LMFDB - Embedded newform 121.11.b.c.120.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,11,Mod(120,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("121.120");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	121.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$76.8782275735$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			120.4
Character	$\chi$	$=$	121.120
Dual form			121.11.b.c.120.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-51.4200i q^{2} -204.299 q^{3} -1620.02 q^{4} +840.263 q^{5} +10505.1i q^{6} -11012.5i q^{7} +30647.2i q^{8} -17310.9 q^{9} +O(q^{10})$	\(q-51.4200i q^{2} -204.299 q^{3} -1620.02 q^{4} +840.263 q^{5} +10505.1i q^{6} -11012.5i q^{7} +30647.2i q^{8} -17310.9 q^{9} -43206.3i q^{10} +330968. q^{12} -334044. i q^{13} -566262. q^{14} -171665. q^{15} -83017.4 q^{16} -1.67073e6i q^{17} +890127. i q^{18} -2.87200e6i q^{19} -1.36124e6 q^{20} +2.24984e6i q^{21} -6.17837e6 q^{23} -6.26120e6i q^{24} -9.05958e6 q^{25} -1.71765e7 q^{26} +1.56003e7 q^{27} +1.78404e7i q^{28} -1.50387e7i q^{29} +8.82701e6i q^{30} -1.32404e7 q^{31} +3.56515e7i q^{32} -8.59090e7 q^{34} -9.25338e6i q^{35} +2.80440e7 q^{36} -1.08560e8 q^{37} -1.47679e8 q^{38} +6.82448e7i q^{39} +2.57517e7i q^{40} +9.74034e7i q^{41} +1.15687e8 q^{42} -1.88418e8i q^{43} -1.45457e7 q^{45} +3.17692e8i q^{46} -7.20878e7 q^{47} +1.69604e7 q^{48} +1.61201e8 q^{49} +4.65844e8i q^{50} +3.41329e8i q^{51} +5.41156e8i q^{52} +7.81424e8 q^{53} -8.02165e8i q^{54} +3.37502e8 q^{56} +5.86748e8i q^{57} -7.73292e8 q^{58} +8.13913e7 q^{59} +2.78100e8 q^{60} +4.54614e8i q^{61} +6.80819e8i q^{62} +1.90636e8i q^{63} +1.74819e9 q^{64} -2.80684e8i q^{65} -1.82676e9 q^{67} +2.70661e9i q^{68} +1.26223e9 q^{69} -4.75809e8 q^{70} +3.52717e8 q^{71} -5.30531e8i q^{72} -3.14963e9i q^{73} +5.58215e9i q^{74} +1.85086e9 q^{75} +4.65270e9i q^{76} +3.50915e9 q^{78} -2.35088e9i q^{79} -6.97564e7 q^{80} -2.16493e9 q^{81} +5.00848e9 q^{82} -1.70477e9i q^{83} -3.64478e9i q^{84} -1.40385e9i q^{85} -9.68847e9 q^{86} +3.07240e9i q^{87} -4.54171e9 q^{89} +7.47941e8i q^{90} -3.67865e9 q^{91} +1.00091e10 q^{92} +2.70499e9 q^{93} +3.70676e9i q^{94} -2.41324e9i q^{95} -7.28357e9i q^{96} -5.00860e9 q^{97} -8.28894e9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 82 q^{3} - 17636 q^{4} + 8836 q^{5} + 444618 q^{9}+O(q^{10}) $ 36 * q + 82 * q^3 - 17636 * q^4 + 8836 * q^5 + 444618 * q^9	$ 36 q + 82 q^{3} - 17636 q^{4} + 8836 q^{5} + 444618 q^{9} - 690462 q^{12} + 2470700 q^{14} - 238640 q^{15} + 5948436 q^{16} - 27229336 q^{20} + 2991652 q^{23} + 64315904 q^{25} - 89638980 q^{26} - 12404744 q^{27} - 144437904 q^{31} + 8404770 q^{34} + 273404882 q^{36} + 87128788 q^{37} + 412794790 q^{38} - 414956240 q^{42} - 1073801424 q^{45} - 954884432 q^{47} + 1236109242 q^{48} - 1072154336 q^{49} + 2521486392 q^{53} + 464386660 q^{56} + 4129717580 q^{58} + 4035534274 q^{59} + 4965057480 q^{60} - 3387556676 q^{64} - 6673767122 q^{67} + 12987260292 q^{69} + 2229687840 q^{70} + 14278430392 q^{71} - 27874531830 q^{75} - 35448700760 q^{78} + 59564874016 q^{80} - 3276118216 q^{81} + 45104764870 q^{82} - 21079852850 q^{86} - 19181286322 q^{89} + 85635114120 q^{91} + 40774045308 q^{92} + 86401354444 q^{93} - 26168299402 q^{97}+O(q^{100}) $ 36 * q + 82 * q^3 - 17636 * q^4 + 8836 * q^5 + 444618 * q^9 - 690462 * q^12 + 2470700 * q^14 - 238640 * q^15 + 5948436 * q^16 - 27229336 * q^20 + 2991652 * q^23 + 64315904 * q^25 - 89638980 * q^26 - 12404744 * q^27 - 144437904 * q^31 + 8404770 * q^34 + 273404882 * q^36 + 87128788 * q^37 + 412794790 * q^38 - 414956240 * q^42 - 1073801424 * q^45 - 954884432 * q^47 + 1236109242 * q^48 - 1072154336 * q^49 + 2521486392 * q^53 + 464386660 * q^56 + 4129717580 * q^58 + 4035534274 * q^59 + 4965057480 * q^60 - 3387556676 * q^64 - 6673767122 * q^67 + 12987260292 * q^69 + 2229687840 * q^70 + 14278430392 * q^71 - 27874531830 * q^75 - 35448700760 * q^78 + 59564874016 * q^80 - 3276118216 * q^81 + 45104764870 * q^82 - 21079852850 * q^86 - 19181286322 * q^89 + 85635114120 * q^91 + 40774045308 * q^92 + 86401354444 * q^93 - 26168299402 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 51.4200i	− 1.60688i	−0.595389	−	0.803438i	$-0.703002\pi$
$2$	− 51.4200i	− 1.60688i	0.595389	−	0.803438i	$-0.296998\pi$
$3$	−204.299	−0.840737	−0.420368	−	0.907354i	$-0.638099\pi$
$3$	−204.299	−0.840737	−0.420368	+	0.907354i	$0.638099\pi$
$4$	−1620.02	−1.58205
$5$	840.263	0.268884	0.134442	−	0.990921i	$-0.457076\pi$
$5$	840.263	0.268884	0.134442	+	0.990921i	$0.457076\pi$
$6$	10505.1i	1.35096i
$7$	− 11012.5i	− 0.655232i	−0.944811	−	0.327616i	$-0.893755\pi$
$7$	− 11012.5i	− 0.655232i	0.944811	−	0.327616i	$-0.106245\pi$
$8$	30647.2i	0.935279i
$9$	−17310.9	−0.293162
$10$	− 43206.3i	− 0.432063i
$11$	0	0
$11$	0	0
$12$	330968.	1.33009
$13$	− 334044.i	− 0.899677i	−0.893110	−	0.449838i	$-0.851482\pi$
$13$	− 334044.i	− 0.899677i	0.893110	−	0.449838i	$-0.148518\pi$
$14$	−566262.	−1.05288
$15$	−171665.	−0.226061
$16$	−83017.4	−0.0791715
$17$	− 1.67073e6i	− 1.17669i	−0.808610	−	0.588345i	$-0.799780\pi$
$17$	− 1.67073e6i	− 1.17669i	0.808610	−	0.588345i	$-0.200220\pi$
$18$	890127.i	0.471074i
$19$	− 2.87200e6i	− 1.15989i	−0.814655	−	0.579945i	$-0.803074\pi$
$19$	− 2.87200e6i	− 1.15989i	0.814655	−	0.579945i	$-0.196926\pi$
$20$	−1.36124e6	−0.425388
$21$	2.24984e6i	0.550877i
$22$	0	0
$23$	−6.17837e6	−0.959919	−0.479960	−	0.877291i	$-0.659349\pi$
$23$	−6.17837e6	−0.959919	−0.479960	+	0.877291i	$0.659349\pi$
$24$	− 6.26120e6i	− 0.786323i
$25$	−9.05958e6	−0.927701
$26$	−1.71765e7	−1.44567
$27$	1.56003e7	1.08721
$28$	1.78404e7i	1.03661i
$29$	− 1.50387e7i	− 0.733199i	−0.930379	−	0.366599i	$-0.880522\pi$
$29$	− 1.50387e7i	− 0.733199i	0.930379	−	0.366599i	$-0.119478\pi$
$30$	8.82701e6i	0.363252i
$31$	−1.32404e7	−0.462478	−0.231239	−	0.972897i	$-0.574278\pi$
$31$	−1.32404e7	−0.462478	−0.231239	+	0.972897i	$0.574278\pi$
$32$	3.56515e7i	1.06250i
$33$	0	0
$34$	−8.59090e7	−1.89079
$35$	− 9.25338e6i	− 0.176181i
$36$	2.80440e7	0.463796
$37$	−1.08560e8	−1.56553	−0.782763	−	0.622319i	$-0.786191\pi$
$37$	−1.08560e8	−1.56553	−0.782763	+	0.622319i	$0.786191\pi$
$38$	−1.47679e8	−1.86380
$39$	6.82448e7i	0.756391i
$40$	2.57517e7i	0.251482i
$41$	9.74034e7i	0.840727i	0.907356	+	0.420363i	$0.138097\pi$
$41$	9.74034e7i	0.840727i	−0.907356	+	0.420363i	$0.861903\pi$
$42$	1.15687e8	0.885191
$43$	− 1.88418e8i	− 1.28168i	−0.767673	−	0.640842i	$-0.778585\pi$
$43$	− 1.88418e8i	− 1.28168i	0.767673	−	0.640842i	$-0.221415\pi$
