LMFDB - Embedded newform 825.4.c.q.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, 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("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$48.6765757547$
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} + 574x^{6} + 121601x^{4} + 11262916x^{2} + 384787456 $ x^8 + 574x^6 + 121601x^4 + 11262916*x^2 + 384787456
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.1
Root			$10.1952i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.q.199.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56155i q^{2} -3.00000i q^{3} +1.43845 q^{4} -7.68466 q^{6} -29.1157i q^{7} -24.1771i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q-2.56155i q^{2} -3.00000i q^{3} +1.43845 q^{4} -7.68466 q^{6} -29.1157i q^{7} -24.1771i q^{8} -9.00000 q^{9} -11.0000 q^{11} -4.31534i q^{12} -39.1577i q^{13} -74.5813 q^{14} -50.4233 q^{16} -46.3467i q^{17} +23.0540i q^{18} -43.5734 q^{19} -87.3470 q^{21} +28.1771i q^{22} +91.3160i q^{23} -72.5312 q^{24} -100.305 q^{26} +27.0000i q^{27} -41.8813i q^{28} +185.921 q^{29} -45.8880 q^{31} -64.2547i q^{32} +33.0000i q^{33} -118.720 q^{34} -12.9460 q^{36} -177.929i q^{37} +111.616i q^{38} -117.473 q^{39} +232.717 q^{41} +223.744i q^{42} +64.1891i q^{43} -15.8229 q^{44} +233.911 q^{46} -16.9819i q^{47} +151.270i q^{48} -504.722 q^{49} -139.040 q^{51} -56.3263i q^{52} -48.7222i q^{53} +69.1619 q^{54} -703.932 q^{56} +130.720i q^{57} -476.246i q^{58} -200.479 q^{59} +521.098 q^{61} +117.545i q^{62} +262.041i q^{63} -567.978 q^{64} +84.5312 q^{66} +338.192i q^{67} -66.6673i q^{68} +273.948 q^{69} +318.476 q^{71} +217.594i q^{72} +1138.17i q^{73} -455.775 q^{74} -62.6781 q^{76} +320.272i q^{77} +300.914i q^{78} -824.862 q^{79} +81.0000 q^{81} -596.117i q^{82} -731.172i q^{83} -125.644 q^{84} +164.424 q^{86} -557.763i q^{87} +265.948i q^{88} -902.495 q^{89} -1140.10 q^{91} +131.353i q^{92} +137.664i q^{93} -43.4999 q^{94} -192.764 q^{96} -1355.74i q^{97} +1292.87i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 28 q^{4} - 12 q^{6} - 72 q^{9}+O(q^{10}) $ 8 * q + 28 * q^4 - 12 * q^6 - 72 * q^9	$ 8 q + 28 q^{4} - 12 q^{6} - 72 q^{9} - 88 q^{11} + 6 q^{14} - 156 q^{16} - 236 q^{19} - 66 q^{21} - 36 q^{24} - 314 q^{26} - 502 q^{29} - 270 q^{31} - 578 q^{34} - 252 q^{36} - 150 q^{39} - 206 q^{41} - 308 q^{44} - 840 q^{46} - 2006 q^{49} + 510 q^{51} + 108 q^{54} + 154 q^{56} - 1902 q^{59} - 700 q^{61} - 3076 q^{64} + 132 q^{66} + 60 q^{69} + 3052 q^{71} - 2182 q^{74} - 792 q^{76} - 5134 q^{79} + 648 q^{81} - 282 q^{84} + 3674 q^{86} - 2106 q^{89} + 4300 q^{91} - 4418 q^{94} + 1476 q^{96} + 792 q^{99}+O(q^{100}) $ 8 * q + 28 * q^4 - 12 * q^6 - 72 * q^9 - 88 * q^11 + 6 * q^14 - 156 * q^16 - 236 * q^19 - 66 * q^21 - 36 * q^24 - 314 * q^26 - 502 * q^29 - 270 * q^31 - 578 * q^34 - 252 * q^36 - 150 * q^39 - 206 * q^41 - 308 * q^44 - 840 * q^46 - 2006 * q^49 + 510 * q^51 + 108 * q^54 + 154 * q^56 - 1902 * q^59 - 700 * q^61 - 3076 * q^64 + 132 * q^66 + 60 * q^69 + 3052 * q^71 - 2182 * q^74 - 792 * q^76 - 5134 * q^79 + 648 * q^81 - 282 * q^84 + 3674 * q^86 - 2106 * q^89 + 4300 * q^91 - 4418 * q^94 + 1476 * q^96 + 792 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	− 2.56155i	− 0.905646i	−0.891601	−	0.452823i	$-0.850417\pi$
$2$	− 2.56155i	− 0.905646i	0.891601	−	0.452823i	$-0.149583\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	1.43845	0.179806
$5$	0	0
$5$	0	0
$6$	−7.68466	−0.522875
$7$	− 29.1157i	− 1.57210i	−0.618164	−	0.786049i	$-0.712123\pi$
$7$	− 29.1157i	− 1.57210i	0.618164	−	0.786049i	$-0.287877\pi$
$8$	− 24.1771i	− 1.06849i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	− 4.31534i	− 0.103811i
$13$	− 39.1577i	− 0.835416i	−0.908581	−	0.417708i	$-0.862834\pi$
$13$	− 39.1577i	− 0.835416i	0.908581	−	0.417708i	$-0.137166\pi$
$14$	−74.5813	−1.42376
$15$	0	0
$16$	−50.4233	−0.787864
$17$	− 46.3467i	− 0.661219i	−0.943768	−	0.330610i	$-0.892746\pi$
$17$	− 46.3467i	− 0.661219i	0.943768	−	0.330610i	$-0.107254\pi$
$18$	23.0540i	0.301882i
$19$	−43.5734	−0.526128	−0.263064	−	0.964778i	$-0.584733\pi$
$19$	−43.5734	−0.526128	−0.263064	+	0.964778i	$0.584733\pi$
$20$	0	0
$21$	−87.3470	−0.907651
$22$	28.1771i	0.273062i
$23$	91.3160i	0.827857i	0.910309	+	0.413928i	$0.135844\pi$
$23$	91.3160i	0.827857i	−0.910309	+	0.413928i	$0.864156\pi$
$24$	−72.5312	−0.616891
$25$	0	0
$26$	−100.305	−0.756591
$27$	27.0000i	0.192450i
$28$	− 41.8813i	− 0.282672i
$29$	185.921	1.19051	0.595253	−	0.803539i	$-0.297052\pi$
$29$	185.921	1.19051	0.595253	+	0.803539i	$0.297052\pi$
$30$	0	0
$31$	−45.8880	−0.265862	−0.132931	−	0.991125i	$-0.542439\pi$
$31$	−45.8880	−0.265862	−0.132931	+	0.991125i	$0.542439\pi$
$32$	− 64.2547i	− 0.354961i
$33$	33.0000i	0.174078i
$34$	−118.720	−0.598830
$35$	0	0
$36$	−12.9460	−0.0599353
$37$	− 177.929i	− 0.790577i	−0.918557	−	0.395289i	$-0.870645\pi$
$37$	− 177.929i	− 0.790577i	0.918557	−	0.395289i	$-0.129355\pi$
$38$	111.616i	0.476486i
$39$	−117.473	−0.482327
$40$	0	0
$41$	232.717	0.886446	0.443223	−	0.896411i	$-0.353835\pi$
$41$	232.717	0.886446	0.443223	+	0.896411i	$0.353835\pi$
$42$	223.744i	0.822010i
$43$	64.1891i	0.227645i	0.993501	+	0.113823i	$0.0363096\pi$
$43$	64.1891i	0.227645i	−0.993501	+	0.113823i	$0.963690\pi$
$44$	−15.8229	−0.0542135
$45$	0	0
$46$	233.911	0.749745
$47$	− 16.9819i	− 0.0527034i	−0.999653	−	0.0263517i	$-0.991611\pi$
$47$	− 16.9819i	− 0.0527034i	0.999653	−	0.0263517i	$-0.00838898\pi$
$48$	151.270i	0.454873i
$49$	−504.722	−1.47149
$50$	0	0
$51$	−139.040	−0.381755
$52$	− 56.3263i	− 0.150213i
$53$	− 48.7222i	− 0.126274i	−0.998005	−	0.0631369i	$-0.979890\pi$
$53$	− 48.7222i	− 0.126274i	0.998005	−	0.0631369i	$-0.0201105\pi$
