LMFDB - Embedded newform 312.4.m.a.181.3

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			181.3
Character	$\chi$	$=$	312.181
Dual form			312.4.m.a.181.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81504 - 0.274823i) q^{2} +3.00000i q^{3} +(7.84894 + 1.54728i) q^{4} -8.71484 q^{5} +(0.824470 - 8.44513i) q^{6} -16.6675i q^{7} +(-21.6699 - 6.51273i) q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+(-2.81504 - 0.274823i) q^{2} +3.00000i q^{3} +(7.84894 + 1.54728i) q^{4} -8.71484 q^{5} +(0.824470 - 8.44513i) q^{6} -16.6675i q^{7} +(-21.6699 - 6.51273i) q^{8} -9.00000 q^{9} +(24.5327 + 2.39504i) q^{10} -35.9563 q^{11} +(-4.64184 + 23.5468i) q^{12} +(46.8360 - 1.83976i) q^{13} +(-4.58062 + 46.9198i) q^{14} -26.1445i q^{15} +(59.2119 + 24.2890i) q^{16} +23.1651 q^{17} +(25.3354 + 2.47341i) q^{18} +30.2303 q^{19} +(-68.4023 - 13.4843i) q^{20} +50.0026 q^{21} +(101.219 + 9.88164i) q^{22} +72.9013 q^{23} +(19.5382 - 65.0097i) q^{24} -49.0516 q^{25} +(-132.351 - 7.69263i) q^{26} -27.0000i q^{27} +(25.7893 - 130.822i) q^{28} +119.929i q^{29} +(-7.18512 + 73.5980i) q^{30} +96.3119i q^{31} +(-160.009 - 84.6474i) q^{32} -107.869i q^{33} +(-65.2108 - 6.36632i) q^{34} +145.255i q^{35} +(-70.6405 - 13.9255i) q^{36} -33.6307 q^{37} +(-85.0997 - 8.30800i) q^{38} +(5.51929 + 140.508i) q^{39} +(188.850 + 56.7574i) q^{40} -60.2958i q^{41} +(-140.759 - 13.7419i) q^{42} -6.93666i q^{43} +(-282.219 - 55.6345i) q^{44} +78.4335 q^{45} +(-205.220 - 20.0350i) q^{46} +452.018i q^{47} +(-72.8670 + 177.636i) q^{48} +65.1938 q^{49} +(138.082 + 13.4805i) q^{50} +69.4954i q^{51} +(370.460 + 58.0283i) q^{52} +308.251i q^{53} +(-7.42023 + 76.0062i) q^{54} +313.354 q^{55} +(-108.551 + 361.183i) q^{56} +90.6910i q^{57} +(32.9594 - 337.607i) q^{58} +92.9154 q^{59} +(40.4529 - 205.207i) q^{60} +538.354i q^{61} +(26.4688 - 271.122i) q^{62} +150.008i q^{63} +(427.169 + 282.260i) q^{64} +(-408.169 + 16.0332i) q^{65} +(-29.6449 + 303.656i) q^{66} +484.925 q^{67} +(181.822 + 35.8429i) q^{68} +218.704i q^{69} +(39.9194 - 408.898i) q^{70} +447.724i q^{71} +(195.029 + 58.6146i) q^{72} +763.242i q^{73} +(94.6719 + 9.24250i) q^{74} -147.155i q^{75} +(237.276 + 46.7748i) q^{76} +599.303i q^{77} +(23.0779 - 397.053i) q^{78} +354.543 q^{79} +(-516.022 - 211.675i) q^{80} +81.0000 q^{81} +(-16.5707 + 169.735i) q^{82} -232.957 q^{83} +(392.467 + 77.3679i) q^{84} -201.880 q^{85} +(-1.90636 + 19.5270i) q^{86} -359.788 q^{87} +(779.170 + 234.174i) q^{88} +1319.37i q^{89} +(-220.794 - 21.5554i) q^{90} +(-30.6643 - 780.641i) q^{91} +(572.198 + 112.799i) q^{92} -288.936 q^{93} +(124.225 - 1272.45i) q^{94} -263.453 q^{95} +(253.942 - 480.026i) q^{96} +1333.11i q^{97} +(-183.523 - 17.9168i) q^{98} +323.607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 756 q^{9}+O(q^{10}) $ 84 * q - 756 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−2.81504	−	0.274823i	−0.995268	−	0.0971647i
$2$	−2.81504	−	0.274823i	−0.995268	−	0.0971647i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	7.84894	+	1.54728i	0.981118	+	0.193410i
$5$	−8.71484			−0.779479			−0.389739	−	0.920925i	$-0.627435\pi$
$5$	−8.71484			−0.779479			−0.389739	+	0.920925i	$0.627435\pi$
$6$	0.824470	−	8.44513i	0.0560981	−	0.574618i
$7$		−	16.6675i		−	0.899962i	−0.893038	−	0.449981i	$-0.851431\pi$
$7$		−	16.6675i		−	0.899962i	0.893038	−	0.449981i	$-0.148569\pi$
$8$	−21.6699	−	6.51273i	−0.957683	−	0.287825i
$9$	−9.00000			−0.333333
$10$	24.5327	+	2.39504i	0.775791	+	0.0757378i
$11$	−35.9563			−0.985568			−0.492784	−	0.870152i	$-0.664021\pi$
$11$	−35.9563			−0.985568			−0.492784	+	0.870152i	$0.664021\pi$
$12$	−4.64184	+	23.5468i	−0.111665	+	0.566449i
$13$	46.8360	−	1.83976i	0.999229	−	0.0392506i
$13$	46.8360	−	1.83976i	0.999229	−	0.0392506i
$14$	−4.58062	+	46.9198i	−0.0874445	+	0.895703i
$15$		−	26.1445i		−	0.450032i
$16$	59.2119	+	24.2890i	0.925185	+	0.379516i
$17$	23.1651			0.330492			0.165246	−	0.986252i	$-0.447158\pi$
$17$	23.1651			0.330492			0.165246	+	0.986252i	$0.447158\pi$
$18$	25.3354	+	2.47341i	0.331756	+	0.0323882i
$19$	30.2303			0.365017			0.182508	−	0.983204i	$-0.441578\pi$
$19$	30.2303			0.365017			0.182508	+	0.983204i	$0.441578\pi$
$20$	−68.4023	−	13.4843i	−0.764761	−	0.150759i
$21$	50.0026			0.519593
$22$	101.219	+	9.88164i	0.980904	+	0.0957624i
$23$	72.9013			0.660912			0.330456	−	0.943821i	$-0.392797\pi$
$23$	72.9013			0.660912			0.330456	+	0.943821i	$0.392797\pi$
$24$	19.5382	−	65.0097i	0.166176	−	0.552919i
$25$	−49.0516			−0.392413
$26$	−132.351	−	7.69263i	−0.998315	−	0.0580249i
$27$		−	27.0000i		−	0.192450i
$28$	25.7893	−	130.822i	0.174061	−	0.882968i
$29$			119.929i			0.767943i	0.923345	+	0.383971i	$0.125444\pi$
$29$			119.929i			0.767943i	−0.923345	+	0.383971i	$0.874556\pi$
$30$	−7.18512	+	73.5980i	−0.0437273	+	0.447903i
$31$			96.3119i			0.558004i	0.960290	+	0.279002i	$0.0900037\pi$
$31$			96.3119i			0.558004i	−0.960290	+	0.279002i	$0.909996\pi$
$32$	−160.009	−	84.6474i	−0.883932	−	0.467615i
$33$		−	107.869i		−	0.569018i
$34$	−65.2108	−	6.36632i	−0.328928	−	0.0321122i
$35$			145.255i			0.701501i
$36$	−70.6405	−	13.9255i	−0.327039	−	0.0644700i
$37$	−33.6307			−0.149428			−0.0747142	−	0.997205i	$-0.523804\pi$
$37$	−33.6307			−0.149428			−0.0747142	+	0.997205i	$0.523804\pi$
$38$	−85.0997	−	8.30800i	−0.363289	−	0.0354667i
$39$	5.51929	+	140.508i	0.0226614	+	0.576905i
$40$	188.850	+	56.7574i	0.746494	+	0.224353i
$41$		−	60.2958i		−	0.229674i	−0.993384	−	0.114837i	$-0.963365\pi$
$41$		−	60.2958i		−	0.229674i	0.993384	−	0.114837i	$-0.0366345\pi$
$42$	−140.759	−	13.7419i	−0.517134	−	0.0504861i
$43$		−	6.93666i		−	0.0246007i	−0.999924	−	0.0123004i	$-0.996085\pi$
$43$		−	6.93666i		−	0.0246007i	0.999924	−	0.0123004i	$-0.00391542\pi$
$44$	−282.219	−	55.6345i	−0.966958	−	0.190619i
$45$	78.4335			0.259826
$46$	−205.220	−	20.0350i	−0.657785	−	0.0642173i
$47$			452.018i			1.40284i	0.712747	+	0.701421i	$0.247451\pi$
$47$			452.018i			1.40284i	−0.712747	+	0.701421i	$0.752549\pi$
$48$	−72.8670	+	177.636i	−0.219114	+	0.534156i
$49$	65.1938			0.190069
$50$	138.082	+	13.4805i	0.390556	+	0.0381287i
$51$			69.4954i			0.190810i
$52$	370.460	+	58.0283i	0.987953	+	0.154751i
$53$			308.251i			0.798897i	0.916756	+	0.399449i	$0.130798\pi$