$44$	0	0
$45$	−1.45457e7	−0.0788265
$46$	3.17692e8i	1.54247i
$47$	−7.20878e7	−0.314320	−0.157160	−	0.987573i	$-0.550234\pi$
$47$	−7.20878e7	−0.314320	−0.157160	+	0.987573i	$0.550234\pi$
$48$	1.69604e7	0.0665624
$49$	1.61201e8	0.570672
$50$	4.65844e8i	1.49070i
$51$	3.41329e8i	0.989286i
$52$	5.41156e8i	1.42333i
$53$	7.81424e8	1.86856	0.934280	−	0.356540i	$-0.116044\pi$
$53$	7.81424e8	1.86856	0.934280	+	0.356540i	$0.116044\pi$
$54$	− 8.02165e8i	− 1.74701i
$55$	0	0
$56$	3.37502e8	0.612824
$57$	5.86748e8i	0.975163i
$58$	−7.73292e8	−1.17816
$59$	8.13913e7	0.113846	0.0569230	−	0.998379i	$-0.481871\pi$
$59$	8.13913e7	0.113846	0.0569230	+	0.998379i	$0.481871\pi$
$60$	2.78100e8	0.357639
$61$	4.54614e8i	0.538261i	0.963104	+	0.269131i	$0.0867364\pi$
$61$	4.54614e8i	0.538261i	−0.963104	+	0.269131i	$0.913264\pi$
$62$	6.80819e8i	0.743145i
$63$	1.90636e8i	0.192089i
$64$	1.74819e9	1.62813
$65$	− 2.80684e8i	− 0.241909i
$66$	0	0
$67$	−1.82676e9	−1.35303	−0.676516	−	0.736428i	$-0.736511\pi$
$67$	−1.82676e9	−1.35303	−0.676516	+	0.736428i	$0.736511\pi$
$68$	2.70661e9i	1.86158i
$69$	1.26223e9	0.807039
$70$	−4.75809e8	−0.283102
$71$	3.52717e8	0.195495	0.0977473	−	0.995211i	$-0.468836\pi$
$71$	3.52717e8	0.195495	0.0977473	+	0.995211i	$0.468836\pi$
$72$	− 5.30531e8i	− 0.274188i
$73$	− 3.14963e9i	− 1.51930i	−0.650330	−	0.759652i	$-0.725369\pi$
$73$	− 3.14963e9i	− 1.51930i	0.650330	−	0.759652i	$-0.274631\pi$
$74$	5.58215e9i	2.51561i
$75$	1.85086e9	0.779953
$76$	4.65270e9i	1.83500i
$77$	0	0
$78$	3.50915e9	1.21543
$79$	− 2.35088e9i	− 0.764002i	−0.924162	−	0.382001i	$-0.875235\pi$
$79$	− 2.35088e9i	− 0.764002i	0.924162	−	0.382001i	$-0.124765\pi$
$80$	−6.97564e7	−0.0212880
$81$	−2.16493e9	−0.620895
$82$	5.00848e9	1.35094
$83$	− 1.70477e9i	− 0.432789i	−0.976306	−	0.216395i	$-0.930570\pi$
$83$	− 1.70477e9i	− 0.432789i	0.976306	−	0.216395i	$-0.0694298\pi$
$84$	− 3.64478e9i	− 0.871514i
$85$	− 1.40385e9i	− 0.316393i
$86$	−9.68847e9	−2.05951
$87$	3.07240e9i	0.616427i
$88$	0	0
$89$	−4.54171e9	−0.813334	−0.406667	−	0.913576i	$-0.633309\pi$
$89$	−4.54171e9	−0.813334	−0.406667	+	0.913576i	$0.633309\pi$
$90$	7.47941e8i	0.126664i
$91$	−3.67865e9	−0.589496
$92$	1.00091e10	1.51864
$93$	2.70499e9	0.388822
$94$	3.70676e9i	0.505074i
$95$	− 2.41324e9i	− 0.311876i
$96$	− 7.28357e9i	− 0.893281i
$97$	−5.00860e9	−0.583254	−0.291627	−	0.956532i	$-0.594197\pi$
$97$	−5.00860e9	−0.583254	−0.291627	+	0.956532i	$0.594197\pi$
$98$	− 8.28894e9i	− 0.916998i
$99$	0	0
$100$	1.46767e10	1.46767
$101$	− 2.45396e9i	− 0.233486i	−0.993162	−	0.116743i	$-0.962755\pi$
$101$	− 2.45396e9i	− 0.233486i	0.993162	−	0.116743i	$-0.0372454\pi$
$102$	1.75511e10	1.58966
$103$	1.94824e10	1.68057	0.840283	−	0.542148i	$-0.182389\pi$
$103$	1.94824e10	1.68057	0.840283	+	0.542148i	$0.182389\pi$
$104$	1.02375e10	0.841449
$105$	1.89046e9i	0.148122i
$106$	− 4.01808e10i	− 3.00254i
$107$	− 1.19739e9i	− 0.0853725i	−0.999089	−	0.0426863i	$-0.986408\pi$
$107$	− 1.19739e9i	− 0.0853725i	0.999089	−	0.0426863i	$-0.0135916\pi$
$108$	−2.52727e10	−1.72002
$109$	− 9.65634e9i	− 0.627596i	−0.949490	−	0.313798i	$-0.898399\pi$
$109$	− 9.65634e9i	− 0.627596i	0.949490	−	0.313798i	$-0.101601\pi$
$110$	0	0
$111$	2.21787e10	1.31620
$112$	9.14227e8i	0.0518757i
$113$	3.00741e10	1.63230	0.816151	−	0.577838i	$-0.196104\pi$
$113$	3.00741e10	1.63230	0.816151	+	0.577838i	$0.196104\pi$
$114$	3.01706e10	1.56697
$115$	−5.19146e9	−0.258107
$116$	2.43630e10i	1.15996i
$117$	5.78260e9i	0.263751i
$118$	− 4.18514e9i	− 0.182936i
$119$	−1.83989e10	−0.771004
$120$	− 5.26105e9i	− 0.211430i
$121$	0	0
$122$	2.33762e10	0.864919
$123$	− 1.98994e10i	− 0.706830i
$124$	2.14496e10	0.731663
$125$	−1.58181e10	−0.518328
$126$	9.80250e9	0.308663
$127$	2.01388e10i	0.609558i	0.952423	+	0.304779i	$0.0985826\pi$
$127$	2.01388e10i	0.609558i	−0.952423	+	0.304779i	$0.901417\pi$
$128$	− 5.33849e10i	− 1.55370i
$129$	3.84937e10i	1.07756i
$130$	−1.44328e10	−0.388717
$131$	7.07549e10i	1.83400i	0.398883	+	0.917002i	$0.369398\pi$
$131$	7.07549e10i	1.83400i	−0.398883	+	0.917002i	$0.630602\pi$
$132$	0	0
$133$	−3.16279e10	−0.759997
$134$	9.39321e10i	2.17415i
$135$	1.31083e10	0.292333
$136$	5.12033e10	1.10053
$137$	3.89074e10	0.806176	0.403088	−	0.915161i	$-0.367937\pi$
$137$	3.89074e10	0.806176	0.403088	+	0.915161i	$0.367937\pi$
$138$	− 6.49041e10i	− 1.29681i
$139$	9.99534e9i	0.192630i	0.995351	+	0.0963149i	$0.0307056\pi$
$139$	9.99534e9i	0.192630i	−0.995351	+	0.0963149i	$0.969294\pi$
$140$	1.49906e10i	0.278727i
$141$	1.47275e10	0.264261
$142$	− 1.81367e10i	− 0.314136i
$143$	0	0
$144$	1.43711e9	0.0232101
$145$	− 1.26365e10i	− 0.197145i
$146$	−1.61954e11	−2.44133
$147$	−3.29331e10	−0.479785
$148$	1.75869e11	2.47674
$149$	− 3.76236e8i	− 0.00512305i	−0.999997	−	0.00256153i	$-0.999185\pi$
$149$	− 3.76236e8i	− 0.00512305i	0.999997	−	0.00256153i	$-0.000815360\pi$
$150$	− 9.51715e10i	− 1.25329i
$151$	5.61366e10i	0.715091i	0.933896	+	0.357545i	$0.116386\pi$
$151$	5.61366e10i	0.715091i	−0.933896	+	0.357545i	$0.883614\pi$
$152$	8.80190e10	1.08482
$153$	2.89219e10i	0.344960i
$154$	0	0
$155$	−1.11254e10	−0.124353
$156$	− 1.10558e11i	− 1.19665i
$157$	4.76554e10	0.499590	0.249795	−	0.968299i	$-0.419637\pi$
$157$	4.76554e10	0.499590	0.249795	+	0.968299i	$0.419637\pi$
$158$	−1.20882e11	−1.22766
$159$	−1.59644e11	−1.57097
$160$	2.99566e10i	0.285689i
$161$	6.80392e10i	0.628969i
$162$	1.11320e11i	0.997700i
$163$	1.63686e11	1.42257	0.711286	−	0.702903i	$-0.248113\pi$
$163$	1.63686e11	1.42257	0.711286	+	0.702903i	$0.248113\pi$
$164$	− 1.57795e11i	− 1.33007i
$165$	0	0
$166$	−8.76595e10	−0.695438
$167$	2.45213e11i	1.88782i	0.330197	+	0.943912i	$0.392885\pi$
$167$	2.45213e11i	1.88782i	−0.330197	+	0.943912i	$0.607115\pi$
$168$	−6.89513e10	−0.515224
$169$	2.62734e10	0.190582
$170$	−7.21862e10	−0.508404
$171$	4.97170e10i	0.340036i
$172$	3.05241e11i	2.02769i
$173$	8.56345e10i	0.552609i	0.961070	+	0.276305i	$0.0891099\pi$
$173$	8.56345e10i	0.552609i	−0.961070	+	0.276305i	$0.910890\pi$
$174$	1.57983e11	0.990521
$175$	9.97684e10i	0.607859i
$176$	0	0
$177$	−1.66282e10	−0.0957146
$178$	2.33535e11i	1.30693i
$179$	2.05280e11	1.11707	0.558537	−	0.829480i	$-0.311363\pi$
$179$	2.05280e11	1.11707	0.558537	+	0.829480i	$0.311363\pi$
$180$	2.35643e10	0.124707
$181$	1.10215e10	0.0567347	0.0283674	−	0.999598i	$-0.490969\pi$
$181$	1.10215e10	0.0567347	0.0283674	+	0.999598i	$0.490969\pi$
$182$	1.89156e11i	0.947247i
$183$	− 9.28771e10i	− 0.452536i
$184$	− 1.89350e11i	− 0.897792i
$185$	−9.12188e10	−0.420945
$186$	− 1.39091e11i	− 0.624789i
