LMFDB - Embedded newform 575.2.p.a.374.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(49,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 16]))

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

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

chi := DirichletCharacter("575.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.p (of order $22$, degree $10$, not 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{22})$
Coefficient field:	$\Q(\zeta_{44})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			374.2
Root			$0.540641 - 0.841254i$ of defining polynomial
Character	$\chi$	$=$	575.374
Dual form			575.2.p.a.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.02730 + 0.925839i) q^{2} +(0.281733 - 0.959493i) q^{3} +(1.94306 + 2.24241i) q^{4} +(1.45949 - 1.68434i) q^{6} +(-0.0872586 - 0.0125459i) q^{7} +(0.607265 + 2.06815i) q^{8} +(1.68251 + 1.08128i) q^{9} +(1.01365 + 2.21959i) q^{11} +(2.69900 - 1.23259i) q^{12} +(3.56484 - 0.512546i) q^{13} +(-0.165284 - 0.106222i) q^{14} +(0.160869 - 1.11887i) q^{16} +(-2.55667 - 2.21537i) q^{17} +(2.40986 + 3.74982i) q^{18} +(-1.87358 - 2.16222i) q^{19} +(-0.0366213 + 0.0801894i) q^{21} +5.43826i q^{22} +(-2.15802 + 4.28287i) q^{23} +2.15546 q^{24} +(7.70154 + 2.26138i) q^{26} +(3.77875 - 3.27430i) q^{27} +(-0.141416 - 0.220047i) q^{28} +(-4.87604 + 5.62725i) q^{29} +(1.65370 - 0.485571i) q^{31} +(3.69269 - 5.74593i) q^{32} +(2.41526 - 0.347262i) q^{33} +(-3.13208 - 6.85830i) q^{34} +(0.844535 + 5.87387i) q^{36} +(-0.382654 + 0.595421i) q^{37} +(-1.79644 - 6.11811i) q^{38} +(0.512546 - 3.56484i) q^{39} +(-4.66991 + 3.00117i) q^{41} +(-0.148485 + 0.128663i) q^{42} +(0.675383 - 2.30014i) q^{43} +(-3.00764 + 6.58582i) q^{44} +(-8.34021 + 6.68469i) q^{46} -11.6146i q^{47} +(-1.02822 - 0.469574i) q^{48} +(-6.70899 - 1.96994i) q^{49} +(-2.84593 + 1.82897i) q^{51} +(8.07603 + 6.99792i) q^{52} +(-10.2695 - 1.47653i) q^{53} +(10.6921 - 3.13950i) q^{54} +(-0.0270422 - 0.188083i) q^{56} +(-2.60249 + 1.18852i) q^{57} +(-15.0951 + 6.89372i) q^{58} +(1.64421 + 11.4357i) q^{59} +(-3.89722 + 1.14433i) q^{61} +(3.80211 + 0.546662i) q^{62} +(-0.133248 - 0.115460i) q^{63} +(10.9041 - 7.00766i) q^{64} +(5.21797 + 1.53213i) q^{66} +(-11.1056 - 5.07177i) q^{67} -10.0377i q^{68} +(3.50140 + 3.27723i) q^{69} +(0.787956 - 1.72538i) q^{71} +(-1.21453 + 4.13631i) q^{72} +(4.16900 - 3.61246i) q^{73} +(-1.32702 + 0.852823i) q^{74} +(1.20812 - 8.40266i) q^{76} +(-0.0606031 - 0.206395i) q^{77} +(4.33955 - 6.75247i) q^{78} +(0.997420 + 6.93721i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-12.2459 + 1.76070i) q^{82} +(2.25587 - 3.51021i) q^{83} +(-0.250975 + 0.0736930i) q^{84} +(3.49877 - 4.03779i) q^{86} +(4.02557 + 6.26391i) q^{87} +(-3.97489 + 3.44426i) q^{88} +(-15.3009 - 4.49275i) q^{89} -0.317493 q^{91} +(-13.7971 + 3.48270i) q^{92} -1.72352i q^{93} +(10.7532 - 23.5463i) q^{94} +(-4.47283 - 5.16192i) q^{96} +(7.77424 + 12.0969i) q^{97} +(-11.7773 - 10.2051i) q^{98} +(-0.694523 + 4.83052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9} + 16 q^{11} + 6 q^{14} + 10 q^{16} + 26 q^{19} + 12 q^{21} + 12 q^{24} + 22 q^{26} - 4 q^{29} - 40 q^{31} - 32 q^{34} + 48 q^{36} - 10 q^{41} - 38 q^{44} - 32 q^{46}+ \cdots - 12 q^{99}+O(q^{100}) $ 20 * q + 2 * q^4 + 12 * q^6 - 4 * q^9 + 16 * q^11 + 6 * q^14 + 10 * q^16 + 26 * q^19 + 12 * q^21 + 12 * q^24 + 22 * q^26 - 4 * q^29 - 40 * q^31 - 32 * q^34 + 48 * q^36 - 10 * q^41 - 38 * q^44 - 32 * q^46 - 8 * q^49 - 20 * q^51 + 60 * q^54 + 6 * q^56 - 10 * q^59 - 6 * q^61 + 68 * q^64 - 8 * q^66 + 2 * q^69 - 44 * q^71 - 2 * q^74 - 4 * q^76 - 102 * q^79 - 2 * q^81 - 12 * q^84 - 18 * q^86 - 114 * q^89 - 44 * q^91 + 162 * q^94 - 14 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$-1$

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 $

$2$	2.02730	+	0.925839i	1.43352	+	0.654667i	0.972538	−	0.232743i	$-0.0747701\pi$
$2$	2.02730	+	0.925839i	1.43352	+	0.654667i	0.460982	+	0.887410i	$0.347497\pi$
$3$	0.281733	−	0.959493i	0.162658	−	0.553964i	−0.837315	−	0.546720i	$-0.815876\pi$
$3$	0.281733	−	0.959493i	0.162658	−	0.553964i	0.999974	−	0.00724338i	$-0.00230566\pi$
$4$	1.94306	+	2.24241i	0.971531	+	1.12121i
$5$		0			0
$5$		0			0
$6$	1.45949	−	1.68434i	0.595836	−	0.687631i
$7$	−0.0872586	−	0.0125459i	−0.0329807	−	0.00474190i	0.125805	−	0.992055i	$-0.459849\pi$
$7$	−0.0872586	−	0.0125459i	−0.0329807	−	0.00474190i	−0.158785	+	0.987313i	$0.550758\pi$
$8$	0.607265	+	2.06815i	0.214700	+	0.731203i
$9$	1.68251	+	1.08128i	0.560836	+	0.360427i
$10$		0			0
$11$	1.01365	+	2.21959i	0.305628	+	0.669231i	0.998664	−	0.0516714i	$-0.0164549\pi$
$11$	1.01365	+	2.21959i	0.305628	+	0.669231i	−0.693037	+	0.720902i	$0.743728\pi$
$12$	2.69900	−	1.23259i	0.779135	−	0.355819i
$13$	3.56484	−	0.512546i	0.988707	−	0.142155i	0.371059	−	0.928609i	$-0.378995\pi$
$13$	3.56484	−	0.512546i	0.988707	−	0.142155i	0.617648	+	0.786455i	$0.288086\pi$
$14$	−0.165284	−	0.106222i	−0.0441741	−	0.0283890i
$15$		0			0
$16$	0.160869	−	1.11887i	0.0402172	−	0.279717i
$17$	−2.55667	−	2.21537i	−0.620084	−	0.537306i	0.287175	−	0.957878i	$-0.407284\pi$
$17$	−2.55667	−	2.21537i	−0.620084	−	0.537306i	−0.907259	+	0.420572i	$0.861829\pi$
$18$	2.40986	+	3.74982i	0.568010	+	0.883840i
$19$	−1.87358	−	2.16222i	−0.429828	−	0.496048i	0.498978	−	0.866615i	$-0.333709\pi$
$19$	−1.87358	−	2.16222i	−0.429828	−	0.496048i	−0.928806	+	0.370567i	$0.879163\pi$
$20$		0			0
$21$	−0.0366213	+	0.0801894i	−0.00799142	+	0.0174988i
$22$			5.43826i			1.15944i
$23$	−2.15802	+	4.28287i	−0.449979	+	0.893039i
$23$	−2.15802	+	4.28287i	−0.449979	+	0.893039i
$24$	2.15546			0.439982
$25$		0			0
$26$	7.70154	+	2.26138i	1.51040	+	0.443492i
$27$	3.77875	−	3.27430i	0.727220	−	0.630140i
$28$	−0.141416	−	0.220047i	−0.0267251	−	0.0415850i
$29$	−4.87604	+	5.62725i	−0.905458	+	1.04495i	0.0933249	+	0.995636i	$0.470250\pi$
$29$	−4.87604	+	5.62725i	−0.905458	+	1.04495i	−0.998783	+	0.0493188i	$0.984295\pi$
$30$		0			0
$31$	1.65370	−	0.485571i	0.297014	−	0.0872110i	−0.129831	−	0.991536i	$-0.541443\pi$
$31$	1.65370	−	0.485571i	0.297014	−	0.0872110i	0.426844	+	0.904325i	$0.359625\pi$
$32$	3.69269	−	5.74593i	0.652781	−	1.01575i
$33$	2.41526	−	0.347262i	0.420442	−	0.0604505i
$34$	−3.13208	−	6.85830i	−0.537147	−	1.17619i
$35$		0			0
$36$	0.844535	+	5.87387i	0.140756	+	0.978979i
$37$	−0.382654	+	0.595421i	−0.0629079	+	0.0978866i	−0.871283	−	0.490782i	$-0.836711\pi$
$37$	−0.382654	+	0.595421i	−0.0629079	+	0.0978866i	0.808375	+	0.588668i	$0.200348\pi$
$38$	−1.79644	−	6.11811i	−0.291421	−	0.992489i
$39$	0.512546	−	3.56484i	0.0820730	−	0.570830i
$40$		0			0
$41$	−4.66991	+	3.00117i	−0.729317	+	0.468704i	−0.851867	−	0.523759i	$-0.824529\pi$
$41$	−4.66991	+	3.00117i	−0.729317	+	0.468704i	0.122550	+	0.992462i	$0.460893\pi$
$42$	−0.148485	+	0.128663i	−0.0229117	+	0.0198531i
$43$	0.675383	−	2.30014i	0.102995	−	0.350768i	−0.891830	−	0.452370i	$-0.850579\pi$
$43$	0.675383	−	2.30014i	0.102995	−	0.350768i	0.994825	+	0.101602i	$0.0323968\pi$
$44$	−3.00764	+	6.58582i	−0.453419	+	0.992850i
$45$		0			0
$46$	−8.34021	+	6.68469i	−1.22970	+	0.985604i
$47$		−	11.6146i		−	1.69416i	−0.531466	−	0.847079i	$-0.678359\pi$
$47$		−	11.6146i		−	1.69416i	0.531466	−	0.847079i	$-0.321641\pi$
$48$	−1.02822	−	0.469574i	−0.148411	−	0.0677772i
$49$	−6.70899	−	1.96994i	−0.958428	−	0.281420i
$50$		0			0
$51$	−2.84593	+	1.82897i	−0.398510	+	0.256107i
$52$	8.07603	+	6.99792i	1.11994	+	0.970437i
$53$	−10.2695	−	1.47653i	−1.41062	−	0.202817i	−0.605462	−	0.795874i	$-0.707012\pi$
$53$	−10.2695	−	1.47653i	−1.41062	−	0.202817i	−0.805160	+	0.593058i	$0.797921\pi$
$54$	10.6921	−	3.13950i	1.45502	−	0.427231i
$55$		0			0
$56$	−0.0270422	−	0.188083i	−0.00361367	−	0.0251336i
$57$	−2.60249	+	1.18852i	−0.344708	+	0.157423i
$58$	−15.0951	+	6.89372i	−1.98209	+	0.905190i
$59$	1.64421	+	11.4357i	0.214058	+	1.48881i	0.759417	+	0.650604i	$0.225484\pi$
$59$	1.64421	+	11.4357i	0.214058	+	1.48881i	−0.545359	+	0.838203i	$0.683607\pi$
$60$		0			0
$61$	−3.89722	+	1.14433i	−0.498988	+	0.146516i	−0.521535	−	0.853230i	$-0.674641\pi$
$61$	−3.89722	+	1.14433i	−0.498988	+	0.146516i	0.0225474	+	0.999746i	$0.492822\pi$
$62$	3.80211	+	0.546662i	0.482869	+	0.0694261i
$63$	−0.133248	−	0.115460i	−0.0167876	−	0.0145466i
$64$	10.9041	−	7.00766i	1.36302	−	0.875958i
$65$		0			0
$66$	5.21797	+	1.53213i	0.642288	+	0.188593i
$67$	−11.1056	−	5.07177i	−1.35677	−	0.619615i	−0.401637	−	0.915799i	$-0.631559\pi$