$53$			308.251i			0.798897i	−0.916756	+	0.399449i	$0.869202\pi$
$54$	−7.42023	+	76.0062i	−0.0186994	+	0.191539i
$55$	313.354			0.768229
$56$	−108.551	+	361.183i	−0.259031	+	0.861878i
$57$			90.6910i			0.210742i
$58$	32.9594	−	337.607i	0.0746169	−	0.764309i
$59$	92.9154			0.205026			0.102513	−	0.994732i	$-0.467312\pi$
$59$	92.9154			0.205026			0.102513	+	0.994732i	$0.467312\pi$
$60$	40.4529	−	205.207i	0.0870407	−	0.441535i
$61$			538.354i			1.12999i	0.825095	+	0.564993i	$0.191121\pi$
$61$			538.354i			1.12999i	−0.825095	+	0.564993i	$0.808879\pi$
$62$	26.4688	−	271.122i	0.0542183	−	0.555364i
$63$			150.008i			0.299987i
$64$	427.169	+	282.260i	0.834314	+	0.551290i
$65$	−408.169	+	16.0332i	−0.778878	+	0.0305950i
$66$	−29.6449	+	303.656i	−0.0552884	+	0.566325i
$67$	484.925			0.884224			0.442112	−	0.896960i	$-0.354229\pi$
$67$	484.925			0.884224			0.442112	+	0.896960i	$0.354229\pi$
$68$	181.822	+	35.8429i	0.324252	+	0.0639205i
$69$			218.704i			0.381578i
$70$	39.9194	−	408.898i	0.0681611	−	0.698182i
$71$			447.724i			0.748381i	0.927352	+	0.374190i	$0.122079\pi$
$71$			447.724i			0.748381i	−0.927352	+	0.374190i	$0.877921\pi$
$72$	195.029	+	58.6146i	0.319228	+	0.0959416i
$73$			763.242i			1.22371i	0.790971	+	0.611854i	$0.209576\pi$
$73$			763.242i			1.22371i	−0.790971	+	0.611854i	$0.790424\pi$
$74$	94.6719	+	9.24250i	0.148721	+	0.0145192i
$75$		−	147.155i		−	0.226560i
$76$	237.276	+	46.7748i	0.358124	+	0.0705978i
$77$			599.303i			0.886973i
$78$	23.0779	−	397.053i	0.0335007	−	0.576378i
$79$	354.543			0.504927			0.252464	−	0.967606i	$-0.418759\pi$
$79$	354.543			0.504927			0.252464	+	0.967606i	$0.418759\pi$
$80$	−516.022	−	211.675i	−0.721162	−	0.295825i
$81$	81.0000			0.111111
$82$	−16.5707	+	169.735i	−0.0223162	+	0.228587i
$83$	−232.957			−0.308076			−0.154038	−	0.988065i	$-0.549228\pi$
$83$	−232.957			−0.308076			−0.154038	+	0.988065i	$0.549228\pi$
$84$	392.467	+	77.3679i	0.509782	+	0.100494i
$85$	−201.880			−0.257612
$86$	−1.90636	+	19.5270i	−0.00239032	+	0.0244843i
$87$	−359.788			−0.443372
$88$	779.170	+	234.174i	0.943862	+	0.283671i
$89$			1319.37i			1.57138i	0.618622	+	0.785689i	$0.287691\pi$
$89$			1319.37i			1.57138i	−0.618622	+	0.785689i	$0.712309\pi$
$90$	−220.794	−	21.5554i	−0.258597	−	0.0252459i
$91$	−30.6643	−	780.641i	−0.0353241	−	0.899268i
$92$	572.198	+	112.799i	0.648433	+	0.127827i
$93$	−288.936			−0.322164
$94$	124.225	−	1272.45i	0.136307	−	1.39620i
$95$	−263.453			−0.284523
$96$	253.942	−	480.026i	0.269978	−	0.510338i
$97$			1333.11i			1.39543i	0.716374	+	0.697716i	$0.245800\pi$
$97$			1333.11i			1.39543i	−0.716374	+	0.697716i	$0.754200\pi$
$98$	−183.523	−	17.9168i	−0.189170	−	0.0184680i
$99$	323.607			0.328523
$100$	−385.003	−	75.8965i	−0.385003	−	0.0758965i
$101$		−	834.686i		−	0.822321i	−0.911563	−	0.411160i	$-0.865124\pi$
$101$		−	834.686i		−	0.822321i	0.911563	−	0.411160i	$-0.134876\pi$
$102$	19.0989	−	195.633i	0.0185400	−	0.189907i
$103$	81.2939			0.0777682			0.0388841	−	0.999244i	$-0.487620\pi$
$103$	81.2939			0.0777682			0.0388841	+	0.999244i	$0.487620\pi$
$104$	−1026.91	−	265.163i	−0.968242	−	0.250013i
$105$	−435.764			−0.405012
$106$	84.7146	−	867.740i	0.0776246	−	0.795117i
$107$		−	1329.88i		−	1.20154i	−0.799423	−	0.600769i	$-0.794861\pi$
$107$		−	1329.88i		−	1.20154i	0.799423	−	0.600769i	$-0.205139\pi$
$108$	41.7765	−	211.921i	0.0372218	−	0.188816i
$109$	−292.074			−0.256657			−0.128329	−	0.991732i	$-0.540961\pi$
$109$	−292.074			−0.256657			−0.128329	+	0.991732i	$0.540961\pi$
$110$	−882.104	−	86.1169i	−0.764594	−	0.0746448i
$111$		−	100.892i		−	0.0862726i
$112$	404.838	−	986.915i	0.341550	−	0.832631i
$113$	383.578			0.319328			0.159664	−	0.987171i	$-0.448959\pi$
$113$	383.578			0.319328			0.159664	+	0.987171i	$0.448959\pi$
$114$	24.9240	−	255.299i	0.0204767	−	0.209745i
$115$	−635.323			−0.515167
$116$	−185.564	+	941.319i	−0.148528	+	0.753442i
$117$	−421.524	+	16.5579i	−0.333076	+	0.0130835i
$118$	−261.561	−	25.5353i	−0.204056	−	0.0199213i
$119$		−	386.105i		−	0.297430i
$120$	−170.272	+	566.549i	−0.129530	+	0.430988i
$121$	−38.1413			−0.0286561
$122$	147.952	−	1515.49i	0.109795	−	1.12464i
$123$	180.887			0.132602
$124$	−149.021	+	755.947i	−0.107924	+	0.547468i
$125$	1516.83			1.08536
$126$	41.2256	−	422.278i	0.0291482	−	0.298568i
$127$	568.964			0.397539			0.198769	−	0.980046i	$-0.436306\pi$
$127$	568.964			0.397539			0.198769	+	0.980046i	$0.436306\pi$
$128$	−1124.93	−	911.971i	−0.776800	−	0.629747i
$129$	20.8100			0.0142032
$130$	1153.42	+	67.0400i	0.778165	+	0.0452292i
$131$		−	1759.15i		−	1.17327i	−0.809853	−	0.586633i	$-0.800453\pi$
$131$		−	1759.15i		−	1.17327i	0.809853	−	0.586633i	$-0.199547\pi$
$132$	166.904	−	846.658i	0.110054	−	0.558274i
$133$		−	503.865i		−	0.328501i
$134$	−1365.08	−	133.269i	−0.880040	−	0.0859153i
$135$			235.301i			0.150011i
$136$	−501.986	−	150.868i	−0.316507	−	0.0951239i
$137$		−	798.340i		−	0.497860i	−0.968521	−	0.248930i	$-0.919921\pi$
$137$		−	798.340i		−	0.497860i	0.968521	−	0.248930i	$-0.0800789\pi$
$138$	60.1049	−	615.661i	0.0370759	−	0.379772i
$139$		−	2438.56i		−	1.48803i	−0.668162	−	0.744016i	$-0.732919\pi$
$139$		−	2438.56i		−	1.48803i	0.668162	−	0.744016i	$-0.267081\pi$
$140$	−224.750	+	1140.10i	−0.135677	+	0.688255i
$141$	−1356.05			−0.809931
$142$	123.045	−	1260.36i	0.0727162	−	0.744840i
$143$	−1684.05	+	66.1511i	−0.984808	+	0.0386841i
$144$	−532.907	−	218.601i	−0.308395	−	0.126505i
$145$		−	1045.17i		−	0.598595i
$146$	209.757	−	2148.56i	0.118901	−	1.21792i
$147$			195.581i			0.109737i
$148$	−263.965	−	52.0361i	−0.146607	−	0.0289009i
$149$	1811.39			0.995938			0.497969	−	0.867195i	$-0.334079\pi$
$149$	1811.39			0.995938			0.497969	+	0.867195i	$0.334079\pi$
$150$	−40.4416	+	414.247i	−0.0220136	+	0.225488i
$151$			341.374i			0.183978i	0.995760	+	0.0919888i	$0.0293224\pi$
$151$			341.374i			0.183978i	−0.995760	+	0.0919888i	$0.970678\pi$
$152$	−655.088	−	196.882i	−0.349570	−	0.105061i
$153$	−208.486			−0.110164
$154$	164.702	−	1687.06i	0.0861825	−	0.882776i
$155$		−	839.343i		−	0.434953i
$156$	−174.085	+	1111.38i	−0.0893457	+	0.570395i
$157$			2602.82i			1.32310i	0.749899	+	0.661552i	$0.230102\pi$
$157$			2602.82i			1.32310i	−0.749899	+	0.661552i	$0.769898\pi$
$158$	−998.055	−	97.4368i	−0.502538	−	0.0490611i
