LMFDB - Embedded newform 1183.2.c.e.337.3

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			337.3
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.e.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205i q^{2} -0.732051 q^{3} -1.00000 q^{4} +1.73205i q^{5} -1.26795i q^{6} +1.00000i q^{7} +1.73205i q^{8} -2.46410 q^{9} +O(q^{10})$	\(q+1.73205i q^{2} -0.732051 q^{3} -1.00000 q^{4} +1.73205i q^{5} -1.26795i q^{6} +1.00000i q^{7} +1.73205i q^{8} -2.46410 q^{9} -3.00000 q^{10} +4.73205i q^{11} +0.732051 q^{12} -1.73205 q^{14} -1.26795i q^{15} -5.00000 q^{16} +4.26795 q^{17} -4.26795i q^{18} -2.00000i q^{19} -1.73205i q^{20} -0.732051i q^{21} -8.19615 q^{22} -1.26795 q^{23} -1.26795i q^{24} +2.00000 q^{25} +4.00000 q^{27} -1.00000i q^{28} -3.00000 q^{29} +2.19615 q^{30} +6.19615i q^{31} -5.19615i q^{32} -3.46410i q^{33} +7.39230i q^{34} -1.73205 q^{35} +2.46410 q^{36} -7.00000i q^{37} +3.46410 q^{38} -3.00000 q^{40} -5.19615i q^{41} +1.26795 q^{42} -10.1962 q^{43} -4.73205i q^{44} -4.26795i q^{45} -2.19615i q^{46} -0.928203i q^{47} +3.66025 q^{48} -1.00000 q^{49} +3.46410i q^{50} -3.12436 q^{51} +3.92820 q^{53} +6.92820i q^{54} -8.19615 q^{55} -1.73205 q^{56} +1.46410i q^{57} -5.19615i q^{58} +10.7321i q^{59} +1.26795i q^{60} -15.1962 q^{61} -10.7321 q^{62} -2.46410i q^{63} -1.00000 q^{64} +6.00000 q^{66} -4.19615i q^{67} -4.26795 q^{68} +0.928203 q^{69} -3.00000i q^{70} -6.00000i q^{71} -4.26795i q^{72} +7.19615i q^{73} +12.1244 q^{74} -1.46410 q^{75} +2.00000i q^{76} -4.73205 q^{77} +5.80385 q^{79} -8.66025i q^{80} +4.46410 q^{81} +9.00000 q^{82} -8.19615i q^{83} +0.732051i q^{84} +7.39230i q^{85} -17.6603i q^{86} +2.19615 q^{87} -8.19615 q^{88} -0.928203i q^{89} +7.39230 q^{90} +1.26795 q^{92} -4.53590i q^{93} +1.60770 q^{94} +3.46410 q^{95} +3.80385i q^{96} +14.3923i q^{97} -1.73205i q^{98} -11.6603i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.209785\pi$
$2$	1.73205i	1.22474i	−0.790569	+	0.612372i	$0.790215\pi$
$3$	−0.732051	−0.422650	−0.211325	−	0.977416i	$-0.567778\pi$
$3$	−0.732051	−0.422650	−0.211325	+	0.977416i	$0.567778\pi$
$4$	−1.00000	−0.500000
$5$	1.73205i	0.774597i	0.921954	+	0.387298i	$0.126592\pi$
$5$	1.73205i	0.774597i	−0.921954	+	0.387298i	$0.873408\pi$
$6$	− 1.26795i	− 0.517638i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	1.73205i	0.612372i
$9$	−2.46410	−0.821367
$10$	−3.00000	−0.948683
$11$	4.73205i	1.42677i	0.700774	+	0.713384i	$0.252838\pi$
$11$	4.73205i	1.42677i	−0.700774	+	0.713384i	$0.747162\pi$
$12$	0.732051	0.211325
$13$	0	0
$13$	0	0
$14$	−1.73205	−0.462910
$15$	− 1.26795i	− 0.327383i
$16$	−5.00000	−1.25000
$17$	4.26795	1.03513	0.517565	−	0.855644i	$-0.326839\pi$
$17$	4.26795	1.03513	0.517565	+	0.855644i	$0.326839\pi$
$18$	− 4.26795i	− 1.00597i
$19$	− 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
$21$	− 0.732051i	− 0.159747i
$22$	−8.19615	−1.74743
$23$	−1.26795	−0.264386	−0.132193	−	0.991224i	$-0.542202\pi$
$23$	−1.26795	−0.264386	−0.132193	+	0.991224i	$0.542202\pi$
$24$	− 1.26795i	− 0.258819i
$25$	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	$0.589851\pi$
$30$	2.19615	0.400961
$31$	6.19615i	1.11286i	0.830894	+	0.556431i	$0.187830\pi$
$31$	6.19615i	1.11286i	−0.830894	+	0.556431i	$0.812170\pi$
$32$	− 5.19615i	− 0.918559i
$33$	− 3.46410i	− 0.603023i
$34$	7.39230i	1.26777i
$35$	−1.73205	−0.292770
$36$	2.46410	0.410684
$37$	− 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	$-0.867010\pi$
$41$	− 5.19615i	− 0.811503i	0.913984	−	0.405751i	$-0.132990\pi$
$42$	1.26795	0.195649
$43$	−10.1962	−1.55490	−0.777449	−	0.628946i	$-0.783487\pi$
$43$	−10.1962	−1.55490	−0.777449	+	0.628946i	$0.783487\pi$
$44$	− 4.73205i	− 0.713384i
$45$	− 4.26795i	− 0.636228i
$46$	− 2.19615i	− 0.323805i
$47$	− 0.928203i	− 0.135392i	−0.997706	−	0.0676962i	$-0.978435\pi$
$47$	− 0.928203i	− 0.135392i	0.997706	−	0.0676962i	$-0.0215649\pi$
$48$	3.66025	0.528312
$49$	−1.00000	−0.142857
$50$	3.46410i	0.489898i
$51$	−3.12436	−0.437497
$52$	0	0
$53$	3.92820	0.539580	0.269790	−	0.962919i	$-0.413046\pi$
$53$	3.92820	0.539580	0.269790	+	0.962919i	$0.413046\pi$
$54$	6.92820i	0.942809i
$55$	−8.19615	−1.10517
$56$	−1.73205	−0.231455
$57$	1.46410i	0.193925i
$58$	− 5.19615i	− 0.682288i
$59$	10.7321i	1.39719i	0.715515	+	0.698597i	$0.246192\pi$
$59$	10.7321i	1.39719i	−0.715515	+	0.698597i	$0.753808\pi$
$60$	1.26795i	0.163692i
$61$	−15.1962	−1.94567	−0.972834	−	0.231504i	$-0.925635\pi$
$61$	−15.1962	−1.94567	−0.972834	+	0.231504i	$0.925635\pi$
$62$	−10.7321	−1.36297
$63$	− 2.46410i	− 0.310448i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	6.00000	0.738549
$67$	− 4.19615i	− 0.512642i	−0.966592	−	0.256321i	$-0.917490\pi$
$67$	− 4.19615i	− 0.512642i	0.966592	−	0.256321i	$-0.0825104\pi$
$68$	−4.26795	−0.517565
$69$	0.928203	0.111743
$70$	− 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	$-0.115871\pi$
$72$	− 4.26795i	− 0.502983i
$73$	7.19615i	0.842246i	0.907004	+	0.421123i	$0.138364\pi$
$73$	7.19615i	0.842246i	−0.907004	+	0.421123i	$0.861636\pi$
$74$	12.1244	1.40943
$75$	−1.46410	−0.169060
$76$	2.00000i	0.229416i
$77$	−4.73205	−0.539267
$78$	0	0
$79$	5.80385	0.652984	0.326492	−	0.945200i	$-0.394133\pi$
$79$	5.80385	0.652984	0.326492	+	0.945200i	$0.394133\pi$
$80$	− 8.66025i	− 0.968246i
$81$	4.46410	0.496011
$82$	9.00000	0.993884
$83$	− 8.19615i	− 0.899645i	−0.893118	−	0.449822i	$-0.851487\pi$
$83$	− 8.19615i	− 0.899645i	0.893118	−	0.449822i	$-0.148513\pi$
$84$	0.732051i	0.0798733i
$85$	7.39230i	0.801808i
$86$	− 17.6603i	− 1.90435i
$87$	2.19615	0.235452
$88$	−8.19615	−0.873713
$89$	− 0.928203i	− 0.0983893i	−0.998789	−	0.0491947i	$-0.984335\pi$
