LMFDB - Embedded newform 867.2.d.d.577.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(577,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, 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("867.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.419904.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 9x^{2} + 1 $ x^6 + 6x^4 + 9x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			577.4
Root			$0.347296i$ of defining polynomial
Character	$\chi$	$=$	867.577
Dual form			867.2.d.d.577.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34730 q^{2} +1.00000i q^{3} -0.184793 q^{4} -2.53209i q^{5} +1.34730i q^{6} -0.184793i q^{7} -2.94356 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.34730 q^{2} +1.00000i q^{3} -0.184793 q^{4} -2.53209i q^{5} +1.34730i q^{6} -0.184793i q^{7} -2.94356 q^{8} -1.00000 q^{9} -3.41147i q^{10} -3.57398i q^{11} -0.184793i q^{12} -6.53209 q^{13} -0.248970i q^{14} +2.53209 q^{15} -3.59627 q^{16} -1.34730 q^{18} -4.63816 q^{19} +0.467911i q^{20} +0.184793 q^{21} -4.81521i q^{22} +3.10607i q^{23} -2.94356i q^{24} -1.41147 q^{25} -8.80066 q^{26} -1.00000i q^{27} +0.0341483i q^{28} +6.35504i q^{29} +3.41147 q^{30} -7.41147i q^{31} +1.04189 q^{32} +3.57398 q^{33} -0.467911 q^{35} +0.184793 q^{36} -8.39693i q^{37} -6.24897 q^{38} -6.53209i q^{39} +7.45336i q^{40} -7.18479i q^{41} +0.248970 q^{42} +4.93582 q^{43} +0.660444i q^{44} +2.53209i q^{45} +4.18479i q^{46} -9.04963 q^{47} -3.59627i q^{48} +6.96585 q^{49} -1.90167 q^{50} +1.20708 q^{52} +7.65270 q^{53} -1.34730i q^{54} -9.04963 q^{55} +0.543948i q^{56} -4.63816i q^{57} +8.56212i q^{58} +6.55438 q^{59} -0.467911 q^{60} -2.98545i q^{61} -9.98545i q^{62} +0.184793i q^{63} +8.59627 q^{64} +16.5398i q^{65} +4.81521 q^{66} -13.5175 q^{67} -3.10607 q^{69} -0.630415 q^{70} -3.61081i q^{71} +2.94356 q^{72} +8.41147i q^{73} -11.3131i q^{74} -1.41147i q^{75} +0.857097 q^{76} -0.660444 q^{77} -8.80066i q^{78} +7.82295i q^{79} +9.10607i q^{80} +1.00000 q^{81} -9.68004i q^{82} -2.51249 q^{83} -0.0341483 q^{84} +6.65002 q^{86} -6.35504 q^{87} +10.5202i q^{88} +1.32770 q^{89} +3.41147i q^{90} +1.20708i q^{91} -0.573978i q^{92} +7.41147 q^{93} -12.1925 q^{94} +11.7442i q^{95} +1.04189i q^{96} -8.75877i q^{97} +9.38507 q^{98} +3.57398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} + 12 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 + 12 * q^8 - 6 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} + 12 q^{8} - 6 q^{9} - 30 q^{13} + 6 q^{15} + 6 q^{16} - 6 q^{18} + 6 q^{19} - 6 q^{21} + 12 q^{25} - 24 q^{26} + 6 q^{33} - 12 q^{35} - 6 q^{36} - 12 q^{38} - 24 q^{42} + 48 q^{43} + 12 q^{50} - 12 q^{52} + 48 q^{53} + 18 q^{59} - 12 q^{60} + 24 q^{64} + 36 q^{66} - 36 q^{67} + 6 q^{69} - 18 q^{70} - 12 q^{72} + 6 q^{76} + 42 q^{77} + 6 q^{81} - 42 q^{84} + 60 q^{86} + 12 q^{87} + 24 q^{93} - 18 q^{94} - 54 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 + 12 * q^8 - 6 * q^9 - 30 * q^13 + 6 * q^15 + 6 * q^16 - 6 * q^18 + 6 * q^19 - 6 * q^21 + 12 * q^25 - 24 * q^26 + 6 * q^33 - 12 * q^35 - 6 * q^36 - 12 * q^38 - 24 * q^42 + 48 * q^43 + 12 * q^50 - 12 * q^52 + 48 * q^53 + 18 * q^59 - 12 * q^60 + 24 * q^64 + 36 * q^66 - 36 * q^67 + 6 * q^69 - 18 * q^70 - 12 * q^72 + 6 * q^76 + 42 * q^77 + 6 * q^81 - 42 * q^84 + 60 * q^86 + 12 * q^87 + 24 * q^93 - 18 * q^94 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.34730	0.952682	0.476341	−	0.879261i	$-0.341963\pi$
$2$	1.34730	0.952682	0.476341	+	0.879261i	$0.341963\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−0.184793	−0.0923963
$5$	− 2.53209i	− 1.13238i	−0.824273	−	0.566192i	$-0.808416\pi$
$5$	− 2.53209i	− 1.13238i	0.824273	−	0.566192i	$-0.191584\pi$
$6$	1.34730i	0.550031i
$7$	− 0.184793i	− 0.0698450i	−0.999390	−	0.0349225i	$-0.988882\pi$
$7$	− 0.184793i	− 0.0698450i	0.999390	−	0.0349225i	$-0.0111184\pi$
$8$	−2.94356	−1.04071
$9$	−1.00000	−0.333333
$10$	− 3.41147i	− 1.07880i
$11$	− 3.57398i	− 1.07759i	−0.842435	−	0.538797i	$-0.818879\pi$
$11$	− 3.57398i	− 1.07759i	0.842435	−	0.538797i	$-0.181121\pi$
$12$	− 0.184793i	− 0.0533450i
$13$	−6.53209	−1.81168	−0.905838	−	0.423625i	$-0.860758\pi$
$13$	−6.53209	−1.81168	−0.905838	+	0.423625i	$0.860758\pi$
$14$	− 0.248970i	− 0.0665401i
$15$	2.53209	0.653783
$16$	−3.59627	−0.899067
$17$	0	0
$17$	0	0
$18$	−1.34730	−0.317561
$19$	−4.63816	−1.06407	−0.532033	−	0.846724i	$-0.678572\pi$
$19$	−4.63816	−1.06407	−0.532033	+	0.846724i	$0.678572\pi$
$20$	0.467911i	0.104628i
$21$	0.184793	0.0403250
$22$	− 4.81521i	− 1.02661i
$23$	3.10607i	0.647660i	0.946115	+	0.323830i	$0.104971\pi$
$23$	3.10607i	0.647660i	−0.946115	+	0.323830i	$0.895029\pi$
$24$	− 2.94356i	− 0.600852i
$25$	−1.41147	−0.282295
$26$	−8.80066	−1.72595
$27$	− 1.00000i	− 0.192450i
$28$	0.0341483i	0.00645342i
$29$	6.35504i	1.18010i	0.807366	+	0.590050i	$0.200892\pi$
$29$	6.35504i	1.18010i	−0.807366	+	0.590050i	$0.799108\pi$
$30$	3.41147	0.622847
$31$	− 7.41147i	− 1.33114i	−0.746335	−	0.665570i	$-0.768188\pi$
$31$	− 7.41147i	− 1.33114i	0.746335	−	0.665570i	$-0.231812\pi$
$32$	1.04189	0.184182
$33$	3.57398	0.622150
$34$	0	0
$35$	−0.467911	−0.0790914
$36$	0.184793	0.0307988
$37$	− 8.39693i	− 1.38045i	−0.723597	−	0.690223i	$-0.757512\pi$
$37$	− 8.39693i	− 1.38045i	0.723597	−	0.690223i	$-0.242488\pi$
$38$	−6.24897	−1.01372
$39$	− 6.53209i	− 1.04597i
$40$	7.45336i	1.17848i
$41$	− 7.18479i	− 1.12208i	−0.827790	−	0.561038i	$-0.810402\pi$
$41$	− 7.18479i	− 1.12208i	0.827790	−	0.561038i	$-0.189598\pi$
$42$	0.248970	0.0384170
$43$	4.93582	0.752706	0.376353	−	0.926476i	$-0.377178\pi$
$43$	4.93582	0.752706	0.376353	+	0.926476i	$0.377178\pi$
$44$	0.660444i	0.0995657i
$45$	2.53209i	0.377462i
$46$	4.18479i	0.617014i
$47$	−9.04963	−1.32002	−0.660012	−	0.751255i	$-0.729449\pi$
$47$	−9.04963	−1.32002	−0.660012	+	0.751255i	$0.729449\pi$
$48$	− 3.59627i	− 0.519076i
$49$	6.96585	0.995122
$50$	−1.90167	−0.268937
$51$	0	0
$52$	1.20708	0.167392
$53$	7.65270	1.05118	0.525590	−	0.850738i	$-0.323845\pi$
$53$	7.65270	1.05118	0.525590	+	0.850738i	$0.323845\pi$
$54$	− 1.34730i	− 0.183344i
$55$	−9.04963	−1.22025
