LMFDB - Embedded newform 1183.2.c.c.337.1

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:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.1
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.c.337.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61803i q^{2} -2.61803 q^{3} -4.85410 q^{4} -2.61803i q^{5} +6.85410i q^{6} +1.00000i q^{7} +7.47214i q^{8} +3.85410 q^{9} +O(q^{10})$	\(q-2.61803i q^{2} -2.61803 q^{3} -4.85410 q^{4} -2.61803i q^{5} +6.85410i q^{6} +1.00000i q^{7} +7.47214i q^{8} +3.85410 q^{9} -6.85410 q^{10} +1.85410i q^{11} +12.7082 q^{12} +2.61803 q^{14} +6.85410i q^{15} +9.85410 q^{16} +1.47214 q^{17} -10.0902i q^{18} +1.85410i q^{19} +12.7082i q^{20} -2.61803i q^{21} +4.85410 q^{22} +4.47214 q^{23} -19.5623i q^{24} -1.85410 q^{25} -2.23607 q^{27} -4.85410i q^{28} +7.09017 q^{29} +17.9443 q^{30} +4.70820i q^{31} -10.8541i q^{32} -4.85410i q^{33} -3.85410i q^{34} +2.61803 q^{35} -18.7082 q^{36} +4.00000i q^{37} +4.85410 q^{38} +19.5623 q^{40} -0.763932i q^{41} -6.85410 q^{42} -12.5623 q^{43} -9.00000i q^{44} -10.0902i q^{45} -11.7082i q^{46} -2.23607i q^{47} -25.7984 q^{48} -1.00000 q^{49} +4.85410i q^{50} -3.85410 q^{51} +3.76393 q^{53} +5.85410i q^{54} +4.85410 q^{55} -7.47214 q^{56} -4.85410i q^{57} -18.5623i q^{58} -2.23607i q^{59} -33.2705i q^{60} -6.00000 q^{61} +12.3262 q^{62} +3.85410i q^{63} -8.70820 q^{64} -12.7082 q^{66} +12.7082i q^{67} -7.14590 q^{68} -11.7082 q^{69} -6.85410i q^{70} +14.1803i q^{71} +28.7984i q^{72} -2.00000i q^{73} +10.4721 q^{74} +4.85410 q^{75} -9.00000i q^{76} -1.85410 q^{77} +4.00000 q^{79} -25.7984i q^{80} -5.70820 q^{81} -2.00000 q^{82} -6.70820i q^{83} +12.7082i q^{84} -3.85410i q^{85} +32.8885i q^{86} -18.5623 q^{87} -13.8541 q^{88} +4.90983i q^{89} -26.4164 q^{90} -21.7082 q^{92} -12.3262i q^{93} -5.85410 q^{94} +4.85410 q^{95} +28.4164i q^{96} -18.8541i q^{97} +2.61803i q^{98} +7.14590i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} - 6 q^{4} + 2 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 - 6 * q^4 + 2 * q^9	$ 4 q - 6 q^{3} - 6 q^{4} + 2 q^{9} - 14 q^{10} + 24 q^{12} + 6 q^{14} + 26 q^{16} - 12 q^{17} + 6 q^{22} + 6 q^{25} + 6 q^{29} + 36 q^{30} + 6 q^{35} - 48 q^{36} + 6 q^{38} + 38 q^{40} - 14 q^{42} - 10 q^{43} - 54 q^{48} - 4 q^{49} - 2 q^{51} + 24 q^{53} + 6 q^{55} - 12 q^{56} - 24 q^{61} + 18 q^{62} - 8 q^{64} - 24 q^{66} - 42 q^{68} - 20 q^{69} + 24 q^{74} + 6 q^{75} + 6 q^{77} + 16 q^{79} + 4 q^{81} - 8 q^{82} - 34 q^{87} - 42 q^{88} - 52 q^{90} - 60 q^{92} - 10 q^{94} + 6 q^{95}+O(q^{100}) $ 4 * q - 6 * q^3 - 6 * q^4 + 2 * q^9 - 14 * q^10 + 24 * q^12 + 6 * q^14 + 26 * q^16 - 12 * q^17 + 6 * q^22 + 6 * q^25 + 6 * q^29 + 36 * q^30 + 6 * q^35 - 48 * q^36 + 6 * q^38 + 38 * q^40 - 14 * q^42 - 10 * q^43 - 54 * q^48 - 4 * q^49 - 2 * q^51 + 24 * q^53 + 6 * q^55 - 12 * q^56 - 24 * q^61 + 18 * q^62 - 8 * q^64 - 24 * q^66 - 42 * q^68 - 20 * q^69 + 24 * q^74 + 6 * q^75 + 6 * q^77 + 16 * q^79 + 4 * q^81 - 8 * q^82 - 34 * q^87 - 42 * q^88 - 52 * q^90 - 60 * q^92 - 10 * q^94 + 6 * q^95

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 $

$2$	− 2.61803i	− 1.85123i	−0.378467	−	0.925615i	$-0.623549\pi$
$2$	− 2.61803i	− 1.85123i	0.378467	−	0.925615i	$-0.376451\pi$
$3$	−2.61803	−1.51152	−0.755761	−	0.654847i	$-0.772733\pi$
$3$	−2.61803	−1.51152	−0.755761	+	0.654847i	$0.772733\pi$
$4$	−4.85410	−2.42705
$5$	− 2.61803i	− 1.17082i	−0.810737	−	0.585410i	$-0.800933\pi$
$5$	− 2.61803i	− 1.17082i	0.810737	−	0.585410i	$-0.199067\pi$
$6$	6.85410i	2.79818i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	7.47214i	2.64180i
$9$	3.85410	1.28470
$10$	−6.85410	−2.16746
$11$	1.85410i	0.559033i	0.960141	+	0.279516i	$0.0901741\pi$
$11$	1.85410i	0.559033i	−0.960141	+	0.279516i	$0.909826\pi$
$12$	12.7082	3.66854
$13$	0	0
$13$	0	0
$14$	2.61803	0.699699
$15$	6.85410i	1.76972i
$16$	9.85410	2.46353
$17$	1.47214	0.357045	0.178523	−	0.983936i	$-0.442868\pi$
$17$	1.47214	0.357045	0.178523	+	0.983936i	$0.442868\pi$
$18$	− 10.0902i	− 2.37828i
$19$	1.85410i	0.425360i	0.977122	+	0.212680i	$0.0682192\pi$
$19$	1.85410i	0.425360i	−0.977122	+	0.212680i	$0.931781\pi$
$20$	12.7082i	2.84164i
$21$	− 2.61803i	− 0.571302i
$22$	4.85410	1.03490
$23$	4.47214	0.932505	0.466252	−	0.884652i	$-0.345604\pi$
$23$	4.47214	0.932505	0.466252	+	0.884652i	$0.345604\pi$
$24$	− 19.5623i	− 3.99314i
$25$	−1.85410	−0.370820
$26$	0	0
$27$	−2.23607	−0.430331
$28$	− 4.85410i	− 0.917339i
$29$	7.09017	1.31661	0.658306	−	0.752751i	$-0.271273\pi$
$29$	7.09017	1.31661	0.658306	+	0.752751i	$0.271273\pi$
$30$	17.9443	3.27616
$31$	4.70820i	0.845618i	0.906219	+	0.422809i	$0.138956\pi$
$31$	4.70820i	0.845618i	−0.906219	+	0.422809i	$0.861044\pi$
$32$	− 10.8541i	− 1.91875i
$33$	− 4.85410i	− 0.844991i
$34$	− 3.85410i	− 0.660973i
$35$	2.61803	0.442529
$36$	−18.7082	−3.11803
$37$	4.00000i	0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$	4.00000i	0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$	4.85410	0.787439
$39$	0	0
$40$	19.5623	3.09307
$41$	− 0.763932i	− 0.119306i	−0.998219	−	0.0596531i	$-0.981001\pi$
$41$	− 0.763932i	− 0.119306i	0.998219	−	0.0596531i	$-0.0189994\pi$
$42$	−6.85410	−1.05761
$43$	−12.5623	−1.91573	−0.957867	−	0.287213i	$-0.907271\pi$
$43$	−12.5623	−1.91573	−0.957867	+	0.287213i	$0.907271\pi$
$44$	− 9.00000i	− 1.35680i
$45$	− 10.0902i	− 1.50415i
$46$	− 11.7082i	− 1.72628i
$47$	− 2.23607i	− 0.326164i	−0.986613	−	0.163082i	$-0.947856\pi$
$47$	− 2.23607i	− 0.326164i	0.986613	−	0.163082i	$-0.0521435\pi$
$48$	−25.7984	−3.72367
$49$	−1.00000	−0.142857
$50$	4.85410i	0.686474i
$51$	−3.85410	−0.539682
$52$	0	0
$53$	3.76393	0.517016	0.258508	−	0.966009i	$-0.416769\pi$
$53$	3.76393	0.517016	0.258508	+	0.966009i	$0.416769\pi$
$54$	5.85410i	0.796642i
$55$	4.85410	0.654527
$56$	−7.47214	−0.998506
$57$	− 4.85410i	− 0.642942i
$58$	− 18.5623i	− 2.43735i
$59$	− 2.23607i	− 0.291111i	−0.989350	−	0.145556i	$-0.953503\pi$
$59$	− 2.23607i	− 0.291111i	0.989350	−	0.145556i	$-0.0464970\pi$
