LMFDB - Embedded newform 960.4.s.a.241.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,4,Mod(241,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("960.241");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	960.s (of order $4$, degree $2$, 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:	$56.6418336055$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			241.10
Character	$\chi$	$=$	960.241
Dual form			960.4.s.a.721.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12132 + 2.12132i) q^{3} +(3.53553 + 3.53553i) q^{5} -13.5482i q^{7} -9.00000i q^{9} +O(q^{10})$	\(q+(-2.12132 + 2.12132i) q^{3} +(3.53553 + 3.53553i) q^{5} -13.5482i q^{7} -9.00000i q^{9} +(-6.01627 - 6.01627i) q^{11} +(-50.8066 + 50.8066i) q^{13} -15.0000 q^{15} +71.8521 q^{17} +(-14.9694 + 14.9694i) q^{19} +(28.7401 + 28.7401i) q^{21} -118.826i q^{23} +25.0000i q^{25} +(19.0919 + 19.0919i) q^{27} +(-26.4309 + 26.4309i) q^{29} +36.4526 q^{31} +25.5249 q^{33} +(47.9002 - 47.9002i) q^{35} +(77.6123 + 77.6123i) q^{37} -215.554i q^{39} -80.6949i q^{41} +(-149.217 - 149.217i) q^{43} +(31.8198 - 31.8198i) q^{45} +157.924 q^{47} +159.445 q^{49} +(-152.421 + 152.421i) q^{51} +(-219.795 - 219.795i) q^{53} -42.5415i q^{55} -63.5098i q^{57} +(-442.628 - 442.628i) q^{59} +(357.164 - 357.164i) q^{61} -121.934 q^{63} -359.257 q^{65} +(-349.879 + 349.879i) q^{67} +(252.068 + 252.068i) q^{69} +511.645i q^{71} -986.665i q^{73} +(-53.0330 - 53.0330i) q^{75} +(-81.5098 + 81.5098i) q^{77} +285.524 q^{79} -81.0000 q^{81} +(229.843 - 229.843i) q^{83} +(254.036 + 254.036i) q^{85} -112.137i q^{87} +34.2296i q^{89} +(688.340 + 688.340i) q^{91} +(-77.3277 + 77.3277i) q^{93} -105.850 q^{95} +1778.37 q^{97} +(-54.1464 + 54.1464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q+O(q^{10}) $ 44 * q	$ 44 q - 40 q^{11} - 660 q^{15} + 408 q^{17} + 340 q^{19} - 400 q^{29} - 528 q^{33} - 16 q^{37} + 808 q^{43} - 588 q^{49} + 300 q^{51} - 752 q^{53} - 688 q^{59} + 1172 q^{61} - 504 q^{63} - 408 q^{67} + 948 q^{69} - 5816 q^{77} + 2632 q^{79} - 3564 q^{81} - 1104 q^{83} - 500 q^{85} - 2648 q^{91} + 2352 q^{93} - 5432 q^{97} - 360 q^{99}+O(q^{100}) $ 44 * q - 40 * q^11 - 660 * q^15 + 408 * q^17 + 340 * q^19 - 400 * q^29 - 528 * q^33 - 16 * q^37 + 808 * q^43 - 588 * q^49 + 300 * q^51 - 752 * q^53 - 688 * q^59 + 1172 * q^61 - 504 * q^63 - 408 * q^67 + 948 * q^69 - 5816 * q^77 + 2632 * q^79 - 3564 * q^81 - 1104 * q^83 - 500 * q^85 - 2648 * q^91 + 2352 * q^93 - 5432 * q^97 - 360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$4$		0			0
$5$	3.53553	+	3.53553i	0.316228	+	0.316228i
$5$	3.53553	+	3.53553i	0.316228	+	0.316228i
$6$		0			0
$7$		−	13.5482i		−	0.731536i	−0.930706	−	0.365768i	$-0.880806\pi$
$7$		−	13.5482i		−	0.731536i	0.930706	−	0.365768i	$-0.119194\pi$
$8$		0			0
$9$		−	9.00000i		−	0.333333i
$10$		0			0
$11$	−6.01627	−	6.01627i	−0.164907	−	0.164907i	0.619830	−	0.784736i	$-0.287202\pi$
$11$	−6.01627	−	6.01627i	−0.164907	−	0.164907i	−0.784736	+	0.619830i	$0.787202\pi$
$12$		0			0
$13$	−50.8066	+	50.8066i	−1.08394	+	1.08394i	−0.0878016	+	0.996138i	$0.527984\pi$
$13$	−50.8066	+	50.8066i	−1.08394	+	1.08394i	−0.996138	+	0.0878016i	$0.972016\pi$
$14$		0			0
$15$	−15.0000			−0.258199
$16$		0			0
$17$	71.8521			1.02510			0.512550	−	0.858657i	$-0.328701\pi$
$17$	71.8521			1.02510			0.512550	+	0.858657i	$0.328701\pi$
$18$		0			0
$19$	−14.9694	+	14.9694i	−0.180748	+	0.180748i	−0.791682	−	0.610934i	$-0.790794\pi$
$19$	−14.9694	+	14.9694i	−0.180748	+	0.180748i	0.610934	+	0.791682i	$0.290794\pi$
$20$		0			0
$21$	28.7401	+	28.7401i	0.298648	+	0.298648i
$22$		0			0
$23$		−	118.826i		−	1.07726i	−0.842544	−	0.538628i	$-0.818943\pi$
$23$		−	118.826i		−	1.07726i	0.842544	−	0.538628i	$-0.181057\pi$
$24$		0			0
$25$			25.0000i			0.200000i
$26$		0			0
$27$	19.0919	+	19.0919i	0.136083	+	0.136083i
$28$		0			0
$29$	−26.4309	+	26.4309i	−0.169244	+	0.169244i	−0.786647	−	0.617403i	$-0.788185\pi$
$29$	−26.4309	+	26.4309i	−0.169244	+	0.169244i	0.617403	+	0.786647i	$0.288185\pi$
$30$		0			0
$31$	36.4526			0.211196			0.105598	−	0.994409i	$-0.466324\pi$
$31$	36.4526			0.211196			0.105598	+	0.994409i	$0.466324\pi$
$32$		0			0
$33$	25.5249			0.134646
$34$		0			0
$35$	47.9002	−	47.9002i	0.231332	−	0.231332i
$36$		0			0
$37$	77.6123	+	77.6123i	0.344848	+	0.344848i	0.858186	−	0.513338i	$-0.171591\pi$
$37$	77.6123	+	77.6123i	0.344848	+	0.344848i	−0.513338	+	0.858186i	$0.671591\pi$
$38$		0			0
$39$		−	215.554i		−	0.885033i
$40$		0			0
$41$		−	80.6949i		−	0.307376i	−0.988119	−	0.153688i	$-0.950885\pi$
$41$		−	80.6949i		−	0.307376i	0.988119	−	0.153688i	$-0.0491151\pi$
$42$		0			0
$43$	−149.217	−	149.217i	−0.529197	−	0.529197i	0.391136	−	0.920333i	$-0.372082\pi$
$43$	−149.217	−	149.217i	−0.529197	−	0.529197i	−0.920333	+	0.391136i	$0.872082\pi$
$44$		0			0
$45$	31.8198	−	31.8198i	0.105409	−	0.105409i
$46$		0			0
$47$	157.924			0.490119			0.245059	−	0.969508i	$-0.421193\pi$
$47$	157.924			0.490119			0.245059	+	0.969508i	$0.421193\pi$
$48$		0			0
$49$	159.445			0.464855
$50$		0			0
$51$	−152.421	+	152.421i	−0.418495	+	0.418495i
$52$		0			0
$53$	−219.795	−	219.795i	−0.569645	−	0.569645i	0.362384	−	0.932029i	$-0.381963\pi$
$53$	−219.795	−	219.795i	−0.569645	−	0.569645i	−0.932029	+	0.362384i	$0.881963\pi$
$54$		0			0
$55$		−	42.5415i		−	0.104296i
$56$		0			0
$57$		−	63.5098i		−	0.147580i
$58$		0			0
$59$	−442.628	−	442.628i	−0.976700	−	0.976700i	0.0230345	−	0.999735i	$-0.492667\pi$
$59$	−442.628	−	442.628i	−0.976700	−	0.976700i	−0.999735	+	0.0230345i	$0.992667\pi$
$60$		0			0
$61$	357.164	−	357.164i	0.749675	−	0.749675i	−0.224743	−	0.974418i	$-0.572154\pi$
$61$	357.164	−	357.164i	0.749675	−	0.749675i	0.974418	+	0.224743i	$0.0721543\pi$
$62$		0			0
$63$	−121.934			−0.243845
$64$		0			0
$65$	−359.257			−0.685544
$66$		0			0
$67$	−349.879	+	349.879i	−0.637978	+	0.637978i	−0.950056	−	0.312078i	$-0.898975\pi$
$67$	−349.879	+	349.879i	−0.637978	+	0.637978i	0.312078	+	0.950056i	$0.398975\pi$
$68$		0			0
$69$	252.068	+	252.068i	0.439788	+	0.439788i
$70$		0			0
$71$			511.645i			0.855227i	0.903962	+	0.427613i	$0.140646\pi$
$71$			511.645i			0.855227i	−0.903962	+	0.427613i	$0.859354\pi$
