LMFDB - Embedded newform 640.4.l.b.161.10

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			161.10
Character	$\chi$	$=$	640.161
Dual form			640.4.l.b.481.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30312 - 1.30312i) q^{3} +(-3.53553 + 3.53553i) q^{5} -17.9744i q^{7} -23.6037i q^{9} +(-9.66542 + 9.66542i) q^{11} +(-19.1969 - 19.1969i) q^{13} +9.21448 q^{15} +103.565 q^{17} +(-16.2553 - 16.2553i) q^{19} +(-23.4229 + 23.4229i) q^{21} -49.6583i q^{23} -25.0000i q^{25} +(-65.9429 + 65.9429i) q^{27} +(68.7899 + 68.7899i) q^{29} -249.904 q^{31} +25.1905 q^{33} +(63.5492 + 63.5492i) q^{35} +(-210.860 + 210.860i) q^{37} +50.0318i q^{39} +129.785i q^{41} +(344.071 - 344.071i) q^{43} +(83.4518 + 83.4518i) q^{45} -174.483 q^{47} +19.9202 q^{49} +(-134.958 - 134.958i) q^{51} +(-322.832 + 322.832i) q^{53} -68.3448i q^{55} +42.3653i q^{57} +(21.0376 - 21.0376i) q^{59} +(-489.653 - 489.653i) q^{61} -424.264 q^{63} +135.742 q^{65} +(-261.470 - 261.470i) q^{67} +(-64.7110 + 64.7110i) q^{69} -218.795i q^{71} +1085.01i q^{73} +(-32.5781 + 32.5781i) q^{75} +(173.730 + 173.730i) q^{77} -1155.60 q^{79} -465.437 q^{81} +(-777.042 - 777.042i) q^{83} +(-366.157 + 366.157i) q^{85} -179.283i q^{87} -15.9331i q^{89} +(-345.052 + 345.052i) q^{91} +(325.656 + 325.656i) q^{93} +114.942 q^{95} -923.624 q^{97} +(228.140 + 228.140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.30312	−	1.30312i	−0.250786	−	0.250786i	0.570507	−	0.821293i	$-0.306747\pi$
$3$	−1.30312	−	1.30312i	−0.250786	−	0.250786i	−0.821293	+	0.570507i	$0.806747\pi$
$4$		0			0
$5$	−3.53553	+	3.53553i	−0.316228	+	0.316228i
$5$	−3.53553	+	3.53553i	−0.316228	+	0.316228i
$6$		0			0
$7$		−	17.9744i		−	0.970528i	−0.874368	−	0.485264i	$-0.838724\pi$
$7$		−	17.9744i		−	0.970528i	0.874368	−	0.485264i	$-0.161276\pi$
$8$		0			0
$9$		−	23.6037i		−	0.874213i
$10$		0			0
$11$	−9.66542	+	9.66542i	−0.264930	+	0.264930i	−0.827054	−	0.562123i	$-0.809985\pi$
$11$	−9.66542	+	9.66542i	−0.264930	+	0.264930i	0.562123	+	0.827054i	$0.309985\pi$
$12$		0			0
$13$	−19.1969	−	19.1969i	−0.409558	−	0.409558i	0.472027	−	0.881584i	$-0.343523\pi$
$13$	−19.1969	−	19.1969i	−0.409558	−	0.409558i	−0.881584	+	0.472027i	$0.843523\pi$
$14$		0			0
$15$	9.21448			0.158611
$16$		0			0
$17$	103.565			1.47754			0.738770	−	0.673957i	$-0.235407\pi$
$17$	103.565			1.47754			0.738770	+	0.673957i	$0.235407\pi$
$18$		0			0
$19$	−16.2553	−	16.2553i	−0.196275	−	0.196275i	0.602126	−	0.798401i	$-0.294320\pi$
$19$	−16.2553	−	16.2553i	−0.196275	−	0.196275i	−0.798401	+	0.602126i	$0.794320\pi$
$20$		0			0
$21$	−23.4229	+	23.4229i	−0.243395	+	0.243395i
$22$		0			0
$23$		−	49.6583i		−	0.450195i	−0.974336	−	0.225097i	$-0.927730\pi$
$23$		−	49.6583i		−	0.450195i	0.974336	−	0.225097i	$-0.0722700\pi$
$24$		0			0
$25$		−	25.0000i		−	0.200000i
$26$		0			0
$27$	−65.9429	+	65.9429i	−0.470027	+	0.470027i
$28$		0			0
$29$	68.7899	+	68.7899i	0.440481	+	0.440481i	0.892174	−	0.451692i	$-0.149180\pi$
$29$	68.7899	+	68.7899i	0.440481	+	0.440481i	−0.451692	+	0.892174i	$0.649180\pi$
$30$		0			0
$31$	−249.904			−1.44787			−0.723937	−	0.689866i	$-0.757670\pi$
$31$	−249.904			−1.44787			−0.723937	+	0.689866i	$0.757670\pi$
$32$		0			0
$33$	25.1905			0.132882
$34$		0			0
$35$	63.5492	+	63.5492i	0.306908	+	0.306908i
$36$		0			0
$37$	−210.860	+	210.860i	−0.936897	+	0.936897i	−0.998124	−	0.0612269i	$-0.980499\pi$
$37$	−210.860	+	210.860i	−0.936897	+	0.936897i	0.0612269	+	0.998124i	$0.480499\pi$
$38$		0			0
$39$			50.0318i			0.205423i
$40$		0			0
$41$			129.785i			0.494367i	0.968969	+	0.247183i	$0.0795050\pi$
$41$			129.785i			0.494367i	−0.968969	+	0.247183i	$0.920495\pi$
$42$		0			0
$43$	344.071	−	344.071i	1.22024	−	1.22024i	0.252696	−	0.967546i	$-0.418683\pi$
$43$	344.071	−	344.071i	1.22024	−	1.22024i	0.967546	−	0.252696i	$-0.0813173\pi$
$44$		0			0
$45$	83.4518	+	83.4518i	0.276450	+	0.276450i
$46$		0			0
$47$	−174.483			−0.541511			−0.270755	−	0.962648i	$-0.587273\pi$
$47$	−174.483			−0.541511			−0.270755	+	0.962648i	$0.587273\pi$
$48$		0			0
$49$	19.9202			0.0580764
$50$		0			0
$51$	−134.958	−	134.958i	−0.370547	−	0.370547i
$52$		0			0
$53$	−322.832	+	322.832i	−0.836687	+	0.836687i	−0.988421	−	0.151735i	$-0.951514\pi$
$53$	−322.832	+	322.832i	−0.836687	+	0.836687i	0.151735	+	0.988421i	$0.451514\pi$
$54$		0			0
$55$		−	68.3448i		−	0.167557i
$56$		0			0
$57$			42.3653i			0.0984461i
$58$		0			0
$59$	21.0376	−	21.0376i	0.0464213	−	0.0464213i	−0.683515	−	0.729936i	$-0.739550\pi$
$59$	21.0376	−	21.0376i	0.0464213	−	0.0464213i	0.729936	+	0.683515i	$0.239550\pi$
$60$		0			0
$61$	−489.653	−	489.653i	−1.02777	−	1.02777i	−0.999603	−	0.0281617i	$-0.991035\pi$
$61$	−489.653	−	489.653i	−1.02777	−	1.02777i	−0.0281617	−	0.999603i	$-0.508965\pi$
$62$		0			0
$63$	−424.264			−0.848447
$64$		0			0
$65$	135.742			0.259027
$66$		0			0
$67$	−261.470	−	261.470i	−0.476771	−	0.476771i	0.427327	−	0.904097i	$-0.359455\pi$
$67$	−261.470	−	261.470i	−0.476771	−	0.476771i	−0.904097	+	0.427327i	$0.859455\pi$
$68$		0			0
$69$	−64.7110	+	64.7110i	−0.112903	+	0.112903i
$70$		0			0
$71$		−	218.795i		−	0.365720i	−0.983139	−	0.182860i	$-0.941464\pi$
$71$		−	218.795i		−	0.365720i	0.983139	−	0.182860i	$-0.0585356\pi$
$72$		0			0
$73$			1085.01i			1.73960i	0.493401	+	0.869802i	$0.335754\pi$
$73$			1085.01i			1.73960i	−0.493401	+	0.869802i	$0.664246\pi$
$74$		0			0
$75$	−32.5781	+	32.5781i	−0.0501573	+	0.0501573i
$76$		0			0
$77$	173.730	+	173.730i	0.257122	+	0.257122i
$78$		0			0
$79$	−1155.60			−1.64576			−0.822880	−	0.568215i	$-0.807634\pi$
$79$	−1155.60			−1.64576			−0.822880	+	0.568215i	$0.807634\pi$
$80$		0			0
$81$	−465.437			−0.638460
$82$		0			0
$83$	−777.042	−	777.042i	−1.02761	−	1.02761i	−0.999608	−	0.0280004i	$-0.991086\pi$
$83$	−777.042	−	777.042i	−1.02761	−	1.02761i	−0.0280004	−	0.999608i	$-0.508914\pi$
$84$		0			0
$85$	−366.157	+	366.157i	−0.467239	+	0.467239i
$86$		0			0
$87$		−	179.283i		−	0.220933i
$88$		0			0
