LMFDB - Embedded newform 1183.2.c.j.337.7

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:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.7
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.j.337.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.35819i q^{2} +3.39737 q^{3} +0.155322 q^{4} -0.772491i q^{5} -4.61428i q^{6} -1.00000i q^{7} -2.92733i q^{8} +8.54215 q^{9} -1.04919 q^{10} +2.11612i q^{11} +0.527686 q^{12} -1.35819 q^{14} -2.62444i q^{15} -3.66523 q^{16} -5.63627 q^{17} -11.6019i q^{18} +2.99988i q^{19} -0.119985i q^{20} -3.39737i q^{21} +2.87409 q^{22} -1.24177 q^{23} -9.94525i q^{24} +4.40326 q^{25} +18.8288 q^{27} -0.155322i q^{28} -7.96564 q^{29} -3.56449 q^{30} +1.26728i q^{31} -0.876591i q^{32} +7.18925i q^{33} +7.65512i q^{34} -0.772491 q^{35} +1.32678 q^{36} +4.54251i q^{37} +4.07440 q^{38} -2.26134 q^{40} +9.82390i q^{41} -4.61428 q^{42} -2.64573 q^{43} +0.328679i q^{44} -6.59873i q^{45} +1.68656i q^{46} -7.68703i q^{47} -12.4522 q^{48} -1.00000 q^{49} -5.98046i q^{50} -19.1485 q^{51} -0.350895 q^{53} -25.5730i q^{54} +1.63468 q^{55} -2.92733 q^{56} +10.1917i q^{57} +10.8188i q^{58} +5.00519i q^{59} -0.407633i q^{60} +4.24504 q^{61} +1.72120 q^{62} -8.54215i q^{63} -8.52104 q^{64} +9.76437 q^{66} -11.3053i q^{67} -0.875435 q^{68} -4.21876 q^{69} +1.04919i q^{70} +11.8975i q^{71} -25.0057i q^{72} -8.99347i q^{73} +6.16959 q^{74} +14.9595 q^{75} +0.465946i q^{76} +2.11612 q^{77} -6.30010 q^{79} +2.83136i q^{80} +38.3419 q^{81} +13.3427 q^{82} +2.92778i q^{83} -0.527686i q^{84} +4.35397i q^{85} +3.59340i q^{86} -27.0622 q^{87} +6.19459 q^{88} +1.97181i q^{89} -8.96233 q^{90} -0.192874 q^{92} +4.30541i q^{93} -10.4404 q^{94} +2.31738 q^{95} -2.97811i q^{96} +7.88255i q^{97} +1.35819i q^{98} +18.0762i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38}+ \cdots - 58 q^{95}+O(q^{100}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

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 $

$2$	− 1.35819i	− 0.960385i	−0.877163	−	0.480192i	$-0.840567\pi$
$2$	− 1.35819i	− 0.960385i	0.877163	−	0.480192i	$-0.159433\pi$
$3$	3.39737	1.96147	0.980737	−	0.195331i	$-0.0625782\pi$
$3$	3.39737	1.96147	0.980737	+	0.195331i	$0.0625782\pi$
$4$	0.155322	0.0776609
$5$	− 0.772491i	− 0.345468i	−0.984968	−	0.172734i	$-0.944740\pi$
$5$	− 0.772491i	− 0.345468i	0.984968	−	0.172734i	$-0.0552602\pi$
$6$	− 4.61428i	− 1.88377i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 2.92733i	− 1.03497i
$9$	8.54215	2.84738
$10$	−1.04919	−0.331783
$11$	2.11612i	0.638034i	0.947749	+	0.319017i	$0.103353\pi$
$11$	2.11612i	0.638034i	−0.947749	+	0.319017i	$0.896647\pi$
$12$	0.527686	0.152330
$13$	0	0
$13$	0	0
$14$	−1.35819	−0.362991
$15$	− 2.62444i	− 0.677627i
$16$	−3.66523	−0.916308
$17$	−5.63627	−1.36700	−0.683498	−	0.729952i	$-0.739542\pi$
$17$	−5.63627	−1.36700	−0.683498	+	0.729952i	$0.739542\pi$
$18$	− 11.6019i	− 2.73458i
$19$	2.99988i	0.688219i	0.938930	+	0.344110i	$0.111819\pi$
$19$	2.99988i	0.688219i	−0.938930	+	0.344110i	$0.888181\pi$
$20$	− 0.119985i	− 0.0268294i
$21$	− 3.39737i	− 0.741368i
$22$	2.87409	0.612759
$23$	−1.24177	−0.258927	−0.129464	−	0.991584i	$-0.541326\pi$
$23$	−1.24177	−0.258927	−0.129464	+	0.991584i	$0.541326\pi$
$24$	− 9.94525i	− 2.03007i
$25$	4.40326	0.880652
$26$	0	0
$27$	18.8288	3.62359
$28$	− 0.155322i	− 0.0293530i
$29$	−7.96564	−1.47918	−0.739591	−	0.673057i	$-0.764981\pi$
$29$	−7.96564	−1.47918	−0.739591	+	0.673057i	$0.764981\pi$
$30$	−3.56449	−0.650783
$31$	1.26728i	0.227609i	0.993503	+	0.113805i	$0.0363038\pi$
$31$	1.26728i	0.227609i	−0.993503	+	0.113805i	$0.963696\pi$
$32$	− 0.876591i	− 0.154961i
$33$	7.18925i	1.25149i
$34$	7.65512i	1.31284i
$35$	−0.772491	−0.130575
$36$	1.32678	0.221130
$37$	4.54251i	0.746784i	0.927674	+	0.373392i	$0.121805\pi$
$37$	4.54251i	0.746784i	−0.927674	+	0.373392i	$0.878195\pi$
$38$	4.07440	0.660955
$39$	0	0
$40$	−2.26134	−0.357549
$41$	9.82390i	1.53424i	0.641506	+	0.767118i	$0.278310\pi$
$41$	9.82390i	1.53424i	−0.641506	+	0.767118i	$0.721690\pi$
$42$	−4.61428	−0.711998
$43$	−2.64573	−0.403470	−0.201735	−	0.979440i	$-0.564658\pi$
$43$	−2.64573	−0.403470	−0.201735	+	0.979440i	$0.564658\pi$
$44$	0.328679i	0.0495503i
$45$	− 6.59873i	− 0.983681i
$46$	1.68656i	0.248670i
$47$	− 7.68703i	− 1.12127i	−0.828064	−	0.560634i	$-0.810557\pi$
$47$	− 7.68703i	− 1.12127i	0.828064	−	0.560634i	$-0.189443\pi$
$48$	−12.4522	−1.79731
$49$	−1.00000	−0.142857
$50$	− 5.98046i	− 0.845764i
$51$	−19.1485	−2.68133
$52$	0	0
$53$	−0.350895	−0.0481991	−0.0240995	−	0.999710i	$-0.507672\pi$
$53$	−0.350895	−0.0481991	−0.0240995	+	0.999710i	$0.507672\pi$
$54$	− 25.5730i	− 3.48005i
$55$	1.63468	0.220421
$56$	−2.92733	−0.391182
$57$	10.1917i	1.34992i
$58$	10.8188i	1.42058i
$59$	5.00519i	0.651621i	0.945435	+	0.325810i	$0.105637\pi$
$59$	5.00519i	0.651621i	−0.945435	+	0.325810i	$0.894363\pi$
$60$	− 0.407633i	− 0.0526251i
$61$	4.24504	0.543522	0.271761	−	0.962365i	$-0.412394\pi$
$61$	4.24504	0.543522	0.271761	+	0.962365i	$0.412394\pi$
$62$	1.72120	0.218593
$63$	− 8.54215i	− 1.07621i
$64$	−8.52104	−1.06513
$65$	0	0
$66$	9.76437	1.20191
$67$	− 11.3053i	− 1.38117i	−0.723253	−	0.690583i	$-0.757354\pi$
$67$	− 11.3053i	− 1.38117i	0.723253	−	0.690583i	$-0.242646\pi$
$68$	−0.875435	−0.106162
$69$	−4.21876	−0.507879
$70$	1.04919i	0.125402i
$71$	11.8975i	1.41198i	0.708223	+	0.705989i	$0.249497\pi$
$71$	11.8975i	1.41198i	−0.708223	+	0.705989i	$0.750503\pi$
$72$	− 25.0057i	− 2.94695i
$73$	− 8.99347i	− 1.05261i	−0.850297	−	0.526303i	$-0.823578\pi$
$73$	− 8.99347i	− 1.05261i	0.850297	−	0.526303i	$-0.176422\pi$
$74$	6.16959	0.717200
$75$	14.9595	1.72738