$67$	−11.1056	−	5.07177i	−1.35677	−	0.619615i	−0.955131	+	0.296184i	$0.904286\pi$
$68$		−	10.0377i		−	1.21725i
$69$	3.50140	+	3.27723i	0.421518	+	0.394532i
$70$		0			0
$71$	0.787956	−	1.72538i	0.0935131	−	0.204765i	−0.857095	−	0.515158i	$-0.827733\pi$
$71$	0.787956	−	1.72538i	0.0935131	−	0.204765i	0.950608	+	0.310393i	$0.100461\pi$
$72$	−1.21453	+	4.13631i	−0.143134	+	0.487468i
$73$	4.16900	−	3.61246i	0.487944	−	0.422806i	−0.375827	−	0.926690i	$-0.622641\pi$
$73$	4.16900	−	3.61246i	0.487944	−	0.422806i	0.863772	+	0.503884i	$0.168096\pi$
$74$	−1.32702	+	0.852823i	−0.154263	+	0.0991387i
$75$		0			0
$76$	1.20812	−	8.40266i	0.138581	−	0.963852i
$77$	−0.0606031	−	0.206395i	−0.00690637	−	0.0235209i
$78$	4.33955	−	6.75247i	0.491357	−	0.764566i
$79$	0.997420	+	6.93721i	0.112219	+	0.780497i	0.965753	+	0.259461i	$0.0835450\pi$
$79$	0.997420	+	6.93721i	0.112219	+	0.780497i	−0.853535	+	0.521036i	$0.825546\pi$
$80$		0			0
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−12.2459	+	1.76070i	−1.35234	+	0.194436i
$83$	2.25587	−	3.51021i	0.247614	−	0.385295i	−0.695091	−	0.718922i	$-0.744636\pi$
$83$	2.25587	−	3.51021i	0.247614	−	0.385295i	0.942705	+	0.333626i	$0.108272\pi$
$84$	−0.250975	+	0.0736930i	−0.0273836	+	0.00804056i
$85$		0			0
$86$	3.49877	−	4.03779i	0.377282	−	0.435406i
$87$	4.02557	+	6.26391i	0.431586	+	0.671561i
$88$	−3.97489	+	3.44426i	−0.423725	+	0.367160i
$89$	−15.3009	−	4.49275i	−1.62189	−	0.476231i	−0.660367	−	0.750943i	$-0.729599\pi$
$89$	−15.3009	−	4.49275i	−1.62189	−	0.476231i	−0.961526	+	0.274713i	$0.911417\pi$
$90$		0			0
$91$	−0.317493			−0.0332823
$92$	−13.7971	+	3.48270i	−1.43845	+	0.363096i
$93$		−	1.72352i		−	0.178720i
$94$	10.7532	−	23.5463i	1.10911	−	2.42861i
$95$		0			0
$96$	−4.47283	−	5.16192i	−0.456506	−	0.526836i
$97$	7.77424	+	12.0969i	0.789354	+	1.22826i	0.969614	+	0.244640i	$0.0786698\pi$
$97$	7.77424	+	12.0969i	0.789354	+	1.22826i	−0.180260	+	0.983619i	$0.557694\pi$
$98$	−11.7773	−	10.2051i	−1.18969	−	1.03087i
$99$	−0.694523	+	4.83052i	−0.0698022	+	0.485485i
$100$		0			0
$101$	14.6237	+	9.39808i	1.45511	+	0.935144i	0.998976	+	0.0452346i	$0.0144035\pi$
$101$	14.6237	+	9.39808i	1.45511	+	0.935144i	0.456137	+	0.889910i	$0.349233\pi$
$102$	−7.46289	+	1.07300i	−0.738937	+	0.106243i
$103$	1.05821	−	0.483270i	0.104269	−	0.0476180i	−0.362598	−	0.931946i	$-0.618110\pi$
$103$	1.05821	−	0.483270i	0.104269	−	0.0476180i	0.466867	+	0.884328i	$0.345383\pi$
$104$	3.22482	+	7.06137i	0.316220	+	0.692425i
$105$		0			0
$106$	−19.4523	−	12.5013i	−1.88938	−	1.21423i
$107$	−4.83181	−	16.4556i	−0.467108	−	1.59083i	−0.770160	−	0.637851i	$-0.779824\pi$
$107$	−4.83181	−	16.4556i	−0.467108	−	1.59083i	0.303051	−	0.952974i	$-0.401995\pi$
$108$	14.6847	+	2.11134i	1.41303	+	0.203164i
$109$	1.71227	−	1.97606i	0.164006	−	0.189273i	−0.667798	−	0.744343i	$-0.732763\pi$
$109$	1.71227	−	1.97606i	0.164006	−	0.189273i	0.831804	+	0.555070i	$0.187308\pi$
$110$		0			0
$111$	0.463496	+	0.534903i	0.0439931	+	0.0507707i
$112$	−0.0280744	+	0.0956126i	−0.00265278	+	0.00903454i
$113$	16.2969	+	7.44256i	1.53309	+	0.700137i	0.990198	−	0.139668i	$-0.0446035\pi$
$113$	16.2969	+	7.44256i	1.53309	+	0.700137i	0.542888	+	0.839805i	$0.317331\pi$
$114$	−6.37640			−0.597205
$115$		0			0
$116$	−22.0931			−2.05129
$117$	6.55207	+	2.99223i	0.605739	+	0.276632i
$118$	−7.25434	+	24.7060i	−0.667816	+	2.27437i
$119$	0.195298	+	0.225386i	0.0179029	+	0.0206611i
$120$		0			0
$121$	3.30439	−	3.81347i	0.300399	−	0.346679i
$122$	−8.96031	−	1.28830i	−0.811228	−	0.116637i
$123$	1.56393	+	5.32627i	0.141015	+	0.480254i
$124$	4.30209	+	2.76479i	0.386339	+	0.248285i
$125$		0			0
$126$	−0.163236	−	0.357438i	−0.0145422	−	0.0318431i
$127$	−2.72142	+	1.24283i	−0.241487	+	0.110283i	−0.532482	−	0.846441i	$-0.678741\pi$
$127$	−2.72142	+	1.24283i	−0.241487	+	0.110283i	0.290996	+	0.956724i	$0.406013\pi$
$128$	15.0726	−	2.16711i	1.33224	−	0.191548i
$129$	−2.01669	−	1.29605i	−0.177560	−	0.114111i
$130$		0			0
$131$	1.91036	−	13.2869i	0.166909	−	1.16088i	−0.718316	−	0.695716i	$-0.755087\pi$
$131$	1.91036	−	13.2869i	0.166909	−	1.16088i	0.885226	−	0.465162i	$-0.154004\pi$
$132$	5.47170	+	4.74125i	0.476250	+	0.412673i
$133$	0.136359	+	0.212178i	0.0118238	+	0.0183982i
$134$	−17.8188	−	20.5640i	−1.53931	−	1.77646i
$135$		0			0
$136$	3.02915	−	6.63291i	0.259747	−	0.568767i
$137$			19.2932i			1.64833i	0.566350	+	0.824165i	$0.308355\pi$
$137$			19.2932i			1.64833i	−0.566350	+	0.824165i	$0.691645\pi$
$138$	4.06421	+	9.88567i	0.345968	+	0.841524i
$139$	−15.4962			−1.31437			−0.657185	−	0.753729i	$-0.728253\pi$
$139$	−15.4962			−1.31437			−0.657185	+	0.753729i	$0.728253\pi$
$140$		0			0
$141$	−11.1441	−	3.27220i	−0.938502	−	0.275569i
$142$	3.19485	−	2.76835i	0.268106	−	0.232315i
$143$	4.75114	+	7.39292i	0.397310	+	0.618227i
$144$	1.48047	−	1.70856i	0.123373	−	0.142380i
$145$		0			0
$146$	11.7964	−	3.46373i	0.976275	−	0.286660i
$147$	−3.78028	+	5.88224i	−0.311793	+	0.485159i
$148$	−2.07870	+	0.298872i	−0.170868	+	0.0245671i
$149$	6.62691	+	14.5109i	0.542898	+	1.18878i	0.960020	+	0.279930i	$0.0903114\pi$
$149$	6.62691	+	14.5109i	0.542898	+	1.18878i	−0.417122	+	0.908850i	$0.636961\pi$
$150$		0			0
$151$	−0.0629411	−	0.437765i	−0.00512208	−	0.0356248i	0.987100	−	0.160104i	$-0.0511830\pi$
$151$	−0.0629411	−	0.437765i	−0.00512208	−	0.0356248i	−0.992222	+	0.124479i	$0.960274\pi$
$152$	3.33405	−	5.18789i	0.270427	−	0.420793i
$153$	−1.90618	−	6.49186i	−0.154106	−	0.524836i
$154$	0.0682278	−	0.474535i	0.00549795	−	0.0382391i
$155$		0			0
$156$	8.98974	−	5.77735i	0.719755	−	0.462559i
$157$	5.37996	−	4.66176i	0.429367	−	0.372049i	−0.413200	−	0.910640i	$-0.635589\pi$
$157$	5.37996	−	4.66176i	0.429367	−	0.372049i	0.842567	+	0.538592i	$0.181043\pi$
$158$	−4.40066	+	14.9873i	−0.350098	+	1.19232i
$159$	−4.30997	+	9.43751i	−0.341803	+	0.748443i
$160$		0			0
$161$	0.242038	−	0.346643i	0.0190753	−	0.0273193i
$162$			2.22871i			0.175104i
$163$	6.50054	+	2.96870i	0.509162	+	0.232526i	0.653395	−	0.757017i	$-0.273344\pi$
$163$	6.50054	+	2.96870i	0.509162	+	0.232526i	−0.144233	+	0.989544i	$0.546071\pi$
$164$	−15.8038	−	4.64041i	−1.23407	−	0.362355i
$165$		0			0
$166$	7.82322	−	5.02768i	0.607200	−	0.390224i
$167$	−1.00714	−	0.872694i	−0.0779351	−	0.0675311i	0.615022	−	0.788510i	$-0.289147\pi$
$167$	−1.00714	−	0.872694i	−0.0779351	−	0.0675311i	−0.692957	+	0.720979i	$0.743693\pi$
$168$	−0.188083	−	0.0270422i	−0.0145109	−	0.00208635i
$169$	−0.0280633	+	0.00824014i	−0.00215872	+	0.000633857i
$170$		0			0
$171$	−0.814334	−	5.66382i	−0.0622737	−	0.433123i
$172$	6.47018	−	2.95483i	0.493346	−	0.225304i
$173$	2.45670	−	1.12194i	0.186779	−	0.0852992i	−0.319830	−	0.947475i	$-0.603626\pi$
$173$	2.45670	−	1.12194i	0.186779	−	0.0852992i	0.506609	+	0.862176i	$0.330899\pi$
$174$	2.36168	+	16.4259i	0.179039	+	1.24524i
$175$		0			0
$176$	2.64649	−	0.777080i	0.199487	−	0.0585746i
$177$	11.4357	+	1.64421i	0.859563	+	0.123587i
$178$	−26.8600	−	23.2743i	−2.01324	−	1.74449i
$179$	16.6467	−	10.6982i	1.24423	−	0.799620i	0.258188	−	0.966095i	$-0.416875\pi$
$179$	16.6467	−	10.6982i	1.24423	−	0.799620i	0.986046	+	0.166474i	$0.0532383\pi$
$180$		0			0
$181$	−3.82402	−	1.12283i	−0.284237	−	0.0834596i	0.136506	−	0.990639i	$-0.456413\pi$
$181$	−3.82402	−	1.12283i	−0.284237	−	0.0834596i	−0.420744	+	0.907180i	$0.638231\pi$
$182$	−0.643655	−	0.293947i	−0.0477109	−	0.0217888i
$183$			4.06175i			0.300253i
$184$	−10.1681	−	1.86229i	−0.749603	−	0.137290i
$185$		0			0
$186$	1.59570	−	3.49409i	0.117002	−	0.256199i
$187$	2.32563	−	7.92038i	0.170067	−	0.579195i
$188$	26.0447	−	22.5678i	1.89950	−	1.64593i
$189$	−0.370807	+	0.238303i	−0.0269723	+	0.0173340i
$190$		0			0
$191$	0.850935	−	5.91838i	0.0615715	−	0.428239i	−0.935599	−	0.353065i	$-0.885140\pi$
$191$	0.850935	−	5.91838i	0.0615715	−	0.428239i	0.997170	−	0.0751744i	$-0.0239513\pi$
$192$	−3.65175	−	12.4367i	−0.263543	−	0.897544i
$193$	5.45312	−	8.48523i	0.392524	−	0.610780i	−0.587603	−	0.809149i	$-0.699928\pi$
$193$	5.45312	−	8.48523i	0.392524	−	0.610780i	0.980127	+	0.198370i	$0.0635646\pi$
$194$	4.56092	+	31.7219i	0.327455	+	2.27750i
$195$		0			0
$196$	−8.61857	−	18.8720i	−0.615612	−	1.34800i
$197$	−5.06355	+	0.728029i	−0.360763	+	0.0518699i	−0.320313	−	0.947312i	$-0.603788\pi$
$197$	−5.06355	+	0.728029i	−0.360763	+	0.0518699i	−0.0404498	+	0.999182i	$0.512879\pi$
$198$	−5.88029	+	9.14991i	−0.417894	+	0.650255i
