LMFDB - Embedded newform 930.2.z.d.349.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.4
Character	$\chi$	$=$	930.349
Dual form			930.2.z.d.469.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.02832 - 1.98559i) q^{5} +1.00000 q^{6} +(0.156978 - 0.216062i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.02832 - 1.98559i) q^{5} +1.00000 q^{6} +(0.156978 - 0.216062i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.364410 + 2.20617i) q^{10} +(2.92003 + 2.12153i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(1.30820 - 0.425060i) q^{13} +(-0.216062 + 0.156978i) q^{14} +(1.59157 + 1.57064i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.769375 + 1.05895i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(-2.05138 + 6.31349i) q^{19} +(0.335171 - 2.21081i) q^{20} +(-0.0825284 + 0.253996i) q^{21} +(-2.12153 - 2.92003i) q^{22} +(-2.85190 - 3.92531i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-2.88512 + 4.08364i) q^{25} -1.37552 q^{26} +(-0.587785 + 0.809017i) q^{27} +(0.253996 - 0.0825284i) q^{28} +(2.66929 - 8.21523i) q^{29} +(-1.02832 - 1.98559i) q^{30} +(5.50694 + 0.820707i) q^{31} -1.00000i q^{32} +(-3.43271 - 1.11535i) q^{33} +(-0.404484 - 1.24487i) q^{34} +(-0.590434 - 0.0895133i) q^{35} +1.00000 q^{36} -8.56433i q^{37} +(3.90195 - 5.37058i) q^{38} +(-1.11282 + 0.808512i) q^{39} +(-1.00194 + 1.99903i) q^{40} +(1.03019 - 3.17061i) q^{41} +(0.156978 - 0.216062i) q^{42} +(3.22692 + 1.04849i) q^{43} +(1.11535 + 3.43271i) q^{44} +(-1.99903 - 1.00194i) q^{45} +(1.49933 + 4.61448i) q^{46} +(6.19452 - 2.01272i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(2.14108 + 6.58956i) q^{49} +(4.00582 - 2.99222i) q^{50} +(-1.05895 - 0.769375i) q^{51} +(1.30820 + 0.425060i) q^{52} +(0.524377 + 0.721743i) q^{53} +(0.809017 - 0.587785i) q^{54} +(1.20975 - 7.97959i) q^{55} -0.267067 q^{56} -6.63840i q^{57} +(-5.07729 + 6.98829i) q^{58} +(-3.87911 - 11.9387i) q^{59} +(0.364410 + 2.20617i) q^{60} +6.82886 q^{61} +(-4.98380 - 2.48228i) q^{62} -0.267067i q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.18924 - 2.16045i) q^{65} +(2.92003 + 2.12153i) q^{66} +9.27905i q^{67} +1.30894i q^{68} +(3.92531 + 2.85190i) q^{69} +(0.533875 + 0.267586i) q^{70} +(6.47371 - 4.70343i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(0.267859 - 0.368676i) q^{73} +(-2.64652 + 8.14516i) q^{74} +(1.48200 - 4.77532i) q^{75} +(-5.37058 + 3.90195i) q^{76} +(0.916764 - 0.297875i) q^{77} +(1.30820 - 0.425060i) q^{78} +(11.4930 - 8.35017i) q^{79} +(1.57064 - 1.59157i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.95954 + 2.69708i) q^{82} +(7.85032 + 2.55072i) q^{83} +(-0.216062 + 0.156978i) q^{84} +(1.31148 - 2.61660i) q^{85} +(-2.74498 - 1.99435i) q^{86} +8.63801i q^{87} -3.60936i q^{88} +(-0.856308 - 0.622145i) q^{89} +(1.59157 + 1.57064i) q^{90} +(0.113520 - 0.349378i) q^{91} -4.85195i q^{92} +(-5.49103 + 0.921201i) q^{93} -6.51331 q^{94} +(14.6455 - 2.41910i) q^{95} +(0.309017 + 0.951057i) q^{96} +(7.31105 - 10.0628i) q^{97} -6.92868i q^{98} +3.60936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.02832	−	1.98559i	−0.459879	−	0.887982i
