LMFDB - Embedded newform 529.2.c.n.170.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,2,Mod(118,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("529.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	529.c (of order $11$, 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:	$4.22408626693$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	20.0.54296067514572573056640625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 2 x^{18} - 3 x^{17} + 5 x^{16} - 8 x^{15} + 13 x^{14} - 21 x^{13} + 34 x^{12} + \cdots + 1 $ x^20 - x^19 + 2x^18 - 3x^17 + 5x^16 - 8x^15 + 13x^14 - 21x^13 + 34x^12 - 55x^11 + 89x^10 + 55x^9 + 34x^8 + 21x^7 + 13x^6 + 8x^5 + 5x^4 + 3x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			170.1
Root			$0.256741 + 0.562183i$ of defining polynomial
Character	$\chi$	$=$	529.170
Dual form			529.2.c.n.501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.592999 + 0.174120i) q^{2} +(1.46431 + 1.68991i) q^{3} +(-1.36118 + 0.874775i) q^{4} +(0.175911 + 1.22349i) q^{5} +(-1.16258 - 0.747147i) q^{6} +(-1.34431 + 2.94363i) q^{7} +(1.46431 - 1.68991i) q^{8} +(-0.284630 + 1.97964i) q^{9} +(-0.317349 - 0.694897i) q^{10} +(-5.02397 - 1.47517i) q^{11} +(-3.47148 - 1.01932i) q^{12} +(1.24625 + 2.72890i) q^{13} +(0.284630 - 1.97964i) q^{14} +(-1.80999 + 2.08884i) q^{15} +(0.770222 - 1.68655i) q^{16} +(-0.642661 - 0.413013i) q^{17} +(-0.175911 - 1.22349i) q^{18} +(1.68251 - 1.08128i) q^{19} +(-1.30972 - 1.51150i) q^{20} +(-6.94296 + 2.03864i) q^{21} +3.23607 q^{22} +5.00000 q^{24} +(3.33149 - 0.978214i) q^{25} +(-1.21418 - 1.40124i) q^{26} +(1.88110 - 1.20891i) q^{27} +(-0.745170 - 5.18277i) q^{28} +(-2.52376 - 1.62192i) q^{29} +(0.709614 - 1.55384i) q^{30} +(-4.39294 + 5.06972i) q^{31} +(-0.799530 + 5.56085i) q^{32} +(-4.86376 - 10.6502i) q^{33} +(0.453011 + 0.133016i) q^{34} +(-3.83797 - 1.12693i) q^{35} +(-1.34431 - 2.94363i) q^{36} +(-0.175911 + 1.22349i) q^{37} +(-0.809452 + 0.934158i) q^{38} +(-2.78669 + 6.10200i) q^{39} +(2.32517 + 1.49429i) q^{40} +(0.494136 + 3.43679i) q^{41} +(3.76220 - 2.41782i) q^{42} +(8.12895 - 2.38688i) q^{44} -2.47214 q^{45} -2.23607 q^{47} +(3.97796 - 1.16803i) q^{48} +(-2.27377 - 2.62407i) q^{49} +(-1.80524 + 1.16016i) q^{50} +(-0.243103 - 1.69082i) q^{51} +(-4.08353 - 2.62433i) q^{52} +(-0.196132 + 0.429470i) q^{53} +(-0.904995 + 1.04442i) q^{54} +(0.921081 - 6.40626i) q^{55} +(3.00597 + 6.58216i) q^{56} +(4.29098 + 1.25995i) q^{57} +(1.77900 + 0.522361i) q^{58} +(2.68862 + 5.88726i) q^{59} +(0.636451 - 4.42662i) q^{60} +(-4.54753 + 5.24813i) q^{61} +(1.72227 - 3.77124i) q^{62} +(-5.44471 - 3.49910i) q^{63} +(0.0335960 + 0.233665i) q^{64} +(-3.11954 + 2.00481i) q^{65} +(4.73862 + 5.46866i) q^{66} +(-2.65197 + 0.778690i) q^{67} +1.23607 q^{68} +2.47214 q^{70} +(-11.7404 + 3.44730i) q^{71} +(2.92863 + 3.37981i) q^{72} +(5.49159 - 3.52923i) q^{73} +(-0.108719 - 0.756156i) q^{74} +(6.53144 + 4.19750i) q^{75} +(-1.34431 + 2.94363i) q^{76} +(11.0961 - 12.8056i) q^{77} +(0.590023 - 4.10370i) q^{78} +(4.54641 + 9.95526i) q^{79} +(2.19896 + 0.645674i) q^{80} +(10.5544 + 3.09906i) q^{81} +(-0.891438 - 1.95198i) q^{82} +(-1.24724 + 8.67473i) q^{83} +(7.66724 - 8.84847i) q^{84} +(0.392265 - 0.858940i) q^{85} +(-0.954677 - 6.63992i) q^{87} +(-9.84957 + 6.32993i) q^{88} +(-6.85779 - 7.91431i) q^{89} +(1.46597 - 0.430449i) q^{90} -9.70820 q^{91} -15.0000 q^{93} +(1.32599 - 0.389345i) q^{94} +(1.61890 + 1.86832i) q^{95} +(-10.5681 + 6.79170i) q^{96} +(2.52014 + 17.5280i) q^{97} +(1.80524 + 1.16016i) q^{98} +(4.35028 - 9.52579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 4 q^{9} + 6 q^{10} - 6 q^{11} - 5 q^{12} - 6 q^{13} + 4 q^{14} - 10 q^{15} + 3 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 4 q^{20} - 10 q^{21} + 20 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) $ 20 * q + q^2 + q^4 - 2 * q^5 + 5 * q^6 + 2 * q^7 - 4 * q^9 + 6 * q^10 - 6 * q^11 - 5 * q^12 - 6 * q^13 + 4 * q^14 - 10 * q^15 + 3 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 4 * q^20 - 10 * q^21 + 20 * q^22 + 100 * q^24 - 2 * q^25 + 3 * q^26 - 6 * q^28 + 6 * q^29 + 10 * q^30 - 9 * q^32 + 10 * q^33 - 8 * q^34 - 8 * q^35 + 2 * q^36 + 2 * q^37 + 2 * q^38 - 10 * q^40 - 2 * q^41 + 8 * q^44 + 40 * q^45 + 15 * q^48 + 2 * q^49 + 11 * q^50 + 10 * q^51 + 3 * q^52 - 8 * q^53 - 5 * q^54 + 4 * q^55 - 10 * q^56 - 3 * q^58 - 4 * q^59 + 4 * q^61 - 15 * q^62 + 4 * q^63 - 4 * q^64 - 6 * q^65 + 10 * q^66 - 10 * q^67 - 20 * q^68 - 40 * q^70 - 20 * q^71 - 22 * q^73 - 6 * q^74 - 20 * q^75 + 2 * q^76 + 16 * q^77 + 15 * q^78 - 4 * q^79 + 18 * q^80 + 22 * q^81 + 11 * q^82 - 22 * q^83 + 10 * q^84 + 16 * q^85 + 10 * q^88 - 12 * q^89 + 12 * q^90 - 60 * q^91 - 300 * q^93 + 5 * q^94 - 4 * q^95 + 5 * q^96 + 22 * q^97 - 11 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/529\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

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

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

$2$	−0.592999	+	0.174120i	−0.419314	+	0.123122i	−0.484581	−	0.874746i	$-0.661028\pi$
$2$	−0.592999	+	0.174120i	−0.419314	+	0.123122i	0.0652676	+	0.997868i	$0.479210\pi$
$3$	1.46431	+	1.68991i	0.845422	+	0.975669i	0.999924	−	0.0123239i	$-0.00392292\pi$
$3$	1.46431	+	1.68991i	0.845422	+	0.975669i	−0.154502	+	0.987992i	$0.549377\pi$
$4$	−1.36118	+	0.874775i	−0.680588	+	0.437388i
$5$	0.175911	+	1.22349i	0.0786697	+	0.547160i	0.990597	+	0.136809i	$0.0436847\pi$
$5$	0.175911	+	1.22349i	0.0786697	+	0.547160i	−0.911928	+	0.410351i	$0.865406\pi$
$6$	−1.16258	−	0.747147i	−0.474623	−	0.305022i
$7$	−1.34431	+	2.94363i	−0.508102	+	1.11259i	0.465649	+	0.884970i	$0.345821\pi$
$7$	−1.34431	+	2.94363i	−0.508102	+	1.11259i	−0.973750	+	0.227618i	$0.926906\pi$
$8$	1.46431	−	1.68991i	0.517713	−	0.597472i
$9$	−0.284630	+	1.97964i	−0.0948766	+	0.659881i
$10$	−0.317349	−	0.694897i	−0.100355	−	0.219746i
$11$	−5.02397	−	1.47517i	−1.51478	−	0.444781i	−0.584430	−	0.811444i	$-0.698682\pi$
$11$	−5.02397	−	1.47517i	−1.51478	−	0.444781i	−0.930354	+	0.366663i	$0.880500\pi$
$12$	−3.47148	−	1.01932i	−1.00213	−	0.294252i
$13$	1.24625	+	2.72890i	0.345646	+	0.756860i	1.00000		0.000670851i	$0.000213539\pi$
$13$	1.24625	+	2.72890i	0.345646	+	0.756860i	−0.654354	+	0.756189i	$0.727059\pi$
$14$	0.284630	−	1.97964i	0.0760705	−	0.529082i
$15$	−1.80999	+	2.08884i	−0.467338	+	0.539336i
$16$	0.770222	−	1.68655i	0.192555	−	0.421638i
$17$	−0.642661	−	0.413013i	−0.155868	−	0.100170i	0.460382	−	0.887721i	$-0.347713\pi$
$17$	−0.642661	−	0.413013i	−0.155868	−	0.100170i	−0.616250	+	0.787551i	$0.711349\pi$
$18$	−0.175911	−	1.22349i	−0.0414626	−	0.288379i
$19$	1.68251	−	1.08128i	0.385994	−	0.248063i	−0.333224	−	0.942848i	$-0.608137\pi$
$19$	1.68251	−	1.08128i	0.385994	−	0.248063i	0.719218	+	0.694785i	$0.244500\pi$
$20$	−1.30972	−	1.51150i	−0.292863	−	0.337981i
$21$	−6.94296	+	2.03864i	−1.51508	+	0.444867i
$22$	3.23607			0.689932
$23$		0			0
$23$		0			0
$24$	5.00000			1.02062
$25$	3.33149	−	0.978214i	0.666298	−	0.195643i
$26$	−1.21418	−	1.40124i	−0.238120	−	0.274805i
$27$	1.88110	−	1.20891i	0.362018	−	0.232655i
$28$	−0.745170	−	5.18277i	−0.140824	−	0.979452i
$29$	−2.52376	−	1.62192i	−0.468651	−	0.301183i	0.284919	−	0.958552i	$-0.408033\pi$
$29$	−2.52376	−	1.62192i	−0.468651	−	0.301183i	−0.753570	+	0.657368i	$0.771670\pi$
$30$	0.709614	−	1.55384i	0.129557	−	0.283691i
$31$	−4.39294	+	5.06972i	−0.788995	+	0.910549i	−0.997724	−	0.0674245i	$-0.978522\pi$
$31$	−4.39294	+	5.06972i	−0.788995	+	0.910549i	0.208729	+	0.977973i	$0.433067\pi$
$32$	−0.799530	+	5.56085i	−0.141338	+	0.983029i
$33$	−4.86376	−	10.6502i	−0.846673	−	1.85395i
$34$	0.453011	+	0.133016i	0.0776908	+	0.0228121i
$35$	−3.83797	−	1.12693i	−0.648736	−	0.190486i
$36$	−1.34431	−	2.94363i	−0.224052	−	0.490605i
$37$	−0.175911	+	1.22349i	−0.0289196	+	0.201140i	−0.999159	−	0.0410084i	$-0.986943\pi$
$37$	−0.175911	+	1.22349i	−0.0289196	+	0.201140i	0.970239	+	0.242148i	$0.0778521\pi$
$38$	−0.809452	+	0.934158i	−0.131311	+	0.151540i
$39$	−2.78669	+	6.10200i	−0.446227	+	0.977102i
$40$	2.32517	+	1.49429i	0.367641	+	0.236269i
$41$	0.494136	+	3.43679i	0.0771712	+	0.536737i	0.991331	+	0.131384i	$0.0419422\pi$
$41$	0.494136	+	3.43679i	0.0771712	+	0.536737i	−0.914160	+	0.405353i	$0.867149\pi$
$42$	3.76220	−	2.41782i	0.580520	−	0.373078i
$43$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$43$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$44$	8.12895	−	2.38688i	1.22549	−	0.359835i
$45$	−2.47214			−0.368524
$46$		0			0
$47$	−2.23607			−0.326164			−0.163082	−	0.986613i	$-0.552144\pi$
$47$	−2.23607			−0.326164			−0.163082	+	0.986613i	$0.552144\pi$
$48$	3.97796	−	1.16803i	0.574169	−	0.168591i
$49$	−2.27377	−	2.62407i	−0.324824	−	0.374866i
$50$	−1.80524	+	1.16016i	−0.255300	+	0.164071i
$51$	−0.243103	−	1.69082i	−0.0340412	−	0.236762i
$52$	−4.08353	−	2.62433i	−0.566284	−	0.363928i
$53$	−0.196132	+	0.429470i	−0.0269409	+	0.0589922i	−0.922624	−	0.385700i	$-0.873960\pi$
$53$	−0.196132	+	0.429470i	−0.0269409	+	0.0589922i	0.895683	+	0.444693i	$0.146687\pi$
$54$	−0.904995	+	1.04442i	−0.123154	+	0.142128i
$55$	0.921081	−	6.40626i	0.124199	−	0.863820i
$56$	3.00597	+	6.58216i	0.401690	+	0.879578i
$57$	4.29098	+	1.25995i	0.568355	+	0.166884i
$58$	1.77900	+	0.522361i	0.233594	+	0.0685893i
$59$	2.68862	+	5.88726i	0.350029	+	0.766456i	0.999979	+	0.00647940i	$0.00206247\pi$
