LMFDB - Embedded newform 425.2.r.a.69.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(69,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([9, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			69.18
Character	$\chi$	$=$	425.69
Dual form			425.2.r.a.154.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.292236 + 0.0949534i) q^{2} +(-0.973705 - 1.34019i) q^{3} +(-1.54165 + 1.12007i) q^{4} +(1.39711 - 1.74587i) q^{5} +(0.411808 + 0.299196i) q^{6} +1.62592i q^{7} +(0.705395 - 0.970893i) q^{8} +(0.0790435 - 0.243271i) q^{9} +(-0.242510 + 0.642869i) q^{10} +(-0.389672 - 1.19929i) q^{11} +(3.00222 + 0.975481i) q^{12} +(-2.15907 - 0.701526i) q^{13} +(-0.154386 - 0.475153i) q^{14} +(-3.70018 - 0.172428i) q^{15} +(1.06376 - 3.27392i) q^{16} +(-0.587785 + 0.809017i) q^{17} +0.0785981i q^{18} +(-3.60186 - 2.61690i) q^{19} +(-0.198347 + 4.25639i) q^{20} +(2.17904 - 1.58316i) q^{21} +(0.227753 + 0.313474i) q^{22} +(-3.44716 + 1.12005i) q^{23} -1.98803 q^{24} +(-1.09616 - 4.87836i) q^{25} +0.697573 q^{26} +(-5.12946 + 1.66666i) q^{27} +(-1.82115 - 2.50659i) q^{28} +(-0.213184 + 0.154887i) q^{29} +(1.09770 - 0.300955i) q^{30} +(-6.37905 - 4.63465i) q^{31} +3.45795i q^{32} +(-1.22785 + 1.68998i) q^{33} +(0.0949534 - 0.292236i) q^{34} +(2.83865 + 2.27159i) q^{35} +(0.150624 + 0.463572i) q^{36} +(-6.04607 - 1.96449i) q^{37} +(1.30108 + 0.422746i) q^{38} +(1.16212 + 3.57665i) q^{39} +(-0.709542 - 2.58798i) q^{40} +(2.73636 - 8.42164i) q^{41} +(-0.486468 + 0.669566i) q^{42} -0.812241i q^{43} +(1.94402 + 1.41242i) q^{44} +(-0.314288 - 0.477877i) q^{45} +(0.901034 - 0.654639i) q^{46} +(5.32740 + 7.33254i) q^{47} +(-5.42347 + 1.76219i) q^{48} +4.35639 q^{49} +(0.783555 + 1.32155i) q^{50} +1.65657 q^{51} +(4.11429 - 1.33681i) q^{52} +(-5.64476 - 7.76935i) q^{53} +(1.34076 - 0.974119i) q^{54} +(-2.63822 - 0.995218i) q^{55} +(1.57859 + 1.14691i) q^{56} +7.37526i q^{57} +(0.0475931 - 0.0655062i) q^{58} +(1.36411 - 4.19831i) q^{59} +(5.89750 - 3.87865i) q^{60} +(2.24358 + 6.90501i) q^{61} +(2.30427 + 0.748701i) q^{62} +(0.395538 + 0.128518i) q^{63} +(1.79918 + 5.53731i) q^{64} +(-4.24124 + 2.78936i) q^{65} +(0.198352 - 0.610463i) q^{66} +(-4.75656 + 6.54685i) q^{67} -1.90558i q^{68} +(4.85760 + 3.52925i) q^{69} +(-1.04525 - 0.394302i) q^{70} +(1.46562 - 1.06483i) q^{71} +(-0.180433 - 0.248345i) q^{72} +(15.3611 - 4.99113i) q^{73} +1.95342 q^{74} +(-5.47060 + 6.21915i) q^{75} +8.48392 q^{76} +(1.94994 - 0.633574i) q^{77} +(-0.679230 - 0.934880i) q^{78} +(13.2522 - 9.62832i) q^{79} +(-4.22966 - 6.43123i) q^{80} +(6.60740 + 4.80056i) q^{81} +2.72094i q^{82} +(-1.68587 + 2.32040i) q^{83} +(-1.58605 + 4.88137i) q^{84} +(0.591241 + 2.15649i) q^{85} +(0.0771250 + 0.237366i) q^{86} +(0.415156 + 0.134893i) q^{87} +(-1.43925 - 0.467641i) q^{88} +(4.18423 + 12.8777i) q^{89} +(0.137222 + 0.109810i) q^{90} +(1.14062 - 3.51048i) q^{91} +(4.05977 - 5.58780i) q^{92} +13.0619i q^{93} +(-2.25311 - 1.63698i) q^{94} +(-9.60098 + 2.63229i) q^{95} +(4.63431 - 3.36702i) q^{96} +(-4.19887 - 5.77924i) q^{97} +(-1.27310 + 0.413654i) q^{98} -0.322552 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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 $

$2$	−0.292236	+	0.0949534i	−0.206642	+	0.0671422i	−0.410509	−	0.911856i	$-0.634649\pi$
$2$	−0.292236	+	0.0949534i	−0.206642	+	0.0671422i	0.203867	+	0.978999i	$0.434649\pi$
$3$	−0.973705	−	1.34019i	−0.562169	−	0.773759i	0.429431	−	0.903099i	$-0.358714\pi$
$3$	−0.973705	−	1.34019i	−0.562169	−	0.773759i	−0.991600	+	0.129341i	$0.958714\pi$
$4$	−1.54165	+	1.12007i	−0.770824	+	0.560036i
$5$	1.39711	−	1.74587i	0.624807	−	0.780779i
$5$	1.39711	−	1.74587i	0.624807	−	0.780779i
$6$	0.411808	+	0.299196i	0.168120	+	0.122146i
$7$			1.62592i			0.614539i	0.951622	+	0.307270i	$0.0994154\pi$
$7$			1.62592i			0.614539i	−0.951622	+	0.307270i	$0.900585\pi$
$8$	0.705395	−	0.970893i	0.249395	−	0.343263i
$9$	0.0790435	−	0.243271i	0.0263478	−	0.0810903i
$10$	−0.242510	+	0.642869i	−0.0766885	+	0.203293i
$11$	−0.389672	−	1.19929i	−0.117490	−	0.361598i	0.874968	−	0.484181i	$-0.160882\pi$
$11$	−0.389672	−	1.19929i	−0.117490	−	0.361598i	−0.992458	+	0.122583i	$0.960882\pi$
$12$	3.00222	+	0.975481i	0.866666	+	0.281597i
$13$	−2.15907	−	0.701526i	−0.598820	−	0.194568i	−0.00610566	−	0.999981i	$-0.501944\pi$
$13$	−2.15907	−	0.701526i	−0.598820	−	0.194568i	−0.592714	+	0.805413i	$0.701944\pi$
$14$	−0.154386	−	0.475153i	−0.0412615	−	0.126990i
$15$	−3.70018	−	0.172428i	−0.955382	−	0.0445206i
$16$	1.06376	−	3.27392i	0.265940	−	0.818480i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$17$	−0.587785	+	0.809017i	−0.142559	+	0.196215i
$18$			0.0785981i			0.0185257i
$19$	−3.60186	−	2.61690i	−0.826323	−	0.600359i	0.0921939	−	0.995741i	$-0.470612\pi$
$19$	−3.60186	−	2.61690i	−0.826323	−	0.600359i	−0.918517	+	0.395383i	$0.870612\pi$
$20$	−0.198347	+	4.25639i	−0.0443518	+	0.951758i
$21$	2.17904	−	1.58316i	0.475505	−	0.345475i
$22$	0.227753	+	0.313474i	0.0485570	+	0.0668330i
$23$	−3.44716	+	1.12005i	−0.718783	+	0.233547i	−0.645495	−	0.763764i	$-0.723349\pi$
$23$	−3.44716	+	1.12005i	−0.718783	+	0.233547i	−0.0732875	+	0.997311i	$0.523349\pi$
$24$	−1.98803			−0.405804
$25$	−1.09616	−	4.87836i	−0.219232	−	0.975673i
$26$	0.697573			0.136805
$27$	−5.12946	+	1.66666i	−0.987164	+	0.320749i
$28$	−1.82115	−	2.50659i	−0.344164	−	0.473702i
$29$	−0.213184	+	0.154887i	−0.0395873	+	0.0287618i	−0.607403	−	0.794394i	$-0.707789\pi$
$29$	−0.213184	+	0.154887i	−0.0395873	+	0.0287618i	0.567816	+	0.823156i	$0.307789\pi$
$30$	1.09770	−	0.300955i	0.200412	−	0.0549466i
$31$	−6.37905	−	4.63465i	−1.14571	−	0.832407i	−0.157806	−	0.987470i	$-0.550442\pi$
$31$	−6.37905	−	4.63465i	−1.14571	−	0.832407i	−0.987905	+	0.155063i	$0.950442\pi$
$32$			3.45795i			0.611284i
$33$	−1.22785	+	1.68998i	−0.213740	+	0.294189i
$34$	0.0949534	−	0.292236i	0.0162844	−	0.0501181i
$35$	2.83865	+	2.27159i	0.479819	+	0.383969i
$36$	0.150624	+	0.463572i	0.0251040	+	0.0772621i
$37$	−6.04607	−	1.96449i	−0.993968	−	0.322960i	−0.233515	−	0.972353i	$-0.575023\pi$
$37$	−6.04607	−	1.96449i	−0.993968	−	0.322960i	−0.760453	+	0.649393i	$0.775023\pi$
$38$	1.30108	+	0.422746i	0.211063	+	0.0685784i
$39$	1.16212	+	3.57665i	0.186089	+	0.572722i
$40$	−0.709542	−	2.58798i	−0.112188	−	0.409195i
$41$	2.73636	−	8.42164i	0.427347	−	1.31524i	−0.473382	−	0.880857i	$-0.656967\pi$
$41$	2.73636	−	8.42164i	0.427347	−	1.31524i	0.900729	−	0.434381i	$-0.143033\pi$
$42$	−0.486468	+	0.669566i	−0.0750636	+	0.103316i
$43$		−	0.812241i		−	0.123866i	−0.998080	−	0.0619328i	$-0.980274\pi$
$43$		−	0.812241i		−	0.123866i	0.998080	−	0.0619328i	$-0.0197264\pi$
$44$	1.94402	+	1.41242i	0.293073	+	0.212930i
$45$	−0.314288	−	0.477877i	−0.0468513	−	0.0712376i
$46$	0.901034	−	0.654639i	0.132850	−	0.0965213i
$47$	5.32740	+	7.33254i	0.777081	+	1.06956i	0.995598	+	0.0937274i	$0.0298782\pi$
$47$	5.32740	+	7.33254i	0.777081	+	1.06956i	−0.218517	+	0.975833i	$0.570122\pi$
$48$	−5.42347	+	1.76219i	−0.782810	+	0.254350i
$49$	4.35639			0.622341
$50$	0.783555	+	1.32155i	0.110811	+	0.186896i
$51$	1.65657			0.231966
$52$	4.11429	−	1.33681i	0.570550	−	0.185383i
$53$	−5.64476	−	7.76935i	−0.775368	−	1.06720i	−0.995778	−	0.0917948i	$-0.970740\pi$
$53$	−5.64476	−	7.76935i	−0.775368	−	1.06720i	0.220410	−	0.975407i	$-0.429260\pi$
$54$	1.34076	−	0.974119i	0.182454	−	0.132561i
$55$	−2.63822	−	0.995218i	−0.355737	−	0.134195i
$56$	1.57859	+	1.14691i	0.210948	+	0.153263i
$57$			7.37526i			0.976877i
$58$	0.0475931	−	0.0655062i	0.00624927	−	0.00860139i
$59$	1.36411	−	4.19831i	0.177593	−	0.546574i	−0.822150	−	0.569271i	$-0.807225\pi$
$59$	1.36411	−	4.19831i	0.177593	−	0.546574i	0.999742	+	0.0226975i	$0.00722545\pi$
$60$	5.89750	−	3.87865i	0.761364	−	0.500731i
$61$	2.24358	+	6.90501i	0.287260	+	0.884097i	0.985712	+	0.168439i	$0.0538727\pi$
$61$	2.24358	+	6.90501i	0.287260	+	0.884097i	−0.698452	+	0.715657i	$0.746127\pi$
$62$	2.30427	+	0.748701i	0.292642	+	0.0950852i
$63$	0.395538	+	0.128518i	0.0498332	+	0.0161918i
$64$	1.79918	+	5.53731i	0.224897	+	0.692163i
$65$	−4.24124	+	2.78936i	−0.526062	+	0.345978i
$66$	0.198352	−	0.610463i	0.0244154	−	0.0751428i
$67$	−4.75656	+	6.54685i	−0.581107	+	0.799825i	−0.993816	−	0.111038i	$-0.964582\pi$
$67$	−4.75656	+	6.54685i	−0.581107	+	0.799825i	0.412710	+	0.910863i	$0.364582\pi$
$68$		−	1.90558i		−	0.231086i
$69$	4.85760	+	3.52925i	0.584786	+	0.424872i
$70$	−1.04525	−	0.394302i	−0.124932	−	0.0471281i
$71$	1.46562	−	1.06483i	0.173937	−	0.126372i	−0.497411	−	0.867515i	$-0.665716\pi$
$71$	1.46562	−	1.06483i	0.173937	−	0.126372i	0.671348	+	0.741143i	$0.265716\pi$
$72$	−0.180433	−	0.248345i	−0.0212642	−	0.0292677i
$73$	15.3611	−	4.99113i	1.79788	−	0.584167i	0.798051	−	0.602590i	$-0.205864\pi$
$73$	15.3611	−	4.99113i	1.79788	−	0.584167i	0.999830	+	0.0184224i	$0.00586437\pi$
$74$	1.95342			0.227080
$75$	−5.47060	+	6.21915i	−0.631690	+	0.718125i
$76$	8.48392			0.973172
