LMFDB - Embedded newform 1014.2.b.e.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(337,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, 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("1014.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.337
Dual form			1014.2.b.e.337.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -0.267949i q^{5} -1.00000i q^{6} +0.732051i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -0.267949i q^{5} -1.00000i q^{6} +0.732051i q^{7} +1.00000i q^{8} +1.00000 q^{9} -0.267949 q^{10} +4.73205i q^{11} -1.00000 q^{12} +0.732051 q^{14} -0.267949i q^{15} +1.00000 q^{16} +2.26795 q^{17} -1.00000i q^{18} -1.26795i q^{19} +0.267949i q^{20} +0.732051i q^{21} +4.73205 q^{22} +6.19615 q^{23} +1.00000i q^{24} +4.92820 q^{25} +1.00000 q^{27} -0.732051i q^{28} +2.46410 q^{29} -0.267949 q^{30} +5.46410i q^{31} -1.00000i q^{32} +4.73205i q^{33} -2.26795i q^{34} +0.196152 q^{35} -1.00000 q^{36} +10.4641i q^{37} -1.26795 q^{38} +0.267949 q^{40} -11.3923i q^{41} +0.732051 q^{42} -7.66025 q^{43} -4.73205i q^{44} -0.267949i q^{45} -6.19615i q^{46} -8.19615i q^{47} +1.00000 q^{48} +6.46410 q^{49} -4.92820i q^{50} +2.26795 q^{51} +0.464102 q^{53} -1.00000i q^{54} +1.26795 q^{55} -0.732051 q^{56} -1.26795i q^{57} -2.46410i q^{58} +8.00000i q^{59} +0.267949i q^{60} +1.19615 q^{61} +5.46410 q^{62} +0.732051i q^{63} -1.00000 q^{64} +4.73205 q^{66} +11.1244i q^{67} -2.26795 q^{68} +6.19615 q^{69} -0.196152i q^{70} -1.26795i q^{71} +1.00000i q^{72} -9.73205i q^{73} +10.4641 q^{74} +4.92820 q^{75} +1.26795i q^{76} -3.46410 q^{77} -9.46410 q^{79} -0.267949i q^{80} +1.00000 q^{81} -11.3923 q^{82} -10.1962i q^{83} -0.732051i q^{84} -0.607695i q^{85} +7.66025i q^{86} +2.46410 q^{87} -4.73205 q^{88} -2.53590i q^{89} -0.267949 q^{90} -6.19615 q^{92} +5.46410i q^{93} -8.19615 q^{94} -0.339746 q^{95} -1.00000i q^{96} +6.00000i q^{97} -6.46410i q^{98} +4.73205i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9	$ 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9} - 8 q^{10} - 4 q^{12} - 4 q^{14} + 4 q^{16} + 16 q^{17} + 12 q^{22} + 4 q^{23} - 8 q^{25} + 4 q^{27} - 4 q^{29} - 8 q^{30} - 20 q^{35} - 4 q^{36} - 12 q^{38} + 8 q^{40} - 4 q^{42} + 4 q^{43} + 4 q^{48} + 12 q^{49} + 16 q^{51} - 12 q^{53} + 12 q^{55} + 4 q^{56} - 16 q^{61} + 8 q^{62} - 4 q^{64} + 12 q^{66} - 16 q^{68} + 4 q^{69} + 28 q^{74} - 8 q^{75} - 24 q^{79} + 4 q^{81} - 4 q^{82} - 4 q^{87} - 12 q^{88} - 8 q^{90} - 4 q^{92} - 12 q^{94} - 36 q^{95}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9 - 8 * q^10 - 4 * q^12 - 4 * q^14 + 4 * q^16 + 16 * q^17 + 12 * q^22 + 4 * q^23 - 8 * q^25 + 4 * q^27 - 4 * q^29 - 8 * q^30 - 20 * q^35 - 4 * q^36 - 12 * q^38 + 8 * q^40 - 4 * q^42 + 4 * q^43 + 4 * q^48 + 12 * q^49 + 16 * q^51 - 12 * q^53 + 12 * q^55 + 4 * q^56 - 16 * q^61 + 8 * q^62 - 4 * q^64 + 12 * q^66 - 16 * q^68 + 4 * q^69 + 28 * q^74 - 8 * q^75 - 24 * q^79 + 4 * q^81 - 4 * q^82 - 4 * q^87 - 12 * q^88 - 8 * q^90 - 4 * q^92 - 12 * q^94 - 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$-1$

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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.00000	−0.500000
$5$	− 0.267949i	− 0.119831i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	− 0.267949i	− 0.119831i	0.998203	−	0.0599153i	$-0.0190830\pi$
$6$	− 1.00000i	− 0.408248i
$7$	0.732051i	0.276689i	0.990384	+	0.138345i	$0.0441781\pi$
$7$	0.732051i	0.276689i	−0.990384	+	0.138345i	$0.955822\pi$
$8$	1.00000i	0.353553i
$9$	1.00000	0.333333
$10$	−0.267949	−0.0847330
$11$	4.73205i	1.42677i	0.700774	+	0.713384i	$0.252838\pi$
$11$	4.73205i	1.42677i	−0.700774	+	0.713384i	$0.747162\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	0.732051	0.195649
$15$	− 0.267949i	− 0.0691842i
$16$	1.00000	0.250000
$17$	2.26795	0.550058	0.275029	−	0.961436i	$-0.411312\pi$
$17$	2.26795	0.550058	0.275029	+	0.961436i	$0.411312\pi$
$18$	− 1.00000i	− 0.235702i
$19$	− 1.26795i	− 0.290887i	−0.989367	−	0.145444i	$-0.953539\pi$
$19$	− 1.26795i	− 0.290887i	0.989367	−	0.145444i	$-0.0464610\pi$
$20$	0.267949i	0.0599153i
$21$	0.732051i	0.159747i
$22$	4.73205	1.00888
$23$	6.19615	1.29199	0.645994	−	0.763343i	$-0.276443\pi$
$23$	6.19615	1.29199	0.645994	+	0.763343i	$0.276443\pi$
$24$	1.00000i	0.204124i
$25$	4.92820	0.985641
$26$	0	0
$27$	1.00000	0.192450
$28$	− 0.732051i	− 0.138345i
$29$	2.46410	0.457572	0.228786	−	0.973477i	$-0.426524\pi$
$29$	2.46410	0.457572	0.228786	+	0.973477i	$0.426524\pi$
$30$	−0.267949	−0.0489206
$31$	5.46410i	0.981382i	0.871334	+	0.490691i	$0.163256\pi$
$31$	5.46410i	0.981382i	−0.871334	+	0.490691i	$0.836744\pi$
$32$	− 1.00000i	− 0.176777i
$33$	4.73205i	0.823744i
$34$	− 2.26795i	− 0.388950i
$35$	0.196152	0.0331558
$36$	−1.00000	−0.166667
$37$	10.4641i	1.72029i	0.510052	+	0.860144i	$0.329626\pi$
$37$	10.4641i	1.72029i	−0.510052	+	0.860144i	$0.670374\pi$
$38$	−1.26795	−0.205689
$39$	0	0
$40$	0.267949	0.0423665
$41$	− 11.3923i	− 1.77918i	−0.456761	−	0.889590i	$-0.650990\pi$
$41$	− 11.3923i	− 1.77918i	0.456761	−	0.889590i	$-0.349010\pi$
$42$	0.732051	0.112958
$43$	−7.66025	−1.16818	−0.584089	−	0.811690i	$-0.698548\pi$
$43$	−7.66025	−1.16818	−0.584089	+	0.811690i	$0.698548\pi$
$44$	− 4.73205i	− 0.713384i
$45$	− 0.267949i	− 0.0399435i
$46$	− 6.19615i	− 0.913573i
$47$	− 8.19615i	− 1.19553i	−0.801671	−	0.597766i	$-0.796055\pi$
$47$	− 8.19615i	− 1.19553i	0.801671	−	0.597766i	$-0.203945\pi$
$48$	1.00000	0.144338
$49$	6.46410	0.923443
$50$	− 4.92820i	− 0.696953i
$51$	2.26795	0.317576
$52$	0	0
$53$	0.464102	0.0637493	0.0318746	−	0.999492i	$-0.489852\pi$
$53$	0.464102	0.0637493	0.0318746	+	0.999492i	$0.489852\pi$
$54$	− 1.00000i	− 0.136083i
$55$	1.26795	0.170970
$56$	−0.732051	−0.0978244
$57$	− 1.26795i	− 0.167944i
$58$	− 2.46410i	− 0.323552i
$59$	8.00000i	1.04151i	0.853706	+	0.520756i	$0.174350\pi$
$59$	8.00000i	1.04151i	−0.853706	+	0.520756i	$0.825650\pi$
$60$	0.267949i	0.0345921i
$61$	1.19615	0.153152	0.0765758	−	0.997064i	$-0.475601\pi$
$61$	1.19615	0.153152	0.0765758	+	0.997064i	$0.475601\pi$
$62$	5.46410	0.693942
$63$	0.732051i	0.0922297i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	4.73205	0.582475
