LMFDB - Embedded newform 120.4.m.b.59.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(59,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("120.59");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.19
Character	$\chi$	$=$	120.59
Dual form			120.4.m.b.59.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65669 + 2.29246i) q^{2} +(-4.82386 - 1.93142i) q^{3} +(-2.51074 - 7.59580i) q^{4} +(-7.20740 + 8.54713i) q^{5} +(12.4193 - 7.85874i) q^{6} -30.0545 q^{7} +(21.5726 + 6.82812i) q^{8} +(19.5392 + 18.6338i) q^{9} +O(q^{10})$	\(q+(-1.65669 + 2.29246i) q^{2} +(-4.82386 - 1.93142i) q^{3} +(-2.51074 - 7.59580i) q^{4} +(-7.20740 + 8.54713i) q^{5} +(12.4193 - 7.85874i) q^{6} -30.0545 q^{7} +(21.5726 + 6.82812i) q^{8} +(19.5392 + 18.6338i) q^{9} +(-7.65352 - 30.6826i) q^{10} -35.6161i q^{11} +(-2.55919 + 41.4904i) q^{12} +58.6475 q^{13} +(49.7911 - 68.8988i) q^{14} +(51.2756 - 27.3096i) q^{15} +(-51.3923 + 38.1422i) q^{16} -14.3949 q^{17} +(-75.0877 + 13.9225i) q^{18} +106.012 q^{19} +(83.0182 + 33.2863i) q^{20} +(144.979 + 58.0479i) q^{21} +(81.6485 + 59.0049i) q^{22} +47.7072i q^{23} +(-90.8752 - 74.6036i) q^{24} +(-21.1068 - 123.205i) q^{25} +(-97.1608 + 134.447i) q^{26} +(-58.2649 - 127.625i) q^{27} +(75.4593 + 228.288i) q^{28} +49.5925 q^{29} +(-22.3415 + 162.791i) q^{30} +181.017i q^{31} +(-2.29829 - 181.005i) q^{32} +(-68.7896 + 171.807i) q^{33} +(23.8480 - 32.9998i) q^{34} +(216.615 - 256.880i) q^{35} +(92.4805 - 195.201i) q^{36} +113.746 q^{37} +(-175.629 + 243.028i) q^{38} +(-282.907 - 113.273i) q^{39} +(-213.843 + 135.171i) q^{40} +53.6178i q^{41} +(-373.258 + 236.191i) q^{42} -490.109i q^{43} +(-270.533 + 89.4229i) q^{44} +(-300.092 + 32.7033i) q^{45} +(-109.367 - 79.0361i) q^{46} -441.575i q^{47} +(321.578 - 84.7326i) q^{48} +560.275 q^{49} +(317.410 + 155.726i) q^{50} +(69.4392 + 27.8027i) q^{51} +(-147.249 - 445.475i) q^{52} -65.6784i q^{53} +(389.103 + 77.8658i) q^{54} +(304.415 + 256.699i) q^{55} +(-648.354 - 205.216i) q^{56} +(-511.387 - 204.754i) q^{57} +(-82.1595 + 113.689i) q^{58} -406.047i q^{59} +(-336.178 - 320.911i) q^{60} +213.568i q^{61} +(-414.975 - 299.890i) q^{62} +(-587.243 - 560.030i) q^{63} +(418.754 + 294.600i) q^{64} +(-422.696 + 501.268i) q^{65} +(-279.898 - 442.329i) q^{66} +825.615i q^{67} +(36.1420 + 109.341i) q^{68} +(92.1426 - 230.133i) q^{69} +(230.023 + 922.152i) q^{70} +157.626 q^{71} +(294.278 + 535.395i) q^{72} +242.743i q^{73} +(-188.442 + 260.758i) q^{74} +(-136.144 + 635.090i) q^{75} +(-266.169 - 805.246i) q^{76} +1070.43i q^{77} +(728.364 - 460.895i) q^{78} +107.503i q^{79} +(44.3984 - 714.163i) q^{80} +(34.5637 + 728.180i) q^{81} +(-122.917 - 88.8281i) q^{82} +1158.62 q^{83} +(76.9153 - 1246.97i) q^{84} +(103.750 - 123.035i) q^{85} +(1123.56 + 811.960i) q^{86} +(-239.227 - 95.7839i) q^{87} +(243.191 - 768.331i) q^{88} -750.147i q^{89} +(422.190 - 742.129i) q^{90} -1762.62 q^{91} +(362.374 - 119.781i) q^{92} +(349.621 - 873.203i) q^{93} +(1012.29 + 731.554i) q^{94} +(-764.070 + 906.098i) q^{95} +(-338.509 + 877.580i) q^{96} -83.2231i q^{97} +(-928.203 + 1284.41i) q^{98} +(663.663 - 695.911i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9}+O(q^{10}) $ 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9	$ 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54} - 2064 q^{60} + 2176 q^{64} - 176 q^{66} + 672 q^{70} - 1600 q^{75} + 2304 q^{76} - 2304 q^{81} - 736 q^{84} - 1432 q^{90} - 2752 q^{91} + 4496 q^{94} + 640 q^{96} + 256 q^{99}+O(q^{100}) $ 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9 - 72 * q^10 - 128 * q^16 + 672 * q^19 - 416 * q^24 + 496 * q^25 - 248 * q^30 + 240 * q^34 - 608 * q^36 - 1344 * q^40 + 336 * q^46 + 3520 * q^49 - 544 * q^51 - 952 * q^54 - 2064 * q^60 + 2176 * q^64 - 176 * q^66 + 672 * q^70 - 1600 * q^75 + 2304 * q^76 - 2304 * q^81 - 736 * q^84 - 1432 * q^90 - 2752 * q^91 + 4496 * q^94 + 640 * q^96 + 256 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−1.65669	+	2.29246i	−0.585729	+	0.810507i
$2$	−1.65669	+	2.29246i	−0.585729	+	0.810507i
$3$	−4.82386	−	1.93142i	−0.928352	−	0.371702i
$3$	−4.82386	−	1.93142i	−0.928352	−	0.371702i
$4$	−2.51074	−	7.59580i	−0.313843	−	0.949475i
$5$	−7.20740	+	8.54713i	−0.644649	+	0.764478i
$5$	−7.20740	+	8.54713i	−0.644649	+	0.764478i
$6$	12.4193	−	7.85874i	0.845030	−	0.534719i
$7$	−30.0545			−1.62279			−0.811396	−	0.584497i	$-0.801292\pi$
$7$	−30.0545			−1.62279			−0.811396	+	0.584497i	$0.801292\pi$
$8$	21.5726	+	6.82812i	0.953383	+	0.301763i
$9$	19.5392	+	18.6338i	0.723676	+	0.690140i
$10$	−7.65352	−	30.6826i	−0.242025	−	0.970270i
$11$		−	35.6161i		−	0.976241i	−0.872776	−	0.488121i	$-0.837683\pi$
$11$		−	35.6161i		−	0.976241i	0.872776	−	0.488121i	$-0.162317\pi$
$12$	−2.55919	+	41.4904i	−0.0615646	+	0.998103i
$13$	58.6475			1.25122			0.625611	−	0.780135i	$-0.284850\pi$
$13$	58.6475			1.25122			0.625611	+	0.780135i	$0.284850\pi$
$14$	49.7911	−	68.8988i	0.950517	−	1.31528i
$15$	51.2756	−	27.3096i	0.882620	−	0.470088i
$16$	−51.3923	+	38.1422i	−0.803005	+	0.595972i
$17$	−14.3949			−0.205370			−0.102685	−	0.994714i	$-0.532743\pi$
$17$	−14.3949			−0.205370			−0.102685	+	0.994714i	$0.532743\pi$
$18$	−75.0877	+	13.9225i	−0.983241	+	0.182309i
$19$	106.012			1.28004			0.640021	−	0.768357i	$-0.278925\pi$
$19$	106.012			1.28004			0.640021	+	0.768357i	$0.278925\pi$
$20$	83.0182	+	33.2863i	0.928172	+	0.372152i
$21$	144.979	+	58.0479i	1.50652	+	0.603195i
$22$	81.6485	+	59.0049i	0.791250	+	0.571813i
$23$			47.7072i			0.432506i	0.976337	+	0.216253i	$0.0693836\pi$
$23$			47.7072i			0.432506i	−0.976337	+	0.216253i	$0.930616\pi$
$24$	−90.8752	−	74.6036i	−0.772909	−	0.634516i
$25$	−21.1068	−	123.205i	−0.168855	−	0.985641i
$26$	−97.1608	+	134.447i	−0.732877	+	1.01412i
$27$	−58.2649	−	127.625i	−0.415299	−	0.909685i
$28$	75.4593	+	228.288i	0.509302	+	1.54080i
$29$	49.5925			0.317555			0.158778	−	0.987314i	$-0.449245\pi$
$29$	49.5925			0.317555			0.158778	+	0.987314i	$0.449245\pi$
$30$	−22.3415	+	162.791i	−0.135966	+	0.990713i
$31$			181.017i			1.04876i	0.851483	+	0.524382i	$0.175704\pi$
$31$			181.017i			1.04876i	−0.851483	+	0.524382i	$0.824296\pi$
$32$	−2.29829	−	181.005i	−0.0126964	−	0.999919i
$33$	−68.7896	+	171.807i	−0.362871	+	0.906296i
$34$	23.8480	−	32.9998i	0.120291	−	0.166454i
$35$	216.615	−	256.880i	1.04613	−	1.24059i
$36$	92.4805	−	195.201i	0.428150	−	0.903708i
$37$	113.746			0.505397			0.252699	−	0.967545i	$-0.418682\pi$
$37$	113.746			0.505397			0.252699	+	0.967545i	$0.418682\pi$
$38$	−175.629	+	243.028i	−0.749758	+	1.03748i
$39$	−282.907	−	113.273i	−1.16158	−	0.465082i
$40$	−213.843	+	135.171i	−0.845289	+	0.534310i
$41$			53.6178i			0.204236i	0.994772	+	0.102118i	$0.0325620\pi$
$41$			53.6178i			0.204236i	−0.994772	+	0.102118i	$0.967438\pi$
