LMFDB - Embedded newform 29.18.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,18,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	29.a (trivial)

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:	yes
Analytic conductor:	$53.1344053299$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-39.6552 q^{2} +13037.0 q^{3} -129499. q^{4} -1.72282e6 q^{5} -516984. q^{6} -1.48112e7 q^{7} +1.03330e7 q^{8} +4.08230e7 q^{9} +O(q^{10})$	\(q-39.6552 q^{2} +13037.0 q^{3} -129499. q^{4} -1.72282e6 q^{5} -516984. q^{6} -1.48112e7 q^{7} +1.03330e7 q^{8} +4.08230e7 q^{9} +6.83187e7 q^{10} -1.36256e9 q^{11} -1.68828e9 q^{12} -2.08559e9 q^{13} +5.87342e8 q^{14} -2.24604e10 q^{15} +1.65640e10 q^{16} +1.13481e10 q^{17} -1.61884e9 q^{18} -3.19108e10 q^{19} +2.23104e11 q^{20} -1.93094e11 q^{21} +5.40326e10 q^{22} +1.33070e11 q^{23} +1.34711e11 q^{24} +2.20516e12 q^{25} +8.27046e10 q^{26} -1.15139e12 q^{27} +1.91805e12 q^{28} +5.00246e11 q^{29} +8.90670e11 q^{30} -6.48836e12 q^{31} -2.01122e12 q^{32} -1.77637e13 q^{33} -4.50011e11 q^{34} +2.55171e13 q^{35} -5.28655e12 q^{36} -3.15023e12 q^{37} +1.26543e12 q^{38} -2.71899e13 q^{39} -1.78019e13 q^{40} -3.85163e13 q^{41} +7.65717e12 q^{42} +9.98982e13 q^{43} +1.76451e14 q^{44} -7.03305e13 q^{45} -5.27690e12 q^{46} -1.87719e14 q^{47} +2.15945e14 q^{48} -1.32578e13 q^{49} -8.74461e13 q^{50} +1.47945e14 q^{51} +2.70083e14 q^{52} -1.38543e14 q^{53} +4.56586e13 q^{54} +2.34744e15 q^{55} -1.53045e14 q^{56} -4.16021e14 q^{57} -1.98374e13 q^{58} -5.88901e14 q^{59} +2.90861e15 q^{60} -1.12663e15 q^{61} +2.57297e14 q^{62} -6.04639e14 q^{63} -2.09132e15 q^{64} +3.59310e15 q^{65} +7.04422e14 q^{66} -4.30664e15 q^{67} -1.46957e15 q^{68} +1.73483e15 q^{69} -1.01188e15 q^{70} -1.20660e15 q^{71} +4.21824e14 q^{72} +4.73658e15 q^{73} +1.24923e14 q^{74} +2.87487e16 q^{75} +4.13244e15 q^{76} +2.01812e16 q^{77} +1.07822e15 q^{78} +1.77579e16 q^{79} -2.85368e16 q^{80} -2.02826e16 q^{81} +1.52737e15 q^{82} +3.58210e16 q^{83} +2.50056e16 q^{84} -1.95507e16 q^{85} -3.96148e15 q^{86} +6.52171e15 q^{87} -1.40793e16 q^{88} -3.89324e16 q^{89} +2.78897e15 q^{90} +3.08902e16 q^{91} -1.72325e16 q^{92} -8.45887e16 q^{93} +7.44405e15 q^{94} +5.49766e16 q^{95} -2.62202e16 q^{96} +1.54936e16 q^{97} +5.25740e14 q^{98} -5.56238e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) $ 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9} - 224469478 q^{10} + 1203139534 q^{11} - 5164251122 q^{12} + 3854339312 q^{13} + 25262272904 q^{14} + 28324474306 q^{15} + 196520815922 q^{16} + 76444714794 q^{17} + 75758949126 q^{18} + 246497292428 q^{19} - 46900976670 q^{20} + 360937126704 q^{21} - 275001533522 q^{22} + 213498528140 q^{23} - 451123453870 q^{24} + 3898884886997 q^{25} - 3609347694206 q^{26} - 2718903745978 q^{27} - 5946174617200 q^{28} + 10505174672181 q^{29} - 20237658929454 q^{30} + 16670029895798 q^{31} - 42141001912046 q^{32} - 7157109761394 q^{33} + 12785761151136 q^{34} + 46677934312888 q^{35} + 132137824374868 q^{36} + 53445659988410 q^{37} + 76581637956388 q^{38} + 79233849032530 q^{39} + 193617444734146 q^{40} - 20814769309298 q^{41} + 76690667258352 q^{42} + 185498647364454 q^{43} + 315429066899678 q^{44} - 486270821438526 q^{45} + 261474367677132 q^{46} + 389503471719450 q^{47} - 101509672247630 q^{48} + 730079062141437 q^{49} + 14\!\cdots\!54 q^{50}+ \cdots - 95\!\cdots\!64 q^{99}+O(q^{100}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9 - 224469478 * q^10 + 1203139534 * q^11 - 5164251122 * q^12 + 3854339312 * q^13 + 25262272904 * q^14 + 28324474306 * q^15 + 196520815922 * q^16 + 76444714794 * q^17 + 75758949126 * q^18 + 246497292428 * q^19 - 46900976670 * q^20 + 360937126704 * q^21 - 275001533522 * q^22 + 213498528140 * q^23 - 451123453870 * q^24 + 3898884886997 * q^25 - 3609347694206 * q^26 - 2718903745978 * q^27 - 5946174617200 * q^28 + 10505174672181 * q^29 - 20237658929454 * q^30 + 16670029895798 * q^31 - 42141001912046 * q^32 - 7157109761394 * q^33 + 12785761151136 * q^34 + 46677934312888 * q^35 + 132137824374868 * q^36 + 53445659988410 * q^37 + 76581637956388 * q^38 + 79233849032530 * q^39 + 193617444734146 * q^40 - 20814769309298 * q^41 + 76690667258352 * q^42 + 185498647364454 * q^43 + 315429066899678 * q^44 - 486270821438526 * q^45 + 261474367677132 * q^46 + 389503471719450 * q^47 - 101509672247630 * q^48 + 730079062141437 * q^49 + 1482269666368354 * q^50 + 718238208473988 * q^51 + 1966802817157170 * q^52 + 747441265526156 * q^53 + 5692893333117030 * q^54 + 1639109418219546 * q^55 + 5657219329125240 * q^56 + 4694352396864932 * q^57 + 128063081718016 * q^58 + 5280258638332960 * q^59 + 15251367906033378 * q^60 + 5813675353074254 * q^61 + 6242066590947250 * q^62 + 10947760075450368 * q^63 + 24583792057508902 * q^64 + 19190799243789974 * q^65 + 41877805444482390 * q^66 + 13420580230958268 * q^67 + 24771837384165388 * q^68 + 30973047049935252 * q^69 + 8505088080182440 * q^70 + 4824462822979508 * q^71 + 1180071997284592 * q^72 + 11228916281304662 * q^73 - 89132715356772 * q^74 + 59161419576630296 * q^75 + 57466858643173460 * q^76 + 58741564492720064 * q^77 + 142050530910210210 * q^78 + 71718598015696758 * q^79 + 48350023652407550 * q^80 + 75805931446703569 * q^81 + 188661890754420812 * q^82 + 50769377111735608 * q^83 + 198832046985593048 * q^84 + 53422044849490784 * q^85 + 35014892323844118 * q^86 + 11988905533023326 * q^87 + 37459283979085258 * q^88 - 70981414576978018 * q^89 + 57211029866143724 * q^90 + 112933943315157320 * q^91 - 103019729095759724 * q^92 - 350358290646906646 * q^93 - 150286322409612578 * q^94 - 102561321856584476 * q^95 - 213770098354021866 * q^96 - 130930167251505210 * q^97 - 537387515497557296 * q^98 - 95267700931431064 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−39.6552	−0.109533	−0.0547665	−	0.998499i	$-0.517441\pi$
$2$	−39.6552	−0.109533	−0.0547665	+	0.998499i	$0.517441\pi$
$3$	13037.0	1.14722	0.573610	−	0.819129i	$-0.305543\pi$
$3$	13037.0	1.14722	0.573610	+	0.819129i	$0.305543\pi$
$4$	−129499.	−0.988003
$5$	−1.72282e6	−1.97240	−0.986199	−	0.165566i	$-0.947055\pi$
$5$	−1.72282e6	−1.97240	−0.986199	+	0.165566i	$0.947055\pi$
$6$	−516984.	−0.125658
$7$	−1.48112e7	−0.971087	−0.485543	−	0.874213i	$-0.661378\pi$
$7$	−1.48112e7	−0.971087	−0.485543	+	0.874213i	$0.661378\pi$
$8$	1.03330e7	0.217752
$9$	4.08230e7	0.316114
$10$	6.83187e7	0.216043
$11$	−1.36256e9	−1.91654	−0.958270	−	0.285864i	$-0.907720\pi$
$11$	−1.36256e9	−1.91654	−0.958270	+	0.285864i	$0.907720\pi$
$12$	−1.68828e9	−1.13346
$13$	−2.08559e9	−0.709106	−0.354553	−	0.935036i	$-0.615367\pi$
$13$	−2.08559e9	−0.709106	−0.354553	+	0.935036i	$0.615367\pi$
$14$	5.87342e8	0.106366
$15$	−2.24604e10	−2.26277
$16$	1.65640e10	0.964152
$17$	1.13481e10	0.394555	0.197278	−	0.980348i	$-0.436790\pi$
$17$	1.13481e10	0.394555	0.197278	+	0.980348i	$0.436790\pi$
$18$	−1.61884e9	−0.0346249
