LMFDB - Embedded newform 10.32.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,32,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 32, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 32 $
Character orbit:	$[\chi]$	$=$	10.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:	$60.8771328190$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 17573188320 $ x^2 - x - 17573188320
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-132563.$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-32768.0 q^{2} +2.09091e7 q^{3} +1.07374e9 q^{4} +3.05176e10 q^{5} -6.85150e11 q^{6} +1.72878e13 q^{7} -3.51844e13 q^{8} -1.80482e14 q^{9} -1.00000e15 q^{10} -1.40404e16 q^{11} +2.24510e16 q^{12} +1.12100e17 q^{13} -5.66487e17 q^{14} +6.38096e17 q^{15} +1.15292e18 q^{16} -1.87926e19 q^{17} +5.91403e18 q^{18} -1.17369e20 q^{19} +3.27680e19 q^{20} +3.61473e20 q^{21} +4.60074e20 q^{22} -2.47133e21 q^{23} -7.35674e20 q^{24} +9.31323e20 q^{25} -3.67328e21 q^{26} -1.66887e22 q^{27} +1.85627e22 q^{28} +6.20136e22 q^{29} -2.09091e22 q^{30} +1.42328e23 q^{31} -3.77789e22 q^{32} -2.93572e23 q^{33} +6.15797e23 q^{34} +5.27582e23 q^{35} -1.93791e23 q^{36} +1.53344e24 q^{37} +3.84596e24 q^{38} +2.34391e24 q^{39} -1.07374e24 q^{40} -6.64565e24 q^{41} -1.18448e25 q^{42} +1.23317e24 q^{43} -1.50757e25 q^{44} -5.50787e24 q^{45} +8.09804e25 q^{46} -1.65205e26 q^{47} +2.41066e25 q^{48} +1.41093e26 q^{49} -3.05176e25 q^{50} -3.92938e26 q^{51} +1.20366e26 q^{52} +2.10693e25 q^{53} +5.46856e26 q^{54} -4.28478e26 q^{55} -6.08261e26 q^{56} -2.45409e27 q^{57} -2.03206e27 q^{58} +2.11570e27 q^{59} +6.85150e26 q^{60} -2.54907e27 q^{61} -4.66380e27 q^{62} -3.12014e27 q^{63} +1.23794e27 q^{64} +3.42101e27 q^{65} +9.61975e27 q^{66} +2.58183e28 q^{67} -2.01784e28 q^{68} -5.16733e28 q^{69} -1.72878e28 q^{70} -6.76939e28 q^{71} +6.35014e27 q^{72} -5.88515e28 q^{73} -5.02476e28 q^{74} +1.94731e28 q^{75} -1.26024e29 q^{76} -2.42727e29 q^{77} -7.68051e28 q^{78} -2.13368e29 q^{79} +3.51844e28 q^{80} -2.37468e29 q^{81} +2.17765e29 q^{82} -1.06637e29 q^{83} +3.88129e29 q^{84} -5.73506e29 q^{85} -4.04086e28 q^{86} +1.29665e30 q^{87} +4.94001e29 q^{88} -5.07280e29 q^{89} +1.80482e29 q^{90} +1.93796e30 q^{91} -2.65357e30 q^{92} +2.97595e30 q^{93} +5.41345e30 q^{94} -3.58183e30 q^{95} -7.89924e29 q^{96} +2.99146e30 q^{97} -4.62334e30 q^{98} +2.53403e30 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 65536 q^{2} - 5904756 q^{3} + 2147483648 q^{4} + 61035156250 q^{5} + 193487044608 q^{6} + 18016565093212 q^{7} - 70368744177664 q^{8} - 79171117705926 q^{9} - 20\!\cdots\!00 q^{10} - 17\!\cdots\!76 q^{11}+ \cdots + 21\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 65536 * q^2 - 5904756 * q^3 + 2147483648 * q^4 + 61035156250 * q^5 + 193487044608 * q^6 + 18016565093212 * q^7 - 70368744177664 * q^8 - 79171117705926 * q^9 - 2000000000000000 * q^10 - 17416121431336176 * q^11 - 6340183477714944 * q^12 - 25489812233411396 * q^13 - 590366804974370816 * q^14 - 180198852539062500 * q^15 + 2305843009213693952 * q^16 - 16396230747963647148 * q^17 + 2594279184987783168 * q^18 - 107880416928265082840 * q^19 + 65536000000000000000 * q^20 + 341932614252792754464 * q^21 + 570691467062023815168 * q^22 - 577071154821832133436 * q^23 + 207755132197763284992 * q^24 + 1862645149230957031250 * q^25 + 835250167264424624128 * q^26 - 2843043459520171719240 * q^27 + 19345139465400182898688 * q^28 + 67048805832697356280140 * q^29 + 5904756000000000000000 * q^30 + 56909800035573417801064 * q^31 - 75557863725914323419136 * q^32 - 203054257469968728424272 * q^33 + 537271689149272789745664 * q^34 + 549821932776245117187500 * q^35 - 85009340333679678849024 * q^36 + 2801153390572259937695932 * q^37 + 3535025501905390234501120 * q^38 + 6033212900355351396566088 * q^39 - 2147483648000000000000000 * q^40 + 1893631200697714321546884 * q^41 - 11204447903835512978276352 * q^42 + 25327635900154956194956684 * q^43 - 18700417992688396375425024 * q^44 - 2416110769834167480468750 * q^45 + 18909467601201795348430848 * q^46 - 204836832883272087160299828 * q^47 - 6807720171856307322617856 * q^48 - 16151031643901179650461214 * q^49 - 61035156250000000000000000 * q^50 - 457194512783561777077087656 * q^51 - 27369477480920666083426304 * q^52 + 93384041038067791074445644 * q^53 + 93160848081556986896056320 * q^54 - 531497846415288574218750000 * q^55 - 633901530002233193224208384 * q^56 - 2708523042419370548680789680 * q^57 - 2197055269525826970587627520 * q^58 + 401993734479158802793910280 * q^59 - 193487044608000000000000000 * q^60 - 523487156255386223571641876 * q^61 - 1864820327565669754505265152 * q^62 - 3046308524664113764706112756 * q^63 + 2475880078570760549798248448 * q^64 - 777887336224713012695312500 * q^65 + 6653681908775935293006544896 * q^66 + 3525975420949577285673481252 * q^67 - 17605318710043370774385917952 * q^68 - 102465607127544429209145592992 * q^69 - 18016565093212000000000000000 * q^70 - 155367638238255137782572480456 * q^71 + 2785586064054015716524818432 * q^72 - 121161803322719279904680358236 * q^73 - 91788194302271813638420299776 * q^74 - 5499232560396194458007812500 * q^75 - 115835715646435827204132700160 * q^76 - 245187227911068920618395555056 * q^77 - 197696320318844154562677571584 * q^78 - 106325261485679876782031095760 * q^79 + 70368744177664000000000000000 * q^80 - 671301359934033052744190089758 * q^81 - 62050507184462702888448294912 * q^82 - 165992230806613806640311266676 * q^83 + 367147348912882089272159502336 * q^84 - 500373252806507786499023437500 * q^85 - 829935973176277604596340621312 * q^86 + 1161637435058040293762416972680 * q^87 + 612775296784413372429927186432 * q^88 + 596773808150426638152387464820 * q^89 + 79171117705926000000000000000 * q^90 + 1837690480870898595062956149224 * q^91 - 619625434356180429977382027264 * q^92 + 5266346212626013088658434510208 * q^93 + 6712093339919059752068704763904 * q^94 - 3292249051765902186279296875000 * q^95 + 223075374591387478347541905408 * q^96 + 8308055695022791533341129836372 * q^97 + 529237004907353854786313060352 * q^98 + 2192029238850361923111708294288 * q^99

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 $

$2$	−32768.0	−0.707107
$2$	−32768.0	−0.707107
$3$	2.09091e7	0.841311	0.420655	−	0.907221i	$-0.361800\pi$
$3$	2.09091e7	0.841311	0.420655	+	0.907221i	$0.361800\pi$
$4$	1.07374e9	0.500000
$5$	3.05176e10	0.447214
$5$	3.05176e10	0.447214
$6$	−6.85150e11	−0.594896
$7$	1.72878e13	1.37632	0.688162	−	0.725557i	$-0.258418\pi$
$7$	1.72878e13	1.37632	0.688162	+	0.725557i	$0.258418\pi$
$8$	−3.51844e13	−0.353553
$9$	−1.80482e14	−0.292196
$10$	−1.00000e15	−0.316228
$11$	−1.40404e16	−1.01342	−0.506712	−	0.862115i	$-0.669139\pi$
$11$	−1.40404e16	−1.01342	−0.506712	+	0.862115i	$0.669139\pi$
$12$	2.24510e16	0.420655
$13$	1.12100e17	0.607410	0.303705	−	0.952766i	$-0.401776\pi$
$13$	1.12100e17	0.607410	0.303705	+	0.952766i	$0.401776\pi$
$14$	−5.66487e17	−0.973208
$15$	6.38096e17	0.376246