$72$		0			0
$73$		−	986.665i		−	1.58192i	−0.611866	−	0.790961i	$-0.709581\pi$
$73$		−	986.665i		−	1.58192i	0.611866	−	0.790961i	$-0.290419\pi$
$74$		0			0
$75$	−53.0330	−	53.0330i	−0.0816497	−	0.0816497i
$76$		0			0
$77$	−81.5098	+	81.5098i	−0.120635	+	0.120635i
$78$		0			0
$79$	285.524			0.406633			0.203316	−	0.979113i	$-0.434828\pi$
$79$	285.524			0.406633			0.203316	+	0.979113i	$0.434828\pi$
$80$		0			0
$81$	−81.0000			−0.111111
$82$		0			0
$83$	229.843	−	229.843i	0.303959	−	0.303959i	−0.538602	−	0.842561i	$-0.681047\pi$
$83$	229.843	−	229.843i	0.303959	−	0.303959i	0.842561	+	0.538602i	$0.181047\pi$
$84$		0			0
$85$	254.036	+	254.036i	0.324165	+	0.324165i
$86$		0			0
$87$		−	112.137i		−	0.138188i
$88$		0			0
$89$			34.2296i			0.0407678i	0.999792	+	0.0203839i	$0.00648884\pi$
$89$			34.2296i			0.0407678i	−0.999792	+	0.0203839i	$0.993511\pi$
$90$		0			0
$91$	688.340	+	688.340i	0.792941	+	0.792941i
$92$		0			0
$93$	−77.3277	+	77.3277i	−0.0862205	+	0.0862205i
$94$		0			0
$95$	−105.850			−0.114315
$96$		0			0
$97$	1778.37			1.86150			0.930751	−	0.365654i	$-0.119155\pi$
$97$	1778.37			1.86150			0.930751	+	0.365654i	$0.119155\pi$
$98$		0			0
$99$	−54.1464	+	54.1464i	−0.0549689	+	0.0549689i
$100$		0			0
$101$	1027.47	+	1027.47i	1.01225	+	1.01225i	0.999924	+	0.0123251i	$0.00392329\pi$
$101$	1027.47	+	1027.47i	1.01225	+	1.01225i	0.0123251	+	0.999924i	$0.496077\pi$
$102$		0			0
$103$		−	924.381i		−	0.884291i	−0.896943	−	0.442145i	$-0.854218\pi$
$103$		−	924.381i		−	0.884291i	0.896943	−	0.442145i	$-0.145782\pi$
$104$		0			0
$105$			203.223i			0.188882i
$106$		0			0
$107$	72.9780	+	72.9780i	0.0659350	+	0.0659350i	0.739305	−	0.673370i	$-0.235154\pi$
$107$	72.9780	+	72.9780i	0.0659350	+	0.0659350i	−0.673370	+	0.739305i	$0.735154\pi$
$108$		0			0
$109$	1195.75	−	1195.75i	1.05075	−	1.05075i	0.0521089	−	0.998641i	$-0.483406\pi$
$109$	1195.75	−	1195.75i	1.05075	−	1.05075i	0.998641	−	0.0521089i	$-0.0165943\pi$
$110$		0			0
$111$	−329.281			−0.281567
$112$		0			0
$113$	1565.59			1.30334			0.651672	−	0.758501i	$-0.274068\pi$
$113$	1565.59			1.30334			0.651672	+	0.758501i	$0.274068\pi$
$114$		0			0
$115$	420.113	−	420.113i	0.340658	−	0.340658i
$116$		0			0
$117$	457.259	+	457.259i	0.361313	+	0.361313i
$118$		0			0
$119$		−	973.470i		−	0.749898i
$120$		0			0
$121$		−	1258.61i		−	0.945612i
$122$		0			0
$123$	171.180	+	171.180i	0.125486	+	0.125486i
$124$		0			0
$125$	−88.3883	+	88.3883i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−1814.14			−1.26755			−0.633775	−	0.773517i	$-0.718496\pi$
$127$	−1814.14			−1.26755			−0.633775	+	0.773517i	$0.718496\pi$
$128$		0			0
$129$	633.076			0.432087
$130$		0			0
$131$	1521.66	−	1521.66i	1.01487	−	1.01487i	0.0149847	−	0.999888i	$-0.495230\pi$
$131$	1521.66	−	1521.66i	1.01487	−	1.01487i	0.999888	−	0.0149847i	$-0.00476996\pi$
$132$		0			0
$133$	202.809	+	202.809i	0.132224	+	0.132224i
$134$		0			0
$135$			135.000i			0.0860663i
$136$		0			0
$137$		−	1064.25i		−	0.663688i	−0.943334	−	0.331844i	$-0.892329\pi$
$137$		−	1064.25i		−	0.663688i	0.943334	−	0.331844i	$-0.107671\pi$
$138$		0			0
$139$	2293.39	+	2293.39i	1.39944	+	1.39944i	0.801656	+	0.597785i	$0.203953\pi$
$139$	2293.39	+	2293.39i	1.39944	+	1.39944i	0.597785	+	0.801656i	$0.296047\pi$
$140$		0			0
$141$	−335.007	+	335.007i	−0.200090	+	0.200090i
$142$		0			0
$143$	611.332			0.357498
$144$		0			0
$145$	−186.894			−0.107040
$146$		0			0
$147$	−338.235	+	338.235i	−0.189776	+	0.189776i
$148$		0			0
$149$	−63.1226	−	63.1226i	−0.0347061	−	0.0347061i	0.689541	−	0.724247i	$-0.257812\pi$
$149$	−63.1226	−	63.1226i	−0.0347061	−	0.0347061i	−0.724247	+	0.689541i	$0.757812\pi$
$150$		0			0
$151$		−	398.151i		−	0.214577i	−0.994228	−	0.107288i	$-0.965783\pi$
$151$		−	398.151i		−	0.214577i	0.994228	−	0.107288i	$-0.0342168\pi$
$152$		0			0
$153$		−	646.669i		−	0.341700i
$154$		0			0
$155$	128.879	+	128.879i	0.0667861	+	0.0667861i
$156$		0			0
$157$	47.7551	−	47.7551i	0.0242756	−	0.0242756i	−0.694865	−	0.719140i	$-0.744536\pi$
$157$	47.7551	−	47.7551i	0.0242756	−	0.0242756i	0.719140	+	0.694865i	$0.244536\pi$
$158$		0			0
$159$	932.512			0.465113
$160$		0			0
$161$	−1609.88			−0.788051
$162$		0			0
$163$	771.180	−	771.180i	0.370573	−	0.370573i	−0.497113	−	0.867686i	$-0.665606\pi$
$163$	771.180	−	771.180i	0.370573	−	0.370573i	0.867686	+	0.497113i	$0.165606\pi$
$164$		0			0
$165$	90.2441	+	90.2441i	0.0425787	+	0.0425787i
$166$		0			0
$167$		−	2277.25i		−	1.05520i	−0.849493	−	0.527600i	$-0.823092\pi$
$167$		−	2277.25i		−	1.05520i	0.849493	−	0.527600i	$-0.176908\pi$
$168$		0			0
$169$		−	2965.62i		−	1.34985i
$170$		0			0
$171$	134.725	+	134.725i	0.0602494	+	0.0602494i
$172$		0			0
$173$	−571.214	+	571.214i	−0.251033	+	0.251033i	−0.821394	−	0.570361i	$-0.806803\pi$
$173$	−571.214	+	571.214i	−0.251033	+	0.251033i	0.570361	+	0.821394i	$0.306803\pi$
$174$		0			0
$175$	338.706			0.146307
$176$		0			0
$177$	1877.91			0.797472
$178$		0			0
$179$	1269.80	−	1269.80i	0.530221	−	0.530221i	−0.390417	−	0.920638i	$-0.627669\pi$
$179$	1269.80	−	1269.80i	0.530221	−	0.530221i	0.920638	+	0.390417i	$0.127669\pi$
$180$		0			0
$181$	−2334.97	−	2334.97i	−0.958880	−	0.958880i	0.0403076	−	0.999187i	$-0.487166\pi$
$181$	−2334.97	−	2334.97i	−0.958880	−	0.958880i	−0.999187	+	0.0403076i	$0.987166\pi$
$182$		0			0
$183$			1515.32i			0.612107i
$184$		0			0
$185$			548.802i			0.218101i
$186$		0			0
$187$	−432.282	−	432.282i	−0.169046	−	0.169046i
$188$		0			0
$189$	258.661	−	258.661i	0.0995494	−	0.0995494i
$190$		0			0
$191$	3591.88			1.36073			0.680364	−	0.732874i	$-0.261822\pi$
$191$	3591.88			1.36073			0.680364	+	0.732874i	$0.261822\pi$
$192$		0			0
$193$	−2429.07			−0.905951			−0.452975	−	0.891523i	$-0.649637\pi$
$193$	−2429.07			−0.905951			−0.452975	+	0.891523i	$0.649637\pi$
$194$		0			0
$195$	762.099	−	762.099i	0.279872	−	0.279872i
$196$		0			0
$197$	3483.32	+	3483.32i	1.25978	+	1.25978i	0.951199	+	0.308577i	$0.0998527\pi$
$197$	3483.32	+	3483.32i	1.25978	+	1.25978i	0.308577	+	0.951199i	$0.400147\pi$
$198$		0			0
$199$		−	822.537i		−	0.293006i	−0.989210	−	0.146503i	$-0.953198\pi$