$42$	−373.258	+	236.191i	−1.37131	+	0.867739i
$43$		−	490.109i		−	1.73816i	−0.494669	−	0.869081i	$-0.664711\pi$
$43$		−	490.109i		−	1.73816i	0.494669	−	0.869081i	$-0.335289\pi$
$44$	−270.533	+	89.4229i	−0.926917	+	0.306387i
$45$	−300.092	+	32.7033i	−0.994114	+	0.108336i
$46$	−109.367	−	79.0361i	−0.350549	−	0.253331i
$47$		−	441.575i		−	1.37043i	−0.728339	−	0.685217i	$-0.759707\pi$
$47$		−	441.575i		−	1.37043i	0.728339	−	0.685217i	$-0.240293\pi$
$48$	321.578	−	84.7326i	0.966995	−	0.254794i
$49$	560.275			1.63346
$50$	317.410	+	155.726i	0.897772	+	0.440461i
$51$	69.4392	+	27.8027i	0.190655	+	0.0763363i
$52$	−147.249	−	445.475i	−0.392688	−	1.18800i
$53$		−	65.6784i		−	0.170219i	−0.996372	−	0.0851097i	$-0.972876\pi$
$53$		−	65.6784i		−	0.170219i	0.996372	−	0.0851097i	$-0.0271241\pi$
$54$	389.103	+	77.8658i	0.980559	+	0.196226i
$55$	304.415	+	256.699i	0.746316	+	0.629333i
$56$	−648.354	−	205.216i	−1.54714	−	0.489699i
$57$	−511.387	−	204.754i	−1.18833	−	0.475794i
$58$	−82.1595	+	113.689i	−0.186001	+	0.257381i
$59$		−	406.047i		−	0.895979i	−0.894039	−	0.447989i	$-0.852140\pi$
$59$		−	406.047i		−	0.895979i	0.894039	−	0.447989i	$-0.147860\pi$
$60$	−336.178	−	320.911i	−0.723341	−	0.690491i
$61$			213.568i			0.448271i	0.974558	+	0.224135i	$0.0719558\pi$
$61$			213.568i			0.448271i	−0.974558	+	0.224135i	$0.928044\pi$
$62$	−414.975	−	299.890i	−0.850031	−	0.614292i
$63$	−587.243	−	560.030i	−1.17438	−	1.11995i
$64$	418.754	+	294.600i	0.817878	+	0.575391i
$65$	−422.696	+	501.268i	−0.806600	+	0.956533i
$66$	−279.898	−	442.329i	−0.522015	−	0.824953i
$67$			825.615i			1.50545i	0.658337	+	0.752723i	$0.271260\pi$
$67$			825.615i			1.50545i	−0.658337	+	0.752723i	$0.728740\pi$
$68$	36.1420	+	109.341i	0.0644539	+	0.194993i
$69$	92.1426	−	230.133i	0.160763	−	0.401518i
$70$	230.023	+	922.152i	0.392757	+	1.57455i
$71$	157.626			0.263476			0.131738	−	0.991285i	$-0.457944\pi$
$71$	157.626			0.263476			0.131738	+	0.991285i	$0.457944\pi$
$72$	294.278	+	535.395i	0.481681	+	0.876347i
$73$			242.743i			0.389190i	0.980884	+	0.194595i	$0.0623393\pi$
$73$			242.743i			0.389190i	−0.980884	+	0.194595i	$0.937661\pi$
$74$	−188.442	+	260.758i	−0.296026	+	0.409628i
$75$	−136.144	+	635.090i	−0.209608	+	0.977786i
$76$	−266.169	−	805.246i	−0.401733	−	1.21537i
$77$			1070.43i			1.58424i
$78$	728.364	−	460.895i	1.05732	−	0.669053i
$79$			107.503i			0.153101i	0.997066	+	0.0765506i	$0.0243907\pi$
$79$			107.503i			0.153101i	−0.997066	+	0.0765506i	$0.975609\pi$
$80$	44.3984	−	714.163i	0.0620486	−	0.998073i
$81$	34.5637	+	728.180i	0.0474125	+	0.998875i
$82$	−122.917	−	88.8281i	−0.165535	−	0.119627i
$83$	1158.62			1.53223			0.766113	−	0.642706i	$-0.222188\pi$
$83$	1158.62			1.53223			0.766113	+	0.642706i	$0.222188\pi$
$84$	76.9153	−	1246.97i	0.0999066	−	1.61971i
$85$	103.750	−	123.035i	0.132391	−	0.157001i
$86$	1123.56	+	811.960i	1.40879	+	1.01809i
$87$	−239.227	−	95.7839i	−0.294803	−	0.118036i
$88$	243.191	−	768.331i	0.294593	−	0.930732i
$89$		−	750.147i		−	0.893431i	−0.894676	−	0.446716i	$-0.852594\pi$
$89$		−	750.147i		−	0.893431i	0.894676	−	0.446716i	$-0.147406\pi$
$90$	422.190	−	742.129i	0.494475	−	0.869192i
$91$	−1762.62			−2.03047
$92$	362.374	−	119.781i	0.410654	−	0.135739i
$93$	349.621	−	873.203i	0.389828	−	0.973623i
$94$	1012.29	+	731.554i	1.11075	+	0.802703i
$95$	−764.070	+	906.098i	−0.825179	+	0.978565i
$96$	−338.509	+	877.580i	−0.359885	+	0.932997i
$97$		−	83.2231i		−	0.0871136i	−0.999051	−	0.0435568i	$-0.986131\pi$
$97$		−	83.2231i		−	0.0871136i	0.999051	−	0.0435568i	$-0.0138690\pi$
$98$	−928.203	+	1284.41i	−0.956762	+	1.32393i
$99$	663.663	−	695.911i	0.673744	−	0.706482i
$100$	−882.847	+	469.660i	−0.882847	+	0.469660i
$101$	978.565			0.964068			0.482034	−	0.876153i	$-0.339898\pi$
$101$	978.565			0.964068			0.482034	+	0.876153i	$0.339898\pi$
$102$	−178.776	+	113.126i	−0.173544	+	0.109815i
$103$	484.228			0.463228			0.231614	−	0.972808i	$-0.425599\pi$
$103$	484.228			0.463228			0.231614	+	0.972808i	$0.425599\pi$
$104$	1265.18	+	400.452i	1.19289	+	0.377573i
$105$	−1541.06	+	820.779i	−1.43231	+	0.762855i
$106$	150.565	+	108.809i	0.137964	+	0.0997024i
$107$	912.615			0.824541			0.412270	−	0.911062i	$-0.364736\pi$
$107$	912.615			0.824541			0.412270	+	0.911062i	$0.364736\pi$
$108$	−823.127	+	763.003i	−0.733384	+	0.679815i
$109$		−	1290.42i		−	1.13395i	−0.823736	−	0.566973i	$-0.808114\pi$
$109$		−	1290.42i		−	1.13395i	0.823736	−	0.566973i	$-0.191886\pi$
$110$	−1092.80	+	272.588i	−0.947218	+	0.236275i
$111$	−548.694	−	219.691i	−0.469187	−	0.187857i
$112$	1544.57	−	1146.35i	1.30311	−	0.967139i
$113$	24.0806			0.0200470			0.0100235	−	0.999950i	$-0.496809\pi$
$113$	24.0806			0.0200470			0.0100235	+	0.999950i	$0.496809\pi$
$114$	1316.60	−	833.120i	1.08167	−	0.684464i
$115$	−407.760	−	343.845i	−0.330642	−	0.278815i
$116$	−124.514	−	376.695i	−0.0996625	−	0.301511i
$117$	1145.93	+	1092.83i	0.905479	+	0.863519i
$118$	930.845	+	672.694i	0.726197	+	0.524801i
$119$	432.633			0.333273
$120$	1292.62	−	239.024i	0.983330	−	0.181832i
$121$	62.4941			0.0469527
$122$	−489.595	−	353.816i	−0.363327	−	0.262565i
$123$	103.558	−	258.645i	0.0759150	−	0.189603i
$124$	1374.97	−	454.489i	0.995775	−	0.329147i
$125$	1205.18	+	707.585i	0.862353	+	0.506307i
$126$	2256.73	−	418.434i	1.59560	−	0.295849i
$127$	−1018.44			−0.711593			−0.355797	−	0.934563i	$-0.615790\pi$
$127$	−1018.44			−0.711593			−0.355797	+	0.934563i	$0.615790\pi$
$128$	−1369.11	+	471.914i	−0.945414	+	0.325873i
$129$	−946.607	+	2364.22i	−0.646078	+	1.61363i
$130$	−448.860	−	1799.46i	−0.302828	−	1.21402i
$131$		−	422.320i		−	0.281666i	−0.990033	−	0.140833i	$-0.955022\pi$
$131$		−	422.320i		−	0.281666i	0.990033	−	0.140833i	$-0.0449781\pi$
$132$	1477.72	+	91.1484i	0.974390	+	0.0601019i
$133$	−3186.14			−2.07724
$134$	−1892.69	−	1367.79i	−1.22017	−	0.881783i
$135$	1510.77	+	421.848i	0.963157	+	0.268940i
$136$	−310.536	−	98.2903i	−0.195796	−	0.0619730i
$137$	2962.29			1.84734			0.923671	−	0.383186i	$-0.125173\pi$
$137$	2962.29			1.84734			0.923671	+	0.383186i	$0.125173\pi$
$138$	374.918	+	592.492i	0.231269	+	0.365481i
$139$	724.141			0.441877			0.220938	−	0.975288i	$-0.429088\pi$
$139$	724.141			0.441877			0.220938	+	0.975288i	$0.429088\pi$
$140$	−2495.07	−	1000.40i	−1.50623	−	0.603925i
$141$	−852.867	+	2130.10i	−0.509393	+	1.27225i
$142$	−261.138	+	361.352i	−0.154325	+	0.213549i
$143$		−	2088.80i		−	1.22150i
$144$	−1714.90	−	212.364i	−0.992420	−	0.122896i
$145$	−357.433	+	423.874i	−0.204712	+	0.242764i
$146$	−556.478	−	402.150i	−0.315441	−	0.227960i
$147$	−2702.69	−	1082.13i	−1.51642	−	0.607158i
$148$	−285.587	−	863.990i	−0.158615	−	0.479862i
$149$	−1917.06			−1.05404			−0.527019	−	0.849854i	$-0.676690\pi$
