LMFDB - Embedded newform 525.4.d.l.274.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.d (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:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.3
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.l.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.82843i q^{2} +3.00000i q^{3} +4.65685 q^{4} -5.48528 q^{6} -7.00000i q^{7} +23.1421i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+1.82843i q^{2} +3.00000i q^{3} +4.65685 q^{4} -5.48528 q^{6} -7.00000i q^{7} +23.1421i q^{8} -9.00000 q^{9} -64.5685 q^{11} +13.9706i q^{12} +32.3431i q^{13} +12.7990 q^{14} -5.05887 q^{16} -56.3431i q^{17} -16.4558i q^{18} +2.74517 q^{19} +21.0000 q^{21} -118.059i q^{22} -88.1665i q^{23} -69.4264 q^{24} -59.1371 q^{26} -27.0000i q^{27} -32.5980i q^{28} -246.735 q^{29} -110.912 q^{31} +175.887i q^{32} -193.706i q^{33} +103.019 q^{34} -41.9117 q^{36} +120.676i q^{37} +5.01934i q^{38} -97.0294 q^{39} -176.274 q^{41} +38.3970i q^{42} +443.362i q^{43} -300.686 q^{44} +161.206 q^{46} -345.206i q^{47} -15.1766i q^{48} -49.0000 q^{49} +169.029 q^{51} +150.617i q^{52} -260.981i q^{53} +49.3675 q^{54} +161.995 q^{56} +8.23550i q^{57} -451.137i q^{58} -628.999 q^{59} -115.206 q^{61} -202.794i q^{62} +63.0000i q^{63} -362.068 q^{64} +354.177 q^{66} -951.480i q^{67} -262.382i q^{68} +264.500 q^{69} +356.264 q^{71} -208.279i q^{72} +656.754i q^{73} -220.648 q^{74} +12.7838 q^{76} +451.980i q^{77} -177.411i q^{78} -440.195 q^{79} +81.0000 q^{81} -322.304i q^{82} +54.4121i q^{83} +97.7939 q^{84} -810.656 q^{86} -740.205i q^{87} -1494.25i q^{88} +1018.78 q^{89} +226.402 q^{91} -410.579i q^{92} -332.735i q^{93} +631.184 q^{94} -527.662 q^{96} -724.108i q^{97} -89.5929i q^{98} +581.117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 12 q^{6} - 36 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 12 * q^6 - 36 * q^9	$ 4 q - 4 q^{4} + 12 q^{6} - 36 q^{9} - 32 q^{11} - 28 q^{14} - 156 q^{16} + 192 q^{19} + 84 q^{21} - 108 q^{24} + 216 q^{26} - 376 q^{29} - 240 q^{31} - 312 q^{34} + 36 q^{36} - 456 q^{39} + 200 q^{41} - 1248 q^{44} + 1120 q^{46} - 196 q^{49} + 744 q^{51} - 108 q^{54} + 252 q^{56} - 208 q^{59} - 936 q^{61} - 68 q^{64} + 1824 q^{66} - 96 q^{69} - 272 q^{71} - 2376 q^{74} - 1216 q^{76} + 864 q^{79} + 324 q^{81} - 84 q^{84} - 912 q^{86} + 2808 q^{89} + 1064 q^{91} - 3200 q^{94} - 2484 q^{96} + 288 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 12 * q^6 - 36 * q^9 - 32 * q^11 - 28 * q^14 - 156 * q^16 + 192 * q^19 + 84 * q^21 - 108 * q^24 + 216 * q^26 - 376 * q^29 - 240 * q^31 - 312 * q^34 + 36 * q^36 - 456 * q^39 + 200 * q^41 - 1248 * q^44 + 1120 * q^46 - 196 * q^49 + 744 * q^51 - 108 * q^54 + 252 * q^56 - 208 * q^59 - 936 * q^61 - 68 * q^64 + 1824 * q^66 - 96 * q^69 - 272 * q^71 - 2376 * q^74 - 1216 * q^76 + 864 * q^79 + 324 * q^81 - 84 * q^84 - 912 * q^86 + 2808 * q^89 + 1064 * q^91 - 3200 * q^94 - 2484 * q^96 + 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	1.82843i	0.646447i	0.946323	+	0.323223i	$0.104766\pi$
$2$	1.82843i	0.646447i	−0.946323	+	0.323223i	$0.895234\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	4.65685	0.582107
$5$	0	0
$5$	0	0
$6$	−5.48528	−0.373226
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	23.1421i	1.02275i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−64.5685	−1.76983	−0.884916	−	0.465751i	$-0.845784\pi$
$11$	−64.5685	−1.76983	−0.884916	+	0.465751i	$0.845784\pi$
$12$	13.9706i	0.336080i
$13$	32.3431i	0.690029i	0.938597	+	0.345014i	$0.112126\pi$
$13$	32.3431i	0.690029i	−0.938597	+	0.345014i	$0.887874\pi$
$14$	12.7990	0.244334
$15$	0	0
$16$	−5.05887	−0.0790449
$17$	− 56.3431i	− 0.803836i	−0.915676	−	0.401918i	$-0.868344\pi$
$17$	− 56.3431i	− 0.803836i	0.915676	−	0.401918i	$-0.131656\pi$
$18$	− 16.4558i	− 0.215482i
$19$	2.74517	0.0331465	0.0165733	−	0.999863i	$-0.494724\pi$
$19$	2.74517	0.0331465	0.0165733	+	0.999863i	$0.494724\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	− 118.059i	− 1.14410i
$23$	− 88.1665i	− 0.799304i	−0.916667	−	0.399652i	$-0.869131\pi$
$23$	− 88.1665i	− 0.799304i	0.916667	−	0.399652i	$-0.130869\pi$
$24$	−69.4264	−0.590484
$25$	0	0
$26$	−59.1371	−0.446067
$27$	− 27.0000i	− 0.192450i
$28$	− 32.5980i	− 0.220016i
$29$	−246.735	−1.57992	−0.789958	−	0.613161i	$-0.789898\pi$
$29$	−246.735	−1.57992	−0.789958	+	0.613161i	$0.789898\pi$
$30$	0	0
$31$	−110.912	−0.642591	−0.321296	−	0.946979i	$-0.604118\pi$
$31$	−110.912	−0.642591	−0.321296	+	0.946979i	$0.604118\pi$
$32$	175.887i	0.971649i
$33$	− 193.706i	− 1.02181i
$34$	103.019	0.519637
$35$	0	0
$36$	−41.9117	−0.194036
$37$	120.676i	0.536190i	0.963392	+	0.268095i	$0.0863942\pi$
$37$	120.676i	0.536190i	−0.963392	+	0.268095i	$0.913606\pi$
$38$	5.01934i	0.0214275i
$39$	−97.0294	−0.398388
$40$	0	0
$41$	−176.274	−0.671449	−0.335724	−	0.941960i	$-0.608981\pi$
$41$	−176.274	−0.671449	−0.335724	+	0.941960i	$0.608981\pi$
$42$	38.3970i	0.141066i
$43$	443.362i	1.57238i	0.617988	+	0.786188i	$0.287948\pi$
$43$	443.362i	1.57238i	−0.617988	+	0.786188i	$0.712052\pi$
$44$	−300.686	−1.03023
$45$	0	0
$46$	161.206	0.516707
$47$	− 345.206i	− 1.07135i	−0.844424	−	0.535675i	$-0.820057\pi$
$47$	− 345.206i	− 1.07135i	0.844424	−	0.535675i	$-0.179943\pi$
$48$	− 15.1766i	− 0.0456366i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	169.029	0.464095
$52$	150.617i	0.401670i
$53$	− 260.981i	− 0.676386i	−0.941077	−	0.338193i	$-0.890184\pi$
$53$	− 260.981i	− 0.676386i	0.941077	−	0.338193i	$-0.109816\pi$
$54$	49.3675	0.124409
$55$	0	0
$56$	161.995	0.386562
$57$	8.23550i	0.0191372i
$58$	− 451.137i	− 1.02133i
$59$	−628.999	−1.38794	−0.693972	−	0.720002i	$-0.744141\pi$