$89$		−	15.9331i		−	0.0189765i	−0.999955	−	0.00948823i	$-0.996980\pi$
$89$		−	15.9331i		−	0.0189765i	0.999955	−	0.00948823i	$-0.00302024\pi$
$90$		0			0
$91$	−345.052	+	345.052i	−0.397487	+	0.397487i
$92$		0			0
$93$	325.656	+	325.656i	0.363107	+	0.363107i
$94$		0			0
$95$	114.942			0.124135
$96$		0			0
$97$	−923.624			−0.966802			−0.483401	−	0.875399i	$-0.660599\pi$
$97$	−923.624			−0.966802			−0.483401	+	0.875399i	$0.660599\pi$
$98$		0			0
$99$	228.140	+	228.140i	0.231605	+	0.231605i
$100$		0			0
$101$	385.353	−	385.353i	0.379644	−	0.379644i	−0.491330	−	0.870974i	$-0.663489\pi$
$101$	385.353	−	385.353i	0.379644	−	0.379644i	0.870974	+	0.491330i	$0.163489\pi$
$102$		0			0
$103$			1445.05i			1.38238i	0.722672	+	0.691191i	$0.242914\pi$
$103$			1445.05i			1.38238i	−0.722672	+	0.691191i	$0.757086\pi$
$104$		0			0
$105$		−	165.625i		−	0.153936i
$106$		0			0
$107$	−488.994	+	488.994i	−0.441802	+	0.441802i	−0.892617	−	0.450815i	$-0.851133\pi$
$107$	−488.994	+	488.994i	−0.441802	+	0.441802i	0.450815	+	0.892617i	$0.351133\pi$
$108$		0			0
$109$	640.953	+	640.953i	0.563231	+	0.563231i	0.930224	−	0.366993i	$-0.119613\pi$
$109$	640.953	+	640.953i	0.563231	+	0.563231i	−0.366993	+	0.930224i	$0.619613\pi$
$110$		0			0
$111$	549.554			0.469922
$112$		0			0
$113$	214.312			0.178414			0.0892069	−	0.996013i	$-0.471567\pi$
$113$	214.312			0.178414			0.0892069	+	0.996013i	$0.471567\pi$
$114$		0			0
$115$	175.569	+	175.569i	0.142364	+	0.142364i
$116$		0			0
$117$	−453.118	+	453.118i	−0.358040	+	0.358040i
$118$		0			0
$119$		−	1861.52i		−	1.43399i
$120$		0			0
$121$			1144.16i			0.859624i
$122$		0			0
$123$	169.126	−	169.126i	0.123980	−	0.123980i
$124$		0			0
$125$	88.3883	+	88.3883i	0.0632456	+	0.0632456i
$126$		0			0
$127$	68.9099			0.0481478			0.0240739	−	0.999710i	$-0.492336\pi$
$127$	68.9099			0.0481478			0.0240739	+	0.999710i	$0.492336\pi$
$128$		0			0
$129$	−896.735			−0.612040
$130$		0			0
$131$	−488.197	−	488.197i	−0.325603	−	0.325603i	0.525309	−	0.850912i	$-0.323950\pi$
$131$	−488.197	−	488.197i	−0.325603	−	0.325603i	−0.850912	+	0.525309i	$0.823950\pi$
$132$		0			0
$133$	−292.180	+	292.180i	−0.190490	+	0.190490i
$134$		0			0
$135$		−	466.287i		−	0.297271i
$136$		0			0
$137$			2605.52i			1.62485i	0.583066	+	0.812425i	$0.301853\pi$
$137$			2605.52i			1.62485i	−0.583066	+	0.812425i	$0.698147\pi$
$138$		0			0
$139$	−2138.54	+	2138.54i	−1.30495	+	1.30495i	−0.379944	+	0.925009i	$0.624057\pi$
$139$	−2138.54	+	2138.54i	−1.30495	+	1.30495i	−0.925009	+	0.379944i	$0.875943\pi$
$140$		0			0
$141$	227.373	+	227.373i	0.135803	+	0.135803i
$142$		0			0
$143$	371.091			0.217009
$144$		0			0
$145$	−486.418			−0.278585
$146$		0			0
$147$	−25.9585	−	25.9585i	−0.0145648	−	0.0145648i
$148$		0			0
$149$	−1394.57	+	1394.57i	−0.766764	+	0.766764i	−0.977535	−	0.210771i	$-0.932402\pi$
$149$	−1394.57	+	1394.57i	−0.766764	+	0.766764i	0.210771	+	0.977535i	$0.432402\pi$
$150$		0			0
$151$		−	1946.09i		−	1.04881i	−0.851469	−	0.524405i	$-0.824288\pi$
$151$		−	1946.09i		−	1.04881i	0.851469	−	0.524405i	$-0.175712\pi$
$152$		0			0
$153$		−	2444.52i		−	1.29168i
$154$		0			0
$155$	883.545	−	883.545i	0.457858	−	0.457858i
$156$		0			0
$157$	514.931	+	514.931i	0.261758	+	0.261758i	0.825768	−	0.564010i	$-0.190742\pi$
$157$	514.931	+	514.931i	0.261758	+	0.261758i	−0.564010	+	0.825768i	$0.690742\pi$
$158$		0			0
$159$	841.380			0.419659
$160$		0			0
$161$	−892.580			−0.436926
$162$		0			0
$163$	−1228.72	−	1228.72i	−0.590433	−	0.590433i	0.347316	−	0.937748i	$-0.387093\pi$
$163$	−1228.72	−	1228.72i	−0.590433	−	0.590433i	−0.937748	+	0.347316i	$0.887093\pi$
$164$		0			0
$165$	−89.0618	+	89.0618i	−0.0420209	+	0.0420209i
$166$		0			0
$167$			587.588i			0.272269i	0.990690	+	0.136135i	$0.0434679\pi$
$167$			587.588i			0.272269i	−0.990690	+	0.136135i	$0.956532\pi$
$168$		0			0
$169$		−	1459.96i		−	0.664525i
$170$		0			0
$171$	−383.686	+	383.686i	−0.171586	+	0.171586i
$172$		0			0
$173$	−1062.06	−	1062.06i	−0.466744	−	0.466744i	0.434114	−	0.900858i	$-0.357062\pi$
$173$	−1062.06	−	1062.06i	−0.466744	−	0.466744i	−0.900858	+	0.434114i	$0.857062\pi$
$174$		0			0
$175$	−449.361			−0.194106
$176$		0			0
$177$	−54.8291			−0.0232836
$178$		0			0
$179$	−1954.76	−	1954.76i	−0.816234	−	0.816234i	0.169326	−	0.985560i	$-0.445841\pi$
$179$	−1954.76	−	1954.76i	−0.816234	−	0.816234i	−0.985560	+	0.169326i	$0.945841\pi$
$180$		0			0
$181$	2384.68	−	2384.68i	0.979293	−	0.979293i	−0.0204973	−	0.999790i	$-0.506525\pi$
$181$	2384.68	−	2384.68i	0.979293	−	0.979293i	0.999790	+	0.0204973i	$0.00652494\pi$
$182$		0			0
$183$			1276.16i			0.515499i
$184$		0			0
$185$		−	1491.01i		−	0.592546i
$186$		0			0
$187$	−1001.00	+	1001.00i	−0.391445	+	0.391445i
$188$		0			0
$189$	1185.29	+	1185.29i	0.456174	+	0.456174i
$190$		0			0
$191$	3326.75			1.26029			0.630145	−	0.776478i	$-0.282996\pi$
$191$	3326.75			1.26029			0.630145	+	0.776478i	$0.282996\pi$
$192$		0			0
$193$	2489.93			0.928648			0.464324	−	0.885665i	$-0.346297\pi$
$193$	2489.93			0.928648			0.464324	+	0.885665i	$0.346297\pi$
$194$		0			0
$195$	−176.889	−	176.889i	−0.0649604	−	0.0649604i
$196$		0			0
$197$	1788.50	−	1788.50i	0.646829	−	0.646829i	−0.305396	−	0.952225i	$-0.598789\pi$
$197$	1788.50	−	1788.50i	0.646829	−	0.646829i	0.952225	+	0.305396i	$0.0987890\pi$
$198$		0			0
$199$		−	1891.36i		−	0.673743i	−0.941551	−	0.336872i	$-0.890631\pi$
$199$		−	1891.36i		−	0.673743i	0.941551	−	0.336872i	$-0.109369\pi$
$200$		0			0
$201$			681.455i			0.239135i
$202$		0			0
$203$	1236.46	−	1236.46i	0.427499	−	0.427499i
$204$		0			0
$205$	−458.860	−	458.860i	−0.156333	−	0.156333i
$206$		0			0
$207$	−1172.12			−0.393566
$208$		0			0
$209$	314.229			0.103998
$210$		0			0
$211$	3007.32	+	3007.32i	0.981197	+	0.981197i	0.999826	−	0.0186292i	$-0.00593020\pi$
$211$	3007.32	+	3007.32i	0.981197	+	0.981197i	−0.0186292	+	0.999826i	$0.505930\pi$
$212$		0			0
$213$	−285.116	+	285.116i	−0.0917176	+	0.0917176i
$214$		0			0
$215$			2432.95i			0.771749i
$216$		0			0
$217$			4491.88i			1.40520i
