LMFDB - Embedded newform 336.3.bv.a.325.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,3,Mod(61,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 0, 10])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.61"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	336.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.15533688251$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			325.11
Character	$\chi$	$=$	336.325
Dual form			336.3.bv.a.61.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.75213 - 0.964387i) q^{2} +(1.67303 - 0.448288i) q^{3} +(2.13992 + 3.37946i) q^{4} +(2.59267 + 0.694703i) q^{5} +(-3.36369 - 0.827992i) q^{6} +(3.44036 - 6.09622i) q^{7} +(-0.490303 - 7.98496i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-3.87272 - 3.71754i) q^{10} +(-3.13303 + 0.839492i) q^{11} +(5.09512 + 4.69465i) q^{12} +(-17.3684 - 17.3684i) q^{13} +(-11.9071 + 7.36353i) q^{14} +4.64904 q^{15} +(-6.84152 + 14.4635i) q^{16} +(25.6090 + 14.7854i) q^{17} +(-5.99875 + 0.122644i) q^{18} +(2.62395 - 9.79272i) q^{19} +(3.20037 + 10.2484i) q^{20} +(3.02298 - 11.7414i) q^{21} +(6.29907 + 1.55055i) q^{22} +(21.8942 - 12.6406i) q^{23} +(-4.39985 - 13.1393i) q^{24} +(-15.4113 - 8.89774i) q^{25} +(13.6818 + 47.1814i) q^{26} +(3.67423 - 3.67423i) q^{27} +(27.9640 - 1.41883i) q^{28} +(11.7835 - 11.7835i) q^{29} +(-8.14572 - 4.48347i) q^{30} +(14.3785 + 8.30144i) q^{31} +(25.9357 - 18.7441i) q^{32} +(-4.86532 + 2.80900i) q^{33} +(-30.6115 - 50.6029i) q^{34} +(13.1548 - 13.4154i) q^{35} +(10.6289 + 5.57022i) q^{36} +(0.644161 - 2.40404i) q^{37} +(-14.0415 + 14.6276i) q^{38} +(-36.8438 - 21.2718i) q^{39} +(4.27598 - 21.0429i) q^{40} -28.8572 q^{41} +(-16.6199 + 17.6572i) q^{42} +(11.7190 + 11.7190i) q^{43} +(-9.54145 - 8.79150i) q^{44} +(7.77800 - 2.08411i) q^{45} +(-50.5519 + 1.03353i) q^{46} +(-9.87222 + 5.69973i) q^{47} +(-4.96226 + 27.2649i) q^{48} +(-25.3278 - 41.9464i) q^{49} +(18.4218 + 30.4525i) q^{50} +(49.4728 + 13.2562i) q^{51} +(21.5289 - 95.8625i) q^{52} +(18.7393 - 5.02118i) q^{53} +(-9.98112 + 2.89435i) q^{54} -8.70609 q^{55} +(-50.3649 - 24.4822i) q^{56} -17.5598i q^{57} +(-32.0100 + 9.28233i) q^{58} +(-9.20202 - 34.3424i) q^{59} +(9.94856 + 15.7113i) q^{60} +(10.8264 - 40.4046i) q^{61} +(-17.1872 - 28.4116i) q^{62} +(-0.206007 - 20.9990i) q^{63} +(-63.5192 + 7.83009i) q^{64} +(-32.9645 - 57.0962i) q^{65} +(11.2336 - 0.229671i) q^{66} +(-17.3101 - 64.6023i) q^{67} +(4.83455 + 118.184i) q^{68} +(30.9631 - 30.9631i) q^{69} +(-35.9865 + 10.8193i) q^{70} +38.1964i q^{71} +(-13.2513 - 20.0101i) q^{72} +(50.1133 - 86.7988i) q^{73} +(-3.44708 + 3.59097i) q^{74} +(-29.7724 - 7.97749i) q^{75} +(38.7092 - 12.0881i) q^{76} +(-5.66102 + 21.9878i) q^{77} +(44.0409 + 72.8027i) q^{78} +(14.7468 + 25.5422i) q^{79} +(-27.7856 + 32.7463i) q^{80} +(4.50000 - 7.79423i) q^{81} +(50.5615 + 27.8295i) q^{82} +(114.783 + 114.783i) q^{83} +(46.1487 - 14.9097i) q^{84} +(56.1241 + 56.1241i) q^{85} +(-9.23160 - 31.8350i) q^{86} +(14.4317 - 24.9965i) q^{87} +(8.23944 + 24.6055i) q^{88} +(45.8318 + 79.3831i) q^{89} +(-15.6379 - 3.84937i) q^{90} +(-165.635 + 46.1279i) q^{91} +(89.5702 + 46.9407i) q^{92} +(27.7772 + 7.44287i) q^{93} +(22.7941 - 0.466025i) q^{94} +(13.6061 - 23.5664i) q^{95} +(34.9885 - 42.9861i) q^{96} +112.019i q^{97} +(3.92504 + 97.9214i) q^{98} +(-6.88061 + 6.88061i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50}+ \cdots + 192 q^{99}+O(q^{100}) $ 256 * q - 12 * q^4 - 24 * q^8 + 108 * q^10 + 32 * q^11 + 32 * q^14 - 4 * q^16 + 12 * q^18 + 48 * q^22 - 64 * q^29 - 96 * q^35 - 96 * q^37 + 60 * q^40 - 60 * q^42 - 192 * q^43 + 228 * q^44 + 180 * q^46 - 32 * q^50 + 720 * q^52 + 160 * q^53 - 56 * q^56 - 312 * q^58 + 384 * q^59 + 72 * q^60 - 96 * q^64 - 216 * q^66 - 320 * q^67 - 780 * q^68 - 828 * q^70 + 60 * q^72 - 88 * q^74 - 72 * q^78 - 612 * q^80 + 1152 * q^81 + 780 * q^82 - 72 * q^84 - 212 * q^86 - 464 * q^88 - 480 * q^91 - 488 * q^92 - 612 * q^94 + 768 * q^95 - 900 * q^96 - 196 * q^98 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.75213	−	0.964387i	−0.876065	−	0.482193i
$2$	−1.75213	−	0.964387i	−0.876065	−	0.482193i
$3$	1.67303	−	0.448288i	0.557678	−	0.149429i
$3$	1.67303	−	0.448288i	0.557678	−	0.149429i
$4$	2.13992	+	3.37946i	0.534979	+	0.844865i
$5$	2.59267	+	0.694703i	0.518533	+	0.138941i	0.508588	−	0.861010i	$-0.330168\pi$
$5$	2.59267	+	0.694703i	0.518533	+	0.138941i	0.00994510	+	0.999951i	$0.496834\pi$
$6$	−3.36369	−	0.827992i	−0.560615	−	0.137999i
$7$	3.44036	−	6.09622i	0.491480	−	0.870889i
$7$	3.44036	−	6.09622i	0.491480	−	0.870889i
$8$	−0.490303	−	7.98496i	−0.0612878	−	0.998120i
$9$	2.59808	−	1.50000i	0.288675	−	0.166667i
$10$	−3.87272	−	3.71754i	−0.387272	−	0.371754i
$11$	−3.13303	+	0.839492i	−0.284821	+	0.0763175i	−0.398401	−	0.917211i	$-0.630435\pi$
$11$	−3.13303	+	0.839492i	−0.284821	+	0.0763175i	0.113580	+	0.993529i	$0.463768\pi$
$12$	5.09512	+	4.69465i	0.424593	+	0.391221i
$13$	−17.3684	−	17.3684i	−1.33603	−	1.33603i	−0.899871	−	0.436156i	$-0.856340\pi$
$13$	−17.3684	−	17.3684i	−1.33603	−	1.33603i	−0.436156	−	0.899871i	$-0.643660\pi$
$14$	−11.9071	+	7.36353i	−0.850505	+	0.525966i
$15$	4.64904			0.309936
$16$	−6.84152	+	14.4635i	−0.427595	+	0.903970i
$17$	25.6090	+	14.7854i	1.50641	+	0.869727i	0.999972	+	0.00745168i	$0.00237197\pi$
$17$	25.6090	+	14.7854i	1.50641	+	0.869727i	0.506439	+	0.862276i	$0.330961\pi$
$18$	−5.99875	+	0.122644i	−0.333264	+	0.00681355i
$19$	2.62395	−	9.79272i	0.138103	−	0.515406i	−0.861863	−	0.507141i	$-0.830702\pi$
$19$	2.62395	−	9.79272i	0.138103	−	0.515406i	0.999966	−	0.00826539i	$-0.00263098\pi$
$20$	3.20037	+	10.2484i	0.160018	+	0.512421i
$21$	3.02298	−	11.7414i	0.143951	−	0.559117i
$22$	6.29907	+	1.55055i	0.286321	+	0.0704796i
$23$	21.8942	−	12.6406i	0.951922	−	0.549592i	0.0582444	−	0.998302i	$-0.481450\pi$
$23$	21.8942	−	12.6406i	0.951922	−	0.549592i	0.893677	+	0.448710i	$0.148116\pi$
$24$	−4.39985	−	13.1393i	−0.183327	−	0.547471i
$25$	−15.4113	−	8.89774i	−0.616453	−	0.355909i
$26$	13.6818	+	47.1814i	0.526223	+	1.81467i
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	27.9640	−	1.41883i	0.998715	−	0.0506725i
$29$	11.7835	−	11.7835i	0.406326	−	0.406326i	−0.474129	−	0.880455i	$-0.657237\pi$
$29$	11.7835	−	11.7835i	0.406326	−	0.406326i	0.880455	+	0.474129i	$0.157237\pi$
$30$	−8.14572	−	4.48347i	−0.271524	−	0.149449i
$31$	14.3785	+	8.30144i	0.463823	+	0.267788i	0.713650	−	0.700502i	$-0.247041\pi$
$31$	14.3785	+	8.30144i	0.463823	+	0.267788i	−0.249827	+	0.968290i	$0.580374\pi$
$32$	25.9357	−	18.7441i	0.810489	−	0.585753i
$33$	−4.86532	+	2.80900i	−0.147434	+	0.0851211i
$34$	−30.6115	−	50.6029i	−0.900338	−	1.48832i
$35$	13.1548	−	13.4154i	0.375851	−	0.383298i
$36$	10.6289	+	5.57022i	0.295246	+	0.154728i
$37$	0.644161	−	2.40404i	0.0174098	−	0.0649741i	−0.956674	−	0.291160i	$-0.905959\pi$
$37$	0.644161	−	2.40404i	0.0174098	−	0.0649741i	0.974084	+	0.226186i	$0.0726256\pi$
$38$	−14.0415	+	14.6276i	−0.369512	+	0.384937i
$39$	−36.8438	−	21.2718i	−0.944714	−	0.545431i
$40$	4.27598	−	21.0429i	0.106900	−	0.526074i
$41$	−28.8572			−0.703834			−0.351917	−	0.936031i	$-0.614470\pi$
$41$	−28.8572			−0.703834			−0.351917	+	0.936031i	$0.614470\pi$
$42$	−16.6199	+	17.6572i	−0.395713	+	0.420410i
$43$	11.7190	+	11.7190i	0.272536	+	0.272536i	0.830120	−	0.557584i	$-0.188272\pi$
$43$	11.7190	+	11.7190i	0.272536	+	0.272536i	−0.557584	+	0.830120i	$0.688272\pi$
$44$	−9.54145	−	8.79150i	−0.216851	−	0.199807i
$45$	7.77800	−	2.08411i	0.172844	−	0.0463135i
$46$	−50.5519	+	1.03353i	−1.09895	+	0.0224681i
$47$	−9.87222	+	5.69973i	−0.210047	+	0.121271i	−0.601333	−	0.798998i	$-0.705364\pi$
$47$	−9.87222	+	5.69973i	−0.210047	+	0.121271i	0.391286	+	0.920269i	$0.372030\pi$
$48$	−4.96226	+	27.2649i	−0.103380	+	0.568019i
$49$	−25.3278	−	41.9464i	−0.516894	−	0.856049i
$50$	18.4218	+	30.4525i	0.368436	+	0.609049i
$51$	49.4728	+	13.2562i	0.970055	+	0.259925i
$52$	21.5289	−	95.8625i	0.414016	−	1.84351i
$53$	18.7393	−	5.02118i	0.353572	−	0.0947392i	−0.0776614	−	0.996980i	$-0.524745\pi$
$53$	18.7393	−	5.02118i	0.353572	−	0.0947392i	0.431233	+	0.902241i	$0.358079\pi$
$54$	−9.98112	+	2.89435i	−0.184836	+	0.0535991i
$55$	−8.70609			−0.158293
$56$	−50.3649	−	24.4822i	−0.899373	−	0.437182i
$57$		−	17.5598i		−	0.308067i
$58$	−32.0100	+	9.28233i	−0.551896	+	0.160040i
$59$	−9.20202	−	34.3424i	−0.155966	−	0.582075i	−0.999021	−	0.0442461i	$-0.985911\pi$
$59$	−9.20202	−	34.3424i	−0.155966	−	0.582075i	0.843054	−	0.537829i	$-0.180755\pi$
$60$	9.94856	+	15.7113i	0.165809	+	0.261854i
$61$	10.8264	−	40.4046i	0.177482	−	0.662370i	−0.818634	−	0.574316i	$-0.805268\pi$
$61$	10.8264	−	40.4046i	0.177482	−	0.662370i	0.996116	−	0.0880548i	$-0.0280651\pi$
$62$	−17.1872	−	28.4116i	−0.277213	−	0.458252i
$63$	−0.206007	−	20.9990i	−0.00326995	−	0.333317i
$64$	−63.5192	+	7.83009i	−0.992488	+	0.122345i
$65$	−32.9645	−	57.0962i	−0.507146	−	0.878402i
$66$	11.2336	−	0.229671i	0.170207	−	0.00347986i
$67$	−17.3101	−	64.6023i	−0.258360	−	0.964214i	−0.966190	−	0.257831i	$-0.916992\pi$
$67$	−17.3101	−	64.6023i	−0.258360	−	0.964214i	0.707830	−	0.706383i	$-0.249674\pi$
$68$	4.83455	+	118.184i	0.0710963	+	1.73800i
$69$	30.9631	−	30.9631i	0.448740	−	0.448740i
$70$	−35.9865	+	10.8193i	−0.514093	+	0.154561i
