LMFDB - Embedded newform 70.3.l.b.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,3,Mod(23,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.23"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	70.l (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.90736185052$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.303595776.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.1
Root			$1.26217 + 1.18614i$ of defining polynomial
Character	$\chi$	$=$	70.37
Dual form			70.3.l.b.53.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 - 0.366025i) q^{2} +(-1.58228 - 0.423972i) q^{3} +(1.73205 - 1.00000i) q^{4} +(4.94253 + 0.755913i) q^{5} -2.31662 q^{6} +(6.42096 - 2.78771i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-5.47036 - 3.15831i) q^{9} +(7.02830 - 0.776495i) q^{10} +(-0.341688 - 0.591820i) q^{11} +(-3.16457 + 0.847944i) q^{12} +(-11.9499 + 11.9499i) q^{13} +(7.75082 - 6.15831i) q^{14} +(-7.50000 - 3.29156i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-8.70832 + 32.4999i) q^{17} +(-8.62867 - 2.31205i) q^{18} +(-8.34264 - 4.81662i) q^{19} +(9.31662 - 3.63325i) q^{20} +(-11.3417 + 1.68864i) q^{21} +(-0.683375 - 0.683375i) q^{22} +(-6.26203 - 23.3702i) q^{23} +(-4.01251 + 2.31662i) q^{24} +(23.8572 + 7.47224i) q^{25} +(-11.9499 + 20.6978i) q^{26} +(17.7414 + 17.7414i) q^{27} +(8.33372 - 11.2494i) q^{28} -16.5330i q^{29} +(-11.4500 - 1.75117i) q^{30} +(-11.9248 - 20.6544i) q^{31} +(1.46410 - 5.46410i) q^{32} +(0.289732 + 1.08129i) q^{33} +47.5831i q^{34} +(33.8430 - 8.92464i) q^{35} -12.6332 q^{36} +(-25.3742 + 6.79899i) q^{37} +(-13.1593 - 3.52601i) q^{38} +(23.9745 - 13.8417i) q^{39} +(11.3969 - 8.37323i) q^{40} +0.200503 q^{41} +(-14.8749 + 6.45807i) q^{42} +(-41.1161 + 41.1161i) q^{43} +(-1.18364 - 0.683375i) q^{44} +(-24.6500 - 19.7452i) q^{45} +(-17.1082 - 29.6322i) q^{46} +(46.1601 - 12.3686i) q^{47} +(-4.63325 + 4.63325i) q^{48} +(33.4574 - 35.7995i) q^{49} +(35.3246 + 1.47494i) q^{50} +(27.5581 - 47.7320i) q^{51} +(-8.74792 + 32.6477i) q^{52} +(90.1000 + 24.1422i) q^{53} +(30.7291 + 17.7414i) q^{54} +(-1.24144 - 3.18338i) q^{55} +(7.26650 - 18.4173i) q^{56} +(11.1583 + 11.1583i) q^{57} +(-6.05150 - 22.5845i) q^{58} +(20.0054 - 11.5501i) q^{59} +(-16.2819 + 1.79885i) q^{60} +(6.08312 - 10.5363i) q^{61} +(-23.8496 - 23.8496i) q^{62} +(-43.9294 - 5.02963i) q^{63} -8.00000i q^{64} +(-68.0957 + 50.0295i) q^{65} +(0.791562 + 1.37103i) q^{66} +(0.363121 - 1.35519i) q^{67} +(17.4166 + 64.9998i) q^{68} +39.6332i q^{69} +(42.9638 - 24.5787i) q^{70} +63.2665 q^{71} +(-17.2573 + 4.62409i) q^{72} +(-45.5005 - 12.1918i) q^{73} +(-32.1732 + 18.5752i) q^{74} +(-34.5808 - 21.9380i) q^{75} -19.2665 q^{76} +(-3.84378 - 2.84753i) q^{77} +(27.6834 - 27.6834i) q^{78} +(-97.2256 - 56.1332i) q^{79} +(12.5036 - 15.6096i) q^{80} +(7.87469 + 13.6394i) q^{81} +(0.273892 - 0.0733890i) q^{82} +(23.1161 - 23.1161i) q^{83} +(-17.9557 + 14.2665i) q^{84} +(-67.6082 + 154.049i) q^{85} +(-41.1161 + 71.2152i) q^{86} +(-7.00952 + 26.1599i) q^{87} +(-1.86702 - 0.500265i) q^{88} +(-69.1518 - 39.9248i) q^{89} +(-40.8997 - 17.9499i) q^{90} +(-43.4169 + 110.042i) q^{91} +(-34.2164 - 34.2164i) q^{92} +(10.1116 + 37.7369i) q^{93} +(58.5287 - 33.7916i) q^{94} +(-37.5928 - 30.1126i) q^{95} +(-4.63325 + 8.02502i) q^{96} +(-50.6834 - 50.6834i) q^{97} +(32.6001 - 61.1493i) q^{98} +4.31662i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 2 q^{3} - 6 q^{5} + 8 q^{6} - 12 q^{7} + 16 q^{8} + 18 q^{10} - 16 q^{11} + 4 q^{12} - 16 q^{13} - 60 q^{15} + 16 q^{16} + 62 q^{17} - 12 q^{18} + 48 q^{20} - 104 q^{21} - 32 q^{22} + 22 q^{23}+ \cdots + 176 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 2 * q^3 - 6 * q^5 + 8 * q^6 - 12 * q^7 + 16 * q^8 + 18 * q^10 - 16 * q^11 + 4 * q^12 - 16 * q^13 - 60 * q^15 + 16 * q^16 + 62 * q^17 - 12 * q^18 + 48 * q^20 - 104 * q^21 - 32 * q^22 + 22 * q^23 - 6 * q^25 - 16 * q^26 - 4 * q^27 + 12 * q^28 - 50 * q^30 + 24 * q^31 - 16 * q^32 + 30 * q^33 + 70 * q^35 - 48 * q^36 - 134 * q^37 - 12 * q^38 + 12 * q^40 + 320 * q^41 - 100 * q^42 + 16 * q^43 - 58 * q^45 - 44 * q^46 + 102 * q^47 + 16 * q^48 + 4 * q^50 + 48 * q^51 + 16 * q^52 + 98 * q^53 + 136 * q^55 - 48 * q^56 + 76 * q^57 - 40 * q^58 + 40 * q^60 - 84 * q^61 + 48 * q^62 - 76 * q^63 - 210 * q^65 - 60 * q^66 - 130 * q^67 - 124 * q^68 + 146 * q^70 + 400 * q^71 - 24 * q^72 - 246 * q^73 + 40 * q^75 - 48 * q^76 + 86 * q^77 + 248 * q^78 + 24 * q^80 - 136 * q^81 + 160 * q^82 - 160 * q^83 - 448 * q^85 + 16 * q^86 + 196 * q^87 - 32 * q^88 - 168 * q^90 - 480 * q^91 - 88 * q^92 - 210 * q^93 - 80 * q^95 + 16 * q^96 - 432 * q^97 + 176 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$3$	−1.58228	−	0.423972i	−0.527428	−	0.141324i	−0.0147277	−	0.999892i	$-0.504688\pi$
$3$	−1.58228	−	0.423972i	−0.527428	−	0.141324i	−0.512700	+	0.858568i	$0.671355\pi$
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	4.94253	+	0.755913i	0.988506	+	0.151183i
$5$	4.94253	+	0.755913i	0.988506	+	0.151183i
$6$	−2.31662			−0.386104
$7$	6.42096	−	2.78771i	0.917280	−	0.398244i
$7$	6.42096	−	2.78771i	0.917280	−	0.398244i
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	−5.47036	−	3.15831i	−0.607818	−	0.350924i
$10$	7.02830	−	0.776495i	0.702830	−	0.0776495i
$11$	−0.341688	−	0.591820i	−0.0310625	−	0.0538018i	0.850076	−	0.526660i	$-0.176556\pi$
$11$	−0.341688	−	0.591820i	−0.0310625	−	0.0538018i	−0.881139	+	0.472858i	$0.843222\pi$
$12$	−3.16457	+	0.847944i	−0.263714	+	0.0706620i
$13$	−11.9499	+	11.9499i	−0.919221	+	0.919221i	−0.996973	−	0.0777517i	$-0.975226\pi$
$13$	−11.9499	+	11.9499i	−0.919221	+	0.919221i	0.0777517	+	0.996973i	$0.475226\pi$
$14$	7.75082	−	6.15831i	0.553630	−	0.439879i
$15$	−7.50000	−	3.29156i	−0.500000	−	0.219437i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−8.70832	+	32.4999i	−0.512254	+	1.91176i	−0.117172	+	0.993112i	$0.537383\pi$
$17$	−8.70832	+	32.4999i	−0.512254	+	1.91176i	−0.395082	+	0.918646i	$0.629284\pi$
$18$	−8.62867	−	2.31205i	−0.479371	−	0.128447i
$19$	−8.34264	−	4.81662i	−0.439086	−	0.253507i	0.264124	−	0.964489i	$-0.414917\pi$
$19$	−8.34264	−	4.81662i	−0.439086	−	0.253507i	−0.703210	+	0.710982i	$0.748251\pi$
$20$	9.31662	−	3.63325i	0.465831	−	0.181662i
$21$	−11.3417	+	1.68864i	−0.540080	+	0.0804115i
$22$	−0.683375	−	0.683375i	−0.0310625	−	0.0310625i
$23$	−6.26203	−	23.3702i	−0.272262	−	1.01610i	−0.957654	−	0.287922i	$-0.907036\pi$
$23$	−6.26203	−	23.3702i	−0.272262	−	1.01610i	0.685392	−	0.728175i	$-0.259631\pi$
$24$	−4.01251	+	2.31662i	−0.167188	+	0.0965260i
$25$	23.8572	+	7.47224i	0.954288	+	0.298890i
$26$	−11.9499	+	20.6978i	−0.459611	+	0.796069i
$27$	17.7414	+	17.7414i	0.657090	+	0.657090i
$28$	8.33372	−	11.2494i	0.297633	−	0.401765i
$29$		−	16.5330i		−	0.570103i	−0.958512	−	0.285052i	$-0.907989\pi$
$29$		−	16.5330i		−	0.570103i	0.958512	−	0.285052i	$-0.0920108\pi$
$30$	−11.4500	−	1.75117i	−0.381666	−	0.0583722i
$31$	−11.9248	−	20.6544i	−0.384671	−	0.666270i	0.607052	−	0.794662i	$-0.292352\pi$
$31$	−11.9248	−	20.6544i	−0.384671	−	0.666270i	−0.991724	+	0.128392i	$0.959019\pi$
$32$	1.46410	−	5.46410i	0.0457532	−	0.170753i
$33$	0.289732	+	1.08129i	0.00877975	+	0.0327665i
$34$			47.5831i			1.39950i
$35$	33.8430	−	8.92464i	0.966944	−	0.254990i
$36$	−12.6332			−0.350924
$37$	−25.3742	+	6.79899i	−0.685789	+	0.183757i	−0.584856	−	0.811137i	$-0.698849\pi$
$37$	−25.3742	+	6.79899i	−0.685789	+	0.183757i	−0.100932	+	0.994893i	$0.532183\pi$
$38$	−13.1593	−	3.52601i	−0.346296	−	0.0927898i
$39$	23.9745	−	13.8417i	0.614731	−	0.354915i
$40$	11.3969	−	8.37323i	0.284922	−	0.209331i
$41$	0.200503			0.00489031			0.00244515	−	0.999997i	$-0.499222\pi$
$41$	0.200503			0.00489031			0.00244515	+	0.999997i	$0.499222\pi$
$42$	−14.8749	+	6.45807i	−0.354165	+	0.153764i
$43$	−41.1161	+	41.1161i	−0.956189	+	0.956189i	−0.999080	−	0.0428909i	$-0.986343\pi$
$43$	−41.1161	+	41.1161i	−0.956189	+	0.956189i	0.0428909	+	0.999080i	$0.486343\pi$
$44$	−1.18364	−	0.683375i	−0.0269009	−	0.0155313i
$45$	−24.6500	−	19.7452i	−0.547778	−	0.438781i
$46$	−17.1082	−	29.6322i	−0.371917	−	0.644179i
$47$	46.1601	−	12.3686i	0.982130	−	0.263161i	0.268189	−	0.963366i	$-0.413575\pi$
$47$	46.1601	−	12.3686i	0.982130	−	0.263161i	0.713942	+	0.700205i	$0.246908\pi$
$48$	−4.63325	+	4.63325i	−0.0965260	+	0.0965260i
$49$	33.4574	−	35.7995i	0.682804	−	0.730602i
$50$	35.3246	+	1.47494i	0.706491	+	0.0294987i
$51$	27.5581	−	47.7320i	0.540354	−	0.935921i
$52$	−8.74792	+	32.6477i	−0.168229	+	0.627840i
$53$	90.1000	+	24.1422i	1.70000	+	0.455514i	0.972940	−	0.231059i	$-0.0742190\pi$
$53$	90.1000	+	24.1422i	1.70000	+	0.455514i	0.727061	+	0.686573i	$0.240886\pi$
$54$	30.7291	+	17.7414i	0.569057	+	0.328545i
$55$	−1.24144	−	3.18338i	−0.0225716	−	0.0578795i
$56$	7.26650	−	18.4173i	0.129759	−	0.328881i
$57$	11.1583	+	11.1583i	0.195760	+	0.195760i
$58$	−6.05150	−	22.5845i	−0.104336	−	0.389388i
$59$	20.0054	−	11.5501i	0.339075	−	0.195765i	−0.320788	−	0.947151i	$-0.603948\pi$
$59$	20.0054	−	11.5501i	0.339075	−	0.195765i	0.659863	+	0.751386i	$0.270614\pi$
$60$	−16.2819	+	1.79885i	−0.271366	+	0.0299808i
$61$	6.08312	−	10.5363i	0.0997233	−	0.172726i	−0.811847	−	0.583871i	$-0.801538\pi$
$61$	6.08312	−	10.5363i	0.0997233	−	0.172726i	0.911570	+	0.411145i	$0.134871\pi$
$62$	−23.8496	−	23.8496i	−0.384671	−	0.384671i
$63$	−43.9294	−	5.02963i	−0.697292	−	0.0798354i
$64$		−	8.00000i		−	0.125000i
