LMFDB - Embedded newform 312.4.m.a.181.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [312,4,Mod(181,312)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(312, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("312.181");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 312 = 2^{3} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	312.m (of order $2$, degree $1$, 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:	$18.4085959218$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.7
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.73458 - 0.722559i) q^{2} -3.00000i q^{3} +(6.95582 + 3.95178i) q^{4} -2.18910 q^{5} +(-2.16768 + 8.20373i) q^{6} -4.02754i q^{7} +(-16.1658 - 15.8324i) q^{8} -9.00000 q^{9} +(5.98626 + 1.58175i) q^{10} +8.07699 q^{11} +(11.8554 - 20.8675i) q^{12} +(-40.2222 + 24.0660i) q^{13} +(-2.91013 + 11.0136i) q^{14} +6.56729i q^{15} +(32.7668 + 54.9758i) q^{16} +130.087 q^{17} +(24.6112 + 6.50303i) q^{18} -109.429 q^{19} +(-15.2270 - 8.65084i) q^{20} -12.0826 q^{21} +(-22.0871 - 5.83610i) q^{22} -77.1254 q^{23} +(-47.4973 + 48.4975i) q^{24} -120.208 q^{25} +(127.380 - 36.7473i) q^{26} +27.0000i q^{27} +(15.9160 - 28.0148i) q^{28} -94.2930i q^{29} +(4.74525 - 17.9588i) q^{30} +171.593i q^{31} +(-49.8802 - 174.011i) q^{32} -24.2310i q^{33} +(-355.734 - 93.9957i) q^{34} +8.81668i q^{35} +(-62.6024 - 35.5661i) q^{36} -18.4611 q^{37} +(299.241 + 79.0686i) q^{38} +(72.1979 + 120.667i) q^{39} +(35.3886 + 34.6588i) q^{40} +345.326i q^{41} +(33.0409 + 8.73040i) q^{42} +272.794i q^{43} +(56.1820 + 31.9185i) q^{44} +19.7019 q^{45} +(210.905 + 55.7276i) q^{46} -278.858i q^{47} +(164.927 - 98.3005i) q^{48} +326.779 q^{49} +(328.718 + 86.8572i) q^{50} -390.262i q^{51} +(-374.882 + 8.44902i) q^{52} +443.813i q^{53} +(19.5091 - 73.8336i) q^{54} -17.6813 q^{55} +(-63.7658 + 65.1085i) q^{56} +328.286i q^{57} +(-68.1322 + 257.851i) q^{58} +25.5699 q^{59} +(-25.9525 + 45.6809i) q^{60} +606.212i q^{61} +(123.986 - 469.234i) q^{62} +36.2479i q^{63} +(10.6677 + 511.889i) q^{64} +(88.0504 - 52.6828i) q^{65} +(-17.5083 + 66.2614i) q^{66} +583.980 q^{67} +(904.864 + 514.077i) q^{68} +231.376i q^{69} +(6.37057 - 24.1099i) q^{70} +847.652i q^{71} +(145.492 + 142.492i) q^{72} +1209.72i q^{73} +(50.4832 + 13.3392i) q^{74} +360.624i q^{75} +(-761.165 - 432.438i) q^{76} -32.5304i q^{77} +(-110.242 - 382.140i) q^{78} -1189.76 q^{79} +(-71.7298 - 120.347i) q^{80} +81.0000 q^{81} +(249.518 - 944.320i) q^{82} +932.173 q^{83} +(-84.0445 - 47.7479i) q^{84} -284.774 q^{85} +(197.109 - 745.975i) q^{86} -282.879 q^{87} +(-130.571 - 127.878i) q^{88} -227.209i q^{89} +(-53.8763 - 14.2358i) q^{90} +(96.9267 + 161.997i) q^{91} +(-536.470 - 304.783i) q^{92} +514.779 q^{93} +(-201.491 + 762.559i) q^{94} +239.550 q^{95} +(-522.034 + 149.640i) q^{96} -710.316i q^{97} +(-893.602 - 236.117i) q^{98} -72.6929 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) $ 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.73458	−	0.722559i	−0.966819	−	0.255463i
$2$	−2.73458	−	0.722559i	−0.966819	−	0.255463i
$3$		−	3.00000i		−	0.577350i
$3$		−	3.00000i		−	0.577350i
$4$	6.95582	+	3.95178i	0.869477	+	0.493973i
$5$	−2.18910			−0.195799			−0.0978994	−	0.995196i	$-0.531212\pi$
$5$	−2.18910			−0.195799			−0.0978994	+	0.995196i	$0.531212\pi$
$6$	−2.16768	+	8.20373i	−0.147492	+	0.558193i
$7$		−	4.02754i		−	0.217467i	−0.994071	−	0.108733i	$-0.965321\pi$
$7$		−	4.02754i		−	0.217467i	0.994071	−	0.108733i	$-0.0346795\pi$
$8$	−16.1658	−	15.8324i	−0.714435	−	0.699702i
$9$	−9.00000			−0.333333
$10$	5.98626	+	1.58175i	0.189302	+	0.0500194i
$11$	8.07699			0.221391			0.110696	−	0.993854i	$-0.464692\pi$
$11$	8.07699			0.221391			0.110696	+	0.993854i	$0.464692\pi$
$12$	11.8554	−	20.8675i	0.285195	−	0.501993i
$13$	−40.2222	+	24.0660i	−0.858126	+	0.513439i
$13$	−40.2222	+	24.0660i	−0.858126	+	0.513439i
$14$	−2.91013	+	11.0136i	−0.0555547	+	0.210251i
$15$			6.56729i			0.113045i
$16$	32.7668	+	54.9758i	0.511982	+	0.858996i
$17$	130.087			1.85593			0.927965	−	0.372668i	$-0.121557\pi$
$17$	130.087			1.85593			0.927965	+	0.372668i	$0.121557\pi$
$18$	24.6112	+	6.50303i	0.322273	+	0.0851543i
$19$	−109.429			−1.32130			−0.660649	−	0.750695i	$-0.729719\pi$
$19$	−109.429			−1.32130			−0.660649	+	0.750695i	$0.729719\pi$
$20$	−15.2270	−	8.65084i	−0.170243	−	0.0967193i
$21$	−12.0826			−0.125555
$22$	−22.0871	−	5.83610i	−0.214045	−	0.0565573i
$23$	−77.1254			−0.699207			−0.349603	−	0.936898i	$-0.613684\pi$
$23$	−77.1254			−0.699207			−0.349603	+	0.936898i	$0.613684\pi$
$24$	−47.4973	+	48.4975i	−0.403973	+	0.412479i
$25$	−120.208			−0.961663
$26$	127.380	−	36.7473i	0.960817	−	0.277183i
$27$			27.0000i			0.192450i
$28$	15.9160	−	28.0148i	0.107423	−	0.189082i
$29$		−	94.2930i		−	0.603785i	−0.953342	−	0.301893i	$-0.902382\pi$
$29$		−	94.2930i		−	0.603785i	0.953342	−	0.301893i	$-0.0976184\pi$
$30$	4.74525	−	17.9588i	0.0288787	−	0.109294i
$31$			171.593i			0.994162i	0.867704	+	0.497081i	$0.165595\pi$
$31$			171.593i			0.994162i	−0.867704	+	0.497081i	$0.834405\pi$
$32$	−49.8802	−	174.011i	−0.275552	−	0.961286i
$33$		−	24.2310i		−	0.127820i
$34$	−355.734	−	93.9957i	−1.79435	−	0.474121i
$35$			8.81668i			0.0425798i
$36$	−62.6024	−	35.5661i	−0.289826	−	0.164658i
$37$	−18.4611			−0.0820264			−0.0410132	−	0.999159i	$-0.513059\pi$
$37$	−18.4611			−0.0820264			−0.0410132	+	0.999159i	$0.513059\pi$
$38$	299.241	+	79.0686i	1.27745	+	0.337543i
$39$	72.1979	+	120.667i	0.296434	+	0.495439i
$40$	35.3886	+	34.6588i	0.139886	+	0.137001i
$41$			345.326i			1.31539i	0.753286	+	0.657693i	$0.228468\pi$
$41$			345.326i			1.31539i	−0.753286	+	0.657693i	$0.771532\pi$
$42$	33.0409	+	8.73040i	0.121388	+	0.0320745i
$43$			272.794i			0.967457i	0.875218	+	0.483728i	$0.160718\pi$
$43$			272.794i			0.967457i	−0.875218	+	0.483728i	$0.839282\pi$
$44$	56.1820	+	31.9185i	0.192495	+	0.109361i
$45$	19.7019			0.0652663
$46$	210.905	+	55.7276i	0.676006	+	0.178621i
$47$		−	278.858i		−	0.865439i	−0.901529	−	0.432719i	$-0.857554\pi$
$47$		−	278.858i		−	0.865439i	0.901529	−	0.432719i	$-0.142446\pi$
$48$	164.927	−	98.3005i	0.495942	−	0.295593i
$49$	326.779			0.952708
$50$	328.718	+	86.8572i	0.929754	+	0.245669i
$51$		−	390.262i		−	1.07152i
