LMFDB - Embedded newform 525.4.d.n.274.4

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 48x^{6} + 668x^{4} + 2217x^{2} + 2116 $ x^8 + 48x^6 + 668x^4 + 2217*x^2 + 2116
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.4
Root			$-1.37627i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.n.274.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.37627i q^{2} +3.00000i q^{3} +6.10588 q^{4} +4.12881 q^{6} -7.00000i q^{7} -19.4135i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-1.37627i q^{2} +3.00000i q^{3} +6.10588 q^{4} +4.12881 q^{6} -7.00000i q^{7} -19.4135i q^{8} -9.00000 q^{9} +15.2804 q^{11} +18.3176i q^{12} +76.7787i q^{13} -9.63389 q^{14} +22.1288 q^{16} +96.7073i q^{17} +12.3864i q^{18} +14.1659 q^{19} +21.0000 q^{21} -21.0300i q^{22} -75.7097i q^{23} +58.2405 q^{24} +105.668 q^{26} -27.0000i q^{27} -42.7412i q^{28} -89.9625 q^{29} +289.563 q^{31} -185.763i q^{32} +45.8412i q^{33} +133.095 q^{34} -54.9529 q^{36} -14.2345i q^{37} -19.4961i q^{38} -230.336 q^{39} +318.710 q^{41} -28.9017i q^{42} +389.707i q^{43} +93.3003 q^{44} -104.197 q^{46} -228.849i q^{47} +66.3864i q^{48} -49.0000 q^{49} -290.122 q^{51} +468.801i q^{52} +679.493i q^{53} -37.1593 q^{54} -135.895 q^{56} +42.4977i q^{57} +123.813i q^{58} +398.628 q^{59} -146.361 q^{61} -398.517i q^{62} +63.0000i q^{63} -78.6300 q^{64} +63.0899 q^{66} -291.493i q^{67} +590.483i q^{68} +227.129 q^{69} +333.233 q^{71} +174.722i q^{72} +891.133i q^{73} -19.5905 q^{74} +86.4953 q^{76} -106.963i q^{77} +317.005i q^{78} +416.731 q^{79} +81.0000 q^{81} -438.631i q^{82} -814.323i q^{83} +128.223 q^{84} +536.342 q^{86} -269.887i q^{87} -296.646i q^{88} +650.076 q^{89} +537.451 q^{91} -462.275i q^{92} +868.690i q^{93} -314.958 q^{94} +557.290 q^{96} +1585.25i q^{97} +67.4372i q^{98} -137.524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} - 72 q^{9}+O(q^{10}) $ 8 * q - 32 * q^4 - 72 * q^9	$ 8 q - 32 q^{4} - 72 q^{9} + 42 q^{11} + 144 q^{16} - 144 q^{19} + 168 q^{21} - 54 q^{24} + 258 q^{26} + 480 q^{29} + 702 q^{31} + 570 q^{34} + 288 q^{36} - 30 q^{39} + 762 q^{41} + 1950 q^{44} + 1100 q^{46} - 392 q^{49} + 594 q^{51} + 126 q^{56} + 1710 q^{59} + 1374 q^{61} + 2570 q^{64} + 1326 q^{66} - 612 q^{69} - 1362 q^{71} + 6738 q^{74} + 3820 q^{76} - 690 q^{79} + 648 q^{81} - 672 q^{84} - 1080 q^{86} + 396 q^{89} + 70 q^{91} + 3464 q^{94} + 432 q^{96} - 378 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 - 72 * q^9 + 42 * q^11 + 144 * q^16 - 144 * q^19 + 168 * q^21 - 54 * q^24 + 258 * q^26 + 480 * q^29 + 702 * q^31 + 570 * q^34 + 288 * q^36 - 30 * q^39 + 762 * q^41 + 1950 * q^44 + 1100 * q^46 - 392 * q^49 + 594 * q^51 + 126 * q^56 + 1710 * q^59 + 1374 * q^61 + 2570 * q^64 + 1326 * q^66 - 612 * q^69 - 1362 * q^71 + 6738 * q^74 + 3820 * q^76 - 690 * q^79 + 648 * q^81 - 672 * q^84 - 1080 * q^86 + 396 * q^89 + 70 * q^91 + 3464 * q^94 + 432 * q^96 - 378 * 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 $

$2$	− 1.37627i	− 0.486585i	−0.969953	−	0.243293i	$-0.921773\pi$
$2$	− 1.37627i	− 0.486585i	0.969953	−	0.243293i	$-0.0782275\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	6.10588	0.763235
$5$	0	0
$5$	0	0
$6$	4.12881	0.280930
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	− 19.4135i	− 0.857964i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	15.2804	0.418838	0.209419	−	0.977826i	$-0.432843\pi$
$11$	15.2804	0.418838	0.209419	+	0.977826i	$0.432843\pi$
$12$	18.3176i	0.440654i
$13$	76.7787i	1.63804i	0.573762	+	0.819022i	$0.305483\pi$
$13$	76.7787i	1.63804i	−0.573762	+	0.819022i	$0.694517\pi$
$14$	−9.63389	−0.183912
$15$	0	0
$16$	22.1288	0.345763
$17$	96.7073i	1.37970i	0.723951	+	0.689852i	$0.242324\pi$
$17$	96.7073i	1.37970i	−0.723951	+	0.689852i	$0.757676\pi$
$18$	12.3864i	0.162195i
$19$	14.1659	0.171046	0.0855232	−	0.996336i	$-0.472744\pi$
$19$	14.1659	0.171046	0.0855232	+	0.996336i	$0.472744\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	− 21.0300i	− 0.203800i
$23$	− 75.7097i	− 0.686373i	−0.939267	−	0.343186i	$-0.888494\pi$
$23$	− 75.7097i	− 0.686373i	0.939267	−	0.343186i	$-0.111506\pi$
$24$	58.2405	0.495346
$25$	0	0
$26$	105.668	0.797048
$27$	− 27.0000i	− 0.192450i
$28$	− 42.7412i	− 0.288476i
$29$	−89.9625	−0.576055	−0.288028	−	0.957622i	$-0.593000\pi$
$29$	−89.9625	−0.576055	−0.288028	+	0.957622i	$0.593000\pi$
$30$	0	0
$31$	289.563	1.67765	0.838824	−	0.544403i	$-0.183244\pi$
$31$	289.563	1.67765	0.838824	+	0.544403i	$0.183244\pi$
$32$	− 185.763i	− 1.02621i
$33$	45.8412i	0.241816i
$34$	133.095	0.671343
$35$	0	0
$36$	−54.9529	−0.254412
$37$	− 14.2345i	− 0.0632470i	−0.999500	−	0.0316235i	$-0.989932\pi$
$37$	− 14.2345i	− 0.0632470i	0.999500	−	0.0316235i	$-0.0100678\pi$
$38$	− 19.4961i	− 0.0832286i
$39$	−230.336	−0.945725
$40$	0	0
$41$	318.710	1.21400	0.607002	−	0.794700i	$-0.292372\pi$
$41$	318.710	1.21400	0.607002	+	0.794700i	$0.292372\pi$
$42$	− 28.9017i	− 0.106182i
$43$	389.707i	1.38209i	0.722813	+	0.691044i	$0.242849\pi$
$43$	389.707i	1.38209i	−0.722813	+	0.691044i	$0.757151\pi$
$44$	93.3003	0.319672
$45$	0	0
$46$	−104.197	−0.333979
$47$	− 228.849i	− 0.710236i	−0.934821	−	0.355118i	$-0.884441\pi$
$47$	− 228.849i	− 0.710236i	0.934821	−	0.355118i	$-0.115559\pi$
$48$	66.3864i	0.199626i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−290.122	−0.796572
$52$	468.801i	1.25021i
$53$	679.493i	1.76105i	0.474002	+	0.880524i	$0.342809\pi$
$53$	679.493i	1.76105i	−0.474002	+	0.880524i	$0.657191\pi$
$54$	−37.1593	−0.0936433
$55$	0	0
$56$	−135.895	−0.324280
$57$	42.4977i	0.0987536i
$58$	123.813i	0.280300i
$59$	398.628	0.879610	0.439805	−	0.898093i	$-0.355048\pi$