$19$	−3.19108e10	−0.431055	−0.215527	−	0.976498i	$-0.569147\pi$
$19$	−3.19108e10	−0.431055	−0.215527	+	0.976498i	$0.569147\pi$
$20$	2.23104e11	1.94873
$21$	−1.93094e11	−1.11405
$22$	5.40326e10	0.209924
$23$	1.33070e11	0.354317	0.177159	−	0.984182i	$-0.443309\pi$
$23$	1.33070e11	0.354317	0.177159	+	0.984182i	$0.443309\pi$
$24$	1.34711e11	0.249809
$25$	2.20516e12	2.89035
$26$	8.27046e10	0.0776705
$27$	−1.15139e12	−0.784568
$28$	1.91805e12	0.959436
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	8.90670e11	0.247848
$31$	−6.48836e12	−1.36635	−0.683173	−	0.730257i	$-0.739400\pi$
$31$	−6.48836e12	−1.36635	−0.683173	+	0.730257i	$0.739400\pi$
$32$	−2.01122e12	−0.323358
$33$	−1.77637e13	−2.19869
$34$	−4.50011e11	−0.0432168
$35$	2.55171e13	1.91537
$36$	−5.28655e12	−0.312321
$37$	−3.15023e12	−0.147444	−0.0737220	−	0.997279i	$-0.523488\pi$
$37$	−3.15023e12	−0.147444	−0.0737220	+	0.997279i	$0.523488\pi$
$38$	1.26543e12	0.0472147
$39$	−2.71899e13	−0.813501
$40$	−1.78019e13	−0.429493
$41$	−3.85163e13	−0.753325	−0.376662	−	0.926351i	$-0.622928\pi$
$41$	−3.85163e13	−0.753325	−0.376662	+	0.926351i	$0.622928\pi$
$42$	7.65717e12	0.122025
$43$	9.98982e13	1.30339	0.651697	−	0.758479i	$-0.274057\pi$
$43$	9.98982e13	1.30339	0.651697	+	0.758479i	$0.274057\pi$
$44$	1.76451e14	1.89355
$45$	−7.03305e13	−0.623502
$46$	−5.27690e12	−0.0388094
$47$	−1.87719e14	−1.14995	−0.574973	−	0.818172i	$-0.694988\pi$
$47$	−1.87719e14	−1.14995	−0.574973	+	0.818172i	$0.694988\pi$
$48$	2.15945e14	1.10609
$49$	−1.32578e13	−0.0569907
$50$	−8.74461e13	−0.316589
$51$	1.47945e14	0.452641
$52$	2.70083e14	0.700599
$53$	−1.38543e14	−0.305661	−0.152831	−	0.988252i	$-0.548839\pi$
$53$	−1.38543e14	−0.305661	−0.152831	+	0.988252i	$0.548839\pi$
$54$	4.56586e13	0.0859361
$55$	2.34744e15	3.78018
$56$	−1.53045e14	−0.211456
$57$	−4.16021e14	−0.494515
$58$	−1.98374e13	−0.0203398
$59$	−5.88901e14	−0.522156	−0.261078	−	0.965318i	$-0.584078\pi$
$59$	−5.88901e14	−0.522156	−0.261078	+	0.965318i	$0.584078\pi$
$60$	2.90861e15	2.23563
$61$	−1.12663e15	−0.752449	−0.376225	−	0.926528i	$-0.622778\pi$
$61$	−1.12663e15	−0.752449	−0.376225	+	0.926528i	$0.622778\pi$
$62$	2.57297e14	0.149660
$63$	−6.04639e14	−0.306974
$64$	−2.09132e15	−0.928733
$65$	3.59310e15	1.39864
$66$	7.04422e14	0.240829
$67$	−4.30664e15	−1.29569	−0.647847	−	0.761771i	$-0.724330\pi$
$67$	−4.30664e15	−1.29569	−0.647847	+	0.761771i	$0.724330\pi$
$68$	−1.46957e15	−0.389821
$69$	1.73483e15	0.406480
$70$	−1.01188e15	−0.209796
$71$	−1.20660e15	−0.221752	−0.110876	−	0.993834i	$-0.535366\pi$
$71$	−1.20660e15	−0.221752	−0.110876	+	0.993834i	$0.535366\pi$
$72$	4.21824e14	0.0688343
$73$	4.73658e15	0.687418	0.343709	−	0.939076i	$-0.388317\pi$
$73$	4.73658e15	0.687418	0.343709	+	0.939076i	$0.388317\pi$
$74$	1.24923e14	0.0161500
$75$	2.87487e16	3.31587
$76$	4.13244e15	0.425883
$77$	2.01812e16	1.86113
$78$	1.07822e15	0.0891052
$79$	1.77579e16	1.31692	0.658461	−	0.752615i	$-0.271208\pi$
$79$	1.77579e16	1.31692	0.658461	+	0.752615i	$0.271208\pi$
$80$	−2.85368e16	−1.90169
$81$	−2.02826e16	−1.21619
$82$	1.52737e15	0.0825139
$83$	3.58210e16	1.74572	0.872858	−	0.487975i	$-0.162264\pi$
$83$	3.58210e16	1.74572	0.872858	+	0.487975i	$0.162264\pi$
$84$	2.50056e16	1.10068
$85$	−1.95507e16	−0.778219
$86$	−3.96148e15	−0.142765
$87$	6.52171e15	0.213033
$88$	−1.40793e16	−0.417330
$89$	−3.89324e16	−1.04832	−0.524162	−	0.851618i	$-0.675622\pi$
$89$	−3.89324e16	−1.04832	−0.524162	+	0.851618i	$0.675622\pi$
$90$	2.78897e15	0.0682940
$91$	3.08902e16	0.688604
$92$	−1.72325e16	−0.350066
$93$	−8.45887e16	−1.56750
$94$	7.44405e15	0.125957
$95$	5.49766e16	0.850212
$96$	−2.62202e16	−0.370963
$97$	1.54936e16	0.200721	0.100360	−	0.994951i	$-0.468000\pi$
$97$	1.54936e16	0.200721	0.100360	+	0.994951i	$0.468000\pi$
$98$	5.25740e14	0.00624237
$99$	−5.56238e16	−0.605844
$100$	−2.85567e17	−2.85567
$101$	7.14290e16	0.656361	0.328181	−	0.944615i	$-0.393565\pi$
$101$	7.14290e16	0.656361	0.328181	+	0.944615i	$0.393565\pi$
$102$	−5.86679e15	−0.0495792
$103$	1.44387e17	1.12309	0.561543	−	0.827448i	$-0.310208\pi$
$103$	1.44387e17	1.12309	0.561543	+	0.827448i	$0.310208\pi$
$104$	−2.15505e16	−0.154409
$105$	3.32666e17	2.19735
$106$	5.49396e15	0.0334800
$107$	−2.55133e16	−0.143551	−0.0717753	−	0.997421i	$-0.522866\pi$
$107$	−2.55133e16	−0.143551	−0.0717753	+	0.997421i	$0.522866\pi$
$108$	1.49104e17	0.775155
$109$	−3.15962e17	−1.51883	−0.759417	−	0.650604i	$-0.774516\pi$
$109$	−3.15962e17	−1.51883	−0.759417	+	0.650604i	$0.774516\pi$
$110$	−9.30883e16	−0.414054
$111$	−4.10695e16	−0.169151
$112$	−2.45333e17	−0.936275
$113$	−3.72174e17	−1.31698	−0.658490	−	0.752589i	$-0.728805\pi$
$113$	−3.72174e17	−1.31698	−0.658490	+	0.752589i	$0.728805\pi$
$114$	1.64974e16	0.0541657
$115$	−2.29255e17	−0.698855
$116$	−6.47816e16	−0.183467
$117$	−8.51402e16	−0.224158
$118$	2.33530e16	0.0571933
$119$	−1.68080e17	−0.383147
$120$	−2.32083e17	−0.492723
$121$	1.35112e18	2.67313
$122$	4.46767e16	0.0824180
$123$	−5.02137e17	−0.864229
$124$	8.40239e17	1.34995
$125$	−2.48469e18	−3.72853
$126$	2.39770e16	0.0336237
$127$	−1.23535e18	−1.61979	−0.809893	−	0.586577i	$-0.800475\pi$
$127$	−1.23535e18	−1.61979	−0.809893	+	0.586577i	$0.800475\pi$
$128$	3.46546e17	0.425085
$129$	1.30237e18	1.49528
$130$	−1.42485e17	−0.153197
$131$	−1.29667e18	−1.30624	−0.653121	−	0.757254i	$-0.726541\pi$
$131$	−1.29667e18	−1.30624	−0.653121	+	0.757254i	$0.726541\pi$
$132$	2.30039e18	2.17231
$133$	4.72639e17	0.418592
$134$	1.70780e17	0.141921
$135$	1.98364e18	1.54748
$136$	1.17260e17	0.0859151
$137$	−9.73668e17	−0.670326	−0.335163	−	0.942160i	$-0.608791\pi$
$137$	−9.73668e17	−0.670326	−0.335163	+	0.942160i	$0.608791\pi$
$138$	−6.87949e16	−0.0445230
$139$	2.80477e18	1.70715	0.853575	−	0.520971i	$-0.174430\pi$
$139$	2.80477e18	1.70715	0.853575	+	0.520971i	$0.174430\pi$
$140$	−3.30445e18	−1.89239
$141$	−2.44730e18	−1.31924
$142$	4.78480e16	0.0242892
$143$	2.84175e18	1.35903
$144$	6.76191e17	0.304781
$145$	−8.61834e17	−0.366265
$146$	−1.87830e17	−0.0752949
$147$	−1.72842e17	−0.0653809
$148$	4.07952e17	0.145675
$149$	1.72769e18	0.582617	0.291308	−	0.956629i	$-0.405909\pi$
$149$	1.72769e18	0.582617	0.291308	+	0.956629i	$0.405909\pi$
$150$	−1.14003e18	−0.363197
$151$	−2.18737e18	−0.658594	−0.329297	−	0.944226i	$-0.606812\pi$
$151$	−2.18737e18	−0.658594	−0.329297	+	0.944226i	$0.606812\pi$
$152$	−3.29735e17	−0.0938630
$153$	4.63263e17	0.124724
$154$	−8.00289e17	−0.203855
$155$	1.11783e19	2.69498
$156$	3.52107e18	0.803741
$157$	−7.41786e17	−0.160373	−0.0801866	−	0.996780i	$-0.525552\pi$
$157$	−7.41786e17	−0.160373	−0.0801866	+	0.996780i	$0.525552\pi$
$158$	−7.04191e17	−0.144246
$159$	−1.80619e18	−0.350661
$160$	3.46496e18	0.637791
$161$	−1.97093e18	−0.344073
$162$	8.04308e17	0.133212
$163$	1.70946e18	0.268698	0.134349	−	0.990934i	$-0.457106\pi$
$163$	1.70946e18	0.268698	0.134349	+	0.990934i	$0.457106\pi$
$164$	4.98784e18	0.744287
$165$	3.06036e19	4.33670