$52$	−374.882	+	8.44902i	−0.999746	+	0.0225321i
$53$			443.813i			1.15023i	0.818071	+	0.575117i	$0.195043\pi$
$53$			443.813i			1.15023i	−0.818071	+	0.575117i	$0.804957\pi$
$54$	19.5091	−	73.8336i	0.0491639	−	0.186064i
$55$	−17.6813			−0.0433481
$56$	−63.7658	+	65.1085i	−0.152162	+	0.155366i
$57$			328.286i			0.762851i
$58$	−68.1322	+	257.851i	−0.154245	+	0.583751i
$59$	25.5699			0.0564224			0.0282112	−	0.999602i	$-0.491019\pi$
$59$	25.5699			0.0564224			0.0282112	+	0.999602i	$0.491019\pi$
$60$	−25.9525	+	45.6809i	−0.0558409	+	0.0982897i
$61$			606.212i			1.27242i	0.771517	+	0.636209i	$0.219498\pi$
$61$			606.212i			1.27242i	−0.771517	+	0.636209i	$0.780502\pi$
$62$	123.986	−	469.234i	0.253972	−	0.961174i
$63$			36.2479i			0.0724889i
$64$	10.6677	+	511.889i	0.0208353	+	0.999783i
$65$	88.0504	−	52.6828i	0.168020	−	0.100531i
$66$	−17.5083	+	66.2614i	−0.0326533	+	0.123579i
$67$	583.980			1.06484			0.532421	−	0.846479i	$-0.321282\pi$
$67$	583.980			1.06484			0.532421	+	0.846479i	$0.321282\pi$
$68$	904.864	+	514.077i	1.61369	+	0.916779i
$69$			231.376i			0.403687i
$70$	6.37057	−	24.1099i	0.0108776	−	0.0411669i
$71$			847.652i			1.41687i	0.705776	+	0.708435i	$0.250598\pi$
$71$			847.652i			1.41687i	−0.705776	+	0.708435i	$0.749402\pi$
$72$	145.492	+	142.492i	0.238145	+	0.233234i
$73$			1209.72i			1.93955i	0.243995	+	0.969776i	$0.421542\pi$
$73$			1209.72i			1.93955i	−0.243995	+	0.969776i	$0.578458\pi$
$74$	50.4832	+	13.3392i	0.0793047	+	0.0209547i
$75$			360.624i			0.555216i
$76$	−761.165	−	432.438i	−1.14884	−	0.652685i
$77$		−	32.5304i		−	0.0481452i
$78$	−110.242	−	382.140i	−0.160031	−	0.554728i
$79$	−1189.76			−1.69442			−0.847208	−	0.531261i	$-0.821718\pi$
$79$	−1189.76			−1.69442			−0.847208	+	0.531261i	$0.821718\pi$
$80$	−71.7298	−	120.347i	−0.100245	−	0.168191i
$81$	81.0000			0.111111
$82$	249.518	−	944.320i	0.336032	−	1.27174i
$83$	932.173			1.23276			0.616381	−	0.787448i	$-0.288598\pi$
$83$	932.173			1.23276			0.616381	+	0.787448i	$0.288598\pi$
$84$	−84.0445	−	47.7479i	−0.109167	−	0.0620205i
$85$	−284.774			−0.363389
$86$	197.109	−	745.975i	0.247149	−	0.935355i
$87$	−282.879			−0.348596
$88$	−130.571	−	127.878i	−0.158170	−	0.154908i
$89$		−	227.209i		−	0.270608i	−0.990804	−	0.135304i	$-0.956799\pi$
$89$		−	227.209i		−	0.270608i	0.990804	−	0.135304i	$-0.0432011\pi$
$90$	−53.8763	−	14.2358i	−0.0631007	−	0.0166731i
$91$	96.9267	+	161.997i	0.111656	+	0.186614i
$92$	−536.470	−	304.783i	−0.607944	−	0.345389i
$93$	514.779			0.573980
$94$	−201.491	+	762.559i	−0.221088	+	0.836723i
$95$	239.550			0.258708
$96$	−522.034	+	149.640i	−0.554999	+	0.159090i
$97$		−	710.316i		−	0.743522i	−0.928329	−	0.371761i	$-0.878754\pi$
$97$		−	710.316i		−	0.743522i	0.928329	−	0.371761i	$-0.121246\pi$
$98$	−893.602	−	236.117i	−0.921096	−	0.243382i
$99$	−72.6929			−0.0737971
$100$	−836.144	−	475.035i	−0.836144	−	0.475035i
$101$			524.495i			0.516725i	0.966048	+	0.258363i	$0.0831829\pi$
$101$			524.495i			0.516725i	−0.966048	+	0.258363i	$0.916817\pi$
$102$	−281.987	+	1067.20i	−0.273734	+	1.03597i
$103$	−613.735			−0.587118			−0.293559	−	0.955941i	$-0.594840\pi$
$103$	−613.735			−0.587118			−0.293559	+	0.955941i	$0.594840\pi$
$104$	1031.25	+	247.770i	0.972329	+	0.233614i
$105$	26.4500			0.0245834
$106$	320.681	−	1213.64i	0.293842	−	1.11207i
$107$		−	416.106i		−	0.375948i	−0.982174	−	0.187974i	$-0.939808\pi$
$107$		−	416.106i		−	0.375948i	0.982174	−	0.187974i	$-0.0601921\pi$
$108$	−106.698	+	187.807i	−0.0950651	+	0.167331i
$109$	485.276			0.426432			0.213216	−	0.977005i	$-0.431606\pi$
$109$	485.276			0.426432			0.213216	+	0.977005i	$0.431606\pi$
$110$	48.3509	+	12.7758i	0.0419098	+	0.0110738i
$111$			55.3832i			0.0473580i
$112$	221.417	−	131.970i	0.186803	−	0.111339i
$113$	−900.530			−0.749688			−0.374844	−	0.927088i	$-0.622304\pi$
$113$	−900.530			−0.749688			−0.374844	+	0.927088i	$0.622304\pi$
$114$	237.206	−	897.723i	0.194880	−	0.737539i
$115$	168.835			0.136904
$116$	372.626	−	655.885i	0.298254	−	0.524978i
$117$	362.000	−	216.594i	0.286042	−	0.171146i
$118$	−69.9230	−	18.4758i	−0.0545503	−	0.0144138i
$119$		−	523.932i		−	0.403603i
$120$	103.976	−	106.166i	0.0790974	−	0.0807630i
$121$	−1265.76			−0.950986
$122$	438.024	−	1657.73i	0.325056	−	1.23020i
$123$	1035.98			0.759438
$124$	−678.098	+	1193.57i	−0.491089	+	0.864401i
$125$	536.784			0.384091
$126$	26.1912	−	99.1226i	0.0185182	−	0.0700837i
$127$	−253.242			−0.176942			−0.0884708	−	0.996079i	$-0.528198\pi$
$127$	−253.242			−0.176942			−0.0884708	+	0.996079i	$0.528198\pi$
$128$	340.698	−	1407.51i	0.235264	−	0.971932i
$129$	818.381			0.558561
$130$	−278.847	+	80.4435i	−0.188127	+	0.0542720i
$131$		−	1768.04i		−	1.17919i	−0.807698	−	0.589597i	$-0.799287\pi$
$131$		−	1768.04i		−	1.17919i	0.807698	−	0.589597i	$-0.200713\pi$
$132$	95.7555	−	168.546i	0.0631397	−	0.111137i
$133$			440.728i			0.287338i
$134$	−1596.94	−	421.960i	−1.02951	−	0.272028i
$135$		−	59.1056i		−	0.0376815i
$136$	−2102.97	−	2059.60i	−1.32594	−	1.29860i
$137$			2297.53i			1.43278i	0.697700	+	0.716390i	$0.254207\pi$
$137$			2297.53i			1.43278i	−0.697700	+	0.716390i	$0.745793\pi$
$138$	167.183	−	632.716i	0.103127	−	0.390292i
$139$		−	2409.47i		−	1.47028i	−0.677915	−	0.735140i	$-0.737116\pi$
$139$		−	2409.47i		−	1.47028i	0.677915	−	0.735140i	$-0.262884\pi$
$140$	−34.8416	+	61.3272i	−0.0210332	+	0.0370221i
$141$	−836.574			−0.499661
$142$	612.478	−	2317.97i	0.361958	−	1.36986i
$143$	−324.874	+	194.381i	−0.189982	+	0.113671i
$144$	−294.901	−	494.782i	−0.170661	−	0.286332i
$145$			206.417i			0.118220i
$146$	874.096	−	3308.08i	0.495484	−	1.87520i
$147$		−	980.337i		−	0.550046i
$148$	−128.412	−	72.9541i	−0.0713201	−	0.0405188i
$149$	−3443.67			−1.89340			−0.946698	−	0.322121i	$-0.895604\pi$
$149$	−3443.67			−1.89340			−0.946698	+	0.322121i	$0.895604\pi$
$150$	260.572	−	986.153i	0.141837	−	0.536794i
$151$		−	2299.02i		−	1.23902i	−0.784989	−	0.619510i	$-0.787331\pi$
$151$		−	2299.02i		−	1.23902i	0.784989	−	0.619510i	$-0.212669\pi$
$152$	1769.00	+	1732.52i	0.943981	+	0.924514i
$153$	−1170.79			−0.618643
$154$	−23.5051	+	88.9569i	−0.0122993	+	0.0465477i
$155$		−	375.634i		−	0.194656i
$156$	25.3470	+	1124.65i	0.0130089	+	0.577204i
$157$			3399.69i			1.72819i	0.503333	+	0.864093i	$0.332107\pi$