$218$		0			0
$219$	1413.91	−	1413.91i	0.436269	−	0.436269i
$220$		0			0
$221$	−1988.12	−	1988.12i	−0.605138	−	0.605138i
$222$		0			0
$223$	−5155.90			−1.54827			−0.774136	−	0.633019i	$-0.781815\pi$
$223$	−5155.90			−1.54827			−0.774136	+	0.633019i	$0.781815\pi$
$224$		0			0
$225$	−590.093			−0.174843
$226$		0			0
$227$	363.535	+	363.535i	0.106294	+	0.106294i	0.758254	−	0.651960i	$-0.226053\pi$
$227$	363.535	+	363.535i	0.106294	+	0.106294i	−0.651960	+	0.758254i	$0.726053\pi$
$228$		0			0
$229$	2227.85	−	2227.85i	0.642884	−	0.642884i	−0.308380	−	0.951263i	$-0.599787\pi$
$229$	2227.85	−	2227.85i	0.642884	−	0.642884i	0.951263	+	0.308380i	$0.0997867\pi$
$230$		0			0
$231$		−	452.784i		−	0.128965i
$232$		0			0
$233$		−	3753.04i		−	1.05524i	−0.849482	−	0.527618i	$-0.823085\pi$
$233$		−	3753.04i		−	1.05524i	0.849482	−	0.527618i	$-0.176915\pi$
$234$		0			0
$235$	616.892	−	616.892i	0.171241	−	0.171241i
$236$		0			0
$237$	1505.89	+	1505.89i	0.412734	+	0.412734i
$238$		0			0
$239$	−1005.32			−0.272088			−0.136044	−	0.990703i	$-0.543439\pi$
$239$	−1005.32			−0.272088			−0.136044	+	0.990703i	$0.543439\pi$
$240$		0			0
$241$	−1393.93			−0.372576			−0.186288	−	0.982495i	$-0.559646\pi$
$241$	−1393.93			−0.372576			−0.186288	+	0.982495i	$0.559646\pi$
$242$		0			0
$243$	2386.98	+	2386.98i	0.630144	+	0.630144i
$244$		0			0
$245$	−70.4285	+	70.4285i	−0.0183654	+	0.0183654i
$246$		0			0
$247$			624.101i			0.160772i
$248$		0			0
$249$			2025.16i			0.515420i
$250$		0			0
$251$	4032.99	−	4032.99i	1.01418	−	1.01418i	0.0142864	−	0.999898i	$-0.495452\pi$
$251$	4032.99	−	4032.99i	1.01418	−	1.01418i	0.999898	−	0.0142864i	$-0.00454766\pi$
$252$		0			0
$253$	479.969	+	479.969i	0.119270	+	0.119270i
$254$		0			0
$255$	954.297			0.234354
$256$		0			0
$257$	2814.94			0.683234			0.341617	−	0.939839i	$-0.389025\pi$
$257$	2814.94			0.683234			0.341617	+	0.939839i	$0.389025\pi$
$258$		0			0
$259$	3790.09	+	3790.09i	0.909284	+	0.909284i
$260$		0			0
$261$	1623.70	−	1623.70i	0.385074	−	0.385074i
$262$		0			0
$263$			5568.12i			1.30549i	0.757576	+	0.652747i	$0.226384\pi$
$263$			5568.12i			1.30549i	−0.757576	+	0.652747i	$0.773616\pi$
$264$		0			0
$265$		−	2282.77i		−	0.529167i
$266$		0			0
$267$	−20.7628	+	20.7628i	−0.00475904	+	0.00475904i
$268$		0			0
$269$	−3381.13	−	3381.13i	−0.766362	−	0.766362i	0.211102	−	0.977464i	$-0.432295\pi$
$269$	−3381.13	−	3381.13i	−0.766362	−	0.766362i	−0.977464	+	0.211102i	$0.932295\pi$
$270$		0			0
$271$	8497.20			1.90468			0.952339	−	0.305040i	$-0.0986699\pi$
$271$	8497.20			1.90468			0.952339	+	0.305040i	$0.0986699\pi$
$272$		0			0
$273$	899.292			0.199369
$274$		0			0
$275$	241.635	+	241.635i	0.0529861	+	0.0529861i
$276$		0			0
$277$	−776.937	+	776.937i	−0.168526	+	0.168526i	−0.786331	−	0.617805i	$-0.788022\pi$
$277$	−776.937	+	776.937i	−0.168526	+	0.168526i	0.617805	+	0.786331i	$0.288022\pi$
$278$		0			0
$279$			5898.67i			1.26575i
$280$		0			0
$281$		−	8079.78i		−	1.71530i	−0.514234	−	0.857650i	$-0.671924\pi$
$281$		−	8079.78i		−	1.71530i	0.514234	−	0.857650i	$-0.328076\pi$
$282$		0			0
$283$	2189.72	−	2189.72i	0.459949	−	0.459949i	−0.438690	−	0.898639i	$-0.644557\pi$
$283$	2189.72	−	2189.72i	0.459949	−	0.459949i	0.898639	+	0.438690i	$0.144557\pi$
$284$		0			0
$285$	−149.784	−	149.784i	−0.0311314	−	0.0311314i
$286$		0			0
$287$	2332.81			0.479797
$288$		0			0
$289$	5812.70			1.18313
$290$		0			0
$291$	1203.60	+	1203.60i	0.242461	+	0.242461i
$292$		0			0
$293$	−5552.61	+	5552.61i	−1.10712	+	1.10712i	−0.113596	+	0.993527i	$0.536237\pi$
$293$	−5552.61	+	5552.61i	−1.10712	+	1.10712i	−0.993527	+	0.113596i	$0.963763\pi$
$294$		0			0
$295$			148.758i			0.0293594i
$296$		0			0
$297$		−	1274.73i		−	0.249049i
$298$		0			0
$299$	−953.284	+	953.284i	−0.184381	+	0.184381i
$300$		0			0
$301$	−6184.48	−	6184.48i	−1.18428	−	1.18428i
$302$		0			0
$303$	−1004.32			−0.190419
$304$		0			0
$305$	3462.37			0.650016
$306$		0			0
$307$	4301.90	+	4301.90i	0.799747	+	0.799747i	0.983055	−	0.183309i	$-0.0586808\pi$
$307$	4301.90	+	4301.90i	0.799747	+	0.799747i	−0.183309	+	0.983055i	$0.558681\pi$
$308$		0			0
$309$	1883.08	−	1883.08i	0.346682	−	0.346682i
$310$		0			0
$311$		−	4756.88i		−	0.867325i	−0.901075	−	0.433663i	$-0.857221\pi$
$311$		−	4756.88i		−	0.867325i	0.901075	−	0.433663i	$-0.142779\pi$
$312$		0			0
$313$		−	5433.84i		−	0.981274i	−0.871364	−	0.490637i	$-0.836764\pi$
$313$		−	5433.84i		−	0.981274i	0.871364	−	0.490637i	$-0.163236\pi$
$314$		0			0
$315$	1500.00	−	1500.00i	0.268303	−	0.268303i
$316$		0			0
$317$	728.663	+	728.663i	0.129103	+	0.129103i	0.768706	−	0.639602i	$-0.220901\pi$
$317$	728.663	+	728.663i	0.129103	+	0.129103i	−0.639602	+	0.768706i	$0.720901\pi$
$318$		0			0
$319$	−1329.77			−0.233394
$320$		0			0
$321$	1274.44			0.221596
$322$		0			0
$323$	−1683.48	−	1683.48i	−0.290004	−	0.290004i
$324$		0			0
$325$	−479.921	+	479.921i	−0.0819115	+	0.0819115i
$326$		0			0
$327$		−	1670.48i		−	0.282501i
$328$		0			0
$329$			3136.24i			0.525551i
$330$		0			0
$331$	−2514.44	+	2514.44i	−0.417541	+	0.417541i	−0.884355	−	0.466814i	$-0.845402\pi$
$331$	−2514.44	+	2514.44i	−0.417541	+	0.417541i	0.466814	+	0.884355i	$0.345402\pi$
$332$		0			0
$333$	4977.09	+	4977.09i	0.819047	+	0.819047i
$334$		0			0
$335$	1848.87			0.301536
$336$		0			0
$337$	82.5425			0.0133424			0.00667118	−	0.999978i	$-0.497876\pi$
$337$	82.5425			0.0133424			0.00667118	+	0.999978i	$0.497876\pi$
$338$		0			0
$339$	−279.275	−	279.275i	−0.0447438	−	0.0447438i
$340$		0			0
$341$	2415.43	−	2415.43i	0.383586	−	0.383586i
$342$		0			0
$343$		−	6523.28i		−	1.02689i
$344$		0			0
$345$		−	457.576i		−	0.0714059i
$346$		0			0
$347$	−7202.76	+	7202.76i	−1.11431	+	1.11431i	−0.121745	+	0.992561i	$0.538849\pi$
$347$	−7202.76	+	7202.76i	−1.11431	+	1.11431i	−0.992561	+	0.121745i	$0.961151\pi$
$348$		0			0
$349$	2134.41	+	2134.41i	0.327370	+	0.327370i	0.851586	−	0.524215i	$-0.175641\pi$
$349$	2134.41	+	2134.41i	0.327370	+	0.327370i	−0.524215	+	0.851586i	$0.675641\pi$