$67$	11.1244i	1.35906i	0.733649	+	0.679528i	$0.237815\pi$
$67$	11.1244i	1.35906i	−0.733649	+	0.679528i	$0.762185\pi$
$68$	−2.26795	−0.275029
$69$	6.19615	0.745929
$70$	− 0.196152i	− 0.0234447i
$71$	− 1.26795i	− 0.150478i	−0.997166	−	0.0752389i	$-0.976028\pi$
$71$	− 1.26795i	− 0.150478i	0.997166	−	0.0752389i	$-0.0239720\pi$
$72$	1.00000i	0.117851i
$73$	− 9.73205i	− 1.13905i	−0.821974	−	0.569525i	$-0.807127\pi$
$73$	− 9.73205i	− 1.13905i	0.821974	−	0.569525i	$-0.192873\pi$
$74$	10.4641	1.21643
$75$	4.92820	0.569060
$76$	1.26795i	0.145444i
$77$	−3.46410	−0.394771
$78$	0	0
$79$	−9.46410	−1.06479	−0.532397	−	0.846495i	$-0.678709\pi$
$79$	−9.46410	−1.06479	−0.532397	+	0.846495i	$0.678709\pi$
$80$	− 0.267949i	− 0.0299576i
$81$	1.00000	0.111111
$82$	−11.3923	−1.25807
$83$	− 10.1962i	− 1.11917i	−0.828772	−	0.559587i	$-0.810960\pi$
$83$	− 10.1962i	− 1.11917i	0.828772	−	0.559587i	$-0.189040\pi$
$84$	− 0.732051i	− 0.0798733i
$85$	− 0.607695i	− 0.0659138i
$86$	7.66025i	0.826026i
$87$	2.46410	0.264179
$88$	−4.73205	−0.504438
$89$	− 2.53590i	− 0.268805i	−0.990927	−	0.134402i	$-0.957089\pi$
$89$	− 2.53590i	− 0.268805i	0.990927	−	0.134402i	$-0.0429115\pi$
$90$	−0.267949	−0.0282443
$91$	0	0
$92$	−6.19615	−0.645994
$93$	5.46410i	0.566601i
$94$	−8.19615	−0.845369
$95$	−0.339746	−0.0348572
$96$	− 1.00000i	− 0.102062i
$97$	6.00000i	0.609208i	0.952479	+	0.304604i	$0.0985241\pi$
$97$	6.00000i	0.609208i	−0.952479	+	0.304604i	$0.901476\pi$
$98$	− 6.46410i	− 0.652973i
$99$	4.73205i	0.475589i
$100$	−4.92820	−0.492820
$101$	11.9282	1.18690	0.593450	−	0.804871i	$-0.297765\pi$
$101$	11.9282	1.18690	0.593450	+	0.804871i	$0.297765\pi$
$102$	− 2.26795i	− 0.224560i
$103$	18.7321	1.84572	0.922862	−	0.385131i	$-0.125844\pi$
$103$	18.7321	1.84572	0.922862	+	0.385131i	$0.125844\pi$
$104$	0	0
$105$	0.196152	0.0191425
$106$	− 0.464102i	− 0.0450775i
$107$	−0.196152	−0.0189628	−0.00948139	−	0.999955i	$-0.503018\pi$
$107$	−0.196152	−0.0189628	−0.00948139	+	0.999955i	$0.503018\pi$
$108$	−1.00000	−0.0962250
$109$	5.46410i	0.523366i	0.965154	+	0.261683i	$0.0842775\pi$
$109$	5.46410i	0.523366i	−0.965154	+	0.261683i	$0.915723\pi$
$110$	− 1.26795i	− 0.120894i
$111$	10.4641i	0.993209i
$112$	0.732051i	0.0691723i
$113$	−18.6603	−1.75541	−0.877705	−	0.479202i	$-0.840926\pi$
$113$	−18.6603	−1.75541	−0.877705	+	0.479202i	$0.840926\pi$
$114$	−1.26795	−0.118754
$115$	− 1.66025i	− 0.154819i
$116$	−2.46410	−0.228786
$117$	0	0
$118$	8.00000	0.736460
$119$	1.66025i	0.152195i
$120$	0.267949	0.0244603
$121$	−11.3923	−1.03566
$122$	− 1.19615i	− 0.108295i
$123$	− 11.3923i	− 1.02721i
$124$	− 5.46410i	− 0.490691i
$125$	− 2.66025i	− 0.237940i
$126$	0.732051	0.0652163
$127$	−17.8564	−1.58450	−0.792250	−	0.610197i	$-0.791090\pi$
$127$	−17.8564	−1.58450	−0.792250	+	0.610197i	$0.791090\pi$
$128$	1.00000i	0.0883883i
$129$	−7.66025	−0.674448
$130$	0	0
$131$	13.4641	1.17636	0.588182	−	0.808729i	$-0.299844\pi$
$131$	13.4641	1.17636	0.588182	+	0.808729i	$0.299844\pi$
$132$	− 4.73205i	− 0.411872i
$133$	0.928203	0.0804854
$134$	11.1244	0.960998
$135$	− 0.267949i	− 0.0230614i
$136$	2.26795i	0.194475i
$137$	− 1.92820i	− 0.164738i	−0.996602	−	0.0823688i	$-0.973751\pi$
$137$	− 1.92820i	− 0.164738i	0.996602	−	0.0823688i	$-0.0262485\pi$
$138$	− 6.19615i	− 0.527452i
$139$	−9.85641	−0.836009	−0.418005	−	0.908445i	$-0.637270\pi$
$139$	−9.85641	−0.836009	−0.418005	+	0.908445i	$0.637270\pi$
$140$	−0.196152	−0.0165779
$141$	− 8.19615i	− 0.690241i
$142$	−1.26795	−0.106404
$143$	0	0
$144$	1.00000	0.0833333
$145$	− 0.660254i	− 0.0548311i
$146$	−9.73205	−0.805430
$147$	6.46410	0.533150
$148$	− 10.4641i	− 0.860144i
$149$	− 2.80385i	− 0.229700i	−0.993383	−	0.114850i	$-0.963361\pi$
$149$	− 2.80385i	− 0.229700i	0.993383	−	0.114850i	$-0.0366388\pi$
$150$	− 4.92820i	− 0.402386i
$151$	3.26795i	0.265942i	0.991120	+	0.132971i	$0.0424517\pi$
$151$	3.26795i	0.265942i	−0.991120	+	0.132971i	$0.957548\pi$
$152$	1.26795	0.102844
$153$	2.26795	0.183353
$154$	3.46410i	0.279145i
$155$	1.46410	0.117599
$156$	0	0
$157$	−23.5885	−1.88256	−0.941282	−	0.337622i	$-0.890378\pi$
$157$	−23.5885	−1.88256	−0.941282	+	0.337622i	$0.890378\pi$
$158$	9.46410i	0.752923i
$159$	0.464102	0.0368057
$160$	−0.267949	−0.0211832
$161$	4.53590i	0.357479i
$162$	− 1.00000i	− 0.0785674i
$163$	− 6.53590i	− 0.511931i	−0.966686	−	0.255966i	$-0.917607\pi$
$163$	− 6.53590i	− 0.511931i	0.966686	−	0.255966i	$-0.0823934\pi$
$164$	11.3923i	0.889590i
$165$	1.26795	0.0987097
$166$	−10.1962	−0.791375
$167$	− 2.53590i	− 0.196234i	−0.995175	−	0.0981169i	$-0.968718\pi$
$167$	− 2.53590i	− 0.196234i	0.995175	−	0.0981169i	$-0.0312819\pi$
$168$	−0.732051	−0.0564789
$169$	0	0
$170$	−0.607695	−0.0466081
$171$	− 1.26795i	− 0.0969625i
$172$	7.66025	0.584089
$173$	16.3923	1.24628	0.623142	−	0.782109i	$-0.285856\pi$
$173$	16.3923	1.24628	0.623142	+	0.782109i	$0.285856\pi$
$174$	− 2.46410i	− 0.186803i
$175$	3.60770i	0.272716i
$176$	4.73205i	0.356692i
$177$	8.00000i	0.601317i
$178$	−2.53590	−0.190074
$179$	−22.0526	−1.64829	−0.824143	−	0.566382i	$-0.808343\pi$
$179$	−22.0526	−1.64829	−0.824143	+	0.566382i	$0.808343\pi$
$180$	0.267949i	0.0199718i
$181$	−8.80385	−0.654385	−0.327192	−	0.944958i	$-0.606103\pi$
$181$	−8.80385	−0.654385	−0.327192	+	0.944958i	$0.606103\pi$
$182$	0	0
$183$	1.19615	0.0884221
$184$	6.19615i	0.456786i
$185$	2.80385	0.206143
$186$	5.46410	0.400647
$187$	10.7321i	0.784805i
$188$	8.19615i	0.597766i
$189$	0.732051i	0.0532489i
$190$	0.339746i	0.0246478i
$191$	6.92820	0.501307	0.250654	−	0.968077i	$-0.419354\pi$
$191$	6.92820	0.501307	0.250654	+	0.968077i	$0.419354\pi$
$192$	−1.00000	−0.0721688
$193$	− 8.26795i	− 0.595140i	−0.954700	−	0.297570i	$-0.903824\pi$
$193$	− 8.26795i	− 0.595140i	0.954700	−	0.297570i	$-0.0961762\pi$
$194$	6.00000	0.430775
$195$	0	0
$196$	−6.46410	−0.461722
$197$	− 9.85641i	− 0.702240i	−0.936330	−	0.351120i	$-0.885801\pi$
$197$	− 9.85641i	− 0.702240i	0.936330	−	0.351120i	$-0.114199\pi$
$198$	4.73205	0.336292
$199$	3.80385	0.269648	0.134824	−	0.990870i	$-0.456953\pi$
$199$	3.80385	0.269648	0.134824	+	0.990870i	$0.456953\pi$
$200$	4.92820i	0.348477i
