LMFDB - Embedded newform 325.4.b.e.274.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,4,Mod(274,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("325.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	325.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.1756207519$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.2
Root			$-1.56155i$ of defining polynomial
Character	$\chi$	$=$	325.274
Dual form			325.4.b.e.274.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.56155i q^{2} -8.68466i q^{3} +5.56155 q^{4} -13.5616 q^{6} -27.1771i q^{7} -21.1771i q^{8} -48.4233 q^{9} +O(q^{10})$	\(q-1.56155i q^{2} -8.68466i q^{3} +5.56155 q^{4} -13.5616 q^{6} -27.1771i q^{7} -21.1771i q^{8} -48.4233 q^{9} +15.2614 q^{11} -48.3002i q^{12} +13.0000i q^{13} -42.4384 q^{14} +11.4233 q^{16} +44.5464i q^{17} +75.6155i q^{18} -23.9697 q^{19} -236.024 q^{21} -23.8314i q^{22} -122.739i q^{23} -183.916 q^{24} +20.3002 q^{26} +186.054i q^{27} -151.147i q^{28} +219.909 q^{29} +27.0928 q^{31} -187.255i q^{32} -132.540i q^{33} +69.5616 q^{34} -269.309 q^{36} +94.1922i q^{37} +37.4299i q^{38} +112.901 q^{39} -160.354 q^{41} +368.563i q^{42} +151.302i q^{43} +84.8769 q^{44} -191.663 q^{46} +466.948i q^{47} -99.2074i q^{48} -395.594 q^{49} +386.870 q^{51} +72.3002i q^{52} +120.847i q^{53} +290.533 q^{54} -575.531 q^{56} +208.169i q^{57} -343.400i q^{58} +439.633 q^{59} -137.305 q^{61} -42.3068i q^{62} +1316.00i q^{63} -201.022 q^{64} -206.968 q^{66} +512.280i q^{67} +247.747i q^{68} -1065.94 q^{69} +410.719 q^{71} +1025.46i q^{72} +308.004i q^{73} +147.086 q^{74} -133.309 q^{76} -414.759i q^{77} -176.300i q^{78} +586.462 q^{79} +308.386 q^{81} +250.401i q^{82} -1354.20i q^{83} -1312.66 q^{84} +236.266 q^{86} -1909.84i q^{87} -323.191i q^{88} -439.882 q^{89} +353.302 q^{91} -682.617i q^{92} -235.292i q^{93} +729.164 q^{94} -1626.24 q^{96} -1511.27i q^{97} +617.740i q^{98} -739.006 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 14 q^{4} - 46 q^{6} - 70 q^{9}+O(q^{10}) $ 4 * q + 14 * q^4 - 46 * q^6 - 70 * q^9	$ 4 q + 14 q^{4} - 46 q^{6} - 70 q^{9} + 160 q^{11} - 178 q^{14} - 78 q^{16} + 168 q^{19} - 606 q^{21} - 546 q^{24} - 26 q^{26} + 88 q^{29} - 172 q^{31} + 270 q^{34} - 500 q^{36} + 130 q^{39} - 460 q^{41} + 356 q^{44} - 8 q^{46} - 766 q^{49} + 962 q^{51} - 182 q^{54} - 2030 q^{56} + 736 q^{59} - 2116 q^{61} - 1538 q^{64} - 1636 q^{66} - 1592 q^{69} - 262 q^{71} - 294 q^{74} + 44 q^{76} + 2016 q^{79} + 244 q^{81} - 2818 q^{84} + 2718 q^{86} + 1440 q^{89} + 234 q^{91} + 1622 q^{94} - 3726 q^{96} + 260 q^{99}+O(q^{100}) $ 4 * q + 14 * q^4 - 46 * q^6 - 70 * q^9 + 160 * q^11 - 178 * q^14 - 78 * q^16 + 168 * q^19 - 606 * q^21 - 546 * q^24 - 26 * q^26 + 88 * q^29 - 172 * q^31 + 270 * q^34 - 500 * q^36 + 130 * q^39 - 460 * q^41 + 356 * q^44 - 8 * q^46 - 766 * q^49 + 962 * q^51 - 182 * q^54 - 2030 * q^56 + 736 * q^59 - 2116 * q^61 - 1538 * q^64 - 1636 * q^66 - 1592 * q^69 - 262 * q^71 - 294 * q^74 + 44 * q^76 + 2016 * q^79 + 244 * q^81 - 2818 * q^84 + 2718 * q^86 + 1440 * q^89 + 234 * q^91 + 1622 * q^94 - 3726 * q^96 + 260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$1$

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 $

$2$	− 1.56155i	− 0.552092i	−0.961144	−	0.276046i	$-0.910976\pi$
$2$	− 1.56155i	− 0.552092i	0.961144	−	0.276046i	$-0.0890243\pi$
$3$	− 8.68466i	− 1.67136i	−0.549214	−	0.835682i	$-0.685073\pi$
$3$	− 8.68466i	− 1.67136i	0.549214	−	0.835682i	$-0.314927\pi$
$4$	5.56155	0.695194
$5$	0	0
$5$	0	0
$6$	−13.5616	−0.922747
$7$	− 27.1771i	− 1.46742i	−0.679460	−	0.733712i	$-0.737786\pi$
$7$	− 27.1771i	− 1.46742i	0.679460	−	0.733712i	$-0.262214\pi$
$8$	− 21.1771i	− 0.935904i
$9$	−48.4233	−1.79346
$10$	0	0
$11$	15.2614	0.418316	0.209158	−	0.977882i	$-0.432928\pi$
$11$	15.2614	0.418316	0.209158	+	0.977882i	$0.432928\pi$
$12$	− 48.3002i	− 1.16192i
$13$	13.0000i	0.277350i
$13$	13.0000i	0.277350i
$14$	−42.4384	−0.810154
$15$	0	0
$16$	11.4233	0.178489
$17$	44.5464i	0.635535i	0.948169	+	0.317767i	$0.102933\pi$
$17$	44.5464i	0.635535i	−0.948169	+	0.317767i	$0.897067\pi$
$18$	75.6155i	0.990153i
$19$	−23.9697	−0.289422	−0.144711	−	0.989474i	$-0.546225\pi$
$19$	−23.9697	−0.289422	−0.144711	+	0.989474i	$0.546225\pi$
$20$	0	0
$21$	−236.024	−2.45260
$22$	− 23.8314i	− 0.230949i
$23$	− 122.739i	− 1.11273i	−0.830938	−	0.556365i	$-0.812196\pi$
$23$	− 122.739i	− 1.11273i	0.830938	−	0.556365i	$-0.187804\pi$
$24$	−183.916	−1.56423
$25$	0	0
$26$	20.3002	0.153123
$27$	186.054i	1.32615i
$28$	− 151.147i	− 1.02014i
$29$	219.909	1.40814	0.704071	−	0.710130i	$-0.251364\pi$
$29$	219.909	1.40814	0.704071	+	0.710130i	$0.251364\pi$
$30$	0	0
$31$	27.0928	0.156968	0.0784840	−	0.996915i	$-0.474992\pi$
$31$	27.0928	0.156968	0.0784840	+	0.996915i	$0.474992\pi$
$32$	− 187.255i	− 1.03445i
$33$	− 132.540i	− 0.699158i
$34$	69.5616	0.350874
$35$	0	0
$36$	−269.309	−1.24680
$37$	94.1922i	0.418516i	0.977860	+	0.209258i	$0.0671049\pi$
$37$	94.1922i	0.418516i	−0.977860	+	0.209258i	$0.932895\pi$
$38$	37.4299i	0.159788i
$39$	112.901	0.463553
$40$	0	0
$41$	−160.354	−0.610808	−0.305404	−	0.952223i	$-0.598791\pi$
$41$	−160.354	−0.610808	−0.305404	+	0.952223i	$0.598791\pi$
$42$	368.563i	1.35406i
$43$	151.302i	0.536589i	0.963337	+	0.268295i	$0.0864601\pi$
$43$	151.302i	0.536589i	−0.963337	+	0.268295i	$0.913540\pi$
$44$	84.8769	0.290811
$45$	0	0
$46$	−191.663	−0.614329
$47$	466.948i	1.44918i	0.689181	+	0.724589i	$0.257970\pi$
$47$	466.948i	1.44918i	−0.689181	+	0.724589i	$0.742030\pi$
$48$	− 99.2074i	− 0.298320i
$49$	−395.594	−1.15333
$50$	0	0
$51$	386.870	1.06221
$52$	72.3002i	0.192812i
$53$	120.847i	0.313199i	0.987662	+	0.156600i	$0.0500532\pi$
$53$	120.847i	0.313199i	−0.987662	+	0.156600i	$0.949947\pi$
$54$	290.533	0.732158
$55$	0	0
$56$	−575.531	−1.37337
$57$	208.169i	0.483730i
