LMFDB - Embedded newform 216.3.x.a.101.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,3,Mod(5,216)] 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("216.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.x (of order $18$, degree $6$, 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:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$70$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.10
Character	$\chi$	$=$	216.101
Dual form			216.3.x.a.77.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.86843 - 0.713426i) q^{2} +(1.83045 - 2.37686i) q^{3} +(2.98205 + 2.66597i) q^{4} +(0.431661 + 2.44807i) q^{5} +(-5.11578 + 3.13509i) q^{6} +(9.31534 + 7.81650i) q^{7} +(-3.66977 - 7.10864i) q^{8} +(-2.29889 - 8.70144i) q^{9} +(0.939989 - 4.88201i) q^{10} +(-3.17501 + 18.0064i) q^{11} +(11.7951 - 2.20797i) q^{12} +(-7.62257 + 20.9428i) q^{13} +(-11.8286 - 21.2504i) q^{14} +(6.60885 + 3.45508i) q^{15} +(1.78522 + 15.9001i) q^{16} +(-4.71393 + 2.72159i) q^{17} +(-1.91252 + 17.8981i) q^{18} +(-3.59403 - 2.07501i) q^{19} +(-5.23925 + 8.45106i) q^{20} +(35.6300 - 7.83350i) q^{21} +(18.7785 - 31.3785i) q^{22} +(-8.24193 - 9.82236i) q^{23} +(-23.6136 - 4.28950i) q^{24} +(17.6856 - 6.43703i) q^{25} +(29.1834 - 33.6921i) q^{26} +(-24.8901 - 10.4634i) q^{27} +(6.94025 + 48.1436i) q^{28} +(17.4981 - 6.36879i) q^{29} +(-9.88322 - 11.1705i) q^{30} +(15.8536 - 13.3028i) q^{31} +(8.00798 - 30.9818i) q^{32} +(36.9869 + 40.5064i) q^{33} +(10.7493 - 1.72206i) q^{34} +(-15.1143 + 26.1787i) q^{35} +(16.3424 - 32.0769i) q^{36} +(23.5765 - 13.6119i) q^{37} +(5.23481 + 6.44108i) q^{38} +(35.8254 + 56.4526i) q^{39} +(15.8184 - 12.0524i) q^{40} +(0.450966 - 1.23902i) q^{41} +(-72.1607 - 10.7830i) q^{42} +(-26.4805 - 4.66923i) q^{43} +(-57.4725 + 45.2314i) q^{44} +(20.3094 - 9.38393i) q^{45} +(8.39194 + 24.2324i) q^{46} +(45.1266 - 53.7798i) q^{47} +(41.0600 + 24.8611i) q^{48} +(17.1692 + 97.3712i) q^{49} +(-37.6366 - 0.590226i) q^{50} +(-2.15980 + 16.1861i) q^{51} +(-78.5638 + 42.1310i) q^{52} -16.1947 q^{53} +(39.0405 + 37.3074i) q^{54} -45.4515 q^{55} +(21.3795 - 94.9042i) q^{56} +(-11.5107 + 4.74428i) q^{57} +(-37.2376 - 0.583969i) q^{58} +(-9.85967 - 55.9170i) q^{59} +(10.4968 + 27.9222i) q^{60} +(44.4475 - 52.9705i) q^{61} +(-39.1118 + 13.5449i) q^{62} +(46.5999 - 99.0262i) q^{63} +(-37.0655 + 52.1742i) q^{64} +(-54.5599 - 9.62039i) q^{65} +(-40.2091 - 102.071i) q^{66} +(28.4769 - 78.2396i) q^{67} +(-21.3128 - 4.45128i) q^{68} +(-38.4328 + 1.61055i) q^{69} +(46.9165 - 38.1301i) q^{70} +(-50.0267 + 28.8829i) q^{71} +(-53.4190 + 48.2743i) q^{72} +(-35.7118 + 61.8546i) q^{73} +(-53.7621 + 8.61278i) q^{74} +(17.0727 - 53.8188i) q^{75} +(-5.18564 - 15.7694i) q^{76} +(-170.323 + 142.918i) q^{77} +(-26.6624 - 131.036i) q^{78} +(-37.1663 + 13.5274i) q^{79} +(-38.1540 + 11.2338i) q^{80} +(-70.4302 + 40.0073i) q^{81} +(-1.72655 + 1.99329i) q^{82} +(-7.73295 + 2.81456i) q^{83} +(127.134 + 71.6285i) q^{84} +(-8.69747 - 10.3652i) q^{85} +(46.1458 + 27.6160i) q^{86} +(16.8917 - 53.2482i) q^{87} +(139.652 - 43.5093i) q^{88} +(46.1603 + 26.6506i) q^{89} +(-44.6414 + 3.04394i) q^{90} +(-234.707 + 135.508i) q^{91} +(1.60825 - 51.2635i) q^{92} +(-2.59947 - 62.0318i) q^{93} +(-122.684 + 68.2892i) q^{94} +(3.52838 - 9.69414i) q^{95} +(-58.9811 - 75.7445i) q^{96} +(30.7051 - 174.137i) q^{97} +(37.3877 - 194.180i) q^{98} +(163.980 - 13.7675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 51 q^{12} + 39 q^{14} - 12 q^{15} - 6 q^{16} - 18 q^{17} - 27 q^{18} + 57 q^{20} - 6 q^{22} - 12 q^{23} + 126 q^{24} - 12 q^{25}+ \cdots - 1548 q^{98}+O(q^{100}) $ 420 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 51 * q^12 + 39 * q^14 - 12 * q^15 - 6 * q^16 - 18 * q^17 - 27 * q^18 + 57 * q^20 - 6 * q^22 - 12 * q^23 + 126 * q^24 - 12 * q^25 - 12 * q^28 + 87 * q^30 - 12 * q^31 + 84 * q^32 - 36 * q^33 - 18 * q^34 - 36 * q^36 - 108 * q^38 - 12 * q^39 + 69 * q^40 - 84 * q^41 + 114 * q^42 - 657 * q^44 - 3 * q^46 - 12 * q^47 - 453 * q^48 - 12 * q^49 + 153 * q^50 + 21 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 66 * q^57 + 129 * q^58 + 210 * q^60 - 900 * q^62 + 468 * q^63 - 3 * q^64 - 12 * q^65 - 855 * q^66 + 279 * q^68 + 153 * q^70 - 18 * q^71 - 156 * q^72 - 6 * q^73 + 423 * q^74 - 54 * q^76 + 642 * q^78 - 12 * q^79 - 12 * q^81 - 12 * q^82 + 192 * q^84 + 606 * q^86 - 588 * q^87 + 186 * q^88 - 18 * q^89 - 534 * q^90 - 735 * q^92 + 345 * q^94 - 162 * q^95 - 486 * q^96 - 12 * q^97 - 1548 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−1.86843	−	0.713426i	−0.934214	−	0.356713i
$2$	−1.86843	−	0.713426i	−0.934214	−	0.356713i
$3$	1.83045	−	2.37686i	0.610151	−	0.792285i
$3$	1.83045	−	2.37686i	0.610151	−	0.792285i
$4$	2.98205	+	2.66597i	0.745512	+	0.666492i
$5$	0.431661	+	2.44807i	0.0863322	+	0.489614i	0.997061	+	0.0766098i	$0.0244096\pi$
$5$	0.431661	+	2.44807i	0.0863322	+	0.489614i	−0.910729	+	0.413005i	$0.864479\pi$
$6$	−5.11578	+	3.13509i	−0.852630	+	0.522516i
$7$	9.31534	+	7.81650i	1.33076	+	1.11664i	0.983899	+	0.178728i	$0.0571981\pi$
$7$	9.31534	+	7.81650i	1.33076	+	1.11664i	0.346865	+	0.937915i	$0.387246\pi$
$8$	−3.66977	−	7.10864i	−0.458722	−	0.888580i
$9$	−2.29889	−	8.70144i	−0.255432	−	0.966827i
$10$	0.939989	−	4.88201i	0.0939989	−	0.488201i
$11$	−3.17501	+	18.0064i	−0.288637	+	1.63694i	0.403358	+	0.915042i	$0.367843\pi$
$11$	−3.17501	+	18.0064i	−0.288637	+	1.63694i	−0.691996	+	0.721902i	$0.743268\pi$
$12$	11.7951	−	2.20797i	0.982927	−	0.183998i
$13$	−7.62257	+	20.9428i	−0.586351	+	1.61099i	0.190769	+	0.981635i	$0.438902\pi$
$13$	−7.62257	+	20.9428i	−0.586351	+	1.61099i	−0.777120	+	0.629352i	$0.783320\pi$
$14$	−11.8286	−	21.2504i	−0.844897	−	1.51788i
$15$	6.60885	+	3.45508i	0.440590	+	0.230339i
$16$	1.78522	+	15.9001i	0.111576	+	0.993756i
$17$	−4.71393	+	2.72159i	−0.277290	+	0.160093i	−0.632196	−	0.774809i	$-0.717846\pi$
$17$	−4.71393	+	2.72159i	−0.277290	+	0.160093i	0.354906	+	0.934902i	$0.384513\pi$
$18$	−1.91252	+	17.8981i	−0.106251	+	0.994339i
$19$	−3.59403	−	2.07501i	−0.189159	−	0.109211i	0.402430	−	0.915451i	$-0.368166\pi$
$19$	−3.59403	−	2.07501i	−0.189159	−	0.109211i	−0.591589	+	0.806240i	$0.701499\pi$
$20$	−5.23925	+	8.45106i	−0.261962	+	0.422553i
$21$	35.6300	−	7.83350i	1.69667	−	0.373024i
$22$	18.7785	−	31.3785i	0.853568	−	1.42630i
$23$	−8.24193	−	9.82236i	−0.358345	−	0.427059i	0.556510	−	0.830841i	$-0.312140\pi$
$23$	−8.24193	−	9.82236i	−0.358345	−	0.427059i	−0.914855	+	0.403782i	$0.867696\pi$
$24$	−23.6136	−	4.28950i	−0.983898	−	0.178729i
$25$	17.6856	−	6.43703i	0.707424	−	0.257481i
$26$	29.1834	−	33.6921i	1.12244	−	1.29585i
$27$	−24.8901	−	10.4634i	−0.921855	−	0.387535i
$28$	6.94025	+	48.1436i	0.247866	+	1.71941i
$29$	17.4981	−	6.36879i	0.603383	−	0.219613i	−0.0222226	−	0.999753i	$-0.507074\pi$
$29$	17.4981	−	6.36879i	0.603383	−	0.219613i	0.625605	+	0.780140i	$0.284852\pi$
$30$	−9.88322	−	11.1705i	−0.329441	−	0.372350i
$31$	15.8536	−	13.3028i	0.511407	−	0.429121i	−0.350217	−	0.936669i	$-0.613892\pi$
$31$	15.8536	−	13.3028i	0.511407	−	0.429121i	0.861624	+	0.507547i	$0.169448\pi$
$32$	8.00798	−	30.9818i	0.250249	−	0.968181i
$33$	36.9869	+	40.5064i	1.12081	+	1.22747i
$34$	10.7493	−	1.72206i	0.316156	−	0.0506487i
$35$	−15.1143	+	26.1787i	−0.431837	+	0.747963i
$36$	16.3424	−	32.0769i	0.453955	−	0.891025i
$37$	23.5765	−	13.6119i	0.637203	−	0.367889i	−0.146333	−	0.989235i	$-0.546747\pi$
$37$	23.5765	−	13.6119i	0.637203	−	0.367889i	0.783536	+	0.621346i	$0.213414\pi$
$38$	5.23481	+	6.44108i	0.137758	+	0.169502i
$39$	35.8254	+	56.4526i	0.918599	+	1.44750i
$40$	15.8184	−	12.0524i	0.395459	−	0.301310i
$41$	0.450966	−	1.23902i	0.0109992	−	0.0302200i	−0.934072	−	0.357086i	$-0.883770\pi$
$41$	0.450966	−	1.23902i	0.0109992	−	0.0302200i	0.945071	+	0.326866i	$0.105993\pi$
$42$	−72.1607	−	10.7830i	−1.71811	−	0.256738i
$43$	−26.4805	−	4.66923i	−0.615826	−	0.108587i	−0.142971	−	0.989727i	$-0.545666\pi$
$43$	−26.4805	−	4.66923i	−0.615826	−	0.108587i	−0.472855	+	0.881140i	$0.656777\pi$
$44$	−57.4725	+	45.2314i	−1.30619	+	1.02799i
$45$	20.3094	−	9.38393i	0.451320	−	0.208532i
$46$	8.39194	+	24.2324i	0.182434	+	0.526791i
$47$	45.1266	−	53.7798i	0.960141	−	1.14425i	−0.0293376	−	0.999570i	$-0.509340\pi$
$47$	45.1266	−	53.7798i	0.960141	−	1.14425i	0.989478	−	0.144682i	$-0.0462158\pi$
$48$	41.0600	+	24.8611i	0.855417	+	0.517940i
$49$	17.1692	+	97.3712i	0.350391	+	1.98717i
$50$	−37.6366	−	0.590226i	−0.752732	−	0.0118045i
$51$	−2.15980	+	16.1861i	−0.0423490	+	0.317374i
$52$	−78.5638	+	42.1310i	−1.51084	+	0.810212i
$53$	−16.1947			−0.305560			−0.152780	−	0.988260i	$-0.548823\pi$
$53$	−16.1947			−0.305560			−0.152780	+	0.988260i	$0.548823\pi$
$54$	39.0405	+	37.3074i	0.722972	+	0.690878i
$55$	−45.4515			−0.826390
$56$	21.3795	−	94.9042i	0.381777	−	1.69472i
$57$	−11.5107	+	4.74428i	−0.201942	+	0.0832329i
$58$	−37.2376	−	0.583969i	−0.642028	−	0.0100684i
$59$	−9.85967	−	55.9170i	−0.167113	−	0.947745i	−0.946859	−	0.321649i	$-0.895763\pi$
$59$	−9.85967	−	55.9170i	−0.167113	−	0.947745i	0.779746	−	0.626096i	$-0.215348\pi$
$60$	10.4968	+	27.9222i	0.174946	+	0.465370i
$61$	44.4475	−	52.9705i	0.728647	−	0.868368i	−0.266793	−	0.963754i	$-0.585964\pi$
$61$	44.4475	−	52.9705i	0.728647	−	0.868368i	0.995440	+	0.0953856i	$0.0304084\pi$
$62$	−39.1118	+	13.5449i	−0.630836	+	0.218466i
$63$	46.5999	−	99.0262i	0.739680	−	1.57184i
$64$	−37.0655	+	52.1742i	−0.579149	+	0.815222i
$65$	−54.5599	−	9.62039i	−0.839384	−	0.148006i