$159$	−924.753			−0.461243
$160$	1394.45	+	737.689i	0.689006	+	0.364496i
$161$		−	1215.08i		−	0.594795i
$162$	−228.019	−	22.2607i	−0.110585	−	0.0107961i
$163$	−280.578			−0.134825			−0.0674127	−	0.997725i	$-0.521474\pi$
$163$	−280.578			−0.134825			−0.0674127	+	0.997725i	$0.521474\pi$
$164$	93.2945	−	473.258i	0.0444212	−	0.225337i
$165$			940.061i			0.443537i
$166$	655.784	+	64.0220i	0.306619	+	0.0299342i
$167$			445.106i			0.206248i	0.994669	+	0.103124i	$0.0328838\pi$
$167$			445.106i			0.206248i	−0.994669	+	0.103124i	$0.967116\pi$
$168$	−1083.55	−	325.653i	−0.497605	−	0.149552i
$169$	2190.23	−	172.334i	0.996919	−	0.0784408i
$170$	568.302	+	55.4814i	0.256393	+	0.0250308i
$171$	−272.073			−0.121672
$172$	10.7329	−	54.4455i	0.00475802	−	0.0241362i
$173$			4293.12i			1.88670i	0.331796	+	0.943351i	$0.392345\pi$
$173$			4293.12i			1.88670i	−0.331796	+	0.943351i	$0.607655\pi$
$174$	1012.82	+	98.8782i	0.441274	+	0.0430801i
$175$			817.569i			0.353156i
$176$	−2129.04	−	873.344i	−0.911833	−	0.374039i
$177$			278.746i			0.118372i
$178$	362.593	−	3714.08i	0.152682	−	1.56394i
$179$			1254.41i			0.523792i	0.965096	+	0.261896i	$0.0843478\pi$
$179$			1254.41i			0.523792i	−0.965096	+	0.261896i	$0.915652\pi$
$180$	615.620	+	121.359i	0.254920	+	0.0502530i
$181$		−	581.299i		−	0.238716i	−0.992851	−	0.119358i	$-0.961916\pi$
$181$		−	581.299i		−	0.238716i	0.992851	−	0.119358i	$-0.0380837\pi$
$182$	−128.217	+	2205.97i	−0.0522202	+	0.898445i
$183$	−1615.06			−0.652398
$184$	−1579.76	−	474.787i	−0.632944	−	0.190227i
$185$	293.086			0.116476
$186$	813.367	+	79.4063i	0.320640	+	0.0313030i
$187$	−832.933			−0.325723
$188$	−699.398	+	3547.86i	−0.271324	+	1.37635i
$189$	−450.023			−0.173198
$190$	741.630	+	72.4029i	0.283176	+	0.0276456i
$191$	−3296.98			−1.24901			−0.624506	−	0.781020i	$-0.714700\pi$
$191$	−3296.98			−1.24901			−0.624506	+	0.781020i	$0.714700\pi$
$192$	−846.781	+	1281.51i	−0.318287	+	0.481691i
$193$			450.627i			0.168067i	0.996463	+	0.0840333i	$0.0267802\pi$
$193$			450.627i			0.168067i	−0.996463	+	0.0840333i	$0.973220\pi$
$194$	366.370	−	3752.77i	0.135587	−	1.38883i
$195$	−48.0997	−	1224.51i	−0.0176640	−	0.449685i
$196$	511.702	+	100.873i	0.186480	+	0.0367613i
$197$	4208.90			1.52219			0.761095	−	0.648640i	$-0.224662\pi$
$197$	4208.90			1.52219			0.761095	+	0.648640i	$0.224662\pi$
$198$	−910.968	−	88.9348i	−0.326968	−	0.0319208i
$199$	4910.70			1.74930			0.874649	−	0.484756i	$-0.161092\pi$
$199$	4910.70			1.74930			0.874649	+	0.484756i	$0.161092\pi$
$200$	1062.94	+	319.460i	0.375807	+	0.112946i
$201$			1454.77i			0.510507i
$202$	−229.391	+	2349.68i	−0.0799006	+	0.818430i
$203$	1998.93			0.691119
$204$	−107.529	+	545.465i	−0.0369045	+	0.187207i
$205$			525.468i			0.179026i
$206$	−228.846	−	22.3415i	−0.0774003	−	0.00755633i
$207$	−656.112			−0.220304
$208$	2817.94	+	1028.67i	0.939369	+	0.342909i
$209$	−1086.97			−0.359749
$210$	1226.70	+	119.758i	0.403095	+	0.0393528i
$211$		−	3970.82i		−	1.29556i	−0.761829	−	0.647778i	$-0.775698\pi$
$211$		−	3970.82i		−	1.29556i	0.761829	−	0.647778i	$-0.224302\pi$
$212$	−476.951	+	2419.45i	−0.154515	+	0.783812i
$213$	−1343.17			−0.432078
$214$	−365.482	+	3743.68i	−0.116747	+	1.19585i
$215$			60.4519i			0.0191757i
$216$	−175.844	+	585.087i	−0.0553919	+	0.184306i
$217$	1605.28			0.502182
$218$	822.202	+	80.2688i	0.255443	+	0.0249380i
$219$	−2289.72			−0.706508
$220$	2459.50	+	484.846i	0.753723	+	0.148583i
$221$	1084.96	−	42.6183i	0.330238	−	0.0129720i
$222$	−27.7275	+	284.016i	−0.00838265	+	0.0858643i
$223$			484.716i			0.145556i	0.997348	+	0.0727780i	$0.0231864\pi$
$223$			484.716i			0.145556i	−0.997348	+	0.0727780i	$0.976814\pi$
$224$	−1410.86	+	2666.95i	−0.420836	+	0.795505i
$225$	441.464			0.130804
$226$	−1079.79	−	105.416i	−0.317817	−	0.0310274i
$227$	6155.05			1.79967			0.899835	−	0.436231i	$-0.143687\pi$
$227$	6155.05			1.79967			0.899835	+	0.436231i	$0.143687\pi$
$228$	−140.324	+	711.829i	−0.0407597	+	0.206763i
$229$	−5029.53			−1.45136			−0.725679	−	0.688034i	$-0.758474\pi$
$229$	−5029.53			−1.45136			−0.725679	+	0.688034i	$0.758474\pi$
$230$	1788.46	+	174.602i	0.512729	+	0.0500560i
$231$	−1797.91			−0.512094
$232$	781.068	−	2598.86i	0.221033	−	0.735446i
$233$	−1563.57			−0.439627			−0.219813	−	0.975542i	$-0.570545\pi$
$233$	−1563.57			−0.439627			−0.219813	+	0.975542i	$0.570545\pi$
$234$	1191.16	+	69.2336i	0.332772	+	0.0193416i
$235$		−	3939.26i		−	1.09349i
$236$	729.288	+	143.766i	0.201155	+	0.0396541i
$237$			1063.63i			0.291520i
$238$	−106.111	+	1086.90i	−0.0288997	+	0.296023i
$239$		−	6996.70i		−	1.89364i	−0.321770	−	0.946818i	$-0.604278\pi$
$239$		−	6996.70i		−	1.89364i	0.321770	−	0.946818i	$-0.395722\pi$
$240$	635.024	−	1548.07i	0.170794	−	0.416363i
$241$		−	3982.68i		−	1.06451i	−0.846584	−	0.532255i	$-0.821345\pi$
$241$		−	3982.68i		−	1.06451i	0.846584	−	0.532255i	$-0.178655\pi$
$242$	107.370	+	10.4821i	0.0285206	+	0.00278437i
$243$			243.000i			0.0641500i
$244$	−832.984	+	4225.51i	−0.218551	+	1.10865i
$245$	−568.153			−0.148155
$246$	−509.206	−	49.7121i	−0.131975	−	0.0128843i
$247$	1415.87	−	55.6166i	0.364735	−	0.0143271i
$248$	627.254	−	2087.07i	0.160607	−	0.534391i
$249$		−	698.871i		−	0.177868i
$250$	−4269.95	−	416.861i	−1.08022	−	0.105458i
$251$		−	1286.97i		−	0.323636i	−0.986821	−	0.161818i	$-0.948264\pi$
$251$		−	1286.97i		−	0.323636i	0.986821	−	0.161818i	$-0.0517358\pi$
$252$	−232.104	+	1177.40i	−0.0580205	+	0.294323i
$253$	−2621.27			−0.651374
$254$	−1601.66	−	156.365i	−0.395658	−	0.0386267i
$255$		−	605.641i		−	0.148732i
$256$	2916.09	+	2876.40i	0.711935	+	0.702245i
$257$	6235.56			1.51348			0.756738	−	0.653718i	$-0.226792\pi$
$257$	6235.56			1.51348			0.756738	+	0.653718i	$0.226792\pi$
$258$	−58.5810	−	5.71907i	−0.0141360	−	0.00138005i
$259$			560.540i			0.134480i
$260$	−3228.50	−	505.707i	−0.770089	−	0.120625i
$261$		−	1079.36i		−	0.255981i
$262$	−483.456	+	4952.09i	−0.114000	+	1.16772i
$263$	692.393			0.162337			0.0811687	−	0.996700i	$-0.474135\pi$
$263$	692.393			0.162337			0.0811687	+	0.996700i	$0.474135\pi$
$264$	−702.522	+	2337.51i	−0.163777	+	0.544939i
$265$		−	2686.36i		−	0.622723i
$266$	−138.474	+	1418.40i	−0.0319187	+	0.326947i
$267$	−3958.10			−0.907235
$268$	3806.15	+	750.314i	0.867528	+	0.171018i
