LMFDB - Embedded newform 575.2.p.a.349.1

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			349.1
Root			$-0.540641 - 0.841254i$ of defining polynomial
Character	$\chi$	$=$	575.349
Dual form			575.2.p.a.374.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.02730 + 0.925839i) q^{2} +(-0.281733 - 0.959493i) q^{3} +(1.94306 - 2.24241i) q^{4} +(1.45949 + 1.68434i) q^{6} +(0.0872586 - 0.0125459i) q^{7} +(-0.607265 + 2.06815i) q^{8} +(1.68251 - 1.08128i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 20 * q + 2 * q^4 + 12 * q^6 - 4 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$-1$

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	$-0.925230\pi$
$2$	−2.02730	+	0.925839i	−1.43352	+	0.654667i	−0.460982	+	0.887410i	$0.652503\pi$
$3$	−0.281733	−	0.959493i	−0.162658	−	0.553964i	−0.999974	−	0.00724338i	$-0.997694\pi$
$3$	−0.281733	−	0.959493i	−0.162658	−	0.553964i	0.837315	−	0.546720i	$-0.184124\pi$
$4$	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	$-0.540151\pi$
$7$	0.0872586	−	0.0125459i	0.0329807	−	0.00474190i	0.158785	+	0.987313i	$0.449242\pi$
$8$	−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	−0.693037	−	0.720902i	$-0.743728\pi$
$11$	1.01365	−	2.21959i	0.305628	−	0.669231i	0.998664	+	0.0516714i	$0.0164549\pi$
$12$	−2.69900	−	1.23259i	−0.779135	−	0.355819i
$13$	−3.56484	−	0.512546i	−0.988707	−	0.142155i	−0.371059	−	0.928609i	$-0.621005\pi$
$13$	−3.56484	−	0.512546i	−0.988707	−	0.142155i	−0.617648	+	0.786455i	$0.711914\pi$
$14$	−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	$-0.592716\pi$
$17$	2.55667	−	2.21537i	0.620084	−	0.537306i	0.907259	+	0.420572i	$0.138171\pi$
$18$	−2.40986	+	3.74982i	−0.568010	+	0.883840i
$19$	−1.87358	+	2.16222i	−0.429828	+	0.496048i	−0.928806	−	0.370567i	$-0.879163\pi$
$19$	−1.87358	+	2.16222i	−0.429828	+	0.496048i	0.498978	+	0.866615i	$0.333709\pi$
$20$		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	−0.998783	−	0.0493188i	$-0.984295\pi$
$29$	−4.87604	−	5.62725i	−0.905458	−	1.04495i	0.0933249	−	0.995636i	$-0.470250\pi$
$30$		0			0
$31$	1.65370	+	0.485571i	0.297014	+	0.0872110i	0.426844	−	0.904325i	$-0.359625\pi$
$31$	1.65370	+	0.485571i	0.297014	+	0.0872110i	−0.129831	+	0.991536i	$0.541443\pi$
$32$	−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	$-0.163289\pi$
$37$	0.382654	+	0.595421i	0.0629079	+	0.0978866i	−0.808375	+	0.588668i	$0.799652\pi$
$38$	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	0.122550	−	0.992462i	$-0.460893\pi$
$41$	−4.66991	−	3.00117i	−0.729317	−	0.468704i	−0.851867	+	0.523759i	$0.824529\pi$
$42$	0.148485	+	0.128663i	0.0229117	+	0.0198531i
$43$	−0.675383	−	2.30014i	−0.102995	−	0.350768i	0.891830	−	0.452370i	$-0.149421\pi$
$43$	−0.675383	−	2.30014i	−0.102995	−	0.350768i	−0.994825	+	0.101602i	$0.967603\pi$
$44$	−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	$-0.292988\pi$
$53$	10.2695	−	1.47653i	1.41062	−	0.202817i	0.805160	+	0.593058i	$0.202079\pi$
$54$	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	−0.545359	−	0.838203i	$-0.683607\pi$
$59$	1.64421	−	11.4357i	0.214058	−	1.48881i	0.759417	−	0.650604i	$-0.225484\pi$
$60$		0			0
$61$	−3.89722	−	1.14433i	−0.498988	−	0.146516i	0.0225474	−	0.999746i	$-0.492822\pi$
$61$	−3.89722	−	1.14433i	−0.498988	−	0.146516i	−0.521535	+	0.853230i	$0.674641\pi$
$62$	−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	$-0.368441\pi$
$67$	11.1056	−	5.07177i	1.35677	−	0.619615i	0.955131	+	0.296184i	$0.0957141\pi$
$68$		−	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	0.950608	−	0.310393i	$-0.100461\pi$
$71$	0.787956	+	1.72538i	0.0935131	+	0.204765i	−0.857095	+	0.515158i	$0.827733\pi$