$199$	25.5033	−	7.48844i	1.80788	−	0.530842i	0.809468	−	0.587164i	$-0.199756\pi$
$199$	25.5033	−	7.48844i	1.80788	−	0.530842i	0.998413	+	0.0563229i	$0.0179376\pi$
$200$		0			0
$201$	−7.99514	+	9.22689i	−0.563934	+	0.650814i
$202$	20.9456	+	32.5920i	1.47373	+	2.29316i
$203$	0.496076	−	0.429852i	0.0348177	−	0.0301697i
$204$	−9.63112	−	2.82795i	−0.674313	−	0.197996i
$205$		0			0
$206$	2.59275			0.180646
$207$	−8.26187	+	4.87252i	−0.574240	+	0.338664i
$208$		−	4.07103i		−	0.282275i
$209$	2.90009	−	6.35031i	0.200603	−	0.439260i
$210$		0			0
$211$	9.65433	+	11.1417i	0.664631	+	0.767026i	0.983526	−	0.180765i	$-0.0578572\pi$
$211$	9.65433	+	11.1417i	0.664631	+	0.767026i	−0.318895	+	0.947790i	$0.603312\pi$
$212$	−16.6432	−	25.8974i	−1.14306	−	1.77864i
$213$	−1.43350	−	1.24213i	−0.0982217	−	0.0851096i
$214$	5.43971	−	37.8340i	0.371851	−	2.58628i
$215$		0			0
$216$	9.06646	+	5.82666i	0.616895	+	0.396454i
$217$	−0.150392	+	0.0216231i	−0.0102092	+	0.00146787i
$218$	5.30081	−	2.42080i	0.359016	−	0.163957i
$219$	−2.29158	−	5.01787i	−0.154851	−	0.339076i
$220$		0			0
$221$	−10.2496	−	6.58702i	−0.689463	−	0.443091i
$222$	0.444413	+	1.51353i	0.0298271	+	0.101582i
$223$	−1.00163	−	0.144012i	−0.0670740	−	0.00964378i	0.108696	−	0.994075i	$-0.465332\pi$
$223$	−1.00163	−	0.144012i	−0.0670740	−	0.00964378i	−0.175770	+	0.984431i	$0.556242\pi$
$224$	−0.394306	+	0.455054i	−0.0263457	+	0.0304046i
$225$		0			0
$226$	26.1482	+	30.1767i	1.73935	+	2.00732i
$227$	1.42057	−	4.83803i	0.0942867	−	0.321111i	−0.898821	−	0.438316i	$-0.855575\pi$
$227$	1.42057	−	4.83803i	0.0942867	−	0.321111i	0.993108	+	0.117205i	$0.0373934\pi$
$228$	−7.72193	−	3.52649i	−0.511397	−	0.233547i
$229$	22.9504			1.51661			0.758304	−	0.651901i	$-0.226028\pi$
$229$	22.9504			1.51661			0.758304	+	0.651901i	$0.226028\pi$
$230$		0			0
$231$	−0.215109			−0.0141531
$232$	−14.5991	−	6.66717i	−0.958476	−	0.437721i
$233$	−6.06370	+	20.6511i	−0.397246	+	1.35290i	0.481850	+	0.876254i	$0.339965\pi$
$233$	−6.06370	+	20.6511i	−0.397246	+	1.35290i	−0.879097	+	0.476644i	$0.841853\pi$
$234$	10.5127	+	12.1323i	0.687237	+	0.793114i
$235$		0			0
$236$	−22.4489	+	25.9074i	−1.46130	+	1.68643i
$237$	6.93721	+	0.997420i	0.450620	+	0.0647894i
$238$	0.187257	+	0.637740i	0.0121381	+	0.0413386i
$239$	7.37760	+	4.74129i	0.477217	+	0.306689i	0.757047	−	0.653361i	$-0.226642\pi$
$239$	7.37760	+	4.74129i	0.477217	+	0.306689i	−0.279830	+	0.960050i	$0.590278\pi$
$240$		0			0
$241$	3.66317	+	8.02123i	0.235966	+	0.516693i	0.990157	−	0.139962i	$-0.0446980\pi$
$241$	3.66317	+	8.02123i	0.235966	+	0.516693i	−0.754191	+	0.656655i	$0.771971\pi$
$242$	10.2296	−	4.67172i	0.657587	−	0.300310i
$243$	15.8371	−	2.27704i	1.01595	−	0.146072i
$244$	−10.1386	−	6.51568i	−0.649057	−	0.417123i
$245$		0			0
$246$	−1.76070	+	12.2459i	−0.112258	+	0.780771i
$247$	−7.78723	−	6.74767i	−0.495490	−	0.429344i
$248$	2.00847	+	3.12524i	0.127538	+	0.198453i
$249$	−2.73247	−	3.15343i	−0.173163	−	0.199841i
$250$		0			0
$251$	−2.44763	+	5.35957i	−0.154493	+	0.338293i	−0.971014	−	0.239023i	$-0.923173\pi$
$251$	−2.44763	+	5.35957i	−0.154493	+	0.338293i	0.816521	+	0.577316i	$0.195900\pi$
$252$		−	0.523141i		−	0.0329548i
$253$	−11.6937	−	0.448583i	−0.735175	−	0.0282022i
$254$	−6.66780			−0.418375
$255$		0			0
$256$	7.68968	+	2.25789i	0.480605	+	0.141118i
$257$	−5.82941	+	5.05121i	−0.363628	+	0.315086i	−0.817442	−	0.576011i	$-0.804609\pi$
$257$	−5.82941	+	5.05121i	−0.363628	+	0.315086i	0.453814	+	0.891097i	$0.350063\pi$
$258$	−2.88852	−	4.49462i	−0.179831	−	0.279823i
$259$	0.0408599	−	0.0471549i	0.00253891	−	0.00293006i
$260$		0			0
$261$	−14.2886	+	4.19552i	−0.884443	+	0.259696i
$262$	16.1744	−	25.1678i	0.999256	−	1.55487i
$263$	−22.1627	+	3.18652i	−1.36661	+	0.196489i	−0.786270	−	0.617883i	$-0.787991\pi$
$263$	−22.1627	+	3.18652i	−1.36661	+	0.196489i	−0.580343	+	0.814372i	$0.697081\pi$
$264$	2.18489	+	4.78424i	0.134471	+	0.294450i
$265$		0			0
$266$	0.0799977	+	0.556396i	0.00490497	+	0.0341148i
$267$	−8.62153	+	13.4154i	−0.527629	+	0.821007i
$268$	−10.2059	−	34.7581i	−0.623425	−	2.12319i
$269$	1.31816	−	9.16802i	0.0803698	−	0.558984i	−0.909357	−	0.416016i	$-0.863426\pi$
$269$	1.31816	−	9.16802i	0.0803698	−	0.558984i	0.989727	−	0.142968i	$-0.0456648\pi$
$270$		0			0
$271$	18.4727	−	11.8717i	1.12214	−	0.721154i	0.158233	−	0.987402i	$-0.449420\pi$
$271$	18.4727	−	11.8717i	1.12214	−	0.721154i	0.963905	+	0.266247i	$0.0857838\pi$
$272$	−2.88999	+	2.50419i	−0.175232	+	0.151839i
$273$	−0.0894481	+	0.304632i	−0.00541365	+	0.0184372i
$274$	−17.8624	+	39.1132i	−1.07911	+	2.36291i
$275$		0			0
$276$	−0.545473	+	14.2194i	−0.0328336	+	0.855909i
$277$			12.5089i			0.751589i	0.926703	+	0.375795i	$0.122630\pi$
$277$			12.5089i			0.751589i	−0.926703	+	0.375795i	$0.877370\pi$
$278$	−31.4155	−	14.3470i	−1.88418	−	0.860474i
$279$	3.30740	+	0.971141i	0.198009	+	0.0581407i
$280$		0			0
$281$	−20.6303	+	13.2583i	−1.23070	+	0.790922i	−0.984000	−	0.178171i	$-0.942982\pi$
$281$	−20.6303	+	13.2583i	−1.23070	+	0.790922i	−0.246699	+	0.969092i	$0.579346\pi$
$282$	−19.5629	−	16.9514i	−1.16496	−	1.00944i
$283$	−17.4860	−	2.51410i	−1.03943	−	0.149448i	−0.398597	−	0.917126i	$-0.630503\pi$
$283$	−17.4860	−	2.51410i	−1.03943	−	0.149448i	−0.640836	+	0.767678i	$0.721412\pi$
$284$	5.40006	−	1.58560i	0.320435	−	0.0940882i
$285$		0			0
$286$	2.78736	+	19.3865i	0.164820	+	1.14635i
$287$	0.445142	−	0.203290i	0.0262759	−	0.0119998i
$288$	12.4259	−	5.67474i	0.732205	−	0.334387i
$289$	−0.790638	−	5.49901i	−0.0465081	−	0.323471i
$290$		0			0
$291$	13.7972	−	4.05122i	0.808806	−	0.237487i
$292$	16.2012	+	2.32939i	0.948106	+	0.136317i
$293$	6.41653	+	5.55996i	0.374858	+	0.324816i	0.821831	−	0.569731i	$-0.192953\pi$
$293$	6.41653	+	5.55996i	0.374858	+	0.324816i	−0.446973	+	0.894547i	$0.647498\pi$
$294$	−13.1098	+	8.42515i	−0.764578	+	0.491365i
$295$		0			0
$296$	−1.46379	−	0.429809i	−0.0850813	−	0.0249821i
$297$	11.0979	+	5.06826i	0.643968	+	0.294090i
$298$			35.5535i			2.05956i
$299$	−5.49782	+	16.3738i	−0.317947	+	0.946921i
$300$		0			0
$301$	−0.0877903	+	0.192234i	−0.00506015	+	0.0110802i
$302$	0.277699	−	0.945756i	0.0159798	−	0.0544222i
$303$	13.1374	−	11.3836i	0.754722	−	0.653970i
$304$	−2.72064	+	1.74845i	−0.156039	+	0.100280i
$305$		0			0
$306$	2.14600	−	14.9258i	0.122679	−	0.853251i
$307$	4.13574	+	14.0850i	0.236039	+	0.803875i	0.989267	+	0.146116i	$0.0466774\pi$
$307$	4.13574	+	14.0850i	0.236039	+	0.803875i	−0.753228	+	0.657759i	$0.771504\pi$
$308$	0.345068	−	0.536936i	0.0196621	−	0.0305948i
$309$	−0.165561	−	1.15150i	−0.00941843	−	0.0655066i
$310$		0			0
$311$	12.5355	+	27.4490i	0.710826	+	1.55649i	0.826332	+	0.563184i	$0.190424\pi$
$311$	12.5355	+	27.4490i	0.710826	+	1.55649i	−0.115506	+	0.993307i	$0.536849\pi$
$312$	7.68388	−	1.10477i	0.435014	−	0.0625455i
$313$	−3.00922	+	4.68243i	−0.170091	+	0.264667i	−0.915826	−	0.401576i	$-0.868462\pi$
$313$	−3.00922	+	4.68243i	−0.170091	+	0.264667i	0.745734	+	0.666243i	$0.232099\pi$
$314$	15.2228	−	4.46983i	0.859074	−	0.252247i
$315$		0			0
$316$	−13.6180	+	15.7160i	−0.766074	+	0.884097i
$317$	1.51979	+	2.36484i	0.0853600	+	0.132823i	0.881308	−	0.472542i	$-0.156664\pi$
$317$	1.51979	+	2.36484i	0.0853600	+	0.132823i	−0.795948	+	0.605365i	$0.793027\pi$
$318$	−17.4752	+	15.1424i	−0.979962	+	0.849142i
$319$	−17.4328	−	5.11873i	−0.976049	−	0.286594i
$320$		0			0
$321$	−17.1503			−0.957238
$322$	0.811620	−	0.478662i	0.0452298	−	0.0266748i
$323$			9.67876i			0.538541i
$324$	−1.23259	+	2.69900i	−0.0684774	+	0.149945i
$325$		0			0
$326$	10.4300	+	12.0369i	0.577667	+	0.666663i
$327$	−1.41362	−	2.19963i	−0.0781732	−	0.121640i
$328$	−9.04274	−	7.83558i	−0.499302	−	0.432648i
$329$	−0.145715	+	1.01347i	−0.00803354	+	0.0558745i
$330$		0			0
$331$	−11.6540	−	7.48954i	−0.640560	−	0.411663i	0.179646	−	0.983731i	$-0.442505\pi$
$331$	−11.6540	−	7.48954i	−0.640560	−	0.411663i	−0.820206	+	0.572069i	$0.806141\pi$
$332$	12.2546	−	1.76195i	0.672560	−	0.0966995i
$333$	−1.28764	+	0.588043i	−0.0705620	+	0.0322246i
$334$	−1.23381	−	2.70167i	−0.0675111	−	0.147829i
$335$		0			0
$336$	0.0838301	+	0.0538744i	0.00457331	+	0.00293909i
$337$	−6.07980	−	20.7059i	−0.331188	−	1.12792i	−0.941851	−	0.336031i	$-0.890915\pi$
$337$	−6.07980	−	20.7059i	−0.331188	−	1.12792i	0.610663	−	0.791890i	$-0.290903\pi$
$338$	−0.0645219	−	0.00927685i	−0.00350953	−	0.000504594i
$339$	11.7325	−	13.5400i	0.637220	−	0.735391i
$340$		0			0
$341$	2.75404	+	3.17834i	0.149140	+	0.172117i
