LMFDB - Embedded newform 310.3.i.a.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [310,3,Mod(99,310)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(310, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("310.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 310 = 2 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	310.i (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.44688819517$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			99.4
Character	$\chi$	$=$	310.99
Dual form			310.3.i.a.119.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-1.60457 - 2.77920i) q^{3} -2.00000 q^{4} +(-2.86911 - 4.09490i) q^{5} +(-3.93038 + 2.26920i) q^{6} +(11.5265 - 6.65484i) q^{7} +2.82843i q^{8} +(-0.649284 + 1.12459i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-1.60457 - 2.77920i) q^{3} -2.00000 q^{4} +(-2.86911 - 4.09490i) q^{5} +(-3.93038 + 2.26920i) q^{6} +(11.5265 - 6.65484i) q^{7} +2.82843i q^{8} +(-0.649284 + 1.12459i) q^{9} +(-5.79106 + 4.05754i) q^{10} +(-16.0693 - 9.27762i) q^{11} +(3.20914 + 5.55839i) q^{12} +(6.09017 - 10.5485i) q^{13} +(-9.41136 - 16.3010i) q^{14} +(-6.77684 + 14.5444i) q^{15} +4.00000 q^{16} +(-1.72538 - 2.98844i) q^{17} +(1.59041 + 0.918227i) q^{18} +(11.1575 + 19.3253i) q^{19} +(5.73822 + 8.18980i) q^{20} +(-36.9902 - 21.3563i) q^{21} +(-13.1205 + 22.7254i) q^{22} +18.9965 q^{23} +(7.86075 - 4.53841i) q^{24} +(-8.53640 + 23.4974i) q^{25} +(-14.9178 - 8.61280i) q^{26} -24.7150 q^{27} +(-23.0530 + 13.3097i) q^{28} +31.8234i q^{29} +(20.5688 + 9.58389i) q^{30} +(2.63262 + 30.8880i) q^{31} -5.65685i q^{32} +59.5463i q^{33} +(-4.22630 + 2.44005i) q^{34} +(-60.3218 - 28.1065i) q^{35} +(1.29857 - 2.24919i) q^{36} +(5.14167 + 8.90563i) q^{37} +(27.3301 - 15.7790i) q^{38} -39.0884 q^{39} +(11.5821 - 8.11507i) q^{40} +(29.1796 - 50.5405i) q^{41} +(-30.2024 + 52.3120i) q^{42} +(3.27107 + 5.66567i) q^{43} +(32.1386 + 18.5552i) q^{44} +(6.46796 - 0.567830i) q^{45} -26.8651i q^{46} -26.7004i q^{47} +(-6.41828 - 11.1168i) q^{48} +(64.0737 - 110.979i) q^{49} +(33.2304 + 12.0723i) q^{50} +(-5.53698 + 9.59032i) q^{51} +(-12.1803 + 21.0970i) q^{52} +(-10.0096 + 17.3372i) q^{53} +34.9522i q^{54} +(8.11372 + 92.4207i) q^{55} +(18.8227 + 32.6019i) q^{56} +(35.8059 - 62.0176i) q^{57} +45.0051 q^{58} +(-22.3434 - 38.6999i) q^{59} +(13.5537 - 29.0887i) q^{60} +56.2901i q^{61} +(43.6822 - 3.72309i) q^{62} +17.2835i q^{63} -8.00000 q^{64} +(-60.6683 + 5.32614i) q^{65} +84.2112 q^{66} +(-92.1079 - 53.1785i) q^{67} +(3.45076 + 5.97688i) q^{68} +(-30.4811 - 52.7949i) q^{69} +(-39.7485 + 85.3078i) q^{70} +(-11.9344 + 20.6710i) q^{71} +(-3.18083 - 1.83645i) q^{72} +(70.4715 - 122.060i) q^{73} +(12.5945 - 7.27142i) q^{74} +(79.0012 - 13.9790i) q^{75} +(-22.3149 - 38.6506i) q^{76} -246.964 q^{77} +55.2793i q^{78} +(21.5684 - 12.4525i) q^{79} +(-11.4764 - 16.3796i) q^{80} +(45.5004 + 78.8090i) q^{81} +(-71.4750 - 41.2661i) q^{82} +(-23.7635 + 41.1597i) q^{83} +(73.9804 + 42.7126i) q^{84} +(-7.28707 + 15.6394i) q^{85} +(8.01246 - 4.62600i) q^{86} +(88.4435 - 51.0629i) q^{87} +(26.2411 - 45.4509i) q^{88} +61.3833i q^{89} +(-0.803033 - 9.14708i) q^{90} -162.116i q^{91} -37.9929 q^{92} +(81.6196 - 56.8785i) q^{93} -37.7600 q^{94} +(47.1231 - 101.135i) q^{95} +(-15.7215 + 9.07681i) q^{96} -10.8007i q^{97} +(-156.948 - 90.6139i) q^{98} +(20.8671 - 12.0476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 128 q^{4} + 6 q^{5} - 56 q^{9}+O(q^{10}) $ 64 * q - 128 * q^4 + 6 * q^5 - 56 * q^9	$ 64 q - 128 q^{4} + 6 q^{5} - 56 q^{9} - 16 q^{10} + 256 q^{16} - 8 q^{19} - 12 q^{20} - 72 q^{21} - 22 q^{25} + 72 q^{31} - 48 q^{34} + 12 q^{35} + 112 q^{36} - 400 q^{39} + 32 q^{40} - 8 q^{41} + 92 q^{45} + 24 q^{49} + 16 q^{50} + 164 q^{51} + 162 q^{55} + 48 q^{59} - 512 q^{64} - 54 q^{65} - 64 q^{66} - 32 q^{69} + 352 q^{70} - 128 q^{71} + 144 q^{74} + 942 q^{75} + 16 q^{76} - 768 q^{79} + 24 q^{80} - 168 q^{81} + 144 q^{84} - 336 q^{86} - 272 q^{90} + 176 q^{94} - 292 q^{95} - 168 q^{99}+O(q^{100}) $ 64 * q - 128 * q^4 + 6 * q^5 - 56 * q^9 - 16 * q^10 + 256 * q^16 - 8 * q^19 - 12 * q^20 - 72 * q^21 - 22 * q^25 + 72 * q^31 - 48 * q^34 + 12 * q^35 + 112 * q^36 - 400 * q^39 + 32 * q^40 - 8 * q^41 + 92 * q^45 + 24 * q^49 + 16 * q^50 + 164 * q^51 + 162 * q^55 + 48 * q^59 - 512 * q^64 - 54 * q^65 - 64 * q^66 - 32 * q^69 + 352 * q^70 - 128 * q^71 + 144 * q^74 + 942 * q^75 + 16 * q^76 - 768 * q^79 + 24 * q^80 - 168 * q^81 + 144 * q^84 - 336 * q^86 - 272 * q^90 + 176 * q^94 - 292 * q^95 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/310\mathbb{Z}\right)^\times$.

$n$	$187$	$251$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−1.60457	−	2.77920i	−0.534856	−	0.926398i	−0.999170	−	0.0407277i	$-0.987032\pi$
$3$	−1.60457	−	2.77920i	−0.534856	−	0.926398i	0.464314	−	0.885671i	$-0.346301\pi$
$4$	−2.00000			−0.500000
$5$	−2.86911	−	4.09490i	−0.573822	−	0.818980i
$5$	−2.86911	−	4.09490i	−0.573822	−	0.818980i
$6$	−3.93038	+	2.26920i	−0.655063	+	0.378201i
$7$	11.5265	−	6.65484i	1.64665	−	0.950691i	0.668253	−	0.743934i	$-0.267042\pi$
$7$	11.5265	−	6.65484i	1.64665	−	0.950691i	0.978392	−	0.206757i	$-0.0662909\pi$
$8$			2.82843i			0.353553i
$9$	−0.649284	+	1.12459i	−0.0721427	+	0.124955i
$10$	−5.79106	+	4.05754i	−0.579106	+	0.405754i
$11$	−16.0693	−	9.27762i	−1.46085	−	0.843420i	−0.461796	−	0.886986i	$-0.652795\pi$
$11$	−16.0693	−	9.27762i	−1.46085	−	0.843420i	−0.999051	+	0.0435664i	$0.986128\pi$
$12$	3.20914	+	5.55839i	0.267428	+	0.463199i
$13$	6.09017	−	10.5485i	0.468474	−	0.811422i	−0.530876	−	0.847449i	$-0.678137\pi$
$13$	6.09017	−	10.5485i	0.468474	−	0.811422i	0.999351	+	0.0360277i	$0.0114705\pi$
$14$	−9.41136	−	16.3010i	−0.672240	−	1.16435i
$15$	−6.77684	+	14.5444i	−0.451789	+	0.969625i
$16$	4.00000			0.250000
$17$	−1.72538	−	2.98844i	−0.101493	−	0.175791i	0.810807	−	0.585313i	$-0.199029\pi$
$17$	−1.72538	−	2.98844i	−0.101493	−	0.175791i	−0.912300	+	0.409523i	$0.865695\pi$
$18$	1.59041	+	0.918227i	0.0883564	+	0.0510126i
$19$	11.1575	+	19.3253i	0.587235	+	1.01712i	0.994593	+	0.103852i	$0.0331169\pi$
$19$	11.1575	+	19.3253i	0.587235	+	1.01712i	−0.407358	+	0.913269i	$0.633550\pi$
$20$	5.73822	+	8.18980i	0.286911	+	0.409490i
$21$	−36.9902	−	21.3563i	−1.76144	−	1.01697i
$22$	−13.1205	+	22.7254i	−0.596388	+	1.03297i
$23$	18.9965			0.825933			0.412967	−	0.910746i	$-0.364493\pi$
$23$	18.9965			0.825933			0.412967	+	0.910746i	$0.364493\pi$
$24$	7.86075	−	4.53841i	0.327531	−	0.189100i
$25$	−8.53640	+	23.4974i	−0.341456	+	0.939898i
$26$	−14.9178	−	8.61280i	−0.573762	−	0.331261i
$27$	−24.7150			−0.915369
$28$	−23.0530	+	13.3097i	−0.823323	+	0.475346i
$29$			31.8234i			1.09736i	0.836033	+	0.548680i	$0.184869\pi$
$29$			31.8234i			1.09736i	−0.836033	+	0.548680i	$0.815131\pi$
$30$	20.5688	+	9.58389i	0.685628	+	0.319463i
$31$	2.63262	+	30.8880i	0.0849233	+	0.996387i
$31$	2.63262	+	30.8880i	0.0849233	+	0.996387i
$32$		−	5.65685i		−	0.176777i
$33$			59.5463i			1.80443i
$34$	−4.22630	+	2.44005i	−0.124303	+	0.0717663i
$35$	−60.3218	−	28.1065i	−1.72348	−	0.803042i
$36$	1.29857	−	2.24919i	0.0360713	−	0.0624774i
$37$	5.14167	+	8.90563i	0.138964	+	0.240693i	0.927105	−	0.374802i	$-0.122289\pi$
$37$	5.14167	+	8.90563i	0.138964	+	0.240693i	−0.788141	+	0.615495i	$0.788956\pi$
$38$	27.3301	−	15.7790i	0.719213	−	0.415238i
$39$	−39.0884			−1.00227
$40$	11.5821	−	8.11507i	0.289553	−	0.202877i
$41$	29.1796	−	50.5405i	0.711696	−	1.23269i	−0.252524	−	0.967591i	$-0.581261\pi$
$41$	29.1796	−	50.5405i	0.711696	−	1.23269i	0.964220	−	0.265104i	$-0.0854062\pi$
$42$	−30.2024	+	52.3120i	−0.719104	+	1.24552i
$43$	3.27107	+	5.66567i	0.0760715	+	0.131760i	0.901552	−	0.432671i	$-0.142429\pi$
$43$	3.27107	+	5.66567i	0.0760715	+	0.131760i	−0.825480	+	0.564431i	$0.809096\pi$
$44$	32.1386	+	18.5552i	0.730423	+	0.421710i
$45$	6.46796	−	0.567830i	0.143733	−	0.0126184i
$46$		−	26.8651i		−	0.584023i
$47$		−	26.7004i		−	0.568093i	−0.958810	−	0.284047i	$-0.908323\pi$
$47$		−	26.7004i		−	0.568093i	0.958810	−	0.284047i	$-0.0916770\pi$
$48$	−6.41828	−	11.1168i	−0.133714	−	0.231600i
$49$	64.0737	−	110.979i	1.30763	−	2.26488i
$50$	33.2304	+	12.0723i	0.664608	+	0.241446i
$51$	−5.53698	+	9.59032i	−0.108568	+	0.188046i
$52$	−12.1803	+	21.0970i	−0.234237	+	0.405711i
$53$	−10.0096	+	17.3372i	−0.188861	+	0.327117i	−0.944871	−	0.327444i	$-0.893813\pi$
$53$	−10.0096	+	17.3372i	−0.188861	+	0.327117i	0.756010	+	0.654560i	$0.227146\pi$
$54$			34.9522i			0.647264i
$55$	8.11372	+	92.4207i	0.147522	+	1.68038i
$56$	18.8227	+	32.6019i	0.336120	+	0.582177i
$57$	35.8059	−	62.0176i	0.628173	−	1.08803i
$58$	45.0051			0.775950
$59$	−22.3434	−	38.6999i	−0.378702	−	0.655931i	0.612172	−	0.790725i	$-0.290296\pi$
$59$	−22.3434	−	38.6999i	−0.378702	−	0.655931i	−0.990874	+	0.134794i	$0.956963\pi$
$60$	13.5537	−	29.0887i	0.225895	−	0.484812i
