LMFDB - Embedded newform 630.2.ba.a.529.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(499,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("630.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ba (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.18
Character	$\chi$	$=$	630.529
Dual form			630.2.ba.a.499.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.32919 + 1.11052i) q^{3} -1.00000 q^{4} +(-1.69883 - 1.45395i) q^{5} +(1.11052 - 1.32919i) q^{6} +(-2.63186 - 0.270774i) q^{7} +1.00000i q^{8} +(0.533495 + 2.95218i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.32919 + 1.11052i) q^{3} -1.00000 q^{4} +(-1.69883 - 1.45395i) q^{5} +(1.11052 - 1.32919i) q^{6} +(-2.63186 - 0.270774i) q^{7} +1.00000i q^{8} +(0.533495 + 2.95218i) q^{9} +(-1.45395 + 1.69883i) q^{10} +(-1.73546 - 3.00590i) q^{11} +(-1.32919 - 1.11052i) q^{12} +(1.09687 - 0.633281i) q^{13} +(-0.270774 + 2.63186i) q^{14} +(-0.643436 - 3.81916i) q^{15} +1.00000 q^{16} +(-4.66021 - 2.69057i) q^{17} +(2.95218 - 0.533495i) q^{18} +(-2.23829 - 3.87684i) q^{19} +(1.69883 + 1.45395i) q^{20} +(-3.19754 - 3.28264i) q^{21} +(-3.00590 + 1.73546i) q^{22} +(-4.15498 - 2.39888i) q^{23} +(-1.11052 + 1.32919i) q^{24} +(0.772070 + 4.94003i) q^{25} +(-0.633281 - 1.09687i) q^{26} +(-2.56934 + 4.51647i) q^{27} +(2.63186 + 0.270774i) q^{28} +(1.04810 - 1.81537i) q^{29} +(-3.81916 + 0.643436i) q^{30} +0.803755 q^{31} -1.00000i q^{32} +(1.03136 - 5.92267i) q^{33} +(-2.69057 + 4.66021i) q^{34} +(4.07740 + 4.28659i) q^{35} +(-0.533495 - 2.95218i) q^{36} +(-5.27556 + 3.04584i) q^{37} +(-3.87684 + 2.23829i) q^{38} +(2.16123 + 0.376349i) q^{39} +(1.45395 - 1.69883i) q^{40} +(2.28878 + 3.96429i) q^{41} +(-3.28264 + 3.19754i) q^{42} +(0.972049 + 0.561213i) q^{43} +(1.73546 + 3.00590i) q^{44} +(3.38600 - 5.79094i) q^{45} +(-2.39888 + 4.15498i) q^{46} -9.74789i q^{47} +(1.32919 + 1.11052i) q^{48} +(6.85336 + 1.42528i) q^{49} +(4.94003 - 0.772070i) q^{50} +(-3.20637 - 8.75153i) q^{51} +(-1.09687 + 0.633281i) q^{52} +(-6.88082 - 3.97264i) q^{53} +(4.51647 + 2.56934i) q^{54} +(-1.42217 + 7.62978i) q^{55} +(0.270774 - 2.63186i) q^{56} +(1.33018 - 7.63872i) q^{57} +(-1.81537 - 1.04810i) q^{58} +12.1347 q^{59} +(0.643436 + 3.81916i) q^{60} -10.6833 q^{61} -0.803755i q^{62} +(-0.604709 - 7.91419i) q^{63} -1.00000 q^{64} +(-2.78416 - 0.518960i) q^{65} +(-5.92267 - 1.03136i) q^{66} +1.64754i q^{67} +(4.66021 + 2.69057i) q^{68} +(-2.85876 - 7.80276i) q^{69} +(4.28659 - 4.07740i) q^{70} +10.0748 q^{71} +(-2.95218 + 0.533495i) q^{72} +(3.28654 + 1.89748i) q^{73} +(3.04584 + 5.27556i) q^{74} +(-4.45977 + 7.42364i) q^{75} +(2.23829 + 3.87684i) q^{76} +(3.75356 + 8.38101i) q^{77} +(0.376349 - 2.16123i) q^{78} -1.59449 q^{79} +(-1.69883 - 1.45395i) q^{80} +(-8.43077 + 3.14995i) q^{81} +(3.96429 - 2.28878i) q^{82} +(9.12037 + 5.26565i) q^{83} +(3.19754 + 3.28264i) q^{84} +(4.00496 + 11.3465i) q^{85} +(0.561213 - 0.972049i) q^{86} +(3.40913 - 1.24903i) q^{87} +(3.00590 - 1.73546i) q^{88} +(-4.84020 - 8.38348i) q^{89} +(-5.79094 - 3.38600i) q^{90} +(-3.05829 + 1.36970i) q^{91} +(4.15498 + 2.39888i) q^{92} +(1.06834 + 0.892585i) q^{93} -9.74789 q^{94} +(-1.83423 + 9.84046i) q^{95} +(1.11052 - 1.32919i) q^{96} +(7.48401 + 4.32089i) q^{97} +(1.42528 - 6.85336i) q^{98} +(7.94810 - 6.72701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9	$ 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9} + 4 q^{11} - 2 q^{14} - 2 q^{15} + 96 q^{16} + 8 q^{21} + 4 q^{24} + 24 q^{26} + 10 q^{29} + 10 q^{30} - 34 q^{35} - 8 q^{36} + 44 q^{39} + 30 q^{41} - 4 q^{44} - 44 q^{45} - 6 q^{46} - 6 q^{49} - 12 q^{50} + 28 q^{51} - 8 q^{54} + 12 q^{55} + 2 q^{56} + 48 q^{59} + 2 q^{60} + 12 q^{61} - 96 q^{64} - 36 q^{65} + 32 q^{66} + 36 q^{69} + 6 q^{70} - 32 q^{71} - 68 q^{75} - 32 q^{81} - 8 q^{84} + 4 q^{86} - 66 q^{89} - 22 q^{90} + 24 q^{94} - 60 q^{95} - 4 q^{96} - 4 q^{99}+O(q^{100}) $ 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9 + 4 * q^11 - 2 * q^14 - 2 * q^15 + 96 * q^16 + 8 * q^21 + 4 * q^24 + 24 * q^26 + 10 * q^29 + 10 * q^30 - 34 * q^35 - 8 * q^36 + 44 * q^39 + 30 * q^41 - 4 * q^44 - 44 * q^45 - 6 * q^46 - 6 * q^49 - 12 * q^50 + 28 * q^51 - 8 * q^54 + 12 * q^55 + 2 * q^56 + 48 * q^59 + 2 * q^60 + 12 * q^61 - 96 * q^64 - 36 * q^65 + 32 * q^66 + 36 * q^69 + 6 * q^70 - 32 * q^71 - 68 * q^75 - 32 * q^81 - 8 * q^84 + 4 * q^86 - 66 * q^89 - 22 * q^90 + 24 * q^94 - 60 * q^95 - 4 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.32919	+	1.11052i	0.767408	+	0.641158i
$3$	1.32919	+	1.11052i	0.767408	+	0.641158i
$4$	−1.00000			−0.500000
$5$	−1.69883	−	1.45395i	−0.759741	−	0.650225i
$5$	−1.69883	−	1.45395i	−0.759741	−	0.650225i
$6$	1.11052	−	1.32919i	0.453368	−	0.542640i
$7$	−2.63186	−	0.270774i	−0.994749	−	0.102343i
$7$	−2.63186	−	0.270774i	−0.994749	−	0.102343i
$8$			1.00000i			0.353553i
$9$	0.533495	+	2.95218i	0.177832	+	0.984061i
$10$	−1.45395	+	1.69883i	−0.459779	+	0.537218i
$11$	−1.73546	−	3.00590i	−0.523260	−	0.906312i	−0.999634	−	0.0270693i	$-0.991383\pi$
$11$	−1.73546	−	3.00590i	−0.523260	−	0.906312i	0.476374	−	0.879243i	$-0.341951\pi$
$12$	−1.32919	−	1.11052i	−0.383704	−	0.320579i
$13$	1.09687	−	0.633281i	0.304218	−	0.175640i	−0.340118	−	0.940383i	$-0.610467\pi$
$13$	1.09687	−	0.633281i	0.304218	−	0.175640i	0.644336	+	0.764742i	$0.277134\pi$
$14$	−0.270774	+	2.63186i	−0.0723674	+	0.703394i
$15$	−0.643436	−	3.81916i	−0.166135	−	0.986103i
$16$	1.00000			0.250000
$17$	−4.66021	−	2.69057i	−1.13027	−	0.652560i	−0.186264	−	0.982500i	$-0.559638\pi$
$17$	−4.66021	−	2.69057i	−1.13027	−	0.652560i	−0.944002	+	0.329940i	$0.892971\pi$
$18$	2.95218	−	0.533495i	0.695836	−	0.125746i
$19$	−2.23829	−	3.87684i	−0.513499	−	0.889407i	−0.999877	−	0.0156586i	$-0.995016\pi$
$19$	−2.23829	−	3.87684i	−0.513499	−	0.889407i	0.486378	−	0.873749i	$-0.338318\pi$
$20$	1.69883	+	1.45395i	0.379871	+	0.325113i
$21$	−3.19754	−	3.28264i	−0.697761	−	0.716331i
$22$	−3.00590	+	1.73546i	−0.640859	+	0.370000i
$23$	−4.15498	−	2.39888i	−0.866374	−	0.500201i	−0.000232275	−	1.00000i	$-0.500074\pi$
$23$	−4.15498	−	2.39888i	−0.866374	−	0.500201i	−0.866142	+	0.499799i	$0.833407\pi$
$24$	−1.11052	+	1.32919i	−0.226684	+	0.271320i
$25$	0.772070	+	4.94003i	0.154414	+	0.988006i
$26$	−0.633281	−	1.09687i	−0.124197	−	0.215115i
$27$	−2.56934	+	4.51647i	−0.494470	+	0.869195i
$28$	2.63186	+	0.270774i	0.497375	+	0.0511715i
$29$	1.04810	−	1.81537i	0.194628	−	0.337105i	−0.752151	−	0.658991i	$-0.770983\pi$
$29$	1.04810	−	1.81537i	0.194628	−	0.337105i	0.946778	+	0.321886i	$0.104317\pi$
$30$	−3.81916	+	0.643436i	−0.697280	+	0.117475i
$31$	0.803755			0.144359			0.0721793	−	0.997392i	$-0.477005\pi$
$31$	0.803755			0.144359			0.0721793	+	0.997392i	$0.477005\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.03136	−	5.92267i	0.179536	−	1.03100i
$34$	−2.69057	+	4.66021i	−0.461429	+	0.799219i
$35$	4.07740	+	4.28659i	0.689206	+	0.724565i
$36$	−0.533495	−	2.95218i	−0.0889158	−	0.492030i
$37$	−5.27556	+	3.04584i	−0.867296	+	0.500734i	−0.866449	−	0.499266i	$-0.833603\pi$
$37$	−5.27556	+	3.04584i	−0.867296	+	0.500734i	−0.000847502		1.00000i	$0.500270\pi$
$38$	−3.87684	+	2.23829i	−0.628906	+	0.363099i
$39$	2.16123	+	0.376349i	0.346073	+	0.0602641i
$40$	1.45395	−	1.69883i	0.229889	−	0.268609i
$41$	2.28878	+	3.96429i	0.357448	+	0.619118i	0.987534	−	0.157407i	$-0.0503136\pi$
$41$	2.28878	+	3.96429i	0.357448	+	0.619118i	−0.630086	+	0.776526i	$0.716980\pi$
$42$	−3.28264	+	3.19754i	−0.506522	+	0.493391i
$43$	0.972049	+	0.561213i	0.148236	+	0.0855841i	0.572283	−	0.820056i	$-0.306058\pi$
$43$	0.972049	+	0.561213i	0.148236	+	0.0855841i	−0.424047	+	0.905640i	$0.639391\pi$
$44$	1.73546	+	3.00590i	0.261630	+	0.453156i
$45$	3.38600	−	5.79094i	0.504755	−	0.863262i
$46$	−2.39888	+	4.15498i	−0.353696	+	0.612619i
$47$		−	9.74789i		−	1.42188i	−0.703255	−	0.710938i	$-0.748271\pi$
$47$		−	9.74789i		−	1.42188i	0.703255	−	0.710938i	$-0.251729\pi$
$48$	1.32919	+	1.11052i	0.191852	+	0.160290i
$49$	6.85336	+	1.42528i	0.979052	+	0.203611i
$50$	4.94003	−	0.772070i	0.698626	−	0.109187i
$51$	−3.20637	−	8.75153i	−0.448982	−	1.22546i
$52$	−1.09687	+	0.633281i	−0.152109	+	0.0878202i
$53$	−6.88082	−	3.97264i	−0.945153	−	0.545684i	−0.0535811	−	0.998564i	$-0.517064\pi$
$53$	−6.88082	−	3.97264i	−0.945153	−	0.545684i	−0.891572	+	0.452879i	$0.850397\pi$
$54$	4.51647	+	2.56934i	0.614614	+	0.349643i
$55$	−1.42217	+	7.62978i	−0.191765	+	1.02880i
$56$	0.270774	−	2.63186i	0.0361837	−	0.351697i
$57$	1.33018	−	7.63872i	0.176187	−	1.01177i
$58$	−1.81537	−	1.04810i	−0.238369	−	0.137623i
$59$	12.1347			1.57981			0.789904	−	0.613231i	$-0.210131\pi$
$59$	12.1347			1.57981			0.789904	+	0.613231i	$0.210131\pi$
$60$	0.643436	+	3.81916i	0.0830673	+	0.493052i
$61$	−10.6833			−1.36785			−0.683927	−	0.729551i	$-0.739729\pi$
$61$	−10.6833			−1.36785			−0.683927	+	0.729551i	$0.739729\pi$
$62$		−	0.803755i		−	0.102077i
$63$	−0.604709	−	7.91419i	−0.0761861	−	0.997094i
$64$	−1.00000			−0.125000
$65$	−2.78416	−	0.518960i	−0.345333	−	0.0643690i
$66$	−5.92267	−	1.03136i	−0.729030	−	0.126951i
$67$			1.64754i			0.201279i	0.994923	+	0.100640i	$0.0320889\pi$
$67$			1.64754i			0.201279i	−0.994923	+	0.100640i	$0.967911\pi$