$89$	− 0.928203i	− 0.0983893i	0.998789	−	0.0491947i	$-0.0156655\pi$
$90$	7.39230	0.779217
$91$	0	0
$92$	1.26795	0.132193
$93$	− 4.53590i	− 0.470351i
$94$	1.60770	0.165821
$95$	3.46410	0.355409
$96$	3.80385i	0.388229i
$97$	14.3923i	1.46132i	0.682743	+	0.730659i	$0.260787\pi$
$97$	14.3923i	1.46132i	−0.682743	+	0.730659i	$0.739213\pi$
$98$	− 1.73205i	− 0.174964i
$99$	− 11.6603i	− 1.17190i
$100$	−2.00000	−0.200000
$101$	4.26795	0.424677	0.212338	−	0.977196i	$-0.431892\pi$
$101$	4.26795	0.424677	0.212338	+	0.977196i	$0.431892\pi$
$102$	− 5.41154i	− 0.535823i
$103$	−6.39230	−0.629853	−0.314926	−	0.949116i	$-0.601980\pi$
$103$	−6.39230	−0.629853	−0.314926	+	0.949116i	$0.601980\pi$
$104$	0	0
$105$	1.26795	0.123739
$106$	6.80385i	0.660848i
$107$	19.8564	1.91959	0.959796	−	0.280700i	$-0.0905665\pi$
$107$	19.8564	1.91959	0.959796	+	0.280700i	$0.0905665\pi$
$108$	−4.00000	−0.384900
$109$	− 12.3923i	− 1.18697i	−0.804846	−	0.593484i	$-0.797752\pi$
$109$	− 12.3923i	− 1.18697i	0.804846	−	0.593484i	$-0.202248\pi$
$110$	− 14.1962i	− 1.35355i
$111$	5.12436i	0.486382i
$112$	− 5.00000i	− 0.472456i
$113$	−7.39230	−0.695410	−0.347705	−	0.937604i	$-0.613039\pi$
$113$	−7.39230	−0.695410	−0.347705	+	0.937604i	$0.613039\pi$
$114$	−2.53590	−0.237509
$115$	− 2.19615i	− 0.204792i
$116$	3.00000	0.278543
$117$	0	0
$118$	−18.5885	−1.71121
$119$	4.26795i	0.391242i
$120$	2.19615	0.200480
$121$	−11.3923	−1.03566
$122$	− 26.3205i	− 2.38295i
$123$	3.80385i	0.342981i
$124$	− 6.19615i	− 0.556431i
$125$	12.1244i	1.08444i
$126$	4.26795	0.380219
$127$	2.39230	0.212283	0.106141	−	0.994351i	$-0.466150\pi$
$127$	2.39230	0.212283	0.106141	+	0.994351i	$0.466150\pi$
$128$	− 12.1244i	− 1.07165i
$129$	7.46410	0.657178
$130$	0	0
$131$	3.46410	0.302660	0.151330	−	0.988483i	$-0.451644\pi$
$131$	3.46410	0.302660	0.151330	+	0.988483i	$0.451644\pi$
$132$	3.46410i	0.301511i
$133$	2.00000	0.173422
$134$	7.26795	0.627855
$135$	6.92820i	0.596285i
$136$	7.39230i	0.633885i
$137$	21.9282i	1.87345i	0.350062	+	0.936726i	$0.386160\pi$
$137$	21.9282i	1.87345i	−0.350062	+	0.936726i	$0.613840\pi$
$138$	1.60770i	0.136856i
$139$	20.5885	1.74629	0.873145	−	0.487460i	$-0.162077\pi$
$139$	20.5885	1.74629	0.873145	+	0.487460i	$0.162077\pi$
$140$	1.73205	0.146385
$141$	0.679492i	0.0572235i
$142$	10.3923	0.872103
$143$	0	0
$144$	12.3205	1.02671
$145$	− 5.19615i	− 0.431517i
$146$	−12.4641	−1.03154
$147$	0.732051	0.0603785
$148$	7.00000i	0.575396i
$149$	− 0.464102i	− 0.0380207i	−0.999819	−	0.0190103i	$-0.993948\pi$
$149$	− 0.464102i	− 0.0380207i	0.999819	−	0.0190103i	$-0.00605154\pi$
$150$	− 2.53590i	− 0.207055i
$151$	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
$153$	−10.5167	−0.850222
$154$	− 8.19615i	− 0.660465i
$155$	−10.7321	−0.862019
$156$	0	0
$157$	−9.19615	−0.733933	−0.366966	−	0.930234i	$-0.619604\pi$
$157$	−9.19615	−0.733933	−0.366966	+	0.930234i	$0.619604\pi$
$158$	10.0526i	0.799739i
$159$	−2.87564	−0.228053
$160$	9.00000	0.711512
$161$	− 1.26795i	− 0.0999284i
$162$	7.73205i	0.607487i
$163$	5.80385i	0.454592i	0.973826	+	0.227296i	$0.0729886\pi$
$163$	5.80385i	0.454592i	−0.973826	+	0.227296i	$0.927011\pi$
$164$	5.19615i	0.405751i
$165$	6.00000	0.467099
$166$	14.1962	1.10184
$167$	24.5885i	1.90271i	0.308094	+	0.951356i	$0.400309\pi$
$167$	24.5885i	1.90271i	−0.308094	+	0.951356i	$0.599691\pi$
$168$	1.26795	0.0978244
$169$	0	0
$170$	−12.8038	−0.982010
$171$	4.92820i	0.376869i
$172$	10.1962	0.777449
$173$	−15.4641	−1.17571	−0.587857	−	0.808965i	$-0.700028\pi$
$173$	−15.4641	−1.17571	−0.587857	+	0.808965i	$0.700028\pi$
$174$	3.80385i	0.288369i
$175$	2.00000i	0.151186i
$176$	− 23.6603i	− 1.78346i
$177$	− 7.85641i	− 0.590524i
$178$	1.60770	0.120502
$179$	−6.92820	−0.517838	−0.258919	−	0.965899i	$-0.583366\pi$
$179$	−6.92820	−0.517838	−0.258919	+	0.965899i	$0.583366\pi$
$180$	4.26795i	0.318114i
$181$	25.5885	1.90198	0.950988	−	0.309229i	$-0.100071\pi$
$181$	25.5885	1.90198	0.950988	+	0.309229i	$0.100071\pi$
$182$	0	0
$183$	11.1244	0.822336
$184$	− 2.19615i	− 0.161903i
$185$	12.1244	0.891400
$186$	7.85641	0.576060
$187$	20.1962i	1.47689i
$188$	0.928203i	0.0676962i
$189$	4.00000i	0.290957i
$190$	6.00000i	0.435286i
$191$	1.26795	0.0917456	0.0458728	−	0.998947i	$-0.485393\pi$
$191$	1.26795	0.0917456	0.0458728	+	0.998947i	$0.485393\pi$
$192$	0.732051	0.0528312
$193$	5.00000i	0.359908i	0.983675	+	0.179954i	$0.0575949\pi$
$193$	5.00000i	0.359908i	−0.983675	+	0.179954i	$0.942405\pi$
$194$	−24.9282	−1.78974
$195$	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	$-0.140599\pi$
$198$	20.1962	1.43528
$199$	−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
$201$	3.07180i	0.216668i
$202$	7.39230i	0.520121i
$203$	− 3.00000i	− 0.210559i
$204$	3.12436	0.218749
$205$	9.00000	0.628587
$206$	− 11.0718i	− 0.771409i
$207$	3.12436	0.217158
$208$	0	0
$209$	9.46410	0.654646
$210$	2.19615i	0.151549i
$211$	−12.1962	−0.839618	−0.419809	−	0.907613i	$-0.637903\pi$
$211$	−12.1962	−0.839618	−0.419809	+	0.907613i	$0.637903\pi$
$212$	−3.92820	−0.269790
$213$	4.39230i	0.300956i
$214$	34.3923i	2.35101i
$215$	− 17.6603i	− 1.20442i
$216$	6.92820i	0.471405i
$217$	−6.19615	−0.420622
$218$	21.4641	1.45373
$219$	− 5.26795i	− 0.355975i
$220$	8.19615	0.552584
$221$	0	0
$222$	−8.87564	−0.595694
$223$	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
$225$	−4.92820	−0.328547
$226$	− 12.8038i	− 0.851699i
$227$	11.6603i	0.773918i	0.922097	+	0.386959i	$0.126475\pi$
$227$	11.6603i	0.773918i	−0.922097	+	0.386959i	$0.873525\pi$
$228$	− 1.46410i	− 0.0969625i
$229$	6.39230i	0.422415i	0.977441	+	0.211208i	$0.0677396\pi$