$60$	− 33.2705i	− 4.29520i
$61$	−6.00000	−0.768221	−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000	−0.768221	−0.384111	+	0.923287i	$0.625492\pi$
$62$	12.3262	1.56543
$63$	3.85410i	0.485571i
$64$	−8.70820	−1.08853
$65$	0	0
$66$	−12.7082	−1.56427
$67$	12.7082i	1.55255i	0.630392	+	0.776277i	$0.282894\pi$
$67$	12.7082i	1.55255i	−0.630392	+	0.776277i	$0.717106\pi$
$68$	−7.14590	−0.866567
$69$	−11.7082	−1.40950
$70$	− 6.85410i	− 0.819222i
$71$	14.1803i	1.68290i	0.540338	+	0.841448i	$0.318297\pi$
$71$	14.1803i	1.68290i	−0.540338	+	0.841448i	$0.681703\pi$
$72$	28.7984i	3.39392i
$73$	− 2.00000i	− 0.234082i	−0.993127	−	0.117041i	$-0.962659\pi$
$73$	− 2.00000i	− 0.234082i	0.993127	−	0.117041i	$-0.0373409\pi$
$74$	10.4721	1.21736
$75$	4.85410	0.560503
$76$	− 9.00000i	− 1.03237i
$77$	−1.85410	−0.211295
$78$	0	0
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	− 25.7984i	− 2.88435i
$81$	−5.70820	−0.634245
$82$	−2.00000	−0.220863
$83$	− 6.70820i	− 0.736321i	−0.929762	−	0.368161i	$-0.879988\pi$
$83$	− 6.70820i	− 0.736321i	0.929762	−	0.368161i	$-0.120012\pi$
$84$	12.7082i	1.38658i
$85$	− 3.85410i	− 0.418036i
$86$	32.8885i	3.54646i
$87$	−18.5623	−1.99009
$88$	−13.8541	−1.47685
$89$	4.90983i	0.520441i	0.965549	+	0.260220i	$0.0837952\pi$
$89$	4.90983i	0.520441i	−0.965549	+	0.260220i	$0.916205\pi$
$90$	−26.4164	−2.78453
$91$	0	0
$92$	−21.7082	−2.26324
$93$	− 12.3262i	− 1.27817i
$94$	−5.85410	−0.603805
$95$	4.85410	0.498020
$96$	28.4164i	2.90024i
$97$	− 18.8541i	− 1.91434i	−0.289520	−	0.957172i	$-0.593496\pi$
$97$	− 18.8541i	− 1.91434i	0.289520	−	0.957172i	$-0.406504\pi$
$98$	2.61803i	0.264461i
$99$	7.14590i	0.718190i
$100$	9.00000	0.900000
$101$	11.5623	1.15049	0.575246	−	0.817980i	$-0.304906\pi$
$101$	11.5623	1.15049	0.575246	+	0.817980i	$0.304906\pi$
$102$	10.0902i	0.999076i
$103$	8.70820	0.858045	0.429022	−	0.903294i	$-0.358858\pi$
$103$	8.70820	0.858045	0.429022	+	0.903294i	$0.358858\pi$
$104$	0	0
$105$	−6.85410	−0.668892
$106$	− 9.85410i	− 0.957115i
$107$	−3.38197	−0.326947	−0.163473	−	0.986548i	$-0.552270\pi$
$107$	−3.38197	−0.326947	−0.163473	+	0.986548i	$0.552270\pi$
$108$	10.8541	1.04444
$109$	2.70820i	0.259399i	0.991553	+	0.129699i	$0.0414012\pi$
$109$	2.70820i	0.259399i	−0.991553	+	0.129699i	$0.958599\pi$
$110$	− 12.7082i	− 1.21168i
$111$	− 10.4721i	− 0.993971i
$112$	9.85410i	0.931125i
$113$	1.47214	0.138487	0.0692435	−	0.997600i	$-0.477941\pi$
$113$	1.47214	0.138487	0.0692435	+	0.997600i	$0.477941\pi$
$114$	−12.7082	−1.19023
$115$	− 11.7082i	− 1.09180i
$116$	−34.4164	−3.19548
$117$	0	0
$118$	−5.85410	−0.538914
$119$	1.47214i	0.134950i
$120$	−51.2148	−4.67525
$121$	7.56231	0.687482
$122$	15.7082i	1.42215i
$123$	2.00000i	0.180334i
$124$	− 22.8541i	− 2.05236i
$125$	− 8.23607i	− 0.736656i
$126$	10.0902	0.898904
$127$	20.8541	1.85050	0.925251	−	0.379355i	$-0.123854\pi$
$127$	20.8541	1.85050	0.925251	+	0.379355i	$0.123854\pi$
$128$	1.09017i	0.0963583i
$129$	32.8885	2.89567
$130$	0	0
$131$	−15.3262	−1.33906	−0.669530	−	0.742785i	$-0.733504\pi$
$131$	−15.3262	−1.33906	−0.669530	+	0.742785i	$0.733504\pi$
$132$	23.5623i	2.05084i
$133$	−1.85410	−0.160771
$134$	33.2705	2.87413
$135$	5.85410i	0.503841i
$136$	11.0000i	0.943242i
$137$	− 2.61803i	− 0.223674i	−0.993727	−	0.111837i	$-0.964327\pi$
$137$	− 2.61803i	− 0.223674i	0.993727	−	0.111837i	$-0.0356734\pi$
$138$	30.6525i	2.60931i
$139$	4.56231	0.386970	0.193485	−	0.981103i	$-0.438021\pi$
$139$	4.56231	0.386970	0.193485	+	0.981103i	$0.438021\pi$
$140$	−12.7082	−1.07404
$141$	5.85410i	0.493004i
$142$	37.1246	3.11543
$143$	0	0
$144$	37.9787	3.16489
$145$	− 18.5623i	− 1.54152i
$146$	−5.23607	−0.433340
$147$	2.61803	0.215932
$148$	− 19.4164i	− 1.59602i
$149$	− 1.85410i	− 0.151894i	−0.997112	−	0.0759470i	$-0.975802\pi$
$149$	− 1.85410i	− 0.151894i	0.997112	−	0.0759470i	$-0.0241980\pi$
$150$	− 12.7082i	− 1.03762i
$151$	− 1.29180i	− 0.105125i	−0.998618	−	0.0525624i	$-0.983261\pi$
$151$	− 1.29180i	− 0.105125i	0.998618	−	0.0525624i	$-0.0167389\pi$
$152$	−13.8541	−1.12372
$153$	5.67376	0.458696
$154$	4.85410i	0.391155i
$155$	12.3262	0.990067
$156$	0	0
$157$	14.8541	1.18549	0.592743	−	0.805392i	$-0.298045\pi$
$157$	14.8541	1.18549	0.592743	+	0.805392i	$0.298045\pi$
$158$	− 10.4721i	− 0.833118i
$159$	−9.85410	−0.781481
$160$	−28.4164	−2.24651
$161$	4.47214i	0.352454i
$162$	14.9443i	1.17413i
$163$	− 3.70820i	− 0.290449i	−0.989399	−	0.145224i	$-0.953610\pi$
$163$	− 3.70820i	− 0.290449i	0.989399	−	0.145224i	$-0.0463904\pi$
$164$	3.70820i	0.289562i
$165$	−12.7082	−0.989332
$166$	−17.5623	−1.36310
$167$	14.2361i	1.10162i	0.834631	+	0.550810i	$0.185681\pi$
$167$	14.2361i	1.10162i	−0.834631	+	0.550810i	$0.814319\pi$
$168$	19.5623	1.50926
$169$	0	0
$170$	−10.0902	−0.773881
$171$	7.14590i	0.546460i
$172$	60.9787	4.64958
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	48.5967i	3.68411i
$175$	− 1.85410i	− 0.140157i
$176$	18.2705i	1.37719i
$177$	5.85410i	0.440021i
$178$	12.8541	0.963456
$179$	9.00000	0.672692	0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000	0.672692	0.336346	+	0.941739i	$0.390809\pi$
$180$	48.9787i	3.65066i
$181$	−9.70820	−0.721605	−0.360803	−	0.932642i	$-0.617497\pi$
$181$	−9.70820	−0.721605	−0.360803	+	0.932642i	$0.617497\pi$
$182$	0	0
$183$	15.7082	1.16118
$184$	33.4164i	2.46349i
$185$	10.4721	0.769927
$186$	−32.2705	−2.36619
$187$	2.72949i	0.199600i
$188$	10.8541i	0.791617i
$189$	− 2.23607i	− 0.162650i
$190$	− 12.7082i	− 0.921950i
$191$	21.3820	1.54714	0.773572	−	0.633708i	$-0.218468\pi$
$191$	21.3820	1.54714	0.773572	+	0.633708i	$0.218468\pi$
$192$	22.7984	1.64533
$193$	− 6.00000i	− 0.431889i	−0.976406	−	0.215945i	$-0.930717\pi$
$193$	− 6.00000i	− 0.431889i	0.976406	−	0.215945i	$-0.0692831\pi$
$194$	−49.3607	−3.54389
$195$	0	0
$196$	4.85410	0.346722
$197$	16.7984i	1.19683i	0.801185	+	0.598417i	$0.204203\pi$
$197$	16.7984i	1.19683i	−0.801185	+	0.598417i	$0.795797\pi$
$198$	18.7082	1.32953
$199$	24.4164	1.73083	0.865417	−	0.501053i	$-0.167054\pi$
