LMFDB - Embedded newform 575.2.k.a.326.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(26,575)]

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([0, 16]))

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

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

chi := DirichletCharacter("575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.k (of order $11$, degree $10$, 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:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 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:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			326.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	575.326
Dual form			575.2.k.a.351.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.925839 - 2.02730i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-1.94306 + 2.24241i) q^{4} +(1.45949 + 1.68434i) q^{6} +(0.0125459 + 0.0872586i) q^{7} +(2.06815 + 0.607265i) q^{8} +(-1.68251 + 1.08128i) q^{9} +(1.01365 - 2.21959i) q^{11} +(1.23259 - 2.69900i) q^{12} +(-0.512546 + 3.56484i) q^{13} +(0.165284 - 0.106222i) q^{14} +(0.160869 + 1.11887i) q^{16} +(2.21537 + 2.55667i) q^{17} +(3.74982 + 2.40986i) q^{18} +(1.87358 - 2.16222i) q^{19} +(-0.0366213 - 0.0801894i) q^{21} -5.43826 q^{22} +(4.28287 - 2.15802i) q^{23} -2.15546 q^{24} +(7.70154 - 2.26138i) q^{26} +(3.27430 - 3.77875i) q^{27} +(-0.220047 - 0.141416i) q^{28} +(4.87604 + 5.62725i) q^{29} +(1.65370 + 0.485571i) q^{31} +(5.74593 - 3.69269i) q^{32} +(-0.347262 + 2.41526i) q^{33} +(3.13208 - 6.85830i) q^{34} +(0.844535 - 5.87387i) q^{36} +(-0.595421 + 0.382654i) q^{37} +(-6.11811 - 1.79644i) q^{38} +(-0.512546 - 3.56484i) q^{39} +(-4.66991 - 3.00117i) q^{41} +(-0.128663 + 0.148485i) q^{42} +(-2.30014 + 0.675383i) q^{43} +(3.00764 + 6.58582i) q^{44} +(-8.34021 - 6.68469i) q^{46} +11.6146 q^{47} +(-0.469574 - 1.02822i) q^{48} +(6.70899 - 1.96994i) q^{49} +(-2.84593 - 1.82897i) q^{51} +(-6.99792 - 8.07603i) q^{52} +(-1.47653 - 10.2695i) q^{53} +(-10.6921 - 3.13950i) q^{54} +(-0.0270422 + 0.188083i) q^{56} +(-1.18852 + 2.60249i) q^{57} +(6.89372 - 15.0951i) q^{58} +(-1.64421 + 11.4357i) q^{59} +(-3.89722 - 1.14433i) q^{61} +(-0.546662 - 3.80211i) q^{62} +(-0.115460 - 0.133248i) q^{63} +(-10.9041 - 7.00766i) q^{64} +(5.21797 - 1.53213i) q^{66} +(5.07177 + 11.1056i) q^{67} -10.0377 q^{68} +(-3.50140 + 3.27723i) q^{69} +(0.787956 + 1.72538i) q^{71} +(-4.13631 + 1.21453i) q^{72} +(-3.61246 + 4.16900i) q^{73} +(1.32702 + 0.852823i) q^{74} +(1.20812 + 8.40266i) q^{76} +(0.206395 + 0.0606031i) q^{77} +(-6.75247 + 4.33955i) q^{78} +(-0.997420 + 6.93721i) q^{79} +(0.415415 - 0.909632i) q^{81} +(-1.76070 + 12.2459i) q^{82} +(-3.51021 + 2.25587i) q^{83} +(0.250975 + 0.0736930i) q^{84} +(3.49877 + 4.03779i) q^{86} +(-6.26391 - 4.02557i) q^{87} +(3.44426 - 3.97489i) q^{88} +(15.3009 - 4.49275i) q^{89} -0.317493 q^{91} +(-3.48270 + 13.7971i) q^{92} -1.72352 q^{93} +(-10.7532 - 23.5463i) q^{94} +(-4.47283 + 5.16192i) q^{96} +(-12.0969 - 7.77424i) q^{97} +(-10.2051 - 11.7773i) q^{98} +(0.694523 + 4.83052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - q^{3} - q^{4} + 6 q^{6} - 5 q^{7} + 16 q^{8} + 2 q^{9} + 8 q^{11} - q^{12} - 3 q^{14} + 5 q^{16} + 23 q^{17} + 10 q^{18} - 13 q^{19} + 6 q^{21} - 4 q^{22} + 21 q^{23} - 6 q^{24} + 11 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - q^3 - q^4 + 6 * q^6 - 5 * q^7 + 16 * q^8 + 2 * q^9 + 8 * q^11 - q^12 - 3 * q^14 + 5 * q^16 + 23 * q^17 + 10 * q^18 - 13 * q^19 + 6 * q^21 - 4 * q^22 + 21 * q^23 - 6 * q^24 + 11 * q^26 + 5 * q^27 + 6 * q^28 + 2 * q^29 - 20 * q^31 + 15 * q^32 - 3 * q^33 + 16 * q^34 + 24 * q^36 - 13 * q^37 - 21 * q^38 - 5 * q^41 - 3 * q^42 - 15 * q^43 + 19 * q^44 - 16 * q^46 + 52 * q^47 - 6 * q^48 + 4 * q^49 - 10 * q^51 - 22 * q^52 - 6 * q^53 - 30 * q^54 + 3 * q^56 - 2 * q^57 - 45 * q^58 + 5 * q^59 - 3 * q^61 + 54 * q^62 + 10 * q^63 - 34 * q^64 - 4 * q^66 - 20 * q^67 - 32 * q^68 - q^69 - 22 * q^71 - 32 * q^72 - 43 * q^73 + q^74 - 2 * q^76 - 4 * q^77 - 11 * q^78 + 51 * q^79 - q^81 - 58 * q^82 + 17 * q^83 + 6 * q^84 - 9 * q^86 + 2 * q^87 - 7 * q^88 + 57 * q^89 - 22 * q^91 + 43 * q^92 - 20 * q^93 - 81 * q^94 - 7 * q^96 - 52 * q^97 - 24 * q^98 + 6 * q^99

Character values

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

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

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 $

$2$	−0.925839	−	2.02730i	−0.654667	−	1.43352i	−0.887410	−	0.460982i	$-0.847497\pi$
$2$	−0.925839	−	2.02730i	−0.654667	−	1.43352i	0.232743	−	0.972538i	$-0.425230\pi$
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i	−0.546720	−	0.837315i	$-0.684124\pi$
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i	−0.00724338	+	0.999974i	$0.502306\pi$
$4$	−1.94306	+	2.24241i	−0.971531	+	1.12121i
$5$		0			0
$5$		0			0
$6$	1.45949	+	1.68434i	0.595836	+	0.687631i
$7$	0.0125459	+	0.0872586i	0.00474190	+	0.0329807i	0.992055	−	0.125805i	$-0.0401513\pi$
$7$	0.0125459	+	0.0872586i	0.00474190	+	0.0329807i	−0.987313	+	0.158785i	$0.949242\pi$
$8$	2.06815	+	0.607265i	0.731203	+	0.214700i
$9$	−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	$0.0164549\pi$
$12$	1.23259	−	2.69900i	0.355819	−	0.779135i
$13$	−0.512546	+	3.56484i	−0.142155	+	0.988707i	0.786455	+	0.617648i	$0.211914\pi$
$13$	−0.512546	+	3.56484i	−0.142155	+	0.988707i	−0.928609	+	0.371059i	$0.878995\pi$
$14$	0.165284	−	0.106222i	0.0441741	−	0.0283890i
$15$		0			0
$16$	0.160869	+	1.11887i	0.0402172	+	0.279717i
$17$	2.21537	+	2.55667i	0.537306	+	0.620084i	0.957878	−	0.287175i	$-0.0927160\pi$
$17$	2.21537	+	2.55667i	0.537306	+	0.620084i	−0.420572	+	0.907259i	$0.638171\pi$
$18$	3.74982	+	2.40986i	0.883840	+	0.568010i
$19$	1.87358	−	2.16222i	0.429828	−	0.496048i	−0.498978	−	0.866615i	$-0.666291\pi$
$19$	1.87358	−	2.16222i	0.429828	−	0.496048i	0.928806	+	0.370567i	$0.120837\pi$
$20$		0			0
$21$	−0.0366213	−	0.0801894i	−0.00799142	−	0.0174988i
$22$	−5.43826			−1.15944
$23$	4.28287	−	2.15802i	0.893039	−	0.449979i
$23$	4.28287	−	2.15802i	0.893039	−	0.449979i
$24$	−2.15546			−0.439982
$25$		0			0
$26$	7.70154	−	2.26138i	1.51040	−	0.443492i
$27$	3.27430	−	3.77875i	0.630140	−	0.727220i
$28$	−0.220047	−	0.141416i	−0.0415850	−	0.0267251i
$29$	4.87604	+	5.62725i	0.905458	+	1.04495i	0.998783	+	0.0493188i	$0.0157050\pi$
$29$	4.87604	+	5.62725i	0.905458	+	1.04495i	−0.0933249	+	0.995636i	$0.529750\pi$
$30$		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	$0.541443\pi$
$32$	5.74593	−	3.69269i	1.01575	−	0.652781i
$33$	−0.347262	+	2.41526i	−0.0604505	+	0.420442i
$34$	3.13208	−	6.85830i	0.537147	−	1.17619i
$35$		0			0
$36$	0.844535	−	5.87387i	0.140756	−	0.978979i
$37$	−0.595421	+	0.382654i	−0.0978866	+	0.0629079i	−0.588668	−	0.808375i	$-0.700348\pi$
$37$	−0.595421	+	0.382654i	−0.0978866	+	0.0629079i	0.490782	+	0.871283i	$0.336711\pi$
$38$	−6.11811	−	1.79644i	−0.992489	−	0.291421i
$39$	−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	$0.824529\pi$
$42$	−0.128663	+	0.148485i	−0.0198531	+	0.0229117i
$43$	−2.30014	+	0.675383i	−0.350768	+	0.102995i	−0.452370	−	0.891830i	$-0.649421\pi$
$43$	−2.30014	+	0.675383i	−0.350768	+	0.102995i	0.101602	+	0.994825i	$0.467603\pi$
$44$	3.00764	+	6.58582i	0.453419	+	0.992850i
$45$		0			0
$46$	−8.34021	−	6.68469i	−1.22970	−	0.985604i
$47$	11.6146			1.69416			0.847079	−	0.531466i	$-0.178359\pi$
$47$	11.6146			1.69416			0.847079	+	0.531466i	$0.178359\pi$
$48$	−0.469574	−	1.02822i	−0.0677772	−	0.148411i
$49$	6.70899	−	1.96994i	0.958428	−	0.281420i
$50$		0			0
$51$	−2.84593	−	1.82897i	−0.398510	−	0.256107i
$52$	−6.99792	−	8.07603i	−0.970437	−	1.11994i
$53$	−1.47653	−	10.2695i	−0.202817	−	1.41062i	−0.795874	−	0.605462i	$-0.792988\pi$
$53$	−1.47653	−	10.2695i	−0.202817	−	1.41062i	0.593058	−	0.805160i	$-0.297921\pi$
$54$	−10.6921	−	3.13950i	−1.45502	−	0.427231i
$55$		0			0