$149$	−1917.06			−1.05404			−0.527019	+	0.849854i	$0.676690\pi$
$150$	−1230.37	−	1364.25i	−0.669729	−	0.742606i
$151$		−	2586.17i		−	1.39377i	−0.717182	−	0.696886i	$-0.754568\pi$
$151$		−	2586.17i		−	1.39377i	0.717182	−	0.696886i	$-0.245432\pi$
$152$	2286.95	+	723.862i	1.22037	+	0.386269i
$153$	−281.266	−	268.232i	−0.148621	−	0.141734i
$154$	−2453.91	−	1773.36i	−1.28404	−	0.927934i
$155$	−1547.18	−	1304.66i	−0.801758	−	0.676085i
$156$	−150.090	+	2433.31i	−0.0770310	+	1.24885i
$157$	1527.70			0.776586			0.388293	−	0.921536i	$-0.373065\pi$
$157$	1527.70			0.776586			0.388293	+	0.921536i	$0.373065\pi$
$158$	−246.446	−	178.099i	−0.124090	−	0.0896758i
$159$	−126.853	+	316.823i	−0.0632708	+	0.158023i
$160$	1563.64	+	1284.93i	0.772602	+	0.634891i
$161$		−	1433.82i		−	0.701868i
$162$	−1726.59	−	1127.13i	−0.837366	−	0.546642i
$163$			2775.55i			1.33373i	0.745179	+	0.666865i	$0.232364\pi$
$163$			2775.55i			1.33373i	−0.745179	+	0.666865i	$0.767636\pi$
$164$	407.270	−	134.621i	0.193917	−	0.0640981i
$165$	−972.663	−	1826.24i	−0.458919	−	0.861650i
$166$	−1919.47	+	2656.08i	−0.897470	+	1.24188i
$167$			1484.84i			0.688025i	0.938965	+	0.344013i	$0.111786\pi$
$167$			1484.84i			0.688025i	−0.938965	+	0.344013i	$0.888214\pi$
$168$	2731.21	+	2242.18i	1.25427	+	1.02969i
$169$	1242.53			0.565558
$170$	110.172	+	441.675i	0.0497047	+	0.199264i
$171$	2071.39	+	1975.40i	0.926336	+	0.883409i
$172$	−3722.77	+	1230.54i	−1.65034	+	0.545510i
$173$		−	4487.55i		−	1.97215i	−0.166292	−	0.986077i	$-0.553179\pi$
$173$		−	4487.55i		−	1.97215i	0.166292	−	0.986077i	$-0.446821\pi$
$174$	615.907	−	389.735i	0.268343	−	0.169803i
$175$	634.356	+	3702.87i	0.274016	+	1.59949i
$176$	1358.48	+	1830.39i	0.581813	+	0.783927i
$177$	−784.246	+	1958.71i	−0.333037	+	0.831784i
$178$	1719.68	+	1242.76i	0.724132	+	0.523309i
$179$			2713.96i			1.13325i	0.823977	+	0.566623i	$0.191750\pi$
$179$			2713.96i			1.13325i	−0.823977	+	0.566623i	$0.808250\pi$
$180$	1001.86	+	2197.33i	0.414858	+	0.909886i
$181$		−	913.737i		−	0.375235i	−0.982242	−	0.187618i	$-0.939923\pi$
$181$		−	913.737i		−	0.375235i	0.982242	−	0.187618i	$-0.0600765\pi$
$182$	2920.12	−	4040.74i	1.18931	−	1.64571i
$183$	412.489	−	1030.22i	0.166623	−	0.416153i
$184$	−325.750	+	1029.17i	−0.130514	+	0.412344i
$185$	−819.811	+	972.200i	−0.325804	+	0.386365i
$186$	1422.57	+	2248.12i	0.560795	+	0.886237i
$187$			512.692i			0.200490i
$188$	−3354.12	+	1108.68i	−1.30119	+	0.430101i
$189$	1751.12	+	3835.72i	0.673945	+	1.47623i
$190$	−811.364	−	3252.73i	−0.309803	−	1.24199i
$191$	−3419.83			−1.29555			−0.647776	−	0.761831i	$-0.724301\pi$
$191$	−3419.83			−1.29555			−0.647776	+	0.761831i	$0.724301\pi$
$192$	−1451.01	−	2229.90i	−0.545405	−	0.838173i
$193$		−	3786.04i		−	1.41205i	−0.708189	−	0.706023i	$-0.750487\pi$
$193$		−	3786.04i		−	1.41205i	0.708189	−	0.706023i	$-0.249513\pi$
$194$	190.786	+	137.875i	0.0706062	+	0.0510250i
$195$	3007.18	−	1601.64i	1.10435	−	0.588185i
$196$	−1406.71	−	4255.74i	−0.512649	−	1.55092i
$197$		−	12.8824i		−	0.00465904i	−0.999997	−	0.00232952i	$-0.999258\pi$
$197$		−	12.8824i		−	0.00465904i	0.999997	−	0.00232952i	$-0.000741510\pi$
$198$	495.864	+	2674.33i	0.177977	+	0.959881i
$199$			1630.96i			0.580983i	0.956878	+	0.290491i	$0.0938187\pi$
$199$			1630.96i			0.580983i	−0.956878	+	0.290491i	$0.906181\pi$
$200$	385.929	−	2801.97i	0.136447	−	0.990647i
$201$	1594.61	−	3982.65i	0.559577	−	1.39758i
$202$	−1621.18	+	2243.32i	−0.564683	+	0.781384i
$203$	−1490.48			−0.515326
$204$	36.8394	−	597.251i	0.0126435	−	0.204980i
$205$	−458.278	−	386.445i	−0.156134	−	0.131661i
$206$	−802.217	+	1110.07i	−0.271326	+	0.375449i
$207$	−888.966	+	932.163i	−0.298490	+	0.312994i
$208$	−3014.03	+	2236.95i	−1.00474	+	0.745694i
$209$		−	3775.73i		−	1.24963i
$210$	671.465	−	4892.60i	0.220645	−	1.60772i
$211$	−2482.49			−0.809960			−0.404980	−	0.914326i	$-0.632721\pi$
$211$	−2482.49			−0.809960			−0.404980	+	0.914326i	$0.632721\pi$
$212$	−498.880	+	164.902i	−0.161619	+	0.0534222i
$213$	−760.367	−	304.442i	−0.244598	−	0.0979345i
$214$	−1511.92	+	2092.13i	−0.482957	+	0.668296i
$215$	4189.03	+	3532.41i	1.32879	+	1.12051i
$216$	−385.485	−	3151.05i	−0.121430	−	0.992600i
$217$		−	5440.40i		−	1.70193i
$218$	2958.24	+	2137.83i	0.919072	+	0.664185i
$219$	468.838	−	1170.96i	0.144663	−	0.361306i
$220$	1185.53	−	2956.78i	0.363310	−	0.906120i
$221$	−844.228			−0.256963
$222$	1412.65	−	893.898i	0.427076	−	0.270246i
$223$	−220.601			−0.0662444			−0.0331222	−	0.999451i	$-0.510545\pi$
$223$	−220.601			−0.0662444			−0.0331222	+	0.999451i	$0.510545\pi$
$224$	69.0740	+	5440.01i	0.0206036	+	1.62266i
$225$	1883.37	−	2800.63i	0.558035	−	0.829818i
$226$	−39.8941	+	55.2038i	−0.0117421	+	0.0162482i
$227$	−1286.28			−0.376094			−0.188047	−	0.982160i	$-0.560216\pi$
$227$	−1286.28			−0.376094			−0.188047	+	0.982160i	$0.560216\pi$
$228$	−271.305	+	4398.48i	−0.0788053	+	1.27761i
$229$		−	3473.66i		−	1.00238i	−0.865336	−	0.501192i	$-0.832895\pi$
$229$		−	3473.66i		−	1.00238i	0.865336	−	0.501192i	$-0.167105\pi$
$230$	1463.78	−	365.128i	0.419648	−	0.104677i
$231$	2067.44	−	5163.58i	0.588864	−	1.47073i
$232$	1069.84	+	338.623i	0.302752	+	0.0958264i
$233$	1374.39			0.386435			0.193218	−	0.981156i	$-0.438108\pi$
$233$	1374.39			0.386435			0.193218	+	0.981156i	$0.438108\pi$
$234$	−4403.71	+	816.519i	−1.23025	+	0.228109i
$235$	3774.20	+	3182.61i	1.04767	+	0.883449i
$236$	−3084.25	+	1019.48i	−0.850709	+	0.281197i
$237$	207.633	−	518.578i	0.0569080	−	0.142132i
$238$	−716.740	+	991.795i	−0.195207	+	0.270120i
$239$	6110.81			1.65387			0.826936	−	0.562296i	$-0.190082\pi$
$239$	6110.81			1.65387			0.826936	+	0.562296i	$0.190082\pi$
$240$	−1593.52	+	3359.27i	−0.428589	+	0.903500i
$241$	7359.10			1.96698			0.983488	−	0.180975i	$-0.0579253\pi$
$241$	7359.10			1.96698			0.983488	+	0.180975i	$0.0579253\pi$
$242$	−103.533	+	143.265i	−0.0275016	+	0.0380555i
$243$	1239.69	−	3579.40i	0.327268	−	0.944931i
$244$	1622.22	−	536.214i	0.425622	−	0.140687i
$245$	−4038.13	+	4788.74i	−1.05301	+	1.24874i
$246$	421.368	+	665.898i	0.109209	+	0.172586i
$247$	6217.34			1.60162
$248$	−1236.01	+	3905.02i	−0.316478	+	0.999874i
$249$	−5589.01	−	2237.78i	−1.42245	−	0.569531i
$250$	−3618.72	+	1590.57i	−0.915471	+	0.402385i
$251$			1602.46i			0.402973i	0.979491	+	0.201486i	$0.0645772\pi$
$251$			1602.46i			0.402973i	−0.979491	+	0.201486i	$0.935423\pi$
$252$	−2779.46	+	5866.67i	−0.694799	+	1.46653i
$253$	1699.14			0.422230
$254$	1687.25	−	2334.74i	0.416801	−	0.576751i
$255$	−738.109	+	393.121i	−0.181263	+	0.0965419i
$256$	1186.34	−	3920.43i	0.289634	−	0.957137i
$257$	−1317.48			−0.319775			−0.159887	−	0.987135i	$-0.551113\pi$
$257$	−1317.48			−0.319775			−0.159887	+	0.987135i	$0.551113\pi$
$258$	−3851.64	−	6086.84i	−0.929429	−	1.46880i
$259$	−3418.58			−0.820155
