LMFDB - Embedded newform 117.3.k.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(29,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.k (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.53953i q^{2} +(0.194193 + 2.99371i) q^{3} -8.52830 q^{4} +(-6.00755 + 3.46846i) q^{5} +(10.5963 - 0.687351i) q^{6} +(-2.39062 - 4.14067i) q^{7} +16.0281i q^{8} +(-8.92458 + 1.16271i) q^{9} +(12.2767 + 21.2639i) q^{10} +14.5808i q^{11} +(-1.65613 - 25.5312i) q^{12} +(8.05780 + 10.2016i) q^{13} +(-14.6561 + 8.46168i) q^{14} +(-11.5502 - 17.3113i) q^{15} +22.6187 q^{16} +(-23.2425 - 13.4191i) q^{17} +(4.11546 + 31.5888i) q^{18} +(5.79181 - 10.0317i) q^{19} +(51.2342 - 29.5801i) q^{20} +(11.9317 - 7.96091i) q^{21} +51.6093 q^{22} +(-27.6664 - 15.9732i) q^{23} +(-47.9833 + 3.11253i) q^{24} +(11.5604 - 20.0233i) q^{25} +(36.1088 - 28.5208i) q^{26} +(-5.21391 - 26.4918i) q^{27} +(20.3879 + 35.3129i) q^{28} +23.2513i q^{29} +(-61.2739 + 40.8823i) q^{30} +(-7.06716 - 12.2407i) q^{31} -15.9473i q^{32} +(-43.6507 + 2.83149i) q^{33} +(-47.4973 + 82.2677i) q^{34} +(28.7235 + 16.5835i) q^{35} +(76.1115 - 9.91595i) q^{36} +(13.2297 + 22.9145i) q^{37} +(-35.5076 - 20.5003i) q^{38} +(-28.9757 + 26.1038i) q^{39} +(-55.5927 - 96.2894i) q^{40} +(0.891522 + 0.514720i) q^{41} +(-28.1779 - 42.2328i) q^{42} +(5.58744 + 9.67774i) q^{43} -124.350i q^{44} +(49.5820 - 37.9396i) q^{45} +(-56.5378 + 97.9263i) q^{46} +(29.9550 + 17.2945i) q^{47} +(4.39238 + 67.7137i) q^{48} +(13.0699 - 22.6377i) q^{49} +(-70.8730 - 40.9186i) q^{50} +(35.6593 - 72.1872i) q^{51} +(-68.7193 - 87.0020i) q^{52} -8.55270i q^{53} +(-93.7686 + 18.4548i) q^{54} +(-50.5730 - 87.5950i) q^{55} +(66.3670 - 38.3170i) q^{56} +(31.1567 + 15.3909i) q^{57} +82.2987 q^{58} +97.6091i q^{59} +(98.5034 + 147.636i) q^{60} +(12.0161 + 20.8125i) q^{61} +(-43.3263 + 25.0144i) q^{62} +(26.1497 + 34.1742i) q^{63} +34.0287 q^{64} +(-83.7913 - 33.3382i) q^{65} +(10.0221 + 154.503i) q^{66} +(-36.0107 + 62.3723i) q^{67} +(198.219 + 114.442i) q^{68} +(42.4466 - 85.9271i) q^{69} +(58.6980 - 101.668i) q^{70} +(60.2943 + 34.8109i) q^{71} +(-18.6360 - 143.044i) q^{72} -64.5728 q^{73} +(81.1067 - 46.8270i) q^{74} +(62.1888 + 30.7202i) q^{75} +(-49.3943 + 85.5534i) q^{76} +(60.3744 - 34.8572i) q^{77} +(92.3952 + 102.561i) q^{78} +(-7.43609 + 12.8797i) q^{79} +(-135.883 + 78.4520i) q^{80} +(78.2962 - 20.7534i) q^{81} +(1.82187 - 3.15557i) q^{82} +(-90.6104 - 52.3140i) q^{83} +(-101.757 + 67.8930i) q^{84} +186.174 q^{85} +(34.2547 - 19.7769i) q^{86} +(-69.6076 + 4.51523i) q^{87} -233.702 q^{88} +(-71.9152 + 41.5203i) q^{89} +(-134.288 - 175.497i) q^{90} +(22.9782 - 57.7528i) q^{91} +(235.948 + 136.224i) q^{92} +(35.2726 - 23.5341i) q^{93} +(61.2146 - 106.027i) q^{94} +80.3547i q^{95} +(47.7416 - 3.09685i) q^{96} +(-13.5762 - 23.5147i) q^{97} +(-80.1268 - 46.2613i) q^{98} +(-16.9533 - 130.128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	3.53953i		−	1.76977i	−0.465813	−	0.884883i	$-0.654238\pi$
$2$		−	3.53953i		−	1.76977i	0.465813	−	0.884883i	$-0.345762\pi$
$3$	0.194193	+	2.99371i	0.0647309	+	0.997903i
$3$	0.194193	+	2.99371i	0.0647309	+	0.997903i
$4$	−8.52830			−2.13207
$5$	−6.00755	+	3.46846i	−1.20151	+	0.693692i	−0.960891	−	0.276927i	$-0.910684\pi$
$5$	−6.00755	+	3.46846i	−1.20151	+	0.693692i	−0.240619	+	0.970620i	$0.577350\pi$
$6$	10.5963	−	0.687351i	1.76606	−	0.114559i
$7$	−2.39062	−	4.14067i	−0.341517	−	0.591525i	0.643198	−	0.765700i	$-0.277607\pi$
$7$	−2.39062	−	4.14067i	−0.341517	−	0.591525i	−0.984715	+	0.174175i	$0.944274\pi$
$8$			16.0281i			2.00351i
$9$	−8.92458	+	1.16271i	−0.991620	+	0.129190i
$10$	12.2767	+	21.2639i	1.22767	+	2.12639i
$11$			14.5808i			1.32553i	0.748828	+	0.662764i	$0.230617\pi$
$11$			14.5808i			1.32553i	−0.748828	+	0.662764i	$0.769383\pi$
$12$	−1.65613	−	25.5312i	−0.138011	−	2.12760i
$13$	8.05780	+	10.2016i	0.619831	+	0.784736i
$13$	8.05780	+	10.2016i	0.619831	+	0.784736i
$14$	−14.6561	+	8.46168i	−1.04686	+	0.604406i
$15$	−11.5502	−	17.3113i	−0.770012	−	1.15409i
$16$	22.6187			1.41367
$17$	−23.2425	−	13.4191i	−1.36721	−	0.789358i	−0.376637	−	0.926361i	$-0.622920\pi$
$17$	−23.2425	−	13.4191i	−1.36721	−	0.789358i	−0.990571	+	0.137003i	$0.956253\pi$
$18$	4.11546	+	31.5888i	0.228637	+	1.75494i
$19$	5.79181	−	10.0317i	0.304832	−	0.527985i	−0.672392	−	0.740195i	$-0.734733\pi$
$19$	5.79181	−	10.0317i	0.304832	−	0.527985i	0.977224	+	0.212211i	$0.0680663\pi$
$20$	51.2342	−	29.5801i	2.56171	−	1.47900i
$21$	11.9317	−	7.96091i	0.568178	−	0.379091i
$22$	51.6093			2.34588
$23$	−27.6664	−	15.9732i	−1.20289	−	0.694488i	−0.241692	−	0.970353i	$-0.577702\pi$
$23$	−27.6664	−	15.9732i	−1.20289	−	0.694488i	−0.961196	+	0.275865i	$0.911036\pi$
$24$	−47.9833	+	3.11253i	−1.99931	+	0.129689i
$25$	11.5604	−	20.0233i	0.462418	−	0.800931i
$26$	36.1088	−	28.5208i	1.38880	−	1.09696i
$27$	−5.21391	−	26.4918i	−0.193108	−	0.981178i
$28$	20.3879	+	35.3129i	0.728140	+	1.26118i
$29$			23.2513i			0.801769i	0.916129	+	0.400884i	$0.131297\pi$
$29$			23.2513i			0.801769i	−0.916129	+	0.400884i	$0.868703\pi$
$30$	−61.2739	+	40.8823i	−2.04246	+	1.36274i
$31$	−7.06716	−	12.2407i	−0.227973	−	0.394861i	0.729234	−	0.684264i	$-0.239876\pi$
$31$	−7.06716	−	12.2407i	−0.227973	−	0.394861i	−0.957207	+	0.289403i	$0.906543\pi$
$32$		−	15.9473i		−	0.498353i
$33$	−43.6507	+	2.83149i	−1.32275	+	0.0858026i
$34$	−47.4973	+	82.2677i	−1.39698	+	2.41964i
$35$	28.7235	+	16.5835i	0.820672	+	0.473815i
$36$	76.1115	−	9.91595i	2.11421	−	0.275443i
$37$	13.2297	+	22.9145i	0.357560	+	0.619312i	0.987553	−	0.157289i	$-0.0502755\pi$
$37$	13.2297	+	22.9145i	0.357560	+	0.619312i	−0.629993	+	0.776601i	$0.716942\pi$
$38$	−35.5076	−	20.5003i	−0.934410	−	0.539482i
$39$	−28.9757	+	26.1038i	−0.742968	+	0.669327i
$40$	−55.5927	−	96.2894i	−1.38982	−	2.40723i
$41$	0.891522	+	0.514720i	0.0217444	+	0.0125542i	0.510833	−	0.859680i	$-0.329337\pi$
$41$	0.891522	+	0.514720i	0.0217444	+	0.0125542i	−0.489088	+	0.872234i	$0.662670\pi$
$42$	−28.1779	−	42.2328i	−0.670902	−	1.00554i
$43$	5.58744	+	9.67774i	0.129941	+	0.225064i	0.923653	−	0.383229i	$-0.125188\pi$
$43$	5.58744	+	9.67774i	0.129941	+	0.225064i	−0.793713	+	0.608293i	$0.791855\pi$
$44$		−	124.350i		−	2.82613i
$45$	49.5820	−	37.9396i	1.10182	−	0.843102i
$46$	−56.5378	+	97.9263i	−1.22908	+	2.12883i
$47$	29.9550	+	17.2945i	0.637341	+	0.367969i	0.783589	−	0.621279i	$-0.213387\pi$
$47$	29.9550	+	17.2945i	0.637341	+	0.367969i	−0.146249	+	0.989248i	$0.546720\pi$
$48$	4.39238	+	67.7137i	0.0915079	+	1.41070i
$49$	13.0699	−	22.6377i	0.266732	−	0.461994i
$50$	−70.8730	−	40.9186i	−1.41746	−	0.818371i
$51$	35.6593	−	72.1872i	0.699202	−	1.41544i
$52$	−68.7193	−	87.0020i	−1.32153	−	1.67311i
$53$		−	8.55270i		−	0.161372i	−0.996740	−	0.0806859i	$-0.974289\pi$
$53$		−	8.55270i		−	0.161372i	0.996740	−	0.0806859i	$-0.0257111\pi$