$56$	−0.0270422	+	0.188083i	−0.00361367	+	0.0251336i
$57$	−1.18852	+	2.60249i	−0.157423	+	0.344708i
$58$	6.89372	−	15.0951i	0.905190	−	1.98209i
$59$	−1.64421	+	11.4357i	−0.214058	+	1.48881i	0.545359	+	0.838203i	$0.316393\pi$
$59$	−1.64421	+	11.4357i	−0.214058	+	1.48881i	−0.759417	+	0.650604i	$0.774516\pi$
$60$		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	$0.674641\pi$
$62$	−0.546662	−	3.80211i	−0.0694261	−	0.482869i
$63$	−0.115460	−	0.133248i	−0.0145466	−	0.0167876i
$64$	−10.9041	−	7.00766i	−1.36302	−	0.875958i
$65$		0			0
$66$	5.21797	−	1.53213i	0.642288	−	0.188593i
$67$	5.07177	+	11.1056i	0.619615	+	1.35677i	0.915799	+	0.401637i	$0.131559\pi$
$67$	5.07177	+	11.1056i	0.619615	+	1.35677i	−0.296184	+	0.955131i	$0.595714\pi$
$68$	−10.0377			−1.21725
$69$	−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	$0.827733\pi$
$72$	−4.13631	+	1.21453i	−0.487468	+	0.143134i
$73$	−3.61246	+	4.16900i	−0.422806	+	0.487944i	−0.926690	−	0.375827i	$-0.877359\pi$
$73$	−3.61246	+	4.16900i	−0.422806	+	0.487944i	0.503884	+	0.863772i	$0.331904\pi$
$74$	1.32702	+	0.852823i	0.154263	+	0.0991387i
$75$		0			0
$76$	1.20812	+	8.40266i	0.138581	+	0.963852i
$77$	0.206395	+	0.0606031i	0.0235209	+	0.00690637i
$78$	−6.75247	+	4.33955i	−0.764566	+	0.491357i
$79$	−0.997420	+	6.93721i	−0.112219	+	0.780497i	0.853535	+	0.521036i	$0.174454\pi$
$79$	−0.997420	+	6.93721i	−0.112219	+	0.780497i	−0.965753	+	0.259461i	$0.916455\pi$
$80$		0			0
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−1.76070	+	12.2459i	−0.194436	+	1.35234i
$83$	−3.51021	+	2.25587i	−0.385295	+	0.247614i	−0.718922	−	0.695091i	$-0.755364\pi$
$83$	−3.51021	+	2.25587i	−0.385295	+	0.247614i	0.333626	+	0.942705i	$0.391728\pi$
$84$	0.250975	+	0.0736930i	0.0273836	+	0.00804056i
$85$		0			0
$86$	3.49877	+	4.03779i	0.377282	+	0.435406i
$87$	−6.26391	−	4.02557i	−0.671561	−	0.431586i
$88$	3.44426	−	3.97489i	0.367160	−	0.423725i
$89$	15.3009	−	4.49275i	1.62189	−	0.476231i	0.660367	−	0.750943i	$-0.270401\pi$
$89$	15.3009	−	4.49275i	1.62189	−	0.476231i	0.961526	+	0.274713i	$0.0885827\pi$
$90$		0			0
$91$	−0.317493			−0.0332823
$92$	−3.48270	+	13.7971i	−0.363096	+	1.43845i
$93$	−1.72352			−0.178720
$94$	−10.7532	−	23.5463i	−1.10911	−	2.42861i
$95$		0			0
$96$	−4.47283	+	5.16192i	−0.456506	+	0.526836i
$97$	−12.0969	−	7.77424i	−1.22826	−	0.789354i	−0.244640	−	0.969614i	$-0.578670\pi$
$97$	−12.0969	−	7.77424i	−1.22826	−	0.789354i	−0.983619	+	0.180260i	$0.942306\pi$
$98$	−10.2051	−	11.7773i	−1.03087	−	1.18969i
$99$	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	$-0.0144035\pi$
$102$	−1.07300	+	7.46289i	−0.106243	+	0.738937i
$103$	−0.483270	+	1.05821i	−0.0476180	+	0.104269i	−0.931946	−	0.362598i	$-0.881890\pi$
$103$	−0.483270	+	1.05821i	−0.0476180	+	0.104269i	0.884328	+	0.466867i	$0.154617\pi$
$104$	−3.22482	+	7.06137i	−0.316220	+	0.692425i
$105$		0			0
$106$	−19.4523	+	12.5013i	−1.88938	+	1.21423i
$107$	16.4556	+	4.83181i	1.59083	+	0.467108i	0.952974	−	0.303051i	$-0.0980053\pi$
$107$	16.4556	+	4.83181i	1.59083	+	0.467108i	0.637851	+	0.770160i	$0.279824\pi$
$108$	2.11134	+	14.6847i	0.203164	+	1.41303i
$109$	−1.71227	−	1.97606i	−0.164006	−	0.189273i	0.667798	−	0.744343i	$-0.267237\pi$
$109$	−1.71227	−	1.97606i	−0.164006	−	0.189273i	−0.831804	+	0.555070i	$0.812692\pi$
$110$		0			0
$111$	0.463496	−	0.534903i	0.0439931	−	0.0507707i
$112$	−0.0956126	+	0.0280744i	−0.00903454	+	0.00265278i
$113$	7.44256	+	16.2969i	0.700137	+	1.53309i	0.839805	+	0.542888i	$0.182669\pi$
$113$	7.44256	+	16.2969i	0.700137	+	1.53309i	−0.139668	+	0.990198i	$0.544604\pi$
$114$	6.37640			0.597205
$115$		0			0
$116$	−22.0931			−2.05129
$117$	−2.99223	−	6.55207i	−0.276632	−	0.605739i
$118$	24.7060	−	7.25434i	2.27437	−	0.667816i
$119$	−0.195298	+	0.225386i	−0.0179029	+	0.0206611i
$120$		0			0
$121$	3.30439	+	3.81347i	0.300399	+	0.346679i
$122$	1.28830	+	8.96031i	0.116637	+	0.811228i
$123$	5.32627	+	1.56393i	0.480254	+	0.141015i
$124$	−4.30209	+	2.76479i	−0.386339	+	0.248285i
$125$		0			0
$126$	−0.163236	+	0.357438i	−0.0145422	+	0.0318431i
$127$	−1.24283	+	2.72142i	−0.110283	+	0.241487i	−0.956724	−	0.290996i	$-0.906013\pi$
$127$	−1.24283	+	2.72142i	−0.110283	+	0.241487i	0.846441	+	0.532482i	$0.178741\pi$
$128$	−2.16711	+	15.0726i	−0.191548	+	1.33224i
$129$	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	$0.755087\pi$
$132$	−4.74125	−	5.47170i	−0.412673	−	0.476250i
$133$	0.212178	+	0.136359i	0.0183982	+	0.0118238i
$134$	17.8188	−	20.5640i	1.53931	−	1.77646i
$135$		0			0
$136$	3.02915	+	6.63291i	0.259747	+	0.568767i
$137$	−19.2932			−1.64833			−0.824165	−	0.566350i	$-0.808355\pi$
$137$	−19.2932			−1.64833			−0.824165	+	0.566350i	$0.808355\pi$
$138$	9.88567	+	4.06421i	0.841524	+	0.345968i
$139$	15.4962			1.31437			0.657185	−	0.753729i	$-0.271747\pi$
$139$	15.4962			1.31437			0.657185	+	0.753729i	$0.271747\pi$
$140$		0			0
$141$	−11.1441	+	3.27220i	−0.938502	+	0.275569i
$142$	2.76835	−	3.19485i	0.232315	−	0.268106i
$143$	7.39292	+	4.75114i	0.618227	+	0.397310i
$144$	−1.48047	−	1.70856i	−0.123373	−	0.142380i
$145$		0			0
$146$	11.7964	+	3.46373i	0.976275	+	0.286660i
$147$	−5.88224	+	3.78028i	−0.485159	+	0.311793i
$148$	0.298872	−	2.07870i	0.0245671	−	0.170868i
$149$	−6.62691	+	14.5109i	−0.542898	+	1.18878i	0.417122	+	0.908850i	$0.363039\pi$
$149$	−6.62691	+	14.5109i	−0.542898	+	1.18878i	−0.960020	+	0.279930i	$0.909689\pi$
$150$		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	$0.0511830\pi$
$152$	5.18789	−	3.33405i	0.420793	−	0.270427i
$153$	−6.49186	−	1.90618i	−0.524836	−	0.154106i
$154$	−0.0682278	−	0.474535i	−0.00549795	−	0.0382391i
$155$		0			0
$156$	8.98974	+	5.77735i	0.719755	+	0.462559i
$157$	4.66176	−	5.37996i	0.372049	−	0.429367i	−0.538592	−	0.842567i	$-0.681043\pi$
$157$	4.66176	−	5.37996i	0.372049	−	0.429367i	0.910640	+	0.413200i	$0.135589\pi$
$158$	14.9873	−	4.40066i	1.19232	−	0.350098i
$159$	4.30997	+	9.43751i	0.341803	+	0.748443i
$160$		0			0
$161$	0.242038	+	0.346643i	0.0190753	+	0.0273193i
$162$	−2.22871			−0.175104
$163$	2.96870	+	6.50054i	0.232526	+	0.509162i	0.989544	−	0.144233i	$-0.0460714\pi$
$163$	2.96870	+	6.50054i	0.232526	+	0.509162i	−0.757017	+	0.653395i	$0.773344\pi$
$164$	15.8038	−	4.64041i	1.23407	−	0.362355i
$165$		0			0
$166$	7.82322	+	5.02768i	0.607200	+	0.390224i
$167$	0.872694	+	1.00714i	0.0675311	+	0.0779351i	0.788510	−	0.615022i	$-0.210853\pi$
$167$	0.872694	+	1.00714i	0.0675311	+	0.0779351i	−0.720979	+	0.692957i	$0.756307\pi$
$168$	−0.0270422	−	0.188083i	−0.00208635	−	0.0145109i
$169$	0.0280633	+	0.00824014i	0.00215872	+	0.000633857i
$170$		0			0
$171$	−0.814334	+	5.66382i	−0.0622737	+	0.433123i
$172$	2.95483	−	6.47018i	0.225304	−	0.493346i
$173$	−1.12194	+	2.45670i	−0.0852992	+	0.186779i	−0.947475	−	0.319830i	$-0.896374\pi$
$173$	−1.12194	+	2.45670i	−0.0852992	+	0.186779i	0.862176	+	0.506609i	$0.169101\pi$
$174$	−2.36168	+	16.4259i	−0.179039	+	1.24524i
$175$		0			0
$176$	2.64649	+	0.777080i	0.199487	+	0.0585746i
$177$	−1.64421	−	11.4357i	−0.123587	−	0.859563i
$178$	−23.2743	−	26.8600i	−1.74449	−	2.01324i
$179$	−16.6467	−	10.6982i	−1.24423	−	0.799620i	−0.258188	−	0.966095i	$-0.583125\pi$
$179$	−16.6467	−	10.6982i	−1.24423	−	0.799620i	−0.986046	+	0.166474i	$0.946762\pi$
$180$		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	$0.456413\pi$
$182$	0.293947	+	0.643655i	0.0217888	+	0.0477109i
$183$	4.06175			0.300253
$184$	10.1681	−	1.86229i	0.749603	−	0.137290i
$185$		0			0
$186$	1.59570	+	3.49409i	0.117002	+	0.256199i
$187$	7.92038	−	2.32563i	0.579195	−	0.170067i
$188$	−22.5678	+	26.0447i	−1.64593	+	1.89950i
$189$	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	$0.885140\pi$
$192$	12.4367	+	3.65175i	0.897544	+	0.263543i
$193$	−8.48523	+	5.45312i	−0.610780	+	0.392524i	−0.809149	−	0.587603i	$-0.800072\pi$
$193$	−8.48523	+	5.45312i	−0.610780	+	0.392524i	0.198370	+	0.980127i	$0.436435\pi$