$56$	0.543948i	0.0726882i
$57$	− 4.63816i	− 0.614339i
$58$	8.56212i	1.12426i
$59$	6.55438	0.853307	0.426654	−	0.904415i	$-0.359692\pi$
$59$	6.55438	0.853307	0.426654	+	0.904415i	$0.359692\pi$
$60$	−0.467911	−0.0604071
$61$	− 2.98545i	− 0.382248i	−0.981566	−	0.191124i	$-0.938787\pi$
$61$	− 2.98545i	− 0.382248i	0.981566	−	0.191124i	$-0.0612133\pi$
$62$	− 9.98545i	− 1.26815i
$63$	0.184793i	0.0232817i
$64$	8.59627	1.07453
$65$	16.5398i	2.05151i
$66$	4.81521	0.592711
$67$	−13.5175	−1.65143	−0.825715	−	0.564087i	$-0.809228\pi$
$67$	−13.5175	−1.65143	−0.825715	+	0.564087i	$0.809228\pi$
$68$	0	0
$69$	−3.10607	−0.373927
$70$	−0.630415	−0.0753490
$71$	− 3.61081i	− 0.428525i	−0.976776	−	0.214262i	$-0.931265\pi$
$71$	− 3.61081i	− 0.428525i	0.976776	−	0.214262i	$-0.0687348\pi$
$72$	2.94356	0.346902
$73$	8.41147i	0.984489i	0.870457	+	0.492244i	$0.163823\pi$
$73$	8.41147i	0.984489i	−0.870457	+	0.492244i	$0.836177\pi$
$74$	− 11.3131i	− 1.31513i
$75$	− 1.41147i	− 0.162983i
$76$	0.857097	0.0983157
$77$	−0.660444	−0.0752646
$78$	− 8.80066i	− 0.996478i
$79$	7.82295i	0.880150i	0.897961	+	0.440075i	$0.145048\pi$
$79$	7.82295i	0.880150i	−0.897961	+	0.440075i	$0.854952\pi$
$80$	9.10607i	1.01809i
$81$	1.00000	0.111111
$82$	− 9.68004i	− 1.06898i
$83$	−2.51249	−0.275781	−0.137891	−	0.990447i	$-0.544032\pi$
$83$	−2.51249	−0.275781	−0.137891	+	0.990447i	$0.544032\pi$
$84$	−0.0341483	−0.00372588
$85$	0	0
$86$	6.65002	0.717090
$87$	−6.35504	−0.681331
$88$	10.5202i	1.12146i
$89$	1.32770	0.140735	0.0703677	−	0.997521i	$-0.477583\pi$
$89$	1.32770	0.140735	0.0703677	+	0.997521i	$0.477583\pi$
$90$	3.41147i	0.359601i
$91$	1.20708i	0.126536i
$92$	− 0.573978i	− 0.0598413i
$93$	7.41147	0.768534
$94$	−12.1925	−1.25756
$95$	11.7442i	1.20493i
$96$	1.04189i	0.106337i
$97$	− 8.75877i	− 0.889318i	−0.895700	−	0.444659i	$-0.853325\pi$
$97$	− 8.75877i	− 0.889318i	0.895700	−	0.444659i	$-0.146675\pi$
$98$	9.38507	0.948035
$99$	3.57398i	0.359198i
$100$	0.260830	0.0260830
$101$	−11.0273	−1.09726	−0.548631	−	0.836065i	$-0.684851\pi$
$101$	−11.0273	−1.09726	−0.548631	+	0.836065i	$0.684851\pi$
$102$	0	0
$103$	6.27126	0.617926	0.308963	−	0.951074i	$-0.400018\pi$
$103$	6.27126	0.617926	0.308963	+	0.951074i	$0.400018\pi$
$104$	19.2276	1.88542
$105$	− 0.467911i	− 0.0456634i
$106$	10.3105	1.00144
$107$	3.55438i	0.343615i	0.985131	+	0.171807i	$0.0549607\pi$
$107$	3.55438i	0.343615i	−0.985131	+	0.171807i	$0.945039\pi$
$108$	0.184793i	0.0177817i
$109$	− 3.59627i	− 0.344460i	−0.985057	−	0.172230i	$-0.944903\pi$
$109$	− 3.59627i	− 0.344460i	0.985057	−	0.172230i	$-0.0550972\pi$
$110$	−12.1925	−1.16251
$111$	8.39693	0.797001
$112$	0.664563i	0.0627953i
$113$	− 4.70914i	− 0.442999i	−0.975161	−	0.221499i	$-0.928905\pi$
$113$	− 4.70914i	− 0.442999i	0.975161	−	0.221499i	$-0.0710951\pi$
$114$	− 6.24897i	− 0.585270i
$115$	7.86484	0.733400
$116$	− 1.17436i	− 0.109037i
$117$	6.53209	0.603892
$118$	8.83069	0.812931
$119$	0	0
$120$	−7.45336	−0.680396
$121$	−1.77332	−0.161211
$122$	− 4.02229i	− 0.364161i
$123$	7.18479	0.647831
$124$	1.36959i	0.122992i
$125$	− 9.08647i	− 0.812718i
$126$	0.248970i	0.0221800i
$127$	7.76651	0.689166	0.344583	−	0.938756i	$-0.388020\pi$
$127$	7.76651	0.689166	0.344583	+	0.938756i	$0.388020\pi$
$128$	9.49794	0.839507
$129$	4.93582i	0.434575i
$130$	22.2841i	1.95444i
$131$	− 4.95130i	− 0.432597i	−0.976327	−	0.216299i	$-0.930601\pi$
$131$	− 4.95130i	− 0.432597i	0.976327	−	0.216299i	$-0.0693985\pi$
$132$	−0.660444	−0.0574843
$133$	0.857097i	0.0743197i
$134$	−18.2121	−1.57329
$135$	−2.53209	−0.217928
$136$	0	0
$137$	−11.5885	−0.990075	−0.495037	−	0.868872i	$-0.664846\pi$
$137$	−11.5885	−0.990075	−0.495037	+	0.868872i	$0.664846\pi$
$138$	−4.18479	−0.356233
$139$	− 2.68954i	− 0.228124i	−0.993474	−	0.114062i	$-0.963614\pi$
$139$	− 2.68954i	− 0.228124i	0.993474	−	0.114062i	$-0.0363862\pi$
$140$	0.0864665	0.00730775
$141$	− 9.04963i	− 0.762116i
$142$	− 4.86484i	− 0.408248i
$143$	23.3455i	1.95225i
$144$	3.59627	0.299689
$145$	16.0915	1.33633
$146$	11.3327i	0.937905i
$147$	6.96585i	0.574534i
$148$	1.55169i	0.127548i
$149$	−15.9290	−1.30496	−0.652478	−	0.757808i	$-0.726270\pi$
$149$	−15.9290	−1.30496	−0.652478	+	0.757808i	$0.726270\pi$
$150$	− 1.90167i	− 0.155271i
$151$	−1.38919	−0.113050	−0.0565252	−	0.998401i	$-0.518002\pi$
$151$	−1.38919	−0.113050	−0.0565252	+	0.998401i	$0.518002\pi$
$152$	13.6527	1.10738
$153$	0	0
$154$	−0.889814	−0.0717033
$155$	−18.7665	−1.50736
$156$	1.20708i	0.0966438i
$157$	1.78106	0.142144	0.0710720	−	0.997471i	$-0.477358\pi$
$157$	1.78106	0.142144	0.0710720	+	0.997471i	$0.477358\pi$
$158$	10.5398i	0.838504i
$159$	7.65270i	0.606899i
$160$	− 2.63816i	− 0.208565i
$161$	0.573978	0.0452358
$162$	1.34730	0.105854
$163$	3.15064i	0.246778i	0.992358	+	0.123389i	$0.0393762\pi$
$163$	3.15064i	0.246778i	−0.992358	+	0.123389i	$0.960624\pi$
$164$	1.32770i	0.103676i
$165$	− 9.04963i	− 0.704513i
$166$	−3.38507	−0.262732
$167$	24.3482i	1.88412i	0.335441	+	0.942061i	$0.391115\pi$
$167$	24.3482i	1.88412i	−0.335441	+	0.942061i	$0.608885\pi$
$168$	−0.543948	−0.0419665
$169$	29.6682	2.28217
$170$	0	0
$171$	4.63816	0.354689
$172$	−0.912103	−0.0695472
$173$	15.0692i	1.14569i	0.819663	+	0.572846i	$0.194161\pi$
$173$	15.0692i	1.14569i	−0.819663	+	0.572846i	$0.805839\pi$
$174$	−8.56212	−0.649093
$175$	0.260830i	0.0197169i
$176$	12.8530i	0.968830i
$177$	6.55438i	0.492657i
$178$	1.78880	0.134076
$179$	−16.9017	−1.26329	−0.631645	−	0.775258i	$-0.717620\pi$
$179$	−16.9017	−1.26329	−0.631645	+	0.775258i	$0.717620\pi$
$180$	− 0.467911i	− 0.0348760i
$181$	− 10.6682i	− 0.792960i	−0.918043	−	0.396480i	$-0.870232\pi$
$181$	− 10.6682i	− 0.792960i	0.918043	−	0.396480i	$-0.129768\pi$
$182$	1.62630i	0.120549i
$183$	2.98545	0.220691
$184$	− 9.14290i	− 0.674024i
$185$	−21.2618	−1.56320
$186$	9.98545	0.732169
$187$	0	0
$188$	1.67230	0.121965
$189$	−0.184793	−0.0134417
$190$	15.8229i	1.14792i
$191$	1.77837	0.128678	0.0643392	−	0.997928i	$-0.479506\pi$
$191$	1.77837	0.128678	0.0643392	+	0.997928i	$0.479506\pi$
$192$	8.59627i	0.620382i
$193$	− 5.06923i	− 0.364891i	−0.983216	−	0.182446i	$-0.941599\pi$