$66$	−40.2091	−	102.071i	−0.609228	−	1.54652i
$67$	28.4769	−	78.2396i	0.425028	−	1.16776i	−0.523766	−	0.851862i	$-0.675473\pi$
$67$	28.4769	−	78.2396i	0.425028	−	1.16776i	0.948795	−	0.315894i	$-0.102304\pi$
$68$	−21.3128	−	4.45128i	−0.313424	−	0.0654600i
$69$	−38.4328	+	1.61055i	−0.556997	+	0.0233412i
$70$	46.9165	−	38.1301i	0.670236	−	0.544716i
$71$	−50.0267	+	28.8829i	−0.704602	+	0.406802i	−0.809059	−	0.587727i	$-0.800023\pi$
$71$	−50.0267	+	28.8829i	−0.704602	+	0.406802i	0.104457	+	0.994529i	$0.466689\pi$
$72$	−53.4190	+	48.2743i	−0.741931	+	0.670477i
$73$	−35.7118	+	61.8546i	−0.489203	+	0.847324i	−0.999923	−	0.0124231i	$-0.996046\pi$
$73$	−35.7118	+	61.8546i	−0.489203	+	0.847324i	0.510720	+	0.859747i	$0.329379\pi$
$74$	−53.7621	+	8.61278i	−0.726514	+	0.116389i
$75$	17.0727	−	53.8188i	0.227636	−	0.717584i
$76$	−5.18564	−	15.7694i	−0.0682321	−	0.207491i
$77$	−170.323	+	142.918i	−2.21199	+	1.85608i
$78$	−26.6624	−	131.036i	−0.341826	−	1.67995i
$79$	−37.1663	+	13.5274i	−0.470460	+	0.171233i	−0.566361	−	0.824157i	$-0.691649\pi$
$79$	−37.1663	+	13.5274i	−0.470460	+	0.171233i	0.0959007	+	0.995391i	$0.469427\pi$
$80$	−38.1540	+	11.2338i	−0.476925	+	0.140423i
$81$	−70.4302	+	40.0073i	−0.869509	+	0.493918i
$82$	−1.72655	+	1.99329i	−0.0210554	+	0.0243084i
$83$	−7.73295	+	2.81456i	−0.0931680	+	0.0339104i	−0.388184	−	0.921582i	$-0.626897\pi$
$83$	−7.73295	+	2.81456i	−0.0931680	+	0.0339104i	0.295016	+	0.955492i	$0.404675\pi$
$84$	127.134	+	71.6285i	1.51350	+	0.852721i
$85$	−8.69747	−	10.3652i	−0.102323	−	0.121944i
$86$	46.1458	+	27.6160i	0.536579	+	0.321116i
$87$	16.8917	−	53.2482i	0.194158	−	0.612049i
$88$	139.652	−	43.5093i	1.58696	−	0.494424i
$89$	46.1603	+	26.6506i	0.518655	+	0.299445i	0.736384	−	0.676564i	$-0.236532\pi$
$89$	46.1603	+	26.6506i	0.518655	+	0.299445i	−0.217729	+	0.976009i	$0.569865\pi$
$90$	−44.6414	+	3.04394i	−0.496016	+	0.0338215i
$91$	−234.707	+	135.508i	−2.57919	+	1.48910i
$92$	1.60825	−	51.2635i	0.0174809	−	0.557212i
$93$	−2.59947	−	62.0318i	−0.0279513	−	0.667009i
$94$	−122.684	+	68.2892i	−1.30515	+	0.726481i
$95$	3.52838	−	9.69414i	0.0371408	−	0.102044i
$96$	−58.9811	−	75.7445i	−0.614386	−	0.789005i
$97$	30.7051	−	174.137i	0.316548	−	1.79523i	−0.246858	−	0.969052i	$-0.579398\pi$
$97$	30.7051	−	174.137i	0.316548	−	1.79523i	0.563406	−	0.826180i	$-0.309491\pi$
$98$	37.3877	−	194.180i	0.381507	−	1.98143i
$99$	163.980	−	13.7675i	1.65637	−	0.139066i
$100$	69.9002	+	27.9537i	0.699002	+	0.279537i
$101$	135.846	+	113.988i	1.34501	+	1.12860i	0.980308	+	0.197473i	$0.0632734\pi$
$101$	135.846	+	113.988i	1.34501	+	1.12860i	0.364701	+	0.931125i	$0.381171\pi$
$102$	15.5830	−	28.7017i	0.152774	−	0.281389i
$103$	8.41299	+	47.7124i	0.0816795	+	0.463227i	0.998024	+	0.0628363i	$0.0200146\pi$
$103$	8.41299	+	47.7124i	0.0816795	+	0.463227i	−0.916344	+	0.400391i	$0.868874\pi$
$104$	176.848	−	22.6693i	1.70046	−	0.217974i
$105$	34.5571	+	83.8433i	0.329115	+	0.798508i
$106$	30.2586	+	11.5537i	0.285458	+	0.108997i
$107$	11.5838			0.108260			0.0541298	−	0.998534i	$-0.482762\pi$
$107$	11.5838			0.108260			0.0541298	+	0.998534i	$0.482762\pi$
$108$	−46.3282	−	97.5587i	−0.428965	−	0.903321i
$109$		−	18.9771i		−	0.174102i	−0.996204	−	0.0870510i	$-0.972256\pi$
$109$		−	18.9771i		−	0.174102i	0.996204	−	0.0870510i	$-0.0277443\pi$
$110$	84.9228	+	32.4262i	0.772025	+	0.294784i
$111$	10.8021	−	80.9539i	0.0973164	−	0.729314i
$112$	−107.653	+	162.069i	−0.961189	+	1.44704i
$113$	96.6737	−	17.0462i	0.855519	−	0.150851i	0.271348	−	0.962481i	$-0.412531\pi$
$113$	96.6737	−	17.0462i	0.855519	−	0.150851i	0.584172	+	0.811630i	$0.301420\pi$
$114$	24.8916	−	0.652311i	0.218347	−	0.00572202i
$115$	20.4881	−	24.4168i	0.178157	−	0.212320i
$116$	69.1592	+	27.6574i	0.596200	+	0.238426i
$117$	199.756	+	18.1820i	1.70732	+	0.155402i
$118$	−21.4705	+	111.511i	−0.181953	+	0.945008i
$119$	−65.1852	−	11.4939i	−0.547775	−	0.0965874i
$120$	0.307955	−	59.6593i	0.00256629	−	0.497161i
$121$	−200.446	−	72.9565i	−1.65658	−	0.602946i
$122$	−120.837	+	67.2615i	−0.990471	+	0.551324i
$123$	−2.11950	−	3.33985i	−0.0172317	−	0.0271532i
$124$	82.7409	+	2.59576i	0.667266	+	0.0209336i
$125$	54.4655	+	94.3369i	0.435724	+	0.754696i
$126$	−157.716	+	151.778i	−1.25172	+	1.20459i
$127$	51.6695	−	89.4942i	0.406847	−	0.704679i	−0.587688	−	0.809088i	$-0.699962\pi$
$127$	51.6695	−	89.4942i	0.406847	−	0.704679i	0.994534	+	0.104409i	$0.0332950\pi$
$128$	106.477	−	71.0402i	0.831849	−	0.555002i
$129$	−59.5694	+	54.3936i	−0.461779	+	0.421656i
$130$	95.0779	+	56.8995i	0.731369	+	0.437688i
$131$	−76.8677	+	64.4997i	−0.586777	+	0.492364i	−0.887165	−	0.461453i	$-0.847328\pi$
$131$	−76.8677	+	64.4997i	−0.586777	+	0.492364i	0.300388	+	0.953817i	$0.402884\pi$
$132$	2.30795	+	219.398i	0.0174845	+	1.66210i
$133$	−17.2603	−	47.4222i	−0.129776	−	0.356558i
$134$	−109.025	+	125.869i	−0.813621	+	0.939321i
$135$	14.8712	−	65.4494i	0.110157	−	0.484810i
$136$	36.6459	+	23.5220i	0.269455	+	0.172956i
$137$	86.3596	+	237.271i	0.630362	+	1.73191i	0.680075	+	0.733142i	$0.261947\pi$
$137$	86.3596	+	237.271i	0.630362	+	1.73191i	−0.0497129	+	0.998764i	$0.515831\pi$
$138$	72.9579	+	24.4097i	0.528681	+	0.176882i
$139$	−113.810	−	135.633i	−0.818776	−	0.975779i	0.181195	−	0.983447i	$-0.442004\pi$
$139$	−113.810	−	135.633i	−0.818776	−	0.975779i	−0.999971	+	0.00766807i	$0.997559\pi$
$140$	−114.863	+	37.7720i	−0.820451	+	0.269800i
$141$	−45.2248	−	205.701i	−0.320743	−	1.45887i
$142$	114.077	−	18.2754i	0.803360	−	0.128700i
$143$	−352.903	−	203.749i	−2.46785	−	1.42482i
$144$	134.250	−	52.0866i	0.932290	−	0.361712i
$145$	23.1445	+	40.0875i	0.159617	+	0.276465i
$146$	110.854	−	90.0933i	0.759271	−	0.617077i
$147$	262.865	+	137.425i	1.78819	+	0.934861i
$148$	106.595	+	22.2629i	0.720237	+	0.150425i
$149$	38.7986	+	14.1215i	0.260393	+	0.0947755i	0.468918	−	0.883242i	$-0.344644\pi$
$149$	38.7986	+	14.1215i	0.260393	+	0.0947755i	−0.208525	+	0.978017i	$0.566866\pi$
$150$	−70.2949	+	88.3764i	−0.468632	+	0.589176i
$151$	−12.1751	+	69.0485i	−0.0806299	+	0.457275i	0.917584	+	0.397541i	$0.130136\pi$
$151$	−12.1751	+	69.0485i	−0.0806299	+	0.457275i	−0.998214	+	0.0597338i	$0.980975\pi$
$152$	−1.56126	+	33.1635i	−0.0102714	+	0.218181i
$153$	34.5186	+	34.7614i	0.225612	+	0.227198i
$154$	420.198	−	145.519i	2.72856	−	0.944931i
$155$	39.4095	+	33.0685i	0.254255	+	0.213345i
$156$	−43.6679	+	263.854i	−0.279923	+	1.69137i
$157$	137.862	−	24.3087i	0.878099	−	0.154833i	0.283613	−	0.958939i	$-0.408467\pi$
$157$	137.862	−	24.3087i	0.878099	−	0.154833i	0.594486	+	0.804106i	$0.297356\pi$
$158$	79.0935	+	1.24036i	0.500592	+	0.00785039i
$159$	−29.6436	+	38.4924i	−0.186438	+	0.242091i
$160$	79.3024	+	6.23046i	0.495640	+	0.0389404i
$161$		−	155.922i		−	0.968458i
$162$	160.136	−	24.5042i	0.988494	−	0.151260i
$163$		−	61.3323i		−	0.376272i	−0.982143	−	0.188136i	$-0.939755\pi$
$163$		−	61.3323i		−	0.376272i	0.982143	−	0.188136i	$-0.0602446\pi$
$164$	4.64799	−	2.49255i	0.0283414	−	0.0151985i
$165$	−83.1967	+	108.032i	−0.504222	+	0.654737i
$166$	16.4564	+	0.258074i	0.0991352	+	0.00155466i
$167$	101.129	−	17.8318i	0.605566	−	0.106778i	0.137546	−	0.990495i	$-0.456079\pi$
$167$	101.129	−	17.8318i	0.605566	−	0.106778i	0.468020	+	0.883718i	$0.344968\pi$
$168$	−186.439	−	224.534i	−1.10976	−	1.33651i
$169$	−251.037	−	210.645i	−1.48543	−	1.24642i
$170$	8.85577	+	25.5717i	0.0520928	+	0.150422i
$171$	−9.79332	+	36.0434i	−0.0572709	+	0.210780i
$172$	−66.5182	−	84.5202i	−0.386734	−	0.491396i
$173$	−28.9499	+	164.183i	−0.167340	+	0.949035i	0.779278	+	0.626678i	$0.215586\pi$
$173$	−28.9499	+	164.183i	−0.167340	+	0.949035i	−0.946618	+	0.322356i	$0.895525\pi$
$174$	−69.5496	+	87.4395i	−0.399711	+	0.502526i
$175$	215.062	+	78.2763i	1.22893	+	0.447293i
$176$	−291.971	−	18.3376i	−1.65893	−	0.104191i
$177$	−150.954	−	78.9183i	−0.852849	−	0.445866i
$178$	−67.2339	−	82.7267i	−0.377719	−	0.464757i
$179$	−93.6982	−	162.290i	−0.523454	−	0.906648i	−0.999627	−	0.0272970i	$-0.991310\pi$
$179$	−93.6982	−	162.290i	−0.523454	−	0.906648i	0.476174	−	0.879351i	$-0.342023\pi$
$180$	85.5809	+	26.1609i	0.475450	+	0.145339i
$181$	−86.7322	−	50.0749i	−0.479183	−	0.276657i	0.240893	−	0.970552i	$-0.422560\pi$
$181$	−86.7322	−	50.0749i	−0.479183	−	0.276657i	−0.720076	+	0.693895i	$0.755893\pi$
$182$	535.207	−	85.7411i	2.94070	−	0.471105i
$183$	−44.5442	−	202.605i	−0.243411	−	1.10713i
$184$	−39.5776	+	94.6348i	−0.215095	+	0.514319i
$185$	43.5000	+	51.8412i	0.235135	+	0.280223i
$186$	−39.3981	+	117.756i	−0.211818	+	0.633099i
$187$	−34.0392	−	93.5219i	−0.182028	−	0.500117i
$188$	277.945	−	40.0678i	1.47843	−	0.213127i
$189$	−150.072	−	292.024i	−0.794033	−	1.54510i
$190$	−13.5086	+	15.5956i	−0.0710977	+	0.0820819i
$191$	70.9312	+	194.882i	0.371368	+	1.02032i	0.974833	+	0.222935i	$0.0715638\pi$
$191$	70.9312	+	194.882i	0.371368	+	1.02032i	−0.603466	+	0.797389i	$0.706214\pi$
$192$	56.1639	+	183.602i	0.292520	+	0.956259i
$193$	242.261	−	203.281i	1.25524	−	1.05327i	0.259067	−	0.965859i	$-0.416585\pi$
$193$	242.261	−	203.281i	1.25524	−	1.05327i	0.996172	−	0.0874113i	$-0.0278594\pi$
$194$	−181.604	+	303.458i	−0.936105	+	1.56421i
$195$	−122.736	+	112.071i	−0.629414	+	0.574726i
$196$	−208.389	+	336.138i	−1.06321	+	1.71499i
$197$	74.3536	−	128.784i	0.377429	−	0.653727i	−0.613258	−	0.789883i	$-0.710141\pi$
$197$	74.3536	−	128.784i	0.377429	−	0.653727i	0.990687	+	0.136156i	$0.0434748\pi$
$198$	−316.208	−	91.2642i	−1.59701	−	0.460930i
