LMFDB - Embedded newform 21.30.e.b.4.17

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			4.17
Character	$\chi$	$=$	21.4
Dual form			21.30.e.b.16.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16582.6 + 28721.9i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-2.81530e8 + 4.87624e8i) q^{4} +(1.20484e10 + 2.08684e10i) q^{5} -1.58628e11 q^{6} +(1.59164e12 - 8.28603e11i) q^{7} -8.68562e11 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})$	\(q+(16582.6 + 28721.9i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-2.81530e8 + 4.87624e8i) q^{4} +(1.20484e10 + 2.08684e10i) q^{5} -1.58628e11 q^{6} +(1.59164e12 - 8.28603e11i) q^{7} -8.68562e11 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-3.99587e14 + 6.92105e14i) q^{10} +(7.46062e14 - 1.29222e15i) q^{11} +(-1.34655e15 - 2.33229e15i) q^{12} +1.20144e16 q^{13} +(5.01926e16 + 3.19746e16i) q^{14} -1.15254e17 q^{15} +(1.36742e17 + 2.36844e17i) q^{16} +(-4.62399e16 + 8.00898e16i) q^{17} +(3.79357e17 - 6.57065e17i) q^{18} +(-2.51134e18 - 4.34977e18i) q^{19} -1.35679e19 q^{20} +(-3.74169e17 + 8.57445e18i) q^{21} +4.94866e19 q^{22} +(3.02777e19 + 5.24425e19i) q^{23} +(2.07715e18 - 3.59773e18i) q^{24} +(-1.97195e20 + 3.41551e20i) q^{25} +(1.99230e20 + 3.45076e20i) q^{26} +1.09419e20 q^{27} +(-4.40478e19 + 1.00940e21i) q^{28} +1.71011e21 q^{29} +(-1.91121e21 - 3.31032e21i) q^{30} +(-2.84538e21 + 4.92834e21i) q^{31} +(-4.76824e21 + 8.25883e21i) q^{32} +(3.56839e21 + 6.18064e21i) q^{33} -3.06711e21 q^{34} +(3.64683e22 + 2.32317e22i) q^{35} +1.28810e22 q^{36} +(-1.28403e22 - 2.22401e22i) q^{37} +(8.32891e22 - 1.44261e23i) q^{38} +(-2.87322e22 + 4.97657e22i) q^{39} +(-1.04648e22 - 1.81255e22i) q^{40} +4.38272e23 q^{41} +(-2.52479e23 + 1.31440e23i) q^{42} -2.80589e23 q^{43} +(4.20078e23 + 7.27596e23i) q^{44} +(2.75628e23 - 4.77402e23i) q^{45} +(-1.00417e24 + 1.73927e24i) q^{46} +(8.39057e23 + 1.45329e24i) q^{47} -1.30807e24 q^{48} +(1.84674e24 - 2.63768e24i) q^{49} -1.30800e25 q^{50} +(-2.21164e23 - 3.83067e23i) q^{51} +(-3.38241e24 + 5.85851e24i) q^{52} +(-9.01576e23 + 1.56157e24i) q^{53} +(1.81445e24 + 3.14272e24i) q^{54} +3.59554e25 q^{55} +(-1.38244e24 + 7.19693e23i) q^{56} +2.40233e25 q^{57} +(2.83581e25 + 4.91177e25i) q^{58} +(-4.24260e25 + 7.34839e25i) q^{59} +(3.24475e25 - 5.62007e25i) q^{60} +(-2.58468e25 - 4.47679e25i) q^{61} -1.88735e26 q^{62} +(-3.46220e25 - 2.20555e25i) q^{63} -1.69453e26 q^{64} +(1.44754e26 + 2.50721e26i) q^{65} +(-1.18346e26 + 2.04982e26i) q^{66} +(-1.31952e26 + 2.28548e26i) q^{67} +(-2.60358e25 - 4.50953e25i) q^{68} -2.89634e26 q^{69} +(-6.25189e25 + 1.43268e27i) q^{70} +4.57120e25 q^{71} +(9.93496e24 + 1.72078e25i) q^{72} +(-7.88211e26 + 1.36522e27i) q^{73} +(4.25852e26 - 7.37597e26i) q^{74} +(-9.43176e26 - 1.63363e27i) q^{75} +2.82807e27 q^{76} +(1.16728e26 - 2.67494e27i) q^{77} -1.90582e27 q^{78} +(-1.69663e27 - 2.93865e27i) q^{79} +(-3.29504e27 + 5.70718e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(7.26769e27 + 1.25880e28i) q^{82} +1.05794e28 q^{83} +(-4.07577e27 - 2.59642e27i) q^{84} -2.22846e27 q^{85} +(-4.65289e27 - 8.05904e27i) q^{86} +(-4.08971e27 + 7.08359e27i) q^{87} +(-6.48001e26 + 1.12237e27i) q^{88} +(-4.73780e27 - 8.20611e27i) q^{89} +1.82825e28 q^{90} +(1.91226e28 - 9.95516e27i) q^{91} -3.40963e28 q^{92} +(-1.36093e28 - 2.35721e28i) q^{93} +(-2.78275e28 + 4.81986e28i) q^{94} +(6.05152e28 - 1.04815e29i) q^{95} +(-2.28063e28 - 3.95017e28i) q^{96} +1.80901e28 q^{97} +(1.06383e29 + 9.30231e27i) q^{98} -3.41350e28 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 $

$2$	16582.6	+	28721.9i	0.715678	+	1.23959i	0.962697	+	0.270580i	$0.0872156\pi$
$2$	16582.6	+	28721.9i	0.715678	+	1.23959i	−0.247019	+	0.969011i	$0.579451\pi$
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$4$	−2.81530e8	+	4.87624e8i	−0.524390	+	0.908271i
$5$	1.20484e10	+	2.08684e10i	0.882803	+	1.52906i	0.848212	+	0.529657i	$0.177679\pi$
$5$	1.20484e10	+	2.08684e10i	0.882803	+	1.52906i	0.0345907	+	0.999402i	$0.488987\pi$
$6$	−1.58628e11			−0.826394
$7$	1.59164e12	−	8.28603e11i	0.887000	−	0.461769i
$7$	1.59164e12	−	8.28603e11i	0.887000	−	0.461769i
$8$	−8.68562e11			−0.0698226
$9$	−1.14384e13	−	1.98119e13i	−0.166667	−	0.288675i
$10$	−3.99587e14	+	6.92105e14i	−1.26360	+	2.18863i
$11$	7.46062e14	−	1.29222e15i	0.592354	−	1.02599i	−0.401561	−	0.915832i	$-0.631532\pi$
$11$	7.46062e14	−	1.29222e15i	0.592354	−	1.02599i	0.993915	−	0.110154i	$-0.0351345\pi$
$12$	−1.34655e15	−	2.33229e15i	−0.302757	−	0.524390i
$13$	1.20144e16			0.846298			0.423149	−	0.906060i	$-0.360925\pi$
$13$	1.20144e16			0.846298			0.423149	+	0.906060i	$0.360925\pi$
$14$	5.01926e16	+	3.19746e16i	1.20721	+	0.769039i
$15$	−1.15254e17			−1.01937
$16$	1.36742e17	+	2.36844e17i	0.474420	+	0.821719i
$17$	−4.62399e16	+	8.00898e16i	−0.0666050	+	0.115363i	−0.897405	−	0.441208i	$-0.854550\pi$
$17$	−4.62399e16	+	8.00898e16i	−0.0666050	+	0.115363i	0.830800	+	0.556571i	$0.187883\pi$
$18$	3.79357e17	−	6.57065e17i	0.238559	−	0.413197i
$19$	−2.51134e18	−	4.34977e18i	−0.721072	−	1.24893i	−0.960571	−	0.278036i	$-0.910316\pi$
$19$	−2.51134e18	−	4.34977e18i	−0.721072	−	1.24893i	0.239499	−	0.970897i	$-0.423017\pi$
$20$	−1.35679e19			−1.85173
$21$	−3.74169e17	+	8.57445e18i	−0.0251703	+	0.576801i
$22$	4.94866e19			1.69574
$23$	3.02777e19	+	5.24425e19i	0.544589	+	0.943256i	0.998633	+	0.0522766i	$0.0166477\pi$
$23$	3.02777e19	+	5.24425e19i	0.544589	+	0.943256i	−0.454043	+	0.890980i	$0.650019\pi$
$24$	2.07715e18	−	3.59773e18i	0.0201560	−	0.0349113i
$25$	−1.97195e20	+	3.41551e20i	−1.05868	+	1.83369i
$26$	1.99230e20	+	3.45076e20i	0.605677	+	1.04906i
$27$	1.09419e20			0.192450
$28$	−4.40478e19	+	1.00940e21i	−0.0457228	+	1.04778i
$29$	1.71011e21			1.06722			0.533610	−	0.845731i	$-0.320835\pi$
$29$	1.71011e21			1.06722			0.533610	+	0.845731i	$0.320835\pi$
$30$	−1.91121e21	−	3.31032e21i	−0.729543	−	1.26360i
$31$	−2.84538e21	+	4.92834e21i	−0.675142	+	1.16938i	0.301285	+	0.953534i	$0.402584\pi$
$31$	−2.84538e21	+	4.92834e21i	−0.675142	+	1.16938i	−0.976427	+	0.215846i	$0.930749\pi$
$32$	−4.76824e21	+	8.25883e21i	−0.713975	+	1.23664i
$33$	3.56839e21	+	6.18064e21i	0.341996	+	0.592354i
$34$	−3.06711e21			−0.190671
$35$	3.64683e22	+	2.32317e22i	1.48912	+	0.948624i
$36$	1.28810e22			0.349594
$37$	−1.28403e22	−	2.22401e22i	−0.234235	−	0.405706i	0.724815	−	0.688943i	$-0.241925\pi$
$37$	−1.28403e22	−	2.22401e22i	−0.234235	−	0.405706i	−0.959050	+	0.283237i	$0.908592\pi$
$38$	8.32891e22	−	1.44261e23i	1.03211	−	1.78767i
$39$	−2.87322e22	+	4.97657e22i	−0.244305	+	0.423149i
$40$	−1.04648e22	−	1.81255e22i	−0.0616396	−	0.106763i
$41$	4.38272e23			1.80459			0.902293	−	0.431123i	$-0.141883\pi$
$41$	4.38272e23			1.80459			0.902293	+	0.431123i	$0.141883\pi$
$42$	−2.52479e23	+	1.31440e23i	−0.733011	+	0.381603i
$43$	−2.80589e23			−0.579132			−0.289566	−	0.957158i	$-0.593511\pi$
$43$	−2.80589e23			−0.579132			−0.289566	+	0.957158i	$0.593511\pi$
$44$	4.20078e23	+	7.27596e23i	0.621249	+	1.07603i
$45$	2.75628e23	−	4.77402e23i	0.294268	−	0.509686i
$46$	−1.00417e24	+	1.73927e24i	−0.779501	+	1.35014i
$47$	8.39057e23	+	1.45329e24i	0.476840	+	0.825911i	0.999648	−	0.0265396i	$-0.00844882\pi$
$47$	8.39057e23	+	1.45329e24i	0.476840	+	0.825911i	−0.522808	+	0.852451i	$0.675115\pi$
$48$	−1.30807e24			−0.547813
$49$	1.84674e24	−	2.63768e24i	0.573538	−	0.819179i
$50$	−1.30800e25			−3.03070
$51$	−2.21164e23	−	3.83067e23i	−0.0384544	−	0.0666050i
$52$	−3.38241e24	+	5.85851e24i	−0.443790	+	0.768667i
$53$	−9.01576e23	+	1.56157e24i	−0.0897433	+	0.155440i	−0.907403	−	0.420262i	$-0.861938\pi$
$53$	−9.01576e23	+	1.56157e24i	−0.0897433	+	0.155440i	0.817659	+	0.575702i	$0.195271\pi$
$54$	1.81445e24	+	3.14272e24i	0.137732	+	0.238559i
$55$	3.59554e25			2.09173
$56$	−1.38244e24	+	7.19693e23i	−0.0619327	+	0.0322419i
$57$	2.40233e25			0.832622
$58$	2.83581e25	+	4.91177e25i	0.763786	+	1.32292i
$59$	−4.24260e25	+	7.34839e25i	−0.891821	+	1.54468i	−0.0541301	+	0.998534i	$0.517239\pi$
$59$	−4.24260e25	+	7.34839e25i	−0.891821	+	1.54468i	−0.837691	+	0.546145i	$0.816095\pi$
$60$	3.24475e25	−	5.62007e25i	0.534549	−	0.925866i
$61$	−2.58468e25	−	4.47679e25i	−0.335061	−	0.580342i	0.648436	−	0.761269i	$-0.275423\pi$
$61$	−2.58468e25	−	4.47679e25i	−0.335061	−	0.580342i	−0.983496	+	0.180927i	$0.942090\pi$
$62$	−1.88735e26			−1.93274
$63$	−3.46220e25	−	2.20555e25i	−0.281135	−	0.179093i
$64$	−1.69453e26			−1.09507
$65$	1.44754e26	+	2.50721e26i	0.747114	+	1.29404i
$66$	−1.18346e26	+	2.04982e26i	−0.489517	+	0.847869i
$67$	−1.31952e26	+	2.28548e26i	−0.438866	+	0.760138i	−0.997602	−	0.0692076i	$-0.977953\pi$
$67$	−1.31952e26	+	2.28548e26i	−0.438866	+	0.760138i	0.558737	+	0.829345i	$0.311286\pi$
$68$	−2.60358e25	−	4.50953e25i	−0.0698541	−	0.120991i
$69$	−2.89634e26			−0.628837
$70$	−6.25189e25	+	1.43268e27i	−0.110177	+	2.52481i
$71$	4.57120e25			0.0655819			0.0327910	−	0.999462i	$-0.489560\pi$
$71$	4.57120e25			0.0655819			0.0327910	+	0.999462i	$0.489560\pi$
$72$	9.93496e24	+	1.72078e25i	0.0116371	+	0.0201560i
$73$	−7.88211e26	+	1.36522e27i	−0.755894	+	1.30925i	0.189035	+	0.981970i	$0.439464\pi$
$73$	−7.88211e26	+	1.36522e27i	−0.755894	+	1.30925i	−0.944929	+	0.327276i	$0.893869\pi$
$74$	4.25852e26	−	7.37597e26i	0.335273	−	0.580710i
