LMFDB - Embedded newform 841.2.b.d.840.10

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 150x^{8} + 523x^{6} + 835x^{4} + 495x^{2} + 81 $ x^12 + 20x^10 + 150x^8 + 523x^6 + 835x^4 + 495*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			840.10
Root			$1.94573i$ of defining polynomial
Character	$\chi$	$=$	841.840
Dual form			841.2.b.d.840.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.94573i q^{2} +2.27154i q^{3} -1.78585 q^{4} -3.21726 q^{5} -4.41979 q^{6} -2.53022 q^{7} +0.416673i q^{8} -2.15987 q^{9} -6.25991i q^{10} +1.12328i q^{11} -4.05663i q^{12} +1.54902 q^{13} -4.92311i q^{14} -7.30813i q^{15} -4.38244 q^{16} -4.41979i q^{17} -4.20253i q^{18} +4.91337i q^{19} +5.74556 q^{20} -5.74748i q^{21} -2.18560 q^{22} +2.47406 q^{23} -0.946487 q^{24} +5.35078 q^{25} +3.01398i q^{26} +1.90838i q^{27} +4.51860 q^{28} +14.2196 q^{30} -1.58761i q^{31} -7.69368i q^{32} -2.55158 q^{33} +8.59970 q^{34} +8.14037 q^{35} +3.85722 q^{36} +8.28372i q^{37} -9.56008 q^{38} +3.51866i q^{39} -1.34055i q^{40} -11.7882i q^{41} +11.1830 q^{42} -1.88390i q^{43} -2.00602i q^{44} +6.94888 q^{45} +4.81385i q^{46} -0.962649i q^{47} -9.95486i q^{48} -0.597997 q^{49} +10.4111i q^{50} +10.0397 q^{51} -2.76633 q^{52} +1.61810 q^{53} -3.71318 q^{54} -3.61390i q^{55} -1.05427i q^{56} -11.1609 q^{57} -13.3686 q^{59} +13.0512i q^{60} +1.92241i q^{61} +3.08905 q^{62} +5.46495 q^{63} +6.20492 q^{64} -4.98362 q^{65} -4.96468i q^{66} +3.02385 q^{67} +7.89309i q^{68} +5.61992i q^{69} +15.8389i q^{70} -4.14265 q^{71} -0.899961i q^{72} -3.79682i q^{73} -16.1178 q^{74} +12.1545i q^{75} -8.77456i q^{76} -2.84215i q^{77} -6.84635 q^{78} +13.2356i q^{79} +14.0994 q^{80} -10.8146 q^{81} +22.9366 q^{82} -9.70833 q^{83} +10.2642i q^{84} +14.2196i q^{85} +3.66555 q^{86} -0.468042 q^{88} -4.87979i q^{89} +13.5206i q^{90} -3.91937 q^{91} -4.41831 q^{92} +3.60630 q^{93} +1.87305 q^{94} -15.8076i q^{95} +17.4765 q^{96} -15.6150i q^{97} -1.16354i q^{98} -2.42615i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{4} + 4 q^{5} + 6 q^{6} - 8 q^{7} - 12 q^{9} + 12 q^{13} + 8 q^{16} - 10 q^{20} + 8 q^{22} - 10 q^{23} - 20 q^{24} + 12 q^{25} + 10 q^{28} + 52 q^{30} - 54 q^{33} + 8 q^{35} - 42 q^{36} - 82 q^{38}+ \cdots + 74 q^{96}+O(q^{100}) $ 12 * q - 16 * q^4 + 4 * q^5 + 6 * q^6 - 8 * q^7 - 12 * q^9 + 12 * q^13 + 8 * q^16 - 10 * q^20 + 8 * q^22 - 10 * q^23 - 20 * q^24 + 12 * q^25 + 10 * q^28 + 52 * q^30 - 54 * q^33 + 8 * q^35 - 42 * q^36 - 82 * q^38 + 42 * q^42 + 32 * q^45 - 24 * q^49 + 46 * q^51 - 26 * q^53 + 38 * q^54 + 32 * q^57 - 34 * q^59 + 18 * q^63 - 2 * q^64 + 64 * q^65 + 18 * q^67 - 72 * q^74 - 10 * q^80 - 44 * q^81 + 38 * q^82 - 48 * q^83 - 34 * q^86 + 42 * q^88 - 32 * q^91 + 46 * q^92 + 24 * q^93 - 74 * q^94 + 74 * q^96

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 $

$2$	1.94573i	1.37584i	0.725788	+	0.687918i	$0.241475\pi$
$2$	1.94573i	1.37584i	−0.725788	+	0.687918i	$0.758525\pi$
$3$	2.27154i	1.31147i	0.754990	+	0.655736i	$0.227642\pi$
$3$	2.27154i	1.31147i	−0.754990	+	0.655736i	$0.772358\pi$
$4$	−1.78585	−0.892926
$5$	−3.21726	−1.43880	−0.719402	−	0.694594i	$-0.755584\pi$
$5$	−3.21726	−1.43880	−0.719402	+	0.694594i	$0.755584\pi$
$6$	−4.41979	−1.80437
$7$	−2.53022	−0.956332	−0.478166	−	0.878269i	$-0.658698\pi$
$7$	−2.53022	−0.956332	−0.478166	+	0.878269i	$0.658698\pi$
$8$	0.416673i	0.147316i
$9$	−2.15987	−0.719958
$10$	− 6.25991i	− 1.97956i
$11$	1.12328i	0.338683i	0.985557	+	0.169341i	$0.0541641\pi$
$11$	1.12328i	0.338683i	−0.985557	+	0.169341i	$0.945836\pi$
$12$	− 4.05663i	− 1.17105i
$13$	1.54902	0.429622	0.214811	−	0.976656i	$-0.431086\pi$
$13$	1.54902	0.429622	0.214811	+	0.976656i	$0.431086\pi$
$14$	− 4.92311i	− 1.31576i
$15$	− 7.30813i	− 1.88695i
$16$	−4.38244	−1.09561
$17$	− 4.41979i	− 1.07196i	−0.844232	−	0.535978i	$-0.819943\pi$
$17$	− 4.41979i	− 1.07196i	0.844232	−	0.535978i	$-0.180057\pi$
$18$	− 4.20253i	− 0.990545i
$19$	4.91337i	1.12721i	0.826046	+	0.563603i	$0.190585\pi$
$19$	4.91337i	1.12721i	−0.826046	+	0.563603i	$0.809415\pi$
$20$	5.74556	1.28475
$21$	− 5.74748i	− 1.25420i
$22$	−2.18560	−0.465972
$23$	2.47406	0.515877	0.257939	−	0.966161i	$-0.416957\pi$
$23$	2.47406	0.515877	0.257939	+	0.966161i	$0.416957\pi$
$24$	−0.946487	−0.193201
$25$	5.35078	1.07016
$26$	3.01398i	0.591089i
$27$	1.90838i	0.367267i
$28$	4.51860	0.853934
$29$	0	0
$29$	0	0
$30$	14.2196	2.59613
$31$	− 1.58761i	− 0.285142i	−0.989785	−	0.142571i	$-0.954463\pi$
$31$	− 1.58761i	− 0.285142i	0.989785	−	0.142571i	$-0.0455370\pi$
$32$	− 7.69368i	− 1.36006i
$33$	−2.55158	−0.444173
$34$	8.59970	1.47484
$35$	8.14037	1.37597
$36$	3.85722	0.642869
$37$	8.28372i	1.36183i	0.732360	+	0.680917i	$0.238419\pi$
$37$	8.28372i	1.36183i	−0.732360	+	0.680917i	$0.761581\pi$
$38$	−9.56008	−1.55085
$39$	3.51866i	0.563437i
$40$	− 1.34055i	− 0.211959i
$41$	− 11.7882i	− 1.84101i	−0.390733	−	0.920504i	$-0.627778\pi$
$41$	− 11.7882i	− 1.84101i	0.390733	−	0.920504i	$-0.372222\pi$
$42$	11.1830	1.72558
$43$	− 1.88390i	− 0.287292i	−0.989629	−	0.143646i	$-0.954117\pi$
$43$	− 1.88390i	− 0.287292i	0.989629	−	0.143646i	$-0.0458827\pi$
$44$	− 2.00602i	− 0.302419i
$45$	6.94888	1.03588
$46$	4.81385i	0.709763i
$47$	− 0.962649i	− 0.140417i	−0.997532	−	0.0702084i	$-0.977634\pi$
$47$	− 0.962649i	− 0.140417i	0.997532	−	0.0702084i	$-0.0223664\pi$
$48$	− 9.95486i	− 1.43686i
$49$	−0.597997	−0.0854282
$50$	10.4111i	1.47236i
$51$	10.0397	1.40584
$52$	−2.76633	−0.383621
$53$	1.61810	0.222263	0.111132	−	0.993806i	$-0.464552\pi$
$53$	1.61810	0.222263	0.111132	+	0.993806i	$0.464552\pi$
$54$	−3.71318	−0.505299
$55$	− 3.61390i	− 0.487298i
$56$	− 1.05427i	− 0.140883i
$57$	−11.1609	−1.47830
$58$	0	0
$59$	−13.3686	−1.74045	−0.870224	−	0.492657i	$-0.836026\pi$
$59$	−13.3686	−1.74045	−0.870224	+	0.492657i	$0.836026\pi$
$60$	13.0512i	1.68491i
$61$	1.92241i	0.246140i	0.992398	+	0.123070i	$0.0392740\pi$
$61$	1.92241i	0.246140i	−0.992398	+	0.123070i	$0.960726\pi$
$62$	3.08905	0.392309
$63$	5.46495	0.688519
$64$	6.20492	0.775615
$65$	−4.98362	−0.618141
$66$	− 4.96468i	− 0.611109i
$67$	3.02385	0.369421	0.184711	−	0.982793i	$-0.440865\pi$
