LMFDB - Embedded newform 2366.2.d.r.337.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(337,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("2366.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.d (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:	$18.8926051182$
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} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.4
Root			$0.500000 + 0.613147i$ of defining polynomial
Character	$\chi$	$=$	2366.337
Dual form			2366.2.d.r.337.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +0.252878 q^{3} -1.00000 q^{4} -1.14776i q^{5} -0.252878i q^{6} +1.00000i q^{7} +1.00000i q^{8} -2.93605 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +0.252878 q^{3} -1.00000 q^{4} -1.14776i q^{5} -0.252878i q^{6} +1.00000i q^{7} +1.00000i q^{8} -2.93605 q^{9} -1.14776 q^{10} +4.44485i q^{11} -0.252878 q^{12} +1.00000 q^{14} -0.290242i q^{15} +1.00000 q^{16} -2.70976 q^{17} +2.93605i q^{18} -6.56298i q^{19} +1.14776i q^{20} +0.252878i q^{21} +4.44485 q^{22} +2.08000 q^{23} +0.252878i q^{24} +3.68266 q^{25} -1.50110 q^{27} -1.00000i q^{28} +7.19919 q^{29} -0.290242 q^{30} +7.90895i q^{31} -1.00000i q^{32} +1.12400i q^{33} +2.70976i q^{34} +1.14776 q^{35} +2.93605 q^{36} -9.64405i q^{37} -6.56298 q^{38} +1.14776 q^{40} -9.49471i q^{41} +0.252878 q^{42} +3.40320 q^{43} -4.44485i q^{44} +3.36987i q^{45} -2.08000i q^{46} -1.67435i q^{47} +0.252878 q^{48} -1.00000 q^{49} -3.68266i q^{50} -0.685238 q^{51} +13.2815 q^{53} +1.50110i q^{54} +5.10160 q^{55} -1.00000 q^{56} -1.65963i q^{57} -7.19919i q^{58} -0.0677585i q^{59} +0.290242i q^{60} +8.10046 q^{61} +7.90895 q^{62} -2.93605i q^{63} -1.00000 q^{64} +1.12400 q^{66} -0.513495i q^{67} +2.70976 q^{68} +0.525985 q^{69} -1.14776i q^{70} -10.7873i q^{71} -2.93605i q^{72} -8.02452i q^{73} -9.64405 q^{74} +0.931263 q^{75} +6.56298i q^{76} -4.44485 q^{77} +10.7404 q^{79} -1.14776i q^{80} +8.42856 q^{81} -9.49471 q^{82} +15.3479i q^{83} -0.252878i q^{84} +3.11014i q^{85} -3.40320i q^{86} +1.82052 q^{87} -4.44485 q^{88} +10.8596i q^{89} +3.36987 q^{90} -2.08000 q^{92} +2.00000i q^{93} -1.67435 q^{94} -7.53270 q^{95} -0.252878i q^{96} -2.12694i q^{97} +1.00000i q^{98} -13.0503i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 - 12 * q^4 + 12 * q^9	$ 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} - 4 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 40 q^{27} + 20 q^{29} - 28 q^{30} - 4 q^{35} - 12 q^{36} + 8 q^{38} - 4 q^{40} + 4 q^{42} - 52 q^{43} + 4 q^{48} - 12 q^{49} - 36 q^{51} + 36 q^{53} + 12 q^{55} - 12 q^{56} + 56 q^{61} + 4 q^{62} - 12 q^{64} + 8 q^{68} - 64 q^{69} + 96 q^{75} - 4 q^{77} + 44 q^{79} + 68 q^{81} - 12 q^{82} - 4 q^{87} - 4 q^{88} + 12 q^{90} - 12 q^{92} - 16 q^{94} - 64 q^{95}+O(q^{100}) $ 12 * q + 4 * q^3 - 12 * q^4 + 12 * q^9 + 4 * q^10 - 4 * q^12 + 12 * q^14 + 12 * q^16 - 8 * q^17 + 4 * q^22 + 12 * q^23 - 24 * q^25 + 40 * q^27 + 20 * q^29 - 28 * q^30 - 4 * q^35 - 12 * q^36 + 8 * q^38 - 4 * q^40 + 4 * q^42 - 52 * q^43 + 4 * q^48 - 12 * q^49 - 36 * q^51 + 36 * q^53 + 12 * q^55 - 12 * q^56 + 56 * q^61 + 4 * q^62 - 12 * q^64 + 8 * q^68 - 64 * q^69 + 96 * q^75 - 4 * q^77 + 44 * q^79 + 68 * q^81 - 12 * q^82 - 4 * q^87 - 4 * q^88 + 12 * q^90 - 12 * q^92 - 16 * q^94 - 64 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2366\mathbb{Z}\right)^\times$.

$n$	$339$	$2199$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	0.252878	0.145999	0.0729996	−	0.997332i	$-0.476743\pi$
$3$	0.252878	0.145999	0.0729996	+	0.997332i	$0.476743\pi$
$4$	−1.00000	−0.500000
$5$	− 1.14776i	− 0.513292i	−0.966505	−	0.256646i	$-0.917383\pi$
$5$	− 1.14776i	− 0.513292i	0.966505	−	0.256646i	$-0.0826174\pi$
$6$	− 0.252878i	− 0.103237i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	1.00000i	0.353553i
$9$	−2.93605	−0.978684
$10$	−1.14776	−0.362952
$11$	4.44485i	1.34017i	0.742283	+	0.670086i	$0.233743\pi$
$11$	4.44485i	1.34017i	−0.742283	+	0.670086i	$0.766257\pi$
$12$	−0.252878	−0.0729996
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	− 0.290242i	− 0.0749402i
$16$	1.00000	0.250000
$17$	−2.70976	−0.657213	−0.328606	−	0.944467i	$-0.606579\pi$
$17$	−2.70976	−0.657213	−0.328606	+	0.944467i	$0.606579\pi$
$18$	2.93605i	0.692034i
$19$	− 6.56298i	− 1.50565i	−0.658220	−	0.752826i	$-0.728690\pi$
$19$	− 6.56298i	− 1.50565i	0.658220	−	0.752826i	$-0.271310\pi$
$20$	1.14776i	0.256646i
$21$	0.252878i	0.0551825i
$22$	4.44485	0.947645
$23$	2.08000	0.433709	0.216855	−	0.976204i	$-0.430420\pi$
$23$	2.08000	0.433709	0.216855	+	0.976204i	$0.430420\pi$
$24$	0.252878i	0.0516185i
$25$	3.68266	0.736531
$26$	0	0
$27$	−1.50110	−0.288886
$28$	− 1.00000i	− 0.188982i
$29$	7.19919	1.33686	0.668428	−	0.743776i	$-0.266967\pi$
$29$	7.19919	1.33686	0.668428	+	0.743776i	$0.266967\pi$
$30$	−0.290242	−0.0529907
$31$	7.90895i	1.42049i	0.703955	+	0.710245i	$0.251416\pi$
$31$	7.90895i	1.42049i	−0.703955	+	0.710245i	$0.748584\pi$
$32$	− 1.00000i	− 0.176777i
$33$	1.12400i	0.195664i
$34$	2.70976i	0.464720i
$35$	1.14776	0.194006
$36$	2.93605	0.489342
$37$	− 9.64405i	− 1.58547i	−0.609566	−	0.792736i	$-0.708656\pi$
$37$	− 9.64405i	− 1.58547i	0.609566	−	0.792736i	$-0.291344\pi$
$38$	−6.56298	−1.06466
$39$	0	0
$40$	1.14776	0.181476
$41$	− 9.49471i	− 1.48282i	−0.671050	−	0.741412i	$-0.734157\pi$
$41$	− 9.49471i	− 1.48282i	0.671050	−	0.741412i	$-0.265843\pi$
$42$	0.252878	0.0390199
$43$	3.40320	0.518983	0.259491	−	0.965745i	$-0.416445\pi$
$43$	3.40320	0.518983	0.259491	+	0.965745i	$0.416445\pi$
$44$	− 4.44485i	− 0.670086i
$45$	3.36987i	0.502351i
$46$	− 2.08000i	− 0.306679i
$47$	− 1.67435i	− 0.244229i	−0.992516	−	0.122114i	$-0.961033\pi$
$47$	− 1.67435i	− 0.244229i	0.992516	−	0.122114i	$-0.0389674\pi$
$48$	0.252878	0.0364998
$49$	−1.00000	−0.142857
$50$	− 3.68266i	− 0.520806i
$51$	−0.685238	−0.0959525
$52$	0	0
$53$	13.2815	1.82436	0.912180	−	0.409789i	$-0.134398\pi$
$53$	13.2815	1.82436	0.912180	+	0.409789i	$0.134398\pi$
$54$	1.50110i	0.204273i
$55$	5.10160	0.687900
$56$	−1.00000	−0.133631
$57$	− 1.65963i	− 0.219824i
$58$	− 7.19919i	− 0.945301i