$350$		0			0
$351$	2531.79			0.385006
$352$		0			0
$353$	705.357			0.106352			0.0531761	−	0.998585i	$-0.483066\pi$
$353$	705.357			0.106352			0.0531761	+	0.998585i	$0.483066\pi$
$354$		0			0
$355$	773.556	+	773.556i	0.115651	+	0.115651i
$356$		0			0
$357$	−2425.79	+	2425.79i	−0.359626	+	0.359626i
$358$		0			0
$359$			11015.7i			1.61946i	0.586803	+	0.809730i	$0.300386\pi$
$359$			11015.7i			1.61946i	−0.586803	+	0.809730i	$0.699614\pi$
$360$		0			0
$361$		−	6330.53i		−	0.922952i
$362$		0			0
$363$	1490.98	−	1490.98i	0.215582	−	0.215582i
$364$		0			0
$365$	−3836.10	−	3836.10i	−0.550111	−	0.550111i
$366$		0			0
$367$	−12269.4			−1.74512			−0.872560	−	0.488506i	$-0.837542\pi$
$367$	−12269.4			−1.74512			−0.872560	+	0.488506i	$0.837542\pi$
$368$		0			0
$369$	3063.42			0.432182
$370$		0			0
$371$	5802.72	+	5802.72i	0.812028	+	0.812028i
$372$		0			0
$373$	1651.92	−	1651.92i	0.229312	−	0.229312i	−0.583093	−	0.812405i	$-0.698158\pi$
$373$	1651.92	−	1651.92i	0.229312	−	0.229312i	0.812405	+	0.583093i	$0.198158\pi$
$374$		0			0
$375$		−	230.362i		−	0.0317222i
$376$		0			0
$377$		−	2641.10i		−	0.360805i
$378$		0			0
$379$	2757.81	−	2757.81i	0.373771	−	0.373771i	−0.495078	−	0.868849i	$-0.664860\pi$
$379$	2757.81	−	2757.81i	0.373771	−	0.373771i	0.868849	+	0.495078i	$0.164860\pi$
$380$		0			0
$381$	−89.7982	−	89.7982i	−0.0120748	−	0.0120748i
$382$		0			0
$383$	10375.4			1.38423			0.692116	−	0.721787i	$-0.256679\pi$
$383$	10375.4			1.38423			0.692116	+	0.721787i	$0.256679\pi$
$384$		0			0
$385$	−1228.46			−0.162618
$386$		0			0
$387$	−8121.37	−	8121.37i	−1.06675	−	1.06675i
$388$		0			0
$389$	2933.34	−	2933.34i	0.382330	−	0.382330i	−0.489611	−	0.871941i	$-0.662861\pi$
$389$	2933.34	−	2933.34i	0.382330	−	0.382330i	0.871941	+	0.489611i	$0.162861\pi$
$390$		0			0
$391$		−	5142.87i		−	0.665181i
$392$		0			0
$393$			1272.36i			0.163313i
$394$		0			0
$395$	4085.66	−	4085.66i	0.520435	−	0.520435i
$396$		0			0
$397$	2310.28	+	2310.28i	0.292065	+	0.292065i	0.837895	−	0.545831i	$-0.183786\pi$
$397$	2310.28	+	2310.28i	0.292065	+	0.292065i	−0.545831	+	0.837895i	$0.683786\pi$
$398$		0			0
$399$	761.492			0.0955446
$400$		0			0
$401$	−15396.7			−1.91740			−0.958698	−	0.284427i	$-0.908197\pi$
$401$	−15396.7			−1.91740			−0.958698	+	0.284427i	$0.908197\pi$
$402$		0			0
$403$	4797.37	+	4797.37i	0.592988	+	0.592988i
$404$		0			0
$405$	1645.57	−	1645.57i	0.201899	−	0.201899i
$406$		0			0
$407$		−	4076.10i		−	0.496425i
$408$		0			0
$409$			12575.6i			1.52036i	0.649715	+	0.760178i	$0.274888\pi$
$409$			12575.6i			1.52036i	−0.649715	+	0.760178i	$0.725112\pi$
$410$		0			0
$411$	3395.31	−	3395.31i	0.407490	−	0.407490i
$412$		0			0
$413$	−378.138	−	378.138i	−0.0450531	−	0.0450531i
$414$		0			0
$415$	5494.52			0.649917
$416$		0			0
$417$	5573.56			0.654529
$418$		0			0
$419$	−8665.37	−	8665.37i	−1.01034	−	1.01034i	−0.999946	−	0.0103906i	$-0.996693\pi$
$419$	−8665.37	−	8665.37i	−1.01034	−	1.01034i	−0.0103906	−	0.999946i	$-0.503307\pi$
$420$		0			0
$421$	7662.55	−	7662.55i	0.887054	−	0.887054i	−0.107185	−	0.994239i	$-0.534184\pi$
$421$	7662.55	−	7662.55i	0.887054	−	0.887054i	0.994239	+	0.107185i	$0.0341837\pi$
$422$		0			0
$423$			4118.46i			0.473395i
$424$		0			0
$425$		−	2589.12i		−	0.295508i
$426$		0			0
$427$	−8801.23	+	8801.23i	−0.997474	+	0.997474i
$428$		0			0
$429$	−483.578	−	483.578i	−0.0544228	−	0.0544228i
$430$		0			0
$431$	−1895.81			−0.211874			−0.105937	−	0.994373i	$-0.533784\pi$
$431$	−1895.81			−0.211874			−0.105937	+	0.994373i	$0.533784\pi$
$432$		0			0
$433$	−2200.34			−0.244207			−0.122104	−	0.992517i	$-0.538964\pi$
$433$	−2200.34			−0.244207			−0.122104	+	0.992517i	$0.538964\pi$
$434$		0			0
$435$	633.863	+	633.863i	0.0698653	+	0.0698653i
$436$		0			0
$437$	−807.211	+	807.211i	−0.0883619	+	0.0883619i
$438$		0			0
$439$		−	6043.58i		−	0.657049i	−0.944495	−	0.328524i	$-0.893449\pi$
$439$		−	6043.58i		−	0.657049i	0.944495	−	0.328524i	$-0.106551\pi$
$440$		0			0
$441$		−	470.191i		−	0.0507711i
$442$		0			0
$443$	2766.30	−	2766.30i	0.296684	−	0.296684i	−0.543030	−	0.839714i	$-0.682723\pi$
$443$	2766.30	−	2766.30i	0.296684	−	0.296684i	0.839714	+	0.543030i	$0.182723\pi$
$444$		0			0
$445$	56.3320	+	56.3320i	0.00600088	+	0.00600088i
$446$		0			0
$447$	3634.60			0.384588
$448$		0			0
$449$	−17830.6			−1.87411			−0.937056	−	0.349179i	$-0.886461\pi$
$449$	−17830.6			−1.87411			−0.937056	+	0.349179i	$0.886461\pi$
$450$		0			0
$451$	−1254.43	−	1254.43i	−0.130973	−	0.130973i
$452$		0			0
$453$	−2535.99	+	2535.99i	−0.263027	+	0.263027i
$454$		0			0
$455$		−	2439.89i		−	0.251393i
$456$		0			0
$457$			14018.4i			1.43491i	0.696606	+	0.717454i	$0.254693\pi$
$457$			14018.4i			1.43491i	−0.696606	+	0.717454i	$0.745307\pi$
$458$		0			0
$459$	−6829.38	+	6829.38i	−0.694484	+	0.694484i
$460$		0			0
$461$	−2477.06	−	2477.06i	−0.250256	−	0.250256i	0.570819	−	0.821076i	$-0.306626\pi$
$461$	−2477.06	−	2477.06i	−0.250256	−	0.250256i	−0.821076	+	0.570819i	$0.806626\pi$
$462$		0			0
$463$	−6279.68			−0.630327			−0.315163	−	0.949037i	$-0.602059\pi$
$463$	−6279.68			−0.630327			−0.315163	+	0.949037i	$0.602059\pi$
$464$		0			0
$465$	−2302.74			−0.229649
$466$		0			0
$467$	−5797.97	−	5797.97i	−0.574514	−	0.574514i	0.358873	−	0.933386i	$-0.383161\pi$
$467$	−5797.97	−	5797.97i	−0.574514	−	0.574514i	−0.933386	+	0.358873i	$0.883161\pi$
$468$		0			0
$469$	−4699.77	+	4699.77i	−0.462719	+	0.462719i
$470$		0			0
$471$		−	1342.04i		−	0.131290i
$472$		0			0
$473$			6651.19i			0.646558i
$474$		0			0
$475$	−406.383	+	406.383i	−0.0392550	+	0.0392550i
$476$		0			0
$477$	7620.04	+	7620.04i	0.731442	+	0.731442i
$478$		0			0
$479$	965.448			0.0920927			0.0460464	−	0.998939i	$-0.485338\pi$
$479$	965.448			0.0920927			0.0460464	+	0.998939i	$0.485338\pi$
$480$		0			0
$481$	8095.70			0.767427
$482$		0			0
$483$	1163.14	+	1163.14i	0.109575	+	0.109575i
$484$		0			0
$485$	3265.50	−	3265.50i	0.305730	−	0.305730i
$486$		0			0
$487$			13452.2i			1.25170i	0.779942	+	0.625852i	$0.215248\pi$