$59$	2.68862	+	5.88726i	0.350029	+	0.766456i	−0.649950	+	0.759977i	$0.725210\pi$
$60$	0.636451	−	4.42662i	0.0821655	−	0.571474i
$61$	−4.54753	+	5.24813i	−0.582252	+	0.671954i	−0.968087	−	0.250613i	$-0.919368\pi$
$61$	−4.54753	+	5.24813i	−0.582252	+	0.671954i	0.385836	+	0.922568i	$0.373913\pi$
$62$	1.72227	−	3.77124i	0.218728	−	0.478948i
$63$	−5.44471	−	3.49910i	−0.685969	−	0.440845i
$64$	0.0335960	+	0.233665i	0.00419950	+	0.0292081i
$65$	−3.11954	+	2.00481i	−0.386931	+	0.248666i
$66$	4.73862	+	5.46866i	0.583283	+	0.673145i
$67$	−2.65197	+	0.778690i	−0.323990	+	0.0951321i	−0.439683	−	0.898153i	$-0.644909\pi$
$67$	−2.65197	+	0.778690i	−0.323990	+	0.0951321i	0.115693	+	0.993285i	$0.463091\pi$
$68$	1.23607			0.149895
$69$		0			0
$70$	2.47214			0.295477
$71$	−11.7404	+	3.44730i	−1.39333	+	0.409119i	−0.890389	−	0.455201i	$-0.849568\pi$
$71$	−11.7404	+	3.44730i	−1.39333	+	0.409119i	−0.502943	+	0.864320i	$0.667749\pi$
$72$	2.92863	+	3.37981i	0.345142	+	0.398315i
$73$	5.49159	−	3.52923i	0.642742	−	0.413065i	−0.178266	−	0.983982i	$-0.557049\pi$
$73$	5.49159	−	3.52923i	0.642742	−	0.413065i	0.821008	+	0.570917i	$0.193412\pi$
$74$	−0.108719	−	0.756156i	−0.0126383	−	0.0879014i
$75$	6.53144	+	4.19750i	0.754185	+	0.484685i
$76$	−1.34431	+	2.94363i	−0.154203	+	0.337658i
$77$	11.0961	−	12.8056i	1.26452	−	1.45934i
$78$	0.590023	−	4.10370i	0.0668069	−	0.464652i
$79$	4.54641	+	9.95526i	0.511512	+	1.12005i	0.972554	+	0.232676i	$0.0747483\pi$
$79$	4.54641	+	9.95526i	0.511512	+	1.12005i	−0.461043	+	0.887378i	$0.652524\pi$
$80$	2.19896	+	0.645674i	0.245851	+	0.0721885i
$81$	10.5544	+	3.09906i	1.17271	+	0.344340i
$82$	−0.891438	−	1.95198i	−0.0984429	−	0.215560i
$83$	−1.24724	+	8.67473i	−0.136902	+	0.952175i	0.799355	+	0.600859i	$0.205175\pi$
$83$	−1.24724	+	8.67473i	−0.136902	+	0.952175i	−0.936257	+	0.351316i	$0.885734\pi$
$84$	7.66724	−	8.84847i	0.836565	−	0.965447i
$85$	0.392265	−	0.858940i	0.0425471	−	0.0931651i
$86$		0			0
$87$	−0.954677	−	6.63992i	−0.102352	−	0.711875i
$88$	−9.84957	+	6.32993i	−1.04997	+	0.674773i
$89$	−6.85779	−	7.91431i	−0.726924	−	0.838915i	0.265197	−	0.964194i	$-0.414563\pi$
$89$	−6.85779	−	7.91431i	−0.726924	−	0.838915i	−0.992122	+	0.125279i	$0.960017\pi$
$90$	1.46597	−	0.430449i	0.154527	−	0.0453733i
$91$	−9.70820			−1.01770
$92$		0			0
$93$	−15.0000			−1.55543
$94$	1.32599	−	0.389345i	0.136765	−	0.0401579i
$95$	1.61890	+	1.86832i	0.166096	+	0.191685i
$96$	−10.5681	+	6.79170i	−1.07860	+	0.693175i
$97$	2.52014	+	17.5280i	0.255881	+	1.77969i	0.561436	+	0.827520i	$0.310249\pi$
$97$	2.52014	+	17.5280i	0.255881	+	1.77969i	−0.305555	+	0.952175i	$0.598842\pi$
$98$	1.80524	+	1.16016i	0.182357	+	0.117194i
$99$	4.35028	−	9.52579i	0.437220	−	0.957378i
$100$	−3.67903	+	4.24583i	−0.367903	+	0.424583i
$101$	−0.636451	+	4.42662i	−0.0633293	+	0.440465i	0.933345	+	0.358980i	$0.116875\pi$
$101$	−0.636451	+	4.42662i	−0.0633293	+	0.440465i	−0.996675	+	0.0814849i	$0.974034\pi$
$102$	0.438565	+	0.960324i	0.0434244	+	0.0950862i
$103$	−4.01101	−	1.17774i	−0.395216	−	0.116046i	0.0780848	−	0.996947i	$-0.475120\pi$
$103$	−4.01101	−	1.17774i	−0.395216	−	0.116046i	−0.473301	+	0.880901i	$0.656938\pi$
$104$	6.43647	+	1.88992i	0.631148	+	0.185322i
$105$	−3.71558	−	8.13600i	−0.362604	−	0.793992i
$106$	0.0415269	−	0.288826i	0.00403345	−	0.0280533i
$107$	8.78588	−	10.1394i	0.849363	−	0.980217i	−0.150602	−	0.988594i	$-0.548121\pi$
$107$	8.78588	−	10.1394i	0.849363	−	0.980217i	0.999965	+	0.00837738i	$0.00266663\pi$
$108$	−1.50299	+	3.29108i	−0.144625	+	0.316684i
$109$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$109$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$110$	0.569259	+	3.95929i	0.0542767	+	0.377503i
$111$	−2.32517	+	1.49429i	−0.220695	+	0.141832i
$112$	3.92916	+	4.53450i	0.371271	+	0.428470i
$113$	8.40893	−	2.46908i	0.791046	−	0.232272i	0.138841	−	0.990315i	$-0.455662\pi$
$113$	8.40893	−	2.46908i	0.791046	−	0.232272i	0.652205	+	0.758043i	$0.273844\pi$
$114$	−2.76393			−0.258866
$115$		0			0
$116$	4.85410			0.450692
$117$	−5.75696	+	1.69040i	−0.532231	+	0.156277i
$118$	−2.61944	−	3.02300i	−0.241139	−	0.278290i
$119$	2.07969	−	1.33654i	0.190645	−	0.122520i
$120$	0.879554	+	6.11743i	0.0802919	+	0.558443i
$121$	13.8104	+	8.87538i	1.25549	+	0.806853i
$122$	1.78288	−	3.90396i	0.161414	−	0.353447i
$123$	−5.08429	+	5.86759i	−0.458435	+	0.529063i
$124$	1.54470	−	10.7436i	0.138718	−	0.964806i
$125$	4.35028	+	9.52579i	0.389101	+	0.852013i
$126$	3.83797	+	1.12693i	0.341914	+	0.100395i
$127$	6.99643	+	2.05434i	0.620833	+	0.182293i	0.576998	−	0.816746i	$-0.304224\pi$
$127$	6.99643	+	2.05434i	0.620833	+	0.182293i	0.0438350	+	0.999039i	$0.486042\pi$
$128$	−4.72824	−	10.3534i	−0.417921	−	0.915120i
$129$		0			0
$130$	1.50081	−	1.73202i	0.131630	−	0.151909i
$131$	7.77167	−	17.0176i	0.679014	−	1.48683i	−0.184671	−	0.982800i	$-0.559122\pi$
$131$	7.77167	−	17.0176i	0.679014	−	1.48683i	0.863685	−	0.504033i	$-0.168151\pi$
$132$	15.9369	+	10.2420i	1.38713	+	0.891456i
$133$	0.921081	+	6.40626i	0.0798679	+	0.555493i
$134$	1.43703	−	0.923525i	0.124141	−	0.0797804i
$135$	1.80999	+	2.08884i	0.155779	+	0.179779i
$136$	−1.63901	+	0.481257i	−0.140544	+	0.0412674i
$137$	21.8885			1.87006			0.935032	−	0.354563i	$-0.115370\pi$
$137$	21.8885			1.87006			0.935032	+	0.354563i	$0.115370\pi$
$138$		0			0
$139$	−10.7082			−0.908258			−0.454129	−	0.890936i	$-0.650049\pi$
$139$	−10.7082			−0.908258			−0.454129	+	0.890936i	$0.650049\pi$
$140$	6.20997	−	1.82341i	0.524838	−	0.154106i
$141$	−3.27430	−	3.77875i	−0.275746	−	0.318228i
$142$	6.36182	−	4.08849i	0.533872	−	0.343099i
$143$	−2.23551	−	15.5483i	−0.186943	−	1.30022i
$144$	3.11954	+	2.00481i	0.259962	+	0.167067i
$145$	1.54044	−	3.37310i	0.127927	−	0.280121i
$146$	−2.64200	+	3.04903i	−0.218653	+	0.252339i
$147$	1.10492	−	7.68491i	0.0911325	−	0.633840i
$148$	−0.830830	−	1.81926i	−0.0682938	−	0.149543i
$149$	22.9209	+	6.73018i	1.87775	+	0.551358i	0.996965	+	0.0778452i	$0.0248040\pi$
$149$	22.9209	+	6.73018i	1.87775	+	0.551358i	0.880787	+	0.473513i	$0.157014\pi$
$150$	−4.60401	−	1.35186i	−0.375916	−	0.110379i
$151$	1.75973	+	3.85326i	0.143204	+	0.313574i	0.967620	−	0.252411i	$-0.0812234\pi$
$151$	1.75973	+	3.85326i	0.143204	+	0.313574i	−0.824416	+	0.565985i	$0.808496\pi$
$152$	0.636451	−	4.42662i	0.0516230	−	0.359046i
$153$	1.00054	−	1.15468i	0.0808887	−	0.0933506i
$154$	−4.35028	+	9.52579i	−0.350556	+	0.767610i
$155$	−6.97550	−	4.48288i	−0.560286	−	0.360074i
$156$	−1.54470	−	10.7436i	−0.123675	−	0.860178i
$157$	9.60409	−	6.17218i	0.766490	−	0.492593i	−0.0980350	−	0.995183i	$-0.531256\pi$
$157$	9.60409	−	6.17218i	0.766490	−	0.492593i	0.864525	+	0.502590i	$0.167619\pi$
$158$	−4.42943	−	5.11184i	−0.352387	−	0.406676i
$159$	−1.01296	+	0.297433i	−0.0803332	+	0.0235880i
$160$	−6.94427			−0.548993
$161$		0			0
$162$	−6.79837			−0.534131
$163$	5.53045	−	1.62389i	0.433178	−	0.127193i	−0.0578716	−	0.998324i	$-0.518431\pi$
$163$	5.53045	−	1.62389i	0.433178	−	0.127193i	0.491050	+	0.871131i	$0.336613\pi$
$164$	−3.67903	−	4.24583i	−0.287284	−	0.331543i
$165$	12.1747	−	7.82423i	0.947802	−	0.609115i
$166$	−0.770835	−	5.36128i	−0.0598284	−	0.416116i
$167$	1.28532	+	0.826026i	0.0994611	+	0.0639198i	0.589426	−	0.807822i	$-0.299354\pi$
$167$	1.28532	+	0.826026i	0.0994611	+	0.0639198i	−0.489965	+	0.871742i	$0.662990\pi$
$168$	−6.72156	+	14.7182i	−0.518579	+	1.13553i
$169$	2.61944	−	3.02300i	0.201496	−	0.232538i
$170$	−0.0830538	+	0.577652i	−0.00636994	+	0.0443039i
$171$	1.66166	+	3.63853i	0.127070	+	0.278245i
$172$		0			0
$173$	−22.0149	−	6.46415i	−1.67376	−	0.491460i	−0.699076	−	0.715048i	$-0.746405\pi$
$173$	−22.0149	−	6.46415i	−1.67376	−	0.491460i	−0.974684	+	0.223588i	$0.928223\pi$
$174$	1.72227	+	3.77124i	0.130565	+	0.285897i
$175$	−1.59906	+	11.1217i	−0.120878	+	0.840722i
$176$	−6.35752	+	7.33697i	−0.479216	+	0.553045i
$177$	−6.01194	+	13.1643i	−0.451885	+	0.989491i
$178$	5.44471	+	3.49910i	0.408098	+	0.262269i
$179$	−0.100788	−	0.700995i	−0.00753324	−	0.0523949i	0.985708	−	0.168462i	$-0.0538802\pi$
$179$	−0.100788	−	0.700995i	−0.00753324	−	0.0523949i	−0.993241	+	0.116068i	$0.962971\pi$
$180$	3.36501	−	2.16256i	0.250813	−	0.161188i
$181$	10.9051	+	12.5851i	0.810566	+	0.935443i	0.998911	−	0.0466598i	$-0.0148577\pi$
$181$	10.9051	+	12.5851i	0.810566	+	0.935443i	−0.188345	+	0.982103i	$0.560312\pi$
$182$	5.75696	−	1.69040i	0.426734	−	0.125300i
$183$	−15.5279			−1.14785
$184$		0			0
$185$	−1.52786			−0.112331
$186$	8.89499	−	2.61180i	0.652212	−	0.191507i
$187$	2.61944	+	3.02300i	0.191553	+	0.221064i
$188$	3.04368	−	1.95606i	0.221983	−	0.142660i
$189$	1.02980	+	7.16242i	0.0749069	+	0.520989i
$190$	−1.28532	−	0.826026i	−0.0932470	−	0.0599262i
$191$	10.8757	−	23.8145i	0.786938	−	1.72315i	0.101725	−	0.994813i	$-0.467564\pi$
$191$	10.8757	−	23.8145i	0.786938	−	1.72315i	0.685213	−	0.728342i	$-0.259709\pi$
$192$	−0.345677	+	0.398933i	−0.0249471	+	0.0287905i
$193$	−1.41522	+	9.84305i	−0.101870	+	0.708518i	0.873320	+	0.487147i	$0.161962\pi$
$193$	−1.41522	+	9.84305i	−0.101870	+	0.708518i	−0.975190	+	0.221371i	$0.928947\pi$
$194$	−4.54641	−	9.95526i	−0.326414	−	0.714746i
$195$	−7.95592	−	2.33607i	−0.569735	−	0.167289i
$196$	5.39046	+	1.58278i	0.385033	+	0.113056i
$197$	−0.611547	−	1.33910i	−0.0435709	−	0.0954071i	0.886595	−	0.462547i	$-0.153064\pi$
$197$	−0.611547	−	1.33910i	−0.0435709	−	0.0954071i	−0.930166	+	0.367140i	$0.880337\pi$
$198$	−0.921081	+	6.40626i	−0.0654584	+	0.455273i
