LMFDB - Embedded newform 21.30.e.b.4.5

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			4.5
Character	$\chi$	$=$	21.4
Dual form			21.30.e.b.16.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15572.5 - 26972.3i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-2.16568e8 + 3.75107e8i) q^{4} +(3.77327e9 + 6.53549e9i) q^{5} +1.48965e11 q^{6} +(1.66300e12 - 6.74056e11i) q^{7} -3.23080e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})$	\(q+(-15572.5 - 26972.3i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-2.16568e8 + 3.75107e8i) q^{4} +(3.77327e9 + 6.53549e9i) q^{5} +1.48965e11 q^{6} +(1.66300e12 - 6.74056e11i) q^{7} -3.23080e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(1.17518e14 - 2.03547e14i) q^{10} +(1.21940e15 - 2.11206e15i) q^{11} +(-1.03584e15 - 1.79413e15i) q^{12} -2.05200e16 q^{13} +(-4.40778e16 - 3.43581e16i) q^{14} -3.60948e16 q^{15} +(1.66581e17 + 2.88526e17i) q^{16} +(2.40948e17 - 4.17335e17i) q^{17} +(-3.56248e17 + 6.17040e17i) q^{18} +(-1.59980e17 - 2.77094e17i) q^{19} -3.26868e18 q^{20} +(-1.18497e18 + 8.50041e18i) q^{21} -7.59563e19 q^{22} +(3.28933e18 + 5.69728e18i) q^{23} +(7.72640e18 - 1.33825e19i) q^{24} +(6.46572e19 - 1.11989e20i) q^{25} +(3.19547e20 + 5.53472e20i) q^{26} +1.09419e20 q^{27} +(-1.07309e20 + 7.69781e20i) q^{28} +6.39356e20 q^{29} +(5.62086e20 + 9.73561e20i) q^{30} +(-5.38240e20 + 9.32260e20i) q^{31} +(4.32089e21 - 7.48400e21i) q^{32} +(5.83236e21 + 1.01019e22i) q^{33} -1.50086e22 q^{34} +(1.06802e22 + 8.32510e21i) q^{35} +9.90878e21 q^{36} +(3.11133e22 + 5.38899e22i) q^{37} +(-4.98258e21 + 8.63009e21i) q^{38} +(4.90733e22 - 8.49974e22i) q^{39} +(-1.21907e22 - 2.11148e22i) q^{40} -1.87058e23 q^{41} +(2.47729e23 - 1.00411e23i) q^{42} -4.01116e22 q^{43} +(5.28167e23 + 9.14812e23i) q^{44} +(8.63203e22 - 1.49511e23i) q^{45} +(1.02446e23 - 1.77442e23i) q^{46} +(-2.82016e23 - 4.88465e23i) q^{47} -1.59350e24 q^{48} +(2.31120e24 - 2.24191e24i) q^{49} -4.02749e24 q^{50} +(1.15245e24 + 1.99610e24i) q^{51} +(4.44398e24 - 7.69720e24i) q^{52} +(-1.47448e24 + 2.55388e24i) q^{53} +(-1.70392e24 - 2.95128e24i) q^{54} +1.84045e25 q^{55} +(-5.37280e24 + 2.17774e24i) q^{56} +1.53036e24 q^{57} +(-9.95635e24 - 1.72449e25i) q^{58} +(3.98213e25 - 6.89725e25i) q^{59} +(7.81700e24 - 1.35394e25i) q^{60} +(-8.08699e24 - 1.40071e25i) q^{61} +3.35269e25 q^{62} +(-3.23763e25 - 2.52369e25i) q^{63} -9.02829e25 q^{64} +(-7.74274e25 - 1.34108e26i) q^{65} +(1.81648e26 - 3.14624e26i) q^{66} +(1.95560e26 - 3.38719e26i) q^{67} +(1.04364e26 + 1.80763e26i) q^{68} -3.14655e25 q^{69} +(5.82297e25 - 4.17712e26i) q^{70} -6.47922e26 q^{71} +(3.69551e25 + 6.40081e25i) q^{72} +(1.03372e26 - 1.79045e26i) q^{73} +(9.69023e26 - 1.67840e27i) q^{74} +(3.09253e26 + 5.35642e26i) q^{75} +1.38587e26 q^{76} +(6.04208e26 - 4.33430e27i) q^{77} -3.05677e27 q^{78} +(7.98832e26 + 1.38362e27i) q^{79} +(-1.25711e27 + 2.17737e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(2.91296e27 + 5.04540e27i) q^{82} +6.96409e27 q^{83} +(-2.93194e27 - 2.28541e27i) q^{84} +3.63665e27 q^{85} +(6.24637e26 + 1.08190e27i) q^{86} +(-1.52901e27 + 2.64832e27i) q^{87} +(-3.93963e27 + 6.82365e27i) q^{88} +(1.23110e28 + 2.13233e28i) q^{89} -5.37688e27 q^{90} +(-3.41247e28 + 1.38316e28i) q^{91} -2.84946e27 q^{92} +(-2.57439e27 - 4.45897e27i) q^{93} +(-8.78336e27 + 1.52132e28i) q^{94} +(1.20730e27 - 2.09110e27i) q^{95} +(2.06667e28 + 3.57957e28i) q^{96} -8.68407e28 q^{97} +(-9.64605e28 - 2.74265e28i) q^{98} -5.57920e28 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 $

$2$	−15572.5	−	26972.3i	−0.672083	−	1.16408i	−0.977312	−	0.211803i	$-0.932067\pi$
$2$	−15572.5	−	26972.3i	−0.672083	−	1.16408i	0.305230	−	0.952279i	$-0.401267\pi$
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$4$	−2.16568e8	+	3.75107e8i	−0.403390	+	0.698692i
$5$	3.77327e9	+	6.53549e9i	0.276473	+	0.478865i	0.970506	−	0.241078i	$-0.0775011\pi$
$5$	3.77327e9	+	6.53549e9i	0.276473	+	0.478865i	−0.694033	+	0.719943i	$0.744168\pi$
$6$	1.48965e11			0.776054
$7$	1.66300e12	−	6.74056e11i	0.926765	−	0.375642i
$7$	1.66300e12	−	6.74056e11i	0.926765	−	0.375642i
$8$	−3.23080e12			−0.259720
$9$	−1.14384e13	−	1.98119e13i	−0.166667	−	0.288675i
$10$	1.17518e14	−	2.03547e14i	0.371625	−	0.643674i
$11$	1.21940e15	−	2.11206e15i	0.968172	−	1.67692i	0.267332	−	0.963604i	$-0.413858\pi$
$11$	1.21940e15	−	2.11206e15i	0.968172	−	1.67692i	0.700840	−	0.713319i	$-0.252809\pi$
$12$	−1.03584e15	−	1.79413e15i	−0.232897	−	0.403390i
$13$	−2.05200e16			−1.44544			−0.722718	−	0.691143i	$-0.757107\pi$
$13$	−2.05200e16			−1.44544			−0.722718	+	0.691143i	$0.757107\pi$
$14$	−4.40778e16	−	3.43581e16i	−1.06014	−	0.826367i
$15$	−3.60948e16			−0.319243
$16$	1.66581e17	+	2.88526e17i	0.577943	+	1.00103i
$17$	2.40948e17	−	4.17335e17i	0.347068	−	0.601139i	−0.638659	−	0.769490i	$-0.720511\pi$
$17$	2.40948e17	−	4.17335e17i	0.347068	−	0.601139i	0.985727	+	0.168350i	$0.0538440\pi$
$18$	−3.56248e17	+	6.17040e17i	−0.224028	+	0.388027i
$19$	−1.59980e17	−	2.77094e17i	−0.0459346	−	0.0795610i	0.842144	−	0.539253i	$-0.181293\pi$
$19$	−1.59980e17	−	2.77094e17i	−0.0459346	−	0.0795610i	−0.888079	+	0.459692i	$0.847960\pi$
$20$	−3.26868e18			−0.446106
$21$	−1.18497e18	+	8.50041e18i	−0.0797127	+	0.571821i
$22$	−7.59563e19			−2.60277
$23$	3.28933e18	+	5.69728e18i	0.0591635	+	0.102474i	0.894090	−	0.447887i	$-0.147823\pi$
$23$	3.28933e18	+	5.69728e18i	0.0591635	+	0.102474i	−0.834927	+	0.550361i	$0.814490\pi$
$24$	7.72640e18	−	1.33825e19i	0.0749746	−	0.129860i
$25$	6.46572e19	−	1.11989e20i	0.347126	−	0.601239i
$26$	3.19547e20	+	5.53472e20i	0.971452	+	1.68260i
$27$	1.09419e20			0.192450
$28$	−1.07309e20	+	7.69781e20i	−0.111389	+	0.799053i
$29$	6.39356e20			0.398999			0.199499	−	0.979898i	$-0.436068\pi$
$29$	6.39356e20			0.398999			0.199499	+	0.979898i	$0.436068\pi$
$30$	5.62086e20	+	9.73561e20i	0.214558	+	0.371625i
$31$	−5.38240e20	+	9.32260e20i	−0.127712	+	0.221204i	−0.922790	−	0.385304i	$-0.874097\pi$
$31$	−5.38240e20	+	9.32260e20i	−0.127712	+	0.221204i	0.795078	+	0.606507i	$0.207430\pi$
$32$	4.32089e21	−	7.48400e21i	0.646991	−	1.12062i
$33$	5.83236e21	+	1.01019e22i	0.558974	+	0.968172i
$34$	−1.50086e22			−0.933033
$35$	1.06802e22	+	8.32510e21i	0.436107	+	0.339940i
$36$	9.90878e21			0.268927
$37$	3.11133e22	+	5.38899e22i	0.567573	+	0.983065i	0.996805	+	0.0798711i	$0.0254509\pi$
$37$	3.11133e22	+	5.38899e22i	0.567573	+	0.983065i	−0.429232	+	0.903194i	$0.641216\pi$
$38$	−4.98258e21	+	8.63009e21i	−0.0617437	+	0.106943i
$39$	4.90733e22	−	8.49974e22i	0.417261	−	0.722718i
$40$	−1.21907e22	−	2.11148e22i	−0.0718054	−	0.124371i
$41$	−1.87058e23			−0.770214			−0.385107	−	0.922872i	$-0.625835\pi$
$41$	−1.87058e23			−0.770214			−0.385107	+	0.922872i	$0.625835\pi$
$42$	2.47729e23	−	1.00411e23i	0.719220	−	0.291519i
$43$	−4.01116e22			−0.0827899			−0.0413949	−	0.999143i	$-0.513180\pi$
$43$	−4.01116e22			−0.0827899			−0.0413949	+	0.999143i	$0.513180\pi$
$44$	5.28167e23	+	9.14812e23i	0.781102	+	1.35291i
$45$	8.63203e22	−	1.49511e23i	0.0921576	−	0.159622i
$46$	1.02446e23	−	1.77442e23i	0.0795255	−	0.137742i
$47$	−2.82016e23	−	4.88465e23i	−0.160271	−	0.277597i	0.774695	−	0.632335i	$-0.217903\pi$
$47$	−2.82016e23	−	4.88465e23i	−0.160271	−	0.277597i	−0.934966	+	0.354738i	$0.884570\pi$
$48$	−1.59350e24			−0.667351
$49$	2.31120e24	−	2.24191e24i	0.717786	−	0.696264i
$50$	−4.02749e24			−0.933188
$51$	1.15245e24	+	1.99610e24i	0.200380	+	0.347068i
$52$	4.44398e24	−	7.69720e24i	0.583074	−	1.00991i
$53$	−1.47448e24	+	2.55388e24i	−0.146771	+	0.254214i	−0.930032	−	0.367478i	$-0.880221\pi$
$53$	−1.47448e24	+	2.55388e24i	−0.146771	+	0.254214i	0.783261	+	0.621692i	$0.213555\pi$
$54$	−1.70392e24	−	2.95128e24i	−0.129342	−	0.224028i
$55$	1.84045e25			1.07069
$56$	−5.37280e24	+	2.17774e24i	−0.240699	+	0.0975617i
$57$	1.53036e24			0.0530407
$58$	−9.95635e24	−	1.72449e25i	−0.268160	−	0.464467i
$59$	3.98213e25	−	6.89725e25i	0.837069	−	1.44985i	−0.0552666	−	0.998472i	$-0.517601\pi$
$59$	3.98213e25	−	6.89725e25i	0.837069	−	1.44985i	0.892335	−	0.451374i	$-0.149066\pi$
$60$	7.81700e24	−	1.35394e25i	0.128780	−	0.223053i
$61$	−8.08699e24	−	1.40071e25i	−0.104835	−	0.181579i	0.808836	−	0.588034i	$-0.200098\pi$
$61$	−8.08699e24	−	1.40071e25i	−0.104835	−	0.181579i	−0.913671	+	0.406455i	$0.866765\pi$
$62$	3.35269e25			0.343332
$63$	−3.23763e25	−	2.52369e25i	−0.262899	−	0.204927i
$64$	−9.02829e25			−0.583440
$65$	−7.74274e25	−	1.34108e26i	−0.399624	−	0.692169i
$66$	1.81648e26	−	3.14624e26i	0.751354	−	1.30138i
$67$	1.95560e26	−	3.38719e26i	0.650421	−	1.12656i	−0.332600	−	0.943068i	$-0.607926\pi$
$67$	1.95560e26	−	3.38719e26i	0.650421	−	1.12656i	0.983021	−	0.183494i	$-0.0587408\pi$
$68$	1.04364e26	+	1.80763e26i	0.280007	+	0.484987i
$69$	−3.14655e25			−0.0683161
$70$	5.82297e25	−	4.17712e26i	0.102618	−	0.736132i
$71$	−6.47922e26			−0.929558			−0.464779	−	0.885427i	$-0.653866\pi$
$71$	−6.47922e26			−0.929558			−0.464779	+	0.885427i	$0.653866\pi$
$72$	3.69551e25	+	6.40081e25i	0.0432866	+	0.0749746i
$73$	1.03372e26	−	1.79045e26i	0.0991333	−	0.171704i	−0.812193	−	0.583389i	$-0.801726\pi$
$73$	1.03372e26	−	1.79045e26i	0.0991333	−	0.171704i	0.911326	+	0.411685i	$0.135060\pi$
$74$	9.69023e26	−	1.67840e27i	0.762912	−	1.32140i