$61$			56.2901i			0.922788i	0.887195	+	0.461394i	$0.152651\pi$
$61$			56.2901i			0.922788i	−0.887195	+	0.461394i	$0.847349\pi$
$62$	43.6822	−	3.72309i	0.704552	−	0.0600498i
$63$			17.2835i			0.274342i
$64$	−8.00000			−0.125000
$65$	−60.6683	+	5.32614i	−0.933359	+	0.0819406i
$66$	84.2112			1.27593
$67$	−92.1079	−	53.1785i	−1.37474	−	0.793709i	−0.383224	−	0.923656i	$-0.625186\pi$
$67$	−92.1079	−	53.1785i	−1.37474	−	0.793709i	−0.991521	+	0.129946i	$0.958520\pi$
$68$	3.45076	+	5.97688i	0.0507464	+	0.0878954i
$69$	−30.4811	−	52.7949i	−0.441756	−	0.765143i
$70$	−39.7485	+	85.3078i	−0.567836	+	1.21868i
$71$	−11.9344	+	20.6710i	−0.168090	+	0.291141i	−0.937748	−	0.347315i	$-0.887093\pi$
$71$	−11.9344	+	20.6710i	−0.168090	+	0.291141i	0.769658	+	0.638456i	$0.220427\pi$
$72$	−3.18083	−	1.83645i	−0.0441782	−	0.0255063i
$73$	70.4715	−	122.060i	0.965363	−	1.67206i	0.256725	−	0.966484i	$-0.417356\pi$
$73$	70.4715	−	122.060i	0.965363	−	1.67206i	0.708637	−	0.705573i	$-0.249310\pi$
$74$	12.5945	−	7.27142i	0.170195	−	0.0982624i
$75$	79.0012	−	13.9790i	1.05335	−	0.186386i
$76$	−22.3149	−	38.6506i	−0.293618	−	0.508561i
$77$	−246.964			−3.20733
$78$			55.2793i			0.708709i
$79$	21.5684	−	12.4525i	0.273018	−	0.157627i	−0.357240	−	0.934012i	$-0.616282\pi$
$79$	21.5684	−	12.4525i	0.273018	−	0.157627i	0.630258	+	0.776386i	$0.282949\pi$
$80$	−11.4764	−	16.3796i	−0.143456	−	0.204745i
$81$	45.5004	+	78.8090i	0.561734	+	0.972951i
$82$	−71.4750	−	41.2661i	−0.871647	−	0.503245i
$83$	−23.7635	+	41.1597i	−0.286308	+	0.495900i	−0.972925	−	0.231119i	$-0.925761\pi$
$83$	−23.7635	+	41.1597i	−0.286308	+	0.495900i	0.686618	+	0.727019i	$0.259095\pi$
$84$	73.9804	+	42.7126i	0.880719	+	0.508483i
$85$	−7.28707	+	15.6394i	−0.0857302	+	0.183993i
$86$	8.01246	−	4.62600i	0.0931682	−	0.0537907i
$87$	88.4435	−	51.0629i	1.01659	−	0.586930i
$88$	26.2411	−	45.4509i	0.298194	−	0.516487i
$89$			61.3833i			0.689700i	0.938658	+	0.344850i	$0.112070\pi$
$89$			61.3833i			0.689700i	−0.938658	+	0.344850i	$0.887930\pi$
$90$	−0.803033	−	9.14708i	−0.00892259	−	0.101634i
$91$		−	162.116i		−	1.78150i
$92$	−37.9929			−0.412967
$93$	81.6196	−	56.8785i	0.877630	−	0.611597i
$94$	−37.7600			−0.401703
$95$	47.1231	−	101.135i	0.496033	−	1.06458i
$96$	−15.7215	+	9.07681i	−0.163766	+	0.0945501i
$97$		−	10.8007i		−	0.111347i	−0.998449	−	0.0556737i	$-0.982269\pi$
$97$		−	10.8007i		−	0.111347i	0.998449	−	0.0556737i	$-0.0177307\pi$
$98$	−156.948	−	90.6139i	−1.60151	−	0.924632i
$99$	20.8671	−	12.0476i	0.210779	−	0.121693i
$100$	17.0728	−	46.9949i	0.170728	−	0.469949i
$101$	81.2791			0.804743			0.402372	−	0.915476i	$-0.368186\pi$
$101$	81.2791			0.804743			0.402372	+	0.915476i	$0.368186\pi$
$102$	13.5628	+	7.83047i	0.132968	+	0.0767693i
$103$	76.7076	+	44.2872i	0.744734	+	0.429972i	0.823788	−	0.566898i	$-0.191857\pi$
$103$	76.7076	+	44.2872i	0.744734	+	0.429972i	−0.0790539	+	0.996870i	$0.525190\pi$
$104$	29.8356	+	17.2256i	0.286881	+	0.165631i
$105$	18.6771	+	212.745i	0.177877	+	2.02614i
$106$	24.5185	+	14.1557i	0.231306	+	0.133545i
$107$	90.6006	−	52.3083i	0.846734	−	0.488862i	−0.0128133	−	0.999918i	$-0.504079\pi$
$107$	90.6006	−	52.3083i	0.846734	−	0.488862i	0.859548	+	0.511056i	$0.170745\pi$
$108$	49.4299			0.457684
$109$	102.299			0.938524			0.469262	−	0.883059i	$-0.344520\pi$
$109$	102.299			0.938524			0.469262	+	0.883059i	$0.344520\pi$
$110$	130.703	−	11.4745i	1.18821	−	0.104314i
$111$	16.5003	−	28.5794i	0.148652	−	0.257472i
$112$	46.1061	−	26.6194i	0.411661	−	0.237673i
$113$	−30.5533	−	17.6400i	−0.270383	−	0.156106i	0.358678	−	0.933461i	$-0.383227\pi$
$113$	−30.5533	−	17.6400i	−0.270383	−	0.156106i	−0.629062	+	0.777355i	$0.716561\pi$
$114$	−87.7061	−	50.6371i	−0.769352	−	0.444185i
$115$	−54.5030	−	77.7886i	−0.473939	−	0.676423i
$116$		−	63.6468i		−	0.548680i
$117$	7.90850	+	13.6979i	0.0675940	+	0.117076i
$118$	−54.7299	+	31.5983i	−0.463813	+	0.267783i
$119$	−39.7752	−	22.9642i	−0.334245	−	0.192977i
$120$	−41.1377	−	19.1678i	−0.342814	−	0.159732i
$121$	111.648	+	193.381i	0.922714	+	1.59819i
$122$	79.6062			0.652510
$123$	−187.282			−1.52262
$124$	−5.26524	−	61.7760i	−0.0424616	−	0.498194i
$125$	120.712	−	32.4611i	0.965692	−	0.259689i
$126$	24.4426			0.193989
$127$	−106.528	−	184.512i	−0.838806	−	1.45285i	−0.890894	−	0.454211i	$-0.849921\pi$
$127$	−106.528	−	184.512i	−0.838806	−	1.45285i	0.0520885	−	0.998642i	$-0.483412\pi$
$128$			11.3137i			0.0883883i
$129$	10.4973	−	18.1819i	0.0813746	−	0.140945i
$130$	7.53230	+	85.7980i	0.0579408	+	0.659984i
$131$	−125.628	−	217.594i	−0.958990	−	1.66102i	−0.724960	−	0.688791i	$-0.758142\pi$
$131$	−125.628	−	217.594i	−0.958990	−	1.66102i	−0.234030	−	0.972229i	$-0.575191\pi$
$132$		−	119.093i		−	0.902217i
$133$	257.213	+	148.502i	1.93394	+	1.11656i
$134$	−75.2058	+	130.260i	−0.561237	+	0.972091i
$135$	70.9100	+	101.205i	0.525259	+	0.749669i
$136$	8.45259	−	4.88011i	0.0621514	−	0.0358831i
$137$	−95.9930	+	166.265i	−0.700679	+	1.21361i	0.267549	+	0.963544i	$0.413786\pi$
$137$	−95.9930	+	166.265i	−0.700679	+	1.21361i	−0.968228	+	0.250068i	$0.919547\pi$
$138$	−74.6633	+	43.1069i	−0.541038	+	0.312369i
$139$			137.526i			0.989393i	0.869066	+	0.494696i	$0.164721\pi$
$139$			137.526i			0.989393i	−0.869066	+	0.494696i	$0.835279\pi$
$140$	120.644	+	56.2129i	0.861739	+	0.401521i
$141$	−74.2056	+	42.8426i	−0.526281	+	0.303848i
$142$	29.2332	+	16.8778i	0.205868	+	0.118858i
$143$	−195.730	+	113.005i	−1.36874	+	0.790241i
$144$	−2.59714	+	4.49837i	−0.0180357	+	0.0312387i
$145$	130.314	−	91.3050i	0.898715	−	0.629689i
$146$	−172.619	−	99.6617i	−1.18232	−	0.682615i
$147$	−411.243			−2.79757
$148$	−10.2833	−	17.8113i	−0.0694820	−	0.120346i
$149$	5.74660	+	9.95340i	0.0385678	+	0.0668013i	0.884665	−	0.466227i	$-0.154387\pi$
$149$	5.74660	+	9.95340i	0.0385678	+	0.0668013i	−0.846097	+	0.533029i	$0.821054\pi$
$150$	−19.7692	−	111.725i	−0.131795	−	0.744831i
$151$		−	115.503i		−	0.764918i	−0.923972	−	0.382459i	$-0.875077\pi$
$151$		−	115.503i		−	0.764918i	0.923972	−	0.382459i	$-0.124923\pi$
$152$	−54.6602	+	31.5581i	−0.359607	+	0.207619i
$153$	4.48104			0.0292879
$154$			349.260i			2.26792i
$155$	118.930	−	99.4015i	0.767290	−	0.641300i
$156$	78.1768			0.501133
$157$			206.924i			1.31799i	0.752148	+	0.658995i	$0.229018\pi$
$157$			206.924i			1.31799i	−0.752148	+	0.658995i	$0.770982\pi$
$158$	−17.6105	−	30.5023i	−0.111459	−	0.193053i
$159$	64.2445			0.404054
$160$	−23.1642	+	16.2301i	−0.144777	+	0.101438i
$161$	218.963	−	126.418i	1.36002	−	0.785208i
$162$	111.453	−	64.3473i	0.687980	−	0.397206i
$163$		−	163.653i		−	1.00401i	−0.864866	−	0.502003i	$-0.832597\pi$
$163$		−	163.653i		−	1.00401i	0.864866	−	0.502003i	$-0.167403\pi$
$164$	−58.3591	+	101.081i	−0.355848	+	0.616347i
$165$	243.836	−	170.845i	1.47780	−	1.03542i
$166$	58.2086	+	33.6067i	0.350654	+	0.202450i
$167$	−22.0692	−	38.2250i	−0.132151	−	0.228892i	0.792355	−	0.610061i	$-0.208855\pi$
$167$	−22.0692	−	38.2250i	−0.132151	−	0.228892i	−0.924506	+	0.381169i	$0.875522\pi$
$168$	60.4047	−	104.624i	0.359552	−	0.622762i
$169$	10.3197	+	17.8743i	0.0610634	+	0.105765i
$170$	22.1175	+	10.3055i	0.130103	+	0.0606204i
$171$	−28.9775			−0.169459
$172$	−6.54215	−	11.3313i	−0.0380357	−	0.0658798i
$173$	132.928	+	76.7461i	0.768370	+	0.443619i	0.832293	−	0.554336i	$-0.187028\pi$
$173$	132.928	+	76.7461i	0.768370	+	0.443619i	−0.0639226	+	0.997955i	$0.520361\pi$
$174$	−72.2138	−	125.078i	−0.415022	−	0.718839i
$175$	57.9767	+	327.652i	0.331296	+	1.87230i
$176$	−64.2772	−	37.1105i	−0.365212	−	0.210855i
$177$	−71.7031	+	124.193i	−0.405102	+	0.701657i
$178$	86.8091			0.487692
$179$	119.514	−	69.0012i	0.667673	−	0.385481i	−0.127521	−	0.991836i	$-0.540702\pi$
$179$	119.514	−	69.0012i	0.667673	−	0.385481i	0.795194	+	0.606354i	$0.207369\pi$
$180$	−12.9359	+	1.13566i	−0.0718663	+	0.00630922i
$181$	−208.176	−	120.190i	−1.15014	−	0.664035i	−0.201221	−	0.979546i	$-0.564491\pi$
$181$	−208.176	−	120.190i	−1.15014	−	0.664035i	−0.948922	+	0.315511i	$0.897824\pi$
$182$	−229.267			−1.25971
$183$	156.441	−	90.3213i	0.854870	−	0.493559i
$184$			53.7301i			0.292012i
$185$	21.7156	−	46.6059i	0.117382	−	0.251924i
$186$	−80.4384	−	115.428i	−0.432464	−	0.620578i
$187$			64.0296i			0.342404i
$188$			53.4008i			0.284047i
$189$	−284.877	+	164.474i	−1.50729	+	0.870233i
$190$	−143.027	−	66.6422i	−0.752772	−	0.350748i
$191$	−95.9025	+	166.108i	−0.502107	+	0.869675i	0.497890	+	0.867240i	$0.334108\pi$
$191$	−95.9025	+	166.108i	−0.502107	+	0.869675i	−0.999997	+	0.00243489i	$0.999225\pi$
$192$	12.8366	+	22.2336i	0.0668570	+	0.115800i
$193$	117.802	−	68.0133i	0.610375	−	0.352400i	−0.162737	−	0.986669i	$-0.552032\pi$
$193$	117.802	−	68.0133i	0.610375	−	0.352400i	0.773112	+	0.634269i	$0.218699\pi$
$194$	−15.2745			−0.0787345
$195$	112.149	+	160.063i	0.575123	+	0.820836i
$196$	−128.147	+	221.958i	−0.653814	+	1.13244i
$197$	21.0292	−	36.4236i	0.106747	−	0.184891i	−0.807704	−	0.589589i	$-0.799290\pi$