$65$	−68.0957	+	50.0295i	−1.04763	+	0.769685i
$66$	0.791562	+	1.37103i	0.0119934	+	0.0207731i
$67$	0.363121	−	1.35519i	0.00541971	−	0.0202266i	−0.963163	−	0.268918i	$-0.913334\pi$
$67$	0.363121	−	1.35519i	0.00541971	−	0.0202266i	0.968583	+	0.248692i	$0.0800005\pi$
$68$	17.4166	+	64.9998i	0.256127	+	0.955879i
$69$			39.6332i			0.574395i
$70$	42.9638	−	24.5787i	0.613769	−	0.351124i
$71$	63.2665			0.891077			0.445539	−	0.895263i	$-0.353012\pi$
$71$	63.2665			0.891077			0.445539	+	0.895263i	$0.353012\pi$
$72$	−17.2573	+	4.62409i	−0.239685	+	0.0642235i
$73$	−45.5005	−	12.1918i	−0.623295	−	0.167011i	−0.0666696	−	0.997775i	$-0.521237\pi$
$73$	−45.5005	−	12.1918i	−0.623295	−	0.167011i	−0.556625	+	0.830764i	$0.687904\pi$
$74$	−32.1732	+	18.5752i	−0.434773	+	0.251016i
$75$	−34.5808	−	21.9380i	−0.461078	−	0.292507i
$76$	−19.2665			−0.253507
$77$	−3.84378	−	2.84753i	−0.0499193	−	0.0369809i
$78$	27.6834	−	27.6834i	0.354915	−	0.354915i
$79$	−97.2256	−	56.1332i	−1.23070	−	0.710547i	−0.263528	−	0.964652i	$-0.584886\pi$
$79$	−97.2256	−	56.1332i	−1.23070	−	0.710547i	−0.967177	+	0.254104i	$0.918219\pi$
$80$	12.5036	−	15.6096i	0.156295	−	0.195120i
$81$	7.87469	+	13.6394i	0.0972183	+	0.168387i
$82$	0.273892	−	0.0733890i	0.00334014	−	0.000894988i
$83$	23.1161	−	23.1161i	0.278507	−	0.278507i	−0.554006	−	0.832513i	$-0.686901\pi$
$83$	23.1161	−	23.1161i	0.278507	−	0.278507i	0.832513	+	0.554006i	$0.186901\pi$
$84$	−17.9557	+	14.2665i	−0.213759	+	0.169839i
$85$	−67.6082	+	154.049i	−0.795390	+	1.81234i
$86$	−41.1161	+	71.2152i	−0.478094	+	0.828084i
$87$	−7.00952	+	26.1599i	−0.0805692	+	0.300689i
$88$	−1.86702	−	0.500265i	−0.0212161	−	0.00568483i
$89$	−69.1518	−	39.9248i	−0.776987	−	0.448593i	0.0583747	−	0.998295i	$-0.481408\pi$
$89$	−69.1518	−	39.9248i	−0.776987	−	0.448593i	−0.835361	+	0.549701i	$0.814742\pi$
$90$	−40.8997	−	17.9499i	−0.454442	−	0.199443i
$91$	−43.4169	+	110.042i	−0.477109	+	1.20926i
$92$	−34.2164	−	34.2164i	−0.371917	−	0.371917i
$93$	10.1116	+	37.7369i	0.108727	+	0.405773i
$94$	58.5287	−	33.7916i	0.622646	−	0.359485i
$95$	−37.5928	−	30.1126i	−0.395714	−	0.316975i
$96$	−4.63325	+	8.02502i	−0.0482630	+	0.0835940i
$97$	−50.6834	−	50.6834i	−0.522509	−	0.522509i	0.395819	−	0.918328i	$-0.370461\pi$
$97$	−50.6834	−	50.6834i	−0.522509	−	0.522509i	−0.918328	+	0.395819i	$0.870461\pi$
$98$	32.6001	−	61.1493i	0.332654	−	0.623972i
$99$			4.31662i			0.0436023i
$100$	48.7941	−	10.9149i	0.487941	−	0.109149i
$101$	27.5000	+	47.6314i	0.272277	+	0.471598i	0.969445	−	0.245310i	$-0.0788899\pi$
$101$	27.5000	+	47.6314i	0.272277	+	0.471598i	−0.697167	+	0.716908i	$0.745557\pi$
$102$	20.1739	−	75.2900i	0.197783	−	0.738137i
$103$	0.0579464	+	0.216259i	0.000562586	+	0.00209960i	0.966207	−	0.257769i	$-0.0829874\pi$
$103$	0.0579464	+	0.216259i	0.000562586	+	0.00209960i	−0.965644	+	0.259869i	$0.916321\pi$
$104$			47.7995i			0.459611i
$105$	−57.3331	−	0.227173i	−0.546029	−	0.00216355i
$106$	131.916			1.24449
$107$	129.989	−	34.8304i	1.21485	−	0.325517i	0.406185	−	0.913791i	$-0.366859\pi$
$107$	129.989	−	34.8304i	1.21485	−	0.325517i	0.808662	+	0.588273i	$0.200192\pi$
$108$	48.4705	+	12.9876i	0.448801	+	0.120256i
$109$	−44.2679	+	25.5581i	−0.406127	+	0.234478i	−0.689124	−	0.724643i	$-0.742005\pi$
$109$	−44.2679	+	25.5581i	−0.406127	+	0.234478i	0.282997	+	0.959121i	$0.408671\pi$
$110$	−2.86103	−	3.89417i	−0.0260094	−	0.0354016i
$111$	43.0317			0.387673
$112$	3.18501	−	27.8183i	0.0284376	−	0.248377i
$113$	63.8496	−	63.8496i	0.565041	−	0.565041i	−0.365694	−	0.930735i	$-0.619168\pi$
$113$	63.8496	−	63.8496i	0.565041	−	0.565041i	0.930735	+	0.365694i	$0.119168\pi$
$114$	19.3268	+	11.1583i	0.169533	+	0.0978799i
$115$	−13.2844	−	120.242i	−0.115517	−	1.04558i
$116$	−16.5330	−	28.6360i	−0.142526	−	0.246862i
$117$	103.112	−	27.6286i	0.881295	−	0.236142i
$118$	23.1003	−	23.1003i	0.195765	−	0.195765i
$119$	34.6844	+	232.957i	0.291466	+	1.95762i
$120$	−21.5831	+	8.41688i	−0.179859	+	0.0701406i
$121$	60.2665	−	104.385i	0.498070	−	0.862683i
$122$	4.45316	−	16.6194i	0.0365013	−	0.136225i
$123$	−0.317252	−	0.0850074i	−0.00257928	−	0.000691117i
$124$	−41.3088	−	23.8496i	−0.333135	−	0.192336i
$125$	112.266	+	54.9657i	0.898132	+	0.439726i
$126$	−61.8496	+	9.20866i	−0.490870	+	0.0730846i
$127$	−108.082	−	108.082i	−0.851038	−	0.851038i	0.139223	−	0.990261i	$-0.455540\pi$
$127$	−108.082	−	108.082i	−0.851038	−	0.851038i	−0.990261	+	0.139223i	$0.955540\pi$
$128$	−2.92820	−	10.9282i	−0.0228766	−	0.0853766i
$129$	82.4895	−	47.6253i	0.639453	−	0.369188i
$130$	−74.7083	+	93.2664i	−0.574679	+	0.717434i
$131$	−29.4419	+	50.9949i	−0.224748	+	0.389274i	−0.956244	−	0.292571i	$-0.905489\pi$
$131$	−29.4419	+	50.9949i	−0.224748	+	0.389274i	0.731496	+	0.681846i	$0.238822\pi$
$132$	1.58312	+	1.58312i	0.0119934	+	0.0119934i
$133$	−66.9951	−	7.67050i	−0.503722	−	0.0576730i
$134$		−	1.98413i		−	0.0148069i
$135$	74.2766	+	101.099i	0.550197	+	0.748878i
$136$	47.5831	+	82.4164i	0.349876	+	0.606003i
$137$	34.1041	−	127.278i	0.248935	−	0.929039i	−0.722429	−	0.691445i	$-0.756975\pi$
$137$	34.1041	−	127.278i	0.248935	−	0.929039i	0.971365	−	0.237594i	$-0.0763588\pi$
$138$	14.5068	+	54.1400i	0.105122	+	0.392319i
$139$		−	68.2322i		−	0.490879i	−0.969412	−	0.245440i	$-0.921068\pi$
$139$		−	68.2322i		−	0.490879i	0.969412	−	0.245440i	$-0.0789323\pi$
$140$	49.6932	−	49.3010i	0.354951	−	0.352150i
$141$	−78.2824			−0.555194
$142$	86.4236	−	23.1571i	0.608617	−	0.163078i
$143$	11.1553	+	2.98905i	0.0780091	+	0.0209025i
$144$	−21.8814	+	12.6332i	−0.151954	+	0.0877309i
$145$	12.4975	−	81.7148i	0.0861897	−	0.563551i
$146$	−66.6174			−0.456283
$147$	−68.1171	+	42.4600i	−0.463381	+	0.288844i
$148$	−37.1504	+	37.1504i	−0.251016	+	0.251016i
$149$	75.7327	+	43.7243i	0.508273	+	0.293452i	0.732124	−	0.681172i	$-0.238529\pi$
$149$	75.7327	+	43.7243i	0.508273	+	0.293452i	−0.223850	+	0.974624i	$0.571863\pi$
$150$	−55.2682	−	17.3104i	−0.368454	−	0.115403i
$151$	117.991	+	204.366i	0.781396	+	1.35342i	0.931129	+	0.364691i	$0.118825\pi$
$151$	117.991	+	204.366i	0.781396	+	1.35342i	−0.149732	+	0.988727i	$0.547841\pi$
$152$	−26.3185	+	7.05203i	−0.173148	+	0.0463949i
$153$	150.282	−	150.282i	0.982238	−	0.982238i
$154$	−6.29297	−	2.48287i	−0.0408635	−	0.0161225i
$155$	−43.3258	−	111.099i	−0.279521	−	0.716768i
$156$	27.6834	−	47.9490i	0.177458	−	0.307365i
$157$	−41.2295	+	153.871i	−0.262609	+	0.980068i	0.701089	+	0.713073i	$0.252697\pi$
$157$	−41.2295	+	153.871i	−0.262609	+	0.980068i	−0.963698	+	0.266995i	$0.913969\pi$
$158$	−153.359	−	41.0924i	−0.970626	−	0.260078i
$159$	−132.328	−	76.3997i	−0.832253	−	0.480502i
$160$	11.3668	−	25.8997i	0.0710422	−	0.161873i
$161$	−105.358	−	132.602i	−0.654395	−	0.823618i
$162$	15.7494	+	15.7494i	0.0972183	+	0.0972183i
$163$	64.6117	+	241.134i	0.396391	+	1.47935i	0.819398	+	0.573225i	$0.194308\pi$
$163$	64.6117	+	241.134i	0.396391	+	1.47935i	−0.423007	+	0.906126i	$0.639025\pi$
$164$	0.347281	−	0.200503i	0.00211756	−	0.00122258i
$165$	0.614644	+	5.56334i	0.00372511	+	0.0337172i
$166$	23.1161	−	40.0383i	0.139254	−	0.241195i
$167$	−202.799	−	202.799i	−1.21437	−	1.21437i	−0.969575	−	0.244793i	$-0.921280\pi$
$167$	−202.799	−	202.799i	−1.21437	−	1.21437i	−0.244793	−	0.969575i	$-0.578720\pi$
$168$	−19.3061	+	26.0607i	−0.114917	+	0.155123i
$169$		−	116.599i		−	0.689935i
$170$	−35.9687	+	235.181i	−0.211581	+	1.38342i
$171$	30.4248	+	52.6973i	0.177923	+	0.308171i
$172$	−30.0991	+	112.331i	−0.174995	+	0.653089i
$173$	−4.05334	−	15.1273i	−0.0234297	−	0.0874409i	0.953221	−	0.302274i	$-0.0977458\pi$
$173$	−4.05334	−	15.1273i	−0.0234297	−	0.0874409i	−0.976651	+	0.214833i	$0.931079\pi$
$174$			38.3008i			0.220119i
$175$	174.016	−	18.5279i	0.994380	−	0.105874i
$176$	−2.73350			−0.0155313
$177$	−36.5512	+	9.79385i	−0.206504	+	0.0553325i
$178$	−109.077	−	29.2270i	−0.612790	−	0.164197i
$179$	−296.960	+	171.450i	−1.65899	+	0.957821i	−0.685813	+	0.727777i	$0.740553\pi$
$179$	−296.960	+	171.450i	−1.65899	+	0.957821i	−0.973180	+	0.230043i	$0.926113\pi$
$180$	−62.4402	−	9.54964i	−0.346890	−	0.0530535i
$181$	−88.1320			−0.486917			−0.243459	−	0.969911i	$-0.578282\pi$
$181$	−88.1320			−0.486917			−0.243459	+	0.969911i	$0.578282\pi$
$182$	−19.0302	+	166.212i	−0.104562	+	0.913255i
$183$	−14.0923	+	14.0923i	−0.0770072	+	0.0770072i
$184$	−59.2645	−	34.2164i	−0.322090	−	0.185959i
$185$	−130.552	+	14.4235i	−0.705687	+	0.0779651i
$186$	27.6253	+	47.8484i	0.148523	+	0.257250i
$187$	22.2096	−	5.95105i	0.118768	−	0.0318238i
$188$	67.5831	−	67.5831i	0.359485	−	0.359485i
$189$	163.375	+	64.4591i	0.864418	+	0.341053i
$190$	−62.3747	−	27.3747i	−0.328288	−	0.144077i
$191$	23.5422	−	40.7763i	0.123258	−	0.213488i	−0.797793	−	0.602932i	$-0.793999\pi$
$191$	23.5422	−	40.7763i	0.123258	−	0.213488i	0.921050	+	0.389443i	$0.127333\pi$
$192$	−3.39177	+	12.6583i	−0.0176655	+	0.0659285i
$193$	98.8657	+	26.4910i	0.512257	+	0.137259i	0.505683	−	0.862719i	$-0.331241\pi$
$193$	98.8657	+	26.4910i	0.512257	+	0.137259i	0.00657446	+	0.999978i	$0.497907\pi$
$194$	−87.7862	−	50.6834i	−0.452506	−	0.261255i
$195$	128.958	−	50.2903i	0.661322	−	0.257899i
$196$	22.1504	−	95.4639i	0.113012	−	0.487061i
$197$	163.148	+	163.148i	0.828162	+	0.828162i	0.987262	−	0.159101i	$-0.0508594\pi$
$197$	163.148	+	163.148i	0.828162	+	0.828162i	−0.159101	+	0.987262i	$0.550859\pi$
$198$	1.57999	+	5.89662i	0.00797977	+	0.0297809i
$199$	295.082	−	170.365i	1.48282	−	0.856108i	0.483013	−	0.875613i	$-0.339542\pi$