$229$	6.39230i	0.422415i	−0.977441	+	0.211208i	$0.932260\pi$
$230$	3.80385	0.250818
$231$	3.46410	0.227921
$232$	− 5.19615i	− 0.341144i
$233$	−25.8564	−1.69391	−0.846955	−	0.531665i	$-0.821567\pi$
$233$	−25.8564	−1.69391	−0.846955	+	0.531665i	$0.821567\pi$
$234$	0	0
$235$	1.60770	0.104874
$236$	− 10.7321i	− 0.698597i
$237$	−4.24871	−0.275983
$238$	−7.39230	−0.479172
$239$	26.1962i	1.69449i	0.531204	+	0.847244i	$0.321740\pi$
$239$	26.1962i	1.69449i	−0.531204	+	0.847244i	$0.678260\pi$
$240$	6.33975i	0.409229i
$241$	− 10.8038i	− 0.695937i	−0.937506	−	0.347969i	$-0.886872\pi$
$241$	− 10.8038i	− 0.695937i	0.937506	−	0.347969i	$-0.113128\pi$
$242$	− 19.7321i	− 1.26842i
$243$	−15.2679	−0.979439
$244$	15.1962	0.972834
$245$	− 1.73205i	− 0.110657i
$246$	−6.58846	−0.420065
$247$	0	0
$248$	−10.7321	−0.681486
$249$	6.00000i	0.380235i
$250$	−21.0000	−1.32816
$251$	22.3923	1.41339	0.706695	−	0.707518i	$-0.250185\pi$
$251$	22.3923	1.41339	0.706695	+	0.707518i	$0.250185\pi$
$252$	2.46410i	0.155224i
$253$	− 6.00000i	− 0.377217i
$254$	4.14359i	0.259992i
$255$	− 5.41154i	− 0.338884i
$256$	19.0000	1.18750
$257$	18.1244	1.13057	0.565283	−	0.824897i	$-0.308767\pi$
$257$	18.1244	1.13057	0.565283	+	0.824897i	$0.308767\pi$
$258$	12.9282i	0.804875i
$259$	7.00000	0.434959
$260$	0	0
$261$	7.39230	0.457572
$262$	6.00000i	0.370681i
$263$	4.73205	0.291791	0.145895	−	0.989300i	$-0.453394\pi$
$263$	4.73205	0.291791	0.145895	+	0.989300i	$0.453394\pi$
$264$	6.00000	0.369274
$265$	6.80385i	0.417957i
$266$	3.46410i	0.212398i
$267$	0.679492i	0.0415842i
$268$	4.19615i	0.256321i
$269$	18.9282	1.15407	0.577036	−	0.816718i	$-0.304209\pi$
$269$	18.9282	1.15407	0.577036	+	0.816718i	$0.304209\pi$
$270$	−12.0000	−0.730297
$271$	16.1962i	0.983846i	0.870639	+	0.491923i	$0.163706\pi$
$271$	16.1962i	0.983846i	−0.870639	+	0.491923i	$0.836294\pi$
$272$	−21.3397	−1.29391
$273$	0	0
$274$	−37.9808	−2.29450
$275$	9.46410i	0.570707i
$276$	−0.928203	−0.0558713
$277$	−17.0000	−1.02143	−0.510716	−	0.859750i	$-0.670619\pi$
$277$	−17.0000	−1.02143	−0.510716	+	0.859750i	$0.670619\pi$
$278$	35.6603i	2.13876i
$279$	− 15.2679i	− 0.914068i
$280$	− 3.00000i	− 0.179284i
$281$	− 7.39230i	− 0.440988i	−0.975388	−	0.220494i	$-0.929233\pi$
$281$	− 7.39230i	− 0.440988i	0.975388	−	0.220494i	$-0.0707669\pi$
$282$	−1.17691	−0.0700842
$283$	0.196152	0.0116601	0.00583003	−	0.999983i	$-0.498144\pi$
$283$	0.196152	0.0116601	0.00583003	+	0.999983i	$0.498144\pi$
$284$	6.00000i	0.356034i
$285$	−2.53590	−0.150214
$286$	0	0
$287$	5.19615	0.306719
$288$	12.8038i	0.754474i
$289$	1.21539	0.0714935
$290$	9.00000	0.528498
$291$	− 10.5359i	− 0.617625i
$292$	− 7.19615i	− 0.421123i
$293$	− 11.1962i	− 0.654086i	−0.945009	−	0.327043i	$-0.893948\pi$
$293$	− 11.1962i	− 0.654086i	0.945009	−	0.327043i	$-0.106052\pi$
$294$	1.26795i	0.0739483i
$295$	−18.5885	−1.08226
$296$	12.1244	0.704714
$297$	18.9282i	1.09833i
$298$	0.803848	0.0465656
$299$	0	0
$300$	1.46410	0.0845299
$301$	− 10.1962i	− 0.587696i
$302$	−3.46410	−0.199337
$303$	−3.12436	−0.179490
$304$	10.0000i	0.573539i
$305$	− 26.3205i	− 1.50711i
$306$	− 18.2154i	− 1.04130i
$307$	26.5885i	1.51748i	0.651392	+	0.758742i	$0.274186\pi$
$307$	26.5885i	1.51748i	−0.651392	+	0.758742i	$0.725814\pi$
$308$	4.73205	0.269634
$309$	4.67949	0.266207
$310$	− 18.5885i	− 1.05575i
$311$	−4.73205	−0.268330	−0.134165	−	0.990959i	$-0.542835\pi$
$311$	−4.73205	−0.268330	−0.134165	+	0.990959i	$0.542835\pi$
$312$	0	0
$313$	−12.7846	−0.722629	−0.361314	−	0.932444i	$-0.617672\pi$
$313$	−12.7846	−0.722629	−0.361314	+	0.932444i	$0.617672\pi$
$314$	− 15.9282i	− 0.898881i
$315$	4.26795	0.240472
$316$	−5.80385	−0.326492
$317$	− 0.464102i	− 0.0260665i	−0.999915	−	0.0130333i	$-0.995851\pi$
$317$	− 0.464102i	− 0.0260665i	0.999915	−	0.0130333i	$-0.00414874\pi$
$318$	− 4.98076i	− 0.279307i
$319$	− 14.1962i	− 0.794832i
$320$	− 1.73205i	− 0.0968246i
$321$	−14.5359	−0.811315
$322$	2.19615	0.122387
$323$	− 8.53590i	− 0.474950i
$324$	−4.46410	−0.248006
$325$	0	0
$326$	−10.0526	−0.556760
$327$	9.07180i	0.501672i
$328$	9.00000	0.496942
$329$	0.928203	0.0511735
$330$	10.3923i	0.572078i
$331$	26.9808i	1.48300i	0.670955	+	0.741498i	$0.265885\pi$
$331$	26.9808i	1.48300i	−0.670955	+	0.741498i	$0.734115\pi$
$332$	8.19615i	0.449822i
$333$	17.2487i	0.945224i
$334$	−42.5885	−2.33034
$335$	7.26795	0.397090
$336$	3.66025i	0.199683i
$337$	−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
$339$	5.41154	0.293915
$340$	− 7.39230i	− 0.400904i
$341$	−29.3205	−1.58779
$342$	−8.53590	−0.461569
$343$	− 1.00000i	− 0.0539949i
$344$	− 17.6603i	− 0.952177i
$345$	1.60770i	0.0865554i
$346$	− 26.7846i	− 1.43995i
$347$	10.7321	0.576127	0.288063	−	0.957611i	$-0.406989\pi$
$347$	10.7321	0.576127	0.288063	+	0.957611i	$0.406989\pi$
$348$	−2.19615	−0.117726
$349$	16.7846i	0.898460i	0.893416	+	0.449230i	$0.148302\pi$
$349$	16.7846i	0.898460i	−0.893416	+	0.449230i	$0.851698\pi$
$350$	−3.46410	−0.185164
$351$	0	0
$352$	24.5885	1.31057
$353$	− 3.33975i	− 0.177757i	−0.996042	−	0.0888784i	$-0.971672\pi$
$353$	− 3.33975i	− 0.177757i	0.996042	−	0.0888784i	$-0.0283282\pi$
$354$	13.6077	0.723241
$355$	10.3923	0.551566
$356$	0.928203i	0.0491947i
$357$	− 3.12436i	− 0.165358i
$358$	− 12.0000i	− 0.634220i
$359$	5.07180i	0.267679i	0.991003	+	0.133840i	$0.0427307\pi$
$359$	5.07180i	0.267679i	−0.991003	+	0.133840i	$0.957269\pi$
$360$	7.39230	0.389609
$361$	15.0000	0.789474
$362$	44.3205i	2.32943i
$363$	8.33975	0.437723
$364$	0	0
$365$	−12.4641	−0.652401
$366$	19.2679i	1.00715i
$367$	−6.19615	−0.323437	−0.161718	−	0.986837i	$-0.551704\pi$
$367$	−6.19615	−0.323437	−0.161718	+	0.986837i	$0.551704\pi$