$197$	21.0292	−	36.4236i	0.106747	−	0.184891i	0.914451	+	0.404697i	$0.132623\pi$
$198$	−17.0379	−	29.5105i	−0.0860501	−	0.149043i
$199$	−80.5883	−	46.5277i	−0.404966	−	0.233807i	0.283658	−	0.958925i	$-0.408452\pi$
$199$	−80.5883	−	46.5277i	−0.404966	−	0.233807i	−0.688625	+	0.725118i	$0.741785\pi$
$200$	−66.4608	−	24.1446i	−0.332304	−	0.120723i
$201$			341.314i			1.69808i
$202$		−	114.946i		−	0.569040i
$203$	211.780	+	366.813i	1.04325	+	1.80696i
$204$	11.0740	−	19.1806i	0.0542841	−	0.0940228i
$205$	−290.678	+	25.5189i	−1.41794	+	0.124482i
$206$	62.6315	−	108.481i	0.304036	−	0.526607i
$207$	−12.3341	+	21.3633i	−0.0595851	+	0.103204i
$208$	24.3607	−	42.1939i	0.117119	−	0.202855i
$209$		−	414.059i		−	1.98114i
$210$	300.866	−	26.4134i	1.43270	−	0.125778i
$211$	−118.605	−	205.429i	−0.562107	−	0.973597i	−0.997312	−	0.0732663i	$-0.976658\pi$
$211$	−118.605	−	205.429i	−0.562107	−	0.973597i	0.435206	−	0.900331i	$-0.356676\pi$
$212$	20.0193	−	34.6744i	0.0944304	−	0.163558i
$213$	76.5984			0.359617
$214$	−73.9751	−	128.129i	−0.345678	−	0.598732i
$215$	13.8153	−	29.6501i	0.0642570	−	0.137908i
$216$		−	69.9045i		−	0.323632i
$217$	235.900	+	338.512i	1.08710	+	1.55996i
$218$		−	144.673i		−	0.663637i
$219$	−452.305			−2.06532
$220$	−16.2274	−	184.841i	−0.0737611	−	0.840188i
$221$	−42.0314			−0.190187
$222$	−40.4174	−	23.3350i	−0.182060	−	0.105113i
$223$	−3.66657	−	6.35068i	−0.0164420	−	0.0284784i	0.857687	−	0.514172i	$-0.171901\pi$
$223$	−3.66657	−	6.35068i	−0.0164420	−	0.0284784i	−0.874129	+	0.485693i	$0.838567\pi$
$224$	−37.6454	−	65.2038i	−0.168060	−	0.291089i
$225$	−20.8825	−	24.8565i	−0.0928112	−	0.110473i
$226$	−24.9467	+	43.2089i	−0.110384	+	0.191190i
$227$	−166.194	−	95.9524i	−0.732134	−	0.422698i	0.0870684	−	0.996202i	$-0.472250\pi$
$227$	−166.194	−	95.9524i	−0.732134	−	0.422698i	−0.819202	+	0.573505i	$0.805583\pi$
$228$	−71.6117	+	124.035i	−0.314086	+	0.544014i
$229$	159.122	−	91.8692i	0.694857	−	0.401176i	−0.110572	−	0.993868i	$-0.535268\pi$
$229$	159.122	−	91.8692i	0.694857	−	0.401176i	0.805429	+	0.592692i	$0.201935\pi$
$230$	−110.010	+	77.0789i	−0.478303	+	0.335126i
$231$	396.271	+	686.362i	1.71546	+	2.97126i
$232$	−90.0102			−0.387975
$233$		−	21.3176i		−	0.0914918i	−0.998953	−	0.0457459i	$-0.985434\pi$
$233$		−	21.3176i		−	0.0914918i	0.998953	−	0.0457459i	$-0.0145665\pi$
$234$	19.3718	−	11.1843i	0.0827854	−	0.0477962i
$235$	−109.335	+	76.6064i	−0.465257	+	0.325985i
$236$	44.6868	+	77.3998i	0.189351	+	0.327965i
$237$	−69.2160	−	39.9619i	−0.292051	−	0.168616i
$238$	−32.4763	+	56.2506i	−0.136455	+	0.236347i
$239$	−50.7063	−	29.2753i	−0.212160	−	0.122491i	0.390155	−	0.920749i	$-0.372421\pi$
$239$	−50.7063	−	29.2753i	−0.212160	−	0.122491i	−0.602315	+	0.798259i	$0.705755\pi$
$240$	−27.1073	+	58.1775i	−0.112947	+	0.242406i
$241$	−347.076	+	200.384i	−1.44015	+	0.831470i	−0.997859	−	0.0654033i	$-0.979167\pi$
$241$	−347.076	+	200.384i	−1.44015	+	0.831470i	−0.442289	+	0.896873i	$0.645833\pi$
$242$	273.482	−	157.895i	1.13009	−	0.652458i
$243$	34.7998	−	60.2751i	0.143209	−	0.248045i
$244$		−	112.580i		−	0.461394i
$245$	−638.282	+	56.0355i	−2.60523	+	0.228716i
$246$			264.857i			1.07666i
$247$	271.803			1.10042
$248$	−87.3645	+	7.44618i	−0.352276	+	0.0300249i
$249$	152.521			0.612534
$250$	−45.9069	−	170.712i	−0.183628	−	0.682848i
$251$	−80.7438	+	46.6174i	−0.321688	+	0.185727i	−0.652145	−	0.758094i	$-0.726131\pi$
$251$	−80.7438	+	46.6174i	−0.321688	+	0.185727i	0.330457	+	0.943821i	$0.392797\pi$
$252$		−	34.5670i		−	0.137171i
$253$	−305.260	−	176.242i	−1.20656	−	0.696609i
$254$	−260.940	+	150.654i	−1.02732	+	0.593125i
$255$	55.1576	−	4.84235i	0.216304	−	0.0189896i
$256$	16.0000			0.0625000
$257$	−4.55008	−	2.62699i	−0.0177046	−	0.0102217i	0.491122	−	0.871091i	$-0.336587\pi$
$257$	−4.55008	−	2.62699i	−0.0177046	−	0.0102217i	−0.508826	+	0.860869i	$0.669920\pi$
$258$	−25.7131	−	14.8455i	−0.0996632	−	0.0575406i
$259$	118.531	+	68.4339i	0.457649	+	0.264224i
$260$	121.337	−	10.6523i	0.466679	−	0.0409703i
$261$	−35.7884	−	20.6624i	−0.137120	−	0.0791665i
$262$	−307.724	+	177.664i	−1.17452	+	0.678109i
$263$	−258.001			−0.980993			−0.490496	−	0.871443i	$-0.663185\pi$
$263$	−258.001			−0.980993			−0.490496	+	0.871443i	$0.663185\pi$
$264$	−168.422			−0.637964
$265$	99.7127	−	8.75390i	0.376274	−	0.0330336i
$266$	210.014	−	363.755i	0.789526	−	1.36750i
$267$	170.596	−	98.4938i	0.638937	−	0.368891i
$268$	184.216	+	106.357i	0.687372	+	0.396855i
$269$	263.400	+	152.074i	0.979183	+	0.565331i	0.902023	−	0.431687i	$-0.142082\pi$
$269$	263.400	+	152.074i	0.979183	+	0.565331i	0.0771595	+	0.997019i	$0.475415\pi$
$270$	143.126	−	100.282i	0.530096	−	0.371414i
$271$			71.7604i			0.264799i	0.991196	+	0.132399i	$0.0422681\pi$
$271$			71.7604i			0.264799i	−0.991196	+	0.132399i	$0.957732\pi$
$272$	−6.90151	−	11.9538i	−0.0253732	−	0.0439477i
$273$	−450.553	+	260.127i	−1.65038	+	0.952846i
$274$	235.134	+	135.755i	0.858153	+	0.495455i
$275$	355.174	−	298.390i	1.29154	−	1.08506i
$276$	60.9623	+	105.590i	0.220878	+	0.382572i
$277$	−32.6897			−0.118013			−0.0590067	−	0.998258i	$-0.518793\pi$
$277$	−32.6897			−0.118013			−0.0590067	+	0.998258i	$0.518793\pi$
$278$	194.491			0.699606
$279$	−36.4458	−	17.0945i	−0.130630	−	0.0612705i
$280$	79.4971	−	170.616i	0.283918	−	0.609342i
$281$	51.0120			0.181538			0.0907688	−	0.995872i	$-0.471068\pi$
$281$	51.0120			0.181538			0.0907688	+	0.995872i	$0.471068\pi$
$282$	60.5886	+	104.943i	0.214853	+	0.372137i
$283$			453.922i			1.60397i	0.597347	+	0.801983i	$0.296221\pi$
$283$			453.922i			1.60397i	−0.597347	+	0.801983i	$0.703779\pi$
$284$	23.8688	−	41.3420i	0.0840451	−	0.145570i
$285$	−356.687	+	31.3139i	−1.25153	+	0.109873i
$286$	159.813	+	276.803i	0.558785	+	0.967844i
$287$		−	776.741i		−	2.70641i
$288$	6.36166	+	3.67291i	0.0220891	+	0.0127531i
$289$	138.546	−	239.969i	0.479398	−	0.830342i
$290$	−129.125	−	184.291i	−0.445258	−	0.635488i
$291$	−30.0173	+	17.3305i	−0.103152	+	0.0595549i
$292$	−140.943	+	244.120i	−0.482681	+	0.836029i
$293$	31.8657	−	18.3977i	0.108757	−	0.0627907i	−0.444635	−	0.895712i	$-0.646667\pi$
$293$	31.8657	−	18.3977i	0.108757	−	0.0627907i	0.553392	+	0.832921i	$0.313333\pi$
$294$			581.585i			1.97818i
$295$	−94.3665	+	202.528i	−0.319886	+	0.686537i
$296$	−25.1889	+	14.5428i	−0.0850977	+	0.0491312i
$297$	397.152	+	229.296i	1.33721	+	0.772040i
$298$	14.0762	−	8.12692i	0.0472357	−	0.0272715i
$299$	115.692	−	200.384i	0.386929	−	0.670180i
$300$	−158.002	+	27.9579i	−0.526675	+	0.0931930i
$301$	75.4082	+	43.5369i	0.250525	+	0.144641i
$302$	−163.345			−0.540879
$303$	−130.418	−	225.890i	−0.430422	−	0.745513i
$304$	44.6299	+	77.3012i	0.146809	+	0.254280i
$305$	230.502	−	161.503i	0.755745	−	0.529516i
$306$		−	6.33715i		−	0.0207096i
$307$	−217.561	+	125.609i	−0.708669	+	0.409150i	−0.810568	−	0.585645i	$-0.800841\pi$
$307$	−217.561	+	125.609i	−0.708669	+	0.409150i	0.101899	+	0.994795i	$0.467508\pi$
$308$	493.928			1.60366
$309$		−	284.247i		−	0.919894i
$310$	−140.575	−	168.192i	−0.453467	−	0.542556i
$311$	493.974			1.58834			0.794171	−	0.607695i	$-0.207906\pi$
$311$	493.974			1.58834			0.794171	+	0.607695i	$0.207906\pi$
$312$		−	110.559i		−	0.354355i
$313$	289.008	+	500.577i	0.923349	+	1.59929i	0.794195	+	0.607663i	$0.207893\pi$
$313$	289.008	+	500.577i	0.923349	+	1.59929i	0.129155	+	0.991624i	$0.458774\pi$
$314$	292.635			0.931959
$315$	70.7743	−	49.5884i	0.224680	−	0.157423i
$316$	−43.1368	+	24.9051i	−0.136509	+	0.0788135i
$317$	151.037	−	87.2013i	0.476458	−	0.275083i	−0.242481	−	0.970156i	$-0.577961\pi$
$317$	151.037	−	87.2013i	0.476458	−	0.275083i	0.718939	+	0.695073i	$0.244628\pi$
$318$		−	90.8555i		−	0.285709i
$319$	295.246	−	511.380i	0.925535	−	1.60307i
$320$	22.9529	+	32.7592i	0.0717278	+	0.102372i
$321$	−290.750	−	167.864i	−0.905763	−	0.522942i
$322$	−178.783	−	309.661i	−0.555226	−	0.961679i
$323$	38.5017	−	66.6869i	0.119200	−	0.206461i
$324$	−91.0008	−	157.618i	−0.280867	−	0.486476i
$325$	195.874	+	233.149i	0.602690	+	0.717383i
$326$	−231.440			−0.709939
$327$	−164.146	−	284.309i	−0.501975	−	0.869447i
$328$	142.950	+	82.5322i	0.435823	+	0.251623i
$329$	−177.687	−	307.762i	−0.540081	−	0.935448i
$330$	−241.611	−	344.836i	−0.732156	−	1.04496i
$331$	−151.323	−	87.3664i	−0.457169	−	0.263947i	0.253684	−	0.967287i	$-0.418358\pi$
$331$	−151.323	−	87.3664i	−0.457169	−	0.263947i	−0.710853	+	0.703340i	$0.751691\pi$
$332$	47.5271	−	82.3193i	0.143154	−	0.247950i
$333$	−13.3536			−0.0401009
$334$	−54.0583	+	31.2106i	−0.161851	+	0.0934449i
$335$	46.5072	+	529.748i	0.138827	+	1.58134i
$336$	−147.961	−	85.4252i	−0.440359	−	0.254242i
$337$	−188.590			−0.559614			−0.279807	−	0.960056i	$-0.590270\pi$
$337$	−188.590			−0.559614			−0.279807	+	0.960056i	$0.590270\pi$
$338$	25.2780	−	14.5943i	0.0747870	−	0.0431783i
$339$			113.218i			0.333977i