$71$			38.1964i			0.537977i	0.963143	+	0.268988i	$0.0866893\pi$
$71$			38.1964i			0.537977i	−0.963143	+	0.268988i	$0.913311\pi$
$72$	−13.2513	−	20.0101i	−0.184046	−	0.277918i
$73$	50.1133	−	86.7988i	0.686484	−	1.18902i	−0.286484	−	0.958085i	$-0.592487\pi$
$73$	50.1133	−	86.7988i	0.686484	−	1.18902i	0.972968	−	0.230940i	$-0.0741801\pi$
$74$	−3.44708	+	3.59097i	−0.0465822	+	0.0485267i
$75$	−29.7724	−	7.97749i	−0.396965	−	0.106367i
$76$	38.7092	−	12.0881i	0.509331	−	0.159053i
$77$	−5.66102	+	21.9878i	−0.0735198	+	0.285556i
$78$	44.0409	+	72.8027i	0.564627	+	0.933367i
$79$	14.7468	+	25.5422i	0.186669	+	0.323319i	0.944138	−	0.329552i	$-0.106898\pi$
$79$	14.7468	+	25.5422i	0.186669	+	0.323319i	−0.757469	+	0.652871i	$0.773564\pi$
$80$	−27.7856	+	32.7463i	−0.347320	+	0.409328i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	50.5615	+	27.8295i	0.616604	+	0.339384i
$83$	114.783	+	114.783i	1.38293	+	1.38293i	0.839372	+	0.543558i	$0.182923\pi$
$83$	114.783	+	114.783i	1.38293	+	1.38293i	0.543558	+	0.839372i	$0.317077\pi$
$84$	46.1487	−	14.9097i	0.549389	−	0.177496i
$85$	56.1241	+	56.1241i	0.660284	+	0.660284i
$86$	−9.23160	−	31.8350i	−0.107344	−	0.370174i
$87$	14.4317	−	24.9965i	0.165882	−	0.287316i
$88$	8.23944	+	24.6055i	0.0936301	+	0.279608i
$89$	45.8318	+	79.3831i	0.514964	+	0.891944i	0.999849	+	0.0173664i	$0.00552818\pi$
$89$	45.8318	+	79.3831i	0.514964	+	0.891944i	−0.484885	+	0.874578i	$0.661138\pi$
$90$	−15.6379	−	3.84937i	−0.173755	−	0.0427708i
$91$	−165.635	+	46.1279i	−1.82016	+	0.506900i
$92$	89.5702	+	46.9407i	0.973590	+	0.510225i
$93$	27.7772	+	7.44287i	0.298679	+	0.0800308i
$94$	22.7941	−	0.466025i	0.242491	−	0.00495771i
$95$	13.6061	−	23.5664i	0.143222	−	0.248067i
$96$	34.9885	−	42.9861i	0.364463	−	0.447772i
$97$			112.019i			1.15483i	0.816450	+	0.577416i	$0.195939\pi$
$97$			112.019i			1.15483i	−0.816450	+	0.577416i	$0.804061\pi$
$98$	3.92504	+	97.9214i	0.0400514	+	0.999198i
$99$	−6.88061	+	6.88061i	−0.0695011	+	0.0695011i
$100$	−2.90940	−	71.1224i	−0.0290940	−	0.711224i
$101$	−21.2603	−	79.3445i	−0.210498	−	0.785589i	−0.987703	−	0.156342i	$-0.950030\pi$
$101$	−21.2603	−	79.3445i	−0.210498	−	0.785589i	0.777205	−	0.629248i	$-0.216637\pi$
$102$	−73.8986	−	70.9375i	−0.724496	−	0.695465i
$103$	70.2432	+	121.665i	0.681973	+	1.18121i	0.974378	+	0.224918i	$0.0722113\pi$
$103$	70.2432	+	121.665i	0.681973	+	1.18121i	−0.292405	+	0.956295i	$0.594455\pi$
$104$	−130.170	+	147.201i	−1.25163	+	1.41540i
$105$	15.9944	−	28.3416i	0.152327	−	0.269920i
$106$	−37.6760	−	9.27417i	−0.355434	−	0.0874922i
$107$	−46.5776	+	173.830i	−0.435304	+	1.62458i	0.305032	+	0.952342i	$0.401333\pi$
$107$	−46.5776	+	173.830i	−0.435304	+	1.62458i	−0.740337	+	0.672236i	$0.765334\pi$
$108$	20.2795	+	4.55438i	0.187773	+	0.0421702i
$109$	−9.73295	−	36.3239i	−0.0892931	−	0.333247i	0.906799	−	0.421562i	$-0.138518\pi$
$109$	−9.73295	−	36.3239i	−0.0892931	−	0.333247i	−0.996093	+	0.0883159i	$0.971852\pi$
$110$	15.2542	+	8.39604i	0.138675	+	0.0763276i
$111$		−	4.31081i		−	0.0388361i
$112$	64.6356	+	91.4672i	0.577103	+	0.816671i
$113$	−177.867			−1.57404			−0.787021	−	0.616926i	$-0.788378\pi$
$113$	−177.867			−1.57404			−0.787021	+	0.616926i	$0.788378\pi$
$114$	−16.9345	+	30.7671i	−0.148548	+	0.269887i
$115$	65.5458	−	17.5629i	0.569964	−	0.152721i
$116$	65.0373	+	14.6061i	0.560667	+	0.125915i
$117$	−71.1768	−	19.0718i	−0.608349	−	0.163007i
$118$	−16.9962	+	69.0466i	−0.144036	+	0.585141i
$119$	178.239	−	105.251i	1.49781	−	0.884463i
$120$	−2.27944	−	37.1224i	−0.0189953	−	0.309353i
$121$	−95.6780	+	55.2397i	−0.790727	+	0.456526i
$122$	−57.9349	+	60.3533i	−0.474876	+	0.494699i
$123$	−48.2790	+	12.9363i	−0.392512	+	0.105173i
$124$	2.71442	+	66.3560i	0.0218905	+	0.535129i
$125$	−81.2242	−	81.2242i	−0.649794	−	0.649794i
$126$	−19.8902	+	36.9916i	−0.157859	+	0.293584i
$127$	181.661			1.43040			0.715199	−	0.698921i	$-0.246336\pi$
$127$	181.661			1.43040			0.715199	+	0.698921i	$0.246336\pi$
$128$	118.845	+	47.5377i	0.928478	+	0.371389i
$129$	24.8599	+	14.3528i	0.192712	+	0.111262i
$130$	2.69526	+	131.830i	0.0207328	+	1.01408i
$131$	−22.0675	+	82.3569i	−0.168454	+	0.628679i	0.829120	+	0.559070i	$0.188842\pi$
$131$	−22.0675	+	82.3569i	−0.168454	+	0.628679i	−0.997574	+	0.0696086i	$0.977825\pi$
$132$	−19.9043	−	10.4312i	−0.150790	−	0.0790239i
$133$	−50.6712	−	49.6867i	−0.380987	−	0.373584i
$134$	−31.9720	+	129.885i	−0.238597	+	0.969293i
$135$	12.0786	−	6.97356i	0.0894708	−	0.0516560i
$136$	105.504	−	211.736i	0.775768	−	1.55688i
$137$	−24.7699	−	14.3009i	−0.180802	−	0.104386i	0.406867	−	0.913487i	$-0.366621\pi$
$137$	−24.7699	−	14.3009i	−0.180802	−	0.104386i	−0.587670	+	0.809101i	$0.699954\pi$
$138$	−84.1117	+	24.3909i	−0.609505	+	0.176746i
$139$	−145.324	+	145.324i	−1.04550	+	1.04550i	−0.0465840	+	0.998914i	$0.514834\pi$
$139$	−145.324	+	145.324i	−1.04550	+	1.04550i	−0.998914	+	0.0465840i	$0.985166\pi$
$140$	73.4870	+	15.7481i	0.524907	+	0.112487i
$141$	−13.9614	+	13.9614i	−0.0990172	+	0.0990172i
$142$	36.8361	−	66.9250i	0.259409	−	0.471303i
$143$	68.9961	+	39.8349i	0.482490	+	0.278566i
$144$	3.92051	+	47.8396i	0.0272258	+	0.332220i
$145$	38.7366	−	22.3646i	0.267149	−	0.154238i
$146$	−171.513	+	103.754i	−1.17474	+	0.710645i
$147$	−61.1783	−	58.8236i	−0.416179	−	0.400160i
$148$	9.50282	−	2.96753i	0.0642082	−	0.0200509i
$149$	40.3877	−	150.729i	0.271058	−	1.01160i	−0.687379	−	0.726299i	$-0.741239\pi$
$149$	40.3877	−	150.729i	0.271058	−	1.01160i	0.958437	−	0.285304i	$-0.0920947\pi$
$150$	44.4717	+	42.6897i	0.296478	+	0.284598i
$151$	196.878	+	113.667i	1.30383	+	0.752765i	0.981058	−	0.193713i	$-0.0620531\pi$
$151$	196.878	+	113.667i	1.30383	+	0.752765i	0.322769	+	0.946478i	$0.395386\pi$
$152$	−79.4810	−	16.1508i	−0.522901	−	0.106255i
$153$	88.7122			0.579818
$154$	31.1236	−	33.0660i	0.202101	−	0.214715i
$155$	31.5116	+	31.5116i	0.203301	+	0.203301i
$156$	−6.95550	−	170.032i	−0.0445865	−	1.08995i
$157$	−133.414	+	35.7480i	−0.849768	+	0.227695i	−0.657319	−	0.753613i	$-0.728310\pi$
$157$	−133.414	+	35.7480i	−0.849768	+	0.227695i	−0.192449	+	0.981307i	$0.561643\pi$
$158$	−1.20574	−	58.9749i	−0.00763126	−	0.373259i
$159$	29.1005	−	16.8012i	0.183022	−	0.105668i
$160$	80.2641	−	30.5796i	0.501650	−	0.191123i
$161$	−1.73604	−	176.960i	−0.0107828	−	1.09913i
$162$	−15.4012	+	9.31676i	−0.0950693	+	0.0575109i
$163$	6.66413	+	1.78565i	0.0408842	+	0.0109549i	0.279203	−	0.960232i	$-0.409930\pi$
$163$	6.66413	+	1.78565i	0.0408842	+	0.0109549i	−0.238319	+	0.971187i	$0.576596\pi$
$164$	−61.7519	−	97.5217i	−0.376536	−	0.594645i
$165$	−14.5656	+	3.90283i	−0.0882762	+	0.0236535i
$166$	−90.4196	−	311.810i	−0.544696	−	1.87838i
$167$	−102.231			−0.612161			−0.306081	−	0.952006i	$-0.599018\pi$
$167$	−102.231			−0.612161			−0.306081	+	0.952006i	$0.599018\pi$
$168$	−95.2372	−	18.3815i	−0.566888	−	0.109414i
$169$			434.319i			2.56994i
$170$	−44.2114	−	152.462i	−0.260067	−	0.896836i
$171$	−7.87185	−	29.3782i	−0.0460342	−	0.171802i
$172$	−14.5263	+	64.6818i	−0.0844552	+	0.376057i
$173$	32.4034	−	120.931i	0.187303	−	0.699024i	−0.806823	−	0.590793i	$-0.798815\pi$
$173$	32.4034	−	120.931i	0.187303	−	0.699024i	0.994126	−	0.108231i	$-0.0345185\pi$
$174$	−49.3925	+	29.8793i	−0.283865	+	0.171720i
$175$	−107.263	+	63.3394i	−0.612932	+	0.361940i
$176$	9.29264	−	51.0580i	0.0527991	−	0.290102i
$177$	−30.7906	−	53.3308i	−0.173958	−	0.301304i
$178$	−3.74733	−	183.289i	−0.0210524	−	1.02971i
$179$	28.1670	+	105.121i	0.157358	+	0.587267i	0.998892	+	0.0470631i	$0.0149862\pi$
$179$	28.1670	+	105.121i	0.157358	+	0.587267i	−0.841534	+	0.540204i	$0.818347\pi$
$180$	23.6874	+	21.8256i	0.131597	+	0.121253i
$181$	100.490	−	100.490i	0.555196	−	0.555196i	−0.372740	−	0.927936i	$-0.621582\pi$
$181$	100.490	−	100.490i	0.555196	−	0.555196i	0.927936	+	0.372740i	$0.121582\pi$
$182$	334.699	+	78.9139i	1.83900	+	0.433593i
$183$		−	72.4515i		−	0.395910i
$184$	−111.670	−	168.627i	−0.606900	−	0.916449i
$185$	3.34019	−	5.78538i	0.0180551	−	0.0312723i
$186$	−41.4914	−	39.8288i	−0.223072	−	0.214133i
$187$	−92.6459	−	24.8244i	−0.495433	−	0.132751i
$188$	−40.3877	−	21.1658i	−0.214828	−	0.112584i
$189$	−9.75825	−	35.0396i	−0.0516309	−	0.185395i
$190$	−46.5667	+	28.1699i	−0.245088	+	0.148262i
$191$	69.1642	+	119.796i	0.362116	+	0.627204i	0.988309	−	0.152465i	$-0.0487210\pi$
$191$	69.1642	+	119.796i	0.362116	+	0.627204i	−0.626193	+	0.779668i	$0.715388\pi$
$192$	−102.760	+	41.5749i	−0.535206	+	0.216536i
$193$	−50.9500	+	88.2480i	−0.263990	+	0.457244i	−0.967298	−	0.253641i	$-0.918372\pi$
$193$	−50.9500	+	88.2480i	−0.263990	+	0.457244i	0.703309	+	0.710885i	$0.251705\pi$
$194$	108.029	−	196.271i	0.556853	−	1.01171i
$195$	−80.7462	−	80.7462i	−0.414083	−	0.414083i
$196$	87.5569	−	175.356i	0.446719	−	0.894674i
$197$	238.379	+	238.379i	1.21004	+	1.21004i	0.971012	+	0.239032i	$0.0768299\pi$
$197$	238.379	+	238.379i	1.21004	+	1.21004i	0.239032	+	0.971012i	$0.423170\pi$
$198$	18.6913	−	5.42015i	0.0944004	−	0.0273745i
$199$	−196.732	+	340.750i	−0.988604	+	1.71231i	−0.363932	+	0.931425i	$0.618566\pi$
$199$	−196.732	+	340.750i	−0.988604	+	1.71231i	−0.624672	+	0.780887i	$0.714767\pi$
$200$	−63.4919	+	127.421i	−0.317459	+	0.637107i
$201$	−57.9209	−	100.322i	−0.288163	−	0.499114i
$202$	−39.2680	+	159.525i	−0.194396	+	0.789728i
$203$	−31.2952	−	112.374i	−0.154164	−	0.553566i