$368$	6.33975	0.330482
$369$	12.8038i	0.666542i
$370$	21.0000i	1.09174i
$371$	3.92820i	0.203942i
$372$	4.53590i	0.235175i
$373$	9.39230	0.486315	0.243158	−	0.969987i	$-0.421817\pi$
$373$	9.39230	0.486315	0.243158	+	0.969987i	$0.421817\pi$
$374$	−34.9808	−1.80881
$375$	− 8.87564i	− 0.458336i
$376$	1.60770	0.0829105
$377$	0	0
$378$	−6.92820	−0.356348
$379$	4.58846i	0.235693i	0.993032	+	0.117847i	$0.0375991\pi$
$379$	4.58846i	0.235693i	−0.993032	+	0.117847i	$0.962401\pi$
$380$	−3.46410	−0.177705
$381$	−1.75129	−0.0897212
$382$	2.19615i	0.112365i
$383$	− 5.66025i	− 0.289225i	−0.989488	−	0.144613i	$-0.953806\pi$
$383$	− 5.66025i	− 0.289225i	0.989488	−	0.144613i	$-0.0461936\pi$
$384$	8.87564i	0.452933i
$385$	− 8.19615i	− 0.417715i
$386$	−8.66025	−0.440795
$387$	25.1244	1.27714
$388$	− 14.3923i	− 0.730659i
$389$	30.4641	1.54459	0.772296	−	0.635263i	$-0.219108\pi$
$389$	30.4641	1.54459	0.772296	+	0.635263i	$0.219108\pi$
$390$	0	0
$391$	−5.41154	−0.273673
$392$	− 1.73205i	− 0.0874818i
$393$	−2.53590	−0.127919
$394$	20.7846	1.04711
$395$	10.0526i	0.505799i
$396$	11.6603i	0.585950i
$397$	22.7846i	1.14353i	0.820419	+	0.571763i	$0.193740\pi$
$397$	22.7846i	1.14353i	−0.820419	+	0.571763i	$0.806260\pi$
$398$	− 3.46410i	− 0.173640i
$399$	−1.46410	−0.0732968
$400$	−10.0000	−0.500000
$401$	16.8564i	0.841769i	0.907114	+	0.420884i	$0.138280\pi$
$401$	16.8564i	0.841769i	−0.907114	+	0.420884i	$0.861720\pi$
$402$	−5.32051	−0.265363
$403$	0	0
$404$	−4.26795	−0.212338
$405$	7.73205i	0.384209i
$406$	5.19615	0.257881
$407$	33.1244	1.64191
$408$	− 5.41154i	− 0.267911i
$409$	27.1962i	1.34476i	0.740205	+	0.672382i	$0.234729\pi$
$409$	27.1962i	1.34476i	−0.740205	+	0.672382i	$0.765271\pi$
$410$	15.5885i	0.769859i
$411$	− 16.0526i	− 0.791814i
$412$	6.39230	0.314926
$413$	−10.7321	−0.528090
$414$	5.41154i	0.265963i
$415$	14.1962	0.696862
$416$	0	0
$417$	−15.0718	−0.738069
$418$	16.3923i	0.801774i
$419$	−21.8038	−1.06519	−0.532594	−	0.846371i	$-0.678783\pi$
$419$	−21.8038	−1.06519	−0.532594	+	0.846371i	$0.678783\pi$
$420$	−1.26795	−0.0618696
$421$	− 30.1769i	− 1.47073i	−0.677670	−	0.735366i	$-0.737010\pi$
$421$	− 30.1769i	− 1.47073i	0.677670	−	0.735366i	$-0.262990\pi$
$422$	− 21.1244i	− 1.02832i
$423$	2.28719i	0.111207i
$424$	6.80385i	0.330424i
$425$	8.53590	0.414052
$426$	−7.60770	−0.368594
$427$	− 15.1962i	− 0.735393i
$428$	−19.8564	−0.959796
$429$	0	0
$430$	30.5885	1.47511
$431$	− 35.3205i	− 1.70133i	−0.525709	−	0.850665i	$-0.676200\pi$
$431$	− 35.3205i	− 1.70133i	0.525709	−	0.850665i	$-0.323800\pi$
$432$	−20.0000	−0.962250
$433$	−17.5885	−0.845247	−0.422624	−	0.906305i	$-0.638891\pi$
$433$	−17.5885	−0.845247	−0.422624	+	0.906305i	$0.638891\pi$
$434$	− 10.7321i	− 0.515155i
$435$	3.80385i	0.182381i
$436$	12.3923i	0.593484i
$437$	2.53590i	0.121308i
$438$	9.12436	0.435979
$439$	16.5885	0.791724	0.395862	−	0.918310i	$-0.370446\pi$
$439$	16.5885	0.791724	0.395862	+	0.918310i	$0.370446\pi$
$440$	− 14.1962i	− 0.676775i
$441$	2.46410	0.117338
$442$	0	0
$443$	−11.3205	−0.537854	−0.268927	−	0.963161i	$-0.586669\pi$
$443$	−11.3205	−0.537854	−0.268927	+	0.963161i	$0.586669\pi$
$444$	− 5.12436i	− 0.243191i
$445$	1.60770	0.0762121
$446$	−17.3205	−0.820150
$447$	0.339746i	0.0160694i
$448$	− 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	$-0.0913819\pi$
$450$	− 8.53590i	− 0.402386i
$451$	24.5885	1.15783
$452$	7.39230	0.347705
$453$	− 1.46410i	− 0.0687895i
$454$	−20.1962	−0.947852
$455$	0	0
$456$	−2.53590	−0.118754
$457$	− 11.0000i	− 0.514558i	−0.966337	−	0.257279i	$-0.917174\pi$
$457$	− 11.0000i	− 0.514558i	0.966337	−	0.257279i	$-0.0828260\pi$
$458$	−11.0718	−0.517351
$459$	17.0718	0.796843
$460$	2.19615i	0.102396i
$461$	− 15.5885i	− 0.726027i	−0.931784	−	0.363013i	$-0.881748\pi$
$461$	− 15.5885i	− 0.726027i	0.931784	−	0.363013i	$-0.118252\pi$
$462$	6.00000i	0.279145i
$463$	26.5885i	1.23567i	0.786308	+	0.617835i	$0.211990\pi$
$463$	26.5885i	1.23567i	−0.786308	+	0.617835i	$0.788010\pi$
$464$	15.0000	0.696358
$465$	7.85641	0.364332
$466$	− 44.7846i	− 2.07461i
$467$	19.5167	0.903123	0.451562	−	0.892240i	$-0.350867\pi$
$467$	19.5167	0.903123	0.451562	+	0.892240i	$0.350867\pi$
$468$	0	0
$469$	4.19615	0.193760
$470$	2.78461i	0.128444i
$471$	6.73205	0.310197
$472$	−18.5885	−0.855603
$473$	− 48.2487i	− 2.21848i
$474$	− 7.35898i	− 0.338009i
$475$	− 4.00000i	− 0.183533i
$476$	− 4.26795i	− 0.195621i
$477$	−9.67949	−0.443193
$478$	−45.3731	−2.07532
$479$	4.73205i	0.216213i	0.994139	+	0.108106i	$0.0344787\pi$
$479$	4.73205i	0.216213i	−0.994139	+	0.108106i	$0.965521\pi$
$480$	−6.58846	−0.300721
$481$	0	0
$482$	18.7128	0.852345
$483$	0.928203i	0.0422347i
$484$	11.3923	0.517832
$485$	−24.9282	−1.13193
$486$	− 26.4449i	− 1.19956i
$487$	0.784610i	0.0355541i	0.999842	+	0.0177770i	$0.00565890\pi$
$487$	0.784610i	0.0355541i	−0.999842	+	0.0177770i	$0.994341\pi$
$488$	− 26.3205i	− 1.19147i
$489$	− 4.24871i	− 0.192133i
$490$	3.00000	0.135526
$491$	−28.3923	−1.28133	−0.640663	−	0.767822i	$-0.721341\pi$
$491$	−28.3923	−1.28133	−0.640663	+	0.767822i	$0.721341\pi$
$492$	− 3.80385i	− 0.171491i
$493$	−12.8038	−0.576656
$494$	0	0
$495$	20.1962	0.907750
$496$	− 30.9808i	− 1.39108i
$497$	6.00000	0.269137
$498$	−10.3923	−0.465690
$499$	− 12.9808i	− 0.581099i	−0.956860	−	0.290549i	$-0.906162\pi$
$499$	− 12.9808i	− 0.581099i	0.956860	−	0.290549i	$-0.0938380\pi$
$500$	− 12.1244i	− 0.542218i
$501$	− 18.0000i	− 0.804181i
$502$	38.7846i	1.73104i
$503$	12.5885	0.561292	0.280646	−	0.959811i	$-0.409451\pi$
$503$	12.5885	0.561292	0.280646	+	0.959811i	$0.409451\pi$
$504$	4.26795	0.190110
$505$	7.39230i	0.328953i
