LMFDB - Embedded newform 121.9.b.b.120.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,9,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, 9, names="a")

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

chi := DirichletCharacter("121.120");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 9 $
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:	$49.2928118174$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			120.17
Character	$\chi$	$=$	121.120
Dual form			121.9.b.b.120.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.02107i q^{2} +77.6168 q^{3} +206.705 q^{4} -703.179 q^{5} +544.953i q^{6} -1344.96i q^{7} +3248.68i q^{8} -536.638 q^{9} +O(q^{10})$	\(q+7.02107i q^{2} +77.6168 q^{3} +206.705 q^{4} -703.179 q^{5} +544.953i q^{6} -1344.96i q^{7} +3248.68i q^{8} -536.638 q^{9} -4937.07i q^{10} +16043.7 q^{12} +19362.2i q^{13} +9443.03 q^{14} -54578.5 q^{15} +30107.1 q^{16} -68446.7i q^{17} -3767.78i q^{18} +199054. i q^{19} -145350. q^{20} -104391. i q^{21} -350509. q^{23} +252152. i q^{24} +103836. q^{25} -135944. q^{26} -550896. q^{27} -278008. i q^{28} +382400. i q^{29} -383200. i q^{30} -1.01139e6 q^{31} +1.04305e6i q^{32} +480569. q^{34} +945744. i q^{35} -110926. q^{36} +384405. q^{37} -1.39758e6 q^{38} +1.50283e6i q^{39} -2.28441e6i q^{40} +3.18937e6i q^{41} +732937. q^{42} -823502. i q^{43} +377353. q^{45} -2.46095e6i q^{46} -507245. q^{47} +2.33682e6 q^{48} +3.95590e6 q^{49} +729040. i q^{50} -5.31261e6i q^{51} +4.00226e6i q^{52} +7.24871e6 q^{53} -3.86788e6i q^{54} +4.36933e6 q^{56} +1.54500e7i q^{57} -2.68486e6 q^{58} -1.94016e7 q^{59} -1.12816e7 q^{60} +2.29541e7i q^{61} -7.10108e6i q^{62} +721754. i q^{63} +384118. q^{64} -1.36151e7i q^{65} -3.55334e7 q^{67} -1.41482e7i q^{68} -2.72054e7 q^{69} -6.64014e6 q^{70} -3.06113e7 q^{71} -1.74337e6i q^{72} -4.83861e7i q^{73} +2.69893e6i q^{74} +8.05941e6 q^{75} +4.11455e7i q^{76} -1.05515e7 q^{78} +4.42610e7i q^{79} -2.11707e7 q^{80} -3.92379e7 q^{81} -2.23928e7 q^{82} -3.91863e7i q^{83} -2.15781e7i q^{84} +4.81303e7i q^{85} +5.78187e6 q^{86} +2.96807e7i q^{87} -2.40233e7 q^{89} +2.64942e6i q^{90} +2.60413e7 q^{91} -7.24519e7 q^{92} -7.85012e7 q^{93} -3.56141e6i q^{94} -1.39971e8i q^{95} +8.09579e7i q^{96} +1.22884e8 q^{97} +2.77746e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 26 q^{3} - 2884 q^{4} + 32 q^{5} + 42270 q^{9}+O(q^{10}) $ 28 * q - 26 * q^3 - 2884 * q^4 + 32 * q^5 + 42270 * q^9	$ 28 q - 26 q^{3} - 2884 q^{4} + 32 q^{5} + 42270 q^{9} + 63954 q^{12} - 148212 q^{14} + 387904 q^{15} - 73580 q^{16} + 1086392 q^{20} + 704764 q^{23} - 466788 q^{25} + 176572 q^{26} - 4112 q^{27} + 189364 q^{31} + 897538 q^{34} - 10359118 q^{36} - 5362896 q^{37} - 9823530 q^{38} + 1736320 q^{42} + 17701416 q^{45} - 34069636 q^{47} - 41699046 q^{48} - 27977884 q^{49} + 31846244 q^{53} + 96646244 q^{56} - 150994100 q^{58} + 2920262 q^{59} - 226082376 q^{60} + 127464764 q^{64} + 105502894 q^{67} - 321764892 q^{69} - 66153280 q^{70} - 240107164 q^{71} + 99947994 q^{75} + 387475480 q^{78} - 662332688 q^{80} - 203047984 q^{81} - 303592570 q^{82} + 71553822 q^{86} + 317966134 q^{89} - 519475368 q^{91} - 177687636 q^{92} - 725795252 q^{93} + 88971434 q^{97}+O(q^{100}) $ 28 * q - 26 * q^3 - 2884 * q^4 + 32 * q^5 + 42270 * q^9 + 63954 * q^12 - 148212 * q^14 + 387904 * q^15 - 73580 * q^16 + 1086392 * q^20 + 704764 * q^23 - 466788 * q^25 + 176572 * q^26 - 4112 * q^27 + 189364 * q^31 + 897538 * q^34 - 10359118 * q^36 - 5362896 * q^37 - 9823530 * q^38 + 1736320 * q^42 + 17701416 * q^45 - 34069636 * q^47 - 41699046 * q^48 - 27977884 * q^49 + 31846244 * q^53 + 96646244 * q^56 - 150994100 * q^58 + 2920262 * q^59 - 226082376 * q^60 + 127464764 * q^64 + 105502894 * q^67 - 321764892 * q^69 - 66153280 * q^70 - 240107164 * q^71 + 99947994 * q^75 + 387475480 * q^78 - 662332688 * q^80 - 203047984 * q^81 - 303592570 * q^82 + 71553822 * q^86 + 317966134 * q^89 - 519475368 * q^91 - 177687636 * q^92 - 725795252 * q^93 + 88971434 * 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 $

$2$	7.02107i	0.438817i	0.975633	+	0.219409i	$0.0704127\pi$
$2$	7.02107i	0.438817i	−0.975633	+	0.219409i	$0.929587\pi$
$3$	77.6168	0.958232	0.479116	−	0.877752i	$-0.340957\pi$
$3$	77.6168	0.958232	0.479116	+	0.877752i	$0.340957\pi$
$4$	206.705	0.807440
$5$	−703.179	−1.12509	−0.562543	−	0.826768i	$-0.690177\pi$
$5$	−703.179	−1.12509	−0.562543	+	0.826768i	$0.690177\pi$
$6$	544.953i	0.420488i
$7$	− 1344.96i	− 0.560165i	−0.959976	−	0.280082i	$-0.909638\pi$
$7$	− 1344.96i	− 0.560165i	0.959976	−	0.280082i	$-0.0903618\pi$
$8$	3248.68i	0.793135i
$9$	−536.638	−0.0817921
$10$	− 4937.07i	− 0.493707i
$11$	0	0
$11$	0	0
$12$	16043.7	0.773714
$13$	19362.2i	0.677926i	0.940800	+	0.338963i	$0.110076\pi$
$13$	19362.2i	0.677926i	−0.940800	+	0.338963i	$0.889924\pi$
$14$	9443.03	0.245810
$15$	−54578.5	−1.07809
$16$	30107.1	0.459398
$17$	− 68446.7i	− 0.819514i	−0.912195	−	0.409757i	$-0.865613\pi$
$17$	− 68446.7i	− 0.819514i	0.912195	−	0.409757i	$-0.134387\pi$
$18$	− 3767.78i	− 0.0358918i
$19$	199054.i	1.52742i	0.645562	+	0.763708i	$0.276623\pi$
$19$	199054.i	1.52742i	−0.645562	+	0.763708i	$0.723377\pi$
$20$	−145350.	−0.908440
$21$	− 104391.i	− 0.536767i
$22$	0	0
$23$	−350509.	−1.25253	−0.626265	−	0.779610i	$-0.715417\pi$
$23$	−350509.	−1.25253	−0.626265	+	0.779610i	$0.715417\pi$
$24$	252152.i	0.760007i
$25$	103836.	0.265820
$26$	−135944.	−0.297485
$27$	−550896.	−1.03661
$28$	− 278008.i	− 0.452299i
$29$	382400.i	0.540662i	0.962767	+	0.270331i	$0.0871332\pi$
$29$	382400.i	0.540662i	−0.962767	+	0.270331i	$0.912867\pi$
$30$	− 383200.i	− 0.473086i
$31$	−1.01139e6	−1.09515	−0.547575	−	0.836756i	$-0.684449\pi$
$31$	−1.01139e6	−1.09515	−0.547575	+	0.836756i	$0.684449\pi$
$32$	1.04305e6i	0.994727i
$33$	0	0
$34$	480569.	0.359617
$35$	945744.i	0.630234i
$36$	−110926.	−0.0660422
$37$	384405.	0.205108	0.102554	−	0.994727i	$-0.467299\pi$
$37$	384405.	0.205108	0.102554	+	0.994727i	$0.467299\pi$
$38$	−1.39758e6	−0.670256
$39$	1.50283e6i	0.649610i
$40$	− 2.28441e6i	− 0.892346i
$41$	3.18937e6i	1.12868i	0.825543	+	0.564339i	$0.190869\pi$
$41$	3.18937e6i	1.12868i	−0.825543	+	0.564339i	$0.809131\pi$
$42$	732937.	0.235543
$43$	− 823502.i	− 0.240875i	−0.992721	−	0.120437i	$-0.961570\pi$
$43$	− 823502.i	− 0.240875i	0.992721	−	0.120437i	$-0.0384297\pi$
$44$	0	0
$45$	377353.	0.0920233
$46$	− 2.46095e6i	− 0.549632i
$47$	−507245.	−0.103951	−0.0519753	−	0.998648i	$-0.516552\pi$
