LMFDB - Embedded newform 312.4.m.a.181.41

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			181.41
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.42

$q$-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} +(122.836 - 49.8741i) 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} +(-148.785 - 344.196i) 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} +(-149.622 - 368.507i) 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	$-0.320042\pi$
$5$	11.9790			1.07143			0.535716	+	0.844398i	$0.320042\pi$
$6$	−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	$-0.391282\pi$
$11$	24.4396			0.669893			0.334946	+	0.942237i	$0.391282\pi$
$12$	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	$-0.556742\pi$
$19$	−29.3706			−0.354636			−0.177318	+	0.984154i	$0.556742\pi$
$20$	−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
$26$	122.836	−	49.8741i	0.926540	−	0.376197i
$27$			27.0000i			0.192450i
$28$	−3.99775	−	89.4826i	−0.0269823	−	0.603951i
$29$			184.758i			1.18306i	0.806284	+	0.591528i	$0.201475\pi$
$29$			184.758i			1.18306i	−0.806284	+	0.591528i	$0.798525\pi$
$30$	−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	$-0.558180\pi$
$37$	−81.8153			−0.363523			−0.181761	+	0.983343i	$0.558180\pi$
$38$	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	$-0.748979\pi$
$43$		−	400.042i		−	1.41874i	0.704835	−	0.709371i	$-0.251021\pi$
$44$	−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
$52$	−148.785	−	344.196i	−0.396785	−	0.917912i
$53$			220.471i			0.571396i	0.958320	+	0.285698i	$0.0922254\pi$
$53$			220.471i			0.571396i	−0.958320	+	0.285698i	$0.907775\pi$
$54$	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	$-0.671333\pi$
$59$	−464.646			−1.02528			−0.512642	+	0.858603i	$0.671333\pi$
$60$	12.8314	+	287.209i	0.0276088	+	0.617975i
$61$			182.988i			0.384085i	0.981387	+	0.192042i	$0.0615111\pi$
$61$			182.988i			0.384085i	−0.981387	+	0.192042i	$0.938489\pi$
$62$	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	$-0.414048\pi$
$67$	292.588			0.533512			0.266756	+	0.963764i	$0.414048\pi$
$68$	−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
$78$	−149.622	−	368.507i	−0.217197	−	0.534938i
$79$	−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	$-0.581271\pi$
$83$	−381.946			−0.505109			−0.252555	+	0.967583i	$0.581271\pi$
$84$	−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	$-0.853945\pi$
$101$		−	899.146i		−	0.885825i	0.896565	−	0.442913i	$-0.146055\pi$
$102$	−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	$0.340674\pi$
$104$	−963.898	+	442.454i	−0.908826	+	0.417175i
$105$	402.367			0.373972
$106$	623.430	−	13.9193i	0.571253	−	0.0127544i
$107$			1222.69i			1.10469i	0.833616	+	0.552344i	$0.186266\pi$
$107$			1222.69i			1.10469i	−0.833616	+	0.552344i	$0.813734\pi$
$108$	−9.64046	−	215.785i	−0.00858938	−	0.192258i
$109$	2007.74			1.76428			0.882142	−	0.470984i	$-0.156101\pi$
$109$	2007.74			1.76428			0.882142	+	0.470984i	$0.156101\pi$
$110$	−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
$130$	1471.44	−	597.441i	0.992725	−	0.403069i
$131$			754.399i			0.503146i	0.967838	+	0.251573i	$0.0809479\pi$
$131$			754.399i			0.503146i	−0.967838	+	0.251573i	$0.919052\pi$
$132$	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	$-0.970283\pi$
$139$		−	305.549i		−	0.186448i	0.995645	−	0.0932242i	$-0.0297173\pi$
$140$	−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	$-0.778275\pi$
$149$	−2790.17			−1.53409			−0.767047	+	0.641591i	$0.778275\pi$
$150$	−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