$59$	− 0.0677585i	− 0.00882140i	−0.999990	−	0.00441070i	$-0.998596\pi$
$59$	− 0.0677585i	− 0.00882140i	0.999990	−	0.00441070i	$-0.00140397\pi$
$60$	0.290242i	0.0374701i
$61$	8.10046	1.03716	0.518579	−	0.855030i	$-0.326461\pi$
$61$	8.10046	1.03716	0.518579	+	0.855030i	$0.326461\pi$
$62$	7.90895	1.00444
$63$	− 2.93605i	− 0.369908i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	1.12400	0.138355
$67$	− 0.513495i	− 0.0627334i	−0.999508	−	0.0313667i	$-0.990014\pi$
$67$	− 0.513495i	− 0.0627334i	0.999508	−	0.0313667i	$-0.00998597\pi$
$68$	2.70976	0.328606
$69$	0.525985	0.0633212
$70$	− 1.14776i	− 0.137183i
$71$	− 10.7873i	− 1.28022i	−0.768284	−	0.640109i	$-0.778889\pi$
$71$	− 10.7873i	− 1.28022i	0.768284	−	0.640109i	$-0.221111\pi$
$72$	− 2.93605i	− 0.346017i
$73$	− 8.02452i	− 0.939199i	−0.882880	−	0.469599i	$-0.844398\pi$
$73$	− 8.02452i	− 0.939199i	0.882880	−	0.469599i	$-0.155602\pi$
$74$	−9.64405	−1.12110
$75$	0.931263	0.107533
$76$	6.56298i	0.752826i
$77$	−4.44485	−0.506538
$78$	0	0
$79$	10.7404	1.20839	0.604193	−	0.796838i	$-0.293496\pi$
$79$	10.7404	1.20839	0.604193	+	0.796838i	$0.293496\pi$
$80$	− 1.14776i	− 0.128323i
$81$	8.42856	0.936507
$82$	−9.49471	−1.04851
$83$	15.3479i	1.68465i	0.538967	+	0.842327i	$0.318815\pi$
$83$	15.3479i	1.68465i	−0.538967	+	0.842327i	$0.681185\pi$
$84$	− 0.252878i	− 0.0275913i
$85$	3.11014i	0.337342i
$86$	− 3.40320i	− 0.366976i
$87$	1.82052	0.195180
$88$	−4.44485	−0.473823
$89$	10.8596i	1.15111i	0.817763	+	0.575555i	$0.195214\pi$
$89$	10.8596i	1.15111i	−0.817763	+	0.575555i	$0.804786\pi$
$90$	3.36987	0.355216
$91$	0	0
$92$	−2.08000	−0.216855
$93$	2.00000i	0.207390i
$94$	−1.67435	−0.172696
$95$	−7.53270	−0.772838
$96$	− 0.252878i	− 0.0258093i
$97$	− 2.12694i	− 0.215958i	−0.994153	−	0.107979i	$-0.965562\pi$
$97$	− 2.12694i	− 0.215958i	0.994153	−	0.107979i	$-0.0344379\pi$
$98$	1.00000i	0.101015i
$99$	− 13.0503i	− 1.31161i
$100$	−3.68266	−0.368266
$101$	6.01888	0.598901	0.299451	−	0.954112i	$-0.403197\pi$
$101$	6.01888	0.598901	0.299451	+	0.954112i	$0.403197\pi$
$102$	0.685238i	0.0678487i
$103$	5.75670	0.567224	0.283612	−	0.958939i	$-0.408467\pi$
$103$	5.75670	0.567224	0.283612	+	0.958939i	$0.408467\pi$
$104$	0	0
$105$	0.290242	0.0283247
$106$	− 13.2815i	− 1.29002i
$107$	−5.54937	−0.536478	−0.268239	−	0.963352i	$-0.586442\pi$
$107$	−5.54937	−0.536478	−0.268239	+	0.963352i	$0.586442\pi$
$108$	1.50110	0.144443
$109$	7.96986i	0.763374i	0.924292	+	0.381687i	$0.124657\pi$
$109$	7.96986i	0.763374i	−0.924292	+	0.381687i	$0.875343\pi$
$110$	− 5.10160i	− 0.486419i
$111$	− 2.43877i	− 0.231477i
$112$	1.00000i	0.0944911i
$113$	−4.37070	−0.411161	−0.205580	−	0.978640i	$-0.565908\pi$
$113$	−4.37070	−0.411161	−0.205580	+	0.978640i	$0.565908\pi$
$114$	−1.65963	−0.155439
$115$	− 2.38733i	− 0.222619i
$116$	−7.19919	−0.668428
$117$	0	0
$118$	−0.0677585	−0.00623767
$119$	− 2.70976i	− 0.248403i
$120$	0.290242	0.0264954
$121$	−8.75670	−0.796063
$122$	− 8.10046i	− 0.733382i
$123$	− 2.40100i	− 0.216491i
$124$	− 7.90895i	− 0.710245i
$125$	− 9.96557i	− 0.891347i
$126$	−2.93605	−0.261564
$127$	−6.86494	−0.609165	−0.304583	−	0.952486i	$-0.598517\pi$
$127$	−6.86494	−0.609165	−0.304583	+	0.952486i	$0.598517\pi$
$128$	1.00000i	0.0883883i
$129$	0.860593	0.0757710
$130$	0	0
$131$	−16.1996	−1.41537	−0.707683	−	0.706530i	$-0.750259\pi$
$131$	−16.1996	−1.41537	−0.707683	+	0.706530i	$0.750259\pi$
$132$	− 1.12400i	− 0.0978321i
$133$	6.56298	0.569083
$134$	−0.513495	−0.0443592
$135$	1.72289i	0.148283i
$136$	− 2.70976i	− 0.232360i
$137$	− 5.20224i	− 0.444457i	−0.974995	−	0.222229i	$-0.928667\pi$
$137$	− 5.20224i	− 0.444457i	0.974995	−	0.222229i	$-0.0713331\pi$
$138$	− 0.525985i	− 0.0447749i
$139$	5.74027	0.486883	0.243442	−	0.969916i	$-0.421724\pi$
$139$	5.74027	0.486883	0.243442	+	0.969916i	$0.421724\pi$
$140$	−1.14776	−0.0970030
$141$	− 0.423405i	− 0.0356572i
$142$	−10.7873	−0.905250
$143$	0	0
$144$	−2.93605	−0.244671
$145$	− 8.26291i	− 0.686198i
$146$	−8.02452	−0.664114
$147$	−0.252878	−0.0208570
$148$	9.64405i	0.792736i
$149$	− 3.02580i	− 0.247883i	−0.992290	−	0.123941i	$-0.960447\pi$
$149$	− 3.02580i	− 0.247883i	0.992290	−	0.123941i	$-0.0395535\pi$
$150$	− 0.931263i	− 0.0760373i
$151$	− 1.27030i	− 0.103376i	−0.998663	−	0.0516879i	$-0.983540\pi$
$151$	− 1.27030i	− 0.103376i	0.998663	−	0.0516879i	$-0.0164601\pi$
$152$	6.56298	0.532328
$153$	7.95599	0.643204
$154$	4.44485i	0.358176i
$155$	9.07754	0.729126
$156$	0	0
$157$	−4.11859	−0.328699	−0.164350	−	0.986402i	$-0.552553\pi$
$157$	−4.11859	−0.328699	−0.164350	+	0.986402i	$0.552553\pi$
$158$	− 10.7404i	− 0.854457i
$159$	3.35861	0.266355
$160$	−1.14776	−0.0907380
$161$	2.08000i	0.163927i
$162$	− 8.42856i	− 0.662211i
$163$	11.2191i	0.878751i	0.898303	+	0.439376i	$0.144800\pi$
$163$	11.2191i	0.878751i	−0.898303	+	0.439376i	$0.855200\pi$
$164$	9.49471i	0.741412i
$165$	1.29008	0.100433
$166$	15.3479	1.19123
$167$	− 3.99739i	− 0.309327i	−0.987967	−	0.154664i	$-0.950571\pi$
$167$	− 3.99739i	− 0.309327i	0.987967	−	0.154664i	$-0.0494293\pi$
$168$	−0.252878	−0.0195100
$169$	0	0
$170$	3.11014	0.238537
$171$	19.2693i	1.47356i
$172$	−3.40320	−0.259491
$173$	12.1679	0.925109	0.462555	−	0.886591i	$-0.346933\pi$
$173$	12.1679	0.925109	0.462555	+	0.886591i	$0.346933\pi$
$174$	− 1.82052i	− 0.138013i
$175$	3.68266i	0.278383i
$176$	4.44485i	0.335043i
$177$	− 0.0171346i	− 0.00128792i
$178$	10.8596	0.813958
$179$	11.8711	0.887285	0.443643	−	0.896204i	$-0.353686\pi$
$179$	11.8711	0.887285	0.443643	+	0.896204i	$0.353686\pi$
$180$	− 3.36987i	− 0.251175i
$181$	−4.79134	−0.356137	−0.178069	−	0.984018i	$-0.556985\pi$
$181$	−4.79134	−0.356137	−0.178069	+	0.984018i	$0.556985\pi$
$182$	0	0
$183$	2.04843	0.151424
$184$	2.08000i	0.153339i
$185$	−11.0690	−0.813809
$186$	2.00000	0.146647
$187$	− 12.0445i	− 0.880779i
$188$	1.67435i	0.122114i
$189$	− 1.50110i	− 0.109189i
$190$	7.53270i	0.546479i
$191$	15.5853	1.12771	0.563855	−	0.825874i	$-0.309318\pi$
$191$	15.5853	1.12771	0.563855	+	0.825874i	$0.309318\pi$
$192$	−0.252878	−0.0182499
$193$	− 17.5855i	− 1.26583i	−0.774221	−	0.632916i	$-0.781858\pi$