$340$	14.5741	−	31.2788i	0.0428651	−	0.0919966i
$341$	244.263	−	520.773i	0.716313	−	1.52719i
$342$			40.9803i			0.119826i
$343$		−	1053.43i		−	3.07122i
$344$	−16.0249	+	9.25199i	−0.0465841	+	0.0268953i
$345$	−128.736	+	276.292i	−0.373148	+	0.800845i
$346$	108.535	−	187.989i	0.313686	−	0.543320i
$347$	−121.524	−	210.485i	−0.350213	−	0.606586i	0.636074	−	0.771628i	$-0.280557\pi$
$347$	−121.524	−	210.485i	−0.350213	−	0.606586i	−0.986287	+	0.165042i	$0.947224\pi$
$348$	−176.887	+	102.126i	−0.508296	+	0.293465i
$349$	−36.9029			−0.105739			−0.0528694	−	0.998601i	$-0.516837\pi$
$349$	−36.9029			−0.105739			−0.0528694	+	0.998601i	$0.516837\pi$
$350$	463.370	−	81.9915i	1.32391	−	0.234261i
$351$	−150.518	+	260.705i	−0.428827	+	0.742750i
$352$	−52.4821	+	90.9017i	−0.149097	+	0.258244i
$353$	−197.861	−	342.705i	−0.560512	−	0.970836i	−0.997452	−	0.0713447i	$-0.977271\pi$
$353$	−197.861	−	342.705i	−0.560512	−	0.970836i	0.436940	−	0.899491i	$-0.356062\pi$
$354$	175.636	+	101.403i	0.496147	+	0.286450i
$355$	118.887	−	10.4372i	0.334893	−	0.0294006i
$356$		−	122.767i		−	0.344850i
$357$			147.391i			0.412859i
$358$	−97.5824	−	169.018i	−0.272577	−	0.472116i
$359$	−63.2842	+	109.611i	−0.176279	+	0.305324i	−0.940603	−	0.339508i	$-0.889739\pi$
$359$	−63.2842	+	109.611i	−0.176279	+	0.305324i	0.764324	+	0.644832i	$0.223073\pi$
$360$	1.60607	+	18.2942i	0.00446129	+	0.0508171i
$361$	−68.4781	+	118.608i	−0.189690	+	0.328553i
$362$	−169.975	+	294.405i	−0.469544	+	0.813274i
$363$	358.295	−	620.586i	0.987039	−	1.70960i
$364$			324.233i			0.890749i
$365$	−702.015	+	61.6307i	−1.92333	+	0.168851i
$366$	−127.734	−	221.241i	−0.348999	−	0.604484i
$367$	−179.132	+	310.266i	−0.488099	+	0.845413i	−0.999906	−	0.0136877i	$-0.995643\pi$
$367$	−179.132	+	310.266i	−0.488099	+	0.845413i	0.511807	+	0.859100i	$0.328976\pi$
$368$	75.9859			0.206483
$369$	37.8916	+	65.6303i	0.102687	+	0.177860i
$370$	−65.9106	−	30.7106i	−0.178137	−	0.0830015i
$371$			266.450i			0.718193i
$372$	−163.239	+	113.757i	−0.438815	+	0.305798i
$373$		−	461.428i		−	1.23707i	−0.785756	−	0.618537i	$-0.787726\pi$
$373$		−	461.428i		−	1.23707i	0.785756	−	0.618537i	$-0.212274\pi$
$374$	90.5515			0.242116
$375$	−283.906	−	283.395i	−0.757082	−	0.755720i
$376$	75.5201			0.200851
$377$	335.689	+	193.810i	0.890421	+	0.514085i
$378$	232.601	+	402.877i	0.615348	+	1.06581i
$379$	186.788	+	323.527i	0.492845	+	0.853632i	0.999966	−	0.00824254i	$-0.00262371\pi$
$379$	186.788	+	323.527i	0.492845	+	0.853632i	−0.507121	+	0.861875i	$0.669290\pi$
$380$	−94.2463	+	202.270i	−0.248017	+	0.532290i
$381$	−341.864	+	592.126i	−0.897281	+	1.55414i
$382$	234.912	+	135.627i	0.614953	+	0.355043i
$383$	−51.7129	+	89.5694i	−0.135021	+	0.233863i	−0.925605	−	0.378490i	$-0.876443\pi$
$383$	−51.7129	+	89.5694i	−0.135021	+	0.233863i	0.790585	+	0.612353i	$0.209777\pi$
$384$	31.4430	−	18.1536i	0.0818828	−	0.0472751i
$385$	708.568	+	1011.29i	1.84044	+	2.62674i
$386$	−96.1853	−	166.598i	−0.249185	−	0.431601i
$387$	−8.49543			−0.0219520
$388$			21.6014i			0.0556737i
$389$	321.229	−	185.462i	0.825781	−	0.476765i	−0.0266248	−	0.999645i	$-0.508476\pi$
$389$	321.229	−	185.462i	0.825781	−	0.476765i	0.852406	+	0.522881i	$0.175143\pi$
$390$	226.363	−	158.603i	0.580419	−	0.406673i
$391$	−32.7761	−	56.7698i	−0.0838263	−	0.145191i
$392$	313.896	+	181.228i	0.800755	+	0.462316i
$393$	−403.157	+	698.288i	−1.02584	+	1.77681i
$394$	−51.5108	−	29.7398i	−0.130738	−	0.0754816i
$395$	−112.874	−	52.5928i	−0.285757	−	0.133146i
$396$	−41.7342	+	24.0952i	−0.105389	+	0.0608466i
$397$	543.458	−	313.766i	1.36891	−	0.790341i	0.378122	−	0.925756i	$-0.376570\pi$
$397$	543.458	−	313.766i	1.36891	−	0.790341i	0.990789	+	0.135414i	$0.0432365\pi$
$398$	−65.8001	+	113.969i	−0.165327	+	0.286355i
$399$		−	953.129i		−	2.38879i
$400$	−34.1456	+	93.9898i	−0.0853640	+	0.234974i
$401$		−	300.235i		−	0.748716i	−0.927284	−	0.374358i	$-0.877863\pi$
$401$		−	300.235i		−	0.748716i	0.927284	−	0.374358i	$-0.122137\pi$
$402$	482.692			1.20073
$403$	341.855	+	160.343i	0.848275	+	0.397874i
$404$	−162.558			−0.402372
$405$	192.169	−	412.432i	0.474492	−	1.01835i
$406$	518.752	−	299.502i	1.27771	−	0.737689i
$407$		−	190.810i		−	0.468820i
$408$	−27.1255	−	15.6609i	−0.0664841	−	0.0383846i
$409$	241.722	−	139.558i	0.591008	−	0.341218i	−0.174488	−	0.984659i	$-0.555827\pi$
$409$	241.722	−	139.558i	0.591008	−	0.341218i	0.765496	+	0.643441i	$0.222494\pi$
$410$	36.0892	+	411.080i	0.0880224	+	1.00263i
$411$	616.110			1.49905
$412$	−153.415	−	88.5743i	−0.372367	−	0.214986i
$413$	−515.083	−	297.383i	−1.24717	−	0.720057i
$414$	30.2123	+	17.4431i	0.0729765	+	0.0421330i
$415$	236.725	−	20.7824i	0.570422	−	0.0500780i
$416$	−59.6712	−	34.4512i	−0.143440	−	0.0828154i
$417$	382.211	−	220.669i	0.916572	−	0.529183i
$418$	−585.568			−1.40088
$419$	726.826			1.73467			0.867334	−	0.497726i	$-0.165832\pi$
$419$	726.826			1.73467			0.867334	+	0.497726i	$0.165832\pi$
$420$	−37.3542	−	425.489i	−0.0889386	−	1.01307i
$421$	249.060	−	431.384i	0.591591	−	1.02467i	−0.402428	−	0.915452i	$-0.631833\pi$
$421$	249.060	−	431.384i	0.591591	−	1.02467i	0.994018	−	0.109213i	$-0.0348332\pi$
$422$	−290.521	+	167.732i	−0.688437	+	0.397469i
$423$	30.0271	+	17.3361i	0.0709860	+	0.0409838i
$424$	−49.0370	−	28.3115i	−0.115653	−	0.0667724i
$425$	84.9493	−	15.0314i	0.199881	−	0.0353681i
$426$		−	108.326i		−	0.254287i
$427$	374.601	+	648.829i	0.877287	+	1.51950i
$428$	−181.201	+	104.617i	−0.423367	+	0.244431i
$429$	628.123	+	362.647i	1.46416	+	0.845331i
$430$	−41.9316	−	19.5377i	−0.0975154	−	0.0454366i
$431$	−145.312	−	251.687i	−0.337150	−	0.583961i	0.646745	−	0.762706i	$-0.276130\pi$
$431$	−145.312	−	251.687i	−0.337150	−	0.583961i	−0.983895	+	0.178745i	$0.942796\pi$
$432$	−98.8598			−0.228842
$433$	316.900			0.731870			0.365935	−	0.930640i	$-0.380749\pi$
$433$	316.900			0.731870			0.365935	+	0.930640i	$0.380749\pi$
$434$	478.728	−	333.613i	1.10306	−	0.768692i
$435$	−462.852	−	215.662i	−1.06403	−	0.495775i
$436$	−204.598			−0.469262
$437$	211.952	+	367.112i	0.485017	+	0.840074i
$438$			639.656i			1.46040i
$439$	68.9844	−	119.485i	0.157140	−	0.272174i	−0.776696	−	0.629875i	$-0.783106\pi$
$439$	68.9844	−	119.485i	0.157140	−	0.272174i	0.933836	+	0.357701i	$0.116439\pi$
$440$	−261.405	+	22.9491i	−0.594103	+	0.0521570i
$441$	83.2041	+	144.114i	0.188671	+	0.326789i
$442$			59.4413i			0.134483i
$443$	11.5976	+	6.69587i	0.0261797	+	0.0151148i	0.513033	−	0.858369i	$-0.328522\pi$
$443$	11.5976	+	6.69587i	0.0261797	+	0.0151148i	−0.486853	+	0.873484i	$0.661855\pi$
$444$	−33.0006	+	57.1588i	−0.0743258	+	0.128736i
$445$	251.359	−	176.116i	0.564851	−	0.395765i
$446$	−8.98122	+	5.18531i	−0.0201373	+	0.0116263i
$447$	18.4416	−	31.9418i	0.0412564	−	0.0714583i
$448$	−92.2121	+	53.2387i	−0.205831	+	0.118836i
$449$			207.108i			0.461264i	0.973041	+	0.230632i	$0.0740794\pi$
$449$			207.108i			0.461264i	−0.973041	+	0.230632i	$0.925921\pi$
$450$	−35.1524	+	29.5323i	−0.0781164	+	0.0656274i
$451$	−937.790	+	541.434i	−2.07936	+	1.20052i
$452$	61.1066	+	35.2799i	0.135192	+	0.0780530i
$453$	−321.004	+	185.332i	−0.708619	+	0.409121i
$454$	−135.697	+	235.034i	−0.298892	+	0.517697i
$455$	−663.850	+	465.130i	−1.45901	+	1.02226i
$456$	175.412	+	101.274i	0.384676	+	0.222093i
$457$	249.642			0.546262			0.273131	−	0.961977i	$-0.411941\pi$
$457$	249.642			0.546262			0.273131	+	0.961977i	$0.411941\pi$
$458$	−129.923	−	225.033i	−0.283674	−	0.491338i
$459$	42.6426	+	73.8592i	0.0929034	+	0.160913i
$460$	109.006	+	155.577i	0.236970	+	0.338211i
$461$			225.102i			0.488291i	0.969739	+	0.244146i	$0.0785075\pi$
$461$			225.102i			0.488291i	−0.969739	+	0.244146i	$0.921492\pi$
$462$	970.662	−	560.412i	2.10100	−	1.21301i
$463$	−266.758			−0.576150			−0.288075	−	0.957608i	$-0.593015\pi$
$463$	−266.758			−0.576150			−0.288075	+	0.957608i	$0.593015\pi$
$464$			127.294i			0.274340i
$465$	−467.088	−	171.033i	−1.00449	−	0.367813i
$466$	−30.1476			−0.0646945
$467$			666.753i			1.42774i	0.700280	+	0.713868i	$0.253058\pi$
$467$			666.753i			1.42774i	−0.700280	+	0.713868i	$0.746942\pi$
$468$	−15.8170	−	27.3958i	−0.0337970	−	0.0585381i
$469$	−1415.58			−3.01829
$470$	108.338	+	154.624i	0.230506	+	0.328986i
$471$	575.083	−	332.024i	1.22098	−	0.704935i
$472$	109.460	−	63.1967i	0.231906	−	0.133891i
$473$		−	121.391i		−	0.256641i
$474$	−56.5146	+	97.8862i	−0.119229	+	0.206511i
$475$	−549.340	+	97.2035i	−1.15650	+	0.204639i
$476$	79.5504	+	45.9284i	0.167123	+	0.0964883i
$477$	−12.9982	−	22.5135i	−0.0272499	−	0.0471981i
$478$	−41.4015	+	71.7095i	−0.0866140	+	0.150020i
$479$	395.020	+	684.194i	0.824675	+	1.42838i	0.902167	+	0.431387i	$0.141976\pi$
$479$	395.020	+	684.194i	0.824675	+	1.42838i	−0.0774916	+	0.996993i	$0.524691\pi$
$480$	82.2754	+	38.3356i	0.171407	+	0.0798658i
$481$	125.254			0.260404
$482$	283.386	+	490.839i	0.587938	+	1.01834i
$483$	−702.683	−	405.694i	−1.45483	−	0.839947i