$156$	−1032.59	+	446.356i	−0.529957	+	0.229084i
$157$		−	1105.94i		−	0.562188i	−0.959680	−	0.281094i	$-0.909303\pi$
$157$		−	1105.94i		−	0.562188i	0.959680	−	0.281094i	$-0.0906973\pi$
$158$	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	$-0.713945\pi$
$163$	−2591.54			−1.24531			−0.622653	+	0.782498i	$0.713945\pi$
$164$	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	$0.142484\pi$
$173$			1969.77i			0.865656i	−0.901476	+	0.432828i	$0.857516\pi$
$174$	−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	$-0.956921\pi$
$179$		−	646.244i		−	0.269846i	0.990856	−	0.134923i	$-0.0430788\pi$
$180$	861.627	−	38.4943i	0.356788	−	0.0159400i
$181$			3540.40i			1.45390i	0.686690	+	0.726950i	$0.259063\pi$
$181$			3540.40i			1.45390i	−0.686690	+	0.726950i	$0.740937\pi$
$182$	558.414	+	1375.33i	0.227431	+	0.560143i
$183$	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	$-0.508739\pi$
$197$	−151.798			−0.0548991			−0.0274496	+	0.999623i	$0.508739\pi$
$198$	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
$208$	1311.99	+	2697.70i	0.437357	+	0.899288i
$209$	−717.806			−0.237568
$210$	−25.4033	−	1137.78i	−0.00834759	−	0.373879i
$211$			1347.84i			0.439760i	0.975527	+	0.219880i	$0.0705665\pi$
$211$			1347.84i			0.439760i	−0.975527	+	0.219880i	$0.929433\pi$
$212$	−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	$-0.296061\pi$
$227$	4088.74			1.19550			0.597751	+	0.801682i	$0.296061\pi$
$228$	−31.4607	−	704.192i	−0.00913831	−	0.204545i
$229$	−1569.92			−0.453026			−0.226513	−	0.974008i	$-0.572733\pi$
$229$	−1569.92			−0.453026			−0.226513	+	0.974008i	$0.572733\pi$
$230$	−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	$0.568823\pi$
$234$	−1105.52	+	448.867i	−0.308847	+	0.125399i
$235$		−	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	$-0.961207\pi$
$251$		−	966.865i		−	0.243139i	0.992583	−	0.121570i	$-0.0387928\pi$
$252$	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
$260$	−1782.30	−	4123.12i	−0.425128	−	0.983481i
$261$		−	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	$-0.997266\pi$
$269$		−	75.7876i		−	0.0171779i	0.999963	−	0.00858895i	$-0.00273398\pi$
$270$	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	$-0.873986\pi$
$277$		−	3555.60i		−	0.771247i	0.922656	−	0.385623i	$-0.126014\pi$
$278$	−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	$-0.930014\pi$
$283$		−	2076.65i		−	0.436198i	0.975927	−	0.218099i	$-0.0699856\pi$
$284$	326.048	+	7298.02i	0.0681246	+	1.52485i
$285$			1055.49i			0.219375i
$286$	3002.05	−	1218.90i	0.620682	−	0.252011i
$287$	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	$-0.745182\pi$
$293$	−6984.62			−1.39265			−0.696324	+	0.717727i	$0.745182\pi$
$294$	−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	$-0.797112\pi$
$307$	−8645.79			−1.60730			−0.803651	+	0.595101i	$0.797112\pi$
$308$	−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	$0.245470\pi$
$312$	1327.36	+	2891.69i	0.240856	+	0.524711i
$313$	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	$-0.663396\pi$
$317$	−5543.27			−0.982148			−0.491074	+	0.871118i	$0.663396\pi$
$318$	−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	$-0.556148\pi$
$331$	−2113.49			−0.350961			−0.175481	+	0.984483i	$0.556148\pi$
$332$	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	$0.483093\pi$
$338$	4231.43	+	4550.77i	0.680945	+	0.732334i
$339$		−	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	$0.214271\pi$
$347$			8059.88i			1.24691i	−0.781860	+	0.623454i	$0.785729\pi$