$75$	3.09253e26	+	5.35642e26i	0.200413	+	0.347126i
$76$	1.38587e26			0.0741182
$77$	6.04208e26	−	4.33430e27i	0.267344	−	1.91780i
$78$	−3.05677e27			−1.12174
$79$	7.98832e26	+	1.38362e27i	0.243704	+	0.422108i	0.961766	−	0.273871i	$-0.0883041\pi$
$79$	7.98832e26	+	1.38362e27i	0.243704	+	0.422108i	−0.718062	+	0.695979i	$0.754971\pi$
$80$	−1.25711e27	+	2.17737e27i	−0.319571	+	0.553513i
$81$	−2.61674e26	+	4.53232e26i	−0.0555556	+	0.0962250i
$82$	2.91296e27	+	5.04540e27i	0.517647	+	0.896592i
$83$	6.96409e27			1.03808			0.519042	−	0.854749i	$-0.326289\pi$
$83$	6.96409e27			1.03808			0.519042	+	0.854749i	$0.326289\pi$
$84$	−2.93194e27	−	2.28541e27i	−0.367371	−	0.286362i
$85$	3.63665e27			0.383819
$86$	6.24637e26	+	1.08190e27i	0.0556416	+	0.0963741i
$87$	−1.52901e27	+	2.64832e27i	−0.115181	+	0.199499i
$88$	−3.93963e27	+	6.82365e27i	−0.251453	+	0.435530i
$89$	1.23110e28	+	2.13233e28i	0.667021	+	1.15531i	0.978733	+	0.205138i	$0.0657643\pi$
$89$	1.23110e28	+	2.13233e28i	0.667021	+	1.15531i	−0.311712	+	0.950177i	$0.600902\pi$
$90$	−5.37688e27			−0.247750
$91$	−3.41247e28	+	1.38316e28i	−1.33958	+	0.542967i
$92$	−2.84946e27			−0.0954638
$93$	−2.57439e27	−	4.45897e27i	−0.0737346	−	0.127712i
$94$	−8.78336e27	+	1.52132e28i	−0.215430	+	0.373136i
$95$	1.20730e27	−	2.09110e27i	0.0253993	−	0.0439929i
$96$	2.06667e28	+	3.57957e28i	0.373540	+	0.646991i
$97$	−8.68407e28			−1.35062			−0.675310	−	0.737534i	$-0.735990\pi$
$97$	−8.68407e28			−1.35062			−0.675310	+	0.737534i	$0.735990\pi$
$98$	−9.64605e28	−	2.74265e28i	−1.29292	−	0.367614i
$99$	−5.57920e28			−0.645448
$100$	2.80054e28	+	4.85068e28i	0.280054	+	0.485068i
$101$	−4.17226e28	+	7.22657e28i	−0.361170	+	0.625565i	−0.988154	−	0.153468i	$-0.950956\pi$
$101$	−4.17226e28	+	7.22657e28i	−0.361170	+	0.625565i	0.626984	+	0.779032i	$0.284289\pi$
$102$	3.58929e28	−	6.21684e28i	0.269343	−	0.466517i
$103$	−9.05033e28	−	1.56756e29i	−0.589555	−	1.02114i	−0.994291	−	0.106706i	$-0.965970\pi$
$103$	−9.05033e28	−	1.56756e29i	−0.589555	−	1.02114i	0.404735	−	0.914434i	$-0.367364\pi$
$104$	6.62959e28			0.375408
$105$	−6.00256e28	+	2.43300e28i	−0.295863	+	0.119921i
$106$	9.18453e28			0.394568
$107$	2.42187e29	+	4.19480e29i	0.908000	+	1.57270i	0.816839	+	0.576865i	$0.195724\pi$
$107$	2.42187e29	+	4.19480e29i	0.908000	+	1.57270i	0.0911603	+	0.995836i	$0.470942\pi$
$108$	−2.36967e28	+	4.10439e28i	−0.0776324	+	0.134463i
$109$	−9.08730e28	+	1.57397e29i	−0.260466	+	0.451140i	−0.966366	−	0.257171i	$-0.917209\pi$
$109$	−9.08730e28	+	1.57397e29i	−0.260466	+	0.451140i	0.705900	+	0.708312i	$0.250543\pi$
$110$	−2.86604e29	−	4.96412e29i	−0.719594	−	1.24637i
$111$	−2.97628e29			−0.655377
$112$	4.71506e29	+	3.67533e29i	0.911645	+	0.710616i
$113$	1.26586e29			0.215153			0.107576	−	0.994197i	$-0.465691\pi$
$113$	1.26586e29			0.215153			0.107576	+	0.994197i	$0.465691\pi$
$114$	−2.38315e28	−	4.12774e28i	−0.0356477	−	0.0617437i
$115$	−2.48230e28	+	4.29947e28i	−0.0327142	+	0.0566626i
$116$	−1.38464e29	+	2.39827e29i	−0.160952	+	0.278777i
$117$	2.34716e29	+	4.06540e29i	0.240906	+	0.417261i
$118$	−2.48046e30			−2.25032
$119$	1.19389e29	−	8.56438e29i	0.0958369	−	0.687488i
$120$	1.16615e29			0.0829137
$121$	−2.18072e30	−	3.77712e30i	−1.37471	−	2.38107i
$122$	−2.51869e29	+	4.36250e29i	−0.140915	+	0.244072i
$123$	4.47347e29	−	7.74828e29i	0.222342	−	0.385107i
$124$	−2.33132e29	−	4.03796e29i	−0.103035	−	0.178463i
$125$	2.38153e30			0.936829
$126$	−1.76519e29	+	1.26627e30i	−0.0618614	+	0.443764i
$127$	7.18061e29			0.224392			0.112196	−	0.993686i	$-0.464212\pi$
$127$	7.18061e29			0.224392			0.112196	+	0.993686i	$0.464212\pi$
$128$	−9.13830e29	−	1.58280e30i	−0.254871	−	0.441450i
$129$	9.59262e28	−	1.66149e29i	0.0238994	−	0.0413949i
$130$	−2.41147e30	+	4.17679e30i	−0.537160	+	0.930389i
$131$	−4.37112e30	−	7.57100e30i	−0.871282	−	1.50910i	−0.860671	−	0.509161i	$-0.829956\pi$
$131$	−4.37112e30	−	7.57100e30i	−0.871282	−	1.50910i	−0.0106103	−	0.999944i	$-0.503377\pi$
$132$	−5.05242e30			−0.901939
$133$	−4.52824e29	−	3.52971e29i	−0.0724570	−	0.0564794i
$134$	−1.21814e31			−1.74855
$135$	4.12867e29	+	7.15107e29i	0.0532072	+	0.0921576i
$136$	−7.78454e29	+	1.34832e30i	−0.0901403	+	0.156128i
$137$	−8.21742e30	+	1.42330e31i	−0.855632	+	1.48200i	0.0204252	+	0.999791i	$0.493498\pi$
$137$	−8.21742e30	+	1.42330e31i	−0.855632	+	1.48200i	−0.876057	+	0.482207i	$0.839835\pi$
$138$	4.89996e29	+	8.48698e29i	0.0459141	+	0.0795255i
$139$	−9.95145e30			−0.839792			−0.419896	−	0.907572i	$-0.637933\pi$
$139$	−9.95145e30			−0.839792			−0.419896	+	0.907572i	$0.637933\pi$
$140$	−5.43580e30	+	2.20328e30i	−0.413435	+	0.167576i
$141$	2.69774e30			0.185065
$142$	1.00897e31	+	1.74759e31i	0.624740	+	1.08208i
$143$	−2.50221e31	+	4.33396e31i	−1.39943	+	2.42388i
$144$	3.81083e30	−	6.60056e30i	0.192648	−	0.333676i
$145$	2.41246e30	+	4.17850e30i	0.110312	+	0.191067i
$146$	−6.43900e30			−0.266503
$147$	3.75916e30	+	1.49349e31i	0.140925	+	0.559887i
$148$	−2.69527e31			−0.915813
$149$	4.75315e30	+	8.23270e30i	0.146481	+	0.253712i	0.929924	−	0.367751i	$-0.119872\pi$
$149$	4.75315e30	+	8.23270e30i	0.146481	+	0.253712i	−0.783444	+	0.621463i	$0.786539\pi$
$150$	9.63167e30	−	1.66826e31i	0.269388	−	0.466594i
$151$	3.25393e31	−	5.63597e31i	0.826498	−	1.43154i	−0.0742706	−	0.997238i	$-0.523663\pi$
$151$	3.25393e31	−	5.63597e31i	0.826498	−	1.43154i	0.900769	−	0.434299i	$-0.143004\pi$
$152$	5.16864e29	+	8.95235e29i	0.0119301	+	0.0206636i
$153$	−1.10242e31			−0.231379
$154$	−1.26315e32	+	5.11989e31i	−2.41215	+	0.977709i
$155$	−8.12370e30			−0.141236
$156$	2.12554e31	+	3.68155e31i	0.336638	+	0.583074i
$157$	−3.03537e31	+	5.25741e31i	−0.438194	+	0.758975i	−0.997550	−	0.0699529i	$-0.977715\pi$
$157$	−3.03537e31	+	5.25741e31i	−0.438194	+	0.758975i	0.559356	+	0.828927i	$0.311048\pi$
$158$	2.48796e31	−	4.30927e31i	0.327579	−	0.567383i
$159$	−7.05240e30	−	1.22151e31i	−0.0847381	−	0.146771i
$160$	6.52155e31			0.715502
$161$	9.31043e30	+	7.25736e30i	0.0933242	+	0.0727451i
$162$	1.62996e31			0.149352
$163$	−9.34855e31	−	1.61922e32i	−0.783473	−	1.35702i	−0.929907	−	0.367795i	$-0.880113\pi$
$163$	−9.34855e31	−	1.61922e32i	−0.783473	−	1.35702i	0.146434	−	0.989220i	$-0.453220\pi$
$164$	4.05109e31	−	7.01670e31i	0.310697	−	0.538142i
$165$	−4.40141e31	+	7.62346e31i	−0.309082	+	0.535347i
$166$	−1.08448e32	−	1.87838e32i	−0.697678	−	1.20841i
$167$	−7.89716e31			−0.465674			−0.232837	−	0.972516i	$-0.574801\pi$
$167$	−7.89716e31			−0.465674			−0.232837	+	0.972516i	$0.574801\pi$
$168$	3.82840e30	−	2.74631e31i	0.0207029	−	0.148513i
$169$	2.19532e32			1.08928
$170$	−5.66316e31	−	9.80888e31i	−0.257958	−	0.446797i
$171$	−3.65984e30	+	6.33903e30i	−0.0153115	+	0.0265203i
$172$	8.68690e30	−	1.50462e31i	0.0333966	−	0.0578446i
$173$	8.29774e31	+	1.43721e32i	0.293286	+	0.507986i	0.974585	−	0.224019i	$-0.0719179\pi$
$173$	8.29774e31	+	1.43721e32i	0.293286	+	0.507986i	−0.681299	+	0.732005i	$0.738585\pi$
$174$	9.52418e31			0.309645
$175$	3.20373e31	−	2.29821e32i	0.0958528	−	0.687602i
$176$	8.12515e32			2.23819
$177$	1.90464e32	+	3.29893e32i	0.483282	+	0.837069i
$178$	3.83427e32	−	6.64115e32i	0.896587	−	1.55293i
$179$	2.48942e32	−	4.31181e32i	0.536698	−	0.929588i	−0.462381	−	0.886681i	$-0.653005\pi$
$179$	2.48942e32	−	4.31181e32i	0.536698	−	0.929588i	0.999079	−	0.0429066i	$-0.0136618\pi$
$180$	3.73885e31	+	6.47587e31i	0.0743509	+	0.128780i
$181$	−9.17921e32			−1.68448			−0.842240	−	0.539103i	$-0.818763\pi$
$181$	−9.17921e32			−1.68448			−0.842240	+	0.539103i	$0.818763\pi$
$182$	9.04477e32	+	7.05028e32i	1.53237	+	1.19446i
$183$	7.73596e31			0.121052
$184$	−1.06271e31	−	1.84068e31i	−0.0153659	−	0.0266145i
$185$	−2.34798e32	+	4.06682e32i	−0.313837	+	0.543582i
$186$	−8.01791e31	+	1.38874e32i	−0.0991114	+	0.171666i
$187$	−5.87625e32	−	1.01780e33i	−0.672043	−	1.16401i
$188$	2.44303e32			0.258606
$189$	1.81963e32	−	7.37546e31i	0.178356	−	0.0722924i
$190$	−7.52025e31			−0.0682818
$191$	−5.77406e32	−	1.00010e33i	−0.485845	−	0.841507i	0.514023	−	0.857776i	$-0.328155\pi$
$191$	−5.77406e32	−	1.00010e33i	−0.485845	−	0.841507i	−0.999868	+	0.0162689i	$0.994821\pi$
$192$	2.15910e32	−	3.73968e32i	0.168425	−	0.291720i
$193$	−9.82525e32	+	1.70178e33i	−0.710825	+	1.23118i	0.253723	+	0.967277i	$0.418345\pi$
$193$	−9.82525e32	+	1.70178e33i	−0.710825	+	1.23118i	−0.964548	+	0.263908i	$0.914988\pi$
$194$	1.35232e33	+	2.34229e33i	0.907728	+	1.57223i
$195$	7.40666e32			0.461446
$196$	3.40422e32	+	1.35247e33i	0.196927	+	0.782377i
$197$	1.88543e33			1.01310			0.506549	−	0.862211i	$-0.330921\pi$
$197$	1.88543e33			1.01310			0.506549	+	0.862211i	$0.330921\pi$
$198$	8.68819e32	+	1.50484e33i	0.433794	+	0.751354i
$199$	1.12120e33	−	1.94197e33i	0.520370	−	0.901307i	−0.479350	−	0.877624i	$-0.659127\pi$
$199$	1.12120e33	−	1.94197e33i	0.520370	−	0.901307i	0.999720	−	0.0236830i	$-0.00753925\pi$
$200$	−2.08894e32	+	3.61815e32i	−0.0901553	+	0.156154i
$201$	9.35355e32	+	1.62008e33i	0.375521	+	0.650421i
$202$	2.59890e33			0.970944
$203$	1.06325e33	−	4.30962e32i	0.369778	−	0.149881i
$204$	−9.98335e32			−0.323325
$205$	−7.05822e32	−	1.22252e33i	−0.212943	−	0.368829i
$206$	−2.81872e33	+	4.88216e33i	−0.792460	+	1.37258i
$207$	7.52493e31	−	1.30336e32i	0.0197212	−	0.0341580i
$208$	−3.41824e33	−	5.92056e33i	−0.835379	−	1.44692i
