LMFDB - Embedded newform 31.3.f.a.15.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,3,Mod(15,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.15"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	31.f (of order $10$, 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:	$0.844688819517$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 20 x^{18} - 33 x^{17} + 250 x^{16} - 510 x^{15} + 2908 x^{14} - 6447 x^{13} + \cdots + 731025 $ x^20 - 2x^19 + 20x^18 - 33x^17 + 250x^16 - 510x^15 + 2908x^14 - 6447x^13 + 39842x^12 - 79034x^11 + 199542x^10 - 173039x^9 + 688988x^8 - 636120x^7 + 3401146x^6 - 2156427x^5 + 7116556x^4 - 6139950x^3 + 6454710x^2 - 3116475*x + 731025
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.4
Root			$-0.453363 - 1.39531i$ of defining polynomial
Character	$\chi$	$=$	31.15
Dual form			31.3.f.a.29.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.18692 - 0.862348i) q^{2} +(1.08425 - 1.49234i) q^{3} +(-0.570933 + 1.75715i) q^{4} -4.14776 q^{5} -2.70629i q^{6} +(1.06697 - 3.28380i) q^{7} +(2.65108 + 8.15917i) q^{8} +(1.72966 + 5.32336i) q^{9} +(-4.92306 + 3.57681i) q^{10} +(-13.6300 - 4.42864i) q^{11} +(2.00324 + 2.75722i) q^{12} +(5.41722 - 7.45616i) q^{13} +(-1.56537 - 4.81771i) q^{14} +(-4.49722 + 6.18989i) q^{15} +(4.20377 + 3.05422i) q^{16} +(-1.46101 + 0.474711i) q^{17} +(6.64356 + 4.82683i) q^{18} +(16.5438 - 12.0198i) q^{19} +(2.36809 - 7.28825i) q^{20} +(-3.74370 - 5.15276i) q^{21} +(-19.9967 + 6.49732i) q^{22} +(17.2964 - 5.61995i) q^{23} +(15.0507 + 4.89028i) q^{24} -7.79606 q^{25} -13.5214i q^{26} +(25.6089 + 8.32083i) q^{27} +(5.16097 + 3.74966i) q^{28} +(-23.9358 - 32.9448i) q^{29} +11.2251i q^{30} +(20.1838 + 23.5290i) q^{31} -26.6929 q^{32} +(-21.3873 + 15.5388i) q^{33} +(-1.32474 + 1.82334i) q^{34} +(-4.42555 + 13.6204i) q^{35} -10.3415 q^{36} +42.0983i q^{37} +(9.27096 - 28.5331i) q^{38} +(-5.25353 - 16.1687i) q^{39} +(-10.9960 - 33.8423i) q^{40} +(-61.3917 + 44.6037i) q^{41} +(-8.88693 - 2.88754i) q^{42} +(15.1894 + 20.9064i) q^{43} +(15.5636 - 21.4214i) q^{44} +(-7.17423 - 22.0800i) q^{45} +(15.6831 - 21.5860i) q^{46} +(-3.99548 - 2.90289i) q^{47} +(9.11588 - 2.96193i) q^{48} +(29.9969 + 21.7940i) q^{49} +(-9.25330 + 6.72292i) q^{50} +(-0.875671 + 2.69504i) q^{51} +(10.0087 + 13.7758i) q^{52} +(38.5605 - 12.5291i) q^{53} +(37.5711 - 12.2076i) q^{54} +(56.5338 + 18.3689i) q^{55} +29.6217 q^{56} -37.7216i q^{57} +(-56.8198 - 18.4619i) q^{58} +(36.1430 + 26.2594i) q^{59} +(-8.30896 - 11.4363i) q^{60} -84.8005i q^{61} +(44.2468 + 10.5215i) q^{62} +19.3264 q^{63} +(-48.4974 + 35.2354i) q^{64} +(-22.4693 + 30.9264i) q^{65} +(-11.9852 + 36.8867i) q^{66} -109.556 q^{67} -2.83825i q^{68} +(10.3668 - 31.9057i) q^{69} +(6.49278 + 19.9827i) q^{70} +(-19.6220 - 60.3903i) q^{71} +(-38.8487 + 28.2252i) q^{72} +(-85.9266 - 27.9192i) q^{73} +(36.3034 + 49.9674i) q^{74} +(-8.45289 + 11.6344i) q^{75} +(11.6752 + 35.9325i) q^{76} +(-29.0856 + 40.0328i) q^{77} +(-20.1786 - 14.6606i) q^{78} +(142.262 - 46.2236i) q^{79} +(-17.4362 - 12.6682i) q^{80} +(-0.570882 + 0.414770i) q^{81} +(-34.4032 + 105.882i) q^{82} +(25.0530 + 34.4824i) q^{83} +(11.1916 - 3.63636i) q^{84} +(6.05993 - 1.96899i) q^{85} +(36.0572 + 11.7157i) q^{86} -75.1175 q^{87} -122.950i q^{88} +(46.3352 + 15.0552i) q^{89} +(-27.5559 - 20.0205i) q^{90} +(-18.7045 - 25.7446i) q^{91} +33.6011i q^{92} +(56.9977 - 4.60992i) q^{93} -7.24561 q^{94} +(-68.6199 + 49.8553i) q^{95} +(-28.9418 + 39.8350i) q^{96} +(15.1554 - 46.6434i) q^{97} +54.3979 q^{98} -80.2172i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9} + 12 q^{10} - 10 q^{11} + 90 q^{12} + 10 q^{13} - 85 q^{15} - 103 q^{16} + 35 q^{17} + 6 q^{18} + 47 q^{19} - 125 q^{20} - 125 q^{21}+ \cdots - 1000 q^{98}+O(q^{100}) $ 20 * q - 3 * q^2 - 5 * q^3 - 11 * q^4 - 14 * q^5 - q^7 - 19 * q^8 + 2 * q^9 + 12 * q^10 - 10 * q^11 + 90 * q^12 + 10 * q^13 - 85 * q^15 - 103 * q^16 + 35 * q^17 + 6 * q^18 + 47 * q^19 - 125 * q^20 - 125 * q^21 + 150 * q^22 + 75 * q^23 + 195 * q^24 + 82 * q^25 + 25 * q^27 + 88 * q^28 + 5 * q^29 + 73 * q^31 + 226 * q^32 - 206 * q^33 - 265 * q^34 - 50 * q^35 - 520 * q^36 + 8 * q^38 + 91 * q^39 - 466 * q^40 - 98 * q^41 + 245 * q^43 + 380 * q^44 - 162 * q^45 - 445 * q^46 - 187 * q^47 + 570 * q^48 + 328 * q^49 - 44 * q^50 + 185 * q^51 - 15 * q^52 + 25 * q^53 + 920 * q^54 + 190 * q^55 + 64 * q^56 - 85 * q^58 - 173 * q^59 + 275 * q^60 - 40 * q^62 + 252 * q^63 - 469 * q^64 - 345 * q^65 - 564 * q^66 + 76 * q^67 - 197 * q^69 - 11 * q^70 - 467 * q^71 - 982 * q^72 - 15 * q^73 + 45 * q^74 - 175 * q^75 + 55 * q^76 - 320 * q^77 - 91 * q^78 + 500 * q^79 + 1030 * q^80 + 117 * q^81 + 178 * q^82 - 50 * q^83 + 65 * q^84 + 20 * q^85 + 1125 * q^86 - 366 * q^87 + 55 * q^89 + 444 * q^90 + 300 * q^91 + 502 * q^93 + 62 * q^94 - 559 * q^95 - 10 * q^96 - 405 * q^97 - 1000 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	1.18692	−	0.862348i	0.593460	−	0.431174i	−0.250092	−	0.968222i	$-0.580461\pi$
$2$	1.18692	−	0.862348i	0.593460	−	0.431174i	0.843551	+	0.537048i	$0.180461\pi$
$3$	1.08425	−	1.49234i	0.361417	−	0.497448i	−0.589126	−	0.808041i	$-0.700528\pi$
$3$	1.08425	−	1.49234i	0.361417	−	0.497448i	0.950543	+	0.310593i	$0.100528\pi$
$4$	−0.570933	+	1.75715i	−0.142733	+	0.439288i
$5$	−4.14776			−0.829553			−0.414776	−	0.909923i	$-0.636140\pi$
$5$	−4.14776			−0.829553			−0.414776	+	0.909923i	$0.636140\pi$
$6$		−	2.70629i		−	0.451049i
$7$	1.06697	−	3.28380i	0.152425	−	0.469115i	−0.845466	−	0.534029i	$-0.820677\pi$
$7$	1.06697	−	3.28380i	0.152425	−	0.469115i	0.997891	+	0.0649142i	$0.0206774\pi$
$8$	2.65108	+	8.15917i	0.331384	+	1.01990i
$9$	1.72966	+	5.32336i	0.192185	+	0.591484i
$10$	−4.92306	+	3.57681i	−0.492306	+	0.357681i
$11$	−13.6300	−	4.42864i	−1.23909	−	0.402604i	−0.385088	−	0.922880i	$-0.625829\pi$
$11$	−13.6300	−	4.42864i	−1.23909	−	0.402604i	−0.853998	+	0.520276i	$0.825829\pi$
$12$	2.00324	+	2.75722i	0.166937	+	0.229768i
$13$	5.41722	−	7.45616i	0.416709	−	0.573551i	−0.548130	−	0.836393i	$-0.684660\pi$
$13$	5.41722	−	7.45616i	0.416709	−	0.573551i	0.964839	+	0.262842i	$0.0846599\pi$
$14$	−1.56537	−	4.81771i	−0.111812	−	0.344122i
$15$	−4.49722	+	6.18989i	−0.299814	+	0.412659i
$16$	4.20377	+	3.05422i	0.262735	+	0.190888i
$17$	−1.46101	+	0.474711i	−0.0859418	+	0.0279242i	−0.351672	−	0.936123i	$-0.614387\pi$
$17$	−1.46101	+	0.474711i	−0.0859418	+	0.0279242i	0.265730	+	0.964047i	$0.414387\pi$
$18$	6.64356	+	4.82683i	0.369086	+	0.268157i
$19$	16.5438	−	12.0198i	0.870728	−	0.632621i	−0.0600541	−	0.998195i	$-0.519127\pi$
$19$	16.5438	−	12.0198i	0.870728	−	0.632621i	0.930782	+	0.365574i	$0.119127\pi$
$20$	2.36809	−	7.28825i	0.118405	−	0.364412i
$21$	−3.74370	−	5.15276i	−0.178271	−	0.245369i
$22$	−19.9967	+	6.49732i	−0.908940	+	0.295333i
$23$	17.2964	−	5.61995i	0.752019	−	0.244346i	0.0921694	−	0.995743i	$-0.470620\pi$
$23$	17.2964	−	5.61995i	0.752019	−	0.244346i	0.659850	+	0.751397i	$0.270620\pi$
$24$	15.0507	+	4.89028i	0.627113	+	0.203761i
$25$	−7.79606			−0.311843
$26$		−	13.5214i		−	0.520054i
$27$	25.6089	+	8.32083i	0.948477	+	0.308179i
$28$	5.16097	+	3.74966i	0.184320	+	0.133917i
$29$	−23.9358	−	32.9448i	−0.825373	−	1.13603i	−0.988767	−	0.149468i	$-0.952244\pi$
$29$	−23.9358	−	32.9448i	−0.825373	−	1.13603i	0.163393	−	0.986561i	$-0.447756\pi$
$30$			11.2251i			0.374169i
$31$	20.1838	+	23.5290i	0.651092	+	0.758999i
$31$	20.1838	+	23.5290i	0.651092	+	0.758999i
$32$	−26.6929			−0.834154
$33$	−21.3873	+	15.5388i	−0.648101	+	0.470873i
$34$	−1.32474	+	1.82334i	−0.0389629	+	0.0536278i
$35$	−4.42555	+	13.6204i	−0.126444	+	0.389155i
$36$	−10.3415			−0.287263
$37$			42.0983i			1.13779i	0.822409	+	0.568897i	$0.192630\pi$
$37$			42.0983i			1.13779i	−0.822409	+	0.568897i	$0.807370\pi$
$38$	9.27096	−	28.5331i	0.243973	−	0.750870i
$39$	−5.25353	−	16.1687i	−0.134706	−	0.414582i
$40$	−10.9960	−	33.8423i	−0.274901	−	0.846058i
$41$	−61.3917	+	44.6037i	−1.49736	+	1.08790i	−0.525941	+	0.850521i	$0.676287\pi$
$41$	−61.3917	+	44.6037i	−1.49736	+	1.08790i	−0.971418	+	0.237374i	$0.923713\pi$
$42$	−8.88693	−	2.88754i	−0.211594	−	0.0687510i
$43$	15.1894	+	20.9064i	0.353242	+	0.486196i	0.948250	−	0.317523i	$-0.102851\pi$
$43$	15.1894	+	20.9064i	0.353242	+	0.486196i	−0.595008	+	0.803720i	$0.702851\pi$
$44$	15.5636	−	21.4214i	0.353718	−	0.486851i
$45$	−7.17423	−	22.0800i	−0.159427	−	0.490667i
$46$	15.6831	−	21.5860i	0.340938	−	0.469260i
$47$	−3.99548	−	2.90289i	−0.0850102	−	0.0617635i	0.544468	−	0.838781i	$-0.316731\pi$
$47$	−3.99548	−	2.90289i	−0.0850102	−	0.0617635i	−0.629479	+	0.777018i	$0.716731\pi$
$48$	9.11588	−	2.96193i	0.189914	−	0.0617069i
$49$	29.9969	+	21.7940i	0.612182	+	0.444776i
$50$	−9.25330	+	6.72292i	−0.185066	+	0.134458i
$51$	−0.875671	+	2.69504i	−0.0171700	+	0.0528439i
$52$	10.0087	+	13.7758i	0.192476	+	0.264920i
$53$	38.5605	−	12.5291i	0.727557	−	0.236398i	0.0782603	−	0.996933i	$-0.475063\pi$
$53$	38.5605	−	12.5291i	0.727557	−	0.236398i	0.649296	+	0.760535i	$0.275063\pi$
$54$	37.5711	−	12.2076i	0.695761	−	0.226067i
$55$	56.5338	+	18.3689i	1.02789	+	0.333981i
$56$	29.6217			0.528959
$57$		−	37.7216i		−	0.661782i