$348$	−4429.77	+	197.905i	−0.682357	+	0.0304852i
$349$	11088.0			1.70065			0.850324	−	0.526259i	$-0.176406\pi$
$349$	11088.0			1.70065			0.850324	+	0.526259i	$0.176406\pi$
$350$	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
$364$	3853.79	−	1665.87i	0.554927	−	0.239877i
$365$			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	$-0.912708\pi$
$373$		−	3901.75i		−	0.541622i	0.962633	−	0.270811i	$-0.0872918\pi$
$374$	−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	$-0.826247\pi$
$379$	−12612.3			−1.70936			−0.854681	+	0.519153i	$0.826247\pi$
$380$	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	$0.147799\pi$
$389$			6871.59i			0.895639i	−0.894124	+	0.447819i	$0.852201\pi$
$390$	−1792.32	−	4414.33i	−0.232712	−	0.573150i
$391$	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	$-0.415884\pi$
$397$	4132.17			0.522387			0.261194	+	0.965286i	$0.415884\pi$
$398$	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
$416$	7545.52	−	3880.27i	0.889301	−	0.457322i
$417$	−916.647			−0.107646
$418$	45.3184	+	2029.76i	0.00530286	+	0.237509i
$419$		−	1295.24i		−	0.151018i	−0.997145	−	0.0755089i	$-0.975942\pi$
$419$		−	1295.24i		−	0.151018i	0.997145	−	0.0755089i	$-0.0240581\pi$
$420$	−3215.73	+	143.667i	−0.373599	+	0.0166910i
$421$	−8747.69			−1.01268			−0.506338	−	0.862335i	$-0.669001\pi$
$421$	−8747.69			−1.01268			−0.506338	+	0.862335i	$0.669001\pi$
$422$	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
$442$	8386.97	−	3405.30i	0.902551	−	0.366457i
$443$			12326.5i			1.32201i	0.750381	+	0.661006i	$0.229870\pi$
$443$			12326.5i			1.32201i	−0.750381	+	0.661006i	$0.770130\pi$
$444$	−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	$-0.211754\pi$
$461$	15574.9			1.57353			0.786765	+	0.617253i	$0.211754\pi$
$462$	−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	$0.257856\pi$
$467$			14620.0i			1.44868i	−0.689441	+	0.724341i	$0.742144\pi$
$468$	1339.07	+	3097.77i	0.132262	+	0.305971i
$469$			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	$-0.749345\pi$
$491$		−	15418.0i		−	1.41712i	0.705650	−	0.708561i	$-0.250655\pi$
$492$	3820.59	−	170.690i	0.350093	−	0.0156408i
$493$			12614.9i			1.15243i
$494$	−3607.75	+	1464.83i	−0.328584	+	0.133413i
$495$	−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	$-0.727422\pi$
$499$	−14607.1			−1.31043			−0.655215	+	0.755442i	$0.727422\pi$
$500$	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	$-0.541340\pi$
$509$	−2974.43			−0.259016			−0.129508	+	0.991578i	$0.541340\pi$
$510$	−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
$520$	−11546.5	+	5300.15i	−0.973746	+	0.446975i
$521$	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	$-0.840134\pi$
$523$		−	11515.3i		−	0.962771i	0.876509	−	0.481385i	$-0.159866\pi$
$524$	−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	$-0.678586\pi$
$541$	−13390.4			−1.06414			−0.532070	+	0.846700i	$0.678586\pi$
$542$	−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
$546$	4125.98	−	1675.24i	0.323399	−	0.131307i
$547$		−	20360.8i		−	1.59152i	−0.605610	−	0.795762i	$-0.707071\pi$
$547$		−	20360.8i		−	1.59152i	0.605610	−	0.795762i	$-0.292929\pi$
$548$	−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	$-0.843727\pi$
$557$	−23186.0			−1.76377			−0.881887	+	0.471461i	$0.843727\pi$
$558$	−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	$-0.825878\pi$
$563$		−	13896.8i		−	1.04029i	0.854079	−	0.520144i	$-0.174122\pi$
$564$	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	$-0.971101\pi$
$571$		−	2474.08i		−	0.181326i	0.995882	−	0.0906628i	$-0.0288986\pi$