$194$	−4.56092	+	31.7219i	−0.327455	+	2.27750i
$195$		0			0
$196$	−8.61857	+	18.8720i	−0.615612	+	1.34800i
$197$	−0.728029	+	5.06355i	−0.0518699	+	0.360763i	0.947312	+	0.320313i	$0.103788\pi$
$197$	−0.728029	+	5.06355i	−0.0518699	+	0.360763i	−0.999182	+	0.0404498i	$0.987121\pi$
$198$	9.14991	−	5.88029i	0.650255	−	0.417894i
$199$	−25.5033	−	7.48844i	−1.80788	−	0.530842i	−0.809468	−	0.587164i	$-0.800244\pi$
$199$	−25.5033	−	7.48844i	−1.80788	−	0.530842i	−0.998413	+	0.0563229i	$0.982062\pi$
$200$		0			0
$201$	−7.99514	−	9.22689i	−0.563934	−	0.650814i
$202$	−32.5920	−	20.9456i	−2.29316	−	1.47373i
$203$	−0.429852	+	0.496076i	−0.0301697	+	0.0348177i
$204$	9.63112	−	2.82795i	0.674313	−	0.197996i
$205$		0			0
$206$	2.59275			0.180646
$207$	−4.87252	+	8.26187i	−0.338664	+	0.574240i
$208$	−4.07103			−0.282275
$209$	−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	$0.0578572\pi$
$212$	25.8974	+	16.6432i	1.77864	+	1.14306i
$213$	−1.24213	−	1.43350i	−0.0851096	−	0.0982217i
$214$	−5.43971	−	37.8340i	−0.371851	−	2.58628i
$215$		0			0
$216$	9.06646	−	5.82666i	0.616895	−	0.396454i
$217$	−0.0216231	+	0.150392i	−0.00146787	+	0.0102092i
$218$	−2.42080	+	5.30081i	−0.163957	+	0.359016i
$219$	2.29158	−	5.01787i	0.154851	−	0.339076i
$220$		0			0
$221$	−10.2496	+	6.58702i	−0.689463	+	0.443091i
$222$	−1.51353	−	0.444413i	−0.101582	−	0.0298271i
$223$	−0.144012	−	1.00163i	−0.00964378	−	0.0670740i	0.984431	−	0.175770i	$-0.0562415\pi$
$223$	−0.144012	−	1.00163i	−0.00964378	−	0.0670740i	−0.994075	+	0.108696i	$0.965332\pi$
$224$	0.394306	+	0.455054i	0.0263457	+	0.0304046i
$225$		0			0
$226$	26.1482	−	30.1767i	1.73935	−	2.00732i
$227$	4.83803	−	1.42057i	0.321111	−	0.0942867i	−0.117205	−	0.993108i	$-0.537393\pi$
$227$	4.83803	−	1.42057i	0.321111	−	0.0942867i	0.438316	+	0.898821i	$0.355575\pi$
$228$	−3.52649	−	7.72193i	−0.233547	−	0.511397i
$229$	−22.9504			−1.51661			−0.758304	−	0.651901i	$-0.773972\pi$
$229$	−22.9504			−1.51661			−0.758304	+	0.651901i	$0.773972\pi$
$230$		0			0
$231$	−0.215109			−0.0141531
$232$	6.66717	+	14.5991i	0.437721	+	0.958476i
$233$	20.6511	−	6.06370i	1.35290	−	0.397246i	0.476644	−	0.879097i	$-0.341853\pi$
$233$	20.6511	−	6.06370i	1.35290	−	0.397246i	0.876254	+	0.481850i	$0.160035\pi$
$234$	−10.5127	+	12.1323i	−0.687237	+	0.793114i
$235$		0			0
$236$	−22.4489	−	25.9074i	−1.46130	−	1.68643i
$237$	−0.997420	−	6.93721i	−0.0647894	−	0.450620i
$238$	0.637740	+	0.187257i	0.0413386	+	0.0121381i
$239$	−7.37760	+	4.74129i	−0.477217	+	0.306689i	−0.757047	−	0.653361i	$-0.773358\pi$
$239$	−7.37760	+	4.74129i	−0.477217	+	0.306689i	0.279830	+	0.960050i	$0.409722\pi$
$240$		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	$0.0446980\pi$
$242$	4.67172	−	10.2296i	0.300310	−	0.657587i
$243$	−2.27704	+	15.8371i	−0.146072	+	1.01595i
$244$	10.1386	−	6.51568i	0.649057	−	0.417123i
$245$		0			0
$246$	−1.76070	−	12.2459i	−0.112258	−	0.780771i
$247$	6.74767	+	7.78723i	0.429344	+	0.495490i
$248$	3.12524	+	2.00847i	0.198453	+	0.127538i
$249$	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	$0.923173\pi$
$252$	0.523141			0.0329548
$253$	−0.448583	−	11.6937i	−0.0282022	−	0.735175i
$254$	6.66780			0.418375
$255$		0			0
$256$	7.68968	−	2.25789i	0.480605	−	0.141118i
$257$	−5.05121	+	5.82941i	−0.315086	+	0.363628i	−0.891097	−	0.453814i	$-0.850063\pi$
$257$	−5.05121	+	5.82941i	−0.315086	+	0.363628i	0.576011	+	0.817442i	$0.304609\pi$
$258$	−4.49462	−	2.88852i	−0.279823	−	0.179831i
$259$	−0.0408599	−	0.0471549i	−0.00253891	−	0.00293006i
$260$		0			0
$261$	−14.2886	−	4.19552i	−0.884443	−	0.259696i
$262$	25.1678	−	16.1744i	1.55487	−	0.999256i
$263$	3.18652	−	22.1627i	0.196489	−	1.36661i	−0.617883	−	0.786270i	$-0.712009\pi$
$263$	3.18652	−	22.1627i	0.196489	−	1.36661i	0.814372	−	0.580343i	$-0.197081\pi$
$264$	−2.18489	+	4.78424i	−0.134471	+	0.294450i
$265$		0			0
$266$	0.0799977	−	0.556396i	0.00490497	−	0.0341148i
$267$	−13.4154	+	8.62153i	−0.821007	+	0.527629i
$268$	−34.7581	−	10.2059i	−2.12319	−	0.623425i
$269$	−1.31816	−	9.16802i	−0.0803698	−	0.558984i	−0.989727	−	0.142968i	$-0.954335\pi$
$269$	−1.31816	−	9.16802i	−0.0803698	−	0.558984i	0.909357	−	0.416016i	$-0.136574\pi$
$270$		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	$0.449420\pi$
$272$	−2.50419	+	2.88999i	−0.151839	+	0.175232i
$273$	0.304632	−	0.0894481i	0.0184372	−	0.00541365i
$274$	17.8624	+	39.1132i	1.07911	+	2.36291i
$275$		0			0
$276$	−0.545473	−	14.2194i	−0.0328336	−	0.855909i
$277$	−12.5089			−0.751589			−0.375795	−	0.926703i	$-0.622630\pi$
$277$	−12.5089			−0.751589			−0.375795	+	0.926703i	$0.622630\pi$
$278$	−14.3470	−	31.4155i	−0.860474	−	1.88418i
$279$	−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	$0.942982\pi$
$282$	16.9514	+	19.5629i	1.00944	+	1.16496i
$283$	−2.51410	−	17.4860i	−0.149448	−	1.03943i	−0.917126	−	0.398597i	$-0.869497\pi$
$283$	−2.51410	−	17.4860i	−0.149448	−	1.03943i	0.767678	−	0.640836i	$-0.221412\pi$
$284$	−5.40006	−	1.58560i	−0.320435	−	0.0940882i
$285$		0			0
$286$	2.78736	−	19.3865i	0.164820	−	1.14635i
$287$	0.203290	−	0.445142i	0.0119998	−	0.0262759i
$288$	−5.67474	+	12.4259i	−0.334387	+	0.732205i
$289$	0.790638	−	5.49901i	0.0465081	−	0.323471i
$290$		0			0
$291$	13.7972	+	4.05122i	0.808806	+	0.237487i
$292$	−2.32939	−	16.2012i	−0.136317	−	0.948106i
$293$	5.55996	+	6.41653i	0.324816	+	0.374858i	0.894547	−	0.446973i	$-0.147498\pi$
$293$	5.55996	+	6.41653i	0.324816	+	0.374858i	−0.569731	+	0.821831i	$0.692953\pi$
$294$	13.1098	+	8.42515i	0.764578	+	0.491365i
$295$		0			0
$296$	−1.46379	+	0.429809i	−0.0850813	+	0.0249821i
$297$	−5.06826	−	11.0979i	−0.294090	−	0.643968i
$298$	35.5535			2.05956
$299$	5.49782	+	16.3738i	0.317947	+	0.946921i
$300$		0			0
$301$	−0.0877903	−	0.192234i	−0.00506015	−	0.0110802i
$302$	0.945756	−	0.277699i	0.0544222	−	0.0159798i
$303$	−11.3836	+	13.1374i	−0.653970	+	0.754722i
$304$	2.72064	+	1.74845i	0.156039	+	0.100280i
$305$		0			0
$306$	2.14600	+	14.9258i	0.122679	+	0.853251i
$307$	−14.0850	−	4.13574i	−0.803875	−	0.236039i	−0.146116	−	0.989267i	$-0.546677\pi$
$307$	−14.0850	−	4.13574i	−0.803875	−	0.236039i	−0.657759	+	0.753228i	$0.728496\pi$
$308$	−0.536936	+	0.345068i	−0.0305948	+	0.0196621i
$309$	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	$-0.190424\pi$
$312$	1.10477	−	7.68388i	0.0625455	−	0.435014i
$313$	4.68243	−	3.00922i	0.264667	−	0.170091i	−0.401576	−	0.915826i	$-0.631538\pi$
$313$	4.68243	−	3.00922i	0.264667	−	0.170091i	0.666243	+	0.745734i	$0.267901\pi$
$314$	−15.2228	−	4.46983i	−0.859074	−	0.252247i
$315$		0			0
$316$	−13.6180	−	15.7160i	−0.766074	−	0.884097i
$317$	−2.36484	−	1.51979i	−0.132823	−	0.0853600i	0.472542	−	0.881308i	$-0.343336\pi$
$317$	−2.36484	−	1.51979i	−0.132823	−	0.0853600i	−0.605365	+	0.795948i	$0.706973\pi$
$318$	15.1424	−	17.4752i	0.849142	−	0.979962i
$319$	17.4328	−	5.11873i	0.976049	−	0.286594i
$320$		0			0
$321$	−17.1503			−0.957238
$322$	0.478662	−	0.811620i	0.0266748	−	0.0452298i
$323$	9.67876			0.538541
$324$	1.23259	+	2.69900i	0.0684774	+	0.149945i
$325$		0			0
$326$	10.4300	−	12.0369i	0.577667	−	0.666663i
$327$	2.19963	+	1.41362i	0.121640	+	0.0781732i
$328$	−7.83558	−	9.04274i	−0.432648	−	0.499302i
$329$	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	$0.442505\pi$
$332$	1.76195	−	12.2546i	0.0966995	−	0.672560i
$333$	0.588043	−	1.28764i	0.0322246	−	0.0705620i
$334$	1.23381	−	2.70167i	0.0675111	−	0.147829i
$335$		0			0
$336$	0.0838301	−	0.0538744i	0.00457331	−	0.00293909i
$337$	20.7059	+	6.07980i	1.12792	+	0.331188i	0.791890	−	0.610663i	$-0.209097\pi$
$337$	20.7059	+	6.07980i	1.12792	+	0.331188i	0.336031	+	0.941851i	$0.390915\pi$
$338$	−0.00927685	−	0.0645219i	−0.000504594	−	0.00350953i
$339$	−11.7325	−	13.5400i	−0.637220	−	0.735391i
$340$		0			0
$341$	2.75404	−	3.17834i	0.149140	−	0.172117i
$342$	12.2362	−	3.59288i	0.661659	−	0.194281i