$58$	−56.8198	−	18.4619i	−0.979652	−	0.318308i
$59$	36.1430	+	26.2594i	0.612592	+	0.445074i	0.850326	−	0.526256i	$-0.176405\pi$
$59$	36.1430	+	26.2594i	0.612592	+	0.445074i	−0.237734	+	0.971330i	$0.576405\pi$
$60$	−8.30896	−	11.4363i	−0.138483	−	0.190605i
$61$		−	84.8005i		−	1.39017i	−0.718927	−	0.695086i	$-0.755366\pi$
$61$		−	84.8005i		−	1.39017i	0.718927	−	0.695086i	$-0.244634\pi$
$62$	44.2468	+	10.5215i	0.713657	+	0.169702i
$63$	19.3264			0.306768
$64$	−48.4974	+	35.2354i	−0.757772	+	0.550554i
$65$	−22.4693	+	30.9264i	−0.345682	+	0.475791i
$66$	−11.9852	+	36.8867i	−0.181594	+	0.558889i
$67$	−109.556			−1.63517			−0.817583	−	0.575811i	$-0.804686\pi$
$67$	−109.556			−1.63517			−0.817583	+	0.575811i	$0.804686\pi$
$68$		−	2.83825i		−	0.0417389i
$69$	10.3668	−	31.9057i	0.150243	−	0.462401i
$70$	6.49278	+	19.9827i	0.0927540	+	0.285467i
$71$	−19.6220	−	60.3903i	−0.276366	−	0.850568i	−0.988855	−	0.148884i	$-0.952432\pi$
$71$	−19.6220	−	60.3903i	−0.276366	−	0.850568i	0.712488	−	0.701684i	$-0.247568\pi$
$72$	−38.8487	+	28.2252i	−0.539565	+	0.392017i
$73$	−85.9266	−	27.9192i	−1.17708	−	0.382455i	−0.345796	−	0.938310i	$-0.612391\pi$
$73$	−85.9266	−	27.9192i	−1.17708	−	0.382455i	−0.831280	+	0.555854i	$0.812391\pi$
$74$	36.3034	+	49.9674i	0.490587	+	0.675235i
$75$	−8.45289	+	11.6344i	−0.112705	+	0.155125i
$76$	11.6752	+	35.9325i	0.153621	+	0.472796i
$77$	−29.0856	+	40.0328i	−0.377735	+	0.519907i
$78$	−20.1786	−	14.6606i	−0.258700	−	0.187956i
$79$	142.262	−	46.2236i	1.80078	−	0.585108i	0.800873	−	0.598834i	$-0.204369\pi$
$79$	142.262	−	46.2236i	1.80078	−	0.585108i	0.999906	+	0.0137258i	$0.00436918\pi$
$80$	−17.4362	−	12.6682i	−0.217953	−	0.158352i
$81$	−0.570882	+	0.414770i	−0.00704793	+	0.00512062i
$82$	−34.4032	+	105.882i	−0.419551	+	1.29124i
$83$	25.0530	+	34.4824i	0.301843	+	0.415451i	0.932816	−	0.360354i	$-0.117344\pi$
$83$	25.0530	+	34.4824i	0.301843	+	0.415451i	−0.630973	+	0.775805i	$0.717344\pi$
$84$	11.1916	−	3.63636i	0.133233	−	0.0432900i
$85$	6.05993	−	1.96899i	0.0712933	−	0.0231646i
$86$	36.0572	+	11.7157i	0.419270	+	0.136229i
$87$	−75.1175			−0.863419
$88$		−	122.950i		−	1.39716i
$89$	46.3352	+	15.0552i	0.520620	+	0.169160i	0.557527	−	0.830159i	$-0.311750\pi$
$89$	46.3352	+	15.0552i	0.520620	+	0.169160i	−0.0369067	+	0.999319i	$0.511750\pi$
$90$	−27.5559	−	20.0205i	−0.306177	−	0.222450i
$91$	−18.7045	−	25.7446i	−0.205544	−	0.282908i
$92$			33.6011i			0.365229i
$93$	56.9977	−	4.60992i	0.612878	−	0.0495690i
$94$	−7.24561			−0.0770810
$95$	−68.6199	+	49.8553i	−0.722315	+	0.524792i
$96$	−28.9418	+	39.8350i	−0.301477	+	0.414948i
$97$	15.1554	−	46.6434i	0.156241	−	0.480860i	−0.842044	−	0.539409i	$-0.818648\pi$
$97$	15.1554	−	46.6434i	0.156241	−	0.480860i	0.998284	+	0.0585497i	$0.0186476\pi$
$98$	54.3979			0.555081
$99$		−	80.2172i		−	0.810274i
$100$	4.45103	−	13.6989i	0.0445103	−	0.136989i
$101$	17.7682	+	54.6850i	0.175923	+	0.541435i	0.999674	−	0.0255158i	$-0.00812281\pi$
$101$	17.7682	+	54.6850i	0.175923	+	0.541435i	−0.823751	+	0.566951i	$0.808123\pi$
$102$	1.28471	+	3.95393i	0.0125952	+	0.0387640i
$103$	51.9380	−	37.7352i	0.504253	−	0.366361i	−0.306386	−	0.951907i	$-0.599120\pi$
$103$	51.9380	−	37.7352i	0.504253	−	0.366361i	0.810639	+	0.585546i	$0.199120\pi$
$104$	75.1976	+	24.4332i	0.723054	+	0.234934i
$105$	15.5280	+	21.3724i	0.147885	+	0.203547i
$106$	34.9638	−	48.1236i	0.329847	−	0.453996i
$107$	−40.4335	−	124.442i	−0.377883	−	1.16300i	−0.941513	−	0.336977i	$-0.890595\pi$
$107$	−40.4335	−	124.442i	−0.377883	−	1.16300i	0.563630	−	0.826028i	$-0.309405\pi$
$108$	−29.2419	+	40.2480i	−0.270758	+	0.372667i
$109$	−123.474	−	89.7092i	−1.13279	−	0.823020i	−0.146692	−	0.989182i	$-0.546863\pi$
$109$	−123.474	−	89.7092i	−1.13279	−	0.823020i	−0.986099	+	0.166162i	$0.946863\pi$
$110$	82.9415	−	26.9493i	0.754014	−	0.244994i
$111$	62.8252	+	45.6452i	0.565993	+	0.411218i
$112$	14.5147	−	10.5456i	0.129596	−	0.0941570i
$113$	−37.7786	+	116.270i	−0.334324	+	1.02894i	0.632731	+	0.774372i	$0.281934\pi$
$113$	−37.7786	+	116.270i	−0.334324	+	1.02894i	−0.967054	+	0.254570i	$0.918066\pi$
$114$	−32.5291	−	44.7725i	−0.285343	−	0.392741i
$115$	−71.7415	+	23.3102i	−0.623839	+	0.202698i
$116$	71.5548	−	23.2496i	0.616852	−	0.200427i
$117$	49.0618	+	15.9411i	0.419331	+	0.136249i
$118$	65.5435			0.555453
$119$			5.30418i			0.0445729i
$120$	−62.4268	−	20.2837i	−0.520224	−	0.169031i
$121$	68.2717	+	49.6023i	0.564229	+	0.409936i
$122$	−73.1275	−	100.651i	−0.599406	−	0.825011i
$123$			139.979i			1.13804i
$124$	−52.8676	+	22.0326i	−0.426351	+	0.177682i
$125$	136.030			1.08824
$126$	22.9388	−	16.6660i	0.182054	−	0.132270i
$127$	−86.5000	+	119.057i	−0.681102	+	0.937457i	−0.999946	−	0.0103505i	$-0.996705\pi$
$127$	−86.5000	+	119.057i	−0.681102	+	0.937457i	0.318844	+	0.947807i	$0.396705\pi$
$128$	5.81691	−	17.9026i	0.0454446	−	0.139864i
$129$	47.6687			0.369525
$130$			56.0835i			0.431412i
$131$	19.6729	−	60.5470i	0.150175	−	0.462191i	−0.847465	−	0.530851i	$-0.821872\pi$
$131$	19.6729	−	60.5470i	0.150175	−	0.462191i	0.997640	+	0.0686600i	$0.0218724\pi$
$132$	−15.0933	−	46.4524i	−0.114343	−	0.351912i
$133$	−21.8188	−	67.1515i	−0.164051	−	0.504898i
$134$	−130.034	+	94.4754i	−0.970405	+	0.705040i
$135$	−106.220	−	34.5128i	−0.786811	−	0.255650i
$136$	−7.74650	−	10.6621i	−0.0569596	−	0.0783981i
$137$	−56.0236	+	77.1098i	−0.408931	+	0.562846i	−0.962957	−	0.269654i	$-0.913091\pi$
$137$	−56.0236	+	77.1098i	−0.408931	+	0.562846i	0.554026	+	0.832499i	$0.313091\pi$
$138$	−15.2092	−	46.8093i	−0.110212	−	0.339198i
$139$	43.4725	−	59.8347i	0.312752	−	0.430466i	−0.623485	−	0.781835i	$-0.714284\pi$
$139$	43.4725	−	59.8347i	0.312752	−	0.430466i	0.936237	+	0.351369i	$0.114284\pi$
$140$	−21.4065	−	15.5527i	−0.152903	−	0.111091i
$141$	−8.66421	+	2.81517i	−0.0614483	+	0.0199658i
$142$	−75.3672	−	54.7575i	−0.530755	−	0.385616i
$143$	−106.857	+	77.6362i	−0.747252	+	0.542911i
$144$	−8.98758	+	27.6609i	−0.0624137	+	0.192090i
$145$	99.2801	+	136.647i	0.684690	+	0.942396i
$146$	−126.064	+	40.9607i	−0.863452	+	0.280553i
$147$	65.0484	−	21.1355i	0.442506	−	0.143779i
$148$	−73.9732	−	24.0353i	−0.499819	−	0.162401i
$149$	−41.6680			−0.279651			−0.139826	−	0.990176i	$-0.544654\pi$
$149$	−41.6680			−0.279651			−0.139826	+	0.990176i	$0.544654\pi$
$150$			21.0984i			0.140656i
$151$	−18.9900	−	6.17023i	−0.125762	−	0.0408624i	0.245460	−	0.969407i	$-0.421061\pi$
$151$	−18.9900	−	6.17023i	−0.125762	−	0.0408624i	−0.371222	+	0.928544i	$0.621061\pi$
$152$	141.931	+	103.119i	0.933754	+	0.678412i
$153$	−5.05412	−	6.95639i	−0.0330334	−	0.0454666i
$154$			72.5976i			0.471413i
$155$	−83.7178	−	97.5926i	−0.540115	−	0.629630i
$156$	31.4103			0.201348
$157$	80.3853	−	58.4034i	0.512009	−	0.371996i	−0.301576	−	0.953442i	$-0.597513\pi$
$157$	80.3853	−	58.4034i	0.512009	−	0.371996i	0.813585	+	0.581446i	$0.197513\pi$
$158$	128.992	−	177.543i	0.816406	−	1.12369i
$159$	23.1116	−	71.1302i	0.145356	−	0.447360i
$160$	110.716			0.691974
$161$		−	62.7944i		−	0.390028i
$162$	−0.319915	+	0.984597i	−0.00197478	+	0.00607776i
$163$	51.9446	+	159.869i	0.318679	+	0.980792i	0.974214	+	0.225627i	$0.0724431\pi$
$163$	51.9446	+	159.869i	0.318679	+	0.980792i	−0.655535	+	0.755165i	$0.727557\pi$
$164$	−43.3249	−	133.340i	−0.264176	−	0.813050i
$165$	88.7096	−	64.4513i	0.537634	−	0.390614i
$166$	59.4717	+	19.3235i	0.358263	+	0.116407i
$167$	−41.7004	−	57.3956i	−0.249703	−	0.343686i	0.665704	−	0.746216i	$-0.268131\pi$
$167$	−41.7004	−	57.3956i	−0.249703	−	0.343686i	−0.915407	+	0.402529i	$0.868131\pi$
$168$	32.1174	−	44.2058i	0.191175	−	0.263130i
$169$	25.9758	+	79.9452i	0.153703	+	0.473049i
$170$	5.49469	−	7.56280i	0.0323217	−	0.0444870i
$171$	92.6010	+	67.2785i	0.541526	+	0.393442i
$172$	−45.4079	+	14.7539i	−0.263999	+	0.0857786i
$173$	166.025	+	120.624i	0.959684	+	0.697251i	0.953077	−	0.302727i	$-0.0978970\pi$
$173$	166.025	+	120.624i	0.959684	+	0.697251i	0.00660682	+	0.999978i	$0.497897\pi$
$174$	−89.1584	+	64.7774i	−0.512405	+	0.372284i
$175$	−8.31818	+	25.6007i	−0.0475325	+	0.146290i
$176$	−43.7711	−	60.2458i	−0.248700	−	0.342306i
$177$	78.3761	−	25.4659i	0.442803	−	0.143875i
$178$	67.9790	−	22.0877i	0.381904	−	0.124088i
$179$	−101.179	−	32.8752i	−0.565248	−	0.183660i	0.0124333	−	0.999923i	$-0.496042\pi$
$179$	−101.179	−	32.8752i	−0.565248	−	0.183660i	−0.577681	+	0.816263i	$0.696042\pi$
$180$	42.8939			0.238300
$181$		−	137.906i		−	0.761913i	−0.924593	−	0.380957i	$-0.875595\pi$
$181$		−	137.906i		−	0.761913i	0.924593	−	0.380957i	$-0.124405\pi$
$182$	−44.4016	−	14.4269i	−0.243965	−	0.0792690i
$183$	−126.552	−	91.9451i	−0.691538	−	0.502432i
$184$	91.7083	+	126.226i	0.498415	+	0.686009i
$185$		−	174.614i		−	0.943859i
$186$	63.6763	−	54.6234i	0.342346	−	0.293674i
$187$	22.0158			0.117732
$188$	7.38196	−	5.36331i	0.0392657	−	0.0285282i
$189$	54.6479	−	75.2164i	0.289142	−	0.397970i
$190$	−38.4537	+	118.348i	−0.202388	+	0.622886i
$191$	−30.5286			−0.159836			−0.0799178	−	0.996801i	$-0.525466\pi$
$191$	−30.5286			−0.159836			−0.0799178	+	0.996801i	$0.525466\pi$
$192$			110.579i			0.575932i
$193$	−55.8889	+	172.008i	−0.289580	+	0.891236i	0.695408	+	0.718615i	$0.255224\pi$