$75$	−9.43176e26	−	1.63363e27i	−0.611229	−	1.05868i
$76$	2.82807e27			1.51249
$77$	1.16728e26	−	2.67494e27i	0.0516487	−	1.18358i
$78$	−1.90582e27			−0.699375
$79$	−1.69663e27	−	2.93865e27i	−0.517600	−	0.896510i	−0.999791	−	0.0204435i	$-0.993492\pi$
$79$	−1.69663e27	−	2.93865e27i	−0.517600	−	0.896510i	0.482191	−	0.876066i	$-0.339841\pi$
$80$	−3.29504e27	+	5.70718e27i	−0.837638	+	1.45083i
$81$	−2.61674e26	+	4.53232e26i	−0.0555556	+	0.0962250i
$82$	7.26769e27	+	1.25880e28i	1.29150	+	2.23695i
$83$	1.05794e28			1.57699			0.788494	−	0.615042i	$-0.210861\pi$
$83$	1.05794e28			1.57699			0.788494	+	0.615042i	$0.210861\pi$
$84$	−4.07577e27	−	2.59642e27i	−0.510693	−	0.325330i
$85$	−2.22846e27			−0.235196
$86$	−4.65289e27	−	8.05904e27i	−0.414472	−	0.717887i
$87$	−4.08971e27	+	7.08359e27i	−0.308080	+	0.533610i
$88$	−6.48001e26	+	1.12237e27i	−0.0413597	+	0.0716371i
$89$	−4.73780e27	−	8.20611e27i	−0.256698	−	0.444613i	0.708658	−	0.705553i	$-0.249301\pi$
$89$	−4.73780e27	−	8.20611e27i	−0.256698	−	0.444613i	−0.965355	+	0.260939i	$0.915968\pi$
$90$	1.82825e28			0.842403
$91$	1.91226e28	−	9.95516e27i	0.750666	−	0.390794i
$92$	−3.40963e28			−1.14231
$93$	−1.36093e28	−	2.35721e28i	−0.389794	−	0.675142i
$94$	−2.78275e28	+	4.81986e28i	−0.682528	+	1.18217i
$95$	6.05152e28	−	1.04815e29i	1.27313	−	2.20512i
$96$	−2.28063e28	−	3.95017e28i	−0.412214	−	0.713975i
$97$	1.80901e28			0.281352			0.140676	−	0.990056i	$-0.455072\pi$
$97$	1.80901e28			0.281352			0.140676	+	0.990056i	$0.455072\pi$
$98$	1.06383e29	+	9.30231e27i	1.42592	+	0.124685i
$99$	−3.41350e28			−0.394902
$100$	−1.11032e29	−	1.92314e29i	−1.11032	−	1.92314i
$101$	6.55591e27	−	1.13552e28i	0.0567510	−	0.0982956i	−0.836254	−	0.548342i	$-0.815259\pi$
$101$	6.55591e27	−	1.13552e28i	0.0567510	−	0.0982956i	0.893005	+	0.450046i	$0.148593\pi$
$102$	7.33494e27	−	1.27045e28i	0.0550420	−	0.0953355i
$103$	−1.31254e29	−	2.27339e29i	−0.855016	−	1.48093i	−0.876630	−	0.481165i	$-0.840214\pi$
$103$	−1.31254e29	−	2.27339e29i	−0.855016	−	1.48093i	0.0216145	−	0.999766i	$-0.493119\pi$
$104$	−1.04352e28			−0.0590907
$105$	−1.83443e29	+	9.54999e28i	−0.904184	+	0.470715i
$106$	−5.98019e28			−0.256909
$107$	−8.54488e28	−	1.48002e29i	−0.320362	−	0.554883i	0.660201	−	0.751089i	$-0.270471\pi$
$107$	−8.54488e28	−	1.48002e29i	−0.320362	−	0.554883i	−0.980563	+	0.196206i	$0.937138\pi$
$108$	−3.08047e28	+	5.33553e28i	−0.100919	+	0.174797i
$109$	−1.56678e28	+	2.71373e28i	−0.0449079	+	0.0777827i	−0.887606	−	0.460604i	$-0.847633\pi$
$109$	−1.56678e28	+	2.71373e28i	−0.0449079	+	0.0777827i	0.842698	+	0.538387i	$0.180966\pi$
$110$	5.96233e29	+	1.03271e30i	1.49700	+	2.59288i
$111$	1.22830e29			0.270471
$112$	4.13895e29	+	2.63666e29i	0.800255	+	0.509793i
$113$	−7.42394e29			−1.26182			−0.630909	−	0.775857i	$-0.717318\pi$
$113$	−7.42394e29			−1.26182			−0.630909	+	0.775857i	$0.717318\pi$
$114$	3.98369e29	+	6.89996e29i	0.595889	+	1.03211i
$115$	−7.29594e29	+	1.26369e30i	−0.961529	+	1.66542i
$116$	−4.81448e29	+	8.33893e29i	−0.559640	+	0.969325i
$117$	−1.37425e29	−	2.38028e29i	−0.141050	−	0.244305i
$118$	−2.81413e30			−2.55303
$119$	−7.23463e27	+	1.65789e29i	−0.00580745	+	0.133083i
$120$	1.00105e29			0.0711752
$121$	−3.20063e29	−	5.54365e29i	−0.201766	−	0.349468i
$122$	8.57213e29	−	1.48474e30i	0.479591	−	0.830676i
$123$	−1.04812e30	+	1.81540e30i	−0.520939	+	0.902293i
$124$	−1.60212e30	−	2.77495e30i	−0.708076	−	1.22642i
$125$	−5.01513e30			−1.97282
$126$	5.93537e28	−	1.36015e30i	0.0208005	−	0.476665i
$127$	2.93591e30			0.917463			0.458731	−	0.888575i	$-0.348304\pi$
$127$	2.93591e30			0.917463			0.458731	+	0.888575i	$0.348304\pi$
$128$	−2.50048e29	−	4.33096e29i	−0.0697395	−	0.120792i
$129$	6.71024e29	−	1.16225e30i	0.167181	−	0.289566i
$130$	−4.80079e30	+	8.31522e30i	−1.06939	+	1.85223i
$131$	1.62657e30	+	2.81729e30i	0.324219	+	0.561563i	0.981354	−	0.192210i	$-0.0615653\pi$
$131$	1.62657e30	+	2.81729e30i	0.324219	+	0.561563i	−0.657135	+	0.753773i	$0.728232\pi$
$132$	−4.01844e30			−0.717357
$133$	−7.60139e30	−	4.84237e30i	−1.21631	−	0.774835i
$134$	−8.75243e30			−1.25635
$135$	1.31832e30	+	2.28340e30i	0.169895	+	0.294268i
$136$	4.01622e28	−	6.95629e28i	0.00465054	−	0.00805497i
$137$	5.33040e30	−	9.23252e30i	0.555023	−	0.961329i	−0.442878	−	0.896582i	$-0.646043\pi$
$137$	5.33040e30	−	9.23252e30i	0.555023	−	0.961329i	0.997902	−	0.0647471i	$-0.0206241\pi$
$138$	−4.80289e30	−	8.31885e30i	−0.450045	−	0.779501i
$139$	1.17501e31			0.991574			0.495787	−	0.868444i	$-0.334880\pi$
$139$	1.17501e31			0.991574			0.495787	+	0.868444i	$0.334880\pi$
$140$	−2.15953e31	+	1.12424e31i	−1.64249	+	0.855073i
$141$	−8.02637e30			−0.550607
$142$	7.58024e29	+	1.31294e30i	0.0469355	+	0.0812947i
$143$	8.96348e30	−	1.55252e31i	0.501307	−	0.868290i
$144$	3.12822e30	−	5.41824e30i	0.158140	−	0.273906i
$145$	2.06041e31	+	3.56873e31i	0.942145	+	1.63184i
$146$	−5.22823e31			−2.16391
$147$	6.50927e30	+	1.39575e31i	0.244023	+	0.523246i
$148$	1.44597e31			0.491321
$149$	−1.74578e31	−	3.02379e31i	−0.538009	−	0.931859i	−0.999011	−	0.0444599i	$-0.985843\pi$
$149$	−1.74578e31	−	3.02379e31i	−0.538009	−	0.931859i	0.461002	−	0.887399i	$-0.347490\pi$
$150$	3.12806e31	−	5.41796e31i	0.874887	−	1.51535i
$151$	−4.07669e30	+	7.06103e30i	−0.103548	+	0.179350i	−0.913144	−	0.407637i	$-0.866353\pi$
$151$	−4.07669e30	+	7.06103e30i	−0.103548	+	0.179350i	0.809596	+	0.586987i	$0.199686\pi$
$152$	2.18126e30	+	3.77805e30i	0.0503471	+	0.0872037i
$153$	2.11564e30			0.0444034
$154$	7.87649e31	−	4.10048e31i	1.50412	−	0.783040i
$155$	−1.37129e32			−2.38407
$156$	−1.61780e31	−	2.80211e31i	−0.256222	−	0.443790i
$157$	−1.59736e31	+	2.76672e31i	−0.230600	+	0.399411i	−0.957985	−	0.286819i	$-0.907402\pi$
$157$	−1.59736e31	+	2.76672e31i	−0.230600	+	0.399411i	0.727385	+	0.686230i	$0.240736\pi$
$158$	5.62691e31	−	9.74609e31i	0.740870	−	1.28322i
$159$	−4.31221e30	−	7.46896e30i	−0.0518133	−	0.0897433i
$160$	−2.29798e32			−2.52120
$161$	9.16452e31	+	5.83815e31i	0.918617	+	0.585194i
$162$	−1.73569e31			−0.159040
$163$	−3.91956e31	−	6.78887e31i	−0.328486	−	0.568954i	0.653726	−	0.756732i	$-0.273205\pi$
$163$	−3.91956e31	−	6.78887e31i	−0.328486	−	0.568954i	−0.982212	+	0.187777i	$0.939872\pi$
$164$	−1.23387e32	+	2.13712e32i	−0.946308	+	1.63905i
$165$	−8.59867e31	+	1.48933e32i	−0.603829	+	1.04586i
$166$	1.75434e32	+	3.03860e32i	1.12862	+	1.95482i
$167$	2.74057e32			1.61604			0.808019	−	0.589156i	$-0.200540\pi$
$167$	2.74057e32			1.61604			0.808019	+	0.589156i	$0.200540\pi$
$168$	3.24989e29	−	7.44744e30i	0.00175745	−	0.0402738i
$169$	−5.71926e31			−0.283780
$170$	−3.69537e31	−	6.40057e31i	−0.168325	−	0.291547i
$171$	−5.74514e31	+	9.95088e31i	−0.240357	+	0.416311i
$172$	7.89941e31	−	1.36822e32i	0.303691	−	0.526009i
$173$	−4.46155e31	−	7.72763e31i	−0.157695	−	0.273135i	0.776342	−	0.630312i	$-0.217073\pi$
$173$	−4.46155e31	−	7.72763e31i	−0.157695	−	0.273135i	−0.934037	+	0.357176i	$0.883740\pi$
$174$	−2.71272e32			−0.881944
$175$	−3.08528e31	+	7.07023e32i	−0.0923088	+	2.11535i
$176$	4.08073e32			1.12410
$177$	−2.02922e32	−	3.51471e32i	−0.514893	−	0.891821i
$178$	1.57130e32	−	2.72157e32i	0.367426	−	0.636400i
$179$	1.72906e32	−	2.99481e32i	0.372769	−	0.645655i	−0.617221	−	0.786790i	$-0.711742\pi$
$179$	1.72906e32	−	2.99481e32i	0.372769	−	0.645655i	0.989990	+	0.141134i	$0.0450749\pi$
$180$	1.55195e32	+	2.68806e32i	0.308622	+	0.534549i
$181$	−1.33696e32			−0.245346			−0.122673	−	0.992447i	$-0.539147\pi$
$181$	−1.33696e32			−0.245346			−0.122673	+	0.992447i	$0.539147\pi$
$182$	6.03034e32	+	3.84155e32i	1.02166	+	0.650836i
$183$	2.47248e32			0.386895
$184$	−2.62980e31	−	4.55496e31i	−0.0380246	−	0.0658606i
$185$	3.09410e32	−	5.35914e32i	0.413566	−	0.716317i
$186$	4.51357e32	−	7.81773e32i	0.557933	−	0.966369i
$187$	6.89956e31	+	1.19504e32i	0.0789075	+	0.136672i
$188$	−9.44879e32			−1.00020
$189$	1.74156e32	−	9.06649e31i	0.170703	−	0.0888675i
$190$	4.01400e33			3.64460
$191$	−7.12552e32	−	1.23418e33i	−0.599560	−	1.03847i	−0.992886	−	0.119069i	$-0.962009\pi$
$191$	−7.12552e32	−	1.23418e33i	−0.599560	−	1.03847i	0.393326	−	0.919399i	$-0.371324\pi$
$192$	4.05245e32	−	7.01905e32i	0.316118	−	0.547533i
$193$	−3.35170e32	+	5.80531e32i	−0.242484	+	0.419995i	−0.961421	−	0.275080i	$-0.911296\pi$
$193$	−3.35170e32	+	5.80531e32i	−0.242484	+	0.419995i	0.718937	+	0.695075i	$0.244629\pi$
$194$	2.99980e32	+	5.19581e32i	0.201357	+	0.348761i
$195$	−1.38471e33			−0.862693
$196$	7.66283e32	+	1.64310e33i	0.443278	+	0.950498i
$197$	−5.22012e32			−0.280492			−0.140246	−	0.990117i	$-0.544789\pi$
$197$	−5.22012e32			−0.280492			−0.140246	+	0.990117i	$0.544789\pi$
$198$	−5.66047e32	−	9.80423e32i	−0.282623	−	0.489517i
$199$	1.23683e33	−	2.14225e33i	0.574038	−	0.994263i	−0.422107	−	0.906546i	$-0.638710\pi$
$199$	1.23683e33	−	2.14225e33i	0.574038	−	0.994263i	0.996145	−	0.0877171i	$-0.0279572\pi$
$200$	1.71276e32	−	2.96658e32i	0.0739198	−	0.128033i
$201$	−6.31123e32	−	1.09314e33i	−0.253379	−	0.438866i
$202$	4.34857e32			0.162462
$203$	2.72189e33	−	1.41701e33i	0.946624	−	0.492809i
$204$	2.49057e32			0.0806606
$205$	5.28047e33	+	9.14603e33i	1.59309	+	2.75932i
$206$	4.35308e33	−	7.53975e33i	1.22383	−	2.11974i
$207$	6.92656e32	−	1.19972e33i	0.181530	−	0.314419i