$199$	150.091	+	259.965i	0.754225	+	1.30636i	0.945758	+	0.324871i	$0.105321\pi$
$199$	150.091	+	259.965i	0.754225	+	1.30636i	−0.191533	+	0.981486i	$0.561346\pi$
$200$	−110.661	−	102.098i	−0.553303	−	0.510490i
$201$	−133.839	−	210.899i	−0.665865	−	1.04925i
$202$	−172.496	−	309.895i	−0.853942	−	1.53413i
$203$	212.782	+	77.4465i	1.04819	+	0.381510i
$204$	−49.5922	+	42.5097i	−0.243099	+	0.208381i
$205$	3.22787	+	0.569161i	0.0157457	+	0.00277640i
$206$	18.3202	−	95.1493i	0.0889330	−	0.461890i
$207$	−66.5213	+	94.2973i	−0.321359	+	0.455542i
$208$	−346.601	−	83.8120i	−1.66635	−	0.402942i
$209$	48.7745	−	58.1272i	0.233371	−	0.278121i
$210$	−4.75140	−	181.309i	−0.0226257	−	0.863377i
$211$	−384.620	+	67.8189i	−1.82284	+	0.321416i	−0.977198	−	0.212329i	$-0.931895\pi$
$211$	−384.620	+	67.8189i	−1.82284	+	0.321416i	−0.845645	+	0.533746i	$0.820784\pi$
$212$	−48.2933	−	43.1745i	−0.227799	−	0.203653i
$213$	−22.9209	+	171.775i	−0.107610	+	0.806456i
$214$	−21.6435	−	8.26416i	−0.101138	−	0.0386176i
$215$		−	66.8418i		−	0.310892i
$216$	16.9602	+	215.333i	0.0785193	+	0.996913i
$217$	251.663			1.15974
$218$	−13.5388	+	35.4574i	−0.0621044	+	0.162649i
$219$	81.6509	+	198.104i	0.372835	+	0.904583i
$220$	−135.538	−	121.172i	−0.616084	−	0.550782i
$221$	−21.0655	−	119.469i	−0.0953192	−	0.540582i
$222$	−77.9376	+	143.550i	−0.351070	+	0.646622i
$223$	−175.898	−	147.596i	−0.788780	−	0.661865i	0.156663	−	0.987652i	$-0.449926\pi$
$223$	−175.898	−	147.596i	−0.788780	−	0.661865i	−0.945443	+	0.325787i	$0.894371\pi$
$224$	316.766	−	226.012i	1.41414	−	1.00898i
$225$	−96.6687	−	139.092i	−0.429639	−	0.618187i
$226$	−192.789	−	37.1199i	−0.853049	−	0.164247i
$227$	50.1373	−	284.343i	0.220869	−	1.25261i	−0.649557	−	0.760313i	$-0.725046\pi$
$227$	50.1373	−	284.343i	0.220869	−	1.25261i	0.870426	−	0.492299i	$-0.163843\pi$
$228$	−46.9736	−	16.5395i	−0.206024	−	0.0725417i
$229$	−58.2137	+	159.941i	−0.254208	+	0.698431i	0.745290	+	0.666741i	$0.232311\pi$
$229$	−58.2137	+	159.941i	−0.254208	+	0.698431i	−0.999498	+	0.0316904i	$0.989911\pi$
$230$	−55.7001	+	31.0043i	−0.242174	+	0.134801i
$231$	27.9274	+	666.439i	0.120898	+	2.88502i
$232$	−109.487	−	101.016i	−0.471929	−	0.435413i
$233$	−286.010	+	165.128i	−1.22751	+	0.708703i	−0.966508	−	0.256635i	$-0.917386\pi$
$233$	−286.010	+	165.128i	−1.22751	+	0.708703i	−0.261001	+	0.965338i	$0.584053\pi$
$234$	−360.259	−	176.483i	−1.53957	−	0.754201i
$235$	151.136	+	87.2585i	0.643133	+	0.371313i
$236$	119.671	−	193.033i	0.507080	−	0.817935i
$237$	−35.8784	+	113.100i	−0.151386	+	0.477217i
$238$	113.594	+	67.9803i	0.477285	+	0.285632i
$239$	145.138	+	172.969i	0.607273	+	0.723720i	0.978826	−	0.204692i	$-0.0656192\pi$
$239$	145.138	+	172.969i	0.607273	+	0.723720i	−0.371554	+	0.928412i	$0.621175\pi$
$240$	−43.1379	+	111.249i	−0.179741	+	0.463539i
$241$	243.524	−	88.6356i	1.01047	−	0.367783i	0.216860	−	0.976203i	$-0.430419\pi$
$241$	243.524	−	88.6356i	1.01047	−	0.367783i	0.793615	+	0.608420i	$0.208196\pi$
$242$	322.470	+	279.317i	1.33252	+	1.15420i
$243$	−33.8274	+	240.634i	−0.139207	+	0.990263i
$244$	273.762	−	39.4648i	1.12198	−	0.161741i
$245$	−230.960	+	84.0627i	−0.942695	+	0.343113i
$246$	1.57740	+	7.75237i	0.00641219	+	0.0315137i
$247$	70.8524	−	59.4522i	0.286852	−	0.240697i
$248$	−152.744	−	63.8795i	−0.615902	−	0.257579i
$249$	−7.46498	+	23.5320i	−0.0299798	+	0.0945061i
$250$	−34.4624	−	215.119i	−0.137850	−	0.860475i
$251$	125.834	−	217.951i	0.501332	−	0.868332i	−0.498667	−	0.866794i	$-0.666177\pi$
$251$	125.834	−	217.951i	0.501332	−	0.868332i	0.999999	−	0.00153847i	$-0.000489712\pi$
$252$	402.964	−	171.067i	1.59906	−	0.678838i
$253$	203.033	−	117.221i	0.802503	−	0.463325i
$254$	−160.388	+	130.351i	−0.631450	+	0.513194i
$255$	−40.5570	+	1.69956i	−0.159047	+	0.00666494i
$256$	−249.626	+	56.7704i	−0.975101	+	0.221759i
$257$	47.2822	−	129.907i	0.183978	−	0.505474i	−0.813078	−	0.582155i	$-0.802210\pi$
$257$	47.2822	−	129.907i	0.183978	−	0.505474i	0.997056	+	0.0766803i	$0.0244321\pi$
$258$	150.107	−	59.1322i	0.581810	−	0.229195i
$259$	326.021	+	57.4862i	1.25877	+	0.221955i
$260$	−137.053	−	174.144i	−0.527126	−	0.669783i
$261$	−95.6439	−	137.618i	−0.366452	−	0.527270i
$262$	189.638	−	65.6736i	0.723808	−	0.250663i
$263$	−148.185	+	176.600i	−0.563443	+	0.671485i	−0.970271	−	0.242020i	$-0.922190\pi$
$263$	−148.185	+	176.600i	−0.563443	+	0.671485i	0.406829	+	0.913504i	$0.366635\pi$
$264$	152.212	−	411.576i	0.576560	−	1.55900i
$265$	−6.99061	−	39.6457i	−0.0263797	−	0.149607i
$266$	−1.58263	+	100.919i	−0.00594975	+	0.379394i
$267$	147.839	−	60.9336i	0.553704	−	0.228216i
$268$	293.504	−	157.396i	1.09516	−	0.587298i
$269$	−292.043			−1.08566			−0.542830	−	0.839843i	$-0.682647\pi$
$269$	−292.043			−1.08566			−0.542830	+	0.839843i	$0.682647\pi$
$270$	−74.4790	+	111.678i	−0.275848	+	0.413622i
$271$	−358.276			−1.32205			−0.661025	−	0.750364i	$-0.729878\pi$
$271$	−358.276			−1.32205			−0.661025	+	0.750364i	$0.729878\pi$
$272$	−51.6889	−	70.0933i	−0.190033	−	0.257696i
$273$	−107.536	+	805.904i	−0.393906	+	2.95203i
$274$	7.91851	−	504.935i	0.0288997	−	1.84283i
$275$	59.7556	+	338.891i	0.217293	+	1.23233i
$276$	−118.902	−	97.6579i	−0.430805	−	0.353833i
$277$	71.6482	−	85.3869i	0.258658	−	0.308256i	−0.621050	−	0.783771i	$-0.713294\pi$
$277$	71.6482	−	85.3869i	0.258658	−	0.308256i	0.879708	+	0.475515i	$0.157738\pi$
$278$	115.881	+	334.616i	0.416839	+	1.20365i
$279$	−152.199	−	107.368i	−0.545516	−	0.384830i
$280$	241.561	+	11.3721i	0.862718	+	0.0406147i
$281$	65.0505	+	11.4702i	0.231496	+	0.0408190i	0.288193	−	0.957572i	$-0.406946\pi$
$281$	65.0505	+	11.4702i	0.231496	+	0.0408190i	−0.0566965	+	0.998391i	$0.518057\pi$
$282$	−62.2530	+	416.602i	−0.220755	+	1.47731i
$283$	−24.1190	+	66.2665i	−0.0852262	+	0.234157i	−0.974984	−	0.222277i	$-0.928651\pi$
$283$	−24.1190	+	66.2665i	−0.0852262	+	0.234157i	0.889757	+	0.456434i	$0.150873\pi$
$284$	−226.183	−	47.2393i	−0.796419	−	0.166336i
$285$	−16.5831	−	26.1311i	−0.0581861	−	0.0916881i
$286$	514.014	+	632.460i	1.79725	+	2.21140i
$287$	13.8857	−	8.01691i	0.0483822	−	0.0279335i
$288$	−287.996	+	1.54288i	−0.999986	+	0.00535723i
$289$	−129.686	+	224.623i	−0.448740	+	0.777241i
$290$	−14.6444	−	91.4124i	−0.0504980	−	0.315215i
$291$	−357.695	−	391.732i	−1.22919	−	1.34616i
$292$	−271.397	+	89.2470i	−0.929441	+	0.305640i
$293$	22.3432	−	18.7482i	0.0762568	−	0.0639871i	−0.603862	−	0.797089i	$-0.706372\pi$
$293$	22.3432	−	18.7482i	0.0762568	−	0.0639871i	0.680119	+	0.733101i	$0.261928\pi$
$294$	−393.101	−	444.302i	−1.33708	−	1.51123i
$295$	132.633	−	48.2744i	0.449603	−	0.163642i
$296$	−183.282	−	117.644i	−0.619198	−	0.397447i
$297$	267.435	−	414.959i	0.900454	−	1.39717i
$298$	−62.4178	−	54.0650i	−0.209456	−	0.181426i
$299$	268.533	−	97.7379i	0.898103	−	0.326883i
$300$	194.391	−	114.975i	0.647970	−	0.383249i
$301$	−210.178	−	250.481i	−0.698266	−	0.832162i
$302$	72.0093	−	120.326i	0.238441	−	0.398431i
$303$	519.593	−	114.236i	1.71483	−	0.377017i
$304$	26.5768	−	60.8497i	0.0874236	−	0.200164i
$305$	148.862	+	85.9454i	0.488071	+	0.281788i
$306$	−39.6958	−	89.5755i	−0.129725	−	0.292730i
$307$	−82.2556	+	47.4903i	−0.267933	+	0.154691i	−0.627948	−	0.778255i	$-0.716105\pi$
$307$	−82.2556	+	47.4903i	−0.267933	+	0.154691i	0.360015	+	0.932947i	$0.382772\pi$
$308$	−888.927	−	27.8876i	−2.88613	−	0.0905441i
$309$	128.805	+	67.3388i	0.416845	+	0.217925i
$310$	−50.0419	−	89.9018i	−0.161425	−	0.290006i
$311$	39.9411	−	109.737i	0.128428	−	0.352853i	−0.858768	−	0.512365i	$-0.828770\pi$
$311$	39.9411	−	109.737i	0.128428	−	0.352853i	0.987196	+	0.159511i	$0.0509919\pi$
$312$	269.830	−	461.838i	0.864841	−	1.48025i
$313$	19.1570	−	108.645i	0.0612043	−	0.347107i	−0.938792	−	0.344484i	$-0.888054\pi$
$313$	19.1570	−	108.645i	0.0612043	−	0.347107i	0.999997	−	0.00262316i	$-0.000834979\pi$
$314$	−274.927	−	52.9349i	−0.875563	−	0.168582i
$315$	262.539	+	71.3341i	0.833456	+	0.226457i
$316$	−146.896	−	58.7448i	−0.464859	−	0.185901i
$317$	−176.283	−	147.919i	−0.556097	−	0.466621i	0.320903	−	0.947112i	$-0.396014\pi$
$317$	−176.283	−	147.919i	−0.556097	−	0.466621i	−0.876999	+	0.480492i	$0.840458\pi$
$318$	82.8484	−	50.7718i	0.260529	−	0.159660i
$319$	59.1222	+	335.298i	0.185336	+	1.05109i
$320$	−143.726	−	68.2175i	−0.449144	−	0.213180i
$321$	21.2036	−	27.5330i	0.0660547	−	0.0857725i
$322$	−111.239	+	291.328i	−0.345461	+	0.904747i
$323$	22.5893			0.0699360
$324$	−316.685	−	68.4609i	−0.977421	−	0.211299i
$325$			419.453i			1.29062i
$326$	−43.7560	+	114.595i	−0.134221	+	0.351519i
$327$	−45.1059	−	34.7367i	−0.137939	−	0.106229i
$328$	−10.4627	+	1.34116i	−0.0318984	+	0.00408891i
$329$	840.740	−	148.245i	2.55544	−	0.450593i
$330$	232.520	−	142.495i	0.704605	−	0.431802i
$331$	−95.9402	+	114.337i	−0.289849	+	0.345429i	−0.891245	−	0.453522i	$-0.850167\pi$
$331$	−95.9402	+	114.337i	−0.289849	+	0.345429i	0.601395	+	0.798952i	$0.294612\pi$
$332$	−30.5636	−	12.2226i	−0.0920589	−	0.0368152i
$333$	−172.643	−	173.857i	−0.518447	−	0.522094i
$334$	−201.675	−	38.8308i	−0.603817	−	0.116260i
$335$	203.829	+	35.9405i	0.608444	+	0.107285i
$336$	188.161	+	552.536i	0.560002	+	1.64445i
$337$	341.384	+	124.254i	1.01301	+	0.368705i	0.794588	−	0.607149i	$-0.207687\pi$
$337$	341.384	+	124.254i	1.01301	+	0.368705i	0.218422	+	0.975854i	$0.429909\pi$
$338$	318.766	+	572.672i	0.943093	+	1.69430i
$339$	136.440	−	260.982i	0.402478	−	0.769857i
$340$	1.69714	−	54.0968i	0.00499157	−	0.159108i
$341$	189.199	+	327.702i	0.554836	+	0.961004i