$166$	−1.42049e18	−0.191213
$167$	−1.75628e18	−0.224649	−0.112324	−	0.993672i	$-0.535830\pi$
$167$	−1.75628e18	−0.224649	−0.112324	+	0.993672i	$0.535830\pi$
$168$	−1.99524e18	−0.242586
$169$	−4.30071e18	−0.497168
$170$	7.75288e17	0.0852407
$171$	−1.30269e18	−0.136262
$172$	−1.29368e19	−1.28776
$173$	5.23272e18	0.495833	0.247917	−	0.968781i	$-0.420254\pi$
$173$	5.23272e18	0.495833	0.247917	+	0.968781i	$0.420254\pi$
$174$	−2.58619e17	−0.0233342
$175$	−3.26612e19	−2.80678
$176$	−2.25695e19	−1.84784
$177$	−7.67750e18	−0.599028
$178$	1.54387e18	0.114826
$179$	−4.74304e18	−0.336362	−0.168181	−	0.985756i	$-0.553789\pi$
$179$	−4.74304e18	−0.336362	−0.168181	+	0.985756i	$0.553789\pi$
$180$	9.10777e18	0.616021
$181$	−1.91932e19	−1.23845	−0.619225	−	0.785213i	$-0.712553\pi$
$181$	−1.91932e19	−1.23845	−0.619225	+	0.785213i	$0.712553\pi$
$182$	−1.22496e18	−0.0754248
$183$	−1.46878e19	−0.863225
$184$	1.37501e18	0.0771533
$185$	5.42727e18	0.290818
$186$	3.35438e18	0.171693
$187$	−1.54625e19	−0.756181
$188$	2.43096e19	1.13615
$189$	1.70535e19	0.761884
$190$	−2.18011e18	−0.0931262
$191$	−3.41661e18	−0.139576	−0.0697882	−	0.997562i	$-0.522232\pi$
$191$	−3.41661e18	−0.139576	−0.0697882	+	0.997562i	$0.522232\pi$
$192$	−2.72645e19	−1.06546
$193$	3.35009e19	1.25262	0.626310	−	0.779574i	$-0.284564\pi$
$193$	3.35009e19	1.25262	0.626310	+	0.779574i	$0.284564\pi$
$194$	−6.14402e17	−0.0219856
$195$	4.68432e19	1.60455
$196$	1.71688e18	0.0563070
$197$	4.66487e18	0.146513	0.0732565	−	0.997313i	$-0.476661\pi$
$197$	4.66487e18	0.146513	0.0732565	+	0.997313i	$0.476661\pi$
$198$	2.20577e18	0.0663600
$199$	−3.56100e19	−1.02641	−0.513204	−	0.858266i	$-0.671542\pi$
$199$	−3.56100e19	−1.02641	−0.513204	+	0.858266i	$0.671542\pi$
$200$	2.27860e19	0.629379
$201$	−5.61456e19	−1.48645
$202$	−2.83253e18	−0.0718932
$203$	−7.40927e18	−0.180326
$204$	−1.91588e19	−0.447211
$205$	6.63566e19	1.48586
$206$	−5.72571e18	−0.123015
$207$	5.43230e18	0.112005
$208$	−3.45458e19	−0.683686
$209$	4.34804e19	0.826134
$210$	−1.31919e19	−0.240682
$211$	−3.47221e19	−0.608422	−0.304211	−	0.952605i	$-0.598393\pi$
$211$	−3.47221e19	−0.608422	−0.304211	+	0.952605i	$0.598393\pi$
$212$	1.79413e19	0.301994
$213$	−1.57305e19	−0.254399
$214$	1.01174e18	0.0157235
$215$	−1.72106e20	−2.57081
$216$	−1.18973e19	−0.170841
$217$	9.61006e19	1.32684
$218$	1.25295e19	0.166362
$219$	6.17508e19	0.788619
$220$	−3.03993e20	−3.73483
$221$	−2.36676e19	−0.279782
$222$	1.62862e18	0.0185276
$223$	−1.50583e20	−1.64887	−0.824434	−	0.565958i	$-0.808506\pi$
$223$	−1.50583e20	−1.64887	−0.824434	+	0.565958i	$0.808506\pi$
$224$	2.97886e19	0.314009
$225$	9.00213e19	0.913679
$226$	1.47586e19	0.144253
$227$	1.37451e20	1.29398	0.646989	−	0.762499i	$-0.276028\pi$
$227$	1.37451e20	1.29398	0.646989	+	0.762499i	$0.276028\pi$
$228$	5.38745e19	0.488582
$229$	2.51294e19	0.219574	0.109787	−	0.993955i	$-0.464983\pi$
$229$	2.51294e19	0.219574	0.109787	+	0.993955i	$0.464983\pi$
$230$	9.09114e18	0.0765476
$231$	2.63102e20	2.13512
$232$	5.16905e18	0.0404355
$233$	−1.35837e19	−0.102445	−0.0512226	−	0.998687i	$-0.516312\pi$
$233$	−1.35837e19	−0.102445	−0.0512226	+	0.998687i	$0.516312\pi$
$234$	3.37625e18	0.0245527
$235$	3.23407e20	2.26815
$236$	7.62624e19	0.515892
$237$	2.31509e20	1.51080
$238$	6.66522e18	0.0419673
$239$	−1.51157e20	−0.918429	−0.459214	−	0.888325i	$-0.651869\pi$
$239$	−1.51157e20	−0.918429	−0.459214	+	0.888325i	$0.651869\pi$
$240$	−3.72033e20	−2.18166
$241$	8.59255e19	0.486382	0.243191	−	0.969978i	$-0.421806\pi$
$241$	8.59255e19	0.486382	0.243191	+	0.969978i	$0.421806\pi$
$242$	−5.35791e19	−0.292796
$243$	−1.15733e20	−0.610664
$244$	1.45898e20	0.743422
$245$	2.28408e19	0.112408
$246$	1.99123e19	0.0946616
$247$	6.65531e19	0.305664
$248$	−6.70443e19	−0.297524
$249$	4.66998e20	2.00272
$250$	9.85308e19	0.408397
$251$	2.06878e20	0.828872	0.414436	−	0.910078i	$-0.363979\pi$
$251$	2.06878e20	0.828872	0.414436	+	0.910078i	$0.363979\pi$
$252$	7.83004e19	0.303291
$253$	−1.81315e20	−0.679064
$254$	4.89879e19	0.177420
$255$	−2.54883e20	−0.892789
$256$	2.60371e20	0.882172
$257$	−1.34320e19	−0.0440260	−0.0220130	−	0.999758i	$-0.507008\pi$
$257$	−1.34320e19	−0.0440260	−0.0220130	+	0.999758i	$0.507008\pi$
$258$	−5.16458e19	−0.163782
$259$	4.66587e19	0.143181
$260$	−4.65305e20	−1.38186
$261$	2.04215e19	0.0587008
$262$	5.14197e19	0.143077
$263$	−3.39929e20	−0.915723	−0.457861	−	0.889024i	$-0.651384\pi$
$263$	−3.39929e20	−0.915723	−0.457861	+	0.889024i	$0.651384\pi$
$264$	−1.83552e20	−0.478770
$265$	2.38685e20	0.602885
$266$	−1.87426e19	−0.0458496
$267$	−5.07561e20	−1.20266
$268$	5.57707e20	1.28015
$269$	6.48823e20	1.44289	0.721443	−	0.692474i	$-0.243479\pi$
$269$	6.48823e20	1.44289	0.721443	+	0.692474i	$0.243479\pi$
$270$	−7.86615e19	−0.169500
$271$	2.67341e20	0.558246	0.279123	−	0.960255i	$-0.409956\pi$
$271$	2.67341e20	0.558246	0.279123	+	0.960255i	$0.409956\pi$
$272$	1.87970e20	0.380411
$273$	4.02716e20	0.789980
$274$	3.86110e19	0.0734228
$275$	−3.00467e21	−5.53948
$276$	−2.24659e20	−0.401603
$277$	−2.37458e20	−0.411631	−0.205815	−	0.978591i	$-0.565985\pi$
$277$	−2.37458e20	−0.411631	−0.205815	+	0.978591i	$0.565985\pi$
$278$	−1.11224e20	−0.186989
$279$	−2.64874e20	−0.431920
$280$	2.63668e20	0.417075
$281$	−3.89911e19	−0.0598359	−0.0299180	−	0.999552i	$-0.509525\pi$
$281$	−3.89911e19	−0.0598359	−0.0299180	+	0.999552i	$0.509525\pi$
$282$	9.70480e19	0.144500
$283$	3.73191e20	0.539196	0.269598	−	0.962973i	$-0.413109\pi$
$283$	3.73191e20	0.539196	0.269598	+	0.962973i	$0.413109\pi$
$284$	1.56254e20	0.219092
$285$	7.16729e20	0.975380
$286$	−1.12690e20	−0.148859
$287$	5.70475e20	0.731543
$288$	−8.21038e19	−0.102218
$289$	−6.98461e20	−0.844326
$290$	3.41762e19	0.0401181
$291$	2.01990e20	0.230271
$292$	−6.13385e20	−0.679170
$293$	−9.30414e20	−1.00069	−0.500347	−	0.865825i	$-0.666794\pi$
$293$	−9.30414e20	−1.00069	−0.500347	+	0.865825i	$0.666794\pi$
$294$	6.85406e18	0.00716137
$295$	1.01457e21	1.02990
$296$	−3.25513e19	−0.0321062
$297$	1.56884e21	1.50366
$298$	−6.85119e19	−0.0638157
$299$	−2.77529e20	−0.251249
$300$	−3.72294e21	−3.27609
$301$	−1.47962e21	−1.26571
$302$	8.67405e19	0.0721378
$303$	9.31219e20	0.752990
$304$	−5.28571e20	−0.415602
$305$	1.94098e21	1.48413
$306$	−1.83708e19	−0.0136614
$307$	1.91006e21	1.38156	0.690780	−	0.723065i	$-0.257267\pi$
$307$	1.91006e21	1.38156	0.690780	+	0.723065i	$0.257267\pi$
$308$	−2.61346e21	−1.83880
$309$	1.88238e21	1.28843
$310$	−4.43276e20	−0.295189
$311$	−8.70765e20	−0.564206	−0.282103	−	0.959384i	$-0.591032\pi$
$311$	−8.70765e20	−0.564206	−0.282103	+	0.959384i	$0.591032\pi$
$312$	−2.80953e20	−0.177141
$313$	1.21509e21	0.745558	0.372779	−	0.927920i	$-0.378405\pi$
$313$	1.21509e21	0.745558	0.372779	+	0.927920i	$0.378405\pi$
$314$	2.94157e19	0.0175662
$315$	1.04168e21	0.605474
$316$	−2.29963e21	−1.30112
$317$	1.32074e21	0.727468	0.363734	−	0.931503i	$-0.381502\pi$