$201$	11.1244i	0.784652i
$202$	− 11.9282i	− 0.839265i
$203$	1.80385i	0.126605i
$204$	−2.26795	−0.158788
$205$	−3.05256	−0.213200
$206$	− 18.7321i	− 1.30512i
$207$	6.19615	0.430662
$208$	0	0
$209$	6.00000	0.415029
$210$	− 0.196152i	− 0.0135358i
$211$	−4.39230	−0.302379	−0.151189	−	0.988505i	$-0.548310\pi$
$211$	−4.39230	−0.302379	−0.151189	+	0.988505i	$0.548310\pi$
$212$	−0.464102	−0.0318746
$213$	− 1.26795i	− 0.0868784i
$214$	0.196152i	0.0134087i
$215$	2.05256i	0.139983i
$216$	1.00000i	0.0680414i
$217$	−4.00000	−0.271538
$218$	5.46410	0.370076
$219$	− 9.73205i	− 0.657631i
$220$	−1.26795	−0.0854851
$221$	0	0
$222$	10.4641	0.702305
$223$	13.0718i	0.875352i	0.899133	+	0.437676i	$0.144198\pi$
$223$	13.0718i	0.875352i	−0.899133	+	0.437676i	$0.855802\pi$
$224$	0.732051	0.0489122
$225$	4.92820	0.328547
$226$	18.6603i	1.24126i
$227$	1.80385i	0.119726i	0.998207	+	0.0598628i	$0.0190663\pi$
$227$	1.80385i	0.119726i	−0.998207	+	0.0598628i	$0.980934\pi$
$228$	1.26795i	0.0839720i
$229$	15.8564i	1.04782i	0.851773	+	0.523910i	$0.175527\pi$
$229$	15.8564i	1.04782i	−0.851773	+	0.523910i	$0.824473\pi$
$230$	−1.66025	−0.109474
$231$	−3.46410	−0.227921
$232$	2.46410i	0.161776i
$233$	−19.8564	−1.30084	−0.650418	−	0.759576i	$-0.725406\pi$
$233$	−19.8564	−1.30084	−0.650418	+	0.759576i	$0.725406\pi$
$234$	0	0
$235$	−2.19615	−0.143261
$236$	− 8.00000i	− 0.520756i
$237$	−9.46410	−0.614759
$238$	1.66025	0.107618
$239$	9.66025i	0.624870i	0.949939	+	0.312435i	$0.101145\pi$
$239$	9.66025i	0.624870i	−0.949939	+	0.312435i	$0.898855\pi$
$240$	− 0.267949i	− 0.0172960i
$241$	− 17.5885i	− 1.13297i	−0.824071	−	0.566486i	$-0.808302\pi$
$241$	− 17.5885i	− 1.13297i	0.824071	−	0.566486i	$-0.191698\pi$
$242$	11.3923i	0.732325i
$243$	1.00000	0.0641500
$244$	−1.19615	−0.0765758
$245$	− 1.73205i	− 0.110657i
$246$	−11.3923	−0.726347
$247$	0	0
$248$	−5.46410	−0.346971
$249$	− 10.1962i	− 0.646155i
$250$	−2.66025	−0.168249
$251$	−6.53590	−0.412542	−0.206271	−	0.978495i	$-0.566133\pi$
$251$	−6.53590	−0.412542	−0.206271	+	0.978495i	$0.566133\pi$
$252$	− 0.732051i	− 0.0461149i
$253$	29.3205i	1.84336i
$254$	17.8564i	1.12041i
$255$	− 0.607695i	− 0.0380553i
$256$	1.00000	0.0625000
$257$	−26.6603	−1.66302	−0.831510	−	0.555509i	$-0.812523\pi$
$257$	−26.6603	−1.66302	−0.831510	+	0.555509i	$0.812523\pi$
$258$	7.66025i	0.476907i
$259$	−7.66025	−0.475985
$260$	0	0
$261$	2.46410	0.152524
$262$	− 13.4641i	− 0.831815i
$263$	28.0526	1.72979	0.864897	−	0.501949i	$-0.167383\pi$
$263$	28.0526	1.72979	0.864897	+	0.501949i	$0.167383\pi$
$264$	−4.73205	−0.291238
$265$	− 0.124356i	− 0.00763911i
$266$	− 0.928203i	− 0.0569118i
$267$	− 2.53590i	− 0.155194i
$268$	− 11.1244i	− 0.679528i
$269$	−1.46410	−0.0892679	−0.0446339	−	0.999003i	$-0.514212\pi$
$269$	−1.46410	−0.0892679	−0.0446339	+	0.999003i	$0.514212\pi$
$270$	−0.267949	−0.0163069
$271$	5.85641i	0.355751i	0.984053	+	0.177876i	$0.0569225\pi$
$271$	5.85641i	0.355751i	−0.984053	+	0.177876i	$0.943078\pi$
$272$	2.26795	0.137515
$273$	0	0
$274$	−1.92820	−0.116487
$275$	23.3205i	1.40628i
$276$	−6.19615	−0.372965
$277$	2.26795	0.136268	0.0681339	−	0.997676i	$-0.478295\pi$
$277$	2.26795	0.136268	0.0681339	+	0.997676i	$0.478295\pi$
$278$	9.85641i	0.591148i
$279$	5.46410i	0.327127i
$280$	0.196152i	0.0117223i
$281$	− 22.3205i	− 1.33153i	−0.746162	−	0.665765i	$-0.768105\pi$
$281$	− 22.3205i	− 1.33153i	0.746162	−	0.665765i	$-0.231895\pi$
$282$	−8.19615	−0.488074
$283$	−8.33975	−0.495746	−0.247873	−	0.968792i	$-0.579732\pi$
$283$	−8.33975	−0.495746	−0.247873	+	0.968792i	$0.579732\pi$
$284$	1.26795i	0.0752389i
$285$	−0.339746	−0.0201248
$286$	0	0
$287$	8.33975	0.492280
$288$	− 1.00000i	− 0.0589256i
$289$	−11.8564	−0.697436
$290$	−0.660254	−0.0387715
$291$	6.00000i	0.351726i
$292$	9.73205i	0.569525i
$293$	− 14.5167i	− 0.848072i	−0.905645	−	0.424036i	$-0.860613\pi$
$293$	− 14.5167i	− 0.848072i	0.905645	−	0.424036i	$-0.139387\pi$
$294$	− 6.46410i	− 0.376994i
$295$	2.14359	0.124805
$296$	−10.4641	−0.608214
$297$	4.73205i	0.274581i
$298$	−2.80385	−0.162423
$299$	0	0
$300$	−4.92820	−0.284530
$301$	− 5.60770i	− 0.323222i
$302$	3.26795	0.188049
$303$	11.9282	0.685257
$304$	− 1.26795i	− 0.0727219i
$305$	− 0.320508i	− 0.0183522i
$306$	− 2.26795i	− 0.129650i
$307$	8.58846i	0.490169i	0.969502	+	0.245085i	$0.0788157\pi$
$307$	8.58846i	0.490169i	−0.969502	+	0.245085i	$0.921184\pi$
$308$	3.46410	0.197386
$309$	18.7321	1.06563
$310$	− 1.46410i	− 0.0831554i
$311$	−15.6603	−0.888012	−0.444006	−	0.896024i	$-0.646443\pi$
$311$	−15.6603	−0.888012	−0.444006	+	0.896024i	$0.646443\pi$
$312$	0	0
$313$	13.4641	0.761036	0.380518	−	0.924774i	$-0.375746\pi$
$313$	13.4641	0.761036	0.380518	+	0.924774i	$0.375746\pi$
$314$	23.5885i	1.33117i
$315$	0.196152	0.0110519
$316$	9.46410	0.532397
$317$	− 3.33975i	− 0.187579i	−0.995592	−	0.0937894i	$-0.970102\pi$
$317$	− 3.33975i	− 0.187579i	0.995592	−	0.0937894i	$-0.0298980\pi$
$318$	− 0.464102i	− 0.0260255i
$319$	11.6603i	0.652849i
$320$	0.267949i	0.0149788i
$321$	−0.196152	−0.0109482
$322$	4.53590	0.252776
$323$	− 2.87564i	− 0.160005i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−6.53590	−0.361990
$327$	5.46410i	0.302166i
$328$	11.3923	0.629035
$329$	6.00000	0.330791
$330$	− 1.26795i	− 0.0697983i
$331$	− 20.0000i	− 1.09930i	−0.835395	−	0.549650i	$-0.814761\pi$
$331$	− 20.0000i	− 1.09930i	0.835395	−	0.549650i	$-0.185239\pi$
$332$	10.1962i	0.559587i
$333$	10.4641i	0.573429i
$334$	−2.53590	−0.138758
$335$	2.98076	0.162856
$336$	0.732051i	0.0399366i
$337$	−6.85641	−0.373492	−0.186746	−	0.982408i	$-0.559794\pi$
$337$	−6.85641	−0.373492	−0.186746	+	0.982408i	$0.559794\pi$
$338$	0	0
$339$	−18.6603	−1.01349
$340$	0.607695i	0.0329569i
$341$	−25.8564	−1.40020
$342$	−1.26795	−0.0685628
$343$	9.85641i	0.532196i
$344$	− 7.66025i	− 0.413013i
$345$	− 1.66025i	− 0.0893851i
$346$	− 16.3923i	− 0.881256i
$347$	8.87564	0.476470	0.238235	−	0.971208i	$-0.423431\pi$
$347$	8.87564	0.476470	0.238235	+	0.971208i	$0.423431\pi$
$348$	−2.46410	−0.132090
$349$	− 19.3205i	− 1.03420i	−0.855924	−	0.517102i	$-0.827011\pi$
$349$	− 19.3205i	− 1.03420i	0.855924	−	0.517102i	$-0.172989\pi$
$350$	3.60770	0.192839
