LMFDB - Embedded newform 21.30.e.b.4.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(4,21)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 30, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$111.883889004$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.9
Character	$\chi$	$=$	21.4
Dual form			21.30.e.b.16.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5215.37 - 9033.29i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(2.14035e8 - 3.70720e8i) q^{4} +(-6.54948e9 - 1.13440e10i) q^{5} +4.98899e10 q^{6} +(1.56106e12 - 8.84875e11i) q^{7} -1.00651e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})$	\(q+(-5215.37 - 9033.29i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(2.14035e8 - 3.70720e8i) q^{4} +(-6.54948e9 - 1.13440e10i) q^{5} +4.98899e10 q^{6} +(1.56106e12 - 8.84875e11i) q^{7} -1.00651e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-6.83160e13 + 1.18327e14i) q^{10} +(-3.73566e14 + 6.47036e14i) q^{11} +(1.02372e15 + 1.77314e15i) q^{12} +1.37529e16 q^{13} +(-1.61348e16 - 9.48654e15i) q^{14} +6.26520e16 q^{15} +(-6.24162e16 - 1.08108e17i) q^{16} +(1.73700e17 - 3.00858e17i) q^{17} +(-1.19311e17 + 2.06653e17i) q^{18} +(-2.08139e18 - 3.60508e18i) q^{19} -5.60728e18 q^{20} +(-6.79416e16 + 8.58234e18i) q^{21} +7.79315e18 q^{22} +(-2.27015e19 - 3.93202e19i) q^{23} +(2.40704e19 - 4.16912e19i) q^{24} +(7.34077e18 - 1.27146e19i) q^{25} +(-7.17265e19 - 1.24234e20i) q^{26} +1.09419e20 q^{27} +(6.08070e18 - 7.68110e20i) q^{28} +1.52744e21 q^{29} +(-3.26753e20 - 5.65953e20i) q^{30} +(2.67664e21 - 4.63608e21i) q^{31} +(-3.35287e21 + 5.80734e21i) q^{32} +(-1.78676e21 - 3.09475e21i) q^{33} -3.62365e21 q^{34} +(-2.02622e22 - 1.19132e22i) q^{35} -9.79288e21 q^{36} +(-6.66601e21 - 1.15459e22i) q^{37} +(-2.17105e22 + 3.76037e22i) q^{38} +(-3.28898e22 + 5.69669e22i) q^{39} +(6.59209e22 + 1.14178e23i) q^{40} +1.78918e23 q^{41} +(7.78811e22 - 4.41464e22i) q^{42} +2.73094e23 q^{43} +(1.59913e23 + 2.76977e23i) q^{44} +(-1.49831e23 + 2.59515e23i) q^{45} +(-2.36794e23 + 4.10139e23i) q^{46} +(3.16869e23 + 5.48834e23i) q^{47} +5.97070e23 q^{48} +(1.65390e24 - 2.76268e24i) q^{49} -1.53140e23 q^{50} +(8.30804e23 + 1.43899e24i) q^{51} +(2.94360e24 - 5.09847e24i) q^{52} +(-5.13092e24 + 8.88702e24i) q^{53} +(-5.70661e23 - 9.88414e23i) q^{54} +9.78667e24 q^{55} +(-1.57121e25 + 8.90632e24i) q^{56} +1.99105e25 q^{57} +(-7.96620e24 - 1.37979e25i) q^{58} +(2.57977e24 - 4.46829e24i) q^{59} +(1.34097e25 - 2.32263e25i) q^{60} +(-4.16403e25 - 7.21230e25i) q^{61} -5.58388e25 q^{62} +(-3.53870e25 - 2.08060e25i) q^{63} +2.92689e24 q^{64} +(-9.00744e25 - 1.56013e26i) q^{65} +(-1.86372e25 + 3.22806e25i) q^{66} +(1.90920e26 - 3.30684e26i) q^{67} +(-7.43560e25 - 1.28788e26i) q^{68} +2.17161e26 q^{69} +(-1.94085e24 + 2.45166e26i) q^{70} +1.14718e27 q^{71} +(1.15128e26 + 1.99408e26i) q^{72} +(8.24643e24 - 1.42832e25i) q^{73} +(-6.95315e25 + 1.20432e26i) q^{74} +(3.51107e25 + 6.08135e25i) q^{75} -1.78197e27 q^{76} +(-1.06130e25 + 1.34062e27i) q^{77} +6.86131e26 q^{78} +(-5.91661e26 - 1.02479e27i) q^{79} +(-8.17588e26 + 1.41610e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(-9.33122e26 - 1.61621e27i) q^{82} +2.16410e27 q^{83} +(3.16710e27 + 1.86211e27i) q^{84} -4.55059e27 q^{85} +(-1.42429e27 - 2.46694e27i) q^{86} +(-3.65286e27 + 6.32694e27i) q^{87} +(3.75997e27 - 6.51245e27i) q^{88} +(-5.27159e27 - 9.13067e27i) q^{89} +3.12570e27 q^{90} +(2.14691e28 - 1.21696e28i) q^{91} -1.94357e28 q^{92} +(1.28023e28 + 2.21742e28i) q^{93} +(3.30518e27 - 5.72474e27i) q^{94} +(-2.72641e28 + 4.72229e28i) q^{95} +(-1.60367e28 - 2.77763e28i) q^{96} -8.93506e28 q^{97} +(-3.35818e28 - 5.31731e26i) q^{98} +1.70920e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9}+O(q^{10}) $ 40 * q - 7743 * q^2 - 95659380 * q^3 - 5985454645 * q^4 + 14215352760 * q^5 + 74069057934 * q^6 - 368001036334 * q^7 + 49989480496086 * q^8 - 457535849099220 * q^9	$ 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9} - 167879133295903 q^{10} - 31\!\cdots\!14 q^{11}+ \cdots + 14\!\cdots\!08 q^{99}+O(q^{100}) $ 40 * q - 7743 * q^2 - 95659380 * q^3 - 5985454645 * q^4 + 14215352760 * q^5 + 74069057934 * q^6 - 368001036334 * q^7 + 49989480496086 * q^8 - 457535849099220 * q^9 - 167879133295903 * q^10 - 3154300361224314 * q^11 - 28628244017941005 * q^12 + 27686480502978220 * q^13 - 214257133773063450 * q^14 - 135983183150288880 * q^15 - 1764048935658629353 * q^16 + 41802108452009436 * q^17 - 177135003978763023 * q^18 - 7235175939726809174 * q^19 - 2944336803535185762 * q^20 + 9048396870023397228 * q^21 + 89086825354637664038 * q^22 + 44902952138264019852 * q^23 - 119549067769441979667 * q^24 - 856461315876501170374 * q^25 + 740598921837346265154 * q^26 + 4376759565260494368360 * q^27 + 837334611372858240643 * q^28 + 3042539991157763918664 * q^29 - 802960690301171876007 * q^30 - 7171021288148722128918 * q^31 - 3221069809618281449199 * q^32 - 15086920844424695908266 * q^33 - 40988792924743489638864 * q^34 + 22734956365007065015692 * q^35 + 273856007324494541487690 * q^36 - 32961210550052530362042 * q^37 - 21824144763887061483774 * q^38 - 66211788982424616967590 * q^39 - 561274593219911517352413 * q^40 - 407158367720211769052760 * q^41 + 261768399564896960899059 * q^42 - 742478352427516947522676 * q^43 - 860699497136335577636151 * q^44 + 325201674764577027042360 * q^45 - 3603590382443692607483880 * q^46 + 5088913555222492904989956 * q^47 + 16874782747476437555778114 * q^48 - 1107011263686123128490044 * q^49 + 20047363110221889541650996 * q^50 + 199938188860599120095484 * q^51 - 15020364113616852849255436 * q^52 + 4503823724603073528076524 * q^53 - 847231232845300197355287 * q^54 - 26118327809723981533730792 * q^55 + 23391818796605514251144607 * q^56 + 69211244458518393496315212 * q^57 - 19344263089875691399511041 * q^58 - 107339818359767325079738806 * q^59 + 7041335828433941954443689 * q^60 - 55695583344240438158518844 * q^61 + 595684893227471470626855138 * q^62 - 34859518397595458196656958 * q^63 + 2556323224325113131258620002 * q^64 + 116576686276646946961533216 * q^65 - 213049761989822976663084411 * q^66 - 395633506213215660680479214 * q^67 - 341809314919360918295601216 * q^68 - 429538856171601041535001176 * q^69 + 3114247010513527110020739673 * q^70 - 357045698249607322103230392 * q^71 - 571799485120140136045891323 * q^72 + 1563411738231613398537297906 * q^73 - 2560064971236623546640897774 * q^74 - 4096427923536512926362560406 * q^75 + 24051365932177387567037871800 * q^76 - 788772365883171194224066980 * q^77 - 7084523369162900456994724452 * q^78 + 5677690363343606232557230766 * q^79 - 3948631034904977500881109899 * q^80 - 10466952660547210744270230420 * q^81 - 14901652274869047200277511964 * q^82 + 21293945454157612982870988948 * q^83 - 13769091913378092591470544324 * q^84 + 8900456942787328180094572008 * q^85 - 1540767080130988487092741200 * q^86 - 7276187229483929466144216708 * q^87 - 63208209978831072085072879725 * q^88 - 11757157651476935757967358112 * q^89 + 7681072179858211493226649566 * q^90 - 1529257930272663641703478390 * q^91 + 158106912155564585073501217248 * q^92 - 34298772519555405332228797542 * q^93 - 133188762499886306919098285406 * q^94 - 159842963957338542634753903584 * q^95 - 15406277046240142004793891831 * q^96 - 390739421663203813144382175132 * q^97 + 239765305290895114544854004019 * q^98 + 144320549408674286727326243508 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5215.37	−	9033.29i	−0.225087	−	0.389862i	0.731259	−	0.682100i	$-0.238933\pi$
$2$	−5215.37	−	9033.29i	−0.225087	−	0.389862i	−0.956346	+	0.292238i	$0.905600\pi$
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$4$	2.14035e8	−	3.70720e8i	0.398672	−	0.690520i
$5$	−6.54948e9	−	1.13440e10i	−0.479890	−	0.831194i	0.519844	−	0.854261i	$-0.325990\pi$
$5$	−6.54948e9	−	1.13440e10i	−0.479890	−	0.831194i	−0.999734	+	0.0230670i	$0.992657\pi$
$6$	4.98899e10			0.259908
$7$	1.56106e12	−	8.84875e11i	0.869956	−	0.493129i
$7$	1.56106e12	−	8.84875e11i	0.869956	−	0.493129i
$8$	−1.00651e13			−0.809117
$9$	−1.14384e13	−	1.98119e13i	−0.166667	−	0.288675i
$10$	−6.83160e13	+	1.18327e14i	−0.216034	+	0.374182i
$11$	−3.73566e14	+	6.47036e14i	−0.296602	+	0.513729i	−0.975356	−	0.220636i	$-0.929187\pi$
$11$	−3.73566e14	+	6.47036e14i	−0.296602	+	0.513729i	0.678754	+	0.734365i	$0.262520\pi$
$12$	1.02372e15	+	1.77314e15i	0.230173	+	0.398672i
$13$	1.37529e16			0.968759			0.484379	−	0.874858i	$-0.339045\pi$
$13$	1.37529e16			0.968759			0.484379	+	0.874858i	$0.339045\pi$
$14$	−1.61348e16	−	9.48654e15i	−0.388068	−	0.228166i
$15$	6.26520e16			0.554130
$16$	−6.24162e16	−	1.08108e17i	−0.216550	−	0.375075i
$17$	1.73700e17	−	3.00858e17i	0.250202	−	0.433363i	−0.713379	−	0.700778i	$-0.752836\pi$
$17$	1.73700e17	−	3.00858e17i	0.250202	−	0.433363i	0.963581	+	0.267415i	$0.0861695\pi$
$18$	−1.19311e17	+	2.06653e17i	−0.0750290	+	0.129954i
$19$	−2.08139e18	−	3.60508e18i	−0.597623	−	1.03511i	−0.993171	−	0.116668i	$-0.962779\pi$
$19$	−2.08139e18	−	3.60508e18i	−0.597623	−	1.03511i	0.395548	−	0.918445i	$-0.370555\pi$
$20$	−5.60728e18			−0.765275
$21$	−6.79416e16	+	8.58234e18i	−0.00457042	+	0.577332i
$22$	7.79315e18			0.267045
$23$	−2.27015e19	−	3.93202e19i	−0.408321	−	0.707232i	0.586381	−	0.810035i	$-0.300552\pi$
$23$	−2.27015e19	−	3.93202e19i	−0.408321	−	0.707232i	−0.994702	+	0.102803i	$0.967219\pi$
$24$	2.40704e19	−	4.16912e19i	0.233572	−	0.404559i
$25$	7.34077e18	−	1.27146e19i	0.0394105	−	0.0682609i
$26$	−7.17265e19	−	1.24234e20i	−0.218055	−	0.377682i
$27$	1.09419e20			0.192450
$28$	6.08070e18	−	7.68110e20i	0.00631193	−	0.797318i
$29$	1.52744e21			0.953223			0.476612	−	0.879114i	$-0.341865\pi$
$29$	1.52744e21			0.953223			0.476612	+	0.879114i	$0.341865\pi$
$30$	−3.26753e20	−	5.65953e20i	−0.124727	−	0.216034i
$31$	2.67664e21	−	4.63608e21i	0.635106	−	1.10004i	−0.351387	−	0.936230i	$-0.614290\pi$
$31$	2.67664e21	−	4.63608e21i	0.635106	−	1.10004i	0.986493	−	0.163805i	$-0.0523769\pi$
$32$	−3.35287e21	+	5.80734e21i	−0.502044	+	0.869565i
$33$	−1.78676e21	−	3.09475e21i	−0.171243	−	0.296602i
$34$	−3.62365e21			−0.225269
$35$	−2.02622e22	−	1.19132e22i	−0.827370	−	0.486455i
$36$	−9.79288e21			−0.265781