$317$	1.32074e21	0.727468	0.363734	+	0.931503i	$0.381502\pi$
$318$	7.16246e19	0.0384089
$319$	−6.81616e20	−0.355893
$320$	3.60297e21	1.83183
$321$	−3.32617e20	−0.164684
$322$	7.81574e19	0.0376873
$323$	−3.62128e20	−0.170075
$324$	2.62658e21	1.20159
$325$	−4.59908e21	−2.04957
$326$	−6.77890e19	−0.0294313
$327$	−4.11920e21	−1.74244
$328$	−3.97990e20	−0.164038
$329$	2.78036e21	1.11670
$330$	−1.21359e21	−0.475011
$331$	−3.80635e19	−0.0145201	−0.00726007	−	0.999974i	$-0.502311\pi$
$331$	−3.80635e19	−0.0145201	−0.00726007	+	0.999974i	$0.502311\pi$
$332$	−4.63880e21	−1.72477
$333$	−1.28602e20	−0.0466090
$334$	6.96456e19	0.0246064
$335$	7.41955e21	2.55562
$336$	−3.19841e21	−1.07411
$337$	3.51161e21	1.14988	0.574940	−	0.818196i	$-0.305025\pi$
$337$	3.51161e21	1.14988	0.574940	+	0.818196i	$0.305025\pi$
$338$	1.70545e20	0.0544563
$339$	−4.85203e21	−1.51087
$340$	2.53181e21	0.768883
$341$	8.84078e21	2.61866
$342$	5.16586e19	0.0149252
$343$	3.64191e21	1.02643
$344$	1.03225e21	0.283817
$345$	−2.98879e21	−0.801740
$346$	−2.07504e20	−0.0543101
$347$	5.47357e21	1.39788	0.698940	−	0.715180i	$-0.253655\pi$
$347$	5.47357e21	1.39788	0.698940	+	0.715180i	$0.253655\pi$
$348$	−8.44558e20	−0.210478
$349$	−2.62794e21	−0.639144	−0.319572	−	0.947562i	$-0.603539\pi$
$349$	−2.62794e21	−0.639144	−0.319572	+	0.947562i	$0.603539\pi$
$350$	1.29519e21	0.307435
$351$	2.40133e21	0.556342
$352$	2.74040e21	0.619729
$353$	−2.46885e21	−0.545016	−0.272508	−	0.962154i	$-0.587853\pi$
$353$	−2.46885e21	−0.545016	−0.272508	+	0.962154i	$0.587853\pi$
$354$	3.04453e20	0.0656133
$355$	2.07876e21	0.437384
$356$	5.04172e21	1.03575
$357$	−2.19125e21	−0.439554
$358$	1.88086e20	0.0368427
$359$	−4.74456e21	−0.907597	−0.453798	−	0.891104i	$-0.649931\pi$
$359$	−4.74456e21	−0.907597	−0.453798	+	0.891104i	$0.649931\pi$
$360$	−7.26726e20	−0.135769
$361$	−4.46209e21	−0.814192
$362$	7.61108e20	0.135651
$363$	1.76146e22	3.06667
$364$	−4.00027e21	−0.680342
$365$	−8.16027e21	−1.35586
$366$	5.82449e20	0.0945516
$367$	8.71292e21	1.38198	0.690991	−	0.722864i	$-0.257175\pi$
$367$	8.71292e21	1.38198	0.690991	+	0.722864i	$0.257175\pi$
$368$	2.20417e21	0.341616
$369$	−1.57235e21	−0.238136
$370$	−2.15219e20	−0.0318542
$371$	2.05200e21	0.296824
$372$	1.09542e22	1.54869
$373$	6.57987e21	0.909269	0.454634	−	0.890678i	$-0.349770\pi$
$373$	6.57987e21	0.909269	0.454634	+	0.890678i	$0.349770\pi$
$374$	6.13168e20	0.0828267
$375$	−3.23929e22	−4.27744
$376$	−1.93971e21	−0.250403
$377$	−1.04331e21	−0.131678
$378$	−6.76260e20	−0.0834514
$379$	6.70258e21	0.808739	0.404370	−	0.914596i	$-0.367491\pi$
$379$	6.70258e21	0.808739	0.404370	+	0.914596i	$0.367491\pi$
$380$	−7.11944e21	−0.840011
$381$	−1.61052e22	−1.85825
$382$	1.35486e20	0.0152882
$383$	5.52437e21	0.609668	0.304834	−	0.952406i	$-0.401399\pi$
$383$	5.52437e21	0.609668	0.304834	+	0.952406i	$0.401399\pi$
$384$	4.51791e21	0.487666
$385$	−3.47686e22	−3.67088
$386$	−1.32848e21	−0.137203
$387$	4.07814e21	0.412021
$388$	−2.00641e21	−0.198313
$389$	−5.40059e21	−0.522240	−0.261120	−	0.965306i	$-0.584092\pi$
$389$	−5.40059e21	−0.522240	−0.261120	+	0.965306i	$0.584092\pi$
$390$	−1.85758e21	−0.175751
$391$	1.51009e21	0.139798
$392$	−1.36993e20	−0.0124098
$393$	−1.69047e22	−1.49855
$394$	−1.84986e20	−0.0160480
$395$	−3.05936e22	−2.59749
$396$	7.20325e21	0.598576
$397$	2.05094e22	1.66814	0.834072	−	0.551655i	$-0.186004\pi$
$397$	2.05094e22	1.66814	0.834072	+	0.551655i	$0.186004\pi$
$398$	1.41212e21	0.112426
$399$	6.16179e21	0.480217
$400$	3.65263e22	2.78674
$401$	6.02787e21	0.450233	0.225116	−	0.974332i	$-0.427724\pi$
$401$	6.02787e21	0.450233	0.225116	+	0.974332i	$0.427724\pi$
$402$	2.22646e21	0.162815
$403$	1.35321e22	0.968884
$404$	−9.25002e21	−0.648486
$405$	3.49432e22	2.39880
$406$	2.93816e20	0.0197517
$407$	4.29237e21	0.282582
$408$	1.52872e21	0.0985635
$409$	−6.57778e21	−0.415366	−0.207683	−	0.978196i	$-0.566592\pi$
$409$	−6.57778e21	−0.415366	−0.207683	+	0.978196i	$0.566592\pi$
$410$	−2.63138e21	−0.162750
$411$	−1.26937e22	−0.769012
$412$	−1.86981e22	−1.10961
$413$	8.72236e21	0.507059
$414$	−2.15419e20	−0.0122682
$415$	−6.17130e22	−3.44325
$416$	4.19458e21	0.229295
$417$	3.65658e22	1.95848
$418$	−1.72422e21	−0.0904889
$419$	−3.38114e22	−1.73878	−0.869388	−	0.494130i	$-0.835487\pi$
$419$	−3.38114e22	−1.73878	−0.869388	+	0.494130i	$0.835487\pi$
$420$	−4.30800e22	−2.17099
$421$	1.24898e22	0.616820	0.308410	−	0.951253i	$-0.400203\pi$
$421$	1.24898e22	0.616820	0.308410	+	0.951253i	$0.400203\pi$
$422$	1.37691e21	0.0666423
$423$	−7.66326e21	−0.363514
$424$	−1.43157e21	−0.0665583
$425$	2.50244e22	1.14040
$426$	6.23794e20	0.0278650
$427$	1.66868e22	0.730693
$428$	3.30396e21	0.141828
$429$	3.70479e22	1.55911
$430$	6.82491e21	0.281589
$431$	−3.83802e22	−1.55257	−0.776284	−	0.630383i	$-0.782898\pi$
$431$	−3.83802e22	−1.55257	−0.776284	+	0.630383i	$0.782898\pi$
$432$	−1.90716e22	−0.756443
$433$	−1.55018e22	−0.602886	−0.301443	−	0.953484i	$-0.597468\pi$
$433$	−1.55018e22	−0.602886	−0.301443	+	0.953484i	$0.597468\pi$
$434$	−3.81089e21	−0.145333
$435$	−1.12357e22	−0.420187
$436$	4.09170e22	1.50061
$437$	−4.24636e21	−0.152730
$438$	−2.44874e21	−0.0863798
$439$	−1.54978e22	−0.536194	−0.268097	−	0.963392i	$-0.586395\pi$
$439$	−1.54978e22	−0.536194	−0.268097	+	0.963392i	$0.586395\pi$
$440$	2.42562e22	0.823141
$441$	−5.41222e20	−0.0180155
$442$	9.38541e20	0.0306453
$443$	−1.49954e22	−0.480315	−0.240157	−	0.970734i	$-0.577199\pi$
$443$	−1.49954e22	−0.480315	−0.240157	+	0.970734i	$0.577199\pi$
$444$	5.31847e21	0.167121
$445$	6.70734e22	2.06771
$446$	5.97141e21	0.180605
$447$	2.25239e22	0.668389
$448$	3.09751e22	0.901880
$449$	−5.48234e22	−1.56629	−0.783144	−	0.621840i	$-0.786385\pi$
$449$	−5.48234e22	−1.56629	−0.783144	+	0.621840i	$0.786385\pi$
$450$	−3.56981e21	−0.100078
$451$	5.24808e22	1.44378
$452$	4.81964e22	1.30118
$453$	−2.85167e22	−0.755552
$454$	−5.45063e21	−0.141733
$455$	−5.32183e22	−1.35820
$456$	−4.29875e21	−0.107681
$457$	1.29767e22	0.319062	0.159531	−	0.987193i	$-0.449002\pi$
$457$	1.29767e22	0.319062	0.159531	+	0.987193i	$0.449002\pi$
$458$	−9.96511e20	−0.0240506
$459$	−1.30661e22	−0.309555
$460$	2.96884e22	0.690470
$461$	−5.04849e22	−1.15267	−0.576333	−	0.817215i	$-0.695517\pi$
$461$	−5.04849e22	−1.15267	−0.576333	+	0.817215i	$0.695517\pi$
$462$	−1.04334e22	−0.233866
$463$	1.59633e21	0.0351306	0.0175653	−	0.999846i	$-0.494409\pi$
$463$	1.59633e21	0.0351306	0.0175653	+	0.999846i	$0.494409\pi$
$464$	8.28608e21	0.179038
$465$	1.45731e23	3.09173
$466$	5.38663e20	0.0112211
$467$	3.79982e22	0.777266	0.388633	−	0.921393i	$-0.372947\pi$
$467$	3.79982e22	0.777266	0.388633	+	0.921393i	$0.372947\pi$
$468$	1.10256e22	0.221469
$469$	6.37866e22	1.25823
$470$	−1.28247e22	−0.248437
$471$	−9.67066e21	−0.183983
$472$	−6.08512e21	−0.113700
$473$	−1.36117e23	−2.49801
$474$	−9.18053e21	−0.165482
$475$	−7.03686e22	−1.24590
$476$	2.17662e22	0.378550
$477$	−5.65574e21	−0.0966237