$58$	− 343.400i	− 0.777424i
$59$	439.633	0.970090	0.485045	−	0.874489i	$-0.338803\pi$
$59$	439.633	0.970090	0.485045	+	0.874489i	$0.338803\pi$
$60$	0	0
$61$	−137.305	−0.288198	−0.144099	−	0.989563i	$-0.546028\pi$
$61$	−137.305	−0.288198	−0.144099	+	0.989563i	$0.546028\pi$
$62$	− 42.3068i	− 0.0866609i
$63$	1316.00i	2.63176i
$64$	−201.022	−0.392621
$65$	0	0
$66$	−206.968	−0.386000
$67$	512.280i	0.934104i	0.884230	+	0.467052i	$0.154684\pi$
$67$	512.280i	0.934104i	−0.884230	+	0.467052i	$0.845316\pi$
$68$	247.747i	0.441820i
$69$	−1065.94	−1.85977
$70$	0	0
$71$	410.719	0.686526	0.343263	−	0.939239i	$-0.388468\pi$
$71$	410.719	0.686526	0.343263	+	0.939239i	$0.388468\pi$
$72$	1025.46i	1.67850i
$73$	308.004i	0.493823i	0.969038	+	0.246912i	$0.0794158\pi$
$73$	308.004i	0.493823i	−0.969038	+	0.246912i	$0.920584\pi$
$74$	147.086	0.231060
$75$	0	0
$76$	−133.309	−0.201205
$77$	− 414.759i	− 0.613847i
$78$	− 176.300i	− 0.255924i
$79$	586.462	0.835217	0.417608	−	0.908627i	$-0.362868\pi$
$79$	586.462	0.835217	0.417608	+	0.908627i	$0.362868\pi$
$80$	0	0
$81$	308.386	0.423027
$82$	250.401i	0.337222i
$83$	− 1354.20i	− 1.79088i	−0.445182	−	0.895440i	$-0.646861\pi$
$83$	− 1354.20i	− 1.79088i	0.445182	−	0.895440i	$-0.353139\pi$
$84$	−1312.66	−1.70503
$85$	0	0
$86$	236.266	0.296247
$87$	− 1909.84i	− 2.35352i
$88$	− 323.191i	− 0.391503i
$89$	−439.882	−0.523904	−0.261952	−	0.965081i	$-0.584366\pi$
$89$	−439.882	−0.523904	−0.261952	+	0.965081i	$0.584366\pi$
$90$	0	0
$91$	353.302	0.406990
$92$	− 682.617i	− 0.773563i
$93$	− 235.292i	− 0.262351i
$94$	729.164	0.800080
$95$	0	0
$96$	−1626.24	−1.72894
$97$	− 1511.27i	− 1.58192i	−0.611869	−	0.790959i	$-0.709582\pi$
$97$	− 1511.27i	− 1.58192i	0.611869	−	0.790959i	$-0.290418\pi$
$98$	617.740i	0.636747i
$99$	−739.006	−0.750231
$100$	0	0
$101$	336.260	0.331278	0.165639	−	0.986186i	$-0.447031\pi$
$101$	336.260	0.331278	0.165639	+	0.986186i	$0.447031\pi$
$102$	− 604.118i	− 0.586438i
$103$	− 322.712i	− 0.308716i	−0.988015	−	0.154358i	$-0.950669\pi$
$103$	− 322.712i	− 0.308716i	0.988015	−	0.154358i	$-0.0493309\pi$
$104$	275.302	0.259573
$105$	0	0
$106$	188.708	0.172915
$107$	1434.62i	1.29617i	0.761570	+	0.648083i	$0.224429\pi$
$107$	1434.62i	1.29617i	−0.761570	+	0.648083i	$0.775571\pi$
$108$	1034.75i	0.921933i
$109$	−849.147	−0.746179	−0.373089	−	0.927795i	$-0.621702\pi$
$109$	−849.147	−0.746179	−0.373089	+	0.927795i	$0.621702\pi$
$110$	0	0
$111$	818.027	0.699493
$112$	− 310.452i	− 0.261919i
$113$	− 1614.53i	− 1.34409i	−0.740511	−	0.672044i	$-0.765417\pi$
$113$	− 1614.53i	− 1.34409i	0.740511	−	0.672044i	$-0.234583\pi$
$114$	325.066	0.267064
$115$	0	0
$116$	1223.04	0.978931
$117$	− 629.503i	− 0.497415i
$118$	− 686.509i	− 0.535579i
$119$	1210.64	0.932599
$120$	0	0
$121$	−1098.09	−0.825012
$122$	214.409i	0.159112i
$123$	1392.62i	1.02088i
$124$	150.678	0.109123
$125$	0	0
$126$	2055.01	1.45297
$127$	865.174i	0.604502i	0.953228	+	0.302251i	$0.0977381\pi$
$127$	865.174i	0.604502i	−0.953228	+	0.302251i	$0.902262\pi$
$128$	− 1184.13i	− 0.817683i
$129$	1314.01	0.896836
$130$	0	0
$131$	−281.400	−0.187680	−0.0938400	−	0.995587i	$-0.529914\pi$
$131$	−281.400	−0.187680	−0.0938400	+	0.995587i	$0.529914\pi$
$132$	− 737.127i	− 0.486050i
$133$	651.426i	0.424705i
$134$	799.953	0.515712
$135$	0	0
$136$	943.363	0.594799
$137$	− 2641.43i	− 1.64725i	−0.567137	−	0.823624i	$-0.691949\pi$
$137$	− 2641.43i	− 1.64725i	0.567137	−	0.823624i	$-0.308051\pi$
$138$	1664.53i	1.02677i
$139$	1998.64	1.21958	0.609791	−	0.792562i	$-0.291253\pi$
$139$	1998.64	1.21958	0.609791	+	0.792562i	$0.291253\pi$
$140$	0	0
$141$	4055.28	2.42210
$142$	− 641.359i	− 0.379026i
$143$	198.398i	0.116020i
$144$	−553.153	−0.320112
$145$	0	0
$146$	480.964	0.272636
$147$	3435.60i	1.92764i
$148$	523.855i	0.290950i
$149$	1752.98	0.963824	0.481912	−	0.876220i	$-0.339942\pi$
$149$	1752.98	0.963824	0.481912	+	0.876220i	$0.339942\pi$
$150$	0	0
$151$	−2794.64	−1.50613	−0.753063	−	0.657949i	$-0.771424\pi$
$151$	−2794.64	−1.50613	−0.753063	+	0.657949i	$0.771424\pi$
$152$	507.608i	0.270871i
$153$	− 2157.08i	− 1.13980i
$154$	−647.669	−0.338900
$155$	0	0
$156$	627.902	0.322259
$157$	3244.87i	1.64949i	0.565508	+	0.824743i	$0.308680\pi$
$157$	3244.87i	1.64949i	−0.565508	+	0.824743i	$0.691320\pi$
$158$	− 915.792i	− 0.461117i
$159$	1049.51	0.523470
$160$	0	0
$161$	−3335.68	−1.63285
$162$	− 481.562i	− 0.233550i
$163$	− 3281.47i	− 1.57684i	−0.615139	−	0.788418i	$-0.710900\pi$
$163$	− 3281.47i	− 1.57684i	0.615139	−	0.788418i	$-0.289100\pi$
$164$	−891.818	−0.424630
$165$	0	0
$166$	−2114.66	−0.988731
$167$	− 3126.52i	− 1.44873i	−0.689418	−	0.724364i	$-0.742134\pi$
$167$	− 3126.52i	− 1.44873i	0.689418	−	0.724364i	$-0.257866\pi$
$168$	4998.29i	2.29540i
$169$	−169.000	−0.0769231
$170$	0	0
$171$	1160.69	0.519066
$172$	841.474i	0.373034i
$173$	− 97.5698i	− 0.0428792i	−0.999770	−	0.0214396i	$-0.993175\pi$
$173$	− 97.5698i	− 0.0428792i	0.999770	−	0.0214396i	$-0.00682496\pi$
$174$	−2982.31	−1.29936
$175$	0	0
$176$	174.335	0.0746648
$177$	− 3818.06i	− 1.62137i
$178$	686.900i	0.289243i
$179$	34.7150	0.0144956	0.00724782	−	0.999974i	$-0.497693\pi$
$179$	34.7150	0.0144956	0.00724782	+	0.999974i	$0.497693\pi$
$180$	0	0
$181$	−1229.35	−0.504843	−0.252422	−	0.967617i	$-0.581227\pi$
$181$	−1229.35	−0.504843	−0.252422	+	0.967617i	$0.581227\pi$
$182$	− 551.700i	− 0.224696i
$183$	1192.45i	0.481684i
$184$	−2599.25	−1.04141
$185$	0	0
$186$	−367.420	−0.144842
$187$	679.839i	0.265854i
$188$	2596.96i	1.00746i
$189$	5056.40	1.94603
$190$	0	0
$191$	4280.80	1.62172	0.810858	−	0.585243i	$-0.199001\pi$
$191$	4280.80	1.62172	0.810858	+	0.585243i	$0.199001\pi$
$192$	1745.81i	0.656212i
$193$	− 472.320i	− 0.176157i	−0.996114	−	0.0880786i	$-0.971927\pi$
$193$	− 472.320i	− 0.176157i	0.996114	−	0.0880786i	$-0.0280727\pi$
$194$	−2359.93	−0.873365
$195$	0	0
