LMFDB - Embedded newform 640.4.l.a.161.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,4,Mod(161,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("640.161");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	640.l (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:	$37.7612224037$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.13
Character	$\chi$	$=$	640.161
Dual form			640.4.l.a.481.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.332572 + 0.332572i) q^{3} +(-3.53553 + 3.53553i) q^{5} -31.6472i q^{7} -26.7788i q^{9} +(27.5498 - 27.5498i) q^{11} +(-17.9171 - 17.9171i) q^{13} -2.35164 q^{15} -87.1912 q^{17} +(-4.04610 - 4.04610i) q^{19} +(10.5250 - 10.5250i) q^{21} +181.039i q^{23} -25.0000i q^{25} +(17.8853 - 17.8853i) q^{27} +(159.995 + 159.995i) q^{29} -99.1025 q^{31} +18.3246 q^{33} +(111.890 + 111.890i) q^{35} +(-137.739 + 137.739i) q^{37} -11.9174i q^{39} -222.109i q^{41} +(-214.011 + 214.011i) q^{43} +(94.6773 + 94.6773i) q^{45} -430.778 q^{47} -658.547 q^{49} +(-28.9973 - 28.9973i) q^{51} +(450.373 - 450.373i) q^{53} +194.807i q^{55} -2.69124i q^{57} +(-147.911 + 147.911i) q^{59} +(-450.412 - 450.412i) q^{61} -847.474 q^{63} +126.693 q^{65} +(160.440 + 160.440i) q^{67} +(-60.2085 + 60.2085i) q^{69} -560.046i q^{71} -232.658i q^{73} +(8.31430 - 8.31430i) q^{75} +(-871.876 - 871.876i) q^{77} +507.981 q^{79} -711.131 q^{81} +(907.140 + 907.140i) q^{83} +(308.267 - 308.267i) q^{85} +106.420i q^{87} -466.938i q^{89} +(-567.025 + 567.025i) q^{91} +(-32.9587 - 32.9587i) q^{93} +28.6103 q^{95} -285.809 q^{97} +(-737.752 - 737.752i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 40 q^{11} - 120 q^{15} + 24 q^{19} - 264 q^{27} - 400 q^{29} - 16 q^{37} + 808 q^{43} - 1880 q^{47} - 2352 q^{49} + 2144 q^{51} - 752 q^{53} - 2728 q^{59} + 912 q^{61} + 2520 q^{63} - 2040 q^{67}+ \cdots - 4456 q^{99}+O(q^{100}) $ 48 * q - 40 * q^11 - 120 * q^15 + 24 * q^19 - 264 * q^27 - 400 * q^29 - 16 * q^37 + 808 * q^43 - 1880 * q^47 - 2352 * q^49 + 2144 * q^51 - 752 * q^53 - 2728 * q^59 + 912 * q^61 + 2520 * q^63 - 2040 * q^67 + 528 * q^69 - 1904 * q^77 - 2832 * q^79 - 3888 * q^81 + 2440 * q^83 + 240 * q^85 - 4448 * q^91 - 4272 * q^93 + 3040 * q^95 - 4456 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.332572	+	0.332572i	0.0640035	+	0.0640035i	0.738384	−	0.674381i	$-0.235589\pi$
$3$	0.332572	+	0.332572i	0.0640035	+	0.0640035i	−0.674381	+	0.738384i	$0.735589\pi$
$4$		0			0
$5$	−3.53553	+	3.53553i	−0.316228	+	0.316228i
$5$	−3.53553	+	3.53553i	−0.316228	+	0.316228i
$6$		0			0
$7$		−	31.6472i		−	1.70879i	−0.519625	−	0.854395i	$-0.673928\pi$
$7$		−	31.6472i		−	1.70879i	0.519625	−	0.854395i	$-0.326072\pi$
$8$		0			0
$9$		−	26.7788i		−	0.991807i
$10$		0			0
$11$	27.5498	−	27.5498i	0.755145	−	0.755145i	−0.220290	−	0.975434i	$-0.570700\pi$
$11$	27.5498	−	27.5498i	0.755145	−	0.755145i	0.975434	+	0.220290i	$0.0707003\pi$
$12$		0			0
$13$	−17.9171	−	17.9171i	−0.382254	−	0.382254i	0.489660	−	0.871914i	$-0.337121\pi$
$13$	−17.9171	−	17.9171i	−0.382254	−	0.382254i	−0.871914	+	0.489660i	$0.837121\pi$
$14$		0			0
$15$	−2.35164			−0.0404794
$16$		0			0
$17$	−87.1912			−1.24394			−0.621970	−	0.783041i	$-0.713667\pi$
$17$	−87.1912			−1.24394			−0.621970	+	0.783041i	$0.713667\pi$
$18$		0			0
$19$	−4.04610	−	4.04610i	−0.0488547	−	0.0488547i	0.682257	−	0.731112i	$-0.260998\pi$
$19$	−4.04610	−	4.04610i	−0.0488547	−	0.0488547i	−0.731112	+	0.682257i	$0.760998\pi$
$20$		0			0
$21$	10.5250	−	10.5250i	0.109368	−	0.109368i
$22$		0			0
$23$			181.039i			1.64127i	0.571451	+	0.820636i	$0.306381\pi$
$23$			181.039i			1.64127i	−0.571451	+	0.820636i	$0.693619\pi$
$24$		0			0
$25$		−	25.0000i		−	0.200000i
$26$		0			0
$27$	17.8853	−	17.8853i	0.127483	−	0.127483i
$28$		0			0
$29$	159.995	+	159.995i	1.02450	+	1.02450i	0.999692	+	0.0248046i	$0.00789636\pi$
$29$	159.995	+	159.995i	1.02450	+	1.02450i	0.0248046	+	0.999692i	$0.492104\pi$
$30$		0			0
$31$	−99.1025			−0.574172			−0.287086	−	0.957905i	$-0.592687\pi$
$31$	−99.1025			−0.574172			−0.287086	+	0.957905i	$0.592687\pi$
$32$		0			0
$33$	18.3246			0.0966638
$34$		0			0
$35$	111.890	+	111.890i	0.540367	+	0.540367i
$36$		0			0
$37$	−137.739	+	137.739i	−0.612003	+	0.612003i	−0.943468	−	0.331465i	$-0.892457\pi$
$37$	−137.739	+	137.739i	−0.612003	+	0.612003i	0.331465	+	0.943468i	$0.392457\pi$
$38$		0			0
$39$		−	11.9174i		−	0.0489312i
$40$		0			0
$41$		−	222.109i		−	0.846038i	−0.906121	−	0.423019i	$-0.860970\pi$
$41$		−	222.109i		−	0.846038i	0.906121	−	0.423019i	$-0.139030\pi$
$42$		0			0
$43$	−214.011	+	214.011i	−0.758985	+	0.758985i	−0.976138	−	0.217153i	$-0.930323\pi$
$43$	−214.011	+	214.011i	−0.758985	+	0.758985i	0.217153	+	0.976138i	$0.430323\pi$
$44$		0			0
$45$	94.6773	+	94.6773i	0.313637	+	0.313637i
$46$		0			0
$47$	−430.778			−1.33693			−0.668463	−	0.743746i	$-0.733047\pi$
$47$	−430.778			−1.33693			−0.668463	+	0.743746i	$0.733047\pi$
$48$		0			0
$49$	−658.547			−1.91996
$50$		0			0
$51$	−28.9973	−	28.9973i	−0.0796165	−	0.0796165i
$52$		0			0
$53$	450.373	−	450.373i	1.16723	−	1.16723i	0.184380	−	0.982855i	$-0.440972\pi$
$53$	450.373	−	450.373i	1.16723	−	1.16723i	0.982855	−	0.184380i	$-0.0590275\pi$
$54$		0			0
$55$			194.807i			0.477595i
$56$		0			0
$57$		−	2.69124i		−	0.00625374i
$58$		0			0
$59$	−147.911	+	147.911i	−0.326379	+	0.326379i	−0.851208	−	0.524829i	$-0.824129\pi$
$59$	−147.911	+	147.911i	−0.326379	+	0.326379i	0.524829	+	0.851208i	$0.324129\pi$
$60$		0			0
$61$	−450.412	−	450.412i	−0.945400	−	0.945400i	0.0531846	−	0.998585i	$-0.483063\pi$
$61$	−450.412	−	450.412i	−0.945400	−	0.945400i	−0.998585	+	0.0531846i	$0.983063\pi$
$62$		0			0
$63$	−847.474			−1.69479
$64$		0			0
$65$	126.693			0.241759
$66$		0			0
$67$	160.440	+	160.440i	0.292551	+	0.292551i	0.838087	−	0.545536i	$-0.183674\pi$
$67$	160.440	+	160.440i	0.292551	+	0.292551i	−0.545536	+	0.838087i	$0.683674\pi$
$68$		0			0
$69$	−60.2085	+	60.2085i	−0.105047	+	0.105047i
$70$		0			0
$71$		−	560.046i		−	0.936130i	−0.883694	−	0.468065i	$-0.844951\pi$
$71$		−	560.046i		−	0.936130i	0.883694	−	0.468065i	$-0.155049\pi$
$72$		0			0
