LMFDB - Embedded newform 312.4.m.a.181.43

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			181.43
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0631346 - 2.82772i) q^{2} +3.00000i q^{3} +(-7.99203 - 0.357054i) q^{4} -11.9790 q^{5} +(8.48317 + 0.189404i) q^{6} +11.1965i q^{7} +(-1.51422 + 22.5767i) q^{8} -9.00000 q^{9} +(-0.756288 + 33.8732i) q^{10} -24.4396 q^{11} +(1.07116 - 23.9761i) q^{12} +(-16.6594 - 43.8117i) q^{13} +(31.6605 + 0.706885i) q^{14} -35.9369i q^{15} +(63.7450 + 5.70717i) q^{16} +68.2781 q^{17} +(-0.568211 + 25.4495i) q^{18} +29.3706 q^{19} +(95.7364 + 4.27714i) q^{20} -33.5894 q^{21} +(-1.54298 + 69.1084i) q^{22} +197.516 q^{23} +(-67.7301 - 4.54267i) q^{24} +18.4960 q^{25} +(-124.939 + 44.3420i) q^{26} -27.0000i q^{27} +(3.99775 - 89.4826i) q^{28} -184.758i q^{29} +(-101.620 - 2.26886i) q^{30} +32.3159i q^{31} +(20.1628 - 179.893i) q^{32} -73.3188i q^{33} +(4.31070 - 193.071i) q^{34} -134.122i q^{35} +(71.9283 + 3.21349i) q^{36} +81.8153 q^{37} +(1.85430 - 83.0519i) q^{38} +(131.435 - 49.9781i) q^{39} +(18.1388 - 270.446i) q^{40} -159.350i q^{41} +(-2.12065 + 94.9816i) q^{42} +400.042i q^{43} +(195.322 + 8.72626i) q^{44} +107.811 q^{45} +(12.4701 - 558.520i) q^{46} -183.327i q^{47} +(-17.1215 + 191.235i) q^{48} +217.639 q^{49} +(1.16774 - 52.3015i) q^{50} +204.834i q^{51} +(117.499 + 356.093i) q^{52} -220.471i q^{53} +(-76.3485 - 1.70463i) q^{54} +292.762 q^{55} +(-252.780 - 16.9540i) q^{56} +88.1118i q^{57} +(-522.443 - 11.6646i) q^{58} +464.646 q^{59} +(-12.8314 + 287.209i) q^{60} -182.988i q^{61} +(91.3805 + 2.04025i) q^{62} -100.768i q^{63} +(-507.414 - 68.3723i) q^{64} +(199.562 + 524.820i) q^{65} +(-207.325 - 4.62895i) q^{66} -292.588 q^{67} +(-545.680 - 24.3790i) q^{68} +592.547i q^{69} +(-379.261 - 8.46776i) q^{70} -913.162i q^{71} +(13.6280 - 203.190i) q^{72} +300.218i q^{73} +(5.16537 - 231.351i) q^{74} +55.4879i q^{75} +(-234.731 - 10.4869i) q^{76} -273.638i q^{77} +(-133.026 - 374.817i) q^{78} -61.6597 q^{79} +(-763.600 - 68.3661i) q^{80} +81.0000 q^{81} +(-450.598 - 10.0605i) q^{82} +381.946 q^{83} +(268.448 + 11.9932i) q^{84} -817.902 q^{85} +(1131.21 + 25.2565i) q^{86} +554.273 q^{87} +(37.0070 - 551.766i) q^{88} +172.439i q^{89} +(6.80659 - 304.859i) q^{90} +(490.537 - 186.526i) q^{91} +(-1578.55 - 70.5238i) q^{92} -96.9478 q^{93} +(-518.397 - 11.5742i) q^{94} -351.830 q^{95} +(539.679 + 60.4884i) q^{96} +933.436i q^{97} +(13.7405 - 615.422i) q^{98} +219.956 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 $

$2$	0.0631346	−	2.82772i	0.0223214	−	0.999751i
$2$	0.0631346	−	2.82772i	0.0223214	−	0.999751i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−7.99203	−	0.357054i	−0.999004	−	0.0446317i
$5$	−11.9790			−1.07143			−0.535716	−	0.844398i	$-0.679958\pi$
$5$	−11.9790			−1.07143			−0.535716	+	0.844398i	$0.679958\pi$
$6$	8.48317	+	0.189404i	0.577206	+	0.0128873i
$7$			11.1965i			0.604553i	0.953220	+	0.302277i	$0.0977466\pi$
$7$			11.1965i			0.604553i	−0.953220	+	0.302277i	$0.902253\pi$
$8$	−1.51422	+	22.5767i	−0.0669198	+	0.997758i
$9$	−9.00000			−0.333333
$10$	−0.756288	+	33.8732i	−0.0239159	+	1.07117i
$11$	−24.4396			−0.669893			−0.334946	−	0.942237i	$-0.608718\pi$
$11$	−24.4396			−0.669893			−0.334946	+	0.942237i	$0.608718\pi$
$12$	1.07116	−	23.9761i	0.0257682	−	0.576775i
$13$	−16.6594	−	43.8117i	−0.355421	−	0.934706i
$13$	−16.6594	−	43.8117i	−0.355421	−	0.934706i
$14$	31.6605	+	0.706885i	0.604403	+	0.0134945i
$15$		−	35.9369i		−	0.618592i
$16$	63.7450	+	5.70717i	0.996016	+	0.0891745i
$17$	68.2781			0.974109			0.487055	−	0.873371i	$-0.338071\pi$
$17$	68.2781			0.974109			0.487055	+	0.873371i	$0.338071\pi$
$18$	−0.568211	+	25.4495i	−0.00744048	+	0.333250i
$19$	29.3706			0.354636			0.177318	−	0.984154i	$-0.443258\pi$
$19$	29.3706			0.354636			0.177318	+	0.984154i	$0.443258\pi$
$20$	95.7364	+	4.27714i	1.07036	+	0.0478199i
$21$	−33.5894			−0.349039
$22$	−1.54298	+	69.1084i	−0.0149530	+	0.669726i
$23$	197.516			1.79065			0.895323	−	0.445417i	$-0.146945\pi$
$23$	197.516			1.79065			0.895323	+	0.445417i	$0.146945\pi$
$24$	−67.7301	−	4.54267i	−0.576056	−	0.0386362i
$25$	18.4960			0.147968
$26$	−124.939	+	44.3420i	−0.942407	+	0.334469i
$27$		−	27.0000i		−	0.192450i
$28$	3.99775	−	89.4826i	0.0269823	−	0.603951i
$29$		−	184.758i		−	1.18306i	−0.806284	−	0.591528i	$-0.798525\pi$
$29$		−	184.758i		−	1.18306i	0.806284	−	0.591528i	$-0.201475\pi$
$30$	−101.620	−	2.26886i	−0.618438	−	0.0138079i
$31$			32.3159i			0.187229i	0.995608	+	0.0936147i	$0.0298422\pi$
$31$			32.3159i			0.187229i	−0.995608	+	0.0936147i	$0.970158\pi$
$32$	20.1628	−	179.893i	0.111385	−	0.993777i
$33$		−	73.3188i		−	0.386763i
$34$	4.31070	−	193.071i	0.0217435	−	0.973867i
$35$		−	134.122i		−	0.647738i
$36$	71.9283	+	3.21349i	0.333001	+	0.0148772i
$37$	81.8153			0.363523			0.181761	−	0.983343i	$-0.441820\pi$
$37$	81.8153			0.363523			0.181761	+	0.983343i	$0.441820\pi$
$38$	1.85430	−	83.0519i	0.00791598	−	0.354547i
$39$	131.435	−	49.9781i	0.539653	−	0.205202i
$40$	18.1388	−	270.446i	0.0717001	−	1.06903i
$41$		−	159.350i		−	0.606983i	−0.952834	−	0.303491i	$-0.901848\pi$
$41$		−	159.350i		−	0.606983i	0.952834	−	0.303491i	$-0.0981524\pi$
$42$	−2.12065	+	94.9816i	−0.00779105	+	0.348952i
$43$			400.042i			1.41874i	0.704835	+	0.709371i	$0.251021\pi$
$43$			400.042i			1.41874i	−0.704835	+	0.709371i	$0.748979\pi$
$44$	195.322	+	8.72626i	0.669225	+	0.0298985i
$45$	107.811			0.357144
$46$	12.4701	−	558.520i	0.0399698	−	1.79020i
$47$		−	183.327i		−	0.568956i	−0.958683	−	0.284478i	$-0.908180\pi$
$47$		−	183.327i		−	0.568956i	0.958683	−	0.284478i	$-0.0918203\pi$
$48$	−17.1215	+	191.235i	−0.0514849	+	0.575050i
$49$	217.639			0.634515
$50$	1.16774	−	52.3015i	0.00330285	−	0.147931i
$51$			204.834i			0.562402i
$52$	117.499	+	356.093i	0.313349	+	0.949638i
$53$		−	220.471i		−	0.571396i	−0.958320	−	0.285698i	$-0.907775\pi$
$53$		−	220.471i		−	0.571396i	0.958320	−	0.285698i	$-0.0922254\pi$
$54$	−76.3485	−	1.70463i	−0.192402	−	0.00429576i
$55$	292.762			0.717745
$56$	−252.780	−	16.9540i	−0.603198	−	0.0404566i
$57$			88.1118i			0.204749i