$193$	− 5.06923i	− 0.364891i	0.983216	−	0.182446i	$-0.0584013\pi$
$194$	− 11.8007i	− 0.847238i
$195$	−16.5398	−1.18444
$196$	−1.28724	−0.0919455
$197$	− 8.04458i	− 0.573152i	−0.958057	−	0.286576i	$-0.907483\pi$
$197$	− 8.04458i	− 0.573152i	0.958057	−	0.286576i	$-0.0925172\pi$
$198$	4.81521i	0.342202i
$199$	− 11.9409i	− 0.846466i	−0.906021	−	0.423233i	$-0.860895\pi$
$199$	− 11.9409i	− 0.846466i	0.906021	−	0.423233i	$-0.139105\pi$
$200$	4.15476	0.293786
$201$	− 13.5175i	− 0.953454i
$202$	−14.8571	−1.04534
$203$	1.17436	0.0824242
$204$	0	0
$205$	−18.1925	−1.27062
$206$	8.44924	0.588687
$207$	− 3.10607i	− 0.215887i
$208$	23.4911	1.62882
$209$	16.5767i	1.14663i
$210$	− 0.630415i	− 0.0435028i
$211$	2.54664i	0.175318i	0.996151	+	0.0876589i	$0.0279385\pi$
$211$	2.54664i	0.175318i	−0.996151	+	0.0876589i	$0.972061\pi$
$212$	−1.41416	−0.0971251
$213$	3.61081	0.247409
$214$	4.78880i	0.327356i
$215$	− 12.4979i	− 0.852352i
$216$	2.94356i	0.200284i
$217$	−1.36959	−0.0929735
$218$	− 4.84524i	− 0.328161i
$219$	−8.41147	−0.568395
$220$	1.67230	0.112747
$221$	0	0
$222$	11.3131	0.759289
$223$	−4.44562	−0.297701	−0.148850	−	0.988860i	$-0.547557\pi$
$223$	−4.44562	−0.297701	−0.148850	+	0.988860i	$0.547557\pi$
$224$	− 0.192533i	− 0.0128642i
$225$	1.41147	0.0940983
$226$	− 6.34461i	− 0.422037i
$227$	7.52023i	0.499135i	0.968357	+	0.249568i	$0.0802885\pi$
$227$	7.52023i	0.499135i	−0.968357	+	0.249568i	$0.919712\pi$
$228$	0.857097i	0.0567626i
$229$	−13.7374	−0.907794	−0.453897	−	0.891054i	$-0.649967\pi$
$229$	−13.7374	−0.907794	−0.453897	+	0.891054i	$0.649967\pi$
$230$	10.5963	0.698697
$231$	− 0.660444i	− 0.0434541i
$232$	− 18.7065i	− 1.22814i
$233$	− 20.5253i	− 1.34466i	−0.740253	−	0.672328i	$-0.765294\pi$
$233$	− 20.5253i	− 1.34466i	0.740253	−	0.672328i	$-0.234706\pi$
$234$	8.80066	0.575317
$235$	22.9145i	1.49478i
$236$	−1.21120	−0.0788424
$237$	−7.82295	−0.508155
$238$	0	0
$239$	25.9145	1.67627	0.838134	−	0.545465i	$-0.183647\pi$
$239$	25.9145	1.67627	0.838134	+	0.545465i	$0.183647\pi$
$240$	−9.10607	−0.587794
$241$	− 11.3773i	− 0.732878i	−0.930442	−	0.366439i	$-0.880577\pi$
$241$	− 11.3773i	− 0.732878i	0.930442	−	0.366439i	$-0.119423\pi$
$242$	−2.38919	−0.153583
$243$	1.00000i	0.0641500i
$244$	0.551689i	0.0353183i
$245$	− 17.6382i	− 1.12686i
$246$	9.68004	0.617177
$247$	30.2968	1.92774
$248$	21.8161i	1.38533i
$249$	− 2.51249i	− 0.159222i
$250$	− 12.2422i	− 0.774262i
$251$	−0.859785	−0.0542691	−0.0271346	−	0.999632i	$-0.508638\pi$
$251$	−0.859785	−0.0542691	−0.0271346	+	0.999632i	$0.508638\pi$
$252$	− 0.0341483i	− 0.00215114i
$253$	11.1010	0.697915
$254$	10.4638	0.656557
$255$	0	0
$256$	−4.39599	−0.274750
$257$	−0.0300295	−0.00187319	−0.000936594	−	1.00000i	$-0.500298\pi$
$257$	−0.0300295	−0.00187319	−0.000936594		1.00000i	$0.500298\pi$
$258$	6.65002i	0.414012i
$259$	−1.55169	−0.0964173
$260$	− 3.05644i	− 0.189552i
$261$	− 6.35504i	− 0.393367i
$262$	− 6.67087i	− 0.412128i
$263$	−12.2422	−0.754884	−0.377442	−	0.926033i	$-0.623196\pi$
$263$	−12.2422	−0.754884	−0.377442	+	0.926033i	$0.623196\pi$
$264$	−10.5202	−0.647475
$265$	− 19.3773i	− 1.19034i
$266$	1.15476i	0.0708031i
$267$	1.32770i	0.0812537i
$268$	2.49794	0.152586
$269$	− 21.5672i	− 1.31497i	−0.753466	−	0.657487i	$-0.771620\pi$
$269$	− 21.5672i	− 1.31497i	0.753466	−	0.657487i	$-0.228380\pi$
$270$	−3.41147	−0.207616
$271$	3.39693	0.206349	0.103174	−	0.994663i	$-0.467100\pi$
$271$	3.39693	0.206349	0.103174	+	0.994663i	$0.467100\pi$
$272$	0	0
$273$	−1.20708	−0.0730559
$274$	−15.6132	−0.943227
$275$	5.04458i	0.304199i
$276$	0.573978	0.0345494
$277$	− 15.9172i	− 0.956369i	−0.878259	−	0.478185i	$-0.841295\pi$
$277$	− 15.9172i	− 0.956369i	0.878259	−	0.478185i	$-0.158705\pi$
$278$	− 3.62361i	− 0.217330i
$279$	7.41147i	0.443713i
$280$	1.37733	0.0823110
$281$	16.0155	0.955404	0.477702	−	0.878522i	$-0.341470\pi$
$281$	16.0155	0.955404	0.477702	+	0.878522i	$0.341470\pi$
$282$	− 12.1925i	− 0.726055i
$283$	− 26.8357i	− 1.59522i	−0.603174	−	0.797610i	$-0.706098\pi$
$283$	− 26.8357i	− 1.59522i	0.603174	−	0.797610i	$-0.293902\pi$
$284$	0.667252i	0.0395941i
$285$	−11.7442	−0.695668
$286$	31.4534i	1.85988i
$287$	−1.32770	−0.0783714
$288$	−1.04189	−0.0613939
$289$	0	0
$290$	21.6800	1.27310
$291$	8.75877	0.513448
$292$	− 1.55438i	− 0.0909631i
$293$	2.40879	0.140723	0.0703614	−	0.997522i	$-0.477585\pi$
$293$	2.40879	0.140723	0.0703614	+	0.997522i	$0.477585\pi$
$294$	9.38507i	0.547348i
$295$	− 16.5963i	− 0.966272i
$296$	24.7169i	1.43664i
$297$	−3.57398	−0.207383
$298$	−21.4611	−1.24321
$299$	− 20.2891i	− 1.17335i
$300$	0.260830i	0.0150590i
$301$	− 0.912103i	− 0.0525727i
$302$	−1.87164	−0.107701
$303$	− 11.0273i	− 0.633504i
$304$	16.6800	0.956666
$305$	−7.55943	−0.432852
$306$	0	0
$307$	−6.41921	−0.366364	−0.183182	−	0.983079i	$-0.558640\pi$
$307$	−6.41921	−0.366364	−0.183182	+	0.983079i	$0.558640\pi$
$308$	0.122045	0.00695417
$309$	6.27126i	0.356759i
$310$	−25.2841	−1.43604
$311$	0.543948i	0.0308445i	0.999881	+	0.0154222i	$0.00490925\pi$
$311$	0.543948i	0.0308445i	−0.999881	+	0.0154222i	$0.995091\pi$
$312$	19.2276i	1.08855i
$313$	− 16.6186i	− 0.939336i	−0.882843	−	0.469668i	$-0.844374\pi$
$313$	− 16.6186i	− 0.939336i	0.882843	−	0.469668i	$-0.155626\pi$
$314$	2.39961	0.135418
$315$	0.467911	0.0263638
$316$	− 1.44562i	− 0.0813226i
$317$	26.0574i	1.46353i	0.681558	+	0.731764i	$0.261303\pi$
$317$	26.0574i	1.46353i	−0.681558	+	0.731764i	$0.738697\pi$
$318$	10.3105i	0.578182i
$319$	22.7128	1.27167
$320$	− 21.7665i	− 1.21678i
$321$	−3.55438	−0.198386
$322$	0.773318	0.0430953
$323$	0	0
$324$	−0.184793	−0.0102663
$325$	9.21987	0.511427
$326$	4.24485i	0.235101i
$327$	3.59627	0.198874
$328$	21.1489i	1.16775i
$329$	1.67230i	0.0921971i
$330$	− 12.1925i	− 0.671177i
$331$	22.5107	1.23730	0.618651	−	0.785666i	$-0.287680\pi$
$331$	22.5107	1.23730	0.618651	+	0.785666i	$0.287680\pi$
$332$	0.464289	0.0254812
$333$	8.39693i	0.460149i
$334$	32.8043i	1.79497i
$335$	34.2276i	1.87005i
$336$	−0.664563	−0.0362549
$337$	0.497007i	0.0270737i	0.999908	+	0.0135368i	$0.00430904\pi$
$337$	0.497007i	0.0270737i	−0.999908	+	0.0135368i	$0.995691\pi$
$338$	39.9718	2.17418
$339$	4.70914	0.255765