$54$	69.1619	0.174292
$55$	0	0
$56$	−703.932	−1.67976
$57$	130.720i	0.303760i
$58$	− 476.246i	− 1.07818i
$59$	−200.479	−0.442375	−0.221187	−	0.975231i	$-0.570993\pi$
$59$	−200.479	−0.442375	−0.221187	+	0.975231i	$0.570993\pi$
$60$	0	0
$61$	521.098	1.09377	0.546883	−	0.837209i	$-0.315814\pi$
$61$	521.098	1.09377	0.546883	+	0.837209i	$0.315814\pi$
$62$	117.545i	0.240777i
$63$	262.041i	0.524033i
$64$	−567.978	−1.10933
$65$	0	0
$66$	84.5312	0.157653
$67$	338.192i	0.616668i	0.951278	+	0.308334i	$0.0997715\pi$
$67$	338.192i	0.616668i	−0.951278	+	0.308334i	$0.900229\pi$
$68$	− 66.6673i	− 0.118891i
$69$	273.948	0.477963
$70$	0	0
$71$	318.476	0.532340	0.266170	−	0.963926i	$-0.414242\pi$
$71$	318.476	0.532340	0.266170	+	0.963926i	$0.414242\pi$
$72$	217.594i	0.356162i
$73$	1138.17i	1.82484i	0.409257	+	0.912419i	$0.365788\pi$
$73$	1138.17i	1.82484i	−0.409257	+	0.912419i	$0.634212\pi$
$74$	−455.775	−0.715983
$75$	0	0
$76$	−62.6781	−0.0946009
$77$	320.272i	0.474005i
$78$	300.914i	0.436818i
$79$	−824.862	−1.17474	−0.587368	−	0.809320i	$-0.699836\pi$
$79$	−824.862	−1.17474	−0.587368	+	0.809320i	$0.699836\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 596.117i	− 0.802806i
$83$	− 731.172i	− 0.966946i	−0.875359	−	0.483473i	$-0.839375\pi$
$83$	− 731.172i	− 0.966946i	0.875359	−	0.483473i	$-0.160625\pi$
$84$	−125.644	−0.163201
$85$	0	0
$86$	164.424	0.206166
$87$	− 557.763i	− 0.687339i
$88$	265.948i	0.322161i
$89$	−902.495	−1.07488	−0.537440	−	0.843302i	$-0.680608\pi$
$89$	−902.495	−1.07488	−0.537440	+	0.843302i	$0.680608\pi$
$90$	0	0
$91$	−1140.10	−1.31336
$92$	131.353i	0.148854i
$93$	137.664i	0.153496i
$94$	−43.4999	−0.0477306
$95$	0	0
$96$	−192.764	−0.204937
$97$	− 1355.74i	− 1.41912i	−0.704645	−	0.709560i	$-0.748894\pi$
$97$	− 1355.74i	− 1.41912i	0.704645	−	0.709560i	$-0.251106\pi$
$98$	1292.87i	1.33265i
$99$	99.0000	0.100504
$100$	0	0
$101$	653.497	0.643816	0.321908	−	0.946771i	$-0.395676\pi$
$101$	653.497	0.643816	0.321908	+	0.946771i	$0.395676\pi$
$102$	356.159i	0.345735i
$103$	801.592i	0.766827i	0.923577	+	0.383414i	$0.125252\pi$
$103$	801.592i	0.766827i	−0.923577	+	0.383414i	$0.874748\pi$
$104$	−946.720	−0.892630
$105$	0	0
$106$	−124.804	−0.114359
$107$	− 478.412i	− 0.432241i	−0.976367	−	0.216121i	$-0.930660\pi$
$107$	− 478.412i	− 0.432241i	0.976367	−	0.216121i	$-0.0693404\pi$
$108$	38.8381i	0.0346037i
$109$	−1019.91	−0.896235	−0.448117	−	0.893975i	$-0.647905\pi$
$109$	−1019.91	−0.896235	−0.448117	+	0.893975i	$0.647905\pi$
$110$	0	0
$111$	−533.787	−0.456440
$112$	1468.11i	1.23860i
$113$	− 448.303i	− 0.373211i	−0.982435	−	0.186605i	$-0.940251\pi$
$113$	− 448.303i	− 0.373211i	0.982435	−	0.186605i	$-0.0597486\pi$
$114$	334.847	0.275099
$115$	0	0
$116$	267.437	0.214060
$117$	352.420i	0.278472i
$118$	513.537i	0.400635i
$119$	−1349.42	−1.03950
$120$	0	0
$121$	121.000	0.0909091
$122$	− 1334.82i	− 0.990565i
$123$	− 698.151i	− 0.511790i
$124$	−66.0075	−0.0478036
$125$	0	0
$126$	671.232	0.474588
$127$	1509.67i	1.05481i	0.849613	+	0.527406i	$0.176835\pi$
$127$	1509.67i	1.05481i	−0.849613	+	0.527406i	$0.823165\pi$
$128$	940.868i	0.649702i
$129$	192.567	0.131431
$130$	0	0
$131$	2829.06	1.88684	0.943419	−	0.331603i	$-0.107590\pi$
$131$	2829.06	1.88684	0.943419	+	0.331603i	$0.107590\pi$
$132$	47.4688i	0.0313002i
$133$	1268.67i	0.827125i
$134$	866.298	0.558483
$135$	0	0
$136$	−1120.53	−0.706504
$137$	− 326.658i	− 0.203710i	−0.994799	−	0.101855i	$-0.967522\pi$
$137$	− 326.658i	− 0.203710i	0.994799	−	0.101855i	$-0.0324778\pi$
$138$	− 701.732i	− 0.432865i
$139$	1226.81	0.748610	0.374305	−	0.927306i	$-0.377881\pi$
$139$	1226.81	0.748610	0.374305	+	0.927306i	$0.377881\pi$
$140$	0	0
$141$	−50.9456	−0.0304283
$142$	− 815.793i	− 0.482111i
$143$	430.735i	0.251887i
$144$	453.810	0.262621
$145$	0	0
$146$	2915.49	1.65266
$147$	1514.16i	0.849566i
$148$	− 255.942i	− 0.142150i
$149$	−1877.36	−1.03221	−0.516106	−	0.856524i	$-0.672619\pi$
$149$	−1877.36	−1.03221	−0.516106	+	0.856524i	$0.672619\pi$
$150$	0	0
$151$	550.749	0.296817	0.148408	−	0.988926i	$-0.452585\pi$
$151$	550.749	0.296817	0.148408	+	0.988926i	$0.452585\pi$
$152$	1053.48i	0.562161i
$153$	417.120i	0.220406i
$154$	820.394	0.429281
$155$	0	0
$156$	−168.979	−0.0867253
$157$	3462.24i	1.75998i	0.474992	+	0.879990i	$0.342451\pi$
$157$	3462.24i	1.75998i	−0.474992	+	0.879990i	$0.657549\pi$
$158$	2112.93i	1.06390i
$159$	−146.167	−0.0729042
$160$	0	0
$161$	2658.73	1.30147
$162$	− 207.486i	− 0.100627i
$163$	1.28644i	0 0.000618173i	1.00000		0.000309086i	$9.83852e-5\pi$
$163$	1.28644i	0 0.000618173i	−1.00000		0.000309086i	$0.999902\pi$
$164$	334.751	0.159388
$165$	0	0
$166$	−1872.94	−0.875711
$167$	4242.05i	1.96563i	0.184604	+	0.982813i	$0.440900\pi$
$167$	4242.05i	1.96563i	−0.184604	+	0.982813i	$0.559100\pi$
$168$	2111.79i	0.969813i
$169$	663.671	0.302081
$170$	0	0
$171$	392.161	0.175376
$172$	92.3326i	0.0409320i
$173$	− 2803.72i	− 1.23216i	−0.787685	−	0.616078i	$-0.788721\pi$
$173$	− 2803.72i	− 1.23216i	0.787685	−	0.616078i	$-0.211279\pi$
$174$	−1428.74	−0.622485
$175$	0	0
$176$	554.656	0.237550
$177$	601.436i	0.255405i
$178$	2311.79i	0.973460i
$179$	3598.59	1.50263	0.751316	−	0.659943i	$-0.229419\pi$
$179$	3598.59	1.50263	0.751316	+	0.659943i	$0.229419\pi$
$180$	0	0
$181$	−3112.78	−1.27829	−0.639147	−	0.769085i	$-0.720712\pi$
$181$	−3112.78	−1.27829	−0.639147	+	0.769085i	$0.720712\pi$
$182$	2920.44i	1.18943i
$183$	− 1563.29i	− 0.631486i
$184$	2207.75	0.884553
$185$	0	0
$186$	352.634	0.139013
$187$	509.814i	0.199365i
$188$	− 24.4275i	− 0.00947638i
$189$	786.123	0.302550
$190$	0	0
$191$	3264.88	1.23685	0.618426	−	0.785843i	$-0.287771\pi$