$67$	3.02385	0.369421	0.184711	+	0.982793i	$0.440865\pi$
$68$	7.89309i	0.957177i
$69$	5.61992i	0.676559i
$70$	15.8389i	1.89312i
$71$	−4.14265	−0.491642	−0.245821	−	0.969315i	$-0.579058\pi$
$71$	−4.14265	−0.491642	−0.245821	+	0.969315i	$0.579058\pi$
$72$	− 0.899961i	− 0.106061i
$73$	− 3.79682i	− 0.444384i	−0.975003	−	0.222192i	$-0.928679\pi$
$73$	− 3.79682i	− 0.444384i	0.975003	−	0.222192i	$-0.0713212\pi$
$74$	−16.1178	−1.87366
$75$	12.1545i	1.40348i
$76$	− 8.77456i	− 1.00651i
$77$	− 2.84215i	− 0.323893i
$78$	−6.84635	−0.775197
$79$	13.2356i	1.48913i	0.667552	+	0.744563i	$0.267342\pi$
$79$	13.2356i	1.48913i	−0.667552	+	0.744563i	$0.732658\pi$
$80$	14.0994	1.57637
$81$	−10.8146	−1.20162
$82$	22.9366	2.53293
$83$	−9.70833	−1.06563	−0.532814	−	0.846232i	$-0.678865\pi$
$83$	−9.70833	−1.06563	−0.532814	+	0.846232i	$0.678865\pi$
$84$	10.2642i	1.11991i
$85$	14.2196i	1.54233i
$86$	3.66555	0.395267
$87$	0	0
$88$	−0.468042	−0.0498934
$89$	− 4.87979i	− 0.517257i	−0.965977	−	0.258628i	$-0.916730\pi$
$89$	− 4.87979i	− 0.517257i	0.965977	−	0.258628i	$-0.0832705\pi$
$90$	13.5206i	1.42520i
$91$	−3.91937	−0.410861
$92$	−4.41831	−0.460640
$93$	3.60630	0.373956
$94$	1.87305	0.193190
$95$	− 15.8076i	− 1.62183i
$96$	17.4765	1.78368
$97$	− 15.6150i	− 1.58546i	−0.609571	−	0.792731i	$-0.708658\pi$
$97$	− 15.6150i	− 1.58546i	0.609571	−	0.792731i	$-0.291342\pi$
$98$	− 1.16354i	− 0.117535i
$99$	− 2.42615i	− 0.243837i
$100$	−9.55570	−0.955570
$101$	11.3941i	1.13376i	0.823800	+	0.566880i	$0.191850\pi$
$101$	11.3941i	1.13376i	−0.823800	+	0.566880i	$0.808150\pi$
$102$	19.5345i	1.93421i
$103$	7.38911	0.728070	0.364035	−	0.931385i	$-0.381399\pi$
$103$	7.38911	0.728070	0.364035	+	0.931385i	$0.381399\pi$
$104$	0.645436i	0.0632902i
$105$	18.4912i	1.80455i
$106$	3.14838i	0.305798i
$107$	−11.9202	−1.15237	−0.576183	−	0.817321i	$-0.695458\pi$
$107$	−11.9202	−1.15237	−0.576183	+	0.817321i	$0.695458\pi$
$108$	− 3.40808i	− 0.327942i
$109$	−16.1719	−1.54898	−0.774492	−	0.632583i	$-0.781995\pi$
$109$	−16.1719	−1.54898	−0.774492	+	0.632583i	$0.781995\pi$
$110$	7.03166	0.670442
$111$	−18.8168	−1.78601
$112$	11.0885	1.04777
$113$	− 6.34816i	− 0.597184i	−0.954381	−	0.298592i	$-0.903483\pi$
$113$	− 6.34816i	− 0.597184i	0.954381	−	0.298592i	$-0.0965171\pi$
$114$	− 21.7161i	− 2.03390i
$115$	−7.95970	−0.742246
$116$	0	0
$117$	−3.34570	−0.309310
$118$	− 26.0117i	− 2.39457i
$119$	11.1830i	1.02515i
$120$	3.04510	0.277978
$121$	9.73823	0.885294
$122$	−3.74049	−0.338648
$123$	26.7773	2.41443
$124$	2.83523i	0.254611i
$125$	−1.12854	−0.100940
$126$	10.6333i	0.947290i
$127$	17.8415i	1.58318i	0.611053	+	0.791590i	$0.290746\pi$
$127$	17.8415i	1.58318i	−0.611053	+	0.791590i	$0.709254\pi$
$128$	− 3.31428i	− 0.292943i
$129$	4.27934	0.376775
$130$	− 9.69675i	− 0.850461i
$131$	0.574730i	0.0502144i	0.999685	+	0.0251072i	$0.00799272\pi$
$131$	0.574730i	0.0502144i	−0.999685	+	0.0251072i	$0.992007\pi$
$132$	4.55674	0.396614
$133$	− 12.4319i	− 1.07798i
$134$	5.88358i	0.508264i
$135$	− 6.13974i	− 0.528425i
$136$	1.84161	0.157916
$137$	− 13.7829i	− 1.17755i	−0.808297	−	0.588774i	$-0.799611\pi$
$137$	− 13.7829i	− 1.17755i	0.808297	−	0.588774i	$-0.200389\pi$
$138$	−10.9348	−0.930834
$139$	10.6013	0.899192	0.449596	−	0.893232i	$-0.351568\pi$
$139$	10.6013	0.899192	0.449596	+	0.893232i	$0.351568\pi$
$140$	−14.5375	−1.22864
$141$	2.18669	0.184153
$142$	− 8.06046i	− 0.676419i
$143$	1.73999i	0.145506i
$144$	9.46551	0.788793
$145$	0	0
$146$	7.38758	0.611400
$147$	− 1.35837i	− 0.112037i
$148$	− 14.7935i	− 1.21602i
$149$	−2.36656	−0.193876	−0.0969381	−	0.995290i	$-0.530905\pi$
$149$	−2.36656	−0.193876	−0.0969381	+	0.995290i	$0.530905\pi$
$150$	−23.6493	−1.93096
$151$	−9.74934	−0.793390	−0.396695	−	0.917950i	$-0.629843\pi$
$151$	−9.74934	−0.793390	−0.396695	+	0.917950i	$0.629843\pi$
$152$	−2.04727	−0.166056
$153$	9.54619i	0.771763i
$154$	5.53005	0.445624
$155$	5.10774i	0.410264i
$156$	− 6.28381i	− 0.503108i
$157$	18.7547i	1.49679i	0.663252	+	0.748396i	$0.269176\pi$
$157$	18.7547i	1.49679i	−0.663252	+	0.748396i	$0.730824\pi$
$158$	−25.7530	−2.04879
$159$	3.67557i	0.291492i
$160$	24.7526i	1.95686i
$161$	−6.25991	−0.493350
$162$	− 21.0422i	− 1.65323i
$163$	− 9.65226i	− 0.756023i	−0.925801	−	0.378012i	$-0.876608\pi$
$163$	− 9.65226i	− 0.756023i	0.925801	−	0.378012i	$-0.123392\pi$
$164$	21.0520i	1.64388i
$165$	8.20910	0.639078
$166$	− 18.8898i	− 1.46613i
$167$	−0.464845	−0.0359708	−0.0179854	−	0.999838i	$-0.505725\pi$
$167$	−0.464845	−0.0359708	−0.0179854	+	0.999838i	$0.505725\pi$
$168$	2.39482	0.184764
$169$	−10.6005	−0.815425
$170$	−27.6675	−2.12200
$171$	− 10.6123i	− 0.811541i
$172$	3.36437i	0.256530i
$173$	22.2914	1.69478	0.847392	−	0.530968i	$-0.178172\pi$
$173$	22.2914	1.69478	0.847392	+	0.530968i	$0.178172\pi$
$174$	0	0
$175$	−13.5386	−1.02342
$176$	− 4.92272i	− 0.371064i
$177$	− 30.3673i	− 2.28255i
$178$	9.49474	0.711661
$179$	−7.50994	−0.561319	−0.280660	−	0.959807i	$-0.590553\pi$
$179$	−7.50994	−0.561319	−0.280660	+	0.959807i	$0.590553\pi$
$180$	−12.4097	−0.924963
$181$	−23.9371	−1.77923	−0.889615	−	0.456711i	$-0.849027\pi$
$181$	−23.9371	−1.77923	−0.889615	+	0.456711i	$0.849027\pi$
$182$	− 7.62602i	− 0.565278i
$183$	−4.36683	−0.322806
$184$	1.03087i	0.0759971i
$185$	− 26.6509i	− 1.95941i
$186$	7.01688i	0.514503i
$187$	4.96468	0.363053
$188$	1.71915i	0.125382i
$189$	− 4.82861i	− 0.351229i
$190$	30.7573	2.23137
$191$	13.4059i	0.970016i	0.874510	+	0.485008i	$0.161183\pi$
$191$	13.4059i	0.970016i	−0.874510	+	0.485008i	$0.838817\pi$
$192$	14.0947i	1.01720i
$193$	12.7705i	0.919243i	0.888115	+	0.459622i	$0.152015\pi$
$193$	12.7705i	0.919243i	−0.888115	+	0.459622i	$0.847985\pi$
$194$	30.3825	2.18134
$195$	− 11.3205i	− 0.810675i
$196$	1.06794	0.0762811
$197$	−4.07710	−0.290481	−0.145241	−	0.989396i	$-0.546396\pi$
$197$	−4.07710	−0.290481	−0.145241	+	0.989396i	$0.546396\pi$
$198$	4.72063	0.335480
$199$	16.9678	1.20282	0.601409	−	0.798941i	$-0.294606\pi$
$199$	16.9678	1.20282	0.601409	+	0.798941i	$0.294606\pi$
$200$	2.22952i	0.157651i
$201$	6.86877i	0.484486i
$202$	−22.1699	−1.55987
$203$	0	0