$68$	4.66021	+	2.69057i	0.565133	+	0.326280i
$69$	−2.85876	−	7.80276i	−0.344154	−	0.939342i
$70$	4.28659	−	4.07740i	0.512345	−	0.487342i
$71$	10.0748			1.19566			0.597829	−	0.801624i	$-0.296030\pi$
$71$	10.0748			1.19566			0.597829	+	0.801624i	$0.296030\pi$
$72$	−2.95218	+	0.533495i	−0.347918	+	0.0628730i
$73$	3.28654	+	1.89748i	0.384660	+	0.222084i	0.679844	−	0.733357i	$-0.262048\pi$
$73$	3.28654	+	1.89748i	0.384660	+	0.222084i	−0.295184	+	0.955440i	$0.595381\pi$
$74$	3.04584	+	5.27556i	0.354072	+	0.613271i
$75$	−4.45977	+	7.42364i	−0.514970	+	0.857208i
$76$	2.23829	+	3.87684i	0.256750	+	0.444704i
$77$	3.75356	+	8.38101i	0.427757	+	0.955105i
$78$	0.376349	−	2.16123i	0.0426131	−	0.244711i
$79$	−1.59449			−0.179394			−0.0896970	−	0.995969i	$-0.528590\pi$
$79$	−1.59449			−0.179394			−0.0896970	+	0.995969i	$0.528590\pi$
$80$	−1.69883	−	1.45395i	−0.189935	−	0.162556i
$81$	−8.43077	+	3.14995i	−0.936752	+	0.349994i
$82$	3.96429	−	2.28878i	0.437783	−	0.252754i
$83$	9.12037	+	5.26565i	1.00109	+	0.577980i	0.908571	−	0.417731i	$-0.137175\pi$
$83$	9.12037	+	5.26565i	1.00109	+	0.577980i	0.0925198	+	0.995711i	$0.470508\pi$
$84$	3.19754	+	3.28264i	0.348880	+	0.358165i
$85$	4.00496	+	11.3465i	0.434399	+	1.23070i
$86$	0.561213	−	0.972049i	0.0605171	−	0.104819i
$87$	3.40913	−	1.24903i	0.365497	−	0.133910i
$88$	3.00590	−	1.73546i	0.320430	−	0.185000i
$89$	−4.84020	−	8.38348i	−0.513061	−	0.888647i	−0.999885	−	0.0151474i	$-0.995178\pi$
$89$	−4.84020	−	8.38348i	−0.513061	−	0.888647i	0.486825	−	0.873500i	$-0.338155\pi$
$90$	−5.79094	−	3.38600i	−0.610419	−	0.356916i
$91$	−3.05829	+	1.36970i	−0.320596	+	0.143584i
$92$	4.15498	+	2.39888i	0.433187	+	0.250101i
$93$	1.06834	+	0.892585i	0.110782	+	0.0925568i
$94$	−9.74789			−1.00542
$95$	−1.83423	+	9.84046i	−0.188188	+	1.00961i
$96$	1.11052	−	1.32919i	0.113342	−	0.135660i
$97$	7.48401	+	4.32089i	0.759886	+	0.438720i	0.829255	−	0.558871i	$-0.188765\pi$
$97$	7.48401	+	4.32089i	0.759886	+	0.438720i	−0.0693689	+	0.997591i	$0.522099\pi$
$98$	1.42528	−	6.85336i	0.143975	−	0.692294i
$99$	7.94810	−	6.72701i	0.798814	−	0.676090i
$100$	−0.772070	−	4.94003i	−0.0772070	−	0.494003i
$101$	−8.36161	−	14.4827i	−0.832011	−	1.44109i	−0.896441	−	0.443164i	$-0.853856\pi$
$101$	−8.36161	−	14.4827i	−0.832011	−	1.44109i	0.0644295	−	0.997922i	$-0.479477\pi$
$102$	−8.75153	+	3.20637i	−0.866531	+	0.317478i
$103$	16.4479	+	9.49620i	1.62066	+	0.935688i	0.986744	+	0.162287i	$0.0518870\pi$
$103$	16.4479	+	9.49620i	1.62066	+	0.935688i	0.633916	+	0.773402i	$0.281446\pi$
$104$	0.633281	+	1.09687i	0.0620983	+	0.107557i
$105$	0.659304	+	10.2257i	0.0643415	+	0.997928i
$106$	−3.97264	+	6.88082i	−0.385857	+	0.668324i
$107$	−6.00586	+	3.46749i	−0.580608	+	0.335214i	−0.761375	−	0.648312i	$-0.775475\pi$
$107$	−6.00586	+	3.46749i	−0.580608	+	0.335214i	0.180767	+	0.983526i	$0.442142\pi$
$108$	2.56934	−	4.51647i	0.247235	−	0.434597i
$109$	−7.96687	+	13.7990i	−0.763088	+	1.32171i	0.178164	+	0.984001i	$0.442984\pi$
$109$	−7.96687	+	13.7990i	−0.763088	+	1.32171i	−0.941252	+	0.337706i	$0.890349\pi$
$110$	7.62978	+	1.42217i	0.727471	+	0.135598i
$111$	−10.3947	−	1.81010i	−0.986620	−	0.171807i
$112$	−2.63186	−	0.270774i	−0.248687	−	0.0255857i
$113$	−6.92378	+	3.99745i	−0.651335	+	0.376048i	−0.788967	−	0.614435i	$-0.789384\pi$
$113$	−6.92378	+	3.99745i	−0.651335	+	0.376048i	0.137633	+	0.990483i	$0.456051\pi$
$114$	−7.63872	−	1.33018i	−0.715432	−	0.124583i
$115$	3.57078	+	10.1164i	0.332977	+	0.943362i
$116$	−1.04810	+	1.81537i	−0.0973139	+	0.168553i
$117$	2.45474	+	2.90032i	0.226941	+	0.268135i
$118$		−	12.1347i		−	1.11709i
$119$	11.5365	+	8.34307i	1.05755	+	0.764808i
$120$	3.81916	−	0.643436i	0.348640	−	0.0587374i
$121$	−0.523611	+	0.906921i	−0.0476010	+	0.0824474i
$122$			10.6833i			0.967218i
$123$	−1.36019	+	7.81103i	−0.122644	+	0.704297i
$124$	−0.803755			−0.0721793
$125$	5.87093	−	9.51484i	0.525112	−	0.851033i
$126$	−7.91419	+	0.604709i	−0.705052	+	0.0538717i
$127$		−	10.7133i		−	0.950654i	−0.879809	−	0.475327i	$-0.842330\pi$
$127$		−	10.7133i		−	0.950654i	0.879809	−	0.475327i	$-0.157670\pi$
$128$			1.00000i			0.0883883i
$129$	0.668801	+	1.82544i	0.0588846	+	0.160721i
$130$	−0.518960	+	2.78416i	−0.0455158	+	0.244187i
$131$	−0.490580	+	0.849709i	−0.0428621	+	0.0742394i	−0.886661	−	0.462421i	$-0.846981\pi$
$131$	−0.490580	+	0.849709i	−0.0428621	+	0.0742394i	0.843798	+	0.536660i	$0.180314\pi$
$132$	−1.03136	+	5.92267i	−0.0897679	+	0.515502i
$133$	4.84112	+	10.8094i	0.419779	+	0.937290i
$134$	1.64754			0.142326
$135$	10.9316	−	3.93704i	0.940842	−	0.338847i
$136$	2.69057	−	4.66021i	0.230715	−	0.399609i
$137$	11.8149	−	6.82131i	1.00941	−	0.582784i	0.0983925	−	0.995148i	$-0.468630\pi$
$137$	11.8149	−	6.82131i	1.00941	−	0.582784i	0.911019	+	0.412363i	$0.135297\pi$
$138$	−7.80276	+	2.85876i	−0.664215	+	0.243354i
$139$	−9.40894	−	16.2968i	−0.798056	−	1.38227i	−0.920881	−	0.389845i	$-0.872529\pi$
$139$	−9.40894	−	16.2968i	−0.798056	−	1.38227i	0.122825	−	0.992428i	$-0.460805\pi$
$140$	−4.07740	−	4.28659i	−0.344603	−	0.362283i
$141$	10.8252	−	12.9568i	0.911648	−	1.09116i
$142$		−	10.0748i		−	0.845458i
$143$	−3.80715	−	2.19806i	−0.318370	−	0.183811i
$144$	0.533495	+	2.95218i	0.0444579	+	0.246015i
$145$	−4.42000	+	1.56012i	−0.367061	+	0.129561i
$146$	1.89748	−	3.28654i	0.157037	−	0.271996i
$147$	7.52663	+	9.50526i	0.620786	+	0.783980i
$148$	5.27556	−	3.04584i	0.433648	−	0.250367i
$149$	−8.16842	+	14.1481i	−0.669183	+	1.15906i	0.308950	+	0.951078i	$0.400022\pi$
$149$	−8.16842	+	14.1481i	−0.669183	+	1.15906i	−0.978133	+	0.207980i	$0.933311\pi$
$150$	7.42364	+	4.45977i	0.606138	+	0.364139i
$151$	−3.81070	−	6.60033i	−0.310111	−	0.537127i	0.668276	−	0.743914i	$-0.267033\pi$
$151$	−3.81070	−	6.60033i	−0.310111	−	0.537127i	−0.978386	+	0.206787i	$0.933699\pi$
$152$	3.87684	−	2.23829i	0.314453	−	0.181549i
$153$	5.45686	−	15.1932i	0.441161	−	1.22830i
$154$	8.38101	−	3.75356i	0.675361	−	0.302470i
$155$	−1.36545	−	1.16862i	−0.109675	−	0.0938657i
$156$	−2.16123	−	0.376349i	−0.173036	−	0.0301320i
$157$		−	22.9337i		−	1.83031i	−0.403100	−	0.915156i	$-0.632067\pi$
$157$		−	22.9337i		−	1.83031i	0.403100	−	0.915156i	$-0.367933\pi$
$158$			1.59449i			0.126851i
$159$	−4.73422	−	12.9217i	−0.375448	−	1.02476i
$160$	−1.45395	+	1.69883i	−0.114945	+	0.134305i
$161$	10.2858	+	7.43858i	0.810633	+	0.586242i
$162$	3.14995	+	8.43077i	0.247483	+	0.662384i
$163$	1.35549	−	0.782594i	0.106170	−	0.0612975i	−0.445975	−	0.895046i	$-0.647143\pi$
$163$	1.35549	−	0.782594i	0.106170	−	0.0612975i	0.552145	+	0.833748i	$0.313810\pi$
$164$	−2.28878	−	3.96429i	−0.178724	−	0.309559i
$165$	−10.3633	+	8.56209i	−0.806786	+	0.666558i
$166$	5.26565	−	9.12037i	0.408693	−	0.707878i
$167$	5.24110	−	3.02595i	0.405568	−	0.234155i	−0.283315	−	0.959027i	$-0.591434\pi$
$167$	5.24110	−	3.02595i	0.405568	−	0.234155i	0.688884	+	0.724872i	$0.258101\pi$
$168$	3.28264	−	3.19754i	0.253261	−	0.246696i
$169$	−5.69791	+	9.86907i	−0.438301	+	0.759159i
$170$	11.3465	−	4.00496i	0.870239	−	0.307167i
$171$	10.2510	−	8.67612i	0.783914	−	0.663479i
$172$	−0.972049	−	0.561213i	−0.0741180	−	0.0427921i
$173$		−	15.3445i		−	1.16662i	−0.812248	−	0.583312i	$-0.801757\pi$
$173$		−	15.3445i		−	1.16662i	0.812248	−	0.583312i	$-0.198243\pi$
$174$	−1.24903	−	3.40913i	−0.0946888	−	0.258445i
$175$	−0.694347	−	13.2105i	−0.0524877	−	0.998622i
$176$	−1.73546	−	3.00590i	−0.130815	−	0.226578i
$177$	16.1294	+	13.4758i	1.21236	+	1.01291i
$178$	−8.38348	+	4.84020i	−0.628368	+	0.362789i
$179$	4.10439	−	7.10902i	0.306777	−	0.531353i	−0.670879	−	0.741567i	$-0.734083\pi$
$179$	4.10439	−	7.10902i	0.306777	−	0.531353i	0.977655	+	0.210214i	$0.0674162\pi$
$180$	−3.38600	+	5.79094i	−0.252378	+	0.431631i
$181$	8.42895			0.626519			0.313260	−	0.949668i	$-0.398579\pi$
$181$	8.42895			0.626519			0.313260	+	0.949668i	$0.398579\pi$
$182$	1.36970	+	3.05829i	0.101529	+	0.226696i
$183$	−14.2001	−	11.8640i	−1.04970	−	0.877011i
$184$	2.39888	−	4.15498i	0.176848	−	0.306309i
$185$	13.3908	+	2.49600i	0.984511	+	0.183510i
$186$	0.892585	−	1.06834i	0.0654475	−	0.0783348i
$187$			18.6775i			1.36583i
$188$			9.74789i			0.710938i
$189$	7.98508	−	11.1910i	0.580829	−	0.814025i
$190$	9.84046	+	1.83423i	0.713902	+	0.133069i
$191$	2.53681			0.183557			0.0917786	−	0.995779i	$-0.470745\pi$
$191$	2.53681			0.183557			0.0917786	+	0.995779i	$0.470745\pi$
$192$	−1.32919	−	1.11052i	−0.0959261	−	0.0801448i
$193$			25.2581i			1.81812i	0.416668	+	0.909059i	$0.363198\pi$
$193$			25.2581i			1.81812i	−0.416668	+	0.909059i	$0.636802\pi$
$194$	4.32089	−	7.48401i	0.310222	−	0.537321i
$195$	−3.12437	−	3.78166i	−0.223741	−	0.270811i
$196$	−6.85336	−	1.42528i	−0.489526	−	0.101806i
$197$		−	5.46911i		−	0.389658i	−0.980837	−	0.194829i	$-0.937585\pi$
$197$		−	5.46911i		−	0.389658i	0.980837	−	0.194829i	$-0.0624152\pi$
$198$	−6.72701	−	7.94810i	−0.478068	−	0.564847i
$199$	0.308443	−	0.534239i	0.0218649	−	0.0378712i	−0.854886	−	0.518816i	$-0.826373\pi$
$199$	0.308443	−	0.534239i	0.0218649	−	0.0378712i	0.876751	+	0.480945i	$0.159706\pi$
$200$	−4.94003	+	0.772070i	−0.349313	+	0.0545936i
$201$	−1.82963	+	2.18990i	−0.129052	+	0.154464i
$202$	−14.4827	+	8.36161i	−1.01900	+	0.588321i
$203$	−3.25001	+	4.49399i	−0.228106	+	0.315416i