$342$	44.0124	−	60.3578i	0.128691	−	0.176485i
$343$	−303.237	+	525.222i	−0.884074	+	1.53126i
$344$	63.9856	+	205.376i	0.186005	+	0.597022i
$345$	−20.5327	−	93.3910i	−0.0595150	−	0.270699i
$346$	171.223	−	286.111i	0.494865	−	0.826909i
$347$	236.019	−	198.043i	0.680169	−	0.570730i	−0.235886	−	0.971781i	$-0.575799\pi$
$347$	236.019	−	198.043i	0.680169	−	0.570730i	0.916056	+	0.401051i	$0.131355\pi$
$348$	192.330	−	113.756i	0.552673	−	0.326885i
$349$	88.3158	+	242.646i	0.253054	+	0.695260i	0.999554	+	0.0298743i	$0.00951069\pi$
$349$	88.3158	+	242.646i	0.253054	+	0.695260i	−0.746500	+	0.665386i	$0.768267\pi$
$350$	−345.984	−	299.685i	−0.988526	−	0.856242i
$351$	408.860	−	441.511i	1.16484	−	1.25787i
$352$	532.445	+	242.562i	1.51263	+	0.689097i
$353$	−128.921	−	354.207i	−0.365214	−	1.00342i	−0.977157	−	0.212516i	$-0.931834\pi$
$353$	−128.921	−	354.207i	−0.365214	−	1.00342i	0.611943	−	0.790902i	$-0.290388\pi$
$354$	225.745	+	255.148i	0.637697	+	0.720757i
$355$	−92.3021	−	110.001i	−0.260006	−	0.309863i
$356$	66.6024	+	202.535i	0.187085	+	0.568919i
$357$	−146.638	+	133.897i	−0.410750	+	0.375061i
$358$	59.2865	+	370.074i	0.165605	+	1.03373i
$359$	−62.1995	−	35.9109i	−0.173258	−	0.100030i	0.410863	−	0.911697i	$-0.365227\pi$
$359$	−62.1995	−	35.9109i	−0.173258	−	0.100030i	−0.584121	+	0.811667i	$0.698561\pi$
$360$	−141.238	−	109.935i	−0.392328	−	0.305376i
$361$	−171.889	−	297.720i	−0.476146	−	0.824709i
$362$	126.328	+	155.438i	0.348973	+	0.429387i
$363$	−540.314	+	342.889i	−1.48847	+	0.944597i
$364$	−1061.17	−	221.629i	−2.91529	−	0.608872i
$365$	−166.840	−	60.7248i	−0.457096	−	0.166369i
$366$	−61.3161	+	410.332i	−0.167530	+	1.12113i
$367$	15.6931	−	89.0001i	0.0427606	−	0.242507i	−0.955934	−	0.293581i	$-0.905153\pi$
$367$	15.6931	−	89.0001i	0.0427606	−	0.242507i	0.998695	+	0.0510733i	$0.0162642\pi$
$368$	141.463	−	148.583i	0.384410	−	0.403757i
$369$	−11.8180	−	1.07568i	−0.0320270	−	0.00291513i
$370$	−44.2917	−	127.896i	−0.119707	−	0.345664i
$371$	−150.859	−	126.586i	−0.406628	−	0.341201i
$372$	157.623	−	191.912i	0.423718	−	0.515892i
$373$	249.197	−	43.9401i	0.668088	−	0.117802i	0.170691	−	0.985325i	$-0.445400\pi$
$373$	249.197	−	43.9401i	0.668088	−	0.117802i	0.497397	+	0.867523i	$0.334289\pi$
$374$	−3.12113	+	199.023i	−0.00834527	+	0.532148i
$375$	323.922	+	43.2227i	0.863791	+	0.115260i
$376$	−547.906	−	123.429i	−1.45720	−	0.328269i
$377$			415.006i			1.10081i
$378$	72.0619	+	652.691i	0.190640	+	1.72670i
$379$			25.6417i			0.0676562i	0.999428	+	0.0338281i	$0.0107699\pi$
$379$			25.6417i			0.0676562i	−0.999428	+	0.0338281i	$0.989230\pi$
$380$	36.3661	−	19.5018i	0.0957002	−	0.0513206i
$381$	−118.136	−	286.626i	−0.310069	−	0.752299i
$382$	6.50385	−	414.727i	0.0170258	−	1.08567i
$383$	−713.042	+	125.729i	−1.86173	+	0.328273i	−0.987547	−	0.157327i	$-0.949712\pi$
$383$	−713.042	+	125.729i	−1.86173	+	0.328273i	−0.874181	+	0.485600i	$0.838601\pi$
$384$	26.0481	−	383.116i	0.0678335	−	0.997697i
$385$	−423.396	−	355.271i	−1.09973	−	0.922783i
$386$	−597.674	+	206.981i	−1.54838	+	0.536221i
$387$	20.2468	+	241.153i	0.0523174	+	0.623134i
$388$	555.809	−	437.427i	1.43250	−	1.12739i
$389$	−46.9195	+	266.094i	−0.120616	+	0.684045i	0.863200	+	0.504862i	$0.168457\pi$
$389$	−46.9195	+	266.094i	−0.120616	+	0.684045i	−0.983816	+	0.179183i	$0.942654\pi$
$390$	309.277	−	121.835i	0.793019	−	0.312397i
$391$	65.5843	+	23.8707i	0.167735	+	0.0610505i
$392$	629.170	−	479.379i	1.60502	−	1.22291i
$393$	12.6038	+	300.767i	0.0320707	+	0.765311i
$394$	−230.802	+	187.578i	−0.585792	+	0.476087i
$395$	−49.1594	−	85.1466i	−0.124454	−	0.215561i
$396$	525.702	+	396.111i	1.32753	+	1.00028i
$397$	−43.4213	−	25.0693i	−0.109374	−	0.0631468i	0.444315	−	0.895870i	$-0.353447\pi$
$397$	−43.4213	−	25.0693i	−0.109374	−	0.0631468i	−0.553689	+	0.832724i	$0.686780\pi$
$398$	−94.9683	−	592.805i	−0.238614	−	1.48946i
$399$	−144.310	−	45.7788i	−0.361679	−	0.114734i
$400$	133.922	+	269.711i	0.334805	+	0.674278i
$401$	94.4109	+	112.515i	0.235439	+	0.280585i	0.870808	−	0.491624i	$-0.163596\pi$
$401$	94.4109	+	112.515i	0.235439	+	0.280585i	−0.635369	+	0.772209i	$0.719152\pi$
$402$	99.6071	+	489.534i	0.247779	+	1.21775i
$403$	157.752	+	433.421i	0.391445	+	1.07549i
$404$	101.210	+	702.080i	0.250520	+	1.73782i
$405$	−128.343	−	155.149i	−0.316896	−	0.383083i
$406$	−342.316	−	296.508i	−0.843144	−	0.730314i
$407$	170.245	+	467.745i	0.418293	+	1.14925i
$408$	122.987	−	44.0460i	0.301439	−	0.107956i
$409$	−238.446	+	200.080i	−0.582998	+	0.489193i	−0.885930	−	0.463819i	$-0.846479\pi$
$409$	−238.446	+	200.080i	−0.582998	+	0.489193i	0.302932	+	0.953012i	$0.402034\pi$
$410$	−5.62500	−	3.36628i	−0.0137195	−	0.00821045i
$411$	722.036	+	229.049i	1.75678	+	0.557297i
$412$	−102.112	+	164.709i	−0.247844	+	0.399780i
$413$	345.229	−	597.954i	0.835905	−	1.44783i
$414$	191.564	−	128.730i	0.462716	−	0.310941i
$415$	−10.2283	−	17.7159i	−0.0246464	−	0.0426889i
$416$	587.806	+	403.871i	1.41299	+	0.970843i
$417$	−530.704	+	22.2394i	−1.27267	+	0.0533320i
$418$	−132.601	+	73.8096i	−0.317228	+	0.176578i
$419$	−306.796	−	111.665i	−0.732210	−	0.266503i	−0.0511098	−	0.998693i	$-0.516276\pi$
$419$	−306.796	−	111.665i	−0.732210	−	0.266503i	−0.681100	+	0.732190i	$0.738498\pi$
$420$	−120.473	+	342.153i	−0.286840	+	0.814650i
$421$	283.538	+	49.9954i	0.673486	+	0.118754i	0.499924	−	0.866069i	$-0.333361\pi$
$421$	283.538	+	49.9954i	0.673486	+	0.118754i	0.173562	+	0.984823i	$0.444472\pi$
$422$	767.018	+	147.683i	1.81758	+	0.349960i
$423$	−571.703	−	269.033i	−1.35154	−	0.636011i
$424$	59.4308	+	115.122i	0.140167	+	0.271514i
$425$	−65.8497	+	78.4766i	−0.154940	+	0.184651i
$426$	165.375	−	304.597i	0.388204	−	0.715017i
$427$	828.087	−	146.014i	1.93931	−	0.341953i
$428$	34.5434	+	30.8820i	0.0807089	+	0.0721542i
$429$	−1130.25	+	465.848i	−2.63462	+	1.08589i
$430$	−47.6866	+	124.889i	−0.110899	+	0.290440i
$431$		−	490.741i		−	1.13861i	−0.822126	−	0.569305i	$-0.807212\pi$
$431$		−	490.741i		−	1.13861i	0.822126	−	0.569305i	$-0.192788\pi$
$432$	121.935	−	414.434i	0.282258	−	0.959339i
$433$	−269.575			−0.622575			−0.311287	−	0.950316i	$-0.600760\pi$
$433$	−269.575			−0.622575			−0.311287	+	0.950316i	$0.600760\pi$
$434$	−470.214	−	179.543i	−1.08344	−	0.413693i
$435$	137.647	+	18.3670i	0.316430	+	0.0422230i
$436$	50.5924	−	56.5907i	0.116038	−	0.129795i
$437$	9.24023	+	52.4039i	0.0211447	+	0.119917i
$438$	−11.2265	−	428.394i	−0.0256313	−	0.978070i
$439$	431.418	+	362.002i	0.982728	+	0.824607i	0.984499	−	0.175391i	$-0.0561191\pi$
$439$	431.418	+	362.002i	0.982728	+	0.824607i	−0.00177037	+	0.999998i	$0.500564\pi$
$440$	166.796	+	323.098i	0.379083	+	0.734314i
$441$	807.799	−	373.242i	1.83174	−	0.846354i
$442$	−45.8725	+	238.247i	−0.103784	+	0.539021i
$443$	17.1447	−	97.2323i	0.0387013	−	0.219486i	−0.959323	−	0.282310i	$-0.908899\pi$
$443$	17.1447	−	97.2323i	0.0387013	−	0.219486i	0.998025	+	0.0628236i	$0.0200106\pi$
$444$	248.033	−	212.610i	0.558633	−	0.478852i
$445$	−45.3171	+	124.508i	−0.101836	+	0.279793i
$446$	223.354	+	401.262i	0.500794	+	0.899691i
$447$	104.584	−	66.3700i	0.233968	−	0.148479i
$448$	−753.098	+	196.298i	−1.68102	+	0.438164i
$449$	−5.24318	+	3.02715i	−0.0116775	+	0.00674199i	−0.505827	−	0.862635i	$-0.668813\pi$
$449$	−5.24318	+	3.02715i	−0.0116775	+	0.00674199i	0.494150	+	0.869377i	$0.335479\pi$
$450$	81.3866	+	328.850i	0.180859	+	0.730777i
$451$	20.8784	+	12.0542i	0.0462936	+	0.0267276i
$452$	333.730	+	206.897i	0.738341	+	0.457736i
$453$	141.832	+	155.328i	0.313096	+	0.342888i
$454$	−296.535	+	495.505i	−0.653162	+	1.09142i
$455$	−433.047	−	516.085i	−0.951751	−	1.13425i
$456$	75.9670	+	64.4150i	0.166594	+	0.141261i
$457$	−75.4501	+	27.4616i	−0.165099	+	0.0600910i	−0.423247	−	0.906014i	$-0.639110\pi$
$457$	−75.4501	+	27.4616i	−0.165099	+	0.0600910i	0.258149	+	0.966105i	$0.416888\pi$
$458$	222.874	−	257.307i	0.486624	−	0.561805i
$459$	145.807	−	18.4167i	0.317663	−	0.0401235i
$460$	126.191	−	18.1913i	0.274328	−	0.0395464i
$461$	−371.652	+	135.270i	−0.806187	+	0.293428i	−0.712048	−	0.702131i	$-0.752232\pi$
$461$	−371.652	+	135.270i	−0.806187	+	0.293428i	−0.0941393	+	0.995559i	$0.530010\pi$
$462$	423.274	−	1265.12i	0.916177	−	2.73835i
$463$	528.701	−	443.633i	1.14190	−	0.958171i	0.142404	−	0.989809i	$-0.454517\pi$
$463$	528.701	−	443.633i	1.14190	−	0.958171i	0.999499	+	0.0316377i	$0.0100723\pi$
$464$	132.502	+	266.852i	0.285565	+	0.575112i
$465$	150.736	−	33.1404i	0.324164	−	0.0712697i
$466$	652.195	−	104.483i	1.39956	−	0.224212i
$467$	248.315	−	430.095i	0.531725	−	0.920974i	−0.467590	−	0.883946i	$-0.654877\pi$
$467$	248.315	−	430.095i	0.531725	−	0.920974i	0.999314	−	0.0370284i	$-0.0117892\pi$
$468$	547.210	+	586.764i	1.16925	+	1.25377i
$469$	876.832	−	506.239i	1.86958	−	1.07940i
$470$	−220.135	−	270.861i	−0.468372	−	0.576300i
$471$	194.571	−	372.173i	0.413101	−	0.790176i
$472$	−361.311	+	275.291i	−0.765489	+	0.583245i
$473$	168.152	−	461.994i	0.355501	−	0.976731i
$474$	147.725	−	185.723i	0.311656	−	0.391821i
$475$	−76.9194	−	13.5630i	−0.161936	−	0.0285536i
$476$	−163.743	−	208.057i	−0.343998	−	0.437095i
$477$	37.2298	+	140.917i	0.0780499	+	0.295424i
$478$	−147.780	−	426.725i	−0.309163	−	0.892731i
$479$	148.733	−	177.253i	0.310508	−	0.370049i	−0.588110	−	0.808781i	$-0.700128\pi$
$479$	148.733	−	177.253i	0.310508	−	0.370049i	0.898618	+	0.438732i	$0.144572\pi$
$480$	159.968	−	177.086i	0.333267	−	0.368929i
$481$	105.358	+	597.516i	0.219040	+	1.24224i