$208$	1.64287e33	+	2.84554e33i	0.401500	+	0.695419i
$209$	−7.49447e33			−1.70852
$210$	−5.78490e33	−	3.68520e33i	−1.23060	−	0.783937i
$211$	3.84335e33			0.763158			0.381579	−	0.924336i	$-0.375380\pi$
$211$	3.84335e33			0.763158			0.381579	+	0.924336i	$0.375380\pi$
$212$	−5.07641e32	−	8.79260e32i	−0.0941211	−	0.163022i
$213$	−1.09320e32	+	1.89347e32i	−0.0189319	+	0.0327910i
$214$	2.83393e33	−	4.90850e33i	0.458552	−	0.794236i
$215$	−3.38064e33	−	5.85544e33i	−0.511259	−	0.885527i
$216$	−9.50372e31			−0.0134374
$217$	−4.45184e32	+	1.02018e34i	−0.0588672	+	1.34900i
$218$	−1.03925e33			−0.128558
$219$	−3.76999e33	−	6.52981e33i	−0.436416	−	0.755894i
$220$	−1.01225e34	+	1.75327e34i	−1.09688	+	1.89985i
$221$	−5.55544e32	+	9.62230e32i	−0.0563677	+	0.0976317i
$222$	2.03684e33	+	3.52790e33i	0.193570	+	0.335273i
$223$	1.03682e34			0.923177			0.461588	−	0.887094i	$-0.347280\pi$
$223$	1.03682e34			0.923177			0.461588	+	0.887094i	$0.347280\pi$
$224$	−7.46032e32	+	1.70961e34i	−0.0622531	+	1.42659i
$225$	9.02236e33			0.705787
$226$	−1.23108e34	−	2.13230e34i	−0.903056	−	1.56414i
$227$	−1.27923e34	+	2.21569e34i	−0.880184	+	1.52452i	−0.0290471	+	0.999578i	$0.509247\pi$
$227$	−1.27923e34	+	2.21569e34i	−0.880184	+	1.52452i	−0.851136	+	0.524945i	$0.824086\pi$
$228$	−6.76329e33	+	1.17144e34i	−0.436619	+	0.756246i
$229$	9.19569e32	+	1.59274e33i	0.0557147	+	0.0965007i	0.892538	−	0.450973i	$-0.148923\pi$
$229$	9.19569e32	+	1.59274e33i	0.0557147	+	0.0965007i	−0.836823	+	0.547474i	$0.815590\pi$
$230$	−4.83943e34			−2.75258
$231$	1.08009e34	+	6.88058e33i	0.576881	+	0.367495i
$232$	−1.48534e33			−0.0745161
$233$	9.84395e33	+	1.70502e34i	0.463990	+	0.803654i	0.999155	−	0.0410931i	$-0.0130840\pi$
$233$	9.84395e33	+	1.70502e34i	0.463990	+	0.803654i	−0.535165	+	0.844747i	$0.679751\pi$
$234$	4.55774e33	−	7.89424e33i	0.201892	−	0.349688i
$235$	−2.02186e34	+	3.50196e34i	−0.841911	+	1.45823i
$236$	−2.38884e34	−	4.13759e34i	−0.935324	−	1.62003i
$237$	1.62299e34			0.597673
$238$	−4.88174e33	+	2.54142e33i	−0.169125	+	0.0880460i
$239$	−2.91386e33			−0.0949945			−0.0474973	−	0.998871i	$-0.515125\pi$
$239$	−2.91386e33			−0.0949945			−0.0474973	+	0.998871i	$0.515125\pi$
$240$	−1.57601e34	−	2.72973e34i	−0.483611	−	0.837638i
$241$	−2.75363e33	+	4.76942e33i	−0.0795532	+	0.137790i	−0.903057	−	0.429520i	$-0.858683\pi$
$241$	−2.75363e33	+	4.76942e33i	−0.0795532	+	0.137790i	0.823504	+	0.567310i	$0.192016\pi$
$242$	1.06149e34	−	1.83856e34i	0.288799	−	0.500214i
$243$	−1.25158e33	−	2.16780e33i	−0.0320750	−	0.0555556i
$244$	2.91065e34			0.702810
$245$	7.72944e34	+	6.75876e33i	1.75889	+	0.153801i
$246$	−6.95222e34			−1.49130
$247$	−3.01722e34	−	5.22598e34i	−0.610241	−	1.05697i
$248$	2.47139e33	−	4.28057e33i	0.0471402	−	0.0816492i
$249$	−2.53005e34	+	4.38217e34i	−0.455237	+	0.788494i
$250$	−8.31639e34	−	1.44044e35i	−1.41190	−	2.44549i
$251$	6.96903e34			1.11662			0.558308	−	0.829634i	$-0.311451\pi$
$251$	6.96903e34			1.11662			0.558308	+	0.829634i	$0.311451\pi$
$252$	2.05019e34	−	1.06732e34i	0.310090	−	0.161432i
$253$	9.03561e34			1.29036
$254$	4.86850e34	+	8.43249e34i	0.656608	+	1.13728i
$255$	5.32933e33	−	9.23067e33i	0.0678954	−	0.117598i
$256$	−3.71944e34	+	6.44225e34i	−0.447711	+	0.775458i
$257$	−4.49470e34	−	7.78506e34i	−0.511294	−	0.885588i	−0.999914	−	0.0130909i	$-0.995833\pi$
$257$	−4.49470e34	−	7.78506e34i	−0.511294	−	0.885588i	0.488620	−	0.872497i	$-0.337500\pi$
$258$	4.45093e34			0.478591
$259$	−3.88654e34	−	2.47587e34i	−0.395109	−	0.251699i
$260$	−1.63010e35			−1.56712
$261$	−1.95610e34	−	3.38806e34i	−0.177870	−	0.308080i
$262$	−5.39454e34	+	9.34362e34i	−0.464072	+	0.803797i
$263$	−5.97001e34	+	1.03404e35i	−0.485978	+	0.841739i	−0.999870	−	0.0161160i	$-0.994870\pi$
$263$	−5.97001e34	+	1.03404e35i	−0.485978	+	0.841739i	0.513892	+	0.857855i	$0.328203\pi$
$264$	−3.09937e33	−	5.36827e33i	−0.0238790	−	0.0413597i
$265$	−4.34501e34			−0.316902
$266$	1.30313e34	−	2.98625e35i	0.0899921	−	2.06226i
$267$	4.53215e34			0.296409
$268$	−7.42969e34	−	1.28686e35i	−0.460274	−	0.797218i
$269$	7.22128e34	−	1.25076e35i	0.423844	−	0.734119i	−0.572468	−	0.819927i	$-0.694014\pi$
$269$	7.22128e34	−	1.25076e35i	0.423844	−	0.734119i	0.996312	+	0.0858079i	$0.0273471\pi$
$270$	−4.37224e34	+	7.57294e34i	−0.243181	+	0.421202i
$271$	5.75888e33	+	9.97467e33i	0.0303587	+	0.0525828i	0.880806	−	0.473478i	$-0.157002\pi$
$271$	5.75888e33	+	9.97467e33i	0.0303587	+	0.0525828i	−0.850447	+	0.526061i	$0.823668\pi$
$272$	−2.52918e34			−0.126395
$273$	−4.49541e33	+	1.03017e35i	−0.0213015	+	0.488146i
$274$	3.53567e35			1.58887
$275$	2.94239e35	+	5.09637e35i	1.25423	+	2.17238i
$276$	8.15408e34	−	1.41233e35i	0.329756	−	0.571155i
$277$	−1.58851e35	+	2.75138e35i	−0.609584	+	1.05583i	0.381725	+	0.924276i	$0.375330\pi$
$277$	−1.58851e35	+	2.75138e35i	−0.609584	+	1.05583i	−0.991309	+	0.131555i	$0.958003\pi$
$278$	1.94846e35	+	3.37484e35i	0.709648	+	1.22915i
$279$	1.30186e35			0.450095
$280$	−3.16750e34	−	2.01782e34i	−0.103974	−	0.0662354i
$281$	−1.19171e35			−0.371475			−0.185738	−	0.982599i	$-0.559467\pi$
$281$	−1.19171e35			−0.371475			−0.185738	+	0.982599i	$0.559467\pi$
$282$	−1.33098e35	−	2.30533e35i	−0.394058	−	0.682528i
$283$	2.57679e35	−	4.46314e35i	0.724730	−	1.25527i	−0.234355	−	0.972151i	$-0.575298\pi$
$283$	2.57679e35	−	4.46314e35i	0.724730	−	1.25527i	0.959085	−	0.283119i	$-0.0913690\pi$
$284$	−1.28693e34	+	2.22903e34i	−0.0343905	+	0.0595661i
$285$	2.89442e35	+	5.01329e35i	0.735041	+	1.27313i
$286$	5.94551e35			1.43510
$287$	6.97572e35	−	3.63153e35i	1.60067	−	0.833302i
$288$	2.18164e35			0.475983
$289$	2.36708e35	+	4.09990e35i	0.491128	+	0.850658i
$290$	−6.83339e35	+	1.18358e36i	−1.34854	+	2.33575i
$291$	−4.32621e34	+	7.49322e34i	−0.0812193	+	0.140676i
$292$	−4.43810e35	−	7.68701e35i	−0.792767	−	1.37311i
$293$	−3.35943e35			−0.571065			−0.285532	−	0.958369i	$-0.592170\pi$
$293$	−3.35943e35			−0.571065			−0.285532	+	0.958369i	$0.592170\pi$
$294$	−2.92945e35	+	4.18410e35i	−0.473969	+	0.676964i
$295$	−2.04466e36			−3.14921
$296$	1.11526e34	+	1.93169e34i	0.0163549	+	0.0283275i
$297$	8.16334e34	−	1.41393e35i	0.113999	−	0.197451i
$298$	5.78993e35	−	1.00284e36i	0.770082	−	1.33382i
$299$	3.63768e35	+	6.30064e35i	0.460885	+	0.798275i
$300$	1.06213e36			1.28209
$301$	−4.46597e35	+	2.32497e35i	−0.513690	+	0.267425i
$302$	−2.70408e35			−0.296428
$303$	3.13567e34	+	5.43115e34i	0.0327652	+	0.0567510i
$304$	6.86813e35	−	1.18959e36i	0.684181	−	1.18504i
$305$	6.22823e35	−	1.07876e36i	0.591585	−	1.02465i
$306$	3.50828e34	+	6.07652e34i	0.0317785	+	0.0550420i
$307$	1.87883e36			1.62323			0.811617	−	0.584189i	$-0.198587\pi$
$307$	1.87883e36			1.62323			0.811617	+	0.584189i	$0.198587\pi$
$308$	1.27150e36	+	8.09994e35i	1.04793	+	0.667569i
$309$	1.25557e36			0.987287
$310$	−2.27395e36	−	3.93860e36i	−1.70623	−	2.95527i
$311$	−6.02493e35	+	1.04355e36i	−0.431446	+	0.747286i	−0.996998	−	0.0774262i	$-0.975330\pi$
$311$	−6.02493e35	+	1.04355e36i	−0.431446	+	0.747286i	0.565552	+	0.824713i	$0.308663\pi$
$312$	2.49557e34	−	4.32246e34i	0.0170580	−	0.0295454i
$313$	−4.39928e35	−	7.61977e35i	−0.287070	−	0.497221i	0.686039	−	0.727565i	$-0.259348\pi$
$313$	−4.39928e35	−	7.61977e35i	−0.287070	−	0.497221i	−0.973109	+	0.230344i	$0.926015\pi$
$314$	−1.05954e36			−0.660141
$315$	4.31244e34	−	9.88240e35i	0.0256579	−	0.587975i
$316$	1.91061e36			1.08570
$317$	7.43057e35	+	1.28701e36i	0.403332	+	0.698591i	0.994126	−	0.108231i	$-0.0345187\pi$
$317$	7.43057e35	+	1.28701e36i	0.403332	+	0.698591i	−0.590794	+	0.806823i	$0.701185\pi$
$318$	1.43015e35	−	2.47710e35i	0.0741633	−	0.128455i
$319$	1.27585e36	−	2.20984e36i	0.632172	−	1.09495i
$320$	−2.04164e36	−	3.53622e36i	−0.966727	−	1.67442i
$321$	8.17398e35			0.369922
$322$	−1.57110e35	+	3.60034e36i	−0.0679665	+	1.55752i
$323$	4.64496e35			0.192108
$324$	−1.47338e35	−	2.55197e35i	−0.0582656	−	0.100919i
$325$	−2.36917e36	+	4.10353e36i	−0.895959	+	1.55185i
$326$	1.29993e36	−	2.25154e36i	0.470180	−	0.814376i
$327$	−7.49384e34	−	1.29797e35i	−0.0259276	−	0.0449079i
$328$	−3.80666e35			−0.126001
$329$	2.53968e36	+	1.61787e36i	0.804337	+	0.512393i
$330$	−5.70353e36			−1.72859
$331$	1.00918e36	+	1.74795e36i	0.292726	+	0.507017i	0.974453	−	0.224590i	$-0.0721042\pi$
$331$	1.00918e36	+	1.74795e36i	0.292726	+	0.507017i	−0.681727	+	0.731607i	$0.738771\pi$
$332$	−2.97842e36	+	5.15877e36i	−0.826957	+	1.43233i
$333$	−2.93745e35	+	5.08782e35i	−0.0780782	+	0.135235i
$334$	4.54457e36	+	7.87143e36i	1.15656	+	2.00323i
$335$	−6.35923e36			−1.54973
$336$	−2.08197e36	+	1.08387e36i	−0.485910	+	0.252963i
$337$	−8.48308e36			−1.89636			−0.948178	−	0.317740i	$-0.897076\pi$
$337$	−8.48308e36			−1.89636			−0.948178	+	0.317740i	$0.897076\pi$
$338$	−9.48401e35	−	1.64268e36i	−0.203095	−	0.351771i
$339$	1.77542e36	−	3.07512e36i	0.364255	−	0.630909i
$340$	6.27379e35	−	1.08665e36i	0.123335	−	0.213622i
$341$	4.24566e36	+	7.35369e36i	0.799846	+	1.38537i
$342$	−3.81078e36			−0.688074
$343$	7.53758e35	−	5.72845e36i	0.130457	−	0.991454i
$344$	2.43709e35			0.0404365
$345$	−3.48963e36	−	6.04421e36i	−0.555139	−	0.961529i
$346$	1.47968e36	−	2.56288e36i	0.225717	−	0.390954i
$347$	1.85388e36	−	3.21102e36i	0.271210	−	0.469749i	−0.697962	−	0.716135i	$-0.745910\pi$