$77$	1.94994	−	0.633574i	0.222216	−	0.0722025i
$78$	−0.679230	−	0.934880i	−0.0769076	−	0.105854i
$79$	13.2522	−	9.62832i	1.49099	−	1.08327i	0.517192	−	0.855869i	$-0.326977\pi$
$79$	13.2522	−	9.62832i	1.49099	−	1.08327i	0.973801	−	0.227401i	$-0.0730228\pi$
$80$	−4.22966	−	6.43123i	−0.472891	−	0.719033i
$81$	6.60740	+	4.80056i	0.734156	+	0.533396i
$82$			2.72094i			0.300477i
$83$	−1.68587	+	2.32040i	−0.185048	+	0.254696i	−0.891455	−	0.453109i	$-0.850315\pi$
$83$	−1.68587	+	2.32040i	−0.185048	+	0.254696i	0.706407	+	0.707806i	$0.250315\pi$
$84$	−1.58605	+	4.88137i	−0.173052	+	0.532601i
$85$	0.591241	+	2.15649i	0.0641291	+	0.233904i
$86$	0.0771250	+	0.237366i	0.00831660	+	0.0255959i
$87$	0.415156	+	0.134893i	0.0445094	+	0.0144620i
$88$	−1.43925	−	0.467641i	−0.153425	−	0.0498507i
$89$	4.18423	+	12.8777i	0.443527	+	1.36504i	0.884091	+	0.467315i	$0.154779\pi$
$89$	4.18423	+	12.8777i	0.443527	+	1.36504i	−0.440564	+	0.897721i	$0.645221\pi$
$90$	0.137222	+	0.109810i	0.0144645	+	0.0115750i
$91$	1.14062	−	3.51048i	0.119570	−	0.367998i
$92$	4.05977	−	5.58780i	0.423260	−	0.582568i
$93$			13.0619i			1.35446i
$94$	−2.25311	−	1.63698i	−0.232391	−	0.168842i
$95$	−9.60098	+	2.63229i	−0.985040	+	0.270067i
$96$	4.63431	−	3.36702i	0.472987	−	0.343645i
$97$	−4.19887	−	5.77924i	−0.426330	−	0.586793i	0.540776	−	0.841167i	$-0.318131\pi$
$97$	−4.19887	−	5.77924i	−0.426330	−	0.586793i	−0.967106	+	0.254373i	$0.918131\pi$
$98$	−1.27310	+	0.413654i	−0.128602	+	0.0417854i
$99$	−0.322552			−0.0324177
$100$	7.15401	+	6.29294i	0.715401	+	0.629294i
$101$	−15.4267			−1.53502			−0.767509	−	0.641039i	$-0.778504\pi$
$101$	−15.4267			−1.53502			−0.767509	+	0.641039i	$0.778504\pi$
$102$	−0.484109	+	0.157297i	−0.0479339	+	0.0155747i
$103$	0.143618	+	0.197674i	0.0141511	+	0.0194774i	0.816034	−	0.578004i	$-0.196168\pi$
$103$	0.143618	+	0.197674i	0.0141511	+	0.0194774i	−0.801883	+	0.597481i	$0.796168\pi$
$104$	−2.20411	+	1.60138i	−0.216131	+	0.157028i
$105$	0.280353	−	6.01619i	0.0273597	−	0.587120i
$106$	2.38733	+	1.73450i	0.231878	+	0.168469i
$107$		−	1.05708i		−	0.102191i	−0.998694	−	0.0510957i	$-0.983729\pi$
$107$		−	1.05708i		−	0.102191i	0.998694	−	0.0510957i	$-0.0162713\pi$
$108$	6.04103	−	8.31477i	0.581299	−	0.800089i
$109$	3.19910	−	9.84581i	0.306418	−	0.943057i	−0.672726	−	0.739891i	$-0.734877\pi$
$109$	3.19910	−	9.84581i	0.306418	−	0.943057i	0.979144	−	0.203166i	$-0.0651231\pi$
$110$	0.865483	+	0.0403314i	0.0825205	+	0.00384544i
$111$	3.25430	+	10.0157i	0.308885	+	0.950649i
$112$	5.32313	+	1.72959i	0.502988	+	0.163431i
$113$	−4.63908	−	1.50733i	−0.436408	−	0.141797i	0.0825700	−	0.996585i	$-0.473687\pi$
$113$	−4.63908	−	1.50733i	−0.436408	−	0.141797i	−0.518978	+	0.854788i	$0.673687\pi$
$114$	−0.700306	−	2.15532i	−0.0655897	−	0.201864i
$115$	−2.86060	+	7.58315i	−0.266752	+	0.707132i
$116$	0.155170	−	0.477563i	0.0144071	−	0.0443406i
$117$	−0.341322	+	0.469789i	−0.0315552	+	0.0434320i
$118$			1.35643i			0.124869i
$119$	−1.31540	−	0.955691i	−0.120582	−	0.0876080i
$120$	−2.77750	+	3.47085i	−0.253550	+	0.316844i
$121$	7.61274	−	5.53098i	0.692068	−	0.502817i
$122$	−1.31131	−	1.80486i	−0.118720	−	0.163405i
$123$	−13.9510	+	4.53295i	−1.25792	+	0.408723i
$124$	15.0254			1.34932
$125$	−10.0485	−	4.90186i	−0.898762	−	0.438436i
$126$	−0.127794			−0.0113848
$127$	−4.79030	+	1.55646i	−0.425070	+	0.138114i	−0.513737	−	0.857948i	$-0.671739\pi$
$127$	−4.79030	+	1.55646i	−0.425070	+	0.138114i	0.0886668	+	0.996061i	$0.471739\pi$
$128$	−5.11663	−	7.04244i	−0.452251	−	0.622470i
$129$	−1.08856	+	0.790883i	−0.0958421	+	0.0696333i
$130$	0.974587	−	1.21787i	0.0854769	−	0.106815i
$131$	2.58581	+	1.87870i	0.225924	+	0.164143i	0.694989	−	0.719020i	$-0.255409\pi$
$131$	2.58581	+	1.87870i	0.225924	+	0.164143i	−0.469066	+	0.883163i	$0.655409\pi$
$132$		−	3.98064i		−	0.346470i
$133$	4.25487	−	5.85632i	0.368944	−	0.507808i
$134$	0.768396	−	2.36488i	0.0663793	−	0.204294i
$135$	−4.25664	+	11.2839i	−0.366353	+	0.971164i
$136$	0.370848	+	1.14135i	0.0318000	+	0.0978702i
$137$	15.9189	+	5.17237i	1.36005	+	0.441906i	0.896058	−	0.443936i	$-0.146418\pi$
$137$	15.9189	+	5.17237i	1.36005	+	0.441906i	0.463987	+	0.885842i	$0.346418\pi$
$138$	−1.75468	−	0.570131i	−0.149368	−	0.0485328i
$139$	4.28631	+	13.1919i	0.363560	+	1.11892i	0.950878	+	0.309566i	$0.100184\pi$
$139$	4.28631	+	13.1919i	0.363560	+	1.11892i	−0.587318	+	0.809356i	$0.699816\pi$
$140$	−6.92054	−	0.322496i	−0.584893	−	0.0272559i
$141$	4.63968	−	14.2795i	0.390731	−	1.20255i
$142$	−0.327197	+	0.450349i	−0.0274578	+	0.0377924i
$143$			2.86271i			0.239392i
$144$	−0.712366	−	0.517564i	−0.0593639	−	0.0431304i
$145$	−0.0274281	+	0.588587i	−0.00227778	+	0.0488795i
$146$	−4.01515	+	2.91718i	−0.332296	+	0.241427i
$147$	−4.24184	−	5.83839i	−0.349861	−	0.481542i
$148$	11.5213	−	3.74349i	0.947043	−	0.307713i
$149$	14.4596			1.18458			0.592290	−	0.805725i	$-0.298224\pi$
$149$	14.4596			1.18458			0.592290	+	0.805725i	$0.298224\pi$
$150$	1.00818	−	2.33691i	0.0823175	−	0.190808i
$151$	−8.64347			−0.703395			−0.351698	−	0.936114i	$-0.614395\pi$
$151$	−8.64347			−0.703395			−0.351698	+	0.936114i	$0.614395\pi$
$152$	−5.08146	+	1.65107i	−0.412161	+	0.133919i
$153$	0.150350	+	0.206939i	0.0121550	+	0.0167300i
$154$	−0.509684	+	0.370307i	−0.0410715	+	0.0298402i
$155$	−17.0038	+	4.66190i	−1.36577	+	0.374453i
$156$	−5.79769	−	4.21227i	−0.464187	−	0.337252i
$157$		−	5.68770i		−	0.453928i	−0.973903	−	0.226964i	$-0.927120\pi$
$157$		−	5.68770i		−	0.453928i	0.973903	−	0.226964i	$-0.0728800\pi$
$158$	−2.95855	+	4.07209i	−0.235369	+	0.323958i
$159$	−4.91607	+	15.1301i	−0.389870	+	1.19990i
$160$	6.03714	+	4.83114i	0.477278	+	0.381935i
$161$	−1.82111	−	5.60480i	−0.143524	−	0.441720i
$162$	−2.38675	−	0.775503i	−0.187521	−	0.0609293i
$163$	−0.969133	−	0.314890i	−0.0759084	−	0.0246641i	0.270817	−	0.962631i	$-0.412706\pi$
$163$	−0.969133	−	0.314890i	−0.0759084	−	0.0246641i	−0.346725	+	0.937967i	$0.612706\pi$
$164$	5.21435	+	16.0481i	0.407172	+	1.25315i
$165$	1.23506	+	4.50476i	0.0961496	+	0.350695i
$166$	0.272342	−	0.838183i	0.0211378	−	0.0650556i
$167$	−4.60354	+	6.33623i	−0.356233	+	0.490312i	−0.949094	−	0.314992i	$-0.897998\pi$
$167$	−4.60354	+	6.33623i	−0.356233	+	0.490312i	0.592862	+	0.805304i	$0.297998\pi$
$168$		−	3.23237i		−	0.249383i
$169$	−6.34776	−	4.61192i	−0.488289	−	0.354763i
$170$	−0.377548	−	0.574064i	−0.0289566	−	0.0440287i
$171$	−0.921319	+	0.669378i	−0.0704550	+	0.0511886i
$172$	0.909769	+	1.25219i	0.0693692	+	0.0954785i
$173$	4.35181	−	1.41399i	0.330862	−	0.107503i	−0.138875	−	0.990310i	$-0.544349\pi$
$173$	4.35181	−	1.41399i	0.330862	−	0.107503i	0.469737	+	0.882806i	$0.344349\pi$
$174$	−0.134132			−0.0101685
$175$	7.93182	−	1.78226i	0.599589	−	0.134727i
$176$	−4.34089			−0.327207
$177$	−6.95478	+	2.25975i	−0.522753	+	0.169853i
$178$	−2.44557	−	3.36603i	−0.183303	−	0.252295i
$179$	12.5163	−	9.09360i	0.935510	−	0.679688i	−0.0118256	−	0.999930i	$-0.503764\pi$
$179$	12.5163	−	9.09360i	0.935510	−	0.679688i	0.947336	+	0.320242i	$0.103764\pi$
$180$	1.01978	+	0.384692i	0.0760097	+	0.0286733i
$181$	−3.56616	−	2.59097i	−0.265070	−	0.192585i	0.447309	−	0.894380i	$-0.352382\pi$
$181$	−3.56616	−	2.59097i	−0.265070	−	0.192585i	−0.712379	+	0.701795i	$0.752382\pi$
$182$			1.13420i			0.0840722i
$183$	7.06945	−	9.73026i	0.522589	−	0.719282i
$184$	−1.34416	+	4.13690i	−0.0990929	+	0.304977i
$185$	−11.8768	+	7.81107i	−0.873198	+	0.574282i
$186$	−1.24027	−	3.81717i	−0.0909412	−	0.279888i
$187$	1.19929	+	0.389672i	0.0877005	+	0.0284956i
$188$	−16.4260	−	5.33712i	−1.19799	−	0.389249i
$189$	−2.70986	−	8.34008i	−0.197113	−	0.606651i
$190$	2.55581	−	1.68090i	0.185418	−	0.121945i
$191$	−2.17070	+	6.68073i	−0.157066	+	0.483401i	−0.998364	−	0.0571710i	$-0.981792\pi$
$191$	−2.17070	+	6.68073i	−0.157066	+	0.483401i	0.841298	+	0.540572i	$0.181792\pi$
$192$	5.66917	−	7.80294i	0.409137	−	0.563129i
$193$			8.13530i			0.585591i	0.956175	+	0.292796i	$0.0945856\pi$
$193$			8.13530i			0.585591i	−0.956175	+	0.292796i	$0.905414\pi$
$194$	1.77582	+	1.29021i	0.127496	+	0.0926316i
$195$	7.86800	+	2.96805i	0.563439	+	0.212547i
$196$	−6.71602	+	4.87947i	−0.479716	+	0.348534i
$197$	−5.76155	−	7.93010i	−0.410494	−	0.564996i	0.552845	−	0.833284i	$-0.313542\pi$
$197$	−5.76155	−	7.93010i	−0.410494	−	0.564996i	−0.963339	+	0.268288i	$0.913542\pi$
$198$	0.0942615	−	0.0306274i	0.00669888	−	0.00217660i
$199$	−3.50272			−0.248301			−0.124151	−	0.992263i	$-0.539621\pi$
$199$	−3.50272			−0.248301			−0.124151	+	0.992263i	$0.539621\pi$
$200$	−5.50960	−	2.37692i	−0.389587	−	0.168074i
$201$	13.4055			0.945551
$202$	4.50825	−	1.46482i	0.317200	−	0.103064i
$203$	−0.251834	−	0.346620i	−0.0176753	−	0.0243279i
$204$	−2.55384	+	1.85547i	−0.178805	+	0.129909i
$205$	−10.8801	−	16.5433i	−0.759901	−	1.15543i
$206$	−0.0607403	−	0.0441304i	−0.00423198	−	0.00307471i
$207$			0.927127i			0.0644398i
$208$	−4.59348	+	6.32238i	−0.318501	+	0.438379i