$59$	−628.999	−1.38794	−0.693972	+	0.720002i	$0.744141\pi$
$60$	0	0
$61$	−115.206	−0.241814	−0.120907	−	0.992664i	$-0.538580\pi$
$61$	−115.206	−0.241814	−0.120907	+	0.992664i	$0.538580\pi$
$62$	− 202.794i	− 0.415401i
$63$	63.0000i	0.125988i
$64$	−362.068	−0.707164
$65$	0	0
$66$	354.177	0.660547
$67$	− 951.480i	− 1.73495i	−0.497479	−	0.867476i	$-0.665741\pi$
$67$	− 951.480i	− 1.73495i	0.497479	−	0.867476i	$-0.334259\pi$
$68$	− 262.382i	− 0.467919i
$69$	264.500	0.461478
$70$	0	0
$71$	356.264	0.595504	0.297752	−	0.954643i	$-0.403763\pi$
$71$	356.264	0.595504	0.297752	+	0.954643i	$0.403763\pi$
$72$	− 208.279i	− 0.340916i
$73$	656.754i	1.05298i	0.850183	+	0.526488i	$0.176491\pi$
$73$	656.754i	1.05298i	−0.850183	+	0.526488i	$0.823509\pi$
$74$	−220.648	−0.346618
$75$	0	0
$76$	12.7838	0.0192948
$77$	451.980i	0.668933i
$78$	− 177.411i	− 0.257537i
$79$	−440.195	−0.626909	−0.313455	−	0.949603i	$-0.601486\pi$
$79$	−440.195	−0.626909	−0.313455	+	0.949603i	$0.601486\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 322.304i	− 0.434056i
$83$	54.4121i	0.0719579i	0.999353	+	0.0359790i	$0.0114549\pi$
$83$	54.4121i	0.0719579i	−0.999353	+	0.0359790i	$0.988545\pi$
$84$	97.7939	0.127026
$85$	0	0
$86$	−810.656	−1.01646
$87$	− 740.205i	− 0.912165i
$88$	− 1494.25i	− 1.81009i
$89$	1018.78	1.21338	0.606690	−	0.794938i	$-0.292497\pi$
$89$	1018.78	1.21338	0.606690	+	0.794938i	$0.292497\pi$
$90$	0	0
$91$	226.402	0.260806
$92$	− 410.579i	− 0.465280i
$93$	− 332.735i	− 0.371000i
$94$	631.184	0.692571
$95$	0	0
$96$	−527.662	−0.560982
$97$	− 724.108i	− 0.757959i	−0.925405	−	0.378979i	$-0.876275\pi$
$97$	− 724.108i	− 0.757959i	0.925405	−	0.378979i	$-0.123725\pi$
$98$	− 89.5929i	− 0.0923495i
$99$	581.117	0.589944
$100$	0	0
$101$	268.725	0.264744	0.132372	−	0.991200i	$-0.457741\pi$
$101$	268.725	0.264744	0.132372	+	0.991200i	$0.457741\pi$
$102$	309.058i	0.300013i
$103$	1840.63i	1.76080i	0.474233	+	0.880399i	$0.342725\pi$
$103$	1840.63i	1.76080i	−0.474233	+	0.880399i	$0.657275\pi$
$104$	−748.489	−0.705725
$105$	0	0
$106$	477.184	0.437247
$107$	− 243.087i	− 0.219627i	−0.993952	−	0.109813i	$-0.964975\pi$
$107$	− 243.087i	− 0.219627i	0.993952	−	0.109813i	$-0.0350253\pi$
$108$	− 125.735i	− 0.112027i
$109$	405.176	0.356044	0.178022	−	0.984027i	$-0.443030\pi$
$109$	405.176	0.356044	0.178022	+	0.984027i	$0.443030\pi$
$110$	0	0
$111$	−362.029	−0.309570
$112$	35.4121i	0.0298762i
$113$	28.1766i	0.0234569i	0.999931	+	0.0117285i	$0.00373337\pi$
$113$	28.1766i	0.0234569i	−0.999931	+	0.0117285i	$0.996267\pi$
$114$	−15.0580	−0.0123712
$115$	0	0
$116$	−1149.01	−0.919680
$117$	− 291.088i	− 0.230010i
$118$	− 1150.08i	− 0.897232i
$119$	−394.402	−0.303822
$120$	0	0
$121$	2838.10	2.13230
$122$	− 210.646i	− 0.156320i
$123$	− 528.823i	− 0.387661i
$124$	−516.500	−0.374057
$125$	0	0
$126$	−115.191	−0.0814446
$127$	− 2740.90i	− 1.91508i	−0.288298	−	0.957541i	$-0.593089\pi$
$127$	− 2740.90i	− 1.91508i	0.288298	−	0.957541i	$-0.406911\pi$
$128$	745.083i	0.514505i
$129$	−1330.09	−0.907811
$130$	0	0
$131$	−1832.04	−1.22188	−0.610938	−	0.791678i	$-0.709208\pi$
$131$	−1832.04	−1.22188	−0.610938	+	0.791678i	$0.709208\pi$
$132$	− 902.059i	− 0.594804i
$133$	− 19.2162i	− 0.0125282i
$134$	1739.71	1.12155
$135$	0	0
$136$	1303.90	0.822122
$137$	382.747i	0.238688i	0.992853	+	0.119344i	$0.0380792\pi$
$137$	382.747i	0.238688i	−0.992853	+	0.119344i	$0.961921\pi$
$138$	483.618i	0.298321i
$139$	−3053.60	−1.86333	−0.931667	−	0.363314i	$-0.881645\pi$
$139$	−3053.60	−1.86333	−0.931667	+	0.363314i	$0.881645\pi$
$140$	0	0
$141$	1035.62	0.618545
$142$	651.403i	0.384961i
$143$	− 2088.35i	− 1.22123i
$144$	45.5299	0.0263483
$145$	0	0
$146$	−1200.83	−0.680692
$147$	− 147.000i	− 0.0824786i
$148$	561.971i	0.312120i
$149$	−3560.60	−1.95769	−0.978843	−	0.204611i	$-0.934407\pi$
$149$	−3560.60	−1.95769	−0.978843	+	0.204611i	$0.934407\pi$
$150$	0	0
$151$	3261.80	1.75789	0.878945	−	0.476923i	$-0.158248\pi$
$151$	3261.80	1.75789	0.878945	+	0.476923i	$0.158248\pi$
$152$	63.5290i	0.0339005i
$153$	507.088i	0.267945i
$154$	−826.412	−0.432430
$155$	0	0
$156$	−451.852	−0.231905
$157$	2878.46i	1.46322i	0.681723	+	0.731611i	$0.261231\pi$
$157$	2878.46i	1.46322i	−0.681723	+	0.731611i	$0.738769\pi$
$158$	− 804.865i	− 0.405263i
$159$	782.942	0.390512
$160$	0	0
$161$	−617.166	−0.302108
$162$	148.103i	0.0718274i
$163$	927.537i	0.445708i	0.974852	+	0.222854i	$0.0715373\pi$
$163$	927.537i	0.445708i	−0.974852	+	0.222854i	$0.928463\pi$
$164$	−820.883	−0.390855
$165$	0	0
$166$	−99.4886	−0.0465169
$167$	1094.52i	0.507164i	0.967314	+	0.253582i	$0.0816087\pi$
$167$	1094.52i	0.507164i	−0.967314	+	0.253582i	$0.918391\pi$
$168$	485.985i	0.223182i
$169$	1150.92	0.523860
$170$	0	0
$171$	−24.7065	−0.0110488
$172$	2064.67i	0.915290i
$173$	1713.25i	0.752926i	0.926432	+	0.376463i	$0.122860\pi$
$173$	1713.25i	0.752926i	−0.926432	+	0.376463i	$0.877140\pi$
$174$	1353.41	0.589666
$175$	0	0
$176$	326.644	0.139896
$177$	− 1887.00i	− 0.801330i
$178$	1862.77i	0.784386i
$179$	4065.58	1.69763	0.848816	−	0.528689i	$-0.177316\pi$
$179$	4065.58	1.69763	0.848816	+	0.528689i	$0.177316\pi$
$180$	0	0
$181$	−2791.40	−1.14631	−0.573157	−	0.819445i	$-0.694282\pi$
$181$	−2791.40	−1.14631	−0.573157	+	0.819445i	$0.694282\pi$
$182$	413.960i	0.168597i
$183$	− 345.618i	− 0.139611i
$184$	2040.36	0.817486
$185$	0	0
$186$	608.382	0.239832
$187$	3637.99i	1.42266i
$188$	− 1607.57i	− 0.623640i
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−634.185	−0.240251	−0.120126	−	0.992759i	$-0.538330\pi$
$191$	−634.185	−0.240251	−0.120126	+	0.992759i	$0.538330\pi$
$192$	− 1086.20i	− 0.408281i
$193$	254.999i	0.0951049i	0.998869	+	0.0475524i	$0.0151421\pi$
$193$	254.999i	0.0951049i	−0.998869	+	0.0475524i	$0.984858\pi$