$260$	4868.81	+	1952.16i	1.16135	+	0.465645i
$261$	969.000	+	924.096i	0.229807	+	0.219158i
$262$	968.151	+	699.654i	0.228292	+	0.164980i
$263$			621.813i			0.145789i	0.997340	+	0.0728947i	$0.0232237\pi$
$263$			621.813i			0.145789i	−0.997340	+	0.0728947i	$0.976776\pi$
$264$	−2657.09	+	3236.62i	−0.619441	+	0.754546i
$265$	561.362	+	473.371i	0.130129	+	0.109732i
$266$	5278.45	−	7304.10i	1.21670	−	1.68362i
$267$	−1448.85	+	3618.60i	−0.332090	+	0.829419i
$268$	6271.20	−	2072.91i	1.42938	−	0.472474i
$269$	105.003			0.0237998			0.0118999	−	0.999929i	$-0.496212\pi$
$269$	105.003			0.0237998			0.0118999	+	0.999929i	$0.496212\pi$
$270$	−3469.95	+	2764.50i	−0.782127	+	0.623119i
$271$		−	979.683i		−	0.219600i	−0.993954	−	0.109800i	$-0.964979\pi$
$271$		−	979.683i		−	0.219600i	0.993954	−	0.109800i	$-0.0350210\pi$
$272$	739.789	−	549.055i	0.164913	−	0.122395i
$273$	8502.65	+	3404.37i	1.88500	+	0.754731i
$274$	−4907.61	+	6790.94i	−1.08204	+	1.49728i
$275$	−4388.08	+	751.743i	−0.962224	+	0.164843i
$276$	−1979.39	−	122.092i	−0.431686	−	0.0266271i
$277$	−7385.36			−1.60196			−0.800981	−	0.598690i	$-0.795688\pi$
$277$	−7385.36			−1.60196			−0.800981	+	0.598690i	$0.795688\pi$
$278$	−1199.68	+	1660.06i	−0.258820	+	0.358144i
$279$	−3373.04	+	3536.94i	−0.723795	+	0.758965i
$280$	6426.95	−	4062.50i	1.37173	−	0.867074i
$281$			2837.82i			0.602457i	0.953552	+	0.301229i	$0.0973967\pi$
$281$			2837.82i			0.602457i	−0.953552	+	0.301229i	$0.902603\pi$
$282$	−3470.22	−	5484.08i	−0.732797	−	1.15806i
$283$		−	3418.04i		−	0.717955i	−0.933346	−	0.358977i	$-0.883126\pi$
$283$		−	3418.04i		−	0.717955i	0.933346	−	0.358977i	$-0.116874\pi$
$284$	−395.759	−	1197.30i	−0.0826901	−	0.250164i
$285$	5435.82	−	2895.15i	1.12979	−	0.601733i
$286$	4788.48	+	3460.49i	0.990030	+	0.715465i
$287$		−	1611.46i		−	0.331433i
$288$	3327.90	−	3579.52i	0.680897	−	0.732379i
$289$	−4705.79			−0.957823
$290$	−379.557	−	1521.63i	−0.0768564	−	0.308114i
$291$	−160.739	+	401.456i	−0.0323803	+	0.0808721i
$292$	1843.82	−	609.465i	0.369526	−	0.122145i
$293$		−	3323.01i		−	0.662569i	−0.943531	−	0.331284i	$-0.892518\pi$
$293$		−	3323.01i		−	0.662569i	0.943531	−	0.331284i	$-0.107482\pi$
$294$	6958.25	−	4403.06i	1.38032	−	0.873440i
$295$	3470.53	+	2926.54i	0.684957	+	0.577592i
$296$	2453.79	+	776.669i	0.481837	+	0.152510i
$297$	−4545.51	+	2075.17i	−0.888072	+	0.405432i
$298$	3175.98	−	4394.78i	0.617381	−	0.854305i
$299$			2797.91i			0.541161i
$300$	5165.84	−	560.425i	0.994167	−	0.107854i
$301$			14730.0i			2.82068i
$302$	5928.69	+	4284.49i	1.12966	+	0.816372i
$303$	−4720.46	−	1890.02i	−0.894995	−	0.358346i
$304$	−5448.20	+	4043.53i	−1.02788	+	0.762870i
$305$	−1825.39	−	1539.27i	−0.342694	−	0.288978i
$306$	1080.88	−	200.413i	0.201928	−	0.0374407i
$307$			455.313i			0.0846452i	0.999104	+	0.0423226i	$0.0134757\pi$
$307$			455.313i			0.0846452i	−0.999104	+	0.0423226i	$0.986524\pi$
$308$	8130.73	−	2687.56i	1.50419	−	0.497202i
$309$	−2335.85	−	935.248i	−0.430038	−	0.172183i
$310$	5554.09	−	1385.42i	1.01758	−	0.253828i
$311$	1672.37			0.304923			0.152462	−	0.988309i	$-0.451280\pi$
$311$	1672.37			0.304923			0.152462	+	0.988309i	$0.451280\pi$
$312$	−5329.60	−	4375.32i	−0.967082	−	0.793921i
$313$			3116.09i			0.562721i	0.959602	+	0.281361i	$0.0907857\pi$
$313$			3116.09i			0.562721i	−0.959602	+	0.281361i	$0.909214\pi$
$314$	−2530.93	+	3502.20i	−0.454869	+	0.629428i
$315$	9019.14	−	982.882i	1.61324	−	0.175807i
$316$	816.569	−	269.912i	0.145366	−	0.0480498i
$317$		−	4710.18i		−	0.834543i	−0.908782	−	0.417272i	$-0.862986\pi$
$317$		−	4710.18i		−	0.834543i	0.908782	−	0.417272i	$-0.137014\pi$
$318$	−516.150	−	815.683i	−0.0910196	−	0.143840i
$319$		−	1766.29i		−	0.310010i
$320$	−5536.11	+	1455.84i	−0.967119	+	0.254325i
$321$	−4402.33	−	1762.64i	−0.765464	−	0.306483i
$322$	3286.97	+	2375.39i	0.568869	+	0.411104i
$323$	−1526.04			−0.262882
$324$	5444.33	−	2090.81i	0.933527	−	0.358507i
$325$	−1237.86	−	7225.67i	−0.211275	−	1.23326i
$326$	−6362.84	−	4598.23i	−1.08100	−	0.781204i
$327$	−2492.35	+	6224.82i	−0.421490	+	1.05270i
$328$	−366.108	+	1156.67i	−0.0616309	+	0.194715i
$329$			13271.3i			2.22393i
$330$	5797.97	+	795.718i	0.967176	+	0.132736i
$331$	−7743.80			−1.28592			−0.642958	−	0.765902i	$-0.722293\pi$
$331$	−7743.80			−1.28592			−0.642958	+	0.765902i	$0.722293\pi$
$332$	−2908.99	−	8800.63i	−0.480879	−	1.45481i
$333$	2222.51	+	2119.52i	0.365744	+	0.348795i
$334$	−3403.93	−	2459.92i	−0.557649	−	0.402996i
$335$	−7056.64	−	5950.53i	−1.15088	−	0.970485i
$336$	−9664.88	+	2546.60i	−1.56923	+	0.413477i
$337$			8409.42i			1.35932i	0.733528	+	0.679659i	$0.237872\pi$
$337$			8409.42i			1.35932i	−0.733528	+	0.679659i	$0.762128\pi$
$338$	−2058.49	+	2848.45i	−0.331264	+	0.458389i
$339$	−116.161	−	46.5098i	−0.0186107	−	0.00745151i
$340$	−1195.04	−	479.154i	−0.190618	−	0.0764288i
$341$	6447.13			1.02385
$342$	−7960.20	+	1475.95i	−1.25859	+	0.233363i
$343$	−6530.10			−1.02797
$344$	3346.52	−	10572.9i	0.524513	−	1.65713i
$345$	1302.87	+	2446.21i	0.203316	+	0.381738i
$346$	10287.5	+	7434.50i	1.59844	+	1.15515i
$347$	4830.70			0.747336			0.373668	−	0.927562i	$-0.378100\pi$
$347$	4830.70			0.747336			0.373668	+	0.927562i	$0.378100\pi$
$348$	−126.917	+	2057.61i	−0.0195501	+	0.316953i
$349$		−	6202.35i		−	0.951301i	−0.879634	−	0.475650i	$-0.842213\pi$
$349$		−	6202.35i		−	0.951301i	0.879634	−	0.475650i	$-0.157787\pi$
$350$	−9539.62	−	4680.28i	−1.45690	−	0.714776i
$351$	−3417.09	−	7484.90i	−0.519632	−	1.13822i
$352$	−6446.68	+	81.8561i	−0.976163	+	0.0123947i
$353$	−7678.75			−1.15779			−0.578893	−	0.815404i	$-0.696515\pi$
$353$	−7678.75			−1.15779			−0.578893	+	0.815404i	$0.696515\pi$
$354$	−3191.01	−	5042.83i	−0.479097	−	0.757129i
$355$	−1136.07	+	1347.25i	−0.169850	+	0.201422i
$356$	−5697.96	+	1883.43i	−0.848291	+	0.280397i
$357$	−2086.96	−	835.596i	−0.309394	−	0.123878i
$358$	−6221.64	−	4496.19i	−0.918503	−	0.663775i
$359$	−12403.8			−1.82352			−0.911762	−	0.410719i	$-0.865278\pi$
$359$	−12403.8			−1.82352			−0.911762	+	0.410719i	$0.865278\pi$
$360$	−6697.08	−	1343.57i	−0.980463	−	0.196701i
$361$	4379.54			0.638509
$362$	2094.71	+	1513.78i	0.304131	+	0.219786i
$363$	−301.463	−	120.702i	−0.0435887	−	0.0174524i
$364$	4425.50	+	13388.5i	0.637250	+	1.92788i
$365$	−2074.75	−	1749.54i	−0.297528	−	0.250891i
$366$	1678.37	+	2652.37i	0.239699	+	0.378802i
$367$	1231.21			0.175119			0.0875597	−	0.996159i	$-0.472093\pi$
$367$	1231.21			0.175119			0.0875597	+	0.996159i	$0.472093\pi$
$368$	−1819.66	−	2451.78i	−0.257762	−	0.347305i
$369$	−999.102	+	1047.65i	−0.140952	+	0.147801i
$370$	−870.555	−	3490.02i	−0.122319	−	0.490372i
$371$			1973.93i			0.276231i
$372$	−7510.48	−	463.258i	−1.04677	−	0.0645667i
$373$	5114.70			0.709998			0.354999	−	0.934867i	$-0.384481\pi$