$196$	−2200.12	−0.801791
$197$	− 4484.37i	− 1.62182i	−0.585173	−	0.810908i	$-0.698974\pi$
$197$	− 4484.37i	− 1.62182i	0.585173	−	0.810908i	$-0.301026\pi$
$198$	1154.00i	0.414197i
$199$	366.240	0.130463	0.0652314	−	0.997870i	$-0.479221\pi$
$199$	366.240	0.130463	0.0652314	+	0.997870i	$0.479221\pi$
$200$	0	0
$201$	4448.98	1.56123
$202$	− 525.087i	− 0.182896i
$203$	− 5976.49i	− 2.06634i
$204$	2151.60	0.738442
$205$	0	0
$206$	−503.932	−0.170440
$207$	5943.41i	1.99563i
$208$	148.503i	0.0495039i
$209$	−365.810	−0.121070
$210$	0	0
$211$	2122.55	0.692524	0.346262	−	0.938138i	$-0.387451\pi$
$211$	2122.55	0.692524	0.346262	+	0.938138i	$0.387451\pi$
$212$	672.095i	0.217734i
$213$	− 3566.95i	− 1.14743i
$214$	2240.23	0.715603
$215$	0	0
$216$	3940.08	1.24115
$217$	− 736.303i	− 0.230339i
$218$	1325.99i	0.411960i
$219$	2674.91	0.825358
$220$	0	0
$221$	−579.103	−0.176266
$222$	− 1277.39i	− 0.386185i
$223$	5926.42i	1.77965i	0.456301	+	0.889826i	$0.349174\pi$
$223$	5926.42i	1.77965i	−0.456301	+	0.889826i	$0.650826\pi$
$224$	−5089.04	−1.51797
$225$	0	0
$226$	−2521.17	−0.742060
$227$	− 895.661i	− 0.261881i	−0.991390	−	0.130941i	$-0.958200\pi$
$227$	− 895.661i	− 0.261881i	0.991390	−	0.130941i	$-0.0417998\pi$
$228$	1157.74i	0.336286i
$229$	−627.717	−0.181138	−0.0905692	−	0.995890i	$-0.528869\pi$
$229$	−627.717	−0.181138	−0.0905692	+	0.995890i	$0.528869\pi$
$230$	0	0
$231$	−3602.04	−1.02596
$232$	− 4657.03i	− 1.31788i
$233$	− 2303.72i	− 0.647734i	−0.946103	−	0.323867i	$-0.895017\pi$
$233$	− 2303.72i	− 0.647734i	0.946103	−	0.323867i	$-0.104983\pi$
$234$	−983.002	−0.274619
$235$	0	0
$236$	2445.04	0.674401
$237$	− 5093.22i	− 1.39595i
$238$	− 1890.48i	− 0.514881i
$239$	−544.622	−0.147400	−0.0737001	−	0.997280i	$-0.523481\pi$
$239$	−544.622	−0.147400	−0.0737001	+	0.997280i	$0.523481\pi$
$240$	0	0
$241$	5426.10	1.45031	0.725157	−	0.688584i	$-0.241767\pi$
$241$	5426.10	1.45031	0.725157	+	0.688584i	$0.241767\pi$
$242$	1714.73i	0.455483i
$243$	2345.23i	0.619121i
$244$	−763.629	−0.200354
$245$	0	0
$246$	2174.65	0.563621
$247$	− 311.606i	− 0.0802713i
$248$	− 573.746i	− 0.146907i
$249$	−11760.8	−2.99321
$250$	0	0
$251$	−5221.22	−1.31299	−0.656494	−	0.754331i	$-0.727961\pi$
$251$	−5221.22	−1.31299	−0.656494	+	0.754331i	$0.727961\pi$
$252$	7319.02i	1.82958i
$253$	− 1873.16i	− 0.465472i
$254$	1351.02	0.333741
$255$	0	0
$256$	−3457.26	−0.844057
$257$	658.206i	0.159758i	0.996805	+	0.0798789i	$0.0254533\pi$
$257$	658.206i	0.159758i	−0.996805	+	0.0798789i	$0.974547\pi$
$258$	− 2051.89i	− 0.495136i
$259$	2559.87	0.614141
$260$	0	0
$261$	−10648.7	−2.52544
$262$	439.422i	0.103617i
$263$	− 3246.45i	− 0.761160i	−0.924748	−	0.380580i	$-0.875724\pi$
$263$	− 3246.45i	− 0.761160i	0.924748	−	0.380580i	$-0.124276\pi$
$264$	−2806.81	−0.654344
$265$	0	0
$266$	1017.24	0.234477
$267$	3820.23i	0.875634i
$268$	2849.07i	0.649384i
$269$	2585.80	0.586093	0.293047	−	0.956098i	$-0.405331\pi$
$269$	2585.80	0.586093	0.293047	+	0.956098i	$0.405331\pi$
$270$	0	0
$271$	988.933	0.221673	0.110836	−	0.993839i	$-0.464647\pi$
$271$	988.933	0.221673	0.110836	+	0.993839i	$0.464647\pi$
$272$	508.867i	0.113436i
$273$	− 3068.31i	− 0.680229i
$274$	−4124.74	−0.909433
$275$	0	0
$276$	−5928.30	−1.29290
$277$	8142.40i	1.76617i	0.469211	+	0.883086i	$0.344538\pi$
$277$	8142.40i	1.76617i	−0.469211	+	0.883086i	$0.655462\pi$
$278$	− 3120.97i	− 0.673322i
$279$	−1311.92	−0.281515
$280$	0	0
$281$	1534.21	0.325705	0.162853	−	0.986650i	$-0.447930\pi$
$281$	1534.21	0.325705	0.162853	+	0.986650i	$0.447930\pi$
$282$	− 6332.54i	− 1.33722i
$283$	6965.00i	1.46299i	0.681847	+	0.731495i	$0.261177\pi$
$283$	6965.00i	1.46299i	−0.681847	+	0.731495i	$0.738823\pi$
$284$	2284.23	0.477269
$285$	0	0
$286$	309.809	0.0640537
$287$	4357.96i	0.896314i
$288$	9067.49i	1.85523i
$289$	2928.62	0.596096
$290$	0	0
$291$	−13124.9	−2.64396
$292$	1712.98i	0.343303i
$293$	− 640.029i	− 0.127614i	−0.997962	−	0.0638070i	$-0.979676\pi$
$293$	− 640.029i	− 0.127614i	0.997962	−	0.0638070i	$-0.0203242\pi$
$294$	5364.87	1.06424
$295$	0	0
$296$	1994.72	0.391691
$297$	2839.44i	0.554750i
$298$	− 2737.37i	− 0.532120i
$299$	1595.60	0.308616
$300$	0	0
$301$	4111.95	0.787404
$302$	4363.99i	0.831520i
$303$	− 2920.30i	− 0.553686i
$304$	−273.813	−0.0516587
$305$	0	0
$306$	−3368.40	−0.629276
$307$	− 100.406i	− 0.0186660i	−0.999956	−	0.00933299i	$-0.997029\pi$
$307$	− 100.406i	− 0.0186660i	0.999956	−	0.00933299i	$-0.00297083\pi$
$308$	− 2306.71i	− 0.426743i
$309$	−2802.64	−0.515977
$310$	0	0
$311$	−3878.92	−0.707245	−0.353623	−	0.935388i	$-0.615050\pi$
$311$	−3878.92	−0.707245	−0.353623	+	0.935388i	$0.615050\pi$
$312$	− 2390.90i	− 0.433841i
$313$	3789.39i	0.684311i	0.939643	+	0.342155i	$0.111157\pi$
$313$	3789.39i	0.684311i	−0.939643	+	0.342155i	$0.888843\pi$
$314$	5067.04	0.910668
$315$	0	0
$316$	3261.64	0.580638
$317$	4406.81i	0.780791i	0.920647	+	0.390396i	$0.127662\pi$
$317$	4406.81i	0.780791i	−0.920647	+	0.390396i	$0.872338\pi$
$318$	− 1638.87i	− 0.289004i
$319$	3356.11	0.589048
$320$	0	0
$321$	12459.2	2.16636
$322$	5208.84i	0.901482i
$323$	− 1067.76i	− 0.183938i
$324$	1715.11	0.294086
$325$	0	0
$326$	−5124.19	−0.870559
$327$	7374.55i	1.24714i
$328$	3395.83i	0.571657i
$329$	12690.3	2.12656
$330$	0	0
$331$	−4131.49	−0.686064	−0.343032	−	0.939324i	$-0.611454\pi$
$331$	−4131.49	−0.686064	−0.343032	+	0.939324i	$0.611454\pi$
$332$	− 7531.47i	− 1.24501i
$333$	− 4561.10i	− 0.750591i
$334$	−4882.23	−0.799831
$335$	0	0
$336$	−2696.17	−0.437762
$337$	− 4560.82i	− 0.737221i	−0.929584	−	0.368611i	$-0.879834\pi$
$337$	− 4560.82i	− 0.737221i	0.929584	−	0.368611i	$-0.120166\pi$
$338$	263.902i	0.0424686i
$339$	−14021.6	−2.24646
$340$	0	0
$341$	413.473	0.0656622
$342$	− 1812.48i	− 0.286572i
$343$	1429.34i	0.225007i
$344$	3204.14	0.502196
$345$	0	0
$346$	−152.360	−0.0236733