$16$	1.15292e18	0.250000
$17$	−1.87926e19	−1.59232	−0.796158	−	0.605088i	$-0.793138\pi$
$17$	−1.87926e19	−1.59232	−0.796158	+	0.605088i	$0.793138\pi$
$18$	5.91403e18	0.206614
$19$	−1.17369e20	−1.77367	−0.886837	−	0.462083i	$-0.847102\pi$
$19$	−1.17369e20	−1.77367	−0.886837	+	0.462083i	$0.847102\pi$
$20$	3.27680e19	0.223607
$21$	3.61473e20	1.15792
$22$	4.60074e20	0.716600
$23$	−2.47133e21	−1.93263	−0.966315	−	0.257363i	$-0.917146\pi$
$23$	−2.47133e21	−1.93263	−0.966315	+	0.257363i	$0.917146\pi$
$24$	−7.35674e20	−0.297448
$25$	9.31323e20	0.200000
$26$	−3.67328e21	−0.429504
$27$	−1.66887e22	−1.08714
$28$	1.85627e22	0.688162
$29$	6.20136e22	1.33450	0.667249	−	0.744835i	$-0.267472\pi$
$29$	6.20136e22	1.33450	0.667249	+	0.744835i	$0.267472\pi$
$30$	−2.09091e22	−0.266046
$31$	1.42328e23	1.08939	0.544696	−	0.838634i	$-0.316645\pi$
$31$	1.42328e23	1.08939	0.544696	+	0.838634i	$0.316645\pi$
$32$	−3.77789e22	−0.176777
$33$	−2.93572e23	−0.852605
$34$	6.15797e23	1.12594
$35$	5.27582e23	0.615511
$36$	−1.93791e23	−0.146098
$37$	1.53344e24	0.756030	0.378015	−	0.925799i	$-0.376607\pi$
$37$	1.53344e24	0.756030	0.378015	+	0.925799i	$0.376607\pi$
$38$	3.84596e24	1.25418
$39$	2.34391e24	0.511021
$40$	−1.07374e24	−0.158114
$41$	−6.64565e24	−0.667403	−0.333701	−	0.942679i	$-0.608298\pi$
$41$	−6.64565e24	−0.667403	−0.333701	+	0.942679i	$0.608298\pi$
$42$	−1.18448e25	−0.818770
$43$	1.23317e24	0.0591920	0.0295960	−	0.999562i	$-0.490578\pi$
$43$	1.23317e24	0.0591920	0.0295960	+	0.999562i	$0.490578\pi$
$44$	−1.50757e25	−0.506712
$45$	−5.50787e24	−0.130674
$46$	8.09804e25	1.36658
$47$	−1.65205e26	−1.99760	−0.998798	−	0.0490256i	$-0.984388\pi$
$47$	−1.65205e26	−1.99760	−0.998798	+	0.0490256i	$0.984388\pi$
$48$	2.41066e25	0.210328
$49$	1.41093e26	0.894267
$50$	−3.05176e25	−0.141421
$51$	−3.92938e26	−1.33963
$52$	1.20366e26	0.303705
$53$	2.10693e25	0.0395708	0.0197854	−	0.999804i	$-0.493702\pi$
$53$	2.10693e25	0.0395708	0.0197854	+	0.999804i	$0.493702\pi$
$54$	5.46856e26	0.768723
$55$	−4.28478e26	−0.453217
$56$	−6.08261e26	−0.486604
$57$	−2.45409e27	−1.49221
$58$	−2.03206e27	−0.943633
$59$	2.11570e27	0.753786	0.376893	−	0.926257i	$-0.376992\pi$
$59$	2.11570e27	0.753786	0.376893	+	0.926257i	$0.376992\pi$
$60$	6.85150e26	0.188123
$61$	−2.54907e27	−0.541712	−0.270856	−	0.962620i	$-0.587307\pi$
$61$	−2.54907e27	−0.541712	−0.270856	+	0.962620i	$0.587307\pi$
$62$	−4.66380e27	−0.770316
$63$	−3.12014e27	−0.402157
$64$	1.23794e27	0.125000
$65$	3.42101e27	0.271642
$66$	9.61975e27	0.602883
$67$	2.58183e28	1.28165	0.640823	−	0.767688i	$-0.278593\pi$
$67$	2.58183e28	1.28165	0.640823	+	0.767688i	$0.278593\pi$
$68$	−2.01784e28	−0.796158
$69$	−5.16733e28	−1.62594
$70$	−1.72878e28	−0.435232
$71$	−6.76939e28	−1.36787	−0.683936	−	0.729542i	$-0.739733\pi$
$71$	−6.76939e28	−1.36787	−0.683936	+	0.729542i	$0.739733\pi$
$72$	6.35014e27	0.103307
$73$	−5.88515e28	−0.773131	−0.386566	−	0.922262i	$-0.626339\pi$
$73$	−5.88515e28	−0.773131	−0.386566	+	0.922262i	$0.626339\pi$
$74$	−5.02476e28	−0.534594
$75$	1.94731e28	0.168262
$76$	−1.26024e29	−0.886837
$77$	−2.42727e29	−1.39480
$78$	−7.68051e28	−0.361346
$79$	−2.13368e29	−0.823965	−0.411982	−	0.911192i	$-0.635163\pi$
$79$	−2.13368e29	−0.823965	−0.411982	+	0.911192i	$0.635163\pi$
$80$	3.51844e28	0.111803
$81$	−2.37468e29	−0.622425
$82$	2.17765e29	0.471925
$83$	−1.06637e29	−0.191513	−0.0957564	−	0.995405i	$-0.530527\pi$
$83$	−1.06637e29	−0.191513	−0.0957564	+	0.995405i	$0.530527\pi$
$84$	3.88129e29	0.578958
$85$	−5.73506e29	−0.712106
$86$	−4.04086e28	−0.0418550
$87$	1.29665e30	1.12273
$88$	4.94001e29	0.358300
$89$	−5.07280e29	−0.308818	−0.154409	−	0.988007i	$-0.549347\pi$
$89$	−5.07280e29	−0.308818	−0.154409	+	0.988007i	$0.549347\pi$
$90$	1.80482e29	0.0924006
$91$	1.93796e30	0.835993
$92$	−2.65357e30	−0.966315
$93$	2.97595e30	0.916517
$94$	5.41345e30	1.41251
$95$	−3.58183e30	−0.793211
$96$	−7.89924e29	−0.148724
$97$	2.99146e30	0.479646	0.239823	−	0.970817i	$-0.422911\pi$
$97$	2.99146e30	0.479646	0.239823	+	0.970817i	$0.422911\pi$
$98$	−4.62334e30	−0.632342
$99$	2.53403e30	0.296119
$100$	1.00000e30	0.100000
$101$	5.56134e30	0.476648	0.238324	−	0.971186i	$-0.423402\pi$
$101$	5.56134e30	0.476648	0.238324	+	0.971186i	$0.423402\pi$
$102$	1.28758e31	0.947264
$103$	−9.44476e30	−0.597330	−0.298665	−	0.954358i	$-0.596541\pi$
$103$	−9.44476e30	−0.597330	−0.298665	+	0.954358i	$0.596541\pi$
$104$	−3.94416e30	−0.214752
$105$	1.10313e31	0.517836
$106$	−6.90400e29	−0.0279808
$107$	3.40170e31	1.19192	0.595961	−	0.803014i	$-0.296771\pi$
$107$	3.40170e31	1.19192	0.595961	+	0.803014i	$0.296771\pi$
$108$	−1.79194e31	−0.543569
$109$	1.12629e31	0.296169	0.148085	−	0.988975i	$-0.452689\pi$
$109$	1.12629e31	0.296169	0.148085	+	0.988975i	$0.452689\pi$
$110$	1.40404e31	0.320473
$111$	3.20628e31	0.636056
$112$	1.99315e31	0.344081
$113$	−1.71220e31	−0.257537	−0.128769	−	0.991675i	$-0.541102\pi$
$113$	−1.71220e31	−0.257537	−0.128769	+	0.991675i	$0.541102\pi$
$114$	8.04156e31	1.05515
$115$	−7.54189e31	−0.864298
$116$	6.65866e31	0.667249
$117$	−2.02320e31	−0.177483
$118$	−6.93273e31	−0.533007
$119$	−3.24884e32	−2.19154
$120$	−2.24510e31	−0.133023
$121$	5.18822e30	0.0270299
$122$	8.35278e31	0.383048
$123$	−1.38955e32	−0.561493
$124$	1.52824e32	0.544696
$125$	2.84217e31	0.0894427
$126$	1.02241e32	0.284368
$127$	−7.80052e32	−1.91940	−0.959701	−	0.281022i	$-0.909327\pi$
$127$	−7.80052e32	−1.91940	−0.959701	+	0.281022i	$0.909327\pi$
$128$	−4.05648e31	−0.0883883
$129$	2.57846e31	0.0497988
$130$	−1.12100e32	−0.192080
$131$	7.18592e32	1.09340	0.546698	−	0.837330i	$-0.315885\pi$
$131$	7.18592e32	1.09340	0.546698	+	0.837330i	$0.315885\pi$
$132$	−3.15220e32	−0.426303
$133$	−2.02906e33	−2.44115
$134$	−8.46014e32	−0.906261
$135$	−5.09300e32	−0.486183
$136$	6.61207e32	0.562969
$137$	1.47730e33	1.12279	0.561395	−	0.827548i	$-0.310265\pi$
$137$	1.47730e33	1.12279	0.561395	+	0.827548i	$0.310265\pi$
$138$	1.69323e33	1.14971
$139$	5.43580e32	0.330016	0.165008	−	0.986292i	$-0.447235\pi$
$139$	5.43580e32	0.330016	0.165008	+	0.986292i	$0.447235\pi$
$140$	5.66487e32	0.307755
$141$	−3.45430e33	−1.68060
$142$	2.21819e33	0.967231
$143$	−1.57392e33	−0.615565
$144$	−2.08081e32	−0.0730491
$145$	1.89251e33	0.596806
$146$	1.92845e33	0.546686
$147$	2.95014e33	0.752356
$148$	1.64651e33	0.378015
$149$	−3.63270e33	−0.751350	−0.375675	−	0.926752i	$-0.622589\pi$
$149$	−3.63270e33	−0.751350	−0.375675	+	0.926752i	$0.622589\pi$
$150$	−6.38096e32	−0.118979
$151$	6.05619e33	1.01872	0.509362	−	0.860552i	$-0.329881\pi$
$151$	6.05619e33	1.01872	0.509362	+	0.860552i	$0.329881\pi$
$152$	4.12957e33	0.627088
$153$	3.39173e33	0.465269
$154$	7.95368e33	0.986273
$155$	4.34351e33	0.487191
$156$	2.51675e33	0.255510
$157$	2.21456e33	0.203631	0.101815	−	0.994803i	$-0.467535\pi$
$157$	2.21456e33	0.203631	0.101815	+	0.994803i	$0.467535\pi$
$158$	6.99163e33	0.582631
$159$	4.40541e32	0.0332913
$160$	−1.15292e33	−0.0790569
$161$	−4.27238e34	−2.65992
