LMFDB - Embedded newform 320.4.l.a.81.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,4,Mod(81,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, 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("320.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	320.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:	$18.8806112018$
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			81.12
Character	$\chi$	$=$	320.81
Dual form			320.4.l.a.241.12

$q$-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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.332572	−	0.332572i	−0.0640035	−	0.0640035i	0.674381	−	0.738384i	$-0.264411\pi$
$3$	−0.332572	−	0.332572i	−0.0640035	−	0.0640035i	−0.738384	+	0.674381i	$0.764411\pi$
$4$		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	−0.975434	−	0.220290i	$-0.929300\pi$
$11$	−27.5498	+	27.5498i	−0.755145	+	0.755145i	0.220290	+	0.975434i	$0.429300\pi$
$12$		0			0
$13$	17.9171	+	17.9171i	0.382254	+	0.382254i	0.871914	−	0.489660i	$-0.162879\pi$
$13$	17.9171	+	17.9171i	0.382254	+	0.382254i	−0.489660	+	0.871914i	$0.662879\pi$
$14$		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	0.731112	−	0.682257i	$-0.239002\pi$
$19$	4.04610	+	4.04610i	0.0488547	+	0.0488547i	−0.682257	+	0.731112i	$0.739002\pi$
$20$		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	$-0.992104\pi$
$29$	−159.995	−	159.995i	−1.02450	−	1.02450i	−0.0248046	−	0.999692i	$-0.507896\pi$
$30$		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	−0.331465	−	0.943468i	$-0.607543\pi$
$37$	137.739	−	137.739i	0.612003	−	0.612003i	0.943468	+	0.331465i	$0.107543\pi$
$38$		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	−0.217153	−	0.976138i	$-0.569677\pi$
$43$	214.011	−	214.011i	0.758985	−	0.758985i	0.976138	+	0.217153i	$0.0696770\pi$
$44$		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	$0.559028\pi$
$53$	−450.373	+	450.373i	−1.16723	+	1.16723i	−0.982855	+	0.184380i	$0.940972\pi$
$54$		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	−0.524829	−	0.851208i	$-0.675871\pi$
$59$	147.911	−	147.911i	0.326379	−	0.326379i	0.851208	+	0.524829i	$0.175871\pi$
$60$		0			0
$61$	450.412	+	450.412i	0.945400	+	0.945400i	0.998585	−	0.0531846i	$-0.0169372\pi$
$61$	450.412	+	450.412i	0.945400	+	0.945400i	−0.0531846	+	0.998585i	$0.516937\pi$
$62$		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	0.545536	−	0.838087i	$-0.316326\pi$
$67$	−160.440	−	160.440i	−0.292551	−	0.292551i	−0.838087	+	0.545536i	$0.816326\pi$
$68$		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	$-0.927635\pi$
$83$	−907.140	−	907.140i	−1.19966	−	1.19966i	−0.225388	−	0.974269i	$-0.572365\pi$
$84$		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	−0.250584	−	0.968095i	$-0.580622\pi$
$101$	728.301	−	728.301i	0.717511	−	0.717511i	0.968095	+	0.250584i	$0.0806225\pi$
$102$		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	−0.426793	−	0.904349i	$-0.640357\pi$
$107$	528.567	−	528.567i	0.477556	−	0.477556i	0.904349	+	0.426793i	$0.140357\pi$
$108$		0			0
$109$	289.467	+	289.467i	0.254366	+	0.254366i	0.822758	−	0.568392i	$-0.192434\pi$
$109$	289.467	+	289.467i	0.254366	+	0.254366i	−0.568392	+	0.822758i	$0.692434\pi$
$110$		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	0.920256	−	0.391317i	$-0.127980\pi$