$199$	295.082	−	170.365i	1.48282	−	0.856108i	0.999810	+	0.0195053i	$0.00620911\pi$
$200$	62.6589	−	32.7699i	0.313294	−	0.163849i
$201$	−1.14912	+	1.99034i	−0.00571702	+	0.00990217i
$202$	55.0000	+	55.0000i	0.272277	+	0.272277i
$203$	−46.0892	−	106.158i	−0.227040	−	0.522944i
$204$		−	110.232i		−	0.540354i
$205$	0.990990	+	0.151562i	0.00483410	+	0.000739329i
$206$	0.158312	+	0.274205i	0.000768507	+	0.00133109i
$207$	−39.5549	+	147.621i	−0.191086	+	0.713144i
$208$	17.4958	+	65.2953i	0.0841146	+	0.313920i
$209$			6.58312i			0.0314982i
$210$	−78.4016	+	20.6750i	−0.373341	+	0.0984526i
$211$	113.799			0.539334			0.269667	−	0.962954i	$-0.413086\pi$
$211$	113.799			0.539334			0.269667	+	0.962954i	$0.413086\pi$
$212$	180.200	−	48.2845i	0.850000	−	0.227757i
$213$	−100.106	−	26.8232i	−0.469979	−	0.125931i
$214$	164.819	−	95.1583i	0.770182	−	0.444665i
$215$	−234.298	+	172.137i	−1.08976	+	0.800639i
$216$	70.9657			0.328545
$217$	−134.147	−	99.3780i	−0.618189	−	0.457963i
$218$	−51.1161	+	51.1161i	−0.234478	+	0.234478i
$219$	66.8258	+	38.5819i	0.305140	+	0.176173i
$220$	−5.33361	−	4.27233i	−0.0242437	−	0.0194197i
$221$	−284.306	−	492.433i	−1.28645	−	2.22820i
$222$	58.7825	−	15.7507i	0.264786	−	0.0709491i
$223$	−158.916	+	158.916i	−0.712626	+	0.712626i	−0.967084	−	0.254458i	$-0.918103\pi$
$223$	−158.916	+	158.916i	−0.712626	+	0.712626i	0.254458	+	0.967084i	$0.418103\pi$
$224$	−5.83138	−	39.1662i	−0.0260330	−	0.174849i
$225$	−106.908	−	116.224i	−0.475145	−	0.516552i
$226$	63.8496	−	110.591i	0.282520	−	0.489340i
$227$	−73.8850	+	275.743i	−0.325485	+	1.21472i	0.588339	+	0.808614i	$0.299782\pi$
$227$	−73.8850	+	275.743i	−0.325485	+	1.21472i	−0.913824	+	0.406111i	$0.866885\pi$
$228$	30.4851	+	8.16845i	0.133706	+	0.0358265i
$229$	271.368	+	156.674i	1.18501	+	0.684167i	0.957169	−	0.289531i	$-0.0934994\pi$
$229$	271.368	+	156.674i	1.18501	+	0.684167i	0.227843	+	0.973698i	$0.426833\pi$
$230$	−62.1583	−	159.391i	−0.270254	−	0.693002i
$231$	4.87469	+	6.13525i	0.0211025	+	0.0265595i
$232$	−33.0660	−	33.0660i	−0.142526	−	0.142526i
$233$	13.0948	+	48.8705i	0.0562009	+	0.209745i	0.988316	−	0.152417i	$-0.0487056\pi$
$233$	13.0948	+	48.8705i	0.0562009	+	0.209745i	−0.932115	+	0.362161i	$0.882039\pi$
$234$	130.740	−	75.4829i	0.558719	−	0.322576i
$235$	237.497	−	26.2390i	1.01063	−	0.111655i
$236$	23.1003	−	40.0108i	0.0978824	−	0.169537i
$237$	130.040	+	130.040i	0.548691	+	0.548691i
$238$	132.648	+	305.529i	0.557344	+	1.28374i
$239$			195.330i			0.817280i	0.912696	+	0.408640i	$0.133997\pi$
$239$			195.330i			0.817280i	−0.912696	+	0.408640i	$0.866003\pi$
$240$	−26.4023	+	19.3976i	−0.110010	+	0.0808235i
$241$	−46.4657	−	80.4810i	−0.192804	−	0.333946i	0.753374	−	0.657592i	$-0.228425\pi$
$241$	−46.4657	−	80.4810i	−0.192804	−	0.333946i	−0.946178	+	0.323646i	$0.895091\pi$
$242$	44.1181	−	164.651i	0.182306	−	0.680377i
$243$	−65.1216	−	243.037i	−0.267990	−	1.00015i
$244$		−	24.3325i		−	0.0997233i
$245$	192.425	−	151.649i	0.785410	−	0.618976i
$246$	−0.464489			−0.00188817
$247$	157.252	−	42.1354i	0.636646	−	0.170589i
$248$	−65.1584	−	17.4591i	−0.262735	−	0.0703997i
$249$	−46.3769	+	26.7757i	−0.186252	+	0.107533i
$250$	173.478	+	33.9922i	0.693911	+	0.135969i
$251$	−332.665			−1.32536			−0.662679	−	0.748903i	$-0.730581\pi$
$251$	−332.665			−1.32536			−0.662679	+	0.748903i	$0.730581\pi$
$252$	−81.1176	+	35.2178i	−0.321895	+	0.139753i
$253$	−11.6913	+	11.6913i	−0.0462107	+	0.0462107i
$254$	−187.203	−	108.082i	−0.737021	−	0.425519i
$255$	172.288	−	215.085i	0.675638	−	0.843471i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−98.8873	+	26.4968i	−0.384776	+	0.103100i	−0.446021	−	0.895022i	$-0.647159\pi$
$257$	−98.8873	+	26.4968i	−0.384776	+	0.103100i	0.0612455	+	0.998123i	$0.480493\pi$
$258$	95.2506	−	95.2506i	0.369188	−	0.369188i
$259$	−143.973	+	114.392i	−0.555880	+	0.441667i
$260$	−67.9156	+	154.749i	−0.261214	+	0.595190i
$261$	−52.2164	+	90.4414i	−0.200063	+	0.346519i
$262$	−21.5530	+	80.4369i	−0.0822633	+	0.307011i
$263$	−193.143	−	51.7525i	−0.734384	−	0.196778i	−0.127804	−	0.991800i	$-0.540793\pi$
$263$	−193.143	−	51.7525i	−0.734384	−	0.196778i	−0.606581	+	0.795022i	$0.707459\pi$
$264$	2.74205	+	1.58312i	0.0103866	+	0.00599668i
$265$	427.073	+	187.431i	1.61160	+	0.707289i
$266$	−94.3246	+	14.0438i	−0.354604	+	0.0527962i
$267$	92.4908	+	92.4908i	0.346408	+	0.346408i
$268$	−0.726242	−	2.71037i	−0.00270986	−	0.0101133i
$269$	198.535	−	114.624i	0.738047	−	0.426112i	−0.0833117	−	0.996524i	$-0.526550\pi$
$269$	198.535	−	114.624i	0.738047	−	0.426112i	0.821359	+	0.570412i	$0.193216\pi$
$270$	138.468	+	110.916i	0.512846	+	0.410800i
$271$	−28.0911	+	48.6551i	−0.103657	+	0.179539i	−0.913189	−	0.407537i	$-0.866388\pi$
$271$	−28.0911	+	48.6551i	−0.103657	+	0.179539i	0.809532	+	0.587076i	$0.199721\pi$
$272$	95.1662	+	95.1662i	0.349876	+	0.349876i
$273$	115.353	−	155.711i	0.422537	−	0.570369i
$274$		−	186.348i		−	0.680104i
$275$	−3.72948	−	16.6723i	−0.0135617	−	0.0606267i
$276$	39.6332	+	68.6468i	0.143599	+	0.248720i
$277$	−21.9644	+	81.9724i	−0.0792940	+	0.295929i	−0.994173	−	0.107800i	$-0.965619\pi$
$277$	−21.9644	+	81.9724i	−0.0792940	+	0.295929i	0.914879	+	0.403729i	$0.132286\pi$
$278$	−24.9747	−	93.2070i	−0.0898372	−	0.335277i
$279$			150.649i			0.539961i
$280$	49.8368	−	85.5353i	0.177989	−	0.305483i
$281$	136.201			0.484699			0.242350	−	0.970189i	$-0.422082\pi$
$281$	136.201			0.484699			0.242350	+	0.970189i	$0.422082\pi$
$282$	−106.936	+	28.6533i	−0.379205	+	0.101608i
$283$	−303.860	−	81.4189i	−1.07371	−	0.287699i	−0.321693	−	0.946844i	$-0.604252\pi$
$283$	−303.860	−	81.4189i	−1.07371	−	0.287699i	−0.752016	+	0.659145i	$0.770918\pi$
$284$	109.581	−	63.2665i	0.385848	−	0.222769i
$285$	46.7156	+	63.5850i	0.163914	+	0.223105i
$286$	16.3325			0.0571066
$287$	1.28742	−	0.558942i	0.00448578	−	0.00194753i
$288$	−25.2665	+	25.2665i	−0.0877309	+	0.0877309i
$289$	−730.126	−	421.538i	−2.52639	−	1.45861i
$290$	−12.8378	−	116.199i	−0.0442682	−	0.400686i
$291$	58.7072	+	101.684i	0.201743	+	0.349429i
$292$	−91.0010	+	24.3837i	−0.311647	+	0.0835057i
$293$	−184.699	+	184.699i	−0.630373	+	0.630373i	−0.948162	−	0.317789i	$-0.897060\pi$
$293$	−184.699	+	184.699i	−0.630373	+	0.630373i	0.317789	+	0.948162i	$0.397060\pi$
$294$	−77.5082	+	82.9340i	−0.263633	+	0.282088i
$295$	107.608	−	41.9645i	0.364774	−	0.142253i
$296$	−37.1504	+	64.3463i	−0.125508	+	0.217386i
$297$	4.43771	−	16.5618i	0.0149418	−	0.0557635i
$298$	119.457	+	32.0084i	0.400863	+	0.107411i
$299$	354.102	+	204.441i	1.18429	+	0.683748i
$300$	−81.8338	−	3.41688i	−0.272779	−	0.0113896i
$301$	−149.385	+	378.625i	−0.496296	+	1.25789i
$302$	235.982	+	235.982i	0.781396	+	0.781396i
$303$	−23.3184	−	87.0256i	−0.0769586	−	0.287213i
$304$	−33.3706	+	19.2665i	−0.109772	+	0.0633766i
$305$	38.0305	−	47.4776i	0.124690	−	0.155664i
$306$	150.282	−	260.297i	0.491119	−	0.850643i
$307$	−370.647	−	370.647i	−1.20732	−	1.20732i	−0.971892	−	0.235426i	$-0.924352\pi$
$307$	−370.647	−	370.647i	−1.20732	−	1.20732i	−0.235426	−	0.971892i	$-0.575648\pi$
$308$	−9.50516	−	1.08828i	−0.0308609	−	0.00353337i
$309$		−	0.366750i		−	0.00118689i
$310$	−99.8492	−	135.906i	−0.322094	−	0.438405i
$311$	219.540	+	380.254i	0.705915	+	1.22268i	0.966360	+	0.257193i	$0.0827975\pi$
$311$	219.540	+	380.254i	0.705915	+	1.22268i	−0.260445	+	0.965489i	$0.583869\pi$
$312$	20.2656	−	75.6324i	0.0649540	−	0.242411i
$313$	53.8502	+	200.972i	0.172045	+	0.642082i	0.997036	+	0.0769359i	$0.0245137\pi$
$313$	53.8502	+	200.972i	0.172045	+	0.642082i	−0.824991	+	0.565146i	$0.808820\pi$
$314$			225.282i			0.717460i
$315$	−213.320	−	58.0659i	−0.677207	−	0.184336i
$316$	−224.533			−0.710547
$317$	−398.433	+	106.760i	−1.25689	+	0.336781i	−0.824993	−	0.565144i	$-0.808821\pi$
$317$	−398.433	+	106.760i	−1.25689	+	0.336781i	−0.431893	+	0.901925i	$0.642154\pi$
$318$	−208.728	−	55.9285i	−0.656377	−	0.175876i
$319$	−9.78456	+	5.64912i	−0.0306726	+	0.0177088i
$320$	6.04730	−	39.5402i	0.0188978	−	0.123563i
$321$	−220.446			−0.686748
$322$	−192.457	−	142.575i	−0.597692	−	0.442779i
$323$	229.190	−	229.190i	0.709567	−	0.709567i
$324$	27.2787	+	15.7494i	0.0841936	+	0.0486092i
$325$	−374.383	+	195.798i	−1.15195	+	0.602456i
$326$	176.523	+	305.746i	0.541480	+	0.937871i
$327$	80.8802	−	21.6718i	0.247340	−	0.0662746i
$328$	0.401005	−	0.401005i	0.00122258	−	0.00122258i
$329$	261.912	−	208.099i	0.796086	−	0.632520i
$330$	2.87594	+	7.37469i	0.00871498	+	0.0223475i
$331$	186.690	−	323.357i	0.564018	−	0.976908i	−0.433122	−	0.901335i	$-0.642588\pi$
$331$	186.690	−	323.357i	0.564018	−	0.976908i	0.997140	−	0.0755730i	$-0.0240786\pi$
$332$	16.9222	−	63.1544i	0.0509704	−	0.190224i
$333$	160.279	+	42.9467i	0.481319	+	0.128969i
$334$	−351.259	−	202.799i	−1.05167	−	0.607184i
$335$	2.81914	−	6.42356i	0.00841534	−	0.0191748i
$336$	−16.8338	+	42.6660i	−0.0501005	+	0.126982i
$337$	259.016	+	259.016i	0.768593	+	0.768593i	0.977859	−	0.209266i	$-0.0671074\pi$
$337$	259.016	+	259.016i	0.768593	+	0.768593i	−0.209266	+	0.977859i	$0.567107\pi$
$338$	−42.6782	−	159.277i	−0.126267	−	0.471234i
$339$	−128.099	+	73.9578i	−0.377872	+	0.218165i
$340$	36.9481	+	334.429i	0.108671	+	0.983614i
$341$	−8.14912	+	14.1147i	−0.0238977	+	0.0413921i
$342$	60.8496	+	60.8496i	0.177923	+	0.177923i
$343$	115.030	−	323.136i	0.335364	−	0.942089i
$344$			164.464i			0.478094i
$345$	−29.9593	+	195.888i	−0.0868385	+	0.567793i