$373$	5114.70			0.709998			0.354999	+	0.934867i	$0.384481\pi$
$374$	−1175.32	−	849.372i	−0.162499	−	0.117433i
$375$	−4446.95	−	5740.99i	−0.612372	−	0.790569i
$376$	3015.13	−	9525.93i	0.413546	−	1.30655i
$377$	2908.48			0.397332
$378$	−11694.3	−	2340.22i	−1.59124	−	0.318434i
$379$	2973.78			0.403041			0.201521	−	0.979484i	$-0.435412\pi$
$379$	2973.78			0.403041			0.201521	+	0.979484i	$0.435412\pi$
$380$	8800.92	+	3528.74i	1.18810	+	0.476370i
$381$	4912.83	+	1967.04i	0.660609	+	0.264500i
$382$	5665.61	−	7839.83i	0.758843	−	1.05005i
$383$			4239.61i			0.565623i	0.959175	+	0.282812i	$0.0912671\pi$
$383$			4239.61i			0.565623i	−0.959175	+	0.282812i	$0.908733\pi$
$384$	7515.84	+	367.869i	0.998804	+	0.0488873i
$385$	−9149.06	−	7714.98i	−1.21112	−	1.02128i
$386$	8679.34	+	6272.30i	1.14447	+	0.827076i
$387$	9132.60	−	9576.37i	1.19958	−	1.25787i
$388$	−632.146	+	208.952i	−0.0827122	+	0.0273400i
$389$	−1866.70			−0.243304			−0.121652	−	0.992573i	$-0.538819\pi$
$389$	−1866.70			−0.243304			−0.121652	+	0.992573i	$0.538819\pi$
$390$	−1310.28	+	9547.28i	−0.170124	+	1.23960i
$391$		−	686.742i		−	0.0888237i
$392$	12086.6	+	3825.62i	1.55731	+	0.492916i
$393$	−815.677	+	2037.21i	−0.104696	+	0.261485i
$394$	29.5323	+	21.3421i	0.00377619	+	0.00272894i
$395$	−918.839	−	774.815i	−0.117043	−	0.0986966i
$396$	−6952.29	−	3293.79i	−0.882237	−	0.417978i
$397$	7085.75			0.895778			0.447889	−	0.894089i	$-0.352176\pi$
$397$	7085.75			0.895778			0.447889	+	0.894089i	$0.352176\pi$
$398$	−3738.91	−	2701.99i	−0.470890	−	0.340298i
$399$	15369.5	+	6153.77i	1.92841	+	0.772115i
$400$	5784.05	+	5526.74i	0.723006	+	0.690842i
$401$		−	4052.17i		−	0.504628i	−0.967645	−	0.252314i	$-0.918808\pi$
$401$		−	4052.17i		−	0.504628i	0.967645	−	0.252314i	$-0.0811915\pi$
$402$	6488.29	+	10253.6i	0.804991	+	1.27215i
$403$			10616.2i			1.31224i
$404$	−2456.93	−	7432.98i	−0.302566	−	0.915358i
$405$	−6472.96	−	4952.86i	−0.794183	−	0.607678i
$406$	2469.27	−	3416.87i	0.301841	−	0.417675i
$407$		−	4051.18i		−	0.493390i
$408$	1308.14	+	1073.91i	0.158732	+	0.130311i
$409$	3577.29			0.432483			0.216242	−	0.976340i	$-0.430620\pi$
$409$	3577.29			0.432483			0.216242	+	0.976340i	$0.430620\pi$
$410$	1645.13	−	410.364i	0.198164	−	0.0494304i
$411$	−14289.7	−	5721.43i	−1.71498	−	0.686660i
$412$	−1215.77	−	3678.10i	−0.145381	−	0.439823i
$413$			12203.5i			1.45399i
$414$	−664.202	−	3582.23i	−0.0788497	−	0.425258i
$415$	−8350.62	+	9902.85i	−0.987749	+	1.17135i
$416$	−134.789	−	10615.5i	−0.0158860	−	1.25112i
$417$	−3493.16	−	1398.62i	−0.410217	−	0.164246i
$418$	8655.71	+	6255.22i	1.01283	+	0.731945i
$419$		−	13722.4i		−	1.59996i	−0.600028	−	0.799979i	$-0.704844\pi$
$419$		−	13722.4i		−	1.59996i	0.600028	−	0.799979i	$-0.295156\pi$
$420$	10103.7	+	9644.84i	1.17383	+	1.12052i
$421$			3588.59i			0.415433i	0.978189	+	0.207717i	$0.0666032\pi$
$421$			3588.59i			0.415433i	−0.978189	+	0.207717i	$0.933397\pi$
$422$	4112.72	−	5691.00i	0.474417	−	0.656478i
$423$	8228.22	−	8628.05i	0.945792	−	0.991749i
$424$	448.460	−	1416.85i	0.0513659	−	0.162284i
$425$	303.832	+	1773.53i	0.0346777	+	0.202421i
$426$	1957.62	−	1238.74i	0.222645	−	0.140886i
$427$		−	6418.68i		−	0.727451i
$428$	−2291.34	−	6932.04i	−0.258776	−	0.782881i
$429$	−4034.34	+	10076.1i	−0.454032	+	1.13398i
$430$	−15037.8	+	3751.06i	−1.68649	+	0.420679i
$431$	−8138.32			−0.909534			−0.454767	−	0.890610i	$-0.650277\pi$
$431$	−8138.32			−0.909534			−0.454767	+	0.890610i	$0.650277\pi$
$432$	7862.28	+	4336.61i	0.875634	+	0.482975i
$433$		−	2624.71i		−	0.291306i	−0.989336	−	0.145653i	$-0.953472\pi$
$433$		−	2624.71i		−	0.291306i	0.989336	−	0.145653i	$-0.0465284\pi$
$434$	12471.9	+	9013.06i	1.37942	+	0.996868i
$435$	2542.88	−	1354.35i	0.280280	−	0.149279i
$436$	−9801.80	+	3239.92i	−1.07665	+	0.355881i
$437$			5057.53i			0.553626i
$438$	1907.65	+	3014.71i	0.208108	+	0.328877i
$439$		−	1733.88i		−	0.188504i	−0.995548	−	0.0942522i	$-0.969954\pi$
$439$		−	1733.88i		−	0.188504i	0.995548	−	0.0942522i	$-0.0300460\pi$
$440$	4814.26	+	7616.25i	0.521615	+	0.825206i
$441$	10947.4	+	10440.1i	1.18209	+	1.12731i
$442$	1398.62	−	1935.36i	0.150511	−	0.208271i
$443$	3608.99			0.387061			0.193531	−	0.981094i	$-0.438006\pi$
$443$	3608.99			0.387061			0.193531	+	0.981094i	$0.438006\pi$
$444$	−291.097	+	4719.36i	−0.0311146	+	0.504438i
$445$	6411.60	+	5406.61i	0.683009	+	0.575950i
$446$	365.467	−	505.718i	0.0388013	−	0.0536916i
$447$	9247.63	+	3702.65i	0.978518	+	0.391788i
$448$	−12585.4	−	8854.08i	−1.32725	−	0.933741i
$449$			1133.13i			0.119100i	0.998225	+	0.0595499i	$0.0189665\pi$
$449$			1133.13i			0.119100i	−0.998225	+	0.0595499i	$0.981033\pi$
$450$	3300.18	+	8957.33i	0.345716	+	0.938339i
$451$	1909.66			0.199384
$452$	−60.4603	−	182.911i	−0.00629162	−	0.0190341i
$453$	−4994.98	+	12475.3i	−0.518067	+	1.29391i
$454$	2130.97	−	2948.74i	0.220289	−	0.304827i
$455$	12703.9	−	15065.4i	1.30894	−	1.55225i
$456$	−9633.86	−	7908.87i	−0.989357	−	0.812208i
$457$			2261.32i			0.231466i	0.993280	+	0.115733i	$0.0369217\pi$
$457$			2261.32i			0.231466i	−0.993280	+	0.115733i	$0.963078\pi$
$458$	7963.22	+	5754.78i	0.812439	+	0.587125i
$459$	838.720	+	1837.16i	0.0852899	+	0.186822i
$460$	−1588.00	+	3960.57i	−0.160958	+	0.401440i
$461$	9091.77			0.918538			0.459269	−	0.888297i	$-0.348111\pi$
$461$	9091.77			0.918538			0.459269	+	0.888297i	$0.348111\pi$
$462$	8412.19	+	13294.0i	0.847122	+	1.33873i
$463$	13361.2			1.34114			0.670568	−	0.741848i	$-0.266050\pi$
$463$	13361.2			1.34114			0.670568	+	0.741848i	$0.266050\pi$
$464$	−2548.67	+	1891.57i	−0.254998	+	0.189254i
$465$	4943.52	+	9281.77i	0.493012	+	0.925660i
$466$	−2276.94	+	3150.74i	−0.226346	+	0.313208i
$467$	11343.7			1.12404			0.562019	−	0.827124i	$-0.310025\pi$
$467$	11343.7			1.12404			0.562019	+	0.827124i	$0.310025\pi$
$468$	5423.75	−	11448.0i	0.535711	−	1.13074i
$469$		−	24813.5i		−	2.44303i
$470$	−13548.7	+	3379.60i	−1.32969	+	0.331680i
$471$	−7369.42	−	2950.63i	−0.720945	−	0.288658i
$472$	2772.53	−	8759.48i	0.270373	−	0.854211i
$473$	−17455.8			−1.69687
$474$	844.835	+	1335.11i	0.0818662	+	0.129375i
$475$	−2237.58	−	13061.2i	−0.216141	−	1.26166i
$476$	−1086.23	−	3286.20i	−0.104595	−	0.316434i
$477$	1223.84	−	1283.31i	0.117475	−	0.123184i
$478$	−10123.7	+	14008.8i	−0.968721	+	1.34048i
$479$	3825.30			0.364890			0.182445	−	0.983216i	$-0.441599\pi$
$479$	3825.30			0.364890			0.182445	+	0.983216i	$0.441599\pi$
$480$	−5061.02	−	9218.35i	−0.481256	−	0.876580i
$481$	6670.91			0.632364
$482$	−12191.8	+	16870.4i	−1.15211	+	1.59425i
$483$	−2769.30	+	6916.54i	−0.260885	+	0.651580i
$484$	−156.907	−	474.692i	−0.0147358	−	0.0445804i
$485$	711.318	+	599.822i	0.0665965	+	0.0561577i
$486$	6151.84	+	8771.90i	0.574183	+	0.818727i