$58$	−522.443	−	11.6646i	−1.18276	−	0.0264075i
$59$	464.646			1.02528			0.512642	−	0.858603i	$-0.328667\pi$
$59$	464.646			1.02528			0.512642	+	0.858603i	$0.328667\pi$
$60$	−12.8314	+	287.209i	−0.0276088	+	0.617975i
$61$		−	182.988i		−	0.384085i	−0.981387	−	0.192042i	$-0.938489\pi$
$61$		−	182.988i		−	0.384085i	0.981387	−	0.192042i	$-0.0615111\pi$
$62$	91.3805	+	2.04025i	0.187183	+	0.00417923i
$63$		−	100.768i		−	0.201518i
$64$	−507.414	−	68.3723i	−0.991043	−	0.133540i
$65$	199.562	+	524.820i	0.380810	+	1.00147i
$66$	−207.325	−	4.62895i	−0.386666	−	0.00863310i
$67$	−292.588			−0.533512			−0.266756	−	0.963764i	$-0.585952\pi$
$67$	−292.588			−0.533512			−0.266756	+	0.963764i	$0.585952\pi$
$68$	−545.680	−	24.3790i	−0.973139	−	0.0434762i
$69$			592.547i			1.03383i
$70$	−379.261	−	8.46776i	−0.647577	−	0.0144584i
$71$		−	913.162i		−	1.52637i	−0.646179	−	0.763186i	$-0.723634\pi$
$71$		−	913.162i		−	1.52637i	0.646179	−	0.763186i	$-0.276366\pi$
$72$	13.6280	−	203.190i	0.0223066	−	0.332586i
$73$			300.218i			0.481341i	0.970607	+	0.240670i	$0.0773672\pi$
$73$			300.218i			0.481341i	−0.970607	+	0.240670i	$0.922633\pi$
$74$	5.16537	−	231.351i	0.00811435	−	0.363432i
$75$			55.4879i			0.0854293i
$76$	−234.731	−	10.4869i	−0.354282	−	0.0158280i
$77$		−	273.638i		−	0.404986i
$78$	−133.026	−	374.817i	−0.193106	−	0.544099i
$79$	−61.6597			−0.0878134			−0.0439067	−	0.999036i	$-0.513980\pi$
$79$	−61.6597			−0.0878134			−0.0439067	+	0.999036i	$0.513980\pi$
$80$	−763.600	−	68.3661i	−1.06716	−	0.0955445i
$81$	81.0000			0.111111
$82$	−450.598	−	10.0605i	−0.606832	−	0.0135487i
$83$	381.946			0.505109			0.252555	−	0.967583i	$-0.418729\pi$
$83$	381.946			0.505109			0.252555	+	0.967583i	$0.418729\pi$
$84$	268.448	+	11.9932i	0.348691	+	0.0155782i
$85$	−817.902			−1.04369
$86$	1131.21	+	25.2565i	1.41839	+	0.0316683i
$87$	554.273			0.683038
$88$	37.0070	−	551.766i	0.0448291	−	0.668391i
$89$			172.439i			0.205376i	0.994714	+	0.102688i	$0.0327443\pi$
$89$			172.439i			0.205376i	−0.994714	+	0.102688i	$0.967256\pi$
$90$	6.80659	−	304.859i	0.00797197	−	0.357055i
$91$	490.537	−	186.526i	0.565080	−	0.214871i
$92$	−1578.55	−	70.5238i	−1.78886	−	0.0799197i
$93$	−96.9478			−0.108097
$94$	−518.397	−	11.5742i	−0.568814	−	0.0126999i
$95$	−351.830			−0.379968
$96$	539.679	+	60.4884i	0.573758	+	0.0643081i
$97$			933.436i			0.977073i	0.872543	+	0.488537i	$0.162469\pi$
$97$			933.436i			0.977073i	−0.872543	+	0.488537i	$0.837531\pi$
$98$	13.7405	−	615.422i	0.0141633	−	0.634357i
$99$	219.956			0.223298
$100$	−147.820	−	6.60406i	−0.147820	−	0.00660406i
$101$			899.146i			0.885825i	0.896565	+	0.442913i	$0.146055\pi$
$101$			899.146i			0.885825i	−0.896565	+	0.442913i	$0.853945\pi$
$102$	579.214	+	12.9321i	0.562262	+	0.0125536i
$103$	1003.31			0.959797			0.479898	−	0.877324i	$-0.340674\pi$
$103$	1003.31			0.959797			0.479898	+	0.877324i	$0.340674\pi$
$104$	1014.35	−	309.773i	0.956396	−	0.292074i
$105$	402.367			0.373972
$106$	−623.430	−	13.9193i	−0.571253	−	0.0127544i
$107$		−	1222.69i		−	1.10469i	−0.833616	−	0.552344i	$-0.813734\pi$
$107$		−	1222.69i		−	1.10469i	0.833616	−	0.552344i	$-0.186266\pi$
$108$	−9.64046	+	215.785i	−0.00858938	+	0.192258i
$109$	−2007.74			−1.76428			−0.882142	−	0.470984i	$-0.843899\pi$
$109$	−2007.74			−1.76428			−0.882142	+	0.470984i	$0.843899\pi$
$110$	18.4834	−	827.849i	0.0160211	−	0.717566i
$111$			245.446i			0.209880i
$112$	−63.9002	+	713.720i	−0.0539108	+	0.602145i
$113$	2054.26			1.71016			0.855080	−	0.518495i	$-0.173508\pi$
$113$	2054.26			1.71016			0.855080	+	0.518495i	$0.173508\pi$
$114$	249.156	+	5.56290i	0.204698	+	0.00457029i
$115$	−2366.04			−1.91856
$116$	−65.9685	+	1476.59i	−0.0528019	+	1.18188i
$117$	149.934	+	394.305i	0.118474	+	0.311569i
$118$	29.3352	−	1313.89i	0.0228858	−	1.02503i
$119$			764.474i			0.588901i
$120$	811.337	+	54.4165i	0.617205	+	0.0413961i
$121$	−733.705			−0.551244
$122$	−517.438	−	11.5528i	−0.383989	−	0.00857333i
$123$	478.050			0.350442
$124$	11.5385	−	258.270i	0.00835638	−	0.187043i
$125$	1275.81			0.912895
$126$	−284.945	−	6.36196i	−0.201468	−	0.00449817i
$127$	2138.45			1.49415			0.747074	−	0.664741i	$-0.231458\pi$
$127$	2138.45			1.49415			0.747074	+	0.664741i	$0.231458\pi$
$128$	−225.373	+	1430.51i	−0.155628	+	0.987816i
$129$	−1200.13			−0.819111
$130$	1496.64	−	531.172i	1.00973	−	0.358361i
$131$		−	754.399i		−	0.503146i	−0.967838	−	0.251573i	$-0.919052\pi$
$131$		−	754.399i		−	0.503146i	0.967838	−	0.251573i	$-0.0809479\pi$
$132$	−26.1788	+	585.966i	−0.0172619	+	0.386377i
$133$			328.847i			0.214396i
$134$	−18.4724	+	827.357i	−0.0119087	+	0.533379i
$135$			323.432i			0.206197i
$136$	−103.388	+	1541.49i	−0.0651872	+	0.971926i
$137$			2675.17i			1.66828i	0.551549	+	0.834142i	$0.314037\pi$
$137$			2675.17i			1.66828i	−0.551549	+	0.834142i	$0.685963\pi$
$138$	1675.56	+	37.4102i	1.03357	+	0.0230766i
$139$			305.549i			0.186448i	0.995645	+	0.0932242i	$0.0297173\pi$
$139$			305.549i			0.186448i	−0.995645	+	0.0932242i	$0.970283\pi$
$140$	−47.8890	+	1071.91i	−0.0289097	+	0.647093i
$141$	549.980			0.328487
$142$	−2582.17	−	57.6521i	−1.52599	−	0.0340708i
$143$	407.148	+	1070.74i	0.238094	+	0.626153i
$144$	−573.705	−	51.3645i	−0.332005	−	0.0297248i
$145$			2213.21i			1.26757i
$146$	848.933	+	18.9541i	0.481221	+	0.0107442i
$147$			652.916i			0.366338i
$148$	−653.870	−	29.2125i	−0.363161	−	0.0162247i
$149$	2790.17			1.53409			0.767047	−	0.641591i	$-0.221725\pi$
$149$	2790.17			1.53409			0.767047	+	0.641591i	$0.221725\pi$
$150$	156.905	+	3.50321i	0.0854080	+	0.00190690i
$151$		−	2393.73i		−	1.29006i	−0.764158	−	0.645029i	$-0.776845\pi$
$151$		−	2393.73i		−	1.29006i	0.764158	−	0.645029i	$-0.223155\pi$
$152$	−44.4736	+	663.091i	−0.0237322	+	0.353841i
$153$	−614.502			−0.324703
$154$	−773.771	−	17.2760i	−0.404885	−	0.00903986i
$155$		−	387.112i		−	0.200604i
$156$	−1068.28	+	352.497i	−0.548274	+	0.180912i
$157$			1105.94i			0.562188i	0.959680	+	0.281094i	$0.0906973\pi$
$157$			1105.94i			0.562188i	−0.959680	+	0.281094i	$0.909303\pi$
$158$	−3.89286	+	174.356i	−0.00196012	+	0.0877915i
$159$	661.412			0.329896
$160$	−241.530	+	2154.93i	−0.119341	+	1.06477i
$161$			2211.48i			1.08254i