$199$	24.4164	1.73083	0.865417	+	0.501053i	$0.167054\pi$
$200$	− 13.8541i	− 0.979633i
$201$	− 33.2705i	− 2.34672i
$202$	− 30.2705i	− 2.12983i
$203$	7.09017i	0.497632i
$204$	18.7082	1.30984
$205$	−2.00000	−0.139686
$206$	− 22.7984i	− 1.58844i
$207$	17.2361	1.19799
$208$	0	0
$209$	−3.43769	−0.237790
$210$	17.9443i	1.23827i
$211$	4.70820	0.324126	0.162063	−	0.986780i	$-0.448185\pi$
$211$	4.70820	0.324126	0.162063	+	0.986780i	$0.448185\pi$
$212$	−18.2705	−1.25482
$213$	− 37.1246i	− 2.54374i
$214$	8.85410i	0.605254i
$215$	32.8885i	2.24298i
$216$	− 16.7082i	− 1.13685i
$217$	−4.70820	−0.319614
$218$	7.09017	0.480207
$219$	5.23607i	0.353821i
$220$	−23.5623	−1.58857
$221$	0	0
$222$	−27.4164	−1.84007
$223$	− 20.2705i	− 1.35741i	−0.734409	−	0.678707i	$-0.762541\pi$
$223$	− 20.2705i	− 1.35741i	0.734409	−	0.678707i	$-0.237459\pi$
$224$	10.8541	0.725220
$225$	−7.14590	−0.476393
$226$	− 3.85410i	− 0.256371i
$227$	− 1.47214i	− 0.0977091i	−0.998806	−	0.0488545i	$-0.984443\pi$
$227$	− 1.47214i	− 0.0977091i	0.998806	−	0.0488545i	$-0.0155571\pi$
$228$	23.5623i	1.56045i
$229$	− 13.1246i	− 0.867299i	−0.901082	−	0.433649i	$-0.857226\pi$
$229$	− 13.1246i	− 0.867299i	0.901082	−	0.433649i	$-0.142774\pi$
$230$	−30.6525	−2.02116
$231$	4.85410	0.319376
$232$	52.9787i	3.47822i
$233$	−2.61803	−0.171513	−0.0857566	−	0.996316i	$-0.527331\pi$
$233$	−2.61803	−0.171513	−0.0857566	+	0.996316i	$0.527331\pi$
$234$	0	0
$235$	−5.85410	−0.381880
$236$	10.8541i	0.706542i
$237$	−10.4721	−0.680238
$238$	3.85410	0.249824
$239$	24.7082i	1.59824i	0.601171	+	0.799120i	$0.294701\pi$
$239$	24.7082i	1.59824i	−0.601171	+	0.799120i	$0.705299\pi$
$240$	67.5410i	4.35975i
$241$	24.5623i	1.58220i	0.611689	+	0.791099i	$0.290491\pi$
$241$	24.5623i	1.58220i	−0.611689	+	0.791099i	$0.709509\pi$
$242$	− 19.7984i	− 1.27269i
$243$	21.6525	1.38901
$244$	29.1246	1.86451
$245$	2.61803i	0.167260i
$246$	5.23607	0.333840
$247$	0	0
$248$	−35.1803	−2.23395
$249$	17.5623i	1.11297i
$250$	−21.5623	−1.36372
$251$	−0.763932	−0.0482190	−0.0241095	−	0.999709i	$-0.507675\pi$
$251$	−0.763932	−0.0482190	−0.0241095	+	0.999709i	$0.507675\pi$
$252$	− 18.7082i	− 1.17851i
$253$	8.29180i	0.521301i
$254$	− 54.5967i	− 3.42570i
$255$	10.0902i	0.631871i
$256$	−14.5623	−0.910144
$257$	−16.7426	−1.04438	−0.522189	−	0.852830i	$-0.674884\pi$
$257$	−16.7426	−1.04438	−0.522189	+	0.852830i	$0.674884\pi$
$258$	− 86.1033i	− 5.36056i
$259$	−4.00000	−0.248548
$260$	0	0
$261$	27.3262	1.69145
$262$	40.1246i	2.47891i
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	36.2705	2.23230
$265$	− 9.85410i	− 0.605333i
$266$	4.85410i	0.297624i
$267$	− 12.8541i	− 0.786658i
$268$	− 61.6869i	− 3.76813i
$269$	−28.7426	−1.75247	−0.876235	−	0.481884i	$-0.839953\pi$
$269$	−28.7426	−1.75247	−0.876235	+	0.481884i	$0.839953\pi$
$270$	15.3262	0.932725
$271$	− 8.41641i	− 0.511260i	−0.966775	−	0.255630i	$-0.917717\pi$
$271$	− 8.41641i	− 0.511260i	0.966775	−	0.255630i	$-0.0822829\pi$
$272$	14.5066	0.879590
$273$	0	0
$274$	−6.85410	−0.414071
$275$	− 3.43769i	− 0.207301i
$276$	56.8328	3.42093
$277$	5.00000	0.300421	0.150210	−	0.988654i	$-0.452005\pi$
$277$	5.00000	0.300421	0.150210	+	0.988654i	$0.452005\pi$
$278$	− 11.9443i	− 0.716370i
$279$	18.1459i	1.08637i
$280$	19.5623i	1.16907i
$281$	20.1803i	1.20386i	0.798550	+	0.601929i	$0.205601\pi$
$281$	20.1803i	1.20386i	−0.798550	+	0.601929i	$0.794399\pi$
$282$	15.3262	0.912664
$283$	−13.4164	−0.797523	−0.398761	−	0.917055i	$-0.630560\pi$
$283$	−13.4164	−0.797523	−0.398761	+	0.917055i	$0.630560\pi$
$284$	− 68.8328i	− 4.08448i
$285$	−12.7082	−0.752769
$286$	0	0
$287$	0.763932	0.0450935
$288$	− 41.8328i	− 2.46502i
$289$	−14.8328	−0.872519
$290$	−48.5967	−2.85370
$291$	49.3607i	2.89357i
$292$	9.70820i	0.568130i
$293$	− 6.76393i	− 0.395153i	−0.980287	−	0.197577i	$-0.936693\pi$
$293$	− 6.76393i	− 0.395153i	0.980287	−	0.197577i	$-0.0633071\pi$
$294$	− 6.85410i	− 0.399739i
$295$	−5.85410	−0.340839
$296$	−29.8885	−1.73724
$297$	− 4.14590i	− 0.240569i
$298$	−4.85410	−0.281191
$299$	0	0
$300$	−23.5623	−1.36037
$301$	− 12.5623i	− 0.724079i
$302$	−3.38197	−0.194610
$303$	−30.2705	−1.73900
$304$	18.2705i	1.04789i
$305$	15.7082i	0.899449i
$306$	− 14.8541i	− 0.849152i
$307$	− 4.85410i	− 0.277038i	−0.990360	−	0.138519i	$-0.955766\pi$
$307$	− 4.85410i	− 0.277038i	0.990360	−	0.138519i	$-0.0442342\pi$
$308$	9.00000	0.512823
$309$	−22.7984	−1.29695
$310$	− 32.2705i	− 1.83284i
$311$	−3.32624	−0.188614	−0.0943068	−	0.995543i	$-0.530063\pi$
$311$	−3.32624	−0.188614	−0.0943068	+	0.995543i	$0.530063\pi$
$312$	0	0
$313$	25.1246	1.42013	0.710064	−	0.704138i	$-0.248666\pi$
$313$	25.1246	1.42013	0.710064	+	0.704138i	$0.248666\pi$
$314$	− 38.8885i	− 2.19461i
$315$	10.0902	0.568517
$316$	−19.4164	−1.09226
$317$	− 26.2361i	− 1.47356i	−0.676130	−	0.736782i	$-0.736344\pi$
$317$	− 26.2361i	− 1.47356i	0.676130	−	0.736782i	$-0.263656\pi$
$318$	25.7984i	1.44670i
$319$	13.1459i	0.736029i
$320$	22.7984i	1.27447i
$321$	8.85410	0.494188
$322$	11.7082	0.652473
$323$	2.72949i	0.151873i
$324$	27.7082	1.53934
$325$	0	0
$326$	−9.70820	−0.537688
$327$	− 7.09017i	− 0.392087i
$328$	5.70820	0.315183
$329$	2.23607	0.123278
$330$	33.2705i	1.83148i
$331$	10.1459i	0.557669i	0.960339	+	0.278834i	$0.0899481\pi$
$331$	10.1459i	0.557669i	−0.960339	+	0.278834i	$0.910052\pi$
$332$	32.5623i	1.78709i
$333$	15.4164i	0.844814i
$334$	37.2705	2.03935
$335$	33.2705	1.81776
$336$	− 25.7984i	− 1.40742i
$337$	11.5623	0.629839	0.314919	−	0.949118i	$-0.398022\pi$
$337$	11.5623	0.629839	0.314919	+	0.949118i	$0.398022\pi$
$338$	0	0
$339$	−3.85410	−0.209326
$340$	18.7082i	1.01459i
$341$	−8.72949	−0.472728
$342$	18.7082	1.01162
$343$	− 1.00000i	− 0.0539949i
$344$	− 93.8673i	− 5.06098i
$345$	30.6525i	1.65027i
$346$	− 23.5623i	− 1.26672i
$347$	30.7639	1.65149	0.825747	−	0.564040i	$-0.190754\pi$
$347$	30.7639	1.65149	0.825747	+	0.564040i	$0.190754\pi$
$348$	90.1033	4.83005
$349$	20.7082i	1.10848i	0.832355	+	0.554242i	$0.186992\pi$
$349$	20.7082i	1.10848i	−0.832355	+	0.554242i	$0.813008\pi$