$72$	1.21453	+	4.13631i	0.143134	+	0.487468i
$73$	−4.16900	−	3.61246i	−0.487944	−	0.422806i	0.375827	−	0.926690i	$-0.377359\pi$
$73$	−4.16900	−	3.61246i	−0.487944	−	0.422806i	−0.863772	+	0.503884i	$0.831904\pi$
$74$	−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	−0.853535	−	0.521036i	$-0.825546\pi$
$79$	0.997420	−	6.93721i	0.112219	−	0.780497i	0.965753	−	0.259461i	$-0.0835450\pi$
$80$		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	$-0.255364\pi$
$83$	−2.25587	−	3.51021i	−0.247614	−	0.385295i	−0.942705	+	0.333626i	$0.891728\pi$
$84$	−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	−0.961526	−	0.274713i	$-0.911417\pi$
$89$	−15.3009	+	4.49275i	−1.62189	+	0.476231i	−0.660367	+	0.750943i	$0.729599\pi$
$90$		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	0.180260	+	0.983619i	$0.442306\pi$
$97$	−7.77424	+	12.0969i	−0.789354	+	1.22826i	−0.969614	+	0.244640i	$0.921330\pi$
$98$	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	0.456137	−	0.889910i	$-0.349233\pi$
$101$	14.6237	−	9.39808i	1.45511	−	0.935144i	0.998976	−	0.0452346i	$-0.0144035\pi$
$102$	7.46289	+	1.07300i	0.738937	+	0.106243i
$103$	−1.05821	−	0.483270i	−0.104269	−	0.0476180i	0.362598	−	0.931946i	$-0.381890\pi$
$103$	−1.05821	−	0.483270i	−0.104269	−	0.0476180i	−0.466867	+	0.884328i	$0.654617\pi$
$104$	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	−0.303051	−	0.952974i	$-0.598005\pi$
$107$	4.83181	−	16.4556i	0.467108	−	1.59083i	0.770160	−	0.637851i	$-0.220176\pi$
$108$	−14.6847	+	2.11134i	−1.41303	+	0.203164i
$109$	1.71227	+	1.97606i	0.164006	+	0.189273i	0.831804	−	0.555070i	$-0.187308\pi$
$109$	1.71227	+	1.97606i	0.164006	+	0.189273i	−0.667798	+	0.744343i	$0.732763\pi$
$110$		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	$-0.955396\pi$
$113$	−16.2969	+	7.44256i	−1.53309	+	0.700137i	−0.542888	+	0.839805i	$0.682669\pi$
$114$	−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	$-0.321259\pi$
$127$	2.72142	+	1.24283i	0.241487	+	0.110283i	−0.290996	+	0.956724i	$0.593987\pi$
$128$	−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	0.885226	+	0.465162i	$0.154004\pi$
$131$	1.91036	+	13.2869i	0.166909	+	1.16088i	−0.718316	+	0.695716i	$0.755087\pi$
$132$	−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	−0.417122	−	0.908850i	$-0.636961\pi$
$149$	6.62691	−	14.5109i	0.542898	−	1.18878i	0.960020	−	0.279930i	$-0.0903114\pi$
$150$		0			0
$151$	−0.0629411	+	0.437765i	−0.00512208	+	0.0356248i	−0.992222	−	0.124479i	$-0.960274\pi$
$151$	−0.0629411	+	0.437765i	−0.00512208	+	0.0356248i	0.987100	+	0.160104i	$0.0511830\pi$
$152$	−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	$-0.364411\pi$
$157$	−5.37996	−	4.66176i	−0.429367	−	0.372049i	−0.842567	+	0.538592i	$0.818957\pi$
$158$	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	$-0.726656\pi$
$163$	−6.50054	+	2.96870i	−0.509162	+	0.232526i	0.144233	+	0.989544i	$0.453929\pi$
$164$	−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	$-0.710853\pi$
$167$	1.00714	−	0.872694i	0.0779351	−	0.0675311i	0.692957	+	0.720979i	$0.256307\pi$
$168$	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	$-0.396374\pi$
$173$	−2.45670	−	1.12194i	−0.186779	−	0.0852992i	−0.506609	+	0.862176i	$0.669101\pi$
$174$	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	0.986046	−	0.166474i	$-0.0532383\pi$
$179$	16.6467	+	10.6982i	1.24423	+	0.799620i	0.258188	+	0.966095i	$0.416875\pi$
$180$		0			0
$181$	−3.82402	+	1.12283i	−0.284237	+	0.0834596i	−0.420744	−	0.907180i	$-0.638231\pi$
$181$	−3.82402	+	1.12283i	−0.284237	+	0.0834596i	0.136506	+	0.990639i	$0.456413\pi$
$182$	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	0.997170	+	0.0751744i	$0.0239513\pi$