$342$	3.59288	−	12.2362i	0.194281	−	0.661659i
$343$	1.12203	+	0.512414i	0.0605839	+	0.0276677i
$344$	5.16718			0.278596
$345$		0			0
$346$	6.01920			0.323594
$347$	17.1989	+	7.85449i	0.923288	+	0.421651i	0.819585	−	0.572957i	$-0.194204\pi$
$347$	17.1989	+	7.85449i	0.923288	+	0.421651i	0.103702	+	0.994608i	$0.466931\pi$
$348$	−6.22434	+	21.1981i	−0.333659	+	1.13634i
$349$	13.7056	+	15.8171i	0.733643	+	0.846669i	0.992877	−	0.119146i	$-0.0380155\pi$
$349$	13.7056	+	15.8171i	0.733643	+	0.846669i	−0.259234	+	0.965815i	$0.583470\pi$
$350$		0			0
$351$	11.7924	−	13.6091i	0.629431	−	0.726402i
$352$	16.4967	+	2.37187i	0.879277	+	0.126421i
$353$	0.454159	+	1.54672i	0.0241724	+	0.0823238i	0.970696	−	0.240311i	$-0.0772495\pi$
$353$	0.454159	+	1.54672i	0.0241724	+	0.0823238i	−0.946523	+	0.322635i	$0.895431\pi$
$354$	21.6615	+	13.9210i	1.15129	+	0.739891i
$355$		0			0
$356$	−19.6560	−	43.0406i	−1.04177	−	2.28115i
$357$	0.271278	−	0.123889i	0.0143576	−	0.00655688i
$358$	43.6527	−	6.27632i	2.30712	−	0.331714i
$359$	−29.2892	−	18.8230i	−1.54583	−	0.993442i	−0.986362	−	0.164588i	$-0.947371\pi$
$359$	−29.2892	−	18.8230i	−1.54583	−	0.993442i	−0.559464	−	0.828854i	$-0.688993\pi$
$360$		0			0
$361$	1.53906	−	10.7044i	0.0810034	−	0.563391i
$362$	−6.71289	−	5.81675i	−0.352822	−	0.305722i
$363$	−2.72804	−	4.24491i	−0.143185	−	0.222800i
$364$	−0.616908	−	0.711950i	−0.0323348	−	0.0373163i
$365$		0			0
$366$	−3.76052	+	8.23440i	−0.196566	+	0.430419i
$367$		−	22.6244i		−	1.18098i	−0.807044	−	0.590491i	$-0.798934\pi$
$367$		−	22.6244i		−	1.18098i	0.807044	−	0.590491i	$-0.201066\pi$
$368$	4.44480	+	3.10352i	0.231701	+	0.161782i
$369$	−11.1023			−0.577961
$370$		0			0
$371$	0.877577	+	0.257680i	0.0455615	+	0.0133781i
$372$	3.86483	−	3.34890i	0.200382	−	0.173632i
$373$	−5.83633	−	9.08151i	−0.302194	−	0.470223i	0.656635	−	0.754209i	$-0.271979\pi$
$373$	−5.83633	−	9.08151i	−0.302194	−	0.470223i	−0.958828	+	0.283986i	$0.908343\pi$
$374$	12.0478	−	13.9038i	0.622974	−	0.718951i
$375$		0			0
$376$	24.0207	−	7.05312i	1.23877	−	0.363737i
$377$	−14.4981	+	22.5594i	−0.746688	+	1.16187i
$378$	−0.972370	+	0.139806i	−0.0500133	+	0.00719083i
$379$	1.53173	+	3.35401i	0.0786795	+	0.172284i	0.944884	−	0.327406i	$-0.106174\pi$
$379$	1.53173	+	3.35401i	0.0786795	+	0.172284i	−0.866204	+	0.499690i	$0.833447\pi$
$380$		0			0
$381$	0.425774	+	2.96133i	0.0218131	+	0.151713i
$382$	7.20457	−	11.2105i	0.368618	−	0.573580i
$383$	−1.67426	−	5.70202i	−0.0855509	−	0.291360i	0.905594	−	0.424146i	$-0.139426\pi$
$383$	−1.67426	−	5.70202i	−0.0855509	−	0.291360i	−0.991145	+	0.132787i	$0.957608\pi$
$384$	2.16711	−	15.0726i	0.110590	−	0.769171i
$385$		0			0
$386$	18.9111	−	12.1534i	0.962549	−	0.618593i
$387$	3.62344	−	3.13973i	0.184190	−	0.159601i
$388$	−12.0205	+	40.9382i	−0.610250	+	2.07832i
$389$	−2.75929	+	6.04199i	−0.139901	+	0.306341i	−0.966594	−	0.256313i	$-0.917492\pi$
$389$	−2.75929	+	6.04199i	−0.139901	+	0.306341i	0.826693	+	0.562654i	$0.190220\pi$
$390$		0			0
$391$	15.0055	−	6.16908i	0.758860	−	0.311984i
$392$		−	15.0715i		−	0.761226i
$393$	−12.2104	−	5.57632i	−0.615935	−	0.281288i
$394$	−10.9394	−	3.21210i	−0.551119	−	0.161823i
$395$		0			0
$396$	−12.1815	+	7.82858i	−0.612144	+	0.393401i
$397$	3.44429	+	2.98449i	0.172864	+	0.149787i	0.736996	−	0.675897i	$-0.236244\pi$
$397$	3.44429	+	2.98449i	0.172864	+	0.149787i	−0.564132	+	0.825685i	$0.690789\pi$
$398$	58.6360	+	8.43058i	2.93916	+	0.422587i
$399$	0.242000	−	0.0710577i	0.0121152	−	0.00355733i
$400$		0			0
$401$	3.97219	+	27.6272i	0.198362	+	1.37964i	0.809038	+	0.587756i	$0.199989\pi$
$401$	3.97219	+	27.6272i	0.198362	+	1.37964i	−0.610676	+	0.791880i	$0.709102\pi$
$402$	−24.7512	+	11.3035i	−1.23448	+	0.563767i
$403$	5.64630	−	2.57858i	0.281262	−	0.128448i
$404$	7.34038	+	51.0534i	0.365197	+	2.54000i
$405$		0			0
$406$	1.40367	−	0.412155i	0.0696629	−	0.0204549i
$407$	−1.70947	−	0.245784i	−0.0847351	−	0.0121831i
$408$	−5.51082	−	4.77515i	−0.272826	−	0.236405i
$409$	−6.83017	+	4.38949i	−0.337730	+	0.217046i	−0.698502	−	0.715608i	$-0.746150\pi$
$409$	−6.83017	+	4.38949i	−0.337730	+	0.217046i	0.360772	+	0.932654i	$0.382513\pi$
$410$		0			0
$411$	18.5117	+	5.43552i	0.913115	+	0.268115i
$412$	3.13987	+	1.43393i	0.154690	+	0.0706446i
$413$		−	1.01850i		−	0.0501169i
$414$	−21.2605	+	2.22893i	−1.04490	+	0.109546i
$415$		0			0
$416$	10.2188	−	22.3760i	0.501016	−	1.09707i
$417$	−4.36578	+	14.8685i	−0.213793	+	0.728113i
$418$	11.7587	−	10.1890i	0.575138	−	0.498360i
$419$	23.3315	−	14.9942i	1.13982	−	0.732517i	0.172232	−	0.985056i	$-0.444902\pi$
$419$	23.3315	−	14.9942i	1.13982	−	0.732517i	0.967587	+	0.252539i	$0.0812658\pi$
$420$		0			0
$421$	4.97445	−	34.5981i	0.242440	−	1.68621i	−0.397359	−	0.917663i	$-0.630073\pi$
$421$	4.97445	−	34.5981i	0.242440	−	1.68621i	0.639799	−	0.768543i	$-0.279018\pi$
$422$	9.25685	+	31.5259i	0.450616	+	1.53466i
$423$	12.5586	−	19.5416i	0.610621	−	0.950145i
$424$	−3.18261	−	22.1355i	−0.154561	−	1.07500i
$425$		0			0
$426$	−1.75612	−	3.84537i	−0.0850844	−	0.186309i
$427$	0.354423	−	0.0509583i	0.0171517	−	0.00246604i
$428$	27.5118	−	42.8092i	1.32983	−	2.06926i
$429$	8.43201	−	2.47586i	0.407101	−	0.119536i
$430$		0			0
$431$	6.06858	−	7.00351i	0.292313	−	0.337347i	−0.590530	−	0.807016i	$-0.701081\pi$
$431$	6.06858	−	7.00351i	0.292313	−	0.337347i	0.882843	+	0.469669i	$0.155627\pi$
$432$	−3.05563	−	4.75465i	−0.147014	−	0.228758i
$433$	−17.1014	+	14.8185i	−0.821841	+	0.712129i	−0.960521	−	0.278208i	$-0.910260\pi$
$433$	−17.1014	+	14.8185i	−0.821841	+	0.712129i	0.138680	+	0.990337i	$0.455714\pi$
$434$	−0.324909	−	0.0954019i	−0.0155961	−	0.00457944i
$435$		0			0
$436$	7.75820			0.371550
$437$	13.3037	−	3.35816i	0.636404	−	0.160642i
$438$		−	12.2944i		−	0.587448i
$439$	7.68428	−	16.8262i	0.366751	−	0.803072i	−0.632835	−	0.774287i	$-0.718109\pi$
$439$	7.68428	−	16.8262i	0.366751	−	0.803072i	0.999586	−	0.0287853i	$-0.00916393\pi$
$440$		0			0
$441$	−9.15787	−	10.5687i	−0.436089	−	0.503274i
$442$	−14.6805	−	22.8434i	−0.698282	−	1.08655i
$443$	−16.9129	−	14.6551i	−0.803554	−	0.696284i	0.152876	−	0.988245i	$-0.451147\pi$
$443$	−16.9129	−	14.6551i	−0.803554	−	0.696284i	−0.956430	+	0.291962i	$0.905692\pi$
$444$	−0.298872	+	2.07870i	−0.0141838	+	0.0986507i
$445$		0			0
$446$	−1.89727	−	1.21930i	−0.0898384	−	0.0577356i
$447$	15.7901	−	2.27028i	0.746848	−	0.107381i
$448$	−1.03940	+	0.474677i	−0.0491069	+	0.0224264i
$449$	−2.04143	−	4.47012i	−0.0963412	−	0.210958i	0.855325	−	0.518092i	$-0.173357\pi$
$449$	−2.04143	−	4.47012i	−0.0963412	−	0.210958i	−0.951666	+	0.307134i	$0.900630\pi$
$450$		0			0
$451$	−11.3950	−	7.32313i	−0.536570	−	0.344833i
$452$	14.9767	+	51.0058i	0.704442	+	2.39911i
$453$	−0.437765	−	0.0629411i	−0.0205680	−	0.00295723i
$454$	7.35916	−	8.49293i	0.345383	−	0.398593i
$455$		0			0
$456$	−4.03843	−	4.66060i	−0.189117	−	0.218252i
$457$	3.26318	−	11.1134i	0.152645	−	0.519861i	−0.847291	−	0.531128i	$-0.821768\pi$
$457$	3.26318	−	11.1134i	0.152645	−	0.519861i	0.999937	+	0.0112669i	$0.00358644\pi$
$458$	46.5275	+	21.2484i	2.17409	+	0.992873i
$459$	−16.9148			−0.789516
$460$		0			0
$461$	−15.5495			−0.724210			−0.362105	−	0.932137i	$-0.617942\pi$
$461$	−15.5495			−0.724210			−0.362105	+	0.932137i	$0.617942\pi$
$462$	−0.436091	−	0.199156i	−0.0202888	−	0.00926558i
$463$	−2.85313	+	9.71687i	−0.132596	+	0.451581i	−0.998846	−	0.0480300i	$-0.984706\pi$
$463$	−2.85313	+	9.71687i	−0.132596	+	0.451581i	0.866250	+	0.499611i	$0.166524\pi$
$464$	5.51175	+	6.36089i	0.255876	+	0.295297i
$465$		0			0
$466$	−31.4125	+	36.2520i	−1.45516	+	1.67934i
$467$	−0.158222	−	0.0227489i	−0.00732164	−	0.00105269i	0.138653	−	0.990341i	$-0.455723\pi$
$467$	−0.158222	−	0.0227489i	−0.00732164	−	0.00105269i	−0.145975	+	0.989288i	$0.546632\pi$
$468$	6.02126	+	20.5065i	0.278333	+	0.947914i
$469$	0.905432	+	0.581886i	0.0418089	+	0.0268690i
$470$		0			0
$471$	−2.95722	−	6.47540i	−0.136261	−	0.298371i
$472$	−22.6524	+	10.3450i	−1.04266	+	0.476168i
$473$	5.78997	−	0.832472i	0.266223	−	0.0382771i
$474$	13.1404	+	8.44481i	0.603558	+	0.387883i
$475$		0			0
$476$	−0.125932	+	0.875877i	−0.00577209	+	0.0401458i
$477$	−15.6819	−	13.5885i	−0.718026	−	0.622173i
$478$	10.5670	+	16.4425i	0.483321	+	0.752063i
$479$	3.84712	+	4.43982i	0.175779	+	0.202860i	0.836802	−	0.547506i	$-0.184423\pi$
$479$	3.84712	+	4.43982i	0.175779	+	0.202860i	−0.661022	+	0.750366i	$0.729877\pi$
$480$		0			0
$481$	−1.05892	+	2.31870i	−0.0482825	+	0.105724i
$482$			19.6530i			0.895169i