$199$		−	822.537i		−	0.293006i	0.989210	−	0.146503i	$-0.0468017\pi$
$200$		0			0
$201$		−	1484.41i		−	0.520907i
$202$		0			0
$203$	358.092	+	358.092i	0.123808	+	0.123808i
$204$		0			0
$205$	285.300	−	285.300i	0.0972009	−	0.0972009i
$206$		0			0
$207$	−1069.43			−0.359085
$208$		0			0
$209$	180.120			0.0596132
$210$		0			0
$211$	3623.66	−	3623.66i	1.18229	−	1.18229i	0.203138	−	0.979150i	$-0.434886\pi$
$211$	3623.66	−	3623.66i	1.18229	−	1.18229i	0.979150	−	0.203138i	$-0.0651140\pi$
$212$		0			0
$213$	−1085.36	−	1085.36i	−0.349145	−	0.349145i
$214$		0			0
$215$		−	1055.13i		−	0.334693i
$216$		0			0
$217$		−	493.868i		−	0.154498i
$218$		0			0
$219$	2093.03	+	2093.03i	0.645817	+	0.645817i
$220$		0			0
$221$	−3650.56	+	3650.56i	−1.11115	+	1.11115i
$222$		0			0
$223$	−694.908			−0.208675			−0.104337	−	0.994542i	$-0.533272\pi$
$223$	−694.908			−0.208675			−0.104337	+	0.994542i	$0.533272\pi$
$224$		0			0
$225$	225.000			0.0666667
$226$		0			0
$227$	1591.61	−	1591.61i	0.465370	−	0.465370i	−0.435041	−	0.900411i	$-0.643266\pi$
$227$	1591.61	−	1591.61i	0.465370	−	0.465370i	0.900411	+	0.435041i	$0.143266\pi$
$228$		0			0
$229$	94.9286	+	94.9286i	0.0273933	+	0.0273933i	0.720671	−	0.693277i	$-0.243834\pi$
$229$	94.9286	+	94.9286i	0.0273933	+	0.0273933i	−0.693277	+	0.720671i	$0.743834\pi$
$230$		0			0
$231$		−	345.817i		−	0.0984982i
$232$		0			0
$233$		−	3358.31i		−	0.944249i	−0.881532	−	0.472125i	$-0.843487\pi$
$233$		−	3358.31i		−	0.944249i	0.881532	−	0.472125i	$-0.156513\pi$
$234$		0			0
$235$	558.345	+	558.345i	0.154989	+	0.154989i
$236$		0			0
$237$	−605.688	+	605.688i	−0.166007	+	0.166007i
$238$		0			0
$239$	−906.113			−0.245237			−0.122618	−	0.992454i	$-0.539129\pi$
$239$	−906.113			−0.245237			−0.122618	+	0.992454i	$0.539129\pi$
$240$		0			0
$241$	1769.39			0.472931			0.236466	−	0.971640i	$-0.424011\pi$
$241$	1769.39			0.472931			0.236466	+	0.971640i	$0.424011\pi$
$242$		0			0
$243$	171.827	−	171.827i	0.0453609	−	0.0453609i
$244$		0			0
$245$	563.725	+	563.725i	0.147000	+	0.147000i
$246$		0			0
$247$		−	1521.09i		−	0.391840i
$248$		0			0
$249$			975.143i			0.248181i
$250$		0			0
$251$	3946.29	+	3946.29i	0.992382	+	0.992382i	0.999971	−	0.00758956i	$-0.00241585\pi$
$251$	3946.29	+	3946.29i	0.992382	+	0.992382i	−0.00758956	+	0.999971i	$0.502416\pi$
$252$		0			0
$253$	−714.888	+	714.888i	−0.177647	+	0.177647i
$254$		0			0
$255$	−1077.78			−0.264680
$256$		0			0
$257$	−1234.85			−0.299720			−0.149860	−	0.988707i	$-0.547882\pi$
$257$	−1234.85			−0.299720			−0.149860	+	0.988707i	$0.547882\pi$
$258$		0			0
$259$	1051.51	−	1051.51i	0.252269	−	0.252269i
$260$		0			0
$261$	237.878	+	237.878i	0.0564148	+	0.0564148i
$262$		0			0
$263$			5718.48i			1.34075i	0.742024	+	0.670374i	$0.233866\pi$
$263$			5718.48i			1.34075i	−0.742024	+	0.670374i	$0.766134\pi$
$264$		0			0
$265$		−	1554.19i		−	0.360275i
$266$		0			0
$267$	−72.6119	−	72.6119i	−0.0166434	−	0.0166434i
$268$		0			0
$269$	−5230.79	+	5230.79i	−1.18560	+	1.18560i	−0.207332	+	0.978271i	$0.566478\pi$
$269$	−5230.79	+	5230.79i	−1.18560	+	1.18560i	−0.978271	+	0.207332i	$0.933522\pi$
$270$		0			0
$271$	−6787.00			−1.52133			−0.760666	−	0.649143i	$-0.775128\pi$
$271$	−6787.00			−1.52133			−0.760666	+	0.649143i	$0.775128\pi$
$272$		0			0
$273$	−2920.38			−0.647433
$274$		0			0
$275$	150.407	−	150.407i	0.0329813	−	0.0329813i
$276$		0			0
$277$	1892.29	+	1892.29i	0.410457	+	0.410457i	0.881898	−	0.471441i	$-0.156266\pi$
$277$	1892.29	+	1892.29i	0.410457	+	0.410457i	−0.471441	+	0.881898i	$0.656266\pi$
$278$		0			0
$279$		−	328.073i		−	0.0703987i
$280$		0			0
$281$			3029.97i			0.643250i	0.946867	+	0.321625i	$0.104229\pi$
$281$			3029.97i			0.643250i	−0.946867	+	0.321625i	$0.895771\pi$
$282$		0			0
$283$	−5398.96	−	5398.96i	−1.13405	−	1.13405i	−0.989498	−	0.144547i	$-0.953827\pi$
$283$	−5398.96	−	5398.96i	−1.13405	−	1.13405i	−0.144547	−	0.989498i	$-0.546173\pi$
$284$		0			0
$285$	224.541	−	224.541i	0.0466690	−	0.0466690i
$286$		0			0
$287$	−1093.27			−0.224857
$288$		0			0
$289$	249.731			0.0508306
$290$		0			0
$291$	−3772.48	+	3772.48i	−0.759955	+	0.759955i
$292$		0			0
$293$	−6707.32	−	6707.32i	−1.33736	−	1.33736i	−0.898610	−	0.438748i	$-0.855422\pi$
$293$	−6707.32	−	6707.32i	−1.33736	−	1.33736i	−0.438748	−	0.898610i	$-0.644578\pi$
$294$		0			0
$295$		−	3129.86i		−	0.617719i
$296$		0			0
$297$		−	229.724i		−	0.0448819i
$298$		0			0
$299$	6037.13	+	6037.13i	1.16768	+	1.16768i
$300$		0			0
$301$	−2021.63	+	2021.63i	−0.387126	+	0.387126i
$302$		0			0
$303$	−4359.19			−0.826498
$304$		0			0
$305$	2525.53			0.474136
$306$		0			0
$307$	2960.73	−	2960.73i	0.550416	−	0.550416i	−0.376145	−	0.926561i	$-0.622751\pi$
$307$	2960.73	−	2960.73i	0.550416	−	0.550416i	0.926561	+	0.376145i	$0.122751\pi$
$308$		0			0
$309$	1960.91	+	1960.91i	0.361010	+	0.361010i
$310$		0			0
$311$		−	985.088i		−	0.179612i	−0.995959	−	0.0898058i	$-0.971375\pi$
$311$		−	985.088i		−	0.179612i	0.995959	−	0.0898058i	$-0.0286247\pi$
$312$		0			0
$313$		−	6501.09i		−	1.17400i	−0.809585	−	0.587002i	$-0.800308\pi$
$313$		−	6501.09i		−	1.17400i	0.809585	−	0.587002i	$-0.199692\pi$
$314$		0			0
$315$	−431.102	−	431.102i	−0.0771106	−	0.0771106i
$316$		0			0
$317$	−6070.48	+	6070.48i	−1.07556	+	1.07556i	−0.0786561	+	0.996902i	$0.525063\pi$
$317$	−6070.48	+	6070.48i	−1.07556	+	1.07556i	−0.996902	+	0.0786561i	$0.974937\pi$
$318$		0			0
$319$	318.031			0.0558191
$320$		0			0
$321$	−309.619			−0.0538357
$322$		0			0
$323$	−1075.58	+	1075.58i	−0.185285	+	0.185285i
$324$		0			0
$325$	−1270.16	−	1270.16i	−0.216788	−	0.216788i
$326$		0			0
$327$			5073.12i			0.857934i
$328$		0			0
$329$		−	2139.59i		−	0.358539i
$330$		0			0
$331$	5023.23	+	5023.23i	0.834144	+	0.834144i	0.988081	−	0.153936i	$-0.0491951\pi$
$331$	5023.23	+	5023.23i	0.834144	+	0.834144i	−0.153936	+	0.988081i	$0.549195\pi$
$332$		0			0
$333$	698.511	−	698.511i	0.114949	−	0.114949i
$334$		0			0
$335$	−2474.02			−0.403493
$336$		0			0
$337$	9173.72			1.48286			0.741431	−	0.671029i	$-0.234148\pi$
$337$	9173.72			1.48286			0.741431	+	0.671029i	$0.234148\pi$
$338$		0			0
$339$	−3321.11	+	3321.11i	−0.532088	+	0.532088i
$340$		0			0
$341$	−219.309	−	219.309i	−0.0348277	−	0.0348277i