$487$			13452.2i			1.25170i	−0.779942	+	0.625852i	$0.784752\pi$
$488$		0			0
$489$			3202.34i			0.296145i
$490$		0			0
$491$	7716.82	−	7716.82i	0.709277	−	0.709277i	−0.257106	−	0.966383i	$-0.582769\pi$
$491$	7716.82	−	7716.82i	0.709277	−	0.709277i	0.966383	+	0.257106i	$0.0827689\pi$
$492$		0			0
$493$	7124.22	+	7124.22i	0.650829	+	0.650829i
$494$		0			0
$495$	−1613.19			−0.146480
$496$		0			0
$497$	−3932.71			−0.354942
$498$		0			0
$499$	−3025.88	−	3025.88i	−0.271457	−	0.271457i	0.558230	−	0.829686i	$-0.311481\pi$
$499$	−3025.88	−	3025.88i	−0.271457	−	0.271457i	−0.829686	+	0.558230i	$0.811481\pi$
$500$		0			0
$501$	765.700	−	765.700i	0.0682813	−	0.0682813i
$502$		0			0
$503$		−	7264.11i		−	0.643918i	−0.946754	−	0.321959i	$-0.895659\pi$
$503$		−	7264.11i		−	0.643918i	0.946754	−	0.321959i	$-0.104341\pi$
$504$		0			0
$505$			2724.86i			0.240108i
$506$		0			0
$507$	−1902.51	+	1902.51i	−0.166654	+	0.166654i
$508$		0			0
$509$	6106.12	+	6106.12i	0.531727	+	0.531727i	0.921086	−	0.389359i	$-0.127303\pi$
$509$	6106.12	+	6106.12i	0.531727	+	0.531727i	−0.389359	+	0.921086i	$0.627303\pi$
$510$		0			0
$511$	19502.5			1.68833
$512$		0			0
$513$	2143.84			0.184509
$514$		0			0
$515$	−5109.04	−	5109.04i	−0.437148	−	0.437148i
$516$		0			0
$517$	1686.45	−	1686.45i	0.143463	−	0.143463i
$518$		0			0
$519$			2767.98i			0.234106i
$520$		0			0
$521$		−	15120.8i		−	1.27151i	−0.771893	−	0.635753i	$-0.780690\pi$
$521$		−	15120.8i		−	1.27151i	0.771893	−	0.635753i	$-0.219310\pi$
$522$		0			0
$523$	−15970.5	+	15970.5i	−1.33526	+	1.33526i	−0.434671	+	0.900589i	$0.643135\pi$
$523$	−15970.5	+	15970.5i	−1.33526	+	1.33526i	−0.900589	+	0.434671i	$0.856865\pi$
$524$		0			0
$525$	585.572	+	585.572i	0.0486790	+	0.0486790i
$526$		0			0
$527$	−25881.3			−2.13929
$528$		0			0
$529$	9701.05			0.797325
$530$		0			0
$531$	−496.565	−	496.565i	−0.0405821	−	0.0405821i
$532$		0			0
$533$	2491.47	−	2491.47i	0.202472	−	0.202472i
$534$		0			0
$535$		−	3457.71i		−	0.279420i
$536$		0			0
$537$			5094.60i			0.409401i
$538$		0			0
$539$	−192.537	+	192.537i	−0.0153862	+	0.0153862i
$540$		0			0
$541$	−16156.7	−	16156.7i	−1.28398	−	1.28398i	−0.938385	−	0.345592i	$-0.887678\pi$
$541$	−16156.7	−	16156.7i	−1.28398	−	1.28398i	−0.345592	−	0.938385i	$-0.612322\pi$
$542$		0			0
$543$	−6215.07			−0.491186
$544$		0			0
$545$	−4532.22			−0.356218
$546$		0			0
$547$	−6368.79	−	6368.79i	−0.497824	−	0.497824i	0.412936	−	0.910760i	$-0.364503\pi$
$547$	−6368.79	−	6368.79i	−0.497824	−	0.497824i	−0.910760	+	0.412936i	$0.864503\pi$
$548$		0			0
$549$	−11557.6	+	11557.6i	−0.898485	+	0.898485i
$550$		0			0
$551$		−	2236.40i		−	0.172911i
$552$		0			0
$553$			20771.2i			1.59726i
$554$		0			0
$555$	−1942.97	+	1942.97i	−0.148602	+	0.148602i
$556$		0			0
$557$	9746.29	+	9746.29i	0.741407	+	0.741407i	0.972849	−	0.231442i	$-0.0743443\pi$
$557$	9746.29	+	9746.29i	0.741407	+	0.741407i	−0.231442	+	0.972849i	$0.574344\pi$
$558$		0			0
$559$	−13210.2			−0.999519
$560$		0			0
$561$	2608.85			0.196338
$562$		0			0
$563$	−7196.60	−	7196.60i	−0.538722	−	0.538722i	0.384431	−	0.923154i	$-0.374398\pi$
$563$	−7196.60	−	7196.60i	−0.538722	−	0.538722i	−0.923154	+	0.384431i	$0.874398\pi$
$564$		0			0
$565$	−757.707	+	757.707i	−0.0564194	+	0.0564194i
$566$		0			0
$567$			8365.97i			0.619643i
$568$		0			0
$569$		−	5236.83i		−	0.385834i	−0.981215	−	0.192917i	$-0.938205\pi$
$569$		−	5236.83i		−	0.385834i	0.981215	−	0.192917i	$-0.0617948\pi$
$570$		0			0
$571$	7407.25	−	7407.25i	0.542879	−	0.542879i	−0.381493	−	0.924372i	$-0.624590\pi$
$571$	7407.25	−	7407.25i	0.542879	−	0.542879i	0.924372	+	0.381493i	$0.124590\pi$
$572$		0			0
$573$	−4335.17	−	4335.17i	−0.316063	−	0.316063i
$574$		0			0
$575$	−1241.46			−0.0900390
$576$		0			0
$577$	−7726.80			−0.557488			−0.278744	−	0.960365i	$-0.589918\pi$
$577$	−7726.80			−0.557488			−0.278744	+	0.960365i	$0.589918\pi$
$578$		0			0
$579$	−3244.69	−	3244.69i	−0.232892	−	0.232892i
$580$		0			0
$581$	−13966.9	+	13966.9i	−0.997322	+	0.997322i
$582$		0			0
$583$		−	6240.62i		−	0.443327i
$584$		0			0
$585$		−	3204.03i		−	0.226445i
$586$		0			0
$587$	8359.85	−	8359.85i	0.587816	−	0.587816i	−0.349224	−	0.937039i	$-0.613555\pi$
$587$	8359.85	−	8359.85i	0.587816	−	0.587816i	0.937039	+	0.349224i	$0.113555\pi$
$588$		0			0
$589$	4062.27	+	4062.27i	0.284181	+	0.284181i
$590$		0			0
$591$	−4661.27			−0.324432
$592$		0			0
$593$	−8292.91			−0.574281			−0.287141	−	0.957888i	$-0.592705\pi$
$593$	−8292.91			−0.574281			−0.287141	+	0.957888i	$0.592705\pi$
$594$		0			0
$595$	6581.47	+	6581.47i	0.453469	+	0.453469i
$596$		0			0
$597$	−2464.68	+	2464.68i	−0.168966	+	0.168966i
$598$		0			0
$599$		−	27431.8i		−	1.87117i	−0.353097	−	0.935587i	$-0.614871\pi$
$599$		−	27431.8i		−	1.87117i	0.353097	−	0.935587i	$-0.385129\pi$
$600$		0			0
$601$		−	2790.89i		−	0.189422i	−0.995505	−	0.0947112i	$-0.969807\pi$
$601$		−	2790.89i		−	0.189422i	0.995505	−	0.0947112i	$-0.0301928\pi$
$602$		0			0
$603$	−6171.67	+	6171.67i	−0.416799	+	0.416799i
$604$		0			0
$605$	−4045.21	−	4045.21i	−0.271837	−	0.271837i
$606$		0			0
$607$	−10317.1			−0.689882			−0.344941	−	0.938624i	$-0.612101\pi$
$607$	−10317.1			−0.689882			−0.344941	+	0.938624i	$0.612101\pi$
$608$		0			0
$609$	−3222.52			−0.214422
$610$		0			0
$611$	3349.53	+	3349.53i	0.221780	+	0.221780i
$612$		0			0
$613$	2563.99	−	2563.99i	0.168938	−	0.168938i	−0.617575	−	0.786512i	$-0.711885\pi$
$613$	2563.99	−	2563.99i	0.168938	−	0.168938i	0.786512	+	0.617575i	$0.211885\pi$
$614$		0			0
$615$			1195.90i			0.0784121i
$616$		0			0
$617$			9519.59i			0.621141i	0.950550	+	0.310571i	$0.100520\pi$
$617$			9519.59i			0.621141i	−0.950550	+	0.310571i	$0.899480\pi$
$618$		0			0
$619$	−5737.81	+	5737.81i	−0.372572	+	0.372572i	−0.868413	−	0.495841i	$-0.834860\pi$
$619$	−5737.81	+	5737.81i	−0.372572	+	0.372572i	0.495841	+	0.868413i	$0.334860\pi$
$620$		0			0
$621$	3274.62	+	3274.62i	0.211604	+	0.211604i
$622$		0			0
$623$	−286.388			−0.0184172
$624$		0			0