$340$	0	0
$341$	−26.4884	−1.43443
$342$	6.24897	0.337906
$343$	− 2.58079i	− 0.139349i
$344$	−14.5289	−0.783346
$345$	7.86484i	0.423429i
$346$	20.3027i	1.09148i
$347$	13.8648i	0.744303i	0.928172	+	0.372152i	$0.121380\pi$
$347$	13.8648i	0.744303i	−0.928172	+	0.372152i	$0.878620\pi$
$348$	1.17436	0.0629525
$349$	−27.0479	−1.44784	−0.723920	−	0.689884i	$-0.757661\pi$
$349$	−27.0479	−1.44784	−0.723920	+	0.689884i	$0.757661\pi$
$350$	0.351415i	0.0187839i
$351$	6.53209i	0.348657i
$352$	− 3.72369i	− 0.198473i
$353$	8.96997	0.477423	0.238712	−	0.971090i	$-0.423275\pi$
$353$	8.96997	0.477423	0.238712	+	0.971090i	$0.423275\pi$
$354$	8.83069i	0.469346i
$355$	−9.14290	−0.485255
$356$	−0.245348	−0.0130034
$357$	0	0
$358$	−22.7716	−1.20351
$359$	−6.12567	−0.323300	−0.161650	−	0.986848i	$-0.551682\pi$
$359$	−6.12567	−0.323300	−0.161650	+	0.986848i	$0.551682\pi$
$360$	− 7.45336i	− 0.392827i
$361$	2.51249	0.132236
$362$	− 14.3732i	− 0.755439i
$363$	− 1.77332i	− 0.0930751i
$364$	− 0.223060i	− 0.0116915i
$365$	21.2986	1.11482
$366$	4.02229	0.210248
$367$	17.9213i	0.935483i	0.883865	+	0.467741i	$0.154932\pi$
$367$	17.9213i	0.935483i	−0.883865	+	0.467741i	$0.845068\pi$
$368$	− 11.1702i	− 0.582289i
$369$	7.18479i	0.374025i
$370$	−28.6459	−1.48923
$371$	− 1.41416i	− 0.0734197i
$372$	−1.36959	−0.0710097
$373$	−15.5389	−0.804574	−0.402287	−	0.915514i	$-0.631785\pi$
$373$	−15.5389	−0.804574	−0.402287	+	0.915514i	$0.631785\pi$
$374$	0	0
$375$	9.08647	0.469223
$376$	26.6382	1.37376
$377$	− 41.5117i	− 2.13796i
$378$	−0.248970	−0.0128057
$379$	− 38.0087i	− 1.95237i	−0.216930	−	0.976187i	$-0.569604\pi$
$379$	− 38.0087i	− 1.95237i	0.216930	−	0.976187i	$-0.430396\pi$
$380$	− 2.17024i	− 0.111331i
$381$	7.76651i	0.397890i
$382$	2.39599	0.122590
$383$	−21.2686	−1.08677	−0.543387	−	0.839483i	$-0.682858\pi$
$383$	−21.2686	−1.08677	−0.543387	+	0.839483i	$0.682858\pi$
$384$	9.49794i	0.484690i
$385$	1.67230i	0.0852285i
$386$	− 6.82976i	− 0.347625i
$387$	−4.93582	−0.250902
$388$	1.61856i	0.0821697i
$389$	−13.8016	−0.699769	−0.349884	−	0.936793i	$-0.613779\pi$
$389$	−13.8016	−0.699769	−0.349884	+	0.936793i	$0.613779\pi$
$390$	−22.2841	−1.12840
$391$	0	0
$392$	−20.5044	−1.03563
$393$	4.95130	0.249760
$394$	− 10.8384i	− 0.546032i
$395$	19.8084	0.996669
$396$	− 0.660444i	− 0.0331886i
$397$	− 28.5621i	− 1.43349i	−0.697335	−	0.716746i	$-0.745631\pi$
$397$	− 28.5621i	− 1.43349i	0.697335	−	0.716746i	$-0.254369\pi$
$398$	− 16.0879i	− 0.806413i
$399$	−0.857097	−0.0429085
$400$	5.07604	0.253802
$401$	− 26.7766i	− 1.33716i	−0.743640	−	0.668580i	$-0.766902\pi$
$401$	− 26.7766i	− 1.33716i	0.743640	−	0.668580i	$-0.233098\pi$
$402$	− 18.2121i	− 0.908339i
$403$	48.4124i	2.41159i
$404$	2.03777	0.101383
$405$	− 2.53209i	− 0.125821i
$406$	1.58222	0.0785240
$407$	−30.0104	−1.48756
$408$	0	0
$409$	38.8357	1.92030	0.960152	−	0.279479i	$-0.0901616\pi$
$409$	38.8357	1.92030	0.960152	+	0.279479i	$0.0901616\pi$
$410$	−24.5107	−1.21050
$411$	− 11.5885i	− 0.571620i
$412$	−1.15888	−0.0570940
$413$	− 1.21120i	− 0.0595993i
$414$	− 4.18479i	− 0.205671i
$415$	6.36184i	0.312291i
$416$	−6.80571	−0.333677
$417$	2.68954	0.131707
$418$	22.3337i	1.09238i
$419$	19.0351i	0.929925i	0.885330	+	0.464962i	$0.153932\pi$
$419$	19.0351i	0.929925i	−0.885330	+	0.464962i	$0.846068\pi$
$420$	0.0864665i	0.00421913i
$421$	6.41653	0.312722	0.156361	−	0.987700i	$-0.450024\pi$
$421$	6.41653	0.312722	0.156361	+	0.987700i	$0.450024\pi$
$422$	3.43107i	0.167022i
$423$	9.04963	0.440008
$424$	−22.5262	−1.09397
$425$	0	0
$426$	4.86484	0.235702
$427$	−0.551689	−0.0266981
$428$	− 0.656822i	− 0.0317487i
$429$	−23.3455	−1.12713
$430$	− 16.8384i	− 0.812021i
$431$	8.65095i	0.416702i	0.978054	+	0.208351i	$0.0668096\pi$
$431$	8.65095i	0.416702i	−0.978054	+	0.208351i	$0.933190\pi$
$432$	3.59627i	0.173025i
$433$	−23.3182	−1.12060	−0.560301	−	0.828289i	$-0.689314\pi$
$433$	−23.3182	−1.12060	−0.560301	+	0.828289i	$0.689314\pi$
$434$	−1.84524	−0.0885742
$435$	16.0915i	0.771529i
$436$	0.664563i	0.0318268i
$437$	− 14.4064i	− 0.689153i
$438$	−11.3327	−0.541500
$439$	− 13.1993i	− 0.629970i	−0.949097	−	0.314985i	$-0.898000\pi$
$439$	− 13.1993i	− 0.629970i	0.949097	−	0.314985i	$-0.102000\pi$
$440$	26.6382	1.26992
$441$	−6.96585	−0.331707
$442$	0	0
$443$	−30.5235	−1.45022	−0.725108	−	0.688635i	$-0.758210\pi$
$443$	−30.5235	−1.45022	−0.725108	+	0.688635i	$0.758210\pi$
$444$	−1.55169	−0.0736399
$445$	− 3.36184i	− 0.159367i
$446$	−5.98957	−0.283614
$447$	− 15.9290i	− 0.753417i
$448$	− 1.58853i	− 0.0750508i
$449$	2.71183i	0.127979i	0.997951	+	0.0639896i	$0.0203824\pi$
$449$	2.71183i	0.127979i	−0.997951	+	0.0639896i	$0.979618\pi$
$450$	1.90167	0.0896458
$451$	−25.6783	−1.20914
$452$	0.870214i	0.0409314i
$453$	− 1.38919i	− 0.0652696i
$454$	10.1320i	0.475517i
$455$	3.05644	0.143288
$456$	13.6527i	0.639346i
$457$	26.2668	1.22871	0.614355	−	0.789030i	$-0.289416\pi$
$457$	26.2668	1.22871	0.614355	+	0.789030i	$0.289416\pi$
$458$	−18.5084	−0.864839
$459$	0	0
$460$	−1.45336	−0.0677634
$461$	25.5202	1.18860	0.594298	−	0.804245i	$-0.297430\pi$
$461$	25.5202	1.18860	0.594298	+	0.804245i	$0.297430\pi$
$462$	− 0.889814i	− 0.0413979i
$463$	−2.82564	−0.131318	−0.0656592	−	0.997842i	$-0.520915\pi$
$463$	−2.82564	−0.131318	−0.0656592	+	0.997842i	$0.520915\pi$
$464$	− 22.8544i	− 1.06099i
$465$	− 18.7665i	− 0.870276i
$466$	− 27.6536i	− 1.28103i
$467$	32.9992	1.52702	0.763510	−	0.645796i	$-0.223474\pi$
$467$	32.9992	1.52702	0.763510	+	0.645796i	$0.223474\pi$
$468$	−1.20708	−0.0557973
$469$	2.49794i	0.115344i
$470$	30.8726i	1.42405i
$471$	1.78106i	0.0820669i
$472$	−19.2932	−0.888043
$473$	− 17.6405i	− 0.811112i
$474$	−10.5398	−0.484110
$475$	6.54664	0.300380
$476$	0	0
$477$	−7.65270	−0.350393
$478$	34.9145	1.59695
$479$	34.8188i	1.59091i	0.606011	+	0.795456i	$0.292769\pi$
$479$	34.8188i	1.59091i	−0.606011	+	0.795456i	$0.707231\pi$
$480$	2.63816	0.120415
$481$	54.8495i	2.50092i
$482$	− 15.3286i	− 0.698200i
$483$	0.573978i	0.0261169i
$484$	0.327696	0.0148953
$485$	−22.1780	−1.00705
$486$	1.34730i	0.0611146i
$487$	− 21.5827i	− 0.978003i	−0.872283	−	0.489002i	$-0.837361\pi$