$191$	3264.88	1.23685	0.618426	+	0.785843i	$0.287771\pi$
$192$	1703.93i	0.640473i
$193$	1105.46i	0.412294i	0.978521	+	0.206147i	$0.0660925\pi$
$193$	1105.46i	0.412294i	−0.978521	+	0.206147i	$0.933907\pi$
$194$	−3472.80	−1.28522
$195$	0	0
$196$	−726.015	−0.264583
$197$	− 1833.05i	− 0.662942i	−0.943465	−	0.331471i	$-0.892455\pi$
$197$	− 1833.05i	− 0.662942i	0.943465	−	0.331471i	$-0.107545\pi$
$198$	− 253.594i	− 0.0910208i
$199$	−5533.14	−1.97102	−0.985512	−	0.169607i	$-0.945750\pi$
$199$	−5533.14	−1.97102	−0.985512	+	0.169607i	$0.945750\pi$
$200$	0	0
$201$	1014.58	0.356034
$202$	− 1673.97i	− 0.583069i
$203$	− 5413.21i	− 1.87159i
$204$	−200.002	−0.0686418
$205$	0	0
$206$	2053.32	0.694474
$207$	− 821.844i	− 0.275952i
$208$	1974.46i	0.658194i
$209$	479.308	0.158634
$210$	0	0
$211$	1746.95	0.569977	0.284988	−	0.958531i	$-0.408010\pi$
$211$	1746.95	0.569977	0.284988	+	0.958531i	$0.408010\pi$
$212$	− 70.0843i	− 0.0227048i
$213$	− 955.428i	− 0.307347i
$214$	−1225.48	−0.391457
$215$	0	0
$216$	652.781	0.205630
$217$	1336.06i	0.417961i
$218$	2612.55i	0.811671i
$219$	3414.52	1.05357
$220$	0	0
$221$	−1814.83	−0.552393
$222$	1367.32i	0.413373i
$223$	− 5621.85i	− 1.68819i	−0.536191	−	0.844097i	$-0.680137\pi$
$223$	− 5621.85i	− 1.68819i	0.536191	−	0.844097i	$-0.319863\pi$
$224$	−1870.82	−0.558033
$225$	0	0
$226$	−1148.35	−0.337997
$227$	3341.93i	0.977143i	0.872524	+	0.488571i	$0.162482\pi$
$227$	3341.93i	0.977143i	−0.872524	+	0.488571i	$0.837518\pi$
$228$	188.034i	0.0546179i
$229$	−2381.21	−0.687140	−0.343570	−	0.939127i	$-0.611636\pi$
$229$	−2381.21	−0.687140	−0.343570	+	0.939127i	$0.611636\pi$
$230$	0	0
$231$	960.817	0.273667
$232$	− 4495.03i	− 1.27204i
$233$	− 6736.45i	− 1.89407i	−0.321124	−	0.947037i	$-0.604061\pi$
$233$	− 6736.45i	− 1.89407i	0.321124	−	0.947037i	$-0.395939\pi$
$234$	902.742	0.252197
$235$	0	0
$236$	−288.378	−0.0795416
$237$	2474.58i	0.678234i
$238$	3456.60i	0.941420i
$239$	−2042.55	−0.552811	−0.276406	−	0.961041i	$-0.589143\pi$
$239$	−2042.55	−0.552811	−0.276406	+	0.961041i	$0.589143\pi$
$240$	0	0
$241$	−5844.87	−1.56225	−0.781123	−	0.624377i	$-0.785353\pi$
$241$	−5844.87	−1.56225	−0.781123	+	0.624377i	$0.785353\pi$
$242$	− 309.948i	− 0.0823314i
$243$	− 243.000i	− 0.0641500i
$244$	749.572	0.196666
$245$	0	0
$246$	−1788.35	−0.463501
$247$	1706.24i	0.439536i
$248$	1109.44i	0.284070i
$249$	−2193.52	−0.558267
$250$	0	0
$251$	−2706.17	−0.680525	−0.340263	−	0.940330i	$-0.610516\pi$
$251$	−2706.17	−0.680525	−0.340263	+	0.940330i	$0.610516\pi$
$252$	376.932i	0.0942241i
$253$	− 1004.48i	− 0.249608i
$254$	3867.09	0.955286
$255$	0	0
$256$	−2133.74	−0.520933
$257$	− 3599.31i	− 0.873613i	−0.899555	−	0.436807i	$-0.856109\pi$
$257$	− 3599.31i	− 0.873613i	0.899555	−	0.436807i	$-0.143891\pi$
$258$	− 493.271i	− 0.119030i
$259$	−5180.52	−1.24286
$260$	0	0
$261$	−1673.29	−0.396835
$262$	− 7246.78i	− 1.70881i
$263$	− 2736.39i	− 0.641570i	−0.947152	−	0.320785i	$-0.896053\pi$
$263$	− 2736.39i	− 0.641570i	0.947152	−	0.320785i	$-0.103947\pi$
$264$	797.844	0.186000
$265$	0	0
$266$	3249.76	0.749082
$267$	2707.48i	0.620582i
$268$	486.472i	0.110881i
$269$	3741.47	0.848035	0.424017	−	0.905654i	$-0.360620\pi$
$269$	3741.47	0.848035	0.424017	+	0.905654i	$0.360620\pi$
$270$	0	0
$271$	4444.66	0.996287	0.498144	−	0.867095i	$-0.334015\pi$
$271$	4444.66	0.996287	0.498144	+	0.867095i	$0.334015\pi$
$272$	2336.95i	0.520951i
$273$	3420.31i	0.758266i
$274$	−836.752	−0.184489
$275$	0	0
$276$	394.060	0.0859406
$277$	− 7723.95i	− 1.67540i	−0.546127	−	0.837702i	$-0.683898\pi$
$277$	− 7723.95i	− 1.67540i	0.546127	−	0.837702i	$-0.316102\pi$
$278$	− 3142.54i	− 0.677976i
$279$	412.992	0.0886208
$280$	0	0
$281$	−8427.77	−1.78918	−0.894588	−	0.446892i	$-0.852531\pi$
$281$	−8427.77	−1.78918	−0.894588	+	0.446892i	$0.852531\pi$
$282$	130.500i	0.0275573i
$283$	4556.14i	0.957013i	0.878084	+	0.478506i	$0.158822\pi$
$283$	4556.14i	0.957013i	−0.878084	+	0.478506i	$0.841178\pi$
$284$	458.111	0.0957179
$285$	0	0
$286$	1103.35	0.228121
$287$	− 6775.71i	− 1.39358i
$288$	578.292i	0.118320i
$289$	2764.98	0.562789
$290$	0	0
$291$	−4067.23	−0.819330
$292$	1637.20i	0.328117i
$293$	− 3542.77i	− 0.706384i	−0.935551	−	0.353192i	$-0.885096\pi$
$293$	− 3542.77i	− 0.706384i	0.935551	−	0.353192i	$-0.114904\pi$
$294$	3878.61	0.769406
$295$	0	0
$296$	−4301.81	−0.844721
$297$	− 297.000i	− 0.0580259i
$298$	4808.97i	0.934819i
$299$	3575.73	0.691604
$300$	0	0
$301$	1868.91	0.357881
$302$	− 1410.77i	− 0.268811i
$303$	− 1960.49i	− 0.371707i
$304$	2197.12	0.414517
$305$	0	0
$306$	1068.48	0.199610
$307$	− 381.342i	− 0.0708936i	−0.999372	−	0.0354468i	$-0.988715\pi$
$307$	− 381.342i	− 0.0708936i	0.999372	−	0.0354468i	$-0.0112854\pi$
$308$	460.695i	0.0852290i
$309$	2404.78	0.442728
$310$	0	0
$311$	7299.83	1.33098	0.665491	−	0.746406i	$-0.268222\pi$
$311$	7299.83	1.33098	0.665491	+	0.746406i	$0.268222\pi$
$312$	2840.16i	0.515360i
$313$	− 188.923i	− 0.0341168i	−0.999854	−	0.0170584i	$-0.994570\pi$
$313$	− 188.923i	− 0.0341168i	0.999854	−	0.0170584i	$-0.00543012\pi$
$314$	8868.71	1.59392
$315$	0	0
$316$	−1186.52	−0.211225
$317$	− 4455.50i	− 0.789418i	−0.918806	−	0.394709i	$-0.870845\pi$
$317$	− 4455.50i	− 0.789418i	0.918806	−	0.394709i	$-0.129155\pi$
$318$	374.413i	0.0660254i
$319$	−2045.13	−0.358951
$320$	0	0
$321$	−1435.23	−0.249555
$322$	− 6810.47i	− 1.17867i
$323$	2019.49i	0.347886i
$324$	116.514	0.0199784
$325$	0	0
$326$	3.29530	0.000559845 0
$327$	3059.73i	0.517441i
$328$	− 5626.42i	− 0.947156i
$329$	−494.438	−0.0828549
$330$	0	0
$331$	5602.25	0.930295	0.465147	−	0.885233i	$-0.346001\pi$
$331$	5602.25	0.930295	0.465147	+	0.885233i	$0.346001\pi$
$332$	− 1051.75i	− 0.173863i
$333$	1601.36i	0.263526i