$37$	−6.66601e21	−	1.15459e22i	−0.121602	−	0.210621i	0.798798	−	0.601600i	$-0.205470\pi$
$37$	−6.66601e21	−	1.15459e22i	−0.121602	−	0.210621i	−0.920400	+	0.390979i	$0.872137\pi$
$38$	−2.17105e22	+	3.76037e22i	−0.269034	+	0.465981i
$39$	−3.28898e22	+	5.69669e22i	−0.279657	+	0.484379i
$40$	6.59209e22	+	1.14178e23i	0.388288	+	0.672534i
$41$	1.78918e23			0.736694			0.368347	−	0.929688i	$-0.379924\pi$
$41$	1.78918e23			0.736694			0.368347	+	0.929688i	$0.379924\pi$
$42$	7.78811e22	−	4.41464e22i	0.226109	−	0.128168i
$43$	2.73094e23			0.563663			0.281831	−	0.959464i	$-0.409058\pi$
$43$	2.73094e23			0.563663			0.281831	+	0.959464i	$0.409058\pi$
$44$	1.59913e23	+	2.76977e23i	0.236493	+	0.409619i
$45$	−1.49831e23	+	2.59515e23i	−0.159963	+	0.277065i
$46$	−2.36794e23	+	4.10139e23i	−0.183815	+	0.318378i
$47$	3.16869e23	+	5.48834e23i	0.180078	+	0.311905i	0.941907	−	0.335874i	$-0.109032\pi$
$47$	3.16869e23	+	5.48834e23i	0.180078	+	0.311905i	−0.761829	+	0.647778i	$0.775698\pi$
$48$	5.97070e23			0.250050
$49$	1.65390e24	−	2.76268e24i	0.513648	−	0.858001i
$50$	−1.53140e23			−0.0354832
$51$	8.30804e23	+	1.43899e24i	0.144454	+	0.250202i
$52$	2.94360e24	−	5.09847e24i	0.386217	−	0.668947i
$53$	−5.13092e24	+	8.88702e24i	−0.510735	+	0.884618i	0.489188	+	0.872178i	$0.337293\pi$
$53$	−5.13092e24	+	8.88702e24i	−0.510735	+	0.884618i	−0.999923	+	0.0124399i	$0.996040\pi$
$54$	−5.70661e23	−	9.88414e23i	−0.0433180	−	0.0750290i
$55$	9.78667e24			0.569345
$56$	−1.57121e25	+	8.90632e24i	−0.703897	+	0.398999i
$57$	1.99105e25			0.690076
$58$	−7.96620e24	−	1.37979e25i	−0.214558	−	0.371626i
$59$	2.57977e24	−	4.46829e24i	0.0542284	−	0.0939263i	−0.837637	−	0.546227i	$-0.816063\pi$
$59$	2.57977e24	−	4.46829e24i	0.0542284	−	0.0939263i	0.891865	+	0.452301i	$0.149397\pi$
$60$	1.34097e25	−	2.32263e25i	0.220916	−	0.382637i
$61$	−4.16403e25	−	7.21230e25i	−0.539797	−	0.934956i	−0.998915	−	0.0465807i	$-0.985168\pi$
$61$	−4.16403e25	−	7.21230e25i	−0.539797	−	0.934956i	0.459117	−	0.888376i	$-0.348166\pi$
$62$	−5.58388e25			−0.571816
$63$	−3.53870e25	−	2.08060e25i	−0.287347	−	0.168947i
$64$	2.92689e24			0.0189146
$65$	−9.00744e25	−	1.56013e26i	−0.464898	−	0.805227i
$66$	−1.86372e25	+	3.22806e25i	−0.0770892	+	0.133522i
$67$	1.90920e26	−	3.30684e26i	0.634991	−	1.09984i	−0.351526	−	0.936178i	$-0.614337\pi$
$67$	1.90920e26	−	3.30684e26i	0.634991	−	1.09984i	0.986517	−	0.163659i	$-0.0523297\pi$
$68$	−7.43560e25	−	1.28788e26i	−0.199497	−	0.345539i
$69$	2.17161e26			0.471488
$70$	−1.94085e24	+	2.45166e26i	−0.00342034	+	0.432055i
$71$	1.14718e27			1.64583			0.822915	−	0.568165i	$-0.192346\pi$
$71$	1.14718e27			1.64583			0.822915	+	0.568165i	$0.192346\pi$
$72$	1.15128e26	+	1.99408e26i	0.134853	+	0.233572i
$73$	8.24643e24	−	1.42832e25i	0.00790833	−	0.0136976i	−0.862044	−	0.506833i	$-0.830816\pi$
$73$	8.24643e24	−	1.42832e25i	0.00790833	−	0.0136976i	0.869952	+	0.493136i	$0.164149\pi$
$74$	−6.95315e25	+	1.20432e26i	−0.0547421	+	0.0948161i
$75$	3.51107e25	+	6.08135e25i	0.0227536	+	0.0394105i
$76$	−1.78197e27			−0.953021
$77$	−1.06130e25	+	1.34062e27i	−0.00469592	+	0.593185i
$78$	6.86131e26			0.251788
$79$	−5.91661e26	−	1.02479e27i	−0.180501	−	0.312637i	0.761550	−	0.648106i	$-0.224439\pi$
$79$	−5.91661e26	−	1.02479e27i	−0.180501	−	0.312637i	−0.942051	+	0.335469i	$0.891105\pi$
$80$	−8.17588e26	+	1.41610e27i	−0.207840	+	0.359990i
$81$	−2.61674e26	+	4.53232e26i	−0.0555556	+	0.0962250i
$82$	−9.33122e26	−	1.61621e27i	−0.165820	−	0.287209i
$83$	2.16410e27			0.322585			0.161293	−	0.986907i	$-0.448434\pi$
$83$	2.16410e27			0.322585			0.161293	+	0.986907i	$0.448434\pi$
$84$	3.16710e27	+	1.86211e27i	0.396837	+	0.233322i
$85$	−4.55059e27			−0.480279
$86$	−1.42429e27	−	2.46694e27i	−0.126873	−	0.219751i
$87$	−3.65286e27	+	6.32694e27i	−0.275172	+	0.476612i
$88$	3.75997e27	−	6.51245e27i	0.239986	−	0.415667i
$89$	−5.27159e27	−	9.13067e27i	−0.285619	−	0.494706i	0.687140	−	0.726525i	$-0.258866\pi$
$89$	−5.27159e27	−	9.13067e27i	−0.285619	−	0.494706i	−0.972759	+	0.231819i	$0.925532\pi$
$90$	3.12570e27			0.144023
$91$	2.14691e28	−	1.21696e28i	0.842778	−	0.477723i
$92$	−1.94357e28			−0.651144
$93$	1.28023e28	+	2.21742e28i	0.366679	+	0.635106i
$94$	3.30518e27	−	5.72474e27i	0.0810665	−	0.140411i
$95$	−2.72641e28	+	4.72229e28i	−0.573587	+	0.993482i
$96$	−1.60367e28	−	2.77763e28i	−0.289855	−	0.502044i
$97$	−8.93506e28			−1.38966			−0.694828	−	0.719176i	$-0.744519\pi$
$97$	−8.93506e28			−1.38966			−0.694828	+	0.719176i	$0.744519\pi$
$98$	−3.35818e28	−	5.31731e26i	−0.450118	−	0.00712712i
$99$	1.70920e28			0.197735
$100$	−3.14237e27	−	5.44274e27i	−0.0314237	−	0.0544274i
$101$	−6.91423e28	+	1.19758e29i	−0.598527	+	1.03668i	0.394512	+	0.918891i	$0.370914\pi$
$101$	−6.91423e28	+	1.19758e29i	−0.598527	+	1.03668i	−0.993039	+	0.117788i	$0.962420\pi$
$102$	8.66590e27	−	1.50098e28i	0.0650296	−	0.112635i
$103$	8.20838e28	+	1.42173e29i	0.534709	+	0.926143i	0.999177	+	0.0405536i	$0.0129122\pi$
$103$	8.20838e28	+	1.42173e29i	0.534709	+	0.926143i	−0.464468	+	0.885590i	$0.653755\pi$
$104$	−1.38424e29			−0.783840
$105$	9.78033e28	−	5.54391e28i	0.482069	−	0.273257i
$106$	1.07039e29			0.459839
$107$	−8.98175e28	−	1.55568e29i	−0.336741	−	0.583253i	0.647077	−	0.762425i	$-0.275991\pi$
$107$	−8.98175e28	−	1.55568e29i	−0.336741	−	0.583253i	−0.983818	+	0.179172i	$0.942658\pi$
$108$	2.34195e28	−	4.05638e28i	0.0767244	−	0.132891i
$109$	−4.07503e28	+	7.05816e28i	−0.116801	+	0.202305i	−0.918498	−	0.395425i	$-0.870597\pi$
$109$	−4.07503e28	+	7.05816e28i	−0.116801	+	0.202305i	0.801697	+	0.597730i	$0.203931\pi$
$110$	−5.10411e28	−	8.84058e28i	−0.128152	−	0.221966i
$111$	6.37667e28			0.140414
$112$	−1.93097e29	−	1.13532e29i	−0.373349	−	0.219512i
$113$	−9.12596e29			−1.55111			−0.775553	−	0.631283i	$-0.782529\pi$
$113$	−9.12596e29			−1.55111			−0.775553	+	0.631283i	$0.782529\pi$
$114$	−1.03841e29	−	1.79857e29i	−0.155327	−	0.269034i
$115$	−2.97367e29	+	5.15054e29i	−0.391898	+	0.678788i
$116$	3.26927e29	−	5.66254e29i	0.380023	−	0.658219i
$117$	−1.57311e29	−	2.72471e29i	−0.161460	−	0.279657i
$118$	−5.38178e28			−0.0488244
$119$	4.93480e27	−	6.23360e29i	0.00396131	−	0.500389i
$120$	−6.30596e29			−0.448356
$121$	5.14051e29	+	8.90363e29i	0.324055	+	0.561279i
$122$	−4.34339e29	+	7.52297e29i	−0.243003	+	0.420893i
$123$	−4.27879e29	+	7.41107e29i	−0.212665	+	0.368347i
$124$	−1.14579e30	−	1.98457e30i	−0.506397	−	0.877106i
$125$	−2.63219e30			−1.03543
$126$	−3.38960e27	+	4.28172e29i	−0.00118789	+	0.150053i
$127$	−1.12370e30			−0.351152			−0.175576	−	0.984466i	$-0.556179\pi$
$127$	−1.12370e30			−0.351152			−0.175576	+	0.984466i	$0.556179\pi$
$128$	1.78479e30	+	3.09135e30i	0.497786	+	0.862191i
$129$	−6.53099e29	+	1.13120e30i	−0.162715	+	0.281831i
$130$	−9.39543e29	+	1.62734e30i	−0.209285	+	0.362492i
$131$	−1.59717e30	−	2.76637e30i	−0.318358	−	0.551413i	0.661787	−	0.749692i	$-0.269798\pi$
$131$	−1.59717e30	−	2.76637e30i	−0.318358	−	0.551413i	−0.980146	+	0.198279i	$0.936465\pi$
$132$	−1.52971e30			−0.273079
$133$	−6.43922e30	−	3.78597e30i	−1.03035	−	0.605798i
$134$	−3.98289e30			−0.571713
$135$	−7.16638e29	−	1.24125e30i	−0.0923549	−	0.159963i
$136$	−1.74830e30	+	3.02815e30i	−0.202443	+	0.350642i
$137$	3.07095e30	−	5.31904e30i	0.319760	−	0.553841i	−0.660678	−	0.750670i	$-0.729731\pi$
$137$	3.07095e30	−	5.31904e30i	0.319760	−	0.553841i	0.980438	+	0.196829i	$0.0630644\pi$
$138$	−1.13258e30	−	1.96168e30i	−0.106126	−	0.183815i
$139$	−1.92487e31			−1.62438			−0.812189	−	0.583395i	$-0.801724\pi$
$139$	−1.92487e31			−1.62438			−0.812189	+	0.583395i	$0.801724\pi$
$140$	−8.75329e30	+	4.96174e30i	−0.665756	+	0.377379i
$141$	−3.03115e30			−0.207936
$142$	−5.98296e30	−	1.03628e31i	−0.370455	−	0.641647i
$143$	−5.13762e30	+	8.89862e30i	−0.287336	+	0.497680i
$144$	−1.42788e30	+	2.47317e30i	−0.0721833	+	0.125025i
$145$	−1.00040e31	−	1.73274e31i	−0.457443	−	0.792314i
$146$	−1.72033e29			−0.00712025
$147$	7.48823e30	+	1.34576e31i	0.280723	+	0.504508i
$148$	−5.70705e30			−0.193917
$149$	7.57270e30	+	1.31163e31i	0.233373	+	0.404213i	0.958798	−	0.284087i	$-0.0916905\pi$
$149$	7.57270e30	+	1.31163e31i	0.233373	+	0.404213i	−0.725426	+	0.688300i	$0.758357\pi$
$150$	3.66231e29	−	6.34330e29i	0.0102431	−	0.0177416i
$151$	−3.72909e31	+	6.45898e31i	−0.947191	+	1.64058i	−0.195888	+	0.980626i	$0.562759\pi$
$151$	−3.72909e31	+	6.45898e31i	−0.947191	+	1.64058i	−0.751303	+	0.659957i	$0.770574\pi$
$152$	2.09494e31	+	3.62854e31i	0.483547	+	0.837528i
$153$	−7.94742e30			−0.166802
$154$	1.21656e31	−	6.89596e30i	0.232317	−	0.131687i
$155$	−7.01226e31			−1.21912
$156$	1.40792e31	+	2.43858e31i	0.222982	+	0.386217i
$157$	−6.79074e30	+	1.17619e31i	−0.0980329	+	0.169798i	−0.910870	−	0.412693i	$-0.864588\pi$
$157$	−6.79074e30	+	1.17619e31i	−0.0980329	+	0.169798i	0.812837	+	0.582491i	$0.197922\pi$
$158$	−6.17146e30	+	1.06893e31i	−0.0812569	+	0.140741i
$159$	−2.45410e31	−	4.25063e31i	−0.294873	−	0.510735i
$160$	8.78382e31			0.963704
$161$	−7.02319e31	−	4.12931e31i	−0.703978	−	0.413907i
$162$	5.45891e30			0.0500193
$163$	−8.54395e31	−	1.47986e32i	−0.716042	−	1.24022i	−0.962556	−	0.271082i	$-0.912618\pi$
$163$	−8.54395e31	−	1.47986e32i	−0.716042	−	1.24022i	0.246514	−	0.969139i	$-0.420715\pi$
$164$	3.82947e31	−	6.63283e31i	0.293699	−	0.508701i
$165$	−2.34047e31	+	4.05381e31i	−0.164356	+	0.284673i
$166$	−1.12866e31	−	1.95489e31i	−0.0726098	−	0.125764i
$167$	2.75598e32			1.62513			0.812564	−	0.582871i	$-0.198071\pi$
$167$	2.75598e32			1.62513			0.812564	+	0.582871i	$0.198071\pi$
$168$	6.83837e29	−	8.63817e31i	0.00369801	−	0.467129i
$169$	−1.23959e31			−0.0615065
$170$	2.37330e31	+	4.11068e31i	0.108105	+	0.187243i
$171$	−4.76156e31	+	8.24727e31i	−0.199208	+	0.345038i
$172$	5.84517e31	−	1.01241e32i	0.224716	−	0.389220i
$173$	−1.61421e32	−	2.79589e32i	−0.570546	−	0.988215i	−0.996510	−	0.0834748i	$-0.973398\pi$
$173$	−1.61421e32	−	2.79589e32i	−0.570546	−	0.988215i	0.425964	−	0.904740i	$-0.359935\pi$
$174$	7.62041e31			0.247750
$175$	2.08550e29	−	2.63439e31i	0.000623963	−	0.0788185i
$176$	9.32664e31			0.256916
$177$	1.23390e31	+	2.13717e31i	0.0313088	+	0.0542284i
$178$	−5.49867e31	+	9.52397e31i	−0.128578	+	0.222704i
$179$	−3.10834e31	+	5.38380e31i	−0.0670131	+	0.116070i	−0.897585	−	0.440841i	$-0.854680\pi$