$483$	−0.264411	−	0.329895i	−0.0120311	−	0.0150107i
$484$	14.9720			0.680545
$485$		0			0
$486$	34.2149	+	10.0464i	1.55202	+	0.455714i
$487$	−5.24040	+	4.54083i	−0.237465	+	0.205765i	−0.765461	−	0.643482i	$-0.777489\pi$
$487$	−5.24040	+	4.54083i	−0.237465	+	0.205765i	0.527996	+	0.849247i	$0.322944\pi$
$488$	−4.73329	−	7.36514i	−0.214266	−	0.333404i
$489$	4.67986	−	5.40085i	0.211631	−	0.244235i
$490$		0			0
$491$	21.0671	−	6.18586i	0.950745	−	0.279164i	0.230648	−	0.973037i	$-0.425915\pi$
$491$	21.0671	−	6.18586i	0.950745	−	0.279164i	0.720097	+	0.693873i	$0.244097\pi$
$492$	−8.90487	+	13.8563i	−0.401463	+	0.624688i
$493$	24.9329	−	3.58481i	1.12292	−	0.161452i
$494$	−9.53982	−	20.8893i	−0.429217	−	0.939854i
$495$		0			0
$496$	−0.277260	−	1.92839i	−0.0124493	−	0.0865871i
$497$	−0.0904024	+	0.140669i	−0.00405510	+	0.00630986i
$498$	−2.61997	−	8.92279i	−0.117404	−	0.399840i
$499$	−4.04910	+	28.1621i	−0.181263	+	1.26071i	0.672520	+	0.740079i	$0.265212\pi$
$499$	−4.04910	+	28.1621i	−0.181263	+	1.26071i	−0.853783	+	0.520630i	$0.825697\pi$
$500$		0			0
$501$	−1.12109	+	0.720480i	−0.0500866	+	0.0321887i
$502$	−9.92419	+	8.59936i	−0.442938	+	0.383808i
$503$	−9.67821	+	32.9609i	−0.431530	+	1.46966i	0.401207	+	0.915987i	$0.368591\pi$
$503$	−9.67821	+	32.9609i	−0.431530	+	1.46966i	−0.832737	+	0.553668i	$0.813227\pi$
$504$	0.157872	−	0.345691i	0.00703217	−	0.0153983i
$505$		0			0
$506$	−23.2913	−	11.7359i	−1.03543	−	0.521723i
$507$			0.0292481i			0.00129895i
$508$	−8.07482	−	3.68765i	−0.358262	−	0.163613i
$509$	−6.60273	−	1.93874i	−0.292661	−	0.0859329i	0.132107	−	0.991236i	$-0.457826\pi$
$509$	−6.60273	−	1.93874i	−0.292661	−	0.0859329i	−0.424767	+	0.905303i	$0.639644\pi$
$510$		0			0
$511$	−0.409102	+	0.262914i	−0.0180976	+	0.0116306i
$512$	−9.51763	−	8.24708i	−0.420624	−	0.364473i
$513$	−14.1595	−	2.03584i	−0.625159	−	0.0898843i
$514$	−16.4946	+	4.84325i	−0.727545	+	0.213626i
$515$		0			0
$516$	−1.01228	−	7.04056i	−0.0445631	−	0.309943i
$517$	25.7796	−	11.7731i	1.13378	−	0.517782i
$518$	0.126493	−	0.0577675i	0.00555779	−	0.00253816i
$519$	−0.384358	−	2.67327i	−0.0168714	−	0.117343i
$520$		0			0
$521$	5.29187	−	1.55383i	0.231841	−	0.0680747i	−0.163748	−	0.986502i	$-0.552358\pi$
$521$	5.29187	−	1.55383i	0.231841	−	0.0680747i	0.395589	+	0.918427i	$0.370540\pi$
$522$	−32.8517	−	4.72337i	−1.43788	−	0.206736i
$523$	−3.59678	−	3.11663i	−0.157276	−	0.136281i	0.572668	−	0.819787i	$-0.305908\pi$
$523$	−3.59678	−	3.11663i	−0.157276	−	0.136281i	−0.729944	+	0.683507i	$0.760454\pi$
$524$	33.5066	−	21.5334i	1.46374	−	0.940689i
$525$		0			0
$526$	−47.8808	−	14.0591i	−2.08770	−	0.613005i
$527$	−5.30369	−	2.42212i	−0.231033	−	0.105509i
$528$		−	2.75822i		−	0.120036i
$529$	−13.6859	−	18.4850i	−0.595039	−	0.803697i
$530$		0			0
$531$	−9.59886	+	21.0186i	−0.416555	+	0.912129i
$532$	−0.210838	+	0.718048i	−0.00914098	+	0.0311313i
$533$	−15.1092	+	13.0922i	−0.654453	+	0.567087i
$534$	−29.8989	+	19.2149i	−1.29385	+	0.831508i
$535$		0			0
$536$	3.74514	−	26.0480i	0.161766	−	1.12510i
$537$	−5.57492	−	18.9864i	−0.240576	−	0.819325i
$538$	11.1604	−	17.3660i	0.481160	−	0.748700i
$539$	−2.42813	−	16.8880i	−0.104587	−	0.727419i
$540$		0			0
$541$	−7.02447	−	15.3814i	−0.302006	−	0.661300i	0.696406	−	0.717648i	$-0.254782\pi$
$541$	−7.02447	−	15.3814i	−0.302006	−	0.661300i	−0.998411	+	0.0563484i	$0.982054\pi$
$542$	48.4411	−	6.96478i	2.08072	−	0.299163i
$543$	−2.15470	+	3.35278i	−0.0924671	+	0.143882i
$544$	−22.1704	+	6.50980i	−0.950546	+	0.279106i
$545$		0			0
$546$	−0.463379	+	0.534768i	−0.0198308	+	0.0228859i
$547$	−20.8518	−	32.4460i	−0.891557	−	1.38729i	−0.921766	−	0.387746i	$-0.873254\pi$
$547$	−20.8518	−	32.4460i	−0.891557	−	1.38729i	0.0302093	−	0.999544i	$-0.490383\pi$
$548$	−43.2633	+	37.4879i	−1.84812	+	1.60140i
$549$	−7.79444	−	2.28865i	−0.332659	−	0.0976774i
$550$		0			0
$551$	21.3030			0.907539
$552$	−4.65154	+	9.23157i	−0.197983	+	0.392922i
$553$		−	0.617845i		−	0.0262734i
$554$	−11.5813	+	25.3594i	−0.492040	+	1.07742i
$555$		0			0
$556$	−30.1100	−	34.7488i	−1.27695	−	1.47368i
$557$	22.7805	+	35.4471i	0.965239	+	1.50194i	0.861764	+	0.507309i	$0.169360\pi$
$557$	22.7805	+	35.4471i	0.965239	+	1.50194i	0.103475	+	0.994632i	$0.467004\pi$
$558$	5.80599	+	5.03092i	0.245787	+	0.212976i
$559$	1.22870	−	8.54579i	0.0519685	−	0.361449i
$560$		0			0
$561$	−6.94434	−	4.46286i	−0.293190	−	0.188422i
$562$	−54.0988	+	7.77824i	−2.28202	+	0.328105i
$563$	−5.47564	+	2.50064i	−0.230771	+	0.105389i	−0.527445	−	0.849589i	$-0.676850\pi$
$563$	−5.47564	+	2.50064i	−0.230771	+	0.105389i	0.296674	+	0.954979i	$0.404123\pi$
$564$	−14.3160	−	31.3477i	−0.602814	−	1.31998i
$565$		0			0
$566$	−33.1217	−	21.2860i	−1.39221	−	0.894719i
$567$	−0.0248364	−	0.0845850i	−0.00104303	−	0.00355224i
$568$	4.04685	+	0.581849i	0.169802	+	0.0244139i
$569$	−11.4512	+	13.2154i	−0.480061	+	0.554020i	−0.943183	−	0.332275i	$-0.892184\pi$
$569$	−11.4512	+	13.2154i	−0.480061	+	0.554020i	0.463121	+	0.886295i	$0.346729\pi$
$570$		0			0
$571$	−8.64327	−	9.97487i	−0.361710	−	0.417435i	0.545502	−	0.838109i	$-0.316339\pi$
$571$	−8.64327	−	9.97487i	−0.361710	−	0.417435i	−0.907212	+	0.420674i	$0.861794\pi$
$572$	−7.34622	+	25.0189i	−0.307161	+	1.04609i
$573$	−5.43891	−	2.48387i	−0.227214	−	0.103765i
$574$	1.09065			0.0455229
$575$		0			0
$576$	25.9235			1.08015
$577$	−29.5506	−	13.4953i	−1.23021	−	0.561818i	−0.309065	−	0.951041i	$-0.600016\pi$
$577$	−29.5506	−	13.4953i	−1.23021	−	0.561818i	−0.921143	+	0.389223i	$0.872743\pi$
$578$	3.48833	−	11.8802i	0.145095	−	0.494149i
$579$	−6.60519	−	7.62280i	−0.274502	−	0.316793i
$580$		0			0
$581$	−0.240883	+	0.277994i	−0.00999351	+	0.0115331i
$582$	31.7219	+	4.56092i	1.31491	+	0.189056i
$583$	−7.13240	−	24.2907i	−0.295394	−	1.00602i
$584$	10.0028	+	6.42841i	0.413919	+	0.266009i
$585$		0			0
$586$	7.86064	+	17.2124i	0.324720	+	0.711037i
$587$	11.9812	−	5.47162i	0.494516	−	0.225838i	−0.152515	−	0.988301i	$-0.548737\pi$
$587$	11.9812	−	5.47162i	0.494516	−	0.225838i	0.647032	+	0.762463i	$0.276010\pi$
$588$	−20.5357	+	2.95259i	−0.846879	+	0.121763i
$589$	−4.14825	−	2.66592i	−0.170926	−	0.109847i
$590$		0			0
$591$	−0.728029	+	5.06355i	−0.0299471	+	0.208287i
$592$	0.604640	+	0.523923i	0.0248505	+	0.0215331i
$593$	−17.0754	−	26.5698i	−0.701202	−	1.09109i	−0.990982	−	0.133999i	$-0.957218\pi$
$593$	−17.0754	−	26.5698i	−0.701202	−	1.09109i	0.289779	−	0.957094i	$-0.406418\pi$
$594$	17.8065	+	20.5498i	0.730610	+	0.843169i
$595$		0			0
$596$	−19.6630	+	43.0559i	−0.805426	+	1.76364i
$597$		−	26.5800i		−	1.08785i
$598$	−26.3053	+	28.1046i	−1.07570	+	1.14928i
$599$	5.38162			0.219887			0.109943	−	0.993938i	$-0.464933\pi$
$599$	5.38162			0.219887			0.109943	+	0.993938i	$0.464933\pi$
$600$		0			0
$601$	−32.4793	−	9.53678i	−1.32486	−	0.389013i	−0.458614	−	0.888636i	$-0.651654\pi$
$601$	−32.4793	−	9.53678i	−1.32486	−	0.389013i	−0.866243	+	0.499622i	$0.833472\pi$
$602$	−0.355955	+	0.308437i	−0.0145077	+	0.0125710i
$603$	−13.2013	−	20.5416i	−0.537598	−	0.836518i
$604$	0.859352	−	0.991745i	0.0349665	−	0.0403535i
$605$		0			0
$606$	37.1728	−	10.9149i	1.51004	−	0.443388i
$607$	−11.7812	+	18.3320i	−0.478186	+	0.744072i	−0.993611	−	0.112863i	$-0.963998\pi$
$607$	−11.7812	+	18.3320i	−0.478186	+	0.744072i	0.515424	+	0.856935i	$0.327634\pi$
$608$	−19.3425	+	2.78103i	−0.784442	+	0.112786i
$609$	−0.272679	−	0.597084i	−0.0110495	−	0.0241951i
$610$		0			0
$611$	−5.95300	−	41.4040i	−0.240833	−	1.67503i
$612$	10.8536	−	16.8885i	0.438731	−	0.682678i
$613$	−1.91064	−	6.50705i	−0.0771701	−	0.262817i	0.911867	−	0.410486i	$-0.134641\pi$
$613$	−1.91064	−	6.50705i	−0.0771701	−	0.262817i	−0.989037	+	0.147669i	$0.952823\pi$
$614$	−4.65607	+	32.3837i	−0.187904	+	1.30690i
$615$		0			0
$616$	0.390055	−	0.250673i	0.0157158	−	0.0100999i
$617$	−24.3863	+	21.1308i	−0.981755	+	0.850695i	−0.988795	−	0.149280i	$-0.952304\pi$
$617$	−24.3863	+	21.1308i	−0.981755	+	0.850695i	0.00704038	+	0.999975i	$0.497759\pi$
$618$	0.730462	−	2.48773i	0.0293835	−	0.100071i
$619$	14.5801	−	31.9260i	0.586024	−	1.28321i	−0.351792	−	0.936078i	$-0.614427\pi$
$619$	14.5801	−	31.9260i	0.586024	−	1.28321i	0.937815	−	0.347134i	$-0.112845\pi$
$620$		0			0
$621$	5.86879	+	23.2499i	0.235506	+	0.932986i
$622$			67.2534i			2.69661i
$623$	1.27877	+	0.583995i	0.0512329	+	0.0233973i
$624$	−3.90613	−	1.14694i	−0.156370	−	0.0459144i
$625$		0			0
$626$	−10.4358	+	6.70667i	−0.417098	+	0.268052i