$193$	−55.8889	+	172.008i	−0.289580	+	0.891236i	−0.984988	+	0.172621i	$0.944776\pi$
$194$	−22.2346	−	68.4311i	−0.114611	−	0.352738i
$195$	21.7904	+	67.0640i	0.111746	+	0.343918i
$196$	−55.4216	+	40.2662i	−0.282763	+	0.205440i
$197$	−54.3265	−	17.6518i	−0.275769	−	0.0896028i	0.167868	−	0.985810i	$-0.446312\pi$
$197$	−54.3265	−	17.6518i	−0.275769	−	0.0896028i	−0.443637	+	0.896207i	$0.646312\pi$
$198$	−69.1751	−	95.2113i	−0.349369	−	0.480865i
$199$	−138.187	+	190.199i	−0.694409	+	0.955773i	0.305584	+	0.952165i	$0.401148\pi$
$199$	−138.187	+	190.199i	−0.694409	+	0.955773i	−0.999993	+	0.00360755i	$0.998852\pi$
$200$	−20.6680	−	63.6094i	−0.103340	−	0.318047i
$201$	−118.786	+	163.495i	−0.590977	+	0.813409i
$202$	68.2469	+	49.5843i	0.337856	+	0.245467i
$203$	−133.723	+	43.4493i	−0.658735	+	0.214036i
$204$	−4.23564	−	3.07737i	−0.0207629	−	0.0150852i
$205$	254.638	−	185.006i	1.24214	−	0.902466i
$206$	29.1054	−	89.5773i	0.141288	−	0.434841i
$207$	59.8341	+	82.3545i	0.289053	+	0.397848i
$208$	45.5455	−	14.7986i	0.218969	−	0.0711472i
$209$	−278.723	+	90.5626i	−1.33360	+	0.433314i
$210$	36.8609	+	11.9768i	0.175528	+	0.0570325i
$211$	−122.713			−0.581578			−0.290789	−	0.956787i	$-0.593918\pi$
$211$	−122.713			−0.581578			−0.290789	+	0.956787i	$0.593918\pi$
$212$			74.9099i			0.353349i
$213$	−111.398	−	36.1955i	−0.522997	−	0.169932i
$214$	−155.303	−	112.834i	−0.725716	−	0.527263i
$215$	−63.0021	−	86.7149i	−0.293033	−	0.403325i
$216$			231.006i			1.06947i
$217$	98.8001	−	41.1750i	0.455300	−	0.189747i
$218$	−223.914			−1.02713
$219$	−134.831	+	97.9605i	−0.615667	+	0.447308i
$220$	−64.5540	+	88.8510i	−0.293427	+	0.403868i
$221$	−4.37509	+	13.4652i	−0.0197968	+	0.0609283i
$222$	113.930			0.513200
$223$		−	310.445i		−	1.39213i	−0.717980	−	0.696064i	$-0.754933\pi$
$223$		−	310.445i		−	1.39213i	0.717980	−	0.696064i	$-0.245067\pi$
$224$	−28.4806	+	87.6543i	−0.127146	+	0.391314i
$225$	−13.4846	−	41.5012i	−0.0599314	−	0.184450i
$226$	55.4254	+	170.582i	0.245245	+	0.754787i
$227$	344.688	−	250.430i	1.51845	−	1.10322i	0.556198	−	0.831050i	$-0.312260\pi$
$227$	344.688	−	250.430i	1.51845	−	1.10322i	0.962250	−	0.272167i	$-0.0877404\pi$
$228$	66.2825	+	21.5365i	0.290713	+	0.0944583i
$229$	0.576116	+	0.792956i	0.00251579	+	0.00346269i	0.810273	−	0.586053i	$-0.199319\pi$
$229$	0.576116	+	0.792956i	0.00251579	+	0.00346269i	−0.807757	+	0.589515i	$0.799319\pi$
$230$	−65.0499	+	89.5335i	−0.282826	+	0.389276i
$231$	28.2067	+	86.8113i	0.122107	+	0.375807i
$232$	205.347	−	282.636i	0.885116	−	1.21826i
$233$	287.434	+	208.833i	1.23362	+	0.896280i	0.997156	−	0.0753591i	$-0.0240103\pi$
$233$	287.434	+	208.833i	1.23362	+	0.896280i	0.236468	+	0.971639i	$0.424010\pi$
$234$	71.9792	−	23.3875i	0.307603	−	0.0999464i
$235$	16.5723	+	12.0405i	0.0705204	+	0.0512361i
$236$	−66.7769	+	48.5163i	−0.282953	+	0.205577i
$237$	85.2658	−	262.421i	0.359771	−	1.10726i
$238$	4.57404	+	6.29563i	0.0192187	+	0.0264522i
$239$	226.754	−	73.6767i	0.948760	−	0.308271i	0.206548	−	0.978436i	$-0.433777\pi$
$239$	226.754	−	73.6767i	0.948760	−	0.308271i	0.742212	+	0.670166i	$0.233777\pi$
$240$	−37.8105	+	12.2854i	−0.157544	+	0.0511891i
$241$	−309.669	−	100.617i	−1.28493	−	0.417500i	−0.414617	−	0.909996i	$-0.636085\pi$
$241$	−309.669	−	100.617i	−1.28493	−	0.417500i	−0.870315	+	0.492496i	$0.836085\pi$
$242$	123.807			0.511601
$243$			243.642i			1.00264i
$244$	149.007	+	48.4154i	0.610686	+	0.198424i
$245$	−124.420	−	90.3964i	−0.507837	−	0.368965i
$246$	120.711	+	166.144i	0.490694	+	0.675382i
$247$		−	188.467i		−	0.763026i
$248$	−138.468	+	227.061i	−0.558339	+	0.915567i
$249$	78.6234			0.315756
$250$	161.457	−	117.305i	0.645828	−	0.469222i
$251$	107.602	−	148.101i	0.428692	−	0.590044i	−0.538960	−	0.842331i	$-0.681183\pi$
$251$	107.602	−	148.101i	0.428692	−	0.590044i	0.967652	+	0.252287i	$0.0811827\pi$
$252$	−11.0341	+	33.9593i	−0.0437859	+	0.134759i
$253$	−260.638			−1.03019
$254$			215.904i			0.850016i
$255$	3.63207	−	11.1784i	0.0142434	−	0.0438368i
$256$	−82.6315	−	254.314i	−0.322779	−	0.993413i
$257$	58.6764	+	180.587i	0.228313	+	0.702675i	0.997938	+	0.0641793i	$0.0204430\pi$
$257$	58.6764	+	180.587i	0.228313	+	0.702675i	−0.769625	+	0.638496i	$0.779557\pi$
$258$	56.5790	−	41.1070i	0.219298	−	0.159330i
$259$	138.243	+	44.9178i	0.533755	+	0.173428i
$260$	−41.5139	−	57.1389i	−0.159669	−	0.219765i
$261$	133.976	−	184.402i	0.513319	−	0.706523i
$262$	−28.8624	−	88.8294i	−0.110162	−	0.339043i
$263$	−16.6417	+	22.9053i	−0.0632762	+	0.0870923i	−0.839482	−	0.543387i	$-0.817142\pi$
$263$	−16.6417	+	22.9053i	−0.0632762	+	0.0870923i	0.776206	+	0.630479i	$0.217142\pi$
$264$	−183.483	−	133.308i	−0.695013	−	0.504956i
$265$	−159.940	+	51.9676i	−0.603547	+	0.196104i
$266$	−83.8051	−	60.8880i	−0.315057	−	0.228902i
$267$	72.7065	−	52.8244i	0.272309	−	0.197844i
$268$	62.5492	−	192.507i	0.233392	−	0.718308i
$269$	−166.176	−	228.722i	−0.617756	−	0.850268i	0.379431	−	0.925220i	$-0.376120\pi$
$269$	−166.176	−	228.722i	−0.617756	−	0.850268i	−0.997187	+	0.0749520i	$0.976120\pi$
$270$	−155.836	+	50.6342i	−0.577171	+	0.187534i
$271$	−70.9562	+	23.0551i	−0.261831	+	0.0850740i	−0.436991	−	0.899466i	$-0.643956\pi$
$271$	−70.9562	+	23.0551i	−0.261831	+	0.0850740i	0.175160	+	0.984540i	$0.443956\pi$
$272$	−7.59162	−	2.46667i	−0.0279104	−	0.00906863i
$273$	−58.7002			−0.215019
$274$			139.835i			0.510347i
$275$	106.260	+	34.5260i	0.386400	+	0.125549i
$276$	50.1444	+	36.4320i	0.181683	+	0.132000i
$277$	253.022	+	348.255i	0.913437	+	1.25724i	0.965979	+	0.258620i	$0.0832678\pi$
$277$	253.022	+	348.255i	0.913437	+	1.25724i	−0.0525416	+	0.998619i	$0.516732\pi$
$278$		−	108.507i		−	0.390314i
$279$	−90.3418	+	148.143i	−0.323806	+	0.530979i
$280$	−122.864			−0.438800
$281$	111.187	−	80.7824i	0.395685	−	0.287482i	−0.372096	−	0.928194i	$-0.621361\pi$
$281$	111.187	−	80.7824i	0.395685	−	0.287482i	0.767781	+	0.640712i	$0.221361\pi$
$282$	−7.85606	+	10.8129i	−0.0278584	+	0.0383438i
$283$	15.0593	−	46.3479i	0.0532132	−	0.163773i	−0.920918	−	0.389756i	$-0.872559\pi$
$283$	15.0593	−	46.3479i	0.0532132	−	0.163773i	0.974131	+	0.225983i	$0.0725593\pi$
$284$	117.318			0.413091
$285$			156.460i			0.548983i
$286$	−59.8814	+	184.296i	−0.209375	+	0.644391i
$287$	80.9665	+	249.189i	0.282113	+	0.868255i
$288$	−46.1698	−	142.096i	−0.160312	−	0.493389i
$289$	−231.897	+	168.483i	−0.802411	+	0.582986i
$290$	235.675	+	76.5755i	0.812673	+	0.264053i
$291$	−53.1757	−	73.1901i	−0.182735	−	0.251512i
$292$	98.1166	−	135.046i	0.336016	−	0.462486i
$293$	126.593	+	389.613i	0.432058	+	1.32974i	0.896072	+	0.443909i	$0.146409\pi$
$293$	126.593	+	389.613i	0.432058	+	1.32974i	−0.464014	+	0.885828i	$0.653591\pi$
$294$	58.9810	−	81.1804i	0.200616	−	0.276124i
$295$	−149.912	−	108.918i	−0.508178	−	0.369213i
$296$	−343.488	+	111.606i	−1.16043	+	0.377047i
$297$	−312.198	−	226.825i	−1.05117	−	0.763720i
$298$	−49.4566	+	35.9323i	−0.165962	+	0.120578i
$299$	51.7953	−	159.410i	0.173229	−	0.533143i
$300$	−15.6174	−	21.4955i	−0.0520579	−	0.0716516i
$301$	84.8593	−	27.5725i	0.281925	−	0.0916028i
$302$	−27.8605	+	9.05242i	−0.0922533	+	0.0299749i
$303$	100.874	+	32.7760i	0.332918	+	0.108171i
$304$	106.257			0.349531
$305$			351.732i			1.15322i
$306$	−11.9977	−	3.89828i	−0.0392080	−	0.0127395i
$307$	45.5020	+	33.0591i	0.148215	+	0.107684i	0.659421	−	0.751773i	$-0.270801\pi$
$307$	45.5020	+	33.0591i	0.148215	+	0.107684i	−0.511207	+	0.859458i	$0.670801\pi$
$308$	−53.7378	−	73.9638i	−0.174474	−	0.240142i
$309$		−	118.424i		−	0.383249i
$310$	−183.525	−	43.6407i	−0.592016	−	0.140776i
$311$	−151.616			−0.487511			−0.243756	−	0.969837i	$-0.578380\pi$
$311$	−151.616			−0.487511			−0.243756	+	0.969837i	$0.578380\pi$
$312$	117.996	−	85.7289i	0.378192	−	0.274772i
$313$	50.3435	−	69.2919i	0.160842	−	0.221380i	−0.720988	−	0.692948i	$-0.756312\pi$
$313$	50.3435	−	69.2919i	0.160842	−	0.221380i	0.881830	+	0.471568i	$0.156312\pi$
$314$	45.0469	−	138.640i	0.143462	−	0.441529i
$315$	−80.1611			−0.254480
$316$			276.366i			0.874575i
$317$	51.1637	−	157.466i	0.161400	−	0.496737i	−0.837353	−	0.546662i	$-0.815898\pi$
$317$	51.1637	−	157.466i	0.161400	−	0.496737i	0.998753	+	0.0499250i	$0.0158982\pi$
$318$	−33.9073	−	104.356i	−0.106627	−	0.328164i
$319$	180.343	+	555.040i	0.565340	+	1.73994i
$320$	201.156	−	146.148i	0.628612	−	0.456713i
$321$	−229.550	−	74.5852i	−0.715108	−	0.232353i
$322$	−54.1506	−	74.5320i	−0.168170	−	0.231466i
$323$	−18.4648	+	25.4146i	−0.0571665	+	0.0786830i
$324$	−0.402878	−	1.23993i	−0.00124345	−	0.00382695i
$325$	−42.2330	+	58.1287i	−0.129948	+	0.178858i
$326$	199.517	+	144.957i	0.612015	+	0.444655i
$327$	−267.754	+	86.9986i	−0.818820	+	0.266051i
$328$	−526.683	−	382.658i	−1.60574	−	1.16664i
$329$	−13.7956	+	10.0231i	−0.0419318	+	0.0304652i
$330$	49.7118	−	152.997i	0.150642	−	0.463628i
$331$	−200.957	−	276.593i	−0.607120	−	0.835630i	0.389216	−	0.921146i	$-0.372746\pi$
$331$	−200.957	−	276.593i	−0.607120	−	0.835630i	−0.996337	+	0.0855168i	$0.972746\pi$
$332$	−74.8944	+	24.3347i	−0.225586	+	0.0732972i
$333$	−224.105	+	72.8160i	−0.672987	+	0.218667i
$334$	−98.9900	−	32.1638i	−0.296377	−	0.0962988i
