LMFDB - Embedded newform 525.4.d.n.274.8

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			274.8
Root			$4.75345i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.n.274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.75345i q^{2} -3.00000i q^{3} -14.5953 q^{4} +14.2604 q^{6} +7.00000i q^{7} -31.3504i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+4.75345i q^{2} -3.00000i q^{3} -14.5953 q^{4} +14.2604 q^{6} +7.00000i q^{7} -31.3504i q^{8} -9.00000 q^{9} +7.31799 q^{11} +43.7859i q^{12} +4.15422i q^{13} -33.2742 q^{14} +32.2604 q^{16} +53.5216i q^{17} -42.7811i q^{18} -88.9019 q^{19} +21.0000 q^{21} +34.7857i q^{22} -156.780i q^{23} -94.0513 q^{24} -19.7469 q^{26} +27.0000i q^{27} -102.167i q^{28} -42.2570 q^{29} -14.0248 q^{31} -97.4554i q^{32} -21.9540i q^{33} -254.412 q^{34} +131.358 q^{36} -293.336i q^{37} -422.591i q^{38} +12.4627 q^{39} -127.214 q^{41} +99.8225i q^{42} +210.189i q^{43} -106.808 q^{44} +745.244 q^{46} -468.688i q^{47} -96.7811i q^{48} -49.0000 q^{49} +160.565 q^{51} -60.6321i q^{52} -115.973i q^{53} -128.343 q^{54} +219.453 q^{56} +266.706i q^{57} -200.867i q^{58} +314.090 q^{59} +768.386 q^{61} -66.6662i q^{62} -63.0000i q^{63} +721.332 q^{64} +104.357 q^{66} -717.081i q^{67} -781.164i q^{68} -470.339 q^{69} -737.783 q^{71} +282.154i q^{72} -477.618i q^{73} +1394.36 q^{74} +1297.55 q^{76} +51.2259i q^{77} +59.2407i q^{78} +279.262 q^{79} +81.0000 q^{81} -604.703i q^{82} -776.981i q^{83} -306.501 q^{84} -999.123 q^{86} +126.771i q^{87} -229.422i q^{88} +29.7626 q^{89} -29.0796 q^{91} +2288.24i q^{92} +42.0744i q^{93} +2227.88 q^{94} -292.366 q^{96} -231.793i q^{97} -232.919i q^{98} -65.8619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.75345i	1.68060i	0.542123	+	0.840299i	$0.317621\pi$
$2$	4.75345i	1.68060i	−0.542123	+	0.840299i	$0.682379\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−14.5953	−1.82441
$5$	0	0
$5$	0	0
$6$	14.2604	0.970294
$7$	7.00000i	0.377964i
$7$	7.00000i	0.377964i
$8$	− 31.3504i	− 1.38551i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	7.31799	0.200587	0.100293	−	0.994958i	$-0.468022\pi$
$11$	7.31799	0.200587	0.100293	+	0.994958i	$0.468022\pi$
$12$	43.7859i	1.05332i
$13$	4.15422i	0.0886288i	0.999018	+	0.0443144i	$0.0141103\pi$
$13$	4.15422i	0.0886288i	−0.999018	+	0.0443144i	$0.985890\pi$
$14$	−33.2742	−0.635207
$15$	0	0
$16$	32.2604	0.504068
$17$	53.5216i	0.763582i	0.924249	+	0.381791i	$0.124693\pi$
$17$	53.5216i	0.763582i	−0.924249	+	0.381791i	$0.875307\pi$
$18$	− 42.7811i	− 0.560200i
$19$	−88.9019	−1.07345	−0.536724	−	0.843758i	$-0.680338\pi$
$19$	−88.9019	−1.07345	−0.536724	+	0.843758i	$0.680338\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	34.7857i	0.337106i
$23$	− 156.780i	− 1.42134i	−0.703526	−	0.710670i	$-0.748392\pi$
$23$	− 156.780i	− 1.42134i	0.703526	−	0.710670i	$-0.251608\pi$
$24$	−94.0513	−0.799922
$25$	0	0
$26$	−19.7469	−0.148949
$27$	27.0000i	0.192450i
$28$	− 102.167i	− 0.689563i
$29$	−42.2570	−0.270584	−0.135292	−	0.990806i	$-0.543197\pi$
$29$	−42.2570	−0.270584	−0.135292	+	0.990806i	$0.543197\pi$
$30$	0	0
$31$	−14.0248	−0.0812557	−0.0406279	−	0.999174i	$-0.512936\pi$
$31$	−14.0248	−0.0812557	−0.0406279	+	0.999174i	$0.512936\pi$
$32$	− 97.4554i	− 0.538370i
$33$	− 21.9540i	− 0.115809i
$34$	−254.412	−1.28328
$35$	0	0
$36$	131.358	0.608137
$37$	− 293.336i	− 1.30335i	−0.758496	−	0.651677i	$-0.774066\pi$
$37$	− 293.336i	− 1.30335i	0.758496	−	0.651677i	$-0.225934\pi$
$38$	− 422.591i	− 1.80403i
$39$	12.4627	0.0511699
$40$	0	0
$41$	−127.214	−0.484571	−0.242286	−	0.970205i	$-0.577897\pi$
$41$	−127.214	−0.484571	−0.242286	+	0.970205i	$0.577897\pi$
$42$	99.8225i	0.366737i
$43$	210.189i	0.745431i	0.927946	+	0.372715i	$0.121573\pi$
$43$	210.189i	0.745431i	−0.927946	+	0.372715i	$0.878427\pi$
$44$	−106.808	−0.365953
$45$	0	0
$46$	745.244	2.38870
$47$	− 468.688i	− 1.45458i	−0.686332	−	0.727289i	$-0.740780\pi$
$47$	− 468.688i	− 1.45458i	0.686332	−	0.727289i	$-0.259220\pi$
$48$	− 96.7811i	− 0.291024i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	160.565	0.440854
$52$	− 60.6321i	− 0.161696i
$53$	− 115.973i	− 0.300569i	−0.988643	−	0.150285i	$-0.951981\pi$
$53$	− 115.973i	− 0.300569i	0.988643	−	0.150285i	$-0.0480190\pi$
$54$	−128.343	−0.323431
$55$	0	0
$56$	219.453	0.523672
$57$	266.706i	0.619755i
$58$	− 200.867i	− 0.454743i
$59$	314.090	0.693069	0.346534	−	0.938037i	$-0.387358\pi$
$59$	314.090	0.693069	0.346534	+	0.938037i	$0.387358\pi$
$60$	0	0
$61$	768.386	1.61281	0.806407	−	0.591361i	$-0.201409\pi$
$61$	768.386	1.61281	0.806407	+	0.591361i	$0.201409\pi$
$62$	− 66.6662i	− 0.136558i
$63$	− 63.0000i	− 0.125988i
$64$	721.332	1.40885
$65$	0	0
$66$	104.357	0.194628
$67$	− 717.081i	− 1.30754i	−0.756692	−	0.653772i	$-0.773186\pi$
$67$	− 717.081i	− 1.30754i	0.756692	−	0.653772i	$-0.226814\pi$
$68$	− 781.164i	− 1.39309i
$69$	−470.339	−0.820610
$70$	0	0
$71$	−737.783	−1.23322	−0.616611	−	0.787268i	$-0.711495\pi$
$71$	−737.783	−1.23322	−0.616611	+	0.787268i	$0.711495\pi$
$72$	282.154i	0.461835i
$73$	− 477.618i	− 0.765767i	−0.923797	−	0.382884i	$-0.874931\pi$
$73$	− 477.618i	− 0.765767i	0.923797	−	0.382884i	$-0.125069\pi$
$74$	1394.36	2.19042
$75$	0	0
$76$	1297.55	1.95841
$77$	51.2259i	0.0758147i
$78$	59.2407i	0.0859960i
$79$	279.262	0.397714	0.198857	−	0.980029i	$-0.436277\pi$