$347$	10069.4i	1.55779i	0.627153	+	0.778896i	$0.284220\pi$
$347$	10069.4i	1.55779i	−0.627153	+	0.778896i	$0.715780\pi$
$348$	− 10621.6i	− 1.63615i
$349$	−5879.32	−0.901757	−0.450878	−	0.892585i	$-0.648889\pi$
$349$	−5879.32	−0.901757	−0.450878	+	0.892585i	$0.648889\pi$
$350$	0	0
$351$	−2418.70	−0.367808
$352$	− 2857.76i	− 0.432725i
$353$	9142.56i	1.37850i	0.724525	+	0.689249i	$0.242059\pi$
$353$	9142.56i	1.37850i	−0.724525	+	0.689249i	$0.757941\pi$
$354$	−5962.10	−0.895147
$355$	0	0
$356$	−2446.43	−0.364215
$357$	− 10514.0i	− 1.55871i
$358$	− 54.2093i	− 0.00800293i
$359$	2754.32	0.404924	0.202462	−	0.979290i	$-0.435106\pi$
$359$	2754.32	0.404924	0.202462	+	0.979290i	$0.435106\pi$
$360$	0	0
$361$	−6284.45	−0.916235
$362$	1919.69i	0.278720i
$363$	9536.54i	1.37889i
$364$	1964.91	0.282937
$365$	0	0
$366$	1862.07	0.265934
$367$	3040.19i	0.432416i	0.976347	+	0.216208i	$0.0693689\pi$
$367$	3040.19i	0.432416i	−0.976347	+	0.216208i	$0.930631\pi$
$368$	− 1402.08i	− 0.198610i
$369$	7764.88	1.09546
$370$	0	0
$371$	3284.26	0.459596
$372$	− 1308.59i	− 0.182385i
$373$	5384.72i	0.747481i	0.927533	+	0.373740i	$0.121925\pi$
$373$	5384.72i	0.747481i	−0.927533	+	0.373740i	$0.878075\pi$
$374$	1061.60	0.146776
$375$	0	0
$376$	9888.59	1.35629
$377$	2858.82i	0.390548i
$378$	− 7895.84i	− 1.07439i
$379$	3424.27	0.464097	0.232049	−	0.972704i	$-0.425457\pi$
$379$	3424.27	0.464097	0.232049	+	0.972704i	$0.425457\pi$
$380$	0	0
$381$	7513.74	1.01034
$382$	− 6684.69i	− 0.895336i
$383$	382.985i	0.0510956i	0.999674	+	0.0255478i	$0.00813301\pi$
$383$	382.985i	0.0510956i	−0.999674	+	0.0255478i	$0.991867\pi$
$384$	−10283.8	−1.36665
$385$	0	0
$386$	−737.553	−0.0972551
$387$	− 7326.54i	− 0.962349i
$388$	− 8405.00i	− 1.09974i
$389$	−8588.34	−1.11940	−0.559699	−	0.828696i	$-0.689083\pi$
$389$	−8588.34	−1.11940	−0.559699	+	0.828696i	$0.689083\pi$
$390$	0	0
$391$	5467.56	0.707178
$392$	8377.52i	1.07941i
$393$	2443.87i	0.313681i
$394$	−7002.57	−0.895392
$395$	0	0
$396$	−4110.02	−0.521556
$397$	− 7239.16i	− 0.915171i	−0.889166	−	0.457586i	$-0.848714\pi$
$397$	− 7239.16i	− 0.915171i	0.889166	−	0.457586i	$-0.151286\pi$
$398$	− 571.904i	− 0.0720275i
$399$	5657.41	0.709837
$400$	0	0
$401$	4269.62	0.531708	0.265854	−	0.964013i	$-0.414346\pi$
$401$	4269.62	0.531708	0.265854	+	0.964013i	$0.414346\pi$
$402$	− 6947.32i	− 0.861942i
$403$	352.206i	0.0435351i
$404$	1870.12	0.230302
$405$	0	0
$406$	−9332.60	−1.14081
$407$	1437.50i	0.175072i
$408$	− 8192.78i	− 0.994125i
$409$	−13562.5	−1.63967	−0.819834	−	0.572602i	$-0.805934\pi$
$409$	−13562.5	−1.63967	−0.819834	+	0.572602i	$0.805934\pi$
$410$	0	0
$411$	−22939.9	−2.75315
$412$	− 1794.78i	− 0.214618i
$413$	− 11947.9i	− 1.42353i
$414$	9280.95	1.10177
$415$	0	0
$416$	2434.31	0.286904
$417$	− 17357.5i	− 2.03837i
$418$	571.232i	0.0668418i
$419$	14576.9	1.69959	0.849794	−	0.527114i	$-0.176726\pi$
$419$	14576.9	1.69959	0.849794	+	0.527114i	$0.176726\pi$
$420$	0	0
$421$	15848.4	1.83469	0.917343	−	0.398099i	$-0.130330\pi$
$421$	15848.4	1.83469	0.917343	+	0.398099i	$0.130330\pi$
$422$	− 3314.48i	− 0.382337i
$423$	− 22611.2i	− 2.59904i
$424$	2559.18	0.293124
$425$	0	0
$426$	−5569.98	−0.633490
$427$	3731.55i	0.422909i
$428$	7978.70i	0.901087i
$429$	1723.02	0.193912
$430$	0	0
$431$	10694.7	1.19524	0.597618	−	0.801781i	$-0.296114\pi$
$431$	10694.7	1.19524	0.597618	+	0.801781i	$0.296114\pi$
$432$	2125.35i	0.236703i
$433$	16079.0i	1.78454i	0.451498	+	0.892272i	$0.350890\pi$
$433$	16079.0i	1.78454i	−0.451498	+	0.892272i	$0.649110\pi$
$434$	−1149.78	−0.127168
$435$	0	0
$436$	−4722.57	−0.518739
$437$	2942.01i	0.322049i
$438$	− 4177.01i	− 0.455674i
$439$	−6035.80	−0.656203	−0.328101	−	0.944643i	$-0.606409\pi$
$439$	−6035.80	−0.656203	−0.328101	+	0.944643i	$0.606409\pi$
$440$	0	0
$441$	19156.0	2.06845
$442$	904.300i	0.0973149i
$443$	− 10201.3i	− 1.09409i	−0.837105	−	0.547043i	$-0.815753\pi$
$443$	− 10201.3i	− 1.09409i	0.837105	−	0.547043i	$-0.184247\pi$
$444$	4549.50	0.486283
$445$	0	0
$446$	9254.41	0.982532
$447$	− 15224.0i	− 1.61090i
$448$	5463.19i	0.576141i
$449$	5822.54	0.611988	0.305994	−	0.952033i	$-0.401011\pi$
$449$	5822.54	0.611988	0.305994	+	0.952033i	$0.401011\pi$
$450$	0	0
$451$	−2447.22	−0.255511
$452$	− 8979.27i	− 0.934402i
$453$	24270.5i	2.51728i
$454$	−1398.62	−0.144583
$455$	0	0
$456$	4408.40	0.452724
$457$	4621.60i	0.473062i	0.971624	+	0.236531i	$0.0760105\pi$
$457$	4621.60i	0.473062i	−0.971624	+	0.236531i	$0.923990\pi$
$458$	980.213i	0.100005i
$459$	−8288.03	−0.842816
$460$	0	0
$461$	5127.77	0.518056	0.259028	−	0.965870i	$-0.416598\pi$
$461$	5127.77	0.518056	0.259028	+	0.965870i	$0.416598\pi$
$462$	5624.78i	0.566425i
$463$	− 6486.27i	− 0.651064i	−0.945531	−	0.325532i	$-0.894457\pi$
$463$	− 6486.27i	− 0.651064i	0.945531	−	0.325532i	$-0.105543\pi$
$464$	2512.09	0.251338
$465$	0	0
$466$	−3597.39	−0.357609
$467$	12978.0i	1.28598i	0.765875	+	0.642990i	$0.222306\pi$
$467$	12978.0i	1.28598i	−0.765875	+	0.642990i	$0.777694\pi$
$468$	− 3501.01i	− 0.345800i
$469$	13922.3	1.37073
$470$	0	0
$471$	28180.6	2.75689
$472$	− 9310.13i	− 0.907910i
$473$	2309.08i	0.224464i
$474$	−7953.34	−0.770694
$475$	0	0
$476$	6733.04	0.648337
$477$	− 5851.79i	− 0.561709i
$478$	850.456i	0.0813786i
$479$	5808.96	0.554109	0.277055	−	0.960854i	$-0.410642\pi$
$479$	5808.96	0.554109	0.277055	+	0.960854i	$0.410642\pi$
$480$	0	0
$481$	−1224.50	−0.116076
$482$	− 8473.14i	− 0.800707i
$483$	28969.2i	2.72908i
$484$	−6107.09	−0.573543
$485$	0	0
$486$	3662.20	0.341812
$487$	− 5387.14i	− 0.501262i	−0.968083	−	0.250631i	$-0.919362\pi$
$487$	− 5387.14i	− 0.501262i	0.968083	−	0.250631i	$-0.0806381\pi$
$488$	2907.72i	0.269726i
$489$	−28498.4	−2.63547
$490$	0	0
$491$	15259.1	1.40251	0.701255	−	0.712911i	$-0.252624\pi$
$491$	15259.1	1.40251	0.701255	+	0.712911i	$0.252624\pi$
$492$	7745.14i	0.709711i
$493$	9796.16i	0.894922i