$76$	0.465946i	0.0534477i
$77$	2.11612	0.241154
$78$	0	0
$79$	−6.30010	−0.708817	−0.354408	−	0.935091i	$-0.615318\pi$
$79$	−6.30010	−0.708817	−0.354408	+	0.935091i	$0.615318\pi$
$80$	2.83136i	0.316555i
$81$	38.3419	4.26021
$82$	13.3427	1.47346
$83$	2.92778i	0.321366i	0.987006	+	0.160683i	$0.0513697\pi$
$83$	2.92778i	0.321366i	−0.987006	+	0.160683i	$0.948630\pi$
$84$	− 0.527686i	− 0.0575753i
$85$	4.35397i	0.472254i
$86$	3.59340i	0.387487i
$87$	−27.0622	−2.90138
$88$	6.19459	0.660346
$89$	1.97181i	0.209012i	0.994524	+	0.104506i	$0.0333261\pi$
$89$	1.97181i	0.209012i	−0.994524	+	0.104506i	$0.966674\pi$
$90$	−8.96233	−0.944712
$91$	0	0
$92$	−0.192874	−0.0201085
$93$	4.30541i	0.446450i
$94$	−10.4404	−1.07685
$95$	2.31738	0.237758
$96$	− 2.97811i	− 0.303952i
$97$	7.88255i	0.800352i	0.916438	+	0.400176i	$0.131051\pi$
$97$	7.88255i	0.800352i	−0.916438	+	0.400176i	$0.868949\pi$
$98$	1.35819i	0.137198i
$99$	18.0762i	1.81673i
$100$	0.683922	0.0683922
$101$	−1.76856	−0.175978	−0.0879890	−	0.996121i	$-0.528044\pi$
$101$	−1.76856	−0.175978	−0.0879890	+	0.996121i	$0.528044\pi$
$102$	26.0073i	2.57511i
$103$	11.4598	1.12917	0.564586	−	0.825375i	$-0.309036\pi$
$103$	11.4598	1.12917	0.564586	+	0.825375i	$0.309036\pi$
$104$	0	0
$105$	−2.62444	−0.256119
$106$	0.476581i	0.0462897i
$107$	−3.29566	−0.318603	−0.159302	−	0.987230i	$-0.550924\pi$
$107$	−3.29566	−0.318603	−0.159302	+	0.987230i	$0.550924\pi$
$108$	2.92451	0.281412
$109$	− 13.1559i	− 1.26011i	−0.776551	−	0.630055i	$-0.783032\pi$
$109$	− 13.1559i	− 1.26011i	0.776551	−	0.630055i	$-0.216968\pi$
$110$	− 2.22021i	− 0.211689i
$111$	15.4326i	1.46480i
$112$	3.66523i	0.346332i
$113$	1.44552	0.135984	0.0679918	−	0.997686i	$-0.478341\pi$
$113$	1.44552	0.135984	0.0679918	+	0.997686i	$0.478341\pi$
$114$	13.8423	1.29645
$115$	0.959257i	0.0894512i
$116$	−1.23724	−0.114875
$117$	0	0
$118$	6.79800	0.625807
$119$	5.63627i	0.516676i
$120$	−7.68261	−0.701324
$121$	6.52203	0.592912
$122$	− 5.76557i	− 0.521990i
$123$	33.3755i	3.00936i
$124$	0.196835i	0.0176763i
$125$	− 7.26393i	− 0.649706i
$126$	−11.6019	−1.03358
$127$	10.9224	0.969209	0.484605	−	0.874733i	$-0.338963\pi$
$127$	10.9224	0.969209	0.484605	+	0.874733i	$0.338963\pi$
$128$	9.82000i	0.867974i
$129$	−8.98854	−0.791397
$130$	0	0
$131$	−2.24077	−0.195777	−0.0978886	−	0.995197i	$-0.531209\pi$
$131$	−2.24077	−0.195777	−0.0978886	+	0.995197i	$0.531209\pi$
$132$	1.11665i	0.0971917i
$133$	2.99988	0.260122
$134$	−15.3548	−1.32645
$135$	− 14.5450i	− 1.25184i
$136$	16.4993i	1.41480i
$137$	− 7.48827i	− 0.639766i	−0.947457	−	0.319883i	$-0.896356\pi$
$137$	− 7.48827i	− 0.639766i	0.947457	−	0.319883i	$-0.103644\pi$
$138$	5.72988i	0.487759i
$139$	3.17757	0.269518	0.134759	−	0.990878i	$-0.456974\pi$
$139$	3.17757	0.269518	0.134759	+	0.990878i	$0.456974\pi$
$140$	−0.119985	−0.0101405
$141$	− 26.1157i	− 2.19934i
$142$	16.1591	1.35604
$143$	0	0
$144$	−31.3090	−2.60908
$145$	6.15338i	0.511010i
$146$	−12.2148	−1.01091
$147$	−3.39737	−0.280211
$148$	0.705550i	0.0579959i
$149$	− 15.6423i	− 1.28147i	−0.767762	−	0.640735i	$-0.778630\pi$
$149$	− 15.6423i	− 1.28147i	0.767762	−	0.640735i	$-0.221370\pi$
$150$	− 20.3179i	− 1.65895i
$151$	− 15.2282i	− 1.23925i	−0.784897	−	0.619626i	$-0.787284\pi$
$151$	− 15.2282i	− 1.23925i	0.784897	−	0.619626i	$-0.212716\pi$
$152$	8.78165	0.712286
$153$	−48.1459	−3.89236
$154$	− 2.87409i	− 0.231601i
$155$	0.978959	0.0786318
$156$	0	0
$157$	−14.4128	−1.15027	−0.575134	−	0.818059i	$-0.695050\pi$
$157$	−14.4128	−1.15027	−0.575134	+	0.818059i	$0.695050\pi$
$158$	8.55673i	0.680737i
$159$	−1.19212	−0.0945413
$160$	−0.677159	−0.0535341
$161$	1.24177i	0.0978653i
$162$	− 52.0755i	− 4.09144i
$163$	10.6875i	0.837113i	0.908191	+	0.418556i	$0.137464\pi$
$163$	10.6875i	0.837113i	−0.908191	+	0.418556i	$0.862536\pi$
$164$	1.52587i	0.119150i
$165$	5.55363	0.432350
$166$	3.97648	0.308635
$167$	− 5.89574i	− 0.456226i	−0.973635	−	0.228113i	$-0.926744\pi$
$167$	− 5.89574i	− 0.456226i	0.973635	−	0.228113i	$-0.0732555\pi$
$168$	−9.94525	−0.767293
$169$	0	0
$170$	5.91351	0.453546
$171$	25.6254i	1.95962i
$172$	−0.410940	−0.0313338
$173$	−5.63112	−0.428126	−0.214063	−	0.976820i	$-0.568670\pi$
$173$	−5.63112	−0.428126	−0.214063	+	0.976820i	$0.568670\pi$
$174$	36.7557i	2.78644i
$175$	− 4.40326i	− 0.332855i
$176$	− 7.75607i	− 0.584636i
$177$	17.0045i	1.27814i
$178$	2.67810	0.200732
$179$	−7.18084	−0.536721	−0.268361	−	0.963318i	$-0.586482\pi$
$179$	−7.18084	−0.536721	−0.268361	+	0.963318i	$0.586482\pi$
$180$	− 1.02493i	− 0.0763935i
$181$	0.567427	0.0421765	0.0210883	−	0.999778i	$-0.493287\pi$
$181$	0.567427	0.0421765	0.0210883	+	0.999778i	$0.493287\pi$
$182$	0	0
$183$	14.4220	1.06611
$184$	3.63508i	0.267982i
$185$	3.50905	0.257990
$186$	5.84756	0.428764
$187$	− 11.9270i	− 0.872191i
$188$	− 1.19396i	− 0.0870787i
$189$	− 18.8288i	− 1.36959i
$190$	− 3.14744i	− 0.228339i
$191$	−7.95163	−0.575360	−0.287680	−	0.957727i	$-0.592884\pi$
$191$	−7.95163	−0.575360	−0.287680	+	0.957727i	$0.592884\pi$
$192$	−28.9492	−2.08923
$193$	20.5748i	1.48100i	0.672054	+	0.740502i	$0.265412\pi$
$193$	20.5748i	1.48100i	−0.672054	+	0.740502i	$0.734588\pi$
$194$	10.7060	0.768646
$195$	0	0
$196$	−0.155322	−0.0110944
$197$	1.52219i	0.108451i	0.998529	+	0.0542256i	$0.0172690\pi$
$197$	1.52219i	0.108451i	−0.998529	+	0.0542256i	$0.982731\pi$
$198$	24.5509	1.74476
$199$	−25.3123	−1.79434	−0.897172	−	0.441681i	$-0.854382\pi$
$199$	−25.3123	−1.79434	−0.897172	+	0.441681i	$0.854382\pi$
$200$	− 12.8898i	− 0.911447i
$201$	− 38.4084i	− 2.70912i
$202$	2.40204i	0.169007i
$203$	7.96564i	0.559078i
$204$	−2.97418	−0.208234
$205$	7.58887	0.530030
