LMFDB - Embedded newform 1183.2.c.e.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (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:	$9.44630255912$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.e.337.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{2} +2.73205 q^{3} -1.00000 q^{4} -1.73205i q^{5} -4.73205i q^{6} +1.00000i q^{7} -1.73205i q^{8} +4.46410 q^{9} +O(q^{10})$	\(q-1.73205i q^{2} +2.73205 q^{3} -1.00000 q^{4} -1.73205i q^{5} -4.73205i q^{6} +1.00000i q^{7} -1.73205i q^{8} +4.46410 q^{9} -3.00000 q^{10} +1.26795i q^{11} -2.73205 q^{12} +1.73205 q^{14} -4.73205i q^{15} -5.00000 q^{16} +7.73205 q^{17} -7.73205i q^{18} -2.00000i q^{19} +1.73205i q^{20} +2.73205i q^{21} +2.19615 q^{22} -4.73205 q^{23} -4.73205i q^{24} +2.00000 q^{25} +4.00000 q^{27} -1.00000i q^{28} -3.00000 q^{29} -8.19615 q^{30} -4.19615i q^{31} +5.19615i q^{32} +3.46410i q^{33} -13.3923i q^{34} +1.73205 q^{35} -4.46410 q^{36} -7.00000i q^{37} -3.46410 q^{38} -3.00000 q^{40} +5.19615i q^{41} +4.73205 q^{42} +0.196152 q^{43} -1.26795i q^{44} -7.73205i q^{45} +8.19615i q^{46} +12.9282i q^{47} -13.6603 q^{48} -1.00000 q^{49} -3.46410i q^{50} +21.1244 q^{51} -9.92820 q^{53} -6.92820i q^{54} +2.19615 q^{55} +1.73205 q^{56} -5.46410i q^{57} +5.19615i q^{58} +7.26795i q^{59} +4.73205i q^{60} -4.80385 q^{61} -7.26795 q^{62} +4.46410i q^{63} -1.00000 q^{64} +6.00000 q^{66} +6.19615i q^{67} -7.73205 q^{68} -12.9282 q^{69} -3.00000i q^{70} -6.00000i q^{71} -7.73205i q^{72} -3.19615i q^{73} -12.1244 q^{74} +5.46410 q^{75} +2.00000i q^{76} -1.26795 q^{77} +16.1962 q^{79} +8.66025i q^{80} -2.46410 q^{81} +9.00000 q^{82} +2.19615i q^{83} -2.73205i q^{84} -13.3923i q^{85} -0.339746i q^{86} -8.19615 q^{87} +2.19615 q^{88} +12.9282i q^{89} -13.3923 q^{90} +4.73205 q^{92} -11.4641i q^{93} +22.3923 q^{94} -3.46410 q^{95} +14.1962i q^{96} -6.39230i q^{97} +1.73205i q^{98} +5.66025i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 12 q^{10} - 4 q^{12} - 20 q^{16} + 24 q^{17} - 12 q^{22} - 12 q^{23} + 8 q^{25} + 16 q^{27} - 12 q^{29} - 12 q^{30} - 4 q^{36} - 12 q^{40} + 12 q^{42} - 20 q^{43} - 20 q^{48} - 4 q^{49} + 36 q^{51} - 12 q^{53} - 12 q^{55} - 40 q^{61} - 36 q^{62} - 4 q^{64} + 24 q^{66} - 24 q^{68} - 24 q^{69} + 8 q^{75} - 12 q^{77} + 44 q^{79} + 4 q^{81} + 36 q^{82} - 12 q^{87} - 12 q^{88} - 12 q^{90} + 12 q^{92} + 48 q^{94}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9 - 12 * q^10 - 4 * q^12 - 20 * q^16 + 24 * q^17 - 12 * q^22 - 12 * q^23 + 8 * q^25 + 16 * q^27 - 12 * q^29 - 12 * q^30 - 4 * q^36 - 12 * q^40 + 12 * q^42 - 20 * q^43 - 20 * q^48 - 4 * q^49 + 36 * q^51 - 12 * q^53 - 12 * q^55 - 40 * q^61 - 36 * q^62 - 4 * q^64 + 24 * q^66 - 24 * q^68 - 24 * q^69 + 8 * q^75 - 12 * q^77 + 44 * q^79 + 4 * q^81 + 36 * q^82 - 12 * q^87 - 12 * q^88 - 12 * q^90 + 12 * q^92 + 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.73205i	− 1.22474i	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	− 1.73205i	− 1.22474i	0.790569	−	0.612372i	$-0.209785\pi$
$3$	2.73205	1.57735	0.788675	−	0.614810i	$-0.210767\pi$
$3$	2.73205	1.57735	0.788675	+	0.614810i	$0.210767\pi$
$4$	−1.00000	−0.500000
$5$	− 1.73205i	− 0.774597i	−0.921954	−	0.387298i	$-0.873408\pi$
$5$	− 1.73205i	− 0.774597i	0.921954	−	0.387298i	$-0.126592\pi$
$6$	− 4.73205i	− 1.93185i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 1.73205i	− 0.612372i
$9$	4.46410	1.48803
$10$	−3.00000	−0.948683
$11$	1.26795i	0.382301i	0.981561	+	0.191151i	$0.0612219\pi$
$11$	1.26795i	0.382301i	−0.981561	+	0.191151i	$0.938778\pi$
$12$	−2.73205	−0.788675
$13$	0	0
$13$	0	0
$14$	1.73205	0.462910
$15$	− 4.73205i	− 1.22181i
$16$	−5.00000	−1.25000
$17$	7.73205	1.87530	0.937649	−	0.347584i	$-0.112998\pi$
$17$	7.73205	1.87530	0.937649	+	0.347584i	$0.112998\pi$
$18$	− 7.73205i	− 1.82246i
$19$	− 2.00000i	− 0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$	− 2.00000i	− 0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$	1.73205i	0.387298i
$21$	2.73205i	0.596182i
$22$	2.19615	0.468221
$23$	−4.73205	−0.986701	−0.493350	−	0.869831i	$-0.664228\pi$
$23$	−4.73205	−0.986701	−0.493350	+	0.869831i	$0.664228\pi$
$24$	− 4.73205i	− 0.965926i
$25$	2.00000	0.400000
$26$	0	0
$27$	4.00000	0.769800
$28$	− 1.00000i	− 0.188982i
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	−8.19615	−1.49641
$31$	− 4.19615i	− 0.753651i	−0.926284	−	0.376826i	$-0.877016\pi$
$31$	− 4.19615i	− 0.753651i	0.926284	−	0.376826i	$-0.122984\pi$
$32$	5.19615i	0.918559i
$33$	3.46410i	0.603023i
$34$	− 13.3923i	− 2.29676i
$35$	1.73205	0.292770
$36$	−4.46410	−0.744017
$37$	− 7.00000i	− 1.15079i	−0.817875	−	0.575396i	$-0.804848\pi$
$37$	− 7.00000i	− 1.15079i	0.817875	−	0.575396i	$-0.195152\pi$
$38$	−3.46410	−0.561951
$39$	0	0
$40$	−3.00000	−0.474342
$41$	5.19615i	0.811503i	0.913984	+	0.405751i	$0.132990\pi$
$41$	5.19615i	0.811503i	−0.913984	+	0.405751i	$0.867010\pi$
$42$	4.73205	0.730171
$43$	0.196152	0.0299130	0.0149565	−	0.999888i	$-0.495239\pi$
$43$	0.196152	0.0299130	0.0149565	+	0.999888i	$0.495239\pi$
$44$	− 1.26795i	− 0.191151i
$45$	− 7.73205i	− 1.15263i
$46$	8.19615i	1.20846i
$47$	12.9282i	1.88577i	0.333115	+	0.942886i	$0.391900\pi$
$47$	12.9282i	1.88577i	−0.333115	+	0.942886i	$0.608100\pi$
$48$	−13.6603	−1.97169
$49$	−1.00000	−0.142857
$50$	− 3.46410i	− 0.489898i
$51$	21.1244	2.95800
$52$	0	0
$53$	−9.92820	−1.36374	−0.681872	−	0.731472i	$-0.738834\pi$
$53$	−9.92820	−1.36374	−0.681872	+	0.731472i	$0.738834\pi$
$54$	− 6.92820i	− 0.942809i
$55$	2.19615	0.296129
$56$	1.73205	0.231455
$57$	− 5.46410i	− 0.723738i
$58$	5.19615i	0.682288i
$59$	7.26795i	0.946206i	0.881007	+	0.473103i	$0.156866\pi$
$59$	7.26795i	0.946206i	−0.881007	+	0.473103i	$0.843134\pi$
$60$	4.73205i	0.610905i
$61$	−4.80385	−0.615070	−0.307535	−	0.951537i	$-0.599504\pi$
$61$	−4.80385	−0.615070	−0.307535	+	0.951537i	$0.599504\pi$
$62$	−7.26795	−0.923030
$63$	4.46410i	0.562424i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	6.00000	0.738549