$350$	−4.85410	−0.259463
$351$	0	0
$352$	20.1246	1.07265
$353$	− 22.1459i	− 1.17871i	−0.807875	−	0.589354i	$-0.799382\pi$
$353$	− 22.1459i	− 1.17871i	0.807875	−	0.589354i	$-0.200618\pi$
$354$	15.3262	0.814580
$355$	37.1246	1.97037
$356$	− 23.8328i	− 1.26314i
$357$	− 3.85410i	− 0.203981i
$358$	− 23.5623i	− 1.24531i
$359$	− 22.0902i	− 1.16587i	−0.812517	−	0.582937i	$-0.801903\pi$
$359$	− 22.0902i	− 1.16587i	0.812517	−	0.582937i	$-0.198097\pi$
$360$	75.3951	3.97367
$361$	15.5623	0.819069
$362$	25.4164i	1.33586i
$363$	−19.7984	−1.03915
$364$	0	0
$365$	−5.23607	−0.274068
$366$	− 41.1246i	− 2.14962i
$367$	−1.41641	−0.0739359	−0.0369679	−	0.999316i	$-0.511770\pi$
$367$	−1.41641	−0.0739359	−0.0369679	+	0.999316i	$0.511770\pi$
$368$	44.0689	2.29725
$369$	− 2.94427i	− 0.153273i
$370$	− 27.4164i	− 1.42531i
$371$	3.76393i	0.195414i
$372$	59.8328i	3.10219i
$373$	−20.5623	−1.06468	−0.532338	−	0.846532i	$-0.678686\pi$
$373$	−20.5623	−1.06468	−0.532338	+	0.846532i	$0.678686\pi$
$374$	7.14590	0.369506
$375$	21.5623i	1.11347i
$376$	16.7082	0.861660
$377$	0	0
$378$	−5.85410	−0.301103
$379$	6.14590i	0.315694i	0.987464	+	0.157847i	$0.0504552\pi$
$379$	6.14590i	0.315694i	−0.987464	+	0.157847i	$0.949545\pi$
$380$	−23.5623	−1.20872
$381$	−54.5967	−2.79708
$382$	− 55.9787i	− 2.86412i
$383$	21.9787i	1.12306i	0.827456	+	0.561530i	$0.189787\pi$
$383$	21.9787i	1.12306i	−0.827456	+	0.561530i	$0.810213\pi$
$384$	− 2.85410i	− 0.145648i
$385$	4.85410i	0.247388i
$386$	−15.7082	−0.799527
$387$	−48.4164	−2.46114
$388$	91.5197i	4.64621i
$389$	11.8885	0.602773	0.301387	−	0.953502i	$-0.402551\pi$
$389$	11.8885	0.602773	0.301387	+	0.953502i	$0.402551\pi$
$390$	0	0
$391$	6.58359	0.332947
$392$	− 7.47214i	− 0.377400i
$393$	40.1246	2.02402
$394$	43.9787	2.21562
$395$	− 10.4721i	− 0.526910i
$396$	− 34.6869i	− 1.74308i
$397$	1.41641i	0.0710875i	0.999368	+	0.0355437i	$0.0113163\pi$
$397$	1.41641i	0.0710875i	−0.999368	+	0.0355437i	$0.988684\pi$
$398$	− 63.9230i	− 3.20417i
$399$	4.85410	0.243009
$400$	−18.2705	−0.913525
$401$	35.4508i	1.77033i	0.465276	+	0.885165i	$0.345955\pi$
$401$	35.4508i	1.77033i	−0.465276	+	0.885165i	$0.654045\pi$
$402$	−87.1033	−4.34432
$403$	0	0
$404$	−56.1246	−2.79230
$405$	14.9443i	0.742587i
$406$	18.5623	0.921232
$407$	−7.41641	−0.367618
$408$	− 28.7984i	− 1.42573i
$409$	− 14.4377i	− 0.713898i	−0.934124	−	0.356949i	$-0.883817\pi$
$409$	− 14.4377i	− 0.713898i	0.934124	−	0.356949i	$-0.116183\pi$
$410$	5.23607i	0.258591i
$411$	6.85410i	0.338088i
$412$	−42.2705	−2.08252
$413$	2.23607	0.110030
$414$	− 45.1246i	− 2.21775i
$415$	−17.5623	−0.862100
$416$	0	0
$417$	−11.9443	−0.584914
$418$	9.00000i	0.440204i
$419$	−11.9443	−0.583516	−0.291758	−	0.956492i	$-0.594240\pi$
$419$	−11.9443	−0.583516	−0.291758	+	0.956492i	$0.594240\pi$
$420$	33.2705	1.62343
$421$	− 1.41641i	− 0.0690315i	−0.999404	−	0.0345157i	$-0.989011\pi$
$421$	− 1.41641i	− 0.0690315i	0.999404	−	0.0345157i	$-0.0109889\pi$
$422$	− 12.3262i	− 0.600032i
$423$	− 8.61803i	− 0.419023i
$424$	28.1246i	1.36585i
$425$	−2.72949	−0.132400
$426$	−97.1935	−4.70904
$427$	− 6.00000i	− 0.290360i
$428$	16.4164	0.793517
$429$	0	0
$430$	86.1033	4.15227
$431$	− 7.79837i	− 0.375634i	−0.982204	−	0.187817i	$-0.939859\pi$
$431$	− 7.79837i	− 0.375634i	0.982204	−	0.187817i	$-0.0601413\pi$
$432$	−22.0344	−1.06013
$433$	−1.00000	−0.0480569	−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000	−0.0480569	−0.0240285	+	0.999711i	$0.507649\pi$
$434$	12.3262i	0.591678i
$435$	48.5967i	2.33004i
$436$	− 13.1459i	− 0.629574i
$437$	8.29180i	0.396650i
$438$	13.7082	0.655003
$439$	−14.8541	−0.708948	−0.354474	−	0.935066i	$-0.615340\pi$
$439$	−14.8541	−0.708948	−0.354474	+	0.935066i	$0.615340\pi$
$440$	36.2705i	1.72913i
$441$	−3.85410	−0.183529
$442$	0	0
$443$	−5.23607	−0.248773	−0.124387	−	0.992234i	$-0.539696\pi$
$443$	−5.23607	−0.248773	−0.124387	+	0.992234i	$0.539696\pi$
$444$	50.8328i	2.41242i
$445$	12.8541	0.609343
$446$	−53.0689	−2.51288
$447$	4.85410i	0.229591i
$448$	− 8.70820i	− 0.411424i
$449$	19.5279i	0.921577i	0.887510	+	0.460788i	$0.152433\pi$
$449$	19.5279i	0.921577i	−0.887510	+	0.460788i	$0.847567\pi$
$450$	18.7082i	0.881913i
$451$	1.41641	0.0666960
$452$	−7.14590	−0.336115
$453$	3.38197i	0.158899i
$454$	−3.85410	−0.180882
$455$	0	0
$456$	36.2705	1.69852
$457$	− 15.4164i	− 0.721149i	−0.932730	−	0.360575i	$-0.882581\pi$
$457$	− 15.4164i	− 0.721149i	0.932730	−	0.360575i	$-0.117419\pi$
$458$	−34.3607	−1.60557
$459$	−3.29180	−0.153648
$460$	56.8328i	2.64984i
$461$	12.2148i	0.568899i	0.958691	+	0.284450i	$0.0918108\pi$
$461$	12.2148i	0.568899i	−0.958691	+	0.284450i	$0.908189\pi$
$462$	− 12.7082i	− 0.591239i
$463$	6.70820i	0.311757i	0.987776	+	0.155878i	$0.0498208\pi$
$463$	6.70820i	0.311757i	−0.987776	+	0.155878i	$0.950179\pi$
$464$	69.8673	3.24351
$465$	−32.2705	−1.49651
$466$	6.85410i	0.317510i
$467$	−2.34752	−0.108630	−0.0543152	−	0.998524i	$-0.517298\pi$
$467$	−2.34752	−0.108630	−0.0543152	+	0.998524i	$0.517298\pi$
$468$	0	0
$469$	−12.7082	−0.586810
$470$	15.3262i	0.706947i
$471$	−38.8885	−1.79189
$472$	16.7082	0.769057
$473$	− 23.2918i	− 1.07096i
$474$	27.4164i	1.25928i
$475$	− 3.43769i	− 0.157732i
$476$	− 7.14590i	− 0.327532i
$477$	14.5066	0.664211
$478$	64.6869	2.95871
$479$	24.9787i	1.14131i	0.821191	+	0.570653i	$0.193310\pi$
$479$	24.9787i	1.14131i	−0.821191	+	0.570653i	$0.806690\pi$
$480$	74.3951	3.39566
$481$	0	0
$482$	64.3050	2.92901
$483$	− 11.7082i	− 0.532742i
$484$	−36.7082	−1.66855
$485$	−49.3607	−2.24135
$486$	− 56.6869i	− 2.57137i
$487$	− 29.9787i	− 1.35847i	−0.733923	−	0.679233i	$-0.762313\pi$
$487$	− 29.9787i	− 1.35847i	0.733923	−	0.679233i	$-0.237687\pi$
$488$	− 44.8328i	− 2.02949i
$489$	9.70820i	0.439020i
$490$	6.85410	0.309637
$491$	−12.3820	−0.558790	−0.279395	−	0.960176i	$-0.590134\pi$
$491$	−12.3820	−0.558790	−0.279395	+	0.960176i	$0.590134\pi$
$492$	− 9.70820i	− 0.437680i
$493$	10.4377	0.470090
$494$	0	0
$495$	18.7082	0.840871
$496$	46.3951i	2.08320i
$497$	−14.1803	−0.636075