$199$	−8.04941	+	9.28952i	−0.570608	+	0.658517i	−0.965559	−	0.260186i	$-0.916216\pi$
$199$	−8.04941	+	9.28952i	−0.570608	+	0.658517i	0.394951	+	0.918702i	$0.370762\pi$
$200$	3.22525	−	7.06232i	0.228060	−	0.499382i
$201$	−5.19923	−	3.34134i	−0.366726	−	0.235680i
$202$	−0.393349	−	2.73580i	−0.0276759	−	0.192490i
$203$	8.16706	−	5.24865i	0.573215	−	0.368383i
$204$	1.80999	+	2.08884i	0.126725	+	0.146248i
$205$	−4.11795	+	1.20914i	−0.287610	+	0.0844499i
$206$	2.58359			0.180007
$207$		0			0
$208$	5.56231			0.385677
$209$	−10.0479	+	2.95034i	−0.695031	+	0.204079i
$210$	3.61998	+	4.17768i	0.249802	+	0.288287i
$211$	−19.6991	+	12.6599i	−1.35614	+	0.871541i	−0.998067	−	0.0621507i	$-0.980204\pi$
$211$	−19.6991	+	12.6599i	−1.35614	+	0.871541i	−0.358078	+	0.933692i	$0.616568\pi$
$212$	−0.108719	−	0.756156i	−0.00746684	−	0.0519330i
$213$	−23.0173	−	14.7923i	−1.57712	−	1.01355i
$214$	−3.44454	+	7.54248i	−0.235464	+	0.515594i
$215$		0			0
$216$	0.711574	−	4.94911i	0.0484165	−	0.336744i
$217$	−9.01791	−	19.7465i	−0.612176	−	1.34048i
$218$		0			0
$219$	14.0055	+	4.11238i	0.946402	+	0.277889i
$220$	4.35028	+	9.52579i	0.293296	+	0.642229i
$221$	0.326157	−	2.26847i	0.0219397	−	0.152594i
$222$	1.11864	−	1.29097i	0.0750779	−	0.0866445i
$223$	1.66166	−	3.63853i	0.111273	−	0.243654i	−0.845800	−	0.533499i	$-0.820877\pi$
$223$	1.66166	−	3.63853i	0.111273	−	0.243654i	0.957073	+	0.289846i	$0.0936039\pi$
$224$	−15.2943	−	9.82903i	−1.02189	−	0.656730i
$225$	0.988273	+	6.87359i	0.0658849	+	0.458239i
$226$	−4.55657	+	2.92833i	−0.303099	+	0.194790i
$227$	−7.97643	−	9.20529i	−0.529414	−	0.610976i	0.426549	−	0.904465i	$-0.359729\pi$
$227$	−7.97643	−	9.20529i	−0.529414	−	0.610976i	−0.955963	+	0.293488i	$0.905184\pi$
$228$	−6.94296	+	2.03864i	−0.459809	+	0.135012i
$229$	12.0000			0.792982			0.396491	−	0.918039i	$-0.370228\pi$
$229$	12.0000			0.792982			0.396491	+	0.918039i	$0.370228\pi$
$230$		0			0
$231$	37.8885			2.49288
$232$	−6.43647	+	1.88992i	−0.422575	+	0.124079i
$233$	4.27484	+	4.93343i	0.280054	+	0.323200i	0.878297	−	0.478115i	$-0.158680\pi$
$233$	4.27484	+	4.93343i	0.280054	+	0.323200i	−0.598243	+	0.801315i	$0.704134\pi$
$234$	3.11954	−	2.00481i	0.203931	−	0.131058i
$235$	−0.393349	−	2.73580i	−0.0256592	−	0.178464i
$236$	−8.80972	−	5.66166i	−0.573464	−	0.368543i
$237$	−10.1661	+	22.2606i	−0.660359	+	1.44598i
$238$	−1.00054	+	1.15468i	−0.0648553	+	0.0748470i
$239$	−1.95881	+	13.6238i	−0.126705	+	0.881253i	0.822985	+	0.568062i	$0.192307\pi$
$239$	−1.95881	+	13.6238i	−0.126705	+	0.881253i	−0.949690	+	0.313190i	$0.898602\pi$
$240$	2.12884	+	4.66151i	0.137416	+	0.300899i
$241$	−22.1879	−	6.51496i	−1.42925	−	0.419665i	−0.526626	−	0.850097i	$-0.676543\pi$
$241$	−22.1879	−	6.51496i	−1.42925	−	0.419665i	−0.902623	+	0.430432i	$0.858361\pi$
$242$	−9.73492	−	2.85843i	−0.625784	−	0.183747i
$243$	7.43117	+	16.2720i	0.476710	+	1.04385i
$244$	1.59906	−	11.1217i	0.102369	−	0.711994i
$245$	2.81053	−	3.24352i	0.179558	−	0.207221i
$246$	1.99332	−	4.36475i	0.127089	−	0.278287i
$247$	5.04752	+	3.24384i	0.321166	+	0.206401i
$248$	2.13472	+	14.8473i	0.135555	+	0.942806i
$249$	−16.4858	+	10.5948i	−1.04475	+	0.671418i
$250$	−4.23835	−	4.89131i	−0.268057	−	0.309354i
$251$	2.19896	−	0.645674i	0.138797	−	0.0407546i	−0.211596	−	0.977357i	$-0.567866\pi$
$251$	2.19896	−	0.645674i	0.138797	−	0.0407546i	0.350393	+	0.936603i	$0.386048\pi$
$252$	10.4721			0.659683
$253$		0			0
$254$	−4.50658			−0.282768
$255$	2.02593	−	0.594866i	0.126868	−	0.0372520i
$256$	4.29740	+	4.95946i	0.268587	+	0.309966i
$257$	−6.28596	+	4.03974i	−0.392107	+	0.251992i	−0.721808	−	0.692093i	$-0.756689\pi$
$257$	−6.28596	+	4.03974i	−0.392107	+	0.251992i	0.329700	+	0.944086i	$0.393052\pi$
$258$		0			0
$259$	−3.36501	−	2.16256i	−0.209092	−	0.134375i
$260$	2.49249	−	5.45779i	0.154578	−	0.338478i
$261$	3.92916	−	4.53450i	0.243209	−	0.280678i
$262$	−1.64549	+	11.4446i	−0.101659	+	0.707051i
$263$	−1.22309	−	2.67820i	−0.0754193	−	0.165145i	0.868167	−	0.496272i	$-0.165298\pi$
$263$	−1.22309	−	2.67820i	−0.0754193	−	0.165145i	−0.943586	+	0.331127i	$0.892571\pi$
$264$	−25.1199	−	7.37585i	−1.54602	−	0.453952i
$265$	−0.559953	−	0.164417i	−0.0343976	−	0.0101001i
$266$	−1.66166	−	3.63853i	−0.101883	−	0.223092i
$267$	3.33250	−	23.1781i	0.203946	−	1.41847i
$268$	2.92863	−	3.37981i	0.178894	−	0.206455i
$269$	−3.30017	+	7.22636i	−0.201215	+	0.440599i	−0.983160	−	0.182749i	$-0.941501\pi$
$269$	−3.30017	+	7.22636i	−0.201215	+	0.440599i	0.781945	+	0.623348i	$0.214228\pi$
$270$	−1.43703	−	0.923525i	−0.0874550	−	0.0562039i
$271$	−1.13852	−	7.91857i	−0.0691601	−	0.481019i	−0.994737	−	0.102460i	$-0.967329\pi$
$271$	−1.13852	−	7.91857i	−0.0691601	−	0.481019i	0.925577	−	0.378559i	$-0.123580\pi$
$272$	−1.19156	+	0.765768i	−0.0722488	+	0.0464315i
$273$	−14.2159	−	16.4060i	−0.860382	−	0.992934i
$274$	−12.9799	+	3.81124i	−0.784144	+	0.230245i
$275$	−18.1803			−1.09632
$276$		0			0
$277$	15.4721			0.929631			0.464815	−	0.885408i	$-0.346121\pi$
$277$	15.4721			0.929631			0.464815	+	0.885408i	$0.346121\pi$
$278$	6.34996	−	1.86452i	0.380845	−	0.111826i
$279$	−8.78588	−	10.1394i	−0.525997	−	0.607033i
$280$	−7.52440	+	4.83564i	−0.449669	+	0.288985i
$281$	−1.24724	−	8.67473i	−0.0744040	−	0.517491i	−0.992606	−	0.121379i	$-0.961268\pi$
$281$	−1.24724	−	8.67473i	−0.0744040	−	0.517491i	0.918202	−	0.396112i	$-0.129641\pi$
$282$	2.59962	+	1.67067i	0.154805	+	0.0994871i
$283$	−11.5104	+	25.2043i	−0.684222	+	1.49824i	0.173884	+	0.984766i	$0.444368\pi$
$283$	−11.5104	+	25.2043i	−0.684222	+	1.49824i	−0.858106	+	0.513472i	$0.828359\pi$
$284$	12.9652	−	14.9626i	0.769342	−	0.887868i
$285$	−0.786697	+	5.47160i	−0.0465999	+	0.324110i
$286$	4.03293	+	8.83089i	0.238472	+	0.522182i
$287$	−10.7809	−	3.16557i	−0.636378	−	0.186857i
$288$	−10.7809	−	3.16557i	−0.635272	−	0.186533i
$289$	−6.81962	−	14.9329i	−0.401154	−	0.878405i
$290$	−0.326157	+	2.26847i	−0.0191526	+	0.133209i
$291$	−25.9304	+	29.9252i	−1.52006	+	1.75425i
$292$	−4.38774	+	9.60781i	−0.256773	+	0.562255i
$293$	1.28532	+	0.826026i	0.0750893	+	0.0482569i	0.577647	−	0.816287i	$-0.303971\pi$
$293$	1.28532	+	0.826026i	0.0750893	+	0.0482569i	−0.502558	+	0.864544i	$0.667607\pi$
$294$	0.682880	+	4.74953i	0.0398264	+	0.276998i
$295$	−6.73003	+	4.32513i	−0.391837	+	0.251819i
$296$	1.80999	+	2.08884i	0.105204	+	0.121411i
$297$	−11.2339	+	3.29858i	−0.651859	+	0.191403i
$298$	−14.7639			−0.855252
$299$		0			0
$300$	−12.5623			−0.725285
$301$		0			0
$302$	−1.71445	−	1.97858i	−0.0986554	−	0.113854i
$303$	−8.41254	+	5.40641i	−0.483288	+	0.310590i
$304$	−0.527732	−	3.67046i	−0.0302675	−	0.210515i
$305$	−7.22098	−	4.64064i	−0.413472	−	0.265722i
$306$	−0.392265	+	0.858940i	−0.0224243	+	0.0491023i
$307$	−6.23942	+	7.20068i	−0.356103	+	0.410964i	−0.905330	−	0.424708i	$-0.860377\pi$
$307$	−6.23942	+	7.20068i	−0.356103	+	0.410964i	0.549227	+	0.835673i	$0.314922\pi$
$308$	−3.90176	+	27.1373i	−0.222324	+	1.54629i
$309$	−3.88310	−	8.50281i	−0.220902	−	0.483708i
$310$	4.91703	+	1.44377i	0.279268	+	0.0820006i
$311$	−12.6464	−	3.71333i	−0.717114	−	0.210564i	−0.0972354	−	0.995261i	$-0.531000\pi$
$311$	−12.6464	−	3.71333i	−0.717114	−	0.210564i	−0.619879	+	0.784698i	$0.712818\pi$
$312$	6.23123	+	13.6445i	0.352774	+	0.772467i
$313$	3.46689	−	24.1127i	0.195960	−	1.36293i	−0.619899	−	0.784681i	$-0.712827\pi$
$313$	3.46689	−	24.1127i	0.195960	−	1.36293i	0.815859	−	0.578250i	$-0.196264\pi$
$314$	−4.62052	+	5.33236i	−0.260751	+	0.300923i
$315$	3.32332	−	7.27706i	0.187248	−	0.410016i
$316$	−14.8971	−	9.57378i	−0.838027	−	0.538567i
$317$	−3.61713	−	25.1577i	−0.203158	−	1.41300i	−0.794837	−	0.606823i	$-0.792444\pi$
$317$	−3.61713	−	25.1577i	−0.203158	−	1.41300i	0.591678	−	0.806174i	$-0.298466\pi$
$318$	0.548898	−	0.352755i	0.0307806	−	0.0197815i
$319$	10.2867	+	11.8715i	0.575944	+	0.664675i
$320$	−0.279976	+	0.0822085i	−0.0156511	+	0.00459559i
$321$	30.0000			1.67444
$322$		0			0
$323$	−1.52786			−0.0850126
$324$	−17.0774	+	5.01438i	−0.948745	+	0.278577i
$325$	6.82130	+	7.87220i	0.378377	+	0.436671i
$326$	−2.99680	+	1.92593i	−0.165978	+	0.106667i
$327$		0			0
$328$	6.53144	+	4.19750i	0.360638	+	0.231768i
$329$	3.00597	−	6.58216i	0.165725	−	0.362886i
$330$	−5.85725	+	6.75963i	−0.322431	+	0.372105i
$331$	2.79684	−	19.4524i	0.153728	−	1.06920i	−0.756171	−	0.654374i	$-0.772932\pi$
$331$	2.79684	−	19.4524i	0.153728	−	1.06920i	0.909899	−	0.414829i	$-0.136159\pi$
$332$	−5.89073	−	12.8989i	−0.323296	−	0.707919i
$333$	−2.37200	−	0.696481i	−0.129985	−	0.0381669i
$334$	−0.906022	−	0.266032i	−0.0495753	−	0.0145566i
$335$	−1.41923	−	3.10767i	−0.0775407	−	0.169790i
$336$	−1.90935	+	13.2798i	−0.104164	+	0.724475i
$337$	15.3345	−	17.6969i	0.835323	−	0.964014i	−0.164427	−	0.986389i	$-0.552577\pi$
$337$	15.3345	−	17.6969i	0.835323	−	0.964014i	0.999750	+	0.0223755i	$0.00712294\pi$
$338$	−1.02696	+	2.24873i	−0.0558594	+	0.122315i
$339$	16.4858	+	10.5948i	0.895388	+	0.575431i
$340$	0.217438	+	1.51231i	0.0117922	+	0.0820167i
$341$	29.5487	−	18.9898i	1.60015	−	1.02836i
$342$	−1.61890	−	1.86832i	−0.0875403	−	0.101027i
$343$	−10.9540	+	3.21637i	−0.591458	+	0.173668i
$344$		0			0
$345$		0			0
$346$	14.1803			0.762340
$347$	9.48799	−	2.78592i	0.509342	−	0.149556i	−0.0169565	−	0.999856i	$-0.505398\pi$
$347$	9.48799	−	2.78592i	0.509342	−	0.149556i	0.526298	+	0.850300i	$0.323579\pi$
$348$	7.10793	+	8.20298i	0.381025	+	0.439726i