$79$	279.262	0.397714	0.198857	+	0.980029i	$0.436277\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 604.703i	− 0.814370i
$83$	− 776.981i	− 1.02753i	−0.857932	−	0.513764i	$-0.828251\pi$
$83$	− 776.981i	− 1.02753i	0.857932	−	0.513764i	$-0.171749\pi$
$84$	−306.501	−0.398119
$85$	0	0
$86$	−999.123	−1.25277
$87$	126.771i	0.156222i
$88$	− 229.422i	− 0.277914i
$89$	29.7626	0.0354476	0.0177238	−	0.999843i	$-0.494358\pi$
$89$	29.7626	0.0354476	0.0177238	+	0.999843i	$0.494358\pi$
$90$	0	0
$91$	−29.0796	−0.0334985
$92$	2288.24i	2.59311i
$93$	42.0744i	0.0469130i
$94$	2227.88	2.44456
$95$	0	0
$96$	−292.366	−0.310828
$97$	− 231.793i	− 0.242629i	−0.992614	−	0.121314i	$-0.961289\pi$
$97$	− 231.793i	− 0.242629i	0.992614	−	0.121314i	$-0.0387109\pi$
$98$	− 232.919i	− 0.240086i
$99$	−65.8619	−0.0668623
$100$	0	0
$101$	−1898.26	−1.87014	−0.935069	−	0.354467i	$-0.884662\pi$
$101$	−1898.26	−1.87014	−0.935069	+	0.354467i	$0.884662\pi$
$102$	763.237i	0.740899i
$103$	− 1375.67i	− 1.31601i	−0.753015	−	0.658003i	$-0.771401\pi$
$103$	− 1375.67i	− 1.31601i	0.753015	−	0.658003i	$-0.228599\pi$
$104$	130.237	0.122796
$105$	0	0
$106$	551.274	0.505136
$107$	166.359i	0.150304i	0.997172	+	0.0751521i	$0.0239442\pi$
$107$	166.359i	0.150304i	−0.997172	+	0.0751521i	$0.976056\pi$
$108$	− 394.073i	− 0.351108i
$109$	1346.00	1.18279	0.591393	−	0.806383i	$-0.298578\pi$
$109$	1346.00	1.18279	0.591393	+	0.806383i	$0.298578\pi$
$110$	0	0
$111$	−880.008	−0.752492
$112$	225.822i	0.190520i
$113$	1322.25i	1.10077i	0.834911	+	0.550386i	$0.185519\pi$
$113$	1322.25i	1.10077i	−0.834911	+	0.550386i	$0.814481\pi$
$114$	−1267.77	−1.04156
$115$	0	0
$116$	616.754	0.493657
$117$	− 37.3880i	− 0.0295429i
$118$	1493.01i	1.16477i
$119$	−374.651	−0.288607
$120$	0	0
$121$	−1277.45	−0.959765
$122$	3652.48i	2.71049i
$123$	381.641i	0.279767i
$124$	204.696	0.148244
$125$	0	0
$126$	299.467	0.211736
$127$	2111.85i	1.47556i	0.675040	+	0.737781i	$0.264126\pi$
$127$	2111.85i	1.47556i	−0.675040	+	0.737781i	$0.735874\pi$
$128$	2649.18i	1.82935i
$129$	630.567	0.430375
$130$	0	0
$131$	−209.773	−0.139908	−0.0699541	−	0.997550i	$-0.522285\pi$
$131$	−209.773	−0.139908	−0.0699541	+	0.997550i	$0.522285\pi$
$132$	320.425i	0.211283i
$133$	− 622.313i	− 0.405725i
$134$	3408.61	2.19746
$135$	0	0
$136$	1677.93	1.05795
$137$	2386.27i	1.48812i	0.668111	+	0.744062i	$0.267103\pi$
$137$	2386.27i	1.48812i	−0.668111	+	0.744062i	$0.732897\pi$
$138$	− 2235.73i	− 1.37912i
$139$	−1215.45	−0.741675	−0.370838	−	0.928698i	$-0.620929\pi$
$139$	−1215.45	−0.741675	−0.370838	+	0.928698i	$0.620929\pi$
$140$	0	0
$141$	−1406.06	−0.839801
$142$	− 3507.01i	− 2.07255i
$143$	30.4006i	0.0177778i
$144$	−290.343	−0.168023
$145$	0	0
$146$	2270.34	1.28695
$147$	147.000i	0.0824786i
$148$	4281.33i	2.37786i
$149$	−2849.51	−1.56672	−0.783359	−	0.621570i	$-0.786495\pi$
$149$	−2849.51	−1.56672	−0.783359	+	0.621570i	$0.786495\pi$
$150$	0	0
$151$	−2643.84	−1.42485	−0.712426	−	0.701747i	$-0.752403\pi$
$151$	−2643.84	−1.42485	−0.712426	+	0.701747i	$0.752403\pi$
$152$	2787.11i	1.48727i
$153$	− 481.695i	− 0.254527i
$154$	−243.500	−0.127414
$155$	0	0
$156$	−181.896	−0.0933549
$157$	− 2563.09i	− 1.30291i	−0.758688	−	0.651454i	$-0.774159\pi$
$157$	− 2563.09i	− 1.30291i	0.758688	−	0.651454i	$-0.225841\pi$
$158$	1327.46i	0.668398i
$159$	−347.920	−0.173534
$160$	0	0
$161$	1097.46	0.537216
$162$	385.030i	0.186733i
$163$	1403.46i	0.674400i	0.941433	+	0.337200i	$0.109480\pi$
$163$	1403.46i	0.674400i	−0.941433	+	0.337200i	$0.890520\pi$
$164$	1856.72	0.884057
$165$	0	0
$166$	3693.34	1.72686
$167$	− 2658.97i	− 1.23208i	−0.787715	−	0.616040i	$-0.788736\pi$
$167$	− 2658.97i	− 1.23208i	0.787715	−	0.616040i	$-0.211264\pi$
$168$	− 658.359i	− 0.302342i
$169$	2179.74	0.992145
$170$	0	0
$171$	800.117	0.357816
$172$	− 3067.77i	− 1.35997i
$173$	− 3763.19i	− 1.65382i	−0.562336	−	0.826909i	$-0.690097\pi$
$173$	− 3763.19i	− 1.65382i	0.562336	−	0.826909i	$-0.309903\pi$
$174$	−602.600	−0.262546
$175$	0	0
$176$	236.081	0.101109
$177$	− 942.270i	− 0.400143i
$178$	141.475i	0.0595731i
$179$	1056.94	0.441336	0.220668	−	0.975349i	$-0.429176\pi$
$179$	1056.94	0.441336	0.220668	+	0.975349i	$0.429176\pi$
$180$	0	0
$181$	537.439	0.220705	0.110352	−	0.993893i	$-0.464802\pi$
$181$	537.439	0.220705	0.110352	+	0.993893i	$0.464802\pi$
$182$	− 138.228i	− 0.0562976i
$183$	− 2305.16i	− 0.931159i
$184$	−4915.11	−1.96927
$185$	0	0
$186$	−199.999	−0.0788420
$187$	391.670i	0.153165i
$188$	6840.64i	2.65375i
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−3236.34	−1.22604	−0.613020	−	0.790068i	$-0.710045\pi$
$191$	−3236.34	−1.22604	−0.613020	+	0.790068i	$0.710045\pi$
$192$	− 2164.00i	− 0.813401i
$193$	− 4620.71i	− 1.72335i	−0.507464	−	0.861673i	$-0.669417\pi$
$193$	− 4620.71i	− 1.72335i	0.507464	−	0.861673i	$-0.330583\pi$
$194$	1101.82	0.407762
$195$	0	0
$196$	715.170	0.260630
$197$	− 2519.57i	− 0.911230i	−0.890177	−	0.455615i	$-0.849419\pi$
$197$	− 2519.57i	− 0.911230i	0.890177	−	0.455615i	$-0.150581\pi$
$198$	− 313.071i	− 0.112369i
$199$	2121.77	0.755819	0.377910	−	0.925842i	$-0.376643\pi$
$199$	2121.77	0.755819	0.377910	+	0.925842i	$0.376643\pi$
$200$	0	0
$201$	−2151.24	−0.754911
$202$	− 9023.28i	− 3.14295i
$203$	− 295.799i	− 0.102271i
$204$	−2343.49	−0.804300
$205$	0	0
$206$	6539.17	2.21168
$207$	1411.02i	0.473780i
$208$	134.017i	0.0446750i
$209$	−650.583	−0.215319
$210$	0	0