$157$			3399.69i			1.72819i	−0.503333	+	0.864093i	$0.667893\pi$
$158$	3253.50	+	859.674i	1.63819	+	0.432861i
$159$	1331.44			0.664088
$160$	109.193	+	380.928i	0.0539527	+	0.188219i
$161$			310.626i			0.152054i
$162$	−221.501	−	58.5272i	−0.107424	−	0.0283848i
$163$	356.404			0.171262			0.0856309	−	0.996327i	$-0.472709\pi$
$163$	356.404			0.171262			0.0856309	+	0.996327i	$0.472709\pi$
$164$	−1364.65	+	2402.02i	−0.649765	+	1.14370i
$165$			53.0439i			0.0250271i
$166$	−2549.10	−	673.549i	−1.19186	−	0.314925i
$167$			2820.49i			1.30692i	0.756960	+	0.653461i	$0.226684\pi$
$167$			2820.49i			1.30692i	−0.756960	+	0.653461i	$0.773316\pi$
$168$	195.326	+	191.297i	0.0897006	+	0.0878507i
$169$	1038.66	−	1935.98i	0.472762	−	0.881190i
$170$	778.736	+	205.766i	0.351331	+	0.0928324i
$171$	984.857			0.440432
$172$	−1078.02	+	1897.50i	−0.477897	+	0.841182i
$173$		−	2319.99i		−	1.01957i	−0.860303	−	0.509784i	$-0.829725\pi$
$173$		−	2319.99i		−	1.01957i	0.860303	−	0.509784i	$-0.170275\pi$
$174$	773.554	+	204.397i	0.337029	+	0.0890533i
$175$			484.142i			0.209130i
$176$	264.657	+	444.039i	0.113348	+	0.190174i
$177$		−	76.7098i		−	0.0325755i
$178$	−164.172	+	621.320i	−0.0691303	+	0.261629i
$179$		−	3439.12i		−	1.43604i	−0.696020	−	0.718022i	$-0.745048\pi$
$179$		−	3439.12i		−	1.43604i	0.696020	−	0.718022i	$-0.254952\pi$
$180$	137.043	+	77.8576i	0.0567476	+	0.0322398i
$181$			2779.16i			1.14129i	0.821197	+	0.570644i	$0.193307\pi$
$181$			2779.16i			1.14129i	−0.821197	+	0.570644i	$0.806693\pi$
$182$	−148.001	−	513.028i	−0.0602780	−	0.208946i
$183$	1818.64			0.734631
$184$	1246.80	+	1221.08i	0.499538	+	0.489236i
$185$	40.4130			0.0160607
$186$	−1407.70	−	371.958i	−0.554934	−	0.146631i
$187$	1050.71			0.410886
$188$	1101.99	−	1939.69i	0.427503	−	0.752480i
$189$	108.744			0.0418515
$190$	−655.068	−	173.089i	−0.250124	−	0.0660904i
$191$	−2194.22			−0.831249			−0.415624	−	0.909536i	$-0.636437\pi$
$191$	−2194.22			−0.831249			−0.415624	+	0.909536i	$0.636437\pi$
$192$	1535.67	−	32.0030i	0.577225	−	0.0120293i
$193$		−	1082.72i		−	0.403814i	−0.979405	−	0.201907i	$-0.935286\pi$
$193$		−	1082.72i		−	0.403814i	0.979405	−	0.201907i	$-0.0647138\pi$
$194$	−513.245	+	1942.41i	−0.189942	+	0.718851i
$195$	−158.048	−	264.151i	−0.0580414	−	0.0970065i
$196$	2273.01	+	1291.36i	0.828358	+	0.470612i
$197$	345.276			0.124873			0.0624363	−	0.998049i	$-0.480113\pi$
$197$	345.276			0.124873			0.0624363	+	0.998049i	$0.480113\pi$
$198$	198.784	+	52.5249i	0.0713484	+	0.0188524i
$199$	−4047.98			−1.44198			−0.720990	−	0.692946i	$-0.756313\pi$
$199$	−4047.98			−1.44198			−0.720990	+	0.692946i	$0.756313\pi$
$200$	1943.26	+	1903.18i	0.687046	+	0.672877i
$201$		−	1751.94i		−	0.614787i
$202$	378.979	−	1434.27i	0.132004	−	0.499579i
$203$	−379.769			−0.131303
$204$	1542.23	−	2714.59i	0.529303	−	0.931664i
$205$		−	755.952i		−	0.257551i
$206$	1678.31	+	443.460i	0.567636	+	0.149987i
$207$	694.128			0.233069
$208$	−2641.00	−	1422.68i	−0.880387	−	0.474256i
$209$	−883.853			−0.292523
$210$	−72.3297	−	19.1117i	−0.0237677	−	0.00628016i
$211$			2356.06i			0.768712i	0.923185	+	0.384356i	$0.125576\pi$
$211$			2356.06i			0.768712i	−0.923185	+	0.384356i	$0.874424\pi$
$212$	−1753.85	+	3087.08i	−0.568184	+	1.00010i
$213$	2542.95			0.818030
$214$	−300.661	+	1137.87i	−0.0960409	+	0.363474i
$215$		−	597.172i		−	0.189427i
$216$	427.476	−	436.477i	0.134658	−	0.137493i
$217$	691.098			0.216197
$218$	−1327.03	−	350.641i	−0.412282	−	0.108937i
$219$	3629.17			1.11980
$220$	−122.988	−	69.8727i	−0.0376902	−	0.0214128i
$221$	−5232.40	+	3130.68i	−1.59262	+	0.952906i
$222$	40.0176	−	151.449i	0.0120982	−	0.0457866i
$223$		−	529.135i		−	0.158895i	−0.996839	−	0.0794473i	$-0.974684\pi$
$223$		−	529.135i		−	0.158895i	0.996839	−	0.0794473i	$-0.0253155\pi$
$224$	−700.838	+	200.894i	−0.209048	+	0.0599233i
$225$	1081.87			0.320554
$226$	2462.57	+	650.686i	0.724813	+	0.191518i
$227$	−2406.64			−0.703676			−0.351838	−	0.936061i	$-0.614443\pi$
$227$	−2406.64			−0.703676			−0.351838	+	0.936061i	$0.614443\pi$
$228$	−1297.31	+	2283.50i	−0.376828	+	0.663282i
$229$	−3225.80			−0.930859			−0.465429	−	0.885085i	$-0.654100\pi$
$229$	−3225.80			−0.930859			−0.465429	+	0.885085i	$0.654100\pi$
$230$	−461.692	−	121.993i	−0.132361	−	0.0349739i
$231$	−97.5912			−0.0277967
$232$	−1492.89	+	1524.32i	−0.422470	+	0.431365i
$233$	2607.36			0.733106			0.366553	−	0.930397i	$-0.380538\pi$
$233$	2607.36			0.733106			0.366553	+	0.930397i	$0.380538\pi$
$234$	−1146.42	+	330.726i	−0.320272	+	0.0923942i
$235$			610.448i			0.169452i
$236$	177.860	+	101.047i	0.0490580	+	0.0278711i
$237$			3569.29i			0.978272i
$238$	−378.572	+	1432.73i	−0.103106	+	0.390211i
$239$			2233.80i			0.604571i	0.953217	+	0.302285i	$0.0977496\pi$
$239$			2233.80i			0.604571i	−0.953217	+	0.302285i	$0.902250\pi$
$240$	−361.042	+	215.189i	−0.0971049	+	0.0578767i
$241$			3747.28i			1.00159i	0.865565	+	0.500796i	$0.166959\pi$
$241$			3747.28i			1.00159i	−0.865565	+	0.500796i	$0.833041\pi$
$242$	3461.32	+	914.587i	0.919431	+	0.242942i
$243$		−	243.000i		−	0.0641500i
$244$	−2395.62	+	4216.70i	−0.628540	+	1.10634i
$245$	−715.351			−0.186539
$246$	−2832.96	−	748.554i	−0.734239	−	0.194008i
$247$	4401.46	−	2633.51i	1.13384	−	0.678405i
$248$	2716.74	−	2773.94i	0.695617	−	0.710264i
$249$		−	2796.52i		−	0.711735i
$250$	−1467.88	−	387.858i	−0.371347	−	0.0981211i
$251$		−	5937.12i		−	1.49302i	−0.665375	−	0.746510i	$-0.731728\pi$
$251$		−	5937.12i		−	1.49302i	0.665375	−	0.746510i	$-0.268272\pi$
$252$	−143.244	+	252.134i	−0.0358076	+	0.0630275i
$253$	−622.941			−0.154798
$254$	692.509	+	182.982i	0.171070	+	0.0452020i
$255$			854.322i			0.209803i
$256$	−1948.67	+	3602.76i	−0.475750	+	0.879581i
$257$	−3657.10			−0.887639			−0.443820	−	0.896116i	$-0.646377\pi$
$257$	−3657.10			−0.887639			−0.443820	+	0.896116i	$0.646377\pi$
$258$	−2237.93	−	591.328i	−0.540028	−	0.142692i
$259$			74.3526i			0.0178380i
$260$	820.654	−	18.4957i	0.195749	−	0.00441175i
$261$			848.637i			0.201262i
$262$	−1277.51	+	4834.84i	−0.301240	+	1.14007i
$263$	4997.53			1.17171			0.585857	−	0.810414i	$-0.300758\pi$
$263$	4997.53			1.17171			0.585857	+	0.810414i	$0.300758\pi$
$264$	−383.635	+	391.713i	−0.0894360	+	0.0913193i
$265$		−	971.550i		−	0.225214i
$266$	318.452	−	1205.21i	0.0734043	−	0.277804i
