LMFDB - Embedded newform 841.2.b.a.840.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(840,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("841.840");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.b (of order $2$, degree $1$, not 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			840.4
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	841.840
Dual form			841.2.b.a.840.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41421i q^{2} -2.41421i q^{3} -3.82843 q^{4} +1.00000 q^{5} +5.82843 q^{6} -2.82843 q^{7} -4.41421i q^{8} -2.82843 q^{9} +O(q^{10})$	\(q+2.41421i q^{2} -2.41421i q^{3} -3.82843 q^{4} +1.00000 q^{5} +5.82843 q^{6} -2.82843 q^{7} -4.41421i q^{8} -2.82843 q^{9} +2.41421i q^{10} +0.414214i q^{11} +9.24264i q^{12} +3.82843 q^{13} -6.82843i q^{14} -2.41421i q^{15} +3.00000 q^{16} -0.828427i q^{17} -6.82843i q^{18} -6.00000i q^{19} -3.82843 q^{20} +6.82843i q^{21} -1.00000 q^{22} +3.65685 q^{23} -10.6569 q^{24} -4.00000 q^{25} +9.24264i q^{26} -0.414214i q^{27} +10.8284 q^{28} +5.82843 q^{30} -10.0711i q^{31} -1.58579i q^{32} +1.00000 q^{33} +2.00000 q^{34} -2.82843 q^{35} +10.8284 q^{36} -4.00000i q^{37} +14.4853 q^{38} -9.24264i q^{39} -4.41421i q^{40} -4.48528i q^{41} -16.4853 q^{42} -3.58579i q^{43} -1.58579i q^{44} -2.82843 q^{45} +8.82843i q^{46} -3.24264i q^{47} -7.24264i q^{48} +1.00000 q^{49} -9.65685i q^{50} -2.00000 q^{51} -14.6569 q^{52} +9.48528 q^{53} +1.00000 q^{54} +0.414214i q^{55} +12.4853i q^{56} -14.4853 q^{57} -3.65685 q^{59} +9.24264i q^{60} +4.82843i q^{61} +24.3137 q^{62} +8.00000 q^{63} +9.82843 q^{64} +3.82843 q^{65} +2.41421i q^{66} -5.65685 q^{67} +3.17157i q^{68} -8.82843i q^{69} -6.82843i q^{70} +8.82843 q^{71} +12.4853i q^{72} +4.00000i q^{73} +9.65685 q^{74} +9.65685i q^{75} +22.9706i q^{76} -1.17157i q^{77} +22.3137 q^{78} +2.41421i q^{79} +3.00000 q^{80} -9.48528 q^{81} +10.8284 q^{82} +7.65685 q^{83} -26.1421i q^{84} -0.828427i q^{85} +8.65685 q^{86} +1.82843 q^{88} +12.4853i q^{89} -6.82843i q^{90} -10.8284 q^{91} -14.0000 q^{92} -24.3137 q^{93} +7.82843 q^{94} -6.00000i q^{95} -3.82843 q^{96} +4.48528i q^{97} +2.41421i q^{98} -1.17157i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{5} + 12 q^{6}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^5 + 12 * q^6	$ 4 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 4 q^{13} + 12 q^{16} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{24} - 16 q^{25} + 32 q^{28} + 12 q^{30} + 4 q^{33} + 8 q^{34} + 32 q^{36} + 24 q^{38} - 32 q^{42} + 4 q^{49} - 8 q^{51} - 36 q^{52} + 4 q^{53} + 4 q^{54} - 24 q^{57} + 8 q^{59} + 52 q^{62} + 32 q^{63} + 28 q^{64} + 4 q^{65} + 24 q^{71} + 16 q^{74} + 44 q^{78} + 12 q^{80} - 4 q^{81} + 32 q^{82} + 8 q^{83} + 12 q^{86} - 4 q^{88} - 32 q^{91} - 56 q^{92} - 52 q^{93} + 20 q^{94} - 4 q^{96}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 4 * q^13 + 12 * q^16 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^24 - 16 * q^25 + 32 * q^28 + 12 * q^30 + 4 * q^33 + 8 * q^34 + 32 * q^36 + 24 * q^38 - 32 * q^42 + 4 * q^49 - 8 * q^51 - 36 * q^52 + 4 * q^53 + 4 * q^54 - 24 * q^57 + 8 * q^59 + 52 * q^62 + 32 * q^63 + 28 * q^64 + 4 * q^65 + 24 * q^71 + 16 * q^74 + 44 * q^78 + 12 * q^80 - 4 * q^81 + 32 * q^82 + 8 * q^83 + 12 * q^86 - 4 * q^88 - 32 * q^91 - 56 * q^92 - 52 * q^93 + 20 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

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

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 $

$2$	2.41421i	1.70711i	0.521005	+	0.853553i	$0.325557\pi$
$2$	2.41421i	1.70711i	−0.521005	+	0.853553i	$0.674443\pi$
$3$	− 2.41421i	− 1.39385i	−0.717146	−	0.696923i	$-0.754552\pi$
$3$	− 2.41421i	− 1.39385i	0.717146	−	0.696923i	$-0.245448\pi$
$4$	−3.82843	−1.91421
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	5.82843	2.37945
$7$	−2.82843	−1.06904	−0.534522	−	0.845154i	$-0.679509\pi$
$7$	−2.82843	−1.06904	−0.534522	+	0.845154i	$0.679509\pi$
$8$	− 4.41421i	− 1.56066i
$9$	−2.82843	−0.942809
$10$	2.41421i	0.763441i
$11$	0.414214i	0.124890i	0.998048	+	0.0624450i	$0.0198898\pi$
$11$	0.414214i	0.124890i	−0.998048	+	0.0624450i	$0.980110\pi$
$12$	9.24264i	2.66812i
$13$	3.82843	1.06181	0.530907	−	0.847430i	$-0.321851\pi$
$13$	3.82843	1.06181	0.530907	+	0.847430i	$0.321851\pi$
$14$	− 6.82843i	− 1.82497i
$15$	− 2.41421i	− 0.623347i
$16$	3.00000	0.750000
$17$	− 0.828427i	− 0.200923i	−0.994941	−	0.100462i	$-0.967968\pi$
$17$	− 0.828427i	− 0.200923i	0.994941	−	0.100462i	$-0.0320319\pi$
$18$	− 6.82843i	− 1.60948i
$19$	− 6.00000i	− 1.37649i	−0.725476	−	0.688247i	$-0.758380\pi$
$19$	− 6.00000i	− 1.37649i	0.725476	−	0.688247i	$-0.241620\pi$
$20$	−3.82843	−0.856062
$21$	6.82843i	1.49008i
$22$	−1.00000	−0.213201
$23$	3.65685	0.762507	0.381253	−	0.924471i	$-0.375493\pi$
$23$	3.65685	0.762507	0.381253	+	0.924471i	$0.375493\pi$
$24$	−10.6569	−2.17532
$25$	−4.00000	−0.800000
$26$	9.24264i	1.81263i
$27$	− 0.414214i	− 0.0797154i
$28$	10.8284	2.04638
$29$	0	0
$29$	0	0
$30$	5.82843	1.06412
$31$	− 10.0711i	− 1.80882i	−0.426667	−	0.904409i	$-0.640313\pi$
$31$	− 10.0711i	− 1.80882i	0.426667	−	0.904409i	$-0.359687\pi$
$32$	− 1.58579i	− 0.280330i
$33$	1.00000	0.174078
$34$	2.00000	0.342997
$35$	−2.82843	−0.478091
$36$	10.8284	1.80474
$37$	− 4.00000i	− 0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$	− 4.00000i	− 0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	14.4853	2.34982
$39$	− 9.24264i	− 1.48001i
$40$	− 4.41421i	− 0.697948i
$41$	− 4.48528i	− 0.700483i	−0.936659	−	0.350242i	$-0.886099\pi$
$41$	− 4.48528i	− 0.700483i	0.936659	−	0.350242i	$-0.113901\pi$
$42$	−16.4853	−2.54373
$43$	− 3.58579i	− 0.546827i	−0.961897	−	0.273414i	$-0.911847\pi$
$43$	− 3.58579i	− 0.546827i	0.961897	−	0.273414i	$-0.0881528\pi$
$44$	− 1.58579i	− 0.239066i
$45$	−2.82843	−0.421637
$46$	8.82843i	1.30168i
$47$	− 3.24264i	− 0.472988i	−0.971633	−	0.236494i	$-0.924002\pi$
$47$	− 3.24264i	− 0.472988i	0.971633	−	0.236494i	$-0.0759983\pi$
$48$	− 7.24264i	− 1.04539i
$49$	1.00000	0.142857
$50$	− 9.65685i	− 1.36569i
$51$	−2.00000	−0.280056
$52$	−14.6569	−2.03254
$53$	9.48528	1.30290	0.651452	−	0.758690i	$-0.274160\pi$
$53$	9.48528	1.30290	0.651452	+	0.758690i	$0.274160\pi$
$54$	1.00000	0.136083
$55$	0.414214i	0.0558525i
$56$	12.4853i	1.66842i
$57$	−14.4853	−1.91862
$58$	0	0