$187$	0	0
$188$	1.16784e11	0.497270
$189$	− 1.71797e11i	− 0.712373i
$190$	−1.24089e11	−0.501146
$191$	−1.99252e11	−0.783854	−0.391927	−	0.919996i	$-0.628191\pi$
$191$	−1.99252e11	−0.783854	−0.391927	+	0.919996i	$0.628191\pi$
$192$	−3.57154e11	−1.36883
$193$	2.36284e11i	0.882363i	0.897418	+	0.441181i	$0.145440\pi$
$193$	2.36284e11i	0.882363i	−0.897418	+	0.441181i	$0.854560\pi$
$194$	2.57542e11i	0.937217i
$195$	5.73436e10i	0.203382i
$196$	−2.61148e11	−0.902830
$197$	− 3.09846e11i	− 1.04427i	−0.852862	−	0.522137i	$-0.825135\pi$
$197$	− 3.09846e11i	− 1.04427i	0.852862	−	0.522137i	$-0.174865\pi$
$198$	0	0
$199$	−1.92515e11	−0.616876	−0.308438	−	0.951244i	$-0.599806\pi$
$199$	−1.92515e11	−0.616876	−0.308438	+	0.951244i	$0.599806\pi$
$200$	− 2.77651e11i	− 0.867660i
$201$	3.73206e11	1.13754
$202$	−1.26183e11	−0.375183
$203$	−1.65614e11	−0.480415
$204$	− 5.52958e11i	− 1.56510i
$205$	8.18445e10i	0.226058i
$206$	− 1.00178e12i	− 2.70046i
$207$	1.06953e11	0.281411
$208$	2.77314e10i	0.0712288i
$209$	0	0
$210$	9.72073e10	0.238014
$211$	− 7.39409e11i	− 1.76796i	−0.467526	−	0.883979i	$-0.654854\pi$
$211$	− 7.39409e11i	− 1.76796i	0.467526	−	0.883979i	$-0.345146\pi$
$212$	−1.26592e12	−2.95615
$213$	−7.20598e10	−0.164360
$214$	−6.15700e10	−0.137183
$215$	− 1.58321e11i	− 0.344625i
$216$	4.78104e11i	1.01684i
$217$	1.45809e11i	0.303030i
$218$	−4.96529e11	−1.00847
$219$	6.43465e11i	1.27733i
$220$	0	0
$221$	−5.58097e11	−1.05864
$222$	− 1.14043e12i	− 2.11496i
$223$	5.26380e11	0.954499	0.477249	−	0.878768i	$-0.341634\pi$
$223$	5.26380e11	0.954499	0.477249	+	0.878768i	$0.341634\pi$
$224$	3.92611e11	0.696182
$225$	1.56830e11	0.271966
$226$	− 1.54641e12i	− 2.62291i
$227$	− 1.01800e12i	− 1.68896i	−0.535585	−	0.844481i	$-0.679909\pi$
$227$	− 1.01800e12i	− 1.68896i	0.535585	−	0.844481i	$-0.320091\pi$
$228$	− 9.50542e11i	− 1.54275i
$229$	−6.03702e11	−0.958617	−0.479309	−	0.877646i	$-0.659113\pi$
$229$	−6.03702e11	−0.958617	−0.479309	+	0.877646i	$0.659113\pi$
$230$	2.66945e11i	0.414746i
$231$	0	0
$232$	4.60896e11	0.685745
$233$	1.06224e12i	1.54683i	0.633897	+	0.773417i	$0.281454\pi$
$233$	1.06224e12i	1.54683i	−0.633897	+	0.773417i	$0.718546\pi$
$234$	2.97341e11	0.423814
$235$	−6.05727e10	−0.0845158
$236$	−1.31855e11	−0.180110
$237$	4.80282e11i	0.642325i
$238$	9.46071e11i	1.23891i
$239$	− 1.94576e11i	− 0.249517i	−0.992187	−	0.124758i	$-0.960184\pi$
$239$	− 1.94576e11i	− 0.249517i	0.992187	−	0.124758i	$-0.0398155\pi$
$240$	1.42512e10	0.0178976
$241$	1.38360e12i	1.70187i	0.525269	+	0.850936i	$0.323965\pi$
$241$	1.38360e12i	1.70187i	−0.525269	+	0.850936i	$0.676035\pi$
$242$	0	0
$243$	−4.78887e11	−0.565200
$244$	− 7.36482e11i	− 0.851556i
$245$	1.35451e11	0.153445
$246$	−1.02323e12	−1.13579
$247$	−9.59375e11	−1.04353
$248$	− 4.05780e11i	− 0.432546i
$249$	3.48284e11i	0.363862i
$250$	8.13368e11i	0.832889i
$251$	−7.67033e11	−0.769919	−0.384960	−	0.922933i	$-0.625785\pi$
$251$	−7.67033e11	−0.769919	−0.384960	+	0.922933i	$0.625785\pi$
$252$	− 3.08833e11i	− 0.303894i
$253$	0	0
$254$	1.03554e12	0.979484
$255$	2.86806e11i	0.266003i
$256$	−9.54902e11	−0.868479
$257$	−8.77465e11	−0.782644	−0.391322	−	0.920254i	$-0.627982\pi$
$257$	−8.77465e11	−0.782644	−0.391322	+	0.920254i	$0.627982\pi$
$258$	1.97935e12	1.73150
$259$	1.19551e12i	1.02578i
$260$	4.54714e11i	0.382711i
$261$	2.60334e11i	0.214946i
$262$	3.63822e12	2.94702
$263$	− 1.73051e12i	− 1.37529i	−0.726047	−	0.687645i	$-0.758645\pi$
$263$	− 1.73051e12i	− 1.37529i	0.726047	−	0.687645i	$-0.241355\pi$
$264$	0	0
$265$	6.56601e11	0.502426
$266$	1.62631e12i	1.22122i
$267$	9.27866e11	0.683800
$268$	2.95939e12	2.14056
$269$	−2.38655e12	−1.69438	−0.847188	−	0.531293i	$-0.821706\pi$
$269$	−2.38655e12	−1.69438	−0.847188	+	0.531293i	$0.821706\pi$
$270$	− 6.74030e11i	− 0.469743i
$271$	7.65517e11i	0.523731i	0.965104	+	0.261866i	$0.0843377\pi$
$271$	7.65517e11i	0.523731i	−0.965104	+	0.261866i	$0.915662\pi$
$272$	1.38700e11i	0.0931603i
$273$	7.51544e11	0.495611
$274$	− 2.00062e12i	− 1.29542i
$275$	0	0
$276$	−2.04484e12	−1.27678
$277$	8.97922e11i	0.550605i	0.961358	+	0.275302i	$0.0887780\pi$
$277$	8.97922e11i	0.550605i	−0.961358	+	0.275302i	$0.911222\pi$
$278$	5.13960e11	0.309532
$279$	2.29202e11	0.135581
$280$	2.83590e11	0.164779
$281$	2.47012e11i	0.140989i	0.997512	+	0.0704947i	$0.0224578\pi$
$281$	2.47012e11i	0.140989i	−0.997512	+	0.0704947i	$0.977542\pi$
$282$	− 7.57287e11i	− 0.424634i
$283$	1.00667e12i	0.554568i	0.960788	+	0.277284i	$0.0894343\pi$
$283$	1.00667e12i	0.554568i	−0.960788	+	0.277284i	$0.910566\pi$
$284$	−5.71408e11	−0.309282
$285$	4.93022e11i	0.262206i
$286$	0	0
$287$	1.07265e12	0.550871
$288$	− 6.17160e11i	− 0.311484i
$289$	−7.75348e11	−0.384598
$290$	−6.49769e11	−0.316788
$291$	1.02325e12	0.490363
$292$	5.10245e12i	2.40361i
$293$	− 1.55385e12i	− 0.719568i	−0.933036	−	0.359784i	$-0.882850\pi$
$293$	− 1.55385e12i	− 0.719568i	0.933036	−	0.359784i	$-0.117150\pi$
$294$	1.69342e12i	0.770954i
$295$	6.83901e10	0.0306114
$296$	− 3.32706e12i	− 1.46420i
$297$	0	0
$298$	−1.93461e10	−0.00823211
$299$	2.06384e12i	0.863617i
$300$	−2.99843e12	−1.23392
$301$	−2.07495e12	−0.839800
$302$	2.88654e12	1.14906
$303$	5.01342e11i	0.196300i
$304$	2.38426e11i	0.0918303i
$305$	3.81995e11i	0.144730i
$306$	1.48716e12	0.554308
$307$	6.56191e11i	0.240624i	0.992736	+	0.120312i	$0.0383894\pi$
$307$	6.56191e11i	0.240624i	−0.992736	+	0.120312i	$0.961611\pi$
$308$	0	0
$309$	−3.98023e12	−1.41291
$310$	5.72067e11i	0.199820i
$311$	6.48085e11	0.222756	0.111378	−	0.993778i	$-0.464473\pi$
$311$	6.48085e11	0.222756	0.111378	+	0.993778i	$0.464473\pi$
$312$	−2.09151e12	−0.707437
$313$	−1.65799e12	−0.551901	−0.275951	−	0.961172i	$-0.588993\pi$
$313$	−1.65799e12	−0.551901	−0.275951	+	0.961172i	$0.588993\pi$
$314$	− 2.45044e12i	− 0.802779i
$315$	1.60184e11i	0.0516496i
$316$	3.80846e12i	1.20869i
$317$	−1.73093e12	−0.540732	−0.270366	−	0.962758i	$-0.587145\pi$
$317$	−1.73093e12	−0.540732	−0.270366	+	0.962758i	$0.587145\pi$
$318$	8.20890e12i	2.52435i
$319$	0	0
$320$	1.46894e12	0.437778
$321$	2.44626e11i	0.0717758i
$322$	3.49857e12	1.01068
$323$	−4.79835e12	−1.36483
$324$	3.50722e12	0.982285
$325$	3.02630e12i	0.834631i
$326$	− 8.41675e12i	− 2.28590i
$327$	1.97278e12i	0.527643i
$328$	−2.98514e12	−0.786314
$329$	7.93865e11i	0.205953i
$330$	0	0
$331$	3.53130e11	0.0888781	0.0444390	−	0.999012i	$-0.485850\pi$
$331$	3.53130e11	0.0888781	0.0444390	+	0.999012i	$0.485850\pi$
$332$	2.76176e12i	0.684693i
$333$	1.87927e12	0.458952
$334$	1.26089e13	3.03350