$209$	−1.73487	+	5.33939i	−0.120004	+	0.369333i
$210$	0.489328	+	1.78477i	0.0337668	+	0.123161i
$211$	−2.96976	−	9.13997i	−0.204446	−	0.629222i	−0.999736	−	0.0229913i	$-0.992681\pi$
$211$	−2.96976	−	9.13997i	−0.204446	−	0.629222i	0.795289	−	0.606230i	$-0.207319\pi$
$212$	17.4045	+	5.65506i	1.19534	+	0.388391i
$213$	−2.85416	−	0.927372i	−0.195564	−	0.0635425i
$214$	0.100373	+	0.308916i	0.00686135	+	0.0211171i
$215$	−1.41807	−	1.13479i	−0.0967116	−	0.0773921i
$216$	−2.00014	+	6.15581i	−0.136093	+	0.418850i
$217$	7.53556	−	10.3718i	0.511547	−	0.704084i
$218$			3.18107i			0.215449i
$219$	−21.6462	−	15.7269i	−1.46272	−	1.06273i
$220$	5.18192	−	1.42072i	0.349365	−	0.0957849i
$221$	1.83662	−	1.33438i	0.123544	−	0.0897602i
$222$	−1.90205	−	2.61795i	−0.127657	−	0.175705i
$223$	23.0414	−	7.48659i	1.54296	−	0.501339i	0.590772	−	0.806839i	$-0.298823\pi$
$223$	23.0414	−	7.48659i	1.54296	−	0.501339i	0.952192	+	0.305500i	$0.0988234\pi$
$224$	−5.62234			−0.375658
$225$	−1.27341	−	0.118939i	−0.0848939	−	0.00792930i
$226$	1.49883			0.0997009
$227$	−22.5679	+	7.33277i	−1.49789	+	0.486693i	−0.939401	−	0.342821i	$-0.888617\pi$
$227$	−22.5679	+	7.33277i	−1.49789	+	0.486693i	−0.558486	+	0.829514i	$0.688617\pi$
$228$	−8.26083	−	11.3701i	−0.547087	−	0.753000i
$229$	9.40074	−	6.83004i	0.621218	−	0.451342i	−0.232129	−	0.972685i	$-0.574569\pi$
$229$	9.40074	−	6.83004i	0.621218	−	0.451342i	0.853347	+	0.521344i	$0.174569\pi$
$230$	0.115926	−	2.48770i	0.00764395	−	0.164034i
$231$	−2.74778	−	1.99638i	−0.180790	−	0.131352i
$232$			0.316235i			0.0207619i
$233$	14.5724	−	20.0571i	0.954668	−	1.31399i	0.00524490	−	0.999986i	$-0.498330\pi$
$233$	14.5724	−	20.0571i	0.954668	−	1.31399i	0.949423	−	0.314001i	$-0.101670\pi$
$234$	0.0551386	−	0.169699i	0.00360452	−	0.0110936i
$235$	20.2447	+	0.943398i	1.32062	+	0.0615405i
$236$	2.59943	+	8.00023i	0.169209	+	0.520770i
$237$	−25.8075	−	8.38538i	−1.67638	−	0.544689i
$238$	0.475153	+	0.154386i	0.0307996	+	0.0100074i
$239$	−3.12486	−	9.61733i	−0.202130	−	0.622093i	−0.999819	−	0.0190238i	$-0.993944\pi$
$239$	−3.12486	−	9.61733i	−0.202130	−	0.622093i	0.797689	−	0.603069i	$-0.206056\pi$
$240$	−4.50062	+	11.9307i	−0.290514	+	0.770122i
$241$	5.57157	−	17.1475i	0.358896	−	1.10457i	−0.594820	−	0.803859i	$-0.702777\pi$
$241$	5.57157	−	17.1475i	0.358896	−	1.10457i	0.953716	−	0.300710i	$-0.0972235\pi$
$242$	−1.69954	+	2.33921i	−0.109250	+	0.150370i
$243$			2.65079i			0.170048i
$244$	−11.1929	−	8.13213i	−0.716553	−	0.520607i
$245$	6.08636	−	7.60571i	0.388843	−	0.485911i
$246$	3.64657	−	2.64939i	0.232497	−	0.168919i
$247$	5.94085	+	8.17688i	0.378007	+	0.520283i
$248$	−8.99950	+	2.92411i	−0.571469	+	0.185681i
$249$	4.75131			0.301102
$250$	3.40198	+	0.478367i	0.215160	+	0.0302546i
$251$	−13.5873			−0.857623			−0.428812	−	0.903394i	$-0.641068\pi$
$251$	−13.5873			−0.857623			−0.428812	+	0.903394i	$0.641068\pi$
$252$	−0.753731	+	0.244902i	−0.0474806	+	0.0154274i
$253$	2.68652	+	3.69768i	0.168900	+	0.232471i
$254$	1.25211	−	0.909710i	0.0785643	−	0.0570803i
$255$	2.31441	−	2.89216i	0.144934	−	0.181114i
$256$	−7.25666	−	5.27227i	−0.453541	−	0.329517i
$257$			18.1352i			1.13125i	0.824664	+	0.565623i	$0.191364\pi$
$257$			18.1352i			1.13125i	−0.824664	+	0.565623i	$0.808636\pi$
$258$	0.243019	−	0.334487i	0.0151297	−	0.0208242i
$259$	3.19410	−	9.83042i	0.198471	−	0.610832i
$260$	3.41421	−	9.05072i	0.211741	−	0.561302i
$261$	0.0208287	+	0.0641043i	0.00128927	+	0.00396795i
$262$	−0.934058	−	0.303494i	−0.0577063	−	0.0187499i
$263$	−1.91294	−	0.621553i	−0.117957	−	0.0383266i	0.249444	−	0.968389i	$-0.419752\pi$
$263$	−1.91294	−	0.621553i	−0.117957	−	0.0383266i	−0.367401	+	0.930063i	$0.619752\pi$
$264$	0.774678	+	2.38421i	0.0476781	+	0.146738i
$265$	−21.4507	−	0.999598i	−1.31770	−	0.0614048i
$266$	−0.687350	+	2.11545i	−0.0421441	+	0.129706i
$267$	13.1844	−	18.1468i	0.806872	−	1.11056i
$268$		−	15.4206i		−	0.941965i
$269$	−17.8188	−	12.9461i	−1.08643	−	0.789340i	−0.107640	−	0.994190i	$-0.534329\pi$
$269$	−17.8188	−	12.9461i	−1.08643	−	0.789340i	−0.978793	+	0.204850i	$0.934329\pi$
$270$	0.172501	−	3.70175i	0.0104981	−	0.225281i
$271$	−2.55313	+	1.85496i	−0.155092	+	0.112681i	−0.662625	−	0.748952i	$-0.730558\pi$
$271$	−2.55313	+	1.85496i	−0.155092	+	0.112681i	0.507533	+	0.861632i	$0.330558\pi$
$272$	2.02339	+	2.78496i	0.122686	+	0.168863i
$273$	−5.81534	+	1.88952i	−0.351960	+	0.114359i
$274$	−5.14322			−0.310714
$275$	−5.42341	+	3.21557i	−0.327044	+	0.193906i
$276$	−11.4417			−0.688711
$277$	−1.19236	+	0.387420i	−0.0716417	+	0.0232778i	−0.344619	−	0.938743i	$-0.611992\pi$
$277$	−1.19236	+	0.387420i	−0.0716417	+	0.0232778i	0.272977	+	0.962021i	$0.411992\pi$
$278$	−2.50523	−	3.44815i	−0.150254	−	0.206806i
$279$	−1.63170	+	1.18550i	−0.0976871	+	0.0709739i
$280$	4.20784	−	1.15366i	0.251467	−	0.0689442i
$281$	1.51731	+	1.10239i	0.0905152	+	0.0657631i	0.632122	−	0.774869i	$-0.282184\pi$
$281$	1.51731	+	1.10239i	0.0905152	+	0.0657631i	−0.541607	+	0.840632i	$0.682184\pi$
$282$			4.61353i			0.274732i
$283$	−1.16165	+	1.59887i	−0.0690527	+	0.0950429i	−0.842146	−	0.539249i	$-0.818708\pi$
$283$	−1.16165	+	1.59887i	−0.0690527	+	0.0950429i	0.773094	+	0.634292i	$0.218708\pi$
$284$	−1.06678	+	3.28320i	−0.0633015	+	0.194822i
$285$	12.8763	+	10.3041i	0.762725	+	0.610360i
$286$	−0.271824	−	0.836589i	−0.0160733	−	0.0494685i
$287$	13.6929	+	4.44909i	0.808266	+	0.262621i
$288$	0.841218	+	0.273328i	0.0495692	+	0.0161060i
$289$	−0.309017	−	0.951057i	−0.0181775	−	0.0559445i
$290$	−0.0478729	−	0.174611i	−0.00281119	−	0.0102535i
$291$	−3.65683	+	11.2546i	−0.214367	+	0.659754i
$292$	−18.0910	+	24.9001i	−1.05870	+	1.45717i
$293$			17.6854i			1.03319i	0.856229	+	0.516596i	$0.172801\pi$
$293$			17.6854i			1.03319i	−0.856229	+	0.516596i	$0.827199\pi$
$294$	1.79399	+	1.30341i	0.104628	+	0.0760166i
$295$	−5.42391	−	8.24708i	−0.315792	−	0.480164i
$296$	−6.17218	+	4.48435i	−0.358750	+	0.260647i
$297$	3.99761	+	5.50223i	0.231965	+	0.319272i
$298$	−4.22564	+	1.37299i	−0.244784	+	0.0795353i
$299$	8.22842			0.475862
$300$	1.46784	−	15.7152i	0.0847458	−	0.907318i
$301$	1.32064			0.0761203
$302$	2.52594	−	0.820726i	0.145351	−	0.0472275i
$303$	15.0211	+	20.6747i	0.862939	+	1.18773i
$304$	−12.3991	+	9.00844i	−0.711134	+	0.516669i
$305$	15.1898	+	5.73007i	0.869766	+	0.328103i
$306$	−0.0635872	−	0.0461988i	−0.00363504	−	0.00264101i
$307$			4.10323i			0.234184i	0.993121	+	0.117092i	$0.0373572\pi$
$307$			4.10323i			0.234184i	−0.993121	+	0.117092i	$0.962643\pi$
$308$	−2.29647	+	3.16082i	−0.130854	+	0.180105i
$309$	0.125078	−	0.384952i	0.00711546	−	0.0218991i
$310$	4.52645	−	2.97694i	0.257085	−	0.169079i
$311$	2.55206	+	7.85442i	0.144714	+	0.445383i	0.996974	−	0.0777347i	$-0.0247687\pi$
$311$	2.55206	+	7.85442i	0.144714	+	0.445383i	−0.852260	+	0.523118i	$0.824769\pi$
$312$	4.29230	+	1.39465i	0.243004	+	0.0789567i
$313$	25.6384	+	8.33043i	1.44917	+	0.470864i	0.924743	−	0.380592i	$-0.124280\pi$
$313$	25.6384	+	8.33043i	1.44917	+	0.470864i	0.524427	+	0.851456i	$0.324280\pi$
$314$	0.540066	+	1.66215i	0.0304777	+	0.0938008i
$315$	0.776988	−	0.511006i	0.0437783	−	0.0287919i
$316$	−9.64587	+	29.6869i	−0.542623	+	1.67002i
$317$	9.82050	−	13.5168i	0.551574	−	0.759177i	−0.438650	−	0.898658i	$-0.644543\pi$
$317$	9.82050	−	13.5168i	0.551574	−	0.759177i	0.990225	+	0.139481i	$0.0445434\pi$
$318$		−	4.88837i		−	0.274126i
$319$	0.268826	+	0.195313i	0.0150514	+	0.0109354i
$320$	12.1811	+	4.59509i	0.680944	+	0.256873i
$321$	−1.41668	+	1.02928i	−0.0790715	+	0.0574488i
$322$	1.06439	+	1.46501i	0.0593161	+	0.0816417i
$323$	4.23424	−	1.37579i	0.235599	−	0.0765508i
$324$	−15.5633			−0.864626
$325$	−1.05561	+	11.3017i	−0.0585547	+	0.626907i
$326$	0.313116			0.0173419
$327$	−16.3102	+	5.29951i	−0.901958	+	0.293064i
$328$	−6.24630	−	8.59729i	−0.344894	−	0.474706i
$329$	−11.9221	+	8.66192i	−0.657287	+	0.477547i
$330$	−0.788673	−	1.19918i	−0.0434150	−	0.0660128i
$331$	20.9611	+	15.2291i	1.15212	+	0.837068i	0.988762	−	0.149498i	$-0.0477659\pi$
$331$	20.9611	+	15.2291i	1.15212	+	0.837068i	0.163363	+	0.986566i	$0.447766\pi$
$332$		−	5.46553i		−	0.299960i
$333$	−0.955805	+	1.31555i	−0.0523778	+	0.0720918i
$334$	0.743676	−	2.28880i	0.0406921	−	0.125238i
$335$	4.78453	+	17.4510i	0.261407	+	0.953452i
$336$	−2.86518	−	8.81811i	−0.156308	−	0.481068i
$337$	7.36348	+	2.39254i	0.401114	+	0.130330i	0.502625	−	0.864505i	$-0.332368\pi$
$337$	7.36348	+	2.39254i	0.401114	+	0.130330i	−0.101511	+	0.994834i	$0.532368\pi$
$338$	2.29296	+	0.745029i	0.124721	+	0.0405242i
$339$	2.49699	+	7.68494i	0.135618	+	0.417388i
$340$	−3.32691	−	2.66231i	−0.180427	−	0.144384i
$341$	−3.07254	+	9.45629i	−0.166387	+	0.512087i
$342$	0.205683	−	0.283099i	0.0111221	−	0.0153082i
$343$			18.4646i			0.996993i
$344$	−0.788599	−	0.572951i	−0.0425184	−	0.0308914i
$345$	12.9482	−	3.55000i	0.697110	−	0.191126i
$346$	−1.13749	+	0.826437i	−0.0611520	+	0.0444296i
$347$	6.55796	+	9.02625i	0.352050	+	0.484555i	0.947912	−	0.318532i	$-0.103190\pi$