$179$	−3.10834e31	+	5.38380e31i	−0.0670131	+	0.116070i	0.830572	+	0.556911i	$0.188014\pi$
$180$	6.41383e31	+	1.11091e32i	0.127546	+	0.220916i
$181$	8.13490e32			1.49284			0.746419	−	0.665476i	$-0.231771\pi$
$181$	8.13490e32			1.49284			0.746419	+	0.665476i	$0.231771\pi$
$182$	−2.21901e32	−	1.30467e32i	−0.375944	−	0.221038i
$183$	3.98328e32			0.623304
$184$	2.28492e32	+	3.95760e32i	0.330379	+	0.572234i
$185$	−8.73179e31	+	1.51239e32i	−0.116711	+	0.202150i
$186$	1.33538e32	−	2.31294e32i	0.165069	−	0.285908i
$187$	1.29777e32	+	2.24781e32i	0.148421	+	0.257073i
$188$	2.71285e32			0.287168
$189$	1.70809e32	−	9.68221e31i	0.167423	−	0.0949027i
$190$	5.68770e32			0.516428
$191$	9.99769e32	+	1.73165e33i	0.841232	+	1.45706i	0.888854	+	0.458191i	$0.151502\pi$
$191$	9.99769e32	+	1.73165e33i	0.841232	+	1.45706i	−0.0476219	+	0.998865i	$0.515164\pi$
$192$	−6.99962e30	+	1.21237e31i	−0.00546018	+	0.00945730i
$193$	4.93245e32	−	8.54326e32i	0.356847	−	0.618077i	−0.630585	−	0.776120i	$-0.717185\pi$
$193$	4.93245e32	−	8.54326e32i	0.356847	−	0.618077i	0.987432	+	0.158043i	$0.0505185\pi$
$194$	4.65997e32	+	8.07130e32i	0.312794	+	0.541774i
$195$	8.61646e32			0.536818
$196$	−6.70189e32	−	1.20444e33i	−0.387689	−	0.696745i
$197$	−6.14162e32			−0.330007			−0.165003	−	0.986293i	$-0.552764\pi$
$197$	−6.14162e32			−0.330007			−0.165003	+	0.986293i	$0.552764\pi$
$198$	−8.91412e31	−	1.54397e32i	−0.0445075	−	0.0770892i
$199$	1.49365e31	−	2.58707e31i	0.00693231	−	0.0120071i	−0.862538	−	0.505992i	$-0.831127\pi$
$199$	1.49365e31	−	2.58707e31i	0.00693231	−	0.0120071i	0.869471	+	0.493984i	$0.164460\pi$
$200$	−7.38853e31	+	1.27973e32i	−0.0318877	+	0.0552311i
$201$	9.13167e32	+	1.58165e33i	0.366612	+	0.634991i
$202$	1.44241e33			0.538883
$203$	2.38443e33	−	1.35160e33i	0.829263	−	0.470062i
$204$	7.11285e32			0.230360
$205$	−1.17182e33	−	2.02965e33i	−0.353532	−	0.612336i
$206$	8.56195e32	−	1.48297e33i	0.240712	−	0.416926i
$207$	−5.19338e32	+	8.99520e32i	−0.136107	+	0.235744i
$208$	−8.58404e32	−	1.48680e33i	−0.209785	−	0.363357i
$209$	3.11016e33			0.709024
$210$	−1.01088e33	−	5.94350e32i	−0.215040	−	0.126434i
$211$	−8.05359e33			−1.59917			−0.799584	−	0.600555i	$-0.794946\pi$
$211$	−8.05359e33			−1.59917			−0.799584	+	0.600555i	$0.794946\pi$
$212$	2.19640e33	+	3.80427e33i	0.407231	+	0.705344i
$213$	−2.74346e33	+	4.75181e33i	−0.475110	+	0.822915i
$214$	−9.36864e32	+	1.62270e33i	−0.151592	+	0.262565i
$215$	−1.78862e33	−	3.09799e33i	−0.270496	−	0.468513i
$216$	−1.10131e33			−0.155715
$217$	7.60430e31	−	9.60569e33i	0.0100553	−	1.27017i
$218$	8.50113e32			0.105162
$219$	3.94424e31	+	6.83163e31i	0.00456587	+	0.00790833i
$220$	2.09469e33	−	3.62811e33i	0.226982	−	0.393144i
$221$	2.38888e33	−	4.13767e33i	0.242386	−	0.419824i
$222$	−3.32567e32	−	5.76023e32i	−0.0316054	−	0.0547421i
$223$	−2.25095e33			−0.200422			−0.100211	−	0.994966i	$-0.531952\pi$
$223$	−2.25095e33			−0.200422			−0.100211	+	0.994966i	$0.531952\pi$
$224$	−9.52543e31	+	1.20325e34i	−0.00794856	+	1.00406i
$225$	−3.35867e32			−0.0262737
$226$	4.75953e33	+	8.24375e33i	0.349134	+	0.604717i
$227$	−8.48860e32	+	1.47027e33i	−0.0584065	+	0.101163i	−0.893750	−	0.448565i	$-0.851935\pi$
$227$	−8.48860e32	+	1.47027e33i	−0.0584065	+	0.101163i	0.835344	+	0.549728i	$0.185269\pi$
$228$	4.26155e33	−	7.38122e33i	0.275114	−	0.476511i
$229$	7.39184e33	+	1.28030e34i	0.447856	+	0.775709i	0.998246	−	0.0591984i	$-0.0188545\pi$
$229$	7.39184e33	+	1.28030e34i	0.447856	+	0.775709i	−0.550390	+	0.834907i	$0.685521\pi$
$230$	6.20351e33			0.352845
$231$	−5.52770e33	−	3.25003e33i	−0.295237	−	0.173586i
$232$	−1.53738e34			−0.771269
$233$	−6.59688e33	−	1.14261e34i	−0.310941	−	0.538565i	0.667625	−	0.744497i	$-0.267311\pi$
$233$	−6.59688e33	−	1.14261e34i	−0.310941	−	0.538565i	−0.978566	+	0.205932i	$0.933977\pi$
$234$	−1.64087e33	+	2.84207e33i	−0.0726850	+	0.125894i
$235$	4.15066e33	−	7.18915e33i	0.172836	−	0.299360i
$236$	−1.10432e33	−	1.91274e33i	−0.0432386	−	0.0748915i
$237$	5.65979e33			0.208425
$238$	−5.65673e33	+	3.20648e33i	−0.195974	+	0.111087i
$239$	−5.71715e34			−1.86385			−0.931923	−	0.362657i	$-0.881870\pi$
$239$	−5.71715e34			−1.86385			−0.931923	+	0.362657i	$0.881870\pi$
$240$	−3.91050e33	−	6.77318e33i	−0.119997	−	0.207840i
$241$	−1.87776e34	+	3.25238e34i	−0.542493	+	0.939625i	0.456267	+	0.889843i	$0.349186\pi$
$241$	−1.87776e34	+	3.25238e34i	−0.542493	+	0.939625i	−0.998760	+	0.0497825i	$0.984147\pi$
$242$	5.36194e33	−	9.28715e33i	0.145881	−	0.252673i
$243$	−1.25158e33	−	2.16780e33i	−0.0320750	−	0.0555556i
$244$	−3.56499e34			−0.860808
$245$	−4.21722e34	−	6.67749e32i	−0.959660	−	0.0151952i
$246$	8.92619e33			0.191473
$247$	−2.86252e34	−	4.95803e34i	−0.578952	−	1.00278i
$248$	−2.69406e34	+	4.66625e34i	−0.513875	+	0.890058i
$249$	−5.17541e33	+	8.96407e33i	−0.0931224	+	0.161293i
$250$	1.37278e34	+	2.37773e34i	0.233062	+	0.403676i
$251$	−2.46630e34			−0.395163			−0.197582	−	0.980286i	$-0.563309\pi$
$251$	−2.46630e34			−0.395163			−0.197582	+	0.980286i	$0.563309\pi$
$252$	−1.52873e34	+	8.66547e33i	−0.231218	+	0.131064i
$253$	3.39221e34			0.484435
$254$	5.86050e33	+	1.01507e34i	0.0790398	+	0.136901i
$255$	1.08827e34	−	1.88493e34i	0.138645	−	0.240139i
$256$	1.94024e34	−	3.36059e34i	0.233548	−	0.404517i
$257$	2.41619e34	+	4.18497e34i	0.274854	+	0.476060i	0.970098	−	0.242713i	$-0.0780373\pi$
$257$	2.41619e34	+	4.18497e34i	0.274854	+	0.476060i	−0.695245	+	0.718773i	$0.744704\pi$
$258$	1.36246e34			0.146500
$259$	−2.06227e34	−	1.21252e34i	−0.209652	−	0.123266i
$260$	−7.71164e34			−0.741367
$261$	−1.74715e34	−	3.02616e34i	−0.158871	−	0.275172i
$262$	−1.66596e34	+	2.88553e34i	−0.143317	+	0.248232i
$263$	7.35281e34	−	1.27354e35i	0.598543	−	1.03671i	−0.394494	−	0.918899i	$-0.629080\pi$
$263$	7.35281e34	−	1.27354e35i	0.598543	−	1.03671i	0.993036	−	0.117808i	$-0.0375867\pi$
$264$	1.79838e34	+	3.11489e34i	0.138556	+	0.239986i
$265$	1.34420e35			0.980386
$266$	−6.16792e32	+	7.79126e34i	−0.00425946	+	0.538052i
$267$	5.04277e34			0.329804
$268$	−8.17274e34	−	1.41556e35i	−0.506306	−	0.876948i
$269$	−2.83137e34	+	4.90409e34i	−0.166184	+	0.287839i	−0.937075	−	0.349128i	$-0.886478\pi$
$269$	−2.83137e34	+	4.90409e34i	−0.166184	+	0.287839i	0.770891	+	0.636967i	$0.219811\pi$
$270$	−7.47507e33	+	1.29472e34i	−0.0415758	+	0.0720114i
$271$	7.77621e34	+	1.34688e35i	0.409934	+	0.710026i	0.994882	−	0.101045i	$-0.0322185\pi$
$271$	7.77621e34	+	1.34688e35i	0.409934	+	0.710026i	−0.584948	+	0.811071i	$0.698885\pi$
$272$	−4.33669e34			−0.216725
$273$	−9.34395e32	+	1.18032e35i	−0.00442764	+	0.559296i
$274$	−6.40646e34			−0.287895
$275$	5.48453e33	+	9.49949e33i	0.0233784	+	0.0404926i
$276$	4.64802e34	−	8.05060e34i	0.187969	−	0.325572i
$277$	−2.74846e34	+	4.76047e34i	−0.105471	+	0.182681i	−0.913930	−	0.405871i	$-0.866968\pi$
$277$	−2.74846e34	+	4.76047e34i	−0.105471	+	0.182681i	0.808460	+	0.588552i	$0.200302\pi$
$278$	1.00389e35	+	1.73879e35i	0.365626	+	0.633283i
$279$	−1.22466e35			−0.423404
$280$	2.03940e35	+	1.19907e35i	0.669439	+	0.393599i
$281$	3.66849e35			1.14352			0.571762	−	0.820420i	$-0.306260\pi$
$281$	3.66849e35			1.14352			0.571762	+	0.820420i	$0.306260\pi$
$282$	1.58086e34	+	2.73813e34i	0.0468038	+	0.0810665i
$283$	1.62440e35	−	2.81354e35i	0.456867	−	0.791317i	−0.541927	−	0.840426i	$-0.682305\pi$
$283$	1.62440e35	−	2.81354e35i	0.456867	−	0.791317i	0.998793	+	0.0491092i	$0.0156382\pi$
$284$	2.45537e35	−	4.25282e35i	0.656146	−	1.13648i
$285$	−1.30403e35	−	2.25865e35i	−0.331161	−	0.573587i
$286$	1.07178e35			0.258702
$287$	2.79301e35	−	1.58320e35i	0.640891	−	0.363285i
$288$	1.53406e35			0.334696
$289$	1.80641e35	+	3.12879e35i	0.374798	+	0.649168i
$290$	−1.04349e35	+	1.80738e35i	−0.205929	+	0.356679i
$291$	2.13681e35	−	3.70106e35i	0.401159	−	0.694828i
$292$	−3.53005e33	−	6.11423e33i	−0.00630565	−	0.0109217i
$293$	−2.19029e35			−0.372323			−0.186162	−	0.982519i	$-0.559605\pi$
$293$	−2.19029e35			−0.372323			−0.186162	+	0.982519i	$0.559605\pi$
$294$	8.25129e34	−	1.37830e35i	0.133501	−	0.223001i
$295$	−6.75846e34			−0.104095
$296$	6.70938e34	+	1.16210e35i	0.0983904	+	0.170417i
$297$	−4.08752e34	+	7.07980e34i	−0.0570810	+	0.0988673i
$298$	7.89889e34	−	1.36813e35i	0.105058	−	0.181966i
$299$	−3.12212e35	−	5.40767e35i	−0.395564	−	0.685137i
$300$	3.00597e34			0.0362849
$301$	4.26315e35	−	2.41654e35i	0.490362	−	0.277958i
$302$	7.77945e35			0.852802
$303$	−3.30705e35	−	5.72798e35i	−0.345560	−	0.598527i
$304$	−2.59826e35	+	4.50031e35i	−0.258830	+	0.448307i
$305$	−5.45444e35	+	9.44737e35i	−0.518087	+	0.897353i
$306$	4.14487e34	+	7.17913e34i	0.0375449	+	0.0650296i
$307$	2.21185e36			1.91095			0.955475	−	0.295072i	$-0.0953436\pi$
$307$	2.21185e36			1.91095			0.955475	+	0.295072i	$0.0953436\pi$
$308$	4.94723e35	+	2.90874e35i	0.407734	+	0.239729i
$309$	−7.85208e35			−0.617429
$310$	3.65715e35	+	6.33438e35i	0.274409	+	0.475291i
$311$	−1.11443e36	+	1.93024e36i	−0.798042	+	1.38225i	0.122848	+	0.992426i	$0.460797\pi$
$311$	−1.11443e36	+	1.93024e36i	−0.798042	+	1.38225i	−0.920890	+	0.389824i	$0.872536\pi$
$312$	3.31038e35	−	5.73375e35i	0.226275	−	0.391920i
$313$	−5.79375e35	−	1.00351e36i	−0.378066	−	0.654829i	0.612715	−	0.790304i	$-0.290077\pi$
$313$	−5.79375e35	−	1.00351e36i	−0.378066	−	0.654829i	−0.990781	+	0.135475i	$0.956744\pi$
$314$	1.41665e35			0.0882637
$315$	−4.25668e33	+	5.37700e35i	−0.00253261	+	0.319917i
$316$	−5.06545e35			−0.287843
$317$	−6.55859e35	−	1.13598e36i	−0.356001	−	0.616611i	0.631288	−	0.775549i	$-0.282527\pi$
$317$	−6.55859e35	−	1.13598e36i	−0.356001	−	0.616611i	−0.987289	+	0.158937i	$0.949193\pi$
$318$	−2.55981e35	+	4.43373e35i	−0.132744	+	0.229919i
$319$	−5.70602e35	+	9.88312e35i	−0.282728	+	0.489699i
$320$	−1.91696e34	−	3.32028e34i	−0.00907694	−	0.0157217i
$321$	8.59189e35			0.388835
$322$	−6.72727e33	+	8.49784e35i	−0.00291024	+	0.367619i
$323$	−1.44616e36			−0.598107
$324$	1.12015e35	+	1.94015e35i	0.0442968	+	0.0767244i
$325$	1.00957e35	−	1.74863e35i	0.0381792	−	0.0661284i
$326$	−8.91198e35	+	1.54360e36i	−0.322344	+	0.558316i
$327$	−1.94908e35	−	3.37590e35i	−0.0674351	−	0.116801i
$328$	−1.80082e36			−0.596072
$329$	9.80300e35	+	5.76372e35i	0.310469	+	0.182542i
$330$	4.88256e35			0.147977
$331$	−2.17402e36	−	3.76550e36i	−0.630604	−	1.09224i	−0.987428	−	0.158067i	$-0.949474\pi$