$269$			7517.66i			1.70394i	0.523591	+	0.851970i	$0.324592\pi$
$269$			7517.66i			1.70394i	−0.523591	+	0.851970i	$0.675408\pi$
$270$	64.6661	−	662.382i	0.0145758	−	0.149301i
$271$			3416.45i			0.765810i	0.923788	+	0.382905i	$0.125076\pi$
$271$			3416.45i			0.765810i	−0.923788	+	0.382905i	$0.874924\pi$
$272$	1371.65	+	562.658i	0.305767	+	0.125427i
$273$	2341.92	−	91.9928i	0.519193	−	0.0203943i
$274$	−219.403	+	2247.36i	−0.0483744	+	0.495504i
$275$	1763.72			0.386749
$276$	−338.396	+	1716.60i	−0.0738009	+	0.374373i
$277$			5784.73i			1.25477i	0.778710	+	0.627385i	$0.215875\pi$
$277$			5784.73i			1.25477i	−0.778710	+	0.627385i	$0.784125\pi$
$278$	−670.174	+	6864.67i	−0.144584	+	1.48099i
$279$		−	866.807i		−	0.186001i
$280$	946.005	−	3147.65i	0.201909	−	0.671816i
$281$		−	3098.96i		−	0.657895i	−0.944348	−	0.328948i	$-0.893306\pi$
$281$		−	3098.96i		−	0.657895i	0.944348	−	0.328948i	$-0.106694\pi$
$282$	3817.35	+	372.675i	0.806099	+	0.0786967i
$283$			8198.04i			1.72199i	0.508614	+	0.860994i	$0.330158\pi$
$283$			8198.04i			1.72199i	−0.508614	+	0.860994i	$0.669842\pi$
$284$	−692.754	+	3514.16i	−0.144744	+	0.734250i
$285$		−	790.358i		−	0.164269i
$286$	4758.86	+	276.599i	0.983907	+	0.0571875i
$287$	−1004.98			−0.206698
$288$	1440.08	+	761.827i	0.294644	+	0.155872i
$289$	−4376.38			−0.890775
$290$	−287.236	+	2942.19i	−0.0581623	+	0.595763i
$291$	−3999.33			−0.805653
$292$	−1180.95	+	5990.64i	−0.236677	+	1.20060i
$293$	−2594.28			−0.517267			−0.258634	−	0.965975i	$-0.583272\pi$
$293$	−2594.28			−0.517267			−0.258634	+	0.965975i	$0.583272\pi$
$294$	53.7503	−	550.570i	0.0106625	−	0.109217i
$295$	−809.743			−0.159814
$296$	728.774	+	219.028i	0.143105	+	0.0430092i
$297$			970.821i			0.189673i
$298$	−5099.14	−	497.812i	−0.991225	−	0.0967700i
$299$	3414.41	−	134.121i	0.660403	−	0.0259412i
$300$	227.690	−	1155.01i	0.0438189	−	0.222282i
$301$	−115.617			−0.0221397
$302$	93.8175	−	960.982i	0.0178761	−	0.183107i
$303$	2504.06			0.474767
$304$	1789.99	+	734.265i	0.337708	+	0.138530i
$305$		−	4691.67i		−	0.880801i
$306$	586.898	+	57.2968i	0.109643	+	0.0107041i
$307$	−2227.35			−0.414076			−0.207038	−	0.978333i	$-0.566382\pi$
$307$	−2227.35			−0.414076			−0.207038	+	0.978333i	$0.566382\pi$
$308$	−927.289	+	4703.90i	−0.171549	+	0.870225i
$309$			243.882i			0.0448995i
$310$	−230.671	+	2362.79i	−0.0422620	+	0.432894i
$311$	6254.74			1.14043			0.570215	−	0.821496i	$-0.306860\pi$
$311$	6254.74			1.14043			0.570215	+	0.821496i	$0.306860\pi$
$312$	795.489	−	3080.74i	0.144345	−	0.559015i
$313$	−8081.71			−1.45944			−0.729720	−	0.683746i	$-0.760350\pi$
$313$	−8081.71			−1.45944			−0.729720	+	0.683746i	$0.760350\pi$
$314$	715.314	−	7327.04i	0.128559	−	1.31684i
$315$		−	1307.29i		−	0.233834i
$316$	2782.79	+	548.577i	0.495393	+	0.0976579i
$317$	−607.880			−0.107703			−0.0538517	−	0.998549i	$-0.517150\pi$
$317$	−607.880			−0.107703			−0.0538517	+	0.998549i	$0.517150\pi$
$318$	2603.22	+	254.144i	0.459061	+	0.0448166i
$319$		−	4312.22i		−	0.756859i
$320$	−3722.71	−	2459.85i	−0.650330	−	0.429719i
$321$	3989.65			0.693708
$322$	−333.933	+	3420.52i	−0.0577931	+	0.591981i
$323$	700.290			0.120635
$324$	635.764	+	125.330i	0.109013	+	0.0214900i
$325$	−2297.38	+	90.2433i	−0.392110	+	0.0154024i
$326$	789.838	+	77.1093i	0.134187	+	0.0131003i
$327$		−	876.223i		−	0.148181i
$328$	−392.690	+	1306.60i	−0.0661058	+	0.219955i
$329$	7534.02			1.26250
$330$	258.351	−	2646.31i	0.0430962	−	0.441439i
$331$	−8021.66			−1.33206			−0.666028	−	0.745927i	$-0.732007\pi$
$331$	−8021.66			−1.33206			−0.666028	+	0.745927i	$0.732007\pi$
$332$	−1828.47	−	360.449i	−0.302259	−	0.0595850i
$333$	302.676			0.0498095
$334$	122.326	−	1252.99i	0.0200400	−	0.205272i
$335$	−4226.04			−0.689234
$336$	2960.74	+	1214.51i	0.480720	+	0.197194i
$337$	−10370.6			−1.67633			−0.838164	−	0.545419i	$-0.816371\pi$
$337$	−10370.6			−1.67633			−0.838164	+	0.545419i	$0.816371\pi$
$338$	−6212.96	−	116.798i	−0.999823	−	0.0187957i
$339$			1150.74i			0.184364i
$340$	−1584.55	−	312.365i	−0.252747	−	0.0498247i
$341$		−	3463.02i		−	0.549951i
$342$	765.898	+	74.7720i	0.121096	+	0.0118222i
$343$		−	6803.58i		−	1.07102i
$344$	−45.1766	+	150.317i	−0.00708069	+	0.0235597i
$345$		−	1905.97i		−	0.297432i
$346$	1179.85	−	12085.3i	0.183321	−	1.87778i
$347$			2078.35i			0.321532i	0.986993	+	0.160766i	$0.0513965\pi$
$347$			2078.35i			0.321532i	−0.986993	+	0.160766i	$0.948604\pi$
$348$	−2823.96	−	556.693i	−0.435000	−	0.0857525i
$349$	5847.40			0.896861			0.448430	−	0.893818i	$-0.351983\pi$
$349$	5847.40			0.896861			0.448430	+	0.893818i	$0.351983\pi$
$350$	224.687	−	2301.49i	0.0343143	−	0.351485i
$351$	−49.6736	−	1264.57i	−0.00755379	−	0.192302i
$352$	5753.33	+	3043.61i	0.871175	+	0.460867i
$353$		−	1046.41i		−	0.157776i	−0.996883	−	0.0788881i	$-0.974863\pi$
$353$		−	1046.41i		−	0.157776i	0.996883	−	0.0788881i	$-0.0251370\pi$
$354$	76.6060	−	784.683i	0.0115016	−	0.117812i
$355$		−	3901.84i		−	0.583347i
$356$	−2041.43	+	10355.6i	−0.303920	+	1.54171i
$357$	1158.32			0.171721
$358$	344.741	−	3531.21i	0.0508941	−	0.521314i
$359$		−	9018.15i		−	1.32579i	−0.748711	−	0.662896i	$-0.769327\pi$
$359$		−	9018.15i		−	1.32579i	0.748711	−	0.662896i	$-0.230673\pi$
$360$	−1699.65	−	510.817i	−0.248831	−	0.0747844i
$361$	−5945.13			−0.866763
$362$	−159.755	+	1636.38i	−0.0231948	+	0.237587i
$363$		−	114.424i		−	0.0165446i
$364$	967.187	−	6174.65i	0.139270	−	0.889120i
$365$		−	6651.53i		−	0.953854i
$366$	4546.47	+	443.857i	0.649311	+	0.0633901i
$367$	−248.518			−0.0353475			−0.0176737	−	0.999844i	$-0.505626\pi$
$367$	−248.518			−0.0353475			−0.0176737	+	0.999844i	$0.505626\pi$
$368$	4316.62	+	1770.70i	0.611466	+	0.250827i
$369$			542.662i			0.0765579i
$370$	−825.050	−	80.5469i	−0.115925	−	0.0113174i
$371$	5137.78			0.718977
$372$	−2267.84	−	447.064i	−0.316081	−	0.0623097i
$373$			5757.08i			0.799170i	0.916696	+	0.399585i	$0.130846\pi$
$373$			5757.08i			0.799170i	−0.916696	+	0.399585i	$0.869154\pi$
$374$	2344.74	+	228.909i	0.324181	+	0.0316487i
$375$			4550.49i			0.626631i
$376$	2943.87	−	9795.18i	0.403773	−	1.34348i
$377$	220.642	+	5617.02i	0.0301422	+	0.767351i
$378$	1266.83	+	123.677i	0.172378	+	0.0168287i
$379$	−6826.63			−0.925226			−0.462613	−	0.886560i	$-0.653088\pi$