$47$	−507245.	−0.103951	−0.0519753	+	0.998648i	$0.516552\pi$
$48$	2.33682e6	0.440210
$49$	3.95590e6	0.686216
$50$	729040.i	0.116646i
$51$	− 5.31261e6i	− 0.785285i
$52$	4.00226e6i	0.547384i
$53$	7.24871e6	0.918666	0.459333	−	0.888264i	$-0.348089\pi$
$53$	7.24871e6	0.918666	0.459333	+	0.888264i	$0.348089\pi$
$54$	− 3.86788e6i	− 0.454881i
$55$	0	0
$56$	4.36933e6	0.444286
$57$	1.54500e7i	1.46362i
$58$	−2.68486e6	−0.237252
$59$	−1.94016e7	−1.60114	−0.800569	−	0.599240i	$-0.795469\pi$
$59$	−1.94016e7	−1.60114	−0.800569	+	0.599240i	$0.795469\pi$
$60$	−1.12816e7	−0.870496
$61$	2.29541e7i	1.65783i	0.559373	+	0.828916i	$0.311042\pi$
$61$	2.29541e7i	1.65783i	−0.559373	+	0.828916i	$0.688958\pi$
$62$	− 7.10108e6i	− 0.480571i
$63$	721754.i	0.0458171i
$64$	384118.	0.0228952
$65$	− 1.36151e7i	− 0.762725i
$66$	0	0
$67$	−3.55334e7	−1.76335	−0.881673	−	0.471861i	$-0.843583\pi$
$67$	−3.55334e7	−1.76335	−0.881673	+	0.471861i	$0.843583\pi$
$68$	− 1.41482e7i	− 0.661708i
$69$	−2.72054e7	−1.20021
$70$	−6.64014e6	−0.276557
$71$	−3.06113e7	−1.20462	−0.602309	−	0.798263i	$-0.705752\pi$
$71$	−3.06113e7	−1.20462	−0.602309	+	0.798263i	$0.705752\pi$
$72$	− 1.74337e6i	− 0.0648722i
$73$	− 4.83861e7i	− 1.70384i	−0.523672	−	0.851920i	$-0.675438\pi$
$73$	− 4.83861e7i	− 1.70384i	0.523672	−	0.851920i	$-0.324562\pi$
$74$	2.69893e6i	0.0900047i
$75$	8.05941e6	0.254717
$76$	4.11455e7i	1.23330i
$77$	0	0
$78$	−1.05515e7	−0.285060
$79$	4.42610e7i	1.13635i	0.822907	+	0.568177i	$0.192351\pi$
$79$	4.42610e7i	1.13635i	−0.822907	+	0.568177i	$0.807649\pi$
$80$	−2.11707e7	−0.516863
$81$	−3.92379e7	−0.911518
$82$	−2.23928e7	−0.495283
$83$	− 3.91863e7i	− 0.825699i	−0.910799	−	0.412849i	$-0.864534\pi$
$83$	− 3.91863e7i	− 0.825699i	0.910799	−	0.412849i	$-0.135466\pi$
$84$	− 2.15781e7i	− 0.433407i
$85$	4.81303e7i	0.922025i
$86$	5.78187e6	0.105700
$87$	2.96807e7i	0.518080i
$88$	0	0
$89$	−2.40233e7	−0.382888	−0.191444	−	0.981503i	$-0.561317\pi$
$89$	−2.40233e7	−0.382888	−0.191444	+	0.981503i	$0.561317\pi$
$90$	2.64942e6i	0.0403814i
$91$	2.60413e7	0.379750
$92$	−7.24519e7	−1.01134
$93$	−7.85012e7	−1.04941
$94$	− 3.56141e6i	− 0.0456153i
$95$	− 1.39971e8i	− 1.71848i
$96$	8.09579e7i	0.953179i
$97$	1.22884e8	1.38806	0.694028	−	0.719948i	$-0.255834\pi$
$97$	1.22884e8	1.38806	0.694028	+	0.719948i	$0.255834\pi$
$98$	2.77746e7i	0.301123i
$99$	0	0
$100$	2.14634e7	0.214634
$101$	1.81445e6i	0.0174365i	0.999962	+	0.00871825i	$0.00277514\pi$
$101$	1.81445e6i	0.0174365i	−0.999962	+	0.00871825i	$0.997225\pi$
$102$	3.73002e7	0.344596
$103$	6.36632e7	0.565640	0.282820	−	0.959173i	$-0.408730\pi$
$103$	6.36632e7	0.565640	0.282820	+	0.959173i	$0.408730\pi$
$104$	−6.29018e7	−0.537687
$105$	7.34056e7i	0.603910i
$106$	5.08937e7i	0.403126i
$107$	− 2.33770e7i	− 0.178342i	−0.996016	−	0.0891710i	$-0.971578\pi$
$107$	− 2.33770e7i	− 0.178342i	0.996016	−	0.0891710i	$-0.0284217\pi$
$108$	−1.13873e8	−0.836998
$109$	− 1.51242e8i	− 1.07144i	−0.844396	−	0.535719i	$-0.820041\pi$
$109$	− 1.51242e8i	− 1.07144i	0.844396	−	0.535719i	$-0.179959\pi$
$110$	0	0
$111$	2.98362e7	0.196541
$112$	− 4.04927e7i	− 0.257339i
$113$	−1.30764e8	−0.802003	−0.401001	−	0.916077i	$-0.631338\pi$
$113$	−1.30764e8	−0.802003	−0.401001	+	0.916077i	$0.631338\pi$
$114$	−1.08475e8	−0.642261
$115$	2.46471e8	1.40921
$116$	7.90439e7i	0.436552i
$117$	− 1.03905e7i	− 0.0554490i
$118$	− 1.36220e8i	− 0.702607i
$119$	−9.20577e7	−0.459063
$120$	− 1.77308e8i	− 0.855074i
$121$	0	0
$122$	−1.61162e8	−0.727485
$123$	2.47549e8i	1.08153i
$124$	−2.09060e8	−0.884268
$125$	2.01664e8	0.826016
$126$	−5.06749e6	−0.0201053
$127$	3.35006e8i	1.28777i	0.765123	+	0.643884i	$0.222678\pi$
$127$	3.35006e8i	1.28777i	−0.765123	+	0.643884i	$0.777322\pi$
$128$	2.69717e8i	1.00477i
$129$	− 6.39176e7i	− 0.230814i
$130$	9.55928e7	0.334697
$131$	3.32594e8i	1.12935i	0.825312	+	0.564677i	$0.190999\pi$
$131$	3.32594e8i	1.12935i	−0.825312	+	0.564677i	$0.809001\pi$
$132$	0	0
$133$	2.67719e8	0.855604
$134$	− 2.49483e8i	− 0.773786i
$135$	3.87378e8	1.16627
$136$	2.22361e8	0.649986
$137$	7.71773e7	0.219082	0.109541	−	0.993982i	$-0.465062\pi$
$137$	7.71773e7	0.219082	0.109541	+	0.993982i	$0.465062\pi$
$138$	− 1.91011e8i	− 0.526675i
$139$	2.97102e8i	0.795878i	0.917412	+	0.397939i	$0.130274\pi$
$139$	2.97102e8i	0.795878i	−0.917412	+	0.397939i	$0.869726\pi$
$140$	1.95490e8i	0.508876i
$141$	−3.93708e7	−0.0996087
$142$	− 2.14924e8i	− 0.528607i
$143$	0	0
$144$	−1.61566e7	−0.0375752
$145$	− 2.68896e8i	− 0.608292i
$146$	3.39722e8	0.747674
$147$	3.07044e8	0.657554
$148$	7.94582e7	0.165612
$149$	− 8.04396e8i	− 1.63202i	−0.578039	−	0.816009i	$-0.696182\pi$
$149$	− 8.04396e8i	− 1.63202i	0.578039	−	0.816009i	$-0.303818\pi$
$150$	5.65857e7i	0.111774i
$151$	− 2.47501e8i	− 0.476069i	−0.971257	−	0.238034i	$-0.923497\pi$
$151$	− 2.47501e8i	− 0.476069i	0.971257	−	0.238034i	$-0.0765031\pi$
$152$	−6.46664e8	−1.21145
$153$	3.67311e7i	0.0670298i
$154$	0	0
$155$	7.11192e8	1.23214
$156$	3.10643e8i	0.524521i
$157$	3.50938e8	0.577606	0.288803	−	0.957389i	$-0.406743\pi$
$157$	3.50938e8	0.577606	0.288803	+	0.957389i	$0.406743\pi$
$158$	−3.10760e8	−0.498651
$159$	5.62622e8	0.880294
$160$	− 7.33449e8i	− 1.11915i
$161$	4.71420e8i	0.701623i
$162$	− 2.75492e8i	− 0.399990i
$163$	4.07923e8	0.577867	0.288934	−	0.957349i	$-0.406699\pi$
$163$	4.07923e8	0.577867	0.288934	+	0.957349i	$0.406699\pi$
$164$	6.59258e8i	0.911339i
$165$	0	0
$166$	2.75130e8	0.362331
$167$	− 1.07018e9i	− 1.37591i	−0.725754	−	0.687955i	$-0.758509\pi$
$167$	− 1.07018e9i	− 1.37591i	0.725754	−	0.687955i	$-0.241491\pi$
$168$	3.39133e8	0.425729
$169$	4.40834e8	0.540416
$170$	−3.37926e8	−0.404600
$171$	− 1.06820e8i	− 0.124931i
$172$	− 1.70222e8i	− 0.194492i
$173$	− 4.59404e7i	− 0.0512873i	−0.999671	−	0.0256437i	$-0.991836\pi$
$173$	− 4.59404e7i	− 0.0512873i	0.999671	−	0.0256437i	$-0.00816352\pi$
$174$	−2.08390e8	−0.227342
$175$	− 1.39655e8i	− 0.148903i
$176$	0	0
$177$	−1.50589e9	−1.53426
$178$	− 1.68669e8i	− 0.168018i
$179$	−1.02935e9	−1.00265	−0.501326	−	0.865258i	$-0.667154\pi$
$179$	−1.02935e9	−1.00265	−0.501326	+	0.865258i	$0.667154\pi$
$180$	7.80005e7	0.0743032
$181$	8.18745e8	0.762842	0.381421	−	0.924402i	$-0.375435\pi$
$181$	8.18745e8	0.762842	0.381421	+	0.924402i	$0.375435\pi$
$182$	1.82838e8i	0.166641i
$183$	1.78162e9i	1.58859i
$184$	− 1.13869e9i	− 0.993426i
$185$	−2.70305e8	−0.230764
$186$	− 5.51162e8i	− 0.460498i
$187$	0	0
$188$	−1.04850e8	−0.0839338
$189$	7.40930e8i	0.580671i