$351$	0	0
$352$	4.73205	0.252219
$353$	− 19.7846i	− 1.05303i	−0.850166	−	0.526514i	$-0.823499\pi$
$353$	− 19.7846i	− 1.05303i	0.850166	−	0.526514i	$-0.176501\pi$
$354$	8.00000	0.425195
$355$	−0.339746	−0.0180318
$356$	2.53590i	0.134402i
$357$	1.66025i	0.0878700i
$358$	22.0526i	1.16551i
$359$	23.1244i	1.22046i	0.792226	+	0.610228i	$0.208922\pi$
$359$	23.1244i	1.22046i	−0.792226	+	0.610228i	$0.791078\pi$
$360$	0.267949	0.0141222
$361$	17.3923	0.915384
$362$	8.80385i	0.462720i
$363$	−11.3923	−0.597941
$364$	0	0
$365$	−2.60770	−0.136493
$366$	− 1.19615i	− 0.0625239i
$367$	−14.7321	−0.769007	−0.384503	−	0.923124i	$-0.625627\pi$
$367$	−14.7321	−0.769007	−0.384503	+	0.923124i	$0.625627\pi$
$368$	6.19615	0.322997
$369$	− 11.3923i	− 0.593060i
$370$	− 2.80385i	− 0.145765i
$371$	0.339746i	0.0176387i
$372$	− 5.46410i	− 0.283300i
$373$	−10.2679	−0.531654	−0.265827	−	0.964021i	$-0.585645\pi$
$373$	−10.2679	−0.531654	−0.265827	+	0.964021i	$0.585645\pi$
$374$	10.7321	0.554941
$375$	− 2.66025i	− 0.137375i
$376$	8.19615	0.422684
$377$	0	0
$378$	0.732051	0.0376526
$379$	− 1.46410i	− 0.0752058i	−0.999293	−	0.0376029i	$-0.988028\pi$
$379$	− 1.46410i	− 0.0752058i	0.999293	−	0.0376029i	$-0.0119722\pi$
$380$	0.339746	0.0174286
$381$	−17.8564	−0.914811
$382$	− 6.92820i	− 0.354478i
$383$	− 5.46410i	− 0.279203i	−0.990208	−	0.139601i	$-0.955418\pi$
$383$	− 5.46410i	− 0.279203i	0.990208	−	0.139601i	$-0.0445821\pi$
$384$	1.00000i	0.0510310i
$385$	0.928203i	0.0473056i
$386$	−8.26795	−0.420828
$387$	−7.66025	−0.389393
$388$	− 6.00000i	− 0.304604i
$389$	29.7846	1.51014	0.755070	−	0.655644i	$-0.227603\pi$
$389$	29.7846	1.51014	0.755070	+	0.655644i	$0.227603\pi$
$390$	0	0
$391$	14.0526	0.710668
$392$	6.46410i	0.326486i
$393$	13.4641	0.679174
$394$	−9.85641	−0.496559
$395$	2.53590i	0.127595i
$396$	− 4.73205i	− 0.237795i
$397$	− 0.392305i	− 0.0196892i	−0.999952	−	0.00984461i	$-0.996866\pi$
$397$	− 0.392305i	− 0.0196892i	0.999952	−	0.00984461i	$-0.00313369\pi$
$398$	− 3.80385i	− 0.190670i
$399$	0.928203	0.0464683
$400$	4.92820	0.246410
$401$	21.9282i	1.09504i	0.836792	+	0.547521i	$0.184428\pi$
$401$	21.9282i	1.09504i	−0.836792	+	0.547521i	$0.815572\pi$
$402$	11.1244	0.554832
$403$	0	0
$404$	−11.9282	−0.593450
$405$	− 0.267949i	− 0.0133145i
$406$	1.80385	0.0895235
$407$	−49.5167	−2.45445
$408$	2.26795i	0.112280i
$409$	− 14.2679i	− 0.705505i	−0.935717	−	0.352752i	$-0.885246\pi$
$409$	− 14.2679i	− 0.705505i	0.935717	−	0.352752i	$-0.114754\pi$
$410$	3.05256i	0.150755i
$411$	− 1.92820i	− 0.0951113i
$412$	−18.7321	−0.922862
$413$	−5.85641	−0.288175
$414$	− 6.19615i	− 0.304524i
$415$	−2.73205	−0.134111
$416$	0	0
$417$	−9.85641	−0.482670
$418$	− 6.00000i	− 0.293470i
$419$	−10.5359	−0.514712	−0.257356	−	0.966317i	$-0.582851\pi$
$419$	−10.5359	−0.514712	−0.257356	+	0.966317i	$0.582851\pi$
$420$	−0.196152	−0.00957126
$421$	− 32.7128i	− 1.59432i	−0.603765	−	0.797162i	$-0.706333\pi$
$421$	− 32.7128i	− 1.59432i	0.603765	−	0.797162i	$-0.293667\pi$
$422$	4.39230i	0.213814i
$423$	− 8.19615i	− 0.398511i
$424$	0.464102i	0.0225388i
$425$	11.1769	0.542160
$426$	−1.26795	−0.0614323
$427$	0.875644i	0.0423754i
$428$	0.196152	0.00948139
$429$	0	0
$430$	2.05256	0.0989832
$431$	11.1244i	0.535841i	0.963441	+	0.267921i	$0.0863365\pi$
$431$	11.1244i	0.535841i	−0.963441	+	0.267921i	$0.913663\pi$
$432$	1.00000	0.0481125
$433$	14.8564	0.713953	0.356977	−	0.934113i	$-0.383808\pi$
$433$	14.8564	0.713953	0.356977	+	0.934113i	$0.383808\pi$
$434$	4.00000i	0.192006i
$435$	− 0.660254i	− 0.0316568i
$436$	− 5.46410i	− 0.261683i
$437$	− 7.85641i	− 0.375823i
$438$	−9.73205	−0.465015
$439$	17.6603	0.842878	0.421439	−	0.906857i	$-0.361525\pi$
$439$	17.6603	0.842878	0.421439	+	0.906857i	$0.361525\pi$
$440$	1.26795i	0.0604471i
$441$	6.46410	0.307814
$442$	0	0
$443$	36.3923	1.72905	0.864525	−	0.502589i	$-0.167619\pi$
$443$	36.3923	1.72905	0.864525	+	0.502589i	$0.167619\pi$
$444$	− 10.4641i	− 0.496604i
$445$	−0.679492	−0.0322110
$446$	13.0718	0.618968
$447$	− 2.80385i	− 0.132617i
$448$	− 0.732051i	− 0.0345861i
$449$	− 23.3205i	− 1.10056i	−0.834979	−	0.550281i	$-0.814520\pi$
$449$	− 23.3205i	− 1.10056i	0.834979	−	0.550281i	$-0.185480\pi$
$450$	− 4.92820i	− 0.232318i
$451$	53.9090	2.53847
$452$	18.6603	0.877705
$453$	3.26795i	0.153542i
$454$	1.80385	0.0846588
$455$	0	0
$456$	1.26795	0.0593772
$457$	− 18.6603i	− 0.872890i	−0.899731	−	0.436445i	$-0.856237\pi$
$457$	− 18.6603i	− 0.872890i	0.899731	−	0.436445i	$-0.143763\pi$
$458$	15.8564	0.740921
$459$	2.26795	0.105859
$460$	1.66025i	0.0774097i
$461$	− 25.7321i	− 1.19846i	−0.800577	−	0.599231i	$-0.795473\pi$
$461$	− 25.7321i	− 1.19846i	0.800577	−	0.599231i	$-0.204527\pi$
$462$	3.46410i	0.161165i
$463$	− 28.0526i	− 1.30371i	−0.758342	−	0.651856i	$-0.773990\pi$
$463$	− 28.0526i	− 1.30371i	0.758342	−	0.651856i	$-0.226010\pi$
$464$	2.46410	0.114393
$465$	1.46410	0.0678961
$466$	19.8564i	0.919830i
$467$	12.5885	0.582524	0.291262	−	0.956643i	$-0.405925\pi$
$467$	12.5885	0.582524	0.291262	+	0.956643i	$0.405925\pi$
$468$	0	0
$469$	−8.14359	−0.376036
$470$	2.19615i	0.101301i
$471$	−23.5885	−1.08690
$472$	−8.00000	−0.368230
$473$	− 36.2487i	− 1.66672i
$474$	9.46410i	0.434701i
$475$	− 6.24871i	− 0.286711i
$476$	− 1.66025i	− 0.0760976i
$477$	0.464102	0.0212498
$478$	9.66025	0.441850
$479$	26.5359i	1.21246i	0.795291	+	0.606228i	$0.207318\pi$
$479$	26.5359i	1.21246i	−0.795291	+	0.606228i	$0.792682\pi$
$480$	−0.267949	−0.0122302
$481$	0	0
$482$	−17.5885	−0.801132
$483$	4.53590i	0.206391i
$484$	11.3923	0.517832
$485$	1.60770	0.0730017
$486$	− 1.00000i	− 0.0453609i
$487$	− 21.1244i	− 0.957236i	−0.878023	−	0.478618i	$-0.841138\pi$
$487$	− 21.1244i	− 0.957236i	0.878023	−	0.478618i	$-0.158862\pi$
$488$	1.19615i	0.0541473i
$489$	− 6.53590i	− 0.295564i
$490$	−1.73205	−0.0782461
$491$	−5.26795	−0.237739	−0.118870	−	0.992910i	$-0.537927\pi$
$491$	−5.26795	−0.237739	−0.118870	+	0.992910i	$0.537927\pi$
$492$	11.3923i	0.513605i
$493$	5.58846	0.251691
$494$	0	0
$495$	1.26795	0.0569901
$496$	5.46410i	0.245345i
$497$	0.928203	0.0416356
$498$	−10.1962	−0.456901
$499$	− 32.0000i	− 1.43252i	−0.697835	−	0.716258i	$-0.745853\pi$