$5$	−1.02832	−	1.98559i	−0.459879	−	0.887982i
$6$	1.00000			0.408248
$7$	0.156978	−	0.216062i	0.0593322	−	0.0816638i	−0.778320	−	0.627868i	$-0.783928\pi$
$7$	0.156978	−	0.216062i	0.0593322	−	0.0816638i	0.837652	+	0.546204i	$0.183928\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	0.364410	+	2.20617i	0.115236	+	0.697654i
$11$	2.92003	+	2.12153i	0.880424	+	0.639665i	0.933363	−	0.358933i	$-0.116859\pi$
$11$	2.92003	+	2.12153i	0.880424	+	0.639665i	−0.0529400	+	0.998598i	$0.516859\pi$
$12$	−0.951057	−	0.309017i	−0.274546	−	0.0892055i
$13$	1.30820	−	0.425060i	0.362829	−	0.117890i	−0.121928	−	0.992539i	$-0.538908\pi$
$13$	1.30820	−	0.425060i	0.362829	−	0.117890i	0.484758	+	0.874648i	$0.338908\pi$
$14$	−0.216062	+	0.156978i	−0.0577450	+	0.0419542i
$15$	1.59157	+	1.57064i	0.410942	+	0.405537i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.769375	+	1.05895i	0.186601	+	0.256834i	0.892060	−	0.451916i	$-0.149259\pi$
$17$	0.769375	+	1.05895i	0.186601	+	0.256834i	−0.705460	+	0.708750i	$0.749259\pi$
$18$	−0.951057	+	0.309017i	−0.224166	+	0.0728360i
$19$	−2.05138	+	6.31349i	−0.470619	+	1.44841i	0.381158	+	0.924510i	$0.375525\pi$
$19$	−2.05138	+	6.31349i	−0.470619	+	1.44841i	−0.851777	+	0.523905i	$0.824475\pi$
$20$	0.335171	−	2.21081i	0.0749465	−	0.494351i
$21$	−0.0825284	+	0.253996i	−0.0180092	+	0.0554265i
$22$	−2.12153	−	2.92003i	−0.452312	−	0.622553i
$23$	−2.85190	−	3.92531i	−0.594663	−	0.818483i	0.400544	−	0.916278i	$-0.368821\pi$
$23$	−2.85190	−	3.92531i	−0.594663	−	0.818483i	−0.995207	+	0.0977943i	$0.968821\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	−2.88512	+	4.08364i	−0.577024	+	0.816728i
$26$	−1.37552			−0.269762
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	0.253996	−	0.0825284i	0.0480008	−	0.0155964i
$29$	2.66929	−	8.21523i	0.495675	−	1.52553i	−0.320227	−	0.947341i	$-0.603759\pi$
$29$	2.66929	−	8.21523i	0.495675	−	1.52553i	0.815902	−	0.578190i	$-0.196241\pi$
$30$	−1.02832	−	1.98559i	−0.187745	−	0.362517i
$31$	5.50694	+	0.820707i	0.989076	+	0.147403i
$31$	5.50694	+	0.820707i	0.989076	+	0.147403i
$32$		−	1.00000i		−	0.176777i
$33$	−3.43271	−	1.11535i	−0.597557	−	0.194158i
$34$	−0.404484	−	1.24487i	−0.0693685	−	0.213494i
$35$	−0.590434	−	0.0895133i	−0.0998016	−	0.0151305i
$36$	1.00000			0.166667
$37$		−	8.56433i		−	1.40797i	−0.710216	−	0.703984i	$-0.751403\pi$
$37$		−	8.56433i		−	1.40797i	0.710216	−	0.703984i	$-0.248597\pi$