$131$	793.072	+	793.072i	0.528939	+	0.528939i	−0.391317	+	0.920256i	$0.627980\pi$
$132$		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	−0.223622	−	0.974676i	$-0.571788\pi$
$139$	1230.82	−	1230.82i	0.751054	−	0.751054i	0.974676	+	0.223622i	$0.0717880\pi$
$140$		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	−0.742919	−	0.669381i	$-0.766559\pi$
$149$	−133.750	+	133.750i	−0.0735385	+	0.0735385i	0.669381	+	0.742919i	$0.266559\pi$
$150$		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	0.647511	−	0.762056i	$-0.275810\pi$
$157$	−225.332	−	225.332i	−0.114544	−	0.114544i	−0.762056	+	0.647511i	$0.775810\pi$
$158$		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	0.718025	−	0.696018i	$-0.245047\pi$
$163$	45.7973	+	45.7973i	0.0220069	+	0.0220069i	−0.696018	+	0.718025i	$0.745047\pi$
$164$		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	$0.0645388\pi$
$173$	2687.05	+	2687.05i	1.18088	+	1.18088i	0.201368	+	0.979516i	$0.435461\pi$
$174$		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	0.763443	−	0.645875i	$-0.223507\pi$
$179$	281.560	+	281.560i	0.117569	+	0.117569i	−0.645875	+	0.763443i	$0.723507\pi$
$180$		0			0
$181$	118.145	−	118.145i	0.0485175	−	0.0485175i	−0.682432	−	0.730949i	$-0.739078\pi$
$181$	118.145	−	118.145i	0.0485175	−	0.0485175i	0.730949	+	0.682432i	$0.239078\pi$
$182$		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	−0.758821	−	0.651300i	$-0.774224\pi$
$197$	−297.298	+	297.298i	−0.107521	+	0.107521i	0.651300	+	0.758821i	$0.274224\pi$
$198$		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	0.718132	−	0.695906i	$-0.244997\pi$
$211$	68.1214	+	68.1214i	0.0222259	+	0.0222259i	−0.695906	+	0.718132i	$0.744997\pi$
$212$		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	0.422019	−	0.906587i	$-0.361322\pi$
$227$	−1657.27	−	1657.27i	−0.484568	−	0.484568i	−0.906587	+	0.422019i	$0.861322\pi$
$228$		0			0
$229$	1654.38	−	1654.38i	0.477401	−	0.477401i	−0.426899	−	0.904299i	$-0.640394\pi$
$229$	1654.38	−	1654.38i	0.477401	−	0.477401i	0.904299	+	0.426899i	$0.140394\pi$
$230$		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	−0.510362	−	0.859959i	$-0.670489\pi$
$251$	1390.20	−	1390.20i	0.349597	−	0.349597i	0.859959	+	0.510362i	$0.170489\pi$
$252$		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	0.105917	−	0.994375i	$-0.466222\pi$
$269$	−3919.81	−	3919.81i	−0.888458	−	0.888458i	−0.994375	+	0.105917i	$0.966222\pi$
$270$		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	$-0.360684\pi$
$277$	6129.60	−	6129.60i	1.32957	−	1.32957i	0.905740	−	0.423834i	$-0.139316\pi$
$278$		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	−0.737050	−	0.675839i	$-0.763782\pi$
$283$	−291.414	+	291.414i	−0.0612112	+	0.0612112i	0.675839	+	0.737050i	$0.263782\pi$
$284$		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	$0.543145\pi$
$293$	−5647.07	+	5647.07i	−1.12596	+	1.12596i	−0.990828	+	0.135129i	$0.956855\pi$
$294$		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	0.615325	−	0.788274i	$-0.289025\pi$
$307$	−930.306	−	930.306i	−0.172949	−	0.172949i	−0.788274	+	0.615325i	$0.789025\pi$
$308$		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	0.887116	−	0.461546i	$-0.152705\pi$
$317$	2401.93	+	2401.93i	0.425571	+	0.425571i	−0.461546	+	0.887116i	$0.652705\pi$