$59$	−3.65685	−0.476082	−0.238041	−	0.971255i	$-0.576505\pi$
$59$	−3.65685	−0.476082	−0.238041	+	0.971255i	$0.576505\pi$
$60$	9.24264i	1.19322i
$61$	4.82843i	0.618217i	0.951027	+	0.309108i	$0.100031\pi$
$61$	4.82843i	0.618217i	−0.951027	+	0.309108i	$0.899969\pi$
$62$	24.3137	3.08784
$63$	8.00000	1.00791
$64$	9.82843	1.22855
$65$	3.82843	0.474858
$66$	2.41421i	0.297169i
$67$	−5.65685	−0.691095	−0.345547	−	0.938401i	$-0.612307\pi$
$67$	−5.65685	−0.691095	−0.345547	+	0.938401i	$0.612307\pi$
$68$	3.17157i	0.384610i
$69$	− 8.82843i	− 1.06282i
$70$	− 6.82843i	− 0.816153i
$71$	8.82843	1.04774	0.523871	−	0.851798i	$-0.324487\pi$
$71$	8.82843	1.04774	0.523871	+	0.851798i	$0.324487\pi$
$72$	12.4853i	1.47140i
$73$	4.00000i	0.468165i	0.972217	+	0.234082i	$0.0752085\pi$
$73$	4.00000i	0.468165i	−0.972217	+	0.234082i	$0.924791\pi$
$74$	9.65685	1.12259
$75$	9.65685i	1.11508i
$76$	22.9706i	2.63490i
$77$	− 1.17157i	− 0.133513i
$78$	22.3137	2.52653
$79$	2.41421i	0.271620i	0.990735	+	0.135810i	$0.0433637\pi$
$79$	2.41421i	0.271620i	−0.990735	+	0.135810i	$0.956636\pi$
$80$	3.00000	0.335410
$81$	−9.48528	−1.05392
$82$	10.8284	1.19580
$83$	7.65685	0.840449	0.420224	−	0.907420i	$-0.361951\pi$
$83$	7.65685	0.840449	0.420224	+	0.907420i	$0.361951\pi$
$84$	− 26.1421i	− 2.85234i
$85$	− 0.828427i	− 0.0898555i
$86$	8.65685	0.933493
$87$	0	0
$88$	1.82843	0.194911
$89$	12.4853i	1.32344i	0.749752	+	0.661719i	$0.230173\pi$
$89$	12.4853i	1.32344i	−0.749752	+	0.661719i	$0.769827\pi$
$90$	− 6.82843i	− 0.719779i
$91$	−10.8284	−1.13513
$92$	−14.0000	−1.45960
$93$	−24.3137	−2.52121
$94$	7.82843	0.807441
$95$	− 6.00000i	− 0.615587i
$96$	−3.82843	−0.390737
$97$	4.48528i	0.455411i	0.973730	+	0.227706i	$0.0731224\pi$
$97$	4.48528i	0.455411i	−0.973730	+	0.227706i	$0.926878\pi$
$98$	2.41421i	0.243872i
$99$	− 1.17157i	− 0.117748i
$100$	15.3137	1.53137
$101$	2.34315i	0.233152i	0.993182	+	0.116576i	$0.0371918\pi$
$101$	2.34315i	0.233152i	−0.993182	+	0.116576i	$0.962808\pi$
$102$	− 4.82843i	− 0.478086i
$103$	−4.82843	−0.475759	−0.237880	−	0.971295i	$-0.576452\pi$
$103$	−4.82843	−0.475759	−0.237880	+	0.971295i	$0.576452\pi$
$104$	− 16.8995i	− 1.65713i
$105$	6.82843i	0.666386i
$106$	22.8995i	2.22420i
$107$	−14.8284	−1.43352	−0.716759	−	0.697321i	$-0.754375\pi$
$107$	−14.8284	−1.43352	−0.716759	+	0.697321i	$0.754375\pi$
$108$	1.58579i	0.152592i
$109$	−12.6569	−1.21231	−0.606153	−	0.795348i	$-0.707288\pi$
$109$	−12.6569	−1.21231	−0.606153	+	0.795348i	$0.707288\pi$
$110$	−1.00000	−0.0953463
$111$	−9.65685	−0.916588
$112$	−8.48528	−0.801784
$113$	− 13.3137i	− 1.25245i	−0.779643	−	0.626224i	$-0.784599\pi$
$113$	− 13.3137i	− 1.25245i	0.779643	−	0.626224i	$-0.215401\pi$
$114$	− 34.9706i	− 3.27529i
$115$	3.65685	0.341003
$116$	0	0
$117$	−10.8284	−1.00109
$118$	− 8.82843i	− 0.812723i
$119$	2.34315i	0.214796i
$120$	−10.6569	−0.972833
$121$	10.8284	0.984402
$122$	−11.6569	−1.05536
$123$	−10.8284	−0.976366
$124$	38.5563i	3.46246i
$125$	−9.00000	−0.804984
$126$	19.3137i	1.72060i
$127$	4.34315i	0.385392i	0.981259	+	0.192696i	$0.0617231\pi$
$127$	4.34315i	0.385392i	−0.981259	+	0.192696i	$0.938277\pi$
$128$	20.5563i	1.81694i
$129$	−8.65685	−0.762194
$130$	9.24264i	0.810633i
$131$	21.3137i	1.86219i	0.364780	+	0.931094i	$0.381144\pi$
$131$	21.3137i	1.86219i	−0.364780	+	0.931094i	$0.618856\pi$
$132$	−3.82843	−0.333222
$133$	16.9706i	1.47153i
$134$	− 13.6569i	− 1.17977i
$135$	− 0.414214i	− 0.0356498i
$136$	−3.65685	−0.313573
$137$	− 12.0000i	− 1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$	− 12.0000i	− 1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$	21.3137	1.81434
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	10.8284	0.915169
$141$	−7.82843	−0.659272
$142$	21.3137i	1.78861i
$143$	1.58579i	0.132610i
$144$	−8.48528	−0.707107
$145$	0	0
$146$	−9.65685	−0.799207
$147$	− 2.41421i	− 0.199121i
$148$	15.3137i	1.25878i
$149$	7.82843	0.641330	0.320665	−	0.947193i	$-0.396094\pi$
$149$	7.82843	0.641330	0.320665	+	0.947193i	$0.396094\pi$
$150$	−23.3137	−1.90356
$151$	14.1421	1.15087	0.575435	−	0.817847i	$-0.304833\pi$
$151$	14.1421	1.15087	0.575435	+	0.817847i	$0.304833\pi$
$152$	−26.4853	−2.14824
$153$	2.34315i	0.189432i
$154$	2.82843	0.227921
$155$	− 10.0711i	− 0.808928i
$156$	35.3848i	2.83305i
$157$	8.48528i	0.677199i	0.940931	+	0.338600i	$0.109953\pi$
$157$	8.48528i	0.677199i	−0.940931	+	0.338600i	$0.890047\pi$
$158$	−5.82843	−0.463685
$159$	− 22.8995i	− 1.81605i
$160$	− 1.58579i	− 0.125367i
$161$	−10.3431	−0.815154
$162$	− 22.8995i	− 1.79915i
$163$	3.92893i	0.307738i	0.988091	+	0.153869i	$0.0491733\pi$
$163$	3.92893i	0.307738i	−0.988091	+	0.153869i	$0.950827\pi$
$164$	17.1716i	1.34087i
$165$	1.00000	0.0778499
$166$	18.4853i	1.43474i
$167$	3.17157	0.245424	0.122712	−	0.992442i	$-0.460841\pi$
$167$	3.17157	0.245424	0.122712	+	0.992442i	$0.460841\pi$
$168$	30.1421	2.32552
$169$	1.65685	0.127450
$170$	2.00000	0.153393
$171$	16.9706i	1.29777i
$172$	13.7279i	1.04674i
$173$	−12.3431	−0.938432	−0.469216	−	0.883083i	$-0.655463\pi$
$173$	−12.3431	−0.938432	−0.469216	+	0.883083i	$0.655463\pi$
$174$	0	0
$175$	11.3137	0.855236
$176$	1.24264i	0.0936676i
$177$	8.82843i	0.663585i
$178$	−30.1421	−2.25925
$179$	6.48528	0.484733	0.242366	−	0.970185i	$-0.422076\pi$
$179$	6.48528	0.484733	0.242366	+	0.970185i	$0.422076\pi$
$180$	10.8284	0.807103
$181$	8.31371	0.617953	0.308977	−	0.951070i	$-0.400014\pi$
$181$	8.31371	0.617953	0.308977	+	0.951070i	$0.400014\pi$
$182$	− 26.1421i	− 1.93778i
$183$	11.6569	0.861699
$184$	− 16.1421i	− 1.19001i
$185$	− 4.00000i	− 0.294086i
$186$	− 58.6985i	− 4.30398i
$187$	0.343146	0.0250933
$188$	12.4142i	0.905400i
$189$	1.17157i	0.0852194i
$190$	14.4853	1.05087
$191$	− 25.3137i	− 1.83164i	−0.401594	−	0.915818i	$-0.631544\pi$
$191$	− 25.3137i	− 1.83164i	0.401594	−	0.915818i	$-0.368456\pi$
$192$	− 23.7279i	− 1.71242i
$193$	5.17157i	0.372258i	0.982525	+	0.186129i	$0.0595942\pi$
$193$	5.17157i	0.372258i	−0.982525	+	0.186129i	$0.940406\pi$
$194$	−10.8284	−0.777436
$195$	− 9.24264i	− 0.661879i
$196$	−3.82843	−0.273459
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	2.82843	0.201008
$199$	−0.485281	−0.0344007	−0.0172003	−	0.999852i	$-0.505475\pi$
$199$	−0.485281	−0.0344007	−0.0172003	+	0.999852i	$0.505475\pi$
$200$	17.6569i	1.24853i
$201$	13.6569i	0.963280i
$202$	−5.65685	−0.398015