$487$	− 21.5827i	− 0.978003i	0.872283	−	0.489002i	$-0.162639\pi$
$488$	8.78787i	0.397808i
$489$	−3.15064	−0.142477
$490$	− 23.7638i	− 1.07354i
$491$	34.3209	1.54888	0.774440	−	0.632647i	$-0.218032\pi$
$491$	34.3209	1.54888	0.774440	+	0.632647i	$0.218032\pi$
$492$	−1.32770	−0.0598572
$493$	0	0
$494$	40.8188	1.83653
$495$	9.04963	0.406751
$496$	26.6536i	1.19678i
$497$	−0.667252	−0.0299303
$498$	− 3.38507i	− 0.151688i
$499$	18.1462i	0.812336i	0.913799	+	0.406168i	$0.133135\pi$
$499$	18.1462i	0.812336i	−0.913799	+	0.406168i	$0.866865\pi$
$500$	1.67911i	0.0750921i
$501$	−24.3482	−1.08780
$502$	−1.15839	−0.0517013
$503$	− 25.2148i	− 1.12427i	−0.827044	−	0.562137i	$-0.809979\pi$
$503$	− 25.2148i	− 1.12427i	0.827044	−	0.562137i	$-0.190021\pi$
$504$	− 0.543948i	− 0.0242294i
$505$	27.9222i	1.24252i
$506$	14.9564	0.664891
$507$	29.6682i	1.31761i
$508$	−1.43519	−0.0636764
$509$	−2.82026	−0.125006	−0.0625029	−	0.998045i	$-0.519908\pi$
$509$	−2.82026	−0.125006	−0.0625029	+	0.998045i	$0.519908\pi$
$510$	0	0
$511$	1.55438	0.0687616
$512$	−24.9186	−1.10126
$513$	4.63816i	0.204780i
$514$	−0.0404586	−0.00178455
$515$	− 15.8794i	− 0.699729i
$516$	− 0.912103i	− 0.0401531i
$517$	32.3432i	1.42245i
$518$	−2.09059	−0.0918550
$519$	−15.0692	−0.661466
$520$	− 48.6860i	− 2.13502i
$521$	− 1.05232i	− 0.0461029i	−0.999734	−	0.0230514i	$-0.992662\pi$
$521$	− 1.05232i	− 0.0461029i	0.999734	−	0.0230514i	$-0.00733815\pi$
$522$	− 8.56212i	− 0.374754i
$523$	15.0915	0.659906	0.329953	−	0.943997i	$-0.392967\pi$
$523$	15.0915	0.659906	0.329953	+	0.943997i	$0.392967\pi$
$524$	0.914964i	0.0399704i
$525$	−0.260830	−0.0113835
$526$	−16.4938	−0.719165
$527$	0	0
$528$	−12.8530	−0.559354
$529$	13.3523	0.580537
$530$	− 26.1070i	− 1.13402i
$531$	−6.55438	−0.284436
$532$	− 0.158385i	− 0.00686686i
$533$	46.9317i	2.03284i
$534$	1.78880i	0.0774089i
$535$	9.00000	0.389104
$536$	39.7897	1.71865
$537$	− 16.9017i	− 0.729361i
$538$	− 29.0574i	− 1.25275i
$539$	− 24.8958i	− 1.07234i
$540$	0.467911	0.0201357
$541$	− 19.3182i	− 0.830554i	−0.909695	−	0.415277i	$-0.863685\pi$
$541$	− 19.3182i	− 0.830554i	0.909695	−	0.415277i	$-0.136315\pi$
$542$	4.57667	0.196585
$543$	10.6682	0.457816
$544$	0	0
$545$	−9.10607	−0.390061
$546$	−1.62630	−0.0695991
$547$	16.7419i	0.715830i	0.933754	+	0.357915i	$0.116512\pi$
$547$	16.7419i	0.715830i	−0.933754	+	0.357915i	$0.883488\pi$
$548$	2.14147	0.0914792
$549$	2.98545i	0.127416i
$550$	6.79654i	0.289805i
$551$	− 29.4757i	− 1.25570i
$552$	9.14290	0.389148
$553$	1.44562	0.0614741
$554$	− 21.4451i	− 0.911116i
$555$	− 21.2618i	− 0.902512i
$556$	0.497007i	0.0210778i
$557$	−19.8084	−0.839309	−0.419654	−	0.907684i	$-0.637849\pi$
$557$	−19.8084	−0.839309	−0.419654	+	0.907684i	$0.637849\pi$
$558$	9.98545i	0.422718i
$559$	−32.2412	−1.36366
$560$	1.68273	0.0711085
$561$	0	0
$562$	21.5776	0.910196
$563$	−35.4020	−1.49202	−0.746008	−	0.665937i	$-0.768032\pi$
$563$	−35.4020	−1.49202	−0.746008	+	0.665937i	$0.768032\pi$
$564$	1.67230i	0.0704167i
$565$	−11.9240	−0.501645
$566$	− 36.1557i	− 1.51974i
$567$	− 0.184793i	− 0.00776056i
$568$	10.6287i	0.445969i
$569$	−18.0060	−0.754850	−0.377425	−	0.926040i	$-0.623190\pi$
$569$	−18.0060	−0.754850	−0.377425	+	0.926040i	$0.623190\pi$
$570$	−15.8229	−0.662750
$571$	13.8922i	0.581370i	0.956819	+	0.290685i	$0.0938831\pi$
$571$	13.8922i	0.581370i	−0.956819	+	0.290685i	$0.906117\pi$
$572$	− 4.31408i	− 0.180381i
$573$	1.77837i	0.0742925i
$574$	−1.78880	−0.0746631
$575$	− 4.38413i	− 0.182831i
$576$	−8.59627	−0.358178
$577$	−4.15570	−0.173004	−0.0865020	−	0.996252i	$-0.527569\pi$
$577$	−4.15570	−0.173004	−0.0865020	+	0.996252i	$0.527569\pi$
$578$	0	0
$579$	5.06923	0.210670
$580$	−2.97359	−0.123472
$581$	0.464289i	0.0192620i
$582$	11.8007	0.489153
$583$	− 27.3506i	− 1.13275i
$584$	− 24.7597i	− 1.02456i
$585$	− 16.5398i	− 0.683838i
$586$	3.24535	0.134064
$587$	25.9341	1.07041	0.535207	−	0.844721i	$-0.320234\pi$
$587$	25.9341	1.07041	0.535207	+	0.844721i	$0.320234\pi$
$588$	− 1.28724i	− 0.0530848i
$589$	34.3756i	1.41642i
$590$	− 22.3601i	− 0.920550i
$591$	8.04458	0.330910
$592$	30.1976i	1.24111i
$593$	37.6459	1.54593	0.772966	−	0.634448i	$-0.218772\pi$
$593$	37.6459	1.54593	0.772966	+	0.634448i	$0.218772\pi$
$594$	−4.81521	−0.197570
$595$	0	0
$596$	2.94356	0.120573
$597$	11.9409	0.488707
$598$	− 27.3354i	− 1.11783i
$599$	−9.59720	−0.392131	−0.196065	−	0.980591i	$-0.562817\pi$
$599$	−9.59720	−0.392131	−0.196065	+	0.980591i	$0.562817\pi$
$600$	4.15476i	0.169617i
$601$	28.1625i	1.14877i	0.818584	+	0.574386i	$0.194759\pi$
$601$	28.1625i	1.14877i	−0.818584	+	0.574386i	$0.805241\pi$
$602$	− 1.22887i	− 0.0500851i
$603$	13.5175	0.550477
$604$	0.256711	0.0104454
$605$	4.49020i	0.182553i
$606$	− 14.8571i	− 0.603528i
$607$	− 16.2686i	− 0.660321i	−0.943925	−	0.330160i	$-0.892897\pi$
$607$	− 16.2686i	− 0.660321i	0.943925	−	0.330160i	$-0.107103\pi$
$608$	−4.83244	−0.195981
$609$	1.17436i	0.0475876i
$610$	−10.1848	−0.412370
$611$	59.1130	2.39146
$612$	0	0
$613$	−4.12330	−0.166539	−0.0832693	−	0.996527i	$-0.526536\pi$
$613$	−4.12330	−0.166539	−0.0832693	+	0.996527i	$0.526536\pi$
$614$	−8.64858	−0.349028
$615$	− 18.1925i	− 0.733594i
$616$	1.94406	0.0783284
$617$	12.6928i	0.510994i	0.966810	+	0.255497i	$0.0822392\pi$
$617$	12.6928i	0.510994i	−0.966810	+	0.255497i	$0.917761\pi$
$618$	8.44924i	0.339878i
$619$	− 25.9240i	− 1.04197i	−0.853565	−	0.520986i	$-0.825564\pi$
$619$	− 25.9240i	− 1.04197i	0.853565	−	0.520986i	$-0.174436\pi$
$620$	3.46791	0.139275
$621$	3.10607	0.124642
$622$	0.732860i	0.0293850i
$623$	− 0.245348i	− 0.00982967i
$624$	23.4911i	0.940398i
$625$	−30.0651	−1.20260
$626$	− 22.3901i	− 0.894889i
$627$	−16.5767	−0.662008
$628$	−0.329126	−0.0131336
$629$	0	0
$630$	0.630415	0.0251163
$631$	−30.1411	−1.19990	−0.599950	−	0.800037i	$-0.704813\pi$
$631$	−30.1411	−1.19990	−0.599950	+	0.800037i	$0.704813\pi$
$632$	− 23.0273i	− 0.915978i
$633$	−2.54664	−0.101220
$634$	35.1070i	1.39428i
$635$	− 19.6655i	− 0.780401i
$636$	− 1.41416i	− 0.0560752i
$637$	−45.5016	−1.80284
$638$	30.6008	1.21150
$639$	3.61081i	0.142842i
$640$	− 24.0496i	− 0.950645i