$59$	398.628	0.879610	0.439805	+	0.898093i	$0.355048\pi$
$60$	0	0
$61$	−146.361	−0.307206	−0.153603	−	0.988133i	$-0.549088\pi$
$61$	−146.361	−0.307206	−0.153603	+	0.988133i	$0.549088\pi$
$62$	− 398.517i	− 0.816318i
$63$	63.0000i	0.125988i
$64$	−78.6300	−0.153574
$65$	0	0
$66$	63.0899	0.117664
$67$	− 291.493i	− 0.531516i	−0.964040	−	0.265758i	$-0.914378\pi$
$67$	− 291.493i	− 0.531516i	0.964040	−	0.265758i	$-0.0856223\pi$
$68$	590.483i	1.05304i
$69$	227.129	0.396278
$70$	0	0
$71$	333.233	0.557007	0.278503	−	0.960435i	$-0.410162\pi$
$71$	333.233	0.557007	0.278503	+	0.960435i	$0.410162\pi$
$72$	174.722i	0.285988i
$73$	891.133i	1.42876i	0.699760	+	0.714378i	$0.253290\pi$
$73$	891.133i	1.42876i	−0.699760	+	0.714378i	$0.746710\pi$
$74$	−19.5905	−0.0307751
$75$	0	0
$76$	86.4953	0.130549
$77$	− 106.963i	− 0.158306i
$78$	317.005i	0.460176i
$79$	416.731	0.593493	0.296746	−	0.954956i	$-0.404098\pi$
$79$	416.731	0.593493	0.296746	+	0.954956i	$0.404098\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 438.631i	− 0.590716i
$83$	− 814.323i	− 1.07691i	−0.842654	−	0.538455i	$-0.819008\pi$
$83$	− 814.323i	− 1.07691i	0.842654	−	0.538455i	$-0.180992\pi$
$84$	128.223	0.166552
$85$	0	0
$86$	536.342	0.672503
$87$	− 269.887i	− 0.332586i
$88$	− 296.646i	− 0.359348i
$89$	650.076	0.774247	0.387123	−	0.922028i	$-0.373469\pi$
$89$	650.076	0.774247	0.387123	+	0.922028i	$0.373469\pi$
$90$	0	0
$91$	537.451	0.619123
$92$	− 462.275i	− 0.523864i
$93$	868.690i	0.968590i
$94$	−314.958	−0.345590
$95$	0	0
$96$	557.290	0.592481
$97$	1585.25i	1.65936i	0.558243	+	0.829678i	$0.311476\pi$
$97$	1585.25i	1.65936i	−0.558243	+	0.829678i	$0.688524\pi$
$98$	67.4372i	0.0695121i
$99$	−137.524	−0.139613
$100$	0	0
$101$	−496.139	−0.488789	−0.244395	−	0.969676i	$-0.578589\pi$
$101$	−496.139	−0.488789	−0.244395	+	0.969676i	$0.578589\pi$
$102$	399.286i	0.387600i
$103$	468.440i	0.448124i	0.974575	+	0.224062i	$0.0719318\pi$
$103$	468.440i	0.448124i	−0.974575	+	0.224062i	$0.928068\pi$
$104$	1490.54	1.40538
$105$	0	0
$106$	935.166	0.856900
$107$	− 1978.79i	− 1.78782i	−0.448249	−	0.893909i	$-0.647952\pi$
$107$	− 1978.79i	− 1.78782i	0.448249	−	0.893909i	$-0.352048\pi$
$108$	− 164.859i	− 0.146885i
$109$	1009.70	0.887260	0.443630	−	0.896210i	$-0.353691\pi$
$109$	1009.70	0.887260	0.443630	+	0.896210i	$0.353691\pi$
$110$	0	0
$111$	42.7035	0.0365157
$112$	− 154.902i	− 0.130686i
$113$	120.953i	0.100693i	0.998732	+	0.0503466i	$0.0160326\pi$
$113$	120.953i	0.100693i	−0.998732	+	0.0503466i	$0.983967\pi$
$114$	58.4883	0.0480520
$115$	0	0
$116$	−549.300	−0.439666
$117$	− 691.008i	− 0.546015i
$118$	− 548.620i	− 0.428005i
$119$	676.951	0.521479
$120$	0	0
$121$	−1097.51	−0.824575
$122$	201.432i	0.149482i
$123$	956.130i	0.700905i
$124$	1768.04	1.28044
$125$	0	0
$126$	86.7050	0.0613040
$127$	1545.52i	1.07986i	0.841709	+	0.539932i	$0.181550\pi$
$127$	1545.52i	1.07986i	−0.841709	+	0.539932i	$0.818450\pi$
$128$	− 1377.89i	− 0.951480i
$129$	−1169.12	−0.797949
$130$	0	0
$131$	−2258.15	−1.50607	−0.753035	−	0.657980i	$-0.771411\pi$
$131$	−2258.15	−1.50607	−0.753035	+	0.657980i	$0.771411\pi$
$132$	279.901i	0.184563i
$133$	− 99.1613i	− 0.0646494i
$134$	−401.174	−0.258628
$135$	0	0
$136$	1877.43	1.18374
$137$	1242.72i	0.774982i	0.921873	+	0.387491i	$0.126658\pi$
$137$	1242.72i	0.774982i	−0.921873	+	0.387491i	$0.873342\pi$
$138$	− 312.591i	− 0.192823i
$139$	−405.672	−0.247544	−0.123772	−	0.992311i	$-0.539499\pi$
$139$	−405.672	−0.247544	−0.123772	+	0.992311i	$0.539499\pi$
$140$	0	0
$141$	686.548	0.410055
$142$	− 458.619i	− 0.271031i
$143$	1173.21i	0.686075i
$144$	−199.159	−0.115254
$145$	0	0
$146$	1226.44	0.695211
$147$	− 147.000i	− 0.0824786i
$148$	− 86.9142i	− 0.0482723i
$149$	−882.453	−0.485191	−0.242595	−	0.970128i	$-0.577999\pi$
$149$	−882.453	−0.485191	−0.242595	+	0.970128i	$0.577999\pi$
$150$	0	0
$151$	2246.66	1.21080	0.605400	−	0.795921i	$-0.293013\pi$
$151$	2246.66	1.21080	0.605400	+	0.795921i	$0.293013\pi$
$152$	− 275.010i	− 0.146752i
$153$	− 870.366i	− 0.459901i
$154$	−147.210	−0.0770292
$155$	0	0
$156$	−1406.40	−0.721811
$157$	− 2953.43i	− 1.50133i	−0.660681	−	0.750667i	$-0.729732\pi$
$157$	− 2953.43i	− 1.50133i	0.660681	−	0.750667i	$-0.270268\pi$
$158$	− 573.535i	− 0.288785i
$159$	−2038.48	−1.01674
$160$	0	0
$161$	−529.968	−0.259425
$162$	− 111.478i	− 0.0540650i
$163$	− 104.301i	− 0.0501197i	−0.999686	−	0.0250599i	$-0.992022\pi$
$163$	− 104.301i	− 0.0501197i	0.999686	−	0.0250599i	$-0.00797763\pi$
$164$	1946.01	0.926570
$165$	0	0
$166$	−1120.73	−0.524008
$167$	− 2220.68i	− 1.02899i	−0.857493	−	0.514495i	$-0.827979\pi$
$167$	− 2220.68i	− 1.02899i	0.857493	−	0.514495i	$-0.172021\pi$
$168$	− 407.684i	− 0.187223i
$169$	−3697.97	−1.68319
$170$	0	0
$171$	−127.493	−0.0570154
$172$	2379.50i	1.05486i
$173$	− 1727.64i	− 0.759247i	−0.925141	−	0.379623i	$-0.876054\pi$
$173$	− 1727.64i	− 0.759247i	0.925141	−	0.379623i	$-0.123946\pi$
$174$	−371.438	−0.161831
$175$	0	0
$176$	338.137	0.144818
$177$	1195.89i	0.507843i
$178$	− 894.681i	− 0.376737i
$179$	3332.33	1.39145	0.695727	−	0.718306i	$-0.255082\pi$
$179$	3332.33	1.39145	0.695727	+	0.718306i	$0.255082\pi$
$180$	0	0
$181$	1308.68	0.537422	0.268711	−	0.963221i	$-0.413402\pi$
$181$	1308.68	0.537422	0.268711	+	0.963221i	$0.413402\pi$
$182$	− 739.678i	− 0.301256i
$183$	− 439.083i	− 0.177366i
$184$	−1469.79	−0.588883
$185$	0	0
$186$	1195.55	0.471302
$187$	1477.73i	0.577872i
$188$	− 1397.33i	− 0.542077i
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−3545.30	−1.34308	−0.671541	−	0.740968i	$-0.734367\pi$
$191$	−3545.30	−1.34308	−0.671541	+	0.740968i	$0.734367\pi$
$192$	− 235.890i	− 0.0886661i