$482$	−518.243	−	8.12721i	−1.07519	−	0.0168614i
$483$	−370.603	−	285.407i	−0.767295	−	0.590905i
$484$	−403.241	−	751.943i	−0.833142	−	1.55360i
$485$	439.555			0.906300
$486$	234.878	−	425.474i	0.483289	−	0.875461i
$487$	−569.784			−1.16999			−0.584994	−	0.811037i	$-0.698903\pi$
$487$	−569.784			−1.16999			−0.584994	+	0.811037i	$0.698903\pi$
$488$	−539.660	−	121.572i	−1.10586	−	0.249122i
$489$	−145.778	−	112.266i	−0.298115	−	0.229583i
$490$	491.505	+	7.70790i	1.00307	+	0.0157304i
$491$	−57.9013	−	328.375i	−0.117925	−	0.668788i	−0.985260	−	0.171063i	$-0.945280\pi$
$491$	−57.9013	−	328.375i	−0.117925	−	0.668788i	0.867335	−	0.497725i	$-0.165831\pi$
$492$	2.58348	−	15.6101i	0.00525098	−	0.0317279i
$493$	−65.1516	+	77.6447i	−0.132153	+	0.157494i
$494$	−174.797	+	60.5343i	−0.353841	+	0.122539i
$495$	104.488	+	395.493i	0.211087	+	0.798976i
$496$	239.817	+	228.325i	0.483502	+	0.460334i
$497$	−691.779	−	121.979i	−1.39191	−	0.245431i
$498$	30.7361	−	38.6422i	0.0617191	−	0.0775948i
$499$	−275.892	+	758.008i	−0.552891	+	1.51905i	0.276854	+	0.960912i	$0.410708\pi$
$499$	−275.892	+	758.008i	−0.552891	+	1.51905i	−0.829745	+	0.558143i	$0.811514\pi$
$500$	−89.0807	+	426.521i	−0.178161	+	0.853041i
$501$	142.729	−	273.010i	0.284888	−	0.544931i
$502$	−390.604	+	317.453i	−0.778096	+	0.632377i
$503$	267.225	−	154.283i	0.531263	−	0.306725i	−0.210268	−	0.977644i	$-0.567434\pi$
$503$	267.225	−	154.283i	0.531263	−	0.306725i	0.741531	+	0.670919i	$0.234100\pi$
$504$	−874.953	+	32.1420i	−1.73602	+	0.0637737i
$505$	−220.412	+	381.765i	−0.436460	+	0.755970i
$506$	−462.982	+	74.1705i	−0.914984	+	0.146582i
$507$	−960.186	+	211.104i	−1.89386	+	0.416378i
$508$	392.670	−	129.127i	0.772972	−	0.254187i
$509$	331.689	−	278.320i	0.651648	−	0.546797i	−0.255923	−	0.966697i	$-0.582379\pi$
$509$	331.689	−	278.320i	0.651648	−	0.546797i	0.907570	+	0.419900i	$0.137935\pi$
$510$	76.9903	+	25.7589i	0.150961	+	0.0505076i
$511$	−816.154	+	297.056i	−1.59717	+	0.581323i
$512$	506.910	+	72.0182i	0.990058	+	0.140661i
$513$	67.7439	+	89.2531i	0.132054	+	0.173983i
$514$	−181.022	+	208.989i	−0.352184	+	0.406594i
$515$	−113.172	+	41.1912i	−0.219751	+	0.0799829i
$516$	−322.651	+	3.39412i	−0.625292	+	0.00657775i
$517$	825.102	+	983.318i	1.59594	+	1.90197i
$518$	−568.134	−	340.000i	−1.09678	−	0.656371i
$519$	337.248	+	369.339i	0.649804	+	0.711636i
$520$	131.835	+	423.152i	0.253528	+	0.813753i
$521$	−795.081	−	459.040i	−1.52607	−	0.881075i	−0.999522	−	0.0309274i	$-0.990154\pi$
$521$	−795.081	−	459.040i	−1.52607	−	0.881075i	−0.526545	−	0.850147i	$-0.676513\pi$
$522$	80.5238	+	325.363i	0.154260	+	0.623301i
$523$	−360.155	+	207.936i	−0.688634	+	0.397583i	−0.803100	−	0.595844i	$-0.796818\pi$
$523$	−360.155	+	207.936i	−0.688634	+	0.397583i	0.114466	+	0.993427i	$0.463484\pi$
$524$	−401.177	−	12.5858i	−0.765606	−	0.0240187i
$525$	579.713	−	367.891i	1.10421	−	0.700745i
$526$	402.865	−	224.246i	0.765903	−	0.426323i
$527$	−38.5282	+	105.855i	−0.0731085	+	0.200864i
$528$	−578.025	+	660.408i	−1.09474	+	1.25077i
$529$	63.3107	−	359.053i	0.119680	−	0.678739i
$530$	−15.2228	+	79.0625i	−0.0287223	+	0.149174i
$531$	−463.892	+	214.340i	−0.873620	+	0.403654i
$532$	74.9551	−	187.430i	0.140893	−	0.352313i
$533$	22.5111	+	18.8890i	0.0422346	+	0.0354391i
$534$	−319.698	+	8.37802i	−0.598685	+	0.0156892i
$535$	5.00027	+	28.3579i	0.00934630	+	0.0530055i
$536$	−660.681	+	84.6896i	−1.23261	+	0.158003i
$537$	−557.250	−	74.3569i	−1.03771	−	0.138467i
$538$	545.661	+	208.351i	1.01424	+	0.387269i
$539$	−1807.81			−3.35402
$540$	218.833	−	155.527i	0.405245	−	0.288013i
$541$		−	615.361i		−	1.13745i	−0.822527	−	0.568726i	$-0.807437\pi$
$541$		−	615.361i		−	1.13745i	0.822527	−	0.568726i	$-0.192563\pi$
$542$	669.413	+	255.603i	1.23508	+	0.471592i
$543$	−277.780	+	114.490i	−0.511565	+	0.210848i
$544$	46.5707	+	167.841i	0.0856079	+	0.308530i
$545$	46.4574	−	8.19169i	0.0852429	−	0.0150306i
$546$	775.876	−	1429.06i	1.42102	−	2.61732i
$547$	34.3201	−	40.9011i	0.0627424	−	0.0747735i	−0.733760	−	0.679408i	$-0.762237\pi$
$547$	34.3201	−	40.9011i	0.0627424	−	0.0747735i	0.796503	+	0.604635i	$0.206681\pi$
$548$	−375.029	+	937.786i	−0.684359	+	1.71129i
$549$	−563.099	−	264.984i	−1.02568	−	0.482667i
$550$	130.124	−	675.825i	0.236590	−	1.22877i
$551$	−76.1040	−	13.4192i	−0.138120	−	0.0243542i
$552$	152.488	+	267.295i	0.276247	+	0.484229i
$553$	−451.954	−	164.498i	−0.817277	−	0.297465i
$554$	−194.787	+	108.424i	−0.351600	+	0.195711i
$555$	202.844	−	8.50027i	0.365484	−	0.0153158i
$556$	22.2077	−	707.879i	0.0399419	−	1.27316i
$557$	0.116057	+	0.201016i	0.000208360	+	0.000360890i	0.866130	−	0.499820i	$-0.166600\pi$
$557$	0.116057	+	0.201016i	0.000208360	+	0.000360890i	−0.865921	+	0.500180i	$0.833267\pi$
$558$	207.774	+	309.191i	0.372355	+	0.554106i
$559$	299.637	−	518.986i	0.536023	−	0.928419i
$560$	−443.226	−	193.584i	−0.791475	−	0.345685i
$561$	−284.595	−	90.2811i	−0.507300	−	0.160929i
$562$	−113.359	−	67.8398i	−0.201706	−	0.120711i
$563$	354.814	−	297.725i	0.630221	−	0.528818i	−0.270777	−	0.962642i	$-0.587280\pi$
$563$	354.814	−	297.725i	0.630221	−	0.528818i	0.900998	+	0.433824i	$0.142836\pi$
$564$	413.529	−	733.978i	0.733208	−	1.30138i
$565$	83.4606	+	229.306i	0.147718	+	0.405851i
$566$	92.3409	−	106.607i	0.163146	−	0.188352i
$567$	−968.799	−	177.835i	−1.70864	−	0.313643i
$568$	388.905	+	249.628i	0.684692	+	0.439486i
$569$	268.047	+	736.453i	0.471084	+	1.29429i	0.916882	+	0.399159i	$0.130698\pi$
$569$	268.047	+	736.453i	0.471084	+	1.29429i	−0.445797	+	0.895134i	$0.647080\pi$
$570$	12.3416	+	60.6549i	0.0216520	+	0.106412i
$571$	−126.691	−	150.985i	−0.221876	−	0.264422i	0.643611	−	0.765353i	$-0.277436\pi$
$571$	−126.691	−	150.985i	−0.221876	−	0.264422i	−0.865487	+	0.500931i	$0.832991\pi$
$572$	−509.186	−	1548.42i	−0.890186	−	2.70702i
$573$	593.043	+	188.129i	1.03498	+	0.328322i
$574$	−31.6639	+	5.07261i	−0.0551636	+	0.00883730i
$575$	−208.990	−	120.661i	−0.363461	−	0.209844i
$576$	539.200	+	202.581i	0.936112	+	0.351703i
$577$	304.421	+	527.272i	0.527592	+	0.913817i	0.999483	+	0.0321596i	$0.0102385\pi$
$577$	304.421	+	527.272i	0.527592	+	0.913817i	−0.471890	+	0.881657i	$0.656428\pi$
$578$	402.560	−	327.170i	0.696471	−	0.566038i
$579$	−39.7229	−	947.917i	−0.0686061	−	1.63716i
$580$	−37.8539	+	181.245i	−0.0652653	+	0.312492i
$581$	−94.0351	−	34.2260i	−0.161850	−	0.0589087i
$582$	388.857	+	987.112i	0.668139	+	1.69607i
$583$	51.4183	−	291.607i	0.0881960	−	0.500184i
$584$	570.757	+	26.8698i	0.977323	+	0.0460100i
$585$	41.7161	+	496.866i	0.0713096	+	0.849344i
$586$	−55.1222	+	19.0894i	−0.0940652	+	0.0325758i
$587$	106.529	+	89.3888i	0.181481	+	0.152281i	0.729003	−	0.684511i	$-0.239984\pi$
$587$	106.529	+	89.3888i	0.181481	+	0.152281i	−0.547522	+	0.836792i	$0.684429\pi$
$588$	417.505	+	1110.60i	0.710043	+	1.88877i
$589$	−84.5817	+	14.9140i	−0.143602	+	0.0253209i
$590$	−282.255	−	4.42639i	−0.478398	−	0.00750235i
$591$	−170.001	−	412.461i	−0.287649	−	0.697904i
$592$	258.520	+	350.568i	0.436689	+	0.592176i
$593$			8.54539i			0.0144104i	0.999974	+	0.00720522i	$0.00229351\pi$
$593$			8.54539i			0.0144104i	−0.999974	+	0.00720522i	$0.997706\pi$
$594$	−795.725	+	584.526i	−1.33960	+	0.984051i
$595$		−	164.539i		−	0.276537i
$596$	78.0518	+	145.547i	0.130959	+	0.244206i
$597$	892.634	+	119.109i	1.49520	+	0.199513i
$598$	−571.463	−	8.96181i	−0.955623	−	0.0149863i
$599$	496.991	−	87.6330i	0.829702	−	0.146299i	0.257362	−	0.966315i	$-0.417147\pi$
$599$	496.991	−	87.6330i	0.829702	−	0.146299i	0.572340	+	0.820016i	$0.306036\pi$
$600$	−445.231	+	76.1388i	−0.742052	+	0.126898i
$601$	256.738	+	215.429i	0.427184	+	0.358450i	0.830888	−	0.556440i	$-0.187833\pi$
$601$	256.738	+	215.429i	0.427184	+	0.358450i	−0.403704	+	0.914890i	$0.632277\pi$
$602$	214.004	+	617.952i	0.355488	+	1.02650i
$603$	−746.263	−	67.9256i	−1.23758	−	0.112646i
$604$	−220.388	+	173.447i	−0.364880	+	0.287165i
$605$	92.0779	−	522.199i	0.152195	−	0.863140i
$606$	−1052.32	−	157.249i	−1.73650	−	0.259487i
$607$	−199.628	−	72.6585i	−0.328876	−	0.119701i	0.172305	−	0.985044i	$-0.444879\pi$
$607$	−199.628	−	72.6585i	−0.328876	−	0.119701i	−0.501181	+	0.865343i	$0.667101\pi$
$608$	−93.0685	+	94.7328i	−0.153073	+	0.155811i
$609$	573.567	−	363.991i	0.941818	−	0.597687i
$610$	−216.822	−	266.785i	−0.355446	−	0.437352i
$611$	782.321	+	1355.02i	1.28039	+	2.21771i
$612$	10.2633	+	195.685i	0.0167702	+	0.319747i
$613$	−199.370	−	115.106i	−0.325237	−	0.187776i	0.328488	−	0.944508i	$-0.393461\pi$
$613$	−199.370	−	115.106i	−0.325237	−	0.187776i	−0.653724	+	0.756733i	$0.726794\pi$
$614$	187.569	−	30.0489i	0.305488	−	0.0489397i
$615$	7.26128	−	6.63037i	0.0118070	−	0.0107811i
$616$	1641.00	+	686.289i	2.66396	+	1.11411i
$617$	−372.007	−	443.340i	−0.602928	−	0.718542i	0.375107	−	0.926981i	$-0.377606\pi$
$617$	−372.007	−	443.340i	−0.602928	−	0.718542i	−0.978035	+	0.208440i	$0.933161\pi$
$618$	−192.622	−	217.711i	−0.311686	−	0.352283i
$619$	−313.531	−	861.418i	−0.506512	−	1.39163i	−0.884813	−	0.465946i	$-0.845714\pi$
$619$	−313.531	−	861.418i	−0.506512	−	1.39163i	0.378301	−	0.925682i	$-0.376508\pi$
$620$	29.3614	+	203.676i	0.0473571	+	0.328510i
$621$	102.367	+	330.718i	0.164842	+	0.532558i
$622$	−152.917	+	176.541i	−0.245847	+	0.283828i
$623$	221.684	+	609.072i	0.355833	+	0.977643i
$624$	−833.646	+	670.407i	−1.33597	+	1.07437i
$625$	153.003	−	128.384i	0.244804	−	0.205415i
$626$	−113.303	+	189.327i	−0.180995	+	0.302440i
$627$	−48.8806	−	222.329i	−0.0779595	−	0.354592i