$334$	10866.2	1.78016
$335$	0	0
$336$	4404.32	0.715106
$337$	− 5486.45i	− 0.886843i	−0.896313	−	0.443422i	$-0.853764\pi$
$337$	− 5486.45i	− 0.886843i	0.896313	−	0.443422i	$-0.146236\pi$
$338$	− 1700.03i	− 0.273578i
$339$	−1344.91	−0.215473
$340$	0	0
$341$	504.768	0.0801605
$342$	− 1004.54i	− 0.158829i
$343$	4708.63i	0.741231i
$344$	1551.91	0.243236
$345$	0	0
$346$	−7181.88	−1.11590
$347$	1679.90i	0.259889i	0.991521	+	0.129945i	$0.0414800\pi$
$347$	1679.90i	0.259889i	−0.991521	+	0.129945i	$0.958520\pi$
$348$	− 802.312i	− 0.123588i
$349$	−11110.4	−1.70408	−0.852040	−	0.523477i	$-0.824635\pi$
$349$	−11110.4	−1.70408	−0.852040	+	0.523477i	$0.824635\pi$
$350$	0	0
$351$	1057.26	0.160776
$352$	706.802i	0.107025i
$353$	− 1156.07i	− 0.174310i	−0.996195	−	0.0871551i	$-0.972222\pi$
$353$	− 1156.07i	− 0.174310i	0.996195	−	0.0871551i	$-0.0277776\pi$
$354$	1540.61	0.231307
$355$	0	0
$356$	−1298.19	−0.193270
$357$	4048.25i	0.600156i
$358$	− 9217.97i	− 1.36085i
$359$	8720.34	1.28201	0.641005	−	0.767536i	$-0.278518\pi$
$359$	8720.34	1.28201	0.641005	+	0.767536i	$0.278518\pi$
$360$	0	0
$361$	−4960.36	−0.723189
$362$	7973.55i	1.15768i
$363$	− 363.000i	− 0.0524864i
$364$	−1639.98	−0.236149
$365$	0	0
$366$	−4004.46	−0.571903
$367$	− 9485.15i	− 1.34910i	−0.738228	−	0.674552i	$-0.764337\pi$
$367$	− 9485.15i	− 1.34910i	0.738228	−	0.674552i	$-0.235663\pi$
$368$	− 4604.45i	− 0.652238i
$369$	−2094.45	−0.295482
$370$	0	0
$371$	−1418.58	−0.198515
$372$	198.022i	0.0275994i
$373$	− 12692.4i	− 1.76190i	−0.473207	−	0.880951i	$-0.656904\pi$
$373$	− 12692.4i	− 1.76190i	0.473207	−	0.880951i	$-0.343096\pi$
$374$	1305.92	0.180554
$375$	0	0
$376$	−410.572	−0.0563128
$377$	− 7280.25i	− 0.994567i
$378$	− 2013.69i	− 0.274003i
$379$	3578.72	0.485030	0.242515	−	0.970148i	$-0.422028\pi$
$379$	3578.72	0.485030	0.242515	+	0.970148i	$0.422028\pi$
$380$	0	0
$381$	4529.00	0.608996
$382$	− 8363.17i	− 1.12015i
$383$	8730.00i	1.16471i	0.812936	+	0.582353i	$0.197868\pi$
$383$	8730.00i	1.16471i	−0.812936	+	0.582353i	$0.802132\pi$
$384$	2822.61	0.375105
$385$	0	0
$386$	2831.69	0.373392
$387$	− 577.702i	− 0.0758818i
$388$	− 1950.16i	− 0.255166i
$389$	−11450.8	−1.49249	−0.746244	−	0.665673i	$-0.768145\pi$
$389$	−11450.8	−1.49249	−0.746244	+	0.665673i	$0.768145\pi$
$390$	0	0
$391$	4232.20	0.547395
$392$	12202.7i	1.57227i
$393$	− 8487.17i	− 1.08937i
$394$	−4695.46	−0.600391
$395$	0	0
$396$	142.406	0.0180712
$397$	− 8248.03i	− 1.04271i	−0.853339	−	0.521356i	$-0.825426\pi$
$397$	− 8248.03i	− 1.04271i	0.853339	−	0.521356i	$-0.174574\pi$
$398$	14173.4i	1.78505i
$399$	3806.01	0.477541
$400$	0	0
$401$	10577.1	1.31719	0.658596	−	0.752497i	$-0.271151\pi$
$401$	10577.1	1.31719	0.658596	+	0.752497i	$0.271151\pi$
$402$	− 2598.89i	− 0.322440i
$403$	1796.87i	0.222106i
$404$	940.021	0.115762
$405$	0	0
$406$	−13866.2	−1.69500
$407$	1957.22i	0.238368i
$408$	3361.58i	0.407900i
$409$	−8285.94	−1.00174	−0.500872	−	0.865521i	$-0.666987\pi$
$409$	−8285.94	−1.00174	−0.500872	+	0.865521i	$0.666987\pi$
$410$	0	0
$411$	−979.974	−0.117612
$412$	1153.05i	0.137880i
$413$	5837.07i	0.695456i
$414$	−2105.20	−0.249915
$415$	0	0
$416$	−2516.07	−0.296540
$417$	− 3680.44i	− 0.432210i
$418$	− 1227.77i	− 0.143666i
$419$	1762.52	0.205500	0.102750	−	0.994707i	$-0.467236\pi$
$419$	1762.52	0.205500	0.102750	+	0.994707i	$0.467236\pi$
$420$	0	0
$421$	−10979.8	−1.27107	−0.635535	−	0.772072i	$-0.719221\pi$
$421$	−10979.8	−1.27107	−0.635535	+	0.772072i	$0.719221\pi$
$422$	− 4474.91i	− 0.516197i
$423$	152.837i	0.0175678i
$424$	−1177.96	−0.134922
$425$	0	0
$426$	−2447.38	−0.278347
$427$	− 15172.1i	− 1.71951i
$428$	− 688.170i	− 0.0777195i
$429$	1292.21	0.145427
$430$	0	0
$431$	−15796.2	−1.76537	−0.882686	−	0.469963i	$-0.844267\pi$
$431$	−15796.2	−1.76537	−0.882686	+	0.469963i	$0.844267\pi$
$432$	− 1361.43i	− 0.151624i
$433$	7143.48i	0.792826i	0.918072	+	0.396413i	$0.129745\pi$
$433$	7143.48i	0.792826i	−0.918072	+	0.396413i	$0.870255\pi$
$434$	3422.39	0.378525
$435$	0	0
$436$	−1467.09	−0.161148
$437$	− 3978.95i	− 0.435559i
$438$	− 8746.48i	− 0.954162i
$439$	9945.41	1.08125	0.540624	−	0.841264i	$-0.318188\pi$
$439$	9945.41	1.08125	0.540624	+	0.841264i	$0.318188\pi$
$440$	0	0
$441$	4542.49	0.490497
$442$	4648.79i	0.500272i
$443$	− 4365.38i	− 0.468184i	−0.972214	−	0.234092i	$-0.924788\pi$
$443$	− 4365.38i	− 0.468184i	0.972214	−	0.234092i	$-0.0752117\pi$
$444$	−767.825	−0.0820706
$445$	0	0
$446$	−14400.7	−1.52891
$447$	5632.09i	0.595948i
$448$	16537.1i	1.74398i
$449$	11845.9	1.24508	0.622540	−	0.782588i	$-0.286101\pi$
$449$	11845.9	1.24508	0.622540	+	0.782588i	$0.286101\pi$
$450$	0	0
$451$	−2559.89	−0.267274
$452$	− 644.861i	− 0.0671055i
$453$	− 1652.25i	− 0.171367i
$454$	8560.52	0.884945
$455$	0	0
$456$	3160.44	0.324564
$457$	− 14283.2i	− 1.46202i	−0.682368	−	0.731009i	$-0.739050\pi$
$457$	− 14283.2i	− 1.46202i	0.682368	−	0.731009i	$-0.260950\pi$
$458$	6099.60i	0.622305i
$459$	1251.36	0.127252
$460$	0	0
$461$	8491.06	0.857848	0.428924	−	0.903340i	$-0.358893\pi$
$461$	8491.06	0.857848	0.428924	+	0.903340i	$0.358893\pi$
$462$	− 2461.18i	− 0.247845i
$463$	8545.74i	0.857784i	0.903356	+	0.428892i	$0.141096\pi$
$463$	8545.74i	0.857784i	−0.903356	+	0.428892i	$0.858904\pi$
$464$	−9374.75	−0.937956
$465$	0	0
$466$	−17255.8	−1.71536
$467$	2090.95i	0.207190i	0.994620	+	0.103595i	$0.0330346\pi$
$467$	2090.95i	0.207190i	−0.994620	+	0.103595i	$0.966965\pi$
$468$	506.937i	0.0500709i
$469$	9846.70	0.969463
$470$	0	0
$471$	10386.7	1.01613
$472$	4846.99i	0.472671i
$473$	− 706.080i	− 0.0686376i
$474$	6338.78	0.614240
$475$	0	0
$476$	−1941.06	−0.186908
$477$	438.500i	0.0420912i
$478$	5232.11i	0.500651i