$487$	−11327.9			−1.05403			−0.527017	−	0.849855i	$-0.676689\pi$
$487$	−11327.9			−1.05403			−0.527017	+	0.849855i	$0.676689\pi$
$488$	−1458.26	+	4607.21i	−0.135272	+	0.427374i
$489$	5360.75	−	13388.9i	0.495750	−	1.23817i
$490$	−4288.07	−	17190.7i	−0.395338	−	1.58489i
$491$			17714.2i			1.62817i	0.580747	+	0.814084i	$0.302761\pi$
$491$			17714.2i			1.62817i	−0.580747	+	0.814084i	$0.697239\pi$
$492$	−2224.62	−	137.218i	−0.203849	−	0.0125737i
$493$	−713.881			−0.0652162
$494$	−10300.2	+	14253.0i	−0.938114	+	1.29812i
$495$	1164.76	+	10688.1i	0.105762	+	0.970496i
$496$	−6904.41	−	9302.91i	−0.625034	−	0.842163i
$497$	−4737.38			−0.427567
$498$	14389.3	−	9105.27i	1.29478	−	0.819311i
$499$	16471.4			1.47768			0.738839	−	0.673882i	$-0.235374\pi$
$499$	16471.4			1.47768			0.738839	+	0.673882i	$0.235374\pi$
$500$	2348.79	−	10930.8i	0.210082	−	0.977684i
$501$	2867.84	−	7162.65i	0.255740	−	0.638730i
$502$	−3673.57	−	2654.78i	−0.326612	−	0.236033i
$503$			14790.4i			1.31108i	0.755162	+	0.655538i	$0.227558\pi$
$503$			14790.4i			1.31108i	−0.755162	+	0.655538i	$0.772442\pi$
$504$	−8844.40	−	16091.1i	−0.781669	−	1.42213i
$505$	−7052.91	+	8363.92i	−0.621486	+	0.737009i
$506$	−2814.96	+	3895.22i	−0.247313	+	0.342221i
$507$	−5993.79	−	2399.85i	−0.525037	−	0.210219i
$508$	2557.05	+	7735.90i	0.223329	+	0.675640i
$509$	14027.9			1.22157			0.610783	−	0.791798i	$-0.290855\pi$
$509$	14027.9			1.22157			0.610783	+	0.791798i	$0.290855\pi$
$510$	321.605	−	2343.36i	0.0279234	−	0.203463i
$511$		−	7295.52i		−	0.631575i
$512$	7022.04	+	9214.59i	0.606119	+	0.795374i
$513$	−6176.77	−	13529.8i	−0.531601	−	1.16444i
$514$	2182.66	−	3020.27i	0.187301	−	0.259180i
$515$	−3490.03	+	4138.76i	−0.298619	+	0.354128i
$516$	20334.8	+	1254.28i	1.73487	+	0.107009i
$517$	−15727.2			−1.33787
$518$	5663.53	−	7836.95i	0.480388	−	0.664741i
$519$	−8667.35	+	21647.3i	−0.733053	+	1.83085i
$520$	−12541.4	+	7927.43i	−1.05764	+	0.668540i
$521$		−	13903.0i		−	1.16910i	−0.811356	−	0.584552i	$-0.801270\pi$
$521$		−	13903.0i		−	1.16910i	0.811356	−	0.584552i	$-0.198730\pi$
$522$	−3723.79	+	690.451i	−0.312233	+	0.0578931i
$523$		−	11850.7i		−	0.990813i	−0.868661	−	0.495407i	$-0.835019\pi$
$523$		−	11850.7i		−	0.990813i	0.868661	−	0.495407i	$-0.164981\pi$
$524$	−3207.86	+	1060.34i	−0.267435	+	0.0883990i
$525$	4091.75	−	19087.3i	0.340150	−	1.58674i
$526$	−1425.48	−	1030.15i	−0.118163	−	0.0853931i
$527$		−	2605.74i		−	0.215384i
$528$	−3017.84	−	11453.3i	−0.248740	−	0.944021i
$529$	9891.02			0.812938
$530$	−2015.19	+	502.671i	−0.165159	+	0.0411974i
$531$	7566.19	−	7933.84i	0.618351	−	0.648398i
$532$	7999.59	+	24201.3i	0.651929	+	1.97229i
$533$			3144.55i			0.255545i
$534$	−5895.21	−	9316.34i	−0.477735	−	0.754976i
$535$	−6577.58	+	7800.24i	−0.531540	+	0.630344i
$536$	−5637.39	+	17810.6i	−0.454288	+	1.43527i
$537$	5241.79	−	13091.8i	0.421229	−	1.05205i
$538$	−173.958	+	240.715i	−0.0139402	+	0.0192899i
$539$		−	19954.8i		−	1.59465i
$540$	−588.876	−	12534.6i	−0.0469282	−	0.998898i
$541$			19263.3i			1.53086i	0.643519	+	0.765430i	$0.277474\pi$
$541$			19263.3i			1.53086i	−0.643519	+	0.765430i	$0.722526\pi$
$542$	2245.88	+	1623.03i	0.177987	+	0.128626i
$543$	−1764.81	+	4407.74i	−0.139476	+	0.348350i
$544$	33.0837	+	2605.55i	0.00260745	+	0.205353i
$545$	11029.4	+	9300.60i	0.866878	+	0.730998i
$546$	−21890.6	+	13852.0i	−1.71581	+	1.08573i
$547$			5317.24i			0.415629i	0.978168	+	0.207814i	$0.0666350\pi$
$547$			5317.24i			0.415629i	−0.978168	+	0.207814i	$0.933365\pi$
$548$	−7437.56	−	22501.0i	−0.579776	−	1.75400i
$549$	−3979.57	+	4172.95i	−0.309370	+	0.324403i
$550$	5546.36	−	11304.9i	0.429996	−	0.876442i
$551$	5257.40			0.406484
$552$	3559.13	−	4335.40i	0.274432	−	0.334288i
$553$		−	3230.94i		−	0.248452i
$554$	12235.3	−	16930.6i	0.938315	−	1.29840i
$555$	5832.38	−	3106.36i	0.446073	−	0.237581i
$556$	−1818.13	−	5500.43i	−0.138680	−	0.419551i
$557$		−	10227.8i		−	0.778039i	−0.921230	−	0.389019i	$-0.872814\pi$
$557$		−	10227.8i		−	0.778039i	0.921230	−	0.389019i	$-0.127186\pi$
$558$	−2520.21	−	13592.2i	−0.191199	−	1.03119i
$559$		−	28743.7i		−	2.17483i
$560$	−1334.37	+	21463.8i	−0.100692	+	1.61967i
$561$	990.222	−	2473.15i	0.0745227	−	0.186126i
$562$	−6505.60	−	4701.40i	−0.488296	−	0.352877i
$563$	6371.34			0.476945			0.238472	−	0.971149i	$-0.423353\pi$
$563$	6371.34			0.476945			0.238472	+	0.971149i	$0.423353\pi$
$564$	18321.1	+	1130.08i	1.36783	+	0.0843702i
$565$	−173.559	+	205.820i	−0.0129233	+	0.0153255i
$566$	7835.71	+	5662.63i	0.581907	+	0.420527i
$567$	−1038.80	−	21885.1i	−0.0769407	−	1.62097i
$568$	3400.41	+	1076.29i	0.251193	+	0.0795073i
$569$		−	3929.11i		−	0.289485i	−0.989469	−	0.144742i	$-0.953765\pi$
$569$		−	3929.11i		−	0.289485i	0.989469	−	0.144742i	$-0.0462353\pi$
$570$	−2368.47	+	17257.8i	−0.174043	+	1.26816i
$571$	−4292.81			−0.314621			−0.157310	−	0.987549i	$-0.550282\pi$
$571$	−4292.81			−0.314621			−0.157310	+	0.987549i	$0.550282\pi$
$572$	−15866.1	+	5244.43i	−1.15978	+	0.383358i
$573$	16496.8	+	6605.14i	1.20273	+	0.481559i
$574$	3694.20	+	2669.69i	0.268629	+	0.194130i
$575$	5877.77	−	1006.95i	0.426296	−	0.0730307i
$576$	2692.61	+	13559.2i	0.194778	+	0.980847i
$577$			1957.65i			0.141244i	0.997503	+	0.0706221i	$0.0224985\pi$
$577$			1957.65i			0.141244i	−0.997503	+	0.0706221i	$0.977502\pi$
$578$	7796.04	−	10787.8i	0.561025	−	0.776322i
$579$	−7312.42	+	18263.3i	−0.524860	+	1.31088i
$580$	4117.08	+	1650.75i	0.294746	+	0.118179i
$581$	−34821.7			−2.48649
$582$	−654.028	−	1033.58i	−0.0465814	−	0.0736136i
$583$	−2339.21			−0.166175
$584$	−1657.48	+	5236.59i	−0.117443	+	0.371047i
$585$	−17599.7	+	1917.97i	−1.24386	+	0.135552i
$586$	7617.88	+	5505.21i	0.537016	+	0.388086i
$587$	−17909.4			−1.25928			−0.629642	−	0.776886i	$-0.716798\pi$
$587$	−17909.4			−1.25928			−0.629642	+	0.776886i	$0.716798\pi$
$588$	−1433.85	+	23246.0i	−0.100563	+	1.63036i
$589$			19190.0i			1.34246i
$590$	−12458.6	+	3107.68i	−0.869341	+	0.216850i
$591$	−24.8813	+	62.1428i	−0.00173177	+	0.00432523i
$592$	−5845.66	+	4338.52i	−0.405836	+	0.301203i
$593$	20213.4			1.39977			0.699887	−	0.714253i	$-0.253233\pi$
$593$	20213.4			1.39977			0.699887	+	0.714253i	$0.253233\pi$
$594$	2773.27	−	13858.3i	0.191564	−	0.957262i
$595$	−3118.16	+	3697.77i	−0.214844	+	0.254780i
$596$	4813.25	+	14561.6i	0.330803	+	1.00078i
$597$	3150.06	−	7867.51i	0.215952	−	0.539356i
$598$	−6414.09	−	4635.27i	−0.438615	−	0.316974i
$599$	−8469.13			−0.577695			−0.288848	−	0.957375i	$-0.593272\pi$
$599$	−8469.13			−0.577695			−0.288848	+	0.957375i	$0.593272\pi$
$600$	−7273.46	+	12770.9i	−0.494896	+	0.868952i
$601$	−16288.3			−1.10551			−0.552756	−	0.833343i	$-0.686424\pi$
$601$	−16288.3			−1.10551			−0.552756	+	0.833343i	$0.686424\pi$
$602$	−33768.0	−	24403.1i	−2.28618	−	1.65215i