$191$	0.850935	+	5.91838i	0.0615715	+	0.428239i	−0.935599	+	0.353065i	$0.885140\pi$
$192$	3.65175	−	12.4367i	0.263543	−	0.897544i
$193$	−5.45312	−	8.48523i	−0.392524	−	0.610780i	0.587603	−	0.809149i	$-0.300072\pi$
$193$	−5.45312	−	8.48523i	−0.392524	−	0.610780i	−0.980127	+	0.198370i	$0.936435\pi$
$194$	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	$-0.396212\pi$
$197$	5.06355	+	0.728029i	0.360763	+	0.0518699i	0.0404498	+	0.999182i	$0.487121\pi$
$198$	5.88029	+	9.14991i	0.417894	+	0.650255i
$199$	25.5033	+	7.48844i	1.80788	+	0.530842i	0.998413	−	0.0563229i	$-0.0179376\pi$
$199$	25.5033	+	7.48844i	1.80788	+	0.530842i	0.809468	+	0.587164i	$0.199756\pi$
$200$		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	−0.318895	−	0.947790i	$-0.603312\pi$
$211$	9.65433	−	11.1417i	0.664631	−	0.767026i	0.983526	+	0.180765i	$0.0578572\pi$
$212$	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	$-0.534668\pi$
$223$	1.00163	−	0.144012i	0.0670740	−	0.00964378i	0.175770	+	0.984431i	$0.443758\pi$
$224$	−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	$-0.144425\pi$
$227$	−1.42057	−	4.83803i	−0.0942867	−	0.321111i	−0.993108	+	0.117205i	$0.962607\pi$
$228$	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	0.879097	+	0.476644i	$0.158147\pi$
$233$	6.06370	+	20.6511i	0.397246	+	1.35290i	−0.481850	+	0.876254i	$0.660035\pi$
$234$	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	−0.279830	−	0.960050i	$-0.590278\pi$
$239$	7.37760	−	4.74129i	0.477217	−	0.306689i	0.757047	+	0.653361i	$0.226642\pi$
$240$		0			0
$241$	3.66317	−	8.02123i	0.235966	−	0.516693i	−0.754191	−	0.656655i	$-0.771971\pi$
$241$	3.66317	−	8.02123i	0.235966	−	0.516693i	0.990157	+	0.139962i	$0.0446980\pi$
$242$	−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	0.816521	−	0.577316i	$-0.195900\pi$
$251$	−2.44763	−	5.35957i	−0.154493	−	0.338293i	−0.971014	+	0.239023i	$0.923173\pi$
$252$		−	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	$-0.195391\pi$
$257$	5.82941	+	5.05121i	0.363628	+	0.315086i	−0.453814	+	0.891097i	$0.649937\pi$
$258$	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	$-0.212009\pi$
$263$	22.1627	+	3.18652i	1.36661	+	0.196489i	0.580343	+	0.814372i	$0.302919\pi$
$264$	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	0.989727	+	0.142968i	$0.0456648\pi$
$269$	1.31816	+	9.16802i	0.0803698	+	0.558984i	−0.909357	+	0.416016i	$0.863426\pi$
$270$		0			0
$271$	18.4727	+	11.8717i	1.12214	+	0.721154i	0.963905	−	0.266247i	$-0.0857838\pi$
$271$	18.4727	+	11.8717i	1.12214	+	0.721154i	0.158233	+	0.987402i	$0.449420\pi$
$272$	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	−0.246699	−	0.969092i	$-0.579346\pi$
$281$	−20.6303	−	13.2583i	−1.23070	−	0.790922i	−0.984000	+	0.178171i	$0.942982\pi$
$282$	19.5629	−	16.9514i	1.16496	−	1.00944i
$283$	17.4860	−	2.51410i	1.03943	−	0.149448i	0.398597	−	0.917126i	$-0.369497\pi$
$283$	17.4860	−	2.51410i	1.03943	−	0.149448i	0.640836	+	0.767678i	$0.278588\pi$
$284$	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	$-0.807047\pi$
$293$	−6.41653	+	5.55996i	−0.374858	+	0.324816i	0.446973	+	0.894547i	$0.352502\pi$
$294$	−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	0.753228	+	0.657759i	$0.228496\pi$
$307$	−4.13574	+	14.0850i	−0.236039	+	0.803875i	−0.989267	+	0.146116i	$0.953323\pi$
$308$	−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	−0.115506	−	0.993307i	$-0.536849\pi$
$311$	12.5355	−	27.4490i	0.710826	−	1.55649i	0.826332	−	0.563184i	$-0.190424\pi$
$312$	−7.68388	−	1.10477i	−0.435014	−	0.0625455i
$313$	3.00922	+	4.68243i	0.170091	+	0.264667i	0.915826	−	0.401576i	$-0.131538\pi$