$162$	7.78135e33	0.440121
$163$	−1.25964e34	−0.647649	−0.323824	−	0.946117i	$-0.604969\pi$
$163$	−1.25964e34	−0.647649	−0.323824	+	0.946117i	$0.604969\pi$
$164$	−7.13572e33	−0.333701
$165$	−8.95909e33	−0.381297
$166$	3.49429e33	0.135420
$167$	−1.61993e34	−0.571992	−0.285996	−	0.958231i	$-0.592324\pi$
$167$	−1.61993e34	−0.571992	−0.285996	+	0.958231i	$0.592324\pi$
$168$	−1.27182e34	−0.409385
$169$	−2.14936e34	−0.631052
$170$	1.87926e34	0.503535
$171$	2.11830e34	0.518261
$172$	1.32411e33	0.0295960
$173$	8.33177e34	1.70225	0.851124	−	0.524965i	$-0.175922\pi$
$173$	8.33177e34	1.70225	0.851124	+	0.524965i	$0.175922\pi$
$174$	−4.24886e34	−0.793888
$175$	1.61005e34	0.275265
$176$	−1.61874e34	−0.253356
$177$	4.42375e34	0.634168
$178$	1.66226e34	0.218367
$179$	−1.19965e35	−1.44488	−0.722442	−	0.691432i	$-0.756980\pi$
$179$	−1.19965e35	−1.44488	−0.722442	+	0.691432i	$0.756980\pi$
$180$	−5.91403e33	−0.0653371
$181$	−9.22700e34	−0.935497	−0.467749	−	0.883861i	$-0.654935\pi$
$181$	−9.22700e34	−0.935497	−0.467749	+	0.883861i	$0.654935\pi$
$182$	−6.35030e34	−0.591137
$183$	−5.32987e34	−0.455748
$184$	8.69521e34	0.683288
$185$	4.67968e34	0.338107
$186$	−9.75160e34	−0.648075
$187$	2.63855e35	1.61369
$188$	−1.77388e35	−0.998798
$189$	−2.88512e35	−1.49625
$190$	1.17369e35	0.560885
$191$	9.20859e34	0.405673	0.202837	−	0.979213i	$-0.434984\pi$
$191$	9.20859e34	0.405673	0.202837	+	0.979213i	$0.434984\pi$
$192$	2.58842e34	0.105164
$193$	−4.07145e35	−1.52620	−0.763098	−	0.646283i	$-0.776323\pi$
$193$	−4.07145e35	−1.52620	−0.763098	+	0.646283i	$0.776323\pi$
$194$	−9.80241e34	−0.339161
$195$	7.15303e34	0.228536
$196$	1.51498e35	0.447133
$197$	1.97536e35	0.538791	0.269395	−	0.963030i	$-0.413176\pi$
$197$	1.97536e35	0.538791	0.269395	+	0.963030i	$0.413176\pi$
$198$	−8.30351e34	−0.209388
$199$	4.46274e35	1.04083	0.520413	−	0.853914i	$-0.325778\pi$
$199$	4.46274e35	1.04083	0.520413	+	0.853914i	$0.325778\pi$
$200$	−3.27680e34	−0.0707107
$201$	5.39838e35	1.07826
$202$	−1.82234e35	−0.337041
$203$	1.07208e36	1.83670
$204$	−4.21914e35	−0.669816
$205$	−2.02809e35	−0.298472
$206$	3.09486e35	0.422376
$207$	4.46030e35	0.564707
$208$	1.29242e35	0.151853
$209$	1.64791e36	1.79748
$210$	−3.61473e35	−0.366165
$211$	3.17406e35	0.298701	0.149351	−	0.988784i	$-0.452282\pi$
$211$	3.17406e35	0.298701	0.149351	+	0.988784i	$0.452282\pi$
$212$	2.26230e34	0.0197854
$213$	−1.41542e36	−1.15080
$214$	−1.11467e36	−0.842815
$215$	3.76334e34	0.0264714
$216$	5.87182e35	0.384362
$217$	2.46054e36	1.49936
$218$	−3.69063e35	−0.209423
$219$	−1.23053e36	−0.650444
$220$	−4.60074e35	−0.226609
$221$	−2.10665e36	−0.967190
$222$	−1.05063e36	−0.449760
$223$	1.18359e36	0.472582	0.236291	−	0.971682i	$-0.424068\pi$
$223$	1.18359e36	0.472582	0.236291	+	0.971682i	$0.424068\pi$
$224$	−6.53115e35	−0.243302
$225$	−1.68087e35	−0.0584393
$226$	5.61055e35	0.182106
$227$	1.73010e34	0.00524408	0.00262204	−	0.999997i	$-0.499165\pi$
$227$	1.73010e34	0.00524408	0.00262204	+	0.999997i	$0.499165\pi$
$228$	−2.63506e36	−0.746105
$229$	−1.57133e36	−0.415737	−0.207868	−	0.978157i	$-0.566653\pi$
$229$	−1.57133e36	−0.415737	−0.207868	+	0.978157i	$0.566653\pi$
$230$	2.47133e36	0.611151
$231$	−5.07521e36	−1.17346
$232$	−2.18191e36	−0.471816
$233$	−6.37806e36	−1.29024	−0.645122	−	0.764080i	$-0.723193\pi$
$233$	−6.37806e36	−1.29024	−0.645122	+	0.764080i	$0.723193\pi$
$234$	6.62961e35	0.125500
$235$	−5.04167e36	−0.893352
$236$	2.27172e36	0.376893
$237$	−4.46133e36	−0.693210
$238$	1.06458e37	1.54965
$239$	3.04721e36	0.415656	0.207828	−	0.978165i	$-0.433361\pi$
$239$	3.04721e36	0.415656	0.207828	+	0.978165i	$0.433361\pi$
$240$	7.35674e35	0.0940614
$241$	1.21299e36	0.145409	0.0727047	−	0.997354i	$-0.476837\pi$
$241$	1.21299e36	0.145409	0.0727047	+	0.997354i	$0.476837\pi$
$242$	−1.70007e35	−0.0191130
$243$	5.34294e36	0.563486
$244$	−2.73704e36	−0.270856
$245$	4.30583e36	0.399928
$246$	4.55327e36	0.397036
$247$	−1.31571e37	−1.07735
$248$	−5.00772e36	−0.385158
$249$	−2.22969e36	−0.161122
$250$	−9.31323e35	−0.0632456
$251$	−5.23269e36	−0.334027	−0.167014	−	0.985955i	$-0.553412\pi$
$251$	−5.23269e36	−0.334027	−0.167014	+	0.985955i	$0.553412\pi$
$252$	−3.35022e36	−0.201078
$253$	3.46983e37	1.95858
$254$	2.55608e37	1.35722
$255$	−1.19915e37	−0.599102
$256$	1.32923e36	0.0625000
$257$	−2.76137e36	−0.122225	−0.0611126	−	0.998131i	$-0.519465\pi$
$257$	−2.76137e36	−0.122225	−0.0611126	+	0.998131i	$0.519465\pi$
$258$	−8.44908e35	−0.0352131
$259$	2.65098e37	1.04054
$260$	3.67328e36	0.135821
$261$	−1.11923e37	−0.389936
$262$	−2.35468e37	−0.773147
$263$	2.48833e37	0.770183	0.385091	−	0.922878i	$-0.374170\pi$
$263$	2.48833e37	0.770183	0.385091	+	0.922878i	$0.374170\pi$
$264$	1.03291e37	0.301441
$265$	6.42985e35	0.0176966
$266$	6.64882e37	1.72615
$267$	−1.06068e37	−0.259812
$268$	2.77222e37	0.640823
$269$	−8.65600e37	−1.88867	−0.944336	−	0.328982i	$-0.893295\pi$
$269$	−8.65600e37	−1.88867	−0.944336	+	0.328982i	$0.893295\pi$
$270$	1.66887e37	0.343783
$271$	−7.04664e36	−0.137075	−0.0685375	−	0.997649i	$-0.521833\pi$
$271$	−7.04664e36	−0.137075	−0.0685375	+	0.997649i	$0.521833\pi$
$272$	−2.16664e37	−0.398079
$273$	4.05210e37	0.703330
$274$	−4.84080e37	−0.793933
$275$	−1.30761e37	−0.202685
$276$	−5.54838e37	−0.812971
$277$	8.82814e37	1.22302	0.611509	−	0.791238i	$-0.290563\pi$
$277$	8.82814e37	1.22302	0.611509	+	0.791238i	$0.290563\pi$
$278$	−1.78120e37	−0.233356
$279$	−2.56876e37	−0.318316
$280$	−1.85627e37	−0.217616
$281$	−2.56349e36	−0.0284370	−0.0142185	−	0.999899i	$-0.504526\pi$
$281$	−2.56349e36	−0.0284370	−0.0142185	+	0.999899i	$0.504526\pi$
$282$	1.13191e38	1.18836
$283$	−1.16177e38	−1.15460	−0.577298	−	0.816533i	$-0.695893\pi$
$283$	−1.16177e38	−1.15460	−0.577298	+	0.816533i	$0.695893\pi$
$284$	−7.26858e37	−0.683936
$285$	−7.48929e37	−0.667337
$286$	5.15742e37	0.435270
$287$	−1.14889e38	−0.918562
$288$	6.81841e36	0.0516535
$289$	2.13874e38	1.53547
$290$	−6.20136e37	−0.422005
$291$	6.25488e37	0.403532
$292$	−6.31913e37	−0.386566
$293$	−1.14934e38	−0.666805	−0.333402	−	0.942785i	$-0.608197\pi$
$293$	−1.14934e38	−0.666805	−0.333402	+	0.942785i	$0.608197\pi$
$294$	−9.66701e37	−0.531996
$295$	6.45661e37	0.337103
$296$	−5.39530e37	−0.267297
$297$	2.34316e38	1.10173
$298$	1.19036e38	0.531285
$299$	−2.77035e38	−1.17390
$300$	2.09091e37	0.0841311
$301$	2.13189e37	0.0814673
$302$	−1.98449e38	−0.720347
$303$	1.16283e38	0.401009
$304$	−1.35318e38	−0.443418
$305$	−7.77913e37	−0.242261
$306$	−1.11140e38	−0.328995
$307$	1.02249e38	0.287749	0.143874	−	0.989596i	$-0.454044\pi$
$307$	1.02249e38	0.287749	0.143874	+	0.989596i	$0.454044\pi$
$308$	−2.60626e38	−0.697400
$309$	−1.97482e38	−0.502540
$310$	−1.42328e38	−0.344496
$311$	5.49215e38	1.26461	0.632305	−	0.774720i	$-0.282109\pi$
$311$	5.49215e38	1.26461	0.632305	+	0.774720i	$0.282109\pi$
$312$	−8.24688e37	−0.180673
$313$	3.18159e38	0.663294	0.331647	−	0.943403i	$-0.392396\pi$
$313$	3.18159e38	0.663294	0.331647	+	0.943403i	$0.392396\pi$
$314$	−7.25667e37	−0.143989