$627$	−5.27603	−	4.57170i	−0.210704	−	0.182576i
$628$	20.9072	+	3.00600i	0.834287	+	0.119952i
$629$	2.29740	−	0.674577i	0.0916033	−	0.0268971i
$630$		0			0
$631$	1.85675	+	12.9139i	0.0739159	+	0.514096i	0.992820	+	0.119616i	$0.0381663\pi$
$631$	1.85675	+	12.9139i	0.0739159	+	0.514096i	−0.918904	+	0.394480i	$0.870925\pi$
$632$	−13.7415	+	6.27554i	−0.546608	+	0.249628i
$633$	13.4103	−	6.12428i	0.533012	−	0.243418i
$634$	0.891617	+	6.20133i	0.0354106	+	0.246286i
$635$		0			0
$636$	−29.5373	+	8.67294i	−1.17123	+	0.343904i
$637$	−24.9261	−	3.58384i	−0.987610	−	0.141997i
$638$	−30.6024	−	26.5172i	−1.21156	−	1.04982i
$639$	3.19136	−	2.05097i	0.126248	−	0.0811349i
$640$		0			0
$641$	34.6688	+	10.1797i	1.36934	+	0.402073i	0.882044	−	0.471166i	$-0.156167\pi$
$641$	34.6688	+	10.1797i	1.36934	+	0.402073i	0.487291	+	0.873239i	$0.337985\pi$
$642$	−34.7689	−	15.8784i	−1.37222	−	0.626672i
$643$		−	31.5510i		−	1.24425i	−0.782917	−	0.622126i	$-0.786269\pi$
$643$		−	31.5510i		−	1.24425i	0.782917	−	0.622126i	$-0.213731\pi$
$644$	1.24761	−	0.130798i	0.0491628	−	0.00515417i
$645$		0			0
$646$	−8.96097	+	19.6218i	−0.352565	+	0.772009i
$647$	−3.90562	+	13.3013i	−0.153546	+	0.522929i	−0.999954	−	0.00960580i	$-0.996942\pi$
$647$	−3.90562	+	13.3013i	−0.153546	+	0.522929i	0.846408	+	0.532535i	$0.178761\pi$
$648$	−1.62899	+	1.41153i	−0.0639928	+	0.0554501i
$649$	−23.7160	+	15.2413i	−0.930934	+	0.598275i
$650$		0			0
$651$	−0.0216231	+	0.150392i	−0.000847474	+	0.00589431i
$652$	5.97391	+	20.3453i	0.233956	+	0.796782i
$653$	−3.05729	+	4.75724i	−0.119641	+	0.186165i	−0.895909	−	0.444239i	$-0.853474\pi$
$653$	−3.05729	+	4.75724i	−0.119641	+	0.186165i	0.776267	+	0.630404i	$0.217111\pi$
$654$	−0.829328	−	5.76810i	−0.0324293	−	0.225551i
$655$		0			0
$656$	2.60667	+	5.70780i	0.101773	+	0.222852i
$657$	10.9204	−	1.57012i	0.426047	−	0.0612564i
$658$	−1.23372	+	1.91971i	−0.0480954	+	0.0748379i
$659$	28.0838	−	8.24614i	1.09399	−	0.321224i	0.315527	−	0.948917i	$-0.397819\pi$
$659$	28.0838	−	8.24614i	1.09399	−	0.321224i	0.778461	+	0.627692i	$0.216000\pi$
$660$		0			0
$661$	−10.5207	+	12.1415i	−0.409207	+	0.472250i	−0.922519	−	0.385952i	$-0.873873\pi$
$661$	−10.5207	+	12.1415i	−0.409207	+	0.472250i	0.513312	+	0.858202i	$0.328418\pi$
$662$	−16.6920	−	25.9733i	−0.648753	−	1.00948i
$663$	−9.20784	+	7.97864i	−0.357603	+	0.309865i
$664$	8.62956	+	2.53387i	0.334892	+	0.0983331i
$665$		0			0
$666$	−3.15486			−0.122248
$667$	−13.5782	−	33.0272i	−0.525749	−	1.27882i
$668$		−	3.95413i		−	0.152990i
$669$	−0.420370	+	0.920482i	−0.0162524	+	0.0355879i
$670$		0			0
$671$	−6.49036	−	7.49027i	−0.250558	−	0.289159i
$672$	0.325532	+	0.506538i	0.0125577	+	0.0195401i
$673$	2.88949	+	2.50376i	0.111382	+	0.0965128i	0.708771	−	0.705438i	$-0.249250\pi$
$673$	2.88949	+	2.50376i	0.111382	+	0.0965128i	−0.597389	+	0.801951i	$0.703795\pi$
$674$	6.84471	−	47.6060i	0.263649	−	1.83372i
$675$		0			0
$676$	−0.0730065	−	0.0469185i	−0.00280794	−	0.00180456i
$677$	16.2586	−	2.33764i	0.624870	−	0.0898428i	0.177396	−	0.984140i	$-0.443233\pi$
$677$	16.2586	−	2.33764i	0.624870	−	0.0898428i	0.447474	+	0.894297i	$0.352324\pi$
$678$	36.3211	−	16.5873i	1.39490	−	0.637031i
$679$	−0.526602	−	1.15310i	−0.0202091	−	0.0442518i
$680$		0			0
$681$	−4.24183	−	2.72606i	−0.162547	−	0.104463i
$682$	2.64066	+	8.99325i	0.101116	+	0.344369i
$683$	7.28651	+	1.04764i	0.278811	+	0.0400869i	0.280302	−	0.959912i	$-0.409566\pi$
$683$	7.28651	+	1.04764i	0.278811	+	0.0400869i	−0.00149105	+	0.999999i	$0.500475\pi$
$684$	11.1183	−	12.8312i	0.425119	−	0.490614i
$685$		0			0
$686$	1.80028	+	2.07764i	0.0687351	+	0.0793245i
$687$	6.46589	−	22.0208i	0.246689	−	0.840145i
$688$	−2.46491	−	1.12569i	−0.0939737	−	0.0429163i
$689$	−37.3658			−1.42352
$690$		0			0
$691$	−9.67502			−0.368055			−0.184028	−	0.982921i	$-0.558914\pi$
$691$	−9.67502			−0.368055			−0.184028	+	0.982921i	$0.558914\pi$
$692$	7.28935	+	3.32894i	0.277100	+	0.126547i
$693$	0.121206	−	0.412791i	0.00460425	−	0.0156806i
$694$	27.5955	+	31.8469i	1.04751	+	1.20889i
$695$		0			0
$696$	−10.5101	+	12.1293i	−0.398386	+	0.459762i
$697$	18.5881	+	2.67257i	0.704076	+	0.101231i
$698$	13.1413	+	44.7552i	0.497406	+	1.69401i
$699$	18.1062	+	11.6362i	0.684840	+	0.440120i
$700$		0			0
$701$	17.6838	+	38.7221i	0.667908	+	1.46252i	0.874965	+	0.484186i	$0.160884\pi$
$701$	17.6838	+	38.7221i	0.667908	+	1.46252i	−0.207057	+	0.978329i	$0.566388\pi$
$702$	36.5066	−	16.6720i	1.37785	−	0.629244i
$703$	2.00436	−	0.288184i	0.0755960	−	0.0108691i
$704$	26.6071	+	17.0994i	1.00279	+	0.644456i
$705$		0			0
$706$	−0.511298	+	3.55616i	−0.0192430	+	0.133838i
$707$	−1.15814	−	1.00353i	−0.0435562	−	0.0377417i
$708$	18.5334	+	28.8385i	0.696526	+	1.08382i
$709$	22.9666	+	26.5049i	0.862529	+	0.995411i	0.999988	+	0.00490358i	$0.00156086\pi$
$709$	22.9666	+	26.5049i	0.862529	+	0.995411i	−0.137459	+	0.990507i	$0.543894\pi$
$710$		0			0
$711$	−5.82291	+	12.7504i	−0.218376	+	0.478177i
$712$		−	34.3729i		−	1.28818i
$713$	−1.48909	+	8.13045i	−0.0557668	+	0.304488i
$714$	0.664664			0.0248744
$715$		0			0
$716$	56.3353	+	16.5415i	2.10535	+	0.618187i
$717$	6.62775	−	5.74298i	0.247518	−	0.214475i
$718$	−41.9511	−	65.2771i	−1.56560	−	2.43612i
$719$	14.5394	−	16.7793i	0.542226	−	0.625763i	−0.416828	−	0.908986i	$-0.636858\pi$
$719$	14.5394	−	16.7793i	0.542226	−	0.625763i	0.959054	+	0.283223i	$0.0914036\pi$
$720$		0			0
$721$	−0.0984013	+	0.0288932i	−0.00366466	+	0.00107604i
$722$	13.0307	−	20.2762i	0.484953	−	0.754602i
$723$	8.72835	−	1.25495i	0.324611	−	0.0466720i
$724$	−4.91245	−	10.7568i	−0.182570	−	0.399772i
$725$		0			0
$726$	−1.60046	−	11.1315i	−0.0593987	−	0.413127i
$727$	−0.377738	+	0.587772i	−0.0140095	+	0.0217993i	−0.848188	−	0.529696i	$-0.822306\pi$
$727$	−0.377738	+	0.587772i	−0.0140095	+	0.0217993i	0.834178	+	0.551495i	$0.185942\pi$
$728$	−0.192802	−	0.656624i	−0.00714573	−	0.0243361i
$729$	1.85009	−	12.8677i	0.0685220	−	0.476581i
$730$		0			0
$731$	−6.82240	+	4.38449i	−0.252336	+	0.162166i
$732$	−9.10812	+	7.89223i	−0.336646	+	0.291705i
$733$	10.5094	−	35.7918i	0.388174	−	1.32200i	−0.501403	−	0.865214i	$-0.667183\pi$
$733$	10.5094	−	35.7918i	0.388174	−	1.32200i	0.889577	−	0.456785i	$-0.150999\pi$
$734$	20.9465	−	45.8664i	0.773149	−	1.69296i
$735$		0			0
$736$	16.6402	+	28.2151i	0.613364	+	1.04002i
$737$		−	29.7909i		−	1.09736i
$738$	−22.5077	−	10.2789i	−0.828518	−	0.378372i
$739$	−23.5752	−	6.92231i	−0.867229	−	0.254641i	−0.182293	−	0.983244i	$-0.558352\pi$
$739$	−23.5752	−	6.92231i	−0.867229	−	0.254641i	−0.684936	+	0.728603i	$0.740170\pi$
$740$		0			0
$741$	−8.66826	+	5.57075i	−0.318437	+	0.204647i
$742$	1.54054	+	1.33489i	0.0565552	+	0.0490053i
$743$	40.9388	+	5.88612i	1.50190	+	0.215941i	0.843665	−	0.536871i	$-0.180394\pi$
$743$	40.9388	+	5.88612i	1.50190	+	0.215941i	0.658236	+	0.752811i	$0.271303\pi$
$744$	3.56450	−	1.04663i	0.130681	−	0.0383713i
$745$		0			0
$746$	−3.42400	−	23.8145i	−0.125362	−	0.871910i
$747$	7.59104	−	3.46671i	0.277742	−	0.126840i
$748$	22.2796	−	10.1748i	0.814623	−	0.372026i
$749$	0.215166	+	1.49651i	0.00786201	+	0.0546815i
$750$		0			0
$751$	39.3106	−	11.5426i	1.43446	−	0.421197i	0.530091	−	0.847941i	$-0.322158\pi$
$751$	39.3106	−	11.5426i	1.43446	−	0.421197i	0.904372	+	0.426744i	$0.140339\pi$
$752$	−12.9952	−	1.86842i	−0.473885	−	0.0681344i
$753$	4.45289	+	3.85845i	0.162272	+	0.140610i
$754$	−50.2783	+	32.3119i	−1.83103	+	1.17673i
$755$		0			0
$756$	−1.25488	−	0.368465i	−0.0456394	−	0.0134009i
$757$	9.08592	+	4.14940i	0.330233	+	0.150812i	0.573630	−	0.819114i	$-0.305535\pi$
$757$	9.08592	+	4.14940i	0.330233	+	0.150812i	−0.243397	+	0.969927i	$0.578262\pi$
$758$			8.21774i			0.298482i
$759$	−3.72490	+	11.0936i	−0.135205	+	0.402673i
$760$		0			0
$761$	−7.00401	+	15.3366i	−0.253895	+	0.555953i	−0.993065	−	0.117566i	$-0.962491\pi$
$761$	−7.00401	+	15.3366i	−0.253895	+	0.555953i	0.739170	+	0.673519i	$0.235218\pi$
$762$	−1.87854	+	6.39771i	−0.0680522	+	0.231764i
$763$	−0.174202	+	0.150947i	−0.00630653	+	0.00546464i
$764$	14.9249	−	9.59163i	0.539963	−	0.347013i
$765$		0			0
$766$	1.88491	−	13.1098i	0.0681045	−	0.473677i
$767$	11.7227	+	39.9238i	0.423282	+	1.44157i
$768$	4.33287	−	6.74207i	0.156349	−	0.243283i
$769$	−6.22901	−	43.3237i	−0.224624	−	1.56229i	−0.720223	−	0.693743i	$-0.755961\pi$
$769$	−6.22901	−	43.3237i	−0.224624	−	1.56229i	0.495599	−	0.868551i	$-0.334949\pi$
$770$		0			0
$771$	3.20427	+	7.01636i	0.115399	+	0.252688i
$772$	29.6231	−	4.25916i	1.06616	−	0.153291i