$346$	−11.0739	−	19.1806i	−0.0320056	−	0.0554353i
$347$	85.7311	−	319.953i	0.247064	−	0.922055i	−0.725271	−	0.688463i	$-0.758286\pi$
$347$	85.7311	−	319.953i	0.247064	−	0.922055i	0.972335	−	0.233591i	$-0.0750477\pi$
$348$	14.0190	+	52.3198i	0.0402846	+	0.150344i
$349$			383.298i			1.09828i	0.835732	+	0.549138i	$0.185044\pi$
$349$			383.298i			1.09828i	−0.835732	+	0.549138i	$0.814956\pi$
$350$	230.929	−	89.0040i	0.659798	−	0.254297i
$351$	−424.016			−1.20802
$352$	−3.73403	+	1.00053i	−0.0106080	+	0.00284242i
$353$	538.726	+	144.351i	1.52614	+	0.408927i	0.921756	−	0.387770i	$-0.126754\pi$
$353$	538.726	+	144.351i	1.52614	+	0.408927i	0.604379	+	0.796697i	$0.293421\pi$
$354$	−46.3450	+	26.7573i	−0.130918	+	0.0755856i
$355$	312.697	+	47.8240i	0.880835	+	0.134715i
$356$	−159.699			−0.448593
$357$	43.8864	−	383.309i	0.122931	−	1.07369i
$358$	−342.900	+	342.900i	−0.957821	+	0.957821i
$359$	−190.670	−	110.083i	−0.531113	−	0.306638i	0.210357	−	0.977625i	$-0.432538\pi$
$359$	−190.670	−	110.083i	−0.531113	−	0.306638i	−0.741470	+	0.670987i	$0.765871\pi$
$360$	−88.7903	+	9.80965i	−0.246640	+	0.0272490i
$361$	−134.100	−	232.268i	−0.371469	−	0.643403i
$362$	−120.391	+	32.2585i	−0.332571	+	0.0891120i
$363$	−139.615	+	139.615i	−0.384614	+	0.384614i
$364$	34.8421	+	234.016i	0.0957202	+	0.642901i
$365$	−215.672	−	94.6529i	−0.590881	−	0.259323i
$366$	−14.0923	+	24.4086i	−0.0385036	+	0.0666902i
$367$	126.983	−	473.906i	0.346002	−	1.29130i	−0.545435	−	0.838153i	$-0.683635\pi$
$367$	126.983	−	473.906i	0.346002	−	1.29130i	0.891437	−	0.453145i	$-0.149698\pi$
$368$	−93.4809	−	25.0481i	−0.254024	−	0.0680656i
$369$	−1.09682	−	0.633250i	−0.00297241	−	0.00171612i
$370$	−173.058	+	67.4883i	−0.467724	+	0.182401i
$371$	645.830	−	96.1563i	1.74078	−	0.259181i
$372$	55.2506	+	55.2506i	0.148523	+	0.148523i
$373$	11.3448	+	42.3394i	0.0304150	+	0.113510i	0.979465	−	0.201617i	$-0.0646195\pi$
$373$	11.3448	+	42.3394i	0.0304150	+	0.113510i	−0.949049	+	0.315127i	$0.897953\pi$
$374$	28.1607	−	16.2586i	0.0752959	−	0.0434721i
$375$	−154.334	−	134.569i	−0.411556	−	0.358851i
$376$	67.5831	−	117.057i	0.179742	−	0.311323i
$377$	197.567	+	197.567i	0.524051	+	0.524051i
$378$	246.768	+	28.2533i	0.652825	+	0.0747443i
$379$		−	393.135i		−	1.03729i	−0.854988	−	0.518647i	$-0.826436\pi$
$379$		−	393.135i		−	1.03729i	0.854988	−	0.518647i	$-0.173564\pi$
$380$	−95.2252	−	14.5638i	−0.250593	−	0.0383258i
$381$	125.193	+	216.840i	0.328589	+	0.569134i
$382$	17.2341	−	64.3185i	0.0451154	−	0.168373i
$383$	30.8833	+	115.258i	0.0806352	+	0.300935i	0.994452	−	0.105192i	$-0.0335458\pi$
$383$	30.8833	+	115.258i	0.0806352	+	0.300935i	−0.913817	+	0.406127i	$0.866879\pi$
$384$			18.5330i			0.0482630i
$385$	−16.8455	−	16.9796i	−0.0437546	−	0.0441027i
$386$	144.749			0.374998
$387$	354.777	−	95.0623i	0.916738	−	0.245639i
$388$	−138.470	−	37.1028i	−0.356880	−	0.0956258i
$389$	369.542	−	213.355i	0.949979	−	0.548471i	0.0569045	−	0.998380i	$-0.481877\pi$
$389$	369.542	−	213.355i	0.949979	−	0.548471i	0.893074	+	0.449909i	$0.148544\pi$
$390$	157.752	−	115.900i	0.404493	−	0.297179i
$391$	814.061			2.08200
$392$	−4.68424	−	138.514i	−0.0119496	−	0.353351i
$393$	68.2059	−	68.2059i	0.173552	−	0.173552i
$394$	282.580	+	163.148i	0.717209	+	0.414081i
$395$	−438.109	−	350.934i	−1.10914	−	0.888441i
$396$	4.31662	+	7.47661i	0.0109006	+	0.0188803i
$397$	106.060	−	28.4186i	0.267153	−	0.0715835i	−0.122756	−	0.992437i	$-0.539173\pi$
$397$	106.060	−	28.4186i	0.267153	−	0.0715835i	0.389909	+	0.920853i	$0.372506\pi$
$398$	340.731	−	340.731i	0.856108	−	0.856108i
$399$	102.753	+	40.5409i	0.257527	+	0.101606i
$400$	73.5990	−	67.6992i	0.183997	−	0.169248i
$401$	−39.4499	+	68.3292i	−0.0983787	+	0.170397i	−0.911014	−	0.412376i	$-0.864699\pi$
$401$	−39.4499	+	68.3292i	−0.0983787	+	0.170397i	0.812635	+	0.582773i	$0.198032\pi$
$402$	−0.841215	+	3.13946i	−0.00209257	+	0.00780959i
$403$	389.317	+	104.317i	0.966048	+	0.258852i
$404$	95.2628	+	55.0000i	0.235799	+	0.136139i
$405$	28.6107	+	73.3655i	0.0706437	+	0.181149i
$406$	−101.815	−	128.144i	−0.250777	−	0.315626i
$407$	12.6938	+	12.6938i	0.0311888	+	0.0311888i
$408$	−40.3478	−	150.580i	−0.0988917	−	0.369069i
$409$	−340.819	+	196.772i	−0.833298	+	0.481105i	−0.854981	−	0.518660i	$-0.826431\pi$
$409$	−340.819	+	196.772i	−0.833298	+	0.481105i	0.0216824	+	0.999765i	$0.493098\pi$
$410$	1.40919	−	0.155689i	0.00343706	−	0.000379730i
$411$	−107.925	+	186.931i	−0.262591	+	0.454821i
$412$	0.316625	+	0.316625i	0.000768507	+	0.000768507i
$413$	96.2555	−	129.932i	0.233064	−	0.314606i
$414$			216.132i			0.522058i
$415$	131.726	−	96.7783i	0.317412	−	0.233201i
$416$	47.7995	+	82.7912i	0.114903	+	0.199017i
$417$	−28.9285	+	107.963i	−0.0693730	+	0.258904i
$418$	2.40959	+	8.99271i	0.00576457	+	0.0215137i
$419$		−	165.330i		−	0.394582i	−0.980345	−	0.197291i	$-0.936786\pi$
$419$		−	165.330i		−	0.394582i	0.980345	−	0.197291i	$-0.0632144\pi$
$420$	−99.5310	+	56.9396i	−0.236979	+	0.135571i
$421$	163.631			0.388672			0.194336	−	0.980935i	$-0.437745\pi$
$421$	163.631			0.388672			0.194336	+	0.980935i	$0.437745\pi$
$422$	155.453	−	41.6535i	0.368372	−	0.0987050i
$423$	−291.576	−	78.1276i	−0.689306	−	0.184699i
$424$	228.485	−	131.916i	0.538879	−	0.311122i
$425$	−450.603	+	710.285i	−1.06024	+	1.67126i
$426$	−146.565			−0.344049
$427$	9.68741	−	84.6110i	0.0226871	−	0.198152i
$428$	190.317	−	190.317i	0.444665	−	0.444665i
$429$	−16.3836	−	9.45907i	−0.0381902	−	0.0220491i
$430$	−257.050	+	320.903i	−0.597791	+	0.746286i
$431$	−209.872	−	363.509i	−0.486942	−	0.843409i	0.512945	−	0.858422i	$-0.328555\pi$
$431$	−209.872	−	363.509i	−0.486942	−	0.843409i	−0.999887	+	0.0150126i	$0.995221\pi$
$432$	96.9410	−	25.9753i	0.224400	−	0.0601279i
$433$	−355.950	+	355.950i	−0.822055	+	0.822055i	−0.986403	−	0.164347i	$-0.947448\pi$
$433$	−355.950	+	355.950i	−0.822055	+	0.822055i	0.164347	+	0.986403i	$0.447448\pi$
$434$	−219.623	−	86.6516i	−0.506044	−	0.199658i
$435$	−54.4194	+	123.997i	−0.125102	+	0.285052i
$436$	−51.1161	+	88.5357i	−0.117239	+	0.203064i
$437$	−60.3237	+	225.131i	−0.138041	+	0.515174i
$438$	105.408	+	28.2439i	0.240657	+	0.0644838i
$439$	−162.609	−	93.8826i	−0.370409	−	0.213856i	0.303228	−	0.952918i	$-0.401936\pi$
$439$	−162.609	−	93.8826i	−0.370409	−	0.213856i	−0.673637	+	0.739062i	$0.735269\pi$
$440$	−8.84962	−	3.88388i	−0.0201128	−	0.00882699i
$441$	−296.090	+	90.1672i	−0.671405	+	0.204461i
$442$	−568.612	−	568.612i	−1.28645	−	1.28645i
$443$	154.855	+	577.926i	0.349560	+	1.30457i	0.887194	+	0.461396i	$0.152651\pi$
$443$	154.855	+	577.926i	0.349560	+	1.30457i	−0.537635	+	0.843178i	$0.680682\pi$
$444$	74.5332	−	43.0317i	0.167867	−	0.0969183i
$445$	−311.605	−	249.602i	−0.700236	−	0.560904i
$446$	−158.916	+	275.250i	−0.356313	+	0.617152i
$447$	−101.293	−	101.293i	−0.226606	−	0.226606i
$448$	−22.3017	−	51.3677i	−0.0497805	−	0.114660i
$449$		−	93.8630i		−	0.209049i	−0.994522	−	0.104524i	$-0.966668\pi$
$449$		−	93.8630i		−	0.209049i	0.994522	−	0.104524i	$-0.0333321\pi$
$450$	−188.580	−	119.634i	−0.419066	−	0.265854i
$451$	−0.0685092	−	0.118661i	−0.000151905	−	0.000263107i
$452$	46.7412	−	174.440i	0.103410	−	0.385930i
$453$	−100.050	−	373.390i	−0.220860	−	0.824260i
$454$			403.715i			0.889240i
$455$	−297.772	+	511.068i	−0.654443	+	1.12323i
$456$	44.6332			0.0978799
$457$	−204.824	+	54.8826i	−0.448194	+	0.120093i	−0.475854	−	0.879524i	$-0.657861\pi$
$457$	−204.824	+	54.8826i	−0.448194	+	0.120093i	0.0276604	+	0.999617i	$0.491194\pi$
$458$	428.042	+	114.693i	0.934589	+	0.250422i
$459$	−731.093	+	422.096i	−1.59279	+	0.919600i
$460$	−143.251	−	194.980i	−0.311415	−	0.423870i
$461$	350.396			0.760078			0.380039	−	0.924970i	$-0.375911\pi$
$461$	350.396			0.760078			0.380039	+	0.924970i	$0.375911\pi$
$462$	8.90460	+	6.59665i	0.0192740	+	0.0142785i
$463$	−327.380	+	327.380i	−0.707084	+	0.707084i	−0.965921	−	0.258837i	$-0.916661\pi$
$463$	−327.380	+	327.380i	−0.707084	+	0.707084i	0.258837	+	0.965921i	$0.416661\pi$
$464$	−57.2720	−	33.0660i	−0.123431	−	0.0712629i
$465$	21.4509	+	194.159i	0.0461310	+	0.417546i
$466$	35.7757	+	61.9653i	0.0767719	+	0.132973i
$467$	−525.495	+	140.806i	−1.12526	+	0.301512i	−0.773009	−	0.634395i	$-0.781249\pi$
$467$	−525.495	+	140.806i	−1.12526	+	0.301512i	−0.352248	+	0.935907i	$0.614582\pi$
$468$	150.966	−	150.966i	0.322576	−	0.322576i
$469$	−1.44628	−	9.71386i	−0.00308375	−	0.0207119i
$470$	314.823	−	122.773i	0.669837	−	0.261220i
$471$	130.474	−	225.987i	0.277014	−	0.479803i
$472$	16.9106	−	63.1111i	0.0358275	−	0.133710i
$473$	38.3822	+	10.2845i	0.0811464	+	0.0217431i
$474$	225.235	+	130.040i	0.475180	+	0.274345i
$475$	−163.041	−	177.249i	−0.343244	−	0.373157i
$476$	293.032	+	368.808i	0.615613	+	0.774807i
$477$	−416.631	−	416.631i	−0.873440	−	0.873440i
$478$	71.4957	+	266.826i	0.149573	+	0.558213i
$479$	−58.5721	+	33.8166i	−0.122280	+	0.0705984i	−0.559892	−	0.828565i	$-0.689158\pi$
$479$	−58.5721	+	33.8166i	−0.122280	+	0.0705984i	0.437612	+	0.899164i	$0.355824\pi$
$480$	−28.9662	+	36.1616i	−0.0603462	+	0.0753366i
$481$	221.971	−	384.465i	0.461479	−	0.799304i
$482$	−92.9315	−	92.9315i	−0.192804	−	0.192804i
$483$	110.486	+	254.483i	0.228749	+	0.526881i
$484$		−	241.066i		−	0.498070i
$485$	−212.192	−	288.816i	−0.437509	−	0.595497i
$486$	−177.916	−	308.159i	−0.366082	−	0.634072i
$487$	−192.958	+	720.130i	−0.396218	+	1.47871i	0.423477	+	0.905907i	$0.360809\pi$