$204$	3.20637	+	8.75153i	0.224491	+	0.612730i
$205$	1.87561	−	10.0624i	0.130998	−	0.702791i
$206$	9.49620	−	16.4479i	0.661632	−	1.14598i
$207$	4.86527	−	13.5461i	0.338160	−	0.941516i
$208$	1.09687	−	0.633281i	0.0760545	−	0.0439101i
$209$	−7.76891	+	13.4562i	−0.537387	+	0.930781i
$210$	10.2257	−	0.659304i	0.705642	−	0.0454963i
$211$	−1.33497	−	2.31223i	−0.0919029	−	0.159180i	0.816409	−	0.577474i	$-0.195962\pi$
$211$	−1.33497	−	2.31223i	−0.0919029	−	0.159180i	−0.908312	+	0.418294i	$0.862628\pi$
$212$	6.88082	+	3.97264i	0.472577	+	0.272842i
$213$	13.3913	+	11.1883i	0.917558	+	0.766606i
$214$	3.46749	+	6.00586i	0.237032	+	0.410552i
$215$	−0.835375	−	2.36672i	−0.0569721	−	0.161409i
$216$	−4.51647	−	2.56934i	−0.307307	−	0.174821i
$217$	−2.11537	−	0.217636i	−0.143601	−	0.0147741i
$218$	13.7990	+	7.96687i	0.934588	+	0.539584i
$219$	2.26124	+	6.17188i	0.152801	+	0.417057i
$220$	1.42217	−	7.62978i	0.0958826	−	0.514400i
$221$	−6.81555			−0.458463
$222$	−1.81010	+	10.3947i	−0.121486	+	0.697646i
$223$	0.443085	+	0.255815i	0.0296712	+	0.0171307i	0.514762	−	0.857333i	$-0.327880\pi$
$223$	0.443085	+	0.255815i	0.0296712	+	0.0171307i	−0.485091	+	0.874464i	$0.661214\pi$
$224$	−0.270774	+	2.63186i	−0.0180919	+	0.175848i
$225$	−14.1720	+	4.91477i	−0.944799	+	0.327652i
$226$	3.99745	+	6.92378i	0.265906	+	0.460563i
$227$	12.0795	−	6.97409i	0.801743	−	0.462887i	−0.0423371	−	0.999103i	$-0.513480\pi$
$227$	12.0795	−	6.97409i	0.801743	−	0.462887i	0.844080	+	0.536217i	$0.180147\pi$
$228$	−1.33018	+	7.63872i	−0.0880935	+	0.505887i
$229$	5.94886	−	10.3037i	0.393111	−	0.680889i	−0.599747	−	0.800190i	$-0.704732\pi$
$229$	5.94886	−	10.3037i	0.393111	−	0.680889i	0.992858	+	0.119301i	$0.0380653\pi$
$230$	10.1164	−	3.57078i	0.667057	−	0.235450i
$231$	−4.31809	+	15.3084i	−0.284109	+	1.00722i
$232$	1.81537	+	1.04810i	0.119185	+	0.0688113i
$233$	−22.7879	+	13.1566i	−1.49288	+	0.861916i	−0.999967	−	0.00816149i	$-0.997402\pi$
$233$	−22.7879	+	13.1566i	−1.49288	+	0.861916i	−0.492915	+	0.870077i	$0.664069\pi$
$234$	2.90032	−	2.45474i	0.189600	−	0.160471i
$235$	−14.1729	+	16.5600i	−0.924539	+	1.08026i
$236$	−12.1347			−0.789904
$237$	−2.11938	−	1.77071i	−0.137668	−	0.115020i
$238$	8.34307	−	11.5365i	0.540801	−	0.747798i
$239$	−5.80430	−	10.0533i	−0.375449	−	0.650297i	0.614945	−	0.788570i	$-0.289178\pi$
$239$	−5.80430	−	10.0533i	−0.375449	−	0.650297i	−0.990394	+	0.138273i	$0.955845\pi$
$240$	−0.643436	−	3.81916i	−0.0415336	−	0.246526i
$241$	−8.91164	−	15.4354i	−0.574049	−	0.994282i	−0.996144	−	0.0877309i	$-0.972038\pi$
$241$	−8.91164	−	15.4354i	−0.574049	−	0.994282i	0.422095	−	0.906552i	$-0.361295\pi$
$242$	0.906921	+	0.523611i	0.0582991	+	0.0336590i
$243$	−14.7042	−	5.17565i	−0.943273	−	0.332018i
$244$	10.6833			0.683927
$245$	−9.57044	−	12.3857i	−0.611433	−	0.791296i
$246$	7.81103	+	1.36019i	0.498013	+	0.0867225i
$247$	−4.91025	−	2.83493i	−0.312432	−	0.180383i
$248$			0.803755i			0.0510385i
$249$	6.27511	+	17.1274i	0.397669	+	1.08540i
$250$	−9.51484	−	5.87093i	−0.601771	−	0.371310i
$251$	−27.6972			−1.74823			−0.874117	−	0.485716i	$-0.838559\pi$
$251$	−27.6972			−1.74823			−0.874117	+	0.485716i	$0.838559\pi$
$252$	0.604709	+	7.91419i	0.0380931	+	0.498547i
$253$			16.6526i			1.04694i
$254$	−10.7133			−0.672214
$255$	−7.27718	+	19.5293i	−0.455715	+	1.22297i
$256$	1.00000			0.0625000
$257$	10.4872	+	6.05481i	0.654176	+	0.377689i	0.790054	−	0.613037i	$-0.210052\pi$
$257$	10.4872	+	6.05481i	0.654176	+	0.377689i	−0.135878	+	0.990726i	$0.543386\pi$
$258$	1.82544	−	0.668801i	0.113647	−	0.0416377i
$259$	14.7093	−	6.58775i	0.913989	−	0.409343i
$260$	2.78416	+	0.518960i	0.172667	+	0.0321845i
$261$	5.91846	+	2.12570i	0.366343	+	0.131578i
$262$	0.849709	+	0.490580i	0.0524952	+	0.0303081i
$263$	16.4181	−	9.47897i	1.01238	−	0.584499i	0.100493	−	0.994938i	$-0.467958\pi$
$263$	16.4181	−	9.47897i	1.01238	−	0.584499i	0.911888	+	0.410439i	$0.134625\pi$
$264$	5.92267	+	1.03136i	0.364515	+	0.0634755i
$265$	5.91335	+	16.7532i	0.363254	+	1.02914i
$266$	10.8094	−	4.84112i	0.662764	−	0.296828i
$267$	2.87646	−	16.5184i	0.176037	−	1.01091i
$268$		−	1.64754i		−	0.100640i
$269$	−14.0626	+	24.3571i	−0.857412	+	1.48508i	0.0169778	+	0.999856i	$0.494596\pi$
$269$	−14.0626	+	24.3571i	−0.857412	+	1.48508i	−0.874389	+	0.485225i	$0.838738\pi$
$270$	−3.93704	−	10.9316i	−0.239601	−	0.665275i
$271$	−5.11495	−	8.85936i	−0.310711	−	0.538168i	0.667805	−	0.744336i	$-0.267234\pi$
$271$	−5.11495	−	8.85936i	−0.310711	−	0.538168i	−0.978517	+	0.206168i	$0.933901\pi$
$272$	−4.66021	−	2.69057i	−0.282567	−	0.163140i
$273$	−5.58613	−	1.57570i	−0.338088	−	0.0953658i
$274$	−6.82131	−	11.8149i	−0.412091	−	0.713762i
$275$	13.5093	−	10.8940i	0.814643	−	0.656931i
$276$	2.85876	+	7.80276i	0.172077	+	0.469671i
$277$	8.21886	−	4.74516i	0.493824	−	0.285109i	−0.232336	−	0.972636i	$-0.574637\pi$
$277$	8.21886	−	4.74516i	0.493824	−	0.285109i	0.726159	+	0.687526i	$0.241303\pi$
$278$	−16.2968	+	9.40894i	−0.977415	+	0.564311i
$279$	0.428799	+	2.37283i	0.0256715	+	0.142058i
$280$	−4.28659	+	4.07740i	−0.256173	+	0.243671i
$281$	−2.73218	+	4.73228i	−0.162988	+	0.282304i	−0.935939	−	0.352162i	$-0.885447\pi$
$281$	−2.73218	+	4.73228i	−0.162988	+	0.282304i	0.772951	+	0.634466i	$0.218780\pi$
$282$	−12.9568	−	10.8252i	−0.771566	−	0.644632i
$283$		−	25.6737i		−	1.52614i	−0.646315	−	0.763071i	$-0.723691\pi$
$283$		−	25.6737i		−	1.52614i	0.646315	−	0.763071i	$-0.276309\pi$
$284$	−10.0748			−0.597829
$285$	−13.3661	+	11.0429i	−0.791737	+	0.654125i
$286$	−2.19806	+	3.80715i	−0.129974	+	0.225122i
$287$	−4.95033	−	11.0532i	−0.292209	−	0.652449i
$288$	2.95218	−	0.533495i	0.173959	−	0.0314365i
$289$	5.97835	+	10.3548i	0.351668	+	0.609107i
$290$	1.56012	+	4.42000i	0.0916134	+	0.259552i
$291$	5.14924	+	14.0544i	0.301854	+	0.823885i
$292$	−3.28654	−	1.89748i	−0.192330	−	0.111042i
$293$	−18.1103	+	10.4560i	−1.05801	+	0.610844i	−0.924882	−	0.380254i	$-0.875836\pi$
$293$	−18.1103	+	10.4560i	−1.05801	+	0.610844i	−0.133131	+	0.991098i	$0.542503\pi$
$294$	9.50526	−	7.52663i	0.554358	−	0.438962i
$295$	−20.6149	−	17.6433i	−1.20024	−	1.02723i
$296$	−3.04584	−	5.27556i	−0.177036	−	0.306636i
$297$	18.0350	−	0.114963i	1.04650	−	0.00667084i
$298$	14.1481	+	8.16842i	0.819578	+	0.473184i
$299$	−6.07666			−0.351422
$300$	4.45977	−	7.42364i	0.257485	−	0.428604i
$301$	−2.40633	−	1.74024i	−0.138699	−	0.100306i
$302$	−6.60033	+	3.81070i	−0.379806	+	0.219281i
$303$	4.96918	−	28.5360i	0.285472	−	1.63935i
$304$	−2.23829	−	3.87684i	−0.128375	−	0.222352i
$305$	18.1491	+	15.5329i	1.03921	+	0.889413i
$306$	−15.1932	−	5.45686i	−0.868537	−	0.311948i
$307$			1.32689i			0.0757295i	0.999283	+	0.0378647i	$0.0120556\pi$
$307$			1.32689i			0.0757295i	−0.999283	+	0.0378647i	$0.987944\pi$
$308$	−3.75356	−	8.38101i	−0.213879	−	0.477553i
$309$	11.3167	+	30.8880i	0.643784	+	1.75716i
$310$	−1.16862	+	1.36545i	−0.0663731	+	0.0775521i
$311$	−22.2201			−1.25998			−0.629992	−	0.776601i	$-0.716942\pi$
$311$	−22.2201			−1.25998			−0.629992	+	0.776601i	$0.716942\pi$
$312$	−0.376349	+	2.16123i	−0.0213066	+	0.122355i
$313$			16.0859i			0.909228i	0.890689	+	0.454614i	$0.150223\pi$
$313$			16.0859i			0.909228i	−0.890689	+	0.454614i	$0.849777\pi$
$314$	−22.9337			−1.29423
$315$	−10.4795	+	14.3241i	−0.590454	+	0.807071i
$316$	1.59449			0.0896970
$317$		−	10.5715i		−	0.593753i	−0.954916	−	0.296876i	$-0.904055\pi$
$317$		−	10.5715i		−	0.593753i	0.954916	−	0.296876i	$-0.0959450\pi$
$318$	−12.9217	+	4.73422i	−0.724612	+	0.265482i
$319$	−7.27575			−0.407364
$320$	1.69883	+	1.45395i	0.0949677	+	0.0812782i
$321$	−11.8336	−	2.06067i	−0.660489	−	0.115016i
$322$	7.43858	−	10.2858i	0.414536	−	0.573204i
$323$			24.0891i			1.34036i
$324$	8.43077	−	3.14995i	0.468376	−	0.174997i
$325$	3.97529	+	4.92966i	0.220509	+	0.273448i
$326$	−0.782594	−	1.35549i	−0.0433439	−	0.0750738i
$327$	−25.9136	+	9.49417i	−1.43302	+	0.525029i
$328$	−3.96429	+	2.28878i	−0.218891	+	0.126377i
$329$	−2.63947	+	25.6551i	−0.145519	+	1.41441i
$330$	8.56209	+	10.3633i	0.471327	+	0.570484i
$331$	−0.764272			−0.0420082			−0.0210041	−	0.999779i	$-0.506686\pi$
$331$	−0.764272			−0.0420082			−0.0210041	+	0.999779i	$0.506686\pi$
$332$	−9.12037	−	5.26565i	−0.500545	−	0.288990i
$333$	−11.8064	−	13.9495i	−0.646985	−	0.764426i
$334$	−3.02595	−	5.24110i	−0.165573	−	0.286780i
$335$	2.39544	−	2.79890i	0.130877	−	0.152920i
$336$	−3.19754	−	3.28264i	−0.174440	−	0.179083i
$337$	−19.0299	+	10.9869i	−1.03662	+	0.598494i	−0.918875	−	0.394549i	$-0.870901\pi$
$337$	−19.0299	+	10.9869i	−1.03662	+	0.598494i	−0.117748	+	0.993044i	$0.537567\pi$
$338$	9.86907	+	5.69791i	0.536807	+	0.309926i
$339$	−13.6423	−	2.37562i	−0.740946	−	0.129026i
$340$	−4.00496	−	11.3465i	−0.217200	−	0.615352i
$341$	−1.39488	−	2.41601i	−0.0755371	−	0.130834i
$342$	−8.67612	−	10.2510i	−0.469151	−	0.554311i
$343$	−17.6512	−	5.60684i	−0.953073	−	0.302741i
$344$	−0.561213	+	0.972049i	−0.0302586	+	0.0524094i
$345$	−6.48824	+	17.4121i	−0.349315	+	0.937435i
$346$	−15.3445			−0.824927
$347$		−	0.172046i		−	0.00923592i	−0.999989	−	0.00461796i	$-0.998530\pi$
$347$		−	0.172046i		−	0.00923592i	0.999989	−	0.00461796i	$-0.00146995\pi$
$348$	−3.40913	+	1.24903i	−0.182749	+	0.0669551i
$349$	8.18168	−	14.1711i	0.437955	−	0.758561i	−0.559576	−	0.828779i	$-0.689036\pi$