$206$	− 15.5646i	− 1.08444i
$207$	−10.6074	−0.737265
$208$	0	0
$209$	−6.34810	−0.439107
$210$	3.56449i	0.245973i
$211$	5.54406	0.381669	0.190834	−	0.981622i	$-0.438881\pi$
$211$	5.54406	0.381669	0.190834	+	0.981622i	$0.438881\pi$
$212$	−0.0545016	−0.00374318
$213$	40.4204i	2.76956i
$214$	4.47612i	0.305982i
$215$	2.04380i	0.139386i
$216$	− 55.1181i	− 3.75031i
$217$	1.26728	0.0860283
$218$	−17.8682	−1.21019
$219$	− 30.5542i	− 2.06466i
$220$	0.253902	0.0171181
$221$	0	0
$222$	20.9604	1.40677
$223$	− 6.89711i	− 0.461865i	−0.972970	−	0.230932i	$-0.925822\pi$
$223$	− 6.89711i	− 0.461865i	0.972970	−	0.230932i	$-0.0741776\pi$
$224$	−0.876591	−0.0585697
$225$	37.6133	2.50755
$226$	− 1.96330i	− 0.130597i
$227$	− 3.16626i	− 0.210152i	−0.994464	−	0.105076i	$-0.966491\pi$
$227$	− 3.16626i	− 0.210152i	0.994464	−	0.105076i	$-0.0335086\pi$
$228$	1.58299i	0.104836i
$229$	23.3695i	1.54430i	0.635442	+	0.772148i	$0.280818\pi$
$229$	23.3695i	1.54430i	−0.635442	+	0.772148i	$0.719182\pi$
$230$	1.30285	0.0859075
$231$	7.18925	0.473018
$232$	23.3181i	1.53091i
$233$	9.65245	0.632353	0.316177	−	0.948700i	$-0.397601\pi$
$233$	9.65245	0.632353	0.316177	+	0.948700i	$0.397601\pi$
$234$	0	0
$235$	−5.93816	−0.387363
$236$	0.777415i	0.0506054i
$237$	−21.4038	−1.39033
$238$	7.65512	0.496208
$239$	− 6.98215i	− 0.451638i	−0.974169	−	0.225819i	$-0.927494\pi$
$239$	− 6.98215i	− 0.451638i	0.974169	−	0.225819i	$-0.0725058\pi$
$240$	9.61918i	0.620915i
$241$	18.5592i	1.19550i	0.801681	+	0.597751i	$0.203939\pi$
$241$	18.5592i	1.19550i	−0.801681	+	0.597751i	$0.796061\pi$
$242$	− 8.85816i	− 0.569424i
$243$	73.7754	4.73269
$244$	0.659348	0.0422104
$245$	0.772491i	0.0493526i
$246$	45.3302	2.89015
$247$	0	0
$248$	3.70974	0.235569
$249$	9.94677i	0.630351i
$250$	−9.86579	−0.623967
$251$	−16.6573	−1.05140	−0.525699	−	0.850671i	$-0.676196\pi$
$251$	−16.6573	−1.05140	−0.525699	+	0.850671i	$0.676196\pi$
$252$	− 1.32678i	− 0.0835794i
$253$	− 2.62774i	− 0.165204i
$254$	− 14.8347i	− 0.930814i
$255$	14.7921i	0.926314i
$256$	−3.70466	−0.231541
$257$	−7.63652	−0.476353	−0.238177	−	0.971222i	$-0.576550\pi$
$257$	−7.63652	−0.476353	−0.238177	+	0.971222i	$0.576550\pi$
$258$	12.2081i	0.760045i
$259$	4.54251	0.282258
$260$	0	0
$261$	−68.0436	−4.21180
$262$	3.04339i	0.188022i
$263$	−18.6358	−1.14913	−0.574567	−	0.818458i	$-0.694830\pi$
$263$	−18.6358	−1.14913	−0.574567	+	0.818458i	$0.694830\pi$
$264$	21.0453	1.29525
$265$	0.271063i	0.0166513i
$266$	− 4.07440i	− 0.249818i
$267$	6.69899i	0.409971i
$268$	− 1.75596i	− 0.107263i
$269$	24.8582	1.51563	0.757817	−	0.652467i	$-0.226266\pi$
$269$	24.8582	1.51563	0.757817	+	0.652467i	$0.226266\pi$
$270$	−19.7549	−1.20225
$271$	22.0518i	1.33955i	0.742562	+	0.669777i	$0.233610\pi$
$271$	22.0518i	1.33955i	−0.742562	+	0.669777i	$0.766390\pi$
$272$	20.6582	1.25259
$273$	0	0
$274$	−10.1705	−0.614421
$275$	9.31782i	0.561886i
$276$	−0.655265	−0.0394423
$277$	19.7139	1.18449	0.592245	−	0.805758i	$-0.298242\pi$
$277$	19.7139	1.18449	0.592245	+	0.805758i	$0.298242\pi$
$278$	− 4.31574i	− 0.258841i
$279$	10.8253i	0.648091i
$280$	2.26134i	0.135141i
$281$	− 4.42005i	− 0.263678i	−0.991271	−	0.131839i	$-0.957912\pi$
$281$	− 4.42005i	− 0.263678i	0.991271	−	0.131839i	$-0.0420882\pi$
$282$	−35.4701	−2.11221
$283$	31.9312	1.89811	0.949057	−	0.315106i	$-0.102040\pi$
$283$	31.9312	1.89811	0.949057	+	0.315106i	$0.102040\pi$
$284$	1.84795i	0.109655i
$285$	7.87300	0.466356
$286$	0	0
$287$	9.82390	0.579887
$288$	− 7.48797i	− 0.441233i
$289$	14.7675	0.868679
$290$	8.35746	0.490767
$291$	26.7800i	1.56987i
$292$	− 1.39688i	− 0.0817463i
$293$	16.2471i	0.949169i	0.880210	+	0.474584i	$0.157402\pi$
$293$	16.2471i	0.949169i	−0.880210	+	0.474584i	$0.842598\pi$
$294$	4.61428i	0.269110i
$295$	3.86647	0.225114
$296$	13.2974	0.772898
$297$	39.8439i	2.31198i
$298$	−21.2453	−1.23071
$299$	0	0
$300$	2.32354	0.134150
$301$	2.64573i	0.152497i
$302$	−20.6828	−1.19016
$303$	−6.00845	−0.345176
$304$	− 10.9952i	− 0.630621i
$305$	− 3.27926i	− 0.187770i
$306$	65.3912i	3.73817i
$307$	13.5052i	0.770782i	0.922753	+	0.385391i	$0.125933\pi$
$307$	13.5052i	0.770782i	−0.922753	+	0.385391i	$0.874067\pi$
$308$	0.328679	0.0187283
$309$	38.9333	2.21484
$310$	− 1.32961i	− 0.0755168i
$311$	−2.26442	−0.128404	−0.0642018	−	0.997937i	$-0.520450\pi$
$311$	−2.26442	−0.128404	−0.0642018	+	0.997937i	$0.520450\pi$
$312$	0	0
$313$	20.1386	1.13830	0.569151	−	0.822233i	$-0.307272\pi$
$313$	20.1386	1.13830	0.569151	+	0.822233i	$0.307272\pi$
$314$	19.5753i	1.10470i
$315$	−6.59873	−0.371796
$316$	−0.978543	−0.0550473
$317$	− 31.3079i	− 1.75843i	−0.476429	−	0.879213i	$-0.658069\pi$
$317$	− 31.3079i	− 1.75843i	0.476429	−	0.879213i	$-0.341931\pi$
$318$	1.61913i	0.0907960i
$319$	− 16.8562i	− 0.943769i
$320$	6.58243i	0.367969i
$321$	−11.1966	−0.624932
$322$	1.68656	0.0939883
$323$	− 16.9081i	− 0.940793i
$324$	5.95532	0.330851
$325$	0	0
$326$	14.5157	0.803950
$327$	− 44.6956i	− 2.47167i
$328$	28.7578	1.58789
$329$	−7.68703	−0.423800
$330$	− 7.54288i	− 0.415222i
$331$	− 5.86072i	− 0.322134i	−0.986943	−	0.161067i	$-0.948506\pi$
$331$	− 5.86072i	− 0.322134i	0.986943	−	0.161067i	$-0.0514936\pi$
$332$	0.454748i	0.0249576i
$333$	38.8028i	2.12638i
$334$	−8.00753	−0.438152
$335$	−8.73327	−0.477149
$336$	12.4522i	0.679321i
$337$	−14.0167	−0.763539	−0.381769	−	0.924258i	$-0.624685\pi$
$337$	−14.0167	−0.763539	−0.381769	+	0.924258i	$0.624685\pi$
$338$	0	0
$339$	4.91099	0.266728
$340$	0.676266i	0.0366757i
$341$	−2.68171	−0.145223
$342$	34.8041	1.88199
$343$	1.00000i	0.0539949i
$344$	7.74494i	0.417579i
$345$	3.25895i	0.175456i
$346$	7.64813i	0.411166i
$347$	−18.4346	−0.989622	−0.494811	−	0.869001i	$-0.664763\pi$