$498$	45.9787	2.06036
$499$	− 14.8541i	− 0.664961i	−0.943110	−	0.332480i	$-0.892114\pi$
$499$	− 14.8541i	− 0.664961i	0.943110	−	0.332480i	$-0.107886\pi$
$500$	39.9787i	1.78790i
$501$	− 37.2705i	− 1.66512i
$502$	2.00000i	0.0892644i
$503$	26.6180	1.18684	0.593420	−	0.804893i	$-0.297777\pi$
$503$	26.6180	1.18684	0.593420	+	0.804893i	$0.297777\pi$
$504$	−28.7984	−1.28278
$505$	− 30.2705i	− 1.34702i
$506$	21.7082	0.965047
$507$	0	0
$508$	−101.228	−4.49126
$509$	18.5967i	0.824286i	0.911119	+	0.412143i	$0.135220\pi$
$509$	18.5967i	0.824286i	−0.911119	+	0.412143i	$0.864780\pi$
$510$	26.4164	1.16974
$511$	2.00000	0.0884748
$512$	40.3050i	1.78124i
$513$	− 4.14590i	− 0.183046i
$514$	43.8328i	1.93338i
$515$	− 22.7984i	− 1.00462i
$516$	−159.644	−7.02795
$517$	4.14590	0.182336
$518$	10.4721i	0.460119i
$519$	−23.5623	−1.03427
$520$	0	0
$521$	18.6525	0.817180	0.408590	−	0.912718i	$-0.366021\pi$
$521$	18.6525	0.817180	0.408590	+	0.912718i	$0.366021\pi$
$522$	− 71.5410i	− 3.13127i
$523$	1.12461	0.0491758	0.0245879	−	0.999698i	$-0.492173\pi$
$523$	1.12461	0.0491758	0.0245879	+	0.999698i	$0.492173\pi$
$524$	74.3951	3.24997
$525$	4.85410i	0.211850i
$526$	− 23.5623i	− 1.02737i
$527$	6.93112i	0.301924i
$528$	− 47.8328i	− 2.08166i
$529$	−3.00000	−0.130435
$530$	−25.7984	−1.12061
$531$	− 8.61803i	− 0.373991i
$532$	9.00000	0.390199
$533$	0	0
$534$	−33.6525	−1.45629
$535$	8.85410i	0.382796i
$536$	−94.9574	−4.10154
$537$	−23.5623	−1.01679
$538$	75.2492i	3.24422i
$539$	− 1.85410i	− 0.0798618i
$540$	− 28.4164i	− 1.22285i
$541$	35.2705i	1.51640i	0.652023	+	0.758199i	$0.273920\pi$
$541$	35.2705i	1.51640i	−0.652023	+	0.758199i	$0.726080\pi$
$542$	−22.0344	−0.946460
$543$	25.4164	1.09072
$544$	− 15.9787i	− 0.685082i
$545$	7.09017	0.303710
$546$	0	0
$547$	−3.00000	−0.128271	−0.0641354	−	0.997941i	$-0.520429\pi$
$547$	−3.00000	−0.128271	−0.0641354	+	0.997941i	$0.520429\pi$
$548$	12.7082i	0.542868i
$549$	−23.1246	−0.986934
$550$	−9.00000	−0.383761
$551$	13.1459i	0.560034i
$552$	− 87.4853i	− 3.72362i
$553$	4.00000i	0.170097i
$554$	− 13.0902i	− 0.556148i
$555$	−27.4164	−1.16376
$556$	−22.1459	−0.939195
$557$	− 27.9787i	− 1.18550i	−0.805388	−	0.592748i	$-0.798043\pi$
$557$	− 27.9787i	− 1.18550i	0.805388	−	0.592748i	$-0.201957\pi$
$558$	47.5066	2.01111
$559$	0	0
$560$	25.7984	1.09018
$561$	− 7.14590i	− 0.301700i
$562$	52.8328	2.22862
$563$	21.0557	0.887393	0.443697	−	0.896177i	$-0.353667\pi$
$563$	21.0557	0.887393	0.443697	+	0.896177i	$0.353667\pi$
$564$	− 28.4164i	− 1.19655i
$565$	− 3.85410i	− 0.162143i
$566$	35.1246i	1.47640i
$567$	− 5.70820i	− 0.239722i
$568$	−105.957	−4.44587
$569$	−14.9443	−0.626496	−0.313248	−	0.949671i	$-0.601417\pi$
$569$	−14.9443	−0.626496	−0.313248	+	0.949671i	$0.601417\pi$
$570$	33.2705i	1.39355i
$571$	−24.6869	−1.03312	−0.516558	−	0.856252i	$-0.672787\pi$
$571$	−24.6869	−1.03312	−0.516558	+	0.856252i	$0.672787\pi$
$572$	0	0
$573$	−55.9787	−2.33854
$574$	− 2.00000i	− 0.0834784i
$575$	−8.29180	−0.345792
$576$	−33.5623	−1.39843
$577$	43.8328i	1.82478i	0.409318	+	0.912392i	$0.365767\pi$
$577$	43.8328i	1.82478i	−0.409318	+	0.912392i	$0.634233\pi$
$578$	38.8328i	1.61523i
$579$	15.7082i	0.652811i
$580$	90.1033i	3.74134i
$581$	6.70820	0.278303
$582$	129.228	5.35667
$583$	6.97871i	0.289029i
$584$	14.9443	0.618398
$585$	0	0
$586$	−17.7082	−0.731519
$587$	19.9098i	0.821767i	0.911688	+	0.410883i	$0.134780\pi$
$587$	19.9098i	0.821767i	−0.911688	+	0.410883i	$0.865220\pi$
$588$	−12.7082	−0.524077
$589$	−8.72949	−0.359692
$590$	15.3262i	0.630971i
$591$	− 43.9787i	− 1.80904i
$592$	39.4164i	1.62000i
$593$	43.7984i	1.79858i	0.437349	+	0.899292i	$0.355917\pi$
$593$	43.7984i	1.79858i	−0.437349	+	0.899292i	$0.644083\pi$
$594$	−10.8541	−0.445349
$595$	3.85410	0.158003
$596$	9.00000i	0.368654i
$597$	−63.9230	−2.61619
$598$	0	0
$599$	29.5066	1.20561	0.602803	−	0.797890i	$-0.294050\pi$
$599$	29.5066	1.20561	0.602803	+	0.797890i	$0.294050\pi$
$600$	36.2705i	1.48074i
$601$	40.3951	1.64775	0.823876	−	0.566771i	$-0.191807\pi$
$601$	40.3951	1.64775	0.823876	+	0.566771i	$0.191807\pi$
$602$	−32.8885	−1.34044
$603$	48.9787i	1.99457i
$604$	6.27051i	0.255143i
$605$	− 19.7984i	− 0.804918i
$606$	79.2492i	3.21928i
$607$	−23.0000	−0.933541	−0.466771	−	0.884378i	$-0.654583\pi$
$607$	−23.0000	−0.933541	−0.466771	+	0.884378i	$0.654583\pi$
$608$	20.1246	0.816161
$609$	− 18.5623i	− 0.752183i
$610$	41.1246	1.66509
$611$	0	0
$612$	−27.5410	−1.11328
$613$	− 34.5623i	− 1.39596i	−0.716118	−	0.697979i	$-0.754083\pi$
$613$	− 34.5623i	− 1.39596i	0.716118	−	0.697979i	$-0.245917\pi$
$614$	−12.7082	−0.512861
$615$	5.23607	0.211139
$616$	− 13.8541i	− 0.558198i
$617$	− 0.0557281i	− 0.00224353i	−0.999999	−	0.00112176i	$-0.999643\pi$
$617$	− 0.0557281i	− 0.00224353i	0.999999	−	0.00112176i	$-0.000357069\pi$
$618$	59.6869i	2.40096i
$619$	9.41641i	0.378477i	0.981931	+	0.189239i	$0.0606020\pi$
$619$	9.41641i	0.378477i	−0.981931	+	0.189239i	$0.939398\pi$
$620$	−59.8328	−2.40294
$621$	−10.0000	−0.401286
$622$	8.70820i	0.349167i
$623$	−4.90983	−0.196708
$624$	0	0
$625$	−30.8328	−1.23331
$626$	− 65.7771i	− 2.62898i
$627$	9.00000	0.359425
$628$	−72.1033	−2.87724
$629$	5.88854i	0.234792i
$630$	− 26.4164i	− 1.05245i
$631$	34.3951i	1.36925i	0.728896	+	0.684624i	$0.240034\pi$
$631$	34.3951i	1.36925i	−0.728896	+	0.684624i	$0.759966\pi$
$632$	29.8885i	1.18890i
$633$	−12.3262	−0.489924
$634$	−68.6869	−2.72791
$635$	− 54.5967i	− 2.16661i
$636$	47.8328	1.89669
$637$	0	0
$638$	34.4164	1.36256
$639$	54.6525i	2.16202i
$640$	2.85410	0.112818
$641$	47.5066	1.87640	0.938199	−	0.346098i	$-0.112493\pi$
$641$	47.5066	1.87640	0.938199	+	0.346098i	$0.112493\pi$
$642$	− 23.1803i	− 0.914855i
$643$	7.00000i	0.276053i	0.990429	+	0.138027i	$0.0440759\pi$
$643$	7.00000i	0.276053i	−0.990429	+	0.138027i	$0.955924\pi$
$644$	− 21.7082i	− 0.855423i
$645$	− 86.1033i	− 3.39032i
$646$	7.14590	0.281152
$647$	−24.7639	−0.973571	−0.486785	−	0.873522i	$-0.661831\pi$
$647$	−24.7639	−0.973571	−0.486785	+	0.873522i	$0.661831\pi$