$347$	6.55796	+	9.02625i	0.352050	+	0.484555i	−0.595863	+	0.803086i	$0.703190\pi$
$348$	−0.791115	+	0.257049i	−0.0424082	+	0.0137793i
$349$	−35.9557			−1.92467			−0.962333	−	0.271872i	$-0.912357\pi$
$349$	−35.9557			−1.92467			−0.962333	+	0.271872i	$0.912357\pi$
$350$	−2.14874	+	1.27400i	−0.114855	+	0.0680979i
$351$	12.2441			0.653541
$352$	4.14707	−	1.34746i	0.221039	−	0.0718201i
$353$	7.73542	+	10.6469i	0.411715	+	0.566677i	0.963636	−	0.267220i	$-0.0861049\pi$
$353$	7.73542	+	10.6469i	0.411715	+	0.566677i	−0.551921	+	0.833897i	$0.686105\pi$
$354$	1.81787	−	1.32076i	0.0966187	−	0.0701976i
$355$	0.188565	−	4.04648i	0.0100080	−	0.214765i
$356$	−20.8746	−	15.1663i	−1.10635	−	0.803811i
$357$			2.69344i			0.142552i
$358$	−2.79424	+	3.84594i	−0.147680	+	0.203265i
$359$	0.258771	−	0.796417i	0.0136574	−	0.0420333i	−0.943996	−	0.329958i	$-0.892965\pi$
$359$	0.258771	−	0.796417i	0.0136574	−	0.0420333i	0.957653	+	0.287925i	$0.0929654\pi$
$360$	−0.685664	−	0.0319518i	−0.0361377	−	0.00168401i
$361$	0.253873	+	0.781340i	0.0133617	+	0.0411231i
$362$	1.28818	+	0.418556i	0.0677054	+	0.0219988i
$363$	−14.8251	−	4.81698i	−0.778118	−	0.252826i
$364$	2.17355	+	6.68950i	0.113925	+	0.350625i
$365$	12.7473	−	33.7917i	0.667224	−	1.76874i
$366$	−1.14203	+	3.51481i	−0.0596948	+	0.183722i
$367$	18.2797	−	25.1598i	0.954190	−	1.31333i	0.00454901	−	0.999990i	$-0.498552\pi$
$367$	18.2797	−	25.1598i	0.954190	−	1.31333i	0.949641	−	0.313340i	$-0.101448\pi$
$368$			12.4772i			0.650419i
$369$	−1.83245	−	1.33135i	−0.0953934	−	0.0693074i
$370$	2.72914	−	3.41042i	0.141881	−	0.177299i
$371$	12.6323	−	9.17792i	0.655838	−	0.476494i
$372$	−14.6303	−	20.1369i	−0.758545	−	1.04405i
$373$	9.97836	−	3.24217i	0.516660	−	0.167873i	−0.0390690	−	0.999237i	$-0.512439\pi$
$373$	9.97836	−	3.24217i	0.516660	−	0.167873i	0.555729	+	0.831364i	$0.312439\pi$
$374$	−0.387476			−0.0200359
$375$	3.21482	+	18.2398i	0.166012	+	0.941900i
$376$	10.8770			0.560940
$377$	0.568937	−	0.184859i	0.0293018	−	0.00952072i
$378$	1.58384	+	2.17996i	0.0814638	+	0.112125i
$379$	21.2741	−	15.4565i	1.09278	−	0.793948i	0.112910	−	0.993605i	$-0.463983\pi$
$379$	21.2741	−	15.4565i	1.09278	−	0.793948i	0.979866	+	0.199657i	$0.0639827\pi$
$380$	11.8530	−	14.8119i	0.608045	−	0.759832i
$381$	6.75029	+	4.90438i	0.345828	+	0.251259i
$382$		−	2.15847i		−	0.110437i
$383$	−14.3159	+	19.7041i	−0.731507	+	1.00683i	0.267556	+	0.963542i	$0.413784\pi$
$383$	−14.3159	+	19.7041i	−0.731507	+	1.00683i	−0.999063	+	0.0432903i	$0.986216\pi$
$384$	−4.45612	+	13.7145i	−0.227400	+	0.699866i
$385$	1.61814	−	4.28953i	0.0824682	−	0.218615i
$386$	−0.772474	−	2.37743i	−0.0393179	−	0.121008i
$387$	−0.197594	−	0.0642023i	−0.0100443	−	0.00326359i
$388$	12.9463	+	4.20652i	0.657251	+	0.213554i
$389$	5.31635	+	16.3620i	0.269550	+	0.829588i	0.990610	+	0.136716i	$0.0436549\pi$
$389$	5.31635	+	16.3620i	0.269550	+	0.829588i	−0.721061	+	0.692872i	$0.756345\pi$
$390$	−2.58114	−	0.120281i	−0.130701	−	0.00609066i
$391$	1.12005	−	3.44716i	0.0566434	−	0.174330i
$392$	3.07298	−	4.22959i	0.155209	−	0.213627i
$393$		−	5.29478i		−	0.267086i
$394$	2.43673	+	1.77038i	0.122760	+	0.0891907i
$395$	1.70502	−	36.5886i	0.0857890	−	1.84097i
$396$	0.497262	−	0.361282i	0.0249884	−	0.0181551i
$397$	−2.16365	−	2.97801i	−0.108590	−	0.149462i	0.751263	−	0.660003i	$-0.229445\pi$
$397$	−2.16365	−	2.97801i	−0.108590	−	0.149462i	−0.859853	+	0.510541i	$0.829445\pi$
$398$	1.02362	−	0.332595i	0.0513096	−	0.0166715i
$399$	−11.9916			−0.600330
$400$	−17.1374	−	1.60068i	−0.856872	−	0.0800340i
$401$	15.8505			0.791535			0.395768	−	0.918351i	$-0.370479\pi$
$401$	15.8505			0.791535			0.395768	+	0.918351i	$0.370479\pi$
$402$	−3.91758	+	1.27290i	−0.195391	+	0.0634864i
$403$	10.5215	+	14.4816i	0.524114	+	0.721381i
$404$	23.7826	−	17.2791i	1.18323	−	0.859665i
$405$	17.6125	−	4.82878i	0.875170	−	0.239944i
$406$	0.106508	+	0.0773824i	0.00528589	+	0.00384042i
$407$			8.01647i			0.397362i
$408$	1.16853	−	1.60835i	0.0578510	−	0.0796251i
$409$	−1.82872	+	5.62822i	−0.0904243	+	0.278297i	−0.986034	−	0.166543i	$-0.946740\pi$
$409$	−1.82872	+	5.62822i	−0.0904243	+	0.278297i	0.895610	+	0.444840i	$0.146740\pi$
$410$	4.75041	+	3.80145i	0.234606	+	0.187740i
$411$	−8.56837	−	26.3707i	−0.422647	−	1.30077i
$412$	−0.442818	−	0.143880i	−0.0218161	−	0.00708847i
$413$	6.82611	+	2.21794i	0.335891	+	0.109138i
$414$	−0.0880338	−	0.270940i	−0.00432663	−	0.0133160i
$415$	1.69578	+	6.18516i	0.0832424	+	0.303618i
$416$	2.42584	−	7.46597i	0.118937	−	0.366049i
$417$	13.5060	−	18.5895i	0.661394	−	0.910330i
$418$		−	1.72510i		−	0.0843772i
$419$	2.12124	+	1.54117i	0.103629	+	0.0752910i	0.638393	−	0.769711i	$-0.279599\pi$
$419$	2.12124	+	1.54117i	0.103629	+	0.0752910i	−0.534764	+	0.845002i	$0.679599\pi$
$420$	6.30636	+	9.58886i	0.307719	+	0.467888i
$421$	8.88464	−	6.45507i	0.433011	−	0.314601i	−0.349841	−	0.936809i	$-0.613764\pi$
$421$	8.88464	−	6.45507i	0.433011	−	0.314601i	0.782852	+	0.622208i	$0.213764\pi$
$422$	1.73574	+	2.38904i	0.0844946	+	0.116297i
$423$	2.20489	−	0.716412i	0.107205	−	0.0348331i
$424$	−11.5250			−0.559703
$425$	4.59099	+	1.98062i	0.222695	+	0.0960742i
$426$	0.922146			0.0446781
$427$	−11.2270	+	3.64787i	−0.543312	+	0.176533i
$428$	1.18400	+	1.62964i	0.0572309	+	0.0787716i
$429$	3.83658	−	2.78744i	0.185232	−	0.134579i
$430$	0.522164	+	0.196977i	0.0251810	+	0.00949906i
$431$	11.9905	+	8.71159i	0.577561	+	0.419622i	0.837844	−	0.545910i	$-0.183816\pi$
$431$	11.9905	+	8.71159i	0.577561	+	0.419622i	−0.260283	+	0.965532i	$0.583816\pi$
$432$			18.5664i			0.893275i
$433$	−16.1264	+	22.1961i	−0.774986	+	1.06668i	0.220831	+	0.975312i	$0.429123\pi$
$433$	−16.1264	+	22.1961i	−0.774986	+	1.06668i	−0.995817	+	0.0913649i	$0.970877\pi$
$434$	−1.21733	+	3.74655i	−0.0584336	+	0.179840i
$435$	0.815525	−	0.536351i	0.0391014	−	0.0257161i
$436$	6.09614	+	18.7620i	0.291952	+	0.898537i
$437$	15.3472	+	4.98662i	0.734158	+	0.238543i
$438$	7.81914	+	2.54059i	0.373613	+	0.121394i
$439$	−11.6028	−	35.7098i	−0.553773	−	1.70434i	−0.699163	−	0.714962i	$-0.746444\pi$
$439$	−11.6028	−	35.7098i	−0.553773	−	1.70434i	0.145391	−	0.989374i	$-0.453556\pi$
$440$	−2.82724	+	1.85941i	−0.134783	+	0.0886437i
$441$	0.344344	−	1.05978i	0.0163973	−	0.0504658i
$442$	−0.410023	+	0.564348i	−0.0195028	+	0.0268433i
$443$		−	6.27766i		−	0.298261i	−0.988818	−	0.149130i	$-0.952353\pi$
$443$		−	6.27766i		−	0.298261i	0.988818	−	0.149130i	$-0.0476474\pi$
$444$	−16.2353	−	11.7956i	−0.770494	−	0.559797i
$445$	28.3287	+	10.6865i	1.34291	+	0.506588i
$446$	−6.02265	+	4.37571i	−0.285181	+	0.207196i
$447$	−14.0794	−	19.3787i	−0.665934	−	0.916580i
$448$	−9.00321	+	2.92532i	−0.425362	+	0.138208i
$449$	2.78860			0.131602			0.0658010	−	0.997833i	$-0.479040\pi$
$449$	2.78860			0.131602			0.0658010	+	0.997833i	$0.479040\pi$
$450$	0.383430	−	0.0861559i	0.0180751	−	0.00406143i
$451$	−11.1662			−0.525797
$452$	8.84014	−	2.87234i	0.415805	−	0.135103i
$453$	8.41619	+	11.5839i	0.395427	+	0.544258i
$454$	5.89890	−	4.28580i	0.276849	−	0.201143i
$455$	−4.53528	−	6.89592i	−0.212617	−	0.323286i
$456$	7.16059	+	5.20247i	0.335325	+	0.243628i
$457$		−	27.0553i		−	1.26560i	−0.774317	−	0.632798i	$-0.781906\pi$
$457$		−	27.0553i		−	1.26560i	0.774317	−	0.632798i	$-0.218094\pi$
$458$	−2.09870	+	2.88862i	−0.0980660	+	0.134976i
$459$	1.66666	−	5.12946i	0.0777931	−	0.239423i
$460$	−4.08364	−	14.8946i	−0.190401	−	0.694466i
$461$	6.30050	+	19.3910i	0.293444	+	0.903127i	0.983740	+	0.179600i	$0.0574803\pi$
$461$	6.30050	+	19.3910i	0.293444	+	0.903127i	−0.690296	+	0.723527i	$0.742520\pi$
$462$	0.992563	+	0.322503i	0.0461782	+	0.0150042i
$463$	−33.6715	−	10.9405i	−1.56485	−	0.508449i	−0.606749	−	0.794894i	$-0.707527\pi$
$463$	−33.6715	−	10.9405i	−1.56485	−	0.508449i	−0.958097	+	0.286445i	$0.907527\pi$
$464$	0.280312	+	0.862711i	0.0130131	+	0.0400503i
$465$	22.8045	+	18.2489i	1.05753	+	0.846275i
$466$	−2.35408	+	7.24512i	−0.109051	+	0.335624i
$467$	6.74496	−	9.28364i	0.312119	−	0.429595i	−0.623921	−	0.781487i	$-0.714461\pi$
$467$	6.74496	−	9.28364i	0.312119	−	0.429595i	0.936041	+	0.351892i	$0.114461\pi$
$468$		−	1.10655i		−	0.0511505i
$469$	−10.6446	−	7.73378i	−0.491524	−	0.357113i
$470$	−6.00581	+	1.64660i	−0.277027	+	0.0759522i
$471$	−7.62260	+	5.53814i	−0.351231	+	0.255184i
$472$	−3.11387	−	4.28588i	−0.143328	−	0.197274i
$473$	−0.974109	+	0.316507i	−0.0447896	+	0.0145530i
$474$	8.33812			0.382983
$475$	−8.81800	+	20.4397i	−0.404597	+	0.937838i
$476$	3.09832			0.142011
$477$	−2.33624	+	0.759090i	−0.106969	+	0.0347563i
$478$	1.82640	+	2.51382i	0.0835374	+	0.114979i
$479$	21.7352	−	15.7915i	0.993106	−	0.721533i	0.0325066	−	0.999472i	$-0.489651\pi$
$479$	21.7352	−	15.7915i	0.993106	−	0.721533i	0.960599	+	0.277938i	$0.0896510\pi$
$480$	0.596246	−	12.7950i	0.0272148	−	0.584010i
$481$	11.6758	+	8.48295i	0.532370	+	0.386789i
$482$			5.54017i			0.252348i
$483$	−5.73828	+	7.89806i	−0.261101	+	0.359374i