$347$	−18.4346	−0.989622	−0.494811	+	0.869001i	$0.664763\pi$
$348$	−4.20335	−0.225323
$349$	− 0.841480i	− 0.0450434i	−0.999746	−	0.0225217i	$-0.992831\pi$
$349$	− 0.841480i	− 0.0450434i	0.999746	−	0.0225217i	$-0.00716948\pi$
$350$	−5.98046	−0.319669
$351$	0	0
$352$	1.85497	0.0988704
$353$	− 4.32366i	− 0.230125i	−0.993358	−	0.115063i	$-0.963293\pi$
$353$	− 4.32366i	− 0.230125i	0.993358	−	0.115063i	$-0.0367069\pi$
$354$	23.0953	1.22750
$355$	9.19074	0.487794
$356$	0.306265i	0.0162320i
$357$	19.1485i	1.01345i
$358$	9.75295i	0.515459i
$359$	− 12.0924i	− 0.638213i	−0.947719	−	0.319107i	$-0.896617\pi$
$359$	− 12.0924i	− 0.638213i	0.947719	−	0.319107i	$-0.103383\pi$
$360$	−19.3167	−1.01808
$361$	10.0007	0.526355
$362$	− 0.770673i	− 0.0405057i
$363$	22.1578	1.16298
$364$	0	0
$365$	−6.94737	−0.363642
$366$	− 19.5878i	− 1.02387i
$367$	−9.05715	−0.472779	−0.236390	−	0.971658i	$-0.575964\pi$
$367$	−9.05715	−0.472779	−0.236390	+	0.971658i	$0.575964\pi$
$368$	4.55138	0.237257
$369$	83.9172i	4.36856i
$370$	− 4.76595i	− 0.247770i
$371$	0.350895i	0.0182175i
$372$	0.668724i	0.0346717i
$373$	−23.0254	−1.19221	−0.596104	−	0.802907i	$-0.703285\pi$
$373$	−23.0254	−1.19221	−0.596104	+	0.802907i	$0.703285\pi$
$374$	−16.1992	−0.837639
$375$	− 24.6783i	− 1.27438i
$376$	−22.5025	−1.16048
$377$	0	0
$378$	−25.5730	−1.31533
$379$	− 29.5778i	− 1.51931i	−0.650326	−	0.759655i	$-0.725368\pi$
$379$	− 29.5778i	− 1.51931i	0.650326	−	0.759655i	$-0.274632\pi$
$380$	0.359939	0.0184645
$381$	37.1076	1.90108
$382$	10.7998i	0.552567i
$383$	− 19.0793i	− 0.974906i	−0.873149	−	0.487453i	$-0.837926\pi$
$383$	− 19.0793i	− 0.974906i	0.873149	−	0.487453i	$-0.162074\pi$
$384$	33.3622i	1.70251i
$385$	− 1.63468i	− 0.0833112i
$386$	27.9444	1.42233
$387$	−22.6002	−1.14883
$388$	1.22433i	0.0621560i
$389$	11.3977	0.577885	0.288942	−	0.957347i	$-0.406696\pi$
$389$	11.3977	0.577885	0.288942	+	0.957347i	$0.406696\pi$
$390$	0	0
$391$	6.99896	0.353953
$392$	2.92733i	0.147853i
$393$	−7.61274	−0.384012
$394$	2.06742	0.104155
$395$	4.86677i	0.244874i
$396$	2.80763i	0.141089i
$397$	− 29.1687i	− 1.46394i	−0.681339	−	0.731968i	$-0.738602\pi$
$397$	− 29.1687i	− 1.46394i	0.681339	−	0.731968i	$-0.261398\pi$
$398$	34.3790i	1.72326i
$399$	10.1917	0.510223
$400$	−16.1390	−0.806948
$401$	− 17.0352i	− 0.850697i	−0.905030	−	0.425349i	$-0.860151\pi$
$401$	− 17.0352i	− 0.850697i	0.905030	−	0.425349i	$-0.139849\pi$
$402$	−52.1659	−2.60180
$403$	0	0
$404$	−0.274695	−0.0136666
$405$	− 29.6187i	− 1.47177i
$406$	10.8188	0.536930
$407$	−9.61250	−0.476474
$408$	56.0541i	2.77509i
$409$	7.21000i	0.356511i	0.983984	+	0.178256i	$0.0570454\pi$
$409$	7.21000i	0.356511i	−0.983984	+	0.178256i	$0.942955\pi$
$410$	− 10.3071i	− 0.509033i
$411$	− 25.4404i	− 1.25488i
$412$	1.77996	0.0876924
$413$	5.00519	0.246289
$414$	14.4069i	0.708058i
$415$	2.26169	0.111022
$416$	0	0
$417$	10.7954	0.528653
$418$	8.62192i	0.421712i
$419$	34.1903	1.67030	0.835152	−	0.550019i	$-0.185379\pi$
$419$	34.1903	1.67030	0.835152	+	0.550019i	$0.185379\pi$
$420$	−0.407633	−0.0198904
$421$	33.3533i	1.62554i	0.582585	+	0.812770i	$0.302041\pi$
$421$	33.3533i	1.62554i	−0.582585	+	0.812770i	$0.697959\pi$
$422$	− 7.52989i	− 0.366549i
$423$	− 65.6638i	− 3.19268i
$424$	1.02719i	0.0498846i
$425$	−24.8180	−1.20385
$426$	54.8985	2.65984
$427$	− 4.24504i	− 0.205432i
$428$	−0.511887	−0.0247430
$429$	0	0
$430$	2.77587	0.133864
$431$	31.8622i	1.53475i	0.641200	+	0.767374i	$0.278437\pi$
$431$	31.8622i	1.53475i	−0.641200	+	0.767374i	$0.721563\pi$
$432$	−69.0117	−3.32033
$433$	−2.69773	−0.129645	−0.0648223	−	0.997897i	$-0.520648\pi$
$433$	−2.69773	−0.129645	−0.0648223	+	0.997897i	$0.520648\pi$
$434$	− 1.72120i	− 0.0826202i
$435$	20.9053i	1.00233i
$436$	− 2.04340i	− 0.0978612i
$437$	− 3.72516i	− 0.178199i
$438$	−41.4983	−1.98287
$439$	21.5226	1.02722	0.513609	−	0.858024i	$-0.328308\pi$
$439$	21.5226	1.02722	0.513609	+	0.858024i	$0.328308\pi$
$440$	− 4.78527i	− 0.228129i
$441$	−8.54215	−0.406769
$442$	0	0
$443$	6.74835	0.320624	0.160312	−	0.987066i	$-0.448750\pi$
$443$	6.74835	0.320624	0.160312	+	0.987066i	$0.448750\pi$
$444$	2.39702i	0.113757i
$445$	1.52321	0.0722069
$446$	−9.36759	−0.443568
$447$	− 53.1429i	− 2.51357i
$448$	8.52104i	0.402581i
$449$	32.3984i	1.52898i	0.644638	+	0.764488i	$0.277008\pi$
$449$	32.3984i	1.52898i	−0.644638	+	0.764488i	$0.722992\pi$
$450$	− 51.0860i	− 2.40822i
$451$	−20.7886	−0.978895
$452$	0.224521	0.0105606
$453$	− 51.7359i	− 2.43076i
$454$	−4.30038	−0.201827
$455$	0	0
$456$	29.8345	1.39713
$457$	5.27900i	0.246941i	0.992348	+	0.123471i	$0.0394025\pi$
$457$	5.27900i	0.246941i	−0.992348	+	0.123471i	$0.960598\pi$
$458$	31.7401	1.48312
$459$	−106.124	−4.95344
$460$	0.148993i	0.00694685i
$461$	− 39.9387i	− 1.86013i	−0.367396	−	0.930065i	$-0.619750\pi$
$461$	− 39.9387i	− 1.86013i	0.367396	−	0.930065i	$-0.380250\pi$
$462$	− 9.76437i	− 0.454279i
$463$	− 7.02805i	− 0.326621i	−0.986575	−	0.163311i	$-0.947783\pi$
$463$	− 7.02805i	− 0.326621i	0.986575	−	0.163311i	$-0.0522173\pi$
$464$	29.1959	1.35539
$465$	3.32589	0.154234
$466$	− 13.1099i	− 0.607302i
$467$	12.7122	0.588252	0.294126	−	0.955767i	$-0.404971\pi$
$467$	12.7122	0.588252	0.294126	+	0.955767i	$0.404971\pi$
$468$	0	0
$469$	−11.3053	−0.522032
$470$	8.06515i	0.372017i
$471$	−48.9657	−2.25622
$472$	14.6519	0.674407
$473$	− 5.59869i	− 0.257428i
$474$	29.0704i	1.33525i
$475$	13.2092i	0.606081i
$476$	0.875435i	0.0401255i
$477$	−2.99739	−0.137241
$478$	−9.48309	−0.433746
$479$	23.9405i	1.09387i	0.837175	+	0.546935i	$0.184206\pi$
$479$	23.9405i	1.09387i	−0.837175	+	0.546935i	$0.815794\pi$
$480$	−2.30056	−0.105006