$349$	8.18168	−	14.1711i	0.437955	−	0.758561i	0.997532	+	0.0702180i	$0.0223695\pi$
$350$	−13.2105	+	0.694347i	−0.706132	+	0.0371144i
$351$	0.0419509	+	6.58111i	0.00223917	+	0.351274i
$352$	−3.00590	+	1.73546i	−0.160215	+	0.0925001i
$353$	−27.4379	+	15.8413i	−1.46037	+	0.843145i	−0.999028	−	0.0440776i	$-0.985965\pi$
$353$	−27.4379	+	15.8413i	−1.46037	+	0.843145i	−0.461342	+	0.887223i	$0.652632\pi$
$354$	13.4758	−	16.1294i	0.716233	−	0.857266i
$355$	−17.1154	−	14.6482i	−0.908391	−	0.777447i
$356$	4.84020	+	8.38348i	0.256530	+	0.444324i
$357$	6.06903	+	23.9010i	0.321207	+	1.26497i
$358$	−7.10902	−	4.10439i	−0.375723	−	0.216924i
$359$	−2.57635	−	4.46237i	−0.135974	−	0.235515i	0.789995	−	0.613113i	$-0.210083\pi$
$359$	−2.57635	−	4.46237i	−0.135974	−	0.235515i	−0.925969	+	0.377599i	$0.876750\pi$
$360$	5.79094	+	3.38600i	0.305209	+	0.178458i
$361$	−0.519903	+	0.900498i	−0.0273633	+	0.0473946i
$362$		−	8.42895i		−	0.443016i
$363$	−1.70313	+	0.623991i	−0.0893913	+	0.0327510i
$364$	3.05829	−	1.36970i	0.160298	−	0.0717918i
$365$	−2.82444	−	8.00196i	−0.147838	−	0.418842i
$366$	−11.8640	+	14.2001i	−0.620140	+	0.742251i
$367$	10.5050	−	6.06508i	0.548358	−	0.316595i	−0.200101	−	0.979775i	$-0.564127\pi$
$367$	10.5050	−	6.06508i	0.548358	−	0.316595i	0.748460	+	0.663180i	$0.230794\pi$
$368$	−4.15498	−	2.39888i	−0.216593	−	0.125050i
$369$	−10.4823	+	8.87184i	−0.545684	+	0.461849i
$370$	2.49600	−	13.3908i	0.129761	−	0.696154i
$371$	17.0337	+	12.3186i	0.884343	+	0.639549i
$372$	−1.06834	−	0.892585i	−0.0553910	−	0.0462784i
$373$	20.1620	+	11.6405i	1.04395	+	0.602723i	0.920949	−	0.389684i	$-0.127416\pi$
$373$	20.1620	+	11.6405i	1.04395	+	0.602723i	0.122998	+	0.992407i	$0.460749\pi$
$374$	18.6775			0.965789
$375$	18.3700	−	6.12726i	0.948623	−	0.316410i
$376$	9.74789			0.502709
$377$		−	2.65497i		−	0.136738i
$378$	−11.1910	−	7.98508i	−0.575603	−	0.410708i
$379$	21.3552			1.09694			0.548472	−	0.836169i	$-0.315210\pi$
$379$	21.3552			1.09694			0.548472	+	0.836169i	$0.315210\pi$
$380$	1.83423	−	9.84046i	0.0940941	−	0.504805i
$381$	11.8974	−	14.2401i	0.609520	−	0.729540i
$382$		−	2.53681i		−	0.129795i
$383$	−32.8633	−	18.9736i	−1.67923	−	0.969506i	−0.962150	−	0.272520i	$-0.912143\pi$
$383$	−32.8633	−	18.9736i	−1.67923	−	0.969506i	−0.717084	−	0.696986i	$-0.754524\pi$
$384$	−1.11052	+	1.32919i	−0.0566709	+	0.0678300i
$385$	5.80889	−	19.6954i	0.296049	−	1.00377i
$386$	25.2581			1.28560
$387$	−1.13822	+	3.16907i	−0.0578589	+	0.161093i
$388$	−7.48401	−	4.32089i	−0.379943	−	0.219360i
$389$	−5.45474	−	9.44789i	−0.276566	−	0.479027i	0.693963	−	0.720011i	$-0.255863\pi$
$389$	−5.45474	−	9.44789i	−0.276566	−	0.479027i	−0.970529	+	0.240984i	$0.922530\pi$
$390$	−3.78166	+	3.12437i	−0.191492	+	0.158209i
$391$	12.9087	+	22.3586i	0.652822	+	1.13072i
$392$	−1.42528	+	6.85336i	−0.0719874	+	0.346147i
$393$	−1.59569	+	0.584627i	−0.0804920	+	0.0294905i
$394$	−5.46911			−0.275530
$395$	2.70877	+	2.31830i	0.136293	+	0.116646i
$396$	−7.94810	+	6.72701i	−0.399407	+	0.338045i
$397$	13.6408	−	7.87551i	0.684611	−	0.395260i	−0.116979	−	0.993134i	$-0.537321\pi$
$397$	13.6408	−	7.87551i	0.684611	−	0.395260i	0.801590	+	0.597874i	$0.203988\pi$
$398$	−0.534239	−	0.308443i	−0.0267790	−	0.0154609i
$399$	−5.56922	+	19.7439i	−0.278810	+	0.988429i
$400$	0.772070	+	4.94003i	0.0386035	+	0.247002i
$401$	10.0216	−	17.3580i	0.500456	−	0.866816i	−0.499543	−	0.866289i	$-0.666499\pi$
$401$	10.0216	−	17.3580i	0.500456	−	0.866816i	1.00000		0.000527125i	$-0.000167789\pi$
$402$	2.18990	+	1.82963i	0.109222	+	0.0912535i
$403$	0.881618	−	0.509003i	0.0439165	−	0.0253552i
$404$	8.36161	+	14.4827i	0.416006	+	0.720543i
$405$	18.9023	+	6.90666i	0.939264	+	0.343195i
$406$	4.49399	+	3.25001i	0.223033	+	0.161296i
$407$	18.3110	+	10.5719i	0.907642	+	0.524027i
$408$	8.75153	−	3.20637i	0.433265	−	0.158739i
$409$	−5.88551			−0.291020			−0.145510	−	0.989357i	$-0.546482\pi$
$409$	−5.88551			−0.291020			−0.145510	+	0.989357i	$0.546482\pi$
$410$	−10.0624	−	1.87561i	−0.496949	−	0.0926297i
$411$	23.2794	+	4.05380i	1.14829	+	0.199959i
$412$	−16.4479	−	9.49620i	−0.810330	−	0.467844i
$413$	−31.9369	−	3.28577i	−1.57151	−	0.161682i
$414$	−13.5461	−	4.86527i	−0.665752	−	0.239115i
$415$	−7.83801	−	22.2060i	−0.384753	−	1.09005i
$416$	−0.633281	−	1.09687i	−0.0310491	−	0.0537787i
$417$	5.59159	−	32.1103i	0.273821	−	1.57245i
$418$	13.4562	+	7.76891i	0.658162	+	0.379990i
$419$	−7.67105	−	13.2867i	−0.374755	−	0.649096i	0.615535	−	0.788110i	$-0.288940\pi$
$419$	−7.67105	−	13.2867i	−0.374755	−	0.649096i	−0.990290	+	0.139014i	$0.955607\pi$
$420$	−0.659304	−	10.2257i	−0.0321707	−	0.498964i
$421$	12.8961	−	22.3367i	0.628518	−	1.08862i	−0.359332	−	0.933210i	$-0.616995\pi$
$421$	12.8961	−	22.3367i	0.628518	−	1.08862i	0.987849	−	0.155415i	$-0.0496713\pi$
$422$	−2.31223	+	1.33497i	−0.112558	+	0.0649851i
$423$	28.7775	−	5.20045i	1.39921	−	0.252854i
$424$	3.97264	−	6.88082i	0.192929	−	0.334162i
$425$	9.69350	−	25.0989i	0.470204	−	1.21747i
$426$	11.1883	−	13.3913i	0.542072	−	0.648812i
$427$	28.1169	+	2.89275i	1.36067	+	0.139990i
$428$	6.00586	−	3.46749i	0.290304	−	0.167607i
$429$	−2.61944	−	7.14956i	−0.126468	−	0.345184i
$430$	−2.36672	+	0.835375i	−0.114133	+	0.0402854i
$431$	−11.7207	+	20.3008i	−0.564565	+	0.977855i	0.432525	+	0.901622i	$0.357623\pi$
$431$	−11.7207	+	20.3008i	−0.564565	+	0.977855i	−0.997090	+	0.0762332i	$0.975711\pi$
$432$	−2.56934	+	4.51647i	−0.123617	+	0.217299i
$433$		−	15.3466i		−	0.737511i	−0.929526	−	0.368755i	$-0.879784\pi$
$433$		−	15.3466i		−	0.737511i	0.929526	−	0.368755i	$-0.120216\pi$
$434$	−0.217636	+	2.11537i	−0.0104469	+	0.101541i
$435$	−7.60757	−	2.83480i	−0.364755	−	0.135918i
$436$	7.96687	−	13.7990i	0.381544	−	0.660853i
$437$			21.4776i			1.02741i
$438$	6.17188	−	2.26124i	0.294904	−	0.108046i
$439$	8.42369			0.402041			0.201020	−	0.979587i	$-0.435574\pi$
$439$	8.42369			0.402041			0.201020	+	0.979587i	$0.435574\pi$
$440$	−7.62978	−	1.42217i	−0.363736	−	0.0677992i
$441$	−0.551448	+	20.9928i	−0.0262594	+	0.999655i
$442$			6.81555i			0.324183i
$443$			34.9512i			1.66058i	0.557329	+	0.830291i	$0.311826\pi$
$443$			34.9512i			1.66058i	−0.557329	+	0.830291i	$0.688174\pi$
$444$	10.3947	+	1.81010i	0.493310	+	0.0859035i
$445$	−3.96644	+	21.2795i	−0.188027	+	1.00875i
$446$	0.255815	−	0.443085i	0.0121132	−	0.0209807i
$447$	−26.5691	+	9.73435i	−1.25668	+	0.460419i
$448$	2.63186	+	0.270774i	0.124344	+	0.0127929i
$449$	−6.45132			−0.304457			−0.152228	−	0.988345i	$-0.548645\pi$
$449$	−6.45132			−0.304457			−0.152228	+	0.988345i	$0.548645\pi$
$450$	4.91477	+	14.1720i	0.231685	+	0.668074i
$451$	7.94417	−	13.7597i	0.374076	−	0.647919i
$452$	6.92378	−	3.99745i	0.325667	−	0.188024i
$453$	2.26464	−	13.0050i	0.106402	−	0.611026i
$454$	−6.97409	−	12.0795i	−0.327310	−	0.566918i
$455$	7.18701	+	2.11971i	0.336932	+	0.0993735i
$456$	7.63872	+	1.33018i	0.357716	+	0.0622915i
$457$		−	8.44609i		−	0.395092i	−0.980294	−	0.197546i	$-0.936703\pi$
$457$		−	8.44609i		−	0.395092i	0.980294	−	0.197546i	$-0.0632971\pi$
$458$	−10.3037	−	5.94886i	−0.481461	−	0.277972i
$459$	24.1255	−	14.1347i	1.12608	−	0.659751i
$460$	−3.57078	−	10.1164i	−0.166488	−	0.471681i
$461$	−2.44623	+	4.23699i	−0.113932	+	0.197336i	−0.917352	−	0.398076i	$-0.869678\pi$
$461$	−2.44623	+	4.23699i	−0.113932	+	0.197336i	0.803420	+	0.595412i	$0.203011\pi$
$462$	15.3084	+	4.31809i	0.712209	+	0.200896i
$463$	1.94441	−	1.12261i	0.0903645	−	0.0521720i	−0.454137	−	0.890932i	$-0.650052\pi$
$463$	1.94441	−	1.12261i	0.0903645	−	0.0521720i	0.544501	+	0.838760i	$0.316719\pi$
$464$	1.04810	−	1.81537i	0.0486570	−	0.0842763i
$465$	−0.517165	−	3.06967i	−0.0239830	−	0.142353i
$466$	13.1566	+	22.7879i	0.609467	+	1.05563i
$467$	17.4863	−	10.0957i	0.809169	−	0.467174i	−0.0374982	−	0.999297i	$-0.511939\pi$
$467$	17.4863	−	10.0957i	0.809169	−	0.467174i	0.846667	+	0.532123i	$0.178606\pi$
$468$	−2.45474	−	2.90032i	−0.113470	−	0.134067i
$469$	0.446112	−	4.33610i	0.0205995	−	0.200223i
$470$	16.5600	+	14.1729i	0.763858	+	0.653748i
$471$	25.4684	−	30.4833i	1.17352	−	1.40460i
$472$			12.1347i			0.558546i
$473$		−	3.89584i		−	0.179131i
$474$	−1.77071	+	2.11938i	−0.0813314	+	0.0973463i
$475$	17.4236	−	14.0504i	0.799448	−	0.644678i
$476$	−11.5365	−	8.34307i	−0.528773	−	0.382404i
$477$	8.05708	−	22.4328i	0.368909	−	1.02713i
$478$	−10.0533	+	5.80430i	−0.459829	+	0.265483i
$479$	3.06078	+	5.30143i	0.139851	+	0.242229i	0.927440	−	0.373972i	$-0.122004\pi$
$479$	3.06078	+	5.30143i	0.139851	+	0.242229i	−0.787589	+	0.616201i	$0.788671\pi$
$480$	−3.81916	+	0.643436i	−0.174320	+	0.0293687i
$481$	−3.85775	+	6.68182i	−0.175898	+	0.304665i
$482$	−15.4354	+	8.91164i	−0.703064	+	0.405914i
$483$	5.41107	+	21.3098i	0.246212	+	0.969631i
$484$	0.523611	−	0.906921i	0.0238005	−	0.0412237i
$485$	−6.43173	−	18.2218i	−0.292050	−	0.827411i
$486$	−5.17565	+	14.7042i	−0.234772	+	0.666995i
$487$	−6.81398	−	3.93405i	−0.308771	−	0.178269i	0.337605	−	0.941288i	$-0.390383\pi$
$487$	−6.81398	−	3.93405i	−0.308771	−	0.178269i	−0.646376	+	0.763019i	$0.723716\pi$
$488$		−	10.6833i		−	0.483609i
$489$	2.67079	+	0.465084i	0.120777	+	0.0210318i
$490$	−12.3857	+	9.57044i	−0.559531	+	0.432348i