$487$	−192.958	+	720.130i	−0.396218	+	1.47871i	−0.819696	+	0.572799i	$0.805857\pi$
$488$	−8.90631	−	33.2388i	−0.0182506	−	0.0681123i
$489$		−	408.937i		−	0.836271i
$490$	207.350	−	277.589i	0.423164	−	0.566509i
$491$	199.061			0.405419			0.202710	−	0.979239i	$-0.435025\pi$
$491$	199.061			0.405419			0.202710	+	0.979239i	$0.435025\pi$
$492$	−0.634504	+	0.170015i	−0.00128964	+	0.000345559i
$493$	537.320	+	143.975i	1.08990	+	0.292038i
$494$	199.387	−	115.116i	0.403617	−	0.233029i
$495$	−3.26299	+	21.3350i	−0.00659190	+	0.0431011i
$496$	−95.3985			−0.192336
$497$	406.231	−	176.368i	0.817367	−	0.354866i
$498$	−53.5514	+	53.5514i	−0.107533	+	0.107533i
$499$	471.810	+	272.400i	0.945511	+	0.545891i	0.891684	−	0.452659i	$-0.149524\pi$
$499$	471.810	+	272.400i	0.945511	+	0.545891i	0.0538277	+	0.998550i	$0.482858\pi$
$500$	249.417	−	17.0630i	0.498834	−	0.0341261i
$501$	234.905	+	406.868i	0.468873	+	0.812111i
$502$	−454.429	+	121.764i	−0.905237	+	0.242557i
$503$	−38.0869	+	38.0869i	−0.0757195	+	0.0757195i	−0.743952	−	0.668233i	$-0.767051\pi$
$503$	−38.0869	+	38.0869i	−0.0757195	+	0.0757195i	0.668233	+	0.743952i	$0.267051\pi$
$504$	−97.9180	+	77.7995i	−0.194282	+	0.154364i
$505$	99.9144	+	256.207i	0.197850	+	0.507341i
$506$	−11.6913	+	20.2499i	−0.0231054	+	0.0400197i
$507$	−49.4347	+	184.493i	−0.0975043	+	0.363891i
$508$	−295.285	−	79.1214i	−0.581270	−	0.155751i
$509$	−149.946	−	86.5714i	−0.294590	−	0.170081i	0.345420	−	0.938448i	$-0.387736\pi$
$509$	−149.946	−	86.5714i	−0.294590	−	0.170081i	−0.640010	+	0.768367i	$0.721070\pi$
$510$	156.623	−	356.873i	0.307104	−	0.699752i
$511$	−326.144	+	48.5589i	−0.638247	+	0.0950273i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−62.5566	−	233.464i	−0.121943	−	0.455096i
$514$	−125.384	+	72.3906i	−0.243938	+	0.140838i
$515$	0.122929	+	1.11267i	0.000238697	+	0.00216052i
$516$	95.2506	−	164.979i	0.184594	−	0.319727i
$517$	−23.0923	−	23.0923i	−0.0446660	−	0.0446660i
$518$	−154.800	+	208.960i	−0.298842	+	0.403397i
$519$			25.6541i			0.0494300i
$520$	−36.1323	+	236.250i	−0.0694851	+	0.454328i
$521$	−121.347	−	210.179i	−0.232912	−	0.403415i	0.725752	−	0.687957i	$-0.241492\pi$
$521$	−121.347	−	210.179i	−0.232912	−	0.403415i	−0.958664	+	0.284541i	$0.908159\pi$
$522$	−38.2250	+	142.658i	−0.0732280	+	0.273291i
$523$	−206.313	−	769.970i	−0.394480	−	1.47222i	−0.822665	−	0.568527i	$-0.807514\pi$
$523$	−206.313	−	769.970i	−0.394480	−	1.47222i	0.428185	−	0.903691i	$-0.359153\pi$
$524$			117.768i			0.224748i
$525$	−283.199	−	44.4616i	−0.539426	−	0.0846888i
$526$	−282.781			−0.537607
$527$	775.110	−	207.690i	1.47080	−	0.394099i
$528$	4.32518	+	1.15893i	0.00819162	+	0.00219494i
$529$	−48.8266	+	28.1901i	−0.0922998	+	0.0532893i
$530$	651.997	+	99.7167i	1.23018	+	0.188145i
$531$	−145.916			−0.274794
$532$	−123.709	+	53.7094i	−0.232536	+	0.100957i
$533$	−2.39598	+	2.39598i	−0.00449527	+	0.00449527i
$534$	160.199	+	92.4908i	0.299998	+	0.173204i
$535$	668.802	−	73.8899i	1.25010	−	0.138112i
$536$	−1.98413	−	3.43661i	−0.00370173	−	0.00641159i
$537$	542.565	−	145.380i	1.01036	−	0.270726i
$538$	229.248	−	229.248i	0.426112	−	0.426112i
$539$	−32.6188	−	7.56851i	−0.0605173	−	0.0140418i
$540$	229.749	+	100.831i	0.425462	+	0.186725i
$541$	−274.812	+	475.988i	−0.507970	+	0.879829i	0.491988	+	0.870602i	$0.336270\pi$
$541$	−274.812	+	475.988i	−0.507970	+	0.879829i	−0.999957	+	0.00922718i	$0.997063\pi$
$542$	−20.5641	+	76.7462i	−0.0379411	+	0.141598i
$543$	139.450	+	37.3655i	0.256814	+	0.0688130i
$544$	164.833	+	95.1662i	0.303001	+	0.174938i
$545$	−238.115	+	92.8588i	−0.436908	+	0.170383i
$546$	100.581	−	254.927i	0.184214	−	0.466899i
$547$	469.765	+	469.765i	0.858803	+	0.858803i	0.991197	−	0.132394i	$-0.0422665\pi$
$547$	469.765	+	469.765i	0.858803	+	0.858803i	−0.132394	+	0.991197i	$0.542266\pi$
$548$	−68.2082	−	254.557i	−0.124468	−	0.464519i
$549$	−66.5537	+	38.4248i	−0.121227	+	0.0699905i
$550$	−11.1971	−	21.4098i	−0.0203583	−	0.0389268i
$551$	−79.6332	+	137.929i	−0.144525	+	0.250325i
$552$	79.2665	+	79.2665i	0.143599	+	0.143599i
$553$	−780.765	−	89.3925i	−1.41187	−	0.161650i
$554$			120.016i			0.216635i
$555$	212.686	+	32.5283i	0.383217	+	0.0586095i
$556$	−68.2322	−	118.182i	−0.122720	−	0.212557i
$557$	−98.7738	+	368.629i	−0.177332	+	0.661811i	0.818811	+	0.574063i	$0.194634\pi$
$557$	−98.7738	+	368.629i	−0.177332	+	0.661811i	−0.996143	+	0.0877479i	$0.972033\pi$
$558$	55.1414	+	205.791i	0.0988197	+	0.368800i
$559$		−	982.665i		−	1.75790i
$560$	36.7702	−	135.085i	0.0656611	−	0.241223i
$561$	−37.6650			−0.0671390
$562$	186.053	−	49.8528i	0.331056	−	0.0887061i
$563$	176.181	+	47.2076i	0.312933	+	0.0838502i	0.411867	−	0.911244i	$-0.364877\pi$
$563$	176.181	+	47.2076i	0.312933	+	0.0838502i	−0.0989343	+	0.995094i	$0.531543\pi$
$564$	−135.589	+	78.2824i	−0.240406	+	0.138799i
$565$	363.843	−	267.314i	0.643971	−	0.473122i
$566$	−444.881			−0.786009
$567$	88.5856	+	65.6254i	0.156236	+	0.115741i
$568$	126.533	−	126.533i	0.222769	−	0.222769i
$569$	647.396	+	373.774i	1.13778	+	0.656897i	0.945880	−	0.324518i	$-0.105202\pi$
$569$	647.396	+	373.774i	1.13778	+	0.656897i	0.191899	+	0.981415i	$0.438535\pi$
$570$	87.0884	+	69.7596i	0.152787	+	0.122385i
$571$	−92.0727	−	159.475i	−0.161248	−	0.279290i	0.774068	−	0.633102i	$-0.218219\pi$
$571$	−92.0727	−	159.475i	−0.161248	−	0.279290i	−0.935317	+	0.353812i	$0.884885\pi$
$572$	22.3106	−	5.97811i	0.0390046	−	0.0104512i
$573$	−54.5384	+	54.5384i	−0.0951805	+	0.0951805i
$574$	1.55406	−	1.23476i	0.00270742	−	0.00215114i
$575$	25.2335	−	604.339i	0.0438843	−	1.05102i
$576$	−25.2665	+	43.7629i	−0.0438654	+	0.0759772i
$577$	256.665	−	957.887i	0.444827	−	1.66012i	−0.271567	−	0.962420i	$-0.587542\pi$
$577$	256.665	−	957.887i	0.444827	−	1.66012i	0.716394	−	0.697696i	$-0.245791\pi$
$578$	−1151.66	−	308.588i	−1.99250	−	0.533888i
$579$	−145.202	−	83.8325i	−0.250781	−	0.144788i
$580$	−60.0685	−	154.032i	−0.103566	−	0.265572i
$581$	83.9866	−	212.869i	0.144555	−	0.366383i
$582$	117.414	+	117.414i	0.201743	+	0.201743i
$583$	−16.4982	−	61.5721i	−0.0282988	−	0.105613i
$584$	−115.385	+	66.6174i	−0.197577	+	0.114071i
$585$	530.517	−	58.6121i	0.906866	−	0.100192i
$586$	−184.699	+	319.908i	−0.315186	+	0.545919i
$587$	−103.786	−	103.786i	−0.176808	−	0.176808i	0.613155	−	0.789963i	$-0.289900\pi$
$587$	−103.786	−	103.786i	−0.176808	−	0.176808i	−0.789963	+	0.613155i	$0.789900\pi$
$588$	−75.5222	+	141.660i	−0.128439	+	0.240918i
$589$			229.749i			0.390067i
$590$	131.635	−	96.7119i	0.223111	−	0.163918i
$591$	−188.976	−	327.316i	−0.319757	−	0.553835i
$592$	−27.1960	+	101.497i	−0.0459391	+	0.171447i
$593$	24.0988	+	89.9380i	0.0406388	+	0.151666i	0.983264	−	0.182187i	$-0.0583177\pi$
$593$	24.0988	+	89.9380i	0.0406388	+	0.151666i	−0.942625	+	0.333853i	$0.891651\pi$
$594$		−	24.2481i		−	0.0408217i
$595$	−4.66609	+	1177.61i	−0.00784217	+	1.97918i
$596$	174.897			0.293452
$597$	−539.133	+	144.460i	−0.903071	+	0.241977i
$598$	558.542	+	149.661i	0.934017	+	0.250269i
$599$	469.928	−	271.313i	0.784520	−	0.452943i	−0.0535096	−	0.998567i	$-0.517041\pi$
$599$	469.928	−	271.313i	0.784520	−	0.452943i	0.838030	+	0.545624i	$0.183707\pi$
$600$	−113.038	+	25.2857i	−0.188396	+	0.0421428i
$601$	422.829			0.703542			0.351771	−	0.936086i	$-0.385580\pi$
$601$	422.829			0.703542			0.351771	+	0.936086i	$0.385580\pi$
$602$	−65.4777	+	571.890i	−0.108767	+	0.949983i
$603$	−6.26650	+	6.26650i	−0.0103922	+	0.0103922i
$604$	408.732	+	235.982i	0.676709	+	0.390698i
$605$	376.775	−	470.368i	0.622768	−	0.777468i
$606$	−63.7072	−	110.344i	−0.105127	−	0.182086i
$607$	198.564	−	53.2050i	0.327123	−	0.0876524i	−0.0915198	−	0.995803i	$-0.529172\pi$
$607$	198.564	−	53.2050i	0.327123	−	0.0876524i	0.418643	+	0.908151i	$0.362506\pi$
$608$	−38.5330	+	38.5330i	−0.0633766	+	0.0633766i
$609$	27.9183	+	187.512i	0.0458428	+	0.307902i
$610$	34.5727	−	78.7757i	0.0566765	−	0.129140i
$611$	−403.805	+	699.411i	−0.660892	+	1.14470i
$612$	110.014	−	410.579i	0.179762	−	0.670881i
$613$	−242.590	−	65.0019i	−0.395743	−	0.106039i	0.0554588	−	0.998461i	$-0.482338\pi$
$613$	−242.590	−	65.0019i	−0.395743	−	0.106039i	−0.451202	+	0.892422i	$0.649005\pi$
$614$	−641.979	−	370.647i	−1.04557	−	0.603659i
$615$	−1.50377	−	0.659966i	−0.00244515	−	0.00107312i
$616$	−13.3826	+	1.99251i	−0.0217250	+	0.00323460i
$617$	206.947	+	206.947i	0.335409	+	0.335409i	0.854636	−	0.519227i	$-0.173780\pi$
$617$	206.947	+	206.947i	0.335409	+	0.335409i	−0.519227	+	0.854636i	$0.673780\pi$
$618$	−0.134240	−	0.500990i	−0.000217217	−	0.000810664i
$619$	408.698	−	235.962i	0.660255	−	0.381199i	−0.132119	−	0.991234i	$-0.542178\pi$
$619$	408.698	−	235.962i	0.660255	−	0.381199i	0.792374	+	0.610035i	$0.208845\pi$
$620$	−186.142	−	149.103i	−0.300228	−	0.240489i
$621$	303.524	−	525.719i	0.488766	−	0.846568i
$622$	439.079	+	439.079i	0.705915	+	0.705915i
$623$	−555.319	−	63.5805i	−0.891363	−	0.102055i
$624$		−	110.734i		−	0.177458i
$625$	513.331	+	356.534i	0.821330	+	0.570454i
$626$	147.122	+	254.822i	0.235018	+	0.407064i
$627$	2.79106	−	10.4164i	0.00445145	−	0.0166130i
$628$	82.4591	+	307.741i	0.131304	+	0.490034i
$629$		−	883.865i		−	1.40519i
$630$	−312.655	−	1.23884i	−0.496277	−	0.00196641i
$631$	−675.457			−1.07045			−0.535227	−	0.844708i	$-0.679774\pi$
$631$	−675.457			−1.07045			−0.535227	+	0.844708i	$0.679774\pi$
$632$	−306.718	+	82.1848i	−0.485313	+	0.130039i
$633$	−180.063	−	48.2478i	−0.284460	−	0.0762208i
$634$	−505.192	+	291.673i	−0.796833	+	0.460052i