$331$	−2.17402e36	−	3.76550e36i	−0.630604	−	1.09224i	0.356825	−	0.934171i	$-0.383859\pi$
$332$	4.63193e35	−	8.02274e35i	0.128606	−	0.222752i
$333$	−1.52497e35	+	2.64133e35i	−0.0405340	+	0.0702070i
$334$	−1.43735e36	−	2.48956e36i	−0.365795	−	0.633576i
$335$	−5.00172e36			−1.21890
$336$	9.32061e35	−	5.28332e35i	0.217533	−	0.123307i
$337$	−1.81574e36			−0.405902			−0.202951	−	0.979189i	$-0.565053\pi$
$337$	−1.81574e36			−0.405902			−0.202951	+	0.979189i	$0.565053\pi$
$338$	6.46493e34	+	1.11976e35i	0.0138443	+	0.0239791i
$339$	2.18246e36	−	3.78013e36i	0.447765	−	0.775553i
$340$	−9.73987e35	+	1.68699e36i	−0.191474	+	0.331642i
$341$	1.99981e36	+	3.46377e36i	0.376747	+	0.652545i
$342$	9.93333e35			0.179356
$343$	1.37204e35	−	5.77620e36i	0.0237466	−	0.999718i
$344$	−2.74870e36			−0.456069
$345$	−1.42230e36	−	2.46349e36i	−0.226263	−	0.391898i
$346$	−1.68374e36	+	2.91632e36i	−0.256845	+	0.444869i
$347$	−6.04876e36	+	1.04768e37i	−0.884890	+	1.53267i	−0.0390502	+	0.999237i	$0.512433\pi$
$347$	−6.04876e36	+	1.04768e37i	−0.884890	+	1.53267i	−0.845840	+	0.533437i	$0.820900\pi$
$348$	1.56368e36	+	2.70838e36i	0.219406	+	0.380023i
$349$	1.07323e37			1.44452			0.722260	−	0.691622i	$-0.243103\pi$
$349$	1.07323e37			1.44452			0.722260	+	0.691622i	$0.243103\pi$
$350$	−2.39060e35	+	1.35509e35i	−0.0308688	+	0.0174978i
$351$	1.50483e36			0.186438
$352$	−2.50504e36	−	4.33885e36i	−0.297814	−	0.515829i
$353$	−7.20014e36	+	1.24710e37i	−0.821500	+	1.42288i	0.0830652	+	0.996544i	$0.473529\pi$
$353$	−7.20014e36	+	1.24710e37i	−0.821500	+	1.42288i	−0.904565	+	0.426335i	$0.859804\pi$
$354$	1.28704e35	−	2.22923e35i	0.0140944	−	0.0244122i
$355$	−7.51343e36	−	1.30136e37i	−0.789818	−	1.36800i
$356$	−4.51323e36			−0.455472
$357$	2.57026e36	+	1.51120e36i	0.249051	+	0.146431i
$358$	6.48446e35			0.0603351
$359$	−1.26713e36	−	2.19473e36i	−0.113227	−	0.196116i	0.803842	−	0.594842i	$-0.202786\pi$
$359$	−1.26713e36	−	2.19473e36i	−0.113227	−	0.196116i	−0.917070	+	0.398727i	$0.869452\pi$
$360$	1.50806e36	−	2.61204e36i	0.129429	−	0.224178i
$361$	−2.59950e36	+	4.50246e36i	−0.214306	+	0.371190i
$362$	−4.24265e36	−	7.34849e36i	−0.336019	−	0.582001i
$363$	−4.91738e36			−0.374186
$364$	8.36273e34	−	1.05637e37i	0.00611474	−	0.772409i
$365$	−2.16039e35			−0.0151805
$366$	−2.07743e36	−	3.59821e36i	−0.140298	−	0.243003i
$367$	9.32627e35	−	1.61536e36i	0.0605411	−	0.104860i	−0.834166	−	0.551513i	$-0.814051\pi$
$367$	9.32627e35	−	1.61536e36i	0.0605411	−	0.104860i	0.894707	+	0.446653i	$0.147384\pi$
$368$	−2.83389e36	+	4.90844e36i	−0.176844	+	0.306302i
$369$	−2.04653e36	−	3.54469e36i	−0.122782	−	0.212665i
$370$	1.82158e36			0.105081
$371$	−1.45769e35	+	1.84134e37i	−0.00808616	+	1.02144i
$372$	1.09606e37			0.584737
$373$	4.45939e36	+	7.72389e36i	0.228822	+	0.396331i	0.957459	−	0.288569i	$-0.0931793\pi$
$373$	4.45939e36	+	7.72389e36i	0.228822	+	0.396331i	−0.728637	+	0.684900i	$0.759846\pi$
$374$	1.35367e36	−	2.34463e36i	0.0668153	−	0.115727i
$375$	6.29483e36	−	1.09030e37i	0.298903	−	0.517716i
$376$	−3.18931e36	−	5.52404e36i	−0.145704	−	0.252367i
$377$	2.10068e37			0.923443
$378$	−1.76546e36	−	1.03801e36i	−0.0746837	−	0.0439106i
$379$	2.84231e37			1.15719			0.578593	−	0.815616i	$-0.303602\pi$
$379$	2.84231e37			1.15719			0.578593	+	0.815616i	$0.303602\pi$
$380$	1.16710e37	+	2.02147e37i	0.457346	+	0.792146i
$381$	2.68731e36	−	4.65455e36i	0.101369	−	0.175576i
$382$	1.04283e37	−	1.80624e37i	0.378701	−	0.655929i
$383$	2.57482e37	+	4.45972e37i	0.900254	+	1.55929i	0.827164	+	0.561960i	$0.189953\pi$
$383$	2.57482e37	+	4.45972e37i	0.900254	+	1.55929i	0.0730898	+	0.997325i	$0.476714\pi$
$384$	−1.70732e37			−0.574794
$385$	1.52776e37	−	8.65998e36i	0.495306	−	0.280761i
$386$	−1.02898e37			−0.321286
$387$	−3.12375e36	−	5.41050e36i	−0.0939438	−	0.162715i
$388$	−1.91242e37	+	3.31240e37i	−0.554016	+	0.959584i
$389$	1.49294e37	−	2.58584e37i	0.416651	−	0.721661i	−0.578949	−	0.815364i	$-0.696537\pi$
$389$	1.49294e37	−	2.58584e37i	0.416651	−	0.721661i	0.995600	+	0.0937029i	$0.0298704\pi$
$390$	−4.49381e36	−	7.78350e36i	−0.120831	−	0.209285i
$391$	−1.57731e37			−0.408651
$392$	−1.66466e37	+	2.78066e37i	−0.415602	+	0.694223i
$393$	1.52784e37			0.367609
$394$	3.20309e36	+	5.54791e36i	0.0742803	+	0.128657i
$395$	−7.75015e36	+	1.34236e37i	−0.173242	+	0.300063i
$396$	3.65829e36	−	6.33634e36i	0.0788312	−	0.136540i
$397$	1.96602e37	+	3.40524e37i	0.408437	+	0.707433i	0.994715	−	0.102677i	$-0.0327408\pi$
$397$	1.96602e37	+	3.40524e37i	0.408437	+	0.707433i	−0.586278	+	0.810110i	$0.699407\pi$
$398$	−3.11597e35			−0.00624149
$399$	3.10814e37	−	1.76183e37i	0.600336	−	0.340296i
$400$	−1.83273e36			−0.0341373
$401$	−8.40594e36	−	1.45595e37i	−0.151006	−	0.261549i	0.780592	−	0.625041i	$-0.214918\pi$
$401$	−8.40594e36	−	1.45595e37i	−0.151006	−	0.261549i	−0.931597	+	0.363492i	$0.881584\pi$
$402$	9.52501e36	−	1.64978e37i	0.165039	−	0.285857i
$403$	3.68116e37	−	6.37596e37i	0.615264	−	1.06567i
$404$	2.95978e37	+	5.12648e37i	0.477231	+	0.826589i
$405$	6.85531e36			0.106642
$406$	−2.46451e37	−	1.44902e37i	−0.369916	−	0.217493i
$407$	9.96079e36			0.144270
$408$	−8.36209e36	−	1.44836e37i	−0.116881	−	0.202443i
$409$	7.35044e37	−	1.27313e38i	0.991574	−	1.71746i	0.383600	−	0.923499i	$-0.374684\pi$
$409$	7.35044e37	−	1.27313e38i	0.991574	−	1.71746i	0.607973	−	0.793957i	$-0.291983\pi$
$410$	−1.22229e37	+	2.11707e37i	−0.159151	+	0.275658i
$411$	1.46882e37	+	2.54408e37i	0.184614	+	0.319760i
$412$	7.02753e37			0.852694
$413$	7.32908e34	−	9.25803e36i	0.000858565	−	0.108453i
$414$	1.08342e37			0.122544
$415$	−1.41737e37	−	2.45496e37i	−0.154806	−	0.268131i
$416$	−4.61116e37	+	7.98677e37i	−0.486359	+	0.842399i
$417$	4.60330e37	−	7.97315e37i	0.468917	−	0.812189i
$418$	−1.62206e37	−	2.80949e37i	−0.159592	−	0.276422i
$419$	−2.05341e38			−1.95152			−0.975758	−	0.218850i	$-0.929769\pi$
$419$	−2.05341e38			−1.95152			−0.975758	+	0.218850i	$0.929769\pi$
$420$	3.80968e35	−	4.81236e37i	0.00349763	−	0.441818i
$421$	6.61041e37			0.586324			0.293162	−	0.956063i	$-0.405292\pi$
$421$	6.61041e37			0.586324			0.293162	+	0.956063i	$0.405292\pi$
$422$	4.20025e37	+	7.27504e37i	0.359952	+	0.623455i
$423$	7.24895e36	−	1.25556e37i	0.0600261	−	0.103968i
$424$	5.16430e37	−	8.94483e37i	0.413244	−	0.715760i
$425$	−2.55019e36	−	4.41706e36i	−0.0197212	−	0.0341581i
$426$	5.72327e37			0.427764
$427$	−1.28823e38	−	7.57418e37i	−0.930654	−	0.547182i
$428$	−7.68964e37			−0.536997
$429$	−2.45731e37	−	4.25618e37i	−0.165893	−	0.287336i
$430$	−1.86567e37	+	3.23143e37i	−0.121770	+	0.210912i
$431$	−1.16916e38	+	2.02504e38i	−0.737824	+	1.27795i	0.215649	+	0.976471i	$0.430813\pi$
$431$	−1.16916e38	+	2.02504e38i	−0.737824	+	1.27795i	−0.953473	+	0.301478i	$0.902520\pi$
$432$	−6.82952e36	−	1.18291e37i	−0.0416750	−	0.0721833i
$433$	−2.80810e37			−0.165706			−0.0828530	−	0.996562i	$-0.526403\pi$
$433$	−2.80810e37			−0.165706			−0.0828530	+	0.996562i	$0.526403\pi$
$434$	−8.71676e37	+	4.94104e37i	−0.497455	+	0.281979i
$435$	9.56974e37			0.528209
$436$	1.74440e37	+	3.02139e37i	0.0931305	+	0.161307i
$437$	−9.45017e37	+	1.63682e38i	−0.488044	+	0.845317i
$438$	4.11414e35	−	7.12590e35i	0.00205544	−	0.00356012i
$439$	1.49739e38	+	2.59355e38i	0.723767	+	1.25360i	0.959480	+	0.281778i	$0.0909242\pi$
$439$	1.49739e38	+	2.59355e38i	0.723767	+	1.25360i	−0.235713	+	0.971823i	$0.575743\pi$
$440$	−9.85034e37			−0.460667
$441$	−7.36519e37	−	1.16620e36i	−0.333292	−	0.00527730i
$442$	−4.98357e37			−0.218232
$443$	−3.26095e37	−	5.64814e37i	−0.138194	−	0.239360i	0.788619	−	0.614883i	$-0.210797\pi$
$443$	−3.26095e37	−	5.64814e37i	−0.138194	−	0.239360i	−0.926813	+	0.375523i	$0.877463\pi$
$444$	1.36483e37	−	2.36396e37i	0.0559791	−	0.0969586i
$445$	−6.90524e37	+	1.19602e38i	−0.274131	+	0.474810i
$446$	1.17395e37	+	2.03335e37i	0.0451124	+	0.0781369i
$447$	−7.24400e37			−0.269475
$448$	4.56905e36	−	2.58993e36i	0.0164549	−	0.00932733i
$449$	4.10554e38			1.43152			0.715762	−	0.698344i	$-0.246080\pi$
$449$	4.10554e38			1.43152			0.715762	+	0.698344i	$0.246080\pi$
$450$	1.75167e36	+	3.03398e36i	0.00591386	+	0.0102431i
$451$	−6.68376e37	+	1.15766e38i	−0.218505	+	0.378461i
$452$	−1.95328e38	+	3.38318e38i	−0.618382	+	1.07107i
$453$	−1.78361e38	−	3.08931e38i	−0.546861	−	0.947191i
$454$	1.77085e37			0.0525862
$455$	−2.78664e38	−	1.63841e38i	−0.801521	−	0.471258i
$456$	−2.00400e38			−0.558352
$457$	−1.54956e38	−	2.68392e38i	−0.418239	−	0.724410i	0.577524	−	0.816374i	$-0.304019\pi$
$457$	−1.54956e38	−	2.68392e38i	−0.418239	−	0.724410i	−0.995762	+	0.0919634i	$0.970686\pi$
$458$	7.71024e37	−	1.33545e38i	0.201613	−	0.349204i
$459$	1.90061e37	−	3.29196e37i	0.0481515	−	0.0834008i
$460$	1.27294e38	+	2.20479e38i	0.312478	+	0.541227i
$461$	−1.32267e38			−0.314621			−0.157310	−	0.987549i	$-0.550282\pi$
$461$	−1.32267e38			−0.314621			−0.157310	+	0.987549i	$0.550282\pi$
$462$	−5.29480e35	+	6.68835e37i	−0.00122051	+	0.154174i
$463$	−4.70054e38			−1.05008			−0.525042	−	0.851076i	$-0.675950\pi$
$463$	−4.70054e38			−1.05008			−0.525042	+	0.851076i	$0.675950\pi$
$464$	−9.53374e37	−	1.65129e38i	−0.206420	−	0.357530i
$465$	1.67697e38	−	2.90460e38i	0.351931	−	0.609562i
$466$	−6.88104e37	+	1.19183e38i	−0.139978	+	0.242448i
$467$	−1.34229e38	−	2.32491e38i	−0.264698	−	0.458471i	0.702786	−	0.711401i	$-0.251939\pi$
$467$	−1.34229e38	−	2.32491e38i	−0.264698	−	0.458471i	−0.967485	+	0.252930i	$0.918606\pi$
$468$	−1.34680e38			−0.257478
$469$	5.42401e36	−	6.85157e38i	0.0100534	−	1.26994i
$470$	−8.65890e37			−0.155612
$471$	−3.24799e37	−	5.62568e37i	−0.0565993	−	0.0980329i
$472$	−2.59655e37	+	4.49736e37i	−0.0438771	+	0.0759974i
$473$	−1.02019e38	+	1.76701e38i	−0.167183	+	0.289570i
$474$	−2.95179e37	−	5.11265e37i	−0.0469137	−	0.0812569i
$475$	−6.11162e37			−0.0942104
$476$	−2.30036e38	−	1.35250e38i	−0.343949	−	0.202226i
$477$	2.34758e38			0.340490
$478$	2.98171e38	+	5.16447e38i	0.419527	+	0.726643i
$479$	−2.24995e38	+	3.89702e38i	−0.307120	+	0.531947i	−0.977731	−	0.209862i	$-0.932698\pi$
$479$	−2.24995e38	+	3.89702e38i	−0.307120	+	0.531947i	0.670611	+	0.741809i	$0.266032\pi$
$480$	−2.10064e38	+	3.63841e38i	−0.278197	+	0.481852i
$481$	−9.16770e37	−	1.58789e38i	−0.117803	−	0.204041i
$482$	3.91730e38			0.488433