$54$	−93.7686	+	18.4548i	−1.73646	+	0.341756i
$55$	−50.5730	−	87.5950i	−0.919509	−	1.59264i
$56$	66.3670	−	38.3170i	1.18512	−	0.684232i
$57$	31.1567	+	15.3909i	0.546610	+	0.270016i
$58$	82.2987			1.41894
$59$			97.6091i			1.65439i	0.561914	+	0.827195i	$0.310065\pi$
$59$			97.6091i			1.65439i	−0.561914	+	0.827195i	$0.689935\pi$
$60$	98.5034	+	147.636i	1.64172	+	2.46060i
$61$	12.0161	+	20.8125i	0.196985	+	0.341188i	0.947549	−	0.319609i	$-0.103552\pi$
$61$	12.0161	+	20.8125i	0.196985	+	0.341188i	−0.750564	+	0.660797i	$0.770218\pi$
$62$	−43.3263	+	25.0144i	−0.698811	+	0.403459i
$63$	26.1497	+	34.1742i	0.415074	+	0.542447i
$64$	34.0287			0.531698
$65$	−83.7913	−	33.3382i	−1.28910	−	0.512896i
$66$	10.0221	+	154.503i	0.151851	+	2.34096i
$67$	−36.0107	+	62.3723i	−0.537473	+	0.930931i	0.461566	+	0.887106i	$0.347288\pi$
$67$	−36.0107	+	62.3723i	−0.537473	+	0.930931i	−0.999039	+	0.0438248i	$0.986046\pi$
$68$	198.219	+	114.442i	2.91499	+	1.68297i
$69$	42.4466	−	85.9271i	0.615168	−	1.24532i
$70$	58.6980	−	101.668i	0.838543	−	1.45240i
$71$	60.2943	+	34.8109i	0.849216	+	0.490295i	0.860386	−	0.509643i	$-0.170222\pi$
$71$	60.2943	+	34.8109i	0.849216	+	0.490295i	−0.0111703	+	0.999938i	$0.503556\pi$
$72$	−18.6360	−	143.044i	−0.258834	−	1.98672i
$73$	−64.5728			−0.884559			−0.442279	−	0.896877i	$-0.645830\pi$
$73$	−64.5728			−0.884559			−0.442279	+	0.896877i	$0.645830\pi$
$74$	81.1067	−	46.8270i	1.09604	−	0.632797i
$75$	62.1888	+	30.7202i	0.829184	+	0.409603i
$76$	−49.3943	+	85.5534i	−0.649925	+	1.12570i
$77$	60.3744	−	34.8572i	0.784083	−	0.452691i
$78$	92.3952	+	102.561i	1.18455	+	1.31488i
$79$	−7.43609	+	12.8797i	−0.0941278	+	0.163034i	−0.909244	−	0.416263i	$-0.863340\pi$
$79$	−7.43609	+	12.8797i	−0.0941278	+	0.163034i	0.815116	+	0.579297i	$0.196673\pi$
$80$	−135.883	+	78.4520i	−1.69854	+	0.980650i
$81$	78.2962	−	20.7534i	0.966620	−	0.256215i
$82$	1.82187	−	3.15557i	0.0222179	−	0.0384826i
$83$	−90.6104	−	52.3140i	−1.09169	−	0.630289i	−0.157665	−	0.987493i	$-0.550397\pi$
$83$	−90.6104	−	52.3140i	−1.09169	−	0.630289i	−0.934026	+	0.357204i	$0.883730\pi$
$84$	−101.757	+	67.8930i	−1.21140	+	0.808250i
$85$	186.174			2.19028
$86$	34.2547	−	19.7769i	0.398310	−	0.229965i
$87$	−69.6076	+	4.51523i	−0.800087	+	0.0518992i
$88$	−233.702			−2.65571
$89$	−71.9152	+	41.5203i	−0.808036	+	0.466520i	−0.846273	−	0.532749i	$-0.821159\pi$
$89$	−71.9152	+	41.5203i	−0.808036	+	0.466520i	0.0382372	+	0.999269i	$0.487826\pi$
$90$	−134.288	−	175.497i	−1.49209	−	1.94997i
$91$	22.9782	−	57.7528i	0.252508	−	0.634646i
$92$	235.948	+	136.224i	2.56465	+	1.48070i
$93$	35.2726	−	23.5341i	0.379276	−	0.253054i
$94$	61.2146	−	106.027i	0.651219	−	1.12794i
$95$			80.3547i			0.845839i
$96$	47.7416	−	3.09685i	0.497308	−	0.0322588i
$97$	−13.5762	−	23.5147i	−0.139961	−	0.242420i	0.787521	−	0.616288i	$-0.211364\pi$
$97$	−13.5762	−	23.5147i	−0.139961	−	0.242420i	−0.927482	+	0.373869i	$0.878031\pi$
$98$	−80.1268	−	46.2613i	−0.817621	−	0.472054i
$99$	−16.9533	−	130.128i	−0.171245	−	1.31442i
$100$	−98.5909	+	170.764i	−0.985909	+	1.70764i
$101$		−	62.6007i		−	0.619809i	−0.950768	−	0.309904i	$-0.899703\pi$
$101$		−	62.6007i		−	0.619809i	0.950768	−	0.309904i	$-0.100297\pi$
$102$	−255.509	−	126.217i	−2.50499	−	1.23742i
$103$	55.1061	+	95.4465i	0.535010	+	0.926665i	0.999163	+	0.0409098i	$0.0130256\pi$
$103$	55.1061	+	95.4465i	0.535010	+	0.926665i	−0.464153	+	0.885755i	$0.653641\pi$
$104$	−163.511	+	129.151i	−1.57222	+	1.24184i
$105$	−44.0684	+	89.2103i	−0.419699	+	0.849622i
$106$	−30.2726			−0.285590
$107$	−89.5094	+	51.6783i	−0.836536	+	0.482974i	−0.856085	−	0.516835i	$-0.827110\pi$
$107$	−89.5094	+	51.6783i	−0.836536	+	0.482974i	0.0195492	+	0.999809i	$0.493777\pi$
$108$	44.4658	+	225.930i	0.411720	+	2.09194i
$109$	−37.3796			−0.342932			−0.171466	−	0.985190i	$-0.554850\pi$
$109$	−37.3796			−0.342932			−0.171466	+	0.985190i	$0.554850\pi$
$110$	−310.045	+	179.005i	−2.81859	+	1.62732i
$111$	−66.0303	+	44.0557i	−0.594868	+	0.396898i
$112$	−54.0726	−	93.6566i	−0.482791	−	0.836219i
$113$		−	185.714i		−	1.64349i	−0.569856	−	0.821745i	$-0.693001\pi$
$113$		−	185.714i		−	1.64349i	0.569856	−	0.821745i	$-0.306999\pi$
$114$	54.4766	−	110.280i	0.477865	−	0.967371i
$115$	221.610			1.92704
$116$		−	198.294i		−	1.70943i
$117$	−83.7739	−	81.6757i	−0.716017	−	0.698083i
$118$	345.491			2.92789
$119$			128.320i			1.07832i
$120$	277.467	−	185.127i	2.31222	−	1.54273i
$121$	−91.6001			−0.757026
$122$	73.6665	−	42.5314i	0.603824	−	0.348618i
$123$	−1.36780	+	2.76891i	−0.0111203	+	0.0225115i
$124$	60.2708	+	104.392i	0.486055	+	0.841872i
$125$		−	13.0353i		−	0.104283i
$126$	120.961	−	92.5577i	0.960005	−	0.734585i
$127$	7.47211	+	12.9421i	0.0588355	+	0.101906i	0.893943	−	0.448181i	$-0.147928\pi$
$127$	7.47211	+	12.9421i	0.0588355	+	0.101906i	−0.835107	+	0.550087i	$0.814595\pi$
$128$		−	184.235i		−	1.43933i
$129$	−27.8873	+	18.6065i	−0.216181	+	0.144237i
$130$	−118.002	+	296.582i	−0.907706	+	2.28140i
$131$	−166.360	+	96.0478i	−1.26992	+	0.733190i	−0.974973	−	0.222323i	$-0.928636\pi$
$131$	−166.360	+	96.0478i	−1.26992	+	0.733190i	−0.294949	+	0.955513i	$0.595303\pi$
$132$	372.266	−	24.1478i	2.82020	−	0.182938i
$133$	−55.3841			−0.416422
$134$	220.769	+	127.461i	1.64753	+	0.951202i
$135$	123.209	+	141.067i	0.912656	+	1.04494i
$136$	215.082	−	372.533i	1.58148	−	2.73921i
$137$	204.623	−	118.139i	1.49360	−	0.862330i	0.493627	−	0.869674i	$-0.335671\pi$
$137$	204.623	−	118.139i	1.49360	−	0.862330i	0.999973	+	0.00734348i	$0.00233752\pi$
$138$	−304.142	−	150.241i	−2.20393	−	1.08870i
$139$	−204.623			−1.47211			−0.736054	−	0.676923i	$-0.763313\pi$
$139$	−204.623			−1.47211			−0.736054	+	0.676923i	$0.763313\pi$
$140$	−244.963	−	141.429i	−1.74973	−	1.01021i
$141$	−45.9577	+	93.0350i	−0.325941	+	0.659823i
$142$	123.215	−	213.414i	0.867708	−	1.50291i
$143$	−148.747	+	117.489i	−1.04019	+	0.821603i
$144$	−201.862	+	26.2990i	−1.40182	+	0.182632i
$145$	−80.6462	−	139.683i	−0.556181	−	0.963333i
$146$			228.558i			1.56546i
$147$	70.3087	+	34.7313i	0.478290	+	0.236267i
$148$	−112.827	−	195.422i	−0.762344	−	1.32042i
$149$			180.830i			1.21362i	0.794846	+	0.606811i	$0.207552\pi$
$149$			180.830i			1.21362i	−0.794846	+	0.606811i	$0.792448\pi$
$150$	108.735	−	220.119i	0.724901	−	1.46746i
$151$	−48.1240	+	83.3533i	−0.318702	+	0.552008i	−0.980218	−	0.197923i	$-0.936580\pi$
$151$	−48.1240	+	83.3533i	−0.318702	+	0.552008i	0.661515	+	0.749932i	$0.269914\pi$
$152$	160.789	+	92.8315i	1.05782	+	0.610734i
$153$	223.032	+	92.7353i	1.45773	+	0.606113i
$154$	−123.378	−	213.697i	−0.801157	−	1.38764i
$155$	84.9126	+	49.0243i	0.547823	+	0.316286i
$156$	247.114	−	222.621i	1.58406	−	1.42706i
$157$	−66.1161	−	114.516i	−0.421122	−	0.729404i	0.574928	−	0.818204i	$-0.305030\pi$
$157$	−66.1161	−	114.516i	−0.421122	−	0.729404i	−0.996049	+	0.0888001i	$0.971697\pi$