$73$		−	232.658i		−	0.373021i	−0.982453	−	0.186510i	$-0.940282\pi$
$73$		−	232.658i		−	0.373021i	0.982453	−	0.186510i	$-0.0597178\pi$
$74$		0			0
$75$	8.31430	−	8.31430i	0.0128007	−	0.0128007i
$76$		0			0
$77$	−871.876	−	871.876i	−1.29038	−	1.29038i
$78$		0			0
$79$	507.981			0.723448			0.361724	−	0.932285i	$-0.382188\pi$
$79$	507.981			0.723448			0.361724	+	0.932285i	$0.382188\pi$
$80$		0			0
$81$	−711.131			−0.975488
$82$		0			0
$83$	907.140	+	907.140i	1.19966	+	1.19966i	0.974269	+	0.225388i	$0.0723651\pi$
$83$	907.140	+	907.140i	1.19966	+	1.19966i	0.225388	+	0.974269i	$0.427635\pi$
$84$		0			0
$85$	308.267	−	308.267i	0.393368	−	0.393368i
$86$		0			0
$87$			106.420i			0.131143i
$88$		0			0
$89$		−	466.938i		−	0.556128i	−0.960563	−	0.278064i	$-0.910307\pi$
$89$		−	466.938i		−	0.556128i	0.960563	−	0.278064i	$-0.0896927\pi$
$90$		0			0
$91$	−567.025	+	567.025i	−0.653191	+	0.653191i
$92$		0			0
$93$	−32.9587	−	32.9587i	−0.0367490	−	0.0367490i
$94$		0			0
$95$	28.6103			0.0308984
$96$		0			0
$97$	−285.809			−0.299170			−0.149585	−	0.988749i	$-0.547794\pi$
$97$	−285.809			−0.299170			−0.149585	+	0.988749i	$0.547794\pi$
$98$		0			0
$99$	−737.752	−	737.752i	−0.748958	−	0.748958i
$100$		0			0
$101$	−728.301	+	728.301i	−0.717511	+	0.717511i	−0.968095	−	0.250584i	$-0.919378\pi$
$101$	−728.301	+	728.301i	−0.717511	+	0.717511i	0.250584	+	0.968095i	$0.419378\pi$
$102$		0			0
$103$			737.304i			0.705327i	0.935750	+	0.352663i	$0.114724\pi$
$103$			737.304i			0.705327i	−0.935750	+	0.352663i	$0.885276\pi$
$104$		0			0
$105$			74.4228i			0.0691707i
$106$		0			0
$107$	−528.567	+	528.567i	−0.477556	+	0.477556i	−0.904349	−	0.426793i	$-0.859643\pi$
$107$	−528.567	+	528.567i	−0.477556	+	0.477556i	0.426793	+	0.904349i	$0.359643\pi$
$108$		0			0
$109$	−289.467	−	289.467i	−0.254366	−	0.254366i	0.568392	−	0.822758i	$-0.307566\pi$
$109$	−289.467	−	289.467i	−0.254366	−	0.254366i	−0.822758	+	0.568392i	$0.807566\pi$
$110$		0			0
$111$	−91.6160			−0.0783406
$112$		0			0
$113$	288.748			0.240382			0.120191	−	0.992751i	$-0.461649\pi$
$113$	288.748			0.240382			0.120191	+	0.992751i	$0.461649\pi$
$114$		0			0
$115$	−640.070	−	640.070i	−0.519016	−	0.519016i
$116$		0			0
$117$	−479.797	+	479.797i	−0.379122	+	0.379122i
$118$		0			0
$119$			2759.36i			2.12563i
$120$		0			0
$121$		−	186.988i		−	0.140487i
$122$		0			0
$123$	73.8672	−	73.8672i	0.0541494	−	0.0541494i
$124$		0			0
$125$	88.3883	+	88.3883i	0.0632456	+	0.0632456i
$126$		0			0
$127$	672.037			0.469556			0.234778	−	0.972049i	$-0.424564\pi$
$127$	672.037			0.469556			0.234778	+	0.972049i	$0.424564\pi$
$128$		0			0
$129$	−142.348			−0.0971554
$130$		0			0
$131$	−793.072	−	793.072i	−0.528939	−	0.528939i	0.391317	−	0.920256i	$-0.372020\pi$
$131$	−793.072	−	793.072i	−0.528939	−	0.528939i	−0.920256	+	0.391317i	$0.872020\pi$
$132$		0			0
$133$	−128.048	+	128.048i	−0.0834824	+	0.0834824i
$134$		0			0
$135$			126.468i			0.0806271i
$136$		0			0
$137$		−	1705.40i		−	1.06352i	−0.846896	−	0.531759i	$-0.821531\pi$
$137$		−	1705.40i		−	1.06352i	0.846896	−	0.531759i	$-0.178469\pi$
$138$		0			0
$139$	−1230.82	+	1230.82i	−0.751054	+	0.751054i	−0.974676	−	0.223622i	$-0.928212\pi$
$139$	−1230.82	+	1230.82i	−0.751054	+	0.751054i	0.223622	+	0.974676i	$0.428212\pi$
$140$		0			0
$141$	−143.265	−	143.265i	−0.0855679	−	0.0855679i
$142$		0			0
$143$	−987.225			−0.577314
$144$		0			0
$145$	−1131.34			−0.647949
$146$		0			0
$147$	−219.014	−	219.014i	−0.122884	−	0.122884i
$148$		0			0
$149$	133.750	−	133.750i	0.0735385	−	0.0735385i	−0.669381	−	0.742919i	$-0.733441\pi$
$149$	133.750	−	133.750i	0.0735385	−	0.0735385i	0.742919	+	0.669381i	$0.233441\pi$
$150$		0			0
$151$		−	1197.57i		−	0.645410i	−0.946500	−	0.322705i	$-0.895408\pi$
$151$		−	1197.57i		−	0.645410i	0.946500	−	0.322705i	$-0.104592\pi$
$152$		0			0
$153$			2334.87i			1.23375i
$154$		0			0
$155$	350.380	−	350.380i	0.181569	−	0.181569i
$156$		0			0
$157$	225.332	+	225.332i	0.114544	+	0.114544i	0.762056	−	0.647511i	$-0.224190\pi$
$157$	225.332	+	225.332i	0.114544	+	0.114544i	−0.647511	+	0.762056i	$0.724190\pi$
$158$		0			0
$159$	299.563			0.149414
$160$		0			0
$161$	5729.38			2.80459
$162$		0			0
$163$	−45.7973	−	45.7973i	−0.0220069	−	0.0220069i	0.696018	−	0.718025i	$-0.254953\pi$
$163$	−45.7973	−	45.7973i	−0.0220069	−	0.0220069i	−0.718025	+	0.696018i	$0.754953\pi$
$164$		0			0
$165$	−64.7873	+	64.7873i	−0.0305678	+	0.0305678i
$166$		0			0
$167$			1967.93i			0.911872i	0.890012	+	0.455936i	$0.150696\pi$
$167$			1967.93i			0.911872i	−0.890012	+	0.455936i	$0.849304\pi$
$168$		0			0
$169$		−	1554.96i		−	0.707764i
$170$		0			0
$171$	−108.350	+	108.350i	−0.0484544	+	0.0484544i
$172$		0			0
$173$	−2687.05	−	2687.05i	−1.18088	−	1.18088i	−0.979516	−	0.201368i	$-0.935461\pi$
$173$	−2687.05	−	2687.05i	−1.18088	−	1.18088i	−0.201368	−	0.979516i	$-0.564539\pi$
$174$		0			0
$175$	−791.181			−0.341758
$176$		0			0
$177$	−98.3819			−0.0417788
$178$		0			0
$179$	−281.560	−	281.560i	−0.117569	−	0.117569i	0.645875	−	0.763443i	$-0.276493\pi$
$179$	−281.560	−	281.560i	−0.117569	−	0.117569i	−0.763443	+	0.645875i	$0.776493\pi$
$180$		0			0
$181$	−118.145	+	118.145i	−0.0485175	+	0.0485175i	−0.730949	−	0.682432i	$-0.760922\pi$
$181$	−118.145	+	118.145i	−0.0485175	+	0.0485175i	0.682432	+	0.730949i	$0.260922\pi$
$182$		0			0
$183$		−	299.589i		−	0.121018i
$184$		0			0
$185$		−	973.959i		−	0.387064i
$186$		0			0
$187$	−2402.10	+	2402.10i	−0.939354	+	0.939354i
$188$		0			0
$189$	−566.021	−	566.021i	−0.217841	−	0.217841i
$190$		0			0
$191$	2149.51			0.814309			0.407154	−	0.913359i	$-0.366521\pi$
$191$	2149.51			0.814309			0.407154	+	0.913359i	$0.366521\pi$
$192$		0			0
$193$	−5077.23			−1.89361			−0.946806	−	0.321805i	$-0.895710\pi$
$193$	−5077.23			−1.89361			−0.946806	+	0.321805i	$0.895710\pi$
$194$		0			0
$195$	42.1345	+	42.1345i	0.0154734	+	0.0154734i
$196$		0			0
$197$	297.298	−	297.298i	0.107521	−	0.107521i	−0.651300	−	0.758821i	$-0.725776\pi$
$197$	297.298	−	297.298i	0.107521	−	0.107521i	0.758821	+	0.651300i	$0.225776\pi$
$198$		0			0
$199$		−	3870.84i		−	1.37888i	−0.724343	−	0.689440i	$-0.757857\pi$
$199$		−	3870.84i		−	1.37888i	0.724343	−	0.689440i	$-0.242143\pi$