$494$	−486.589	−0.0443172
$495$	0	0
$496$	309.489	0.0280171
$497$	− 11162.1i	− 1.00742i
$498$	18365.1i	1.65253i
$499$	−1856.04	−0.166509	−0.0832544	−	0.996528i	$-0.526531\pi$
$499$	−1856.04	−0.166509	−0.0832544	+	0.996528i	$0.526531\pi$
$500$	0	0
$501$	−27152.8	−2.42135
$502$	8153.20i	0.724891i
$503$	− 1049.46i	− 0.0930283i	−0.998918	−	0.0465142i	$-0.985189\pi$
$503$	− 1049.46i	− 0.0930283i	0.998918	−	0.0465142i	$-0.0148113\pi$
$504$	27869.1	2.46307
$505$	0	0
$506$	−2925.04	−0.256984
$507$	1467.71i	0.128566i
$508$	4811.71i	0.420246i
$509$	551.106	0.0479909	0.0239954	−	0.999712i	$-0.492361\pi$
$509$	551.106	0.0479909	0.0239954	+	0.999712i	$0.492361\pi$
$510$	0	0
$511$	8370.64	0.724649
$512$	− 4074.36i	− 0.351686i
$513$	− 4459.66i	− 0.383818i
$514$	1027.82	0.0882010
$515$	0	0
$516$	7307.92	0.623475
$517$	7126.26i	0.606214i
$518$	− 3997.37i	− 0.339063i
$519$	−847.361	−0.0716667
$520$	0	0
$521$	−8995.30	−0.756413	−0.378206	−	0.925721i	$-0.623459\pi$
$521$	−8995.30	−0.756413	−0.378206	+	0.925721i	$0.623459\pi$
$522$	16628.5i	1.39427i
$523$	− 2663.91i	− 0.222724i	−0.993780	−	0.111362i	$-0.964479\pi$
$523$	− 2663.91i	− 0.222724i	0.993780	−	0.111362i	$-0.0355213\pi$
$524$	−1565.02	−0.130474
$525$	0	0
$526$	−5069.51	−0.420230
$527$	1206.89i	0.0997586i
$528$	− 1514.04i	− 0.124792i
$529$	−2897.77	−0.238167
$530$	0	0
$531$	−21288.5	−1.73981
$532$	3622.94i	0.295253i
$533$	− 2084.60i	− 0.169408i
$534$	5965.49	0.483431
$535$	0	0
$536$	10848.6	0.874232
$537$	− 301.488i	− 0.0242275i
$538$	− 4037.86i	− 0.323577i
$539$	−6037.30	−0.482458
$540$	0	0
$541$	−6169.23	−0.490270	−0.245135	−	0.969489i	$-0.578832\pi$
$541$	−6169.23	−0.490270	−0.245135	+	0.969489i	$0.578832\pi$
$542$	− 1544.27i	− 0.122384i
$543$	10676.5i	0.843776i
$544$	8341.52	0.657426
$545$	0	0
$546$	−4791.32	−0.375549
$547$	5140.42i	0.401807i	0.979611	+	0.200904i	$0.0643878\pi$
$547$	5140.42i	0.401807i	−0.979611	+	0.200904i	$0.935612\pi$
$548$	− 14690.5i	− 1.14516i
$549$	6648.76	0.516871
$550$	0	0
$551$	−5271.15	−0.407547
$552$	22573.6i	1.74057i
$553$	− 15938.3i	− 1.22562i
$554$	12714.8	0.975090
$555$	0	0
$556$	11115.5	0.847847
$557$	2778.56i	0.211367i	0.994400	+	0.105683i	$0.0337030\pi$
$557$	2778.56i	0.211367i	−0.994400	+	0.105683i	$0.966297\pi$
$558$	2048.64i	0.155422i
$559$	−1966.93	−0.148823
$560$	0	0
$561$	5904.17	0.444339
$562$	− 2395.75i	− 0.179819i
$563$	− 4906.14i	− 0.367263i	−0.982995	−	0.183632i	$-0.941215\pi$
$563$	− 4906.14i	− 0.367263i	0.982995	−	0.183632i	$-0.0587854\pi$
$564$	22553.7	1.68383
$565$	0	0
$566$	10876.2	0.807706
$567$	− 8381.04i	− 0.620759i
$568$	− 8697.82i	− 0.642522i
$569$	9363.15	0.689849	0.344924	−	0.938631i	$-0.387905\pi$
$569$	9363.15	0.689849	0.344924	+	0.938631i	$0.387905\pi$
$570$	0	0
$571$	7199.32	0.527640	0.263820	−	0.964572i	$-0.415018\pi$
$571$	7199.32	0.527640	0.263820	+	0.964572i	$0.415018\pi$
$572$	1103.40i	0.0806564i
$573$	− 37177.3i	− 2.71048i
$574$	6805.18	0.494848
$575$	0	0
$576$	9734.14	0.704148
$577$	− 11449.6i	− 0.826086i	−0.910711	−	0.413043i	$-0.864466\pi$
$577$	− 11449.6i	− 0.826086i	0.910711	−	0.413043i	$-0.135534\pi$
$578$	− 4573.19i	− 0.329100i
$579$	−4101.94	−0.294423
$580$	0	0
$581$	−36803.3	−2.62798
$582$	20495.2i	1.45971i
$583$	1844.28i	0.131016i
$584$	6522.62	0.462171
$585$	0	0
$586$	−999.439	−0.0704547
$587$	− 5439.39i	− 0.382466i	−0.981545	−	0.191233i	$-0.938751\pi$
$587$	− 5439.39i	− 0.382466i	0.981545	−	0.191233i	$-0.0612487\pi$
$588$	19107.3i	1.34008i
$589$	−649.406	−0.0454301
$590$	0	0
$591$	−38945.2	−2.71064
$592$	1075.99i	0.0747006i
$593$	28405.8i	1.96709i	0.180651	+	0.983547i	$0.442180\pi$
$593$	28405.8i	1.96709i	−0.180651	+	0.983547i	$0.557820\pi$
$594$	4433.93	0.306273
$595$	0	0
$596$	9749.30	0.670045
$597$	− 3180.67i	− 0.218051i
$598$	− 2491.62i	− 0.170384i
$599$	10482.3	0.715020	0.357510	−	0.933909i	$-0.383626\pi$
$599$	10482.3	0.715020	0.357510	+	0.933909i	$0.383626\pi$
$600$	0	0
$601$	3199.54	0.217158	0.108579	−	0.994088i	$-0.465370\pi$
$601$	3199.54	0.217158	0.108579	+	0.994088i	$0.465370\pi$
$602$	− 6421.02i	− 0.434720i
$603$	− 24806.3i	− 1.67527i
$604$	−15542.6	−1.04705
$605$	0	0
$606$	−4560.20	−0.305686
$607$	11342.8i	0.758468i	0.925301	+	0.379234i	$0.123812\pi$
$607$	11342.8i	0.758468i	−0.925301	+	0.379234i	$0.876188\pi$
$608$	4488.44i	0.299392i
$609$	−51903.7	−3.45361
$610$	0	0
$611$	−6070.32	−0.401930
$612$	− 11996.7i	− 0.792384i
$613$	− 14385.4i	− 0.947831i	−0.880570	−	0.473916i	$-0.842840\pi$
$613$	− 14385.4i	− 0.947831i	0.880570	−	0.473916i	$-0.157160\pi$
$614$	−156.789	−0.0103053
$615$	0	0
$616$	−8783.39	−0.574502
$617$	22056.8i	1.43918i	0.694401	+	0.719588i	$0.255669\pi$
$617$	22056.8i	1.43918i	−0.694401	+	0.719588i	$0.744331\pi$
$618$	4376.48i	0.284867i
$619$	−13621.4	−0.884477	−0.442238	−	0.896898i	$-0.645815\pi$
$619$	−13621.4	−0.884477	−0.442238	+	0.896898i	$0.645815\pi$
$620$	0	0
$621$	22836.0	1.47565
$622$	6057.14i	0.390465i
$623$	11954.7i	0.768789i
$624$	1289.70	0.0827390
$625$	0	0
$626$	5917.34	0.377803
$627$	3176.94i	0.202352i
$628$	18046.5i	1.14671i
$629$	−4195.92	−0.265982
$630$	0	0
$631$	−18737.5	−1.18214	−0.591068	−	0.806622i	$-0.701293\pi$
$631$	−18737.5	−1.18214	−0.591068	+	0.806622i	$0.701293\pi$
$632$	− 12419.6i	− 0.781683i
$633$	− 18433.7i	− 1.15746i
$634$	6881.46	0.431069
$635$	0	0
$636$	5836.91	0.363913
$637$	− 5142.72i	− 0.319877i
$638$	− 5240.75i	− 0.325209i
$639$	−19888.4	−1.23125
$640$	0	0
$641$	29798.7	1.83616	0.918081	−	0.396394i	$-0.129739\pi$
$641$	29798.7	1.83616	0.918081	+	0.396394i	$0.129739\pi$
$642$	− 19455.6i	− 1.19603i
$643$	22983.5i	1.40961i	0.709399	+	0.704807i	$0.248966\pi$
$643$	22983.5i	1.40961i	−0.709399	+	0.704807i	$0.751034\pi$
$644$	−18551.5	−1.13515
$645$	0	0
$646$	−1667.37	−0.101551
$647$	− 24905.4i	− 1.51334i	−0.653794	−	0.756672i	$-0.726824\pi$