$484$	−5.54107	+	17.0537i	−0.251867	+	0.775166i
$485$	−15.9561	−	0.743553i	−0.724530	−	0.0337630i
$486$	−0.251701	−	0.774656i	−0.0114174	−	0.0351391i
$487$	−17.9419	−	5.82968i	−0.813026	−	0.264168i	−0.127147	−	0.991884i	$-0.540582\pi$
$487$	−17.9419	−	5.82968i	−0.813026	−	0.264168i	−0.685879	+	0.727716i	$0.740582\pi$
$488$	8.28664	+	2.69249i	0.375119	+	0.121883i
$489$	0.521637	+	1.60543i	0.0235892	+	0.0726002i
$490$	−1.05647	+	2.80059i	−0.0477264	+	0.126518i
$491$	−9.34393	+	28.7577i	−0.421686	+	1.29782i	0.484447	+	0.874821i	$0.339021\pi$
$491$	−9.34393	+	28.7577i	−0.421686	+	1.29782i	−0.906132	+	0.422994i	$0.860979\pi$
$492$	16.4303	−	22.6143i	0.740734	−	1.01953i
$493$		−	0.263510i		−	0.0118679i
$494$	−2.51256	−	1.82548i	−0.113045	−	0.0821322i
$495$	−0.450642	+	0.563136i	−0.0202548	+	0.0253111i
$496$	−21.9593	+	15.9543i	−0.986000	+	0.716371i
$497$	1.73133	+	2.38297i	0.0776609	+	0.106891i
$498$	−1.38850	+	0.451153i	−0.0622204	+	0.0202166i
$499$	−9.75671			−0.436770			−0.218385	−	0.975863i	$-0.570079\pi$
$499$	−9.75671			−0.436770			−0.218385	+	0.975863i	$0.570079\pi$
$500$	20.9816	−	3.69807i	0.938328	−	0.165383i
$501$	12.9742			0.579646
$502$	3.97071	−	1.29016i	0.177221	−	0.0575827i
$503$	−16.0480	−	22.0882i	−0.715546	−	0.984865i	−0.999660	−	0.0260741i	$-0.991699\pi$
$503$	−16.0480	−	22.0882i	−0.715546	−	0.984865i	0.284114	−	0.958791i	$-0.408301\pi$
$504$	0.403788	−	0.293369i	0.0179862	−	0.0130677i
$505$	−21.5529	+	26.9331i	−0.959090	+	1.19851i
$506$	−1.13621	−	0.825503i	−0.0505106	−	0.0366981i
$507$			12.9978i			0.577254i
$508$	5.64160	−	7.76500i	0.250306	−	0.344516i
$509$	−9.82910	+	30.2509i	−0.435667	+	1.34085i	0.456734	+	0.889603i	$0.349019\pi$
$509$	−9.82910	+	30.2509i	−0.435667	+	1.34085i	−0.892401	+	0.451243i	$0.850981\pi$
$510$	−0.401734	+	1.06495i	−0.0177891	+	0.0471570i
$511$	8.11516	+	24.9759i	0.358994	+	1.10487i
$512$	19.1790	+	6.23165i	0.847602	+	0.275403i
$513$	22.8371	+	7.42021i	1.00828	+	0.327610i
$514$	−1.72200	−	5.29978i	−0.0759543	−	0.233763i
$515$	0.545765	+	0.0254325i	0.0240493	+	0.00112069i
$516$	0.792325	−	2.43853i	0.0348802	−	0.107350i
$517$	6.71787	−	9.24636i	0.295452	−	0.406654i
$518$			3.17610i			0.139550i
$519$	−6.13239	−	4.45544i	−0.269182	−	0.195572i
$520$	−0.283579	+	6.08540i	−0.0124357	+	0.266862i
$521$	−22.5291	+	16.3684i	−0.987019	+	0.717111i	−0.959266	−	0.282503i	$-0.908835\pi$
$521$	−22.5291	+	16.3684i	−0.987019	+	0.717111i	−0.0277529	+	0.999615i	$0.508835\pi$
$522$	−0.0121738	−	0.0167558i	−0.000532834	−	0.000733383i
$523$	22.8220	−	7.41533i	0.997938	−	0.324250i	0.235897	−	0.971778i	$-0.424197\pi$
$523$	22.8220	−	7.41533i	0.997938	−	0.324250i	0.762041	+	0.647528i	$0.224197\pi$
$524$	−6.09070			−0.266073
$525$	−10.1118	−	8.89475i	−0.441316	−	0.388199i
$526$	0.618050			0.0269483
$527$	7.49902	−	2.43658i	0.326662	−	0.106139i
$528$	4.22674	+	5.81761i	0.183945	+	0.253179i
$529$	−7.97898	+	5.79707i	−0.346912	+	0.252046i
$530$	6.36358	−	1.74469i	0.276416	−	0.0757847i
$531$	−0.913503	−	0.663698i	−0.0396426	−	0.0288021i
$532$			13.7942i			0.598052i
$533$	−11.8160	+	16.2633i	−0.511807	+	0.704442i
$534$	−2.12986	+	6.55505i	−0.0921682	+	0.283665i
$535$	−1.84552	−	1.47685i	−0.0797889	−	0.0638499i
$536$	3.00103	+	9.23623i	0.129625	+	0.398944i
$537$	−24.3743	−	7.91969i	−1.05183	−	0.341760i
$538$	6.43659	+	2.09138i	0.277501	+	0.0901656i
$539$	−1.69756	−	5.22456i	−0.0731191	−	0.225038i
$540$	−6.07655	−	22.1636i	−0.261493	−	0.953767i
$541$	13.7528	−	42.3267i	0.591278	−	1.81977i	0.0188356	−	0.999823i	$-0.494004\pi$
$541$	13.7528	−	42.3267i	0.591278	−	1.81977i	0.572443	−	0.819945i	$-0.305996\pi$
$542$	0.569984	−	0.784515i	0.0244829	−	0.0336978i
$543$			7.30216i			0.313366i
$544$	−2.79754	−	2.03253i	−0.119943	−	0.0871440i
$545$	−12.7201	−	19.3409i	−0.544867	−	0.828474i
$546$	1.52004	−	1.10437i	0.0650516	−	0.0472628i
$547$	−19.5171	−	26.8630i	−0.834490	−	1.14858i	−0.987071	−	0.160287i	$-0.948758\pi$
$547$	−19.5171	−	26.8630i	−0.834490	−	1.14858i	0.152580	−	0.988291i	$-0.451242\pi$
$548$	−30.3348	+	9.85638i	−1.29584	+	0.421044i
$549$	1.85713			0.0792603
$550$	1.27959	−	1.45468i	0.0545619	−	0.0620276i
$551$	1.17318			0.0499793
$552$	6.85305	−	2.22669i	0.291685	−	0.0947743i
$553$	15.6549	+	21.5471i	0.665712	+	0.916274i
$554$	0.311663	−	0.226436i	0.0132413	−	0.00962036i
$555$	22.0328	+	8.31146i	0.935240	+	0.352802i
$556$	−21.3839	−	15.5363i	−0.906877	−	0.658885i
$557$		−	33.3269i		−	1.41210i	−0.708160	−	0.706052i	$-0.750474\pi$
$557$		−	33.3269i		−	1.41210i	0.708160	−	0.706052i	$-0.249526\pi$
$558$	0.364274	−	0.501381i	0.0154210	−	0.0212251i
$559$	−0.569808	+	1.75369i	−0.0241003	+	0.0741731i
$560$	10.4567	−	6.87709i	0.441874	−	0.290610i
$561$	−0.645517	−	1.98670i	−0.0272537	−	0.0838784i
$562$	−0.548089	−	0.178085i	−0.0231197	−	0.00751206i
$563$	−21.9439	−	7.13002i	−0.924826	−	0.300494i	−0.192381	−	0.981320i	$-0.561621\pi$
$563$	−21.9439	−	7.13002i	−0.924826	−	0.300494i	−0.732445	+	0.680826i	$0.761621\pi$
$564$	8.84128	+	27.2107i	0.372285	+	1.14578i
$565$	−9.11291	+	5.99334i	−0.383383	+	0.252142i
$566$	0.187657	−	0.577550i	0.00788783	−	0.0242762i
$567$	−7.80532	+	10.7431i	−0.327793	+	0.451168i
$568$		−	2.17409i		−	0.0912227i
$569$	−34.0916	−	24.7690i	−1.42920	−	1.03837i	−0.990166	−	0.139899i	$-0.955322\pi$
$569$	−34.0916	−	24.7690i	−1.42920	−	1.03837i	−0.439030	−	0.898473i	$-0.644678\pi$
$570$	−4.74133	−	1.78858i	−0.198592	−	0.0749152i
$571$	−20.6550	+	15.0068i	−0.864386	+	0.628013i	−0.929075	−	0.369892i	$-0.879395\pi$
$571$	−20.6550	+	15.0068i	−0.864386	+	0.628013i	0.0646885	+	0.997906i	$0.479395\pi$
$572$	−3.20645	−	4.41329i	−0.134068	−	0.184529i
$573$	11.0671	−	3.59591i	0.462333	−	0.150221i
$574$	−4.42402			−0.184655
$575$	9.24265	+	15.5888i	0.385445	+	0.650096i
$576$	1.48928			0.0620533
$577$	−36.5263	+	11.8681i	−1.52061	+	0.494076i	−0.945949	−	0.324315i	$-0.894866\pi$
$577$	−36.5263	+	11.8681i	−1.52061	+	0.494076i	−0.574661	+	0.818391i	$0.694866\pi$
$578$	0.180612	+	0.248591i	0.00751247	+	0.0103400i
$579$	10.9028	−	7.92138i	0.453107	−	0.329201i
$580$	−0.616976	−	0.938116i	−0.0256185	−	0.0389531i
$581$	−3.77277	−	2.74108i	−0.156521	−	0.113719i
$582$		−	3.63622i		−	0.150726i
$583$	−7.11807	+	9.79718i	−0.294800	+	0.405758i
$584$	5.98980	−	18.4347i	0.247860	−	0.762834i
$585$	0.343328	+	1.25225i	0.0141949	+	0.0517743i
$586$	−1.67929	−	5.16832i	−0.0693708	−	0.213501i
$587$	7.91504	+	2.57175i	0.326688	+	0.106148i	0.467769	−	0.883851i	$-0.345058\pi$
$587$	7.91504	+	2.57175i	0.326688	+	0.106148i	−0.141081	+	0.989998i	$0.545058\pi$
$588$	13.0788	+	4.24957i	0.539362	+	0.175249i
$589$	10.8480	+	33.3867i	0.446984	+	1.37567i
$590$	2.36815	+	1.89508i	0.0974953	+	0.0780192i
$591$	−5.01778	+	15.4431i	−0.206404	+	0.635246i
$592$	−12.8632	+	17.7046i	−0.528672	+	0.727655i
$593$		−	30.6734i		−	1.25961i	−0.776754	−	0.629804i	$-0.783135\pi$
$593$		−	30.6734i		−	1.25961i	0.776754	−	0.629804i	$-0.216865\pi$
$594$	−1.69070	−	1.22837i	−0.0693704	−	0.0504005i
$595$	−3.50627	+	0.961309i	−0.143743	+	0.0394098i
$596$	−22.2917	+	16.1959i	−0.913103	+	0.663408i
$597$	3.41062	+	4.69431i	0.139587	+	0.192125i
$598$	−2.40465	+	0.781317i	−0.0983333	+	0.0319504i
$599$	30.2644			1.23657			0.618285	−	0.785954i	$-0.287828\pi$
$599$	30.2644			1.23657			0.618285	+	0.785954i	$0.287828\pi$
$600$	2.17919	+	9.69832i	0.0889652	+	0.395932i
$601$	5.40895			0.220636			0.110318	−	0.993896i	$-0.464813\pi$
$601$	5.40895			0.220636			0.110318	+	0.993896i	$0.464813\pi$
$602$	−0.385938	+	0.125399i	−0.0157297	+	0.00511088i
$603$	1.21668	+	1.67462i	0.0495471	+	0.0681957i
$604$	13.3252	−	9.68131i	0.542194	−	0.393927i
$605$	0.979449	−	21.0183i	0.0398203	−	0.854515i
$606$	−6.35285	−	4.61561i	−0.258067	−	0.187496i
$607$		−	18.4222i		−	0.747735i	−0.927482	−	0.373868i	$-0.878031\pi$
$607$		−	18.4222i		−	0.747735i	0.927482	−	0.373868i	$-0.121969\pi$
$608$	9.04911	−	12.4550i	0.366990	−	0.505118i
$609$	−0.219324	+	0.675010i	−0.00888746	+	0.0273528i
$610$	−4.98311	−	0.232212i	−0.201760	−	0.00940199i
$611$	−6.35829	−	19.5688i	−0.257229	−	0.791669i
$612$	−0.463572	−	0.150624i	−0.0187388	−	0.00608861i
$613$	−1.42032	−	0.461489i	−0.0573661	−	0.0186394i	0.280193	−	0.959944i	$-0.409601\pi$
$613$	−1.42032	−	0.461489i	−0.0573661	−	0.0186394i	−0.337559	+	0.941304i	$0.609601\pi$
$614$	−0.389615	−	1.19911i	−0.0157236	−	0.0483922i
$615$	−11.5771	+	30.6897i	−0.466835	+	1.23753i
$616$	0.760346	−	2.34010i	0.0306352	−	0.0942855i
$617$	15.8990	−	21.8831i	0.640068	−	0.880978i	−0.358551	−	0.933510i	$-0.616729\pi$
$617$	15.8990	−	21.8831i	0.640068	−	0.880978i	0.998619	+	0.0525317i	$0.0167291\pi$
$618$			0.124374i			0.00500304i
$619$	−8.54582	−	6.20890i	−0.343486	−	0.249557i	0.402645	−	0.915356i	$-0.368091\pi$
$619$	−8.54582	−	6.20890i	−0.343486	−	0.249557i	−0.746131	+	0.665799i	$0.768091\pi$
$620$	20.9921	−	26.2324i	0.843065	−	1.05352i
$621$	15.8153	−	11.4905i	0.634647	−	0.461098i
$622$	−1.49161	−	2.05302i	−0.0598080	−	0.0823187i