$203$	0	0
$204$	7.65685	0.536087
$205$	− 4.48528i	− 0.313266i
$206$	− 11.6569i	− 0.812172i
$207$	−10.3431	−0.718898
$208$	11.4853	0.796361
$209$	2.48528	0.171911
$210$	−16.4853	−1.13759
$211$	− 19.3848i	− 1.33450i	−0.744832	−	0.667252i	$-0.767471\pi$
$211$	− 19.3848i	− 1.33450i	0.744832	−	0.667252i	$-0.232529\pi$
$212$	−36.3137	−2.49404
$213$	− 21.3137i	− 1.46039i
$214$	− 35.7990i	− 2.44717i
$215$	− 3.58579i	− 0.244549i
$216$	−1.82843	−0.124409
$217$	28.4853i	1.93371i
$218$	− 30.5563i	− 2.06954i
$219$	9.65685	0.652550
$220$	− 1.58579i	− 0.106914i
$221$	− 3.17157i	− 0.213343i
$222$	− 23.3137i	− 1.56471i
$223$	−3.17157	−0.212384	−0.106192	−	0.994346i	$-0.533866\pi$
$223$	−3.17157	−0.212384	−0.106192	+	0.994346i	$0.533866\pi$
$224$	4.48528i	0.299685i
$225$	11.3137	0.754247
$226$	32.1421	2.13806
$227$	−8.14214	−0.540413	−0.270206	−	0.962802i	$-0.587092\pi$
$227$	−8.14214	−0.540413	−0.270206	+	0.962802i	$0.587092\pi$
$228$	55.4558	3.67265
$229$	− 3.51472i	− 0.232259i	−0.993234	−	0.116130i	$-0.962951\pi$
$229$	− 3.51472i	− 0.232259i	0.993234	−	0.116130i	$-0.0370488\pi$
$230$	8.82843i	0.582129i
$231$	−2.82843	−0.186097
$232$	0	0
$233$	18.3137	1.19977	0.599885	−	0.800086i	$-0.295213\pi$
$233$	18.3137	1.19977	0.599885	+	0.800086i	$0.295213\pi$
$234$	− 26.1421i	− 1.70896i
$235$	− 3.24264i	− 0.211527i
$236$	14.0000	0.911322
$237$	5.82843	0.378597
$238$	−5.65685	−0.366679
$239$	−19.6569	−1.27150	−0.635748	−	0.771897i	$-0.719308\pi$
$239$	−19.6569	−1.27150	−0.635748	+	0.771897i	$0.719308\pi$
$240$	− 7.24264i	− 0.467510i
$241$	18.3137	1.17969	0.589845	−	0.807517i	$-0.299189\pi$
$241$	18.3137	1.17969	0.589845	+	0.807517i	$0.299189\pi$
$242$	26.1421i	1.68048i
$243$	21.6569i	1.38929i
$244$	− 18.4853i	− 1.18340i
$245$	1.00000	0.0638877
$246$	− 26.1421i	− 1.66676i
$247$	− 22.9706i	− 1.46158i
$248$	−44.4558	−2.82295
$249$	− 18.4853i	− 1.17146i
$250$	− 21.7279i	− 1.37419i
$251$	− 20.0711i	− 1.26687i	−0.773794	−	0.633437i	$-0.781643\pi$
$251$	− 20.0711i	− 1.26687i	0.773794	−	0.633437i	$-0.218357\pi$
$252$	−30.6274	−1.92935
$253$	1.51472i	0.0952295i
$254$	−10.4853	−0.657905
$255$	−2.00000	−0.125245
$256$	−29.9706	−1.87316
$257$	−18.1716	−1.13351	−0.566756	−	0.823886i	$-0.691802\pi$
$257$	−18.1716	−1.13351	−0.566756	+	0.823886i	$0.691802\pi$
$258$	− 20.8995i	− 1.30115i
$259$	11.3137i	0.703000i
$260$	−14.6569	−0.908980
$261$	0	0
$262$	−51.4558	−3.17895
$263$	− 2.75736i	− 0.170026i	−0.996380	−	0.0850130i	$-0.972907\pi$
$263$	− 2.75736i	− 0.170026i	0.996380	−	0.0850130i	$-0.0270932\pi$
$264$	− 4.41421i	− 0.271676i
$265$	9.48528	0.582676
$266$	−40.9706	−2.51207
$267$	30.1421	1.84467
$268$	21.6569	1.32290
$269$	31.4558i	1.91790i	0.283581	+	0.958948i	$0.408478\pi$
$269$	31.4558i	1.91790i	−0.283581	+	0.958948i	$0.591522\pi$
$270$	1.00000	0.0608581
$271$	16.5563i	1.00573i	0.864366	+	0.502863i	$0.167720\pi$
$271$	16.5563i	1.00573i	−0.864366	+	0.502863i	$0.832280\pi$
$272$	− 2.48528i	− 0.150692i
$273$	26.1421i	1.58219i
$274$	28.9706	1.75018
$275$	− 1.65685i	− 0.0999121i
$276$	33.7990i	2.03446i
$277$	−17.3137	−1.04028	−0.520140	−	0.854081i	$-0.674120\pi$
$277$	−17.3137	−1.04028	−0.520140	+	0.854081i	$0.674120\pi$
$278$	33.7990i	2.02713i
$279$	28.4853i	1.70537i
$280$	12.4853i	0.746138i
$281$	31.9706	1.90720	0.953602	−	0.301070i	$-0.0973439\pi$
$281$	31.9706	1.90720	0.953602	+	0.301070i	$0.0973439\pi$
$282$	− 18.8995i	− 1.12545i
$283$	−11.6569	−0.692928	−0.346464	−	0.938063i	$-0.612618\pi$
$283$	−11.6569	−0.692928	−0.346464	+	0.938063i	$0.612618\pi$
$284$	−33.7990	−2.00560
$285$	−14.4853	−0.858034
$286$	−3.82843	−0.226380
$287$	12.6863i	0.748848i
$288$	4.48528i	0.264298i
$289$	16.3137	0.959630
$290$	0	0
$291$	10.8284	0.634774
$292$	− 15.3137i	− 0.896167i
$293$	− 7.65685i	− 0.447318i	−0.974667	−	0.223659i	$-0.928200\pi$
$293$	− 7.65685i	− 0.447318i	0.974667	−	0.223659i	$-0.0718002\pi$
$294$	5.82843	0.339921
$295$	−3.65685	−0.212910
$296$	−17.6569	−1.02628
$297$	0.171573	0.00995567
$298$	18.8995i	1.09482i
$299$	14.0000	0.809641
$300$	− 36.9706i	− 2.13450i
$301$	10.1421i	0.584583i
$302$	34.1421i	1.96466i
$303$	5.65685	0.324978
$304$	− 18.0000i	− 1.03237i
$305$	4.82843i	0.276475i
$306$	−5.65685	−0.323381
$307$	− 2.89949i	− 0.165483i	−0.996571	−	0.0827415i	$-0.973632\pi$
$307$	− 2.89949i	− 0.165483i	0.996571	−	0.0827415i	$-0.0263676\pi$
$308$	4.48528i	0.255573i
$309$	11.6569i	0.663135i
$310$	24.3137	1.38093
$311$	− 2.68629i	− 0.152326i	−0.997095	−	0.0761628i	$-0.975733\pi$
$311$	− 2.68629i	− 0.152326i	0.997095	−	0.0761628i	$-0.0242669\pi$
$312$	−40.7990	−2.30979
$313$	9.82843	0.555536	0.277768	−	0.960648i	$-0.410405\pi$
$313$	9.82843	0.555536	0.277768	+	0.960648i	$0.410405\pi$
$314$	−20.4853	−1.15605
$315$	8.00000	0.450749
$316$	− 9.24264i	− 0.519939i
$317$	− 31.4558i	− 1.76674i	−0.468680	−	0.883368i	$-0.655270\pi$
$317$	− 31.4558i	− 1.76674i	0.468680	−	0.883368i	$-0.344730\pi$
$318$	55.2843	3.10019
$319$	0	0
$320$	9.82843	0.549426
$321$	35.7990i	1.99810i
$322$	− 24.9706i	− 1.39156i
$323$	−4.97056	−0.276570
$324$	36.3137	2.01743
$325$	−15.3137	−0.849452
$326$	−9.48528	−0.525341
$327$	30.5563i	1.68977i
$328$	−19.7990	−1.09322
$329$	9.17157i	0.505645i
$330$	2.41421i	0.132898i
$331$	− 2.41421i	− 0.132697i	−0.997797	−	0.0663486i	$-0.978865\pi$
$331$	− 2.41421i	− 0.132697i	0.997797	−	0.0663486i	$-0.0211349\pi$
$332$	−29.3137	−1.60880
$333$	11.3137i	0.619987i
$334$	7.65685i	0.418964i
$335$	−5.65685	−0.309067
$336$	20.4853i	1.11756i
$337$	21.7990i	1.18747i	0.804662	+	0.593733i	$0.202347\pi$
$337$	21.7990i	1.18747i	−0.804662	+	0.593733i	$0.797653\pi$
$338$	4.00000i	0.217571i
$339$	−32.1421	−1.74572
$340$	3.17157i	0.172003i
$341$	4.17157	0.225903
$342$	−40.9706	−2.21543
$343$	16.9706	0.916324
$344$	−15.8284	−0.853412
$345$	− 8.82843i	− 0.475307i
$346$	− 29.7990i	− 1.60200i
$347$	−2.48528	−0.133417	−0.0667084	−	0.997773i	$-0.521250\pi$
$347$	−2.48528	−0.133417	−0.0667084	+	0.997773i	$0.521250\pi$
$348$	0	0
$349$	−5.14214	−0.275252	−0.137626	−	0.990484i	$-0.543947\pi$
$349$	−5.14214	−0.275252	−0.137626	+	0.990484i	$0.543947\pi$
$350$	27.3137i	1.45998i
$351$	− 1.58579i	− 0.0846430i
$352$	0.656854	0.0350104
$353$	−26.9706	−1.43550	−0.717749	−	0.696302i	$-0.754828\pi$
$353$	−26.9706	−1.43550	−0.717749	+	0.696302i	$0.754828\pi$
$354$	−21.3137	−1.13281
$355$	8.82843	0.468564