$773$	18.1814	−	28.2907i	0.653938	−	1.01755i	−0.342999	−	0.939336i	$-0.611443\pi$
$773$	18.1814	−	28.2907i	0.653938	−	1.01755i	0.996937	−	0.0782114i	$-0.0249209\pi$
$774$	10.2527	−	3.01046i	0.368525	−	0.108209i
$775$		0			0
$776$	−20.2973	+	23.4244i	−0.728632	+	0.840886i
$777$	−0.0337332	−	0.0524899i	−0.00121017	−	0.00188306i
$778$	−11.1878	+	9.69430i	−0.401103	+	0.347558i
$779$	15.2386	+	4.47446i	0.545980	+	0.160314i
$780$		0			0
$781$	4.62835			0.165615
$782$	36.1323	+	1.38607i	1.29209	+	0.0495659i
$783$			37.2296i			1.33048i
$784$	−3.28337	+	7.18957i	−0.117263	+	0.256770i
$785$		0			0
$786$	−19.5915	−	22.6098i	−0.698805	−	0.806464i
$787$	0.676215	+	1.05221i	0.0241045	+	0.0375073i	0.853097	−	0.521753i	$-0.174722\pi$
$787$	0.676215	+	1.05221i	0.0241045	+	0.0375073i	−0.828992	+	0.559260i	$0.811085\pi$
$788$	−11.4713	−	9.93997i	−0.408649	−	0.354097i
$789$	−3.18652	+	22.1627i	−0.113443	+	0.789014i
$790$		0			0
$791$	−1.32867	−	0.853887i	−0.0472422	−	0.0303607i
$792$	−10.4120	+	1.49702i	−0.369975	+	0.0531943i
$793$	−13.3064	+	6.07684i	−0.472525	+	0.215795i
$794$	4.21946	+	9.23933i	0.149743	+	0.327892i
$795$		0			0
$796$	66.3466	+	42.6384i	2.35159	+	1.51128i
$797$	3.44308	+	11.7261i	0.121960	+	0.415358i	0.997728	−	0.0673749i	$-0.0214624\pi$
$797$	3.44308	+	11.7261i	0.121960	+	0.415358i	−0.875768	+	0.482733i	$0.839644\pi$
$798$	0.556396	+	0.0799977i	0.0196962	+	0.00283189i
$799$	−25.7306	+	29.6947i	−0.910282	+	1.05052i
$800$		0			0
$801$	−20.8860	−	24.1037i	−0.737969	−	0.851662i
$802$	−17.5255	+	59.6863i	−0.618846	+	2.10760i
$803$	12.2441	+	5.59168i	0.432084	+	0.197326i
$804$	−36.2255			−1.27758
$805$		0			0
$806$	13.8341			0.487285
$807$	−8.42528	−	3.84770i	−0.296584	−	0.135445i
$808$	−10.5562	+	35.9512i	−0.371367	+	1.26476i
$809$	−17.5520	−	20.2561i	−0.617097	−	0.712167i	0.358056	−	0.933700i	$-0.383440\pi$
$809$	−17.5520	−	20.2561i	−0.617097	−	0.712167i	−0.975153	+	0.221533i	$0.928894\pi$
$810$		0			0
$811$	25.9259	−	29.9201i	0.910381	−	1.05064i	−0.0881316	−	0.996109i	$-0.528090\pi$
$811$	25.9259	−	29.9201i	0.910381	−	1.05064i	0.998512	−	0.0545266i	$-0.0173650\pi$
$812$	1.92781	+	0.277177i	0.0676529	+	0.00972702i
$813$	−6.18644	−	21.0691i	−0.216968	−	0.738925i
$814$	−3.23805	−	2.08097i	−0.113494	−	0.0729379i
$815$		0			0
$816$	1.58855	+	3.47844i	0.0556104	+	0.121770i
$817$	−6.23880	+	2.84917i	−0.218268	+	0.0996797i
$818$	−17.9108	+	2.57518i	−0.626236	+	0.0900392i
$819$	−0.534184	−	0.343299i	−0.0186659	−	0.0119958i
$820$		0			0
$821$	4.50608	−	31.3404i	0.157263	−	1.09379i	−0.746385	−	0.665514i	$-0.768212\pi$
$821$	4.50608	−	31.3404i	0.157263	−	1.09379i	0.903648	−	0.428275i	$-0.140879\pi$
$822$	32.4964	+	28.1583i	1.13344	+	0.982134i
$823$	25.3640	+	39.4672i	0.884134	+	1.37574i	0.926363	+	0.376632i	$0.122918\pi$
$823$	25.3640	+	39.4672i	0.884134	+	1.37574i	−0.0422285	+	0.999108i	$0.513446\pi$
$824$	1.64209	+	1.89508i	0.0572050	+	0.0660181i
$825$		0			0
$826$	0.942962	−	2.06480i	0.0328099	−	0.0718436i
$827$		−	24.2676i		−	0.843869i	−0.906626	−	0.421934i	$-0.861351\pi$
$827$		−	24.2676i		−	0.843869i	0.906626	−	0.421934i	$-0.138649\pi$
$828$	−26.9795	−	9.05891i	−0.937603	−	0.314819i
$829$	21.8597			0.759220			0.379610	−	0.925147i	$-0.376058\pi$
$829$	21.8597			0.759220			0.379610	+	0.925147i	$0.376058\pi$
$830$		0			0
$831$	12.0022	+	3.52417i	0.416353	+	0.122252i
$832$	35.2797	−	30.5700i	1.22310	−	1.05983i
$833$	12.7886	+	19.8994i	0.443098	+	0.689473i
$834$	−22.6166	+	26.1009i	−0.783148	+	0.903801i
$835$		0			0
$836$	19.8751	−	5.83585i	0.687393	−	0.201837i
$837$	4.65902	−	7.24957i	0.161039	−	0.250582i
$838$	61.1823	−	8.79669i	2.11351	−	0.303876i
$839$	11.3411	+	24.8335i	0.391538	+	0.857348i	0.998059	+	0.0622806i	$0.0198374\pi$
$839$	11.3411	+	24.8335i	0.391538	+	0.857348i	−0.606521	+	0.795068i	$0.707435\pi$
$840$		0			0
$841$	−3.76305	−	26.1726i	−0.129760	−	0.902504i
$842$	42.1169	−	65.5352i	1.45145	−	2.25849i
$843$	6.90899	+	23.5299i	0.237958	+	0.810412i
$844$	−6.22531	+	43.2980i	−0.214284	+	1.49038i
$845$		0			0
$846$	43.5525	−	27.9895i	1.49737	−	0.962298i
$847$	−0.336180	+	0.291301i	−0.0115513	+	0.0100092i
$848$	−3.30408	+	11.2527i	−0.113463	+	0.386418i
$849$	−7.33863	+	16.0694i	−0.251861	+	0.551499i
$850$		0			0
$851$	−1.72433	−	2.92379i	−0.0591094	−	0.100226i
$852$		−	5.62804i		−	0.192813i
$853$	25.6230	+	11.7016i	0.877316	+	0.400657i	0.802578	−	0.596547i	$-0.203461\pi$
$853$	25.6230	+	11.7016i	0.877316	+	0.400657i	0.0747372	+	0.997203i	$0.476188\pi$
$854$	0.765701	+	0.224830i	0.0262018	+	0.00769353i
$855$		0			0
$856$	31.0986	−	19.9858i	1.06293	−	0.683102i
$857$	8.49369	+	7.35982i	0.290139	+	0.251407i	0.787752	−	0.615992i	$-0.211245\pi$
$857$	8.49369	+	7.35982i	0.290139	+	0.251407i	−0.497613	+	0.867399i	$0.665790\pi$
$858$	19.3865	+	2.78736i	0.661844	+	0.0951588i
$859$	−8.44772	+	2.48047i	−0.288233	+	0.0846327i	−0.422653	−	0.906292i	$-0.638901\pi$
$859$	−8.44772	+	2.48047i	−0.288233	+	0.0846327i	0.134420	+	0.990924i	$0.457083\pi$
$860$		0			0
$861$	−0.0696439	−	0.484384i	−0.00237346	−	0.0165078i
$862$	18.7870	−	8.57972i	0.639887	−	0.292226i
$863$	−43.5371	+	19.8827i	−1.48202	+	0.676816i	−0.981945	−	0.189166i	$-0.939421\pi$
$863$	−43.5371	+	19.8827i	−1.48202	+	0.676816i	−0.500075	+	0.865982i	$0.666694\pi$
$864$	−4.86019	−	33.8034i	−0.165347	−	1.15001i
$865$		0			0
$866$	−48.3892	+	14.2084i	−1.64433	+	0.482820i
$867$	−5.49901	−	0.790638i	−0.186756	−	0.0268515i
$868$	−0.340708	−	0.295225i	−0.0115644	−	0.0100206i
$869$	−14.3867	+	9.24578i	−0.488036	+	0.313641i
$870$		0			0
$871$	−42.1892	−	12.3879i	−1.42953	−	0.419747i
$872$	5.12661	+	2.34124i	0.173609	+	0.0792845i
$873$			28.7593i			0.973356i
$874$	30.0798	+	5.50910i	1.01746	+	0.186348i
$875$		0			0
$876$	6.79944	−	14.8887i	0.229732	−	0.503043i
$877$	−13.2847	+	45.2435i	−0.448592	+	1.52776i	0.356317	+	0.934365i	$0.384032\pi$
$877$	−13.2847	+	45.2435i	−0.448592	+	1.52776i	−0.804909	+	0.593398i	$0.797786\pi$
$878$	31.1567	−	26.9975i	1.05149	−	0.911121i
$879$	7.14248	−	4.59020i	0.240910	−	0.154823i
$880$		0			0
$881$	−5.26169	+	36.5959i	−0.177271	+	1.23295i	0.685773	+	0.727816i	$0.259464\pi$
$881$	−5.26169	+	36.5959i	−0.177271	+	1.23295i	−0.863043	+	0.505130i	$0.831445\pi$
$882$	−8.78083	−	29.9048i	−0.295666	−	1.00695i
$883$	−29.4975	+	45.8990i	−0.992670	+	1.54462i	−0.162807	+	0.986658i	$0.552055\pi$
$883$	−29.4975	+	45.8990i	−0.992670	+	1.54462i	−0.829863	+	0.557967i	$0.811582\pi$
$884$	−5.14479	−	35.7828i	−0.173038	−	1.20351i
$885$		0			0
$886$	−20.7193	−	45.3689i	−0.696077	−	1.52420i
$887$	−14.0346	+	2.01788i	−0.471237	+	0.0677537i	−0.373843	−	0.927492i	$-0.621960\pi$
$887$	−14.0346	+	2.01788i	−0.471237	+	0.0677537i	−0.0973946	+	0.995246i	$0.531051\pi$
$888$	−0.824797	+	1.28341i	−0.0276784	+	0.0430684i
$889$	0.253060	−	0.0743050i	0.00848734	−	0.00249211i
$890$		0			0
$891$	−1.59792	+	1.84410i	−0.0535324	+	0.0617797i
$892$	−1.62329	−	2.52589i	−0.0543517	−	0.0845730i
$893$	−25.1133	+	21.7608i	−0.840384	+	0.728197i
$894$	34.1133	+	10.0166i	1.14092	+	0.335004i
$895$		0			0
$896$	−1.34240			−0.0448465
$897$	14.1616	+	9.88816i	0.472843	+	0.330156i
$898$		−	10.9523i		−	0.365484i
$899$	−5.33109	+	11.6735i	−0.177802	+	0.389332i
$900$		0			0
$901$	22.9847	+	26.5257i	0.765730	+	0.883699i
$902$	−16.3211	−	25.3962i	−0.543434	−	0.845600i
$903$	0.159714	+	0.138393i	0.00531494	+	0.00460542i
$904$	−5.49580	+	38.2242i	−0.182788	+	1.27132i
$905$		0			0
$906$	−0.829210	−	0.532901i	−0.0275486	−	0.0177044i
$907$	49.3023	−	7.08860i	1.63706	−	0.235373i	0.738506	−	0.674246i	$-0.235531\pi$
$907$	49.3023	−	7.08860i	1.63706	−	0.235373i	0.898549	+	0.438873i	$0.144622\pi$
$908$	13.6091	−	6.21507i	0.451634	−	0.206254i
$909$	14.4425	+	31.6247i	0.479028	+	1.04892i
$910$		0			0
$911$	−17.7763	−	11.4241i	−0.588955	−	0.378498i	0.211959	−	0.977279i	$-0.432016\pi$
$911$	−17.7763	−	11.4241i	−0.588955	−	0.378498i	−0.800913	+	0.598781i	$0.795652\pi$
$912$	0.911132	+	3.10303i	0.0301706	+	0.102752i
$913$	10.0779	+	1.44898i	0.333529	+	0.0479543i
$914$	16.9046	−	19.5090i	0.559156	−	0.645300i
$915$		0			0
$916$	44.5941	+	51.4644i	1.47343	+	1.70043i
$917$	−0.333391	+	1.13543i	−0.0110095	+	0.0374951i
$918$	−34.2915	−	15.6604i	−1.13179	−	0.516870i
$919$	1.66022			0.0547657			0.0273829	−	0.999625i	$-0.491283\pi$
$919$	1.66022			0.0547657			0.0273829	+	0.999625i	$0.491283\pi$
$920$		0			0
$921$	14.6797			0.483711
$922$	−31.5235	−	14.3963i	−1.03817	−	0.474116i