$318$		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	$0.540166\pi$
$331$	−6732.01	+	6732.01i	−1.11790	+	1.11790i	−0.992049	+	0.125850i	$0.959834\pi$
$332$		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	−0.932955	−	0.359993i	$-0.882779\pi$
$347$	−3703.57	+	3703.57i	−0.572962	+	0.572962i	0.359993	+	0.932955i	$0.382779\pi$
$348$		0			0
$349$	7885.04	+	7885.04i	1.20939	+	1.20939i	0.971225	+	0.238164i	$0.0765455\pi$
$349$	7885.04	+	7885.04i	1.20939	+	1.20939i	0.238164	+	0.971225i	$0.423455\pi$
$350$		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	−0.721365	−	0.692555i	$-0.756485\pi$
$373$	−207.539	+	207.539i	−0.0288095	+	0.0288095i	0.692555	+	0.721365i	$0.256485\pi$
$374$		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	−0.508709	−	0.860939i	$-0.669877\pi$
$379$	2598.87	−	2598.87i	0.352230	−	0.352230i	0.860939	+	0.508709i	$0.169877\pi$
$380$		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	−0.383899	−	0.923375i	$-0.625419\pi$
$389$	4139.02	−	4139.02i	0.539477	−	0.539477i	0.923375	+	0.383899i	$0.125419\pi$
$390$		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	0.755309	−	0.655369i	$-0.227487\pi$
$397$	790.544	+	790.544i	0.0999402	+	0.0999402i	−0.655369	+	0.755309i	$0.727487\pi$
$398$		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	0.758725	−	0.651411i	$-0.225823\pi$
$419$	920.398	+	920.398i	0.107314	+	0.107314i	−0.651411	+	0.758725i	$0.725823\pi$
$420$		0			0
$421$	−767.503	+	767.503i	−0.0888498	+	0.0888498i	−0.750135	−	0.661285i	$-0.770011\pi$
$421$	−767.503	+	767.503i	−0.0888498	+	0.0888498i	0.661285	+	0.750135i	$0.270011\pi$
$422$		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	−0.151275	−	0.988492i	$-0.548338\pi$
$443$	7806.27	−	7806.27i	0.837217	−	0.837217i	0.988492	+	0.151275i	$0.0483379\pi$
$444$		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	0.925395	−	0.379005i	$-0.123734\pi$
$461$	5408.22	+	5408.22i	0.546390	+	0.546390i	−0.379005	+	0.925395i	$0.623734\pi$
$462$		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	0.816200	−	0.577769i	$-0.196077\pi$
$467$	2406.24	+	2406.24i	0.238431	+	0.238431i	−0.577769	+	0.816200i	$0.696077\pi$
$468$		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	−0.967226	−	0.253918i	$-0.918281\pi$
$491$	−7760.67	+	7760.67i	−0.713308	+	0.713308i	0.253918	+	0.967226i	$0.418281\pi$
$492$		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	$-0.998413\pi$
$499$	−11202.3	−	11202.3i	−1.00497	−	1.00497i	−0.00498630	−	0.999988i	$-0.501587\pi$
$500$		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	0.989104	−	0.147215i	$-0.0470311\pi$
$509$	9667.89	+	9667.89i	0.841889	+	0.841889i	−0.147215	+	0.989104i	$0.547031\pi$
$510$		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	−0.624546	−	0.780988i	$-0.714716\pi$
$523$	1871.14	−	1871.14i	0.156442	−	0.156442i	0.780988	+	0.624546i	$0.214716\pi$
$524$		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	0.194898	−	0.980823i	$-0.437562\pi$
$541$	−9889.56	−	9889.56i	−0.785925	−	0.785925i	−0.980823	+	0.194898i	$0.937562\pi$
$542$		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	0.496397	−	0.868096i	$-0.334656\pi$
$547$	−4755.24	−	4755.24i	−0.371699	−	0.371699i	−0.868096	+	0.496397i	$0.834656\pi$