$211$	−1557.91	−0.508297	−0.254149	−	0.967165i	$-0.581795\pi$
$211$	−1557.91	−0.508297	−0.254149	+	0.967165i	$0.581795\pi$
$212$	1692.67i	0.548362i
$213$	2213.35i	0.712001i
$214$	−790.780	−0.252601
$215$	0	0
$216$	846.462	0.266641
$217$	− 98.1736i	− 0.0307118i
$218$	6398.16i	1.98779i
$219$	−1432.85	−0.442116
$220$	0	0
$221$	−222.341	−0.0676754
$222$	− 4183.07i	− 1.26464i
$223$	− 1319.83i	− 0.396333i	−0.980168	−	0.198167i	$-0.936501\pi$
$223$	− 1319.83i	− 0.396333i	0.980168	−	0.198167i	$-0.0634987\pi$
$224$	682.188	0.203485
$225$	0	0
$226$	−6285.27	−1.84995
$227$	6442.42i	1.88369i	0.336043	+	0.941847i	$0.390911\pi$
$227$	6442.42i	1.88369i	−0.336043	+	0.941847i	$0.609089\pi$
$228$	− 3892.65i	− 1.13069i
$229$	−4654.11	−1.34302	−0.671511	−	0.740995i	$-0.734354\pi$
$229$	−4654.11	−1.34302	−0.671511	+	0.740995i	$0.734354\pi$
$230$	0	0
$231$	153.678	0.0437716
$232$	1324.78i	0.374896i
$233$	2628.61i	0.739080i	0.929215	+	0.369540i	$0.120485\pi$
$233$	2628.61i	0.739080i	−0.929215	+	0.369540i	$0.879515\pi$
$234$	177.722	0.0496498
$235$	0	0
$236$	−4584.24	−1.26444
$237$	− 837.786i	− 0.229620i
$238$	− 1780.89i	− 0.485033i
$239$	−586.369	−0.158699	−0.0793495	−	0.996847i	$-0.525284\pi$
$239$	−586.369	−0.158699	−0.0793495	+	0.996847i	$0.525284\pi$
$240$	0	0
$241$	3141.71	0.839731	0.419865	−	0.907586i	$-0.362077\pi$
$241$	3141.71	0.839731	0.419865	+	0.907586i	$0.362077\pi$
$242$	− 6072.28i	− 1.61298i
$243$	− 243.000i	− 0.0641500i
$244$	−11214.8	−2.94244
$245$	0	0
$246$	−1814.11	−0.470176
$247$	− 369.318i	− 0.0951383i
$248$	439.683i	0.112580i
$249$	−2330.94	−0.593243
$250$	0	0
$251$	−2929.38	−0.736656	−0.368328	−	0.929696i	$-0.620070\pi$
$251$	−2929.38	−0.736656	−0.368328	+	0.929696i	$0.620070\pi$
$252$	919.504i	0.229854i
$253$	− 1147.31i	− 0.285102i
$254$	−10038.6	−2.47983
$255$	0	0
$256$	−6822.07	−1.66554
$257$	− 388.552i	− 0.0943081i	−0.998888	−	0.0471541i	$-0.984985\pi$
$257$	− 388.552i	− 0.0943081i	0.998888	−	0.0471541i	$-0.0150152\pi$
$258$	2997.37i	0.723287i
$259$	2053.35	0.492622
$260$	0	0
$261$	380.313	0.0901946
$262$	− 997.147i	− 0.235130i
$263$	− 766.349i	− 0.179677i	−0.995956	−	0.0898387i	$-0.971365\pi$
$263$	− 766.349i	− 0.179677i	0.995956	−	0.0898387i	$-0.0286351\pi$
$264$	−688.266	−0.160454
$265$	0	0
$266$	2958.14	0.681861
$267$	− 89.2879i	− 0.0204657i
$268$	10466.0i	2.38550i
$269$	−2842.03	−0.644170	−0.322085	−	0.946711i	$-0.604384\pi$
$269$	−2842.03	−0.644170	−0.322085	+	0.946711i	$0.604384\pi$
$270$	0	0
$271$	3512.72	0.787390	0.393695	−	0.919241i	$-0.371197\pi$
$271$	3512.72	0.787390	0.393695	+	0.919241i	$0.371197\pi$
$272$	1726.63i	0.384897i
$273$	87.2387i	0.0193404i
$274$	−11343.0	−2.50094
$275$	0	0
$276$	6864.73	1.49713
$277$	6388.71i	1.38578i	0.721044	+	0.692889i	$0.243663\pi$
$277$	6388.71i	1.38578i	−0.721044	+	0.692889i	$0.756337\pi$
$278$	− 5777.57i	− 1.24646i
$279$	126.223	0.0270852
$280$	0	0
$281$	−2126.77	−0.451503	−0.225752	−	0.974185i	$-0.572484\pi$
$281$	−2126.77	−0.451503	−0.225752	+	0.974185i	$0.572484\pi$
$282$	− 6683.65i	− 1.41137i
$283$	− 8332.13i	− 1.75015i	−0.483983	−	0.875077i	$-0.660810\pi$
$283$	− 8332.13i	− 1.75015i	0.483983	−	0.875077i	$-0.339190\pi$
$284$	10768.2	2.24990
$285$	0	0
$286$	−144.508	−0.0298773
$287$	− 890.495i	− 0.183151i
$288$	877.099i	0.179457i
$289$	2048.44	0.416942
$290$	0	0
$291$	−695.379	−0.140082
$292$	6970.98i	1.39707i
$293$	8654.11i	1.72552i	0.505610	+	0.862762i	$0.331267\pi$
$293$	8654.11i	1.72552i	−0.505610	+	0.862762i	$0.668733\pi$
$294$	−698.757	−0.138613
$295$	0	0
$296$	−9196.21	−1.80581
$297$	197.586i	0.0386030i
$298$	− 13545.0i	− 2.63302i
$299$	651.297	0.125972
$300$	0	0
$301$	−1471.32	−0.281746
$302$	− 12567.4i	− 2.39460i
$303$	5694.78i	1.07972i
$304$	−2868.01	−0.541090
$305$	0	0
$306$	2289.71	0.427758
$307$	5318.56i	0.988749i	0.869249	+	0.494375i	$0.164603\pi$
$307$	5318.56i	0.988749i	−0.869249	+	0.494375i	$0.835397\pi$
$308$	− 747.657i	− 0.138317i
$309$	−4127.00	−0.759796
$310$	0	0
$311$	−7097.87	−1.29416	−0.647079	−	0.762423i	$-0.724010\pi$
$311$	−7097.87	−1.29416	−0.647079	+	0.762423i	$0.724010\pi$
$312$	− 390.710i	− 0.0708962i
$313$	2080.78i	0.375759i	0.982192	+	0.187879i	$0.0601614\pi$
$313$	2080.78i	0.375759i	−0.982192	+	0.187879i	$0.939839\pi$
$314$	12183.5	2.18967
$315$	0	0
$316$	−4075.91	−0.725595
$317$	2644.61i	0.468568i	0.972168	+	0.234284i	$0.0752745\pi$
$317$	2644.61i	0.468568i	−0.972168	+	0.234284i	$0.924725\pi$
$318$	− 1653.82i	− 0.291641i
$319$	−309.236	−0.0542756
$320$	0	0
$321$	499.078	0.0867782
$322$	5216.71i	0.902844i
$323$	− 4758.17i	− 0.819665i
$324$	−1182.22	−0.202712
$325$	0	0
$326$	−6671.26	−1.13340
$327$	− 4038.01i	− 0.682882i
$328$	3988.20i	0.671376i
$329$	3280.81	0.549779
$330$	0	0
$331$	−1831.16	−0.304077	−0.152039	−	0.988375i	$-0.548584\pi$
$331$	−1831.16	−0.304077	−0.152039	+	0.988375i	$0.548584\pi$
$332$	11340.3i	1.87463i
$333$	2640.02i	0.434452i
$334$	12639.3	2.07063
$335$	0	0
$336$	677.467	0.109997
$337$	9307.67i	1.50451i	0.658870	+	0.752257i	$0.271035\pi$
$337$	9307.67i	1.50451i	−0.658870	+	0.752257i	$0.728965\pi$
$338$	10361.3i	1.66740i
$339$	3966.76	0.635531
$340$	0	0
$341$	−102.633	−0.0162988
$342$	3803.32i	0.601345i
$343$	− 343.000i	− 0.0539949i
$344$	6589.52	1.03280
$345$	0	0
$346$	17888.2	2.77940
$347$	− 10802.7i	− 1.67124i	−0.549310	−	0.835619i	$-0.685109\pi$
$347$	− 10802.7i	− 1.67124i	0.549310	−	0.835619i	$-0.314891\pi$