$335$	454.413			1.35646
$336$		−	33.0950i		−	0.0984972i
$337$	444.678	+	144.485i	1.31952	+	0.428738i	0.882330	−	0.470632i	$-0.155974\pi$
$337$	444.678	+	144.485i	1.31952	+	0.428738i	0.437189	+	0.899369i	$0.355974\pi$
$338$	99.7717	+	72.4884i	0.295183	+	0.214463i
$339$	132.554	+	182.445i	0.391015	+	0.538186i
$340$			11.7724i			0.0346246i
$341$	−170.904	−	410.086i	−0.501183	−	1.20260i
$342$	167.927			0.491016
$343$	240.448	−	174.696i	0.701015	−	0.509317i
$344$	−130.311	+	179.358i	−0.378811	+	0.521388i
$345$	−42.9990	+	132.337i	−0.124635	+	0.383586i
$346$	301.079			0.870171
$347$		−	279.411i		−	0.805218i	−0.915372	−	0.402609i	$-0.868103\pi$
$347$		−	279.411i		−	0.805218i	0.915372	−	0.402609i	$-0.131897\pi$
$348$	42.8870	−	131.993i	0.123239	−	0.379290i
$349$	−95.5019	−	293.925i	−0.273644	−	0.842191i	−0.989575	−	0.144019i	$-0.953997\pi$
$349$	−95.5019	−	293.925i	−0.273644	−	0.842191i	0.715930	−	0.698172i	$-0.246003\pi$
$350$	12.2037	+	37.5592i	0.0348678	+	0.107312i
$351$	200.770	−	145.868i	0.571995	−	0.415579i
$352$	363.823	+	118.213i	1.03359	+	0.335833i
$353$	345.083	+	474.966i	0.977572	+	1.34551i	0.938127	+	0.346291i	$0.112559\pi$
$353$	345.083	+	474.966i	0.977572	+	1.34551i	0.0394454	+	0.999222i	$0.487441\pi$
$354$	71.0656	−	97.8134i	0.200750	−	0.276309i
$355$	81.3875	+	250.485i	0.229260	+	0.705591i
$356$	−52.9086	+	72.8224i	−0.148620	+	0.204557i
$357$	7.91566	+	5.75106i	0.0221727	+	0.0161094i
$358$	−148.442	+	48.2316i	−0.414641	+	0.134725i
$359$	208.797	+	151.700i	0.581609	+	0.422563i	0.839304	−	0.543663i	$-0.182963\pi$
$359$	208.797	+	151.700i	0.581609	+	0.422563i	−0.257695	+	0.966226i	$0.582963\pi$
$360$	161.135	−	117.072i	0.447598	−	0.325199i
$361$	17.6678	−	54.3758i	0.0489412	−	0.150625i
$362$	−118.923	−	163.684i	−0.328517	−	0.452165i
$363$	148.047	−	48.1035i	0.407844	−	0.132517i
$364$	55.9162	−	18.1683i	0.153616	−	0.0499128i
$365$	356.403	+	115.802i	0.976447	+	0.317267i
$366$	−229.495			−0.627036
$367$			79.9018i			0.217716i	0.994057	+	0.108858i	$0.0347194\pi$
$367$			79.9018i			0.217716i	−0.994057	+	0.108858i	$0.965281\pi$
$368$	89.8748	+	29.2021i	0.244225	+	0.0793535i
$369$	−343.628	−	249.661i	−0.931242	−	0.676587i
$370$	−150.578	−	207.253i	−0.406967	−	0.560143i
$371$		−	139.993i		−	0.377340i
$372$	−24.4415	+	102.785i	−0.0657030	+	0.276305i
$373$	−381.373			−1.02245			−0.511224	−	0.859447i	$-0.670808\pi$
$373$	−381.373			−1.02245			−0.511224	+	0.859447i	$0.670808\pi$
$374$	26.1310	−	18.9853i	0.0698691	−	0.0507629i
$375$	147.491	−	203.004i	0.393309	−	0.541344i
$376$	13.0928	−	40.2956i	0.0348213	−	0.107169i
$377$	−375.308			−0.995511
$378$		−	136.401i		−	0.360850i
$379$	−111.049	+	341.775i	−0.293006	+	0.901781i	0.690877	+	0.722972i	$0.257224\pi$
$379$	−111.049	+	341.775i	−0.293006	+	0.901781i	−0.983884	+	0.178809i	$0.942776\pi$
$380$	−48.4259	−	149.040i	−0.127437	−	0.392209i
$381$	83.8863	+	258.175i	0.220174	+	0.677626i
$382$	−36.2350	+	26.3263i	−0.0948560	+	0.0689169i
$383$	11.2735	+	3.66299i	0.0294348	+	0.00956395i	0.323697	−	0.946161i	$-0.395074\pi$
$383$	11.2735	+	3.66299i	0.0294348	+	0.00956395i	−0.294263	+	0.955725i	$0.595074\pi$
$384$	−20.4099	−	28.0918i	−0.0531507	−	0.0731556i
$385$	120.640	−	166.047i	0.313351	−	0.431290i
$386$	81.9954	+	252.356i	0.212423	+	0.653772i
$387$	−85.0199	+	117.020i	−0.219690	+	0.302377i
$388$	73.3068	+	53.2605i	0.188935	+	0.137269i
$389$	−195.309	+	63.4597i	−0.502079	+	0.163135i	−0.549097	−	0.835759i	$-0.685028\pi$
$389$	−195.309	+	63.4597i	−0.502079	+	0.163135i	0.0470179	+	0.998894i	$0.485028\pi$
$390$	83.6959	+	60.8086i	0.214605	+	0.155920i
$391$	−22.6024	+	16.4216i	−0.0578068	+	0.0419991i
$392$	−98.2971	+	302.527i	−0.250758	+	0.771754i
$393$	−69.0266	−	95.0070i	−0.175640	−	0.241748i
$394$	−79.7031	+	25.8971i	−0.202292	+	0.0657287i
$395$	−590.067	+	191.724i	−1.49384	+	0.485378i
$396$	140.954	+	45.7986i	0.355944	+	0.115653i
$397$	−710.602			−1.78993			−0.894964	−	0.446137i	$-0.852799\pi$
$397$	−710.602			−1.78993			−0.894964	+	0.446137i	$0.852799\pi$
$398$			344.916i			0.866624i
$399$	−123.870	−	40.2479i	−0.310452	−	0.100872i
$400$	−32.7728	−	23.8109i	−0.0819321	−	0.0595272i
$401$	−46.2384	−	63.6417i	−0.115308	−	0.158708i	0.747462	−	0.664305i	$-0.231272\pi$
$401$	−46.2384	−	63.6417i	−0.115308	−	0.158708i	−0.862770	+	0.505597i	$0.831272\pi$
$402$			296.491i			0.737540i
$403$	284.776	−	23.0324i	0.706641	−	0.0571525i
$404$	−106.234			−0.262956
$405$	2.36788	−	1.72037i	0.00584662	−	0.00424782i
$406$	−121.250	+	166.887i	−0.298646	+	0.411051i
$407$	186.438	−	573.798i	0.458080	−	1.40982i
$408$	−24.3107			−0.0595852
$409$		−	480.633i		−	1.17514i	−0.809173	−	0.587571i	$-0.800084\pi$
$409$		−	480.633i		−	1.17514i	0.809173	−	0.587571i	$-0.199916\pi$
$410$	142.696	−	439.173i	0.348039	−	1.07115i
$411$	54.3308	+	167.213i	0.132192	+	0.406844i
$412$	36.6533	+	112.807i	0.0889643	+	0.273804i
$413$	124.794	−	90.6683i	0.302165	−	0.219536i
$414$	142.036	+	46.1504i	0.343083	+	0.111474i
$415$	−103.914	−	143.025i	−0.250395	−	0.344639i
$416$	−144.601	+	199.027i	−0.347599	+	0.478430i
$417$	−42.1589	−	129.752i	−0.101100	−	0.311155i
$418$	−252.725	+	347.847i	−0.604606	+	0.832169i
$419$	−69.0155	−	50.1427i	−0.164715	−	0.119672i	0.502374	−	0.864650i	$-0.332460\pi$
$419$	−69.0155	−	50.1427i	−0.164715	−	0.119672i	−0.667089	+	0.744978i	$0.732460\pi$
$420$	−46.4200	+	15.0828i	−0.110524	+	0.0359114i
$421$	248.970	+	180.888i	0.591379	+	0.429662i	0.842808	−	0.538214i	$-0.180901\pi$
$421$	248.970	+	180.888i	0.591379	+	0.429662i	−0.251430	+	0.967876i	$0.580901\pi$
$422$	−145.651	+	105.821i	−0.345143	+	0.250761i
$423$	8.54226	−	26.2904i	0.0201945	−	0.0621522i
$424$	204.454	+	281.406i	0.482202	+	0.663694i
$425$	11.3901	−	3.70088i	0.0268003	−	0.00870795i
$426$	−163.434	+	53.1029i	−0.383648	+	0.124655i
$427$	−278.468	−	90.4798i	−0.652150	−	0.211896i
$428$	241.747			0.564830
$429$			243.645i			0.567936i
$430$	−149.557	−	48.5940i	−0.347807	−	0.113009i
$431$	−11.4520	−	8.32036i	−0.0265707	−	0.0193048i	0.574421	−	0.818560i	$-0.305227\pi$
$431$	−11.4520	−	8.32036i	−0.0265707	−	0.0193048i	−0.600991	+	0.799256i	$0.705227\pi$
$432$	82.2401	+	113.194i	0.190371	+	0.262023i
$433$		−	414.463i		−	0.957190i	−0.878036	−	0.478595i	$-0.841146\pi$
$433$		−	414.463i		−	0.957190i	0.878036	−	0.478595i	$-0.158854\pi$
$434$	81.7606	−	134.071i	0.188388	−	0.308920i
$435$	311.569			0.716252
$436$	228.128	−	165.745i	0.523230	−	0.380149i
$437$	218.599	−	300.875i	0.500226	−	0.688502i
$438$	−75.5576	+	232.543i	−0.172506	+	0.530919i
$439$	354.356			0.807190			0.403595	−	0.914938i	$-0.367760\pi$
$439$	354.356			0.807190			0.403595	+	0.914938i	$0.367760\pi$
$440$			509.967i			1.15901i
$441$	−64.1328	+	197.381i	−0.145426	+	0.447575i
$442$	6.41876	+	19.7549i	0.0145221	+	0.0446944i
$443$	22.0099	+	67.7395i	0.0496837	+	0.152911i	0.972820	−	0.231561i	$-0.0743834\pi$
$443$	22.0099	+	67.7395i	0.0496837	+	0.152911i	−0.923137	+	0.384472i	$0.874383\pi$
$444$	−116.074	+	84.3330i	−0.261429	+	0.189939i
$445$	−192.187	−	62.4455i	−0.431882	−	0.140327i
$446$	−267.711	−	368.473i	−0.600249	−	0.826172i
$447$	−45.1786	+	62.1830i	−0.101071	+	0.139112i
$448$	63.9608	+	196.851i	0.142770	+	0.439400i
$449$	388.723	−	535.031i	0.865752	−	1.19161i	−0.114415	−	0.993433i	$-0.536500\pi$
$449$	388.723	−	535.031i	0.865752	−	1.19161i	0.980167	−	0.198172i	$-0.0635005\pi$
$450$	−51.7936	−	37.6302i	−0.115097	−	0.0836228i
$451$	1034.30	−	336.064i	2.29335	−	0.745154i
$452$	−182.736	−	132.765i	−0.404283	−	0.293729i
$453$	−29.7980	+	21.6495i	−0.0657793	+	0.0477915i
$454$	193.159	−	594.481i	0.425460	−	1.30943i
$455$	77.5820	+	106.782i	0.170510	+	0.234687i
$456$	307.777	−	100.003i	0.674949	−	0.219304i
$457$	78.2123	−	25.4127i	0.171143	−	0.0556077i	−0.222192	−	0.975003i	$-0.571321\pi$
$457$	78.2123	−	25.4127i	0.171143	−	0.0556077i	0.393335	+	0.919395i	$0.371321\pi$
$458$	1.36761	+	0.444363i	0.00298604	+	0.000970224i
$459$	−41.3648			−0.0901195
$460$		−	139.369i		−	0.302977i
$461$	26.7061	+	8.67734i	0.0579308	+	0.0188229i	0.337839	−	0.941204i	$-0.390304\pi$
$461$	26.7061	+	8.67734i	0.0579308	+	0.0188229i	−0.279908	+	0.960027i	$0.590304\pi$
$462$	108.341	+	78.7141i	0.234504	+	0.170377i
$463$	213.250	+	293.513i	0.460583	+	0.633938i	0.974630	−	0.223824i	$-0.0718542\pi$
$463$	213.250	+	293.513i	0.460583	+	0.633938i	−0.514047	+	0.857762i	$0.671854\pi$
$464$		−	211.598i		−	0.456029i
$465$	−236.413	+	19.1209i	−0.508415	+	0.0411201i
$466$	521.248			1.11856
$467$	−576.186	+	418.624i	−1.23380	+	0.896411i	−0.997169	−	0.0751878i	$-0.976044\pi$
$467$	−576.186	+	418.624i	−1.23380	+	0.896411i	−0.236634	+	0.971599i	$0.576044\pi$
$468$	−56.0220	+	77.1077i	−0.119705	+	0.164760i
$469$	−116.893	+	359.760i	−0.249239	+	0.767080i
$470$	30.0531			0.0639427
$471$		−	183.286i		−	0.389143i
$472$	−118.437	+	364.512i	−0.250926	+	0.772272i
$473$	−114.444	−	352.222i	−0.241953	−	0.744656i
$474$	−125.095	−	385.001i	−0.263913	−	0.812239i
$475$	−128.977	+	93.7071i	−0.271530	+	0.197278i
$476$	−9.32024	−	3.02833i	−0.0195803	−	0.00636204i
$477$	133.393	+	183.600i	0.279651	+	0.384906i
$478$	205.603	−	282.989i	0.430133	−	0.592027i