$193$	1077.32i	0.401798i	0.979612	+	0.200899i	$0.0643863\pi$
$193$	1077.32i	0.401798i	−0.979612	+	0.200899i	$0.935614\pi$
$194$	2181.73	0.807417
$195$	0	0
$196$	−299.188	−0.109034
$197$	− 3800.24i	− 1.37439i	−0.726471	−	0.687197i	$-0.758841\pi$
$197$	− 3800.24i	− 1.37439i	0.726471	−	0.687197i	$-0.241159\pi$
$198$	189.270i	0.0679334i
$199$	−2494.27	−0.888513	−0.444256	−	0.895900i	$-0.646532\pi$
$199$	−2494.27	−0.888513	−0.444256	+	0.895900i	$0.646532\pi$
$200$	0	0
$201$	874.480	0.306871
$202$	682.822i	0.237838i
$203$	629.737i	0.217728i
$204$	−1771.45	−0.607972
$205$	0	0
$206$	644.700	0.218050
$207$	681.388i	0.228791i
$208$	1699.02i	0.566375i
$209$	216.461	0.0716407
$210$	0	0
$211$	−4235.73	−1.38199	−0.690995	−	0.722859i	$-0.742827\pi$
$211$	−4235.73	−1.38199	−0.690995	+	0.722859i	$0.742827\pi$
$212$	4148.90i	1.34409i
$213$	999.699i	0.321588i
$214$	−2723.34	−0.869925
$215$	0	0
$216$	−524.165	−0.165115
$217$	− 2026.94i	− 0.634091i
$218$	− 1389.61i	− 0.431727i
$219$	−2673.40	−0.824893
$220$	0	0
$221$	−7425.06	−2.26002
$222$	− 58.7716i	− 0.0177680i
$223$	− 1274.70i	− 0.382781i	−0.981514	−	0.191391i	$-0.938700\pi$
$223$	− 1274.70i	− 0.382781i	0.981514	−	0.191391i	$-0.0612997\pi$
$224$	−1300.34	−0.387870
$225$	0	0
$226$	166.465	0.0489958
$227$	2710.17i	0.792425i	0.918159	+	0.396213i	$0.129676\pi$
$227$	2710.17i	0.792425i	−0.918159	+	0.396213i	$0.870324\pi$
$228$	259.486i	0.0753722i
$229$	−1396.94	−0.403111	−0.201555	−	0.979477i	$-0.564600\pi$
$229$	−1396.94	−0.403111	−0.201555	+	0.979477i	$0.564600\pi$
$230$	0	0
$231$	320.889	0.0913979
$232$	1746.49i	0.494235i
$233$	− 5628.80i	− 1.58264i	−0.611403	−	0.791319i	$-0.709395\pi$
$233$	− 5628.80i	− 1.58264i	0.611403	−	0.791319i	$-0.290605\pi$
$234$	−951.014	−0.265683
$235$	0	0
$236$	2433.98	0.671349
$237$	1250.19i	0.342653i
$238$	− 931.668i	− 0.253744i
$239$	−3490.10	−0.944585	−0.472293	−	0.881442i	$-0.656573\pi$
$239$	−3490.10	−0.944585	−0.472293	+	0.881442i	$0.656573\pi$
$240$	0	0
$241$	3077.81	0.822653	0.411326	−	0.911488i	$-0.365066\pi$
$241$	3077.81	0.822653	0.411326	+	0.911488i	$0.365066\pi$
$242$	1510.47i	0.401226i
$243$	243.000i	0.0641500i
$244$	−893.662	−0.234471
$245$	0	0
$246$	1315.89	0.341050
$247$	1087.64i	0.280181i
$248$	− 5621.44i	− 1.43936i
$249$	2442.97	0.621754
$250$	0	0
$251$	−3094.27	−0.778123	−0.389061	−	0.921212i	$-0.627201\pi$
$251$	−3094.27	−0.778123	−0.389061	+	0.921212i	$0.627201\pi$
$252$	384.670i	0.0961586i
$253$	− 1156.88i	− 0.287479i
$254$	2127.05	0.525445
$255$	0	0
$256$	−2525.39	−0.616550
$257$	− 1966.11i	− 0.477208i	−0.971117	−	0.238604i	$-0.923310\pi$
$257$	− 1966.11i	− 0.477208i	0.971117	−	0.238604i	$-0.0766899\pi$
$258$	1609.03i	0.388270i
$259$	−99.6416	−0.0239051
$260$	0	0
$261$	809.662	0.192018
$262$	3107.82i	0.732831i
$263$	2828.34i	0.663129i	0.943432	+	0.331565i	$0.107577\pi$
$263$	2828.34i	0.663129i	−0.943432	+	0.331565i	$0.892423\pi$
$264$	889.939	0.207469
$265$	0	0
$266$	−136.473	−0.0314574
$267$	1950.23i	0.447011i
$268$	− 1779.82i	− 0.405672i
$269$	1653.14	0.374698	0.187349	−	0.982293i	$-0.440011\pi$
$269$	1653.14	0.374698	0.187349	+	0.982293i	$0.440011\pi$
$270$	0	0
$271$	−5326.26	−1.19390	−0.596950	−	0.802278i	$-0.703621\pi$
$271$	−5326.26	−1.19390	−0.596950	+	0.802278i	$0.703621\pi$
$272$	2140.02i	0.477050i
$273$	1612.35i	0.357451i
$274$	1710.32	0.377095
$275$	0	0
$276$	1386.82	0.302453
$277$	5317.24i	1.15336i	0.816968	+	0.576682i	$0.195653\pi$
$277$	5317.24i	1.15336i	−0.816968	+	0.576682i	$0.804347\pi$
$278$	558.314i	0.120451i
$279$	−2606.07	−0.559216
$280$	0	0
$281$	−3584.56	−0.760985	−0.380493	−	0.924784i	$-0.624246\pi$
$281$	−3584.56	−0.760985	−0.380493	+	0.924784i	$0.624246\pi$
$282$	− 944.875i	− 0.199527i
$283$	− 1230.41i	− 0.258446i	−0.991616	−	0.129223i	$-0.958752\pi$
$283$	− 1230.41i	− 0.258446i	0.991616	−	0.129223i	$-0.0412483\pi$
$284$	2034.68	0.425127
$285$	0	0
$286$	1614.65	0.333834
$287$	− 2230.97i	− 0.458850i
$288$	1671.87i	0.342069i
$289$	−4439.30	−0.903582
$290$	0	0
$291$	−4755.74	−0.958029
$292$	5441.15i	1.09048i
$293$	− 8544.91i	− 1.70375i	−0.523745	−	0.851875i	$-0.675465\pi$
$293$	− 8544.91i	− 1.70375i	0.523745	−	0.851875i	$-0.324535\pi$
$294$	−202.312	−0.0401329
$295$	0	0
$296$	−276.342	−0.0542636
$297$	− 412.571i	− 0.0806054i
$298$	1214.49i	0.236086i
$299$	5812.89	1.12431
$300$	0	0
$301$	2727.95	0.522380
$302$	− 3092.02i	− 0.589158i
$303$	− 1488.42i	− 0.282203i
$304$	313.474	0.0591414
$305$	0	0
$306$	−1197.86	−0.223781
$307$	− 2066.36i	− 0.384148i	−0.981380	−	0.192074i	$-0.938479\pi$
$307$	− 2066.36i	− 0.384148i	0.981380	−	0.192074i	$-0.0615213\pi$
$308$	− 653.102i	− 0.120825i
$309$	−1405.32	−0.258725
$310$	0	0
$311$	7346.18	1.33943	0.669717	−	0.742617i	$-0.266416\pi$
$311$	7346.18	1.33943	0.669717	+	0.742617i	$0.266416\pi$
$312$	4471.63i	0.811398i
$313$	6421.62i	1.15965i	0.814740	+	0.579826i	$0.196880\pi$
$313$	6421.62i	1.15965i	−0.814740	+	0.579826i	$0.803120\pi$
$314$	−4064.72	−0.730526
$315$	0	0
$316$	2544.51	0.452974
$317$	799.972i	0.141738i	0.997486	+	0.0708689i	$0.0225772\pi$
$317$	799.972i	0.141738i	−0.997486	+	0.0708689i	$0.977423\pi$
$318$	2805.50i	0.494731i
$319$	−1374.66	−0.241274
$320$	0	0
$321$	5936.36	1.03220
$322$	729.380i	0.126232i
$323$	1369.95i	0.235993i
$324$	494.576	0.0848039
$325$	0	0
$326$	−143.547	−0.0243875
$327$	3029.09i	0.512260i
$328$	− 6187.28i	− 1.04157i
$329$	−1601.94	−0.268444
$330$	0	0
$331$	−4453.67	−0.739565	−0.369782	−	0.929118i	$-0.620568\pi$
$331$	−4453.67	−0.739565	−0.369782	+	0.929118i	$0.620568\pi$
$332$	− 4972.16i	− 0.821935i
$333$	128.111i	0.0210823i
$334$	−3056.25	−0.500691
$335$	0	0
$336$	464.705	0.0754516