$484$	−223.297	−	386.762i	−0.461357	−	0.799094i
$485$	−44.2278	+	30.9884i	−0.0911913	+	0.0638936i
$486$	−85.2418	−	49.2144i	−0.175395	−	0.101264i
$487$	348.871	−	604.262i	0.716367	−	1.24078i	−0.246063	−	0.969254i	$-0.579137\pi$
$487$	348.871	−	604.262i	0.716367	−	1.24078i	0.962430	−	0.271530i	$-0.0875297\pi$
$488$	−159.212			−0.326255
$489$	−454.823	+	262.592i	−0.930109	+	0.536999i
$490$	79.2462	+	902.667i	0.161727	+	1.84218i
$491$	−560.115	−	323.382i	−1.14076	−	0.658620i	−0.194143	−	0.980973i	$-0.562193\pi$
$491$	−560.115	−	323.382i	−1.14076	−	0.658620i	−0.946619	+	0.322353i	$0.895526\pi$
$492$	374.565			0.761311
$493$	95.1025	−	54.9074i	0.192906	−	0.111374i
$494$		−	384.388i		−	0.778113i
$495$	−109.204	−	50.8827i	−0.220614	−	0.102793i
$496$	10.5305	+	123.552i	0.0212308	+	0.249097i
$497$			317.686i			0.639208i
$498$		−	215.697i		−	0.433127i
$499$	−352.089	+	203.279i	−0.705590	+	0.407373i	−0.809426	−	0.587222i	$-0.800222\pi$
$499$	−352.089	+	203.279i	−0.705590	+	0.407373i	0.103836	+	0.994594i	$0.466888\pi$
$500$	−241.423	+	64.9222i	−0.482846	+	0.129844i
$501$	−70.8232	+	122.669i	−0.141364	+	0.244849i
$502$	65.9270	+	114.189i	0.131329	+	0.227468i
$503$	−447.678	+	258.467i	−0.890017	+	0.513851i	−0.873948	−	0.486019i	$-0.838448\pi$
$503$	−447.678	+	258.467i	−0.890017	+	0.513851i	−0.0160689	+	0.999871i	$0.505115\pi$
$504$	−48.8852			−0.0969944
$505$	−233.199	−	332.830i	−0.461780	−	0.659069i
$506$	−249.244	+	431.703i	−0.492577	+	0.853168i
$507$	33.1174	−	57.3610i	0.0653203	−	0.113138i
$508$	213.057	+	369.025i	0.419403	+	0.726427i
$509$	−169.334	−	97.7649i	−0.332679	−	0.192072i	0.324351	−	0.945937i	$-0.394854\pi$
$509$	−169.334	−	97.7649i	−0.332679	−	0.192072i	−0.657030	+	0.753864i	$0.728188\pi$
$510$	−6.84812	−	78.0046i	−0.0134277	−	0.152950i
$511$		−	1875.90i		−	3.67105i
$512$		−	22.6274i		−	0.0441942i
$513$	−275.756	−	477.624i	−0.537537	−	0.931041i
$514$	−3.71512	+	6.43478i	−0.00722787	+	0.0125190i
$515$	−38.7312	−	441.175i	−0.0752063	−	0.856650i
$516$	−20.9947	+	36.3638i	−0.0406873	+	0.0704725i
$517$	−247.716	+	429.057i	−0.479141	+	0.829897i
$518$	96.7802	−	167.628i	0.186834	−	0.323607i
$519$		−	492.577i		−	0.949089i
$520$	−15.0646	−	171.596i	−0.0289704	−	0.329992i
$521$	−266.430	−	461.470i	−0.511381	−	0.885738i	−0.999913	−	0.0131920i	$-0.995801\pi$
$521$	−266.430	−	461.470i	−0.511381	−	0.885738i	0.488532	−	0.872546i	$-0.337533\pi$
$522$	−29.2211	+	50.6125i	−0.0559791	+	0.0969587i
$523$	−11.4682			−0.0219277			−0.0109639	−	0.999940i	$-0.503490\pi$
$523$	−11.4682			−0.0219277			−0.0109639	+	0.999940i	$0.503490\pi$
$524$	251.255	+	435.187i	0.479495	+	0.830510i
$525$	817.581	−	686.869i	1.55730	−	1.30832i
$526$			364.869i			0.693667i
$527$	87.7648	−	61.1609i	0.166537	−	0.116055i
$528$			238.185i			0.451109i
$529$	−168.134			−0.317834
$530$	−12.3799	−	141.015i	−0.0233583	−	0.266066i
$531$	58.0289			0.109282
$532$	−514.427	−	297.005i	−0.966968	−	0.558279i
$533$	−355.417	−	615.600i	−0.666823	−	1.15497i
$534$	−139.291	−	241.260i	−0.260845	−	0.451797i
$535$	−474.140	−	220.922i	−0.886243	−	0.412938i
$536$	150.412	−	260.520i	0.280619	−	0.486046i
$537$	−383.535	−	221.434i	−0.714219	−	0.412354i
$538$	215.065	−	372.504i	0.399750	−	0.692387i
$539$	−2059.24	+	1188.90i	−3.82048	+	2.20576i
$540$	−141.820	−	202.411i	−0.262630	−	0.374834i
$541$	368.624	+	638.475i	0.681375	+	1.18018i	0.974561	+	0.224121i	$0.0719511\pi$
$541$	368.624	+	638.475i	0.681375	+	1.18018i	−0.293186	+	0.956055i	$0.594716\pi$
$542$	101.485			0.187241
$543$			771.415i			1.42065i
$544$	−16.9052	+	9.76021i	−0.0310757	+	0.0179416i
$545$	−293.508	−	418.904i	−0.538546	−	0.768632i
$546$	367.875	+	637.178i	0.673764	+	1.16699i
$547$	−501.167	−	289.349i	−0.916211	−	0.528975i	−0.0337865	−	0.999429i	$-0.510757\pi$
$547$	−501.167	−	289.349i	−0.916211	−	0.528975i	−0.882424	+	0.470455i	$0.844090\pi$
$548$	191.986	−	332.530i	0.350340	−	0.606806i
$549$	−63.3034	−	36.5483i	−0.115307	−	0.0665724i
$550$	−421.987	−	502.292i	−0.767250	−	0.913259i
$551$	−614.997	+	355.069i	−1.11615	+	0.644408i
$552$	149.327	−	86.2137i	0.270519	−	0.156184i
$553$	165.739	−	287.069i	0.299709	−	0.519111i
$554$			46.2302i			0.0834480i
$555$	−164.371	+	14.4303i	−0.296164	+	0.0260006i
$556$		−	275.051i		−	0.494696i
$557$	843.552			1.51446			0.757228	−	0.653150i	$-0.226553\pi$
$557$	843.552			1.51446			0.757228	+	0.653150i	$0.226553\pi$
$558$	−24.1752	+	51.5421i	−0.0433248	+	0.0923694i
$559$	79.6855			0.142550
$560$	−241.287	−	112.426i	−0.430870	−	0.200760i
$561$	177.951	−	102.740i	0.317203	−	0.183137i
$562$		−	72.1419i		−	0.128366i
$563$	814.216	+	470.088i	1.44621	+	0.834969i	0.998253	−	0.0590861i	$-0.0188187\pi$
$563$	814.216	+	470.088i	1.44621	+	0.834969i	0.447956	+	0.894055i	$0.352152\pi$
$564$	148.411	−	85.6852i	0.263140	−	0.151924i
$565$	15.4270	+	175.724i	0.0273044	+	0.311016i
$566$	641.943			1.13417
$567$	1048.92	+	605.596i	1.84995	+	1.06807i
$568$	−58.4664	−	33.7556i	−0.102934	−	0.0594289i
$569$	551.132	+	318.196i	0.968597	+	0.559220i	0.898808	−	0.438342i	$-0.144434\pi$
$569$	551.132	+	318.196i	0.968597	+	0.559220i	0.0697886	+	0.997562i	$0.477768\pi$
$570$	44.2846	+	504.431i	0.0776922	+	0.884967i
$571$	848.500	+	489.882i	1.48599	+	0.857937i	0.999873	−	0.0159566i	$-0.00507935\pi$
$571$	848.500	+	489.882i	1.48599	+	0.857937i	0.486118	+	0.873893i	$0.338413\pi$
$572$	391.459	−	226.009i	0.684369	−	0.395121i
$573$	615.529			1.07422
$574$	−1098.48			−1.91372
$575$	−162.161	+	446.369i	−0.282020	+	0.776293i
$576$	5.19427	−	8.99675i	0.00901784	−	0.0156194i
$577$	−117.735	+	67.9742i	−0.204046	+	0.117806i	−0.598541	−	0.801092i	$-0.704253\pi$
$577$	−117.735	+	67.9742i	−0.204046	+	0.117806i	0.394495	+	0.918898i	$0.370920\pi$
$578$	−339.367	−	195.934i	−0.587141	−	0.338986i
$579$	−378.044	−	218.264i	−0.652926	−	0.376967i
$580$	−260.627	+	182.610i	−0.449358	+	0.314845i
$581$			632.570i			1.08876i
$582$	24.5090	+	42.4508i	0.0421117	+	0.0729395i
$583$	321.696	−	185.731i	0.551793	−	0.318578i
$584$	345.238	+	199.323i	0.591161	+	0.341307i
$585$	33.4012	−	71.6854i	0.0570961	−	0.122539i
$586$	−26.0182	−	45.0649i	−0.0443997	−	0.0769025i
$587$	−892.966			−1.52124			−0.760619	−	0.649199i	$-0.775104\pi$
$587$	−892.966			−1.52124			−0.760619	+	0.649199i	$0.775104\pi$
$588$	822.486			1.39879
$589$	−567.547	+	395.508i	−0.963577	+	0.671491i
$590$	286.418	+	133.454i	0.485455	+	0.226194i
$591$	−134.971			−0.228378
$592$	20.5667	+	35.6225i	0.0347410	+	0.0601732i
$593$			242.804i			0.409451i	0.978819	+	0.204726i	$0.0656302\pi$
$593$			242.804i			0.409451i	−0.978819	+	0.204726i	$0.934370\pi$
$594$	324.273	−	561.658i	0.545915	−	0.945552i
$595$	20.0833	+	228.762i	0.0337535	+	0.384474i
$596$	−11.4932	−	19.9068i	−0.0192839	−	0.0334007i
$597$			298.628i			0.500214i
$598$	−283.386	−	163.613i	−0.473889	−	0.273600i
$599$	−60.4487	+	104.700i	−0.100916	+	0.174792i	−0.912062	−	0.410052i	$-0.865511\pi$
$599$	−60.4487	+	104.700i	−0.100916	+	0.174792i	0.811146	+	0.584843i	$0.198844\pi$
$600$	39.5385	+	223.449i	0.0658974	+	0.372415i
$601$	−354.693	+	204.782i	−0.590171	+	0.340735i	−0.765165	−	0.643834i	$-0.777343\pi$
$601$	−354.693	+	204.782i	−0.590171	+	0.340735i	0.174994	+	0.984569i	$0.444009\pi$
$602$	61.5705	−	106.643i	0.102277	−	0.177148i
$603$	119.608	−	69.0560i	0.198356	−	0.114521i
$604$			231.005i			0.382459i
$605$	471.543	−	1012.02i	0.779410	−	1.67276i
$606$	−319.457	+	184.439i	−0.527157	+	0.304354i
$607$	1040.64	+	600.815i	1.71440	+	0.989811i	0.928396	+	0.371592i	$0.121188\pi$
$607$	1040.64	+	600.815i	1.71440	+	0.989811i	0.786006	+	0.618219i	$0.212146\pi$
$608$	109.320	−	63.1162i	0.179803	−	0.103809i
$609$	679.630	−	1177.15i	1.11598	−	1.93293i
$610$	−228.399	−	325.979i	−0.374425	−	0.534392i
$611$	−281.648	−	162.610i	−0.460963	−	0.266137i
$612$	−8.96208			−0.0146439
$613$	−225.077	−	389.845i	−0.367173	−	0.635963i	0.621949	−	0.783058i	$-0.286341\pi$
$613$	−225.077	−	389.845i	−0.367173	−	0.635963i	−0.989122	+	0.147095i	$0.953008\pi$
$614$	177.638	+	307.678i	0.289313	+	0.501104i
$615$	537.334	+	766.903i	0.873714	+	1.24700i
$616$		−	698.520i		−	1.13396i
$617$	−162.284	+	93.6949i	−0.263022	+	0.151856i	−0.625712	−	0.780054i	$-0.715192\pi$
$617$	−162.284	+	93.6949i	−0.263022	+	0.151856i	0.362691	+	0.931910i	$0.381858\pi$
$618$	−401.986			−0.650463
$619$			344.602i			0.556707i	0.960479	+	0.278354i	$0.0897888\pi$
$619$			344.602i			0.556707i	−0.960479	+	0.278354i	$0.910211\pi$
$620$	−237.860	+	198.803i	−0.383645	+	0.320650i
$621$	−469.497			−0.756034
$622$		−	698.585i		−	1.12313i
$623$	408.496	+	707.536i	0.655692	+	1.13569i
$624$	−156.354			−0.250567
$625$	−479.260	−	401.167i	−0.766816	−	0.641867i
$626$	707.923	−	408.719i	1.13087	−	0.652907i
$627$	−1150.75	+	664.386i	−1.83533	+	1.05963i
$628$		−	413.849i		−	0.658995i
$629$	17.7426	−	30.7312i	0.0282077	−	0.0488572i
$630$	−70.1285	−	100.090i	−0.111315	−	0.158873i