$158$	45.5881	+	26.3203i	0.288532	+	0.166584i
$159$	25.6043	−	1.66087i	0.161033	−	0.0104457i
$160$	55.3126	+	95.8042i	0.345704	+	0.598776i
$161$			152.744i			0.948718i
$162$	−73.4574	−	277.132i	−0.453441	−	1.71069i
$163$	−0.785540	+	1.36060i	−0.00481926	+	0.00834721i	−0.868425	−	0.495821i	$-0.834867\pi$
$163$	−0.785540	+	1.36060i	−0.00481926	+	0.00834721i	0.863606	+	0.504168i	$0.168201\pi$
$164$	−7.60316	−	4.38969i	−0.0463608	−	0.0267664i
$165$	252.413	−	168.411i	1.52977	−	1.02067i
$166$	−185.167	+	320.719i	−1.11546	+	1.93204i
$167$	238.739	+	137.836i	1.42958	+	0.825366i	0.997087	−	0.0762737i	$-0.0243023\pi$
$167$	238.739	+	137.836i	1.42958	+	0.825366i	0.432488	+	0.901639i	$0.357636\pi$
$168$	127.598	+	191.243i	0.759511	+	1.13835i
$169$	−39.1438	+	164.404i	−0.231620	+	0.972806i
$170$		−	658.970i		−	3.87629i
$171$	−40.0255	+	96.2630i	−0.234067	+	0.562942i
$172$	−47.6514	−	82.5346i	−0.277043	−	0.479853i
$173$	50.4722	−	29.1401i	0.291747	−	0.168440i	−0.346983	−	0.937872i	$-0.612794\pi$
$173$	50.4722	−	29.1401i	0.291747	−	0.168440i	0.638729	+	0.769431i	$0.279460\pi$
$174$	15.9818	+	246.378i	0.0918495	+	1.41597i
$175$	−110.546			−0.631694
$176$			329.799i			1.87386i
$177$	−292.213	+	18.9550i	−1.65092	+	0.107090i
$178$	146.962	+	254.546i	0.825632	+	1.43004i
$179$	7.54922	−	4.35854i	0.0421744	−	0.0243494i	−0.478765	−	0.877943i	$-0.658915\pi$
$179$	7.54922	−	4.35854i	0.0421744	−	0.0243494i	0.520939	+	0.853594i	$0.325582\pi$
$180$	−422.850	+	323.560i	−2.34917	+	1.79756i
$181$	−319.717			−1.76639			−0.883195	−	0.469006i	$-0.844612\pi$
$181$	−319.717			−1.76639			−0.883195	+	0.469006i	$0.844612\pi$
$182$	−204.418	−	81.3322i	−1.12318	−	0.446880i
$183$	−59.9731	+	40.0143i	−0.327722	+	0.218657i
$184$	256.020	−	443.439i	1.39141	−	2.41000i
$185$	−158.956	−	91.7735i	−0.859223	−	0.496073i
$186$	−83.2996	−	124.849i	−0.447847	−	0.671229i
$187$	195.661	−	338.895i	1.04632	−	1.81227i
$188$	−255.465	−	147.493i	−1.35886	−	0.784537i
$189$	−97.2294	+	84.9209i	−0.514441	+	0.449317i
$190$	284.418			1.49694
$191$	−18.6864	+	10.7886i	−0.0978346	+	0.0564848i	−0.548119	−	0.836400i	$-0.684656\pi$
$191$	−18.6864	+	10.7886i	−0.0978346	+	0.0564848i	0.450284	+	0.892885i	$0.351323\pi$
$192$	6.60812	+	101.872i	0.0344173	+	0.530583i
$193$	−4.45316	+	7.71309i	−0.0230733	+	0.0399642i	−0.877332	−	0.479885i	$-0.840678\pi$
$193$	−4.45316	+	7.71309i	−0.0230733	+	0.0399642i	0.854258	+	0.519849i	$0.174012\pi$
$194$	−83.2311	+	48.0535i	−0.429026	+	0.247698i
$195$	83.5333	−	257.321i	0.428376	−	1.31959i
$196$	−111.464	+	193.061i	−0.568693	+	0.985005i
$197$	13.8582	−	8.00106i	0.0703464	−	0.0406145i	−0.464414	−	0.885618i	$-0.653735\pi$
$197$	13.8582	−	8.00106i	0.0703464	−	0.0406145i	0.534761	+	0.845004i	$0.320402\pi$
$198$	−460.591	+	60.0067i	−2.32622	+	0.303064i
$199$	−86.1243	+	149.172i	−0.432786	+	0.749607i	−0.997112	−	0.0759451i	$-0.975803\pi$
$199$	−86.1243	+	149.172i	−0.432786	+	0.749607i	0.564326	+	0.825552i	$0.309136\pi$
$200$	320.934	+	185.291i	1.60467	+	0.926457i
$201$	−193.718	−	95.6933i	−0.963769	−	0.476086i
$202$	−221.577			−1.09692
$203$	96.2761	−	55.5850i	0.474266	−	0.273818i
$204$	−304.113	+	615.634i	−1.49075	+	3.01781i
$205$	−7.14115			−0.0348349
$206$	337.836	−	195.050i	1.63998	−	0.946843i
$207$	265.484	+	110.386i	1.28253	+	0.533267i
$208$	182.257	+	230.746i	0.876234	+	1.10935i
$209$	146.271	+	84.4493i	0.699859	+	0.404064i
$210$	315.763	+	155.982i	1.50363	+	0.742769i
$211$	39.4983	−	68.4130i	0.187196	−	0.324232i	−0.757119	−	0.653277i	$-0.773394\pi$
$211$	39.4983	−	68.4130i	0.187196	−	0.324232i	0.944314	+	0.329045i	$0.106727\pi$
$212$			72.9400i			0.344057i
$213$	−92.5051	+	187.264i	−0.434296	+	0.879172i
$214$	182.917	+	316.821i	0.854752	+	1.48047i
$215$	−67.1337	−	38.7597i	−0.312250	−	0.180278i
$216$	424.612	−	83.5688i	1.96580	−	0.386893i
$217$	−33.7898	+	58.5256i	−0.155713	+	0.269703i
$218$			132.306i			0.606910i
$219$	−12.5396	−	193.312i	−0.0572583	−	0.882704i
$220$	431.301	+	747.036i	1.96046	+	3.39562i
$221$	−50.3880	−	345.238i	−0.228000	−	1.56216i
$222$	155.937	+	233.716i	0.702418	+	1.05278i
$223$	136.653			0.612793			0.306396	−	0.951904i	$-0.400877\pi$
$223$	136.653			0.612793			0.306396	+	0.951904i	$0.400877\pi$
$224$	−66.0326	+	38.1239i	−0.294788	+	0.170196i
$225$	−79.8908	+	192.141i	−0.355070	+	0.853959i
$226$	−657.342			−2.90859
$227$	78.8649	−	45.5326i	0.347422	−	0.200584i	−0.316127	−	0.948717i	$-0.602383\pi$
$227$	78.8649	−	45.5326i	0.347422	−	0.200584i	0.663549	+	0.748133i	$0.269049\pi$
$228$	−265.714	−	131.258i	−1.16541	−	0.575694i
$229$	104.863	+	181.628i	0.457918	+	0.793137i	0.998851	−	0.0479288i	$-0.0152620\pi$
$229$	104.863	+	181.628i	0.457918	+	0.793137i	−0.540933	+	0.841066i	$0.681929\pi$
$230$		−	784.396i		−	3.41042i
$231$	116.076	+	173.974i	0.502496	+	0.753136i
$232$	−372.673			−1.60635
$233$		−	308.839i		−	1.32549i	−0.748845	−	0.662745i	$-0.769391\pi$
$233$		−	308.839i		−	1.32549i	0.748845	−	0.662745i	$-0.230609\pi$
$234$	−289.094	+	296.521i	−1.23544	+	1.26718i
$235$	−239.942			−1.02103
$236$		−	832.439i		−	3.52728i
$237$	−40.0021	−	19.7604i	−0.168785	−	0.0833770i
$238$	454.192			1.90837
$239$	167.140	−	96.4983i	0.699331	−	0.403759i	−0.107767	−	0.994176i	$-0.534370\pi$
$239$	167.140	−	96.4983i	0.699331	−	0.403759i	0.807098	+	0.590417i	$0.201037\pi$
$240$	−261.250	−	391.559i	−1.08854	−	1.63149i
$241$	−156.704	−	271.420i	−0.650225	−	1.12622i	−0.983068	−	0.183241i	$-0.941341\pi$
$241$	−156.704	−	271.420i	−0.650225	−	1.12622i	0.332843	−	0.942982i	$-0.391992\pi$
$242$			324.222i			1.33976i
$243$	77.3342	+	230.366i	0.318248	+	0.948008i
$244$	−102.477	−	177.495i	−0.419987	−	0.727439i
$245$			181.329i			0.740120i
$246$	9.80066	+	4.84136i	0.0398401	+	0.0196803i
$247$	149.008	−	21.7480i	0.603273	−	0.0880485i
$248$	196.194	−	113.273i	0.791106	−	0.456745i
$249$	139.017	−	281.420i	0.558301	−	1.13020i
$250$	−46.1390			−0.184556
$251$	231.469	+	133.638i	0.922186	+	0.532424i	0.884332	−	0.466859i	$-0.154614\pi$
$251$	231.469	+	133.638i	0.922186	+	0.532424i	0.0378541	+	0.999283i	$0.487948\pi$
$252$	−223.012	−	291.448i	−0.884969	−	1.15654i
$253$	232.903	−	403.399i	0.920564	−	1.59446i
$254$	45.8089	−	26.4478i	0.180350	−	0.104125i
$255$	36.1536	+	557.351i	0.141779	+	2.18569i
$256$	−515.991			−2.01559
$257$	−63.6103	−	36.7254i	−0.247511	−	0.142901i	0.371113	−	0.928588i	$-0.378976\pi$
$257$	−63.6103	−	36.7254i	−0.247511	−	0.142901i	−0.618624	+	0.785687i	$0.712310\pi$
$258$	65.8584	+	98.7080i	0.255265	+	0.382589i
$259$	63.2544	−	109.560i	0.244226	−	0.423011i
$260$	714.598	+	284.318i	2.74845	+	1.09353i
$261$	−27.0346	−	207.508i	−0.103581	−	0.795050i
$262$	339.965	+	588.836i	1.29757	+	2.24747i
$263$		−	6.08203i		−	0.0231256i	−0.999933	−	0.0115628i	$-0.996319\pi$