$204$	−17.9294	−1.25531
$205$	37.9258i	2.64885i
$206$	14.3772i	1.00171i
$207$	−5.34366	−0.371410
$208$	−6.78850	−0.470698
$209$	−5.51911	−0.381765
$210$	−35.9787	−2.48277
$211$	− 4.41621i	− 0.304024i	−0.988379	−	0.152012i	$-0.951425\pi$
$211$	− 4.41621i	− 0.304024i	0.988379	−	0.152012i	$-0.0485753\pi$
$212$	−2.88969	−0.198465
$213$	− 9.41017i	− 0.644774i
$214$	− 23.1934i	− 1.58547i
$215$	6.06100i	0.413357i
$216$	−0.795168	−0.0541044
$217$	4.01699i	0.272691i
$218$	− 31.4660i	− 2.13115i
$219$	8.62462	0.582798
$220$	6.45389i	0.435121i
$221$	− 6.84635i	− 0.460536i
$222$	− 36.6123i	− 2.45725i
$223$	−17.0683	−1.14298	−0.571488	−	0.820611i	$-0.693634\pi$
$223$	−17.0683	−1.14298	−0.571488	+	0.820611i	$0.693634\pi$
$224$	19.4667i	1.30067i
$225$	−11.5570	−0.770467
$226$	12.3518	0.821628
$227$	−9.78008	−0.649127	−0.324563	−	0.945864i	$-0.605217\pi$
$227$	−9.78008	−0.649127	−0.324563	+	0.945864i	$0.605217\pi$
$228$	19.9317	1.32001
$229$	3.43919i	0.227268i	0.993523	+	0.113634i	$0.0362492\pi$
$229$	3.43919i	0.227268i	−0.993523	+	0.113634i	$0.963751\pi$
$230$	− 15.4874i	− 1.02121i
$231$	6.45605	0.424777
$232$	0	0
$233$	−4.39157	−0.287702	−0.143851	−	0.989599i	$-0.545949\pi$
$233$	−4.39157	−0.287702	−0.143851	+	0.989599i	$0.545949\pi$
$234$	− 6.50981i	− 0.425560i
$235$	3.09709i	0.202032i
$236$	23.8744	1.55409
$237$	−30.0652	−1.95295
$238$	−21.7591	−1.41043
$239$	17.6803	1.14364	0.571821	−	0.820378i	$-0.306237\pi$
$239$	17.6803	1.14364	0.571821	+	0.820378i	$0.306237\pi$
$240$	32.0274i	2.06736i
$241$	−11.4068	−0.734778	−0.367389	−	0.930067i	$-0.619748\pi$
$241$	−11.4068	−0.734778	−0.367389	+	0.930067i	$0.619748\pi$
$242$	18.9479i	1.21802i
$243$	− 18.8405i	− 1.20862i
$244$	− 3.43315i	− 0.219785i
$245$	1.92391	0.122914
$246$	52.1014i	3.32186i
$247$	7.61093i	0.484272i
$248$	0.661512	0.0420061
$249$	− 22.0528i	− 1.39754i
$250$	− 2.19583i	− 0.138877i
$251$	25.5356i	1.61179i	0.592056	+	0.805897i	$0.298317\pi$
$251$	25.5356i	1.61179i	−0.592056	+	0.805897i	$0.701683\pi$
$252$	−9.75960	−0.614797
$253$	2.77907i	0.174719i
$254$	−34.7147	−2.17820
$255$	−32.3004	−2.02273
$256$	18.8585	1.17866
$257$	0.178617	0.0111418	0.00557091	−	0.999984i	$-0.498227\pi$
$257$	0.178617	0.0111418	0.00557091	+	0.999984i	$0.498227\pi$
$258$	8.32643i	0.518381i
$259$	− 20.9596i	− 1.30237i
$260$	8.90000	0.551955
$261$	0	0
$262$	−1.11827	−0.0690869
$263$	5.63230i	0.347303i	0.984807	+	0.173651i	$0.0555566\pi$
$263$	5.63230i	0.347303i	−0.984807	+	0.173651i	$0.944443\pi$
$264$	− 1.06317i	− 0.0654338i
$265$	−5.20585	−0.319793
$266$	24.1891	1.48313
$267$	11.0846	0.678367
$268$	−5.40014	−0.329866
$269$	1.94833i	0.118792i	0.998235	+	0.0593958i	$0.0189174\pi$
$269$	1.94833i	0.118792i	−0.998235	+	0.0593958i	$0.981083\pi$
$270$	11.9463	0.727026
$271$	17.4418i	1.05951i	0.848150	+	0.529756i	$0.177716\pi$
$271$	17.4418i	1.05951i	−0.848150	+	0.529756i	$0.822284\pi$
$272$	19.3694i	1.17444i
$273$	− 8.90298i	− 0.538833i
$274$	26.8177	1.62011
$275$	6.01044i	0.362443i
$276$	− 10.0363i	− 0.604117i
$277$	−15.3445	−0.921964	−0.460982	−	0.887409i	$-0.652503\pi$
$277$	−15.3445	−0.921964	−0.460982	+	0.887409i	$0.652503\pi$
$278$	20.6273i	1.23714i
$279$	3.42903i	0.205291i
$280$	3.39187i	0.202703i
$281$	−13.2112	−0.788114	−0.394057	−	0.919086i	$-0.628929\pi$
$281$	−13.2112	−0.788114	−0.394057	+	0.919086i	$0.628929\pi$
$282$	4.25470i	0.253364i
$283$	11.1563	0.663170	0.331585	−	0.943425i	$-0.392417\pi$
$283$	11.1563	0.663170	0.331585	+	0.943425i	$0.392417\pi$
$284$	7.39816	0.439000
$285$	35.9076	2.12698
$286$	−3.38555	−0.200192
$287$	29.8267i	1.76062i
$288$	16.6174i	0.979188i
$289$	−2.53452	−0.149090
$290$	0	0
$291$	35.4700	2.07929
$292$	6.78056i	0.396802i
$293$	− 6.80277i	− 0.397422i	−0.980058	−	0.198711i	$-0.936324\pi$
$293$	− 6.80277i	− 0.397422i	0.980058	−	0.198711i	$-0.0636755\pi$
$294$	2.64302	0.154144
$295$	43.0104	2.50416
$296$	−3.45160	−0.200620
$297$	−2.14365	−0.124387
$298$	− 4.60468i	− 0.266742i
$299$	3.83238	0.221632
$300$	− 21.7061i	− 1.25320i
$301$	4.76668i	0.274747i
$302$	− 18.9695i	− 1.09157i
$303$	−25.8822	−1.48689
$304$	− 21.5325i	− 1.23498i
$305$	− 6.18491i	− 0.354147i
$306$	−18.5743	−1.06182
$307$	− 16.1578i	− 0.922176i	−0.887354	−	0.461088i	$-0.847459\pi$
$307$	− 16.1578i	− 0.922176i	0.887354	−	0.461088i	$-0.152541\pi$
$308$	5.07567i	0.289213i
$309$	16.7846i	0.954844i
$310$	−9.93827	−0.564456
$311$	− 4.33954i	− 0.246073i	−0.992402	−	0.123036i	$-0.960737\pi$
$311$	− 4.33954i	− 0.246073i	0.992402	−	0.123036i	$-0.0392632\pi$
$312$	−1.46613	−0.0830033
$313$	1.07340	0.0606724	0.0303362	−	0.999540i	$-0.490342\pi$
$313$	1.07340	0.0606724	0.0303362	+	0.999540i	$0.490342\pi$
$314$	−36.4916	−2.05934
$315$	−17.5822	−0.990644
$316$	− 23.6369i	− 1.32968i
$317$	− 7.79415i	− 0.437763i	−0.975751	−	0.218882i	$-0.929759\pi$
$317$	− 7.79415i	− 0.437763i	0.975751	−	0.218882i	$-0.0702408\pi$
$318$	−7.15166	−0.401045
$319$	0	0
$320$	−19.9629	−1.11596
$321$	− 27.0771i	− 1.51130i
$322$	− 12.1801i	− 0.678769i
$323$	21.7161	1.20831
$324$	19.3132	1.07296
$325$	8.28848	0.459762
$326$	18.7807	1.04016
$327$	− 36.7350i	− 2.03145i
$328$	4.91183	0.271210
$329$	2.43571i	0.134285i
$330$	15.9727i	0.879266i
$331$	9.95716i	0.547295i	0.961830	+	0.273648i	$0.0882302\pi$
$331$	9.95716i	0.547295i	−0.961830	+	0.273648i	$0.911770\pi$
$332$	17.3377	0.951527
$333$	− 17.8918i	− 0.980464i
$334$	− 0.904461i	− 0.0494899i
$335$	−9.72850	−0.531525
$336$	25.1880i	1.37412i
$337$	21.3599i	1.16355i	0.813350	+	0.581774i	$0.197641\pi$
$337$	21.3599i	1.16355i	−0.813350	+	0.581774i	$0.802359\pi$
$338$	− 20.6257i	− 1.12189i
$339$	14.4201	0.783191
$340$	− 25.3941i	− 1.37719i
$341$	1.78333	0.0965728
$342$	20.6486	1.11655
$343$	19.2246	1.03803
$344$	0.784970	0.0423227
$345$	− 18.0807i	− 0.973435i
$346$	43.3730i	2.33174i
$347$	−26.9149	−1.44487	−0.722434	−	0.691440i	$-0.756977\pi$
$347$	−26.9149	−1.44487	−0.722434	+	0.691440i	$0.756977\pi$
$348$	0	0
$349$	18.7783	1.00518	0.502591	−	0.864524i	$-0.332380\pi$
$349$	18.7783	1.00518	0.502591	+	0.864524i	$0.332380\pi$
$350$	− 26.3425i	− 1.40806i
$351$	2.95612i	0.157786i
$352$	8.64218	0.460630