$38$	3.90195	−	5.37058i	0.632981	−	0.871223i
$39$	−1.11282	+	0.808512i	−0.178194	+	0.129466i
$40$	−1.00194	+	1.99903i	−0.158421	+	0.316074i
$41$	1.03019	−	3.17061i	0.160889	−	0.495166i	−0.837821	−	0.545945i	$-0.816171\pi$
$41$	1.03019	−	3.17061i	0.160889	−	0.495166i	0.998710	+	0.0507796i	$0.0161706\pi$
$42$	0.156978	−	0.216062i	0.0242223	−	0.0333391i
$43$	3.22692	+	1.04849i	0.492101	+	0.159893i	0.544547	−	0.838730i	$-0.316702\pi$
$43$	3.22692	+	1.04849i	0.492101	+	0.159893i	−0.0524457	+	0.998624i	$0.516702\pi$
$44$	1.11535	+	3.43271i	0.168146	+	0.517500i
$45$	−1.99903	−	1.00194i	−0.297997	−	0.149361i
$46$	1.49933	+	4.61448i	0.221065	+	0.680367i
$47$	6.19452	−	2.01272i	0.903564	−	0.293586i	0.179857	−	0.983693i	$-0.442437\pi$
$47$	6.19452	−	2.01272i	0.903564	−	0.293586i	0.723707	+	0.690107i	$0.242437\pi$
$48$	−0.587785	−	0.809017i	−0.0848395	−	0.116772i
$49$	2.14108	+	6.58956i	0.305868	+	0.941366i
$50$	4.00582	−	2.99222i	0.566509	−	0.423164i
$51$	−1.05895	−	0.769375i	−0.148283	−	0.107734i
$52$	1.30820	+	0.425060i	0.181415	+	0.0589452i
$53$	0.524377	+	0.721743i	0.0720288	+	0.0991391i	0.843511	−	0.537111i	$-0.180485\pi$
$53$	0.524377	+	0.721743i	0.0720288	+	0.0991391i	−0.771483	+	0.636250i	$0.780485\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	1.20975	−	7.97959i	0.163123	−	1.07597i
$56$	−0.267067			−0.0356884
$57$		−	6.63840i		−	0.879278i
$58$	−5.07729	+	6.98829i	−0.666681	+	0.917608i
$59$	−3.87911	−	11.9387i	−0.505017	−	1.55428i	−0.800742	−	0.599010i	$-0.795561\pi$
$59$	−3.87911	−	11.9387i	−0.505017	−	1.55428i	0.295725	−	0.955273i	$-0.404439\pi$
$60$	0.364410	+	2.20617i	0.0470451	+	0.284816i
$61$	6.82886			0.874346			0.437173	−	0.899377i	$-0.355980\pi$
$61$	6.82886			0.874346			0.437173	+	0.899377i	$0.355980\pi$
$62$	−4.98380	−	2.48228i	−0.632944	−	0.315250i
$63$		−	0.267067i		−	0.0336473i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−2.18924	−	2.16045i	−0.271542	−	0.267971i
$66$	2.92003	+	2.12153i	0.359431	+	0.261142i
$67$			9.27905i			1.13362i	0.823850	+	0.566808i	$0.191822\pi$
$67$			9.27905i			1.13362i	−0.823850	+	0.566808i	$0.808178\pi$
$68$			1.30894i			0.158732i
$69$	3.92531	+	2.85190i	0.472552	+	0.343329i
$70$	0.533875	+	0.267586i	0.0638103	+	0.0319827i
$71$	6.47371	−	4.70343i	0.768288	−	0.558194i	−0.133153	−	0.991095i	$-0.542510\pi$
$71$	6.47371	−	4.70343i	0.768288	−	0.558194i	0.901441	+	0.432901i	$0.142510\pi$
$72$	−0.951057	−	0.309017i	−0.112083	−	0.0364180i
$73$	0.267859	−	0.368676i	0.0313505	−	0.0431502i	−0.793054	−	0.609151i	$-0.791510\pi$
$73$	0.267859	−	0.368676i	0.0313505	−	0.0431502i	0.824405	+	0.566001i	$0.191510\pi$
$74$	−2.64652	+	8.14516i	−0.307652	+	0.946856i
$75$	1.48200	−	4.77532i	0.171126	−	0.551407i
$76$	−5.37058	+	3.90195i	−0.616048	+	0.447585i