$263$		−	6.08203i		−	0.0231256i	0.999933	−	0.0115628i	$-0.00368063\pi$
$264$	−45.3832	−	699.636i	−0.171906	−	2.65014i
$265$	29.6647	+	51.3808i	0.111942	+	0.193890i
$266$			196.034i			0.736969i
$267$	−138.265	−	207.230i	−0.517846	−	0.776143i
$268$	307.110	−	531.930i	1.14593	−	1.98481i
$269$	−154.391	−	89.1378i	−0.573945	−	0.331367i	0.184778	−	0.982780i	$-0.440843\pi$
$269$	−154.391	−	89.1378i	−0.573945	−	0.331367i	−0.758723	+	0.651413i	$0.774177\pi$
$270$	499.310	−	436.101i	1.84930	−	1.61519i
$271$	117.638	+	203.755i	0.434088	+	0.751863i	0.997221	−	0.0745036i	$-0.0237372\pi$
$271$	117.638	+	203.755i	0.434088	+	0.751863i	−0.563132	+	0.826367i	$0.690404\pi$
$272$	−525.715	−	303.522i	−1.93278	−	1.11589i
$273$	177.357	+	57.5749i	0.649660	+	0.210897i
$274$	−418.158	−	724.271i	−1.52612	−	2.64332i
$275$	291.956	+	168.561i	1.06166	+	0.612948i
$276$	−361.997	+	732.812i	−1.31158	+	2.65512i
$277$	108.786	+	188.423i	0.392729	+	0.680226i	0.992808	−	0.119714i	$-0.0381978\pi$
$277$	108.786	+	188.423i	0.392729	+	0.680226i	−0.600080	+	0.799940i	$0.704864\pi$
$278$			724.270i			2.60529i
$279$	77.3038	+	101.026i	0.277075	+	0.362100i
$280$	−265.802	+	460.383i	−0.949293	+	1.64422i
$281$	−104.650	−	60.4199i	−0.372421	−	0.215018i	0.302094	−	0.953278i	$-0.402314\pi$
$281$	−104.650	−	60.4199i	−0.372421	−	0.215018i	−0.674516	+	0.738260i	$0.735648\pi$
$282$	329.301	+	162.669i	1.16773	+	0.576840i
$283$	6.33735	−	10.9766i	0.0223935	−	0.0387866i	−0.854611	−	0.519268i	$-0.826205\pi$
$283$	6.33735	−	10.9766i	0.0223935	−	0.0387866i	0.877005	+	0.480481i	$0.159538\pi$
$284$	−514.208	−	296.878i	−1.81059	−	1.04535i
$285$	−240.558	+	15.6043i	−0.844065	+	0.0547519i
$286$	415.857	+	526.495i	1.45405	+	1.84089i
$287$		−	4.92200i		−	0.0171498i
$288$	18.5421	+	142.323i	0.0643823	+	0.494177i
$289$	215.643	+	373.505i	0.746171	+	1.29241i
$290$	−494.414	+	285.450i	−1.70488	+	0.984310i
$291$	67.7598	−	45.2096i	0.232852	−	0.155360i
$292$	550.696			1.88595
$293$			197.967i			0.675655i	0.941208	+	0.337827i	$0.109692\pi$
$293$			197.967i			0.675655i	−0.941208	+	0.337827i	$0.890308\pi$
$294$	122.933	−	248.860i	0.418138	−	0.846463i
$295$	−338.553	−	586.391i	−1.14764	−	1.98777i
$296$	−367.275	+	212.047i	−1.24080	+	0.716374i
$297$	386.272	−	76.0230i	1.30058	−	0.255970i
$298$	640.053			2.14783
$299$	−59.9787	−	410.950i	−0.200598	−	1.37441i
$300$	−530.364	−	261.991i	−1.76788	−	0.873304i
$301$	26.7149	−	46.2716i	0.0887539	−	0.153726i
$302$	295.032	+	170.337i	0.976926	+	0.564028i
$303$	187.408	−	12.1566i	0.618509	−	0.0401207i
$304$	131.003	−	226.904i	0.430931	−	0.746395i
$305$	−144.375	−	83.3547i	−0.473359	−	0.273294i
$306$	328.240	−	789.430i	1.07268	−	2.57984i
$307$	−543.817			−1.77139			−0.885696	−	0.464265i	$-0.846318\pi$
$307$	−543.817			−1.77139			−0.885696	+	0.464265i	$0.846318\pi$
$308$	−514.891	+	297.272i	−1.67172	+	0.965170i
$309$	−275.038	+	183.506i	−0.890090	+	0.593872i
$310$	173.523	−	300.551i	0.559752	−	0.969520i
$311$	−375.320	+	216.691i	−1.20682	+	0.696756i	−0.962063	−	0.272829i	$-0.912041\pi$
$311$	−375.320	+	216.691i	−1.20682	+	0.696756i	−0.244754	+	0.969585i	$0.578707\pi$
$312$	−418.393	−	464.425i	−1.34100	−	1.48854i
$313$	−63.3667	+	109.754i	−0.202450	+	0.350653i	−0.949317	−	0.314320i	$-0.898224\pi$
$313$	−63.3667	+	109.754i	−0.202450	+	0.350653i	0.746868	+	0.664973i	$0.231557\pi$
$314$	−405.335	+	234.020i	−1.29087	+	0.745287i
$315$	−275.627	−	114.604i	−0.875007	−	0.363822i
$316$	63.4172	−	109.842i	0.200687	−	0.347601i
$317$	356.487	+	205.818i	1.12457	+	0.649268i	0.942563	−	0.334030i	$-0.108409\pi$
$317$	356.487	+	205.818i	1.12457	+	0.649268i	0.182003	+	0.983298i	$0.441742\pi$
$318$	−5.87871	−	90.6273i	−0.0184865	−	0.284991i
$319$	−339.023			−1.06277
$320$	−204.429	+	118.027i	−0.638841	+	0.368835i
$321$	−172.092	−	257.929i	−0.536111	−	0.803518i
$322$	540.641			1.67901
$323$	−269.233	+	155.442i	−0.833538	+	0.481243i
$324$	−667.733	+	176.991i	−2.06091	+	0.546270i
$325$	297.420	−	43.4089i	0.915139	−	0.133566i
$326$	4.81587	+	2.78045i	0.0147726	+	0.00852897i
$327$	−7.25885	−	111.904i	−0.0221983	−	0.342213i
$328$	−8.24997	+	14.2894i	−0.0251524	+	0.0435652i
$329$		−	165.379i		−	0.502671i
$330$	−596.096	−	893.424i	−1.80635	−	2.70734i
$331$	61.2192	+	106.035i	0.184952	+	0.320346i	0.943560	−	0.331201i	$-0.107454\pi$
$331$	61.2192	+	106.035i	0.184952	+	0.320346i	−0.758608	+	0.651547i	$0.774120\pi$
$332$	772.753	+	446.149i	2.32757	+	1.34382i
$333$	−144.713	−	189.120i	−0.434572	−	0.567928i
$334$	487.875	−	845.025i	1.46070	−	2.53002i
$335$		−	499.607i		−	1.49136i
$336$	269.880	−	180.065i	0.803214	−	0.535908i
$337$	2.95144	+	5.11204i	0.00875797	+	0.0151693i	0.870371	−	0.492396i	$-0.163879\pi$
$337$	2.95144	+	5.11204i	0.00875797	+	0.0151693i	−0.861613	+	0.507565i	$0.830546\pi$
$338$	581.914	+	138.551i	1.72164	+	0.409913i
$339$	555.975	−	36.0643i	1.64004	−	0.106384i
$340$	−1587.75			−4.66985
$341$	178.479	−	103.045i	0.523399	−	0.302185i
$342$	340.726	+	141.672i	0.996275	+	0.414244i
$343$	−359.261			−1.04741
$344$	−155.115	+	89.5559i	−0.450917	+	0.260337i
$345$	43.0350	+	663.436i	0.124739	+	1.92300i
$346$	−103.142	−	178.648i	−0.298100	−	0.516324i
$347$			143.359i			0.413138i	0.978432	+	0.206569i	$0.0662298\pi$
$347$			143.359i			0.413138i	−0.978432	+	0.206569i	$0.933770\pi$
$348$	593.634	−	38.5072i	1.70585	−	0.110653i
$349$	273.417			0.783429			0.391715	−	0.920087i	$-0.371882\pi$
$349$	273.417			0.783429			0.391715	+	0.920087i	$0.371882\pi$
$350$			391.283i			1.11795i
$351$	228.245	−	266.656i	0.650271	−	0.759702i
$352$	232.525			0.660581
$353$		−	488.715i		−	1.38446i	−0.721676	−	0.692231i	$-0.756628\pi$
$353$		−	488.715i		−	1.38446i	0.721676	−	0.692231i	$-0.243372\pi$
$354$	67.0917	+	1034.30i	0.189525	+	2.92175i
$355$	−482.962			−1.36046
$356$	613.315	−	354.097i	1.72279	−	0.994655i
$357$	−384.152	+	24.9187i	−1.07605	+	0.0698003i
$358$	−15.4272	−	26.7207i	−0.0430928	−	0.0746389i
$359$		−	539.571i		−	1.50298i	−0.659742	−	0.751492i	$-0.729335\pi$
$359$		−	539.571i		−	1.50298i	0.659742	−	0.751492i	$-0.270665\pi$
$360$	608.098	+	794.704i	1.68916	+	2.20751i
$361$	113.410	+	196.432i	0.314155	+	0.544132i
$362$			1131.65i			3.12610i
$363$	−17.7881	−	274.224i	−0.0490029	−	0.755438i
$364$	−195.965	+	492.533i	−0.538366	+	1.35311i
$365$	387.924	−	223.968i	1.06281	−	0.613611i
$366$	141.632	+	212.277i	0.386973	+	0.579991i
$367$	52.0141			0.141728			0.0708639	−	0.997486i	$-0.477424\pi$
$367$	52.0141			0.141728			0.0708639	+	0.997486i	$0.477424\pi$
$368$	−625.778	−	361.293i	−1.70048	−	0.981775i
$369$	−8.55493	−	3.55708i	−0.0231841	−	0.00963978i
$370$	−324.835	+	562.631i	−0.877933	+	1.52062i
$371$	−35.4140	+	20.4463i	−0.0954554	+	0.0551112i
$372$	−300.815	+	200.705i	−0.808644	+	0.539531i
$373$	613.654			1.64518			0.822592	−	0.568631i	$-0.192527\pi$
$373$	613.654			1.64518			0.822592	+	0.568631i	$0.192527\pi$