$506$	10.3923	0.461994
$507$	0	0
$508$	−2.39230	−0.106141
$509$	− 10.2679i	− 0.455119i	−0.973764	−	0.227559i	$-0.926925\pi$
$509$	− 10.2679i	− 0.455119i	0.973764	−	0.227559i	$-0.0730746\pi$
$510$	9.37307	0.415046
$511$	−7.19615	−0.318339
$512$	8.66025i	0.382733i
$513$	− 8.00000i	− 0.353209i
$514$	31.3923i	1.38466i
$515$	− 11.0718i	− 0.487882i
$516$	−7.46410	−0.328589
$517$	4.39230	0.193173
$518$	12.1244i	0.532714i
$519$	11.3205	0.496915
$520$	0	0
$521$	0.124356	0.00544812	0.00272406	−	0.999996i	$-0.499133\pi$
$521$	0.124356	0.00544812	0.00272406	+	0.999996i	$0.499133\pi$
$522$	12.8038i	0.560409i
$523$	33.1769	1.45073	0.725363	−	0.688367i	$-0.241672\pi$
$523$	33.1769	1.45073	0.725363	+	0.688367i	$0.241672\pi$
$524$	−3.46410	−0.151330
$525$	− 1.46410i	− 0.0638986i
$526$	8.19615i	0.357369i
$527$	26.4449i	1.15196i
$528$	17.3205i	0.753778i
$529$	−21.3923	−0.930100
$530$	−11.7846	−0.511891
$531$	− 26.4449i	− 1.14761i
$532$	−2.00000	−0.0867110
$533$	0	0
$534$	−1.17691	−0.0509301
$535$	34.3923i	1.48691i
$536$	7.26795	0.313928
$537$	5.07180	0.218864
$538$	32.7846i	1.41344i
$539$	− 4.73205i	− 0.203824i
$540$	− 6.92820i	− 0.298142i
$541$	− 35.3923i	− 1.52163i	−0.648966	−	0.760817i	$-0.724798\pi$
$541$	− 35.3923i	− 1.52163i	0.648966	−	0.760817i	$-0.275202\pi$
$542$	−28.0526	−1.20496
$543$	−18.7321	−0.803869
$544$	− 22.1769i	− 0.950827i
$545$	21.4641	0.919421
$546$	0	0
$547$	28.1962	1.20558	0.602790	−	0.797900i	$-0.294056\pi$
$547$	28.1962	1.20558	0.602790	+	0.797900i	$0.294056\pi$
$548$	− 21.9282i	− 0.936726i
$549$	37.4449	1.59811
$550$	−16.3923	−0.698970
$551$	6.00000i	0.255609i
$552$	1.60770i	0.0684280i
$553$	5.80385i	0.246805i
$554$	− 29.4449i	− 1.25099i
$555$	−8.87564	−0.376750
$556$	−20.5885	−0.873145
$557$	− 25.6410i	− 1.08644i	−0.839589	−	0.543222i	$-0.817204\pi$
$557$	− 25.6410i	− 1.08644i	0.839589	−	0.543222i	$-0.182796\pi$
$558$	26.4449	1.11950
$559$	0	0
$560$	8.66025	0.365963
$561$	− 14.7846i	− 0.624207i
$562$	12.8038	0.540098
$563$	10.0526	0.423665	0.211832	−	0.977306i	$-0.432057\pi$
$563$	10.0526	0.423665	0.211832	+	0.977306i	$0.432057\pi$
$564$	− 0.679492i	− 0.0286118i
$565$	− 12.8038i	− 0.538662i
$566$	0.339746i	0.0142806i
$567$	4.46410i	0.187475i
$568$	10.3923	0.436051
$569$	−29.0718	−1.21875	−0.609377	−	0.792881i	$-0.708580\pi$
$569$	−29.0718	−1.21875	−0.609377	+	0.792881i	$0.708580\pi$
$570$	− 4.39230i	− 0.183973i
$571$	24.7846	1.03720	0.518602	−	0.855016i	$-0.326453\pi$
$571$	24.7846	1.03720	0.518602	+	0.855016i	$0.326453\pi$
$572$	0	0
$573$	−0.928203	−0.0387762
$574$	9.00000i	0.375653i
$575$	−2.53590	−0.105754
$576$	2.46410	0.102671
$577$	− 32.8038i	− 1.36564i	−0.730586	−	0.682821i	$-0.760753\pi$
$577$	− 32.8038i	− 1.36564i	0.730586	−	0.682821i	$-0.239247\pi$
$578$	2.10512i	0.0875614i
$579$	− 3.66025i	− 0.152115i
$580$	5.19615i	0.215758i
$581$	8.19615	0.340034
$582$	18.2487	0.756433
$583$	18.5885i	0.769855i
$584$	−12.4641	−0.515768
$585$	0	0
$586$	19.3923	0.801089
$587$	4.39230i	0.181290i	0.995883	+	0.0906449i	$0.0288928\pi$
$587$	4.39230i	0.181290i	−0.995883	+	0.0906449i	$0.971107\pi$
$588$	−0.732051	−0.0301893
$589$	12.3923	0.510616
$590$	− 32.1962i	− 1.32549i
$591$	8.78461i	0.361351i
$592$	35.0000i	1.43849i
$593$	41.4449i	1.70194i	0.525217	+	0.850968i	$0.323984\pi$
$593$	41.4449i	1.70194i	−0.525217	+	0.850968i	$0.676016\pi$
$594$	−32.7846	−1.34517
$595$	−7.39230	−0.303055
$596$	0.464102i	0.0190103i
$597$	1.46410	0.0599217
$598$	0	0
$599$	16.1436	0.659609	0.329805	−	0.944049i	$-0.393017\pi$
$599$	16.1436	0.659609	0.329805	+	0.944049i	$0.393017\pi$
$600$	− 2.53590i	− 0.103528i
$601$	21.9808	0.896614	0.448307	−	0.893880i	$-0.352027\pi$
$601$	21.9808	0.896614	0.448307	+	0.893880i	$0.352027\pi$
$602$	17.6603	0.719778
$603$	10.3397i	0.421067i
$604$	− 2.00000i	− 0.0813788i
$605$	− 19.7321i	− 0.802222i
$606$	− 5.41154i	− 0.219829i
$607$	6.39230	0.259456	0.129728	−	0.991550i	$-0.458590\pi$
$607$	6.39230	0.259456	0.129728	+	0.991550i	$0.458590\pi$
$608$	−10.3923	−0.421464
$609$	2.19615i	0.0889926i
$610$	45.5885	1.84582
$611$	0	0
$612$	10.5167	0.425111
$613$	17.3923i	0.702469i	0.936288	+	0.351234i	$0.114238\pi$
$613$	17.3923i	0.702469i	−0.936288	+	0.351234i	$0.885762\pi$
$614$	−46.0526	−1.85853
$615$	−6.58846	−0.265672
$616$	− 8.19615i	− 0.330232i
$617$	− 28.6077i	− 1.15170i	−0.817555	−	0.575851i	$-0.804671\pi$
$617$	− 28.6077i	− 1.15170i	0.817555	−	0.575851i	$-0.195329\pi$
$618$	8.10512i	0.326036i
$619$	− 37.3731i	− 1.50215i	−0.660217	−	0.751075i	$-0.729536\pi$
$619$	− 37.3731i	− 1.50215i	0.660217	−	0.751075i	$-0.270464\pi$
$620$	10.7321	0.431010
$621$	−5.07180	−0.203524
$622$	− 8.19615i	− 0.328636i
$623$	0.928203	0.0371877
$624$	0	0
$625$	−11.0000	−0.440000
$626$	− 22.1436i	− 0.885036i
$627$	−6.92820	−0.276686
$628$	9.19615	0.366966
$629$	− 29.8756i	− 1.19122i
$630$	7.39230i	0.294516i
$631$	28.7846i	1.14590i	0.819591	+	0.572949i	$0.194201\pi$
$631$	28.7846i	1.14590i	−0.819591	+	0.572949i	$0.805799\pi$
$632$	10.0526i	0.399869i
$633$	8.92820	0.354864
$634$	0.803848	0.0319249
$635$	4.14359i	0.164433i
$636$	2.87564	0.114027
$637$	0	0
$638$	24.5885	0.973466
$639$	14.7846i	0.584870i
$640$	21.0000	0.830098
$641$	−1.14359	−0.0451692	−0.0225846	−	0.999745i	$-0.507190\pi$
$641$	−1.14359	−0.0451692	−0.0225846	+	0.999745i	$0.507190\pi$
$642$	− 25.1769i	− 0.993654i
$643$	− 40.7846i	− 1.60839i	−0.594367	−	0.804194i	$-0.702597\pi$
$643$	− 40.7846i	− 1.60839i	0.594367	−	0.804194i	$-0.297403\pi$
$644$	1.26795i	0.0499642i
$645$	12.9282i	0.509048i
$646$	14.7846	0.581693
$647$	45.0333	1.77044	0.885221	−	0.465170i	$-0.154007\pi$
$647$	45.0333	1.77044	0.885221	+	0.465170i	$0.154007\pi$