$348$	− 1850.26i	− 0.285013i
$349$	−2242.94	−0.344017	−0.172009	−	0.985095i	$-0.555026\pi$
$349$	−2242.94	−0.344017	−0.172009	+	0.985095i	$0.555026\pi$
$350$	0	0
$351$	−112.164	−0.0170566
$352$	− 713.177i	− 0.107990i
$353$	− 3295.68i	− 0.496916i	−0.968643	−	0.248458i	$-0.920076\pi$
$353$	− 3295.68i	− 0.496916i	0.968643	−	0.248458i	$-0.0799238\pi$
$354$	4479.04	0.672480
$355$	0	0
$356$	−434.395	−0.0646710
$357$	1123.95i	0.166627i
$358$	5024.09i	0.741709i
$359$	4634.55	0.681344	0.340672	−	0.940182i	$-0.389345\pi$
$359$	4634.55	0.681344	0.340672	+	0.940182i	$0.389345\pi$
$360$	0	0
$361$	1044.55	0.152289
$362$	2554.69i	0.370916i
$363$	3832.34i	0.554121i
$364$	424.425	0.0611152
$365$	0	0
$366$	10957.4	1.56490
$367$	6316.17i	0.898369i	0.893439	+	0.449185i	$0.148285\pi$
$367$	6316.17i	0.898369i	−0.893439	+	0.449185i	$0.851715\pi$
$368$	− 5057.76i	− 0.716452i
$369$	1144.92	0.161524
$370$	0	0
$371$	811.814	0.113604
$372$	− 614.088i	− 0.0855887i
$373$	7880.83i	1.09398i	0.837140	+	0.546989i	$0.184226\pi$
$373$	7880.83i	1.09398i	−0.837140	+	0.546989i	$0.815774\pi$
$374$	−1861.79	−0.257408
$375$	0	0
$376$	−14693.6	−2.01533
$377$	− 175.545i	− 0.0239815i
$378$	− 898.402i	− 0.122246i
$379$	−9853.13	−1.33541	−0.667706	−	0.744425i	$-0.732724\pi$
$379$	−9853.13	−1.33541	−0.667706	+	0.744425i	$0.732724\pi$
$380$	0	0
$381$	6335.55	0.851916
$382$	− 15383.8i	− 2.06048i
$383$	− 1193.49i	− 0.159228i	−0.996826	−	0.0796141i	$-0.974631\pi$
$383$	− 1193.49i	− 0.159228i	0.996826	−	0.0796141i	$-0.0253688\pi$
$384$	7947.53	1.05617
$385$	0	0
$386$	21964.3	2.89625
$387$	− 1891.70i	− 0.248477i
$388$	3383.09i	0.442655i
$389$	10425.7	1.35888	0.679442	−	0.733729i	$-0.262222\pi$
$389$	10425.7	1.35888	0.679442	+	0.733729i	$0.262222\pi$
$390$	0	0
$391$	8391.09	1.08531
$392$	1536.17i	0.197929i
$393$	629.320i	0.0807761i
$394$	11976.7	1.53141
$395$	0	0
$396$	961.274	0.121984
$397$	3650.05i	0.461437i	0.973021	+	0.230719i	$0.0741077\pi$
$397$	3650.05i	0.461437i	−0.973021	+	0.230719i	$0.925892\pi$
$398$	10085.7i	1.27023i
$399$	−1866.94	−0.234245
$400$	0	0
$401$	−8202.17	−1.02144	−0.510719	−	0.859747i	$-0.670621\pi$
$401$	−8202.17	−1.02144	−0.510719	+	0.859747i	$0.670621\pi$
$402$	− 10225.8i	− 1.26870i
$403$	− 58.2622i	− 0.00720160i
$404$	27705.7	3.41190
$405$	0	0
$406$	1406.07	0.171877
$407$	− 2146.63i	− 0.261436i
$408$	− 5033.78i	− 0.610807i
$409$	−9097.72	−1.09989	−0.549943	−	0.835202i	$-0.685351\pi$
$409$	−9097.72	−1.09989	−0.549943	+	0.835202i	$0.685351\pi$
$410$	0	0
$411$	7158.81	0.859169
$412$	20078.3i	2.40094i
$413$	2198.63i	0.261955i
$414$	−6707.20	−0.796234
$415$	0	0
$416$	404.852	0.0477151
$417$	3646.34i	0.428206i
$418$	− 3092.51i	− 0.361866i
$419$	4704.01	0.548462	0.274231	−	0.961664i	$-0.411577\pi$
$419$	4704.01	0.548462	0.274231	+	0.961664i	$0.411577\pi$
$420$	0	0
$421$	1596.95	0.184871	0.0924355	−	0.995719i	$-0.470535\pi$
$421$	1596.95	0.184871	0.0924355	+	0.995719i	$0.470535\pi$
$422$	− 7405.44i	− 0.854244i
$423$	4218.19i	0.484859i
$424$	−3635.82	−0.416441
$425$	0	0
$426$	−10521.0	−1.19659
$427$	5378.70i	0.609587i
$428$	− 2428.06i	− 0.274217i
$429$	91.2017	0.0102640
$430$	0	0
$431$	6235.23	0.696845	0.348423	−	0.937338i	$-0.386717\pi$
$431$	6235.23	0.696845	0.348423	+	0.937338i	$0.386717\pi$
$432$	871.030i	0.0970079i
$433$	− 2363.94i	− 0.262364i	−0.991358	−	0.131182i	$-0.958123\pi$
$433$	− 2363.94i	− 0.262364i	0.991358	−	0.131182i	$-0.0418772\pi$
$434$	466.663	0.0516142
$435$	0	0
$436$	−19645.3	−2.15789
$437$	13938.0i	1.52573i
$438$	− 6811.01i	− 0.743019i
$439$	17537.7	1.90667	0.953335	−	0.301916i	$-0.0976261\pi$
$439$	17537.7	1.90667	0.953335	+	0.301916i	$0.0976261\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	− 1056.89i	− 0.113735i
$443$	4488.83i	0.481424i	0.970597	+	0.240712i	$0.0773809\pi$
$443$	4488.83i	0.481424i	−0.970597	+	0.240712i	$0.922619\pi$
$444$	12844.0	1.37286
$445$	0	0
$446$	6273.74	0.666077
$447$	8548.53i	0.904544i
$448$	5049.33i	0.532496i
$449$	−13188.3	−1.38618	−0.693090	−	0.720851i	$-0.743751\pi$
$449$	−13188.3	−1.38618	−0.693090	+	0.720851i	$0.743751\pi$
$450$	0	0
$451$	−930.947	−0.0971986
$452$	− 19298.7i	− 2.00826i
$453$	7931.52i	0.822638i
$454$	−30623.7	−3.16573
$455$	0	0
$456$	8361.34	0.858674
$457$	8085.04i	0.827576i	0.910373	+	0.413788i	$0.135794\pi$
$457$	8085.04i	0.827576i	−0.910373	+	0.413788i	$0.864206\pi$
$458$	− 22123.1i	− 2.25708i
$459$	−1445.08	−0.146951
$460$	0	0
$461$	−825.258	−0.0833754	−0.0416877	−	0.999131i	$-0.513273\pi$
$461$	−825.258	−0.0833754	−0.0416877	+	0.999131i	$0.513273\pi$
$462$	730.499i	0.0735626i
$463$	− 16607.8i	− 1.66702i	−0.552505	−	0.833509i	$-0.686328\pi$
$463$	− 16607.8i	− 1.66702i	0.552505	−	0.833509i	$-0.313672\pi$
$464$	−1363.23	−0.136393
$465$	0	0
$466$	−12495.0	−1.24210
$467$	6003.84i	0.594914i	0.954735	+	0.297457i	$0.0961385\pi$
$467$	6003.84i	0.594914i	−0.954735	+	0.297457i	$0.903862\pi$
$468$	545.689i	0.0538985i
$469$	5019.57	0.494205
$470$	0	0
$471$	−7689.26	−0.752235
$472$	− 9846.86i	− 0.960251i
$473$	1538.16i	0.149524i
$474$	3982.37	0.385900
$475$	0	0
$476$	5468.15	0.526538
$477$	1043.76i	0.100190i
$478$	− 2787.28i	− 0.266709i
$479$	−20386.0	−1.94459	−0.972295	−	0.233759i	$-0.924897\pi$
$479$	−20386.0	−1.94459	−0.972295	+	0.233759i	$0.924897\pi$
$480$	0	0
$481$	1218.58	0.115515
$482$	14933.9i	1.41125i
$483$	− 3292.37i	− 0.310162i
$484$	18644.7	1.75101