$641$	− 0.598021i	− 0.0236204i	−0.999930	−	0.0118102i	$-0.996241\pi$
$641$	− 0.598021i	− 0.0236204i	0.999930	−	0.0118102i	$-0.00375939\pi$
$642$	−4.78880	−0.188999
$643$	− 32.5827i	− 1.28493i	−0.766313	−	0.642467i	$-0.777911\pi$
$643$	− 32.5827i	− 1.28493i	0.766313	−	0.642467i	$-0.222089\pi$
$644$	−0.106067	−0.00417962
$645$	12.4979	0.492106
$646$	0	0
$647$	−13.8648	−0.545083	−0.272542	−	0.962144i	$-0.587864\pi$
$647$	−13.8648	−0.545083	−0.272542	+	0.962144i	$0.587864\pi$
$648$	−2.94356	−0.115634
$649$	− 23.4252i	− 0.919520i
$650$	12.4219	0.487227
$651$	− 1.36959i	− 0.0536783i
$652$	− 0.582216i	− 0.0228013i
$653$	− 1.49619i	− 0.0585503i	−0.999571	−	0.0292751i	$-0.990680\pi$
$653$	− 1.49619i	− 0.0585503i	0.999571	−	0.0292751i	$-0.00931990\pi$
$654$	4.84524	0.189464
$655$	−12.5371	−0.489867
$656$	25.8384i	1.00882i
$657$	− 8.41147i	− 0.328163i
$658$	2.25309i	0.0878346i
$659$	49.3441	1.92217	0.961087	−	0.276246i	$-0.0890906\pi$
$659$	49.3441	1.92217	0.961087	+	0.276246i	$0.0890906\pi$
$660$	1.67230i	0.0650943i
$661$	−45.9077	−1.78560	−0.892801	−	0.450452i	$-0.851263\pi$
$661$	−45.9077	−1.78560	−0.892801	+	0.450452i	$0.851263\pi$
$662$	30.3286	1.17876
$663$	0	0
$664$	7.39567	0.287008
$665$	2.17024	0.0841585
$666$	11.3131i	0.438376i
$667$	−19.7392	−0.764304
$668$	− 4.49937i	− 0.174086i
$669$	− 4.44562i	− 0.171878i
$670$	46.1147i	1.78157i
$671$	−10.6699	−0.411908
$672$	0.192533	0.00742713
$673$	34.7965i	1.34131i	0.741770	+	0.670654i	$0.233986\pi$
$673$	34.7965i	1.34131i	−0.741770	+	0.670654i	$0.766014\pi$
$674$	0.669616i	0.0257926i
$675$	1.41147i	0.0543277i
$676$	−5.48246	−0.210864
$677$	− 14.1875i	− 0.545269i	−0.962118	−	0.272635i	$-0.912105\pi$
$677$	− 14.1875i	− 0.545269i	0.962118	−	0.272635i	$-0.0878950\pi$
$678$	6.34461	0.243663
$679$	−1.61856	−0.0621145
$680$	0	0
$681$	−7.52023	−0.288176
$682$	−35.6878	−1.36656
$683$	44.5289i	1.70385i	0.523663	+	0.851926i	$0.324565\pi$
$683$	44.5289i	1.70385i	−0.523663	+	0.851926i	$0.675435\pi$
$684$	−0.857097	−0.0327719
$685$	29.3432i	1.12115i
$686$	− 3.47708i	− 0.132756i
$687$	− 13.7374i	− 0.524115i
$688$	−17.7505	−0.676733
$689$	−49.9881	−1.90440
$690$	10.5963i	0.403393i
$691$	− 5.98782i	− 0.227787i	−0.993493	−	0.113894i	$-0.963668\pi$
$691$	− 5.98782i	− 0.227787i	0.993493	−	0.113894i	$-0.0363323\pi$
$692$	− 2.78468i	− 0.105858i
$693$	0.660444	0.0250882
$694$	18.6800i	0.709085i
$695$	−6.81016	−0.258324
$696$	18.7065	0.709066
$697$	0	0
$698$	−36.4415	−1.37933
$699$	20.5253	0.776337
$700$	− 0.0481994i	− 0.00182177i
$701$	15.4739	0.584441	0.292221	−	0.956351i	$-0.405606\pi$
$701$	15.4739	0.584441	0.292221	+	0.956351i	$0.405606\pi$
$702$	8.80066i	0.332159i
$703$	38.9463i	1.46889i
$704$	− 30.7229i	− 1.15791i
$705$	−22.9145	−0.863009
$706$	12.0852	0.454833
$707$	2.03777i	0.0766382i
$708$	− 1.21120i	− 0.0455197i
$709$	− 31.9982i	− 1.20172i	−0.799355	−	0.600860i	$-0.794825\pi$
$709$	− 31.9982i	− 1.20172i	0.799355	−	0.600860i	$-0.205175\pi$
$710$	−12.3182	−0.462294
$711$	− 7.82295i	− 0.293383i
$712$	−3.90816	−0.146464
$713$	23.0205	0.862126
$714$	0	0
$715$	59.1130	2.21070
$716$	3.12330	0.116723
$717$	25.9145i	0.967794i
$718$	−8.25309	−0.308003
$719$	23.3364i	0.870300i	0.900358	+	0.435150i	$0.143305\pi$
$719$	23.3364i	0.870300i	−0.900358	+	0.435150i	$0.856695\pi$
$720$	− 9.10607i	− 0.339363i
$721$	− 1.15888i	− 0.0431590i
$722$	3.38507	0.125979
$723$	11.3773	0.423127
$724$	1.97140i	0.0732665i
$725$	− 8.96997i	− 0.333136i
$726$	− 2.38919i	− 0.0886710i
$727$	−4.75372	−0.176306	−0.0881528	−	0.996107i	$-0.528096\pi$
$727$	−4.75372	−0.176306	−0.0881528	+	0.996107i	$0.528096\pi$
$728$	− 3.55312i	− 0.131687i
$729$	−1.00000	−0.0370370
$730$	28.6955	1.06207
$731$	0	0
$732$	−0.551689	−0.0203910
$733$	0.982764	0.0362992	0.0181496	−	0.999835i	$-0.494222\pi$
$733$	0.982764	0.0362992	0.0181496	+	0.999835i	$0.494222\pi$
$734$	24.1453i	0.891218i
$735$	17.6382	0.650593
$736$	3.23618i	0.119287i
$737$	48.3114i	1.77957i
$738$	9.68004i	0.356327i
$739$	9.95636	0.366250	0.183125	−	0.983090i	$-0.441379\pi$
$739$	9.95636	0.366250	0.183125	+	0.983090i	$0.441379\pi$
$740$	3.92902	0.144433
$741$	30.2968i	1.11298i
$742$	− 1.90530i	− 0.0699456i
$743$	46.5262i	1.70688i	0.521190	+	0.853441i	$0.325488\pi$
$743$	46.5262i	1.70688i	−0.521190	+	0.853441i	$0.674512\pi$
$744$	−21.8161	−0.799819
$745$	40.3337i	1.47771i
$746$	−20.9355	−0.766503
$747$	2.51249	0.0919271
$748$	0	0
$749$	0.656822	0.0239998
$750$	12.2422	0.447021
$751$	13.3155i	0.485890i	0.970040	+	0.242945i	$0.0781134\pi$
$751$	13.3155i	0.485890i	−0.970040	+	0.242945i	$0.921887\pi$
$752$	32.5449	1.18679
$753$	− 0.859785i	− 0.0313323i
$754$	− 55.9285i	− 2.03680i
$755$	3.51754i	0.128016i
$756$	0.0341483	0.00124196
$757$	45.0874	1.63873	0.819365	−	0.573273i	$-0.194326\pi$
$757$	45.0874	1.63873	0.819365	+	0.573273i	$0.194326\pi$
$758$	− 51.2089i	− 1.85999i
$759$	11.1010i	0.402941i
$760$	− 34.5699i	− 1.25398i
$761$	24.0036	0.870131	0.435065	−	0.900399i	$-0.356725\pi$
$761$	24.0036	0.870131	0.435065	+	0.900399i	$0.356725\pi$
$762$	10.4638i	0.379063i
$763$	−0.664563	−0.0240588
$764$	−0.328630	−0.0118894
$765$	0	0
$766$	−28.6551	−1.03535
$767$	−42.8138	−1.54592
$768$	− 4.39599i	− 0.158627i
$769$	−30.5773	−1.10264	−0.551322	−	0.834292i	$-0.685877\pi$
$769$	−30.5773	−1.10264	−0.551322	+	0.834292i	$0.685877\pi$
$770$	2.25309i	0.0811957i
$771$	− 0.0300295i	− 0.00108149i
$772$	0.936756i	0.0337146i
$773$	45.3346	1.63057	0.815286	−	0.579058i	$-0.196579\pi$
$773$	45.3346	1.63057	0.815286	+	0.579058i	$0.196579\pi$
$774$	−6.65002	−0.239030
$775$	10.4611i	0.375774i
$776$	25.7820i	0.925520i
$777$	− 1.55169i	− 0.0556665i
$778$	−18.5948	−0.666657
$779$	33.3242i	1.19396i
$780$	3.05644	0.109438
$781$	−12.9050	−0.461776
$782$	0	0
$783$	6.35504	0.227110
$784$	−25.0511	−0.894681
$785$	− 4.50980i	− 0.160962i
$786$	6.67087	0.237942
$787$	− 18.7442i	− 0.668159i	−0.942545	−	0.334080i	$-0.891575\pi$
$787$	− 18.7442i	− 0.668159i	0.942545	−	0.334080i	$-0.108425\pi$
$788$	1.48658i	0.0529571i
$789$	− 12.2422i	− 0.435833i
$790$	26.6878	0.949509
$791$	−0.870214	−0.0309412
$792$	− 10.5202i	− 0.373820i
$793$	19.5012i	0.692509i
$794$	− 38.4816i	− 1.36566i