$335$	−1.53496e12	−0.363809
$336$	− 1.86776e11i	− 0.0436138i
$337$	− 1.00456e12i	− 0.231114i	−0.993301	−	0.115557i	$-0.963135\pi$
$337$	− 1.00456e12i	− 0.231114i	0.993301	−	0.115557i	$-0.0368653\pi$
$338$	− 1.35098e12i	− 0.306242i
$339$	−6.14411e12	−1.37234
$340$	2.27427e12i	0.500549i
$341$	0	0
$342$	2.55645e12	0.546395
$343$	− 4.88597e12i	− 1.02915i
$344$	5.77450e12	1.19873
$345$	1.06061e12	0.217000
$346$	4.40333e12	0.887974
$347$	2.55743e11i	0.0508343i	0.999677	+	0.0254171i	$0.00809140\pi$
$347$	2.55743e11i	0.0508343i	−0.999677	+	0.0254171i	$0.991909\pi$
$348$	− 4.97734e12i	− 0.975217i
$349$	− 4.01874e12i	− 0.776181i	−0.921621	−	0.388091i	$-0.873135\pi$
$349$	− 4.01874e12i	− 0.776181i	0.921621	−	0.388091i	$-0.126865\pi$
$350$	5.13009e12	0.976754
$351$	− 5.21117e12i	− 0.978136i
$352$	0	0
$353$	6.05587e12	1.10485	0.552425	−	0.833563i	$-0.313703\pi$
$353$	6.05587e12	1.10485	0.552425	+	0.833563i	$0.313703\pi$
$354$	8.55021e11i	0.153801i
$355$	2.96375e11	0.0525654
$356$	7.35764e12	1.28673
$357$	3.75887e12	0.648212
$358$	− 1.05555e13i	− 1.79500i
$359$	− 6.26135e11i	− 0.105002i	−0.998621	−	0.0525008i	$-0.983281\pi$
$359$	− 6.26135e11i	− 0.105002i	0.998621	−	0.0525008i	$-0.0167192\pi$
$360$	− 4.45786e11i	− 0.0737248i
$361$	−2.11735e12	−0.345347
$362$	− 5.66727e11i	− 0.0911656i
$363$	0	0
$364$	5.95947e12	0.932612
$365$	− 2.64651e12i	− 0.408517i
$366$	−4.77574e12	−0.727169
$367$	8.71197e12	1.30854	0.654268	−	0.756262i	$-0.272977\pi$
$367$	8.71197e12	1.30854	0.654268	+	0.756262i	$0.272977\pi$
$368$	5.12912e11	0.0759983
$369$	− 1.68614e12i	− 0.246469i
$370$	4.69047e12i	0.676407i
$371$	− 8.60541e12i	− 1.22434i
$372$	−4.38213e12	−0.615136
$373$	− 1.07207e13i	− 1.48483i	−0.669938	−	0.742417i	$-0.733679\pi$
$373$	− 1.07207e13i	− 1.48483i	0.669938	−	0.742417i	$-0.266321\pi$
$374$	0	0
$375$	3.23163e12	0.435778
$376$	− 2.20929e12i	− 0.293977i
$377$	−5.02360e12	−0.659642
$378$	−8.83383e12	−1.14470
$379$	2.99054e11	0.0382431	0.0191215	−	0.999817i	$-0.493913\pi$
$379$	2.99054e11	0.0382431	0.0191215	+	0.999817i	$0.493913\pi$
$380$	3.90949e12i	0.493403i
$381$	− 4.11434e12i	− 0.512478i
$382$	1.02455e13i	1.25956i
$383$	3.51394e12	0.426384	0.213192	−	0.977010i	$-0.431614\pi$
$383$	3.51394e12	0.426384	0.213192	+	0.977010i	$0.431614\pi$
$384$	1.09065e13i	1.30626i
$385$	0	0
$386$	1.21497e13	1.41785
$387$	3.26169e12i	0.375741i
$388$	8.11402e12	0.922736
$389$	1.04694e13	1.17537	0.587684	−	0.809091i	$-0.300040\pi$
$389$	1.04694e13	1.17537	0.587684	+	0.809091i	$0.300040\pi$
$390$	2.94861e12	0.326809
$391$	1.03224e13i	1.12953i
$392$	4.94035e12i	0.533737i
$393$	− 1.44552e13i	− 1.54191i
$394$	−1.59323e13	−1.67802
$395$	− 1.97536e12i	− 0.205428i
$396$	0	0
$397$	−1.72874e13	−1.75298	−0.876492	−	0.481416i	$-0.840123\pi$
$397$	−1.72874e13	−1.75298	−0.876492	+	0.481416i	$0.840123\pi$
$398$	9.89910e12i	0.991243i
$399$	6.46155e12	0.638958
$400$	7.52103e11	0.0734475
$401$	−4.09452e12	−0.394894	−0.197447	−	0.980314i	$-0.563265\pi$
$401$	−4.09452e12	−0.394894	−0.197447	+	0.980314i	$0.563265\pi$
$402$	− 1.91902e13i	− 1.82789i
$403$	4.42286e12i	0.416081i
$404$	3.97546e12i	0.369386i
$405$	−1.81911e12	−0.166949
$406$	8.51587e12i	0.771967i
$407$	0	0
$408$	−1.04608e13	−0.925259
$409$	− 1.74501e13i	− 1.52469i	−0.647172	−	0.762344i	$-0.724048\pi$
$409$	− 1.74501e13i	− 1.52469i	0.647172	−	0.762344i	$-0.275952\pi$
$410$	4.20844e12	0.363247
$411$	−7.94875e12	−0.677782
$412$	−3.15618e13	−2.65874
$413$	− 8.96320e11i	− 0.0745955i
$414$	− 5.49953e12i	− 0.452193i
$415$	− 1.43246e12i	− 0.116370i
$416$	1.19092e13	0.955904
$417$	− 2.04204e12i	− 0.161951i
$418$	0	0
$419$	−8.69601e12	−0.673364	−0.336682	−	0.941618i	$-0.609305\pi$
$419$	−8.69601e12	−0.673364	−0.336682	+	0.941618i	$0.609305\pi$
$420$	− 3.06257e12i	− 0.234336i
$421$	−2.14703e13	−1.62341	−0.811704	−	0.584069i	$-0.801460\pi$
$421$	−2.14703e13	−1.62341	−0.811704	+	0.584069i	$0.801460\pi$
$422$	−3.80204e13	−2.84089
$423$	1.24791e12	0.0921467
$424$	2.39485e13i	1.74763i
$425$	1.51361e13i	1.09162i
$426$	3.70531e12i	0.264105i
$427$	5.00642e12	0.352686
$428$	1.93980e12i	0.135063i
$429$	0	0
$430$	−8.14087e12	−0.553769
$431$	− 2.07224e13i	− 1.39333i	−0.717399	−	0.696663i	$-0.754667\pi$
$431$	− 2.07224e13i	− 1.39333i	0.717399	−	0.696663i	$-0.245333\pi$
$432$	−1.29509e12	−0.0860760
$433$	−8.67744e12	−0.570101	−0.285051	−	0.958512i	$-0.592010\pi$
$433$	−8.67744e12	−0.570101	−0.285051	+	0.958512i	$0.592010\pi$
$434$	7.49750e12	0.486932
$435$	2.58163e12i	0.165747i
$436$	1.56434e13i	0.992887i
$437$	1.77443e13i	1.11340i
$438$	3.30870e13	2.05252
$439$	4.19959e12i	0.257564i	0.991673	+	0.128782i	$0.0411067\pi$
$439$	4.19959e12i	0.257564i	−0.991673	+	0.128782i	$0.958893\pi$
$440$	0	0
$441$	−2.79053e12	−0.167299
$442$	2.86974e13i	1.70110i
$443$	2.87506e12	0.168511	0.0842556	−	0.996444i	$-0.473149\pi$
$443$	2.87506e12	0.168511	0.0842556	+	0.996444i	$0.473149\pi$
$444$	−3.59298e13	−2.08229
$445$	−3.81623e12	−0.218693
$446$	− 2.70665e13i	− 1.53376i
$447$	7.68647e10i	0.00430714i
$448$	− 1.92519e13i	− 1.06680i
$449$	−3.31999e12	−0.181930	−0.0909652	−	0.995854i	$-0.528995\pi$
$449$	−3.31999e12	−0.181930	−0.0909652	+	0.995854i	$0.528995\pi$
$450$	− 8.06418e12i	− 0.437016i
$451$	0	0
$452$	−4.87206e13	−2.58238
$453$	− 1.14687e13i	− 0.601203i
$454$	−5.23458e13	−2.71395
$455$	−3.09103e12	−0.158506
$456$	−1.79822e13	−0.912049
$457$	2.23705e13i	1.12226i	0.827727	+	0.561130i	$0.189633\pi$
$457$	2.23705e13i	1.12226i	−0.827727	+	0.561130i	$0.810367\pi$
$458$	3.10424e13i	1.54038i
$459$	− 2.60638e13i	− 1.27931i
$460$	8.41025e12	0.408338
$461$	− 3.55379e13i	− 1.70682i	−0.521242	−	0.853409i	$-0.674531\pi$
$461$	− 3.55379e13i	− 1.70682i	0.521242	−	0.853409i	$-0.325469\pi$
$462$	0	0
$463$	2.97354e13	1.39755	0.698776	−	0.715340i	$-0.253728\pi$
$463$	2.97354e13	1.39755	0.698776	+	0.715340i	$0.253728\pi$
$464$	1.24848e12i	0.0580485i
$465$	2.27290e12	0.104548
$466$	5.46205e13	2.48557
$467$	2.31178e13	1.04079	0.520394	−	0.853927i	$-0.325785\pi$
$467$	2.31178e13	1.04079	0.520394	+	0.853927i	$0.325785\pi$
$468$	− 9.36791e12i	− 0.417266i
$469$	2.01172e13i	0.886549i
$470$	3.11465e12i	0.135806i
$471$	−9.73595e12	−0.420024
$472$	2.49442e12i	0.106478i
$473$	0	0
$474$	2.46961e13	1.03214
$475$	2.60192e13i	1.07603i
$476$	2.98065e13	1.21977
$477$	−1.35271e13	−0.547790
$478$	−1.00051e13	−0.400942
$479$	8.81053e12i	0.349401i	0.984622	+	0.174701i	$0.0558958\pi$
$479$	8.81053e12i	0.349401i	−0.984622	+	0.174701i	$0.944104\pi$
$480$	− 6.12011e12i	− 0.240189i
$481$	3.62637e13i	1.40847i