$162$	5.11390	−	229.046i	0.00248016	−	0.111083i
$163$	2591.54			1.24531			0.622653	−	0.782498i	$-0.286055\pi$
$163$	2591.54			1.24531			0.622653	+	0.782498i	$0.286055\pi$
$164$	−56.8966	+	1273.53i	−0.0270907	+	0.606378i
$165$			878.285i			0.414390i
$166$	24.1140	−	1080.04i	0.0112748	−	0.504983i
$167$		−	2755.28i		−	1.27670i	−0.769744	−	0.638352i	$-0.779616\pi$
$167$		−	2755.28i		−	1.27670i	0.769744	−	0.638352i	$-0.220384\pi$
$168$	50.8619	−	758.339i	0.0233576	−	0.348257i
$169$	−1641.93	+	1459.75i	−0.747352	+	0.664429i
$170$	−51.6378	+	2312.80i	−0.0232967	+	1.04343i
$171$	−264.335			−0.118212
$172$	142.837	−	3197.15i	0.0633209	−	1.41733i
$173$		−	1969.77i		−	0.865656i	−0.901476	−	0.432828i	$-0.857516\pi$
$173$		−	1969.77i		−	0.865656i	0.901476	−	0.432828i	$-0.142484\pi$
$174$	34.9938	−	1567.33i	0.0152464	−	0.682868i
$175$			207.090i			0.0894544i
$176$	−1557.90	−	139.481i	−0.667224	−	0.0597374i
$177$			1393.94i			0.591948i
$178$	487.609	+	10.8868i	0.205325	+	0.00458429i
$179$			646.244i			0.269846i	0.990856	+	0.134923i	$0.0430788\pi$
$179$			646.244i			0.269846i	−0.990856	+	0.134923i	$0.956921\pi$
$180$	−861.627	−	38.4943i	−0.356788	−	0.0159400i
$181$		−	3540.40i		−	1.45390i	−0.686690	−	0.726950i	$-0.740937\pi$
$181$		−	3540.40i		−	1.45390i	0.686690	−	0.726950i	$-0.259063\pi$
$182$	−496.474	−	1398.88i	−0.202204	−	0.569735i
$183$	548.963			0.221752
$184$	−299.083	+	4459.25i	−0.119830	+	1.78663i
$185$	−980.064			−0.389490
$186$	−6.12076	+	274.142i	−0.00241288	+	0.108070i
$187$	−1668.69			−0.652549
$188$	−65.4575	+	1465.15i	−0.0253935	+	0.568389i
$189$	302.305			0.116346
$190$	−22.2126	+	994.877i	−0.00848144	+	0.379874i
$191$	−81.5830			−0.0309065			−0.0154532	−	0.999881i	$-0.504919\pi$
$191$	−81.5830			−0.0309065			−0.0154532	+	0.999881i	$0.504919\pi$
$192$	205.117	−	1522.24i	0.0770991	−	0.572179i
$193$		−	2902.47i		−	1.08251i	−0.840859	−	0.541255i	$-0.817949\pi$
$193$		−	2902.47i		−	1.08251i	0.840859	−	0.541255i	$-0.182051\pi$
$194$	2639.50	+	58.9321i	0.976830	+	0.0218097i
$195$	−1574.46	+	598.686i	−0.578202	+	0.219861i
$196$	−1739.38	−	77.7088i	−0.633883	−	0.0283195i
$197$	151.798			0.0548991			0.0274496	−	0.999623i	$-0.491261\pi$
$197$	151.798			0.0548991			0.0274496	+	0.999623i	$0.491261\pi$
$198$	13.8869	−	621.976i	0.00498432	−	0.223242i
$199$	−1551.21			−0.552575			−0.276288	−	0.961075i	$-0.589104\pi$
$199$	−1551.21			−0.552575			−0.276288	+	0.961075i	$0.589104\pi$
$200$	−28.0070	+	417.578i	−0.00990198	+	0.147636i
$201$		−	877.763i		−	0.308023i
$202$	2542.53	+	56.7672i	0.885604	+	0.0197729i
$203$	2068.64			0.715221
$204$	73.1369	−	1637.04i	0.0251010	−	0.561842i
$205$			1908.85i			0.650341i
$206$	63.3435	−	2837.08i	0.0214240	−	0.959558i
$207$	−1777.64			−0.596882
$208$	−811.910	−	2887.86i	−0.270653	−	0.962677i
$209$	−717.806			−0.237568
$210$	25.4033	−	1137.78i	0.00834759	−	0.373879i
$211$		−	1347.84i		−	0.439760i	−0.975527	−	0.219880i	$-0.929433\pi$
$211$		−	1347.84i		−	0.439760i	0.975527	−	0.219880i	$-0.0705665\pi$
$212$	−78.7199	+	1762.01i	−0.0255024	+	0.570826i
$213$	2739.49			0.881251
$214$	−3457.42	−	77.1938i	−1.10441	−	0.0246582i
$215$		−	4792.10i		−	1.52009i
$216$	609.571	+	40.8840i	0.192019	+	0.0128787i
$217$	−361.825			−0.113190
$218$	−126.758	+	5677.34i	−0.0393813	+	1.76384i
$219$	−900.654			−0.277902
$220$	−2339.76	−	104.532i	−0.717030	−	0.0320342i
$221$	−1137.47	−	2991.38i	−0.346219	−	0.910506i
$222$	694.053	+	15.4961i	0.209828	+	0.00468482i
$223$		−	2120.01i		−	0.636619i	−0.947987	−	0.318310i	$-0.896885\pi$
$223$		−	2120.01i		−	0.636619i	0.947987	−	0.318310i	$-0.103115\pi$
$224$	2014.17	+	225.753i	0.600791	+	0.0673381i
$225$	−166.464			−0.0493226
$226$	129.695	−	5808.87i	0.0381732	−	1.70973i
$227$	−4088.74			−1.19550			−0.597751	−	0.801682i	$-0.703939\pi$
$227$	−4088.74			−1.19550			−0.597751	+	0.801682i	$0.703939\pi$
$228$	31.4607	−	704.192i	0.00913831	−	0.204545i
$229$	1569.92			0.453026			0.226513	−	0.974008i	$-0.427267\pi$
$229$	1569.92			0.453026			0.226513	+	0.974008i	$0.427267\pi$
$230$	−149.379	+	6690.49i	−0.0428249	+	1.91808i
$231$	820.913			0.233819
$232$	4171.22	+	279.764i	1.18040	+	0.0791699i
$233$	−1526.02			−0.429068			−0.214534	−	0.976716i	$-0.568823\pi$
$233$	−1526.02			−0.429068			−0.214534	+	0.976716i	$0.568823\pi$
$234$	1124.45	−	399.078i	0.314136	−	0.111490i
$235$			2196.07i			0.609598i
$236$	−3713.46	−	165.904i	−1.02426	−	0.0457602i
$237$		−	184.979i		−	0.0506991i
$238$	2161.72	+	48.2647i	0.588754	+	0.0131451i
$239$		−	706.224i		−	0.191137i	−0.995423	−	0.0955687i	$-0.969533\pi$
$239$		−	706.224i		−	0.191137i	0.995423	−	0.0955687i	$-0.0304670\pi$
$240$	205.098	−	2290.80i	0.0551627	−	0.616127i
$241$		−	624.829i		−	0.167007i	−0.996507	−	0.0835037i	$-0.973389\pi$
$241$		−	624.829i		−	0.167007i	0.996507	−	0.0835037i	$-0.0266110\pi$
$242$	−46.3222	+	2074.72i	−0.0123046	+	0.551106i
$243$			243.000i			0.0641500i
$244$	−65.3365	+	1462.44i	−0.0171424	+	0.383702i
$245$	−2607.09			−0.679840
$246$	30.1815	−	1351.79i	0.00782236	−	0.350354i
$247$	−489.295	−	1286.78i	−0.126045	−	0.331480i
$248$	−729.587	−	48.9335i	−0.186810	−	0.0125294i
$249$			1145.84i			0.291625i
$250$	80.5477	−	3607.64i	0.0203771	−	0.912668i
$251$			966.865i			0.243139i	0.992583	+	0.121570i	$0.0387928\pi$
$251$			966.865i			0.243139i	−0.992583	+	0.121570i	$0.961207\pi$
$252$	−35.9797	+	805.343i	−0.00899409	+	0.201317i
$253$	−4827.21			−1.19954
$254$	135.010	−	6046.94i	0.0333515	−	1.49378i
$255$		−	2453.70i		−	0.602576i
$256$	4030.86	+	727.607i	0.984096	+	0.177639i
$257$	−7870.71			−1.91035			−0.955177	−	0.296034i	$-0.904336\pi$
$257$	−7870.71			−1.91035			−0.955177	+	0.296034i	$0.904336\pi$
$258$	−75.7695	+	3393.63i	−0.0182837	+	0.818907i
$259$			916.043i			0.219769i
$260$	−1407.52	−	4265.63i	−0.335733	−	1.01747i
$261$			1662.82i			0.394352i
$262$	−2133.23	−	47.6287i	−0.503021	−	0.0112309i
$263$	−4964.41			−1.16395			−0.581975	−	0.813207i	$-0.697720\pi$
$263$	−4964.41			−1.16395			−0.581975	+	0.813207i	$0.697720\pi$
$264$	1655.30	+	111.021i	0.385896	+	0.0258821i
$265$			2641.01i			0.612212i
$266$	929.889	+	20.7616i	0.214343	+	0.00478563i