$349$	20.5404	−	13.2005i	1.09950	−	0.706607i	0.140521	−	0.990078i	$-0.455122\pi$
$349$	20.5404	−	13.2005i	1.09950	−	0.706607i	0.958981	+	0.283471i	$0.0914859\pi$
$350$	−0.988273	−	6.87359i	−0.0528254	−	0.367409i
$351$	5.64330	+	3.62673i	0.301217	+	0.193580i
$352$	12.2200	−	26.7581i	0.651329	−	1.42621i
$353$	−6.12994	+	7.07433i	−0.326264	+	0.376529i	−0.895057	−	0.445952i	$-0.852865\pi$
$353$	−6.12994	+	7.07433i	−0.326264	+	0.376529i	0.568793	+	0.822481i	$0.307411\pi$
$354$	1.27290	−	8.85323i	0.0676540	−	0.470544i
$355$	−6.28299	−	13.7578i	−0.333467	−	0.730190i
$356$	16.2579	+	4.77375i	0.861667	+	0.253008i
$357$	5.30395	+	1.55738i	0.280715	+	0.0824253i
$358$	0.181825	+	0.398141i	0.00960973	+	0.0210424i
$359$	−2.83043	+	19.6861i	−0.149385	+	1.03899i	0.767845	+	0.640635i	$0.221329\pi$
$359$	−2.83043	+	19.6861i	−0.149385	+	1.03899i	−0.917230	+	0.398358i	$0.869580\pi$
$360$	−3.61998	+	4.17768i	−0.190790	+	0.220183i
$361$	−6.23123	+	13.6445i	−0.327959	+	0.718131i
$362$	−8.65801	−	5.56417i	−0.455055	−	0.292446i
$363$	5.22412	+	36.3346i	0.274195	+	1.90707i
$364$	13.2146	−	8.49250i	0.692632	−	0.445128i
$365$	5.28400	+	6.09806i	0.276577	+	0.319187i
$366$	9.20801	−	2.70372i	0.481310	−	0.141326i
$367$	4.18034			0.218212			0.109106	−	0.994030i	$-0.465201\pi$
$367$	4.18034			0.218212			0.109106	+	0.994030i	$0.465201\pi$
$368$		0			0
$369$	−6.94427			−0.361504
$370$	0.906022	−	0.266032i	0.0471019	−	0.0138304i
$371$	−1.00054	−	1.15468i	−0.0519454	−	0.0599481i
$372$	20.4177	−	13.1216i	1.05861	−	0.680325i
$373$	1.09699	+	7.62975i	0.0568001	+	0.395053i	0.998312	+	0.0580743i	$0.0184960\pi$
$373$	1.09699	+	7.62975i	0.0568001	+	0.395053i	−0.941512	+	0.336979i	$0.890595\pi$
$374$	−2.07969	−	1.33654i	−0.107538	−	0.0691107i
$375$	−9.72753	+	21.3003i	−0.502327	+	1.09994i
$376$	−3.27430	+	3.77875i	−0.168859	+	0.194874i
$377$	1.28083	−	8.90839i	0.0659663	−	0.458806i
$378$	−1.85779	−	4.06800i	−0.0955545	−	0.209235i
$379$	23.3739	+	6.86320i	1.20064	+	0.352539i	0.820096	−	0.572226i	$-0.193920\pi$
$379$	23.3739	+	6.86320i	1.20064	+	0.352539i	0.380540	+	0.924764i	$0.375738\pi$
$380$	−3.83797	−	1.12693i	−0.196884	−	0.0578103i
$381$	6.77332	+	14.8315i	0.347008	+	0.759841i
$382$	−2.30270	+	16.0156i	−0.117817	+	0.819432i
$383$	4.62052	−	5.33236i	0.236098	−	0.272471i	−0.625320	−	0.780368i	$-0.715032\pi$
$383$	4.62052	−	5.33236i	0.236098	−	0.272471i	0.861418	+	0.507897i	$0.169577\pi$
$384$	10.5727	−	23.1509i	0.539534	−	1.18141i
$385$	17.6194	+	11.3233i	0.897970	+	0.577090i
$386$	−0.874652	−	6.08334i	−0.0445186	−	0.309634i
$387$		0			0
$388$	−18.7634	−	21.6541i	−0.952566	−	1.09932i
$389$	24.4938	−	7.19203i	1.24189	−	0.364650i	0.406162	−	0.913801i	$-0.366867\pi$
$389$	24.4938	−	7.19203i	1.24189	−	0.364650i	0.835723	+	0.549151i	$0.185049\pi$
$390$	5.12461			0.259495
$391$		0			0
$392$	−7.76393			−0.392138
$393$	40.1383	−	11.7857i	2.02471	−	0.594508i
$394$	0.595812	+	0.687604i	0.0300166	+	0.0346410i
$395$	−11.3804	+	7.31372i	−0.572608	+	0.367993i
$396$	2.41142	+	16.7718i	0.121178	+	0.842815i
$397$	−20.5404	−	13.2005i	−1.03089	−	0.662514i	−0.0881745	−	0.996105i	$-0.528103\pi$
$397$	−20.5404	−	13.2005i	−1.03089	−	0.662514i	−0.942718	+	0.333591i	$0.891740\pi$
$398$	3.15580	−	6.91024i	0.158186	−	0.346379i
$399$	−9.47723	+	10.9373i	−0.474455	+	0.547550i
$400$	0.916179	−	6.37217i	0.0458090	−	0.318608i
$401$	5.89073	+	12.8989i	0.294169	+	0.644140i	0.997791	−	0.0664346i	$-0.0211624\pi$
$401$	5.89073	+	12.8989i	0.294169	+	0.644140i	−0.703622	+	0.710575i	$0.748435\pi$
$402$	3.66494	+	1.07612i	0.182790	+	0.0536721i
$403$	−19.3094	−	5.66976i	−0.961871	−	0.282431i
$404$	−3.00597	−	6.58216i	−0.149553	−	0.327475i
$405$	−1.93502	+	13.4584i	−0.0961519	+	0.668751i
$406$	−3.92916	+	4.53450i	−0.195001	+	0.225043i
$407$	2.68862	−	5.88726i	0.133270	−	0.291821i
$408$	−3.21330	−	2.06506i	−0.159082	−	0.102236i
$409$	−3.03994	−	21.1433i	−0.150315	−	1.04547i	−0.915691	−	0.401883i	$-0.868356\pi$
$409$	−3.03994	−	21.1433i	−0.150315	−	1.04547i	0.765376	−	0.643584i	$-0.222553\pi$
$410$	2.23140	−	1.43404i	0.110201	−	0.0708220i
$411$	32.0517	+	36.9896i	1.58099	+	1.82456i
$412$	6.48995	−	1.90562i	0.319737	−	0.0938832i
$413$	−20.9443			−1.03060
$414$		0			0
$415$	−10.8328			−0.531762
$416$	−16.1714	+	4.74835i	−0.792868	+	0.232807i
$417$	−15.6802	−	18.0959i	−0.767861	−	0.886159i
$418$	5.44471	−	3.49910i	0.266309	−	0.171147i
$419$	−0.652313	−	4.53694i	−0.0318676	−	0.221644i	0.967664	−	0.252242i	$-0.0811679\pi$
$419$	−0.652313	−	4.53694i	−0.0318676	−	0.221644i	−0.999532	+	0.0305981i	$0.990259\pi$
$420$	12.1747	+	7.82423i	0.594066	+	0.381783i
$421$	4.27537	−	9.36175i	0.208369	−	0.456264i	−0.776376	−	0.630270i	$-0.782944\pi$
$421$	4.27537	−	9.36175i	0.208369	−	0.456264i	0.984744	+	0.174007i	$0.0556714\pi$
$422$	9.47723	−	10.9373i	0.461345	−	0.532420i
$423$	0.636451	−	4.42662i	0.0309453	−	0.215229i
$424$	0.438565	+	0.960324i	0.0212986	+	0.0466375i
$425$	−2.54503	−	0.747289i	−0.123452	−	0.0362488i
$426$	16.2249	+	4.76405i	0.786097	+	0.230819i
$427$	−9.33526	−	20.4414i	−0.451765	−	0.989227i
$428$	−3.08940	+	21.4872i	−0.149332	+	1.03863i
$429$	23.0017	−	26.5454i	1.11053	−	1.28162i
$430$		0			0
$431$	14.7454	+	9.47628i	0.710260	+	0.456456i	0.845236	−	0.534392i	$-0.179460\pi$
$431$	14.7454	+	9.47628i	0.710260	+	0.456456i	−0.134977	+	0.990849i	$0.543096\pi$
$432$	−0.590023	−	4.10370i	−0.0283875	−	0.197439i
$433$	−14.9909	+	9.63404i	−0.720414	+	0.462982i	−0.848781	−	0.528745i	$-0.822663\pi$
$433$	−14.9909	+	9.63404i	−0.720414	+	0.462982i	0.128367	+	0.991727i	$0.459027\pi$
$434$	8.78588	+	10.1394i	0.421736	+	0.486709i
$435$	7.95592	−	2.33607i	0.381457	−	0.112006i
$436$		0			0
$437$		0			0
$438$	−9.02129			−0.431054
$439$	17.9504	−	5.27071i	0.856725	−	0.251557i	0.176266	−	0.984343i	$-0.443598\pi$
$439$	17.9504	−	5.27071i	0.856725	−	0.251557i	0.680460	+	0.732785i	$0.261780\pi$
$440$	−9.47723	−	10.9373i	−0.451809	−	0.521416i
$441$	5.84189	−	3.75436i	0.278185	−	0.178779i
$442$	0.201576	+	1.40199i	0.00958799	+	0.0666859i
$443$	32.0725	+	20.6117i	1.52381	+	0.979292i	0.991118	+	0.132982i	$0.0424553\pi$
$443$	32.0725	+	20.6117i	1.52381	+	0.979292i	0.532690	+	0.846310i	$0.321181\pi$
$444$	1.85779	−	4.06800i	0.0881669	−	0.193059i
$445$	8.47670	−	9.78263i	0.401834	−	0.463741i
$446$	−0.351822	+	2.44697i	−0.0166592	+	0.115868i
$447$	22.1900	+	48.5893i	1.04955	+	2.29819i
$448$	−0.732987	−	0.215225i	−0.0346304	−	0.0101684i
$449$	14.3389	+	4.21029i	0.676696	+	0.198696i	0.601982	−	0.798509i	$-0.294378\pi$
$449$	14.3389	+	4.21029i	0.676696	+	0.198696i	0.0747132	+	0.997205i	$0.476196\pi$
$450$	−1.78288	−	3.90396i	−0.0840456	−	0.184034i
$451$	2.58733	−	17.9953i	0.121833	−	0.847365i
$452$	−9.28615	+	10.7168i	−0.436784	+	0.504075i
$453$	−3.93487	+	8.61616i	−0.184876	+	0.404822i
$454$	6.33284	+	4.06987i	0.297215	+	0.191008i
$455$	−1.70778	−	11.8779i	−0.0800619	−	0.556843i
$456$	8.41254	−	5.40641i	0.393953	−	0.253178i
$457$	−3.35591	−	3.87292i	−0.156983	−	0.181168i	0.671810	−	0.740724i	$-0.265517\pi$
$457$	−3.35591	−	3.87292i	−0.156983	−	0.181168i	−0.828793	+	0.559556i	$0.810972\pi$
$458$	−7.11599	+	2.08944i	−0.332508	+	0.0976333i
$459$	−1.70820			−0.0797321
$460$		0			0
$461$	−1.47214			−0.0685642			−0.0342821	−	0.999412i	$-0.510914\pi$
$461$	−1.47214			−0.0685642			−0.0342821	+	0.999412i	$0.510914\pi$
$462$	−22.4679	+	6.59716i	−1.04530	+	0.306928i
$463$	13.0972	+	15.1150i	0.608679	+	0.702453i	0.973516	−	0.228618i	$-0.0734207\pi$
$463$	13.0972	+	15.1150i	0.608679	+	0.702453i	−0.364837	+	0.931071i	$0.618875\pi$
$464$	−4.67931	+	3.00721i	−0.217231	+	0.139606i
$465$	−2.63866	−	18.3523i	−0.122365	−	0.851067i
$466$	−3.39399	−	2.18118i	−0.157223	−	0.101041i
$467$	5.42355	−	11.8759i	0.250972	−	0.549551i	−0.741652	−	0.670784i	$-0.765958\pi$
$467$	5.42355	−	11.8759i	0.250972	−	0.549551i	0.992624	+	0.121233i	$0.0386848\pi$
$468$	6.35752	−	7.33697i	0.293877	−	0.339152i
$469$	1.27290	−	8.85323i	0.0587772	−	0.408804i
$470$	0.709614	+	1.55384i	0.0327320	+	0.0716732i
$471$	24.4938	+	7.19203i	1.12862	+	0.331391i
$472$	13.8859	+	4.07727i	0.639151	+	0.187672i
$473$		0			0
$474$	2.15246	−	14.9707i	0.0988656	−	0.687625i
$475$	4.54753	−	5.24813i	0.208655	−	0.240801i
$476$	−1.66166	+	3.63853i	−0.0761621	+	0.166772i
$477$	−0.794372	−	0.510512i	−0.0363718	−	0.0233747i
$478$	−1.21061	−	8.41999i	−0.0553721	−	0.385122i
$479$	−26.5809	+	17.0825i	−1.21451	+	0.780519i	−0.981408	−	0.191933i	$-0.938524\pi$
$479$	−26.5809	+	17.0825i	−1.21451	+	0.780519i	−0.233103	+	0.972452i	$0.574888\pi$
$480$	−10.1686	−	11.7352i	−0.464130	−	0.535635i
$481$	−3.55800	+	1.04472i	−0.162231	+	0.0476352i
$482$	14.2918			0.650973
$483$		0			0
$484$	−26.5623			−1.20738
$485$	−21.0019	+	6.16672i	−0.953647	+	0.280016i
$486$	−7.23996	−	8.35536i	−0.328411	−	0.379007i
$487$	−12.3733	+	7.95186i	−0.560689	+	0.360333i	−0.790082	−	0.613001i	$-0.789962\pi$
$487$	−12.3733	+	7.95186i	−0.560689	+	0.360333i	0.229393	+	0.973334i	$0.426326\pi$
$488$	2.20985	+	15.3698i	0.100035	+	0.695759i
$489$	10.8425	+	6.96807i	0.490316	+	0.315107i
$490$	−1.10188	+	2.41278i	−0.0497778	+	0.108998i
$491$	−5.46647	+	6.30864i	−0.246698	+	0.284705i	−0.865571	−	0.500786i	$-0.833044\pi$
$491$	−5.46647	+	6.30864i	−0.246698	+	0.284705i	0.618873	+	0.785491i	$0.287590\pi$
$492$	1.78780	−	12.4344i	0.0806004	−	0.560588i
$493$	0.952046	+	2.08469i	0.0428780	+	0.0938898i
$494$	−3.55800	−	1.04472i	−0.160082	−	0.0470043i
$495$	12.4199	+	3.64682i	0.558235	+	0.163912i