$623$	−20.9381	+	6.80321i	−0.838868	+	0.272565i
$624$	12.9459			0.518250
$625$	−22.5969	+	10.6949i	−0.903875	+	0.427797i
$626$	−8.28349			−0.331075
$627$	8.84505	−	2.87393i	0.353237	−	0.114774i
$628$	6.37064	+	8.76843i	0.254216	+	0.349899i
$629$	5.14309	−	3.73668i	0.205069	−	0.148991i
$630$	−0.178542	+	0.223112i	−0.00711330	+	0.00888901i
$631$	−26.4354	−	19.2064i	−1.05238	−	0.764596i	−0.0797134	−	0.996818i	$-0.525401\pi$
$631$	−26.4354	−	19.2064i	−1.05238	−	0.764596i	−0.972663	+	0.232222i	$0.925401\pi$
$632$		−	19.6583i		−	0.781964i
$633$	−9.35763	+	12.8797i	−0.371932	+	0.511921i
$634$	−1.58645	+	4.88258i	−0.0630058	+	0.193912i
$635$	−3.97519	+	10.5378i	−0.157751	+	0.418180i
$636$	−9.36797	−	28.8316i	−0.371464	−	1.14325i
$637$	−9.40577	−	3.05612i	−0.372670	−	0.121088i
$638$	−0.0971063	−	0.0315518i	−0.00384448	−	0.00124915i
$639$	−0.143195	−	0.440710i	−0.00566472	−	0.0174342i
$640$	−19.4437	−	0.906075i	−0.768581	−	0.0358157i
$641$	−10.9862	+	33.8121i	−0.433930	+	1.33550i	0.460249	+	0.887790i	$0.347760\pi$
$641$	−10.9862	+	33.8121i	−0.433930	+	1.33550i	−0.894179	+	0.447709i	$0.852240\pi$
$642$	0.316273	−	0.435312i	0.0124823	−	0.0171804i
$643$		−	38.1043i		−	1.50269i	−0.659911	−	0.751344i	$-0.729406\pi$
$643$		−	38.1043i		−	1.50269i	0.659911	−	0.751344i	$-0.270594\pi$
$644$	9.08530	+	6.60086i	0.358011	+	0.260110i
$645$	−0.140053	+	3.00544i	−0.00551457	+	0.118339i
$646$	−1.10676	+	0.804110i	−0.0435450	+	0.0316373i
$647$	−20.1603	−	27.7482i	−0.792582	−	1.09090i	−0.993782	−	0.111345i	$-0.964484\pi$
$647$	−20.1603	−	27.7482i	−0.792582	−	1.09090i	0.201200	−	0.979550i	$-0.435516\pi$
$648$	9.32166	−	3.02879i	0.366189	−	0.118982i
$649$	−5.56653			−0.218506
$650$	−0.764650	−	3.40301i	−0.0299920	−	0.133477i
$651$	−21.2376			−0.832367
$652$	1.84676	−	0.600050i	0.0723248	−	0.0234998i
$653$	9.95976	+	13.7084i	0.389755	+	0.536452i	0.958136	−	0.286314i	$-0.0924299\pi$
$653$	9.95976	+	13.7084i	0.389755	+	0.536452i	−0.568381	+	0.822766i	$0.692430\pi$
$654$	4.26324	−	3.09742i	0.166706	−	0.121119i
$655$	6.89265	−	1.88975i	0.269318	−	0.0738386i
$656$	−24.6609	−	17.9172i	−0.962848	−	0.699550i
$657$		−	4.13143i		−	0.161182i
$658$	2.66160	−	3.66337i	0.103760	−	0.142813i
$659$	−5.83334	+	17.9532i	−0.227234	+	0.699356i	0.770823	+	0.637050i	$0.219845\pi$
$659$	−5.83334	+	17.9532i	−0.227234	+	0.699356i	−0.998057	+	0.0623060i	$0.980155\pi$
$660$	−6.94970	−	5.56139i	−0.270517	−	0.216477i
$661$	−1.07593	−	3.31136i	−0.0418486	−	0.128797i	0.927949	−	0.372706i	$-0.121570\pi$
$661$	−1.07593	−	3.31136i	−0.0418486	−	0.128797i	−0.969798	+	0.243909i	$0.921570\pi$
$662$	−7.57164	−	2.46018i	−0.294280	−	0.0956175i
$663$	−3.57665	−	1.16212i	−0.138906	−	0.0451331i
$664$	1.06365	+	3.27359i	0.0412778	+	0.127040i
$665$	−4.27988	−	15.6104i	−0.165967	−	0.605346i
$666$	0.154405	−	0.475209i	0.00598307	−	0.0184140i
$667$	0.561398	−	0.772698i	0.0217374	−	0.0299190i
$668$		−	14.9245i		−	0.577448i
$669$	−32.4689	−	23.5901i	−1.25532	−	0.912045i
$670$	−3.05525	−	4.64552i	−0.118035	−	0.179472i
$671$	7.40683	−	5.38138i	0.285937	−	0.207746i
$672$	5.47450	+	7.53500i	0.211183	+	0.290669i
$673$	25.9272	−	8.42424i	0.999418	−	0.324731i	0.236785	−	0.971562i	$-0.423906\pi$
$673$	25.9272	−	8.42424i	0.999418	−	0.324731i	0.762633	+	0.646831i	$0.223906\pi$
$674$	−2.37906			−0.0916378
$675$	13.7533	+	23.1964i	0.529364	+	0.892831i
$676$	14.9517			0.575065
$677$	−31.7265	+	10.3086i	−1.21935	+	0.396191i	−0.846845	−	0.531839i	$-0.821501\pi$
$677$	−31.7265	+	10.3086i	−1.21935	+	0.396191i	−0.372505	+	0.928030i	$0.621501\pi$
$678$	−1.45942	−	2.00872i	−0.0560487	−	0.0771445i
$679$	9.39658	−	6.82701i	0.360608	−	0.261997i
$680$	2.51078	+	0.947143i	0.0962839	+	0.0363213i
$681$	31.8018	+	23.1054i	1.21865	+	0.885400i
$682$		−	3.05522i		−	0.116990i
$683$	16.8424	−	23.1816i	0.644457	−	0.887019i	−0.354386	−	0.935099i	$-0.615310\pi$
$683$	16.8424	−	23.1816i	0.644457	−	0.887019i	0.998843	+	0.0480799i	$0.0153102\pi$
$684$	0.670598	−	2.06389i	0.0256410	−	0.0789148i
$685$	31.2708	−	20.5661i	1.19480	−	0.785789i
$686$	−1.75327	−	5.39602i	−0.0669403	−	0.206021i
$687$	−18.3071	−	5.94833i	−0.698459	−	0.226943i
$688$	−2.65921	−	0.864031i	−0.101382	−	0.0329409i
$689$	6.73706	+	20.7345i	0.256662	+	0.789923i
$690$	−3.44686	+	2.26692i	−0.131220	+	0.0863001i
$691$	3.78994	−	11.6642i	0.144176	−	0.443729i	−0.852728	−	0.522355i	$-0.825053\pi$
$691$	3.78994	−	11.6642i	0.144176	−	0.443729i	0.996904	+	0.0786266i	$0.0250535\pi$
$692$	−5.12518	+	7.05421i	−0.194830	+	0.268161i
$693$		−	0.524444i		−	0.0199220i
$694$	−2.77355	−	2.01510i	−0.105282	−	0.0764922i
$695$	29.0198	+	10.9472i	1.10079	+	0.415251i
$696$	0.423816	−	0.307920i	0.0160647	−	0.0116717i
$697$	5.20486	+	7.16387i	0.197148	+	0.271351i
$698$	10.5076	−	3.41412i	0.397718	−	0.129226i
$699$	−41.0696			−1.55339
$700$	−10.2318	+	11.6318i	−0.386726	+	0.439642i
$701$	8.58406			0.324216			0.162108	−	0.986773i	$-0.448171\pi$
$701$	8.58406			0.324216			0.162108	+	0.986773i	$0.448171\pi$
$702$	−3.57817	+	1.16262i	−0.135049	+	0.0438802i
$703$	16.6362	+	22.8978i	0.627446	+	0.863606i
$704$	5.93972	−	4.31546i	0.223862	−	0.162645i
$705$	−18.4480	−	28.0503i	−0.694792	−	1.05644i
$706$	−3.27153	−	2.37691i	−0.123126	−	0.0894560i
$707$		−	25.0826i		−	0.943328i
$708$	8.19074	−	11.2736i	0.307827	−	0.423688i
$709$	−1.49331	+	4.59593i	−0.0560824	+	0.172604i	−0.975174	−	0.221440i	$-0.928924\pi$
$709$	−1.49331	+	4.59593i	−0.0560824	+	0.172604i	0.919092	+	0.394044i	$0.128924\pi$
$710$	0.329121	+	1.20043i	0.0123517	+	0.0450514i
$711$	−1.29479	−	3.98494i	−0.0485582	−	0.149447i
$712$	15.4544	+	5.02145i	0.579179	+	0.188187i
$713$	27.1806	+	8.83153i	1.01792	+	0.330743i
$714$	−0.255751	−	0.787122i	−0.00957125	−	0.0294573i
$715$	4.99794	+	3.99953i	0.186912	+	0.149574i
$716$	−9.11019	+	28.0383i	−0.340464	+	1.04784i
$717$	−9.84635	+	13.5523i	−0.367719	+	0.506122i
$718$			0.257313i			0.00960284i
$719$	29.7275	+	21.5983i	1.10865	+	0.805481i	0.982450	−	0.186524i	$-0.0597222\pi$
$719$	29.7275	+	21.5983i	1.10865	+	0.805481i	0.126199	+	0.992005i	$0.459722\pi$
$720$	−1.89886	+	0.520607i	−0.0707663	+	0.0194019i
$721$	−0.321401	+	0.233512i	−0.0119696	+	0.00869643i
$722$	−0.148382	−	0.204230i	−0.00552219	−	0.00760065i
$723$	−28.4060	+	9.22967i	−1.05643	+	0.343255i
$724$	8.39983			0.312177
$725$	0.989279	+	0.870208i	0.0367409	+	0.0323187i
$726$	4.78983			0.177767
$727$	8.56722	−	2.78366i	0.317741	−	0.103240i	−0.145805	−	0.989313i	$-0.546577\pi$
$727$	8.56722	−	2.78366i	0.317741	−	0.103240i	0.463545	+	0.886073i	$0.346577\pi$
$728$	−2.60371	−	3.58370i	−0.0964999	−	0.132821i
$729$	23.3748	−	16.9828i	0.865732	−	0.628991i
$730$	−0.516586	+	11.0856i	−0.0191197	+	0.410296i
$731$	0.657117	+	0.477423i	0.0243043	+	0.0176581i
$732$			22.9189i			0.847108i
$733$	−1.50589	+	2.07268i	−0.0556214	+	0.0765563i	−0.835922	−	0.548849i	$-0.815066\pi$
$733$	−1.50589	+	2.07268i	−0.0556214	+	0.0765563i	0.780300	+	0.625405i	$0.215066\pi$
$734$	−2.95297	+	9.08832i	−0.108996	+	0.335456i
$735$	−16.1194	−	0.751162i	−0.594574	−	0.0277070i
$736$	−3.87308	−	11.9201i	−0.142763	−	0.439381i
$737$	9.70504	+	3.15336i	0.357490	+	0.116155i
$738$	0.661924	+	0.215072i	0.0243658	+	0.00791692i
$739$	−5.57735	−	17.1653i	−0.205166	−	0.631436i	−0.999707	−	0.0242249i	$-0.992288\pi$
$739$	−5.57735	−	17.1653i	−0.205166	−	0.631436i	0.794541	−	0.607211i	$-0.207712\pi$
$740$	9.56085	−	25.3448i	0.351464	−	0.931693i
$741$	5.17394	−	15.9237i	0.190069	−	0.584973i
$742$	−2.82015	+	3.88161i	−0.103531	+	0.142498i
$743$		−	41.8213i		−	1.53427i	−0.641483	−	0.767137i	$-0.721681\pi$
$743$		−	41.8213i		−	1.53427i	0.641483	−	0.767137i	$-0.278319\pi$
$744$	12.6817	+	9.21381i	0.464934	+	0.337795i
$745$	20.2017	−	25.2447i	0.740134	−	0.924895i
$746$	−2.60819	+	1.89496i	−0.0954925	+	0.0693794i
$747$	0.431228	+	0.593534i	0.0157778	+	0.0217163i
$748$	−2.28534	+	0.742551i	−0.0835602	+	0.0271504i
$749$	1.71872			0.0628006
$750$	−2.67142	−	5.02508i	−0.0975465	−	0.183490i
$751$	−40.9365			−1.49379			−0.746897	−	0.664939i	$-0.768457\pi$
$751$	−40.9365			−1.49379			−0.746897	+	0.664939i	$0.768457\pi$
$752$	29.6732	−	9.64142i	1.08207	−	0.351586i
$753$	13.2300	+	18.2096i	0.482129	+	0.663594i
$754$	−0.148711	+	0.108045i	−0.00541574	+	0.00393477i
$755$	−12.0759	+	15.0904i	−0.439487	+	0.549196i
$756$	13.5191	+	9.82223i	0.491686	+	0.357231i
$757$			43.0585i			1.56499i	0.622658	+	0.782494i	$0.286053\pi$
$757$			43.0585i			1.56499i	−0.622658	+	0.782494i	$0.713947\pi$
$758$	−4.74941	+	6.53701i	−0.172506	+	0.237435i
$759$	2.33971	−	7.20090i	0.0849262	−	0.261376i
$760$	−4.21682	+	11.1783i	−0.152960	+	0.405481i
$761$	−0.149790	−	0.461006i	−0.00542988	−	0.0167115i	0.948305	−	0.317361i	$-0.102797\pi$
$761$	−0.149790	−	0.461006i	−0.00542988	−	0.0167115i	−0.953735	+	0.300649i	$0.902797\pi$
$762$	−2.43837	−	0.792274i	−0.0883328	−	0.0287011i
$763$	16.0085	+	5.20147i	0.579546	+	0.188306i
$764$	−4.13645	−	12.7307i	−0.149651	−	0.460580i