$356$	− 47.7990i	− 2.53334i
$357$	5.65685	0.299392
$358$	15.6569i	0.827490i
$359$	− 3.92893i	− 0.207361i	−0.994611	−	0.103681i	$-0.966938\pi$
$359$	− 3.92893i	− 0.207361i	0.994611	−	0.103681i	$-0.0330620\pi$
$360$	12.4853i	0.658032i
$361$	−17.0000	−0.894737
$362$	20.0711i	1.05491i
$363$	− 26.1421i	− 1.37211i
$364$	41.4558	2.17288
$365$	4.00000i	0.209370i
$366$	28.1421i	1.47101i
$367$	− 18.0000i	− 0.939592i	−0.882775	−	0.469796i	$-0.844327\pi$
$367$	− 18.0000i	− 0.939592i	0.882775	−	0.469796i	$-0.155673\pi$
$368$	10.9706	0.571880
$369$	12.6863i	0.660422i
$370$	9.65685	0.502036
$371$	−26.8284	−1.39286
$372$	93.0833	4.82614
$373$	−26.3137	−1.36247	−0.681236	−	0.732064i	$-0.738557\pi$
$373$	−26.3137	−1.36247	−0.681236	+	0.732064i	$0.738557\pi$
$374$	0.828427i	0.0428369i
$375$	21.7279i	1.12203i
$376$	−14.3137	−0.738173
$377$	0	0
$378$	−2.82843	−0.145479
$379$	6.97056i	0.358054i	0.983844	+	0.179027i	$0.0572949\pi$
$379$	6.97056i	0.358054i	−0.983844	+	0.179027i	$0.942705\pi$
$380$	22.9706i	1.17837i
$381$	10.4853	0.537177
$382$	61.1127	3.12680
$383$	3.51472	0.179594	0.0897969	−	0.995960i	$-0.471378\pi$
$383$	3.51472	0.179594	0.0897969	+	0.995960i	$0.471378\pi$
$384$	49.6274	2.53254
$385$	− 1.17157i	− 0.0597089i
$386$	−12.4853	−0.635484
$387$	10.1421i	0.515554i
$388$	− 17.1716i	− 0.871755i
$389$	3.02944i	0.153599i	0.997047	+	0.0767993i	$0.0244701\pi$
$389$	3.02944i	0.153599i	−0.997047	+	0.0767993i	$0.975530\pi$
$390$	22.3137	1.12990
$391$	− 3.02944i	− 0.153205i
$392$	− 4.41421i	− 0.222951i
$393$	51.4558	2.59560
$394$	4.82843i	0.243253i
$395$	2.41421i	0.121472i
$396$	4.48528i	0.225394i
$397$	19.3431	0.970805	0.485402	−	0.874291i	$-0.338673\pi$
$397$	19.3431	0.970805	0.485402	+	0.874291i	$0.338673\pi$
$398$	− 1.17157i	− 0.0587256i
$399$	40.9706	2.05109
$400$	−12.0000	−0.600000
$401$	−18.6569	−0.931679	−0.465839	−	0.884869i	$-0.654248\pi$
$401$	−18.6569	−0.931679	−0.465839	+	0.884869i	$0.654248\pi$
$402$	−32.9706	−1.64442
$403$	− 38.5563i	− 1.92063i
$404$	− 8.97056i	− 0.446302i
$405$	−9.48528	−0.471327
$406$	0	0
$407$	1.65685	0.0821272
$408$	8.82843i	0.437072i
$409$	18.9706i	0.938034i	0.883189	+	0.469017i	$0.155392\pi$
$409$	18.9706i	0.938034i	−0.883189	+	0.469017i	$0.844608\pi$
$410$	10.8284	0.534778
$411$	−28.9706	−1.42901
$412$	18.4853	0.910704
$413$	10.3431	0.508953
$414$	− 24.9706i	− 1.22724i
$415$	7.65685	0.375860
$416$	− 6.07107i	− 0.297659i
$417$	− 33.7990i	− 1.65514i
$418$	6.00000i	0.293470i
$419$	9.51472	0.464824	0.232412	−	0.972617i	$-0.425338\pi$
$419$	9.51472	0.464824	0.232412	+	0.972617i	$0.425338\pi$
$420$	− 26.1421i	− 1.27561i
$421$	37.1127i	1.80876i	0.426726	+	0.904381i	$0.359667\pi$
$421$	37.1127i	1.80876i	−0.426726	+	0.904381i	$0.640333\pi$
$422$	46.7990	2.27814
$423$	9.17157i	0.445937i
$424$	− 41.8701i	− 2.03339i
$425$	3.31371i	0.160738i
$426$	51.4558	2.49304
$427$	− 13.6569i	− 0.660901i
$428$	56.7696	2.74406
$429$	3.82843	0.184838
$430$	8.65685	0.417471
$431$	19.6569	0.946837	0.473419	−	0.880838i	$-0.343020\pi$
$431$	19.6569	0.946837	0.473419	+	0.880838i	$0.343020\pi$
$432$	− 1.24264i	− 0.0597866i
$433$	30.6274i	1.47186i	0.677058	+	0.735930i	$0.263255\pi$
$433$	30.6274i	1.47186i	−0.677058	+	0.735930i	$0.736745\pi$
$434$	−68.7696	−3.30104
$435$	0	0
$436$	48.4558	2.32061
$437$	− 21.9411i	− 1.04959i
$438$	23.3137i	1.11397i
$439$	0.343146	0.0163775	0.00818873	−	0.999966i	$-0.497393\pi$
$439$	0.343146	0.0163775	0.00818873	+	0.999966i	$0.497393\pi$
$440$	1.82843	0.0871668
$441$	−2.82843	−0.134687
$442$	7.65685	0.364199
$443$	− 24.3431i	− 1.15658i	−0.815832	−	0.578289i	$-0.803721\pi$
$443$	− 24.3431i	− 1.15658i	0.815832	−	0.578289i	$-0.196279\pi$
$444$	36.9706	1.75455
$445$	12.4853i	0.591859i
$446$	− 7.65685i	− 0.362563i
$447$	− 18.8995i	− 0.893915i
$448$	−27.7990	−1.31338
$449$	34.9706i	1.65036i	0.564868	+	0.825181i	$0.308927\pi$
$449$	34.9706i	1.65036i	−0.564868	+	0.825181i	$0.691073\pi$
$450$	27.3137i	1.28758i
$451$	1.85786	0.0874834
$452$	50.9706i	2.39745i
$453$	− 34.1421i	− 1.60414i
$454$	− 19.6569i	− 0.922542i
$455$	−10.8284	−0.507644
$456$	63.9411i	2.99432i
$457$	−1.02944	−0.0481550	−0.0240775	−	0.999710i	$-0.507665\pi$
$457$	−1.02944	−0.0481550	−0.0240775	+	0.999710i	$0.507665\pi$
$458$	8.48528	0.396491
$459$	−0.343146	−0.0160167
$460$	−14.0000	−0.652753
$461$	14.0000i	0.652045i	0.945362	+	0.326023i	$0.105709\pi$
$461$	14.0000i	0.652045i	−0.945362	+	0.326023i	$0.894291\pi$
$462$	− 6.82843i	− 0.317687i
$463$	26.0000	1.20832	0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000	1.20832	0.604161	+	0.796862i	$0.293508\pi$
$464$	0	0
$465$	−24.3137	−1.12752
$466$	44.2132i	2.04814i
$467$	38.3553i	1.77487i	0.460930	+	0.887437i	$0.347516\pi$
$467$	38.3553i	1.77487i	−0.460930	+	0.887437i	$0.652484\pi$
$468$	41.4558	1.91630
$469$	16.0000	0.738811
$470$	7.82843	0.361098
$471$	20.4853	0.943912
$472$	16.1421i	0.743002i
$473$	1.48528	0.0682933
$474$	14.0711i	0.646306i
$475$	24.0000i	1.10120i
$476$	− 8.97056i	− 0.411165i
$477$	−26.8284	−1.22839
$478$	− 47.4558i	− 2.17058i
$479$	6.89949i	0.315246i	0.987499	+	0.157623i	$0.0503831\pi$
$479$	6.89949i	0.315246i	−0.987499	+	0.157623i	$0.949617\pi$
$480$	−3.82843	−0.174743
$481$	− 15.3137i	− 0.698245i
$482$	44.2132i	2.01386i
$483$	24.9706i	1.13620i
$484$	−41.4558	−1.88436
$485$	4.48528i	0.203666i
$486$	−52.2843	−2.37166
$487$	−11.5147	−0.521782	−0.260891	−	0.965368i	$-0.584016\pi$
$487$	−11.5147	−0.521782	−0.260891	+	0.965368i	$0.584016\pi$
$488$	21.3137	0.964826
$489$	9.48528	0.428939
$490$	2.41421i	0.109063i
$491$	− 21.2426i	− 0.958667i	−0.877633	−	0.479333i	$-0.840878\pi$
$491$	− 21.2426i	− 0.958667i	0.877633	−	0.479333i	$-0.159122\pi$
$492$	41.4558	1.86897
$493$	0	0
$494$	55.4558	2.49508
$495$	− 1.17157i	− 0.0526583i
$496$	− 30.2132i	− 1.35661i
$497$	−24.9706	−1.12008
$498$	44.6274	1.99980
$499$	−18.9706	−0.849239	−0.424620	−	0.905372i	$-0.639592\pi$
$499$	−18.9706	−0.849239	−0.424620	+	0.905372i	$0.639592\pi$
$500$	34.4558	1.54091
$501$	− 7.65685i	− 0.342083i
$502$	48.4558	2.16269
$503$	0.272078i	0.0121314i	0.999982	+	0.00606568i	$0.00193078\pi$
$503$	0.272078i	0.0121314i	−0.999982	+	0.00606568i	$0.998069\pi$
$504$	− 35.3137i	− 1.57300i
$505$	2.34315i	0.104269i
$506$	−3.65685	−0.162567
$507$	− 4.00000i	− 0.177646i
$508$	− 16.6274i	− 0.737722i
$509$	−10.5147	−0.466057	−0.233028	−	0.972470i	$-0.574863\pi$