$485$	0	0
$486$	1155.09	0.107810
$487$	9422.61i	0.876754i	0.898791	+	0.438377i	$0.144447\pi$
$487$	9422.61i	0.876754i	−0.898791	+	0.438377i	$0.855553\pi$
$488$	− 24089.2i	− 2.23456i
$489$	4210.37	0.389365
$490$	0	0
$491$	5908.30	0.543051	0.271525	−	0.962431i	$-0.412472\pi$
$491$	5908.30	0.543051	0.271525	+	0.962431i	$0.412472\pi$
$492$	− 5570.16i	− 0.510411i
$493$	− 2261.66i	− 0.206613i
$494$	1755.54	0.159889
$495$	0	0
$496$	−452.445	−0.0409584
$497$	− 5164.48i	− 0.466114i
$498$	− 11080.0i	− 0.997003i
$499$	3237.65	0.290455	0.145227	−	0.989398i	$-0.453609\pi$
$499$	3237.65	0.290455	0.145227	+	0.989398i	$0.453609\pi$
$500$	0	0
$501$	−7976.92	−0.711342
$502$	− 13924.7i	− 1.23802i
$503$	− 1112.05i	− 0.0985760i	−0.998785	−	0.0492880i	$-0.984305\pi$
$503$	− 1112.05i	− 0.0985760i	0.998785	−	0.0492880i	$-0.0156952\pi$
$504$	−1975.08	−0.174557
$505$	0	0
$506$	5453.68	0.479142
$507$	− 6539.23i	− 0.572815i
$508$	− 30823.1i	− 2.69203i
$509$	−15737.5	−1.37044	−0.685220	−	0.728336i	$-0.740294\pi$
$509$	−15737.5	−1.37044	−0.685220	+	0.728336i	$0.740294\pi$
$510$	0	0
$511$	3343.33	0.289433
$512$	− 11235.0i	− 0.969765i
$513$	− 2400.35i	− 0.206585i
$514$	1846.96	0.158494
$515$	0	0
$516$	−9203.32	−0.785181
$517$	− 3429.85i	− 0.291769i
$518$	9760.51i	0.827900i
$519$	−11289.6	−0.954832
$520$	0	0
$521$	−5009.73	−0.421267	−0.210633	−	0.977565i	$-0.567553\pi$
$521$	−5009.73	−0.421267	−0.210633	+	0.977565i	$0.567553\pi$
$522$	1807.80i	0.151581i
$523$	− 14162.2i	− 1.18407i	−0.805912	−	0.592035i	$-0.798325\pi$
$523$	− 14162.2i	− 1.18407i	0.805912	−	0.592035i	$-0.201675\pi$
$524$	3061.70	0.255250
$525$	0	0
$526$	3642.80	0.301965
$527$	− 750.630i	− 0.0620454i
$528$	− 708.242i	− 0.0583756i
$529$	−12412.8	−1.02020
$530$	0	0
$531$	−2826.81	−0.231023
$532$	9082.85i	0.740209i
$533$	− 528.474i	− 0.0429470i
$534$	424.426	0.0343946
$535$	0	0
$536$	−22480.8	−1.81161
$537$	− 3170.81i	− 0.254805i
$538$	− 13509.5i	− 1.08259i
$539$	−358.581	−0.0286553
$540$	0	0
$541$	14815.3	1.17738	0.588689	−	0.808360i	$-0.299644\pi$
$541$	14815.3	1.17738	0.588689	+	0.808360i	$0.299644\pi$
$542$	16697.5i	1.32329i
$543$	− 1612.32i	− 0.127424i
$544$	5215.97	0.411090
$545$	0	0
$546$	−414.685	−0.0325034
$547$	14248.3i	1.11373i	0.830601	+	0.556867i	$0.187997\pi$
$547$	14248.3i	1.11373i	−0.830601	+	0.556867i	$0.812003\pi$
$548$	− 34828.3i	− 2.71495i
$549$	−6915.47	−0.537605
$550$	0	0
$551$	3756.73	0.290458
$552$	14745.3i	1.13696i
$553$	1954.83i	0.150322i
$554$	−30368.4	−2.32894
$555$	0	0
$556$	17739.8	1.35312
$557$	9394.37i	0.714636i	0.933983	+	0.357318i	$0.116309\pi$
$557$	9394.37i	0.714636i	−0.933983	+	0.357318i	$0.883691\pi$
$558$	599.996i	0.0455194i
$559$	−873.173	−0.0660667
$560$	0	0
$561$	1175.01	0.0884296
$562$	− 10109.5i	− 0.758796i
$563$	8572.89i	0.641748i	0.947122	+	0.320874i	$0.103977\pi$
$563$	8572.89i	0.641748i	−0.947122	+	0.320874i	$0.896023\pi$
$564$	20521.9	1.53214
$565$	0	0
$566$	39606.4	2.94131
$567$	567.000i	0.0419961i
$568$	23129.8i	1.70864i
$569$	−8954.65	−0.659751	−0.329876	−	0.944024i	$-0.607007\pi$
$569$	−8954.65	−0.659751	−0.329876	+	0.944024i	$0.607007\pi$
$570$	0	0
$571$	21592.5	1.58252	0.791260	−	0.611479i	$-0.209425\pi$
$571$	21592.5	1.58252	0.791260	+	0.611479i	$0.209425\pi$
$572$	− 443.705i	− 0.0324340i
$573$	9709.03i	0.707854i
$574$	4232.92	0.307803
$575$	0	0
$576$	−6491.99	−0.469617
$577$	− 17587.5i	− 1.26894i	−0.772947	−	0.634470i	$-0.781218\pi$
$577$	− 17587.5i	− 1.26894i	0.772947	−	0.634470i	$-0.218782\pi$
$578$	9737.14i	0.700712i
$579$	−13862.1	−0.994974
$580$	0	0
$581$	5438.87	0.388369
$582$	− 3305.45i	− 0.235421i
$583$	− 848.692i	− 0.0602903i
$584$	−14973.5	−1.06098
$585$	0	0
$586$	−41136.9	−2.89991
$587$	− 4613.88i	− 0.324421i	−0.986756	−	0.162210i	$-0.948138\pi$
$587$	− 4613.88i	− 0.324421i	0.986756	−	0.162210i	$-0.0518623\pi$
$588$	− 2145.51i	− 0.150475i
$589$	1246.83	0.0872237
$590$	0	0
$591$	−7558.72	−0.526099
$592$	− 9463.12i	− 0.656980i
$593$	8688.07i	0.601647i	0.953680	+	0.300823i	$0.0972614\pi$
$593$	8688.07i	0.601647i	−0.953680	+	0.300823i	$0.902739\pi$
$594$	−939.214	−0.0648761
$595$	0	0
$596$	41589.4	2.85834
$597$	− 6365.30i	− 0.436372i
$598$	3095.91i	0.211708i
$599$	−7361.43	−0.502137	−0.251068	−	0.967969i	$-0.580782\pi$
$599$	−7361.43	−0.502137	−0.251068	+	0.967969i	$0.580782\pi$
$600$	0	0
$601$	16441.9	1.11594	0.557971	−	0.829861i	$-0.311580\pi$
$601$	16441.9	1.11594	0.557971	+	0.829861i	$0.311580\pi$
$602$	− 6993.86i	− 0.473503i
$603$	6453.73i	0.435848i
$604$	38587.6	2.59952
$605$	0	0
$606$	−27069.9	−1.81458
$607$	− 21024.5i	− 1.40586i	−0.711258	−	0.702931i	$-0.751874\pi$
$607$	− 21024.5i	− 1.40586i	0.711258	−	0.702931i	$-0.248126\pi$
$608$	8663.97i	0.577912i
$609$	−887.398	−0.0590463
$610$	0	0
$611$	1947.03	0.128917
$612$	7030.48i	0.464363i
$613$	− 3278.79i	− 0.216034i	−0.994149	−	0.108017i	$-0.965550\pi$
$613$	− 3278.79i	− 0.216034i	0.994149	−	0.108017i	$-0.0344501\pi$
$614$	−25281.5	−1.66169
$615$	0	0
$616$	1605.95	0.105042
$617$	136.641i	0.00891567i	0.999990	+	0.00445783i	$0.00141898\pi$
$617$	136.641i	0.00891567i	−0.999990	+	0.00445783i	$0.998581\pi$
$618$	− 19617.5i	− 1.27691i
$619$	13109.0	0.851205	0.425603	−	0.904910i	$-0.360062\pi$
$619$	13109.0	0.851205	0.425603	+	0.904910i	$0.360062\pi$
$620$	0	0
$621$	4233.05	0.273537
$622$	− 33739.4i	− 2.17496i
$623$	208.338i	0.0133979i