$353$	−29.5764	−1.57419	−0.787095	−	0.616831i	$-0.788416\pi$
$353$	−29.5764	−1.57419	−0.787095	+	0.616831i	$0.788416\pi$
$354$	59.0865	3.14041
$355$	13.3280	0.707376
$356$	8.71458i	0.461872i
$357$	−25.4026	−1.34445
$358$	− 14.6123i	− 0.772283i
$359$	20.2837i	1.07053i	0.844683	+	0.535267i	$0.179789\pi$
$359$	20.2837i	1.07053i	−0.844683	+	0.535267i	$0.820211\pi$
$360$	2.89541i	0.152602i
$361$	−5.14124	−0.270592
$362$	− 46.5750i	− 2.44793i
$363$	22.1207i	1.16104i
$364$	6.99941	0.366869
$365$	12.2154i	0.639382i
$366$	− 8.49667i	− 0.444128i
$367$	− 16.9933i	− 0.887044i	−0.896263	−	0.443522i	$-0.853729\pi$
$367$	− 16.9933i	− 0.887044i	0.896263	−	0.443522i	$-0.146271\pi$
$368$	−10.8424	−0.565200
$369$	25.4610i	1.32545i
$370$	51.8553	2.69583
$371$	−4.09415	−0.212558
$372$	−6.44033	−0.333915
$373$	−10.4156	−0.539300	−0.269650	−	0.962958i	$-0.586908\pi$
$373$	−10.4156	−0.539300	−0.269650	+	0.962958i	$0.586908\pi$
$374$	9.65990i	0.499502i
$375$	− 2.56352i	− 0.132380i
$376$	0.401110	0.0206856
$377$	0	0
$378$	9.39515	0.483234
$379$	22.8981i	1.17619i	0.808790	+	0.588097i	$0.200123\pi$
$379$	22.8981i	1.17619i	−0.808790	+	0.588097i	$0.799877\pi$
$380$	28.2301i	1.44817i
$381$	−40.5277	−2.07630
$382$	−26.0842	−1.33458
$383$	2.90269	0.148320	0.0741602	−	0.997246i	$-0.476372\pi$
$383$	2.90269	0.148320	0.0741602	+	0.997246i	$0.476372\pi$
$384$	7.52849	0.384187
$385$	9.14395i	0.466019i
$386$	−24.8480	−1.26473
$387$	4.06899i	0.206838i
$388$	27.8861i	1.41570i
$389$	3.15385i	0.159907i	0.996799	+	0.0799533i	$0.0254771\pi$
$389$	3.15385i	0.159907i	−0.996799	+	0.0799533i	$0.974523\pi$
$390$	22.0265	1.11536
$391$	− 10.9348i	− 0.552998i
$392$	− 0.249169i	− 0.0125850i
$393$	−1.30552	−0.0658548
$394$	− 7.93292i	− 0.399655i
$395$	− 42.5826i	− 2.14256i
$396$	4.33275i	0.217729i
$397$	21.2009	1.06404	0.532021	−	0.846731i	$-0.321433\pi$
$397$	21.2009	1.06404	0.532021	+	0.846731i	$0.321433\pi$
$398$	33.0148i	1.65488i
$399$	28.2395	1.41374
$400$	−23.4494	−1.17247
$401$	−4.29991	−0.214728	−0.107364	−	0.994220i	$-0.534241\pi$
$401$	−4.29991	−0.214728	−0.107364	+	0.994220i	$0.534241\pi$
$402$	−13.3648	−0.666573
$403$	− 2.45924i	− 0.122503i
$404$	− 20.3483i	− 1.01236i
$405$	34.7933	1.72889
$406$	0	0
$407$	−9.30497	−0.461230
$408$	4.18327i	0.207103i
$409$	25.4982i	1.26081i	0.776268	+	0.630403i	$0.217110\pi$
$409$	25.4982i	1.26081i	−0.776268	+	0.630403i	$0.782890\pi$
$410$	−73.7931	−3.64438
$411$	31.3082	1.54432
$412$	−13.1959	−0.650113
$413$	33.8255	1.66445
$414$	− 10.3973i	− 0.511000i
$415$	31.2343	1.53323
$416$	− 11.9177i	− 0.584313i
$417$	24.0813i	1.17927i
$418$	− 10.7387i	− 0.525246i
$419$	−6.74628	−0.329578	−0.164789	−	0.986329i	$-0.552694\pi$
$419$	−6.74628	−0.329578	−0.164789	+	0.986329i	$0.552694\pi$
$420$	− 33.0225i	− 1.61133i
$421$	34.5466i	1.68370i	0.539713	+	0.841849i	$0.318533\pi$
$421$	34.5466i	1.68370i	−0.539713	+	0.841849i	$0.681467\pi$
$422$	8.59273	0.418288
$423$	2.07920i	0.101094i
$424$	0.674219i	0.0327430i
$425$	− 23.6493i	− 1.14716i
$426$	18.3096	0.887104
$427$	− 4.86413i	− 0.235392i
$428$	21.2877	1.02898
$429$	−3.95246	−0.190826
$430$	−11.7930	−0.568711
$431$	9.87958	0.475882	0.237941	−	0.971280i	$-0.423527\pi$
$431$	9.87958	0.475882	0.237941	+	0.971280i	$0.423527\pi$
$432$	− 8.36333i	− 0.402381i
$433$	− 3.20188i	− 0.153873i	−0.997036	−	0.0769363i	$-0.975486\pi$
$433$	− 3.20188i	− 0.153873i	0.997036	−	0.0769363i	$-0.0245138\pi$
$434$	−7.81596	−0.375178
$435$	0	0
$436$	28.8806	1.38313
$437$	12.1560i	0.581500i
$438$	16.7811i	0.801834i
$439$	−6.41437	−0.306141	−0.153071	−	0.988215i	$-0.548916\pi$
$439$	−6.41437	−0.306141	−0.153071	+	0.988215i	$0.548916\pi$
$440$	1.50581	0.0717869
$441$	1.29160	0.0615047
$442$	13.3211	0.633622
$443$	8.49949i	0.403823i	0.979404	+	0.201911i	$0.0647153\pi$
$443$	8.49949i	0.403823i	−0.979404	+	0.201911i	$0.935285\pi$
$444$	33.6040	1.59477
$445$	15.6996i	0.744231i
$446$	− 33.2102i	− 1.57255i
$447$	− 5.37573i	− 0.254263i
$448$	−15.6998	−0.741746
$449$	16.9423i	0.799555i	0.916612	+	0.399778i	$0.130913\pi$
$449$	16.9423i	0.799555i	−0.916612	+	0.399778i	$0.869087\pi$
$450$	− 22.4868i	− 1.06004i
$451$	13.2415	0.623518
$452$	11.3369i	0.533242i
$453$	− 22.1460i	− 1.04051i
$454$	− 19.0294i	− 0.893092i
$455$	12.6096	0.591149
$456$	− 4.65045i	− 0.217777i
$457$	−0.505911	−0.0236655	−0.0118328	−	0.999930i	$-0.503767\pi$
$457$	−0.505911	−0.0236655	−0.0118328	+	0.999930i	$0.503767\pi$
$458$	−6.69173	−0.312684
$459$	8.43461	0.393694
$460$	14.2149	0.662771
$461$	− 5.50088i	− 0.256201i	−0.991761	−	0.128101i	$-0.959112\pi$
$461$	− 5.50088i	− 0.256201i	0.991761	−	0.128101i	$-0.0408881\pi$
$462$	12.5617i	0.584424i
$463$	6.56599	0.305148	0.152574	−	0.988292i	$-0.451244\pi$
$463$	6.56599	0.305148	0.152574	+	0.988292i	$0.451244\pi$
$464$	0	0
$465$	−11.6024	−0.538050
$466$	− 8.54480i	− 0.395830i
$467$	− 4.47819i	− 0.207226i	−0.994618	−	0.103613i	$-0.966960\pi$
$467$	− 4.47819i	− 0.207226i	0.994618	−	0.103613i	$-0.0330403\pi$
$468$	5.97492	0.276191
$469$	−7.65099	−0.353290
$470$	−6.02610	−0.277963
$471$	−42.6021	−1.96300
$472$	− 5.57035i	− 0.256396i
$473$	2.11615	0.0973008
$474$	− 58.4988i	− 2.68694i
$475$	26.2904i	1.20628i
$476$	− 19.9712i	− 0.915380i
$477$	−3.49489	−0.160020
$478$	34.4010i	1.57347i
$479$	− 9.27693i	− 0.423874i	−0.977283	−	0.211937i	$-0.932023\pi$
$479$	− 9.27693i	− 0.423874i	0.977283	−	0.211937i	$-0.0679771\pi$
$480$	−56.2264	−2.56637
$481$	12.8317i	0.585074i
$482$	− 22.1946i	− 1.01093i
$483$	− 14.2196i	− 0.647015i
$484$	−17.3910	−0.790502
$485$	50.2375i	2.28117i
$486$	36.6586	1.66287
$487$	38.0837	1.72574	0.862869	−	0.505428i	$-0.168665\pi$
$487$	38.0837	1.72574	0.862869	+	0.505428i	$0.168665\pi$
$488$	−0.801018	−0.0362604
$489$	21.9254	0.991503
$490$	3.74341i	0.169110i
$491$	31.5938i	1.42581i	0.701262	+	0.712904i	$0.252620\pi$
$491$	31.5938i	1.42581i	−0.701262	+	0.712904i	$0.747380\pi$
$492$	−47.8204	−2.15591
$493$	0	0
$494$	−14.8088	−0.666279
$495$	7.80557i	0.350834i
$496$	6.95758i	0.312405i
$497$	10.4818	0.470173
$498$	42.9088	1.92279
$499$	21.0654	0.943016	0.471508	−	0.881862i	$-0.343710\pi$
$499$	21.0654	0.943016	0.471508	+	0.881862i	$0.343710\pi$