$625$	−625.000			−0.0400000
$626$		0			0
$627$	−409.479	−	409.479i	−0.0260814	−	0.0260814i
$628$		0			0
$629$	−21837.7	+	21837.7i	−1.38430	+	1.38430i
$630$		0			0
$631$			2962.42i			0.186897i	0.995624	+	0.0934485i	$0.0297890\pi$
$631$			2962.42i			0.186897i	−0.995624	+	0.0934485i	$0.970211\pi$
$632$		0			0
$633$		−	7837.83i		−	0.492142i
$634$		0			0
$635$	−243.633	+	243.633i	−0.0152257	+	0.0152257i
$636$		0			0
$637$	−382.405	−	382.405i	−0.0237856	−	0.0237856i
$638$		0			0
$639$	−5164.37			−0.319717
$640$		0			0
$641$	−14378.2			−0.885964			−0.442982	−	0.896530i	$-0.646079\pi$
$641$	−14378.2			−0.885964			−0.442982	+	0.896530i	$0.646079\pi$
$642$		0			0
$643$	−6022.70	−	6022.70i	−0.369381	−	0.369381i	0.497870	−	0.867251i	$-0.334116\pi$
$643$	−6022.70	−	6022.70i	−0.369381	−	0.369381i	−0.867251	+	0.497870i	$0.834116\pi$
$644$		0			0
$645$	3170.44	−	3170.44i	0.193544	−	0.193544i
$646$		0			0
$647$		−	14764.5i		−	0.897147i	−0.893746	−	0.448573i	$-0.851932\pi$
$647$		−	14764.5i		−	0.897147i	0.893746	−	0.448573i	$-0.148068\pi$
$648$		0			0
$649$			406.674i			0.0245968i
$650$		0			0
$651$	5853.48	−	5853.48i	0.352405	−	0.352405i
$652$		0			0
$653$	−9815.04	−	9815.04i	−0.588197	−	0.588197i	0.348946	−	0.937143i	$-0.386540\pi$
$653$	−9815.04	−	9815.04i	−0.588197	−	0.588197i	−0.937143	+	0.348946i	$0.886540\pi$
$654$		0			0
$655$	3452.08			0.205929
$656$		0			0
$657$	25610.4			1.52078
$658$		0			0
$659$	19820.3	+	19820.3i	1.17161	+	1.17161i	0.981826	+	0.189783i	$0.0607786\pi$
$659$	19820.3	+	19820.3i	1.17161	+	1.17161i	0.189783	+	0.981826i	$0.439221\pi$
$660$		0			0
$661$	−12939.4	+	12939.4i	−0.761397	+	0.761397i	−0.976575	−	0.215178i	$-0.930967\pi$
$661$	−12939.4	+	12939.4i	−0.761397	+	0.761397i	0.215178	+	0.976575i	$0.430967\pi$
$662$		0			0
$663$			5181.54i			0.303521i
$664$		0			0
$665$		−	2066.02i		−	0.120477i
$666$		0			0
$667$	3415.99	−	3415.99i	0.198302	−	0.198302i
$668$		0			0
$669$	6718.78	+	6718.78i	0.388285	+	0.388285i
$670$		0			0
$671$	9465.41			0.544572
$672$		0			0
$673$	−3822.26			−0.218926			−0.109463	−	0.993991i	$-0.534913\pi$
$673$	−3822.26			−0.218926			−0.109463	+	0.993991i	$0.534913\pi$
$674$		0			0
$675$	1648.57	+	1648.57i	0.0940053	+	0.0940053i
$676$		0			0
$677$	−20574.4	+	20574.4i	−1.16800	+	1.16800i	−0.185324	+	0.982677i	$0.559334\pi$
$677$	−20574.4	+	20574.4i	−1.16800	+	1.16800i	−0.982677	+	0.185324i	$0.940666\pi$
$678$		0			0
$679$			16601.6i			0.938308i
$680$		0			0
$681$		−	947.463i		−	0.0533140i
$682$		0			0
$683$	−5442.92	+	5442.92i	−0.304931	+	0.304931i	−0.842939	−	0.538009i	$-0.819177\pi$
$683$	−5442.92	+	5442.92i	−0.304931	+	0.304931i	0.538009	+	0.842939i	$0.319177\pi$
$684$		0			0
$685$	−9211.90	−	9211.90i	−0.513823	−	0.513823i
$686$		0			0
$687$	−5806.33			−0.322453
$688$		0			0
$689$	12394.7			0.685343
$690$		0			0
$691$	−7826.48	−	7826.48i	−0.430873	−	0.430873i	0.458052	−	0.888925i	$-0.348547\pi$
$691$	−7826.48	−	7826.48i	−0.430873	−	0.430873i	−0.888925	+	0.458052i	$0.848547\pi$
$692$		0			0
$693$	4100.69	−	4100.69i	0.224779	−	0.224779i
$694$		0			0
$695$		−	15121.8i		−	0.825325i
$696$		0			0
$697$			13441.2i			0.730447i
$698$		0			0
$699$	−4890.68	+	4890.68i	−0.264639	+	0.264639i
$700$		0			0
$701$	5762.25	+	5762.25i	0.310467	+	0.310467i	0.845090	−	0.534624i	$-0.179547\pi$
$701$	5762.25	+	5762.25i	0.310467	+	0.310467i	−0.534624	+	0.845090i	$0.679547\pi$
$702$		0			0
$703$	6855.19			0.367779
$704$		0			0
$705$	−1607.77			−0.0858896
$706$		0			0
$707$	−6926.49	−	6926.49i	−0.368455	−	0.368455i
$708$		0			0
$709$	16981.3	−	16981.3i	0.899502	−	0.899502i	−0.0958899	−	0.995392i	$-0.530570\pi$
$709$	16981.3	−	16981.3i	0.899502	−	0.899502i	0.995392	+	0.0958899i	$0.0305697\pi$
$710$		0			0
$711$			27276.5i			1.43874i
$712$		0			0
$713$			12409.8i			0.651826i
$714$		0			0
$715$	−1312.01	+	1312.01i	−0.0686241	+	0.0686241i
$716$		0			0
$717$	1310.06	+	1310.06i	0.0682359	+	0.0682359i
$718$		0			0
$719$	−1795.42			−0.0931262			−0.0465631	−	0.998915i	$-0.514827\pi$
$719$	−1795.42			−0.0931262			−0.0465631	+	0.998915i	$0.514827\pi$
$720$		0			0
$721$	25974.0			1.34164
$722$		0			0
$723$	1816.46	+	1816.46i	0.0934368	+	0.0934368i
$724$		0			0
$725$	1719.75	−	1719.75i	0.0880963	−	0.0880963i
$726$		0			0
$727$			15599.8i			0.795825i	0.917423	+	0.397912i	$0.130265\pi$
$727$			15599.8i			0.795825i	−0.917423	+	0.397912i	$0.869735\pi$
$728$		0			0
$729$			6345.74i			0.322397i
$730$		0			0
$731$	35633.7	−	35633.7i	1.80296	−	1.80296i
$732$		0			0
$733$	−12450.9	−	12450.9i	−0.627401	−	0.627401i	0.320013	−	0.947413i	$-0.396313\pi$
$733$	−12450.9	−	12450.9i	−0.627401	−	0.627401i	−0.947413	+	0.320013i	$0.896313\pi$
$734$		0			0
$735$	183.554			0.00921156
$736$		0			0
$737$	5054.43			0.252622
$738$		0			0
$739$	−637.719	−	637.719i	−0.0317441	−	0.0317441i	0.691057	−	0.722801i	$-0.257146\pi$
$739$	−637.719	−	637.719i	−0.0317441	−	0.0317441i	−0.722801	+	0.691057i	$0.757146\pi$
$740$		0			0
$741$	813.281	−	813.281i	0.0403193	−	0.0403193i
$742$		0			0
$743$			1952.47i			0.0964053i	0.998838	+	0.0482026i	$0.0153493\pi$
$743$			1952.47i			0.0964053i	−0.998838	+	0.0482026i	$0.984651\pi$
$744$		0			0
$745$		−	9861.12i		−	0.484944i
$746$		0			0
$747$	−18341.1	+	18341.1i	−0.898348	+	0.898348i
$748$		0			0
$749$	8789.38	+	8789.38i	0.428781	+	0.428781i
$750$		0			0
$751$	−13710.1			−0.666161			−0.333081	−	0.942898i	$-0.608088\pi$
$751$	−13710.1			−0.666161			−0.333081	+	0.942898i	$0.608088\pi$
$752$		0			0
$753$	−10511.0			−0.508687
$754$		0			0
$755$	6880.46	+	6880.46i	0.331663	+	0.331663i
$756$		0			0
$757$	−5425.87	+	5425.87i	−0.260510	+	0.260510i	−0.825261	−	0.564751i	$-0.808972\pi$
$757$	−5425.87	+	5425.87i	−0.260510	+	0.260510i	0.564751	+	0.825261i	$0.308972\pi$
$758$		0			0
$759$		−	1250.92i		−	0.0598227i
$760$		0			0
$761$		−	18568.0i		−	0.884481i	−0.896896	−	0.442241i	$-0.854184\pi$
$761$		−	18568.0i		−	0.884481i	0.896896	−	0.442241i	$-0.145816\pi$
$762$		0			0
$763$	11520.8	−	11520.8i	0.546631	−	0.546631i