$315$	−9.52191e37	−0.179850
$316$	−2.29102e38	−0.411982
$317$	4.84708e38	0.829968	0.414984	−	0.909829i	$-0.363787\pi$
$317$	4.84708e38	0.829968	0.414984	+	0.909829i	$0.363787\pi$
$318$	−1.44357e37	−0.0235405
$319$	−8.70693e38	−1.35241
$320$	3.77789e37	0.0559017
$321$	7.11266e38	1.00278
$322$	1.39997e39	1.88085
$323$	2.20568e39	2.82425
$324$	−2.54979e38	−0.311212
$325$	1.04401e38	0.121482
$326$	4.12760e38	0.457957
$327$	2.35497e38	0.249170
$328$	2.33823e38	0.235962
$329$	−2.85604e39	−2.74934
$330$	2.93572e38	0.269617
$331$	1.17621e39	1.03074	0.515371	−	0.856967i	$-0.327654\pi$
$331$	1.17621e39	1.03074	0.515371	+	0.856967i	$0.327654\pi$
$332$	−1.14501e38	−0.0957564
$333$	−2.76758e38	−0.220909
$334$	5.30817e38	0.404459
$335$	7.87912e38	0.573170
$336$	4.16750e38	0.289479
$337$	3.32696e38	0.220690	0.110345	−	0.993893i	$-0.464804\pi$
$337$	3.32696e38	0.220690	0.110345	+	0.993893i	$0.464804\pi$
$338$	7.04303e38	0.446221
$339$	−3.58007e38	−0.216669
$340$	−6.15797e38	−0.356053
$341$	−1.99834e39	−1.10402
$342$	−6.94126e38	−0.366466
$343$	−2.88397e38	−0.145523
$344$	−4.33884e37	−0.0209275
$345$	−1.57694e39	−0.727143
$346$	−2.73015e39	−1.20367
$347$	−2.52708e39	−1.06540	−0.532700	−	0.846304i	$-0.678823\pi$
$347$	−2.52708e39	−1.06540	−0.532700	+	0.846304i	$0.678823\pi$
$348$	1.39227e39	0.561364
$349$	−2.89784e39	−1.11758	−0.558792	−	0.829308i	$-0.688735\pi$
$349$	−2.89784e39	−1.11758	−0.558792	+	0.829308i	$0.688735\pi$
$350$	−5.27582e38	−0.194642
$351$	−1.87080e39	−0.660339
$352$	5.30430e38	0.179150
$353$	4.87022e39	1.57413	0.787065	−	0.616871i	$-0.211600\pi$
$353$	4.87022e39	1.57413	0.787065	+	0.616871i	$0.211600\pi$
$354$	−1.44957e39	−0.448425
$355$	−2.06585e39	−0.611731
$356$	−5.44688e38	−0.154409
$357$	−6.79303e39	−1.84377
$358$	3.93101e39	1.02169
$359$	−4.94989e39	−1.23206	−0.616030	−	0.787723i	$-0.711260\pi$
$359$	−4.94989e39	−1.23206	−0.616030	+	0.787723i	$0.711260\pi$
$360$	1.93791e38	0.0462003
$361$	9.39669e39	2.14592
$362$	3.02350e39	0.661497
$363$	1.08481e38	0.0227406
$364$	2.08087e39	0.417997
$365$	−1.79601e39	−0.345755
$366$	1.74649e39	0.322263
$367$	2.60673e39	0.461076	0.230538	−	0.973063i	$-0.425951\pi$
$367$	2.60673e39	0.461076	0.230538	+	0.973063i	$0.425951\pi$
$368$	−2.84925e39	−0.483157
$369$	1.19942e39	0.195013
$370$	−1.53344e39	−0.239078
$371$	3.64243e38	0.0544622
$372$	3.19541e39	0.458258
$373$	5.14959e39	0.708412	0.354206	−	0.935167i	$-0.384751\pi$
$373$	5.14959e39	0.708412	0.354206	+	0.935167i	$0.384751\pi$
$374$	−8.64601e39	−1.14105
$375$	5.94273e38	0.0752491
$376$	5.81265e39	0.706257
$377$	6.95170e39	0.810588
$378$	9.45395e39	1.05801
$379$	−1.10887e40	−1.19117	−0.595584	−	0.803293i	$-0.703079\pi$
$379$	−1.10887e40	−1.19117	−0.595584	+	0.803293i	$0.703079\pi$
$380$	−3.84596e39	−0.396605
$381$	−1.63102e40	−1.61481
$382$	−3.01747e39	−0.286854
$383$	1.77078e39	0.161653	0.0808266	−	0.996728i	$-0.474244\pi$
$383$	1.77078e39	0.161653	0.0808266	+	0.996728i	$0.474244\pi$
$384$	−8.48175e38	−0.0743621
$385$	−7.40744e39	−0.623774
$386$	1.33413e40	1.07918
$387$	−2.22565e38	−0.0172957
$388$	3.21205e39	0.239823
$389$	1.78976e40	1.28403	0.642015	−	0.766692i	$-0.278099\pi$
$389$	1.78976e40	1.28403	0.642015	+	0.766692i	$0.278099\pi$
$390$	−2.34391e39	−0.161599
$391$	4.64427e40	3.07736
$392$	−4.96428e39	−0.316171
$393$	1.50251e40	0.919885
$394$	−6.47287e39	−0.380983
$395$	−6.51146e39	−0.368488
$396$	2.72089e39	0.148060
$397$	1.42952e40	0.748063	0.374032	−	0.927416i	$-0.377975\pi$
$397$	1.42952e40	0.748063	0.374032	+	0.927416i	$0.377975\pi$
$398$	−1.46235e40	−0.735976
$399$	−4.24258e40	−2.05376
$400$	1.07374e39	0.0500000
$401$	1.59146e38	0.00712948	0.00356474	−	0.999994i	$-0.498865\pi$
$401$	1.59146e38	0.00712948	0.00356474	+	0.999994i	$0.498865\pi$
$402$	−1.76894e40	−0.762447
$403$	1.59549e40	0.661708
$404$	5.97144e39	0.238324
$405$	−7.24694e39	−0.278357
$406$	−3.51299e40	−1.29874
$407$	−2.15300e40	−0.766180
$408$	1.38253e40	0.473632
$409$	6.33912e39	0.209083	0.104541	−	0.994521i	$-0.466663\pi$
$409$	6.33912e39	0.209083	0.104541	+	0.994521i	$0.466663\pi$
$410$	6.64565e39	0.211051
$411$	3.08890e40	0.944616
$412$	−1.01412e40	−0.298665
$413$	3.65759e40	1.03745
$414$	−1.46155e40	−0.399308
$415$	−3.25431e39	−0.0856472
$416$	−4.23501e39	−0.107376
$417$	1.13658e40	0.277646
$418$	−5.39986e40	−1.27101
$419$	−9.89389e39	−0.224414	−0.112207	−	0.993685i	$-0.535792\pi$
$419$	−9.89389e39	−0.224414	−0.112207	+	0.993685i	$0.535792\pi$
$420$	1.18448e40	0.258918
$421$	−4.00753e40	−0.844315	−0.422157	−	0.906523i	$-0.638727\pi$
$421$	−4.00753e40	−0.844315	−0.422157	+	0.906523i	$0.638727\pi$
$422$	−1.04008e40	−0.211214
$423$	2.98166e40	0.583690
$424$	−7.41311e38	−0.0139904
$425$	−1.75020e40	−0.318463
$426$	4.63805e40	0.813742
$427$	−4.40678e40	−0.745571
$428$	3.65255e40	0.595961
$429$	−3.29093e40	−0.517881
$430$	−1.23317e39	−0.0187181
$431$	−1.32321e41	−1.93745	−0.968725	−	0.248136i	$-0.920182\pi$
$431$	−1.32321e41	−1.93745	−0.968725	+	0.248136i	$0.920182\pi$
$432$	−1.92408e40	−0.271785
$433$	−7.69902e40	−1.04924	−0.524618	−	0.851338i	$-0.675792\pi$
$433$	−7.69902e40	−1.04924	−0.524618	+	0.851338i	$0.675792\pi$
$434$	−8.06270e40	−1.06020
$435$	3.95706e40	0.502099
$436$	1.20934e40	0.148085
$437$	2.90058e41	3.42785
$438$	4.03221e40	0.459933
$439$	−6.36959e40	−0.701313	−0.350656	−	0.936504i	$-0.614041\pi$
$439$	−6.36959e40	−0.701313	−0.350656	+	0.936504i	$0.614041\pi$
$440$	1.50757e40	0.160237
$441$	−2.54648e40	−0.261301
$442$	6.90306e40	0.683906
$443$	6.37157e39	0.0609521	0.0304761	−	0.999535i	$-0.490298\pi$
$443$	6.37157e39	0.0609521	0.0304761	+	0.999535i	$0.490298\pi$
$444$	3.44272e40	0.318028
$445$	−1.54810e40	−0.138108
$446$	−3.87840e40	−0.334166
$447$	−7.59565e40	−0.632119
$448$	2.14013e40	0.172040
$449$	−1.42862e41	−1.10943	−0.554715	−	0.832040i	$-0.687173\pi$
$449$	−1.42862e41	−1.10943	−0.554715	+	0.832040i	$0.687173\pi$
$450$	5.50787e39	0.0413228
$451$	9.33074e40	0.676362
$452$	−1.83847e40	−0.128769
$453$	1.26630e41	0.857064
$454$	−5.66918e38	−0.00370812
$455$	5.91418e40	0.373868
$456$	8.63456e40	0.527576
$457$	−5.32708e40	−0.314621	−0.157311	−	0.987549i	$-0.550282\pi$
$457$	−5.32708e40	−0.314621	−0.157311	+	0.987549i	$0.550282\pi$
$458$	5.14895e40	0.293970
$459$	3.13625e41	1.73107
$460$	−8.09804e40	−0.432149
$461$	−1.55667e41	−0.803214	−0.401607	−	0.915812i	$-0.631548\pi$
$461$	−1.55667e41	−0.803214	−0.401607	+	0.915812i	$0.631548\pi$
$462$	1.66305e41	0.829762
$463$	−2.90324e41	−1.40080	−0.700401	−	0.713749i	$-0.746996\pi$
$463$	−2.90324e41	−1.40080	−0.700401	+	0.713749i	$0.746996\pi$
$464$	7.14968e40	0.333625
$465$	9.08189e40	0.409879
$466$	2.08996e41	0.912340
$467$	−1.49482e41	−0.631216	−0.315608	−	0.948890i	$-0.602209\pi$
$467$	−1.49482e41	−0.631216	−0.315608	+	0.948890i	$0.602209\pi$
$468$	−2.17239e40	−0.0887416
$469$	4.46342e41	1.76396
$470$	1.65205e41	0.631695
$471$	4.63045e40	0.171317
$472$	−7.44396e40	−0.266504
$473$	−1.73142e40	−0.0599866
$474$	1.46189e41	0.490174