$496$	5.16680	+	11.3137i	0.231996	+	0.508001i
$497$	5.63520	−	39.1937i	0.252773	−	1.75808i
$498$	7.93132	−	9.15323i	0.355411	−	0.410166i
$499$	8.01410	−	17.5484i	0.358760	−	0.785576i	−0.641076	−	0.767478i	$-0.721512\pi$
$499$	8.01410	−	17.5484i	0.358760	−	0.785576i	0.999836	−	0.0180982i	$-0.00576116\pi$
$500$	−14.2544	−	9.16077i	−0.637477	−	0.409682i
$501$	0.486206	+	3.38163i	0.0217221	+	0.151080i
$502$	−1.19156	+	0.765768i	−0.0531818	+	0.0341779i
$503$	−17.6447	−	20.3631i	−0.786740	−	0.907947i	0.210836	−	0.977521i	$-0.432381\pi$
$503$	−17.6447	−	20.3631i	−0.786740	−	0.907947i	−0.997577	+	0.0695746i	$0.977836\pi$
$504$	−13.8859	+	4.07727i	−0.618528	+	0.181616i
$505$	−5.52786			−0.245987
$506$		0			0
$507$	8.94427			0.397229
$508$	−11.3205	+	3.32399i	−0.502264	+	0.147478i
$509$	18.5358	+	21.3915i	0.821585	+	0.948160i	0.999355	−	0.0359125i	$-0.0114338\pi$
$509$	18.5358	+	21.3915i	0.821585	+	0.948160i	−0.177770	+	0.984072i	$0.556888\pi$
$510$	−1.09780	+	0.705510i	−0.0486112	+	0.0312405i
$511$	3.00635	+	20.9096i	0.132993	+	0.924986i
$512$	15.7383	+	10.1144i	0.695543	+	0.446998i
$513$	1.85779	−	4.06800i	0.0820235	−	0.179606i
$514$	3.02417	−	3.49008i	0.133390	−	0.153941i
$515$	0.735367	−	5.11459i	0.0324041	−	0.225376i
$516$		0			0
$517$	11.2339	+	3.29858i	0.494068	+	0.145071i
$518$	2.37200	+	0.696481i	0.104220	+	0.0306016i
$519$	−21.3128	−	46.6686i	−0.935530	−	2.04853i
$520$	−1.18005	+	8.20740i	−0.0517484	+	0.359918i
$521$	20.5734	−	23.7429i	0.901336	−	1.04020i	−0.0976523	−	0.995221i	$-0.531133\pi$
$521$	20.5734	−	23.7429i	0.901336	−	1.04020i	0.998988	−	0.0449764i	$-0.0143212\pi$
$522$	−1.54044	+	3.37310i	−0.0674234	+	0.147637i
$523$	−34.5962	−	22.2336i	−1.51279	−	0.972209i	−0.993026	−	0.117898i	$-0.962384\pi$
$523$	−34.5962	−	22.2336i	−1.51279	−	0.972209i	−0.519762	−	0.854311i	$-0.673979\pi$
$524$	4.30794	+	29.9624i	0.188193	+	1.30891i
$525$	−21.1362	+	13.5834i	−0.922458	+	0.592828i
$526$	1.19162	+	1.37521i	0.0519573	+	0.0599619i
$527$	4.91703	−	1.44377i	0.214189	−	0.0628916i
$528$	−21.7082			−0.944728
$529$		0			0
$530$	0.360680			0.0156669
$531$	−12.4199	+	3.64682i	−0.538979	+	0.158259i
$532$	−6.85779	−	7.91431i	−0.297323	−	0.343129i
$533$	−8.76284	+	5.63154i	−0.379561	+	0.243929i
$534$	2.05960	+	14.3248i	0.0891276	+	0.619896i
$535$	13.9510	+	8.96577i	0.603155	+	0.387624i
$536$	−2.56741	+	5.62183i	−0.110895	+	0.242826i
$537$	1.03703	−	1.19680i	0.0447512	−	0.0516457i
$538$	0.698742	−	4.85986i	0.0301249	−	0.209523i
$539$	7.55239	+	16.5374i	0.325304	+	0.712317i
$540$	−4.29098	−	1.25995i	−0.184655	−	0.0542195i
$541$	33.0223	+	9.69622i	1.41974	+	0.416873i	0.899415	−	0.437095i	$-0.143993\pi$
$541$	33.0223	+	9.69622i	1.41974	+	0.416873i	0.520325	+	0.853969i	$0.325811\pi$
$542$	2.05392	+	4.49747i	0.0882236	+	0.193183i
$543$	−5.29924	+	36.8571i	−0.227412	+	1.58169i
$544$	2.81053	−	3.24352i	0.120500	−	0.139065i
$545$		0			0
$546$	11.2866	+	7.25346i	0.483022	+	0.310419i
$547$	4.20413	+	29.2403i	0.179755	+	1.25023i	0.857328	+	0.514771i	$0.172123\pi$
$547$	4.20413	+	29.2403i	0.179755	+	1.25023i	−0.677573	+	0.735456i	$0.736968\pi$
$548$	−29.7942	+	19.1476i	−1.27274	+	0.817943i
$549$	−9.09506	−	10.4963i	−0.388168	−	0.447970i
$550$	10.7809	−	3.16557i	0.459700	−	0.134980i
$551$	−6.00000			−0.255609
$552$		0			0
$553$	−35.4164			−1.50606
$554$	−9.17497	+	2.69401i	−0.389807	+	0.114458i
$555$	−2.23727	−	2.58195i	−0.0949669	−	0.109598i
$556$	14.5758	−	9.36727i	0.618150	−	0.397261i
$557$	−1.05546	−	7.34092i	−0.0447215	−	0.311045i	−0.999888	−	0.0149752i	$-0.995233\pi$
$557$	−1.05546	−	7.34092i	−0.0447215	−	0.311045i	0.955166	−	0.296070i	$-0.0956760\pi$
$558$	6.97550	+	4.48288i	0.295297	+	0.189776i
$559$		0			0
$560$	−4.85671	+	5.60495i	−0.205234	+	0.236852i
$561$	−1.27290	+	8.85323i	−0.0537420	+	0.373784i
$562$	2.25006	+	4.92694i	0.0949129	+	0.207830i
$563$	−31.6098	−	9.28147i	−1.33219	−	0.391167i	−0.463316	−	0.886193i	$-0.653340\pi$
$563$	−31.6098	−	9.28147i	−1.33219	−	0.391167i	−0.868878	+	0.495026i	$0.835159\pi$
$564$	7.76246	+	2.27926i	0.326859	+	0.0959743i
$565$	4.50011	+	9.85388i	0.189321	+	0.414556i
$566$	2.43709	−	16.9503i	0.102438	−	0.712475i
$567$	−23.3109	+	26.9022i	−0.978966	+	1.12979i
$568$	−11.3660	+	24.8881i	−0.476908	+	1.04428i
$569$	18.6593	+	11.9916i	0.782238	+	0.502714i	0.869776	−	0.493447i	$-0.164263\pi$
$569$	18.6593	+	11.9916i	0.782238	+	0.502714i	−0.0875376	+	0.996161i	$0.527900\pi$
$570$	−0.486206	−	3.38163i	−0.0203649	−	0.141641i
$571$	12.0230	−	7.72673i	0.503148	−	0.323354i	−0.264326	−	0.964433i	$-0.585150\pi$
$571$	12.0230	−	7.72673i	0.503148	−	0.323354i	0.767474	+	0.641080i	$0.221513\pi$
$572$	16.6442	+	19.2084i	0.695929	+	0.803145i
$573$	56.1697	−	16.4929i	2.34652	−	0.689001i
$574$	6.94427			0.289848
$575$		0			0
$576$	−0.472136			−0.0196723
$577$	−21.9614	+	6.44845i	−0.914265	+	0.268452i	−0.704835	−	0.709371i	$-0.748979\pi$
$577$	−21.9614	+	6.44845i	−0.914265	+	0.268452i	−0.209430	+	0.977824i	$0.567161\pi$
$578$	6.64415	+	7.66776i	0.276360	+	0.318937i
$579$	−18.7062	+	12.0217i	−0.777402	+	0.499606i
$580$	0.853889	+	5.93893i	0.0354558	+	0.246601i
$581$	−23.8585	−	15.3329i	−0.989818	−	0.636118i
$582$	10.1661	−	22.2606i	0.421398	−	0.922733i
$583$	1.61890	−	1.86832i	0.0670482	−	0.0773777i
$584$	2.07733	−	14.4482i	0.0859607	−	0.597870i
$585$	−3.08089	−	6.74620i	−0.127379	−	0.278921i
$586$	−0.906022	−	0.266032i	−0.0374274	−	0.0109897i
$587$	23.7073	+	6.96111i	0.978507	+	0.287316i	0.731608	−	0.681726i	$-0.238770\pi$
$587$	23.7073	+	6.96111i	0.978507	+	0.287316i	0.246899	+	0.969041i	$0.420588\pi$
$588$	5.21857	+	11.4271i	0.215210	+	0.471245i
$589$	−1.90935	+	13.2798i	−0.0786736	+	0.547187i
$590$	3.23781	−	3.73663i	0.133299	−	0.153835i
$591$	1.36746	−	2.99432i	0.0562499	−	0.123170i
$592$	1.92798	+	1.23904i	0.0792396	+	0.0509242i
$593$	0.419014	+	2.91430i	0.0172068	+	0.119676i	0.996614	−	0.0822165i	$-0.0261999\pi$
$593$	0.419014	+	2.91430i	0.0172068	+	0.119676i	−0.979408	+	0.201893i	$0.935291\pi$
$594$	6.08737	−	3.91211i	0.249768	−	0.160516i
$595$	2.00108	+	2.30937i	0.0820361	+	0.0946747i
$596$	−37.0868	+	10.8897i	−1.51913	+	0.446058i
$597$	−27.4853			−1.12490
$598$		0			0
$599$	33.8885			1.38465			0.692324	−	0.721587i	$-0.256587\pi$
$599$	33.8885			1.38465			0.692324	+	0.721587i	$0.256587\pi$
$600$	16.6575	−	4.89107i	0.680038	−	0.199677i
$601$	−30.7055	−	35.4360i	−1.25250	−	1.44546i	−0.847193	−	0.531285i	$-0.821710\pi$
$601$	−30.7055	−	35.4360i	−1.25250	−	1.44546i	−0.405309	−	0.914180i	$-0.632836\pi$
$602$		0			0
$603$	−0.786697	−	5.47160i	−0.0320368	−	0.222821i
$604$	−5.76604	−	3.70561i	−0.234617	−	0.150779i
$605$	−8.42952	+	18.4581i	−0.342709	+	0.750427i
$606$	4.04726	−	4.67079i	0.164409	−	0.189738i
$607$	−3.76738	+	26.2027i	−0.152913	+	1.06353i	0.758391	+	0.651800i	$0.225986\pi$
$607$	−3.76738	+	26.2027i	−0.152913	+	1.06353i	−0.911304	+	0.411734i	$0.864923\pi$
$608$	4.66763	+	10.2207i	0.189297	+	0.414504i
$609$	20.8289	+	6.11591i	0.844028	+	0.247829i
$610$	5.09006	+	1.49458i	0.206091	+	0.0605137i
$611$	−2.78669	−	6.10200i	−0.112737	−	0.246860i
$612$	−0.351822	+	2.44697i	−0.0142215	+	0.0989130i
$613$	3.73808	−	4.31397i	0.150980	−	0.174240i	−0.675222	−	0.737615i	$-0.735952\pi$
$613$	3.73808	−	4.31397i	0.150980	−	0.174240i	0.826201	+	0.563375i	$0.190497\pi$
$614$	2.44619	−	5.35641i	0.0987202	−	0.216167i
$615$	−8.07330	−	5.18839i	−0.325547	−	0.209216i
$616$	−5.39210	−	37.5029i	−0.217254	−	1.51103i
$617$	6.33284	−	4.06987i	0.254951	−	0.163847i	−0.406923	−	0.913463i	$-0.633398\pi$
$617$	6.33284	−	4.06987i	0.254951	−	0.163847i	0.661873	+	0.749616i	$0.269762\pi$
$618$	3.78319	+	4.36603i	0.152182	+	0.175628i
$619$	18.6299	−	5.47023i	0.748799	−	0.219867i	0.115001	−	0.993365i	$-0.463313\pi$
$619$	18.6299	−	5.47023i	0.748799	−	0.219867i	0.633799	+	0.773498i	$0.281495\pi$
$620$	13.4164			0.538816
$621$		0			0
$622$	8.14590			0.326621
$623$	32.5158	−	9.54751i	1.30272	−	0.382513i
$624$	8.14496	+	9.39978i	0.326059	+	0.376292i
$625$	3.71532	−	2.38769i	0.148613	−	0.0955076i
$626$	2.14265	+	14.9025i	0.0856377	+	0.595623i
$627$	−19.6991	−	12.6599i	−0.786708	−	0.505586i
$628$	−7.67360	+	16.8028i	−0.306210	+	0.670507i
$629$	0.618367	−	0.713633i	0.0246559	−	0.0284544i
$630$	−0.703643	+	4.89395i	−0.0280338	+	0.194979i
$631$	−5.13481	−	11.2437i	−0.204414	−	0.447603i	0.779464	−	0.626447i	$-0.215492\pi$
$631$	−5.13481	−	11.2437i	−0.204414	−	0.447603i	−0.983877	+	0.178844i	$0.942764\pi$
$632$	23.4808	+	6.89460i	0.934018	+	0.274252i
$633$	−50.2397	−	14.7517i	−1.99685	−	0.586328i
$634$	6.52542	+	14.2887i	0.259158	+	0.567476i
$635$	−1.28271	+	8.92141i	−0.0509026	+	0.354036i
$636$	1.11864	−	1.29097i	0.0443568	−	0.0511905i
$637$	4.32713	−	9.47510i	0.171447	−	0.375417i
$638$	−8.16706	−	5.24865i	−0.323337	−	0.207796i
$639$	−3.48275	−	24.2230i	−0.137775	−	0.958249i
$640$	11.8355	−	7.60621i	0.467839	−	0.300662i
$641$	−11.3323	−	13.0782i	−0.447600	−	0.516558i	0.486446	−	0.873711i	$-0.338293\pi$
$641$	−11.3323	−	13.0782i	−0.447600	−	0.516558i	−0.934046	+	0.357153i	$0.883748\pi$
$642$	−17.7900	+	5.22361i	−0.702114	+	0.206159i
$643$	29.5967			1.16718			0.583591	−	0.812048i	$-0.301647\pi$
$643$	29.5967			1.16718			0.583591	+	0.812048i	$0.301647\pi$
$644$		0			0
$645$		0			0
$646$	0.906022	−	0.266032i	0.0356470	−	0.0104669i
$647$	−4.39294	−	5.06972i	−0.172704	−	0.199311i	0.662798	−	0.748798i	$-0.269369\pi$
$647$	−4.39294	−	5.06972i	−0.172704	−	0.199311i	−0.835502	+	0.549487i	$0.814823\pi$