$628$	475.916	+	295.045i	0.757828	+	0.469817i
$629$	−74.0920	+	128.331i	−0.117793	+	0.204024i
$630$	−439.643	−	320.584i	−0.697846	−	0.508864i
$631$	−250.496	−	433.871i	−0.396982	−	0.687593i	0.596370	−	0.802710i	$-0.296609\pi$
$631$	−250.496	−	433.871i	−0.396982	−	0.687593i	−0.993352	+	0.115117i	$0.963276\pi$
$632$	232.554	+	214.560i	0.367965	+	0.339493i
$633$	−542.833	+	1038.33i	−0.857555	+	1.64032i
$634$	223.843	+	402.140i	0.353064	+	0.634290i
$635$	241.392	+	87.8595i	0.380145	+	0.138361i
$636$	−191.018	+	35.7574i	−0.300343	+	0.0562223i
$637$	−2170.10	−	382.647i	−3.40675	−	0.600702i
$638$	128.745	−	668.660i	0.201795	−	1.04806i
$639$	366.329	+	368.906i	0.573285	+	0.577317i
$640$	219.873	+	229.997i	0.343552	+	0.359371i
$641$	−708.740	+	844.643i	−1.10568	+	1.31770i	−0.162015	+	0.986788i	$0.551799\pi$
$641$	−708.740	+	844.643i	−1.10568	+	1.31770i	−0.943663	+	0.330908i	$0.892645\pi$
$642$	−59.2600	+	36.3162i	−0.0923054	+	0.0565674i
$643$	428.029	−	75.4731i	0.665675	−	0.117377i	0.169408	−	0.985546i	$-0.445815\pi$
$643$	428.029	−	75.4731i	0.665675	−	0.117377i	0.496268	+	0.868170i	$0.334703\pi$
$644$	415.682	−	464.966i	0.645469	−	0.721997i
$645$	−158.873	−	122.351i	−0.246315	−	0.189691i
$646$	−42.2065	−	16.1158i	−0.0653352	−	0.0249471i
$647$		−	1236.49i		−	1.91111i	−0.294808	−	0.955557i	$-0.595256\pi$
$647$		−	1236.49i		−	1.91111i	0.294808	−	0.955557i	$-0.404744\pi$
$648$	542.861	+	353.845i	0.837748	+	0.546057i
$649$	1038.17			1.59964
$650$	299.249	−	783.718i	0.460382	−	1.20572i
$651$	460.657	−	598.166i	0.707614	−	0.918842i
$652$	163.510	−	182.896i	0.250782	−	0.280515i
$653$	−102.303	−	580.190i	−0.156666	−	0.888499i	−0.957247	−	0.289273i	$-0.906586\pi$
$653$	−102.303	−	580.190i	−0.156666	−	0.888499i	0.800580	−	0.599225i	$-0.204525\pi$
$654$	59.4951	+	97.0828i	0.0909711	+	0.148445i
$655$	−191.081	−	160.336i	−0.291726	−	0.244787i
$656$	20.5056	+	4.95848i	0.0312585	+	0.00755866i
$657$	620.322	+	168.547i	0.944174	+	0.256540i
$658$	−1676.62	−	322.820i	−2.54806	−	0.490608i
$659$	181.192	−	1027.59i	0.274951	−	1.55932i	−0.464168	−	0.885747i	$-0.653647\pi$
$659$	181.192	−	1027.59i	0.274951	−	1.55932i	0.739119	−	0.673575i	$-0.235242\pi$
$660$	−536.105	+	100.356i	−0.812281	+	0.152054i
$661$	−191.300	+	525.592i	−0.289410	+	0.795147i	0.706739	+	0.707474i	$0.250165\pi$
$661$	−191.300	+	525.592i	−0.289410	+	0.795147i	−0.996149	+	0.0876732i	$0.972057\pi$
$662$	260.828	−	145.184i	0.394000	−	0.219312i
$663$	−322.519	−	168.612i	−0.486454	−	0.254316i
$664$	48.3859	+	44.6419i	0.0728703	+	0.0672318i
$665$	108.642	−	62.7247i	0.163372	−	0.0943228i
$666$	198.537	+	448.008i	0.298103	+	0.672684i
$667$	−206.775	−	119.381i	−0.310007	−	0.178983i
$668$	349.112	+	216.433i	0.522623	+	0.324001i
$669$	−672.787	+	147.917i	−1.00566	+	0.221102i
$670$	−355.198	−	212.569i	−0.530147	−	0.317267i
$671$	812.685	+	968.520i	1.21116	+	1.44340i
$672$	42.6280	−	1166.61i	0.0634345	−	1.73603i
$673$	219.027	−	79.7195i	0.325449	−	0.118454i	−0.174128	−	0.984723i	$-0.555711\pi$
$673$	219.027	−	79.7195i	0.325449	−	0.118454i	0.499578	+	0.866269i	$0.333489\pi$
$674$	−549.206	−	475.711i	−0.814846	−	0.705803i
$675$	−507.549	−	24.8338i	−0.751925	−	0.0367909i
$676$	−187.032	−	1297.41i	−0.276674	−	1.91925i
$677$	457.775	−	166.616i	0.676182	−	0.246110i	0.0189744	−	0.999820i	$-0.493960\pi$
$677$	457.775	−	166.616i	0.676182	−	0.246110i	0.657207	+	0.753710i	$0.271738\pi$
$678$	−441.120	+	390.286i	−0.650619	+	0.575642i
$679$	1647.17	−	1382.14i	2.42588	−	2.03556i
$680$	−41.7650	+	99.8652i	−0.0614192	+	0.146861i
$681$	−584.068	−	639.645i	−0.857662	−	0.939273i
$682$	−119.714	−	747.268i	−0.175533	−	1.09570i
$683$	−439.183	+	760.687i	−0.643020	+	1.11374i	0.341735	+	0.939796i	$0.388985\pi$
$683$	−439.183	+	760.687i	−0.643020	+	1.11374i	−0.984755	+	0.173947i	$0.944348\pi$
$684$	−125.295	+	81.3746i	−0.183180	+	0.118969i
$685$	−543.579	+	313.835i	−0.793546	+	0.458154i
$686$	941.284	−	765.003i	1.37213	−	1.11517i
$687$	273.599	+	431.129i	0.398252	+	0.627554i
$688$	26.9676	−	429.379i	0.0391971	−	0.624097i
$689$	123.445	−	339.162i	0.179166	−	0.492253i
$690$	−28.2637	+	189.143i	−0.0409619	+	0.274120i
$691$	1192.42	+	210.255i	1.72564	+	0.304277i	0.946531	−	0.322614i	$-0.104562\pi$
$691$	1192.42	+	210.255i	1.72564	+	0.304277i	0.779107	+	0.626890i	$0.215673\pi$
$692$	−524.037	+	412.422i	−0.757279	+	0.595986i
$693$	1635.15	+	1153.50i	2.35952	+	1.66451i
$694$	−582.273	+	201.648i	−0.839011	+	0.290559i
$695$	282.913	−	337.162i	0.407069	−	0.485126i
$696$	−440.511	+	75.3316i	−0.632919	+	0.108235i
$697$	1.24628	+	7.06800i	0.00178806	+	0.0101406i
$698$	8.09788	−	516.373i	0.0116016	−	0.739789i
$699$	−131.042	+	982.063i	−0.187471	+	1.40495i
$700$	432.644	+	806.773i	0.618063	+	1.15253i
$701$	438.504			0.625540			0.312770	−	0.949829i	$-0.398743\pi$
$701$	438.504			0.625540			0.312770	+	0.949829i	$0.398743\pi$
$702$	−1078.91	+	533.240i	−1.53691	+	0.759601i
$703$	−112.979			−0.160710
$704$	−821.785	−	833.070i	−1.16731	−	1.18334i
$705$	484.049	−	199.507i	0.686594	−	0.282988i
$706$	−11.8210	+	753.785i	−0.0167437	+	1.06768i
$707$	374.462	+	2123.68i	0.529649	+	3.00379i
$708$	−239.759	−	637.778i	−0.338643	−	0.900816i
$709$	−258.161	+	307.664i	−0.364119	+	0.433941i	−0.916735	−	0.399496i	$-0.869185\pi$
$709$	−258.161	+	307.664i	−0.364119	+	0.433941i	0.552616	+	0.833436i	$0.313630\pi$
$710$	93.9821	+	271.380i	0.132369	+	0.382226i
$711$	203.150	+	292.303i	0.285724	+	0.411115i
$712$	20.0522	−	425.939i	0.0281631	−	0.598228i
$713$	−261.329	−	46.0793i	−0.366520	−	0.0646274i
$714$	369.507	−	145.561i	0.517517	−	0.203868i
$715$	346.457	−	951.882i	0.484555	−	1.33130i
$716$	153.248	−	733.753i	0.214033	−	1.02479i
$717$	676.791	−	28.3613i	0.943920	−	0.0395555i
$718$	90.5956	+	111.472i	0.126178	+	0.155253i
$719$	−911.473	+	526.239i	−1.26770	+	0.731905i	−0.974552	−	0.224164i	$-0.928035\pi$
$719$	−911.473	+	526.239i	−1.26770	+	0.731905i	−0.293144	+	0.956068i	$0.594702\pi$
$720$	185.462	+	306.169i	0.257586	+	0.425235i
$721$	−294.574	+	510.218i	−0.408563	+	0.707653i
$722$	108.761	+	678.898i	0.150638	+	0.940302i
$723$	235.086	−	741.066i	0.325153	−	1.02499i
$724$	−125.142	−	380.551i	−0.172847	−	0.525623i
$725$	268.468	−	225.272i	0.370301	−	0.310719i
$726$	1254.16	−	255.189i	1.72750	−	0.351500i
$727$	−465.844	+	169.553i	−0.640776	+	0.233223i	−0.641915	−	0.766776i	$-0.721860\pi$
$727$	−465.844	+	169.553i	−0.640776	+	0.233223i	0.00113892	+	0.999999i	$0.499637\pi$
$728$	1824.60	+	1171.16i	2.50631	+	1.60874i
$729$	510.033	+	520.872i	0.699634	+	0.714502i
$730$	268.406	+	232.488i	0.367679	+	0.318477i
$731$	137.535	−	50.0587i	0.188147	−	0.0684798i
$732$	407.306	−	722.932i	0.556429	−	0.987612i
$733$	262.058	+	312.309i	0.357515	+	0.426070i	0.914584	−	0.404397i	$-0.132519\pi$
$733$	262.058	+	312.309i	0.357515	+	0.426070i	−0.557069	+	0.830466i	$0.688074\pi$
$734$	−92.8164	+	155.094i	−0.126453	+	0.211300i
$735$	−222.957	+	702.832i	−0.303343	+	0.956234i
$736$	−370.316	+	176.693i	−0.503146	+	0.240072i
$737$	1318.40	+	761.178i	1.78887	+	1.03281i
$738$	21.3136	+	10.4411i	0.0288802	+	0.0141478i
$739$	351.045	−	202.676i	0.475028	−	0.274257i	−0.243314	−	0.969947i	$-0.578235\pi$
$739$	351.045	−	202.676i	0.475028	−	0.274257i	0.718342	+	0.695690i	$0.244901\pi$
$740$	−8.48814	+	270.563i	−0.0114705	+	0.365625i
$741$	−11.6175	−	277.230i	−0.0156781	−	0.374130i
$742$	191.560	+	344.143i	0.258167	+	0.463804i
$743$	172.658	−	474.373i	0.232379	−	0.638456i	−0.767618	−	0.640908i	$-0.778558\pi$
$743$	172.658	−	474.373i	0.232379	−	0.638456i	0.999997	+	0.00245157i	$0.000780360\pi$
$744$	−431.422	+	246.121i	−0.579869	+	0.330808i
$745$	−17.8227	+	101.078i	−0.0239231	+	0.135675i
$746$	−496.954	−	95.6844i	−0.666159	−	0.128263i
$747$	42.2680	+	60.8174i	0.0565836	+	0.0814156i
$748$	147.820	−	369.634i	0.197620	−	0.494163i
$749$	107.907	+	90.5446i	0.144068	+	0.120887i
$750$	−574.388	−	311.853i	−0.765851	−	0.415803i
$751$	132.345	+	750.569i	0.176226	+	0.999425i	0.936720	+	0.350080i	$0.113846\pi$
$751$	132.345	+	750.569i	0.176226	+	0.999425i	−0.760494	+	0.649345i	$0.775043\pi$
$752$	935.665	+	621.509i	1.24424	+	0.826474i
$753$	−287.705	−	698.039i	−0.382079	−	0.927011i
$754$	296.076	−	775.410i	0.392674	−	1.02839i
$755$	−174.291			−0.230849
$756$	331.004	−	1270.92i	0.437836	−	1.68111i
$757$		−	87.8735i		−	0.116081i	−0.998314	−	0.0580406i	$-0.981515\pi$
$757$		−	87.8735i		−	0.116081i	0.998314	−	0.0580406i	$-0.0184853\pi$
$758$	18.2934	−	47.9097i	0.0241338	−	0.0632053i
$759$	93.0244	−	697.149i	0.122562	−	0.918510i
$760$	−81.8605	+	10.4933i	−0.107711	+	0.0138070i
$761$	−139.257	+	24.5548i	−0.182992	+	0.0322665i	−0.264393	−	0.964415i	$-0.585172\pi$
$761$	−139.257	+	24.5548i	−0.182992	+	0.0322665i	0.0814009	+	0.996681i	$0.474061\pi$
$762$	16.2431	+	619.821i	0.0213164	+	0.813414i
$763$	148.335	−	176.778i	0.194410	−	0.231689i
$764$	−308.029	+	770.248i	−0.403179	+	1.00818i
$765$	−70.1980	+	99.5091i	−0.0917621	+	0.130077i
$766$	1421.97	+	273.788i	1.85635	+	0.357425i
$767$	1246.22	+	219.742i	1.62479	+	0.286495i
$768$	−321.993	+	697.240i	−0.419262	+	0.907865i
$769$	−1151.42	−	419.081i	−1.49729	−	0.544969i	−0.541933	−	0.840421i	$-0.682308\pi$
$769$	−1151.42	−	419.081i	−1.49729	−	0.544969i	−0.955358	+	0.295452i	$0.904530\pi$
$770$	537.625	+	965.860i	0.698214	+	1.25436i
$771$	−222.222	−	350.171i	−0.288226	−	0.454178i
$772$	1264.38	+	39.6662i	1.63779	+	0.0513811i
$773$	380.773	+	659.518i	0.492591	+	0.853193i	0.999964	−	0.00853372i	$-0.00271640\pi$