$200$		0			0
$201$			106.716i			0.0374486i
$202$		0			0
$203$	5063.41	−	5063.41i	1.75065	−	1.75065i
$204$		0			0
$205$	785.273	+	785.273i	0.267541	+	0.267541i
$206$		0			0
$207$	4848.01			1.62783
$208$		0			0
$209$	−222.939			−0.0737847
$210$		0			0
$211$	−68.1214	−	68.1214i	−0.0222259	−	0.0222259i	0.695906	−	0.718132i	$-0.255003\pi$
$211$	−68.1214	−	68.1214i	−0.0222259	−	0.0222259i	−0.718132	+	0.695906i	$0.755003\pi$
$212$		0			0
$213$	186.256	−	186.256i	0.0599156	−	0.0599156i
$214$		0			0
$215$		−	1513.29i		−	0.480024i
$216$		0			0
$217$			3136.32i			0.981139i
$218$		0			0
$219$	77.3754	−	77.3754i	0.0238746	−	0.0238746i
$220$		0			0
$221$	1562.21	+	1562.21i	0.475500	+	0.475500i
$222$		0			0
$223$	−3027.13			−0.909020			−0.454510	−	0.890742i	$-0.650186\pi$
$223$	−3027.13			−0.909020			−0.454510	+	0.890742i	$0.650186\pi$
$224$		0			0
$225$	−669.470			−0.198361
$226$		0			0
$227$	1657.27	+	1657.27i	0.484568	+	0.484568i	0.906587	−	0.422019i	$-0.138678\pi$
$227$	1657.27	+	1657.27i	0.484568	+	0.484568i	−0.422019	+	0.906587i	$0.638678\pi$
$228$		0			0
$229$	−1654.38	+	1654.38i	−0.477401	+	0.477401i	−0.904299	−	0.426899i	$-0.859606\pi$
$229$	−1654.38	+	1654.38i	−0.477401	+	0.477401i	0.426899	+	0.904299i	$0.359606\pi$
$230$		0			0
$231$		−	579.923i		−	0.165178i
$232$		0			0
$233$			2988.64i			0.840311i	0.907452	+	0.420156i	$0.138025\pi$
$233$			2988.64i			0.840311i	−0.907452	+	0.420156i	$0.861975\pi$
$234$		0			0
$235$	1523.03	−	1523.03i	0.422773	−	0.422773i
$236$		0			0
$237$	168.940	+	168.940i	0.0463032	+	0.0463032i
$238$		0			0
$239$	−3559.69			−0.963419			−0.481709	−	0.876331i	$-0.659984\pi$
$239$	−3559.69			−0.963419			−0.481709	+	0.876331i	$0.659984\pi$
$240$		0			0
$241$	6527.63			1.74474			0.872369	−	0.488849i	$-0.162583\pi$
$241$	6527.63			1.74474			0.872369	+	0.488849i	$0.162583\pi$
$242$		0			0
$243$	−719.406	−	719.406i	−0.189917	−	0.189917i
$244$		0			0
$245$	2328.31	−	2328.31i	0.607145	−	0.607145i
$246$		0			0
$247$			144.989i			0.0373498i
$248$		0			0
$249$			603.379i			0.153565i
$250$		0			0
$251$	−1390.20	+	1390.20i	−0.349597	+	0.349597i	−0.859959	−	0.510362i	$-0.829511\pi$
$251$	−1390.20	+	1390.20i	−0.349597	+	0.349597i	0.510362	+	0.859959i	$0.329511\pi$
$252$		0			0
$253$	4987.60	+	4987.60i	1.23940	+	1.23940i
$254$		0			0
$255$	205.042			0.0503539
$256$		0			0
$257$	−2047.61			−0.496990			−0.248495	−	0.968633i	$-0.579936\pi$
$257$	−2047.61			−0.496990			−0.248495	+	0.968633i	$0.579936\pi$
$258$		0			0
$259$	4359.05	+	4359.05i	1.04578	+	1.04578i
$260$		0			0
$261$	4284.49	−	4284.49i	1.01610	−	1.01610i
$262$		0			0
$263$		−	3771.96i		−	0.884370i	−0.896924	−	0.442185i	$-0.854203\pi$
$263$		−	3771.96i		−	0.884370i	0.896924	−	0.442185i	$-0.145797\pi$
$264$		0			0
$265$			3184.62i			0.738224i
$266$		0			0
$267$	155.291	−	155.291i	0.0355941	−	0.0355941i
$268$		0			0
$269$	3919.81	+	3919.81i	0.888458	+	0.888458i	0.994375	−	0.105917i	$-0.0337777\pi$
$269$	3919.81	+	3919.81i	0.888458	+	0.888458i	−0.105917	+	0.994375i	$0.533778\pi$
$270$		0			0
$271$	4414.42			0.989510			0.494755	−	0.869033i	$-0.335258\pi$
$271$	4414.42			0.989510			0.494755	+	0.869033i	$0.335258\pi$
$272$		0			0
$273$	−377.153			−0.0836130
$274$		0			0
$275$	−688.746	−	688.746i	−0.151029	−	0.151029i
$276$		0			0
$277$	−6129.60	+	6129.60i	−1.32957	+	1.32957i	−0.423834	+	0.905740i	$0.639316\pi$
$277$	−6129.60	+	6129.60i	−1.32957	+	1.32957i	−0.905740	+	0.423834i	$0.860684\pi$
$278$		0			0
$279$			2653.84i			0.569468i
$280$		0			0
$281$		−	2156.72i		−	0.457862i	−0.973443	−	0.228931i	$-0.926477\pi$
$281$		−	2156.72i		−	0.457862i	0.973443	−	0.228931i	$-0.0735231\pi$
$282$		0			0
$283$	291.414	−	291.414i	0.0612112	−	0.0612112i	−0.675839	−	0.737050i	$-0.736218\pi$
$283$	291.414	−	291.414i	0.0612112	−	0.0612112i	0.737050	+	0.675839i	$0.236218\pi$
$284$		0			0
$285$	9.51497	+	9.51497i	0.00197761	+	0.00197761i
$286$		0			0
$287$	−7029.13			−1.44570
$288$		0			0
$289$	2689.30			0.547384
$290$		0			0
$291$	−95.0521	−	95.0521i	−0.0191479	−	0.0191479i
$292$		0			0
$293$	5647.07	−	5647.07i	1.12596	−	1.12596i	0.135129	−	0.990828i	$-0.456855\pi$
$293$	5647.07	−	5647.07i	1.12596	−	1.12596i	0.990828	−	0.135129i	$-0.0431449\pi$
$294$		0			0
$295$		−	1045.89i		−	0.206420i
$296$		0			0
$297$		−	985.475i		−	0.192536i
$298$		0			0
$299$	3243.69	−	3243.69i	0.627383	−	0.627383i
$300$		0			0
$301$	6772.85	+	6772.85i	1.29695	+	1.29695i
$302$		0			0
$303$	−484.425			−0.0918465
$304$		0			0
$305$	3184.90			0.597923
$306$		0			0
$307$	930.306	+	930.306i	0.172949	+	0.172949i	0.788274	−	0.615325i	$-0.210975\pi$
$307$	930.306	+	930.306i	0.172949	+	0.172949i	−0.615325	+	0.788274i	$0.710975\pi$
$308$		0			0
$309$	−245.206	+	245.206i	−0.0451434	+	0.0451434i
$310$		0			0
$311$		−	9791.82i		−	1.78535i	−0.450704	−	0.892673i	$-0.648827\pi$
$311$		−	9791.82i		−	1.78535i	0.450704	−	0.892673i	$-0.351173\pi$
$312$		0			0
$313$		−	5708.35i		−	1.03085i	−0.856936	−	0.515423i	$-0.827635\pi$
$313$		−	5708.35i		−	1.03085i	0.856936	−	0.515423i	$-0.172365\pi$
$314$		0			0
$315$	2996.27	−	2996.27i	0.535939	−	0.535939i
$316$		0			0
$317$	−2401.93	−	2401.93i	−0.425571	−	0.425571i	0.461546	−	0.887116i	$-0.347295\pi$
$317$	−2401.93	−	2401.93i	−0.425571	−	0.425571i	−0.887116	+	0.461546i	$0.847295\pi$
$318$		0			0
$319$	8815.70			1.54729
$320$		0			0
$321$	−351.573			−0.0611305
$322$		0			0
$323$	352.784	+	352.784i	0.0607723	+	0.0607723i
$324$		0			0
$325$	−447.927	+	447.927i	−0.0764508	+	0.0764508i
$326$		0			0
$327$		−	192.537i		−	0.0325607i
$328$		0			0
$329$			13632.9i			2.28452i
$330$		0			0
$331$	6732.01	−	6732.01i	1.11790	−	1.11790i	0.125850	−	0.992049i	$-0.459834\pi$
$331$	6732.01	−	6732.01i	1.11790	−	1.11790i	0.992049	−	0.125850i	$-0.0401658\pi$
$332$		0			0
$333$	3688.48	+	3688.48i	0.606989	+	0.606989i
$334$		0			0
$335$	−1134.48			−0.185025
$336$		0			0
$337$	−1392.53			−0.225092			−0.112546	−	0.993647i	$-0.535901\pi$
$337$	−1392.53			−0.225092			−0.112546	+	0.993647i	$0.535901\pi$
$338$		0			0
$339$	96.0295	+	96.0295i	0.0153853	+	0.0153853i
$340$		0			0
$341$	−2730.26	+	2730.26i	−0.433583	+	0.433583i