$483$	3.39002e38	−	1.92161e38i	0.410174	−	0.232504i
$484$	4.40100e38			0.516766
$485$	5.85200e38	+	1.01360e39i	0.666882	+	1.15507i
$486$	−1.30549e37	+	2.26117e37i	−0.0144393	+	0.0250097i
$487$	7.41227e38	−	1.28384e39i	0.795759	−	1.37830i	−0.126597	−	0.991954i	$-0.540406\pi$
$487$	7.41227e38	−	1.28384e39i	0.795759	−	1.37830i	0.922356	−	0.386341i	$-0.126261\pi$
$488$	4.19112e38	+	7.25923e38i	0.436759	+	0.756489i
$489$	8.17309e38			0.826814
$490$	2.13912e38	+	3.84436e38i	0.210083	+	0.377556i
$491$	5.32051e38			0.507308			0.253654	−	0.967295i	$-0.418368\pi$
$491$	5.32051e38			0.507308			0.253654	+	0.967295i	$0.418368\pi$
$492$	1.83162e38	+	3.17246e38i	0.169567	+	0.293699i
$493$	2.65318e38	−	4.59544e38i	0.238499	−	0.413092i
$494$	−2.98582e38	+	5.17160e38i	−0.260629	+	0.451423i
$495$	−1.11944e38	−	1.93892e38i	−0.0948909	−	0.164356i
$496$	−6.68264e38			−0.550128
$497$	1.79081e39	−	1.01511e39i	1.43180	−	0.811606i
$498$	1.07967e38			0.0838426
$499$	−8.86554e38	−	1.53556e39i	−0.668725	−	1.15827i	−0.978261	−	0.207377i	$-0.933507\pi$
$499$	−8.86554e38	−	1.53556e39i	−0.668725	−	1.15827i	0.309536	−	0.950888i	$-0.399826\pi$
$500$	−5.63380e38	+	9.75804e38i	−0.412797	+	0.714986i
$501$	−6.59089e38	+	1.14158e39i	−0.469134	+	0.812564i
$502$	1.28627e38	+	2.22788e38i	0.0889461	+	0.154059i
$503$	8.12320e38			0.545747			0.272873	−	0.962050i	$-0.412026\pi$
$503$	8.12320e38			0.545747			0.272873	+	0.962050i	$0.412026\pi$
$504$	3.56173e38	+	2.09413e38i	0.232497	+	0.136698i
$505$	1.81138e39			1.14891
$506$	−1.76916e38	−	3.06428e38i	−0.109040	−	0.188863i
$507$	2.96446e37	−	5.13460e37i	0.0177554	−	0.0307532i
$508$	−2.40511e38	+	4.16577e38i	−0.139994	+	0.242478i
$509$	−1.22392e39	−	2.11989e39i	−0.692382	−	1.19924i	−0.971055	−	0.238855i	$-0.923228\pi$
$509$	−1.22392e39	−	2.11989e39i	−0.692382	−	1.19924i	0.278673	−	0.960386i	$-0.410105\pi$
$510$	−2.27029e38			−0.124828
$511$	2.34280e35	−	2.95940e37i	0.000125208	−	0.0158162i
$512$	1.51164e39			0.785298
$513$	−2.27744e38	−	3.94464e38i	−0.115013	−	0.199208i
$514$	2.52027e38	−	4.36524e38i	0.123732	−	0.214310i
$515$	1.07521e39	−	1.86232e39i	0.513204	−	0.888895i
$516$	2.79573e38	+	4.84234e38i	0.129740	+	0.224716i
$517$	−4.73487e38			−0.213646
$518$	−1.97538e36	+	2.49528e38i	−0.000866700	+	0.109481i
$519$	1.54414e39			0.658810
$520$	9.06604e38	+	1.57028e39i	0.376157	+	0.651523i
$521$	3.36828e38	−	5.83404e38i	0.135913	−	0.235409i	−0.790033	−	0.613065i	$-0.789936\pi$
$521$	3.36828e38	−	5.83404e38i	0.135913	−	0.235409i	0.925946	+	0.377656i	$0.123270\pi$
$522$	−1.82241e38	+	3.15651e38i	−0.0715194	+	0.123875i
$523$	9.69937e38	+	1.67998e39i	0.370228	+	0.641253i	0.989600	−	0.143844i	$-0.0459463\pi$
$523$	9.69937e38	+	1.67998e39i	0.370228	+	0.641253i	−0.619373	+	0.785097i	$0.712613\pi$
$524$	−1.36740e39			−0.507682
$525$	1.08622e38	+	6.38648e37i	0.0392291	+	0.0230649i
$526$	−1.53391e39			−0.538897
$527$	−9.29868e38	−	1.61058e39i	−0.317810	−	0.550463i
$528$	−2.23045e38	+	3.86326e38i	−0.0741653	+	0.128458i
$529$	5.14811e38	−	8.91678e38i	0.166548	−	0.288470i
$530$	−7.01048e38	−	1.21425e39i	−0.220672	−	0.382216i
$531$	−1.18034e38			−0.0361522
$532$	−2.78175e39	+	1.57682e39i	−0.829087	+	0.469962i
$533$	2.46063e39			0.713679
$534$	−2.62999e38	−	4.55528e38i	−0.0742346	−	0.128578i
$535$	−1.17652e39	+	2.03779e39i	−0.323198	+	0.559795i
$536$	−1.92163e39	+	3.32835e39i	−0.513782	+	0.889897i
$537$	−1.48671e38	−	2.57506e38i	−0.0386900	−	0.0670131i
$538$	5.90667e38			0.149623
$539$	1.16971e39	+	2.10218e39i	0.288431	+	0.518361i
$540$	−6.13543e38			−0.147277
$541$	−1.14086e39	−	1.97602e39i	−0.266606	−	0.461776i	0.701377	−	0.712791i	$-0.252569\pi$
$541$	−1.14086e39	−	1.97602e39i	−0.266606	−	0.461776i	−0.967983	+	0.251015i	$0.919236\pi$
$542$	8.11117e38	−	1.40490e39i	0.184541	−	0.319635i
$543$	−1.94545e39	+	3.36962e39i	−0.430945	+	0.746419i
$544$	1.16479e39	+	2.01747e39i	0.251225	+	0.435135i
$545$	1.06757e39			0.224207
$546$	1.07109e39	−	6.07140e38i	0.219045	−	0.124164i
$547$	1.30481e39			0.259856			0.129928	−	0.991523i	$-0.458525\pi$
$547$	1.30481e39			0.259856			0.129928	+	0.991523i	$0.458525\pi$
$548$	−1.31458e39	−	2.27692e39i	−0.254959	−	0.441601i
$549$	−9.52595e38	+	1.64994e39i	−0.179932	+	0.311652i
$550$	5.72078e37	−	9.90867e37i	0.0105244	−	0.0182287i
$551$	−3.17922e39	−	5.50656e39i	−0.569668	−	0.986694i
$552$	−2.18574e39			−0.381489
$553$	−1.83042e39	−	1.07621e39i	−0.311198	−	0.182970i
$554$	5.73370e38			0.0949605
$555$	−4.17639e38	−	7.23372e38i	−0.0673833	−	0.116711i
$556$	−4.11990e39	+	7.13588e39i	−0.647593	+	1.12166i
$557$	3.24463e39	−	5.61987e39i	0.496896	−	0.860649i	−0.503098	−	0.864230i	$-0.667806\pi$
$557$	3.24463e39	−	5.61987e39i	0.496896	−	0.860649i	0.999994	+	0.00358069i	$0.00113977\pi$
$558$	6.38706e38	+	1.10627e39i	0.0953027	+	0.165069i
$559$	3.75583e39			0.546053
$560$	−2.32275e37	+	2.93408e39i	−0.00329061	+	0.415668i
$561$	−1.24144e39			−0.171382
$562$	−1.91325e39	−	3.31385e39i	−0.257392	−	0.445817i
$563$	3.92236e39	−	6.79373e39i	0.514252	−	0.890710i	−0.485612	−	0.874175i	$-0.661403\pi$
$563$	3.92236e39	−	6.79373e39i	0.514252	−	0.890710i	0.999863	−	0.0165354i	$-0.00526363\pi$
$564$	−6.48773e38	+	1.12371e39i	−0.0828983	+	0.143584i
$565$	5.97703e39	+	1.03525e40i	0.744360	+	1.28927i
$566$	−3.38874e39			−0.411339
$567$	−7.43411e36	+	9.39071e38i	−0.000879578	+	0.111108i
$568$	−1.15464e40			−1.33167
$569$	−5.05754e39	−	8.75991e39i	−0.568606	−	0.984854i	−0.996704	−	0.0811220i	$-0.974150\pi$
$569$	−5.05754e39	−	8.75991e39i	−0.568606	−	0.984854i	0.428098	−	0.903732i	$-0.359184\pi$
$570$	−1.36021e39	+	2.35595e39i	−0.149080	+	0.258214i
$571$	5.79091e39	−	1.00302e40i	0.618762	−	1.07173i	−0.370951	−	0.928653i	$-0.620968\pi$
$571$	5.79091e39	−	1.00302e40i	0.618762	−	1.07173i	0.989712	−	0.143074i	$-0.0456986\pi$
$572$	2.19926e39	+	3.80924e39i	0.229105	+	0.396822i
$573$	−9.56373e39			−0.971371
$574$	−2.88681e39	−	1.69731e39i	−0.285887	−	0.168089i
$575$	−6.66587e38			−0.0643685
$576$	−3.34790e37	−	5.79873e37i	−0.00315243	−	0.00546018i
$577$	−5.75575e39	+	9.96925e39i	−0.528509	+	0.915405i	0.470938	+	0.882166i	$0.343915\pi$
$577$	−5.75575e39	+	9.96925e39i	−0.528509	+	0.915405i	−0.999447	+	0.0332385i	$0.989418\pi$
$578$	1.88422e39	−	3.26356e39i	0.168724	−	0.292239i
$579$	2.35918e39	+	4.08621e39i	0.206026	+	0.356847i
$580$	−8.56481e39			−0.729478
$581$	3.37828e39	−	1.91496e39i	0.280635	−	0.159076i
$582$	−4.45770e39			−0.361183
$583$	−3.83348e39	−	6.63978e39i	−0.302970	−	0.524759i
$584$	−8.30008e37	+	1.43762e38i	−0.00639876	+	0.0110830i
$585$	−2.06061e39	+	3.56909e39i	−0.154966	+	0.268409i
$586$	1.14232e39	+	1.97855e39i	0.0838052	+	0.145155i
$587$	6.11164e39			0.437427			0.218713	−	0.975789i	$-0.429814\pi$
$587$	6.11164e39			0.437427			0.218713	+	0.975789i	$0.429814\pi$
$588$	6.59176e39	+	1.04373e38i	0.460289	+	0.00728816i
$589$	−2.22846e40			−1.51822
$590$	3.52479e38	+	6.10511e38i	0.0234304	+	0.0405826i
$591$	1.46876e39	−	2.54397e39i	0.0952648	−	0.165003i
$592$	−8.32135e38	+	1.44130e39i	−0.0526658	+	0.0912199i
$593$	−8.50521e39	−	1.47315e40i	−0.525281	−	0.909814i	−0.999566	−	0.0294426i	$-0.990627\pi$
$593$	−8.50521e39	−	1.47315e40i	−0.525281	−	0.909814i	0.474285	−	0.880371i	$-0.342707\pi$
$594$	8.52719e38			0.0513928
$595$	−7.10374e39	+	4.02670e39i	−0.417822	+	0.236839i
$596$	6.48330e39			0.372156
$597$	7.14406e37	+	1.23739e38i	0.00400237	+	0.00693231i
$598$	−3.25660e39	+	5.64060e39i	−0.178073	+	0.308431i
$599$	9.91482e39	−	1.71730e40i	0.529171	−	0.916551i	−0.470250	−	0.882533i	$-0.655836\pi$
$599$	9.91482e39	−	1.71730e40i	0.529171	−	0.916551i	0.999421	−	0.0340176i	$-0.0108302\pi$
$600$	−3.53391e38	−	6.12091e38i	−0.0184104	−	0.0318877i
$601$	2.36605e40			1.20322			0.601609	−	0.798791i	$-0.294527\pi$
$601$	2.36605e40			1.20322			0.601609	+	0.798791i	$0.294527\pi$
$602$	−4.40632e39	−	2.59071e39i	−0.218739	−	0.128609i
$603$	−8.73529e39			−0.423328
$604$	1.59632e40	+	2.76490e40i	0.755237	+	1.30811i
$605$	6.73354e39	−	1.16628e40i	0.311022	−	0.538705i
$606$	−3.44950e39	+	5.97472e39i	−0.155562	+	0.269441i
$607$	7.02209e39	+	1.21626e40i	0.309194	+	0.535539i	0.978186	−	0.207730i	$-0.0666076\pi$
$607$	7.02209e39	+	1.21626e40i	0.309194	+	0.535539i	−0.668993	+	0.743269i	$0.733274\pi$
$608$	2.79146e40			1.20013
$609$	−1.03777e38	+	1.31090e40i	−0.00435663	+	0.550326i
$610$	1.13788e40			0.466459
$611$	4.35787e39	+	7.54805e39i	0.174452	+	0.302160i
$612$	−1.70103e39	+	2.94627e39i	−0.0664991	+	0.115180i
$613$	4.06051e37	−	7.03302e37i	0.00155026	−	0.00268513i	−0.865249	−	0.501342i	$-0.832840\pi$
$613$	4.06051e37	−	7.03302e37i	0.00155026	−	0.00268513i	0.866799	+	0.498657i	$0.166173\pi$
$614$	−1.15356e40	−	1.99803e40i	−0.430130	−	0.745007i
$615$	1.12095e40			0.408224
$616$	1.06820e38	−	1.34934e40i	0.00379955	−	0.479956i
$617$	1.33377e40			0.463388			0.231694	−	0.972789i	$-0.425573\pi$
$617$	1.33377e40			0.463388			0.231694	+	0.972789i	$0.425573\pi$
$618$	4.09516e39	+	7.09302e39i	0.138975	+	0.240712i
$619$	2.60196e39	−	4.50672e39i	0.0862553	−	0.149399i	−0.819670	−	0.572836i	$-0.805843\pi$
$619$	2.60196e39	−	4.50672e39i	0.0862553	−	0.149399i	0.905925	+	0.423437i	$0.139177\pi$
$620$	−1.50087e40	+	2.59958e40i	−0.486030	+	0.841829i
$621$	−2.48398e39	−	4.30238e39i	−0.0785814	−	0.136107i
$622$	2.32486e40			0.718516
$623$	−1.63088e40	−	9.58880e39i	−0.492430	−	0.289526i
$624$	8.21144e39			0.242238
$625$	1.58721e40	+	2.74913e40i	0.457483	+	0.792384i
$626$	−6.04332e39	+	1.04673e40i	−0.170195	+	0.294787i
$627$	−7.43789e39	+	1.28828e40i	−0.204678	+	0.354512i
$628$	2.90691e39	+	5.03492e39i	0.0781659	+	0.135387i
$629$	−4.63156e39			−0.121701
$630$	4.87940e39	−	2.76586e39i	0.125294	−	0.0710218i
$631$	−3.97463e39			−0.0997403			−0.0498702	−	0.998756i	$-0.515881\pi$
$631$	−3.97463e39			−0.0997403			−0.0498702	+	0.998756i	$0.515881\pi$
$632$	5.95510e39	+	1.03145e40i	0.146047	+	0.252960i
$633$	1.92600e40	−	3.33594e40i	0.461640	−	0.799584i
$634$	−6.84110e39	+	1.18491e40i	−0.160262	+	0.277582i
$635$	7.35964e39	+	1.27473e40i	0.168515	+	0.291876i
$636$	−2.10106e40			−0.470230
$637$	2.27459e40	−	3.79949e40i	0.497601	−	0.831196i
$638$	1.19036e40			0.254553
$639$	−1.31219e40	−	2.27278e40i	−0.274305	−	0.475110i
$640$	2.33789e40	−	4.04935e40i	0.477766	−	0.827515i