$631$	354.198	+	204.496i	0.561327	+	0.324083i	0.753678	−	0.657244i	$-0.228278\pi$
$631$	354.198	+	204.496i	0.561327	+	0.324083i	−0.192351	+	0.981326i	$0.561611\pi$
$632$	35.2211	+	61.0047i	0.0557295	+	0.0965264i
$633$	−380.618	+	659.250i	−0.601293	+	1.04147i
$634$	−123.321	−	213.599i	−0.194513	−	0.336906i
$635$	−449.918	+	965.609i	−0.708533	+	1.52064i
$636$	−128.489			−0.202027
$637$	−780.440	−	1351.76i	−1.22518	−	2.12207i
$638$	−723.201	−	417.540i	−1.13354	−	0.654452i
$639$	−15.4976	−	26.8427i	−0.0242530	−	0.0420074i
$640$	46.3285	−	32.4603i	0.0723883	−	0.0507192i
$641$	312.280	+	180.295i	0.487177	+	0.281272i	0.723402	−	0.690427i	$-0.242577\pi$
$641$	312.280	+	180.295i	0.487177	+	0.281272i	−0.236226	+	0.971698i	$0.575911\pi$
$642$	−237.396	+	411.182i	−0.369776	+	0.640471i
$643$	638.692			0.993301			0.496650	−	0.867951i	$-0.334563\pi$
$643$	638.692			0.993301			0.496650	+	0.867951i	$0.334563\pi$
$644$	−437.926	+	252.837i	−0.680010	+	0.392604i
$645$	−104.571	+	9.18041i	−0.162126	+	0.0142332i
$646$	−94.3095	−	54.4496i	−0.145990	−	0.0842873i
$647$	490.354			0.757889			0.378945	−	0.925419i	$-0.376287\pi$
$647$	490.354			0.757889			0.378945	+	0.925419i	$0.376287\pi$
$648$	−222.906	+	128.695i	−0.343990	+	0.198603i
$649$			829.174i			1.27762i
$650$	329.723	−	277.008i	0.507266	−	0.426166i
$651$	562.272	−	1198.78i	0.863706	−	1.84144i
$652$			327.306i			0.502003i
$653$			649.320i			0.994364i	0.867646	+	0.497182i	$0.165632\pi$
$653$			649.320i			0.994364i	−0.867646	+	0.497182i	$0.834368\pi$
$654$	−402.074	+	232.137i	−0.614792	+	0.354950i
$655$	−530.584	+	1138.73i	−0.810052	+	1.73852i
$656$	116.718	−	202.162i	0.177924	−	0.308174i
$657$	91.5120	+	158.503i	0.139288	+	0.241253i
$658$	−435.242	+	251.287i	−0.661462	+	0.381895i
$659$	772.386			1.17206			0.586028	−	0.810290i	$-0.300691\pi$
$659$	772.386			1.17206			0.586028	+	0.810290i	$0.300691\pi$
$660$	−487.672	+	341.690i	−0.738898	+	0.517712i
$661$	−163.986	+	284.031i	−0.248087	+	0.429700i	−0.962995	−	0.269519i	$-0.913135\pi$
$661$	−163.986	+	284.031i	−0.248087	+	0.429700i	0.714908	+	0.699219i	$0.246469\pi$
$662$	−123.555	+	214.003i	−0.186639	+	0.323268i
$663$	67.4422	+	116.813i	0.101723	+	0.176189i
$664$	−116.417	−	67.2135i	−0.175327	−	0.101225i
$665$	−129.872	−	1479.33i	−0.195297	−	2.22456i
$666$			18.8849i			0.0283557i
$667$			604.533i			0.906346i
$668$	44.1384	+	76.4500i	0.0660755	+	0.114446i
$669$	−11.7665	+	20.3802i	−0.0175882	+	0.0304637i
$670$	749.176	−	65.7710i	1.11817	−	0.0981657i
$671$	522.238	−	904.543i	0.778298	−	1.34805i
$672$	−120.809	+	209.248i	−0.179776	+	0.311381i
$673$	−380.612	+	659.239i	−0.565545	+	0.979553i	0.431454	+	0.902135i	$0.358001\pi$
$673$	−380.612	+	659.239i	−0.565545	+	0.979553i	−0.996999	+	0.0774177i	$0.975332\pi$
$674$			266.706i			0.395707i
$675$	210.977	−	580.738i	0.312558	−	0.860353i
$676$	−20.6394	−	35.7485i	−0.0305317	−	0.0528824i
$677$	598.812	−	1037.17i	0.884507	−	1.53201i	0.0382303	−	0.999269i	$-0.487828\pi$
$677$	598.812	−	1037.17i	0.884507	−	1.53201i	0.846277	−	0.532743i	$-0.178839\pi$
$678$	160.115			0.236157
$679$	−71.8769	−	124.494i	−0.105857	−	0.183350i
$680$	−44.2350	−	20.6109i	−0.0650514	−	0.0303102i
$681$			615.849i			0.904330i
$682$	−736.485	−	345.440i	−1.07989	−	0.506510i
$683$		−	283.559i		−	0.415167i	−0.978217	−	0.207583i	$-0.933440\pi$
$683$		−	283.559i		−	0.415167i	0.978217	−	0.207583i	$-0.0665599\pi$
$684$	57.9549			0.0847294
$685$	956.252	−	83.9505i	1.39599	−	0.122555i
$686$	−1489.77			−2.17168
$687$	−510.645	−	294.821i	−0.743297	−	0.429143i
$688$	13.0843	+	22.6627i	0.0190179	+	0.0329399i
$689$	121.921	+	211.173i	0.176953	+	0.306492i
$690$	390.735	+	182.060i	0.566283	+	0.263855i
$691$	407.370	−	705.586i	0.589537	−	1.02111i	−0.404755	−	0.914425i	$-0.632643\pi$
$691$	407.370	−	705.586i	0.589537	−	1.02111i	0.994293	−	0.106684i	$-0.0340233\pi$
$692$	−265.856	−	153.492i	−0.384185	−	0.221809i
$693$	160.350	−	277.734i	0.231385	−	0.400771i
$694$	−297.671	+	171.861i	−0.428921	+	0.247638i
$695$	563.153	−	394.576i	0.810293	−	0.567736i
$696$	144.428	+	250.156i	0.207511	+	0.359420i
$697$	−201.383			−0.288928
$698$			52.1885i			0.0747687i
$699$	−59.2457	+	34.2055i	−0.0847579	+	0.0489350i
$700$	−115.953	−	655.304i	−0.165648	−	0.936149i
$701$	421.037	+	729.257i	0.600623	+	1.04031i	0.992727	+	0.120389i	$0.0384142\pi$
$701$	421.037	+	729.257i	0.600623	+	1.04031i	−0.392103	+	0.919921i	$0.628252\pi$
$702$	368.693	+	212.865i	0.525204	+	0.303226i
$703$	−114.736	+	198.729i	−0.163209	+	0.282686i
$704$	128.554	+	74.2210i	0.182606	+	0.105427i
$705$	388.340	+	180.944i	0.550837	+	0.256658i
$706$	−484.658	+	279.817i	−0.686484	+	0.396342i
$707$	936.865	−	540.899i	1.32513	−	0.765062i
$708$	143.406	−	248.387i	0.202551	−	0.350829i
$709$		−	776.028i		−	1.09454i	−0.836957	−	0.547269i	$-0.815667\pi$
$709$		−	776.028i		−	1.09454i	0.836957	−	0.547269i	$-0.184333\pi$
$710$	−14.7604	−	168.131i	−0.0207894	−	0.236805i
$711$			32.3409i			0.0454865i
$712$	−173.618			−0.243846
$713$	50.0105	+	586.763i	0.0701410	+	0.822950i
$714$	208.442			0.291935
$715$	1024.31	+	477.270i	1.43260	+	0.667511i
$716$	−239.027	+	138.002i	−0.333837	+	0.192741i
$717$			187.897i			0.262060i
$718$	155.014	+	89.4973i	0.215897	+	0.124648i
$719$	−504.385	+	291.207i	−0.701509	+	0.405017i	−0.807909	−	0.589307i	$-0.799401\pi$
$719$	−504.385	+	291.207i	−0.701509	+	0.405017i	0.106400	+	0.994323i	$0.466068\pi$
$720$	25.8719	−	2.27132i	0.0359331	−	0.00315461i
$721$	1178.90			1.63508
$722$	167.736	+	96.8427i	0.232322	+	0.134131i
$723$	1113.81	+	643.060i	1.54054	+	0.889434i
$724$	416.352	+	240.381i	0.575071	+	0.332018i
$725$	−747.769	−	271.657i	−1.03141	−	0.374700i
$726$	−877.641	−	506.706i	−1.20887	−	0.697942i
$727$	−639.144	+	369.010i	−0.879152	+	0.507579i	−0.870379	−	0.492383i	$-0.836126\pi$
$727$	−639.144	+	369.010i	−0.879152	+	0.507579i	−0.00877344	+	0.999962i	$0.502793\pi$
$728$	458.534			0.629855
$729$	595.653			0.817082
$730$	87.1589	+	992.799i	0.119396	+	1.36000i
$731$	11.2877	−	19.5508i	0.0154414	−	0.0267453i
$732$	−312.882	+	180.643i	−0.427435	+	0.246780i
$733$	−1100.47	−	635.354i	−1.50132	−	0.866786i	−0.999999	−	0.00152335i	$-0.999515\pi$
$733$	−1100.47	−	635.354i	−1.50132	−	0.866786i	−0.501319	−	0.865263i	$-0.667152\pi$
$734$	438.783	+	253.332i	0.597797	+	0.345138i
$735$	1179.90	+	1684.00i	1.60531	+	2.29115i
$736$		−	107.460i		−	0.146006i
$737$	986.740	+	1709.08i	1.33886	+	2.31897i
$738$	92.8152	−	53.5869i	0.125766	−	0.0726109i
$739$	−653.593	−	377.352i	−0.884429	−	0.510625i	−0.0123126	−	0.999924i	$-0.503919\pi$
$739$	−653.593	−	377.352i	−0.884429	−	0.510625i	−0.872116	+	0.489299i	$0.837253\pi$
$740$	−43.4313	+	93.2117i	−0.0586909	+	0.125962i
$741$	−436.127	−	755.395i	−0.588566	−	1.01943i
$742$	376.817			0.507839
$743$	−645.991			−0.869436			−0.434718	−	0.900567i	$-0.643152\pi$
$743$	−645.991			−0.869436			−0.434718	+	0.900567i	$0.643152\pi$
$744$	160.877	+	230.855i	0.216232	+	0.310289i
$745$	24.2705	−	52.0892i	0.0325779	−	0.0699183i
$746$	−652.558			−0.874743
$747$	−30.8586	−	53.4486i	−0.0413100	−	0.0715511i
$748$		−	128.059i		−	0.171202i
$749$	696.206	−	1205.86i	0.929514	−	1.60997i
$750$	−400.781	+	401.503i	−0.534375	+	0.535338i
$751$	−230.998	−	400.099i	−0.307587	−	0.532756i	0.670247	−	0.742138i	$-0.266188\pi$
$751$	−230.998	−	400.099i	−0.307587	−	0.532756i	−0.977834	+	0.209382i	$0.932855\pi$
$752$		−	106.802i		−	0.142023i
$753$	259.118	+	149.602i	0.344114	+	0.198674i
$754$	274.089	−	474.736i	0.363513	−	0.629623i
$755$	−472.972	+	331.390i	−0.626452	+	0.438927i
$756$	569.755	−	328.948i	0.753644	−	0.435117i
$757$	231.415	−	400.823i	0.305701	−	0.529489i	−0.671716	−	0.740808i	$-0.734443\pi$
$757$	231.415	−	400.823i	0.305701	−	0.529489i	0.977417	+	0.211319i	$0.0677760\pi$
$758$	457.536	−	264.158i	0.603609	−	0.348494i
$759$			1131.17i			1.49034i
$760$	286.053	+	133.284i	0.376386	+	0.175374i
$761$	−507.324	+	292.904i	−0.666654	+	0.384893i	−0.794808	−	0.606861i	$-0.792428\pi$
$761$	−507.324	+	292.904i	−0.666654	+	0.384893i	0.128154	+	0.991754i	$0.459095\pi$
$762$	837.392	+	483.469i	1.09894	+	0.634473i
$763$	1179.15	−	680.784i	1.54542	−	0.892246i
$764$	191.805	−	332.216i	0.251054	−	0.434838i
$765$	−12.8566	−	18.3494i	−0.0168060	−	0.0239862i
$766$	126.670	+	73.1331i	0.165366	+	0.0954740i
$767$	−544.300			−0.709648
$768$	−25.6731	−	44.4671i	−0.0334285	−	0.0578999i
$769$	20.6627	+	35.7889i	0.0268696	+	0.0465396i	0.879148	−	0.476550i	$-0.158113\pi$
$769$	20.6627	+	35.7889i	0.0268696	+	0.0465396i	−0.852278	+	0.523089i	$0.824779\pi$
$770$	1430.18	−	1002.07i	1.85738	−	1.30138i
$771$			16.8607i			0.0218687i
$772$	−235.605	+	136.027i	−0.305188	+	0.176200i
$773$	532.081			0.688333			0.344166	−	0.938909i	$-0.388162\pi$
$773$	532.081			0.688333			0.344166	+	0.938909i	$0.388162\pi$
$774$			12.0143i			0.0155224i
$775$	−748.262	−	201.813i	−0.965500	−	0.260403i