$194$	1323.98	0.489980
$195$	0	0
$196$	−228.186	−0.0831581
$197$	4172.37i	1.50898i	0.656311	+	0.754490i	$0.272116\pi$
$197$	4172.37i	1.50898i	−0.656311	+	0.754490i	$0.727884\pi$
$198$	1062.53i	0.381367i
$199$	4626.48	1.64805	0.824026	−	0.566552i	$-0.191723\pi$
$199$	4626.48	1.64805	0.824026	+	0.566552i	$0.191723\pi$
$200$	0	0
$201$	2854.44	1.00168
$202$	491.344i	0.171143i
$203$	1727.15i	0.597152i
$204$	787.145	0.270153
$205$	0	0
$206$	−3365.45	−1.13826
$207$	793.499i	0.266435i
$208$	− 163.620i	− 0.0545433i
$209$	−177.251	−0.0586638
$210$	0	0
$211$	−1562.64	−0.509843	−0.254921	−	0.966962i	$-0.582050\pi$
$211$	−1562.64	−0.509843	−0.254921	+	0.966962i	$0.582050\pi$
$212$	− 1215.35i	− 0.393729i
$213$	1068.79i	0.343814i
$214$	444.466	0.141977
$215$	0	0
$216$	624.838	0.196828
$217$	776.382i	0.242877i
$218$	740.834i	0.230163i
$219$	−1970.26	−0.607935
$220$	0	0
$221$	1822.31	0.554670
$222$	− 661.943i	− 0.200120i
$223$	1236.39i	0.371278i	0.982618	+	0.185639i	$0.0594355\pi$
$223$	1236.39i	0.371278i	−0.982618	+	0.185639i	$0.940564\pi$
$224$	1231.21	0.367249
$225$	0	0
$226$	−51.5189	−0.0151637
$227$	4181.82i	1.22272i	0.791353	+	0.611359i	$0.209377\pi$
$227$	4181.82i	1.22272i	−0.791353	+	0.611359i	$0.790623\pi$
$228$	38.3515i	0.0111399i
$229$	484.774	0.139890	0.0699449	−	0.997551i	$-0.477718\pi$
$229$	484.774	0.139890	0.0699449	+	0.997551i	$0.477718\pi$
$230$	0	0
$231$	−1355.94	−0.386209
$232$	− 5709.98i	− 1.61585i
$233$	− 2080.54i	− 0.584982i	−0.956268	−	0.292491i	$-0.905516\pi$
$233$	− 2080.54i	− 0.584982i	0.956268	−	0.292491i	$-0.0944842\pi$
$234$	532.234	0.148689
$235$	0	0
$236$	−2929.16	−0.807932
$237$	− 1320.59i	− 0.361946i
$238$	− 721.135i	− 0.196404i
$239$	−6814.10	−1.84422	−0.922108	−	0.386933i	$-0.873534\pi$
$239$	−6814.10	−1.84422	−0.922108	+	0.386933i	$0.873534\pi$
$240$	0	0
$241$	−3921.84	−1.04825	−0.524125	−	0.851642i	$-0.675607\pi$
$241$	−3921.84	−1.04825	−0.524125	+	0.851642i	$0.675607\pi$
$242$	5189.25i	1.37842i
$243$	243.000i	0.0641500i
$244$	−536.498	−0.140761
$245$	0	0
$246$	966.913	0.250602
$247$	88.7873i	0.0228721i
$248$	− 2566.73i	− 0.657209i
$249$	−163.236	−0.0415449
$250$	0	0
$251$	−5219.10	−1.31246	−0.656228	−	0.754562i	$-0.727849\pi$
$251$	−5219.10	−1.31246	−0.656228	+	0.754562i	$0.727849\pi$
$252$	293.382i	0.0733386i
$253$	5692.78i	1.41463i
$254$	5011.53	1.23800
$255$	0	0
$256$	−4258.88	−1.03976
$257$	6975.71i	1.69312i	0.532289	+	0.846562i	$0.321332\pi$
$257$	6975.71i	1.69312i	−0.532289	+	0.846562i	$0.678668\pi$
$258$	− 2431.97i	− 0.586852i
$259$	844.733	0.202661
$260$	0	0
$261$	2220.62	0.526639
$262$	− 3349.75i	− 0.789878i
$263$	3607.36i	0.845776i	0.906182	+	0.422888i	$0.138984\pi$
$263$	3607.36i	0.845776i	−0.906182	+	0.422888i	$0.861016\pi$
$264$	4482.76	1.04506
$265$	0	0
$266$	35.1354	0.00809882
$267$	3056.35i	0.700546i
$268$	− 4430.90i	− 1.00993i
$269$	−5.88572	−0.00133405	−0.000667023	−	1.00000i	$-0.500212\pi$
$269$	−5.88572	−0.00133405	−0.000667023		1.00000i	$0.500212\pi$
$270$	0	0
$271$	6916.32	1.55032	0.775160	−	0.631765i	$-0.217669\pi$
$271$	6916.32	1.55032	0.775160	+	0.631765i	$0.217669\pi$
$272$	285.033i	0.0635392i
$273$	679.206i	0.150577i
$274$	−699.825	−0.154299
$275$	0	0
$276$	1231.74	0.268630
$277$	− 2119.46i	− 0.459733i	−0.973222	−	0.229867i	$-0.926171\pi$
$277$	− 2119.46i	− 0.459733i	0.973222	−	0.229867i	$-0.0738290\pi$
$278$	− 5583.29i	− 1.20455i
$279$	998.205	0.214197
$280$	0	0
$281$	−239.917	−0.0509334	−0.0254667	−	0.999676i	$-0.508107\pi$
$281$	−239.917	−0.0509334	−0.0254667	+	0.999676i	$0.508107\pi$
$282$	1893.55i	0.399856i
$283$	4542.12i	0.954067i	0.878885	+	0.477034i	$0.158288\pi$
$283$	4542.12i	0.954067i	−0.878885	+	0.477034i	$0.841712\pi$
$284$	1659.07	0.346647
$285$	0	0
$286$	3818.40	0.789463
$287$	1233.92i	0.253784i
$288$	− 1582.99i	− 0.323883i
$289$	1738.45	0.353847
$290$	0	0
$291$	2172.32	0.437608
$292$	3058.41i	0.612944i
$293$	2171.70i	0.433010i	0.976281	+	0.216505i	$0.0694658\pi$
$293$	2171.70i	0.433010i	−0.976281	+	0.216505i	$0.930534\pi$
$294$	268.779	0.0533180
$295$	0	0
$296$	−2792.70	−0.548387
$297$	1743.35i	0.340604i
$298$	− 6510.29i	− 1.26554i
$299$	2851.58	0.551543
$300$	0	0
$301$	3103.54	0.594302
$302$	5963.96i	1.13638i
$303$	806.175i	0.152850i
$304$	−13.8875	−0.00262007
$305$	0	0
$306$	−927.174	−0.173212
$307$	− 3508.64i	− 0.652276i	−0.945322	−	0.326138i	$-0.894253\pi$
$307$	− 3508.64i	− 0.652276i	0.945322	−	0.326138i	$-0.105747\pi$
$308$	2104.80i	0.389391i
$309$	−5521.88	−1.01660
$310$	0	0
$311$	−3133.25	−0.571287	−0.285643	−	0.958336i	$-0.592207\pi$
$311$	−3133.25	−0.571287	−0.285643	+	0.958336i	$0.592207\pi$
$312$	− 2245.47i	− 0.407451i
$313$	− 6389.59i	− 1.15387i	−0.816790	−	0.576935i	$-0.804249\pi$
$313$	− 6389.59i	− 1.15387i	0.816790	−	0.576935i	$-0.195751\pi$
$314$	−5263.05	−0.945895
$315$	0	0
$316$	−2049.92	−0.364928
$317$	1634.44i	0.289587i	0.989462	+	0.144794i	$0.0462518\pi$
$317$	1634.44i	0.289587i	−0.989462	+	0.144794i	$0.953748\pi$
$318$	1431.55i	0.252445i
$319$	15931.3	2.79618
$320$	0	0
$321$	729.260	0.126802
$322$	− 1128.44i	− 0.195297i
$323$	− 154.671i	− 0.0266444i
$324$	377.205	0.0646785
$325$	0	0
$326$	−1695.93	−0.288126
$327$	1215.53i	0.205562i
$328$	− 4079.36i	− 0.686723i
$329$	−2416.44	−0.404932
$330$	0	0
$331$	4386.17	0.728355	0.364177	−	0.931330i	$-0.381350\pi$
$331$	4386.17	0.728355	0.364177	+	0.931330i	$0.381350\pi$
$332$	253.389i	0.0418872i
$333$	− 1086.09i	− 0.178730i
$334$	−2001.25	−0.327854
$335$	0	0
$336$	−106.236	−0.0172490
$337$	1713.98i	0.277051i	0.990359	+	0.138526i	$0.0442363\pi$
$337$	1713.98i	0.277051i	−0.990359	+	0.138526i	$0.955764\pi$
$338$	2104.38i	0.338648i
$339$	−84.5299	−0.0135429