$347$	1.85388e36	−	3.21102e36i	0.271210	−	0.469749i	0.969172	+	0.246386i	$0.0792430\pi$
$348$	−2.30275e36	−	3.98848e36i	−0.323108	−	0.559640i
$349$	−9.13360e36			−1.22934			−0.614672	−	0.788783i	$-0.710712\pi$
$349$	−9.13360e36			−1.22934			−0.614672	+	0.788783i	$0.710712\pi$
$350$	−2.08187e37	+	1.08381e37i	−2.68823	+	1.39948i
$351$	1.31460e36			0.162870
$352$	7.11480e36	+	1.23232e37i	0.845852	+	1.46506i
$353$	1.13420e36	−	1.96449e36i	0.129406	−	0.224139i	−0.794040	−	0.607865i	$-0.792026\pi$
$353$	1.13420e36	−	1.96449e36i	0.129406	−	0.224139i	0.923447	+	0.383727i	$0.125359\pi$
$354$	6.72995e36	−	1.16566e37i	0.736995	−	1.27651i
$355$	5.50755e35	+	9.53936e35i	0.0578959	+	0.100279i
$356$	5.33533e36			0.538439
$357$	−6.69424e35	−	4.26448e35i	−0.0648653	−	0.0413216i
$358$	1.14689e37			1.06713
$359$	−3.84947e36	−	6.66748e36i	−0.343979	−	0.595788i	0.641189	−	0.767383i	$-0.278441\pi$
$359$	−3.84947e36	−	6.66748e36i	−0.343979	−	0.595788i	−0.985168	+	0.171595i	$0.945108\pi$
$360$	−2.39400e35	+	4.14653e35i	−0.0205465	+	0.0355876i
$361$	−6.54876e36	+	1.13428e37i	−0.539889	+	0.935115i
$362$	−2.21703e36	−	3.84000e36i	−0.175589	−	0.304128i
$363$	3.06170e36			0.232979
$364$	−5.29208e35	+	1.21273e37i	−0.0386951	+	0.886737i
$365$	−3.79866e37			−2.66922
$366$	4.10002e36	+	7.10145e36i	0.276892	+	0.479591i
$367$	1.15018e37	−	1.99218e37i	0.746637	−	1.29321i	−0.202789	−	0.979223i	$-0.565000\pi$
$367$	1.15018e37	−	1.99218e37i	0.746637	−	1.29321i	0.949426	−	0.313991i	$-0.101666\pi$
$368$	−8.28047e36	+	1.43422e37i	−0.516728	+	0.894999i
$369$	−5.01313e36	−	8.68299e36i	−0.300764	−	0.520939i
$370$	2.05233e37			1.18392
$371$	−1.41059e35	+	3.23252e36i	−0.00782493	+	0.179316i
$372$	1.53258e37			0.817616
$373$	−8.89632e36	−	1.54089e37i	−0.456491	−	0.790666i	0.542281	−	0.840197i	$-0.317561\pi$
$373$	−8.89632e36	−	1.54089e37i	−0.456491	−	0.790666i	−0.998773	+	0.0495309i	$0.984227\pi$
$374$	−2.28825e36	+	3.96337e36i	−0.112945	+	0.195626i
$375$	1.19936e37	−	2.07735e37i	0.569504	−	0.986409i
$376$	−7.28773e35	−	1.26227e36i	−0.0332942	−	0.0576672i
$377$	2.05460e37			0.903186
$378$	5.49203e36	+	3.49863e36i	0.232328	+	0.148002i
$379$	2.10804e37			0.858244			0.429122	−	0.903246i	$-0.358823\pi$
$379$	2.10804e37			0.858244			0.429122	+	0.903246i	$0.358823\pi$
$380$	3.40737e37	+	5.90173e37i	1.33523	+	2.31269i
$381$	−7.02118e36	+	1.21610e37i	−0.264849	+	0.458731i
$382$	2.36319e37	−	4.09317e37i	0.858184	−	1.48642i
$383$	8.24794e36	+	1.42858e37i	0.288379	+	0.499487i	0.973423	−	0.229015i	$-0.0735505\pi$
$383$	8.24794e36	+	1.42858e37i	0.288379	+	0.499487i	−0.685044	+	0.728501i	$0.740217\pi$
$384$	2.39194e36			0.0805283
$385$	5.72280e37	−	2.97927e37i	1.85536	−	0.965894i
$386$	−2.22319e37			−0.694163
$387$	3.20949e36	+	5.55899e36i	0.0965220	+	0.167181i
$388$	−5.09289e36	+	8.82115e36i	−0.147538	+	0.255544i
$389$	4.29643e36	−	7.44164e36i	0.119905	−	0.207682i	−0.799825	−	0.600234i	$-0.795074\pi$
$389$	4.29643e36	−	7.44164e36i	0.119905	−	0.207682i	0.919730	+	0.392551i	$0.128408\pi$
$390$	−2.29620e37	−	3.97714e37i	−0.617410	−	1.06939i
$391$	−5.60014e36			−0.145090
$392$	−1.60401e36	+	2.29099e36i	−0.0400459	+	0.0571972i
$393$	−1.55596e37			−0.374375
$394$	−8.65632e36	−	1.49932e37i	−0.200742	−	0.347695i
$395$	4.08833e37	−	7.08119e37i	0.913877	−	1.58288i
$396$	9.61003e36	−	1.66451e37i	0.207083	−	0.358678i
$397$	−2.17964e37	−	3.77525e37i	−0.452817	−	0.784303i	0.545742	−	0.837953i	$-0.316248\pi$
$397$	−2.17964e37	−	3.77525e37i	−0.452817	−	0.784303i	−0.998560	+	0.0536503i	$0.982914\pi$
$398$	8.20395e37			1.64331
$399$	3.82365e37	−	1.99058e37i	0.738536	−	0.384479i
$400$	−1.07859e38			−2.00904
$401$	−4.93815e37	−	8.55313e37i	−0.887097	−	1.53650i	−0.843292	−	0.537456i	$-0.819385\pi$
$401$	−4.93815e37	−	8.55313e37i	−0.887097	−	1.53650i	−0.0438052	−	0.999040i	$-0.513948\pi$
$402$	2.09313e37	−	3.62541e37i	0.362676	−	0.628173i
$403$	−3.41855e37	+	5.92110e37i	−0.571371	+	0.989644i
$404$	3.69137e36	+	6.39364e36i	0.0595193	+	0.103091i
$405$	−1.26110e37			−0.196178
$406$	8.58351e37	+	5.46802e37i	1.28836	+	0.820734i
$407$	−3.83187e37			−0.554999
$408$	1.92094e35	+	3.32717e35i	0.00268499	+	0.00465054i
$409$	4.57366e37	−	7.92182e37i	0.616987	−	1.06865i	−0.373045	−	0.927813i	$-0.621686\pi$
$409$	4.57366e37	−	7.92182e37i	0.616987	−	1.06865i	0.990032	−	0.140840i	$-0.0449803\pi$
$410$	−1.75128e38	+	3.03330e38i	−2.28028	+	3.94957i
$411$	2.54951e37	+	4.41588e37i	0.320443	+	0.555023i
$412$	1.47808e38			1.79345
$413$	−6.63791e36	+	1.52114e38i	−0.0777599	+	1.78195i
$414$	4.59442e37			0.519667
$415$	1.27465e38	+	2.20775e38i	1.39217	+	2.41131i
$416$	−5.72875e37	+	9.92248e37i	−0.604235	+	1.04657i
$417$	−2.81001e37	+	4.86708e37i	−0.286243	+	0.495787i
$418$	−1.24278e38	−	2.15255e38i	−1.22275	−	2.11786i
$419$	5.07305e37			0.482131			0.241066	−	0.970509i	$-0.422503\pi$
$419$	5.07305e37			0.482131			0.241066	+	0.970509i	$0.422503\pi$
$420$	5.07669e36	−	1.16337e38i	0.0466086	−	1.06808i
$421$	−9.73267e37			−0.863260			−0.431630	−	0.902051i	$-0.642061\pi$
$421$	−9.73267e37			−0.863260			−0.431630	+	0.902051i	$0.642061\pi$
$422$	6.37328e37	+	1.10388e38i	0.546176	+	0.946004i
$423$	1.91949e37	−	3.32466e37i	0.158947	−	0.275304i
$424$	7.83074e35	−	1.35632e36i	0.00626611	−	0.0108532i
$425$	−1.82365e37	−	3.15865e37i	−0.141027	−	0.244266i
$426$	−7.25121e36			−0.0541965
$427$	−7.82336e37	−	4.98377e37i	−0.565183	−	0.360043i
$428$	9.62255e37			0.671979
$429$	4.28721e37	+	7.42566e37i	0.289430	+	0.501307i
$430$	1.12120e38	−	1.94197e38i	0.731794	−	1.26750i
$431$	−1.17720e37	+	2.03898e37i	−0.0742901	+	0.128674i	−0.900777	−	0.434281i	$-0.857002\pi$
$431$	−1.17720e37	+	2.03898e37i	−0.0742901	+	0.128674i	0.826487	+	0.562955i	$0.190336\pi$
$432$	1.49622e37	+	2.59153e37i	0.0913021	+	0.158140i
$433$	−2.74521e38			−1.61995			−0.809975	−	0.586465i	$-0.800519\pi$
$433$	−2.74521e38			−1.61995			−0.809975	+	0.586465i	$0.800519\pi$
$434$	−3.00398e38	+	1.56386e38i	−1.71434	+	0.892479i
$435$	−1.97098e38			−1.08789
$436$	−8.82188e36	−	1.52799e37i	−0.0470985	−	0.0815770i
$437$	1.52075e38	−	2.63402e38i	0.785376	−	1.36031i
$438$	1.25032e38	−	2.16562e38i	0.624666	−	1.08195i
$439$	−1.33675e38	−	2.31532e38i	−0.646123	−	1.11912i	−0.984041	−	0.177942i	$-0.943056\pi$
$439$	−1.33675e38	−	2.31532e38i	−0.646123	−	1.11912i	0.337918	−	0.941176i	$-0.390277\pi$
$440$	−3.12295e37			−0.146050
$441$	−7.33811e37	−	6.41658e36i	−0.332066	−	0.0290365i
$442$	−3.68494e37			−0.161364
$443$	9.77348e37	+	1.69282e38i	0.414186	+	0.717391i	0.995343	−	0.0964009i	$-0.0307331\pi$
$443$	9.77348e37	+	1.69282e38i	0.414186	+	0.717391i	−0.581157	+	0.813792i	$0.697400\pi$
$444$	−3.45802e37	+	5.98947e37i	−0.141832	+	0.245661i
$445$	1.14166e38	−	1.97741e38i	0.453227	−	0.785011i
$446$	1.71932e38	+	2.97796e38i	0.660697	+	1.14436i
$447$	1.67001e38			0.621239
$448$	−2.69709e38	+	1.40409e38i	−0.971323	+	0.505668i
$449$	−2.92798e38			−1.02093			−0.510465	−	0.859899i	$-0.670527\pi$
$449$	−2.92798e38			−1.02093			−0.510465	+	0.859899i	$0.670527\pi$
$450$	1.49614e38	+	2.59139e38i	0.505116	+	0.874887i
$451$	3.26978e38	−	5.66343e38i	1.06895	−	1.85148i
$452$	2.09006e38	−	3.62009e38i	0.661685	−	1.14607i
$453$	−1.94987e37	−	3.37727e37i	−0.0597835	−	0.103548i
$454$	−8.48518e38			−2.51971
$455$	4.38145e38	+	2.79115e38i	1.26024	+	0.802818i
$456$	−2.08658e37			−0.0581358
$457$	−1.54010e38	−	2.66753e38i	−0.415684	−	0.719986i	0.579816	−	0.814748i	$-0.303124\pi$
$457$	−1.54010e38	−	2.66753e38i	−0.415684	−	0.719986i	−0.995500	+	0.0947616i	$0.969791\pi$
$458$	−3.04977e37	+	5.28236e37i	−0.0797476	+	0.138127i
$459$	−5.05952e36	+	8.76334e36i	−0.0128181	+	0.0222017i
$460$	−4.10805e38	−	7.11535e38i	−1.00843	−	1.74666i
$461$	−6.08998e38			−1.44861			−0.724306	−	0.689478i	$-0.757840\pi$
$461$	−6.08998e38			−1.44861			−0.724306	+	0.689478i	$0.757840\pi$
$462$	−1.85163e37	+	4.24320e38i	−0.0426822	+	0.978104i
$463$	4.46272e38			0.996954			0.498477	−	0.866903i	$-0.333893\pi$
$463$	4.46272e38			0.996954			0.498477	+	0.866903i	$0.333893\pi$
$464$	2.33845e38	+	4.05031e38i	0.506310	+	0.876955i
$465$	3.27941e38	−	5.68011e38i	0.688221	−	1.19203i
$466$	−3.26477e38	+	5.65474e38i	−0.664135	+	1.15032i
$467$	−5.75791e37	−	9.97299e37i	−0.113546	−	0.196667i	0.803652	−	0.595100i	$-0.202887\pi$
$467$	−5.75791e37	−	9.97299e37i	−0.113546	−	0.196667i	−0.917197	+	0.398433i	$0.869554\pi$
$468$	1.54757e38			0.295860
$469$	−2.06451e37	+	4.73102e38i	−0.0382657	+	0.876897i
$470$	−1.34111e39			−2.41015
$471$	−7.64015e37	−	1.32331e38i	−0.133137	−	0.230600i
$472$	3.68496e37	−	6.38254e37i	0.0622692	−	0.107854i
$473$	−2.09337e38	+	3.62582e38i	−0.343051	+	0.594182i
$474$	2.69133e38	+	4.66153e38i	0.427742	+	0.740870i
$475$	1.98089e39			3.05354
$476$	−7.88058e37	−	5.02023e37i	−0.117830	−	0.0750624i
$477$	4.12503e37			0.0598289
$478$	−4.83193e37	−	8.36915e37i	−0.0679855	−	0.117754i
$479$	−5.19912e38	+	9.00514e38i	−0.709684	+	1.22921i	0.255291	+	0.966864i	$0.417829\pi$
$479$	−5.19912e38	+	9.00514e38i	−0.709684	+	1.22921i	−0.964974	+	0.262344i	$0.915504\pi$
$480$	5.49559e38	−	9.51863e38i	0.727807	−	1.26060i
$481$	−1.54269e38	−	2.67201e38i	−0.198232	−	0.343348i
$482$	−1.82649e38			−0.227738
$483$	−4.60994e38	+	2.39992e38i	−0.557779	+	0.290378i
$484$	3.60429e38			0.423216
$485$	2.17956e38	+	3.77511e38i	0.248378	+	0.430204i