$482$	7.11450e13	2.73470
$483$	− 1.39003e13i	− 0.528798i
$484$	0	0
$485$	−4.20854e12	−0.156828
$486$	2.46244e13i	0.908205i
$487$	−3.51109e13	−1.28173	−0.640867	−	0.767652i	$-0.721425\pi$
$487$	−3.51109e13	−1.28173	−0.640867	+	0.767652i	$0.721425\pi$
$488$	−1.39326e13	−0.503425
$489$	−3.34410e13	−1.19601
$490$	− 6.96489e12i	− 0.246566i
$491$	1.81567e13i	0.636251i	0.948049	+	0.318126i	$0.103053\pi$
$491$	1.81567e13i	0.636251i	−0.948049	+	0.318126i	$0.896947\pi$
$492$	3.22374e13i	1.11824i
$493$	−2.51257e13	−0.862747
$494$	4.93311e13i	1.67682i
$495$	0	0
$496$	1.09918e12	0.0366151
$497$	− 3.88429e12i	− 0.128094i
$498$	1.79088e13	0.584680
$499$	1.39152e13	0.449765	0.224882	−	0.974386i	$-0.427800\pi$
$499$	1.39152e13	0.449765	0.224882	+	0.974386i	$0.427800\pi$
$500$	2.56256e13	0.820020
$501$	− 5.00968e13i	− 1.58716i
$502$	3.94408e13i	1.23716i
$503$	− 5.84810e13i	− 1.81625i	−0.418703	−	0.908123i	$-0.637515\pi$
$503$	− 5.84810e13i	− 1.81625i	0.418703	−	0.908123i	$-0.362485\pi$
$504$	−5.84246e12	−0.179657
$505$	− 2.06197e12i	− 0.0627807i
$506$	0	0
$507$	−5.36762e12	−0.160229
$508$	− 3.26252e13i	− 0.964350i
$509$	4.61710e13	1.35139	0.675694	−	0.737182i	$-0.263844\pi$
$509$	4.61710e13	1.35139	0.675694	+	0.737182i	$0.263844\pi$
$510$	1.47476e13	0.427434
$511$	−3.46852e13	−0.995496
$512$	− 5.56501e12i	− 0.158167i
$513$	− 4.48040e13i	− 1.26104i
$514$	4.51192e13i	1.25761i
$515$	1.63703e13	0.451878
$516$	− 6.23604e13i	− 1.70475i
$517$	0	0
$518$	6.14733e13	1.64830
$519$	− 1.74950e13i	− 0.464599i
$520$	8.60220e12	0.226252
$521$	−1.02829e13	−0.267873	−0.133936	−	0.990990i	$-0.542762\pi$
$521$	−1.02829e13	−0.267873	−0.133936	+	0.990990i	$0.542762\pi$
$522$	1.33864e13	0.345391
$523$	6.74856e13i	1.72466i	0.506349	+	0.862328i	$0.330995\pi$
$523$	6.74856e13i	1.72466i	−0.506349	+	0.862328i	$0.669005\pi$
$524$	− 1.14624e14i	− 2.90148i
$525$	− 2.03826e13i	− 0.511050i
$526$	−8.89826e13	−2.20992
$527$	2.21211e13i	0.544193i
$528$	0	0
$529$	−3.25426e12	−0.0785550
$530$	− 3.37624e13i	− 0.807336i
$531$	−1.40896e12	−0.0333753
$532$	5.12377e13	1.20235
$533$	3.25370e13	0.756382
$534$	− 4.77109e13i	− 1.09878i
$535$	− 1.00613e12i	− 0.0229553i
$536$	− 5.59852e13i	− 1.26546i
$537$	−4.19385e13	−0.939165
$538$	1.22717e14i	2.72265i
$539$	0	0
$540$	−2.12357e13	−0.462485
$541$	− 3.60954e12i	− 0.0778872i	−0.999241	−	0.0389436i	$-0.987601\pi$
$541$	− 3.60954e12i	− 0.0778872i	0.999241	−	0.0389436i	$-0.0123993\pi$
$542$	3.93629e13	0.841570
$543$	−2.25169e12	−0.0476990
$544$	5.95641e13	1.25023
$545$	− 8.11386e12i	− 0.168751i
$546$	− 3.86444e13i	− 0.796386i
$547$	− 2.59261e13i	− 0.529421i	−0.964328	−	0.264711i	$-0.914724\pi$
$547$	− 2.59261e13i	− 0.529421i	0.964328	−	0.264711i	$-0.0852764\pi$
$548$	−6.30307e13	−1.27541
$549$	− 7.86977e12i	− 0.157798i
$550$	0	0
$551$	−4.31914e13	−0.850430
$552$	3.86840e13i	0.754807i
$553$	−2.58890e13	−0.500598
$554$	4.61712e13	0.884753
$555$	1.86359e13	0.353904
$556$	− 1.61926e13i	− 0.304750i
$557$	− 6.91195e12i	− 0.128921i	−0.997920	−	0.0644607i	$-0.979467\pi$
$557$	− 6.91195e12i	− 0.128921i	0.997920	−	0.0644607i	$-0.0205327\pi$
$558$	− 1.17856e13i	− 0.217861i
$559$	−6.29399e13	−1.15310
$560$	7.68191e11i	0.0139485i
$561$	0	0
$562$	1.27014e13	0.226552
$563$	− 3.72286e13i	− 0.658165i	−0.944301	−	0.329082i	$-0.893261\pi$
$563$	− 3.72286e13i	− 0.658165i	0.944301	−	0.329082i	$-0.106739\pi$
$564$	−2.38588e13	−0.418073
$565$	2.52702e13	0.438900
$566$	5.17630e13	0.891121
$567$	2.38412e13i	0.406830i
$568$	1.08098e13i	0.182842i
$569$	− 1.44818e13i	− 0.242808i	−0.992603	−	0.121404i	$-0.961260\pi$
$569$	− 1.44818e13i	− 0.242808i	0.992603	−	0.121404i	$-0.0387396\pi$
$570$	2.53512e13	0.421332
$571$	1.02782e13i	0.169330i	0.996409	+	0.0846652i	$0.0269821\pi$
$571$	1.02782e13i	0.169330i	−0.996409	+	0.0846652i	$0.973018\pi$
$572$	0	0
$573$	4.07069e13	0.659015
$574$	− 5.51558e13i	− 0.885180i
$575$	5.59735e13	0.890518
$576$	−3.02628e13	−0.477305
$577$	−7.22988e13	−1.13045	−0.565226	−	0.824936i	$-0.691211\pi$
$577$	−7.22988e13	−1.13045	−0.565226	+	0.824936i	$0.691211\pi$
$578$	3.98684e13i	0.618002i
$579$	− 4.82725e13i	− 0.741835i
$580$	2.04714e13i	0.311894i
$581$	−1.87738e13	−0.283577
$582$	− 5.26156e13i	− 0.787952i
$583$	0	0
$584$	9.65273e13	1.42097
$585$	4.85890e12i	0.0709184i
$586$	−7.98992e13	−1.15626
$587$	−7.99968e13	−1.14784	−0.573921	−	0.818911i	$-0.694578\pi$
$587$	−7.99968e13	−1.14784	−0.573921	+	0.818911i	$0.694578\pi$
$588$	5.33522e13	0.759042
$589$	3.80264e13i	0.536424i
$590$	− 3.51662e12i	− 0.0491887i
$591$	6.33012e13i	0.877959i
$592$	9.01235e12	0.123945
$593$	− 2.33053e13i	− 0.317820i	−0.987293	−	0.158910i	$-0.949202\pi$
$593$	− 2.33053e13i	− 0.317820i	0.987293	−	0.158910i	$-0.0507980\pi$
$594$	0	0
$595$	−1.54599e13	−0.207311
$596$	6.09509e11i	0.00810492i
$597$	3.93305e13	0.518631
$598$	1.06123e14	1.38772
$599$	−2.43715e13	−0.316044	−0.158022	−	0.987436i	$-0.550512\pi$
$599$	−2.43715e13	−0.316044	−0.158022	+	0.987436i	$0.550512\pi$
$600$	5.67238e13i	0.729473i
$601$	− 8.17240e13i	− 1.04226i	−0.853477	−	0.521131i	$-0.825510\pi$
$601$	− 8.17240e13i	− 1.04226i	0.853477	−	0.521131i	$-0.174490\pi$
$602$	1.06694e14i	1.34945i
$603$	3.16229e13	0.396657
$604$	− 9.09423e13i	− 1.13131i
$605$	0	0
$606$	2.57790e13	0.315430
$607$	8.84677e13i	1.07360i	0.843710	+	0.536799i	$0.180367\pi$
$607$	8.84677e13i	1.07360i	−0.843710	+	0.536799i	$0.819633\pi$
$608$	1.02391e14	1.23238
$609$	3.38347e13	0.403902
$610$	1.96422e13	0.232563
$611$	2.40805e13i	0.282787i
$612$	− 4.68539e13i	− 0.545744i
$613$	7.12369e13i	0.823005i	0.911409	+	0.411503i	$0.134996\pi$
$613$	7.12369e13i	0.823005i	−0.911409	+	0.411503i	$0.865004\pi$
$614$	3.37413e13	0.386652
$615$	− 1.67207e13i	− 0.190055i
$616$	0	0
$617$	−6.17669e13	−0.690764	−0.345382	−	0.938462i	$-0.612251\pi$
$617$	−6.17669e13	−0.690764	−0.345382	+	0.938462i	$0.612251\pi$
$618$	2.04663e14i	2.27038i
$619$	1.52405e14	1.67705	0.838523	−	0.544866i	$-0.183420\pi$
$619$	1.52405e14	1.67705	0.838523	+	0.544866i	$0.183420\pi$
$620$	1.80233e13	0.196732
$621$	−9.63841e13	−1.04363
$622$	− 3.33246e13i	− 0.357942i
$623$	5.00154e13i	0.532922i
$624$	− 5.66550e12i	− 0.0598846i
$625$	7.51811e13	0.788331
$626$	8.52541e13i	0.886837i
$627$	0	0
$628$	−7.72025e13	−0.790375
$629$	1.81374e14i	1.84214i
$630$	8.23668e12	0.0829945
$631$	1.66382e13	0.166325	0.0831627	−	0.996536i	$-0.473498\pi$
$631$	1.66382e13	0.166325	0.0831627	+	0.996536i	$0.473498\pi$
$632$	7.20479e13	0.714555
$633$	1.51060e14i	1.48639i
$634$	8.90042e13i	0.868889i
$635$	1.69219e13i	0.163901i