$340$	0	0
$341$	7161.41	1.13728
$342$	− 45.1740i	− 0.00714249i
$343$	343.000i	0.0539949i
$344$	−10260.4	−1.60814
$345$	0	0
$346$	−3132.56	−0.486727
$347$	− 1744.83i	− 0.269935i	−0.990850	−	0.134967i	$-0.956907\pi$
$347$	− 1744.83i	− 0.269935i	0.990850	−	0.134967i	$-0.0430930\pi$
$348$	− 3447.03i	− 0.530977i
$349$	−7046.78	−1.08082	−0.540409	−	0.841403i	$-0.681730\pi$
$349$	−7046.78	−1.08082	−0.540409	+	0.841403i	$0.681730\pi$
$350$	0	0
$351$	873.265	0.132796
$352$	− 11356.8i	− 1.71966i
$353$	12668.5i	1.91013i	0.296400	+	0.955064i	$0.404214\pi$
$353$	12668.5i	1.91013i	−0.296400	+	0.955064i	$0.595786\pi$
$354$	3450.24	0.518017
$355$	0	0
$356$	4744.33	0.706317
$357$	− 1183.21i	− 0.175411i
$358$	7433.62i	1.09743i
$359$	−37.7844	−0.00555483	−0.00277742	−	0.999996i	$-0.500884\pi$
$359$	−37.7844	−0.00555483	−0.00277742	+	0.999996i	$0.500884\pi$
$360$	0	0
$361$	−6851.46	−0.998901
$362$	− 5103.87i	− 0.741031i
$363$	8514.29i	1.23109i
$364$	1054.32	0.151817
$365$	0	0
$366$	631.938	0.0902511
$367$	− 759.829i	− 0.108073i	−0.998539	−	0.0540364i	$-0.982791\pi$
$367$	− 759.829i	− 0.108073i	0.998539	−	0.0540364i	$-0.0172087\pi$
$368$	446.023i	0.0631809i
$369$	1586.47	0.223816
$370$	0	0
$371$	−1826.86	−0.255650
$372$	− 1549.50i	− 0.215962i
$373$	− 719.320i	− 0.0998525i	−0.998753	−	0.0499263i	$-0.984101\pi$
$373$	− 719.320i	− 0.0998525i	0.998753	−	0.0499263i	$-0.0158986\pi$
$374$	−6651.81	−0.919671
$375$	0	0
$376$	7988.81	1.09572
$377$	− 7980.19i	− 1.09019i
$378$	− 345.573i	− 0.0470221i
$379$	−572.559	−0.0775999	−0.0388000	−	0.999247i	$-0.512354\pi$
$379$	−572.559	−0.0775999	−0.0388000	+	0.999247i	$0.512354\pi$
$380$	0	0
$381$	8222.69	1.10567
$382$	− 1159.56i	− 0.155310i
$383$	− 4513.18i	− 0.602122i	−0.953605	−	0.301061i	$-0.902659\pi$
$383$	− 4513.18i	− 0.602122i	0.953605	−	0.301061i	$-0.0973408\pi$
$384$	−2235.25	−0.297050
$385$	0	0
$386$	−466.247	−0.0614802
$387$	− 3990.26i	− 0.524125i
$388$	− 3372.06i	− 0.441213i
$389$	6902.13	0.899619	0.449810	−	0.893124i	$-0.351492\pi$
$389$	6902.13	0.899619	0.449810	+	0.893124i	$0.351492\pi$
$390$	0	0
$391$	−4967.58	−0.642510
$392$	− 1133.96i	− 0.146107i
$393$	− 5496.11i	− 0.705451i
$394$	−7628.88	−0.975475
$395$	0	0
$396$	2706.18	0.343410
$397$	4124.58i	0.521427i	0.965416	+	0.260714i	$0.0839579\pi$
$397$	4124.58i	0.521427i	−0.965416	+	0.260714i	$0.916042\pi$
$398$	8459.18i	1.06538i
$399$	57.6485	0.00723317
$400$	0	0
$401$	−1002.50	−0.124844	−0.0624219	−	0.998050i	$-0.519882\pi$
$401$	−1002.50	−0.124844	−0.0624219	+	0.998050i	$0.519882\pi$
$402$	5219.14i	0.647530i
$403$	− 3587.23i	− 0.443406i
$404$	1251.41	0.154109
$405$	0	0
$406$	−3157.96	−0.386027
$407$	− 7791.89i	− 0.948967i
$408$	3911.70i	0.474652i
$409$	−10335.0	−1.24947	−0.624736	−	0.780836i	$-0.714794\pi$
$409$	−10335.0	−1.24947	−0.624736	+	0.780836i	$0.714794\pi$
$410$	0	0
$411$	−1148.24	−0.137807
$412$	8571.53i	1.02497i
$413$	4402.99i	0.524594i
$414$	−1450.85	−0.172236
$415$	0	0
$416$	−5688.75	−0.670466
$417$	− 9160.81i	− 1.07580i
$418$	− 324.091i	− 0.0379230i
$419$	−3183.21	−0.371145	−0.185573	−	0.982631i	$-0.559414\pi$
$419$	−3183.21	−0.371145	−0.185573	+	0.982631i	$0.559414\pi$
$420$	0	0
$421$	−6944.34	−0.803911	−0.401956	−	0.915659i	$-0.631669\pi$
$421$	−6944.34	−0.803911	−0.401956	+	0.915659i	$0.631669\pi$
$422$	− 2857.18i	− 0.329586i
$423$	3106.85i	0.357117i
$424$	6039.65	0.691772
$425$	0	0
$426$	−1954.21	−0.222258
$427$	806.442i	0.0913969i
$428$	− 1132.02i	− 0.127846i
$429$	6265.05	0.705080
$430$	0	0
$431$	3868.41	0.432331	0.216166	−	0.976357i	$-0.430645\pi$
$431$	3868.41	0.432331	0.216166	+	0.976357i	$0.430645\pi$
$432$	136.590i	0.0152122i
$433$	6132.96i	0.680673i	0.940304	+	0.340336i	$0.110541\pi$
$433$	6132.96i	0.680673i	−0.940304	+	0.340336i	$0.889459\pi$
$434$	−1419.56	−0.157007
$435$	0	0
$436$	1886.84	0.207256
$437$	− 242.032i	− 0.0264942i
$438$	− 3602.48i	− 0.392998i
$439$	4090.14	0.444673	0.222337	−	0.974970i	$-0.428632\pi$
$439$	4090.14	0.444673	0.222337	+	0.974970i	$0.428632\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	3331.97i	0.358565i
$443$	− 12434.5i	− 1.33359i	−0.745241	−	0.666795i	$-0.767666\pi$
$443$	− 12434.5i	− 1.33359i	0.745241	−	0.666795i	$-0.232334\pi$
$444$	−1685.91	−0.180203
$445$	0	0
$446$	−2260.66	−0.240012
$447$	− 10681.8i	− 1.13027i
$448$	2534.48i	0.267283i
$449$	−883.046	−0.0928141	−0.0464071	−	0.998923i	$-0.514777\pi$
$449$	−883.046	−0.0928141	−0.0464071	+	0.998923i	$0.514777\pi$
$450$	0	0
$451$	11381.8	1.18835
$452$	131.214i	0.0136544i
$453$	9785.40i	1.01492i
$454$	−7646.15	−0.790422
$455$	0	0
$456$	−190.587	−0.0195725
$457$	− 9068.44i	− 0.928235i	−0.885774	−	0.464118i	$-0.846371\pi$
$457$	− 9068.44i	− 0.928235i	0.885774	−	0.464118i	$-0.153629\pi$
$458$	886.373i	0.0904312i
$459$	−1521.26	−0.154698
$460$	0	0
$461$	12508.9	1.26377	0.631885	−	0.775063i	$-0.282282\pi$
$461$	12508.9	1.26377	0.631885	+	0.775063i	$0.282282\pi$
$462$	− 2479.24i	− 0.249663i
$463$	− 12688.7i	− 1.27363i	−0.771015	−	0.636817i	$-0.780251\pi$
$463$	− 12688.7i	− 1.27363i	0.771015	−	0.636817i	$-0.219749\pi$
$464$	1248.20	0.124884
$465$	0	0
$466$	3804.12	0.378160
$467$	− 10136.5i	− 1.00442i	−0.864747	−	0.502208i	$-0.832521\pi$
$467$	− 10136.5i	− 1.00442i	0.864747	−	0.502208i	$-0.167479\pi$
$468$	− 1355.56i	− 0.133890i
$469$	−6660.36	−0.655750
$470$	0	0
$471$	−8635.37	−0.844791
$472$	− 14556.4i	− 1.41952i
$473$	− 28627.3i	− 2.78284i
$474$	2414.59	0.233979
$475$	0	0
$476$	−1836.67	−0.176857
$477$	2348.83i	0.225462i
$478$	− 12459.1i	− 1.19219i
$479$	11361.1	1.08372	0.541861	−	0.840468i	$-0.317720\pi$
$479$	11361.1	1.08372	0.541861	+	0.840468i	$0.317720\pi$
$480$	0	0
$481$	−3903.05	−0.369987
$482$	− 7170.80i	− 0.677637i