$342$		0			0
$343$			9986.17i			1.57202i
$344$		0			0
$345$		−	425.739i		−	0.0664377i
$346$		0			0
$347$	3703.57	−	3703.57i	0.572962	−	0.572962i	−0.359993	−	0.932955i	$-0.617221\pi$
$347$	3703.57	−	3703.57i	0.572962	−	0.572962i	0.932955	+	0.359993i	$0.117221\pi$
$348$		0			0
$349$	−7885.04	−	7885.04i	−1.20939	−	1.20939i	−0.971225	−	0.238164i	$-0.923455\pi$
$349$	−7885.04	−	7885.04i	−1.20939	−	1.20939i	−0.238164	−	0.971225i	$-0.576545\pi$
$350$		0			0
$351$	−640.905			−0.0974614
$352$		0			0
$353$	−8895.49			−1.34124			−0.670622	−	0.741799i	$-0.733973\pi$
$353$	−8895.49			−1.34124			−0.670622	+	0.741799i	$0.733973\pi$
$354$		0			0
$355$	1980.06	+	1980.06i	0.296030	+	0.296030i
$356$		0			0
$357$	−917.685	+	917.685i	−0.136048	+	0.136048i
$358$		0			0
$359$			336.118i			0.0494140i	0.999695	+	0.0247070i	$0.00786528\pi$
$359$			336.118i			0.0494140i	−0.999695	+	0.0247070i	$0.992135\pi$
$360$		0			0
$361$		−	6826.26i		−	0.995226i
$362$		0			0
$363$	62.1870	−	62.1870i	0.00899165	−	0.00899165i
$364$		0			0
$365$	822.569	+	822.569i	0.117960	+	0.117960i
$366$		0			0
$367$	6382.36			0.907783			0.453892	−	0.891057i	$-0.350035\pi$
$367$	6382.36			0.907783			0.453892	+	0.891057i	$0.350035\pi$
$368$		0			0
$369$	−5947.81			−0.839107
$370$		0			0
$371$	−14253.0	−	14253.0i	−1.99456	−	1.99456i
$372$		0			0
$373$	207.539	−	207.539i	0.0288095	−	0.0288095i	−0.692555	−	0.721365i	$-0.743515\pi$
$373$	207.539	−	207.539i	0.0288095	−	0.0288095i	0.721365	+	0.692555i	$0.243515\pi$
$374$		0			0
$375$			58.7910i			0.00809587i
$376$		0			0
$377$		−	5733.30i		−	0.783236i
$378$		0			0
$379$	−2598.87	+	2598.87i	−0.352230	+	0.352230i	−0.860939	−	0.508709i	$-0.830123\pi$
$379$	−2598.87	+	2598.87i	−0.352230	+	0.352230i	0.508709	+	0.860939i	$0.330123\pi$
$380$		0			0
$381$	223.501	+	223.501i	0.0300533	+	0.0300533i
$382$		0			0
$383$	1522.49			0.203121			0.101561	−	0.994829i	$-0.467616\pi$
$383$	1522.49			0.203121			0.101561	+	0.994829i	$0.467616\pi$
$384$		0			0
$385$	6165.09			0.816110
$386$		0			0
$387$	5730.95	+	5730.95i	0.752767	+	0.752767i
$388$		0			0
$389$	−4139.02	+	4139.02i	−0.539477	+	0.539477i	−0.923375	−	0.383899i	$-0.874581\pi$
$389$	−4139.02	+	4139.02i	−0.539477	+	0.539477i	0.383899	+	0.923375i	$0.374581\pi$
$390$		0			0
$391$		−	15785.0i		−	2.04164i
$392$		0			0
$393$		−	527.507i		−	0.0677079i
$394$		0			0
$395$	−1795.99	+	1795.99i	−0.228774	+	0.228774i
$396$		0			0
$397$	−790.544	−	790.544i	−0.0999402	−	0.0999402i	0.655369	−	0.755309i	$-0.272513\pi$
$397$	−790.544	−	790.544i	−0.0999402	−	0.0999402i	−0.755309	+	0.655369i	$0.772513\pi$
$398$		0			0
$399$	−85.1702			−0.0106863
$400$		0			0
$401$	8488.83			1.05714			0.528569	−	0.848891i	$-0.322729\pi$
$401$	8488.83			1.05714			0.528569	+	0.848891i	$0.322729\pi$
$402$		0			0
$403$	1775.63	+	1775.63i	0.219479	+	0.219479i
$404$		0			0
$405$	2514.23	−	2514.23i	0.308477	−	0.308477i
$406$		0			0
$407$			7589.36i			0.924301i
$408$		0			0
$409$		−	11390.7i		−	1.37710i	−0.725191	−	0.688548i	$-0.758248\pi$
$409$		−	11390.7i		−	1.37710i	0.725191	−	0.688548i	$-0.241752\pi$
$410$		0			0
$411$	567.167	−	567.167i	0.0680689	−	0.0680689i
$412$		0			0
$413$	4680.97	+	4680.97i	0.557712	+	0.557712i
$414$		0			0
$415$	−6414.45			−0.758730
$416$		0			0
$417$	−818.670			−0.0961402
$418$		0			0
$419$	−920.398	−	920.398i	−0.107314	−	0.107314i	0.651411	−	0.758725i	$-0.274177\pi$
$419$	−920.398	−	920.398i	−0.107314	−	0.107314i	−0.758725	+	0.651411i	$0.774177\pi$
$420$		0			0
$421$	767.503	−	767.503i	0.0888498	−	0.0888498i	−0.661285	−	0.750135i	$-0.729989\pi$
$421$	767.503	−	767.503i	0.0888498	−	0.0888498i	0.750135	+	0.661285i	$0.229989\pi$
$422$		0			0
$423$			11535.7i			1.32597i
$424$		0			0
$425$			2179.78i			0.248788i
$426$		0			0
$427$	−14254.3	+	14254.3i	−1.61549	+	1.61549i
$428$		0			0
$429$	−328.323	−	328.323i	−0.0369501	−	0.0369501i
$430$		0			0
$431$	2092.47			0.233853			0.116927	−	0.993141i	$-0.462696\pi$
$431$	2092.47			0.233853			0.116927	+	0.993141i	$0.462696\pi$
$432$		0			0
$433$	12347.8			1.37043			0.685215	−	0.728340i	$-0.259708\pi$
$433$	12347.8			1.37043			0.685215	+	0.728340i	$0.259708\pi$
$434$		0			0
$435$	−376.251	−	376.251i	−0.0414710	−	0.0414710i
$436$		0			0
$437$	732.503	−	732.503i	0.0801839	−	0.0801839i
$438$		0			0
$439$		−	106.069i		−	0.0115316i	−0.999983	−	0.00576582i	$-0.998165\pi$
$439$		−	106.069i		−	0.0115316i	0.999983	−	0.00576582i	$-0.00183533\pi$
$440$		0			0
$441$			17635.1i			1.90423i
$442$		0			0
$443$	−7806.27	+	7806.27i	−0.837217	+	0.837217i	−0.988492	−	0.151275i	$-0.951662\pi$
$443$	−7806.27	+	7806.27i	−0.837217	+	0.837217i	0.151275	+	0.988492i	$0.451662\pi$
$444$		0			0
$445$	1650.88	+	1650.88i	0.175863	+	0.175863i
$446$		0			0
$447$	88.9630			0.00941344
$448$		0			0
$449$	8260.92			0.868278			0.434139	−	0.900846i	$-0.357053\pi$
$449$	8260.92			0.868278			0.434139	+	0.900846i	$0.357053\pi$
$450$		0			0
$451$	−6119.07	−	6119.07i	−0.638881	−	0.638881i
$452$		0			0
$453$	398.278	−	398.278i	0.0413085	−	0.0413085i
$454$		0			0
$455$		−	4009.47i		−	0.413114i
$456$		0			0
$457$			11303.0i			1.15696i	0.815695	+	0.578482i	$0.196355\pi$
$457$			11303.0i			1.15696i	−0.815695	+	0.578482i	$0.803645\pi$
$458$		0			0
$459$	−1559.44	+	1559.44i	−0.158581	+	0.158581i
$460$		0			0
$461$	−5408.22	−	5408.22i	−0.546390	−	0.546390i	0.379005	−	0.925395i	$-0.376266\pi$
$461$	−5408.22	−	5408.22i	−0.546390	−	0.546390i	−0.925395	+	0.379005i	$0.876266\pi$
$462$		0			0
$463$	10798.3			1.08388			0.541941	−	0.840416i	$-0.317690\pi$
$463$	10798.3			1.08388			0.541941	+	0.840416i	$0.317690\pi$
$464$		0			0
$465$	233.053			0.0232421
$466$		0			0
$467$	−2406.24	−	2406.24i	−0.238431	−	0.238431i	0.577769	−	0.816200i	$-0.303923\pi$
$467$	−2406.24	−	2406.24i	−0.238431	−	0.238431i	−0.816200	+	0.577769i	$0.803923\pi$
$468$		0			0
$469$	5077.49	−	5077.49i	0.499908	−	0.499908i
$470$		0			0
$471$			149.878i			0.0146625i
$472$		0			0
$473$			11791.9i			1.14629i
$474$		0			0
$475$	−101.153	+	101.153i	−0.00977094	+	0.00977094i
$476$		0			0
$477$	−12060.4	−	12060.4i	−1.15767	−	1.15767i
$478$		0			0
$479$	−18643.4			−1.77836			−0.889182	−	0.457553i	$-0.848726\pi$