$379$	−6826.63			−0.925226			−0.462613	+	0.886560i	$0.653088\pi$
$380$	−2067.82	−	407.635i	−0.279150	−	0.0550295i
$381$			1706.89i			0.229519i
$382$	9281.15	+	906.087i	1.24310	+	0.121360i
$383$		−	1577.59i		−	0.210472i	−0.994447	−	0.105236i	$-0.966440\pi$
$383$		−	1577.59i		−	0.210472i	0.994447	−	0.105236i	$-0.0335598\pi$
$384$	2735.91	−	3374.78i	0.363585	−	0.448486i
$385$		−	5222.83i		−	0.691377i
$386$	123.843	−	1268.53i	0.0163301	−	0.167271i
$387$			62.4299i			0.00820024i
$388$	−2062.70	+	10463.5i	−0.269890	+	1.36908i
$389$		−	4906.45i		−	0.639504i	−0.947501	−	0.319752i	$-0.896400\pi$
$389$		−	4906.45i		−	0.639504i	0.947501	−	0.319752i	$-0.103600\pi$
$390$	−201.120	+	3460.26i	−0.0261131	+	0.449274i
$391$	1688.77			0.218426
$392$	−1412.74	−	424.589i	−0.182026	−	0.0547066i
$393$	5277.46			0.677386
$394$	−11848.2	−	1156.70i	−1.51499	−	0.147903i
$395$	−3089.79			−0.393580
$396$	2539.97	+	500.711i	0.322319	+	0.0635395i
$397$	−807.657			−0.102104			−0.0510518	−	0.998696i	$-0.516257\pi$
$397$	−807.657			−0.102104			−0.0510518	+	0.998696i	$0.516257\pi$
$398$	−13823.8	−	1349.58i	−1.74102	−	0.169970i
$399$	1511.59			0.189660
$400$	−2904.44	−	1191.42i	−0.363055	−	0.148927i
$401$			6460.01i			0.804483i	0.915534	+	0.402241i	$0.131769\pi$
$401$			6460.01i			0.804483i	−0.915534	+	0.402241i	$0.868231\pi$
$402$	399.806	−	4095.25i	0.0496032	−	0.508091i
$403$	177.191	+	4510.87i	0.0219020	+	0.557574i
$404$	1291.49	−	6551.41i	0.159045	−	0.806794i
$405$	−705.902			−0.0866088
$406$	−5627.06	−	549.351i	−0.687849	−	0.0671523i
$407$	1209.24			0.147272
$408$	452.605	−	1505.96i	0.0549198	−	0.182735i
$409$			6999.02i			0.846159i	0.906093	+	0.423079i	$0.139051\pi$
$409$			6999.02i			0.846159i	−0.906093	+	0.423079i	$0.860949\pi$
$410$	144.411	−	1479.22i	0.0173950	−	0.178179i
$411$	2395.02			0.287440
$412$	638.072	+	125.784i	0.0762998	+	0.0150411i
$413$		−	1548.67i		−	0.184516i
$414$	1846.98	+	180.315i	0.219262	+	0.0214058i
$415$	2030.18			0.240139
$416$	−7649.91	−	3670.17i	−0.901605	−	0.432560i
$417$	7315.69			0.859115
$418$	3059.88	+	298.725i	0.358046	+	0.0349549i
$419$		−	12515.6i		−	1.45925i	−0.683848	−	0.729624i	$-0.739695\pi$
$419$		−	12515.6i		−	1.45925i	0.683848	−	0.729624i	$-0.260305\pi$
$420$	−3420.29	−	674.249i	−0.397364	−	0.0783333i
$421$	12863.5			1.48914			0.744571	−	0.667543i	$-0.232654\pi$
$421$	12863.5			1.48914			0.744571	+	0.667543i	$0.232654\pi$
$422$	−1091.27	+	11178.0i	−0.125882	+	1.28943i
$423$		−	4068.16i		−	0.467614i
$424$	2007.56	−	6679.77i	0.229942	−	0.765090i
$425$	−1136.29			−0.129689
$426$	3781.09	+	369.135i	0.430033	+	0.0419827i
$427$	8973.03			1.01694
$428$	2057.70	−	10438.2i	0.232389	−	1.17885i
$429$	−198.453	−	5052.16i	−0.0223343	−	0.568579i
$430$	16.6136	−	170.175i	0.00186320	−	0.0190850i
$431$			13608.6i			1.52089i	0.649401	+	0.760446i	$0.275020\pi$
$431$			13608.6i			1.52089i	−0.649401	+	0.760446i	$0.724980\pi$
$432$	655.803	−	1598.72i	0.0730379	−	0.178052i
$433$	−12975.4			−1.44009			−0.720043	−	0.693929i	$-0.755878\pi$
$433$	−12975.4			−1.44009			−0.720043	+	0.693929i	$0.755878\pi$
$434$	−4518.94	−	441.169i	−0.499806	−	0.0487944i
$435$	3135.50			0.345599
$436$	−2292.47	−	451.920i	−0.251811	−	0.0496401i
$437$	2203.83			0.241244
$438$	6445.68	+	629.270i	0.703165	+	0.0686476i
$439$	10025.0			1.08991			0.544953	−	0.838467i	$-0.316548\pi$
$439$	10025.0			1.08991			0.544953	+	0.838467i	$0.316548\pi$
$440$	−6790.34	−	2040.79i	−0.735720	−	0.221115i
$441$	−586.744			−0.0633564
$442$	−3065.93	−	178.201i	−0.329935	−	0.0191768i
$443$			7965.70i			0.854315i	0.904177	+	0.427158i	$0.140485\pi$
$443$			7965.70i			0.854315i	−0.904177	+	0.427158i	$0.859515\pi$
$444$	156.108	−	791.896i	0.0166860	−	0.0846436i
$445$		−	11498.1i		−	1.22486i
$446$	133.211	−	1364.50i	0.0141429	−	0.144867i
$447$			5434.17i			0.575005i
$448$	4704.58	−	7119.84i	0.496140	−	0.750850i
$449$		−	2522.14i		−	0.265094i	−0.991177	−	0.132547i	$-0.957684\pi$
$449$		−	2522.14i		−	0.265094i	0.991177	−	0.132547i	$-0.0423155\pi$
$450$	−1242.74	−	121.325i	−0.130185	−	0.0127096i
$451$			2168.02i			0.226359i
$452$	3010.69	+	593.503i	0.313298	+	0.0617611i
$453$	−1024.12			−0.106219
$454$	−17326.7	−	1691.55i	−1.79115	−	0.174864i
$455$	267.234	+	6803.16i	0.0275343	+	0.700960i
$456$	590.646	−	1965.26i	0.0606569	−	0.201824i
$457$			9207.77i			0.942497i	0.882000	+	0.471249i	$0.156197\pi$
$457$			9207.77i			0.942497i	−0.882000	+	0.471249i	$0.843803\pi$
$458$	14158.4	+	1382.23i	1.44449	+	0.141021i
$459$		−	625.458i		−	0.0636033i
$460$	−4986.62	−	983.022i	−0.505440	−	0.0996384i
$461$	−4470.19			−0.451622			−0.225811	−	0.974171i	$-0.572503\pi$
$461$	−4470.19			−0.451622			−0.225811	+	0.974171i	$0.572503\pi$
$462$	5061.19	+	494.107i	0.509671	+	0.0497575i
$463$		−	8509.64i		−	0.854161i	−0.904214	−	0.427081i	$-0.859542\pi$
$463$		−	8509.64i		−	0.854161i	0.904214	−	0.427081i	$-0.140458\pi$
$464$	−2912.97	+	7101.24i	−0.291446	+	0.710489i
$465$	2518.03			0.251120
$466$	4401.52	+	429.706i	0.437546	+	0.0427162i
$467$			3571.08i			0.353854i	0.984224	+	0.176927i	$0.0566157\pi$
$467$			3571.08i			0.353854i	−0.984224	+	0.176927i	$0.943384\pi$
$468$	−3334.14	−	522.254i	−0.329318	−	0.0515838i
$469$		−	8082.49i		−	0.795767i
$470$	−1082.60	+	11089.2i	−0.106248	+	1.08831i
$471$	−7808.45			−0.763895
$472$	−2013.47	−	605.133i	−0.196350	−	0.0590117i
$473$			249.417i			0.0242457i
$474$	292.310	−	2994.16i	0.0283254	−	0.290140i
$475$	−1482.85			−0.143237
$476$	597.413	−	3030.52i	0.0575260	−	0.291814i
$477$		−	2774.26i		−	0.266299i
$478$	−1922.86	+	19696.0i	−0.183995	+	1.88468i
$479$			4738.57i			0.452006i	0.974127	+	0.226003i	$0.0725659\pi$
$479$			4738.57i			0.452006i	−0.974127	+	0.226003i	$0.927434\pi$
$480$	−2213.07	+	4183.35i	−0.210442	+	0.397798i
$481$	−1575.13	+	61.8725i	−0.149313	+	0.00586516i
$482$	−1094.53	+	11211.4i	−0.103433	+	1.05947i
$483$	3645.25			0.343405
$484$	−299.369	−	59.0153i	−0.0281151	−	0.00554238i
$485$		−	11617.8i		−	1.08771i
$486$	66.7821	−	684.056i	0.00623312	−	0.0638465i
$487$			20179.6i			1.87767i	0.344371	+	0.938834i	$0.388092\pi$
$487$			20179.6i			1.87767i	−0.344371	+	0.938834i	$0.611908\pi$
$488$	3506.16	−	11666.1i	0.325238	−	1.08217i
$489$		−	841.733i		−	0.0778415i
$490$	1599.38	+	156.142i	0.147454	+	0.0143954i