$636$	2.58626e14	2.48535
$637$	− 5.38480e13i	− 0.513420i
$638$	0	0
$639$	−6.10585e12	−0.0573115
$640$	− 4.48573e13i	− 0.417766i
$641$	−2.13998e14	−1.97752	−0.988758	−	0.149526i	$-0.952225\pi$
$641$	−2.13998e14	−1.97752	−0.988758	+	0.149526i	$0.952225\pi$
$642$	1.25787e13	0.115335
$643$	3.83482e13	0.348891	0.174445	−	0.984667i	$-0.444187\pi$
$643$	3.83482e13	0.348891	0.174445	+	0.984667i	$0.444187\pi$
$644$	− 1.10225e14i	− 0.995060i
$645$	3.23448e13i	0.289739i
$646$	2.46731e14i	2.19311i
$647$	5.94428e13	0.524297	0.262149	−	0.965028i	$-0.415569\pi$
$647$	5.94428e13	0.524297	0.262149	+	0.965028i	$0.415569\pi$
$648$	− 6.63490e13i	− 0.580710i
$649$	0	0
$650$	1.55612e14	1.34115
$651$	− 2.97887e13i	− 0.254769i
$652$	−2.65175e14	−2.25058
$653$	−1.40281e14	−1.18149	−0.590747	−	0.806857i	$-0.701167\pi$
$653$	−1.40281e14	−1.18149	−0.590747	+	0.806857i	$0.701167\pi$
$654$	1.01440e14	0.847856
$655$	5.94528e13i	0.493135i
$656$	− 8.08617e12i	− 0.0665616i
$657$	5.45229e13i	0.445402i
$658$	4.08206e13	0.330940
$659$	− 3.84162e13i	− 0.309092i	−0.987986	−	0.154546i	$-0.950609\pi$
$659$	− 3.84162e13i	− 0.309092i	0.987986	−	0.154546i	$-0.0493914\pi$
$660$	0	0
$661$	−2.10584e14	−1.66885	−0.834427	−	0.551118i	$-0.814201\pi$
$661$	−2.10584e14	−1.66885	−0.834427	+	0.551118i	$0.814201\pi$
$662$	− 1.81579e13i	− 0.142816i
$663$	1.14019e14	0.890038
$664$	5.22466e13	0.404779
$665$	−2.65757e13	−0.204351
$666$	− 9.66320e13i	− 0.737479i
$667$	9.29149e13i	0.703811i
$668$	− 3.97250e14i	− 2.98663i
$669$	−1.07539e14	−0.802482
$670$	7.89277e13i	0.584595i
$671$	0	0
$672$	−8.02101e13	−0.585306
$673$	− 1.14689e14i	− 0.830704i	−0.909661	−	0.415352i	$-0.863658\pi$
$673$	− 1.14689e14i	− 0.830704i	0.909661	−	0.415352i	$-0.136342\pi$
$674$	−5.16544e13	−0.371371
$675$	−1.41332e14	−1.00860
$676$	−4.25633e13	−0.301510
$677$	− 7.50743e13i	− 0.527895i	−0.964537	−	0.263948i	$-0.914975\pi$
$677$	− 7.50743e13i	− 0.527895i	0.964537	−	0.263948i	$-0.0850246\pi$
$678$	3.15930e14i	2.20517i
$679$	5.51571e13i	0.382166i
$680$	4.30242e13	0.295916
$681$	2.07977e14i	1.41997i
$682$	0	0
$683$	2.09453e14	1.40924	0.704618	−	0.709587i	$-0.251118\pi$
$683$	2.09453e14	1.40924	0.704618	+	0.709587i	$0.251118\pi$
$684$	− 8.05424e13i	− 0.537953i
$685$	3.26925e13	0.216768
$686$	−2.51237e14	−1.65372
$687$	1.23336e14	0.805945
$688$	1.56420e13i	0.101473i
$689$	− 2.61030e14i	− 1.68110i
$690$	− 5.45365e13i	− 0.348692i
$691$	−5.23051e13	−0.332012	−0.166006	−	0.986125i	$-0.553087\pi$
$691$	−5.23051e13	−0.332012	−0.166006	+	0.986125i	$0.553087\pi$
$692$	− 1.38729e14i	− 0.874254i
$693$	0	0
$694$	1.31503e13	0.0816843
$695$	8.39871e12i	0.0517951i
$696$	−9.41606e13	−0.576531
$697$	1.62735e14	0.989274
$698$	−2.06644e14	−1.24723
$699$	− 2.17015e14i	− 1.30048i
$700$	− 1.61627e14i	− 0.961663i
$701$	1.30133e14i	0.768775i	0.923172	+	0.384387i	$0.125587\pi$
$701$	1.30133e14i	0.768775i	−0.923172	+	0.384387i	$0.874413\pi$
$702$	−2.67958e14	−1.57174
$703$	3.11784e14i	1.81584i
$704$	0	0
$705$	1.23750e13	0.0710555
$706$	− 3.11393e14i	− 1.77536i
$707$	−2.70242e13	−0.152987
$708$	2.69379e13	0.151425
$709$	−7.36630e13	−0.411167	−0.205584	−	0.978640i	$-0.565909\pi$
$709$	−7.36630e13	−0.411167	−0.205584	+	0.978640i	$0.565909\pi$
$710$	− 1.52396e13i	− 0.0844661i
$711$	4.06958e13i	0.223976i
$712$	− 1.39191e14i	− 0.760694i
$713$	8.18038e13	0.443942
$714$	− 1.93281e14i	− 1.04160i
$715$	0	0
$716$	−3.32557e14	−1.76726
$717$	3.97517e13i	0.209778i
$718$	−3.21959e13	−0.168724
$719$	−7.25746e13	−0.377694	−0.188847	−	0.982006i	$-0.560475\pi$
$719$	−7.25746e13	−0.377694	−0.188847	+	0.982006i	$0.560475\pi$
$720$	1.20755e12	0.00624082
$721$	− 2.14549e14i	− 1.10116i
$722$	1.08874e14i	0.554930i
$723$	− 2.82669e14i	− 1.43083i
$724$	−1.78551e13	−0.0897571
$725$	1.36245e14i	0.680189i
$726$	0	0
$727$	8.09116e12	0.0398418	0.0199209	−	0.999802i	$-0.493659\pi$
$727$	8.09116e12	0.0398418	0.0199209	+	0.999802i	$0.493659\pi$
$728$	− 1.12740e14i	− 0.551344i
$729$	2.25673e14	1.09608
$730$	−1.36084e14	−0.656435
$731$	−3.14796e14	−1.50814
$732$	1.50463e14i	0.715934i
$733$	2.79180e14i	1.31936i	0.751545	+	0.659682i	$0.229309\pi$
$733$	2.79180e14i	1.31936i	−0.751545	+	0.659682i	$0.770691\pi$
$734$	− 4.47969e14i	− 2.10266i
$735$	−2.76725e13	−0.129006
$736$	− 2.20268e14i	− 1.01991i
$737$	0	0
$738$	−8.67014e13	−0.396045
$739$	4.90436e12i	0.0222516i	0.999938	+	0.0111258i	$0.00354152\pi$
$739$	4.90436e12i	0.0222516i	−0.999938	+	0.0111258i	$0.996458\pi$
$740$	1.47776e14	0.665956
$741$	1.95999e14	0.877331
$742$	−4.42490e14	−1.96736
$743$	1.74731e14i	0.771659i	0.922570	+	0.385830i	$0.126085\pi$
$743$	1.74731e14i	0.771659i	−0.922570	+	0.385830i	$0.873915\pi$
$744$	8.29005e13i	0.363657i
$745$	− 3.16137e11i	− 0.00137751i
$746$	−5.51257e14	−2.38594
$747$	2.95112e13i	0.126877i
$748$	0	0
$749$	−1.31863e13	−0.0559388
$750$	− 1.66170e14i	− 0.700240i
$751$	1.52973e14	0.640348	0.320174	−	0.947359i	$-0.396259\pi$
$751$	1.52973e14	0.640348	0.320174	+	0.947359i	$0.396259\pi$
$752$	5.98454e12	0.0248852
$753$	1.56704e14	0.647299
$754$	2.58313e14i	1.05996i
$755$	4.71695e13i	0.192277i
$756$	2.78315e14i	1.12701i
$757$	−1.12720e14	−0.453440	−0.226720	−	0.973960i	$-0.572800\pi$
$757$	−1.12720e14	−0.453440	−0.226720	+	0.973960i	$0.572800\pi$
$758$	− 1.53773e13i	− 0.0614519i
$759$	0	0
$760$	7.39591e13	0.291691
$761$	6.06067e13i	0.237464i	0.992926	+	0.118732i	$0.0378829\pi$
$761$	6.06067e13i	0.237464i	−0.992926	+	0.118732i	$0.962117\pi$
$762$	−2.11559e14	−0.823488
$763$	−1.06340e14	−0.411220
$764$	3.22791e14	1.24009
$765$	2.43020e13i	0.0927543i
$766$	− 1.80687e14i	− 0.685145i
$767$	− 2.71882e13i	− 0.102425i
$768$	1.95086e14	0.730162
$769$	− 1.11982e14i	− 0.416406i	−0.978086	−	0.208203i	$-0.933239\pi$
$769$	− 1.11982e14i	− 0.416406i	0.978086	−	0.208203i	$-0.0667615\pi$
$770$	0	0
$771$	1.79265e14	0.657997
$772$	− 3.82784e14i	− 1.39594i
$773$	5.53174e13	0.200431	0.100215	−	0.994966i	$-0.468047\pi$
$773$	5.53174e13	0.200431	0.100215	+	0.994966i	$0.468047\pi$
$774$	1.67716e14	0.603768
$775$	1.19952e14	0.429042
$776$	− 1.53500e14i	− 0.545505i
$777$	− 2.44242e14i	− 0.862413i
$778$	− 5.38337e14i	− 1.88867i
$779$	2.79743e14	0.975151
$780$	− 9.28976e13i	− 0.321760i
$781$	0	0
$782$	5.30778e14	1.81501
$783$	− 2.34608e14i	− 0.797140i
$784$	−1.33824e13	−0.0451809
$785$	4.00430e13	0.134332
$786$	−7.43285e14	−2.47766
$787$	− 3.24246e14i	− 1.07399i	−0.843585	−	0.536996i	$-0.819559\pi$
$787$	− 3.24246e14i	− 1.07399i	0.843585	−	0.536996i	$-0.180441\pi$
$788$	5.01955e14i	1.65209i