$313$	3.00922	+	4.68243i	0.170091	+	0.264667i	−0.745734	+	0.666243i	$0.767901\pi$
$314$	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	$-0.843336\pi$
$317$	−1.51979	+	2.36484i	−0.0853600	+	0.132823i	0.795948	+	0.605365i	$0.206973\pi$
$318$	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	−0.820206	−	0.572069i	$-0.806141\pi$
$331$	−11.6540	+	7.48954i	−0.640560	+	0.411663i	0.179646	+	0.983731i	$0.442505\pi$
$332$	−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	−0.610663	−	0.791890i	$-0.709097\pi$
$337$	6.07980	−	20.7059i	0.331188	−	1.12792i	0.941851	−	0.336031i	$-0.109085\pi$
$338$	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	$-0.805796\pi$
$347$	−17.1989	+	7.85449i	−0.923288	+	0.421651i	−0.103702	+	0.994608i	$0.533069\pi$
$348$	6.22434	+	21.1981i	0.333659	+	1.13634i
$349$	13.7056	−	15.8171i	0.733643	−	0.846669i	−0.259234	−	0.965815i	$-0.583470\pi$
$349$	13.7056	−	15.8171i	0.733643	−	0.846669i	0.992877	+	0.119146i	$0.0380155\pi$
$350$		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	$-0.922750\pi$
$353$	−0.454159	+	1.54672i	−0.0241724	+	0.0823238i	0.946523	+	0.322635i	$0.104569\pi$
$354$	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	−0.559464	+	0.828854i	$0.688993\pi$
$359$	−29.2892	+	18.8230i	−1.54583	+	0.993442i	−0.986362	+	0.164588i	$0.947371\pi$
$360$		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	$-0.728021\pi$
$373$	5.83633	−	9.08151i	0.302194	−	0.470223i	0.958828	+	0.283986i	$0.0916570\pi$
$374$	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	−0.866204	−	0.499690i	$-0.833447\pi$
$379$	1.53173	−	3.35401i	0.0786795	−	0.172284i	0.944884	+	0.327406i	$0.106174\pi$
$380$		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	$-0.860574\pi$
$383$	1.67426	−	5.70202i	0.0855509	−	0.291360i	0.991145	+	0.132787i	$0.0423925\pi$
$384$	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	0.826693	−	0.562654i	$-0.190220\pi$
$389$	−2.75929	−	6.04199i	−0.139901	−	0.306341i	−0.966594	+	0.256313i	$0.917492\pi$
$390$		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	$-0.763756\pi$
$397$	−3.44429	+	2.98449i	−0.172864	+	0.149787i	0.564132	+	0.825685i	$0.309211\pi$
$398$	−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	−0.610676	−	0.791880i	$-0.709102\pi$
$401$	3.97219	−	27.6272i	0.198362	−	1.37964i	0.809038	−	0.587756i	$-0.199989\pi$
$402$	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	0.360772	−	0.932654i	$-0.382513\pi$
$409$	−6.83017	−	4.38949i	−0.337730	−	0.217046i	−0.698502	+	0.715608i	$0.746150\pi$
$410$		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	0.967587	−	0.252539i	$-0.0812658\pi$
$419$	23.3315	+	14.9942i	1.13982	+	0.732517i	0.172232	+	0.985056i	$0.444902\pi$
$420$		0			0
$421$	4.97445	+	34.5981i	0.242440	+	1.68621i	0.639799	+	0.768543i	$0.279018\pi$
$421$	4.97445	+	34.5981i	0.242440	+	1.68621i	−0.397359	+	0.917663i	$0.630073\pi$
$422$	−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	0.882843	−	0.469669i	$-0.155627\pi$
$431$	6.06858	+	7.00351i	0.292313	+	0.337347i	−0.590530	+	0.807016i	$0.701081\pi$
$432$	3.05563	−	4.75465i	0.147014	−	0.228758i
$433$	17.1014	+	14.8185i	0.821841	+	0.712129i	0.960521	−	0.278208i	$-0.0897404\pi$
$433$	17.1014	+	14.8185i	0.821841	+	0.712129i	−0.138680	+	0.990337i	$0.544286\pi$
$434$	−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	0.999586	+	0.0287853i	$0.00916393\pi$
$439$	7.68428	+	16.8262i	0.366751	+	0.803072i	−0.632835	+	0.774287i	$0.718109\pi$
$440$		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	$-0.548853\pi$
$443$	16.9129	−	14.6551i	0.803554	−	0.696284i	0.956430	+	0.291962i	$0.0943080\pi$