$499$	− 32.0000i	− 1.43252i	0.697835	−	0.716258i	$-0.254147\pi$
$500$	2.66025i	0.118970i
$501$	− 2.53590i	− 0.113296i
$502$	6.53590i	0.291711i
$503$	−10.9808	−0.489608	−0.244804	−	0.969573i	$-0.578724\pi$
$503$	−10.9808	−0.489608	−0.244804	+	0.969573i	$0.578724\pi$
$504$	−0.732051	−0.0326081
$505$	− 3.19615i	− 0.142227i
$506$	29.3205	1.30346
$507$	0	0
$508$	17.8564	0.792250
$509$	− 10.2679i	− 0.455119i	−0.973764	−	0.227559i	$-0.926925\pi$
$509$	− 10.2679i	− 0.455119i	0.973764	−	0.227559i	$-0.0730746\pi$
$510$	−0.607695	−0.0269092
$511$	7.12436	0.315163
$512$	− 1.00000i	− 0.0441942i
$513$	− 1.26795i	− 0.0559813i
$514$	26.6603i	1.17593i
$515$	− 5.01924i	− 0.221174i
$516$	7.66025	0.337224
$517$	38.7846	1.70575
$518$	7.66025i	0.336572i
$519$	16.3923	0.719542
$520$	0	0
$521$	−17.4449	−0.764273	−0.382137	−	0.924106i	$-0.624812\pi$
$521$	−17.4449	−0.764273	−0.382137	+	0.924106i	$0.624812\pi$
$522$	− 2.46410i	− 0.107851i
$523$	36.4449	1.59362	0.796811	−	0.604228i	$-0.206518\pi$
$523$	36.4449	1.59362	0.796811	+	0.604228i	$0.206518\pi$
$524$	−13.4641	−0.588182
$525$	3.60770i	0.157453i
$526$	− 28.0526i	− 1.22315i
$527$	12.3923i	0.539817i
$528$	4.73205i	0.205936i
$529$	15.3923	0.669231
$530$	−0.124356	−0.00540166
$531$	8.00000i	0.347170i
$532$	−0.928203	−0.0402427
$533$	0	0
$534$	−2.53590	−0.109739
$535$	0.0525589i	0.00227232i
$536$	−11.1244	−0.480499
$537$	−22.0526	−0.951638
$538$	1.46410i	0.0631219i
$539$	30.5885i	1.31754i
$540$	0.267949i	0.0115307i
$541$	40.3205i	1.73351i	0.498731	+	0.866757i	$0.333800\pi$
$541$	40.3205i	1.73351i	−0.498731	+	0.866757i	$0.666200\pi$
$542$	5.85641	0.251554
$543$	−8.80385	−0.377809
$544$	− 2.26795i	− 0.0972375i
$545$	1.46410	0.0627152
$546$	0	0
$547$	6.19615	0.264928	0.132464	−	0.991188i	$-0.457711\pi$
$547$	6.19615	0.264928	0.132464	+	0.991188i	$0.457711\pi$
$548$	1.92820i	0.0823688i
$549$	1.19615	0.0510505
$550$	23.3205	0.994390
$551$	− 3.12436i	− 0.133102i
$552$	6.19615i	0.263726i
$553$	− 6.92820i	− 0.294617i
$554$	− 2.26795i	− 0.0963559i
$555$	2.80385	0.119017
$556$	9.85641	0.418005
$557$	− 30.3731i	− 1.28695i	−0.765468	−	0.643474i	$-0.777492\pi$
$557$	− 30.3731i	− 1.28695i	0.765468	−	0.643474i	$-0.222508\pi$
$558$	5.46410	0.231314
$559$	0	0
$560$	0.196152	0.00828895
$561$	10.7321i	0.453108i
$562$	−22.3205	−0.941534
$563$	−21.0718	−0.888070	−0.444035	−	0.896009i	$-0.646453\pi$
$563$	−21.0718	−0.888070	−0.444035	+	0.896009i	$0.646453\pi$
$564$	8.19615i	0.345120i
$565$	5.00000i	0.210352i
$566$	8.33975i	0.350546i
$567$	0.732051i	0.0307432i
$568$	1.26795	0.0532020
$569$	38.6410	1.61992	0.809958	−	0.586488i	$-0.199490\pi$
$569$	38.6410	1.61992	0.809958	+	0.586488i	$0.199490\pi$
$570$	0.339746i	0.0142304i
$571$	24.0526	1.00657	0.503284	−	0.864121i	$-0.332125\pi$
$571$	24.0526	1.00657	0.503284	+	0.864121i	$0.332125\pi$
$572$	0	0
$573$	6.92820	0.289430
$574$	− 8.33975i	− 0.348094i
$575$	30.5359	1.27343
$576$	−1.00000	−0.0416667
$577$	− 0.267949i	− 0.0111549i	−0.999984	−	0.00557744i	$-0.998225\pi$
$577$	− 0.267949i	− 0.0111549i	0.999984	−	0.00557744i	$-0.00177536\pi$
$578$	11.8564i	0.493161i
$579$	− 8.26795i	− 0.343604i
$580$	0.660254i	0.0274156i
$581$	7.46410	0.309663
$582$	6.00000	0.248708
$583$	2.19615i	0.0909553i
$584$	9.73205	0.402715
$585$	0	0
$586$	−14.5167	−0.599678
$587$	− 16.0000i	− 0.660391i	−0.943913	−	0.330195i	$-0.892885\pi$
$587$	− 16.0000i	− 0.660391i	0.943913	−	0.330195i	$-0.107115\pi$
$588$	−6.46410	−0.266575
$589$	6.92820	0.285472
$590$	− 2.14359i	− 0.0882503i
$591$	− 9.85641i	− 0.405438i
$592$	10.4641i	0.430072i
$593$	− 36.8564i	− 1.51351i	−0.653698	−	0.756756i	$-0.726783\pi$
$593$	− 36.8564i	− 1.51351i	0.653698	−	0.756756i	$-0.273217\pi$
$594$	4.73205	0.194158
$595$	0.444864	0.0182376
$596$	2.80385i	0.114850i
$597$	3.80385	0.155681
$598$	0	0
$599$	−9.46410	−0.386693	−0.193346	−	0.981131i	$-0.561934\pi$
$599$	−9.46410	−0.386693	−0.193346	+	0.981131i	$0.561934\pi$
$600$	4.92820i	0.201193i
$601$	−5.92820	−0.241816	−0.120908	−	0.992664i	$-0.538581\pi$
$601$	−5.92820	−0.241816	−0.120908	+	0.992664i	$0.538581\pi$
$602$	−5.60770	−0.228553
$603$	11.1244i	0.453019i
$604$	− 3.26795i	− 0.132971i
$605$	3.05256i	0.124104i
$606$	− 11.9282i	− 0.484550i
$607$	0.784610	0.0318463	0.0159232	−	0.999873i	$-0.494931\pi$
$607$	0.784610	0.0318463	0.0159232	+	0.999873i	$0.494931\pi$
$608$	−1.26795	−0.0514221
$609$	1.80385i	0.0730956i
$610$	−0.320508	−0.0129770
$611$	0	0
$612$	−2.26795	−0.0916764
$613$	− 11.3923i	− 0.460131i	−0.973175	−	0.230065i	$-0.926106\pi$
$613$	− 11.3923i	− 0.460131i	0.973175	−	0.230065i	$-0.0738940\pi$
$614$	8.58846	0.346602
$615$	−3.05256	−0.123091
$616$	− 3.46410i	− 0.139573i
$617$	− 35.2487i	− 1.41906i	−0.704675	−	0.709530i	$-0.748907\pi$
$617$	− 35.2487i	− 1.41906i	0.704675	−	0.709530i	$-0.251093\pi$
$618$	− 18.7321i	− 0.753514i
$619$	10.5359i	0.423474i	0.977327	+	0.211737i	$0.0679119\pi$
$619$	10.5359i	0.423474i	−0.977327	+	0.211737i	$0.932088\pi$
$620$	−1.46410	−0.0587997
$621$	6.19615	0.248643
$622$	15.6603i	0.627919i
$623$	1.85641	0.0743754
$624$	0	0
$625$	23.9282	0.957128
$626$	− 13.4641i	− 0.538134i
$627$	6.00000	0.239617
$628$	23.5885	0.941282
$629$	23.7321i	0.946259i
$630$	− 0.196152i	− 0.00781490i
$631$	47.7128i	1.89942i	0.313135	+	0.949709i	$0.398621\pi$
$631$	47.7128i	1.89942i	−0.313135	+	0.949709i	$0.601379\pi$
$632$	− 9.46410i	− 0.376462i
$633$	−4.39230	−0.174578
$634$	−3.33975	−0.132638
$635$	4.78461i	0.189871i
$636$	−0.464102	−0.0184028
$637$	0	0
$638$	11.6603	0.461634
$639$	− 1.26795i	− 0.0501593i
$640$	0.267949	0.0105916
$641$	−25.9808	−1.02618	−0.513089	−	0.858335i	$-0.671499\pi$
$641$	−25.9808	−1.02618	−0.513089	+	0.858335i	$0.671499\pi$
$642$	0.196152i	0.00774152i
$643$	− 13.8564i	− 0.546443i	−0.961951	−	0.273222i	$-0.911911\pi$
$643$	− 13.8564i	− 0.546443i	0.961951	−	0.273222i	$-0.0880892\pi$
$644$	− 4.53590i	− 0.178739i
$645$	2.05256i	0.0808194i
$646$	−2.87564	−0.113141
$647$	−26.2487	−1.03194	−0.515972	−	0.856606i	$-0.672569\pi$
$647$	−26.2487	−1.03194	−0.515972	+	0.856606i	$0.672569\pi$
$648$	1.00000i	0.0392837i
$649$	−37.8564	−1.48599
$650$	0	0
$651$	−4.00000	−0.156772