$491$	−2.26524	−	3.92352i	−0.102229	−	0.177066i	0.810374	−	0.585913i	$-0.199264\pi$
$491$	−2.26524	−	3.92352i	−0.102229	−	0.177066i	−0.912603	+	0.408848i	$0.865931\pi$
$492$	1.36019	−	7.81103i	0.0613221	−	0.352149i
$493$	−9.76876	+	5.63999i	−0.439963	+	0.254013i
$494$	−2.83493	+	4.91025i	−0.127550	+	0.220923i
$495$	−23.2832	−	0.128053i	−1.04650	−	0.00575554i
$496$	0.803755			0.0360897
$497$	−26.5154	−	2.72799i	−1.18938	−	0.122367i
$498$	17.1274	−	6.27511i	0.767497	−	0.281194i
$499$	−15.4231	+	26.7136i	−0.690432	+	1.19586i	0.281264	+	0.959630i	$0.409246\pi$
$499$	−15.4231	+	26.7136i	−0.690432	+	1.19586i	−0.971696	+	0.236233i	$0.924087\pi$
$500$	−5.87093	+	9.51484i	−0.262556	+	0.425517i
$501$	10.3268	+	1.79828i	0.461367	+	0.0803410i
$502$			27.6972i			1.23619i
$503$			13.8010i			0.615357i	0.951490	+	0.307678i	$0.0995521\pi$
$503$			13.8010i			0.615357i	−0.951490	+	0.307678i	$0.900448\pi$
$504$	7.91419	−	0.604709i	0.352526	−	0.0269359i
$505$	−6.85216	+	36.7611i	−0.304917	+	1.63585i
$506$	16.6526			0.740298
$507$	−18.5334	+	6.79024i	−0.823097	+	0.301565i
$508$			10.7133i			0.475327i
$509$	13.2412	−	22.9345i	0.586907	−	1.01655i	−0.407727	−	0.913104i	$-0.633679\pi$
$509$	13.2412	−	22.9345i	0.586907	−	1.01655i	0.994635	−	0.103450i	$-0.0329881\pi$
$510$	19.5293	+	7.27718i	0.864772	+	0.322239i
$511$	−8.13591	−	5.88381i	−0.359911	−	0.260285i
$512$		−	1.00000i		−	0.0441942i
$513$	23.2605	−	0.148273i	1.02698	−	0.00654641i
$514$	6.05481	−	10.4872i	0.267066	−	0.462573i
$515$	−14.1353	−	40.0469i	−0.622874	−	1.76468i
$516$	−0.668801	−	1.82544i	−0.0294423	−	0.0803604i
$517$	−29.3011	+	16.9170i	−1.28866	+	0.744010i
$518$	−6.58775	−	14.7093i	−0.289449	−	0.646288i
$519$	17.0404	−	20.3958i	0.747990	−	0.895277i
$520$	0.518960	−	2.78416i	0.0227579	−	0.122094i
$521$	−19.1388	+	33.1494i	−0.838486	+	1.45230i	0.0526739	+	0.998612i	$0.483226\pi$
$521$	−19.1388	+	33.1494i	−0.838486	+	1.45230i	−0.891160	+	0.453689i	$0.850108\pi$
$522$	2.12570	−	5.91846i	0.0930395	−	0.259044i
$523$	27.4538	−	15.8505i	1.20047	−	0.693093i	0.239812	−	0.970819i	$-0.422914\pi$
$523$	27.4538	−	15.8505i	1.20047	−	0.693093i	0.960660	+	0.277727i	$0.0895810\pi$
$524$	0.490580	−	0.849709i	0.0214311	−	0.0371197i
$525$	13.7476	−	18.3304i	0.599995	−	0.800004i
$526$	−9.47897	−	16.4181i	−0.413303	−	0.715862i
$527$	−3.74567	−	2.16256i	−0.163164	−	0.0942026i
$528$	1.03136	−	5.92267i	0.0448840	−	0.257751i
$529$	0.00925444	+	0.0160292i	0.000402367	+	0.000696920i
$530$	16.7532	−	5.91335i	0.727713	−	0.256859i
$531$	6.47382	+	35.8239i	0.280940	+	1.55463i
$532$	−4.84112	−	10.8094i	−0.209889	−	0.468645i
$533$	5.02102	+	2.89888i	0.217484	+	0.125565i
$534$	−16.5184	−	2.87646i	−0.714820	−	0.124477i
$535$	15.2445	+	2.84153i	0.659077	+	0.122850i
$536$	−1.64754			−0.0711630
$537$	13.3502	−	4.89123i	0.576105	−	0.211072i
$538$	24.3571	+	14.0626i	1.05011	+	0.606282i
$539$	−7.60947	−	23.0740i	−0.327763	−	0.993868i
$540$	−10.9316	+	3.93704i	−0.470421	+	0.169423i
$541$	11.9014	+	20.6137i	0.511679	+	0.886254i	0.999908	+	0.0135387i	$0.00430964\pi$
$541$	11.9014	+	20.6137i	0.511679	+	0.886254i	−0.488229	+	0.872715i	$0.662357\pi$
$542$	−8.85936	+	5.11495i	−0.380542	+	0.219706i
$543$	11.2037	+	9.36051i	0.480796	+	0.401698i
$544$	−2.69057	+	4.66021i	−0.115357	+	0.199805i
$545$	33.5974	−	11.8588i	1.43916	−	0.507976i
$546$	−1.57570	+	5.58613i	−0.0674338	+	0.239064i
$547$	−35.3481	−	20.4082i	−1.51137	−	0.872593i	−0.999912	−	0.0132874i	$-0.995770\pi$
$547$	−35.3481	−	20.4082i	−1.51137	−	0.872593i	−0.511463	−	0.859305i	$-0.670896\pi$
$548$	−11.8149	+	6.82131i	−0.504706	+	0.291392i
$549$	−5.69947	−	31.5390i	−0.243247	−	1.34605i
$550$	−10.8940	−	13.5093i	−0.464520	−	0.576040i
$551$	−9.38384			−0.399765
$552$	7.80276	−	2.85876i	0.332107	−	0.121677i
$553$	4.19647	+	0.431746i	0.178452	+	0.0183597i
$554$	−4.74516	−	8.21886i	−0.201603	−	0.349186i
$555$	15.0271	+	18.1884i	0.637863	+	0.772054i
$556$	9.40894	+	16.2968i	0.399028	+	0.691137i
$557$	−33.1268	−	19.1258i	−1.40363	−	0.810384i	−0.408864	−	0.912595i	$-0.634075\pi$
$557$	−33.1268	−	19.1258i	−1.40363	−	0.810384i	−0.994763	+	0.102211i	$0.967408\pi$
$558$	2.37283	−	0.428799i	0.100450	−	0.0181525i
$559$	1.42162			0.0601281
$560$	4.07740	+	4.28659i	0.172302	+	0.181141i
$561$	−20.7417	+	24.8259i	−0.875715	+	1.04815i
$562$	4.73228	+	2.73218i	0.199619	+	0.115250i
$563$		−	17.9127i		−	0.754930i	−0.926024	−	0.377465i	$-0.876796\pi$
$563$		−	17.9127i		−	0.754930i	0.926024	−	0.377465i	$-0.123204\pi$
$564$	−10.8252	+	12.9568i	−0.455824	+	0.545580i
$565$	17.5744	+	3.27582i	0.739362	+	0.137815i
$566$	−25.6737			−1.07914
$567$	23.0415	−	6.00739i	0.967653	−	0.252287i
$568$			10.0748i			0.422729i
$569$	−25.2417			−1.05819			−0.529094	−	0.848563i	$-0.677468\pi$
$569$	−25.2417			−1.05819			−0.529094	+	0.848563i	$0.677468\pi$
$570$	11.0429	+	13.3661i	0.462536	+	0.559843i
$571$	10.1448			0.424545			0.212272	−	0.977211i	$-0.431914\pi$
$571$	10.1448			0.424545			0.212272	+	0.977211i	$0.431914\pi$
$572$	3.80715	+	2.19806i	0.159185	+	0.0919055i
$573$	3.37190	+	2.81718i	0.140863	+	0.117689i
$574$	−11.0532	+	4.95033i	−0.461351	+	0.206623i
$575$	8.64261	−	22.3778i	0.360422	−	0.933221i
$576$	−0.533495	−	2.95218i	−0.0222290	−	0.123008i
$577$	12.4685	+	7.19867i	0.519069	+	0.299685i	0.736554	−	0.676379i	$-0.236452\pi$
$577$	12.4685	+	7.19867i	0.519069	+	0.299685i	−0.217485	+	0.976064i	$0.569785\pi$
$578$	10.3548	−	5.97835i	0.430703	−	0.248667i
$579$	−28.0496	+	33.5728i	−1.16570	+	1.39524i
$580$	4.42000	−	1.56012i	0.183531	−	0.0647805i
$581$	−22.5777	−	16.3280i	−0.936682	−	0.677400i
$582$	14.0544	−	5.14924i	0.582575	−	0.213443i
$583$			27.5774i			1.14214i
$584$	−1.89748	+	3.28654i	−0.0785184	+	0.135998i
$585$	0.0467274	−	8.49622i	0.00193194	−	0.351276i
$586$	10.4560	+	18.1103i	0.431932	+	0.748128i
$587$	13.2170	+	7.63087i	0.545526	+	0.314960i	0.747316	−	0.664469i	$-0.231342\pi$
$587$	13.2170	+	7.63087i	0.545526	+	0.314960i	−0.201790	+	0.979429i	$0.564676\pi$
$588$	−7.52663	−	9.50526i	−0.310393	−	0.391990i
$589$	−1.79904	−	3.11603i	−0.0741281	−	0.128394i
$590$	−17.6433	+	20.6149i	−0.726362	+	0.848701i
$591$	6.07355	−	7.26949i	0.249833	−	0.299027i
$592$	−5.27556	+	3.04584i	−0.216824	+	0.125183i
$593$	24.0106	−	13.8625i	0.985996	−	0.569265i	0.0819210	−	0.996639i	$-0.473894\pi$
$593$	24.0106	−	13.8625i	0.985996	−	0.569265i	0.904075	+	0.427374i	$0.140561\pi$
$594$	−0.114963	−	18.0350i	−0.00471699	−	0.739986i
$595$	−7.46815	−	30.9469i	−0.306164	−	1.26870i
$596$	8.16842	−	14.1481i	0.334591	−	0.579529i
$597$	1.00326	−	0.367574i	0.0410608	−	0.0150438i
$598$			6.07666i			0.248493i
$599$	15.7443			0.643295			0.321648	−	0.946859i	$-0.395763\pi$
$599$	15.7443			0.643295			0.321648	+	0.946859i	$0.395763\pi$
$600$	−7.42364	−	4.45977i	−0.303069	−	0.182069i
$601$	9.82777	−	17.0222i	0.400883	−	0.694350i	−0.592950	−	0.805239i	$-0.702037\pi$
$601$	9.82777	−	17.0222i	0.400883	−	0.694350i	0.993833	+	0.110890i	$0.0353701\pi$
$602$	−1.74024	+	2.40633i	−0.0709268	+	0.0980748i
$603$	−4.86385	+	0.878956i	−0.198071	+	0.0357938i
$604$	3.81070	+	6.60033i	0.155055	+	0.268564i
$605$	2.20815	−	0.779405i	0.0897739	−	0.0316873i
$606$	−28.5360	−	4.96918i	−1.15920	−	0.201859i
$607$	26.4012	+	15.2428i	1.07159	+	0.618684i	0.928616	−	0.371042i	$-0.120999\pi$
$607$	26.4012	+	15.2428i	1.07159	+	0.618684i	0.142976	+	0.989726i	$0.454333\pi$
$608$	−3.87684	+	2.23829i	−0.157226	+	0.0907747i
$609$	−9.31055	+	2.36417i	−0.377283	+	0.0958010i
$610$	15.5329	−	18.1491i	0.628910	−	0.734836i
$611$	−6.17315	−	10.6922i	−0.249739	−	0.432560i
$612$	−5.45686	+	15.1932i	−0.220581	+	0.614148i
$613$	−16.0145	−	9.24599i	−0.646821	−	0.373442i	0.140416	−	0.990093i	$-0.455156\pi$
$613$	−16.0145	−	9.24599i	−0.646821	−	0.373442i	−0.787237	+	0.616650i	$0.788489\pi$
$614$	1.32689			0.0535488
$615$	13.6676	−	11.2920i	0.551130	−	0.455337i
$616$	−8.38101	+	3.75356i	−0.337681	+	0.151235i
$617$	23.0855	−	13.3284i	0.929386	−	0.536582i	0.0427690	−	0.999085i	$-0.486382\pi$
$617$	23.0855	−	13.3284i	0.929386	−	0.536582i	0.886617	+	0.462503i	$0.153049\pi$
$618$	30.8880	−	11.3167i	1.24250	−	0.455224i
$619$	8.89728	+	15.4105i	0.357612	+	0.619402i	0.987561	−	0.157234i	$-0.0502578\pi$
$619$	8.89728	+	15.4105i	0.357612	+	0.619402i	−0.629950	+	0.776636i	$0.716924\pi$
$620$	1.36545	+	1.16862i	0.0548376	+	0.0469328i
$621$	21.5100	−	12.6023i	0.863168	−	0.505714i
$622$			22.2201i			0.890944i
$623$	10.4687	+	23.3747i	0.419420	+	0.936489i
$624$	2.16123	+	0.376349i	0.0865182	+	0.0150660i
$625$	−23.8078	+	7.62810i	−0.952313	+	0.305124i
$626$	16.0859			0.642921
$627$	−25.2697	+	9.25826i	−1.00917	+	0.369739i
$628$			22.9337i			0.915156i
$629$	32.7803			1.30703
$630$	14.3241	+	10.4795i	0.570686	+	0.417514i
$631$	−47.9581			−1.90918			−0.954592	−	0.297917i	$-0.903708\pi$
$631$	−47.9581			−1.90918			−0.954592	+	0.297917i	$0.903708\pi$
$632$		−	1.59449i		−	0.0634253i
$633$	0.793350	−	4.55590i	0.0315328	−	0.181081i
$634$	−10.5715			−0.419847
$635$	−15.5766	+	18.2002i	−0.618139	+	0.722251i
$636$	4.73422	+	12.9217i	0.187724	+	0.512378i
$637$	8.41988	−	2.77675i	0.333608	−	0.110019i
$638$			7.27575i			0.288050i
$639$	5.37485	+	29.7426i	0.212626	+	1.17660i
$640$	1.45395	−	1.69883i	0.0574723	−	0.0671523i
$641$	22.8076	+	39.5039i	0.900847	+	1.56031i	0.826398	+	0.563087i	$0.190386\pi$