$374$	−1199.53	−	692.549i	−3.20730	−	1.85174i
$375$	39.0240	−	2.53136i	0.104064	−	0.00675030i
$376$	−277.198	+	480.121i	−0.737228	+	1.27692i
$377$	−237.200	+	187.354i	−0.629177	+	0.496961i
$378$	300.580	+	344.147i	0.795186	+	0.910441i
$379$	68.7440	+	119.068i	0.181382	+	0.314164i	0.942352	−	0.334624i	$-0.108609\pi$
$379$	68.7440	+	119.068i	0.181382	+	0.314164i	−0.760969	+	0.648788i	$0.775276\pi$
$380$		−	685.289i		−	1.80339i
$381$	−37.2938	+	24.8826i	−0.0978839	+	0.0653086i
$382$	38.1866	+	66.1412i	0.0999650	+	0.173144i
$383$		−	77.9413i		−	0.203502i	−0.994810	−	0.101751i	$-0.967555\pi$
$383$		−	77.9413i		−	0.203502i	0.994810	−	0.101751i	$-0.0324445\pi$
$384$	551.545	−	35.7770i	1.43632	−	0.0931694i
$385$	−241.802	+	418.812i	−0.628056	+	1.08782i
$386$	27.3007	+	15.7621i	0.0707273	+	0.0408344i
$387$	−61.1180	−	79.8731i	−0.157928	−	0.206391i
$388$	115.782	+	200.540i	0.298407	+	0.516857i
$389$	308.392	+	178.050i	0.792781	+	0.457712i	0.840941	−	0.541127i	$-0.182002\pi$
$389$	308.392	+	178.050i	0.792781	+	0.457712i	−0.0481597	+	0.998840i	$0.515336\pi$
$390$	−910.796	−	295.669i	−2.33537	−	0.758126i
$391$	428.692	+	742.516i	1.09640	+	1.89902i
$392$	362.838	+	209.485i	0.925608	+	0.534400i
$393$	−319.845	−	479.381i	−0.813855	−	1.21980i
$394$	−28.3200	−	49.0517i	−0.0718782	−	0.124497i
$395$		−	103.167i		−	0.261183i
$396$	144.583	+	1109.77i	0.365108	+	2.80244i
$397$	149.918	−	259.665i	0.377626	−	0.654068i	−0.613090	−	0.790013i	$-0.710074\pi$
$397$	149.918	−	259.665i	0.377626	−	0.654068i	0.990716	+	0.135945i	$0.0434071\pi$
$398$	527.998	+	304.840i	1.32663	+	0.765930i
$399$	−10.7552	−	165.804i	−0.0269553	−	0.415548i
$400$	261.482	−	452.900i	0.653704	−	1.13225i
$401$	599.374	+	346.049i	1.49470	+	0.862964i	0.999981	−	0.00609030i	$-0.00193861\pi$
$401$	599.374	+	346.049i	1.49470	+	0.862964i	0.494716	+	0.869054i	$0.335272\pi$
$402$	−338.709	+	685.670i	−0.842561	+	1.70565i
$403$	67.9283	−	170.729i	0.168557	−	0.423645i
$404$			533.877i			1.32148i
$405$	−398.386	+	396.245i	−0.983669	+	0.978382i
$406$	−196.745	−	340.772i	−0.484594	−	0.839341i
$407$	−334.112	+	192.900i	−0.820915	+	0.473956i
$408$	1157.02	+	571.549i	2.83584	+	1.40086i
$409$	−38.5099			−0.0941562			−0.0470781	−	0.998891i	$-0.514991\pi$
$409$	−38.5099			−0.0941562			−0.0470781	+	0.998891i	$0.514991\pi$
$410$			25.2763i			0.0616496i
$411$	393.411	+	589.640i	0.957204	+	1.43465i
$412$	−469.961	−	813.996i	−1.14068	−	1.97572i
$413$	404.167	−	233.346i	0.978613	−	0.565003i
$414$	390.716	−	939.688i	0.943758	−	2.26978i
$415$	725.796			1.74890
$416$	162.687	−	128.500i	0.391075	−	0.308895i
$417$	−39.7363	−	612.581i	−0.0952908	−	1.46902i
$418$	298.911	−	517.729i	0.715099	−	1.23859i
$419$	−367.296	−	212.058i	−0.876601	−	0.506106i	−0.00706489	−	0.999975i	$-0.502249\pi$
$419$	−367.296	−	212.058i	−0.876601	−	0.506106i	−0.869536	+	0.493869i	$0.835582\pi$
$420$	375.828	−	760.812i	0.894829	−	1.81146i
$421$	−179.602	+	311.079i	−0.426607	+	0.738905i	−0.996569	−	0.0827660i	$-0.973625\pi$
$421$	−179.602	+	311.079i	−0.426607	+	0.738905i	0.569962	+	0.821671i	$0.306958\pi$
$422$	−242.150	−	139.805i	−0.573815	−	0.331292i
$423$	−287.444	−	119.517i	−0.679538	−	0.282547i
$424$	137.083			0.323310
$425$	−537.388	+	310.261i	−1.26444	+	0.730026i
$426$	662.826	+	327.425i	1.55593	+	0.768603i
$427$	57.4518	−	99.5094i	0.134548	−	0.233043i
$428$	763.362	−	440.728i	1.78356	−	1.02974i
$429$	−380.614	−	422.490i	−0.887212	−	0.984825i
$430$	−137.191	+	237.622i	−0.319049	+	0.552609i
$431$	−720.368	+	415.905i	−1.67139	+	0.964976i	−0.704525	+	0.709679i	$0.748840\pi$
$431$	−720.368	+	415.905i	−1.67139	+	0.964976i	−0.966863	+	0.255298i	$0.917827\pi$
$432$	−117.932	−	599.209i	−0.272990	−	1.38706i
$433$	148.493	−	257.198i	0.342941	−	0.593990i	−0.642037	−	0.766674i	$-0.721910\pi$
$433$	148.493	−	257.198i	0.342941	−	0.593990i	0.984977	+	0.172683i	$0.0552437\pi$
$434$	207.153	+	119.600i	0.477312	+	0.275576i
$435$	402.510	−	268.557i	0.925311	−	0.617372i
$436$	318.785			0.731158
$437$	−320.478	+	185.028i	−0.733358	+	0.423405i
$438$	−684.235	+	44.3842i	−1.56218	+	0.101334i
$439$	−446.011			−1.01597			−0.507985	−	0.861366i	$-0.669610\pi$
$439$	−446.011			−1.01597			−0.507985	+	0.861366i	$0.669610\pi$
$440$	1403.98	−	810.587i	3.19086	−	1.84224i
$441$	−90.3220	+	217.228i	−0.204812	+	0.492581i
$442$	−1221.98	+	178.350i	−2.76467	+	0.403507i
$443$	−293.632	−	169.529i	−0.662826	−	0.382683i	0.130527	−	0.991445i	$-0.458333\pi$
$443$	−293.632	−	169.529i	−0.662826	−	0.382683i	−0.793353	+	0.608762i	$0.791666\pi$
$444$	563.126	−	375.720i	1.26830	−	0.846217i
$445$	288.023	−	498.870i	0.647242	−	1.12106i
$446$		−	483.687i		−	1.08450i
$447$	−541.351	+	35.1158i	−1.21108	+	0.0785588i
$448$	−81.3496	−	140.902i	−0.181584	−	0.314513i
$449$	−75.7448	−	43.7313i	−0.168697	−	0.0973971i	0.413274	−	0.910607i	$-0.364385\pi$
$449$	−75.7448	−	43.7313i	−0.168697	−	0.0973971i	−0.581971	+	0.813209i	$0.697718\pi$
$450$	680.088	+	282.776i	1.51131	+	0.628391i
$451$	−7.50504	+	12.9991i	−0.0166409	+	0.0288229i
$452$			1583.83i			3.50404i
$453$	−258.881	−	127.883i	−0.571480	−	0.282302i
$454$	−161.164	−	279.145i	−0.354987	−	0.614856i
$455$	62.2704	+	426.652i	0.136858	+	0.937696i
$456$	−246.686	+	499.382i	−0.540979	+	1.09514i
$457$	−0.590571			−0.00129228			−0.000646139	−	1.00000i	$-0.500206\pi$
$457$	−0.590571			−0.00129228			−0.000646139		1.00000i	$0.500206\pi$
$458$	642.880	−	371.167i	1.40367	−	0.810408i
$459$	−234.311	+	685.702i	−0.510482	+	1.49390i
$460$	−1889.96			−4.10860
$461$	−51.3324	+	29.6368i	−0.111350	+	0.0642880i	−0.554641	−	0.832090i	$-0.687144\pi$
$461$	−51.3324	+	29.6368i	−0.111350	+	0.0642880i	0.443291	+	0.896378i	$0.353811\pi$
$462$	615.788	−	410.857i	1.33287	−	0.889300i
$463$	−113.399	−	196.412i	−0.244922	−	0.424217i	0.717188	−	0.696880i	$-0.245429\pi$
$463$	−113.399	−	196.412i	−0.244922	−	0.424217i	−0.962110	+	0.272663i	$0.912096\pi$
$464$			525.913i			1.13343i
$465$	−130.275	+	263.724i	−0.280162	+	0.567148i
$466$	−1093.15			−2.34581
$467$		−	67.2592i		−	0.144024i	−0.997404	−	0.0720119i	$-0.977058\pi$
$467$		−	67.2592i		−	0.144024i	0.997404	−	0.0720119i	$-0.0229420\pi$
$468$	714.449	+	696.555i	1.52660	+	1.48837i
$469$	344.351			0.734225
$470$			849.282i			1.80698i
$471$	329.990	−	220.171i	0.700615	−	0.467453i
$472$	−1564.48			−3.31458
$473$	−141.109	+	81.4695i	−0.298328	+	0.172240i
$474$	−69.9424	+	141.589i	−0.147558	+	0.298710i
$475$	−133.912	−	231.942i	−0.281919	−	0.488299i
$476$		−	1094.35i		−	2.29905i
$477$	9.94433	+	76.3293i	0.0208477	+	0.160019i
$478$	−341.559	−	591.598i	−0.714559	−	1.23765i
$479$		−	29.6998i		−	0.0620038i	−0.999519	−	0.0310019i	$-0.990130\pi$
$479$		−	29.6998i		−	0.0620038i	0.999519	−	0.0310019i	$-0.00986979\pi$
$480$	−276.069	+	184.194i	−0.575143	+	0.383738i
$481$	−127.162	+	319.604i	−0.264369	+	0.664458i