$483$	− 1851.50i	− 0.174422i
$484$	13216.6	1.24123
$485$	0	0
$486$	−444.308	−0.0414696
$487$	7929.53i	0.737826i	0.929464	+	0.368913i	$0.120270\pi$
$487$	7929.53i	0.737826i	−0.929464	+	0.368913i	$0.879730\pi$
$488$	− 2666.11i	− 0.247314i
$489$	−2782.61	−0.257329
$490$	0	0
$491$	8111.51	0.745555	0.372777	−	0.927921i	$-0.378405\pi$
$491$	8111.51	0.745555	0.372777	+	0.927921i	$0.378405\pi$
$492$	− 2462.65i	− 0.225660i
$493$	13901.8i	1.26999i
$494$	−162.341	−0.0147856
$495$	0	0
$496$	561.088	0.0507936
$497$	− 2493.85i	− 0.225079i
$498$	− 298.466i	− 0.0268566i
$499$	−16816.6	−1.50865	−0.754324	−	0.656502i	$-0.772035\pi$
$499$	−16816.6	−1.50865	−0.754324	+	0.656502i	$0.772035\pi$
$500$	0	0
$501$	−3283.55	−0.292811
$502$	− 9542.74i	− 0.848433i
$503$	17764.6i	1.57472i	0.616491	+	0.787362i	$0.288554\pi$
$503$	17764.6i	1.57472i	−0.616491	+	0.787362i	$0.711446\pi$
$504$	−1457.95	−0.128854
$505$	0	0
$506$	−10408.8	−0.914485
$507$	3452.76i	0.302451i
$508$	− 12764.0i	− 1.11478i
$509$	−13908.8	−1.21120	−0.605598	−	0.795771i	$-0.707066\pi$
$509$	−13908.8	−1.21120	−0.605598	+	0.795771i	$0.707066\pi$
$510$	0	0
$511$	4597.27	0.397987
$512$	− 1826.38i	− 0.157647i
$513$	− 74.1195i	− 0.00637905i
$514$	−12754.6	−1.09451
$515$	0	0
$516$	−6194.02	−0.528443
$517$	22289.5i	1.89611i
$518$	1544.53i	0.131009i
$519$	−5139.76	−0.434702
$520$	0	0
$521$	−8639.68	−0.726510	−0.363255	−	0.931690i	$-0.618335\pi$
$521$	−8639.68	−0.726510	−0.363255	+	0.931690i	$0.618335\pi$
$522$	4060.23i	0.340444i
$523$	− 23242.2i	− 1.94323i	−0.236561	−	0.971617i	$-0.576020\pi$
$523$	− 23242.2i	− 1.94323i	0.236561	−	0.971617i	$-0.423980\pi$
$524$	−8531.53	−0.711263
$525$	0	0
$526$	−6595.79	−0.546749
$527$	6249.11i	0.516538i
$528$	979.932i	0.0807691i
$529$	4393.66	0.361113
$530$	0	0
$531$	5660.99	0.462648
$532$	− 89.4869i	− 0.00729276i
$533$	− 5701.26i	− 0.463319i
$534$	−5588.32	−0.452865
$535$	0	0
$536$	22019.3	1.77442
$537$	12196.8i	0.980128i
$538$	− 10.7616i	0 0.000862390i
$539$	3163.86	0.252833
$540$	0	0
$541$	11395.2	0.905577	0.452789	−	0.891618i	$-0.350429\pi$
$541$	11395.2	0.905577	0.452789	+	0.891618i	$0.350429\pi$
$542$	12646.0i	1.00220i
$543$	− 8374.19i	− 0.661825i
$544$	9910.04	0.781047
$545$	0	0
$546$	−1241.88	−0.0973398
$547$	− 7870.21i	− 0.615184i	−0.951518	−	0.307592i	$-0.900477\pi$
$547$	− 7870.21i	− 0.615184i	0.951518	−	0.307592i	$-0.0995232\pi$
$548$	1782.40i	0.138942i
$549$	1036.85	0.0806045
$550$	0	0
$551$	−677.329	−0.0523687
$552$	6121.08i	0.471976i
$553$	3081.37i	0.236949i
$554$	3875.28	0.297193
$555$	0	0
$556$	−14220.2	−1.08466
$557$	17769.8i	1.35176i	0.737012	+	0.675880i	$0.236236\pi$
$557$	17769.8i	1.35176i	−0.737012	+	0.675880i	$0.763764\pi$
$558$	1825.15i	0.138467i
$559$	−14339.7	−1.08498
$560$	0	0
$561$	−10914.0	−0.821370
$562$	− 438.672i	− 0.0329257i
$563$	− 15192.8i	− 1.13730i	−0.822579	−	0.568651i	$-0.807466\pi$
$563$	− 15192.8i	− 1.13730i	0.822579	−	0.568651i	$-0.192534\pi$
$564$	4822.72	0.360059
$565$	0	0
$566$	−8304.93	−0.616753
$567$	− 567.000i	− 0.0419961i
$568$	8244.71i	0.609050i
$569$	23300.0	1.71667	0.858335	−	0.513090i	$-0.171499\pi$
$569$	23300.0	1.71667	0.858335	+	0.513090i	$0.171499\pi$
$570$	0	0
$571$	10638.2	0.779673	0.389837	−	0.920884i	$-0.372531\pi$
$571$	10638.2	0.779673	0.389837	+	0.920884i	$0.372531\pi$
$572$	− 9725.14i	− 0.710889i
$573$	− 1902.55i	− 0.138709i
$574$	−2256.13	−0.164058
$575$	0	0
$576$	3258.61	0.235721
$577$	− 897.258i	− 0.0647372i	−0.999476	−	0.0323686i	$-0.989695\pi$
$577$	− 897.258i	− 0.0647372i	0.999476	−	0.0323686i	$-0.0103050\pi$
$578$	3178.63i	0.228743i
$579$	−764.997	−0.0549088
$580$	0	0
$581$	380.885	0.0271975
$582$	3971.93i	0.282890i
$583$	16851.1i	1.19709i
$584$	−15198.7	−1.07693
$585$	0	0
$586$	−3970.79	−0.279918
$587$	− 14712.9i	− 1.03452i	−0.855828	−	0.517261i	$-0.826952\pi$
$587$	− 14712.9i	− 1.03452i	0.855828	−	0.517261i	$-0.173048\pi$
$588$	− 684.558i	− 0.0480114i
$589$	−304.471	−0.0212997
$590$	0	0
$591$	−12517.1	−0.871210
$592$	− 610.486i	− 0.0423831i
$593$	7216.29i	0.499726i	0.968281	+	0.249863i	$0.0803856\pi$
$593$	7216.29i	0.499726i	−0.968281	+	0.249863i	$0.919614\pi$
$594$	−3187.59	−0.220182
$595$	0	0
$596$	−16581.2	−1.13958
$597$	13879.4i	0.951503i
$598$	5213.91i	0.356543i
$599$	20885.5	1.42464	0.712320	−	0.701855i	$-0.247645\pi$
$599$	20885.5	1.42464	0.712320	+	0.701855i	$0.247645\pi$
$600$	0	0
$601$	−11047.7	−0.749823	−0.374911	−	0.927061i	$-0.622327\pi$
$601$	−11047.7	−0.749823	−0.374911	+	0.927061i	$0.622327\pi$
$602$	5674.59i	0.384185i
$603$	8563.32i	0.578317i
$604$	15189.7	1.02328
$605$	0	0
$606$	−1474.03	−0.0988093
$607$	− 9434.94i	− 0.630894i	−0.948943	−	0.315447i	$-0.897846\pi$
$607$	− 9434.94i	− 0.630894i	0.948943	−	0.315447i	$-0.102154\pi$
$608$	482.840i	0.0322068i
$609$	−5181.44	−0.344766
$610$	0	0
$611$	11165.0	0.739263
$612$	2361.44i	0.155973i
$613$	17662.6i	1.16376i	0.813274	+	0.581881i	$0.197683\pi$
$613$	17662.6i	1.16376i	−0.813274	+	0.581881i	$0.802317\pi$
$614$	6415.30	0.421662
$615$	0	0
$616$	−10459.8	−0.684150
$617$	− 10817.4i	− 0.705820i	−0.935657	−	0.352910i	$-0.885192\pi$
$617$	− 10817.4i	− 0.705820i	0.935657	−	0.352910i	$-0.114808\pi$
$618$	− 10096.3i	− 0.657176i
$619$	−29073.9	−1.88785	−0.943926	−	0.330158i	$-0.892898\pi$
$619$	−29073.9	−1.88785	−0.943926	+	0.330158i	$0.892898\pi$
$620$	0	0
$621$	−2380.50	−0.153826
$622$	− 5728.92i	− 0.369306i
$623$	− 7131.49i	− 0.458615i
$624$	490.860	0.0314906
$625$	0	0
$626$	11682.9	0.745915
$627$	− 531.754i	− 0.0338696i
$628$	13404.5i	0.851751i
$629$	6799.28	0.431009
$630$	0	0
$631$	−2203.17	−0.138996	−0.0694981	−	0.997582i	$-0.522140\pi$
$631$	−2203.17	−0.138996	−0.0694981	+	0.997582i	$0.522140\pi$
$632$	− 10187.1i	− 0.641170i