$193$	− 17.5855i	− 1.26583i	0.774221	−	0.632916i	$-0.218142\pi$
$194$	−2.12694	−0.152705
$195$	0	0
$196$	1.00000	0.0714286
$197$	− 0.529815i	− 0.0377477i	−0.999822	−	0.0188739i	$-0.993992\pi$
$197$	− 0.529815i	− 0.0377477i	0.999822	−	0.0188739i	$-0.00600809\pi$
$198$	−13.0503	−0.927446
$199$	−25.1465	−1.78259	−0.891294	−	0.453426i	$-0.850201\pi$
$199$	−25.1465	−1.78259	−0.891294	+	0.453426i	$0.850201\pi$
$200$	3.68266i	0.260403i
$201$	− 0.129852i	− 0.00915902i
$202$	− 6.01888i	− 0.423487i
$203$	7.19919i	0.505284i
$204$	0.685238	0.0479763
$205$	−10.8976	−0.761121
$206$	− 5.75670i	− 0.401088i
$207$	−6.10698	−0.424465
$208$	0	0
$209$	29.1715	2.01783
$210$	− 0.290242i	− 0.0200286i
$211$	5.44170	0.374622	0.187311	−	0.982301i	$-0.440023\pi$
$211$	5.44170	0.374622	0.187311	+	0.982301i	$0.440023\pi$
$212$	−13.2815	−0.912180
$213$	− 2.72787i	− 0.186911i
$214$	5.54937i	0.379347i
$215$	− 3.90604i	− 0.266390i
$216$	− 1.50110i	− 0.102137i
$217$	−7.90895	−0.536895
$218$	7.96986	0.539787
$219$	− 2.02922i	− 0.137122i
$220$	−5.10160	−0.343950
$221$	0	0
$222$	−2.43877	−0.163679
$223$	9.24550i	0.619124i	0.950879	+	0.309562i	$0.100182\pi$
$223$	9.24550i	0.619124i	−0.950879	+	0.309562i	$0.899818\pi$
$224$	1.00000	0.0668153
$225$	−10.8125	−0.720832
$226$	4.37070i	0.290735i
$227$	1.50478i	0.0998756i	0.998752	+	0.0499378i	$0.0159023\pi$
$227$	1.50478i	0.0998756i	−0.998752	+	0.0499378i	$0.984098\pi$
$228$	1.65963i	0.109912i
$229$	− 25.4380i	− 1.68099i	−0.541818	−	0.840496i	$-0.682264\pi$
$229$	− 25.4380i	− 1.68099i	0.541818	−	0.840496i	$-0.317736\pi$
$230$	−2.38733	−0.157416
$231$	−1.12400	−0.0739541
$232$	7.19919i	0.472650i
$233$	12.1004	0.792724	0.396362	−	0.918094i	$-0.370273\pi$
$233$	12.1004	0.792724	0.396362	+	0.918094i	$0.370273\pi$
$234$	0	0
$235$	−1.92174	−0.125361
$236$	0.0677585i	0.00441070i
$237$	2.71600	0.176423
$238$	−2.70976	−0.175648
$239$	− 5.57964i	− 0.360917i	−0.983583	−	0.180458i	$-0.942242\pi$
$239$	− 5.57964i	− 0.360917i	0.983583	−	0.180458i	$-0.0577581\pi$
$240$	− 0.290242i	− 0.0187350i
$241$	− 23.2430i	− 1.49722i	−0.663013	−	0.748608i	$-0.730723\pi$
$241$	− 23.2430i	− 1.49722i	0.663013	−	0.748608i	$-0.269277\pi$
$242$	8.75670i	0.562902i
$243$	6.63469	0.425616
$244$	−8.10046	−0.518579
$245$	1.14776i	0.0733274i
$246$	−2.40100	−0.153082
$247$	0	0
$248$	−7.90895	−0.502219
$249$	3.88115i	0.245958i
$250$	−9.96557	−0.630278
$251$	23.7414	1.49855	0.749273	−	0.662261i	$-0.230403\pi$
$251$	23.7414	1.49855	0.749273	+	0.662261i	$0.230403\pi$
$252$	2.93605i	0.184954i
$253$	9.24528i	0.581246i
$254$	6.86494i	0.430745i
$255$	0.786486i	0.0492517i
$256$	1.00000	0.0625000
$257$	−7.01039	−0.437296	−0.218648	−	0.975804i	$-0.570165\pi$
$257$	−7.01039	−0.437296	−0.218648	+	0.975804i	$0.570165\pi$
$258$	− 0.860593i	− 0.0535782i
$259$	9.64405	0.599252
$260$	0	0
$261$	−21.1372	−1.30836
$262$	16.1996i	1.00081i
$263$	30.8452	1.90200	0.950998	−	0.309196i	$-0.100060\pi$
$263$	30.8452	1.90200	0.950998	+	0.309196i	$0.100060\pi$
$264$	−1.12400	−0.0691777
$265$	− 15.2440i	− 0.936429i
$266$	− 6.56298i	− 0.402402i
$267$	2.74614i	0.168061i
$268$	0.513495i	0.0313667i
$269$	−5.63191	−0.343383	−0.171692	−	0.985151i	$-0.554923\pi$
$269$	−5.63191	−0.343383	−0.171692	+	0.985151i	$0.554923\pi$
$270$	1.72289	0.104852
$271$	− 3.00481i	− 0.182529i	−0.995827	−	0.0912645i	$-0.970909\pi$
$271$	− 3.00481i	− 0.182529i	0.995827	−	0.0912645i	$-0.0290909\pi$
$272$	−2.70976	−0.164303
$273$	0	0
$274$	−5.20224	−0.314279
$275$	16.3689i	0.987080i
$276$	−0.525985	−0.0316606
$277$	24.1732	1.45243	0.726214	−	0.687469i	$-0.241278\pi$
$277$	24.1732	1.45243	0.726214	+	0.687469i	$0.241278\pi$
$278$	− 5.74027i	− 0.344278i
$279$	− 23.2211i	− 1.39021i
$280$	1.14776i	0.0685915i
$281$	1.74575i	0.104143i	0.998643	+	0.0520713i	$0.0165823\pi$
$281$	1.74575i	0.104143i	−0.998643	+	0.0520713i	$0.983418\pi$
$282$	−0.423405	−0.0252134
$283$	−26.1143	−1.55233	−0.776167	−	0.630527i	$-0.782839\pi$
$283$	−26.1143	−1.55233	−0.776167	+	0.630527i	$0.782839\pi$
$284$	10.7873i	0.640109i
$285$	−1.90485	−0.112834
$286$	0	0
$287$	9.49471	0.560455
$288$	2.93605i	0.173009i
$289$	−9.65721	−0.568071
$290$	−8.26291	−0.485215
$291$	− 0.537855i	− 0.0315296i
$292$	8.02452i	0.469599i
$293$	5.65535i	0.330389i	0.986261	+	0.165194i	$0.0528252\pi$
$293$	5.65535i	0.330389i	−0.986261	+	0.165194i	$0.947175\pi$
$294$	0.252878i	0.0147481i
$295$	−0.0777701	−0.00452795
$296$	9.64405	0.560549
$297$	− 6.67215i	− 0.387158i
$298$	−3.02580	−0.175280
$299$	0	0
$300$	−0.931263	−0.0537665
$301$	3.40320i	0.196157i
$302$	−1.27030	−0.0730977
$303$	1.52204	0.0874391
$304$	− 6.56298i	− 0.376413i
$305$	− 9.29735i	− 0.532365i
$306$	− 7.95599i	− 0.454814i
$307$	− 20.4767i	− 1.16867i	−0.811514	−	0.584333i	$-0.801356\pi$
$307$	− 20.4767i	− 1.16867i	0.811514	−	0.584333i	$-0.198644\pi$
$308$	4.44485	0.253269
$309$	1.45574	0.0828143
$310$	− 9.07754i	− 0.515570i
$311$	1.23712	0.0701506	0.0350753	−	0.999385i	$-0.488833\pi$
$311$	1.23712	0.0701506	0.0350753	+	0.999385i	$0.488833\pi$
$312$	0	0
$313$	−9.01151	−0.509361	−0.254680	−	0.967025i	$-0.581970\pi$
$313$	−9.01151	−0.509361	−0.254680	+	0.967025i	$0.581970\pi$
$314$	4.11859i	0.232426i
$315$	−3.36987	−0.189871
$316$	−10.7404	−0.604193
$317$	− 0.580644i	− 0.0326122i	−0.999867	−	0.0163061i	$-0.994809\pi$
$317$	− 0.580644i	− 0.0326122i	0.999867	−	0.0163061i	$-0.00519062\pi$
$318$	− 3.35861i	− 0.188342i
$319$	31.9993i	1.79162i
$320$	1.14776i	0.0641615i
$321$	−1.40331	−0.0783253
$322$	2.08000	0.115914
$323$	17.7841i	0.989533i
$324$	−8.42856	−0.468254
$325$	0	0
$326$	11.2191	0.621371
$327$	2.01540i	0.111452i
$328$	9.49471	0.524257
$329$	1.67435	0.0923097
$330$	− 1.29008i	− 0.0710167i
$331$	31.3654i	1.72400i	0.506910	+	0.861999i	$0.330788\pi$
$331$	31.3654i	1.72400i	−0.506910	+	0.861999i	$0.669212\pi$
$332$	− 15.3479i	− 0.842327i
$333$	28.3154i	1.55168i
$334$	−3.99739	−0.218727
$335$	−0.589367	−0.0322005
$336$	0.252878i	0.0137956i
$337$	9.43033	0.513703	0.256851	−	0.966451i	$-0.417315\pi$
$337$	9.43033	0.513703	0.256851	+	0.966451i	$0.417315\pi$
$338$	0	0
$339$	−1.10525	−0.0600292
$340$	− 3.11014i	− 0.168671i
$341$	−35.1541	−1.90370