$500$	2.01541	0.0901318
$501$	− 1.05591i	− 0.0471746i
$502$	−49.6853	−2.21757
$503$	− 26.2365i	− 1.16983i	−0.811095	−	0.584915i	$-0.801128\pi$
$503$	− 26.2365i	− 1.16983i	0.811095	−	0.584915i	$-0.198872\pi$
$504$	2.27710i	0.101430i
$505$	− 36.6580i	− 1.63126i
$506$	−5.40732	−0.240384
$507$	− 24.0795i	− 1.06941i
$508$	− 31.8623i	− 1.41366i
$509$	−20.9900	−0.930366	−0.465183	−	0.885215i	$-0.654011\pi$
$509$	−20.9900	−0.930366	−0.465183	+	0.885215i	$0.654011\pi$
$510$	− 62.8477i	− 2.78294i
$511$	9.60679i	0.424979i
$512$	30.0650i	1.32870i
$513$	−9.37656	−0.413985
$514$	0.347540i	0.0153293i
$515$	−23.7727	−1.04755
$516$	−7.64228	−0.336432
$517$	1.08133	0.0475567
$518$	40.7817	1.79184
$519$	50.6357i	2.22266i
$520$	− 2.07654i	− 0.0910622i
$521$	37.4112	1.63901	0.819507	−	0.573069i	$-0.194247\pi$
$521$	37.4112	1.63901	0.819507	+	0.573069i	$0.194247\pi$
$522$	0	0
$523$	17.4633	0.763618	0.381809	−	0.924241i	$-0.375301\pi$
$523$	17.4633	0.763618	0.381809	+	0.924241i	$0.375301\pi$
$524$	− 1.02638i	− 0.0448378i
$525$	− 30.7535i	− 1.34219i
$526$	−10.9589	−0.477832
$527$	−7.01688	−0.305660
$528$	11.1821	0.486640
$529$	−16.8790	−0.733871
$530$	− 10.1292i	− 0.439983i
$531$	28.8746	1.25305
$532$	22.2015i	0.962559i
$533$	− 18.2602i	− 0.790937i
$534$	21.5676i	0.933323i
$535$	38.3503	1.65803
$536$	1.25995i	0.0544217i
$537$	− 17.0591i	− 0.736154i
$538$	−3.79091	−0.163438
$539$	− 0.671721i	− 0.0289331i
$540$	10.9647i	0.471845i
$541$	− 5.69494i	− 0.244845i	−0.992478	−	0.122422i	$-0.960934\pi$
$541$	− 5.69494i	− 0.244845i	0.992478	−	0.122422i	$-0.0390662\pi$
$542$	−33.9369	−1.45771
$543$	− 54.3740i	− 2.33341i
$544$	−34.0044	−1.45793
$545$	52.0292	2.22868
$546$	17.3228	0.741346
$547$	−26.1122	−1.11648	−0.558238	−	0.829681i	$-0.688522\pi$
$547$	−26.1122	−1.11648	−0.558238	+	0.829681i	$0.688522\pi$
$548$	24.6141i	1.05146i
$549$	− 4.15217i	− 0.177210i
$550$	−11.6947	−0.498663
$551$	0	0
$552$	−2.34167	−0.0996680
$553$	− 33.4891i	− 1.42410i
$554$	− 29.8563i	− 1.26847i
$555$	60.5385	2.56971
$556$	−18.9324	−0.802912
$557$	−28.6514	−1.21400	−0.606998	−	0.794703i	$-0.707627\pi$
$557$	−28.6514	−1.21400	−0.606998	+	0.794703i	$0.707627\pi$
$558$	−6.67195	−0.282446
$559$	− 2.91820i	− 0.123427i
$560$	−35.6747	−1.50753
$561$	11.2774i	0.476134i
$562$	− 25.7054i	− 1.08432i
$563$	2.23595i	0.0942341i	0.998889	+	0.0471170i	$0.0150034\pi$
$563$	2.23595i	0.0942341i	−0.998889	+	0.0471170i	$0.984997\pi$
$564$	−3.90511	−0.164435
$565$	20.4237i	0.859231i
$566$	21.7070i	0.912414i
$567$	27.3632	1.14915
$568$	− 1.72613i	− 0.0724268i
$569$	14.6792i	0.615385i	0.951486	+	0.307692i	$0.0995568\pi$
$569$	14.6792i	0.615385i	−0.951486	+	0.307692i	$0.900443\pi$
$570$	69.8663i	2.92638i
$571$	20.8600	0.872962	0.436481	−	0.899714i	$-0.356225\pi$
$571$	20.8600	0.872962	0.436481	+	0.899714i	$0.356225\pi$
$572$	− 3.10737i	− 0.129926i
$573$	−30.4520	−1.27215
$574$	−58.0347	−2.42232
$575$	13.2381	0.552069
$576$	−13.4018	−0.558410
$577$	22.4919i	0.936348i	0.883636	+	0.468174i	$0.155088\pi$
$577$	22.4919i	0.936348i	−0.883636	+	0.468174i	$0.844912\pi$
$578$	− 4.93149i	− 0.205123i
$579$	−29.0087	−1.20556
$580$	0	0
$581$	24.5642	1.01909
$582$	69.0150i	2.86076i
$583$	1.81759i	0.0752767i
$584$	1.58203	0.0654650
$585$	10.7640	0.445036
$586$	13.2363	0.546788
$587$	16.4960	0.680864	0.340432	−	0.940269i	$-0.389427\pi$
$587$	16.4960	0.680864	0.340432	+	0.940269i	$0.389427\pi$
$588$	2.42585i	0.100040i
$589$	7.80050	0.321414
$590$	83.6865i	3.44532i
$591$	− 9.26127i	− 0.380958i
$592$	− 36.3029i	− 1.49204i
$593$	45.1022	1.85212	0.926062	−	0.377371i	$-0.123172\pi$
$593$	45.1022	1.85212	0.926062	+	0.377371i	$0.123172\pi$
$594$	− 4.17095i	− 0.171136i
$595$	− 35.9787i	− 1.47498i
$596$	4.22633	0.173117
$597$	38.5431i	1.57746i
$598$	7.45676i	0.304930i
$599$	− 10.5711i	− 0.431925i	−0.976402	−	0.215963i	$-0.930711\pi$
$599$	− 10.5711i	− 0.431925i	0.976402	−	0.215963i	$-0.0692889\pi$
$600$	−5.06444	−0.206755
$601$	0.743399i	0.0303239i	0.999885	+	0.0151619i	$0.00482638\pi$
$601$	0.743399i	0.0303239i	−0.999885	+	0.0151619i	$0.995174\pi$
$602$	−9.27465	−0.378006
$603$	−6.53113	−0.265968
$604$	17.4109	0.708439
$605$	−31.3305	−1.27376
$606$	− 50.3597i	− 2.04572i
$607$	− 32.6175i	− 1.32390i	−0.749546	−	0.661952i	$-0.769728\pi$
$607$	− 32.6175i	− 1.32390i	0.749546	−	0.661952i	$-0.230272\pi$
$608$	37.8019	1.53307
$609$	0	0
$610$	12.0342	0.487248
$611$	− 1.49117i	− 0.0603261i
$612$	− 17.0481i	− 0.689128i
$613$	−15.0054	−0.606064	−0.303032	−	0.952980i	$-0.597999\pi$
$613$	−15.0054	−0.606064	−0.303032	+	0.952980i	$0.597999\pi$
$614$	31.4387	1.26876
$615$	−86.1497	−3.47389
$616$	1.18425	0.0477147
$617$	41.5249i	1.67173i	0.548936	+	0.835864i	$0.315033\pi$
$617$	41.5249i	1.67173i	−0.548936	+	0.835864i	$0.684967\pi$
$618$	−32.6583	−1.31371
$619$	− 21.3783i	− 0.859268i	−0.903003	−	0.429634i	$-0.858643\pi$
$619$	− 21.3783i	− 0.859268i	0.903003	−	0.429634i	$-0.141357\pi$
$620$	− 9.12168i	− 0.366335i
$621$	4.72144i	0.189465i
$622$	8.44356	0.338556
$623$	12.3469i	0.494669i
$624$	− 15.4203i	− 0.617307i
$625$	−23.1231	−0.924923
$626$	2.08855i	0.0834752i
$627$	− 12.5369i	− 0.500674i
$628$	− 33.4932i	− 1.33652i
$629$	36.6123	1.45983
$630$	− 34.2101i	− 1.36296i
$631$	−22.2833	−0.887085	−0.443542	−	0.896253i	$-0.646278\pi$
$631$	−22.2833	−0.887085	−0.443542	+	0.896253i	$0.646278\pi$
$632$	−5.51494	−0.219372
$633$	10.0316	0.398719
$634$	15.1653	0.602290
$635$	− 57.4009i	− 2.27788i
$636$	− 6.56403i	− 0.260281i
$637$	−0.926312	−0.0367018
$638$	0	0
$639$	8.94760	0.353962
$640$	10.6629i	0.421488i
$641$	26.5934i	1.05038i	0.850986	+	0.525188i	$0.176005\pi$
$641$	26.5934i	1.05038i	−0.850986	+	0.525188i	$0.823995\pi$
$642$	52.6846	2.07930
$643$	−38.2237	−1.50740	−0.753699	−	0.657220i	$-0.771732\pi$
$643$	−38.2237	−1.50740	−0.753699	+	0.657220i	$0.771732\pi$
$644$	11.1793	0.440525
$645$	−13.7678	−0.542106
$646$	42.2535i	1.66244i
$647$	−32.8334	−1.29081	−0.645407	−	0.763839i	$-0.723312\pi$
$647$	−32.8334	−1.29081	−0.645407	+	0.763839i	$0.723312\pi$
$648$	− 4.50614i	− 0.177018i
$649$	− 15.0168i	− 0.589460i
$650$	16.1271i	0.632558i
$651$	−9.12473	−0.357626