$795$	19.3773	0.687243
$796$	2.20658i	0.0782103i
$797$	−44.5681	−1.57868	−0.789342	−	0.613954i	$-0.789578\pi$
$797$	−44.5681	−1.57868	−0.789342	+	0.613954i	$0.789578\pi$
$798$	−1.15476	−0.0408782
$799$	0	0
$800$	−1.47060	−0.0519935
$801$	−1.32770	−0.0469118
$802$	− 36.0760i	− 1.27389i
$803$	30.0624	1.06088
$804$	2.49794i	0.0880956i
$805$	− 1.45336i	− 0.0512243i
$806$	65.2259i	2.29748i
$807$	21.5672	0.759200
$808$	32.4597	1.14193
$809$	− 8.46522i	− 0.297621i	−0.988866	−	0.148811i	$-0.952455\pi$
$809$	− 8.46522i	− 0.297621i	0.988866	−	0.148811i	$-0.0475445\pi$
$810$	− 3.41147i	− 0.119867i
$811$	− 10.9314i	− 0.383853i	−0.981409	−	0.191926i	$-0.938527\pi$
$811$	− 10.9314i	− 0.383853i	0.981409	−	0.191926i	$-0.0614735\pi$
$812$	−0.217014	−0.00761568
$813$	3.39693i	0.119135i
$814$	−40.4329	−1.41717
$815$	7.97771	0.279447
$816$	0	0
$817$	−22.8931	−0.800929
$818$	52.3233	1.82944
$819$	− 1.20708i	− 0.0421788i
$820$	3.36184	0.117401
$821$	12.5680i	0.438626i	0.975655	+	0.219313i	$0.0703816\pi$
$821$	12.5680i	0.438626i	−0.975655	+	0.219313i	$0.929618\pi$
$822$	− 15.6132i	− 0.544572i
$823$	51.2695i	1.78714i	0.448921	+	0.893571i	$0.351808\pi$
$823$	51.2695i	1.78714i	−0.448921	+	0.893571i	$0.648192\pi$
$824$	−18.4598	−0.643079
$825$	−5.04458	−0.175630
$826$	− 1.63185i	− 0.0567792i
$827$	28.5458i	0.992635i	0.868141	+	0.496318i	$0.165315\pi$
$827$	28.5458i	0.992635i	−0.868141	+	0.496318i	$0.834685\pi$
$828$	0.573978i	0.0199471i
$829$	4.09865	0.142352	0.0711760	−	0.997464i	$-0.477325\pi$
$829$	4.09865	0.142352	0.0711760	+	0.997464i	$0.477325\pi$
$830$	8.57129i	0.297514i
$831$	15.9172	0.552160
$832$	−56.1516	−1.94671
$833$	0	0
$834$	3.62361	0.125475
$835$	61.6519	2.13355
$836$	− 3.06324i	− 0.105945i
$837$	−7.41147	−0.256178
$838$	25.6459i	0.885923i
$839$	− 37.3969i	− 1.29109i	−0.763724	−	0.645543i	$-0.776631\pi$
$839$	− 37.3969i	− 1.29109i	0.763724	−	0.645543i	$-0.223369\pi$
$840$	1.37733i	0.0475223i
$841$	−11.3865	−0.392638
$842$	8.64496	0.297925
$843$	16.0155i	0.551602i
$844$	− 0.470599i	− 0.0161987i
$845$	− 75.1225i	− 2.58429i
$846$	12.1925	0.419188
$847$	0.327696i	0.0112598i
$848$	−27.5212	−0.945081
$849$	26.8357	0.921000
$850$	0	0
$851$	26.0814	0.894059
$852$	−0.667252	−0.0228597
$853$	56.2586i	1.92626i	0.269042	+	0.963129i	$0.413293\pi$
$853$	56.2586i	1.92626i	−0.269042	+	0.963129i	$0.586707\pi$
$854$	−0.743289	−0.0254348
$855$	− 11.7442i	− 0.401644i
$856$	− 10.4625i	− 0.357602i
$857$	− 17.8203i	− 0.608728i	−0.952556	−	0.304364i	$-0.901556\pi$
$857$	− 17.8203i	− 0.608728i	0.952556	−	0.304364i	$-0.0984440\pi$
$858$	−31.4534	−1.07380
$859$	5.45935	0.186271	0.0931353	−	0.995653i	$-0.470311\pi$
$859$	5.45935	0.186271	0.0931353	+	0.995653i	$0.470311\pi$
$860$	2.30953i	0.0787542i
$861$	− 1.32770i	− 0.0452478i
$862$	11.6554i	0.396984i
$863$	8.23947	0.280475	0.140237	−	0.990118i	$-0.455213\pi$
$863$	8.23947	0.280475	0.140237	+	0.990118i	$0.455213\pi$
$864$	− 1.04189i	− 0.0354458i
$865$	38.1566	1.29736
$866$	−31.4165	−1.06758
$867$	0	0
$868$	0.253089	0.00859040
$869$	27.9590	0.948446
$870$	21.6800i	0.735022i
$871$	88.2978	2.99186
$872$	10.5858i	0.358482i
$873$	8.75877i	0.296439i
$874$	− 19.4097i	− 0.656544i
$875$	−1.67911	−0.0567643
$876$	1.55438	0.0525176
$877$	8.15032i	0.275217i	0.990487	+	0.137608i	$0.0439415\pi$
$877$	8.15032i	0.275217i	−0.990487	+	0.137608i	$0.956058\pi$
$878$	− 17.7834i	− 0.600161i
$879$	2.40879i	0.0812463i
$880$	32.5449	1.09709
$881$	− 18.8553i	− 0.635253i	−0.948216	−	0.317626i	$-0.897114\pi$
$881$	− 18.8553i	− 0.635253i	0.948216	−	0.317626i	$-0.102886\pi$
$882$	−9.38507	−0.316012
$883$	17.2189	0.579463	0.289732	−	0.957108i	$-0.406434\pi$
$883$	17.2189	0.579463	0.289732	+	0.957108i	$0.406434\pi$
$884$	0	0
$885$	16.5963	0.557877
$886$	−41.1242	−1.38160
$887$	11.1898i	0.375718i	0.982196	+	0.187859i	$0.0601548\pi$
$887$	11.1898i	0.375718i	−0.982196	+	0.187859i	$0.939845\pi$
$888$	−24.7169	−0.829444
$889$	− 1.43519i	− 0.0481348i
$890$	− 4.52940i	− 0.151826i
$891$	− 3.57398i	− 0.119733i
$892$	0.821518	0.0275065
$893$	41.9736	1.40459
$894$	− 21.4611i	− 0.717767i
$895$	42.7965i	1.43053i
$896$	− 1.75515i	− 0.0586354i
$897$	20.2891	0.677433
$898$	3.65364i	0.121923i
$899$	47.1002	1.57088
$900$	−0.260830	−0.00869433
$901$	0	0
$902$	−34.5963	−1.15193
$903$	0.912103	0.0303529
$904$	13.8617i	0.461032i
$905$	−27.0128	−0.897936
$906$	− 1.87164i	− 0.0621812i
$907$	− 41.0797i	− 1.36403i	−0.731339	−	0.682014i	$-0.761104\pi$
$907$	− 41.0797i	− 1.36403i	0.731339	−	0.682014i	$-0.238896\pi$
$908$	− 1.38968i	− 0.0461182i
$909$	11.0273	0.365754
$910$	4.11793	0.136508
$911$	38.3688i	1.27121i	0.772013	+	0.635607i	$0.219250\pi$
$911$	38.3688i	1.27121i	−0.772013	+	0.635607i	$0.780750\pi$
$912$	16.6800i	0.552331i
$913$	8.97958i	0.297181i
$914$	35.3892	1.17057
$915$	− 7.55943i	− 0.249907i
$916$	2.53857	0.0838768
$917$	−0.914964	−0.0302148
$918$	0	0
$919$	22.7110	0.749167	0.374584	−	0.927193i	$-0.377786\pi$
$919$	22.7110	0.749167	0.374584	+	0.927193i	$0.377786\pi$
$920$	−23.1506	−0.763254
$921$	− 6.41921i	− 0.211520i
$922$	34.3833	1.13235
$923$	23.5862i	0.776348i
$924$	0.122045i	0.00401499i
$925$	11.8520i	0.389693i
$926$	−3.80697	−0.125105
$927$	−6.27126	−0.205975
$928$	6.62124i	0.217353i
$929$	21.5439i	0.706834i	0.935466	+	0.353417i	$0.114980\pi$
$929$	21.5439i	0.706834i	−0.935466	+	0.353417i	$0.885020\pi$
$930$	− 25.2841i	− 0.829097i
$931$	−32.3087	−1.05888
$932$	3.79292i	0.124241i
$933$	−0.543948	−0.0178081
$934$	44.4597	1.45476
$935$	0	0
$936$	−19.2276	−0.628474
$937$	37.5476	1.22663	0.613313	−	0.789840i	$-0.289837\pi$
$937$	37.5476	1.22663	0.613313	+	0.789840i	$0.289837\pi$
$938$	3.36547i	0.109886i
$939$	16.6186	0.542326
$940$	− 4.23442i	− 0.138112i
$941$	− 38.8735i	− 1.26724i	−0.773644	−	0.633620i	$-0.781568\pi$
$941$	− 38.8735i	− 1.26724i	0.773644	−	0.633620i	$-0.218432\pi$
$942$	2.39961i	0.0781837i
$943$	22.3164	0.726723
$944$	−23.5713	−0.767180
$945$	0.467911i	0.0152211i
$946$	− 23.7670i	− 0.772732i
$947$	47.5313i	1.54456i	0.635283	+	0.772279i	$0.280883\pi$
$947$	47.5313i	1.54456i	−0.635283	+	0.772279i	$0.719117\pi$
$948$	1.44562	0.0469516
$949$	− 54.9445i	− 1.78357i