$209$	−7.80321e32			−0.177890
$210$	1.59098e33	+	1.24015e33i	0.338443	+	0.263812i
$211$	−2.42971e33			−0.482457			−0.241229	−	0.970468i	$-0.577550\pi$
$211$	−2.42971e33			−0.482457			−0.241229	+	0.970468i	$0.577550\pi$
$212$	−6.38652e32	−	1.10618e33i	−0.118412	−	0.205095i
$213$	1.54949e33	−	2.68380e33i	0.268340	−	0.464779i
$214$	7.54289e33	−	1.30647e34i	1.22050	−	2.11397i
$215$	−1.51352e32	−	2.62149e32i	−0.0228892	−	0.0396452i
$216$	−3.53510e32			−0.0499830
$217$	−2.66696e32	+	1.91315e33i	−0.0352655	+	0.252978i
$218$	5.66047e33			0.700218
$219$	4.94423e32	+	8.56366e32i	0.0572347	+	0.0991333i
$220$	−3.98583e33	+	6.90366e33i	−0.431907	+	0.748085i
$221$	−4.94426e33	+	8.56371e33i	−0.501664	+	0.868908i
$222$	4.63481e33	+	8.02773e33i	0.440467	+	0.762912i
$223$	−2.18474e34			−1.94527			−0.972636	−	0.232335i	$-0.925363\pi$
$223$	−2.18474e34			−1.94527			−0.972636	+	0.232335i	$0.925363\pi$
$224$	2.14098e33	−	1.53584e34i	0.178656	−	1.28159i
$225$	−2.95830e33			−0.231417
$226$	−1.97125e33	−	3.41431e33i	−0.144600	−	0.250455i
$227$	8.67766e33	−	1.50301e34i	0.597073	−	1.03416i	−0.396178	−	0.918174i	$-0.629664\pi$
$227$	8.67766e33	−	1.50301e34i	0.597073	−	1.03416i	0.993251	−	0.115987i	$-0.0370031\pi$
$228$	−3.31428e32	+	5.74051e32i	−0.0213961	+	0.0370591i
$229$	−1.13534e34	−	1.96646e34i	−0.687877	−	1.19144i	−0.972523	−	0.232806i	$-0.925209\pi$
$229$	−1.13534e34	−	1.96646e34i	−0.687877	−	1.19144i	0.284646	−	0.958633i	$-0.408124\pi$
$230$	1.54622e33			0.0879465
$231$	1.65085e34	+	1.28681e34i	0.881724	+	0.687293i
$232$	−2.06563e33			−0.103628
$233$	−8.15428e33	−	1.41236e34i	−0.384348	−	0.665710i	0.607331	−	0.794449i	$-0.292240\pi$
$233$	−8.15428e33	−	1.41236e34i	−0.384348	−	0.665710i	−0.991679	+	0.128739i	$0.958907\pi$
$234$	7.31021e33	−	1.26617e34i	0.323817	−	0.560868i
$235$	2.12824e33	−	3.68622e33i	0.0886210	−	0.153496i
$236$	1.72481e34	+	2.98745e34i	0.675330	+	1.16971i
$237$	−7.64158e33			−0.281405
$238$	−2.49593e34	+	1.01167e34i	−0.864702	+	0.350487i
$239$	−2.44546e34			−0.797244			−0.398622	−	0.917115i	$-0.630511\pi$
$239$	−2.44546e34			−0.797244			−0.398622	+	0.917115i	$0.630511\pi$
$240$	−6.01270e33	−	1.04143e34i	−0.184504	−	0.319571i
$241$	3.99172e33	−	6.91385e33i	0.115322	−	0.199744i	−0.802586	−	0.596536i	$-0.796543\pi$
$241$	3.99172e33	−	6.91385e33i	0.115322	−	0.199744i	0.917908	+	0.396792i	$0.129877\pi$
$242$	−6.79184e34	+	1.17638e35i	−1.84784	+	3.20056i
$243$	−1.25158e33	−	2.16780e33i	−0.0320750	−	0.0555556i
$244$	7.00554e33			0.169157
$245$	2.33727e34	+	6.64553e33i	0.531865	+	0.151224i
$246$	−2.78652e34			−0.597728
$247$	3.28280e33	+	5.68597e33i	0.0663955	+	0.115000i
$248$	1.73894e33	−	3.01194e33i	0.0331693	−	0.0574509i
$249$	−1.66545e34	+	2.88465e34i	−0.299669	+	0.519042i
$250$	−3.70863e34	−	6.42353e34i	−0.629626	−	1.09054i
$251$	−4.66328e34			−0.747175			−0.373587	−	0.927595i	$-0.621872\pi$
$251$	−4.66328e34			−0.747175			−0.373587	+	0.927595i	$0.621872\pi$
$252$	1.64783e34	−	6.67908e33i	0.249232	−	0.101020i
$253$	1.60440e34			0.229122
$254$	−1.11820e34	−	1.93678e34i	−0.150810	−	0.261211i
$255$	−8.69699e33	+	1.50636e34i	−0.110799	+	0.191910i
$256$	−5.26963e34	+	9.12727e34i	−0.634309	+	1.09866i
$257$	−4.09887e34	−	7.09944e34i	−0.466266	−	0.807596i	0.532992	−	0.846120i	$-0.321068\pi$
$257$	−4.09887e34	−	7.09944e34i	−0.466266	−	0.807596i	−0.999258	+	0.0385246i	$0.987734\pi$
$258$	−5.97523e33			−0.0642494
$259$	8.80662e34	+	6.86465e34i	0.895288	+	0.697866i
$260$	6.70733e34			0.644817
$261$	−7.31320e33	−	1.26668e34i	−0.0664998	−	0.115181i
$262$	−1.36138e35	+	2.35798e35i	−1.17115	+	2.02849i
$263$	5.27231e34	−	9.13191e34i	0.429183	−	0.743367i	−0.567618	−	0.823292i	$-0.692135\pi$
$263$	5.27231e34	−	9.13191e34i	0.429183	−	0.743367i	0.996801	+	0.0799252i	$0.0254682\pi$
$264$	−1.88431e34	−	3.26373e34i	−0.145177	−	0.251453i
$265$	−2.22545e34			−0.162312
$266$	−2.46885e33	+	1.77103e34i	−0.0170495	+	0.122305i
$267$	−1.17767e35			−0.770210
$268$	8.47040e34	+	1.46712e35i	0.524747	+	0.908888i
$269$	1.06569e34	−	1.84582e34i	0.0625491	−	0.108338i	−0.833055	−	0.553190i	$-0.813410\pi$
$269$	1.06569e34	−	1.84582e34i	0.0625491	−	0.108338i	0.895604	+	0.444852i	$0.146744\pi$
$270$	1.28587e34	−	2.22720e34i	0.0715193	−	0.123875i
$271$	−1.67168e35	−	2.89544e35i	−0.881249	−	1.52637i	−0.849953	−	0.526858i	$-0.823370\pi$
$271$	−1.67168e35	−	2.89544e35i	−0.881249	−	1.52637i	−0.0312960	−	0.999510i	$-0.509963\pi$
$272$	1.60549e35			0.802342
$273$	2.43156e34	−	1.74428e35i	0.115220	−	0.826530i
$274$	5.11862e35			2.30022
$275$	−1.57686e35	−	2.73120e35i	−0.672154	−	1.16421i
$276$	6.81443e33	−	1.18029e34i	0.0275580	−	0.0477319i
$277$	1.00980e35	−	1.74903e35i	0.387508	−	0.671183i	−0.604606	−	0.796525i	$-0.706669\pi$
$277$	1.00980e35	−	1.74903e35i	0.387508	−	0.671183i	0.992114	+	0.125342i	$0.0400027\pi$
$278$	1.54969e35	+	2.68414e35i	0.564410	+	0.977586i
$279$	2.46264e34			0.0851413
$280$	−3.45056e34	−	2.68967e34i	−0.113266	−	0.0882891i
$281$	7.42310e34			0.231389			0.115695	−	0.993285i	$-0.463091\pi$
$281$	7.42310e34			0.231389			0.115695	+	0.993285i	$0.463091\pi$
$282$	−4.20105e34	−	7.27644e34i	−0.124379	−	0.215430i
$283$	−1.09414e35	+	1.89510e35i	−0.307729	+	0.533002i	−0.977865	−	0.209236i	$-0.932902\pi$
$283$	−1.09414e35	+	1.89510e35i	−0.307729	+	0.533002i	0.670136	+	0.742238i	$0.266236\pi$
$284$	1.40319e35	−	2.43040e35i	0.374974	−	0.649475i
$285$	5.77447e33	+	1.00017e34i	0.0146643	+	0.0253993i
$286$	1.55862e36			3.76213
$287$	−3.11077e35	+	1.26088e35i	−0.713807	+	0.289325i
$288$	−1.97696e35			−0.431327
$289$	1.24872e35	+	2.16285e35i	0.259088	+	0.448753i
$290$	7.51359e34	−	1.30139e35i	0.148278	−	0.256825i
$291$	2.07678e35	−	3.59709e35i	0.389890	−	0.675310i
$292$	4.47740e34	+	7.75509e34i	0.0799788	+	0.138527i
$293$	−2.47324e35			−0.420422			−0.210211	−	0.977656i	$-0.567415\pi$
$293$	−2.47324e35			−0.420422			−0.210211	+	0.977656i	$0.567415\pi$
$294$	3.44289e35	−	3.33966e35i	0.557040	−	0.540339i
$295$	6.01025e35			0.925707
$296$	−1.00521e35	−	1.74107e35i	−0.147410	−	0.255321i
$297$	1.33426e35	−	2.31100e35i	0.186325	−	0.322724i
$298$	1.48037e35	−	2.56407e35i	0.196894	−	0.341031i
$299$	−6.74970e34	−	1.16908e35i	−0.0855170	−	0.148120i
$300$	−2.67898e35			−0.323378
$301$	−6.67054e34	+	2.70375e34i	−0.0767267	+	0.0310994i
$302$	−2.02687e36			−2.22190
$303$	−1.99558e35	−	3.45645e35i	−0.208522	−	0.361170i
$304$	5.32993e34	−	9.23171e34i	0.0530951	−	0.0919635i
$305$	6.10287e34	−	1.05705e35i	0.0579678	−	0.100403i
$306$	1.71675e35	+	2.97349e35i	0.155506	+	0.269343i
$307$	−1.88840e36			−1.63150			−0.815749	−	0.578406i	$-0.803675\pi$
$307$	−1.88840e36			−1.63150			−0.815749	+	0.578406i	$0.803675\pi$
$308$	1.49497e36	+	1.16531e36i	1.23211	+	0.960412i
$309$	8.65749e35			0.680760
$310$	1.26506e35	+	2.19115e35i	0.0949220	+	0.164410i
$311$	−5.60189e35	+	9.70277e35i	−0.401152	+	0.694816i	−0.993865	−	0.110598i	$-0.964724\pi$
$311$	−5.60189e35	+	9.70277e35i	−0.401152	+	0.694816i	0.592713	+	0.805414i	$0.298057\pi$
$312$	−1.58546e35	+	2.74609e35i	−0.108371	+	0.187704i
$313$	8.16955e35	+	1.41501e36i	0.533096	+	0.923349i	0.999253	+	0.0386470i	$0.0123048\pi$
$313$	8.16955e35	+	1.41501e36i	0.533096	+	0.923349i	−0.466157	+	0.884702i	$0.654362\pi$
$314$	1.89073e36			1.17801
$315$	4.27713e34	−	3.06821e35i	0.0254478	−	0.182550i
$316$	−6.92007e35			−0.393231
$317$	6.24055e35	+	1.08089e36i	0.338737	+	0.586711i	0.984196	−	0.177085i	$-0.0566668\pi$
$317$	6.24055e35	+	1.08089e36i	0.338737	+	0.586711i	−0.645458	+	0.763796i	$0.723333\pi$
$318$	−2.19647e35	+	3.80439e35i	−0.113902	+	0.197284i
$319$	7.79631e35	−	1.35036e36i	0.386299	−	0.669090i
$320$	−3.40662e35	−	5.90043e35i	−0.161305	−	0.279389i
$321$	−2.31674e36			−1.04847
$322$	5.07615e34	−	3.64139e35i	0.0219596	−	0.157528i
$323$	−1.54188e35			−0.0637697
$324$	−1.13341e35	−	1.96312e35i	−0.0448211	−	0.0776324i
$325$	−1.32677e36	+	2.29802e36i	−0.501748	+	0.869052i
$326$	−2.91160e36	+	5.04304e36i	−1.05312	+	1.82405i
$327$	−4.34643e35	−	7.52824e35i	−0.150380	−	0.260466i
$328$	6.04348e35			0.200040
$329$	−7.98244e35	−	6.22221e35i	−0.252810	−	0.197063i
$330$	2.74163e36			0.830916
$331$	−1.65492e36	−	2.86641e36i	−0.480033	−	0.831442i	0.519704	−	0.854346i	$-0.326042\pi$
$331$	−1.65492e36	−	2.86641e36i	−0.480033	−	0.831442i	−0.999738	+	0.0229041i	$0.992709\pi$
$332$	−1.50820e36	+	2.61228e36i	−0.418753	+	0.725301i
$333$	7.11774e35	−	1.23283e36i	0.189191	−	0.327688i
$334$	1.22978e36	+	2.13005e36i	0.312972	+	0.542083i
$335$	2.95159e36			0.719295
$336$	−2.64998e36	+	1.07411e36i	−0.618477	+	0.250685i
$337$	−2.98285e36			−0.666804			−0.333402	−	0.942785i	$-0.608197\pi$
$337$	−2.98285e36			−0.666804			−0.333402	+	0.942785i	$0.608197\pi$
$338$	−3.41866e36	−	5.92129e36i	−0.732089	−	1.26801i
$339$	−3.02728e35	+	5.24340e35i	−0.0621093	+	0.107576i
$340$	−7.87583e35	+	1.36413e36i	−0.154829	+	0.268172i
$341$	1.31266e36	+	2.27360e36i	0.247294	+	0.428326i
$342$	2.27971e35			0.0411624
$343$	2.33235e36	−	5.28616e36i	0.403672	−	0.914904i
$344$	1.29592e35			0.0215021
$345$	−1.18728e35	−	2.05643e35i	−0.0188875	−	0.0327142i
$346$	2.58433e36	−	4.47618e36i	0.394225	−	0.682817i
$347$	4.89702e36	−	8.48189e36i	0.716398	−	1.24084i	−0.246020	−	0.969265i	$-0.579123\pi$
$347$	4.89702e36	−	8.48189e36i	0.716398	−	1.24084i	0.962418	−	0.271573i	$-0.0875438\pi$