$764$		0			0
$765$	8642.68	+	8642.68i	0.408467	+	0.408467i
$766$		0			0
$767$	−807.710			−0.0380244
$768$		0			0
$769$	13501.1			0.633110			0.316555	−	0.948574i	$-0.397474\pi$
$769$	13501.1			0.633110			0.316555	+	0.948574i	$0.397474\pi$
$770$		0			0
$771$	−3668.22	−	3668.22i	−0.171346	−	0.171346i
$772$		0			0
$773$	19002.7	−	19002.7i	0.884191	−	0.884191i	−0.109767	−	0.993957i	$-0.535010\pi$
$773$	19002.7	−	19002.7i	0.884191	−	0.884191i	0.993957	+	0.109767i	$0.0350103\pi$
$774$		0			0
$775$			6247.60i			0.289575i
$776$		0			0
$777$		−	9877.91i		−	0.456072i
$778$		0			0
$779$	2109.70	−	2109.70i	0.0970318	−	0.0970318i
$780$		0			0
$781$	2114.74	+	2114.74i	0.0968904	+	0.0968904i
$782$		0			0
$783$	−9072.41			−0.414076
$784$		0			0
$785$	−3641.11			−0.165550
$786$		0			0
$787$	18237.9	+	18237.9i	0.826061	+	0.826061i	0.986969	−	0.160908i	$-0.0514424\pi$
$787$	18237.9	+	18237.9i	0.826061	+	0.826061i	−0.160908	+	0.986969i	$0.551442\pi$
$788$		0			0
$789$	7255.95	−	7255.95i	0.327400	−	0.327400i
$790$		0			0
$791$		−	3852.13i		−	0.173156i
$792$		0			0
$793$			18799.6i			0.841858i
$794$		0			0
$795$	−2974.73	+	2974.73i	−0.132708	+	0.132708i
$796$		0			0
$797$	−14529.0	−	14529.0i	−0.645727	−	0.645727i	0.306230	−	0.951958i	$-0.400932\pi$
$797$	−14529.0	−	14529.0i	−0.645727	−	0.645727i	−0.951958	+	0.306230i	$0.900932\pi$
$798$		0			0
$799$	−18070.4			−0.800104
$800$		0			0
$801$	−376.081			−0.0165895
$802$		0			0
$803$	−10487.1	−	10487.1i	−0.460874	−	0.460874i
$804$		0			0
$805$	3155.75	−	3155.75i	0.138168	−	0.138168i
$806$		0			0
$807$			8812.07i			0.384386i
$808$		0			0
$809$		−	35390.4i		−	1.53802i	−0.639234	−	0.769012i	$-0.720748\pi$
$809$		−	35390.4i		−	1.53802i	0.639234	−	0.769012i	$-0.279252\pi$
$810$		0			0
$811$	−3671.23	+	3671.23i	−0.158957	+	0.158957i	−0.782104	−	0.623147i	$-0.785854\pi$
$811$	−3671.23	+	3671.23i	−0.158957	+	0.158957i	0.623147	+	0.782104i	$0.285854\pi$
$812$		0			0
$813$	−11072.9	−	11072.9i	−0.477667	−	0.477667i
$814$		0			0
$815$	8688.34			0.373422
$816$		0			0
$817$	−11186.0			−0.479006
$818$		0			0
$819$	8144.53	+	8144.53i	0.347488	+	0.347488i
$820$		0			0
$821$	32787.6	−	32787.6i	1.39378	−	1.39378i	0.577131	−	0.816652i	$-0.304172\pi$
$821$	32787.6	−	32787.6i	1.39378	−	1.39378i	0.816652	−	0.577131i	$-0.195828\pi$
$822$		0			0
$823$		−	24158.6i		−	1.02323i	−0.859216	−	0.511613i	$-0.829048\pi$
$823$		−	24158.6i		−	1.02323i	0.859216	−	0.511613i	$-0.170952\pi$
$824$		0			0
$825$		−	629.762i		−	0.0265764i
$826$		0			0
$827$	24624.9	−	24624.9i	1.03542	−	1.03542i	0.0360706	−	0.999349i	$-0.488516\pi$
$827$	24624.9	−	24624.9i	1.03542	−	1.03542i	0.999349	−	0.0360706i	$-0.0114841\pi$
$828$		0			0
$829$	−2211.20	−	2211.20i	−0.0926394	−	0.0926394i	0.659268	−	0.751908i	$-0.270866\pi$
$829$	−2211.20	−	2211.20i	−0.0926394	−	0.0926394i	−0.751908	+	0.659268i	$0.770866\pi$
$830$		0			0
$831$	2024.89			0.0845279
$832$		0			0
$833$	2063.03			0.0858102
$834$		0			0
$835$	−2077.44	−	2077.44i	−0.0860990	−	0.0860990i
$836$		0			0
$837$	16479.4	−	16479.4i	0.680540	−	0.680540i
$838$		0			0
$839$			14313.9i			0.589001i	0.955651	+	0.294501i	$0.0951533\pi$
$839$			14313.9i			0.589001i	−0.955651	+	0.294501i	$0.904847\pi$
$840$		0			0
$841$		−	14924.9i		−	0.611952i
$842$		0			0
$843$	−10529.0	+	10529.0i	−0.430174	+	0.430174i
$844$		0			0
$845$	5161.74	+	5161.74i	0.210141	+	0.210141i
$846$		0			0
$847$	20565.6			0.834289
$848$		0			0
$849$	−5706.96			−0.230698
$850$		0			0
$851$	10471.0	+	10471.0i	0.421786	+	0.421786i
$852$		0			0
$853$	21680.6	−	21680.6i	0.870257	−	0.870257i	−0.122243	−	0.992500i	$-0.539009\pi$
$853$	21680.6	−	21680.6i	0.870257	−	0.870257i	0.992500	+	0.122243i	$0.0390088\pi$
$854$		0			0
$855$		−	2713.07i		−	0.108520i
$856$		0			0
$857$		−	19741.2i		−	0.786870i	−0.919352	−	0.393435i	$-0.871287\pi$
$857$		−	19741.2i		−	0.786870i	0.919352	−	0.393435i	$-0.128713\pi$
$858$		0			0
$859$	4986.65	−	4986.65i	0.198070	−	0.198070i	−0.601102	−	0.799172i	$-0.705271\pi$
$859$	4986.65	−	4986.65i	0.198070	−	0.198070i	0.799172	+	0.601102i	$0.205271\pi$
$860$		0			0
$861$	−3039.94	−	3039.94i	−0.120326	−	0.120326i
$862$		0			0
$863$	38207.3			1.50706			0.753529	−	0.657415i	$-0.228350\pi$
$863$	38207.3			1.50706			0.753529	+	0.657415i	$0.228350\pi$
$864$		0			0
$865$	7509.88			0.295195
$866$		0			0
$867$	−7574.67	−	7574.67i	−0.296712	−	0.296712i
$868$		0			0
$869$	11169.4	−	11169.4i	0.436012	−	0.436012i
$870$		0			0
$871$			10038.8i			0.390530i
$872$		0			0
$873$			21801.0i			0.845190i
$874$		0			0
$875$	1588.73	−	1588.73i	0.0613815	−	0.0613815i
$876$		0			0
$877$	24917.7	+	24917.7i	0.959421	+	0.959421i	0.999208	−	0.0397868i	$-0.0126679\pi$
$877$	24917.7	+	24917.7i	0.959421	+	0.959421i	−0.0397868	+	0.999208i	$0.512668\pi$
$878$		0			0
$879$	14471.5			0.555302
$880$		0			0
$881$	−28327.0			−1.08327			−0.541635	−	0.840614i	$-0.682195\pi$
$881$	−28327.0			−1.08327			−0.541635	+	0.840614i	$0.682195\pi$
$882$		0			0
$883$	18768.9	+	18768.9i	0.715314	+	0.715314i	0.967642	−	0.252328i	$-0.0811961\pi$
$883$	18768.9	+	18768.9i	0.715314	+	0.715314i	−0.252328	+	0.967642i	$0.581196\pi$
$884$		0			0
$885$	193.850	−	193.850i	0.00736293	−	0.00736293i
$886$		0			0
$887$		−	26017.3i		−	0.984865i	−0.870351	−	0.492433i	$-0.836108\pi$
$887$		−	26017.3i		−	0.984865i	0.870351	−	0.492433i	$-0.163892\pi$
$888$		0			0
$889$		−	1238.62i		−	0.0467288i
$890$		0			0
$891$	4498.65	−	4498.65i	0.169147	−	0.169147i
$892$		0			0
$893$	2836.28	+	2836.28i	0.106285	+	0.106285i
$894$		0			0
$895$	13822.3			0.516232
$896$		0			0
$897$	2484.49			0.0924803
$898$		0			0
$899$	−17190.9	−	17190.9i	−0.637762	−	0.637762i
$900$		0			0
$901$	−33434.1	+	33434.1i	−1.23624	+	1.23624i
$902$		0			0
$903$			16118.3i			0.594001i
$904$		0			0
$905$			16862.2i			0.619359i
$906$		0			0
$907$	−26216.3	+	26216.3i	−0.959757	+	0.959757i	−0.999221	−	0.0394644i	$-0.987435\pi$
$907$	−26216.3	+	26216.3i	−0.959757	+	0.959757i	0.0394644	+	0.999221i	$0.487435\pi$