$481$	0	0
$482$	25.2069	1.14814
$483$	4.21876i	0.191960i
$484$	1.01301	0.0460461
$485$	6.08920	0.276496
$486$	− 100.201i	− 4.54521i
$487$	− 10.6960i	− 0.484683i	−0.970191	−	0.242342i	$-0.922084\pi$
$487$	− 10.6960i	− 0.484683i	0.970191	−	0.242342i	$-0.0779155\pi$
$488$	− 12.4267i	− 0.562529i
$489$	36.3096i	1.64198i
$490$	1.04919	0.0473975
$491$	−13.8352	−0.624373	−0.312187	−	0.950021i	$-0.601061\pi$
$491$	−13.8352	−0.624373	−0.312187	+	0.950021i	$0.601061\pi$
$492$	5.18393i	0.233710i
$493$	44.8965	2.02204
$494$	0	0
$495$	13.9637	0.627622
$496$	− 4.64486i	− 0.208560i
$497$	11.8975	0.533677
$498$	13.5096	0.605380
$499$	− 14.6054i	− 0.653827i	−0.945054	−	0.326913i	$-0.893991\pi$
$499$	− 14.6054i	− 0.653827i	0.945054	−	0.326913i	$-0.106009\pi$
$500$	− 1.12825i	− 0.0504567i
$501$	− 20.0300i	− 0.894875i
$502$	22.6237i	1.00975i
$503$	9.63765	0.429721	0.214861	−	0.976645i	$-0.431070\pi$
$503$	9.63765	0.429721	0.214861	+	0.976645i	$0.431070\pi$
$504$	−25.0057	−1.11384
$505$	1.36619i	0.0607948i
$506$	−3.56897	−0.158660
$507$	0	0
$508$	1.69649	0.0752696
$509$	6.16582i	0.273295i	0.990620	+	0.136648i	$0.0436328\pi$
$509$	6.16582i	0.273295i	−0.990620	+	0.136648i	$0.956367\pi$
$510$	20.0904	0.889618
$511$	−8.99347	−0.397848
$512$	24.6716i	1.09034i
$513$	56.4839i	2.49383i
$514$	10.3718i	0.457482i
$515$	− 8.85262i	− 0.390093i
$516$	−1.39612	−0.0614606
$517$	16.2667	0.715408
$518$	− 6.16959i	− 0.271076i
$519$	−19.1310	−0.839759
$520$	0	0
$521$	−30.1162	−1.31942	−0.659708	−	0.751522i	$-0.729320\pi$
$521$	−30.1162	−1.31942	−0.659708	+	0.751522i	$0.729320\pi$
$522$	92.4162i	4.04495i
$523$	6.30225	0.275578	0.137789	−	0.990462i	$-0.456000\pi$
$523$	6.30225	0.275578	0.137789	+	0.990462i	$0.456000\pi$
$524$	−0.348041	−0.0152042
$525$	− 14.9595i	− 0.652887i
$526$	25.3110i	1.10361i
$527$	− 7.14271i	− 0.311141i
$528$	− 26.3503i	− 1.14675i
$529$	−21.4580	−0.932957
$530$	0.368155	0.0159916
$531$	42.7551i	1.85541i
$532$	0.465946	0.0202013
$533$	0	0
$534$	9.09849	0.393730
$535$	2.54586i	0.110067i
$536$	−33.0945	−1.42946
$537$	−24.3960	−1.05277
$538$	− 33.7622i	− 1.45559i
$539$	− 2.11612i	− 0.0911478i
$540$	− 2.25916i	− 0.0972188i
$541$	1.95419i	0.0840171i	0.999117	+	0.0420086i	$0.0133757\pi$
$541$	1.95419i	0.0840171i	−0.999117	+	0.0420086i	$0.986624\pi$
$542$	29.9506	1.28649
$543$	1.92776	0.0827282
$544$	4.94071i	0.211831i
$545$	−10.1628	−0.435328
$546$	0	0
$547$	−45.2888	−1.93641	−0.968204	−	0.250162i	$-0.919516\pi$
$547$	−45.2888	−1.93641	−0.968204	+	0.250162i	$0.919516\pi$
$548$	− 1.16309i	− 0.0496848i
$549$	36.2618	1.54762
$550$	12.6554	0.539627
$551$	− 23.8959i	− 1.01800i
$552$	12.3497i	0.525639i
$553$	6.30010i	0.267908i
$554$	− 26.7751i	− 1.13757i
$555$	11.9215	0.506041
$556$	0.493546	0.0209310
$557$	− 4.02083i	− 0.170368i	−0.996365	−	0.0851841i	$-0.972852\pi$
$557$	− 4.02083i	− 0.170368i	0.996365	−	0.0851841i	$-0.0271478\pi$
$558$	14.7027	0.622417
$559$	0	0
$560$	2.83136	0.119647
$561$	− 40.5206i	− 1.71078i
$562$	−6.00326	−0.253232
$563$	−14.4667	−0.609700	−0.304850	−	0.952400i	$-0.598606\pi$
$563$	−14.4667	−0.609700	−0.304850	+	0.952400i	$0.598606\pi$
$564$	− 4.05634i	− 0.170803i
$565$	− 1.11665i	− 0.0469780i
$566$	− 43.3686i	− 1.82292i
$567$	− 38.3419i	− 1.61021i
$568$	34.8281	1.46135
$569$	−39.0095	−1.63536	−0.817682	−	0.575670i	$-0.804741\pi$
$569$	−39.0095	−1.63536	−0.817682	+	0.575670i	$0.804741\pi$
$570$	− 10.6930i	− 0.447881i
$571$	13.5719	0.567966	0.283983	−	0.958829i	$-0.408344\pi$
$571$	13.5719	0.567966	0.283983	+	0.958829i	$0.408344\pi$
$572$	0	0
$573$	−27.0147	−1.12855
$574$	− 13.3427i	− 0.556914i
$575$	−5.46784	−0.228025
$576$	−72.7880	−3.03283
$577$	8.39100i	0.349322i	0.984629	+	0.174661i	$0.0558829\pi$
$577$	8.39100i	0.349322i	−0.984629	+	0.174661i	$0.944117\pi$
$578$	− 20.0571i	− 0.834266i
$579$	69.9002i	2.90495i
$580$	0.955754i	0.0396855i
$581$	2.92778	0.121465
$582$	36.3723	1.50768
$583$	− 0.742535i	− 0.0307527i
$584$	−26.3269	−1.08941
$585$	0	0
$586$	22.0667	0.911567
$587$	− 22.1640i	− 0.914808i	−0.889259	−	0.457404i	$-0.848779\pi$
$587$	− 22.1640i	− 0.914808i	0.889259	−	0.457404i	$-0.151221\pi$
$588$	−0.527686	−0.0217614
$589$	−3.80167	−0.156645
$590$	− 5.25139i	− 0.216196i
$591$	5.17143i	0.212724i
$592$	− 16.6494i	− 0.684284i
$593$	− 39.0195i	− 1.60234i	−0.598437	−	0.801170i	$-0.704211\pi$
$593$	− 39.0195i	− 1.60234i	0.598437	−	0.801170i	$-0.295789\pi$
$594$	54.1156	2.22039
$595$	4.35397	0.178495
$596$	− 2.42960i	− 0.0995201i
$597$	−85.9955	−3.51956
$598$	0	0
$599$	31.3114	1.27935	0.639674	−	0.768646i	$-0.279069\pi$
$599$	31.3114	1.27935	0.639674	+	0.768646i	$0.279069\pi$
$600$	− 43.7915i	− 1.78778i
$601$	24.7669	1.01026	0.505132	−	0.863042i	$-0.331444\pi$
$601$	24.7669	1.01026	0.505132	+	0.863042i	$0.331444\pi$
$602$	3.59340	0.146456
$603$	− 96.5718i	− 3.93271i
$604$	− 2.36527i	− 0.0962415i
$605$	− 5.03821i	− 0.204832i
$606$	8.16061i	0.331502i
$607$	4.33301	0.175871	0.0879357	−	0.996126i	$-0.471973\pi$
$607$	4.33301	0.175871	0.0879357	+	0.996126i	$0.471973\pi$
$608$	2.62967	0.106647
$609$	27.0622i	1.09662i
$610$	−4.45385	−0.180331
$611$	0	0
$612$	−7.47810	−0.302284
$613$	− 45.9015i	− 1.85394i	−0.375131	−	0.926972i	$-0.622402\pi$
$613$	− 45.9015i	− 1.85394i	0.375131	−	0.926972i	$-0.377598\pi$
$614$	18.3426	0.740247
$615$	25.7822	1.03964
$616$	− 6.19459i	− 0.249587i
$617$	− 29.0145i	− 1.16808i	−0.811725	−	0.584040i	$-0.801471\pi$
$617$	− 29.0145i	− 1.16808i	0.811725	−	0.584040i	$-0.198529\pi$
$618$	− 52.8789i	− 2.12710i
$619$	8.57642i	0.344715i	0.985034	+	0.172358i	$0.0551385\pi$
$619$	8.57642i	0.344715i	−0.985034	+	0.172358i	$0.944861\pi$
$620$	0.152054	0.00610662