$342$	19.2693	1.04196
$343$	− 1.00000i	− 0.0539949i
$344$	3.40320i	0.183488i
$345$	− 0.603703i	− 0.0325023i
$346$	− 12.1679i	− 0.654151i
$347$	6.47300	0.347489	0.173744	−	0.984791i	$-0.444413\pi$
$347$	6.47300	0.347489	0.173744	+	0.984791i	$0.444413\pi$
$348$	−1.82052	−0.0975900
$349$	9.90515i	0.530211i	0.964219	+	0.265105i	$0.0854067\pi$
$349$	9.90515i	0.530211i	−0.964219	+	0.265105i	$0.914593\pi$
$350$	3.68266	0.196846
$351$	0	0
$352$	4.44485	0.236911
$353$	28.7758i	1.53158i	0.643090	+	0.765790i	$0.277652\pi$
$353$	28.7758i	1.53158i	−0.643090	+	0.765790i	$0.722348\pi$
$354$	−0.0171346	−0.000910695 0
$355$	−12.3812	−0.657125
$356$	− 10.8596i	− 0.575555i
$357$	− 0.685238i	− 0.0362666i
$358$	− 11.8711i	− 0.627406i
$359$	12.1382i	0.640631i	0.947311	+	0.320315i	$0.103789\pi$
$359$	12.1382i	0.640631i	−0.947311	+	0.320315i	$0.896211\pi$
$360$	−3.36987	−0.177608
$361$	−24.0727	−1.26699
$362$	4.79134i	0.251827i
$363$	−2.21438	−0.116225
$364$	0	0
$365$	−9.21019	−0.482083
$366$	− 2.04843i	− 0.107073i
$367$	−27.0775	−1.41343	−0.706717	−	0.707496i	$-0.749825\pi$
$367$	−27.0775	−1.41343	−0.706717	+	0.707496i	$0.749825\pi$
$368$	2.08000	0.108427
$369$	27.8770i	1.45122i
$370$	11.0690i	0.575450i
$371$	13.2815i	0.689543i
$372$	− 2.00000i	− 0.103695i
$373$	−15.6332	−0.809457	−0.404729	−	0.914437i	$-0.632634\pi$
$373$	−15.6332	−0.809457	−0.404729	+	0.914437i	$0.632634\pi$
$374$	−12.0445	−0.622805
$375$	− 2.52007i	− 0.130136i
$376$	1.67435	0.0863478
$377$	0	0
$378$	−1.50110	−0.0772081
$379$	− 37.3308i	− 1.91756i	−0.284155	−	0.958778i	$-0.591713\pi$
$379$	− 37.3308i	− 1.91756i	0.284155	−	0.958778i	$-0.408287\pi$
$380$	7.53270	0.386419
$381$	−1.73599	−0.0889376
$382$	− 15.5853i	− 0.797411i
$383$	37.8964i	1.93642i	0.250144	+	0.968209i	$0.419522\pi$
$383$	37.8964i	1.93642i	−0.250144	+	0.968209i	$0.580478\pi$
$384$	0.252878i	0.0129046i
$385$	5.10160i	0.260002i
$386$	−17.5855	−0.895078
$387$	−9.99196	−0.507920
$388$	2.12694i	0.107979i
$389$	−10.1053	−0.512361	−0.256180	−	0.966629i	$-0.582464\pi$
$389$	−10.1053	−0.512361	−0.256180	+	0.966629i	$0.582464\pi$
$390$	0	0
$391$	−5.63629	−0.285039
$392$	− 1.00000i	− 0.0505076i
$393$	−4.09652	−0.206642
$394$	−0.529815	−0.0266917
$395$	− 12.3273i	− 0.620254i
$396$	13.0503i	0.655803i
$397$	− 5.50839i	− 0.276458i	−0.990400	−	0.138229i	$-0.955859\pi$
$397$	− 5.50839i	− 0.276458i	0.990400	−	0.138229i	$-0.0441410\pi$
$398$	25.1465i	1.26048i
$399$	1.65963	0.0830856
$400$	3.68266	0.184133
$401$	− 26.7495i	− 1.33581i	−0.744249	−	0.667903i	$-0.767192\pi$
$401$	− 26.7495i	− 1.33581i	0.744249	−	0.667903i	$-0.232808\pi$
$402$	−0.129852	−0.00647641
$403$	0	0
$404$	−6.01888	−0.299451
$405$	− 9.67393i	− 0.480701i
$406$	7.19919	0.357290
$407$	42.8663	2.12481
$408$	− 0.685238i	− 0.0339243i
$409$	31.9995i	1.58227i	0.611639	+	0.791137i	$0.290510\pi$
$409$	31.9995i	1.58227i	−0.611639	+	0.791137i	$0.709490\pi$
$410$	10.8976i	0.538194i
$411$	− 1.31553i	− 0.0648904i
$412$	−5.75670	−0.283612
$413$	0.0677585	0.00333418
$414$	6.10698i	0.300142i
$415$	17.6157	0.864719
$416$	0	0
$417$	1.45159	0.0710846
$418$	− 29.1715i	− 1.42682i
$419$	11.6956	0.571370	0.285685	−	0.958324i	$-0.407779\pi$
$419$	11.6956	0.571370	0.285685	+	0.958324i	$0.407779\pi$
$420$	−0.290242	−0.0141624
$421$	25.8565i	1.26017i	0.776527	+	0.630084i	$0.216979\pi$
$421$	25.8565i	1.26017i	−0.776527	+	0.630084i	$0.783021\pi$
$422$	− 5.44170i	− 0.264898i
$423$	4.91597i	0.239023i
$424$	13.2815i	0.645009i
$425$	−9.97911	−0.484058
$426$	−2.72787	−0.132166
$427$	8.10046i	0.392009i
$428$	5.54937	0.268239
$429$	0	0
$430$	−3.90604	−0.188366
$431$	10.7062i	0.515700i	0.966185	+	0.257850i	$0.0830141\pi$
$431$	10.7062i	0.515700i	−0.966185	+	0.257850i	$0.916986\pi$
$432$	−1.50110	−0.0722216
$433$	−22.4299	−1.07791	−0.538956	−	0.842334i	$-0.681181\pi$
$433$	−22.4299	−1.07791	−0.538956	+	0.842334i	$0.681181\pi$
$434$	7.90895i	0.379642i
$435$	− 2.08951i	− 0.100184i
$436$	− 7.96986i	− 0.381687i
$437$	− 13.6510i	− 0.653015i
$438$	−2.02922	−0.0969601
$439$	12.7183	0.607009	0.303505	−	0.952830i	$-0.401843\pi$
$439$	12.7183	0.607009	0.303505	+	0.952830i	$0.401843\pi$
$440$	5.10160i	0.243209i
$441$	2.93605	0.139812
$442$	0	0
$443$	−7.86448	−0.373653	−0.186826	−	0.982393i	$-0.559820\pi$
$443$	−7.86448	−0.373653	−0.186826	+	0.982393i	$0.559820\pi$
$444$	2.43877i	0.115739i
$445$	12.4641	0.590856
$446$	9.24550	0.437787
$447$	− 0.765157i	− 0.0361907i
$448$	− 1.00000i	− 0.0472456i
$449$	16.8373i	0.794600i	0.917689	+	0.397300i	$0.130053\pi$
$449$	16.8373i	0.794600i	−0.917689	+	0.397300i	$0.869947\pi$
$450$	10.8125i	0.509705i
$451$	42.2025	1.98724
$452$	4.37070	0.205580
$453$	− 0.321232i	− 0.0150928i
$454$	1.50478	0.0706227
$455$	0	0
$456$	1.65963	0.0777195
$457$	9.19764i	0.430248i	0.976587	+	0.215124i	$0.0690155\pi$
$457$	9.19764i	0.430248i	−0.976587	+	0.215124i	$0.930985\pi$
$458$	−25.4380	−1.18864
$459$	4.06761	0.189860
$460$	2.38733i	0.111310i
$461$	21.8021i	1.01542i	0.861527	+	0.507712i	$0.169509\pi$
$461$	21.8021i	1.01542i	−0.861527	+	0.507712i	$0.830491\pi$
$462$	1.12400i	0.0522934i
$463$	26.0636i	1.21128i	0.795740	+	0.605638i	$0.207082\pi$
$463$	26.0636i	1.21128i	−0.795740	+	0.605638i	$0.792918\pi$
$464$	7.19919	0.334214
$465$	2.29551	0.106452
$466$	− 12.1004i	− 0.560541i
$467$	28.6668	1.32654	0.663271	−	0.748379i	$-0.269168\pi$
$467$	28.6668	1.32654	0.663271	+	0.748379i	$0.269168\pi$
$468$	0	0
$469$	0.513495	0.0237110
$470$	1.92174i	0.0886433i
$471$	−1.04150	−0.0479898
$472$	0.0677585	0.00311884
$473$	15.1267i	0.695526i
$474$	− 2.71600i	− 0.124750i
$475$	− 24.1692i	− 1.10896i
$476$	2.70976i	0.124202i
$477$	−38.9953	−1.78547
$478$	−5.57964	−0.255207
$479$	− 17.9762i	− 0.821356i	−0.911781	−	0.410678i	$-0.865292\pi$
$479$	− 17.9762i	− 0.821356i	0.911781	−	0.410678i	$-0.134708\pi$
$480$	−0.290242	−0.0132477
$481$	0	0
$482$	−23.2430	−1.05869
$483$	0.525985i	0.0239332i
$484$	8.75670	0.398032
$485$	−2.44120	−0.110849
$486$	− 6.63469i	− 0.300956i
$487$	− 21.9216i	− 0.993363i	−0.867933	−	0.496681i	$-0.834552\pi$
$487$	− 21.9216i	− 0.993363i	0.867933	−	0.496681i	$-0.165448\pi$