$77$	0.916764	−	0.297875i	0.104475	−	0.0339460i
$78$	1.30820	−	0.425060i	0.148124	−	0.0481286i
$79$	11.4930	−	8.35017i	1.29307	−	0.939468i	0.293204	−	0.956050i	$-0.405279\pi$
$79$	11.4930	−	8.35017i	1.29307	−	0.939468i	0.999863	+	0.0165822i	$0.00527851\pi$
$80$	1.57064	−	1.59157i	0.175603	−	0.177943i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−1.95954	+	2.69708i	−0.216395	+	0.297843i
$83$	7.85032	+	2.55072i	0.861685	+	0.279978i	0.706332	−	0.707881i	$-0.250349\pi$
$83$	7.85032	+	2.55072i	0.861685	+	0.279978i	0.155353	+	0.987859i	$0.450349\pi$
$84$	−0.216062	+	0.156978i	−0.0235743	+	0.0171277i
$85$	1.31148	−	2.61660i	0.142250	−	0.283811i
$86$	−2.74498	−	1.99435i	−0.295999	−	0.215056i
$87$			8.63801i			0.926092i
$88$		−	3.60936i		−	0.384759i
$89$	−0.856308	−	0.622145i	−0.0907685	−	0.0659472i	0.541475	−	0.840717i	$-0.317866\pi$
$89$	−0.856308	−	0.622145i	−0.0907685	−	0.0659472i	−0.632244	+	0.774769i	$0.717866\pi$
$90$	1.59157	+	1.57064i	0.167766	+	0.165560i
$91$	0.113520	−	0.349378i	0.0119001	−	0.0366247i
$92$		−	4.85195i		−	0.505851i
$93$	−5.49103	+	0.921201i	−0.569393	+	0.0955241i
$94$	−6.51331			−0.671796
$95$	14.6455	−	2.41910i	1.50259	−	0.248194i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	7.31105	−	10.0628i	0.742325	−	1.02172i	−0.256157	−	0.966635i	$-0.582456\pi$
$97$	7.31105	−	10.0628i	0.742325	−	1.02172i	0.998482	−	0.0550872i	$-0.0175437\pi$
$98$		−	6.92868i		−	0.699902i
$99$	3.60936			0.362754
$100$	−4.73441	+	1.60790i	−0.473441	+	0.160790i
$101$	4.94756	−	3.59462i	0.492301	−	0.357678i	−0.313768	−	0.949500i	$-0.601591\pi$
$101$	4.94756	−	3.59462i	0.492301	−	0.357678i	0.806069	+	0.591822i	$0.201591\pi$
$102$	0.769375	+	1.05895i	0.0761794	+	0.104852i
$103$	−12.1094	−	3.93460i	−1.19318	−	0.387687i	−0.355932	−	0.934512i	$-0.615836\pi$
$103$	−12.1094	−	3.93460i	−1.19318	−	0.387687i	−0.837247	+	0.546825i	$0.815836\pi$
$104$	−1.11282	−	0.808512i	−0.109121	−	0.0792811i
$105$	0.589197	−	0.0973219i	0.0574998	−	0.00949765i
$106$	−0.275681	−	0.848460i	−0.0267765	−	0.0824097i
$107$	0.482239	+	0.663746i	0.0466198	+	0.0641667i	0.831690	−	0.555240i	$-0.187373\pi$
$107$	0.482239	+	0.663746i	0.0466198	+	0.0641667i	−0.785071	+	0.619406i	$0.787373\pi$
$108$	−0.951057	+	0.309017i	−0.0915155	+	0.0297352i
$109$	−5.64316	−	17.3679i	−0.540516	−	1.66354i	−0.731418	−	0.681930i	$-0.761141\pi$
$109$	−5.64316	−	17.3679i	−0.540516	−	1.66354i	0.190901	−	0.981609i	$-0.438859\pi$
$110$	−3.61637	+	7.21521i	−0.344808	+	0.687943i
$111$	2.64652	+	8.14516i	0.251197	+	0.773105i
$112$	0.253996	+	0.0825284i	0.0240004	+	0.00779820i
$113$	−2.31315	+	3.18377i	−0.217602	+	0.299504i	−0.903838	−	0.427876i	$-0.859262\pi$
$113$	−2.31315	+	3.18377i	−0.217602	+	0.299504i	0.686235	+	0.727380i	$0.259262\pi$
$114$	−2.05138	+	6.31349i	−0.192129	+	0.591313i