$621$	−23.3810	−0.938247
$622$	3.07551i	0.123317i
$623$	1.97181	0.0789990
$624$	0	0
$625$	16.4050	0.656199
$626$	− 27.3521i	− 1.09321i
$627$	−21.5669	−0.861298
$628$	−2.23862	−0.0893308
$629$	− 25.6028i	− 1.02085i
$630$	8.96233i	0.357068i
$631$	− 31.4081i	− 1.25034i	−0.780490	−	0.625168i	$-0.785030\pi$
$631$	− 31.4081i	− 1.25034i	0.780490	−	0.625168i	$-0.214970\pi$
$632$	18.4425i	0.733604i
$633$	18.8353	0.748634
$634$	−42.5220	−1.68877
$635$	− 8.43748i	− 0.334831i
$636$	−0.185162	−0.00734216
$637$	0	0
$638$	−22.8940	−0.906381
$639$	101.631i	4.02044i
$640$	7.58586	0.299858
$641$	−7.67208	−0.303029	−0.151514	−	0.988455i	$-0.548415\pi$
$641$	−7.67208	−0.303029	−0.151514	+	0.988455i	$0.548415\pi$
$642$	15.2071i	0.600175i
$643$	7.48239i	0.295076i	0.989056	+	0.147538i	$0.0471350\pi$
$643$	7.48239i	0.295076i	−0.989056	+	0.147538i	$0.952865\pi$
$644$	0.192874i	0.00760030i
$645$	6.94356i	0.273403i
$646$	−22.9644	−0.903523
$647$	−23.9406	−0.941201	−0.470600	−	0.882346i	$-0.655963\pi$
$647$	−23.9406	−0.941201	−0.470600	+	0.882346i	$0.655963\pi$
$648$	− 112.239i	− 4.40918i
$649$	−10.5916	−0.415756
$650$	0	0
$651$	4.30541	0.168742
$652$	1.66001i	0.0650109i
$653$	34.2885	1.34181	0.670907	−	0.741541i	$-0.265905\pi$
$653$	34.2885	1.34181	0.670907	+	0.741541i	$0.265905\pi$
$654$	−60.7051	−2.37376
$655$	1.73098i	0.0676349i
$656$	− 36.0069i	− 1.40583i
$657$	− 76.8235i	− 2.99717i
$658$	10.4404i	0.407011i
$659$	−8.82716	−0.343857	−0.171929	−	0.985109i	$-0.555000\pi$
$659$	−8.82716	−0.343857	−0.171929	+	0.985109i	$0.555000\pi$
$660$	0.862600	0.0335766
$661$	− 33.3881i	− 1.29865i	−0.760512	−	0.649324i	$-0.775052\pi$
$661$	− 33.3881i	− 1.29865i	0.760512	−	0.649324i	$-0.224948\pi$
$662$	−7.95997	−0.309373
$663$	0	0
$664$	8.57060	0.332604
$665$	− 2.31738i	− 0.0898640i
$666$	52.7015	2.04214
$667$	9.89150	0.383000
$668$	− 0.915736i	− 0.0354309i
$669$	− 23.4321i	− 0.905936i
$670$	11.8614i	0.458247i
$671$	8.98302i	0.346786i
$672$	−2.97811	−0.114883
$673$	−33.1395	−1.27743	−0.638717	−	0.769442i	$-0.720534\pi$
$673$	−33.1395	−1.27743	−0.638717	+	0.769442i	$0.720534\pi$
$674$	19.0373i	0.733291i
$675$	82.9079	3.19112
$676$	0	0
$677$	28.8217	1.10771	0.553854	−	0.832614i	$-0.313157\pi$
$677$	28.8217	1.10771	0.553854	+	0.832614i	$0.313157\pi$
$678$	− 6.67005i	− 0.256162i
$679$	7.88255	0.302505
$680$	12.7455	0.488768
$681$	− 10.7570i	− 0.412207i
$682$	3.64227i	0.139470i
$683$	− 17.0467i	− 0.652274i	−0.945323	−	0.326137i	$-0.894253\pi$
$683$	− 17.0467i	− 0.652274i	0.945323	−	0.326137i	$-0.105747\pi$
$684$	3.98018i	0.152186i
$685$	−5.78462	−0.221019
$686$	1.35819	0.0518559
$687$	79.3948i	3.02910i
$688$	9.69722	0.369703
$689$	0	0
$690$	4.42628	0.168505
$691$	3.56418i	0.135588i	0.997699	+	0.0677939i	$0.0215960\pi$
$691$	3.56418i	0.135588i	−0.997699	+	0.0677939i	$0.978404\pi$
$692$	−0.874636	−0.0332487
$693$	18.0762	0.686659
$694$	25.0377i	0.950418i
$695$	− 2.45464i	− 0.0931099i
$696$	79.2203i	3.00284i
$697$	− 55.3702i	− 2.09729i
$698$	−1.14289	−0.0432590
$699$	32.7930	1.24034
$700$	− 0.683922i	− 0.0258498i
$701$	−5.75672	−0.217428	−0.108714	−	0.994073i	$-0.534673\pi$
$701$	−5.75672	−0.217428	−0.108714	+	0.994073i	$0.534673\pi$
$702$	0	0
$703$	−13.6270	−0.513951
$704$	− 18.0315i	− 0.679590i
$705$	−20.1741	−0.759802
$706$	−5.87235	−0.221009
$707$	1.76856i	0.0665134i
$708$	2.64117i	0.0992613i
$709$	5.47541i	0.205633i	0.994700	+	0.102817i	$0.0327855\pi$
$709$	5.47541i	0.205633i	−0.994700	+	0.102817i	$0.967214\pi$
$710$	− 12.4828i	− 0.468470i
$711$	−53.8164	−2.01827
$712$	5.77216	0.216321
$713$	− 1.57367i	− 0.0589343i
$714$	26.0073	0.973299
$715$	0	0
$716$	−1.11534	−0.0416823
$717$	− 23.7210i	− 0.885876i
$718$	−16.4238	−0.612930
$719$	45.1042	1.68210	0.841051	−	0.540955i	$-0.181937\pi$
$719$	45.1042	1.68210	0.841051	+	0.540955i	$0.181937\pi$
$720$	24.1859i	0.901354i
$721$	− 11.4598i	− 0.426787i
$722$	− 13.5829i	− 0.505503i
$723$	63.0525i	2.34495i
$724$	0.0881337	0.00327546
$725$	−35.0748	−1.30264
$726$	− 30.0945i	− 1.11691i
$727$	−35.7464	−1.32576	−0.662880	−	0.748725i	$-0.730666\pi$
$727$	−35.7464	−1.32576	−0.662880	+	0.748725i	$0.730666\pi$
$728$	0	0
$729$	135.617	5.02285
$730$	9.43584i	0.349236i
$731$	14.9121	0.551542
$732$	2.24005	0.0827946
$733$	30.7972i	1.13752i	0.822503	+	0.568761i	$0.192577\pi$
$733$	30.7972i	1.13752i	−0.822503	+	0.568761i	$0.807423\pi$
$734$	12.3013i	0.454050i
$735$	2.62444i	0.0968039i
$736$	1.08853i	0.0401236i
$737$	23.9234	0.881231
$738$	113.975	4.19550
$739$	− 38.1399i	− 1.40300i	−0.712670	−	0.701499i	$-0.752514\pi$
$739$	− 38.1399i	− 1.40300i	0.712670	−	0.701499i	$-0.247486\pi$
$740$	0.545031	0.0200357
$741$	0	0
$742$	0.476581	0.0174959
$743$	19.8187i	0.727079i	0.931579	+	0.363539i	$0.118432\pi$
$743$	19.8187i	0.727079i	−0.931579	+	0.363539i	$0.881568\pi$
$744$	12.6034	0.462062
$745$	−12.0836	−0.442708
$746$	31.2728i	1.14498i
$747$	25.0096i	0.915052i
$748$	− 1.85253i	− 0.0677351i
$749$	3.29566i	0.120421i
$750$	−33.5178	−1.22390
$751$	−11.0353	−0.402683	−0.201341	−	0.979521i	$-0.564530\pi$
$751$	−11.0353	−0.402683	−0.201341	+	0.979521i	$0.564530\pi$
$752$	28.1747i	1.02743i
$753$	−56.5910	−2.06229
$754$	0	0
$755$	−11.7636	−0.428123
$756$	− 2.92451i	− 0.106364i
$757$	−5.63273	−0.204725	−0.102363	−	0.994747i	$-0.532640\pi$
$757$	−5.63273	−0.204725	−0.102363	+	0.994747i	$0.532640\pi$
$758$	−40.1723	−1.45912
$759$	− 8.92741i	− 0.324044i
$760$	− 6.78374i	− 0.246072i
$761$	6.45648i	0.234047i	0.993129	+	0.117024i	$0.0373353\pi$
$761$	6.45648i	0.234047i	−0.993129	+	0.117024i	$0.962665\pi$
$762$	− 50.3991i	− 1.82577i
$763$	−13.1559	−0.476277
$764$	−1.23506	−0.0446830
$765$	37.1922i	1.34469i