$648$	7.73205i	0.303744i
$649$	−50.7846	−1.99347
$650$	0	0
$651$	4.53590	0.177776
$652$	− 5.80385i	− 0.227296i
$653$	−10.1436	−0.396949	−0.198475	−	0.980106i	$-0.563599\pi$
$653$	−10.1436	−0.396949	−0.198475	+	0.980106i	$0.563599\pi$
$654$	−15.7128	−0.614420
$655$	6.00000i	0.234439i
$656$	25.9808i	1.01438i
$657$	− 17.7321i	− 0.691793i
$658$	1.60770i	0.0626745i
$659$	7.60770	0.296354	0.148177	−	0.988961i	$-0.452660\pi$
$659$	7.60770	0.296354	0.148177	+	0.988961i	$0.452660\pi$
$660$	−6.00000	−0.233550
$661$	− 22.8038i	− 0.886967i	−0.896283	−	0.443483i	$-0.853742\pi$
$661$	− 22.8038i	− 0.886967i	0.896283	−	0.443483i	$-0.146258\pi$
$662$	−46.7321	−1.81629
$663$	0	0
$664$	14.1962	0.550918
$665$	3.46410i	0.134332i
$666$	−29.8756	−1.15766
$667$	3.80385	0.147286
$668$	− 24.5885i	− 0.951356i
$669$	− 7.32051i	− 0.283027i
$670$	12.5885i	0.486335i
$671$	− 71.9090i	− 2.77601i
$672$	−3.80385	−0.146737
$673$	−18.1769	−0.700669	−0.350334	−	0.936625i	$-0.613932\pi$
$673$	−18.1769	−0.700669	−0.350334	+	0.936625i	$0.613932\pi$
$674$	− 19.0526i	− 0.733877i
$675$	8.00000	0.307920
$676$	0	0
$677$	−36.9282	−1.41927	−0.709633	−	0.704571i	$-0.751139\pi$
$677$	−36.9282	−1.41927	−0.709633	+	0.704571i	$0.751139\pi$
$678$	9.37307i	0.359970i
$679$	−14.3923	−0.552326
$680$	−12.8038	−0.491005
$681$	− 8.53590i	− 0.327096i
$682$	− 50.7846i	− 1.94464i
$683$	8.53590i	0.326617i	0.986575	+	0.163309i	$0.0522166\pi$
$683$	8.53590i	0.326617i	−0.986575	+	0.163309i	$0.947783\pi$
$684$	− 4.92820i	− 0.188435i
$685$	−37.9808	−1.45117
$686$	1.73205	0.0661300
$687$	− 4.67949i	− 0.178534i
$688$	50.9808	1.94362
$689$	0	0
$690$	−2.78461	−0.106008
$691$	20.3923i	0.775760i	0.921710	+	0.387880i	$0.126792\pi$
$691$	20.3923i	0.775760i	−0.921710	+	0.387880i	$0.873208\pi$
$692$	15.4641	0.587857
$693$	11.6603	0.442936
$694$	18.5885i	0.705608i
$695$	35.6603i	1.35267i
$696$	3.80385i	0.144184i
$697$	− 22.1769i	− 0.840011i
$698$	−29.0718	−1.10038
$699$	18.9282	0.715930
$700$	− 2.00000i	− 0.0755929i
$701$	20.7846	0.785024	0.392512	−	0.919747i	$-0.371606\pi$
$701$	20.7846	0.785024	0.392512	+	0.919747i	$0.371606\pi$
$702$	0	0
$703$	−14.0000	−0.528020
$704$	− 4.73205i	− 0.178346i
$705$	−1.17691	−0.0443252
$706$	5.78461	0.217707
$707$	4.26795i	0.160513i
$708$	7.85641i	0.295262i
$709$	− 32.1769i	− 1.20843i	−0.796822	−	0.604215i	$-0.793487\pi$
$709$	− 32.1769i	− 1.20843i	0.796822	−	0.604215i	$-0.206513\pi$
$710$	18.0000i	0.675528i
$711$	−14.3013	−0.536340
$712$	1.60770	0.0602509
$713$	− 7.85641i	− 0.294225i
$714$	5.41154	0.202522
$715$	0	0
$716$	6.92820	0.258919
$717$	− 19.1769i	− 0.716175i
$718$	−8.78461	−0.327839
$719$	10.7321	0.400238	0.200119	−	0.979772i	$-0.435867\pi$
$719$	10.7321	0.400238	0.200119	+	0.979772i	$0.435867\pi$
$720$	21.3397i	0.795285i
$721$	− 6.39230i	− 0.238062i
$722$	25.9808i	0.966904i
$723$	7.90897i	0.294138i
$724$	−25.5885	−0.950988
$725$	−6.00000	−0.222834
$726$	14.4449i	0.536099i
$727$	−21.1769	−0.785408	−0.392704	−	0.919665i	$-0.628460\pi$
$727$	−21.1769	−0.785408	−0.392704	+	0.919665i	$0.628460\pi$
$728$	0	0
$729$	−2.21539	−0.0820515
$730$	− 21.5885i	− 0.799025i
$731$	−43.5167	−1.60952
$732$	−11.1244	−0.411168
$733$	7.58846i	0.280286i	0.990131	+	0.140143i	$0.0447562\pi$
$733$	7.58846i	0.280286i	−0.990131	+	0.140143i	$0.955244\pi$
$734$	− 10.7321i	− 0.396127i
$735$	1.26795i	0.0467690i
$736$	6.58846i	0.242854i
$737$	19.8564	0.731420
$738$	−22.1769	−0.816344
$739$	− 0.784610i	− 0.0288623i	−0.999896	−	0.0144312i	$-0.995406\pi$
$739$	− 0.784610i	− 0.0288623i	0.999896	−	0.0144312i	$-0.00459374\pi$
$740$	−12.1244	−0.445700
$741$	0	0
$742$	−6.80385	−0.249777
$743$	28.3923i	1.04161i	0.853675	+	0.520806i	$0.174369\pi$
$743$	28.3923i	1.04161i	−0.853675	+	0.520806i	$0.825631\pi$
$744$	7.85641	0.288030
$745$	0.803848	0.0294507
$746$	16.2679i	0.595612i
$747$	20.1962i	0.738939i
$748$	− 20.1962i	− 0.738444i
$749$	19.8564i	0.725537i
$750$	15.3731	0.561345
$751$	−46.1962	−1.68572	−0.842861	−	0.538132i	$-0.819130\pi$
$751$	−46.1962	−1.68572	−0.842861	+	0.538132i	$0.819130\pi$
$752$	4.64102i	0.169240i
$753$	−16.3923	−0.597369
$754$	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	$0.593910\pi$
$758$	−7.94744	−0.288664
$759$	4.39230i	0.159431i
$760$	6.00000i	0.217643i
$761$	6.67949i	0.242131i	0.992644	+	0.121066i	$0.0386312\pi$
$761$	6.67949i	0.242131i	−0.992644	+	0.121066i	$0.961369\pi$
$762$	− 3.03332i	− 0.109886i
$763$	12.3923	0.448632
$764$	−1.26795	−0.0458728
$765$	− 18.2154i	− 0.658579i
$766$	9.80385	0.354227
$767$	0	0
$768$	−13.9090	−0.501897
$769$	47.1769i	1.70124i	0.525778	+	0.850622i	$0.323774\pi$
$769$	47.1769i	1.70124i	−0.525778	+	0.850622i	$0.676226\pi$
$770$	14.1962	0.511594
$771$	−13.2679	−0.477834
$772$	− 5.00000i	− 0.179954i
$773$	− 0.928203i	− 0.0333851i	−0.999861	−	0.0166926i	$-0.994686\pi$
$773$	− 0.928203i	− 0.0333851i	0.999861	−	0.0166926i	$-0.00531366\pi$
$774$	43.5167i	1.56417i
$775$	12.3923i	0.445145i
$776$	−24.9282	−0.894870
$777$	−5.12436	−0.183835
$778$	52.7654i	1.89173i
$779$	−10.3923	−0.372343
$780$	0	0
$781$	28.3923	1.01596
$782$	− 9.37307i	− 0.335180i
$783$	−12.0000	−0.428845
$784$	5.00000	0.178571
$785$	− 15.9282i	− 0.568502i
$786$	− 4.39230i	− 0.156668i
$787$	− 38.9808i	− 1.38951i	−0.719244	−	0.694757i	$-0.755512\pi$
$787$	− 38.9808i	− 1.38951i	0.719244	−	0.694757i	$-0.244488\pi$
$788$	12.0000i	0.427482i
$789$	−3.46410	−0.123325
$790$	−17.4115	−0.619475
$791$	− 7.39230i	− 0.262840i
$792$	20.1962	0.717639
$793$	0	0
$794$	−39.4641	−1.40053
$795$	− 4.98076i	− 0.176649i
$796$	2.00000	0.0708881
$797$	13.6077	0.482009	0.241005	−	0.970524i	$-0.422523\pi$