$190$	9.82746e8	0.754096
$191$	6.67535e8	0.501581	0.250790	−	0.968041i	$-0.419310\pi$
$191$	6.67535e8	0.501581	0.250790	+	0.968041i	$0.419310\pi$
$192$	2.98140e7	0.0219389
$193$	2.20519e9i	1.58934i	0.607040	+	0.794671i	$0.292357\pi$
$193$	2.20519e9i	1.58934i	−0.607040	+	0.794671i	$0.707643\pi$
$194$	8.62775e8i	0.609103i
$195$	− 1.05676e9i	− 0.730868i
$196$	8.17702e8	0.554078
$197$	− 2.23782e8i	− 0.148580i	−0.997237	−	0.0742899i	$-0.976331\pi$
$197$	− 2.23782e8i	− 0.148580i	0.997237	−	0.0742899i	$-0.0236690\pi$
$198$	0	0
$199$	1.49591e9	0.953880	0.476940	−	0.878936i	$-0.341746\pi$
$199$	1.49591e9	0.953880	0.476940	+	0.878936i	$0.341746\pi$
$200$	3.37330e8i	0.210831i
$201$	−2.75799e9	−1.68969
$202$	−1.27394e7	−0.00765143
$203$	5.14311e8	0.302860
$204$	− 1.09814e9i	− 0.634070i
$205$	− 2.24270e9i	− 1.26986i
$206$	4.46984e8i	0.248212i
$207$	1.88097e8	0.102447
$208$	5.82942e8i	0.311438i
$209$	0	0
$210$	−5.15386e8	−0.265006
$211$	− 1.54592e9i	− 0.779933i	−0.920829	−	0.389966i	$-0.872487\pi$
$211$	− 1.54592e9i	− 0.779933i	0.920829	−	0.389966i	$-0.127513\pi$
$212$	1.49834e9	0.741767
$213$	−2.37595e9	−1.15430
$214$	1.64132e8	0.0782595
$215$	5.79070e8i	0.271005i
$216$	− 1.78968e9i	− 0.822170i
$217$	1.36028e9i	0.613465i
$218$	1.06188e9	0.470165
$219$	− 3.75557e9i	− 1.63267i
$220$	0	0
$221$	1.32528e9	0.555570
$222$	2.09482e8i	0.0862454i
$223$	1.96463e9	0.794440	0.397220	−	0.917723i	$-0.369975\pi$
$223$	1.96463e9	0.794440	0.397220	+	0.917723i	$0.369975\pi$
$224$	1.40285e9	0.557211
$225$	−5.57224e7	−0.0217420
$226$	− 9.18106e8i	− 0.351932i
$227$	− 6.58101e8i	− 0.247850i	−0.992292	−	0.123925i	$-0.960452\pi$
$227$	− 6.58101e8i	− 0.247850i	0.992292	−	0.123925i	$-0.0395482\pi$
$228$	3.19358e9i	1.18178i
$229$	1.18612e8	0.0431306	0.0215653	−	0.999767i	$-0.493135\pi$
$229$	1.18612e8	0.0431306	0.0215653	+	0.999767i	$0.493135\pi$
$230$	1.73049e9i	0.618383i
$231$	0	0
$232$	−1.24230e9	−0.428818
$233$	− 1.88981e7i	− 0.00641203i	−0.999995	−	0.00320601i	$-0.998979\pi$
$233$	− 1.88981e7i	− 0.00641203i	0.999995	−	0.00320601i	$-0.00102051\pi$
$234$	7.29526e7	0.0243320
$235$	3.56684e8	0.116953
$236$	−4.01039e9	−1.29282
$237$	3.43540e9i	1.08889i
$238$	− 6.46344e8i	− 0.201445i
$239$	1.34719e9i	0.412894i	0.978458	+	0.206447i	$0.0661900\pi$
$239$	1.34719e9i	0.412894i	−0.978458	+	0.206447i	$0.933810\pi$
$240$	−1.64320e9	−0.495274
$241$	5.25935e9i	1.55906i	0.626363	+	0.779531i	$0.284543\pi$
$241$	5.25935e9i	1.55906i	−0.626363	+	0.779531i	$0.715457\pi$
$242$	0	0
$243$	5.68911e8	0.163162
$244$	4.74471e9i	1.33860i
$245$	−2.78170e9	−0.772052
$246$	−1.73806e9	−0.474596
$247$	−3.85414e9	−1.03548
$248$	− 3.28570e9i	− 0.868603i
$249$	− 3.04151e9i	− 0.791211i
$250$	1.41590e9i	0.362470i
$251$	5.98408e7	0.0150766	0.00753828	−	0.999972i	$-0.497600\pi$
$251$	5.98408e7	0.0150766	0.00753828	+	0.999972i	$0.497600\pi$
$252$	1.49190e8i	0.0369945i
$253$	0	0
$254$	−2.35210e9	−0.565095
$255$	3.73572e9i	0.883513i
$256$	−1.79537e9	−0.418017
$257$	−1.20842e9	−0.277004	−0.138502	−	0.990362i	$-0.544229\pi$
$257$	−1.20842e9	−0.277004	−0.138502	+	0.990362i	$0.544229\pi$
$258$	4.48770e8	0.101285
$259$	− 5.17007e8i	− 0.114894i
$260$	− 2.81431e9i	− 0.615855i
$261$	− 2.05211e8i	− 0.0442219i
$262$	−2.33517e9	−0.495580
$263$	− 4.22692e8i	− 0.0883490i	−0.999024	−	0.0441745i	$-0.985934\pi$
$263$	− 4.22692e8i	− 0.0883490i	0.999024	−	0.0441745i	$-0.0140658\pi$
$264$	0	0
$265$	−5.09714e9	−1.03358
$266$	1.87968e9i	0.375454i
$267$	−1.86461e9	−0.366896
$268$	−7.34492e9	−1.42380
$269$	−4.44912e9	−0.849700	−0.424850	−	0.905264i	$-0.639673\pi$
$269$	−4.44912e9	−0.849700	−0.424850	+	0.905264i	$0.639673\pi$
$270$	2.71981e9i	0.511781i
$271$	1.41774e9i	0.262857i	0.991326	+	0.131428i	$0.0419563\pi$
$271$	1.41774e9i	0.262857i	−0.991326	+	0.131428i	$0.958044\pi$
$272$	− 2.06073e9i	− 0.376484i
$273$	2.02124e9	0.363889
$274$	5.41868e8i	0.0961371i
$275$	0	0
$276$	−5.62348e9	−0.969101
$277$	− 3.39043e9i	− 0.575885i	−0.957648	−	0.287943i	$-0.907029\pi$
$277$	− 3.39043e9i	− 0.575885i	0.957648	−	0.287943i	$-0.0929713\pi$
$278$	−2.08597e9	−0.349245
$279$	5.42753e8	0.0895747
$280$	−3.07242e9	−0.499861
$281$	9.12882e9i	1.46416i	0.681217	+	0.732081i	$0.261451\pi$
$281$	9.12882e9i	1.46416i	−0.681217	+	0.732081i	$0.738549\pi$
$282$	− 2.76425e8i	− 0.0437100i
$283$	6.49110e9i	1.01198i	0.862539	+	0.505991i	$0.168873\pi$
$283$	6.49110e9i	1.01198i	−0.862539	+	0.505991i	$0.831127\pi$
$284$	−6.32750e9	−0.972656
$285$	− 1.08641e10i	− 1.64670i
$286$	0	0
$287$	4.28956e9	0.632245
$288$	− 5.59739e8i	− 0.0813609i
$289$	2.29081e9	0.328396
$290$	1.88794e9	0.266929
$291$	9.53783e9	1.33008
$292$	− 1.00016e10i	− 1.37575i
$293$	− 9.28248e9i	− 1.25949i	−0.776803	−	0.629743i	$-0.783160\pi$
$293$	− 9.28248e9i	− 1.25949i	0.776803	−	0.629743i	$-0.216840\pi$
$294$	2.15578e9i	0.288546i
$295$	1.36428e10	1.80142
$296$	1.24881e9i	0.162678i
$297$	0	0
$298$	5.64773e9	0.716157
$299$	− 6.78665e9i	− 0.849123i
$300$	1.66592e9	0.205669
$301$	−1.10757e9	−0.134929
$302$	1.73772e9	0.208907
$303$	1.40832e8i	0.0167082i
$304$	5.99296e9i	0.701693i
$305$	− 1.61408e10i	− 1.86520i
$306$	−2.57892e8	−0.0294138
$307$	3.17364e9i	0.357276i	0.983915	+	0.178638i	$0.0571691\pi$
$307$	3.17364e9i	0.357276i	−0.983915	+	0.178638i	$0.942831\pi$
$308$	0	0
$309$	4.94133e9	0.542014
$310$	4.99333e9i	0.540684i
$311$	1.86968e9	0.199859	0.0999297	−	0.994994i	$-0.468138\pi$
$311$	1.86968e9	0.199859	0.0999297	+	0.994994i	$0.468138\pi$
$312$	−4.88223e9	−0.515229
$313$	1.75095e9	0.182430	0.0912152	−	0.995831i	$-0.470925\pi$
$313$	1.75095e9	0.182430	0.0912152	+	0.995831i	$0.470925\pi$
$314$	2.46396e9i	0.253463i
$315$	− 5.07523e8i	− 0.0515482i
$316$	9.14896e9i	0.917537i
$317$	1.68758e10	1.67119	0.835596	−	0.549344i	$-0.185122\pi$
$317$	1.68758e10	1.67119	0.835596	+	0.549344i	$0.185122\pi$
$318$	3.95021e9i	0.386288i
$319$	0	0
$320$	−2.70104e8	−0.0257591
$321$	− 1.81445e9i	− 0.170893i
$322$	−3.30987e9	−0.307884
$323$	1.36246e10	1.25174
$324$	−8.11064e9	−0.735996
$325$	2.01050e9i	0.180206i
$326$	2.86406e9i	0.253578i
$327$	− 1.17389e10i	− 1.02669i
$328$	−1.03613e10	−0.895194
$329$	6.82222e8i	0.0582294i
$330$	0	0
$331$	3.80681e9	0.317138	0.158569	−	0.987348i	$-0.449312\pi$
$331$	3.80681e9	0.317138	0.158569	+	0.987348i	$0.449312\pi$
$332$	− 8.09998e9i	− 0.666702i
$333$	−2.06286e8	−0.0167762
$334$	7.51379e9	0.603773
$335$	2.49863e10	1.98392
$336$	− 3.14292e9i	− 0.246590i
$337$	1.61926e10i	1.25544i	0.778439	+	0.627720i	$0.216012\pi$