$482$	−960.699	+	554.660i	−1.99315	+	1.15075i
$483$	−457.270	+	29.6617i	−0.946729	+	0.0614114i
$484$	781.193			1.61403
$485$	163.120	+	94.1772i	0.336329	+	0.194180i
$486$	815.388	−	273.727i	1.67775	−	0.563225i
$487$	−17.9042	+	31.0109i	−0.0367642	+	0.0636775i	−0.883822	−	0.467823i	$-0.845038\pi$
$487$	−17.9042	+	31.0109i	−0.0367642	+	0.0636775i	0.847058	+	0.531501i	$0.178372\pi$
$488$	−333.584	+	192.595i	−0.683573	+	0.394661i
$489$	−4.22577	−	2.08746i	−0.00864166	−	0.00426884i
$490$	641.821			1.30984
$491$	708.405	+	408.998i	1.44278	+	0.832989i	0.998034	−	0.0626676i	$-0.0199608\pi$
$491$	708.405	+	408.998i	1.44278	+	0.832989i	0.444746	+	0.895657i	$0.353294\pi$
$492$	11.6650	−	23.6141i	0.0237093	−	0.0479961i
$493$	312.011	−	540.419i	0.632882	−	1.09618i
$494$	−76.9777	−	527.420i	−0.155825	−	1.06765i
$495$	553.190	+	722.946i	1.11756	+	1.46050i
$496$	−159.850	−	276.868i	−0.322278	−	0.558201i
$497$		−	332.879i		−	0.669777i
$498$	−996.096	−	492.055i	−2.00019	−	0.988062i
$499$	171.943	+	297.814i	0.344575	+	0.596822i	0.985276	−	0.170968i	$-0.0546896\pi$
$499$	171.943	+	297.814i	0.344575	+	0.596822i	−0.640701	+	0.767790i	$0.721356\pi$
$500$			111.169i			0.222338i
$501$	−366.280	+	741.482i	−0.731097	+	1.48000i
$502$	473.018	−	819.291i	0.942267	−	1.63205i
$503$	667.525	+	385.396i	1.32709	+	0.766195i	0.984848	−	0.173418i	$-0.0554812\pi$
$503$	667.525	+	385.396i	1.32709	+	0.766195i	0.342240	+	0.939613i	$0.388815\pi$
$504$	−547.746	+	419.129i	−1.08680	+	0.831605i
$505$	217.128	+	376.077i	0.429956	+	0.744706i
$506$	−1427.84	−	824.367i	−2.82183	−	1.62918i
$507$	−499.780	−	85.2589i	−0.985759	−	0.168164i
$508$	−63.7244	−	110.374i	−0.125442	−	0.217271i
$509$	−327.879	−	189.301i	−0.644164	−	0.371908i	0.142053	−	0.989859i	$-0.454630\pi$
$509$	−327.879	−	189.301i	−0.644164	−	0.371908i	−0.786217	+	0.617951i	$0.787963\pi$
$510$	1972.76	−	127.967i	3.86816	−	0.250916i
$511$	154.369	+	267.375i	0.302092	+	0.523239i
$512$			1089.43i			2.12779i
$513$	−295.956	−	101.131i	−0.576912	−	0.197137i
$514$	−129.991	+	225.151i	−0.252901	+	0.438037i
$515$	−662.105	−	382.266i	−1.28564	−	0.742265i
$516$	237.831	−	158.682i	0.460913	−	0.307523i
$517$	−252.168	+	436.768i	−0.487753	+	0.844813i
$518$	−387.791	−	223.891i	−0.748631	−	0.432222i
$519$	97.0384	+	145.440i	0.186972	+	0.280232i
$520$	534.347	−	1343.01i	1.02759	−	2.58272i
$521$		−	941.779i		−	1.80764i	−0.427915	−	0.903819i	$-0.640752\pi$
$521$		−	941.779i		−	1.80764i	0.427915	−	0.903819i	$-0.359248\pi$
$522$	−734.482	+	95.6897i	−1.40705	+	0.183314i
$523$	28.7721	+	49.8347i	0.0550135	+	0.0952862i	0.892221	−	0.451600i	$-0.149146\pi$
$523$	28.7721	+	49.8347i	0.0550135	+	0.0952862i	−0.837207	+	0.546886i	$0.815813\pi$
$524$	1418.77	−	819.125i	2.70757	−	1.56321i
$525$	−21.4673	−	330.944i	−0.0408901	−	0.630369i
$526$	−21.5276			−0.0409269
$527$			379.339i			0.719808i
$528$	−987.321	+	64.0444i	−1.86993	+	0.121296i
$529$	245.788	+	425.717i	0.464628	+	0.804758i
$530$	181.864	−	104.999i	0.343140	−	0.198112i
$531$	−113.491	−	871.120i	−0.213731	−	1.64053i
$532$	472.332			0.887842
$533$	1.93275	+	13.2424i	0.00362618	+	0.0248451i
$534$	−733.499	+	489.394i	−1.37359	+	0.916467i
$535$	358.488	−	620.919i	0.670071	−	1.16060i
$536$	−999.708	−	577.182i	−1.86513	−	1.07683i
$537$	14.5142	+	21.7538i	0.0270283	+	0.0405098i
$538$	−315.506	+	546.473i	−0.586443	+	1.01575i
$539$	330.076	+	190.569i	0.612386	+	0.353561i
$540$	−1050.76	−	1203.06i	−1.94585	−	2.22788i
$541$	376.905			0.696683			0.348341	−	0.937368i	$-0.386745\pi$
$541$	376.905			0.696683			0.348341	+	0.937368i	$0.386745\pi$
$542$	721.197	−	416.383i	1.33062	−	0.768235i
$543$	−62.0866	−	957.138i	−0.114340	−	1.76269i
$544$	−213.998	+	370.656i	−0.393379	+	0.681352i
$545$	224.560	−	129.650i	0.412037	−	0.237890i
$546$	203.788	−	627.762i	0.373239	−	1.14975i
$547$	−399.375	+	691.739i	−0.730120	+	1.26460i	0.226712	+	0.973962i	$0.427202\pi$
$547$	−399.375	+	691.739i	−0.730120	+	1.26460i	−0.956832	+	0.290643i	$0.906131\pi$
$548$	−1745.09	+	1007.53i	−3.18447	+	1.83855i
$549$	−131.437	−	171.771i	−0.239412	−	0.312880i
$550$	596.626	−	1033.39i	1.08477	−	1.87888i
$551$	233.250	+	134.667i	0.423322	+	0.244405i
$552$	1377.25	+	680.336i	2.49501	+	1.23249i
$553$	71.1075			0.128585
$554$	666.928	−	385.051i	1.20384	−	0.695038i
$555$	243.875	−	493.690i	0.439414	−	0.889532i
$556$	1745.09			3.13864
$557$	−357.720	+	206.530i	−0.642226	+	0.370789i	−0.785472	−	0.618898i	$-0.787580\pi$
$557$	−357.720	+	206.530i	−0.642226	+	0.370789i	0.143245	+	0.989687i	$0.454246\pi$
$558$	357.584	−	273.619i	0.640832	−	0.490357i
$559$	−53.7055	+	134.982i	−0.0960743	+	0.241470i
$560$	649.688	+	375.098i	1.16016	+	0.669817i
$561$	1052.55	+	519.941i	1.87620	+	0.926812i
$562$	−213.858	+	370.414i	−0.380531	+	0.659099i
$563$		−	331.849i		−	0.589430i	−0.955585	−	0.294715i	$-0.904775\pi$
$563$		−	331.849i		−	0.589430i	0.955585	−	0.294715i	$-0.0952247\pi$
$564$	391.941	−	793.430i	0.694932	−	1.40679i
$565$	644.143	+	1115.69i	1.14008	+	1.97467i
$566$	−38.8521	−	22.4313i	−0.0686433	−	0.0396312i
$567$	−273.110	−	274.586i	−0.481675	−	0.484278i
$568$	−557.952	+	966.401i	−0.982310	+	1.70141i
$569$			299.019i			0.525517i	0.964862	+	0.262759i	$0.0846323\pi$
$569$			299.019i			0.525517i	−0.964862	+	0.262759i	$0.915368\pi$
$570$	55.2319	+	851.465i	0.0968980	+	1.49380i
$571$	−115.115	−	199.385i	−0.201602	−	0.349186i	0.747442	−	0.664327i	$-0.231282\pi$
$571$	−115.115	−	199.385i	−0.201602	−	0.349186i	−0.949045	+	0.315141i	$0.897948\pi$
$572$	1268.56	−	1001.98i	2.21776	−	1.75172i
$573$	−35.9267	−	53.8466i	−0.0626993	−	0.0939731i
$574$	−17.4216			−0.0303512
$575$	−639.672	+	369.315i	−1.11247	+	0.642287i
$576$	−303.692	+	39.5656i	−0.527242	+	0.0686902i
$577$	903.438			1.56575			0.782876	−	0.622178i	$-0.213752\pi$
$577$	903.438			1.56575			0.782876	+	0.622178i	$0.213752\pi$
$578$	1322.03	−	763.277i	2.28726	−	1.32055i
$579$	−23.9555	−	11.8336i	−0.0413740	−	0.0204380i
$580$	687.775	+	1191.26i	1.18582	+	2.05390i
$581$			500.251i			0.861017i
$582$	−160.021	−	239.838i	−0.274950	−	0.412093i
$583$	124.705			0.213903
$584$		−	1034.98i		−	1.77222i
$585$	786.565	+	200.105i	1.34456	+	0.342059i
$586$	700.710			1.19575
$587$		−	206.546i		−	0.351868i	−0.984402	−	0.175934i	$-0.943706\pi$
$587$		−	206.546i		−	0.351868i	0.984402	−	0.175934i	$-0.0562945\pi$
$588$	−599.614	−	296.199i	−1.01975	−	0.503740i
$589$	−163.727			−0.277974
$590$	−2075.55	+	1198.32i	−3.51788	+	2.03105i
$591$	26.6440	+	39.9338i	0.0450829	+	0.0675698i
$592$	299.238	+	518.296i	0.505470	+	0.875500i
$593$			854.227i			1.44052i	0.693705	+	0.720259i	$0.255977\pi$
$593$			854.227i			1.44052i	−0.693705	+	0.720259i	$0.744023\pi$
$594$	−269.086	−	1367.22i	−0.453007	−	2.30172i
$595$	−445.072	−	770.887i	−0.748020	−	1.29561i
$596$		−	1542.17i		−	2.58753i
$597$	−463.301	−	228.863i	−0.776049	−	0.383355i