$648$	20.6921	−	13.2980i	0.812862	−	0.522395i
$649$	−4.82284	−	33.5436i	−0.189313	−	1.31670i
$650$	−5.41573	−	3.48048i	−0.212423	−	0.136516i
$651$	20.1647	−	44.1545i	0.790316	−	1.73055i
$652$	−6.10739	+	7.04830i	−0.239184	+	0.276033i
$653$	5.45136	−	37.9151i	0.213328	−	1.48373i	−0.548608	−	0.836079i	$-0.684842\pi$
$653$	5.45136	−	37.9151i	0.213328	−	1.48373i	0.761937	−	0.647652i	$-0.224249\pi$
$654$		0			0
$655$	22.1879	+	6.51496i	0.866953	+	0.254560i
$656$	6.17692	+	1.81371i	0.241168	+	0.0708134i
$657$	5.42355	+	11.8759i	0.211593	+	0.463323i
$658$	−0.636451	+	4.42662i	−0.0248115	+	0.172567i
$659$	−6.97589	+	8.05060i	−0.271742	+	0.313607i	−0.875175	−	0.483807i	$-0.839254\pi$
$659$	−6.97589	+	8.05060i	−0.271742	+	0.313607i	0.603433	+	0.797414i	$0.293799\pi$
$660$	−9.72753	+	21.3003i	−0.378643	+	0.829114i
$661$	19.3019	+	12.4046i	0.750759	+	0.482483i	0.859213	−	0.511618i	$-0.170954\pi$
$661$	19.3019	+	12.4046i	0.750759	+	0.482483i	−0.108454	+	0.994101i	$0.534590\pi$
$662$	1.72854	+	12.0223i	0.0671817	+	0.467259i
$663$	4.31110	−	2.77057i	0.167429	−	0.107600i
$664$	12.8331	+	14.8102i	0.498022	+	0.574749i
$665$	−7.67594	+	2.25386i	−0.297660	+	0.0874010i
$666$	1.52786			0.0592035
$667$		0			0
$668$	−2.47214			−0.0956498
$669$	8.58197	−	2.51989i	0.331798	−	0.0974247i
$670$	1.38271	+	1.59573i	0.0534187	+	0.0616485i
$671$	30.5886	−	19.6581i	1.18086	−	0.758891i
$672$	−5.78545	−	40.2387i	−0.223179	−	1.55224i
$673$	2.52376	+	1.62192i	0.0972838	+	0.0625205i	0.588378	−	0.808586i	$-0.299767\pi$
$673$	2.52376	+	1.62192i	0.0972838	+	0.0625205i	−0.491094	+	0.871106i	$0.663403\pi$
$674$	−6.01194	+	13.1643i	−0.231571	+	0.507071i
$675$	5.08429	−	5.86759i	0.195695	−	0.225844i
$676$	−0.921081	+	6.40626i	−0.0354262	+	0.246395i
$677$	−7.47747	−	16.3734i	−0.287383	−	0.629280i	0.709791	−	0.704412i	$-0.248789\pi$
$677$	−7.47747	−	16.3734i	−0.287383	−	0.629280i	−0.997174	+	0.0751323i	$0.976062\pi$
$678$	−11.6209	−	3.41219i	−0.446296	−	0.131044i
$679$	−54.9837	−	16.1447i	−2.11008	−	0.619576i
$680$	−0.877131	−	1.92065i	−0.0336364	−	0.0736535i
$681$	3.87610	−	26.9588i	0.148532	−	1.03307i
$682$	−14.2159	+	16.4060i	−0.544353	+	0.628217i
$683$	11.0487	−	24.1933i	0.422766	−	0.925729i	−0.571679	−	0.820477i	$-0.693708\pi$
$683$	11.0487	−	24.1933i	0.422766	−	0.925729i	0.994446	−	0.105252i	$-0.0335649\pi$
$684$	−5.44471	−	3.49910i	−0.208184	−	0.133791i
$685$	3.85043	+	26.7803i	0.147117	+	1.02322i
$686$	5.93566	−	3.81461i	0.226624	−	0.145643i
$687$	17.5718	+	20.2789i	0.670404	+	0.773688i
$688$		0			0
$689$	−1.41641			−0.0539608
$690$		0			0
$691$	7.05573			0.268413			0.134206	−	0.990953i	$-0.457152\pi$
$691$	7.05573			0.268413			0.134206	+	0.990953i	$0.457152\pi$
$692$	35.6208	−	10.4592i	1.35410	−	0.397600i
$693$	22.1923	+	25.6113i	0.843015	+	0.972891i
$694$	−5.14128	+	3.30410i	−0.195160	+	0.125422i
$695$	−1.88369	−	13.1013i	−0.0714524	−	0.496962i
$696$	−12.6188	−	8.10961i	−0.478314	−	0.307394i
$697$	1.10188	−	2.41278i	0.0417366	−	0.0913904i
$698$	−9.88196	+	11.4044i	−0.374038	+	0.431663i
$699$	−2.07733	+	14.4482i	−0.0785720	+	0.546480i
$700$	−7.55239	−	16.5374i	−0.285453	−	0.625056i
$701$	−3.66494	−	1.07612i	−0.138423	−	0.0406446i	0.211787	−	0.977316i	$-0.432072\pi$
$701$	−3.66494	−	1.07612i	−0.138423	−	0.0406446i	−0.350210	+	0.936671i	$0.613890\pi$
$702$	−3.97796	−	1.16803i	−0.150138	−	0.0440846i
$703$	1.02696	+	2.24873i	0.0387326	+	0.0848126i
$704$	0.175911	−	1.22349i	0.00662989	−	0.0461119i
$705$	4.04726	−	4.67079i	0.152429	−	0.175912i
$706$	2.40327	−	5.26242i	0.0904481	−	0.198054i
$707$	−12.1747	−	7.82423i	−0.457878	−	0.294260i
$708$	−3.33250	−	23.1781i	−0.125243	−	0.871085i
$709$	35.3906	−	22.7442i	1.32912	−	0.854175i	0.333066	−	0.942904i	$-0.391917\pi$
$709$	35.3906	−	22.7442i	1.32912	−	0.854175i	0.996056	+	0.0887288i	$0.0282805\pi$
$710$	6.12133	+	7.06439i	0.229729	+	0.265122i
$711$	−21.0019	+	6.16672i	−0.787633	+	0.231270i
$712$	−23.4164			−0.877567
$713$		0			0
$714$	−3.41641			−0.127856
$715$	18.6299	−	5.47023i	0.696719	−	0.204575i
$716$	0.750404	+	0.866012i	0.0280439	+	0.0323644i
$717$	−25.8913	+	16.6393i	−0.966930	+	0.621408i
$718$	−1.74930	−	12.1667i	−0.0652835	−	0.454057i
$719$	−2.57064	−	1.65205i	−0.0958688	−	0.0616111i	0.491828	−	0.870692i	$-0.336329\pi$
$719$	−2.57064	−	1.65205i	−0.0958688	−	0.0616111i	−0.587697	+	0.809081i	$0.699965\pi$
$720$	−1.90409	+	4.16938i	−0.0709614	+	0.155384i
$721$	8.85887	−	10.2237i	0.329921	−	0.380750i
$722$	1.31933	−	9.17615i	0.0491004	−	0.341501i
$723$	−21.4804	−	47.0354i	−0.798863	−	1.74927i
$724$	−25.8528	−	7.59108i	−0.960813	−	0.282120i
$725$	−9.99447	−	2.93464i	−0.371185	−	0.108990i
$726$	−9.42449	−	20.6367i	−0.349775	−	0.765901i
$727$	−3.94329	+	27.4262i	−0.146248	+	1.01718i	0.776041	+	0.630682i	$0.217225\pi$
$727$	−3.94329	+	27.4262i	−0.146248	+	1.01718i	−0.922290	+	0.386499i	$0.873684\pi$
$728$	−14.2159	+	16.4060i	−0.526874	+	0.608046i
$729$	−2.90791	+	6.36742i	−0.107700	+	0.235831i
$730$	−4.19520	−	2.69609i	−0.155271	−	0.0997868i
$731$		0			0
$732$	21.1362	−	13.5834i	0.781215	−	0.502057i
$733$	−20.4553	−	23.6066i	−0.755533	−	0.871931i	0.239560	−	0.970882i	$-0.422997\pi$
$733$	−20.4553	−	23.6066i	−0.755533	−	0.871931i	−0.995092	+	0.0989503i	$0.968452\pi$
$734$	−2.47894	+	0.727882i	−0.0914993	+	0.0268666i
$735$	9.59675			0.353981
$736$		0			0
$737$	14.4721			0.533088
$738$	4.11795	−	1.20914i	0.151584	−	0.0445090i
$739$	−17.5631	−	20.2689i	−0.646071	−	0.745605i	0.334365	−	0.942444i	$-0.391478\pi$
$739$	−17.5631	−	20.2689i	−0.646071	−	0.745605i	−0.980436	+	0.196838i	$0.936933\pi$
$740$	2.07969	−	1.33654i	0.0764510	−	0.0491321i
$741$	1.90935	+	13.2798i	0.0701419	+	0.487847i
$742$	0.794372	+	0.510512i	0.0291623	+	0.0187415i
$743$	−17.0838	+	37.4083i	−0.626743	+	1.37238i	0.283769	+	0.958893i	$0.408415\pi$
$743$	−17.0838	+	37.4083i	−0.626743	+	1.37238i	−0.910512	+	0.413483i	$0.864312\pi$
$744$	−21.9647	+	25.3486i	−0.805265	+	0.929325i
$745$	−4.20225	+	29.2273i	−0.153959	+	1.07081i
$746$	−1.97901	−	4.33342i	−0.0724567	−	0.158658i
$747$	−16.8179	−	4.93817i	−0.615333	−	0.180678i
$748$	−6.20997	−	1.82341i	−0.227059	−	0.0666705i
$749$	18.0358	+	39.4930i	0.659015	+	1.44304i
$750$	2.05960	−	14.3248i	0.0752059	−	0.523069i
$751$	0.236195	−	0.272584i	0.00861888	−	0.00994672i	−0.751424	−	0.659820i	$-0.770633\pi$
$751$	0.236195	−	0.272584i	0.00861888	−	0.00994672i	0.760043	+	0.649873i	$0.225178\pi$
$752$	−1.72227	+	3.77124i	−0.0628047	+	0.137523i
$753$	4.31110	+	2.77057i	0.157105	+	0.100965i
$754$	0.791599	+	5.50569i	0.0288283	+	0.200505i
$755$	−4.40486	+	2.83083i	−0.160309	+	0.103025i
$756$	−7.66724	−	8.84847i	−0.278855	−	0.321816i
$757$	1.53207	−	0.449856i	0.0556840	−	0.0163503i	−0.253772	−	0.967264i	$-0.581671\pi$
$757$	1.53207	−	0.449856i	0.0556840	−	0.0163503i	0.309456	+	0.950914i	$0.399853\pi$
$758$	−15.0557			−0.546849
$759$		0			0
$760$	5.52786			0.200517
$761$	−44.4293	+	13.0456i	−1.61056	+	0.472903i	−0.958459	−	0.285229i	$-0.907930\pi$
$761$	−44.4293	+	13.0456i	−1.61056	+	0.472903i	−0.652101	+	0.758132i	$0.726112\pi$
$762$	−6.59904	−	7.61570i	−0.239058	−	0.275888i
$763$		0			0
$764$	6.02855	+	41.9295i	0.218105	+	1.51696i
$765$	1.58874	+	1.02102i	0.0574412	+	0.0369152i
$766$	−1.81149	+	3.96661i	−0.0654519	+	0.143320i
$767$	−12.7150	+	14.6739i	−0.459114	+	0.529845i
$768$	−2.08829	+	14.5244i	−0.0753548	+	0.524104i
$769$	9.60631	+	21.0349i	0.346412	+	0.758537i	0.999999	+	0.00168529i	$0.000536444\pi$
$769$	9.60631	+	21.0349i	0.346412	+	0.758537i	−0.653586	+	0.756852i	$0.726736\pi$
$770$	−12.4199	−	3.64682i	−0.447583	−	0.131422i
$771$	−16.0314	−	4.70725i	−0.577357	−	0.169527i
$772$	−6.68410	−	14.6361i	−0.240566	−	0.526766i
$773$	−0.786697	+	5.47160i	−0.0282955	+	0.196800i	−0.999066	−	0.0432100i	$-0.986242\pi$
$773$	−0.786697	+	5.47160i	−0.0282955	+	0.196800i	0.970770	+	0.240010i	$0.0771506\pi$
$774$		0			0
$775$	−9.67576	+	21.1870i	−0.347564	+	0.761058i
$776$	33.3109	+	21.4076i	1.19579	+	0.768489i
$777$	−1.27290	−	8.85323i	−0.0456651	−	0.317608i
$778$	−13.2725	+	8.52974i	−0.475843	+	0.305806i
$779$	4.54753	+	5.24813i	0.162932	+	0.188034i
$780$	12.8729	−	3.77984i	0.460926	−	0.135340i
$781$	64.0689			2.29256
$782$		0			0
$783$	−6.70820			−0.239732
$784$	−6.17692	+	1.81371i	−0.220604	+	0.0647753i
$785$	9.24104	+	10.6647i	0.329827	+	0.380640i
$786$	−21.7499	+	13.9778i	−0.775792	+	0.498571i
$787$	3.49861	+	24.3334i	0.124712	+	0.867391i	0.952106	+	0.305769i	$0.0989134\pi$
$787$	3.49861	+	24.3334i	0.124712	+	0.867391i	−0.827394	+	0.561622i	$0.810177\pi$
$788$	2.00384	+	1.28779i	0.0713837	+	0.0458755i
$789$	2.73492	−	5.98865i	0.0973658	−	0.213201i
$790$	5.47508	−	6.31858i	0.194795	−	0.224805i
$791$	−4.03615	+	28.0720i	−0.143509	+	0.998126i
$792$	−9.72753	−	21.3003i	−0.345653	−	0.756874i
$793$	−19.9889	−	5.86928i	−0.709828	−	0.208424i
$794$	14.4789	+	4.25139i	0.513837	+	0.150876i
$795$	−0.542097	−	1.18703i	−0.0192262	−	0.0420995i
$796$	2.83043	−	19.6861i	0.100322	−	0.697756i
$797$	−22.5015	+	25.9681i	−0.797043	+	0.919836i	−0.998215	−	0.0597196i	$-0.980979\pi$
$797$	−22.5015	+	25.9681i	−0.797043	+	0.919836i	0.201173	+	0.979556i	$0.435525\pi$
$798$	3.71558	−	8.13600i	0.131530	−	0.288011i
$799$	1.43703	+	0.923525i	0.0508386	+	0.0326720i
$800$	2.77608	+	19.3080i	0.0981491	+	0.682642i
$801$	17.6194	−	11.3233i	0.622552	−	0.400090i
$802$	−5.73915	−	6.62334i	−0.202657	−	0.233878i