$475$	−1.09309e41	−0.354735
$476$	−3.48841e41	−1.09577
$477$	−3.80263e39	−0.0115624
$478$	−9.98509e40	−0.293913
$479$	9.00830e40	0.256710	0.128355	−	0.991728i	$-0.459030\pi$
$479$	9.00830e40	0.256710	0.128355	+	0.991728i	$0.459030\pi$
$480$	−2.41066e40	−0.0665114
$481$	1.71898e41	0.459221
$482$	−3.97472e40	−0.102820
$483$	−8.93318e41	−2.23782
$484$	5.57081e39	0.0135150
$485$	9.12921e40	0.214504
$486$	−1.75077e41	−0.398445
$487$	2.08879e41	0.460463	0.230232	−	0.973136i	$-0.426052\pi$
$487$	2.08879e41	0.460463	0.230232	+	0.973136i	$0.426052\pi$
$488$	8.96873e40	0.191524
$489$	−2.63380e41	−0.544874
$490$	−1.41093e41	−0.282792
$491$	5.18801e41	1.00748	0.503742	−	0.863854i	$-0.331956\pi$
$491$	5.18801e41	1.00748	0.503742	+	0.863854i	$0.331956\pi$
$492$	−1.49202e41	−0.280747
$493$	−1.16540e42	−2.12494
$494$	4.31130e41	0.761800
$495$	7.73325e40	0.132428
$496$	1.64093e41	0.272348
$497$	−1.17028e42	−1.88263
$498$	7.30624e40	0.113930
$499$	−3.17894e41	−0.480534	−0.240267	−	0.970707i	$-0.577235\pi$
$499$	−3.17894e41	−0.480534	−0.240267	+	0.970707i	$0.577235\pi$
$500$	3.05176e40	0.0447214
$501$	−3.38712e41	−0.481223
$502$	1.71465e41	0.236193
$503$	−2.67214e39	−0.00356908	−0.00178454	−	0.999998i	$-0.500568\pi$
$503$	−2.67214e39	−0.00356908	−0.00178454	+	0.999998i	$0.500568\pi$
$504$	1.09780e41	0.142184
$505$	1.69719e41	0.213164
$506$	−1.13699e42	−1.38492
$507$	−4.49413e41	−0.530911
$508$	−8.37575e41	−0.959701
$509$	1.25901e42	1.39928	0.699638	−	0.714498i	$-0.253345\pi$
$509$	1.25901e42	1.39928	0.699638	+	0.714498i	$0.253345\pi$
$510$	3.92938e41	0.423629
$511$	−1.01741e42	−1.06408
$512$	−4.35561e40	−0.0441942
$513$	1.95874e42	1.92823
$514$	9.04845e40	0.0864263
$515$	−2.88231e41	−0.267134
$516$	2.76860e40	0.0248994
$517$	2.31954e42	2.02441
$518$	−8.68672e41	−0.735774
$519$	1.74210e42	1.43212
$520$	−1.20366e41	−0.0960400
$521$	1.93165e42	1.49604	0.748020	−	0.663676i	$-0.231005\pi$
$521$	1.93165e42	1.49604	0.748020	+	0.663676i	$0.231005\pi$
$522$	3.66750e41	0.275726
$523$	5.98151e41	0.436551	0.218275	−	0.975887i	$-0.429957\pi$
$523$	5.98151e41	0.436551	0.218275	+	0.975887i	$0.429957\pi$
$524$	7.71582e41	0.546698
$525$	3.36648e41	0.231583
$526$	−8.15376e41	−0.544602
$527$	−2.67472e42	−1.73466
$528$	−3.38465e41	−0.213151
$529$	4.47228e42	2.73506
$530$	−2.10693e40	−0.0125134
$531$	−3.81846e41	−0.220254
$532$	−2.17869e42	−1.22057
$533$	−7.44976e41	−0.405387
$534$	3.47563e41	0.183715
$535$	1.03812e42	0.533043
$536$	−9.08401e41	−0.453131
$537$	−2.50836e42	−1.21560
$538$	2.83640e42	1.33549
$539$	−1.98100e42	−0.906272
$540$	−5.46856e41	−0.243092
$541$	9.64612e41	0.416673	0.208336	−	0.978057i	$-0.433195\pi$
$541$	9.64612e41	0.416673	0.208336	+	0.978057i	$0.433195\pi$
$542$	2.30904e41	0.0969266
$543$	−1.92928e42	−0.787044
$544$	7.09966e41	0.281484
$545$	3.43717e41	0.132451
$546$	−1.32779e42	−0.497330
$547$	4.34799e42	1.58302	0.791508	−	0.611159i	$-0.209297\pi$
$547$	4.34799e42	1.58302	0.791508	+	0.611159i	$0.209297\pi$
$548$	1.58623e42	0.561395
$549$	4.60060e41	0.158286
$550$	4.28478e41	0.143320
$551$	−7.27849e42	−2.36696
$552$	1.81809e42	0.574857
$553$	−3.68866e42	−1.13404
$554$	−2.89280e42	−0.864804
$555$	9.78479e41	0.284453
$556$	5.83665e41	0.165008
$557$	4.75748e42	1.30804	0.654021	−	0.756476i	$-0.273081\pi$
$557$	4.75748e42	1.30804	0.654021	+	0.756476i	$0.273081\pi$
$558$	8.41732e41	0.225084
$559$	1.38238e41	0.0359538
$560$	6.08261e41	0.153878
$561$	5.51698e42	1.35762
$562$	8.40004e40	0.0201080
$563$	−7.57947e42	−1.76506	−0.882529	−	0.470259i	$-0.844161\pi$
$563$	−7.57947e42	−1.76506	−0.882529	+	0.470259i	$0.844161\pi$
$564$	−3.70903e42	−0.840299
$565$	−5.22523e41	−0.115174
$566$	3.80689e42	0.816423
$567$	−4.10530e42	−0.856658
$568$	2.38177e42	0.483615
$569$	−1.13132e41	−0.0223536	−0.0111768	−	0.999938i	$-0.503558\pi$
$569$	−1.13132e41	−0.0223536	−0.0111768	+	0.999938i	$0.503558\pi$
$570$	2.45409e42	0.471878
$571$	−3.31794e41	−0.0620882	−0.0310441	−	0.999518i	$-0.509883\pi$
$571$	−3.31794e41	−0.0620882	−0.0310441	+	0.999518i	$0.509883\pi$
$572$	−1.68998e42	−0.307782
$573$	1.92544e42	0.341297
$574$	3.76468e42	0.649522
$575$	−2.30160e42	−0.386526
$576$	−2.23426e41	−0.0365245
$577$	−1.34557e40	−0.00214131	−0.00107066	−	0.999999i	$-0.500341\pi$
$577$	−1.34557e40	−0.00214131	−0.00107066	+	0.999999i	$0.500341\pi$
$578$	−7.00823e42	−1.08574
$579$	−8.51304e42	−1.28401
$580$	2.03206e42	0.298403
$581$	−1.84352e42	−0.263584
$582$	−2.04960e42	−0.285340
$583$	−2.95821e41	−0.0401020
$584$	2.07065e42	0.273343
$585$	−6.17430e41	−0.0793729
$586$	3.76614e42	0.471502
$587$	1.52213e42	0.185593	0.0927965	−	0.995685i	$-0.470419\pi$
$587$	1.52213e42	0.185593	0.0927965	+	0.995685i	$0.470419\pi$
$588$	3.16769e42	0.376178
$589$	−1.67049e43	−1.93223
$590$	−2.11570e42	−0.238368
$591$	4.13031e42	0.453290
$592$	1.76793e42	0.189008
$593$	1.84601e42	0.192259	0.0961296	−	0.995369i	$-0.469354\pi$
$593$	1.84601e42	0.192259	0.0961296	+	0.995369i	$0.469354\pi$
$594$	−7.67806e42	−0.779043
$595$	−9.91466e42	−0.980088
$596$	−3.90058e42	−0.375675
$597$	9.33119e42	0.875659
$598$	9.07788e42	0.830072
$599$	−9.39650e41	−0.0837241	−0.0418620	−	0.999123i	$-0.513329\pi$
$599$	−9.39650e41	−0.0837241	−0.0418620	+	0.999123i	$0.513329\pi$
$600$	−6.85150e41	−0.0594896
$601$	1.58484e43	1.34101	0.670505	−	0.741905i	$-0.266077\pi$
$601$	1.58484e43	1.34101	0.670505	+	0.741905i	$0.266077\pi$
$602$	−6.98576e41	−0.0576061
$603$	−4.65974e42	−0.374492
$604$	6.50278e42	0.509362
$605$	1.58332e41	0.0120882
$606$	−3.81035e42	−0.283556
$607$	1.95801e43	1.42033	0.710167	−	0.704034i	$-0.248620\pi$
$607$	1.95801e43	1.42033	0.710167	+	0.704034i	$0.248620\pi$
$608$	4.43409e42	0.313544
$609$	2.24163e43	1.54524
$610$	2.54907e42	0.171304
$611$	−1.85195e43	−1.21336
$612$	3.64184e42	0.232635
$613$	1.98433e43	1.23588	0.617939	−	0.786226i	$-0.287968\pi$
$613$	1.98433e43	1.23588	0.617939	+	0.786226i	$0.287968\pi$
$614$	−3.35049e42	−0.203469
$615$	−4.24056e42	−0.251107
$616$	8.54020e42	0.493136
$617$	−2.01865e43	−1.13669	−0.568344	−	0.822791i	$-0.692416\pi$
$617$	−2.01865e43	−1.13669	−0.568344	+	0.822791i	$0.692416\pi$
$618$	6.47108e42	0.355349
$619$	−1.28098e43	−0.686020	−0.343010	−	0.939332i	$-0.611447\pi$
$619$	−1.28098e43	−0.686020	−0.343010	+	0.939332i	$0.611447\pi$
$620$	4.66380e42	0.243595
$621$	4.12433e43	2.10104
$622$	−1.79967e43	−0.894214
$623$	−8.76977e42	−0.425034
$624$	2.70234e42	0.127755
$625$	8.67362e41	0.0400000
$626$	−1.04254e43	−0.469020
$627$	3.44563e43	1.51224
$628$	2.37787e42	0.101815
$629$	−2.88173e43	−1.20384
$630$	3.12014e42	0.127173
$631$	−9.11677e42	−0.362565	−0.181283	−	0.983431i	$-0.558025\pi$
$631$	−9.11677e42	−0.362565	−0.181283	+	0.983431i	$0.558025\pi$
$632$	7.50720e42	0.291315
$633$	6.63668e42	0.251300
$634$	−1.58829e43	−0.586876
$635$	−2.38053e43	−0.858383
$636$	4.73028e41	0.0166457
$637$	1.58165e43	0.543187
$638$	2.85309e43	0.956301
$639$	1.22175e43	0.399687
$640$	−1.23794e42	−0.0395285
$641$	−7.56603e42	−0.235813	−0.117907	−	0.993025i	$-0.537618\pi$