$603$	−15384.3	+	16131.9i	−1.03897	+	1.08945i
$604$	−19644.0	+	6493.21i	−1.32335	+	0.437426i
$605$	−450.420	+	534.145i	−0.0302680	+	0.0358943i
$606$	12153.1	−	7690.29i	0.814666	−	0.515506i
$607$	−6769.57			−0.452666			−0.226333	−	0.974050i	$-0.572674\pi$
$607$	−6769.57			−0.452666			−0.226333	+	0.974050i	$0.572674\pi$
$608$	−243.646	−	19188.7i	−0.0162519	−	1.27994i
$609$	7189.87	+	2878.74i	0.478404	+	0.191548i
$610$	6552.82	−	1634.54i	0.434944	−	0.108493i
$611$		−	25897.3i		−	1.71472i
$612$	−1331.25	+	2809.90i	−0.0879291	+	0.185594i
$613$	−8543.04			−0.562887			−0.281444	−	0.959578i	$-0.590813\pi$
$613$	−8543.04			−0.562887			−0.281444	+	0.959578i	$0.590813\pi$
$614$	−1043.79	−	754.313i	−0.0686055	−	0.0495791i
$615$	1464.28	+	2749.28i	0.0960090	+	0.180263i
$616$	−7308.99	+	23091.8i	−0.478064	+	1.51038i
$617$	9253.24			0.603763			0.301881	−	0.953346i	$-0.402385\pi$
$617$	9253.24			0.603763			0.301881	+	0.953346i	$0.402385\pi$
$618$	6013.80	−	3805.42i	0.391441	−	0.247697i
$619$	16231.5			1.05396			0.526980	−	0.849878i	$-0.323324\pi$
$619$	16231.5			1.05396			0.526980	+	0.849878i	$0.323324\pi$
$620$	−6025.40	+	15027.7i	−0.390300	+	0.973433i
$621$	6088.64	−	2779.65i	0.393444	−	0.179619i
$622$	−2770.59	+	3833.83i	−0.178602	+	0.247143i
$623$			22545.3i			1.44985i
$624$	18859.7	−	4969.36i	1.20993	−	0.318804i
$625$	−14734.0	+	5200.94i	−0.942976	+	0.332860i
$626$	−7143.51	−	5162.40i	−0.456090	−	0.329602i
$627$	−7292.52	+	18213.6i	−0.464490	+	1.16010i
$628$	−3835.67	−	11604.1i	−0.243726	−	0.737349i
$629$	−1637.36			−0.103793
$630$	−12688.7	+	22304.3i	−0.802430	+	1.41052i
$631$		−	12901.7i		−	0.813960i	−0.913437	−	0.406980i	$-0.866582\pi$
$631$		−	12901.7i		−	0.813960i	0.913437	−	0.406980i	$-0.133418\pi$
$632$	−734.041	+	2319.11i	−0.0462003	+	0.145964i
$633$	11975.2	+	4794.72i	0.751928	+	0.301064i
$634$	10797.9	+	7803.32i	0.676403	+	0.488816i
$635$	7340.33	−	8704.78i	0.458728	−	0.543998i
$636$	2725.02	+	168.084i	0.169896	+	0.0104795i
$637$	32858.7			2.04382
$638$	4049.15	+	2926.20i	0.251266	+	0.181582i
$639$	3079.90	+	2937.17i	0.190671	+	0.181835i
$640$	5834.18	−	15103.2i	0.360338	−	0.932822i
$641$			13164.5i			0.811182i	0.914055	+	0.405591i	$0.132934\pi$
$641$			13164.5i			0.811182i	−0.914055	+	0.405591i	$0.867066\pi$
$642$	11334.1	−	7172.00i	0.696761	−	0.440898i
$643$		−	22712.5i		−	1.39299i	−0.717561	−	0.696496i	$-0.754741\pi$
$643$		−	22712.5i		−	1.39299i	0.717561	−	0.696496i	$-0.245259\pi$
$644$	−10891.0	+	3599.95i	−0.666406	+	0.220276i
$645$	−13384.7	−	25130.6i	−0.817089	−	1.53414i
$646$	2528.17	−	3498.38i	0.153978	−	0.213068i
$647$		−	2451.48i		−	0.148961i	−0.997222	−	0.0744803i	$-0.976270\pi$
$647$		−	2451.48i		−	0.148961i	0.997222	−	0.0744803i	$-0.0237298\pi$
$648$	−4226.47	+	15944.7i	−0.256221	+	0.966618i
$649$	−14461.8			−0.874692
$650$	18615.3	+	9132.96i	1.12331	+	0.551114i
$651$	−10507.7	+	26243.7i	−0.632609	+	1.57999i
$652$	21082.5	−	6968.70i	1.26634	−	0.418582i
$653$		−	26329.5i		−	1.57787i	−0.614474	−	0.788937i	$-0.710632\pi$
$653$		−	26329.5i		−	1.57787i	0.614474	−	0.788937i	$-0.289368\pi$
$654$	−10141.1	−	16026.2i	−0.606343	−	0.958218i
$655$	3609.62	+	3043.83i	0.215328	+	0.181576i
$656$	−2045.10	−	2755.54i	−0.121719	−	0.164003i
$657$	−4523.22	+	4743.01i	−0.268596	+	0.281647i
$658$	−30424.0	−	21986.5i	−1.80251	−	1.30262i
$659$			29804.9i			1.76181i	0.473292	+	0.880906i	$0.343066\pi$
$659$			29804.9i			1.76181i	−0.473292	+	0.880906i	$0.656934\pi$
$660$	−11429.6	+	11973.4i	−0.674086	+	0.706155i
$661$		−	8483.43i		−	0.499194i	−0.968350	−	0.249597i	$-0.919702\pi$
$661$		−	8483.43i		−	0.499194i	0.968350	−	0.249597i	$-0.0802981\pi$
$662$	12829.1	−	17752.4i	0.753198	−	1.04224i
$663$	4072.43	+	1630.56i	0.238552	+	0.0955137i
$664$	24994.4	+	7911.17i	1.46080	+	0.462369i
$665$	22963.8	−	27232.4i	1.33909	−	1.58801i
$666$	−8540.91	+	1583.62i	−0.496927	+	0.0921384i
$667$			2365.92i			0.137345i
$668$	11278.5	−	3728.05i	0.653262	−	0.215932i
$669$	1064.15	+	426.072i	0.0614981	+	0.0246232i
$670$	25332.0	−	6318.85i	1.46069	−	0.364356i
$671$	7606.44			0.437621
$672$	10173.7	−	26375.3i	0.584019	−	1.51406i
$673$			32692.9i			1.87254i	0.351285	+	0.936268i	$0.385745\pi$
$673$			32692.9i			1.87254i	−0.351285	+	0.936268i	$0.614255\pi$
$674$	−19278.3	−	13931.8i	−1.10174	−	0.796193i
$675$	−14494.3	+	9872.30i	−0.826497	+	0.562941i
$676$	−3119.68	−	9438.01i	−0.177496	−	0.536983i
$677$			16192.2i			0.919226i	0.888119	+	0.459613i	$0.152012\pi$
$677$			16192.2i			0.919226i	−0.888119	+	0.459613i	$0.847988\pi$
$678$	299.065	−	189.243i	0.0169403	−	0.0107195i
$679$			2501.23i			0.141367i
$680$	3078.26	−	1945.78i	0.173597	−	0.109731i
$681$	6204.82	+	2484.34i	0.349147	+	0.139795i
$682$	−10680.9	+	14779.8i	−0.599697	+	0.829835i
$683$	14545.0			0.814862			0.407431	−	0.913236i	$-0.366425\pi$
$683$	14545.0			0.814862			0.407431	+	0.913236i	$0.366425\pi$
$684$	9804.04	−	20693.6i	0.548051	−	1.15678i
$685$	−21350.4	+	25319.1i	−1.19089	+	1.41225i
$686$	10818.4	−	14970.0i	0.602110	−	0.833174i
$687$	−6709.09	+	16756.4i	−0.372588	+	0.930565i
$688$	18693.9	+	25187.9i	1.03590	+	1.39575i
$689$		−	3851.88i		−	0.212982i
$690$	−7766.30	−	1065.85i	−0.428490	−	0.0588062i
$691$	8218.62			0.452462			0.226231	−	0.974074i	$-0.427360\pi$
$691$	8218.62			0.452462			0.226231	+	0.974074i	$0.427360\pi$
$692$	−34086.6	+	11267.1i	−1.87251	+	0.618947i
$693$	−19946.1	+	20915.3i	−1.09335	+	1.14647i
$694$	−8002.98	+	11074.2i	−0.437736	+	0.605721i
$695$	−5219.17	+	6189.33i	−0.284856	+	0.337805i
$696$	−4506.73	−	3699.78i	−0.245441	−	0.201494i
$697$		−	771.825i		−	0.0419440i
$698$	14218.6	+	10275.4i	0.771036	+	0.557205i
$699$	−6629.87	−	2654.53i	−0.358748	−	0.143639i
$700$	26533.6	−	14115.4i	1.43268	−	0.762161i
$701$	22746.0			1.22554			0.612770	−	0.790261i	$-0.290055\pi$
$701$	22746.0			1.22554			0.612770	+	0.790261i	$0.290055\pi$
$702$	22819.9	+	4566.63i	1.22690	+	0.245522i
$703$	12058.4			0.646930
$704$	10492.5	−	14914.4i	0.561721	−	0.798447i
$705$	−12059.3	−	22642.0i	−0.644224	−	1.20957i
$706$	12721.3	−	17603.2i	0.678149	−	0.938393i
$707$	−29410.3			−1.56448
$708$	16847.0	+	1039.15i	0.894279	+	0.0551606i
$709$		−	16822.0i		−	0.891062i	−0.895266	−	0.445531i	$-0.853015\pi$
$709$		−	16822.0i		−	0.891062i	0.895266	−	0.445531i	$-0.146985\pi$
$710$	−1206.39	−	4836.39i	−0.0637679	−	0.255643i
$711$	−2003.18	+	2100.52i	−0.105661	+	0.110796i
$712$	5122.09	−	16182.6i	0.269604	−	0.851782i
$713$	−8635.84			−0.453597
$714$	5373.02	−	3399.95i	0.281625	−	0.178207i
$715$	17853.2	+	15054.8i	0.933807	+	0.787436i
$716$	20614.7	−	6814.06i	1.07599	−	0.355661i
$717$	−29477.7	−	11802.5i	−1.53538	−	0.614747i
$718$	20549.2	−	28435.1i	1.06809	−	1.47798i
$719$	24046.5			1.24726			0.623631	−	0.781719i	$-0.285657\pi$