$342$		0			0
$343$		−	6807.25i		−	1.07159i
$344$		0			0
$345$			1782.39i			0.278146i
$346$		0			0
$347$	−6259.49	−	6259.49i	−0.968378	−	0.968378i	0.0311371	−	0.999515i	$-0.490087\pi$
$347$	−6259.49	−	6259.49i	−0.968378	−	0.968378i	−0.999515	+	0.0311371i	$0.990087\pi$
$348$		0			0
$349$	5943.39	−	5943.39i	0.911583	−	0.911583i	−0.0848143	−	0.996397i	$-0.527030\pi$
$349$	5943.39	−	5943.39i	0.911583	−	0.911583i	0.996397	+	0.0848143i	$0.0270297\pi$
$350$		0			0
$351$	−1939.99			−0.295011
$352$		0			0
$353$	−1094.98			−0.165099			−0.0825497	−	0.996587i	$-0.526306\pi$
$353$	−1094.98			−0.165099			−0.0825497	+	0.996587i	$0.526306\pi$
$354$		0			0
$355$	−1808.94	+	1808.94i	−0.270446	+	0.270446i
$356$		0			0
$357$	2065.04	+	2065.04i	0.306144	+	0.306144i
$358$		0			0
$359$			10707.2i			1.57410i	0.616886	+	0.787052i	$0.288394\pi$
$359$			10707.2i			1.57410i	−0.616886	+	0.787052i	$0.711606\pi$
$360$		0			0
$361$			6410.83i			0.934660i
$362$		0			0
$363$	2669.91	+	2669.91i	0.386044	+	0.386044i
$364$		0			0
$365$	3488.39	−	3488.39i	0.500248	−	0.500248i
$366$		0			0
$367$	−8688.58			−1.23580			−0.617902	−	0.786255i	$-0.712017\pi$
$367$	−8688.58			−1.23580			−0.617902	+	0.786255i	$0.712017\pi$
$368$		0			0
$369$	−726.254			−0.102459
$370$		0			0
$371$	−2977.84	+	2977.84i	−0.416716	+	0.416716i
$372$		0			0
$373$	5686.96	+	5686.96i	0.789436	+	0.789436i	0.981402	−	0.191966i	$-0.0614862\pi$
$373$	5686.96	+	5686.96i	0.789436	+	0.789436i	−0.191966	+	0.981402i	$0.561486\pi$
$374$		0			0
$375$		−	375.000i		−	0.0516398i
$376$		0			0
$377$		−	2685.72i		−	0.366902i
$378$		0			0
$379$	3375.73	+	3375.73i	0.457519	+	0.457519i	0.897840	−	0.440321i	$-0.145135\pi$
$379$	3375.73	+	3375.73i	0.457519	+	0.457519i	−0.440321	+	0.897840i	$0.645135\pi$
$380$		0			0
$381$	3848.37	−	3848.37i	0.517475	−	0.517475i
$382$		0			0
$383$	−13409.1			−1.78896			−0.894482	−	0.447103i	$-0.852456\pi$
$383$	−13409.1			−1.78896			−0.894482	+	0.447103i	$0.852456\pi$
$384$		0			0
$385$	−576.362			−0.0762964
$386$		0			0
$387$	−1342.96	+	1342.96i	−0.176399	+	0.176399i
$388$		0			0
$389$	−322.490	−	322.490i	−0.0420332	−	0.0420332i	0.685778	−	0.727811i	$-0.259462\pi$
$389$	−322.490	−	322.490i	−0.0420332	−	0.0420332i	−0.727811	+	0.685778i	$0.759462\pi$
$390$		0			0
$391$		−	8537.89i		−	1.10430i
$392$		0			0
$393$			6455.87i			0.828640i
$394$		0			0
$395$	1009.48	+	1009.48i	0.128589	+	0.128589i
$396$		0			0
$397$	113.547	−	113.547i	0.0143546	−	0.0143546i	−0.699893	−	0.714248i	$-0.746769\pi$
$397$	113.547	−	113.547i	0.0143546	−	0.0143546i	0.714248	+	0.699893i	$0.246769\pi$
$398$		0			0
$399$	−860.446			−0.107960
$400$		0			0
$401$	9904.26			1.23340			0.616702	−	0.787197i	$-0.288468\pi$
$401$	9904.26			1.23340			0.616702	+	0.787197i	$0.288468\pi$
$402$		0			0
$403$	−1852.03	+	1852.03i	−0.228924	+	0.228924i
$404$		0			0
$405$	−286.378	−	286.378i	−0.0351364	−	0.0351364i
$406$		0			0
$407$		−	933.874i		−	0.113736i
$408$		0			0
$409$		−	10584.4i		−	1.27962i	−0.768534	−	0.639809i	$-0.779013\pi$
$409$		−	10584.4i		−	1.27962i	0.768534	−	0.639809i	$-0.220987\pi$
$410$		0			0
$411$	2257.62	+	2257.62i	0.270949	+	0.270949i
$412$		0			0
$413$	−5996.83	+	5996.83i	−0.714491	+	0.714491i
$414$		0			0
$415$	1625.24			0.192240
$416$		0			0
$417$	−9730.01			−1.14264
$418$		0			0
$419$	2538.61	−	2538.61i	0.295988	−	0.295988i	−0.543452	−	0.839440i	$-0.682883\pi$
$419$	2538.61	−	2538.61i	0.295988	−	0.295988i	0.839440	+	0.543452i	$0.182883\pi$
$420$		0			0
$421$	−6034.45	−	6034.45i	−0.698578	−	0.698578i	0.265526	−	0.964104i	$-0.414454\pi$
$421$	−6034.45	−	6034.45i	−0.698578	−	0.698578i	−0.964104	+	0.265526i	$0.914454\pi$
$422$		0			0
$423$		−	1421.32i		−	0.163373i
$424$		0			0
$425$			1796.30i			0.205020i
$426$		0			0
$427$	−4838.94	−	4838.94i	−0.548414	−	0.548414i
$428$		0			0
$429$	−1296.83	+	1296.83i	−0.145948	+	0.145948i
$430$		0			0
$431$	−15334.7			−1.71379			−0.856896	−	0.515489i	$-0.827610\pi$
$431$	−15334.7			−1.71379			−0.856896	+	0.515489i	$0.827610\pi$
$432$		0			0
$433$	−14712.7			−1.63290			−0.816450	−	0.577415i	$-0.804061\pi$
$433$	−14712.7			−1.63290			−0.816450	+	0.577415i	$0.804061\pi$
$434$		0			0
$435$	396.463	−	396.463i	0.0436987	−	0.0436987i
$436$		0			0
$437$	1778.75	+	1778.75i	0.194712	+	0.194712i
$438$		0			0
$439$			10178.2i			1.10656i	0.832995	+	0.553280i	$0.186624\pi$
$439$			10178.2i			1.10656i	−0.832995	+	0.553280i	$0.813376\pi$
$440$		0			0
$441$		−	1435.01i		−	0.154952i
$442$		0			0
$443$	−5291.14	−	5291.14i	−0.567471	−	0.567471i	0.363948	−	0.931419i	$-0.381429\pi$
$443$	−5291.14	−	5291.14i	−0.567471	−	0.567471i	−0.931419	+	0.363948i	$0.881429\pi$
$444$		0			0
$445$	−121.020	+	121.020i	−0.0128919	+	0.0128919i
$446$		0			0
$447$	267.807			0.0283374
$448$		0			0
$449$	8514.28			0.894908			0.447454	−	0.894307i	$-0.352331\pi$
$449$	8514.28			0.894908			0.447454	+	0.894307i	$0.352331\pi$
$450$		0			0
$451$	−485.482	+	485.482i	−0.0506884	+	0.0506884i
$452$		0			0
$453$	844.606	+	844.606i	0.0876006	+	0.0876006i
$454$		0			0
$455$			4867.30i			0.501500i
$456$		0			0
$457$			820.612i			0.0839970i	0.999118	+	0.0419985i	$0.0133725\pi$
$457$			820.612i			0.0839970i	−0.999118	+	0.0419985i	$0.986628\pi$
$458$		0			0
$459$	1371.79	+	1371.79i	0.139498	+	0.139498i
$460$		0			0
$461$	−10004.4	+	10004.4i	−1.01074	+	1.01074i	−0.0108013	+	0.999942i	$0.503438\pi$
$461$	−10004.4	+	10004.4i	−1.01074	+	1.01074i	−0.999942	+	0.0108013i	$0.996562\pi$
$462$		0			0
$463$	3531.86			0.354512			0.177256	−	0.984165i	$-0.443278\pi$
$463$	3531.86			0.354512			0.177256	+	0.984165i	$0.443278\pi$
$464$		0			0
$465$	−546.789			−0.0545306
$466$		0			0
$467$	−3208.50	+	3208.50i	−0.317926	+	0.317926i	−0.847970	−	0.530044i	$-0.822175\pi$
$467$	−3208.50	+	3208.50i	−0.317926	+	0.317926i	0.530044	+	0.847970i	$0.322175\pi$
$468$		0			0
$469$	4740.25	+	4740.25i	0.466704	+	0.466704i
$470$		0			0
$471$			202.608i			0.0198210i
$472$		0			0
$473$			1795.47i			0.174536i
$474$		0			0
$475$	−374.235	−	374.235i	−0.0361496	−	0.0361496i
$476$		0			0
$477$	−1978.16	+	1978.16i	−0.189882	+	0.189882i
$478$		0			0
$479$	17257.4			1.64616			0.823078	−	0.567928i	$-0.192255\pi$