$67$	6.19615i	0.756980i	0.925605	+	0.378490i	$0.123557\pi$
$67$	6.19615i	0.756980i	−0.925605	+	0.378490i	$0.876443\pi$
$68$	−7.73205	−0.937649
$69$	−12.9282	−1.55637
$70$	− 3.00000i	− 0.358569i
$71$	− 6.00000i	− 0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$	− 6.00000i	− 0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$	− 7.73205i	− 0.911231i
$73$	− 3.19615i	− 0.374081i	−0.982352	−	0.187041i	$-0.940110\pi$
$73$	− 3.19615i	− 0.374081i	0.982352	−	0.187041i	$-0.0598896\pi$
$74$	−12.1244	−1.40943
$75$	5.46410	0.630940
$76$	2.00000i	0.229416i
$77$	−1.26795	−0.144496
$78$	0	0
$79$	16.1962	1.82221	0.911105	−	0.412175i	$-0.135231\pi$
$79$	16.1962	1.82221	0.911105	+	0.412175i	$0.135231\pi$
$80$	8.66025i	0.968246i
$81$	−2.46410	−0.273789
$82$	9.00000	0.993884
$83$	2.19615i	0.241059i	0.992710	+	0.120530i	$0.0384592\pi$
$83$	2.19615i	0.241059i	−0.992710	+	0.120530i	$0.961541\pi$
$84$	− 2.73205i	− 0.298091i
$85$	− 13.3923i	− 1.45260i
$86$	− 0.339746i	− 0.0366357i
$87$	−8.19615	−0.878720
$88$	2.19615	0.234111
$89$	12.9282i	1.37039i	0.728361	+	0.685193i	$0.240282\pi$
$89$	12.9282i	1.37039i	−0.728361	+	0.685193i	$0.759718\pi$
$90$	−13.3923	−1.41167
$91$	0	0
$92$	4.73205	0.493350
$93$	− 11.4641i	− 1.18877i
$94$	22.3923	2.30959
$95$	−3.46410	−0.355409
$96$	14.1962i	1.44889i
$97$	− 6.39230i	− 0.649040i	−0.945879	−	0.324520i	$-0.894797\pi$
$97$	− 6.39230i	− 0.649040i	0.945879	−	0.324520i	$-0.105203\pi$
$98$	1.73205i	0.174964i
$99$	5.66025i	0.568877i
$100$	−2.00000	−0.200000
$101$	7.73205	0.769368	0.384684	−	0.923048i	$-0.374310\pi$
$101$	7.73205	0.769368	0.384684	+	0.923048i	$0.374310\pi$
$102$	− 36.5885i	− 3.62280i
$103$	14.3923	1.41812	0.709058	−	0.705150i	$-0.249120\pi$
$103$	14.3923	1.41812	0.709058	+	0.705150i	$0.249120\pi$
$104$	0	0
$105$	4.73205	0.461801
$106$	17.1962i	1.67024i
$107$	−7.85641	−0.759507	−0.379754	−	0.925088i	$-0.623991\pi$
$107$	−7.85641	−0.759507	−0.379754	+	0.925088i	$0.623991\pi$
$108$	−4.00000	−0.384900
$109$	8.39230i	0.803837i	0.915675	+	0.401919i	$0.131656\pi$
$109$	8.39230i	0.803837i	−0.915675	+	0.401919i	$0.868344\pi$
$110$	− 3.80385i	− 0.362683i
$111$	− 19.1244i	− 1.81520i
$112$	− 5.00000i	− 0.472456i
$113$	13.3923	1.25984	0.629921	−	0.776659i	$-0.283087\pi$
$113$	13.3923	1.25984	0.629921	+	0.776659i	$0.283087\pi$
$114$	−9.46410	−0.886394
$115$	8.19615i	0.764295i
$116$	3.00000	0.278543
$117$	0	0
$118$	12.5885	1.15886
$119$	7.73205i	0.708796i
$120$	−8.19615	−0.748203
$121$	9.39230	0.853846
$122$	8.32051i	0.753303i
$123$	14.1962i	1.28002i
$124$	4.19615i	0.376826i
$125$	− 12.1244i	− 1.08444i
$126$	7.73205	0.688826
$127$	−18.3923	−1.63205	−0.816027	−	0.578014i	$-0.803828\pi$
$127$	−18.3923	−1.63205	−0.816027	+	0.578014i	$0.803828\pi$
$128$	12.1244i	1.07165i
$129$	0.535898	0.0471832
$130$	0	0
$131$	−3.46410	−0.302660	−0.151330	−	0.988483i	$-0.548356\pi$
$131$	−3.46410	−0.302660	−0.151330	+	0.988483i	$0.548356\pi$
$132$	− 3.46410i	− 0.301511i
$133$	2.00000	0.173422
$134$	10.7321	0.927108
$135$	− 6.92820i	− 0.596285i
$136$	− 13.3923i	− 1.14838i
$137$	8.07180i	0.689620i	0.938672	+	0.344810i	$0.112057\pi$
$137$	8.07180i	0.689620i	−0.938672	+	0.344810i	$0.887943\pi$
$138$	22.3923i	1.90616i
$139$	−10.5885	−0.898101	−0.449051	−	0.893506i	$-0.648238\pi$
$139$	−10.5885	−0.898101	−0.449051	+	0.893506i	$0.648238\pi$
$140$	−1.73205	−0.146385
$141$	35.3205i	2.97452i
$142$	−10.3923	−0.872103
$143$	0	0
$144$	−22.3205	−1.86004
$145$	5.19615i	0.431517i
$146$	−5.53590	−0.458154
$147$	−2.73205	−0.225336
$148$	7.00000i	0.575396i
$149$	6.46410i	0.529560i	0.964309	+	0.264780i	$0.0852993\pi$
$149$	6.46410i	0.529560i	−0.964309	+	0.264780i	$0.914701\pi$
$150$	− 9.46410i	− 0.772741i
$151$	2.00000i	0.162758i	0.996683	+	0.0813788i	$0.0259324\pi$
$151$	2.00000i	0.162758i	−0.996683	+	0.0813788i	$0.974068\pi$
$152$	−3.46410	−0.280976
$153$	34.5167	2.79051
$154$	2.19615i	0.176971i
$155$	−7.26795	−0.583776
$156$	0	0
$157$	1.19615	0.0954634	0.0477317	−	0.998860i	$-0.484801\pi$
$157$	1.19615	0.0954634	0.0477317	+	0.998860i	$0.484801\pi$
$158$	− 28.0526i	− 2.23174i
$159$	−27.1244	−2.15110
$160$	9.00000	0.711512
$161$	− 4.73205i	− 0.372938i
$162$	4.26795i	0.335322i
$163$	16.1962i	1.26858i	0.773095	+	0.634290i	$0.218708\pi$
$163$	16.1962i	1.26858i	−0.773095	+	0.634290i	$0.781292\pi$
$164$	− 5.19615i	− 0.405751i
$165$	6.00000	0.467099
$166$	3.80385	0.295236
$167$	− 6.58846i	− 0.509830i	−0.966963	−	0.254915i	$-0.917952\pi$
$167$	− 6.58846i	− 0.509830i	0.966963	−	0.254915i	$-0.0820475\pi$
$168$	4.73205	0.365086
$169$	0	0
$170$	−23.1962	−1.77906
$171$	− 8.92820i	− 0.682757i
$172$	−0.196152	−0.0149565
$173$	−8.53590	−0.648972	−0.324486	−	0.945890i	$-0.605191\pi$
$173$	−8.53590	−0.648972	−0.324486	+	0.945890i	$0.605191\pi$
$174$	14.1962i	1.07621i
$175$	2.00000i	0.151186i
$176$	− 6.33975i	− 0.477876i
$177$	19.8564i	1.49250i
$178$	22.3923	1.67837
$179$	6.92820	0.517838	0.258919	−	0.965899i	$-0.416634\pi$
$179$	6.92820	0.517838	0.258919	+	0.965899i	$0.416634\pi$
$180$	7.73205i	0.576313i
$181$	−5.58846	−0.415387	−0.207693	−	0.978194i	$-0.566596\pi$
$181$	−5.58846	−0.415387	−0.207693	+	0.978194i	$0.566596\pi$
$182$	0	0
$183$	−13.1244	−0.970180
$184$	8.19615i	0.604228i
$185$	−12.1244	−0.891400
$186$	−19.8564	−1.45594
$187$	9.80385i	0.716928i
$188$	− 12.9282i	− 0.942886i
$189$	4.00000i	0.290957i
$190$	6.00000i	0.435286i
$191$	4.73205	0.342399	0.171200	−	0.985236i	$-0.445236\pi$
$191$	4.73205	0.342399	0.171200	+	0.985236i	$0.445236\pi$
$192$	−2.73205	−0.197169
$193$	5.00000i	0.359908i	0.983675	+	0.179954i	$0.0575949\pi$
$193$	5.00000i	0.359908i	−0.983675	+	0.179954i	$0.942405\pi$
$194$	−11.0718	−0.794909
$195$	0	0
$196$	1.00000	0.0714286
$197$	− 12.0000i	− 0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$	− 12.0000i	− 0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$	9.80385	0.696729
$199$	−2.00000	−0.141776	−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000	−0.141776	−0.0708881	+	0.997484i	$0.522583\pi$