$343$	0.512414	+	1.12203i	0.0276677	+	0.0605839i
$344$	−5.16718			−0.278596
$345$		0			0
$346$	6.01920			0.323594
$347$	−7.85449	−	17.1989i	−0.421651	−	0.923288i	−0.994608	−	0.103702i	$-0.966931\pi$
$347$	−7.85449	−	17.1989i	−0.421651	−	0.923288i	0.572957	−	0.819585i	$-0.305796\pi$
$348$	21.1981	−	6.22434i	1.13634	−	0.333659i
$349$	−13.7056	+	15.8171i	−0.733643	+	0.846669i	−0.992877	−	0.119146i	$-0.961984\pi$
$349$	−13.7056	+	15.8171i	−0.733643	+	0.846669i	0.259234	+	0.965815i	$0.416530\pi$
$350$		0			0
$351$	11.7924	+	13.6091i	0.629431	+	0.726402i
$352$	−2.37187	−	16.4967i	−0.126421	−	0.879277i
$353$	1.54672	+	0.454159i	0.0823238	+	0.0241724i	0.322635	−	0.946523i	$-0.395431\pi$
$353$	1.54672	+	0.454159i	0.0823238	+	0.0241724i	−0.240311	+	0.970696i	$0.577250\pi$
$354$	−21.6615	+	13.9210i	−1.15129	+	0.739891i
$355$		0			0
$356$	−19.6560	+	43.0406i	−1.04177	+	2.28115i
$357$	0.123889	−	0.271278i	0.00655688	−	0.0143576i
$358$	−6.27632	+	43.6527i	−0.331714	+	2.30712i
$359$	29.2892	−	18.8230i	1.54583	−	0.993442i	0.559464	−	0.828854i	$-0.311007\pi$
$359$	29.2892	−	18.8230i	1.54583	−	0.993442i	0.986362	−	0.164588i	$-0.0526294\pi$
$360$		0			0
$361$	1.53906	+	10.7044i	0.0810034	+	0.563391i
$362$	5.81675	+	6.71289i	0.305722	+	0.352822i
$363$	−4.24491	−	2.72804i	−0.222800	−	0.143185i
$364$	0.616908	−	0.711950i	0.0323348	−	0.0373163i
$365$		0			0
$366$	−3.76052	−	8.23440i	−0.196566	−	0.430419i
$367$	22.6244			1.18098			0.590491	−	0.807044i	$-0.298934\pi$
$367$	22.6244			1.18098			0.590491	+	0.807044i	$0.298934\pi$
$368$	3.10352	+	4.44480i	0.161782	+	0.231701i
$369$	11.1023			0.577961
$370$		0			0
$371$	0.877577	−	0.257680i	0.0455615	−	0.0133781i
$372$	3.34890	−	3.86483i	0.173632	−	0.200382i
$373$	−9.08151	−	5.83633i	−0.470223	−	0.302194i	0.283986	−	0.958828i	$-0.408343\pi$
$373$	−9.08151	−	5.83633i	−0.470223	−	0.302194i	−0.754209	+	0.656635i	$0.771979\pi$
$374$	−12.0478	−	13.9038i	−0.622974	−	0.718951i
$375$		0			0
$376$	24.0207	+	7.05312i	1.23877	+	0.363737i
$377$	−22.5594	+	14.4981i	−1.16187	+	0.746688i
$378$	0.139806	−	0.972370i	0.00719083	−	0.0500133i
$379$	−1.53173	+	3.35401i	−0.0786795	+	0.172284i	−0.944884	−	0.327406i	$-0.893826\pi$
$379$	−1.53173	+	3.35401i	−0.0786795	+	0.172284i	0.866204	+	0.499690i	$0.166553\pi$
$380$		0			0
$381$	0.425774	−	2.96133i	0.0218131	−	0.151713i
$382$	11.2105	−	7.20457i	0.573580	−	0.368618i
$383$	−5.70202	−	1.67426i	−0.291360	−	0.0855509i	0.132787	−	0.991145i	$-0.457608\pi$
$383$	−5.70202	−	1.67426i	−0.291360	−	0.0855509i	−0.424146	+	0.905594i	$0.639426\pi$
$384$	−2.16711	−	15.0726i	−0.110590	−	0.769171i
$385$		0			0
$386$	18.9111	+	12.1534i	0.962549	+	0.618593i
$387$	3.13973	−	3.62344i	0.159601	−	0.184190i
$388$	40.9382	−	12.0205i	2.07832	−	0.610250i
$389$	2.75929	+	6.04199i	0.139901	+	0.306341i	0.966594	−	0.256313i	$-0.0825077\pi$
$389$	2.75929	+	6.04199i	0.139901	+	0.306341i	−0.826693	+	0.562654i	$0.809780\pi$
$390$		0			0
$391$	15.0055	+	6.16908i	0.758860	+	0.311984i
$392$	15.0715			0.761226
$393$	−5.57632	−	12.2104i	−0.281288	−	0.615935i
$394$	10.9394	−	3.21210i	0.551119	−	0.161823i
$395$		0			0
$396$	−12.1815	−	7.82858i	−0.612144	−	0.393401i
$397$	−2.98449	−	3.44429i	−0.149787	−	0.172864i	0.675897	−	0.736996i	$-0.263756\pi$
$397$	−2.98449	−	3.44429i	−0.149787	−	0.172864i	−0.825685	+	0.564132i	$0.809211\pi$
$398$	8.43058	+	58.6360i	0.422587	+	2.93916i
$399$	−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	$-0.199989\pi$
$402$	−11.3035	+	24.7512i	−0.563767	+	1.23448i
$403$	−2.57858	+	5.64630i	−0.128448	+	0.281262i
$404$	−7.34038	+	51.0534i	−0.365197	+	2.54000i
$405$		0			0
$406$	1.40367	+	0.412155i	0.0696629	+	0.0204549i
$407$	0.245784	+	1.70947i	0.0121831	+	0.0847351i
$408$	−4.77515	−	5.51082i	−0.236405	−	0.272826i
$409$	6.83017	+	4.38949i	0.337730	+	0.217046i	0.698502	−	0.715608i	$-0.253850\pi$
$409$	6.83017	+	4.38949i	0.337730	+	0.217046i	−0.360772	+	0.932654i	$0.617487\pi$
$410$		0			0
$411$	18.5117	−	5.43552i	0.913115	−	0.268115i
$412$	−1.43393	−	3.13987i	−0.0706446	−	0.154690i
$413$	−1.01850			−0.0501169
$414$	21.2605	+	2.22893i	1.04490	+	0.109546i
$415$		0			0
$416$	10.2188	+	22.3760i	0.501016	+	1.09707i
$417$	−14.8685	+	4.36578i	−0.728113	+	0.213793i
$418$	−10.1890	+	11.7587i	−0.498360	+	0.575138i
$419$	−23.3315	−	14.9942i	−1.13982	−	0.732517i	−0.172232	−	0.985056i	$-0.555098\pi$
$419$	−23.3315	−	14.9942i	−1.13982	−	0.732517i	−0.967587	+	0.252539i	$0.918734\pi$
$420$		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	$0.630073\pi$
$422$	−31.5259	−	9.25685i	−1.53466	−	0.450616i
$423$	−19.5416	+	12.5586i	−0.950145	+	0.610621i
$424$	3.18261	−	22.1355i	0.154561	−	1.07500i
$425$		0			0
$426$	−1.75612	+	3.84537i	−0.0850844	+	0.186309i
$427$	0.0509583	−	0.354423i	0.00246604	−	0.0171517i
$428$	−42.8092	+	27.5118i	−2.06926	+	1.32983i
$429$	−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	$0.701081\pi$
$432$	4.75465	+	3.05563i	0.228758	+	0.147014i
$433$	14.8185	−	17.1014i	0.712129	−	0.821841i	−0.278208	−	0.960521i	$-0.589740\pi$
$433$	14.8185	−	17.1014i	0.712129	−	0.821841i	0.990337	+	0.138680i	$0.0442859\pi$
$434$	0.324909	−	0.0954019i	0.0155961	−	0.00457944i
$435$		0			0
$436$	7.75820			0.371550
$437$	3.35816	−	13.3037i	0.160642	−	0.636404i
$438$	−12.2944			−0.587448
$439$	−7.68428	−	16.8262i	−0.366751	−	0.803072i	−0.999586	−	0.0287853i	$-0.990836\pi$
$439$	−7.68428	−	16.8262i	−0.366751	−	0.803072i	0.632835	−	0.774287i	$-0.281891\pi$
$440$		0			0
$441$	−9.15787	+	10.5687i	−0.436089	+	0.503274i
$442$	22.8434	+	14.6805i	1.08655	+	0.698282i
$443$	−14.6551	−	16.9129i	−0.696284	−	0.803554i	0.291962	−	0.956430i	$-0.405692\pi$
$443$	−14.6551	−	16.9129i	−0.696284	−	0.803554i	−0.988245	+	0.152876i	$0.951147\pi$
$444$	0.298872	+	2.07870i	0.0141838	+	0.0986507i
$445$		0			0
$446$	−1.89727	+	1.21930i	−0.0898384	+	0.0577356i
$447$	2.27028	−	15.7901i	0.107381	−	0.746848i
$448$	0.474677	−	1.03940i	0.0224264	−	0.0491069i
$449$	2.04143	−	4.47012i	0.0963412	−	0.210958i	−0.855325	−	0.518092i	$-0.826643\pi$
$449$	2.04143	−	4.47012i	0.0963412	−	0.210958i	0.951666	+	0.307134i	$0.0993699\pi$
$450$		0			0
$451$	−11.3950	+	7.32313i	−0.536570	+	0.344833i
$452$	−51.0058	−	14.9767i	−2.39911	−	0.704442i
$453$	−0.0629411	−	0.437765i	−0.00295723	−	0.0205680i
$454$	−7.35916	−	8.49293i	−0.345383	−	0.398593i
$455$		0			0
$456$	−4.03843	+	4.66060i	−0.189117	+	0.218252i
$457$	11.1134	−	3.26318i	0.519861	−	0.152645i	−0.0112669	−	0.999937i	$-0.503586\pi$
$457$	11.1134	−	3.26318i	0.519861	−	0.152645i	0.531128	+	0.847291i	$0.321768\pi$
$458$	21.2484	+	46.5275i	0.992873	+	2.17409i
$459$	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	$0.617942\pi$
$462$	0.199156	+	0.436091i	0.00926558	+	0.0202888i
$463$	9.71687	−	2.85313i	0.451581	−	0.132596i	−0.0480300	−	0.998846i	$-0.515294\pi$
$463$	9.71687	−	2.85313i	0.451581	−	0.132596i	0.499611	+	0.866250i	$0.333476\pi$
$464$	−5.51175	+	6.36089i	−0.255876	+	0.295297i
$465$		0			0
$466$	−31.4125	−	36.2520i	−1.45516	−	1.67934i
$467$	0.0227489	+	0.158222i	0.00105269	+	0.00732164i	0.990341	−	0.138653i	$-0.0442773\pi$
$467$	0.0227489	+	0.158222i	0.00105269	+	0.00732164i	−0.989288	+	0.145975i	$0.953368\pi$
$468$	20.5065	+	6.02126i	0.947914	+	0.278333i
$469$	−0.905432	+	0.581886i	−0.0418089	+	0.0268690i
$470$		0			0
$471$	−2.95722	+	6.47540i	−0.136261	+	0.298371i
$472$	−10.3450	+	22.6524i	−0.476168	+	1.04266i
$473$	−0.832472	+	5.78997i	−0.0382771	+	0.266223i
$474$	−13.1404	+	8.44481i	−0.603558	+	0.387883i
$475$		0			0
$476$	−0.125932	−	0.875877i	−0.00577209	−	0.0401458i
$477$	13.5885	+	15.6819i	0.622173	+	0.718026i
$478$	16.4425	+	10.5670i	0.752063	+	0.483321i
$479$	−3.84712	+	4.43982i	−0.175779	+	0.202860i	−0.836802	−	0.547506i	$-0.815577\pi$
$479$	−3.84712	+	4.43982i	−0.175779	+	0.202860i	0.661022	+	0.750366i	$0.270123\pi$
$480$		0			0