$444$	−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	−0.951666	−	0.307134i	$-0.900630\pi$
$449$	−2.04143	+	4.47012i	−0.0963412	+	0.210958i	0.855325	+	0.518092i	$0.173357\pi$
$450$		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	$-0.178232\pi$
$457$	−3.26318	−	11.1134i	−0.152645	−	0.519861i	−0.999937	+	0.0112669i	$0.996414\pi$
$458$	−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	$-0.0152943\pi$
$463$	2.85313	+	9.71687i	0.132596	+	0.451581i	−0.866250	+	0.499611i	$0.833476\pi$
$464$	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	$-0.544277\pi$
$467$	0.158222	−	0.0227489i	0.00732164	−	0.00105269i	0.145975	+	0.989288i	$0.453368\pi$
$468$	−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	−0.661022	−	0.750366i	$-0.729877\pi$
$479$	3.84712	−	4.43982i	0.175779	−	0.202860i	0.836802	+	0.547506i	$0.184423\pi$
$480$		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	$-0.222511\pi$
$487$	5.24040	+	4.54083i	0.237465	+	0.205765i	−0.527996	+	0.849247i	$0.677056\pi$
$488$	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	0.720097	−	0.693873i	$-0.244097\pi$
$491$	21.0671	+	6.18586i	0.950745	+	0.279164i	0.230648	+	0.973037i	$0.425915\pi$
$492$	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	−0.853783	−	0.520630i	$-0.825697\pi$
$499$	−4.04910	−	28.1621i	−0.181263	−	1.26071i	0.672520	−	0.740079i	$-0.265212\pi$
$500$		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	0.832737	+	0.553668i	$0.186773\pi$
$503$	9.67821	+	32.9609i	0.431530	+	1.46966i	−0.401207	+	0.915987i	$0.631409\pi$
$504$	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	−0.424767	−	0.905303i	$-0.639644\pi$
$509$	−6.60273	+	1.93874i	−0.292661	+	0.0859329i	0.132107	+	0.991236i	$0.457826\pi$
$510$		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	0.395589	−	0.918427i	$-0.370540\pi$
$521$	5.29187	+	1.55383i	0.231841	+	0.0680747i	−0.163748	+	0.986502i	$0.552358\pi$
$522$	32.8517	−	4.72337i	1.43788	−	0.206736i
$523$	3.59678	−	3.11663i	0.157276	−	0.136281i	−0.572668	−	0.819787i	$-0.694092\pi$
$523$	3.59678	−	3.11663i	0.157276	−	0.136281i	0.729944	+	0.683507i	$0.239546\pi$
$524$	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	−0.998411	−	0.0563484i	$-0.982054\pi$
$541$	−7.02447	+	15.3814i	−0.302006	+	0.661300i	0.696406	+	0.717648i	$0.254782\pi$
$542$	−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	−0.0302093	−	0.999544i	$-0.509617\pi$
$547$	20.8518	−	32.4460i	0.891557	−	1.38729i	0.921766	−	0.387746i	$-0.126746\pi$
$548$	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	−0.103475	+	0.994632i	$0.532996\pi$
$557$	−22.7805	+	35.4471i	−0.965239	+	1.50194i	−0.861764	+	0.507309i	$0.830640\pi$
$558$	−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	$-0.323150\pi$
$563$	5.47564	+	2.50064i	0.230771	+	0.105389i	−0.296674	+	0.954979i	$0.595877\pi$
$564$	−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	0.463121	−	0.886295i	$-0.346729\pi$
$569$	−11.4512	−	13.2154i	−0.480061	−	0.554020i	−0.943183	+	0.332275i	$0.892184\pi$
$570$		0			0
$571$	−8.64327	+	9.97487i	−0.361710	+	0.417435i	−0.907212	−	0.420674i	$-0.861794\pi$
$571$	−8.64327	+	9.97487i	−0.361710	+	0.417435i	0.545502	+	0.838109i	$0.316339\pi$
$572$	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	$-0.399984\pi$
$577$	29.5506	−	13.4953i	1.23021	−	0.561818i	0.921143	+	0.389223i	$0.127257\pi$
$578$	−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	$-0.451263\pi$
$587$	−11.9812	−	5.47162i	−0.494516	−	0.225838i	−0.647032	+	0.762463i	$0.723990\pi$
$588$	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	−0.289779	−	0.957094i	$-0.593582\pi$
$593$	17.0754	−	26.5698i	0.701202	−	1.09109i	0.990982	−	0.133999i	$-0.0427818\pi$