$765$	0.571344	+	0.0266245i	0.0206570	+	0.000962612i
$766$	2.31265	−	7.11760i	0.0835594	−	0.257169i
$767$	−5.89045	+	8.10751i	−0.212692	+	0.292745i
$768$			14.8589i			0.536176i
$769$	20.8561	+	15.1528i	0.752090	+	0.546426i	0.896474	−	0.443096i	$-0.146120\pi$
$769$	20.8561	+	15.1528i	0.752090	+	0.546426i	−0.144384	+	0.989522i	$0.546120\pi$
$770$	−0.0655755	+	1.40720i	−0.00236318	+	0.0507121i
$771$	24.3047	−	17.6584i	0.875311	−	0.635951i
$772$	−9.11212	−	12.5418i	−0.327952	−	0.451388i
$773$	−22.4258	+	7.28659i	−0.806600	+	0.262080i	−0.683157	−	0.730271i	$-0.739394\pi$
$773$	−22.4258	+	7.28659i	−0.806600	+	0.262080i	−0.123443	+	0.992352i	$0.539394\pi$
$774$	0.0638405			0.00229470
$775$	−15.6171	+	36.1996i	−0.560981	+	1.30033i
$776$	−8.57289			−0.307749
$777$	−16.2847	+	5.29123i	−0.584211	+	0.189822i
$778$	−3.10726	−	4.27678i	−0.111401	−	0.153330i
$779$	−31.8946	+	23.1728i	−1.14274	+	0.830250i
$780$	−15.4541	+	4.23703i	−0.553346	+	0.151710i
$781$	−1.84815	−	1.34276i	−0.0661320	−	0.0480477i
$782$			1.11374i			0.0398272i
$783$	0.835373	−	1.14979i	0.0298538	−	0.0410902i
$784$	4.63416	−	14.2625i	0.165506	−	0.509374i
$785$	−9.93002	−	7.94635i	−0.354417	−	0.283618i
$786$	0.502758	+	1.54733i	0.0179328	+	0.0551914i
$787$	23.6623	+	7.68835i	0.843470	+	0.274060i	0.698709	−	0.715406i	$-0.253758\pi$
$787$	23.6623	+	7.68835i	0.843470	+	0.274060i	0.144762	+	0.989467i	$0.453758\pi$
$788$	17.7646	+	5.77206i	0.632837	+	0.205621i
$789$	1.02964	+	3.16891i	0.0366562	+	0.112816i
$790$	2.97594	+	10.8544i	0.105879	+	0.386183i
$791$	2.45079	−	7.54276i	0.0871401	−	0.268190i
$792$	−0.227527	+	0.313164i	−0.00808481	+	0.0111278i
$793$		−	16.4824i		−	0.585306i
$794$	0.915069	+	0.664837i	0.0324746	+	0.0235942i
$795$	19.5470	+	29.7213i	0.693260	+	1.05411i
$796$	5.39997	−	3.92330i	0.191397	−	0.139058i
$797$	−0.239995	−	0.330324i	−0.00850104	−	0.0117007i	0.804745	−	0.593620i	$-0.202302\pi$
$797$	−0.239995	−	0.330324i	−0.00850104	−	0.0117007i	−0.813246	+	0.581920i	$0.802302\pi$
$798$	3.50438	−	1.13864i	0.124054	−	0.0403074i
$799$	−9.06352			−0.320644
$800$	16.8691	−	3.79046i	0.596414	−	0.134013i
$801$	3.46351			0.122377
$802$	−4.63209	+	1.50506i	−0.163565	+	0.0531454i
$803$	−11.9716	−	16.4775i	−0.422468	−	0.581477i
$804$	−20.6666	+	15.0151i	−0.728854	+	0.529543i
$805$	−12.3296	−	4.65110i	−0.434561	−	0.163930i
$806$	−4.44985	−	3.23300i	−0.156739	−	0.113878i
$807$			36.4863i			1.28438i
$808$	−10.8819	+	14.9777i	−0.382825	+	0.526914i
$809$	−4.24448	+	13.0632i	−0.149228	+	0.459276i	−0.997530	−	0.0702355i	$-0.977625\pi$
$809$	−4.24448	+	13.0632i	−0.149228	+	0.459276i	0.848302	+	0.529512i	$0.177625\pi$
$810$	−4.68849	+	3.08351i	−0.164737	+	0.108343i
$811$	−10.8192	−	33.2982i	−0.379915	−	1.16926i	−0.940103	−	0.340891i	$-0.889271\pi$
$811$	−10.8192	−	33.2982i	−0.379915	−	1.16926i	0.560188	−	0.828365i	$-0.310729\pi$
$812$	0.776478	+	0.252293i	0.0272491	+	0.00885375i
$813$	4.97199	+	1.61550i	0.174375	+	0.0566580i
$814$	−0.761191	−	2.34271i	−0.0266797	−	0.0821118i
$815$	−1.90375	+	1.25205i	−0.0666853	+	0.0438573i
$816$	1.76219	−	5.42347i	0.0616890	−	0.189859i
$817$	−2.12555	+	2.92557i	−0.0743637	+	0.102353i
$818$		−	1.81841i		−	0.0635793i
$819$	−0.763838	−	0.554961i	−0.0266907	−	0.0193919i
$820$	35.3030	+	13.3174i	1.23284	+	0.465064i
$821$	−37.5481	+	27.2803i	−1.31044	+	0.952090i	−0.310441	+	0.950593i	$0.600477\pi$
$821$	−37.5481	+	27.2803i	−1.31044	+	0.952090i	−0.999999	+	0.00149716i	$0.999523\pi$
$822$	5.00798	+	6.89290i	0.174673	+	0.240417i
$823$	−20.8902	+	6.78763i	−0.728186	+	0.236602i	−0.649569	−	0.760303i	$-0.725050\pi$
$823$	−20.8902	+	6.78763i	−0.728186	+	0.236602i	−0.0786172	+	0.996905i	$0.525050\pi$
$824$	0.293228			0.0102151
$825$	9.59027	+	4.13739i	0.333890	+	0.144045i
$826$	−2.20544			−0.0767371
$827$	34.5742	−	11.2338i	1.20226	−	0.390639i	0.361670	−	0.932306i	$-0.382207\pi$
$827$	34.5742	−	11.2338i	1.20226	−	0.390639i	0.840593	+	0.541667i	$0.182207\pi$
$828$	−1.03845	−	1.42930i	−0.0360886	−	0.0496717i
$829$	−12.3444	+	8.96872i	−0.428738	+	0.311496i	−0.781144	−	0.624351i	$-0.785364\pi$
$829$	−12.3444	+	8.96872i	−0.428738	+	0.311496i	0.352406	+	0.935847i	$0.385364\pi$
$830$	−1.08287	−	1.64651i	−0.0375870	−	0.0571512i
$831$	1.68022	+	1.22075i	0.0582861	+	0.0423473i
$832$		−	13.2176i		−	0.458239i
$833$	−2.56062	+	3.52439i	−0.0887203	+	0.122113i
$834$	−2.18182	+	6.71497i	−0.0755504	+	0.232520i
$835$	4.63061	+	16.8896i	0.160249	+	0.584490i
$836$	−3.30594	−	10.1746i	−0.114338	−	0.351897i
$837$	40.4454	+	13.1415i	1.39800	+	0.454237i
$838$	−0.766242	−	0.248967i	−0.0264694	−	0.00860042i
$839$	7.96688	+	24.5195i	0.275047	+	0.846509i	0.989207	+	0.146526i	$0.0468091\pi$
$839$	7.96688	+	24.5195i	0.275047	+	0.846509i	−0.714159	+	0.699983i	$0.753191\pi$
$840$	−5.64332	−	4.51598i	−0.194713	−	0.155816i
$841$	−8.94004	+	27.5146i	−0.308277	+	0.948779i
$842$	−1.98348	+	2.73003i	−0.0683554	+	0.0940831i
$843$		−	3.10689i		−	0.107007i
$844$	14.8158	+	10.7643i	0.509979	+	0.370522i
$845$	−16.9204	+	4.63903i	−0.582078	+	0.159587i
$846$	−0.576323	+	0.418723i	−0.0198144	+	0.0143960i
$847$	8.99293	+	12.3777i	0.309001	+	0.425303i
$848$	−31.4409	+	10.2158i	−1.07969	+	0.350811i
$849$	3.27389			0.112360
$850$	−1.52972	−	0.142880i	−0.0524690	−	0.00490073i
$851$	23.0421			0.789873
$852$	5.43883	−	1.76718i	0.186331	−	0.0605427i
$853$	−23.2038	−	31.9373i	−0.794484	−	1.09351i	−0.993535	−	0.113524i	$-0.963786\pi$
$853$	−23.2038	−	31.9373i	−0.794484	−	1.09351i	0.199051	−	0.979989i	$-0.436214\pi$
$854$	2.93456	−	2.13208i	0.100419	−	0.0729583i
$855$	−0.118536	+	2.54370i	−0.00405385	+	0.0869928i
$856$	−1.02631	−	0.745656i	−0.0350785	−	0.0254860i
$857$			5.44576i			0.186024i	0.995665	+	0.0930118i	$0.0296494\pi$
$857$			5.44576i			0.186024i	−0.995665	+	0.0930118i	$0.970351\pi$
$858$	−0.856511	+	1.17889i	−0.0292408	+	0.0402465i
$859$	3.96445	−	12.2013i	0.135265	−	0.416304i	−0.860366	−	0.509677i	$-0.829765\pi$
$859$	3.96445	−	12.2013i	0.135265	−	0.416304i	0.995631	+	0.0933730i	$0.0297649\pi$
$860$	3.45721	+	0.161106i	0.117890	+	0.00549366i
$861$	−7.37021	−	22.6832i	−0.251176	−	0.773041i
$862$	−4.33125	−	1.40731i	−0.147523	−	0.0479331i
$863$	−31.6484	−	10.2832i	−1.07732	−	0.350044i	−0.283988	−	0.958828i	$-0.591657\pi$
$863$	−31.6484	−	10.2832i	−1.07732	−	0.350044i	−0.793336	+	0.608784i	$0.791657\pi$
$864$	−5.76323	−	17.7374i	−0.196069	−	0.603438i
$865$	3.61131	−	9.57321i	0.122788	−	0.325499i
$866$	2.60513	−	8.01777i	0.0885260	−	0.272455i
$867$	−0.973705	+	1.34019i	−0.0330688	+	0.0455152i
$868$			24.4301i			0.829210i
$869$	−16.7111	−	12.1413i	−0.566886	−	0.411867i
$870$	−0.187398	+	0.234178i	−0.00635338	+	0.00793939i
$871$	14.8626	−	10.7983i	0.503598	−	0.365886i
$872$	−7.30260	−	10.0512i	−0.247297	−	0.340375i
$873$	−1.73781	+	0.564650i	−0.0588161	+	0.0191105i
$874$	−4.95852			−0.167725
$875$	7.97003	−	16.3380i	0.269436	−	0.552325i
$876$	50.9862			1.72266
$877$	16.1444	−	5.24563i	0.545158	−	0.177132i	−0.0234744	−	0.999724i	$-0.507473\pi$
$877$	16.1444	−	5.24563i	0.545158	−	0.177132i	0.568632	+	0.822592i	$0.307473\pi$
$878$	6.78154	+	9.33398i	0.228866	+	0.315007i
$879$	23.7018	−	17.2204i	0.799442	−	0.580829i
$880$	−6.06470	+	7.57864i	−0.204441	+	0.255476i
$881$	14.7453	+	10.7131i	0.496783	+	0.360934i	0.807787	−	0.589475i	$-0.200665\pi$
$881$	14.7453	+	10.7131i	0.496783	+	0.360934i	−0.311004	+	0.950409i	$0.600665\pi$
$882$			0.342404i			0.0115293i
$883$	33.7622	−	46.4697i	1.13619	−	1.56383i	0.360444	−	0.932781i	$-0.382625\pi$
$883$	33.7622	−	46.4697i	1.13619	−	1.56383i	0.775744	−	0.631048i	$-0.217375\pi$
$884$	−1.33681	+	4.11429i	−0.0449619	+	0.138379i
$885$	−5.77137	+	15.2993i	−0.194003	+	0.514280i
$886$	0.596085	+	1.83456i	0.0200259	+	0.0616333i
$887$	−0.242428	−	0.0787695i	−0.00813992	−	0.00264482i	0.304944	−	0.952370i	$-0.401362\pi$
$887$	−0.242428	−	0.0787695i	−0.00813992	−	0.00264482i	−0.313084	+	0.949725i	$0.601362\pi$
$888$	12.0198	+	3.90546i	0.403357	+	0.131058i
$889$	−2.53068	−	7.78864i	−0.0848763	−	0.261222i
$890$	−9.29340	−	0.433071i	−0.311516	−	0.0145166i
$891$	3.18253	−	9.79481i	0.106619	−	0.328138i
$892$	−27.1361	+	37.3497i	−0.908585	+	1.25056i
$893$		−	40.3520i		−	1.35033i
$894$	5.95459	+	4.32626i	0.199151	+	0.144692i
$895$	1.61033	−	34.5566i	0.0538275	−	1.15510i
$896$	11.4504	−	8.31923i	0.382532	−	0.277926i
$897$	−8.01206	−	11.0277i	−0.267515	−	0.368203i
$898$	−0.814930	+	0.264787i	−0.0271946	+	0.00883605i
$899$	2.07776			0.0692971
$900$	2.09637	−	1.24295i	0.0698789	−	0.0414316i
$901$	9.60344			0.319937
$902$	3.26318	−	1.06027i	0.108652	−	0.0353032i
$903$	−1.28591	−	1.76990i	−0.0427924	−	0.0588987i
$904$	−4.73584	+	3.44079i	−0.157512	+	0.114439i
$905$	−9.50582	+	2.60620i	−0.315984	+	0.0866330i
$906$	−3.55945	−	2.58609i	−0.118255	−	0.0859170i
$907$			11.6864i			0.388042i	0.980997	+	0.194021i	$0.0621530\pi$
$907$			11.6864i			0.388042i	−0.980997	+	0.194021i	$0.937847\pi$
$908$	26.5786	−	36.5823i	0.882041	−	1.21403i