$200$	− 3.46410i	− 0.244949i
$201$	16.9282i	1.19402i
$202$	− 13.3923i	− 0.942279i
$203$	− 3.00000i	− 0.210559i
$204$	−21.1244	−1.47900
$205$	9.00000	0.628587
$206$	− 24.9282i	− 1.73683i
$207$	−21.1244	−1.46824
$208$	0	0
$209$	2.53590	0.175412
$210$	− 8.19615i	− 0.565588i
$211$	−1.80385	−0.124182	−0.0620910	−	0.998070i	$-0.519777\pi$
$211$	−1.80385	−0.124182	−0.0620910	+	0.998070i	$0.519777\pi$
$212$	9.92820	0.681872
$213$	− 16.3923i	− 1.12318i
$214$	13.6077i	0.930203i
$215$	− 0.339746i	− 0.0231705i
$216$	− 6.92820i	− 0.471405i
$217$	4.19615	0.284853
$218$	14.5359	0.984495
$219$	− 8.73205i	− 0.590057i
$220$	−2.19615	−0.148065
$221$	0	0
$222$	−33.1244	−2.22316
$223$	10.0000i	0.669650i	0.942280	+	0.334825i	$0.108677\pi$
$223$	10.0000i	0.669650i	−0.942280	+	0.334825i	$0.891323\pi$
$224$	−5.19615	−0.347183
$225$	8.92820	0.595214
$226$	− 23.1962i	− 1.54299i
$227$	− 5.66025i	− 0.375684i	−0.982199	−	0.187842i	$-0.939851\pi$
$227$	− 5.66025i	− 0.375684i	0.982199	−	0.187842i	$-0.0601493\pi$
$228$	5.46410i	0.361869i
$229$	− 14.3923i	− 0.951070i	−0.879697	−	0.475535i	$-0.842254\pi$
$229$	− 14.3923i	− 0.951070i	0.879697	−	0.475535i	$-0.157746\pi$
$230$	14.1962	0.936067
$231$	−3.46410	−0.227921
$232$	5.19615i	0.341144i
$233$	1.85641	0.121617	0.0608086	−	0.998149i	$-0.480632\pi$
$233$	1.85641	0.121617	0.0608086	+	0.998149i	$0.480632\pi$
$234$	0	0
$235$	22.3923	1.46071
$236$	− 7.26795i	− 0.473103i
$237$	44.2487	2.87426
$238$	13.3923	0.868094
$239$	15.8038i	1.02227i	0.859502	+	0.511133i	$0.170774\pi$
$239$	15.8038i	1.02227i	−0.859502	+	0.511133i	$0.829226\pi$
$240$	23.6603i	1.52726i
$241$	− 21.1962i	− 1.36536i	−0.730716	−	0.682682i	$-0.760813\pi$
$241$	− 21.1962i	− 1.36536i	0.730716	−	0.682682i	$-0.239187\pi$
$242$	− 16.2679i	− 1.04574i
$243$	−18.7321	−1.20166
$244$	4.80385	0.307535
$245$	1.73205i	0.110657i
$246$	24.5885	1.56770
$247$	0	0
$248$	−7.26795	−0.461515
$249$	6.00000i	0.380235i
$250$	−21.0000	−1.32816
$251$	1.60770	0.101477	0.0507384	−	0.998712i	$-0.483843\pi$
$251$	1.60770	0.101477	0.0507384	+	0.998712i	$0.483843\pi$
$252$	− 4.46410i	− 0.281212i
$253$	− 6.00000i	− 0.377217i
$254$	31.8564i	1.99885i
$255$	− 36.5885i	− 2.29126i
$256$	19.0000	1.18750
$257$	−6.12436	−0.382027	−0.191013	−	0.981587i	$-0.561177\pi$
$257$	−6.12436	−0.382027	−0.191013	+	0.981587i	$0.561177\pi$
$258$	− 0.928203i	− 0.0577874i
$259$	7.00000	0.434959
$260$	0	0
$261$	−13.3923	−0.828963
$262$	6.00000i	0.370681i
$263$	1.26795	0.0781851	0.0390925	−	0.999236i	$-0.487553\pi$
$263$	1.26795	0.0781851	0.0390925	+	0.999236i	$0.487553\pi$
$264$	6.00000	0.369274
$265$	17.1962i	1.05635i
$266$	− 3.46410i	− 0.212398i
$267$	35.3205i	2.16158i
$268$	− 6.19615i	− 0.378490i
$269$	5.07180	0.309233	0.154616	−	0.987975i	$-0.450586\pi$
$269$	5.07180	0.309233	0.154616	+	0.987975i	$0.450586\pi$
$270$	−12.0000	−0.730297
$271$	5.80385i	0.352559i	0.984340	+	0.176279i	$0.0564062\pi$
$271$	5.80385i	0.352559i	−0.984340	+	0.176279i	$0.943594\pi$
$272$	−38.6603	−2.34412
$273$	0	0
$274$	13.9808	0.844609
$275$	2.53590i	0.152920i
$276$	12.9282	0.778186
$277$	−17.0000	−1.02143	−0.510716	−	0.859750i	$-0.670619\pi$
$277$	−17.0000	−1.02143	−0.510716	+	0.859750i	$0.670619\pi$
$278$	18.3397i	1.09994i
$279$	− 18.7321i	− 1.12146i
$280$	− 3.00000i	− 0.179284i
$281$	13.3923i	0.798918i	0.916751	+	0.399459i	$0.130802\pi$
$281$	13.3923i	0.798918i	−0.916751	+	0.399459i	$0.869198\pi$
$282$	61.1769	3.64303
$283$	−10.1962	−0.606098	−0.303049	−	0.952975i	$-0.598005\pi$
$283$	−10.1962	−0.606098	−0.303049	+	0.952975i	$0.598005\pi$
$284$	6.00000i	0.356034i
$285$	−9.46410	−0.560605
$286$	0	0
$287$	−5.19615	−0.306719
$288$	23.1962i	1.36685i
$289$	42.7846	2.51674
$290$	9.00000	0.528498
$291$	− 17.4641i	− 1.02376i
$292$	3.19615i	0.187041i
$293$	− 0.803848i	− 0.0469613i	−0.999724	−	0.0234806i	$-0.992525\pi$
$293$	− 0.803848i	− 0.0469613i	0.999724	−	0.0234806i	$-0.00747481\pi$
$294$	4.73205i	0.275979i
$295$	12.5885	0.732928
$296$	−12.1244	−0.704714
$297$	5.07180i	0.294295i
$298$	11.1962	0.648576
$299$	0	0
$300$	−5.46410	−0.315470
$301$	0.196152i	0.0113060i
$302$	3.46410	0.199337
$303$	21.1244	1.21356
$304$	10.0000i	0.573539i
$305$	8.32051i	0.476431i
$306$	− 59.7846i	− 3.41766i
$307$	− 4.58846i	− 0.261877i	−0.991390	−	0.130939i	$-0.958201\pi$
$307$	− 4.58846i	− 0.261877i	0.991390	−	0.130939i	$-0.0417991\pi$
$308$	1.26795	0.0722481
$309$	39.3205	2.23687
$310$	12.5885i	0.714976i
$311$	−1.26795	−0.0718988	−0.0359494	−	0.999354i	$-0.511446\pi$
$311$	−1.26795	−0.0718988	−0.0359494	+	0.999354i	$0.511446\pi$
$312$	0	0
$313$	28.7846	1.62700	0.813501	−	0.581563i	$-0.197559\pi$
$313$	28.7846	1.62700	0.813501	+	0.581563i	$0.197559\pi$
$314$	− 2.07180i	− 0.116918i
$315$	7.73205	0.435652
$316$	−16.1962	−0.911105
$317$	6.46410i	0.363060i	0.983385	+	0.181530i	$0.0581050\pi$
$317$	6.46410i	0.363060i	−0.983385	+	0.181530i	$0.941895\pi$
$318$	46.9808i	2.63455i
$319$	− 3.80385i	− 0.212975i
$320$	1.73205i	0.0968246i
$321$	−21.4641	−1.19801
$322$	−8.19615	−0.456754
$323$	− 15.4641i	− 0.860446i
$324$	2.46410	0.136895
$325$	0	0
$326$	28.0526	1.55369
$327$	22.9282i	1.26793i
$328$	9.00000	0.496942
$329$	−12.9282	−0.712755
$330$	− 10.3923i	− 0.572078i
$331$	− 24.9808i	− 1.37307i	−0.727098	−	0.686533i	$-0.759132\pi$
$331$	− 24.9808i	− 1.37307i	0.727098	−	0.686533i	$-0.240868\pi$
$332$	− 2.19615i	− 0.120530i
$333$	− 31.2487i	− 1.71242i
$334$	−11.4115	−0.624412
$335$	10.7321	0.586355
$336$	− 13.6603i	− 0.745228i
$337$	−11.0000	−0.599208	−0.299604	−	0.954064i	$-0.596855\pi$
$337$	−11.0000	−0.599208	−0.299604	+	0.954064i	$0.596855\pi$
$338$	0	0
$339$	36.5885	1.98721
$340$	13.3923i	0.726300i
$341$	5.32051	0.288122
$342$	−15.4641	−0.836203
$343$	− 1.00000i	− 0.0539949i
$344$	− 0.339746i	− 0.0183179i
$345$	22.3923i	1.20556i
$346$	14.7846i	0.794826i
$347$	7.26795	0.390164	0.195082	−	0.980787i	$-0.437503\pi$
$347$	7.26795	0.390164	0.195082	+	0.980787i	$0.437503\pi$
$348$	8.19615	0.439360
$349$	− 24.7846i	− 1.32669i	−0.748314	−	0.663345i	$-0.769136\pi$