$479$	17257.4			1.64616			0.823078	+	0.567928i	$0.192255\pi$
$480$		0			0
$481$	−7886.44			−0.747589
$482$		0			0
$483$	3415.07	−	3415.07i	0.321721	−	0.321721i
$484$		0			0
$485$	6287.47	+	6287.47i	0.588659	+	0.588659i
$486$		0			0
$487$		−	17541.7i		−	1.63222i	−0.577896	−	0.816111i	$-0.696126\pi$
$487$		−	17541.7i		−	1.63222i	0.577896	−	0.816111i	$-0.303874\pi$
$488$		0			0
$489$			3271.84i			0.302572i
$490$		0			0
$491$	−3262.01	−	3262.01i	−0.299821	−	0.299821i	0.541122	−	0.840944i	$-0.318000\pi$
$491$	−3262.01	−	3262.01i	−0.299821	−	0.299821i	−0.840944	+	0.541122i	$0.818000\pi$
$492$		0			0
$493$	−1899.11	+	1899.11i	−0.173493	+	0.173493i
$494$		0			0
$495$	−382.873			−0.0347654
$496$		0			0
$497$	6931.89			0.625629
$498$		0			0
$499$	5408.23	−	5408.23i	0.485182	−	0.485182i	−0.421600	−	0.906782i	$-0.638531\pi$
$499$	5408.23	−	5408.23i	0.485182	−	0.485182i	0.906782	+	0.421600i	$0.138531\pi$
$500$		0			0
$501$	4830.77	+	4830.77i	0.430784	+	0.430784i
$502$		0			0
$503$			12087.6i			1.07149i	0.844379	+	0.535747i	$0.179970\pi$
$503$			12087.6i			1.07149i	−0.844379	+	0.535747i	$0.820030\pi$
$504$		0			0
$505$			7265.32i			0.640203i
$506$		0			0
$507$	6291.03	+	6291.03i	0.551074	+	0.551074i
$508$		0			0
$509$	−4156.78	+	4156.78i	−0.361977	+	0.361977i	−0.864540	−	0.502564i	$-0.832390\pi$
$509$	−4156.78	+	4156.78i	−0.361977	+	0.361977i	0.502564	+	0.864540i	$0.332390\pi$
$510$		0			0
$511$	−13367.6			−1.15723
$512$		0			0
$513$	−571.588			−0.0491934
$514$		0			0
$515$	3268.18	−	3268.18i	0.279637	−	0.279637i
$516$		0			0
$517$	−950.113	−	950.113i	−0.0808238	−	0.0808238i
$518$		0			0
$519$		−	2423.46i		−	0.204967i
$520$		0			0
$521$		−	1176.74i		−	0.0989520i	−0.998775	−	0.0494760i	$-0.984245\pi$
$521$		−	1176.74i		−	0.0989520i	0.998775	−	0.0494760i	$-0.0157551\pi$
$522$		0			0
$523$	2214.14	+	2214.14i	0.185120	+	0.185120i	0.793582	−	0.608463i	$-0.208214\pi$
$523$	2214.14	+	2214.14i	0.185120	+	0.185120i	−0.608463	+	0.793582i	$0.708214\pi$
$524$		0			0
$525$	−718.504	+	718.504i	−0.0597297	+	0.0597297i
$526$		0			0
$527$	2619.20			0.216497
$528$		0			0
$529$	−1952.57			−0.160481
$530$		0			0
$531$	−3983.66	+	3983.66i	−0.325567	+	0.325567i
$532$		0			0
$533$	4099.83	+	4099.83i	0.333177	+	0.333177i
$534$		0			0
$535$			516.032i			0.0417010i
$536$		0			0
$537$			5387.31i			0.432923i
$538$		0			0
$539$	−959.267	−	959.267i	−0.0766578	−	0.0766578i
$540$		0			0
$541$	6650.21	−	6650.21i	0.528493	−	0.528493i	−0.391630	−	0.920123i	$-0.628089\pi$
$541$	6650.21	−	6650.21i	0.528493	−	0.528493i	0.920123	+	0.391630i	$0.128089\pi$
$542$		0			0
$543$	9906.45			0.782922
$544$		0			0
$545$	8455.21			0.664553
$546$		0			0
$547$	−13262.5	+	13262.5i	−1.03668	+	1.03668i	−0.0373742	+	0.999301i	$0.511899\pi$
$547$	−13262.5	+	13262.5i	−1.03668	+	1.03668i	−0.999301	+	0.0373742i	$0.988101\pi$
$548$		0			0
$549$	−3214.48	−	3214.48i	−0.249892	−	0.249892i
$550$		0			0
$551$		−	791.309i		−	0.0611813i
$552$		0			0
$553$		−	3868.35i		−	0.297466i
$554$		0			0
$555$	−1164.18	−	1164.18i	−0.0890395	−	0.0890395i
$556$		0			0
$557$	−9488.83	+	9488.83i	−0.721822	+	0.721822i	−0.968976	−	0.247155i	$-0.920504\pi$
$557$	−9488.83	+	9488.83i	−0.721822	+	0.721822i	0.247155	+	0.968976i	$0.420504\pi$
$558$		0			0
$559$	15162.5			1.14723
$560$		0			0
$561$	1834.02			0.138025
$562$		0			0
$563$	−14911.6	+	14911.6i	−1.11625	+	1.11625i	−0.123962	+	0.992287i	$0.539560\pi$
$563$	−14911.6	+	14911.6i	−1.11625	+	1.11625i	−0.992287	+	0.123962i	$0.960440\pi$
$564$		0			0
$565$	5535.18	+	5535.18i	0.412154	+	0.412154i
$566$		0			0
$567$			1097.41i			0.0812818i
$568$		0			0
$569$		−	10582.4i		−	0.779677i	−0.920883	−	0.389838i	$-0.872531\pi$
$569$		−	10582.4i		−	0.779677i	0.920883	−	0.389838i	$-0.127469\pi$
$570$		0			0
$571$	−2988.97	−	2988.97i	−0.219062	−	0.219062i	0.589041	−	0.808103i	$-0.299506\pi$
$571$	−2988.97	−	2988.97i	−0.219062	−	0.219062i	−0.808103	+	0.589041i	$0.799506\pi$
$572$		0			0
$573$	−7619.52	+	7619.52i	−0.555515	+	0.555515i
$574$		0			0
$575$	2970.64			0.215451
$576$		0			0
$577$	2968.32			0.214165			0.107082	−	0.994250i	$-0.465849\pi$
$577$	2968.32			0.214165			0.107082	+	0.994250i	$0.465849\pi$
$578$		0			0
$579$	5152.84	−	5152.84i	0.369853	−	0.369853i
$580$		0			0
$581$	−3113.97	−	3113.97i	−0.222357	−	0.222357i
$582$		0			0
$583$			2644.70i			0.187877i
$584$		0			0
$585$			3233.31i			0.228515i
$586$		0			0
$587$	456.790	+	456.790i	0.0321188	+	0.0321188i	0.722984	−	0.690865i	$-0.242770\pi$
$587$	456.790	+	456.790i	0.0321188	+	0.0321188i	−0.690865	+	0.722984i	$0.742770\pi$
$588$		0			0
$589$	−545.674	+	545.674i	−0.0381733	+	0.0381733i
$590$		0			0
$591$	−14778.5			−1.02860
$592$		0			0
$593$	−23340.2			−1.61630			−0.808151	−	0.588975i	$-0.799532\pi$
$593$	−23340.2			−1.61630			−0.808151	+	0.588975i	$0.799532\pi$
$594$		0			0
$595$	3441.73	−	3441.73i	0.237138	−	0.237138i
$596$		0			0
$597$	1744.87	+	1744.87i	0.119619	+	0.119619i
$598$		0			0
$599$			5118.48i			0.349141i	0.984645	+	0.174570i	$0.0558537\pi$
$599$			5118.48i			0.349141i	−0.984645	+	0.174570i	$0.944146\pi$
$600$		0			0
$601$		−	26059.2i		−	1.76868i	−0.466843	−	0.884340i	$-0.654609\pi$
$601$		−	26059.2i		−	1.76868i	0.466843	−	0.884340i	$-0.345391\pi$
$602$		0			0
$603$	3148.91	+	3148.91i	0.212659	+	0.212659i
$604$		0			0
$605$	4449.85	−	4449.85i	0.299029	−	0.299029i
$606$		0			0
$607$	6835.97			0.457106			0.228553	−	0.973531i	$-0.426601\pi$
$607$	6835.97			0.457106			0.228553	+	0.973531i	$0.426601\pi$
$608$		0			0
$609$	−1519.25			−0.101089
$610$		0			0
$611$	−8023.58	+	8023.58i	−0.531259	+	0.531259i
$612$		0			0
$613$	−15841.9	−	15841.9i	−1.04380	−	1.04380i	−0.998996	−	0.0448044i	$-0.985734\pi$
$613$	−15841.9	−	15841.9i	−1.04380	−	1.04380i	−0.0448044	−	0.998996i	$-0.514266\pi$
$614$		0			0
$615$			1210.42i			0.0793642i
$616$		0			0
$617$		−	2925.70i		−	0.190898i	−0.995434	−	0.0954490i	$-0.969571\pi$
$617$		−	2925.70i		−	0.190898i	0.995434	−	0.0954490i	$-0.0304287\pi$
$618$		0			0
$619$	−1311.22	−	1311.22i	−0.0851414	−	0.0851414i	0.663253	−	0.748395i	$-0.269175\pi$
$619$	−1311.22	−	1311.22i	−0.0851414	−	0.0851414i	−0.748395	+	0.663253i	$0.769175\pi$