$348$	−6.62270e35	−	1.14709e36i	−0.0929258	−	0.160952i
$349$	−9.31737e36			−1.25408			−0.627039	−	0.778988i	$-0.715733\pi$
$349$	−9.31737e36			−1.25408			−0.627039	+	0.778988i	$0.715733\pi$
$350$	−6.69769e36	+	2.71475e36i	−0.864846	+	0.350545i
$351$	−2.24528e36			−0.278174
$352$	−1.05378e37	−	1.82520e37i	−1.25280	−	2.16991i
$353$	−6.68209e36	+	1.15737e37i	−0.762394	+	1.32050i	0.179220	+	0.983809i	$0.442643\pi$
$353$	−6.68209e36	+	1.15737e37i	−0.762394	+	1.32050i	−0.941614	+	0.336695i	$0.890691\pi$
$354$	5.93199e36	−	1.02745e37i	0.649610	−	1.12516i
$355$	−2.44478e36	−	4.23449e36i	−0.256998	−	0.445133i
$356$	−1.06647e37			−1.07628
$357$	3.26200e36	+	2.54269e36i	0.316078	+	0.246379i
$358$	−1.55066e37			−1.44282
$359$	7.90101e36	+	1.36850e37i	0.706014	+	1.22285i	0.966324	+	0.257327i	$0.0828417\pi$
$359$	7.90101e36	+	1.36850e37i	0.706014	+	1.22285i	−0.260311	+	0.965525i	$0.583825\pi$
$360$	−2.78883e35	+	4.83040e35i	−0.0239351	+	0.0414569i
$361$	6.01372e36	−	1.04161e37i	0.495780	−	0.858716i
$362$	1.42943e37	+	2.47584e37i	1.13211	+	1.96087i
$363$	2.08606e37			1.58738
$364$	2.20197e36	−	1.57959e37i	0.161006	−	1.15498i
$365$	1.56019e36			0.109631
$366$	−1.20468e36	−	2.08657e36i	−0.0813573	−	0.140915i
$367$	−1.92503e36	+	3.33424e36i	−0.124962	+	0.216441i	−0.921718	−	0.387860i	$-0.873214\pi$
$367$	−1.92503e36	+	3.33424e36i	−0.124962	+	0.216441i	0.796756	+	0.604301i	$0.206548\pi$
$368$	−1.09588e36	+	1.89812e36i	−0.0683862	+	0.118448i
$369$	2.13965e36	+	3.70598e36i	0.128369	+	0.222342i
$370$	1.46255e37			0.843698
$371$	−7.30599e35	+	5.24097e36i	−0.0405282	+	0.290730i
$372$	2.23012e36			0.118975
$373$	5.14746e36	+	8.91565e36i	0.264128	+	0.457483i	0.967335	−	0.253502i	$-0.0815825\pi$
$373$	5.14746e36	+	8.91565e36i	0.264128	+	0.457483i	−0.703207	+	0.710985i	$0.748249\pi$
$374$	−1.83015e37	+	3.16992e37i	−0.903336	+	1.56462i
$375$	−5.69538e36	+	9.86469e36i	−0.270439	+	0.468414i
$376$	9.11134e35	+	1.57813e36i	0.0416254	+	0.0720974i
$377$	−1.31196e37			−0.576727
$378$	−4.82295e36	−	3.75943e36i	−0.204024	−	0.159034i
$379$	1.10807e37			0.451129			0.225564	−	0.974228i	$-0.427577\pi$
$379$	1.10807e37			0.451129			0.225564	+	0.974228i	$0.427577\pi$
$380$	5.22925e35	+	9.05733e35i	0.0204917	+	0.0354926i
$381$	−1.71723e36	+	2.97433e36i	−0.0647764	+	0.112196i
$382$	−1.79833e37	+	3.11479e37i	−0.653055	+	1.13112i
$383$	5.39693e36	+	9.34776e36i	0.188697	+	0.326832i	0.944816	−	0.327601i	$-0.106240\pi$
$383$	5.39693e36	+	9.34776e36i	0.188697	+	0.326832i	−0.756119	+	0.654434i	$0.772907\pi$
$384$	8.74164e36			0.294300
$385$	3.06066e37	−	1.24057e37i	0.992281	−	0.402198i
$386$	6.12014e37			1.91093
$387$	4.58812e35	+	7.94686e35i	0.0137983	+	0.0238994i
$388$	1.88070e37	−	3.25746e37i	0.544827	−	0.943668i
$389$	−2.18671e37	+	3.78750e37i	−0.610270	+	1.05702i	0.380924	+	0.924606i	$0.375606\pi$
$389$	−2.18671e37	+	3.78750e37i	−0.610270	+	1.05702i	−0.991195	+	0.132413i	$0.957727\pi$
$390$	−1.15340e37	−	1.99775e37i	−0.310130	−	0.537160i
$391$	3.17023e36			0.0821349
$392$	−7.46702e36	+	7.24314e36i	−0.186423	+	0.180833i
$393$	4.18138e37			1.00607
$394$	−2.93609e37	−	5.08545e37i	−0.680885	−	1.17933i
$395$	−6.02842e36	+	1.04415e37i	−0.134755	+	0.233403i
$396$	1.20828e37	−	2.09280e37i	0.260367	−	0.450969i
$397$	−1.39139e37	−	2.40996e37i	−0.289059	−	0.500665i	0.684526	−	0.728988i	$-0.260009\pi$
$397$	−1.39139e37	−	2.40996e37i	−0.289059	−	0.500665i	−0.973585	+	0.228323i	$0.926676\pi$
$398$	−6.98392e37			−1.39893
$399$	2.54499e36	−	1.03155e36i	0.0491562	−	0.0199243i
$400$	4.30826e37			0.802475
$401$	1.89073e37	+	3.27484e37i	0.339654	+	0.588298i	0.984368	−	0.176126i	$-0.0563568\pi$
$401$	1.89073e37	+	3.27484e37i	0.339654	+	0.588298i	−0.644714	+	0.764424i	$0.723023\pi$
$402$	2.91316e37	−	5.04574e37i	0.504762	−	0.874273i
$403$	1.10447e37	−	1.91300e37i	0.184599	−	0.319736i
$404$	−1.80716e37	−	3.13009e37i	−0.291385	−	0.504693i
$405$	−3.94946e36			−0.0614384
$406$	−2.81814e37	−	2.19671e37i	−0.422995	−	0.329719i
$407$	1.51759e38			2.19803
$408$	−3.72332e36	−	6.44898e36i	−0.0520425	−	0.0901403i
$409$	1.89439e36	−	3.28118e36i	0.0255554	−	0.0442632i	−0.852965	−	0.521968i	$-0.825198\pi$
$409$	1.89439e36	−	3.28118e36i	0.0255554	−	0.0442632i	0.878520	+	0.477705i	$0.158531\pi$
$410$	−2.19828e37	+	3.80753e37i	−0.286231	+	0.495766i
$411$	−3.93036e37	−	6.80759e37i	−0.493999	−	0.855632i
$412$	7.84006e37			0.951283
$413$	1.97313e37	−	1.41543e38i	0.231142	−	1.65810i
$414$	−4.68727e36			−0.0530170
$415$	2.62774e37	+	4.55138e37i	0.287002	+	0.497102i
$416$	−8.86646e37	+	1.53572e38i	−0.935184	+	1.61979i
$417$	2.37987e37	−	4.12206e37i	0.242427	−	0.419896i
$418$	1.21515e37	+	2.10471e37i	0.119557	+	0.207079i
$419$	1.88180e37			0.178842			0.0894211	−	0.995994i	$-0.471498\pi$
$419$	1.88180e37			0.178842			0.0894211	+	0.995994i	$0.471498\pi$
$420$	3.87329e36	−	2.77851e37i	0.0355603	−	0.255093i
$421$	2.15515e38			1.91155			0.955777	−	0.294091i	$-0.0950170\pi$
$421$	2.15515e38			1.91155			0.955777	+	0.294091i	$0.0950170\pi$
$422$	3.78366e37	+	6.55349e37i	0.324251	+	0.561620i
$423$	−6.45161e36	+	1.11745e37i	−0.0534236	+	0.0925323i
$424$	4.76375e36	−	8.25106e36i	0.0381192	−	0.0660244i
$425$	−3.11581e37	−	5.39673e37i	−0.240952	−	0.417341i
$426$	−9.65179e37			−0.721387
$427$	−2.28902e37	−	1.78426e37i	−0.165366	−	0.128900i
$428$	−2.09800e38			−1.46511
$429$	−1.19680e38	−	2.07292e38i	−0.807961	−	1.39943i
$430$	−4.71384e36	+	8.16461e36i	−0.0307668	+	0.0532897i
$431$	−1.54022e38	+	2.66774e38i	−0.971993	+	1.68354i	−0.282473	+	0.959275i	$0.591155\pi$
$431$	−1.54022e38	+	2.66774e38i	−0.971993	+	1.68354i	−0.689520	+	0.724266i	$0.742179\pi$
$432$	1.82271e37	+	3.15703e37i	0.111225	+	0.192648i
$433$	−8.25735e37			−0.487266			−0.243633	−	0.969867i	$-0.578339\pi$
$433$	−8.25735e37			−0.487266			−0.243633	+	0.969867i	$0.578339\pi$
$434$	5.57551e37	−	2.25990e37i	0.318188	−	0.128970i
$435$	−2.30774e37			−0.127378
$436$	−3.93605e37	−	6.81743e37i	−0.210139	−	0.363971i
$437$	1.05246e36	−	1.82291e36i	0.00543530	−	0.00941421i
$438$	1.53988e37	−	2.66715e37i	0.0769328	−	0.133252i
$439$	5.49424e37	+	9.51630e37i	0.265566	+	0.459973i	0.967712	−	0.252060i	$-0.0811080\pi$
$439$	5.49424e37	+	9.51630e37i	0.265566	+	0.459973i	−0.702146	+	0.712033i	$0.747775\pi$
$440$	−5.94612e37			−0.278080
$441$	−7.08528e37	−	2.01455e37i	−0.320625	−	0.0911628i
$442$	3.07977e38			1.34864
$443$	−2.00091e38	−	3.46568e38i	−0.847958	−	1.46871i	−0.883028	−	0.469321i	$-0.844499\pi$
$443$	−2.00091e38	−	3.46568e38i	−0.847958	−	1.46871i	0.0350701	−	0.999385i	$-0.488835\pi$
$444$	6.44569e37	−	1.11643e38i	0.264372	−	0.457907i
$445$	−9.29057e37	+	1.60917e38i	−0.368827	+	0.638826i
$446$	3.40219e38	+	5.89276e38i	1.30738	+	2.26445i
$447$	−4.54683e37			−0.169141
$448$	−1.50140e38	+	6.08558e37i	−0.540711	+	0.219165i
$449$	−1.81601e38			−0.633209			−0.316605	−	0.948558i	$-0.602543\pi$
$449$	−1.81601e38			−0.633209			−0.316605	+	0.948558i	$0.602543\pi$
$450$	4.60680e37	+	7.97921e37i	0.155531	+	0.269388i
$451$	−2.28099e38	+	3.95079e38i	−0.745700	+	1.29159i
$452$	−2.74144e37	+	4.74832e37i	−0.0867905	+	0.150326i
$453$	1.55634e38	+	2.69566e38i	0.477179	+	0.826498i
$454$	−5.40530e38			−1.60513
$455$	−2.19158e38	−	1.70831e38i	−0.630365	−	0.491362i
$456$	−4.94429e36			−0.0137757
$457$	−1.91569e38	−	3.31807e38i	−0.517059	−	0.895572i	−0.999804	−	0.0198109i	$-0.993694\pi$
$457$	−1.91569e38	−	3.31807e38i	−0.517059	−	0.895572i	0.482745	−	0.875761i	$-0.339640\pi$
$458$	−3.53601e38	+	6.12454e38i	−0.924621	+	1.60149i
$459$	2.63643e37	−	4.56643e37i	0.0667932	−	0.115689i
$460$	−1.07518e37	−	1.86226e37i	−0.0263932	−	0.0457143i
$461$	−6.29745e38			−1.49796			−0.748982	−	0.662590i	$-0.769457\pi$
$461$	−6.29745e38			−1.49796			−0.748982	+	0.662590i	$0.769457\pi$
$462$	9.00060e37	−	6.45660e38i	0.207474	−	1.48832i
$463$	7.08265e38			1.58224			0.791118	−	0.611664i	$-0.209499\pi$
$463$	7.08265e38			1.58224			0.791118	+	0.611664i	$0.209499\pi$
$464$	1.06504e38	+	1.84471e38i	0.230599	+	0.399408i
$465$	1.94277e37	−	3.36498e37i	0.0407712	−	0.0706178i
$466$	−2.53965e38	+	4.39879e38i	−0.516627	+	0.894825i
$467$	1.54182e38	+	2.67051e38i	0.304045	+	0.526622i	0.977048	−	0.213018i	$-0.0683292\pi$
$467$	1.54182e38	+	2.67051e38i	0.304045	+	0.526622i	−0.673003	+	0.739640i	$0.734996\pi$
$468$	−2.03328e38			−0.388716
$469$	9.68989e37	−	6.95107e38i	0.179603	−	1.28838i
$470$	−1.32568e38			−0.238242
$471$	−1.45181e38	−	2.51460e38i	−0.252992	−	0.438194i
$472$	−1.28654e38	+	2.22836e38i	−0.217403	+	0.376553i
$473$	−4.89121e37	+	8.47182e37i	−0.0801548	+	0.138832i
$474$	1.18998e38	+	2.06111e38i	0.189128	+	0.327579i
$475$	−4.13755e37			−0.0637803
$476$	2.95400e38	+	2.30261e38i	0.441683	+	0.344286i
$477$	6.74628e37			0.0978471
$478$	3.80819e38	+	6.59597e38i	0.535814	+	0.928057i
$479$	5.61142e38	−	9.71926e38i	0.765963	−	1.32669i	−0.173773	−	0.984786i	$-0.555596\pi$
$479$	5.61142e38	−	9.71926e38i	0.765963	−	1.32669i	0.939736	−	0.341901i	$-0.111071\pi$
$480$	−1.55962e38	+	2.70134e38i	−0.206548	+	0.357751i
$481$	−6.38446e38	−	1.10582e39i	−0.820390	−	1.42096i
$482$	−2.48644e38			−0.310024
$483$	−5.23270e37	+	2.12095e37i	−0.0633129	+	0.0256624i
$484$	1.88910e39			2.21818
$485$	−3.27673e38	−	5.67547e38i	−0.373410	−	0.646765i