$481$	−1.05892	−	2.31870i	−0.0482825	−	0.105724i
$482$	−19.6530			−0.895169
$483$	−0.329895	−	0.264411i	−0.0150107	−	0.0120311i
$484$	−14.9720			−0.680545
$485$		0			0
$486$	34.2149	−	10.0464i	1.55202	−	0.455714i
$487$	−4.54083	+	5.24040i	−0.205765	+	0.237465i	−0.849247	−	0.527996i	$-0.822944\pi$
$487$	−4.54083	+	5.24040i	−0.205765	+	0.237465i	0.643482	+	0.765461i	$0.277489\pi$
$488$	−7.36514	−	4.73329i	−0.333404	−	0.214266i
$489$	−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	$0.425915\pi$
$492$	−13.8563	+	8.90487i	−0.624688	+	0.401463i
$493$	−3.58481	+	24.9329i	−0.161452	+	1.12292i
$494$	9.53982	−	20.8893i	0.429217	−	0.939854i
$495$		0			0
$496$	−0.277260	+	1.92839i	−0.0124493	+	0.0865871i
$497$	−0.140669	+	0.0904024i	−0.00630986	+	0.00405510i
$498$	−8.92279	−	2.61997i	−0.399840	−	0.117404i
$499$	4.04910	+	28.1621i	0.181263	+	1.26071i	0.853783	+	0.520630i	$0.174303\pi$
$499$	4.04910	+	28.1621i	0.181263	+	1.26071i	−0.672520	+	0.740079i	$0.734788\pi$
$500$		0			0
$501$	−1.12109	−	0.720480i	−0.0500866	−	0.0321887i
$502$	−8.59936	+	9.92419i	−0.383808	+	0.442938i
$503$	32.9609	−	9.67821i	1.46966	−	0.431530i	0.553668	−	0.832737i	$-0.313227\pi$
$503$	32.9609	−	9.67821i	1.46966	−	0.431530i	0.915987	+	0.401207i	$0.131409\pi$
$504$	−0.157872	−	0.345691i	−0.00703217	−	0.0153983i
$505$		0			0
$506$	−23.2913	+	11.7359i	−1.03543	+	0.521723i
$507$	−0.0292481			−0.00129895
$508$	−3.68765	−	8.07482i	−0.163613	−	0.358262i
$509$	6.60273	−	1.93874i	0.292661	−	0.0859329i	−0.132107	−	0.991236i	$-0.542174\pi$
$509$	6.60273	−	1.93874i	0.292661	−	0.0859329i	0.424767	+	0.905303i	$0.360356\pi$
$510$		0			0
$511$	−0.409102	−	0.262914i	−0.0180976	−	0.0116306i
$512$	8.24708	+	9.51763i	0.364473	+	0.420624i
$513$	−2.03584	−	14.1595i	−0.0898843	−	0.625159i
$514$	16.4946	+	4.84325i	0.727545	+	0.213626i
$515$		0			0
$516$	−1.01228	+	7.04056i	−0.0445631	+	0.309943i
$517$	11.7731	−	25.7796i	0.517782	−	1.13378i
$518$	−0.0577675	+	0.126493i	−0.00253816	+	0.00555779i
$519$	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	$0.552358\pi$
$522$	4.72337	+	32.8517i	0.206736	+	1.43788i
$523$	−3.11663	−	3.59678i	−0.136281	−	0.157276i	0.683507	−	0.729944i	$-0.260454\pi$
$523$	−3.11663	−	3.59678i	−0.136281	−	0.157276i	−0.819787	+	0.572668i	$0.805908\pi$
$524$	−33.5066	−	21.5334i	−1.46374	−	0.940689i
$525$		0			0
$526$	−47.8808	+	14.0591i	−2.08770	+	0.613005i
$527$	2.42212	+	5.30369i	0.105509	+	0.231033i
$528$	−2.75822			−0.120036
$529$	13.6859	−	18.4850i	0.595039	−	0.803697i
$530$		0			0
$531$	−9.59886	−	21.0186i	−0.416555	−	0.912129i
$532$	−0.718048	+	0.210838i	−0.0311313	+	0.00914098i
$533$	13.0922	−	15.1092i	0.567087	−	0.654453i
$534$	29.8989	+	19.2149i	1.29385	+	0.831508i
$535$		0			0
$536$	3.74514	+	26.0480i	0.161766	+	1.12510i
$537$	18.9864	+	5.57492i	0.819325	+	0.240576i
$538$	−17.3660	+	11.1604i	−0.748700	+	0.481160i
$539$	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	$0.254782\pi$
$542$	6.96478	−	48.4411i	0.299163	−	2.08072i
$543$	3.35278	−	2.15470i	0.143882	−	0.0924671i
$544$	22.1704	+	6.50980i	0.950546	+	0.279106i
$545$		0			0
$546$	−0.463379	−	0.534768i	−0.0198308	−	0.0228859i
$547$	32.4460	+	20.8518i	1.38729	+	0.891557i	0.999544	−	0.0302093i	$-0.00961739\pi$
$547$	32.4460	+	20.8518i	1.38729	+	0.891557i	0.387746	+	0.921766i	$0.373254\pi$
$548$	37.4879	−	43.2633i	1.60140	−	1.84812i
$549$	7.79444	−	2.28865i	0.332659	−	0.0976774i
$550$		0			0
$551$	21.3030			0.907539
$552$	−9.23157	+	4.65154i	−0.392922	+	0.197983i
$553$	−0.617845			−0.0262734
$554$	11.5813	+	25.3594i	0.492040	+	1.07742i
$555$		0			0
$556$	−30.1100	+	34.7488i	−1.27695	+	1.47368i
$557$	−35.4471	−	22.7805i	−1.50194	−	0.965239i	−0.994632	−	0.103475i	$-0.967004\pi$
$557$	−35.4471	−	22.7805i	−1.50194	−	0.965239i	−0.507309	−	0.861764i	$-0.669360\pi$
$558$	5.03092	+	5.80599i	0.212976	+	0.245787i
$559$	−1.22870	−	8.54579i	−0.0519685	−	0.361449i
$560$		0			0
$561$	−6.94434	+	4.46286i	−0.293190	+	0.188422i
$562$	−7.77824	+	54.0988i	−0.328105	+	2.28202i
$563$	2.50064	−	5.47564i	0.105389	−	0.230771i	−0.849589	−	0.527445i	$-0.823150\pi$
$563$	2.50064	−	5.47564i	0.105389	−	0.230771i	0.954979	+	0.296674i	$0.0958775\pi$
$564$	14.3160	−	31.3477i	0.602814	−	1.31998i
$565$		0			0
$566$	−33.1217	+	21.2860i	−1.39221	+	0.894719i
$567$	0.0845850	+	0.0248364i	0.00355224	+	0.00104303i
$568$	0.581849	+	4.04685i	0.0244139	+	0.169802i
$569$	11.4512	+	13.2154i	0.480061	+	0.554020i	0.943183	−	0.332275i	$-0.107816\pi$
$569$	11.4512	+	13.2154i	0.480061	+	0.554020i	−0.463121	+	0.886295i	$0.653271\pi$
$570$		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	$0.316339\pi$
$572$	−25.0189	+	7.34622i	−1.04609	+	0.307161i
$573$	−2.48387	−	5.43891i	−0.103765	−	0.227214i
$574$	−1.09065			−0.0455229
$575$		0			0
$576$	25.9235			1.08015
$577$	13.4953	+	29.5506i	0.561818	+	1.23021i	0.951041	+	0.309065i	$0.100016\pi$
$577$	13.4953	+	29.5506i	0.561818	+	1.23021i	−0.389223	+	0.921143i	$0.627257\pi$
$578$	−11.8802	+	3.48833i	−0.494149	+	0.145095i
$579$	6.60519	−	7.62280i	0.274502	−	0.316793i
$580$		0			0
$581$	−0.240883	−	0.277994i	−0.00999351	−	0.0115331i
$582$	−4.56092	−	31.7219i	−0.189056	−	1.31491i
$583$	−24.2907	−	7.13240i	−1.00602	−	0.295394i
$584$	−10.0028	+	6.42841i	−0.413919	+	0.266009i
$585$		0			0
$586$	7.86064	−	17.2124i	0.324720	−	0.711037i
$587$	5.47162	−	11.9812i	0.225838	−	0.494516i	−0.762463	−	0.647032i	$-0.776010\pi$
$587$	5.47162	−	11.9812i	0.225838	−	0.494516i	0.988301	+	0.152515i	$0.0487374\pi$
$588$	2.95259	−	20.5357i	0.121763	−	0.846879i
$589$	4.14825	−	2.66592i	0.170926	−	0.109847i
$590$		0			0
$591$	−0.728029	−	5.06355i	−0.0299471	−	0.208287i
$592$	−0.523923	−	0.604640i	−0.0215331	−	0.0248505i
$593$	−26.5698	−	17.0754i	−1.09109	−	0.701202i	−0.133999	−	0.990982i	$-0.542782\pi$
$593$	−26.5698	−	17.0754i	−1.09109	−	0.701202i	−0.957094	+	0.289779i	$0.906418\pi$
$594$	−17.8065	+	20.5498i	−0.730610	+	0.843169i
$595$		0			0
$596$	−19.6630	−	43.0559i	−0.805426	−	1.76364i
$597$	26.5800			1.08785
$598$	28.1046	−	26.3053i	1.14928	−	1.07570i
$599$	−5.38162			−0.219887			−0.109943	−	0.993938i	$-0.535067\pi$
$599$	−5.38162			−0.219887			−0.109943	+	0.993938i	$0.535067\pi$
$600$		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	$0.651654\pi$
$602$	−0.308437	+	0.355955i	−0.0125710	+	0.0145077i
$603$	−20.5416	−	13.2013i	−0.836518	−	0.537598i
$604$	−0.859352	−	0.991745i	−0.0349665	−	0.0403535i
$605$		0			0
$606$	37.1728	+	10.9149i	1.51004	+	0.443388i
$607$	−18.3320	+	11.7812i	−0.744072	+	0.478186i	−0.856935	−	0.515424i	$-0.827634\pi$
$607$	−18.3320	+	11.7812i	−0.744072	+	0.478186i	0.112863	+	0.993611i	$0.463998\pi$
$608$	2.78103	−	19.3425i	0.112786	−	0.784442i
$609$	0.272679	−	0.597084i	0.0110495	−	0.0241951i
$610$		0			0
$611$	−5.95300	+	41.4040i	−0.240833	+	1.67503i
$612$	16.8885	−	10.8536i	0.682678	−	0.438731i
$613$	−6.50705	−	1.91064i	−0.262817	−	0.0771701i	0.147669	−	0.989037i	$-0.452823\pi$
$613$	−6.50705	−	1.91064i	−0.262817	−	0.0771701i	−0.410486	+	0.911867i	$0.634641\pi$
$614$	4.65607	+	32.3837i	0.187904	+	1.30690i
$615$		0			0
$616$	0.390055	+	0.250673i	0.0157158	+	0.0100999i
$617$	−21.1308	+	24.3863i	−0.850695	+	0.981755i	−0.999975	−	0.00704038i	$-0.997759\pi$
$617$	−21.1308	+	24.3863i	−0.850695	+	0.981755i	0.149280	+	0.988795i	$0.452304\pi$
$618$	−2.48773	+	0.730462i	−0.100071	+	0.0293835i
$619$	−14.5801	−	31.9260i	−0.586024	−	1.28321i	−0.937815	−	0.347134i	$-0.887155\pi$
$619$	−14.5801	−	31.9260i	−0.586024	−	1.28321i	0.351792	−	0.936078i	$-0.385573\pi$
$620$		0			0
$621$	5.86879	−	23.2499i	0.235506	−	0.932986i
$622$	−67.2534			−2.69661
$623$	0.583995	+	1.27877i	0.0233973	+	0.0512329i
$624$	3.90613	−	1.14694i	0.156370	−	0.0459144i
$625$		0			0
$626$	−10.4358	−	6.70667i	−0.417098	−	0.268052i
$627$	4.57170	+	5.27603i	0.182576	+	0.210704i
$628$	3.00600	+	20.9072i	0.119952	+	0.834287i