$204$	61.0688	+	195.559i	0.299357	+	0.958620i
$205$	−74.8170	−	20.0472i	−0.364961	−	0.0977910i
$206$	−5.74327	−	280.914i	−0.0278800	−	1.36366i
$207$	37.9219	−	65.6826i	0.183197	−	0.317307i
$208$	370.033	−	132.382i	1.77901	−	0.636451i
$209$			32.8837i			0.157338i
$210$	−55.3565	+	34.2333i	−0.263602	+	0.163016i
$211$	34.5596	−	34.5596i	0.163789	−	0.163789i	−0.620454	−	0.784243i	$-0.713052\pi$
$211$	34.5596	−	34.5596i	0.163789	−	0.163789i	0.784243	+	0.620454i	$0.213052\pi$
$212$	57.0694	+	52.5838i	0.269195	+	0.248037i
$213$	17.1230	+	63.9037i	0.0803895	+	0.300018i
$214$	249.249	−	259.654i	1.16472	−	1.21333i
$215$	22.2423	+	38.5248i	0.103453	+	0.179185i
$216$	−31.1401	−	27.5371i	−0.144167	−	0.127487i
$217$	100.075	−	59.0946i	0.461174	−	0.272326i
$218$	−17.9769	+	73.0305i	−0.0824627	+	0.335002i
$219$	44.9304	−	167.682i	0.205162	−	0.765673i
$220$	−18.6303	−	29.4219i	−0.0846832	−	0.133736i
$221$	−187.989	−	701.583i	−0.850628	−	3.17459i
$222$	−4.15729	+	7.55310i	−0.0187265	+	0.0340230i
$223$		−	311.228i		−	1.39564i	−0.716273	−	0.697820i	$-0.754154\pi$
$223$		−	311.228i		−	1.39564i	0.716273	−	0.697820i	$-0.245846\pi$
$224$	−25.0401	−	222.596i	−0.111786	−	0.993732i
$225$	−53.3864			−0.237273
$226$	311.646	+	171.532i	1.37896	+	0.758993i
$227$	−138.877	+	37.2120i	−0.611793	+	0.163929i	−0.551394	−	0.834245i	$-0.685904\pi$
$227$	−138.877	+	37.2120i	−0.611793	+	0.163929i	−0.0603988	+	0.998174i	$0.519237\pi$
$228$	59.3428	−	37.5766i	0.260275	−	0.164809i
$229$	−186.293	−	49.9169i	−0.813505	−	0.217978i	−0.172000	−	0.985097i	$-0.555023\pi$
$229$	−186.293	−	49.9169i	−0.813505	−	0.217978i	−0.641505	+	0.767119i	$0.721690\pi$
$230$	−131.782	−	32.4390i	−0.572966	−	0.141039i
$231$	0.385782	+	39.3240i	0.00167005	+	0.170234i
$232$	−99.8679	−	88.3130i	−0.430465	−	0.380659i
$233$	115.145	−	66.4791i	0.494186	−	0.285318i	−0.232124	−	0.972686i	$-0.574567\pi$
$233$	115.145	−	66.4791i	0.494186	−	0.285318i	0.726309	+	0.687368i	$0.241234\pi$
$234$	106.318	+	102.058i	0.454352	+	0.436146i
$235$	−29.5550	+	7.91923i	−0.125766	+	0.0336989i
$236$	96.3673	−	104.588i	0.408336	−	0.443168i
$237$	36.1222	+	36.1222i	0.152414	+	0.152414i
$238$	−413.801	+	12.5222i	−1.73866	+	0.0526141i
$239$	−75.8800			−0.317490			−0.158745	−	0.987320i	$-0.550745\pi$
$239$	−75.8800			−0.317490			−0.158745	+	0.987320i	$0.550745\pi$
$240$	−31.8065	+	67.2415i	−0.132527	+	0.280173i
$241$	−160.154	−	92.4650i	−0.664539	−	0.383672i	0.129465	−	0.991584i	$-0.458674\pi$
$241$	−160.154	−	92.4650i	−0.664539	−	0.383672i	−0.794004	+	0.607912i	$0.792007\pi$
$242$	220.913	−	4.51654i	0.912862	−	0.0186634i
$243$	4.03459	−	15.0573i	0.0166032	−	0.0619642i
$244$	159.713	−	49.8751i	0.654563	−	0.204406i
$245$	−36.5263	−	126.348i	−0.149087	−	0.515707i
$246$	97.0667	+	23.8935i	0.394580	+	0.0971282i
$247$	−215.657	+	124.510i	−0.873106	+	0.504088i
$248$	59.2368	−	118.882i	0.238858	−	0.479363i
$249$	243.492	+	140.580i	0.977879	+	0.564579i
$250$	63.9838	+	220.647i	0.255935	+	0.882588i
$251$	−60.4131	+	60.4131i	−0.240689	+	0.240689i	−0.817135	−	0.576446i	$-0.804439\pi$
$251$	−60.4131	+	60.4131i	−0.240689	+	0.240689i	0.576446	+	0.817135i	$0.304439\pi$
$252$	70.5244	−	45.6323i	0.279859	−	0.181080i
$253$	−57.9834	+	57.9834i	−0.229184	+	0.229184i
$254$	−318.293	−	175.191i	−1.25312	−	0.689729i
$255$	119.057	+	68.7377i	0.466891	+	0.269560i
$256$	−162.387	−	197.905i	−0.634325	−	0.773066i
$257$	−394.122	+	227.546i	−1.53355	+	0.885395i	−0.534354	+	0.845261i	$0.679445\pi$
$257$	−394.122	+	227.546i	−1.53355	+	0.885395i	−0.999194	+	0.0401337i	$0.987222\pi$
$258$	−29.7160	−	49.1226i	−0.115178	−	0.190398i
$259$	−12.4394	−	12.1977i	−0.0480287	−	0.0470955i
$260$	122.413	−	233.583i	0.470819	−	0.898397i
$261$	12.9391	−	48.2895i	0.0495752	−	0.185017i
$262$	118.089	−	123.018i	0.450721	−	0.469536i
$263$	421.365	+	243.275i	1.60215	+	0.925001i	0.991057	+	0.133441i	$0.0426026\pi$
$263$	421.365	+	243.275i	1.60215	+	0.925001i	0.611091	+	0.791560i	$0.290731\pi$
$264$	24.8152	+	37.4722i	0.0939970	+	0.141940i
$265$	52.0730			0.196502
$266$	40.8654	+	135.924i	0.153629	+	0.510993i
$267$	112.265	+	112.265i	0.420467	+	0.420467i
$268$	181.279	−	196.743i	0.676413	−	0.734114i
$269$	−17.7363	+	4.75244i	−0.0659343	+	0.0176671i	−0.291635	−	0.956530i	$-0.594199\pi$
$269$	−17.7363	+	4.75244i	−0.0659343	+	0.0176671i	0.225701	+	0.974197i	$0.427533\pi$
$270$	−27.8884	+	0.570177i	−0.103290	+	0.00211177i
$271$	109.594	−	63.2740i	0.404405	−	0.233483i	−0.283978	−	0.958831i	$-0.591654\pi$
$271$	109.594	−	63.2740i	0.404405	−	0.233483i	0.688383	+	0.725348i	$0.258321\pi$
$272$	−389.053	+	269.242i	−1.43034	+	0.989861i
$273$	−256.434	+	151.425i	−0.939318	+	0.554672i
$274$	29.6085	+	48.9448i	0.108060	+	0.178631i
$275$	55.7537	+	14.9392i	0.202741	+	0.0543242i
$276$	170.897	+	38.3801i	0.619192	+	0.139058i
$277$	22.5022	−	6.02944i	0.0812353	−	0.0217669i	−0.217972	−	0.975955i	$-0.569944\pi$
$277$	22.5022	−	6.02944i	0.0812353	−	0.0217669i	0.299208	+	0.954188i	$0.403278\pi$
$278$	394.776	−	114.478i	1.42006	−	0.411792i
$279$	49.8086			0.178526
$280$	−113.572	−	98.4627i	−0.405613	−	0.351652i
$281$			37.5067i			0.133476i	0.997771	+	0.0667379i	$0.0212591\pi$
$281$			37.5067i			0.133476i	−0.997771	+	0.0667379i	$0.978741\pi$
$282$	37.9264	−	10.9980i	0.134491	−	0.0390000i
$283$	28.0317	+	104.616i	0.0990520	+	0.369667i	0.997603	−	0.0692028i	$-0.0220455\pi$
$283$	28.0317	+	104.616i	0.0990520	+	0.369667i	−0.898551	+	0.438870i	$0.855379\pi$
$284$	−129.083	+	81.7370i	−0.454518	+	0.287806i
$285$	12.1989	−	45.5268i	0.0428030	−	0.159743i
$286$	−82.4739	−	136.335i	−0.288370	−	0.476695i
$287$	−99.2792	+	175.920i	−0.345920	+	0.612961i
$288$	39.2667	−	87.6021i	0.136343	−	0.304174i
$289$	292.714	+	506.995i	1.01285	+	1.75431i
$290$	−89.4396	+	1.82859i	−0.308412	+	0.00630547i
$291$	50.2166	+	187.411i	0.172566	+	0.644024i
$292$	400.572	−	16.3862i	1.37182	−	0.0561170i
$293$	−310.989	+	310.989i	−1.06140	+	1.06140i	−0.0634093	+	0.997988i	$0.520197\pi$
$293$	−310.989	+	310.989i	−1.06140	+	1.06140i	−0.997988	+	0.0634093i	$0.979803\pi$
$294$	50.4637	+	162.066i	0.171645	+	0.551245i
$295$		−	95.4310i		−	0.323495i
$296$	−19.5120	−	3.96489i	−0.0659190	−	0.0133949i
$297$	−8.42699	+	14.5960i	−0.0283737	+	0.0491447i
$298$	−216.125	+	225.147i	−0.725253	+	0.755528i
$299$	−599.813	−	160.719i	−2.00606	−	0.537523i
$300$	−36.7508	−	117.686i	−0.122503	−	0.392286i
$301$	111.760	−	31.1241i	0.371295	−	0.103402i
$302$	−235.336	−	389.027i	−0.779259	−	1.28817i
$303$	−71.1384	−	123.215i	−0.234780	−	0.406651i
$304$	123.685	+	104.949i	0.406860	+	0.345226i
$305$	56.1383	−	97.2345i	0.184060	−	0.318802i
$306$	−155.435	−	85.5529i	−0.507958	−	0.279584i
$307$	−402.113	−	402.113i	−1.30982	−	1.30982i	−0.921545	−	0.388270i	$-0.873073\pi$
$307$	−402.113	−	402.113i	−1.30982	−	1.30982i	−0.388270	−	0.921545i	$-0.626927\pi$
$308$	−86.4210	+	27.9208i	−0.280588	+	0.0906520i
$309$	172.060	+	172.060i	0.556829	+	0.556829i
$310$	−24.8231	−	85.6019i	−0.0800744	−	0.276135i
$311$	105.424	−	182.600i	0.338984	−	0.587137i	−0.645258	−	0.763965i	$-0.723250\pi$
$311$	105.424	−	182.600i	0.338984	−	0.587137i	0.984242	+	0.176828i	$0.0565835\pi$
$312$	−151.790	+	304.626i	−0.486506	+	0.976366i
$313$	198.089	+	343.100i	0.632873	+	1.09617i	0.986962	+	0.160956i	$0.0514576\pi$
$313$	198.089	+	343.100i	0.632873	+	1.09617i	−0.354089	+	0.935212i	$0.615209\pi$
$314$	268.233	+	66.0270i	0.854244	+	0.210277i
$315$	14.0539	−	54.5865i	0.0446157	−	0.173290i
$316$	−54.7620	+	104.495i	−0.173298	+	0.330679i
$317$	−114.669	−	30.7254i	−0.361731	−	0.0969256i	0.0733756	−	0.997304i	$-0.476623\pi$
$317$	−114.669	−	30.7254i	−0.361731	−	0.0969256i	−0.435107	+	0.900379i	$0.643289\pi$
$318$	−67.1907	+	1.37371i	−0.211292	+	0.00431984i
$319$	−27.0258	+	46.8100i	−0.0847203	+	0.146740i
$320$	−170.124	−	23.8261i	−0.531636	−	0.0744567i
$321$			311.703i			0.971038i
$322$	−167.616	+	311.731i	−0.520548	+	0.968110i
$323$	211.986	−	211.986i	0.656302	−	0.656302i
$324$	35.9699	−	1.47142i	0.111018	−	0.00454142i
$325$	113.130	+	422.208i	0.348094	+	1.29910i
$326$	−9.95437	−	9.55549i	−0.0305349	−	0.0293113i
$327$	−32.5671	−	56.4079i	−0.0995936	−	0.172501i
$328$	14.1487	+	230.423i	0.0431364	+	0.702511i
$329$	0.782789	+	79.7923i	0.00237930	+	0.242530i
$330$	29.2846	+	7.20858i	0.0887412	+	0.0218442i
$331$	64.5775	−	241.007i	0.195098	−	0.728117i	−0.797143	−	0.603790i	$-0.793656\pi$
$331$	64.5775	−	241.007i	0.195098	−	0.728117i	0.992241	−	0.124326i	$-0.0396769\pi$
$332$	−142.279	+	633.532i	−0.428551	+	1.90823i
$333$	−1.93248	−	7.21213i	−0.00580325	−	0.0216580i
$334$	179.122	+	98.5902i	0.536293	+	0.295180i
$335$		−	179.518i		−	0.535873i
$336$	149.141	+	124.052i	0.443872	+	0.369203i
$337$	523.677			1.55394			0.776969	−	0.629538i	$-0.216756\pi$
$337$	523.677			1.55394			0.776969	+	0.629538i	$0.216756\pi$
$338$	418.852	−	760.984i	1.23921	−	2.25143i
$339$	−297.577	+	79.7355i	−0.877808	+	0.235208i
$340$	−69.5684	+	309.770i	−0.204613	+	0.911089i
$341$	−52.0173	−	13.9380i	−0.152543	−	0.0408739i
$342$	−14.5394	+	59.0659i	−0.0425129	+	0.172707i
$343$	−342.851	+	10.0930i	−0.999567	+	0.0294258i
$344$	87.8303	−	99.3220i	0.255321	−	0.288727i
$345$	101.787	−	58.7668i	0.295035	−	0.170338i
$346$	−173.399	+	180.638i	−0.501154	+	0.522074i