$479$	−200.415	−	616.813i	−0.418402	−	1.28771i	−0.909172	−	0.416420i	$-0.863285\pi$
$479$	−200.415	−	616.813i	−0.418402	−	1.28771i	0.490770	−	0.871289i	$-0.336715\pi$
$480$	120.044	−	165.226i	0.250091	−	0.344221i
$481$	313.892	+	228.056i	0.652582	+	0.474129i
$482$	−454.319	+	147.617i	−0.942570	+	0.306260i
$483$	−93.7109	−	68.0849i	−0.194018	−	0.140963i
$484$	−126.137	+	91.6441i	−0.260614	+	0.189347i
$485$	−62.8608	+	193.466i	−0.129610	+	0.398898i
$486$	210.105	+	289.184i	0.432314	+	0.595029i
$487$	−684.840	+	222.518i	−1.40624	+	0.456916i	−0.911204	−	0.411955i	$-0.864846\pi$
$487$	−684.840	+	222.518i	−1.40624	+	0.456916i	−0.495038	+	0.868871i	$0.664846\pi$
$488$	691.902	−	224.813i	1.41783	−	0.460681i
$489$	294.901	+	95.8190i	0.603069	+	0.195949i
$490$	−225.630			−0.460469
$491$		−	201.155i		−	0.409684i	−0.978795	−	0.204842i	$-0.934332\pi$
$491$		−	201.155i		−	0.409684i	0.978795	−	0.204842i	$-0.0656681\pi$
$492$	−245.965	−	79.9187i	−0.499928	−	0.162436i
$493$	50.6098	+	36.7702i	0.102657	+	0.0745845i
$494$	−162.524	−	223.696i	−0.328997	−	0.452825i
$495$			332.722i			0.672165i
$496$	12.9856	+	160.556i	0.0261807	+	0.323702i
$497$	−219.246			−0.441139
$498$	93.3196	−	67.8007i	0.187389	−	0.136146i
$499$	−43.0223	+	59.2151i	−0.0862170	+	0.118668i	−0.849947	−	0.526869i	$-0.823366\pi$
$499$	−43.0223	+	59.2151i	−0.0862170	+	0.118668i	0.763730	+	0.645536i	$0.223366\pi$
$500$	−77.6642	+	239.026i	−0.155328	+	0.478052i
$501$	−130.868			−0.261213
$502$		−	268.574i		−	0.535008i
$503$	9.73355	−	29.9568i	0.0193510	−	0.0595562i	−0.940915	−	0.338644i	$-0.890032\pi$
$503$	9.73355	−	29.9568i	0.0193510	−	0.0595562i	0.960266	+	0.279087i	$0.0900319\pi$
$504$	51.2356	+	157.687i	0.101658	+	0.312871i
$505$	−73.6984	−	226.820i	−0.145937	−	0.449149i
$506$	−309.357	+	224.761i	−0.611377	+	0.444192i
$507$	147.470	+	47.9159i	0.290868	+	0.0945087i
$508$	−159.815	−	219.967i	−0.314597	−	0.433006i
$509$	−526.782	+	725.053i	−1.03494	+	1.42447i	−0.133759	+	0.991014i	$0.542705\pi$
$509$	−526.782	+	725.053i	−1.03494	+	1.42447i	−0.901177	+	0.433452i	$0.857295\pi$
$510$	−5.32867	−	16.3999i	−0.0104484	−	0.0321568i
$511$	−183.362	+	252.377i	−0.358831	+	0.493888i
$512$	−256.468	−	186.335i	−0.500915	−	0.363936i
$513$	523.684	−	170.155i	1.02083	−	0.331686i
$514$	225.373	+	163.743i	0.438470	+	0.318567i
$515$	−215.427	+	156.517i	−0.418304	+	0.303916i
$516$	−27.2157	+	83.7612i	−0.0527435	+	0.162328i
$517$	41.6024	+	57.2607i	0.0804688	+	0.110756i
$518$	202.818	−	65.8994i	0.391540	−	0.127219i
$519$	360.026	−	116.980i	0.693693	−	0.225394i
$520$	−311.902	−	101.343i	−0.599811	−	0.194890i
$521$	854.877			1.64084			0.820420	−	0.571762i	$-0.193740\pi$
$521$	854.877			1.64084			0.820420	+	0.571762i	$0.193740\pi$
$522$		−	334.405i		−	0.640622i
$523$	−613.920	−	199.475i	−1.17384	−	0.381405i	−0.343768	−	0.939055i	$-0.611703\pi$
$523$	−613.920	−	199.475i	−1.17384	−	0.381405i	−0.830076	+	0.557650i	$0.811703\pi$
$524$	95.1584	+	69.1366i	0.181600	+	0.131940i
$525$	29.1861	+	40.1712i	0.0555926	+	0.0765166i
$526$			41.5376i			0.0789688i
$527$	−40.6583	−	24.7946i	−0.0771505	−	0.0470486i
$528$	−137.366			−0.260164
$529$	−160.387	+	116.528i	−0.303189	+	0.220280i
$530$	−145.022	+	199.605i	−0.273626	+	0.376613i
$531$	−77.2730	+	237.822i	−0.145523	+	0.447875i
$532$	130.452			0.245211
$533$			699.375i			1.31215i
$534$	40.7438	−	125.397i	0.0762993	−	0.234825i
$535$	167.709	+	516.154i	0.313474	+	0.964774i
$536$	−290.441	−	893.887i	−0.541868	−	1.66770i
$537$	−158.765	+	115.349i	−0.295652	+	0.214803i
$538$	−394.476	−	128.173i	−0.733227	−	0.238240i
$539$	−312.338	−	429.897i	−0.579478	−	0.797583i
$540$	121.288	−	166.939i	0.224608	−	0.309147i
$541$	−21.6931	−	66.7644i	−0.0400981	−	0.123409i	0.929004	−	0.370071i	$-0.120666\pi$
$541$	−21.6931	−	66.7644i	−0.0400981	−	0.123409i	−0.969102	+	0.246661i	$0.920666\pi$
$542$	−64.3378	+	88.5534i	−0.118704	+	0.163383i
$543$	−205.804	−	149.525i	−0.379012	−	0.275368i
$544$	38.9986	−	12.6714i	0.0716887	−	0.0232931i
$545$	512.142	+	372.093i	0.939709	+	0.682739i
$546$	−69.6724	+	50.6200i	−0.127605	+	0.0927106i
$547$	−215.959	+	664.654i	−0.394807	+	1.21509i	0.534305	+	0.845292i	$0.320573\pi$
$547$	−215.959	+	664.654i	−0.394807	+	1.21509i	−0.929112	+	0.369799i	$0.879427\pi$
$548$	−103.508	−	142.466i	−0.188883	−	0.259975i
$549$	451.423	−	146.676i	0.822265	−	0.267170i
$550$	155.895	−	50.6535i	0.283446	−	0.0920973i
$551$	−791.981	−	257.330i	−1.43735	−	0.467024i
$552$	287.807			0.521390
$553$		−	516.478i		−	0.933957i
$554$	600.634	+	195.158i	1.08418	+	0.352270i
$555$	−260.584	−	189.325i	−0.469521	−	0.341127i
$556$	80.3188	+	110.549i	0.144458	+	0.198830i
$557$			744.534i			1.33669i	0.743853	+	0.668343i	$0.232996\pi$
$557$			744.534i			1.33669i	−0.743853	+	0.668343i	$0.767004\pi$
$558$	20.5223	+	253.740i	0.0367783	+	0.454731i
$559$	238.166			0.426058
$560$	−60.2037	+	43.7406i	−0.107507	+	0.0781081i
$561$	23.8707	−	32.8552i	0.0425503	−	0.0585654i
$562$	62.3081	−	191.764i	0.110868	−	0.341218i
$563$	672.379			1.19428			0.597140	−	0.802137i	$-0.296304\pi$
$563$	672.379			1.19428			0.597140	+	0.802137i	$0.296304\pi$
$564$		−	16.8316i		−	0.0298433i
$565$	156.697	−	482.262i	0.277339	−	0.853562i
$566$	−22.0938	−	67.9976i	−0.0390349	−	0.120137i
$567$	0.752908	+	2.31721i	0.00132788	+	0.00408679i
$568$	440.716	−	320.199i	0.775908	−	0.563730i
$569$	81.1903	+	26.3803i	0.142689	+	0.0463626i	0.379491	−	0.925195i	$-0.376099\pi$
$569$	81.1903	+	26.3803i	0.142689	+	0.0463626i	−0.236802	+	0.971558i	$0.576099\pi$
$570$	134.923	+	185.706i	0.236707	+	0.325799i
$571$	−16.3121	+	22.4517i	−0.0285676	+	0.0393199i	−0.823062	−	0.567952i	$-0.807736\pi$
$571$	−16.3121	+	22.4517i	−0.0285676	+	0.0393199i	0.794494	+	0.607272i	$0.207736\pi$
$572$	−75.4104	−	232.089i	−0.131836	−	0.405750i
$573$	−33.1007	+	45.5592i	−0.0577673	+	0.0795099i
$574$	310.988	+	225.946i	0.541792	+	0.393635i
$575$	−134.844	+	43.8135i	−0.234512	+	0.0761974i
$576$	−271.455	−	197.224i	−0.471276	−	0.342402i
$577$	632.893	−	459.823i	1.09687	−	0.796921i	0.116322	−	0.993212i	$-0.462890\pi$
$577$	632.893	−	459.823i	1.09687	−	0.796921i	0.980546	+	0.196291i	$0.0628896\pi$
$578$	−129.952	+	399.951i	−0.224830	+	0.691957i
$579$	196.098	+	269.906i	0.338684	+	0.466159i
$580$	−296.792	+	96.4337i	−0.511711	+	0.166265i
$581$	139.964	−	45.4772i	0.240902	−	0.0782740i
$582$	−126.231	−	41.0148i	−0.216891	−	0.0704722i
$583$	−581.065			−0.996680
$584$		−	775.106i		−	1.32724i
$585$	−203.497	−	66.1201i	−0.347858	−	0.113026i
$586$	486.237	+	353.272i	0.829756	+	0.602853i
$587$	−642.042	−	883.695i	−1.09377	−	1.50544i	−0.843395	−	0.537294i	$-0.819447\pi$
$587$	−642.042	−	883.695i	−1.09377	−	1.50544i	−0.250373	−	0.968149i	$-0.580553\pi$
$588$			126.367i			0.214909i
$589$	616.732	+	146.654i	1.04708	+	0.248987i
$590$	−271.859			−0.460778
$591$	−85.2461	+	61.9349i	−0.144240	+	0.104797i
$592$	−128.577	+	176.972i	−0.217192	+	0.298939i
$593$	129.086	−	397.287i	0.217684	−	0.669962i	−0.781268	−	0.624195i	$-0.785427\pi$
$593$	129.086	−	397.287i	0.217684	−	0.669962i	0.998952	−	0.0457665i	$-0.0145730\pi$
$594$	−566.156			−0.953124
$595$		−	22.0005i		−	0.0369756i
$596$	23.7897	−	73.2170i	0.0399155	−	0.122847i
$597$	134.012	+	412.447i	0.224476	+	0.690865i
$598$	−75.9896	−	233.872i	−0.127073	−	0.391090i
$599$	478.000	−	347.288i	0.797997	−	0.579779i	−0.112329	−	0.993671i	$-0.535831\pi$
$599$	478.000	−	347.288i	0.797997	−	0.579779i	0.910326	+	0.413892i	$0.135831\pi$
$600$	−117.336	−	38.1249i	−0.195561	−	0.0635415i
$601$	194.037	+	267.069i	0.322857	+	0.444375i	0.939337	−	0.342996i	$-0.111442\pi$
$601$	194.037	+	267.069i	0.322857	+	0.444375i	−0.616480	+	0.787371i	$0.711442\pi$
$602$	76.9441	−	105.905i	0.127814	−	0.175921i
$603$	−189.495	−	583.206i	−0.314254	−	0.967174i
$604$	21.6840	−	29.8455i	0.0359007	−	0.0494131i
$605$	−283.175	−	205.739i	−0.468058	−	0.340064i
$606$	147.994	−	48.0860i	0.244214	−	0.0793499i
$607$	439.177	+	319.081i	0.723520	+	0.525668i	0.887507	−	0.460794i	$-0.152435\pi$
$607$	439.177	+	319.081i	0.723520	+	0.525668i	−0.163987	+	0.986463i	$0.552435\pi$
$608$	−441.603	+	320.843i	−0.726321	+	0.527703i
$609$	−80.1482	+	246.671i	−0.131606	+	0.405043i
$610$	303.316	+	417.478i	0.497239	+	0.684390i
$611$	−43.2888	+	14.0654i	−0.0708491	+	0.0230203i
$612$	15.1090	−	4.90921i	0.0246879	−	0.00802159i
$613$	523.889	+	170.222i	0.854631	+	0.277686i	0.703384	−	0.710810i	$-0.251671\pi$
$613$	523.889	+	170.222i	0.854631	+	0.277686i	0.151247	+	0.988496i	$0.451671\pi$
$614$	82.5156			0.134390
$615$		−	580.600i		−	0.944066i
$616$	−403.743	−	131.184i	−0.655427	−	0.212961i
$617$	432.605	+	314.306i	0.701143	+	0.509410i	0.880304	−	0.474409i	$-0.157338\pi$
$617$	432.605	+	314.306i	0.701143	+	0.509410i	−0.179161	+	0.983820i	$0.557338\pi$
$618$	−102.123	−	140.560i	−0.165247	−	0.227443i
$619$			410.084i			0.662495i	0.943544	+	0.331247i	$0.107469\pi$
$619$			410.084i			0.662495i	−0.943544	+	0.331247i	$0.892531\pi$
$620$	219.282	−	91.3860i	0.353681	−	0.147397i
$621$	489.705			0.788575
$622$	−179.956	+	130.746i	−0.289318	+	0.210202i
$623$	98.8767	−	136.092i	0.158711	−	0.218446i
$624$	27.2981	−	84.0149i	0.0437470	−	0.134639i