$548$		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	0.827983	−	0.560753i	$-0.189488\pi$
$557$	3512.91	+	3512.91i	0.267230	+	0.267230i	−0.560753	+	0.827983i	$0.689488\pi$
$558$		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	$0.00343293\pi$
$563$	13501.9	+	13501.9i	1.01073	+	1.01073i	0.0107847	+	0.999942i	$0.496567\pi$
$564$		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	−0.655665	−	0.755052i	$-0.727611\pi$
$571$	1356.08	−	1356.08i	0.0993877	−	0.0993877i	0.755052	+	0.655665i	$0.227611\pi$
$572$		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	−0.821227	−	0.570601i	$-0.806710\pi$
$587$	−3564.37	+	3564.37i	−0.250626	+	0.250626i	0.570601	+	0.821227i	$0.306710\pi$
$588$		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	$-0.490134\pi$
$613$	15640.2	−	15640.2i	1.03051	−	1.03051i	0.999520	−	0.0309891i	$-0.00986572\pi$
$614$		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	$0.537566\pi$
$619$	−17106.7	+	17106.7i	−1.11079	+	1.11079i	−0.993044	+	0.117744i	$0.962434\pi$
$620$		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	$-0.985538\pi$
$643$	−17028.5	−	17028.5i	−1.04438	−	1.04438i	−0.0454166	−	0.998968i	$-0.514462\pi$
$644$		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	$0.00435618\pi$
$653$	16913.5	+	16913.5i	1.01359	+	1.01359i	0.0136849	+	0.999906i	$0.495644\pi$
$654$		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	$0.0973122\pi$
$659$	21224.4	+	21224.4i	1.25461	+	1.25461i	0.300975	+	0.953632i	$0.402688\pi$
$660$		0			0
$661$	−8991.82	+	8991.82i	−0.529110	+	0.529110i	−0.920307	−	0.391197i	$-0.872061\pi$
$661$	−8991.82	+	8991.82i	−0.529110	+	0.529110i	0.391197	+	0.920307i	$0.372061\pi$
$662$		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	−0.935687	−	0.352832i	$-0.885219\pi$
$677$	−10267.0	+	10267.0i	−0.582855	+	0.582855i	0.352832	+	0.935687i	$0.385219\pi$
$678$		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	−0.254529	−	0.967065i	$-0.581920\pi$
$683$	12718.6	−	12718.6i	0.712537	−	0.712537i	0.967065	+	0.254529i	$0.0819203\pi$
$684$		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	0.496312	−	0.868144i	$-0.334687\pi$
$691$	−6754.05	−	6754.05i	−0.371832	−	0.371832i	−0.868144	+	0.496312i	$0.834687\pi$
$692$		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	$-0.998541\pi$
$701$	−18644.8	−	18644.8i	−1.00457	−	1.00457i	−0.00458335	−	0.999989i	$-0.501459\pi$
$702$		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	−0.390093	−	0.920776i	$-0.627557\pi$
$709$	10018.5	−	10018.5i	0.530683	−	0.530683i	0.920776	+	0.390093i	$0.127557\pi$
$710$		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	0.846042	−	0.533117i	$-0.178979\pi$
$733$	6210.06	+	6210.06i	0.312924	+	0.312924i	−0.533117	+	0.846042i	$0.678979\pi$
$734$		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	0.344347	−	0.938842i	$-0.388100\pi$
$739$	−11943.0	−	11943.0i	−0.594495	−	0.594495i	−0.938842	+	0.344347i	$0.888100\pi$
$740$		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	−0.812479	−	0.582990i	$-0.801883\pi$
$757$	−4779.77	+	4779.77i	−0.229490	+	0.229490i	0.582990	+	0.812479i	$0.301883\pi$
$758$		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	−0.970496	−	0.241118i	$-0.922486\pi$
$773$	−15675.5	+	15675.5i	−0.729378	+	0.729378i	0.241118	+	0.970496i	$0.422486\pi$