$337$	− 10777.5i	− 1.74210i	−0.491193	−	0.871051i	$-0.663439\pi$
$337$	− 10777.5i	− 1.74210i	0.491193	−	0.871051i	$-0.336561\pi$
$338$	5089.40i	0.819015i
$339$	−362.860	−0.0581353
$340$	0	0
$341$	4424.64	0.702662
$342$	175.465i	0.0277429i
$343$	343.000i	0.0539949i
$344$	7565.58	1.18578
$345$	0	0
$346$	−2377.69	−0.369438
$347$	− 7096.10i	− 1.09781i	−0.835886	−	0.548903i	$-0.815046\pi$
$347$	− 7096.10i	− 1.09781i	0.835886	−	0.548903i	$-0.184954\pi$
$348$	− 1647.90i	− 0.253841i
$349$	−8300.35	−1.27309	−0.636543	−	0.771241i	$-0.719636\pi$
$349$	−8300.35	−1.27309	−0.636543	+	0.771241i	$0.719636\pi$
$350$	0	0
$351$	2073.02	0.315242
$352$	− 2838.54i	− 0.429814i
$353$	− 9084.35i	− 1.36972i	−0.728674	−	0.684860i	$-0.759863\pi$
$353$	− 9084.35i	− 1.36972i	0.728674	−	0.684860i	$-0.240137\pi$
$354$	1645.86	0.247109
$355$	0	0
$356$	3969.29	0.590932
$357$	2030.85i	0.301076i
$358$	− 4586.19i	− 0.677061i
$359$	5129.81	0.754153	0.377077	−	0.926182i	$-0.376929\pi$
$359$	5129.81	0.754153	0.377077	+	0.926182i	$0.376929\pi$
$360$	0	0
$361$	−6658.33	−0.970743
$362$	− 1801.10i	− 0.261501i
$363$	− 3292.53i	− 0.476069i
$364$	3281.61	0.472536
$365$	0	0
$366$	−604.296	−0.0863035
$367$	− 13074.0i	− 1.85956i	−0.368116	−	0.929780i	$-0.619997\pi$
$367$	− 13074.0i	− 1.85956i	0.368116	−	0.929780i	$-0.380003\pi$
$368$	− 1675.37i	− 0.237322i
$369$	−2868.39	−0.404668
$370$	0	0
$371$	4756.45	0.665614
$372$	5304.11i	0.739262i
$373$	− 4056.31i	− 0.563076i	−0.959550	−	0.281538i	$-0.909155\pi$
$373$	− 4056.31i	− 0.563076i	0.959550	−	0.281538i	$-0.0908446\pi$
$374$	2033.75	0.281184
$375$	0	0
$376$	−4442.77	−0.609357
$377$	− 6907.20i	− 0.943604i
$378$	260.115i	0.0353939i
$379$	11594.6	1.57143	0.785715	−	0.618588i	$-0.212295\pi$
$379$	11594.6	1.57143	0.785715	+	0.618588i	$0.212295\pi$
$380$	0	0
$381$	−4636.56	−0.623460
$382$	4879.29i	0.653523i
$383$	10950.0i	1.46089i	0.682972	+	0.730444i	$0.260687\pi$
$383$	10950.0i	1.46089i	−0.682972	+	0.730444i	$0.739313\pi$
$384$	4133.67	0.549337
$385$	0	0
$386$	1482.68	0.195509
$387$	− 3507.36i	− 0.460696i
$388$	9679.33i	1.26648i
$389$	2180.03	0.284143	0.142072	−	0.989856i	$-0.454624\pi$
$389$	2180.03	0.284143	0.142072	+	0.989856i	$0.454624\pi$
$390$	0	0
$391$	7321.68	0.946991
$392$	951.262i	0.122566i
$393$	− 6774.44i	− 0.869530i
$394$	−5230.16	−0.668760
$395$	0	0
$396$	−839.703	−0.106557
$397$	− 6139.23i	− 0.776119i	−0.921634	−	0.388059i	$-0.873146\pi$
$397$	− 6139.23i	− 0.776119i	0.921634	−	0.388059i	$-0.126854\pi$
$398$	3432.79i	0.432337i
$399$	297.484	0.0373254
$400$	0	0
$401$	−11689.1	−1.45567	−0.727835	−	0.685752i	$-0.759473\pi$
$401$	−11689.1	−1.45567	−0.727835	+	0.685752i	$0.759473\pi$
$402$	− 1203.52i	− 0.149319i
$403$	22232.3i	2.74806i
$404$	−3029.37	−0.373061
$405$	0	0
$406$	866.689	0.105943
$407$	− 217.509i	− 0.0264902i
$408$	5632.28i	0.683430i
$409$	−662.397	−0.0800818	−0.0400409	−	0.999198i	$-0.512749\pi$
$409$	−662.397	−0.0800818	−0.0400409	+	0.999198i	$0.512749\pi$
$410$	0	0
$411$	−3728.15	−0.447436
$412$	2860.24i	0.342024i
$413$	− 2790.40i	− 0.332461i
$414$	937.774	0.111326
$415$	0	0
$416$	14262.7	1.68097
$417$	− 1217.01i	− 0.142920i
$418$	− 297.908i	− 0.0348593i
$419$	7414.29	0.864467	0.432234	−	0.901762i	$-0.357726\pi$
$419$	7414.29	0.864467	0.432234	+	0.901762i	$0.357726\pi$
$420$	0	0
$421$	9767.88	1.13078	0.565389	−	0.824825i	$-0.308726\pi$
$421$	9767.88	1.13078	0.565389	+	0.824825i	$0.308726\pi$
$422$	5829.52i	0.672456i
$423$	2059.64i	0.236745i
$424$	13191.3	1.51092
$425$	0	0
$426$	1375.86	0.156480
$427$	1024.53i	0.116113i
$428$	− 12082.2i	− 1.36452i
$429$	−3519.63	−0.396106
$430$	0	0
$431$	−16905.3	−1.88933	−0.944664	−	0.328041i	$-0.893612\pi$
$431$	−16905.3	−1.88933	−0.944664	+	0.328041i	$0.893612\pi$
$432$	− 597.478i	− 0.0665421i
$433$	11118.3i	1.23397i	0.786975	+	0.616985i	$0.211646\pi$
$433$	11118.3i	1.23397i	−0.786975	+	0.616985i	$0.788354\pi$
$434$	−2789.62	−0.308539
$435$	0	0
$436$	6165.08	0.677188
$437$	− 1072.50i	− 0.117402i
$438$	3679.32i	0.401380i
$439$	−2480.01	−0.269623	−0.134811	−	0.990871i	$-0.543043\pi$
$439$	−2480.01	−0.269623	−0.134811	+	0.990871i	$0.543043\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	10218.9i	1.09969i
$443$	1734.62i	0.186036i	0.995664	+	0.0930182i	$0.0296515\pi$
$443$	1734.62i	0.186036i	−0.995664	+	0.0930182i	$0.970349\pi$
$444$	260.743	0.0278700
$445$	0	0
$446$	−1754.33	−0.186256
$447$	− 2647.36i	− 0.280125i
$448$	550.410i	0.0580456i
$449$	−3488.08	−0.366621	−0.183311	−	0.983055i	$-0.558681\pi$
$449$	−3488.08	−0.366621	−0.183311	+	0.983055i	$0.558681\pi$
$450$	0	0
$451$	4870.02	0.508471
$452$	738.527i	0.0768526i
$453$	6739.99i	0.699056i
$454$	3729.93	0.385582
$455$	0	0
$456$	825.029	0.0847270
$457$	− 3634.10i	− 0.371983i	−0.982551	−	0.185991i	$-0.940450\pi$
$457$	− 3634.10i	− 0.371983i	0.982551	−	0.185991i	$-0.0595497\pi$
$458$	1922.57i	0.196148i
$459$	2611.10	0.265524
$460$	0	0
$461$	7589.30	0.766744	0.383372	−	0.923594i	$-0.374763\pi$
$461$	7589.30	0.766744	0.383372	+	0.923594i	$0.374763\pi$
$462$	− 441.629i	− 0.0444729i
$463$	− 6275.14i	− 0.629871i	−0.949113	−	0.314936i	$-0.898017\pi$
$463$	− 6275.14i	− 0.629871i	0.949113	−	0.314936i	$-0.101983\pi$
$464$	−1990.76	−0.199178
$465$	0	0
$466$	−7746.75	−0.770088
$467$	11705.9i	1.15992i	0.814644	+	0.579962i	$0.196933\pi$
$467$	11705.9i	1.15992i	−0.814644	+	0.579962i	$0.803067\pi$
$468$	− 4219.21i	− 0.416738i
$469$	−2040.45	−0.200894
$470$	0	0
$471$	8860.29	0.866795
$472$	− 7738.77i	− 0.754674i
$473$	5954.88i	0.578871i
$474$	1720.60	0.166730
$475$	0	0
$476$	4133.38	0.398011
$477$	− 6115.44i	− 0.587016i
$478$	4803.32i	0.459621i
$479$	842.832	0.0803966	0.0401983	−	0.999192i	$-0.487201\pi$