$486$	4.15088e37	−	7.18954e37i	0.0459108	−	0.0795198i
$487$	4.42619e38	−	7.66638e38i	0.475182	−	0.823039i	−0.524414	−	0.851463i	$-0.675716\pi$
$487$	4.42619e38	−	7.66638e38i	0.475182	−	0.823039i	0.999596	+	0.0284243i	$0.00904896\pi$
$488$	2.24495e37	+	3.88837e37i	0.0233948	+	0.0405210i
$489$	3.74942e38			0.379303
$490$	1.08762e39	+	2.33212e39i	1.06815	+	2.29038i
$491$	−1.70669e39			−1.62732			−0.813662	−	0.581338i	$-0.802529\pi$
$491$	−1.70669e39			−1.62732			−0.813662	+	0.581338i	$0.802529\pi$
$492$	−5.90154e38	−	1.02218e39i	−0.546351	−	0.946308i
$493$	−7.90754e37	+	1.36963e38i	−0.0710822	+	0.123118i
$494$	1.00067e39	−	1.73321e39i	0.873473	−	1.51290i
$495$	−4.11272e38	−	7.12343e38i	−0.348621	−	0.603829i
$496$	−1.55633e39			−1.28120
$497$	7.27571e37	−	3.78771e37i	0.0581712	−	0.0302837i
$498$	−1.67819e39			−1.30321
$499$	1.12506e39	+	1.94865e39i	0.848626	+	1.46986i	0.882435	+	0.470435i	$0.155903\pi$
$499$	1.12506e39	+	1.94865e39i	0.848626	+	1.46986i	−0.0338085	+	0.999428i	$0.510764\pi$
$500$	1.41191e39	−	2.44550e39i	1.03453	−	1.79185i
$501$	−6.55402e38	+	1.13519e39i	−0.466510	+	0.808019i
$502$	1.15565e39	+	2.00164e39i	0.799137	+	1.38415i
$503$	2.22794e39			1.49681			0.748405	−	0.663242i	$-0.230820\pi$
$503$	2.22794e39			1.49681			0.748405	+	0.663242i	$0.230820\pi$
$504$	3.00714e37	+	1.91566e37i	0.0196296	+	0.0125048i
$505$	3.15953e38			0.200400
$506$	1.49834e39	+	2.59520e39i	0.923481	+	1.59952i
$507$	1.36775e38	−	2.36901e38i	0.0819203	−	0.141890i
$508$	−8.26546e38	+	1.43162e39i	−0.481109	+	0.833304i
$509$	9.20913e38	+	1.59507e39i	0.520968	+	0.902343i	0.999703	+	0.0243833i	$0.00776222\pi$
$509$	9.20913e38	+	1.59507e39i	0.520968	+	0.902343i	−0.478735	+	0.877960i	$0.658904\pi$
$510$	3.53497e38			0.194365
$511$	−1.23322e38	+	2.82606e39i	−0.0659081	+	1.51035i
$512$	−2.73560e39			−1.42115
$513$	−2.74788e38	−	4.75947e38i	−0.138770	−	0.240357i
$514$	1.49068e39	−	2.58193e39i	0.731844	−	1.26759i
$515$	3.16281e39	−	5.47814e39i	1.50962	−	2.61474i
$516$	3.77826e38	+	6.54415e38i	0.175336	+	0.303691i
$517$	2.50395e39			1.12983
$518$	6.66282e37	−	1.52685e39i	0.0292332	−	0.669909i
$519$	4.26789e38			0.182090
$520$	−1.25728e38	−	2.17767e38i	−0.0521654	−	0.0903532i
$521$	1.13962e39	−	1.97389e39i	0.459848	−	0.796480i	−0.539104	−	0.842239i	$-0.681237\pi$
$521$	1.13962e39	−	1.97389e39i	0.459848	−	0.796480i	0.998953	+	0.0457586i	$0.0145705\pi$
$522$	6.48743e38	−	1.12366e39i	0.254595	−	0.440972i
$523$	−1.27467e39	−	2.20780e39i	−0.486546	−	0.842722i	0.513335	−	0.858189i	$-0.328410\pi$
$523$	−1.27467e39	−	2.20780e39i	−0.486546	−	0.842722i	−0.999880	+	0.0154664i	$0.995077\pi$
$524$	−1.83171e39			−0.680068
$525$	−2.85483e39	−	1.81863e39i	−1.03103	−	0.656803i
$526$	−3.95993e39			−1.39122
$527$	−2.63140e38	−	4.55771e38i	−0.0899357	−	0.155773i
$528$	−9.75900e38	+	1.69031e39i	−0.324499	+	0.562049i
$529$	−2.87947e38	+	4.98739e38i	−0.0931548	+	0.161349i
$530$	−7.20516e38	−	1.24797e39i	−0.226800	−	0.392829i
$531$	1.94114e39			0.594547
$532$	4.50127e39	−	2.34335e39i	1.34158	−	0.698422i
$533$	5.26557e39			1.52722
$534$	7.51549e38	+	1.30172e39i	0.212133	+	0.367426i
$535$	2.05904e39	−	3.56636e39i	0.565633	−	0.979705i
$536$	1.14609e38	−	1.98508e38i	0.0306427	−	0.0530748i
$537$	8.27002e38	+	1.43241e39i	0.215218	+	0.372769i
$538$	4.78990e39			1.21334
$539$	−2.03067e39	−	4.35426e39i	−0.500729	−	1.07369i
$540$	−1.48459e39			−0.356366
$541$	−4.30889e38	−	7.46322e38i	−0.100694	−	0.174408i	0.811277	−	0.584663i	$-0.198773\pi$
$541$	−4.30889e38	−	7.46322e38i	−0.100694	−	0.174408i	−0.911971	+	0.410255i	$0.865440\pi$
$542$	−1.90994e38	+	3.30812e38i	−0.0434541	+	0.0752648i
$543$	3.19732e38	−	5.53791e38i	0.0708252	−	0.122673i
$544$	−4.40965e38	−	7.63774e38i	−0.0951087	−	0.164733i
$545$	−7.55084e38			−0.158579
$546$	−3.03338e39	+	1.57917e39i	−0.620346	+	0.322950i
$547$	−3.11433e39			−0.620224			−0.310112	−	0.950700i	$-0.600367\pi$
$547$	−3.11433e39			−0.620224			−0.310112	+	0.950700i	$0.600367\pi$
$548$	3.00133e39	+	5.19846e39i	0.582098	+	1.00822i
$549$	−5.91291e38	+	1.02415e39i	−0.111687	+	0.193447i
$550$	−9.75849e39	+	1.69022e40i	−1.79525	+	3.10946i
$551$	−4.29468e39	−	7.43860e39i	−0.769542	−	1.33289i
$552$	2.51565e38			0.0439071
$553$	−5.13540e39	−	3.27144e39i	−0.873092	−	0.556192i
$554$	−1.05367e40			−1.74506
$555$	1.47990e39	+	2.56326e39i	0.238772	+	0.413566i
$556$	−3.30799e39	+	5.72961e39i	−0.519972	+	0.900618i
$557$	2.22021e39	−	3.84552e39i	0.340012	−	0.588918i	−0.644423	−	0.764669i	$-0.722902\pi$
$557$	2.22021e39	−	3.84552e39i	0.340012	−	0.588918i	0.984435	+	0.175752i	$0.0562356\pi$
$558$	2.15883e39	+	3.73920e39i	0.322123	+	0.557933i
$559$	−3.37110e39			−0.490118
$560$	−5.15538e38	+	1.18141e40i	−0.0730356	+	1.67368i
$561$	−6.60008e38			−0.0911145
$562$	−1.97617e39	−	3.42283e39i	−0.265857	−	0.460477i
$563$	4.25322e38	−	7.36679e38i	0.0557630	−	0.0965844i	−0.836796	−	0.547514i	$-0.815574\pi$
$563$	4.25322e38	−	7.36679e38i	0.0557630	−	0.0965844i	0.892559	+	0.450930i	$0.148908\pi$
$564$	2.25966e39	−	3.91385e39i	0.288733	−	0.500100i
$565$	−8.94464e39	−	1.54926e40i	−1.11394	−	1.92939i
$566$	1.70920e40			2.07469
$567$	−4.09411e37	+	9.38207e38i	−0.00484402	+	0.111005i
$568$	−3.97037e37			−0.00457910
$569$	−1.68521e39	−	2.91888e39i	−0.189464	−	0.328162i	0.755607	−	0.655025i	$-0.227342\pi$
$569$	−1.68521e39	−	2.91888e39i	−0.189464	−	0.328162i	−0.945072	+	0.326863i	$0.894008\pi$
$570$	−9.59941e39	+	1.66267e40i	−1.05211	+	1.82230i
$571$	−6.56874e39	+	1.13774e40i	−0.701873	+	1.21568i	0.265935	+	0.963991i	$0.414319\pi$
$571$	−6.56874e39	+	1.13774e40i	−0.701873	+	1.21568i	−0.967808	+	0.251689i	$0.919014\pi$
$572$	5.04698e39	+	8.74162e39i	0.525762	+	0.910646i
$573$	6.81623e39			0.692312
$574$	2.19980e40	+	1.40136e40i	2.17852	+	1.38780i
$575$	−2.38824e40			−2.30618
$576$	1.93827e39	+	3.35719e39i	0.182511	+	0.316118i
$577$	2.04630e39	−	3.54429e39i	0.187897	−	0.325447i	−0.756652	−	0.653818i	$-0.773166\pi$
$577$	2.04630e39	−	3.54429e39i	0.187897	−	0.325447i	0.944549	+	0.328371i	$0.106500\pi$
$578$	−7.85047e39	+	1.35974e40i	−0.702978	+	1.21759i
$579$	−1.60311e39	−	2.77666e39i	−0.139998	−	0.242484i
$580$	−2.32027e40			−1.97621
$581$	1.68386e40	−	8.76612e39i	1.39879	−	0.728205i
$582$	−2.86959e39			−0.232508
$583$	1.34526e39	+	2.33006e39i	0.106320	+	0.184151i
$584$	6.84610e38	−	1.18578e39i	0.0527785	−	0.0914150i
$585$	3.31151e39	−	5.73570e39i	0.249038	−	0.431346i
$586$	−5.57081e39	−	9.64893e39i	−0.408699	−	0.707887i
$587$	3.48058e39			0.249115			0.124557	−	0.992212i	$-0.460249\pi$
$587$	3.48058e39			0.249115			0.124557	+	0.992212i	$0.460249\pi$
$588$	−8.63856e39	−	7.55371e38i	−0.603212	−	0.0527460i
$589$	2.85828e40			1.94730
$590$	−3.39057e40	−	5.87264e40i	−2.25382	−	3.90373i
$591$	1.24838e39	−	2.16227e39i	0.0809711	−	0.140246i
$592$	3.51163e39	−	6.08232e39i	0.222251	−	0.384950i
$593$	−4.32088e39	−	7.48398e39i	−0.266857	−	0.462210i	0.701191	−	0.712973i	$-0.252652\pi$
$593$	−4.32088e39	−	7.48398e39i	−0.266857	−	0.462210i	−0.968049	+	0.250763i	$0.919319\pi$
$594$	5.41477e39			0.326345
$595$	−3.54691e39	+	1.84651e39i	−0.208619	+	0.108606i
$596$	1.96596e40			1.12851
$597$	5.91572e39	+	1.02463e40i	0.331421	+	0.574038i
$598$	−1.20644e40	+	2.08962e40i	−0.659690	+	1.14262i
$599$	−3.23041e39	+	5.59523e39i	−0.172412	+	0.298627i	−0.939263	−	0.343199i	$-0.888489\pi$
$599$	−3.23041e39	+	5.59523e39i	−0.172412	+	0.298627i	0.766850	+	0.641826i	$0.221823\pi$
$600$	8.19207e38	+	1.41891e39i	0.0426776	+	0.0739198i
$601$	−2.00447e40			−1.01934			−0.509670	−	0.860370i	$-0.670233\pi$
$601$	−2.00447e40			−1.01934			−0.509670	+	0.860370i	$0.670233\pi$
$602$	−1.40835e40	−	8.97171e39i	−0.699135	−	0.445375i
$603$	6.03728e39			0.292577
$604$	−2.29542e39	−	3.97578e39i	−0.108599	−	0.188099i
$605$	7.71248e39	−	1.33584e40i	0.356239	−	0.617023i
$606$	−1.03995e39	+	1.80125e39i	−0.0468987	+	0.0812309i
$607$	−1.72452e40	−	2.98695e40i	−0.759331	−	1.31520i	−0.943192	−	0.332248i	$-0.892193\pi$
$607$	−1.72452e40	−	2.98695e40i	−0.759331	−	1.31520i	0.183861	−	0.982952i	$-0.441140\pi$
$608$	4.78987e40			2.05931
$609$	−6.39871e38	+	1.46633e40i	−0.0268622	+	0.615574i
$610$	4.13121e40			1.69354
$611$	1.00808e40	+	1.74604e40i	0.403548	+	0.698966i
$612$	−5.95616e38	+	1.03164e39i	−0.0232847	+	0.0403303i
$613$	8.64552e39	−	1.49745e40i	0.330076	−	0.571709i	−0.652450	−	0.757832i	$-0.726259\pi$
$613$	8.64552e39	−	1.49745e40i	0.330076	−	0.571709i	0.982527	+	0.186123i	$0.0595922\pi$
$614$	3.11559e40	+	5.39636e40i	1.16171	+	2.01215i
$615$	−5.05126e40			−1.83955
$616$	−1.01385e38	+	2.32335e39i	−0.00360625	+	0.0826407i
$617$	3.98390e40			1.38412			0.692060	−	0.721840i	$-0.256703\pi$
$617$	3.98390e40			1.38412			0.692060	+	0.721840i	$0.256703\pi$
$618$	2.08206e40	+	3.60624e40i	0.706580	+	1.22383i
$619$	1.71637e39	−	2.97284e39i	0.0568980	−	0.0985502i	−0.836173	−	0.548465i	$-0.815212\pi$
$619$	1.71637e39	−	2.97284e39i	0.0568980	−	0.0985502i	0.893071	+	0.449915i	$0.148546\pi$
$620$	3.86058e40	−	6.68673e40i	1.25018	−	2.16538i
$621$	3.31295e39	+	5.73820e39i	0.104806	+	0.181530i
$622$	−3.99636e40			−1.23511
$623$	−1.43405e40	−	9.13543e39i	−0.432999	−	0.275837i
$624$	−1.57156e40			−0.463613
$625$	−2.36938e40	−	4.10389e40i	−0.682928	−	1.18287i