$648$	− 42.6525i	− 1.67555i
$649$	4.14590	0.162741
$650$	0	0
$651$	12.3262	0.483103
$652$	18.0000i	0.704934i
$653$	−0.381966	−0.0149475	−0.00747374	−	0.999972i	$-0.502379\pi$
$653$	−0.381966	−0.0149475	−0.00747374	+	0.999972i	$0.502379\pi$
$654$	−18.5623	−0.725844
$655$	40.1246i	1.56780i
$656$	− 7.52786i	− 0.293914i
$657$	− 7.70820i	− 0.300726i
$658$	− 5.85410i	− 0.228217i
$659$	−23.8885	−0.930566	−0.465283	−	0.885162i	$-0.654047\pi$
$659$	−23.8885	−0.930566	−0.465283	+	0.885162i	$0.654047\pi$
$660$	61.6869	2.40116
$661$	− 48.5410i	− 1.88803i	−0.329907	−	0.944013i	$-0.607017\pi$
$661$	− 48.5410i	− 1.88803i	0.329907	−	0.944013i	$-0.392983\pi$
$662$	26.5623	1.03237
$663$	0	0
$664$	50.1246	1.94521
$665$	4.85410i	0.188234i
$666$	40.3607	1.56394
$667$	31.7082	1.22775
$668$	− 69.1033i	− 2.67369i
$669$	53.0689i	2.05176i
$670$	− 87.1033i	− 3.36510i
$671$	− 11.1246i	− 0.429461i
$672$	−28.4164	−1.09619
$673$	39.2492	1.51295	0.756473	−	0.654025i	$-0.226921\pi$
$673$	39.2492	1.51295	0.756473	+	0.654025i	$0.226921\pi$
$674$	− 30.2705i	− 1.16598i
$675$	4.14590	0.159576
$676$	0	0
$677$	43.7426	1.68117	0.840583	−	0.541682i	$-0.182212\pi$
$677$	43.7426	1.68117	0.840583	+	0.541682i	$0.182212\pi$
$678$	10.0902i	0.387511i
$679$	18.8541	0.723554
$680$	28.7984	1.10437
$681$	3.85410i	0.147690i
$682$	22.8541i	0.875129i
$683$	1.47214i	0.0563297i	0.999603	+	0.0281649i	$0.00896634\pi$
$683$	1.47214i	0.0563297i	−0.999603	+	0.0281649i	$0.991034\pi$
$684$	− 34.6869i	− 1.32629i
$685$	−6.85410	−0.261882
$686$	−2.61803	−0.0999570
$687$	34.3607i	1.31094i
$688$	−123.790	−4.71946
$689$	0	0
$690$	80.2492	3.05504
$691$	5.85410i	0.222701i	0.993781	+	0.111350i	$0.0355175\pi$
$691$	5.85410i	0.222701i	−0.993781	+	0.111350i	$0.964482\pi$
$692$	−43.6869	−1.66073
$693$	−7.14590	−0.271450
$694$	− 80.5410i	− 3.05730i
$695$	− 11.9443i	− 0.453072i
$696$	− 138.700i	− 5.25741i
$697$	− 1.12461i	− 0.0425977i
$698$	54.2148	2.05206
$699$	6.85410	0.259246
$700$	9.00000i	0.340168i
$701$	−11.2361	−0.424380	−0.212190	−	0.977228i	$-0.568060\pi$
$701$	−11.2361	−0.424380	−0.212190	+	0.977228i	$0.568060\pi$
$702$	0	0
$703$	−7.41641	−0.279715
$704$	− 16.1459i	− 0.608521i
$705$	15.3262	0.577220
$706$	−57.9787	−2.18206
$707$	11.5623i	0.434845i
$708$	− 28.4164i	− 1.06795i
$709$	23.5623i	0.884901i	0.896793	+	0.442450i	$0.145891\pi$
$709$	23.5623i	0.884901i	−0.896793	+	0.442450i	$0.854109\pi$
$710$	− 97.1935i	− 3.64761i
$711$	15.4164	0.578160
$712$	−36.6869	−1.37490
$713$	21.0557i	0.788543i
$714$	−10.0902	−0.377615
$715$	0	0
$716$	−43.6869	−1.63266
$717$	− 64.6869i	− 2.41578i
$718$	−57.8328	−2.15830
$719$	−8.12461	−0.302997	−0.151498	−	0.988457i	$-0.548410\pi$
$719$	−8.12461	−0.302997	−0.151498	+	0.988457i	$0.548410\pi$
$720$	− 99.4296i	− 3.70552i
$721$	8.70820i	0.324310i
$722$	− 40.7426i	− 1.51628i
$723$	− 64.3050i	− 2.39153i
$724$	47.1246	1.75137
$725$	−13.1459	−0.488226
$726$	51.8328i	1.92370i
$727$	30.7082	1.13890	0.569452	−	0.822025i	$-0.307155\pi$
$727$	30.7082	1.13890	0.569452	+	0.822025i	$0.307155\pi$
$728$	0	0
$729$	−39.5623	−1.46527
$730$	13.7082i	0.507363i
$731$	−18.4934	−0.684004
$732$	−76.2492	−2.81825
$733$	32.2705i	1.19194i	0.803007	+	0.595969i	$0.203232\pi$
$733$	32.2705i	1.19194i	−0.803007	+	0.595969i	$0.796768\pi$
$734$	3.70820i	0.136872i
$735$	− 6.85410i	− 0.252817i
$736$	− 48.5410i	− 1.78925i
$737$	−23.5623	−0.867929
$738$	−7.70820	−0.283743
$739$	− 6.87539i	− 0.252915i	−0.991972	−	0.126458i	$-0.959639\pi$
$739$	− 6.87539i	− 0.252915i	0.991972	−	0.126458i	$-0.0403608\pi$
$740$	−50.8328	−1.86865
$741$	0	0
$742$	9.85410	0.361755
$743$	− 39.3262i	− 1.44274i	−0.692550	−	0.721370i	$-0.743513\pi$
$743$	− 39.3262i	− 1.44274i	0.692550	−	0.721370i	$-0.256487\pi$
$744$	92.1033	3.37667
$745$	−4.85410	−0.177841
$746$	53.8328i	1.97096i
$747$	− 25.8541i	− 0.945952i
$748$	− 13.2492i	− 0.484440i
$749$	− 3.38197i	− 0.123574i
$750$	56.4508	2.06129
$751$	−22.7082	−0.828634	−0.414317	−	0.910133i	$-0.635980\pi$
$751$	−22.7082	−0.828634	−0.414317	+	0.910133i	$0.635980\pi$
$752$	− 22.0344i	− 0.803513i
$753$	2.00000	0.0728841
$754$	0	0
$755$	−3.38197	−0.123082
$756$	10.8541i	0.394760i
$757$	28.0000	1.01768	0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000	1.01768	0.508839	+	0.860862i	$0.330075\pi$
$758$	16.0902	0.584421
$759$	− 21.7082i	− 0.787958i
$760$	36.2705i	1.31567i
$761$	− 28.8541i	− 1.04596i	−0.852345	−	0.522980i	$-0.824820\pi$
$761$	− 28.8541i	− 1.04596i	0.852345	−	0.522980i	$-0.175180\pi$
$762$	142.936i	5.17803i
$763$	−2.70820	−0.0980436
$764$	−103.790	−3.75500
$765$	− 14.8541i	− 0.537051i
$766$	57.5410	2.07904
$767$	0	0
$768$	38.1246	1.37570
$769$	18.4164i	0.664113i	0.943260	+	0.332056i	$0.107742\pi$
$769$	18.4164i	0.664113i	−0.943260	+	0.332056i	$0.892258\pi$
$770$	12.7082	0.457972
$771$	43.8328	1.57860
$772$	29.1246i	1.04822i
$773$	− 25.3607i	− 0.912160i	−0.889939	−	0.456080i	$-0.849253\pi$
$773$	− 25.3607i	− 0.912160i	0.889939	−	0.456080i	$-0.150747\pi$
$774$	126.756i	4.55614i
$775$	− 8.72949i	− 0.313573i
$776$	140.880	5.05731
$777$	10.4721	0.375686
$778$	− 31.1246i	− 1.11587i
$779$	1.41641	0.0507481
$780$	0	0
$781$	−26.2918	−0.940794
$782$	− 17.2361i	− 0.616361i
$783$	−15.8541	−0.566579
$784$	−9.85410	−0.351932
$785$	− 38.8885i	− 1.38799i
$786$	− 105.048i	− 3.74692i
$787$	2.58359i	0.0920951i	0.998939	+	0.0460476i	$0.0146626\pi$
$787$	2.58359i	0.0920951i	−0.998939	+	0.0460476i	$0.985337\pi$
$788$	− 81.5410i	− 2.90478i
$789$	−23.5623	−0.838840
$790$	−27.4164	−0.975432
$791$	1.47214i	0.0523431i
$792$	−53.3951	−1.89731
$793$	0	0
$794$	3.70820	0.131599
$795$	25.7984i	0.914974i
$796$	−118.520	−4.20082
$797$	8.18034	0.289763	0.144881	−	0.989449i	$-0.453720\pi$
$797$	8.18034	0.289763	0.144881	+	0.989449i	$0.453720\pi$
$798$	− 12.7082i	− 0.449866i
$799$	− 3.29180i	− 0.116455i
$800$	20.1246i	0.711512i
$801$	18.9230i	0.668611i
$802$	92.8115	3.27729
$803$	3.70820	0.130860
$804$	161.498i	5.69561i
$805$	11.7082	0.412660
$806$	0	0
$807$	75.2492	2.64890