$909$	−1.21938	+	3.75287i	−0.0404444	+	0.124475i
$910$	1.98016	+	1.58460i	0.0656418	+	0.0525289i
$911$	10.7400	+	33.0544i	0.355833	+	1.09514i	0.955525	+	0.294910i	$0.0952898\pi$
$911$	10.7400	+	33.0544i	0.355833	+	1.09514i	−0.599692	+	0.800231i	$0.704710\pi$
$912$	24.1460	+	7.84552i	0.799555	+	0.259791i
$913$	3.43975	+	1.11764i	0.113839	+	0.0369886i
$914$	2.56900	+	7.90656i	0.0849748	+	0.261526i
$915$	−7.11101	−	25.9366i	−0.235083	−	0.857439i
$916$	−6.84249	+	21.0590i	−0.226082	+	0.695810i
$917$	−3.05462	+	4.20432i	−0.100872	+	0.138839i
$918$			1.65727i			0.0546980i
$919$	2.99311	+	2.17462i	0.0987335	+	0.0717341i	0.636057	−	0.771642i	$-0.280564\pi$
$919$	2.99311	+	2.17462i	0.0987335	+	0.0717341i	−0.537323	+	0.843376i	$0.680564\pi$
$920$	5.34457	+	8.12646i	0.176205	+	0.267921i
$921$	5.49910	−	3.99533i	0.181202	−	0.131651i
$922$	−3.68247	−	5.06849i	−0.121276	−	0.166922i
$923$	−3.91139	+	1.27089i	−0.128745	+	0.0418317i
$924$	6.47219			0.212919
$925$	−2.95603	+	31.6483i	−0.0971937	+	1.04059i
$926$	10.8789			0.357502
$927$	0.0594404	−	0.0193133i	0.00195228	−	0.000634334i
$928$	−0.535592	−	0.737179i	−0.0175817	−	0.0241991i
$929$	−1.61057	+	1.17014i	−0.0528410	+	0.0383912i	−0.613892	−	0.789390i	$-0.710397\pi$
$929$	−1.61057	+	1.17014i	−0.0528410	+	0.0383912i	0.561051	+	0.827781i	$0.310397\pi$
$930$	−8.39710	−	3.16765i	−0.275352	−	0.103871i
$931$	−15.6911	−	11.4002i	−0.514255	−	0.373628i
$932$			47.2432i			1.54750i
$933$	8.04146	−	11.0681i	0.263266	−	0.362354i
$934$	−1.08961	+	3.35347i	−0.0356531	+	0.109729i
$935$	2.35585	−	1.54939i	0.0770447	−	0.0506704i
$936$	0.215348	+	0.662774i	0.00703888	+	0.0216634i
$937$	18.1507	+	5.89752i	0.592957	+	0.192663i	0.590097	−	0.807332i	$-0.299090\pi$
$937$	18.1507	+	5.89752i	0.592957	+	0.192663i	0.00286029	+	0.999996i	$0.499090\pi$
$938$	3.84510	+	1.24935i	0.125547	+	0.0407927i
$939$	−13.7999	−	42.4717i	−0.450343	−	1.38601i
$940$	−32.2668	+	21.2211i	−1.05243	+	0.692156i
$941$	−2.91223	+	8.96293i	−0.0949360	+	0.292183i	−0.987237	−	0.159258i	$-0.949090\pi$
$941$	−2.91223	+	8.96293i	−0.0949360	+	0.292183i	0.892301	+	0.451441i	$0.149090\pi$
$942$	1.70174	−	2.34224i	0.0554456	−	0.0763143i
$943$			32.0956i			1.04518i
$944$	−12.2939	−	8.93201i	−0.400131	−	0.290712i
$945$	−18.3467	−	6.92095i	−0.596818	−	0.225139i
$946$	0.254617	−	0.184990i	0.00827830	−	0.00601454i
$947$	−24.1461	−	33.2343i	−0.784644	−	1.07997i	−0.994754	−	0.102292i	$-0.967382\pi$
$947$	−24.1461	−	33.2343i	−0.784644	−	1.07997i	0.210111	−	0.977678i	$-0.432618\pi$
$948$	49.1784	−	15.9790i	1.59724	−	0.518975i
$949$	−36.6672			−1.19027
$950$	0.636120	−	6.81053i	0.0206385	−	0.220963i
$951$	−27.6773			−0.897498
$952$	−1.85575	+	0.602969i	−0.0601451	+	0.0195423i
$953$	−2.93608	−	4.04117i	−0.0951089	−	0.130906i	0.758810	−	0.651312i	$-0.225781\pi$
$953$	−2.93608	−	4.04117i	−0.0951089	−	0.130906i	−0.853919	+	0.520405i	$0.825781\pi$
$954$	0.610656	−	0.443667i	0.0197707	−	0.0143643i
$955$	8.63101	+	13.1235i	0.279293	+	0.424666i
$956$	15.5895	+	11.3265i	0.504202	+	0.366324i
$957$		−	0.550455i		−	0.0177937i
$958$	−4.85235	+	6.67869i	−0.156772	+	0.215779i
$959$	−8.40985	+	25.8829i	−0.271568	+	0.835801i
$960$	−5.70250	−	20.7992i	−0.184047	−	0.671293i
$961$	9.63274	+	29.6465i	0.310734	+	0.956340i
$962$	−4.21757	−	1.37037i	−0.135980	−	0.0441826i
$963$	−0.257156	−	0.0835550i	−0.00828673	−	0.00269252i
$964$	10.6171	+	32.6760i	0.341953	+	1.05242i
$965$	14.2032	+	11.3659i	0.457217	+	0.365882i
$966$	0.926986	−	2.85297i	0.0298253	−	0.0917928i
$967$	−25.4407	+	35.0161i	−0.818117	+	1.12604i	0.171902	+	0.985114i	$0.445009\pi$
$967$	−25.4407	+	35.0161i	−0.818117	+	1.12604i	−0.990020	+	0.140928i	$0.954991\pi$
$968$		−	11.2927i		−	0.362961i
$969$	−5.96671	−	4.33507i	−0.191678	−	0.139263i
$970$	4.73356	−	1.29779i	0.151986	−	0.0416697i
$971$	45.7621	−	33.2481i	1.46858	−	1.06698i	0.487553	−	0.873094i	$-0.337890\pi$
$971$	45.7621	−	33.2481i	1.46858	−	1.06698i	0.981023	−	0.193889i	$-0.0621103\pi$
$972$	−2.96907	−	4.08658i	−0.0952330	−	0.131077i
$973$	−21.4489	+	6.96918i	−0.687621	+	0.223422i
$974$	5.79683			0.185742
$975$	16.1743	−	9.58984i	0.517993	−	0.307121i
$976$	24.9931			0.800010
$977$	5.12615	−	1.66559i	0.164000	−	0.0532869i	−0.225866	−	0.974158i	$-0.572521\pi$
$977$	5.12615	−	1.66559i	0.164000	−	0.0532869i	0.389866	+	0.920871i	$0.372521\pi$
$978$	−0.304883	−	0.419635i	−0.00974907	−	0.0134184i
$979$	13.8136	−	10.0362i	0.441485	−	0.320757i
$980$	−0.864078	+	18.5425i	−0.0276019	+	0.592318i
$981$	−2.14233	−	1.55649i	−0.0683993	−	0.0496950i
$982$		−	9.29128i		−	0.296497i
$983$	−29.1933	+	40.1812i	−0.931123	+	1.28158i	0.0282971	+	0.999600i	$0.490992\pi$
$983$	−29.1933	+	40.1812i	−0.931123	+	1.28158i	−0.959420	+	0.281981i	$0.909008\pi$
$984$	−5.43995	+	16.7424i	−0.173419	+	0.533730i
$985$	−21.8945	−	1.02028i	−0.697616	−	0.0325088i
$986$	0.0250211	+	0.0770072i	0.000796836	+	0.00245241i
$987$	23.2172	+	7.54374i	0.739013	+	0.240120i
$988$	−18.3174	−	5.95169i	−0.582754	−	0.189348i
$989$	0.909751	+	2.79993i	0.0289284	+	0.0890324i
$990$	0.0782222	−	0.207359i	0.00248607	−	0.00659029i
$991$	6.98139	−	21.4865i	0.221771	−	0.682542i	−0.776832	−	0.629708i	$-0.783175\pi$
$991$	6.98139	−	21.4865i	0.221771	−	0.682542i	0.998603	−	0.0528338i	$-0.0168254\pi$
$992$	16.0264	−	22.0584i	0.508838	−	0.700355i
$993$		−	42.9205i		−	1.36204i
$994$	−0.732230	−	0.531996i	−0.0232249	−	0.0168739i
$995$	−4.89369	+	6.11532i	−0.155141	+	0.193869i
$996$	−7.32484	+	5.32181i	−0.232096	+	0.168628i
$997$	−7.15369	−	9.84621i	−0.226560	−	0.311833i	0.680571	−	0.732682i	$-0.261732\pi$
$997$	−7.15369	−	9.84621i	−0.226560	−	0.311833i	−0.907130	+	0.420850i	$0.861732\pi$
$998$	2.85126	−	0.926432i	0.0902552	−	0.0293257i
$999$	34.2872			1.08480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.r.a.69.18	✓	160
25.4	even	10	inner	425.2.r.a.154.18	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.r.a.69.18	✓	160	1.1	even	1	trivial
425.2.r.a.154.18	yes	160	25.4	even	10	inner

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292236 + 0.0949534i) q^{2} +(-0.973705 - 1.34019i) q^{3} +(-1.54165 + 1.12007i) q^{4} +(1.39711 - 1.74587i) q^{5} +(0.411808 + 0.299196i) q^{6} +1.62592i q^{7} +(0.705395 - 0.970893i) q^{8} +(0.0790435 - 0.243271i) q^{9} +(-0.242510 + 0.642869i) q^{10} +(-0.389672 - 1.19929i) q^{11} +(3.00222 + 0.975481i) q^{12} +(-2.15907 - 0.701526i) q^{13} +(-0.154386 - 0.475153i) q^{14} +(-3.70018 - 0.172428i) q^{15} +(1.06376 - 3.27392i) q^{16} +(-0.587785 + 0.809017i) q^{17} +0.0785981i q^{18} +(-3.60186 - 2.61690i) q^{19} +(-0.198347 + 4.25639i) q^{20} +(2.17904 - 1.58316i) q^{21} +(0.227753 + 0.313474i) q^{22} +(-3.44716 + 1.12005i) q^{23} -1.98803 q^{24} +(-1.09616 - 4.87836i) q^{25} +0.697573 q^{26} +(-5.12946 + 1.66666i) q^{27} +(-1.82115 - 2.50659i) q^{28} +(-0.213184 + 0.154887i) q^{29} +(1.09770 - 0.300955i) q^{30} +(-6.37905 - 4.63465i) q^{31} +3.45795i q^{32} +(-1.22785 + 1.68998i) q^{33} +(0.0949534 - 0.292236i) q^{34} +(2.83865 + 2.27159i) q^{35} +(0.150624 + 0.463572i) q^{36} +(-6.04607 - 1.96449i) q^{37} +(1.30108 + 0.422746i) q^{38} +(1.16212 + 3.57665i) q^{39} +(-0.709542 - 2.58798i) q^{40} +(2.73636 - 8.42164i) q^{41} +(-0.486468 + 0.669566i) q^{42} -0.812241i q^{43} +(1.94402 + 1.41242i) q^{44} +(-0.314288 - 0.477877i) q^{45} +(0.901034 - 0.654639i) q^{46} +(5.32740 + 7.33254i) q^{47} +(-5.42347 + 1.76219i) q^{48} +4.35639 q^{49} +(0.783555 + 1.32155i) q^{50} +1.65657 q^{51} +(4.11429 - 1.33681i) q^{52} +(-5.64476 - 7.76935i) q^{53} +(1.34076 - 0.974119i) q^{54} +(-2.63822 - 0.995218i) q^{55} +(1.57859 + 1.14691i) q^{56} +7.37526i q^{57} +(0.0475931 - 0.0655062i) q^{58} +(1.36411 - 4.19831i) q^{59} +(5.89750 - 3.87865i) q^{60} +(2.24358 + 6.90501i) q^{61} +(2.30427 + 0.748701i) q^{62} +(0.395538 + 0.128518i) q^{63} +(1.79918 + 5.53731i) q^{64} +(-4.24124 + 2.78936i) q^{65} +(0.198352 - 0.610463i) q^{66} +(-4.75656 + 6.54685i) q^{67} -1.90558i q^{68} +(4.85760 + 3.52925i) q^{69} +(-1.04525 - 0.394302i) q^{70} +(1.46562 - 1.06483i) q^{71} +(-0.180433 - 0.248345i) q^{72} +(15.3611 - 4.99113i) q^{73} +1.95342 q^{74} +(-5.47060 + 6.21915i) q^{75} +8.48392 q^{76} +(1.94994 - 0.633574i) q^{77} +(-0.679230 - 0.934880i) q^{78} +(13.2522 - 9.62832i) q^{79} +(-4.22966 - 6.43123i) q^{80} +(6.60740 + 4.80056i) q^{81} +2.72094i q^{82} +(-1.68587 + 2.32040i) q^{83} +(-1.58605 + 4.88137i) q^{84} +(0.591241 + 2.15649i) q^{85} +(0.0771250 + 0.237366i) q^{86} +(0.415156 + 0.134893i) q^{87} +(-1.43925 - 0.467641i) q^{88} +(4.18423 + 12.8777i) q^{89} +(0.137222 + 0.109810i) q^{90} +(1.14062 - 3.51048i) q^{91} +(4.05977 - 5.58780i) q^{92} +13.0619i q^{93} +(-2.25311 - 1.63698i) q^{94} +(-9.60098 + 2.63229i) q^{95} +(4.63431 - 3.36702i) q^{96} +(-4.19887 - 5.77924i) q^{97} +(-1.27310 + 0.413654i) q^{98} -0.322552 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

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