$641$	3.63350e40	−	6.29340e40i	0.725911	−	1.25732i	−0.232687	−	0.972552i	$-0.574752\pi$
$641$	3.63350e40	−	6.29340e40i	0.725911	−	1.25732i	0.958598	−	0.284763i	$-0.0919150\pi$
$642$	−4.48099e39	−	7.76130e39i	−0.0875218	−	0.151592i
$643$	4.92461e40			0.940401			0.470200	−	0.882560i	$-0.344182\pi$
$643$	4.92461e40			0.940401			0.470200	+	0.882560i	$0.344182\pi$
$644$	−3.03403e40	+	1.71982e40i	−0.566467	+	0.321098i
$645$	1.71099e40			0.312342
$646$	7.54225e39	+	1.30636e40i	0.134626	+	0.233179i
$647$	−2.44848e40	+	4.24089e40i	−0.427350	+	0.740192i	−0.996637	−	0.0819468i	$-0.973886\pi$
$647$	−2.44848e40	+	4.24089e40i	−0.427350	+	0.740192i	0.569286	+	0.822139i	$0.307220\pi$
$648$	2.63376e39	−	4.56181e39i	0.0449510	−	0.0778574i
$649$	1.92743e39	+	3.33841e39i	0.0321685	+	0.0557174i
$650$	−2.10611e39			−0.0343746
$651$	3.96066e40	+	2.32868e40i	0.632183	+	0.371695i
$652$	−7.31483e40			−1.14186
$653$	−3.34048e40	−	5.78588e40i	−0.509997	−	0.883341i	−0.999933	−	0.0115824i	$-0.996313\pi$
$653$	−3.34048e40	−	5.78588e40i	−0.509997	−	0.883341i	0.489936	−	0.871759i	$-0.337020\pi$
$654$	−2.03303e39	+	3.52131e39i	−0.0303575	+	0.0525808i
$655$	−2.09212e40	+	3.62366e40i	−0.305554	+	0.529235i
$656$	−1.11674e40	−	1.93424e40i	−0.159531	−	0.276316i
$657$	−3.77304e38			−0.00527222
$658$	9.38997e37	−	1.18613e40i	0.00128348	−	0.162128i
$659$	1.09483e41			1.46389			0.731943	−	0.681366i	$-0.238614\pi$
$659$	1.09483e41			1.46389			0.731943	+	0.681366i	$0.238614\pi$
$660$	1.00188e40	+	1.73531e40i	0.131048	+	0.226982i
$661$	5.36247e40	−	9.28807e40i	0.686189	−	1.18851i	−0.286873	−	0.957969i	$-0.592616\pi$
$661$	5.36247e40	−	9.28807e40i	0.686189	−	1.18851i	0.973062	−	0.230545i	$-0.0740510\pi$
$662$	−2.26766e40	+	3.92770e40i	−0.283882	+	0.491697i
$663$	1.14260e40	+	1.97903e40i	0.139941	+	0.242386i
$664$	−2.17818e40			−0.261009
$665$	−7.74569e38	+	9.78430e40i	−0.00908126	+	1.14714i
$666$	3.18132e39			0.0364948
$667$	−3.46753e40	−	6.00594e40i	−0.389221	−	0.674150i
$668$	5.89878e40	−	1.02170e41i	0.647893	−	1.12218i
$669$	5.38311e39	−	9.32382e39i	0.0578568	−	0.100211i
$670$	2.60858e40	+	4.51820e40i	0.274360	+	0.475205i
$671$	6.22216e40			0.640419
$672$	−4.96127e40	−	2.91700e40i	−0.499734	−	0.293820i
$673$	−1.59158e41			−1.56896			−0.784478	−	0.620156i	$-0.787069\pi$
$673$	−1.59158e41			−1.56896			−0.784478	+	0.620156i	$0.787069\pi$
$674$	9.46978e39	+	1.64021e40i	0.0913632	+	0.158246i
$675$	8.03220e38	−	1.39122e39i	0.00758455	−	0.0131368i
$676$	−2.65316e39	+	4.59541e39i	−0.0245209	+	0.0424714i
$677$	−2.03065e40	−	3.51719e40i	−0.183696	−	0.318171i	0.759440	−	0.650577i	$-0.225473\pi$
$677$	−2.03065e40	−	3.51719e40i	−0.183696	−	0.318171i	−0.943136	+	0.332406i	$0.892140\pi$
$678$	−4.55294e40			−0.403145
$679$	−1.39481e41	+	7.90641e40i	−1.20894	+	0.685279i
$680$	4.58020e40			0.388602
$681$	−4.06007e39	−	7.03225e39i	−0.0337210	−	0.0584065i
$682$	2.08595e40	−	3.61297e40i	0.169602	−	0.293759i
$683$	−1.16516e41	+	2.01811e41i	−0.927436	+	1.60637i	−0.139839	+	0.990174i	$0.544659\pi$
$683$	−1.16516e41	+	2.01811e41i	−0.927436	+	1.60637i	−0.787596	+	0.616192i	$0.788675\pi$
$684$	2.03828e40	+	3.53041e40i	0.158837	+	0.275114i
$685$	−8.04525e40			−0.613799
$686$	−5.28937e40	+	2.88856e40i	−0.395097	+	0.215766i
$687$	−7.07099e40			−0.517139
$688$	−1.70455e40	−	2.95236e40i	−0.122061	−	0.211416i
$689$	−7.05650e40	+	1.22222e41i	−0.494779	+	0.856982i
$690$	−1.48356e40	+	2.56960e40i	−0.101858	+	0.176423i
$691$	−9.86141e40	−	1.70805e41i	−0.662991	−	1.14833i	−0.979826	−	0.199853i	$-0.935954\pi$
$691$	−9.86141e40	−	1.70805e41i	−0.662991	−	1.14833i	0.316835	−	0.948481i	$-0.397380\pi$
$692$	−1.38199e41			−0.909842
$693$	2.66816e40	−	1.51243e40i	0.172020	−	0.0975086i
$694$	1.26186e41			0.796709
$695$	1.26069e41	+	2.18358e41i	0.779523	+	1.35017i
$696$	3.67663e40	−	6.36810e40i	0.222646	−	0.385635i
$697$	3.10781e40	−	5.38288e40i	0.184323	−	0.319256i
$698$	−5.59729e40	−	9.69479e40i	−0.325143	−	0.563164i
$699$	6.31054e40			0.359044
$700$	−9.72156e39	−	5.71583e39i	−0.0541769	−	0.0318536i
$701$	−1.70938e41			−0.933100			−0.466550	−	0.884495i	$-0.654503\pi$
$701$	−1.70938e41			−0.933100			−0.466550	+	0.884495i	$0.654503\pi$
$702$	−7.84824e39	−	1.35936e40i	−0.0419647	−	0.0726850i
$703$	−2.77492e40	+	4.80630e40i	−0.145344	+	0.251744i
$704$	−1.09339e39	+	1.89380e39i	−0.00561010	+	0.00971699i
$705$	1.98525e40	+	3.43855e40i	0.0997867	+	0.172836i
$706$	1.50206e41			0.739636
$707$	−1.96432e39	+	2.48131e41i	−0.00947612	+	1.19702i
$708$	1.05639e40			0.0499277
$709$	−1.83114e41	−	3.17163e41i	−0.847914	−	1.46863i	−0.883066	−	0.469249i	$-0.844525\pi$
$709$	−1.83114e41	−	3.17163e41i	−0.847914	−	1.46863i	0.0351517	−	0.999382i	$-0.488809\pi$
$710$	−7.83706e40	+	1.35742e41i	−0.355555	+	0.615840i
$711$	−1.35353e40	+	2.34438e40i	−0.0601671	+	0.104212i
$712$	5.30589e40	+	9.19007e40i	0.231099	+	0.400275i
$713$	−2.43056e41			−1.03731
$714$	2.46197e38	−	3.10994e40i	0.00102958	−	0.130055i
$715$	1.34595e41			0.551558
$716$	1.33059e40	+	2.30465e40i	0.0534324	+	0.0925477i
$717$	1.36725e41	−	2.36814e41i	0.538046	−	0.931923i
$718$	−1.32171e40	+	2.28927e40i	−0.0509720	+	0.0882862i
$719$	−9.87507e40	−	1.71041e41i	−0.373225	−	0.646445i	0.616834	−	0.787093i	$-0.288415\pi$
$719$	−9.87507e40	−	1.71041e41i	−0.373225	−	0.646445i	−0.990060	+	0.140648i	$0.955082\pi$
$720$	3.74076e40			0.138560
$721$	2.53943e41	+	1.49307e41i	0.921882	+	0.542024i
$722$	5.42294e40			0.192950
$723$	−8.98129e40	−	1.55561e41i	−0.313208	−	0.542493i
$724$	1.74116e41	−	3.01577e41i	0.595152	−	1.03083i
$725$	1.12126e40	−	1.94208e40i	0.0375670	−	0.0650679i
$726$	2.56460e40	+	4.44201e40i	0.0842245	+	0.145881i
$727$	−3.95078e41			−1.27184			−0.635921	−	0.771754i	$-0.719380\pi$
$727$	−3.95078e41			−1.27184			−0.635921	+	0.771754i	$0.719380\pi$
$728$	−2.16087e41	+	1.22488e41i	−0.681906	+	0.386534i
$729$	1.19725e40			0.0370370
$730$	1.12673e39	+	1.95155e39i	0.00341694	+	0.00591831i
$731$	4.74365e40	−	8.21624e40i	0.141030	−	0.244271i
$732$	8.52562e40	−	1.47668e41i	0.248494	−	0.430404i
$733$	2.68123e41	+	4.64402e41i	0.766171	+	1.32705i	0.939625	+	0.342206i	$0.111174\pi$
$733$	2.68123e41	+	4.64402e41i	0.766171	+	1.32705i	−0.173454	+	0.984842i	$0.555493\pi$
$734$	−1.94560e40			−0.0545081
$735$	1.03620e41	−	1.73087e41i	0.284628	−	0.475444i
$736$	3.04461e41			0.819980
$737$	1.42643e41	+	2.47065e41i	0.376679	+	0.652427i
$738$	−2.13468e40	+	3.69738e40i	−0.0552734	+	0.0957364i
$739$	−1.94126e41	+	3.36237e41i	−0.492879	+	0.853692i	−0.999966	−	0.00820315i	$-0.997389\pi$
$739$	−1.94126e41	+	3.36237e41i	−0.492879	+	0.853692i	0.507087	+	0.861895i	$0.330722\pi$
$740$	3.73782e40	+	6.47410e40i	0.0930590	+	0.161183i
$741$	2.73827e41			0.668517
$742$	1.67094e41	−	9.47158e40i	0.400040	−	0.226760i
$743$	−5.84810e41			−1.37302			−0.686511	−	0.727120i	$-0.740858\pi$
$743$	−5.84810e41			−1.37302			−0.686511	+	0.727120i	$0.740858\pi$
$744$	−1.28856e41	−	2.23185e41i	−0.296686	−	0.513875i
$745$	9.91945e40	−	1.71810e41i	0.223986	−	0.387956i
$746$	4.65148e40	−	8.05660e40i	0.103010	−	0.178418i
$747$	−2.47538e40	−	4.28749e40i	−0.0537642	−	0.0931224i
$748$	1.11108e41			0.236685
$749$	−2.77869e41	−	1.63374e41i	−0.580569	−	0.341348i
$750$	−1.31320e41			−0.269117
$751$	4.64451e40	+	8.04453e40i	0.0933601	+	0.161704i	0.908923	−	0.416964i	$-0.136906\pi$
$751$	4.64451e40	+	8.04453e40i	0.0933601	+	0.161704i	−0.815563	+	0.578668i	$0.803573\pi$
$752$	3.95556e40	−	6.85123e40i	0.0779918	−	0.135086i
$753$	5.89811e40	−	1.02158e41i	0.114074	−	0.197582i
$754$	−1.09558e41	−	1.89761e41i	−0.207855	−	0.360016i
$755$	9.76946e41			1.81819
$756$	6.65344e38	−	8.40458e40i	0.00121473	−	0.153444i
$757$	3.80552e41			0.681590			0.340795	−	0.940138i	$-0.389304\pi$
$757$	3.80552e41			0.681590			0.340795	+	0.940138i	$0.389304\pi$
$758$	−1.48237e41	−	2.56754e41i	−0.260468	−	0.451143i
$759$	−8.11242e40	+	1.40511e41i	−0.139844	+	0.242217i
$760$	2.74415e41	−	4.75301e41i	0.464099	−	0.803843i
$761$	3.59126e41	+	6.22024e41i	0.595894	+	1.03212i	0.993420	+	0.114528i	$0.0365357\pi$
$761$	3.59126e41	+	6.22024e41i	0.595894	+	1.03212i	−0.397526	+	0.917591i	$0.630131\pi$
$762$	−5.60612e40			−0.0912673
$763$	−1.15771e39	+	1.46241e41i	−0.00184924	+	0.233595i
$764$	8.55943e41			1.34150
$765$	5.20515e40	+	9.01558e40i	0.0800465	+	0.138645i
$766$	2.68573e41	−	4.65182e41i	0.405271	−	0.701950i
$767$	3.54793e40	−	6.14519e40i	0.0525342	−	0.0909919i
$768$	9.28010e40	+	1.60736e41i	0.134839	+	0.233548i
$769$	1.02094e42			1.45569			0.727845	−	0.685742i	$-0.240522\pi$
$769$	1.02094e42			1.45569			0.727845	+	0.685742i	$0.240522\pi$
$770$	−1.57906e41	−	9.28416e40i	−0.220945	−	0.129905i
$771$	−2.31132e41			−0.317374
$772$	−2.11144e41	−	3.65712e41i	−0.284529	−	0.492819i
$773$	−5.73071e41	+	9.92588e41i	−0.757889	+	1.31270i	0.186036	+	0.982543i	$0.440436\pi$
$773$	−5.73071e41	+	9.92588e41i	−0.757889	+	1.31270i	−0.943925	+	0.330159i	$0.892898\pi$
$774$	−3.25831e40	+	5.64356e40i	−0.0422910	+	0.0732502i
$775$	−3.92973e40	−	6.80649e40i	−0.0500596	−	0.0867059i
$776$	8.99319e41			1.12439
$777$	9.95435e40	−	5.64255e40i	0.122154	−	0.0692422i
$778$	−3.11449e41			−0.375131
$779$	−3.72398e41	−	6.45012e41i	−0.440265	−	0.762562i
$780$	1.84423e41	−	3.19429e41i	0.214014	−	0.370683i
$781$	−4.28547e41	+	7.42265e41i	−0.488156	+	0.845511i
$782$	8.22624e40	+	1.42483e41i	0.0919821	+	0.159318i
$783$	1.67131e41			0.183448
$784$	−4.01898e41	−	6.36362e39i	−0.433045	−	0.00685679i
$785$	1.77903e41			0.188180
$786$	−7.96825e40	−	1.38014e41i	−0.0827439	−	0.143317i
$787$	−6.75528e41	+	1.17005e42i	−0.688668	+	1.19281i	0.283601	+	0.958942i	$0.408471\pi$
$787$	−6.75528e41	+	1.17005e42i	−0.688668	+	1.19281i	−0.972269	+	0.233865i	$0.924862\pi$
$788$	−1.31452e41	+	2.27682e41i	−0.131564	+	0.227876i
$789$	3.51683e41	+	6.09132e41i	0.345569	+	0.598543i
$790$	1.61680e41			0.155978
$791$	−1.42462e42	+	8.07533e41i	−1.34939	+	0.764894i
$792$	−1.72032e41			−0.159990
$793$	−5.72674e41	−	9.91901e41i	−0.522933	−	0.905747i
$794$	2.05070e41	−	3.55192e41i	0.183868	−	0.318468i
$795$	−3.21462e41	+	5.56789e41i	−0.283013	+	0.490193i
$796$	−6.39385e39	−	1.10745e40i	−0.00552743	−	0.00957379i
$797$	1.97798e42			1.67910			0.839548	−	0.543286i	$-0.182820\pi$
$797$	1.97798e42			1.67910			0.839548	+	0.543286i	$0.182820\pi$