$479$	−18643.4			−1.77836			−0.889182	+	0.457553i	$0.848726\pi$
$480$		0			0
$481$	4935.75			0.467881
$482$		0			0
$483$	1905.43	+	1905.43i	0.179503	+	0.179503i
$484$		0			0
$485$	1010.49	−	1010.49i	0.0946059	−	0.0946059i
$486$		0			0
$487$			9243.23i			0.860063i	0.902814	+	0.430032i	$0.141498\pi$
$487$			9243.23i			0.860063i	−0.902814	+	0.430032i	$0.858502\pi$
$488$		0			0
$489$		−	30.4618i		−	0.00281703i
$490$		0			0
$491$	7760.67	−	7760.67i	0.713308	−	0.713308i	−0.253918	−	0.967226i	$-0.581719\pi$
$491$	7760.67	−	7760.67i	0.713308	−	0.713308i	0.967226	+	0.253918i	$0.0817193\pi$
$492$		0			0
$493$	−13950.2	−	13950.2i	−1.27441	−	1.27441i
$494$		0			0
$495$	5216.69			0.473683
$496$		0			0
$497$	−17723.9			−1.59965
$498$		0			0
$499$	11202.3	+	11202.3i	1.00497	+	1.00497i	0.999988	+	0.00498630i	$0.00158720\pi$
$499$	11202.3	+	11202.3i	1.00497	+	1.00497i	0.00498630	+	0.999988i	$0.498413\pi$
$500$		0			0
$501$	−654.477	+	654.477i	−0.0583630	+	0.0583630i
$502$		0			0
$503$			421.544i			0.0373672i	0.999825	+	0.0186836i	$0.00594752\pi$
$503$			421.544i			0.0373672i	−0.999825	+	0.0186836i	$0.994052\pi$
$504$		0			0
$505$		−	5149.87i		−	0.453794i
$506$		0			0
$507$	517.135	−	517.135i	0.0452994	−	0.0452994i
$508$		0			0
$509$	−9667.89	−	9667.89i	−0.841889	−	0.841889i	0.147215	−	0.989104i	$-0.452969\pi$
$509$	−9667.89	−	9667.89i	−0.841889	−	0.841889i	−0.989104	+	0.147215i	$0.952969\pi$
$510$		0			0
$511$	−7362.97			−0.637414
$512$		0			0
$513$	−144.732			−0.0124563
$514$		0			0
$515$	−2606.76	−	2606.76i	−0.223044	−	0.223044i
$516$		0			0
$517$	−11867.9	+	11867.9i	−1.00957	+	1.00957i
$518$		0			0
$519$		−	1787.28i		−	0.151161i
$520$		0			0
$521$		−	15435.0i		−	1.29793i	−0.760819	−	0.648964i	$-0.775202\pi$
$521$		−	15435.0i		−	1.29793i	0.760819	−	0.648964i	$-0.224798\pi$
$522$		0			0
$523$	−1871.14	+	1871.14i	−0.156442	+	0.156442i	−0.780988	−	0.624546i	$-0.785284\pi$
$523$	−1871.14	+	1871.14i	−0.156442	+	0.156442i	0.624546	+	0.780988i	$0.285284\pi$
$524$		0			0
$525$	−263.124	−	263.124i	−0.0218737	−	0.0218737i
$526$		0			0
$527$	8640.86			0.714235
$528$		0			0
$529$	−20608.2			−1.69377
$530$		0			0
$531$	3960.87	+	3960.87i	0.323705	+	0.323705i
$532$		0			0
$533$	−3979.54	+	3979.54i	−0.323401	+	0.323401i
$534$		0			0
$535$		−	3737.53i		−	0.302033i
$536$		0			0
$537$		−	187.278i		−	0.0150496i
$538$		0			0
$539$	−18142.9	+	18142.9i	−1.44985	+	1.44985i
$540$		0			0
$541$	9889.56	+	9889.56i	0.785925	+	0.785925i	0.980823	−	0.194898i	$-0.0624377\pi$
$541$	9889.56	+	9889.56i	0.785925	+	0.785925i	−0.194898	+	0.980823i	$0.562438\pi$
$542$		0			0
$543$	−78.5836			−0.00621058
$544$		0			0
$545$	2046.84			0.160875
$546$		0			0
$547$	4755.24	+	4755.24i	0.371699	+	0.371699i	0.868096	−	0.496397i	$-0.165344\pi$
$547$	4755.24	+	4755.24i	0.371699	+	0.371699i	−0.496397	+	0.868096i	$0.665344\pi$
$548$		0			0
$549$	−12061.5	+	12061.5i	−0.937654	+	0.937654i
$550$		0			0
$551$		−	1294.72i		−	0.100103i
$552$		0			0
$553$		−	16076.2i		−	1.23622i
$554$		0			0
$555$	323.912	−	323.912i	0.0247735	−	0.0247735i
$556$		0			0
$557$	−3512.91	−	3512.91i	−0.267230	−	0.267230i	0.560753	−	0.827983i	$-0.310512\pi$
$557$	−3512.91	−	3512.91i	−0.267230	−	0.267230i	−0.827983	+	0.560753i	$0.810512\pi$
$558$		0			0
$559$	7668.89			0.580250
$560$		0			0
$561$	−1597.74			−0.120244
$562$		0			0
$563$	−13501.9	−	13501.9i	−1.01073	−	1.01073i	−0.999942	−	0.0107847i	$-0.996567\pi$
$563$	−13501.9	−	13501.9i	−1.01073	−	1.01073i	−0.0107847	−	0.999942i	$-0.503433\pi$
$564$		0			0
$565$	−1020.88	+	1020.88i	−0.0760154	+	0.0760154i
$566$		0			0
$567$			22505.3i			1.66690i
$568$		0			0
$569$		−	16173.2i		−	1.19159i	−0.803135	−	0.595797i	$-0.796836\pi$
$569$		−	16173.2i		−	1.19159i	0.803135	−	0.595797i	$-0.203164\pi$
$570$		0			0
$571$	−1356.08	+	1356.08i	−0.0993877	+	0.0993877i	−0.755052	−	0.655665i	$-0.772389\pi$
$571$	−1356.08	+	1356.08i	−0.0993877	+	0.0993877i	0.655665	+	0.755052i	$0.272389\pi$
$572$		0			0
$573$	714.866	+	714.866i	0.0521186	+	0.0521186i
$574$		0			0
$575$	4525.98			0.328254
$576$		0			0
$577$	−20526.2			−1.48096			−0.740482	−	0.672076i	$-0.765403\pi$
$577$	−20526.2			−1.48096			−0.740482	+	0.672076i	$0.765403\pi$
$578$		0			0
$579$	−1688.54	−	1688.54i	−0.121198	−	0.121198i
$580$		0			0
$581$	28708.5	−	28708.5i	2.04996	−	2.04996i
$582$		0			0
$583$		−	24815.4i		−	1.76286i
$584$		0			0
$585$		−	3392.68i		−	0.239778i
$586$		0			0
$587$	3564.37	−	3564.37i	0.250626	−	0.250626i	−0.570601	−	0.821227i	$-0.693290\pi$
$587$	3564.37	−	3564.37i	0.250626	−	0.250626i	0.821227	+	0.570601i	$0.193290\pi$
$588$		0			0
$589$	400.979	+	400.979i	0.0280510	+	0.0280510i
$590$		0			0
$591$	197.746			0.0137634
$592$		0			0
$593$	5234.00			0.362453			0.181226	−	0.983441i	$-0.441993\pi$
$593$	5234.00			0.362453			0.181226	+	0.983441i	$0.441993\pi$
$594$		0			0
$595$	−9755.80	−	9755.80i	−0.672183	−	0.672183i
$596$		0			0
$597$	1287.33	−	1287.33i	0.0882531	−	0.0882531i
$598$		0			0
$599$			26166.9i			1.78489i	0.451152	+	0.892447i	$0.351013\pi$
$599$			26166.9i			1.78489i	−0.451152	+	0.892447i	$0.648987\pi$
$600$		0			0
$601$		−	1111.03i		−	0.0754077i	−0.999289	−	0.0377038i	$-0.987996\pi$
$601$		−	1111.03i		−	0.0754077i	0.999289	−	0.0377038i	$-0.0120043\pi$
$602$		0			0
$603$	4296.40	−	4296.40i	0.290154	−	0.290154i
$604$		0			0
$605$	661.103	+	661.103i	0.0444259	+	0.0444259i
$606$		0			0
$607$	−28038.7			−1.87488			−0.937441	−	0.348143i	$-0.886812\pi$
$607$	−28038.7			−1.87488			−0.937441	+	0.348143i	$0.886812\pi$
$608$		0			0
$609$	3367.90			0.224095
$610$		0			0
$611$	7718.28	+	7718.28i	0.511045	+	0.511045i
$612$		0			0
$613$	−15640.2	+	15640.2i	−1.03051	+	1.03051i	−0.0309891	+	0.999520i	$0.509866\pi$
$613$	−15640.2	+	15640.2i	−1.03051	+	1.03051i	−0.999520	+	0.0309891i	$0.990134\pi$
$614$		0			0
$615$			522.320i			0.0342471i
$616$		0			0
$617$		−	20190.6i		−	1.31741i	−0.752400	−	0.658706i	$-0.771104\pi$
$617$		−	20190.6i		−	1.31741i	0.752400	−	0.658706i	$-0.228896\pi$
$618$		0			0
$619$	17106.7	−	17106.7i	1.11079	−	1.11079i	0.117744	−	0.993044i	$-0.462434\pi$
$619$	17106.7	−	17106.7i	1.11079	−	1.11079i	0.993044	−	0.117744i	$-0.0375664\pi$