$635$	−452.497	−	615.898i	−0.712594	−	0.969919i
$636$	−305.599			−0.480502
$637$	27.9881	+	827.611i	0.0439373	+	1.29923i
$638$	−11.2982	+	11.2982i	−0.0177088	+	0.0177088i
$639$	−346.090	−	199.815i	−0.541612	−	0.312700i
$640$	−6.21196	−	56.2264i	−0.00970619	−	0.0878538i
$641$	−21.7481	−	37.6688i	−0.0339284	−	0.0587657i	0.848563	−	0.529095i	$-0.177468\pi$
$641$	−21.7481	−	37.6688i	−0.0339284	−	0.0587657i	−0.882491	+	0.470329i	$0.844135\pi$
$642$	−301.135	+	80.6889i	−0.469058	+	0.125684i
$643$	344.145	−	344.145i	0.535218	−	0.535218i	−0.386902	−	0.922121i	$-0.626455\pi$
$643$	344.145	−	344.145i	0.535218	−	0.535218i	0.922121	+	0.386902i	$0.126455\pi$
$644$	−315.087	−	124.317i	−0.489266	−	0.193038i
$645$	443.707	−	173.035i	0.687918	−	0.268271i
$646$	229.190	−	396.969i	0.354783	−	0.614503i
$647$	−240.882	+	898.982i	−0.372305	+	1.38946i	0.484937	+	0.874549i	$0.338843\pi$
$647$	−240.882	+	898.982i	−0.372305	+	1.38946i	−0.857242	+	0.514913i	$0.827824\pi$
$648$	43.0281	+	11.5293i	0.0664014	+	0.0177922i
$649$	−13.6712	−	7.89307i	−0.0210650	−	0.0121619i
$650$	−439.749	+	404.499i	−0.676537	+	0.622306i
$651$	170.125	+	214.119i	0.261329	+	0.328908i
$652$	353.045	+	353.045i	0.541480	+	0.541480i
$653$	−150.489	−	561.631i	−0.230457	−	0.860078i	−0.980144	−	0.198286i	$-0.936463\pi$
$653$	−150.489	−	561.631i	−0.230457	−	0.860078i	0.749687	−	0.661793i	$-0.230204\pi$
$654$	102.552	−	59.2084i	0.156807	−	0.0905328i
$655$	−184.065	+	229.788i	−0.281016	+	0.350822i
$656$	0.401005	−	0.694561i	0.000611288	−	0.00105878i
$657$	210.398	+	210.398i	0.320241	+	0.320241i
$658$	281.609	−	380.135i	0.427978	−	0.577713i
$659$			217.266i			0.329691i	0.986319	+	0.164846i	$0.0527126\pi$
$659$			217.266i			0.329691i	−0.986319	+	0.164846i	$0.947287\pi$
$660$	6.62793	+	9.02134i	0.0100423	+	0.0136687i
$661$	−61.8693	−	107.161i	−0.0935995	−	0.162119i	0.815424	−	0.578865i	$-0.196504\pi$
$661$	−61.8693	−	107.161i	−0.0935995	−	0.162119i	−0.909023	+	0.416745i	$0.863171\pi$
$662$	136.667	−	510.047i	0.206445	−	0.770463i
$663$	241.076	+	899.706i	0.363613	+	1.35702i
$664$		−	92.4645i		−	0.139254i
$665$	−325.327	−	88.5541i	−0.489213	−	0.133164i
$666$	234.665			0.352350
$667$	−386.380	+	103.530i	−0.579280	+	0.155218i
$668$	−554.059	−	148.460i	−0.829429	−	0.222245i
$669$	318.825	−	184.074i	0.476570	−	0.275148i
$670$	1.49983	−	9.80662i	0.00223855	−	0.0146367i
$671$	−8.31411			−0.0123906
$672$	−7.37848	+	64.4445i	−0.0109799	+	0.0958995i
$673$	−129.111	+	129.111i	−0.191844	+	0.191844i	−0.796493	−	0.604648i	$-0.793314\pi$
$673$	−129.111	+	129.111i	−0.191844	+	0.191844i	0.604648	+	0.796493i	$0.293314\pi$
$674$	448.629	+	259.016i	0.665621	+	0.384297i
$675$	290.692	+	555.829i	0.430656	+	0.823451i
$676$	−116.599	−	201.955i	−0.172484	−	0.298751i
$677$	−425.912	+	114.123i	−0.629116	+	0.168571i	−0.559269	−	0.828986i	$-0.688918\pi$
$677$	−425.912	+	114.123i	−0.629116	+	0.168571i	−0.0698477	+	0.997558i	$0.522251\pi$
$678$	−147.916	+	147.916i	−0.218165	+	0.218165i
$679$	−466.726	−	184.145i	−0.687373	−	0.271201i
$680$	172.881	+	443.314i	0.254237	+	0.651933i
$681$	233.814	−	404.978i	0.343339	−	0.594681i
$682$	−5.96557	+	22.2638i	−0.00874717	+	0.0326449i
$683$	48.1139	+	12.8921i	0.0704449	+	0.0188757i	0.293869	−	0.955846i	$-0.405057\pi$
$683$	48.1139	+	12.8921i	0.0704449	+	0.0188757i	−0.223424	+	0.974721i	$0.571724\pi$
$684$	105.395	+	60.8496i	0.154086	+	0.0889614i
$685$	264.772	−	603.297i	0.386528	−	0.880726i
$686$	38.8576	−	483.516i	0.0566437	−	0.704834i
$687$	−362.955	−	362.955i	−0.528319	−	0.528319i
$688$	60.1982	+	224.663i	0.0874974	+	0.326545i
$689$	−1365.18	+	788.188i	−1.98139	+	1.14396i
$690$	30.7750	+	278.555i	0.0446015	+	0.403702i
$691$	−163.975	+	284.013i	−0.237301	+	0.411017i	−0.959939	−	0.280209i	$-0.909596\pi$
$691$	−163.975	+	284.013i	−0.237301	+	0.411017i	0.722638	+	0.691227i	$0.242929\pi$
$692$	−22.1479	−	22.1479i	−0.0320056	−	0.0320056i
$693$	12.0335	+	27.7169i	0.0173643	+	0.0399955i
$694$		−	468.444i		−	0.674991i
$695$	51.5776	−	337.240i	0.0742124	−	0.485237i
$696$	38.3008	+	66.3389i	0.0550298	+	0.0953144i
$697$	−1.74604	+	6.51631i	−0.00250508	+	0.00934908i
$698$	140.297	+	523.595i	0.200998	+	0.750136i
$699$		−	82.8789i		−	0.118568i
$700$	282.877	−	206.108i	0.404111	−	0.294440i
$701$	−85.2715			−0.121643			−0.0608213	−	0.998149i	$-0.519372\pi$
$701$	−85.2715			−0.121643			−0.0608213	+	0.998149i	$0.519372\pi$
$702$	−579.216	+	155.201i	−0.825095	+	0.221083i
$703$	244.436	+	65.4964i	0.347704	+	0.0931670i
$704$	−4.73456	+	2.73350i	−0.00672523	+	0.00388281i
$705$	−386.913	−	59.1747i	−0.548813	−	0.0839357i
$706$	788.749			1.11721
$707$	309.359	+	229.177i	0.437565	+	0.324154i
$708$	−53.5146	+	53.5146i	−0.0755856	+	0.0755856i
$709$	185.775	+	107.257i	0.262024	+	0.151280i	0.625258	−	0.780418i	$-0.284994\pi$
$709$	185.775	+	107.257i	0.262024	+	0.151280i	−0.363233	+	0.931698i	$0.618327\pi$
$710$	444.656	−	49.1261i	0.626276	−	0.0691917i
$711$	354.573	+	614.138i	0.498696	+	0.863766i
$712$	−218.153	+	58.4540i	−0.306395	+	0.0820983i
$713$	−408.024	+	408.024i	−0.572263	+	0.572263i
$714$	−80.3508	−	539.673i	−0.112536	−	0.755844i
$715$	52.8759	+	23.2059i	0.0739524	+	0.0324558i
$716$	−342.900	+	593.920i	−0.478910	+	0.829497i
$717$	82.8144	−	309.068i	0.115501	−	0.431057i
$718$	−300.753	−	80.5864i	−0.418876	−	0.112237i
$719$	849.937	+	490.711i	1.18211	+	0.682491i	0.956502	−	0.291727i	$-0.0942298\pi$
$719$	849.937	+	490.711i	1.18211	+	0.682491i	0.225608	+	0.974218i	$0.427563\pi$
$720$	−117.699	+	45.8997i	−0.163471	+	0.0637497i
$721$	0.974937	+	1.22705i	0.00135220	+	0.00170187i
$722$	−268.201	−	268.201i	−0.371469	−	0.371469i
$723$	39.4003	+	147.044i	0.0544956	+	0.203380i
$724$	−152.649	+	88.1320i	−0.210841	+	0.121729i
$725$	123.539	−	394.431i	0.170398	−	0.544043i
$726$	−139.615	+	241.820i	−0.192307	+	0.333085i
$727$	10.5831	+	10.5831i	0.0145573	+	0.0145573i	0.714348	−	0.699791i	$-0.246723\pi$
$727$	10.5831	+	10.5831i	0.0145573	+	0.0145573i	−0.699791	+	0.714348i	$0.746723\pi$
$728$	133.251	+	306.919i	0.183037	+	0.421591i
$729$			270.419i			0.370946i
$730$	−329.258	−	50.3569i	−0.451039	−	0.0689821i
$731$	−978.217	−	1694.32i	−1.33819	−	2.31781i
$732$	−10.3163	+	38.5009i	−0.0140933	+	0.0525969i
$733$	−281.561	−	1050.80i	−0.384121	−	1.43356i	−0.839548	−	0.543285i	$-0.817180\pi$
$733$	−281.561	−	1050.80i	−0.384121	−	1.43356i	0.455427	−	0.890273i	$-0.349486\pi$
$734$		−	693.847i		−	0.945296i
$735$	−368.767	+	158.369i	−0.501723	+	0.215468i
$736$	−136.865			−0.185959
$737$	−0.926100	+	0.248148i	−0.00125658	+	0.000336700i
$738$	−1.73007	−	0.463571i	−0.00234427	−	0.000628145i
$739$	319.303	−	184.350i	0.432074	−	0.249458i	−0.268156	−	0.963376i	$-0.586414\pi$
$739$	319.303	−	184.350i	0.432074	−	0.249458i	0.700230	+	0.713917i	$0.253081\pi$
$740$	−211.699	+	155.534i	−0.286080	+	0.210182i
$741$	−266.681			−0.359893
$742$	847.025	−	367.742i	1.14154	−	0.495609i
$743$	−45.4536	+	45.4536i	−0.0611758	+	0.0611758i	−0.737033	−	0.675857i	$-0.763774\pi$
$743$	−45.4536	+	45.4536i	−0.0611758	+	0.0611758i	0.675857	+	0.737033i	$0.263774\pi$
$744$	95.6969	+	55.2506i	0.128625	+	0.0742616i
$745$	341.259	+	273.356i	0.458066	+	0.366921i
$746$	30.9946	+	53.6842i	0.0415477	+	0.0719627i
$747$	−199.461	+	53.4455i	−0.267017	+	0.0715469i
$748$	32.5171	−	32.5171i	0.0434721	−	0.0434721i
$749$	737.555	−	586.015i	0.984719	−	0.782396i
$750$	−260.079	−	127.335i	−0.346772	−	0.169780i
$751$	−392.273	+	679.437i	−0.522334	+	0.904710i	0.477328	+	0.878725i	$0.341605\pi$
$751$	−392.273	+	679.437i	−0.522334	+	0.904710i	−0.999662	+	0.0259846i	$0.991728\pi$
$752$	49.4743	−	184.641i	0.0657903	−	0.245533i
$753$	526.371	+	141.041i	0.699031	+	0.187305i
$754$	342.197	+	197.567i	0.453842	+	0.262026i
$755$	428.690	+	1099.28i	0.567801	+	1.45599i
$756$	347.433	−	51.7286i	0.459567	−	0.0684240i
$757$	−535.185	−	535.185i	−0.706981	−	0.706981i	0.258918	−	0.965899i	$-0.416634\pi$
$757$	−535.185	−	535.185i	−0.706981	−	0.706981i	−0.965899	+	0.258918i	$0.916634\pi$
$758$	−143.897	−	537.032i	−0.189838	−	0.708485i
$759$	23.4558	−	13.5422i	0.0309035	−	0.0178421i
$760$	−135.411	+	14.9603i	−0.178172	+	0.0196847i
$761$	44.4816	−	77.0444i	0.0584515	−	0.101241i	−0.835319	−	0.549766i	$-0.814717\pi$
$761$	44.4816	−	77.0444i	0.0584515	−	0.101241i	0.893770	+	0.448525i	$0.148050\pi$
$762$	250.385	+	250.385i	0.328589	+	0.328589i
$763$	−212.994	+	287.513i	−0.279153	+	0.376819i
$764$		−	94.1688i		−	0.123258i
$765$	856.375	−	629.175i	1.11944	−	0.822450i
$766$	84.3747	+	146.141i	0.110150	+	0.190785i
$767$	−101.040	+	377.085i	−0.131733	+	0.491636i
$768$	6.78355	+	25.3165i	0.00883275	+	0.0329643i
$769$			999.457i			1.29968i	0.760069	+	0.649842i	$0.225165\pi$
$769$			999.457i			1.29968i	−0.760069	+	0.649842i	$0.774835\pi$
$770$	−29.2264	−	17.0286i	−0.0379563	−	0.0221151i
$771$	167.702			0.217512
$772$	197.731	−	52.9819i	0.256129	−	0.0686295i
$773$	−347.180	−	93.0266i	−0.449133	−	0.120345i	0.0271607	−	0.999631i	$-0.491353\pi$
$773$	−347.180	−	93.0266i	−0.449133	−	0.120345i	−0.476294	+	0.879286i	$0.658020\pi$
$774$	449.840	−	259.715i	0.581188	−	0.335549i
$775$	−130.158	−	581.861i	−0.167946	−	0.750788i
$776$	−202.734			−0.261255
$777$	276.305	−	119.960i	0.355605	−	0.154389i
$778$	426.710	−	426.710i	0.548471	−	0.548471i
$779$	−1.67272	−	0.965745i	−0.00214727	−	0.00123972i
$780$	173.071	−	216.063i	0.221886	−	0.277004i
$781$	−21.6174	−	37.4424i	−0.0276791	−	0.0479416i