$509$	−10.5147	−0.466057	−0.233028	+	0.972470i	$0.574863\pi$
$510$	− 4.82843i	− 0.213806i
$511$	− 11.3137i	− 0.500489i
$512$	− 31.2426i	− 1.38074i
$513$	−2.48528	−0.109728
$514$	− 43.8701i	− 1.93503i
$515$	−4.82843	−0.212766
$516$	33.1421	1.45900
$517$	1.34315	0.0590715
$518$	−27.3137	−1.20010
$519$	29.7990i	1.30803i
$520$	− 16.8995i	− 0.741092i
$521$	29.1421	1.27674	0.638370	−	0.769730i	$-0.279609\pi$
$521$	29.1421	1.27674	0.638370	+	0.769730i	$0.279609\pi$
$522$	0	0
$523$	4.68629	0.204917	0.102459	−	0.994737i	$-0.467329\pi$
$523$	4.68629	0.204917	0.102459	+	0.994737i	$0.467329\pi$
$524$	− 81.5980i	− 3.56462i
$525$	− 27.3137i	− 1.19207i
$526$	6.65685	0.290253
$527$	−8.34315	−0.363433
$528$	3.00000	0.130558
$529$	−9.62742	−0.418583
$530$	22.8995i	0.994690i
$531$	10.3431	0.448854
$532$	− 64.9706i	− 2.81683i
$533$	− 17.1716i	− 0.743783i
$534$	72.7696i	3.14905i
$535$	−14.8284	−0.641089
$536$	24.9706i	1.07856i
$537$	− 15.6569i	− 0.675643i
$538$	−75.9411	−3.27405
$539$	0.414214i	0.0178414i
$540$	1.58579i	0.0682414i
$541$	10.3431i	0.444687i	0.974968	+	0.222343i	$0.0713706\pi$
$541$	10.3431i	0.444687i	−0.974968	+	0.222343i	$0.928629\pi$
$542$	−39.9706	−1.71688
$543$	− 20.0711i	− 0.861332i
$544$	−1.31371	−0.0563248
$545$	−12.6569	−0.542160
$546$	−63.1127	−2.70097
$547$	35.7990	1.53065	0.765327	−	0.643641i	$-0.222577\pi$
$547$	35.7990	1.53065	0.765327	+	0.643641i	$0.222577\pi$
$548$	45.9411i	1.96251i
$549$	− 13.6569i	− 0.582860i
$550$	4.00000	0.170561
$551$	0	0
$552$	−38.9706	−1.65870
$553$	− 6.82843i	− 0.290374i
$554$	− 41.7990i	− 1.77587i
$555$	−9.65685	−0.409911
$556$	−53.5980	−2.27306
$557$	17.3137	0.733605	0.366803	−	0.930299i	$-0.380452\pi$
$557$	17.3137	0.733605	0.366803	+	0.930299i	$0.380452\pi$
$558$	−68.7696	−2.91125
$559$	− 13.7279i	− 0.580629i
$560$	−8.48528	−0.358569
$561$	− 0.828427i	− 0.0349762i
$562$	77.1838i	3.25580i
$563$	− 0.757359i	− 0.0319189i	−0.999873	−	0.0159594i	$-0.994920\pi$
$563$	− 0.757359i	− 0.0319189i	0.999873	−	0.0159594i	$-0.00508026\pi$
$564$	29.9706	1.26199
$565$	− 13.3137i	− 0.560112i
$566$	− 28.1421i	− 1.18290i
$567$	26.8284	1.12669
$568$	− 38.9706i	− 1.63517i
$569$	− 39.6569i	− 1.66250i	−0.555897	−	0.831251i	$-0.687625\pi$
$569$	− 39.6569i	− 1.66250i	0.555897	−	0.831251i	$-0.312375\pi$
$570$	− 34.9706i	− 1.46476i
$571$	14.6274	0.612138	0.306069	−	0.952009i	$-0.400986\pi$
$571$	14.6274	0.612138	0.306069	+	0.952009i	$0.400986\pi$
$572$	− 6.07107i	− 0.253844i
$573$	−61.1127	−2.55302
$574$	−30.6274	−1.27836
$575$	−14.6274	−0.610005
$576$	−27.7990	−1.15829
$577$	− 29.7990i	− 1.24055i	−0.784385	−	0.620274i	$-0.787021\pi$
$577$	− 29.7990i	− 1.24055i	0.784385	−	0.620274i	$-0.212979\pi$
$578$	39.3848i	1.63819i
$579$	12.4853	0.518871
$580$	0	0
$581$	−21.6569	−0.898478
$582$	26.1421i	1.08363i
$583$	3.92893i	0.162720i
$584$	17.6569	0.730646
$585$	−10.8284	−0.447700
$586$	18.4853	0.763620
$587$	7.65685	0.316032	0.158016	−	0.987437i	$-0.449490\pi$
$587$	7.65685	0.316032	0.158016	+	0.987437i	$0.449490\pi$
$588$	9.24264i	0.381160i
$589$	−60.4264	−2.48983
$590$	− 8.82843i	− 0.363461i
$591$	− 4.82843i	− 0.198615i
$592$	− 12.0000i	− 0.493197i
$593$	19.4853	0.800165	0.400082	−	0.916479i	$-0.368982\pi$
$593$	19.4853	0.800165	0.400082	+	0.916479i	$0.368982\pi$
$594$	0.414214i	0.0169954i
$595$	2.34315i	0.0960596i
$596$	−29.9706	−1.22764
$597$	1.17157i	0.0479493i
$598$	33.7990i	1.38214i
$599$	− 9.87006i	− 0.403280i	−0.979460	−	0.201640i	$-0.935373\pi$
$599$	− 9.87006i	− 0.403280i	0.979460	−	0.201640i	$-0.0646270\pi$
$600$	42.6274	1.74026
$601$	17.1716i	0.700443i	0.936667	+	0.350222i	$0.113894\pi$
$601$	17.1716i	0.700443i	−0.936667	+	0.350222i	$0.886106\pi$
$602$	−24.4853	−0.997946
$603$	16.0000	0.651570
$604$	−54.1421	−2.20301
$605$	10.8284	0.440238
$606$	13.6569i	0.554772i
$607$	− 7.72792i	− 0.313667i	−0.987625	−	0.156833i	$-0.949871\pi$
$607$	− 7.72792i	− 0.313667i	0.987625	−	0.156833i	$-0.0501286\pi$
$608$	−9.51472	−0.385873
$609$	0	0
$610$	−11.6569	−0.471972
$611$	− 12.4142i	− 0.502225i
$612$	− 8.97056i	− 0.362614i
$613$	9.00000	0.363507	0.181753	−	0.983344i	$-0.441823\pi$
$613$	9.00000	0.363507	0.181753	+	0.983344i	$0.441823\pi$
$614$	7.00000	0.282497
$615$	−10.8284	−0.436644
$616$	−5.17157	−0.208369
$617$	0.686292i	0.0276291i	0.999905	+	0.0138145i	$0.00439744\pi$
$617$	0.686292i	0.0276291i	−0.999905	+	0.0138145i	$0.995603\pi$
$618$	−28.1421	−1.13204
$619$	33.5858i	1.34993i	0.737851	+	0.674963i	$0.235841\pi$
$619$	33.5858i	1.34993i	−0.737851	+	0.674963i	$0.764159\pi$
$620$	38.5563i	1.54846i
$621$	− 1.51472i	− 0.0607836i
$622$	6.48528	0.260036
$623$	− 35.3137i	− 1.41481i
$624$	− 27.7279i	− 1.11001i
$625$	11.0000	0.440000
$626$	23.7279i	0.948358i
$627$	− 6.00000i	− 0.239617i
$628$	− 32.4853i	− 1.29630i
$629$	−3.31371	−0.132126
$630$	19.3137i	0.769477i
$631$	36.8284	1.46612	0.733058	−	0.680166i	$-0.238092\pi$
$631$	36.8284	1.46612	0.733058	+	0.680166i	$0.238092\pi$
$632$	10.6569	0.423907
$633$	−46.7990	−1.86009
$634$	75.9411	3.01601
$635$	4.34315i	0.172352i
$636$	87.6690i	3.47630i
$637$	3.82843	0.151688
$638$	0	0
$639$	−24.9706	−0.987820
$640$	20.5563i	0.812561i
$641$	− 17.7990i	− 0.703018i	−0.936185	−	0.351509i	$-0.885669\pi$
$641$	− 17.7990i	− 0.703018i	0.936185	−	0.351509i	$-0.114331\pi$
$642$	−86.4264	−3.41098
$643$	−32.4853	−1.28109	−0.640547	−	0.767919i	$-0.721292\pi$
$643$	−32.4853	−1.28109	−0.640547	+	0.767919i	$0.721292\pi$
$644$	39.5980	1.56038
$645$	−8.65685	−0.340863
$646$	− 12.0000i	− 0.472134i
$647$	−39.6569	−1.55907	−0.779536	−	0.626358i	$-0.784545\pi$
$647$	−39.6569	−1.55907	−0.779536	+	0.626358i	$0.784545\pi$
$648$	41.8701i	1.64481i
$649$	− 1.51472i	− 0.0594579i
$650$	− 36.9706i	− 1.45010i
$651$	68.7696	2.69529
$652$	− 15.0416i	− 0.589076i
$653$	− 30.1421i	− 1.17955i	−0.807567	−	0.589776i	$-0.799216\pi$
$653$	− 30.1421i	− 1.17955i	0.807567	−	0.589776i	$-0.200784\pi$
$654$	−73.7696	−2.88462
$655$	21.3137i	0.832796i
$656$	− 13.4558i	− 0.525362i
$657$	− 11.3137i	− 0.441390i
$658$	−22.1421	−0.863190
$659$	− 14.4142i	− 0.561498i	−0.959781	−	0.280749i	$-0.909417\pi$
$659$	− 14.4142i	− 0.561498i	0.959781	−	0.280749i	$-0.0905829\pi$
$660$	−3.82843	−0.149021
$661$	33.3137	1.29575	0.647877	−	0.761745i	$-0.275657\pi$
$661$	33.3137	1.29575	0.647877	+	0.761745i	$0.275657\pi$
$662$	5.82843	0.226528