$486$	−3.89803e37	+	6.75159e37i	−0.0431141	+	0.0746758i
$487$	7.67660e38	−	1.32963e39i	0.824136	−	1.42745i	−0.0784415	−	0.996919i	$-0.524994\pi$
$487$	7.67660e38	−	1.32963e39i	0.824136	−	1.42745i	0.902578	−	0.430527i	$-0.141672\pi$
$488$	2.61274e37	+	4.52540e37i	0.0272276	+	0.0471595i
$489$	8.94277e38			0.904677
$490$	−1.84726e38	−	7.33904e38i	−0.181420	−	0.720769i
$491$	1.56499e39			1.49221			0.746106	−	0.665828i	$-0.231921\pi$
$491$	1.56499e39			1.49221			0.746106	+	0.665828i	$0.231921\pi$
$492$	1.93763e38	+	3.35607e38i	0.179381	+	0.310697i
$493$	1.54052e38	−	2.66825e38i	0.138480	−	0.239854i
$494$	1.02243e38	−	1.77089e38i	0.0892465	−	0.154579i
$495$	−2.10518e38	−	3.64628e38i	−0.178449	−	0.309082i
$496$	−3.58642e38			−0.295241
$497$	−1.07749e39	+	4.36736e38i	−0.861481	+	0.349181i
$498$	1.03741e39			0.805609
$499$	−1.26739e39	−	2.19518e39i	−0.955988	−	1.65582i	−0.732091	−	0.681207i	$-0.761455\pi$
$499$	−1.26739e39	−	2.19518e39i	−0.955988	−	1.65582i	−0.223897	−	0.974613i	$-0.571878\pi$
$500$	−5.15763e38	+	8.93328e38i	−0.377907	+	0.654555i
$501$	1.88859e38	−	3.27114e38i	0.134429	−	0.232837i
$502$	7.26187e38	+	1.25779e39i	0.502163	+	0.869772i
$503$	8.76629e38			0.588952			0.294476	−	0.955659i	$-0.404855\pi$
$503$	8.76629e38			0.588952			0.294476	+	0.955659i	$0.404855\pi$
$504$	1.04601e38	+	8.15354e37i	0.0682801	+	0.0532235i
$505$	−6.29723e38			−0.399415
$506$	−2.49845e38	−	4.32745e38i	−0.153989	−	0.266716i
$507$	−5.25008e38	+	9.09340e38i	−0.314449	+	0.544642i
$508$	−1.55509e38	+	2.69350e38i	−0.0905176	+	0.156781i
$509$	1.52917e39	+	2.64860e39i	0.865062	+	1.49833i	0.866985	+	0.498334i	$0.166055\pi$
$509$	1.52917e39	+	2.64860e39i	0.865062	+	1.49833i	−0.00192287	+	0.999998i	$0.500612\pi$
$510$	5.41734e38			0.297865
$511$	5.12202e37	−	3.67429e38i	0.0273740	−	0.196368i
$512$	2.30123e39			1.19549
$513$	−1.75049e37	−	3.03194e37i	−0.00884011	−	0.0153115i
$514$	−1.27659e39	+	2.21112e39i	−0.626738	+	1.08554i
$515$	6.82986e38	−	1.18297e39i	0.325992	−	0.564635i
$516$	4.15492e37	+	7.19653e37i	0.0192815	+	0.0333966i
$517$	−1.37556e39			−0.620678
$518$	4.80147e38	−	3.44434e39i	0.210665	−	1.51121i
$519$	−7.93756e38			−0.338657
$520$	2.50152e38	+	4.33276e38i	0.103790	+	0.179770i
$521$	7.44514e38	−	1.28954e39i	0.300418	−	0.520339i	−0.675813	−	0.737073i	$-0.736207\pi$
$521$	7.44514e38	−	1.28954e39i	0.300418	−	0.520339i	0.976231	+	0.216734i	$0.0695405\pi$
$522$	−2.27769e38	+	3.94508e38i	−0.0893867	+	0.154822i
$523$	1.16680e39	+	2.02095e39i	0.445370	+	0.771404i	0.998078	−	0.0619712i	$-0.0197387\pi$
$523$	1.16680e39	+	2.02095e39i	0.445370	+	0.771404i	−0.552708	+	0.833375i	$0.686405\pi$
$524$	3.78658e39			1.40587
$525$	8.75340e38	+	6.82317e38i	0.316131	+	0.246420i
$526$	−3.28412e39			−1.15379
$527$	2.59376e38	+	4.49253e38i	0.0886495	+	0.153545i
$528$	−1.94312e39	+	3.36558e39i	−0.646111	+	1.11910i
$529$	1.52389e39	−	2.63945e39i	0.492999	−	0.853900i
$530$	3.46557e38	+	6.00254e38i	0.109087	+	0.188945i
$531$	−1.82197e39			−0.558046
$532$	2.30469e38	−	9.34153e37i	0.0686901	−	0.0278419i
$533$	3.83844e39			1.11329
$534$	1.83392e39	+	3.17644e39i	0.517645	+	0.896587i
$535$	−1.82767e39	+	3.16562e39i	−0.502074	+	0.869619i
$536$	−6.31813e38	+	1.09433e39i	−0.168927	+	0.292590i
$537$	1.19068e39	+	2.06232e39i	0.309863	+	0.536698i
$538$	−6.63815e38			−0.168153
$539$	−1.91677e39	−	7.61519e39i	−0.472642	−	1.87777i
$540$	−3.57656e38			−0.0858531
$541$	−2.49107e39	−	4.31465e39i	−0.582137	−	1.00829i	−0.995226	−	0.0975996i	$-0.968884\pi$
$541$	−2.49107e39	−	4.31465e39i	−0.582137	−	1.00829i	0.413089	−	0.910691i	$-0.364450\pi$
$542$	−5.20644e39	+	9.01782e39i	−1.18454	+	2.05169i
$543$	2.19519e39	−	3.80219e39i	0.486267	−	0.842240i
$544$	−2.08222e39	−	3.60651e39i	−0.449100	−	0.777863i
$545$	−1.37155e39			−0.288047
$546$	−5.08339e39	+	2.06043e39i	−1.03959	+	0.421372i
$547$	3.62400e39			0.721726			0.360863	−	0.932619i	$-0.382482\pi$
$547$	3.62400e39			0.721726			0.360863	+	0.932619i	$0.382482\pi$
$548$	−3.55927e39	−	6.16483e39i	−0.690307	−	1.19565i
$549$	−1.85004e38	+	3.20437e38i	−0.0349448	+	0.0605262i
$550$	−4.91112e39	+	8.50631e39i	−0.903487	+	1.56488i
$551$	−1.02284e38	−	1.77162e38i	−0.0183278	−	0.0317448i
$552$	1.01659e38			0.0177430
$553$	2.26109e39	+	1.76249e39i	0.384418	+	0.299649i
$554$	−6.29006e39			−1.04175
$555$	−1.12303e39	−	1.94515e39i	−0.181194	−	0.313837i
$556$	2.15517e39	−	3.73286e39i	0.338764	−	0.586756i
$557$	5.12842e38	−	8.88268e38i	0.0785386	−	0.136033i	−0.824081	−	0.566472i	$-0.808308\pi$
$557$	5.12842e38	−	8.88268e38i	0.0785386	−	0.136033i	0.902620	+	0.430439i	$0.141641\pi$
$558$	−3.83494e38	−	6.64232e38i	−0.0572220	−	0.0991114i
$559$	8.23090e38			0.119667
$560$	−6.22891e38	+	4.46832e39i	−0.0882441	+	0.633021i
$561$	5.62118e39			0.776008
$562$	−1.15596e39	−	2.00218e39i	−0.155513	−	0.269356i
$563$	3.14261e39	−	5.44317e39i	0.412021	−	0.713641i	−0.583090	−	0.812408i	$-0.698156\pi$
$563$	3.14261e39	−	5.44317e39i	0.412021	−	0.713641i	0.995111	+	0.0987666i	$0.0314897\pi$
$564$	−5.84246e38	+	1.01194e39i	−0.0746532	+	0.129303i
$565$	4.77641e38	+	8.27299e38i	0.0594839	+	0.103029i
$566$	6.81537e39			0.827277
$567$	−1.29658e38	+	9.30106e38i	−0.0153407	+	0.110047i
$568$	2.09330e39			0.241424
$569$	−2.96358e39	−	5.13308e39i	−0.333188	−	0.577099i	0.649947	−	0.759980i	$-0.274791\pi$
$569$	−2.96358e39	−	5.13308e39i	−0.333188	−	0.577099i	−0.983135	+	0.182881i	$0.941458\pi$
$570$	1.79846e38	−	3.11502e38i	0.0197113	−	0.0341409i
$571$	−9.30975e39	+	1.61250e40i	−0.994751	+	1.72296i	−0.408761	+	0.912641i	$0.634039\pi$
$571$	−9.30975e39	+	1.61250e40i	−0.994751	+	1.72296i	−0.585990	+	0.810318i	$0.699294\pi$
$572$	−1.08380e40	−	1.87720e40i	−1.12903	−	1.95554i
$573$	5.52343e39			0.561005
$574$	8.24513e39	+	6.42697e39i	0.816535	+	0.636479i
$575$	8.50715e38			0.0821486
$576$	1.03269e39	+	1.78868e39i	0.0972400	+	0.168425i
$577$	3.18844e39	−	5.52254e39i	0.292771	−	0.507095i	−0.681693	−	0.731639i	$-0.738756\pi$
$577$	3.18844e39	−	5.52254e39i	0.292771	−	0.507095i	0.974464	+	0.224544i	$0.0720892\pi$
$578$	3.88914e39	−	6.73618e39i	0.348257	−	0.603199i
$579$	−4.69939e39	−	8.13958e39i	−0.410395	−	0.710825i
$580$	−2.08985e39			−0.177996
$581$	1.15813e40	−	4.69419e39i	0.962059	−	0.389948i
$582$	−1.29363e40			−1.04815
$583$	3.59597e39	+	6.22840e39i	0.284199	+	0.492246i
$584$	−3.33972e38	+	5.78457e38i	−0.0257469	+	0.0445949i
$585$	−1.77129e39	+	3.06797e39i	−0.133208	+	0.230723i
$586$	3.85145e39	+	6.67090e39i	0.282559	+	0.489406i
$587$	−2.27430e40			−1.62778			−0.813888	−	0.581022i	$-0.802653\pi$
$587$	−2.27430e40			−1.62778			−0.813888	+	0.581022i	$0.802653\pi$
$588$	−6.41630e39	−	1.82434e39i	−0.448036	−	0.127389i
$589$	3.44432e38			0.0234656
$590$	−9.35945e39	−	1.62110e40i	−0.622151	−	1.07760i
$591$	−4.50899e39	+	7.80979e39i	−0.292456	+	0.506549i
$592$	−1.03658e40	+	1.79540e40i	−0.656050	+	1.13631i
$593$	−1.69422e39	−	2.93448e39i	−0.104635	−	0.181233i	0.808954	−	0.587872i	$-0.200034\pi$
$593$	−1.69422e39	−	2.93448e39i	−0.104635	−	0.181233i	−0.913589	+	0.406639i	$0.866701\pi$
$594$	−8.31107e39			−0.500903
$595$	6.04773e39	−	2.45131e39i	0.355710	−	0.144179i
$596$	−4.11753e39			−0.236355
$597$	5.36265e39	+	9.28838e39i	0.300436	+	0.520370i
$598$	−2.10219e39	+	3.64110e39i	−0.114949	+	0.199097i
$599$	9.44477e39	−	1.63588e40i	0.504083	−	0.873098i	−0.495905	−	0.868377i	$-0.665164\pi$
$599$	9.44477e39	−	1.63588e40i	0.504083	−	0.873098i	0.999989	−	0.00472154i	$-0.00150292\pi$
$600$	−9.99134e38	−	1.73055e39i	−0.0520512	−	0.0901553i
$601$	1.32903e39			0.0675857			0.0337929	−	0.999429i	$-0.489241\pi$
$601$	1.32903e39			0.0675857			0.0337929	+	0.999429i	$0.489241\pi$
$602$	1.76803e39	+	1.37816e39i	0.0877689	+	0.0684148i
$603$	−8.94755e39			−0.433614
$604$	1.40939e40	+	2.44114e40i	0.666802	+	1.15494i
$605$	1.64569e40	−	2.85042e40i	0.760142	−	1.31660i
$606$	−6.21522e39	+	1.07651e40i	−0.280288	+	0.485472i
$607$	8.91435e39	+	1.54401e40i	0.392513	+	0.679852i	0.992780	−	0.119947i	$-0.0382725\pi$
$607$	8.91435e39	+	1.54401e40i	0.392513	+	0.679852i	−0.600267	+	0.799799i	$0.704939\pi$
$608$	−2.76503e39			−0.118877
$609$	−7.57617e38	+	5.43479e39i	−0.0318053	+	0.228156i
$610$	−3.80147e39			−0.155837
$611$	5.78696e39	+	1.00233e40i	0.231661	+	0.401249i
$612$	2.38750e39	−	4.13528e39i	0.0933358	−	0.161662i
$613$	7.91971e39	−	1.37173e40i	0.302366	−	0.523713i	−0.674306	−	0.738452i	$-0.735557\pi$
$613$	7.91971e39	−	1.37173e40i	0.302366	−	0.523713i	0.976671	+	0.214740i	$0.0688903\pi$
$614$	2.94070e40	+	5.09344e40i	1.09650	+	1.89920i
$615$	6.75184e39			0.245886
$616$	−1.95207e39	+	1.40032e40i	−0.0694345	+	0.498090i
$617$	−2.27097e40			−0.789000			−0.394500	−	0.918896i	$-0.629082\pi$
$617$	−2.27097e40			−0.789000			−0.394500	+	0.918896i	$0.629082\pi$
$618$	−1.34818e40	−	2.33512e40i	−0.457527	−	0.792460i
$619$	−1.23401e40	+	2.13737e40i	−0.409077	+	0.708542i	−0.994787	−	0.101979i	$-0.967483\pi$
$619$	−1.23401e40	+	2.13737e40i	−0.409077	+	0.708542i	0.585709	+	0.810521i	$0.300816\pi$
$620$	1.75934e39	−	3.04726e39i	0.0569730	−	0.0986802i
$621$	3.59915e38	+	6.23391e38i	0.0113860	+	0.0197212i
$622$	3.48941e40			1.07843
$623$	3.48463e40	+	2.71623e40i	1.05216	+	0.820143i
$624$	3.26986e40			0.964613
$625$	−3.05720e39	−	5.29522e39i	−0.0881178	−	0.152624i
$626$	2.54440e40	−	4.40703e40i	0.716569	−	1.24113i