$267$	−681.627			−0.156236
$268$	4062.06	+	2307.76i	0.925857	+	0.526004i
$269$			1428.50i			0.323782i	0.986809	+	0.161891i	$0.0517592\pi$
$269$			1428.50i			0.323782i	−0.986809	+	0.161891i	$0.948241\pi$
$270$	−42.7073	+	161.629i	−0.00962623	+	0.0364312i
$271$		−	6676.48i		−	1.49656i	−0.663384	−	0.748279i	$-0.730880\pi$
$271$		−	6676.48i		−	1.49656i	0.663384	−	0.748279i	$-0.269120\pi$
$272$	4262.55	+	7151.65i	0.950202	+	1.59424i
$273$	485.990	−	290.780i	0.107742	−	0.0644645i
$274$	1660.10	−	6282.76i	0.366022	−	1.38524i
$275$	−970.917			−0.212904
$276$	−914.348	+	1609.41i	−0.199411	+	0.350997i
$277$		−	26.6863i		−	0.00578854i	−0.999996	−	0.00289427i	$-0.999079\pi$
$277$		−	26.6863i		−	0.00578854i	0.999996	−	0.00289427i	$-0.000921275\pi$
$278$	−1740.99	+	6588.89i	−0.375602	+	1.42149i
$279$		−	1544.34i		−	0.331387i
$280$	139.590	−	142.529i	0.0297931	−	0.0304205i
$281$		−	795.130i		−	0.168802i	−0.996432	−	0.0844012i	$-0.973102\pi$
$281$		−	795.130i		−	0.168802i	0.996432	−	0.0844012i	$-0.0268977\pi$
$282$	2287.68	+	604.474i	0.483082	+	0.127645i
$283$			549.921i			0.115510i	0.998331	+	0.0577551i	$0.0183943\pi$
$283$			549.921i			0.115510i	−0.998331	+	0.0577551i	$0.981606\pi$
$284$	−3349.74	+	5896.11i	−0.699895	+	1.23194i
$285$		−	718.650i		−	0.149365i
$286$	1028.85	−	296.808i	0.212716	−	0.0613658i
$287$	1390.81			0.286053
$288$	448.921	+	1566.10i	0.0918505	+	0.320429i
$289$	12009.7			2.44448
$290$	149.148	−	564.462i	0.0302010	−	0.114298i
$291$	−2130.95			−0.429273
$292$	−4780.56	+	8414.61i	−0.958087	+	1.68640i
$293$	−972.414			−0.193888			−0.0969438	−	0.995290i	$-0.530907\pi$
$293$	−972.414			−0.193888			−0.0969438	+	0.995290i	$0.530907\pi$
$294$	−708.351	+	2680.81i	−0.140516	+	0.531795i
$295$	−55.9751			−0.0110474
$296$	298.438	+	292.283i	0.0586026	+	0.0573940i
$297$			218.079i			0.0426068i
$298$	9416.97	+	2488.25i	1.83057	+	0.483693i
$299$	3102.16	−	1856.10i	0.600008	−	0.359000i
$300$	−1425.11	+	2508.43i	−0.274262	+	0.482748i
$301$	1098.69			0.210390
$302$	−1661.18	+	6286.86i	−0.316524	+	1.19791i
$303$	1573.49			0.298331
$304$	−3585.63	−	6015.92i	−0.676480	−	1.13499i
$305$		−	1327.06i		−	0.249138i
$306$	3201.60	+	845.961i	0.598116	+	0.158040i
$307$	9425.92			1.75233			0.876166	−	0.482010i	$-0.160093\pi$
$307$	9425.92			1.75233			0.876166	+	0.482010i	$0.160093\pi$
$308$	128.553	−	226.276i	0.0237824	−	0.0418612i
$309$			1841.21i			0.338973i
$310$	−271.417	+	1027.20i	−0.0497273	+	0.188197i
$311$	287.018			0.0523321			0.0261661	−	0.999658i	$-0.491670\pi$
$311$	287.018			0.0523321			0.0261661	+	0.999658i	$0.491670\pi$
$312$	743.309	−	3093.75i	0.134877	−	0.561375i
$313$	6365.91			1.14959			0.574796	−	0.818296i	$-0.305081\pi$
$313$	6365.91			1.14959			0.574796	+	0.818296i	$0.305081\pi$
$314$	2456.48	−	9296.72i	0.441487	−	1.67084i
$315$		−	79.3501i		−	0.0141933i
$316$	−8275.78	−	4701.69i	−1.47326	−	0.836996i
$317$	−7432.89			−1.31695			−0.658474	−	0.752603i	$-0.728798\pi$
$317$	−7432.89			−1.31695			−0.658474	+	0.752603i	$0.728798\pi$
$318$	−3640.92	−	962.042i	−0.642052	−	0.169650i
$319$		−	761.603i		−	0.133673i
$320$	−23.3526	−	1120.57i	−0.00407953	−	0.195756i
$321$	−1248.32			−0.217054
$322$	224.445	−	849.430i	0.0388442	−	0.147009i
$323$	−14235.3			−2.45223
$324$	563.421	+	320.094i	0.0966086	+	0.0548859i
$325$	4835.03	−	2892.92i	0.825228	−	0.493755i
$326$	−974.613	−	257.522i	−0.165579	−	0.0437511i
$327$		−	1455.83i		−	0.246200i
$328$	5467.35	−	5582.47i	0.920378	−	0.939758i
$329$	−1123.11			−0.188204
$330$	38.3274	−	145.053i	0.00639349	−	0.0241966i
$331$	−2577.56			−0.428023			−0.214012	−	0.976831i	$-0.568653\pi$
$331$	−2577.56			−0.428023			−0.214012	+	0.976831i	$0.568653\pi$
$332$	6484.02	+	3683.74i	1.07186	+	0.608951i
$333$	166.149			0.0273421
$334$	2037.97	−	7712.85i	0.333870	−	1.26356i
$335$	−1278.39			−0.208495
$336$	−395.909	−	664.252i	−0.0642816	−	0.107851i
$337$	−3146.09			−0.508542			−0.254271	−	0.967133i	$-0.581836\pi$
$337$	−3146.09			−0.508542			−0.254271	+	0.967133i	$0.581836\pi$
$338$	−4239.14	+	4543.58i	−0.682186	+	0.731178i
$339$			2701.59i			0.432833i
$340$	−1980.84	−	1125.36i	−0.315958	−	0.179504i
$341$			1385.95i			0.220099i
$342$	−2693.17	−	711.617i	−0.425818	−	0.112514i
$343$		−	2697.56i		−	0.424649i
$344$	4318.99	−	4409.93i	0.676931	−	0.691185i
$345$		−	506.505i		−	0.0790415i
$346$	−1676.33	+	6344.18i	−0.260462	+	0.985737i
$347$			4209.15i			0.651179i	0.945511	+	0.325590i	$0.105563\pi$
$347$			4209.15i			0.651179i	−0.945511	+	0.325590i	$0.894437\pi$
$348$	−1967.66	−	1117.88i	−0.303096	−	0.172197i
$349$	−2651.37			−0.406661			−0.203330	−	0.979110i	$-0.565177\pi$
$349$	−2651.37			−0.406661			−0.203330	+	0.979110i	$0.565177\pi$
$350$	349.821	−	1323.92i	0.0534249	−	0.202191i
$351$	−649.781	−	1086.00i	−0.0988113	−	0.165146i
$352$	−402.881	−	1405.49i	−0.0610047	−	0.212820i
$353$		−	2792.23i		−	0.421006i	−0.977593	−	0.210503i	$-0.932490\pi$
$353$		−	2792.23i		−	0.421006i	0.977593	−	0.210503i	$-0.0675102\pi$
$354$	−55.4273	+	209.769i	−0.00832184	+	0.0314946i
$355$		−	1855.59i		−	0.277421i
$356$	897.880	−	1580.42i	0.133673	−	0.235287i
$357$	−1571.80			−0.233020
$358$	−2484.97	+	9404.54i	−0.366856	+	1.38839i
$359$			9136.75i			1.34323i	0.740901	+	0.671615i	$0.234399\pi$
$359$			9136.75i			1.34323i	−0.740901	+	0.671615i	$0.765601\pi$
$360$	−318.497	−	311.929i	−0.0466285	−	0.0456669i
$361$	5115.62			0.745826
$362$	2008.11	−	7599.82i	0.291557	−	1.10342i
$363$			3797.29i			0.549052i
$364$	34.0288	+	1509.85i	0.00489998	+	0.217412i
$365$		−	2648.20i		−	0.379762i
$366$	−4973.20	−	1314.07i	−0.710255	−	0.187671i
$367$	−1655.13			−0.235414			−0.117707	−	0.993048i	$-0.537554\pi$
$367$	−1655.13			−0.235414			−0.117707	+	0.993048i	$0.537554\pi$
$368$	−2527.15	−	4240.03i	−0.357981	−	0.600616i
$369$		−	3107.93i		−	0.438462i
$370$	−110.513	−	29.2008i	−0.0155278	−	0.00410291i
$371$	1787.47			0.250138
$372$	3580.71	+	2034.30i	0.499062	+	0.283530i
$373$		−	7639.53i		−	1.06048i	−0.847847	−	0.530241i	$-0.822101\pi$
$373$		−	7639.53i		−	1.06048i	0.847847	−	0.530241i	$-0.177899\pi$
$374$	−2873.26	−	759.202i	−0.397253	−	0.104966i
$375$		−	1610.35i		−	0.221755i
$376$	−4415.00	+	4507.97i	−0.605549	+	0.618300i
$377$	2269.25	+	3792.68i	0.310007	+	0.518124i