$652$	17.2375i	0.675073i
$653$	1.30358i	0.0510131i	0.999675	+	0.0255066i	$0.00811987\pi$
$653$	1.30358i	0.0510131i	−0.999675	+	0.0255066i	$0.991880\pi$
$654$	71.4762	2.79494
$655$	− 1.84906i	− 0.0722487i
$656$	51.6611i	2.01703i
$657$	8.20066i	0.319938i
$658$	−4.73923	−0.184754
$659$	− 19.7479i	− 0.769267i	−0.923069	−	0.384634i	$-0.874328\pi$
$659$	− 19.7479i	− 0.769267i	0.923069	−	0.384634i	$-0.125672\pi$
$660$	−14.6602	−0.570649
$661$	−42.1752	−1.64042	−0.820212	−	0.572059i	$-0.806145\pi$
$661$	−42.1752	−1.64042	−0.820212	+	0.572059i	$0.806145\pi$
$662$	−19.3739	−0.752989
$663$	15.5517	0.603980
$664$	− 4.04520i	− 0.156984i
$665$	39.9967i	1.55101i
$666$	34.8125	1.34896
$667$	0	0
$668$	0.830144	0.0321192
$669$	− 38.7712i	− 1.49898i
$670$	− 18.9290i	− 0.731291i
$671$	−2.15942	−0.0833634
$672$	−44.2193	−1.70579
$673$	41.6873	1.60693	0.803464	−	0.595353i	$-0.202988\pi$
$673$	41.6873	1.60693	0.803464	+	0.595353i	$0.202988\pi$
$674$	−41.5605	−1.60085
$675$	10.2113i	0.393033i
$676$	18.9310	0.728114
$677$	24.5737i	0.944443i	0.881480	+	0.472221i	$0.156548\pi$
$677$	24.5737i	0.944443i	−0.881480	+	0.472221i	$0.843452\pi$
$678$	28.0575i	1.07754i
$679$	39.5093i	1.51623i
$680$	−5.92493	−0.227211
$681$	− 22.2158i	− 0.851311i
$682$	3.46988i	0.132868i
$683$	43.1311	1.65036	0.825182	−	0.564867i	$-0.191072\pi$
$683$	43.1311	1.65036	0.825182	+	0.564867i	$0.191072\pi$
$684$	18.9519i	0.724646i
$685$	44.3431i	1.69426i
$686$	37.4058i	1.42816i
$687$	−7.81225	−0.298056
$688$	8.25607i	0.314760i
$689$	2.50648	0.0954891
$690$	35.1802	1.33929
$691$	−41.0599	−1.56199	−0.780996	−	0.624536i	$-0.785288\pi$
$691$	−41.0599	−1.56199	−0.780996	+	0.624536i	$0.785288\pi$
$692$	−39.8091	−1.51332
$693$	6.13869i	0.233190i
$694$	− 52.3691i	− 1.98790i
$695$	−34.1072	−1.29376
$696$	0	0
$697$	−52.1014	−1.97348
$698$	36.5375i	1.38297i
$699$	− 9.97562i	− 0.377313i
$700$	24.1780	0.913842
$701$	−1.11188	−0.0419949	−0.0209975	−	0.999780i	$-0.506684\pi$
$701$	−1.11188	−0.0419949	−0.0209975	+	0.999780i	$0.506684\pi$
$702$	−5.75180	−0.217088
$703$	−40.7010	−1.53507
$704$	6.96989i	0.262687i
$705$	−7.03516	−0.264959
$706$	− 57.5475i	− 2.16583i
$707$	− 28.8297i	− 1.08425i
$708$	54.2315i	2.03815i
$709$	−29.9385	−1.12437	−0.562183	−	0.827013i	$-0.690038\pi$
$709$	−29.9385	−1.12437	−0.562183	+	0.827013i	$0.690038\pi$
$710$	25.9326i	0.973234i
$711$	− 28.5873i	− 1.07211i
$712$	2.03328	0.0762002
$713$	− 3.92783i	− 0.147099i
$714$	− 49.4266i	− 1.84974i
$715$	− 5.59801i	− 0.209354i
$716$	13.4116	0.501217
$717$	40.1614i	1.49986i
$718$	−39.4666	−1.47288
$719$	−5.03075	−0.187615	−0.0938076	−	0.995590i	$-0.529904\pi$
$719$	−5.03075	−0.187615	−0.0938076	+	0.995590i	$0.529904\pi$
$720$	−30.4530	−1.13492
$721$	−18.6961	−0.696277
$722$	− 10.0034i	− 0.372290i
$723$	− 25.9110i	− 0.963640i
$724$	42.7481	1.58872
$725$	0	0
$726$	−43.0409	−1.59740
$727$	0.650727i	0.0241341i	0.999927	+	0.0120671i	$0.00384116\pi$
$727$	0.650727i	0.0241341i	−0.999927	+	0.0120671i	$0.996159\pi$
$728$	− 1.63309i	− 0.0605265i
$729$	10.3533	0.383455
$730$	−23.7678	−0.879685
$731$	−8.32643	−0.307964
$732$	7.79852	0.288242
$733$	− 11.3833i	− 0.420451i	−0.977653	−	0.210225i	$-0.932580\pi$
$733$	− 11.3833i	− 0.420451i	0.977653	−	0.210225i	$-0.0674198\pi$
$734$	33.0644	1.22043
$735$	4.37024i	0.161199i
$736$	− 19.0346i	− 0.701626i
$737$	3.39664i	0.125117i
$738$	−49.5402	−1.82360
$739$	− 19.1778i	− 0.705465i	−0.935724	−	0.352732i	$-0.885253\pi$
$739$	− 19.1778i	− 0.705465i	0.935724	−	0.352732i	$-0.114747\pi$
$740$	47.5946i	1.74961i
$741$	−17.2885	−0.635109
$742$	− 7.96609i	− 0.292444i
$743$	− 32.1621i	− 1.17991i	−0.807436	−	0.589956i	$-0.799145\pi$
$743$	− 32.1621i	− 1.17991i	0.807436	−	0.589956i	$-0.200855\pi$
$744$	1.50265i	0.0550898i
$745$	7.61385	0.278950
$746$	− 20.2659i	− 0.741988i
$747$	20.9688	0.767208
$748$	−8.86618	−0.324180
$749$	30.1606	1.10205
$750$	4.98792	0.182133
$751$	38.3085i	1.39790i	0.715172	+	0.698949i	$0.246348\pi$
$751$	38.3085i	1.39790i	−0.715172	+	0.698949i	$0.753652\pi$
$752$	4.21875i	0.153842i
$753$	−58.0051	−2.11382
$754$	0	0
$755$	31.3662	1.14153
$756$	8.62318i	0.313622i
$757$	− 11.3624i	− 0.412975i	−0.978449	−	0.206487i	$-0.933797\pi$
$757$	− 11.3624i	− 0.412975i	0.978449	−	0.206487i	$-0.0662032\pi$
$758$	−44.5534	−1.61825
$759$	−6.31276	−0.229139
$760$	6.58660	0.238921
$761$	−15.6194	−0.566205	−0.283102	−	0.959090i	$-0.591364\pi$
$761$	−15.6194	−0.566205	−0.283102	+	0.959090i	$0.591364\pi$
$762$	− 78.8558i	− 2.85664i
$763$	40.9184	1.48134
$764$	− 23.9409i	− 0.866153i
$765$	− 30.7126i	− 1.11042i
$766$	5.64784i	0.204065i
$767$	−20.7083	−0.747734
$768$	42.8378i	1.54578i
$769$	9.65324i	0.348105i	0.984736	+	0.174052i	$0.0556862\pi$
$769$	9.65324i	0.348105i	−0.984736	+	0.174052i	$0.944314\pi$
$770$	−17.7916	−0.641166
$771$	0.405735i	0.0146122i
$772$	− 22.8063i	− 0.820816i
$773$	15.7145i	0.565211i	0.959236	+	0.282605i	$0.0911987\pi$
$773$	15.7145i	0.565211i	−0.959236	+	0.282605i	$0.908801\pi$
$774$	−7.91713	−0.284576
$775$	− 8.49493i	− 0.305147i
$776$	6.50635	0.233564
$777$	47.6105	1.70802
$778$	−6.13653	−0.220005
$779$	57.9199	2.07519
$780$	20.2167i	0.723873i
$781$	− 4.65337i	− 0.166511i
$782$	21.2762	0.760835
$783$	0	0
$784$	2.62069	0.0935959
$785$	− 60.3389i	− 2.15359i
$786$	− 2.54019i	− 0.0906055i
$787$	−5.12572	−0.182712	−0.0913560	−	0.995818i	$-0.529120\pi$
$787$	−5.12572	−0.182712	−0.0913560	+	0.995818i	$0.529120\pi$
$788$	7.28109	0.259378
$789$	−12.7940	−0.455477
$790$	82.8540	2.94781
$791$	16.0622i	0.571107i
$792$	1.01091	0.0359212
$793$	2.97787i	0.105747i
$794$	41.2511i	1.46395i
$795$	− 11.8253i	− 0.419400i
$796$	−30.3021	−1.07403
$797$	− 40.5663i	− 1.43693i	−0.695562	−	0.718466i	$-0.744844\pi$
$797$	− 40.5663i	− 1.43693i	0.695562	−	0.718466i	$-0.255156\pi$
$798$	54.9464i	1.94508i
$799$	−4.25470	−0.150521
$800$	− 41.1672i	− 1.45548i
$801$	10.5397i	0.372403i
$802$	− 8.36646i	− 0.295430i
$803$	4.26491	0.150505
$804$	− 12.2666i	− 0.432610i
$805$	20.1398	0.709834
$806$	4.78501	0.168545
$807$	−4.42569	−0.155792
$808$	−4.74763	−0.167021
$809$	− 31.0217i	− 1.09066i	−0.838220	−	0.545332i	$-0.816403\pi$