$479$	842.832	0.0803966	0.0401983	+	0.999192i	$0.487201\pi$
$480$	0	0
$481$	1092.91	0.103601
$482$	− 4235.90i	− 0.400290i
$483$	− 1589.90i	− 0.149779i
$484$	−6701.26	−0.629344
$485$	0	0
$486$	334.434	0.0312144
$487$	− 1570.99i	− 0.146177i	−0.997325	−	0.0730885i	$-0.976714\pi$
$487$	− 1570.99i	− 0.146177i	0.997325	−	0.0730885i	$-0.0232856\pi$
$488$	2841.38i	0.263572i
$489$	312.904	0.0289366
$490$	0	0
$491$	12555.4	1.15400	0.577001	−	0.816743i	$-0.304223\pi$
$491$	12555.4	1.15400	0.577001	+	0.816743i	$0.304223\pi$
$492$	5838.02i	0.534955i
$493$	− 8700.02i	− 0.794786i
$494$	1496.89	0.136332
$495$	0	0
$496$	6407.69	0.580068
$497$	− 2332.63i	− 0.210529i
$498$	− 3362.18i	− 0.302536i
$499$	19319.0	1.73314	0.866570	−	0.499055i	$-0.166320\pi$
$499$	19319.0	1.73314	0.866570	+	0.499055i	$0.166320\pi$
$500$	0	0
$501$	6662.04	0.594088
$502$	4258.56i	0.378623i
$503$	12824.8i	1.13684i	0.822738	+	0.568421i	$0.192446\pi$
$503$	12824.8i	1.13684i	−0.822738	+	0.568421i	$0.807554\pi$
$504$	1223.05	0.108093
$505$	0	0
$506$	−1592.17	−0.139883
$507$	− 11093.9i	− 0.971790i
$508$	9436.76i	0.824190i
$509$	5978.67	0.520628	0.260314	−	0.965524i	$-0.416174\pi$
$509$	5978.67	0.520628	0.260314	+	0.965524i	$0.416174\pi$
$510$	0	0
$511$	6237.93	0.540019
$512$	− 7547.50i	− 0.651476i
$513$	− 382.479i	− 0.0329179i
$514$	−2705.90	−0.232202
$515$	0	0
$516$	−7138.51	−0.609022
$517$	− 3496.91i	− 0.297474i
$518$	137.134i	0.0116319i
$519$	5182.91	0.438351
$520$	0	0
$521$	4380.56	0.368361	0.184180	−	0.982892i	$-0.441037\pi$
$521$	4380.56	0.368361	0.184180	+	0.982892i	$0.441037\pi$
$522$	− 1114.31i	− 0.0934333i
$523$	− 3438.46i	− 0.287482i	−0.989615	−	0.143741i	$-0.954087\pi$
$523$	− 3438.46i	− 0.287482i	0.989615	−	0.143741i	$-0.0459133\pi$
$524$	−13788.0	−1.14949
$525$	0	0
$526$	3892.56	0.322669
$527$	28002.9i	2.31466i
$528$	1014.41i	0.0836110i
$529$	6435.03	0.528892
$530$	0	0
$531$	−3587.66	−0.293203
$532$	− 605.467i	− 0.0493427i
$533$	24470.1i	1.98859i
$534$	2684.04	0.217509
$535$	0	0
$536$	−5658.91	−0.456022
$537$	9997.00i	0.803357i
$538$	− 2275.17i	− 0.182322i
$539$	−748.740	−0.0598340
$540$	0	0
$541$	−13321.2	−1.05864	−0.529319	−	0.848423i	$-0.677552\pi$
$541$	−13321.2	−1.05864	−0.529319	+	0.848423i	$0.677552\pi$
$542$	7330.37i	0.580934i
$543$	3926.04i	0.310281i
$544$	17964.7	1.41586
$545$	0	0
$546$	2219.03	0.173930
$547$	− 14729.0i	− 1.15131i	−0.817693	−	0.575655i	$-0.804747\pi$
$547$	− 14729.0i	− 1.15131i	0.817693	−	0.575655i	$-0.195253\pi$
$548$	7587.88i	0.591493i
$549$	1317.25	0.102402
$550$	0	0
$551$	−1274.40	−0.0985322
$552$	− 4409.37i	− 0.339992i
$553$	− 2917.12i	− 0.224319i
$554$	7317.96	0.561210
$555$	0	0
$556$	−2476.98	−0.188934
$557$	18675.8i	1.42068i	0.703858	+	0.710341i	$0.251459\pi$
$557$	18675.8i	1.42068i	−0.703858	+	0.710341i	$0.748541\pi$
$558$	3586.66i	0.272106i
$559$	−29921.2	−2.26392
$560$	0	0
$561$	−4433.18	−0.333635
$562$	4933.32i	0.370284i
$563$	− 952.378i	− 0.0712929i	−0.999364	−	0.0356465i	$-0.988651\pi$
$563$	− 952.378i	− 0.0712929i	0.999364	−	0.0356465i	$-0.0113490\pi$
$564$	4191.98	0.312968
$565$	0	0
$566$	−1693.38	−0.125756
$567$	− 567.000i	− 0.0419961i
$568$	− 6469.22i	− 0.477892i
$569$	−9623.89	−0.709059	−0.354530	−	0.935045i	$-0.615359\pi$
$569$	−9623.89	−0.709059	−0.354530	+	0.935045i	$0.615359\pi$
$570$	0	0
$571$	−13532.6	−0.991804	−0.495902	−	0.868378i	$-0.665163\pi$
$571$	−13532.6	−0.991804	−0.495902	+	0.868378i	$0.665163\pi$
$572$	7163.48i	0.523636i
$573$	− 10635.9i	− 0.775429i
$574$	−3070.42	−0.223270
$575$	0	0
$576$	707.670	0.0511914
$577$	14504.0i	1.04646i	0.852191	+	0.523230i	$0.175273\pi$
$577$	14504.0i	1.04646i	−0.852191	+	0.523230i	$0.824727\pi$
$578$	6109.68i	0.439670i
$579$	−3231.95	−0.231978
$580$	0	0
$581$	−5700.26	−0.407034
$582$	6545.19i	0.466163i
$583$	10382.9i	0.737593i
$584$	17300.0	1.22582
$585$	0	0
$586$	−11760.1	−0.829019
$587$	− 25601.0i	− 1.80011i	−0.435775	−	0.900056i	$-0.643525\pi$
$587$	− 25601.0i	− 1.80011i	0.435775	−	0.900056i	$-0.356475\pi$
$588$	− 897.564i	− 0.0629506i
$589$	4101.92	0.286955
$590$	0	0
$591$	11400.7	0.793507
$592$	− 314.993i	− 0.0218685i
$593$	27481.9i	1.90311i	0.307475	+	0.951556i	$0.400516\pi$
$593$	27481.9i	1.90311i	−0.307475	+	0.951556i	$0.599484\pi$
$594$	−567.809	−0.0392214
$595$	0	0
$596$	−5388.15	−0.370314
$597$	− 7482.81i	− 0.512983i
$598$	− 8000.11i	− 0.547072i
$599$	−23862.6	−1.62771	−0.813855	−	0.581067i	$-0.802635\pi$
$599$	−23862.6	−1.62771	−0.813855	+	0.581067i	$0.802635\pi$
$600$	0	0
$601$	22709.4	1.54132	0.770661	−	0.637245i	$-0.219926\pi$
$601$	22709.4	1.54132	0.770661	+	0.637245i	$0.219926\pi$
$602$	− 3754.40i	− 0.254182i
$603$	2623.44i	0.177172i
$604$	13717.9	0.924126
$605$	0	0
$606$	−2048.47	−0.137316
$607$	7717.69i	0.516065i	0.966136	+	0.258032i	$0.0830741\pi$
$607$	7717.69i	0.516065i	−0.966136	+	0.258032i	$0.916926\pi$
$608$	− 2631.50i	− 0.175529i
$609$	−1889.21	−0.125706
$610$	0	0
$611$	17570.7	1.16340
$612$	− 5314.35i	− 0.351013i
$613$	− 12662.3i	− 0.834296i	−0.908839	−	0.417148i	$-0.863030\pi$
$613$	− 12662.3i	− 0.834296i	0.908839	−	0.417148i	$-0.136970\pi$
$614$	−2843.87	−0.186921
$615$	0	0
$616$	−2076.52	−0.135821
$617$	− 7990.11i	− 0.521345i	−0.965427	−	0.260672i	$-0.916056\pi$
$617$	− 7990.11i	− 0.521345i	0.965427	−	0.260672i	$-0.0839442\pi$
$618$	1934.10i	0.125891i
$619$	−16702.4	−1.08453	−0.542266	−	0.840207i	$-0.682433\pi$
$619$	−16702.4	−1.08453	−0.542266	+	0.840207i	$0.682433\pi$
$620$	0	0
$621$	−2044.16	−0.132093
$622$	− 10110.3i	− 0.651748i
$623$	− 4550.53i	− 0.292638i
$624$	−5097.06	−0.326997
$625$	0	0
$626$	8837.88	0.564270
$627$	649.382i	0.0413618i
$628$	− 18033.3i	− 1.14587i