$774$		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	0.866881	−	0.498516i	$-0.166121\pi$
$787$	8132.80	+	8132.80i	0.368365	+	0.368365i	−0.498516	+	0.866881i	$0.666121\pi$
$788$		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	0.760008	−	0.649914i	$-0.225195\pi$
$797$	2477.13	+	2477.13i	0.110093	+	0.110093i	−0.649914	+	0.760008i	$0.725195\pi$
$798$		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	$0.511178\pi$
$811$	−23892.3	+	23892.3i	−1.03449	+	1.03449i	−0.999383	+	0.0351095i	$0.988822\pi$
$812$		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	−0.999119	−	0.0419667i	$-0.986638\pi$
$821$	−22516.2	+	22516.2i	−0.957152	+	0.957152i	0.0419667	+	0.999119i	$0.486638\pi$
$822$		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	−0.845568	−	0.533867i	$-0.820738\pi$
$827$	−7413.04	+	7413.04i	−0.311701	+	0.311701i	0.533867	+	0.845568i	$0.320738\pi$
$828$		0			0
$829$	−20805.8	−	20805.8i	−0.871670	−	0.871670i	0.120984	−	0.992654i	$-0.461395\pi$
$829$	−20805.8	−	20805.8i	−0.871670	−	0.871670i	−0.992654	+	0.120984i	$0.961395\pi$
$830$		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	−0.757190	−	0.653194i	$-0.773429\pi$
$853$	−2590.84	+	2590.84i	−0.103996	+	0.103996i	0.653194	+	0.757190i	$0.273429\pi$
$854$		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	−0.538897	−	0.842371i	$-0.681159\pi$
$859$	7640.32	−	7640.32i	0.303474	−	0.303474i	0.842371	+	0.538897i	$0.181159\pi$
$860$		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	0.988190	−	0.153235i	$-0.0489691\pi$
$877$	21685.2	+	21685.2i	0.834955	+	0.834955i	−0.153235	+	0.988190i	$0.548969\pi$
$878$		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	0.978465	−	0.206414i	$-0.0661792\pi$
$883$	20257.6	+	20257.6i	0.772051	+	0.772051i	−0.206414	+	0.978465i	$0.566179\pi$
$884$		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	−0.999355	−	0.0359230i	$-0.988563\pi$
$907$	−26316.7	+	26316.7i	−0.963432	+	0.963432i	0.0359230	+	0.999355i	$0.488563\pi$
$908$		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	0.291412	−	0.956598i	$-0.405875\pi$
$941$	−19201.2	−	19201.2i	−0.665186	−	0.665186i	−0.956598	+	0.291412i	$0.905875\pi$
$942$		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	0.791287	−	0.611444i	$-0.209411\pi$
$947$	5241.06	+	5241.06i	0.179843	+	0.179843i	−0.611444	+	0.791287i	$0.709411\pi$
$948$		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	−0.846190	−	0.532882i	$-0.821109\pi$
$971$	−9479.83	+	9479.83i	−0.313308	+	0.313308i	0.532882	+	0.846190i	$0.321109\pi$
$972$		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	−0.956628	−	0.291311i	$-0.905909\pi$
$997$	−20944.6	+	20944.6i	−0.665317	+	0.665317i	0.291311	+	0.956628i	$0.405909\pi$
$998$		0			0
$999$			4927.00i			0.156039i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.4.l.a.21.22	✓	48	16.11	odd	4
80.4.l.a.61.22	yes	48	4.3	odd	2
320.4.l.a.81.12		48	1.1	even	1	trivial
320.4.l.a.241.12		48	16.5	even	4	inner
640.4.l.a.161.13		48	8.5	even	2
640.4.l.a.481.13		48	16.13	even	4
640.4.l.b.161.12		48	8.3	odd	2
640.4.l.b.481.12		48	16.3	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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	320.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

Modular forms

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