$626$	1.45903e40	−	2.52711e40i	0.410900	−	0.711700i
$627$	1.79229e40	−	3.10434e40i	0.493207	−	0.854259i
$628$	−8.99412e39	−	1.55783e40i	−0.241849	−	0.418894i
$629$	2.37494e39			0.0624048
$630$	2.90992e40	−	1.51490e40i	0.747212	−	0.388996i
$631$	3.31054e40			0.830756			0.415378	−	0.909649i	$-0.363649\pi$
$631$	3.31054e40			0.830756			0.415378	+	0.909649i	$0.363649\pi$
$632$	1.47363e39	+	2.55240e39i	0.0361402	+	0.0625966i
$633$	−9.19132e39	+	1.59198e40i	−0.220305	+	0.381579i
$634$	−2.46436e40	+	4.26840e40i	−0.577312	+	0.999933i
$635$	3.53729e40	+	6.12677e40i	0.809938	+	1.40285i
$636$	4.85606e39			0.108682
$637$	2.21874e40	−	3.16901e40i	0.485384	−	0.693269i
$638$	8.46277e40			1.80973
$639$	−5.22872e38	−	9.05641e38i	−0.0109303	−	0.0189319i
$640$	6.02535e39	−	1.04362e40i	0.123132	−	0.213272i
$641$	−3.32565e40	+	5.76019e40i	−0.664408	+	1.15079i	0.315037	+	0.949079i	$0.397983\pi$
$641$	−3.32565e40	+	5.76019e40i	−0.664408	+	1.15079i	−0.979445	+	0.201710i	$0.935350\pi$
$642$	1.35546e40	+	2.34772e40i	0.264745	+	0.458552i
$643$	1.84727e40			0.352753			0.176377	−	0.984323i	$-0.443562\pi$
$643$	1.84727e40			0.352753			0.176377	+	0.984323i	$0.443562\pi$
$644$	−5.42691e40	+	2.82523e40i	−1.01323	+	0.527483i
$645$	3.23390e40			0.590351
$646$	7.70256e39	+	1.33412e40i	0.137488	+	0.238135i
$647$	2.13523e40	−	3.69833e40i	0.372678	−	0.645497i	−0.617299	−	0.786729i	$-0.711773\pi$
$647$	2.13523e40	−	3.69833e40i	0.372678	−	0.645497i	0.989977	+	0.141232i	$0.0451063\pi$
$648$	2.27280e38	−	3.93660e38i	0.00387903	−	0.00671868i
$649$	6.33048e40	+	1.09647e41i	1.05655	+	1.82999i
$650$	−1.57148e41			−2.56487
$651$	−4.11931e40	−	2.62416e40i	−0.657507	−	0.418857i
$652$	4.41389e40			0.689019
$653$	−3.56014e40	−	6.16635e40i	−0.543534	−	0.941428i	−0.998698	−	0.0510202i	$-0.983753\pi$
$653$	−3.56014e40	−	6.16635e40i	−0.543534	−	0.941428i	0.455164	−	0.890408i	$-0.349581\pi$
$654$	2.48535e39	−	4.30475e39i	0.0371116	−	0.0642792i
$655$	−3.91950e40	+	6.78877e40i	−0.572442	+	0.991498i
$656$	5.99303e40	+	1.03802e41i	0.856132	+	1.48286i
$657$	3.60635e40			0.503929
$658$	−4.35385e39	+	9.97729e40i	−0.0595112	+	1.36376i
$659$	−1.33834e41			−1.78948			−0.894740	−	0.446587i	$-0.852639\pi$
$659$	−1.33834e41			−1.78948			−0.894740	+	0.446587i	$0.852639\pi$
$660$	−4.84156e40	−	8.38584e40i	−0.633284	−	1.09688i
$661$	2.58237e40	−	4.47279e40i	0.330443	−	0.572344i	−0.652156	−	0.758085i	$-0.726135\pi$
$661$	2.58237e40	−	4.47279e40i	0.330443	−	0.572344i	0.982599	+	0.185741i	$0.0594685\pi$
$662$	−3.34696e40	+	5.79710e40i	−0.418996	+	0.725722i
$663$	−2.65715e39	−	4.60232e39i	−0.0325439	−	0.0563677i
$664$	−9.18886e39			−0.110109
$665$	9.46813e39	−	2.16972e41i	0.111007	−	2.54383i
$666$	−1.94843e40			−0.223515
$667$	5.17783e40	+	8.96826e40i	0.581196	+	1.00666i
$668$	−7.71552e40	+	1.33637e41i	−0.847435	+	1.46780i
$669$	−2.47955e40	+	4.29471e40i	−0.266498	+	0.461588i
$670$	−1.05453e41	−	1.82649e41i	−1.10911	−	1.92103i
$671$	−7.71331e40			−0.793898
$672$	−6.90307e40	−	4.39752e40i	−0.695325	−	0.442948i
$673$	9.71248e40			0.957440			0.478720	−	0.877968i	$-0.341101\pi$
$673$	9.71248e40			0.957440			0.478720	+	0.877968i	$0.341101\pi$
$674$	−1.40671e41	−	2.43650e41i	−1.35718	−	2.35071i
$675$	−2.15768e40	+	3.73722e40i	−0.203743	+	0.352894i
$676$	1.61014e40	−	2.78885e40i	0.148812	−	0.257749i
$677$	9.64386e40	+	1.67036e41i	0.872399	+	1.51104i	0.859508	+	0.511122i	$0.170770\pi$
$677$	9.64386e40	+	1.67036e41i	0.872399	+	1.51104i	0.0128904	+	0.999917i	$0.495897\pi$
$678$	1.17765e41			1.04276
$679$	2.87929e40	−	1.49895e40i	0.249559	−	0.129920i
$680$	1.93556e39			0.0164220
$681$	−6.11851e40	−	1.05976e41i	−0.508174	−	0.880184i
$682$	−1.40808e41	+	2.43887e41i	−1.14486	+	1.98296i
$683$	2.07204e40	−	3.58889e40i	0.164930	−	0.285667i	−0.771701	−	0.635986i	$-0.780594\pi$
$683$	2.07204e40	−	3.58889e40i	0.164930	−	0.285667i	0.936630	+	0.350319i	$0.113927\pi$
$684$	−3.23486e40	−	5.60294e40i	−0.252082	−	0.436619i
$685$	2.56891e41			1.95990
$686$	1.77031e41	−	7.33433e40i	1.32236	−	0.547849i
$687$	−8.79654e39			−0.0643338
$688$	−3.83683e40	−	6.64559e40i	−0.274752	−	0.475884i
$689$	−1.08319e40	+	1.87614e40i	−0.0759495	+	0.131548i
$690$	1.15734e41	−	2.00457e41i	0.794602	−	1.37629i
$691$	6.94683e40	+	1.20323e41i	0.467041	+	0.808939i	0.999291	−	0.0376485i	$-0.0119867\pi$
$691$	6.94683e40	+	1.20323e41i	0.467041	+	0.808939i	−0.532250	+	0.846587i	$0.678653\pi$
$692$	5.02424e40			0.330774
$693$	−5.43307e40	+	2.82844e40i	−0.350278	+	0.182354i
$694$	1.22969e41			0.776395
$695$	1.41569e41	+	2.45205e41i	0.875364	+	1.51618i
$696$	3.55217e39	−	6.15253e39i	0.0215109	−	0.0372580i
$697$	−2.02656e40	+	3.51011e40i	−0.120195	+	0.208183i
$698$	−1.51459e41	−	2.62335e41i	−0.879815	−	1.52388i
$699$	−9.41666e40			−0.535769
$700$	−3.36075e41	−	2.14093e41i	−1.87290	−	1.19311i
$701$	−2.47927e41			−1.35336			−0.676680	−	0.736277i	$-0.736582\pi$
$701$	−2.47927e41			−1.35336			−0.676680	+	0.736277i	$0.736582\pi$
$702$	2.17995e40	+	3.77579e40i	0.116563	+	0.201892i
$703$	−6.44929e40	+	1.11705e41i	−0.337800	+	0.585086i
$704$	−1.26423e41	+	2.18970e41i	−0.648666	+	1.12352i
$705$	−9.67047e40	−	1.67497e41i	−0.486077	−	0.841911i
$706$	7.52319e40			0.370454
$707$	1.02573e39	−	2.35056e40i	0.00494825	−	0.113394i
$708$	2.28515e41			1.08002
$709$	6.16640e39	+	1.06805e40i	0.0285536	+	0.0494564i	0.879949	−	0.475068i	$-0.157577\pi$
$709$	6.16640e39	+	1.06805e40i	0.0285536	+	0.0494564i	−0.851395	+	0.524524i	$0.824243\pi$
$710$	−1.82659e40	+	3.16375e40i	−0.0828696	+	0.143534i
$711$	−3.88135e40	+	6.72269e40i	−0.172533	+	0.298837i
$712$	4.11507e39	+	7.12752e39i	0.0179233	+	0.0310441i
$713$	−3.44606e41			−1.47070
$714$	1.14762e39	−	2.62988e40i	0.00479924	−	0.109979i
$715$	4.31982e41			1.77022
$716$	9.73562e40	+	1.68626e41i	0.390953	+	0.677151i
$717$	6.96844e39	−	1.20697e40i	0.0274226	−	0.0474973i
$718$	1.27668e41	−	2.21128e41i	0.492356	−	0.852785i
$719$	1.30911e41	+	2.26744e41i	0.494774	+	0.856974i	0.999982	−	0.00602366i	$-0.00191740\pi$
$719$	1.30911e41	+	2.26744e41i	0.494774	+	0.856974i	−0.505208	+	0.862998i	$0.668584\pi$
$720$	1.50760e41			0.558425
$721$	−3.97284e41	−	2.53085e41i	−1.44225	−	0.918766i
$722$	−4.34382e41			−1.54555
$723$	−1.31705e40	−	2.28120e40i	−0.0459301	−	0.0795532i
$724$	3.76394e40	−	6.51933e40i	0.128657	−	0.222840i
$725$	−3.37225e41	+	5.84091e41i	−1.12985	+	1.95695i
$726$	5.07710e40	+	8.79379e40i	0.166738	+	0.288799i
$727$	−3.99601e40			−0.128640			−0.0643202	−	0.997929i	$-0.520488\pi$
$727$	−3.99601e40			−0.128640			−0.0643202	+	0.997929i	$0.520488\pi$
$728$	−1.66092e40	+	8.64668e39i	−0.0524135	+	0.0272863i
$729$	1.19725e40			0.0370370
$730$	−6.29917e41	−	1.09105e42i	−1.91030	−	3.30874i
$731$	1.29744e40	−	2.24723e40i	0.0385731	−	0.0668106i
$732$	−6.96078e40	+	1.20564e41i	−0.202884	+	0.351405i
$733$	1.55062e41	+	2.68575e41i	0.443095	+	0.767463i	0.997917	−	0.0645058i	$-0.0205471\pi$
$733$	1.55062e41	+	2.68575e41i	0.443095	+	0.767463i	−0.554822	+	0.831969i	$0.687214\pi$
$734$	7.62922e41			2.13741
$735$	−2.12844e41	+	3.04003e41i	−0.584649	+	0.835048i
$736$	−5.77485e41			−1.55529
$737$	1.96889e41	+	3.41022e41i	0.519927	+	0.900541i
$738$	1.66261e41	−	2.87973e41i	0.430501	−	0.745650i
$739$	3.15215e40	−	5.45968e40i	0.0800317	−	0.138619i	−0.823232	−	0.567706i	$-0.807831\pi$
$739$	3.15215e40	−	5.45968e40i	0.0800317	−	0.138619i	0.903263	+	0.429087i	$0.141165\pi$
$740$	1.74216e41	+	3.01752e41i	0.433740	+	0.751259i
$741$	2.88626e41			0.704646
$742$	−9.51832e40	+	4.95520e40i	−0.227879	+	0.118633i
$743$	6.65512e41			1.56249			0.781246	−	0.624223i	$-0.214584\pi$
$743$	6.65512e41			1.56249			0.781246	+	0.624223i	$0.214584\pi$
$744$	1.18206e40	+	2.04738e40i	0.0272164	+	0.0471402i
$745$	4.20677e41	−	7.28634e41i	0.949911	−	1.64529i
$746$	2.95048e41	−	5.11039e41i	0.653402	−	1.13172i
$747$	−1.21011e41	−	2.09598e41i	−0.262831	−	0.455237i
$748$	−7.76973e40			−0.165513
$749$	−2.58638e41	−	1.64762e41i	−0.540389	−	0.344248i
$750$	7.95541e41			1.63033
$751$	3.24661e41	+	5.62329e41i	0.652606	+	1.13035i	0.982488	+	0.186325i	$0.0596576\pi$
$751$	3.24661e41	+	5.62329e41i	0.652606	+	1.13035i	−0.329882	+	0.944022i	$0.607009\pi$
$752$	−2.29469e41	+	3.97452e41i	−0.452445	+	0.783657i
$753$	−1.66663e41	+	2.88669e41i	−0.322339	+	0.558308i
$754$	3.40706e41	+	5.90120e41i	0.646390	+	1.11958i
$755$	−1.96470e41			−0.365650
$756$	−4.81967e39	+	1.10447e41i	−0.00879936	+	0.201646i
$757$	−1.69944e41			−0.304380			−0.152190	−	0.988351i	$-0.548633\pi$
$757$	−1.69944e41			−0.304380			−0.152190	+	0.988351i	$0.548633\pi$
$758$	3.49568e41	+	6.05470e41i	0.614227	+	1.06387i
$759$	−2.16085e41	+	3.74271e41i	−0.372494	+	0.645179i
$760$	−5.25612e40	+	9.10386e40i	−0.0888931	+	0.153967i
$761$	−6.59221e40	−	1.14180e41i	−0.109384	−	0.189459i	0.806137	−	0.591729i	$-0.201554\pi$
$761$	−6.59221e40	−	1.14180e41i	−0.109384	−	0.189459i	−0.915521	+	0.402270i	$0.868221\pi$
$762$	−4.65718e41			−0.758186
$763$	−2.45136e39	+	5.61753e40i	−0.00391562	+	0.0897304i
$764$	8.02419e41			1.25761
$765$	2.54900e40	+	4.41500e40i	0.0391994	+	0.0678954i
$766$	−2.73545e41	+	4.73793e41i	−0.412773	+	0.714943i
$767$	−5.09722e41	+	8.82865e41i	−0.754746	+	1.30726i
$768$	−1.77899e41	−	3.08131e41i	−0.258486	−	0.447711i
$769$	3.21719e41			0.458716			0.229358	−	0.973342i	$-0.426337\pi$