$641$	22.8076	+	39.5039i	0.900847	+	1.56031i	0.0744490	+	0.997225i	$0.476280\pi$
$642$	−2.06067	+	11.8336i	−0.0813283	+	0.467037i
$643$	26.8259	−	15.4880i	1.05791	−	0.610786i	0.133058	−	0.991108i	$-0.457520\pi$
$643$	26.8259	−	15.4880i	1.05791	−	0.610786i	0.924854	+	0.380323i	$0.124187\pi$
$644$	−10.2858	−	7.43858i	−0.405316	−	0.293121i
$645$	1.51791	−	4.07352i	0.0597676	−	0.160394i
$646$	24.0891			0.947775
$647$	−20.4304	−	11.7955i	−0.803203	−	0.463729i	0.0413872	−	0.999143i	$-0.486822\pi$
$647$	−20.4304	−	11.7955i	−0.803203	−	0.463729i	−0.844590	+	0.535414i	$0.820156\pi$
$648$	−3.14995	−	8.43077i	−0.123742	−	0.331192i
$649$	−21.0593	−	36.4757i	−0.826649	−	1.43180i
$650$	4.92966	−	3.97529i	0.193357	−	0.155924i
$651$	−2.57004	−	2.63844i	−0.100728	−	0.103409i
$652$	−1.35549	+	0.782594i	−0.0530852	+	0.0306487i
$653$	35.6266	+	20.5690i	1.39418	+	0.804929i	0.993775	−	0.111410i	$-0.0355367\pi$
$653$	35.6266	+	20.5690i	1.39418	+	0.804929i	0.400403	+	0.916339i	$0.368870\pi$
$654$	9.49417	+	25.9136i	0.371251	+	1.01330i
$655$	2.06885	−	0.730237i	0.0808365	−	0.0285327i
$656$	2.28878	+	3.96429i	0.0893620	+	0.154780i
$657$	−3.84837	+	10.7148i	−0.150139	+	0.418022i
$658$	25.6551	+	2.63947i	1.00014	+	0.102897i
$659$	3.78262	−	6.55169i	0.147350	−	0.255218i	−0.782897	−	0.622151i	$-0.786259\pi$
$659$	3.78262	−	6.55169i	0.147350	−	0.255218i	0.930247	+	0.366933i	$0.119592\pi$
$660$	10.3633	−	8.56209i	0.403393	−	0.333279i
$661$	31.6888			1.23255			0.616275	−	0.787531i	$-0.288641\pi$
$661$	31.6888			1.23255			0.616275	+	0.787531i	$0.288641\pi$
$662$			0.764272i			0.0297043i
$663$	−9.05916	−	7.56880i	−0.351829	−	0.293948i
$664$	−5.26565	+	9.12037i	−0.204347	+	0.353939i
$665$	7.49198	−	25.4020i	0.290527	−	0.985049i
$666$	−13.9495	+	11.8064i	−0.540531	+	0.457488i
$667$	−8.70970	+	5.02855i	−0.337241	+	0.194706i
$668$	−5.24110	+	3.02595i	−0.202784	+	0.117077i
$669$	0.304857	+	0.832081i	0.0117864	+	0.0321701i
$670$	−2.79890	−	2.39544i	−0.108131	−	0.0925440i
$671$	18.5403	+	32.1128i	0.715742	+	1.23970i
$672$	−3.28264	+	3.19754i	−0.126631	+	0.123348i
$673$	−25.5771	−	14.7669i	−0.985924	−	0.569223i	−0.0818702	−	0.996643i	$-0.526089\pi$
$673$	−25.5771	−	14.7669i	−0.985924	−	0.569223i	−0.904053	+	0.427420i	$0.859423\pi$
$674$	10.9869	+	19.0299i	0.423199	+	0.733003i
$675$	−24.2952	−	9.20558i	−0.935123	−	0.354323i
$676$	5.69791	−	9.86907i	0.219150	−	0.379580i
$677$		−	9.95446i		−	0.382581i	−0.981533	−	0.191290i	$-0.938733\pi$
$677$		−	9.95446i		−	0.382581i	0.981533	−	0.191290i	$-0.0612672\pi$
$678$	−2.37562	+	13.6423i	−0.0912352	+	0.523928i
$679$	−18.5269	−	13.3985i	−0.710996	−	0.514186i
$680$	−11.3465	+	4.00496i	−0.435120	+	0.153583i
$681$	23.8008	+	4.14460i	0.912048	+	0.158821i
$682$	−2.41601	+	1.39488i	−0.0925136	+	0.0534128i
$683$	19.6627	+	11.3523i	0.752372	+	0.434382i	0.826550	−	0.562863i	$-0.190300\pi$
$683$	19.6627	+	11.3523i	0.752372	+	0.434382i	−0.0741781	+	0.997245i	$0.523633\pi$
$684$	−10.2510	+	8.67612i	−0.391957	+	0.331740i
$685$	−29.9893	−	5.58992i	−1.14583	−	0.213580i
$686$	−5.60684	+	17.6512i	−0.214070	+	0.673924i
$687$	19.3496	−	7.08929i	0.738235	−	0.270473i
$688$	0.972049	+	0.561213i	0.0370590	+	0.0213960i
$689$	−10.0632			−0.383377
$690$	17.4121	+	6.48824i	0.662866	+	0.247003i
$691$	40.1065			1.52572			0.762861	−	0.646562i	$-0.223794\pi$
$691$	40.1065			1.52572			0.762861	+	0.646562i	$0.223794\pi$
$692$			15.3445i			0.583312i
$693$	−22.7398	+	15.5524i	−0.863813	+	0.590787i
$694$	−0.172046			−0.00653079
$695$	−7.71042	+	41.3656i	−0.292473	+	1.56909i
$696$	1.24903	+	3.40913i	0.0473444	+	0.129223i
$697$		−	24.6326i		−	0.933024i
$698$	−14.1711	−	8.18168i	−0.536383	−	0.309681i
$699$	−44.9000	−	7.81875i	−1.69827	−	0.295732i
$700$	0.694347	+	13.2105i	0.0262439	+	0.499311i
$701$	11.4107			0.430976			0.215488	−	0.976507i	$-0.430866\pi$
$701$	11.4107			0.430976			0.215488	+	0.976507i	$0.430866\pi$
$702$	6.58111	−	0.0419509i	0.248388	−	0.00158333i
$703$	23.6165	+	13.6350i	0.890712	+	0.514253i
$704$	1.73546	+	3.00590i	0.0654074	+	0.113289i
$705$	−37.2287	+	6.27214i	−1.40212	+	0.236223i
$706$	15.8413	+	27.4379i	0.596194	+	1.03264i
$707$	18.0850	+	40.3806i	0.680158	+	1.51867i
$708$	−16.1294	−	13.4758i	−0.606179	−	0.506453i
$709$	−9.72088			−0.365075			−0.182538	−	0.983199i	$-0.558431\pi$
$709$	−9.72088			−0.365075			−0.182538	+	0.983199i	$0.558431\pi$
$710$	−14.6482	+	17.1154i	−0.549738	+	0.642329i
$711$	−0.850651	−	4.70722i	−0.0319019	−	0.176535i
$712$	8.38348	−	4.84020i	0.314184	−	0.181394i
$713$	−3.33959	−	1.92811i	−0.125069	−	0.0722084i
$714$	23.9010	−	6.06903i	0.894472	−	0.227128i
$715$	3.27185	+	9.26954i	0.122360	+	0.346661i
$716$	−4.10439	+	7.10902i	−0.153388	+	0.265676i
$717$	3.44941	−	19.8086i	0.128821	−	0.739766i
$718$	−4.46237	+	2.57635i	−0.166534	+	0.0961485i
$719$	5.60867	+	9.71450i	0.209168	+	0.362290i	0.951453	−	0.307795i	$-0.0995911\pi$
$719$	5.60867	+	9.71450i	0.209168	+	0.362290i	−0.742285	+	0.670085i	$0.766258\pi$
$720$	3.38600	−	5.79094i	0.126189	−	0.215816i
$721$	−40.7172	−	29.4463i	−1.51639	−	1.09664i
$722$	0.900498	+	0.519903i	0.0335131	+	0.0193488i
$723$	5.29605	−	30.4132i	0.196962	−	1.13108i
$724$	−8.42895			−0.313260
$725$	9.77718	+	3.77607i	0.363115	+	0.140240i
$726$	0.623991	+	1.70313i	0.0231585	+	0.0632092i
$727$	−33.4268	−	19.2990i	−1.23973	−	0.715760i	−0.270693	−	0.962666i	$-0.587253\pi$
$727$	−33.4268	−	19.2990i	−1.23973	−	0.715760i	−0.969039	+	0.246906i	$0.920586\pi$
$728$	−1.36970	−	3.05829i	−0.0507645	−	0.113348i
$729$	−13.7970	−	23.2087i	−0.511000	−	0.859581i
$730$	−8.00196	+	2.82444i	−0.296166	+	0.104537i
$731$	−3.01997	−	5.23073i	−0.111697	−	0.193466i
$732$	14.2001	+	11.8640i	0.524851	+	0.438505i
$733$	26.7479	+	15.4429i	0.987957	+	0.570397i	0.904663	−	0.426128i	$-0.140123\pi$
$733$	26.7479	+	15.4429i	0.987957	+	0.570397i	0.0832939	+	0.996525i	$0.473456\pi$
$734$	−6.06508	−	10.5050i	−0.223866	−	0.387748i
$735$	1.03366	−	27.0912i	0.0381273	−	0.999273i
$736$	−2.39888	+	4.15498i	−0.0884239	+	0.153155i
$737$	4.95234	−	2.85924i	0.182422	−	0.105321i
$738$	8.87184	+	10.4823i	0.326577	+	0.385857i
$739$	23.3669	−	40.4726i	0.859564	−	1.48881i	−0.0127823	−	0.999918i	$-0.504069\pi$
$739$	23.3669	−	40.4726i	0.859564	−	1.48881i	0.872346	−	0.488889i	$-0.162598\pi$
$740$	−13.3908	−	2.49600i	−0.492255	−	0.0917549i
$741$	−3.37841	−	9.22109i	−0.124109	−	0.338745i
$742$	12.3186	−	17.0337i	0.452229	−	0.625325i
$743$	−3.00097	+	1.73261i	−0.110095	+	0.0635633i	−0.554036	−	0.832492i	$-0.686913\pi$
$743$	−3.00097	+	1.73261i	−0.110095	+	0.0635633i	0.443941	+	0.896056i	$0.353580\pi$
$744$	−0.892585	+	1.06834i	−0.0327238	+	0.0391674i
$745$	34.4474	−	12.1588i	1.26206	−	0.445465i
$746$	11.6405	−	20.1620i	0.426189	−	0.738182i
$747$	−10.6795	+	29.7342i	−0.390742	+	1.08792i
$748$		−	18.6775i		−	0.682916i
$749$	16.7455	−	7.49970i	0.611867	−	0.274033i
$750$	−6.12726	−	18.3700i	−0.223736	−	0.670777i
$751$	−9.91531	+	17.1738i	−0.361815	+	0.626682i	−0.988260	−	0.152784i	$-0.951176\pi$
$751$	−9.91531	+	17.1738i	−0.361815	+	0.626682i	0.626445	+	0.779466i	$0.284509\pi$
$752$		−	9.74789i		−	0.355469i
$753$	−36.8149	−	30.7583i	−1.34161	−	1.12089i
$754$	−2.65497			−0.0966884
$755$	−3.12279	+	16.7534i	−0.113650	+	0.609719i
$756$	−7.98508	+	11.1910i	−0.290415	+	0.407013i
$757$			38.7051i			1.40676i	0.710813	+	0.703381i	$0.248327\pi$
$757$			38.7051i			1.40676i	−0.710813	+	0.703381i	$0.751673\pi$
$758$		−	21.3552i		−	0.775657i
$759$	−18.4930	+	22.1345i	−0.671254	+	0.803431i
$760$	−9.84046	−	1.83423i	−0.356951	−	0.0665346i
$761$	−3.27287	+	5.66877i	−0.118641	+	0.205493i	−0.919229	−	0.393722i	$-0.871187\pi$
$761$	−3.27287	+	5.66877i	−0.118641	+	0.205493i	0.800588	+	0.599215i	$0.204521\pi$
$762$	−14.2401	−	11.8974i	−0.515863	−	0.430996i
$763$	24.7041	−	34.1599i	0.894348	−	1.23667i
$764$	−2.53681			−0.0917786
$765$	−31.3604	+	17.8767i	−1.13384	+	0.646334i
$766$	−18.9736	+	32.8633i	−0.685545	+	1.18740i
$767$	13.3103	−	7.68469i	0.480606	−	0.277478i
$768$	1.32919	+	1.11052i	0.0479630	+	0.0400724i
$769$	7.72709	+	13.3837i	0.278646	+	0.482629i	0.971049	−	0.238882i	$-0.0767810\pi$
$769$	7.72709	+	13.3837i	0.278646	+	0.482629i	−0.692402	+	0.721511i	$0.743448\pi$
$770$	−19.6954	−	5.80889i	−0.709774	−	0.209338i
$771$	7.21556	+	19.6943i	0.259862	+	0.709272i
$772$		−	25.2581i		−	0.909059i
$773$	27.8499	+	16.0792i	1.00169	+	0.578327i	0.908749	−	0.417344i	$-0.137039\pi$
$773$	27.8499	+	16.0792i	1.00169	+	0.578327i	0.0929440	+	0.995671i	$0.470372\pi$
$774$	3.16907	+	1.13822i	0.113910	+	0.0409124i
$775$	0.620555	+	3.97058i	0.0222910	+	0.142627i
$776$	−4.32089	+	7.48401i	−0.155111	+	0.268660i
$777$	26.8672	+	7.57854i	0.963856	+	0.271879i
$778$	−9.44789	+	5.45474i	−0.338723	+	0.195562i
$779$	10.2459	−	17.7465i	0.367099	−	0.635834i
$780$	3.12437	+	3.78166i	0.111870	+	0.135405i
$781$	−17.4844	−	30.2838i	−0.625639	−	1.08364i
$782$	22.3586	−	12.9087i	0.799540	−	0.461615i
$783$	5.50612	+	9.39802i	0.196773	+	0.335858i
$784$	6.85336	+	1.42528i	0.244763	+	0.0509028i
$785$	−33.3445	+	38.9606i	−1.19012	+	1.39056i
$786$	0.584627	+	1.59569i	0.0208530	+	0.0569164i
$787$		−	33.6062i		−	1.19793i	−0.800774	−	0.598967i	$-0.795578\pi$
$787$		−	33.6062i		−	1.19793i	0.800774	−	0.598967i	$-0.204422\pi$