$629$	1376.58	0.0872621
$630$	0	0
$631$	12762.2	0.805162	0.402581	−	0.915384i	$-0.368113\pi$
$631$	12762.2	0.805162	0.402581	+	0.915384i	$0.368113\pi$
$632$	− 8090.21i	− 0.509195i
$633$	− 12707.2i	− 0.797893i
$634$	1100.98	0.0689675
$635$	0	0
$636$	−12446.7	−0.776013
$637$	− 3762.16i	− 0.234006i
$638$	1891.91i	0.117400i
$639$	−2999.10	−0.185669
$640$	0	0
$641$	−29847.0	−1.83914	−0.919568	−	0.392931i	$-0.871461\pi$
$641$	−29847.0	−1.83914	−0.919568	+	0.392931i	$0.871461\pi$
$642$	− 8170.03i	− 0.502251i
$643$	− 11676.6i	− 0.716141i	−0.933695	−	0.358070i	$-0.883435\pi$
$643$	− 11676.6i	− 0.716141i	0.933695	−	0.358070i	$-0.116565\pi$
$644$	−3235.92	−0.198002
$645$	0	0
$646$	1885.42	0.114831
$647$	7200.41i	0.437523i	0.975778	+	0.218762i	$0.0702017\pi$
$647$	7200.41i	0.437523i	−0.975778	+	0.218762i	$0.929798\pi$
$648$	− 1572.49i	− 0.0953293i
$649$	6091.20	0.368414
$650$	0	0
$651$	6080.83	0.366093
$652$	− 636.852i	− 0.0382531i
$653$	− 18481.6i	− 1.10756i	−0.832662	−	0.553782i	$-0.813184\pi$
$653$	− 18481.6i	− 1.10756i	0.832662	−	0.553782i	$-0.186816\pi$
$654$	4168.84	0.249258
$655$	0	0
$656$	7052.67	0.419757
$657$	− 8020.19i	− 0.476252i
$658$	2204.71i	0.130621i
$659$	−26203.7	−1.54894	−0.774470	−	0.632611i	$-0.781983\pi$
$659$	−26203.7	−1.54894	−0.774470	+	0.632611i	$0.781983\pi$
$660$	0	0
$661$	4432.97	0.260851	0.130426	−	0.991458i	$-0.458366\pi$
$661$	4432.97	0.260851	0.130426	+	0.991458i	$0.458366\pi$
$662$	6129.46i	0.359861i
$663$	− 22275.2i	− 1.30482i
$664$	−15808.9	−0.923950
$665$	0	0
$666$	176.315	0.0102584
$667$	6811.03i	0.395389i
$668$	− 13559.2i	− 0.785361i
$669$	3824.10	0.220999
$670$	0	0
$671$	−2236.45	−0.128670
$672$	− 3901.03i	− 0.223937i
$673$	− 14535.9i	− 0.832570i	−0.909234	−	0.416285i	$-0.863332\pi$
$673$	− 14535.9i	− 0.832570i	0.909234	−	0.416285i	$-0.136668\pi$
$674$	−14832.8	−0.847681
$675$	0	0
$676$	−22579.3	−1.28467
$677$	14611.2i	0.829475i	0.909941	+	0.414737i	$0.136127\pi$
$677$	14611.2i	0.829475i	−0.909941	+	0.414737i	$0.863873\pi$
$678$	499.394i	0.0282878i
$679$	11096.7	0.627177
$680$	0	0
$681$	−8130.52	−0.457507
$682$	− 6089.51i	− 0.341905i
$683$	15735.8i	0.881570i	0.897613	+	0.440785i	$0.145300\pi$
$683$	15735.8i	0.881570i	−0.897613	+	0.440785i	$0.854700\pi$
$684$	−778.457	−0.0435162
$685$	0	0
$686$	472.061	0.0262731
$687$	− 4190.82i	− 0.232736i
$688$	8623.75i	0.477874i
$689$	−52170.6	−2.88467
$690$	0	0
$691$	18704.7	1.02975	0.514877	−	0.857264i	$-0.327838\pi$
$691$	18704.7	1.02975	0.514877	+	0.857264i	$0.327838\pi$
$692$	− 10548.7i	− 0.579484i
$693$	962.666i	0.0527686i
$694$	−9766.15	−0.534176
$695$	0	0
$696$	−5239.46	−0.285347
$697$	30821.6i	1.67497i
$698$	11423.5i	0.619465i
$699$	16886.4	0.913737
$700$	0	0
$701$	14341.3	0.772699	0.386349	−	0.922353i	$-0.373736\pi$
$701$	14341.3	0.772699	0.386349	+	0.922353i	$0.373736\pi$
$702$	− 2853.04i	− 0.153392i
$703$	− 201.645i	− 0.0108182i
$704$	−1201.50	−0.0643227
$705$	0	0
$706$	−12502.5	−0.666486
$707$	3472.98i	0.184745i
$708$	7301.93i	0.387604i
$709$	21041.9	1.11459	0.557295	−	0.830315i	$-0.311839\pi$
$709$	21041.9	1.11459	0.557295	+	0.830315i	$0.311839\pi$
$710$	0	0
$711$	−3750.58	−0.197831
$712$	− 12620.3i	− 0.664276i
$713$	− 21922.8i	− 1.15149i
$714$	2795.00	0.146499
$715$	0	0
$716$	20346.8	1.06201
$717$	− 10470.3i	− 0.545356i
$718$	− 7060.01i	− 0.366960i
$719$	18439.2	0.956422	0.478211	−	0.878245i	$-0.341285\pi$
$719$	18439.2	0.956422	0.478211	+	0.878245i	$0.341285\pi$
$720$	0	0
$721$	3279.08	0.169375
$722$	9163.66i	0.472349i
$723$	9233.43i	0.474959i
$724$	7990.64	0.410179
$725$	0	0
$726$	−4531.41	−0.231648
$727$	− 5826.21i	− 0.297224i	−0.988896	−	0.148612i	$-0.952519\pi$
$727$	− 5826.21i	− 0.297224i	0.988896	−	0.148612i	$-0.0474806\pi$
$728$	− 10433.8i	− 0.531185i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−37687.5	−1.90687
$732$	− 2680.99i	− 0.135372i
$733$	− 27711.8i	− 1.39640i	−0.715905	−	0.698198i	$-0.753986\pi$
$733$	− 27711.8i	− 1.39640i	0.715905	−	0.698198i	$-0.246014\pi$
$734$	−17993.4	−0.904834
$735$	0	0
$736$	−14064.1	−0.704360
$737$	− 4454.14i	− 0.222619i
$738$	3947.68i	0.196905i
$739$	32108.2	1.59827	0.799133	−	0.601154i	$-0.205292\pi$
$739$	32108.2	1.59827	0.799133	+	0.601154i	$0.205292\pi$
$740$	0	0
$741$	−3262.92	−0.161763
$742$	− 6546.16i	− 0.323878i
$743$	− 3004.06i	− 0.148329i	−0.997246	−	0.0741643i	$-0.976371\pi$
$743$	− 3004.06i	− 0.148329i	0.997246	−	0.0741643i	$-0.0236289\pi$
$744$	16864.3	0.831016
$745$	0	0
$746$	−5582.57	−0.273985
$747$	7328.91i	0.358970i
$748$	9022.82i	0.441052i
$749$	−13851.5	−0.675731
$750$	0	0
$751$	−12573.6	−0.610942	−0.305471	−	0.952201i	$-0.598814\pi$
$751$	−12573.6	−0.610942	−0.305471	+	0.952201i	$0.598814\pi$
$752$	− 5064.16i	− 0.245573i
$753$	− 9282.82i	− 0.449249i
$754$	−9506.17	−0.459144
$755$	0	0
$756$	−1154.01	−0.0555172
$757$	7518.76i	0.360996i	0.983575	+	0.180498i	$0.0577709\pi$
$757$	7518.76i	0.360996i	−0.983575	+	0.180498i	$0.942229\pi$
$758$	− 15957.2i	− 0.764635i
$759$	3470.63	0.165976
$760$	0	0
$761$	−41187.7	−1.96196	−0.980981	−	0.194105i	$-0.937820\pi$
$761$	−41187.7	−1.96196	−0.980981	+	0.194105i	$0.937820\pi$
$762$	6381.16i	0.303366i
$763$	− 7067.87i	− 0.335353i
$764$	−21647.1	−1.02509
$765$	0	0
$766$	15070.2	0.710847
$767$	30606.2i	1.44084i
$768$	− 7576.17i	− 0.355965i
$769$	28909.5	1.35566	0.677832	−	0.735217i	$-0.262920\pi$
$769$	28909.5	1.35566	0.677832	+	0.735217i	$0.262920\pi$
$770$	0	0
$771$	5898.33	0.275516
$772$	6577.97i	0.306666i
$773$	− 17242.4i	− 0.802285i	−0.916016	−	0.401142i	$-0.868613\pi$
$773$	− 17242.4i	− 0.802285i	0.916016	−	0.401142i	$-0.131387\pi$
$774$	−4827.08	−0.224168
$775$	0	0