$594$	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	−0.866243	−	0.499622i	$-0.833472\pi$
$601$	−32.4793	+	9.53678i	−1.32486	+	0.389013i	−0.458614	+	0.888636i	$0.651654\pi$
$602$	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	$-0.0360021\pi$
$607$	11.7812	+	18.3320i	0.478186	+	0.744072i	−0.515424	+	0.856935i	$0.672366\pi$
$608$	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	$-0.865359\pi$
$613$	1.91064	−	6.50705i	0.0771701	−	0.262817i	0.989037	+	0.147669i	$0.0471771\pi$
$614$	−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	$-0.0476956\pi$
$617$	24.3863	+	21.1308i	0.981755	+	0.850695i	−0.00704038	+	0.999975i	$0.502241\pi$
$618$	−0.730462	−	2.48773i	−0.0293835	−	0.100071i
$619$	14.5801	+	31.9260i	0.586024	+	1.28321i	0.937815	+	0.347134i	$0.112845\pi$
$619$	14.5801	+	31.9260i	0.586024	+	1.28321i	−0.351792	+	0.936078i	$0.614427\pi$
$620$		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	−0.918904	−	0.394480i	$-0.870925\pi$
$631$	1.85675	−	12.9139i	0.0739159	−	0.514096i	0.992820	−	0.119616i	$-0.0381663\pi$
$632$	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	0.487291	−	0.873239i	$-0.337985\pi$
$641$	34.6688	−	10.1797i	1.36934	−	0.402073i	0.882044	+	0.471166i	$0.156167\pi$
$642$	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	$-0.00305767\pi$
$647$	3.90562	+	13.3013i	0.153546	+	0.522929i	−0.846408	+	0.532535i	$0.821239\pi$
$648$	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	$-0.146526\pi$
$653$	3.05729	+	4.75724i	0.119641	+	0.186165i	−0.776267	+	0.630404i	$0.782889\pi$
$654$	−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	0.778461	−	0.627692i	$-0.216000\pi$
$659$	28.0838	+	8.24614i	1.09399	+	0.321224i	0.315527	+	0.948917i	$0.397819\pi$
$660$		0			0
$661$	−10.5207	−	12.1415i	−0.409207	−	0.472250i	0.513312	−	0.858202i	$-0.328418\pi$
$661$	−10.5207	−	12.1415i	−0.409207	−	0.472250i	−0.922519	+	0.385952i	$0.873873\pi$
$662$	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	$-0.750750\pi$
$673$	−2.88949	+	2.50376i	−0.111382	+	0.0965128i	0.597389	+	0.801951i	$0.296205\pi$
$674$	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	$-0.556767\pi$
$677$	−16.2586	−	2.33764i	−0.624870	−	0.0898428i	−0.447474	+	0.894297i	$0.647676\pi$
$678$	−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	$-0.590434\pi$
$683$	−7.28651	+	1.04764i	−0.278811	+	0.0400869i	0.00149105	+	0.999999i	$0.499525\pi$
$684$	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	−0.207057	−	0.978329i	$-0.566388\pi$
$701$	17.6838	−	38.7221i	0.667908	−	1.46252i	0.874965	−	0.484186i	$-0.160884\pi$
$702$	−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	−0.137459	−	0.990507i	$-0.543894\pi$
$709$	22.9666	−	26.5049i	0.862529	−	0.995411i	0.999988	−	0.00490358i	$-0.00156086\pi$
$710$		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	0.959054	−	0.283223i	$-0.0914036\pi$
$719$	14.5394	+	16.7793i	0.542226	+	0.625763i	−0.416828	+	0.908986i	$0.636858\pi$
$720$		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	$-0.177694\pi$
$727$	0.377738	+	0.587772i	0.0140095	+	0.0217993i	−0.834178	+	0.551495i	$0.814058\pi$
$728$	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	−0.889577	−	0.456785i	$-0.849001\pi$
$733$	−10.5094	−	35.7918i	−0.388174	−	1.32200i	0.501403	−	0.865214i	$-0.332817\pi$
$734$	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	−0.684936	−	0.728603i	$-0.740170\pi$
$739$	−23.5752	+	6.92231i	−0.867229	+	0.254641i	−0.182293	+	0.983244i	$0.558352\pi$
$740$		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	$-0.819606\pi$
$743$	−40.9388	+	5.88612i	−1.50190	+	0.215941i	−0.658236	+	0.752811i	$0.728697\pi$