$629$	−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	$-0.0381663\pi$
$632$	−6.27554	+	13.7415i	−0.249628	+	0.546608i
$633$	−6.12428	+	13.4103i	−0.243418	+	0.533012i
$634$	−0.891617	+	6.20133i	−0.0354106	+	0.246286i
$635$		0			0
$636$	−29.5373	−	8.67294i	−1.17123	−	0.343904i
$637$	3.58384	+	24.9261i	0.141997	+	0.987610i
$638$	−26.5172	−	30.6024i	−1.04982	−	1.21156i
$639$	−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	$0.156167\pi$
$642$	15.8784	+	34.7689i	0.626672	+	1.37222i
$643$	−31.5510			−1.24425			−0.622126	−	0.782917i	$-0.713731\pi$
$643$	−31.5510			−1.24425			−0.622126	+	0.782917i	$0.713731\pi$
$644$	−1.24761	−	0.130798i	−0.0491628	−	0.00515417i
$645$		0			0
$646$	−8.96097	−	19.6218i	−0.352565	−	0.772009i
$647$	−13.3013	+	3.90562i	−0.522929	+	0.153546i	−0.532535	−	0.846408i	$-0.678761\pi$
$647$	−13.3013	+	3.90562i	−0.522929	+	0.153546i	0.00960580	+	0.999954i	$0.496942\pi$
$648$	1.41153	−	1.62899i	0.0554501	−	0.0639928i
$649$	23.7160	+	15.2413i	0.930934	+	0.598275i
$650$		0			0
$651$	−0.0216231	−	0.150392i	−0.000847474	−	0.00589431i
$652$	−20.3453	−	5.97391i	−0.796782	−	0.233956i
$653$	4.75724	−	3.05729i	0.186165	−	0.119641i	−0.444239	−	0.895909i	$-0.646526\pi$
$653$	4.75724	−	3.05729i	0.186165	−	0.119641i	0.630404	+	0.776267i	$0.282889\pi$
$654$	0.829328	−	5.76810i	0.0324293	−	0.225551i
$655$		0			0
$656$	2.60667	−	5.70780i	0.101773	−	0.222852i
$657$	1.57012	−	10.9204i	0.0612564	−	0.426047i
$658$	1.91971	−	1.23372i	0.0748379	−	0.0480954i
$659$	−28.0838	−	8.24614i	−1.09399	−	0.321224i	−0.315527	−	0.948917i	$-0.602181\pi$
$659$	−28.0838	−	8.24614i	−1.09399	−	0.321224i	−0.778461	+	0.627692i	$0.784000\pi$
$660$		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	$0.873873\pi$
$662$	25.9733	+	16.6920i	1.00948	+	0.648753i
$663$	7.97864	−	9.20784i	0.309865	−	0.357603i
$664$	−8.62956	+	2.53387i	−0.334892	+	0.0983331i
$665$		0			0
$666$	−3.15486			−0.122248
$667$	33.0272	+	13.5782i	1.27882	+	0.525749i
$668$	−3.95413			−0.152990
$669$	0.420370	+	0.920482i	0.0162524	+	0.0355879i
$670$		0			0
$671$	−6.49036	+	7.49027i	−0.250558	+	0.289159i
$672$	−0.506538	−	0.325532i	−0.0195401	−	0.0125577i
$673$	2.50376	+	2.88949i	0.0965128	+	0.111382i	0.801951	−	0.597389i	$-0.203795\pi$
$673$	2.50376	+	2.88949i	0.0965128	+	0.111382i	−0.705438	+	0.708771i	$0.749250\pi$
$674$	−6.84471	−	47.6060i	−0.263649	−	1.83372i
$675$		0			0
$676$	−0.0730065	+	0.0469185i	−0.00280794	+	0.00180456i
$677$	2.33764	−	16.2586i	0.0898428	−	0.624870i	−0.894297	−	0.447474i	$-0.852324\pi$
$677$	2.33764	−	16.2586i	0.0898428	−	0.624870i	0.984140	−	0.177396i	$-0.0567673\pi$
$678$	−16.5873	+	36.3211i	−0.637031	+	1.39490i
$679$	0.526602	−	1.15310i	0.0202091	−	0.0442518i
$680$		0			0
$681$	−4.24183	+	2.72606i	−0.162547	+	0.104463i
$682$	−8.99325	−	2.64066i	−0.344369	−	0.101116i
$683$	1.04764	+	7.28651i	0.0400869	+	0.278811i	0.999999	−	0.00149105i	$-0.000474615\pi$
$683$	1.04764	+	7.28651i	0.0400869	+	0.278811i	−0.959912	+	0.280302i	$0.909566\pi$
$684$	−11.1183	−	12.8312i	−0.425119	−	0.490614i
$685$		0			0
$686$	1.80028	−	2.07764i	0.0687351	−	0.0793245i
$687$	22.0208	−	6.46589i	0.840145	−	0.246689i
$688$	−1.12569	−	2.46491i	−0.0429163	−	0.0939737i
$689$	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	$0.558914\pi$
$692$	−3.32894	−	7.28935i	−0.126547	−	0.277100i
$693$	−0.412791	+	0.121206i	−0.0156806	+	0.00460425i
$694$	−27.5955	+	31.8469i	−1.04751	+	1.20889i
$695$		0			0
$696$	−10.5101	−	12.1293i	−0.398386	−	0.459762i
$697$	−2.67257	−	18.5881i	−0.101231	−	0.704076i
$698$	44.7552	+	13.1413i	1.69401	+	0.497406i
$699$	−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	$-0.160884\pi$
$702$	16.6720	−	36.5066i	0.629244	−	1.37785i
$703$	−0.288184	+	2.00436i	−0.0108691	+	0.0755960i
$704$	−26.6071	+	17.0994i	−1.00279	+	0.644456i
$705$		0			0
$706$	−0.511298	−	3.55616i	−0.0192430	−	0.133838i
$707$	1.00353	+	1.15814i	0.0377417	+	0.0435562i
$708$	28.8385	+	18.5334i	1.08382	+	0.696526i
$709$	−22.9666	+	26.5049i	−0.862529	+	0.995411i	0.137459	+	0.990507i	$0.456106\pi$
$709$	−22.9666	+	26.5049i	−0.862529	+	0.995411i	−0.999988	+	0.00490358i	$0.998439\pi$
$710$		0			0
$711$	−5.82291	−	12.7504i	−0.218376	−	0.478177i
$712$	34.3729			1.28818
$713$	8.13045	−	1.48909i	0.304488	−	0.0557668i
$714$	−0.664664			−0.0248744
$715$		0			0
$716$	56.3353	−	16.5415i	2.10535	−	0.618187i
$717$	5.74298	−	6.62775i	0.214475	−	0.247518i
$718$	−65.2771	−	41.9511i	−2.43612	−	1.56560i
$719$	−14.5394	−	16.7793i	−0.542226	−	0.625763i	0.416828	−	0.908986i	$-0.363142\pi$
$719$	−14.5394	−	16.7793i	−0.542226	−	0.625763i	−0.959054	+	0.283223i	$0.908596\pi$
$720$		0			0
$721$	−0.0984013	−	0.0288932i	−0.00366466	−	0.00107604i
$722$	20.2762	−	13.0307i	0.754602	−	0.484953i
$723$	−1.25495	+	8.72835i	−0.0466720	+	0.324611i
$724$	4.91245	−	10.7568i	0.182570	−	0.399772i
$725$		0			0
$726$	−1.60046	+	11.1315i	−0.0593987	+	0.413127i
$727$	−0.587772	+	0.377738i	−0.0217993	+	0.0140095i	−0.551495	−	0.834178i	$-0.685942\pi$
$727$	−0.587772	+	0.377738i	−0.0217993	+	0.0140095i	0.529696	+	0.848188i	$0.322306\pi$
$728$	−0.656624	−	0.192802i	−0.0243361	−	0.00714573i
$729$	−1.85009	−	12.8677i	−0.0685220	−	0.476581i
$730$		0			0
$731$	−6.82240	−	4.38449i	−0.252336	−	0.162166i
$732$	−7.89223	+	9.10812i	−0.291705	+	0.336646i
$733$	−35.7918	+	10.5094i	−1.32200	+	0.388174i	−0.865214	−	0.501403i	$-0.832817\pi$
$733$	−35.7918	+	10.5094i	−1.32200	+	0.388174i	−0.456785	+	0.889577i	$0.650999\pi$
$734$	−20.9465	−	45.8664i	−0.773149	−	1.69296i
$735$		0			0
$736$	16.6402	−	28.2151i	0.613364	−	1.04002i
$737$	29.7909			1.09736
$738$	−10.2789	−	22.5077i	−0.378372	−	0.828518i
$739$	23.5752	−	6.92231i	0.867229	−	0.254641i	0.182293	−	0.983244i	$-0.441648\pi$
$739$	23.5752	−	6.92231i	0.867229	−	0.254641i	0.684936	+	0.728603i	$0.259830\pi$
$740$		0			0
$741$	−8.66826	−	5.57075i	−0.318437	−	0.204647i
$742$	−1.33489	−	1.54054i	−0.0490053	−	0.0565552i
$743$	5.88612	+	40.9388i	0.215941	+	1.50190i	0.752811	+	0.658236i	$0.228697\pi$
$743$	5.88612	+	40.9388i	0.215941	+	1.50190i	−0.536871	+	0.843665i	$0.680394\pi$
$744$	−3.56450	−	1.04663i	−0.130681	−	0.0383713i
$745$		0			0
$746$	−3.42400	+	23.8145i	−0.125362	+	0.871910i
$747$	3.46671	−	7.59104i	0.126840	−	0.277742i
$748$	−10.1748	+	22.2796i	−0.372026	+	0.814623i
$749$	−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	$0.322158\pi$
$752$	1.86842	+	12.9952i	0.0681344	+	0.473885i
$753$	3.85845	+	4.45289i	0.140610	+	0.162272i
$754$	50.2783	+	32.3119i	1.83103	+	1.17673i
$755$		0			0
$756$	−1.25488	+	0.368465i	−0.0456394	+	0.0134009i
$757$	−4.14940	−	9.08592i	−0.150812	−	0.330233i	0.819114	−	0.573630i	$-0.194465\pi$
$757$	−4.14940	−	9.08592i	−0.150812	−	0.330233i	−0.969927	+	0.243397i	$0.921738\pi$
$758$	8.21774			0.298482
$759$	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	$0.962491\pi$
$762$	−6.39771	+	1.87854i	−0.231764	+	0.0680522i
$763$	0.150947	−	0.174202i	0.00546464	−	0.00630653i
$764$	−14.9249	−	9.59163i	−0.539963	−	0.347013i
$765$		0			0
$766$	1.88491	+	13.1098i	0.0681045	+	0.473677i
$767$	−39.9238	−	11.7227i	−1.44157	−	0.423282i
$768$	−6.74207	+	4.33287i	−0.243283	+	0.156349i
$769$	6.22901	−	43.3237i	0.224624	−	1.56229i	−0.495599	−	0.868551i	$-0.665051\pi$
$769$	6.22901	−	43.3237i	0.224624	−	1.56229i	0.720223	−	0.693743i	$-0.244039\pi$
$770$		0			0
$771$	3.20427	−	7.01636i	0.115399	−	0.252688i
$772$	4.25916	−	29.6231i	0.153291	−	1.06616i
$773$	−28.2907	+	18.1814i	−1.01755	+	0.653938i	−0.939336	−	0.342999i	$-0.888557\pi$
$773$	−28.2907	+	18.1814i	−1.01755	+	0.653938i	−0.0782114	+	0.996937i	$0.524921\pi$
$774$	−10.2527	−	3.01046i	−0.368525	−	0.108209i
$775$		0			0
$776$	−20.2973	−	23.4244i	−0.728632	−	0.840886i
$777$	0.0524899	+	0.0337332i	0.00188306	+	0.00121017i
$778$	9.69430	−	11.1878i	0.347558	−	0.401103i
$779$	−15.2386	+	4.47446i	−0.545980	+	0.160314i
$780$		0			0
$781$	4.62835			0.165615