$479$	−3450.92	−0.329178	−0.164589	−	0.986362i	$-0.552630\pi$
$479$	−3450.92	−0.329178	−0.164589	+	0.986362i	$0.552630\pi$
$480$	0	0
$481$	−6967.30	−0.660461
$482$	14972.0i	1.41484i
$483$	− 7976.18i	− 0.751405i
$484$	174.052	0.0163460
$485$	0	0
$486$	−622.457	−0.0580972
$487$	− 19723.1i	− 1.83519i	−0.397518	−	0.917594i	$-0.630128\pi$
$487$	− 19723.1i	− 1.83519i	0.397518	−	0.917594i	$-0.369872\pi$
$488$	− 12598.6i	− 1.16867i
$489$	3.85933	0.000356902 0
$490$	0	0
$491$	7425.33	0.682485	0.341243	−	0.939975i	$-0.389152\pi$
$491$	7425.33	0.682485	0.341243	+	0.939975i	$0.389152\pi$
$492$	− 1004.25i	− 0.0920229i
$493$	− 8616.83i	− 0.787185i
$494$	4370.62	0.398064
$495$	0	0
$496$	2313.82	0.209463
$497$	− 9272.64i	− 0.836891i
$498$	5618.81i	0.505592i
$499$	−8724.18	−0.782661	−0.391331	−	0.920250i	$-0.627985\pi$
$499$	−8724.18	−0.782661	−0.391331	+	0.920250i	$0.627985\pi$
$500$	0	0
$501$	12726.1	1.13485
$502$	6932.00i	0.616315i
$503$	− 21389.8i	− 1.89607i	−0.318170	−	0.948034i	$-0.603068\pi$
$503$	− 21389.8i	− 1.89607i	0.318170	−	0.948034i	$-0.396932\pi$
$504$	6335.38	0.559922
$505$	0	0
$506$	−2573.02	−0.226057
$507$	− 1991.01i	− 0.174406i
$508$	2171.57i	0.189662i
$509$	7599.47	0.661769	0.330885	−	0.943671i	$-0.392653\pi$
$509$	7599.47	0.661769	0.330885	+	0.943671i	$0.392653\pi$
$510$	0	0
$511$	33138.7	2.86882
$512$	12992.6i	1.12148i
$513$	− 1176.48i	− 0.101253i
$514$	−9219.81	−0.791184
$515$	0	0
$516$	276.998	0.0236321
$517$	186.800i	0.0158907i
$518$	13270.2i	1.12560i
$519$	−8411.17	−0.711386
$520$	0	0
$521$	7789.58	0.655025	0.327512	−	0.944847i	$-0.393790\pi$
$521$	7789.58	0.655025	0.327512	+	0.944847i	$0.393790\pi$
$522$	4286.22i	0.359392i
$523$	− 10408.6i	− 0.870238i	−0.900373	−	0.435119i	$-0.856706\pi$
$523$	− 10408.6i	− 0.870238i	0.900373	−	0.435119i	$-0.143294\pi$
$524$	4069.45	0.339265
$525$	0	0
$526$	−7009.41	−0.581035
$527$	2126.76i	0.175793i
$528$	− 1663.97i	− 0.137150i
$529$	3828.39	0.314653
$530$	0	0
$531$	1804.31	0.147458
$532$	1824.91i	0.148722i
$533$	− 9112.68i	− 0.740551i
$534$	6935.36	0.562027
$535$	0	0
$536$	8176.51	0.658902
$537$	− 10795.8i	− 0.867545i
$538$	− 9583.97i	− 0.768019i
$539$	5551.94	0.443671
$540$	0	0
$541$	−9679.94	−0.769267	−0.384633	−	0.923069i	$-0.625672\pi$
$541$	−9679.94	−0.769267	−0.384633	+	0.923069i	$0.625672\pi$
$542$	− 11385.2i	− 0.902283i
$543$	9338.34i	0.738023i
$544$	−2978.00	−0.234707
$545$	0	0
$546$	8761.31	0.686720
$547$	16026.2i	1.25271i	0.779538	+	0.626355i	$0.215454\pi$
$547$	16026.2i	1.25271i	−0.779538	+	0.626355i	$0.784546\pi$
$548$	− 469.880i	− 0.0366283i
$549$	−4689.88	−0.364589
$550$	0	0
$551$	−8101.22	−0.626358
$552$	− 6623.26i	− 0.510697i
$553$	24016.4i	1.84680i
$554$	−19785.3	−1.51732
$555$	0	0
$556$	1764.70	0.134605
$557$	24999.9i	1.90176i	0.309558	+	0.950880i	$0.399819\pi$
$557$	24999.9i	1.90176i	−0.309558	+	0.950880i	$0.600181\pi$
$558$	− 1057.90i	− 0.0802590i
$559$	2513.50	0.190178
$560$	0	0
$561$	1529.44	0.115104
$562$	21588.2i	1.62036i
$563$	5310.86i	0.397560i	0.980044	+	0.198780i	$0.0636978\pi$
$563$	5310.86i	0.397560i	−0.980044	+	0.198780i	$0.936302\pi$
$564$	−73.2825	−0.00547119
$565$	0	0
$566$	11670.8	0.866714
$567$	− 2358.37i	− 0.174678i
$568$	− 7699.82i	− 0.568798i
$569$	−2807.53	−0.206850	−0.103425	−	0.994637i	$-0.532980\pi$
$569$	−2807.53	−0.206850	−0.103425	+	0.994637i	$0.532980\pi$
$570$	0	0
$571$	10299.0	0.754817	0.377408	−	0.926047i	$-0.376815\pi$
$571$	10299.0	0.754817	0.377408	+	0.926047i	$0.376815\pi$
$572$	619.590i	0.0452908i
$573$	− 9794.65i	− 0.714097i
$574$	−17356.3	−1.26209
$575$	0	0
$576$	5111.80	0.369777
$577$	20030.7i	1.44522i	0.691258	+	0.722608i	$0.257057\pi$
$577$	20030.7i	1.44522i	−0.691258	+	0.722608i	$0.742943\pi$
$578$	− 7082.65i	− 0.509687i
$579$	3316.38	0.238038
$580$	0	0
$581$	−21288.6	−1.52013
$582$	10418.4i	0.742023i
$583$	535.944i	0.0380730i
$584$	27517.7	1.94981
$585$	0	0
$586$	−9074.98	−0.639734
$587$	19678.0i	1.38364i	0.722069	+	0.691821i	$0.243191\pi$
$587$	19678.0i	1.38364i	−0.722069	+	0.691821i	$0.756809\pi$
$588$	2178.05i	0.152757i
$589$	1999.50	0.139878
$590$	0	0
$591$	−5499.16	−0.382750
$592$	8971.77i	0.622867i
$593$	− 24115.8i	− 1.67001i	−0.550239	−	0.835007i	$-0.685463\pi$
$593$	− 24115.8i	− 1.67001i	0.550239	−	0.835007i	$-0.314537\pi$
$594$	−760.781	−0.0525509
$595$	0	0
$596$	−2700.49	−0.185598
$597$	16599.4i	1.13797i
$598$	− 9159.42i	− 0.626349i
$599$	6551.51	0.446890	0.223445	−	0.974717i	$-0.428270\pi$
$599$	6551.51	0.446890	0.223445	+	0.974717i	$0.428270\pi$
$600$	0	0
$601$	19752.3	1.34062	0.670312	−	0.742080i	$-0.266160\pi$
$601$	19752.3	1.34062	0.670312	+	0.742080i	$0.266160\pi$
$602$	− 4787.31i	− 0.324113i
$603$	− 3043.73i	− 0.205556i
$604$	792.223	0.0533694
$605$	0	0
$606$	−5021.90	−0.336635
$607$	− 18626.1i	− 1.24548i	−0.782427	−	0.622742i	$-0.786019\pi$
$607$	− 18626.1i	− 1.24548i	0.782427	−	0.622742i	$-0.213981\pi$
$608$	2799.80i	0.186755i
$609$	−16239.6	−1.08056
$610$	0	0
$611$	−664.971	−0.0440292
$612$	600.006i	0.0396304i
$613$	− 13813.6i	− 0.910153i	−0.890452	−	0.455077i	$-0.849612\pi$
$613$	− 13813.6i	− 0.910153i	0.890452	−	0.455077i	$-0.150388\pi$
$614$	−976.827	−0.0642044
$615$	0	0
$616$	7743.25	0.506468
$617$	12406.3i	0.809498i	0.914428	+	0.404749i	$0.132641\pi$
$617$	12406.3i	0.809498i	−0.914428	+	0.404749i	$0.867359\pi$
$618$	− 6159.96i	− 0.400955i
$619$	3686.88	0.239400	0.119700	−	0.992810i	$-0.461807\pi$
$619$	3686.88	0.239400	0.119700	+	0.992810i	$0.461807\pi$
$620$	0	0
$621$	−2465.53	−0.159321
$622$	− 18698.9i	− 1.20540i
$623$	26276.7i	1.68982i
$624$	5923.39	0.380008
$625$	0	0
$626$	−483.936	−0.0308977
$627$	− 1437.92i	− 0.0915871i
$628$	4980.25i	0.316455i
$629$	−8246.43	−0.522745
$630$	0	0