$789$	3.53541e14i	1.15626i
$790$	−1.01573e14	−0.330097
$791$	− 3.31191e14i	− 1.06954i
$792$	0	0
$793$	1.51861e14	0.484261
$794$	8.88920e14i	2.81683i
$795$	−1.34143e14	−0.422408
$796$	3.11877e14	0.975928
$797$	5.29249e14	1.64577	0.822884	−	0.568209i	$-0.192363\pi$
$797$	5.29249e14	1.64577	0.822884	+	0.568209i	$0.192363\pi$
$798$	− 3.32253e14i	− 1.02673i
$799$	1.20439e14i	0.369858i
$800$	− 3.22988e14i	− 0.985681i
$801$	7.86210e13	0.238438
$802$	2.10540e14i	0.634546i
$803$	0	0
$804$	−6.04600e14	−1.79965
$805$	5.71708e13i	0.169120i
$806$	2.27423e14	0.668590
$807$	4.87571e14	1.42452
$808$	7.52071e13	0.218375
$809$	3.98534e13i	0.115007i	0.998345	+	0.0575033i	$0.0183140\pi$
$809$	3.98534e13i	0.115007i	−0.998345	+	0.0575033i	$0.981686\pi$
$810$	9.35385e13i	0.268266i
$811$	1.88482e14i	0.537237i	0.963247	+	0.268619i	$0.0865672\pi$
$811$	1.88482e14i	0.537237i	−0.963247	+	0.268619i	$0.913433\pi$
$812$	2.68297e14	0.760040
$813$	− 1.56394e14i	− 0.440320i
$814$	0	0
$815$	1.37540e14	0.382507
$816$	− 2.83362e13i	− 0.0783233i
$817$	−5.41138e14	−1.48661
$818$	−8.97284e14	−2.44998
$819$	6.36807e13	0.172818
$820$	− 1.32589e14i	− 0.357635i
$821$	2.20191e14i	0.590314i	0.955449	+	0.295157i	$0.0953719\pi$
$821$	2.20191e14i	0.590314i	−0.955449	+	0.295157i	$0.904628\pi$
$822$	4.08725e14i	1.08911i
$823$	5.05209e14	1.33805	0.669025	−	0.743240i	$-0.266712\pi$
$823$	5.05209e14	1.33805	0.669025	+	0.743240i	$0.266712\pi$
$824$	5.97081e14i	1.57180i
$825$	0	0
$826$	−4.60888e13	−0.119866
$827$	− 3.12471e14i	− 0.807759i	−0.914812	−	0.403880i	$-0.867661\pi$
$827$	− 3.12471e14i	− 0.807759i	0.914812	−	0.403880i	$-0.132339\pi$
$828$	−1.73266e14	−0.445207
$829$	−5.25198e14	−1.34137	−0.670687	−	0.741740i	$-0.734001\pi$
$829$	−5.25198e14	−1.34137	−0.670687	+	0.741740i	$0.734001\pi$
$830$	−7.36570e13	−0.186992
$831$	− 1.83445e14i	− 0.462914i
$832$	− 5.83972e14i	− 1.46479i
$833$	− 2.69323e14i	− 0.671503i
$834$	−1.05002e14	−0.260235
$835$	2.06044e14i	0.507606i
$836$	0	0
$837$	−2.06553e14	−0.502810
$838$	4.47149e14i	1.08201i
$839$	−4.76192e14	−1.14544	−0.572720	−	0.819751i	$-0.694112\pi$
$839$	−4.76192e14	−1.14544	−0.572720	+	0.819751i	$0.694112\pi$
$840$	−5.79372e13	−0.138536
$841$	1.94543e14	0.462420
$842$	1.10400e15i	2.60861i
$843$	− 5.04643e13i	− 0.118535i
$844$	1.19785e15i	2.79700i
$845$	2.20765e13	0.0512445
$846$	− 6.41673e13i	− 0.148068i
$847$	0	0
$848$	−6.48717e13	−0.147937
$849$	− 2.05662e14i	− 0.466246i
$850$	7.78300e14	1.75409
$851$	6.70723e14	1.50278
$852$	1.16738e14	0.260025
$853$	− 4.79250e14i	− 1.06125i	−0.847607	−	0.530625i	$-0.821957\pi$
$853$	− 4.79250e14i	− 1.06125i	0.847607	−	0.530625i	$-0.178043\pi$
$854$	− 2.57430e14i	− 0.566722i
$855$	4.17753e13i	0.0914302i
$856$	3.66968e13	0.0798472
$857$	3.50986e14i	0.759251i	0.925140	+	0.379625i	$0.123947\pi$
$857$	3.50986e14i	0.759251i	−0.925140	+	0.379625i	$0.876053\pi$
$858$	0	0
$859$	−5.55923e14	−1.18864	−0.594318	−	0.804230i	$-0.702578\pi$
$859$	−5.55923e14	−1.18864	−0.594318	+	0.804230i	$0.702578\pi$
$860$	2.56483e14i	0.545213i
$861$	−2.19142e14	−0.463137
$862$	−1.06554e15	−2.23890
$863$	3.72266e14	0.777678	0.388839	−	0.921306i	$-0.372876\pi$
$863$	3.72266e14	0.777678	0.388839	+	0.921306i	$0.372876\pi$
$864$	5.56173e14i	1.15516i
$865$	7.19555e13i	0.148588i
$866$	4.46194e14i	0.916082i
$867$	1.58403e14	0.323346
$868$	− 2.36213e14i	− 0.479408i
$869$	0	0
$870$	1.32747e14	0.266336
$871$	6.10218e14i	1.21729i
$872$	2.95940e14	0.586977
$873$	8.67034e13	0.170988
$874$	9.12412e14	1.78910
$875$	1.74197e14i	0.339625i
$876$	− 1.04243e15i	− 2.02080i
$877$	− 1.94216e14i	− 0.374359i	−0.982326	−	0.187179i	$-0.940065\pi$
$877$	− 1.94216e14i	− 0.374359i	0.982326	−	0.187179i	$-0.0599346\pi$
$878$	2.15943e14	0.413873
$879$	3.17451e14i	0.604968i
$880$	0	0
$881$	1.12274e14	0.211543	0.105772	−	0.994390i	$-0.466269\pi$
$881$	1.12274e14	0.211543	0.105772	+	0.994390i	$0.466269\pi$
$882$	1.43489e14i	0.268829i
$883$	−2.16715e13	−0.0403725	−0.0201862	−	0.999796i	$-0.506426\pi$
$883$	−2.16715e13	−0.0403725	−0.0201862	+	0.999796i	$0.506426\pi$
$884$	9.04127e14	1.67482
$885$	−1.39720e13	−0.0257361
$886$	− 1.47836e14i	− 0.270777i
$887$	1.10130e14i	0.200580i	0.994958	+	0.100290i	$0.0319770\pi$
$887$	1.10130e14i	0.200580i	−0.994958	+	0.100290i	$0.968023\pi$
$888$	6.79715e14i	1.23101i
$889$	2.21778e14	0.399402
$890$	1.96230e14i	0.351412i
$891$	0	0
$892$	−8.52745e14	−1.51006
$893$	2.07037e14i	0.364577i
$894$	3.95238e12	0.00692104
$895$	1.72489e14	0.300363
$896$	−5.87900e14	−1.01804
$897$	− 4.21642e14i	− 0.726074i
$898$	1.70714e14i	0.292340i
$899$	1.99118e14i	0.339088i
$900$	−2.54067e14	−0.430264
$901$	− 1.30555e15i	− 2.19872i
$902$	0	0
$903$	4.23911e14	0.706051
$904$	9.21688e14i	1.52666i
$905$	9.26098e12	0.0152551
$906$	−5.89718e14	−0.966059
$907$	3.04606e14	0.496252	0.248126	−	0.968728i	$-0.420185\pi$
$907$	3.04606e14	0.496252	0.248126	+	0.968728i	$0.420185\pi$
$908$	1.64918e15i	2.67202i
$909$	4.24803e13i	0.0684492i
$910$	1.58941e14i	0.254700i
$911$	5.91306e14	0.942368	0.471184	−	0.882035i	$-0.343827\pi$
$911$	5.91306e14	0.942368	0.471184	+	0.882035i	$0.343827\pi$
$912$	− 4.87103e13i	− 0.0772051i
$913$	0	0
$914$	1.15029e15	1.80333
$915$	− 7.80412e13i	− 0.121680i
$916$	9.78008e14	1.51658
$917$	7.79187e14	1.20170
$918$	−1.34020e15	−2.05569
$919$	2.13901e14i	0.326313i	0.986600	+	0.163157i	$0.0521676\pi$
$919$	2.13901e14i	0.326313i	−0.986600	+	0.163157i	$0.947832\pi$
$920$	− 1.59104e14i	− 0.241402i
$921$	− 1.34059e14i	− 0.202301i
$922$	−1.82736e15	−2.74264
$923$	− 1.17823e14i	− 0.175882i
$924$	0	0
$925$	9.83507e14	1.45234
$926$	− 1.52899e15i	− 2.24569i
$927$	−3.37257e14	−0.492678
$928$	5.36154e14	0.779022
$929$	−9.09805e12	−0.0131483	−0.00657415	−	0.999978i	$-0.502093\pi$
$929$	−9.09805e12	−0.0131483	−0.00657415	+	0.999978i	$0.502093\pi$
$930$	− 1.16873e14i	− 0.167996i
$931$	− 4.62969e14i	− 0.661917i
$932$	− 1.72085e15i	− 2.44717i
$933$	−1.32403e14	−0.187280
$934$	− 1.18872e15i	− 1.67242i
$935$	0	0
$936$	−1.77221e14	−0.246680
$937$	6.74632e14i	0.934047i	0.884245	+	0.467024i	$0.154674\pi$
$937$	6.74632e14i	0.934047i	−0.884245	+	0.467024i	$0.845326\pi$
$938$	1.03443e15	1.42457
$939$	3.38727e14	0.464004
$940$	9.81289e13	0.133708
$941$	− 7.69837e14i	− 1.04340i	−0.853129	−	0.521700i	$-0.825298\pi$
$941$	− 7.69837e14i	− 1.04340i	0.853129	−	0.521700i	$-0.174702\pi$
$942$	5.00623e14i	0.674926i
$943$	− 6.01794e14i	− 0.807030i
$944$	−6.75689e12	−0.00901337
$945$	− 1.44355e14i	− 0.191546i
$946$	0	0
$947$	5.88390e13	0.0772530	0.0386265	−	0.999254i	$-0.487702\pi$