$776$	30.5490			0.0393673
$777$		−	439.228i		−	0.565287i
$778$	−262.282	−	454.286i	−0.337124	−	0.583915i
$779$	1302.28			1.67173
$780$	−224.298	−	320.126i	−0.287561	−	0.410418i
$781$	383.555	−	221.446i	0.491108	−	0.283541i
$782$	−80.2847	+	46.3524i	−0.102666	+	0.0592742i
$783$		−	786.515i		−	1.00449i
$784$	256.295	−	443.916i	0.326907	−	0.566219i
$785$	847.334	−	593.689i	1.07941	−	0.756292i
$786$	987.528	+	570.150i	1.25640	+	0.725381i
$787$	−470.094	−	814.227i	−0.597324	−	1.03460i	−0.993214	−	0.116298i	$-0.962897\pi$
$787$	−470.094	−	814.227i	−0.597324	−	1.03460i	0.395890	−	0.918298i	$-0.370436\pi$
$788$	−42.0584	+	72.8472i	−0.0533736	+	0.0924457i
$789$	413.981	+	717.035i	0.524690	+	0.908790i
$790$	−74.3774	+	159.628i	−0.0941487	+	0.202061i
$791$	−469.564			−0.593634
$792$	34.0758	+	59.0211i	0.0430250	+	0.0745215i
$793$	593.775	+	342.816i	0.748770	+	0.432303i
$794$	−443.732	−	768.566i	−0.558856	−	0.967967i
$795$	−184.325	−	263.075i	−0.231855	−	0.330912i
$796$	161.177	+	93.0554i	0.202483	+	0.116904i
$797$	376.917	−	652.840i	0.472920	−	0.819121i	−0.526600	−	0.850113i	$-0.676533\pi$
$797$	376.917	−	652.840i	0.472920	−	0.819121i	0.999520	+	0.0309921i	$0.00986667\pi$
$798$	−1347.93			−1.68913
$799$	−79.7925	+	46.0682i	−0.0998655	+	0.0576574i
$800$	132.922	+	48.2892i	0.166152	+	0.0603615i
$801$	−69.0313	−	39.8552i	−0.0861814	−	0.0497568i
$802$	−424.596			−0.529422
$803$	−2264.86	+	1307.62i	−2.82049	+	1.62841i
$804$		−	682.629i		−	0.849041i
$805$	−1145.90	−	533.923i	−1.42348	−	0.663259i
$806$	226.759	−	483.456i	0.281339	−	0.599821i
$807$		−	976.054i		−	1.20948i
$808$			229.892i			0.284520i
$809$	−346.784	+	200.216i	−0.428658	+	0.247486i	−0.698775	−	0.715342i	$-0.746271\pi$
$809$	−346.784	+	200.216i	−0.428658	+	0.247486i	0.270117	+	0.962828i	$0.412938\pi$
$810$	−583.266	−	271.768i	−0.720082	−	0.335517i
$811$	586.815	−	1016.39i	0.723569	−	1.25326i	−0.235991	−	0.971755i	$-0.575834\pi$
$811$	586.815	−	1016.39i	0.723569	−	1.25326i	0.959560	−	0.281503i	$-0.0908330\pi$
$812$	−423.559	−	733.626i	−0.521625	−	0.903481i
$813$	199.436	−	115.145i	0.245309	−	0.141629i
$814$	−269.846			−0.331506
$815$	−670.142	+	469.538i	−0.822260	+	0.576121i
$816$	−22.1479	+	38.3613i	−0.0271420	+	0.0470114i
$817$	−72.9938	+	126.429i	−0.0893437	+	0.154748i
$818$	−197.365	−	341.847i	−0.241278	−	0.417906i
$819$	182.315	+	105.260i	0.222607	+	0.128522i
$820$	581.355	−	51.0378i	0.708970	−	0.0622412i
$821$			1402.81i			1.70865i	0.519736	+	0.854327i	$0.326030\pi$
$821$			1402.81i			1.70865i	−0.519736	+	0.854327i	$0.673970\pi$
$822$		−	871.311i		−	1.05999i
$823$	57.7149	+	99.9651i	0.0701274	+	0.121464i	0.898957	−	0.438037i	$-0.144326\pi$
$823$	57.7149	+	99.9651i	0.0701274	+	0.121464i	−0.828830	+	0.559501i	$0.810993\pi$
$824$	−125.263	+	216.962i	−0.152018	+	0.263303i
$825$	−1399.19	−	508.311i	−1.69598	−	0.616135i
$826$	−420.564	+	728.438i	−0.509157	+	0.881886i
$827$	667.700	−	1156.49i	0.807376	−	1.39842i	−0.107299	−	0.994227i	$-0.534220\pi$
$827$	667.700	−	1156.49i	0.807376	−	1.39842i	0.914675	−	0.404189i	$-0.132446\pi$
$828$	24.6682	−	42.7266i	0.0297925	−	0.0516022i
$829$			1128.90i			1.36176i	0.732394	+	0.680881i	$0.238403\pi$
$829$			1128.90i			1.36176i	−0.732394	+	0.680881i	$0.761597\pi$
$830$	−29.3907	−	334.780i	−0.0354105	−	0.403349i
$831$	52.4529	+	90.8510i	0.0631202	+	0.109327i
$832$	−48.7213	+	84.3878i	−0.0585593	+	0.101428i
$833$	−442.206			−0.530859
$834$	−312.074	−	540.527i	−0.374189	−	0.648114i
$835$	−93.2085	+	200.043i	−0.111627	+	0.239572i
$836$			828.118i			0.990572i
$837$	−65.0651	−	763.396i	−0.0777361	−	0.912062i
$838$		−	1027.89i		−	1.22660i
$839$	363.867			0.433692			0.216846	−	0.976206i	$-0.430423\pi$
$839$	363.867			0.433692			0.216846	+	0.976206i	$0.430423\pi$
$840$	−601.733	+	52.8268i	−0.716349	+	0.0628891i
$841$	−171.730			−0.204198
$842$	−610.069	−	352.224i	−0.724548	−	0.418318i
$843$	−81.8523	−	141.772i	−0.0970965	−	0.168176i
$844$	237.209	+	410.858i	0.281053	+	0.486799i
$845$	43.5849	−	93.5414i	0.0515798	−	0.110700i
$846$	24.5170	−	42.4647i	0.0289799	−	0.0501947i
$847$	2573.84	+	1486.00i	3.03877	+	1.75443i
$848$	−40.0385	+	69.3487i	−0.0472152	+	0.0817792i
$849$	1261.54	−	728.349i	1.48591	−	0.857891i
$850$	−21.2577	−	120.136i	−0.0250090	−	0.141337i
$851$	97.6735	+	169.176i	0.114775	+	0.198796i
$852$	−153.197			−0.179808
$853$		−	126.716i		−	0.148554i	−0.997238	−	0.0742768i	$-0.976335\pi$
$853$		−	126.716i		−	0.148554i	0.997238	−	0.0742768i	$-0.0236648\pi$
$854$	917.582	−	529.766i	1.07445	−	0.620335i
$855$	83.1396	+	118.660i	0.0972393	+	0.138783i
$856$	147.950	+	256.257i	0.172839	+	0.299366i
$857$	−257.501	−	148.669i	−0.300468	−	0.173476i	0.342185	−	0.939633i	$-0.388833\pi$
$857$	−257.501	−	148.669i	−0.300468	−	0.173476i	−0.642653	+	0.766157i	$0.722166\pi$
$858$	512.860	−	888.300i	0.597739	−	1.03532i
$859$	1337.20	+	772.033i	1.55669	+	0.898758i	0.997570	+	0.0696744i	$0.0221960\pi$
$859$	1337.20	+	772.033i	1.55669	+	0.898758i	0.559125	+	0.829084i	$0.311137\pi$
$860$	−27.6305	+	59.3003i	−0.0321285	+	0.0689538i
$861$	−2158.71	+	1246.33i	−2.50722	+	1.44754i
$862$	−355.939	+	205.502i	−0.412923	+	0.238401i
$863$	−17.6246	+	30.5267i	−0.0204225	+	0.0353727i	−0.876056	−	0.482209i	$-0.839834\pi$
$863$	−17.6246	+	30.5267i	−0.0204225	+	0.0353727i	0.855634	+	0.517582i	$0.173168\pi$
$864$			139.809i			0.161816i
$865$	−67.1181	−	764.520i	−0.0775932	−	0.883838i
$866$		−	448.164i		−	0.517510i
$867$	−889.227			−1.02564
$868$	−471.799	−	677.023i	−0.543548	−	0.779980i
$869$	−462.119			−0.531783
$870$	−304.992	+	654.571i	−0.350566	+	0.752381i
$871$	−1121.91	+	647.732i	−1.28807	+	0.743665i
$872$			289.346i			0.331818i
$873$	12.1464	+	7.01272i	0.0139134	+	0.00803290i
$874$	519.175	−	299.746i	0.594022	−	0.342959i
$875$	1175.36	−	1177.48i	1.34327	−	1.34569i
$876$	904.611			1.03266
$877$	469.998	+	271.354i	0.535916	+	0.309411i	0.743422	−	0.668823i	$-0.233201\pi$
$877$	469.998	+	271.354i	0.535916	+	0.309411i	−0.207506	+	0.978234i	$0.566535\pi$
$878$	−168.977	−	97.5587i	−0.192456	−	0.111115i
$879$	−102.261	−	59.0406i	−0.116338	−	0.0671680i
$880$	32.4549	+	369.683i	0.0368805	+	0.420094i
$881$	−303.779	−	175.387i	−0.344812	−	0.199077i	0.317586	−	0.948229i	$-0.397128\pi$
$881$	−303.779	−	175.387i	−0.344812	−	0.199077i	−0.662398	+	0.749152i	$0.730461\pi$
$882$	203.808	−	117.668i	0.231074	−	0.133411i
$883$	1318.86			1.49362			0.746808	−	0.665039i	$-0.231585\pi$
$883$	1318.86			1.49362			0.746808	+	0.665039i	$0.231585\pi$
$884$	84.0627			0.0950936
$885$	714.283	−	62.7077i	0.807100	−	0.0708562i
$886$	9.46939	−	16.4015i	0.0106878	−	0.0185118i
$887$	−785.043	+	453.245i	−0.885054	+	0.510986i	−0.872321	−	0.488933i	$-0.837386\pi$
$887$	−785.043	+	453.245i	−0.885054	+	0.510986i	−0.0127323	+	0.999919i	$0.504053\pi$
$888$	80.8347	+	46.6700i	0.0910301	+	0.0525563i
$889$	−2455.80	−	1417.86i	−2.76243	−	1.59489i
$890$	−249.065	−	355.475i	−0.279848	−	0.399410i
$891$		−	1688.54i		−	1.89511i
$892$	7.33313	+	12.7014i	0.00822100	+	0.0142392i
$893$	515.993	−	297.909i	0.577819	−	0.333604i
$894$	−45.1726	−	26.0804i	−0.0505286	−	0.0291727i
$895$	−625.450	−	291.424i	−0.698827	−	0.325613i
$896$	75.2909	+	130.408i	0.0840300	+	0.145544i
$897$	−742.541			−0.827805
$898$	292.894			0.326163
$899$	−982.962	+	83.7790i	−1.09340	+	0.0931913i
$900$	41.7650	+	49.7130i	0.0464056	+	0.0552367i
$901$	69.0815			0.0766721
$902$	765.703	+	1326.24i	0.848894	+	1.47033i
$903$		−	279.432i		−	0.309449i
$904$	49.8934	−	86.4178i	0.0551918	−	0.0955950i
$905$	105.112	+	1197.30i	0.116146	+	1.32298i
$906$	262.099	+	453.969i	0.289292	+	0.501069i
$907$			1011.56i			1.11528i	0.830084	+	0.557638i	$0.188292\pi$
$907$			1011.56i			1.11528i	−0.830084	+	0.557638i	$0.811708\pi$
$908$	332.389	+	191.905i	0.366067	+	0.211349i
$909$	−52.7732	+	91.4059i	−0.0580564	+	0.100557i
$910$	657.793	+	938.826i	0.722849	+	1.03168i
$911$	662.879	−	382.713i	0.727639	−	0.420102i	−0.0899191	−	0.995949i	$-0.528661\pi$
$911$	662.879	−	382.713i	0.727639	−	0.420102i	0.817558	+	0.575847i	$0.195328\pi$
$912$	143.223	−	248.070i	0.157043	−	0.272007i
$913$	763.728	−	440.938i	0.836503	−	0.482955i
$914$		−	353.047i		−	0.386266i
$915$	−818.704	−	381.469i	−0.894758	−	0.416906i
$916$	−318.244	+	183.738i	−0.347428	+	0.200588i
$917$	−2896.10	−	1672.06i	−3.15823	−	1.82341i
$918$	104.453	−	60.3058i	0.113783	−	0.0656926i
$919$	528.993	−	916.243i	0.575618	−	0.997000i	−0.420356	−	0.907359i	$-0.638095\pi$
$919$	528.993	−	916.243i	0.575618	−	0.997000i	0.995974	−	0.0896407i	$-0.0285719\pi$
$920$	220.019	−	154.158i	0.239152	−	0.167563i
$921$	698.184	+	403.097i	0.758072	+	0.437673i
$922$	318.343			0.345274
$923$	145.365	+	251.780i	0.157492	+	0.272784i
$924$	−792.542	−	1372.72i	−0.857730	−	1.48563i
$925$	−253.151	+	44.7940i	−0.273677	+	0.0484260i
$926$			377.252i			0.407400i
$927$	−99.6101	+	57.5099i	−0.107454	+	0.0620387i