$950$	8.82026	0.286167
$951$	−26.0574	−0.844968
$952$	0	0
$953$	48.6332	1.57538	0.787692	−	0.616069i	$-0.211276\pi$
$953$	48.6332	1.57538	0.787692	+	0.616069i	$0.211276\pi$
$954$	−10.3105	−0.333813
$955$	− 4.50299i	− 0.145713i
$956$	−4.78880	−0.154881
$957$	22.7128i	0.734199i
$958$	46.9113i	1.51563i
$959$	2.14147i	0.0691518i
$960$	21.7665	0.702511
$961$	−23.9299	−0.771934
$962$	73.8985i	2.38258i
$963$	− 3.55438i	− 0.114538i
$964$	2.10244i	0.0677152i
$965$	−12.8357	−0.413197
$966$	0.773318i	0.0248811i
$967$	−1.39281	−0.0447897	−0.0223948	−	0.999749i	$-0.507129\pi$
$967$	−1.39281	−0.0447897	−0.0223948	+	0.999749i	$0.507129\pi$
$968$	5.21987	0.167773
$969$	0	0
$970$	−29.8803	−0.959399
$971$	−13.0892	−0.420051	−0.210025	−	0.977696i	$-0.567355\pi$
$971$	−13.0892	−0.420051	−0.210025	+	0.977696i	$0.567355\pi$
$972$	− 0.184793i	− 0.00592722i
$973$	−0.497007	−0.0159333
$974$	− 29.0782i	− 0.931727i
$975$	9.21987i	0.295272i
$976$	10.7365i	0.343666i
$977$	−3.40230	−0.108849	−0.0544247	−	0.998518i	$-0.517332\pi$
$977$	−3.40230	−0.108849	−0.0544247	+	0.998518i	$0.517332\pi$
$978$	−4.24485	−0.135735
$979$	− 4.74516i	− 0.151656i
$980$	3.25940i	0.104118i
$981$	3.59627i	0.114820i
$982$	46.2404	1.47559
$983$	14.6622i	0.467652i	0.972279	+	0.233826i	$0.0751245\pi$
$983$	14.6622i	0.467652i	−0.972279	+	0.233826i	$0.924875\pi$
$984$	−21.1489	−0.674202
$985$	−20.3696	−0.649029
$986$	0	0
$987$	−1.67230	−0.0532300
$988$	−5.59863	−0.178116
$989$	15.3310i	0.487497i
$990$	12.1925	0.387504
$991$	46.6674i	1.48244i	0.671263	+	0.741219i	$0.265752\pi$
$991$	46.6674i	1.48244i	−0.671263	+	0.741219i	$0.734248\pi$
$992$	− 7.72193i	− 0.245172i
$993$	22.5107i	0.714357i
$994$	−0.898986	−0.0285141
$995$	−30.2354	−0.958525
$996$	0.464289i	0.0147116i
$997$	1.54993i	0.0490869i	0.999699	+	0.0245435i	$0.00781321\pi$
$997$	1.54993i	0.0490869i	−0.999699	+	0.0245435i	$0.992187\pi$
$998$	24.4483i	0.773898i
$999$	−8.39693	−0.265667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.d.d.577.4		6
17.2	even	8		867.2.e.j.829.4		12
17.3	odd	16		867.2.h.l.688.3		24
17.4	even	4		867.2.a.j.1.2	yes	3
17.5	odd	16		867.2.h.l.757.3		24
17.6	odd	16		867.2.h.l.712.4		24
17.7	odd	16		867.2.h.l.733.4		24
17.8	even	8		867.2.e.j.616.4		12
17.9	even	8		867.2.e.j.616.3		12
17.10	odd	16		867.2.h.l.733.3		24
17.11	odd	16		867.2.h.l.712.3		24
17.12	odd	16		867.2.h.l.757.4		24
17.13	even	4		867.2.a.i.1.2	✓	3
17.14	odd	16		867.2.h.l.688.4		24
17.15	even	8		867.2.e.j.829.3		12
17.16	even	2	inner	867.2.d.d.577.3		6
51.38	odd	4		2601.2.a.z.1.2		3
51.47	odd	4		2601.2.a.y.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.i.1.2	✓	3	17.13	even	4
867.2.a.j.1.2	yes	3	17.4	even	4
867.2.d.d.577.3		6	17.16	even	2	inner
867.2.d.d.577.4		6	1.1	even	1	trivial
867.2.e.j.616.3		12	17.9	even	8
867.2.e.j.616.4		12	17.8	even	8
867.2.e.j.829.3		12	17.15	even	8
867.2.e.j.829.4		12	17.2	even	8
867.2.h.l.688.3		24	17.3	odd	16
867.2.h.l.688.4		24	17.14	odd	16
867.2.h.l.712.3		24	17.11	odd	16
867.2.h.l.712.4		24	17.6	odd	16
867.2.h.l.733.3		24	17.10	odd	16
867.2.h.l.733.4		24	17.7	odd	16
867.2.h.l.757.3		24	17.5	odd	16
867.2.h.l.757.4		24	17.12	odd	16
2601.2.a.y.1.2		3	51.47	odd	4
2601.2.a.z.1.2		3	51.38	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.34730 q^{2} +1.00000i q^{3} -0.184793 q^{4} -2.53209i q^{5} +1.34730i q^{6} -0.184793i q^{7} -2.94356 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.34730 q^{2} +1.00000i q^{3} -0.184793 q^{4} -2.53209i q^{5} +1.34730i q^{6} -0.184793i q^{7} -2.94356 q^{8} -1.00000 q^{9} -3.41147i q^{10} -3.57398i q^{11} -0.184793i q^{12} -6.53209 q^{13} -0.248970i q^{14} +2.53209 q^{15} -3.59627 q^{16} -1.34730 q^{18} -4.63816 q^{19} +0.467911i q^{20} +0.184793 q^{21} -4.81521i q^{22} +3.10607i q^{23} -2.94356i q^{24} -1.41147 q^{25} -8.80066 q^{26} -1.00000i q^{27} +0.0341483i q^{28} +6.35504i q^{29} +3.41147 q^{30} -7.41147i q^{31} +1.04189 q^{32} +3.57398 q^{33} -0.467911 q^{35} +0.184793 q^{36} -8.39693i q^{37} -6.24897 q^{38} -6.53209i q^{39} +7.45336i q^{40} -7.18479i q^{41} +0.248970 q^{42} +4.93582 q^{43} +0.660444i q^{44} +2.53209i q^{45} +4.18479i q^{46} -9.04963 q^{47} -3.59627i q^{48} +6.96585 q^{49} -1.90167 q^{50} +1.20708 q^{52} +7.65270 q^{53} -1.34730i q^{54} -9.04963 q^{55} +0.543948i q^{56} -4.63816i q^{57} +8.56212i q^{58} +6.55438 q^{59} -0.467911 q^{60} -2.98545i q^{61} -9.98545i q^{62} +0.184793i q^{63} +8.59627 q^{64} +16.5398i q^{65} +4.81521 q^{66} -13.5175 q^{67} -3.10607 q^{69} -0.630415 q^{70} -3.61081i q^{71} +2.94356 q^{72} +8.41147i q^{73} -11.3131i q^{74} -1.41147i q^{75} +0.857097 q^{76} -0.660444 q^{77} -8.80066i q^{78} +7.82295i q^{79} +9.10607i q^{80} +1.00000 q^{81} -9.68004i q^{82} -2.51249 q^{83} -0.0341483 q^{84} +6.65002 q^{86} -6.35504 q^{87} +10.5202i q^{88} +1.32770 q^{89} +3.41147i q^{90} +1.20708i q^{91} -0.573978i q^{92} +7.41147 q^{93} -12.1925 q^{94} +11.7442i q^{95} +1.04189i q^{96} -8.75877i q^{97} +9.38507 q^{98} +3.57398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} + 12 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 + 12 * q^8 - 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} + 12 q^{8} - 6 q^{9} - 30 q^{13} + 6 q^{15} + 6 q^{16} - 6 q^{18} + 6 q^{19} - 6 q^{21} + 12 q^{25} - 24 q^{26} + 6 q^{33} - 12 q^{35} - 6 q^{36} - 12 q^{38} - 24 q^{42} + 48 q^{43} + 12 q^{50} - 12 q^{52} + 48 q^{53} + 18 q^{59} - 12 q^{60} + 24 q^{64} + 36 q^{66} - 36 q^{67} + 6 q^{69} - 18 q^{70} - 12 q^{72} + 6 q^{76} + 42 q^{77} + 6 q^{81} - 42 q^{84} + 60 q^{86} + 12 q^{87} + 24 q^{93} - 18 q^{94} - 54 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 + 12 * q^8 - 6 * q^9 - 30 * q^13 + 6 * q^15 + 6 * q^16 - 6 * q^18 + 6 * q^19 - 6 * q^21 + 12 * q^25 - 24 * q^26 + 6 * q^33 - 12 * q^35 - 6 * q^36 - 12 * q^38 - 24 * q^42 + 48 * q^43 + 12 * q^50 - 12 * q^52 + 48 * q^53 + 18 * q^59 - 12 * q^60 + 24 * q^64 + 36 * q^66 - 36 * q^67 + 6 * q^69 - 18 * q^70 - 12 * q^72 + 6 * q^76 + 42 * q^77 + 6 * q^81 - 42 * q^84 + 60 * q^86 + 12 * q^87 + 24 * q^93 - 18 * q^94 - 54 * q^98

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