$769$	3.21719e41			0.458716			0.229358	+	0.973342i	$0.426337\pi$
$770$	1.80469e42	+	1.14966e42i	2.52515	+	1.60862i
$771$	4.29961e41			0.590392
$772$	−1.88721e41	−	3.26874e41i	−0.254313	−	0.440483i
$773$	2.27458e41	−	3.93969e41i	0.300814	−	0.521026i	−0.675506	−	0.737354i	$-0.736075\pi$
$773$	2.27458e41	−	3.93969e41i	0.300814	−	0.521026i	0.976321	+	0.216329i	$0.0694082\pi$
$774$	−1.06443e41	+	1.84365e41i	−0.138157	+	0.239296i
$775$	−1.12219e42	−	1.94368e42i	−1.42952	−	2.47600i
$776$	−1.57123e40			−0.0196447
$777$	1.95501e41	−	1.01777e41i	0.239908	−	0.124895i
$778$	2.84984e41			0.343255
$779$	−1.10065e42	−	1.90638e42i	−1.30124	−	2.25381i
$780$	3.89837e41	−	6.75217e41i	0.452388	−	0.783558i
$781$	3.41040e40	−	5.90698e40i	0.0388477	−	0.0672862i
$782$	−9.28649e40	−	1.60847e41i	−0.103837	−	0.179852i
$783$	1.87119e41			0.205387
$784$	8.77247e41	+	7.67080e40i	0.945233	+	0.0826529i
$785$	−7.69826e41			−0.814297
$786$	−2.58019e41	−	4.46902e41i	−0.267932	−	0.464072i
$787$	2.76932e41	−	4.79660e41i	0.282318	−	0.488990i	−0.689637	−	0.724155i	$-0.742230\pi$
$787$	2.76932e41	−	4.79660e41i	0.282318	−	0.488990i	0.971955	+	0.235165i	$0.0755632\pi$
$788$	1.46962e41	−	2.54546e41i	0.147087	−	0.254763i
$789$	−2.85544e41	−	4.94576e41i	−0.280580	−	0.485978i
$790$	2.71181e42			2.61617
$791$	−1.18162e42	+	6.15150e41i	−1.11923	+	0.582669i
$792$	2.96484e40			0.0275731
$793$	−3.10533e41	−	5.37859e41i	−0.283561	−	0.491142i
$794$	7.22883e41	−	1.25207e42i	0.648143	−	1.12262i
$795$	1.03910e41	−	1.79978e41i	0.0914819	−	0.158451i
$796$	6.96410e41	+	1.20622e42i	0.602040	+	1.04276i
$797$	−2.02750e42			−1.72114			−0.860568	−	0.509336i	$-0.829891\pi$
$797$	−2.02750e42			−1.72114			−0.860568	+	0.509336i	$0.829891\pi$
$798$	1.20579e42	+	7.68136e41i	1.00515	+	0.640319i
$799$	−1.55192e41			−0.127040
$800$	−1.88054e42	−	3.25719e42i	−1.51174	−	2.61842i
$801$	−1.08386e41	+	1.87730e41i	−0.0855659	+	0.148204i
$802$	1.63775e42	−	2.83666e42i	1.26975	−	2.19927i
$803$	1.17611e42	+	2.03708e42i	0.895513	+	1.55107i
$804$	7.10720e41			0.531478
$805$	−1.14151e41	+	2.61589e42i	−0.0838380	+	1.92123i
$806$	−2.26754e42			−1.63567
$807$	3.45392e41	+	5.98236e41i	0.244706	+	0.423844i
$808$	−5.69422e39	+	9.86268e39i	−0.00396250	+	0.00686325i
$809$	−4.13922e40	+	7.16935e40i	−0.0282921	+	0.0490034i	−0.879825	−	0.475298i	$-0.842340\pi$
$809$	−4.13922e40	+	7.16935e40i	−0.0282921	+	0.0490034i	0.851533	+	0.524302i	$0.175674\pi$
$810$	−2.09123e41	−	3.62211e41i	−0.140401	−	0.243181i
$811$	−1.00340e42			−0.661717			−0.330859	−	0.943680i	$-0.607338\pi$
$811$	−1.00340e42			−0.661717			−0.330859	+	0.943680i	$0.607338\pi$
$812$	−7.53268e40	+	1.72619e42i	−0.0487963	+	1.11822i
$813$	−5.50891e40			−0.0350552
$814$	−6.35424e41	−	1.10059e42i	−0.397200	−	0.687971i
$815$	9.44486e41	−	1.63590e42i	0.579976	−	1.00455i
$816$	6.04849e40	−	1.04763e41i	0.0364871	−	0.0631975i
$817$	7.04654e41	+	1.22050e42i	0.417596	+	0.723297i
$818$	3.03373e42			1.76626
$819$	−4.15962e41	−	2.64984e41i	−0.237924	−	0.151566i
$820$	−5.94644e42			−3.34161
$821$	−1.63090e41	−	2.82480e41i	−0.0900434	−	0.155960i	0.817486	−	0.575949i	$-0.195367\pi$
$821$	−1.63090e41	−	2.82480e41i	−0.0900434	−	0.155960i	−0.907529	+	0.419989i	$0.862034\pi$
$822$	−8.45551e41	+	1.46454e42i	−0.458668	+	0.794436i
$823$	2.88326e41	−	4.99395e41i	0.153669	−	0.266162i	−0.778905	−	0.627142i	$-0.784224\pi$
$823$	2.88326e41	−	4.99395e41i	0.153669	−	0.266162i	0.932573	+	0.360980i	$0.117558\pi$
$824$	1.14003e41	+	1.97458e41i	0.0596994	+	0.103402i
$825$	−2.81467e42			−1.44826
$826$	−4.47909e42	+	2.33180e42i	−2.26453	+	1.17891i
$827$	1.98381e42			0.985532			0.492766	−	0.870162i	$-0.335986\pi$
$827$	1.98381e42			0.985532			0.492766	+	0.870162i	$0.335986\pi$
$828$	3.90007e41	+	6.75512e41i	0.190385	+	0.329756i
$829$	−7.29402e41	+	1.26336e42i	−0.349886	+	0.606020i	−0.986229	−	0.165386i	$-0.947113\pi$
$829$	−7.29402e41	+	1.26336e42i	−0.349886	+	0.606020i	0.636343	+	0.771406i	$0.280446\pi$
$830$	−4.22739e42	+	7.32205e42i	−1.99269	+	3.45144i
$831$	−7.59780e41	−	1.31598e42i	−0.351944	−	0.609584i
$832$	−2.03588e42			−0.926752
$833$	1.25858e41	+	2.69871e41i	0.0563026	+	0.120727i
$834$	−1.86389e42			−0.819431
$835$	3.30194e42	+	5.71913e42i	1.42664	+	2.47102i
$836$	2.10992e42	−	3.65448e42i	0.895930	−	1.55180i
$837$	−3.11338e41	+	5.39254e41i	−0.129931	+	0.225047i
$838$	8.41243e41	+	1.45708e42i	0.345051	+	0.597646i
$839$	3.45784e42			1.39398			0.696990	−	0.717081i	$-0.254522\pi$
$839$	3.45784e42			1.39398			0.696990	+	0.717081i	$0.254522\pi$
$840$	1.59332e41	−	8.29476e40i	0.0631324	−	0.0328665i
$841$	3.56802e41			0.138959
$842$	−1.61393e42	−	2.79541e42i	−0.617816	−	1.07009i
$843$	2.84996e41	−	4.93628e41i	0.107236	−	0.185738i
$844$	−1.08202e42	+	1.87411e42i	−0.400193	+	0.693154i
$845$	−6.89078e41	−	1.19352e42i	−0.250522	−	0.433917i
$846$	1.27321e42			0.455019
$847$	−9.68774e41	−	6.17145e41i	−0.340340	−	0.216809i
$848$	−4.93134e41			−0.170304
$849$	1.23247e42	+	2.13471e42i	0.418423	+	0.724730i
$850$	6.04817e41	−	1.04757e42i	0.201860	−	0.349631i
$851$	7.77550e41	−	1.34676e42i	0.255123	−	0.441886i
$852$	−6.15534e40	−	1.06614e41i	−0.0198554	−	0.0343905i
$853$	4.64526e42			1.47316			0.736579	−	0.676352i	$-0.236440\pi$
$853$	4.64526e42			1.47316			0.736579	+	0.676352i	$0.236440\pi$
$854$	1.34118e41	−	3.07346e42i	0.0418167	−	0.958270i
$855$	−2.76879e42			−0.848752
$856$	7.42176e40	+	1.28549e41i	0.0223685	+	0.0387434i
$857$	2.93887e42	−	5.09027e42i	0.870880	−	1.50841i	0.00979166	−	0.999952i	$-0.496883\pi$
$857$	2.93887e42	−	5.09027e42i	0.870880	−	1.50841i	0.861088	−	0.508456i	$-0.169783\pi$
$858$	−1.42186e42	+	2.46273e42i	−0.414277	+	0.717550i
$859$	−1.39413e42	−	2.41470e42i	−0.399394	−	0.691771i	0.594257	−	0.804275i	$-0.297446\pi$
$859$	−1.39413e42	−	2.41470e42i	−0.399394	−	0.691771i	−0.993651	+	0.112504i	$0.964113\pi$
$860$	3.80700e42			1.07240
$861$	−1.63988e41	+	3.75794e42i	−0.0454219	+	1.04089i
$862$	−7.80844e41			−0.212671
$863$	8.21472e41	+	1.42283e42i	0.220007	+	0.381063i	0.954810	−	0.297218i	$-0.0960587\pi$
$863$	8.21472e41	+	1.42283e42i	0.220007	+	0.381063i	−0.734803	+	0.678281i	$0.762725\pi$
$864$	−5.21736e41	+	9.03673e41i	−0.137405	+	0.237992i
$865$	1.07509e42	−	1.86211e42i	0.278426	−	0.482249i
$866$	−4.55228e42	−	7.88478e42i	−1.15936	−	2.00807i
$867$	−2.26433e42			−0.567105
$868$	−4.84933e42	−	3.08920e42i	−1.19439	−	0.760870i
$869$	−5.06317e42			−1.22641
$870$	−3.26839e42	−	5.66102e42i	−0.778582	−	1.34854i
$871$	−1.58532e42	+	2.74586e42i	−0.371411	+	0.643303i
$872$	1.36084e40	−	2.35705e40i	0.00313558	−	0.00543099i
$873$	−2.06921e41	−	3.58398e41i	−0.0468920	−	0.0812193i
$874$	1.00872e43			2.24830
$875$	−7.98229e42	+	4.15555e42i	−1.74989	+	0.910987i
$876$	4.24546e42			0.915409
$877$	1.91709e42	+	3.32050e42i	0.406582	+	0.704221i	0.994504	−	0.104697i	$-0.0333872\pi$
$877$	1.91709e42	+	3.32050e42i	0.406582	+	0.704221i	−0.587922	+	0.808918i	$0.700054\pi$
$878$	4.43336e42	−	7.67881e42i	0.924832	−	1.60186i
$879$	8.03403e41	−	1.39153e42i	0.164852	−	0.285532i
$880$	4.91662e42	+	8.51583e42i	0.992356	+	1.71881i
$881$	−1.44138e42			−0.286173			−0.143086	−	0.989710i	$-0.545703\pi$
$881$	−1.44138e42			−0.286173			−0.143086	+	0.989710i	$0.545703\pi$
$882$	−1.03255e42	−	2.21405e42i	−0.201659	−	0.432407i
$883$	1.83612e42			0.352752			0.176376	−	0.984323i	$-0.443563\pi$
$883$	1.83612e42			0.352752			0.176376	+	0.984323i	$0.443563\pi$
$884$	−3.12804e41	−	5.41793e41i	−0.0591173	−	0.102394i
$885$	4.88976e42	−	8.46932e42i	0.909098	−	1.57460i
$886$	−3.24139e42	+	5.61426e42i	−0.592847	+	1.02684i
$887$	2.63870e42	+	4.57036e42i	0.474785	+	0.822352i	0.999583	−	0.0288747i	$-0.00919237\pi$
$887$	2.63870e42	+	4.57036e42i	0.474785	+	0.822352i	−0.524798	+	0.851227i	$0.675859\pi$
$888$	−1.06685e41			−0.0188850
$889$	4.67291e42	−	2.43270e42i	0.813789	−	0.423656i
$890$	7.57265e42			1.29746
$891$	3.90450e41	+	6.76279e41i	0.0658171	+	0.113999i
$892$	−2.91897e42	+	5.05581e42i	−0.484105	+	0.838494i
$893$	4.21432e42	−	7.29941e42i	0.687672	−	1.19108i
$894$	2.76930e42	+	4.79658e42i	0.444607	+	0.770082i
$895$	8.33293e42			1.31633
$896$	−7.56852e41	−	4.82143e41i	−0.117637	−	0.0749393i
$897$	−3.47978e42			−0.532184
$898$	−4.85535e42	−	8.40971e42i	−0.730657	−	1.26554i
$899$	−4.86592e42	+	8.42802e42i	−0.720525	+	1.24799i
$900$	−2.54006e42	+	4.39952e42i	−0.370108	+	0.641046i
$901$	−8.33775e40	−	1.44414e41i	−0.0119547	−	0.0207062i
$902$	2.16886e43			3.06011
$903$	1.04987e41	−	2.40589e42i	0.0145769	−	0.334044i
$904$	6.44815e41			0.0881034
$905$	−1.61082e42	−	2.79002e42i	−0.216592	−	0.375148i
$906$	6.46678e41	−	1.12008e42i	0.0855715	−	0.148214i
$907$	1.10670e42	−	1.91686e42i	0.144120	−	0.249624i	−0.784924	−	0.619592i	$-0.787298\pi$
$907$	1.10670e42	−	1.91686e42i	0.144120	−	0.249624i	0.929044	+	0.369968i	$0.120631\pi$
$908$	−7.20282e42	−	1.24757e43i	−0.923120	−	1.59889i
$909$	−2.99957e41			−0.0378340
$910$	−7.51126e41	+	1.72128e43i	−0.0932422	+	2.13674i
$911$	−2.45484e42			−0.299921			−0.149961	−	0.988692i	$-0.547915\pi$
$911$	−2.45484e42			−0.299921			−0.149961	+	0.988692i	$0.547915\pi$
$912$	3.28500e42	+	5.68979e42i	0.395012	+	0.684181i
$913$	7.89288e42	−	1.36709e43i	0.934135	−	1.61797i
$914$	5.10777e42	−	8.84691e42i	0.594992	−	1.03056i