$627$	1.86613e39	−	3.23222e39i	0.0513525	−	0.0889451i
$628$	−1.31473e40	−	2.27718e40i	−0.353526	−	0.612326i
$629$	2.99868e40			0.787945
$630$	−8.94173e39	+	3.62432e39i	−0.229606	+	0.0930655i
$631$	1.26415e40			0.317230			0.158615	−	0.987340i	$-0.449297\pi$
$631$	1.26415e40			0.317230			0.158615	+	0.987340i	$0.449297\pi$
$632$	−2.58086e39	−	4.47019e39i	−0.0632947	−	0.109630i
$633$	5.81062e39	−	1.00643e40i	0.139273	−	0.241229i
$634$	1.94361e40	−	3.36644e40i	0.455319	−	0.788636i
$635$	2.70944e39	+	4.69288e39i	0.0620383	+	0.107454i
$636$	6.10931e39			0.136730
$637$	−4.74259e40	+	4.60039e40i	−1.03751	+	1.00641i
$638$	−4.85631e40			−1.03850
$639$	7.41118e39	+	1.28365e40i	0.154926	+	0.268340i
$640$	6.89625e39	−	1.19447e40i	0.140930	−	0.244098i
$641$	1.79616e40	−	3.11104e40i	0.358842	−	0.621533i	−0.628925	−	0.777466i	$-0.716505\pi$
$641$	1.79616e40	−	3.11104e40i	0.358842	−	0.621533i	0.987768	+	0.155932i	$0.0498382\pi$
$642$	3.60774e40	+	6.24879e40i	0.704657	+	1.22050i
$643$	1.00443e40			0.191806			0.0959029	−	0.995391i	$-0.469426\pi$
$643$	1.00443e40			0.191806			0.0959029	+	0.995391i	$0.469426\pi$
$644$	−4.73864e39	+	1.92070e39i	−0.0884725	+	0.0358603i
$645$	1.44782e39			0.0264301
$646$	2.40109e39	+	4.15881e39i	0.0428585	+	0.0742331i
$647$	3.97876e40	−	6.89141e40i	0.694441	−	1.20281i	−0.275928	−	0.961178i	$-0.588985\pi$
$647$	3.97876e40	−	6.89141e40i	0.694441	−	1.20281i	0.970369	−	0.241629i	$-0.0776816\pi$
$648$	8.45414e38	−	1.46430e39i	0.0144289	−	0.0249915i
$649$	−9.71162e40	−	1.68210e41i	−1.62085	−	2.80740i
$650$	8.26440e40			1.34886
$651$	−7.28679e39	−	5.67996e39i	−0.116309	−	0.0906611i
$652$	8.09840e40			1.26418
$653$	4.76696e40	+	8.25661e40i	0.727780	+	1.26055i	0.957820	+	0.287370i	$0.0927810\pi$
$653$	4.76696e40	+	8.25661e40i	0.727780	+	1.26055i	−0.230040	+	0.973181i	$0.573886\pi$
$654$	−1.35369e40	+	2.34467e40i	−0.202136	+	0.350109i
$655$	3.29868e40	−	5.71348e40i	0.481772	−	0.834453i
$656$	−3.11603e40	−	5.39713e40i	−0.445140	−	0.771005i
$657$	−4.72962e39			−0.0660889
$658$	−4.35212e39	+	3.12200e40i	−0.0594874	+	0.426734i
$659$	−1.34465e41			−1.79792			−0.898958	−	0.438035i	$-0.855675\pi$
$659$	−1.34465e41			−1.79792			−0.898958	+	0.438035i	$0.855675\pi$
$660$	−1.90641e40	−	3.30200e40i	−0.249362	−	0.431907i
$661$	3.49215e40	−	6.04858e40i	0.446860	−	0.773984i	−0.551320	−	0.834294i	$-0.685876\pi$
$661$	3.49215e40	−	6.04858e40i	0.446860	−	0.773984i	0.998180	+	0.0603098i	$0.0192089\pi$
$662$	−5.15424e40	+	8.92741e40i	−0.645244	+	1.11760i
$663$	−2.36482e40	−	4.09599e40i	−0.289636	−	0.501664i
$664$	−2.24996e40			−0.269611
$665$	5.98211e38	−	4.29128e39i	0.00701359	−	0.0503122i
$666$	−4.43363e40			−0.508608
$667$	2.10305e39	+	3.64259e39i	0.0236062	+	0.0408871i
$668$	1.71028e40	−	2.96228e40i	0.187848	−	0.325363i
$669$	5.22478e40	−	9.04959e40i	0.561552	−	0.972636i
$670$	−4.59636e40	−	7.96113e40i	−0.483426	−	0.837318i
$671$	−3.94451e40			−0.405991
$672$	5.84969e40	+	4.55976e40i	0.589221	+	0.459291i
$673$	1.24043e40			0.122280			0.0611399	−	0.998129i	$-0.480526\pi$
$673$	1.24043e40			0.122280			0.0611399	+	0.998129i	$0.480526\pi$
$674$	4.64504e40	+	8.04544e40i	0.448147	+	0.776214i
$675$	7.07472e39	−	1.22538e40i	0.0668043	−	0.115709i
$676$	−4.75437e40	+	8.23482e40i	−0.439406	+	0.761074i
$677$	5.39120e40	+	9.33783e40i	0.487697	+	0.844715i	0.999900	−	0.0141489i	$-0.00450390\pi$
$677$	5.39120e40	+	9.33783e40i	0.487697	+	0.844715i	−0.512203	+	0.858864i	$0.671171\pi$
$678$	1.88569e40			0.166970
$679$	−1.44416e41	+	5.85355e40i	−1.25171	+	0.507350i
$680$	−1.17493e40			−0.0996854
$681$	4.15050e40	+	7.18887e40i	0.344720	+	0.597073i
$682$	4.08828e40	−	7.08110e40i	0.332404	−	0.575741i
$683$	−8.17067e40	+	1.41520e41i	−0.650365	+	1.12647i	0.332669	+	0.943044i	$0.392051\pi$
$683$	−8.17067e40	+	1.41520e41i	−0.650365	+	1.12647i	−0.983034	+	0.183422i	$0.941282\pi$
$684$	−1.58521e39	−	2.74567e39i	−0.0123530	−	0.0213961i
$685$	−1.24026e41			−0.946236
$686$	−1.78900e41	+	1.94098e40i	−1.33632	+	0.144984i
$687$	1.08606e41			0.794292
$688$	−6.68182e39	−	1.15732e40i	−0.0478478	−	0.0828749i
$689$	3.02564e40	−	5.24056e40i	0.212148	−	0.367450i
$690$	−3.69777e39	+	6.40473e39i	−0.0253880	+	0.0439733i
$691$	3.46645e40	+	6.00407e40i	0.233052	+	0.403658i	0.958705	−	0.284403i	$-0.0917954\pi$
$691$	3.46645e40	+	6.00407e40i	0.233052	+	0.403658i	−0.725653	+	0.688061i	$0.758462\pi$
$692$	−7.18811e40			−0.473234
$693$	−9.27818e40	+	3.76069e40i	−0.598178	+	0.242458i
$694$	−3.05035e41			−1.92591
$695$	−3.75495e40	−	6.50376e40i	−0.232180	−	0.402147i
$696$	4.93992e39	−	8.55618e39i	0.0299148	−	0.0518139i
$697$	−4.50714e40	+	7.80660e40i	−0.267317	+	0.463006i
$698$	1.45095e41	+	2.51311e41i	0.842844	+	1.45985i
$699$	7.80033e40			0.443807
$700$	7.92691e40	+	6.17893e40i	0.441756	+	0.344343i
$701$	−1.20465e41			−0.657579			−0.328789	−	0.944403i	$-0.606641\pi$
$701$	−1.20465e41			−0.657579			−0.328789	+	0.944403i	$0.606641\pi$
$702$	3.49645e40	+	6.05603e40i	0.186956	+	0.323817i
$703$	9.95506e39	−	1.72427e40i	0.0521425	−	0.0903134i
$704$	−1.10091e41	+	1.90683e41i	−0.564870	+	0.978384i
$705$	1.01793e40	+	1.76311e40i	0.0511654	+	0.0886210i
$706$	4.16227e41			2.04957
$707$	−2.06734e40	+	1.48301e41i	−0.0997309	+	0.715422i
$708$	−1.64994e41			−0.779804
$709$	2.69006e40	+	4.65933e40i	0.124564	+	0.215751i	0.921562	−	0.388230i	$-0.126913\pi$
$709$	2.69006e40	+	4.65933e40i	0.124564	+	0.215751i	−0.796998	+	0.603981i	$0.793580\pi$
$710$	−7.61426e40	+	1.31883e41i	−0.345447	+	0.598332i
$711$	1.82747e40	−	3.16528e40i	0.0812347	−	0.140703i
$712$	−3.97745e40	−	6.88914e40i	−0.173238	−	0.300058i
$713$	−7.08180e39			−0.0302235
$714$	1.77848e40	−	1.27580e41i	0.0743746	−	0.533528i
$715$	−3.77660e41			−1.54762
$716$	1.07826e41	+	1.86760e41i	0.432997	+	0.749973i
$717$	5.84828e40	−	1.01295e41i	0.230144	−	0.398622i
$718$	2.46077e41	−	4.26217e41i	0.948999	−	1.64371i
$719$	1.52856e41	+	2.64754e41i	0.577714	+	1.00063i	0.995741	+	0.0921957i	$0.0293885\pi$
$719$	1.52856e41	+	2.64754e41i	0.577714	+	1.00063i	−0.418027	+	0.908435i	$0.637278\pi$
$720$	5.75172e40			0.213047
$721$	−2.56169e41	−	1.99681e41i	−0.929962	−	0.724894i
$722$	−3.74594e41			−1.33282
$723$	1.90922e40	+	3.30687e40i	0.0665812	+	0.115322i
$724$	1.98793e41	−	3.44319e41i	0.679502	−	1.17693i
$725$	4.13389e40	−	7.16011e40i	0.138503	−	0.239894i
$726$	−3.24852e41	−	5.62660e41i	−1.06685	−	1.84784i
$727$	−3.14695e40			−0.101307			−0.0506536	−	0.998716i	$-0.516130\pi$
$727$	−3.14695e40			−0.101307			−0.0506536	+	0.998716i	$0.516130\pi$
$728$	1.10250e41	−	4.46872e40i	0.347915	−	0.141019i
$729$	1.19725e40			0.0370370
$730$	−2.42961e40	−	4.20821e40i	−0.0736809	−	0.127619i
$731$	−9.66482e39	+	1.67400e40i	−0.0287337	+	0.0497682i
$732$	−1.67537e40	+	2.90182e40i	−0.0488314	+	0.0845784i
$733$	1.53108e41	+	2.65190e41i	0.437512	+	0.757792i	0.997497	−	0.0707103i	$-0.0225266\pi$
$733$	1.53108e41	+	2.65190e41i	0.437512	+	0.757792i	−0.559985	+	0.828503i	$0.689193\pi$
$734$	1.19910e41			0.335940
$735$	−8.34225e40	+	8.09212e40i	−0.229148	+	0.222278i
$736$	5.68513e40			0.153113
$737$	−4.76931e41	−	8.26069e41i	−1.25944	−	2.18141i
$738$	6.66392e40	−	1.15423e41i	0.172549	−	0.298864i
$739$	−3.02678e40	+	5.24255e40i	−0.0768488	+	0.133106i	−0.901889	−	0.431968i	$-0.857819\pi$
$739$	−3.02678e40	+	5.24255e40i	−0.0768488	+	0.133106i	0.825040	+	0.565074i	$0.191153\pi$
$740$	−1.01700e41	−	1.76149e41i	−0.253197	−	0.438551i
$741$	−3.14031e40			−0.0766669
$742$	1.52738e41	−	6.19089e40i	0.365672	−	0.148217i
$743$	3.62832e41			0.851860			0.425930	−	0.904756i	$-0.359947\pi$
$743$	3.62832e41			0.851860			0.425930	+	0.904756i	$0.359947\pi$
$744$	8.31732e39	+	1.44060e40i	0.0191503	+	0.0331693i
$745$	−3.58698e40	+	6.21283e40i	−0.0809959	+	0.140289i
$746$	1.60317e41	−	2.77678e41i	0.355032	−	0.614933i
$747$	−7.96581e40	−	1.37972e41i	−0.173014	−	0.299669i
$748$	5.09044e41			1.08438
$749$	6.85509e41	+	5.34345e41i	1.43228	+	1.11644i
$750$	3.54765e41			0.727030
$751$	1.54069e41	+	2.66855e41i	0.309696	+	0.536410i	0.978296	−	0.207213i	$-0.0664393\pi$
$751$	1.54069e41	+	2.66855e41i	0.309696	+	0.536410i	−0.668600	+	0.743623i	$0.733106\pi$
$752$	9.39567e40	−	1.62738e41i	0.185255	−	0.320870i
$753$	1.11522e41	−	1.93161e41i	0.215691	−	0.373587i
$754$	2.04304e41	+	3.53865e41i	0.387608	+	0.671357i
$755$	4.91117e41			0.914017
$756$	−1.17416e40	+	8.42287e40i	−0.0214369	+	0.153778i
$757$	6.99897e41			1.25356			0.626778	−	0.779198i	$-0.284373\pi$
$757$	6.99897e41			1.25356			0.626778	+	0.779198i	$0.284373\pi$
$758$	−1.72555e41	−	2.98873e41i	−0.303196	−	0.525151i
$759$	−3.83691e40	+	6.64572e40i	−0.0661417	+	0.114561i
$760$	−3.90053e39	+	6.75592e39i	−0.00659670	+	0.0114258i
$761$	1.52310e41	+	2.63808e41i	0.252726	+	0.437734i	0.964275	−	0.264902i	$-0.0853396\pi$
$761$	1.52310e41	+	2.63808e41i	0.252726	+	0.437734i	−0.711550	+	0.702636i	$0.752006\pi$
$762$	1.06966e41			0.174140
$763$	−4.50272e40	+	3.23004e41i	−0.0719232	+	0.515943i
$764$	5.00191e41			0.783939
$765$	−4.15974e40	−	7.20489e40i	−0.0639699	−	0.110799i
$766$	1.68087e41	−	2.91135e41i	0.253640	−	0.439317i
$767$	−8.17133e41	+	1.41532e42i	−1.20993	+	2.09566i
$768$	−2.52045e41	−	4.36555e41i	−0.366219	−	0.634309i
$769$	−3.98276e40			−0.0567875			−0.0283937	−	0.999597i	$-0.509039\pi$