$652$	6.53590i	0.255966i
$653$	−10.5359	−0.412302	−0.206151	−	0.978520i	$-0.566094\pi$
$653$	−10.5359	−0.412302	−0.206151	+	0.978520i	$0.566094\pi$
$654$	5.46410	0.213663
$655$	− 3.60770i	− 0.140964i
$656$	− 11.3923i	− 0.444795i
$657$	− 9.73205i	− 0.379683i
$658$	− 6.00000i	− 0.233904i
$659$	38.2487	1.48996	0.744979	−	0.667088i	$-0.232459\pi$
$659$	38.2487	1.48996	0.744979	+	0.667088i	$0.232459\pi$
$660$	−1.26795	−0.0493549
$661$	− 9.39230i	− 0.365318i	−0.983176	−	0.182659i	$-0.941530\pi$
$661$	− 9.39230i	− 0.365318i	0.983176	−	0.182659i	$-0.0584705\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	10.1962	0.395687
$665$	− 0.248711i	− 0.00964461i
$666$	10.4641	0.405476
$667$	15.2679	0.591177
$668$	2.53590i	0.0981169i
$669$	13.0718i	0.505385i
$670$	− 2.98076i	− 0.115157i
$671$	5.66025i	0.218512i
$672$	0.732051	0.0282395
$673$	−14.0718	−0.542428	−0.271214	−	0.962519i	$-0.587425\pi$
$673$	−14.0718	−0.542428	−0.271214	+	0.962519i	$0.587425\pi$
$674$	6.85641i	0.264099i
$675$	4.92820	0.189687
$676$	0	0
$677$	−38.5359	−1.48105	−0.740527	−	0.672026i	$-0.765424\pi$
$677$	−38.5359	−1.48105	−0.740527	+	0.672026i	$0.765424\pi$
$678$	18.6603i	0.716643i
$679$	−4.39230	−0.168561
$680$	0.607695	0.0233040
$681$	1.80385i	0.0691236i
$682$	25.8564i	0.990093i
$683$	− 37.8564i	− 1.44854i	−0.689519	−	0.724268i	$-0.742178\pi$
$683$	− 37.8564i	− 1.44854i	0.689519	−	0.724268i	$-0.257822\pi$
$684$	1.26795i	0.0484812i
$685$	−0.516660	−0.0197406
$686$	9.85641	0.376319
$687$	15.8564i	0.604960i
$688$	−7.66025	−0.292044
$689$	0	0
$690$	−1.66025	−0.0632048
$691$	− 26.3397i	− 1.00201i	−0.865444	−	0.501006i	$-0.832964\pi$
$691$	− 26.3397i	− 1.00201i	0.865444	−	0.501006i	$-0.167036\pi$
$692$	−16.3923	−0.623142
$693$	−3.46410	−0.131590
$694$	− 8.87564i	− 0.336915i
$695$	2.64102i	0.100179i
$696$	2.46410i	0.0934015i
$697$	− 25.8372i	− 0.978653i
$698$	−19.3205	−0.731292
$699$	−19.8564	−0.751038
$700$	− 3.60770i	− 0.136358i
$701$	−31.3205	−1.18296	−0.591480	−	0.806320i	$-0.701456\pi$
$701$	−31.3205	−1.18296	−0.591480	+	0.806320i	$0.701456\pi$
$702$	0	0
$703$	13.2679	0.500410
$704$	− 4.73205i	− 0.178346i
$705$	−2.19615	−0.0827119
$706$	−19.7846	−0.744604
$707$	8.73205i	0.328403i
$708$	− 8.00000i	− 0.300658i
$709$	40.8564i	1.53439i	0.641411	+	0.767197i	$0.278349\pi$
$709$	40.8564i	1.53439i	−0.641411	+	0.767197i	$0.721651\pi$
$710$	0.339746i	0.0127504i
$711$	−9.46410	−0.354932
$712$	2.53590	0.0950368
$713$	33.8564i	1.26793i
$714$	1.66025	0.0621334
$715$	0	0
$716$	22.0526	0.824143
$717$	9.66025i	0.360769i
$718$	23.1244	0.862993
$719$	22.5359	0.840447	0.420224	−	0.907421i	$-0.361952\pi$
$719$	22.5359	0.840447	0.420224	+	0.907421i	$0.361952\pi$
$720$	− 0.267949i	− 0.00998588i
$721$	13.7128i	0.510692i
$722$	− 17.3923i	− 0.647275i
$723$	− 17.5885i	− 0.654122i
$724$	8.80385	0.327192
$725$	12.1436	0.451002
$726$	11.3923i	0.422808i
$727$	−20.9808	−0.778133	−0.389067	−	0.921210i	$-0.627202\pi$
$727$	−20.9808	−0.778133	−0.389067	+	0.921210i	$0.627202\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.60770i	0.0965151i
$731$	−17.3731	−0.642566
$732$	−1.19615	−0.0442111
$733$	− 19.0000i	− 0.701781i	−0.936416	−	0.350891i	$-0.885879\pi$
$733$	− 19.0000i	− 0.701781i	0.936416	−	0.350891i	$-0.114121\pi$
$734$	14.7321i	0.543770i
$735$	− 1.73205i	− 0.0638877i
$736$	− 6.19615i	− 0.228393i
$737$	−52.6410	−1.93906
$738$	−11.3923	−0.419357
$739$	− 10.9282i	− 0.402000i	−0.979591	−	0.201000i	$-0.935581\pi$
$739$	− 10.9282i	− 0.402000i	0.979591	−	0.201000i	$-0.0644192\pi$
$740$	−2.80385	−0.103071
$741$	0	0
$742$	0.339746	0.0124725
$743$	27.6077i	1.01283i	0.862290	+	0.506414i	$0.169029\pi$
$743$	27.6077i	1.01283i	−0.862290	+	0.506414i	$0.830971\pi$
$744$	−5.46410	−0.200324
$745$	−0.751289	−0.0275251
$746$	10.2679i	0.375936i
$747$	− 10.1962i	− 0.373058i
$748$	− 10.7321i	− 0.392403i
$749$	− 0.143594i	− 0.00524679i
$750$	−2.66025	−0.0971387
$751$	−15.9090	−0.580526	−0.290263	−	0.956947i	$-0.593743\pi$
$751$	−15.9090	−0.580526	−0.290263	+	0.956947i	$0.593743\pi$
$752$	− 8.19615i	− 0.298883i
$753$	−6.53590	−0.238181
$754$	0	0
$755$	0.875644	0.0318680
$756$	− 0.732051i	− 0.0266244i
$757$	7.07180	0.257029	0.128514	−	0.991708i	$-0.458979\pi$
$757$	7.07180	0.257029	0.128514	+	0.991708i	$0.458979\pi$
$758$	−1.46410	−0.0531786
$759$	29.3205i	1.06427i
$760$	− 0.339746i	− 0.0123239i
$761$	− 23.3205i	− 0.845368i	−0.906277	−	0.422684i	$-0.861088\pi$
$761$	− 23.3205i	− 0.845368i	0.906277	−	0.422684i	$-0.138912\pi$
$762$	17.8564i	0.646869i
$763$	−4.00000	−0.144810
$764$	−6.92820	−0.250654
$765$	− 0.607695i	− 0.0219713i
$766$	−5.46410	−0.197426
$767$	0	0
$768$	1.00000	0.0360844
$769$	16.1436i	0.582153i	0.956700	+	0.291076i	$0.0940134\pi$
$769$	16.1436i	0.582153i	−0.956700	+	0.291076i	$0.905987\pi$
$770$	0.928203	0.0334501
$771$	−26.6603	−0.960146
$772$	8.26795i	0.297570i
$773$	35.0718i	1.26144i	0.776009	+	0.630722i	$0.217241\pi$
$773$	35.0718i	1.26144i	−0.776009	+	0.630722i	$0.782759\pi$
$774$	7.66025i	0.275342i
$775$	26.9282i	0.967290i
$776$	−6.00000	−0.215387
$777$	−7.66025	−0.274810
$778$	− 29.7846i	− 1.06783i
$779$	−14.4449	−0.517541
$780$	0	0
$781$	6.00000	0.214697
$782$	− 14.0526i	− 0.502518i
$783$	2.46410	0.0880598
$784$	6.46410	0.230861
$785$	6.32051i	0.225589i
$786$	− 13.4641i	− 0.480249i
$787$	39.3205i	1.40162i	0.713346	+	0.700812i	$0.247179\pi$
$787$	39.3205i	1.40162i	−0.713346	+	0.700812i	$0.752821\pi$
$788$	9.85641i	0.351120i
$789$	28.0526	0.998698
$790$	2.53590	0.0902232
$791$	− 13.6603i	− 0.485703i
$792$	−4.73205	−0.168146
$793$	0	0
$794$	−0.392305	−0.0139224
$795$	− 0.124356i	− 0.00441044i
$796$	−3.80385	−0.134824
$797$	34.0000	1.20434	0.602171	−	0.798367i	$-0.294303\pi$
$797$	34.0000	1.20434	0.602171	+	0.798367i	$0.294303\pi$
$798$	− 0.928203i	− 0.0328580i
$799$	− 18.5885i	− 0.657612i
$800$	− 4.92820i	− 0.174238i
$801$	− 2.53590i	− 0.0896016i
$802$	21.9282	0.774312
$803$	46.0526	1.62516
$804$	− 11.1244i	− 0.392326i
$805$	1.21539	0.0428369
$806$	0	0
$807$	−1.46410	−0.0515388
$808$	11.9282i	0.419633i
$809$	−22.4115	−0.787948	−0.393974	−	0.919122i	$-0.628900\pi$
$809$	−22.4115	−0.787948	−0.393974	+	0.919122i	$0.628900\pi$