$766$	−25.9133	−0.936285
$767$	0	0
$768$	−12.5861	−0.454162
$769$	− 8.81720i	− 0.317956i	−0.987282	−	0.158978i	$-0.949180\pi$
$769$	− 8.81720i	− 0.317956i	0.987282	−	0.158978i	$-0.0508199\pi$
$770$	−2.22021	−0.0800108
$771$	−25.9441	−0.934355
$772$	3.19571i	0.115016i
$773$	46.0758i	1.65723i	0.559818	+	0.828616i	$0.310871\pi$
$773$	46.0758i	1.65723i	−0.559818	+	0.828616i	$0.689129\pi$
$774$	30.6954i	1.10332i
$775$	5.58014i	0.200445i
$776$	23.0749	0.828340
$777$	15.4326	0.553642
$778$	− 15.4802i	− 0.554992i
$779$	−29.4705	−1.05589
$780$	0	0
$781$	−25.1766	−0.900890
$782$	− 9.50591i	− 0.339931i
$783$	−149.983	−5.35995
$784$	3.66523	0.130901
$785$	11.1338i	0.397381i
$786$	10.3395i	0.368799i
$787$	− 2.92457i	− 0.104250i	−0.998641	−	0.0521248i	$-0.983401\pi$
$787$	− 2.92457i	− 0.104250i	0.998641	−	0.0521248i	$-0.0165994\pi$
$788$	0.236429i	0.00842242i
$789$	−63.3129	−2.25400
$790$	6.61000	0.235173
$791$	− 1.44552i	− 0.0513970i
$792$	52.9151	1.88026
$793$	0	0
$794$	−39.6166	−1.40594
$795$	0.920902i	0.0326610i
$796$	−3.93156	−0.139350
$797$	−34.7197	−1.22984	−0.614918	−	0.788591i	$-0.710811\pi$
$797$	−34.7197	−1.22984	−0.614918	+	0.788591i	$0.710811\pi$
$798$	− 13.8423i	− 0.490011i
$799$	43.3262i	1.53277i
$800$	− 3.85986i	− 0.136467i
$801$	16.8435i	0.595136i
$802$	−23.1370	−0.816997
$803$	19.0313	0.671599
$804$	− 5.96567i	− 0.210393i
$805$	0.959257	0.0338094
$806$	0	0
$807$	84.4528	2.97288
$808$	5.17716i	0.182132i
$809$	−36.7435	−1.29183	−0.645917	−	0.763407i	$-0.723525\pi$
$809$	−36.7435	−1.29183	−0.645917	+	0.763407i	$0.723525\pi$
$810$	−40.2278	−1.41346
$811$	49.5717i	1.74070i	0.492437	+	0.870348i	$0.336106\pi$
$811$	49.5717i	1.74070i	−0.492437	+	0.870348i	$0.663894\pi$
$812$	1.23724i	0.0434185i
$813$	74.9183i	2.62750i
$814$	13.0556i	0.457598i
$815$	8.25603	0.289196
$816$	70.1838	2.45692
$817$	− 7.93687i	− 0.277676i
$818$	9.79254	0.342388
$819$	0	0
$820$	1.17872	0.0411626
$821$	− 31.7074i	− 1.10660i	−0.832983	−	0.553299i	$-0.813369\pi$
$821$	− 31.7074i	− 1.10660i	0.832983	−	0.553299i	$-0.186631\pi$
$822$	−34.5529	−1.20517
$823$	28.7128	1.00086	0.500432	−	0.865776i	$-0.333174\pi$
$823$	28.7128	1.00086	0.500432	+	0.865776i	$0.333174\pi$
$824$	− 33.5468i	− 1.16866i
$825$	31.6561i	1.10213i
$826$	− 6.79800i	− 0.236533i
$827$	− 30.8034i	− 1.07114i	−0.844491	−	0.535569i	$-0.820097\pi$
$827$	− 30.8034i	− 1.07114i	0.844491	−	0.535569i	$-0.179903\pi$
$828$	−1.64756	−0.0572566
$829$	−30.9789	−1.07594	−0.537970	−	0.842964i	$-0.680809\pi$
$829$	−30.9789	−1.07594	−0.537970	+	0.842964i	$0.680809\pi$
$830$	− 3.07180i	− 0.106624i
$831$	66.9753	2.32335
$832$	0	0
$833$	5.63627	0.195285
$834$	− 14.6622i	− 0.507710i
$835$	−4.55440	−0.157612
$836$	−0.985998	−0.0341015
$837$	23.8612i	0.824764i
$838$	− 46.4369i	− 1.60414i
$839$	48.0432i	1.65863i	0.558778	+	0.829317i	$0.311270\pi$
$839$	48.0432i	1.65863i	−0.558778	+	0.829317i	$0.688730\pi$
$840$	7.68261i	0.265075i
$841$	34.4514	1.18798
$842$	45.3001	1.56114
$843$	− 15.0166i	− 0.517198i
$844$	0.861113	0.0296407
$845$	0	0
$846$	−89.1838	−3.06620
$847$	− 6.52203i	− 0.224100i
$848$	1.28611	0.0441652
$849$	108.482	3.72310
$850$	33.7075i	1.15616i
$851$	− 5.64076i	− 0.193363i
$852$	6.27816i	0.215086i
$853$	10.1693i	0.348189i	0.984729	+	0.174095i	$0.0556998\pi$
$853$	10.1693i	0.348189i	−0.984729	+	0.174095i	$0.944300\pi$
$854$	−5.76557	−0.197294
$855$	19.7954	0.676988
$856$	9.64749i	0.329744i
$857$	4.52581	0.154599	0.0772993	−	0.997008i	$-0.475370\pi$
$857$	4.52581	0.154599	0.0772993	+	0.997008i	$0.475370\pi$
$858$	0	0
$859$	29.8293	1.01776	0.508881	−	0.860837i	$-0.330059\pi$
$859$	29.8293	1.01776	0.508881	+	0.860837i	$0.330059\pi$
$860$	0.317447i	0.0108249i
$861$	33.3755	1.13743
$862$	43.2749	1.47395
$863$	34.3352i	1.16879i	0.811471	+	0.584393i	$0.198667\pi$
$863$	34.3352i	1.16879i	−0.811471	+	0.584393i	$0.801333\pi$
$864$	− 16.5051i	− 0.561516i
$865$	4.34999i	0.147904i
$866$	3.66403i	0.124509i
$867$	50.1709	1.70389
$868$	0.196835	0.00668103
$869$	− 13.3318i	− 0.452249i
$870$	28.3934	0.962626
$871$	0	0
$872$	−38.5118	−1.30417
$873$	67.3340i	2.27891i
$874$	−5.05947	−0.171139
$875$	−7.26393	−0.245566
$876$	− 4.74573i	− 0.160343i
$877$	− 29.0504i	− 0.980963i	−0.871452	−	0.490481i	$-0.836821\pi$
$877$	− 29.0504i	− 0.980963i	0.871452	−	0.490481i	$-0.163179\pi$
$878$	− 29.2318i	− 0.986524i
$879$	55.1976i	1.86177i
$880$	−5.99149	−0.201973
$881$	−18.4225	−0.620669	−0.310335	−	0.950627i	$-0.600441\pi$
$881$	−18.4225	−0.620669	−0.310335	+	0.950627i	$0.600441\pi$
$882$	11.6019i	0.390655i
$883$	−33.6175	−1.13132	−0.565659	−	0.824639i	$-0.691378\pi$
$883$	−33.6175	−1.13132	−0.565659	+	0.824639i	$0.691378\pi$
$884$	0	0
$885$	13.1358	0.441556
$886$	− 9.16554i	− 0.307922i
$887$	35.9829	1.20819	0.604094	−	0.796913i	$-0.293535\pi$
$887$	35.9829	1.20819	0.604094	+	0.796913i	$0.293535\pi$
$888$	45.1764	1.51602
$889$	− 10.9224i	− 0.366327i
$890$	− 2.06880i	− 0.0693465i
$891$	81.1360i	2.71816i
$892$	− 1.07127i	− 0.0358688i
$893$	23.0601	0.771678
$894$	−72.1781	−2.41400
$895$	5.54714i	0.185420i
$896$	9.82000	0.328063
$897$	0	0
$898$	44.0032	1.46841
$899$	− 10.0947i	− 0.336676i
$900$	5.84216	0.194739
$901$	1.97774	0.0658880
$902$	28.2348i	0.940116i
$903$	8.98854i	0.299120i
$904$	− 4.23154i	− 0.140739i
$905$	− 0.438332i	− 0.0145706i
$906$	−70.2671	−2.33447
$907$	26.2877	0.872868	0.436434	−	0.899736i	$-0.356241\pi$
$907$	26.2877	0.872868	0.436434	+	0.899736i	$0.356241\pi$
$908$	− 0.491788i	− 0.0163206i
$909$	−15.1073	−0.501077
$910$	0	0
$911$	−39.8689	−1.32092	−0.660458	−	0.750863i	$-0.729638\pi$
$911$	−39.8689	−1.32092	−0.660458	+	0.750863i	$0.729638\pi$