$788$			5.46911i			0.194829i
$789$	32.3493	+	5.63321i	1.15167	+	0.200548i
$790$	2.31830	−	2.70877i	0.0824815	−	0.0963737i
$791$	19.3048	−	8.64594i	0.686400	−	0.307414i
$792$	6.72701	+	7.94810i	0.239034	+	0.282423i
$793$	−11.7182	+	6.76551i	−0.416126	+	0.240250i
$794$	−7.87551	−	13.6408i	−0.279491	−	0.484093i
$795$	−10.7448	+	28.8351i	−0.381078	+	1.02268i
$796$	−0.308443	+	0.534239i	−0.0109325	+	0.0189356i
$797$	−28.6922	+	16.5655i	−1.01633	+	0.586779i	−0.913039	−	0.407872i	$-0.866271\pi$
$797$	−28.6922	+	16.5655i	−1.01633	+	0.586779i	−0.103292	+	0.994651i	$0.532938\pi$
$798$	19.7439	+	5.56922i	0.698925	+	0.197148i
$799$	−26.2274	+	45.4272i	−0.927858	+	1.60710i
$800$	4.94003	−	0.772070i	0.174656	−	0.0272968i
$801$	22.1673	−	18.7617i	0.783244	−	0.662912i
$802$	−17.3580	−	10.0216i	−0.612931	−	0.353876i
$803$		−	13.1720i		−	0.464829i
$804$	1.82963	−	2.18990i	0.0645260	−	0.0772318i
$805$	−6.65851	−	27.5919i	−0.234682	−	0.972486i
$806$	−0.509003	−	0.881618i	−0.0179288	−	0.0310537i
$807$	−45.7409	+	16.7585i	−1.61016	+	0.589927i
$808$	14.4827	−	8.36161i	0.509501	−	0.294160i
$809$	23.6277	−	40.9244i	0.830707	−	1.43883i	−0.0667716	−	0.997768i	$-0.521270\pi$
$809$	23.6277	−	40.9244i	0.830707	−	1.43883i	0.897478	−	0.441058i	$-0.145397\pi$
$810$	6.90666	−	18.9023i	0.242675	−	0.664160i
$811$	−15.8024			−0.554898			−0.277449	−	0.960740i	$-0.589489\pi$
$811$	−15.8024			−0.554898			−0.277449	+	0.960740i	$0.589489\pi$
$812$	3.25001	−	4.49399i	0.114053	−	0.157708i
$813$	3.03974	−	17.4560i	0.106608	−	0.612210i
$814$	10.5719	−	18.3110i	0.370543	−	0.641800i
$815$	−3.44061	−	0.641319i	−0.120519	−	0.0224644i
$816$	−3.20637	−	8.75153i	−0.112245	−	0.306365i
$817$		−	5.02463i		−	0.175790i
$818$			5.88551i			0.205782i
$819$	−5.67519	−	8.29792i	−0.198307	−	0.289953i
$820$	−1.87561	+	10.0624i	−0.0654991	+	0.351396i
$821$	26.8515			0.937124			0.468562	−	0.883431i	$-0.344772\pi$
$821$	26.8515			0.937124			0.468562	+	0.883431i	$0.344772\pi$
$822$	4.05380	−	23.2794i	0.141393	−	0.811962i
$823$			40.6272i			1.41618i	0.706125	+	0.708088i	$0.250442\pi$
$823$			40.6272i			1.41618i	−0.706125	+	0.708088i	$0.749558\pi$
$824$	−9.49620	+	16.4479i	−0.330816	+	0.572990i
$825$	30.0544	+	0.522212i	1.04636	+	0.0181811i
$826$	−3.28577	+	31.9369i	−0.114327	+	1.11123i
$827$			17.9942i			0.625721i	0.949799	+	0.312860i	$0.101287\pi$
$827$			17.9942i			0.625721i	−0.949799	+	0.312860i	$0.898713\pi$
$828$	−4.86527	+	13.5461i	−0.169080	+	0.470758i
$829$	1.45002	−	2.51150i	0.0503611	−	0.0872280i	−0.839746	−	0.542980i	$-0.817296\pi$
$829$	1.45002	−	2.51150i	0.0503611	−	0.0872280i	0.890107	+	0.455752i	$0.150629\pi$
$830$	−22.2060	+	7.83801i	−0.770782	+	0.272061i
$831$	16.1940	+	2.81998i	0.561765	+	0.0978240i
$832$	−1.09687	+	0.633281i	−0.0380273	+	0.0219551i
$833$	−28.1033	−	25.0816i	−0.973721	−	0.869024i
$834$	−32.1103	−	5.59159i	−1.11189	−	0.193621i
$835$	−13.3033	−	2.47970i	−0.460381	−	0.0858136i
$836$	7.76891	−	13.4562i	0.268693	−	0.465391i
$837$	−2.06512	+	3.63014i	−0.0713810	+	0.125476i
$838$	−13.2867	+	7.67105i	−0.458980	+	0.264992i
$839$	13.7374	−	23.7938i	0.474267	−	0.821454i	−0.525299	−	0.850918i	$-0.676047\pi$
$839$	13.7374	−	23.7938i	0.474267	−	0.821454i	0.999566	+	0.0294638i	$0.00937998\pi$
$840$	−10.2257	+	0.659304i	−0.352821	+	0.0227481i
$841$	12.3030	+	21.3094i	0.424240	+	0.734805i
$842$	−22.3367	−	12.8961i	−0.769774	−	0.444429i
$843$	−8.88688	+	3.25596i	−0.306080	+	0.112141i
$844$	1.33497	+	2.31223i	0.0459514	+	0.0795902i
$845$	24.0289	−	8.48144i	0.826620	−	0.291770i
$846$	−5.20045	−	28.7775i	−0.178795	−	0.989392i
$847$	1.62364	−	2.24511i	0.0557890	−	0.0771429i
$848$	−6.88082	−	3.97264i	−0.236288	−	0.136421i
$849$	28.5111	−	34.1252i	0.978499	−	1.17117i
$850$	−25.0989	−	9.69350i	−0.860884	−	0.332484i
$851$	29.2265			1.00187
$852$	−13.3913	−	11.1883i	−0.458779	−	0.383303i
$853$	8.41825	+	4.86028i	0.288235	+	0.166413i	0.637146	−	0.770743i	$-0.280115\pi$
$853$	8.41825	+	4.86028i	0.288235	+	0.166413i	−0.348910	+	0.937156i	$0.613448\pi$
$854$	2.89275	−	28.1169i	0.0989880	−	0.962139i
$855$	−30.0294	−	0.165155i	−1.02698	−	0.00564819i
$856$	−3.46749	−	6.00586i	−0.118516	−	0.205276i
$857$	−7.92952	+	4.57811i	−0.270867	+	0.156385i	−0.629282	−	0.777177i	$-0.716651\pi$
$857$	−7.92952	+	4.57811i	−0.270867	+	0.156385i	0.358414	+	0.933563i	$0.383318\pi$
$858$	−7.14956	+	2.61944i	−0.244082	+	0.0894263i
$859$	−2.08393	+	3.60948i	−0.0711029	+	0.123154i	−0.899385	−	0.437158i	$-0.855985\pi$
$859$	−2.08393	+	3.60948i	−0.0711029	+	0.123154i	0.828282	+	0.560311i	$0.189319\pi$
$860$	0.835375	+	2.36672i	0.0284860	+	0.0807043i
$861$	5.69485	−	20.1892i	0.194080	−	0.688047i
$862$	20.3008	+	11.7207i	0.691448	+	0.399208i
$863$	17.7700	−	10.2595i	0.604897	−	0.349237i	−0.166069	−	0.986114i	$-0.553107\pi$
$863$	17.7700	−	10.2595i	0.604897	−	0.349237i	0.770966	+	0.636877i	$0.219774\pi$
$864$	4.51647	+	2.56934i	0.153653	+	0.0874107i
$865$	−22.3102	+	26.0678i	−0.758568	+	0.886332i
$866$	−15.3466			−0.521499
$867$	−3.55285	+	20.4026i	−0.120661	+	0.692908i
$868$	2.11537	+	0.217636i	0.0718003	+	0.00738705i
$869$	2.76716	+	4.79287i	0.0938696	+	0.162587i
$870$	−2.83480	+	7.60757i	−0.0961088	+	0.257921i
$871$	1.04336	+	1.80715i	0.0353528	+	0.0612329i
$872$	−13.7990	−	7.96687i	−0.467294	−	0.269792i
$873$	−8.76339	+	24.3993i	−0.296596	+	0.825792i
$874$	21.4776			0.726490
$875$	−18.0278	+	23.4520i	−0.609452	+	0.792823i
$876$	−2.26124	−	6.17188i	−0.0764003	−	0.208528i
$877$	−25.9278	−	14.9694i	−0.875521	−	0.505482i	−0.00634187	−	0.999980i	$-0.502019\pi$
$877$	−25.9278	−	14.9694i	−0.875521	−	0.505482i	−0.869179	+	0.494498i	$0.835352\pi$
$878$		−	8.42369i		−	0.284286i
$879$	−35.6835	−	6.21382i	−1.20358	−	0.209587i
$880$	−1.42217	+	7.62978i	−0.0479413	+	0.257200i
$881$	20.5399			0.692006			0.346003	−	0.938233i	$-0.387539\pi$
$881$	20.5399			0.692006			0.346003	+	0.938233i	$0.387539\pi$
$882$	20.9928	+	0.551448i	0.706863	+	0.0185682i
$883$		−	45.7939i		−	1.54109i	−0.637387	−	0.770543i	$-0.719985\pi$
$883$		−	45.7939i		−	1.54109i	0.637387	−	0.770543i	$-0.280015\pi$
$884$	6.81555			0.229232
$885$	−7.80792	−	46.3445i	−0.262461	−	1.55785i
$886$	34.9512			1.17421
$887$	35.9167	+	20.7365i	1.20597	+	0.696264i	0.961875	−	0.273488i	$-0.0881775\pi$
$887$	35.9167	+	20.7365i	1.20597	+	0.696264i	0.244090	+	0.969753i	$0.421511\pi$
$888$	1.81010	−	10.3947i	0.0607430	−	0.348823i
$889$	−2.90089	+	28.1960i	−0.0972928	+	0.945662i
$890$	21.2795	+	3.96644i	0.713292	+	0.132955i
$891$	24.0996	+	19.8754i	0.807368	+	0.665852i
$892$	−0.443085	−	0.255815i	−0.0148356	−	0.00856533i
$893$	−37.7910	+	21.8186i	−1.26463	+	0.730132i
$894$	9.73435	+	26.5691i	0.325566	+	0.888605i
$895$	−17.3088	+	6.10946i	−0.578570	+	0.204217i
$896$	0.270774	−	2.63186i	0.00904593	−	0.0879242i
$897$	−8.07704	−	6.74824i	−0.269684	−	0.225317i
$898$			6.45132i			0.215283i
$899$	0.842418	−	1.45911i	0.0280962	−	0.0486641i
$900$	14.1720	−	4.91477i	0.472399	−	0.163826i
$901$	21.3774	+	37.0267i	0.712183	+	1.23354i
$902$	−13.7597	−	7.94417i	−0.458148	−	0.264512i
$903$	−1.26591	−	4.98539i	−0.0421268	−	0.165903i
$904$	−3.99745	−	6.92378i	−0.132953	−	0.230282i
$905$	−14.3194	−	12.2553i	−0.475992	−	0.407379i
$906$	−13.0050	−	2.26464i	−0.432061	−	0.0752377i
$907$	36.4636	−	21.0523i	1.21075	−	0.699029i	0.247831	−	0.968803i	$-0.420282\pi$
$907$	36.4636	−	21.0523i	1.21075	−	0.699029i	0.962924	+	0.269774i	$0.0869490\pi$
$908$	−12.0795	+	6.97409i	−0.400872	+	0.231443i
$909$	38.2948	−	32.4115i	1.27016	−	1.07502i
$910$	2.11971	−	7.18701i	0.0702676	−	0.238247i
$911$	3.01653	−	5.22479i	0.0999422	−	0.173105i	−0.811718	−	0.584049i	$-0.801468\pi$
$911$	3.01653	−	5.22479i	0.0999422	−	0.173105i	0.911661	+	0.410944i	$0.134801\pi$
$912$	1.33018	−	7.63872i	0.0440468	−	0.252943i
$913$		−	36.5532i		−	1.20973i
$914$	−8.44609			−0.279372
$915$	6.87401	+	40.8011i	0.227248	+	1.34884i
$916$	−5.94886	+	10.3037i	−0.196556	+	0.340445i
$917$	1.52122	−	2.10348i	0.0502350	−	0.0694630i
$918$	−14.1347	−	24.1255i	−0.466514	−	0.796261i
$919$	9.15312	+	15.8537i	0.301933	+	0.522964i	0.976574	−	0.215182i	$-0.0690346\pi$
$919$	9.15312	+	15.8537i	0.301933	+	0.522964i	−0.674640	+	0.738147i	$0.735701\pi$
$920$	−10.1164	+	3.57078i	−0.333529	+	0.117725i
$921$	−1.47353	+	1.76369i	−0.0485546	+	0.0581154i
$922$	4.23699	+	2.44623i	0.139538	+	0.0805621i
$923$	11.0508	−	6.38017i	0.363741	−	0.210006i
$924$	4.31809	−	15.3084i	0.142055	−	0.503608i
$925$	−19.1197	−	23.7098i	−0.628651	−	0.779574i
$926$	−1.12261	−	1.94441i	−0.0368912	−	0.0638974i
$927$	−19.2596	+	53.6234i	−0.632570	+	1.76122i
$928$	−1.81537	−	1.04810i	−0.0595924	−	0.0344057i
$929$	24.2860			0.796798			0.398399	−	0.917212i	$-0.369566\pi$
$929$	24.2860			0.796798			0.398399	+	0.917212i	$0.369566\pi$
$930$	−3.06967	+	0.517165i	−0.100658	+	0.0169585i
$931$	−9.81426	−	29.7595i	−0.321649	−	0.975330i
$932$	22.7879	−	13.1566i	0.746441	−	0.430958i
$933$	−29.5347	−	24.6758i	−0.966923	−	0.807850i
$934$	−10.0957	−	17.4863i	−0.330342	−	0.572169i
$935$	27.1561	−	31.7299i	0.888099	−	1.03768i
$936$	−2.90032	+	2.45474i	−0.0948000	+	0.0802356i
$937$			30.0447i			0.981519i	0.871295	+	0.490759i	$0.163281\pi$
$937$			30.0447i			0.981519i	−0.871295	+	0.490759i	$0.836719\pi$