$782$	−1.38607	−	36.1323i	−0.0495659	−	1.29209i
$783$	37.2296			1.33048
$784$	3.28337	+	7.18957i	0.117263	+	0.256770i
$785$		0			0
$786$	−19.5915	+	22.6098i	−0.698805	+	0.806464i
$787$	−1.05221	−	0.676215i	−0.0375073	−	0.0241045i	0.521753	−	0.853097i	$-0.325278\pi$
$787$	−1.05221	−	0.676215i	−0.0375073	−	0.0241045i	−0.559260	+	0.828992i	$0.688915\pi$
$788$	−9.93997	−	11.4713i	−0.354097	−	0.408649i
$789$	3.18652	+	22.1627i	0.113443	+	0.789014i
$790$		0			0
$791$	−1.32867	+	0.853887i	−0.0472422	+	0.0303607i
$792$	−1.49702	+	10.4120i	−0.0531943	+	0.369975i
$793$	6.07684	−	13.3064i	0.215795	−	0.472525i
$794$	−4.21946	+	9.23933i	−0.149743	+	0.327892i
$795$		0			0
$796$	66.3466	−	42.6384i	2.35159	−	1.51128i
$797$	−11.7261	−	3.44308i	−0.415358	−	0.121960i	0.0673749	−	0.997728i	$-0.478538\pi$
$797$	−11.7261	−	3.44308i	−0.415358	−	0.121960i	−0.482733	+	0.875768i	$0.660356\pi$
$798$	0.0799977	+	0.556396i	0.00283189	+	0.0196962i
$799$	25.7306	+	29.6947i	0.910282	+	1.05052i
$800$		0			0
$801$	−20.8860	+	24.1037i	−0.737969	+	0.851662i
$802$	−59.6863	+	17.5255i	−2.10760	+	0.618846i
$803$	5.59168	+	12.2441i	0.197326	+	0.432084i
$804$	36.2255			1.27758
$805$		0			0
$806$	13.8341			0.487285
$807$	3.84770	+	8.42528i	0.135445	+	0.296584i
$808$	35.9512	−	10.5562i	1.26476	−	0.371367i
$809$	17.5520	−	20.2561i	0.617097	−	0.712167i	−0.358056	−	0.933700i	$-0.616560\pi$
$809$	17.5520	−	20.2561i	0.617097	−	0.712167i	0.975153	+	0.221533i	$0.0711059\pi$
$810$		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	$0.528090\pi$
$812$	−0.277177	−	1.92781i	−0.00972702	−	0.0676529i
$813$	−21.0691	−	6.18644i	−0.738925	−	0.216968i
$814$	3.23805	−	2.08097i	0.113494	−	0.0729379i
$815$		0			0
$816$	1.58855	−	3.47844i	0.0556104	−	0.121770i
$817$	−2.84917	+	6.23880i	−0.0996797	+	0.218268i
$818$	2.57518	−	17.9108i	0.0900392	−	0.626236i
$819$	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	$0.768212\pi$
$822$	−28.1583	−	32.4964i	−0.982134	−	1.13344i
$823$	39.4672	+	25.3640i	1.37574	+	0.884134i	0.999108	−	0.0422285i	$-0.0134457\pi$
$823$	39.4672	+	25.3640i	1.37574	+	0.884134i	0.376632	+	0.926363i	$0.377082\pi$
$824$	−1.64209	+	1.89508i	−0.0572050	+	0.0660181i
$825$		0			0
$826$	0.942962	+	2.06480i	0.0328099	+	0.0718436i
$827$	24.2676			0.843869			0.421934	−	0.906626i	$-0.361351\pi$
$827$	24.2676			0.843869			0.421934	+	0.906626i	$0.361351\pi$
$828$	−9.05891	−	26.9795i	−0.314819	−	0.937603i
$829$	−21.8597			−0.759220			−0.379610	−	0.925147i	$-0.623942\pi$
$829$	−21.8597			−0.759220			−0.379610	+	0.925147i	$0.623942\pi$
$830$		0			0
$831$	12.0022	−	3.52417i	0.416353	−	0.122252i
$832$	30.5700	−	35.2797i	1.05983	−	1.22310i
$833$	19.8994	+	12.7886i	0.689473	+	0.443098i
$834$	22.6166	+	26.1009i	0.783148	+	0.903801i
$835$		0			0
$836$	19.8751	+	5.83585i	0.687393	+	0.201837i
$837$	7.24957	−	4.65902i	0.250582	−	0.161039i
$838$	−8.79669	+	61.1823i	−0.303876	+	2.11351i
$839$	−11.3411	+	24.8335i	−0.391538	+	0.857348i	0.606521	+	0.795068i	$0.292565\pi$
$839$	−11.3411	+	24.8335i	−0.391538	+	0.857348i	−0.998059	+	0.0622806i	$0.980163\pi$
$840$		0			0
$841$	−3.76305	+	26.1726i	−0.129760	+	0.902504i
$842$	65.5352	−	42.1169i	2.25849	−	1.45145i
$843$	23.5299	+	6.90899i	0.810412	+	0.237958i
$844$	6.22531	+	43.2980i	0.214284	+	1.49038i
$845$		0			0
$846$	43.5525	+	27.9895i	1.49737	+	0.962298i
$847$	−0.291301	+	0.336180i	−0.0100092	+	0.0115513i
$848$	11.2527	−	3.30408i	0.386418	−	0.113463i
$849$	7.33863	+	16.0694i	0.251861	+	0.551499i
$850$		0			0
$851$	−1.72433	+	2.92379i	−0.0591094	+	0.100226i
$852$	5.62804			0.192813
$853$	11.7016	+	25.6230i	0.400657	+	0.877316i	0.997203	+	0.0747372i	$0.0238118\pi$
$853$	11.7016	+	25.6230i	0.400657	+	0.877316i	−0.596547	+	0.802578i	$0.703461\pi$
$854$	−0.765701	+	0.224830i	−0.0262018	+	0.00769353i
$855$		0			0
$856$	31.0986	+	19.9858i	1.06293	+	0.683102i
$857$	−7.35982	−	8.49369i	−0.251407	−	0.290139i	0.615992	−	0.787752i	$-0.288755\pi$
$857$	−7.35982	−	8.49369i	−0.251407	−	0.290139i	−0.867399	+	0.497613i	$0.834210\pi$
$858$	2.78736	+	19.3865i	0.0951588	+	0.661844i
$859$	8.44772	+	2.48047i	0.288233	+	0.0846327i	0.422653	−	0.906292i	$-0.361099\pi$
$859$	8.44772	+	2.48047i	0.288233	+	0.0846327i	−0.134420	+	0.990924i	$0.542917\pi$
$860$		0			0
$861$	−0.0696439	+	0.484384i	−0.00237346	+	0.0165078i
$862$	8.57972	−	18.7870i	0.292226	−	0.639887i
$863$	19.8827	−	43.5371i	0.676816	−	1.48202i	−0.189166	−	0.981945i	$-0.560579\pi$
$863$	19.8827	−	43.5371i	0.676816	−	1.48202i	0.865982	−	0.500075i	$-0.166694\pi$
$864$	4.86019	−	33.8034i	0.165347	−	1.15001i
$865$		0			0
$866$	−48.3892	−	14.2084i	−1.64433	−	0.482820i
$867$	0.790638	+	5.49901i	0.0268515	+	0.186756i
$868$	−0.295225	−	0.340708i	−0.0100206	−	0.0115644i
$869$	14.3867	+	9.24578i	0.488036	+	0.313641i
$870$		0			0
$871$	−42.1892	+	12.3879i	−1.42953	+	0.419747i
$872$	−2.34124	−	5.12661i	−0.0792845	−	0.173609i
$873$	28.7593			0.973356
$874$	−30.0798	+	5.50910i	−1.01746	+	0.186348i
$875$		0			0
$876$	6.79944	+	14.8887i	0.229732	+	0.503043i
$877$	−45.2435	+	13.2847i	−1.52776	+	0.448592i	−0.934365	−	0.356317i	$-0.884032\pi$
$877$	−45.2435	+	13.2847i	−1.52776	+	0.448592i	−0.593398	+	0.804909i	$0.702214\pi$
$878$	−26.9975	+	31.1567i	−0.911121	+	1.05149i
$879$	−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	$-0.259464\pi$
$882$	29.9048	+	8.78083i	1.00695	+	0.295666i
$883$	45.8990	−	29.4975i	1.54462	−	0.992670i	0.557967	−	0.829863i	$-0.311582\pi$
$883$	45.8990	−	29.4975i	1.54462	−	0.992670i	0.986658	−	0.162807i	$-0.0520548\pi$
$884$	5.14479	−	35.7828i	0.173038	−	1.20351i
$885$		0			0
$886$	−20.7193	+	45.3689i	−0.696077	+	1.52420i
$887$	−2.01788	+	14.0346i	−0.0677537	+	0.471237i	0.927492	+	0.373843i	$0.121960\pi$
$887$	−2.01788	+	14.0346i	−0.0677537	+	0.471237i	−0.995246	+	0.0973946i	$0.968949\pi$
$888$	1.28341	−	0.824797i	0.0430684	−	0.0276784i
$889$	−0.253060	−	0.0743050i	−0.00848734	−	0.00249211i
$890$		0			0
$891$	−1.59792	−	1.84410i	−0.0535324	−	0.0617797i
$892$	2.52589	+	1.62329i	0.0845730	+	0.0543517i
$893$	21.7608	−	25.1133i	0.728197	−	0.840384i
$894$	−34.1133	+	10.0166i	−1.14092	+	0.335004i
$895$		0			0
$896$	−1.34240			−0.0448465
$897$	−9.88816	−	14.1616i	−0.330156	−	0.472843i
$898$	−10.9523			−0.365484
$899$	5.33109	+	11.6735i	0.177802	+	0.389332i
$900$		0			0
$901$	22.9847	−	26.5257i	0.765730	−	0.883699i
$902$	25.3962	+	16.3211i	0.845600	+	0.543434i
$903$	0.138393	+	0.159714i	0.00460542	+	0.00531494i
$904$	5.49580	+	38.2242i	0.182788	+	1.27132i
$905$		0			0
$906$	−0.829210	+	0.532901i	−0.0275486	+	0.0177044i
$907$	7.08860	−	49.3023i	0.235373	−	1.63706i	−0.438873	−	0.898549i	$-0.644622\pi$
$907$	7.08860	−	49.3023i	0.235373	−	1.63706i	0.674246	−	0.738506i	$-0.264469\pi$
$908$	−6.21507	+	13.6091i	−0.206254	+	0.451634i
$909$	−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	$0.432016\pi$
$912$	−3.10303	−	0.911132i	−0.102752	−	0.0301706i
$913$	1.44898	+	10.0779i	0.0479543	+	0.333529i
$914$	−16.9046	−	19.5090i	−0.559156	−	0.645300i
$915$		0			0
$916$	44.5941	−	51.4644i	1.47343	−	1.70043i
$917$	−1.13543	+	0.333391i	−0.0374951	+	0.0110095i
$918$	−15.6604	−	34.2915i	−0.516870	−	1.13179i
$919$	−1.66022			−0.0547657			−0.0273829	−	0.999625i	$-0.508717\pi$
$919$	−1.66022			−0.0547657			−0.0273829	+	0.999625i	$0.508717\pi$
$920$		0			0
$921$	14.6797			0.483711
$922$	14.3963	+	31.5235i	0.474116	+	1.03817i
$923$	−6.55457	+	1.92459i	−0.215746	+	0.0633488i
$924$	0.417970	−	0.482363i	0.0137502	−	0.0158686i
$925$		0			0
$926$	−14.7804	−	17.0575i	−0.485715	−	0.560545i
$927$	−0.331122	−	2.30300i	−0.0108755	−	0.0756406i
$928$	48.7971	+	14.3281i	1.60184	+	0.470343i
$929$	24.5455	−	15.7744i	0.805311	−	0.517542i	−0.0720340	−	0.997402i	$-0.522949\pi$
$929$	24.5455	−	15.7744i	0.805311	−	0.517542i	0.877345	+	0.479860i	$0.159313\pi$
$930$		0			0
$931$	8.31037	−	18.1972i	0.272361	−	0.596388i