$378$	−297.368	−	78.5736i	−0.0404628	−	0.0106915i
$379$	−9088.73			−1.23181			−0.615906	−	0.787819i	$-0.711210\pi$
$379$	−9088.73			−1.23181			−0.615906	+	0.787819i	$0.711210\pi$
$380$	1666.27	+	946.649i	0.224941	+	0.127795i
$381$			759.726i			0.102157i
$382$	6000.27	+	1585.46i	0.803667	+	0.212353i
$383$		−	14687.1i		−	1.95946i	−0.200320	−	0.979731i	$-0.564198\pi$
$383$		−	14687.1i		−	1.95946i	0.200320	−	0.979731i	$-0.435802\pi$
$384$	−4222.52	−	1022.09i	−0.561145	−	0.135830i
$385$			71.2122i			0.00942678i
$386$	−782.330	+	2960.79i	−0.103159	+	0.390415i
$387$		−	2455.14i		−	0.322486i
$388$	2807.01	−	4940.83i	0.367280	−	0.646475i
$389$		−	5135.82i		−	0.669400i	−0.942325	−	0.334700i	$-0.891365\pi$
$389$		−	5135.82i		−	0.669400i	0.942325	−	0.334700i	$-0.108635\pi$
$390$	241.331	+	836.541i	0.0313340	+	0.108615i
$391$	−10033.0			−1.29768
$392$	−5282.65	−	5173.71i	−0.680648	−	0.666611i
$393$	−5304.12			−0.680808
$394$	−944.184	−	249.482i	−0.120729	−	0.0319004i
$395$	2604.51			0.331765
$396$	−505.638	−	287.266i	−0.0641649	−	0.0364537i
$397$	4691.05			0.593041			0.296520	−	0.955026i	$-0.404174\pi$
$397$	4691.05			0.593041			0.296520	+	0.955026i	$0.404174\pi$
$398$	11069.5	+	2924.91i	1.39413	+	0.368373i
$399$	1322.18			0.165895
$400$	−3938.83	−	6608.52i	−0.492354	−	0.826065i
$401$		−	6989.97i		−	0.870479i	−0.900315	−	0.435240i	$-0.856664\pi$
$401$		−	6989.97i		−	0.870479i	0.900315	−	0.435240i	$-0.143336\pi$
$402$	−1265.88	+	4790.81i	−0.157055	+	0.594388i
$403$	−4129.55	−	6901.85i	−0.510441	−	0.853116i
$404$	−2072.69	+	3648.29i	−0.255248	+	0.449281i
$405$	−177.317			−0.0217554
$406$	1038.51	+	274.405i	0.126946	+	0.0335431i
$407$	−149.110			−0.0181599
$408$	−6178.80	+	6308.91i	−0.749745	+	0.765533i
$409$			8687.87i			1.05034i	0.850998	+	0.525168i	$0.175998\pi$
$409$			8687.87i			1.05034i	−0.850998	+	0.525168i	$0.824002\pi$
$410$	−546.219	+	2067.21i	−0.0657948	+	0.249005i
$411$	6892.58			0.827216
$412$	−4269.03	−	2425.35i	−0.510485	−	0.290020i
$413$		−	102.984i		−	0.0122700i
$414$	−1898.15	−	501.548i	−0.225335	−	0.0595405i
$415$	−2040.62			−0.241373
$416$	6194.05	+	5798.71i	0.730020	+	0.683426i
$417$	−7228.42			−0.848867
$418$	2416.96	+	638.636i	0.282817	+	0.0747289i
$419$			1379.30i			0.160819i	0.996762	+	0.0804094i	$0.0256228\pi$
$419$			1379.30i			0.160819i	−0.996762	+	0.0804094i	$0.974377\pi$
$420$	183.982	+	104.525i	0.0213747	+	0.0121436i
$421$	12625.1			1.46154			0.730769	−	0.682625i	$-0.239162\pi$
$421$	12625.1			1.46154			0.730769	+	0.682625i	$0.239162\pi$
$422$	1702.39	−	6442.84i	0.196377	−	0.743205i
$423$			2509.72i			0.288480i
$424$	7026.64	−	7174.60i	0.804820	−	0.821767i
$425$	−15637.5			−1.78478
$426$	−6953.90	−	1837.43i	−0.790887	−	0.208976i
$427$	2441.54			0.276709
$428$	1644.36	−	2894.36i	0.185708	−	0.326878i
$429$	583.142	+	974.623i	0.0656279	+	0.109686i
$430$	−431.492	+	1633.01i	−0.0483916	+	0.183142i
$431$		−	849.996i		−	0.0949951i	−0.998871	−	0.0474975i	$-0.984875\pi$
$431$		−	849.996i		−	0.0949951i	0.998871	−	0.0474975i	$-0.0151246\pi$
$432$	−1484.35	+	884.704i	−0.165314	+	0.0985309i
$433$	9796.64			1.08729			0.543645	−	0.839315i	$-0.317044\pi$
$433$	9796.64			1.08729			0.543645	+	0.839315i	$0.317044\pi$
$434$	−1889.86	−	499.359i	−0.209023	−	0.0552304i
$435$	619.250			0.0682546
$436$	3375.49	+	1917.71i	0.370773	+	0.210646i
$437$	8439.72			0.923860
$438$	−9924.24	−	2622.29i	−1.08265	−	0.286068i
$439$	−8458.42			−0.919586			−0.459793	−	0.888026i	$-0.652076\pi$
$439$	−8458.42			−0.919586			−0.459793	+	0.888026i	$0.652076\pi$
$440$	285.833	+	279.938i	0.0309694	+	0.0303308i
$441$	−2941.01			−0.317569
$442$	16570.5	−	4780.36i	1.78321	−	0.514431i
$443$			7815.21i			0.838176i	0.907946	+	0.419088i	$0.137650\pi$
$443$			7815.21i			0.838176i	−0.907946	+	0.419088i	$0.862350\pi$
$444$	−218.862	+	385.235i	−0.0233936	+	0.0411767i
$445$			497.383i			0.0529847i
$446$	−382.331	+	1446.96i	−0.0405917	+	0.153622i
$447$			10331.0i			1.09315i
$448$	2061.65	−	42.9645i	0.217420	−	0.00453099i
$449$		−	1877.83i		−	0.197373i	−0.995119	−	0.0986864i	$-0.968536\pi$
$449$		−	1877.83i		−	0.197373i	0.995119	−	0.0986864i	$-0.0314641\pi$
$450$	−2958.46	−	781.715i	−0.309918	−	0.0818898i
$451$			2789.19i			0.291215i
$452$	−6263.93	−	3558.70i	−0.651837	−	0.370326i
$453$	−6897.07			−0.715348
$454$	6581.15	+	1738.94i	0.680327	+	0.179763i
$455$	−212.182	−	354.627i	−0.0218621	−	0.0365388i
$456$	5197.57	−	5307.01i	0.533768	−	0.545008i
$457$			13143.5i			1.34536i	0.739935	+	0.672679i	$0.234856\pi$
$457$			13143.5i			1.34536i	−0.739935	+	0.672679i	$0.765144\pi$
$458$	8821.19	+	2330.83i	0.899972	+	0.237800i
$459$			3512.36i			0.357174i
$460$	1174.39	+	667.199i	0.119035	+	0.0676268i
$461$	−1158.28			−0.117021			−0.0585105	−	0.998287i	$-0.518635\pi$
$461$	−1158.28			−0.117021			−0.0585105	+	0.998287i	$0.518635\pi$
$462$	266.871	+	70.5153i	0.0268743	+	0.00710102i
$463$			15029.1i			1.50856i	0.656555	+	0.754278i	$0.272013\pi$
$463$			15029.1i			1.50856i	−0.656555	+	0.754278i	$0.727987\pi$
$464$	5183.83	−	3089.68i	0.518649	−	0.309127i
$465$	−1126.90			−0.112385
$466$	−7130.02	−	1883.97i	−0.708781	−	0.187281i
$467$		−	8548.28i		−	0.847039i	−0.905887	−	0.423519i	$-0.860795\pi$
$467$		−	8548.28i		−	0.847039i	0.905887	−	0.423519i	$-0.139205\pi$
$468$	3373.94	−	76.0411i	0.333249	−	0.00751069i
$469$		−	2352.00i		−	0.231568i
$470$	441.084	−	1669.32i	0.0432887	−	0.163829i
$471$	10199.1			0.997768
$472$	−413.359	−	404.835i	−0.0403102	−	0.0394789i
$473$			2203.35i			0.214186i
$474$	2579.02	−	9760.50i	0.249912	−	0.945812i
$475$	13154.2			1.27064
$476$	2070.47	−	3644.38i	0.199369	−	0.350924i
$477$		−	3994.31i		−	0.383411i
$478$	1614.05	−	6108.49i	0.154445	−	0.584510i
$479$			545.299i			0.0520153i	0.999662	+	0.0260077i	$0.00827943\pi$
$479$			545.299i			0.0520153i	−0.999662	+	0.0260077i	$0.991721\pi$
$480$	1142.78	−	327.578i	0.108668	−	0.0311496i
$481$	742.545	−	444.283i	0.0703890	−	0.0421155i
$482$	2707.63	−	10247.2i	0.255870	−	0.968358i
$483$	931.877			0.0877886
$484$	−8804.41	−	5002.02i	−0.826861	−	0.469761i
$485$			1554.95i			0.145581i
$486$	−175.582	+	664.502i	−0.0163880	+	0.0620215i
$487$		−	7160.39i		−	0.666260i	−0.942881	−	0.333130i	$-0.891895\pi$
$487$		−	7160.39i		−	0.666260i	0.942881	−	0.333130i	$-0.108105\pi$