$337$	1.61926e10i	1.25544i	−0.778439	+	0.627720i	$0.783988\pi$
$338$	3.09513e9i	0.237144i
$339$	−1.01495e10	−0.768504
$340$	9.94874e9i	0.744479i
$341$	0	0
$342$	7.49992e8	0.0548217
$343$	− 1.30739e10i	− 0.944558i
$344$	2.67530e9	0.191046
$345$	1.91303e10	1.35035
$346$	3.22551e8	0.0225057
$347$	− 5.67555e9i	− 0.391462i	−0.980658	−	0.195731i	$-0.937292\pi$
$347$	− 5.67555e9i	− 0.391462i	0.980658	−	0.195731i	$-0.0627080\pi$
$348$	6.13513e9i	0.418318i
$349$	− 1.48337e10i	− 0.999880i	−0.866060	−	0.499940i	$-0.833355\pi$
$349$	− 1.48337e10i	− 0.999880i	0.866060	−	0.499940i	$-0.166645\pi$
$350$	9.80526e8	0.0653412
$351$	− 1.06666e10i	− 0.702743i
$352$	0	0
$353$	−9.89071e9	−0.636984	−0.318492	−	0.947926i	$-0.603176\pi$
$353$	−9.89071e9	−0.636984	−0.318492	+	0.947926i	$0.603176\pi$
$354$	− 1.05729e10i	− 0.673260i
$355$	2.15253e10	1.35530
$356$	−4.96572e9	−0.309159
$357$	−7.14522e9	−0.439889
$358$	− 7.22714e9i	− 0.439981i
$359$	1.29873e10i	0.781881i	0.920416	+	0.390940i	$0.127850\pi$
$359$	1.29873e10i	0.781881i	−0.920416	+	0.390940i	$0.872150\pi$
$360$	1.22590e9i	0.0729869i
$361$	−2.26391e10	−1.33300
$362$	5.74847e9i	0.334748i
$363$	0	0
$364$	5.38286e9	0.306625
$365$	3.40241e10i	1.91697i
$366$	−1.25089e10	−0.697099
$367$	−1.78932e10	−0.986336	−0.493168	−	0.869934i	$-0.664161\pi$
$367$	−1.78932e10	−0.986336	−0.493168	+	0.869934i	$0.664161\pi$
$368$	−1.05528e10	−0.575411
$369$	− 1.71154e9i	− 0.0923170i
$370$	− 1.89783e9i	− 0.101263i
$371$	− 9.74919e9i	− 0.514604i
$372$	−1.62266e10	−0.847334
$373$	− 1.91399e10i	− 0.988789i	−0.869238	−	0.494394i	$-0.835390\pi$
$373$	− 1.91399e10i	− 0.988789i	0.869238	−	0.494394i	$-0.164610\pi$
$374$	0	0
$375$	1.56525e10	0.791515
$376$	− 1.64788e9i	− 0.0824468i
$377$	−7.40413e9	−0.366529
$378$	−5.20212e9	−0.254808
$379$	2.33972e10	1.13398	0.566992	−	0.823723i	$-0.308107\pi$
$379$	2.33972e10	1.13398	0.566992	+	0.823723i	$0.308107\pi$
$380$	− 2.89326e10i	− 1.38757i
$381$	2.60021e10i	1.23398i
$382$	4.68681e9i	0.220102i
$383$	−4.28407e9	−0.199096	−0.0995478	−	0.995033i	$-0.531740\pi$
$383$	−4.28407e9	−0.199096	−0.0995478	+	0.995033i	$0.531740\pi$
$384$	2.09346e10i	0.962806i
$385$	0	0
$386$	−1.54828e10	−0.697431
$387$	4.41923e8i	0.0197017i
$388$	2.54006e10	1.12077
$389$	2.43100e10	1.06166	0.530831	−	0.847478i	$-0.321880\pi$
$389$	2.43100e10	1.06166	0.530831	+	0.847478i	$0.321880\pi$
$390$	7.41960e9	0.320717
$391$	2.39912e10i	1.02647i
$392$	1.28515e10i	0.544262i
$393$	2.58149e10i	1.08218i
$394$	1.57119e9	0.0651993
$395$	− 3.11234e10i	− 1.27850i
$396$	0	0
$397$	9.11498e9	0.366939	0.183469	−	0.983025i	$-0.441267\pi$
$397$	9.11498e9	0.366939	0.183469	+	0.983025i	$0.441267\pi$
$398$	1.05029e10i	0.418579i
$399$	2.07795e10	0.819867
$400$	3.12620e9	0.122117
$401$	−7.76346e9	−0.300247	−0.150123	−	0.988667i	$-0.547967\pi$
$401$	−7.76346e9	−0.300247	−0.150123	+	0.988667i	$0.547967\pi$
$402$	− 1.93640e10i	− 0.741467i
$403$	− 1.95829e10i	− 0.742431i
$404$	3.75055e8i	0.0140789i
$405$	2.75912e10	1.02554
$406$	3.61102e9i	0.132900i
$407$	0	0
$408$	1.72590e10	0.622837
$409$	− 3.88260e10i	− 1.38749i	−0.720221	−	0.693745i	$-0.755959\pi$
$409$	− 3.88260e10i	− 1.38749i	0.720221	−	0.693745i	$-0.244041\pi$
$410$	1.57462e10	0.557236
$411$	5.99025e9	0.209932
$412$	1.31595e10	0.456720
$413$	2.60942e10i	0.896901i
$414$	1.32064e9i	0.0449556i
$415$	2.75550e10i	0.928983i
$416$	−2.01957e10	−0.674351
$417$	2.30601e10i	0.762635i
$418$	0	0
$419$	−2.41027e9	−0.0782005	−0.0391003	−	0.999235i	$-0.512449\pi$
$419$	−2.41027e9	−0.0782005	−0.0391003	+	0.999235i	$0.512449\pi$
$420$	1.51733e10i	0.487621i
$421$	−4.87583e10	−1.55210	−0.776051	−	0.630670i	$-0.782780\pi$
$421$	−4.87583e10	−1.55210	−0.776051	+	0.630670i	$0.782780\pi$
$422$	1.08540e10	0.342248
$423$	2.72207e8	0.00850234
$424$	2.35488e10i	0.728626i
$425$	− 7.10722e9i	− 0.217843i
$426$	− 1.66817e10i	− 0.506528i
$427$	3.08722e10	0.928659
$428$	− 4.83213e9i	− 0.144000i
$429$	0	0
$430$	−4.06569e9	−0.118922
$431$	− 6.82411e9i	− 0.197759i	−0.995099	−	0.0988796i	$-0.968474\pi$
$431$	− 6.82411e9i	− 0.197759i	0.995099	−	0.0988796i	$-0.0315259\pi$
$432$	−1.65859e10	−0.476216
$433$	−3.12920e10	−0.890188	−0.445094	−	0.895484i	$-0.646830\pi$
$433$	−3.12920e10	−0.890188	−0.445094	+	0.895484i	$0.646830\pi$
$434$	−9.55063e9	−0.269199
$435$	− 2.08708e10i	− 0.582885i
$436$	− 3.12625e10i	− 0.865122i
$437$	− 6.97705e10i	− 1.91314i
$438$	2.63681e10	0.716445
$439$	− 3.21529e9i	− 0.0865689i	−0.999063	−	0.0432845i	$-0.986218\pi$
$439$	− 3.21529e9i	− 0.0865689i	0.999063	−	0.0432845i	$-0.0137822\pi$
$440$	0	0
$441$	−2.12289e9	−0.0561271
$442$	9.30489e9i	0.243794i
$443$	−4.82442e10	−1.25265	−0.626326	−	0.779561i	$-0.715442\pi$
$443$	−4.82442e10	−1.25265	−0.626326	+	0.779561i	$0.715442\pi$
$444$	6.16729e9	0.158695
$445$	1.68927e10	0.430783
$446$	1.37938e10i	0.348614i
$447$	− 6.24346e10i	− 1.56385i
$448$	− 5.16621e8i	− 0.0128251i
$449$	−3.15412e10	−0.776056	−0.388028	−	0.921648i	$-0.626844\pi$
$449$	−3.15412e10	−0.776056	−0.388028	+	0.921648i	$0.626844\pi$
$450$	− 3.91231e8i	− 0.00954076i
$451$	0	0
$452$	−2.70296e10	−0.647569
$453$	− 1.92102e10i	− 0.456184i
$454$	4.62057e9	0.108761
$455$	−1.83117e10	−0.427252
$456$	−5.01920e10	−1.16085
$457$	5.03796e10i	1.15502i	0.816383	+	0.577510i	$0.195976\pi$
$457$	5.03796e10i	1.15502i	−0.816383	+	0.577510i	$0.804024\pi$
$458$	8.32782e8i	0.0189265i
$459$	3.77070e10i	0.849515i
$460$	5.09467e10	1.13785
$461$	5.01336e10i	1.11001i	0.831849	+	0.555003i	$0.187283\pi$
$461$	5.01336e10i	1.11001i	−0.831849	+	0.555003i	$0.812717\pi$
$462$	0	0
$463$	2.36331e10	0.514276	0.257138	−	0.966375i	$-0.417221\pi$
$463$	2.36331e10	0.514276	0.257138	+	0.966375i	$0.417221\pi$
$464$	1.15130e10i	0.248379i
$465$	5.52004e10	1.18068
$466$	1.32685e8	0.00281371
$467$	−8.22609e10	−1.72952	−0.864760	−	0.502185i	$-0.832530\pi$
$467$	−8.22609e10	−1.72952	−0.864760	+	0.502185i	$0.832530\pi$
$468$	− 2.14777e9i	− 0.0447717i
$469$	4.77908e10i	0.987764i
$470$	2.50431e9i	0.0513211i
$471$	2.72387e10	0.553480
$472$	− 6.30295e10i	− 1.26992i
$473$	0	0
$474$	−2.41202e10	−0.477823
$475$	2.06690e10i	0.406018i
$476$	−1.90287e10	−0.370666
$477$	−3.88994e9	−0.0751396
$478$	−9.45874e9	−0.181185
$479$	6.36700e9i	0.120946i	0.998170	+	0.0604732i	$0.0192610\pi$
$479$	6.36700e9i	0.120946i	−0.998170	+	0.0604732i	$0.980739\pi$
$480$	− 5.69279e10i	− 1.07241i
$481$	7.44294e9i	0.139048i
$482$	−3.69263e10	−0.684143
$483$	3.65901e10i	0.672318i
$484$	0	0