$491$			5526.37i			0.507946i	0.967211	+	0.253973i	$0.0817375\pi$
$491$			5526.37i			0.507946i	−0.967211	+	0.253973i	$0.918263\pi$
$492$	1419.78	+	279.883i	0.130098	+	0.0256466i
$493$			2778.18i			0.253799i
$494$	−4001.02	−	232.551i	−0.364402	−	0.0211801i
$495$	−2820.18			−0.256076
$496$	−2339.32	+	5702.81i	−0.211771	+	0.516257i
$497$	7462.45			0.673514
$498$	−192.066	+	1967.35i	−0.0172825	+	0.177026i
$499$	11790.6			1.05776			0.528878	−	0.848698i	$-0.322613\pi$
$499$	11790.6			1.05776			0.528878	+	0.848698i	$0.322613\pi$
$500$	11905.5	+	2346.96i	1.06486	+	0.209919i
$501$	−1335.32			−0.119077
$502$	−353.689	+	3622.87i	−0.0314460	+	0.322105i
$503$	−17921.2			−1.58860			−0.794301	−	0.607525i	$-0.792163\pi$
$503$	−17921.2			−1.58860			−0.794301	+	0.607525i	$0.792163\pi$
$504$	976.960	−	3250.65i	0.0863437	−	0.287293i
$505$			7274.16i			0.640982i
$506$	7378.98	+	720.385i	0.648292	+	0.0632905i
$507$	517.003	+	6570.69i	0.0452878	+	0.575571i
$508$	4465.77	+	880.347i	0.390032	+	0.0768879i
$509$	7918.98			0.689593			0.344796	−	0.938677i	$-0.387948\pi$
$509$	7918.98			0.689593			0.344796	+	0.938677i	$0.387948\pi$
$510$	−166.444	+	1704.91i	−0.0144515	+	0.148028i
$511$	12721.3			1.10129
$512$	−7418.41	−	8898.59i	−0.640333	−	0.768097i
$513$		−	816.219i		−	0.0702475i
$514$	−17553.4	−	1713.68i	−1.50631	−	0.147056i
$515$	−708.463			−0.0606187
$516$	163.336	+	32.1988i	0.0139350	+	0.00274704i
$517$		−	16252.9i		−	1.38260i
$518$	154.050	−	1577.95i	0.0130667	−	0.133844i
$519$	−12879.3			−1.08929
$520$	8949.39	+	2310.85i	0.754724	+	0.194880i
$521$	−9351.85			−0.786395			−0.393198	−	0.919454i	$-0.628631\pi$
$521$	−9351.85			−0.786395			−0.393198	+	0.919454i	$0.628631\pi$
$522$	−296.635	+	3038.46i	−0.0248723	+	0.254770i
$523$		−	10017.4i		−	0.837531i	−0.908094	−	0.418766i	$-0.862463\pi$
$523$		−	10017.4i		−	0.837531i	0.908094	−	0.418766i	$-0.137537\pi$
$524$	2721.90	−	13807.5i	0.226921	−	1.15111i
$525$	−2452.71			−0.203895
$526$	−1949.12	−	190.286i	−0.161569	−	0.0157735i
$527$			2231.08i			0.184416i
$528$	2620.03	−	6387.13i	0.215951	−	0.526447i
$529$	−6852.40			−0.563195
$530$	−738.274	+	7562.22i	−0.0605067	+	0.619777i
$531$	−836.239			−0.0683421
$532$	779.620	−	3954.81i	0.0635353	−	0.322298i
$533$	−110.930	−	2824.02i	−0.00901484	−	0.229497i
$534$	11142.2	+	1087.78i	0.902943	+	0.0881512i
$535$			11589.7i			0.936573i
$536$	−10508.3	−	3158.18i	−0.846806	−	0.254502i
$537$	−3763.22			−0.302412
$538$	2066.03	−	21162.5i	0.165563	−	1.69588i
$539$	−2344.13			−0.187326
$540$	−364.076	+	1846.86i	−0.0290136	+	0.147178i
$541$	−18747.9			−1.48990			−0.744951	−	0.667119i	$-0.767527\pi$
$541$	−18747.9			−1.48990			−0.744951	+	0.667119i	$0.767527\pi$
$542$	938.919	−	9617.45i	0.0744097	−	0.762186i
$543$	1743.90			0.137823
$544$	−3706.62	−	1960.87i	−0.292133	−	0.154543i
$545$	2545.38			0.200059
$546$	−6617.90	−	384.651i	−0.518718	−	0.0301493i
$547$			7024.44i			0.549074i	0.961577	+	0.274537i	$0.0885246\pi$
$547$			7024.44i			0.549074i	−0.961577	+	0.274537i	$0.911475\pi$
$548$	1235.26	−	6266.13i	0.0962910	−	0.488459i
$549$		−	4845.19i		−	0.376662i
$550$	−4964.94	−	484.710i	−0.384919	−	0.0375784i
$551$			3625.51i			0.280312i
$552$	1424.36	−	4739.29i	0.109828	−	0.365431i
$553$		−	5909.36i		−	0.454415i
$554$	1589.78	−	16284.3i	0.121919	−	1.24883i
$555$			879.258i			0.0672476i
$556$	3773.14	−	19140.2i	0.287800	−	1.45993i
$557$	11378.9			0.865604			0.432802	−	0.901489i	$-0.357525\pi$
$557$	11378.9			0.865604			0.432802	+	0.901489i	$0.357525\pi$
$558$	−238.219	+	2440.10i	−0.0180728	+	0.185121i
$559$	−12.7618	−	324.886i	−0.000965593	−	0.0245818i
$560$	−3528.09	+	8600.80i	−0.266231	+	0.649018i
$561$		−	2498.80i		−	0.188056i
$562$	−851.667	+	8723.71i	−0.0639242	+	0.654782i
$563$			15789.5i			1.18197i	0.806683	+	0.590985i	$0.201261\pi$
$563$			15789.5i			1.18197i	−0.806683	+	0.590985i	$0.798739\pi$
$564$	−10643.6	−	2098.19i	−0.794638	−	0.156649i
$565$	−3342.82			−0.248909
$566$	2253.01	−	23077.8i	0.167317	−	1.71384i
$567$		−	1350.07i		−	0.0999957i
$568$	2915.90	−	9702.13i	0.215403	−	0.716712i
$569$	13400.2			0.987284			0.493642	−	0.869665i	$-0.335665\pi$
$569$	13400.2			0.987284			0.493642	+	0.869665i	$0.335665\pi$
$570$	−217.209	+	2224.89i	−0.0159612	+	0.163492i
$571$			22295.1i			1.63401i	0.576630	+	0.817005i	$0.304367\pi$
$571$			22295.1i			1.63401i	−0.576630	+	0.817005i	$0.695633\pi$
$572$	−13320.4	−	2086.48i	−0.973695	−	0.152518i
$573$		−	9890.95i		−	0.721117i
$574$	2829.07	+	276.192i	0.205720	+	0.0200837i
$575$	−3575.93			−0.259350
$576$	−3844.52	−	2540.34i	−0.278105	−	0.183763i
$577$			7646.84i			0.551719i	0.961198	+	0.275860i	$0.0889625\pi$
$577$			7646.84i			0.551719i	−0.961198	+	0.275860i	$0.911038\pi$
$578$	12319.7	+	1202.73i	0.886560	+	0.0865519i
$579$	−1351.88			−0.0970332
$580$	1617.16	−	8203.45i	0.115774	−	0.587292i
$581$			3882.81i			0.277257i
$582$	11258.3	+	1099.11i	0.801841	+	0.0782811i
$583$		−	11083.6i		−	0.787367i
$584$	4970.79	−	16539.4i	0.352213	−	1.17192i
$585$	3673.52	−	144.299i	0.259626	−	0.0101983i
$586$	7303.01	+	712.968i	0.514820	+	0.0502601i
$587$	−7365.05			−0.517867			−0.258934	−	0.965895i	$-0.583371\pi$
$587$	−7365.05			−0.517867			−0.258934	+	0.965895i	$0.583371\pi$
$588$	−302.619	+	1535.11i	−0.0212241	+	0.107665i
$589$			2911.54i			0.203681i
$590$	2279.46	+	222.536i	0.159058	+	0.0155283i
$591$			12626.7i			0.878837i
$592$	−1991.34	−	816.857i	−0.138249	−	0.0567105i
$593$		−	16147.1i		−	1.11818i	−0.829106	−	0.559092i	$-0.811150\pi$
$593$		−	16147.1i		−	1.11818i	0.829106	−	0.559092i	$-0.188850\pi$
$594$	266.804	−	2732.90i	0.0184295	−	0.188775i
$595$			3364.84i			0.231841i
$596$	14217.5	+	2802.72i	0.977133	+	0.192624i
$597$			14732.1i			1.00996i
$598$	−9648.57	−	560.803i	−0.659798	−	0.0383494i
$599$	−6027.18			−0.411125			−0.205562	−	0.978644i	$-0.565902\pi$
$599$	−6027.18			−0.411125			−0.205562	+	0.978644i	$0.565902\pi$
$600$	−958.380	+	3188.83i	−0.0652095	+	0.216972i
$601$	−2117.99			−0.143751			−0.0718757	−	0.997414i	$-0.522899\pi$
$601$	−2117.99			−0.143751			−0.0718757	+	0.997414i	$0.522899\pi$
$602$	325.467	+	31.7742i	0.0220349	+	0.00215120i
$603$	−4364.32			−0.294741
$604$	−528.201	+	2679.42i	−0.0355831	+	0.180504i
$605$	332.395			0.0223369
$606$	−7049.04	−	688.174i	−0.472521	−	0.0461306i