$624$	402.050	0.0257931
$625$	0	0
$626$	−9890.87	−0.631500
$627$	1951.75i	0.124315i
$628$	37409.0i	2.37704i
$629$	15699.8	0.995219
$630$	0	0
$631$	−351.608	−0.0221827	−0.0110913	−	0.999938i	$-0.503531\pi$
$631$	−351.608	−0.0221827	−0.0110913	+	0.999938i	$0.503531\pi$
$632$	− 8754.98i	− 0.551035i
$633$	4673.72i	0.293466i
$634$	−12571.0	−0.787474
$635$	0	0
$636$	5078.00	0.316597
$637$	− 203.557i	− 0.0126613i
$638$	− 1469.94i	− 0.0912155i
$639$	6640.04	0.411074
$640$	0	0
$641$	−17551.0	−1.08147	−0.540736	−	0.841192i	$-0.681854\pi$
$641$	−17551.0	−1.08147	−0.540736	+	0.841192i	$0.681854\pi$
$642$	2372.34i	0.145839i
$643$	− 20683.7i	− 1.26856i	−0.773103	−	0.634281i	$-0.781296\pi$
$643$	− 20683.7i	− 1.26856i	0.773103	−	0.634281i	$-0.218704\pi$
$644$	−16017.7	−0.980103
$645$	0	0
$646$	22617.7	1.37753
$647$	1782.40i	0.108305i	0.998533	+	0.0541526i	$0.0172457\pi$
$647$	1782.40i	0.108305i	−0.998533	+	0.0541526i	$0.982754\pi$
$648$	− 2539.38i	− 0.153945i
$649$	2298.51	0.139020
$650$	0	0
$651$	−294.521	−0.0177315
$652$	− 20483.9i	− 1.23038i
$653$	3642.28i	0.218275i	0.994027	+	0.109137i	$0.0348088\pi$
$653$	3642.28i	0.218275i	−0.994027	+	0.109137i	$0.965191\pi$
$654$	19194.5	1.14765
$655$	0	0
$656$	−4103.95	−0.244257
$657$	4298.56i	0.255256i
$658$	15595.2i	0.923957i
$659$	14883.2	0.879768	0.439884	−	0.898055i	$-0.355020\pi$
$659$	14883.2	0.879768	0.439884	+	0.898055i	$0.355020\pi$
$660$	0	0
$661$	−1871.82	−0.110145	−0.0550723	−	0.998482i	$-0.517539\pi$
$661$	−1871.82	−0.110145	−0.0550723	+	0.998482i	$0.517539\pi$
$662$	− 8704.33i	− 0.511032i
$663$	667.022i	0.0390724i
$664$	−24358.7	−1.42365
$665$	0	0
$666$	−12549.2	−0.730139
$667$	6625.04i	0.384592i
$668$	38808.5i	2.24782i
$669$	−3959.49	−0.228823
$670$	0	0
$671$	5623.03	0.323509
$672$	− 2046.56i	− 0.117482i
$673$	22208.8i	1.27205i	0.771670	+	0.636023i	$0.219422\pi$
$673$	22208.8i	1.27205i	−0.771670	+	0.636023i	$0.780578\pi$
$674$	−44243.6	−2.52848
$675$	0	0
$676$	−31814.0	−1.81008
$677$	− 31340.2i	− 1.77918i	−0.456762	−	0.889589i	$-0.650991\pi$
$677$	− 31340.2i	− 1.77918i	0.456762	−	0.889589i	$-0.349009\pi$
$678$	18855.8i	1.06807i
$679$	1622.55	0.0917051
$680$	0	0
$681$	19327.3	1.08755
$682$	− 487.862i	− 0.0273918i
$683$	− 27666.5i	− 1.54997i	−0.631979	−	0.774985i	$-0.717757\pi$
$683$	− 27666.5i	− 1.54997i	0.631979	−	0.774985i	$-0.282243\pi$
$684$	−11677.9	−0.652803
$685$	0	0
$686$	1630.43	0.0907438
$687$	13962.3i	0.775394i
$688$	6780.77i	0.375748i
$689$	481.780	0.0266391
$690$	0	0
$691$	−7978.64	−0.439250	−0.219625	−	0.975584i	$-0.570483\pi$
$691$	−7978.64	−0.439250	−0.219625	+	0.975584i	$0.570483\pi$
$692$	54925.0i	3.01724i
$693$	− 461.033i	− 0.0252716i
$694$	51350.1	2.80868
$695$	0	0
$696$	3974.33	0.216446
$697$	− 6808.67i	− 0.370010i
$698$	− 10661.7i	− 0.578155i
$699$	7885.82	0.426708
$700$	0	0
$701$	−16299.3	−0.878197	−0.439099	−	0.898439i	$-0.644702\pi$
$701$	−16299.3	−0.878197	−0.439099	+	0.898439i	$0.644702\pi$
$702$	− 533.166i	− 0.0286653i
$703$	26078.1i	1.39908i
$704$	5278.70	0.282597
$705$	0	0
$706$	15665.8	0.835116
$707$	− 13287.8i	− 0.706845i
$708$	13752.7i	0.730026i
$709$	36223.4	1.91876	0.959379	−	0.282122i	$-0.0910382\pi$
$709$	36223.4	1.91876	0.959379	+	0.282122i	$0.0910382\pi$
$710$	0	0
$711$	−2513.36	−0.132571
$712$	− 933.071i	− 0.0491128i
$713$	2198.80i	0.115492i
$714$	−5342.66	−0.280034
$715$	0	0
$716$	−15426.3	−0.805179
$717$	1759.11i	0.0916249i
$718$	22030.1i	1.14507i
$719$	636.264	0.0330023	0.0165011	−	0.999864i	$-0.494747\pi$
$719$	636.264	0.0330023	0.0165011	+	0.999864i	$0.494747\pi$
$720$	0	0
$721$	9629.67	0.497403
$722$	4965.21i	0.255936i
$723$	− 9425.12i	− 0.484819i
$724$	−7844.08	−0.402656
$725$	0	0
$726$	−18216.8	−0.931254
$727$	− 33098.8i	− 1.68854i	−0.535918	−	0.844270i	$-0.680035\pi$
$727$	− 33098.8i	− 1.68854i	0.535918	−	0.844270i	$-0.319965\pi$
$728$	911.657i	0.0464124i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−11249.7	−0.569198
$732$	33644.4i	1.69882i
$733$	12019.8i	0.605678i	0.953042	+	0.302839i	$0.0979345\pi$
$733$	12019.8i	0.605678i	−0.953042	+	0.302839i	$0.902066\pi$
$734$	−30023.6	−1.50980
$735$	0	0
$736$	−15279.0	−0.765207
$737$	− 5247.59i	− 0.262276i
$738$	5442.33i	0.271457i
$739$	−5332.38	−0.265433	−0.132716	−	0.991154i	$-0.542370\pi$
$739$	−5332.38	−0.265433	−0.132716	+	0.991154i	$0.542370\pi$
$740$	0	0
$741$	−1107.96	−0.0549281
$742$	3858.92i	0.190924i
$743$	− 6547.51i	− 0.323290i	−0.986849	−	0.161645i	$-0.948320\pi$
$743$	− 6547.51i	− 0.323290i	0.986849	−	0.161645i	$-0.0516800\pi$
$744$	1319.05	0.0649983
$745$	0	0
$746$	−37461.1	−1.83854
$747$	6992.83i	0.342509i
$748$	− 5716.55i	− 0.279435i
$749$	−1164.51	−0.0568097
$750$	0	0
$751$	19316.3	0.938565	0.469282	−	0.883048i	$-0.344513\pi$
$751$	19316.3	0.938565	0.469282	+	0.883048i	$0.344513\pi$
$752$	− 15120.0i	− 0.733206i
$753$	8788.14i	0.425309i
$754$	834.446	0.0403033
$755$	0	0
$756$	2758.51	0.132706
$757$	40483.3i	1.94371i	0.235573	+	0.971857i	$0.424303\pi$
$757$	40483.3i	1.94371i	−0.235573	+	0.971857i	$0.575697\pi$
$758$	− 46836.3i	− 2.24429i
$759$	−3441.93	−0.164604
$760$	0	0
$761$	−5470.00	−0.260561	−0.130281	−	0.991477i	$-0.541588\pi$
$761$	−5470.00	−0.260561	−0.130281	+	0.991477i	$0.541588\pi$
$762$	30115.7i	1.43173i
$763$	9422.02i	0.447051i
$764$	47235.4	2.23680
$765$	0	0
$766$	5673.19	0.267599
$767$	1304.80i	0.0614258i
$768$	20466.2i	0.961602i