$347$	573.375	−	153.635i	1.65238	−	0.442753i	0.692101	−	0.721801i	$-0.256685\pi$
$347$	573.375	−	153.635i	1.65238	−	0.442753i	0.960277	+	0.279047i	$0.0900186\pi$
$348$	115.357	−	4.71892i	0.331487	−	0.0135601i
$349$	−2.16598	−	2.16598i	−0.00620624	−	0.00620624i	0.703997	−	0.710203i	$-0.251397\pi$
$349$	−2.16598	−	2.16598i	−0.00620624	−	0.00620624i	−0.710203	+	0.703997i	$0.751397\pi$
$350$	249.023	−	7.53576i	0.711493	−	0.0215307i
$351$	−127.631			−0.363620
$352$	−65.5216	+	80.4986i	−0.186141	+	0.228689i
$353$	134.739	+	77.7917i	0.381697	+	0.220373i	0.678557	−	0.734548i	$-0.262606\pi$
$353$	134.739	+	77.7917i	0.381697	+	0.220373i	−0.296859	+	0.954921i	$0.595939\pi$
$354$	2.51752	+	123.136i	0.00711163	+	0.347843i
$355$	−26.5351	+	99.0304i	−0.0747468	+	0.278959i
$356$	−170.196	+	324.760i	−0.478078	+	0.912247i
$357$	251.017	−	255.991i	0.703129	−	0.717061i
$358$	52.0248	−	211.349i	0.145321	−	0.590361i
$359$	323.980	−	187.050i	0.902450	−	0.521030i	0.0244561	−	0.999701i	$-0.492215\pi$
$359$	323.980	−	187.050i	0.902450	−	0.521030i	0.877994	+	0.478671i	$0.158881\pi$
$360$	−20.4551	−	61.0852i	−0.0568197	−	0.169681i
$361$	223.623	+	129.109i	0.619454	+	0.357642i
$362$	−272.984	+	79.1607i	−0.754100	+	0.218676i
$363$	−135.309	+	135.309i	−0.372752	+	0.372752i
$364$	−510.332	−	461.046i	−1.40201	−	1.26661i
$365$	190.226	−	190.226i	0.521168	−	0.521168i
$366$	−69.8713	+	126.944i	−0.190905	+	0.346843i
$367$	−394.495	−	227.762i	−1.07492	−	0.620604i	−0.145396	−	0.989374i	$-0.546446\pi$
$367$	−394.495	−	227.762i	−1.07492	−	0.620604i	−0.929521	+	0.368770i	$0.879779\pi$
$368$	33.0384	+	403.148i	0.0897784	+	1.09551i
$369$	−74.9732	+	43.2858i	−0.203179	+	0.117306i
$370$	−11.4318	+	6.91550i	−0.0308967	+	0.0186905i
$371$	33.8598	−	131.514i	0.0912662	−	0.354484i
$372$	34.2879	+	109.799i	0.0921718	+	0.295158i
$373$	−107.686	+	401.891i	−0.288703	+	1.07745i	0.657388	+	0.753553i	$0.271661\pi$
$373$	−107.686	+	401.891i	−0.288703	+	1.07745i	−0.946091	+	0.323902i	$0.895005\pi$
$374$	138.387	+	132.842i	0.370020	+	0.355193i
$375$	−172.303	−	99.4789i	−0.459474	−	0.265277i
$376$	50.3525	+	76.0347i	0.133916	+	0.202220i
$377$	−409.318			−1.08573
$378$	−16.6941	+	70.8047i	−0.0441642	+	0.187314i
$379$	−64.6594	−	64.6594i	−0.170605	−	0.170605i	0.616640	−	0.787245i	$-0.288493\pi$
$379$	−64.6594	−	64.6594i	−0.170605	−	0.170605i	−0.787245	+	0.616640i	$0.788493\pi$
$380$	108.757	−	4.44894i	0.286204	−	0.0117077i
$381$	303.924	−	81.4362i	0.797701	−	0.213743i
$382$	−5.65505	−	276.599i	−0.0148038	−	0.724081i
$383$	−41.9522	+	24.2211i	−0.109536	+	0.0632406i	−0.553767	−	0.832672i	$-0.686810\pi$
$383$	−41.9522	+	24.2211i	−0.109536	+	0.0632406i	0.444231	+	0.895912i	$0.353477\pi$
$384$	220.142	+	26.2554i	0.573287	+	0.0683734i
$385$	−29.9521	+	53.0742i	−0.0777977	+	0.137855i
$386$	174.376	−	105.486i	0.451752	−	0.273281i
$387$	48.0255	+	12.8684i	0.124097	+	0.0332517i
$388$	−378.563	+	239.711i	−0.975678	+	0.617811i
$389$	118.866	−	31.8500i	0.305568	−	0.0818767i	−0.102777	−	0.994704i	$-0.532773\pi$
$389$	118.866	−	31.8500i	0.305568	−	0.0818767i	0.408345	+	0.912828i	$0.366106\pi$
$390$	63.6072	+	219.348i	0.163095	+	0.562431i
$391$	747.585			1.91198
$392$	−322.522	+	222.808i	−0.822761	+	0.568388i
$393$			147.678i			0.375772i
$394$	−187.781	−	647.559i	−0.476601	−	1.64355i
$395$	20.4893	+	76.4671i	0.0518717	+	0.193588i
$396$	−37.9767	−	8.52882i	−0.0959007	−	0.0215374i
$397$	−113.902	+	425.086i	−0.286906	+	1.07075i	0.660530	+	0.750800i	$0.270332\pi$
$397$	−113.902	+	425.086i	−0.286906	+	1.07075i	−0.947436	+	0.319947i	$0.896335\pi$
$398$	673.315	−	407.313i	1.69175	−	1.02340i
$399$	−107.049	−	60.4122i	−0.268292	−	0.151409i
$400$	234.130	−	162.028i	0.585324	−	0.405071i
$401$	217.295	+	376.367i	0.541884	+	0.938570i	0.998796	+	0.0490584i	$0.0156220\pi$
$401$	217.295	+	376.367i	0.541884	+	0.938570i	−0.456912	+	0.889512i	$0.651045\pi$
$402$	4.73576	+	231.635i	0.0117805	+	0.576207i
$403$	−105.549	−	393.913i	−0.261908	−	0.977453i
$404$	222.646	−	241.639i	0.551105	−	0.598116i
$405$	17.0817	−	17.0817i	0.0421770	−	0.0421770i
$406$	−53.5387	+	227.074i	−0.131869	+	0.559296i
$407$			8.07270i			0.0198346i
$408$	81.5936	−	401.538i	0.199984	−	0.984161i
$409$	378.899	−	656.273i	0.926404	−	1.60458i	0.137117	−	0.990555i	$-0.456216\pi$
$409$	378.899	−	656.273i	0.926404	−	1.60458i	0.789287	−	0.614024i	$-0.210450\pi$
$410$	111.756	+	107.278i	0.272575	+	0.261653i
$411$	−47.8518	−	12.8218i	−0.116428	−	0.0311967i
$412$	−260.847	+	497.737i	−0.633124	+	1.20810i
$413$	−241.017	−	62.0528i	−0.583577	−	0.150249i
$414$	−129.787	+	78.5131i	−0.313496	+	0.189645i
$415$	217.854	+	377.334i	0.524950	+	0.909240i
$416$	−776.014	−	124.905i	−1.86542	−	0.300253i
$417$	−177.985	+	308.279i	−0.426823	+	0.739279i
$418$	31.7126	−	57.6164i	0.0758674	−	0.137838i
$419$	248.941	+	248.941i	0.594130	+	0.594130i	0.938744	−	0.344614i	$-0.111990\pi$
$419$	248.941	+	248.941i	0.594130	+	0.594130i	−0.344614	+	0.938744i	$0.611990\pi$
$420$	130.006	−	6.59619i	0.309538	−	0.0157052i
$421$	−573.306	−	573.306i	−1.36177	−	1.36177i	−0.871660	−	0.490112i	$-0.836956\pi$
$421$	−573.306	−	573.306i	−1.36177	−	1.36177i	−0.490112	−	0.871660i	$-0.663044\pi$
$422$	−93.8816	+	27.2241i	−0.222468	+	0.0645120i
$423$	−17.0992	+	29.6167i	−0.0404236	+	0.0700157i
$424$	−49.2819	−	147.171i	−0.116231	−	0.347101i
$425$	−263.113	−	455.724i	−0.619088	−	1.07229i
$426$	31.6263	−	128.481i	0.0742401	−	0.301598i
$427$	−209.069	−	205.006i	−0.489622	−	0.480109i
$428$	−687.123	+	214.574i	−1.60543	+	0.501342i
$429$	133.290	+	35.7150i	0.310700	+	0.0832518i
$430$	−1.81859	−	88.9507i	−0.00422928	−	0.206862i
$431$	272.662	−	472.264i	0.632626	−	1.09574i	−0.354386	−	0.935099i	$-0.615310\pi$
$431$	272.662	−	472.264i	0.632626	−	1.09574i	0.987013	−	0.160642i	$-0.0513564\pi$
$432$	28.0051	+	78.2797i	0.0648265	+	0.181203i
$433$		−	800.418i		−	1.84854i	−0.381739	−	0.924270i	$-0.624675\pi$
$433$		−	800.418i		−	1.84854i	0.381739	−	0.924270i	$-0.375325\pi$
$434$	−232.334	+	7.03073i	−0.535332	+	0.0161998i
$435$	54.7818	−	54.7818i	0.125935	−	0.125935i
$436$	101.927	−	110.622i	0.233778	−	0.253721i
$437$	−66.3368	−	247.572i	−0.151800	−	0.566527i
$438$	−240.435	+	250.471i	−0.548937	+	0.571852i
$439$	−20.5394	−	35.5753i	−0.0467868	−	0.0810371i	0.841684	−	0.539971i	$-0.181565\pi$
$439$	−20.5394	−	35.5753i	−0.0467868	−	0.0810371i	−0.888470	+	0.458934i	$0.848231\pi$
$440$	4.26862	+	69.5178i	0.00970141	+	0.157995i
$441$	−128.723	−	70.9883i	−0.291889	−	0.160971i
$442$	−347.217	+	1410.56i	−0.785559	+	3.19131i
$443$	34.6675	−	129.381i	0.0782563	−	0.292056i	−0.915696	−	0.401872i	$-0.868360\pi$
$443$	34.6675	−	129.381i	0.0782563	−	0.292056i	0.993952	+	0.109816i	$0.0350262\pi$
$444$	14.5682	−	9.22477i	0.0328113	−	0.0207765i
$445$	63.6790	+	237.653i	0.143099	+	0.534052i
$446$	−300.144	+	545.311i	−0.672968	+	1.22267i
$447$		−	270.280i		−	0.604653i
$448$	−170.795	+	414.165i	−0.381239	+	0.924476i
$449$	−220.962			−0.492121			−0.246060	−	0.969255i	$-0.579136\pi$
$449$	−220.962			−0.492121			−0.246060	+	0.969255i	$0.579136\pi$
$450$	93.5399	+	51.4852i	0.207867	+	0.114411i
$451$	90.4103	−	24.2254i	0.200466	−	0.0537148i
$452$	−380.620	−	601.094i	−0.842080	−	1.32985i
$453$	380.339	+	101.911i	0.839600	+	0.224970i
$454$	279.217	+	68.7309i	0.615016	+	0.151390i
$455$	−461.481	+	4.52727i	−1.01424	+	0.00995005i
$456$	−140.215	+	8.60963i	−0.307488	+	0.0188808i
$457$	−154.109	+	88.9751i	−0.337220	+	0.194694i	−0.659042	−	0.752106i	$-0.729038\pi$
$457$	−154.109	+	88.9751i	−0.337220	+	0.194694i	0.321822	+	0.946800i	$0.395705\pi$
$458$	278.269	+	267.119i	0.607575	+	0.583229i
$459$	148.418	−	39.7686i	0.323352	−	0.0866418i
$460$	199.616	+	183.926i	0.433947	+	0.399840i
$461$	506.634	+	506.634i	1.09899	+	1.09899i	0.994529	+	0.104460i	$0.0333114\pi$
$461$	506.634	+	506.634i	1.09899	+	1.09899i	0.104460	+	0.994529i	$0.466689\pi$
$462$	37.2477	−	69.2729i	0.0806226	−	0.149941i
$463$	412.331			0.890563			0.445282	−	0.895391i	$-0.353104\pi$
$463$	412.331			0.890563			0.445282	+	0.895391i	$0.353104\pi$
$464$	89.8136	+	251.047i	0.193564	+	0.541050i
$465$	66.8463	+	38.5937i	0.143755	+	0.0829973i
$466$	−265.861	+	5.43551i	−0.570517	+	0.0116642i
$467$	−72.9312	+	272.183i	−0.156170	+	0.582833i	0.842833	+	0.538175i	$0.180886\pi$
$467$	−72.9312	+	272.183i	−0.156170	+	0.582833i	−0.999002	+	0.0446573i	$0.985780\pi$
$468$	−87.8601	−	281.351i	−0.187735	−	0.601178i
$469$	−453.383	−	116.729i	−0.966702	−	0.248889i
$470$	59.4213	+	14.6269i	0.126428	+	0.0311211i
$471$	−207.180	+	119.615i	−0.439872	+	0.253960i
$472$	−269.711	+	90.3159i	−0.571422	+	0.191347i
$473$	−46.5542	−	26.8781i	−0.0984232	−	0.0568246i
$474$	−28.4550	−	98.1265i	−0.0600316	−	0.207018i
$475$	−127.572	+	127.572i	−0.268572	+	0.268572i
$476$	737.109	+	377.124i	1.54855	+	0.792276i
$477$	41.1544	−	41.1544i	0.0862775	−	0.0862775i
$478$	132.952	+	73.1777i	0.278141	+	0.153091i
$479$	−162.395	−	93.7586i	−0.339029	−	0.195738i	0.320814	−	0.947142i	$-0.396044\pi$
$479$	−162.395	−	93.7586i	−0.339029	−	0.195738i	−0.659842	+	0.751404i	$0.729377\pi$
$480$	120.576	−	87.1421i	0.251200	−	0.181546i
$481$	−52.9423	+	30.5662i	−0.110067	+	0.0635473i
$482$	191.439	+	316.461i	0.397175	+	0.656558i
$483$	−82.2335	−	295.282i	−0.170256	−	0.611350i
$484$	−391.423	−	205.132i	−0.808726	−	0.423826i
$485$	−77.8197	+	290.427i	−0.160453	+	0.598819i