$809$	− 31.0217i	− 1.09066i	0.838220	−	0.545332i	$-0.183597\pi$
$810$	67.6982i	2.37867i
$811$	45.3970	1.59410	0.797052	−	0.603910i	$-0.206391\pi$
$811$	45.3970	1.59410	0.797052	+	0.603910i	$0.206391\pi$
$812$	0	0
$813$	−39.6196	−1.38952
$814$	− 18.1049i	− 0.634577i
$815$	31.0538i	1.08777i
$816$	−43.9984	−1.54025
$817$	9.25630	0.323837
$818$	−49.6125	−1.73466
$819$	8.46534	0.295803
$820$	− 67.7298i	− 2.36523i
$821$	26.4086	0.921665	0.460833	−	0.887487i	$-0.347551\pi$
$821$	26.4086	0.921665	0.460833	+	0.887487i	$0.347551\pi$
$822$	60.9173i	2.12473i
$823$	− 34.3735i	− 1.19818i	−0.800680	−	0.599092i	$-0.795528\pi$
$823$	− 34.3735i	− 1.19818i	0.800680	−	0.599092i	$-0.204472\pi$
$824$	3.07884i	0.107257i
$825$	−13.6529	−0.475334
$826$	65.8153i	2.29001i
$827$	40.3495i	1.40309i	0.712626	+	0.701545i	$0.247506\pi$
$827$	40.3495i	1.40309i	−0.712626	+	0.701545i	$0.752494\pi$
$828$	9.54299	0.331642
$829$	− 41.4695i	− 1.44029i	−0.693821	−	0.720147i	$-0.744074\pi$
$829$	− 41.4695i	− 1.44029i	0.693821	−	0.720147i	$-0.255926\pi$
$830$	60.7733i	2.10947i
$831$	− 34.8557i	− 1.20913i
$832$	9.61157	0.333221
$833$	2.64302i	0.0915753i
$834$	−46.8556	−1.62248
$835$	1.49553	0.0517549
$836$	9.85632	0.340888
$837$	3.02975	0.104723
$838$	− 13.1264i	− 0.453445i
$839$	− 12.9838i	− 0.448250i	−0.974560	−	0.224125i	$-0.928048\pi$
$839$	− 12.9838i	− 0.448250i	0.974560	−	0.224125i	$-0.0719523\pi$
$840$	−7.70476	−0.265840
$841$	0	0
$842$	−67.2183	−2.31649
$843$	− 30.0097i	− 1.03359i
$844$	7.88669i	0.271471i
$845$	34.1047	1.17324
$846$	−4.04556	−0.139089
$847$	−24.6399	−0.846635
$848$	−7.09122	−0.243514
$849$	25.3418i	0.869729i
$850$	46.0151	1.57830
$851$	20.4944i	0.702540i
$852$	16.8052i	0.575736i
$853$	− 8.15508i	− 0.279225i	−0.990206	−	0.139612i	$-0.955414\pi$
$853$	− 8.15508i	− 0.279225i	0.990206	−	0.139612i	$-0.0445856\pi$
$854$	9.46426	0.323860
$855$	34.1425i	1.16765i
$856$	− 4.96681i	− 0.169762i
$857$	−29.3691	−1.00323	−0.501615	−	0.865091i	$-0.667261\pi$
$857$	−29.3691	−1.00323	−0.501615	+	0.865091i	$0.667261\pi$
$858$	− 7.69040i	− 0.262546i
$859$	19.4101i	0.662265i	0.943584	+	0.331133i	$0.107431\pi$
$859$	19.4101i	0.662265i	−0.943584	+	0.331133i	$0.892569\pi$
$860$	− 10.8240i	− 0.369097i
$861$	−67.7525	−2.30900
$862$	19.2230i	0.654736i
$863$	50.6162	1.72300	0.861498	−	0.507760i	$-0.169526\pi$
$863$	50.6162	1.72300	0.861498	+	0.507760i	$0.169526\pi$
$864$	14.6824	0.499506
$865$	−71.7173	−2.43846
$866$	6.22999	0.211704
$867$	− 5.75726i	− 0.195527i
$868$	− 7.17375i	− 0.243493i
$869$	−14.8674	−0.504342
$870$	0	0
$871$	4.68401	0.158712
$872$	− 6.73838i	− 0.228190i
$873$	33.7264i	1.14147i
$874$	−23.6522	−0.800048
$875$	2.85546	0.0965321
$876$	−15.4023	−0.520395
$877$	35.1220	1.18598	0.592992	−	0.805208i	$-0.297946\pi$
$877$	35.1220	1.18598	0.592992	+	0.805208i	$0.297946\pi$
$878$	− 12.4806i	− 0.421200i
$879$	15.4527	0.521208
$880$	15.8377i	0.533888i
$881$	32.1831i	1.08428i	0.840289	+	0.542138i	$0.182385\pi$
$881$	32.1831i	1.08428i	−0.840289	+	0.542138i	$0.817615\pi$
$882$	2.51310i	0.0846204i
$883$	46.8381	1.57623	0.788113	−	0.615530i	$-0.211058\pi$
$883$	46.8381	1.57623	0.788113	+	0.615530i	$0.211058\pi$
$884$	12.2266i	0.411224i
$885$	97.6996i	3.28414i
$886$	−16.5377	−0.555594
$887$	− 6.85131i	− 0.230045i	−0.993363	−	0.115022i	$-0.963306\pi$
$887$	− 6.85131i	− 0.230045i	0.993363	−	0.115022i	$-0.0366939\pi$
$888$	− 7.84043i	− 0.263108i
$889$	− 45.1429i	− 1.51405i
$890$	−30.5471	−1.02394
$891$	− 12.1478i	− 0.406968i
$892$	30.4814	1.02059
$893$	4.72985	0.158278
$894$	10.4597	0.349825
$895$	24.1614	0.807628
$896$	8.38584i	0.280151i
$897$	8.70538i	0.290664i
$898$	−32.9650	−1.10006
$899$	0	0
$900$	20.6391	0.687970
$901$	− 7.15166i	− 0.238256i
$902$	25.7643i	0.857859i
$903$	−10.8277	−0.360322
$904$	2.64511	0.0879749
$905$	77.0119	2.55996
$906$	43.0900	1.43157
$907$	12.2503i	0.406764i	0.979099	+	0.203382i	$0.0651933\pi$
$907$	12.2503i	0.406764i	−0.979099	+	0.203382i	$0.934807\pi$
$908$	17.4658	0.579622
$909$	− 24.6099i	− 0.816260i
$910$	24.5349i	0.813324i
$911$	− 19.8474i	− 0.657572i	−0.944404	−	0.328786i	$-0.893360\pi$
$911$	− 19.8474i	− 0.657572i	0.944404	−	0.328786i	$-0.106640\pi$
$912$	48.9119	1.61964
$913$	− 10.9052i	− 0.360910i
$914$	− 0.984364i	− 0.0325599i
$915$	14.0493	0.464454
$916$	− 6.14189i	− 0.202934i
$917$	− 1.45419i	− 0.0480217i
$918$	16.4115i	0.541659i
$919$	−30.5383	−1.00736	−0.503682	−	0.863889i	$-0.668022\pi$
$919$	−30.5383	−1.00736	−0.503682	+	0.863889i	$0.668022\pi$
$920$	− 3.31659i	− 0.109345i
$921$	36.7031	1.20941
$922$	10.7032	0.352491
$923$	−6.41706	−0.211220
$924$	−11.5296	−0.379294
$925$	44.3243i	1.45737i
$926$	12.7756i	0.419833i
$927$	−15.9595	−0.524180
$928$	0	0
$929$	−8.90962	−0.292315	−0.146158	−	0.989261i	$-0.546691\pi$
$929$	−8.90962	−0.292315	−0.146158	+	0.989261i	$0.546691\pi$
$930$	− 22.5751i	− 0.740268i
$931$	− 2.93818i	− 0.0962951i
$932$	7.84270	0.256896
$933$	9.85742	0.322717
$934$	8.71333	0.285109
$935$	−15.9727	−0.522362
$936$	− 1.39406i	− 0.0455663i
$937$	−15.3972	−0.503006	−0.251503	−	0.967857i	$-0.580925\pi$
$937$	−15.3972	−0.503006	−0.251503	+	0.967857i	$0.580925\pi$
$938$	− 14.8867i	− 0.486069i
$939$	2.43827i	0.0795701i
$940$	− 5.53095i	− 0.180400i
$941$	−46.5126	−1.51627	−0.758133	−	0.652100i	$-0.773888\pi$
$941$	−46.5126	−1.51627	−0.758133	+	0.652100i	$0.773888\pi$
$942$	− 82.8920i	− 2.70077i
$943$	− 29.1647i	− 0.949735i
$944$	58.5872	1.90685
$945$	15.5349i	0.505350i
$946$	4.11746i	0.133870i
$947$	31.2180i	1.01445i	0.861814	+	0.507224i	$0.169328\pi$
$947$	31.2180i	1.01445i	−0.861814	+	0.507224i	$0.830672\pi$
$948$	53.6921	1.74384
$949$	− 5.88137i	− 0.190917i
$950$	−51.1539	−1.65965
$951$	17.7047	0.574114
$952$	−4.65966	−0.151021
$953$	−24.5654	−0.795752	−0.397876	−	0.917439i	$-0.630253\pi$
$953$	−24.5654	−0.795752	−0.397876	+	0.917439i	$0.630253\pi$
$954$	− 6.80011i	− 0.220162i
$955$	− 43.1303i	− 1.39566i
$956$	−31.5744	−1.02119
$957$	0	0
$958$	18.0504	0.583181
$959$	34.8736i	1.12613i
$960$	− 45.3463i	− 1.46355i
$961$	28.4795	0.918694
$962$	−24.9669	−0.804966
$963$	25.7461	0.829655
$964$	20.3709	0.656102