$798$	−3.21253e41	−	1.88882e41i	−0.267796	−	0.157452i
$799$	2.20161e41			0.180224
$800$	4.92253e40	+	8.52607e40i	0.0395716	+	0.0685400i
$801$	−1.20597e41	+	2.08880e41i	−0.0952063	+	0.164902i
$802$	−8.76803e40	+	1.51867e41i	−0.0679788	+	0.117743i
$803$	6.16118e39	+	1.06715e40i	0.00469125	+	0.00812548i
$804$	7.81799e41			0.584632
$805$	−8.44813e39	+	1.06716e42i	−0.00620469	+	0.783772i
$806$	−7.67945e41			−0.553952
$807$	−1.35424e41	−	2.34561e41i	−0.0959464	−	0.166184i
$808$	6.95921e41	−	1.20537e42i	0.484279	−	0.838795i
$809$	1.51370e41	−	2.62181e41i	0.103464	−	0.179204i	−0.809646	−	0.586919i	$-0.800341\pi$
$809$	1.51370e41	−	2.62181e41i	0.103464	−	0.179204i	0.913109	+	0.407715i	$0.133674\pi$
$810$	−3.57530e40	−	6.19261e40i	−0.0240038	−	0.0415758i
$811$	−8.78138e40			−0.0579109			−0.0289554	−	0.999581i	$-0.509218\pi$
$811$	−8.78138e40			−0.0579109			−0.0289554	+	0.999581i	$0.509218\pi$
$812$	9.28794e39	−	1.17325e42i	0.00601668	−	0.760022i
$813$	−7.43868e41			−0.473351
$814$	−5.19493e40	−	8.99787e40i	−0.0324732	−	0.0562453i
$815$	−1.11917e42	+	1.93846e42i	−0.687244	+	1.19034i
$816$	1.03711e41	−	1.79633e41i	0.0625632	−	0.108363i
$817$	−5.68416e41	−	9.84525e41i	−0.336858	−	0.583455i
$818$	−1.53341e42			−0.892762
$819$	−4.86674e41	−	2.86142e41i	−0.278370	−	0.163669i
$820$	−1.00324e42			−0.563773
$821$	−1.79836e42	−	3.11485e42i	−0.992891	−	1.71974i	−0.599529	−	0.800353i	$-0.704645\pi$
$821$	−1.79836e42	−	3.11485e42i	−0.992891	−	1.71974i	−0.393362	−	0.919384i	$-0.628688\pi$
$822$	1.53209e41	−	2.65366e41i	0.0831082	−	0.143948i
$823$	−8.78764e41	+	1.52206e42i	−0.468354	+	0.811214i	−0.999346	−	0.0361635i	$-0.988486\pi$
$823$	−8.78764e41	+	1.52206e42i	−0.468354	+	0.811214i	0.530991	+	0.847377i	$0.321820\pi$
$824$	−8.26178e41	−	1.43098e42i	−0.432642	−	0.749359i
$825$	−5.24647e40			−0.0269951
$826$	−8.40127e40	+	4.76220e40i	−0.0424751	+	0.0240767i
$827$	2.54097e42			1.26232			0.631160	−	0.775652i	$-0.282579\pi$
$827$	2.54097e42			1.26232			0.631160	+	0.775652i	$0.282579\pi$
$828$	2.22313e41	+	3.85058e41i	0.108524	+	0.187969i
$829$	−4.46683e41	+	7.73677e41i	−0.214269	+	0.371124i	−0.953046	−	0.302825i	$-0.902070\pi$
$829$	−4.46683e41	+	7.73677e41i	−0.214269	+	0.371124i	0.738777	+	0.673949i	$0.235403\pi$
$830$	−1.47843e41	+	2.56071e41i	−0.0696895	+	0.120706i
$831$	−1.31458e41	−	2.27692e41i	−0.0608936	−	0.105471i
$832$	4.02533e40			0.0183237
$833$	−5.43892e41	−	9.77468e41i	−0.243310	−	0.437270i
$834$	−9.60317e41			−0.422189
$835$	−1.80503e42	−	3.12640e42i	−0.779884	−	1.35080i
$836$	6.65683e41	−	1.15300e42i	0.282668	−	0.489595i
$837$	2.92876e41	−	5.07276e41i	0.122226	−	0.211702i
$838$	1.07093e42	+	1.85491e42i	0.439261	+	0.760823i
$839$	1.87727e42			0.756794			0.378397	−	0.925643i	$-0.376475\pi$
$839$	1.87727e42			0.756794			0.378397	+	0.925643i	$0.376475\pi$
$840$	−9.84396e41	+	5.57998e41i	−0.390050	+	0.221097i
$841$	−2.34598e41			−0.0913657
$842$	−3.44757e41	−	5.97137e41i	−0.131974	−	0.228586i
$843$	−8.77313e41	+	1.51955e42i	−0.330107	+	0.571762i
$844$	−1.72375e42	+	2.98563e42i	−0.637543	+	1.10426i
$845$	8.11868e40	+	1.40620e41i	0.0295164	+	0.0511239i
$846$	−1.51224e41			−0.0540444
$847$	1.59032e42	+	9.35037e41i	0.558696	+	0.328488i
$848$	1.28101e42			0.442398
$849$	7.76946e41	+	1.34571e42i	0.263772	+	0.456867i
$850$	−2.66004e40	+	4.60732e40i	−0.00887797	+	0.0153771i
$851$	−3.02657e41	+	5.24218e41i	−0.0993053	+	0.172002i
$852$	1.17439e42	+	2.03411e42i	0.378826	+	0.656146i
$853$	−1.54366e42			−0.489543			−0.244772	−	0.969581i	$-0.578713\pi$
$853$	−1.54366e42			−0.489543			−0.244772	+	0.969581i	$0.578713\pi$
$854$	−1.23395e40	+	1.55872e42i	−0.00384732	+	0.485990i
$855$	1.24743e42			0.382391
$856$	9.04018e41	+	1.56581e42i	0.272463	+	0.471920i
$857$	1.62870e42	−	2.82099e42i	0.482634	−	0.835947i	−0.517167	−	0.855885i	$-0.673013\pi$
$857$	1.62870e42	−	2.82099e42i	0.482634	−	0.835947i	0.999801	+	0.0199373i	$0.00634666\pi$
$858$	−2.56316e41	+	4.43952e41i	−0.0746809	+	0.129351i
$859$	8.13380e41	+	1.40882e42i	0.233020	+	0.403602i	0.958695	−	0.284435i	$-0.0918060\pi$
$859$	8.13380e41	+	1.40882e42i	0.233020	+	0.403602i	−0.725676	+	0.688037i	$0.758473\pi$
$860$	−1.53131e42			−0.431357
$861$	−1.21560e40	+	1.53553e42i	−0.00336700	+	0.425317i
$862$	2.43904e42			0.664298
$863$	−1.76183e42	−	3.05157e42i	−0.471852	−	0.817272i	0.527629	−	0.849475i	$-0.323081\pi$
$863$	−1.76183e42	−	3.05157e42i	−0.471852	−	0.817272i	−0.999481	+	0.0322025i	$0.989748\pi$
$864$	−3.66867e41	+	6.35433e41i	−0.0966184	+	0.167348i
$865$	−2.11445e42	+	3.66233e42i	−0.547599	+	0.948470i
$866$	1.46453e41	+	2.53664e41i	0.0372983	+	0.0646025i
$867$	−1.72800e42			−0.432779
$868$	−3.54474e42	−	2.08415e42i	−0.873070	−	0.513325i
$869$	8.84098e41			0.214148
$870$	−4.99098e41	−	8.64463e41i	−0.118893	−	0.205929i
$871$	2.62571e42	−	4.54786e42i	0.615153	−	1.06548i
$872$	4.10154e41	−	7.10408e41i	0.0945058	−	0.163689i
$873$	1.02203e42	+	1.77020e42i	0.231609	+	0.401159i
$874$	1.97145e42			0.439409
$875$	−4.10900e42	+	2.32916e42i	−0.900780	+	0.510601i
$876$	3.37683e40			0.00728114
$877$	−3.57204e42	−	6.18695e42i	−0.757569	−	1.31215i	−0.944087	−	0.329696i	$-0.893054\pi$
$877$	−3.57204e42	−	6.18695e42i	−0.757569	−	1.31215i	0.186518	−	0.982452i	$-0.440280\pi$
$878$	1.56189e42	−	2.70527e42i	0.325821	−	0.564339i
$879$	5.23804e41	−	9.07254e41i	0.107481	−	0.186162i
$880$	−6.10847e41	−	1.05802e42i	−0.123292	−	0.213547i
$881$	3.57230e42			0.709246			0.354623	−	0.935009i	$-0.384609\pi$
$881$	3.57230e42			0.709246			0.354623	+	0.935009i	$0.384609\pi$
$882$	3.73588e41	+	6.71401e41i	0.0729622	+	0.131126i
$883$	1.93134e42			0.371046			0.185523	−	0.982640i	$-0.440602\pi$
$883$	1.93134e42			0.371046			0.185523	+	0.982640i	$0.440602\pi$
$884$	−1.02261e42	−	1.77121e42i	−0.193265	−	0.334744i
$885$	1.61628e41	−	2.79947e41i	0.0300495	−	0.0520473i
$886$	−3.40142e41	+	5.89143e41i	−0.0622116	+	0.107754i
$887$	2.63785e42	+	4.56889e42i	0.474633	+	0.822089i	0.999578	−	0.0290475i	$-0.00924741\pi$
$887$	2.63785e42	+	4.56889e42i	0.474633	+	0.822089i	−0.524945	+	0.851136i	$0.675914\pi$
$888$	−6.41815e41			−0.113611
$889$	−1.75416e42	+	9.94332e41i	−0.305487	+	0.173163i
$890$	1.44054e42			0.246814
$891$	−1.95505e41	−	3.38625e41i	−0.0329558	−	0.0570810i
$892$	−4.81782e41	+	8.34472e41i	−0.0799025	+	0.138395i
$893$	1.31906e42	−	2.28468e42i	0.215238	−	0.372803i
$894$	3.77801e41	+	6.54371e41i	0.0606554	+	0.105058i
$895$	8.14321e41			0.128636
$896$	5.52162e42	+	3.24646e42i	0.858224	+	0.504596i
$897$	2.98660e42			0.456758
$898$	−2.14119e42	−	3.70866e42i	−0.322217	−	0.558097i
$899$	4.08843e42	−	7.08136e42i	0.605398	−	1.04858i
$900$	−7.18873e40	+	1.24512e41i	−0.0104746	+	0.0181425i
$901$	1.78249e42	+	3.08736e42i	0.255574	+	0.442667i
$902$	1.39433e42			0.196730
$903$	−1.85544e40	+	2.34378e42i	−0.00257618	+	0.325421i
$904$	9.18533e42			1.25503
$905$	−5.32794e42	−	9.22826e42i	−0.716399	−	1.24084i
$906$	−1.86044e42	+	3.22238e42i	−0.246183	+	0.426401i
$907$	−3.51254e42	+	6.08390e42i	−0.457421	+	0.792276i	−0.998824	−	0.0484872i	$-0.984560\pi$
$907$	−3.51254e42	+	6.08390e42i	−0.457421	+	0.792276i	0.541403	+	0.840763i	$0.317893\pi$
$908$	3.63372e41	+	6.29378e41i	0.0465700	+	0.0806616i
$909$	3.16351e42			0.399018
$910$	−2.66923e40	+	3.37175e42i	−0.00331349	+	0.418557i
$911$	1.14433e43			1.39809			0.699044	−	0.715078i	$-0.253609\pi$
$911$	1.14433e43			1.39809			0.699044	+	0.715078i	$0.253609\pi$
$912$	−1.24274e42	−	2.15249e42i	−0.149436	−	0.258830i
$913$	−8.08434e41	+	1.40025e42i	−0.0956794	+	0.165722i
$914$	−1.61631e42	+	2.79953e42i	−0.188280	+	0.326111i
$915$	−2.60884e42	−	4.51865e42i	−0.299118	−	0.518087i
$916$	6.32846e42			0.714190
$917$	−4.94116e42	−	2.90518e42i	−0.548875	−	0.322713i
$918$	−3.96496e41			−0.0433531
$919$	3.90233e42	+	6.75904e42i	0.420000	+	0.727462i	0.995939	−	0.0900311i	$-0.0286966\pi$
$919$	3.90233e42	+	6.75904e42i	0.420000	+	0.727462i	−0.575939	+	0.817493i	$0.695363\pi$
$920$	2.99301e42	−	5.18405e42i	0.317092	−	0.549219i
$921$	−5.28961e42	+	9.16187e42i	−0.551644	+	0.955475i
$922$	6.89821e41	+	1.19480e42i	0.0708171	+	0.122659i
$923$	1.57770e43			1.59441
$924$	−2.38797e42	+	1.35361e42i	−0.237567	+	0.134663i
$925$	−1.95735e41			−0.0191696
$926$	2.45151e42	+	4.24614e42i	0.236360	+	0.409388i
$927$	1.87781e42	−	3.25247e42i	0.178236	−	0.308714i
$928$	−5.12132e42	+	8.87038e42i	−0.478560	+	0.828890i
$929$	4.12752e42	+	7.14907e42i	0.379718	+	0.657691i	0.991021	−	0.133706i	$-0.0426877\pi$
$929$	4.12752e42	+	7.14907e42i	0.379718	+	0.657691i	−0.611303	+	0.791396i	$0.709354\pi$
$930$	−3.49841e42			−0.316860
$931$	−1.34021e43	−	2.12208e41i	−1.19510	−	0.0189230i
$932$	−5.64786e42			−0.495853
$933$	−5.33027e42	−	9.23229e42i	−0.460750	−	0.798042i
$934$	−1.40011e42	+	2.42506e42i	−0.119160	+	0.206392i
$935$	1.69995e42	−	2.94440e42i	0.142452	−	0.246733i
$936$	1.58335e42	+	2.74244e42i	0.130640	+	0.226275i
$937$	2.01280e43			1.63522			0.817611	−	0.575771i	$-0.195298\pi$
$937$	2.01280e43			1.63522			0.817611	+	0.575771i	$0.195298\pi$
$938$	−6.21752e42	+	3.52436e42i	−0.497366	+	0.281928i
$939$	5.54227e42			0.436552
$940$	−1.77677e42	−	3.07746e42i	−0.137809	−	0.238693i
$941$	9.82581e42	−	1.70188e43i	0.750445	−	1.29981i	−0.197162	−	0.980371i	$-0.563173\pi$
$941$	9.82581e42	−	1.70188e43i	0.750445	−	1.29981i	0.947607	−	0.319438i	$-0.103494\pi$
$942$	−3.38789e41	+	5.86800e41i	−0.0254795	+	0.0441319i
$943$	−4.06170e42	−	7.03507e42i	−0.300807	−	0.521014i
$944$	−6.44078e41			−0.0469726
$945$	−2.21707e42	−	1.30353e42i	−0.159227	−	0.0936184i
$946$	2.12826e42			0.150523
$947$	−4.51635e42	−	7.82254e42i	−0.314567	−	0.544845i	0.664779	−	0.747040i	$-0.268526\pi$
$947$	−4.51635e42	−	7.82254e42i	−0.314567	−	0.544845i	−0.979345	+	0.202195i	$0.935193\pi$
$948$	1.21139e42	−	2.09820e42i	0.0830931	−	0.143921i
$949$	1.13412e41	−	1.96436e41i	0.00766126	−	0.0132697i
$950$	3.18744e41	+	5.52080e41i	0.0212055	+	0.0367291i
$951$	6.27390e42			0.411074
$952$	−4.96690e40	+	6.27415e42i	−0.00320516	+	0.404874i
$953$	−2.34761e43			−1.49204			−0.746018	−	0.665926i	$-0.768037\pi$
$953$	−2.34761e43			−1.49204			−0.746018	+	0.665926i	$0.768037\pi$
$954$	−1.22435e42	−	2.12064e42i	−0.0766398	−	0.132744i
$955$	1.30959e43	−	2.26828e43i	0.807398	−	1.39845i