$641$	−7.56603e42	−0.235813	−0.117907	+	0.993025i	$0.537618\pi$
$642$	−2.33068e43	−0.709070
$643$	5.52599e43	1.64112	0.820559	−	0.571561i	$-0.193662\pi$
$643$	5.52599e43	1.64112	0.820559	+	0.571561i	$0.193662\pi$
$644$	−4.58744e43	−1.32996
$645$	7.86882e41	0.0222707
$646$	−7.22757e43	−1.99705
$647$	−5.65084e43	−1.52439	−0.762197	−	0.647346i	$-0.775879\pi$
$647$	−5.65084e43	−1.52439	−0.762197	+	0.647346i	$0.775879\pi$
$648$	8.35516e42	0.220060
$649$	−2.97052e43	−0.763905
$650$	−3.42101e42	−0.0859008
$651$	5.14477e43	1.26142
$652$	−1.35253e43	−0.323824
$653$	−9.93457e42	−0.232271	−0.116135	−	0.993233i	$-0.537051\pi$
$653$	−9.93457e42	−0.232271	−0.116135	+	0.993233i	$0.537051\pi$
$654$	−7.71678e42	−0.176190
$655$	2.19297e43	0.488981
$656$	−7.66192e42	−0.166851
$657$	1.06216e43	0.225906
$658$	9.35868e43	1.94408
$659$	−2.37067e43	−0.481003	−0.240501	−	0.970649i	$-0.577312\pi$
$659$	−2.37067e43	−0.481003	−0.240501	+	0.970649i	$0.577312\pi$
$660$	−9.61975e42	−0.190648
$661$	3.30974e43	0.640725	0.320363	−	0.947295i	$-0.396195\pi$
$661$	3.30974e43	0.640725	0.320363	+	0.947295i	$0.396195\pi$
$662$	−3.85420e43	−0.728845
$663$	−4.40482e43	−0.813707
$664$	3.75196e42	0.0677100
$665$	−6.19220e43	−1.09171
$666$	9.06879e42	0.156206
$667$	−1.53256e44	−2.57909
$668$	−1.73938e43	−0.285996
$669$	2.47479e43	0.397588
$670$	−2.58183e43	−0.405292
$671$	3.57898e43	0.548985
$672$	−1.36561e43	−0.204693
$673$	3.83414e43	0.561609	0.280805	−	0.959765i	$-0.409399\pi$
$673$	3.83414e43	0.561609	0.280805	+	0.959765i	$0.409399\pi$
$674$	−1.09018e43	−0.156052
$675$	−1.55426e43	−0.217428
$676$	−2.30786e43	−0.315526
$677$	1.18717e44	1.58631	0.793153	−	0.609022i	$-0.208438\pi$
$677$	1.18717e44	1.58631	0.793153	+	0.609022i	$0.208438\pi$
$678$	1.17312e43	0.153208
$679$	5.17158e43	0.660149
$680$	2.01784e43	0.251767
$681$	3.61748e41	0.00441190
$682$	6.54815e43	0.780658
$683$	−1.22953e44	−1.43291	−0.716453	−	0.697635i	$-0.754236\pi$
$683$	−1.22953e44	−1.43291	−0.716453	+	0.697635i	$0.754236\pi$
$684$	2.27451e43	0.259130
$685$	4.50835e43	0.502127
$686$	9.45020e42	0.102900
$687$	−3.28552e43	−0.349764
$688$	1.42175e42	0.0147980
$689$	2.36187e42	0.0240357
$690$	5.16733e43	0.514168
$691$	1.32263e44	1.28686	0.643428	−	0.765507i	$-0.277512\pi$
$691$	1.32263e44	1.28686	0.643428	+	0.765507i	$0.277512\pi$
$692$	8.94617e43	0.851124
$693$	4.38079e43	0.407556
$694$	8.28075e43	0.753352
$695$	1.65888e43	0.147587
$696$	−4.56218e43	−0.396944
$697$	1.24889e44	1.06272
$698$	9.49564e43	0.790252
$699$	−1.33360e44	−1.08550
$700$	1.72878e43	0.137632
$701$	1.62662e44	1.26665	0.633325	−	0.773886i	$-0.281690\pi$
$701$	1.62662e44	1.26665	0.633325	+	0.773886i	$0.281690\pi$
$702$	6.13024e43	0.466930
$703$	−1.79978e44	−1.34095
$704$	−1.73811e43	−0.126678
$705$	−1.05417e44	−0.751586
$706$	−1.59587e44	−1.11308
$707$	9.61434e43	0.656022
$708$	4.74996e43	0.317084
$709$	−2.46555e43	−0.161027	−0.0805133	−	0.996754i	$-0.525656\pi$
$709$	−2.46555e43	−0.161027	−0.0805133	+	0.996754i	$0.525656\pi$
$710$	6.76939e43	0.432559
$711$	3.85090e43	0.240759
$712$	1.78483e43	0.109184
$713$	−3.51739e44	−2.10539
$714$	2.22594e44	1.30374
$715$	−4.80322e43	−0.275289
$716$	−1.28811e44	−0.722442
$717$	6.37144e43	0.349696
$718$	1.62198e44	0.871198
$719$	−1.33187e44	−0.700108	−0.350054	−	0.936729i	$-0.613837\pi$
$719$	−1.33187e44	−0.700108	−0.350054	+	0.936729i	$0.613837\pi$
$720$	−6.35014e42	−0.0326685
$721$	−1.63279e44	−0.822119
$722$	−3.07911e44	−1.51739
$723$	2.53625e43	0.122335
$724$	−9.90742e43	−0.467749
$725$	5.77547e43	0.266900
$726$	−3.55471e42	−0.0160800
$727$	3.69856e44	1.63775	0.818877	−	0.573969i	$-0.194597\pi$
$727$	3.69856e44	1.63775	0.818877	+	0.573969i	$0.194597\pi$
$728$	−6.81858e43	−0.295568
$729$	2.58394e44	1.09649
$730$	5.88515e43	0.244486
$731$	−2.31746e43	−0.0942523
$732$	−5.72291e43	−0.227874
$733$	−2.48074e44	−0.967095	−0.483547	−	0.875318i	$-0.660652\pi$
$733$	−2.48074e44	−0.967095	−0.483547	+	0.875318i	$0.660652\pi$
$734$	−8.54174e43	−0.326030
$735$	9.00310e43	0.336464
$736$	9.33641e43	0.341644
$737$	−3.62498e44	−1.29885
$738$	−3.93026e43	−0.137895
$739$	7.67405e43	0.263655	0.131827	−	0.991273i	$-0.457916\pi$
$739$	7.67405e43	0.263655	0.131827	+	0.991273i	$0.457916\pi$
$740$	5.02476e43	0.169053
$741$	−2.75103e44	−0.906384
$742$	−1.19355e43	−0.0385106
$743$	−5.47245e44	−1.72924	−0.864620	−	0.502427i	$-0.832441\pi$
$743$	−5.47245e44	−1.72924	−0.864620	+	0.502427i	$0.832441\pi$
$744$	−1.04707e44	−0.324038
$745$	−1.10861e44	−0.336014
$746$	−1.68742e44	−0.500923
$747$	1.92461e43	0.0559594
$748$	2.83313e44	0.806847
$749$	5.88080e44	1.64047
$750$	−1.94731e43	−0.0532092
$751$	4.53013e44	1.21253	0.606263	−	0.795264i	$-0.292668\pi$
$751$	4.53013e44	1.21253	0.606263	+	0.795264i	$0.292668\pi$
$752$	−1.90469e44	−0.499399
$753$	−1.09411e44	−0.281021
$754$	−2.27793e44	−0.573173
$755$	1.84820e44	0.455587
$756$	−3.09787e44	−0.748127
$757$	−3.88934e44	−0.920215	−0.460108	−	0.887863i	$-0.652189\pi$
$757$	−3.88934e44	−0.920215	−0.460108	+	0.887863i	$0.652189\pi$
$758$	3.63354e44	0.842282
$759$	7.25511e44	1.64777
$760$	1.26024e44	0.280442
$761$	−5.46740e44	−1.19212	−0.596058	−	0.802941i	$-0.703267\pi$
$761$	−5.46740e44	−1.19212	−0.596058	+	0.802941i	$0.703267\pi$
$762$	5.34453e44	1.14185
$763$	1.94711e44	0.407624
$764$	9.88765e43	0.202837
$765$	1.03507e44	0.208075
$766$	−5.80250e43	−0.114306
$767$	2.37169e44	0.457858
$768$	2.77930e43	0.0525819
$769$	−8.57160e44	−1.58929	−0.794646	−	0.607073i	$-0.792343\pi$
$769$	−8.57160e44	−1.58929	−0.794646	+	0.607073i	$0.792343\pi$
$770$	2.42727e44	0.441075
$771$	−5.77378e43	−0.102829
$772$	−4.37168e44	−0.763098
$773$	−2.48088e44	−0.424447	−0.212224	−	0.977221i	$-0.568071\pi$
$773$	−2.48088e44	−0.424447	−0.212224	+	0.977221i	$0.568071\pi$
$774$	7.29302e42	0.0122299
$775$	1.32553e44	0.217878
$776$	−1.05253e44	−0.169581
$777$	5.54296e44	0.875419
$778$	−5.86467e44	−0.907946
$779$	7.79996e44	1.18375
$780$	7.68051e43	0.114268
$781$	9.50447e44	1.38623
$782$	−1.52184e45	−2.17602
$783$	−1.03493e45	−1.45078
$784$	1.62669e44	0.223567
$785$	6.75830e43	0.0910664
$786$	−4.92343e44	−0.650457
$787$	7.42427e44	0.961713	0.480857	−	0.876799i	$-0.340326\pi$
$787$	7.42427e44	0.961713	0.480857	+	0.876799i	$0.340326\pi$
$788$	2.12103e44	0.269395
$789$	5.20288e44	0.647963
$790$	2.13368e44	0.260560
$791$	−2.96003e44	−0.354454
$792$	−8.91583e43	−0.104694
$793$	−2.85749e44	−0.329042
$794$	−4.68426e44	−0.528961
$795$	1.34443e43	0.0148883
$796$	4.79183e44	0.520413
$797$	6.95745e44	0.741047	0.370524	−	0.928823i	$-0.379178\pi$
$797$	6.95745e44	0.741047	0.370524	+	0.928823i	$0.379178\pi$
$798$	1.39021e45	1.45223
$799$	3.10465e45	3.18080
$800$	−3.51844e43	−0.0353553
$801$	9.15549e43	0.0902355
$802$	−5.21489e42	−0.00504130
$803$	8.26296e44	0.783510
$804$	5.79647e44	0.539132
$805$	−1.30383e45	−1.18955
$806$	−5.22811e44	−0.467898
$807$	−1.80989e45	−1.58896
$808$	−1.95672e44	−0.168521
$809$	−5.39805e44	−0.456073	−0.228037	−	0.973653i	$-0.573231\pi$