$769$	−17692.4	−0.829653	−0.414826	−	0.909901i	$-0.636158\pi$
$769$	−17692.4	−0.829653	−0.414826	+	0.909901i	$0.636158\pi$
$770$	0	0
$771$	−1165.65	−0.0544488
$772$	67440.6i	3.14409i
$773$	3338.50i	0.155340i	0.996979	+	0.0776699i	$0.0247480\pi$
$773$	3338.50i	0.155340i	−0.996979	+	0.0776699i	$0.975252\pi$
$774$	8992.11	0.417590
$775$	0	0
$776$	−7266.81	−0.336164
$777$	− 6160.05i	− 0.284415i
$778$	49558.2i	2.28374i
$779$	11309.5	0.520161
$780$	0	0
$781$	−5399.08	−0.247368
$782$	39886.7i	1.82397i
$783$	− 1140.94i	− 0.0520739i
$784$	−1580.76	−0.0720097
$785$	0	0
$786$	−2991.44	−0.135752
$787$	11738.0i	0.531657i	0.964020	+	0.265829i	$0.0856456\pi$
$787$	11738.0i	0.531657i	−0.964020	+	0.265829i	$0.914354\pi$
$788$	36773.9i	1.66246i
$789$	−2299.05	−0.103737
$790$	0	0
$791$	−9255.77	−0.416052
$792$	2064.80i	0.0926381i
$793$	3192.05i	0.142942i
$794$	−17350.3	−0.775491
$795$	0	0
$796$	−30967.8	−1.37893
$797$	− 20150.5i	− 0.895568i	−0.894142	−	0.447784i	$-0.852213\pi$
$797$	− 20150.5i	− 0.895568i	0.894142	−	0.447784i	$-0.147787\pi$
$798$	− 8874.41i	− 0.393672i
$799$	25084.9	1.11069
$800$	0	0
$801$	−267.864	−0.0118159
$802$	− 38988.6i	− 1.71663i
$803$	− 3495.20i	− 0.153603i
$804$	31398.0	1.37727
$805$	0	0
$806$	276.946	0.0121030
$807$	8526.09i	0.371912i
$808$	59511.3i	2.59109i
$809$	3381.53	0.146957	0.0734785	−	0.997297i	$-0.476590\pi$
$809$	3381.53	0.146957	0.0734785	+	0.997297i	$0.476590\pi$
$810$	0	0
$811$	11375.3	0.492528	0.246264	−	0.969203i	$-0.420797\pi$
$811$	11375.3	0.492528	0.246264	+	0.969203i	$0.420797\pi$
$812$	4317.28i	0.186585i
$813$	− 10538.2i	− 0.454600i
$814$	10203.9	0.439369
$815$	0	0
$816$	5179.88	0.222221
$817$	− 18686.2i	− 0.800181i
$818$	− 43245.6i	− 1.84847i
$819$	261.716	0.0111662
$820$	0	0
$821$	−9610.94	−0.408556	−0.204278	−	0.978913i	$-0.565485\pi$
$821$	−9610.94	−0.408556	−0.204278	+	0.978913i	$0.565485\pi$
$822$	34029.1i	1.44392i
$823$	− 13767.3i	− 0.583109i	−0.956554	−	0.291555i	$-0.905827\pi$
$823$	− 13767.3i	− 0.583109i	0.956554	−	0.291555i	$-0.0941725\pi$
$824$	−43127.8	−1.82333
$825$	0	0
$826$	−10451.1	−0.440242
$827$	31978.6i	1.34462i	0.740268	+	0.672312i	$0.234699\pi$
$827$	31978.6i	1.34462i	−0.740268	+	0.672312i	$0.765301\pi$
$828$	− 20594.2i	− 0.864369i
$829$	−18477.2	−0.774111	−0.387055	−	0.922056i	$-0.626508\pi$
$829$	−18477.2	−0.774111	−0.387055	+	0.922056i	$0.626508\pi$
$830$	0	0
$831$	19166.1	0.800080
$832$	2996.58i	0.124865i
$833$	− 2622.56i	− 0.109083i
$834$	−17332.7	−0.719643
$835$	0	0
$836$	9495.45	0.392831
$837$	− 378.669i	− 0.0156377i
$838$	22360.3i	0.921745i
$839$	38552.6	1.58639	0.793196	−	0.608967i	$-0.208416\pi$
$839$	38552.6	1.58639	0.793196	+	0.608967i	$0.208416\pi$
$840$	0	0
$841$	−22603.3	−0.926784
$842$	7591.04i	0.310694i
$843$	6380.31i	0.260676i
$844$	22738.1	0.927344
$845$	0	0
$846$	−20051.0	−0.814854
$847$	− 8942.13i	− 0.362757i
$848$	− 3741.34i	− 0.151507i
$849$	−24996.4	−1.01045
$850$	0	0
$851$	−45989.1	−1.85251
$852$	− 32304.5i	− 1.29898i
$853$	− 3080.15i	− 0.123637i	−0.998087	−	0.0618185i	$-0.980310\pi$
$853$	− 3080.15i	− 0.123637i	0.998087	−	0.0618185i	$-0.0196900\pi$
$854$	−25567.4	−1.02447
$855$	0	0
$856$	5215.43	0.208247
$857$	− 28362.3i	− 1.13050i	−0.824920	−	0.565249i	$-0.808780\pi$
$857$	− 28362.3i	− 1.13050i	0.824920	−	0.565249i	$-0.191220\pi$
$858$	433.523i	0.0172497i
$859$	4928.50	0.195761	0.0978803	−	0.995198i	$-0.468794\pi$
$859$	4928.50	0.195761	0.0978803	+	0.995198i	$0.468794\pi$
$860$	0	0
$861$	−2671.48	−0.105742
$862$	29638.9i	1.17112i
$863$	− 39910.8i	− 1.57425i	−0.616792	−	0.787126i	$-0.711568\pi$
$863$	− 39910.8i	− 1.57425i	0.616792	−	0.787126i	$-0.288432\pi$
$864$	2631.30	0.103609
$865$	0	0
$866$	11236.9	0.440928
$867$	− 6145.31i	− 0.240722i
$868$	1432.87i	0.0560309i
$869$	2043.63	0.0797762
$870$	0	0
$871$	2978.92	0.115886
$872$	− 42197.8i	− 1.63876i
$873$	2086.14i	0.0808763i
$874$	−66253.6	−2.56414
$875$	0	0
$876$	20912.9	0.806602
$877$	− 29231.5i	− 1.12552i	−0.826621	−	0.562759i	$-0.809740\pi$
$877$	− 29231.5i	− 1.12552i	0.826621	−	0.562759i	$-0.190260\pi$
$878$	83364.5i	3.20435i
$879$	25962.3	0.996232
$880$	0	0
$881$	−23473.3	−0.897657	−0.448829	−	0.893618i	$-0.648159\pi$
$881$	−23473.3	−0.897657	−0.448829	+	0.893618i	$0.648159\pi$
$882$	2096.27i	0.0800285i
$883$	− 21250.7i	− 0.809902i	−0.914338	−	0.404951i	$-0.867289\pi$
$883$	− 21250.7i	− 0.809902i	0.914338	−	0.404951i	$-0.132711\pi$
$884$	3245.13	0.123468
$885$	0	0
$886$	−21337.4	−0.809080
$887$	− 48748.6i	− 1.84534i	−0.385588	−	0.922671i	$-0.626001\pi$
$887$	− 48748.6i	− 1.84534i	0.385588	−	0.922671i	$-0.373999\pi$
$888$	27588.6i	1.04258i
$889$	−14783.0	−0.557710
$890$	0	0
$891$	592.757	0.0222874
$892$	19263.3i	0.723075i
$893$	41667.2i	1.56141i
$894$	−40635.0	−1.52018
$895$	0	0
$896$	−18544.2	−0.691428
$897$	− 1953.89i	− 0.0727297i
$898$	− 62690.0i	− 2.32961i
$899$	592.646	0.0219865
$900$	0	0
$901$	6207.08	0.229509
$902$	− 4425.21i	− 0.163352i
$903$	4413.97i	0.162666i
$904$	41453.2	1.52513
$905$	0	0
$906$	−37702.1	−1.38253
$907$	− 13144.5i	− 0.481209i	−0.970623	−	0.240604i	$-0.922654\pi$
$907$	− 13144.5i	− 0.481209i	0.970623	−	0.240604i	$-0.0773456\pi$
$908$	− 94029.0i	− 3.43663i
$909$	17084.3	0.623379
$910$	0	0
$911$	−29731.7	−1.08129	−0.540644	−	0.841251i	$-0.681819\pi$
$911$	−29731.7	−1.08129	−0.540644	+	0.841251i	$0.681819\pi$
$912$	8604.02i	0.312399i