$349$	− 24.7846i	− 1.32669i	0.748314	−	0.663345i	$-0.230864\pi$
$350$	3.46410	0.185164
$351$	0	0
$352$	−6.58846	−0.351166
$353$	− 20.6603i	− 1.09963i	−0.835285	−	0.549817i	$-0.814697\pi$
$353$	− 20.6603i	− 1.09963i	0.835285	−	0.549817i	$-0.185303\pi$
$354$	34.3923	1.82793
$355$	−10.3923	−0.551566
$356$	− 12.9282i	− 0.685193i
$357$	21.1244i	1.11802i
$358$	− 12.0000i	− 0.634220i
$359$	18.9282i	0.998992i	0.866316	+	0.499496i	$0.166482\pi$
$359$	18.9282i	0.998992i	−0.866316	+	0.499496i	$0.833518\pi$
$360$	−13.3923	−0.705836
$361$	15.0000	0.789474
$362$	9.67949i	0.508743i
$363$	25.6603	1.34681
$364$	0	0
$365$	−5.53590	−0.289762
$366$	22.7321i	1.18822i
$367$	4.19615	0.219037	0.109519	−	0.993985i	$-0.465069\pi$
$367$	4.19615	0.219037	0.109519	+	0.993985i	$0.465069\pi$
$368$	23.6603	1.23338
$369$	23.1962i	1.20754i
$370$	21.0000i	1.09174i
$371$	− 9.92820i	− 0.515447i
$372$	11.4641i	0.594386i
$373$	−11.3923	−0.589871	−0.294936	−	0.955517i	$-0.595298\pi$
$373$	−11.3923	−0.589871	−0.294936	+	0.955517i	$0.595298\pi$
$374$	16.9808	0.878054
$375$	− 33.1244i	− 1.71053i
$376$	22.3923	1.15479
$377$	0	0
$378$	6.92820	0.356348
$379$	− 26.5885i	− 1.36576i	−0.730532	−	0.682879i	$-0.760728\pi$
$379$	− 26.5885i	− 1.36576i	0.730532	−	0.682879i	$-0.239272\pi$
$380$	3.46410	0.177705
$381$	−50.2487	−2.57432
$382$	− 8.19615i	− 0.419352i
$383$	11.6603i	0.595811i	0.954595	+	0.297906i	$0.0962881\pi$
$383$	11.6603i	0.595811i	−0.954595	+	0.297906i	$0.903712\pi$
$384$	33.1244i	1.69037i
$385$	2.19615i	0.111926i
$386$	8.66025	0.440795
$387$	0.875644	0.0445115
$388$	6.39230i	0.324520i
$389$	23.5359	1.19332	0.596659	−	0.802495i	$-0.296495\pi$
$389$	23.5359	1.19332	0.596659	+	0.802495i	$0.296495\pi$
$390$	0	0
$391$	−36.5885	−1.85036
$392$	1.73205i	0.0874818i
$393$	−9.46410	−0.477401
$394$	−20.7846	−1.04711
$395$	− 28.0526i	− 1.41148i
$396$	− 5.66025i	− 0.284438i
$397$	− 18.7846i	− 0.942773i	−0.881927	−	0.471386i	$-0.843754\pi$
$397$	− 18.7846i	− 0.942773i	0.881927	−	0.471386i	$-0.156246\pi$
$398$	3.46410i	0.173640i
$399$	5.46410	0.273547
$400$	−10.0000	−0.500000
$401$	− 10.8564i	− 0.542143i	−0.962559	−	0.271072i	$-0.912622\pi$
$401$	− 10.8564i	− 0.542143i	0.962559	−	0.271072i	$-0.0873780\pi$
$402$	29.3205	1.46237
$403$	0	0
$404$	−7.73205	−0.384684
$405$	4.26795i	0.212076i
$406$	−5.19615	−0.257881
$407$	8.87564	0.439949
$408$	− 36.5885i	− 1.81140i
$409$	16.8038i	0.830897i	0.909617	+	0.415448i	$0.136375\pi$
$409$	16.8038i	0.830897i	−0.909617	+	0.415448i	$0.863625\pi$
$410$	− 15.5885i	− 0.769859i
$411$	22.0526i	1.08777i
$412$	−14.3923	−0.709058
$413$	−7.26795	−0.357632
$414$	36.5885i	1.79822i
$415$	3.80385	0.186724
$416$	0	0
$417$	−28.9282	−1.41662
$418$	− 4.39230i	− 0.214835i
$419$	−32.1962	−1.57288	−0.786442	−	0.617664i	$-0.788079\pi$
$419$	−32.1962	−1.57288	−0.786442	+	0.617664i	$0.788079\pi$
$420$	−4.73205	−0.230900
$421$	32.1769i	1.56821i	0.620630	+	0.784103i	$0.286877\pi$
$421$	32.1769i	1.56821i	−0.620630	+	0.784103i	$0.713123\pi$
$422$	3.12436i	0.152091i
$423$	57.7128i	2.80609i
$424$	17.1962i	0.835119i
$425$	15.4641	0.750119
$426$	−28.3923	−1.37561
$427$	− 4.80385i	− 0.232474i
$428$	7.85641	0.379754
$429$	0	0
$430$	−0.588457	−0.0283779
$431$	− 0.679492i	− 0.0327300i	−0.999866	−	0.0163650i	$-0.994791\pi$
$431$	− 0.679492i	− 0.0327300i	0.999866	−	0.0163650i	$-0.00520937\pi$
$432$	−20.0000	−0.962250
$433$	13.5885	0.653020	0.326510	−	0.945194i	$-0.394127\pi$
$433$	13.5885	0.653020	0.326510	+	0.945194i	$0.394127\pi$
$434$	− 7.26795i	− 0.348873i
$435$	14.1962i	0.680653i
$436$	− 8.39230i	− 0.401919i
$437$	9.46410i	0.452729i
$438$	−15.1244	−0.722670
$439$	−14.5885	−0.696269	−0.348135	−	0.937445i	$-0.613185\pi$
$439$	−14.5885	−0.696269	−0.348135	+	0.937445i	$0.613185\pi$
$440$	− 3.80385i	− 0.181341i
$441$	−4.46410	−0.212576
$442$	0	0
$443$	23.3205	1.10799	0.553995	−	0.832520i	$-0.313103\pi$
$443$	23.3205	1.10799	0.553995	+	0.832520i	$0.313103\pi$
$444$	19.1244i	0.907602i
$445$	22.3923	1.06150
$446$	17.3205	0.820150
$447$	17.6603i	0.835301i
$448$	− 1.00000i	− 0.0472456i
$449$	− 12.0000i	− 0.566315i	−0.959073	−	0.283158i	$-0.908618\pi$
$449$	− 12.0000i	− 0.566315i	0.959073	−	0.283158i	$-0.0913819\pi$
$450$	− 15.4641i	− 0.728985i
$451$	−6.58846	−0.310238
$452$	−13.3923	−0.629921
$453$	5.46410i	0.256726i
$454$	−9.80385	−0.460117
$455$	0	0
$456$	−9.46410	−0.443197
$457$	− 11.0000i	− 0.514558i	−0.966337	−	0.257279i	$-0.917174\pi$
$457$	− 11.0000i	− 0.514558i	0.966337	−	0.257279i	$-0.0828260\pi$
$458$	−24.9282	−1.16482
$459$	30.9282	1.44360
$460$	− 8.19615i	− 0.382148i
$461$	15.5885i	0.726027i	0.931784	+	0.363013i	$0.118252\pi$
$461$	15.5885i	0.726027i	−0.931784	+	0.363013i	$0.881748\pi$
$462$	6.00000i	0.279145i
$463$	− 4.58846i	− 0.213244i	−0.994300	−	0.106622i	$-0.965997\pi$
$463$	− 4.58846i	− 0.213244i	0.994300	−	0.106622i	$-0.0340034\pi$
$464$	15.0000	0.696358
$465$	−19.8564	−0.920819
$466$	− 3.21539i	− 0.148950i
$467$	−25.5167	−1.18077	−0.590385	−	0.807122i	$-0.701024\pi$
$467$	−25.5167	−1.18077	−0.590385	+	0.807122i	$0.701024\pi$
$468$	0	0
$469$	−6.19615	−0.286112
$470$	− 38.7846i	− 1.78900i
$471$	3.26795	0.150579
$472$	12.5885	0.579431
$473$	0.248711i	0.0114358i
$474$	− 76.6410i	− 3.52024i
$475$	− 4.00000i	− 0.183533i
$476$	− 7.73205i	− 0.354398i
$477$	−44.3205	−2.02930
$478$	27.3731	1.25201
$479$	1.26795i	0.0579341i	0.999580	+	0.0289670i	$0.00922178\pi$
$479$	1.26795i	0.0579341i	−0.999580	+	0.0289670i	$0.990778\pi$
$480$	24.5885	1.12230
$481$	0	0
$482$	−36.7128	−1.67222
$483$	− 12.9282i	− 0.588254i
$484$	−9.39230	−0.426923
$485$	−11.0718	−0.502744
$486$	32.4449i	1.47173i
$487$	− 40.7846i	− 1.84813i	−0.382239	−	0.924064i	$-0.624847\pi$
$487$	− 40.7846i	− 1.84813i	0.382239	−	0.924064i	$-0.375153\pi$
$488$	8.32051i	0.376652i
$489$	44.2487i	2.00100i
$490$	3.00000	0.135526
$491$	−7.60770	−0.343330	−0.171665	−	0.985155i	$-0.554915\pi$
$491$	−7.60770	−0.343330	−0.171665	+	0.985155i	$0.554915\pi$
$492$	− 14.1962i	− 0.640012i
$493$	−23.1962	−1.04470