$625$	−369.320			−0.590912
$626$		−	125.657i		−	0.200731i
$627$	−167.055	+	514.143i	−0.266436	+	0.820005i
$628$	56.7289	+	174.594i	0.0903326	+	0.278015i
$629$	−19.9846	−	61.5062i	−0.0317720	−	0.0977840i
$630$	−95.1448	+	69.1268i	−0.151024	+	0.109725i
$631$	−769.194	−	249.926i	−1.21901	−	0.396080i	−0.372288	−	0.928117i	$-0.621427\pi$
$631$	−769.194	−	249.926i	−1.21901	−	0.396080i	−0.846721	+	0.532037i	$0.821427\pi$
$632$	754.292	+	1038.19i	1.19350	+	1.64271i
$633$	−133.052	+	183.130i	−0.210192	+	0.289305i
$634$	−75.0629	−	231.020i	−0.118396	−	0.364385i
$635$	358.781	−	493.820i	0.565010	−	0.777669i
$636$	111.791	+	81.2212i	0.175773	+	0.127706i
$637$	325.000	−	105.599i	0.510203	−	0.165775i
$638$	692.690	+	503.269i	1.08572	+	0.788823i
$639$	287.540	−	208.910i	0.449984	−	0.326933i
$640$	−24.1272	+	74.2558i	−0.0376987	+	0.116025i
$641$	−455.154	−	626.465i	−0.710068	−	0.977325i	−0.999796	−	0.0202159i	$-0.993565\pi$
$641$	−455.154	−	626.465i	−0.710068	−	0.977325i	0.289727	−	0.957109i	$-0.406435\pi$
$642$	−336.775	+	109.425i	−0.524572	+	0.170444i
$643$	264.903	−	86.0723i	0.411980	−	0.133861i	−0.0956915	−	0.995411i	$-0.530506\pi$
$643$	264.903	−	86.0723i	0.411980	−	0.133861i	0.507672	+	0.861550i	$0.330506\pi$
$644$	110.339	+	35.8514i	0.171334	+	0.0556699i
$645$	−197.719			−0.306540
$646$			46.0882i			0.0713439i
$647$	−244.776	−	79.5325i	−0.378324	−	0.122925i	0.113681	−	0.993517i	$-0.463736\pi$
$647$	−244.776	−	79.5325i	−0.378324	−	0.122925i	−0.492005	+	0.870592i	$0.663736\pi$
$648$	−4.89763	−	3.55834i	−0.00755807	−	0.00549126i
$649$	−376.333	−	517.978i	−0.579866	−	0.798118i
$650$			105.414i			0.162175i
$651$	45.6769	−	192.088i	0.0701641	−	0.295066i
$652$	−310.571			−0.476336
$653$	−462.588	+	336.090i	−0.708405	+	0.514686i	−0.882659	−	0.470015i	$-0.844249\pi$
$653$	−462.588	+	336.090i	−0.708405	+	0.514686i	0.174254	+	0.984701i	$0.444249\pi$
$654$	−242.780	+	334.157i	−0.371223	+	0.510944i
$655$	−81.5986	+	251.135i	−0.124578	+	0.383412i
$656$	−394.306			−0.601076
$657$		−	505.709i		−	0.769724i
$658$	−7.73086	+	23.7932i	−0.0117490	+	0.0361598i
$659$	234.466	+	721.613i	0.355791	+	1.09501i	0.955549	+	0.294831i	$0.0952633\pi$
$659$	234.466	+	721.613i	0.355791	+	1.09501i	−0.599759	+	0.800181i	$0.704737\pi$
$660$	62.6035	+	192.674i	0.0948537	+	0.291930i
$661$	−815.622	+	592.584i	−1.23392	+	0.896497i	−0.997178	−	0.0750752i	$-0.976080\pi$
$661$	−815.622	+	592.584i	−1.23392	+	0.896497i	−0.236744	+	0.971572i	$0.576080\pi$
$662$	−477.039	−	154.999i	−0.720603	−	0.234138i
$663$	15.3509	+	21.1288i	0.0231538	+	0.0318684i
$664$	−214.931	+	295.827i	−0.323691	+	0.445522i
$665$	90.4994	+	278.528i	0.136089	+	0.418840i
$666$	−203.201	+	279.683i	−0.305107	+	0.419944i
$667$	−599.153	−	435.310i	−0.898280	−	0.652639i
$668$	124.661	−	40.5048i	0.186618	−	0.0606359i
$669$	−463.290	−	336.600i	−0.692511	−	0.503139i
$670$	539.351	−	391.862i	0.805002	−	0.584868i
$671$	−375.551	+	1155.83i	−0.559688	+	1.72254i
$672$	99.9302	+	137.542i	0.148706	+	0.204676i
$673$	−649.297	+	210.969i	−0.964780	+	0.313476i	−0.748707	−	0.662901i	$-0.769325\pi$
$673$	−649.297	+	210.969i	−0.964780	+	0.313476i	−0.216073	+	0.976377i	$0.569325\pi$
$674$	652.393	−	211.975i	0.967942	−	0.314503i
$675$	−199.648	−	64.8697i	−0.295775	−	0.0961032i
$676$	−155.306			−0.229743
$677$			149.853i			0.221349i	0.993857	+	0.110675i	$0.0353011\pi$
$677$			149.853i			0.221349i	−0.993857	+	0.110675i	$0.964699\pi$
$678$	314.662	+	102.240i	0.464103	+	0.150796i
$679$	−136.997	−	99.5344i	−0.201763	−	0.146590i
$680$	32.1307	+	44.2241i	0.0472510	+	0.0650354i
$681$		−	785.922i		−	1.15407i
$682$	−556.485	−	339.361i	−0.815961	−	0.497596i
$683$	619.114			0.906462			0.453231	−	0.891393i	$-0.350271\pi$
$683$	619.114			0.906462			0.453231	+	0.891393i	$0.350271\pi$
$684$	−171.088	+	124.302i	−0.250128	+	0.181729i
$685$	232.373	−	319.833i	0.339230	−	0.466910i
$686$	134.744	−	414.700i	0.196420	−	0.604519i
$687$	1.80802			0.00263176
$688$			134.278i			0.195171i
$689$	115.472	−	355.386i	0.167594	−	0.515800i
$690$	63.0844	+	194.154i	0.0914266	+	0.281382i
$691$	−154.326	−	474.965i	−0.223337	−	0.687359i	−0.998456	−	0.0555447i	$-0.982310\pi$
$691$	−154.326	−	474.965i	−0.223337	−	0.687359i	0.775120	−	0.631814i	$-0.217690\pi$
$692$	−306.745	+	222.863i	−0.443273	+	0.322057i
$693$	−263.417	−	85.5895i	−0.380112	−	0.123506i
$694$	−240.949	−	331.638i	−0.347189	−	0.477865i
$695$	−180.313	+	248.180i	−0.259444	+	0.357094i
$696$	−199.142	−	612.896i	−0.286124	−	0.880598i
$697$	68.5201	−	94.3099i	0.0983072	−	0.135308i
$698$	−366.818	−	266.509i	−0.525528	−	0.381818i
$699$	623.302	−	202.523i	0.891706	−	0.289733i
$700$	−40.2352	−	29.2326i	−0.0574789	−	0.0417609i
$701$	−327.624	+	238.033i	−0.467367	+	0.339562i	−0.796414	−	0.604751i	$-0.793272\pi$
$701$	−327.624	+	238.033i	−0.467367	+	0.339562i	0.329047	+	0.944313i	$0.393272\pi$
$702$	112.509	−	346.268i	0.160269	−	0.493259i
$703$	506.014	+	696.468i	0.719792	+	0.990708i
$704$	817.062	−	265.480i	1.16060	−	0.377102i
$705$	35.9371	−	11.6767i	0.0509746	−	0.0165626i
$706$	819.172	+	266.165i	1.16030	+	0.377004i
$707$	198.533			0.280810
$708$			152.258i			0.215054i
$709$	−132.389	−	43.0157i	−0.186726	−	0.0606709i	0.214161	−	0.976798i	$-0.431298\pi$
$709$	−132.389	−	43.0157i	−0.186726	−	0.0606709i	−0.400887	+	0.916127i	$0.631298\pi$
$710$	312.605	+	227.121i	0.440289	+	0.319889i
$711$	492.129	+	677.358i	0.692165	+	0.952683i
$712$			417.969i			0.587035i
$713$	481.340	+	293.535i	0.675092	+	0.411690i
$714$	14.3547			0.0201046
$715$	443.218	−	322.017i	0.619885	−	0.450373i
$716$	115.533	−	159.018i	0.161359	−	0.222092i
$717$	135.907	−	418.279i	0.189549	−	0.583373i
$718$	378.644			0.527360
$719$			372.976i			0.518742i	0.965778	+	0.259371i	$0.0835153\pi$
$719$			372.976i			0.518742i	−0.965778	+	0.259371i	$0.916485\pi$
$720$	37.2783	−	114.731i	0.0517755	−	0.159349i
$721$	−68.4985	−	210.817i	−0.0950048	−	0.292395i
$722$	−25.9206	−	79.7754i	−0.0359011	−	0.110492i
$723$	−485.914	+	353.037i	−0.672081	+	0.488295i
$724$	242.322	+	78.7353i	0.334699	+	0.108750i
$725$	186.605	+	256.840i	0.257386	+	0.354262i
$726$	134.238	−	184.763i	0.184901	−	0.254495i
$727$	−94.1007	−	289.612i	−0.129437	−	0.398366i	0.865246	−	0.501347i	$-0.167162\pi$
$727$	−94.1007	−	289.612i	−0.129437	−	0.398366i	−0.994683	+	0.102981i	$0.967162\pi$
$728$	160.467	−	220.864i	0.220422	−	0.303385i
$729$	358.460	+	260.437i	0.491715	+	0.357252i
$730$	522.884	−	169.895i	0.716279	−	0.232733i
$731$	−32.1164	−	23.3340i	−0.0439349	−	0.0319206i
$732$	233.814	−	169.876i	0.319418	−	0.232071i
$733$	53.3882	−	164.312i	0.0728352	−	0.224164i	−0.908011	−	0.418945i	$-0.862400\pi$
$733$	53.3882	−	164.312i	0.0728352	−	0.224164i	0.980847	+	0.194782i	$0.0623998\pi$
$734$	68.9032	+	94.8371i	0.0938735	+	0.129206i
$735$	−269.805	+	87.6650i	−0.367082	+	0.119272i
$736$	−461.692	+	150.013i	−0.627299	+	0.203822i
$737$	1493.24	+	485.184i	2.02611	+	0.658323i
$738$	−623.154			−0.844382
$739$		−	709.952i		−	0.960693i	−0.877079	−	0.480346i	$-0.840511\pi$
$739$		−	709.952i		−	0.960693i	0.877079	−	0.480346i	$-0.159489\pi$
$740$	306.823	+	99.6929i	0.414626	+	0.134720i
$741$	−281.258	−	204.346i	−0.379566	−	0.275771i
$742$	−120.723	−	166.161i	−0.162699	−	0.223936i
$743$		−	782.674i		−	1.05340i	−0.850052	−	0.526698i	$-0.823430\pi$
$743$		−	782.674i		−	1.05340i	0.850052	−	0.526698i	$-0.176570\pi$
$744$	188.718	+	452.833i	0.253654	+	0.608646i
$745$	172.829			0.231985
$746$	−452.659	+	328.876i	−0.606782	+	0.440853i
$747$	−140.229	+	193.009i	−0.187723	+	0.258379i
$748$	−12.5696	+	38.6852i	−0.0168042	+	0.0517181i
$749$	−451.783			−0.603181
$750$		−	368.138i		−	0.490851i
$751$	281.220	−	865.505i	0.374460	−	1.15247i	−0.569382	−	0.822073i	$-0.692817\pi$
$751$	281.220	−	865.505i	0.374460	−	1.15247i	0.943842	−	0.330397i	$-0.107183\pi$
$752$	−7.93003	−	24.4061i	−0.0105452	−	0.0324549i
$753$	−104.350	−	321.157i	−0.138580	−	0.426504i
$754$	−445.460	+	323.646i	−0.590796	+	0.429238i
$755$	78.7660	+	25.5926i	0.104326	+	0.0338975i
$756$	100.966	+	138.968i	0.133553	+	0.183820i
$757$	843.357	−	1160.78i	1.11408	−	1.53340i	0.298809	−	0.954313i	$-0.403411\pi$
$757$	843.357	−	1160.78i	1.11408	−	1.53340i	0.815268	−	0.579083i	$-0.196589\pi$
$758$	162.922	+	501.423i	0.214937	+	0.661508i
$759$	−282.598	+	388.962i	−0.372329	+	0.512467i
$760$	−588.694	−	427.711i	−0.774598	−	0.562778i
$761$	−805.298	+	261.657i	−1.05821	+	0.343834i	−0.785886	−	0.618372i	$-0.787793\pi$
$761$	−805.298	+	261.657i	−1.05821	+	0.343834i	−0.272325	+	0.962205i	$0.587793\pi$
$762$	322.203	+	234.094i	0.422839	+	0.307210i
$763$	−426.331	+	309.748i	−0.558756	+	0.405960i
$764$	17.4298	−	53.6434i	0.0228139	−	0.0702138i
$765$	20.9633	+	28.8535i	0.0274030	+	0.0377170i
$766$	16.5396	−	5.37403i	0.0215921	−	0.00701570i
$767$	391.589	−	127.235i	0.510546	−	0.165886i
$768$	−469.117	−	152.425i	−0.610829	−	0.198470i
$769$	−214.787			−0.279307			−0.139654	−	0.990200i	$-0.544599\pi$
$769$	−214.787			−0.279307			−0.139654	+	0.990200i	$0.544599\pi$
$770$		−	301.118i		−	0.391062i
$771$	333.119	+	108.237i	0.432060	+	0.140385i
$772$	−270.336	−	196.411i	−0.350176	−	0.254418i