$913$	− 5685.94i	− 0.206108i
$914$	−38431.8	−1.39082
$915$	0	0
$916$	67928.1	2.45022
$917$	− 1468.41i	− 0.0528803i
$918$	− 6869.13i	− 0.246966i
$919$	47715.4	1.71272	0.856358	−	0.516383i	$-0.172722\pi$
$919$	47715.4	1.71272	0.856358	+	0.516383i	$0.172722\pi$
$920$	0	0
$921$	15955.7	0.570855
$922$	− 3922.82i	− 0.140121i
$923$	− 3064.92i	− 0.109299i
$924$	−2242.97	−0.0798575
$925$	0	0
$926$	78944.4	2.80159
$927$	12381.0i	0.438669i
$928$	4118.18i	0.145674i
$929$	19795.2	0.699094	0.349547	−	0.936919i	$-0.386335\pi$
$929$	19795.2	0.699094	0.349547	+	0.936919i	$0.386335\pi$
$930$	0	0
$931$	4356.19	0.153350
$932$	− 38365.3i	− 1.34839i
$933$	21293.6i	0.747183i
$934$	−28539.0	−0.999811
$935$	0	0
$936$	−1172.13	−0.0409319
$937$	− 17993.9i	− 0.627359i	−0.949529	−	0.313680i	$-0.898438\pi$
$937$	− 17993.9i	− 0.627359i	0.949529	−	0.313680i	$-0.101562\pi$
$938$	23860.3i	0.830560i
$939$	6242.33	0.216944
$940$	0	0
$941$	−34667.7	−1.20099	−0.600497	−	0.799627i	$-0.705030\pi$
$941$	−34667.7	−1.20099	−0.600497	+	0.799627i	$0.705030\pi$
$942$	− 36550.5i	− 1.26420i
$943$	19944.5i	0.688740i
$944$	10132.7	0.349354
$945$	0	0
$946$	−7311.57	−0.251289
$947$	− 56727.3i	− 1.94656i	−0.229627	−	0.973279i	$-0.573751\pi$
$947$	− 56727.3i	− 1.94656i	0.229627	−	0.973279i	$-0.426249\pi$
$948$	12227.7i	0.418922i
$949$	1984.13	0.0678690
$950$	0	0
$951$	7933.82	0.270528
$952$	11745.5i	0.399867i
$953$	− 46267.5i	− 1.57267i	−0.617802	−	0.786333i	$-0.711977\pi$
$953$	− 46267.5i	− 1.57267i	0.617802	−	0.786333i	$-0.288023\pi$
$954$	−4961.46	−0.168379
$955$	0	0
$956$	8558.23	0.289532
$957$	927.709i	0.0313360i
$958$	− 96903.7i	− 3.26807i
$959$	−16703.9	−0.562458
$960$	0	0
$961$	−29594.3	−0.993398
$962$	5792.48i	0.194134i
$963$	− 1497.23i	− 0.0501014i
$964$	−45854.1	−1.53201
$965$	0	0
$966$	15650.1	0.521257
$967$	26514.2i	0.881738i	0.897571	+	0.440869i	$0.145330\pi$
$967$	26514.2i	0.881738i	−0.897571	+	0.440869i	$0.854670\pi$
$968$	40048.5i	1.32976i
$969$	−14274.5	−0.473234
$970$	0	0
$971$	38864.6	1.28447	0.642237	−	0.766506i	$-0.278006\pi$
$971$	38864.6	1.28447	0.642237	+	0.766506i	$0.278006\pi$
$972$	3546.66i	0.117036i
$973$	− 8508.13i	− 0.280327i
$974$	−44789.9	−1.47347
$975$	0	0
$976$	24788.4	0.812968
$977$	− 33774.5i	− 1.10598i	−0.833188	−	0.552990i	$-0.813487\pi$
$977$	− 33774.5i	− 1.10598i	0.833188	−	0.552990i	$-0.186513\pi$
$978$	20013.8i	0.654367i
$979$	217.803	0.00711032
$980$	0	0
$981$	−12114.0	−0.394262
$982$	28084.8i	0.912651i
$983$	− 23536.8i	− 0.763691i	−0.924226	−	0.381846i	$-0.875289\pi$
$983$	− 23536.8i	− 0.763691i	0.924226	−	0.381846i	$-0.124711\pi$
$984$	11964.6	0.387619
$985$	0	0
$986$	10750.7	0.347234
$987$	− 9842.44i	− 0.317415i
$988$	5390.31i	0.173572i
$989$	32953.3	1.05951
$990$	0	0
$991$	29012.6	0.929984	0.464992	−	0.885315i	$-0.346057\pi$
$991$	29012.6	0.929984	0.464992	+	0.885315i	$0.346057\pi$
$992$	1366.79i	0.0437457i
$993$	5493.48i	0.175559i
$994$	24549.1	0.783350
$995$	0	0
$996$	34020.8	1.08232
$997$	14027.1i	0.445579i	0.974867	+	0.222790i	$0.0715163\pi$
$997$	14027.1i	0.445579i	−0.974867	+	0.222790i	$0.928484\pi$
$998$	15390.0i	0.488138i
$999$	7920.07	0.250831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.n.274.8		8
5.2	odd	4		525.4.a.t.1.1	✓	4
5.3	odd	4		525.4.a.u.1.4	yes	4
5.4	even	2	inner	525.4.d.n.274.1		8
15.2	even	4		1575.4.a.bj.1.4		4
15.8	even	4		1575.4.a.bk.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.t.1.1	✓	4	5.2	odd	4
525.4.a.u.1.4	yes	4	5.3	odd	4
525.4.d.n.274.1		8	5.4	even	2	inner
525.4.d.n.274.8		8	1.1	even	1	trivial
1575.4.a.bj.1.4		4	15.2	even	4
1575.4.a.bk.1.1		4	15.8	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)

\(f(q)\)	\(=\)	\(q+4.75345i q^{2} -3.00000i q^{3} -14.5953 q^{4} +14.2604 q^{6} +7.00000i q^{7} -31.3504i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+4.75345i q^{2} -3.00000i q^{3} -14.5953 q^{4} +14.2604 q^{6} +7.00000i q^{7} -31.3504i q^{8} -9.00000 q^{9} +7.31799 q^{11} +43.7859i q^{12} +4.15422i q^{13} -33.2742 q^{14} +32.2604 q^{16} +53.5216i q^{17} -42.7811i q^{18} -88.9019 q^{19} +21.0000 q^{21} +34.7857i q^{22} -156.780i q^{23} -94.0513 q^{24} -19.7469 q^{26} +27.0000i q^{27} -102.167i q^{28} -42.2570 q^{29} -14.0248 q^{31} -97.4554i q^{32} -21.9540i q^{33} -254.412 q^{34} +131.358 q^{36} -293.336i q^{37} -422.591i q^{38} +12.4627 q^{39} -127.214 q^{41} +99.8225i q^{42} +210.189i q^{43} -106.808 q^{44} +745.244 q^{46} -468.688i q^{47} -96.7811i q^{48} -49.0000 q^{49} +160.565 q^{51} -60.6321i q^{52} -115.973i q^{53} -128.343 q^{54} +219.453 q^{56} +266.706i q^{57} -200.867i q^{58} +314.090 q^{59} +768.386 q^{61} -66.6662i q^{62} -63.0000i q^{63} +721.332 q^{64} +104.357 q^{66} -717.081i q^{67} -781.164i q^{68} -470.339 q^{69} -737.783 q^{71} +282.154i q^{72} -477.618i q^{73} +1394.36 q^{74} +1297.55 q^{76} +51.2259i q^{77} +59.2407i q^{78} +279.262 q^{79} +81.0000 q^{81} -604.703i q^{82} -776.981i q^{83} -306.501 q^{84} -999.123 q^{86} +126.771i q^{87} -229.422i q^{88} +29.7626 q^{89} -29.0796 q^{91} +2288.24i q^{92} +42.0744i q^{93} +2227.88 q^{94} -292.366 q^{96} -231.793i q^{97} -232.919i q^{98} -65.8619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} - 72 q^{9}+O(q^{10}) \) 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

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Database

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