$478$	5.99415e21	0.100598
$479$	9.41564e22	1.55238	0.776190	−	0.630499i	$-0.217150\pi$
$479$	9.41564e22	1.55238	0.776190	+	0.630499i	$0.217150\pi$
$480$	4.51727e22	0.731687
$481$	6.57009e21	0.104553
$482$	−3.40739e21	−0.0532749
$483$	−2.56949e22	−0.394727
$484$	−1.74970e23	−2.64106
$485$	−2.66927e22	−0.395902
$486$	4.58940e21	0.0668879
$487$	8.15814e22	1.16841	0.584205	−	0.811606i	$-0.301406\pi$
$487$	8.15814e22	1.16841	0.584205	+	0.811606i	$0.301406\pi$
$488$	−1.16415e22	−0.163847
$489$	2.22862e22	0.308256
$490$	−9.05754e20	−0.0123124
$491$	−7.34666e22	−0.981516	−0.490758	−	0.871296i	$-0.663280\pi$
$491$	−7.34666e22	−0.981516	−0.490758	+	0.871296i	$0.663280\pi$
$492$	6.50265e22	0.853860
$493$	5.67685e21	0.0732670
$494$	−2.63917e21	−0.0334803
$495$	9.58296e22	1.19497
$496$	−1.07473e23	−1.31736
$497$	1.78713e22	0.215341
$498$	−1.85189e22	−0.219364
$499$	6.11596e22	0.712213	0.356106	−	0.934445i	$-0.384104\pi$
$499$	6.11596e22	0.712213	0.356106	+	0.934445i	$0.384104\pi$
$500$	3.21766e23	3.68379
$501$	−2.28966e22	−0.257721
$502$	−8.20378e21	−0.0907888
$503$	−7.58881e22	−0.825744	−0.412872	−	0.910789i	$-0.635474\pi$
$503$	−7.58881e22	−0.825744	−0.412872	+	0.910789i	$0.635474\pi$
$504$	−6.24773e21	−0.0668441
$505$	−1.23059e23	−1.29460
$506$	7.19010e21	0.0743799
$507$	−5.60683e22	−0.570361
$508$	1.59977e23	1.60035
$509$	−2.57607e21	−0.0253429	−0.0126715	−	0.999920i	$-0.504034\pi$
$509$	−2.57607e21	−0.0253429	−0.0126715	+	0.999920i	$0.504034\pi$
$510$	1.01074e22	0.0977898
$511$	−7.01546e22	−0.667542
$512$	−5.57475e22	−0.521712
$513$	3.67418e22	0.338192
$514$	5.32648e20	0.00482230
$515$	−2.48753e23	−2.21517
$516$	−1.68656e23	−1.47734
$517$	2.55779e23	2.20392
$518$	−1.85026e21	−0.0156830
$519$	6.82189e22	0.568830
$520$	3.71275e22	0.304556
$521$	−1.96244e23	−1.58371	−0.791853	−	0.610711i	$-0.790884\pi$
$521$	−1.96244e23	−1.58371	−0.791853	+	0.610711i	$0.790884\pi$
$522$	−8.09820e20	−0.00642968
$523$	8.75782e22	0.684119	0.342060	−	0.939678i	$-0.388876\pi$
$523$	8.75782e22	0.684119	0.342060	+	0.939678i	$0.388876\pi$
$524$	1.67918e23	1.29057
$525$	−4.25804e23	−3.22000
$526$	1.34799e22	0.100302
$527$	−7.36306e22	−0.539098
$528$	−2.94238e23	−2.11987
$529$	−1.23343e23	−0.874459
$530$	−9.46509e21	−0.0660358
$531$	−2.40407e22	−0.165061
$532$	−6.12065e22	−0.413570
$533$	8.03295e22	0.534187
$534$	2.01274e22	0.131731
$535$	4.39549e22	0.283139
$536$	−4.45005e22	−0.282140
$537$	−6.18350e22	−0.385881
$538$	−2.57292e22	−0.158044
$539$	1.80645e22	0.109225
$540$	−2.56880e23	−1.52891
$541$	−2.04101e22	−0.119583	−0.0597914	−	0.998211i	$-0.519044\pi$
$541$	−2.04101e22	−0.119583	−0.0597914	+	0.998211i	$0.519044\pi$
$542$	−1.06014e22	−0.0611464
$543$	−2.50221e23	−1.42077
$544$	−2.28235e22	−0.127583
$545$	5.44346e23	2.99574
$546$	−1.59698e22	−0.0865289
$547$	1.71075e23	0.912630	0.456315	−	0.889818i	$-0.349169\pi$
$547$	1.71075e23	0.912630	0.456315	+	0.889818i	$0.349169\pi$
$548$	1.26090e23	0.662284
$549$	−4.59923e22	−0.237859
$550$	1.19151e23	0.606755
$551$	−1.59633e22	−0.0800449
$552$	1.79260e22	0.0885118
$553$	−2.63016e23	−1.27885
$554$	9.41642e21	0.0450872
$555$	7.07552e22	0.333632
$556$	−3.63216e23	−1.68667
$557$	2.52649e23	1.15544	0.577721	−	0.816235i	$-0.303942\pi$
$557$	2.52649e23	1.15544	0.577721	+	0.816235i	$0.303942\pi$
$558$	1.05036e22	0.0473095
$559$	−2.08347e23	−0.924245
$560$	4.22665e23	1.84671
$561$	−2.01584e23	−0.867506
$562$	1.54620e21	0.00655401
$563$	2.97994e23	1.24419	0.622094	−	0.782943i	$-0.286282\pi$
$563$	2.97994e23	1.24419	0.622094	+	0.782943i	$0.286282\pi$
$564$	3.16924e23	1.30341
$565$	6.41188e23	2.59761
$566$	−1.47990e22	−0.0590597
$567$	3.00410e23	1.18102
$568$	−1.24678e22	−0.0482870
$569$	−2.14953e23	−0.820142	−0.410071	−	0.912054i	$-0.634496\pi$
$569$	−2.14953e23	−0.820142	−0.410071	+	0.912054i	$0.634496\pi$
$570$	−2.84220e22	−0.106836
$571$	1.26560e23	0.468693	0.234346	−	0.972153i	$-0.424705\pi$
$571$	1.26560e23	0.468693	0.234346	+	0.972153i	$0.424705\pi$
$572$	−3.68005e23	−1.34273
$573$	−4.45424e22	−0.160125
$574$	−2.26223e22	−0.0801281
$575$	2.93440e23	1.02410
$576$	−8.53739e22	−0.293585
$577$	3.09050e23	1.04721	0.523606	−	0.851960i	$-0.324586\pi$
$577$	3.09050e23	1.04721	0.523606	+	0.851960i	$0.324586\pi$
$578$	2.76976e22	0.0924816
$579$	4.36751e23	1.43703
$580$	1.11607e23	0.361871
$581$	−5.30553e23	−1.69524
$582$	−8.00995e21	−0.0252223
$583$	1.88774e23	0.585812
$584$	4.89431e22	0.149686
$585$	1.46681e23	0.442129
$586$	3.68957e22	0.109609
$587$	−3.75584e23	−1.09972	−0.549862	−	0.835256i	$-0.685320\pi$
$587$	−3.75584e23	−1.09972	−0.549862	+	0.835256i	$0.685320\pi$
$588$	2.23829e22	0.0645965
$589$	2.07049e23	0.588970
$590$	−4.02329e22	−0.112808
$591$	6.08158e22	0.168083
$592$	−5.21803e22	−0.142158
$593$	2.44159e23	0.655704	0.327852	−	0.944729i	$-0.393675\pi$
$593$	2.44159e23	0.655704	0.327852	+	0.944729i	$0.393675\pi$
$594$	−6.22126e22	−0.164700
$595$	2.89570e23	0.755718
$596$	−2.23735e23	−0.575627
$597$	−4.64247e23	−1.17752
$598$	1.10055e22	0.0275200
$599$	−6.58649e23	−1.62378	−0.811888	−	0.583813i	$-0.801560\pi$
$599$	−6.58649e23	−1.62378	−0.811888	+	0.583813i	$0.801560\pi$
$600$	2.97060e23	0.722037
$601$	−4.62604e22	−0.110860	−0.0554302	−	0.998463i	$-0.517653\pi$
$601$	−4.62604e22	−0.110860	−0.0554302	+	0.998463i	$0.517653\pi$
$602$	5.86744e22	0.138637
$603$	−1.75810e23	−0.409586
$604$	2.83263e23	0.650693
$605$	−2.32774e24	−5.27247
$606$	−3.69277e22	−0.0824773
$607$	8.34589e22	0.183810	0.0919049	−	0.995768i	$-0.470704\pi$
$607$	8.34589e22	0.183810	0.0919049	+	0.995768i	$0.470704\pi$
$608$	6.41796e22	0.139385
$609$	−9.65946e22	−0.206874
$610$	−7.69698e22	−0.162561
$611$	3.91507e23	0.815434
$612$	−5.99924e22	−0.123228
$613$	2.75906e23	0.558916	0.279458	−	0.960158i	$-0.409845\pi$
$613$	2.75906e23	0.558916	0.279458	+	0.960158i	$0.409845\pi$
$614$	−7.57436e22	−0.151326
$615$	8.65091e23	1.70460
$616$	2.08533e23	0.405264
$617$	8.15987e23	1.56408	0.782041	−	0.623227i	$-0.214179\pi$
$617$	8.15987e23	1.56408	0.782041	+	0.623227i	$0.214179\pi$
$618$	−7.46460e22	−0.141125
$619$	6.79999e23	1.26805	0.634027	−	0.773311i	$-0.281401\pi$
$619$	6.79999e23	1.26805	0.634027	+	0.773311i	$0.281401\pi$
$620$	−1.44758e24	−2.66264
$621$	−1.53215e23	−0.277986
$622$	3.45303e22	0.0617992
$623$	5.76637e23	1.01801
$624$	−4.50373e23	−0.784338
$625$	2.59826e24	4.46378
$626$	−4.81846e22	−0.0816632
$627$	5.66854e23	0.947758
$628$	9.60609e22	0.158449
$629$	−3.57491e22	−0.0581748
$630$	−4.13081e22	−0.0663194
$631$	−8.95788e23	−1.41891	−0.709456	−	0.704749i	$-0.751059\pi$
$631$	−8.95788e23	−1.41891	−0.709456	+	0.704749i	$0.751059\pi$
$632$	1.83492e23	0.286762
$633$	−4.52671e23	−0.697994
$634$	−5.23742e22	−0.0796818
$635$	2.12828e24	3.19486
$636$	2.33900e23	0.346454
$637$	2.76504e22	0.0404125
$638$	2.70296e22	0.0389820
$639$	−4.92571e22	−0.0700989
$640$	−5.97036e23	−0.838437
$641$	−1.00910e24	−1.39844	−0.699218	−	0.714908i	$-0.746468\pi$