$488$	8.10046i	0.366691i
$489$	2.83707i	0.128297i
$490$	1.14776	0.0518503
$491$	21.6006	0.974822	0.487411	−	0.873173i	$-0.337941\pi$
$491$	21.6006	0.974822	0.487411	+	0.873173i	$0.337941\pi$
$492$	2.40100i	0.108246i
$493$	−19.5081	−0.878599
$494$	0	0
$495$	−14.9786	−0.673237
$496$	7.90895i	0.355122i
$497$	10.7873	0.483877
$498$	3.88115	0.173919
$499$	− 38.6105i	− 1.72844i	−0.503112	−	0.864221i	$-0.667812\pi$
$499$	− 38.6105i	− 1.72844i	0.503112	−	0.864221i	$-0.332188\pi$
$500$	9.96557i	0.445674i
$501$	− 1.01085i	− 0.0451615i
$502$	− 23.7414i	− 1.05963i
$503$	−9.47007	−0.422249	−0.211125	−	0.977459i	$-0.567713\pi$
$503$	−9.47007	−0.422249	−0.211125	+	0.977459i	$0.567713\pi$
$504$	2.93605	0.130782
$505$	− 6.90820i	− 0.307411i
$506$	9.24528	0.411003
$507$	0	0
$508$	6.86494	0.304583
$509$	13.0530i	0.578565i	0.957244	+	0.289283i	$0.0934167\pi$
$509$	13.0530i	0.578565i	−0.957244	+	0.289283i	$0.906583\pi$
$510$	0.786486	0.0348262
$511$	8.02452	0.354984
$512$	− 1.00000i	− 0.0441942i
$513$	9.85167i	0.434962i
$514$	7.01039i	0.309215i
$515$	− 6.60728i	− 0.291152i
$516$	−0.860593	−0.0378855
$517$	7.44222	0.327309
$518$	− 9.64405i	− 0.423735i
$519$	3.07700	0.135065
$520$	0	0
$521$	10.3444	0.453196	0.226598	−	0.973988i	$-0.427240\pi$
$521$	10.3444	0.453196	0.226598	+	0.973988i	$0.427240\pi$
$522$	21.1372i	0.925151i
$523$	−2.13368	−0.0932993	−0.0466497	−	0.998911i	$-0.514854\pi$
$523$	−2.13368	−0.0932993	−0.0466497	+	0.998911i	$0.514854\pi$
$524$	16.1996	0.707683
$525$	0.931263i	0.0406437i
$526$	− 30.8452i	− 1.34491i
$527$	− 21.4313i	− 0.933564i
$528$	1.12400i	0.0489160i
$529$	−18.6736	−0.811896
$530$	−15.2440	−0.662156
$531$	0.198942i	0.00863336i
$532$	−6.56298	−0.284541
$533$	0	0
$534$	2.74614	0.118837
$535$	6.36932i	0.275370i
$536$	0.513495	0.0221796
$537$	3.00193	0.129543
$538$	5.63191i	0.242809i
$539$	− 4.44485i	− 0.191453i
$540$	− 1.72289i	− 0.0741415i
$541$	8.41225i	0.361671i	0.983513	+	0.180836i	$0.0578802\pi$
$541$	8.41225i	0.361671i	−0.983513	+	0.180836i	$0.942120\pi$
$542$	−3.00481	−0.129068
$543$	−1.21162	−0.0519958
$544$	2.70976i	0.116180i
$545$	9.14745	0.391834
$546$	0	0
$547$	−1.00730	−0.0430692	−0.0215346	−	0.999768i	$-0.506855\pi$
$547$	−1.00730	−0.0430692	−0.0215346	+	0.999768i	$0.506855\pi$
$548$	5.20224i	0.222229i
$549$	−23.7834	−1.01505
$550$	16.3689	0.697971
$551$	− 47.2482i	− 2.01284i
$552$	0.525985i	0.0223874i
$553$	10.7404i	0.456727i
$554$	− 24.1732i	− 1.02702i
$555$	−2.79911	−0.118816
$556$	−5.74027	−0.243442
$557$	43.7905i	1.85546i	0.373247	+	0.927732i	$0.378244\pi$
$557$	43.7905i	1.85546i	−0.373247	+	0.927732i	$0.621756\pi$
$558$	−23.2211	−0.983028
$559$	0	0
$560$	1.14776	0.0485015
$561$	− 3.04578i	− 0.128593i
$562$	1.74575	0.0736399
$563$	−4.22667	−0.178133	−0.0890665	−	0.996026i	$-0.528388\pi$
$563$	−4.22667	−0.178133	−0.0890665	+	0.996026i	$0.528388\pi$
$564$	0.423405i	0.0178286i
$565$	5.01650i	0.211046i
$566$	26.1143i	1.09767i
$567$	8.42856i	0.353966i
$568$	10.7873	0.452625
$569$	−9.42639	−0.395175	−0.197587	−	0.980285i	$-0.563311\pi$
$569$	−9.42639	−0.395175	−0.197587	+	0.980285i	$0.563311\pi$
$570$	1.90485i	0.0797855i
$571$	25.5304	1.06842	0.534208	−	0.845353i	$-0.320610\pi$
$571$	25.5304	1.06842	0.534208	+	0.845353i	$0.320610\pi$
$572$	0	0
$573$	3.94117	0.164645
$574$	− 9.49471i	− 0.396301i
$575$	7.65992	0.319441
$576$	2.93605	0.122336
$577$	− 31.7623i	− 1.32228i	−0.750262	−	0.661141i	$-0.770073\pi$
$577$	− 31.7623i	− 1.32228i	0.750262	−	0.661141i	$-0.229927\pi$
$578$	9.65721i	0.401687i
$579$	− 4.44698i	− 0.184810i
$580$	8.26291i	0.343099i
$581$	−15.3479	−0.636739
$582$	−0.537855	−0.0222948
$583$	59.0345i	2.44496i
$584$	8.02452	0.332057
$585$	0	0
$586$	5.65535	0.233620
$587$	− 34.3442i	− 1.41754i	−0.705441	−	0.708768i	$-0.749251\pi$
$587$	− 34.3442i	− 1.41754i	0.705441	−	0.708768i	$-0.250749\pi$
$588$	0.252878	0.0104285
$589$	51.9063	2.13876
$590$	0.0777701i	0.00320175i
$591$	− 0.133978i	− 0.00551114i
$592$	− 9.64405i	− 0.396368i
$593$	− 15.1751i	− 0.623168i	−0.950219	−	0.311584i	$-0.899140\pi$
$593$	− 15.1751i	− 0.623168i	0.950219	−	0.311584i	$-0.100860\pi$
$594$	−6.67215	−0.273762
$595$	−3.11014	−0.127503
$596$	3.02580i	0.123941i
$597$	−6.35899	−0.260256
$598$	0	0
$599$	7.48641	0.305886	0.152943	−	0.988235i	$-0.451125\pi$
$599$	7.48641	0.305886	0.152943	+	0.988235i	$0.451125\pi$
$600$	0.931263i	0.0380187i
$601$	36.4142	1.48537	0.742683	−	0.669643i	$-0.233553\pi$
$601$	36.4142	1.48537	0.742683	+	0.669643i	$0.233553\pi$
$602$	3.40320	0.138704
$603$	1.50765i	0.0613962i
$604$	1.27030i	0.0516879i
$605$	10.0505i	0.408613i
$606$	− 1.52204i	− 0.0618288i
$607$	4.52337	0.183598	0.0917989	−	0.995778i	$-0.470738\pi$
$607$	4.52337	0.183598	0.0917989	+	0.995778i	$0.470738\pi$
$608$	−6.56298	−0.266164
$609$	1.82052i	0.0737711i
$610$	−9.29735	−0.376439
$611$	0	0
$612$	−7.95599	−0.321602
$613$	− 40.2337i	− 1.62502i	−0.582945	−	0.812512i	$-0.698100\pi$
$613$	− 40.2337i	− 1.62502i	0.582945	−	0.812512i	$-0.301900\pi$
$614$	−20.4767	−0.826372
$615$	−2.75576	−0.111123
$616$	− 4.44485i	− 0.179088i
$617$	39.5031i	1.59034i	0.606390	+	0.795168i	$0.292617\pi$
$617$	39.5031i	1.59034i	−0.606390	+	0.795168i	$0.707383\pi$
$618$	− 1.45574i	− 0.0585585i
$619$	22.9229i	0.921348i	0.887569	+	0.460674i	$0.152392\pi$
$619$	22.9229i	0.921348i	−0.887569	+	0.460674i	$0.847608\pi$
$620$	−9.07754	−0.364563
$621$	−3.12228	−0.125293
$622$	− 1.23712i	− 0.0496039i
$623$	−10.8596	−0.435079
$624$	0	0
$625$	6.97525	0.279010
$626$	9.01151i	0.360172i
$627$	7.37682	0.294602
$628$	4.11859	0.164350
$629$	26.1330i	1.04199i
$630$	3.36987i	0.134259i
$631$	− 3.60147i	− 0.143372i	−0.997427	−	0.0716862i	$-0.977162\pi$
$631$	− 3.60147i	− 0.143372i	0.997427	−	0.0716862i	$-0.0228380\pi$
$632$	10.7404i	0.427229i
$633$	1.37609	0.0546945
$634$	−0.580644	−0.0230603
$635$	7.87928i	0.312680i
$636$	−3.35861	−0.133178
$637$	0	0
$638$	31.9993	1.26687
$639$	31.6721i	1.25293i
$640$	1.14776	0.0453690
$641$	−5.21856	−0.206121	−0.103060	−	0.994675i	$-0.532863\pi$
$641$	−5.21856	−0.206121	−0.103060	+	0.994675i	$0.532863\pi$
$642$	1.40331i	0.0553843i
$643$	− 20.9008i	− 0.824248i	−0.911128	−	0.412124i	$-0.864787\pi$