$647$	− 24905.4i	− 1.51334i	0.653794	−	0.756672i	$-0.273176\pi$
$648$	− 6530.72i	− 0.395912i
$649$	6709.39	0.405804
$650$	0	0
$651$	−6394.54	−0.384980
$652$	− 18250.1i	− 1.09621i
$653$	− 10077.8i	− 0.603946i	−0.953316	−	0.301973i	$-0.902355\pi$
$653$	− 10077.8i	− 0.603946i	0.953316	−	0.301973i	$-0.0976452\pi$
$654$	11515.7	0.688534
$655$	0	0
$656$	−1831.77	−0.109022
$657$	− 14914.6i	− 0.885650i
$658$	− 19816.5i	− 1.17406i
$659$	−12334.6	−0.729116	−0.364558	−	0.931181i	$-0.618780\pi$
$659$	−12334.6	−0.729116	−0.364558	+	0.931181i	$0.618780\pi$
$660$	0	0
$661$	−12749.1	−0.750202	−0.375101	−	0.926984i	$-0.622392\pi$
$661$	−12749.1	−0.750202	−0.375101	+	0.926984i	$0.622392\pi$
$662$	6451.54i	0.378771i
$663$	5029.31i	0.294604i
$664$	−28678.1	−1.67609
$665$	0	0
$666$	−7122.40	−0.414395
$667$	− 26991.3i	− 1.56688i
$668$	− 17388.3i	− 1.00715i
$669$	51468.9	2.97444
$670$	0	0
$671$	−2095.46	−0.120558
$672$	44196.5i	2.53708i
$673$	13618.2i	0.780007i	0.920813	+	0.390004i	$0.127526\pi$
$673$	13618.2i	0.780007i	−0.920813	+	0.390004i	$0.872474\pi$
$674$	−7121.96	−0.407014
$675$	0	0
$676$	−939.902	−0.0534765
$677$	9655.67i	0.548150i	0.961708	+	0.274075i	$0.0883716\pi$
$677$	9655.67i	0.548150i	−0.961708	+	0.274075i	$0.911628\pi$
$678$	21895.5i	1.24025i
$679$	−41071.9	−2.32135
$680$	0	0
$681$	−7778.51	−0.437699
$682$	− 645.660i	− 0.0362516i
$683$	− 16316.8i	− 0.914119i	−0.889436	−	0.457060i	$-0.848903\pi$
$683$	− 16316.8i	− 0.914119i	0.889436	−	0.457060i	$-0.151097\pi$
$684$	6455.25	0.360852
$685$	0	0
$686$	2232.00	0.124225
$687$	5451.51i	0.302748i
$688$	1728.37i	0.0957753i
$689$	−1571.01	−0.0868658
$690$	0	0
$691$	2350.84	0.129421	0.0647106	−	0.997904i	$-0.479388\pi$
$691$	2350.84	0.129421	0.0647106	+	0.997904i	$0.479388\pi$
$692$	− 542.640i	− 0.0298093i
$693$	20084.0i	1.10091i
$694$	15723.9	0.860045
$695$	0	0
$696$	−40444.7	−2.20266
$697$	− 7143.20i	− 0.388189i
$698$	9180.88i	0.497853i
$699$	−20007.1	−1.08260
$700$	0	0
$701$	−8076.90	−0.435179	−0.217589	−	0.976040i	$-0.569819\pi$
$701$	−8076.90	−0.435179	−0.217589	+	0.976040i	$0.569819\pi$
$702$	3776.93i	0.203064i
$703$	− 2257.76i	− 0.121128i
$704$	−3067.87	−0.164239
$705$	0	0
$706$	14276.6	0.761058
$707$	− 9138.55i	− 0.486125i
$708$	− 21234.3i	− 1.12717i
$709$	13624.9	0.721712	0.360856	−	0.932622i	$-0.382485\pi$
$709$	13624.9	0.721712	0.360856	+	0.932622i	$0.382485\pi$
$710$	0	0
$711$	−28398.4	−1.49792
$712$	9315.43i	0.490324i
$713$	− 3325.33i	− 0.174663i
$714$	−16418.2	−0.860553
$715$	0	0
$716$	193.069	0.0100773
$717$	4729.86i	0.246359i
$718$	− 4301.02i	− 0.223555i
$719$	−16235.8	−0.842131	−0.421066	−	0.907030i	$-0.638344\pi$
$719$	−16235.8	−0.842131	−0.421066	+	0.907030i	$0.638344\pi$
$720$	0	0
$721$	−8770.37	−0.453018
$722$	9813.51i	0.505846i
$723$	− 47123.8i	− 2.42400i
$724$	−6837.08	−0.350964
$725$	0	0
$726$	14891.8	0.761277
$727$	24181.2i	1.23361i	0.787118	+	0.616803i	$0.211572\pi$
$727$	24181.2i	1.23361i	−0.787118	+	0.616803i	$0.788428\pi$
$728$	− 7481.91i	− 0.380904i
$729$	28693.9	1.45780
$730$	0	0
$731$	−6739.96	−0.341021
$732$	6631.86i	0.334864i
$733$	− 3053.70i	− 0.153876i	−0.997036	−	0.0769379i	$-0.975486\pi$
$733$	− 3053.70i	− 0.153876i	0.997036	−	0.0769379i	$-0.0245143\pi$
$734$	4747.41	0.238733
$735$	0	0
$736$	−22983.4	−1.15106
$737$	7818.10i	0.390751i
$738$	− 12125.3i	− 0.604793i
$739$	8033.62	0.399894	0.199947	−	0.979807i	$-0.435923\pi$
$739$	8033.62	0.399894	0.199947	+	0.979807i	$0.435923\pi$
$740$	0	0
$741$	−2706.19	−0.134163
$742$	− 5128.54i	− 0.253739i
$743$	16139.6i	0.796912i	0.917187	+	0.398456i	$0.130454\pi$
$743$	16139.6i	0.796912i	−0.917187	+	0.398456i	$0.869546\pi$
$744$	−4982.79	−0.245535
$745$	0	0
$746$	8408.53	0.412678
$747$	65574.9i	3.21186i
$748$	3780.96i	0.184820i
$749$	38988.7	1.90202
$750$	0	0
$751$	−18491.1	−0.898469	−0.449235	−	0.893414i	$-0.648303\pi$
$751$	−18491.1	−0.898469	−0.449235	+	0.893414i	$0.648303\pi$
$752$	5334.08i	0.258662i
$753$	45344.5i	2.19448i
$754$	4464.20	0.215619
$755$	0	0
$756$	28121.5	1.35287
$757$	160.630i	0.00771227i	0.999993	+	0.00385613i	$0.00122745\pi$
$757$	160.630i	0.00771227i	−0.999993	+	0.00385613i	$0.998773\pi$
$758$	− 5347.17i	− 0.256224i
$759$	−16267.7	−0.777973
$760$	0	0
$761$	26799.1	1.27656	0.638282	−	0.769803i	$-0.279645\pi$
$761$	26799.1	1.27656	0.638282	+	0.769803i	$0.279645\pi$
$762$	− 11733.1i	− 0.557803i
$763$	23077.3i	1.09496i
$764$	23807.9	1.12741
$765$	0	0
$766$	598.052	0.0282095
$767$	5715.22i	0.269054i
$768$	30025.1i	1.41073i
$769$	5145.82	0.241304	0.120652	−	0.992695i	$-0.461501\pi$
$769$	5145.82	0.241304	0.120652	+	0.992695i	$0.461501\pi$
$770$	0	0
$771$	5716.29	0.267013
$772$	− 2626.83i	− 0.122463i
$773$	− 12810.6i	− 0.596072i	−0.954555	−	0.298036i	$-0.903668\pi$
$773$	− 12810.6i	− 0.596072i	0.954555	−	0.298036i	$-0.0963316\pi$
$774$	−11440.8	−0.531306
$775$	0	0
$776$	−32004.3	−1.48052
$777$	− 22231.6i	− 1.02645i
$778$	13411.1i	0.618011i
$779$	3843.64	0.176781
$780$	0	0
$781$	6268.13	0.287185
$782$	− 8537.89i	− 0.390428i
$783$	40915.0i	1.86741i
$784$	−4518.98	−0.205857
$785$	0	0
$786$	3816.23	0.173181
$787$	28073.0i	1.27153i	0.771883	+	0.635764i	$0.219315\pi$
$787$	28073.0i	1.27153i	−0.771883	+	0.635764i	$0.780685\pi$
$788$	− 24940.0i	− 1.12748i
$789$	−28194.3	−1.27217
$790$	0	0
$791$	−43878.1	−1.97235
$792$	15650.0i	0.702144i
$793$	− 1784.96i	− 0.0799318i
$794$	−11304.3	−0.505259
$795$	0	0
$796$	2036.87	0.0906970
$797$	30093.1i	1.33746i	0.743507	+	0.668729i	$0.233161\pi$
$797$	30093.1i	1.33746i	−0.743507	+	0.668729i	$0.766839\pi$
$798$	− 8834.35i	− 0.391896i
$799$	−20800.8	−0.921003
$800$	0	0
$801$	21300.6	0.939598
$802$	− 6667.24i	− 0.293552i
$803$	4700.56i	0.206574i
$804$	24743.2	1.08536
$805$	0	0
$806$	549.989	0.0240354
$807$	− 22456.8i	− 0.979575i
$808$	− 7120.99i	− 0.310044i
$809$	24337.1	1.05766	0.528831	−	0.848727i	$-0.322631\pi$