$607$	11132.7			0.744418			0.372209	−	0.928149i	$-0.378601\pi$
$607$	11132.7			0.744418			0.372209	+	0.928149i	$0.378601\pi$
$608$	−4837.12	−	2558.92i	−0.322650	−	0.170687i
$609$			5996.78i			0.399018i
$610$	−1289.38	+	13207.3i	−0.0855827	+	0.876633i
$611$	831.605	+	21170.7i	0.0550624	+	1.40176i
$612$	−1636.40	−	322.586i	−0.108084	−	0.0213068i
$613$	−17390.2			−1.14581			−0.572906	−	0.819621i	$-0.694184\pi$
$613$	−17390.2			−1.14581			−0.572906	+	0.819621i	$0.694184\pi$
$614$	6270.08	+	612.127i	0.412117	+	0.0402336i
$615$	−1576.40			−0.103361
$616$	3903.10	−	12986.8i	0.255293	−	0.849439i
$617$			17583.9i			1.14733i	0.819090	+	0.573665i	$0.194479\pi$
$617$			17583.9i			1.14733i	−0.819090	+	0.573665i	$0.805521\pi$
$618$	67.0244	−	686.538i	0.00436265	−	0.0446871i
$619$	−9088.88			−0.590166			−0.295083	−	0.955472i	$-0.595347\pi$
$619$	−9088.88			−0.590166			−0.295083	+	0.955472i	$0.595347\pi$
$620$	1298.70	−	6587.96i	0.0841241	−	0.426740i
$621$		−	1968.34i		−	0.127193i
$622$	−17607.4	−	1718.95i	−1.13503	−	0.110809i
$623$	21990.6			1.41418
$624$	−3086.00	+	8453.81i	−0.197979	+	0.542345i
$625$	−7087.49			−0.453599
$626$	22750.4	+	2221.04i	1.45254	+	0.141806i
$627$		−	3260.92i		−	0.207701i
$628$	−4027.28	+	20429.4i	−0.255901	+	1.29812i
$629$	−779.059			−0.0493849
$630$	−359.274	+	3680.09i	−0.0227204	+	0.232727i
$631$		−	8004.69i		−	0.505011i	−0.967596	−	0.252505i	$-0.918745\pi$
$631$		−	8004.69i		−	0.505011i	0.967596	−	0.252505i	$-0.0812545\pi$
$632$	−7682.92	−	2309.05i	−0.483560	−	0.145331i
$633$	11912.5			0.747990
$634$	1711.21	+	167.060i	0.107194	+	0.0104650i
$635$	−4958.43			−0.309873
$636$	−7258.34	−	1430.85i	−0.452534	−	0.0892090i
$637$	3053.42	−	119.941i	0.189923	−	0.00746034i
$638$	−1185.10	+	12139.1i	−0.0735400	+	0.753278i
$639$		−	4029.51i		−	0.249460i
$640$	9803.55	+	7947.68i	0.605499	+	0.490875i
$641$	31376.8			1.93340			0.966699	−	0.255917i	$-0.0823775\pi$
$641$	31376.8			1.93340			0.966699	+	0.255917i	$0.0823775\pi$
$642$	−11231.0	−	1096.45i	−0.690426	−	0.0674039i
$643$	24518.9			1.50378			0.751891	−	0.659288i	$-0.229142\pi$
$643$	24518.9			1.50378			0.751891	+	0.659288i	$0.229142\pi$
$644$	1880.07	−	9537.13i	0.115039	−	0.583564i
$645$	−181.356			−0.0110711
$646$	−1971.35	−	192.456i	−0.120064	−	0.0117215i
$647$	−19032.6			−1.15649			−0.578243	−	0.815864i	$-0.696262\pi$
$647$	−19032.6			−1.15649			−0.578243	+	0.815864i	$0.696262\pi$
$648$	−1755.26	−	527.531i	−0.106409	−	0.0319805i
$649$	−3340.90			−0.202067
$650$	6492.04	+	377.336i	0.391752	+	0.0227697i
$651$			4815.84i			0.289935i
$652$	−2202.24	−	434.132i	−0.132280	−	0.0260766i
$653$		−	1630.31i		−	0.0977012i	−0.998806	−	0.0488506i	$-0.984444\pi$
$653$		−	1630.31i		−	0.0977012i	0.998806	−	0.0488506i	$-0.0155558\pi$
$654$	−240.806	+	2466.61i	−0.0143980	+	0.147480i
$655$			15330.7i			0.914536i
$656$	1464.53	−	3570.23i	0.0871648	−	0.212491i
$657$		−	6869.17i		−	0.407903i
$658$	−21208.6	−	2070.52i	−1.25653	−	0.122671i
$659$			6216.87i			0.367489i	0.982974	+	0.183744i	$0.0588218\pi$
$659$			6216.87i			0.367489i	−0.982974	+	0.183744i	$0.941178\pi$
$660$	−1454.54	+	7378.49i	−0.0857845	+	0.435162i
$661$	17029.9			1.00210			0.501050	−	0.865418i	$-0.332947\pi$
$661$	17029.9			1.00210			0.501050	+	0.865418i	$0.332947\pi$
$662$	22581.3	+	2204.54i	1.32575	+	0.129429i
$663$	127.855	+	3254.89i	0.00748940	+	0.190663i
$664$	5048.15	+	1517.19i	0.295040	+	0.0886720i
$665$			4391.10i			0.256059i
$666$	−852.047	−	83.1825i	−0.0495738	−	0.00483972i
$667$			8743.01i			0.507542i
$668$	−688.704	+	3493.62i	−0.0398903	+	0.202353i
$669$	−1454.15			−0.0840368
$670$	11896.5	+	1161.41i	0.685972	+	0.0669692i
$671$		−	19357.2i		−	1.11368i
$672$	−8000.85	−	4232.59i	−0.459285	−	0.242970i
$673$	−8854.72			−0.507168			−0.253584	−	0.967313i	$-0.581609\pi$
$673$	−8854.72			−0.507168			−0.253584	+	0.967313i	$0.581609\pi$
$674$	29193.7	+	2850.08i	1.66840	+	0.162880i
$675$			1324.39i			0.0755199i
$676$	17457.6	+	2036.26i	0.993266	+	0.115854i
$677$		−	25869.2i		−	1.46859i	−0.678830	−	0.734295i	$-0.737513\pi$
$677$		−	25869.2i		−	1.46859i	0.678830	−	0.734295i	$-0.262487\pi$
$678$	316.249	−	3239.37i	0.0179137	−	0.183492i
$679$	22219.7			1.25584
$680$	4374.73	+	1314.79i	0.246710	+	0.0741470i
$681$			18465.1i			1.03904i
$682$	−951.720	+	9748.57i	−0.0534358	+	0.547349i
$683$	−14554.1			−0.815370			−0.407685	−	0.913123i	$-0.633664\pi$
$683$	−14554.1			−0.815370			−0.407685	+	0.913123i	$0.633664\pi$
$684$	−2135.49	−	420.973i	−0.119375	−	0.0235326i
$685$			6957.41i			0.388071i
$686$	−1869.78	+	19152.4i	−0.104065	+	1.06595i
$687$		−	15088.6i		−	0.837942i
$688$	168.485	−	410.732i	0.00933636	−	0.0227602i
$689$	567.109	+	14437.3i	0.0313572	+	0.798281i
$690$	−523.805	+	5365.39i	−0.0288999	+	0.296024i
$691$	−31889.4			−1.75561			−0.877807	−	0.479015i	$-0.840994\pi$
$691$	−31889.4			−1.75561			−0.877807	+	0.479015i	$0.840994\pi$
$692$	−6642.65	+	33696.4i	−0.364907	+	1.85108i
$693$		−	5393.73i		−	0.295658i
$694$	571.179	−	5850.65i	0.0312416	−	0.320011i
$695$			21251.7i			1.15989i
$696$	7796.57	+	2343.20i	0.424610	+	0.127613i
$697$		−	1396.76i		−	0.0759054i
$698$	−16460.7	−	1607.00i	−0.892617	−	0.0871432i
$699$		−	4690.72i		−	0.253819i
$700$	−1265.01	+	6417.05i	−0.0683040	+	0.346488i
$701$			24149.2i			1.30115i	0.759443	+	0.650574i	$0.225471\pi$
$701$			24149.2i			1.30115i	−0.759443	+	0.650574i	$0.774529\pi$
$702$	−207.701	+	3573.48i	−0.0111669	+	0.192126i
$703$	−1016.67			−0.0545439
$704$	−15359.4	−	10149.1i	−0.822273	−	0.543334i
$705$	11817.8			0.631324
$706$	−287.579	+	2945.70i	−0.0153303	+	0.157030i
$707$	−13912.2			−0.740057
$708$	−431.298	+	2187.86i	−0.0228943	+	0.116137i
$709$	10731.6			0.568454			0.284227	−	0.958757i	$-0.408263\pi$
$709$	10731.6			0.568454			0.284227	+	0.958757i	$0.408263\pi$
$710$	−1072.32	+	10983.9i	−0.0566807	+	0.580587i
$711$	−3190.89			−0.168309
$712$	8592.68	−	28590.5i	0.452281	−	1.50488i
$713$			7021.27i			0.368792i
$714$	−3260.71	−	318.332i	−0.170909	−	0.0166853i
$715$	14676.2	−	576.496i	0.767637	−	0.0301535i
$716$	−1940.92	+	9845.78i	−0.101307	+	0.513902i
$717$	20990.1			1.09329
$718$	−2478.40	+	25386.5i	−0.128820	+	1.31952i
$719$	−21369.6			−1.10842			−0.554208	−	0.832378i	$-0.686979\pi$