$663$	−7.65685	−0.297368
$664$	− 33.7990i	− 1.31166i
$665$	16.9706i	0.658090i
$666$	−27.3137	−1.05838
$667$	0	0
$668$	−12.1421	−0.469793
$669$	7.65685i	0.296031i
$670$	− 13.6569i	− 0.527610i
$671$	−2.00000	−0.0772091
$672$	10.8284	0.417716
$673$	21.6274	0.833676	0.416838	−	0.908981i	$-0.363138\pi$
$673$	21.6274	0.833676	0.416838	+	0.908981i	$0.363138\pi$
$674$	−52.6274	−2.02713
$675$	1.65685i	0.0637723i
$676$	−6.34315	−0.243967
$677$	− 22.0000i	− 0.845529i	−0.906240	−	0.422764i	$-0.861060\pi$
$677$	− 22.0000i	− 0.845529i	0.906240	−	0.422764i	$-0.138940\pi$
$678$	− 77.5980i	− 2.98013i
$679$	− 12.6863i	− 0.486855i
$680$	−3.65685	−0.140234
$681$	19.6569i	0.753252i
$682$	10.0711i	0.385641i
$683$	20.9706	0.802416	0.401208	−	0.915987i	$-0.368590\pi$
$683$	20.9706	0.802416	0.401208	+	0.915987i	$0.368590\pi$
$684$	− 64.9706i	− 2.48421i
$685$	− 12.0000i	− 0.458496i
$686$	40.9706i	1.56426i
$687$	−8.48528	−0.323734
$688$	− 10.7574i	− 0.410120i
$689$	36.3137	1.38344
$690$	21.3137	0.811399
$691$	48.0000	1.82601	0.913003	−	0.407953i	$-0.133757\pi$
$691$	48.0000	1.82601	0.913003	+	0.407953i	$0.133757\pi$
$692$	47.2548	1.79636
$693$	3.31371i	0.125877i
$694$	− 6.00000i	− 0.227757i
$695$	14.0000	0.531050
$696$	0	0
$697$	−3.71573	−0.140743
$698$	− 12.4142i	− 0.469885i
$699$	− 44.2132i	− 1.67230i
$700$	−43.3137	−1.63710
$701$	40.1127	1.51504	0.757518	−	0.652814i	$-0.226412\pi$
$701$	40.1127	1.51504	0.757518	+	0.652814i	$0.226412\pi$
$702$	3.82843	0.144495
$703$	−24.0000	−0.905177
$704$	4.07107i	0.153434i
$705$	−7.82843	−0.294836
$706$	− 65.1127i	− 2.45055i
$707$	− 6.62742i	− 0.249250i
$708$	− 33.7990i	− 1.27024i
$709$	−29.1421	−1.09446	−0.547228	−	0.836984i	$-0.684317\pi$
$709$	−29.1421	−1.09446	−0.547228	+	0.836984i	$0.684317\pi$
$710$	21.3137i	0.799889i
$711$	− 6.82843i	− 0.256086i
$712$	55.1127	2.06544
$713$	− 36.8284i	− 1.37924i
$714$	13.6569i	0.511095i
$715$	1.58579i	0.0593051i
$716$	−24.8284	−0.927882
$717$	47.4558i	1.77227i
$718$	9.48528	0.353988
$719$	−20.1421	−0.751175	−0.375587	−	0.926787i	$-0.622559\pi$
$719$	−20.1421	−0.751175	−0.375587	+	0.926787i	$0.622559\pi$
$720$	−8.48528	−0.316228
$721$	13.6569	0.508608
$722$	− 41.0416i	− 1.52741i
$723$	− 44.2132i	− 1.64431i
$724$	−31.8284	−1.18289
$725$	0	0
$726$	63.1127	2.34233
$727$	− 1.31371i	− 0.0487228i	−0.999703	−	0.0243614i	$-0.992245\pi$
$727$	− 1.31371i	− 0.0487228i	0.999703	−	0.0243614i	$-0.00775523\pi$
$728$	47.7990i	1.77155i
$729$	23.8284	0.882534
$730$	−9.65685	−0.357416
$731$	−2.97056	−0.109870
$732$	−44.6274	−1.64948
$733$	− 41.2548i	− 1.52378i	−0.647705	−	0.761891i	$-0.724271\pi$
$733$	− 41.2548i	− 1.52378i	0.647705	−	0.761891i	$-0.275729\pi$
$734$	43.4558	1.60398
$735$	− 2.41421i	− 0.0890496i
$736$	− 5.79899i	− 0.213754i
$737$	− 2.34315i	− 0.0863109i
$738$	−30.6274	−1.12741
$739$	− 4.07107i	− 0.149757i	−0.997193	−	0.0748783i	$-0.976143\pi$
$739$	− 4.07107i	− 0.149757i	0.997193	−	0.0748783i	$-0.0238568\pi$
$740$	15.3137i	0.562943i
$741$	−55.4558	−2.03722
$742$	− 64.7696i	− 2.37777i
$743$	23.6569i	0.867886i	0.900940	+	0.433943i	$0.142878\pi$
$743$	23.6569i	0.867886i	−0.900940	+	0.433943i	$0.857122\pi$
$744$	107.326i	3.93476i
$745$	7.82843	0.286811
$746$	− 63.5269i	− 2.32589i
$747$	−21.6569	−0.792383
$748$	−1.31371	−0.0480339
$749$	41.9411	1.53250
$750$	−52.4558	−1.91542
$751$	25.3137i	0.923710i	0.886955	+	0.461855i	$0.152816\pi$
$751$	25.3137i	0.923710i	−0.886955	+	0.461855i	$0.847184\pi$
$752$	− 9.72792i	− 0.354741i
$753$	−48.4558	−1.76583
$754$	0	0
$755$	14.1421	0.514685
$756$	− 4.48528i	− 0.163128i
$757$	− 25.5147i	− 0.927348i	−0.886006	−	0.463674i	$-0.846531\pi$
$757$	− 25.5147i	− 0.927348i	0.886006	−	0.463674i	$-0.153469\pi$
$758$	−16.8284	−0.611236
$759$	3.65685	0.132735
$760$	−26.4853	−0.960722
$761$	45.5980	1.65293	0.826463	−	0.562991i	$-0.190350\pi$
$761$	45.5980	1.65293	0.826463	+	0.562991i	$0.190350\pi$
$762$	25.3137i	0.917019i
$763$	35.7990	1.29601
$764$	96.9117i	3.50614i
$765$	2.34315i	0.0847166i
$766$	8.48528i	0.306586i
$767$	−14.0000	−0.505511
$768$	72.3553i	2.61090i
$769$	− 49.1127i	− 1.77105i	−0.464592	−	0.885525i	$-0.653799\pi$
$769$	− 49.1127i	− 1.77105i	0.464592	−	0.885525i	$-0.346201\pi$
$770$	2.82843	0.101929
$771$	43.8701i	1.57994i
$772$	− 19.7990i	− 0.712581i
$773$	19.5147i	0.701896i	0.936395	+	0.350948i	$0.114141\pi$
$773$	19.5147i	0.701896i	−0.936395	+	0.350948i	$0.885859\pi$
$774$	−24.4853	−0.880105
$775$	40.2843i	1.44705i
$776$	19.7990	0.710742
$777$	27.3137	0.979874
$778$	−7.31371	−0.262209
$779$	−26.9117	−0.964211
$780$	35.3848i	1.26698i
$781$	3.65685i	0.130853i
$782$	7.31371	0.261538
$783$	0	0
$784$	3.00000	0.107143
$785$	8.48528i	0.302853i
$786$	124.225i	4.43097i
$787$	54.0833	1.92786	0.963930	−	0.266156i	$-0.0857536\pi$
$787$	54.0833	1.92786	0.963930	+	0.266156i	$0.0857536\pi$
$788$	−7.65685	−0.272764
$789$	−6.65685	−0.236990
$790$	−5.82843	−0.207366
$791$	37.6569i	1.33892i
$792$	−5.17157	−0.183764
$793$	18.4853i	0.656432i
$794$	46.6985i	1.65727i
$795$	− 22.8995i	− 0.812161i
$796$	1.85786	0.0658503
$797$	− 51.7401i	− 1.83273i	−0.400345	−	0.916364i	$-0.631110\pi$
$797$	− 51.7401i	− 1.83273i	0.400345	−	0.916364i	$-0.368890\pi$
$798$	98.9117i	3.50144i
$799$	−2.68629	−0.0950342
$800$	6.34315i	0.224264i
$801$	− 35.3137i	− 1.24775i
$802$	− 45.0416i	− 1.59048i
$803$	−1.65685	−0.0584691
$804$	− 52.2843i	− 1.84392i
$805$	−10.3431	−0.364548
$806$	93.0833	3.27872
$807$	75.9411	2.67325
$808$	10.3431	0.363871
$809$	36.2843i	1.27569i	0.770166	+	0.637844i	$0.220173\pi$
$809$	36.2843i	1.27569i	−0.770166	+	0.637844i	$0.779827\pi$
$810$	− 22.8995i	− 0.804606i
$811$	−10.8284	−0.380238	−0.190119	−	0.981761i	$-0.560887\pi$
$811$	−10.8284	−0.380238	−0.190119	+	0.981761i	$0.560887\pi$
$812$	0	0
$813$	39.9706	1.40183
$814$	4.00000i	0.140200i
$815$	3.92893i	0.137624i
$816$	−6.00000	−0.210042
$817$	−21.5147	−0.752705
$818$	−45.7990	−1.60132
$819$	30.6274	1.07021
$820$	17.1716i	0.599657i
$821$	1.48528	0.0518367	0.0259183	−	0.999664i	$-0.491749\pi$
$821$	1.48528	0.0518367	0.0259183	+	0.999664i	$0.491749\pi$
$822$	− 69.9411i	− 2.43948i
$823$	54.2843i	1.89223i	0.323830	+	0.946115i	$0.395029\pi$
$823$	54.2843i	1.89223i	−0.323830	+	0.946115i	$0.604971\pi$
$824$	21.3137i	0.742498i
$825$	−4.00000	−0.139262
$826$	24.9706i	0.868837i
$827$	32.8995i	1.14403i	0.820244	+	0.572014i	$0.193838\pi$