$744$	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	0.904372	−	0.426744i	$-0.140339\pi$
$751$	39.3106	+	11.5426i	1.43446	+	0.421197i	0.530091	+	0.847941i	$0.322158\pi$
$752$	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	$-0.694465\pi$
$757$	−9.08592	+	4.14940i	−0.330233	+	0.150812i	0.243397	+	0.969927i	$0.421738\pi$
$758$			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	0.739170	−	0.673519i	$-0.235218\pi$
$761$	−7.00401	−	15.3366i	−0.253895	−	0.555953i	−0.993065	+	0.117566i	$0.962491\pi$
$762$	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	0.495599	+	0.868551i	$0.334949\pi$
$769$	−6.22901	+	43.3237i	−0.224624	+	1.56229i	−0.720223	+	0.693743i	$0.755961\pi$
$770$		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	−0.996937	−	0.0782114i	$-0.975079\pi$
$773$	−18.1814	−	28.2907i	−0.653938	−	1.01755i	0.342999	−	0.939336i	$-0.388557\pi$
$774$	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	$-0.825278\pi$
$787$	−0.676215	+	1.05221i	−0.0241045	+	0.0375073i	0.828992	+	0.559260i	$0.188915\pi$
$788$	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	$-0.978538\pi$
$797$	−3.44308	+	11.7261i	−0.121960	+	0.415358i	0.875768	+	0.482733i	$0.160356\pi$
$798$	−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	−0.975153	−	0.221533i	$-0.928894\pi$
$809$	−17.5520	+	20.2561i	−0.617097	+	0.712167i	0.358056	+	0.933700i	$0.383440\pi$
$810$		0			0
$811$	25.9259	+	29.9201i	0.910381	+	1.05064i	0.998512	+	0.0545266i	$0.0173650\pi$
$811$	25.9259	+	29.9201i	0.910381	+	1.05064i	−0.0881316	+	0.996109i	$0.528090\pi$
$812$	−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	0.903648	+	0.428275i	$0.140879\pi$
$821$	4.50608	+	31.3404i	0.157263	+	1.09379i	−0.746385	+	0.665514i	$0.768212\pi$
$822$	−32.4964	+	28.1583i	−1.13344	+	0.982134i
$823$	−25.3640	+	39.4672i	−0.884134	+	1.37574i	0.0422285	+	0.999108i	$0.486554\pi$
$823$	−25.3640	+	39.4672i	−0.884134	+	1.37574i	−0.926363	+	0.376632i	$0.877082\pi$
$824$	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	−0.606521	−	0.795068i	$-0.707435\pi$
$839$	11.3411	−	24.8335i	0.391538	−	0.857348i	0.998059	−	0.0622806i	$-0.0198374\pi$
$840$		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	$-0.796539\pi$
$853$	−25.6230	+	11.7016i	−0.877316	+	0.400657i	−0.0747372	+	0.997203i	$0.523812\pi$
$854$	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	$-0.788755\pi$
$857$	−8.49369	+	7.35982i	−0.290139	+	0.251407i	0.497613	+	0.867399i	$0.334210\pi$
$858$	−19.3865	+	2.78736i	−0.661844	+	0.0951588i
$859$	−8.44772	−	2.48047i	−0.288233	−	0.0846327i	0.134420	−	0.990924i	$-0.457083\pi$
$859$	−8.44772	−	2.48047i	−0.288233	−	0.0846327i	−0.422653	+	0.906292i	$0.638901\pi$
$860$		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	$-0.0605786\pi$
$863$	43.5371	+	19.8827i	1.48202	+	0.676816i	0.500075	+	0.865982i	$0.333306\pi$
$864$	−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	0.804909	+	0.593398i	$0.202214\pi$
$877$	13.2847	+	45.2435i	0.448592	+	1.52776i	−0.356317	+	0.934365i	$0.615968\pi$
$878$	−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	−0.863043	−	0.505130i	$-0.831445\pi$
$881$	−5.26169	−	36.5959i	−0.177271	−	1.23295i	0.685773	−	0.727816i	$-0.259464\pi$
$882$	8.78083	−	29.9048i	0.295666	−	1.00695i
$883$	29.4975	+	45.8990i	0.992670	+	1.54462i	0.829863	+	0.557967i	$0.188418\pi$
$883$	29.4975	+	45.8990i	0.992670	+	1.54462i	0.162807	+	0.986658i	$0.447945\pi$
$884$	−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	$-0.378040\pi$
$887$	14.0346	+	2.01788i	0.471237	+	0.0677537i	0.0973946	+	0.995246i	$0.468949\pi$
$888$	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	$-0.764469\pi$