$965$	− 41.0862i	− 1.32261i
$966$	27.6675	0.890187
$967$	25.3774i	0.816082i	0.912964	+	0.408041i	$0.133788\pi$
$967$	25.3774i	0.816082i	−0.912964	+	0.408041i	$0.866212\pi$
$968$	4.05766i	0.130418i
$969$	49.3288i	1.58467i
$970$	−97.7485	−3.13852
$971$	− 11.0345i	− 0.354115i	−0.984200	−	0.177058i	$-0.943342\pi$
$971$	− 11.0345i	− 0.354115i	0.984200	−	0.177058i	$-0.0566579\pi$
$972$	33.6464i	1.07921i
$973$	−26.8237	−0.859927
$974$	74.1005i	2.37433i
$975$	18.8276i	0.602965i
$976$	− 8.42486i	− 0.269673i
$977$	−52.4730	−1.67876	−0.839380	−	0.543545i	$-0.817082\pi$
$977$	−52.4730	−1.67876	−0.839380	+	0.543545i	$0.817082\pi$
$978$	42.6609i	1.36415i
$979$	5.48139	0.175186
$980$	−3.43583	−0.109753
$981$	34.9292	1.11520
$982$	−61.4729	−1.96168
$983$	− 46.0772i	− 1.46964i	−0.678265	−	0.734818i	$-0.737268\pi$
$983$	− 46.0772i	− 1.46964i	0.678265	−	0.734818i	$-0.262732\pi$
$984$	11.1574i	0.355685i
$985$	13.1171	0.417945
$986$	0	0
$987$	−5.53280	−0.176111
$988$	− 13.5920i	− 0.432419i
$989$	− 4.66088i	− 0.148207i
$990$	−15.1875	−0.482690
$991$	−0.807143	−0.0256397	−0.0128199	−	0.999918i	$-0.504081\pi$
$991$	−0.807143	−0.0256397	−0.0128199	+	0.999918i	$0.504081\pi$
$992$	−12.2145	−0.387812
$993$	−22.6181	−0.717762
$994$	20.3947i	0.646881i
$995$	−54.5900	−1.73062
$996$	39.3831i	1.24790i
$997$	30.6050i	0.969270i	0.874716	+	0.484635i	$0.161048\pi$
$997$	30.6050i	0.969270i	−0.874716	+	0.484635i	$0.838952\pi$
$998$	40.9875i	1.29744i
$999$	−15.8084	−0.500157

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.b.d.840.10		12
29.2	odd	28		841.2.d.n.605.2		36
29.3	odd	28		841.2.d.n.571.2		36
29.4	even	14		841.2.e.l.651.3		72
29.5	even	14		841.2.e.l.236.10		72
29.6	even	14		841.2.e.l.196.3		72
29.7	even	7		841.2.e.l.270.3		72
29.8	odd	28		841.2.d.o.574.2		36
29.9	even	14		841.2.e.l.267.3		72
29.10	odd	28		841.2.d.o.190.5		36
29.11	odd	28		841.2.d.n.778.5		36
29.12	odd	4		841.2.a.g.1.2	✓	6
29.13	even	14		841.2.e.l.63.10		72
29.14	odd	28		841.2.d.n.645.2		36
29.15	odd	28		841.2.d.o.645.5		36
29.16	even	7		841.2.e.l.63.3		72
29.17	odd	4		841.2.a.h.1.5	yes	6
29.18	odd	28		841.2.d.o.778.2		36
29.19	odd	28		841.2.d.n.190.2		36
29.20	even	7		841.2.e.l.267.10		72
29.21	odd	28		841.2.d.n.574.5		36
29.22	even	14		841.2.e.l.270.10		72
29.23	even	7		841.2.e.l.196.10		72
29.24	even	7		841.2.e.l.236.3		72
29.25	even	7		841.2.e.l.651.10		72
29.26	odd	28		841.2.d.o.571.5		36
29.27	odd	28		841.2.d.o.605.5		36
29.28	even	2	inner	841.2.b.d.840.3		12
87.17	even	4		7569.2.a.y.1.2		6
87.41	even	4		7569.2.a.bc.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
841.2.a.g.1.2	✓	6	29.12	odd	4
841.2.a.h.1.5	yes	6	29.17	odd	4
841.2.b.d.840.3		12	29.28	even	2	inner
841.2.b.d.840.10		12	1.1	even	1	trivial
841.2.d.n.190.2		36	29.19	odd	28
841.2.d.n.571.2		36	29.3	odd	28
841.2.d.n.574.5		36	29.21	odd	28
841.2.d.n.605.2		36	29.2	odd	28
841.2.d.n.645.2		36	29.14	odd	28
841.2.d.n.778.5		36	29.11	odd	28
841.2.d.o.190.5		36	29.10	odd	28
841.2.d.o.571.5		36	29.26	odd	28
841.2.d.o.574.2		36	29.8	odd	28
841.2.d.o.605.5		36	29.27	odd	28
841.2.d.o.645.5		36	29.15	odd	28
841.2.d.o.778.2		36	29.18	odd	28
841.2.e.l.63.3		72	29.16	even	7
841.2.e.l.63.10		72	29.13	even	14
841.2.e.l.196.3		72	29.6	even	14
841.2.e.l.196.10		72	29.23	even	7
841.2.e.l.236.3		72	29.24	even	7
841.2.e.l.236.10		72	29.5	even	14
841.2.e.l.267.3		72	29.9	even	14
841.2.e.l.267.10		72	29.20	even	7
841.2.e.l.270.3		72	29.7	even	7
841.2.e.l.270.10		72	29.22	even	14
841.2.e.l.651.3		72	29.4	even	14
841.2.e.l.651.10		72	29.25	even	7
7569.2.a.y.1.2		6	87.17	even	4
7569.2.a.bc.1.5		6	87.41	even	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)

\(f(q)\)	\(=\)	\(q+1.94573i q^{2} +2.27154i q^{3} -1.78585 q^{4} -3.21726 q^{5} -4.41979 q^{6} -2.53022 q^{7} +0.416673i q^{8} -2.15987 q^{9} -6.25991i q^{10} +1.12328i q^{11} -4.05663i q^{12} +1.54902 q^{13} -4.92311i q^{14} -7.30813i q^{15} -4.38244 q^{16} -4.41979i q^{17} -4.20253i q^{18} +4.91337i q^{19} +5.74556 q^{20} -5.74748i q^{21} -2.18560 q^{22} +2.47406 q^{23} -0.946487 q^{24} +5.35078 q^{25} +3.01398i q^{26} +1.90838i q^{27} +4.51860 q^{28} +14.2196 q^{30} -1.58761i q^{31} -7.69368i q^{32} -2.55158 q^{33} +8.59970 q^{34} +8.14037 q^{35} +3.85722 q^{36} +8.28372i q^{37} -9.56008 q^{38} +3.51866i q^{39} -1.34055i q^{40} -11.7882i q^{41} +11.1830 q^{42} -1.88390i q^{43} -2.00602i q^{44} +6.94888 q^{45} +4.81385i q^{46} -0.962649i q^{47} -9.95486i q^{48} -0.597997 q^{49} +10.4111i q^{50} +10.0397 q^{51} -2.76633 q^{52} +1.61810 q^{53} -3.71318 q^{54} -3.61390i q^{55} -1.05427i q^{56} -11.1609 q^{57} -13.3686 q^{59} +13.0512i q^{60} +1.92241i q^{61} +3.08905 q^{62} +5.46495 q^{63} +6.20492 q^{64} -4.98362 q^{65} -4.96468i q^{66} +3.02385 q^{67} +7.89309i q^{68} +5.61992i q^{69} +15.8389i q^{70} -4.14265 q^{71} -0.899961i q^{72} -3.79682i q^{73} -16.1178 q^{74} +12.1545i q^{75} -8.77456i q^{76} -2.84215i q^{77} -6.84635 q^{78} +13.2356i q^{79} +14.0994 q^{80} -10.8146 q^{81} +22.9366 q^{82} -9.70833 q^{83} +10.2642i q^{84} +14.2196i q^{85} +3.66555 q^{86} -0.468042 q^{88} -4.87979i q^{89} +13.5206i q^{90} -3.91937 q^{91} -4.41831 q^{92} +3.60630 q^{93} +1.87305 q^{94} -15.8076i q^{95} +17.4765 q^{96} -15.6150i q^{97} -1.16354i q^{98} -2.42615i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} + 4 q^{5} + 6 q^{6} - 8 q^{7} - 12 q^{9} + 12 q^{13} + 8 q^{16} - 10 q^{20} + 8 q^{22} - 10 q^{23} - 20 q^{24} + 12 q^{25} + 10 q^{28} + 52 q^{30} - 54 q^{33} + 8 q^{35} - 42 q^{36} - 82 q^{38}+ \cdots + 74 q^{96}+O(q^{100}) \) 12 * q - 16 * q^4 + 4 * q^5 + 6 * q^6 - 8 * q^7 - 12 * q^9 + 12 * q^13 + 8 * q^16 - 10 * q^20 + 8 * q^22 - 10 * q^23 - 20 * q^24 + 12 * q^25 + 10 * q^28 + 52 * q^30 - 54 * q^33 + 8 * q^35 - 42 * q^36 - 82 * q^38 + 42 * q^42 + 32 * q^45 - 24 * q^49 + 46 * q^51 - 26 * q^53 + 38 * q^54 + 32 * q^57 - 34 * q^59 + 18 * q^63 - 2 * q^64 + 64 * q^65 + 18 * q^67 - 72 * q^74 - 10 * q^80 - 44 * q^81 + 38 * q^82 - 48 * q^83 - 34 * q^86 + 42 * q^88 - 32 * q^91 + 46 * q^92 + 24 * q^93 - 74 * q^94 + 74 * q^96

Introduction

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