$485$	−8.64092e10	−1.56168
$486$	3.99437e9i	0.0715983i
$487$	−4.68524e10	−0.832944	−0.416472	−	0.909149i	$-0.636734\pi$
$487$	−4.68524e10	−0.832944	−0.416472	+	0.909149i	$0.636734\pi$
$488$	−7.45705e10	−1.31488
$489$	3.16617e10	0.553731
$490$	− 1.95305e10i	− 0.338790i
$491$	− 4.92867e10i	− 0.848016i	−0.905659	−	0.424008i	$-0.860623\pi$
$491$	− 4.92867e10i	− 0.848016i	0.905659	−	0.424008i	$-0.139377\pi$
$492$	5.11695e10i	0.873274i
$493$	2.61740e10	0.443081
$494$	− 2.70602e10i	− 0.454384i
$495$	0	0
$496$	−3.04502e10	−0.503110
$497$	4.11709e10i	0.674784i
$498$	2.13547e10	0.347197
$499$	−9.36586e10	−1.51059	−0.755293	−	0.655388i	$-0.772505\pi$
$499$	−9.36586e10	−1.51059	−0.755293	+	0.655388i	$0.772505\pi$
$500$	4.16849e10	0.666958
$501$	− 8.30637e10i	− 1.31844i
$502$	4.20147e8i	0.00661585i
$503$	1.16402e11i	1.81840i	0.416361	+	0.909199i	$0.363305\pi$
$503$	1.16402e11i	1.81840i	−0.416361	+	0.909199i	$0.636695\pi$
$504$	−2.34475e9	−0.0363391
$505$	− 1.27588e9i	− 0.0196176i
$506$	0	0
$507$	3.42161e10	0.517844
$508$	6.92473e10i	1.03980i
$509$	−5.87268e10	−0.874913	−0.437457	−	0.899240i	$-0.644121\pi$
$509$	−5.87268e10	−0.874913	−0.437457	+	0.899240i	$0.644121\pi$
$510$	−2.62287e10	−0.387701
$511$	−6.50771e10	−0.954431
$512$	5.64421e10i	0.821341i
$513$	− 1.09658e11i	− 1.58333i
$514$	− 8.48442e9i	− 0.121554i
$515$	−4.47667e10	−0.636394
$516$	− 1.32121e10i	− 0.186368i
$517$	0	0
$518$	3.62994e9	0.0504174
$519$	− 3.56574e9i	− 0.0491451i
$520$	4.42312e10	0.604944
$521$	3.75217e10	0.509251	0.254625	−	0.967040i	$-0.418048\pi$
$521$	3.75217e10	0.509251	0.254625	+	0.967040i	$0.418048\pi$
$522$	1.44080e9	0.0194053
$523$	− 7.09987e10i	− 0.948951i	−0.880269	−	0.474475i	$-0.842638\pi$
$523$	− 7.09987e10i	− 0.948951i	0.880269	−	0.474475i	$-0.157362\pi$
$524$	6.87488e10i	0.911885i
$525$	− 1.08395e10i	− 0.142684i
$526$	2.96775e9	0.0387690
$527$	6.92266e10i	0.897492i
$528$	0	0
$529$	4.45459e10	0.568833
$530$	− 3.57874e10i	− 0.453552i
$531$	1.04116e10	0.130961
$532$	5.53388e10	0.690849
$533$	−6.17534e10	−0.765160
$534$	− 1.30916e10i	− 0.161000i
$535$	1.64382e10i	0.200650i
$536$	− 1.15437e11i	− 1.39857i
$537$	−7.98948e10	−0.960774
$538$	− 3.12376e10i	− 0.372863i
$539$	0	0
$540$	8.00729e10	0.941695
$541$	1.02085e10i	0.119172i	0.998223	+	0.0595860i	$0.0189781\pi$
$541$	1.02085e10i	0.119172i	−0.998223	+	0.0595860i	$0.981022\pi$
$542$	−9.95405e9	−0.115346
$543$	6.35483e10	0.730979
$544$	7.13931e10	0.815193
$545$	1.06350e11i	1.20546i
$546$	1.41913e10i	0.159680i
$547$	1.07484e11i	1.20059i	0.799779	+	0.600295i	$0.204950\pi$
$547$	1.07484e11i	1.20059i	−0.799779	+	0.600295i	$0.795050\pi$
$548$	1.59529e10	0.176896
$549$	− 1.23180e10i	− 0.135598i
$550$	0	0
$551$	−7.61185e10	−0.825817
$552$	− 8.83817e10i	− 0.951933i
$553$	5.95291e10	0.636545
$554$	2.38045e10	0.252708
$555$	−2.09802e10	−0.221125
$556$	6.14123e10i	0.642623i
$557$	1.21741e11i	1.26478i	0.774648	+	0.632392i	$0.217927\pi$
$557$	1.21741e11i	1.26478i	−0.774648	+	0.632392i	$0.782073\pi$
$558$	3.81071e9i	0.0393069i
$559$	1.59449e10	0.163295
$560$	2.84737e10i	0.289528i
$561$	0	0
$562$	−6.40941e10	−0.642499
$563$	2.54979e9i	0.0253787i	0.999919	+	0.0126894i	$0.00403926\pi$
$563$	2.54979e9i	0.0253787i	−0.999919	+	0.0126894i	$0.995961\pi$
$564$	−8.13811e9	−0.0804280
$565$	9.19508e10	0.902322
$566$	−4.55745e10	−0.444075
$567$	5.27732e10i	0.510600i
$568$	− 9.94465e10i	− 0.955424i
$569$	− 2.01383e11i	− 1.92120i	−0.277928	−	0.960602i	$-0.589648\pi$
$569$	− 2.01383e11i	− 1.92120i	0.277928	−	0.960602i	$-0.410352\pi$
$570$	7.62776e10	0.722599
$571$	− 1.60852e10i	− 0.151315i	−0.997134	−	0.0756575i	$-0.975894\pi$
$571$	− 1.60852e10i	− 0.151315i	0.997134	−	0.0756575i	$-0.0241056\pi$
$572$	0	0
$573$	5.18119e10	0.480631
$574$	3.01173e10i	0.277440i
$575$	−3.63955e10	−0.332948
$576$	−2.06132e8	−0.00187265
$577$	9.97880e10	0.900274	0.450137	−	0.892959i	$-0.351375\pi$
$577$	9.97880e10	0.900274	0.450137	+	0.892959i	$0.351375\pi$
$578$	1.60840e10i	0.144106i
$579$	1.71160e11i	1.52296i
$580$	− 5.55820e10i	− 0.491159i
$581$	−5.27038e10	−0.462527
$582$	6.69658e10i	0.583662i
$583$	0	0
$584$	1.57191e11	1.35138
$585$	7.30640e9i	0.0623849i
$586$	6.51729e10	0.552684
$587$	1.55828e10	0.131248	0.0656241	−	0.997844i	$-0.479096\pi$
$587$	1.55828e10	0.131248	0.0656241	+	0.997844i	$0.479096\pi$
$588$	6.34674e10	0.530935
$589$	− 2.01323e11i	− 1.67275i
$590$	9.57870e10i	0.790494i
$591$	− 1.73692e10i	− 0.142374i
$592$	1.15733e10	0.0942261
$593$	− 5.77849e10i	− 0.467300i	−0.972321	−	0.233650i	$-0.924933\pi$
$593$	− 5.77849e10i	− 0.467300i	0.972321	−	0.233650i	$-0.0750670\pi$
$594$	0	0
$595$	6.47330e10	0.516486
$596$	− 1.66272e11i	− 1.31776i
$597$	1.16108e11	0.914038
$598$	4.76496e10	0.372610
$599$	1.55883e11	1.21085	0.605425	−	0.795902i	$-0.293003\pi$
$599$	1.55883e11	1.21085	0.605425	+	0.795902i	$0.293003\pi$
$600$	2.61825e10i	0.202025i
$601$	− 2.12533e10i	− 0.162903i	−0.996677	−	0.0814513i	$-0.974044\pi$
$601$	− 2.12533e10i	− 0.162903i	0.996677	−	0.0814513i	$-0.0259555\pi$
$602$	− 7.77636e9i	− 0.0592093i
$603$	1.90686e10	0.144228
$604$	− 5.11596e10i	− 0.384397i
$605$	0	0
$606$	−9.88789e8	−0.00733184
$607$	2.67103e10i	0.196754i	0.995149	+	0.0983772i	$0.0313652\pi$
$607$	2.67103e10i	0.196754i	−0.995149	+	0.0983772i	$0.968635\pi$
$608$	−2.07623e11	−1.51936
$609$	3.99192e10	0.290210
$610$	1.13326e11	0.818483
$611$	− 9.82141e9i	− 0.0704708i
$612$	7.59248e9i	0.0541225i
$613$	1.43939e11i	1.01938i	0.860358	+	0.509690i	$0.170240\pi$
$613$	1.43939e11i	1.01938i	−0.860358	+	0.509690i	$0.829760\pi$
$614$	−2.22823e10	−0.156779
$615$	− 1.74071e11i	− 1.21682i
$616$	0	0
$617$	−1.08135e11	−0.746152	−0.373076	−	0.927801i	$-0.621697\pi$
$617$	−1.08135e11	−0.746152	−0.373076	+	0.927801i	$0.621697\pi$
$618$	3.46935e10i	0.237845i
$619$	1.70618e11	1.16215	0.581074	−	0.813851i	$-0.302633\pi$
$619$	1.70618e11	1.16215	0.581074	+	0.813851i	$0.302633\pi$
$620$	1.47007e11	0.994878
$621$	1.93094e11	1.29838
$622$	1.31271e10i	0.0877017i
$623$	3.23102e10i	0.214481i
$624$	4.52460e10i	0.298430i
$625$	−1.82367e11	−1.19516
$626$	1.22936e10i	0.0800536i
$627$	0	0
$628$	7.25405e10	0.466382
$629$	− 2.63112e10i	− 0.168089i
$630$	3.56335e9	0.0226202
$631$	−1.99135e11	−1.25612	−0.628060	−	0.778165i	$-0.716151\pi$
$631$	−1.99135e11	−1.25612	−0.628060	+	0.778165i	$0.716151\pi$
$632$	−1.43790e11	−0.901282
$633$	− 1.19989e11i	− 0.747356i
$634$	1.18486e11i	0.733348i
$635$	− 2.35569e11i	− 1.44885i
$636$	1.16296e11	0.710785