$267$	−517.316			−0.118574
$268$	2338.37	+	104.470i	0.532980	+	0.0238116i
$269$			75.7876i			0.0171779i	0.999963	+	0.00858895i	$0.00273398\pi$
$269$			75.7876i			0.0171779i	−0.999963	+	0.00858895i	$0.997266\pi$
$270$	914.577	+	20.4198i	0.206146	+	0.00460262i
$271$		−	7195.32i		−	1.61286i	−0.591331	−	0.806429i	$-0.701397\pi$
$271$		−	7195.32i		−	1.61286i	0.591331	−	0.806429i	$-0.298603\pi$
$272$	4352.39	+	389.675i	0.970229	+	0.0868658i
$273$	559.579	+	1471.61i	0.124056	+	0.326249i
$274$	7564.63	+	168.896i	1.66787	+	0.0372385i
$275$	−452.035			−0.0991226
$276$	211.571	−	4735.65i	0.0461416	−	1.03280i
$277$			3555.60i			0.771247i	0.922656	+	0.385623i	$0.126014\pi$
$277$			3555.60i			0.771247i	−0.922656	+	0.385623i	$0.873986\pi$
$278$	864.008	+	19.2907i	0.186402	+	0.00416180i
$279$		−	290.843i		−	0.0624098i
$280$	3028.04	+	203.091i	0.646286	+	0.0433465i
$281$		−	4630.12i		−	0.982953i	−0.870891	−	0.491476i	$-0.836457\pi$
$281$		−	4630.12i		−	0.982953i	0.870891	−	0.491476i	$-0.163543\pi$
$282$	34.7227	−	1555.19i	0.00733230	−	0.328405i
$283$			2076.65i			0.436198i	0.975927	+	0.218099i	$0.0699856\pi$
$283$			2076.65i			0.436198i	−0.975927	+	0.218099i	$0.930014\pi$
$284$	−326.048	+	7298.02i	−0.0681246	+	1.52485i
$285$		−	1055.49i		−	0.219375i
$286$	3053.46	−	1083.70i	0.631312	−	0.224058i
$287$	1784.16			0.366954
$288$	−181.465	+	1619.04i	−0.0371283	+	0.331259i
$289$	−251.107			−0.0511108
$290$	6258.34	+	139.730i	1.26725	+	0.0282939i
$291$	−2800.31			−0.564113
$292$	107.194	−	2399.35i	0.0214831	−	0.480861i
$293$	6984.62			1.39265			0.696324	−	0.717727i	$-0.254818\pi$
$293$	6984.62			1.39265			0.696324	+	0.717727i	$0.254818\pi$
$294$	1846.27	+	41.2216i	0.366246	+	0.00817718i
$295$	−5565.98			−1.09852
$296$	−123.887	+	1847.12i	−0.0243269	+	0.362708i
$297$			659.869i			0.128921i
$298$	176.156	−	7889.84i	0.0342432	−	1.53371i
$299$	−3290.48	−	8653.50i	−0.636434	−	1.67373i
$300$	19.8122	−	443.461i	0.00381286	−	0.0853442i
$301$	−4479.07			−0.857705
$302$	−6768.79	−	151.127i	−1.28974	−	0.0287959i
$303$	−2697.44			−0.511431
$304$	1872.23	+	167.623i	0.353223	+	0.0316245i
$305$			2192.01i			0.411521i
$306$	−38.7963	+	1737.64i	−0.00724784	+	0.324622i
$307$	8645.79			1.60730			0.803651	−	0.595101i	$-0.202888\pi$
$307$	8645.79			1.60730			0.803651	+	0.595101i	$0.202888\pi$
$308$	−97.7034	+	2186.92i	−0.0180752	+	0.404582i
$309$			3009.93i			0.554139i
$310$	−1094.65	−	24.4401i	−0.200554	−	0.00447776i
$311$	7865.90			1.43419			0.717097	−	0.696973i	$-0.245470\pi$
$311$	7865.90			1.43419			0.717097	+	0.696973i	$0.245470\pi$
$312$	929.318	+	3043.05i	0.168629	+	0.552175i
$313$	2251.25			0.406543			0.203272	−	0.979122i	$-0.434843\pi$
$313$	2251.25			0.406543			0.203272	+	0.979122i	$0.434843\pi$
$314$	3127.29	+	69.8230i	0.562048	+	0.0125488i
$315$			1207.10i			0.215913i
$316$	492.786	+	22.0158i	0.0877259	+	0.00391926i
$317$	5543.27			0.982148			0.491074	−	0.871118i	$-0.336604\pi$
$317$	5543.27			0.982148			0.491074	+	0.871118i	$0.336604\pi$
$318$	41.7580	−	1870.29i	0.00736374	−	0.329813i
$319$			4515.41i			0.792521i
$320$	6078.31	+	819.030i	1.06184	+	0.143079i
$321$	3668.06			0.637792
$322$	6253.45	+	139.621i	1.08227	+	0.0241639i
$323$	2005.37			0.345454
$324$	−647.354	−	28.9214i	−0.111000	−	0.00495908i
$325$	−308.131	−	810.341i	−0.0525909	−	0.138306i
$326$	163.616	−	7328.15i	0.0277970	−	1.24500i
$327$		−	6023.23i		−	1.01861i
$328$	3597.60	+	241.292i	0.605622	+	0.0406192i
$329$	2052.61			0.343964
$330$	2483.55	+	55.4501i	0.414287	+	0.00924978i
$331$	2113.49			0.350961			0.175481	−	0.984483i	$-0.443852\pi$
$331$	2113.49			0.350961			0.175481	+	0.984483i	$0.443852\pi$
$332$	−3052.53	−	136.375i	−0.504606	−	0.0225439i
$333$	−736.338			−0.121174
$334$	−7791.16	−	173.953i	−1.27639	−	0.0284979i
$335$	3504.90			0.571622
$336$	−2141.16	−	191.701i	−0.347648	−	0.0311254i
$337$	656.888			0.106181			0.0530905	−	0.998590i	$-0.483093\pi$
$337$	656.888			0.106181			0.0530905	+	0.998590i	$0.483093\pi$
$338$	4024.10	+	4735.09i	0.647581	+	0.761996i
$339$			6162.77i			0.987362i
$340$	6536.69	+	292.035i	1.04265	+	0.0465818i
$341$		−	789.789i		−	0.125424i
$342$	−16.6887	+	747.467i	−0.00263866	+	0.118182i
$343$			6277.18i			0.988152i
$344$	−9031.63	−	605.753i	−1.41556	−	0.0949419i
$345$		−	7098.11i		−	1.10768i
$346$	−5569.95	−	124.360i	−0.865441	−	0.0193227i
$347$		−	8059.88i		−	1.24691i	−0.781860	−	0.623454i	$-0.785729\pi$
$347$		−	8059.88i		−	1.24691i	0.781860	−	0.623454i	$-0.214271\pi$
$348$	−4429.77	−	197.905i	−0.682357	−	0.0304852i
$349$	−11088.0			−1.70065			−0.850324	−	0.526259i	$-0.823594\pi$
$349$	−11088.0			−1.70065			−0.850324	+	0.526259i	$0.823594\pi$
$350$	585.593	+	13.0745i	0.0894322	+	0.00199675i
$351$	−1182.92	+	449.803i	−0.179884	+	0.0684008i
$352$	−492.771	+	4396.51i	−0.0746159	+	0.665724i
$353$		−	10003.2i		−	1.50827i	−0.656721	−	0.754134i	$-0.728057\pi$
$353$		−	10003.2i		−	1.50827i	0.656721	−	0.754134i	$-0.271943\pi$
$354$	3941.67	+	88.0056i	0.591800	+	0.0132131i
$355$			10938.7i			1.63540i
$356$	61.5699	−	1378.14i	0.00916629	−	0.205171i
$357$	−2293.42			−0.340002
$358$	1827.40	+	40.8003i	0.269779	+	0.00602336i
$359$			2760.83i			0.405881i	0.979191	+	0.202941i	$0.0650498\pi$
$359$			2760.83i			0.405881i	−0.979191	+	0.202941i	$0.934950\pi$
$360$	−163.250	+	2434.01i	−0.0239000	+	0.356344i
$361$	−5996.37			−0.874234
$362$	−10011.3	−	223.522i	−1.45354	−	0.0324531i
$363$		−	2201.12i		−	0.318261i
$364$	−3986.99	+	1315.57i	−0.574107	+	0.189436i
$365$		−	3596.31i		−	0.515724i
$366$	34.6585	−	1552.32i	0.00494981	−	0.221696i
$367$	−9356.73			−1.33084			−0.665418	−	0.746471i	$-0.731747\pi$
$367$	−9356.73			−1.33084			−0.665418	+	0.746471i	$0.731747\pi$
$368$	12590.6	+	1127.26i	1.78351	+	0.159680i
$369$			1434.15i			0.202328i
$370$	−61.8759	+	2771.35i	−0.00869398	+	0.389393i
$371$	2468.50			0.345439
$372$	774.810	+	34.6156i	0.107989	+	0.00482456i
$373$			3901.75i			0.541622i	0.962633	+	0.270811i	$0.0872918\pi$
$373$			3901.75i			0.541622i	−0.962633	+	0.270811i	$0.912708\pi$
$374$	−105.352	+	4718.59i	−0.0145658	+	0.652386i
$375$			3827.43i			0.527060i
$376$	4138.91	+	277.597i	0.567681	+	0.0380744i