$808$	86.3951i	3.03937i
$809$	−4.41641	−0.155273	−0.0776363	−	0.996982i	$-0.524737\pi$
$809$	−4.41641	−0.155273	−0.0776363	+	0.996982i	$0.524737\pi$
$810$	39.1246	1.37470
$811$	− 39.2705i	− 1.37897i	−0.724298	−	0.689487i	$-0.757836\pi$
$811$	− 39.2705i	− 1.37897i	0.724298	−	0.689487i	$-0.242164\pi$
$812$	− 34.4164i	− 1.20778i
$813$	22.0344i	0.772782i
$814$	19.4164i	0.680545i
$815$	−9.70820	−0.340064
$816$	−37.9787	−1.32952
$817$	− 23.2918i	− 0.814877i
$818$	−37.7984	−1.32159
$819$	0	0
$820$	9.70820	0.339025
$821$	7.36068i	0.256889i	0.991717	+	0.128445i	$0.0409985\pi$
$821$	7.36068i	0.256889i	−0.991717	+	0.128445i	$0.959002\pi$
$822$	17.9443	0.625878
$823$	38.4164	1.33911	0.669556	−	0.742762i	$-0.266484\pi$
$823$	38.4164	1.33911	0.669556	+	0.742762i	$0.266484\pi$
$824$	65.0689i	2.26678i
$825$	9.00000i	0.313340i
$826$	− 5.85410i	− 0.203690i
$827$	15.9787i	0.555634i	0.960634	+	0.277817i	$0.0896109\pi$
$827$	15.9787i	0.555634i	−0.960634	+	0.277817i	$0.910389\pi$
$828$	−83.6656	−2.90758
$829$	−7.56231	−0.262650	−0.131325	−	0.991339i	$-0.541923\pi$
$829$	−7.56231	−0.262650	−0.131325	+	0.991339i	$0.541923\pi$
$830$	45.9787i	1.59594i
$831$	−13.0902	−0.454093
$832$	0	0
$833$	−1.47214	−0.0510065
$834$	31.2705i	1.08281i
$835$	37.2705	1.28980
$836$	16.6869	0.577129
$837$	− 10.5279i	− 0.363896i
$838$	31.2705i	1.08022i
$839$	13.7426i	0.474449i	0.971455	+	0.237224i	$0.0762377\pi$
$839$	13.7426i	0.474449i	−0.971455	+	0.237224i	$0.923762\pi$
$840$	− 51.2148i	− 1.76708i
$841$	21.2705	0.733466
$842$	−3.70820	−0.127793
$843$	− 52.8328i	− 1.81966i
$844$	−22.8541	−0.786671
$845$	0	0
$846$	−22.5623	−0.775708
$847$	7.56231i	0.259844i
$848$	37.0902	1.27368
$849$	35.1246	1.20547
$850$	7.14590i	0.245102i
$851$	17.8885i	0.613211i
$852$	180.207i	6.17378i
$853$	14.1246i	0.483617i	0.970324	+	0.241809i	$0.0777407\pi$
$853$	14.1246i	0.483617i	−0.970324	+	0.241809i	$0.922259\pi$
$854$	−15.7082	−0.537524
$855$	18.7082	0.639807
$856$	− 25.2705i	− 0.863728i
$857$	26.4508	0.903544	0.451772	−	0.892133i	$-0.350792\pi$
$857$	26.4508	0.903544	0.451772	+	0.892133i	$0.350792\pi$
$858$	0	0
$859$	−44.2492	−1.50976	−0.754882	−	0.655861i	$-0.772306\pi$
$859$	−44.2492	−1.50976	−0.754882	+	0.655861i	$0.772306\pi$
$860$	− 159.644i	− 5.44383i
$861$	−2.00000	−0.0681598
$862$	−20.4164	−0.695386
$863$	− 11.8885i	− 0.404691i	−0.979314	−	0.202345i	$-0.935144\pi$
$863$	− 11.8885i	− 0.404691i	0.979314	−	0.202345i	$-0.0648564\pi$
$864$	24.2705i	0.825700i
$865$	− 23.5623i	− 0.801142i
$866$	2.61803i	0.0889644i
$867$	38.8328	1.31883
$868$	22.8541	0.775719
$869$	7.41641i	0.251584i
$870$	127.228	4.31343
$871$	0	0
$872$	−20.2361	−0.685280
$873$	− 72.6656i	− 2.45936i
$874$	21.7082	0.734291
$875$	8.23607	0.278430
$876$	− 25.4164i	− 0.858741i
$877$	− 0.708204i	− 0.0239143i	−0.999929	−	0.0119572i	$-0.996194\pi$
$877$	− 0.708204i	− 0.0239143i	0.999929	−	0.0119572i	$-0.00380618\pi$
$878$	38.8885i	1.31242i
$879$	17.7082i	0.597283i
$880$	47.8328	1.61244
$881$	36.5967	1.23298	0.616488	−	0.787364i	$-0.288555\pi$
$881$	36.5967	1.23298	0.616488	+	0.787364i	$0.288555\pi$
$882$	10.0902i	0.339754i
$883$	−29.0000	−0.975928	−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000	−0.975928	−0.487964	+	0.872864i	$0.662260\pi$
$884$	0	0
$885$	15.3262	0.515186
$886$	13.7082i	0.460536i
$887$	54.6525	1.83505	0.917525	−	0.397677i	$-0.130184\pi$
$887$	54.6525	1.83505	0.917525	+	0.397677i	$0.130184\pi$
$888$	78.2492	2.62587
$889$	20.8541i	0.699424i
$890$	− 33.6525i	− 1.12803i
$891$	− 10.5836i	− 0.354564i
$892$	98.3951i	3.29451i
$893$	4.14590	0.138737
$894$	12.7082	0.425026
$895$	− 23.5623i	− 0.787601i
$896$	−1.09017	−0.0364200
$897$	0	0
$898$	51.1246	1.70605
$899$	33.3820i	1.11335i
$900$	34.6869	1.15623
$901$	5.54102	0.184598
$902$	− 3.70820i	− 0.123470i
$903$	32.8885i	1.09446i
$904$	11.0000i	0.365855i
$905$	25.4164i	0.844870i
$906$	8.85410	0.294158
$907$	24.0000	0.796907	0.398453	−	0.917189i	$-0.369547\pi$
$907$	24.0000	0.796907	0.398453	+	0.917189i	$0.369547\pi$
$908$	7.14590i	0.237145i
$909$	44.5623	1.47804
$910$	0	0
$911$	−22.6869	−0.751651	−0.375826	−	0.926690i	$-0.622641\pi$
$911$	−22.6869	−0.751651	−0.375826	+	0.926690i	$0.622641\pi$
$912$	− 47.8328i	− 1.58390i
$913$	12.4377	0.411628
$914$	−40.3607	−1.33501
$915$	− 41.1246i	− 1.35954i
$916$	63.7082i	2.10498i
$917$	− 15.3262i	− 0.506117i
$918$	8.61803i	0.284438i
$919$	−30.0000	−0.989609	−0.494804	−	0.869004i	$-0.664760\pi$
$919$	−30.0000	−0.989609	−0.494804	+	0.869004i	$0.664760\pi$
$920$	87.4853	2.88430
$921$	12.7082i	0.418750i
$922$	31.9787	1.05316
$923$	0	0
$924$	−23.5623	−0.775143
$925$	− 7.41641i	− 0.243850i
$926$	17.5623	0.577133
$927$	33.5623	1.10233
$928$	− 76.9574i	− 2.52625i
$929$	− 11.0689i	− 0.363158i	−0.983376	−	0.181579i	$-0.941879\pi$
$929$	− 11.0689i	− 0.363158i	0.983376	−	0.181579i	$-0.0581209\pi$
$930$	84.4853i	2.77038i
$931$	− 1.85410i	− 0.0607657i
$932$	12.7082	0.416271
$933$	8.70820	0.285094
$934$	6.14590i	0.201100i
$935$	7.14590	0.233696
$936$	0	0
$937$	−15.8754	−0.518626	−0.259313	−	0.965793i	$-0.583496\pi$
$937$	−15.8754	−0.518626	−0.259313	+	0.965793i	$0.583496\pi$
$938$	33.2705i	1.08632i
$939$	−65.7771	−2.14655
$940$	28.4164	0.926841
$941$	− 20.3475i	− 0.663310i	−0.943401	−	0.331655i	$-0.892393\pi$
$941$	− 20.3475i	− 0.663310i	0.943401	−	0.331655i	$-0.107607\pi$
$942$	101.812i	3.31720i
$943$	− 3.41641i	− 0.111254i
$944$	− 22.0344i	− 0.717160i
$945$	−5.85410	−0.190434
$946$	−60.9787	−1.98259
$947$	− 36.8673i	− 1.19802i	−0.800740	−	0.599012i	$-0.795560\pi$
$947$	− 36.8673i	− 1.19802i	0.800740	−	0.599012i	$-0.204440\pi$
$948$	50.8328	1.65097
$949$	0	0
$950$	−9.00000	−0.291999
$951$	68.6869i	2.22733i
$952$	−11.0000	−0.356512
$953$	−26.7771	−0.867395	−0.433697	−	0.901059i	$-0.642791\pi$
$953$	−26.7771	−0.867395	−0.433697	+	0.901059i	$0.642791\pi$
$954$	− 37.9787i	− 1.22961i
$955$	− 55.9787i	− 1.81143i
$956$	− 119.936i	− 3.87901i
$957$	− 34.4164i	− 1.11252i
$958$	65.3951	2.11282
$959$	2.61803	0.0845407
$960$	− 59.6869i	− 1.92639i