$932$	−26.5290	+	58.0904i	−0.868986	+	1.90281i
$933$	−4.29449	+	29.8688i	−0.140595	+	0.977861i
$934$	0.299702	−	0.192607i	0.00980656	−	0.00630229i
$935$		0			0
$936$	−2.20955	−	15.3678i	−0.0722214	−	0.502311i
$937$	12.0573	+	13.9149i	0.393895	+	0.454580i	0.917709	−	0.397253i	$-0.130037\pi$
$937$	12.0573	+	13.9149i	0.393895	+	0.454580i	−0.523813	+	0.851833i	$0.675491\pi$
$938$	2.01794	+	1.29685i	0.0658881	+	0.0423437i
$939$	−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	$0.614176\pi$
$942$	15.8655			0.516926
$943$	−26.4772	−	2.77584i	−0.862215	−	0.0903937i
$944$	−13.0596			−0.425053
$945$		0			0
$946$	12.5088	−	3.67290i	0.406695	−	0.119416i
$947$	−13.8033	+	15.9299i	−0.448548	+	0.517652i	−0.934321	−	0.356433i	$-0.883993\pi$
$947$	−13.8033	+	15.9299i	−0.448548	+	0.517652i	0.485773	+	0.874085i	$0.338538\pi$
$948$	17.4941	+	11.2428i	0.568183	+	0.365149i
$949$	−13.0102	−	15.0146i	−0.422330	−	0.487395i
$950$		0			0
$951$	2.69722	+	0.791977i	0.0874635	+	0.0256816i
$952$	−0.540775	+	0.347535i	−0.0175266	+	0.0112637i
$953$	2.09831	−	14.5941i	0.0679710	−	0.472749i	−0.927198	−	0.374572i	$-0.877790\pi$
$953$	2.09831	−	14.5941i	0.0679710	−	0.472749i	0.995169	−	0.0981772i	$-0.0313012\pi$
$954$	19.2113	−	42.0669i	0.621989	−	1.36197i
$955$		0			0
$956$	3.70319	−	25.7562i	0.119770	−	0.833016i
$957$	−15.2845	+	9.82277i	−0.494079	+	0.317525i
$958$	12.5627	+	3.68873i	0.405881	+	0.119178i
$959$	−0.242051	−	1.68350i	−0.00781622	−	0.0543630i
$960$		0			0
$961$	−23.5799	−	15.1539i	−0.760642	−	0.488835i
$962$	−3.72033	+	4.29349i	−0.119948	+	0.138428i
$963$	−32.9113	+	9.66362i	−1.06055	+	0.311406i
$964$	10.8691	+	23.8001i	0.350071	+	0.766549i
$965$		0			0
$966$	−0.230613	+	0.913599i	−0.00741984	+	0.0293946i
$967$	25.3720			0.815909			0.407955	−	0.913002i	$-0.366242\pi$
$967$	25.3720			0.815909			0.407955	+	0.913002i	$0.366242\pi$
$968$	4.51820	+	9.89347i	0.145220	+	0.317988i
$969$	−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	$0.897760\pi$
$972$	−31.0890	−	35.8786i	−0.997180	−	1.15081i
$973$	0.194414	+	1.35218i	0.00623261	+	0.0433488i
$974$	14.8280	+	4.35388i	0.475118	+	0.139507i
$975$		0			0
$976$	0.653409	−	4.54456i	0.0209151	−	0.145468i
$977$	9.66014	−	21.1528i	0.309055	−	0.676736i	−0.689829	−	0.723973i	$-0.742314\pi$
$977$	9.66014	−	21.1528i	0.309055	−	0.676736i	0.998884	+	0.0472363i	$0.0150414\pi$
$978$	−6.61636	+	14.4878i	−0.211568	+	0.463269i
$979$	5.53774	−	38.5158i	0.176987	−	1.23097i
$980$		0			0
$981$	5.01759	+	1.47330i	0.160199	+	0.0470387i
$982$	−6.96412	−	48.4365i	−0.222234	−	1.54567i
$983$	0.430697	+	0.497051i	0.0137371	+	0.0158535i	0.762577	−	0.646898i	$-0.223934\pi$
$983$	0.430697	+	0.497051i	0.0137371	+	0.0158535i	−0.748839	+	0.662751i	$0.769389\pi$
$984$	10.0658	+	6.46891i	0.320887	+	0.206221i
$985$		0			0
$986$	53.8655	−	15.8163i	1.71543	−	0.503695i
$987$	−0.425341	−	0.931366i	−0.0135387	−	0.0296457i
$988$	−30.5733			−0.972667
$989$	−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	$0.847670\pi$
$992$	11.2951	−	3.31654i	0.358620	−	0.105300i
$993$	9.07184	−	10.4695i	0.287886	−	0.332238i
$994$	0.313510	+	0.201480i	0.00994392	+	0.00639057i
$995$		0			0
$996$	1.76195	+	12.2546i	0.0558295	+	0.388303i
$997$	−8.45136	−	2.48154i	−0.267657	−	0.0785913i	0.145150	−	0.989410i	$-0.453634\pi$
$997$	−8.45136	−	2.48154i	−0.267657	−	0.0785913i	−0.412807	+	0.910818i	$0.635452\pi$
$998$	53.3443	−	34.2823i	1.68858	−	1.08519i
$999$	−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.k.a.326.1		10
5.2	odd	4		575.2.p.a.349.2		20
5.3	odd	4		575.2.p.a.349.1		20
5.4	even	2		115.2.g.a.96.1	yes	10
23.6	even	11	inner	575.2.k.a.351.1		10
115.29	even	22		115.2.g.a.6.1	✓	10
115.34	odd	22		2645.2.a.o.1.5		5
115.52	odd	44		575.2.p.a.374.1		20
115.98	odd	44		575.2.p.a.374.2		20
115.104	even	22		2645.2.a.n.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.a.6.1	✓	10	115.29	even	22
115.2.g.a.96.1	yes	10	5.4	even	2
575.2.k.a.326.1		10	1.1	even	1	trivial
575.2.k.a.351.1		10	23.6	even	11	inner
575.2.p.a.349.1		20	5.3	odd	4
575.2.p.a.349.2		20	5.2	odd	4
575.2.p.a.374.1		20	115.52	odd	44
575.2.p.a.374.2		20	115.98	odd	44
2645.2.a.n.1.5		5	115.104	even	22
2645.2.a.o.1.5		5	115.34	odd	22

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.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.925839 - 2.02730i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-1.94306 + 2.24241i) q^{4} +(1.45949 + 1.68434i) q^{6} +(0.0125459 + 0.0872586i) q^{7} +(2.06815 + 0.607265i) q^{8} +(-1.68251 + 1.08128i) q^{9} +(1.01365 - 2.21959i) q^{11} +(1.23259 - 2.69900i) q^{12} +(-0.512546 + 3.56484i) q^{13} +(0.165284 - 0.106222i) q^{14} +(0.160869 + 1.11887i) q^{16} +(2.21537 + 2.55667i) q^{17} +(3.74982 + 2.40986i) q^{18} +(1.87358 - 2.16222i) q^{19} +(-0.0366213 - 0.0801894i) q^{21} -5.43826 q^{22} +(4.28287 - 2.15802i) q^{23} -2.15546 q^{24} +(7.70154 - 2.26138i) q^{26} +(3.27430 - 3.77875i) q^{27} +(-0.220047 - 0.141416i) q^{28} +(4.87604 + 5.62725i) q^{29} +(1.65370 + 0.485571i) q^{31} +(5.74593 - 3.69269i) q^{32} +(-0.347262 + 2.41526i) q^{33} +(3.13208 - 6.85830i) q^{34} +(0.844535 - 5.87387i) q^{36} +(-0.595421 + 0.382654i) q^{37} +(-6.11811 - 1.79644i) q^{38} +(-0.512546 - 3.56484i) q^{39} +(-4.66991 - 3.00117i) q^{41} +(-0.128663 + 0.148485i) q^{42} +(-2.30014 + 0.675383i) q^{43} +(3.00764 + 6.58582i) q^{44} +(-8.34021 - 6.68469i) q^{46} +11.6146 q^{47} +(-0.469574 - 1.02822i) q^{48} +(6.70899 - 1.96994i) q^{49} +(-2.84593 - 1.82897i) q^{51} +(-6.99792 - 8.07603i) q^{52} +(-1.47653 - 10.2695i) q^{53} +(-10.6921 - 3.13950i) q^{54} +(-0.0270422 + 0.188083i) q^{56} +(-1.18852 + 2.60249i) q^{57} +(6.89372 - 15.0951i) q^{58} +(-1.64421 + 11.4357i) q^{59} +(-3.89722 - 1.14433i) q^{61} +(-0.546662 - 3.80211i) q^{62} +(-0.115460 - 0.133248i) q^{63} +(-10.9041 - 7.00766i) q^{64} +(5.21797 - 1.53213i) q^{66} +(5.07177 + 11.1056i) q^{67} -10.0377 q^{68} +(-3.50140 + 3.27723i) q^{69} +(0.787956 + 1.72538i) q^{71} +(-4.13631 + 1.21453i) q^{72} +(-3.61246 + 4.16900i) q^{73} +(1.32702 + 0.852823i) q^{74} +(1.20812 + 8.40266i) q^{76} +(0.206395 + 0.0606031i) q^{77} +(-6.75247 + 4.33955i) q^{78} +(-0.997420 + 6.93721i) q^{79} +(0.415415 - 0.909632i) q^{81} +(-1.76070 + 12.2459i) q^{82} +(-3.51021 + 2.25587i) q^{83} +(0.250975 + 0.0736930i) q^{84} +(3.49877 + 4.03779i) q^{86} +(-6.26391 - 4.02557i) q^{87} +(3.44426 - 3.97489i) q^{88} +(15.3009 - 4.49275i) q^{89} -0.317493 q^{91} +(-3.48270 + 13.7971i) q^{92} -1.72352 q^{93} +(-10.7532 - 23.5463i) q^{94} +(-4.47283 + 5.16192i) q^{96} +(-12.0969 - 7.77424i) q^{97} +(-10.2051 - 11.7773i) q^{98} +(0.694523 + 4.83052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - q^{3} - q^{4} + 6 q^{6} - 5 q^{7} + 16 q^{8} + 2 q^{9} + 8 q^{11} - q^{12} - 3 q^{14} + 5 q^{16} + 23 q^{17} + 10 q^{18} - 13 q^{19} + 6 q^{21} - 4 q^{22} + 21 q^{23} - 6 q^{24} + 11 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - q^3 - q^4 + 6 * q^6 - 5 * q^7 + 16 * q^8 + 2 * q^9 + 8 * q^11 - q^12 - 3 * q^14 + 5 * q^16 + 23 * q^17 + 10 * q^18 - 13 * q^19 + 6 * q^21 - 4 * q^22 + 21 * q^23 - 6 * q^24 + 11 * q^26 + 5 * q^27 + 6 * q^28 + 2 * q^29 - 20 * q^31 + 15 * q^32 - 3 * q^33 + 16 * q^34 + 24 * q^36 - 13 * q^37 - 21 * q^38 - 5 * q^41 - 3 * q^42 - 15 * q^43 + 19 * q^44 - 16 * q^46 + 52 * q^47 - 6 * q^48 + 4 * q^49 - 10 * q^51 - 22 * q^52 - 6 * q^53 - 30 * q^54 + 3 * q^56 - 2 * q^57 - 45 * q^58 + 5 * q^59 - 3 * q^61 + 54 * q^62 + 10 * q^63 - 34 * q^64 - 4 * q^66 - 20 * q^67 - 32 * q^68 - q^69 - 22 * q^71 - 32 * q^72 - 43 * q^73 + q^74 - 2 * q^76 - 4 * q^77 - 11 * q^78 + 51 * q^79 - q^81 - 58 * q^82 + 17 * q^83 + 6 * q^84 - 9 * q^86 + 2 * q^87 - 7 * q^88 + 57 * q^89 - 22 * q^91 + 43 * q^92 - 20 * q^93 - 81 * q^94 - 7 * q^96 - 52 * q^97 - 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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