$912$	− 37.3550i	− 1.23695i
$913$	−6.19554	−0.205043
$914$	7.16989	0.237159
$915$	− 11.1409i	− 0.368306i
$916$	3.62978i	0.119931i
$917$	2.24077i	0.0739969i
$918$	144.136i	4.75721i
$919$	−27.5349	−0.908292	−0.454146	−	0.890927i	$-0.650056\pi$
$919$	−27.5349	−0.908292	−0.454146	+	0.890927i	$0.650056\pi$
$920$	2.80807	0.0925792
$921$	45.8822i	1.51187i
$922$	−54.2443	−1.78644
$923$	0	0
$924$	1.11665	0.0367350
$925$	20.0018i	0.657657i
$926$	−9.54542	−0.313682
$927$	97.8916	3.21518
$928$	6.98261i	0.229215i
$929$	14.5572i	0.477607i	0.971068	+	0.238804i	$0.0767552\pi$
$929$	14.5572i	0.477607i	−0.971068	+	0.238804i	$0.923245\pi$
$930$	− 4.51719i	− 0.148124i
$931$	− 2.99988i	− 0.0983170i
$932$	1.49924	0.0491091
$933$	−7.69308	−0.251860
$934$	− 17.2656i	− 0.564949i
$935$	−9.21352	−0.301314
$936$	0	0
$937$	−1.11811	−0.0365270	−0.0182635	−	0.999833i	$-0.505814\pi$
$937$	−1.11811	−0.0365270	−0.0182635	+	0.999833i	$0.505814\pi$
$938$	15.3548i	0.501351i
$939$	68.4184	2.23275
$940$	−0.922325	−0.0300829
$941$	− 30.8810i	− 1.00669i	−0.864085	−	0.503346i	$-0.832102\pi$
$941$	− 30.8810i	− 1.00669i	0.864085	−	0.503346i	$-0.167898\pi$
$942$	66.5047i	2.16684i
$943$	− 12.1990i	− 0.397255i
$944$	− 18.3452i	− 0.597085i
$945$	−14.5450	−0.473150
$946$	−7.60408	−0.247230
$947$	20.2675i	0.658604i	0.944225	+	0.329302i	$0.106813\pi$
$947$	20.2675i	0.658604i	−0.944225	+	0.329302i	$0.893187\pi$
$948$	−3.32448	−0.107974
$949$	0	0
$950$	17.9406	0.582071
$951$	− 106.365i	− 3.44911i
$952$	16.4993	0.534744
$953$	−30.7177	−0.995043	−0.497522	−	0.867452i	$-0.665757\pi$
$953$	−30.7177	−0.995043	−0.497522	+	0.867452i	$0.665757\pi$
$954$	4.07103i	0.131804i
$955$	6.14256i	0.198769i
$956$	− 1.08448i	− 0.0350746i
$957$	− 57.2670i	− 1.85118i
$958$	32.5158	1.05054
$959$	−7.48827	−0.241809
$960$	22.3630i	0.721761i
$961$	29.3940	0.948194
$962$	0	0
$963$	−28.1520	−0.907185
$964$	2.88265i	0.0928438i
$965$	15.8938	0.511640
$966$	5.72988	0.184356
$967$	20.0281i	0.644060i	0.946729	+	0.322030i	$0.104365\pi$
$967$	20.0281i	0.644060i	−0.946729	+	0.322030i	$0.895635\pi$
$968$	− 19.0922i	− 0.613646i
$969$	− 57.4432i	− 1.84534i
$970$	− 8.27029i	− 0.265543i
$971$	−9.01006	−0.289146	−0.144573	−	0.989494i	$-0.546181\pi$
$971$	−9.01006	−0.289146	−0.144573	+	0.989494i	$0.546181\pi$
$972$	11.4589	0.367545
$973$	− 3.17757i	− 0.101868i
$974$	−14.5272	−0.465483
$975$	0	0
$976$	−15.5591	−0.498034
$977$	− 15.4962i	− 0.495766i	−0.968790	−	0.247883i	$-0.920265\pi$
$977$	− 15.4962i	− 0.495766i	0.968790	−	0.247883i	$-0.0797349\pi$
$978$	49.3153	1.57693
$979$	−4.17259	−0.133357
$980$	0.119985i	0.00383277i
$981$	− 112.380i	− 3.58801i
$982$	18.7908i	0.599639i
$983$	− 45.8307i	− 1.46177i	−0.682499	−	0.730886i	$-0.739107\pi$
$983$	− 45.8307i	− 1.46177i	0.682499	−	0.730886i	$-0.260893\pi$
$984$	97.7012	3.11460
$985$	1.17587	0.0374665
$986$	− 60.9779i	− 1.94193i
$987$	−26.1157	−0.831272
$988$	0	0
$989$	3.28539	0.104469
$990$	− 18.9654i	− 0.602759i
$991$	5.91658	0.187946	0.0939731	−	0.995575i	$-0.470043\pi$
$991$	5.91658	0.187946	0.0939731	+	0.995575i	$0.470043\pi$
$992$	1.11088	0.0352706
$993$	− 19.9111i	− 0.631858i
$994$	− 16.1591i	− 0.512536i
$995$	19.5536i	0.619889i
$996$	1.54495i	0.0489536i
$997$	27.0852	0.857798	0.428899	−	0.903352i	$-0.358902\pi$
$997$	27.0852	0.857798	0.428899	+	0.903352i	$0.358902\pi$
$998$	−19.8369	−0.627925
$999$	85.5298i	2.70604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.j.337.7		24
13.5	odd	4		1183.2.a.r.1.3	yes	12
13.8	odd	4		1183.2.a.q.1.10	✓	12
13.12	even	2	inner	1183.2.c.j.337.18		24
91.34	even	4		8281.2.a.cn.1.10		12
91.83	even	4		8281.2.a.cq.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.10	✓	12	13.8	odd	4
1183.2.a.r.1.3	yes	12	13.5	odd	4
1183.2.c.j.337.7		24	1.1	even	1	trivial
1183.2.c.j.337.18		24	13.12	even	2	inner
8281.2.a.cn.1.10		12	91.34	even	4
8281.2.a.cq.1.3		12	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)

\(f(q)\)	\(=\)	\(q-1.35819i q^{2} +3.39737 q^{3} +0.155322 q^{4} -0.772491i q^{5} -4.61428i q^{6} -1.00000i q^{7} -2.92733i q^{8} +8.54215 q^{9} -1.04919 q^{10} +2.11612i q^{11} +0.527686 q^{12} -1.35819 q^{14} -2.62444i q^{15} -3.66523 q^{16} -5.63627 q^{17} -11.6019i q^{18} +2.99988i q^{19} -0.119985i q^{20} -3.39737i q^{21} +2.87409 q^{22} -1.24177 q^{23} -9.94525i q^{24} +4.40326 q^{25} +18.8288 q^{27} -0.155322i q^{28} -7.96564 q^{29} -3.56449 q^{30} +1.26728i q^{31} -0.876591i q^{32} +7.18925i q^{33} +7.65512i q^{34} -0.772491 q^{35} +1.32678 q^{36} +4.54251i q^{37} +4.07440 q^{38} -2.26134 q^{40} +9.82390i q^{41} -4.61428 q^{42} -2.64573 q^{43} +0.328679i q^{44} -6.59873i q^{45} +1.68656i q^{46} -7.68703i q^{47} -12.4522 q^{48} -1.00000 q^{49} -5.98046i q^{50} -19.1485 q^{51} -0.350895 q^{53} -25.5730i q^{54} +1.63468 q^{55} -2.92733 q^{56} +10.1917i q^{57} +10.8188i q^{58} +5.00519i q^{59} -0.407633i q^{60} +4.24504 q^{61} +1.72120 q^{62} -8.54215i q^{63} -8.52104 q^{64} +9.76437 q^{66} -11.3053i q^{67} -0.875435 q^{68} -4.21876 q^{69} +1.04919i q^{70} +11.8975i q^{71} -25.0057i q^{72} -8.99347i q^{73} +6.16959 q^{74} +14.9595 q^{75} +0.465946i q^{76} +2.11612 q^{77} -6.30010 q^{79} +2.83136i q^{80} +38.3419 q^{81} +13.3427 q^{82} +2.92778i q^{83} -0.527686i q^{84} +4.35397i q^{85} +3.59340i q^{86} -27.0622 q^{87} +6.19459 q^{88} +1.97181i q^{89} -8.96233 q^{90} -0.192874 q^{92} +4.30541i q^{93} -10.4404 q^{94} +2.31738 q^{95} -2.97811i q^{96} +7.88255i q^{97} +1.35819i q^{98} +18.0762i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38}+ \cdots - 58 q^{95}+O(q^{100}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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