$782$	1112.03	−	297.967i	1.42203	−	0.381032i
$783$	293.319	−	293.319i	0.374609	−	0.374609i
$784$	−57.0983	−	187.499i	−0.0728295	−	0.239157i
$785$	−320.091	+	729.345i	−0.407759	+	0.929101i
$786$	68.2059	−	118.136i	0.0867760	−	0.150300i
$787$	−20.5997	+	76.8792i	−0.0261750	+	0.0976864i	−0.977778	−	0.209645i	$-0.932769\pi$
$787$	−20.5997	+	76.8792i	−0.0261750	+	0.0976864i	0.951603	+	0.307331i	$0.0994359\pi$
$788$	445.728	+	119.433i	0.565645	+	0.151564i
$789$	283.666	+	163.774i	0.359526	+	0.207572i
$790$	−726.919	−	319.026i	−0.920150	−	0.403831i
$791$	231.982	−	587.970i	0.293276	−	0.743325i
$792$	8.63325	+	8.63325i	0.0109006	+	0.0109006i
$793$	53.2147	+	198.600i	0.0671055	+	0.250441i
$794$	134.478	−	77.6412i	0.169368	−	0.0977849i
$795$	−596.285	−	477.637i	−0.750044	−	0.600801i
$796$	340.731	−	590.163i	0.428054	−	0.741411i
$797$	−320.109	−	320.109i	−0.401642	−	0.401642i	0.477169	−	0.878811i	$-0.341663\pi$
$797$	−320.109	−	320.109i	−0.401642	−	0.401642i	−0.878811	+	0.477169i	$0.841663\pi$
$798$	155.202	+	17.7697i	0.194489	+	0.0222678i
$799$			1607.91i			2.01240i
$800$	75.7585	−	119.418i	0.0946981	−	0.149272i
$801$	252.190	+	436.806i	0.314844	+	0.545326i
$802$	−28.8793	+	107.779i	−0.0360091	+	0.134388i
$803$	8.33159	+	31.0939i	0.0103756	+	0.0387222i
$804$			4.59648i			0.00571702i
$805$	−420.497	−	735.033i	−0.522356	−	0.913084i
$806$	570.000			0.707196
$807$	−362.736	+	97.1947i	−0.449487	+	0.120440i
$808$	150.263	+	40.2628i	0.185969	+	0.0498302i
$809$	−1001.47	+	578.200i	−1.23791	+	0.714709i	−0.968667	−	0.248363i	$-0.920108\pi$
$809$	−1001.47	+	578.200i	−1.23791	+	0.714709i	−0.269245	+	0.963072i	$0.586774\pi$
$810$	65.9366	+	89.7469i	0.0814032	+	0.110799i
$811$	−143.794			−0.177305			−0.0886526	−	0.996063i	$-0.528256\pi$
$811$	−143.794			−0.177305			−0.0886526	+	0.996063i	$0.528256\pi$
$812$	−185.986	−	137.781i	−0.229047	−	0.169681i
$813$	65.0764	−	65.0764i	0.0800448	−	0.0800448i
$814$	21.9863	+	12.6938i	0.0270103	+	0.0155944i
$815$	137.069	+	1240.65i	0.168183	+	1.52228i
$816$	−110.232	−	190.928i	−0.135089	−	0.233980i
$817$	541.058	−	144.976i	0.662250	−	0.177449i
$818$	−393.544	+	393.544i	−0.481105	+	0.481105i
$819$	585.054	−	464.847i	0.714352	−	0.567579i
$820$	1.86801	−	0.728476i	0.00227806	−	0.000888385i
$821$	254.012	−	439.962i	0.309394	−	0.535885i	−0.668836	−	0.743410i	$-0.733207\pi$
$821$	254.012	−	439.962i	0.309394	−	0.535885i	0.978230	+	0.207524i	$0.0665406\pi$
$822$	−79.0064	+	294.856i	−0.0961149	+	0.358706i
$823$	1406.28	+	376.812i	1.70873	+	0.457852i	0.975112	−	0.221714i	$-0.0711650\pi$
$823$	1406.28	+	376.812i	1.70873	+	0.457852i	0.733615	+	0.679566i	$0.237832\pi$
$824$	0.548410	+	0.316625i	0.000665546	+	0.000384253i
$825$	−1.16750	+	27.9616i	−0.00141516	+	0.0338928i
$826$	83.9290	−	212.722i	0.101609	−	0.257533i
$827$	−969.412	−	969.412i	−1.17220	−	1.17220i	−0.981683	−	0.190520i	$-0.938983\pi$
$827$	−969.412	−	969.412i	−1.17220	−	1.17220i	−0.190520	−	0.981683i	$-0.561017\pi$
$828$	79.1098	+	295.242i	0.0955432	+	0.356572i
$829$	−747.599	+	431.627i	−0.901808	+	0.520659i	−0.877786	−	0.479052i	$-0.840980\pi$
$829$	−747.599	+	431.627i	−0.901808	+	0.520659i	−0.0240219	+	0.999711i	$0.507647\pi$
$830$	144.518	−	180.417i	0.174118	−	0.217369i
$831$	69.5079	−	120.391i	0.0836437	−	0.144875i
$832$	95.5990	+	95.5990i	0.114903	+	0.114903i
$833$	872.122	+	1399.11i	1.04697	+	1.67961i
$834$			158.069i			0.189531i
$835$	−849.044	−	1155.64i	−1.01682	−	1.38400i
$836$	6.58312	+	11.4023i	0.00787455	+	0.0136391i
$837$	154.875	−	578.002i	0.185036	−	0.690563i
$838$	−60.5150	−	225.845i	−0.0722136	−	0.269505i
$839$			541.425i			0.645322i	0.946515	+	0.322661i	$0.104577\pi$
$839$			541.425i			0.645322i	−0.946515	+	0.322661i	$0.895423\pi$
$840$	−115.121	+	114.212i	−0.137048	+	0.135966i
$841$	567.660			0.674982
$842$	223.524	−	59.8930i	0.265468	−	0.0711318i
$843$	−215.508	−	57.7452i	−0.255644	−	0.0684996i
$844$	197.107	−	113.799i	0.233539	−	0.134834i
$845$	88.1387	−	576.294i	0.104306	−	0.682005i
$846$	−426.897			−0.504607
$847$	95.9748	−	838.255i	0.113311	−	0.989675i
$848$	263.831	−	263.831i	0.311122	−	0.311122i
$849$	446.273	+	257.656i	0.525645	+	0.303482i
$850$	−355.553	+	1135.20i	−0.418297	+	1.33553i
$851$	317.788	+	550.425i	0.373429	+	0.646797i
$852$	−200.211	+	53.6464i	−0.234990	+	0.0629653i
$853$	203.211	−	203.211i	0.238231	−	0.238231i	−0.577886	−	0.816117i	$-0.696122\pi$
$853$	203.211	−	203.211i	0.238231	−	0.238231i	0.816117	+	0.577886i	$0.196122\pi$
$854$	−17.7365	−	119.127i	−0.0207687	−	0.139492i
$855$	110.541	+	283.457i	0.129288	+	0.331528i
$856$	190.317	−	329.638i	0.222333	−	0.385091i
$857$	303.758	−	1133.64i	0.354443	−	1.32280i	−0.526741	−	0.850026i	$-0.676586\pi$
$857$	303.758	−	1133.64i	0.354443	−	1.32280i	0.881184	−	0.472774i	$-0.156747\pi$
$858$	−25.8426	−	6.92452i	−0.0301196	−	0.00807053i
$859$	−254.787	−	147.102i	−0.296609	−	0.171247i	0.344309	−	0.938856i	$-0.388113\pi$
$859$	−254.787	−	147.102i	−0.296609	−	0.171247i	−0.640919	+	0.767609i	$0.721446\pi$
$860$	−233.678	+	532.449i	−0.271719	+	0.619126i
$861$	−2.27404	+	0.338577i	−0.00264116	+	0.000393237i
$862$	−419.744	−	419.744i	−0.486942	−	0.486942i
$863$	−367.260	−	1370.63i	−0.425562	−	1.58822i	−0.762693	−	0.646760i	$-0.776123\pi$
$863$	−367.260	−	1370.63i	−0.425562	−	1.58822i	0.337132	−	0.941457i	$-0.390543\pi$
$864$	122.916	−	70.9657i	0.142264	−	0.0821363i
$865$	−8.59885	−	77.8310i	−0.00994087	−	0.0899780i
$866$	−355.950	+	616.523i	−0.411028	+	0.711921i
$867$	976.546	+	976.546i	1.12635	+	1.12635i
$868$	−331.728	−	37.9807i	−0.382175	−	0.0437565i
$869$			76.7201i			0.0882855i
$870$	−28.9520	+	189.303i	−0.0332782	+	0.217589i
$871$	11.8550	+	20.5335i	0.0136108	+	0.0235747i
$872$	−37.4196	+	139.652i	−0.0429124	+	0.160151i
$873$	117.182	+	437.330i	0.134229	+	0.500951i
$874$			329.615i			0.377134i
$875$	874.087	+	39.9665i	0.998956	+	0.0456760i
$876$	154.327			0.176173
$877$	−1352.53	+	362.410i	−1.54222	+	0.413238i	−0.926984	−	0.375101i	$-0.877608\pi$
$877$	−1352.53	+	362.410i	−1.54222	+	0.413238i	−0.615241	+	0.788339i	$0.710941\pi$
$878$	−256.492	−	68.7268i	−0.292132	−	0.0782766i
$879$	370.554	−	213.939i	0.421563	−	0.243390i
$880$	−13.5104	−	2.06629i	−0.0153527	−	0.00234806i
$881$	1069.93			1.21445			0.607223	−	0.794532i	$-0.292284\pi$
$881$	1069.93			1.21445			0.607223	+	0.794532i	$0.292284\pi$
$882$	−371.463	+	231.547i	−0.421160	+	0.262525i
$883$	1198.71	−	1198.71i	1.35754	−	1.35754i	0.480593	−	0.876944i	$-0.340421\pi$
$883$	1198.71	−	1198.71i	1.35754	−	1.35754i	0.876944	−	0.480593i	$-0.159579\pi$
$884$	−984.865	−	568.612i	−1.11410	−	0.643227i
$885$	−188.058	+	20.7769i	−0.212495	+	0.0234767i
$886$	423.071	+	732.781i	0.477507	+	0.827067i
$887$	74.4895	−	19.9594i	0.0839791	−	0.0225021i	−0.216585	−	0.976264i	$-0.569492\pi$
$887$	74.4895	−	19.9594i	0.0839791	−	0.0225021i	0.300564	+	0.953762i	$0.402825\pi$
$888$	86.0635	−	86.0635i	0.0969183	−	0.0969183i
$889$	−995.290	−	392.688i	−1.11956	−	0.441719i
$890$	−517.021	−	226.908i	−0.580923	−	0.254952i
$891$	5.38137	−	9.32080i	0.00603969	−	0.0104611i
$892$	−116.334	+	434.166i	−0.130420	+	0.486733i
$893$	−444.672	−	119.150i	−0.497953	−	0.133426i
$894$	−175.444	−	101.293i	−0.196246	−	0.113303i
$895$	−1597.33	+	622.920i	−1.78473	+	0.696000i
$896$	−49.2665	−	62.0065i	−0.0549849	−	0.0692037i
$897$	−473.612	−	473.612i	−0.527996	−	0.527996i
$898$	−34.3562	−	128.219i	−0.0382586	−	0.142783i
$899$	−341.479	+	197.153i	−0.379843	+	0.219302i
$900$	−301.394	−	94.3987i	−0.334882	−	0.104887i
$901$	−1569.24	+	2718.00i	−1.74166	+	3.01665i
$902$	−0.137018	−	0.137018i	−0.000151905	−	0.000151905i
$903$	396.896	−	535.757i	0.439530	−	0.593307i
$904$		−	255.398i		−	0.282520i
$905$	−435.595	−	66.6201i	−0.481320	−	0.0736134i
$906$	−273.340	−	473.440i	−0.301700	−	0.522560i
$907$	260.960	−	973.915i	0.287717	−	1.07378i	−0.659113	−	0.752044i	$-0.729068\pi$
$907$	260.960	−	973.915i	0.287717	−	1.07378i	0.946831	−	0.321732i	$-0.104265\pi$
$908$	147.770	+	551.485i	0.162742	+	0.607362i
$909$		−	347.414i		−	0.382194i
$910$	−219.700	+	807.124i	−0.241428	+	0.886950i
$911$	−1241.02			−1.36226			−0.681130	−	0.732162i	$-0.738511\pi$
$911$	−1241.02			−1.36226			−0.681130	+	0.732162i	$0.738511\pi$
$912$	60.9702	−	16.3369i	0.0668532	−	0.0179133i
$913$	−21.5791	−	5.78210i	−0.0236354	−	0.00633308i
$914$	−259.707	+	149.942i	−0.284143	+	0.164050i
$915$	−80.3042	+	58.9991i	−0.0877642	+	0.0644799i
$916$	626.697			0.684167
$917$	−46.8865	+	409.512i	−0.0511303	+	0.446578i
$918$	−844.193	+	844.193i	−0.919600	+	0.919600i
$919$	5.83356	+	3.36801i	0.00634772	+	0.00366486i	0.503171	−	0.864187i	$-0.332167\pi$
$919$	5.83356	+	3.36801i	0.00634772	+	0.00366486i	−0.496823	+	0.867852i	$0.665500\pi$
$920$	−267.052	−	213.914i	−0.290274	−	0.232515i
$921$	429.325	+	743.612i	0.466150	+	0.807396i
$922$	478.650	−	128.254i	0.519143	−	0.139104i
$923$	−756.027	+	756.027i	−0.819097	+	0.819097i
$924$	14.5785	+	5.75188i	0.0157776	+	0.00622498i
$925$	−656.160	−	27.3972i	−0.709363	−	0.0296186i
$926$	−327.380	+	567.039i	−0.353542	+	0.612353i
$927$	0.366025	−	1.36603i	0.000394849	−	0.00147360i
$928$	−90.3380	−	24.2060i	−0.0973470	−	0.0260840i
$929$	−361.434	−	208.674i	−0.389057	−	0.224622i	0.292694	−	0.956206i	$-0.405448\pi$
$929$	−361.434	−	208.674i	−0.389057	−	0.224622i	−0.681752	+	0.731584i	$0.738782\pi$
$930$	100.370	+	257.375i	0.107924	+	0.276747i
$931$	−451.556	+	137.511i	−0.485022	+	0.147702i