$827$	32.8995i	1.14403i	−0.820244	+	0.572014i	$0.806162\pi$
$828$	39.5980	1.37612
$829$	29.7990i	1.03496i	0.855695	+	0.517481i	$0.173130\pi$
$829$	29.7990i	1.03496i	−0.855695	+	0.517481i	$0.826870\pi$
$830$	18.4853i	0.641633i
$831$	41.7990i	1.44999i
$832$	37.6274	1.30450
$833$	− 0.828427i	− 0.0287033i
$834$	81.5980	2.82551
$835$	3.17157	0.109757
$836$	−9.51472	−0.329073
$837$	−4.17157	−0.144191
$838$	22.9706i	0.793505i
$839$	− 7.92893i	− 0.273737i	−0.990589	−	0.136869i	$-0.956296\pi$
$839$	− 7.92893i	− 0.273737i	0.990589	−	0.136869i	$-0.0437038\pi$
$840$	30.1421	1.04000
$841$	0	0
$842$	−89.5980	−3.08775
$843$	− 77.1838i	− 2.65835i
$844$	74.2132i	2.55452i
$845$	1.65685	0.0569975
$846$	−22.1421	−0.761262
$847$	−30.6274	−1.05237
$848$	28.4558	0.977178
$849$	28.1421i	0.965836i
$850$	−8.00000	−0.274398
$851$	− 14.6274i	− 0.501421i
$852$	81.5980i	2.79550i
$853$	− 22.9706i	− 0.786497i	−0.919432	−	0.393249i	$-0.871351\pi$
$853$	− 22.9706i	− 0.786497i	0.919432	−	0.393249i	$-0.128649\pi$
$854$	32.9706	1.12823
$855$	16.9706i	0.580381i
$856$	65.4558i	2.23723i
$857$	−6.17157	−0.210817	−0.105408	−	0.994429i	$-0.533615\pi$
$857$	−6.17157	−0.210817	−0.105408	+	0.994429i	$0.533615\pi$
$858$	9.24264i	0.315539i
$859$	19.7279i	0.673108i	0.941664	+	0.336554i	$0.109261\pi$
$859$	19.7279i	0.673108i	−0.941664	+	0.336554i	$0.890739\pi$
$860$	13.7279i	0.468118i
$861$	30.6274	1.04378
$862$	47.4558i	1.61635i
$863$	−17.1127	−0.582523	−0.291262	−	0.956643i	$-0.594075\pi$
$863$	−17.1127	−0.582523	−0.291262	+	0.956643i	$0.594075\pi$
$864$	−0.656854	−0.0223466
$865$	−12.3431	−0.419680
$866$	−73.9411	−2.51262
$867$	− 39.3848i	− 1.33758i
$868$	− 109.054i	− 3.70153i
$869$	−1.00000	−0.0339227
$870$	0	0
$871$	−21.6569	−0.733815
$872$	55.8701i	1.89200i
$873$	− 12.6863i	− 0.429366i
$874$	52.9706	1.79176
$875$	25.4558	0.860565
$876$	−36.9706	−1.24912
$877$	−37.1421	−1.25420	−0.627100	−	0.778938i	$-0.715758\pi$
$877$	−37.1421	−1.25420	−0.627100	+	0.778938i	$0.715758\pi$
$878$	0.828427i	0.0279581i
$879$	−18.4853	−0.623493
$880$	1.24264i	0.0418894i
$881$	− 14.0000i	− 0.471672i	−0.971793	−	0.235836i	$-0.924217\pi$
$881$	− 14.0000i	− 0.471672i	0.971793	−	0.235836i	$-0.0757828\pi$
$882$	− 6.82843i	− 0.229925i
$883$	−38.4264	−1.29315	−0.646576	−	0.762850i	$-0.723800\pi$
$883$	−38.4264	−1.29315	−0.646576	+	0.762850i	$0.723800\pi$
$884$	12.1421i	0.408384i
$885$	8.82843i	0.296764i
$886$	58.7696	1.97440
$887$	− 17.1005i	− 0.574179i	−0.957904	−	0.287089i	$-0.907312\pi$
$887$	− 17.1005i	− 0.574179i	0.957904	−	0.287089i	$-0.0926877\pi$
$888$	42.6274i	1.43048i
$889$	− 12.2843i	− 0.412001i
$890$	−30.1421	−1.01037
$891$	− 3.92893i	− 0.131624i
$892$	12.1421	0.406549
$893$	−19.4558	−0.651065
$894$	45.6274	1.52601
$895$	6.48528	0.216779
$896$	− 58.1421i	− 1.94239i
$897$	− 33.7990i	− 1.12852i
$898$	−84.4264	−2.81735
$899$	0	0
$900$	−43.3137	−1.44379
$901$	− 7.85786i	− 0.261783i
$902$	4.48528i	0.149344i
$903$	24.4853	0.814819
$904$	−58.7696	−1.95465
$905$	8.31371	0.276357
$906$	82.4264	2.73843
$907$	22.2843i	0.739937i	0.929044	+	0.369969i	$0.120632\pi$
$907$	22.2843i	0.739937i	−0.929044	+	0.369969i	$0.879368\pi$
$908$	31.1716	1.03446
$909$	− 6.62742i	− 0.219818i
$910$	− 26.1421i	− 0.866603i
$911$	− 15.4437i	− 0.511671i	−0.966720	−	0.255835i	$-0.917649\pi$
$911$	− 15.4437i	− 0.511671i	0.966720	−	0.255835i	$-0.0823505\pi$
$912$	−43.4558	−1.43897
$913$	3.17157i	0.104964i
$914$	− 2.48528i	− 0.0822058i
$915$	11.6569	0.385364
$916$	13.4558i	0.444594i
$917$	− 60.2843i	− 1.99076i
$918$	− 0.828427i	− 0.0273422i
$919$	8.14214	0.268584	0.134292	−	0.990942i	$-0.457124\pi$
$919$	8.14214	0.268584	0.134292	+	0.990942i	$0.457124\pi$
$920$	− 16.1421i	− 0.532190i
$921$	−7.00000	−0.230658
$922$	−33.7990	−1.11311
$923$	33.7990	1.11251
$924$	10.8284	0.356229
$925$	16.0000i	0.526077i
$926$	62.7696i	2.06274i
$927$	13.6569	0.448550
$928$	0	0
$929$	18.6863	0.613077	0.306539	−	0.951858i	$-0.400829\pi$
$929$	18.6863	0.613077	0.306539	+	0.951858i	$0.400829\pi$
$930$	− 58.6985i	− 1.92480i
$931$	− 6.00000i	− 0.196642i
$932$	−70.1127	−2.29662
$933$	−6.48528	−0.212319
$934$	−92.5980	−3.02990
$935$	0.343146	0.0112221
$936$	47.7990i	1.56236i
$937$	16.6274	0.543194	0.271597	−	0.962411i	$-0.412448\pi$
$937$	16.6274	0.543194	0.271597	+	0.962411i	$0.412448\pi$
$938$	38.6274i	1.26123i
$939$	− 23.7279i	− 0.774331i
$940$	12.4142i	0.404907i
$941$	56.5980	1.84504	0.922521	−	0.385948i	$-0.126125\pi$
$941$	56.5980	1.84504	0.922521	+	0.385948i	$0.126125\pi$
$942$	49.4558i	1.61136i
$943$	− 16.4020i	− 0.534123i
$944$	−10.9706	−0.357061
$945$	1.17157i	0.0381113i
$946$	3.58579i	0.116584i
$947$	− 2.61522i	− 0.0849834i	−0.999097	−	0.0424917i	$-0.986470\pi$
$947$	− 2.61522i	− 0.0849834i	0.999097	−	0.0424917i	$-0.0135296\pi$
$948$	−22.3137	−0.724716
$949$	15.3137i	0.497104i
$950$	−57.9411	−1.87986
$951$	−75.9411	−2.46256
$952$	10.3431	0.335223
$953$	−35.6274	−1.15409	−0.577043	−	0.816714i	$-0.695793\pi$
$953$	−35.6274	−1.15409	−0.577043	+	0.816714i	$0.695793\pi$
$954$	− 64.7696i	− 2.09699i
$955$	− 25.3137i	− 0.819132i
$956$	75.2548	2.43392
$957$	0	0
$958$	−16.6569	−0.538159
$959$	33.9411i	1.09602i
$960$	− 23.7279i	− 0.765815i
$961$	−70.4264	−2.27182
$962$	36.9706	1.19198
$963$	41.9411	1.35153
$964$	−70.1127	−2.25818
$965$	5.17157i	0.166479i
$966$	−60.2843	−1.93961
$967$	− 35.2426i	− 1.13333i	−0.823949	−	0.566663i	$-0.808234\pi$
$967$	− 35.2426i	− 1.13333i	0.823949	−	0.566663i	$-0.191766\pi$
$968$	− 47.7990i	− 1.53632i
$969$	12.0000i	0.385496i
$970$	−10.8284	−0.347680
$971$	15.6569i	0.502452i	0.967928	+	0.251226i	$0.0808338\pi$
$971$	15.6569i	0.502452i	−0.967928	+	0.251226i	$0.919166\pi$
$972$	− 82.9117i	− 2.65939i
$973$	−39.5980	−1.26945
$974$	− 27.7990i	− 0.890737i
$975$	36.9706i	1.18401i
$976$	14.4853i	0.463663i
$977$	36.1716	1.15723	0.578616	−	0.815600i	$-0.303593\pi$
$977$	36.1716	1.15723	0.578616	+	0.815600i	$0.303593\pi$
$978$	22.8995i	0.732245i
$979$	−5.17157	−0.165284
$980$	−3.82843	−0.122295
$981$	35.7990	1.14297
$982$	51.2843	1.63655
$983$	− 21.8701i	− 0.697547i	−0.937207	−	0.348773i	$-0.886598\pi$
$983$	− 21.8701i	− 0.697547i	0.937207	−	0.348773i	$-0.113402\pi$
$984$	47.7990i	1.52378i
$985$	2.00000	0.0637253
$986$	0	0
$987$	22.1421	0.704792
$988$	87.9411i	2.79778i
$989$	− 13.1127i	− 0.416960i
$990$	2.82843	0.0898933