$773$	−432.607	−	595.433i	−0.559647	−	0.770289i	0.431634	−	0.902049i	$-0.357937\pi$
$773$	−432.607	−	595.433i	−0.559647	−	0.770289i	−0.991282	+	0.131760i	$0.957937\pi$
$774$			212.210i			0.274173i
$775$	−157.355	−	183.433i	−0.203038	−	0.236688i
$776$	420.749			0.542203
$777$	216.923	−	157.603i	0.279180	−	0.202836i
$778$	−177.092	+	243.746i	−0.227624	+	0.313298i
$779$	−479.527	+	1475.83i	−0.615567	+	1.89452i
$780$	−130.282			−0.167029
$781$			910.016i			1.16519i
$782$	−12.6661	+	38.9823i	−0.0161971	+	0.0498495i
$783$	−338.841	−	1042.85i	−0.432747	−	1.33186i
$784$	59.5363	+	183.234i	0.0759392	+	0.233717i
$785$	−333.419	+	242.243i	−0.424738	+	0.308590i
$786$	−163.858	−	53.2407i	−0.208471	−	0.0677363i
$787$	124.783	+	171.749i	0.158555	+	0.218232i	0.880902	−	0.473298i	$-0.156937\pi$
$787$	124.783	+	171.749i	0.158555	+	0.218232i	−0.722347	+	0.691530i	$0.756937\pi$
$788$	62.0336	−	85.3819i	0.0787228	−	0.108353i
$789$	16.1388	+	49.6701i	0.0204548	+	0.0629533i
$790$	−535.029	+	736.404i	−0.677252	+	0.932157i
$791$	341.501	+	248.115i	0.431733	+	0.313672i
$792$	654.506	−	212.662i	0.826396	−	0.268512i
$793$	−632.286	−	459.383i	−0.797335	−	0.579298i
$794$	−843.427	+	612.786i	−1.06225	+	0.771770i
$795$	−95.8614	+	295.031i	−0.120580	+	0.371108i
$796$	−255.312	−	351.407i	−0.320744	−	0.441466i
$797$	−80.3901	+	26.1203i	−0.100866	+	0.0327733i	−0.359015	−	0.933332i	$-0.616887\pi$
$797$	−80.3901	+	26.1203i	−0.100866	+	0.0327733i	0.258149	+	0.966105i	$0.416887\pi$
$798$	−181.732	+	59.0482i	−0.227734	+	0.0739952i
$799$	7.21547	+	2.34445i	0.00903063	+	0.00293423i
$800$	208.100			0.260125
$801$			272.699i			0.340448i
$802$	−109.763	−	35.6640i	−0.136861	−	0.0444689i
$803$	1047.53	+	761.076i	1.30452	+	0.947790i
$804$	−219.467	−	302.070i	−0.272969	−	0.375709i
$805$			260.456i			0.323548i
$806$	318.144	−	272.914i	0.394720	−	0.338603i
$807$	−521.509			−0.646232
$808$	−399.079	+	289.948i	−0.493910	+	0.358847i
$809$	−531.248	+	731.201i	−0.656673	+	0.903833i	−0.999366	−	0.0356150i	$-0.988661\pi$
$809$	−531.248	+	731.201i	−0.656673	+	0.903833i	0.342693	+	0.939448i	$0.388661\pi$
$810$	1.32693	−	4.08388i	0.00163819	−	0.00504182i
$811$	−13.2753			−0.0163690			−0.00818450	−	0.999967i	$-0.502605\pi$
$811$	−13.2753			−0.0163690			−0.00818450	+	0.999967i	$0.502605\pi$
$812$		−	259.778i		−	0.319924i
$813$	−42.5282	+	130.888i	−0.0523103	+	0.160994i
$814$	−273.526	−	841.827i	−0.336027	−	1.03419i
$815$	−215.454	−	663.099i	−0.264361	−	0.813618i
$816$	−11.9123	+	8.65482i	−0.0145985	+	0.0106064i
$817$	502.582	+	163.299i	0.615156	+	0.199876i
$818$	−414.472	−	570.472i	−0.506690	−	0.697399i
$819$	104.695	−	144.100i	0.127833	−	0.175947i
$820$	179.701	+	553.064i	0.219148	+	0.674468i
$821$	−290.078	+	399.258i	−0.353323	+	0.486307i	−0.948273	−	0.317455i	$-0.897172\pi$
$821$	−290.078	+	399.258i	−0.353323	+	0.486307i	0.594950	+	0.803762i	$0.297172\pi$
$822$	208.682	+	151.616i	0.253871	+	0.184448i
$823$	920.846	−	299.201i	1.11889	−	0.363549i	0.309546	−	0.950885i	$-0.399823\pi$
$823$	920.846	−	299.201i	1.11889	−	0.363549i	0.809344	+	0.587335i	$0.199823\pi$
$824$	445.580	+	323.732i	0.540752	+	0.392879i
$825$	166.737	−	121.142i	0.202106	−	0.146838i
$826$	69.9331	−	215.232i	0.0846648	−	0.260571i
$827$	−606.565	−	834.865i	−0.733452	−	1.00951i	−0.998969	−	0.0454043i	$-0.985542\pi$
$827$	−606.565	−	834.865i	−0.733452	−	1.00951i	0.265516	−	0.964106i	$-0.414458\pi$
$828$	−178.871	+	58.1186i	−0.216027	+	0.0701915i
$829$	−184.738	+	60.0251i	−0.222845	+	0.0724067i	−0.418311	−	0.908304i	$-0.637378\pi$
$829$	−184.738	+	60.0251i	−0.222845	+	0.0724067i	0.195467	+	0.980710i	$0.437378\pi$
$830$	−246.675	−	80.1494i	−0.297198	−	0.0965656i
$831$	794.056			0.955543
$832$			552.483i			0.664042i
$833$	−54.1717	−	17.6014i	−0.0650320	−	0.0211302i
$834$	−161.930	−	117.649i	−0.194161	−	0.141066i
$835$	172.963	+	238.063i	0.207142	+	0.285106i
$836$		−	541.464i		−	0.647684i
$837$	321.105	+	770.497i	0.383638	+	0.920545i
$838$	−125.156			−0.149351
$839$	−126.468	+	91.8842i	−0.150736	+	0.109516i	−0.660597	−	0.750740i	$-0.729697\pi$
$839$	−126.468	+	91.8842i	−0.150736	+	0.109516i	0.509861	+	0.860257i	$0.329697\pi$
$840$	−133.215	+	183.355i	−0.158590	+	0.218280i
$841$	−252.555	+	777.285i	−0.300303	+	0.924239i
$842$	451.496			0.536218
$843$		−	253.518i		−	0.300734i
$844$	70.0609	−	215.625i	0.0830106	−	0.255480i
$845$	−107.741	−	331.594i	−0.127505	−	0.392419i
$846$	−12.5325	−	38.5710i	−0.0148138	−	0.0455922i
$847$	235.728	−	171.267i	0.278310	−	0.202204i
$848$	200.366	+	65.1028i	0.236281	+	0.0767722i
$849$	−52.8389	−	72.7265i	−0.0622366	−	0.0856614i
$850$	10.3277	−	14.2149i	0.0121503	−	0.0167234i
$851$	236.591	+	728.152i	0.278015	+	0.855642i
$852$	127.202	−	175.079i	0.149298	−	0.205491i
$853$	262.545	+	190.750i	0.307790	+	0.223623i	0.730948	−	0.682433i	$-0.239078\pi$
$853$	262.545	+	190.750i	0.307790	+	0.223623i	−0.423158	+	0.906056i	$0.639078\pi$
$854$	−408.544	+	132.744i	−0.478389	+	0.155438i
$855$	−384.087	−	279.055i	−0.449224	−	0.326381i
$856$	908.147	−	659.808i	1.06092	−	0.770803i
$857$	292.610	−	900.560i	0.341435	−	1.05083i	−0.622030	−	0.782993i	$-0.713692\pi$
$857$	292.610	−	900.560i	0.341435	−	1.05083i	0.963465	−	0.267835i	$-0.0863081\pi$
$858$	210.106	+	289.187i	0.244879	+	0.337047i
$859$	934.896	−	303.766i	1.08835	−	0.353628i	0.290744	−	0.956801i	$-0.406097\pi$
$859$	934.896	−	303.766i	1.08835	−	0.353628i	0.797610	+	0.603173i	$0.206097\pi$
$860$	188.341	−	61.1958i	0.219001	−	0.0711579i
$861$	459.664	+	149.354i	0.533872	+	0.173466i
$862$	−20.7676			−0.0240924
$863$			581.969i			0.674355i	0.941441	+	0.337178i	$0.109472\pi$
$863$			581.969i			0.674355i	−0.941441	+	0.337178i	$0.890528\pi$
$864$	−683.575	−	222.107i	−0.791175	−	0.257068i
$865$	−688.634	−	500.322i	−0.796108	−	0.578407i
$866$	−357.411	−	491.935i	−0.412715	−	0.568054i
$867$			528.747i			0.609859i
$868$	15.9425	+	197.115i	0.0183669	+	0.227091i
$869$	−2143.73			−2.46689
$870$	369.808	−	268.681i	0.425067	−	0.308829i
$871$	−593.489	+	816.868i	−0.681388	+	0.937851i
$872$	404.614	−	1245.27i	0.464007	−	1.42807i
$873$	274.513			0.314448
$874$		−	545.623i		−	0.624283i
$875$	145.141	−	446.697i	0.165875	−	0.510510i
$876$	−95.1519	−	292.847i	−0.108621	−	0.334301i
$877$	443.166	+	1363.93i	0.505321	+	1.55522i	0.800230	+	0.599693i	$0.204711\pi$
$877$	443.166	+	1363.93i	0.505321	+	1.55522i	−0.294909	+	0.955525i	$0.595289\pi$
$878$	420.593	−	305.578i	0.479035	−	0.348039i
$879$	718.695	+	233.518i	0.817628	+	0.265663i
$880$	181.552	+	249.885i	0.206309	+	0.283960i
$881$	594.355	−	818.060i	0.674637	−	0.928559i	−0.325217	−	0.945639i	$-0.605437\pi$
$881$	594.355	−	818.060i	0.674637	−	0.928559i	0.999854	+	0.0170809i	$0.00543729\pi$
$882$	94.0901	+	289.580i	0.106678	+	0.328322i
$883$	253.066	−	348.316i	0.286598	−	0.394468i	−0.641307	−	0.767284i	$-0.721608\pi$
$883$	253.066	−	348.316i	0.286598	−	0.394468i	0.927905	+	0.372816i	$0.121608\pi$
$884$	−21.1624	−	15.3754i	−0.0239394	−	0.0173930i
$885$	−325.085	+	105.627i	−0.367328	+	0.119352i
$886$	84.5389	+	61.4211i	0.0954164	+	0.0693241i
$887$	−637.301	+	463.026i	−0.718490	+	0.522014i	−0.885901	−	0.463874i	$-0.846459\pi$
$887$	−637.301	+	463.026i	−0.718490	+	0.522014i	0.167411	+	0.985887i	$0.446459\pi$
$888$	−205.873	+	633.610i	−0.231838	+	0.713525i
$889$	298.667	+	411.079i	0.335958	+	0.462406i
$890$	−281.961	+	91.6146i	−0.316810	+	0.102938i
$891$	9.61796	−	3.12506i	0.0107946	−	0.00350737i
$892$	545.498	+	177.243i	0.611545	+	0.198703i
$893$	−100.993			−0.113094
$894$			112.766i			0.126136i
$895$	419.668	+	136.358i	0.468903	+	0.152356i
$896$	−52.5822	−	38.2032i	−0.0586855	−	0.0426375i
$897$	−181.735	−	250.137i	−0.202603	−	0.278859i
$898$		−	970.252i		−	1.08046i
$899$	292.041	−	1228.14i	0.324851	−	1.36612i
$900$	80.6227			0.0895808
$901$	−50.3897	+	36.6102i	−0.0559264	+	0.0406329i
$902$	937.827	−	1290.81i	1.03972	−	1.43105i
$903$	50.8612	−	156.535i	0.0563247	−	0.173350i
$904$	−1048.82			−1.16020
$905$			572.003i			0.632047i
$906$	−16.6984	+	51.3925i	−0.0184310	+	0.0567247i
$907$	300.044	+	923.442i	0.330810	+	1.01813i	0.968749	+	0.248042i	$0.0797869\pi$
$907$	300.044	+	923.442i	0.330810	+	1.01813i	−0.637940	+	0.770086i	$0.720213\pi$
$908$	243.250	+	748.647i	0.267897	+	0.824501i
$909$	−260.375	+	189.173i	−0.286441	+	0.208111i
$910$	184.167	+	59.8396i	0.202382	+	0.0657578i
$911$	78.3571	+	107.849i	0.0860122	+	0.118386i	0.849855	−	0.527017i	$-0.176690\pi$
$911$	78.3571	+	107.849i	0.0860122	+	0.118386i	−0.763843	+	0.645403i	$0.776690\pi$
$912$	115.210	−	158.573i	0.126327	−	0.173874i
$913$	−188.760	−	580.945i	−0.206747	−	0.636303i
$914$	70.9171	−	97.6091i	0.0775899	−	0.106793i
$915$	524.906	+	381.366i	0.573667	+	0.416794i
$916$	−1.72227	+	0.559599i	−0.00188020	+	0.000610916i
$917$	−177.834	−	129.204i	−0.193930	−	0.140899i
$918$	−49.0967	+	35.6709i	−0.0534823	+	0.0388572i
$919$	354.402	−	1090.74i	0.385638	−	1.18687i	−0.550378	−	0.834916i	$-0.685516\pi$
$919$	354.402	−	1090.74i	0.385638	−	1.18687i	0.936016	−	0.351957i	$-0.114484\pi$
$920$	−380.384	−	523.554i	−0.413461	−	0.569081i
$921$	98.6711	−	32.0602i	0.107135	−	0.0348102i
$922$	39.1809	−	12.7306i	0.0424956	−	0.0138076i