$620$		0			0
$621$	3237.94	+	3237.94i	0.209234	+	0.209234i
$622$		0			0
$623$	−14777.3			−0.950305
$624$		0			0
$625$	−625.000			−0.0400000
$626$		0			0
$627$	−74.1432	−	74.1432i	−0.00472248	−	0.00472248i
$628$		0			0
$629$	12009.6	−	12009.6i	0.761294	−	0.761294i
$630$		0			0
$631$			15692.0i			0.989995i	0.868894	+	0.494998i	$0.164831\pi$
$631$			15692.0i			0.989995i	−0.868894	+	0.494998i	$0.835169\pi$
$632$		0			0
$633$		−	45.3105i		−	0.00284508i
$634$		0			0
$635$	−2376.01	+	2376.01i	−0.148487	+	0.148487i
$636$		0			0
$637$	11799.2	+	11799.2i	0.733912	+	0.733912i
$638$		0			0
$639$	−14997.3			−0.928460
$640$		0			0
$641$	6940.06			0.427638			0.213819	−	0.976873i	$-0.431410\pi$
$641$	6940.06			0.427638			0.213819	+	0.976873i	$0.431410\pi$
$642$		0			0
$643$	17028.5	+	17028.5i	1.04438	+	1.04438i	0.998968	+	0.0454166i	$0.0144615\pi$
$643$	17028.5	+	17028.5i	1.04438	+	1.04438i	0.0454166	+	0.998968i	$0.485538\pi$
$644$		0			0
$645$	503.276	−	503.276i	0.0307232	−	0.0307232i
$646$		0			0
$647$			7772.42i			0.472280i	0.971719	+	0.236140i	$0.0758824\pi$
$647$			7772.42i			0.472280i	−0.971719	+	0.236140i	$0.924118\pi$
$648$		0			0
$649$			8149.84i			0.492926i
$650$		0			0
$651$	−1043.05	+	1043.05i	−0.0627963	+	0.0627963i
$652$		0			0
$653$	−16913.5	−	16913.5i	−1.01359	−	1.01359i	−0.999906	−	0.0136849i	$-0.995644\pi$
$653$	−16913.5	−	16913.5i	−1.01359	−	1.01359i	−0.0136849	−	0.999906i	$-0.504356\pi$
$654$		0			0
$655$	5607.86			0.334530
$656$		0			0
$657$	−6230.29			−0.369965
$658$		0			0
$659$	−21224.4	−	21224.4i	−1.25461	−	1.25461i	−0.953632	−	0.300975i	$-0.902688\pi$
$659$	−21224.4	−	21224.4i	−1.25461	−	1.25461i	−0.300975	−	0.953632i	$-0.597312\pi$
$660$		0			0
$661$	8991.82	−	8991.82i	0.529110	−	0.529110i	−0.391197	−	0.920307i	$-0.627939\pi$
$661$	8991.82	−	8991.82i	0.529110	−	0.529110i	0.920307	+	0.391197i	$0.127939\pi$
$662$		0			0
$663$			1039.09i			0.0608674i
$664$		0			0
$665$		−	905.435i		−	0.0527989i
$666$		0			0
$667$	−28965.4	+	28965.4i	−1.68148	+	1.68148i
$668$		0			0
$669$	−1006.74	−	1006.74i	−0.0581805	−	0.0581805i
$670$		0			0
$671$	−24817.6			−1.42783
$672$		0			0
$673$	−21613.3			−1.23794			−0.618968	−	0.785416i	$-0.712449\pi$
$673$	−21613.3			−1.23794			−0.618968	+	0.785416i	$0.712449\pi$
$674$		0			0
$675$	−447.133	−	447.133i	−0.0254965	−	0.0254965i
$676$		0			0
$677$	10267.0	−	10267.0i	0.582855	−	0.582855i	−0.352832	−	0.935687i	$-0.614781\pi$
$677$	10267.0	−	10267.0i	0.582855	−	0.582855i	0.935687	+	0.352832i	$0.114781\pi$
$678$		0			0
$679$			9045.06i			0.511219i
$680$		0			0
$681$			1102.32i			0.0620282i
$682$		0			0
$683$	−12718.6	+	12718.6i	−0.712537	+	0.712537i	−0.967065	−	0.254529i	$-0.918080\pi$
$683$	−12718.6	+	12718.6i	−0.712537	+	0.712537i	0.254529	+	0.967065i	$0.418080\pi$
$684$		0			0
$685$	6029.49	+	6029.49i	0.336314	+	0.336314i
$686$		0			0
$687$	−1100.40			−0.0611106
$688$		0			0
$689$	−16138.7			−0.892360
$690$		0			0
$691$	6754.05	+	6754.05i	0.371832	+	0.371832i	0.868144	−	0.496312i	$-0.165313\pi$
$691$	6754.05	+	6754.05i	0.371832	+	0.371832i	−0.496312	+	0.868144i	$0.665313\pi$
$692$		0			0
$693$	−23347.8	+	23347.8i	−1.27981	+	1.27981i
$694$		0			0
$695$		−	8703.19i		−	0.475008i
$696$		0			0
$697$			19365.9i			1.05242i
$698$		0			0
$699$	−993.939	+	993.939i	−0.0537829	+	0.0537829i
$700$		0			0
$701$	18644.8	+	18644.8i	1.00457	+	1.00457i	0.999989	+	0.00458335i	$0.00145893\pi$
$701$	18644.8	+	18644.8i	1.00457	+	1.00457i	0.00458335	+	0.999989i	$0.498541\pi$
$702$		0			0
$703$	1114.61			0.0597984
$704$		0			0
$705$	1013.03			0.0541179
$706$		0			0
$707$	23048.7	+	23048.7i	1.22608	+	1.22608i
$708$		0			0
$709$	−10018.5	+	10018.5i	−0.530683	+	0.530683i	−0.920776	−	0.390093i	$-0.872443\pi$
$709$	−10018.5	+	10018.5i	−0.530683	+	0.530683i	0.390093	+	0.920776i	$0.372443\pi$
$710$		0			0
$711$		−	13603.1i		−	0.717521i
$712$		0			0
$713$		−	17941.4i		−	0.942372i
$714$		0			0
$715$	3490.37	−	3490.37i	0.182563	−	0.182563i
$716$		0			0
$717$	−1183.85	−	1183.85i	−0.0616622	−	0.0616622i
$718$		0			0
$719$	23147.6			1.20064			0.600320	−	0.799760i	$-0.295040\pi$
$719$	23147.6			1.20064			0.600320	+	0.799760i	$0.295040\pi$
$720$		0			0
$721$	23333.6			1.20526
$722$		0			0
$723$	2170.91	+	2170.91i	0.111669	+	0.111669i
$724$		0			0
$725$	3999.89	−	3999.89i	0.204899	−	0.204899i
$726$		0			0
$727$		−	14506.3i		−	0.740041i	−0.929024	−	0.370020i	$-0.879351\pi$
$727$		−	14506.3i		−	0.740041i	0.929024	−	0.370020i	$-0.120649\pi$
$728$		0			0
$729$			18722.0i			0.951178i
$730$		0			0
$731$	18659.9	−	18659.9i	0.944131	−	0.944131i
$732$		0			0
$733$	−6210.06	−	6210.06i	−0.312924	−	0.312924i	0.533117	−	0.846042i	$-0.321021\pi$
$733$	−6210.06	−	6210.06i	−0.312924	−	0.312924i	−0.846042	+	0.533117i	$0.821021\pi$
$734$		0			0
$735$	1548.66			0.0777188
$736$		0			0
$737$	8840.22			0.441837
$738$		0			0
$739$	11943.0	+	11943.0i	0.594495	+	0.594495i	0.938842	−	0.344347i	$-0.111900\pi$
$739$	11943.0	+	11943.0i	0.594495	+	0.594495i	−0.344347	+	0.938842i	$0.611900\pi$
$740$		0			0
$741$	−48.2191	+	48.2191i	−0.00239052	+	0.00239052i
$742$		0			0
$743$		−	36602.4i		−	1.80729i	−0.428286	−	0.903643i	$-0.640883\pi$
$743$		−	36602.4i		−	1.80729i	0.428286	−	0.903643i	$-0.359117\pi$
$744$		0			0
$745$			945.756i			0.0465098i
$746$		0			0
$747$	24292.1	−	24292.1i	1.18983	−	1.18983i
$748$		0			0
$749$	16727.7	+	16727.7i	0.816042	+	0.816042i
$750$		0			0
$751$	−14798.3			−0.719040			−0.359520	−	0.933137i	$-0.617060\pi$
$751$	−14798.3			−0.719040			−0.359520	+	0.933137i	$0.617060\pi$
$752$		0			0
$753$	−924.685			−0.0447509
$754$		0			0
$755$	4234.05	+	4234.05i	0.204096	+	0.204096i
$756$		0			0
$757$	4779.77	−	4779.77i	0.229490	−	0.229490i	−0.582990	−	0.812479i	$-0.698117\pi$
$757$	4779.77	−	4779.77i	0.229490	−	0.229490i	0.812479	+	0.582990i	$0.198117\pi$
$758$		0			0
$759$			3317.47i			0.158652i
$760$		0			0
$761$			9090.72i			0.433033i	0.976279	+	0.216517i	$0.0694696\pi$
$761$			9090.72i			0.433033i	−0.976279	+	0.216517i	$0.930530\pi$
$762$		0			0
$763$	−9160.83	+	9160.83i	−0.434658	+	0.434658i
$764$		0			0
$765$	−8255.03	−	8255.03i	−0.390145	−	0.390145i