$115$	−4.86138	+	9.69918i	−0.453326	+	0.904453i
$116$	6.98829	−	5.07729i	0.648847	−	0.471415i
$117$	0.808512	−	1.11282i	0.0747470	−	0.102880i
$118$			12.5531i			1.15560i
$119$	0.349575			0.0320455
$120$	0.335171	−	2.21081i	0.0305968	−	0.201818i
$121$	0.626528	+	1.92826i	0.0569571	+	0.175296i
$122$	−6.49463	−	2.11023i	−0.587996	−	0.191052i
$123$			3.33377i			0.300596i
$124$	3.97281	+	3.90087i	0.356769	+	0.350308i
$125$	11.0752	+	1.52937i	0.990600	+	0.136791i
$126$	−0.0825284	+	0.253996i	−0.00735221	+	0.0226278i
$127$	−5.60840	+	1.82228i	−0.497665	+	0.161701i	−0.547085	−	0.837077i	$-0.684263\pi$
$127$	−5.60840	+	1.82228i	−0.497665	+	0.161701i	0.0494201	+	0.998778i	$0.484263\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−3.39299			−0.298736
$130$	1.41448	+	2.73122i	0.124058	+	0.239544i
$131$	2.18429	+	1.58698i	0.190842	+	0.138655i	0.679104	−	0.734042i	$-0.262369\pi$
$131$	2.18429	+	1.58698i	0.190842	+	0.138655i	−0.488261	+	0.872697i	$0.662369\pi$
$132$	−2.12153	−	2.92003i	−0.184655	−	0.254156i
$133$	1.04208	+	1.43431i	0.0903602	+	0.124370i
$134$	2.86738	−	8.82490i	0.247704	−	0.762355i
$135$	2.21081	+	0.335171i	0.190276	+	0.0288469i
$136$	0.404484	−	1.24487i	0.0346842	−	0.106747i
$137$	−6.45825	+	2.09841i	−0.551766	+	0.179280i	−0.571613	−	0.820523i	$-0.693682\pi$
$137$	−6.45825	+	2.09841i	−0.551766	+	0.179280i	0.0198470	+	0.999803i	$0.493682\pi$
$138$	−2.85190	−	3.92531i	−0.242770	−	0.334144i
$139$	−4.73424	−	14.5705i	−0.401553	−	1.23585i	−0.923740	−	0.383021i	$-0.874884\pi$
$139$	−4.73424	−	14.5705i	−0.401553	−	1.23585i	0.522187	−	0.852831i	$-0.325116\pi$
$140$	−0.425057	−	0.419466i	−0.0359238	−	0.0354514i
$141$	−5.26937	+	3.82842i	−0.443761	+	0.322412i
$142$	−7.61031	+	2.47274i	−0.638643	+	0.207508i
$143$	4.72177	+	1.53419i	0.394854	+	0.128296i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$	−19.0570	+	3.14777i	−1.58259	+	0.261408i
$146$	−0.368676	+	0.267859i	−0.0305118	+	0.0221681i
$147$	−4.07257	−	5.60542i	−0.335900	−	0.462327i
$148$	5.03399	−	6.92869i	0.413791	−	0.569535i
$149$	−18.9768			−1.55464			−0.777320	−	0.629105i	$-0.783421\pi$
$149$	−18.9768			−1.55464			−0.777320	+	0.629105i	$0.783421\pi$
$150$	−2.88512	+	4.08364i	−0.235569	+	0.333428i
$151$	2.23149	+	1.62127i	0.181596	+	0.131937i	0.674870	−	0.737937i	$-0.264200\pi$
$151$	2.23149	+	1.62127i	0.181596	+	0.131937i	−0.493273	+	0.869874i	$0.664200\pi$
$152$	6.31349	−	2.05138i	0.512092	−	0.166389i
$153$	1.24487	+	0.404484i	0.100642	+	0.0327006i
$154$	−0.963943			−0.0776767
$155$	−4.03331	−	11.7785i	−0.323964	−	0.946070i
$156$	−1.37552			−0.110130
$157$	14.3053	+	4.64808i	1.14169	+	0.370957i	0.818007	−	0.575209i	$-0.195079\pi$
$157$	14.3053	+	4.64808i	1.14169	+	0.370957i	0.323682	+	0.946166i	$0.395079\pi$