$377$	−8094.55	+	3077.94i	−1.10581	+	0.420483i
$378$	19.0859	−	854.835i	0.00259702	−	0.116317i
$379$	12612.3			1.70936			0.854681	−	0.519153i	$-0.173753\pi$
$379$	12612.3			1.70936			0.854681	+	0.519153i	$0.173753\pi$
$380$	2811.83	+	125.622i	0.379590	+	0.0169586i
$381$			6415.35i			0.862646i
$382$	−5.15071	+	230.694i	−0.000689877	+	0.0308988i
$383$		−	7774.87i		−	1.03728i	−0.854993	−	0.518639i	$-0.826439\pi$
$383$		−	7774.87i		−	1.03728i	0.854993	−	0.518639i	$-0.173561\pi$
$384$	−4291.53	−	676.120i	−0.570316	−	0.0898518i
$385$			3277.90i			0.433915i
$386$	−8207.38	−	183.246i	−1.08224	−	0.0241632i
$387$		−	3600.38i		−	0.472914i
$388$	333.287	−	7460.05i	0.0436085	−	0.976099i
$389$		−	6871.59i		−	0.895639i	−0.894124	−	0.447819i	$-0.852201\pi$
$389$		−	6871.59i		−	0.895639i	0.894124	−	0.447819i	$-0.147799\pi$
$390$	1593.52	+	4489.93i	0.206900	+	0.582965i
$391$	13486.0			1.74429
$392$	−329.554	+	4913.56i	−0.0424617	+	0.633093i
$393$	2263.20			0.290492
$394$	9.58367	−	429.241i	0.00122543	−	0.0548855i
$395$	738.620			0.0940861
$396$	−1757.90	−	78.5363i	−0.223075	−	0.00996616i
$397$	−4132.17			−0.522387			−0.261194	−	0.965286i	$-0.584116\pi$
$397$	−4132.17			−0.522387			−0.261194	+	0.965286i	$0.584116\pi$
$398$	−97.9351	+	4386.40i	−0.0123343	+	0.552438i
$399$	−986.542			−0.123782
$400$	1179.03	+	105.560i	0.147378	+	0.0131950i
$401$		−	813.908i		−	0.101358i	−0.998715	−	0.0506791i	$-0.983861\pi$
$401$		−	813.908i		−	0.101358i	0.998715	−	0.0506791i	$-0.0161386\pi$
$402$	−2482.07	−	55.4172i	−0.307946	−	0.00687552i
$403$	1415.82	−	538.363i	0.175005	−	0.0665453i
$404$	321.044	−	7186.00i	0.0395359	−	0.884942i
$405$	−970.297			−0.119048
$406$	130.602	−	5849.53i	0.0159648	−	0.715042i
$407$	−1999.53			−0.243521
$408$	−4624.48	−	310.165i	−0.561142	−	0.0376359i
$409$			6461.65i			0.781194i	0.920562	+	0.390597i	$0.127731\pi$
$409$			6461.65i			0.781194i	−0.920562	+	0.390597i	$0.872269\pi$
$410$	5397.70	+	120.514i	0.650179	+	0.0145166i
$411$	−8025.50			−0.963185
$412$	−8018.48	−	358.236i	−0.958840	−	0.0428374i
$413$			5202.40i			0.619839i
$414$	−112.231	+	5026.68i	−0.0133233	+	0.596733i
$415$	−4575.33			−0.541190
$416$	−8217.32	+	2113.53i	−0.968478	+	0.249097i
$417$	−916.647			−0.107646
$418$	−45.3184	+	2029.76i	−0.00530286	+	0.237509i
$419$			1295.24i			0.151018i	0.997145	+	0.0755089i	$0.0240581\pi$
$419$			1295.24i			0.151018i	−0.997145	+	0.0755089i	$0.975942\pi$
$420$	−3215.73	−	143.667i	−0.373599	−	0.0166910i
$421$	8747.69			1.01268			0.506338	−	0.862335i	$-0.330999\pi$
$421$	8747.69			1.01268			0.506338	+	0.862335i	$0.330999\pi$
$422$	−3811.32	−	85.0954i	−0.439650	−	0.00981607i
$423$			1649.94i			0.189652i
$424$	4977.50	+	333.842i	0.570115	+	0.0382377i
$425$	1262.87			0.144137
$426$	172.956	−	7746.50i	0.0196708	−	0.881031i
$427$	2048.82			0.232200
$428$	−436.565	+	9771.74i	−0.0493041	+	1.10359i
$429$	−3212.22	+	1221.44i	−0.361510	+	0.137464i
$430$	−13550.7	−	302.547i	−1.51971	−	0.0339305i
$431$			14848.5i			1.65946i	0.558166	+	0.829729i	$0.311505\pi$
$431$			14848.5i			1.65946i	−0.558166	+	0.829729i	$0.688495\pi$
$432$	154.094	−	1721.12i	0.0171616	−	0.191683i
$433$	1906.25			0.211567			0.105784	−	0.994389i	$-0.466265\pi$
$433$	1906.25			0.211567			0.105784	+	0.994389i	$0.466265\pi$
$434$	−22.8437	+	1023.14i	−0.00252657	+	0.113162i
$435$	−6639.63			−0.731829
$436$	16045.9	+	716.873i	1.76253	+	0.0787431i
$437$	5801.15			0.635027
$438$	−56.8624	+	2546.80i	−0.00620317	+	0.277833i
$439$	967.841			0.105222			0.0526111	−	0.998615i	$-0.483246\pi$
$439$	967.841			0.105222			0.0526111	+	0.998615i	$0.483246\pi$
$440$	−443.306	+	6609.59i	−0.0480314	+	0.716136i
$441$	−1958.75			−0.211505
$442$	−8530.60	+	3027.59i	−0.918007	+	0.325809i
$443$		−	12326.5i		−	1.32201i	−0.750381	−	0.661006i	$-0.770130\pi$
$443$		−	12326.5i		−	1.32201i	0.750381	−	0.661006i	$-0.229870\pi$
$444$	87.6374	−	1961.61i	0.00936731	−	0.209671i
$445$		−	2065.64i		−	0.220047i
$446$	−5994.79	−	133.846i	−0.636461	−	0.0142103i
$447$			8370.52i			0.885709i
$448$	765.529	−	5681.25i	0.0807318	−	0.599139i
$449$			10237.6i			1.07604i	0.842932	+	0.538020i	$0.180827\pi$
$449$			10237.6i			1.07604i	−0.842932	+	0.538020i	$0.819173\pi$
$450$	−10.5096	+	470.714i	−0.00110095	+	0.0493103i
$451$			3894.45i			0.406613i
$452$	−16417.7	−	733.480i	−1.70846	−	0.0763275i
$453$	7181.18			0.744815
$454$	−258.141	+	11561.8i	−0.0266853	+	1.19520i
$455$	−5876.13	+	2234.39i	−0.605445	+	0.230220i
$456$	−1989.27	−	133.421i	−0.204290	−	0.0137018i
$457$		−	5667.78i		−	0.580148i	−0.957004	−	0.290074i	$-0.906320\pi$
$457$		−	5667.78i		−	0.580148i	0.957004	−	0.290074i	$-0.0936798\pi$
$458$	99.1159	−	4439.28i	0.0101122	−	0.452913i
$459$		−	1843.51i		−	0.187467i
$460$	18909.4	+	844.803i	1.91665	+	0.0856285i
$461$	−15574.9			−1.57353			−0.786765	−	0.617253i	$-0.788246\pi$
$461$	−15574.9			−1.57353			−0.786765	+	0.617253i	$0.788246\pi$
$462$	51.8280	−	2321.31i	0.00521917	−	0.233760i
$463$		−	9059.56i		−	0.909359i	−0.890655	−	0.454680i	$-0.849754\pi$
$463$		−	9059.56i		−	0.909359i	0.890655	−	0.454680i	$-0.150246\pi$
$464$	1054.44	−	11777.4i	0.105499	−	1.17834i
$465$	1161.34			0.115819
$466$	−96.3446	+	4315.16i	−0.00957742	+	0.428961i
$467$		−	14620.0i		−	1.44868i	−0.689441	−	0.724341i	$-0.742144\pi$
$467$		−	14620.0i		−	1.44868i	0.689441	−	0.724341i	$-0.257856\pi$
$468$	−1057.49	−	3204.83i	−0.104450	−	0.316546i
$469$		−	3275.95i		−	0.322536i
$470$	6209.87	+	138.648i	0.609446	+	0.0136071i
$471$	−3317.82			−0.324580
$472$	−703.577	+	10490.2i	−0.0686118	+	1.02299i
$473$		−	9776.88i		−	0.950405i
$474$	−523.069	−	11.6786i	−0.0506864	−	0.00113168i
$475$	543.238			0.0524747
$476$	272.958	−	6109.70i	0.0262837	−	0.588314i
$477$			1984.24i			0.190465i
$478$	−1997.01	−	44.5872i	−0.191090	−	0.00426646i
$479$			19198.4i			1.83131i	0.401966	+	0.915655i	$0.368327\pi$
$479$			19198.4i			1.83131i	−0.401966	+	0.915655i	$0.631673\pi$
$480$	−6464.80	−	724.590i	−0.614743	−	0.0689018i
$481$	−1362.99	−	3584.47i	−0.129204	−	0.339787i
$482$	−1766.84	−	39.4483i	−0.166966	−	0.00372784i
$483$	−6634.44			−0.625005
$484$	5863.79	+	261.972i	0.550694	+	0.0246030i
$485$		−	11181.6i		−	1.04687i