$956$	−1.22367e43	+	2.11946e43i	−0.743062	+	1.28702i
$957$	−2.72917e42	−	4.72706e42i	−0.163233	−	0.282728i
$958$	4.69373e42			0.276515
$959$	8.72451e40	−	1.10207e43i	0.00506257	−	0.639500i
$960$	1.83376e41			0.0104811
$961$	−5.44790e42	−	9.43605e42i	−0.306719	−	0.531253i
$962$	−9.56260e41	+	1.65629e42i	−0.0530319	+	0.0918540i
$963$	−2.05474e42	+	3.55891e42i	−0.112247	+	0.194418i
$964$	8.03816e42	+	1.39225e43i	0.432553	+	0.749204i
$965$	−1.29220e43			−0.684989
$966$	−3.50386e42	−	2.06011e42i	−0.182970	−	0.107578i
$967$	−1.23748e43			−0.636584			−0.318292	−	0.947993i	$-0.603109\pi$
$967$	−1.23748e43			−0.636584			−0.318292	+	0.947993i	$0.603109\pi$
$968$	−5.17395e42	−	8.96155e42i	−0.262198	−	0.454141i
$969$	3.45846e42	−	5.99023e42i	0.172659	−	0.299053i
$970$	6.10408e42	−	1.05726e43i	0.300213	−	0.519984i
$971$	−6.18205e42	−	1.07076e43i	−0.299539	−	0.518817i	0.676492	−	0.736450i	$-0.263500\pi$
$971$	−6.18205e42	−	1.07076e43i	−0.299539	−	0.518817i	−0.976031	+	0.217634i	$0.930166\pi$
$972$	−1.07153e42			−0.0511496
$973$	−3.00484e43	+	1.70327e43i	−1.41314	+	0.801027i
$974$	−1.54631e43			−0.716460
$975$	4.82874e41	+	8.36362e41i	0.0220428	+	0.0381792i
$976$	−5.19806e42	+	9.00330e42i	−0.233786	+	0.404929i
$977$	−1.96112e43	+	3.39676e43i	−0.869026	+	1.50520i	−0.00603357	+	0.999982i	$0.501921\pi$
$977$	−1.96112e43	+	3.39676e43i	−0.869026	+	1.50520i	−0.862993	+	0.505216i	$0.831413\pi$
$978$	−4.26257e42	−	7.38299e42i	−0.186105	−	0.322344i
$979$	7.87716e42			0.338860
$980$	−9.27387e42	+	1.54911e43i	−0.393082	+	0.656606i
$981$	1.86447e42			0.0778674
$982$	−2.77484e42	−	4.80617e42i	−0.114188	−	0.197780i
$983$	−1.23411e43	+	2.13754e43i	−0.500412	+	0.866739i	0.499588	+	0.866263i	$0.333485\pi$
$983$	−1.23411e43	+	2.13754e43i	−0.500412	+	0.866739i	−1.00000		0.000475819i	$0.999849\pi$
$984$	4.30662e42	−	7.45929e42i	0.172071	−	0.298036i
$985$	4.02245e42	+	6.96708e42i	0.158367	+	0.274300i
$986$	−5.53493e42			−0.214732
$987$	−4.73180e42	+	2.68219e42i	−0.180896	+	0.102539i
$988$	−2.45072e43			−0.923248
$989$	−6.19965e42	−	1.07381e43i	−0.230155	−	0.398640i
$990$	−1.16766e42	+	2.02244e42i	−0.0427174	+	0.0739887i
$991$	8.13032e42	−	1.40821e43i	0.293116	−	0.507692i	−0.681429	−	0.731884i	$-0.738641\pi$
$991$	8.13032e42	−	1.40821e43i	0.293116	−	0.507692i	0.974545	+	0.224193i	$0.0719744\pi$
$992$	1.79489e43	+	3.10883e43i	0.637702	+	1.10453i
$993$	2.07965e43			0.728159
$994$	−1.85095e43	−	1.08828e43i	−0.638694	−	0.375523i
$995$	−3.91304e41			−0.0133070
$996$	2.21544e42	+	3.83725e42i	0.0742505	+	0.128606i
$997$	−3.34037e42	+	5.78569e42i	−0.110335	+	0.191106i	−0.915905	−	0.401394i	$-0.868526\pi$
$997$	−3.34037e42	+	5.78569e42i	−0.110335	+	0.191106i	0.805570	+	0.592500i	$0.201859\pi$
$998$	−9.24742e42	+	1.60170e43i	−0.301043	+	0.521421i
$999$	−7.29388e41	−	1.26334e42i	−0.0234023	−	0.0405340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.e.b.4.9	✓	40
7.2	even	3	inner	21.30.e.b.16.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.e.b.4.9	✓	40	1.1	even	1	trivial
21.30.e.b.16.9	yes	40	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5215.37 - 9033.29i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(2.14035e8 - 3.70720e8i) q^{4} +(-6.54948e9 - 1.13440e10i) q^{5} +4.98899e10 q^{6} +(1.56106e12 - 8.84875e11i) q^{7} -1.00651e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\)	\(q+(-5215.37 - 9033.29i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(2.14035e8 - 3.70720e8i) q^{4} +(-6.54948e9 - 1.13440e10i) q^{5} +4.98899e10 q^{6} +(1.56106e12 - 8.84875e11i) q^{7} -1.00651e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-6.83160e13 + 1.18327e14i) q^{10} +(-3.73566e14 + 6.47036e14i) q^{11} +(1.02372e15 + 1.77314e15i) q^{12} +1.37529e16 q^{13} +(-1.61348e16 - 9.48654e15i) q^{14} +6.26520e16 q^{15} +(-6.24162e16 - 1.08108e17i) q^{16} +(1.73700e17 - 3.00858e17i) q^{17} +(-1.19311e17 + 2.06653e17i) q^{18} +(-2.08139e18 - 3.60508e18i) q^{19} -5.60728e18 q^{20} +(-6.79416e16 + 8.58234e18i) q^{21} +7.79315e18 q^{22} +(-2.27015e19 - 3.93202e19i) q^{23} +(2.40704e19 - 4.16912e19i) q^{24} +(7.34077e18 - 1.27146e19i) q^{25} +(-7.17265e19 - 1.24234e20i) q^{26} +1.09419e20 q^{27} +(6.08070e18 - 7.68110e20i) q^{28} +1.52744e21 q^{29} +(-3.26753e20 - 5.65953e20i) q^{30} +(2.67664e21 - 4.63608e21i) q^{31} +(-3.35287e21 + 5.80734e21i) q^{32} +(-1.78676e21 - 3.09475e21i) q^{33} -3.62365e21 q^{34} +(-2.02622e22 - 1.19132e22i) q^{35} -9.79288e21 q^{36} +(-6.66601e21 - 1.15459e22i) q^{37} +(-2.17105e22 + 3.76037e22i) q^{38} +(-3.28898e22 + 5.69669e22i) q^{39} +(6.59209e22 + 1.14178e23i) q^{40} +1.78918e23 q^{41} +(7.78811e22 - 4.41464e22i) q^{42} +2.73094e23 q^{43} +(1.59913e23 + 2.76977e23i) q^{44} +(-1.49831e23 + 2.59515e23i) q^{45} +(-2.36794e23 + 4.10139e23i) q^{46} +(3.16869e23 + 5.48834e23i) q^{47} +5.97070e23 q^{48} +(1.65390e24 - 2.76268e24i) q^{49} -1.53140e23 q^{50} +(8.30804e23 + 1.43899e24i) q^{51} +(2.94360e24 - 5.09847e24i) q^{52} +(-5.13092e24 + 8.88702e24i) q^{53} +(-5.70661e23 - 9.88414e23i) q^{54} +9.78667e24 q^{55} +(-1.57121e25 + 8.90632e24i) q^{56} +1.99105e25 q^{57} +(-7.96620e24 - 1.37979e25i) q^{58} +(2.57977e24 - 4.46829e24i) q^{59} +(1.34097e25 - 2.32263e25i) q^{60} +(-4.16403e25 - 7.21230e25i) q^{61} -5.58388e25 q^{62} +(-3.53870e25 - 2.08060e25i) q^{63} +2.92689e24 q^{64} +(-9.00744e25 - 1.56013e26i) q^{65} +(-1.86372e25 + 3.22806e25i) q^{66} +(1.90920e26 - 3.30684e26i) q^{67} +(-7.43560e25 - 1.28788e26i) q^{68} +2.17161e26 q^{69} +(-1.94085e24 + 2.45166e26i) q^{70} +1.14718e27 q^{71} +(1.15128e26 + 1.99408e26i) q^{72} +(8.24643e24 - 1.42832e25i) q^{73} +(-6.95315e25 + 1.20432e26i) q^{74} +(3.51107e25 + 6.08135e25i) q^{75} -1.78197e27 q^{76} +(-1.06130e25 + 1.34062e27i) q^{77} +6.86131e26 q^{78} +(-5.91661e26 - 1.02479e27i) q^{79} +(-8.17588e26 + 1.41610e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(-9.33122e26 - 1.61621e27i) q^{82} +2.16410e27 q^{83} +(3.16710e27 + 1.86211e27i) q^{84} -4.55059e27 q^{85} +(-1.42429e27 - 2.46694e27i) q^{86} +(-3.65286e27 + 6.32694e27i) q^{87} +(3.75997e27 - 6.51245e27i) q^{88} +(-5.27159e27 - 9.13067e27i) q^{89} +3.12570e27 q^{90} +(2.14691e28 - 1.21696e28i) q^{91} -1.94357e28 q^{92} +(1.28023e28 + 2.21742e28i) q^{93} +(3.30518e27 - 5.72474e27i) q^{94} +(-2.72641e28 + 4.72229e28i) q^{95} +(-1.60367e28 - 2.77763e28i) q^{96} -8.93506e28 q^{97} +(-3.35818e28 - 5.31731e26i) q^{98} +1.70920e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9}+O(q^{10}) \) 40 * q - 7743 * q^2 - 95659380 * q^3 - 5985454645 * q^4 + 14215352760 * q^5 + 74069057934 * q^6 - 368001036334 * q^7 + 49989480496086 * q^8 - 457535849099220 * q^9	\( 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9} - 167879133295903 q^{10} - 31\!\cdots\!14 q^{11}+ \cdots + 14\!\cdots\!08 q^{99}+O(q^{100}) \) 40 * q - 7743 * q^2 - 95659380 * q^3 - 5985454645 * q^4 + 14215352760 * q^5 + 74069057934 * q^6 - 368001036334 * q^7 + 49989480496086 * q^8 - 457535849099220 * q^9 - 167879133295903 * q^10 - 3154300361224314 * q^11 - 28628244017941005 * q^12 + 27686480502978220 * q^13 - 214257133773063450 * q^14 - 135983183150288880 * q^15 - 1764048935658629353 * q^16 + 41802108452009436 * q^17 - 177135003978763023 * q^18 - 7235175939726809174 * q^19 - 2944336803535185762 * q^20 + 9048396870023397228 * q^21 + 89086825354637664038 * q^22 + 44902952138264019852 * q^23 - 119549067769441979667 * q^24 - 856461315876501170374 * q^25 + 740598921837346265154 * q^26 + 4376759565260494368360 * q^27 + 837334611372858240643 * q^28 + 3042539991157763918664 * q^29 - 802960690301171876007 * q^30 - 7171021288148722128918 * q^31 - 3221069809618281449199 * q^32 - 15086920844424695908266 * q^33 - 40988792924743489638864 * q^34 + 22734956365007065015692 * q^35 + 273856007324494541487690 * q^36 - 32961210550052530362042 * q^37 - 21824144763887061483774 * q^38 - 66211788982424616967590 * q^39 - 561274593219911517352413 * q^40 - 407158367720211769052760 * q^41 + 261768399564896960899059 * q^42 - 742478352427516947522676 * q^43 - 860699497136335577636151 * q^44 + 325201674764577027042360 * q^45 - 3603590382443692607483880 * q^46 + 5088913555222492904989956 * q^47 + 16874782747476437555778114 * q^48 - 1107011263686123128490044 * q^49 + 20047363110221889541650996 * q^50 + 199938188860599120095484 * q^51 - 15020364113616852849255436 * q^52 + 4503823724603073528076524 * q^53 - 847231232845300197355287 * q^54 - 26118327809723981533730792 * q^55 + 23391818796605514251144607 * q^56 + 69211244458518393496315212 * q^57 - 19344263089875691399511041 * q^58 - 107339818359767325079738806 * q^59 + 7041335828433941954443689 * q^60 - 55695583344240438158518844 * q^61 + 595684893227471470626855138 * q^62 - 34859518397595458196656958 * q^63 + 2556323224325113131258620002 * q^64 + 116576686276646946961533216 * q^65 - 213049761989822976663084411 * q^66 - 395633506213215660680479214 * q^67 - 341809314919360918295601216 * q^68 - 429538856171601041535001176 * q^69 + 3114247010513527110020739673 * q^70 - 357045698249607322103230392 * q^71 - 571799485120140136045891323 * q^72 + 1563411738231613398537297906 * q^73 - 2560064971236623546640897774 * q^74 - 4096427923536512926362560406 * q^75 + 24051365932177387567037871800 * q^76 - 788772365883171194224066980 * q^77 - 7084523369162900456994724452 * q^78 + 5677690363343606232557230766 * q^79 - 3948631034904977500881109899 * q^80 - 10466952660547210744270230420 * q^81 - 14901652274869047200277511964 * q^82 + 21293945454157612982870988948 * q^83 - 13769091913378092591470544324 * q^84 + 8900456942787328180094572008 * q^85 - 1540767080130988487092741200 * q^86 - 7276187229483929466144216708 * q^87 - 63208209978831072085072879725 * q^88 - 11757157651476935757967358112 * q^89 + 7681072179858211493226649566 * q^90 - 1529257930272663641703478390 * q^91 + 158106912155564585073501217248 * q^92 - 34298772519555405332228797542 * q^93 - 133188762499886306919098285406 * q^94 - 159842963957338542634753903584 * q^95 - 15406277046240142004793891831 * q^96 - 390739421663203813144382175132 * q^97 + 239765305290895114544854004019 * q^98 + 144320549408674286727326243508 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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