$633$	− 4687.93i	− 0.294358i
$634$	−2988.45	−0.187203
$635$	0	0
$636$	3646.05	0.227319
$637$	− 1584.81i	− 0.0985755i
$638$	29129.3i	1.80758i
$639$	−3206.38	−0.198501
$640$	0	0
$641$	22466.5	1.38436	0.692180	−	0.721725i	$-0.256651\pi$
$641$	22466.5	1.38436	0.692180	+	0.721725i	$0.256651\pi$
$642$	1333.40i	0.0819705i
$643$	12347.0i	0.757257i	0.925549	+	0.378629i	$0.123604\pi$
$643$	12347.0i	0.757257i	−0.925549	+	0.378629i	$0.876396\pi$
$644$	−2874.05	−0.175859
$645$	0	0
$646$	282.805	0.0172242
$647$	− 24114.0i	− 1.46525i	−0.680631	−	0.732626i	$-0.738294\pi$
$647$	− 24114.0i	− 1.46525i	0.680631	−	0.732626i	$-0.261706\pi$
$648$	1874.51i	0.113639i
$649$	40613.6	2.45643
$650$	0	0
$651$	−2329.15	−0.140225
$652$	4319.41i	0.259449i
$653$	− 7843.33i	− 0.470035i	−0.971991	−	0.235018i	$-0.924485\pi$
$653$	− 7843.33i	− 0.470035i	0.971991	−	0.235018i	$-0.0755148\pi$
$654$	−2222.50	−0.132885
$655$	0	0
$656$	891.749	0.0530746
$657$	− 5910.78i	− 0.350992i
$658$	− 4418.29i	− 0.261767i
$659$	−21242.8	−1.25569	−0.627846	−	0.778338i	$-0.716063\pi$
$659$	−21242.8	−1.25569	−0.627846	+	0.778338i	$0.716063\pi$
$660$	0	0
$661$	−22221.7	−1.30760	−0.653801	−	0.756667i	$-0.726827\pi$
$661$	−22221.7	−1.30760	−0.653801	+	0.756667i	$0.726827\pi$
$662$	8019.79i	0.470843i
$663$	5466.94i	0.320239i
$664$	−1259.21	−0.0735948
$665$	0	0
$666$	1985.83	0.115539
$667$	21753.8i	1.26283i
$668$	5097.01i	0.295223i
$669$	−3709.18	−0.214358
$670$	0	0
$671$	7438.69	0.427969
$672$	3693.63i	0.212031i
$673$	3787.85i	0.216955i	0.994099	+	0.108478i	$0.0345976\pi$
$673$	3787.85i	0.216955i	−0.994099	+	0.108478i	$0.965402\pi$
$674$	−3133.88	−0.179099
$675$	0	0
$676$	5359.67	0.304943
$677$	− 11296.8i	− 0.641314i	−0.947195	−	0.320657i	$-0.896096\pi$
$677$	− 11296.8i	− 0.641314i	0.947195	−	0.320657i	$-0.103904\pi$
$678$	− 154.557i	− 0.00875474i
$679$	−5068.75	−0.286481
$680$	0	0
$681$	−12545.5	−0.705937
$682$	13094.1i	0.735190i
$683$	− 4807.14i	− 0.269312i	−0.990892	−	0.134656i	$-0.957007\pi$
$683$	− 4807.14i	− 0.269312i	0.990892	−	0.134656i	$-0.0429929\pi$
$684$	−115.055	−0.00643161
$685$	0	0
$686$	−627.151	−0.0349048
$687$	1454.32i	0.0807654i
$688$	− 2242.92i	− 0.124288i
$689$	8440.94	0.466726
$690$	0	0
$691$	5393.47	0.296928	0.148464	−	0.988918i	$-0.452567\pi$
$691$	5393.47	0.296928	0.148464	+	0.988918i	$0.452567\pi$
$692$	7978.37i	0.438283i
$693$	− 4067.82i	− 0.222978i
$694$	3190.29	0.174498
$695$	0	0
$696$	17129.9	0.932914
$697$	9931.84i	0.539735i
$698$	− 12884.5i	− 0.698691i
$699$	6241.63	0.337740
$700$	0	0
$701$	2404.77	0.129568	0.0647838	−	0.997899i	$-0.479364\pi$
$701$	2404.77	0.129568	0.0647838	+	0.997899i	$0.479364\pi$
$702$	1596.70i	0.0858456i
$703$	331.276i	0.0177729i
$704$	23378.2	1.25156
$705$	0	0
$706$	−23163.4	−1.23480
$707$	− 1881.07i	− 0.100064i
$708$	− 8787.47i	− 0.466460i
$709$	21617.3	1.14507	0.572535	−	0.819881i	$-0.305960\pi$
$709$	21617.3	1.14507	0.572535	+	0.819881i	$0.305960\pi$
$710$	0	0
$711$	3961.76	0.208970
$712$	23576.8i	1.24098i
$713$	9778.70i	0.513626i
$714$	2163.41	0.113394
$715$	0	0
$716$	18932.8	0.988203
$717$	− 20442.3i	− 1.06476i
$718$	− 69.0860i	− 0.00359090i
$719$	18228.6	0.945498	0.472749	−	0.881197i	$-0.343262\pi$
$719$	18228.6	0.945498	0.472749	+	0.881197i	$0.343262\pi$
$720$	0	0
$721$	12884.4	0.665519
$722$	− 12527.4i	− 0.645736i
$723$	− 11765.5i	− 0.605207i
$724$	−12999.1	−0.667278
$725$	0	0
$726$	−15567.8	−0.795832
$727$	20196.5i	1.03033i	0.857092	+	0.515164i	$0.172269\pi$
$727$	20196.5i	1.03033i	−0.857092	+	0.515164i	$0.827731\pi$
$728$	5239.43i	0.266739i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	24980.4	1.26393
$732$	− 1609.49i	− 0.0812686i
$733$	15264.9i	0.769196i	0.923084	+	0.384598i	$0.125660\pi$
$733$	15264.9i	0.769196i	−0.923084	+	0.384598i	$0.874340\pi$
$734$	1389.29	0.0698633
$735$	0	0
$736$	15507.4	0.776643
$737$	61435.7i	3.07057i
$738$	2900.74i	0.144685i
$739$	−13906.0	−0.692207	−0.346103	−	0.938196i	$-0.612495\pi$
$739$	−13906.0	−0.692207	−0.346103	+	0.938196i	$0.612495\pi$
$740$	0	0
$741$	−266.362	−0.0132052
$742$	− 3340.29i	− 0.165264i
$743$	− 4592.87i	− 0.226778i	−0.993551	−	0.113389i	$-0.963829\pi$
$743$	− 4592.87i	− 0.226778i	0.993551	−	0.113389i	$-0.0361706\pi$
$744$	7700.20	0.379440
$745$	0	0
$746$	1315.22	0.0645493
$747$	− 489.709i	− 0.0239860i
$748$	16941.6i	0.828137i
$749$	−1701.61	−0.0830111
$750$	0	0
$751$	−8390.80	−0.407702	−0.203851	−	0.979002i	$-0.565346\pi$
$751$	−8390.80	−0.407702	−0.203851	+	0.979002i	$0.565346\pi$
$752$	1746.35i	0.0846848i
$753$	− 15657.3i	− 0.757747i
$754$	14591.2	0.704748
$755$	0	0
$756$	−880.145	−0.0423420
$757$	− 1368.89i	− 0.0657240i	−0.999460	−	0.0328620i	$-0.989538\pi$
$757$	− 1368.89i	− 0.0657240i	0.999460	−	0.0328620i	$-0.0104622\pi$
$758$	− 1046.88i	− 0.0501642i
$759$	−17078.4	−0.816739
$760$	0	0
$761$	−1623.77	−0.0773478	−0.0386739	−	0.999252i	$-0.512313\pi$
$761$	−1623.77	−0.0773478	−0.0386739	+	0.999252i	$0.512313\pi$
$762$	15034.6i	0.714759i
$763$	− 2836.23i	− 0.134572i
$764$	−2953.31	−0.139852
$765$	0	0
$766$	8252.03	0.389240
$767$	− 20343.8i	− 0.957722i
$768$	− 12776.6i	− 0.600308i
$769$	26842.5	1.25873	0.629366	−	0.777109i	$-0.283315\pi$
$769$	26842.5	1.25873	0.629366	+	0.777109i	$0.283315\pi$
$770$	0	0
$771$	−20927.1	−0.977526
$772$	1187.49i	0.0553612i
$773$	20961.4i	0.975330i	0.873031	+	0.487665i	$0.162151\pi$
$773$	20961.4i	0.975330i	−0.873031	+	0.487665i	$0.837849\pi$
$774$	7295.90	0.338819
$775$	0	0
$776$	16757.4	0.775200
$777$	2534.20i	0.117006i
$778$	12620.0i	0.581556i
$779$	−483.902	−0.0222562
$780$	0	0
$781$	−23003.5	−1.05394
$782$	− 9082.86i	− 0.415348i
$783$	6661.85i	0.304055i
$784$	247.885	0.0112921
$785$	0	0
$786$	10049.2	0.456036