$932$	71.5514	+	71.5514i	0.0767719	+	0.0767719i
$933$	−186.157	−	694.748i	−0.199525	−	0.744639i
$934$	−666.301	+	384.689i	−0.713384	+	0.411872i
$935$	114.270	−	12.6247i	0.122214	−	0.0135023i
$936$	150.966	−	261.480i	0.161288	−	0.279359i
$937$	−46.4937	−	46.4937i	−0.0496198	−	0.0496198i	0.681862	−	0.731481i	$-0.261171\pi$
$937$	−46.4937	−	46.4937i	−0.0496198	−	0.0496198i	−0.731481	+	0.681862i	$0.761171\pi$
$938$	−5.53117	−	12.7400i	−0.00589677	−	0.0135821i
$939$		−	340.825i		−	0.362966i
$940$	385.119	−	282.945i	0.409701	−	0.301005i
$941$	720.442	+	1247.84i	0.765614	+	1.32608i	0.939922	+	0.341390i	$0.110898\pi$
$941$	720.442	+	1247.84i	0.765614	+	1.32608i	−0.174308	+	0.984691i	$0.555769\pi$
$942$	95.5134	−	356.461i	0.101394	−	0.378408i
$943$	−1.25555	−	4.68579i	−0.00133145	−	0.00496902i
$944$		−	92.4010i		−	0.0978824i
$945$	758.760	+	442.088i	0.802921	+	0.467818i
$946$	56.1955			0.0594033
$947$	−539.920	+	144.671i	−0.570137	+	0.152768i	−0.532359	−	0.846518i	$-0.678694\pi$
$947$	−539.920	+	144.671i	−0.570137	+	0.152768i	−0.0377774	+	0.999286i	$0.512028\pi$
$948$	355.275	+	95.1957i	0.374763	+	0.100417i
$949$	689.416	−	398.035i	0.726466	−	0.419425i
$950$	−287.596	−	182.450i	−0.302732	−	0.192053i
$951$	675.697			0.710512
$952$	535.282	+	396.544i	0.562271	+	0.416538i
$953$	27.0794	−	27.0794i	0.0284149	−	0.0284149i	−0.692757	−	0.721171i	$-0.743604\pi$
$953$	27.0794	−	27.0794i	0.0284149	−	0.0284149i	0.721171	+	0.692757i	$0.243604\pi$
$954$	−721.626	−	416.631i	−0.756421	−	0.436720i
$955$	147.181	−	183.742i	0.154117	−	0.192400i
$956$	195.330	+	338.321i	0.204320	+	0.353893i
$957$	17.8770	−	4.79014i	0.0186803	−	0.00500537i
$958$	−67.6332	+	67.6332i	−0.0705984	+	0.0705984i
$959$	−135.834	−	912.321i	−0.141641	−	0.951325i
$960$	−26.3325	+	60.0000i	−0.0274297	+	0.0625000i
$961$	196.098	−	339.651i	0.204056	−	0.353435i
$962$	162.494	−	606.437i	0.168913	−	0.630391i
$963$	−821.090	−	220.010i	−0.852637	−	0.228463i
$964$	−160.962	−	92.9315i	−0.166973	−	0.0964020i
$965$	468.622	+	205.666i	0.485618	+	0.213126i
$966$	244.074	+	307.190i	0.252665	+	0.318002i
$967$	1012.58	+	1012.58i	1.04713	+	1.04713i	0.998833	+	0.0483007i	$0.0153806\pi$
$967$	1012.58	+	1012.58i	1.04713	+	1.04713i	0.0483007	+	0.998833i	$0.484619\pi$
$968$	−88.2363	−	329.302i	−0.0911532	−	0.340188i
$969$	−459.814	+	265.474i	−0.474524	+	0.273967i
$970$	−395.574	−	316.863i	−0.407808	−	0.326663i
$971$	676.674	−	1172.03i	0.696884	−	1.20704i	−0.272658	−	0.962111i	$-0.587903\pi$
$971$	676.674	−	1172.03i	0.696884	−	1.20704i	0.969542	−	0.244927i	$-0.0787640\pi$
$972$	−355.831	−	355.831i	−0.366082	−	0.366082i
$973$	−190.212	−	438.116i	−0.195490	−	0.450274i
$974$			1054.34i			1.08249i
$975$	675.393	−	151.080i	0.692711	−	0.154954i
$976$	−24.3325	−	42.1451i	−0.0249308	−	0.0431815i
$977$	160.479	−	598.914i	0.164256	−	0.613014i	−0.833877	−	0.551950i	$-0.813884\pi$
$977$	160.479	−	598.914i	0.164256	−	0.613014i	0.998134	−	0.0610638i	$-0.0194493\pi$
$978$	−149.681	−	558.618i	−0.153048	−	0.571184i
$979$			54.5673i			0.0557377i
$980$	181.641	−	455.089i	0.185348	−	0.464377i
$981$	322.881			0.329135
$982$	271.922	−	72.8614i	0.276907	−	0.0741969i
$983$	1296.21	+	347.318i	1.31862	+	0.353324i	0.848462	−	0.529256i	$-0.177529\pi$
$983$	1296.21	+	347.318i	1.31862	+	0.353324i	0.470161	+	0.882580i	$0.344196\pi$
$984$	−0.804519	+	0.464489i	−0.000817600	+	0.000472042i
$985$	683.038	+	929.689i	0.693439	+	0.943846i
$986$	786.692			0.797862
$987$	−502.648	+	218.228i	−0.509268	+	0.221103i
$988$	230.232	−	230.232i	0.233029	−	0.233029i
$989$	1218.36	+	703.422i	1.23191	+	0.711246i
$990$	3.35184	+	30.3386i	0.00338569	+	0.0306450i
$991$	−727.843	−	1260.66i	−0.734453	−	1.27211i	−0.954963	−	0.296725i	$-0.904105\pi$
$991$	−727.843	−	1260.66i	−0.734453	−	1.27211i	0.220510	−	0.975385i	$-0.429228\pi$
$992$	−130.317	+	34.9183i	−0.131368	+	0.0351999i
$993$	−432.491	+	432.491i	−0.435540	+	0.435540i
$994$	490.367	−	389.615i	0.493327	−	0.391967i
$995$	1587.23	−	618.980i	1.59521	−	0.622091i
$996$	−53.5514	+	92.7537i	−0.0537664	+	0.0931262i
$997$	237.255	−	885.448i	0.237969	−	0.888112i	−0.738819	−	0.673904i	$-0.764616\pi$
$997$	237.255	−	885.448i	0.237969	−	0.888112i	0.976788	−	0.214208i	$-0.0687171\pi$
$998$	744.210	+	199.410i	0.745701	+	0.199810i
$999$	−570.798	−	329.551i	−0.571370	−	0.329880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.3.l.b.37.1	yes	8
5.2	odd	4		350.3.p.b.93.1		8
5.3	odd	4	inner	70.3.l.b.23.2	✓	8
5.4	even	2		350.3.p.b.107.2		8
7.2	even	3		490.3.f.f.197.2		4
7.4	even	3	inner	70.3.l.b.67.2	yes	8
7.5	odd	6		490.3.f.k.197.1		4
35.4	even	6		350.3.p.b.207.1		8
35.18	odd	12	inner	70.3.l.b.53.1	yes	8
35.23	odd	12		490.3.f.f.393.2		4
35.32	odd	12		350.3.p.b.193.2		8
35.33	even	12		490.3.f.k.393.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.b.23.2	✓	8	5.3	odd	4	inner
70.3.l.b.37.1	yes	8	1.1	even	1	trivial
70.3.l.b.53.1	yes	8	35.18	odd	12	inner
70.3.l.b.67.2	yes	8	7.4	even	3	inner
350.3.p.b.93.1		8	5.2	odd	4
350.3.p.b.107.2		8	5.4	even	2
350.3.p.b.193.2		8	35.32	odd	12
350.3.p.b.207.1		8	35.4	even	6
490.3.f.f.197.2		4	7.2	even	3
490.3.f.f.393.2		4	35.23	odd	12
490.3.f.k.197.1		4	7.5	odd	6
490.3.f.k.393.1		4	35.33	even	12

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(-1.58228 - 0.423972i) q^{3} +(1.73205 - 1.00000i) q^{4} +(4.94253 + 0.755913i) q^{5} -2.31662 q^{6} +(6.42096 - 2.78771i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-5.47036 - 3.15831i) q^{9} +(7.02830 - 0.776495i) q^{10} +(-0.341688 - 0.591820i) q^{11} +(-3.16457 + 0.847944i) q^{12} +(-11.9499 + 11.9499i) q^{13} +(7.75082 - 6.15831i) q^{14} +(-7.50000 - 3.29156i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-8.70832 + 32.4999i) q^{17} +(-8.62867 - 2.31205i) q^{18} +(-8.34264 - 4.81662i) q^{19} +(9.31662 - 3.63325i) q^{20} +(-11.3417 + 1.68864i) q^{21} +(-0.683375 - 0.683375i) q^{22} +(-6.26203 - 23.3702i) q^{23} +(-4.01251 + 2.31662i) q^{24} +(23.8572 + 7.47224i) q^{25} +(-11.9499 + 20.6978i) q^{26} +(17.7414 + 17.7414i) q^{27} +(8.33372 - 11.2494i) q^{28} -16.5330i q^{29} +(-11.4500 - 1.75117i) q^{30} +(-11.9248 - 20.6544i) q^{31} +(1.46410 - 5.46410i) q^{32} +(0.289732 + 1.08129i) q^{33} +47.5831i q^{34} +(33.8430 - 8.92464i) q^{35} -12.6332 q^{36} +(-25.3742 + 6.79899i) q^{37} +(-13.1593 - 3.52601i) q^{38} +(23.9745 - 13.8417i) q^{39} +(11.3969 - 8.37323i) q^{40} +0.200503 q^{41} +(-14.8749 + 6.45807i) q^{42} +(-41.1161 + 41.1161i) q^{43} +(-1.18364 - 0.683375i) q^{44} +(-24.6500 - 19.7452i) q^{45} +(-17.1082 - 29.6322i) q^{46} +(46.1601 - 12.3686i) q^{47} +(-4.63325 + 4.63325i) q^{48} +(33.4574 - 35.7995i) q^{49} +(35.3246 + 1.47494i) q^{50} +(27.5581 - 47.7320i) q^{51} +(-8.74792 + 32.6477i) q^{52} +(90.1000 + 24.1422i) q^{53} +(30.7291 + 17.7414i) q^{54} +(-1.24144 - 3.18338i) q^{55} +(7.26650 - 18.4173i) q^{56} +(11.1583 + 11.1583i) q^{57} +(-6.05150 - 22.5845i) q^{58} +(20.0054 - 11.5501i) q^{59} +(-16.2819 + 1.79885i) q^{60} +(6.08312 - 10.5363i) q^{61} +(-23.8496 - 23.8496i) q^{62} +(-43.9294 - 5.02963i) q^{63} -8.00000i q^{64} +(-68.0957 + 50.0295i) q^{65} +(0.791562 + 1.37103i) q^{66} +(0.363121 - 1.35519i) q^{67} +(17.4166 + 64.9998i) q^{68} +39.6332i q^{69} +(42.9638 - 24.5787i) q^{70} +63.2665 q^{71} +(-17.2573 + 4.62409i) q^{72} +(-45.5005 - 12.1918i) q^{73} +(-32.1732 + 18.5752i) q^{74} +(-34.5808 - 21.9380i) q^{75} -19.2665 q^{76} +(-3.84378 - 2.84753i) q^{77} +(27.6834 - 27.6834i) q^{78} +(-97.2256 - 56.1332i) q^{79} +(12.5036 - 15.6096i) q^{80} +(7.87469 + 13.6394i) q^{81} +(0.273892 - 0.0733890i) q^{82} +(23.1161 - 23.1161i) q^{83} +(-17.9557 + 14.2665i) q^{84} +(-67.6082 + 154.049i) q^{85} +(-41.1161 + 71.2152i) q^{86} +(-7.00952 + 26.1599i) q^{87} +(-1.86702 - 0.500265i) q^{88} +(-69.1518 - 39.9248i) q^{89} +(-40.8997 - 17.9499i) q^{90} +(-43.4169 + 110.042i) q^{91} +(-34.2164 - 34.2164i) q^{92} +(10.1116 + 37.7369i) q^{93} +(58.5287 - 33.7916i) q^{94} +(-37.5928 - 30.1126i) q^{95} +(-4.63325 + 8.02502i) q^{96} +(-50.6834 - 50.6834i) q^{97} +(32.6001 - 61.1493i) q^{98} +4.31662i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 2 q^{3} - 6 q^{5} + 8 q^{6} - 12 q^{7} + 16 q^{8} + 18 q^{10} - 16 q^{11} + 4 q^{12} - 16 q^{13} - 60 q^{15} + 16 q^{16} + 62 q^{17} - 12 q^{18} + 48 q^{20} - 104 q^{21} - 32 q^{22} + 22 q^{23}+ \cdots + 176 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 2 * q^3 - 6 * q^5 + 8 * q^6 - 12 * q^7 + 16 * q^8 + 18 * q^10 - 16 * q^11 + 4 * q^12 - 16 * q^13 - 60 * q^15 + 16 * q^16 + 62 * q^17 - 12 * q^18 + 48 * q^20 - 104 * q^21 - 32 * q^22 + 22 * q^23 - 6 * q^25 - 16 * q^26 - 4 * q^27 + 12 * q^28 - 50 * q^30 + 24 * q^31 - 16 * q^32 + 30 * q^33 + 70 * q^35 - 48 * q^36 - 134 * q^37 - 12 * q^38 + 12 * q^40 + 320 * q^41 - 100 * q^42 + 16 * q^43 - 58 * q^45 - 44 * q^46 + 102 * q^47 + 16 * q^48 + 4 * q^50 + 48 * q^51 + 16 * q^52 + 98 * q^53 + 136 * q^55 - 48 * q^56 + 76 * q^57 - 40 * q^58 + 40 * q^60 - 84 * q^61 + 48 * q^62 - 76 * q^63 - 210 * q^65 - 60 * q^66 - 130 * q^67 - 124 * q^68 + 146 * q^70 + 400 * q^71 - 24 * q^72 - 246 * q^73 + 40 * q^75 - 48 * q^76 + 86 * q^77 + 248 * q^78 + 24 * q^80 - 136 * q^81 + 160 * q^82 - 160 * q^83 - 448 * q^85 + 16 * q^86 + 196 * q^87 - 32 * q^88 - 168 * q^90 - 480 * q^91 - 88 * q^92 - 210 * q^93 - 80 * q^95 + 16 * q^96 - 432 * q^97 + 176 * q^98

Introduction

L-functions

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