$486$	687.137	+	15.3417i	0.0641340	+	0.00143192i
$487$			14357.2i			1.33591i	0.744204	+	0.667953i	$0.232829\pi$
$487$			14357.2i			1.33591i	−0.744204	+	0.667953i	$0.767171\pi$
$488$	4131.26	+	277.084i	0.383224	+	0.0257029i
$489$			7774.62i			0.718978i
$490$	−164.598	+	7372.13i	−0.0151750	+	0.679671i
$491$			15418.0i			1.41712i	0.705650	+	0.708561i	$0.250655\pi$
$491$			15418.0i			1.41712i	−0.705650	+	0.708561i	$0.749345\pi$
$492$	−3820.59	−	170.690i	−0.350093	−	0.0156408i
$493$		−	12614.9i		−	1.15243i
$494$	−3669.54	+	1302.35i	−0.334211	+	0.118614i
$495$	−2634.85			−0.239248
$496$	−184.433	+	2059.98i	−0.0166961	+	0.186484i
$497$	10224.2			0.922773
$498$	3240.11	+	72.3420i	0.291552	+	0.00650948i
$499$	14607.1			1.31043			0.655215	−	0.755442i	$-0.272578\pi$
$499$	14607.1			1.31043			0.655215	+	0.755442i	$0.272578\pi$
$500$	−10196.3	−	455.533i	−0.911985	−	0.0407441i
$501$	8265.83			0.737106
$502$	2734.02	+	61.0426i	0.243079	+	0.00542722i
$503$	−11828.8			−1.04855			−0.524274	−	0.851550i	$-0.675663\pi$
$503$	−11828.8			−1.04855			−0.524274	+	0.851550i	$0.675663\pi$
$504$	2275.02	+	152.586i	0.201066	+	0.0134855i
$505$		−	10770.8i		−	0.949102i
$506$	−304.764	+	13650.0i	−0.0267755	+	1.19924i
$507$	−4379.25	−	4925.79i	−0.383608	−	0.431484i
$508$	−17090.5	−	763.542i	−1.49266	−	0.0666864i
$509$	2974.43			0.259016			0.129508	−	0.991578i	$-0.458660\pi$
$509$	2974.43			0.259016			0.129508	+	0.991578i	$0.458660\pi$
$510$	−6938.40	−	154.914i	−0.602426	−	0.0134504i
$511$	−3361.39			−0.290996
$512$	2311.96	−	11352.2i	0.199561	−	0.979885i
$513$		−	793.006i		−	0.0682497i
$514$	−496.914	+	22256.2i	−0.0426419	+	1.90988i
$515$	−12018.6			−1.02836
$516$	9591.45	+	428.510i	0.818295	+	0.0365583i
$517$			4480.43i			0.381140i
$518$	2590.32	+	57.8340i	0.219714	+	0.00490556i
$519$	5909.30			0.499787
$520$	−12150.9	+	3710.76i	−1.02471	+	0.312938i
$521$	3470.83			0.291861			0.145931	−	0.989295i	$-0.453382\pi$
$521$	3470.83			0.291861			0.145931	+	0.989295i	$0.453382\pi$
$522$	4701.99	+	104.981i	0.394254	+	0.00880251i
$523$			11515.3i			0.962771i	0.876509	+	0.481385i	$0.159866\pi$
$523$			11515.3i			0.962771i	−0.876509	+	0.481385i	$0.840134\pi$
$524$	−269.361	+	6029.18i	−0.0224563	+	0.502645i
$525$	−621.270			−0.0516465
$526$	−313.426	+	14038.0i	−0.0259810	+	1.16366i
$527$			2206.47i			0.182382i
$528$	418.443	−	4673.71i	0.0344894	−	0.385222i
$529$	26845.4			2.20641
$530$	7468.06	+	166.739i	0.612060	+	0.0136655i
$531$	−4181.81			−0.341761
$532$	117.416	−	2628.16i	0.00956887	−	0.214183i
$533$	−6981.40	+	2654.67i	−0.567351	+	0.215735i
$534$	−32.6605	+	1462.83i	−0.00264674	+	0.118544i
$535$			14646.5i			1.18360i
$536$	443.043	−	6605.66i	0.0357025	−	0.532316i
$537$	−1938.73			−0.155796
$538$	214.306	+	4.78482i	0.0171736	+	0.000383435i
$539$	−5319.01			−0.425057
$540$	115.483	−	2584.88i	0.00920295	−	0.205992i
$541$	13390.4			1.06414			0.532070	−	0.846700i	$-0.321414\pi$
$541$	13390.4			1.06414			0.532070	+	0.846700i	$0.321414\pi$
$542$	−20346.4	−	454.273i	−1.61246	−	0.0360013i
$543$	10621.2			0.839409
$544$	1376.68	−	12282.7i	0.108501	−	0.968048i
$545$	24050.7			1.89031
$546$	4196.64	−	1489.42i	0.328937	−	0.116743i
$547$			20360.8i			1.59152i	0.605610	+	0.795762i	$0.292929\pi$
$547$			20360.8i			1.59152i	−0.605610	+	0.795762i	$0.707071\pi$
$548$	955.179	−	21380.0i	0.0744585	−	1.66662i
$549$			1646.89i			0.128028i
$550$	−28.5390	+	1278.23i	−0.00221256	+	0.0990979i
$551$		−	5426.44i		−	0.419554i
$552$	−13377.8	−	897.248i	−1.03151	−	0.0691837i
$553$		−	690.371i		−	0.0530879i
$554$	10054.3	+	224.481i	0.771055	+	0.0172153i
$555$		−	2940.19i		−	0.224872i
$556$	109.098	−	2441.96i	0.00832152	−	0.186263i
$557$	23186.0			1.76377			0.881887	−	0.471461i	$-0.156273\pi$
$557$	23186.0			1.76377			0.881887	+	0.471461i	$0.156273\pi$
$558$	−822.425	−	18.3623i	−0.0623943	−	0.00139308i
$559$	17526.5	−	6664.45i	1.32611	−	0.504251i
$560$	765.460	−	8549.64i	0.0577617	−	0.645157i
$561$		−	5006.07i		−	0.376749i
$562$	−13092.7	−	292.320i	−0.982708	−	0.0219409i
$563$			13896.8i			1.04029i	0.854079	+	0.520144i	$0.174122\pi$
$563$			13896.8i			1.04029i	−0.854079	+	0.520144i	$0.825878\pi$
$564$	−4395.45	−	196.372i	−0.328160	−	0.0146609i
$565$	−24607.9			−1.83232
$566$	5872.19	+	131.108i	0.436089	+	0.00973656i
$567$			906.915i			0.0671726i
$568$	20616.2	+	1382.73i	1.52295	+	0.102145i
$569$	−1366.99			−0.100716			−0.0503579	−	0.998731i	$-0.516036\pi$
$569$	−1366.99			−0.100716			−0.0503579	+	0.998731i	$0.516036\pi$
$570$	−2984.63	−	66.6379i	−0.219320	−	0.00489676i
$571$			2474.08i			0.181326i	0.995882	+	0.0906628i	$0.0288986\pi$
$571$			2474.08i			0.181326i	−0.995882	+	0.0906628i	$0.971101\pi$
$572$	−2871.63	−	8702.77i	−0.209910	−	0.636156i
$573$		−	244.749i		−	0.0178439i
$574$	112.642	−	5045.11i	0.00819093	−	0.366862i
$575$	3653.25			0.264958
$576$	4566.73	+	615.351i	0.330348	+	0.0445132i
$577$		−	24519.4i		−	1.76907i	−0.466472	−	0.884536i	$-0.654475\pi$
$577$		−	24519.4i		−	1.76907i	0.466472	−	0.884536i	$-0.345525\pi$
$578$	−15.8535	+	710.061i	−0.00114087	+	0.0510980i
$579$	8707.41			0.624987
$580$	790.235	−	17688.0i	0.0565737	−	1.26630i
$581$			4276.45i			0.305365i
$582$	−176.796	+	7918.50i	−0.0125918	+	0.563973i
$583$			5388.22i			0.382774i
$584$	−6777.93	−	454.597i	−0.480262	−	0.0322112i
$585$	−1796.06	−	4723.38i	−0.126937	−	0.333825i
$586$	440.971	−	19750.6i	0.0310859	−	1.39230i
$587$	−9480.60			−0.666621			−0.333310	−	0.942817i	$-0.608166\pi$
$587$	−9480.60			−0.666621			−0.333310	+	0.942817i	$0.608166\pi$
$588$	233.126	−	5218.13i	0.0163503	−	0.365973i
$589$			949.139i			0.0663983i
$590$	−351.406	+	15739.1i	−0.0245206	+	1.09825i
$591$			455.393i			0.0316960i
$592$	5215.32	+	466.934i	0.362075	+	0.0324170i
$593$			3068.45i			0.212490i	0.994340	+	0.106245i	$0.0338827\pi$
$593$			3068.45i			0.212490i	−0.994340	+	0.106245i	$0.966117\pi$
$594$	1865.93	+	41.6606i	0.128889	+	0.00287770i
$595$		−	9157.62i		−	0.630968i
$596$	−22299.1	−	996.243i	−1.53256	−	0.0684693i
$597$		−	4653.64i		−	0.319030i
$598$	−24677.4	+	8758.24i	−1.68752	+	0.598915i
$599$	11040.5			0.753095			0.376548	−	0.926397i	$-0.377111\pi$