$787$	35333.2i	1.60037i	0.599751	+	0.800187i	$0.295266\pi$
$787$	35333.2i	1.60037i	−0.599751	+	0.800187i	$0.704734\pi$
$788$	19430.1i	0.878388i
$789$	−10822.1	−0.488309
$790$	0	0
$791$	197.236	0.00886589
$792$	13448.3i	0.603364i
$793$	− 3726.13i	− 0.166858i
$794$	−7541.49	−0.337075
$795$	0	0
$796$	21544.8	0.959342
$797$	− 8137.04i	− 0.361642i	−0.983516	−	0.180821i	$-0.942125\pi$
$797$	− 8137.04i	− 0.361642i	0.983516	−	0.180821i	$-0.0578755\pi$
$798$	105.406i	0.00467586i
$799$	−19450.0	−0.861191
$800$	0	0
$801$	−9169.05	−0.404460
$802$	− 1832.99i	− 0.0807049i
$803$	− 42405.6i	− 1.86359i
$804$	13292.7	0.583082
$805$	0	0
$806$	6558.99	0.286639
$807$	− 17.6572i	0 0.000770212i
$808$	6218.87i	0.270766i
$809$	36281.0	1.57673	0.788364	−	0.615209i	$-0.210928\pi$
$809$	36281.0	1.57673	0.788364	+	0.615209i	$0.210928\pi$
$810$	0	0
$811$	−34237.2	−1.48240	−0.741202	−	0.671282i	$-0.765744\pi$
$811$	−34237.2	−1.48240	−0.741202	+	0.671282i	$0.765744\pi$
$812$	8043.06i	0.347606i
$813$	20749.0i	0.895077i
$814$	14246.9	0.613456
$815$	0	0
$816$	−855.099	−0.0366844
$817$	1217.10i	0.0521188i
$818$	− 18896.8i	− 0.807717i
$819$	−2037.62	−0.0869355
$820$	0	0
$821$	−23247.8	−0.988250	−0.494125	−	0.869391i	$-0.664511\pi$
$821$	−23247.8	−0.988250	−0.494125	+	0.869391i	$0.664511\pi$
$822$	− 2099.47i	− 0.0890846i
$823$	− 42934.0i	− 1.81845i	−0.416306	−	0.909225i	$-0.636675\pi$
$823$	− 42934.0i	− 1.81845i	0.416306	−	0.909225i	$-0.363325\pi$
$824$	−42596.0	−1.80085
$825$	0	0
$826$	−8050.55	−0.339122
$827$	− 781.391i	− 0.0328557i	−0.999865	−	0.0164278i	$-0.994771\pi$
$827$	− 781.391i	− 0.0328557i	0.999865	−	0.0164278i	$-0.00522938\pi$
$828$	3695.21i	0.155093i
$829$	33493.3	1.40322	0.701611	−	0.712561i	$-0.252465\pi$
$829$	33493.3	1.40322	0.701611	+	0.712561i	$0.252465\pi$
$830$	0	0
$831$	6358.39	0.265427
$832$	− 11710.4i	− 0.487964i
$833$	2760.81i	0.114834i
$834$	16749.9	0.695445
$835$	0	0
$836$	−825.434	−0.0341486
$837$	2994.62i	0.123667i
$838$	− 5820.27i	− 0.239926i
$839$	−15155.7	−0.623639	−0.311819	−	0.950141i	$-0.600938\pi$
$839$	−15155.7	−0.623639	−0.311819	+	0.950141i	$0.600938\pi$
$840$	0	0
$841$	36489.2	1.49613
$842$	− 12697.2i	− 0.519686i
$843$	− 719.752i	− 0.0294064i
$844$	−7277.01	−0.296783
$845$	0	0
$846$	−5680.66	−0.230857
$847$	− 19866.7i	− 0.805935i
$848$	1320.27i	0.0534649i
$849$	−13626.4	−0.550831
$850$	0	0
$851$	10639.6	0.428579
$852$	4977.21i	0.200137i
$853$	2917.48i	0.117107i	0.998284	+	0.0585537i	$0.0186489\pi$
$853$	2917.48i	0.117107i	−0.998284	+	0.0585537i	$0.981351\pi$
$854$	−1474.52	−0.0590832
$855$	0	0
$856$	5625.54	0.224623
$857$	− 31560.7i	− 1.25799i	−0.777411	−	0.628993i	$-0.783468\pi$
$857$	− 31560.7i	− 1.25799i	0.777411	−	0.628993i	$-0.216532\pi$
$858$	11455.2i	0.455797i
$859$	1404.81	0.0557991	0.0278995	−	0.999611i	$-0.491118\pi$
$859$	1404.81	0.0557991	0.0278995	+	0.999611i	$0.491118\pi$
$860$	0	0
$861$	−3701.76	−0.146522
$862$	7073.11i	0.279479i
$863$	9808.24i	0.386879i	0.981112	+	0.193439i	$0.0619643\pi$
$863$	9808.24i	0.386879i	−0.981112	+	0.193439i	$0.938036\pi$
$864$	4748.96	0.186994
$865$	0	0
$866$	−11213.7	−0.440018
$867$	5215.35i	0.204294i
$868$	3615.50i	0.141380i
$869$	28422.8	1.10952
$870$	0	0
$871$	30773.9	1.19717
$872$	9376.63i	0.364143i
$873$	6516.97i	0.252653i
$874$	442.537	0.0171271
$875$	0	0
$876$	−9175.22	−0.353883
$877$	− 7196.05i	− 0.277073i	−0.990357	−	0.138537i	$-0.955760\pi$
$877$	− 7196.05i	− 0.277073i	0.990357	−	0.138537i	$-0.0442399\pi$
$878$	7478.52i	0.287458i
$879$	−6515.10	−0.249999
$880$	0	0
$881$	−3183.27	−0.121733	−0.0608667	−	0.998146i	$-0.519386\pi$
$881$	−3183.27	−0.121733	−0.0608667	+	0.998146i	$0.519386\pi$
$882$	806.336i	0.0307832i
$883$	− 25392.5i	− 0.967751i	−0.875137	−	0.483876i	$-0.839229\pi$
$883$	− 25392.5i	− 0.967751i	0.875137	−	0.483876i	$-0.160771\pi$
$884$	8486.25	0.322877
$885$	0	0
$886$	22735.6	0.862095
$887$	− 30634.2i	− 1.15964i	−0.814746	−	0.579818i	$-0.803124\pi$
$887$	− 30634.2i	− 1.15964i	0.814746	−	0.579818i	$-0.196876\pi$
$888$	− 8378.11i	− 0.316612i
$889$	−19186.3	−0.723833
$890$	0	0
$891$	−5230.05	−0.196648
$892$	5757.71i	0.216124i
$893$	− 947.648i	− 0.0355116i
$894$	19530.9	0.730660
$895$	0	0
$896$	5215.58	0.194465
$897$	8554.75i	0.318433i
$898$	− 1614.59i	− 0.0599994i
$899$	27365.8	1.01524
$900$	0	0
$901$	−14704.5	−0.543704
$902$	20810.7i	0.768206i
$903$	9310.61i	0.343120i
$904$	−652.067	−0.0239905
$905$	0	0
$906$	−17891.9	−0.656091
$907$	− 28089.9i	− 1.02834i	−0.857687	−	0.514172i	$-0.828099\pi$
$907$	− 28089.9i	− 1.02834i	0.857687	−	0.514172i	$-0.171901\pi$
$908$	19474.1i	0.711753i
$909$	−2418.52	−0.0882480
$910$	0	0
$911$	−36102.7	−1.31299	−0.656495	−	0.754330i	$-0.727962\pi$
$911$	−36102.7	−1.31299	−0.656495	+	0.754330i	$0.727962\pi$
$912$	− 41.6624i	− 0.00151270i
$913$	− 3513.31i	− 0.127353i
$914$	16581.0	0.600055
$915$	0	0
$916$	2257.52	0.0814308
$917$	12824.3i	0.461826i
$918$	− 2781.52i	− 0.100004i
$919$	14533.8	0.521682	0.260841	−	0.965382i	$-0.416000\pi$
$919$	14533.8	0.521682	0.260841	+	0.965382i	$0.416000\pi$
$920$	0	0
$921$	10525.9	0.376592
$922$	22871.6i	0.816959i
$923$	11522.7i	0.410915i
$924$	−6314.41	−0.224815
$925$	0	0
$926$	23200.3	0.823336
$927$	− 16565.6i	− 0.586933i
$928$	− 43397.6i	− 1.53512i
$929$	−16539.6	−0.584118	−0.292059	−	0.956400i	$-0.594340\pi$
$929$	−16539.6	−0.584118	−0.292059	+	0.956400i	$0.594340\pi$
$930$	0	0
$931$	−134.513	−0.00473522
$932$	− 9688.79i	− 0.340522i
$933$	− 9399.74i	− 0.329833i
$934$	18533.9	0.649301
$935$	0	0
$936$	6736.41	0.235242
$937$	30212.3i	1.05335i	0.850065	+	0.526677i	$0.176562\pi$
$937$	30212.3i	1.05335i	−0.850065	+	0.526677i	$0.823438\pi$
$938$	− 12178.0i	− 0.423908i
$939$	19168.8	0.666187
$940$	0	0