$809$	24337.1	1.05766	0.528831	+	0.848727i	$0.322631\pi$
$810$	0	0
$811$	19078.7	0.826071	0.413035	−	0.910715i	$-0.364469\pi$
$811$	19078.7	0.826071	0.413035	+	0.910715i	$0.364469\pi$
$812$	− 33238.5i	− 1.43651i
$813$	− 8588.54i	− 0.370496i
$814$	2244.74	0.0966559
$815$	0	0
$816$	4419.33	0.189593
$817$	− 3626.66i	− 0.155301i
$818$	21178.6i	0.905248i
$819$	−17108.0	−0.729919
$820$	0	0
$821$	2013.92	0.0856104	0.0428052	−	0.999083i	$-0.486371\pi$
$821$	2013.92	0.0856104	0.0428052	+	0.999083i	$0.486371\pi$
$822$	35821.9i	1.51999i
$823$	7692.10i	0.325795i	0.986643	+	0.162898i	$0.0520841\pi$
$823$	7692.10i	0.325795i	−0.986643	+	0.162898i	$0.947916\pi$
$824$	−6834.10	−0.288929
$825$	0	0
$826$	−18657.3	−0.785922
$827$	− 4762.76i	− 0.200263i	−0.994974	−	0.100131i	$-0.968074\pi$
$827$	− 4762.76i	− 0.200263i	0.994974	−	0.100131i	$-0.0319263\pi$
$828$	33054.6i	1.38735i
$829$	−19977.7	−0.836976	−0.418488	−	0.908222i	$-0.637440\pi$
$829$	−19977.7	−0.836976	−0.418488	+	0.908222i	$0.637440\pi$
$830$	0	0
$831$	70714.0	2.95191
$832$	− 2613.28i	− 0.108893i
$833$	− 17622.3i	− 0.732984i
$834$	−27104.6	−1.12537
$835$	0	0
$836$	−2034.47	−0.0841671
$837$	5040.72i	0.208164i
$838$	− 22762.6i	− 0.938330i
$839$	30615.8	1.25980	0.629901	−	0.776676i	$-0.283095\pi$
$839$	30615.8	1.25980	0.629901	+	0.776676i	$0.283095\pi$
$840$	0	0
$841$	23971.0	0.982861
$842$	− 24748.1i	− 1.01292i
$843$	− 13324.1i	− 0.544372i
$844$	11804.7	0.481439
$845$	0	0
$846$	−35308.5	−1.43491
$847$	29842.9i	1.21064i
$848$	1380.47i	0.0559026i
$849$	60488.6	2.44519
$850$	0	0
$851$	11561.0	0.465696
$852$	− 19837.8i	− 0.797690i
$853$	− 5660.88i	− 0.227227i	−0.993525	−	0.113614i	$-0.963757\pi$
$853$	− 5660.88i	− 0.227227i	0.993525	−	0.113614i	$-0.0362426\pi$
$854$	5827.01	0.233485
$855$	0	0
$856$	30381.0	1.21309
$857$	41346.1i	1.64802i	0.566572	+	0.824012i	$0.308269\pi$
$857$	41346.1i	1.64802i	−0.566572	+	0.824012i	$0.691731\pi$
$858$	− 2690.58i	− 0.107057i
$859$	34810.5	1.38268	0.691339	−	0.722530i	$-0.257021\pi$
$859$	34810.5	1.38268	0.691339	+	0.722530i	$0.257021\pi$
$860$	0	0
$861$	37847.4	1.49807
$862$	− 16700.4i	− 0.659880i
$863$	8360.51i	0.329774i	0.986312	+	0.164887i	$0.0527260\pi$
$863$	8360.51i	0.329774i	−0.986312	+	0.164887i	$0.947274\pi$
$864$	34839.5	1.37183
$865$	0	0
$866$	25108.2	0.985233
$867$	− 25434.1i	− 0.996293i
$868$	− 4094.99i	− 0.160130i
$869$	8950.21	0.349385
$870$	0	0
$871$	−6659.64	−0.259074
$872$	17982.4i	0.698352i
$873$	73180.6i	2.83710i
$874$	4594.10	0.177801
$875$	0	0
$876$	14876.6	0.573784
$877$	− 40579.3i	− 1.56245i	−0.624251	−	0.781223i	$-0.714596\pi$
$877$	− 40579.3i	− 1.56245i	0.624251	−	0.781223i	$-0.285404\pi$
$878$	9425.22i	0.362285i
$879$	−5558.43	−0.213289
$880$	0	0
$881$	10445.2	0.399442	0.199721	−	0.979853i	$-0.435996\pi$
$881$	10445.2	0.399442	0.199721	+	0.979853i	$0.435996\pi$
$882$	− 29913.0i	− 1.14198i
$883$	− 18227.6i	− 0.694685i	−0.937738	−	0.347343i	$-0.887084\pi$
$883$	− 18227.6i	− 0.694685i	0.937738	−	0.347343i	$-0.112916\pi$
$884$	−3220.71	−0.122539
$885$	0	0
$886$	−15929.9	−0.604036
$887$	− 23517.7i	− 0.890245i	−0.895470	−	0.445122i	$-0.853160\pi$
$887$	− 23517.7i	− 0.890245i	0.895470	−	0.445122i	$-0.146840\pi$
$888$	− 17323.4i	− 0.654658i
$889$	23512.9	0.887061
$890$	0	0
$891$	4706.40	0.176959
$892$	32960.1i	1.23720i
$893$	− 11192.6i	− 0.419424i
$894$	−23773.1	−0.889366
$895$	0	0
$896$	−32181.2	−1.19989
$897$	− 13857.3i	− 0.515809i
$898$	− 9092.21i	− 0.337874i
$899$	5957.95	0.221033
$900$	0	0
$901$	−5383.28	−0.199049
$902$	3821.47i	0.141065i
$903$	− 35710.9i	− 1.31604i
$904$	−34191.0	−1.25794
$905$	0	0
$906$	37899.7	1.38977
$907$	− 30564.6i	− 1.11894i	−0.828850	−	0.559471i	$-0.811004\pi$
$907$	− 30564.6i	− 1.11894i	0.828850	−	0.559471i	$-0.188996\pi$
$908$	− 4981.26i	− 0.182058i
$909$	−16282.8	−0.594132
$910$	0	0
$911$	−32766.5	−1.19166	−0.595831	−	0.803110i	$-0.703177\pi$
$911$	−32766.5	−1.19166	−0.595831	+	0.803110i	$0.703177\pi$
$912$	2377.97i	0.0863404i
$913$	− 20667.0i	− 0.749154i
$914$	7216.87	0.261174
$915$	0	0
$916$	−3491.08	−0.125926
$917$	7647.64i	0.275406i
$918$	12942.2i	0.465312i
$919$	−20686.7	−0.742538	−0.371269	−	0.928525i	$-0.621077\pi$
$919$	−20686.7	−0.742538	−0.371269	+	0.928525i	$0.621077\pi$
$920$	0	0
$921$	−871.989	−0.0311976
$922$	− 8007.28i	− 0.286015i
$923$	5339.34i	0.190408i
$924$	−20033.0	−0.713242
$925$	0	0
$926$	−10128.6	−0.359447
$927$	15626.8i	0.553669i
$928$	− 41179.0i	− 1.45665i
$929$	−45632.2	−1.61156	−0.805782	−	0.592212i	$-0.798255\pi$
$929$	−45632.2	−1.61156	−0.805782	+	0.592212i	$0.798255\pi$
$930$	0	0
$931$	9482.26	0.333801
$932$	− 12812.3i	− 0.450301i
$933$	33687.1i	1.18206i
$934$	20265.9	0.709979
$935$	0	0
$936$	−13331.0	−0.465532
$937$	− 17761.4i	− 0.619253i	−0.950858	−	0.309626i	$-0.899796\pi$
$937$	− 17761.4i	− 0.619253i	0.950858	−	0.309626i	$-0.100204\pi$
$938$	− 21740.4i	− 0.756768i
$939$	32909.6	1.14373
$940$	0	0
$941$	−44888.3	−1.55507	−0.777534	−	0.628841i	$-0.783530\pi$
$941$	−44888.3	−1.55507	−0.777534	+	0.628841i	$0.783530\pi$
$942$	− 44005.5i	− 1.52206i
$943$	19681.7i	0.679664i
$944$	5022.05	0.173150
$945$	0	0
$946$	3605.74	0.123925
$947$	16069.6i	0.551415i	0.961242	+	0.275708i	$0.0889122\pi$
$947$	16069.6i	0.551415i	−0.961242	+	0.275708i	$0.911088\pi$
$948$	− 28326.2i	− 0.970457i
$949$	−4004.05	−0.136962
$950$	0	0
$951$	38271.6	1.30499
$952$	− 25637.8i	− 0.872823i
$953$	− 3512.03i	− 0.119377i	−0.998217	−	0.0596883i	$-0.980989\pi$
$953$	− 3512.03i	− 0.119377i	0.998217	−	0.0596883i	$-0.0190107\pi$
$954$	−9137.88	−0.310115
$955$	0	0
$956$	−3028.94	−0.102472
$957$	− 29146.7i	− 0.984513i
$958$	− 9071.00i	− 0.305919i
$959$	−71786.5	−2.41721
$960$	0	0
$961$	−29057.0	−0.975361
$962$	1912.12i	0.0640844i
$963$	− 69468.9i	− 2.32461i
$964$	30177.5	1.00825
$965$	0	0
$966$	45237.0	1.50670