$637$	7.65950e10i	0.465203i
$638$	0	0
$639$	1.64272e10	0.0985282
$640$	− 1.89659e11i	− 1.13046i
$641$	−2.83608e10	−0.167991	−0.0839957	−	0.996466i	$-0.526768\pi$
$641$	−2.83608e10	−0.167991	−0.0839957	+	0.996466i	$0.526768\pi$
$642$	1.27394e10	0.0749907
$643$	−1.99392e11	−1.16644	−0.583221	−	0.812313i	$-0.698208\pi$
$643$	−1.99392e11	−1.16644	−0.583221	+	0.812313i	$0.698208\pi$
$644$	9.74446e10i	0.566519i
$645$	4.49455e10i	0.259685i
$646$	9.56594e10i	0.549285i
$647$	−2.79365e10	−0.159425	−0.0797123	−	0.996818i	$-0.525400\pi$
$647$	−2.79365e10	−0.159425	−0.0797123	+	0.996818i	$0.525400\pi$
$648$	− 1.27471e11i	− 0.722957i
$649$	0	0
$650$	−1.41158e10	−0.0790776
$651$	1.05581e11i	0.587841i
$652$	8.43196e10	0.466593
$653$	−1.92931e11	−1.06108	−0.530542	−	0.847659i	$-0.678011\pi$
$653$	−1.92931e11	−1.06108	−0.530542	+	0.847659i	$0.678011\pi$
$654$	8.24199e10	0.450527
$655$	− 2.33874e11i	− 1.27062i
$656$	9.60229e10i	0.518513i
$657$	2.59658e10i	0.139361i
$658$	−4.78993e9	−0.0255521
$659$	2.89730e11i	1.53621i	0.640322	+	0.768107i	$0.278801\pi$
$659$	2.89730e11i	1.53621i	−0.640322	+	0.768107i	$0.721199\pi$
$660$	0	0
$661$	−5.56337e10	−0.291428	−0.145714	−	0.989327i	$-0.546548\pi$
$661$	−5.56337e10	−0.291428	−0.145714	+	0.989327i	$0.546548\pi$
$662$	2.67279e10i	0.139166i
$663$	1.02864e11	0.532365
$664$	1.27304e11	0.654891
$665$	−1.88255e11	−0.962629
$666$	− 1.44835e9i	− 0.00736168i
$667$	− 1.34035e11i	− 0.677196i
$668$	− 2.21211e11i	− 1.11096i
$669$	1.52488e11	0.761258
$670$	1.75431e11i	0.870577i
$671$	0	0
$672$	1.08885e11	0.533937
$673$	1.72745e11i	0.842064i	0.907046	+	0.421032i	$0.138332\pi$
$673$	1.72745e11i	0.842064i	−0.907046	+	0.421032i	$0.861668\pi$
$674$	−1.13689e11	−0.550909
$675$	−5.72028e10	−0.275551
$676$	9.11225e10	0.436354
$677$	− 7.32817e10i	− 0.348852i	−0.984670	−	0.174426i	$-0.944193\pi$
$677$	− 7.32817e10i	− 0.348852i	0.984670	−	0.174426i	$-0.0558069\pi$
$678$	− 7.12604e10i	− 0.337233i
$679$	− 1.65273e11i	− 0.777540i
$680$	−1.56360e11	−0.731290
$681$	− 5.10797e10i	− 0.237498i
$682$	0	0
$683$	−3.37571e11	−1.55125	−0.775625	−	0.631194i	$-0.782565\pi$
$683$	−3.37571e11	−1.55125	−0.775625	+	0.631194i	$0.782565\pi$
$684$	− 2.20802e10i	− 0.100874i
$685$	−5.42695e10	−0.246487
$686$	9.17928e10	0.414488
$687$	9.20626e9	0.0413291
$688$	− 2.47933e10i	− 0.110657i
$689$	1.40351e11i	0.622787i
$690$	1.34315e11i	0.592555i
$691$	−2.55262e11	−1.11963	−0.559813	−	0.828619i	$-0.689127\pi$
$691$	−2.55262e11	−1.11963	−0.559813	+	0.828619i	$0.689127\pi$
$692$	− 9.49608e9i	− 0.0414114i
$693$	0	0
$694$	3.98484e10	0.171780
$695$	− 2.08916e11i	− 0.895431i
$696$	−9.64231e10	−0.410907
$697$	2.18302e11	0.924968
$698$	1.04149e11	0.438764
$699$	− 1.46681e9i	− 0.00614421i
$700$	− 2.88673e10i	− 0.120230i
$701$	4.73174e10i	0.195951i	0.995189	+	0.0979757i	$0.0312367\pi$
$701$	4.73174e10i	0.195951i	−0.995189	+	0.0979757i	$0.968763\pi$
$702$	7.48908e10	0.308376
$703$	7.65174e10i	0.313285i
$704$	0	0
$705$	2.76847e10	0.112068
$706$	− 6.94434e10i	− 0.279519i
$707$	2.44035e9	0.00976731
$708$	−3.11274e11	−1.23882
$709$	−3.31666e11	−1.31255	−0.656276	−	0.754521i	$-0.727869\pi$
$709$	−3.31666e11	−1.31255	−0.656276	+	0.754521i	$0.727869\pi$
$710$	1.51130e11i	0.594728i
$711$	− 2.37522e10i	− 0.0929448i
$712$	− 7.80440e10i	− 0.303682i
$713$	3.54503e11	1.37171
$714$	− 5.01671e10i	− 0.193031i
$715$	0	0
$716$	−2.12771e11	−0.809582
$717$	1.04565e11i	0.395648i
$718$	−9.11846e10	−0.343102
$719$	3.88790e11	1.45479	0.727394	−	0.686220i	$-0.240731\pi$
$719$	3.88790e11	1.45479	0.727394	+	0.686220i	$0.240731\pi$
$720$	1.13610e10	0.0422753
$721$	− 8.56242e10i	− 0.316851i
$722$	− 1.58951e11i	− 0.584943i
$723$	4.08213e11i	1.49394i
$724$	1.69238e11	0.615949
$725$	3.97069e10i	0.143719i
$726$	0	0
$727$	3.54660e11	1.26962	0.634812	−	0.772667i	$-0.281078\pi$
$727$	3.54660e11	1.26962	0.634812	+	0.772667i	$0.281078\pi$
$728$	8.46001e10i	0.301193i
$729$	3.01597e11	1.06787
$730$	−2.38886e11	−0.841198
$731$	−5.63660e10	−0.197400
$732$	3.68269e11i	1.28269i
$733$	− 5.63516e11i	− 1.95205i	−0.217664	−	0.976024i	$-0.569844\pi$
$733$	− 5.63516e11i	− 1.95205i	0.217664	−	0.976024i	$-0.430156\pi$
$734$	− 1.25630e11i	− 0.432821i
$735$	−2.15907e11	−0.739805
$736$	− 3.65598e11i	− 1.24593i
$737$	0	0
$738$	1.20168e10	0.0405103
$739$	− 1.88021e11i	− 0.630420i	−0.949022	−	0.315210i	$-0.897925\pi$
$739$	− 1.88021e11i	− 0.630420i	0.949022	−	0.315210i	$-0.102075\pi$
$740$	−5.58733e10	−0.186328
$741$	−2.99146e11	−0.992225
$742$	6.84498e10	0.225817
$743$	4.07212e11i	1.33618i	0.744080	+	0.668090i	$0.232888\pi$
$743$	4.07212e11i	1.33618i	−0.744080	+	0.668090i	$0.767112\pi$
$744$	− 2.55025e11i	− 0.832323i
$745$	5.65635e11i	1.83616i
$746$	1.34382e11	0.433897
$747$	2.10289e10i	0.0675357i
$748$	0	0
$749$	−3.14410e10	−0.0999008
$750$	1.09897e11i	0.347330i
$751$	−3.75624e11	−1.18085	−0.590424	−	0.807094i	$-0.701039\pi$
$751$	−3.75624e11	−1.18085	−0.590424	+	0.807094i	$0.701039\pi$
$752$	−1.52717e10	−0.0477547
$753$	4.64465e9	0.0144468
$754$	− 5.19849e10i	− 0.160839i
$755$	1.74038e11i	0.535619i
$756$	1.53154e11i	0.468857i
$757$	4.01108e11	1.22146	0.610728	−	0.791841i	$-0.290877\pi$
$757$	4.01108e11	1.22146	0.610728	+	0.791841i	$0.290877\pi$
$758$	1.64273e11i	0.497611i
$759$	0	0
$760$	4.54721e11	1.36298
$761$	5.63938e11i	1.68148i	0.541437	+	0.840741i	$0.317880\pi$
$761$	5.63938e11i	1.68148i	−0.541437	+	0.840741i	$0.682120\pi$
$762$	−1.82562e11	−0.541491
$763$	−2.03414e11	−0.600182
$764$	1.37983e11	0.404996
$765$	− 2.58285e10i	− 0.0754144i
$766$	− 3.00788e10i	− 0.0873665i
$767$	− 3.75658e11i	− 1.08545i
$768$	−1.39351e11	−0.400557
$769$	− 3.98817e11i	− 1.14043i	−0.821495	−	0.570215i	$-0.806860\pi$
$769$	− 3.98817e11i	− 1.14043i	0.821495	−	0.570215i	$-0.193140\pi$
$770$	0	0
$771$	−9.37938e10	−0.265434
$772$	4.55824e11i	1.28330i
$773$	1.42881e11	0.400180	0.200090	−	0.979777i	$-0.435877\pi$
$773$	1.42881e11	0.400180	0.200090	+	0.979777i	$0.435877\pi$
$774$	−3.10277e9	−0.00864542
$775$	−1.05019e11	−0.291113
$776$	3.99210e11i	1.10092i
$777$	− 4.01284e10i	− 0.110095i
$778$	1.70682e11i	0.465876i
$779$	−6.34859e11	−1.72396
$780$	− 2.18437e11i	− 0.590131i
$781$	0	0
$782$	−1.68444e11	−0.450431
$783$	− 2.10663e11i	− 0.560455i
$784$	1.19101e11	0.315246
$785$	−2.46772e11	−0.649857
$786$	−1.81248e11	−0.474880
$787$	− 2.65211e11i	− 0.691342i	−0.938356	−	0.345671i	$-0.887651\pi$
$787$	− 2.65211e11i	− 0.691342i	0.938356	−	0.345671i	$-0.112349\pi$
$788$	− 4.62567e10i	− 0.119969i