$769$	−3.98276e40			−0.0567875			−0.0283937	+	0.999597i	$0.509039\pi$
$770$	−8.11230e41	−	6.32344e41i	−1.13509	−	0.884785i
$771$	3.92095e41			0.538397
$772$	−4.25568e41	−	7.37105e41i	−0.573479	−	0.993295i
$773$	4.90144e40	−	8.48954e40i	0.0648218	−	0.112275i	−0.831793	−	0.555086i	$-0.812685\pi$
$773$	4.90144e40	−	8.48954e40i	0.0648218	−	0.112275i	0.896615	+	0.442811i	$0.146019\pi$
$774$	1.42897e40	−	2.47505e40i	0.0185472	−	0.0321247i
$775$	6.96022e40	+	1.20555e41i	0.0886642	+	0.153571i
$776$	2.80565e41			0.350782
$777$	−4.94955e41	+	2.00618e41i	−0.607380	+	0.246187i
$778$	1.36210e42			1.64061
$779$	2.99257e40	+	5.18328e40i	0.0353795	+	0.0612790i
$780$	−1.60405e41	+	2.77829e41i	−0.186143	+	0.322408i
$781$	−7.90076e41	+	1.36845e42i	−0.899972	+	1.55880i
$782$	−4.93683e40	−	8.55085e40i	−0.0552015	−	0.0956117i
$783$	6.99577e40			0.0767874
$784$	1.03185e42	+	2.93384e41i	1.11182	+	0.316121i
$785$	−4.58130e41			−0.484595
$786$	−6.51145e41	−	1.12782e42i	−0.676162	−	1.17115i
$787$	−3.67955e41	+	6.37316e41i	−0.375112	+	0.649713i	−0.990344	−	0.138633i	$-0.955729\pi$
$787$	−3.67955e41	+	6.37316e41i	−0.375112	+	0.649713i	0.615232	+	0.788346i	$0.289062\pi$
$788$	−4.08325e41	+	7.07240e41i	−0.408673	+	0.707843i
$789$	2.52173e41	+	4.36776e41i	0.247789	+	0.429183i
$790$	3.75509e41			0.362266
$791$	2.10511e41	−	8.53258e40i	0.199396	−	0.0808205i
$792$	1.80252e41			0.167635
$793$	1.65945e41	+	2.87425e41i	0.151532	+	0.262460i
$794$	−4.33348e41	+	7.50581e41i	−0.388543	+	0.672977i
$795$	5.32212e40	−	9.21818e40i	0.0468556	−	0.0811562i
$796$	4.85631e41	+	8.41138e41i	0.419824	+	0.727157i
$797$	−1.12283e42			−0.953167			−0.476584	−	0.879129i	$-0.658125\pi$
$797$	−1.12283e42			−0.953167			−0.476584	+	0.879129i	$0.658125\pi$
$798$	−6.74551e40	−	5.25804e40i	−0.0562306	−	0.0438311i
$799$	−2.71805e41			−0.222499
$800$	−5.58753e41	−	9.67788e41i	−0.449174	−	0.777993i
$801$	2.81637e41	−	4.87810e41i	0.222340	−	0.385105i
$802$	5.88867e41	−	1.01995e42i	0.456551	−	0.790769i
$803$	−2.52103e41	−	4.36655e41i	−0.191956	−	0.332478i
$804$	−8.10274e41			−0.605925
$805$	−1.22997e40	+	8.82322e40i	−0.00903346	+	0.0648018i
$806$	−6.87973e41			−0.496264
$807$	5.09714e40	+	8.82851e40i	0.0361127	+	0.0625491i
$808$	1.34797e41	−	2.33476e41i	0.0938029	−	0.162471i
$809$	−2.27908e41	+	3.94748e41i	−0.155778	+	0.269815i	−0.933342	−	0.358988i	$-0.883122\pi$
$809$	−2.27908e41	+	3.94748e41i	−0.155778	+	0.269815i	0.777564	+	0.628804i	$0.216455\pi$
$810$	6.15029e40	+	1.06526e41i	0.0412917	+	0.0715193i
$811$	−1.75289e42			−1.15599			−0.577993	−	0.816042i	$-0.696164\pi$
$811$	−1.75289e42			−1.15599			−0.577993	+	0.816042i	$0.696164\pi$
$812$	−6.86084e40	+	4.92164e41i	−0.0444442	+	0.318821i
$813$	1.59912e42			1.01758
$814$	−2.36326e42	−	4.09328e42i	−1.47726	−	2.55869i
$815$	7.05492e41	−	1.22195e42i	0.433218	−	0.750356i
$816$	−3.83951e41	+	6.65023e41i	−0.231616	+	0.401171i
$817$	6.41707e39	+	1.11147e40i	0.00380292	+	0.00658685i
$818$	−1.18002e41			−0.0687013
$819$	6.64362e41	+	5.17862e41i	0.380004	+	0.296209i
$820$	6.11434e41			0.343597
$821$	5.37754e41	+	9.31417e41i	0.296898	+	0.514243i	0.975425	−	0.220333i	$-0.0707144\pi$
$821$	5.37754e41	+	9.31417e41i	0.296898	+	0.514243i	−0.678526	+	0.734576i	$0.737381\pi$
$822$	−1.22411e42	+	2.12022e42i	−0.664017	+	1.15011i
$823$	−1.23391e41	+	2.13720e41i	−0.0657639	+	0.113906i	−0.897033	−	0.441964i	$-0.854282\pi$
$823$	−1.23391e41	+	2.13720e41i	−0.0657639	+	0.113906i	0.831269	+	0.555871i	$0.187615\pi$
$824$	2.92397e41	+	5.06447e41i	0.153119	+	0.265210i
$825$	1.50841e42			0.776137
$826$	−4.12500e42	+	1.67197e42i	−2.08551	+	0.845314i
$827$	2.92746e42			1.45432			0.727161	−	0.686467i	$-0.240839\pi$
$827$	2.92746e42			1.45432			0.727161	+	0.686467i	$0.240839\pi$
$828$	3.25932e40	+	5.64531e40i	0.0159106	+	0.0275580i
$829$	−1.53887e42	+	2.66539e42i	−0.738176	+	1.27856i	0.215140	+	0.976583i	$0.430979\pi$
$829$	−1.53887e42	+	2.66539e42i	−0.738176	+	1.27856i	−0.953316	+	0.301975i	$0.902354\pi$
$830$	8.18408e41	−	1.41752e42i	0.385778	−	0.668187i
$831$	4.82986e41	+	8.36556e41i	0.223728	+	0.387508i
$832$	1.85261e42			0.843325
$833$	−3.78745e41	−	1.50473e42i	−0.169431	−	0.673140i
$834$	−1.48242e42			−0.651724
$835$	−2.97981e41	−	5.16118e41i	−0.128746	−	0.222995i
$836$	1.68993e41	−	2.92704e41i	0.0717592	−	0.124291i
$837$	−5.88937e40	+	1.02007e41i	−0.0245782	+	0.0425707i
$838$	−2.93043e41	−	5.07565e41i	−0.120197	−	0.208187i
$839$	3.93960e42			1.58819			0.794097	−	0.607792i	$-0.207944\pi$
$839$	3.93960e42			1.58819			0.794097	+	0.607792i	$0.207944\pi$
$840$	1.93930e41	−	7.86051e40i	0.0768415	−	0.0311459i
$841$	−2.15891e42			−0.840800
$842$	−3.35610e42	−	5.81293e42i	−1.28472	−	2.22520i
$843$	−1.77522e41	+	3.07478e41i	−0.0667964	+	0.115695i
$844$	5.26198e41	−	9.11402e41i	0.194618	−	0.337089i
$845$	8.28354e41	+	1.43475e42i	0.301157	+	0.521620i
$846$	4.01870e41			0.143620
$847$	−6.17252e42	−	4.81140e42i	−2.16847	−	1.69029i
$848$	−9.82481e41			−0.339300
$849$	−5.23322e41	−	9.06421e41i	−0.177667	−	0.307729i
$850$	−9.70416e41	+	1.68081e42i	−0.323880	+	0.560976i
$851$	−2.04684e41	+	3.54523e41i	−0.0671592	+	0.116323i
$852$	6.71143e41	+	1.16245e42i	0.216492	+	0.374974i
$853$	3.36280e42			1.06645			0.533225	−	0.845974i	$-0.320980\pi$
$853$	3.36280e42			1.06645			0.533225	+	0.845974i	$0.320980\pi$
$854$	−1.24800e41	+	8.95255e41i	−0.0389112	+	0.279131i
$855$	−5.52382e40			−0.0169329
$856$	−7.82456e41	−	1.35525e42i	−0.235825	−	0.408461i
$857$	7.92318e41	−	1.37234e42i	0.234789	−	0.406666i	−0.724422	−	0.689356i	$-0.757893\pi$
$857$	7.92318e41	−	1.37234e42i	0.234789	−	0.406666i	0.959211	+	0.282690i	$0.0912268\pi$
$858$	−3.72743e42	+	6.45609e42i	−1.08603	+	1.88107i
$859$	−1.69899e42	−	2.94275e42i	−0.486733	−	0.843047i	0.513150	−	0.858299i	$-0.328478\pi$
$859$	−1.69899e42	−	2.94275e42i	−0.486733	−	0.843047i	−0.999884	+	0.0152518i	$0.995145\pi$
$860$	1.31112e41			0.0369330
$861$	2.21659e41	−	1.59007e42i	0.0613958	−	0.440425i
$862$	9.59403e42			2.61304
$863$	−2.28581e41	−	3.95914e41i	−0.0612186	−	0.106034i	0.833792	−	0.552079i	$-0.186165\pi$
$863$	−2.28581e41	−	3.95914e41i	−0.0612186	−	0.106034i	−0.895010	+	0.446045i	$0.852832\pi$
$864$	4.72787e41	−	8.18891e41i	0.124513	−	0.215664i
$865$	−6.26192e41	+	1.08460e42i	−0.162171	+	0.280889i
$866$	1.28587e42	+	2.22720e42i	0.327483	+	0.567217i
$867$	−1.19452e42			−0.299169
$868$	−6.59878e41	−	5.14367e41i	−0.162528	−	0.126688i
$869$	3.89639e42			0.943790
$870$	3.59373e41	+	6.22452e41i	0.0856083	+	0.148278i
$871$	−4.01288e42	+	6.95052e42i	−0.940142	+	1.62837i
$872$	2.93592e41	−	5.08517e41i	0.0676481	−	0.117170i
$873$	9.93318e41	+	1.72048e42i	0.225103	+	0.389890i
$874$	−6.55574e40			−0.0146119
$875$	3.96047e42	−	1.60528e42i	0.868220	−	0.351913i
$876$	−4.28306e41			−0.0923515
$877$	−2.35409e42	−	4.07740e42i	−0.499262	−	0.864748i	0.500737	−	0.865599i	$-0.333062\pi$
$877$	−2.35409e42	−	4.07740e42i	−0.499262	−	0.864748i	−1.00000		0.000851407i	$0.999729\pi$
$878$	1.71118e42	−	2.96385e42i	0.356964	−	0.618280i
$879$	5.91472e41	−	1.02446e42i	0.121365	−	0.210211i
$880$	3.06583e42	+	5.31018e42i	0.618800	+	1.07179i
$881$	−8.69613e42			−1.72653			−0.863267	−	0.504748i	$-0.831586\pi$
$881$	−8.69613e42			−1.72653			−0.863267	+	0.504748i	$0.831586\pi$
$882$	5.59984e41	+	2.22478e42i	0.109366	+	0.434503i
$883$	−3.97193e42			−0.763083			−0.381541	−	0.924352i	$-0.624607\pi$
$883$	−3.97193e42			−0.763083			−0.381541	+	0.924352i	$0.624607\pi$
$884$	−2.14154e42	−	3.70926e42i	−0.404733	−	0.701018i
$885$	−1.43734e42	+	2.48955e42i	−0.267229	+	0.462853i
$886$	−6.23183e42	+	1.07939e43i	−1.13980	+	1.97418i
$887$	2.12553e42	+	3.68153e42i	0.382451	+	0.662424i	0.991412	−	0.130776i	$-0.0417469\pi$
$887$	2.12553e42	+	3.68153e42i	0.382451	+	0.662424i	−0.608961	+	0.793200i	$0.708414\pi$
$888$	9.61576e41			0.170214
$889$	1.19413e42	−	4.84014e41i	0.207959	−	0.0842912i
$890$	5.78709e42			0.991528
$891$	6.38170e41	+	1.10534e42i	0.107575	+	0.186325i
$892$	4.73147e42	−	8.19514e42i	0.784703	−	1.35915i
$893$	−9.02340e40	+	1.56290e41i	−0.0147239	+	0.0255026i
$894$	7.08054e41	+	1.22639e42i	0.113677	+	0.196894i
$895$	3.75730e42			0.593529
$896$	−2.58659e42	−	2.01622e42i	−0.402033	−	0.313380i
$897$	6.45672e41			0.0987465
$898$	2.82798e42	+	4.89821e42i	0.425569	+	0.737107i
$899$	−3.44127e41	+	5.96046e41i	−0.0509569	+	0.0882600i
$900$	6.40674e41	−	1.10968e42i	0.0933513	−	0.161689i
$901$	7.10548e41	+	1.23070e42i	0.101879	+	0.176459i
$902$	1.42083e43			2.00469
$903$	4.75310e40	−	3.40965e41i	0.00659940	−	0.0473410i
$904$	−4.08972e41			−0.0558794
$905$	−3.46356e42	−	5.99906e42i	−0.465713	−	0.806638i
$906$	4.84722e42	−	8.39563e42i	0.641407	−	1.11095i
$907$	−1.52410e42	+	2.63982e42i	−0.198476	+	0.343770i	−0.948034	−	0.318168i	$-0.896932\pi$
$907$	−1.52410e42	+	2.63982e42i	−0.198476	+	0.343770i	0.749559	+	0.661938i	$0.230266\pi$
$908$	3.75861e42	+	6.51011e42i	0.481707	+	0.834340i
$909$	1.90896e42			0.240780
$910$	−1.19487e42	+	8.57146e42i	−0.148328	+	1.06403i
$911$	−3.46058e42			−0.422798			−0.211399	−	0.977400i	$-0.567802\pi$
$911$	−3.46058e42			−0.422798			−0.211399	+	0.977400i	$0.567802\pi$
$912$	2.54929e41	+	4.41550e41i	0.0306545	+	0.0530951i
$913$	8.49202e42	−	1.47086e43i	1.00504	−	1.74079i
$914$	−5.96640e42	+	1.03341e43i	−0.695012	+	1.20380i