$938$	−4.33610	−	0.446112i	−0.141579	−	0.0145661i
$939$	−17.8637	+	21.3812i	−0.582959	+	0.697749i
$940$	14.1729	−	16.5600i	0.462270	−	0.540129i
$941$	17.3678			0.566173			0.283087	−	0.959094i	$-0.408642\pi$
$941$	17.3678			0.566173			0.283087	+	0.959094i	$0.408642\pi$
$942$	−30.4833	−	25.4684i	−0.993200	−	0.829804i
$943$		−	21.9621i		−	0.715184i
$944$	12.1347			0.394952
$945$	−29.8365	+	7.40175i	−0.970580	+	0.240779i
$946$	−3.89584			−0.126665
$947$		−	12.2953i		−	0.399543i	−0.979843	−	0.199771i	$-0.935980\pi$
$947$		−	12.2953i		−	0.399543i	0.979843	−	0.199771i	$-0.0640199\pi$
$948$	2.11938	+	1.77071i	0.0688342	+	0.0575100i
$949$	4.80656			0.156027
$950$	−14.0504	−	17.4236i	−0.455856	−	0.565295i
$951$	11.7398	−	14.0515i	0.380690	−	0.455651i
$952$	−8.34307	+	11.5365i	−0.270400	+	0.373899i
$953$			13.8549i			0.448804i	0.974497	+	0.224402i	$0.0720428\pi$
$953$			13.8549i			0.448804i	−0.974497	+	0.224402i	$0.927957\pi$
$954$	−22.4328	−	8.05708i	−0.726289	−	0.260858i
$955$	−4.30962	−	3.68839i	−0.139456	−	0.119354i
$956$	5.80430	+	10.0533i	0.187724	+	0.325148i
$957$	−9.67085	−	8.07985i	−0.312614	−	0.261185i
$958$	5.30143	−	3.06078i	0.171282	−	0.0988894i
$959$	−32.9421	+	14.7536i	−1.06376	+	0.476418i
$960$	0.643436	+	3.81916i	0.0207668	+	0.123263i
$961$	−30.3540			−0.979161
$962$	6.68182	+	3.85775i	0.215430	+	0.124379i
$963$	−13.4407	−	15.8805i	−0.433122	−	0.511742i
$964$	8.91164	+	15.4354i	0.287025	+	0.497141i
$965$	36.7240	−	42.9093i	1.18219	−	1.38130i
$966$	21.3098	−	5.41107i	0.685633	−	0.174098i
$967$	17.6627	−	10.1976i	0.567994	−	0.327932i	−0.188354	−	0.982101i	$-0.560315\pi$
$967$	17.6627	−	10.1976i	0.567994	−	0.327932i	0.756348	+	0.654170i	$0.226982\pi$
$968$	−0.906921	−	0.523611i	−0.0291496	−	0.0168295i
$969$	−26.7515	+	32.0191i	−0.859380	+	1.02860i
$970$	−18.2218	+	6.43173i	−0.585068	+	0.206510i
$971$	18.1140	+	31.3744i	0.581306	+	1.00685i	0.995325	+	0.0965834i	$0.0307914\pi$
$971$	18.1140	+	31.3744i	0.581306	+	1.00685i	−0.414019	+	0.910268i	$0.635875\pi$
$972$	14.7042	+	5.17565i	0.471637	+	0.166009i
$973$	20.3503	+	45.4385i	0.652399	+	1.45669i
$974$	−3.93405	+	6.81398i	−0.126055	+	0.218334i
$975$	−0.190559	+	10.9671i	−0.00610278	+	0.351228i
$976$	−10.6833			−0.341963
$977$		−	22.0431i		−	0.705222i	−0.935770	−	0.352611i	$-0.885294\pi$
$977$		−	22.0431i		−	0.705222i	0.935770	−	0.352611i	$-0.114706\pi$
$978$	0.465084	−	2.67079i	0.0148717	−	0.0854025i
$979$	−16.7999	+	29.0983i	−0.536928	+	0.929986i
$980$	9.57044	+	12.3857i	0.305717	+	0.395648i
$981$	−44.9875	−	16.1579i	−1.43634	−	0.515884i
$982$	−3.92352	+	2.26524i	−0.125204	+	0.0722868i
$983$	−9.19736	+	5.31010i	−0.293350	+	0.169366i	−0.639452	−	0.768831i	$-0.720839\pi$
$983$	−9.19736	+	5.31010i	−0.293350	+	0.169366i	0.346102	+	0.938197i	$0.387505\pi$
$984$	−7.81103	−	1.36019i	−0.249007	−	0.0433613i
$985$	−7.95180	+	9.29111i	−0.253365	+	0.296039i
$986$	5.63999	+	9.76876i	0.179614	+	0.311101i
$987$	−31.9988	+	31.1693i	−1.01853	+	0.992129i
$988$	4.91025	+	2.83493i	0.156216	+	0.0901913i
$989$	−2.69256	−	4.66366i	−0.0856185	−	0.148296i
$990$	−0.128053	+	23.2832i	−0.00406978	+	0.739990i
$991$	16.2764	−	28.1916i	0.517038	−	0.895535i	−0.482767	−	0.875749i	$-0.660368\pi$
$991$	16.2764	−	28.1916i	0.517038	−	0.895535i	0.999804	−	0.0197864i	$-0.00629862\pi$
$992$		−	0.803755i		−	0.0255193i
$993$	−1.01586	−	0.848739i	−0.0322375	−	0.0269339i
$994$	−2.72799	+	26.5154i	−0.0865267	+	0.841019i
$995$	−1.30075	+	0.459123i	−0.0412365	+	0.0145552i
$996$	−6.27511	−	17.1274i	−0.198834	−	0.542702i
$997$	−2.61817	+	1.51160i	−0.0829183	+	0.0478729i	−0.540886	−	0.841096i	$-0.681911\pi$
$997$	−2.61817	+	1.51160i	−0.0829183	+	0.0478729i	0.457968	+	0.888969i	$0.348578\pi$
$998$	26.7136	+	15.4231i	0.845603	+	0.488209i
$999$	−0.201768	−	31.6527i	−0.00638366	−	1.00145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ba.a.529.18	yes	96
3.2	odd	2		1890.2.ba.a.1369.32		96
5.4	even	2	inner	630.2.ba.a.529.31	yes	96
7.2	even	3		630.2.bq.a.79.3	yes	96
9.4	even	3		630.2.bq.a.319.46	yes	96
9.5	odd	6		1890.2.bq.a.739.7		96
15.14	odd	2		1890.2.ba.a.1369.23		96
21.2	odd	6		1890.2.bq.a.289.33		96
35.9	even	6		630.2.bq.a.79.46	yes	96
45.4	even	6		630.2.bq.a.319.3	yes	96
45.14	odd	6		1890.2.bq.a.739.33		96
63.23	odd	6		1890.2.ba.a.1549.23		96
63.58	even	3	inner	630.2.ba.a.499.7	✓	96
105.44	odd	6		1890.2.bq.a.289.7		96
315.149	odd	6		1890.2.ba.a.1549.32		96
315.184	even	6	inner	630.2.ba.a.499.42	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ba.a.499.7	✓	96	63.58	even	3	inner
630.2.ba.a.499.42	yes	96	315.184	even	6	inner
630.2.ba.a.529.18	yes	96	1.1	even	1	trivial
630.2.ba.a.529.31	yes	96	5.4	even	2	inner
630.2.bq.a.79.3	yes	96	7.2	even	3
630.2.bq.a.79.46	yes	96	35.9	even	6
630.2.bq.a.319.3	yes	96	45.4	even	6
630.2.bq.a.319.46	yes	96	9.4	even	3
1890.2.ba.a.1369.23		96	15.14	odd	2
1890.2.ba.a.1369.32		96	3.2	odd	2
1890.2.ba.a.1549.23		96	63.23	odd	6
1890.2.ba.a.1549.32		96	315.149	odd	6
1890.2.bq.a.289.7		96	105.44	odd	6
1890.2.bq.a.289.33		96	21.2	odd	6
1890.2.bq.a.739.7		96	9.5	odd	6
1890.2.bq.a.739.33		96	45.14	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.32919 + 1.11052i) q^{3} -1.00000 q^{4} +(-1.69883 - 1.45395i) q^{5} +(1.11052 - 1.32919i) q^{6} +(-2.63186 - 0.270774i) q^{7} +1.00000i q^{8} +(0.533495 + 2.95218i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.32919 + 1.11052i) q^{3} -1.00000 q^{4} +(-1.69883 - 1.45395i) q^{5} +(1.11052 - 1.32919i) q^{6} +(-2.63186 - 0.270774i) q^{7} +1.00000i q^{8} +(0.533495 + 2.95218i) q^{9} +(-1.45395 + 1.69883i) q^{10} +(-1.73546 - 3.00590i) q^{11} +(-1.32919 - 1.11052i) q^{12} +(1.09687 - 0.633281i) q^{13} +(-0.270774 + 2.63186i) q^{14} +(-0.643436 - 3.81916i) q^{15} +1.00000 q^{16} +(-4.66021 - 2.69057i) q^{17} +(2.95218 - 0.533495i) q^{18} +(-2.23829 - 3.87684i) q^{19} +(1.69883 + 1.45395i) q^{20} +(-3.19754 - 3.28264i) q^{21} +(-3.00590 + 1.73546i) q^{22} +(-4.15498 - 2.39888i) q^{23} +(-1.11052 + 1.32919i) q^{24} +(0.772070 + 4.94003i) q^{25} +(-0.633281 - 1.09687i) q^{26} +(-2.56934 + 4.51647i) q^{27} +(2.63186 + 0.270774i) q^{28} +(1.04810 - 1.81537i) q^{29} +(-3.81916 + 0.643436i) q^{30} +0.803755 q^{31} -1.00000i q^{32} +(1.03136 - 5.92267i) q^{33} +(-2.69057 + 4.66021i) q^{34} +(4.07740 + 4.28659i) q^{35} +(-0.533495 - 2.95218i) q^{36} +(-5.27556 + 3.04584i) q^{37} +(-3.87684 + 2.23829i) q^{38} +(2.16123 + 0.376349i) q^{39} +(1.45395 - 1.69883i) q^{40} +(2.28878 + 3.96429i) q^{41} +(-3.28264 + 3.19754i) q^{42} +(0.972049 + 0.561213i) q^{43} +(1.73546 + 3.00590i) q^{44} +(3.38600 - 5.79094i) q^{45} +(-2.39888 + 4.15498i) q^{46} -9.74789i q^{47} +(1.32919 + 1.11052i) q^{48} +(6.85336 + 1.42528i) q^{49} +(4.94003 - 0.772070i) q^{50} +(-3.20637 - 8.75153i) q^{51} +(-1.09687 + 0.633281i) q^{52} +(-6.88082 - 3.97264i) q^{53} +(4.51647 + 2.56934i) q^{54} +(-1.42217 + 7.62978i) q^{55} +(0.270774 - 2.63186i) q^{56} +(1.33018 - 7.63872i) q^{57} +(-1.81537 - 1.04810i) q^{58} +12.1347 q^{59} +(0.643436 + 3.81916i) q^{60} -10.6833 q^{61} -0.803755i q^{62} +(-0.604709 - 7.91419i) q^{63} -1.00000 q^{64} +(-2.78416 - 0.518960i) q^{65} +(-5.92267 - 1.03136i) q^{66} +1.64754i q^{67} +(4.66021 + 2.69057i) q^{68} +(-2.85876 - 7.80276i) q^{69} +(4.28659 - 4.07740i) q^{70} +10.0748 q^{71} +(-2.95218 + 0.533495i) q^{72} +(3.28654 + 1.89748i) q^{73} +(3.04584 + 5.27556i) q^{74} +(-4.45977 + 7.42364i) q^{75} +(2.23829 + 3.87684i) q^{76} +(3.75356 + 8.38101i) q^{77} +(0.376349 - 2.16123i) q^{78} -1.59449 q^{79} +(-1.69883 - 1.45395i) q^{80} +(-8.43077 + 3.14995i) q^{81} +(3.96429 - 2.28878i) q^{82} +(9.12037 + 5.26565i) q^{83} +(3.19754 + 3.28264i) q^{84} +(4.00496 + 11.3465i) q^{85} +(0.561213 - 0.972049i) q^{86} +(3.40913 - 1.24903i) q^{87} +(3.00590 - 1.73546i) q^{88} +(-4.84020 - 8.38348i) q^{89} +(-5.79094 - 3.38600i) q^{90} +(-3.05829 + 1.36970i) q^{91} +(4.15498 + 2.39888i) q^{92} +(1.06834 + 0.892585i) q^{93} -9.74789 q^{94} +(-1.83423 + 9.84046i) q^{95} +(1.11052 - 1.32919i) q^{96} +(7.48401 + 4.32089i) q^{97} +(1.42528 - 6.85336i) q^{98} +(7.94810 - 6.72701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9	\( 96 q - 96 q^{4} - 4 q^{6} + 8 q^{9} + 4 q^{11} - 2 q^{14} - 2 q^{15} + 96 q^{16} + 8 q^{21} + 4 q^{24} + 24 q^{26} + 10 q^{29} + 10 q^{30} - 34 q^{35} - 8 q^{36} + 44 q^{39} + 30 q^{41} - 4 q^{44} - 44 q^{45} - 6 q^{46} - 6 q^{49} - 12 q^{50} + 28 q^{51} - 8 q^{54} + 12 q^{55} + 2 q^{56} + 48 q^{59} + 2 q^{60} + 12 q^{61} - 96 q^{64} - 36 q^{65} + 32 q^{66} + 36 q^{69} + 6 q^{70} - 32 q^{71} - 68 q^{75} - 32 q^{81} - 8 q^{84} + 4 q^{86} - 66 q^{89} - 22 q^{90} + 24 q^{94} - 60 q^{95} - 4 q^{96} - 4 q^{99}+O(q^{100}) \) 96 * q - 96 * q^4 - 4 * q^6 + 8 * q^9 + 4 * q^11 - 2 * q^14 - 2 * q^15 + 96 * q^16 + 8 * q^21 + 4 * q^24 + 24 * q^26 + 10 * q^29 + 10 * q^30 - 34 * q^35 - 8 * q^36 + 44 * q^39 + 30 * q^41 - 4 * q^44 - 44 * q^45 - 6 * q^46 - 6 * q^49 - 12 * q^50 + 28 * q^51 - 8 * q^54 + 12 * q^55 + 2 * q^56 + 48 * q^59 + 2 * q^60 + 12 * q^61 - 96 * q^64 - 36 * q^65 + 32 * q^66 + 36 * q^69 + 6 * q^70 - 32 * q^71 - 68 * q^75 - 32 * q^81 - 8 * q^84 + 4 * q^86 - 66 * q^89 - 22 * q^90 + 24 * q^94 - 60 * q^95 - 4 * q^96 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more