$488$	9597.82	−	9799.92i	0.890313	−	0.909060i
$489$		−	1069.21i		−	0.0988781i
$490$	1956.18	+	516.883i	0.180350	+	0.0476539i
$491$			9108.23i			0.837166i	0.908178	+	0.418583i	$0.137473\pi$
$491$			9108.23i			0.837166i	−0.908178	+	0.418583i	$0.862527\pi$
$492$	7206.07	+	4093.96i	0.660314	+	0.375142i
$493$		−	12266.3i		−	1.12058i
$494$	−13939.0	+	4021.21i	−1.26952	+	0.366241i
$495$	159.132			0.0144494
$496$	−9433.46	+	5622.56i	−0.853981	+	0.508992i
$497$	3413.95			0.308122
$498$	−2020.65	+	7647.29i	−0.181822	+	0.688119i
$499$	−9728.13			−0.872727			−0.436364	−	0.899770i	$-0.643734\pi$
$499$	−9728.13			−0.872727			−0.436364	+	0.899770i	$0.643734\pi$
$500$	3733.77	+	2121.25i	0.333959	+	0.189731i
$501$	8461.47			0.754552
$502$	−4289.92	+	16235.5i	−0.381411	+	1.44348i
$503$	−3985.42			−0.353282			−0.176641	−	0.984275i	$-0.556523\pi$
$503$	−3985.42			−0.353282			−0.176641	+	0.984275i	$0.556523\pi$
$504$	573.892	−	585.977i	0.0507206	−	0.0517886i
$505$		−	1148.17i		−	0.101174i
$506$	1703.48	+	450.111i	0.149662	+	0.0395452i
$507$	−5807.93	−	3115.97i	−0.508756	−	0.272949i
$508$	−1761.50	−	1000.76i	−0.153847	−	0.0874044i
$509$	5335.24			0.464598			0.232299	−	0.972644i	$-0.425375\pi$
$509$	5335.24			0.464598			0.232299	+	0.972644i	$0.425375\pi$
$510$	617.297	−	2336.21i	0.0535968	−	0.202841i
$511$	4872.21			0.421788
$512$	7932.00	−	8444.00i	0.684664	−	0.728859i
$513$		−	2954.57i		−	0.254284i
$514$	10000.6	+	2642.47i	0.858187	+	0.226759i
$515$	1343.53			0.114957
$516$	5692.51	+	3234.06i	0.485656	+	0.275914i
$517$		−	2252.33i		−	0.191601i
$518$	53.7241	−	203.323i	0.00455696	−	0.0172461i
$519$	−6959.96			−0.588648
$520$	−2257.50	−	542.392i	−0.190381	−	0.0457413i
$521$	−12965.4			−1.09026			−0.545128	−	0.838353i	$-0.683519\pi$
$521$	−12965.4			−1.09026			−0.545128	+	0.838353i	$0.683519\pi$
$522$	613.190	−	2320.66i	0.0514149	−	0.194584i
$523$			14908.4i			1.24646i	0.782040	+	0.623228i	$0.214179\pi$
$523$			14908.4i			1.24646i	−0.782040	+	0.623228i	$0.785821\pi$
$524$	6986.91	−	12298.2i	0.582490	−	1.02528i
$525$	1452.43			0.120741
$526$	−13666.1	−	3611.01i	−1.13284	−	0.299330i
$527$			22322.1i			1.84509i
$528$	1332.12	−	793.971i	0.109797	−	0.0654416i
$529$	−6218.68			−0.511110
$530$	−702.001	+	2656.78i	−0.0575339	+	0.217742i
$531$	−230.129			−0.0188075
$532$	−1741.66	+	3065.63i	−0.141937	+	0.249834i
$533$	−8310.60	−	13889.8i	−0.675370	−	1.12877i
$534$	1863.96	+	492.515i	0.151051	+	0.0399124i
$535$			910.896i			0.0736102i
$536$	−9440.51	−	9245.82i	−0.760761	−	0.745072i
$537$	−10317.4			−0.829101
$538$	1032.18	−	3906.35i	0.0827142	−	0.313038i
$539$	2639.39			0.210921
$540$	233.573	−	411.128i	0.0186136	−	0.0327632i
$541$	9863.25			0.783834			0.391917	−	0.920001i	$-0.371812\pi$
$541$	9863.25			0.783834			0.391917	+	0.920001i	$0.371812\pi$
$542$	−4824.15	+	18257.3i	−0.382315	+	1.44690i
$543$	8337.48			0.658923
$544$	−6488.78	−	22636.7i	−0.511404	−	1.78408i
$545$	−1062.32			−0.0834948
$546$	−1539.08	+	444.004i	−0.120635	+	0.0348015i
$547$			19142.7i			1.49631i	0.663525	+	0.748154i	$0.269060\pi$
$547$			19142.7i			1.49631i	−0.663525	+	0.748154i	$0.730940\pi$
$548$	−9079.32	+	15981.2i	−0.707754	+	1.24577i
$549$		−	5455.91i		−	0.424139i
$550$	2655.05	+	701.544i	0.205839	+	0.0543890i
$551$			10318.4i			0.797780i
$552$	3663.25	−	3740.39i	0.282461	−	0.288408i
$553$			4791.82i			0.368479i
$554$	−19.2824	+	72.9757i	−0.00147876	+	0.00559647i
$555$		−	121.239i		−	0.00927264i
$556$	9521.72	−	16759.9i	0.726278	−	1.27838i
$557$	21532.3			1.63797			0.818987	−	0.573812i	$-0.194536\pi$
$557$	21532.3			1.63797			0.818987	+	0.573812i	$0.194536\pi$
$558$	−1115.87	+	4223.11i	−0.0846572	+	0.320391i
$559$	−6565.05	−	10972.4i	−0.496730	−	0.830200i
$560$	−484.704	+	288.895i	−0.0365759	+	0.0218000i
$561$		−	3152.14i		−	0.237225i
$562$	−574.528	+	2174.34i	−0.0431228	+	0.163201i
$563$			3177.08i			0.237830i	0.992904	+	0.118915i	$0.0379416\pi$
$563$			3177.08i			0.237830i	−0.992904	+	0.118915i	$0.962058\pi$
$564$	−5819.06	−	3305.96i	−0.434444	−	0.246819i
$565$	1971.35			0.146788
$566$	397.350	−	1503.80i	0.0295086	−	0.111678i
$567$		−	326.231i		−	0.0241630i
$568$	13420.4	−	13703.0i	0.991386	−	1.01226i
$569$	−7839.52			−0.577592			−0.288796	−	0.957391i	$-0.593255\pi$
$569$	−7839.52			−0.577592			−0.288796	+	0.957391i	$0.593255\pi$
$570$	−519.267	+	1965.20i	−0.0381573	+	0.144409i
$571$			7143.10i			0.523519i	0.965133	+	0.261760i	$0.0843027\pi$
$571$			7143.10i			0.523519i	−0.965133	+	0.261760i	$0.915697\pi$
$572$	−3027.92	+	68.2426i	−0.221335	+	0.00498840i
$573$			6582.67i			0.479922i
$574$	−3803.29	−	1004.94i	−0.276561	−	0.0730759i
$575$	9271.08			0.672401
$576$	−96.0091	−	4607.00i	−0.00694510	−	0.333261i
$577$		−	6948.29i		−	0.501319i	−0.968075	−	0.250659i	$-0.919353\pi$
$577$		−	6948.29i		−	0.501319i	0.968075	−	0.250659i	$-0.0806474\pi$
$578$	−32841.5	−	8677.72i	−2.36337	−	0.624473i
$579$	−3248.17			−0.233142
$580$	−815.714	+	1435.80i	−0.0583977	+	0.102790i
$581$		−	3754.36i		−	0.268085i
$582$	5827.24	+	1539.73i	0.415029	+	0.109663i
$583$			3584.67i			0.254651i
$584$	19152.9	−	19556.2i	1.35711	−	1.38568i
$585$	−792.454	+	474.145i	−0.0560067	+	0.0335102i
$586$	2659.14	+	702.626i	0.187454	+	0.0495311i
$587$	−17711.1			−1.24534			−0.622672	−	0.782483i	$-0.713953\pi$
$587$	−17711.1			−1.24534			−0.622672	+	0.782483i	$0.713953\pi$
$588$	3874.08	−	6819.04i	0.271708	−	0.478253i
$589$		−	18777.2i		−	1.31358i
$590$	153.068	+	40.4453i	0.0106809	+	0.00282221i
$591$		−	1035.83i		−	0.0720953i
$592$	−604.910	−	1014.91i	−0.0419960	−	0.0704604i
$593$			9951.18i			0.689117i	0.938765	+	0.344558i	$0.111971\pi$
$593$			9951.18i			0.689117i	−0.938765	+	0.344558i	$0.888029\pi$
$594$	157.575	−	596.353i	0.0108844	−	0.0411930i
$595$			1146.94i			0.0790250i
$596$	−23953.5	−	13608.6i	−1.64627	−	0.935287i
$597$			12144.0i			0.832528i
$598$	−9824.22	+	2834.15i	−0.671810	+	0.193808i
$599$	11352.6			0.774379			0.387190	−	0.922000i	$-0.373446\pi$
$599$	11352.6			0.774379			0.387190	+	0.922000i	$0.373446\pi$
$600$	5709.55	−	5829.78i	0.388486	−	0.396666i
$601$	3952.91			0.268291			0.134145	−	0.990962i	$-0.457171\pi$
$601$	3952.91			0.268291			0.134145	+	0.990962i	$0.457171\pi$
$602$	−3004.45	−	793.866i	−0.203409	−	0.0537468i
$603$	−5255.82			−0.354948