$923$	1.92459	−	6.55457i	0.0633488	−	0.215746i
$924$	−0.417970	−	0.482363i	−0.0137502	−	0.0158686i
$925$		0			0
$926$	−14.7804	+	17.0575i	−0.485715	+	0.560545i
$927$	2.30300	+	0.331122i	0.0756406	+	0.0108755i
$928$	14.3281	+	48.7971i	0.470343	+	1.60184i
$929$	−24.5455	−	15.7744i	−0.805311	−	0.517542i	0.0720340	−	0.997402i	$-0.477051\pi$
$929$	−24.5455	−	15.7744i	−0.805311	−	0.517542i	−0.877345	+	0.479860i	$0.840687\pi$
$930$		0			0
$931$	8.31037	+	18.1972i	0.272361	+	0.596388i
$932$	−58.0904	+	26.5290i	−1.90281	+	0.868986i
$933$	29.8688	−	4.29449i	0.977861	−	0.140595i
$934$	−0.299702	−	0.192607i	−0.00980656	−	0.00630229i
$935$		0			0
$936$	−2.20955	+	15.3678i	−0.0722214	+	0.502311i
$937$	−13.9149	−	12.0573i	−0.454580	−	0.393895i	0.397253	−	0.917709i	$-0.369963\pi$
$937$	−13.9149	−	12.0573i	−0.454580	−	0.393895i	−0.851833	+	0.523813i	$0.824509\pi$
$938$	1.29685	+	2.01794i	0.0423437	+	0.0658881i
$939$	3.64497	+	4.20652i	0.118949	+	0.137275i
$940$		0			0
$941$	17.9910	−	39.3947i	0.586489	−	1.28423i	−0.351052	−	0.936356i	$-0.614176\pi$
$941$	17.9910	−	39.3947i	0.586489	−	1.28423i	0.937541	−	0.347876i	$-0.113097\pi$
$942$		−	15.8655i		−	0.516926i
$943$	−2.77584	−	26.4772i	−0.0903937	−	0.862215i
$944$	13.0596			0.425053
$945$		0			0
$946$	12.5088	+	3.67290i	0.406695	+	0.119416i
$947$	−15.9299	+	13.8033i	−0.517652	+	0.448548i	−0.874085	−	0.485773i	$-0.838538\pi$
$947$	−15.9299	+	13.8033i	−0.517652	+	0.448548i	0.356433	+	0.934321i	$0.383993\pi$
$948$	11.2428	+	17.4941i	0.365149	+	0.568183i
$949$	13.0102	−	15.0146i	0.422330	−	0.487395i
$950$		0			0
$951$	2.69722	−	0.791977i	0.0874635	−	0.0256816i
$952$	−0.347535	+	0.540775i	−0.0112637	+	0.0175266i
$953$	−14.5941	+	2.09831i	−0.472749	+	0.0679710i	−0.374572	−	0.927198i	$-0.622210\pi$
$953$	−14.5941	+	2.09831i	−0.472749	+	0.0679710i	−0.0981772	+	0.995169i	$0.531301\pi$
$954$	−19.2113	−	42.0669i	−0.621989	−	1.36197i
$955$		0			0
$956$	3.70319	+	25.7562i	0.119770	+	0.833016i
$957$	−9.82277	+	15.2845i	−0.317525	+	0.494079i
$958$	3.68873	+	12.5627i	0.119178	+	0.405881i
$959$	0.242051	−	1.68350i	0.00781622	−	0.0543630i
$960$		0			0
$961$	−23.5799	+	15.1539i	−0.760642	+	0.488835i
$962$	−4.29349	+	3.72033i	−0.138428	+	0.119948i
$963$	9.66362	−	32.9113i	0.311406	−	1.06055i
$964$	−10.8691	+	23.8001i	−0.350071	+	0.766549i
$965$		0			0
$966$	−0.230613	−	0.913599i	−0.00741984	−	0.0293946i
$967$		−	25.3720i		−	0.815909i	−0.913002	−	0.407955i	$-0.866242\pi$
$967$		−	25.3720i		−	0.815909i	0.913002	−	0.407955i	$-0.133758\pi$
$968$	9.89347	+	4.51820i	0.317988	+	0.145220i
$969$	9.28671	+	2.72682i	0.298332	+	0.0875982i
$970$		0			0
$971$	−32.9014	+	21.1444i	−1.05586	+	0.678557i	−0.948858	−	0.315702i	$-0.897760\pi$
$971$	−32.9014	+	21.1444i	−1.05586	+	0.678557i	−0.106997	+	0.994259i	$0.534124\pi$
$972$	35.8786	+	31.0890i	1.15081	+	0.997180i
$973$	1.35218	+	0.194414i	0.0433488	+	0.00623261i
$974$	−14.8280	+	4.35388i	−0.475118	+	0.139507i
$975$		0			0
$976$	0.653409	+	4.54456i	0.0209151	+	0.145468i
$977$	21.1528	−	9.66014i	0.676736	−	0.309055i	−0.0472363	−	0.998884i	$-0.515041\pi$
$977$	21.1528	−	9.66014i	0.676736	−	0.309055i	0.723973	+	0.689829i	$0.242314\pi$
$978$	14.4878	−	6.61636i	0.463269	−	0.211568i
$979$	−5.53774	−	38.5158i	−0.176987	−	1.23097i
$980$		0			0
$981$	5.01759	−	1.47330i	0.160199	−	0.0470387i
$982$	48.4365	+	6.96412i	1.54567	+	0.222234i
$983$	0.497051	+	0.430697i	0.0158535	+	0.0137371i	0.662751	−	0.748839i	$-0.269389\pi$
$983$	0.497051	+	0.430697i	0.0158535	+	0.0137371i	−0.646898	+	0.762577i	$0.723934\pi$
$984$	−10.0658	+	6.46891i	−0.320887	+	0.206221i
$985$		0			0
$986$	53.8655	+	15.8163i	1.71543	+	0.503695i
$987$	0.931366	+	0.425341i	0.0296457	+	0.0135387i
$988$		−	30.5733i		−	0.972667i
$989$	8.39371	+	7.85633i	0.266905	+	0.249817i
$990$		0			0
$991$	1.31140	−	2.87157i	0.0416581	−	0.0912185i	−0.887659	−	0.460502i	$-0.847670\pi$
$991$	1.31140	−	2.87157i	0.0416581	−	0.0912185i	0.929317	+	0.369283i	$0.120397\pi$
$992$	3.31654	−	11.2951i	0.105300	−	0.358620i
$993$	−10.4695	+	9.07184i	−0.332238	+	0.287886i
$994$	−0.313510	+	0.201480i	−0.00994392	+	0.00639057i
$995$		0			0
$996$	1.76195	−	12.2546i	0.0558295	−	0.388303i
$997$	2.48154	+	8.45136i	0.0785913	+	0.267657i	0.989410	−	0.145150i	$-0.0463665\pi$
$997$	2.48154	+	8.45136i	0.0785913	+	0.267657i	−0.910818	+	0.412807i	$0.864548\pi$
$998$	−34.2823	+	53.3443i	−1.08519	+	1.68858i
$999$	0.503637	+	3.50287i	0.0159344	+	0.110826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.p.a.374.2		20
5.2	odd	4		575.2.k.a.351.1		10
5.3	odd	4		115.2.g.a.6.1	✓	10
5.4	even	2	inner	575.2.p.a.374.1		20
23.4	even	11	inner	575.2.p.a.349.1		20
115.4	even	22	inner	575.2.p.a.349.2		20
115.27	odd	44		575.2.k.a.326.1		10
115.48	odd	44		2645.2.a.n.1.5		5
115.73	odd	44		115.2.g.a.96.1	yes	10
115.113	even	44		2645.2.a.o.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.6.1	✓	10	5.3	odd	4
115.2.g.a.96.1	yes	10	115.73	odd	44
575.2.k.a.326.1		10	115.27	odd	44
575.2.k.a.351.1		10	5.2	odd	4
575.2.p.a.349.1		20	23.4	even	11	inner
575.2.p.a.349.2		20	115.4	even	22	inner
575.2.p.a.374.1		20	5.4	even	2	inner
575.2.p.a.374.2		20	1.1	even	1	trivial
2645.2.a.n.1.5		5	115.48	odd	44
2645.2.a.o.1.5		5	115.113	even	44

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.p (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.02730 + 0.925839i) q^{2} +(0.281733 - 0.959493i) q^{3} +(1.94306 + 2.24241i) q^{4} +(1.45949 - 1.68434i) q^{6} +(-0.0872586 - 0.0125459i) q^{7} +(0.607265 + 2.06815i) q^{8} +(1.68251 + 1.08128i) q^{9} +(1.01365 + 2.21959i) q^{11} +(2.69900 - 1.23259i) q^{12} +(3.56484 - 0.512546i) q^{13} +(-0.165284 - 0.106222i) q^{14} +(0.160869 - 1.11887i) q^{16} +(-2.55667 - 2.21537i) q^{17} +(2.40986 + 3.74982i) q^{18} +(-1.87358 - 2.16222i) q^{19} +(-0.0366213 + 0.0801894i) q^{21} +5.43826i q^{22} +(-2.15802 + 4.28287i) q^{23} +2.15546 q^{24} +(7.70154 + 2.26138i) q^{26} +(3.77875 - 3.27430i) q^{27} +(-0.141416 - 0.220047i) q^{28} +(-4.87604 + 5.62725i) q^{29} +(1.65370 - 0.485571i) q^{31} +(3.69269 - 5.74593i) q^{32} +(2.41526 - 0.347262i) q^{33} +(-3.13208 - 6.85830i) q^{34} +(0.844535 + 5.87387i) q^{36} +(-0.382654 + 0.595421i) q^{37} +(-1.79644 - 6.11811i) q^{38} +(0.512546 - 3.56484i) q^{39} +(-4.66991 + 3.00117i) q^{41} +(-0.148485 + 0.128663i) q^{42} +(0.675383 - 2.30014i) q^{43} +(-3.00764 + 6.58582i) q^{44} +(-8.34021 + 6.68469i) q^{46} -11.6146i q^{47} +(-1.02822 - 0.469574i) q^{48} +(-6.70899 - 1.96994i) q^{49} +(-2.84593 + 1.82897i) q^{51} +(8.07603 + 6.99792i) q^{52} +(-10.2695 - 1.47653i) q^{53} +(10.6921 - 3.13950i) q^{54} +(-0.0270422 - 0.188083i) q^{56} +(-2.60249 + 1.18852i) q^{57} +(-15.0951 + 6.89372i) q^{58} +(1.64421 + 11.4357i) q^{59} +(-3.89722 + 1.14433i) q^{61} +(3.80211 + 0.546662i) q^{62} +(-0.133248 - 0.115460i) q^{63} +(10.9041 - 7.00766i) q^{64} +(5.21797 + 1.53213i) q^{66} +(-11.1056 - 5.07177i) q^{67} -10.0377i q^{68} +(3.50140 + 3.27723i) q^{69} +(0.787956 - 1.72538i) q^{71} +(-1.21453 + 4.13631i) q^{72} +(4.16900 - 3.61246i) q^{73} +(-1.32702 + 0.852823i) q^{74} +(1.20812 - 8.40266i) q^{76} +(-0.0606031 - 0.206395i) q^{77} +(4.33955 - 6.75247i) q^{78} +(0.997420 + 6.93721i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-12.2459 + 1.76070i) q^{82} +(2.25587 - 3.51021i) q^{83} +(-0.250975 + 0.0736930i) q^{84} +(3.49877 - 4.03779i) q^{86} +(4.02557 + 6.26391i) q^{87} +(-3.97489 + 3.44426i) q^{88} +(-15.3009 - 4.49275i) q^{89} -0.317493 q^{91} +(-13.7971 + 3.48270i) q^{92} -1.72352i q^{93} +(10.7532 - 23.5463i) q^{94} +(-4.47283 - 5.16192i) q^{96} +(7.77424 + 12.0969i) q^{97} +(-11.7773 - 10.2051i) q^{98} +(-0.694523 + 4.83052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9} + 16 q^{11} + 6 q^{14} + 10 q^{16} + 26 q^{19} + 12 q^{21} + 12 q^{24} + 22 q^{26} - 4 q^{29} - 40 q^{31} - 32 q^{34} + 48 q^{36} - 10 q^{41} - 38 q^{44} - 32 q^{46}+ \cdots - 12 q^{99}+O(q^{100}) \) 20 * q + 2 * q^4 + 12 * q^6 - 4 * q^9 + 16 * q^11 + 6 * q^14 + 10 * q^16 + 26 * q^19 + 12 * q^21 + 12 * q^24 + 22 * q^26 - 4 * q^29 - 40 * q^31 - 32 * q^34 + 48 * q^36 - 10 * q^41 - 38 * q^44 - 32 * q^46 - 8 * q^49 - 20 * q^51 + 60 * q^54 + 6 * q^56 - 10 * q^59 - 6 * q^61 + 68 * q^64 - 8 * q^66 + 2 * q^69 - 44 * q^71 - 2 * q^74 - 4 * q^76 - 102 * q^79 - 2 * q^81 - 12 * q^84 - 18 * q^86 - 114 * q^89 - 44 * q^91 + 162 * q^94 - 14 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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