$797$	13.6077	0.482009	0.241005	+	0.970524i	$0.422523\pi$
$798$	− 2.53590i	− 0.0897698i
$799$	− 3.96152i	− 0.140149i
$800$	− 10.3923i	− 0.367423i
$801$	2.28719i	0.0808138i
$802$	−29.1962	−1.03095
$803$	−34.0526	−1.20169
$804$	− 3.07180i	− 0.108334i
$805$	2.19615	0.0774042
$806$	0	0
$807$	−13.8564	−0.487769
$808$	7.39230i	0.260060i
$809$	15.9282	0.560006	0.280003	−	0.959999i	$-0.409665\pi$
$809$	15.9282	0.560006	0.280003	+	0.959999i	$0.409665\pi$
$810$	−13.3923	−0.470558
$811$	− 14.5885i	− 0.512270i	−0.966641	−	0.256135i	$-0.917551\pi$
$811$	− 14.5885i	− 0.512270i	0.966641	−	0.256135i	$-0.0824492\pi$
$812$	3.00000i	0.105279i
$813$	− 11.8564i	− 0.415822i
$814$	57.3731i	2.01092i
$815$	−10.0526	−0.352126
$816$	15.6218	0.546872
$817$	20.3923i	0.713436i
$818$	−47.1051	−1.64699
$819$	0	0
$820$	−9.00000	−0.314294
$821$	− 31.8564i	− 1.11180i	−0.831250	−	0.555898i	$-0.812374\pi$
$821$	− 31.8564i	− 1.11180i	0.831250	−	0.555898i	$-0.187626\pi$
$822$	27.8038	0.969771
$823$	−21.1769	−0.738181	−0.369090	−	0.929393i	$-0.620331\pi$
$823$	−21.1769	−0.738181	−0.369090	+	0.929393i	$0.620331\pi$
$824$	− 11.0718i	− 0.385704i
$825$	− 6.92820i	− 0.241209i
$826$	− 18.5885i	− 0.646775i
$827$	34.9808i	1.21640i	0.793784	+	0.608200i	$0.208108\pi$
$827$	34.9808i	1.21640i	−0.793784	+	0.608200i	$0.791892\pi$
$828$	−3.12436	−0.108579
$829$	31.5885	1.09711	0.548556	−	0.836114i	$-0.315178\pi$
$829$	31.5885	1.09711	0.548556	+	0.836114i	$0.315178\pi$
$830$	24.5885i	0.853478i
$831$	12.4449	0.431708
$832$	0	0
$833$	−4.26795	−0.147876
$834$	− 26.1051i	− 0.903946i
$835$	−42.5885	−1.47383
$836$	−9.46410	−0.327323
$837$	24.7846i	0.856681i
$838$	− 37.7654i	− 1.30458i
$839$	− 18.0000i	− 0.621429i	−0.950503	−	0.310715i	$-0.899432\pi$
$839$	− 18.0000i	− 0.621429i	0.950503	−	0.310715i	$-0.100568\pi$
$840$	2.19615i	0.0757745i
$841$	−20.0000	−0.689655
$842$	52.2679	1.80127
$843$	5.41154i	0.186383i
$844$	12.1962	0.419809
$845$	0	0
$846$	−3.96152	−0.136200
$847$	− 11.3923i	− 0.391444i
$848$	−19.6410	−0.674475
$849$	−0.143594	−0.00492812
$850$	14.7846i	0.507108i
$851$	8.87564i	0.304253i
$852$	− 4.39230i	− 0.150478i
$853$	− 25.5885i	− 0.876132i	−0.898943	−	0.438066i	$-0.855664\pi$
$853$	− 25.5885i	− 0.876132i	0.898943	−	0.438066i	$-0.144336\pi$
$854$	26.3205	0.900669
$855$	−8.53590	−0.291922
$856$	34.3923i	1.17550i
$857$	5.87564	0.200708	0.100354	−	0.994952i	$-0.468002\pi$
$857$	5.87564	0.200708	0.100354	+	0.994952i	$0.468002\pi$
$858$	0	0
$859$	−18.1962	−0.620845	−0.310422	−	0.950599i	$-0.600470\pi$
$859$	−18.1962	−0.620845	−0.310422	+	0.950599i	$0.600470\pi$
$860$	17.6603i	0.602210i
$861$	−3.80385	−0.129635
$862$	61.1769	2.08369
$863$	37.5167i	1.27708i	0.769588	+	0.638541i	$0.220462\pi$
$863$	37.5167i	1.27708i	−0.769588	+	0.638541i	$0.779538\pi$
$864$	− 20.7846i	− 0.707107i
$865$	− 26.7846i	− 0.910704i
$866$	− 30.4641i	− 1.03521i
$867$	−0.889727	−0.0302167
$868$	6.19615	0.210311
$869$	27.4641i	0.931656i
$870$	−6.58846	−0.223370
$871$	0	0
$872$	21.4641	0.726866
$873$	− 35.4641i	− 1.20028i
$874$	−4.39230	−0.148572
$875$	−12.1244	−0.409878
$876$	5.26795i	0.177988i
$877$	21.7846i	0.735614i	0.929902	+	0.367807i	$0.119891\pi$
$877$	21.7846i	0.735614i	−0.929902	+	0.367807i	$0.880109\pi$
$878$	28.7321i	0.969660i
$879$	8.19615i	0.276449i
$880$	40.9808	1.38146
$881$	39.5885	1.33377	0.666885	−	0.745161i	$-0.267627\pi$
$881$	39.5885	1.33377	0.666885	+	0.745161i	$0.267627\pi$
$882$	4.26795i	0.143709i
$883$	−45.7654	−1.54013	−0.770064	−	0.637967i	$-0.779776\pi$
$883$	−45.7654	−1.54013	−0.770064	+	0.637967i	$0.779776\pi$
$884$	0	0
$885$	13.6077	0.457418
$886$	− 19.6077i	− 0.658733i
$887$	−23.3205	−0.783026	−0.391513	−	0.920173i	$-0.628048\pi$
$887$	−23.3205	−0.783026	−0.391513	+	0.920173i	$0.628048\pi$
$888$	−8.87564	−0.297847
$889$	2.39230i	0.0802353i
$890$	2.78461i	0.0933403i
$891$	21.1244i	0.707693i
$892$	− 10.0000i	− 0.334825i
$893$	−1.85641	−0.0621223
$894$	−0.588457	−0.0196810
$895$	− 12.0000i	− 0.401116i
$896$	12.1244	0.405046
$897$	0	0
$898$	20.7846	0.693591
$899$	− 18.5885i	− 0.619960i
$900$	4.92820	0.164273
$901$	16.7654	0.558536
$902$	42.5885i	1.41804i
$903$	7.46410i	0.248390i
$904$	− 12.8038i	− 0.425850i
$905$	44.3205i	1.47326i
$906$	2.53590	0.0842496
$907$	−14.5885	−0.484402	−0.242201	−	0.970226i	$-0.577869\pi$
$907$	−14.5885	−0.484402	−0.242201	+	0.970226i	$0.577869\pi$
$908$	− 11.6603i	− 0.386959i
$909$	−10.5167	−0.348816
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	− 7.32051i	− 0.242406i
$913$	38.7846	1.28358
$914$	19.0526	0.630203
$915$	19.2679i	0.636979i
$916$	− 6.39230i	− 0.211208i
$917$	3.46410i	0.114395i
$918$	29.5692i	0.975930i
$919$	43.5692	1.43722	0.718608	−	0.695415i	$-0.244780\pi$
$919$	43.5692	1.43722	0.718608	+	0.695415i	$0.244780\pi$
$920$	3.80385	0.125409
$921$	− 19.4641i	− 0.641364i
$922$	27.0000	0.889198
$923$	0	0
$924$	−3.46410	−0.113961
$925$	− 14.0000i	− 0.460317i
$926$	−46.0526	−1.51338
$927$	15.7513	0.517340
$928$	15.5885i	0.511716i
$929$	− 7.48334i	− 0.245520i	−0.992436	−	0.122760i	$-0.960825\pi$
$929$	− 7.48334i	− 0.245520i	0.992436	−	0.122760i	$-0.0391746\pi$
$930$	13.6077i	0.446214i
$931$	2.00000i	0.0655474i
$932$	25.8564	0.846955
$933$	3.46410	0.113410
$934$	33.8038i	1.10610i
$935$	−34.9808	−1.14399
$936$	0	0
$937$	−40.8038	−1.33300	−0.666502	−	0.745503i	$-0.732209\pi$
$937$	−40.8038	−1.33300	−0.666502	+	0.745503i	$0.732209\pi$
$938$	7.26795i	0.237307i
$939$	9.35898	0.305419
$940$	−1.60770	−0.0524372
$941$	55.8564i	1.82087i	0.413656	+	0.910433i	$0.364252\pi$
$941$	55.8564i	1.82087i	−0.413656	+	0.910433i	$0.635748\pi$
$942$	11.6603i	0.379912i
$943$	6.58846i	0.214550i