$486$	−21.5902	+	22.4914i	−0.0444242	+	0.0462787i
$487$	421.219	+	243.191i	0.864926	+	0.499366i	0.865659	−	0.500634i	$-0.166900\pi$
$487$	421.219	+	243.191i	0.864926	+	0.499366i	−0.000732469		1.00000i	$0.500233\pi$
$488$	−327.937	−	66.6377i	−0.672003	−	0.136553i
$489$	11.9498			0.0244372
$490$	−57.8499	+	256.604i	−0.118061	+	0.523682i
$491$	−217.930	−	217.930i	−0.443848	−	0.443848i	0.449455	−	0.893303i	$-0.351618\pi$
$491$	−217.930	−	217.930i	−0.443848	−	0.443848i	−0.893303	+	0.449455i	$0.851618\pi$
$492$	−147.031	−	135.474i	−0.298843	−	0.275354i
$493$	475.985	−	127.540i	0.965487	−	0.258702i
$494$	497.935	−	10.1802i	1.00797	−	0.0206078i
$495$	−22.6191	+	13.0591i	−0.0456951	+	0.0263821i
$496$	−218.439	+	151.170i	−0.440401	+	0.304777i
$497$	232.853	+	131.409i	0.468518	+	0.264405i
$498$	−291.056	−	481.135i	−0.584449	−	0.966134i
$499$	−301.038	−	80.6629i	−0.603282	−	0.161649i	−0.0557658	−	0.998444i	$-0.517760\pi$
$499$	−301.038	−	80.6629i	−0.603282	−	0.161649i	−0.547517	+	0.836795i	$0.684427\pi$
$500$	100.681	−	448.307i	0.201362	−	0.896614i
$501$	−171.036	+	45.8289i	−0.341389	+	0.0914748i
$502$	164.113	−	47.5900i	0.326918	−	0.0948007i
$503$	375.338			0.746198			0.373099	−	0.927791i	$-0.378295\pi$
$503$	375.338			0.746198			0.373099	+	0.927791i	$0.378295\pi$
$504$	−167.575	+	11.9408i	−0.332490	+	0.0236921i
$505$		−	220.483i		−	0.436601i
$506$	157.513	−	45.6760i	0.311290	−	0.0902688i
$507$	194.700	+	726.630i	0.384024	+	1.43320i
$508$	388.738	+	613.915i	0.765233	+	1.20849i
$509$	232.132	−	866.327i	0.456054	−	1.70202i	−0.228916	−	0.973446i	$-0.573518\pi$
$509$	232.132	−	866.327i	0.456054	−	1.70202i	0.684970	−	0.728571i	$-0.259815\pi$
$510$	−142.314	−	235.255i	−0.279047	−	0.461284i
$511$	−356.737	−	604.121i	−0.698115	−	1.18223i
$512$	93.6666	+	503.359i	0.182943	+	0.983124i
$513$	−26.3397	−	45.6218i	−0.0513445	−	0.0889313i
$514$	909.995	−	18.6048i	1.77042	−	0.0361961i
$515$	97.5963	+	364.234i	0.189507	+	0.707251i
$516$	4.69312	+	114.727i	0.00909520	+	0.222339i
$517$	26.1451	−	26.1451i	0.0505707	−	0.0505707i
$518$	10.0322	+	33.3684i	0.0193671	+	0.0644178i
$519$		−	216.848i		−	0.417818i
$520$	−439.748	+	291.215i	−0.845669	+	0.560028i
$521$	359.037	−	621.871i	0.689131	−	1.19361i	−0.282988	−	0.959123i	$-0.591326\pi$
$521$	359.037	−	621.871i	0.689131	−	1.19361i	0.972119	−	0.234487i	$-0.0753411\pi$
$522$	−69.2408	+	72.1311i	−0.132645	+	0.138182i
$523$	−696.523	−	186.633i	−1.33178	−	0.356851i	−0.478404	−	0.878140i	$-0.658785\pi$
$523$	−696.523	−	186.633i	−1.33178	−	0.356851i	−0.853380	+	0.521289i	$0.825451\pi$
$524$	−325.544	+	101.661i	−0.621268	+	0.194009i
$525$	−151.060	+	154.054i	−0.287734	+	0.293436i
$526$	−503.675	−	832.609i	−0.957556	−	1.58291i
$527$	245.480	+	425.183i	0.465806	+	0.806799i
$528$	−7.34179	−	89.5875i	−0.0139049	−	0.169673i
$529$	55.0707	−	95.3852i	0.104103	−	0.180312i
$530$	−91.2386	−	50.2185i	−0.172148	−	0.0947518i
$531$	−75.4211	−	75.4211i	−0.142036	−	0.142036i
$532$	59.4821	−	277.567i	0.111808	−	0.521742i
$533$	501.202	+	501.202i	0.940341	+	0.940341i
$534$	−88.4356	−	304.969i	−0.165610	−	0.571102i
$535$	−241.520	+	418.325i	−0.451439	+	0.781916i
$536$	−507.360	+	169.895i	−0.946567	+	0.316969i
$537$	94.2487	+	163.244i	0.175510	+	0.303992i
$538$	35.6595	+	8.77780i	0.0662817	+	0.0163156i
$539$	114.566	+	110.157i	0.212554	+	0.204373i
$540$	49.4140	+	25.8962i	0.0915074	+	0.0479559i
$541$	714.509	+	191.452i	1.32072	+	0.353886i	0.849247	−	0.527995i	$-0.177056\pi$
$541$	714.509	+	191.452i	1.32072	+	0.353886i	0.471472	+	0.881881i	$0.343723\pi$
$542$	−253.043	+	5.17345i	−0.466869	+	0.00954510i
$543$	123.075	−	213.173i	0.226658	−	0.392583i
$544$	941.325	−	96.5496i	1.73038	−	0.177481i
$545$		−	100.937i		−	0.185206i
$546$	595.338	−	18.0157i	1.09036	−	0.0329958i
$547$	660.682	−	660.682i	1.20783	−	1.20783i	0.236099	−	0.971729i	$-0.424131\pi$
$547$	660.682	−	660.682i	1.20783	−	1.20783i	0.971729	−	0.236099i	$-0.0758691\pi$
$548$	−4.67614	−	114.312i	−0.00853311	−	0.208598i
$549$	−32.4791	−	121.214i	−0.0591605	−	0.220790i
$550$	−83.2806	−	79.9435i	−0.151419	−	0.145352i
$551$	−84.4729	−	146.311i	−0.153308	−	0.265538i
$552$	−262.420	−	232.058i	−0.475399	−	0.420394i
$553$	206.445	−	2.02530i	0.373319	−	0.00366238i
$554$	−45.2415	−	11.1364i	−0.0816633	−	0.0201019i
$555$	2.99473	−	11.1765i	0.00539591	−	0.0201378i
$556$	−802.100	−	180.136i	−1.44263	−	0.323986i
$557$	−41.4292	−	154.616i	−0.0743792	−	0.277587i	0.918713	−	0.394927i	$-0.129230\pi$
$557$	−41.4292	−	154.616i	−0.0743792	−	0.277587i	−0.993092	+	0.117340i	$0.962563\pi$
$558$	−87.2712	−	48.0348i	−0.156400	−	0.0860839i
$559$		−	407.081i		−	0.728231i
$560$	104.036	+	282.046i	0.185778	+	0.503654i
$561$	−166.128			−0.296128
$562$	36.1710	−	65.7166i	0.0643612	−	0.116933i
$563$	−594.327	+	159.249i	−1.05564	+	0.282858i	−0.744581	−	0.667532i	$-0.767351\pi$
$563$	−594.327	+	159.249i	−1.05564	+	0.282858i	−0.311061	+	0.950390i	$0.600684\pi$
$564$	−77.0584	−	17.3058i	−0.136628	−	0.0306841i
$565$	−461.149	−	123.565i	−0.816193	−	0.218698i
$566$	51.7749	−	210.334i	0.0914751	−	0.371615i
$567$	−32.0337	−	54.2480i	−0.0564968	−	0.0956754i
$568$	304.996	−	18.7278i	0.536965	−	0.0329714i
$569$	−823.633	+	475.525i	−1.44751	+	0.835720i	−0.998333	−	0.0577228i	$-0.981616\pi$
$569$	−823.633	+	475.525i	−1.44751	+	0.835720i	−0.449177	+	0.893443i	$0.648283\pi$
$570$	−65.2794	+	68.0044i	−0.114525	+	0.119306i
$571$	637.894	−	170.923i	1.11715	−	0.299340i	0.347422	−	0.937709i	$-0.387057\pi$
$571$	637.894	−	170.923i	1.11715	−	0.299340i	0.769730	+	0.638369i	$0.220391\pi$
$572$	13.0253	+	318.413i	0.0227715	+	0.556666i
$573$	169.417	+	169.417i	0.295667	+	0.295667i
$574$	343.605	−	212.491i	0.598614	−	0.370193i
$575$	−449.892			−0.782420
$576$	−153.283	+	115.622i	−0.266116	+	0.200733i
$577$	551.086	+	318.170i	0.955088	+	0.551420i	0.894658	−	0.446752i	$-0.147419\pi$
$577$	551.086	+	318.170i	0.955088	+	0.551420i	0.0604303	+	0.998172i	$0.480753\pi$
$578$	−23.9331	−	1170.61i	−0.0414067	−	2.02528i
$579$	−45.6805	+	170.482i	−0.0788956	+	0.294442i
$580$	158.473	+	83.0504i	0.273230	+	0.143190i
$581$	1094.64	−	304.848i	1.88406	−	0.524695i
$582$	92.7507	−	376.797i	0.159365	−	0.647417i
$583$	−54.4955	+	31.4630i	−0.0934743	+	0.0539674i
$584$	−717.656	−	357.595i	−1.22886	−	0.612321i
$585$	−171.288	−	98.8934i	−0.292801	−	0.169049i
$586$	844.808	−	244.980i	1.44165	−	0.418054i
$587$	−329.887	+	329.887i	−0.561988	+	0.561988i	−0.929872	−	0.367884i	$-0.880082\pi$
$587$	−329.887	+	329.887i	−0.561988	+	0.561988i	0.367884	+	0.929872i	$0.380082\pi$
$588$	67.8755	−	332.627i	0.115435	−	0.565693i
$589$	119.022	−	119.022i	0.202075	−	0.202075i
$590$	−92.0324	+	167.208i	−0.155987	+	0.283403i
$591$	505.677	+	291.953i	0.855630	+	0.493998i
$592$	30.3639	+	25.7641i	0.0512904	+	0.0435205i
$593$	−252.258	+	145.641i	−0.425393	+	0.245601i	−0.697382	−	0.716699i	$-0.745652\pi$
$593$	−252.258	+	145.641i	−0.425393	+	0.245601i	0.271989	+	0.962300i	$0.412319\pi$
$594$	28.8413	−	17.4472i	0.0485544	−	0.0293723i
$595$	535.232	−	149.058i	0.899550	−	0.250517i
$596$	595.809	−	186.059i	0.999679	−	0.312179i
$597$	−176.385	+	658.279i	−0.295453	+	1.10264i
$598$	895.954	+	860.053i	1.49825	+	1.43822i
$599$	−489.133	−	282.401i	−0.816583	−	0.471455i	0.0326534	−	0.999467i	$-0.489604\pi$
$599$	−489.133	−	282.401i	−0.816583	−	0.471455i	−0.849237	+	0.528012i	$0.822938\pi$
$600$	−49.1025	+	241.643i	−0.0818375	+	0.402738i
$601$	−103.843			−0.172783			−0.0863916	−	0.996261i	$-0.527534\pi$
$601$	−103.843			−0.172783			−0.0863916	+	0.996261i	$0.527534\pi$
$602$	−225.833	−	53.2460i	−0.375138	−	0.0884486i
$603$	−141.877	−	141.877i	−0.235285	−	0.235285i
$604$	37.1673	+	908.580i	0.0615352	+	1.50427i
$605$	−286.436	+	76.7503i	−0.473448	+	0.126860i
$606$	5.81646	+	284.494i	0.00959812	+	0.469462i
$607$	−399.001	+	230.363i	−0.657332	+	0.379511i	−0.791260	−	0.611480i	$-0.790574\pi$
$607$	−399.001	+	230.363i	−0.657332	+	0.379511i	0.133927	+	0.990991i	$0.457241\pi$
$608$	−115.502	−	303.164i	−0.189970	−	0.498625i
$609$	−102.734	−	173.976i	−0.168692	−	0.285675i
$610$	−192.133	+	116.228i	−0.314973	+	0.190538i
$611$	270.459	+	72.4693i	0.442650	+	0.118608i
$612$	189.837	+	299.799i	0.310191	+	0.489868i
$613$	−151.046	+	40.4725i	−0.246404	+	0.0660237i	−0.379907	−	0.925025i	$-0.624044\pi$
$613$	−151.046	+	40.4725i	−0.246404	+	0.0660237i	0.133503	+	0.991048i	$0.457377\pi$
$614$	316.762	+	1092.35i	0.515899	+	1.77907i
$615$	−134.158			−0.218143
$616$	178.347	+	34.4224i	0.289525	+	0.0558805i
$617$			742.291i			1.20307i	0.798848	+	0.601533i	$0.205443\pi$
$617$			742.291i			1.20307i	−0.798848	+	0.601533i	$0.794557\pi$
$618$	−135.539	−	467.404i	−0.219319	−	0.756317i
$619$	−82.5439	−	308.058i	−0.133350	−	0.497671i	0.866649	−	0.498919i	$-0.166269\pi$
$619$	−82.5439	−	308.058i	−0.133350	−	0.497671i	−0.999999	+	0.00124813i	$0.999603\pi$
$620$	−39.0601	+	173.925i	−0.0630002	+	0.280524i
$621$	33.9998	−	126.889i	0.0547501	−	0.204330i
$622$	−360.813	+	218.269i	−0.580085	+	0.350914i
$623$	641.615	−	6.29445i	1.02988	−	0.0101034i
$624$	559.733	−	387.360i	0.897008	−	0.620770i
$625$	68.2829	+	118.269i	0.109253	+	0.189231i
$626$	−16.1963	−	792.191i	−0.0258727	−	1.26548i
$627$	14.7413	+	55.0154i	0.0235109	+	0.0877439i
$628$	−406.303	−	374.368i	−0.646979	−	0.596127i
$629$	52.0410	−	52.0410i	0.0827360	−	0.0827360i