$947$	5.88390e13	0.0772530	0.0386265	+	0.999254i	$0.487702\pi$
$948$	− 7.78066e14i	− 1.01619i
$949$	−1.05211e15	−1.36688
$950$	1.33791e15	1.72905
$951$	3.53627e14	0.454613
$952$	− 5.63875e14i	− 0.721104i
$953$	4.75944e14i	0.605468i	0.953075	+	0.302734i	$0.0978994\pi$
$953$	4.75944e14i	0.605468i	−0.953075	+	0.302734i	$0.902101\pi$
$954$	6.95566e14i	0.880231i
$955$	−1.67424e14	−0.210766
$956$	3.15216e14i	0.394747i
$957$	0	0
$958$	4.53038e14	0.561445
$959$	− 4.28467e14i	− 0.528232i
$960$	−3.00103e14	−0.368056
$961$	−6.44321e14	−0.786114
$962$	1.86468e15	2.26323
$963$	2.07280e13i	0.0250280i
$964$	− 2.24146e15i	− 2.69244i
$965$	1.98540e14i	0.237253i
$966$	−7.14755e14	−0.849712
$967$	1.21859e14i	0.144121i	0.997400	+	0.0720604i	$0.0229574\pi$
$967$	1.21859e14i	0.144121i	−0.997400	+	0.0720604i	$0.977043\pi$
$968$	0	0
$969$	9.80298e14	1.14746
$970$	2.16403e14i	0.252003i
$971$	5.05819e14	0.586001	0.293001	−	0.956112i	$-0.405346\pi$
$971$	5.05819e14	0.586001	0.293001	+	0.956112i	$0.405346\pi$
$972$	7.75806e14	0.894173
$973$	1.10073e14	0.126217
$974$	1.80540e15i	2.05959i
$975$	− 6.18269e14i	− 0.701705i
$976$	− 3.77408e13i	− 0.0426150i
$977$	−1.28713e15	−1.44593	−0.722967	−	0.690882i	$-0.757222\pi$
$977$	−1.28713e15	−1.44593	−0.722967	+	0.690882i	$0.757222\pi$
$978$	1.71953e15i	1.92184i
$979$	0	0
$980$	−2.19433e14	−0.242757
$981$	1.67160e14i	0.183987i
$982$	9.33616e14	1.02238
$983$	−8.40111e14	−0.915312	−0.457656	−	0.889129i	$-0.651311\pi$
$983$	−8.40111e14	−0.915312	−0.457656	+	0.889129i	$0.651311\pi$
$984$	6.09862e14	0.661083
$985$	− 2.60352e14i	− 0.280789i
$986$	1.29196e15i	1.38633i
$987$	− 1.62186e14i	− 0.173152i
$988$	1.55420e15	1.65091
$989$	1.16412e15i	1.23031i
$990$	0	0
$991$	−6.54919e12	−0.00685203	−0.00342602	−	0.999994i	$-0.501091\pi$
$991$	−6.54919e12	−0.00685203	−0.00342602	+	0.999994i	$0.501091\pi$
$992$	− 4.72039e14i	− 0.491382i
$993$	−7.21441e13	−0.0747231
$994$	−1.99730e14	−0.205832
$995$	−1.61763e14	−0.165868
$996$	− 5.64226e14i	− 0.575647i
$997$	− 8.17355e14i	− 0.829726i	−0.909884	−	0.414863i	$-0.863829\pi$
$997$	− 8.17355e14i	− 0.829726i	0.909884	−	0.414863i	$-0.136171\pi$
$998$	− 7.15518e14i	− 0.722716i
$999$	−1.69356e15	−1.70205

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.11.b.c.120.4		36
11.4	even	5		11.11.d.a.6.9	yes	36
11.8	odd	10		11.11.d.a.2.9	✓	36
11.10	odd	2	inner	121.11.b.c.120.33		36
33.8	even	10		99.11.k.a.46.1		36
33.26	odd	10		99.11.k.a.28.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.11.d.a.2.9	✓	36	11.8	odd	10
11.11.d.a.6.9	yes	36	11.4	even	5
99.11.k.a.28.1		36	33.26	odd	10
99.11.k.a.46.1		36	33.8	even	10
121.11.b.c.120.4		36	1.1	even	1	trivial
121.11.b.c.120.33		36	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	121.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-51.4200i q^{2} -204.299 q^{3} -1620.02 q^{4} +840.263 q^{5} +10505.1i q^{6} -11012.5i q^{7} +30647.2i q^{8} -17310.9 q^{9} +O(q^{10})\)	\(q-51.4200i q^{2} -204.299 q^{3} -1620.02 q^{4} +840.263 q^{5} +10505.1i q^{6} -11012.5i q^{7} +30647.2i q^{8} -17310.9 q^{9} -43206.3i q^{10} +330968. q^{12} -334044. i q^{13} -566262. q^{14} -171665. q^{15} -83017.4 q^{16} -1.67073e6i q^{17} +890127. i q^{18} -2.87200e6i q^{19} -1.36124e6 q^{20} +2.24984e6i q^{21} -6.17837e6 q^{23} -6.26120e6i q^{24} -9.05958e6 q^{25} -1.71765e7 q^{26} +1.56003e7 q^{27} +1.78404e7i q^{28} -1.50387e7i q^{29} +8.82701e6i q^{30} -1.32404e7 q^{31} +3.56515e7i q^{32} -8.59090e7 q^{34} -9.25338e6i q^{35} +2.80440e7 q^{36} -1.08560e8 q^{37} -1.47679e8 q^{38} +6.82448e7i q^{39} +2.57517e7i q^{40} +9.74034e7i q^{41} +1.15687e8 q^{42} -1.88418e8i q^{43} -1.45457e7 q^{45} +3.17692e8i q^{46} -7.20878e7 q^{47} +1.69604e7 q^{48} +1.61201e8 q^{49} +4.65844e8i q^{50} +3.41329e8i q^{51} +5.41156e8i q^{52} +7.81424e8 q^{53} -8.02165e8i q^{54} +3.37502e8 q^{56} +5.86748e8i q^{57} -7.73292e8 q^{58} +8.13913e7 q^{59} +2.78100e8 q^{60} +4.54614e8i q^{61} +6.80819e8i q^{62} +1.90636e8i q^{63} +1.74819e9 q^{64} -2.80684e8i q^{65} -1.82676e9 q^{67} +2.70661e9i q^{68} +1.26223e9 q^{69} -4.75809e8 q^{70} +3.52717e8 q^{71} -5.30531e8i q^{72} -3.14963e9i q^{73} +5.58215e9i q^{74} +1.85086e9 q^{75} +4.65270e9i q^{76} +3.50915e9 q^{78} -2.35088e9i q^{79} -6.97564e7 q^{80} -2.16493e9 q^{81} +5.00848e9 q^{82} -1.70477e9i q^{83} -3.64478e9i q^{84} -1.40385e9i q^{85} -9.68847e9 q^{86} +3.07240e9i q^{87} -4.54171e9 q^{89} +7.47941e8i q^{90} -3.67865e9 q^{91} +1.00091e10 q^{92} +2.70499e9 q^{93} +3.70676e9i q^{94} -2.41324e9i q^{95} -7.28357e9i q^{96} -5.00860e9 q^{97} -8.28894e9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 82 q^{3} - 17636 q^{4} + 8836 q^{5} + 444618 q^{9}+O(q^{10}) \) 36 * q + 82 * q^3 - 17636 * q^4 + 8836 * q^5 + 444618 * q^9	\( 36 q + 82 q^{3} - 17636 q^{4} + 8836 q^{5} + 444618 q^{9} - 690462 q^{12} + 2470700 q^{14} - 238640 q^{15} + 5948436 q^{16} - 27229336 q^{20} + 2991652 q^{23} + 64315904 q^{25} - 89638980 q^{26} - 12404744 q^{27} - 144437904 q^{31} + 8404770 q^{34} + 273404882 q^{36} + 87128788 q^{37} + 412794790 q^{38} - 414956240 q^{42} - 1073801424 q^{45} - 954884432 q^{47} + 1236109242 q^{48} - 1072154336 q^{49} + 2521486392 q^{53} + 464386660 q^{56} + 4129717580 q^{58} + 4035534274 q^{59} + 4965057480 q^{60} - 3387556676 q^{64} - 6673767122 q^{67} + 12987260292 q^{69} + 2229687840 q^{70} + 14278430392 q^{71} - 27874531830 q^{75} - 35448700760 q^{78} + 59564874016 q^{80} - 3276118216 q^{81} + 45104764870 q^{82} - 21079852850 q^{86} - 19181286322 q^{89} + 85635114120 q^{91} + 40774045308 q^{92} + 86401354444 q^{93} - 26168299402 q^{97}+O(q^{100}) \) 36 * q + 82 * q^3 - 17636 * q^4 + 8836 * q^5 + 444618 * q^9 - 690462 * q^12 + 2470700 * q^14 - 238640 * q^15 + 5948436 * q^16 - 27229336 * q^20 + 2991652 * q^23 + 64315904 * q^25 - 89638980 * q^26 - 12404744 * q^27 - 144437904 * q^31 + 8404770 * q^34 + 273404882 * q^36 + 87128788 * q^37 + 412794790 * q^38 - 414956240 * q^42 - 1073801424 * q^45 - 954884432 * q^47 + 1236109242 * q^48 - 1072154336 * q^49 + 2521486392 * q^53 + 464386660 * q^56 + 4129717580 * q^58 + 4035534274 * q^59 + 4965057480 * q^60 - 3387556676 * q^64 - 6673767122 * q^67 + 12987260292 * q^69 + 2229687840 * q^70 + 14278430392 * q^71 - 27874531830 * q^75 - 35448700760 * q^78 + 59564874016 * q^80 - 3276118216 * q^81 + 45104764870 * q^82 - 21079852850 * q^86 - 19181286322 * q^89 + 85635114120 * q^91 + 40774045308 * q^92 + 86401354444 * q^93 - 26168299402 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more