$631$	−13764.1	−0.868369	−0.434184	−	0.900824i	$-0.642963\pi$
$631$	−13764.1	−0.868369	−0.434184	+	0.900824i	$0.642963\pi$
$632$	19942.7i	1.25519i
$633$	− 5240.85i	− 0.329076i
$634$	−11413.0	−0.714933
$635$	0	0
$636$	−210.253	−0.0131086
$637$	19763.8i	1.22931i
$638$	5238.71i	0.325082i
$639$	−2866.28	−0.177447
$640$	0	0
$641$	7042.47	0.433948	0.216974	−	0.976177i	$-0.430381\pi$
$641$	7042.47	0.433948	0.216974	+	0.976177i	$0.430381\pi$
$642$	3676.43i	0.226008i
$643$	− 12564.8i	− 0.770619i	−0.922787	−	0.385310i	$-0.874095\pi$
$643$	− 12564.8i	− 0.770619i	0.922787	−	0.385310i	$-0.125905\pi$
$644$	3824.44	0.234012
$645$	0	0
$646$	5173.02	0.315062
$647$	− 3832.93i	− 0.232903i	−0.993196	−	0.116451i	$-0.962848\pi$
$647$	− 3832.93i	− 0.232903i	0.993196	−	0.116451i	$-0.0371519\pi$
$648$	− 1958.34i	− 0.118721i
$649$	2205.27	0.133381
$650$	0	0
$651$	4008.18	0.241310
$652$	1.85048i	0 0.000111151i
$653$	10886.5i	0.652406i	0.945300	+	0.326203i	$0.105769\pi$
$653$	10886.5i	0.652406i	−0.945300	+	0.326203i	$0.894231\pi$
$654$	7837.65	0.468619
$655$	0	0
$656$	−11734.4	−0.698399
$657$	− 10243.6i	− 0.608280i
$658$	1266.53i	0.0750372i
$659$	8961.77	0.529743	0.264872	−	0.964284i	$-0.414670\pi$
$659$	8961.77	0.529743	0.264872	+	0.964284i	$0.414670\pi$
$660$	0	0
$661$	−891.146	−0.0524380	−0.0262190	−	0.999656i	$-0.508347\pi$
$661$	−891.146	−0.0524380	−0.0262190	+	0.999656i	$0.508347\pi$
$662$	− 14350.5i	− 0.842518i
$663$	5444.50i	0.318924i
$664$	−17677.6	−1.03317
$665$	0	0
$666$	4101.97	0.238661
$667$	16977.6i	0.985568i
$668$	6101.96i	0.353431i
$669$	−16865.6	−0.974679
$670$	0	0
$671$	−5732.08	−0.329783
$672$	5612.46i	0.322180i
$673$	8725.08i	0.499743i	0.968279	+	0.249872i	$0.0803884\pi$
$673$	8725.08i	0.499743i	−0.968279	+	0.249872i	$0.919612\pi$
$674$	−14053.8	−0.803166
$675$	0	0
$676$	954.656	0.0543159
$677$	2431.71i	0.138048i	0.997615	+	0.0690238i	$0.0219884\pi$
$677$	2431.71i	0.138048i	−0.997615	+	0.0690238i	$0.978012\pi$
$678$	3445.06i	0.195143i
$679$	−39473.3	−2.23100
$680$	0	0
$681$	10025.8	0.564154
$682$	− 1292.99i	− 0.0725970i
$683$	6843.80i	0.383412i	0.981452	+	0.191706i	$0.0614021\pi$
$683$	6843.80i	0.383412i	−0.981452	+	0.191706i	$0.938598\pi$
$684$	564.103	0.0315336
$685$	0	0
$686$	12061.4	0.671292
$687$	7143.64i	0.396720i
$688$	− 3236.63i	− 0.179354i
$689$	−1907.85	−0.105491
$690$	0	0
$691$	17520.9	0.964584	0.482292	−	0.876011i	$-0.339804\pi$
$691$	17520.9	0.964584	0.482292	+	0.876011i	$0.339804\pi$
$692$	− 4033.01i	− 0.221549i
$693$	− 2882.45i	− 0.158002i
$694$	4303.14	0.235368
$695$	0	0
$696$	−13485.1	−0.734412
$697$	− 10785.7i	− 0.586136i
$698$	28459.8i	1.54329i
$699$	−20209.3	−1.09354
$700$	0	0
$701$	14700.6	0.792062	0.396031	−	0.918237i	$-0.370387\pi$
$701$	14700.6	0.792062	0.396031	+	0.918237i	$0.370387\pi$
$702$	− 2708.22i	− 0.145606i
$703$	7752.98i	0.415945i
$704$	6247.76	0.334476
$705$	0	0
$706$	−2961.34	−0.157863
$707$	− 19027.0i	− 1.01214i
$708$	865.134i	0.0459234i
$709$	2976.09	0.157644	0.0788219	−	0.996889i	$-0.474884\pi$
$709$	2976.09	0.157644	0.0788219	+	0.996889i	$0.474884\pi$
$710$	0	0
$711$	7423.75	0.391579
$712$	21819.7i	1.14849i
$713$	− 4190.31i	− 0.220096i
$714$	10369.8	0.543529
$715$	0	0
$716$	5176.38	0.270182
$717$	6127.66i	0.319166i
$718$	− 22337.6i	− 1.16105i
$719$	−9293.43	−0.482039	−0.241020	−	0.970520i	$-0.577482\pi$
$719$	−9293.43	−0.482039	−0.241020	+	0.970520i	$0.577482\pi$
$720$	0	0
$721$	23338.9	1.20553
$722$	12706.2i	0.654953i
$723$	17534.6i	0.901964i
$724$	−4477.57	−0.229845
$725$	0	0
$726$	−929.844	−0.0475341
$727$	− 20756.6i	− 1.05890i	−0.848342	−	0.529449i	$-0.822399\pi$
$727$	− 20756.6i	− 1.05890i	0.848342	−	0.529449i	$-0.177601\pi$
$728$	27564.4i	1.40330i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	2974.95	0.150523
$732$	− 2248.72i	− 0.113545i
$733$	11613.2i	0.585188i	0.956237	+	0.292594i	$0.0945185\pi$
$733$	11613.2i	0.585188i	−0.956237	+	0.292594i	$0.905482\pi$
$734$	−24296.7	−1.22181
$735$	0	0
$736$	5867.48	0.293856
$737$	− 3720.12i	− 0.185933i
$738$	5365.05i	0.267602i
$739$	−21437.8	−1.06712	−0.533561	−	0.845761i	$-0.679147\pi$
$739$	−21437.8	−1.06712	−0.533561	+	0.845761i	$0.679147\pi$
$740$	0	0
$741$	5118.71	0.253766
$742$	3633.76i	0.179784i
$743$	29767.7i	1.46981i	0.678168	+	0.734907i	$0.262774\pi$
$743$	29767.7i	1.46981i	−0.678168	+	0.734907i	$0.737226\pi$
$744$	3328.31	0.164008
$745$	0	0
$746$	−32512.4	−1.59566
$747$	6580.55i	0.322315i
$748$	733.340i	0.0358470i
$749$	−13929.3	−0.679525
$750$	0	0
$751$	14231.8	0.691512	0.345756	−	0.938325i	$-0.387623\pi$
$751$	14231.8	0.691512	0.345756	+	0.938325i	$0.387623\pi$
$752$	856.281i	0.0415231i
$753$	8118.51i	0.392902i
$754$	−18648.7	−0.900725
$755$	0	0
$756$	1130.80	0.0544003
$757$	− 37423.1i	− 1.79678i	−0.439194	−	0.898392i	$-0.644736\pi$
$757$	− 37423.1i	− 1.79678i	0.439194	−	0.898392i	$-0.355264\pi$
$758$	− 9167.07i	− 0.439265i
$759$	−3013.43	−0.144111
$760$	0	0
$761$	−13970.6	−0.665485	−0.332743	−	0.943018i	$-0.607974\pi$
$761$	−13970.6	−0.665485	−0.332743	+	0.943018i	$0.607974\pi$
$762$	− 11601.3i	− 0.551535i
$763$	29695.3i	1.40897i
$764$	4696.36	0.222393
$765$	0	0
$766$	22362.4	1.05481
$767$	7850.29i	0.369567i
$768$	6401.22i	0.300761i
$769$	34261.1	1.60661	0.803307	−	0.595565i	$-0.203072\pi$
$769$	34261.1	1.60661	0.803307	+	0.595565i	$0.203072\pi$
$770$	0	0
$771$	−10797.9	−0.504381
$772$	1590.15i	0.0741329i
$773$	− 26487.5i	− 1.23246i	−0.787568	−	0.616228i	$-0.788660\pi$
$773$	− 26487.5i	− 1.23246i	0.787568	−	0.616228i	$-0.211340\pi$
$774$	−1479.81	−0.0687220
$775$	0	0
$776$	−32777.9	−1.51631
$777$	15541.6i	0.717568i
$778$	29331.8i	1.35166i
$779$	−10140.3	−0.466384
$780$	0	0
$781$	−3503.24	−0.160507