$915$	2.91899e41	+	5.05583e41i	0.0334677	+	0.0579678i
$916$	9.83514e42			1.10993
$917$	−1.23724e43	−	9.64415e42i	−1.37436	−	1.07129i
$918$	−1.64223e42			−0.179562
$919$	−1.42644e42	−	2.47066e42i	−0.153524	−	0.265912i	0.778996	−	0.627028i	$-0.215729\pi$
$919$	−1.42644e42	−	2.47066e42i	−0.153524	−	0.265912i	−0.932521	+	0.361116i	$0.882396\pi$
$920$	8.01981e40	−	1.38907e41i	0.00849651	−	0.0147164i
$921$	4.51607e42	−	7.82206e42i	0.470973	−	0.815749i
$922$	9.80669e42	+	1.69857e43i	1.00676	+	1.74375i
$923$	1.32954e43			1.34362
$924$	−8.40214e42	+	3.40561e42i	−0.835885	+	0.338806i
$925$	8.04680e42			0.788076
$926$	−1.10294e43	−	1.91035e43i	−1.06339	−	1.84185i
$927$	−2.07042e42	+	3.58608e42i	−0.196518	+	0.340380i
$928$	2.76258e42	−	4.78494e42i	0.258149	−	0.447127i
$929$	−9.46668e42	−	1.63968e43i	−0.870903	−	1.50845i	−0.861064	−	0.508497i	$-0.830201\pi$
$929$	−9.46668e42	−	1.63968e43i	−0.870903	−	1.50845i	−0.00983974	−	0.999952i	$-0.503132\pi$
$930$	−1.21015e42			−0.109606
$931$	−9.90966e41	−	2.81760e41i	−0.0883667	−	0.0251251i
$932$	7.06383e42			0.620169
$933$	−2.67937e42	−	4.64080e42i	−0.231605	−	0.401152i
$934$	4.80198e42	−	8.31728e42i	0.408687	−	0.707867i
$935$	4.43453e42	−	7.68083e42i	0.371603	−	0.643636i
$936$	−7.58319e41	−	1.31345e42i	−0.0625680	−	0.108371i
$937$	−2.67382e42			−0.217224			−0.108612	−	0.994084i	$-0.534641\pi$
$937$	−2.67382e42			−0.217224			−0.108612	+	0.994084i	$0.534641\pi$
$938$	−2.02576e43	+	8.21094e42i	−1.62049	+	0.656828i
$939$	−7.81494e42			−0.615566
$940$	9.21819e41	+	1.59664e42i	0.0714976	+	0.123838i
$941$	5.21074e42	−	9.02527e42i	0.397970	−	0.689303i	−0.595506	−	0.803351i	$-0.703048\pi$
$941$	5.21074e42	−	9.02527e42i	0.397970	−	0.689303i	0.993475	+	0.114048i	$0.0363816\pi$
$942$	−4.52165e42	+	7.83172e42i	−0.340062	+	0.589005i
$943$	−6.15297e41	−	1.06573e42i	−0.0455685	−	0.0789270i
$944$	2.65338e43			1.93511
$945$	1.16862e42	+	9.10924e41i	0.0839289	+	0.0654215i
$946$	3.04673e42			0.215483
$947$	−6.93790e41	−	1.20168e42i	−0.0483229	−	0.0836978i	0.840852	−	0.541265i	$-0.182054\pi$
$947$	−6.93790e41	−	1.20168e42i	−0.0483229	−	0.0836978i	−0.889175	+	0.457567i	$0.848721\pi$
$948$	1.65492e42	−	2.86641e42i	0.113516	−	0.196616i
$949$	−2.12118e42	+	3.67400e42i	−0.143291	+	0.248187i
$950$	6.44319e41	+	1.11599e42i	0.0428656	+	0.0742454i
$951$	−5.96967e42			−0.391140
$952$	−3.85721e41	+	2.76698e42i	−0.0248907	+	0.178554i
$953$	2.53814e43			1.61313			0.806564	−	0.591147i	$-0.201325\pi$
$953$	2.53814e43			1.61313			0.806564	+	0.591147i	$0.201325\pi$
$954$	−1.05056e42	−	1.81963e42i	−0.0657614	−	0.113902i
$955$	4.35741e42	−	7.54726e42i	0.268646	−	0.465308i
$956$	5.29609e42	−	9.17311e42i	0.321600	−	0.557028i
$957$	3.72895e42	+	6.45873e42i	0.223030	+	0.386299i
$958$	−3.49535e43			−2.05916
$959$	−4.07169e42	+	2.92084e43i	−0.236268	+	1.69488i
$960$	3.25875e42			0.186259
$961$	8.30154e42	+	1.43787e43i	0.467379	+	0.809525i
$962$	−1.98844e43	+	3.44407e43i	−1.10274	+	1.91000i
$963$	5.54046e42	−	9.59635e42i	0.302667	−	0.524234i
$964$	1.72896e42	+	2.99464e42i	0.0930395	+	0.161149i
$965$	−1.48293e43			−0.786095
$966$	1.38693e42	+	1.08110e42i	0.0724247	+	0.0564541i
$967$	−3.08713e43			−1.58807			−0.794037	−	0.607870i	$-0.792024\pi$
$967$	−3.08713e43			−1.58807			−0.794037	+	0.607870i	$0.792024\pi$
$968$	7.04546e42	+	1.22031e43i	0.357040	+	0.618411i
$969$	3.68738e41	−	6.38673e41i	0.0184087	−	0.0318848i
$970$	−1.02054e43	+	1.76762e43i	−0.501924	+	0.869359i
$971$	−1.61545e43	−	2.79805e43i	−0.782737	−	1.35574i	−0.930342	−	0.366694i	$-0.880490\pi$
$971$	−1.61545e43	−	2.79805e43i	−0.782737	−	1.35574i	0.147604	−	0.989046i	$-0.452844\pi$
$972$	1.08421e42			0.0517550
$973$	−1.65492e43	+	6.70784e42i	−0.778290	+	0.315462i
$974$	−4.78175e43			−2.21555
$975$	−6.34588e42	−	1.09914e43i	−0.289684	−	0.501748i
$976$	2.69427e42	−	4.66662e42i	0.121177	−	0.209884i
$977$	−9.79949e42	+	1.69732e43i	−0.434242	+	0.752130i	−0.997233	−	0.0743331i	$-0.976317\pi$
$977$	−9.79949e42	+	1.69732e43i	−0.434242	+	0.752130i	0.562991	+	0.826463i	$0.309651\pi$
$978$	−1.39261e43	−	2.41207e43i	−0.608017	−	1.05312i
$979$	6.00484e43			2.58317
$980$	−7.55458e42	+	7.32807e42i	−0.320208	+	0.310607i
$981$	4.15777e42			0.173644
$982$	−2.43708e43	−	4.22114e43i	−1.00289	−	1.73706i
$983$	2.08810e43	−	3.61670e43i	0.846692	−	1.46651i	−0.0374509	−	0.999298i	$-0.511924\pi$
$983$	2.08810e43	−	3.61670e43i	0.846692	−	1.46651i	0.884143	−	0.467216i	$-0.154743\pi$
$984$	−1.44529e42	+	2.50331e42i	−0.0577465	+	0.100020i
$985$	7.11425e42	+	1.23222e43i	0.280094	+	0.485137i
$986$	−9.59586e42			−0.372279
$987$	4.48633e42	−	1.81843e42i	0.171511	−	0.0695181i
$988$	−2.84380e42			−0.107133
$989$	−1.31940e41	−	2.28527e41i	−0.00489814	−	0.00848382i
$990$	−6.55657e42	+	1.13563e43i	−0.239865	+	0.415458i
$991$	−2.23753e43	+	3.87552e43i	−0.806680	+	1.39721i	0.108471	+	0.994100i	$0.465405\pi$
$991$	−2.23753e43	+	3.87552e43i	−0.806680	+	1.39721i	−0.915151	+	0.403112i	$0.867929\pi$
$992$	4.65135e42	+	8.05638e42i	0.165257	+	0.286234i
$993$	1.58309e43			0.554295
$994$	2.85590e43	+	2.22614e43i	0.985462	+	0.768156i
$995$	1.69223e43			0.575473
$996$	−7.21369e42	−	1.24945e43i	−0.241767	−	0.418753i
$997$	5.14181e39	−	8.90587e39i	0.000169838	−	0.000294169i	−0.865940	−	0.500147i	$-0.833279\pi$
$997$	5.14181e39	−	8.90587e39i	0.000169838	−	0.000294169i	0.866110	+	0.499853i	$0.166613\pi$
$998$	−3.94728e43	+	6.83689e43i	−1.28501	+	2.22570i
$999$	3.40439e42	+	5.89658e42i	0.109229	+	0.189191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.e.b.4.5	✓	40
7.2	even	3	inner	21.30.e.b.16.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.e.b.4.5	✓	40	1.1	even	1	trivial
21.30.e.b.16.5	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)

\(f(q)\)	\(=\)	\(q+(-15572.5 - 26972.3i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-2.16568e8 + 3.75107e8i) q^{4} +(3.77327e9 + 6.53549e9i) q^{5} +1.48965e11 q^{6} +(1.66300e12 - 6.74056e11i) q^{7} -3.23080e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\)	\(q+(-15572.5 - 26972.3i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-2.16568e8 + 3.75107e8i) q^{4} +(3.77327e9 + 6.53549e9i) q^{5} +1.48965e11 q^{6} +(1.66300e12 - 6.74056e11i) q^{7} -3.23080e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(1.17518e14 - 2.03547e14i) q^{10} +(1.21940e15 - 2.11206e15i) q^{11} +(-1.03584e15 - 1.79413e15i) q^{12} -2.05200e16 q^{13} +(-4.40778e16 - 3.43581e16i) q^{14} -3.60948e16 q^{15} +(1.66581e17 + 2.88526e17i) q^{16} +(2.40948e17 - 4.17335e17i) q^{17} +(-3.56248e17 + 6.17040e17i) q^{18} +(-1.59980e17 - 2.77094e17i) q^{19} -3.26868e18 q^{20} +(-1.18497e18 + 8.50041e18i) q^{21} -7.59563e19 q^{22} +(3.28933e18 + 5.69728e18i) q^{23} +(7.72640e18 - 1.33825e19i) q^{24} +(6.46572e19 - 1.11989e20i) q^{25} +(3.19547e20 + 5.53472e20i) q^{26} +1.09419e20 q^{27} +(-1.07309e20 + 7.69781e20i) q^{28} +6.39356e20 q^{29} +(5.62086e20 + 9.73561e20i) q^{30} +(-5.38240e20 + 9.32260e20i) q^{31} +(4.32089e21 - 7.48400e21i) q^{32} +(5.83236e21 + 1.01019e22i) q^{33} -1.50086e22 q^{34} +(1.06802e22 + 8.32510e21i) q^{35} +9.90878e21 q^{36} +(3.11133e22 + 5.38899e22i) q^{37} +(-4.98258e21 + 8.63009e21i) q^{38} +(4.90733e22 - 8.49974e22i) q^{39} +(-1.21907e22 - 2.11148e22i) q^{40} -1.87058e23 q^{41} +(2.47729e23 - 1.00411e23i) q^{42} -4.01116e22 q^{43} +(5.28167e23 + 9.14812e23i) q^{44} +(8.63203e22 - 1.49511e23i) q^{45} +(1.02446e23 - 1.77442e23i) q^{46} +(-2.82016e23 - 4.88465e23i) q^{47} -1.59350e24 q^{48} +(2.31120e24 - 2.24191e24i) q^{49} -4.02749e24 q^{50} +(1.15245e24 + 1.99610e24i) q^{51} +(4.44398e24 - 7.69720e24i) q^{52} +(-1.47448e24 + 2.55388e24i) q^{53} +(-1.70392e24 - 2.95128e24i) q^{54} +1.84045e25 q^{55} +(-5.37280e24 + 2.17774e24i) q^{56} +1.53036e24 q^{57} +(-9.95635e24 - 1.72449e25i) q^{58} +(3.98213e25 - 6.89725e25i) q^{59} +(7.81700e24 - 1.35394e25i) q^{60} +(-8.08699e24 - 1.40071e25i) q^{61} +3.35269e25 q^{62} +(-3.23763e25 - 2.52369e25i) q^{63} -9.02829e25 q^{64} +(-7.74274e25 - 1.34108e26i) q^{65} +(1.81648e26 - 3.14624e26i) q^{66} +(1.95560e26 - 3.38719e26i) q^{67} +(1.04364e26 + 1.80763e26i) q^{68} -3.14655e25 q^{69} +(5.82297e25 - 4.17712e26i) q^{70} -6.47922e26 q^{71} +(3.69551e25 + 6.40081e25i) q^{72} +(1.03372e26 - 1.79045e26i) q^{73} +(9.69023e26 - 1.67840e27i) q^{74} +(3.09253e26 + 5.35642e26i) q^{75} +1.38587e26 q^{76} +(6.04208e26 - 4.33430e27i) q^{77} -3.05677e27 q^{78} +(7.98832e26 + 1.38362e27i) q^{79} +(-1.25711e27 + 2.17737e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(2.91296e27 + 5.04540e27i) q^{82} +6.96409e27 q^{83} +(-2.93194e27 - 2.28541e27i) q^{84} +3.63665e27 q^{85} +(6.24637e26 + 1.08190e27i) q^{86} +(-1.52901e27 + 2.64832e27i) q^{87} +(-3.93963e27 + 6.82365e27i) q^{88} +(1.23110e28 + 2.13233e28i) q^{89} -5.37688e27 q^{90} +(-3.41247e28 + 1.38316e28i) q^{91} -2.84946e27 q^{92} +(-2.57439e27 - 4.45897e27i) q^{93} +(-8.78336e27 + 1.52132e28i) q^{94} +(1.20730e27 - 2.09110e27i) q^{95} +(2.06667e28 + 3.57957e28i) q^{96} -8.68407e28 q^{97} +(-9.64605e28 - 2.74265e28i) q^{98} -5.57920e28 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

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Groups

Database

Properties

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