$928$	180.020			0.193988
$929$			1788.07i			1.92472i	0.271772	+	0.962362i	$0.412390\pi$
$929$			1788.07i			1.92472i	−0.271772	+	0.962362i	$0.587610\pi$
$930$	−241.877	+	660.562i	−0.260083	+	0.710281i
$931$	2859.60			3.07154
$932$			42.6352i			0.0457459i
$933$	−792.616	−	1372.85i	−0.849534	−	1.47144i
$934$	942.931			1.00956
$935$	262.195	−	183.708i	0.280422	−	0.196479i
$936$	−38.7436	+	22.3686i	−0.0413927	+	0.0238981i
$937$	−304.504	+	175.806i	−0.324978	+	0.187626i	−0.653609	−	0.756832i	$-0.726746\pi$
$937$	−304.504	+	175.806i	−0.324978	+	0.187626i	0.328631	+	0.944458i	$0.393413\pi$
$938$			2001.93i			2.13425i
$939$	927.468	−	1606.42i	0.987719	−	1.71078i
$940$	218.671	−	153.213i	0.232628	−	0.162992i
$941$	−464.398	−	268.120i	−0.493515	−	0.284931i	0.232516	−	0.972593i	$-0.425304\pi$
$941$	−464.398	−	268.120i	−0.493515	−	0.284931i	−0.726032	+	0.687661i	$0.758637\pi$
$942$	−469.553	−	813.290i	−0.498464	−	0.863366i
$943$	554.309	−	960.091i	0.587814	−	1.01812i
$944$	−89.3736	−	154.800i	−0.0946754	−	0.163983i
$945$	1490.85	+	694.650i	1.57762	+	0.735079i
$946$	−171.673			−0.181472
$947$	378.914	+	656.298i	0.400120	+	0.693028i	0.993740	−	0.111717i	$-0.0356351\pi$
$947$	378.914	+	656.298i	0.400120	+	0.693028i	−0.593620	+	0.804745i	$0.702302\pi$
$948$	138.432	+	79.9238i	0.146025	+	0.0843078i
$949$	−858.366	−	1486.73i	−0.904496	−	1.56663i
$950$	137.467	+	776.884i	0.144702	+	0.817772i
$951$	−484.699	−	279.841i	−0.509673	−	0.294260i
$952$	64.9526	−	112.501i	0.0682275	−	0.118174i
$953$	−121.540			−0.127534			−0.0637671	−	0.997965i	$-0.520311\pi$
$953$	−121.540			−0.127534			−0.0637671	+	0.997965i	$0.520311\pi$
$954$	−31.8389	+	18.3822i	−0.0333741	+	0.0192686i
$955$	955.350	−	83.8713i	1.00037	−	0.0878233i
$956$	101.413	+	58.5505i	0.106080	+	0.0612453i
$957$	−1894.97			−1.98011
$958$	967.596	−	558.642i	1.01002	−	0.583134i
$959$			2555.27i			2.66452i
$960$	54.2147	−	116.355i	0.0564736	−	0.121203i
$961$	−947.139	+	162.633i	−0.985576	+	0.169233i
$962$		−	177.137i		−	0.184134i
$963$			135.852i			0.141071i
$964$	694.151	−	400.768i	0.720074	−	0.415735i
$965$	−616.496	−	287.252i	−0.638856	−	0.297670i
$966$	−573.738	+	993.744i	−0.593932	+	1.02872i
$967$	195.370	+	338.390i	0.202037	+	0.349938i	0.949185	−	0.314720i	$-0.101911\pi$
$967$	195.370	+	338.390i	0.202037	+	0.349938i	−0.747148	+	0.664658i	$0.768577\pi$
$968$	−546.963	+	315.789i	−0.565045	+	0.326229i
$969$	−247.114			−0.255020
$970$	43.8242	+	62.5475i	0.0451796	+	0.0644820i
$971$	−360.083	+	623.682i	−0.370837	+	0.642309i	−0.989695	−	0.143195i	$-0.954262\pi$
$971$	−360.083	+	623.682i	−0.370837	+	0.642309i	0.618858	+	0.785503i	$0.287596\pi$
$972$	−69.5996	+	120.550i	−0.0716046	+	0.124023i
$973$	915.211	+	1585.19i	0.940607	+	1.62918i
$974$	−854.555	−	493.378i	−0.877367	−	0.506548i
$975$	333.674	−	918.477i	0.342230	−	0.942028i
$976$			225.160i			0.230697i
$977$			426.175i			0.436208i	0.975926	+	0.218104i	$0.0699871\pi$
$977$			426.175i			0.436208i	−0.975926	+	0.218104i	$0.930013\pi$
$978$	371.362	+	643.217i	0.379715	+	0.657687i
$979$	569.491	−	986.388i	0.581707	−	1.00755i
$980$	1276.56	−	112.071i	1.30262	−	0.114358i
$981$	−66.4212	+	115.045i	−0.0677076	+	0.117273i
$982$	−457.332	+	792.122i	−0.465715	+	0.806641i
$983$	−886.219	+	1534.98i	−0.901546	+	1.56152i	−0.0760577	+	0.997103i	$0.524233\pi$
$983$	−886.219	+	1534.98i	−0.901546	+	1.56152i	−0.825488	+	0.564420i	$0.809100\pi$
$984$		−	529.715i		−	0.538328i
$985$	−209.486	+	18.3910i	−0.212676	+	0.0186711i
$986$	−77.6508	−	134.495i	−0.0787534	−	0.136405i
$987$	−570.221	+	987.652i	−0.577732	+	1.00066i
$988$	−543.607			−0.550209
$989$	62.1389	+	107.628i	0.0628300	+	0.108825i
$990$	−71.9590	+	154.438i	−0.0726858	+	0.155998i
$991$			906.978i			0.915214i	0.889154	+	0.457607i	$0.151293\pi$
$991$			906.978i			0.915214i	−0.889154	+	0.457607i	$0.848707\pi$
$992$	174.729	−	14.8924i	0.176138	−	0.0150125i
$993$			560.742i			0.564695i
$994$	449.276			0.451988
$995$	40.6907	+	463.494i	0.0408952	+	0.465823i
$996$	−305.042			−0.306267
$997$	50.9639	+	29.4240i	0.0511173	+	0.0295126i	0.525341	−	0.850892i	$-0.323938\pi$
$997$	50.9639	+	29.4240i	0.0511173	+	0.0295126i	−0.474224	+	0.880404i	$0.657271\pi$
$998$	287.480	+	497.930i	0.288056	+	0.498928i
$999$	−127.076	−	220.102i	−0.127203	−	0.220323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	310.3.i.a.99.4	✓	64
5.4	even	2	inner	310.3.i.a.99.29	yes	64
31.26	odd	6	inner	310.3.i.a.119.13	yes	64
155.119	odd	6	inner	310.3.i.a.119.20	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
310.3.i.a.99.4	✓	64	1.1	even	1	trivial
310.3.i.a.99.29	yes	64	5.4	even	2	inner
310.3.i.a.119.13	yes	64	31.26	odd	6	inner
310.3.i.a.119.20	yes	64	155.119	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	310.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-1.60457 - 2.77920i) q^{3} -2.00000 q^{4} +(-2.86911 - 4.09490i) q^{5} +(-3.93038 + 2.26920i) q^{6} +(11.5265 - 6.65484i) q^{7} +2.82843i q^{8} +(-0.649284 + 1.12459i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-1.60457 - 2.77920i) q^{3} -2.00000 q^{4} +(-2.86911 - 4.09490i) q^{5} +(-3.93038 + 2.26920i) q^{6} +(11.5265 - 6.65484i) q^{7} +2.82843i q^{8} +(-0.649284 + 1.12459i) q^{9} +(-5.79106 + 4.05754i) q^{10} +(-16.0693 - 9.27762i) q^{11} +(3.20914 + 5.55839i) q^{12} +(6.09017 - 10.5485i) q^{13} +(-9.41136 - 16.3010i) q^{14} +(-6.77684 + 14.5444i) q^{15} +4.00000 q^{16} +(-1.72538 - 2.98844i) q^{17} +(1.59041 + 0.918227i) q^{18} +(11.1575 + 19.3253i) q^{19} +(5.73822 + 8.18980i) q^{20} +(-36.9902 - 21.3563i) q^{21} +(-13.1205 + 22.7254i) q^{22} +18.9965 q^{23} +(7.86075 - 4.53841i) q^{24} +(-8.53640 + 23.4974i) q^{25} +(-14.9178 - 8.61280i) q^{26} -24.7150 q^{27} +(-23.0530 + 13.3097i) q^{28} +31.8234i q^{29} +(20.5688 + 9.58389i) q^{30} +(2.63262 + 30.8880i) q^{31} -5.65685i q^{32} +59.5463i q^{33} +(-4.22630 + 2.44005i) q^{34} +(-60.3218 - 28.1065i) q^{35} +(1.29857 - 2.24919i) q^{36} +(5.14167 + 8.90563i) q^{37} +(27.3301 - 15.7790i) q^{38} -39.0884 q^{39} +(11.5821 - 8.11507i) q^{40} +(29.1796 - 50.5405i) q^{41} +(-30.2024 + 52.3120i) q^{42} +(3.27107 + 5.66567i) q^{43} +(32.1386 + 18.5552i) q^{44} +(6.46796 - 0.567830i) q^{45} -26.8651i q^{46} -26.7004i q^{47} +(-6.41828 - 11.1168i) q^{48} +(64.0737 - 110.979i) q^{49} +(33.2304 + 12.0723i) q^{50} +(-5.53698 + 9.59032i) q^{51} +(-12.1803 + 21.0970i) q^{52} +(-10.0096 + 17.3372i) q^{53} +34.9522i q^{54} +(8.11372 + 92.4207i) q^{55} +(18.8227 + 32.6019i) q^{56} +(35.8059 - 62.0176i) q^{57} +45.0051 q^{58} +(-22.3434 - 38.6999i) q^{59} +(13.5537 - 29.0887i) q^{60} +56.2901i q^{61} +(43.6822 - 3.72309i) q^{62} +17.2835i q^{63} -8.00000 q^{64} +(-60.6683 + 5.32614i) q^{65} +84.2112 q^{66} +(-92.1079 - 53.1785i) q^{67} +(3.45076 + 5.97688i) q^{68} +(-30.4811 - 52.7949i) q^{69} +(-39.7485 + 85.3078i) q^{70} +(-11.9344 + 20.6710i) q^{71} +(-3.18083 - 1.83645i) q^{72} +(70.4715 - 122.060i) q^{73} +(12.5945 - 7.27142i) q^{74} +(79.0012 - 13.9790i) q^{75} +(-22.3149 - 38.6506i) q^{76} -246.964 q^{77} +55.2793i q^{78} +(21.5684 - 12.4525i) q^{79} +(-11.4764 - 16.3796i) q^{80} +(45.5004 + 78.8090i) q^{81} +(-71.4750 - 41.2661i) q^{82} +(-23.7635 + 41.1597i) q^{83} +(73.9804 + 42.7126i) q^{84} +(-7.28707 + 15.6394i) q^{85} +(8.01246 - 4.62600i) q^{86} +(88.4435 - 51.0629i) q^{87} +(26.2411 - 45.4509i) q^{88} +61.3833i q^{89} +(-0.803033 - 9.14708i) q^{90} -162.116i q^{91} -37.9929 q^{92} +(81.6196 - 56.8785i) q^{93} -37.7600 q^{94} +(47.1231 - 101.135i) q^{95} +(-15.7215 + 9.07681i) q^{96} -10.8007i q^{97} +(-156.948 - 90.6139i) q^{98} +(20.8671 - 12.0476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 128 q^{4} + 6 q^{5} - 56 q^{9}+O(q^{10}) \) 64 * q - 128 * q^4 + 6 * q^5 - 56 * q^9	\( 64 q - 128 q^{4} + 6 q^{5} - 56 q^{9} - 16 q^{10} + 256 q^{16} - 8 q^{19} - 12 q^{20} - 72 q^{21} - 22 q^{25} + 72 q^{31} - 48 q^{34} + 12 q^{35} + 112 q^{36} - 400 q^{39} + 32 q^{40} - 8 q^{41} + 92 q^{45} + 24 q^{49} + 16 q^{50} + 164 q^{51} + 162 q^{55} + 48 q^{59} - 512 q^{64} - 54 q^{65} - 64 q^{66} - 32 q^{69} + 352 q^{70} - 128 q^{71} + 144 q^{74} + 942 q^{75} + 16 q^{76} - 768 q^{79} + 24 q^{80} - 168 q^{81} + 144 q^{84} - 336 q^{86} - 272 q^{90} + 176 q^{94} - 292 q^{95} - 168 q^{99}+O(q^{100}) \) 64 * q - 128 * q^4 + 6 * q^5 - 56 * q^9 - 16 * q^10 + 256 * q^16 - 8 * q^19 - 12 * q^20 - 72 * q^21 - 22 * q^25 + 72 * q^31 - 48 * q^34 + 12 * q^35 + 112 * q^36 - 400 * q^39 + 32 * q^40 - 8 * q^41 + 92 * q^45 + 24 * q^49 + 16 * q^50 + 164 * q^51 + 162 * q^55 + 48 * q^59 - 512 * q^64 - 54 * q^65 - 64 * q^66 - 32 * q^69 + 352 * q^70 - 128 * q^71 + 144 * q^74 + 942 * q^75 + 16 * q^76 - 768 * q^79 + 24 * q^80 - 168 * q^81 + 144 * q^84 - 336 * q^86 - 272 * q^90 + 176 * q^94 - 292 * q^95 - 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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