$572$	−3636.25	−	8412.02i	−0.265803	−	0.614902i
$573$			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	$-0.391834\pi$
$587$	9480.60			0.666621			0.333310	+	0.942817i	$0.391834\pi$
$588$	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
$598$	24262.0	−	9850.91i	1.65911	−	0.673635i
$599$	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	$-0.478638\pi$
$613$	2035.60			0.134123			0.0670613	+	0.997749i	$0.478638\pi$
$614$	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	$-0.871662\pi$
$619$	−28331.3			−1.83963			−0.919815	+	0.392352i	$0.871662\pi$
$620$	−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
$624$	8093.10	−	3935.98i	0.519204	−	0.252508i
$625$	−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	$-0.471365\pi$
$643$	2929.61			0.179677			0.0898385	+	0.995956i	$0.471365\pi$
$644$	−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
$650$	2271.96	−	922.470i	0.137098	−	0.0556650i
$651$			1085.47i			0.0653504i
$652$	20711.7	−	925.319i	1.24407	−	0.0555802i
$653$		−	25437.8i		−	1.52444i	−0.647318	−	0.762220i	$-0.724109\pi$
$653$		−	25437.8i		−	1.52444i	0.647318	−	0.762220i	$-0.275891\pi$
$654$	−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	$0.0995954\pi$
$659$			10414.5i			0.615616i	−0.951449	+	0.307808i	$0.900405\pi$
$660$	313.595	+	7019.28i	0.0184950	+	0.413977i
$661$	16499.4			0.970881			0.485441	−	0.874270i	$-0.338659\pi$
$661$	16499.4			0.970881			0.485441	+	0.874270i	$0.338659\pi$
$662$	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
$676$	12601.2	−	12252.6i	0.716952	−	0.697122i
$677$		−	30368.7i		−	1.72403i	−0.506887	−	0.862013i	$-0.669204\pi$
$677$		−	30368.7i		−	1.72403i	0.506887	−	0.862013i	$-0.330796\pi$
$678$	−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	$-0.683193\pi$
$683$	−19430.1			−1.08854			−0.544269	+	0.838911i	$0.683193\pi$
$684$	−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	$-0.606313\pi$
$691$	−11909.1			−0.655635			−0.327818	+	0.944741i	$0.606313\pi$
$692$	−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	$-0.718972\pi$
$701$		−	28677.7i		−	1.54514i	0.634932	−	0.772568i	$-0.281028\pi$
$702$	1346.60	+	3316.56i	0.0723991	+	0.178313i
$703$	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	$-0.305372\pi$
$709$	21674.5			1.14810			0.574049	+	0.818821i	$0.305372\pi$
$710$	−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	$0.670905\pi$
$728$	−4953.93	−	10792.3i	−0.252204	−	0.549434i
$729$	−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	$-0.373598\pi$
$733$	15350.2			0.773496			0.386748	+	0.922185i	$0.373598\pi$
$734$	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	$-0.265299\pi$
$739$	27012.8			1.34463			0.672316	+	0.740264i	$0.265299\pi$
$740$	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
$754$	9214.62	+	22694.8i	0.445062	+	1.09615i
$755$		−	28674.4i		−	1.38221i
$756$	2416.03	−	107.939i	0.116230	−	0.00519274i
$757$		−	20512.3i		−	0.984849i	−0.870355	−	0.492424i	$-0.836111\pi$
$757$		−	20512.3i		−	0.984849i	0.870355	−	0.492424i	$-0.163889\pi$
$758$	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	$-0.381968\pi$
$773$	15575.8			0.724736			0.362368	+	0.932035i	$0.381968\pi$
$774$	10180.9	−	227.308i

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} +(122.836 - 49.8741i) 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} +(-148.785 - 344.196i) 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} +(-149.622 - 368.507i) 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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