$908$		0			0
$909$	−9095.77	−	9095.77i	−0.331889	−	0.331889i
$910$		0			0
$911$	1507.54			0.0548265			0.0274132	−	0.999624i	$-0.491273\pi$
$911$	1507.54			0.0548265			0.0274132	+	0.999624i	$0.491273\pi$
$912$		0			0
$913$	15020.9			0.544489
$914$		0			0
$915$	−4511.90	−	4511.90i	−0.163015	−	0.163015i
$916$		0			0
$917$	−8775.06	+	8775.06i	−0.316007	+	0.316007i
$918$		0			0
$919$		−	2424.43i		−	0.0870236i	−0.999053	−	0.0435118i	$-0.986145\pi$
$919$		−	2424.43i		−	0.0870236i	0.999053	−	0.0435118i	$-0.0138546\pi$
$920$		0			0
$921$		−	11211.8i		−	0.401131i
$922$		0			0
$923$	−4200.17	+	4200.17i	−0.149784	+	0.149784i
$924$		0			0
$925$	5271.50	+	5271.50i	0.187379	+	0.187379i
$926$		0			0
$927$	34108.7			1.20850
$928$		0			0
$929$	−31265.1			−1.10417			−0.552086	−	0.833787i	$-0.686168\pi$
$929$	−31265.1			−1.10417			−0.552086	+	0.833787i	$0.686168\pi$
$930$		0			0
$931$	−323.809	−	323.809i	−0.0113989	−	0.0113989i
$932$		0			0
$933$	−6198.81	+	6198.81i	−0.217513	+	0.217513i
$934$		0			0
$935$		−	7078.13i		−	0.247572i
$936$		0			0
$937$		−	24317.7i		−	0.847839i	−0.905700	−	0.423919i	$-0.860654\pi$
$937$		−	24317.7i		−	0.847839i	0.905700	−	0.423919i	$-0.139346\pi$
$938$		0			0
$939$	−7080.97	+	7080.97i	−0.246090	+	0.246090i
$940$		0			0
$941$	−26684.6	−	26684.6i	−0.924433	−	0.924433i	0.0729055	−	0.997339i	$-0.476773\pi$
$941$	−26684.6	−	26684.6i	−0.924433	−	0.924433i	−0.997339	+	0.0729055i	$0.976773\pi$
$942$		0			0
$943$	6444.92			0.222561
$944$		0			0
$945$	−8381.24			−0.288510
$946$		0			0
$947$	12759.1	+	12759.1i	0.437819	+	0.437819i	0.891278	−	0.453458i	$-0.149810\pi$
$947$	12759.1	+	12759.1i	0.437819	+	0.437819i	−0.453458	+	0.891278i	$0.649810\pi$
$948$		0			0
$949$	20828.8	−	20828.8i	0.712468	−	0.712468i
$950$		0			0
$951$		−	1899.08i		−	0.0647547i
$952$		0			0
$953$		−	4436.11i		−	0.150787i	−0.997154	−	0.0753933i	$-0.975979\pi$
$953$		−	4436.11i		−	0.150787i	0.997154	−	0.0753933i	$-0.0240212\pi$
$954$		0			0
$955$	−11761.8	+	11761.8i	−0.398539	+	0.398539i
$956$		0			0
$957$	1732.85	+	1732.85i	0.0585320	+	0.0585320i
$958$		0			0
$959$	46832.7			1.57696
$960$		0			0
$961$	32661.1			1.09634
$962$		0			0
$963$	11542.1	+	11542.1i	0.386229	+	0.386229i
$964$		0			0
$965$	−8803.23	+	8803.23i	−0.293664	+	0.293664i
$966$		0			0
$967$			37242.9i			1.23852i	0.785185	+	0.619261i	$0.212568\pi$
$967$			37242.9i			1.23852i	−0.785185	+	0.619261i	$0.787432\pi$
$968$		0			0
$969$			4387.57i			0.145458i
$970$		0			0
$971$	−28061.0	+	28061.0i	−0.927414	+	0.927414i	−0.997538	−	0.0701242i	$-0.977660\pi$
$971$	−28061.0	+	28061.0i	−0.927414	+	0.927414i	0.0701242	+	0.997538i	$0.477660\pi$
$972$		0			0
$973$	38439.0	+	38439.0i	1.26649	+	1.26649i
$974$		0			0
$975$	1250.79			0.0410846
$976$		0			0
$977$	11806.4			0.386611			0.193306	−	0.981139i	$-0.438079\pi$
$977$	11806.4			0.386611			0.193306	+	0.981139i	$0.438079\pi$
$978$		0			0
$979$	154.000	+	154.000i	0.00502744	+	0.00502744i
$980$		0			0
$981$	15128.9	−	15128.9i	0.492383	−	0.492383i
$982$		0			0
$983$		−	28865.2i		−	0.936579i	−0.883575	−	0.468290i	$-0.844870\pi$
$983$		−	28865.2i		−	0.936579i	0.883575	−	0.468290i	$-0.155130\pi$
$984$		0			0
$985$			12646.6i			0.409091i
$986$		0			0
$987$	4086.90	−	4086.90i	0.131801	−	0.131801i
$988$		0			0
$989$	−17086.0	−	17086.0i	−0.549347	−	0.549347i
$990$		0			0
$991$	37756.7			1.21027			0.605137	−	0.796121i	$-0.293118\pi$
$991$	37756.7			1.21027			0.605137	+	0.796121i	$0.293118\pi$
$992$		0			0
$993$	6553.25			0.209427
$994$		0			0
$995$	6686.97	+	6686.97i	0.213056	+	0.213056i
$996$		0			0
$997$	11348.0	−	11348.0i	0.360478	−	0.360478i	−0.503511	−	0.863989i	$-0.667959\pi$
$997$	11348.0	−	11348.0i	0.360478	−	0.360478i	0.863989	+	0.503511i	$0.167959\pi$
$998$		0			0
$999$		−	27809.5i		−	0.880733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.4.l.b.161.10		48
4.3	odd	2		640.4.l.a.161.15		48
8.3	odd	2		320.4.l.a.81.10		48
8.5	even	2		80.4.l.a.61.7	yes	48
16.3	odd	4		320.4.l.a.241.10		48
16.5	even	4	inner	640.4.l.b.481.10		48
16.11	odd	4		640.4.l.a.481.15		48
16.13	even	4		80.4.l.a.21.7	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.4.l.a.21.7	✓	48	16.13	even	4
80.4.l.a.61.7	yes	48	8.5	even	2
320.4.l.a.81.10		48	8.3	odd	2
320.4.l.a.241.10		48	16.3	odd	4
640.4.l.a.161.15		48	4.3	odd	2
640.4.l.a.481.15		48	16.11	odd	4
640.4.l.b.161.10		48	1.1	even	1	trivial
640.4.l.b.481.10		48	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.30312 - 1.30312i) q^{3} +(-3.53553 + 3.53553i) q^{5} -17.9744i q^{7} -23.6037i q^{9} +(-9.66542 + 9.66542i) q^{11} +(-19.1969 - 19.1969i) q^{13} +9.21448 q^{15} +103.565 q^{17} +(-16.2553 - 16.2553i) q^{19} +(-23.4229 + 23.4229i) q^{21} -49.6583i q^{23} -25.0000i q^{25} +(-65.9429 + 65.9429i) q^{27} +(68.7899 + 68.7899i) q^{29} -249.904 q^{31} +25.1905 q^{33} +(63.5492 + 63.5492i) q^{35} +(-210.860 + 210.860i) q^{37} +50.0318i q^{39} +129.785i q^{41} +(344.071 - 344.071i) q^{43} +(83.4518 + 83.4518i) q^{45} -174.483 q^{47} +19.9202 q^{49} +(-134.958 - 134.958i) q^{51} +(-322.832 + 322.832i) q^{53} -68.3448i q^{55} +42.3653i q^{57} +(21.0376 - 21.0376i) q^{59} +(-489.653 - 489.653i) q^{61} -424.264 q^{63} +135.742 q^{65} +(-261.470 - 261.470i) q^{67} +(-64.7110 + 64.7110i) q^{69} -218.795i q^{71} +1085.01i q^{73} +(-32.5781 + 32.5781i) q^{75} +(173.730 + 173.730i) q^{77} -1155.60 q^{79} -465.437 q^{81} +(-777.042 - 777.042i) q^{83} +(-366.157 + 366.157i) q^{85} -179.283i q^{87} -15.9331i q^{89} +(-345.052 + 345.052i) q^{91} +(325.656 + 325.656i) q^{93} +114.942 q^{95} -923.624 q^{97} +(228.140 + 228.140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 40 q^{11} + 120 q^{15} - 24 q^{19} + 264 q^{27} - 400 q^{29} - 16 q^{37} - 808 q^{43} + 1880 q^{47} - 2352 q^{49} - 2144 q^{51} - 752 q^{53} + 2728 q^{59} + 912 q^{61} - 2520 q^{63} + 2040 q^{67}+ \cdots + 4456 q^{99}+O(q^{100}) \) 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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