$809$	−5.39805e44	−0.456073	−0.228037	+	0.973653i	$0.573231\pi$
$810$	2.37468e44	0.196828
$811$	6.12229e44	0.497841	0.248920	−	0.968524i	$-0.419924\pi$
$811$	6.12229e44	0.497841	0.248920	+	0.968524i	$0.419924\pi$
$812$	1.15114e45	0.918351
$813$	−1.47339e44	−0.115323
$814$	7.05495e44	0.541771
$815$	−3.84412e44	−0.289637
$816$	−4.53026e44	−0.334908
$817$	−1.44737e44	−0.104987
$818$	−2.07720e44	−0.147844
$819$	−3.49766e44	−0.244274
$820$	−2.17765e44	−0.149236
$821$	2.89962e44	0.194995	0.0974973	−	0.995236i	$-0.468916\pi$
$821$	2.89962e44	0.194995	0.0974973	+	0.995236i	$0.468916\pi$
$822$	−1.01217e45	−0.667944
$823$	−9.30283e44	−0.602445	−0.301223	−	0.953554i	$-0.597395\pi$
$823$	−9.30283e44	−0.602445	−0.301223	+	0.953554i	$0.597395\pi$
$824$	3.32308e44	0.211188
$825$	−2.73410e44	−0.170521
$826$	−1.19852e45	−0.733590
$827$	4.60750e44	0.276777	0.138389	−	0.990378i	$-0.455808\pi$
$827$	4.60750e44	0.276777	0.138389	+	0.990378i	$0.455808\pi$
$828$	4.78921e44	0.282354
$829$	−3.33913e45	−1.93214	−0.966069	−	0.258284i	$-0.916843\pi$
$829$	−3.33913e45	−1.93214	−0.966069	+	0.258284i	$0.916843\pi$
$830$	1.06637e44	0.0605617
$831$	1.84589e45	1.02894
$832$	1.38773e44	0.0759263
$833$	−2.65151e45	−1.42396
$834$	−3.72434e44	−0.196325
$835$	−4.94362e44	−0.255803
$836$	1.76943e45	0.898742
$837$	−2.37527e45	−1.18432
$838$	3.24203e44	0.158684
$839$	−3.12484e45	−1.50147	−0.750737	−	0.660601i	$-0.770302\pi$
$839$	−3.12484e45	−1.50147	−0.750737	+	0.660601i	$0.770302\pi$
$840$	−3.88129e44	−0.183083
$841$	1.68626e45	0.780886
$842$	1.31319e45	0.597021
$843$	−5.36003e43	−0.0239243
$844$	3.40812e44	0.149351
$845$	−6.55933e44	−0.282215
$846$	−9.77030e44	−0.412731
$847$	8.96929e43	0.0372019
$848$	2.42913e43	0.00989270
$849$	−2.42916e45	−0.971375
$850$	5.73506e44	0.225188
$851$	−3.78962e45	−1.46113
$852$	−1.51980e45	−0.575402
$853$	−1.87985e44	−0.0698896	−0.0349448	−	0.999389i	$-0.511126\pi$
$853$	−1.87985e44	−0.0698896	−0.0349448	+	0.999389i	$0.511126\pi$
$854$	1.44401e45	0.527198
$855$	6.46455e44	0.231773
$856$	−1.19687e45	−0.421408
$857$	1.66635e45	0.576186	0.288093	−	0.957602i	$-0.406979\pi$
$857$	1.66635e45	0.576186	0.288093	+	0.957602i	$0.406979\pi$
$858$	1.07837e45	0.366197
$859$	1.58190e45	0.527576	0.263788	−	0.964581i	$-0.415028\pi$
$859$	1.58190e45	0.527576	0.263788	+	0.964581i	$0.415028\pi$
$860$	4.04086e43	0.0132357
$861$	−2.40223e45	−0.772796
$862$	4.33589e45	1.36998
$863$	4.50883e45	1.39925	0.699627	−	0.714508i	$-0.253350\pi$
$863$	4.50883e45	1.39925	0.699627	+	0.714508i	$0.253350\pi$
$864$	6.30482e44	0.192181
$865$	2.54265e45	0.761268
$866$	2.52281e45	0.741922
$867$	4.47192e45	1.29181
$868$	2.64198e45	0.749678
$869$	2.99576e45	0.835026
$870$	−1.29665e45	−0.355038
$871$	2.89422e45	0.778486
$872$	−3.96278e44	−0.104712
$873$	−5.39904e44	−0.140151
$874$	−9.50462e45	−2.42386
$875$	4.91349e44	0.123102
$876$	−1.32128e45	−0.325222
$877$	−3.33310e45	−0.806036	−0.403018	−	0.915192i	$-0.632039\pi$
$877$	−3.33310e45	−0.806036	−0.403018	+	0.915192i	$0.632039\pi$
$878$	2.08719e45	0.495903
$879$	−2.40316e45	−0.560990
$880$	−4.94001e44	−0.113304
$881$	8.52925e45	1.92214	0.961068	−	0.276311i	$-0.0891121\pi$
$881$	8.52925e45	1.92214	0.961068	+	0.276311i	$0.0891121\pi$
$882$	8.34430e44	0.184768
$883$	−3.84364e45	−0.836280	−0.418140	−	0.908383i	$-0.637318\pi$
$883$	−3.84364e45	−0.836280	−0.418140	+	0.908383i	$0.637318\pi$
$884$	−2.26200e45	−0.483595
$885$	1.35002e45	0.283609
$886$	−2.08784e44	−0.0430997
$887$	2.95824e45	0.600092	0.300046	−	0.953925i	$-0.402998\pi$
$887$	2.95824e45	0.600092	0.300046	+	0.953925i	$0.402998\pi$
$888$	−1.12811e45	−0.224880
$889$	−1.34854e46	−2.64172
$890$	5.07280e44	0.0976569
$891$	3.33413e45	0.630781
$892$	1.27087e45	0.236291
$893$	1.93900e46	3.54308
$894$	2.48894e45	0.446975
$895$	−3.66104e45	−0.646171
$896$	−7.01277e44	−0.121651
$897$	−5.79256e45	−0.987614
$898$	4.68132e45	0.784485
$899$	8.82627e45	1.45379
$900$	−1.80482e44	−0.0292196
$901$	−3.95948e44	−0.0630092
$902$	−3.05750e45	−0.478261
$903$	4.45759e44	0.0685393
$904$	6.02428e44	0.0910531
$905$	−2.81586e45	−0.418367
$906$	−4.14940e45	−0.606036
$907$	−8.06932e44	−0.115858	−0.0579288	−	0.998321i	$-0.518450\pi$
$907$	−8.06932e44	−0.115858	−0.0579288	+	0.998321i	$0.518450\pi$
$908$	1.85768e43	0.00262204
$909$	−1.00372e45	−0.139275
$910$	−1.93796e45	−0.264364
$911$	−5.29138e45	−0.709634	−0.354817	−	0.934936i	$-0.615457\pi$
$911$	−5.29138e45	−0.709634	−0.354817	+	0.934936i	$0.615457\pi$
$912$	−2.82937e45	−0.373053
$913$	1.49722e45	0.194084
$914$	1.74558e45	0.222471
$915$	−1.62655e45	−0.203817
$916$	−1.68721e45	−0.207868
$917$	1.24229e46	1.50487
$918$	−1.02769e46	−1.22405
$919$	−1.26770e46	−1.48465	−0.742326	−	0.670039i	$-0.766278\pi$
$919$	−1.26770e46	−1.48465	−0.742326	+	0.670039i	$0.766278\pi$
$920$	2.65357e45	0.305576
$921$	2.13793e45	0.242086
$922$	5.10089e45	0.567958
$923$	−7.58846e45	−0.830859
$924$	−5.44947e45	−0.586730
$925$	1.42812e45	0.151206
$926$	9.51332e45	0.990517
$927$	1.70461e45	0.174538
$928$	−2.34281e45	−0.235908
$929$	−1.42045e46	−1.40664	−0.703320	−	0.710873i	$-0.748300\pi$
$929$	−1.42045e46	−1.40664	−0.703320	+	0.710873i	$0.748300\pi$
$930$	−2.97595e45	−0.289828
$931$	−1.65600e46	−1.58614
$932$	−6.84839e45	−0.645122
$933$	1.14836e46	1.06393
$934$	4.89824e45	0.446337
$935$	8.05223e45	0.721666
$936$	7.11849e44	0.0627498
$937$	−5.11233e45	−0.443256	−0.221628	−	0.975131i	$-0.571137\pi$
$937$	−5.11233e45	−0.443256	−0.221628	+	0.975131i	$0.571137\pi$
$938$	−1.46257e46	−1.24731
$939$	6.65242e45	0.558037
$940$	−5.41345e45	−0.446676
$941$	−3.09574e45	−0.251262	−0.125631	−	0.992077i	$-0.540095\pi$
$941$	−3.09574e45	−0.251262	−0.125631	+	0.992077i	$0.540095\pi$
$942$	−1.51731e45	−0.121139
$943$	1.64236e46	1.28984
$944$	2.43924e45	0.188447
$945$	−8.80468e45	−0.669145
$946$	5.67351e44	0.0424169
$947$	9.70650e45	0.713901	0.356951	−	0.934123i	$-0.383816\pi$
$947$	9.70650e45	0.713901	0.356951	+	0.934123i	$0.383816\pi$
$948$	−4.79032e45	−0.346605
$949$	−6.59723e45	−0.469608
$950$	3.58183e45	0.250835
$951$	1.01348e46	0.698261
$952$	1.14308e46	0.774827
$953$	−1.66762e46	−1.11213	−0.556067	−	0.831137i	$-0.687690\pi$
$953$	−1.66762e46	−1.11213	−0.556067	+	0.831137i	$0.687690\pi$
$954$	1.24605e44	0.00817588
$955$	2.81024e45	0.181422
$956$	3.27191e45	0.207828
$957$	−1.82054e46	−1.13780
$958$	−2.95184e45	−0.181521
$959$	2.55392e46	1.54532
$960$	7.89924e44	0.0470307
$961$	3.18808e45	0.186774
$962$	−5.63274e45	−0.324718
$963$	−6.13945e45	−0.348275
$964$	1.30244e45	0.0727047
$965$	−1.24251e46	−0.682536
$966$	2.92722e46	1.58238
$967$	−1.87173e46	−0.995712	−0.497856	−	0.867260i	$-0.665879\pi$
$967$	−1.87173e46	−0.995712	−0.497856	+	0.867260i	$0.665879\pi$
$968$	−1.82544e44	−0.00955652
$969$	4.61188e46	2.37607
$970$	−2.99146e45	−0.151677
$971$	−7.35947e45	−0.367239	−0.183619	−	0.982997i	$-0.558781\pi$
$971$	−7.35947e45	−0.367239	−0.183619	+	0.982997i	$0.558781\pi$
$972$	5.73694e45	0.281743
$973$	9.39732e45	0.454208
$974$	−6.84454e45	−0.325597