$599$	11040.5			0.753095			0.376548	+	0.926397i	$0.377111\pi$
$600$	−1252.73	−	84.0211i	−0.0852378	−	0.00571691i
$601$	16272.6			1.10445			0.552225	−	0.833695i	$-0.313779\pi$
$601$	16272.6			1.10445			0.552225	+	0.833695i	$0.313779\pi$
$602$	−282.784	+	12665.6i	−0.0191452	+	0.857491i
$603$	2633.29			0.177837
$604$	−854.689	+	19130.7i	−0.0575775	+	1.28877i
$605$	8789.04			0.590621
$606$	−170.301	+	7627.60i	−0.0114159	+	0.511304i
$607$	11654.6			0.779321			0.389660	−	0.920959i	$-0.372592\pi$
$607$	11654.6			0.779321			0.389660	+	0.920959i	$0.372592\pi$
$608$	592.194	−	5283.56i	0.0395010	−	0.352429i
$609$			6205.91i			0.412933i
$610$	6198.39	+	138.391i	0.411419	+	0.00918574i
$611$	−8031.85	+	3054.10i	−0.531807	+	0.202219i
$612$	4911.12	+	219.411i	0.324380	+	0.0144921i
$613$	−2035.60			−0.134123			−0.0670613	−	0.997749i	$-0.521362\pi$
$613$	−2035.60			−0.134123			−0.0670613	+	0.997749i	$0.521362\pi$
$614$	545.848	−	24447.9i	0.0358773	−	1.60690i
$615$	−5726.55			−0.375475
$616$	6177.83	+	414.348i	0.404078	+	0.0271016i
$617$		−	13740.1i		−	0.896522i	−0.893903	−	0.448261i	$-0.852044\pi$
$617$		−	13740.1i		−	0.896522i	0.893903	−	0.448261i	$-0.147956\pi$
$618$	8511.25	+	190.031i	0.554001	+	0.0123692i
$619$	28331.3			1.83963			0.919815	−	0.392352i	$-0.128338\pi$
$619$	28331.3			1.83963			0.919815	+	0.392352i	$0.128338\pi$
$620$	−138.220	+	3093.81i	−0.00895330	+	0.200404i
$621$		−	5332.92i		−	0.344610i
$622$	496.610	−	22242.6i	0.0320133	−	1.43384i
$623$	−1930.71			−0.124161
$624$	8663.57	−	2435.73i	0.555802	−	0.156262i
$625$	−17594.9			−1.12607
$626$	142.132	−	6365.90i	0.00907463	−	0.406442i
$627$		−	2153.42i		−	0.137160i
$628$	394.880	−	8838.70i	0.0250914	−	0.561628i
$629$	5586.19			0.354111
$630$	3413.35	+	76.2098i	0.215859	+	0.00481948i
$631$			6978.73i			0.440284i	0.975468	+	0.220142i	$0.0706520\pi$
$631$			6978.73i			0.440284i	−0.975468	+	0.220142i	$0.929348\pi$
$632$	93.3665	−	1392.07i	0.00587645	−	0.0876165i
$633$	4043.53			0.253895
$634$	349.972	−	15674.8i	0.0219230	−	0.981904i
$635$	−25616.4			−1.60088
$636$	−5286.02	−	236.160i	−0.329567	−	0.0147238i
$637$	−3625.72	−	9535.13i	−0.225520	−	0.593086i
$638$	12768.3	+	285.078i	0.792323	+	0.0176902i
$639$			8218.46i			0.508790i
$640$	2699.74	−	17136.1i	0.166745	−	1.05838i
$641$	15556.2			0.958552			0.479276	−	0.877664i	$-0.340899\pi$
$641$	15556.2			0.958552			0.479276	+	0.877664i	$0.340899\pi$
$642$	231.581	−	10372.3i	0.0142364	−	0.637633i
$643$	−2929.61			−0.179677			−0.0898385	−	0.995956i	$-0.528635\pi$
$643$	−2929.61			−0.179677			−0.0898385	+	0.995956i	$0.528635\pi$
$644$	789.618	−	17674.2i	0.0483157	−	1.08146i
$645$	14376.3			0.877622
$646$	126.608	−	5670.62i	0.00771103	−	0.345368i
$647$	−2017.91			−0.122615			−0.0613077	−	0.998119i	$-0.519527\pi$
$647$	−2017.91			−0.122615			−0.0613077	+	0.998119i	$0.519527\pi$
$648$	−122.652	+	1828.71i	−0.00743554	+	0.110862i
$649$	−11355.8			−0.686830
$650$	−2310.87	+	820.149i	−0.139446	+	0.0494906i
$651$		−	1085.47i		−	0.0653504i
$652$	−20711.7	−	925.319i	−1.24407	−	0.0555802i
$653$			25437.8i			1.52444i	0.647318	+	0.762220i	$0.275891\pi$
$653$			25437.8i			1.52444i	−0.647318	+	0.762220i	$0.724109\pi$
$654$	−17032.0	−	380.274i	−1.01836	−	0.0227368i
$655$			9036.94i			0.539087i
$656$	909.438	−	10157.8i	0.0541274	−	0.604565i
$657$		−	2701.96i		−	0.160447i
$658$	129.591	−	5804.22i	0.00767778	−	0.343879i
$659$		−	10414.5i		−	0.615616i	−0.951449	−	0.307808i	$-0.900405\pi$
$659$		−	10414.5i		−	0.615616i	0.951449	−	0.307808i	$-0.0995954\pi$
$660$	313.595	−	7019.28i	0.0184950	−	0.413977i
$661$	−16499.4			−0.970881			−0.485441	−	0.874270i	$-0.661341\pi$
$661$	−16499.4			−0.970881			−0.485441	+	0.874270i	$0.661341\pi$
$662$	133.435	−	5976.38i	0.00783396	−	0.350874i
$663$	8974.13	−	3412.41i	0.525681	−	0.199890i
$664$	−578.352	+	8623.08i	−0.0338018	+	0.503977i
$665$		−	3939.26i		−	0.229711i
$666$	−46.4883	+	2082.16i	−0.00270478	+	0.121144i
$667$		−	36492.5i		−	2.11844i
$668$	−983.783	+	22020.2i	−0.0569816	+	1.27543i
$669$	6360.02			0.367552
$670$	221.280	−	9910.89i	0.0127594	−	0.571479i
$671$			4472.15i			0.257296i
$672$	−677.258	+	6042.50i	−0.0388776	+	0.346867i
$673$	23193.1			1.32842			0.664212	−	0.747544i	$-0.268767\pi$
$673$	23193.1			1.32842			0.664212	+	0.747544i	$0.268767\pi$
$674$	41.4723	−	1857.50i	0.00237011	−	0.106154i
$675$		−	499.392i		−	0.0284764i
$676$	13643.6	−	11080.1i	0.776262	−	0.630411i
$677$			30368.7i			1.72403i	0.506887	+	0.862013i	$0.330796\pi$
$677$			30368.7i			1.72403i	−0.506887	+	0.862013i	$0.669204\pi$
$678$	17426.6	+	389.084i	0.987116	+	0.0220393i
$679$	−10451.2			−0.590693
$680$	1238.48	−	18465.5i	0.0698437	−	1.04135i
$681$		−	12266.2i		−	0.690224i
$682$	−2233.30	−	49.8630i	−0.125392	−	0.00279964i
$683$	19430.1			1.08854			0.544269	−	0.838911i	$-0.316807\pi$
$683$	19430.1			1.08854			0.544269	+	0.838911i	$0.316807\pi$
$684$	2112.58	+	94.3820i	0.118094	+	0.00527600i
$685$		−	32045.8i		−	1.78745i
$686$	17750.1	+	396.307i	0.987905	+	0.0220570i
$687$			4709.75i			0.261555i
$688$	−2283.11	+	25500.7i	−0.126516	+	1.41309i
$689$	−9659.20	+	3672.90i	−0.534087	+	0.203086i
$690$	−20071.5	−	448.136i	−1.10740	−	0.0247250i
$691$	11909.1			0.655635			0.327818	−	0.944741i	$-0.393687\pi$
$691$	11909.1			0.655635			0.327818	+	0.944741i	$0.393687\pi$
$692$	−703.313	+	15742.4i	−0.0386358	+	0.864794i
$693$			2462.74i			0.134995i
$694$	−22791.1	−	508.857i	−1.24660	−	0.0278328i
$695$		−	3660.17i		−	0.199767i
$696$	−839.293	+	12513.7i	−0.0457088	+	0.681507i
$697$		−	10880.1i		−	0.591268i
$698$	−700.035	+	31353.8i	−0.0379609	+	1.70023i
$699$		−	4578.06i		−	0.247723i
$700$	73.9423	−	1655.07i	0.00399251	−	0.0893653i
$701$			28677.7i			1.54514i	0.634932	+	0.772568i	$0.281028\pi$
$701$			28677.7i			1.54514i	−0.634932	+	0.772568i	$0.718972\pi$
$702$	1197.23	+	3373.36i	0.0643685	+	0.181366i
$703$	2402.96			0.128918
$704$	12401.0	+	1670.99i	0.663893	+	0.0894572i
$705$	−6588.20			−0.351952
$706$	−28286.4	−	631.550i	−1.50789	−	0.0336667i
$707$	−10067.3			−0.535528
$708$	497.711	−	11140.4i	0.0264197	−	0.591358i
$709$	−21674.5			−1.14810			−0.574049	−	0.818821i	$-0.694628\pi$