$766$		0			0
$767$	5300.25			0.249519
$768$		0			0
$769$	−15770.0			−0.739508			−0.369754	−	0.929130i	$-0.620558\pi$
$769$	−15770.0			−0.739508			−0.369754	+	0.929130i	$0.620558\pi$
$770$		0			0
$771$	−680.978	−	680.978i	−0.0318091	−	0.0318091i
$772$		0			0
$773$	15675.5	−	15675.5i	0.729378	−	0.729378i	−0.241118	−	0.970496i	$-0.577514\pi$
$773$	15675.5	−	15675.5i	0.729378	−	0.729378i	0.970496	+	0.241118i	$0.0775140\pi$
$774$		0			0
$775$			2477.56i			0.114834i
$776$		0			0
$777$			2899.39i			0.133868i
$778$		0			0
$779$	−898.675	+	898.675i	−0.0413330	+	0.0413330i
$780$		0			0
$781$	−15429.2	−	15429.2i	−0.706913	−	0.706913i
$782$		0			0
$783$	5723.14			0.261211
$784$		0			0
$785$	−1593.34			−0.0724442
$786$		0			0
$787$	−8132.80	−	8132.80i	−0.368365	−	0.368365i	0.498516	−	0.866881i	$-0.333879\pi$
$787$	−8132.80	−	8132.80i	−0.368365	−	0.368365i	−0.866881	+	0.498516i	$0.833879\pi$
$788$		0			0
$789$	1254.45	−	1254.45i	0.0566028	−	0.0566028i
$790$		0			0
$791$		−	9138.07i		−	0.410762i
$792$		0			0
$793$			16140.1i			0.722766i
$794$		0			0
$795$	−1059.11	+	1059.11i	−0.0472489	+	0.0472489i
$796$		0			0
$797$	−2477.13	−	2477.13i	−0.110093	−	0.110093i	0.649914	−	0.760008i	$-0.274805\pi$
$797$	−2477.13	−	2477.13i	−0.110093	−	0.110093i	−0.760008	+	0.649914i	$0.774805\pi$
$798$		0			0
$799$	37560.1			1.66305
$800$		0			0
$801$	−12504.0			−0.551571
$802$		0			0
$803$	−6409.68	−	6409.68i	−0.281685	−	0.281685i
$804$		0			0
$805$	−20256.4	+	20256.4i	−0.886889	+	0.886889i
$806$		0			0
$807$			2607.24i			0.113729i
$808$		0			0
$809$		−	6243.83i		−	0.271349i	−0.990753	−	0.135674i	$-0.956680\pi$
$809$		−	6243.83i		−	0.271349i	0.990753	−	0.135674i	$-0.0433201\pi$
$810$		0			0
$811$	23892.3	−	23892.3i	1.03449	−	1.03449i	0.0351095	−	0.999383i	$-0.488822\pi$
$811$	23892.3	−	23892.3i	1.03449	−	1.03449i	0.999383	−	0.0351095i	$-0.0111780\pi$
$812$		0			0
$813$	1468.11	+	1468.11i	0.0633321	+	0.0633321i
$814$		0			0
$815$	323.836			0.0139184
$816$		0			0
$817$	1731.82			0.0741600
$818$		0			0
$819$	15184.3	+	15184.3i	0.647840	+	0.647840i
$820$		0			0
$821$	22516.2	−	22516.2i	0.957152	−	0.957152i	−0.0419667	−	0.999119i	$-0.513362\pi$
$821$	22516.2	−	22516.2i	0.957152	−	0.957152i	0.999119	+	0.0419667i	$0.0133623\pi$
$822$		0			0
$823$			21821.0i			0.924221i	0.886822	+	0.462110i	$0.152908\pi$
$823$			21821.0i			0.924221i	−0.886822	+	0.462110i	$0.847092\pi$
$824$		0			0
$825$		−	458.115i		−	0.0193328i
$826$		0			0
$827$	7413.04	−	7413.04i	0.311701	−	0.311701i	−0.533867	−	0.845568i	$-0.679262\pi$
$827$	7413.04	−	7413.04i	0.311701	−	0.311701i	0.845568	+	0.533867i	$0.179262\pi$
$828$		0			0
$829$	20805.8	+	20805.8i	0.871670	+	0.871670i	0.992654	−	0.120984i	$-0.0386051\pi$
$829$	20805.8	+	20805.8i	0.871670	+	0.871670i	−0.120984	+	0.992654i	$0.538605\pi$
$830$		0			0
$831$	−4077.07			−0.170195
$832$		0			0
$833$	57419.4			2.38831
$834$		0			0
$835$	−6957.67	−	6957.67i	−0.288359	−	0.288359i
$836$		0			0
$837$	−1772.48	+	1772.48i	−0.0731969	+	0.0731969i
$838$		0			0
$839$		−	22077.5i		−	0.908464i	−0.890883	−	0.454232i	$-0.849914\pi$
$839$		−	22077.5i		−	0.908464i	0.890883	−	0.454232i	$-0.150086\pi$
$840$		0			0
$841$			26808.1i			1.09919i
$842$		0			0
$843$	717.265	−	717.265i	0.0293048	−	0.0293048i
$844$		0			0
$845$	5497.61	+	5497.61i	0.223815	+	0.223815i
$846$		0			0
$847$	−5917.65			−0.240063
$848$		0			0
$849$	193.832			0.00783546
$850$		0			0
$851$	−24936.1	−	24936.1i	−1.00446	−	1.00446i
$852$		0			0
$853$	2590.84	−	2590.84i	0.103996	−	0.103996i	−0.653194	−	0.757190i	$-0.726571\pi$
$853$	2590.84	−	2590.84i	0.103996	−	0.103996i	0.757190	+	0.653194i	$0.226571\pi$
$854$		0			0
$855$		−	766.148i		−	0.0306453i
$856$		0			0
$857$		−	14022.9i		−	0.558940i	−0.960154	−	0.279470i	$-0.909841\pi$
$857$		−	14022.9i		−	0.558940i	0.960154	−	0.279470i	$-0.0901588\pi$
$858$		0			0
$859$	−7640.32	+	7640.32i	−0.303474	+	0.303474i	−0.842371	−	0.538897i	$-0.818841\pi$
$859$	−7640.32	+	7640.32i	−0.303474	+	0.303474i	0.538897	+	0.842371i	$0.318841\pi$
$860$		0			0
$861$	−2337.69	−	2337.69i	−0.0925300	−	0.0925300i
$862$		0			0
$863$	27256.7			1.07512			0.537560	−	0.843225i	$-0.319346\pi$
$863$	27256.7			1.07512			0.537560	+	0.843225i	$0.319346\pi$
$864$		0			0
$865$	19000.3			0.746857
$866$		0			0
$867$	894.386	+	894.386i	0.0350345	+	0.0350345i
$868$		0			0
$869$	13994.8	−	13994.8i	0.546308	−	0.546308i
$870$		0			0
$871$		−	5749.24i		−	0.223657i
$872$		0			0
$873$			7653.62i			0.296719i
$874$		0			0
$875$	2797.25	−	2797.25i	0.108073	−	0.108073i
$876$		0			0
$877$	−21685.2	−	21685.2i	−0.834955	−	0.834955i	0.153235	−	0.988190i	$-0.451031\pi$
$877$	−21685.2	−	21685.2i	−0.834955	−	0.834955i	−0.988190	+	0.153235i	$0.951031\pi$
$878$		0			0
$879$	3756.11			0.144130
$880$		0			0
$881$	−28719.6			−1.09828			−0.549141	−	0.835730i	$-0.685045\pi$
$881$	−28719.6			−1.09828			−0.549141	+	0.835730i	$0.685045\pi$
$882$		0			0
$883$	−20257.6	−	20257.6i	−0.772051	−	0.772051i	0.206414	−	0.978465i	$-0.433821\pi$
$883$	−20257.6	−	20257.6i	−0.772051	−	0.772051i	−0.978465	+	0.206414i	$0.933821\pi$
$884$		0			0
$885$	347.833	−	347.833i	0.0132116	−	0.0132116i
$886$		0			0
$887$		−	4768.95i		−	0.180525i	−0.995918	−	0.0902625i	$-0.971229\pi$
$887$		−	4768.95i		−	0.180525i	0.995918	−	0.0902625i	$-0.0287706\pi$
$888$		0			0
$889$		−	21268.1i		−	0.802373i
$890$		0			0
$891$	−19591.6	+	19591.6i	−0.736635	+	0.736635i
$892$		0			0
$893$	1742.97	+	1742.97i	0.0653151	+	0.0653151i
$894$		0			0
$895$	1990.93			0.0743570
$896$		0			0
$897$	2157.52			0.0803094
$898$		0			0
$899$	−15855.9	−	15855.9i	−0.588237	−	0.588237i
$900$		0			0
$901$	−39268.5	+	39268.5i	−1.45197	+	1.45197i
$902$		0			0
$903$			4504.92i			0.166018i
$904$		0			0
$905$		−	835.413i		−	0.0306852i
$906$		0			0
$907$	26316.7	−	26316.7i	0.963432	−	0.963432i	−0.0359230	−	0.999355i	$-0.511437\pi$
$907$	26316.7	−	26316.7i	0.963432	−	0.963432i	0.999355	+	0.0359230i	$0.0114371\pi$
$908$		0			0
$909$	19503.0	+	19503.0i	0.711633	+	0.711633i
$910$		0			0
$911$	20400.3			0.741922			0.370961	−	0.928649i	$-0.379028\pi$
$911$	20400.3			0.741922			0.370961	+	0.928649i	$0.379028\pi$