$641$	−1.00910e24	−1.39844	−0.699218	+	0.714908i	$0.746468\pi$
$642$	1.31900e22	0.0180384
$643$	−1.13798e23	−0.153583	−0.0767915	−	0.997047i	$-0.524468\pi$
$643$	−1.13798e23	−0.153583	−0.0767915	+	0.997047i	$0.524468\pi$
$644$	2.55234e23	0.339945
$645$	−2.24375e24	−2.94929
$646$	1.43602e22	0.0186288
$647$	−1.42896e24	−1.82950	−0.914751	−	0.404018i	$-0.867613\pi$
$647$	−1.42896e24	−1.82950	−0.914751	+	0.404018i	$0.867613\pi$
$648$	−2.09580e23	−0.264827
$649$	8.02414e23	1.00073
$650$	1.82377e23	0.224495
$651$	1.25286e24	1.52218
$652$	−2.21374e23	−0.265474
$653$	−9.77912e23	−1.15755	−0.578773	−	0.815489i	$-0.696468\pi$
$653$	−9.77912e23	−1.15755	−0.578773	+	0.815489i	$0.696468\pi$
$654$	1.63348e23	0.190854
$655$	2.23393e24	2.57643
$656$	−6.37984e23	−0.726319
$657$	1.93361e23	0.217302
$658$	−1.10256e23	−0.122315
$659$	3.90965e23	0.428166	0.214083	−	0.976815i	$-0.431324\pi$
$659$	3.90965e23	0.428166	0.214083	+	0.976815i	$0.431324\pi$
$660$	−3.96315e24	−4.28467
$661$	−1.52760e24	−1.63041	−0.815207	−	0.579169i	$-0.803377\pi$
$661$	−1.52760e24	−1.63041	−0.815207	+	0.579169i	$0.803377\pi$
$662$	1.50942e21	0.00159044
$663$	−3.08554e23	−0.320971
$664$	3.70138e23	0.380133
$665$	−8.14271e23	−0.825629
$666$	5.09972e21	0.00510523
$667$	6.65676e22	0.0657951
$668$	2.27437e23	0.221953
$669$	−1.96316e24	−1.89161
$670$	−2.94224e23	−0.279925
$671$	1.53510e24	1.44210
$672$	3.88354e23	0.360237
$673$	−1.29525e24	−1.18639	−0.593195	−	0.805059i	$-0.702134\pi$
$673$	−1.29525e24	−1.18639	−0.593195	+	0.805059i	$0.702134\pi$
$674$	−1.39254e23	−0.125950
$675$	−2.53900e24	−2.26768
$676$	5.56940e23	0.491203
$677$	3.75391e23	0.326949	0.163475	−	0.986548i	$-0.447730\pi$
$677$	3.75391e23	0.326949	0.163475	+	0.986548i	$0.447730\pi$
$678$	1.92408e23	0.165490
$679$	−2.29479e23	−0.194917
$680$	−2.02018e23	−0.169459
$681$	1.79194e24	1.48448
$682$	−3.50583e23	−0.286829
$683$	−4.14269e22	−0.0334739	−0.0167370	−	0.999860i	$-0.505328\pi$
$683$	−4.14269e22	−0.0334739	−0.0167370	+	0.999860i	$0.505328\pi$
$684$	1.68698e23	0.134627
$685$	1.67745e24	1.32215
$686$	−1.44421e23	−0.112428
$687$	3.27612e23	0.251899
$688$	1.65471e24	1.25667
$689$	2.88945e23	0.216746
$690$	1.18521e23	0.0878170
$691$	1.26980e24	0.929331	0.464665	−	0.885486i	$-0.346175\pi$
$691$	1.26980e24	0.929331	0.464665	+	0.885486i	$0.346175\pi$
$692$	−6.77634e23	−0.489884
$693$	8.23857e23	0.588327
$694$	−2.17055e23	−0.153114
$695$	−4.83211e24	−3.36718
$696$	6.73889e22	0.0463884
$697$	−4.37087e23	−0.297228
$698$	1.04211e23	0.0700073
$699$	−1.77090e23	−0.117527
$700$	4.22961e24	2.77311
$701$	−1.47749e24	−0.957018	−0.478509	−	0.878083i	$-0.658823\pi$
$701$	−1.47749e24	−0.957018	−0.478509	+	0.878083i	$0.658823\pi$
$702$	−9.52253e22	−0.0609378
$703$	1.00526e23	0.0635564
$704$	2.84955e24	1.77995
$705$	4.21625e24	2.60207
$706$	9.79026e22	0.0596972
$707$	−1.05795e24	−0.637383
$708$	9.94232e23	0.591841
$709$	1.33012e24	0.782344	0.391172	−	0.920318i	$-0.372070\pi$
$709$	1.33012e24	0.782344	0.391172	+	0.920318i	$0.372070\pi$
$710$	−8.24334e22	−0.0479079
$711$	7.24928e23	0.416297
$712$	−4.02289e23	−0.228275
$713$	−8.63404e23	−0.484120
$714$	8.68944e22	0.0481457
$715$	−4.89582e24	−2.68055
$716$	6.14222e23	0.332326
$717$	−1.97063e24	−1.05364
$718$	1.88146e23	0.0994118
$719$	9.55366e23	0.498855	0.249427	−	0.968393i	$-0.419758\pi$
$719$	9.55366e23	0.498855	0.249427	+	0.968393i	$0.419758\pi$
$720$	−1.16495e24	−0.601150
$721$	−2.13856e24	−1.09061
$722$	1.76945e23	0.0891808
$723$	1.12021e24	0.557987
$724$	2.48550e24	1.22359
$725$	1.10313e24	0.536725
$726$	−6.98510e23	−0.335901
$727$	−5.35923e23	−0.254718	−0.127359	−	0.991857i	$-0.540650\pi$
$727$	−5.35923e23	−0.254718	−0.127359	+	0.991857i	$0.540650\pi$
$728$	3.19189e23	0.149945
$729$	1.11049e24	0.515619
$730$	3.23597e23	0.148512
$731$	1.13366e24	0.514261
$732$	1.90207e24	0.852868
$733$	−1.18095e24	−0.523417	−0.261709	−	0.965147i	$-0.584286\pi$
$733$	−1.18095e24	−0.523417	−0.261709	+	0.965147i	$0.584286\pi$
$734$	−3.45512e23	−0.151373
$735$	2.97775e23	0.128957
$736$	−2.67632e23	−0.114571
$737$	5.86805e24	2.48325
$738$	6.23518e22	0.0260838
$739$	−2.48284e23	−0.102676	−0.0513382	−	0.998681i	$-0.516349\pi$
$739$	−2.48284e23	−0.102676	−0.0513382	+	0.998681i	$0.516349\pi$
$740$	−7.02828e23	−0.287329
$741$	8.67652e23	0.350664
$742$	−8.13723e22	−0.0325120
$743$	−1.04416e24	−0.412440	−0.206220	−	0.978506i	$-0.566116\pi$
$743$	−1.04416e24	−0.412440	−0.206220	+	0.978506i	$0.566116\pi$
$744$	−8.74055e23	−0.341326
$745$	−2.97650e24	−1.14915
$746$	−2.60926e23	−0.0995949
$747$	1.46232e24	0.551844
$748$	2.00238e24	0.747109
$749$	3.77884e23	0.139400
$750$	1.28455e24	0.468521
$751$	−3.49972e24	−1.26210	−0.631050	−	0.775742i	$-0.717376\pi$
$751$	−3.49972e24	−1.26210	−0.631050	+	0.775742i	$0.717376\pi$
$752$	−3.10938e24	−1.10872
$753$	2.69707e24	0.950898
$754$	4.13727e22	0.0144231
$755$	3.76844e24	1.29901
$756$	−2.20842e24	−0.752743
$757$	2.21632e24	0.746994	0.373497	−	0.927631i	$-0.378159\pi$
$757$	2.21632e24	0.746994	0.373497	+	0.927631i	$0.378159\pi$
$758$	−2.65792e23	−0.0885836
$759$	−2.36381e24	−0.779035
$760$	5.68073e23	0.185135
$761$	−3.07616e24	−0.991380	−0.495690	−	0.868500i	$-0.665085\pi$
$761$	−3.07616e24	−0.991380	−0.495690	+	0.868500i	$0.665085\pi$
$762$	6.38655e23	0.203540
$763$	4.67979e24	1.47492
$764$	4.42450e23	0.137902
$765$	−7.98119e23	−0.246006
$766$	−2.19070e23	−0.0667787
$767$	1.22821e24	0.370264
$768$	3.39446e24	1.01205
$769$	6.22500e24	1.83555	0.917773	−	0.397105i	$-0.129985\pi$
$769$	6.22500e24	1.83555	0.917773	+	0.397105i	$0.129985\pi$
$770$	1.37875e24	0.402083
$771$	−1.75113e23	−0.0505075
$772$	−4.33835e24	−1.23759
$773$	−3.54530e24	−1.00029	−0.500147	−	0.865940i	$-0.666721\pi$
$773$	−3.54530e24	−1.00029	−0.500147	+	0.865940i	$0.666721\pi$
$774$	−1.61719e23	−0.0451298
$775$	−1.43079e25	−3.94922
$776$	1.60096e23	0.0437074
$777$	6.08289e23	0.164260
$778$	2.14161e23	0.0572025
$779$	1.22909e24	0.324724
$780$	−6.06617e24	−1.58530
$781$	1.64407e24	0.424997
$782$	−5.98828e22	−0.0153125
$783$	−5.75979e23	−0.145691
$784$	−2.19602e23	−0.0549477
$785$	1.27796e24	0.316320
$786$	6.70358e23	0.164140
$787$	−3.21325e24	−0.778321	−0.389161	−	0.921170i	$-0.627235\pi$
$787$	−3.21325e24	−0.778321	−0.389161	+	0.921170i	$0.627235\pi$
$788$	−6.04098e23	−0.144755
$789$	−4.43165e24	−1.05054
$790$	1.21319e24	0.284511
$791$	5.51236e24	1.27890
$792$	−5.74761e23	−0.131924
$793$	2.34969e24	0.533567
$794$	−8.13304e23	−0.182717
$795$	3.11173e24	0.691642
$796$	4.61147e24	1.01409
$797$	−1.20704e24	−0.262620	−0.131310	−	0.991341i	$-0.541918\pi$
$797$	−1.20704e24	−0.262620	−0.131310	+	0.991341i	$0.541918\pi$
$798$	−2.44347e23	−0.0525996
$799$	−2.13026e24	−0.453717
$800$	−4.43506e24	−0.934619
$801$	−1.58934e24	−0.331390
$802$	−2.39036e23	−0.0493153
$803$	−6.45388e24	−1.31746
$804$	7.27082e24	1.46861
$805$	3.39555e24	0.678648
$806$	−5.36617e23	−0.106125
$807$	8.45870e24	1.65531