$789$	− 3.28080e10i	− 0.0846588i
$790$	2.18520e11	0.561026
$791$	1.75872e11i	0.449253i
$792$	0	0
$793$	−4.44442e11	−1.12389
$794$	6.39969e10i	0.161019i
$795$	−3.95624e11	−0.990408
$796$	3.09212e11	0.770200
$797$	−4.31220e11	−1.06872	−0.534362	−	0.845256i	$-0.679448\pi$
$797$	−4.31220e11	−1.06872	−0.534362	+	0.845256i	$0.679448\pi$
$798$	1.45894e11i	0.359772i
$799$	3.47193e10i	0.0851890i
$800$	1.08306e11i	0.264418i
$801$	1.28918e10	0.0313173
$802$	− 5.45078e10i	− 0.131753i
$803$	0	0
$804$	−5.70089e11	−1.36433
$805$	− 3.31492e11i	− 0.789387i
$806$	1.37493e11	0.325791
$807$	−3.45327e11	−0.814209
$808$	−5.89457e9	−0.0138295
$809$	6.85663e10i	0.160072i	0.996792	+	0.0800362i	$0.0255036\pi$
$809$	6.85663e10i	0.160072i	−0.996792	+	0.0800362i	$0.974496\pi$
$810$	1.93720e11i	0.450023i
$811$	1.82889e11i	0.422770i	0.977403	+	0.211385i	$0.0677973\pi$
$811$	1.82889e11i	0.422770i	−0.977403	+	0.211385i	$0.932203\pi$
$812$	1.06310e11	0.244541
$813$	1.10040e11i	0.251878i
$814$	0	0
$815$	−2.86843e11	−0.650151
$816$	− 1.59947e11i	− 0.360758i
$817$	1.63922e11	0.367916
$818$	2.72600e11	0.608854
$819$	−1.39748e10	−0.0310606
$820$	− 4.63577e11i	− 1.02534i
$821$	− 8.72789e11i	− 1.92104i	−0.278208	−	0.960521i	$-0.589740\pi$
$821$	− 8.72789e11i	− 1.92104i	0.278208	−	0.960521i	$-0.410260\pi$
$822$	4.20580e10i	0.0921216i
$823$	7.70194e10	0.167881	0.0839404	−	0.996471i	$-0.473249\pi$
$823$	7.70194e10	0.167881	0.0839404	+	0.996471i	$0.473249\pi$
$824$	2.06822e11i	0.448629i
$825$	0	0
$826$	−1.83210e11	−0.393575
$827$	− 2.53077e10i	− 0.0541042i	−0.999634	−	0.0270521i	$-0.991388\pi$
$827$	− 2.53077e10i	− 0.0541042i	0.999634	−	0.0270521i	$-0.00861200\pi$
$828$	3.88805e10	0.0827199
$829$	5.47357e10	0.115892	0.0579459	−	0.998320i	$-0.481545\pi$
$829$	5.47357e10	0.115892	0.0579459	+	0.998320i	$0.481545\pi$
$830$	−1.93465e11	−0.407653
$831$	− 2.63154e11i	− 0.551832i
$832$	7.43738e9i	0.0155212i
$833$	− 2.70768e11i	− 0.562364i
$834$	−1.61907e11	−0.334657
$835$	7.52526e11i	1.54802i
$836$	0	0
$837$	5.57173e11	1.13524
$838$	− 1.69227e10i	− 0.0343157i
$839$	−5.10452e11	−1.03017	−0.515083	−	0.857141i	$-0.672239\pi$
$839$	−5.10452e11	−1.03017	−0.515083	+	0.857141i	$0.672239\pi$
$840$	−2.38472e11	−0.478982
$841$	3.54016e11	0.707684
$842$	− 3.42336e11i	− 0.681089i
$843$	7.08549e11i	1.40301i
$844$	− 3.19549e11i	− 0.629749i
$845$	−3.09986e11	−0.608015
$846$	1.91119e9i	0.00373097i
$847$	0	0
$848$	2.18238e11	0.422033
$849$	5.03818e11i	0.969713i
$850$	4.99003e10	0.0955934
$851$	−1.34737e11	−0.256904
$852$	−4.91120e11	−0.932029
$853$	7.88006e11i	1.48845i	0.667931	+	0.744224i	$0.267180\pi$
$853$	7.88006e11i	1.48845i	−0.667931	+	0.744224i	$0.732820\pi$
$854$	2.16756e11i	0.407511i
$855$	7.51137e10i	0.140558i
$856$	7.59444e10	0.141449
$857$	1.32237e11i	0.245150i	0.992459	+	0.122575i	$0.0391151\pi$
$857$	1.32237e11i	0.245150i	−0.992459	+	0.122575i	$0.960885\pi$
$858$	0	0
$859$	3.70268e11	0.680055	0.340027	−	0.940416i	$-0.389564\pi$
$859$	3.70268e11	0.680055	0.340027	+	0.940416i	$0.389564\pi$
$860$	1.19696e11i	0.218820i
$861$	3.32942e11	0.605837
$862$	4.79126e10	0.0867801
$863$	−5.12080e11	−0.923198	−0.461599	−	0.887089i	$-0.652724\pi$
$863$	−5.12080e11	−0.923198	−0.461599	+	0.887089i	$0.652724\pi$
$864$	− 5.74610e11i	− 1.03114i
$865$	3.23043e10i	0.0577027i
$866$	− 2.19703e11i	− 0.390630i
$867$	1.77806e11	0.314680
$868$	2.81176e11i	0.495336i
$869$	0	0
$870$	1.46536e11	0.255780
$871$	− 6.88006e11i	− 1.19542i
$872$	4.91338e11	0.849796
$873$	−6.59441e10	−0.113532
$874$	4.89863e11	0.839517
$875$	− 2.71229e11i	− 0.462705i
$876$	− 7.76293e11i	− 1.31829i
$877$	1.31113e11i	0.221640i	0.993841	+	0.110820i	$0.0353477\pi$
$877$	1.31113e11i	0.221640i	−0.993841	+	0.110820i	$0.964652\pi$
$878$	2.25748e10	0.0379879
$879$	− 7.20476e11i	− 1.20688i
$880$	0	0
$881$	1.82199e11	0.302443	0.151221	−	0.988500i	$-0.451679\pi$
$881$	1.82199e11	0.302443	0.151221	+	0.988500i	$0.451679\pi$
$882$	− 1.49049e10i	− 0.0246295i
$883$	1.32669e11	0.218236	0.109118	−	0.994029i	$-0.465197\pi$
$883$	1.32669e11	0.218236	0.109118	+	0.994029i	$0.465197\pi$
$884$	2.73942e11	0.448589
$885$	1.05891e12	1.72618
$886$	− 3.38726e11i	− 0.549685i
$887$	9.20909e11i	1.48772i	0.668333	+	0.743862i	$0.267008\pi$
$887$	9.20909e11i	1.48772i	−0.668333	+	0.743862i	$0.732992\pi$
$888$	9.69285e10i	0.155883i
$889$	4.50568e11	0.721362
$890$	1.18605e11i	0.189035i
$891$	0	0
$892$	4.06098e11	0.641463
$893$	− 1.00969e11i	− 0.158776i
$894$	4.38358e11	0.686245
$895$	7.23817e11	1.12807
$896$	3.62757e11	0.562839
$897$	− 5.26758e11i	− 0.813657i
$898$	− 2.21453e11i	− 0.340546i
$899$	− 3.86758e11i	− 0.592107i
$900$	−1.15181e10	−0.0175553
$901$	− 4.96150e11i	− 0.752860i
$902$	0	0
$903$	−8.59663e10	−0.129294
$904$	− 4.24812e11i	− 0.636097i
$905$	−5.75724e11	−0.858263
$906$	1.34877e11	0.200181
$907$	3.25840e11	0.481477	0.240738	−	0.970590i	$-0.422610\pi$
$907$	3.25840e11	0.481477	0.240738	+	0.970590i	$0.422610\pi$
$908$	− 1.36032e11i	− 0.200124i
$909$	− 9.73703e8i	− 0.00142617i
$910$	− 1.28568e11i	− 0.187485i
$911$	3.29495e11	0.478382	0.239191	−	0.970972i	$-0.423118\pi$
$911$	3.29495e11	0.478382	0.239191	+	0.970972i	$0.423118\pi$
$912$	4.65154e11i	0.672384i
$913$	0	0
$914$	−3.53719e11	−0.506843
$915$	− 1.25280e12i	− 1.78730i
$916$	2.45176e10	0.0348254
$917$	4.47325e11	0.632624
$918$	−2.64743e11	−0.372781
$919$	1.27480e12i	1.78723i	0.448839	+	0.893613i	$0.351838\pi$
$919$	1.27480e12i	1.78723i	−0.448839	+	0.893613i	$0.648162\pi$
$920$	8.00706e11i	1.11769i
$921$	2.46328e11i	0.342353i
$922$	−3.51991e11	−0.487089
$923$	− 5.92704e11i	− 0.816641i
$924$	0	0
$925$	3.99150e10	0.0545217
$926$	1.65930e11i	0.225673i
$927$	−3.41641e10	−0.0462649
$928$	−3.98861e11	−0.537812
$929$	5.43531e11	0.729729	0.364865	−	0.931061i	$-0.381115\pi$
$929$	5.43531e11	0.729729	0.364865	+	0.931061i	$0.381115\pi$
$930$	3.87566e11i	0.518100i
$931$	7.87439e11i	1.04814i
$932$	− 3.90633e9i	− 0.00517733i
$933$	1.45118e11	0.191512
$934$	− 5.77560e11i	− 0.758943i
$935$	0	0
$936$	3.37555e10	0.0439786
$937$	7.40437e11i	0.960571i	0.877112	+	0.480286i	$0.159467\pi$
$937$	7.40437e11i	0.960571i	−0.877112	+	0.480286i	$0.840533\pi$
$938$	−3.35543e11	−0.433448
$939$	1.35903e11	0.174811
$940$	7.37283e10	0.0944328
$941$	1.94941e11i	0.248625i	0.992243	+	0.124312i	$0.0396725\pi$
$941$	1.94941e11i	0.248625i	−0.992243	+	0.124312i	$0.960327\pi$
$942$	1.91245e11i	0.242877i
$943$	− 1.11791e12i	− 1.41370i
$944$	−5.84126e11	−0.735560