$604$	9085.24	−	15991.6i	0.612042	−	1.07730i
$605$	2770.88			0.186202
$606$	−4302.82	−	1136.94i	−0.288432	−	0.0762126i
$607$	−11301.7			−0.755719			−0.377860	−	0.925863i	$-0.623340\pi$
$607$	−11301.7			−0.755719			−0.377860	+	0.925863i	$0.623340\pi$
$608$	5458.32	+	19041.8i	0.364085	+	1.27014i
$609$			1139.31i			0.0758080i
$610$	−958.877	+	3628.94i	−0.0636455	+	0.240871i
$611$	6710.99	+	11216.3i	0.444350	+	0.742656i
$612$	−8143.77	−	4626.69i	−0.537896	−	0.305593i
$613$	−1858.88			−0.122479			−0.0612393	−	0.998123i	$-0.519505\pi$
$613$	−1858.88			−0.122479			−0.0612393	+	0.998123i	$0.519505\pi$
$614$	−25775.9	−	6810.78i	−1.69419	−	0.447656i
$615$	−2267.86			−0.148697
$616$	−515.036	+	525.881i	−0.0336873	+	0.0343966i
$617$		−	5899.45i		−	0.384932i	−0.981304	−	0.192466i	$-0.938351\pi$
$617$		−	5899.45i		−	0.384932i	0.981304	−	0.192466i	$-0.0616485\pi$
$618$	1330.38	−	5034.92i	0.0865949	−	0.327725i
$619$	7343.08			0.476807			0.238403	−	0.971166i	$-0.423376\pi$
$619$	7343.08			0.476807			0.238403	+	0.971166i	$0.423376\pi$
$620$	1484.42	−	2612.84i	0.0961547	−	0.169249i
$621$		−	2082.39i		−	0.134562i
$622$	−784.872	−	207.387i	−0.0505957	−	0.0133689i
$623$	−915.093			−0.0588482
$624$	−4268.05	+	7923.00i	−0.273812	+	0.508292i
$625$	13850.9			0.886458
$626$	−17408.1	−	4599.74i	−1.11145	−	0.293678i
$627$			2651.56i			0.168889i
$628$	−13434.9	+	23647.7i	−0.853677	+	1.50262i
$629$	−2401.55			−0.152235
$630$	−57.3351	+	216.989i	−0.00362585	+	0.0137223i
$631$		−	629.449i		−	0.0397116i	−0.999803	−	0.0198558i	$-0.993679\pi$
$631$		−	629.449i		−	0.0397116i	0.999803	−	0.0198558i	$-0.00632071\pi$
$632$	19233.5	+	18836.9i	1.21055	+	1.18559i
$633$	7068.19			0.443816
$634$	20325.8	+	5370.70i	1.27325	+	0.336432i
$635$	554.371			0.0346450
$636$	9261.24	+	5261.56i	0.577409	+	0.328041i
$637$	−13143.8	+	7864.26i	−0.817544	+	0.489157i
$638$	−550.303	+	2082.66i	−0.0341484	+	0.129237i
$639$		−	7628.86i		−	0.472290i
$640$	−745.821	+	3081.17i	−0.0460643	+	0.190303i
$641$	−7948.77			−0.489793			−0.244897	−	0.969549i	$-0.578754\pi$
$641$	−7948.77			−0.489793			−0.244897	+	0.969549i	$0.578754\pi$
$642$	3413.62	+	901.982i	0.209852	+	0.0554492i
$643$	−11127.9			−0.682494			−0.341247	−	0.939974i	$-0.610849\pi$
$643$	−11127.9			−0.682494			−0.341247	+	0.939974i	$0.610849\pi$
$644$	−1227.53	+	2160.66i	−0.0751107	+	0.132208i
$645$	−1791.52			−0.109366
$646$	38927.4	+	10285.8i	2.37087	+	0.626455i
$647$	21992.8			1.33636			0.668181	−	0.743999i	$-0.267073\pi$
$647$	21992.8			1.33636			0.668181	+	0.743999i	$0.267073\pi$
$648$	−1309.43	−	1282.43i	−0.0793817	−	0.0777446i
$649$	206.528			0.0124914
$650$	−15312.1	+	4417.32i	−0.923982	+	0.266556i
$651$		−	2073.29i		−	0.124821i
$652$	2479.08	+	1408.43i	0.148908	+	0.0845987i
$653$			21999.4i			1.31838i	0.751976	+	0.659191i	$0.229101\pi$
$653$			21999.4i			1.31838i	−0.751976	+	0.659191i	$0.770899\pi$
$654$	−1051.92	+	3981.08i	−0.0628951	+	0.238031i
$655$			3870.41i			0.230885i
$656$	−18984.5	+	11315.2i	−1.12991	+	0.673453i
$657$		−	10887.5i		−	0.646518i
$658$	3071.24	+	811.515i	0.181959	+	0.0480792i
$659$		−	49.4921i		−	0.00292555i	−0.999999	−	0.00146278i	$-0.999534\pi$
$659$		−	49.4921i		−	0.00292555i	0.999999	−	0.00146278i	$-0.000465616\pi$
$660$	−209.618	+	368.964i	−0.0123627	+	0.0217605i
$661$	−13469.3			−0.792580			−0.396290	−	0.918125i	$-0.629703\pi$
$661$	−13469.3			−0.792580			−0.396290	+	0.918125i	$0.629703\pi$
$662$	7048.54	+	1862.44i	0.413821	+	0.109344i
$663$	9392.04	+	15697.2i	0.550161	+	0.919501i
$664$	−15069.3	−	14758.6i	−0.880728	−	0.862565i
$665$		−	964.797i		−	0.0562605i
$666$	−454.348	−	120.053i	−0.0264349	−	0.00698491i
$667$			7272.38i			0.422171i
$668$	−11146.0	+	19618.8i	−0.645584	+	1.13634i
$669$	−1587.40			−0.0917378
$670$	3495.85	+	923.711i	0.201577	+	0.0532628i
$671$			4896.37i			0.281702i
$672$	602.683	+	2102.51i	0.0345967	+	0.120694i
$673$	8390.33			0.480570			0.240285	−	0.970702i	$-0.422759\pi$
$673$	8390.33			0.480570			0.240285	+	0.970702i	$0.422759\pi$
$674$	8603.24	+	2273.24i	0.491668	+	0.129914i
$675$		−	3245.61i		−	0.185072i
$676$	14875.3	−	9361.74i	0.846340	−	0.532644i
$677$			26739.0i			1.51797i	0.651109	+	0.758984i	$0.274304\pi$
$677$			26739.0i			1.51797i	−0.651109	+	0.758984i	$0.725696\pi$
$678$	1952.06	−	7387.71i	0.110573	−	0.418471i
$679$	−2860.83			−0.161691
$680$	4603.60	+	4508.67i	0.259618	+	0.254264i
$681$			7219.93i			0.406267i
$682$	1001.43	−	3790.00i	0.0562271	−	0.212795i
$683$	15962.9			0.894296			0.447148	−	0.894460i	$-0.352440\pi$
$683$	15962.9			0.894296			0.447148	+	0.894460i	$0.352440\pi$
$684$	6850.49	+	3891.94i	0.382946	+	0.217562i
$685$		−	5029.51i		−	0.280537i
$686$	−1949.15	+	7376.69i	−0.108482	+	0.410559i
$687$			9677.39i			0.537432i
$688$	−14997.0	+	8938.58i	−0.831042	+	0.495320i
$689$	−10680.8	−	17851.1i	−0.590574	−	0.987045i
$690$	−365.980	+	1385.08i	−0.0201922	+	0.0764188i
$691$	−15520.7			−0.854466			−0.427233	−	0.904142i	$-0.640512\pi$
$691$	−15520.7			−0.854466			−0.427233	+	0.904142i	$0.640512\pi$
$692$	9168.08	−	16137.4i	0.503639	−	0.886491i
$693$			292.774i			0.0160484i
$694$	3041.36	−	11510.2i	0.166352	−	0.629572i
$695$			5274.57i			0.287879i
$696$	4572.97	+	4478.67i	0.249049	+	0.243913i
$697$			44922.5i			2.44126i
$698$	7250.38	+	1915.77i	0.393167	+	0.103887i
$699$		−	7822.07i		−	0.423259i
$700$	−1913.22	+	3367.60i	−0.103304	+	0.181834i
$701$		−	31246.8i		−	1.68356i	−0.539822	−	0.841779i	$-0.681508\pi$
$701$		−	31246.8i		−	1.68356i	0.539822	−	0.841779i	$-0.318492\pi$
$702$	992.178	+	3439.26i	0.0533438	+	0.184909i
$703$	2020.17			0.108381
$704$	86.1627	+	4134.52i	0.00461275	+	0.221343i
$705$	1831.34			0.0978331
$706$	−2017.55	+	7635.56i	−0.107552	+	0.407037i
$707$	2112.43			0.112371
$708$	303.141	−	533.580i	0.0160914	−	0.0283237i
$709$	25294.8			1.33987			0.669934	−	0.742421i	$-0.266323\pi$
$709$	25294.8			1.33987			0.669934	+	0.742421i	$0.266323\pi$
$710$	−1340.77	+	5074.26i	−0.0708709	+	0.268216i
$711$	10707.9			0.564805
$712$	−3597.27	+	3673.02i	−0.189345	+	0.193332i
$713$		−	13234.2i		−	0.695124i
$714$	4298.20	+	1135.71i	0.225288	+	0.0595281i
$715$	711.182	−	425.518i	0.0371982	−	0.0222566i
$716$	13590.7	−	23921.9i	0.709367	−	1.24861i
$717$	6701.40			0.349049
$718$	6601.84	−	24985.2i	0.343145	−	1.29866i