$803$	−32.7958	+	9.62971i	−1.15734	+	0.339825i
$804$	10.0000			0.352673
$805$		0			0
$806$	12.4377			0.438099
$807$	−17.0444	+	5.00468i	−0.599990	+	0.176173i
$808$	6.54861	+	7.55750i	0.230379	+	0.265872i
$809$	10.1888	−	6.54795i	0.358219	−	0.230214i	−0.349135	−	0.937072i	$-0.613525\pi$
$809$	10.1888	−	6.54795i	0.358219	−	0.230214i	0.707355	+	0.706859i	$0.249888\pi$
$810$	−1.19591	−	8.31772i	−0.0420199	−	0.292255i
$811$	−20.4824	−	13.1633i	−0.719236	−	0.462225i	0.129135	−	0.991627i	$-0.458780\pi$
$811$	−20.4824	−	13.1633i	−0.719236	−	0.462225i	−0.848371	+	0.529402i	$0.822416\pi$
$812$	−6.52542	+	14.2887i	−0.228997	+	0.501435i
$813$	11.7145	−	13.5193i	0.410846	−	0.474141i
$814$	−0.569259	+	3.95929i	−0.0199525	+	0.138773i
$815$	2.95967	+	6.48077i	0.103673	+	0.227012i
$816$	−3.03889	−	0.892299i	−0.106382	−	0.0312367i
$817$		0			0
$818$	5.48415	+	12.0086i	0.191749	+	0.419872i
$819$	2.76324	−	19.2188i	0.0965555	−	0.671558i
$820$	4.54753	−	5.24813i	0.158807	−	0.183273i
$821$	−16.1780	+	35.4250i	−0.564617	+	1.23634i	0.384997	+	0.922918i	$0.374203\pi$
$821$	−16.1780	+	35.4250i	−0.564617	+	1.23634i	−0.949614	+	0.313422i	$0.898525\pi$
$822$	−25.4473	−	16.3540i	−0.887575	−	0.570410i
$823$	5.62727	+	39.1385i	0.196154	+	1.36428i	0.815314	+	0.579019i	$0.196564\pi$
$823$	5.62727	+	39.1385i	0.196154	+	1.36428i	−0.619160	+	0.785265i	$0.712527\pi$
$824$	−7.86364	+	5.05365i	−0.273943	+	0.176052i
$825$	−26.6217	−	30.7231i	−0.926849	−	1.06964i
$826$	12.4199	−	3.64682i	0.432145	−	0.126889i
$827$	−1.52786			−0.0531290			−0.0265645	−	0.999647i	$-0.508457\pi$
$827$	−1.52786			−0.0531290			−0.0265645	+	0.999647i	$0.508457\pi$
$828$		0			0
$829$	40.2492			1.39791			0.698957	−	0.715164i	$-0.253648\pi$
$829$	40.2492			1.39791			0.698957	+	0.715164i	$0.253648\pi$
$830$	6.42385	−	1.88621i	0.222975	−	0.0654714i
$831$	22.6561	+	26.1465i	0.785930	+	0.907011i
$832$	−0.595779	+	0.382884i	−0.0206549	+	0.0132741i
$833$	0.377487	+	2.62548i	0.0130791	+	0.0909674i
$834$	12.4492	+	8.00060i	0.431080	+	0.277038i
$835$	−0.784529	+	1.71788i	−0.0271498	+	0.0594497i
$836$	11.0961	−	12.8056i	0.383768	−	0.442892i
$837$	−2.13472	+	14.8473i	−0.0737868	+	0.513199i
$838$	1.17679	+	2.57682i	0.0406517	+	0.0890148i
$839$	−39.4588	−	11.5861i	−1.36227	−	0.399998i	−0.482706	−	0.875782i	$-0.660346\pi$
$839$	−39.4588	−	11.5861i	−1.36227	−	0.399998i	−0.879562	+	0.475784i	$0.842164\pi$
$840$	−19.1899	−	5.63465i	−0.662113	−	0.194414i
$841$	−8.30830	−	18.1926i	−0.286493	−	0.627332i
$842$	−0.905219	+	6.29594i	−0.0311959	+	0.216972i
$843$	12.8331	−	14.8102i	0.441997	−	0.510092i
$844$	15.7395	−	34.4646i	0.541775	−	1.18632i
$845$	4.15939	+	2.67308i	0.143087	+	0.0919566i
$846$	0.393349	+	2.73580i	0.0135236	+	0.0940587i
$847$	−44.6913	+	28.7213i	−1.53561	+	0.986877i
$848$	0.573257	+	0.661574i	0.0196857	+	0.0227186i
$849$	−59.4477	+	17.4554i	−2.04024	+	0.599069i
$850$	1.63932			0.0562282
$851$		0			0
$852$	44.2705			1.51668
$853$	10.1549	−	2.98174i	0.347697	−	0.102093i	−0.103221	−	0.994658i	$-0.532915\pi$
$853$	10.1549	−	2.98174i	0.347697	−	0.102093i	0.450918	+	0.892566i	$0.351097\pi$
$854$	9.09506	+	10.4963i	0.311227	+	0.359175i
$855$	−4.15939	+	2.67308i	−0.142248	+	0.0914172i
$856$	−4.26945	−	29.6946i	−0.145927	−	1.01494i
$857$	1.23844	+	0.795897i	0.0423043	+	0.0271873i	0.561622	−	0.827394i	$-0.310178\pi$
$857$	1.23844	+	0.795897i	0.0423043	+	0.0271873i	−0.519318	+	0.854581i	$0.673814\pi$
$858$	−9.01791	+	19.7465i	−0.307867	+	0.674134i
$859$	10.9415	−	12.6272i	0.373321	−	0.430835i	−0.537738	−	0.843112i	$-0.680721\pi$
$859$	10.9415	−	12.6272i	0.373321	−	0.430835i	0.911059	+	0.412277i	$0.135266\pi$
$860$		0			0
$861$	−10.4371	−	22.8542i	−0.355697	−	0.778867i
$862$	−10.3940	−	3.05196i	−0.354021	−	0.103950i
$863$	20.6685	+	6.06881i	0.703562	+	0.206585i	0.613896	−	0.789387i	$-0.289602\pi$
$863$	20.6685	+	6.06881i	0.703562	+	0.206585i	0.0896669	+	0.995972i	$0.471420\pi$
$864$	5.21857	+	11.4271i	0.177539	+	0.388757i
$865$	4.03615	−	28.0720i	0.137233	−	0.954477i
$866$	7.21208	−	8.32319i	0.245077	−	0.282833i
$867$	15.2491	−	33.3910i	0.517888	−	1.13402i
$868$	29.5487	+	18.9898i	1.00295	+	0.644556i
$869$	−8.15534	−	56.7217i	−0.276651	−	1.92415i
$870$	−4.31110	+	2.77057i	−0.146160	+	0.0939313i
$871$	−5.42997	−	6.26652i	−0.183988	−	0.212333i
$872$		0			0
$873$	−35.4164			−1.19866
$874$		0			0
$875$	−33.8885			−1.14564
$876$	−22.6613	+	6.65397i	−0.765656	+	0.224817i
$877$	23.8842	+	27.5638i	0.806511	+	0.930763i	0.998719	−	0.0505907i	$-0.0161104\pi$
$877$	23.8842	+	27.5638i	0.806511	+	0.930763i	−0.192208	+	0.981354i	$0.561565\pi$
$878$	−9.72683	+	6.25105i	−0.328265	+	0.210963i
$879$	0.486206	+	3.38163i	0.0163993	+	0.114060i
$880$	−10.0950	−	6.48769i	−0.340304	−	0.218700i
$881$	−18.3532	+	40.1879i	−0.618334	+	1.35396i	0.298391	+	0.954444i	$0.403550\pi$
$881$	−18.3532	+	40.1879i	−0.618334	+	1.35396i	−0.916725	+	0.399519i	$0.869177\pi$
$882$	−2.81053	+	3.24352i	−0.0946354	+	0.109215i
$883$	−0.569259	+	3.95929i	−0.0191571	+	0.133241i	−0.997155	−	0.0753718i	$-0.975986\pi$
$883$	−0.569259	+	3.95929i	−0.0191571	+	0.133241i	0.977998	+	0.208612i	$0.0668947\pi$
$884$	1.54044	+	3.37310i	0.0518107	+	0.113450i
$885$	−17.1639	−	5.03979i	−0.576959	−	0.169411i
$886$	−22.6079	−	6.63827i	−0.759526	−	0.223017i
$887$	9.58316	+	20.9842i	0.321771	+	0.704580i	0.999528	−	0.0307053i	$-0.00977532\pi$
$887$	9.58316	+	20.9842i	0.321771	+	0.704580i	−0.677757	+	0.735286i	$0.737048\pi$
$888$	−0.879554	+	6.11743i	−0.0295159	+	0.205288i
$889$	−15.4526	+	17.8332i	−0.518263	+	0.598107i
$890$	−3.32332	+	7.27706i	−0.111398	+	0.243927i
$891$	−48.4535	−	31.1392i	−1.62325	−	1.04320i
$892$	0.921081	+	6.40626i	0.0308401	+	0.214497i
$893$	−3.76220	+	2.41782i	−0.125897	+	0.0809092i
$894$	−21.6190	−	24.9497i	−0.723048	−	0.834442i
$895$	0.839929	−	0.246625i	0.0280757	−	0.00824378i
$896$	36.8328			1.23050
$897$		0			0
$898$	−9.23607			−0.308212
$899$	19.3094	−	5.66976i	0.644005	−	0.189097i
$900$	−7.35806	−	8.49165i	−0.245269	−	0.283055i
$901$	0.303423	−	0.194998i	0.0101085	−	0.00649633i
$902$	1.59906	+	11.1217i	0.0532428	+	0.370312i
$903$		0			0
$904$	8.14078	−	17.8258i	0.270758	−	0.592878i
$905$	−13.4794	+	15.5560i	−0.448070	+	0.517100i
$906$	0.833126	−	5.79452i	0.0276787	−	0.192510i
$907$	16.7201	+	36.6120i	0.555183	+	1.21568i	0.954319	+	0.298789i	$0.0965828\pi$
$907$	16.7201	+	36.6120i	0.555183	+	1.21568i	−0.399136	+	0.916892i	$0.630690\pi$
$908$	18.9099	+	5.55244i	0.627547	+	0.184264i
$909$	−8.58197	−	2.51989i	−0.284646	−	0.0835796i
$910$	3.08089	+	6.74620i	0.102130	+	0.223634i
$911$	4.45516	−	30.9863i	0.147606	−	1.02662i	−0.772517	−	0.634994i	$-0.781003\pi$
$911$	4.45516	−	30.9863i	0.147606	−	1.02662i	0.920123	−	0.391629i	$-0.128088\pi$
$912$	5.42997	−	6.26652i	0.179804	−	0.207505i
$913$	19.0628	−	41.7417i	0.630886	−	1.38145i
$914$	2.66440	+	1.71231i	0.0881307	+	0.0566382i
$915$	−2.73152	−	18.9981i	−0.0903012	−	0.628059i
$916$	−16.3341	+	10.4973i	−0.539695	+	0.346841i
$917$	39.6459	+	45.7538i	1.30922	+	1.51093i
$918$	1.01296	−	0.297433i	0.0334328	−	0.00981675i
$919$	−41.1246			−1.35658			−0.678288	−	0.734796i	$-0.737278\pi$
$919$	−41.1246			−1.35658			−0.678288	+	0.734796i	$0.737278\pi$
$920$		0			0
$921$	−21.3050			−0.702022
$922$	0.872976	−	0.256329i	0.0287499	−	0.00844174i
$923$	−24.0388	−	27.7422i	−0.791245	−	0.913146i
$924$	−51.5730	+	33.1440i	−1.69663	+	1.09036i
$925$	0.610786	+	4.24811i	0.0200825	+	0.139677i
$926$	−10.3985	−	6.68269i	−0.341715	−	0.219607i
$927$	3.47315	−	7.60514i	0.114073	−	0.249786i
$928$	11.0371	−	12.7375i	0.362310	−	0.418128i
$929$	3.42349	−	23.8109i	0.112321	−	0.781209i	−0.853331	−	0.521370i	$-0.825421\pi$
$929$	3.42349	−	23.8109i	0.112321	−	0.781209i	0.965652	−	0.259840i	$-0.0836697\pi$
$930$	4.76023	+	10.4235i	0.156094	+	0.341799i
$931$	−6.66298	−	1.95643i	−0.218370	−	0.0641193i
$932$	−10.1345	−	2.97575i	−0.331965	−	0.0974738i
$933$	−12.2432	−	26.8088i	−0.400823	−	0.877681i
$934$	−1.14832	+	7.98675i	−0.0375742	+	0.261335i
$935$	−3.23781	+	3.73663i	−0.105888	+	0.122201i
$936$	−5.57338	+	12.2040i	−0.182172	+	0.398900i
$937$	−28.7543	−	18.4793i	−0.939363	−	0.603692i	−0.0211489	−	0.999776i	$-0.506732\pi$
$937$	−28.7543	−	18.4793i	−0.939363	−	0.603692i	−0.918214	+	0.396084i	$0.870369\pi$
$938$	0.786697	+	5.47160i	0.0256866	+	0.178654i
$939$	45.8249	−	29.4499i	1.49544	−	0.961060i
$940$	2.92863	+	3.37981i	0.0955213	+	0.110237i
$941$	6.38300	−	1.87422i	0.208080	−	0.0610978i	−0.176031	−	0.984385i	$-0.556326\pi$
$941$	6.38300	−	1.87422i	0.208080	−	0.0610978i	0.384111	+	0.923287i	$0.374508\pi$
$942$	−15.7771			−0.514045
$943$		0			0
$944$	12.0000			0.390567
$945$	−8.58197	+	2.51989i	−0.279171	+	0.0819721i
$946$		0			0
$947$	−9.10208	+	5.84955i	−0.295778	+	0.190085i	−0.680110	−	0.733110i	$-0.738068\pi$
$947$	−9.10208	+	5.84955i	−0.295778	+	0.190085i	0.384332	+	0.923195i	$0.374432\pi$
$948$	−5.63520	−	39.1937i	−0.183023	−	1.27295i
$949$	16.4748	+	10.5877i	0.534794	+	0.343691i
$950$	−1.78288	+	3.90396i	−0.0578442	+	0.126661i
$951$	37.2176	−	42.9514i	1.20686	−	1.39279i
$952$	0.786697	−	5.47160i	0.0254970	−	0.177336i
$953$	−8.50443	−	18.6221i	−0.275486	−	0.603229i	0.720429	−	0.693529i	$-0.243945\pi$
$953$	−8.50443	−	18.6221i	−0.275486	−	0.603229i	−0.995915	+	0.0902993i	$0.971218\pi$
$954$	0.559953	+	0.164417i	0.0181291	+	0.00532319i
$955$	31.0498	+	9.11706i	1.00475	+	0.295021i
$956$	−9.25150	−	20.2580i	−0.299215	−	0.655190i
$957$	−4.99875	+	34.7671i	−0.161587	+	1.12386i