$158$	−13.5109	+	4.38995i	−1.07487	+	0.349245i
$159$	−0.721743	−	0.524377i	−0.0572380	−	0.0415858i
$160$	−1.98559	+	1.02832i	−0.156974	+	0.0812958i
$161$	−1.29580			−0.102123
$162$	−0.587785	+	0.809017i	−0.0461808	+	0.0635624i
$163$	2.16931	+	2.98580i	0.169913	+	0.233866i	0.885479	−	0.464680i	$-0.153831\pi$
$163$	2.16931	+	2.98580i	0.169913	+	0.233866i	−0.715565	+	0.698546i	$0.753831\pi$
$164$	2.69708	−	1.95954i	0.210607	−	0.153015i
$165$	1.31529	+	7.96288i	0.102395	+	0.619909i
$166$	−6.67788	−	4.85177i	−0.518304	−	0.376570i
$167$	18.6094	+	6.04655i	1.44004	+	0.467896i	0.921908	−	0.387408i	$-0.126630\pi$
$167$	18.6094	+	6.04655i	1.44004	+	0.467896i	0.518127	+	0.855304i	$0.326630\pi$
$168$	0.253996	−	0.0825284i	0.0195962	−	0.00636720i
$169$	−8.98651	+	6.52908i	−0.691270	+	0.502237i
$170$	−2.05587	+	2.08327i	−0.157678	+	0.159779i
$171$	2.05138	+	6.31349i	0.156873	+	0.482805i
$172$	1.99435	+	2.74498i	0.152068	+	0.209303i
$173$	−19.1437	+	6.22016i	−1.45547	+	0.472910i	−0.926682	−	0.375846i	$-0.877352\pi$
$173$	−19.1437	+	6.22016i	−1.45547	+	0.472910i	−0.528785	+	0.848756i	$0.677352\pi$
$174$	2.66929	−	8.21523i	0.202358	−	0.622795i
$175$	0.429418	+	1.26441i	0.0324610	+	0.0955802i
$176$	−1.11535	+	3.43271i	−0.0840730	+	0.258750i
$177$	7.37851	+	10.1556i	0.554602	+	0.763345i
$178$	0.622145	+	0.856308i	0.0466317	+	0.0641830i
$179$	−6.37078	−	4.62864i	−0.476175	−	0.345961i	0.323668	−	0.946171i	$-0.395084\pi$
$179$	−6.37078	−	4.62864i	−0.476175	−	0.345961i	−0.799843	+	0.600210i	$0.795084\pi$
$180$	−1.02832	−	1.98559i	−0.0766464	−	0.147997i
$181$	−3.35943			−0.249705			−0.124852	−	0.992175i	$-0.539846\pi$
$181$	−3.35943			−0.249705			−0.124852	+	0.992175i	$0.539846\pi$
$182$	−0.215927	+	0.297198i	−0.0160056	+	0.0220298i
$183$	−6.49463	+	2.11023i	−0.480097	+	0.155993i
$184$	−1.49933	+	4.61448i	−0.110532	+	0.340184i
$185$	−17.0052	+	8.80687i	−1.25025	+	0.647494i
$186$	5.50694	+	0.820707i	0.403789	+	0.0601771i
$187$			4.72443i			0.345485i
$188$	6.19452	+	2.01272i	0.451782	+	0.146793i
$189$	0.0825284	+	0.253996i	0.00600305	+	0.0184755i
$190$	−14.6762	−	2.22500i	−1.06472	−	0.161419i
$191$	17.7427			1.28382			0.641909	−	0.766781i	$-0.278143\pi$
$191$	17.7427			1.28382			0.641909	+	0.766781i	$0.278143\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	7.98331	−	10.9881i	0.574651	−	0.790939i	−0.418445	−	0.908242i	$-0.637425\pi$
$193$	7.98331	−	10.9881i	0.574651	−	0.790939i	0.993096	+	0.117303i	$0.0374248\pi$
$194$	−10.0628	+	7.31105i	−0.722467	+	0.524903i
$195$	2.74971	+	1.37820i	0.196911	+	0.0986947i
$196$	−2.14108	+	6.58956i	−0.152934	+	0.470683i
$197$	−3.12925	+	4.30704i	−0.222950	+	0.306864i	−0.905809	−	0.423686i	$-0.860736\pi$
$197$	−3.12925	+	4.30704i	−0.222950	+	0.306864i	0.682860	+	0.730550i	$0.260736\pi$