$494$	0	0
$495$	9.80385	0.440650
$496$	20.9808i	0.942064i
$497$	6.00000	0.269137
$498$	10.3923	0.465690
$499$	38.9808i	1.74502i	0.488598	+	0.872509i	$0.337509\pi$
$499$	38.9808i	1.74502i	−0.488598	+	0.872509i	$0.662491\pi$
$500$	12.1244i	0.542218i
$501$	− 18.0000i	− 0.804181i
$502$	− 2.78461i	− 0.124283i
$503$	−18.5885	−0.828818	−0.414409	−	0.910091i	$-0.636012\pi$
$503$	−18.5885	−0.828818	−0.414409	+	0.910091i	$0.636012\pi$
$504$	7.73205	0.344413
$505$	− 13.3923i	− 0.595950i
$506$	−10.3923	−0.461994
$507$	0	0
$508$	18.3923	0.816027
$509$	− 13.7321i	− 0.608662i	−0.952566	−	0.304331i	$-0.901567\pi$
$509$	− 13.7321i	− 0.608662i	0.952566	−	0.304331i	$-0.0984330\pi$
$510$	−63.3731	−2.80621
$511$	3.19615	0.141389
$512$	− 8.66025i	− 0.382733i
$513$	− 8.00000i	− 0.353209i
$514$	10.6077i	0.467885i
$515$	− 24.9282i	− 1.09847i
$516$	−0.535898	−0.0235916
$517$	−16.3923	−0.720933
$518$	− 12.1244i	− 0.532714i
$519$	−23.3205	−1.02366
$520$	0	0
$521$	−24.1244	−1.05691	−0.528454	−	0.848962i	$-0.677228\pi$
$521$	−24.1244	−1.05691	−0.528454	+	0.848962i	$0.677228\pi$
$522$	23.1962i	1.01527i
$523$	−29.1769	−1.27582	−0.637909	−	0.770112i	$-0.720200\pi$
$523$	−29.1769	−1.27582	−0.637909	+	0.770112i	$0.720200\pi$
$524$	3.46410	0.151330
$525$	5.46410i	0.238473i
$526$	− 2.19615i	− 0.0957568i
$527$	− 32.4449i	− 1.41332i
$528$	− 17.3205i	− 0.753778i
$529$	−0.607695	−0.0264215
$530$	29.7846	1.29376
$531$	32.4449i	1.40799i
$532$	−2.00000	−0.0867110
$533$	0	0
$534$	61.1769	2.64738
$535$	13.6077i	0.588312i
$536$	10.7321	0.463554
$537$	18.9282	0.816812
$538$	− 8.78461i	− 0.378731i
$539$	− 1.26795i	− 0.0546144i
$540$	6.92820i	0.298142i
$541$	− 14.6077i	− 0.628034i	−0.949417	−	0.314017i	$-0.898325\pi$
$541$	− 14.6077i	− 0.628034i	0.949417	−	0.314017i	$-0.101675\pi$
$542$	10.0526	0.431794
$543$	−15.2679	−0.655210
$544$	40.1769i	1.72257i
$545$	14.5359	0.622649
$546$	0	0
$547$	17.8038	0.761238	0.380619	−	0.924732i	$-0.375711\pi$
$547$	17.8038	0.761238	0.380619	+	0.924732i	$0.375711\pi$
$548$	− 8.07180i	− 0.344810i
$549$	−21.4449	−0.915244
$550$	4.39230	0.187289
$551$	6.00000i	0.255609i
$552$	22.3923i	0.953080i
$553$	16.1962i	0.688730i
$554$	29.4449i	1.25099i
$555$	−33.1244	−1.40605
$556$	10.5885	0.449051
$557$	43.6410i	1.84913i	0.381025	+	0.924565i	$0.375571\pi$
$557$	43.6410i	1.84913i	−0.381025	+	0.924565i	$0.624429\pi$
$558$	−32.4449	−1.37350
$559$	0	0
$560$	−8.66025	−0.365963
$561$	26.7846i	1.13085i
$562$	23.1962	0.978471
$563$	−28.0526	−1.18227	−0.591137	−	0.806571i	$-0.701321\pi$
$563$	−28.0526	−1.18227	−0.591137	+	0.806571i	$0.701321\pi$
$564$	− 35.3205i	− 1.48726i
$565$	− 23.1962i	− 0.975869i
$566$	17.6603i	0.742316i
$567$	− 2.46410i	− 0.103483i
$568$	−10.3923	−0.436051
$569$	−42.9282	−1.79964	−0.899822	−	0.436257i	$-0.856304\pi$
$569$	−42.9282	−1.79964	−0.899822	+	0.436257i	$0.856304\pi$
$570$	16.3923i	0.686598i
$571$	−16.7846	−0.702414	−0.351207	−	0.936298i	$-0.614229\pi$
$571$	−16.7846	−0.702414	−0.351207	+	0.936298i	$0.614229\pi$
$572$	0	0
$573$	12.9282	0.540083
$574$	9.00000i	0.375653i
$575$	−9.46410	−0.394680
$576$	−4.46410	−0.186004
$577$	− 43.1962i	− 1.79828i	−0.437662	−	0.899140i	$-0.644193\pi$
$577$	− 43.1962i	− 1.79828i	0.437662	−	0.899140i	$-0.355807\pi$
$578$	− 74.1051i	− 3.08237i
$579$	13.6603i	0.567701i
$580$	− 5.19615i	− 0.215758i
$581$	−2.19615	−0.0911118
$582$	−30.2487	−1.25385
$583$	− 12.5885i	− 0.521361i
$584$	−5.53590	−0.229077
$585$	0	0
$586$	−1.39230	−0.0575156
$587$	− 16.3923i	− 0.676583i	−0.941041	−	0.338291i	$-0.890151\pi$
$587$	− 16.3923i	− 0.676583i	0.941041	−	0.338291i	$-0.109849\pi$
$588$	2.73205	0.112668
$589$	−8.39230	−0.345799
$590$	− 21.8038i	− 0.897650i
$591$	− 32.7846i	− 1.34858i
$592$	35.0000i	1.43849i
$593$	− 17.4449i	− 0.716375i	−0.933650	−	0.358187i	$-0.883395\pi$
$593$	− 17.4449i	− 0.716375i	0.933650	−	0.358187i	$-0.116605\pi$
$594$	8.78461	0.360437
$595$	13.3923	0.549031
$596$	− 6.46410i	− 0.264780i
$597$	−5.46410	−0.223631
$598$	0	0
$599$	43.8564	1.79192	0.895962	−	0.444131i	$-0.146487\pi$
$599$	43.8564	1.79192	0.895962	+	0.444131i	$0.146487\pi$
$600$	− 9.46410i	− 0.386370i
$601$	−29.9808	−1.22294	−0.611470	−	0.791267i	$-0.709422\pi$
$601$	−29.9808	−1.22294	−0.611470	+	0.791267i	$0.709422\pi$
$602$	0.339746	0.0138470
$603$	27.6603i	1.12641i
$604$	− 2.00000i	− 0.0813788i
$605$	− 16.2679i	− 0.661386i
$606$	− 36.5885i	− 1.48630i
$607$	−14.3923	−0.584166	−0.292083	−	0.956393i	$-0.594348\pi$
$607$	−14.3923	−0.584166	−0.292083	+	0.956393i	$0.594348\pi$
$608$	10.3923	0.421464
$609$	− 8.19615i	− 0.332125i
$610$	14.4115	0.583506
$611$	0	0
$612$	−34.5167	−1.39525
$613$	− 3.39230i	− 0.137014i	−0.997651	−	0.0685070i	$-0.978176\pi$
$613$	− 3.39230i	− 0.137014i	0.997651	−	0.0685070i	$-0.0218235\pi$
$614$	−7.94744	−0.320733
$615$	24.5885	0.991502
$616$	2.19615i	0.0884855i
$617$	− 49.3923i	− 1.98846i	−0.107272	−	0.994230i	$-0.534212\pi$
$617$	− 49.3923i	− 1.98846i	0.107272	−	0.994230i	$-0.465788\pi$
$618$	− 68.1051i	− 2.73959i
$619$	35.3731i	1.42176i	0.703311	+	0.710882i	$0.251704\pi$
$619$	35.3731i	1.42176i	−0.703311	+	0.710882i	$0.748296\pi$
$620$	7.26795	0.291888
$621$	−18.9282	−0.759563
$622$	2.19615i	0.0880577i
$623$	−12.9282	−0.517958
$624$	0	0
$625$	−11.0000	−0.440000
$626$	− 49.8564i	− 1.99266i
$627$	6.92820	0.276686
$628$	−1.19615	−0.0477317
$629$	− 54.1244i	− 2.15808i
$630$	− 13.3923i	− 0.533562i
$631$	− 12.7846i	− 0.508947i	−0.967080	−	0.254474i	$-0.918098\pi$
$631$	− 12.7846i	− 0.508947i	0.967080	−	0.254474i	$-0.0819022\pi$
$632$	− 28.0526i	− 1.11587i
$633$	−4.92820	−0.195878
$634$	11.1962	0.444656
$635$	31.8564i	1.26418i
$636$	27.1244	1.07555
$637$	0	0
$638$	−6.58846	−0.260840
$639$	− 26.7846i	− 1.05958i
$640$	21.0000	0.830098
$641$	−28.8564	−1.13976	−0.569880	−	0.821728i	$-0.693010\pi$
$641$	−28.8564	−1.13976	−0.569880	+	0.821728i	$0.693010\pi$
$642$	37.1769i	1.46726i
$643$	0.784610i	0.0309420i	0.999880	+	0.0154710i	$0.00492477\pi$
$643$	0.784610i	0.0309420i	−0.999880	+	0.0154710i	$0.995075\pi$