$907$	−49.3023	−	7.08860i	−1.63706	−	0.235373i	−0.898549	+	0.438873i	$0.855378\pi$
$908$	−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	−0.800913	−	0.598781i	$-0.795652\pi$
$911$	−17.7763	+	11.4241i	−0.588955	+	0.378498i	0.211959	+	0.977279i	$0.432016\pi$
$912$	−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	−0.877345	−	0.479860i	$-0.840687\pi$
$929$	−24.5455	+	15.7744i	−0.805311	+	0.517542i	0.0720340	+	0.997402i	$0.477051\pi$
$930$		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	$-0.630037\pi$
$937$	13.9149	−	12.0573i	0.454580	−	0.393895i	0.851833	+	0.523813i	$0.175491\pi$
$938$	−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	0.937541	+	0.347876i	$0.113097\pi$
$941$	17.9910	+	39.3947i	0.586489	+	1.28423i	−0.351052	+	0.936356i	$0.614176\pi$
$942$		−	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	$-0.161462\pi$
$947$	15.9299	+	13.8033i	0.517652	+	0.448548i	−0.356433	+	0.934321i	$0.616007\pi$
$948$	−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	$-0.377790\pi$
$953$	14.5941	+	2.09831i	0.472749	+	0.0679710i	0.0981772	+	0.995169i	$0.468699\pi$
$954$	−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	−0.106997	−	0.994259i	$-0.534124\pi$
$971$	−32.9014	−	21.1444i	−1.05586	−	0.678557i	−0.948858	+	0.315702i	$0.897760\pi$
$972$	−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	$-0.484959\pi$
$977$	−21.1528	−	9.66014i	−0.676736	−	0.309055i	−0.723973	+	0.689829i	$0.757686\pi$
$978$	−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	$-0.730611\pi$
$983$	−0.497051	+	0.430697i	−0.0158535	+	0.0137371i	0.646898	+	0.762577i	$0.276066\pi$
$984$	−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	0.929317	−	0.369283i	$-0.120397\pi$
$991$	1.31140	+	2.87157i	0.0416581	+	0.0912185i	−0.887659	+	0.460502i	$0.847670\pi$
$992$	−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	$-0.953634\pi$
$997$	−2.48154	+	8.45136i	−0.0785913	+	0.267657i	0.910818	+	0.412807i	$0.135452\pi$
$998$	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.349.1		20
5.2	odd	4		575.2.k.a.326.1		10
5.3	odd	4		115.2.g.a.96.1	yes	10
5.4	even	2	inner	575.2.p.a.349.2		20
23.6	even	11	inner	575.2.p.a.374.2		20
115.29	even	22	inner	575.2.p.a.374.1		20
115.52	odd	44		575.2.k.a.351.1		10
115.58	odd	44		2645.2.a.n.1.5		5
115.98	odd	44		115.2.g.a.6.1	✓	10
115.103	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	115.98	odd	44
115.2.g.a.96.1	yes	10	5.3	odd	4
575.2.k.a.326.1		10	5.2	odd	4
575.2.k.a.351.1		10	115.52	odd	44
575.2.p.a.349.1		20	1.1	even	1	trivial
575.2.p.a.349.2		20	5.4	even	2	inner
575.2.p.a.374.1		20	115.29	even	22	inner
575.2.p.a.374.2		20	23.6	even	11	inner
2645.2.a.n.1.5		5	115.58	odd	44
2645.2.a.o.1.5		5	115.103	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.02730 + 0.925839i) q^{2} +(-0.281733 - 0.959493i) q^{3} +(1.94306 - 2.24241i) q^{4} +(1.45949 + 1.68434i) q^{6} +(0.0872586 - 0.0125459i) q^{7} +(-0.607265 + 2.06815i) q^{8} +(1.68251 - 1.08128i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9}+O(q^{10}) \) 20 * q + 2 * q^4 + 12 * q^6 - 4 * q^9	\( 20 q + 2 q^{4} + 12 q^{6} - 4 q^{9} + 16 q^{11} + 6 q^{14} + 10 q^{16} + 26 q^{19} + 12 q^{21} + 12 q^{24} + 22 q^{26} - 4 q^{29} - 40 q^{31} - 32 q^{34} + 48 q^{36} - 10 q^{41} - 38 q^{44} - 32 q^{46} - 8 q^{49} - 20 q^{51} + 60 q^{54} + 6 q^{56} - 10 q^{59} - 6 q^{61} + 68 q^{64} - 8 q^{66} + 2 q^{69} - 44 q^{71} - 2 q^{74} - 4 q^{76} - 102 q^{79} - 2 q^{81} - 12 q^{84} - 18 q^{86} - 114 q^{89} - 44 q^{91} + 162 q^{94} - 14 q^{96} - 12 q^{99}+O(q^{100}) \) 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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