$967$	− 37011.9i	− 1.23084i	−0.788199	−	0.615421i	$-0.788986\pi$
$967$	− 37011.9i	− 1.23084i	0.788199	−	0.615421i	$-0.211014\pi$
$968$	23254.4i	0.772132i
$969$	−9273.16	−0.307427
$970$	0	0
$971$	19532.3	0.645542	0.322771	−	0.946477i	$-0.395386\pi$
$971$	19532.3	0.645542	0.322771	+	0.946477i	$0.395386\pi$
$972$	13043.1i	0.430409i
$973$	− 54317.1i	− 1.78965i
$974$	−8412.30	−0.276743
$975$	0	0
$976$	−1568.47	−0.0514402
$977$	30201.2i	0.988970i	0.869186	+	0.494485i	$0.164643\pi$
$977$	30201.2i	0.988970i	−0.869186	+	0.494485i	$0.835357\pi$
$978$	44501.8i	1.45502i
$979$	−6713.21	−0.219157
$980$	0	0
$981$	41118.5	1.33824
$982$	− 23827.8i	− 0.774315i
$983$	38774.9i	1.25812i	0.777359	+	0.629058i	$0.216559\pi$
$983$	38774.9i	1.25812i	−0.777359	+	0.629058i	$0.783441\pi$
$984$	29491.7	0.955447
$985$	0	0
$986$	15297.2	0.494080
$987$	− 110211.i	− 3.55425i
$988$	− 1733.01i	− 0.0558041i
$989$	18570.6	0.597079
$990$	0	0
$991$	−27728.9	−0.888838	−0.444419	−	0.895819i	$-0.646590\pi$
$991$	−27728.9	−0.888838	−0.444419	+	0.895819i	$0.646590\pi$
$992$	− 5073.25i	− 0.162375i
$993$	35880.6i	1.14666i
$994$	−17430.3	−0.556192
$995$	0	0
$996$	−65408.2	−2.08086
$997$	− 48918.2i	− 1.55392i	−0.629552	−	0.776958i	$-0.716761\pi$
$997$	− 48918.2i	− 1.55392i	0.629552	−	0.776958i	$-0.283239\pi$
$998$	2898.31i	0.0919283i
$999$	−17524.8	−0.555016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.4.b.e.274.2		4
5.2	odd	4		325.4.a.f.1.2		2
5.3	odd	4		13.4.a.b.1.1	✓	2
5.4	even	2	inner	325.4.b.e.274.3		4
15.8	even	4		117.4.a.d.1.2		2
20.3	even	4		208.4.a.h.1.1		2
35.13	even	4		637.4.a.b.1.1		2
40.3	even	4		832.4.a.z.1.2		2
40.13	odd	4		832.4.a.s.1.1		2
55.43	even	4		1573.4.a.b.1.2		2
60.23	odd	4		1872.4.a.bb.1.2		2
65.3	odd	12		169.4.c.g.22.2		4
65.8	even	4		169.4.b.f.168.2		4
65.18	even	4		169.4.b.f.168.3		4
65.23	odd	12		169.4.c.j.22.1		4
65.28	even	12		169.4.e.f.147.2		8
65.33	even	12		169.4.e.f.23.2		8
65.38	odd	4		169.4.a.g.1.2		2
65.43	odd	12		169.4.c.j.146.1		4
65.48	odd	12		169.4.c.g.146.2		4
65.58	even	12		169.4.e.f.23.3		8
65.63	even	12		169.4.e.f.147.3		8
195.38	even	4		1521.4.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.4.a.b.1.1	✓	2	5.3	odd	4
117.4.a.d.1.2		2	15.8	even	4
169.4.a.g.1.2		2	65.38	odd	4
169.4.b.f.168.2		4	65.8	even	4
169.4.b.f.168.3		4	65.18	even	4
169.4.c.g.22.2		4	65.3	odd	12
169.4.c.g.146.2		4	65.48	odd	12
169.4.c.j.22.1		4	65.23	odd	12
169.4.c.j.146.1		4	65.43	odd	12
169.4.e.f.23.2		8	65.33	even	12
169.4.e.f.23.3		8	65.58	even	12
169.4.e.f.147.2		8	65.28	even	12
169.4.e.f.147.3		8	65.63	even	12
208.4.a.h.1.1		2	20.3	even	4
325.4.a.f.1.2		2	5.2	odd	4
325.4.b.e.274.2		4	1.1	even	1	trivial
325.4.b.e.274.3		4	5.4	even	2	inner
637.4.a.b.1.1		2	35.13	even	4
832.4.a.s.1.1		2	40.13	odd	4
832.4.a.z.1.2		2	40.3	even	4
1521.4.a.r.1.1		2	195.38	even	4
1573.4.a.b.1.2		2	55.43	even	4
1872.4.a.bb.1.2		2	60.23	odd	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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	325.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.56155i q^{2} -8.68466i q^{3} +5.56155 q^{4} -13.5616 q^{6} -27.1771i q^{7} -21.1771i q^{8} -48.4233 q^{9} +O(q^{10})\)	\(q-1.56155i q^{2} -8.68466i q^{3} +5.56155 q^{4} -13.5616 q^{6} -27.1771i q^{7} -21.1771i q^{8} -48.4233 q^{9} +15.2614 q^{11} -48.3002i q^{12} +13.0000i q^{13} -42.4384 q^{14} +11.4233 q^{16} +44.5464i q^{17} +75.6155i q^{18} -23.9697 q^{19} -236.024 q^{21} -23.8314i q^{22} -122.739i q^{23} -183.916 q^{24} +20.3002 q^{26} +186.054i q^{27} -151.147i q^{28} +219.909 q^{29} +27.0928 q^{31} -187.255i q^{32} -132.540i q^{33} +69.5616 q^{34} -269.309 q^{36} +94.1922i q^{37} +37.4299i q^{38} +112.901 q^{39} -160.354 q^{41} +368.563i q^{42} +151.302i q^{43} +84.8769 q^{44} -191.663 q^{46} +466.948i q^{47} -99.2074i q^{48} -395.594 q^{49} +386.870 q^{51} +72.3002i q^{52} +120.847i q^{53} +290.533 q^{54} -575.531 q^{56} +208.169i q^{57} -343.400i q^{58} +439.633 q^{59} -137.305 q^{61} -42.3068i q^{62} +1316.00i q^{63} -201.022 q^{64} -206.968 q^{66} +512.280i q^{67} +247.747i q^{68} -1065.94 q^{69} +410.719 q^{71} +1025.46i q^{72} +308.004i q^{73} +147.086 q^{74} -133.309 q^{76} -414.759i q^{77} -176.300i q^{78} +586.462 q^{79} +308.386 q^{81} +250.401i q^{82} -1354.20i q^{83} -1312.66 q^{84} +236.266 q^{86} -1909.84i q^{87} -323.191i q^{88} -439.882 q^{89} +353.302 q^{91} -682.617i q^{92} -235.292i q^{93} +729.164 q^{94} -1626.24 q^{96} -1511.27i q^{97} +617.740i q^{98} -739.006 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 14 q^{4} - 46 q^{6} - 70 q^{9}+O(q^{10}) \) 4 * q + 14 * q^4 - 46 * q^6 - 70 * q^9	\( 4 q + 14 q^{4} - 46 q^{6} - 70 q^{9} + 160 q^{11} - 178 q^{14} - 78 q^{16} + 168 q^{19} - 606 q^{21} - 546 q^{24} - 26 q^{26} + 88 q^{29} - 172 q^{31} + 270 q^{34} - 500 q^{36} + 130 q^{39} - 460 q^{41} + 356 q^{44} - 8 q^{46} - 766 q^{49} + 962 q^{51} - 182 q^{54} - 2030 q^{56} + 736 q^{59} - 2116 q^{61} - 1538 q^{64} - 1636 q^{66} - 1592 q^{69} - 262 q^{71} - 294 q^{74} + 44 q^{76} + 2016 q^{79} + 244 q^{81} - 2818 q^{84} + 2718 q^{86} + 1440 q^{89} + 234 q^{91} + 1622 q^{94} - 3726 q^{96} + 260 q^{99}+O(q^{100}) \) 4 * q + 14 * q^4 - 46 * q^6 - 70 * q^9 + 160 * q^11 - 178 * q^14 - 78 * q^16 + 168 * q^19 - 606 * q^21 - 546 * q^24 - 26 * q^26 + 88 * q^29 - 172 * q^31 + 270 * q^34 - 500 * q^36 + 130 * q^39 - 460 * q^41 + 356 * q^44 - 8 * q^46 - 766 * q^49 + 962 * q^51 - 182 * q^54 - 2030 * q^56 + 736 * q^59 - 2116 * q^61 - 1538 * q^64 - 1636 * q^66 - 1592 * q^69 - 262 * q^71 - 294 * q^74 + 44 * q^76 + 2016 * q^79 + 244 * q^81 - 2818 * q^84 + 2718 * q^86 + 1440 * q^89 + 234 * q^91 + 1622 * q^94 - 3726 * q^96 + 260 * q^99

Introduction

L-functions

Modular forms

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Database

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