$620$		0			0
$621$	2268.61	−	2268.61i	0.146596	−	0.146596i
$622$		0			0
$623$	463.751			0.0298231
$624$		0			0
$625$	−625.000			−0.0400000
$626$		0			0
$627$	−382.092	+	382.092i	−0.0243370	+	0.0243370i
$628$		0			0
$629$	5576.61	+	5576.61i	0.353504	+	0.353504i
$630$		0			0
$631$			5926.85i			0.373921i	0.982367	+	0.186961i	$0.0598637\pi$
$631$			5926.85i			0.373921i	−0.982367	+	0.186961i	$0.940136\pi$
$632$		0			0
$633$			15373.9i			0.965334i
$634$		0			0
$635$	−6413.96	−	6413.96i	−0.400835	−	0.400835i
$636$		0			0
$637$	−8100.88	+	8100.88i	−0.503875	+	0.503875i
$638$		0			0
$639$	4604.81			0.285076
$640$		0			0
$641$	−8705.13			−0.536400			−0.268200	−	0.963363i	$-0.586429\pi$
$641$	−8705.13			−0.536400			−0.268200	+	0.963363i	$0.586429\pi$
$642$		0			0
$643$	8872.86	−	8872.86i	0.544186	−	0.544186i	−0.380567	−	0.924753i	$-0.624271\pi$
$643$	8872.86	−	8872.86i	0.544186	−	0.544186i	0.924753	+	0.380567i	$0.124271\pi$
$644$		0			0
$645$	2238.26	+	2238.26i	0.136638	+	0.136638i
$646$		0			0
$647$			4760.17i			0.289245i	0.989487	+	0.144622i	$0.0461968\pi$
$647$			4760.17i			0.289245i	−0.989487	+	0.144622i	$0.953803\pi$
$648$		0			0
$649$			5325.95i			0.322129i
$650$		0			0
$651$	1047.65	+	1047.65i	0.0630734	+	0.0630734i
$652$		0			0
$653$	18719.0	−	18719.0i	1.12179	−	1.12179i	0.130323	−	0.991472i	$-0.458398\pi$
$653$	18719.0	−	18719.0i	1.12179	−	1.12179i	0.991472	−	0.130323i	$-0.0416015\pi$
$654$		0			0
$655$	10759.8			0.641862
$656$		0			0
$657$	−8879.98			−0.527308
$658$		0			0
$659$	−3631.83	+	3631.83i	−0.214683	+	0.214683i	−0.806253	−	0.591571i	$-0.798508\pi$
$659$	−3631.83	+	3631.83i	−0.214683	+	0.214683i	0.591571	+	0.806253i	$0.298508\pi$
$660$		0			0
$661$	−6613.83	−	6613.83i	−0.389181	−	0.389181i	0.485215	−	0.874395i	$-0.338741\pi$
$661$	−6613.83	−	6613.83i	−0.389181	−	0.389181i	−0.874395	+	0.485215i	$0.838741\pi$
$662$		0			0
$663$		−	15488.0i		−	0.907248i
$664$		0			0
$665$			1434.08i			0.0836257i
$666$		0			0
$667$	3140.67	+	3140.67i	0.182320	+	0.182320i
$668$		0			0
$669$	1474.12	−	1474.12i	0.0851911	−	0.0851911i
$670$		0			0
$671$	−4297.59			−0.247253
$672$		0			0
$673$	−19572.3			−1.12103			−0.560517	−	0.828143i	$-0.689398\pi$
$673$	−19572.3			−1.12103			−0.560517	+	0.828143i	$0.689398\pi$
$674$		0			0
$675$	−477.297	+	477.297i	−0.0272166	+	0.0272166i
$676$		0			0
$677$	−8675.06	−	8675.06i	−0.492481	−	0.492481i	0.416606	−	0.909087i	$-0.363219\pi$
$677$	−8675.06	−	8675.06i	−0.492481	−	0.492481i	−0.909087	+	0.416606i	$0.863219\pi$
$678$		0			0
$679$		−	24093.7i		−	1.36176i
$680$		0			0
$681$			6752.64i			0.379973i
$682$		0			0
$683$	−21353.3	−	21353.3i	−1.19628	−	1.19628i	−0.975271	−	0.221014i	$-0.929063\pi$
$683$	−21353.3	−	21353.3i	−1.19628	−	1.19628i	−0.221014	−	0.975271i	$-0.570937\pi$
$684$		0			0
$685$	3762.70	−	3762.70i	0.209876	−	0.209876i
$686$		0			0
$687$	−402.748			−0.0223665
$688$		0			0
$689$	22334.1			1.23492
$690$		0			0
$691$	6965.64	−	6965.64i	0.383481	−	0.383481i	−0.488873	−	0.872355i	$-0.662592\pi$
$691$	6965.64	−	6965.64i	0.383481	−	0.383481i	0.872355	+	0.488873i	$0.162592\pi$
$692$		0			0
$693$	733.589	+	733.589i	0.0402117	+	0.0402117i
$694$		0			0
$695$			16216.7i			0.885085i
$696$		0			0
$697$		−	5798.10i		−	0.315091i
$698$		0			0
$699$	7124.05	+	7124.05i	0.385488	+	0.385488i
$700$		0			0
$701$	6147.41	−	6147.41i	0.331219	−	0.331219i	−0.521830	−	0.853049i	$-0.674751\pi$
$701$	6147.41	−	6147.41i	0.331219	−	0.331219i	0.853049	+	0.521830i	$0.174751\pi$
$702$		0			0
$703$	−2323.62			−0.124661
$704$		0			0
$705$	−2368.86			−0.126548
$706$		0			0
$707$	13920.4	−	13920.4i	0.740497	−	0.740497i
$708$		0			0
$709$	7200.09	+	7200.09i	0.381390	+	0.381390i	0.871603	−	0.490213i	$-0.163081\pi$
$709$	7200.09	+	7200.09i	0.381390	+	0.381390i	−0.490213	+	0.871603i	$0.663081\pi$
$710$		0			0
$711$		−	2569.72i		−	0.135544i
$712$		0			0
$713$		−	4331.51i		−	0.227512i
$714$		0			0
$715$	2161.39	+	2161.39i	0.113051	+	0.113051i
$716$		0			0
$717$	1922.16	−	1922.16i	0.100117	−	0.100117i
$718$		0			0
$719$	23244.7			1.20567			0.602837	−	0.797864i	$-0.294037\pi$
$719$	23244.7			1.20567			0.602837	+	0.797864i	$0.294037\pi$
$720$		0			0
$721$	−12523.7			−0.646890
$722$		0			0
$723$	−3753.44	+	3753.44i	−0.193073	+	0.193073i
$724$		0			0
$725$	−660.772	−	660.772i	−0.0338489	−	0.0338489i
$726$		0			0
$727$		−	6957.04i		−	0.354914i	−0.984129	−	0.177457i	$-0.943213\pi$
$727$		−	6957.04i		−	0.354914i	0.984129	−	0.177457i	$-0.0567871\pi$
$728$		0			0
$729$			729.000i			0.0370370i
$730$		0			0
$731$	−10721.6	−	10721.6i	−0.542480	−	0.542480i
$732$		0			0
$733$	21507.9	−	21507.9i	1.08378	−	1.08378i	0.0876296	−	0.996153i	$-0.472071\pi$
$733$	21507.9	−	21507.9i	1.08378	−	1.08378i	0.996153	−	0.0876296i	$-0.0279292\pi$
$734$		0			0
$735$	−2391.68			−0.120025
$736$		0			0
$737$	4209.94			0.210414
$738$		0			0
$739$	10124.0	−	10124.0i	0.503948	−	0.503948i	−0.408715	−	0.912662i	$-0.634023\pi$
$739$	10124.0	−	10124.0i	0.503948	−	0.503948i	0.912662	+	0.408715i	$0.134023\pi$
$740$		0			0
$741$	3226.72	+	3226.72i	0.159968	+	0.159968i
$742$		0			0
$743$			31456.3i			1.55319i	0.630000	+	0.776595i	$0.283055\pi$
$743$			31456.3i			1.55319i	−0.630000	+	0.776595i	$0.716945\pi$
$744$		0			0
$745$		−	446.344i		−	0.0219501i
$746$		0			0
$747$	−2068.59	−	2068.59i	−0.101320	−	0.101320i
$748$		0			0
$749$	988.723	−	988.723i	0.0482338	−	0.0482338i
$750$		0			0
$751$	19589.8			0.951852			0.475926	−	0.879485i	$-0.342113\pi$
$751$	19589.8			0.951852			0.475926	+	0.879485i	$0.342113\pi$
$752$		0			0
$753$	−16742.7			−0.810276
$754$		0			0
$755$	1407.68	−	1407.68i	0.0678551	−	0.0678551i
$756$		0			0
$757$	−16905.0	−	16905.0i	−0.811655	−	0.811655i	0.173227	−	0.984882i	$-0.444581\pi$
$757$	−16905.0	−	16905.0i	−0.811655	−	0.811655i	−0.984882	+	0.173227i	$0.944581\pi$
$758$		0			0
$759$		−	3033.01i		−	0.145048i
$760$		0			0
$761$			1966.50i			0.0936734i	0.998903	+	0.0468367i	$0.0149140\pi$
$761$			1966.50i			0.0936734i	−0.998903	+	0.0468367i	$0.985086\pi$
$762$		0			0
$763$	−16200.3	−	16200.3i	−0.768661	−	0.768661i
$764$		0			0
$765$	2286.32	−	2286.32i	0.108055	−	0.108055i
$766$		0			0
$767$	44976.9			2.11737