$643$	− 20.9008i	− 0.824248i	0.911128	−	0.412124i	$-0.135213\pi$
$644$	− 2.08000i	− 0.0819634i
$645$	− 0.987751i	− 0.0388927i
$646$	17.7841	0.699706
$647$	7.62110	0.299617	0.149808	−	0.988715i	$-0.452134\pi$
$647$	7.62110	0.299617	0.149808	+	0.988715i	$0.452134\pi$
$648$	8.42856i	0.331105i
$649$	0.301176	0.0118222
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	− 11.2191i	− 0.439376i
$653$	−25.7819	−1.00892	−0.504462	−	0.863434i	$-0.668309\pi$
$653$	−25.7819	−1.00892	−0.504462	+	0.863434i	$0.668309\pi$
$654$	2.01540	0.0788084
$655$	18.5932i	0.726495i
$656$	− 9.49471i	− 0.370706i
$657$	23.5604i	0.919179i
$658$	− 1.67435i	− 0.0652728i
$659$	15.6593	0.609999	0.305000	−	0.952352i	$-0.401344\pi$
$659$	15.6593	0.609999	0.305000	+	0.952352i	$0.401344\pi$
$660$	−1.29008	−0.0502164
$661$	− 31.6889i	− 1.23255i	−0.787529	−	0.616277i	$-0.788640\pi$
$661$	− 31.6889i	− 1.23255i	0.787529	−	0.616277i	$-0.211360\pi$
$662$	31.3654	1.21905
$663$	0	0
$664$	−15.3479	−0.595615
$665$	− 7.53270i	− 0.292105i
$666$	28.3154	1.09720
$667$	14.9743	0.579807
$668$	3.99739i	0.154664i
$669$	2.33798i	0.0903916i
$670$	0.589367i	0.0227692i
$671$	36.0054i	1.38997i
$672$	0.252878	0.00975498
$673$	−16.7728	−0.646546	−0.323273	−	0.946306i	$-0.604783\pi$
$673$	−16.7728	−0.646546	−0.323273	+	0.946306i	$0.604783\pi$
$674$	− 9.43033i	− 0.363243i
$675$	−5.52803	−0.212774
$676$	0	0
$677$	−8.34791	−0.320836	−0.160418	−	0.987049i	$-0.551284\pi$
$677$	−8.34791	−0.320836	−0.160418	+	0.987049i	$0.551284\pi$
$678$	1.10525i	0.0424470i
$679$	2.12694	0.0816243
$680$	−3.11014	−0.119268
$681$	0.380525i	0.0145818i
$682$	35.1541i	1.34612i
$683$	27.1789i	1.03997i	0.854175	+	0.519986i	$0.174063\pi$
$683$	27.1789i	1.03997i	−0.854175	+	0.519986i	$0.825937\pi$
$684$	− 19.2693i	− 0.736778i
$685$	−5.97090	−0.228136
$686$	−1.00000	−0.0381802
$687$	− 6.43271i	− 0.245423i
$688$	3.40320	0.129746
$689$	0	0
$690$	−0.603703	−0.0229826
$691$	26.2582i	0.998909i	0.866340	+	0.499454i	$0.166466\pi$
$691$	26.2582i	0.998909i	−0.866340	+	0.499454i	$0.833534\pi$
$692$	−12.1679	−0.462555
$693$	13.0503	0.495741
$694$	− 6.47300i	− 0.245712i
$695$	− 6.58842i	− 0.249913i
$696$	1.82052i	0.0690066i
$697$	25.7284i	0.974531i
$698$	9.90515	0.374916
$699$	3.05993	0.115737
$700$	− 3.68266i	− 0.139191i
$701$	−26.4443	−0.998786	−0.499393	−	0.866376i	$-0.666444\pi$
$701$	−26.4443	−0.998786	−0.499393	+	0.866376i	$0.666444\pi$
$702$	0	0
$703$	−63.2937	−2.38717
$704$	− 4.44485i	− 0.167522i
$705$	−0.485966	−0.0183025
$706$	28.7758	1.08299
$707$	6.01888i	0.226363i
$708$	0.0171346i	0 0.000643959i
$709$	− 11.6264i	− 0.436640i	−0.975877	−	0.218320i	$-0.929942\pi$
$709$	− 11.6264i	− 0.436640i	0.975877	−	0.218320i	$-0.0700576\pi$
$710$	12.3812i	0.464658i
$711$	−31.5343	−1.18263
$712$	−10.8596	−0.406979
$713$	16.4506i	0.616080i
$714$	−0.685238	−0.0256444
$715$	0	0
$716$	−11.8711	−0.443643
$717$	− 1.41097i	− 0.0526935i
$718$	12.1382	0.452994
$719$	44.8758	1.67359	0.836793	−	0.547519i	$-0.184428\pi$
$719$	44.8758	1.67359	0.836793	+	0.547519i	$0.184428\pi$
$720$	3.36987i	0.125588i
$721$	5.75670i	0.214391i
$722$	24.0727i	0.895894i
$723$	− 5.87765i	− 0.218592i
$724$	4.79134	0.178069
$725$	26.5122	0.984637
$726$	2.21438i	0.0821832i
$727$	19.5156	0.723793	0.361896	−	0.932218i	$-0.382129\pi$
$727$	19.5156	0.723793	0.361896	+	0.932218i	$0.382129\pi$
$728$	0	0
$729$	−23.6079	−0.874368
$730$	9.21019i	0.340884i
$731$	−9.22184	−0.341082
$732$	−2.04843	−0.0757121
$733$	− 10.7037i	− 0.395349i	−0.980268	−	0.197675i	$-0.936661\pi$
$733$	− 10.7037i	− 0.395349i	0.980268	−	0.197675i	$-0.0633390\pi$
$734$	27.0775i	0.999449i
$735$	0.290242i	0.0107057i
$736$	− 2.08000i	− 0.0766697i
$737$	2.28241	0.0840736
$738$	27.8770	1.02616
$739$	0.477606i	0.0175690i	0.999961	+	0.00878452i	$0.00279623\pi$
$739$	0.477606i	0.0175690i	−0.999961	+	0.00878452i	$0.997204\pi$
$740$	11.0690	0.406905
$741$	0	0
$742$	13.2815	0.487581
$743$	9.73434i	0.357118i	0.983929	+	0.178559i	$0.0571436\pi$
$743$	9.73434i	0.357118i	−0.983929	+	0.178559i	$0.942856\pi$
$744$	−2.00000	−0.0733236
$745$	−3.47287	−0.127236
$746$	15.6332i	0.572373i
$747$	− 45.0623i	− 1.64874i
$748$	12.0445i	0.440389i
$749$	− 5.54937i	− 0.202769i
$750$	−2.52007	−0.0920200
$751$	−36.2167	−1.32157	−0.660784	−	0.750576i	$-0.729776\pi$
$751$	−36.2167	−1.32157	−0.660784	+	0.750576i	$0.729776\pi$
$752$	− 1.67435i	− 0.0610571i
$753$	6.00369	0.218787
$754$	0	0
$755$	−1.45800	−0.0530619
$756$	1.50110i	0.0545944i
$757$	46.4694	1.68896	0.844479	−	0.535589i	$-0.179910\pi$
$757$	46.4694	1.68896	0.844479	+	0.535589i	$0.179910\pi$
$758$	−37.3308	−1.35592
$759$	2.33793i	0.0848614i
$760$	− 7.53270i	− 0.273240i
$761$	− 21.3663i	− 0.774527i	−0.921969	−	0.387263i	$-0.873420\pi$
$761$	− 21.3663i	− 0.774527i	0.921969	−	0.387263i	$-0.126580\pi$
$762$	1.73599i	0.0628884i
$763$	−7.96986	−0.288528
$764$	−15.5853	−0.563855
$765$	− 9.13153i	− 0.330151i
$766$	37.8964	1.36925
$767$	0	0
$768$	0.252878	0.00912495
$769$	− 45.9914i	− 1.65849i	−0.558884	−	0.829246i	$-0.688770\pi$
$769$	− 45.9914i	− 1.65849i	0.558884	−	0.829246i	$-0.311230\pi$
$770$	5.10160	0.183849
$771$	−1.77277	−0.0638449
$772$	17.5855i	0.632916i
$773$	− 19.9479i	− 0.717475i	−0.933439	−	0.358737i	$-0.883207\pi$
$773$	− 19.9479i	− 0.717475i	0.933439	−	0.358737i	$-0.116793\pi$
$774$	9.99196i	0.359154i
$775$	29.1260i	1.04624i
$776$	2.12694	0.0763526
$777$	2.43877	0.0874903
$778$	10.1053i	0.362294i
$779$	−62.3136	−2.23262
$780$	0	0
$781$	47.9479	1.71571
$782$	5.63629i	0.201553i
$783$	−10.8067	−0.386200
$784$	−1.00000	−0.0357143
$785$	4.72714i	0.168719i
$786$	4.09652i	0.146118i
$787$	− 43.9625i	− 1.56709i	−0.621334	−	0.783546i	$-0.713409\pi$
$787$	− 43.9625i	− 1.56709i	0.621334	−	0.783546i	$-0.286591\pi$
$788$	0.529815i	0.0188739i
$789$	7.80007	0.277690
$790$	−12.3273	−0.438586
$791$	− 4.37070i	− 0.155404i
$792$	13.0503	0.463723
$793$	0	0
$794$	−5.50839	−0.195485
$795$	− 3.85486i	− 0.136718i
$796$	25.1465	0.891294
$797$	−31.9724	−1.13252	−0.566260	−	0.824226i	$-0.691610\pi$
$797$	−31.9724	−1.13252	−0.566260	+	0.824226i	$0.691610\pi$