$630$	−77.2668	+	82.0891i	−0.122646	+	0.130300i
$631$		−	528.131i		−	0.836974i	−0.908223	−	0.418487i	$-0.862560\pi$
$631$		−	528.131i		−	0.836974i	0.908223	−	0.418487i	$-0.137440\pi$
$632$	196.723	−	130.276i	0.311271	−	0.206133i
$633$	42.3267	−	73.3119i	0.0668668	−	0.115817i
$634$	171.284	+	164.420i	0.270163	+	0.259338i
$635$	470.985	+	126.200i	0.741709	+	0.198740i
$636$	119.052	+	62.3909i	0.187188	+	0.0980990i
$637$	−288.638	+	1168.44i	−0.453121	+	1.83429i
$638$	92.4956	−	55.9539i	0.144977	−	0.0877021i
$639$	57.2945	+	99.2370i	0.0896628	+	0.155301i
$640$	275.101	+	205.811i	0.429845	+	0.321580i
$641$	240.007	−	415.705i	0.374426	−	0.648526i	−0.615815	−	0.787891i	$-0.711173\pi$
$641$	240.007	−	415.705i	0.374426	−	0.648526i	0.990241	+	0.139366i	$0.0445063\pi$
$642$	300.602	−	546.144i	0.468228	−	0.850692i
$643$	−106.599	−	106.599i	−0.165783	−	0.165783i	0.619340	−	0.785123i	$-0.287400\pi$
$643$	−106.599	−	106.599i	−0.165783	−	0.165783i	−0.785123	+	0.619340i	$0.787400\pi$
$644$	594.315	−	384.547i	0.922850	−	0.597122i
$645$	54.4823	+	54.4823i	0.0844687	+	0.0844687i
$646$	−575.863	+	166.990i	−0.891428	+	0.258499i
$647$	−197.154	+	341.481i	−0.304721	+	0.527792i	−0.977199	−	0.212325i	$-0.931897\pi$
$647$	−197.154	+	341.481i	−0.304721	+	0.527792i	0.672478	+	0.740117i	$0.265230\pi$
$648$	−64.4430	−	32.1108i	−0.0994490	−	0.0495537i
$649$	57.6604	+	99.8707i	0.0888449	+	0.153884i
$650$	208.953	−	848.865i	0.321466	−	1.30595i
$651$	140.937	−	143.730i	0.216493	−	0.220783i
$652$	8.22615	+	26.3423i	0.0126168	+	0.0404023i
$653$	−947.259	−	253.817i	−1.45063	−	0.388694i	−0.554385	−	0.832260i	$-0.687046\pi$
$653$	−947.259	−	253.817i	−1.45063	−	0.388694i	−0.896242	+	0.443566i	$0.853713\pi$
$654$	2.66277	+	130.241i	0.00407152	+	0.199146i
$655$	−114.427	+	198.194i	−0.174698	+	0.302586i
$656$	197.427	−	417.377i	0.300956	−	0.636245i
$657$		−	300.680i		−	0.457656i
$658$	75.5791	−	140.561i	0.114862	−	0.213619i
$659$	−527.788	+	527.788i	−0.800892	+	0.800892i	−0.983235	−	0.182343i	$-0.941632\pi$
$659$	−527.788	+	527.788i	−0.800892	+	0.800892i	0.182343	+	0.983235i	$0.441632\pi$
$660$	−44.3586	−	40.8721i	−0.0672100	−	0.0619274i
$661$	−262.466	−	979.538i	−0.397075	−	1.48190i	−0.818217	−	0.574909i	$-0.805037\pi$
$661$	−262.466	−	979.538i	−0.397075	−	1.48190i	0.421143	−	0.906994i	$-0.361629\pi$
$662$	−345.572	+	359.997i	−0.522012	+	0.543802i
$663$	−629.022	−	1089.50i	−0.948752	−	1.64329i
$664$	860.261	−	972.818i	1.29557	−	1.46509i
$665$	−96.8561	−	164.022i	−0.145648	−	0.246650i
$666$	−3.56932	+	14.5002i	−0.00535934	+	0.0217721i
$667$	109.039	−	406.940i	0.163477	−	0.610104i
$668$	−218.766	−	345.486i	−0.327494	−	0.517194i
$669$	−139.520	−	520.694i	−0.208549	−	0.778317i
$670$	−173.124	+	314.538i	−0.258395	+	0.469460i
$671$			135.677i			0.202202i
$672$	−141.680	−	361.185i	−0.210833	−	0.537478i
$673$	127.571			0.189556			0.0947781	−	0.995498i	$-0.469786\pi$
$673$	127.571			0.189556			0.0947781	+	0.995498i	$0.469786\pi$
$674$	−917.551	−	505.028i	−1.36135	−	0.749299i
$675$	−89.3172	+	23.9325i	−0.132322	+	0.0354555i
$676$	−1467.76	+	929.407i	−2.17125	+	1.37486i
$677$	−579.596	−	155.302i	−0.856124	−	0.229398i	−0.196046	−	0.980595i	$-0.562810\pi$
$677$	−579.596	−	155.302i	−0.856124	−	0.229398i	−0.660078	+	0.751197i	$0.729477\pi$
$678$	598.289	+	147.272i	0.882433	+	0.217216i
$679$	682.891	+	385.385i	1.00573	+	0.567578i
$680$	420.631	−	475.667i	0.618575	−	0.699510i
$681$	−215.664	+	124.514i	−0.316687	+	0.182840i
$682$	77.6994	+	74.5859i	0.113929	+	0.109364i
$683$	1069.55	−	286.586i	1.56596	−	0.419599i	0.631418	−	0.775442i	$-0.282473\pi$
$683$	1069.55	−	286.586i	1.56596	−	0.419599i	0.934545	+	0.355844i	$0.115806\pi$
$684$	82.4373	−	89.4694i	0.120522	−	0.130803i
$685$	−54.2852	−	54.2852i	−0.0792485	−	0.0792485i
$686$	610.454	+	312.957i	0.889874	+	0.456206i
$687$	−334.051			−0.486246
$688$	−249.675	+	89.3227i	−0.362899	+	0.129830i
$689$	−412.680	−	238.261i	−0.598955	−	0.345807i
$690$	−235.018	+	4.80493i	−0.340606	+	0.00696366i
$691$	25.7823	−	96.2210i	0.0373116	−	0.139249i	−0.944757	−	0.327770i	$-0.893703\pi$
$691$	25.7823	−	96.2210i	0.0373116	−	0.139249i	0.982069	+	0.188521i	$0.0603695\pi$
$692$	478.023	−	149.276i	0.690784	−	0.215717i
$693$	18.2739	+	65.6175i	0.0263693	+	0.0946861i
$694$	−1152.79	−	283.766i	−1.66108	−	0.408885i
$695$	−477.734	+	275.820i	−0.687388	+	0.396863i
$696$	−206.672	−	102.981i	−0.296942	−	0.147961i
$697$	−739.004	−	426.664i	−1.06026	−	0.612143i
$698$	1.70623	+	5.88391i	0.00244446	+	0.00842967i
$699$	162.840	−	162.840i	0.232961	−	0.232961i
$700$	−443.587	−	226.951i	−0.633696	−	0.324215i
$701$	−748.657	+	748.657i	−1.06798	+	1.06798i	−0.0704706	+	0.997514i	$0.522450\pi$
$701$	−748.657	+	748.657i	−1.06798	+	1.06798i	−0.997514	+	0.0704706i	$0.977550\pi$
$702$	223.626	+	123.085i	0.318555	+	0.175335i
$703$	−21.8519	−	12.6162i	−0.0310837	−	0.0179462i
$704$	192.434	−	77.8558i	0.273344	−	0.110591i
$705$	−45.8963	+	26.4983i	−0.0651012	+	0.0375862i
$706$	−161.059	−	266.242i	−0.228129	−	0.377113i
$707$	−556.845	−	143.366i	−0.787617	−	0.202781i
$708$	114.340	−	218.179i	0.161497	−	0.308162i
$709$	181.758	−	678.330i	0.256358	−	0.956742i	−0.710972	−	0.703221i	$-0.751745\pi$
$709$	181.758	−	678.330i	0.256358	−	0.956742i	0.967330	−	0.253521i	$-0.0815888\pi$
$710$	141.997	−	147.924i	0.199995	−	0.208344i
$711$	76.6267	+	44.2404i	0.107773	+	0.0622229i
$712$	611.399	−	404.887i	0.858707	−	0.568662i
$713$	419.741			0.588698
$714$	−686.689	+	206.452i	−0.961749	+	0.289148i
$715$	151.210	+	151.210i	0.211483	+	0.211483i
$716$	−294.977	+	320.139i	−0.411978	+	0.447122i
$717$	−126.950	+	34.0161i	−0.177057	+	0.0474422i
$718$	−748.043	+	15.2937i	−1.04184	+	0.0213004i
$719$	108.937	−	62.8947i	0.151511	−	0.0874752i	−0.422328	−	0.906443i	$-0.638787\pi$
$719$	108.937	−	62.8947i	0.151511	−	0.0874752i	0.573839	+	0.818968i	$0.305453\pi$
$720$	−23.0697	+	126.756i	−0.0320413	+	0.176050i
$721$	983.358	−	9.64706i	1.36388	−	0.0133801i
$722$	−267.306	−	441.874i	−0.370229	−	0.612014i
$723$	−309.394	−	82.9018i	−0.427931	−	0.114664i
$724$	554.645	+	124.562i	0.766084	+	0.172048i
$725$	−286.445	+	76.7527i	−0.395096	+	0.105866i
$726$	367.569	−	106.589i	0.506294	−	0.146816i
$727$	−183.967			−0.253050			−0.126525	−	0.991963i	$-0.540382\pi$
$727$	−183.967			−0.253050			−0.126525	+	0.991963i	$0.540382\pi$
$728$	449.540	+	1299.97i	0.617501	+	1.78567i
$729$		−	27.0000i		−	0.0370370i
$730$	−516.753	+	149.849i	−0.707881	+	0.205273i
$731$	126.843	+	473.383i	0.173519	+	0.647583i
$732$	244.847	−	155.040i	0.334491	−	0.211804i
$733$	−4.92059	+	18.3639i	−0.00671295	+	0.0250531i	−0.969201	−	0.246271i	$-0.920795\pi$
$733$	−4.92059	+	18.3639i	−0.00671295	+	0.0250531i	0.962488	+	0.271324i	$0.0874614\pi$
$734$	471.555	+	779.513i	0.642446	+	1.06201i
$735$	−117.750	−	195.011i	−0.160204	−	0.265321i
$736$	330.903	−	738.230i	0.449597	−	1.00303i
$737$	108.466	+	187.869i	0.147173	+	0.254911i
$738$	173.107	−	3.53916i	0.234562	−	0.00479561i
$739$	176.850	+	660.013i	0.239310	+	0.893117i	0.976159	+	0.217059i	$0.0696463\pi$
$739$	176.850	+	660.013i	0.239310	+	0.893117i	−0.736849	+	0.676058i	$0.763687\pi$
$740$	26.6992	−	1.09218i	0.0360800	−	0.00147592i
$741$	−304.985	+	304.985i	−0.411586	+	0.411586i
$742$	−186.157	+	197.775i	−0.250885	+	0.266543i
$743$		−	1259.69i		−	1.69541i	−0.530465	−	0.847707i	$-0.677983\pi$
$743$		−	1259.69i		−	1.69541i	0.530465	−	0.847707i	$-0.322017\pi$
$744$	45.8118	−	225.449i	0.0615750	−	0.303023i
$745$	209.424	−	362.732i	0.281105	−	0.486889i
$746$	576.258	−	600.313i	0.772464	−	0.804709i
$747$	470.390	+	126.041i	0.629706	+	0.168729i
$748$	−114.361	−	366.215i	−0.152890	−	0.489593i
$749$	899.461	+	881.985i	1.20088	+	1.17755i
$750$	205.960	+	340.466i	0.274614	+	0.453955i
$751$	−202.972	−	351.558i	−0.270269	−	0.468119i	0.698662	−	0.715452i	$-0.253779\pi$
$751$	−202.972	−	351.558i	−0.270269	−	0.468119i	−0.968931	+	0.247333i	$0.920446\pi$
$752$	−14.8972	−	181.782i	−0.0198101	−	0.241731i
$753$	−73.9906	+	128.155i	−0.0982611	+	0.170193i
$754$	717.179	+	394.741i	0.951166	+	0.523530i
$755$	431.473	+	431.473i	0.571488	+	0.571488i
$756$	97.5333	−	107.960i	0.129012	−	0.142804i
$757$	376.328	+	376.328i	0.497131	+	0.497131i	0.910544	−	0.413413i	$-0.135663\pi$
$757$	376.328	+	376.328i	0.497131	+	0.497131i	−0.413413	+	0.910544i	$0.635663\pi$
$758$	50.9350	+	175.648i	0.0671966	+	0.231726i
$759$	−71.0149	+	123.001i	−0.0935638	+	0.162057i
$760$	−194.848	−	97.0892i	−0.256379	−	0.127749i
$761$	289.244	+	500.985i	0.380084	+	0.658324i	0.991074	−	0.133314i	$-0.0425619\pi$
$761$	289.244	+	500.985i	0.380084	+	0.658324i	−0.610990	+	0.791638i	$0.709229\pi$
$762$	−611.050	−	150.414i	−0.801903	−	0.197393i
$763$	−254.923	−	65.6331i	−0.334106	−	0.0860198i
$764$	−256.840	+	490.091i	−0.336178	+	0.641480i
$765$	230.001	+	61.6286i	0.300655	+	0.0805602i
$766$	96.8643	−	1.98038i	0.126455	−	0.00258536i
$767$	−436.647	+	756.295i	−0.569292	+	0.986043i
$768$	−360.398	−	258.305i	−0.469268	−	0.336335i
$769$		−	817.307i		−	1.06282i	−0.847115	−	0.531409i	$-0.821663\pi$
$769$		−	817.307i		−	1.06282i	0.847115	−	0.531409i	$-0.178337\pi$
$770$	103.664	−	64.1075i	0.134629	−	0.0832565i
$771$	−557.373	+	557.373i	−0.722922	+	0.722922i
$772$	−407.260	+	16.6598i	−0.527538	+	0.0215800i