$719$	24046.5			1.24726			0.623631	+	0.781719i	$0.285657\pi$
$720$	14175.1	−	13126.9i	0.733714	−	0.679459i
$721$	−14553.3			−0.751722
$722$	−7255.54	+	10039.9i	−0.373994	+	0.517516i
$723$	−35499.2	−	14213.5i	−1.82605	−	0.731128i
$724$	−6940.56	+	2294.16i	−0.356276	+	0.117765i
$725$	−1046.74	−	6110.05i	−0.0536207	−	0.312995i
$726$	776.136	−	491.125i	0.0396764	−	0.0251065i
$727$	−2465.88			−0.125797			−0.0628986	−	0.998020i	$-0.520034\pi$
$727$	−2465.88			−0.125797			−0.0628986	+	0.998020i	$0.520034\pi$
$728$	−38024.4	−	12035.4i	−1.93582	−	0.612722i
$729$	−12893.4	+	14872.1i	−0.655053	+	0.755583i
$730$	7447.98	−	1857.83i	0.377620	−	0.0941939i
$731$			7055.10i			0.356966i
$732$	−8861.00	−	546.561i	−0.447421	−	0.0275976i
$733$	31105.2			1.56739			0.783696	−	0.621145i	$-0.213332\pi$
$733$	31105.2			1.56739			0.783696	+	0.621145i	$0.213332\pi$
$734$	−2039.74	+	2822.51i	−0.102573	+	0.141936i
$735$	28728.4	−	15300.9i	1.44172	−	0.767868i
$736$	8635.23	−	109.645i	0.432471	−	0.00549126i
$737$	29405.2			1.46968
$738$	−746.492	−	4026.04i	−0.0372341	−	0.200814i
$739$	−12767.8			−0.635548			−0.317774	−	0.948167i	$-0.602935\pi$
$739$	−12767.8			−0.635548			−0.317774	+	0.948167i	$0.602935\pi$
$740$	9442.97	+	3786.17i	0.469095	+	0.188085i
$741$	−29991.6	−	12008.3i	−1.48687	−	0.595324i
$742$	−4525.17	−	3270.20i	−0.223887	−	0.161796i
$743$			26197.5i			1.29353i	0.762690	+	0.646764i	$0.223878\pi$
$743$			26197.5i			1.29353i	−0.762690	+	0.646764i	$0.776122\pi$
$744$	13504.6	−	16450.0i	0.665458	−	0.810600i
$745$	13817.0	−	16385.4i	0.679485	−	0.805789i
$746$	−8473.48	+	11725.2i	−0.415866	+	0.575458i
$747$	22638.5	+	21589.4i	1.10883	+	1.05745i
$748$	3894.30	−	1287.24i	0.190361	−	0.0629226i
$749$	−27428.2			−1.33806
$750$	20528.2	−	683.408i	0.999446	−	0.0332727i
$751$			7833.34i			0.380616i	0.981724	+	0.190308i	$0.0609486\pi$
$751$			7833.34i			0.380616i	−0.981724	+	0.190308i	$0.939051\pi$
$752$	16842.7	+	22693.6i	0.816740	+	1.10047i
$753$	3095.02	−	7730.03i	0.149786	−	0.374101i
$754$	−4818.45	+	6667.57i	−0.232729	+	0.322040i
$755$	22104.3	+	18639.6i	1.06551	+	0.898494i
$756$	24738.7	−	22931.7i	1.19013	−	1.10320i
$757$	−10981.8			−0.527266			−0.263633	−	0.964623i	$-0.584921\pi$
$757$	−10981.8			−0.527266			−0.263633	+	0.964623i	$0.584921\pi$
$758$	−4926.63	+	6817.26i	−0.236073	+	0.326668i
$759$	−8196.43	−	3281.76i	−0.391978	−	0.156944i
$760$	−22669.9	+	14329.7i	−1.08201	+	0.683939i
$761$		−	24605.3i		−	1.17206i	−0.810288	−	0.586032i	$-0.800689\pi$
$761$		−	24605.3i		−	1.17206i	0.810288	−	0.586032i	$-0.199311\pi$
$762$	−12648.4	+	8003.69i	−0.601317	+	0.380503i
$763$			38783.1i			1.84016i
$764$	8586.33	+	25976.4i	0.406600	+	1.23009i
$765$	4319.81	−	470.762i	0.204161	−	0.0222489i
$766$	−9719.13	−	7023.72i	−0.458442	−	0.331302i
$767$		−	23813.6i		−	1.12107i
$768$	−13294.7	+	16620.3i	−0.624652	+	0.780903i
$769$	−17233.6			−0.808140			−0.404070	−	0.914728i	$-0.632405\pi$
$769$	−17233.6			−0.808140			−0.404070	+	0.914728i	$0.632405\pi$
$770$	32843.5	−	8192.51i	1.53714	−	0.383426i

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65669 + 2.29246i) q^{2} +(-4.82386 - 1.93142i) q^{3} +(-2.51074 - 7.59580i) q^{4} +(-7.20740 + 8.54713i) q^{5} +(12.4193 - 7.85874i) q^{6} -30.0545 q^{7} +(21.5726 + 6.82812i) q^{8} +(19.5392 + 18.6338i) q^{9} +O(q^{10})\)	\(q+(-1.65669 + 2.29246i) q^{2} +(-4.82386 - 1.93142i) q^{3} +(-2.51074 - 7.59580i) q^{4} +(-7.20740 + 8.54713i) q^{5} +(12.4193 - 7.85874i) q^{6} -30.0545 q^{7} +(21.5726 + 6.82812i) q^{8} +(19.5392 + 18.6338i) q^{9} +(-7.65352 - 30.6826i) q^{10} -35.6161i q^{11} +(-2.55919 + 41.4904i) q^{12} +58.6475 q^{13} +(49.7911 - 68.8988i) q^{14} +(51.2756 - 27.3096i) q^{15} +(-51.3923 + 38.1422i) q^{16} -14.3949 q^{17} +(-75.0877 + 13.9225i) q^{18} +106.012 q^{19} +(83.0182 + 33.2863i) q^{20} +(144.979 + 58.0479i) q^{21} +(81.6485 + 59.0049i) q^{22} +47.7072i q^{23} +(-90.8752 - 74.6036i) q^{24} +(-21.1068 - 123.205i) q^{25} +(-97.1608 + 134.447i) q^{26} +(-58.2649 - 127.625i) q^{27} +(75.4593 + 228.288i) q^{28} +49.5925 q^{29} +(-22.3415 + 162.791i) q^{30} +181.017i q^{31} +(-2.29829 - 181.005i) q^{32} +(-68.7896 + 171.807i) q^{33} +(23.8480 - 32.9998i) q^{34} +(216.615 - 256.880i) q^{35} +(92.4805 - 195.201i) q^{36} +113.746 q^{37} +(-175.629 + 243.028i) q^{38} +(-282.907 - 113.273i) q^{39} +(-213.843 + 135.171i) q^{40} +53.6178i q^{41} +(-373.258 + 236.191i) q^{42} -490.109i q^{43} +(-270.533 + 89.4229i) q^{44} +(-300.092 + 32.7033i) q^{45} +(-109.367 - 79.0361i) q^{46} -441.575i q^{47} +(321.578 - 84.7326i) q^{48} +560.275 q^{49} +(317.410 + 155.726i) q^{50} +(69.4392 + 27.8027i) q^{51} +(-147.249 - 445.475i) q^{52} -65.6784i q^{53} +(389.103 + 77.8658i) q^{54} +(304.415 + 256.699i) q^{55} +(-648.354 - 205.216i) q^{56} +(-511.387 - 204.754i) q^{57} +(-82.1595 + 113.689i) q^{58} -406.047i q^{59} +(-336.178 - 320.911i) q^{60} +213.568i q^{61} +(-414.975 - 299.890i) q^{62} +(-587.243 - 560.030i) q^{63} +(418.754 + 294.600i) q^{64} +(-422.696 + 501.268i) q^{65} +(-279.898 - 442.329i) q^{66} +825.615i q^{67} +(36.1420 + 109.341i) q^{68} +(92.1426 - 230.133i) q^{69} +(230.023 + 922.152i) q^{70} +157.626 q^{71} +(294.278 + 535.395i) q^{72} +242.743i q^{73} +(-188.442 + 260.758i) q^{74} +(-136.144 + 635.090i) q^{75} +(-266.169 - 805.246i) q^{76} +1070.43i q^{77} +(728.364 - 460.895i) q^{78} +107.503i q^{79} +(44.3984 - 714.163i) q^{80} +(34.5637 + 728.180i) q^{81} +(-122.917 - 88.8281i) q^{82} +1158.62 q^{83} +(76.9153 - 1246.97i) q^{84} +(103.750 - 123.035i) q^{85} +(1123.56 + 811.960i) q^{86} +(-239.227 - 95.7839i) q^{87} +(243.191 - 768.331i) q^{88} -750.147i q^{89} +(422.190 - 742.129i) q^{90} -1762.62 q^{91} +(362.374 - 119.781i) q^{92} +(349.621 - 873.203i) q^{93} +(1012.29 + 731.554i) q^{94} +(-764.070 + 906.098i) q^{95} +(-338.509 + 877.580i) q^{96} -83.2231i q^{97} +(-928.203 + 1284.41i) q^{98} +(663.663 - 695.911i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9}+O(q^{10}) \) 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9	\( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54} - 2064 q^{60} + 2176 q^{64} - 176 q^{66} + 672 q^{70} - 1600 q^{75} + 2304 q^{76} - 2304 q^{81} - 736 q^{84} - 1432 q^{90} - 2752 q^{91} + 4496 q^{94} + 640 q^{96} + 256 q^{99}+O(q^{100}) \) 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9 - 72 * q^10 - 128 * q^16 + 672 * q^19 - 416 * q^24 + 496 * q^25 - 248 * q^30 + 240 * q^34 - 608 * q^36 - 1344 * q^40 + 336 * q^46 + 3520 * q^49 - 544 * q^51 - 952 * q^54 - 2064 * q^60 + 2176 * q^64 - 176 * q^66 + 672 * q^70 - 1600 * q^75 + 2304 * q^76 - 2304 * q^81 - 736 * q^84 - 1432 * q^90 - 2752 * q^91 + 4496 * q^94 + 640 * q^96 + 256 * q^99

Introduction

L-functions

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