$782$	− 10841.0i	− 0.495746i
$783$	5019.87i	0.229113i
$784$	25449.7	1.15933
$785$	0	0
$786$	−21740.3	−0.986580
$787$	− 7240.36i	− 0.327943i	−0.986465	−	0.163971i	$-0.947570\pi$
$787$	− 7240.36i	− 0.327943i	0.986465	−	0.163971i	$-0.0524304\pi$
$788$	− 2636.75i	− 0.119201i
$789$	−8209.17	−0.370411
$790$	0	0
$791$	−13052.6	−0.586724
$792$	− 2393.53i	− 0.107387i
$793$	− 20405.0i	− 0.913749i
$794$	−21127.8	−0.944328
$795$	0	0
$796$	−7959.13	−0.354402
$797$	31135.2i	1.38377i	0.722008	+	0.691885i	$0.243220\pi$
$797$	31135.2i	1.38377i	−0.722008	+	0.691885i	$0.756780\pi$
$798$	− 9749.29i	− 0.432483i
$799$	−787.054	−0.0348485
$800$	0	0
$801$	8122.45	0.358293
$802$	− 27093.7i	− 1.19291i
$803$	− 12519.9i	− 0.550210i
$804$	1459.42	0.0640170
$805$	0	0
$806$	4602.78	0.201149
$807$	− 11224.4i	− 0.489613i
$808$	− 15799.7i	− 0.687908i
$809$	27485.1	1.19447	0.597234	−	0.802067i	$-0.296267\pi$
$809$	27485.1	1.19447	0.597234	+	0.802067i	$0.296267\pi$
$810$	0	0
$811$	−8650.17	−0.374536	−0.187268	−	0.982309i	$-0.559963\pi$
$811$	−8650.17	−0.374536	−0.187268	+	0.982309i	$0.559963\pi$
$812$	− 7786.62i	− 0.336523i
$813$	− 13334.0i	− 0.575207i
$814$	5013.52	0.215877
$815$	0	0
$816$	7010.86	0.300771
$817$	− 2796.94i	− 0.119771i
$818$	21224.9i	0.907226i
$819$	10260.9	0.437785
$820$	0	0
$821$	30823.1	1.31027	0.655136	−	0.755511i	$-0.272611\pi$
$821$	30823.1	1.31027	0.655136	+	0.755511i	$0.272611\pi$
$822$	2510.26i	0.106515i
$823$	22842.2i	0.967473i	0.875214	+	0.483737i	$0.160721\pi$
$823$	22842.2i	0.967473i	−0.875214	+	0.483737i	$0.839279\pi$
$824$	19380.2	0.819344
$825$	0	0
$826$	14952.0	0.629837
$827$	− 17998.5i	− 0.756795i	−0.925643	−	0.378398i	$-0.876475\pi$
$827$	− 17998.5i	− 0.756795i	0.925643	−	0.378398i	$-0.123525\pi$
$828$	− 1182.18i	− 0.0496178i
$829$	6850.35	0.287000	0.143500	−	0.989650i	$-0.454164\pi$
$829$	6850.35	0.287000	0.143500	+	0.989650i	$0.454164\pi$
$830$	0	0
$831$	−23171.9	−0.967296
$832$	22240.7i	0.926754i
$833$	23392.2i	0.972979i
$834$	−9427.63	−0.391430
$835$	0	0
$836$	689.459	0.0285233
$837$	− 1238.98i	− 0.0511652i
$838$	− 4514.78i	− 0.186110i
$839$	−4326.89	−0.178046	−0.0890231	−	0.996030i	$-0.528374\pi$
$839$	−4326.89	−0.178046	−0.0890231	+	0.996030i	$0.528374\pi$
$840$	0	0
$841$	10177.6	0.417303
$842$	28125.2i	1.15114i
$843$	25283.3i	1.03298i
$844$	2512.90	0.102485
$845$	0	0
$846$	391.499	0.0159102
$847$	− 3522.99i	− 0.142918i
$848$	2456.73i	0.0994865i
$849$	13668.4	0.552531
$850$	0	0
$851$	16247.8	0.654485
$852$	− 1374.33i	− 0.0552627i
$853$	6548.50i	0.262856i	0.991326	+	0.131428i	$0.0419563\pi$
$853$	6548.50i	0.262856i	−0.991326	+	0.131428i	$0.958044\pi$
$854$	−38864.1	−1.55726
$855$	0	0
$856$	−11566.6	−0.461844
$857$	− 20052.3i	− 0.799270i	−0.916674	−	0.399635i	$-0.869137\pi$
$857$	− 20052.3i	− 0.799270i	0.916674	−	0.399635i	$-0.130863\pi$
$858$	− 3310.05i	− 0.131706i
$859$	−44548.8	−1.76948	−0.884741	−	0.466083i	$-0.845665\pi$
$859$	−44548.8	−1.76948	−0.884741	+	0.466083i	$0.845665\pi$
$860$	0	0
$861$	−20327.1	−0.804584
$862$	40462.8i	1.59880i
$863$	− 15292.0i	− 0.603182i	−0.953437	−	0.301591i	$-0.902482\pi$
$863$	− 15292.0i	− 0.603182i	0.953437	−	0.301591i	$-0.0975177\pi$
$864$	1734.88	0.0683122
$865$	0	0
$866$	18298.4	0.718020
$867$	− 8294.95i	− 0.324926i
$868$	1921.85i	0.0751519i
$869$	9073.48	0.354196
$870$	0	0
$871$	13242.9	0.515174
$872$	24658.4i	0.957614i
$873$	12201.7i	0.473040i
$874$	−10192.3	−0.394462
$875$	0	0
$876$	4911.61	0.189438
$877$	35175.0i	1.35436i	0.735816	+	0.677182i	$0.236799\pi$
$877$	35175.0i	1.35436i	−0.735816	+	0.677182i	$0.763201\pi$
$878$	− 25475.7i	− 0.979228i
$879$	−10628.3	−0.407831
$880$	0	0
$881$	−803.187	−0.0307152	−0.0153576	−	0.999882i	$-0.504889\pi$
$881$	−803.187	−0.0307152	−0.0153576	+	0.999882i	$0.504889\pi$
$882$	− 11635.8i	− 0.444217i
$883$	12620.8i	0.481001i	0.970649	+	0.240500i	$0.0773115\pi$
$883$	12620.8i	0.481001i	−0.970649	+	0.240500i	$0.922688\pi$
$884$	−2610.54	−0.0993235
$885$	0	0
$886$	−11182.2	−0.424009
$887$	10683.1i	0.404401i	0.979344	+	0.202201i	$0.0648093\pi$
$887$	10683.1i	0.404401i	−0.979344	+	0.202201i	$0.935191\pi$
$888$	12905.4i	0.487700i
$889$	43954.9	1.65827
$890$	0	0
$891$	−891.000	−0.0335013
$892$	− 8086.74i	− 0.303547i
$893$	739.958i	0.0277287i
$894$	14426.9	0.539718
$895$	0	0
$896$	27394.0	1.02139
$897$	− 10727.2i	− 0.399298i
$898$	− 30343.8i	− 1.12760i
$899$	−8531.54	−0.316510
$900$	0	0
$901$	−2258.11	−0.0834946
$902$	6557.29i	0.242055i
$903$	− 5606.72i	− 0.206622i
$904$	−10838.7	−0.398771
$905$	0	0
$906$	−4232.32	−0.155198
$907$	− 3608.81i	− 0.132115i	−0.997816	−	0.0660576i	$-0.978958\pi$
$907$	− 3608.81i	− 0.132115i	0.997816	−	0.0660576i	$-0.0210421\pi$
$908$	4807.18i	0.175696i
$909$	−5881.48	−0.214605
$910$	0	0
$911$	−1664.67	−0.0605413	−0.0302706	−	0.999542i	$-0.509637\pi$
$911$	−1664.67	−0.0605413	−0.0302706	+	0.999542i	$0.509637\pi$
$912$	− 6591.35i	− 0.239322i
$913$	8042.89i	0.291545i
$914$	−36587.3	−1.32407
$915$	0	0
$916$	−3425.25	−0.123552
$917$	− 82369.8i	− 2.96629i
$918$	− 3205.43i	− 0.115245i
$919$	34708.0	1.24582	0.622911	−	0.782293i	$-0.285950\pi$
$919$	34708.0	1.24582	0.622911	+	0.782293i	$0.285950\pi$
$920$	0	0
$921$	−1144.03	−0.0409304
$922$	− 21750.3i	− 0.776907i
$923$	− 12470.8i	− 0.444725i
$924$	1382.08	0.0492070
$925$	0	0
$926$	21890.4	0.776849
$927$	− 7214.33i	− 0.255609i
$928$	− 11946.3i	− 0.422582i
$929$	−32947.1	−1.16357	−0.581787	−	0.813341i	$-0.697646\pi$
$929$	−32947.1	−1.16357	−0.581787	+	0.813341i	$0.697646\pi$
$930$	0	0
$931$	21992.5	0.774193
$932$	− 9690.02i	− 0.340566i
$933$	− 21899.5i	− 0.768443i
$934$	5356.08	0.187641
$935$	0	0
$936$	8520.48	0.297543
$937$	39010.8i	1.36012i	0.733159	+	0.680058i	$0.238045\pi$