$198$	−3.43271	−	1.11535i	−0.243952	−	0.0792648i
$199$	7.49245	+	23.0594i	0.531126	+	1.63464i	0.751875	+	0.659306i	$0.229150\pi$
$199$	7.49245	+	23.0594i	0.531126	+	1.63464i	−0.220749	+	0.975331i	$0.570850\pi$
$200$	4.99956	−	0.0661929i	0.353522	−	0.00468054i
$201$	−2.86738	−	8.82490i	−0.202250	−	0.622460i
$202$	−5.81621	+	1.88980i	−0.409227	+	0.132966i
$203$	−1.35598	−	1.86635i	−0.0951711	−	0.130992i
$204$	−0.404484	−	1.24487i	−0.0283196	−	0.0871586i
$205$	−7.35489	+	1.21486i	−0.513688	+	0.0848495i
$206$	10.3009	+	7.48405i	0.717698	+	0.521438i
$207$	−4.61448	−	1.49933i	−0.320728	−	0.104211i
$208$	0.808512	+	1.11282i	0.0560602	+	0.0771603i
$209$	−19.3844	+	14.0836i	−1.34084	+	0.974180i
$210$	−0.590434	−	0.0895133i	−0.0407438	−	0.00617700i
$211$	23.2415			1.60001			0.800006	−	0.599992i	$-0.204830\pi$
$211$	23.2415			1.60001			0.800006	+	0.599992i	$0.204830\pi$
$212$			0.892124i			0.0612713i
$213$	−4.70343	+	6.47371i	−0.322274	+	0.443571i
$214$	−0.253528	−	0.780280i	−0.0173308	−	0.0533388i
$215$	−1.23644	−	7.48552i	−0.0843243	−	0.510508i
$216$	1.00000			0.0680414
$217$	1.04179	−	1.06101i	0.0707216	−	0.0720260i
$218$			18.2616i			1.23683i
$219$	−0.140822	+	0.433404i	−0.00951585	+	0.0292868i
$220$	5.66900	−	5.74455i	0.382204	−	0.387298i
$221$	1.45661	+	1.05829i	0.0979825	+	0.0711885i
$222$		−	8.56433i		−	0.574800i
$223$			15.8319i			1.06018i	0.847941	+	0.530090i	$0.177842\pi$
$223$			15.8319i			1.06018i	−0.847941	+	0.530090i	$0.822158\pi$
$224$	−0.216062	−	0.156978i	−0.0144363	−	0.0104886i
$225$	0.0661929	+	4.99956i	0.00441286	+	0.333304i
$226$	3.18377	−	2.31315i	0.211781	−	0.153868i
$227$	6.73170	+	2.18726i	0.446799	+	0.145174i	0.523770	−	0.851860i	$-0.324525\pi$
$227$	6.73170	+	2.18726i	0.446799	+	0.145174i	−0.0769714	+	0.997033i	$0.524525\pi$
$228$	3.90195	−	5.37058i	0.258413	−	0.355675i
$229$	−7.12266	+	21.9213i	−0.470679	+	1.44860i	0.381019	+	0.924567i	$0.375573\pi$
$229$	−7.12266	+	21.9213i	−0.470679	+	1.44860i	−0.851698	+	0.524033i	$0.824427\pi$
$230$	7.62065	−	7.72222i	0.502491	−	0.509188i
$231$	−0.779846	+	0.566591i	−0.0513101	+	0.0372790i
$232$	−8.21523	+	2.66929i	−0.539356	+	0.175248i
$233$	−6.93605	+	2.25366i	−0.454396	+	0.147642i	−0.527268	−	0.849699i	$-0.676784\pi$
$233$	−6.93605	+	2.25366i	−0.454396	+	0.147642i	0.0728720	+	0.997341i	$0.476784\pi$
$234$	−1.11282	+	0.808512i	−0.0727474	+	0.0528541i
$235$	−10.3664	−	10.2300i	−0.676228	−	0.667335i
$236$	3.87911	−	11.9387i	0.252509	−	0.777141i
$237$	−8.35017	+	11.4930i	−0.542402	+	0.746552i
$238$	−0.332465	−	0.108025i	−0.0215505	−	0.00700219i
$239$	−11.2805	+	8.19576i	−0.729675	+	0.530140i	−0.889461	−	0.457012i	$-0.848920\pi$
$239$	−11.2805	+	8.19576i	−0.729675	+	0.530140i	0.159786	+	0.987152i	$0.448920\pi$
$240$	−1.00194	+	1.99903i	−0.0646752	+	0.129037i