$773$	61.5702	+	229.783i	0.0796510	+	0.297261i	0.994248	−	0.107106i	$-0.0341584\pi$
$773$	61.5702	+	229.783i	0.0796510	+	0.297261i	−0.914597	+	0.404367i	$0.867492\pi$
$774$	−71.7369	−	68.8623i	−0.0926833	−	0.0889694i
$775$	−147.728	−	255.872i	−0.190617	−	0.330158i
$776$	894.465	−	54.9231i	1.15266	−	0.0707772i
$777$	−26.2797	−	14.8308i	−0.0338219	−	0.0190872i
$778$	−238.984	−	58.8274i	−0.307178	−	0.0756136i
$779$	−75.7198	+	282.590i	−0.0972013	+	0.362760i
$780$	100.089	−	445.669i	0.128319	−	0.571370i
$781$	−32.0655	−	119.670i	−0.0410570	−	0.153227i
$782$	−1309.87	−	720.961i	−1.67502	−	0.921945i
$783$		−	86.5904i		−	0.110588i
$784$	779.974	−	79.3524i	0.994865	−	0.101215i
$785$	−370.731			−0.472269
$786$	142.419	−	258.752i	0.181195	−	0.329200i
$787$	937.322	−	251.155i	1.19101	−	0.319129i	0.391723	−	0.920083i	$-0.371879\pi$
$787$	937.322	−	251.155i	1.19101	−	0.319129i	0.799284	+	0.600954i	$0.205212\pi$
$788$	−295.481	+	1315.70i	−0.374976	+	1.66967i
$789$	814.015	+	218.115i	1.03170	+	0.276444i
$790$	37.8440	−	153.740i	0.0479038	−	0.194607i
$791$	−611.926	+	1084.32i	−0.773611	+	1.37082i
$792$	58.3150	+	51.5678i	0.0736300	+	0.0651109i
$793$	−889.797	+	513.725i	−1.12206	+	0.647824i
$794$	609.518	−	634.961i	0.767655	−	0.799699i
$795$	87.1198	−	23.3437i	0.109585	−	0.0293631i
$796$	−1572.54	+	64.3279i	−1.97556	+	0.0808140i
$797$	407.402	+	407.402i	0.511169	+	0.511169i	0.914885	−	0.403715i	$-0.132281\pi$
$797$	407.402	+	407.402i	0.511169	+	0.511169i	−0.403715	+	0.914885i	$0.632281\pi$
$798$	129.302	+	209.086i	0.162033	+	0.262013i
$799$	−337.090			−0.421890
$800$	−566.483	+	58.1030i	−0.708104	+	0.0726287i
$801$	238.149	+	137.495i	0.297315	+	0.171655i
$802$	−17.7666	−	869.000i	−0.0221529	−	1.08354i
$803$	−84.1395	+	314.013i	−0.104781	+	0.391050i
$804$	215.088	−	410.422i	0.267523	−	0.510475i
$805$	118.434	−	460.005i	0.147123	−	0.571434i
$806$	−194.950	+	791.977i	−0.241873	+	0.982602i
$807$	−27.5430	+	15.9020i	−0.0341301	+	0.0197050i
$808$	−623.139	+	208.666i	−0.771212	+	0.258249i
$809$	−327.398	−	189.023i	−0.404695	−	0.233651i	0.283813	−	0.958880i	$-0.408400\pi$
$809$	−327.398	−	189.023i	−0.404695	−	0.233651i	−0.688508	+	0.725229i	$0.741734\pi$
$810$	−46.4026	+	13.4560i	−0.0572872	+	0.0166123i
$811$	131.050	−	131.050i	0.161590	−	0.161590i	−0.621681	−	0.783271i	$-0.713550\pi$
$811$	131.050	−	131.050i	0.161590	−	0.161590i	0.783271	+	0.621681i	$0.213550\pi$
$812$	312.794	−	346.232i	0.385215	−	0.426394i
$813$	154.989	−	154.989i	0.190638	−	0.190638i
$814$	7.78520	−	14.1444i	0.00956413	−	0.0173764i
$815$	16.0374	+	9.25918i	0.0196778	+	0.0113610i
$816$	−530.200	+	624.859i	−0.649755	+	0.765758i
$817$	145.512	−	84.0111i	0.178105	−	0.102829i
$818$	−1296.78	+	784.470i	−1.58531	+	0.959009i
$819$	−361.140	+	368.296i	−0.440952	+	0.449690i
$820$	−92.3535	−	295.740i	−0.112626	−	0.360659i
$821$	−193.937	+	723.781i	−0.236220	+	0.881585i	0.741375	+	0.671091i	$0.234174\pi$
$821$	−193.937	+	723.781i	−0.236220	+	0.881585i	−0.977595	+	0.210494i	$0.932493\pi$
$822$	71.4773	+	68.6132i	0.0869554	+	0.0834710i
$823$	274.488	+	158.475i	0.333521	+	0.192558i	0.657403	−	0.753539i	$-0.271655\pi$
$823$	274.488	+	158.475i	0.333521	+	0.192558i	−0.323882	+	0.946097i	$0.604988\pi$
$824$	937.049	−	620.542i	1.13720	−	0.753085i
$825$	99.9748			0.121182
$826$	362.450	+	341.158i	0.438802	+	0.413025i
$827$	756.036	+	756.036i	0.914192	+	0.914192i	0.996599	−	0.0824072i	$-0.0262608\pi$
$827$	756.036	+	756.036i	0.914192	+	0.914192i	−0.0824072	+	0.996599i	$0.526261\pi$
$828$	303.121	−	12.3998i	0.366089	−	0.0149756i
$829$	−937.744	+	251.268i	−1.13117	+	0.303097i	−0.775398	−	0.631473i	$-0.782451\pi$
$829$	−937.744	+	251.268i	−1.13117	+	0.303097i	−0.355777	+	0.934571i	$0.615784\pi$
$830$	−17.8123	−	871.235i	−0.0214606	−	1.04968i
$831$	34.9440	−	20.1749i	0.0420505	−	0.0242779i
$832$	1239.22	+	967.228i	1.48945	+	1.16253i
$833$	−28.4269	−	1448.69i	−0.0341259	−	1.73912i
$834$	609.154	−	368.499i	0.730400	−	0.441845i
$835$	−265.051	−	71.0201i	−0.317426	−	0.0850540i
$836$	−111.129	+	70.3683i	−0.132929	+	0.0841726i
$837$	83.3315	−	22.3286i	0.0995597	−	0.0266769i
$838$	−196.101	−	676.251i	−0.234011	−	0.806982i
$839$	534.596			0.637182			0.318591	−	0.947892i	$-0.396790\pi$
$839$	534.596			0.637182			0.318591	+	0.947892i	$0.396790\pi$
$840$	−234.148	−	113.819i	−0.278748	−	0.135498i
$841$			563.300i			0.669798i
$842$	451.617	+	1557.39i	0.536363	+	1.84964i
$843$	16.8138	+	62.7499i	0.0199452	+	0.0744365i
$844$	190.747	+	42.8382i	0.226004	+	0.0507561i
$845$	−301.723	+	1126.04i	−0.357068	+	1.33260i
$846$	58.5219	−	35.4020i	0.0691748	−	0.0418463i
$847$	7.58651	+	773.319i	0.00895691	+	0.913009i
$848$	−55.5813	+	305.389i	−0.0655439	+	0.360128i
$849$	93.7960	+	162.459i	0.110478	+	0.191354i
$850$	21.5128	+	1052.23i	0.0253091	+	1.23792i
$851$	−16.2852	−	60.7772i	−0.0191365	−	0.0714185i
$852$	−179.319	+	194.615i	−0.210468	+	0.228421i
$853$	568.904	−	568.904i	0.666945	−	0.666945i	−0.290062	−	0.957008i	$-0.593676\pi$
$853$	568.904	−	568.904i	0.666945	−	0.666945i	0.957008	+	0.290062i	$0.0936761\pi$
$854$	168.610	+	560.821i	0.197435	+	0.656699i
$855$		−	81.6363i		−	0.0954811i
$856$	1410.86	+	286.691i	1.64820	+	0.334919i
$857$	−137.166	+	237.579i	−0.160054	+	0.277222i	−0.934888	−	0.354943i	$-0.884500\pi$
$857$	−137.166	+	237.579i	−0.160054	+	0.277222i	0.774834	+	0.632165i	$0.217834\pi$
$858$	−199.099	−	191.121i	−0.232050	−	0.222751i
$859$	−627.833	−	168.227i	−0.730888	−	0.195841i	−0.125863	−	0.992048i	$-0.540170\pi$
$859$	−627.833	−	168.227i	−0.730888	−	0.195841i	−0.605025	+	0.796207i	$0.706837\pi$
$860$	−82.5965	+	157.607i	−0.0960424	+	0.183264i
$861$	−87.2346	+	338.825i	−0.101318	+	0.393525i
$862$	−933.184	+	564.517i	−1.08258	+	0.654892i
$863$	603.008	+	1044.44i	0.698734	+	1.21024i	0.968905	+	0.247431i	$0.0795864\pi$
$863$	603.008	+	1044.44i	0.698734	+	1.21024i	−0.270171	+	0.962812i	$0.587080\pi$
$864$	26.4235	−	164.164i	0.0305827	−	0.190005i
$865$	168.022	−	291.023i	0.194245	−	0.336443i
$866$	−771.912	+	1402.44i	−0.891354	+	1.61944i
$867$	717.000	+	717.000i	0.826989	+	0.826989i
$868$	413.860	+	211.741i	0.476797	+	0.243941i
$869$	−67.6447	−	67.6447i	−0.0778420	−	0.0778420i
$870$	−148.816	+	43.1539i	−0.171052	+	0.0496022i
$871$	−821.387	+	1422.68i	−0.943039	+	1.63339i
$872$	−285.273	+	95.5269i	−0.327148	+	0.109549i
$873$	168.028	+	291.033i	0.192472	+	0.333371i
$874$	−122.525	+	497.753i	−0.140188	+	0.569511i
$875$	−774.602	+	215.720i	−0.885259	+	0.246537i
$876$	662.824	−	206.986i	0.756648	−	0.236285i
$877$	−1120.99	−	300.367i	−1.27820	−	0.342494i	−0.445036	−	0.895513i	$-0.646809\pi$
$877$	−1120.99	−	300.367i	−1.27820	−	0.342494i	−0.833169	+	0.553019i	$0.813476\pi$
$878$	1.67936	+	82.1404i	0.00191271	+	0.0935540i
$879$	−380.883	+	659.708i	−0.433313	+	0.750521i
$880$	59.5629	−	125.921i	0.0676851	−	0.143092i
$881$		−	350.940i		−	0.398343i	−0.979965	−	0.199171i	$-0.936175\pi$
$881$		−	350.940i		−	0.398343i	0.979965	−	0.199171i	$-0.0638251\pi$
$882$	157.080	+	248.520i	0.178095	+	0.281768i
$883$	720.133	−	720.133i	0.815553	−	0.815553i	−0.169907	−	0.985460i	$-0.554347\pi$
$883$	720.133	−	720.133i	0.815553	−	0.815553i	0.985460	+	0.169907i	$0.0543467\pi$
$884$	1968.69	−	2136.63i	2.22703	−	2.41700i
$885$	−42.7806	−	159.659i	−0.0483396	−	0.180406i
$886$	−185.515	+	193.259i	−0.209385	+	0.218126i
$887$	−42.7120	−	73.9794i	−0.0481533	−	0.0834040i	0.840944	−	0.541122i	$-0.182000\pi$
$887$	−42.7120	−	73.9794i	−0.0481533	−	0.0834040i	−0.889097	+	0.457718i	$0.848667\pi$
$888$	−34.4217	+	2.11360i	−0.0387631	+	0.00238018i
$889$	624.978	−	1107.44i	0.703013	−	1.24572i
$890$	117.616	−	477.810i	0.132153	−	0.536866i
$891$	−7.55543	+	28.1973i	−0.00847972	+	0.0316467i
$892$	1051.78	−	666.001i	1.17913	−	0.746638i
$893$	29.9116	+	111.632i	0.0334957	+	0.125007i
$894$	−260.654	+	473.565i	−0.291560	+	0.529715i
$895$			292.111i			0.326381i
$896$	698.671	−	560.959i	0.779767	−	0.626070i
$897$	−1075.56			−1.19906
$898$	387.154	+	213.093i	0.431130	+	0.237297i
$899$	267.248	−	71.6090i	0.297273	−	0.0796540i
$900$	−114.242	−	180.417i	−0.126936	−	0.200464i
$901$	554.135	+	148.480i	0.615022	+	0.164795i
$902$	−181.773	−	44.7445i	−0.201522	−	0.0496059i
$903$	173.025	−	102.172i	0.191611	−	0.113147i
$904$	87.2086	+	1420.26i	0.0964696	+	1.57108i
$905$	330.349	−	190.727i	0.365027	−	0.210748i
$906$	−568.121	−	545.356i	−0.627065	−	0.601938i
$907$	−415.298	+	111.279i	−0.457881	+	0.122689i	−0.480385	−	0.877058i	$-0.659503\pi$
$907$	−415.298	+	111.279i	−0.457881	+	0.122689i	0.0225038	+	0.999747i	$0.492836\pi$
$908$	−422.942	−	389.699i	−0.465795	−	0.429184i
$909$	−174.253	−	174.253i	−0.191697	−	0.191697i
$910$	812.940	+	437.113i	0.893340	+	0.480344i
$911$	−1360.44			−1.49334			−0.746672	−	0.665192i	$-0.768350\pi$
$911$	−1360.44			−1.49334			−0.746672	+	0.665192i	$0.768350\pi$
$912$	253.977	+	120.136i	0.278484	+	0.131728i
$913$	−455.978	−	263.259i	−0.499429	−	0.288345i
$914$	355.826	−	7.27484i	0.389307	−	0.00795935i
$915$	50.3323	−	187.843i	0.0550079	−	0.205292i
$916$	−229.958	−	736.387i	−0.251046	−	0.803916i
$917$	426.146	+	417.866i	0.464717	+	0.455688i
$918$	−298.400	−	73.4530i	−0.325055	−	0.0800142i
$919$	406.223	−	234.533i	0.442027	−	0.255204i	−0.262430	−	0.964951i	$-0.584524\pi$
$919$	406.223	−	234.533i	0.442027	−	0.255204i	0.704457	+	0.709747i	$0.251191\pi$