$644$	4.73205i	0.186469i
$645$	− 0.928203i	− 0.0365480i
$646$	−26.7846	−1.05383
$647$	−45.0333	−1.77044	−0.885221	−	0.465170i	$-0.845993\pi$
$647$	−45.0333	−1.77044	−0.885221	+	0.465170i	$0.845993\pi$
$648$	4.26795i	0.167661i
$649$	−9.21539	−0.361736
$650$	0	0
$651$	11.4641	0.449314
$652$	− 16.1962i	− 0.634290i
$653$	−37.8564	−1.48144	−0.740718	−	0.671816i	$-0.765514\pi$
$653$	−37.8564	−1.48144	−0.740718	+	0.671816i	$0.765514\pi$
$654$	39.7128	1.55289
$655$	6.00000i	0.234439i
$656$	− 25.9808i	− 1.01438i
$657$	− 14.2679i	− 0.556646i
$658$	22.3923i	0.872943i
$659$	28.3923	1.10601	0.553004	−	0.833179i	$-0.313482\pi$
$659$	28.3923	1.10601	0.553004	+	0.833179i	$0.313482\pi$
$660$	−6.00000	−0.233550
$661$	− 33.1962i	− 1.29118i	−0.763684	−	0.645590i	$-0.776611\pi$
$661$	− 33.1962i	− 1.29118i	0.763684	−	0.645590i	$-0.223389\pi$
$662$	−43.2679	−1.68166
$663$	0	0
$664$	3.80385	0.147618
$665$	− 3.46410i	− 0.134332i
$666$	−54.1244	−2.09728
$667$	14.1962	0.549677
$668$	6.58846i	0.254915i
$669$	27.3205i	1.05627i
$670$	− 18.5885i	− 0.718135i
$671$	− 6.09103i	− 0.235142i
$672$	−14.1962	−0.547628
$673$	44.1769	1.70289	0.851447	−	0.524440i	$-0.175725\pi$
$673$	44.1769	1.70289	0.851447	+	0.524440i	$0.175725\pi$
$674$	19.0526i	0.733877i
$675$	8.00000	0.307920
$676$	0	0
$677$	−23.0718	−0.886721	−0.443361	−	0.896343i	$-0.646214\pi$
$677$	−23.0718	−0.886721	−0.443361	+	0.896343i	$0.646214\pi$
$678$	− 63.3731i	− 2.43383i
$679$	6.39230	0.245314
$680$	−23.1962	−0.889532
$681$	− 15.4641i	− 0.592586i
$682$	− 9.21539i	− 0.352876i
$683$	15.4641i	0.591717i	0.955232	+	0.295859i	$0.0956058\pi$
$683$	15.4641i	0.591717i	−0.955232	+	0.295859i	$0.904394\pi$
$684$	8.92820i	0.341378i
$685$	13.9808	0.534177
$686$	−1.73205	−0.0661300
$687$	− 39.3205i	− 1.50017i
$688$	−0.980762	−0.0373912
$689$	0	0
$690$	38.7846	1.47650
$691$	− 0.392305i	− 0.0149240i	−0.999972	−	0.00746199i	$-0.997625\pi$
$691$	− 0.392305i	− 0.0149240i	0.999972	−	0.00746199i	$-0.00237525\pi$
$692$	8.53590	0.324486
$693$	−5.66025	−0.215015
$694$	− 12.5885i	− 0.477851i
$695$	18.3397i	0.695666i
$696$	14.1962i	0.538104i
$697$	40.1769i	1.52181i
$698$	−42.9282	−1.62486
$699$	5.07180	0.191833
$700$	− 2.00000i	− 0.0755929i
$701$	−20.7846	−0.785024	−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846	−0.785024	−0.392512	+	0.919747i	$0.628394\pi$
$702$	0	0
$703$	−14.0000	−0.528020
$704$	− 1.26795i	− 0.0477876i
$705$	61.1769	2.30406
$706$	−35.7846	−1.34677
$707$	7.73205i	0.290794i
$708$	− 19.8564i	− 0.746249i
$709$	30.1769i	1.13332i	0.823952	+	0.566659i	$0.191764\pi$
$709$	30.1769i	1.13332i	−0.823952	+	0.566659i	$0.808236\pi$
$710$	18.0000i	0.675528i
$711$	72.3013	2.71151
$712$	22.3923	0.839187
$713$	19.8564i	0.743628i
$714$	36.5885	1.36929
$715$	0	0
$716$	−6.92820	−0.258919
$717$	43.1769i	1.61247i
$718$	32.7846	1.22351
$719$	7.26795	0.271049	0.135524	−	0.990774i	$-0.456728\pi$
$719$	7.26795	0.271049	0.135524	+	0.990774i	$0.456728\pi$
$720$	38.6603i	1.44078i
$721$	14.3923i	0.535997i
$722$	− 25.9808i	− 0.966904i
$723$	− 57.9090i	− 2.15366i
$724$	5.58846	0.207693
$725$	−6.00000	−0.222834
$726$	− 44.4449i	− 1.64950i
$727$	41.1769	1.52717	0.763584	−	0.645709i	$-0.223438\pi$
$727$	41.1769	1.52717	0.763584	+	0.645709i	$0.223438\pi$
$728$	0	0
$729$	−43.7846	−1.62165
$730$	9.58846i	0.354885i
$731$	1.51666	0.0560957
$732$	13.1244	0.485090
$733$	− 23.5885i	− 0.871260i	−0.900126	−	0.435630i	$-0.856526\pi$
$733$	− 23.5885i	− 0.871260i	0.900126	−	0.435630i	$-0.143474\pi$
$734$	− 7.26795i	− 0.268265i
$735$	4.73205i	0.174544i
$736$	− 24.5885i	− 0.906343i
$737$	−7.85641	−0.289394
$738$	40.1769	1.47893
$739$	40.7846i	1.50029i	0.661276	+	0.750143i	$0.270015\pi$
$739$	40.7846i	1.50029i	−0.661276	+	0.750143i	$0.729985\pi$
$740$	12.1244	0.445700
$741$	0	0
$742$	−17.1962	−0.631291
$743$	7.60770i	0.279099i	0.990215	+	0.139550i	$0.0445655\pi$
$743$	7.60770i	0.279099i	−0.990215	+	0.139550i	$0.955435\pi$
$744$	−19.8564	−0.727971
$745$	11.1962	0.410195
$746$	19.7321i	0.722442i
$747$	9.80385i	0.358704i
$748$	− 9.80385i	− 0.358464i
$749$	− 7.85641i	− 0.287067i
$750$	−57.3731	−2.09497
$751$	−35.8038	−1.30650	−0.653250	−	0.757142i	$-0.726595\pi$
$751$	−35.8038	−1.30650	−0.653250	+	0.757142i	$0.726595\pi$
$752$	− 64.6410i	− 2.35722i
$753$	4.39230	0.160064
$754$	0	0
$755$	3.46410	0.126072
$756$	− 4.00000i	− 0.145479i
$757$	−16.0000	−0.581530	−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000	−0.581530	−0.290765	+	0.956795i	$0.593910\pi$
$758$	−46.0526	−1.67270
$759$	− 16.3923i	− 0.595003i
$760$	6.00000i	0.217643i
$761$	41.3205i	1.49787i	0.662645	+	0.748934i	$0.269434\pi$
$761$	41.3205i	1.49787i	−0.662645	+	0.748934i	$0.730566\pi$
$762$	87.0333i	3.15288i
$763$	−8.39230	−0.303822
$764$	−4.73205	−0.171200
$765$	− 59.7846i	− 2.16152i
$766$	20.1962	0.729717
$767$	0	0
$768$	51.9090	1.87310
$769$	− 15.1769i	− 0.547294i	−0.961830	−	0.273647i	$-0.911770\pi$
$769$	− 15.1769i	− 0.547294i	0.961830	−	0.273647i	$-0.0882299\pi$
$770$	3.80385	0.137081
$771$	−16.7321	−0.602590
$772$	− 5.00000i	− 0.179954i
$773$	12.9282i	0.464995i	0.972597	+	0.232498i	$0.0746898\pi$
$773$	12.9282i	0.464995i	−0.972597	+	0.232498i	$0.925310\pi$
$774$	− 1.51666i	− 0.0545152i
$775$	− 8.39230i	− 0.301460i
$776$	−11.0718	−0.397454
$777$	19.1244	0.686082
$778$	− 40.7654i	− 1.46151i
$779$	10.3923	0.372343
$780$	0	0
$781$	7.60770	0.272225
$782$	63.3731i	2.26622i
$783$	−12.0000	−0.428845
$784$	5.00000	0.178571
$785$	− 2.07180i	− 0.0739456i
$786$	16.3923i	0.584694i
$787$	12.9808i	0.462714i	0.972869	+	0.231357i	$0.0743166\pi$
$787$	12.9808i	0.462714i	−0.972869	+	0.231357i	$0.925683\pi$
$788$	12.0000i	0.427482i
$789$	3.46410	0.123325
$790$	−48.5885	−1.72870
$791$	13.3923i	0.476176i
$792$	9.80385	0.348365
$793$	0	0
$794$	−32.5359	−1.15466
$795$	46.9808i	1.66624i
$796$	2.00000	0.0708881
$797$	34.3923	1.21824	0.609119	−	0.793079i	$-0.291523\pi$
$797$	34.3923	1.21824	0.609119	+	0.793079i	$0.291523\pi$
$798$	− 9.46410i	− 0.335026i
$799$	99.9615i	3.53638i