$941$	−26414.4	−0.915074	−0.457537	−	0.889191i	$-0.651268\pi$
$941$	−26414.4	−0.915074	−0.457537	+	0.889191i	$0.651268\pi$
$942$	− 15789.1i	− 0.546112i
$943$	15541.5i	0.536692i
$944$	3182.03	0.109710
$945$	0	0
$946$	52342.9	1.79896
$947$	10187.3i	0.349570i	0.984607	+	0.174785i	$0.0559231\pi$
$947$	10187.3i	0.349570i	−0.984607	+	0.174785i	$0.944077\pi$
$948$	− 6149.77i	− 0.210691i
$949$	−21241.5	−0.726583
$950$	0	0
$951$	−4903.31	−0.167193
$952$	− 9127.31i	− 0.310733i
$953$	− 2211.39i	− 0.0751669i	−0.999293	−	0.0375834i	$-0.988034\pi$
$953$	− 2211.39i	− 0.0751669i	0.999293	−	0.0375834i	$-0.0119660\pi$
$954$	−4294.66	−0.145749
$955$	0	0
$956$	−31732.3	−1.07353
$957$	47794.0i	1.61438i
$958$	20773.0i	0.700569i
$959$	2679.23	0.0902156
$960$	0	0
$961$	−17489.6	−0.587077
$962$	− 7136.44i	− 0.239177i
$963$	2187.78i	0.0732089i
$964$	−18263.4	−0.610193
$965$	0	0
$966$	3385.33	0.112755
$967$	7955.89i	0.264575i	0.991211	+	0.132287i	$0.0422322\pi$
$967$	7955.89i	0.264575i	−0.991211	+	0.132287i	$0.957768\pi$
$968$	65679.6i	2.18081i
$969$	464.014	0.0153832
$970$	0	0
$971$	53071.2	1.75400	0.877001	−	0.480488i	$-0.159541\pi$
$971$	53071.2	1.75400	0.877001	+	0.480488i	$0.159541\pi$
$972$	1131.62i	0.0373422i
$973$	21375.2i	0.704274i
$974$	−14498.6	−0.476965
$975$	0	0
$976$	582.813	0.0191141
$977$	− 22448.2i	− 0.735089i	−0.930006	−	0.367545i	$-0.880199\pi$
$977$	− 22448.2i	− 0.735089i	0.930006	−	0.367545i	$-0.119801\pi$
$978$	− 5087.80i	− 0.166350i
$979$	−65781.4	−2.14748
$980$	0	0
$981$	−3646.58	−0.118681
$982$	14831.3i	0.481961i
$983$	− 21712.8i	− 0.704509i	−0.935904	−	0.352254i	$-0.885415\pi$
$983$	− 21712.8i	− 0.704509i	0.935904	−	0.352254i	$-0.114585\pi$
$984$	12238.1	0.396479
$985$	0	0
$986$	−25418.5	−0.820983
$987$	− 7249.33i	− 0.233788i
$988$	413.470i	0.0133140i
$989$	39089.7	1.25681
$990$	0	0
$991$	−37849.2	−1.21324	−0.606620	−	0.794992i	$-0.707475\pi$
$991$	−37849.2	−1.21324	−0.606620	+	0.794992i	$0.707475\pi$
$992$	− 19508.0i	− 0.624373i
$993$	13158.5i	0.420516i
$994$	4559.82	0.145502
$995$	0	0
$996$	−760.168	−0.0241836
$997$	− 39573.1i	− 1.25707i	−0.777783	−	0.628533i	$-0.783656\pi$
$997$	− 39573.1i	− 1.25707i	0.777783	−	0.628533i	$-0.216344\pi$
$998$	− 30748.0i	− 0.975261i
$999$	3258.26	0.103190

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.l.274.3		4
5.2	odd	4		525.4.a.l.1.1		2
5.3	odd	4		105.4.a.e.1.2	✓	2
5.4	even	2	inner	525.4.d.l.274.2		4
15.2	even	4		1575.4.a.q.1.2		2
15.8	even	4		315.4.a.k.1.1		2
20.3	even	4		1680.4.a.bo.1.2		2
35.13	even	4		735.4.a.o.1.2		2
105.83	odd	4		2205.4.a.bb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.e.1.2	✓	2	5.3	odd	4
315.4.a.k.1.1		2	15.8	even	4
525.4.a.l.1.1		2	5.2	odd	4
525.4.d.l.274.2		4	5.4	even	2	inner
525.4.d.l.274.3		4	1.1	even	1	trivial
735.4.a.o.1.2		2	35.13	even	4
1575.4.a.q.1.2		2	15.2	even	4
1680.4.a.bo.1.2		2	20.3	even	4
2205.4.a.bb.1.1		2	105.83	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.82843i q^{2} +3.00000i q^{3} +4.65685 q^{4} -5.48528 q^{6} -7.00000i q^{7} +23.1421i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+1.82843i q^{2} +3.00000i q^{3} +4.65685 q^{4} -5.48528 q^{6} -7.00000i q^{7} +23.1421i q^{8} -9.00000 q^{9} -64.5685 q^{11} +13.9706i q^{12} +32.3431i q^{13} +12.7990 q^{14} -5.05887 q^{16} -56.3431i q^{17} -16.4558i q^{18} +2.74517 q^{19} +21.0000 q^{21} -118.059i q^{22} -88.1665i q^{23} -69.4264 q^{24} -59.1371 q^{26} -27.0000i q^{27} -32.5980i q^{28} -246.735 q^{29} -110.912 q^{31} +175.887i q^{32} -193.706i q^{33} +103.019 q^{34} -41.9117 q^{36} +120.676i q^{37} +5.01934i q^{38} -97.0294 q^{39} -176.274 q^{41} +38.3970i q^{42} +443.362i q^{43} -300.686 q^{44} +161.206 q^{46} -345.206i q^{47} -15.1766i q^{48} -49.0000 q^{49} +169.029 q^{51} +150.617i q^{52} -260.981i q^{53} +49.3675 q^{54} +161.995 q^{56} +8.23550i q^{57} -451.137i q^{58} -628.999 q^{59} -115.206 q^{61} -202.794i q^{62} +63.0000i q^{63} -362.068 q^{64} +354.177 q^{66} -951.480i q^{67} -262.382i q^{68} +264.500 q^{69} +356.264 q^{71} -208.279i q^{72} +656.754i q^{73} -220.648 q^{74} +12.7838 q^{76} +451.980i q^{77} -177.411i q^{78} -440.195 q^{79} +81.0000 q^{81} -322.304i q^{82} +54.4121i q^{83} +97.7939 q^{84} -810.656 q^{86} -740.205i q^{87} -1494.25i q^{88} +1018.78 q^{89} +226.402 q^{91} -410.579i q^{92} -332.735i q^{93} +631.184 q^{94} -527.662 q^{96} -724.108i q^{97} -89.5929i q^{98} +581.117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 12 q^{6} - 36 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 12 * q^6 - 36 * q^9	\( 4 q - 4 q^{4} + 12 q^{6} - 36 q^{9} - 32 q^{11} - 28 q^{14} - 156 q^{16} + 192 q^{19} + 84 q^{21} - 108 q^{24} + 216 q^{26} - 376 q^{29} - 240 q^{31} - 312 q^{34} + 36 q^{36} - 456 q^{39} + 200 q^{41} - 1248 q^{44} + 1120 q^{46} - 196 q^{49} + 744 q^{51} - 108 q^{54} + 252 q^{56} - 208 q^{59} - 936 q^{61} - 68 q^{64} + 1824 q^{66} - 96 q^{69} - 272 q^{71} - 2376 q^{74} - 1216 q^{76} + 864 q^{79} + 324 q^{81} - 84 q^{84} - 912 q^{86} + 2808 q^{89} + 1064 q^{91} - 3200 q^{94} - 2484 q^{96} + 288 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 12 * q^6 - 36 * q^9 - 32 * q^11 - 28 * q^14 - 156 * q^16 + 192 * q^19 + 84 * q^21 - 108 * q^24 + 216 * q^26 - 376 * q^29 - 240 * q^31 - 312 * q^34 + 36 * q^36 - 456 * q^39 + 200 * q^41 - 1248 * q^44 + 1120 * q^46 - 196 * q^49 + 744 * q^51 - 108 * q^54 + 252 * q^56 - 208 * q^59 - 936 * q^61 - 68 * q^64 + 1824 * q^66 - 96 * q^69 - 272 * q^71 - 2376 * q^74 - 1216 * q^76 + 864 * q^79 + 324 * q^81 - 84 * q^84 - 912 * q^86 + 2808 * q^89 + 1064 * q^91 - 3200 * q^94 - 2484 * q^96 + 288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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