$798$	− 1.65963i	− 0.0587504i
$799$	4.53707i	0.160510i
$800$	− 3.68266i	− 0.130202i
$801$	− 31.8842i	− 1.12657i
$802$	−26.7495	−0.944557
$803$	35.6678	1.25869
$804$	0.129852i	0.00457951i
$805$	2.38733	0.0841423
$806$	0	0
$807$	−1.42419	−0.0501337
$808$	6.01888i	0.211744i
$809$	−28.1731	−0.990514	−0.495257	−	0.868746i	$-0.664926\pi$
$809$	−28.1731	−0.990514	−0.495257	+	0.868746i	$0.664926\pi$
$810$	−9.67393	−0.339907
$811$	39.0534i	1.37135i	0.727908	+	0.685675i	$0.240493\pi$
$811$	39.0534i	1.37135i	−0.727908	+	0.685675i	$0.759507\pi$
$812$	− 7.19919i	− 0.252642i
$813$	− 0.759850i	− 0.0266491i
$814$	− 42.8663i	− 1.50246i
$815$	12.8768	0.451056
$816$	−0.685238	−0.0239881
$817$	− 22.3351i	− 0.781407i
$818$	31.9995	1.11884
$819$	0	0
$820$	10.8976	0.380561
$821$	23.5839i	0.823084i	0.911391	+	0.411542i	$0.135010\pi$
$821$	23.5839i	0.823084i	−0.911391	+	0.411542i	$0.864990\pi$
$822$	−1.31553	−0.0458844
$823$	−24.7133	−0.861450	−0.430725	−	0.902483i	$-0.641742\pi$
$823$	−24.7133	−0.861450	−0.430725	+	0.902483i	$0.641742\pi$
$824$	5.75670i	0.200544i
$825$	4.13933i	0.144113i
$826$	− 0.0677585i	− 0.00235762i
$827$	45.2456i	1.57334i	0.617371	+	0.786672i	$0.288198\pi$
$827$	45.2456i	1.57334i	−0.617371	+	0.786672i	$0.711802\pi$
$828$	6.10698	0.212232
$829$	−44.8129	−1.55642	−0.778208	−	0.628006i	$-0.783871\pi$
$829$	−44.8129	−1.55642	−0.778208	+	0.628006i	$0.783871\pi$
$830$	− 17.6157i	− 0.611449i
$831$	6.11287	0.212053
$832$	0	0
$833$	2.70976	0.0938875
$834$	− 1.45159i	− 0.0502644i
$835$	−4.58802	−0.158775
$836$	−29.1715	−1.00892
$837$	− 11.8721i	− 0.410360i
$838$	− 11.6956i	− 0.404019i
$839$	30.8895i	1.06642i	0.845982	+	0.533212i	$0.179015\pi$
$839$	30.8895i	1.06642i	−0.845982	+	0.533212i	$0.820985\pi$
$840$	0.290242i	0.0100143i
$841$	22.8284	0.787186
$842$	25.8565	0.891073
$843$	0.441461i	0.0152047i
$844$	−5.44170	−0.187311
$845$	0	0
$846$	4.91597	0.169015
$847$	− 8.75670i	− 0.300884i
$848$	13.2815	0.456090
$849$	−6.60373	−0.226640
$850$	9.97911i	0.342281i
$851$	− 20.0596i	− 0.687634i
$852$	2.72787i	0.0934553i
$853$	− 27.9201i	− 0.955965i	−0.878369	−	0.477982i	$-0.841368\pi$
$853$	− 27.9201i	− 0.955965i	0.878369	−	0.477982i	$-0.158632\pi$
$854$	8.10046	0.277192
$855$	22.1164	0.756365
$856$	− 5.54937i	− 0.189673i
$857$	−17.5921	−0.600935	−0.300468	−	0.953792i	$-0.597143\pi$
$857$	−17.5921	−0.600935	−0.300468	+	0.953792i	$0.597143\pi$
$858$	0	0
$859$	22.1337	0.755193	0.377596	−	0.925970i	$-0.376751\pi$
$859$	22.1337	0.755193	0.377596	+	0.925970i	$0.376751\pi$
$860$	3.90604i	0.133195i
$861$	2.40100	0.0818259
$862$	10.7062	0.364655
$863$	− 4.58867i	− 0.156200i	−0.996946	−	0.0781000i	$-0.975115\pi$
$863$	− 4.58867i	− 0.156200i	0.996946	−	0.0781000i	$-0.0248854\pi$
$864$	1.50110i	0.0510684i
$865$	− 13.9658i	− 0.474851i
$866$	22.4299i	0.762199i
$867$	−2.44210	−0.0829379
$868$	7.90895	0.268447
$869$	47.7393i	1.61944i
$870$	−2.08951	−0.0708410
$871$	0	0
$872$	−7.96986	−0.269893
$873$	6.24480i	0.211354i
$874$	−13.6510	−0.461751
$875$	9.96557	0.336898
$876$	2.02922i	0.0685611i
$877$	39.9812i	1.35007i	0.737786	+	0.675035i	$0.235872\pi$
$877$	39.9812i	1.35007i	−0.737786	+	0.675035i	$0.764128\pi$
$878$	− 12.7183i	− 0.429220i
$879$	1.43011i	0.0482365i
$880$	5.10160	0.171975
$881$	47.9096	1.61412	0.807058	−	0.590472i	$-0.201058\pi$
$881$	47.9096	1.61412	0.807058	+	0.590472i	$0.201058\pi$
$882$	− 2.93605i	− 0.0988620i
$883$	34.0091	1.14450	0.572248	−	0.820080i	$-0.306071\pi$
$883$	34.0091	1.14450	0.572248	+	0.820080i	$0.306071\pi$
$884$	0	0
$885$	−0.0196664	−0.000661077 0
$886$	7.86448i	0.264212i
$887$	3.77343	0.126699	0.0633497	−	0.997991i	$-0.479822\pi$
$887$	3.77343	0.126699	0.0633497	+	0.997991i	$0.479822\pi$
$888$	2.43877	0.0818397
$889$	− 6.86494i	− 0.230243i
$890$	− 12.4641i	− 0.417798i
$891$	37.4637i	1.25508i
$892$	− 9.24550i	− 0.309562i
$893$	−10.9887	−0.367723
$894$	−0.765157	−0.0255907
$895$	− 13.6251i	− 0.455436i
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	16.8373	0.561867
$899$	56.9381i	1.89899i
$900$	10.8125	0.360416
$901$	−35.9898	−1.19899
$902$	− 42.2025i	− 1.40519i
$903$	0.860593i	0.0286388i
$904$	− 4.37070i	− 0.145367i
$905$	5.49929i	0.182802i
$906$	−0.321232	−0.0106722
$907$	−14.2751	−0.473996	−0.236998	−	0.971510i	$-0.576163\pi$
$907$	−14.2751	−0.473996	−0.236998	+	0.971510i	$0.576163\pi$
$908$	− 1.50478i	− 0.0499378i
$909$	−17.6718	−0.586135
$910$	0	0
$911$	17.4161	0.577020	0.288510	−	0.957477i	$-0.406840\pi$
$911$	17.4161	0.577020	0.288510	+	0.957477i	$0.406840\pi$
$912$	− 1.65963i	− 0.0549560i
$913$	−68.2192	−2.25773
$914$	9.19764	0.304231
$915$	− 2.35110i	− 0.0777248i
$916$	25.4380i	0.840496i
$917$	− 16.1996i	− 0.534958i
$918$	− 4.06761i	− 0.134251i
$919$	36.2358	1.19531	0.597654	−	0.801754i	$-0.296100\pi$
$919$	36.2358	1.19531	0.597654	+	0.801754i	$0.296100\pi$
$920$	2.38733	0.0787079
$921$	− 5.17810i	− 0.170624i
$922$	21.8021	0.718013
$923$	0	0
$924$	1.12400	0.0369770
$925$	− 35.5157i	− 1.16775i
$926$	26.0636	0.856502
$927$	−16.9020	−0.555133
$928$	− 7.19919i	− 0.236325i
$929$	14.3940i	0.472253i	0.971722	+	0.236126i	$0.0758779\pi$
$929$	14.3940i	0.472253i	−0.971722	+	0.236126i	$0.924122\pi$
$930$	− 2.29551i	− 0.0752728i
$931$	6.56298i	0.215093i
$932$	−12.1004	−0.396362
$933$	0.312840	0.0102419
$934$	− 28.6668i	− 0.938007i
$935$	−13.8241	−0.452097
$936$	0	0
$937$	−6.25633	−0.204385	−0.102193	−	0.994765i	$-0.532586\pi$
$937$	−6.25633	−0.204385	−0.102193	+	0.994765i	$0.532586\pi$
$938$	− 0.513495i	− 0.0167662i
$939$	−2.27881	−0.0743663
$940$	1.92174	0.0626803
$941$	− 29.1506i	− 0.950284i	−0.879909	−	0.475142i	$-0.842397\pi$
$941$	− 29.1506i	− 0.950284i	0.879909	−	0.475142i	$-0.157603\pi$
$942$	1.04150i	0.0339339i
$943$	− 19.7490i	− 0.643115i
$944$	− 0.0677585i	− 0.00220535i
$945$	−1.72289	−0.0560457
$946$	15.1267	0.491811
$947$	− 10.8994i	− 0.354183i	−0.984194	−	0.177091i	$-0.943331\pi$
$947$	− 10.8994i	− 0.354183i	0.984194	−	0.177091i	$-0.0566688\pi$
$948$	−2.71600	−0.0882116
$949$	0	0
$950$	−24.1692	−0.784153
$951$	− 0.146832i	− 0.00476135i
$952$	2.70976	0.0878238
$953$	−27.5305	−0.891799	−0.445900	−	0.895083i	$-0.647116\pi$