$961$	8.83282	0.284930
$962$	0	0
$963$	−13.0344	−0.420029
$964$	− 119.228i	− 3.84007i
$965$	−15.7082	−0.505665
$966$	−30.6525	−0.986227
$967$	39.0000i	1.25416i	0.778957	+	0.627078i	$0.215749\pi$
$967$	39.0000i	1.25416i	−0.778957	+	0.627078i	$0.784251\pi$
$968$	56.5066i	1.81619i
$969$	− 7.14590i	− 0.229559i
$970$	129.228i	4.14926i
$971$	31.5836	1.01357	0.506783	−	0.862074i	$-0.330835\pi$
$971$	31.5836	1.01357	0.506783	+	0.862074i	$0.330835\pi$
$972$	−105.103	−3.37119
$973$	4.56231i	0.146261i
$974$	−78.4853	−2.51483
$975$	0	0
$976$	−59.1246	−1.89253
$977$	22.5279i	0.720730i	0.932811	+	0.360365i	$0.117348\pi$
$977$	22.5279i	0.720730i	−0.932811	+	0.360365i	$0.882652\pi$
$978$	25.4164	0.812727
$979$	−9.10333	−0.290944
$980$	− 12.7082i	− 0.405949i
$981$	10.4377i	0.333250i
$982$	32.4164i	1.03445i
$983$	18.3820i	0.586294i	0.956067	+	0.293147i	$0.0947025\pi$
$983$	18.3820i	0.586294i	−0.956067	+	0.293147i	$0.905298\pi$
$984$	−14.9443	−0.476406
$985$	43.9787	1.40128
$986$	− 27.3262i	− 0.870245i
$987$	−5.85410	−0.186338
$988$	0	0
$989$	−56.1803	−1.78643
$990$	− 48.9787i	− 1.55665i
$991$	−16.1459	−0.512891	−0.256446	−	0.966559i	$-0.582551\pi$
$991$	−16.1459	−0.512891	−0.256446	+	0.966559i	$0.582551\pi$
$992$	51.1033	1.62253
$993$	− 26.5623i	− 0.842929i
$994$	37.1246i	1.17752i
$995$	− 63.9230i	− 2.02649i
$996$	− 85.2492i	− 2.70123i
$997$	49.0000	1.55185	0.775923	−	0.630828i	$-0.217285\pi$
$997$	49.0000	1.55185	0.775923	+	0.630828i	$0.217285\pi$
$998$	−38.8885	−1.23100
$999$	− 8.94427i	− 0.282984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.c.337.1		4
13.5	odd	4		1183.2.a.c.1.1		2
13.7	odd	12		91.2.f.a.29.1	yes	4
13.8	odd	4		1183.2.a.g.1.2		2
13.11	odd	12		91.2.f.a.22.1	✓	4
13.12	even	2	inner	1183.2.c.c.337.4		4
39.11	even	12		819.2.o.c.568.2		4
39.20	even	12		819.2.o.c.757.2		4
52.7	even	12		1456.2.s.h.1121.1		4
52.11	even	12		1456.2.s.h.113.1		4
91.11	odd	12		637.2.g.b.373.1		4
91.20	even	12		637.2.f.c.393.1		4
91.24	even	12		637.2.g.c.373.1		4
91.33	even	12		637.2.g.c.263.1		4
91.34	even	4		8281.2.a.bb.1.2		2
91.37	odd	12		637.2.h.g.165.2		4
91.46	odd	12		637.2.h.g.471.2		4
91.59	even	12		637.2.h.f.471.2		4
91.72	odd	12		637.2.g.b.263.1		4
91.76	even	12		637.2.f.c.295.1		4
91.83	even	4		8281.2.a.n.1.1		2
91.89	even	12		637.2.h.f.165.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.1	✓	4	13.11	odd	12
91.2.f.a.29.1	yes	4	13.7	odd	12
637.2.f.c.295.1		4	91.76	even	12
637.2.f.c.393.1		4	91.20	even	12
637.2.g.b.263.1		4	91.72	odd	12
637.2.g.b.373.1		4	91.11	odd	12
637.2.g.c.263.1		4	91.33	even	12
637.2.g.c.373.1		4	91.24	even	12
637.2.h.f.165.2		4	91.89	even	12
637.2.h.f.471.2		4	91.59	even	12
637.2.h.g.165.2		4	91.37	odd	12
637.2.h.g.471.2		4	91.46	odd	12
819.2.o.c.568.2		4	39.11	even	12
819.2.o.c.757.2		4	39.20	even	12
1183.2.a.c.1.1		2	13.5	odd	4
1183.2.a.g.1.2		2	13.8	odd	4
1183.2.c.c.337.1		4	1.1	even	1	trivial
1183.2.c.c.337.4		4	13.12	even	2	inner
1456.2.s.h.113.1		4	52.11	even	12
1456.2.s.h.1121.1		4	52.7	even	12
8281.2.a.n.1.1		2	91.83	even	4
8281.2.a.bb.1.2		2	91.34	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)

\(f(q)\)	\(=\)	\(q-2.61803i q^{2} -2.61803 q^{3} -4.85410 q^{4} -2.61803i q^{5} +6.85410i q^{6} +1.00000i q^{7} +7.47214i q^{8} +3.85410 q^{9} +O(q^{10})\)	\(q-2.61803i q^{2} -2.61803 q^{3} -4.85410 q^{4} -2.61803i q^{5} +6.85410i q^{6} +1.00000i q^{7} +7.47214i q^{8} +3.85410 q^{9} -6.85410 q^{10} +1.85410i q^{11} +12.7082 q^{12} +2.61803 q^{14} +6.85410i q^{15} +9.85410 q^{16} +1.47214 q^{17} -10.0902i q^{18} +1.85410i q^{19} +12.7082i q^{20} -2.61803i q^{21} +4.85410 q^{22} +4.47214 q^{23} -19.5623i q^{24} -1.85410 q^{25} -2.23607 q^{27} -4.85410i q^{28} +7.09017 q^{29} +17.9443 q^{30} +4.70820i q^{31} -10.8541i q^{32} -4.85410i q^{33} -3.85410i q^{34} +2.61803 q^{35} -18.7082 q^{36} +4.00000i q^{37} +4.85410 q^{38} +19.5623 q^{40} -0.763932i q^{41} -6.85410 q^{42} -12.5623 q^{43} -9.00000i q^{44} -10.0902i q^{45} -11.7082i q^{46} -2.23607i q^{47} -25.7984 q^{48} -1.00000 q^{49} +4.85410i q^{50} -3.85410 q^{51} +3.76393 q^{53} +5.85410i q^{54} +4.85410 q^{55} -7.47214 q^{56} -4.85410i q^{57} -18.5623i q^{58} -2.23607i q^{59} -33.2705i q^{60} -6.00000 q^{61} +12.3262 q^{62} +3.85410i q^{63} -8.70820 q^{64} -12.7082 q^{66} +12.7082i q^{67} -7.14590 q^{68} -11.7082 q^{69} -6.85410i q^{70} +14.1803i q^{71} +28.7984i q^{72} -2.00000i q^{73} +10.4721 q^{74} +4.85410 q^{75} -9.00000i q^{76} -1.85410 q^{77} +4.00000 q^{79} -25.7984i q^{80} -5.70820 q^{81} -2.00000 q^{82} -6.70820i q^{83} +12.7082i q^{84} -3.85410i q^{85} +32.8885i q^{86} -18.5623 q^{87} -13.8541 q^{88} +4.90983i q^{89} -26.4164 q^{90} -21.7082 q^{92} -12.3262i q^{93} -5.85410 q^{94} +4.85410 q^{95} +28.4164i q^{96} -18.8541i q^{97} +2.61803i q^{98} +7.14590i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} - 6 q^{4} + 2 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 - 6 * q^4 + 2 * q^9	\( 4 q - 6 q^{3} - 6 q^{4} + 2 q^{9} - 14 q^{10} + 24 q^{12} + 6 q^{14} + 26 q^{16} - 12 q^{17} + 6 q^{22} + 6 q^{25} + 6 q^{29} + 36 q^{30} + 6 q^{35} - 48 q^{36} + 6 q^{38} + 38 q^{40} - 14 q^{42} - 10 q^{43} - 54 q^{48} - 4 q^{49} - 2 q^{51} + 24 q^{53} + 6 q^{55} - 12 q^{56} - 24 q^{61} + 18 q^{62} - 8 q^{64} - 24 q^{66} - 42 q^{68} - 20 q^{69} + 24 q^{74} + 6 q^{75} + 6 q^{77} + 16 q^{79} + 4 q^{81} - 8 q^{82} - 34 q^{87} - 42 q^{88} - 52 q^{90} - 60 q^{92} - 10 q^{94} + 6 q^{95}+O(q^{100}) \) 4 * q - 6 * q^3 - 6 * q^4 + 2 * q^9 - 14 * q^10 + 24 * q^12 + 6 * q^14 + 26 * q^16 - 12 * q^17 + 6 * q^22 + 6 * q^25 + 6 * q^29 + 36 * q^30 + 6 * q^35 - 48 * q^36 + 6 * q^38 + 38 * q^40 - 14 * q^42 - 10 * q^43 - 54 * q^48 - 4 * q^49 - 2 * q^51 + 24 * q^53 + 6 * q^55 - 12 * q^56 - 24 * q^61 + 18 * q^62 - 8 * q^64 - 24 * q^66 - 42 * q^68 - 20 * q^69 + 24 * q^74 + 6 * q^75 + 6 * q^77 + 16 * q^79 + 4 * q^81 - 8 * q^82 - 34 * q^87 - 42 * q^88 - 52 * q^90 - 60 * q^92 - 10 * q^94 + 6 * q^95

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