$975$	2.18293e45	0.102204
$976$	−2.93887e45	−0.135428
$977$	2.82554e46	1.28155	0.640775	−	0.767728i	$-0.278613\pi$
$977$	2.82554e46	1.28155	0.640775	+	0.767728i	$0.278613\pi$
$978$	8.63044e45	0.385284
$979$	7.12240e45	0.312964
$980$	4.62334e45	0.199964
$981$	−2.03275e45	−0.0865395
$982$	−1.70001e46	−0.712399
$983$	−7.33102e45	−0.302402	−0.151201	−	0.988503i	$-0.548314\pi$
$983$	−7.33102e45	−0.302402	−0.151201	+	0.988503i	$0.548314\pi$
$984$	4.88904e45	0.198518
$985$	6.02833e45	0.240955
$986$	3.81878e46	1.50256
$987$	−5.97173e46	−2.31305
$988$	−1.41273e46	−0.538674
$989$	−3.04757e45	−0.114396
$990$	−2.53403e45	−0.0936411
$991$	−4.55867e46	−1.65843	−0.829213	−	0.558933i	$-0.811211\pi$
$991$	−4.55867e46	−1.65843	−0.829213	+	0.558933i	$0.811211\pi$
$992$	−5.37700e45	−0.192579
$993$	2.45935e46	0.867174
$994$	3.83477e46	1.33122
$995$	1.36192e46	0.465472
$996$	−2.39411e45	−0.0805609
$997$	9.50456e45	0.314889	0.157444	−	0.987528i	$-0.449674\pi$
$997$	9.50456e45	0.314889	0.157444	+	0.987528i	$0.449674\pi$
$998$	1.04168e46	0.339789
$999$	−2.55911e46	−0.821909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.32.a.a.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.32.a.a.1.2	✓	2	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-32768.0 q^{2} +2.09091e7 q^{3} +1.07374e9 q^{4} +3.05176e10 q^{5} -6.85150e11 q^{6} +1.72878e13 q^{7} -3.51844e13 q^{8} -1.80482e14 q^{9} -1.00000e15 q^{10} -1.40404e16 q^{11} +2.24510e16 q^{12} +1.12100e17 q^{13} -5.66487e17 q^{14} +6.38096e17 q^{15} +1.15292e18 q^{16} -1.87926e19 q^{17} +5.91403e18 q^{18} -1.17369e20 q^{19} +3.27680e19 q^{20} +3.61473e20 q^{21} +4.60074e20 q^{22} -2.47133e21 q^{23} -7.35674e20 q^{24} +9.31323e20 q^{25} -3.67328e21 q^{26} -1.66887e22 q^{27} +1.85627e22 q^{28} +6.20136e22 q^{29} -2.09091e22 q^{30} +1.42328e23 q^{31} -3.77789e22 q^{32} -2.93572e23 q^{33} +6.15797e23 q^{34} +5.27582e23 q^{35} -1.93791e23 q^{36} +1.53344e24 q^{37} +3.84596e24 q^{38} +2.34391e24 q^{39} -1.07374e24 q^{40} -6.64565e24 q^{41} -1.18448e25 q^{42} +1.23317e24 q^{43} -1.50757e25 q^{44} -5.50787e24 q^{45} +8.09804e25 q^{46} -1.65205e26 q^{47} +2.41066e25 q^{48} +1.41093e26 q^{49} -3.05176e25 q^{50} -3.92938e26 q^{51} +1.20366e26 q^{52} +2.10693e25 q^{53} +5.46856e26 q^{54} -4.28478e26 q^{55} -6.08261e26 q^{56} -2.45409e27 q^{57} -2.03206e27 q^{58} +2.11570e27 q^{59} +6.85150e26 q^{60} -2.54907e27 q^{61} -4.66380e27 q^{62} -3.12014e27 q^{63} +1.23794e27 q^{64} +3.42101e27 q^{65} +9.61975e27 q^{66} +2.58183e28 q^{67} -2.01784e28 q^{68} -5.16733e28 q^{69} -1.72878e28 q^{70} -6.76939e28 q^{71} +6.35014e27 q^{72} -5.88515e28 q^{73} -5.02476e28 q^{74} +1.94731e28 q^{75} -1.26024e29 q^{76} -2.42727e29 q^{77} -7.68051e28 q^{78} -2.13368e29 q^{79} +3.51844e28 q^{80} -2.37468e29 q^{81} +2.17765e29 q^{82} -1.06637e29 q^{83} +3.88129e29 q^{84} -5.73506e29 q^{85} -4.04086e28 q^{86} +1.29665e30 q^{87} +4.94001e29 q^{88} -5.07280e29 q^{89} +1.80482e29 q^{90} +1.93796e30 q^{91} -2.65357e30 q^{92} +2.97595e30 q^{93} +5.41345e30 q^{94} -3.58183e30 q^{95} -7.89924e29 q^{96} +2.99146e30 q^{97} -4.62334e30 q^{98} +2.53403e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 65536 q^{2} - 5904756 q^{3} + 2147483648 q^{4} + 61035156250 q^{5} + 193487044608 q^{6} + 18016565093212 q^{7} - 70368744177664 q^{8} - 79171117705926 q^{9} - 20\!\cdots\!00 q^{10} - 17\!\cdots\!76 q^{11}+ \cdots + 21\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 65536 * q^2 - 5904756 * q^3 + 2147483648 * q^4 + 61035156250 * q^5 + 193487044608 * q^6 + 18016565093212 * q^7 - 70368744177664 * q^8 - 79171117705926 * q^9 - 2000000000000000 * q^10 - 17416121431336176 * q^11 - 6340183477714944 * q^12 - 25489812233411396 * q^13 - 590366804974370816 * q^14 - 180198852539062500 * q^15 + 2305843009213693952 * q^16 - 16396230747963647148 * q^17 + 2594279184987783168 * q^18 - 107880416928265082840 * q^19 + 65536000000000000000 * q^20 + 341932614252792754464 * q^21 + 570691467062023815168 * q^22 - 577071154821832133436 * q^23 + 207755132197763284992 * q^24 + 1862645149230957031250 * q^25 + 835250167264424624128 * q^26 - 2843043459520171719240 * q^27 + 19345139465400182898688 * q^28 + 67048805832697356280140 * q^29 + 5904756000000000000000 * q^30 + 56909800035573417801064 * q^31 - 75557863725914323419136 * q^32 - 203054257469968728424272 * q^33 + 537271689149272789745664 * q^34 + 549821932776245117187500 * q^35 - 85009340333679678849024 * q^36 + 2801153390572259937695932 * q^37 + 3535025501905390234501120 * q^38 + 6033212900355351396566088 * q^39 - 2147483648000000000000000 * q^40 + 1893631200697714321546884 * q^41 - 11204447903835512978276352 * q^42 + 25327635900154956194956684 * q^43 - 18700417992688396375425024 * q^44 - 2416110769834167480468750 * q^45 + 18909467601201795348430848 * q^46 - 204836832883272087160299828 * q^47 - 6807720171856307322617856 * q^48 - 16151031643901179650461214 * q^49 - 61035156250000000000000000 * q^50 - 457194512783561777077087656 * q^51 - 27369477480920666083426304 * q^52 + 93384041038067791074445644 * q^53 + 93160848081556986896056320 * q^54 - 531497846415288574218750000 * q^55 - 633901530002233193224208384 * q^56 - 2708523042419370548680789680 * q^57 - 2197055269525826970587627520 * q^58 + 401993734479158802793910280 * q^59 - 193487044608000000000000000 * q^60 - 523487156255386223571641876 * q^61 - 1864820327565669754505265152 * q^62 - 3046308524664113764706112756 * q^63 + 2475880078570760549798248448 * q^64 - 777887336224713012695312500 * q^65 + 6653681908775935293006544896 * q^66 + 3525975420949577285673481252 * q^67 - 17605318710043370774385917952 * q^68 - 102465607127544429209145592992 * q^69 - 18016565093212000000000000000 * q^70 - 155367638238255137782572480456 * q^71 + 2785586064054015716524818432 * q^72 - 121161803322719279904680358236 * q^73 - 91788194302271813638420299776 * q^74 - 5499232560396194458007812500 * q^75 - 115835715646435827204132700160 * q^76 - 245187227911068920618395555056 * q^77 - 197696320318844154562677571584 * q^78 - 106325261485679876782031095760 * q^79 + 70368744177664000000000000000 * q^80 - 671301359934033052744190089758 * q^81 - 62050507184462702888448294912 * q^82 - 165992230806613806640311266676 * q^83 + 367147348912882089272159502336 * q^84 - 500373252806507786499023437500 * q^85 - 829935973176277604596340621312 * q^86 + 1161637435058040293762416972680 * q^87 + 612775296784413372429927186432 * q^88 + 596773808150426638152387464820 * q^89 + 79171117705926000000000000000 * q^90 + 1837690480870898595062956149224 * q^91 - 619625434356180429977382027264 * q^92 + 5266346212626013088658434510208 * q^93 + 6712093339919059752068704763904 * q^94 - 3292249051765902186279296875000 * q^95 + 223075374591387478347541905408 * q^96 + 8308055695022791533341129836372 * q^97 + 529237004907353854786313060352 * q^98 + 2192029238850361923111708294288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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