$915$	2.97894e42	+	5.15968e42i	0.341552	+	0.591585i
$916$	−1.03555e42			−0.116865
$917$	4.92333e42	+	3.13635e42i	0.546894	+	0.348392i
$918$	−3.35600e41			−0.0366947
$919$	−6.95369e42	−	1.20442e43i	−0.748412	−	1.29629i	−0.948584	−	0.316527i	$-0.897483\pi$
$919$	−6.95369e42	−	1.20442e43i	−0.748412	−	1.29629i	0.200172	−	0.979761i	$-0.435850\pi$
$920$	6.33698e41	−	1.09760e42i	0.0671365	−	0.116284i
$921$	−4.49320e42	+	7.78244e42i	−0.468588	+	0.811617i
$922$	−1.00988e43	−	1.74916e43i	−1.03674	−	1.79569i
$923$	5.49202e41			0.0555018
$924$	−6.39591e42	+	3.32969e42i	−0.636295	+	0.331253i
$925$	1.01282e43			0.991918
$926$	7.40035e42	+	1.28178e43i	0.713498	+	1.23581i
$927$	−3.00268e42	+	5.20079e42i	−0.285005	+	0.493644i
$928$	−8.15423e42	+	1.41235e43i	−0.761969	+	1.31977i
$929$	1.72025e42	+	2.97956e42i	0.158257	+	0.274109i	0.934240	−	0.356644i	$-0.116079\pi$
$929$	1.72025e42	+	2.97956e42i	0.158257	+	0.274109i	−0.775983	+	0.630754i	$0.782746\pi$
$930$	2.17525e43			1.97018
$931$	−1.61111e43	−	1.40878e42i	−1.43666	−	0.125624i
$932$	−1.10855e43			−0.973247
$933$	−2.88171e42	−	4.99126e42i	−0.249095	−	0.431446i
$934$	1.90962e42	−	3.30756e42i	0.162524	−	0.281500i
$935$	−1.66257e42	+	2.87966e42i	−0.139319	+	0.241308i
$936$	1.19362e41	+	2.06742e41i	0.00984845	+	0.0170580i
$937$	1.09691e43			0.891144			0.445572	−	0.895246i	$-0.353000\pi$
$937$	1.09691e43			0.891144			0.445572	+	0.895246i	$0.353000\pi$
$938$	−1.39307e43	+	7.25229e42i	−1.11438	+	0.580142i
$939$	4.20832e42			0.331480
$940$	−1.13843e43	−	1.97181e43i	−0.882980	−	1.52937i
$941$	−9.03548e42	+	1.56499e43i	−0.690083	+	1.19526i	0.281727	+	0.959495i	$0.409093\pi$
$941$	−9.03548e42	+	1.56499e43i	−0.690083	+	1.19526i	−0.971810	+	0.235765i	$0.924240\pi$
$942$	2.53387e42	−	4.38879e42i	0.190566	−	0.330071i
$943$	1.32699e43	+	2.29841e43i	0.982758	+	1.70219i
$944$	−2.32057e43			−1.69239
$945$	3.99033e42	+	2.54199e42i	0.286581	+	0.182563i
$946$	−1.38854e43			−0.982056
$947$	−6.62375e42	−	1.14727e43i	−0.461348	−	0.799079i	0.537680	−	0.843149i	$-0.319301\pi$
$947$	−6.62375e42	−	1.14727e43i	−0.461348	−	0.799079i	−0.999028	+	0.0440702i	$0.985967\pi$
$948$	−4.56919e42	+	7.91407e42i	−0.313414	+	0.542849i
$949$	−9.46987e42	+	1.64023e43i	−0.639711	+	1.10801i
$950$	3.28483e43	+	5.68950e43i	2.18535	+	3.78514i
$951$	−7.10803e42			−0.465728
$952$	6.28372e39	−	1.43998e41i	0.000405491	−	0.00929223i
$953$	2.10967e43			1.34081			0.670405	−	0.741996i	$-0.266121\pi$
$953$	2.10967e43			1.34081			0.670405	+	0.741996i	$0.266121\pi$
$954$	6.84038e41	+	1.18479e42i	0.0428182	+	0.0741633i
$955$	1.71702e43	−	2.97396e43i	1.05859	−	1.83352i
$956$	8.20338e41	−	1.42087e42i	0.0498142	−	0.0862807i
$957$	6.10236e42	+	1.05696e43i	0.364984	+	0.632172i
$958$	−3.44860e43			−2.03162
$959$	8.33987e41	−	1.91116e43i	0.0483938	−	1.10899i
$960$	1.95302e43			1.11628
$961$	−7.31139e42	−	1.26637e43i	−0.411634	−	0.712971i
$962$	5.11635e42	−	8.86178e42i	0.283741	−	0.491454i
$963$	−1.95479e42	+	3.38580e42i	−0.106787	+	0.184961i
$964$	−1.55046e42	−	2.68547e42i	−0.0834339	−	0.144512i
$965$	−1.61530e43			−0.856263
$966$	−1.45375e43	−	9.26094e42i	−0.759140	−	0.483601i
$967$	−1.74371e43			−0.896996			−0.448498	−	0.893784i	$-0.648041\pi$
$967$	−1.74371e43			−0.896996			−0.448498	+	0.893784i	$0.648041\pi$
$968$	2.77994e41	+	4.81500e41i	0.0140878	+	0.0244008i
$969$	−1.11084e42	+	1.92402e42i	−0.0554568	+	0.0960540i
$970$	−7.22855e42	+	1.25202e43i	−0.355518	+	0.615775i
$971$	−8.58436e42	−	1.48685e43i	−0.415938	−	0.720426i	0.579588	−	0.814910i	$-0.303213\pi$
$971$	−8.58436e42	−	1.48685e43i	−0.415938	−	0.720426i	−0.995526	+	0.0944833i	$0.969880\pi$
$972$	1.40943e42			0.0672793
$973$	1.87019e43	−	9.73613e42i	0.879527	−	0.457879i
$974$	2.93591e43			1.36031
$975$	−1.13317e43	−	1.96270e43i	−0.517282	−	0.895959i
$976$	7.06869e42	−	1.22433e43i	0.317919	−	0.550652i
$977$	−3.72633e42	+	6.45419e42i	−0.165124	+	0.286003i	−0.936699	−	0.350135i	$-0.886136\pi$
$977$	−3.72633e42	+	6.45419e42i	−0.165124	+	0.286003i	0.771575	+	0.636138i	$0.219469\pi$
$978$	6.21752e42	+	1.07691e43i	0.271459	+	0.470180i
$979$	−1.41388e43			−0.608223
$980$	−2.50564e43	+	3.57878e43i	−1.06204	+	1.51690i
$981$	7.16856e41			0.0299386
$982$	−2.83014e43	−	4.90195e43i	−1.16464	−	2.01722i
$983$	1.17342e43	−	2.03242e43i	0.475802	−	0.824114i	−0.523813	−	0.851833i	$-0.675491\pi$
$983$	1.17342e43	−	2.03242e43i	0.475802	−	0.824114i	0.999616	+	0.0277192i	$0.00882442\pi$
$984$	9.10358e41	−	1.57679e42i	0.0363733	−	0.0630005i
$985$	−6.28940e42	−	1.08936e43i	−0.247619	−	0.428889i
$986$	−5.24510e42			−0.203488
$987$	−1.27751e43	+	6.65067e42i	−0.488389	+	0.254254i
$988$	3.39775e43			1.28002
$989$	−8.49558e42	−	1.47148e43i	−0.315389	−	0.546270i
$990$	1.36399e43	−	2.36250e43i	0.499001	−	0.864294i
$991$	−2.94676e42	+	5.10393e42i	−0.106237	+	0.184008i	−0.914243	−	0.405166i	$-0.867214\pi$
$991$	−2.94676e42	+	5.10393e42i	−0.106237	+	0.184008i	0.808006	+	0.589174i	$0.200547\pi$
$992$	−2.71349e43	−	4.69990e43i	−0.964069	−	1.66982i
$993$	−9.65373e42			−0.338011
$994$	2.29440e42	+	1.46162e42i	0.0791712	+	0.0504351i
$995$	5.96072e43			2.02705
$996$	−1.42457e43	−	2.46742e43i	−0.477444	−	0.826957i
$997$	1.80273e42	−	3.12243e42i	0.0595459	−	0.103137i	−0.834716	−	0.550681i	$-0.814368\pi$
$997$	1.80273e42	−	3.12243e42i	0.0595459	−	0.103137i	0.894262	+	0.447545i	$0.147701\pi$
$998$	−3.73127e43	+	6.46275e43i	−1.21469	+	2.10390i
$999$	−1.40498e42	−	2.43349e42i	−0.0450785	−	0.0780782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.e.b.4.17	✓	40
7.2	even	3	inner	21.30.e.b.16.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.e.b.4.17	✓	40	1.1	even	1	trivial
21.30.e.b.16.17	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)

\(f(q)\)	\(=\)	\(q+(16582.6 + 28721.9i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-2.81530e8 + 4.87624e8i) q^{4} +(1.20484e10 + 2.08684e10i) q^{5} -1.58628e11 q^{6} +(1.59164e12 - 8.28603e11i) q^{7} -8.68562e11 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\)	\(q+(16582.6 + 28721.9i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-2.81530e8 + 4.87624e8i) q^{4} +(1.20484e10 + 2.08684e10i) q^{5} -1.58628e11 q^{6} +(1.59164e12 - 8.28603e11i) q^{7} -8.68562e11 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-3.99587e14 + 6.92105e14i) q^{10} +(7.46062e14 - 1.29222e15i) q^{11} +(-1.34655e15 - 2.33229e15i) q^{12} +1.20144e16 q^{13} +(5.01926e16 + 3.19746e16i) q^{14} -1.15254e17 q^{15} +(1.36742e17 + 2.36844e17i) q^{16} +(-4.62399e16 + 8.00898e16i) q^{17} +(3.79357e17 - 6.57065e17i) q^{18} +(-2.51134e18 - 4.34977e18i) q^{19} -1.35679e19 q^{20} +(-3.74169e17 + 8.57445e18i) q^{21} +4.94866e19 q^{22} +(3.02777e19 + 5.24425e19i) q^{23} +(2.07715e18 - 3.59773e18i) q^{24} +(-1.97195e20 + 3.41551e20i) q^{25} +(1.99230e20 + 3.45076e20i) q^{26} +1.09419e20 q^{27} +(-4.40478e19 + 1.00940e21i) q^{28} +1.71011e21 q^{29} +(-1.91121e21 - 3.31032e21i) q^{30} +(-2.84538e21 + 4.92834e21i) q^{31} +(-4.76824e21 + 8.25883e21i) q^{32} +(3.56839e21 + 6.18064e21i) q^{33} -3.06711e21 q^{34} +(3.64683e22 + 2.32317e22i) q^{35} +1.28810e22 q^{36} +(-1.28403e22 - 2.22401e22i) q^{37} +(8.32891e22 - 1.44261e23i) q^{38} +(-2.87322e22 + 4.97657e22i) q^{39} +(-1.04648e22 - 1.81255e22i) q^{40} +4.38272e23 q^{41} +(-2.52479e23 + 1.31440e23i) q^{42} -2.80589e23 q^{43} +(4.20078e23 + 7.27596e23i) q^{44} +(2.75628e23 - 4.77402e23i) q^{45} +(-1.00417e24 + 1.73927e24i) q^{46} +(8.39057e23 + 1.45329e24i) q^{47} -1.30807e24 q^{48} +(1.84674e24 - 2.63768e24i) q^{49} -1.30800e25 q^{50} +(-2.21164e23 - 3.83067e23i) q^{51} +(-3.38241e24 + 5.85851e24i) q^{52} +(-9.01576e23 + 1.56157e24i) q^{53} +(1.81445e24 + 3.14272e24i) q^{54} +3.59554e25 q^{55} +(-1.38244e24 + 7.19693e23i) q^{56} +2.40233e25 q^{57} +(2.83581e25 + 4.91177e25i) q^{58} +(-4.24260e25 + 7.34839e25i) q^{59} +(3.24475e25 - 5.62007e25i) q^{60} +(-2.58468e25 - 4.47679e25i) q^{61} -1.88735e26 q^{62} +(-3.46220e25 - 2.20555e25i) q^{63} -1.69453e26 q^{64} +(1.44754e26 + 2.50721e26i) q^{65} +(-1.18346e26 + 2.04982e26i) q^{66} +(-1.31952e26 + 2.28548e26i) q^{67} +(-2.60358e25 - 4.50953e25i) q^{68} -2.89634e26 q^{69} +(-6.25189e25 + 1.43268e27i) q^{70} +4.57120e25 q^{71} +(9.93496e24 + 1.72078e25i) q^{72} +(-7.88211e26 + 1.36522e27i) q^{73} +(4.25852e26 - 7.37597e26i) q^{74} +(-9.43176e26 - 1.63363e27i) q^{75} +2.82807e27 q^{76} +(1.16728e26 - 2.67494e27i) q^{77} -1.90582e27 q^{78} +(-1.69663e27 - 2.93865e27i) q^{79} +(-3.29504e27 + 5.70718e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(7.26769e27 + 1.25880e28i) q^{82} +1.05794e28 q^{83} +(-4.07577e27 - 2.59642e27i) q^{84} -2.22846e27 q^{85} +(-4.65289e27 - 8.05904e27i) q^{86} +(-4.08971e27 + 7.08359e27i) q^{87} +(-6.48001e26 + 1.12237e27i) q^{88} +(-4.73780e27 - 8.20611e27i) q^{89} +1.82825e28 q^{90} +(1.91226e28 - 9.95516e27i) q^{91} -3.40963e28 q^{92} +(-1.36093e28 - 2.35721e28i) q^{93} +(-2.78275e28 + 4.81986e28i) q^{94} +(6.05152e28 - 1.04815e29i) q^{95} +(-2.28063e28 - 3.95017e28i) q^{96} +1.80901e28 q^{97} +(1.06383e29 + 9.30231e27i) q^{98} -3.41350e28 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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Database

Properties

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