$598$	−1454.57	+	212.297i	−2.43239	+	0.355011i
$599$	170.718	−	98.5643i	0.285006	−	0.164548i	−0.350682	−	0.936495i	$-0.614050\pi$
$599$	170.718	−	98.5643i	0.285006	−	0.164548i	0.635687	+	0.771947i	$0.280717\pi$
$600$	−492.385	+	996.765i	−0.820642	+	1.66128i
$601$	−590.228			−0.982077			−0.491038	−	0.871138i	$-0.663383\pi$
$601$	−590.228			−0.982077			−0.491038	+	0.871138i	$0.663383\pi$
$602$	−163.780	−	94.5583i	−0.272060	−	0.157074i
$603$	248.859	−	598.517i	0.412702	−	0.992565i
$604$	410.416	−	710.861i	0.679497	−	1.17692i
$605$	550.292	−	317.711i	0.909574	−	0.525143i
$606$	−43.0286	−	663.337i	−0.0710044	−	1.09462i
$607$	−42.1306			−0.0694079			−0.0347040	−	0.999398i	$-0.511049\pi$
$607$	−42.1306			−0.0694079			−0.0347040	+	0.999398i	$0.511049\pi$
$608$	−159.979	−	92.3638i	−0.263123	−	0.151914i
$609$	185.101	+	277.428i	0.303943	+	0.455547i
$610$	−295.037	+	511.018i	−0.483667	+	0.837735i
$611$	64.9402	+	444.944i	0.106285	+	0.728222i
$612$	−1902.09	−	790.874i	−3.10798	−	1.29228i
$613$	217.681	+	377.035i	0.355108	+	0.615066i	0.987137	−	0.159880i	$-0.0511106\pi$
$613$	217.681	+	377.035i	0.355108	+	0.615066i	−0.632028	+	0.774945i	$0.717777\pi$
$614$			1924.86i			3.13495i
$615$	−1.38676	−	21.3785i	−0.00225489	−	0.0347618i
$616$	558.693	+	967.685i	0.906969	+	1.57092i
$617$			210.880i			0.341783i	0.985290	+	0.170891i	$0.0546647\pi$
$617$			210.880i			0.341783i	−0.985290	+	0.170891i	$0.945335\pi$
$618$	649.527	+	973.505i	1.05102	+	1.57525i
$619$	62.1645	−	107.672i	0.100427	−	0.173945i	−0.811433	−	0.584445i	$-0.801312\pi$
$619$	62.1645	−	107.672i	0.100427	−	0.173945i	0.911861	+	0.410500i	$0.134646\pi$
$620$	−724.160	−	418.094i	−1.16800	−	0.674345i
$621$	−278.909	+	816.217i	−0.449129	+	1.31436i
$622$	766.986	+	1328.46i	1.23310	+	2.13578i
$623$	343.844	+	198.518i	0.551916	+	0.318649i
$624$	−655.393	+	590.433i	−1.05031	+	0.946206i
$625$	334.223	+	578.892i	0.534758	+	0.926227i
$626$	388.479	+	224.289i	0.620574	+	0.358288i
$627$	−224.412	+	454.291i	−0.357914	+	0.724546i
$628$	563.858	+	976.630i	0.897863	+	1.55514i
$629$		−	710.122i		−	1.12897i
$630$	−405.644	+	975.592i	−0.643880	+	1.54856i
$631$	272.744	−	472.406i	0.432241	−	0.748663i	−0.564825	−	0.825210i	$-0.691056\pi$
$631$	272.744	−	472.406i	0.432241	−	0.748663i	0.997066	+	0.0765478i	$0.0243898\pi$
$632$	−206.436	−	119.186i	−0.326640	−	0.188586i
$633$	212.479	+	104.961i	0.335670	+	0.165815i
$634$	728.500	−	1261.80i	1.14905	−	1.99022i
$635$	−89.7782	−	51.8335i	−0.141383	−	0.0816275i
$636$	−218.361	+	14.1644i	−0.343335	+	0.0222711i
$637$	336.254	−	49.0768i	0.527872	−	0.0770436i
$638$			1199.98i			1.88085i
$639$	−578.577	−	240.568i	−0.905441	−	0.376476i
$640$	639.011	+	1106.80i	0.998455	+	1.72938i
$641$	443.357	−	255.972i	0.691665	−	0.399333i	−0.112571	−	0.993644i	$-0.535908\pi$
$641$	443.357	−	255.972i	0.691665	−	0.399333i	0.804235	+	0.594311i	$0.202575\pi$
$642$	−912.950	+	609.124i	−1.42204	+	0.948792i
$643$	−565.972			−0.880206			−0.440103	−	0.897947i	$-0.645058\pi$
$643$	−565.972			−0.880206			−0.440103	+	0.897947i	$0.645058\pi$
$644$		−	1302.64i		−	2.02274i
$645$	102.998	−	208.506i	0.159687	−	0.323264i
$646$	550.191	+	952.958i	0.851688	+	1.47517i
$647$	443.043	−	255.791i	0.684765	−	0.395349i	−0.116883	−	0.993146i	$-0.537290\pi$
$647$	443.043	−	255.791i	0.684765	−	0.395349i	0.801648	+	0.597796i	$0.203957\pi$
$648$	332.637	+	1254.94i	0.513329	+	1.93663i
$649$	−1423.22			−2.19294
$650$	−153.647	−	1052.73i	−0.236380	−	1.61958i
$651$	−181.770	−	89.7915i	−0.279217	−	0.137929i
$652$	6.69932	−	11.6036i	0.0102750	−	0.0177969i
$653$	−91.9247	−	53.0728i	−0.140773	−	0.0812753i	0.427959	−	0.903798i	$-0.359233\pi$
$653$	−91.9247	−	53.0728i	−0.140773	−	0.0812753i	−0.568732	+	0.822523i	$0.692566\pi$
$654$	−396.087	+	25.6929i	−0.605638	+	0.0392858i
$655$	666.276	−	1154.02i	1.01722	−	1.76187i
$656$	20.1650	+	11.6423i	0.0307394	+	0.0177474i
$657$	576.285	−	75.0796i	0.877146	−	0.114276i
$658$	−585.363			−0.889610
$659$	−762.630	+	440.305i	−1.15725	+	0.668141i	−0.950644	−	0.310283i	$-0.899576\pi$
$659$	−762.630	+	440.305i	−1.15725	+	0.668141i	−0.206610	+	0.978423i	$0.566243\pi$
$660$	−2152.65	+	1436.26i	−3.26159	+	2.17615i
$661$	36.9113	−	63.9322i	0.0558416	−	0.0967205i	−0.836753	−	0.547580i	$-0.815549\pi$
$661$	36.9113	−	63.9322i	0.0558416	−	0.0967205i	0.892595	+	0.450860i	$0.148882\pi$
$662$	375.313	−	216.687i	0.566939	−	0.327322i
$663$	1023.76	−	217.890i	1.54413	−	0.328642i
$664$	838.491	−	1452.31i	1.26279	−	2.18721i
$665$	332.723	−	192.097i	0.500335	−	0.288868i
$666$	−669.397	+	512.215i	−1.00510	+	0.769092i
$667$	371.398	−	643.281i	0.556819	−	0.964439i
$668$	−2036.04	−	1175.51i	−3.04796	−	1.75974i
$669$	26.5370	+	409.099i	0.0396666	+	0.611507i
$670$	−1768.37			−2.63936
$671$	−303.463	+	175.204i	−0.452255	+	0.261109i
$672$	−126.955	−	190.279i	−0.188921	−	0.283153i
$673$	−984.011			−1.46213			−0.731063	−	0.682310i	$-0.760976\pi$
$673$	−984.011			−1.46213			−0.731063	+	0.682310i	$0.760976\pi$
$674$	18.0942	−	10.4467i	0.0268460	−	0.0154996i
$675$	−590.727	−	201.857i	−0.875152	−	0.299048i
$676$	333.830	−	1402.09i	0.493831	−	2.07410i
$677$	−976.039	−	563.516i	−1.44171	−	0.832372i	−0.443747	−	0.896152i	$-0.646351\pi$
$677$	−976.039	−	563.516i	−1.44171	−	0.832372i	−0.997964	+	0.0637796i	$0.979685\pi$
$678$	−127.651	−	1967.89i	−0.188276	−	2.90249i
$679$	−64.9112	+	112.429i	−0.0955982	+	0.165581i
$680$			2984.01i			4.38825i
$681$	151.626	+	227.256i	0.222653	+	0.333710i
$682$	−364.731	−	631.733i	−0.534796	−	0.926294i
$683$	590.806	+	341.102i	0.865016	+	0.499417i	0.865689	−	0.500583i	$-0.166881\pi$
$683$	590.806	+	341.102i	0.865016	+	0.499417i	−0.000672920		1.00000i	$0.500214\pi$
$684$	341.349	−	820.960i	0.499049	−	1.20023i
$685$	−819.523	+	1419.45i	−1.19638	+	2.07220i
$686$			1271.62i			1.85367i
$687$	−523.379	+	349.201i	−0.761832	+	0.508298i
$688$	126.381	+	218.898i	0.183693	+	0.318165i
$689$	87.2509	−	68.9160i	0.126634	−	0.100023i
$690$	2348.25	−	152.324i	3.40327	−	0.220759i
$691$	478.083			0.691872			0.345936	−	0.938258i	$-0.387561\pi$
$691$	478.083			0.691872			0.345936	+	0.938258i	$0.387561\pi$
$692$	−430.442	+	248.516i	−0.622026	+	0.359127i
$693$	−498.287	+	381.284i	−0.719029	+	0.550193i
$694$	507.423			0.731158
$695$	1229.28	−	709.727i	1.76875	−	1.02119i
$696$	−72.3704	−	1115.67i	−0.103980	−	1.60298i
$697$	−13.8141	−	23.9268i	−0.0198194	−	0.0343283i
$698$		−	967.768i		−	1.38649i
$699$	924.574	−	59.9743i	1.32271	−	0.0858001i
$700$	942.773			1.34682
$701$		−	573.375i		−	0.817939i	−0.912548	−	0.408970i	$-0.865888\pi$
$701$		−	573.375i		−	0.817939i	0.912548	−	0.408970i	$-0.134112\pi$
$702$	−943.836	−	807.881i	−1.34450	−	1.15083i
$703$	306.496			0.435983
$704$			496.166i			0.704781i
$705$	−46.5949	−	718.315i	−0.0660920	−	1.01889i
$706$	−1729.82			−2.45018