$808$	7.38076e23	0.142924
$809$	−1.46536e24	−0.280790	−0.140395	−	0.990096i	$-0.544837\pi$
$809$	−1.46536e24	−0.280790	−0.140395	+	0.990096i	$0.544837\pi$
$810$	−1.38568e24	−0.262748
$811$	5.50245e24	1.03247	0.516237	−	0.856446i	$-0.327332\pi$
$811$	5.50245e24	1.03247	0.516237	+	0.856446i	$0.327332\pi$
$812$	9.59496e23	0.178163
$813$	3.48532e24	0.640431
$814$	−1.70215e23	−0.0309521
$815$	−2.94509e24	−0.529979
$816$	2.45056e24	0.436415
$817$	−3.18784e24	−0.561834
$818$	2.60843e23	0.0454963
$819$	1.26103e24	0.217677
$820$	−8.59315e24	−1.46803
$821$	−2.12500e23	−0.0359288	−0.0179644	−	0.999839i	$-0.505719\pi$
$821$	−2.12500e23	−0.0359288	−0.0179644	+	0.999839i	$0.505719\pi$
$822$	5.03371e23	0.0842321
$823$	3.09753e24	0.512999	0.256499	−	0.966544i	$-0.417431\pi$
$823$	3.09753e24	0.512999	0.256499	+	0.966544i	$0.417431\pi$
$824$	1.49196e24	0.244554
$825$	−3.91718e25	−6.35500
$826$	−3.45887e23	−0.0555397
$827$	2.74674e23	0.0436537	0.0218269	−	0.999762i	$-0.493052\pi$
$827$	2.74674e23	0.0436537	0.0218269	+	0.999762i	$0.493052\pi$
$828$	−7.03480e23	−0.110661
$829$	6.12050e24	0.952956	0.476478	−	0.879186i	$-0.341913\pi$
$829$	6.12050e24	0.952956	0.476478	+	0.879186i	$0.341913\pi$
$830$	2.44724e24	0.377149
$831$	−3.09573e24	−0.472231
$832$	4.36165e24	0.658571
$833$	−1.50451e23	−0.0224860
$834$	−1.45002e24	−0.214518
$835$	3.02575e24	0.443097
$836$	−5.63069e24	−0.816223
$837$	7.47063e24	1.07199
$838$	1.34080e24	0.190453
$839$	−1.30278e25	−1.83187	−0.915936	−	0.401325i	$-0.868550\pi$
$839$	−1.30278e25	−1.83187	−0.915936	+	0.401325i	$0.868550\pi$
$840$	3.43744e24	0.478477
$841$	2.50246e23	0.0344828
$842$	−4.95286e23	−0.0675622
$843$	−5.08327e23	−0.0686450
$844$	4.49649e24	0.601122
$845$	7.40934e24	0.980613
$846$	3.03888e23	0.0398167
$847$	−2.00118e25	−2.59584
$848$	−2.29483e24	−0.294704
$849$	4.86529e24	0.618576
$850$	−9.92348e23	−0.124912
$851$	−4.19199e23	−0.0522420
$852$	2.03709e24	0.251346
$853$	1.37978e25	1.68556	0.842780	−	0.538259i	$-0.180918\pi$
$853$	1.37978e25	1.68556	0.842780	+	0.538259i	$0.180918\pi$
$854$	−6.61717e23	−0.0800350
$855$	2.24431e24	0.268763
$856$	−2.63630e23	−0.0312584
$857$	−7.78222e24	−0.913622	−0.456811	−	0.889564i	$-0.651008\pi$
$857$	−7.78222e24	−0.913622	−0.456811	+	0.889564i	$0.651008\pi$
$858$	−1.46914e24	−0.170774
$859$	9.17775e23	0.105632	0.0528159	−	0.998604i	$-0.483180\pi$
$859$	9.17775e23	0.105632	0.0528159	+	0.998604i	$0.483180\pi$
$860$	2.22877e25	2.53997
$861$	7.43727e24	0.839241
$862$	1.52197e24	0.170057
$863$	−1.11360e25	−1.23208	−0.616040	−	0.787715i	$-0.711264\pi$
$863$	−1.11360e25	−1.23208	−0.616040	+	0.787715i	$0.711264\pi$
$864$	2.31570e24	0.253697
$865$	−9.01503e24	−0.977980
$866$	6.14727e23	0.0660359
$867$	−9.10583e24	−0.968628
$868$	−1.24450e25	−1.31092
$869$	−2.41961e25	−2.52393
$870$	4.45554e23	0.0460243
$871$	8.98190e24	0.918785
$872$	−3.26484e24	−0.330729
$873$	6.32495e23	0.0634506
$874$	1.68390e23	0.0167290
$875$	3.68013e25	3.62072
$876$	−7.99669e24	−0.779158
$877$	−1.03750e25	−1.00113	−0.500567	−	0.865698i	$-0.666875\pi$
$877$	−1.03750e25	−1.00113	−0.500567	+	0.865698i	$0.666875\pi$
$878$	6.14569e23	0.0587309
$879$	−1.21298e25	−1.14802
$880$	3.88831e25	3.64467
$881$	−1.28400e25	−1.19198	−0.595990	−	0.802992i	$-0.703240\pi$
$881$	−1.28400e25	−1.19198	−0.595990	+	0.802992i	$0.703240\pi$
$882$	2.14623e22	0.00197330
$883$	3.45324e24	0.314456	0.157228	−	0.987562i	$-0.449744\pi$
$883$	3.45324e24	0.314456	0.157228	+	0.987562i	$0.449744\pi$
$884$	3.06494e24	0.276425
$885$	1.32269e25	1.18152
$886$	5.94645e23	0.0526103
$887$	1.35495e25	1.18733	0.593666	−	0.804712i	$-0.297680\pi$
$887$	1.35495e25	1.18733	0.593666	+	0.804712i	$0.297680\pi$
$888$	−4.24371e23	−0.0368329
$889$	1.82970e25	1.57295
$890$	−2.65981e24	−0.226483
$891$	2.76362e25	2.33087
$892$	1.95005e25	1.62909
$893$	5.99029e24	0.495690
$894$	−8.93189e23	−0.0732107
$895$	8.17140e24	0.663439
$896$	−5.13277e24	−0.412795
$897$	−3.61815e24	−0.288238
$898$	2.17403e24	0.171560
$899$	−3.24578e24	−0.253724
$900$	−1.16577e25	−0.902718
$901$	−1.57220e24	−0.120600
$902$	−2.08114e24	−0.158141
$903$	−1.92897e25	−1.45205
$904$	−3.84568e24	−0.286775
$905$	3.30663e25	2.44272
$906$	1.13083e24	0.0827579
$907$	−2.28285e25	−1.65506	−0.827532	−	0.561419i	$-0.810256\pi$
$907$	−2.28285e25	−1.65506	−0.827532	+	0.561419i	$0.810256\pi$
$908$	−1.77998e25	−1.27845
$909$	2.91594e24	0.207485
$910$	2.11038e24	0.148768
$911$	1.88135e25	1.31390	0.656952	−	0.753932i	$-0.271845\pi$
$911$	1.88135e25	1.31390	0.656952	+	0.753932i	$0.271845\pi$
$912$	−6.89097e24	−0.476787
$913$	−4.88082e25	−3.34573
$914$	−5.14591e23	−0.0349478
$915$	2.53045e25	1.70262
$916$	−3.25424e24	−0.216939
$917$	1.92053e25	1.26847
$918$	5.18139e23	0.0339065
$919$	6.79357e24	0.440470	0.220235	−	0.975447i	$-0.429318\pi$
$919$	6.79357e24	0.440470	0.220235	+	0.975447i	$0.429318\pi$
$920$	−2.36889e24	−0.152177
$921$	2.49014e25	1.58495
$922$	2.00199e24	0.126255
$923$	2.51648e24	0.157246
$924$	−3.40716e25	−2.10951
$925$	−6.94676e24	−0.426165
$926$	−6.33029e22	−0.00384796
$927$	5.89432e24	0.355023
$928$	−1.00610e24	−0.0600461
$929$	−1.44967e24	−0.0857303	−0.0428651	−	0.999081i	$-0.513649\pi$
$929$	−1.44967e24	−0.0857303	−0.0428651	+	0.999081i	$0.513649\pi$
$930$	−5.77898e24	−0.338646
$931$	4.23067e23	0.0245661
$932$	1.75908e24	0.101216
$933$	−1.13522e25	−0.647268
$934$	−1.50683e24	−0.0851362
$935$	2.66391e25	1.49149
$936$	−8.79754e23	−0.0488109
$937$	−7.59096e24	−0.417359	−0.208680	−	0.977984i	$-0.566917\pi$
$937$	−7.59096e24	−0.417359	−0.208680	+	0.977984i	$0.566917\pi$
$938$	−2.52947e24	−0.137818
$939$	1.58411e25	0.855319
$940$	−4.18810e25	−2.24094
$941$	1.13386e25	0.601239	0.300619	−	0.953744i	$-0.402807\pi$
$941$	1.13386e25	0.601239	0.300619	+	0.953744i	$0.402807\pi$
$942$	3.83492e23	0.0201522
$943$	−5.12536e24	−0.266916
$944$	−9.75456e24	−0.503438
$945$	−2.93801e25	−1.50274
$946$	5.39776e24	0.273614
$947$	−1.58031e25	−0.793901	−0.396950	−	0.917840i	$-0.629932\pi$
$947$	−1.58031e25	−0.793901	−0.396950	+	0.917840i	$0.629932\pi$
$948$	−2.99803e25	−1.49267
$949$	−9.87859e24	−0.487452
$950$	2.79048e24	0.136467
$951$	1.72185e25	0.834566
$952$	−1.73677e24	−0.0834310
$953$	1.76120e25	0.838529	0.419265	−	0.907864i	$-0.362288\pi$
$953$	1.76120e25	0.838529	0.419265	+	0.907864i	$0.362288\pi$
$954$	2.24280e23	0.0105835
$955$	5.88620e24	0.275300
$956$	1.95747e25	0.907410
$957$	−8.88622e24	−0.408287
$958$	−3.73379e24	−0.170037
$959$	1.44212e25	0.650945
$960$	4.69718e25	2.10151
$961$	1.95487e25	0.866899
$962$	−2.60538e23	−0.0114521
$963$	−1.04153e24	−0.0453783
$964$	−1.11273e25	−0.480547
$965$	−5.77160e25	−2.47067
$966$	1.01894e24	0.0432357
$967$	−2.10371e25	−0.884832	−0.442416	−	0.896810i	$-0.645878\pi$
$967$	−2.10371e25	−0.884832	−0.442416	+	0.896810i	$0.645878\pi$
$968$	1.39612e25	0.582079
$969$	−4.72105e24	−0.195113
$970$	1.05850e24	0.0433643
$971$	9.13544e24	0.370993	0.185497	−	0.982645i	$-0.440611\pi$