$768$		0			0
$769$	28969.8			1.35849			0.679244	−	0.733913i	$-0.262308\pi$
$769$	28969.8			1.35849			0.679244	+	0.733913i	$0.262308\pi$
$770$		0			0
$771$	2619.52	−	2619.52i	0.122360	−	0.122360i
$772$		0			0
$773$	−10711.8	−	10711.8i	−0.498419	−	0.498419i	0.412527	−	0.910945i	$-0.364646\pi$
$773$	−10711.8	−	10711.8i	−0.498419	−	0.498419i	−0.910945	+	0.412527i	$0.864646\pi$
$774$		0			0
$775$			911.315i			0.0422392i
$776$		0			0
$777$			4461.18i			0.205977i
$778$		0			0
$779$	1207.95	+	1207.95i	0.0555577	+	0.0555577i
$780$		0			0
$781$	3078.20	−	3078.20i	0.141033	−	0.141033i
$782$		0			0
$783$	−1009.23			−0.0460625
$784$		0			0
$785$	337.679			0.0153532
$786$		0			0
$787$	−21559.5	+	21559.5i	−0.976511	+	0.976511i	−0.999730	−	0.0232197i	$-0.992608\pi$
$787$	−21559.5	+	21559.5i	−0.976511	+	0.976511i	0.0232197	+	0.999730i	$0.492608\pi$
$788$		0			0
$789$	−12130.7	−	12130.7i	−0.547358	−	0.547358i
$790$		0			0
$791$		−	21210.9i		−	0.953443i
$792$		0			0
$793$			36292.6i			1.62520i
$794$		0			0
$795$	3296.93	+	3296.93i	0.147082	+	0.147082i
$796$		0			0
$797$	−451.603	+	451.603i	−0.0200710	+	0.0200710i	−0.717071	−	0.697000i	$-0.754518\pi$
$797$	−451.603	+	451.603i	−0.0200710	+	0.0200710i	0.697000	+	0.717071i	$0.254518\pi$
$798$		0			0
$799$	11347.2			0.502421
$800$		0			0
$801$	308.066			0.0135893
$802$		0			0
$803$	−5936.04	+	5936.04i	−0.260870	+	0.260870i
$804$		0			0
$805$	−5691.78	−	5691.78i	−0.249204	−	0.249204i
$806$		0			0
$807$		−	22192.4i		−	0.968041i
$808$		0			0
$809$			29253.6i			1.27133i	0.771966	+	0.635663i	$0.219273\pi$
$809$			29253.6i			1.27133i	−0.771966	+	0.635663i	$0.780727\pi$
$810$		0			0
$811$	27705.5	+	27705.5i	1.19960	+	1.19960i	0.974288	+	0.225308i	$0.0723388\pi$
$811$	27705.5	+	27705.5i	1.19960	+	1.19960i	0.225308	+	0.974288i	$0.427661\pi$
$812$		0			0
$813$	14397.4	−	14397.4i	0.621081	−	0.621081i
$814$		0			0
$815$	5453.06			0.234371
$816$		0			0
$817$	4467.39			0.191303
$818$		0			0
$819$	6195.06	−	6195.06i	0.264314	−	0.264314i
$820$		0			0
$821$	−11645.8	−	11645.8i	−0.495055	−	0.495055i	0.414840	−	0.909894i	$-0.363838\pi$
$821$	−11645.8	−	11645.8i	−0.495055	−	0.495055i	−0.909894	+	0.414840i	$0.863838\pi$
$822$		0			0
$823$			29867.1i			1.26501i	0.774556	+	0.632505i	$0.217973\pi$
$823$			29867.1i			1.26501i	−0.774556	+	0.632505i	$0.782027\pi$
$824$		0			0
$825$			638.122i			0.0269292i
$826$		0			0
$827$	−513.304	−	513.304i	−0.0215832	−	0.0215832i	0.696233	−	0.717816i	$-0.254858\pi$
$827$	−513.304	−	513.304i	−0.0215832	−	0.0215832i	−0.717816	+	0.696233i	$0.754858\pi$
$828$		0			0
$829$	21364.6	−	21364.6i	0.895081	−	0.895081i	−0.0999154	−	0.994996i	$-0.531857\pi$
$829$	21364.6	−	21364.6i	0.895081	−	0.895081i	0.994996	+	0.0999154i	$0.0318572\pi$
$830$		0			0
$831$	−8028.29			−0.335136
$832$		0			0
$833$	11456.5			0.476523
$834$		0			0
$835$	8051.28	−	8051.28i	0.333684	−	0.333684i
$836$		0			0
$837$	695.949	+	695.949i	0.0287402	+	0.0287402i
$838$		0			0
$839$			11943.3i			0.491452i	0.969339	+	0.245726i	$0.0790263\pi$
$839$			11943.3i			0.491452i	−0.969339	+	0.245726i	$0.920974\pi$
$840$		0			0
$841$			22991.8i			0.942713i
$842$		0			0
$843$	−6427.55	−	6427.55i	−0.262606	−	0.262606i
$844$		0			0
$845$	10485.1	−	10485.1i	0.426860	−	0.426860i
$846$		0			0
$847$	−17051.9			−0.691749
$848$		0			0
$849$	22905.8			0.925944
$850$		0			0
$851$	9222.35	−	9222.35i	0.371490	−	0.371490i
$852$		0			0
$853$	1752.54	+	1752.54i	0.0703466	+	0.0703466i	0.741405	−	0.671058i	$-0.234160\pi$
$853$	1752.54	+	1752.54i	0.0703466	+	0.0703466i	−0.671058	+	0.741405i	$0.734160\pi$
$854$		0			0
$855$			952.647i			0.0381051i
$856$		0			0
$857$		−	9668.29i		−	0.385371i	−0.981261	−	0.192685i	$-0.938280\pi$
$857$		−	9668.29i		−	0.385371i	0.981261	−	0.192685i	$-0.0617197\pi$
$858$		0			0
$859$	−1861.23	−	1861.23i	−0.0739284	−	0.0739284i	0.669176	−	0.743104i	$-0.266647\pi$
$859$	−1861.23	−	1861.23i	−0.0739284	−	0.0739284i	−0.743104	+	0.669176i	$0.766647\pi$
$860$		0			0
$861$	2319.18	−	2319.18i	0.0917974	−	0.0917974i
$862$		0			0
$863$	23439.1			0.924536			0.462268	−	0.886740i	$-0.347036\pi$
$863$	23439.1			0.924536			0.462268	+	0.886740i	$0.347036\pi$
$864$		0			0
$865$	−4039.10			−0.158767
$866$		0			0
$867$	−529.759	+	529.759i	−0.0207515	+	0.0207515i
$868$		0			0
$869$	−1717.79	−	1717.79i	−0.0670564	−	0.0670564i
$870$		0			0
$871$		−	35552.3i		−	1.38306i
$872$		0			0
$873$		−	16005.3i		−	0.620501i
$874$		0			0
$875$	1197.51	+	1197.51i	0.0462664	+	0.0462664i
$876$		0			0
$877$	18283.8	−	18283.8i	0.703992	−	0.703992i	−0.261273	−	0.965265i	$-0.584142\pi$
$877$	18283.8	−	18283.8i	0.703992	−	0.703992i	0.965265	+	0.261273i	$0.0841422\pi$
$878$		0			0
$879$	28456.8			1.09195
$880$		0			0
$881$	42175.8			1.61287			0.806435	−	0.591323i	$-0.201394\pi$
$881$	42175.8			1.61287			0.806435	+	0.591323i	$0.201394\pi$
$882$		0			0
$883$	−458.170	+	458.170i	−0.0174617	+	0.0174617i	−0.715784	−	0.698322i	$-0.753930\pi$
$883$	−458.170	+	458.170i	−0.0174617	+	0.0174617i	0.698322	+	0.715784i	$0.253930\pi$
$884$		0			0
$885$	6639.43	+	6639.43i	0.252183	+	0.252183i
$886$		0			0
$887$			37943.2i			1.43631i	0.695882	+	0.718156i	$0.255014\pi$
$887$			37943.2i			1.43631i	−0.695882	+	0.718156i	$0.744986\pi$
$888$		0			0
$889$			24578.4i			0.927259i
$890$		0			0
$891$	487.318	+	487.318i	0.0183230	+	0.0183230i
$892$		0			0
$893$	−2364.03	+	2364.03i	−0.0885881	+	0.0885881i
$894$		0			0
$895$	8978.86			0.335341
$896$		0			0
$897$	−25613.4			−0.953407
$898$		0			0
$899$	−963.474	+	963.474i	−0.0357438	+	0.0357438i
$900$		0			0
$901$	−15792.8	−	15792.8i	−0.583943	−	0.583943i
$902$		0			0
$903$		−	8577.06i		−	0.316087i
$904$		0			0
$905$		−	16510.8i		−	0.606449i
$906$		0			0
$907$	3788.29	+	3788.29i	0.138686	+	0.138686i	0.773041	−	0.634356i	$-0.218734\pi$
$907$	3788.29	+	3788.29i	0.138686	+	0.138686i	−0.634356	+	0.773041i	$0.718734\pi$
$908$		0			0
$909$	9247.24	−	9247.24i	0.337416	−	0.337416i
$910$		0			0
$911$	−6162.22			−0.224109			−0.112055	−	0.993702i	$-0.535743\pi$
$911$	−6162.22			−0.224109			−0.112055	+	0.993702i	$0.535743\pi$
$912$		0			0
$913$	−2765.60			−0.100250
$914$		0			0