$776$	30775.2	1.42367
$777$	− 298.925i	− 0.0138016i
$778$	− 3000.31i	− 0.138260i
$779$	4514.81	0.207651
$780$	0	0
$781$	5091.93	0.233295
$782$	− 10076.6i	− 0.460792i
$783$	2428.99i	0.110862i
$784$	−1084.31	−0.0493947
$785$	0	0
$786$	−9323.46	−0.423100
$787$	− 19396.4i	− 0.878535i	−0.898356	−	0.439267i	$-0.855238\pi$
$787$	− 19396.4i	− 0.878535i	0.898356	−	0.439267i	$-0.144762\pi$
$788$	− 23203.8i	− 1.04899i
$789$	−8485.03	−0.382858
$790$	0	0
$791$	846.674	0.0380585
$792$	2669.82i	0.119783i
$793$	− 11237.4i	− 0.503218i
$794$	−8449.24	−0.377648
$795$	0	0
$796$	−15229.7	−0.678144
$797$	14898.8i	0.662161i	0.943603	+	0.331080i	$0.107413\pi$
$797$	14898.8i	0.662161i	−0.943603	+	0.331080i	$0.892587\pi$
$798$	− 409.418i	− 0.0181620i
$799$	22131.4	0.979915
$800$	0	0
$801$	−5850.69	−0.258082
$802$	16087.3i	0.708307i
$803$	13616.9i	0.598417i
$804$	5339.47	0.234215
$805$	0	0
$806$	30597.6	1.33717
$807$	4959.42i	0.216332i
$808$	9631.80i	0.419363i
$809$	12088.9	0.525367	0.262684	−	0.964882i	$-0.415392\pi$
$809$	12088.9	0.525367	0.262684	+	0.964882i	$0.415392\pi$
$810$	0	0
$811$	9177.34	0.397361	0.198681	−	0.980064i	$-0.436334\pi$
$811$	9177.34	0.397361	0.198681	+	0.980064i	$0.436334\pi$
$812$	3845.10i	0.166178i
$813$	− 15978.8i	− 0.689299i
$814$	−299.351	−0.0128898
$815$	0	0
$816$	−6420.05	−0.275425
$817$	5520.55i	0.236401i
$818$	911.638i	0.0389666i
$819$	−4837.06	−0.206374
$820$	0	0
$821$	−5604.88	−0.238260	−0.119130	−	0.992879i	$-0.538011\pi$
$821$	−5604.88	−0.238260	−0.119130	+	0.992879i	$0.538011\pi$
$822$	5130.95i	0.217716i
$823$	39788.8i	1.68524i	0.538511	+	0.842619i	$0.318987\pi$
$823$	39788.8i	1.68524i	−0.538511	+	0.842619i	$0.681013\pi$
$824$	9094.06	0.384474
$825$	0	0
$826$	−3840.34	−0.161771
$827$	36668.7i	1.54183i	0.636937	+	0.770916i	$0.280201\pi$
$827$	36668.7i	1.54183i	−0.636937	+	0.770916i	$0.719799\pi$
$828$	4160.47i	0.174621i
$829$	−16027.0	−0.671460	−0.335730	−	0.941958i	$-0.608983\pi$
$829$	−16027.0	−0.671460	−0.335730	+	0.941958i	$0.608983\pi$
$830$	0	0
$831$	−15951.7	−0.665895
$832$	− 6037.11i	− 0.251561i
$833$	− 4738.66i	− 0.197101i
$834$	−1674.94	−0.0695425
$835$	0	0
$836$	1321.68	0.0546787
$837$	− 7818.21i	− 0.322863i
$838$	− 10204.1i	− 0.420637i
$839$	26562.9	1.09303	0.546515	−	0.837449i	$-0.315954\pi$
$839$	26562.9	1.09303	0.546515	+	0.837449i	$0.315954\pi$
$840$	0	0
$841$	−16295.8	−0.668160
$842$	− 13443.2i	− 0.550219i
$843$	− 10753.7i	− 0.439355i
$844$	−25862.9	−1.05478
$845$	0	0
$846$	2834.63	0.115197
$847$	7682.56i	0.311660i
$848$	15036.4i	0.608905i
$849$	3691.23	0.149214
$850$	0	0
$851$	−1077.69	−0.0434110
$852$	6104.04i	0.245447i
$853$	− 26089.3i	− 1.04722i	−0.851957	−	0.523611i	$-0.824584\pi$
$853$	− 26089.3i	− 1.04722i	0.851957	−	0.523611i	$-0.175416\pi$
$854$	1410.03	0.0564989
$855$	0	0
$856$	−38415.2	−1.53388
$857$	9551.99i	0.380735i	0.981713	+	0.190367i	$0.0609680\pi$
$857$	9551.99i	0.380735i	−0.981713	+	0.190367i	$0.939032\pi$
$858$	4843.96i	0.192739i
$859$	−29646.7	−1.17757	−0.588784	−	0.808290i	$-0.700393\pi$
$859$	−29646.7	−1.17757	−0.588784	+	0.808290i	$0.700393\pi$
$860$	0	0
$861$	6692.91	0.264917
$862$	23266.3i	0.919318i
$863$	5981.74i	0.235945i	0.993017	+	0.117973i	$0.0376395\pi$
$863$	5981.74i	0.235945i	−0.993017	+	0.117973i	$0.962360\pi$
$864$	−5015.61	−0.197494
$865$	0	0
$866$	15301.7	0.600431
$867$	− 13317.9i	− 0.521683i
$868$	− 12376.3i	− 0.483961i
$869$	6367.82	0.248577
$870$	0	0
$871$	22380.5	0.870647
$872$	− 19601.7i	− 0.761237i
$873$	− 14267.2i	− 0.553118i
$874$	−1476.05	−0.0571258
$875$	0	0
$876$	−16323.4	−0.629587
$877$	− 27503.4i	− 1.05898i	−0.848317	−	0.529488i	$-0.822384\pi$
$877$	− 27503.4i	− 1.05898i	0.848317	−	0.529488i	$-0.177616\pi$
$878$	3413.16i	0.131194i
$879$	25634.7	0.983661
$880$	0	0
$881$	27005.9	1.03275	0.516374	−	0.856363i	$-0.327281\pi$
$881$	27005.9	1.03275	0.516374	+	0.856363i	$0.327281\pi$
$882$	− 606.935i	− 0.0231707i
$883$	− 11434.3i	− 0.435782i	−0.975973	−	0.217891i	$-0.930082\pi$
$883$	− 11434.3i	− 0.435782i	0.975973	−	0.217891i	$-0.0699178\pi$
$884$	−45336.5	−1.72492
$885$	0	0
$886$	2387.30	0.0905225
$887$	13464.3i	0.509683i	0.966983	+	0.254841i	$0.0820233\pi$
$887$	13464.3i	0.509683i	−0.966983	+	0.254841i	$0.917977\pi$
$888$	− 829.025i	− 0.0313291i
$889$	10818.6	0.408150
$890$	0	0
$891$	1237.71	0.0465375
$892$	− 7783.16i	− 0.292152i
$893$	− 3241.85i	− 0.121483i
$894$	−3643.48	−0.136305
$895$	0	0
$896$	−9645.23	−0.359626
$897$	17438.7i	0.649120i
$898$	4800.55i	0.178392i
$899$	−26049.8	−0.966418
$900$	0	0
$901$	−65711.9	−2.42972
$902$	− 6702.46i	− 0.247414i
$903$	8183.85i	0.301596i
$904$	2348.13	0.0863912
$905$	0	0
$906$	9276.05	0.340150
$907$	− 1220.35i	− 0.0446760i	−0.999750	−	0.0223380i	$-0.992889\pi$
$907$	− 1220.35i	− 0.0446760i	0.999750	−	0.0223380i	$-0.00711100\pi$
$908$	16548.0i	0.604807i
$909$	4465.25	0.162930
$910$	0	0
$911$	−2651.77	−0.0964403	−0.0482201	−	0.998837i	$-0.515355\pi$
$911$	−2651.77	−0.0964403	−0.0482201	+	0.998837i	$0.515355\pi$
$912$	940.423i	0.0341453i
$913$	− 12443.2i	− 0.451051i
$914$	−5001.51	−0.181001
$915$	0	0
$916$	−8529.54	−0.307668
$917$	15807.0i	0.569241i
$918$	− 3593.57i	− 0.129200i
$919$	47600.3	1.70858	0.854291	−	0.519795i	$-0.173992\pi$
$919$	47600.3	1.70858	0.854291	+	0.519795i	$0.173992\pi$
$920$	0	0
$921$	6199.08	0.221788
$922$	− 10444.9i	− 0.373086i
$923$	25585.2i	0.912402i
$924$	1959.31	0.0697581
$925$	0	0
$926$	−8636.28	−0.306486
$927$	− 4215.96i	− 0.149375i
$928$	16711.7i	0.591152i
$929$	−1545.26	−0.0545729	−0.0272865	−	0.999628i	$-0.508687\pi$
$929$	−1545.26	−0.0545729	−0.0272865	+	0.999628i	$0.508687\pi$
$930$	0	0
$931$	−694.129	−0.0244352
$932$	− 34368.8i	− 1.20793i