$800$	10.3923i	0.367423i
$801$	57.7128i	2.03918i
$802$	−18.8038	−0.663987
$803$	4.05256	0.143012
$804$	− 16.9282i	− 0.597012i
$805$	−8.19615	−0.288876
$806$	0	0
$807$	13.8564	0.487769
$808$	− 13.3923i	− 0.471140i
$809$	2.07180	0.0728405	0.0364202	−	0.999337i	$-0.488405\pi$
$809$	2.07180	0.0728405	0.0364202	+	0.999337i	$0.488405\pi$
$810$	7.39230	0.259739
$811$	16.5885i	0.582500i	0.956647	+	0.291250i	$0.0940711\pi$
$811$	16.5885i	0.582500i	−0.956647	+	0.291250i	$0.905929\pi$
$812$	3.00000i	0.105279i
$813$	15.8564i	0.556108i
$814$	− 15.3731i	− 0.538826i
$815$	28.0526	0.982638
$816$	−105.622	−3.69750
$817$	− 0.392305i	− 0.0137250i
$818$	29.1051	1.01764
$819$	0	0
$820$	−9.00000	−0.314294
$821$	− 4.14359i	− 0.144612i	−0.997382	−	0.0723062i	$-0.976964\pi$
$821$	− 4.14359i	− 0.144612i	0.997382	−	0.0723062i	$-0.0230359\pi$
$822$	38.1962	1.33224
$823$	41.1769	1.43534	0.717669	−	0.696385i	$-0.245209\pi$
$823$	41.1769	1.43534	0.717669	+	0.696385i	$0.245209\pi$
$824$	− 24.9282i	− 0.868415i
$825$	6.92820i	0.241209i
$826$	12.5885i	0.438008i
$827$	− 16.9808i	− 0.590479i	−0.955423	−	0.295239i	$-0.904601\pi$
$827$	− 16.9808i	− 0.590479i	0.955423	−	0.295239i	$-0.0953994\pi$
$828$	21.1244	0.734122
$829$	0.411543	0.0142935	0.00714673	−	0.999974i	$-0.497725\pi$
$829$	0.411543	0.0142935	0.00714673	+	0.999974i	$0.497725\pi$
$830$	− 6.58846i	− 0.228689i
$831$	−46.4449	−1.61115
$832$	0	0
$833$	−7.73205	−0.267900
$834$	50.1051i	1.73500i
$835$	−11.4115	−0.394913
$836$	−2.53590	−0.0877059
$837$	− 16.7846i	− 0.580161i
$838$	55.7654i	1.92638i
$839$	− 18.0000i	− 0.621429i	−0.950503	−	0.310715i	$-0.899432\pi$
$839$	− 18.0000i	− 0.621429i	0.950503	−	0.310715i	$-0.100568\pi$
$840$	− 8.19615i	− 0.282794i
$841$	−20.0000	−0.689655
$842$	55.7321	1.92065
$843$	36.5885i	1.26017i
$844$	1.80385	0.0620910
$845$	0	0
$846$	99.9615	3.43675
$847$	9.39230i	0.322723i
$848$	49.6410	1.70468
$849$	−27.8564	−0.956029
$850$	− 26.7846i	− 0.918705i
$851$	33.1244i	1.13549i
$852$	16.3923i	0.561591i
$853$	5.58846i	0.191345i	0.995413	+	0.0956726i	$0.0305002\pi$
$853$	5.58846i	0.191345i	−0.995413	+	0.0956726i	$0.969500\pi$
$854$	−8.32051	−0.284722
$855$	−15.4641	−0.528861
$856$	13.6077i	0.465101i
$857$	30.1244	1.02903	0.514514	−	0.857482i	$-0.327972\pi$
$857$	30.1244	1.02903	0.514514	+	0.857482i	$0.327972\pi$
$858$	0	0
$859$	−7.80385	−0.266264	−0.133132	−	0.991098i	$-0.542503\pi$
$859$	−7.80385	−0.266264	−0.133132	+	0.991098i	$0.542503\pi$
$860$	0.339746i	0.0115852i
$861$	−14.1962	−0.483804
$862$	−1.17691	−0.0400859
$863$	− 7.51666i	− 0.255870i	−0.991783	−	0.127935i	$-0.959165\pi$
$863$	− 7.51666i	− 0.255870i	0.991783	−	0.127935i	$-0.0408349\pi$
$864$	20.7846i	0.707107i
$865$	14.7846i	0.502692i
$866$	− 23.5359i	− 0.799782i
$867$	116.890	3.96978
$868$	−4.19615	−0.142427
$869$	20.5359i	0.696633i
$870$	24.5885	0.833627
$871$	0	0
$872$	14.5359	0.492248
$873$	− 28.5359i	− 0.965794i
$874$	16.3923	0.554478
$875$	12.1244	0.409878
$876$	8.73205i	0.295029i
$877$	− 19.7846i	− 0.668079i	−0.942559	−	0.334039i	$-0.891588\pi$
$877$	− 19.7846i	− 0.668079i	0.942559	−	0.334039i	$-0.108412\pi$
$878$	25.2679i	0.852752i
$879$	− 2.19615i	− 0.0740744i
$880$	−10.9808	−0.370161
$881$	8.41154	0.283392	0.141696	−	0.989910i	$-0.454744\pi$
$881$	8.41154	0.283392	0.141696	+	0.989910i	$0.454744\pi$
$882$	7.73205i	0.260352i
$883$	47.7654	1.60743	0.803716	−	0.595013i	$-0.202853\pi$
$883$	47.7654	1.60743	0.803716	+	0.595013i	$0.202853\pi$
$884$	0	0
$885$	34.3923	1.15608
$886$	− 40.3923i	− 1.35701i
$887$	11.3205	0.380105	0.190053	−	0.981774i	$-0.439134\pi$
$887$	11.3205	0.380105	0.190053	+	0.981774i	$0.439134\pi$
$888$	−33.1244	−1.11158
$889$	− 18.3923i	− 0.616858i
$890$	− 38.7846i	− 1.30006i
$891$	− 3.12436i	− 0.104670i
$892$	− 10.0000i	− 0.334825i
$893$	25.8564	0.865252
$894$	30.5885	1.02303
$895$	− 12.0000i	− 0.401116i
$896$	−12.1244	−0.405046
$897$	0	0
$898$	−20.7846	−0.693591
$899$	12.5885i	0.419849i
$900$	−8.92820	−0.297607
$901$	−76.7654	−2.55743
$902$	11.4115i	0.379963i
$903$	0.535898i	0.0178336i
$904$	− 23.1962i	− 0.771493i
$905$	9.67949i	0.321757i
$906$	9.46410	0.314424
$907$	16.5885	0.550811	0.275405	−	0.961328i	$-0.411188\pi$
$907$	16.5885	0.550811	0.275405	+	0.961328i	$0.411188\pi$
$908$	5.66025i	0.187842i
$909$	34.5167	1.14485
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	27.3205i	0.904672i
$913$	−2.78461	−0.0921571
$914$	−19.0526	−0.630203
$915$	22.7321i	0.751498i
$916$	14.3923i	0.475535i
$917$	− 3.46410i	− 0.114395i
$918$	− 53.5692i	− 1.76805i
$919$	−39.5692	−1.30527	−0.652634	−	0.757673i	$-0.726336\pi$
$919$	−39.5692	−1.30527	−0.652634	+	0.757673i	$0.726336\pi$
$920$	14.1962	0.468033
$921$	− 12.5359i	− 0.413072i
$922$	27.0000	0.889198
$923$	0	0
$924$	3.46410	0.113961
$925$	− 14.0000i	− 0.460317i
$926$	−7.94744	−0.261169
$927$	64.2487	2.11020
$928$	− 15.5885i	− 0.511716i
$929$	− 52.5167i	− 1.72302i	−0.507744	−	0.861508i	$-0.669520\pi$
$929$	− 52.5167i	− 1.72302i	0.507744	−	0.861508i	$-0.330480\pi$
$930$	34.3923i	1.12777i
$931$	2.00000i	0.0655474i
$932$	−1.85641	−0.0608086
$933$	−3.46410	−0.113410
$934$	44.1962i	1.44614i
$935$	16.9808	0.555330
$936$	0	0
$937$	−51.1962	−1.67251	−0.836253	−	0.548344i	$-0.815258\pi$
$937$	−51.1962	−1.67251	−0.836253	+	0.548344i	$0.815258\pi$
$938$	10.7321i	0.350414i
$939$	78.6410	2.56635
$940$	−22.3923	−0.730356
$941$	28.1436i	0.917455i	0.888577	+	0.458727i	$0.151695\pi$
$941$	28.1436i	0.917455i	−0.888577	+	0.458727i	$0.848305\pi$
$942$	− 5.66025i	− 0.184421i
$943$	− 24.5885i	− 0.800710i
$944$	− 36.3397i	− 1.18276i
$945$	6.92820	0.225374
$946$	0.430781	0.0140059
$947$	− 7.26795i	− 0.236177i	−0.993003	−	0.118088i	$-0.962323\pi$
$947$	− 7.26795i	− 0.236177i	0.993003	−	0.118088i	$-0.0376766\pi$
$948$	−44.2487	−1.43713
$949$	0	0
$950$	−6.92820	−0.224781
$951$	17.6603i	0.572673i
$952$	13.3923	0.434047
$953$	25.1769	0.815560	0.407780	−	0.913080i	$-0.366303\pi$
$953$	25.1769	0.815560	0.407780	+	0.913080i	$0.366303\pi$
$954$	76.7654i	2.48537i