$709$	−21674.5			−1.14810			−0.574049	+	0.818821i	$0.694628\pi$
$710$	30931.7	+	690.613i	1.63500	+	0.0365046i
$711$	554.937			0.0292711
$712$	−3893.10	−	261.111i	−0.204916	−	0.0137437i
$713$			6382.91i			0.335262i
$714$	−144.794	+	6485.16i	−0.00758934	+	0.339917i
$715$	−4877.22	−	12826.4i	−0.255102	−	0.670881i
$716$	230.744	−	5164.80i	0.0120437	−	0.269578i
$717$	2118.67			0.110353
$718$	7806.87	+	174.304i	0.405780	+	0.00905985i
$719$	2708.77			0.140501			0.0702504	−	0.997529i	$-0.477620\pi$
$719$	2708.77			0.140501			0.0702504	+	0.997529i	$0.477620\pi$
$720$	6872.40	+	615.295i	0.355721	+	0.0318482i
$721$			11233.5i			0.580248i
$722$	−378.578	+	16956.1i	−0.0195141	+	0.874016i
$723$	1874.49			0.0964217
$724$	−1264.11	+	28295.0i	−0.0648901	+	1.45245i
$725$		−	3417.27i		−	0.175054i
$726$	−6224.15	−	138.966i	−0.318181	−	0.00710404i
$727$	−20052.4			−1.02298			−0.511488	−	0.859291i	$-0.670905\pi$
$727$	−20052.4			−1.02298			−0.511488	+	0.859291i	$0.670905\pi$
$728$	3468.36	+	11357.1i	0.176574	+	0.578192i
$729$	−729.000			−0.0370370
$730$	−10169.4	−	227.051i	−0.515596	−	0.0115117i
$731$			27314.1i			1.38201i
$732$	−4387.33	−	196.009i	−0.221531	−	0.00989716i
$733$	−15350.2			−0.773496			−0.386748	−	0.922185i	$-0.626402\pi$
$733$	−15350.2			−0.773496			−0.386748	+	0.922185i	$0.626402\pi$
$734$	−590.733	+	26458.2i	−0.0297062	+	1.33051i
$735$		−	7821.27i		−	0.392506i
$736$	3982.47	−	35531.7i	0.199451	−	1.77950i
$737$	7150.73			0.357396
$738$	4055.38	+	90.5445i	0.202277	+	0.00451624i
$739$	−27012.8			−1.34463			−0.672316	−	0.740264i	$-0.734701\pi$
$739$	−27012.8			−1.34463			−0.672316	+	0.740264i	$0.734701\pi$
$740$	7832.70	+	349.936i	0.389102	+	0.0173836i
$741$	3860.33	−	1467.89i	0.191380	−	0.0727721i
$742$	155.847	−	6980.22i	0.00771070	−	0.345353i
$743$		−	7434.49i		−	0.367086i	−0.983012	−	0.183543i	$-0.941243\pi$
$743$		−	7434.49i		−	0.367086i	0.983012	−	0.183543i	$-0.0587567\pi$
$744$	146.801	−	2188.76i	0.00723383	−	0.107855i
$745$	−33423.4			−1.64368
$746$	11033.1	+	246.335i	0.541487	+	0.0120898i
$747$	−3437.52			−0.168370
$748$	13336.2	+	595.812i	0.651899	+	0.0291244i
$749$	13689.8			0.667842
$750$	10822.9	+	241.643i	0.526929	+	0.0117647i
$751$	818.664			0.0397783			0.0198891	−	0.999802i	$-0.493669\pi$
$751$	818.664			0.0397783			0.0198891	+	0.999802i	$0.493669\pi$
$752$	1046.28	−	11686.2i	0.0507364	−	0.566689i
$753$	−2900.59			−0.140377
$754$	8192.53	+	23083.5i	0.395695	+	1.11492i
$755$			28674.4i			1.38221i
$756$	−2416.03	−	107.939i	−0.116230	−	0.00519274i
$757$			20512.3i			0.984849i	0.870355	+	0.492424i	$0.163889\pi$
$757$			20512.3i			0.984849i	−0.870355	+	0.492424i	$0.836111\pi$
$758$	796.269	−	35664.0i	0.0381554	−	1.70894i
$759$		−	14481.6i		−	0.692555i
$760$	532.749	−	7943.16i	0.0254274	−	0.379116i
$761$		−	29099.9i		−	1.38616i	−0.720859	−	0.693082i	$-0.756252\pi$
$761$		−	29099.9i		−	1.38616i	0.720859	−	0.693082i	$-0.243748\pi$
$762$	18140.8	+	405.030i	0.862431	+	0.0192555i
$763$		−	22479.7i		−	1.06660i
$764$	652.014	+	29.1295i	0.0308757	+	0.00137941i
$765$	7361.11			0.347898
$766$	−21985.2	−	490.863i	−1.03702	−	0.0231535i
$767$	−7740.70	−	20356.9i	−0.364408	−	0.958339i
$768$	−2182.82	+	12092.6i	−0.102560	+	0.568168i
$769$		−	6398.15i		−	0.300030i	−0.988684	−	0.150015i	$-0.952068\pi$
$769$		−	6398.15i		−	0.300030i	0.988684	−	0.150015i	$-0.0479323\pi$
$770$	9268.99	+	206.949i	0.433807	+	0.00968561i
$771$		−	23612.1i		−	1.10294i
$772$	−1036.34	+	23196.6i	−0.0483143	+	1.08143i
$773$	−15575.8			−0.724736			−0.362368	−	0.932035i	$-0.618032\pi$
$773$	−15575.8			−0.724736			−0.362368	+	0.932035i	$0.618032\pi$
$774$	−10180.9	−	227.308i	−0.472796

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+(0.0631346 - 2.82772i) q^{2} +3.00000i q^{3} +(-7.99203 - 0.357054i) q^{4} -11.9790 q^{5} +(8.48317 + 0.189404i) q^{6} +11.1965i q^{7} +(-1.51422 + 22.5767i) q^{8} -9.00000 q^{9} +(-0.756288 + 33.8732i) q^{10} -24.4396 q^{11} +(1.07116 - 23.9761i) q^{12} +(-16.6594 - 43.8117i) q^{13} +(31.6605 + 0.706885i) q^{14} -35.9369i q^{15} +(63.7450 + 5.70717i) q^{16} +68.2781 q^{17} +(-0.568211 + 25.4495i) q^{18} +29.3706 q^{19} +(95.7364 + 4.27714i) q^{20} -33.5894 q^{21} +(-1.54298 + 69.1084i) q^{22} +197.516 q^{23} +(-67.7301 - 4.54267i) q^{24} +18.4960 q^{25} +(-124.939 + 44.3420i) q^{26} -27.0000i q^{27} +(3.99775 - 89.4826i) q^{28} -184.758i q^{29} +(-101.620 - 2.26886i) q^{30} +32.3159i q^{31} +(20.1628 - 179.893i) q^{32} -73.3188i q^{33} +(4.31070 - 193.071i) q^{34} -134.122i q^{35} +(71.9283 + 3.21349i) q^{36} +81.8153 q^{37} +(1.85430 - 83.0519i) q^{38} +(131.435 - 49.9781i) q^{39} +(18.1388 - 270.446i) q^{40} -159.350i q^{41} +(-2.12065 + 94.9816i) q^{42} +400.042i q^{43} +(195.322 + 8.72626i) q^{44} +107.811 q^{45} +(12.4701 - 558.520i) q^{46} -183.327i q^{47} +(-17.1215 + 191.235i) q^{48} +217.639 q^{49} +(1.16774 - 52.3015i) q^{50} +204.834i q^{51} +(117.499 + 356.093i) q^{52} -220.471i q^{53} +(-76.3485 - 1.70463i) q^{54} +292.762 q^{55} +(-252.780 - 16.9540i) q^{56} +88.1118i q^{57} +(-522.443 - 11.6646i) q^{58} +464.646 q^{59} +(-12.8314 + 287.209i) q^{60} -182.988i q^{61} +(91.3805 + 2.04025i) q^{62} -100.768i q^{63} +(-507.414 - 68.3723i) q^{64} +(199.562 + 524.820i) q^{65} +(-207.325 - 4.62895i) q^{66} -292.588 q^{67} +(-545.680 - 24.3790i) q^{68} +592.547i q^{69} +(-379.261 - 8.46776i) q^{70} -913.162i q^{71} +(13.6280 - 203.190i) q^{72} +300.218i q^{73} +(5.16537 - 231.351i) q^{74} +55.4879i q^{75} +(-234.731 - 10.4869i) q^{76} -273.638i q^{77} +(-133.026 - 374.817i) q^{78} -61.6597 q^{79} +(-763.600 - 68.3661i) q^{80} +81.0000 q^{81} +(-450.598 - 10.0605i) q^{82} +381.946 q^{83} +(268.448 + 11.9932i) q^{84} -817.902 q^{85} +(1131.21 + 25.2565i) q^{86} +554.273 q^{87} +(37.0070 - 551.766i) q^{88} +172.439i q^{89} +(6.80659 - 304.859i) q^{90} +(490.537 - 186.526i) q^{91} +(-1578.55 - 70.5238i) q^{92} -96.9478 q^{93} +(-518.397 - 11.5742i) q^{94} -351.830 q^{95} +(539.679 + 60.4884i) q^{96} +933.436i q^{97} +(13.7405 - 615.422i) q^{98} +219.956 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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