$958$	12.7880	−	14.7582i	0.413163	−	0.476815i
$959$	−29.4250	+	64.4318i	−0.950183	+	2.08061i
$960$	−0.548898	−	0.352755i	−0.0177156	−	0.0113851i
$961$	−1.99241	−	13.8575i	−0.0642712	−	0.447016i
$962$	1.92798	−	1.23904i	0.0621606	−	0.0399482i
$963$	17.5718	+	20.2789i	0.566242	+	0.653478i
$964$	35.9008	−	10.5414i	1.15629	−	0.339516i
$965$	−12.2918			−0.395687
$966$		0			0
$967$	27.5410			0.885659			0.442830	−	0.896606i	$-0.353975\pi$
$967$	27.5410			0.885659			0.442830	+	0.896606i	$0.353975\pi$
$968$	35.2213	−	10.3419i	1.13205	−	0.332401i
$969$	−2.23727	−	2.58195i	−0.0718715	−	0.0829441i
$970$	11.3804	−	7.31372i	0.365401	−	0.234829i
$971$	2.34423	+	16.3045i	0.0752299	+	0.523235i	0.992237	+	0.124364i	$0.0396890\pi$
$971$	2.34423	+	16.3045i	0.0752299	+	0.523235i	−0.917007	+	0.398872i	$0.869402\pi$
$972$	−24.3495	−	15.6485i	−0.781010	−	0.501924i
$973$	14.3952	−	31.5210i	0.461488	−	1.01052i
$974$	5.95280	−	6.86989i	0.190740	−	0.220126i
$975$	−3.31477	+	23.0547i	−0.106158	+	0.738342i
$976$	5.34863	+	11.7119i	0.171205	+	0.374888i
$977$	−22.4018	−	6.57776i	−0.716697	−	0.210441i	−0.0970020	−	0.995284i	$-0.530925\pi$
$977$	−22.4018	−	6.57776i	−0.716697	−	0.210441i	−0.619695	+	0.784843i	$0.712744\pi$
$978$	−7.64290	−	2.24416i	−0.244393	−	0.0717602i
$979$	22.7784	+	49.8777i	0.728000	+	1.59410i
$980$	−0.988273	+	6.87359i	−0.0315692	+	0.219569i
$981$		0			0
$982$	2.14315	−	4.69284i	0.0683906	−	0.149755i
$983$	34.0473	+	21.8809i	1.08594	+	0.697892i	0.955922	−	0.293620i	$-0.0948599\pi$
$983$	34.0473	+	21.8809i	1.08594	+	0.697892i	0.130019	+	0.991512i	$0.458496\pi$
$984$	2.47068	+	17.1840i	0.0787625	+	0.547805i
$985$	1.53080	−	0.983783i	0.0487752	−	0.0313459i
$986$	−0.927550	−	1.07045i	−0.0295392	−	0.0340901i
$987$	15.5249	−	4.55853i	0.494164	−	0.145100i
$988$	−9.70820			−0.308859
$989$		0			0
$990$	−8.00000			−0.254257
$991$	−23.0278	+	6.76158i	−0.731503	+	0.214789i	−0.626212	−	0.779653i	$-0.715396\pi$
$991$	−23.0278	+	6.76158i	−0.731503	+	0.214789i	−0.105291	+	0.994441i	$0.533577\pi$
$992$	−24.6797	−	28.4819i	−0.783581	−	0.904300i
$993$	36.9683	−	23.7581i	1.17315	−	0.753939i
$994$	3.48275	+	24.2230i	0.110466	+	0.768308i
$995$	−12.7816	−	8.21422i	−0.405203	−	0.260408i
$996$	13.1721	−	28.8428i	0.417373	−	0.913919i
$997$	−11.0232	+	12.7214i	−0.349107	+	0.402891i	−0.902961	−	0.429723i	$-0.858611\pi$
$997$	−11.0232	+	12.7214i	−0.349107	+	0.402891i	0.553854	+	0.832614i	$0.313157\pi$
$998$	−1.69682	+	11.8016i	−0.0537118	+	0.373574i
$999$	1.14818	+	2.51416i	0.0363268	+	0.0795445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.2.c.n.170.1		20
23.2	even	11	inner	529.2.c.n.266.1		20
23.3	even	11	inner	529.2.c.n.334.2		20
23.4	even	11	inner	529.2.c.n.466.2		20
23.5	odd	22		529.2.c.o.501.1		20
23.6	even	11	inner	529.2.c.n.255.2		20
23.7	odd	22		529.2.c.o.487.2		20
23.8	even	11		529.2.a.a.1.2		2
23.9	even	11	inner	529.2.c.n.177.1		20
23.10	odd	22		529.2.c.o.118.1		20
23.11	odd	22		529.2.c.o.399.1		20
23.12	even	11	inner	529.2.c.n.399.1		20
23.13	even	11	inner	529.2.c.n.118.1		20
23.14	odd	22		529.2.c.o.177.1		20
23.15	odd	22		23.2.a.a.1.2	✓	2
23.16	even	11	inner	529.2.c.n.487.2		20
23.17	odd	22		529.2.c.o.255.2		20
23.18	even	11	inner	529.2.c.n.501.1		20
23.19	odd	22		529.2.c.o.466.2		20
23.20	odd	22		529.2.c.o.334.2		20
23.21	odd	22		529.2.c.o.266.1		20
23.22	odd	2		529.2.c.o.170.1		20
69.8	odd	22		4761.2.a.w.1.1		2
69.38	even	22		207.2.a.d.1.1		2
92.15	even	22		368.2.a.h.1.2		2
92.31	odd	22		8464.2.a.bb.1.2		2
115.38	even	44		575.2.b.d.24.2		4
115.84	odd	22		575.2.a.f.1.1		2
115.107	even	44		575.2.b.d.24.3		4
161.153	even	22		1127.2.a.c.1.2		2
184.61	odd	22		1472.2.a.t.1.2		2
184.107	even	22		1472.2.a.s.1.1		2
253.153	even	22		2783.2.a.c.1.1		2
276.107	odd	22		3312.2.a.ba.1.1		2
299.38	odd	22		3887.2.a.i.1.1		2
345.314	even	22		5175.2.a.be.1.2		2
391.84	odd	22		6647.2.a.b.1.2		2
437.360	even	22		8303.2.a.e.1.1		2
460.199	even	22		9200.2.a.bt.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.a.a.1.2	✓	2	23.15	odd	22
207.2.a.d.1.1		2	69.38	even	22
368.2.a.h.1.2		2	92.15	even	22
529.2.a.a.1.2		2	23.8	even	11
529.2.c.n.118.1		20	23.13	even	11	inner
529.2.c.n.170.1		20	1.1	even	1	trivial
529.2.c.n.177.1		20	23.9	even	11	inner
529.2.c.n.255.2		20	23.6	even	11	inner
529.2.c.n.266.1		20	23.2	even	11	inner
529.2.c.n.334.2		20	23.3	even	11	inner
529.2.c.n.399.1		20	23.12	even	11	inner
529.2.c.n.466.2		20	23.4	even	11	inner
529.2.c.n.487.2		20	23.16	even	11	inner
529.2.c.n.501.1		20	23.18	even	11	inner
529.2.c.o.118.1		20	23.10	odd	22
529.2.c.o.170.1		20	23.22	odd	2
529.2.c.o.177.1		20	23.14	odd	22
529.2.c.o.255.2		20	23.17	odd	22
529.2.c.o.266.1		20	23.21	odd	22
529.2.c.o.334.2		20	23.20	odd	22
529.2.c.o.399.1		20	23.11	odd	22
529.2.c.o.466.2		20	23.19	odd	22
529.2.c.o.487.2		20	23.7	odd	22
529.2.c.o.501.1		20	23.5	odd	22
575.2.a.f.1.1		2	115.84	odd	22
575.2.b.d.24.2		4	115.38	even	44
575.2.b.d.24.3		4	115.107	even	44
1127.2.a.c.1.2		2	161.153	even	22
1472.2.a.s.1.1		2	184.107	even	22
1472.2.a.t.1.2		2	184.61	odd	22
2783.2.a.c.1.1		2	253.153	even	22
3312.2.a.ba.1.1		2	276.107	odd	22
3887.2.a.i.1.1		2	299.38	odd	22
4761.2.a.w.1.1		2	69.8	odd	22
5175.2.a.be.1.2		2	345.314	even	22
6647.2.a.b.1.2		2	391.84	odd	22
8303.2.a.e.1.1		2	437.360	even	22
8464.2.a.bb.1.2		2	92.31	odd	22
9200.2.a.bt.1.1		2	460.199	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	529.c (of order \(11\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.592999 + 0.174120i) q^{2} +(1.46431 + 1.68991i) q^{3} +(-1.36118 + 0.874775i) q^{4} +(0.175911 + 1.22349i) q^{5} +(-1.16258 - 0.747147i) q^{6} +(-1.34431 + 2.94363i) q^{7} +(1.46431 - 1.68991i) q^{8} +(-0.284630 + 1.97964i) q^{9} +(-0.317349 - 0.694897i) q^{10} +(-5.02397 - 1.47517i) q^{11} +(-3.47148 - 1.01932i) q^{12} +(1.24625 + 2.72890i) q^{13} +(0.284630 - 1.97964i) q^{14} +(-1.80999 + 2.08884i) q^{15} +(0.770222 - 1.68655i) q^{16} +(-0.642661 - 0.413013i) q^{17} +(-0.175911 - 1.22349i) q^{18} +(1.68251 - 1.08128i) q^{19} +(-1.30972 - 1.51150i) q^{20} +(-6.94296 + 2.03864i) q^{21} +3.23607 q^{22} +5.00000 q^{24} +(3.33149 - 0.978214i) q^{25} +(-1.21418 - 1.40124i) q^{26} +(1.88110 - 1.20891i) q^{27} +(-0.745170 - 5.18277i) q^{28} +(-2.52376 - 1.62192i) q^{29} +(0.709614 - 1.55384i) q^{30} +(-4.39294 + 5.06972i) q^{31} +(-0.799530 + 5.56085i) q^{32} +(-4.86376 - 10.6502i) q^{33} +(0.453011 + 0.133016i) q^{34} +(-3.83797 - 1.12693i) q^{35} +(-1.34431 - 2.94363i) q^{36} +(-0.175911 + 1.22349i) q^{37} +(-0.809452 + 0.934158i) q^{38} +(-2.78669 + 6.10200i) q^{39} +(2.32517 + 1.49429i) q^{40} +(0.494136 + 3.43679i) q^{41} +(3.76220 - 2.41782i) q^{42} +(8.12895 - 2.38688i) q^{44} -2.47214 q^{45} -2.23607 q^{47} +(3.97796 - 1.16803i) q^{48} +(-2.27377 - 2.62407i) q^{49} +(-1.80524 + 1.16016i) q^{50} +(-0.243103 - 1.69082i) q^{51} +(-4.08353 - 2.62433i) q^{52} +(-0.196132 + 0.429470i) q^{53} +(-0.904995 + 1.04442i) q^{54} +(0.921081 - 6.40626i) q^{55} +(3.00597 + 6.58216i) q^{56} +(4.29098 + 1.25995i) q^{57} +(1.77900 + 0.522361i) q^{58} +(2.68862 + 5.88726i) q^{59} +(0.636451 - 4.42662i) q^{60} +(-4.54753 + 5.24813i) q^{61} +(1.72227 - 3.77124i) q^{62} +(-5.44471 - 3.49910i) q^{63} +(0.0335960 + 0.233665i) q^{64} +(-3.11954 + 2.00481i) q^{65} +(4.73862 + 5.46866i) q^{66} +(-2.65197 + 0.778690i) q^{67} +1.23607 q^{68} +2.47214 q^{70} +(-11.7404 + 3.44730i) q^{71} +(2.92863 + 3.37981i) q^{72} +(5.49159 - 3.52923i) q^{73} +(-0.108719 - 0.756156i) q^{74} +(6.53144 + 4.19750i) q^{75} +(-1.34431 + 2.94363i) q^{76} +(11.0961 - 12.8056i) q^{77} +(0.590023 - 4.10370i) q^{78} +(4.54641 + 9.95526i) q^{79} +(2.19896 + 0.645674i) q^{80} +(10.5544 + 3.09906i) q^{81} +(-0.891438 - 1.95198i) q^{82} +(-1.24724 + 8.67473i) q^{83} +(7.66724 - 8.84847i) q^{84} +(0.392265 - 0.858940i) q^{85} +(-0.954677 - 6.63992i) q^{87} +(-9.84957 + 6.32993i) q^{88} +(-6.85779 - 7.91431i) q^{89} +(1.46597 - 0.430449i) q^{90} -9.70820 q^{91} -15.0000 q^{93} +(1.32599 - 0.389345i) q^{94} +(1.61890 + 1.86832i) q^{95} +(-10.5681 + 6.79170i) q^{96} +(2.52014 + 17.5280i) q^{97} +(1.80524 + 1.16016i) q^{98} +(4.35028 - 9.52579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 4 q^{9} + 6 q^{10} - 6 q^{11} - 5 q^{12} - 6 q^{13} + 4 q^{14} - 10 q^{15} + 3 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 4 q^{20} - 10 q^{21} + 20 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) \) 20 * q + q^2 + q^4 - 2 * q^5 + 5 * q^6 + 2 * q^7 - 4 * q^9 + 6 * q^10 - 6 * q^11 - 5 * q^12 - 6 * q^13 + 4 * q^14 - 10 * q^15 + 3 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 4 * q^20 - 10 * q^21 + 20 * q^22 + 100 * q^24 - 2 * q^25 + 3 * q^26 - 6 * q^28 + 6 * q^29 + 10 * q^30 - 9 * q^32 + 10 * q^33 - 8 * q^34 - 8 * q^35 + 2 * q^36 + 2 * q^37 + 2 * q^38 - 10 * q^40 - 2 * q^41 + 8 * q^44 + 40 * q^45 + 15 * q^48 + 2 * q^49 + 11 * q^50 + 10 * q^51 + 3 * q^52 - 8 * q^53 - 5 * q^54 + 4 * q^55 - 10 * q^56 - 3 * q^58 - 4 * q^59 + 4 * q^61 - 15 * q^62 + 4 * q^63 - 4 * q^64 - 6 * q^65 + 10 * q^66 - 10 * q^67 - 20 * q^68 - 40 * q^70 - 20 * q^71 - 22 * q^73 - 6 * q^74 - 20 * q^75 + 2 * q^76 + 16 * q^77 + 15 * q^78 - 4 * q^79 + 18 * q^80 + 22 * q^81 + 11 * q^82 - 22 * q^83 + 10 * q^84 + 16 * q^85 + 10 * q^88 - 12 * q^89 + 12 * q^90 - 60 * q^91 - 300 * q^93 + 5 * q^94 - 4 * q^95 + 5 * q^96 + 22 * q^97 - 11 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more