$773$	380.773	+	659.518i	0.492591	+	0.853193i	−0.507372	+	0.861727i	$0.669383\pi$
$774$	134.215	−	465.022i	0.173404	−	0.600803i
$775$	194.750	−	337.317i	0.251291	−	0.435248i
$776$	−1350.56	+	420.773i	−1.74041	+	0.542233i
$777$	733.401	−	669.678i	0.943889	−	0.861877i
$778$	277.504	−	463.703i	0.356689	−	0.596020i
$779$	−4.19177	+	3.51731i	−0.00538096	+	0.00451516i
$780$	−664.783	+	6.99317i	−0.852285	+	0.00896561i
$781$	−361.242	−	992.504i	−0.462538	−	1.27081i
$782$	−105.510	−	91.3903i	−0.134923	−	0.116867i
$783$	−502.169	−	24.5706i	−0.641339	−	0.0313800i
$784$	−1517.56	+	446.820i	−1.93566	+	0.569924i
$785$	119.019	+	327.002i	0.151617	+	0.416563i
$786$	191.026	−	570.954i	0.243035	−	0.726404i
$787$	−708.273	−	844.087i	−0.899966	−	1.07254i	−0.997011	−	0.0772576i	$-0.975384\pi$
$787$	−708.273	−	844.087i	−0.899966	−	1.07254i	0.0970453	−	0.995280i	$-0.469061\pi$
$788$	565.061	−	185.816i	0.717082	−	0.235807i
$789$	148.508	+	675.474i	0.188223	+	0.856114i
$790$	31.1051	+	194.162i	0.0393735	+	0.245775i
$791$	1033.79	+	596.859i	1.30694	+	0.754562i
$792$	−699.640	−	1115.15i	−0.883383	−	1.40802i
$793$	770.548	+	1334.63i	0.971687	+	1.68301i
$794$	63.2445	+	77.8180i	0.0796530	+	0.0980076i
$795$	−107.028	−	55.9539i	−0.134627	−	0.0703823i
$796$	−245.480	+	1175.37i	−0.308392	+	1.47659i
$797$	−735.234	−	267.603i	−0.922502	−	0.335763i	−0.163268	−	0.986582i	$-0.552204\pi$
$797$	−735.234	−	267.603i	−0.922502	−	0.335763i	−0.759233	+	0.650818i	$0.774426\pi$
$798$	236.973	+	188.489i	0.296958	+	0.236201i
$799$	−66.3572	+	376.330i	−0.0830503	+	0.471002i
$800$	−57.8050	−	599.479i	−0.0722562	−	0.749349i
$801$	125.782	−	462.928i	0.157031	−	0.577937i
$802$	−96.1293	−	277.581i	−0.119862	−	0.346110i
$803$	−1000.39	−	839.429i	−1.24582	−	1.04537i
$804$	163.138	−	985.722i	0.202907	−	1.22602i
$805$	381.708	−	67.3053i	0.474171	−	0.0836091i
$806$	14.4647	−	922.360i	0.0179462	−	1.14437i
$807$	−534.570	+	694.143i	−0.662416	+	0.860153i
$808$	311.778	−	1383.99i	0.385864	−	1.71286i
$809$			1050.33i			1.29831i	0.760657	+	0.649154i	$0.224877\pi$
$809$			1050.33i			1.29831i	−0.760657	+	0.649154i	$0.775123\pi$
$810$	129.112	+	381.447i	0.159398	+	0.470922i
$811$			1307.30i			1.61197i	0.591939	+	0.805983i	$0.298363\pi$
$811$			1307.30i			1.61197i	−0.591939	+	0.805983i	$0.701637\pi$
$812$	428.058	+	798.220i	0.527164	+	0.983030i
$813$	−655.807	+	851.570i	−0.806650	+	1.04744i
$814$	15.6102	−	995.406i	0.0191771	−	1.22286i
$815$	150.146	−	26.4748i	0.184228	−	0.0324844i
$816$	−261.216	−	5.44526i	−0.320117	−	0.00667311i
$817$	85.4831	+	71.7288i	0.104630	+	0.0877953i
$818$	588.262	−	203.722i	0.719146	−	0.249048i
$819$	1718.68	+	1730.77i	2.09851	+	2.11327i
$820$	8.10831	+	10.3027i	0.00988818	+	0.0125642i
$821$	−222.056	+	1259.34i	−0.270470	+	1.53391i	0.482524	+	0.875883i	$0.339720\pi$
$821$	−222.056	+	1259.34i	−0.270470	+	1.53391i	−0.752994	+	0.658028i	$0.771391\pi$
$822$	−1185.66	−	943.081i	−1.44241	−	1.14730i
$823$	−99.1110	−	36.0734i	−0.120426	−	0.0438317i	0.281104	−	0.959677i	$-0.409299\pi$
$823$	−99.1110	−	36.0734i	−0.120426	−	0.0438317i	−0.401530	+	0.915846i	$0.631522\pi$
$824$	308.297	−	234.899i	0.374146	−	0.285071i
$825$	914.875	+	478.293i	1.10894	+	0.579749i
$826$	−1071.63	+	870.939i	−1.29737	+	1.05441i
$827$	489.700	+	848.186i	0.592141	+	1.02562i	0.993944	+	0.109892i	$0.0350504\pi$
$827$	489.700	+	848.186i	0.592141	+	1.02562i	−0.401803	+	0.915726i	$0.631616\pi$
$828$	−449.763	+	103.855i	−0.543192	+	0.125429i
$829$	135.647	+	78.3157i	0.163627	+	0.0944701i	0.579577	−	0.814917i	$-0.303218\pi$
$829$	135.647	+	78.3157i	0.163627	+	0.0944701i	−0.415950	+	0.909387i	$0.636551\pi$
$830$	6.47182	+	40.3980i	0.00779738	+	0.0486722i
$831$	−71.8040	−	326.594i	−0.0864067	−	0.393013i
$832$	−810.141	−	1173.96i	−0.973727	−	1.41101i
$833$	−345.939	−	412.273i	−0.415292	−	0.494926i
$834$	1007.45	+	337.065i	1.20797	+	0.404155i
$835$	87.3073	+	239.875i	0.104560	+	0.287275i
$836$	300.413	−	43.3068i	0.359346	−	0.0518024i
$837$	−533.790	+	165.224i	−0.637742	+	0.197400i
$838$	493.562	+	427.513i	0.588976	+	0.510159i
$839$	−327.573	−	900.000i	−0.390433	−	1.07271i	−0.966804	−	0.255517i	$-0.917754\pi$
$839$	−327.573	−	900.000i	−0.390433	−	1.07271i	0.576372	−	0.817188i	$-0.304468\pi$
$840$	469.196	−	553.340i	0.558566	−	0.658738i
$841$	−378.621	+	317.701i	−0.450204	+	0.377766i
$842$	−494.102	−	295.696i	−0.586820	−	0.351183i
$843$	146.335	−	133.620i	0.173588	−	0.158505i
$844$	−1327.76	−	823.146i	−1.57317	−	0.975291i
$845$	407.312	−	705.485i	0.482026	−	0.834893i
$846$	876.251	+	910.536i	1.03576	+	1.07628i
$847$	−1296.96	−	2246.40i	−1.53124	−	2.65219i
$848$	−28.9111	−	257.497i	−0.0340932	−	0.303652i
$849$	113.357	+	178.625i	0.133518	+	0.210395i
$850$	179.023	−	99.6491i	0.210615	−	0.117234i
$851$	−328.017	−	119.388i	−0.385449	−	0.140292i
$852$	−526.298	+	451.135i	−0.617721	+	0.529501i
$853$	−1257.60	−	221.750i	−1.47433	−	0.259964i	−0.622020	−	0.783001i	$-0.713688\pi$
$853$	−1257.60	−	221.750i	−1.47433	−	0.259964i	−0.852310	+	0.523037i	$0.824799\pi$
$854$	−1651.39	−	317.962i	−1.93371	−	0.372320i
$855$	−92.4644	−	8.41620i	−0.108145	−	0.00984351i
$856$	−42.5098	−	82.3449i	−0.0496610	−	0.0961973i
$857$	23.0085	−	27.4204i	0.0268477	−	0.0319958i	−0.752454	−	0.658645i	$-0.771130\pi$
$857$	23.0085	−	27.4204i	0.0268477	−	0.0319958i	0.779301	+	0.626650i	$0.215574\pi$
$858$	2444.14	−	64.0514i	2.84865	−	0.0746519i
$859$	−470.369	+	82.9388i	−0.547578	+	0.0965528i	−0.440591	−	0.897708i	$-0.645231\pi$
$859$	−470.369	+	82.9388i	−0.547578	+	0.0965528i	−0.106986	+	0.994260i	$0.534120\pi$
$860$	178.198	−	199.325i	0.207207	−	0.231774i
$861$	6.36206	−	47.6789i	0.00738915	−	0.0553762i
$862$	−350.107	+	916.915i	−0.406157	+	1.06371i
$863$			594.240i			0.688574i	0.938864	+	0.344287i	$0.111879\pi$
$863$			594.240i			0.688574i	−0.938864	+	0.344287i	$0.888121\pi$
$864$	−523.495	+	687.349i	−0.605897	+	0.795543i
$865$	−414.428			−0.479108
$866$	503.681	+	192.322i	0.581618	+	0.222080i
$867$	296.512	+	719.406i	0.341997	+	0.829764i
$868$	750.470	+	670.925i	0.864597	+	0.772955i
$869$	−125.577	−	712.181i	−0.144507	−	0.819541i
$870$	−244.080	−	132.518i	−0.280552	−	0.152320i
$871$	1421.49	+	1192.77i	1.63202	+	1.36943i
$872$	−134.902	+	69.6417i	−0.154704	+	0.0798644i
$873$	−1585.83	+	133.144i	−1.81653	+	0.152513i
$874$	20.1216	−	104.505i	0.0230224	−	0.119571i
$875$	−230.020	+	1304.51i	−0.262880	+	1.49087i
$876$	−284.652	+	808.434i	−0.324945	+	0.922869i
$877$	−94.3960	+	259.351i	−0.107635	+	0.295725i	−0.981804	−	0.189897i	$-0.939185\pi$
$877$	−94.3960	+	259.351i	−0.107635	+	0.295725i	0.874169	+	0.485622i	$0.161407\pi$
$878$	−547.811	−	984.160i	−0.623931	−	1.12091i
$879$	−3.66356	−	87.4244i	−0.00416788	−	0.0994589i
$880$	−81.1409	−	722.682i	−0.0922055	−	0.821230i
$881$	98.6095	−	56.9322i	0.111929	−	0.0646223i	−0.442990	−	0.896526i	$-0.646082\pi$
$881$	98.6095	−	56.9322i	0.111929	−	0.0646223i	0.554919	+	0.831904i	$0.312749\pi$
$882$	−1775.60	+	121.072i	−2.01315	+	0.137269i
$883$	−966.884	−	558.231i	−1.09500	−	0.632198i	−0.160096	−	0.987101i	$-0.551180\pi$
$883$	−966.884	−	558.231i	−1.09500	−	0.632198i	−0.934903	+	0.354904i	$0.884514\pi$
$884$	255.681	−	412.421i	0.289232	−	0.466540i
$885$	128.037	−	403.613i	0.144674	−	0.456060i
$886$	−101.402	+	169.440i	−0.114449	+	0.191242i
$887$	274.263	+	326.854i	0.309203	+	0.368494i	0.898159	−	0.439672i	$-0.144905\pi$
$887$	274.263	+	326.854i	0.309203	+	0.368494i	−0.588956	+	0.808165i	$0.700461\pi$
$888$	−615.113	+	220.294i	−0.692695	+	0.248079i
$889$	1180.85	−	429.795i	1.32829	−	0.483458i
$890$	173.499	−	200.303i	0.194942	−	0.225060i
$891$	−496.771	−	1395.22i	−0.557543	−	1.56590i
$892$	−131.050	−	909.076i	−0.146917	−	1.01914i
$893$	−273.780	+	99.6478i	−0.306585	+	0.111588i
$894$	−242.758	+	49.3947i	−0.271541	+	0.0552513i
$895$	356.852	−	299.434i	0.398717	−	0.334563i
$896$	1547.15	+	170.511i	1.72673	+	0.190303i
$897$	259.227	−	817.168i	0.288994	−	0.911001i
$898$	11.9562	−	1.91540i	0.0133142	−	0.00213296i
$899$	192.686	−	333.741i	0.214333	−	0.371236i
$900$	82.5445	−	672.495i	0.0917162	−	0.747217i
$901$	76.3406	−	44.0753i	0.0847287	−	0.0489181i
$902$	−30.4101	−	37.4176i	−0.0337141	−	0.0414829i
$903$	−980.077	+	41.0706i	−1.08536	+	0.0454824i
$904$	−475.946	−	624.663i	−0.526488	−	0.690999i
$905$	85.1479	−	233.942i	0.0940861	−	0.258499i
$906$	−154.188	−	391.407i	−0.170186	−	0.432016i
$907$	792.825	+	139.796i	0.874118	+	0.154131i	0.592670	−	0.805446i	$-0.298074\pi$
$907$	792.825	+	139.796i	0.874118	+	0.154131i	0.281449	+	0.959576i	$0.409185\pi$
$908$	907.561	−	714.259i	0.999516	−	0.786629i
$909$	679.568	−	1444.10i	0.747599	−	1.58867i
$910$	440.929	+	1273.21i	0.484537	+	1.39914i
$911$	−896.763	+	1068.72i	−0.984372	+	1.17313i	0.000526787		1.00000i	$0.499832\pi$
$911$	−896.763	+	1068.72i	−0.984372	+	1.17313i	−0.984899	+	0.173129i	$0.944612\pi$
$912$	−95.9836	−	174.552i	−0.105245	−	0.191394i
$913$	−26.1279	−	148.179i	−0.0286176	−	0.162299i
$914$	160.565	+	2.51802i	0.175673	+	0.00275494i
$915$	476.764	−	196.504i	0.521054	−	0.214759i
$916$	−599.993	+	321.755i	−0.655014	+	0.351261i
$917$	−1220.21			−1.33066
$918$	−285.569	−	69.6124i	−0.311078	−	0.0758305i
$919$	−143.881			−0.156563			−0.0782814	−	0.996931i	$-0.524943\pi$
$919$	−143.881			−0.156563			−0.0782814	+	0.996931i	$0.524943\pi$
$920$	−248.757	−	56.0386i	−0.270388	−	0.0609115i
$921$	−37.6873	+	282.438i	−0.0409200	+	0.306665i
$922$	790.911	+	12.4033i	0.857821	+	0.0134526i