$719$	10905.7			0.565664			0.282832	−	0.959169i	$-0.408726\pi$
$719$	10905.7			0.565664			0.282832	+	0.959169i	$0.408726\pi$
$720$	645.568	+	1083.13i	0.0334151	+	0.0560635i
$721$			2471.84i			0.127679i
$722$	−13989.1	−	3696.33i	−0.721078	−	0.190531i
$723$	11241.9			0.578270
$724$	−10982.6	+	19331.3i	−0.563766	+	0.992325i
$725$			11334.8i			0.580638i
$726$	2743.76	−	10384.0i	0.140262	−	0.530834i
$727$	−8503.83			−0.433823			−0.216912	−	0.976191i	$-0.569598\pi$
$727$	−8503.83			−0.433823			−0.216912	+	0.976191i	$0.569598\pi$
$728$	997.903	−	4153.40i	0.0508032	−	0.211449i
$729$	−729.000			−0.0370370
$730$	−1913.48	+	7241.71i	−0.0970152	+	0.367161i
$731$			35487.0i			1.79553i
$732$	12650.1	+	7186.86i	0.638745	+	0.362888i
$733$	21415.4			1.07912			0.539562	−	0.841946i	$-0.318590\pi$
$733$	21415.4			1.07912			0.539562	+	0.841946i	$0.318590\pi$
$734$	4526.07	+	1195.93i	0.227602	+	0.0601395i
$735$			2146.05i			0.107698i
$736$	3847.03	+	13420.7i	0.192667	+	0.672138i
$737$	4716.80			0.235747
$738$	−2245.66	+	8498.88i	−0.112011	+	0.423913i
$739$	−21527.1			−1.07157			−0.535784	−	0.844355i	$-0.679984\pi$
$739$	−21527.1			−1.07157			−0.535784	+	0.844355i	$0.679984\pi$
$740$	281.106	+	159.704i	0.0139644	+	0.00793354i
$741$	−7900.52	−	13204.4i	−0.391677	−	0.654623i
$742$	−4887.99	−	1291.55i	−0.241838	−	0.0639009i
$743$		−	3606.40i		−	0.178070i	−0.996028	−	0.0890351i	$-0.971622\pi$
$743$		−	3606.40i		−	0.178070i	0.996028	−	0.0890351i	$-0.0283783\pi$
$744$	−8321.83	−	8150.21i	−0.410071	−	0.401614i
$745$	7538.52			0.370725
$746$	−5520.01	+	20890.9i	−0.270914	+	1.02529i
$747$	−8389.55			−0.410921
$748$	7308.57	+	4152.19i	0.357256	+	0.202967i
$749$	−1675.88			−0.0817562
$750$	−1163.57	+	4403.63i	−0.0566503	+	0.214397i
$751$	−11630.5			−0.565116			−0.282558	−	0.959250i	$-0.591183\pi$
$751$	−11630.5			−0.565116			−0.282558	+	0.959250i	$0.591183\pi$
$752$	15330.4	−	9137.29i	0.743409	−	0.443089i
$753$	−17811.4			−0.861995
$754$	−3465.02	−	12011.0i	−0.167359	−	0.580127i
$755$			5032.79i			0.242599i
$756$	756.401	+	429.731i	0.0363889	+	0.0206735i
$757$		−	7346.59i		−	0.352729i	−0.984325	−	0.176365i	$-0.943566\pi$
$757$		−	7346.59i		−	0.352729i	0.984325	−	0.176365i	$-0.0564338\pi$
$758$	24853.8	+	6567.14i	1.19094	+	0.314683i
$759$			1868.82i			0.0893728i
$760$	−3872.52	−	3792.66i	−0.184830	−	0.181019i
$761$			22964.8i			1.09392i	0.837159	+	0.546960i	$0.184215\pi$
$761$			22964.8i			1.09392i	−0.837159	+	0.546960i	$0.815785\pi$
$762$	548.946	−	2077.53i	0.0260974	−	0.0987676i
$763$		−	1954.47i		−	0.0927347i
$764$	−15262.6	−	8671.10i	−0.722752	−	0.410614i
$765$	2562.96			0.121130
$766$	−10612.3	+	40162.9i	−0.500570	+	1.89444i
$767$	−1028.48	+	615.366i	−0.0484176	+	0.0289694i
$768$	10808.3	+	5846.01i	0.507826	+	0.274674i
$769$			4707.99i			0.220773i	0.993889	+	0.110387i	$0.0352089\pi$
$769$			4707.99i			0.220773i	−0.993889	+	0.110387i	$0.964791\pi$
$770$	51.4550	−	194.735i	0.00240819	−	0.00911399i
$771$			10971.3i			0.512479i
$772$	4278.68	−	7531.22i	0.199473	−	0.351107i
$773$	−12304.9			−0.572543			−0.286271	−	0.958149i	$-0.592416\pi$
$773$	−12304.9			−0.572543			−0.286271	+	0.958149i	$0.592416\pi$
$774$	−1773.98	+	6713.78i	−0.0823831	+

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:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.73458 - 0.722559i) q^{2} -3.00000i q^{3} +(6.95582 + 3.95178i) q^{4} -2.18910 q^{5} +(-2.16768 + 8.20373i) q^{6} -4.02754i q^{7} +(-16.1658 - 15.8324i) q^{8} -9.00000 q^{9} +(5.98626 + 1.58175i) q^{10} +8.07699 q^{11} +(11.8554 - 20.8675i) q^{12} +(-40.2222 + 24.0660i) q^{13} +(-2.91013 + 11.0136i) q^{14} +6.56729i q^{15} +(32.7668 + 54.9758i) q^{16} +130.087 q^{17} +(24.6112 + 6.50303i) q^{18} -109.429 q^{19} +(-15.2270 - 8.65084i) q^{20} -12.0826 q^{21} +(-22.0871 - 5.83610i) q^{22} -77.1254 q^{23} +(-47.4973 + 48.4975i) q^{24} -120.208 q^{25} +(127.380 - 36.7473i) q^{26} +27.0000i q^{27} +(15.9160 - 28.0148i) q^{28} -94.2930i q^{29} +(4.74525 - 17.9588i) q^{30} +171.593i q^{31} +(-49.8802 - 174.011i) q^{32} -24.2310i q^{33} +(-355.734 - 93.9957i) q^{34} +8.81668i q^{35} +(-62.6024 - 35.5661i) q^{36} -18.4611 q^{37} +(299.241 + 79.0686i) q^{38} +(72.1979 + 120.667i) q^{39} +(35.3886 + 34.6588i) q^{40} +345.326i q^{41} +(33.0409 + 8.73040i) q^{42} +272.794i q^{43} +(56.1820 + 31.9185i) q^{44} +19.7019 q^{45} +(210.905 + 55.7276i) q^{46} -278.858i q^{47} +(164.927 - 98.3005i) q^{48} +326.779 q^{49} +(328.718 + 86.8572i) q^{50} -390.262i q^{51} +(-374.882 + 8.44902i) q^{52} +443.813i q^{53} +(19.5091 - 73.8336i) q^{54} -17.6813 q^{55} +(-63.7658 + 65.1085i) q^{56} +328.286i q^{57} +(-68.1322 + 257.851i) q^{58} +25.5699 q^{59} +(-25.9525 + 45.6809i) q^{60} +606.212i q^{61} +(123.986 - 469.234i) q^{62} +36.2479i q^{63} +(10.6677 + 511.889i) q^{64} +(88.0504 - 52.6828i) q^{65} +(-17.5083 + 66.2614i) q^{66} +583.980 q^{67} +(904.864 + 514.077i) q^{68} +231.376i q^{69} +(6.37057 - 24.1099i) q^{70} +847.652i q^{71} +(145.492 + 142.492i) q^{72} +1209.72i q^{73} +(50.4832 + 13.3392i) q^{74} +360.624i q^{75} +(-761.165 - 432.438i) q^{76} -32.5304i q^{77} +(-110.242 - 382.140i) q^{78} -1189.76 q^{79} +(-71.7298 - 120.347i) q^{80} +81.0000 q^{81} +(249.518 - 944.320i) q^{82} +932.173 q^{83} +(-84.0445 - 47.7479i) q^{84} -284.774 q^{85} +(197.109 - 745.975i) q^{86} -282.879 q^{87} +(-130.571 - 127.878i) q^{88} -227.209i q^{89} +(-53.8763 - 14.2358i) q^{90} +(96.9267 + 161.997i) q^{91} +(-536.470 - 304.783i) q^{92} +514.779 q^{93} +(-201.491 + 762.559i) q^{94} +239.550 q^{95} +(-522.034 + 149.640i) q^{96} -710.316i q^{97} +(-893.602 - 236.117i) q^{98} -72.6929 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52}+ \cdots + 2480 q^{95}+O(q^{100}) \) 84 * q - 756 * q^9 - 36 * q^10 + 12 * q^12 - 208 * q^14 - 148 * q^16 - 104 * q^17 + 620 * q^22 + 2188 * q^25 + 444 * q^26 - 204 * q^30 - 40 * q^38 - 1924 * q^40 + 192 * q^42 + 624 * q^48 - 3396 * q^49 - 1292 * q^52 - 1616 * q^55 + 608 * q^56 - 2120 * q^62 - 2856 * q^64 + 696 * q^65 - 396 * q^66 - 2536 * q^68 - 3936 * q^74 - 156 * q^78 + 3160 * q^79 + 6804 * q^81 + 4276 * q^82 - 2088 * q^87 + 1780 * q^88 + 324 * q^90 + 4792 * q^92 - 860 * q^94 + 2480 * q^95

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