$971$	9.13544e24	0.370993	0.185497	+	0.982645i	$0.440611\pi$
$972$	1.49873e25	0.603338
$973$	−4.15421e25	−1.65779
$974$	−3.23513e24	−0.127979
$975$	−5.99581e25	−2.35130
$976$	−1.86615e25	−0.725475
$977$	2.48344e25	0.957084	0.478542	−	0.878065i	$-0.341165\pi$
$977$	2.48344e25	0.957084	0.478542	+	0.878065i	$0.341165\pi$
$978$	−8.83764e23	−0.0337642
$979$	5.30477e25	2.00916
$980$	−2.95787e24	−0.111060
$981$	−1.28985e25	−0.480124
$982$	2.91333e24	0.107508
$983$	4.12557e24	0.150931	0.0754656	−	0.997148i	$-0.475956\pi$
$983$	4.12557e24	0.150931	0.0754656	+	0.997148i	$0.475956\pi$
$984$	−5.18859e24	−0.188187
$985$	−8.03672e24	−0.288982
$986$	−2.25116e23	−0.00802516
$987$	3.62475e25	1.28110
$988$	−8.61859e24	−0.301997
$989$	1.32934e25	0.461815
$990$	−3.80014e24	−0.130888
$991$	−2.57452e25	−0.879165	−0.439582	−	0.898202i	$-0.644874\pi$
$991$	−2.57452e25	−0.879165	−0.439582	+	0.898202i	$0.644874\pi$
$992$	1.30495e25	0.441819
$993$	−4.96234e23	−0.0166578
$994$	−7.08688e23	−0.0235869
$995$	6.13495e25	2.02449
$996$	−6.04759e25	−1.97869
$997$	−4.71280e25	−1.52887	−0.764434	−	0.644702i	$-0.776982\pi$
$997$	−4.71280e25	−1.52887	−0.764434	+	0.644702i	$0.776982\pi$
$998$	−2.42529e24	−0.0780108
$999$	3.62714e24	0.115680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.10	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.10	✓	21	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-39.6552 q^{2} +13037.0 q^{3} -129499. q^{4} -1.72282e6 q^{5} -516984. q^{6} -1.48112e7 q^{7} +1.03330e7 q^{8} +4.08230e7 q^{9} +O(q^{10})\)	\(q-39.6552 q^{2} +13037.0 q^{3} -129499. q^{4} -1.72282e6 q^{5} -516984. q^{6} -1.48112e7 q^{7} +1.03330e7 q^{8} +4.08230e7 q^{9} +6.83187e7 q^{10} -1.36256e9 q^{11} -1.68828e9 q^{12} -2.08559e9 q^{13} +5.87342e8 q^{14} -2.24604e10 q^{15} +1.65640e10 q^{16} +1.13481e10 q^{17} -1.61884e9 q^{18} -3.19108e10 q^{19} +2.23104e11 q^{20} -1.93094e11 q^{21} +5.40326e10 q^{22} +1.33070e11 q^{23} +1.34711e11 q^{24} +2.20516e12 q^{25} +8.27046e10 q^{26} -1.15139e12 q^{27} +1.91805e12 q^{28} +5.00246e11 q^{29} +8.90670e11 q^{30} -6.48836e12 q^{31} -2.01122e12 q^{32} -1.77637e13 q^{33} -4.50011e11 q^{34} +2.55171e13 q^{35} -5.28655e12 q^{36} -3.15023e12 q^{37} +1.26543e12 q^{38} -2.71899e13 q^{39} -1.78019e13 q^{40} -3.85163e13 q^{41} +7.65717e12 q^{42} +9.98982e13 q^{43} +1.76451e14 q^{44} -7.03305e13 q^{45} -5.27690e12 q^{46} -1.87719e14 q^{47} +2.15945e14 q^{48} -1.32578e13 q^{49} -8.74461e13 q^{50} +1.47945e14 q^{51} +2.70083e14 q^{52} -1.38543e14 q^{53} +4.56586e13 q^{54} +2.34744e15 q^{55} -1.53045e14 q^{56} -4.16021e14 q^{57} -1.98374e13 q^{58} -5.88901e14 q^{59} +2.90861e15 q^{60} -1.12663e15 q^{61} +2.57297e14 q^{62} -6.04639e14 q^{63} -2.09132e15 q^{64} +3.59310e15 q^{65} +7.04422e14 q^{66} -4.30664e15 q^{67} -1.46957e15 q^{68} +1.73483e15 q^{69} -1.01188e15 q^{70} -1.20660e15 q^{71} +4.21824e14 q^{72} +4.73658e15 q^{73} +1.24923e14 q^{74} +2.87487e16 q^{75} +4.13244e15 q^{76} +2.01812e16 q^{77} +1.07822e15 q^{78} +1.77579e16 q^{79} -2.85368e16 q^{80} -2.02826e16 q^{81} +1.52737e15 q^{82} +3.58210e16 q^{83} +2.50056e16 q^{84} -1.95507e16 q^{85} -3.96148e15 q^{86} +6.52171e15 q^{87} -1.40793e16 q^{88} -3.89324e16 q^{89} +2.78897e15 q^{90} +3.08902e16 q^{91} -1.72325e16 q^{92} -8.45887e16 q^{93} +7.44405e15 q^{94} +5.49766e16 q^{95} -2.62202e16 q^{96} +1.54936e16 q^{97} +5.25740e14 q^{98} -5.56238e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9} - 224469478 q^{10} + 1203139534 q^{11} - 5164251122 q^{12} + 3854339312 q^{13} + 25262272904 q^{14} + 28324474306 q^{15} + 196520815922 q^{16} + 76444714794 q^{17} + 75758949126 q^{18} + 246497292428 q^{19} - 46900976670 q^{20} + 360937126704 q^{21} - 275001533522 q^{22} + 213498528140 q^{23} - 451123453870 q^{24} + 3898884886997 q^{25} - 3609347694206 q^{26} - 2718903745978 q^{27} - 5946174617200 q^{28} + 10505174672181 q^{29} - 20237658929454 q^{30} + 16670029895798 q^{31} - 42141001912046 q^{32} - 7157109761394 q^{33} + 12785761151136 q^{34} + 46677934312888 q^{35} + 132137824374868 q^{36} + 53445659988410 q^{37} + 76581637956388 q^{38} + 79233849032530 q^{39} + 193617444734146 q^{40} - 20814769309298 q^{41} + 76690667258352 q^{42} + 185498647364454 q^{43} + 315429066899678 q^{44} - 486270821438526 q^{45} + 261474367677132 q^{46} + 389503471719450 q^{47} - 101509672247630 q^{48} + 730079062141437 q^{49} + 14\!\cdots\!54 q^{50}+ \cdots - 95\!\cdots\!64 q^{99}+O(q^{100}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9 - 224469478 * q^10 + 1203139534 * q^11 - 5164251122 * q^12 + 3854339312 * q^13 + 25262272904 * q^14 + 28324474306 * q^15 + 196520815922 * q^16 + 76444714794 * q^17 + 75758949126 * q^18 + 246497292428 * q^19 - 46900976670 * q^20 + 360937126704 * q^21 - 275001533522 * q^22 + 213498528140 * q^23 - 451123453870 * q^24 + 3898884886997 * q^25 - 3609347694206 * q^26 - 2718903745978 * q^27 - 5946174617200 * q^28 + 10505174672181 * q^29 - 20237658929454 * q^30 + 16670029895798 * q^31 - 42141001912046 * q^32 - 7157109761394 * q^33 + 12785761151136 * q^34 + 46677934312888 * q^35 + 132137824374868 * q^36 + 53445659988410 * q^37 + 76581637956388 * q^38 + 79233849032530 * q^39 + 193617444734146 * q^40 - 20814769309298 * q^41 + 76690667258352 * q^42 + 185498647364454 * q^43 + 315429066899678 * q^44 - 486270821438526 * q^45 + 261474367677132 * q^46 + 389503471719450 * q^47 - 101509672247630 * q^48 + 730079062141437 * q^49 + 1482269666368354 * q^50 + 718238208473988 * q^51 + 1966802817157170 * q^52 + 747441265526156 * q^53 + 5692893333117030 * q^54 + 1639109418219546 * q^55 + 5657219329125240 * q^56 + 4694352396864932 * q^57 + 128063081718016 * q^58 + 5280258638332960 * q^59 + 15251367906033378 * q^60 + 5813675353074254 * q^61 + 6242066590947250 * q^62 + 10947760075450368 * q^63 + 24583792057508902 * q^64 + 19190799243789974 * q^65 + 41877805444482390 * q^66 + 13420580230958268 * q^67 + 24771837384165388 * q^68 + 30973047049935252 * q^69 + 8505088080182440 * q^70 + 4824462822979508 * q^71 + 1180071997284592 * q^72 + 11228916281304662 * q^73 - 89132715356772 * q^74 + 59161419576630296 * q^75 + 57466858643173460 * q^76 + 58741564492720064 * q^77 + 142050530910210210 * q^78 + 71718598015696758 * q^79 + 48350023652407550 * q^80 + 75805931446703569 * q^81 + 188661890754420812 * q^82 + 50769377111735608 * q^83 + 198832046985593048 * q^84 + 53422044849490784 * q^85 + 35014892323844118 * q^86 + 11988905533023326 * q^87 + 37459283979085258 * q^88 - 70981414576978018 * q^89 + 57211029866143724 * q^90 + 112933943315157320 * q^91 - 103019729095759724 * q^92 - 350358290646906646 * q^93 - 150286322409612578 * q^94 - 102561321856584476 * q^95 - 213770098354021866 * q^96 - 130930167251505210 * q^97 - 537387515497557296 * q^98 - 95267700931431064 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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