$923$	−223.559	−	1267.86i	−0.242209	−	1.37363i
$924$	−1693.42	+	2061.81i	−1.83271	+	2.23139i
$925$	329.344	−	392.497i	0.356048	−	0.424321i
$926$	−1304.34	+	451.708i	−1.40857	+	0.487805i
$927$	395.826	−	182.891i	0.426997	−	0.197293i
$928$	−57.1922	−	593.124i	−0.0616295	−	0.639142i
$929$	78.2949	+	13.8055i	0.0842787	+	0.0148606i	0.215628	−	0.976475i	$-0.430820\pi$
$929$	78.2949	+	13.8055i	0.0842787	+	0.0148606i	−0.131350	+	0.991336i	$0.541931\pi$
$930$	−305.283	−	45.6186i	−0.328261	−	0.0490522i
$931$	140.340	−	385.581i	0.150741	−	0.414158i
$932$	−1293.12	−	270.074i	−1.38747	−	0.289779i
$933$	−187.720	−	295.803i	−0.201200	−	0.317045i
$934$	−770.800	+	626.447i	−0.825268	+	0.670714i
$935$	214.255	−	123.700i	0.229150	−	0.132300i
$936$	−603.811	−	1486.72i	−0.645097	−	1.58838i
$937$	913.972	−	1583.05i	0.975424	−	1.68948i	0.296894	−	0.954910i	$-0.404049\pi$
$937$	913.972	−	1583.05i	0.975424	−	1.68948i	0.678529	−	0.734573i	$-0.262618\pi$
$938$	−1999.46	+	320.317i	−2.13162	+	0.341490i
$939$	−223.167	−	244.402i	−0.237664	−	0.260279i
$940$	218.067	+	663.134i	0.231986	+	0.705461i
$941$	−195.208	+	163.799i	−0.207448	+	0.174069i	−0.740592	−	0.671955i	$-0.765455\pi$
$941$	−195.208	+	163.799i	−0.207448	+	0.174069i	0.533144	+	0.846024i	$0.321010\pi$
$942$	−629.059	+	556.567i	−0.667791	+	0.590835i
$943$	−15.8869	+	5.78237i	−0.0168472	+	0.00613188i
$944$	871.483	−	256.594i	0.923182	−	0.271816i
$945$	650.115	−	493.443i	0.687953	−	0.522162i
$946$	−643.778	+	743.238i	−0.680527	+	0.785664i
$947$	−486.208	+	176.965i	−0.513420	+	0.186869i	−0.585720	−	0.810513i	$-0.699188\pi$
$947$	−486.208	+	176.965i	−0.513420	+	0.186869i	0.0723005	+	0.997383i	$0.476966\pi$
$948$	−408.513	+	241.620i	−0.430921	+	0.254873i
$949$	−1023.20	−	1219.40i	−1.07818	−	1.28493i
$950$	134.042	+	80.2177i	0.141097	+	0.0844397i
$951$	−674.259	+	148.240i	−0.709000	+	0.155879i
$952$	157.509	+	505.558i	0.165450	+	0.531048i
$953$	−459.475	−	265.278i	−0.482135	−	0.278361i	0.239171	−	0.970977i	$-0.423124\pi$
$953$	−459.475	−	265.278i	−0.482135	−	0.278361i	−0.721306	+	0.692617i	$0.756458\pi$
$954$	30.9726	−	289.854i	0.0324660	−	0.303830i
$955$	−446.467	+	257.768i	−0.467504	+	0.269914i
$956$	−28.3208	+	902.736i	−0.0296243	+	0.944284i
$957$	905.177	+	473.223i	0.945848	+	0.494486i
$958$	−404.354	+	225.075i	−0.422082	+	0.234943i
$959$	−1050.16	+	2885.29i	−1.09506	+	3.00865i
$960$	−425.227	+	216.747i	−0.442944	+	0.225778i
$961$	−92.5024	+	524.607i	−0.0962564	+	0.545897i
$962$	229.429	−	1191.58i	0.238492	−	1.23865i
$963$	−26.6299	−	100.796i	−0.0276530	−	0.104668i
$964$	962.501	+	384.913i	0.998445	+	0.399287i
$965$	602.222	+	505.324i	0.624064	+	0.523652i
$966$	488.829	+	797.661i	0.506034	+	0.825736i
$967$	−0.598590	−	3.39477i	−0.000619017	−	0.00351062i	0.984497	−	0.175403i	$-0.0561229\pi$
$967$	−0.598590	−	3.39477i	−0.000619017	−	0.00351062i	−0.985116	+	0.171893i	$0.945012\pi$
$968$	216.971	+	1692.63i	0.224143	+	1.74859i
$969$	41.3487	−	53.6916i	0.0426715	−	0.0554093i
$970$	−821.278	−	313.590i	−0.846678	−	0.323289i
$971$	−525.039			−0.540720			−0.270360	−	0.962759i	$-0.587143\pi$
$971$	−525.039			−0.540720			−0.270360	+	0.962759i	$0.587143\pi$
$972$	−742.397	+	627.399i	−0.763783	+	0.645473i
$973$		−	2153.07i		−	2.21281i
$974$	1064.60	+	406.499i	1.09302	+	0.417350i
$975$	996.980	+	767.789i	1.02254	+	0.787476i
$976$	921.584	+	612.155i	0.944246	+	0.627208i
$977$	−815.378	+	143.773i	−0.834573	+	0.147158i	−0.574576	−	0.818452i	$-0.694833\pi$
$977$	−815.378	+	143.773i	−0.834573	+	0.147158i	−0.259997	+	0.965609i	$0.583722\pi$
$978$	192.283	+	313.763i	0.196608	+	0.320821i
$979$	−626.441	+	746.563i	−0.639878	+	0.762577i
$980$	−912.843	−	365.054i	−0.931473	−	0.372504i
$981$	−165.128	+	43.6264i	−0.168327	+	0.0444713i
$982$	−126.086	+	654.853i	−0.128398	+	0.666856i
$983$	1084.92	+	191.300i	1.10368	+	0.194608i	0.695664	−	0.718367i	$-0.255110\pi$
$983$	1084.92	+	191.300i	1.10368	+	0.194608i	0.408014	+	0.912976i	$0.366221\pi$
$984$	−15.9637	+	27.3232i	−0.0162233	+	0.0277675i
$985$	347.368	+	126.432i	0.352658	+	0.128357i
$986$	177.125	−	98.5927i	0.179640	−	0.0999926i
$987$	1186.58	−	2269.67i	1.20220	−	2.29957i
$988$	369.783	+	11.6009i	0.374274	+	0.0117418i
$989$	172.388	+	298.585i	0.174305	+	0.301906i
$990$	86.9267	−	813.495i	0.0878047	−	0.821712i
$991$	−310.959	+	538.597i	−0.313783	+	0.543488i	−0.979178	−	0.203003i	$-0.934930\pi$
$991$	−310.959	+	538.597i	−0.313783	+	0.543488i	0.665395	+	0.746491i	$0.268263\pi$
$992$	−285.188	−	597.701i	−0.287488	−	0.602522i
$993$	96.1489	+	437.324i	0.0968266	+	0.440407i
$994$	1205.52	+	721.443i	1.21279	+	0.725798i
$995$	−571.625	+	479.650i	−0.574497	+	0.482060i
$996$	−84.9966	+	50.2722i	−0.0853379	+	0.0504741i
$997$	93.9672	+	258.173i	0.0942500	+	0.258950i	0.977855	−	0.209283i	$-0.0671131\pi$
$997$	93.9672	+	258.173i	0.0942500	+	0.258950i	−0.883605	+	0.468233i	$0.844891\pi$
$998$	1056.27	−	1219.46i	1.05838	−	1.22190i
$999$	−729.248	+	92.1102i	−0.729978	+	0.0922024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.x.a.101.10	yes	420
8.5	even	2	inner	216.3.x.a.101.48	yes	420
27.23	odd	18	inner	216.3.x.a.77.48	yes	420
216.77	odd	18	inner	216.3.x.a.77.10	✓	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.3.x.a.77.10	✓	420	216.77	odd	18	inner
216.3.x.a.77.48	yes	420	27.23	odd	18	inner
216.3.x.a.101.10	yes	420	1.1	even	1	trivial
216.3.x.a.101.48	yes	420	8.5	even	2	inner

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86843 - 0.713426i) q^{2} +(1.83045 - 2.37686i) q^{3} +(2.98205 + 2.66597i) q^{4} +(0.431661 + 2.44807i) q^{5} +(-5.11578 + 3.13509i) q^{6} +(9.31534 + 7.81650i) q^{7} +(-3.66977 - 7.10864i) q^{8} +(-2.29889 - 8.70144i) q^{9} +(0.939989 - 4.88201i) q^{10} +(-3.17501 + 18.0064i) q^{11} +(11.7951 - 2.20797i) q^{12} +(-7.62257 + 20.9428i) q^{13} +(-11.8286 - 21.2504i) q^{14} +(6.60885 + 3.45508i) q^{15} +(1.78522 + 15.9001i) q^{16} +(-4.71393 + 2.72159i) q^{17} +(-1.91252 + 17.8981i) q^{18} +(-3.59403 - 2.07501i) q^{19} +(-5.23925 + 8.45106i) q^{20} +(35.6300 - 7.83350i) q^{21} +(18.7785 - 31.3785i) q^{22} +(-8.24193 - 9.82236i) q^{23} +(-23.6136 - 4.28950i) q^{24} +(17.6856 - 6.43703i) q^{25} +(29.1834 - 33.6921i) q^{26} +(-24.8901 - 10.4634i) q^{27} +(6.94025 + 48.1436i) q^{28} +(17.4981 - 6.36879i) q^{29} +(-9.88322 - 11.1705i) q^{30} +(15.8536 - 13.3028i) q^{31} +(8.00798 - 30.9818i) q^{32} +(36.9869 + 40.5064i) q^{33} +(10.7493 - 1.72206i) q^{34} +(-15.1143 + 26.1787i) q^{35} +(16.3424 - 32.0769i) q^{36} +(23.5765 - 13.6119i) q^{37} +(5.23481 + 6.44108i) q^{38} +(35.8254 + 56.4526i) q^{39} +(15.8184 - 12.0524i) q^{40} +(0.450966 - 1.23902i) q^{41} +(-72.1607 - 10.7830i) q^{42} +(-26.4805 - 4.66923i) q^{43} +(-57.4725 + 45.2314i) q^{44} +(20.3094 - 9.38393i) q^{45} +(8.39194 + 24.2324i) q^{46} +(45.1266 - 53.7798i) q^{47} +(41.0600 + 24.8611i) q^{48} +(17.1692 + 97.3712i) q^{49} +(-37.6366 - 0.590226i) q^{50} +(-2.15980 + 16.1861i) q^{51} +(-78.5638 + 42.1310i) q^{52} -16.1947 q^{53} +(39.0405 + 37.3074i) q^{54} -45.4515 q^{55} +(21.3795 - 94.9042i) q^{56} +(-11.5107 + 4.74428i) q^{57} +(-37.2376 - 0.583969i) q^{58} +(-9.85967 - 55.9170i) q^{59} +(10.4968 + 27.9222i) q^{60} +(44.4475 - 52.9705i) q^{61} +(-39.1118 + 13.5449i) q^{62} +(46.5999 - 99.0262i) q^{63} +(-37.0655 + 52.1742i) q^{64} +(-54.5599 - 9.62039i) q^{65} +(-40.2091 - 102.071i) q^{66} +(28.4769 - 78.2396i) q^{67} +(-21.3128 - 4.45128i) q^{68} +(-38.4328 + 1.61055i) q^{69} +(46.9165 - 38.1301i) q^{70} +(-50.0267 + 28.8829i) q^{71} +(-53.4190 + 48.2743i) q^{72} +(-35.7118 + 61.8546i) q^{73} +(-53.7621 + 8.61278i) q^{74} +(17.0727 - 53.8188i) q^{75} +(-5.18564 - 15.7694i) q^{76} +(-170.323 + 142.918i) q^{77} +(-26.6624 - 131.036i) q^{78} +(-37.1663 + 13.5274i) q^{79} +(-38.1540 + 11.2338i) q^{80} +(-70.4302 + 40.0073i) q^{81} +(-1.72655 + 1.99329i) q^{82} +(-7.73295 + 2.81456i) q^{83} +(127.134 + 71.6285i) q^{84} +(-8.69747 - 10.3652i) q^{85} +(46.1458 + 27.6160i) q^{86} +(16.8917 - 53.2482i) q^{87} +(139.652 - 43.5093i) q^{88} +(46.1603 + 26.6506i) q^{89} +(-44.6414 + 3.04394i) q^{90} +(-234.707 + 135.508i) q^{91} +(1.60825 - 51.2635i) q^{92} +(-2.59947 - 62.0318i) q^{93} +(-122.684 + 68.2892i) q^{94} +(3.52838 - 9.69414i) q^{95} +(-58.9811 - 75.7445i) q^{96} +(30.7051 - 174.137i) q^{97} +(37.3877 - 194.180i) q^{98} +(163.980 - 13.7675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 51 q^{12} + 39 q^{14} - 12 q^{15} - 6 q^{16} - 18 q^{17} - 27 q^{18} + 57 q^{20} - 6 q^{22} - 12 q^{23} + 126 q^{24} - 12 q^{25}+ \cdots - 1548 q^{98}+O(q^{100}) \) 420 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 51 * q^12 + 39 * q^14 - 12 * q^15 - 6 * q^16 - 18 * q^17 - 27 * q^18 + 57 * q^20 - 6 * q^22 - 12 * q^23 + 126 * q^24 - 12 * q^25 - 12 * q^28 + 87 * q^30 - 12 * q^31 + 84 * q^32 - 36 * q^33 - 18 * q^34 - 36 * q^36 - 108 * q^38 - 12 * q^39 + 69 * q^40 - 84 * q^41 + 114 * q^42 - 657 * q^44 - 3 * q^46 - 12 * q^47 - 453 * q^48 - 12 * q^49 + 153 * q^50 + 21 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 66 * q^57 + 129 * q^58 + 210 * q^60 - 900 * q^62 + 468 * q^63 - 3 * q^64 - 12 * q^65 - 855 * q^66 + 279 * q^68 + 153 * q^70 - 18 * q^71 - 156 * q^72 - 6 * q^73 + 423 * q^74 - 54 * q^76 + 642 * q^78 - 12 * q^79 - 12 * q^81 - 12 * q^82 + 192 * q^84 + 606 * q^86 - 588 * q^87 + 186 * q^88 - 18 * q^89 - 534 * q^90 - 735 * q^92 + 345 * q^94 - 162 * q^95 - 486 * q^96 - 12 * q^97 - 1548 * q^98

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