$955$	− 8.19615i	− 0.265221i
$956$	− 15.8038i	− 0.511133i
$957$	− 10.3923i	− 0.335936i
$958$	2.19615	0.0709545
$959$	−8.07180	−0.260652
$960$	4.73205i	0.152726i
$961$	13.3923	0.432010
$962$	0	0
$963$	−35.0718	−1.13017
$964$	21.1962i	0.682682i
$965$	8.66025	0.278783
$966$	−22.3923	−0.720461
$967$	− 54.9808i	− 1.76806i	−0.467428	−	0.884031i	$-0.654819\pi$
$967$	− 54.9808i	− 1.76806i	0.467428	−	0.884031i	$-0.345181\pi$
$968$	− 16.2679i	− 0.522872i
$969$	− 42.2487i	− 1.35722i
$970$	19.1769i	0.615734i
$971$	−52.6410	−1.68933	−0.844665	−	0.535295i	$-0.820201\pi$
$971$	−52.6410	−1.68933	−0.844665	+	0.535295i	$0.820201\pi$
$972$	18.7321	0.600831
$973$	− 10.5885i	− 0.339450i
$974$	−70.6410	−2.26348
$975$	0	0
$976$	24.0192	0.768837
$977$	− 31.6410i	− 1.01229i	−0.862450	−	0.506143i	$-0.831071\pi$
$977$	− 31.6410i	− 1.01229i	0.862450	−	0.506143i	$-0.168929\pi$
$978$	76.6410	2.45071
$979$	−16.3923	−0.523900
$980$	− 1.73205i	− 0.0553283i
$981$	37.4641i	1.19614i
$982$	13.1769i	0.420492i
$983$	− 17.3205i	− 0.552438i	−0.961095	−	0.276219i	$-0.910918\pi$
$983$	− 17.3205i	− 0.552438i	0.961095	−	0.276219i	$-0.0890816\pi$
$984$	24.5885	0.783851
$985$	−20.7846	−0.662253
$986$	40.1769i	1.27949i
$987$	−35.3205	−1.12426
$988$	0	0
$989$	−0.928203	−0.0295151
$990$	− 16.9808i	− 0.539684i
$991$	18.9808	0.602944	0.301472	−	0.953475i	$-0.402522\pi$
$991$	18.9808	0.602944	0.301472	+	0.953475i	$0.402522\pi$
$992$	21.8038	0.692273
$993$	− 68.2487i	− 2.16581i
$994$	− 10.3923i	− 0.329624i
$995$	3.46410i	0.109819i
$996$	− 6.00000i	− 0.190117i
$997$	−4.80385	−0.152139	−0.0760697	−	0.997103i	$-0.524237\pi$
$997$	−4.80385	−0.152139	−0.0760697	+	0.997103i	$0.524237\pi$
$998$	67.5167	2.13720
$999$	− 28.0000i	− 0.885881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.e.337.2		4
13.5	odd	4		1183.2.a.e.1.1		2
13.7	odd	12		91.2.f.b.29.1	yes	4
13.8	odd	4		1183.2.a.f.1.2		2
13.11	odd	12		91.2.f.b.22.1	✓	4
13.12	even	2	inner	1183.2.c.e.337.4		4
39.11	even	12		819.2.o.b.568.2		4
39.20	even	12		819.2.o.b.757.2		4
52.7	even	12		1456.2.s.o.1121.2		4
52.11	even	12		1456.2.s.o.113.2		4
91.11	odd	12		637.2.g.e.373.1		4
91.20	even	12		637.2.f.d.393.1		4
91.24	even	12		637.2.g.d.373.1		4
91.33	even	12		637.2.g.d.263.1		4
91.34	even	4		8281.2.a.r.1.2		2
91.37	odd	12		637.2.h.d.165.2		4
91.46	odd	12		637.2.h.d.471.2		4
91.59	even	12		637.2.h.e.471.2		4
91.72	odd	12		637.2.g.e.263.1		4
91.76	even	12		637.2.f.d.295.1		4
91.83	even	4		8281.2.a.t.1.1		2
91.89	even	12		637.2.h.e.165.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.b.22.1	✓	4	13.11	odd	12
91.2.f.b.29.1	yes	4	13.7	odd	12
637.2.f.d.295.1		4	91.76	even	12
637.2.f.d.393.1		4	91.20	even	12
637.2.g.d.263.1		4	91.33	even	12
637.2.g.d.373.1		4	91.24	even	12
637.2.g.e.263.1		4	91.72	odd	12
637.2.g.e.373.1		4	91.11	odd	12
637.2.h.d.165.2		4	91.37	odd	12
637.2.h.d.471.2		4	91.46	odd	12
637.2.h.e.165.2		4	91.89	even	12
637.2.h.e.471.2		4	91.59	even	12
819.2.o.b.568.2		4	39.11	even	12
819.2.o.b.757.2		4	39.20	even	12
1183.2.a.e.1.1		2	13.5	odd	4
1183.2.a.f.1.2		2	13.8	odd	4
1183.2.c.e.337.2		4	1.1	even	1	trivial
1183.2.c.e.337.4		4	13.12	even	2	inner
1456.2.s.o.113.2		4	52.11	even	12
1456.2.s.o.1121.2		4	52.7	even	12
8281.2.a.r.1.2		2	91.34	even	4
8281.2.a.t.1.1		2	91.83	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{2} +2.73205 q^{3} -1.00000 q^{4} -1.73205i q^{5} -4.73205i q^{6} +1.00000i q^{7} -1.73205i q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q-1.73205i q^{2} +2.73205 q^{3} -1.00000 q^{4} -1.73205i q^{5} -4.73205i q^{6} +1.00000i q^{7} -1.73205i q^{8} +4.46410 q^{9} -3.00000 q^{10} +1.26795i q^{11} -2.73205 q^{12} +1.73205 q^{14} -4.73205i q^{15} -5.00000 q^{16} +7.73205 q^{17} -7.73205i q^{18} -2.00000i q^{19} +1.73205i q^{20} +2.73205i q^{21} +2.19615 q^{22} -4.73205 q^{23} -4.73205i q^{24} +2.00000 q^{25} +4.00000 q^{27} -1.00000i q^{28} -3.00000 q^{29} -8.19615 q^{30} -4.19615i q^{31} +5.19615i q^{32} +3.46410i q^{33} -13.3923i q^{34} +1.73205 q^{35} -4.46410 q^{36} -7.00000i q^{37} -3.46410 q^{38} -3.00000 q^{40} +5.19615i q^{41} +4.73205 q^{42} +0.196152 q^{43} -1.26795i q^{44} -7.73205i q^{45} +8.19615i q^{46} +12.9282i q^{47} -13.6603 q^{48} -1.00000 q^{49} -3.46410i q^{50} +21.1244 q^{51} -9.92820 q^{53} -6.92820i q^{54} +2.19615 q^{55} +1.73205 q^{56} -5.46410i q^{57} +5.19615i q^{58} +7.26795i q^{59} +4.73205i q^{60} -4.80385 q^{61} -7.26795 q^{62} +4.46410i q^{63} -1.00000 q^{64} +6.00000 q^{66} +6.19615i q^{67} -7.73205 q^{68} -12.9282 q^{69} -3.00000i q^{70} -6.00000i q^{71} -7.73205i q^{72} -3.19615i q^{73} -12.1244 q^{74} +5.46410 q^{75} +2.00000i q^{76} -1.26795 q^{77} +16.1962 q^{79} +8.66025i q^{80} -2.46410 q^{81} +9.00000 q^{82} +2.19615i q^{83} -2.73205i q^{84} -13.3923i q^{85} -0.339746i q^{86} -8.19615 q^{87} +2.19615 q^{88} +12.9282i q^{89} -13.3923 q^{90} +4.73205 q^{92} -11.4641i q^{93} +22.3923 q^{94} -3.46410 q^{95} +14.1962i q^{96} -6.39230i q^{97} +1.73205i q^{98} +5.66025i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9} - 12 q^{10} - 4 q^{12} - 20 q^{16} + 24 q^{17} - 12 q^{22} - 12 q^{23} + 8 q^{25} + 16 q^{27} - 12 q^{29} - 12 q^{30} - 4 q^{36} - 12 q^{40} + 12 q^{42} - 20 q^{43} - 20 q^{48} - 4 q^{49} + 36 q^{51} - 12 q^{53} - 12 q^{55} - 40 q^{61} - 36 q^{62} - 4 q^{64} + 24 q^{66} - 24 q^{68} - 24 q^{69} + 8 q^{75} - 12 q^{77} + 44 q^{79} + 4 q^{81} + 36 q^{82} - 12 q^{87} - 12 q^{88} - 12 q^{90} + 12 q^{92} + 48 q^{94}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9 - 12 * q^10 - 4 * q^12 - 20 * q^16 + 24 * q^17 - 12 * q^22 - 12 * q^23 + 8 * q^25 + 16 * q^27 - 12 * q^29 - 12 * q^30 - 4 * q^36 - 12 * q^40 + 12 * q^42 - 20 * q^43 - 20 * q^48 - 4 * q^49 + 36 * q^51 - 12 * q^53 - 12 * q^55 - 40 * q^61 - 36 * q^62 - 4 * q^64 + 24 * q^66 - 24 * q^68 - 24 * q^69 + 8 * q^75 - 12 * q^77 + 44 * q^79 + 4 * q^81 + 36 * q^82 - 12 * q^87 - 12 * q^88 - 12 * q^90 + 12 * q^92 + 48 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more