$719$	−21369.6			−1.10842			−0.554208	+	0.832378i	$0.686979\pi$
$720$	4644.20	+	1905.07i	0.240387	+	0.0986082i
$721$		−	1354.97i		−	0.0699884i
$722$	16735.8	+	1633.86i	0.862662	+	0.0842188i
$723$	11948.0			0.614596
$724$	899.432	−	4562.59i	0.0461701	−	0.234209i
$725$		−	5882.73i		−	0.301351i
$726$	−31.4464	+	322.109i	−0.00160755	+	0.0164663i
$727$	6216.16			0.317118			0.158559	−	0.987350i	$-0.449315\pi$
$727$	6216.16			0.317118			0.158559	+	0.987350i	$0.449315\pi$
$728$	−4419.61	+	17116.1i	−0.225002	+	0.871381i
$729$	−729.000			−0.0370370
$730$	−1827.99	+	18724.3i	−0.0926810	+	0.949341i
$731$		−	160.689i		−	0.00813035i
$732$	−12676.5	−	2498.95i	−0.640080	−	0.126180i
$733$	18224.5			0.918333			0.459166	−	0.888350i	$-0.348148\pi$
$733$	18224.5			0.918333			0.459166	+	0.888350i	$0.348148\pi$
$734$	699.589	+	68.2985i	0.0351802	+	0.00343453i
$735$		−	1704.46i		−	0.0855373i
$736$	−11664.9	−	6170.91i	−0.584201	−	0.309053i
$737$	−17436.1			−0.871462
$738$	149.136	−	1527.62i	0.00743873	−	0.0761957i
$739$	2355.87			0.117269			0.0586346	−	0.998280i	$-0.481325\pi$
$739$	2355.87			0.117269			0.0586346	+	0.998280i	$0.481325\pi$
$740$	2300.42	+	453.486i	0.114277	+	0.0225277i
$741$	166.850	+	4247.61i	0.00827177	+	0.210580i
$742$	−14463.1	−	1411.98i	−0.715575	−	0.0698591i
$743$		−	16897.0i		−	0.834306i	−0.908836	−	0.417153i	$-0.863028\pi$
$743$		−	16897.0i		−	0.834306i	0.908836	−	0.417153i	$-0.136972\pi$
$744$	6261.21	+	1881.76i	0.308531	+	0.0927268i
$745$	−15786.0			−0.776312
$746$	1582.18	−	16206.4i	0.0776511	−	0.795389i
$747$	2096.61			0.102692
$748$	−6537.65	−	1288.78i	−0.319572	−	0.0629980i
$749$	−22165.8			−1.08134
$750$	1250.58	−	12809.8i	0.0608864	−	0.623666i
$751$	6055.22			0.294218			0.147109	−	0.989120i	$-0.453003\pi$
$751$	6055.22			0.294218			0.147109	+	0.989120i	$0.453003\pi$
$752$	−10979.1	+	26764.8i	−0.532401	+	1.29789i
$753$	3860.91			0.186852
$754$	922.572	−	15872.8i	0.0445598	−	0.766649i
$755$		−	2975.02i		−	0.143407i
$756$	−3532.21	−	696.311i	−0.169927	−	0.0334981i
$757$			14120.5i			0.677965i	0.940793	+	0.338982i	$0.110083\pi$
$757$			14120.5i			0.677965i	−0.940793	+	0.338982i	$0.889917\pi$
$758$	19217.3	+	1876.12i	0.920848	+	0.0898993i
$759$		−	7863.80i		−	0.376071i
$760$	5708.99	+	1715.80i	0.272483	+	0.0818927i
$761$			5880.45i			0.280113i	0.990143	+	0.140057i	$0.0447285\pi$
$761$			5880.45i			0.280113i	−0.990143	+	0.140057i	$0.955272\pi$
$762$	469.094	−	4804.98i	0.0223012	−	0.228433i
$763$			4868.15i			0.230982i
$764$	−25877.8	−	5101.35i	−1.22543	−	0.241571i
$765$	1816.92			0.0858706
$766$	−433.557	+	4440.97i	−0.0204505	+	0.209476i
$767$	4351.79	−	170.942i	0.204868	−	0.00804741i
$768$	−8629.19	+	8748.26i	−0.405441	+	0.411036i
$769$		−	36398.3i		−	1.70683i	−0.521229	−	0.853417i	$-0.674526\pi$
$769$		−	36398.3i		−	1.70683i	0.521229	−	0.853417i	$-0.325474\pi$
$770$	−1435.35	+	14702.5i	−0.0671774	+	0.688105i
$771$			18706.7i			0.873806i
$772$	−697.246	+	3536.95i	−0.0325057	+	0.164893i
$773$	−7579.44			−0.352669

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.81504 - 0.274823i) q^{2} +3.00000i q^{3} +(7.84894 + 1.54728i) q^{4} -8.71484 q^{5} +(0.824470 - 8.44513i) q^{6} -16.6675i q^{7} +(-21.6699 - 6.51273i) q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+(-2.81504 - 0.274823i) q^{2} +3.00000i q^{3} +(7.84894 + 1.54728i) q^{4} -8.71484 q^{5} +(0.824470 - 8.44513i) q^{6} -16.6675i q^{7} +(-21.6699 - 6.51273i) q^{8} -9.00000 q^{9} +(24.5327 + 2.39504i) q^{10} -35.9563 q^{11} +(-4.64184 + 23.5468i) q^{12} +(46.8360 - 1.83976i) q^{13} +(-4.58062 + 46.9198i) q^{14} -26.1445i q^{15} +(59.2119 + 24.2890i) q^{16} +23.1651 q^{17} +(25.3354 + 2.47341i) q^{18} +30.2303 q^{19} +(-68.4023 - 13.4843i) q^{20} +50.0026 q^{21} +(101.219 + 9.88164i) q^{22} +72.9013 q^{23} +(19.5382 - 65.0097i) q^{24} -49.0516 q^{25} +(-132.351 - 7.69263i) q^{26} -27.0000i q^{27} +(25.7893 - 130.822i) q^{28} +119.929i q^{29} +(-7.18512 + 73.5980i) q^{30} +96.3119i q^{31} +(-160.009 - 84.6474i) q^{32} -107.869i q^{33} +(-65.2108 - 6.36632i) q^{34} +145.255i q^{35} +(-70.6405 - 13.9255i) q^{36} -33.6307 q^{37} +(-85.0997 - 8.30800i) q^{38} +(5.51929 + 140.508i) q^{39} +(188.850 + 56.7574i) q^{40} -60.2958i q^{41} +(-140.759 - 13.7419i) q^{42} -6.93666i q^{43} +(-282.219 - 55.6345i) q^{44} +78.4335 q^{45} +(-205.220 - 20.0350i) q^{46} +452.018i q^{47} +(-72.8670 + 177.636i) q^{48} +65.1938 q^{49} +(138.082 + 13.4805i) q^{50} +69.4954i q^{51} +(370.460 + 58.0283i) q^{52} +308.251i q^{53} +(-7.42023 + 76.0062i) q^{54} +313.354 q^{55} +(-108.551 + 361.183i) q^{56} +90.6910i q^{57} +(32.9594 - 337.607i) q^{58} +92.9154 q^{59} +(40.4529 - 205.207i) q^{60} +538.354i q^{61} +(26.4688 - 271.122i) q^{62} +150.008i q^{63} +(427.169 + 282.260i) q^{64} +(-408.169 + 16.0332i) q^{65} +(-29.6449 + 303.656i) q^{66} +484.925 q^{67} +(181.822 + 35.8429i) q^{68} +218.704i q^{69} +(39.9194 - 408.898i) q^{70} +447.724i q^{71} +(195.029 + 58.6146i) q^{72} +763.242i q^{73} +(94.6719 + 9.24250i) q^{74} -147.155i q^{75} +(237.276 + 46.7748i) q^{76} +599.303i q^{77} +(23.0779 - 397.053i) q^{78} +354.543 q^{79} +(-516.022 - 211.675i) q^{80} +81.0000 q^{81} +(-16.5707 + 169.735i) q^{82} -232.957 q^{83} +(392.467 + 77.3679i) q^{84} -201.880 q^{85} +(-1.90636 + 19.5270i) q^{86} -359.788 q^{87} +(779.170 + 234.174i) q^{88} +1319.37i q^{89} +(-220.794 - 21.5554i) q^{90} +(-30.6643 - 780.641i) q^{91} +(572.198 + 112.799i) q^{92} -288.936 q^{93} +(124.225 - 1272.45i) q^{94} -263.453 q^{95} +(253.942 - 480.026i) q^{96} +1333.11i q^{97} +(-183.523 - 17.9168i) q^{98} +323.607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 756 q^{9}+O(q^{10}) \) 84 * q - 756 * q^9	\( 84 q - 756 q^{9} - 36 q^{10} + 12 q^{12} - 208 q^{14} - 148 q^{16} - 104 q^{17} + 620 q^{22} + 2188 q^{25} + 444 q^{26} - 204 q^{30} - 40 q^{38} - 1924 q^{40} + 192 q^{42} + 624 q^{48} - 3396 q^{49} - 1292 q^{52} - 1616 q^{55} + 608 q^{56} - 2120 q^{62} - 2856 q^{64} + 696 q^{65} - 396 q^{66} - 2536 q^{68} - 3936 q^{74} - 156 q^{78} + 3160 q^{79} + 6804 q^{81} + 4276 q^{82} - 2088 q^{87} + 1780 q^{88} + 324 q^{90} + 4792 q^{92} - 860 q^{94} + 2480 q^{95}+O(q^{100}) \) 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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