$991$	12.8284	0.407508	0.203754	−	0.979022i	$-0.434686\pi$
$991$	12.8284	0.407508	0.203754	+	0.979022i	$0.434686\pi$
$992$	−15.9706	−0.507066
$993$	−5.82843	−0.184960
$994$	− 60.2843i	− 1.91210i
$995$	−0.485281	−0.0153845
$996$	70.7696i	2.24242i
$997$	− 28.2843i	− 0.895772i	−0.894091	−	0.447886i	$-0.852177\pi$
$997$	− 28.2843i	− 0.895772i	0.894091	−	0.447886i	$-0.147823\pi$
$998$	− 45.7990i	− 1.44974i
$999$	−1.65685	−0.0524205

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.b.a.840.4		4
29.2	odd	28		841.2.d.f.605.1		12
29.3	odd	28		841.2.d.f.571.1		12
29.4	even	14		841.2.e.k.651.1		24
29.5	even	14		841.2.e.k.236.4		24
29.6	even	14		841.2.e.k.196.1		24
29.7	even	7		841.2.e.k.270.1		24
29.8	odd	28		841.2.d.j.574.1		12
29.9	even	14		841.2.e.k.267.1		24
29.10	odd	28		841.2.d.j.190.2		12
29.11	odd	28		841.2.d.f.778.2		12
29.12	odd	4		29.2.a.a.1.1	✓	2
29.13	even	14		841.2.e.k.63.4		24
29.14	odd	28		841.2.d.f.645.1		12
29.15	odd	28		841.2.d.j.645.2		12
29.16	even	7		841.2.e.k.63.1		24
29.17	odd	4		841.2.a.d.1.2		2
29.18	odd	28		841.2.d.j.778.1		12
29.19	odd	28		841.2.d.f.190.1		12
29.20	even	7		841.2.e.k.267.4		24
29.21	odd	28		841.2.d.f.574.2		12
29.22	even	14		841.2.e.k.270.4		24
29.23	even	7		841.2.e.k.196.4		24
29.24	even	7		841.2.e.k.236.1		24
29.25	even	7		841.2.e.k.651.4		24
29.26	odd	28		841.2.d.j.571.2		12
29.27	odd	28		841.2.d.j.605.2		12
29.28	even	2	inner	841.2.b.a.840.1		4
87.17	even	4		7569.2.a.c.1.1		2
87.41	even	4		261.2.a.d.1.2		2
116.99	even	4		464.2.a.h.1.1		2
145.12	even	4		725.2.b.b.349.1		4
145.99	odd	4		725.2.a.b.1.2		2
145.128	even	4		725.2.b.b.349.4		4
203.41	even	4		1421.2.a.j.1.1		2
232.99	even	4		1856.2.a.w.1.2		2
232.157	odd	4		1856.2.a.r.1.1		2
319.186	even	4		3509.2.a.j.1.2		2
348.215	odd	4		4176.2.a.bq.1.2		2
377.12	odd	4		4901.2.a.g.1.2		2
435.389	even	4		6525.2.a.o.1.1		2
493.186	odd	4		8381.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.1	✓	2	29.12	odd	4
261.2.a.d.1.2		2	87.41	even	4
464.2.a.h.1.1		2	116.99	even	4
725.2.a.b.1.2		2	145.99	odd	4
725.2.b.b.349.1		4	145.12	even	4
725.2.b.b.349.4		4	145.128	even	4
841.2.a.d.1.2		2	29.17	odd	4
841.2.b.a.840.1		4	29.28	even	2	inner
841.2.b.a.840.4		4	1.1	even	1	trivial
841.2.d.f.190.1		12	29.19	odd	28
841.2.d.f.571.1		12	29.3	odd	28
841.2.d.f.574.2		12	29.21	odd	28
841.2.d.f.605.1		12	29.2	odd	28
841.2.d.f.645.1		12	29.14	odd	28
841.2.d.f.778.2		12	29.11	odd	28
841.2.d.j.190.2		12	29.10	odd	28
841.2.d.j.571.2		12	29.26	odd	28
841.2.d.j.574.1		12	29.8	odd	28
841.2.d.j.605.2		12	29.27	odd	28
841.2.d.j.645.2		12	29.15	odd	28
841.2.d.j.778.1		12	29.18	odd	28
841.2.e.k.63.1		24	29.16	even	7
841.2.e.k.63.4		24	29.13	even	14
841.2.e.k.196.1		24	29.6	even	14
841.2.e.k.196.4		24	29.23	even	7
841.2.e.k.236.1		24	29.24	even	7
841.2.e.k.236.4		24	29.5	even	14
841.2.e.k.267.1		24	29.9	even	14
841.2.e.k.267.4		24	29.20	even	7
841.2.e.k.270.1		24	29.7	even	7
841.2.e.k.270.4		24	29.22	even	14
841.2.e.k.651.1		24	29.4	even	14
841.2.e.k.651.4		24	29.25	even	7
1421.2.a.j.1.1		2	203.41	even	4
1856.2.a.r.1.1		2	232.157	odd	4
1856.2.a.w.1.2		2	232.99	even	4
3509.2.a.j.1.2		2	319.186	even	4
4176.2.a.bq.1.2		2	348.215	odd	4
4901.2.a.g.1.2		2	377.12	odd	4
6525.2.a.o.1.1		2	435.389	even	4
7569.2.a.c.1.1		2	87.17	even	4
8381.2.a.e.1.1		2	493.186	odd	4

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.41421i q^{2} -2.41421i q^{3} -3.82843 q^{4} +1.00000 q^{5} +5.82843 q^{6} -2.82843 q^{7} -4.41421i q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q+2.41421i q^{2} -2.41421i q^{3} -3.82843 q^{4} +1.00000 q^{5} +5.82843 q^{6} -2.82843 q^{7} -4.41421i q^{8} -2.82843 q^{9} +2.41421i q^{10} +0.414214i q^{11} +9.24264i q^{12} +3.82843 q^{13} -6.82843i q^{14} -2.41421i q^{15} +3.00000 q^{16} -0.828427i q^{17} -6.82843i q^{18} -6.00000i q^{19} -3.82843 q^{20} +6.82843i q^{21} -1.00000 q^{22} +3.65685 q^{23} -10.6569 q^{24} -4.00000 q^{25} +9.24264i q^{26} -0.414214i q^{27} +10.8284 q^{28} +5.82843 q^{30} -10.0711i q^{31} -1.58579i q^{32} +1.00000 q^{33} +2.00000 q^{34} -2.82843 q^{35} +10.8284 q^{36} -4.00000i q^{37} +14.4853 q^{38} -9.24264i q^{39} -4.41421i q^{40} -4.48528i q^{41} -16.4853 q^{42} -3.58579i q^{43} -1.58579i q^{44} -2.82843 q^{45} +8.82843i q^{46} -3.24264i q^{47} -7.24264i q^{48} +1.00000 q^{49} -9.65685i q^{50} -2.00000 q^{51} -14.6569 q^{52} +9.48528 q^{53} +1.00000 q^{54} +0.414214i q^{55} +12.4853i q^{56} -14.4853 q^{57} -3.65685 q^{59} +9.24264i q^{60} +4.82843i q^{61} +24.3137 q^{62} +8.00000 q^{63} +9.82843 q^{64} +3.82843 q^{65} +2.41421i q^{66} -5.65685 q^{67} +3.17157i q^{68} -8.82843i q^{69} -6.82843i q^{70} +8.82843 q^{71} +12.4853i q^{72} +4.00000i q^{73} +9.65685 q^{74} +9.65685i q^{75} +22.9706i q^{76} -1.17157i q^{77} +22.3137 q^{78} +2.41421i q^{79} +3.00000 q^{80} -9.48528 q^{81} +10.8284 q^{82} +7.65685 q^{83} -26.1421i q^{84} -0.828427i q^{85} +8.65685 q^{86} +1.82843 q^{88} +12.4853i q^{89} -6.82843i q^{90} -10.8284 q^{91} -14.0000 q^{92} -24.3137 q^{93} +7.82843 q^{94} -6.00000i q^{95} -3.82843 q^{96} +4.48528i q^{97} +2.41421i q^{98} -1.17157i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{5} + 12 q^{6}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^5 + 12 * q^6	\( 4 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 4 q^{13} + 12 q^{16} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{24} - 16 q^{25} + 32 q^{28} + 12 q^{30} + 4 q^{33} + 8 q^{34} + 32 q^{36} + 24 q^{38} - 32 q^{42} + 4 q^{49} - 8 q^{51} - 36 q^{52} + 4 q^{53} + 4 q^{54} - 24 q^{57} + 8 q^{59} + 52 q^{62} + 32 q^{63} + 28 q^{64} + 4 q^{65} + 24 q^{71} + 16 q^{74} + 44 q^{78} + 12 q^{80} - 4 q^{81} + 32 q^{82} + 8 q^{83} + 12 q^{86} - 4 q^{88} - 32 q^{91} - 56 q^{92} - 52 q^{93} + 20 q^{94} - 4 q^{96}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 4 * q^13 + 12 * q^16 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^24 - 16 * q^25 + 32 * q^28 + 12 * q^30 + 4 * q^33 + 8 * q^34 + 32 * q^36 + 24 * q^38 - 32 * q^42 + 4 * q^49 - 8 * q^51 - 36 * q^52 + 4 * q^53 + 4 * q^54 - 24 * q^57 + 8 * q^59 + 52 * q^62 + 32 * q^63 + 28 * q^64 + 4 * q^65 + 24 * q^71 + 16 * q^74 + 44 * q^78 + 12 * q^80 - 4 * q^81 + 32 * q^82 + 8 * q^83 + 12 * q^86 - 4 * q^88 - 32 * q^91 - 56 * q^92 - 52 * q^93 + 20 * q^94 - 4 * q^96

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