$912$		0			0
$913$	49983.1			1.81183
$914$		0			0
$915$	1059.21	+	1059.21i	0.0382692	+	0.0382692i
$916$		0			0
$917$	−25098.5	+	25098.5i	−0.903845	+	0.903845i
$918$		0			0
$919$		−	9542.94i		−	0.342538i	−0.985224	−	0.171269i	$-0.945213\pi$
$919$		−	9542.94i		−	0.342538i	0.985224	−	0.171269i	$-0.0547867\pi$
$920$		0			0
$921$			618.788i			0.0221387i
$922$		0			0
$923$	−10034.4	+	10034.4i	−0.357839	+	0.357839i
$924$		0			0
$925$	3443.47	+	3443.47i	0.122401	+	0.122401i
$926$		0			0
$927$	19744.1			0.699548
$928$		0			0
$929$	28626.1			1.01097			0.505485	−	0.862835i	$-0.331313\pi$
$929$	28626.1			1.01097			0.505485	+	0.862835i	$0.331313\pi$
$930$		0			0
$931$	2664.55	+	2664.55i	0.0937991	+	0.0937991i
$932$		0			0
$933$	3256.48	−	3256.48i	0.114268	−	0.114268i
$934$		0			0
$935$		−	16985.4i		−	0.594100i
$936$		0			0
$937$			45776.8i			1.59601i	0.602649	+	0.798006i	$0.294112\pi$
$937$			45776.8i			1.59601i	−0.602649	+	0.798006i	$0.705888\pi$
$938$		0			0
$939$	1898.44	−	1898.44i	0.0659778	−	0.0659778i
$940$		0			0
$941$	19201.2	+	19201.2i	0.665186	+	0.665186i	0.956598	−	0.291412i	$-0.0941249\pi$
$941$	19201.2	+	19201.2i	0.665186	+	0.665186i	−0.291412	+	0.956598i	$0.594125\pi$
$942$		0			0
$943$	40210.4			1.38858
$944$		0			0
$945$	4002.37			0.137775
$946$		0			0
$947$	−5241.06	−	5241.06i	−0.179843	−	0.179843i	0.611444	−	0.791287i	$-0.290589\pi$
$947$	−5241.06	−	5241.06i	−0.179843	−	0.179843i	−0.791287	+	0.611444i	$0.790589\pi$
$948$		0			0
$949$	−4168.54	+	4168.54i	−0.142589	+	0.142589i
$950$		0			0
$951$		−	1597.63i		−	0.0544760i
$952$		0			0
$953$			3874.03i			0.131681i	0.997830	+	0.0658406i	$0.0209729\pi$
$953$			3874.03i			0.131681i	−0.997830	+	0.0658406i	$0.979027\pi$
$954$		0			0
$955$	−7599.66	+	7599.66i	−0.257507	+	0.257507i
$956$		0			0
$957$	2931.85	+	2931.85i	0.0990318	+	0.0990318i
$958$		0			0
$959$	−53971.1			−1.81733
$960$		0			0
$961$	−19969.7			−0.670327
$962$		0			0
$963$	14154.4	+	14154.4i	0.473643	+	0.473643i
$964$		0			0
$965$	17950.7	−	17950.7i	0.598813	−	0.598813i
$966$		0			0
$967$			4333.33i			0.144106i	0.997401	+	0.0720531i	$0.0229551\pi$
$967$			4333.33i			0.144106i	−0.997401	+	0.0720531i	$0.977045\pi$
$968$		0			0
$969$			234.652i			0.00777928i
$970$		0			0
$971$	9479.83	−	9479.83i	0.313308	−	0.313308i	−0.532882	−	0.846190i	$-0.678891\pi$
$971$	9479.83	−	9479.83i	0.313308	−	0.313308i	0.846190	+	0.532882i	$0.178891\pi$
$972$		0			0
$973$	38951.9	+	38951.9i	1.28339	+	1.28339i
$974$		0			0
$975$	−297.936			−0.00978623
$976$		0			0
$977$	49089.2			1.60747			0.803737	−	0.594985i	$-0.202842\pi$
$977$	49089.2			1.60747			0.803737	+	0.594985i	$0.202842\pi$
$978$		0			0
$979$	−12864.1	−	12864.1i	−0.419957	−	0.419957i
$980$		0			0
$981$	−7751.58	+	7751.58i	−0.252282	+	0.252282i
$982$		0			0
$983$			32020.3i			1.03895i	0.854485	+	0.519476i	$0.173873\pi$
$983$			32020.3i			1.03895i	−0.854485	+	0.519476i	$0.826127\pi$
$984$		0			0
$985$			2102.21i			0.0680021i
$986$		0			0
$987$	−4533.93	+	4533.93i	−0.146217	+	0.146217i
$988$		0			0
$989$	−38744.3	−	38744.3i	−1.24570	−	1.24570i
$990$		0			0
$991$	4667.61			0.149618			0.0748090	−	0.997198i	$-0.476165\pi$
$991$	4667.61			0.149618			0.0748090	+	0.997198i	$0.476165\pi$
$992$		0			0
$993$	4477.75			0.143099
$994$		0			0
$995$	13685.5	+	13685.5i	0.436040	+	0.436040i
$996$		0			0
$997$	20944.6	−	20944.6i	0.665317	−	0.665317i	−0.291311	−	0.956628i	$-0.594091\pi$
$997$	20944.6	−	20944.6i	0.665317	−	0.665317i	0.956628	+	0.291311i	$0.0940915\pi$
$998$		0			0
$999$			4927.00i			0.156039i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.4.l.a.161.13		48
4.3	odd	2		640.4.l.b.161.12		48
8.3	odd	2		80.4.l.a.61.22	yes	48
8.5	even	2		320.4.l.a.81.12		48
16.3	odd	4		80.4.l.a.21.22	✓	48
16.5	even	4	inner	640.4.l.a.481.13		48
16.11	odd	4		640.4.l.b.481.12		48
16.13	even	4		320.4.l.a.241.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.4.l.a.21.22	✓	48	16.3	odd	4
80.4.l.a.61.22	yes	48	8.3	odd	2
320.4.l.a.81.12		48	8.5	even	2
320.4.l.a.241.12		48	16.13	even	4
640.4.l.a.161.13		48	1.1	even	1	trivial
640.4.l.a.481.13		48	16.5	even	4	inner
640.4.l.b.161.12		48	4.3	odd	2
640.4.l.b.481.12		48	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	640.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.332572 + 0.332572i) q^{3} +(-3.53553 + 3.53553i) q^{5} -31.6472i q^{7} -26.7788i q^{9} +(27.5498 - 27.5498i) q^{11} +(-17.9171 - 17.9171i) q^{13} -2.35164 q^{15} -87.1912 q^{17} +(-4.04610 - 4.04610i) q^{19} +(10.5250 - 10.5250i) q^{21} +181.039i q^{23} -25.0000i q^{25} +(17.8853 - 17.8853i) q^{27} +(159.995 + 159.995i) q^{29} -99.1025 q^{31} +18.3246 q^{33} +(111.890 + 111.890i) q^{35} +(-137.739 + 137.739i) q^{37} -11.9174i q^{39} -222.109i q^{41} +(-214.011 + 214.011i) q^{43} +(94.6773 + 94.6773i) q^{45} -430.778 q^{47} -658.547 q^{49} +(-28.9973 - 28.9973i) q^{51} +(450.373 - 450.373i) q^{53} +194.807i q^{55} -2.69124i q^{57} +(-147.911 + 147.911i) q^{59} +(-450.412 - 450.412i) q^{61} -847.474 q^{63} +126.693 q^{65} +(160.440 + 160.440i) q^{67} +(-60.2085 + 60.2085i) q^{69} -560.046i q^{71} -232.658i q^{73} +(8.31430 - 8.31430i) q^{75} +(-871.876 - 871.876i) q^{77} +507.981 q^{79} -711.131 q^{81} +(907.140 + 907.140i) q^{83} +(308.267 - 308.267i) q^{85} +106.420i q^{87} -466.938i q^{89} +(-567.025 + 567.025i) q^{91} +(-32.9587 - 32.9587i) q^{93} +28.6103 q^{95} -285.809 q^{97} +(-737.752 - 737.752i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 40 q^{11} - 120 q^{15} + 24 q^{19} - 264 q^{27} - 400 q^{29} - 16 q^{37} + 808 q^{43} - 1880 q^{47} - 2352 q^{49} + 2144 q^{51} - 752 q^{53} - 2728 q^{59} + 912 q^{61} + 2520 q^{63} - 2040 q^{67}+ \cdots - 4456 q^{99}+O(q^{100}) \) 48 * q - 40 * q^11 - 120 * q^15 + 24 * q^19 - 264 * q^27 - 400 * q^29 - 16 * q^37 + 808 * q^43 - 1880 * q^47 - 2352 * q^49 + 2144 * q^51 - 752 * q^53 - 2728 * q^59 + 912 * q^61 + 2520 * q^63 - 2040 * q^67 + 528 * q^69 - 1904 * q^77 - 2832 * q^79 - 3888 * q^81 + 2440 * q^83 + 240 * q^85 - 4448 * q^91 - 4272 * q^93 + 3040 * q^95 - 4456 * q^99

Introduction

L-functions

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