$810$	−0.267949	−0.00941477
$811$	45.1769i	1.58638i	0.608977	+	0.793188i	$0.291580\pi$
$811$	45.1769i	1.58638i	−0.608977	+	0.793188i	$0.708420\pi$
$812$	− 1.80385i	− 0.0633026i
$813$	5.85641i	0.205393i
$814$	49.5167i	1.73556i
$815$	−1.75129	−0.0613450
$816$	2.26795	0.0793941
$817$	9.71281i	0.339808i
$818$	−14.2679	−0.498867
$819$	0	0
$820$	3.05256	0.106600
$821$	− 12.9282i	− 0.451197i	−0.974220	−	0.225599i	$-0.927566\pi$
$821$	− 12.9282i	− 0.451197i	0.974220	−	0.225599i	$-0.0724338\pi$
$822$	−1.92820	−0.0672538
$823$	41.5692	1.44901	0.724506	−	0.689269i	$-0.242068\pi$
$823$	41.5692	1.44901	0.724506	+	0.689269i	$0.242068\pi$
$824$	18.7321i	0.652562i
$825$	23.3205i	0.811916i
$826$	5.85641i	0.203770i
$827$	33.4641i	1.16366i	0.813310	+	0.581830i	$0.197663\pi$
$827$	33.4641i	1.16366i	−0.813310	+	0.581830i	$0.802337\pi$
$828$	−6.19615	−0.215331
$829$	−12.1244	−0.421096	−0.210548	−	0.977583i	$-0.567525\pi$
$829$	−12.1244	−0.421096	−0.210548	+	0.977583i	$0.567525\pi$
$830$	2.73205i	0.0948309i
$831$	2.26795	0.0786743
$832$	0	0
$833$	14.6603	0.507948
$834$	9.85641i	0.341299i
$835$	−0.679492	−0.0235148
$836$	−6.00000	−0.207514
$837$	5.46410i	0.188867i
$838$	10.5359i	0.363957i
$839$	14.1436i	0.488291i	0.969739	+	0.244146i	$0.0785075\pi$
$839$	14.1436i	0.488291i	−0.969739	+	0.244146i	$0.921493\pi$
$840$	0.196152i	0.00676790i
$841$	−22.9282	−0.790628
$842$	−32.7128	−1.12736
$843$	− 22.3205i	− 0.768759i
$844$	4.39230	0.151189
$845$	0	0
$846$	−8.19615	−0.281790
$847$	− 8.33975i	− 0.286557i
$848$	0.464102	0.0159373
$849$	−8.33975	−0.286219
$850$	− 11.1769i	− 0.383365i
$851$	64.8372i	2.22259i
$852$	1.26795i	0.0434392i
$853$	8.17691i	0.279972i	0.990153	+	0.139986i	$0.0447058\pi$
$853$	8.17691i	0.279972i	−0.990153	+	0.139986i	$0.955294\pi$
$854$	0.875644	0.0299639
$855$	−0.339746	−0.0116191
$856$	− 0.196152i	− 0.00670435i
$857$	19.4449	0.664224	0.332112	−	0.943240i	$-0.392239\pi$
$857$	19.4449	0.664224	0.332112	+	0.943240i	$0.392239\pi$
$858$	0	0
$859$	−22.8756	−0.780507	−0.390253	−	0.920707i	$-0.627613\pi$
$859$	−22.8756	−0.780507	−0.390253	+	0.920707i	$0.627613\pi$
$860$	− 2.05256i	− 0.0699917i
$861$	8.33975	0.284218
$862$	11.1244	0.378897
$863$	− 7.12436i	− 0.242516i	−0.992621	−	0.121258i	$-0.961307\pi$
$863$	− 7.12436i	− 0.242516i	0.992621	−	0.121258i	$-0.0386928\pi$
$864$	− 1.00000i	− 0.0340207i
$865$	− 4.39230i	− 0.149343i
$866$	− 14.8564i	− 0.504841i
$867$	−11.8564	−0.402665
$868$	4.00000	0.135769
$869$	− 44.7846i	− 1.51921i
$870$	−0.660254	−0.0223847
$871$	0	0
$872$	−5.46410	−0.185038
$873$	6.00000i	0.203069i
$874$	−7.85641	−0.265747
$875$	1.94744	0.0658355
$876$	9.73205i	0.328816i
$877$	− 10.0718i	− 0.340100i	−0.985435	−	0.170050i	$-0.945607\pi$
$877$	− 10.0718i	− 0.340100i	0.985435	−	0.170050i	$-0.0543930\pi$
$878$	− 17.6603i	− 0.596005i
$879$	− 14.5167i	− 0.489635i
$880$	1.26795	0.0427426
$881$	−51.8372	−1.74644	−0.873219	−	0.487327i	$-0.837972\pi$
$881$	−51.8372	−1.74644	−0.873219	+	0.487327i	$0.837972\pi$
$882$	− 6.46410i	− 0.217658i
$883$	−29.0718	−0.978344	−0.489172	−	0.872187i	$-0.662701\pi$
$883$	−29.0718	−0.978344	−0.489172	+	0.872187i	$0.662701\pi$
$884$	0	0
$885$	2.14359	0.0720561
$886$	− 36.3923i	− 1.22262i
$887$	10.1436	0.340589	0.170294	−	0.985393i	$-0.445528\pi$
$887$	10.1436	0.340589	0.170294	+	0.985393i	$0.445528\pi$
$888$	−10.4641	−0.351152
$889$	− 13.0718i	− 0.438414i
$890$	0.679492i	0.0227766i
$891$	4.73205i	0.158530i
$892$	− 13.0718i	− 0.437676i
$893$	−10.3923	−0.347765
$894$	−2.80385	−0.0937747
$895$	5.90897i	0.197515i
$896$	−0.732051	−0.0244561
$897$	0	0
$898$	−23.3205	−0.778215
$899$	13.4641i	0.449053i
$900$	−4.92820	−0.164273
$901$	1.05256	0.0350658
$902$	− 53.9090i	− 1.79497i
$903$	− 5.60770i	− 0.186612i
$904$	− 18.6603i	− 0.620631i
$905$	2.35898i	0.0784153i
$906$	3.26795	0.108570
$907$	−15.6077	−0.518245	−0.259123	−	0.965844i	$-0.583433\pi$
$907$	−15.6077	−0.518245	−0.259123	+	0.965844i	$0.583433\pi$
$908$	− 1.80385i	− 0.0598628i
$909$	11.9282	0.395634
$910$	0	0
$911$	−9.46410	−0.313560	−0.156780	−	0.987634i	$-0.550111\pi$
$911$	−9.46410	−0.313560	−0.156780	+	0.987634i	$0.550111\pi$
$912$	− 1.26795i	− 0.0419860i
$913$	48.2487	1.59680
$914$	−18.6603	−0.617226
$915$	− 0.320508i	− 0.0105957i
$916$	− 15.8564i	− 0.523910i
$917$	9.85641i	0.325487i
$918$	− 2.26795i	− 0.0748535i
$919$	−57.9615	−1.91197	−0.955987	−	0.293409i	$-0.905210\pi$
$919$	−57.9615	−1.91197	−0.955987	+	0.293409i	$0.905210\pi$
$920$	1.66025	0.0547370
$921$	8.58846i	0.282999i
$922$	−25.7321	−0.847440
$923$	0	0
$924$	3.46410	0.113961
$925$	51.5692i	1.69559i
$926$	−28.0526	−0.921864
$927$	18.7321	0.615241
$928$	− 2.46410i	− 0.0808881i
$929$	− 9.24871i	− 0.303440i	−0.988423	−	0.151720i	$-0.951519\pi$
$929$	− 9.24871i	− 0.303440i	0.988423	−	0.151720i	$-0.0484813\pi$
$930$	− 1.46410i	− 0.0480098i
$931$	− 8.19615i	− 0.268618i
$932$	19.8564	0.650418
$933$	−15.6603	−0.512694
$934$	− 12.5885i	− 0.411907i
$935$	2.87564	0.0940436
$936$	0	0
$937$	43.2487	1.41287	0.706437	−	0.707776i	$-0.250301\pi$
$937$	43.2487	1.41287	0.706437	+	0.707776i	$0.250301\pi$
$938$	8.14359i	0.265898i
$939$	13.4641	0.439384
$940$	2.19615	0.0716306
$941$	56.6410i	1.84644i	0.384267	+	0.923222i	$0.374454\pi$
$941$	56.6410i	1.84644i	−0.384267	+	0.923222i	$0.625546\pi$
$942$	23.5885i	0.768553i
$943$	− 70.5885i	− 2.29868i
$944$	8.00000i	0.260378i
$945$	0.196152	0.00638084
$946$	−36.2487	−1.17855
$947$	34.9282i	1.13501i	0.823369	+	0.567507i	$0.192092\pi$
$947$	34.9282i	1.13501i	−0.823369	+	0.567507i	$0.807908\pi$
$948$	9.46410	0.307380
$949$	0	0
$950$	−6.24871	−0.202735
$951$	− 3.33975i	− 0.108299i
$952$	−1.66025	−0.0538091
$953$	41.5692	1.34656	0.673280	−	0.739388i	$-0.264885\pi$
$953$	41.5692	1.34656	0.673280	+	0.739388i	$0.264885\pi$
$954$	− 0.464102i	− 0.0150258i
$955$	− 1.85641i	− 0.0600719i
$956$	− 9.66025i	− 0.312435i
$957$	11.6603i	0.376922i
$958$	26.5359	0.857336
$959$	1.41154	0.0455811
$960$	0.267949i	0.00864802i
$961$	1.14359	0.0368901
$962$	0	0
$963$	−0.196152	−0.00632092
$964$	17.5885i	0.566486i
$965$	−2.21539	−0.0713159
$966$	4.53590	0.145940
$967$	18.8756i	0.607000i	0.952831	+	0.303500i	$0.0981552\pi$