$923$	−556.577	−	180.843i	−0.603009	−	0.195929i
$924$	−168.645			−0.182516
$925$		−	328.201i		−	0.354812i
$926$	506.221	+	164.481i	0.546675	+	0.177625i
$927$	290.713	+	211.216i	0.313606	+	0.227848i
$928$	638.917	+	879.394i	0.688488	+	0.947622i
$929$		−	1665.59i		−	1.79288i	−0.443162	−	0.896441i	$-0.646143\pi$
$929$		−	1665.59i		−	1.79288i	0.443162	−	0.896441i	$-0.353857\pi$
$930$	−264.114	+	226.565i	−0.283994	+	0.243618i
$931$	758.224			0.814419
$932$	−531.058	+	385.836i	−0.569804	+	0.413987i
$933$	−164.390	+	226.263i	−0.176195	+	0.242512i
$934$	−322.888	+	993.746i	−0.345704	+	1.06397i
$935$	−91.3165			−0.0976647
$936$			442.565i			0.472826i
$937$	173.875	−	535.132i	0.185566	−	0.571112i	−0.814392	−	0.580315i	$-0.802929\pi$
$937$	173.875	−	535.132i	0.185566	−	0.571112i	0.999958	+	0.00920275i	$0.00292937\pi$
$938$	171.496	+	527.809i	0.182831	+	0.562697i
$939$	−48.8223	−	150.260i	−0.0519939	−	0.160021i
$940$	−30.6186	+	22.2457i	−0.0325730	+	0.0236657i
$941$	−567.485	−	184.387i	−0.603066	−	0.195948i	−0.00845860	−	0.999964i	$-0.502692\pi$
$941$	−567.485	−	184.387i	−0.603066	−	0.195948i	−0.594607	+	0.804016i	$0.702692\pi$
$942$	−158.057	−	217.546i	−0.167788	−	0.230941i
$943$	−811.188	+	1116.50i	−0.860220	+	1.18399i
$944$	71.7347	+	220.777i	0.0759902	+	0.233874i
$945$	−226.667	+	311.980i	−0.239859	+	0.330137i
$946$	−439.574	−	319.369i	−0.464666	−	0.337599i
$947$	−1296.15	+	421.143i	−1.36869	+	0.444713i	−0.898933	−	0.438086i	$-0.855657\pi$
$947$	−1296.15	+	421.143i	−1.36869	+	0.444713i	−0.469752	+	0.882798i	$0.655657\pi$
$948$	412.432	+	299.650i	0.435055	+	0.316086i
$949$	−673.653	+	489.438i	−0.709856	+	0.515741i
$950$	−72.2770	+	222.446i	−0.0760810	+	0.234153i
$951$	−179.519	−	247.086i	−0.188768	−	0.259817i
$952$	−43.2777	+	14.0618i	−0.0454598	+	0.0147708i
$953$	−603.483	+	196.083i	−0.633245	+	0.205754i	−0.608012	−	0.793928i	$-0.708033\pi$
$953$	−603.483	+	196.083i	−0.633245	+	0.205754i	−0.0252332	+	0.999682i	$0.508033\pi$
$954$	316.655	+	102.887i	0.331923	+	0.107848i
$955$	126.625			0.132592
$956$			440.505i			0.460779i
$957$	1023.85	+	332.668i	1.06985	+	0.347616i
$958$	−769.783	−	559.280i	−0.803531	−	0.583800i
$959$	193.438	+	266.244i	0.201708	+	0.277627i
$960$		−	458.655i		−	0.477766i
$961$	−146.225	+	949.810i	−0.152159	+	0.988356i
$962$	569.228			0.591713
$963$	592.510	−	430.484i	0.615276	−	0.447024i
$964$	353.600	−	486.689i	0.366805	−	0.504864i
$965$	231.814	−	713.450i	0.240222	−	0.739327i
$966$	−169.940			−0.175922
$967$		−	535.924i		−	0.554213i	−0.960839	−	0.277107i	$-0.910624\pi$
$967$		−	535.924i		−	0.554213i	0.960839	−	0.277107i	$-0.0893755\pi$
$968$	−223.720	+	688.540i	−0.231116	+	0.711302i
$969$	17.9069	+	55.1116i	0.0184797	+	0.0568748i
$970$	92.2239	+	283.836i	0.0950762	+	0.292614i
$971$	842.284	−	611.955i	0.867439	−	0.630232i	−0.0624592	−	0.998048i	$-0.519894\pi$
$971$	842.284	−	611.955i	0.867439	−	0.630232i	0.929899	+	0.367816i	$0.119894\pi$
$972$	−428.117	−	139.104i	−0.440449	−	0.143111i
$973$	−150.101	−	206.597i	−0.154267	−	0.212330i
$974$	−620.962	+	854.681i	−0.637538	+	0.877496i
$975$	40.9569	+	126.052i	0.0420070	+	0.129284i
$976$	258.999	−	356.482i	0.265368	−	0.365248i
$977$	−504.334	−	366.420i	−0.516207	−	0.375046i	0.298966	−	0.954264i	$-0.403358\pi$
$977$	−504.334	−	366.420i	−0.516207	−	0.375046i	−0.815173	+	0.579218i	$0.803358\pi$
$978$	432.653	−	140.577i	0.442385	−	0.143740i
$979$	−564.872	−	410.404i	−0.576989	−	0.419207i
$980$	229.876	−	167.015i	0.234567	−	0.170423i
$981$	263.986	−	812.464i	0.269098	−	0.828200i
$982$	−173.465	−	238.755i	−0.176645	−	0.243131i
$983$	−478.127	+	155.353i	−0.486395	+	0.158039i	−0.541941	−	0.840417i	$-0.682310\pi$
$983$	−478.127	+	155.353i	−0.486395	+	0.158039i	0.0555453	+	0.998456i	$0.482310\pi$
$984$	−1142.11	+	371.095i	−1.16069	+	0.377129i
$985$	225.333	+	73.2153i	0.228765	+	0.0743302i
$986$	91.7784			0.0930816
$987$			31.4553i			0.0318696i
$988$	331.166	+	107.602i	0.335188	+	0.108909i
$989$	380.216	+	276.243i	0.384445	+	0.279316i
$990$	286.922	+	394.914i	0.289820	+	0.398903i
$991$			1685.38i			1.70068i	0.526232	+	0.850341i	$0.323604\pi$
$991$			1685.38i			1.70068i	−0.526232	+	0.850341i	$0.676396\pi$
$992$	−538.766	−	628.057i	−0.543110	−	0.633122i
$993$	−630.660			−0.635106
$994$	−260.228	+	189.066i	−0.261798	+	0.190208i
$995$	573.169	−	788.899i	0.576049	−	0.792864i
$996$	−44.8887	+	138.153i	−0.0450690	+	0.138708i
$997$	−368.804			−0.369913			−0.184957	−	0.982747i	$-0.559214\pi$
$997$	−368.804			−0.369913			−0.184957	+	0.982747i	$0.559214\pi$
$998$			107.384i			0.107599i
$999$	−350.293	+	1078.09i	−0.350644	+	1.07917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.3.f.a.15.4	✓	20
3.2	odd	2		279.3.v.a.46.2		20
31.29	odd	10	inner	31.3.f.a.29.4	yes	20
93.29	even	10		279.3.v.a.91.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.3.f.a.15.4	✓	20	1.1	even	1	trivial
31.3.f.a.29.4	yes	20	31.29	odd	10	inner
279.3.v.a.46.2		20	3.2	odd	2
279.3.v.a.91.2		20	93.29	even	10

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	31.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18692 - 0.862348i) q^{2} +(1.08425 - 1.49234i) q^{3} +(-0.570933 + 1.75715i) q^{4} -4.14776 q^{5} -2.70629i q^{6} +(1.06697 - 3.28380i) q^{7} +(2.65108 + 8.15917i) q^{8} +(1.72966 + 5.32336i) q^{9} +(-4.92306 + 3.57681i) q^{10} +(-13.6300 - 4.42864i) q^{11} +(2.00324 + 2.75722i) q^{12} +(5.41722 - 7.45616i) q^{13} +(-1.56537 - 4.81771i) q^{14} +(-4.49722 + 6.18989i) q^{15} +(4.20377 + 3.05422i) q^{16} +(-1.46101 + 0.474711i) q^{17} +(6.64356 + 4.82683i) q^{18} +(16.5438 - 12.0198i) q^{19} +(2.36809 - 7.28825i) q^{20} +(-3.74370 - 5.15276i) q^{21} +(-19.9967 + 6.49732i) q^{22} +(17.2964 - 5.61995i) q^{23} +(15.0507 + 4.89028i) q^{24} -7.79606 q^{25} -13.5214i q^{26} +(25.6089 + 8.32083i) q^{27} +(5.16097 + 3.74966i) q^{28} +(-23.9358 - 32.9448i) q^{29} +11.2251i q^{30} +(20.1838 + 23.5290i) q^{31} -26.6929 q^{32} +(-21.3873 + 15.5388i) q^{33} +(-1.32474 + 1.82334i) q^{34} +(-4.42555 + 13.6204i) q^{35} -10.3415 q^{36} +42.0983i q^{37} +(9.27096 - 28.5331i) q^{38} +(-5.25353 - 16.1687i) q^{39} +(-10.9960 - 33.8423i) q^{40} +(-61.3917 + 44.6037i) q^{41} +(-8.88693 - 2.88754i) q^{42} +(15.1894 + 20.9064i) q^{43} +(15.5636 - 21.4214i) q^{44} +(-7.17423 - 22.0800i) q^{45} +(15.6831 - 21.5860i) q^{46} +(-3.99548 - 2.90289i) q^{47} +(9.11588 - 2.96193i) q^{48} +(29.9969 + 21.7940i) q^{49} +(-9.25330 + 6.72292i) q^{50} +(-0.875671 + 2.69504i) q^{51} +(10.0087 + 13.7758i) q^{52} +(38.5605 - 12.5291i) q^{53} +(37.5711 - 12.2076i) q^{54} +(56.5338 + 18.3689i) q^{55} +29.6217 q^{56} -37.7216i q^{57} +(-56.8198 - 18.4619i) q^{58} +(36.1430 + 26.2594i) q^{59} +(-8.30896 - 11.4363i) q^{60} -84.8005i q^{61} +(44.2468 + 10.5215i) q^{62} +19.3264 q^{63} +(-48.4974 + 35.2354i) q^{64} +(-22.4693 + 30.9264i) q^{65} +(-11.9852 + 36.8867i) q^{66} -109.556 q^{67} -2.83825i q^{68} +(10.3668 - 31.9057i) q^{69} +(6.49278 + 19.9827i) q^{70} +(-19.6220 - 60.3903i) q^{71} +(-38.8487 + 28.2252i) q^{72} +(-85.9266 - 27.9192i) q^{73} +(36.3034 + 49.9674i) q^{74} +(-8.45289 + 11.6344i) q^{75} +(11.6752 + 35.9325i) q^{76} +(-29.0856 + 40.0328i) q^{77} +(-20.1786 - 14.6606i) q^{78} +(142.262 - 46.2236i) q^{79} +(-17.4362 - 12.6682i) q^{80} +(-0.570882 + 0.414770i) q^{81} +(-34.4032 + 105.882i) q^{82} +(25.0530 + 34.4824i) q^{83} +(11.1916 - 3.63636i) q^{84} +(6.05993 - 1.96899i) q^{85} +(36.0572 + 11.7157i) q^{86} -75.1175 q^{87} -122.950i q^{88} +(46.3352 + 15.0552i) q^{89} +(-27.5559 - 20.0205i) q^{90} +(-18.7045 - 25.7446i) q^{91} +33.6011i q^{92} +(56.9977 - 4.60992i) q^{93} -7.24561 q^{94} +(-68.6199 + 49.8553i) q^{95} +(-28.9418 + 39.8350i) q^{96} +(15.1554 - 46.6434i) q^{97} +54.3979 q^{98} -80.2172i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9} + 12 q^{10} - 10 q^{11} + 90 q^{12} + 10 q^{13} - 85 q^{15} - 103 q^{16} + 35 q^{17} + 6 q^{18} + 47 q^{19} - 125 q^{20} - 125 q^{21}+ \cdots - 1000 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 5 * q^3 - 11 * q^4 - 14 * q^5 - q^7 - 19 * q^8 + 2 * q^9 + 12 * q^10 - 10 * q^11 + 90 * q^12 + 10 * q^13 - 85 * q^15 - 103 * q^16 + 35 * q^17 + 6 * q^18 + 47 * q^19 - 125 * q^20 - 125 * q^21 + 150 * q^22 + 75 * q^23 + 195 * q^24 + 82 * q^25 + 25 * q^27 + 88 * q^28 + 5 * q^29 + 73 * q^31 + 226 * q^32 - 206 * q^33 - 265 * q^34 - 50 * q^35 - 520 * q^36 + 8 * q^38 + 91 * q^39 - 466 * q^40 - 98 * q^41 + 245 * q^43 + 380 * q^44 - 162 * q^45 - 445 * q^46 - 187 * q^47 + 570 * q^48 + 328 * q^49 - 44 * q^50 + 185 * q^51 - 15 * q^52 + 25 * q^53 + 920 * q^54 + 190 * q^55 + 64 * q^56 - 85 * q^58 - 173 * q^59 + 275 * q^60 - 40 * q^62 + 252 * q^63 - 469 * q^64 - 345 * q^65 - 564 * q^66 + 76 * q^67 - 197 * q^69 - 11 * q^70 - 467 * q^71 - 982 * q^72 - 15 * q^73 + 45 * q^74 - 175 * q^75 + 55 * q^76 - 320 * q^77 - 91 * q^78 + 500 * q^79 + 1030 * q^80 + 117 * q^81 + 178 * q^82 - 50 * q^83 + 65 * q^84 + 20 * q^85 + 1125 * q^86 - 366 * q^87 + 55 * q^89 + 444 * q^90 + 300 * q^91 + 502 * q^93 + 62 * q^94 - 559 * q^95 - 10 * q^96 - 405 * q^97 - 1000 * q^98

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