$707$	−259.209	+	149.654i	−0.366632	+	0.211675i
$708$	2492.08	−	161.653i	3.51989	−	0.228324i
$709$	511.795	+	886.454i	0.721854	+	1.25029i	0.960256	+	0.279121i	$0.0900431\pi$
$709$	511.795	+	886.454i	0.721854	+	1.25029i	−0.238402	+	0.971167i	$0.576624\pi$
$710$			1709.46i			2.40769i
$711$	51.3886	−	123.592i	0.0722765	−	0.173828i
$712$	−665.490	−	1152.66i	−0.934676	−	1.61891i
$713$			451.541i			0.633298i
$714$	88.2007	+	1359.72i	0.123530	+	1.90437i
$715$	486.099	−	1221.75i	0.679858	−	1.70874i
$716$	−64.3820	+	37.1710i	−0.0899190	+	0.0519147i
$717$	321.345	+	481.629i	0.448180	+	0.671728i
$718$	−1909.83			−2.65993
$719$	116.126	+	67.0454i	0.161511	+	0.0932482i	0.578577	−	0.815628i	$-0.303608\pi$
$719$	116.126	+	67.0454i	0.161511	+	0.0932482i	−0.417066	+	0.908876i	$0.636942\pi$
$720$	1121.48	−	858.143i	1.55761	−	1.19187i
$721$	263.475	−	456.353i	0.365430	−	0.632944i
$722$	695.276	−	401.418i	0.962987	−	0.555981i
$723$	782.121	−	521.834i	1.08177	−	0.721763i
$724$	2726.64			3.76608
$725$	465.567	+	268.795i	0.642161	+	0.370752i
$726$	−970.625	+	62.9614i	−1.33695	+	0.0867237i
$727$	−104.008	+	180.148i	−0.143065	+	0.247796i	−0.928649	−	0.370958i	$-0.879029\pi$
$727$	−104.008	+	180.148i	−0.143065	+	0.247796i	0.785584	+	0.618755i	$0.212363\pi$
$728$	925.665	+	368.296i	1.27152	+	0.505902i
$729$	−674.630	+	276.252i	−0.925419	+	0.378946i
$730$	−792.743	−	1373.07i	−1.08595	−	1.88092i
$731$		−	299.913i		−	0.410278i
$732$	511.468	−	341.254i	0.698727	−	0.466194i
$733$	30.2381	+	52.3739i	0.0412525	+	0.0714515i	0.885914	−	0.463849i	$-0.153532\pi$
$733$	30.2381	+	52.3739i	0.0412525	+	0.0714515i	−0.844662	+	0.535300i	$0.820199\pi$
$734$		−	184.106i		−	0.250825i
$735$	−542.847	+	35.2128i	−0.738568	+	0.0479086i
$736$	−254.730	+	441.205i	−0.346100	+	0.599463i
$737$	−909.439	−	525.065i	−1.23397	−	0.712436i
$738$	−12.5904	+	30.2805i	−0.0170602	+	0.0410304i
$739$	−62.0946	−	107.551i	−0.0840251	−	0.145536i	0.820950	−	0.571000i	$-0.193444\pi$
$739$	−62.0946	−	107.551i	−0.0840251	−	0.145536i	−0.904975	+	0.425464i	$0.860111\pi$
$740$	1355.63	+	782.671i	1.83193	+	1.05766i
$741$	94.0434	+	441.864i	0.126914	+	0.596308i
$742$	72.3702	+	125.349i	0.0975340	+	0.168934i
$743$	−188.132	−	108.618i	−0.253206	−	0.146189i	0.368025	−	0.929816i	$-0.380034\pi$
$743$	−188.132	−	108.618i	−0.253206	−	0.146189i	−0.621231	+	0.783627i	$0.713367\pi$
$744$	377.205	+	565.352i	0.506996	+	0.759882i
$745$	−627.201	−	1086.34i	−0.841880	−	1.45818i
$746$		−	2172.05i		−	2.91159i
$747$	869.486	+	361.526i	1.16397	+	0.483971i
$748$	−1668.66	+	2890.20i	−2.23082	+	3.86390i
$749$	427.966	+	247.086i	0.571383	+	0.329888i
$750$	−8.95985	−	138.127i	−0.0119465	−	0.184169i
$751$	−478.854	+	829.400i	−0.637622	+	1.10439i	0.348331	+	0.937372i	$0.386749\pi$
$751$	−478.854	+	829.400i	−0.637622	+	1.10439i	−0.985953	+	0.167022i	$0.946585\pi$
$752$	677.543	+	391.179i	0.900987	+	0.520185i
$753$	−355.125	+	718.901i	−0.471614	+	0.954716i
$754$	663.147	+	839.576i	0.879505	+	1.11350i
$755$		−	667.665i		−	0.884325i
$756$	829.202	−	724.231i	1.09683	−	0.957977i
$757$	−23.2017	−	40.1865i	−0.0306496	−	0.0530866i	0.850294	−	0.526308i	$-0.176424\pi$
$757$	−23.2017	−	40.1865i	−0.0306496	−	0.0530866i	−0.880943	+	0.473222i	$0.843091\pi$
$758$	421.445	−	243.322i	0.555996	−	0.321005i
$759$	1252.89	+	618.905i	1.65071	+	0.815422i
$760$	−1287.93			−1.69464
$761$		−	901.092i		−	1.18409i	−0.805905	−	0.592044i	$-0.798321\pi$
$761$		−	901.092i		−	1.18409i	0.805905	−	0.592044i	$-0.201679\pi$
$762$	88.0727	+	132.003i	0.115581	+	0.173232i
$763$	89.3605	+	154.777i	0.117117	+	0.202853i
$764$	159.363	−	92.0084i	0.208591	−	0.120430i
$765$	−1661.53	+	216.467i	−2.17193	+	0.282963i
$766$	−275.876			−0.360151
$767$	−995.765	+	786.514i	−1.29826	+	1.02544i
$768$	−100.202	−	1544.73i	−0.130471	−	2.01136i
$769$	73.2129	−	126.809i	0.0952054	−	0.164901i	−0.814489	−	0.580179i	$-0.802983\pi$
$769$	73.2129	−	126.809i	0.0952054	−	0.164901i	0.909694	+	0.415279i	$0.136316\pi$
$770$	1482.40

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.53953i q^{2} +(0.194193 + 2.99371i) q^{3} -8.52830 q^{4} +(-6.00755 + 3.46846i) q^{5} +(10.5963 - 0.687351i) q^{6} +(-2.39062 - 4.14067i) q^{7} +16.0281i q^{8} +(-8.92458 + 1.16271i) q^{9} +(12.2767 + 21.2639i) q^{10} +14.5808i q^{11} +(-1.65613 - 25.5312i) q^{12} +(8.05780 + 10.2016i) q^{13} +(-14.6561 + 8.46168i) q^{14} +(-11.5502 - 17.3113i) q^{15} +22.6187 q^{16} +(-23.2425 - 13.4191i) q^{17} +(4.11546 + 31.5888i) q^{18} +(5.79181 - 10.0317i) q^{19} +(51.2342 - 29.5801i) q^{20} +(11.9317 - 7.96091i) q^{21} +51.6093 q^{22} +(-27.6664 - 15.9732i) q^{23} +(-47.9833 + 3.11253i) q^{24} +(11.5604 - 20.0233i) q^{25} +(36.1088 - 28.5208i) q^{26} +(-5.21391 - 26.4918i) q^{27} +(20.3879 + 35.3129i) q^{28} +23.2513i q^{29} +(-61.2739 + 40.8823i) q^{30} +(-7.06716 - 12.2407i) q^{31} -15.9473i q^{32} +(-43.6507 + 2.83149i) q^{33} +(-47.4973 + 82.2677i) q^{34} +(28.7235 + 16.5835i) q^{35} +(76.1115 - 9.91595i) q^{36} +(13.2297 + 22.9145i) q^{37} +(-35.5076 - 20.5003i) q^{38} +(-28.9757 + 26.1038i) q^{39} +(-55.5927 - 96.2894i) q^{40} +(0.891522 + 0.514720i) q^{41} +(-28.1779 - 42.2328i) q^{42} +(5.58744 + 9.67774i) q^{43} -124.350i q^{44} +(49.5820 - 37.9396i) q^{45} +(-56.5378 + 97.9263i) q^{46} +(29.9550 + 17.2945i) q^{47} +(4.39238 + 67.7137i) q^{48} +(13.0699 - 22.6377i) q^{49} +(-70.8730 - 40.9186i) q^{50} +(35.6593 - 72.1872i) q^{51} +(-68.7193 - 87.0020i) q^{52} -8.55270i q^{53} +(-93.7686 + 18.4548i) q^{54} +(-50.5730 - 87.5950i) q^{55} +(66.3670 - 38.3170i) q^{56} +(31.1567 + 15.3909i) q^{57} +82.2987 q^{58} +97.6091i q^{59} +(98.5034 + 147.636i) q^{60} +(12.0161 + 20.8125i) q^{61} +(-43.3263 + 25.0144i) q^{62} +(26.1497 + 34.1742i) q^{63} +34.0287 q^{64} +(-83.7913 - 33.3382i) q^{65} +(10.0221 + 154.503i) q^{66} +(-36.0107 + 62.3723i) q^{67} +(198.219 + 114.442i) q^{68} +(42.4466 - 85.9271i) q^{69} +(58.6980 - 101.668i) q^{70} +(60.2943 + 34.8109i) q^{71} +(-18.6360 - 143.044i) q^{72} -64.5728 q^{73} +(81.1067 - 46.8270i) q^{74} +(62.1888 + 30.7202i) q^{75} +(-49.3943 + 85.5534i) q^{76} +(60.3744 - 34.8572i) q^{77} +(92.3952 + 102.561i) q^{78} +(-7.43609 + 12.8797i) q^{79} +(-135.883 + 78.4520i) q^{80} +(78.2962 - 20.7534i) q^{81} +(1.82187 - 3.15557i) q^{82} +(-90.6104 - 52.3140i) q^{83} +(-101.757 + 67.8930i) q^{84} +186.174 q^{85} +(34.2547 - 19.7769i) q^{86} +(-69.6076 + 4.51523i) q^{87} -233.702 q^{88} +(-71.9152 + 41.5203i) q^{89} +(-134.288 - 175.497i) q^{90} +(22.9782 - 57.7528i) q^{91} +(235.948 + 136.224i) q^{92} +(35.2726 - 23.5341i) q^{93} +(61.2146 - 106.027i) q^{94} +80.3547i q^{95} +(47.7416 - 3.09685i) q^{96} +(-13.5762 - 23.5147i) q^{97} +(-80.1268 - 46.2613i) q^{98} +(-16.9533 - 130.128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

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