$953$	−27.5305	−0.891799	−0.445900	+	0.895083i	$0.647116\pi$
$954$	38.9953i	1.26252i
$955$	− 17.8881i	− 0.578844i
$956$	5.57964i	0.180458i
$957$	8.09193i	0.261575i
$958$	−17.9762	−0.580786
$959$	5.20224	0.167989
$960$	0.290242i	0.00936752i
$961$	−31.5515	−1.01779
$962$	0	0
$963$	16.2932	0.525042
$964$	23.2430i	0.748608i
$965$	−20.1838	−0.649741
$966$	0.525985	0.0169233
$967$	− 21.0297i	− 0.676271i	−0.941097	−	0.338135i	$-0.890204\pi$
$967$	− 21.0297i	− 0.676271i	0.941097	−	0.338135i	$-0.109796\pi$
$968$	− 8.75670i	− 0.281451i
$969$	4.49720i	0.144471i
$970$	2.44120i	0.0783823i
$971$	4.36820	0.140182	0.0700911	−	0.997541i	$-0.477671\pi$
$971$	4.36820	0.140182	0.0700911	+	0.997541i	$0.477671\pi$
$972$	−6.63469	−0.212808
$973$	5.74027i	0.184025i
$974$	−21.9216	−0.702414
$975$	0	0
$976$	8.10046	0.259290
$977$	− 54.1358i	− 1.73196i	−0.500082	−	0.865978i	$-0.666697\pi$
$977$	− 54.1358i	− 1.73196i	0.500082	−	0.865978i	$-0.333303\pi$
$978$	2.83707	0.0907196
$979$	−48.2691	−1.54269
$980$	− 1.14776i	− 0.0366637i
$981$	− 23.3999i	− 0.747102i
$982$	− 21.6006i	− 0.689303i
$983$	− 44.3574i	− 1.41478i	−0.706823	−	0.707391i	$-0.749872\pi$
$983$	− 44.3574i	− 1.41478i	0.706823	−	0.707391i	$-0.250128\pi$
$984$	2.40100	0.0765411
$985$	−0.608097	−0.0193756
$986$	19.5081i	0.621264i
$987$	0.423405	0.0134771
$988$	0	0
$989$	7.07864	0.225088
$990$	14.9786i	0.476050i
$991$	27.3873	0.869985	0.434992	−	0.900434i	$-0.356751\pi$
$991$	27.3873	0.869985	0.434992	+	0.900434i	$0.356751\pi$
$992$	7.90895	0.251109
$993$	7.93162i	0.251702i
$994$	− 10.7873i	− 0.342152i
$995$	28.8620i	0.914988i
$996$	− 3.88115i	− 0.122979i
$997$	−45.8033	−1.45061	−0.725303	−	0.688430i	$-0.758300\pi$
$997$	−45.8033	−1.45061	−0.725303	+	0.688430i	$0.758300\pi$
$998$	−38.6105	−1.22219
$999$	14.4766i	0.458021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.d.r.337.4		12
13.5	odd	4		2366.2.a.bf.1.4		6
13.8	odd	4		2366.2.a.bh.1.4		6
13.9	even	3		182.2.m.b.127.2	yes	12
13.10	even	6		182.2.m.b.43.2	✓	12
13.12	even	2	inner	2366.2.d.r.337.10		12
39.23	odd	6		1638.2.bj.g.1135.5		12
39.35	odd	6		1638.2.bj.g.127.5		12
52.23	odd	6		1456.2.cc.d.225.4		12
52.35	odd	6		1456.2.cc.d.673.4		12
91.9	even	3		1274.2.v.e.361.5		12
91.10	odd	6		1274.2.v.d.667.5		12
91.23	even	6		1274.2.o.d.459.5		12
91.48	odd	6		1274.2.m.c.491.2		12
91.61	odd	6		1274.2.v.d.361.5		12
91.62	odd	6		1274.2.m.c.589.2		12
91.74	even	3		1274.2.o.d.569.2		12
91.75	odd	6		1274.2.o.e.459.5		12
91.87	odd	6		1274.2.o.e.569.2		12
91.88	even	6		1274.2.v.e.667.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.2	✓	12	13.10	even	6
182.2.m.b.127.2	yes	12	13.9	even	3
1274.2.m.c.491.2		12	91.48	odd	6
1274.2.m.c.589.2		12	91.62	odd	6
1274.2.o.d.459.5		12	91.23	even	6
1274.2.o.d.569.2		12	91.74	even	3
1274.2.o.e.459.5		12	91.75	odd	6
1274.2.o.e.569.2		12	91.87	odd	6
1274.2.v.d.361.5		12	91.61	odd	6
1274.2.v.d.667.5		12	91.10	odd	6
1274.2.v.e.361.5		12	91.9	even	3
1274.2.v.e.667.5		12	91.88	even	6
1456.2.cc.d.225.4		12	52.23	odd	6
1456.2.cc.d.673.4		12	52.35	odd	6
1638.2.bj.g.127.5		12	39.35	odd	6
1638.2.bj.g.1135.5		12	39.23	odd	6
2366.2.a.bf.1.4		6	13.5	odd	4
2366.2.a.bh.1.4		6	13.8	odd	4
2366.2.d.r.337.4		12	1.1	even	1	trivial
2366.2.d.r.337.10		12	13.12	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +0.252878 q^{3} -1.00000 q^{4} -1.14776i q^{5} -0.252878i q^{6} +1.00000i q^{7} +1.00000i q^{8} -2.93605 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +0.252878 q^{3} -1.00000 q^{4} -1.14776i q^{5} -0.252878i q^{6} +1.00000i q^{7} +1.00000i q^{8} -2.93605 q^{9} -1.14776 q^{10} +4.44485i q^{11} -0.252878 q^{12} +1.00000 q^{14} -0.290242i q^{15} +1.00000 q^{16} -2.70976 q^{17} +2.93605i q^{18} -6.56298i q^{19} +1.14776i q^{20} +0.252878i q^{21} +4.44485 q^{22} +2.08000 q^{23} +0.252878i q^{24} +3.68266 q^{25} -1.50110 q^{27} -1.00000i q^{28} +7.19919 q^{29} -0.290242 q^{30} +7.90895i q^{31} -1.00000i q^{32} +1.12400i q^{33} +2.70976i q^{34} +1.14776 q^{35} +2.93605 q^{36} -9.64405i q^{37} -6.56298 q^{38} +1.14776 q^{40} -9.49471i q^{41} +0.252878 q^{42} +3.40320 q^{43} -4.44485i q^{44} +3.36987i q^{45} -2.08000i q^{46} -1.67435i q^{47} +0.252878 q^{48} -1.00000 q^{49} -3.68266i q^{50} -0.685238 q^{51} +13.2815 q^{53} +1.50110i q^{54} +5.10160 q^{55} -1.00000 q^{56} -1.65963i q^{57} -7.19919i q^{58} -0.0677585i q^{59} +0.290242i q^{60} +8.10046 q^{61} +7.90895 q^{62} -2.93605i q^{63} -1.00000 q^{64} +1.12400 q^{66} -0.513495i q^{67} +2.70976 q^{68} +0.525985 q^{69} -1.14776i q^{70} -10.7873i q^{71} -2.93605i q^{72} -8.02452i q^{73} -9.64405 q^{74} +0.931263 q^{75} +6.56298i q^{76} -4.44485 q^{77} +10.7404 q^{79} -1.14776i q^{80} +8.42856 q^{81} -9.49471 q^{82} +15.3479i q^{83} -0.252878i q^{84} +3.11014i q^{85} -3.40320i q^{86} +1.82052 q^{87} -4.44485 q^{88} +10.8596i q^{89} +3.36987 q^{90} -2.08000 q^{92} +2.00000i q^{93} -1.67435 q^{94} -7.53270 q^{95} -0.252878i q^{96} -2.12694i q^{97} +1.00000i q^{98} -13.0503i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 - 12 * q^4 + 12 * q^9	\( 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} - 4 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 40 q^{27} + 20 q^{29} - 28 q^{30} - 4 q^{35} - 12 q^{36} + 8 q^{38} - 4 q^{40} + 4 q^{42} - 52 q^{43} + 4 q^{48} - 12 q^{49} - 36 q^{51} + 36 q^{53} + 12 q^{55} - 12 q^{56} + 56 q^{61} + 4 q^{62} - 12 q^{64} + 8 q^{68} - 64 q^{69} + 96 q^{75} - 4 q^{77} + 44 q^{79} + 68 q^{81} - 12 q^{82} - 4 q^{87} - 4 q^{88} + 12 q^{90} - 12 q^{92} - 16 q^{94} - 64 q^{95}+O(q^{100}) \) 12 * q + 4 * q^3 - 12 * q^4 + 12 * q^9 + 4 * q^10 - 4 * q^12 + 12 * q^14 + 12 * q^16 - 8 * q^17 + 4 * q^22 + 12 * q^23 - 24 * q^25 + 40 * q^27 + 20 * q^29 - 28 * q^30 - 4 * q^35 - 12 * q^36 + 8 * q^38 - 4 * q^40 + 4 * q^42 - 52 * q^43 + 4 * q^48 - 12 * q^49 - 36 * q^51 + 36 * q^53 + 12 * q^55 - 12 * q^56 + 56 * q^61 + 4 * q^62 - 12 * q^64 + 8 * q^68 - 64 * q^69 + 96 * q^75 - 4 * q^77 + 44 * q^79 + 68 * q^81 - 12 * q^82 - 4 * q^87 - 4 * q^88 + 12 * q^90 - 12 * q^92 - 16 * q^94 - 64 * q^95

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