$944$	− 53.6603i	− 1.74649i
$945$	−6.92820	−0.225374
$946$	83.5692	2.71707
$947$	− 10.7321i	− 0.348745i	−0.984680	−	0.174372i	$-0.944210\pi$
$947$	− 10.7321i	− 0.348745i	0.984680	−	0.174372i	$-0.0557897\pi$
$948$	4.24871	0.137992
$949$	0	0
$950$	6.92820	0.224781
$951$	0.339746i	0.0110170i
$952$	−7.39230	−0.239586
$953$	−37.1769	−1.20428	−0.602139	−	0.798391i	$-0.705685\pi$
$953$	−37.1769	−1.20428	−0.602139	+	0.798391i	$0.705685\pi$
$954$	− 16.7654i	− 0.542799i
$955$	2.19615i	0.0710658i
$956$	− 26.1962i	− 0.847244i
$957$	10.3923i	0.335936i
$958$	−8.19615	−0.264806
$959$	−21.9282	−0.708099
$960$	1.26795i	0.0409229i
$961$	−7.39230	−0.238461
$962$	0	0
$963$	−48.9282	−1.57669
$964$	10.8038i	0.347969i
$965$	−8.66025	−0.278783
$966$	−1.60770	−0.0517267
$967$	− 3.01924i	− 0.0970921i	−0.998821	−	0.0485461i	$-0.984541\pi$
$967$	− 3.01924i	− 0.0970921i	0.998821	−	0.0485461i	$-0.0154588\pi$
$968$	− 19.7321i	− 0.634212i
$969$	6.24871i	0.200738i
$970$	− 43.1769i	− 1.38633i
$971$	16.6410	0.534036	0.267018	−	0.963692i	$-0.413962\pi$
$971$	16.6410	0.534036	0.267018	+	0.963692i	$0.413962\pi$
$972$	15.2679	0.489720
$973$	20.5885i	0.660036i
$974$	−1.35898	−0.0435447
$975$	0	0
$976$	75.9808	2.43208
$977$	37.6410i	1.20424i	0.798405	+	0.602121i	$0.205678\pi$
$977$	37.6410i	1.20424i	−0.798405	+	0.602121i	$0.794322\pi$
$978$	7.35898	0.235314
$979$	4.39230	0.140379
$980$	1.73205i	0.0553283i
$981$	30.5359i	0.974936i
$982$	− 49.1769i	− 1.56930i
$983$	17.3205i	0.552438i	0.961095	+	0.276219i	$0.0890816\pi$
$983$	17.3205i	0.552438i	−0.961095	+	0.276219i	$0.910918\pi$
$984$	−6.58846	−0.210032
$985$	20.7846	0.662253
$986$	− 22.1769i	− 0.706257i
$987$	−0.679492	−0.0216285
$988$	0	0
$989$	12.9282	0.411093
$990$	34.9808i	1.11176i
$991$	−32.9808	−1.04767	−0.523834	−	0.851820i	$-0.675499\pi$
$991$	−32.9808	−1.04767	−0.523834	+	0.851820i	$0.675499\pi$
$992$	32.1962	1.02223
$993$	− 19.7513i	− 0.626788i
$994$	10.3923i	0.329624i
$995$	− 3.46410i	− 0.109819i
$996$	− 6.00000i	− 0.190117i
$997$	−15.1962	−0.481267	−0.240633	−	0.970616i	$-0.577355\pi$
$997$	−15.1962	−0.481267	−0.240633	+	0.970616i	$0.577355\pi$
$998$	22.4833	0.711698
$999$	− 28.0000i	− 0.885881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.e.337.3		4
13.5	odd	4		1183.2.a.e.1.2		2
13.7	odd	12		91.2.f.b.29.2	yes	4
13.8	odd	4		1183.2.a.f.1.1		2
13.11	odd	12		91.2.f.b.22.2	✓	4
13.12	even	2	inner	1183.2.c.e.337.1		4
39.11	even	12		819.2.o.b.568.1		4
39.20	even	12		819.2.o.b.757.1		4
52.7	even	12		1456.2.s.o.1121.1		4
52.11	even	12		1456.2.s.o.113.1		4
91.11	odd	12		637.2.g.e.373.2		4
91.20	even	12		637.2.f.d.393.2		4
91.24	even	12		637.2.g.d.373.2		4
91.33	even	12		637.2.g.d.263.2		4
91.34	even	4		8281.2.a.r.1.1		2
91.37	odd	12		637.2.h.d.165.1		4
91.46	odd	12		637.2.h.d.471.1		4
91.59	even	12		637.2.h.e.471.1		4
91.72	odd	12		637.2.g.e.263.2		4
91.76	even	12		637.2.f.d.295.2		4
91.83	even	4		8281.2.a.t.1.2		2
91.89	even	12		637.2.h.e.165.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.b.22.2	✓	4	13.11	odd	12
91.2.f.b.29.2	yes	4	13.7	odd	12
637.2.f.d.295.2		4	91.76	even	12
637.2.f.d.393.2		4	91.20	even	12
637.2.g.d.263.2		4	91.33	even	12
637.2.g.d.373.2		4	91.24	even	12
637.2.g.e.263.2		4	91.72	odd	12
637.2.g.e.373.2		4	91.11	odd	12
637.2.h.d.165.1		4	91.37	odd	12
637.2.h.d.471.1		4	91.46	odd	12
637.2.h.e.165.1		4	91.89	even	12
637.2.h.e.471.1		4	91.59	even	12
819.2.o.b.568.1		4	39.11	even	12
819.2.o.b.757.1		4	39.20	even	12
1183.2.a.e.1.2		2	13.5	odd	4
1183.2.a.f.1.1		2	13.8	odd	4
1183.2.c.e.337.1		4	13.12	even	2	inner
1183.2.c.e.337.3		4	1.1	even	1	trivial
1456.2.s.o.113.1		4	52.11	even	12
1456.2.s.o.1121.1		4	52.7	even	12
8281.2.a.r.1.1		2	91.34	even	4
8281.2.a.t.1.2		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)

\(f(q)\)	\(=\)	\(q+1.73205i q^{2} -0.732051 q^{3} -1.00000 q^{4} +1.73205i q^{5} -1.26795i q^{6} +1.00000i q^{7} +1.73205i q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q+1.73205i q^{2} -0.732051 q^{3} -1.00000 q^{4} +1.73205i q^{5} -1.26795i q^{6} +1.00000i q^{7} +1.73205i q^{8} -2.46410 q^{9} -3.00000 q^{10} +4.73205i q^{11} +0.732051 q^{12} -1.73205 q^{14} -1.26795i q^{15} -5.00000 q^{16} +4.26795 q^{17} -4.26795i q^{18} -2.00000i q^{19} -1.73205i q^{20} -0.732051i q^{21} -8.19615 q^{22} -1.26795 q^{23} -1.26795i q^{24} +2.00000 q^{25} +4.00000 q^{27} -1.00000i q^{28} -3.00000 q^{29} +2.19615 q^{30} +6.19615i q^{31} -5.19615i q^{32} -3.46410i q^{33} +7.39230i q^{34} -1.73205 q^{35} +2.46410 q^{36} -7.00000i q^{37} +3.46410 q^{38} -3.00000 q^{40} -5.19615i q^{41} +1.26795 q^{42} -10.1962 q^{43} -4.73205i q^{44} -4.26795i q^{45} -2.19615i q^{46} -0.928203i q^{47} +3.66025 q^{48} -1.00000 q^{49} +3.46410i q^{50} -3.12436 q^{51} +3.92820 q^{53} +6.92820i q^{54} -8.19615 q^{55} -1.73205 q^{56} +1.46410i q^{57} -5.19615i q^{58} +10.7321i q^{59} +1.26795i q^{60} -15.1962 q^{61} -10.7321 q^{62} -2.46410i q^{63} -1.00000 q^{64} +6.00000 q^{66} -4.19615i q^{67} -4.26795 q^{68} +0.928203 q^{69} -3.00000i q^{70} -6.00000i q^{71} -4.26795i q^{72} +7.19615i q^{73} +12.1244 q^{74} -1.46410 q^{75} +2.00000i q^{76} -4.73205 q^{77} +5.80385 q^{79} -8.66025i q^{80} +4.46410 q^{81} +9.00000 q^{82} -8.19615i q^{83} +0.732051i q^{84} +7.39230i q^{85} -17.6603i q^{86} +2.19615 q^{87} -8.19615 q^{88} -0.928203i q^{89} +7.39230 q^{90} +1.26795 q^{92} -4.53590i q^{93} +1.60770 q^{94} +3.46410 q^{95} +3.80385i q^{96} +14.3923i q^{97} -1.73205i q^{98} -11.6603i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 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

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