$945$	− 5.21007e11i	− 0.653305i
$946$	0	0
$947$	−3.03034e11	−0.376783	−0.188392	−	0.982094i	$-0.560327\pi$
$947$	−3.03034e11	−0.376783	−0.188392	+	0.982094i	$0.560327\pi$
$948$	7.10113e11i	0.879213i
$949$	9.36863e11	1.15508
$950$	−1.45119e11	−0.178168
$951$	1.30984e12	1.60139
$952$	− 2.99066e11i	− 0.364099i
$953$	3.77448e11i	0.457600i	0.973473	+	0.228800i	$0.0734802\pi$
$953$	3.77448e11i	0.457600i	−0.973473	+	0.228800i	$0.926520\pi$
$954$	− 2.73115e10i	− 0.0329725i
$955$	−4.69397e11	−0.564322
$956$	2.78471e11i	0.333387i
$957$	0	0
$958$	−4.47032e10	−0.0530734
$959$	− 1.03800e11i	− 0.122722i
$960$	−2.09646e10	−0.0246832
$961$	1.70028e11	0.199355
$962$	−5.22574e10	−0.0610165
$963$	1.25450e10i	0.0145870i
$964$	1.08713e12i	1.25885i
$965$	− 1.55065e12i	− 1.78815i
$966$	−2.56901e11	−0.295024
$967$	− 9.05058e10i	− 0.103507i	−0.998660	−	0.0517536i	$-0.983519\pi$
$967$	− 9.05058e10i	− 0.103507i	0.998660	−	0.0517536i	$-0.0164810\pi$
$968$	0	0
$969$	1.05750e12	1.19946
$970$	− 6.06685e11i	− 0.685294i
$971$	−7.80333e11	−0.877815	−0.438907	−	0.898532i	$-0.644634\pi$
$971$	−7.80333e11	−0.877815	−0.438907	+	0.898532i	$0.644634\pi$
$972$	1.17597e11	0.131744
$973$	3.99589e11	0.445822
$974$	− 3.28954e11i	− 0.365510i
$975$	1.56048e11i	0.172679i
$976$	6.91081e11i	0.761605i
$977$	3.35549e11	0.368280	0.184140	−	0.982900i	$-0.441050\pi$
$977$	3.35549e11	0.368280	0.184140	+	0.982900i	$0.441050\pi$
$978$	2.22299e11i	0.242986i
$979$	0	0
$980$	−5.74991e11	−0.623385
$981$	8.11624e10i	0.0876352i
$982$	3.46046e11	0.372124
$983$	1.01732e12	1.08954	0.544769	−	0.838586i	$-0.316617\pi$
$983$	1.01732e12	1.08954	0.544769	+	0.838586i	$0.316617\pi$
$984$	−8.04208e11	−0.857803
$985$	1.57359e11i	0.167165i
$986$	1.83770e11i	0.194431i
$987$	5.29519e10i	0.0557973i
$988$	−7.96668e11	−0.836084
$989$	2.88645e11i	0.301703i
$990$	0	0
$991$	9.14619e11	0.948299	0.474150	−	0.880444i	$-0.342756\pi$
$991$	9.14619e11	0.948299	0.474150	+	0.880444i	$0.342756\pi$
$992$	− 1.05493e12i	− 1.08938i
$993$	2.95472e11	0.303892
$994$	−2.89064e11	−0.296107
$995$	−1.05189e12	−1.07320
$996$	− 6.28694e11i	− 0.638855i
$997$	− 1.32177e12i	− 1.33775i	−0.743376	−	0.668874i	$-0.766777\pi$
$997$	− 1.32177e12i	− 1.33775i	0.743376	−	0.668874i	$-0.233223\pi$
$998$	− 6.57583e11i	− 0.662871i
$999$	−2.11767e11	−0.212616

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.9.b.b.120.17		28
11.3	even	5		11.9.d.a.2.5	✓	28
11.7	odd	10		11.9.d.a.6.5	yes	28
11.10	odd	2	inner	121.9.b.b.120.12		28
33.14	odd	10		99.9.k.a.46.3		28
33.29	even	10		99.9.k.a.28.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.9.d.a.2.5	✓	28	11.3	even	5
11.9.d.a.6.5	yes	28	11.7	odd	10
99.9.k.a.28.3		28	33.29	even	10
99.9.k.a.46.3		28	33.14	odd	10
121.9.b.b.120.12		28	11.10	odd	2	inner
121.9.b.b.120.17		28	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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	121.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+7.02107i q^{2} +77.6168 q^{3} +206.705 q^{4} -703.179 q^{5} +544.953i q^{6} -1344.96i q^{7} +3248.68i q^{8} -536.638 q^{9} +O(q^{10})\)	\(q+7.02107i q^{2} +77.6168 q^{3} +206.705 q^{4} -703.179 q^{5} +544.953i q^{6} -1344.96i q^{7} +3248.68i q^{8} -536.638 q^{9} -4937.07i q^{10} +16043.7 q^{12} +19362.2i q^{13} +9443.03 q^{14} -54578.5 q^{15} +30107.1 q^{16} -68446.7i q^{17} -3767.78i q^{18} +199054. i q^{19} -145350. q^{20} -104391. i q^{21} -350509. q^{23} +252152. i q^{24} +103836. q^{25} -135944. q^{26} -550896. q^{27} -278008. i q^{28} +382400. i q^{29} -383200. i q^{30} -1.01139e6 q^{31} +1.04305e6i q^{32} +480569. q^{34} +945744. i q^{35} -110926. q^{36} +384405. q^{37} -1.39758e6 q^{38} +1.50283e6i q^{39} -2.28441e6i q^{40} +3.18937e6i q^{41} +732937. q^{42} -823502. i q^{43} +377353. q^{45} -2.46095e6i q^{46} -507245. q^{47} +2.33682e6 q^{48} +3.95590e6 q^{49} +729040. i q^{50} -5.31261e6i q^{51} +4.00226e6i q^{52} +7.24871e6 q^{53} -3.86788e6i q^{54} +4.36933e6 q^{56} +1.54500e7i q^{57} -2.68486e6 q^{58} -1.94016e7 q^{59} -1.12816e7 q^{60} +2.29541e7i q^{61} -7.10108e6i q^{62} +721754. i q^{63} +384118. q^{64} -1.36151e7i q^{65} -3.55334e7 q^{67} -1.41482e7i q^{68} -2.72054e7 q^{69} -6.64014e6 q^{70} -3.06113e7 q^{71} -1.74337e6i q^{72} -4.83861e7i q^{73} +2.69893e6i q^{74} +8.05941e6 q^{75} +4.11455e7i q^{76} -1.05515e7 q^{78} +4.42610e7i q^{79} -2.11707e7 q^{80} -3.92379e7 q^{81} -2.23928e7 q^{82} -3.91863e7i q^{83} -2.15781e7i q^{84} +4.81303e7i q^{85} +5.78187e6 q^{86} +2.96807e7i q^{87} -2.40233e7 q^{89} +2.64942e6i q^{90} +2.60413e7 q^{91} -7.24519e7 q^{92} -7.85012e7 q^{93} -3.56141e6i q^{94} -1.39971e8i q^{95} +8.09579e7i q^{96} +1.22884e8 q^{97} +2.77746e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 26 q^{3} - 2884 q^{4} + 32 q^{5} + 42270 q^{9}+O(q^{10}) \) 28 * q - 26 * q^3 - 2884 * q^4 + 32 * q^5 + 42270 * q^9	\( 28 q - 26 q^{3} - 2884 q^{4} + 32 q^{5} + 42270 q^{9} + 63954 q^{12} - 148212 q^{14} + 387904 q^{15} - 73580 q^{16} + 1086392 q^{20} + 704764 q^{23} - 466788 q^{25} + 176572 q^{26} - 4112 q^{27} + 189364 q^{31} + 897538 q^{34} - 10359118 q^{36} - 5362896 q^{37} - 9823530 q^{38} + 1736320 q^{42} + 17701416 q^{45} - 34069636 q^{47} - 41699046 q^{48} - 27977884 q^{49} + 31846244 q^{53} + 96646244 q^{56} - 150994100 q^{58} + 2920262 q^{59} - 226082376 q^{60} + 127464764 q^{64} + 105502894 q^{67} - 321764892 q^{69} - 66153280 q^{70} - 240107164 q^{71} + 99947994 q^{75} + 387475480 q^{78} - 662332688 q^{80} - 203047984 q^{81} - 303592570 q^{82} + 71553822 q^{86} + 317966134 q^{89} - 519475368 q^{91} - 177687636 q^{92} - 725795252 q^{93} + 88971434 q^{97}+O(q^{100}) \) 28 * q - 26 * q^3 - 2884 * q^4 + 32 * q^5 + 42270 * q^9 + 63954 * q^12 - 148212 * q^14 + 387904 * q^15 - 73580 * q^16 + 1086392 * q^20 + 704764 * q^23 - 466788 * q^25 + 176572 * q^26 - 4112 * q^27 + 189364 * q^31 + 897538 * q^34 - 10359118 * q^36 - 5362896 * q^37 - 9823530 * q^38 + 1736320 * q^42 + 17701416 * q^45 - 34069636 * q^47 - 41699046 * q^48 - 27977884 * q^49 + 31846244 * q^53 + 96646244 * q^56 - 150994100 * q^58 + 2920262 * q^59 - 226082376 * q^60 + 127464764 * q^64 + 105502894 * q^67 - 321764892 * q^69 - 66153280 * q^70 - 240107164 * q^71 + 99947994 * q^75 + 387475480 * q^78 - 662332688 * q^80 - 203047984 * q^81 - 303592570 * q^82 + 71553822 * q^86 + 317966134 * q^89 - 519475368 * q^91 - 177687636 * q^92 - 725795252 * q^93 + 88971434 * q^97

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