$937$	39010.8i	1.36012i	−0.733159	+	0.680058i	$0.761955\pi$
$938$	− 25222.8i	− 0.877990i
$939$	−566.768	−0.0196973
$940$	0	0
$941$	−34916.1	−1.20960	−0.604800	−	0.796378i	$-0.706747\pi$
$941$	−34916.1	−1.20960	−0.604800	+	0.796378i	$0.706747\pi$
$942$	− 26606.1i	− 0.920249i
$943$	21250.8i	0.733851i
$944$	10108.8	0.348531
$945$	0	0
$946$	−1808.66	−0.0621614
$947$	− 37085.2i	− 1.27255i	−0.771462	−	0.636275i	$-0.780474\pi$
$947$	− 37085.2i	− 1.27255i	0.771462	−	0.636275i	$-0.219526\pi$
$948$	3559.56i	0.121951i
$949$	44568.3	1.52450
$950$	0	0
$951$	−13366.5	−0.455771
$952$	32624.9i	1.11069i
$953$	698.553i	0.0237443i	0.999930	+	0.0118722i	$0.00377912\pi$
$953$	698.553i	0.0237443i	−0.999930	+	0.0118722i	$0.996221\pi$
$954$	1123.24	0.0381198
$955$	0	0
$956$	−2938.11	−0.0993987
$957$	6135.39i	0.207240i
$958$	8839.71i	0.298119i
$959$	−9510.87	−0.320252
$960$	0	0
$961$	−27685.3	−0.929317
$962$	17847.1i	0.598143i
$963$	4305.70i	0.144080i
$964$	−8407.54	−0.280901
$965$	0	0
$966$	−20431.4	−0.680507
$967$	49745.5i	1.65430i	0.561982	+	0.827149i	$0.310039\pi$
$967$	49745.5i	1.65430i	−0.561982	+	0.827149i	$0.689961\pi$
$968$	− 2925.43i	− 0.0971351i
$969$	6058.46	0.200852
$970$	0	0
$971$	−18700.1	−0.618039	−0.309019	−	0.951056i	$-0.600001\pi$
$971$	−18700.1	−0.618039	−0.309019	+	0.951056i	$0.600001\pi$
$972$	− 349.543i	− 0.0115346i
$973$	− 35719.4i	− 1.17689i
$974$	−50521.6	−1.66203
$975$	0	0
$976$	−26275.5	−0.861739
$977$	− 30573.7i	− 1.00117i	−0.865689	−	0.500583i	$-0.833119\pi$
$977$	− 30573.7i	− 1.00117i	0.865689	−	0.500583i	$-0.166881\pi$
$978$	− 9.88589i	0 0.000323227i
$979$	9927.44	0.324088
$980$	0	0
$981$	9179.18	0.298745
$982$	− 19020.4i	− 0.618090i
$983$	5278.61i	0.171273i	0.996326	+	0.0856365i	$0.0272924\pi$
$983$	5278.61i	0.171273i	−0.996326	+	0.0856365i	$0.972708\pi$
$984$	−16879.3	−0.546841
$985$	0	0
$986$	−22072.5	−0.712911
$987$	1483.31i	0.0478363i
$988$	2454.33i	0.0790311i
$989$	−5861.49	−0.188458
$990$	0	0
$991$	8366.63	0.268188	0.134094	−	0.990969i	$-0.457188\pi$
$991$	8366.63	0.268188	0.134094	+	0.990969i	$0.457188\pi$
$992$	2948.52i	0.0943706i
$993$	− 16806.8i	− 0.537106i
$994$	−23752.3	−0.757926
$995$	0	0
$996$	−3155.26	−0.100380
$997$	32383.2i	1.02867i	0.857588	+	0.514337i	$0.171962\pi$
$997$	32383.2i	1.02867i	−0.857588	+	0.514337i	$0.828038\pi$
$998$	22347.4i	0.708814i
$999$	4804.08	0.152147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.q.199.1		8
5.2	odd	4		825.4.a.v.1.4	yes	4
5.3	odd	4		825.4.a.u.1.1	✓	4
5.4	even	2	inner	825.4.c.q.199.8		8
15.2	even	4		2475.4.a.bb.1.2		4
15.8	even	4		2475.4.a.bd.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.4.a.u.1.1	✓	4	5.3	odd	4
825.4.a.v.1.4	yes	4	5.2	odd	4
825.4.c.q.199.1		8	1.1	even	1	trivial
825.4.c.q.199.8		8	5.4	even	2	inner
2475.4.a.bb.1.2		4	15.2	even	4
2475.4.a.bd.1.3		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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.56155i q^{2} -3.00000i q^{3} +1.43845 q^{4} -7.68466 q^{6} -29.1157i q^{7} -24.1771i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q-2.56155i q^{2} -3.00000i q^{3} +1.43845 q^{4} -7.68466 q^{6} -29.1157i q^{7} -24.1771i q^{8} -9.00000 q^{9} -11.0000 q^{11} -4.31534i q^{12} -39.1577i q^{13} -74.5813 q^{14} -50.4233 q^{16} -46.3467i q^{17} +23.0540i q^{18} -43.5734 q^{19} -87.3470 q^{21} +28.1771i q^{22} +91.3160i q^{23} -72.5312 q^{24} -100.305 q^{26} +27.0000i q^{27} -41.8813i q^{28} +185.921 q^{29} -45.8880 q^{31} -64.2547i q^{32} +33.0000i q^{33} -118.720 q^{34} -12.9460 q^{36} -177.929i q^{37} +111.616i q^{38} -117.473 q^{39} +232.717 q^{41} +223.744i q^{42} +64.1891i q^{43} -15.8229 q^{44} +233.911 q^{46} -16.9819i q^{47} +151.270i q^{48} -504.722 q^{49} -139.040 q^{51} -56.3263i q^{52} -48.7222i q^{53} +69.1619 q^{54} -703.932 q^{56} +130.720i q^{57} -476.246i q^{58} -200.479 q^{59} +521.098 q^{61} +117.545i q^{62} +262.041i q^{63} -567.978 q^{64} +84.5312 q^{66} +338.192i q^{67} -66.6673i q^{68} +273.948 q^{69} +318.476 q^{71} +217.594i q^{72} +1138.17i q^{73} -455.775 q^{74} -62.6781 q^{76} +320.272i q^{77} +300.914i q^{78} -824.862 q^{79} +81.0000 q^{81} -596.117i q^{82} -731.172i q^{83} -125.644 q^{84} +164.424 q^{86} -557.763i q^{87} +265.948i q^{88} -902.495 q^{89} -1140.10 q^{91} +131.353i q^{92} +137.664i q^{93} -43.4999 q^{94} -192.764 q^{96} -1355.74i q^{97} +1292.87i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 28 q^{4} - 12 q^{6} - 72 q^{9}+O(q^{10}) \) 8 * q + 28 * q^4 - 12 * q^6 - 72 * q^9	\( 8 q + 28 q^{4} - 12 q^{6} - 72 q^{9} - 88 q^{11} + 6 q^{14} - 156 q^{16} - 236 q^{19} - 66 q^{21} - 36 q^{24} - 314 q^{26} - 502 q^{29} - 270 q^{31} - 578 q^{34} - 252 q^{36} - 150 q^{39} - 206 q^{41} - 308 q^{44} - 840 q^{46} - 2006 q^{49} + 510 q^{51} + 108 q^{54} + 154 q^{56} - 1902 q^{59} - 700 q^{61} - 3076 q^{64} + 132 q^{66} + 60 q^{69} + 3052 q^{71} - 2182 q^{74} - 792 q^{76} - 5134 q^{79} + 648 q^{81} - 282 q^{84} + 3674 q^{86} - 2106 q^{89} + 4300 q^{91} - 4418 q^{94} + 1476 q^{96} + 792 q^{99}+O(q^{100}) \) 8 * q + 28 * q^4 - 12 * q^6 - 72 * q^9 - 88 * q^11 + 6 * q^14 - 156 * q^16 - 236 * q^19 - 66 * q^21 - 36 * q^24 - 314 * q^26 - 502 * q^29 - 270 * q^31 - 578 * q^34 - 252 * q^36 - 150 * q^39 - 206 * q^41 - 308 * q^44 - 840 * q^46 - 2006 * q^49 + 510 * q^51 + 108 * q^54 + 154 * q^56 - 1902 * q^59 - 700 * q^61 - 3076 * q^64 + 132 * q^66 + 60 * q^69 + 3052 * q^71 - 2182 * q^74 - 792 * q^76 - 5134 * q^79 + 648 * q^81 - 282 * q^84 + 3674 * q^86 - 2106 * q^89 + 4300 * q^91 - 4418 * q^94 + 1476 * q^96 + 792 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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