$915$	−5357.46	+	5357.46i	−0.193565	+	0.193565i
$916$		0			0
$917$	−20615.8	−	20615.8i	−0.742416	−	0.742416i
$918$		0			0
$919$		−	19109.9i		−	0.685939i	−0.939346	−	0.342970i	$-0.888567\pi$
$919$		−	19109.9i		−	0.685939i	0.939346	−	0.342970i	$-0.111433\pi$
$920$		0			0
$921$			12561.3i			0.449412i
$922$		0			0
$923$	−25994.9	−	25994.9i	−0.927014	−	0.927014i
$924$		0			0
$925$	−1940.31	+	1940.31i	−0.0689697	+	0.0689697i
$926$		0			0
$927$	−8319.43			−0.294764
$928$		0			0
$929$	24397.3			0.861625			0.430813	−	0.902441i	$-0.358227\pi$
$929$	24397.3			0.861625			0.430813	+	0.902441i	$0.358227\pi$
$930$		0			0
$931$	−2386.80	+	2386.80i	−0.0840218	+	0.0840218i
$932$		0			0
$933$	2089.69	+	2089.69i	0.0733262	+	0.0733262i
$934$		0			0
$935$		−	3056.70i		−	0.106914i
$936$		0			0
$937$		−	1868.57i		−	0.0651479i	−0.999469	−	0.0325740i	$-0.989630\pi$
$937$		−	1868.57i		−	0.0651479i	0.999469	−	0.0325740i	$-0.0103704\pi$
$938$		0			0
$939$	13790.9	+	13790.9i	0.479285	+	0.479285i
$940$		0			0
$941$	−20605.9	+	20605.9i	−0.713850	+	0.713850i	−0.967338	−	0.253488i	$-0.918422\pi$
$941$	−20605.9	+	20605.9i	−0.713850	+	0.713850i	0.253488	+	0.967338i	$0.418422\pi$
$942$		0			0
$943$	−9588.63			−0.331123
$944$		0			0
$945$	1829.01			0.0629606
$946$		0			0
$947$	38688.2	−	38688.2i	1.32756	−	1.32756i	0.420062	−	0.907495i	$-0.362008\pi$
$947$	38688.2	−	38688.2i	1.32756	−	1.32756i	0.907495	−	0.420062i	$-0.137992\pi$
$948$		0			0
$949$	50129.1	+	50129.1i	1.71471	+	1.71471i
$950$		0			0
$951$		−	25754.8i		−	0.878189i
$952$		0			0
$953$			11686.8i			0.397243i	0.980076	+	0.198622i	$0.0636465\pi$
$953$			11686.8i			0.397243i	−0.980076	+	0.198622i	$0.936354\pi$
$954$		0			0
$955$	12699.2	+	12699.2i	0.430300	+	0.430300i
$956$		0			0
$957$	−674.645	+	674.645i	−0.0227881	+	0.0227881i
$958$		0			0
$959$	−14418.7			−0.485511
$960$		0			0
$961$	−28462.2			−0.955396
$962$		0			0
$963$	656.802	−	656.802i	0.0219783	−	0.0219783i
$964$		0			0
$965$	−8588.07	−	8588.07i	−0.286487	−	0.286487i
$966$		0			0
$967$		−	13147.8i		−	0.437232i	−0.975811	−	0.218616i	$-0.929846\pi$
$967$		−	13147.8i		−	0.437232i	0.975811	−	0.218616i	$-0.0701542\pi$
$968$		0			0
$969$		−	4563.32i		−	0.151285i
$970$		0			0
$971$	−20142.1	−	20142.1i	−0.665696	−	0.665696i	0.291020	−	0.956717i	$-0.406005\pi$
$971$	−20142.1	−	20142.1i	−0.665696	−	0.665696i	−0.956717	+	0.291020i	$0.906005\pi$
$972$		0			0
$973$	31071.3	−	31071.3i	1.02374	−	1.02374i
$974$		0			0
$975$	5388.85			0.177007
$976$		0			0
$977$	48223.2			1.57912			0.789559	−	0.613675i	$-0.210309\pi$
$977$	48223.2			1.57912			0.789559	+	0.613675i	$0.210309\pi$
$978$		0			0
$979$	205.935	−	205.935i	0.00672288	−	0.00672288i
$980$		0			0
$981$	−10761.7	−	10761.7i	−0.350250	−	0.350250i
$982$		0			0
$983$			11696.4i			0.379510i	0.981831	+	0.189755i	$0.0607694\pi$
$983$			11696.4i			0.379510i	−0.981831	+	0.189755i	$0.939231\pi$
$984$		0			0
$985$			24630.8i			0.796752i
$986$		0			0
$987$	4538.76	+	4538.76i	0.146373	+	0.146373i
$988$		0			0
$989$	−17730.9	+	17730.9i	−0.570080	+	0.570080i
$990$		0			0
$991$	41886.5			1.34265			0.671326	−	0.741163i	$-0.265725\pi$
$991$	41886.5			1.34265			0.671326	+	0.741163i	$0.265725\pi$
$992$		0			0
$993$	−21311.8			−0.681076
$994$		0			0
$995$	2908.11	−	2908.11i	0.0926565	−	0.0926565i
$996$		0			0
$997$	28568.1	+	28568.1i	0.907483	+	0.907483i	0.996069	−	0.0885853i	$-0.0282346\pi$
$997$	28568.1	+	28568.1i	0.907483	+	0.907483i	−0.0885853	+	0.996069i	$0.528235\pi$
$998$		0			0
$999$			2963.53i			0.0938558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.4.s.a.241.10		44
4.3	odd	2		240.4.s.a.181.16	yes	44
16.3	odd	4		240.4.s.a.61.16	✓	44
16.13	even	4	inner	960.4.s.a.721.10		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.4.s.a.61.16	✓	44	16.3	odd	4
240.4.s.a.181.16	yes	44	4.3	odd	2
960.4.s.a.241.10		44	1.1	even	1	trivial
960.4.s.a.721.10		44	16.13	even	4	inner

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	960.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.12132 + 2.12132i) q^{3} +(3.53553 + 3.53553i) q^{5} -13.5482i q^{7} -9.00000i q^{9} +O(q^{10})\)	\(q+(-2.12132 + 2.12132i) q^{3} +(3.53553 + 3.53553i) q^{5} -13.5482i q^{7} -9.00000i q^{9} +(-6.01627 - 6.01627i) q^{11} +(-50.8066 + 50.8066i) q^{13} -15.0000 q^{15} +71.8521 q^{17} +(-14.9694 + 14.9694i) q^{19} +(28.7401 + 28.7401i) q^{21} -118.826i q^{23} +25.0000i q^{25} +(19.0919 + 19.0919i) q^{27} +(-26.4309 + 26.4309i) q^{29} +36.4526 q^{31} +25.5249 q^{33} +(47.9002 - 47.9002i) q^{35} +(77.6123 + 77.6123i) q^{37} -215.554i q^{39} -80.6949i q^{41} +(-149.217 - 149.217i) q^{43} +(31.8198 - 31.8198i) q^{45} +157.924 q^{47} +159.445 q^{49} +(-152.421 + 152.421i) q^{51} +(-219.795 - 219.795i) q^{53} -42.5415i q^{55} -63.5098i q^{57} +(-442.628 - 442.628i) q^{59} +(357.164 - 357.164i) q^{61} -121.934 q^{63} -359.257 q^{65} +(-349.879 + 349.879i) q^{67} +(252.068 + 252.068i) q^{69} +511.645i q^{71} -986.665i q^{73} +(-53.0330 - 53.0330i) q^{75} +(-81.5098 + 81.5098i) q^{77} +285.524 q^{79} -81.0000 q^{81} +(229.843 - 229.843i) q^{83} +(254.036 + 254.036i) q^{85} -112.137i q^{87} +34.2296i q^{89} +(688.340 + 688.340i) q^{91} +(-77.3277 + 77.3277i) q^{93} -105.850 q^{95} +1778.37 q^{97} +(-54.1464 + 54.1464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 44 * q	\( 44 q - 40 q^{11} - 660 q^{15} + 408 q^{17} + 340 q^{19} - 400 q^{29} - 528 q^{33} - 16 q^{37} + 808 q^{43} - 588 q^{49} + 300 q^{51} - 752 q^{53} - 688 q^{59} + 1172 q^{61} - 504 q^{63} - 408 q^{67} + 948 q^{69} - 5816 q^{77} + 2632 q^{79} - 3564 q^{81} - 1104 q^{83} - 500 q^{85} - 2648 q^{91} + 2352 q^{93} - 5432 q^{97} - 360 q^{99}+O(q^{100}) \) 44 * q - 40 * q^11 - 660 * q^15 + 408 * q^17 + 340 * q^19 - 400 * q^29 - 528 * q^33 - 16 * q^37 + 808 * q^43 - 588 * q^49 + 300 * q^51 - 752 * q^53 - 688 * q^59 + 1172 * q^61 - 504 * q^63 - 408 * q^67 + 948 * q^69 - 5816 * q^77 + 2632 * q^79 - 3564 * q^81 - 1104 * q^83 - 500 * q^85 - 2648 * q^91 + 2352 * q^93 - 5432 * q^97 - 360 * q^99

Introduction

L-functions

Modular forms

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Database

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