$920$	−172.377	−	514.770i	−0.187366	−	0.559532i
$921$	−853.012	−	492.486i	−0.926180	−	0.534730i
$922$	−399.097	−	1376.28i	−0.432860	−	1.49271i
$923$	663.408	−	663.408i	0.718751	−	0.718751i
$924$	−132.069	+	85.4539i	−0.142931	+	0.0924826i
$925$	−31.3179	+	31.3179i	−0.0338572	+	0.0338572i
$926$	−722.457	−	397.646i	−0.780191	−	0.429424i
$927$	364.995	+	210.730i	0.393737	+	0.227324i
$928$	84.7414	−	526.482i	0.0913161	−	0.567330i
$929$	−205.104	+	118.417i	−0.220779	+	0.127467i	−0.606311	−	0.795228i	$-0.707351\pi$
$929$	−205.104	+	118.417i	−0.220779	+	0.127467i	0.385532	+	0.922695i	$0.374018\pi$
$930$	−79.9041	−	132.087i	−0.0859184	−	0.142029i
$931$	−477.228	+	137.963i	−0.512598	+	0.148188i
$932$	471.065	+	246.869i	0.505434	+	0.264881i
$933$	94.5205	−	352.755i	0.101308	−	0.378087i
$934$	390.274	−	406.566i	0.417853	−	0.435295i
$935$	−222.954	−	128.723i	−0.238454	−	0.137671i
$936$	−117.389	+	577.695i	−0.125416	+	0.617196i
$937$	−787.723			−0.840686			−0.420343	−	0.907365i	$-0.638090\pi$
$937$	−787.723			−0.840686			−0.420343	+	0.907365i	$0.638090\pi$
$938$	681.814	+	641.761i	0.726881	+	0.684180i
$939$	485.217	+	485.217i	0.516738	+	0.516738i
$940$	−90.0079	−	82.9334i	−0.0957531	−	0.0882270i
$941$	−102.586	+	27.4879i	−0.109018	+	0.0292114i	−0.312916	−	0.949781i	$-0.601306\pi$
$941$	−102.586	+	27.4879i	−0.109018	+	0.0292114i	0.203897	+	0.978992i	$0.434639\pi$
$942$	478.361	−	9.78006i	0.507814	−	0.0103822i
$943$	−631.805	+	364.773i	−0.669995	+	0.386822i
$944$	559.668	+	101.860i	0.592869	+	0.107903i
$945$	−0.957734	−	97.6252i	−0.00101348	−	0.103307i
$946$	55.6481	+	91.9900i	0.0588246	+	0.0972411i
$947$	1359.68	+	364.324i	1.43577	+	0.384714i	0.891051	−	0.453904i	$-0.149969\pi$
$947$	1359.68	+	364.324i	1.43577	+	0.384714i	0.544721	+	0.838617i	$0.316636\pi$
$948$	−44.7751	+	199.372i	−0.0472311	+	0.210308i
$949$	−2377.94	+	637.167i	−2.50573	+	0.671408i
$950$	346.550	−	100.494i	0.364790	−	0.105783i
$951$	−205.619			−0.216213
$952$	−927.817	−	1371.63i	−0.974598	−	1.44078i
$953$		−	488.000i		−	0.512068i	−0.966668	−	0.256034i	$-0.917584\pi$
$953$		−	488.000i		−	0.512068i	0.966668	−	0.256034i	$-0.0824158\pi$
$954$	−111.796	+	32.4190i	−0.117187	+	0.0339822i
$955$	96.0971	+	358.639i	0.100625	+	0.375538i
$956$	−162.377	−	256.434i	−0.169850	−	0.268236i
$957$	−24.2306	+	90.4300i	−0.0253194	+	0.0944932i
$958$	194.117	+	320.889i	0.202627	+	0.334957i
$959$	−172.399	+	101.802i	−0.179770	+	0.106155i
$960$	−295.303	+	36.4024i	−0.307608	+	0.0379192i
$961$	−342.672	−	593.526i	−0.356579	−	0.617613i
$962$	122.239	−	2.49918i	0.127068	−	0.00259790i
$963$	139.733	+	521.490i	0.145101	+	0.541526i
$964$	−30.2344	−	739.102i	−0.0313635	−	0.766703i
$965$	−193.403	+	193.403i	−0.200417	+	0.200417i
$966$	−140.682	+	596.677i	−0.145634	+	0.617678i
$967$			98.4354i			0.101795i	0.998704	+	0.0508973i	$0.0162081\pi$
$967$			98.4354i			0.101795i	−0.998704	+	0.0508973i	$0.983792\pi$
$968$	487.998	+	736.901i	0.504130	+	0.761261i
$969$	259.628	−	449.690i	0.267934	−	0.464076i
$970$	416.434	−	433.818i	0.429314	−	0.447235i
$971$	1024.82	+	274.599i	1.05542	+	0.282800i	0.744491	−	0.667632i	$-0.232692\pi$
$971$	1024.82	+	274.599i	1.05542	+	0.282800i	0.310932	+	0.950432i	$0.399359\pi$
$972$	59.5192	−	18.5866i	0.0612338	−	0.0191220i
$973$	385.961	+	1385.90i	0.396671	+	1.42435i
$974$	−503.500	−	832.320i	−0.516941	−	0.854538i
$975$	378.542	+	655.654i	0.388248	+	0.672465i
$976$	510.324	+	433.016i	0.522873	+	0.443664i
$977$	169.443	−	293.484i	0.173432	−	0.300393i	−0.766186	−	0.642619i	$-0.777848\pi$
$977$	169.443	−	293.484i	0.173432	−	0.300393i	0.939617	+	0.342227i	$0.111181\pi$
$978$	−20.9376	−	11.5242i	−0.0214086	−	0.0117835i
$979$	−210.234	−	210.234i	−0.214743	−	0.214743i
$980$	348.826	−	393.814i	0.355945	−	0.401851i
$981$	−79.7728	−	79.7728i	−0.0813178	−	0.0813178i
$982$	171.672	+	592.009i	0.174819	+	0.602861i
$983$	142.571	−	246.941i	0.145037	−	0.251211i	−0.784350	−	0.620319i	$-0.787003\pi$
$983$	142.571	−	246.941i	0.145037	−	0.251211i	0.929387	+	0.369107i	$0.120337\pi$
$984$	126.967	+	379.163i	0.129032	+	0.385329i
$985$	452.434	+	783.638i	0.459323	+	0.795572i
$986$	−956.986	−	235.568i	−0.970574	−	0.238912i
$987$	37.0796	+	133.144i	0.0375679	+	0.134898i
$988$	−882.264	−	462.365i	−0.892980	−	0.467980i
$989$	404.715	+	108.443i	0.409217	+	0.109649i
$990$	52.2256	−	1.06775i	0.0527532	−	0.00107853i
$991$	−713.221	+	1235.33i	−0.719698	+	1.24655i	0.241422	+	0.970420i	$0.422386\pi$
$991$	−713.221	+	1235.33i	−0.719698	+	1.24655i	−0.961119	+	0.276133i	$0.910947\pi$
$992$	528.519	−	54.2091i	0.532782	−	0.0546463i
$993$		−	432.161i		−	0.435208i
$994$	−281.260	−	454.807i	−0.282958	−	0.457552i
$995$	−746.781	+	746.781i	−0.750534	+	0.750534i
$996$	45.9672	+	1123.70i	0.0461518	+	1.12821i
$997$	−220.960	−	824.633i	−0.221625	−	0.827115i	−0.983729	−	0.179660i	$-0.942500\pi$
$997$	−220.960	−	824.633i	−0.221625	−	0.827115i	0.762104	−	0.647455i	$-0.224166\pi$
$998$	449.667	+	431.649i	0.450568	+	0.432514i
$999$	−6.46622	−	11.1998i	−0.00647269	−	0.0112110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.3.bv.a.325.11	yes	256
7.5	odd	6	inner	336.3.bv.a.229.33	yes	256
16.13	even	4	inner	336.3.bv.a.157.33	yes	256
112.61	odd	12	inner	336.3.bv.a.61.11	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.3.bv.a.61.11	✓	256	112.61	odd	12	inner
336.3.bv.a.157.33	yes	256	16.13	even	4	inner
336.3.bv.a.229.33	yes	256	7.5	odd	6	inner
336.3.bv.a.325.11	yes	256	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75213 - 0.964387i) q^{2} +(1.67303 - 0.448288i) q^{3} +(2.13992 + 3.37946i) q^{4} +(2.59267 + 0.694703i) q^{5} +(-3.36369 - 0.827992i) q^{6} +(3.44036 - 6.09622i) q^{7} +(-0.490303 - 7.98496i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-3.87272 - 3.71754i) q^{10} +(-3.13303 + 0.839492i) q^{11} +(5.09512 + 4.69465i) q^{12} +(-17.3684 - 17.3684i) q^{13} +(-11.9071 + 7.36353i) q^{14} +4.64904 q^{15} +(-6.84152 + 14.4635i) q^{16} +(25.6090 + 14.7854i) q^{17} +(-5.99875 + 0.122644i) q^{18} +(2.62395 - 9.79272i) q^{19} +(3.20037 + 10.2484i) q^{20} +(3.02298 - 11.7414i) q^{21} +(6.29907 + 1.55055i) q^{22} +(21.8942 - 12.6406i) q^{23} +(-4.39985 - 13.1393i) q^{24} +(-15.4113 - 8.89774i) q^{25} +(13.6818 + 47.1814i) q^{26} +(3.67423 - 3.67423i) q^{27} +(27.9640 - 1.41883i) q^{28} +(11.7835 - 11.7835i) q^{29} +(-8.14572 - 4.48347i) q^{30} +(14.3785 + 8.30144i) q^{31} +(25.9357 - 18.7441i) q^{32} +(-4.86532 + 2.80900i) q^{33} +(-30.6115 - 50.6029i) q^{34} +(13.1548 - 13.4154i) q^{35} +(10.6289 + 5.57022i) q^{36} +(0.644161 - 2.40404i) q^{37} +(-14.0415 + 14.6276i) q^{38} +(-36.8438 - 21.2718i) q^{39} +(4.27598 - 21.0429i) q^{40} -28.8572 q^{41} +(-16.6199 + 17.6572i) q^{42} +(11.7190 + 11.7190i) q^{43} +(-9.54145 - 8.79150i) q^{44} +(7.77800 - 2.08411i) q^{45} +(-50.5519 + 1.03353i) q^{46} +(-9.87222 + 5.69973i) q^{47} +(-4.96226 + 27.2649i) q^{48} +(-25.3278 - 41.9464i) q^{49} +(18.4218 + 30.4525i) q^{50} +(49.4728 + 13.2562i) q^{51} +(21.5289 - 95.8625i) q^{52} +(18.7393 - 5.02118i) q^{53} +(-9.98112 + 2.89435i) q^{54} -8.70609 q^{55} +(-50.3649 - 24.4822i) q^{56} -17.5598i q^{57} +(-32.0100 + 9.28233i) q^{58} +(-9.20202 - 34.3424i) q^{59} +(9.94856 + 15.7113i) q^{60} +(10.8264 - 40.4046i) q^{61} +(-17.1872 - 28.4116i) q^{62} +(-0.206007 - 20.9990i) q^{63} +(-63.5192 + 7.83009i) q^{64} +(-32.9645 - 57.0962i) q^{65} +(11.2336 - 0.229671i) q^{66} +(-17.3101 - 64.6023i) q^{67} +(4.83455 + 118.184i) q^{68} +(30.9631 - 30.9631i) q^{69} +(-35.9865 + 10.8193i) q^{70} +38.1964i q^{71} +(-13.2513 - 20.0101i) q^{72} +(50.1133 - 86.7988i) q^{73} +(-3.44708 + 3.59097i) q^{74} +(-29.7724 - 7.97749i) q^{75} +(38.7092 - 12.0881i) q^{76} +(-5.66102 + 21.9878i) q^{77} +(44.0409 + 72.8027i) q^{78} +(14.7468 + 25.5422i) q^{79} +(-27.7856 + 32.7463i) q^{80} +(4.50000 - 7.79423i) q^{81} +(50.5615 + 27.8295i) q^{82} +(114.783 + 114.783i) q^{83} +(46.1487 - 14.9097i) q^{84} +(56.1241 + 56.1241i) q^{85} +(-9.23160 - 31.8350i) q^{86} +(14.4317 - 24.9965i) q^{87} +(8.23944 + 24.6055i) q^{88} +(45.8318 + 79.3831i) q^{89} +(-15.6379 - 3.84937i) q^{90} +(-165.635 + 46.1279i) q^{91} +(89.5702 + 46.9407i) q^{92} +(27.7772 + 7.44287i) q^{93} +(22.7941 - 0.466025i) q^{94} +(13.6061 - 23.5664i) q^{95} +(34.9885 - 42.9861i) q^{96} +112.019i q^{97} +(3.92504 + 97.9214i) q^{98} +(-6.88061 + 6.88061i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 12 q^{4} - 24 q^{8} + 108 q^{10} + 32 q^{11} + 32 q^{14} - 4 q^{16} + 12 q^{18} + 48 q^{22} - 64 q^{29} - 96 q^{35} - 96 q^{37} + 60 q^{40} - 60 q^{42} - 192 q^{43} + 228 q^{44} + 180 q^{46} - 32 q^{50}+ \cdots + 192 q^{99}+O(q^{100}) \) 256 * q - 12 * q^4 - 24 * q^8 + 108 * q^10 + 32 * q^11 + 32 * q^14 - 4 * q^16 + 12 * q^18 + 48 * q^22 - 64 * q^29 - 96 * q^35 - 96 * q^37 + 60 * q^40 - 60 * q^42 - 192 * q^43 + 228 * q^44 + 180 * q^46 - 32 * q^50 + 720 * q^52 + 160 * q^53 - 56 * q^56 - 312 * q^58 + 384 * q^59 + 72 * q^60 - 96 * q^64 - 216 * q^66 - 320 * q^67 - 780 * q^68 - 828 * q^70 + 60 * q^72 - 88 * q^74 - 72 * q^78 - 612 * q^80 + 1152 * q^81 + 780 * q^82 - 72 * q^84 - 212 * q^86 - 464 * q^88 - 480 * q^91 - 488 * q^92 - 612 * q^94 + 768 * q^95 - 900 * q^96 - 196 * q^98 + 192 * q^99

Introduction

L-functions

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