$967$	18.8756i	0.607000i	−0.952831	+	0.303500i	$0.901845\pi$
$968$	− 11.3923i	− 0.366163i
$969$	− 2.87564i	− 0.0923790i
$970$	− 1.60770i	− 0.0516200i
$971$	−18.2487	−0.585629	−0.292815	−	0.956169i	$-0.594592\pi$
$971$	−18.2487	−0.585629	−0.292815	+	0.956169i	$0.594592\pi$
$972$	−1.00000	−0.0320750
$973$	− 7.21539i	− 0.231315i
$974$	−21.1244	−0.676868
$975$	0	0
$976$	1.19615	0.0382879
$977$	− 32.0718i	− 1.02607i	−0.858368	−	0.513034i	$-0.828522\pi$
$977$	− 32.0718i	− 1.02607i	0.858368	−	0.513034i	$-0.171478\pi$
$978$	−6.53590	−0.208995
$979$	12.0000	0.383522
$980$	1.73205i	0.0553283i
$981$	5.46410i	0.174455i
$982$	5.26795i	0.168107i
$983$	− 20.7846i	− 0.662926i	−0.943468	−	0.331463i	$-0.892458\pi$
$983$	− 20.7846i	− 0.662926i	0.943468	−	0.331463i	$-0.107542\pi$
$984$	11.3923	0.363173
$985$	−2.64102	−0.0841498
$986$	− 5.58846i	− 0.177973i
$987$	6.00000	0.190982
$988$	0	0
$989$	−47.4641	−1.50927
$990$	− 1.26795i	− 0.0402981i
$991$	−8.58846	−0.272821	−0.136411	−	0.990652i	$-0.543557\pi$
$991$	−8.58846	−0.272821	−0.136411	+	0.990652i	$0.543557\pi$
$992$	5.46410	0.173485
$993$	− 20.0000i	− 0.634681i
$994$	− 0.928203i	− 0.0294408i
$995$	− 1.01924i	− 0.0323120i
$996$	10.1962i	0.323077i
$997$	38.6603	1.22438	0.612191	−	0.790710i	$-0.290288\pi$
$997$	38.6603	1.22438	0.612191	+	0.790710i	$0.290288\pi$
$998$	−32.0000	−1.01294
$999$	10.4641i	0.331070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.b.e.337.2		4
3.2	odd	2		3042.2.b.i.1351.3		4
13.2	odd	12		1014.2.e.i.529.2		4
13.3	even	3		78.2.i.a.43.2	✓	4
13.4	even	6		78.2.i.a.49.2	yes	4
13.5	odd	4		1014.2.a.i.1.2		2
13.6	odd	12		1014.2.e.i.991.2		4
13.7	odd	12		1014.2.e.g.991.1		4
13.8	odd	4		1014.2.a.k.1.1		2
13.9	even	3		1014.2.i.a.361.1		4
13.10	even	6		1014.2.i.a.823.1		4
13.11	odd	12		1014.2.e.g.529.1		4
13.12	even	2	inner	1014.2.b.e.337.3		4
39.5	even	4		3042.2.a.y.1.1		2
39.8	even	4		3042.2.a.p.1.2		2
39.17	odd	6		234.2.l.c.127.1		4
39.29	odd	6		234.2.l.c.199.1		4
39.38	odd	2		3042.2.b.i.1351.2		4
52.3	odd	6		624.2.bv.e.433.1		4
52.31	even	4		8112.2.a.bj.1.2		2
52.43	odd	6		624.2.bv.e.49.2		4
52.47	even	4		8112.2.a.bp.1.1		2
65.3	odd	12		1950.2.y.g.199.1		4
65.4	even	6		1950.2.bc.d.751.1		4
65.17	odd	12		1950.2.y.g.49.1		4
65.29	even	6		1950.2.bc.d.901.1		4
65.42	odd	12		1950.2.y.b.199.2		4
65.43	odd	12		1950.2.y.b.49.2		4
156.95	even	6		1872.2.by.h.1297.1		4
156.107	even	6		1872.2.by.h.433.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.i.a.43.2	✓	4	13.3	even	3
78.2.i.a.49.2	yes	4	13.4	even	6
234.2.l.c.127.1		4	39.17	odd	6
234.2.l.c.199.1		4	39.29	odd	6
624.2.bv.e.49.2		4	52.43	odd	6
624.2.bv.e.433.1		4	52.3	odd	6
1014.2.a.i.1.2		2	13.5	odd	4
1014.2.a.k.1.1		2	13.8	odd	4
1014.2.b.e.337.2		4	1.1	even	1	trivial
1014.2.b.e.337.3		4	13.12	even	2	inner
1014.2.e.g.529.1		4	13.11	odd	12
1014.2.e.g.991.1		4	13.7	odd	12
1014.2.e.i.529.2		4	13.2	odd	12
1014.2.e.i.991.2		4	13.6	odd	12
1014.2.i.a.361.1		4	13.9	even	3
1014.2.i.a.823.1		4	13.10	even	6
1872.2.by.h.433.2		4	156.107	even	6
1872.2.by.h.1297.1		4	156.95	even	6
1950.2.y.b.49.2		4	65.43	odd	12
1950.2.y.b.199.2		4	65.42	odd	12
1950.2.y.g.49.1		4	65.17	odd	12
1950.2.y.g.199.1		4	65.3	odd	12
1950.2.bc.d.751.1		4	65.4	even	6
1950.2.bc.d.901.1		4	65.29	even	6
3042.2.a.p.1.2		2	39.8	even	4
3042.2.a.y.1.1		2	39.5	even	4
3042.2.b.i.1351.2		4	39.38	odd	2
3042.2.b.i.1351.3		4	3.2	odd	2
8112.2.a.bj.1.2		2	52.31	even	4
8112.2.a.bp.1.1		2	52.47	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -0.267949i q^{5} -1.00000i q^{6} +0.732051i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -0.267949i q^{5} -1.00000i q^{6} +0.732051i q^{7} +1.00000i q^{8} +1.00000 q^{9} -0.267949 q^{10} +4.73205i q^{11} -1.00000 q^{12} +0.732051 q^{14} -0.267949i q^{15} +1.00000 q^{16} +2.26795 q^{17} -1.00000i q^{18} -1.26795i q^{19} +0.267949i q^{20} +0.732051i q^{21} +4.73205 q^{22} +6.19615 q^{23} +1.00000i q^{24} +4.92820 q^{25} +1.00000 q^{27} -0.732051i q^{28} +2.46410 q^{29} -0.267949 q^{30} +5.46410i q^{31} -1.00000i q^{32} +4.73205i q^{33} -2.26795i q^{34} +0.196152 q^{35} -1.00000 q^{36} +10.4641i q^{37} -1.26795 q^{38} +0.267949 q^{40} -11.3923i q^{41} +0.732051 q^{42} -7.66025 q^{43} -4.73205i q^{44} -0.267949i q^{45} -6.19615i q^{46} -8.19615i q^{47} +1.00000 q^{48} +6.46410 q^{49} -4.92820i q^{50} +2.26795 q^{51} +0.464102 q^{53} -1.00000i q^{54} +1.26795 q^{55} -0.732051 q^{56} -1.26795i q^{57} -2.46410i q^{58} +8.00000i q^{59} +0.267949i q^{60} +1.19615 q^{61} +5.46410 q^{62} +0.732051i q^{63} -1.00000 q^{64} +4.73205 q^{66} +11.1244i q^{67} -2.26795 q^{68} +6.19615 q^{69} -0.196152i q^{70} -1.26795i q^{71} +1.00000i q^{72} -9.73205i q^{73} +10.4641 q^{74} +4.92820 q^{75} +1.26795i q^{76} -3.46410 q^{77} -9.46410 q^{79} -0.267949i q^{80} +1.00000 q^{81} -11.3923 q^{82} -10.1962i q^{83} -0.732051i q^{84} -0.607695i q^{85} +7.66025i q^{86} +2.46410 q^{87} -4.73205 q^{88} -2.53590i q^{89} -0.267949 q^{90} -6.19615 q^{92} +5.46410i q^{93} -8.19615 q^{94} -0.339746 q^{95} -1.00000i q^{96} +6.00000i q^{97} -6.46410i q^{98} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9} - 8 q^{10} - 4 q^{12} - 4 q^{14} + 4 q^{16} + 16 q^{17} + 12 q^{22} + 4 q^{23} - 8 q^{25} + 4 q^{27} - 4 q^{29} - 8 q^{30} - 20 q^{35} - 4 q^{36} - 12 q^{38} + 8 q^{40} - 4 q^{42} + 4 q^{43} + 4 q^{48} + 12 q^{49} + 16 q^{51} - 12 q^{53} + 12 q^{55} + 4 q^{56} - 16 q^{61} + 8 q^{62} - 4 q^{64} + 12 q^{66} - 16 q^{68} + 4 q^{69} + 28 q^{74} - 8 q^{75} - 24 q^{79} + 4 q^{81} - 4 q^{82} - 4 q^{87} - 12 q^{88} - 8 q^{90} - 4 q^{92} - 12 q^{94} - 36 q^{95}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9 - 8 * q^10 - 4 * q^12 - 4 * q^14 + 4 * q^16 + 16 * q^17 + 12 * q^22 + 4 * q^23 - 8 * q^25 + 4 * q^27 - 4 * q^29 - 8 * q^30 - 20 * q^35 - 4 * q^36 - 12 * q^38 + 8 * q^40 - 4 * q^42 + 4 * q^43 + 4 * q^48 + 12 * q^49 + 16 * q^51 - 12 * q^53 + 12 * q^55 + 4 * q^56 - 16 * q^61 + 8 * q^62 - 4 * q^64 + 12 * q^66 - 16 * q^68 + 4 * q^69 + 28 * q^74 - 8 * q^75 - 24 * q^79 + 4 * q^81 - 4 * q^82 - 4 * q^87 - 12 * q^88 - 8 * q^90 - 4 * q^92 - 12 * q^94 - 36 * q^95

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