$933$	22038.5i	0.773322i
$934$	16110.5	0.564402
$935$	0	0
$936$	−13414.9	−0.468461
$937$	53013.1i	1.84830i	0.382025	+	0.924152i	$0.375227\pi$
$937$	53013.1i	1.84830i	−0.382025	+	0.924152i	$0.624773\pi$
$938$	2808.22i	0.0977522i
$939$	−19264.9	−0.669526
$940$	0	0
$941$	19832.7	0.687066	0.343533	−	0.939141i	$-0.388376\pi$
$941$	19832.7	0.687066	0.343533	+	0.939141i	$0.388376\pi$
$942$	− 12194.2i	− 0.421770i
$943$	− 24129.5i	− 0.833259i
$944$	8821.17	0.304136
$945$	0	0
$946$	8195.53	0.281670
$947$	− 14700.2i	− 0.504428i	−0.967671	−	0.252214i	$-0.918841\pi$
$947$	− 14700.2i	− 0.504428i	0.967671	−	0.252214i	$-0.0811587\pi$
$948$	7633.53i	0.261525i
$949$	−68420.0	−2.34037
$950$	0	0
$951$	−2399.92	−0.0818324
$952$	− 13142.0i	− 0.447410i
$953$	39820.9i	1.35354i	0.736194	+	0.676770i	$0.236621\pi$
$953$	39820.9i	1.35354i	−0.736194	+	0.676770i	$0.763379\pi$
$954$	−8416.49	−0.285633
$955$	0	0
$956$	−21310.1	−0.720940
$957$	− 4123.99i	− 0.139299i
$958$	− 1159.96i	− 0.0391198i
$959$	8699.02	0.292916
$960$	0	0
$961$	54055.8	1.81450
$962$	− 1504.14i	− 0.0504109i
$963$	17809.1i	0.595939i
$964$	18792.7	0.627877
$965$	0	0
$966$	−2188.14	−0.0728801
$967$	− 50708.3i	− 1.68632i	−0.537663	−	0.843160i	$-0.680693\pi$
$967$	− 50708.3i	− 1.68632i	0.537663	−	0.843160i	$-0.319307\pi$
$968$	21306.5i	0.707455i
$969$	−4109.84	−0.136251
$970$	0	0
$971$	58395.2	1.92996	0.964980	−	0.262325i	$-0.0844892\pi$
$971$	58395.2	1.92996	0.964980	+	0.262325i	$0.0844892\pi$
$972$	1483.73i	0.0489615i
$973$	2839.70i	0.0935628i
$974$	−2162.10	−0.0711275
$975$	0	0
$976$	−3238.79	−0.106221
$977$	31028.9i	1.01607i	0.861336	+	0.508036i	$0.169628\pi$
$977$	31028.9i	1.01607i	−0.861336	+	0.508036i	$0.830372\pi$
$978$	− 430.641i	− 0.0140801i
$979$	9933.43	0.324284
$980$	0	0
$981$	−9087.26	−0.295753
$982$	− 17279.6i	− 0.561520i
$983$	− 4769.34i	− 0.154749i	−0.997002	−	0.0773746i	$-0.975346\pi$
$983$	− 4769.34i	− 0.154749i	0.997002	−	0.0773746i	$-0.0246537\pi$
$984$	18561.8	0.601351
$985$	0	0
$986$	−11973.6	−0.386731
$987$	− 4805.83i	− 0.154986i
$988$	6640.99i	0.213844i
$989$	29504.6	0.948627
$990$	0	0
$991$	6849.75	0.219566	0.109783	−	0.993956i	$-0.464984\pi$
$991$	6849.75	0.219566	0.109783	+	0.993956i	$0.464984\pi$
$992$	− 53790.2i	− 1.72161i
$993$	− 13361.0i	− 0.426988i
$994$	−3210.33	−0.102440
$995$	0	0
$996$	14916.5	0.474545
$997$	37344.1i	1.18626i	0.805107	+	0.593130i	$0.202108\pi$
$997$	37344.1i	1.18626i	−0.805107	+	0.593130i	$0.797892\pi$
$998$	− 26588.2i	− 0.843320i
$999$	−384.332	−0.0121719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.n.274.4		8
5.2	odd	4		525.4.a.u.1.3	yes	4
5.3	odd	4		525.4.a.t.1.2	✓	4
5.4	even	2	inner	525.4.d.n.274.5		8
15.2	even	4		1575.4.a.bk.1.2		4
15.8	even	4		1575.4.a.bj.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.t.1.2	✓	4	5.3	odd	4
525.4.a.u.1.3	yes	4	5.2	odd	4
525.4.d.n.274.4		8	1.1	even	1	trivial
525.4.d.n.274.5		8	5.4	even	2	inner
1575.4.a.bj.1.3		4	15.8	even	4
1575.4.a.bk.1.2		4	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.37627i q^{2} +3.00000i q^{3} +6.10588 q^{4} +4.12881 q^{6} -7.00000i q^{7} -19.4135i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-1.37627i q^{2} +3.00000i q^{3} +6.10588 q^{4} +4.12881 q^{6} -7.00000i q^{7} -19.4135i q^{8} -9.00000 q^{9} +15.2804 q^{11} +18.3176i q^{12} +76.7787i q^{13} -9.63389 q^{14} +22.1288 q^{16} +96.7073i q^{17} +12.3864i q^{18} +14.1659 q^{19} +21.0000 q^{21} -21.0300i q^{22} -75.7097i q^{23} +58.2405 q^{24} +105.668 q^{26} -27.0000i q^{27} -42.7412i q^{28} -89.9625 q^{29} +289.563 q^{31} -185.763i q^{32} +45.8412i q^{33} +133.095 q^{34} -54.9529 q^{36} -14.2345i q^{37} -19.4961i q^{38} -230.336 q^{39} +318.710 q^{41} -28.9017i q^{42} +389.707i q^{43} +93.3003 q^{44} -104.197 q^{46} -228.849i q^{47} +66.3864i q^{48} -49.0000 q^{49} -290.122 q^{51} +468.801i q^{52} +679.493i q^{53} -37.1593 q^{54} -135.895 q^{56} +42.4977i q^{57} +123.813i q^{58} +398.628 q^{59} -146.361 q^{61} -398.517i q^{62} +63.0000i q^{63} -78.6300 q^{64} +63.0899 q^{66} -291.493i q^{67} +590.483i q^{68} +227.129 q^{69} +333.233 q^{71} +174.722i q^{72} +891.133i q^{73} -19.5905 q^{74} +86.4953 q^{76} -106.963i q^{77} +317.005i q^{78} +416.731 q^{79} +81.0000 q^{81} -438.631i q^{82} -814.323i q^{83} +128.223 q^{84} +536.342 q^{86} -269.887i q^{87} -296.646i q^{88} +650.076 q^{89} +537.451 q^{91} -462.275i q^{92} +868.690i q^{93} -314.958 q^{94} +557.290 q^{96} +1585.25i q^{97} +67.4372i q^{98} -137.524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} - 72 q^{9}+O(q^{10}) \) 8 * q - 32 * q^4 - 72 * q^9	\( 8 q - 32 q^{4} - 72 q^{9} + 42 q^{11} + 144 q^{16} - 144 q^{19} + 168 q^{21} - 54 q^{24} + 258 q^{26} + 480 q^{29} + 702 q^{31} + 570 q^{34} + 288 q^{36} - 30 q^{39} + 762 q^{41} + 1950 q^{44} + 1100 q^{46} - 392 q^{49} + 594 q^{51} + 126 q^{56} + 1710 q^{59} + 1374 q^{61} + 2570 q^{64} + 1326 q^{66} - 612 q^{69} - 1362 q^{71} + 6738 q^{74} + 3820 q^{76} - 690 q^{79} + 648 q^{81} - 672 q^{84} - 1080 q^{86} + 396 q^{89} + 70 q^{91} + 3464 q^{94} + 432 q^{96} - 378 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 - 72 * q^9 + 42 * q^11 + 144 * q^16 - 144 * q^19 + 168 * q^21 - 54 * q^24 + 258 * q^26 + 480 * q^29 + 702 * q^31 + 570 * q^34 + 288 * q^36 - 30 * q^39 + 762 * q^41 + 1950 * q^44 + 1100 * q^46 - 392 * q^49 + 594 * q^51 + 126 * q^56 + 1710 * q^59 + 1374 * q^61 + 2570 * q^64 + 1326 * q^66 - 612 * q^69 - 1362 * q^71 + 6738 * q^74 + 3820 * q^76 - 690 * q^79 + 648 * q^81 - 672 * q^84 - 1080 * q^86 + 396 * q^89 + 70 * q^91 + 3464 * q^94 + 432 * q^96 - 378 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more