$241$	15.1745	+	11.0249i	0.977472	+	0.710175i	0.957142	−	0.289618i	$-0.0935283\pi$
$241$	15.1745	+	11.0249i	0.977472	+	0.710175i	0.0203300	+	0.999793i	$0.493528\pi$
$242$		−	2.02749i		−	0.130332i
$243$			1.00000i			0.0641500i
$244$	5.52467	+	4.01390i	0.353680	+	0.256964i
$245$	10.8824	−	11.0275i	0.695254	−	0.704519i
$246$	1.03019	−	3.17061i	0.0656827	−	0.202151i
$247$			9.13127i			0.581009i
$248$	−2.57294	−	4.93761i	−0.163382	−	0.313539i
$249$	−8.25432			−0.523096
$250$	−10.0606	−	4.87696i	−0.636287	−	0.308446i
$251$	−5.00839	−	15.4143i	−0.316127	−	0.972939i	−0.975288	−	0.220937i	$-0.929088\pi$
$251$	−5.00839	−	15.4143i	−0.316127	−	0.972939i	0.659161	−	0.752002i	$-0.270912\pi$
$252$	0.156978	−	0.216062i	0.00988870	−	0.0136106i
$253$		−	17.5124i		−	1.10100i
$254$	5.89702			0.370012
$255$	−0.438718	+	2.89381i	−0.0274736	+	0.181217i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	13.1831	+	18.1449i	0.822337	+	1.13185i	0.989301	+	0.145887i	$0.0466036\pi$
$257$	13.1831	+	18.1449i	0.822337	+	1.13185i	−0.166964	+	0.985963i	$0.553396\pi$
$258$	3.22692	+	1.04849i	0.200899	+	0.0652762i
$259$	−1.85043	−	1.34441i	−0.114980	−	0.0835378i
$260$	−0.501254	−	3.03464i	−0.0310864	−	0.188201i
$261$	−2.66929	−	8.21523i	−0.165225	−	0.508510i
$262$	−1.58698	−	2.18429i	−0.0980439	−	0.134946i
$263$	−7.14753	+	2.32237i	−0.440735	+	0.143204i	−0.520975	−	0.853572i	$-0.674431\pi$
$263$	−7.14753	+	2.32237i	−0.440735	+	0.143204i	0.0802396	+	0.996776i	$0.474431\pi$
$264$	1.11535	+	3.43271i	0.0686453	+	0.211268i
$265$	0.893857	−	1.78338i	0.0549092	−	0.109552i
$266$	−0.547856	−	1.68613i	−0.0335912	−	0.103383i
$267$	1.00665	+	0.327081i	0.0616060	+	0.0200170i
$268$	−5.45409	+	7.50691i	−0.333161	+	0.458557i
$269$	0.932760	−	2.87074i	0.0568714	−	0.175032i	−0.918586	−	0.395222i	$-0.870668\pi$
$269$	0.932760	−	2.87074i	0.0568714	−	0.175032i	0.975457	+	0.220190i	$0.0706677\pi$
$270$	−1.99903	−	1.00194i	−0.121657	−	0.0609763i
$271$	−0.529635	+	0.384802i	−0.0321730	+	0.0233751i	−0.603756	−	0.797170i	$-0.706330\pi$
$271$	−0.529635	+	0.384802i	−0.0321730	+	0.0233751i	0.571583	+	0.820545i	$0.306330\pi$
$272$	−0.769375	+	1.05895i	−0.0466502	+	0.0642085i
$273$			0.367357i			0.0222335i
$274$	6.79061			0.410236
$275$	−17.0882	+	5.80350i	−1.03046	+	0.349964i
$276$	1.49933	+	4.61448i	0.0902493	+	0.277759i
$277$	−22.2394	−	7.22602i	−1.33624	−	0.434169i	−0.448196	−	0.893935i	$-0.647933\pi$
$277$	−22.2394	−	7.22602i	−1.33624	−	0.434169i	−0.888040	+	0.459766i	$0.847933\pi$
$278$			15.3203i			0.918851i
$279$	4.93761	−	2.57294i	0.295607	−	0.154038i
$280$	0.274631	+	0.530286i	0.0164123	+	0.0316906i
$281$	0.0409262	−	0.125958i	0.00244145	−	0.00751401i	−0.949828	−	0.312772i	$-0.898743\pi$
$281$	0.0409262	−	0.125958i	0.00244145	−	0.00751401i	0.952270	+	0.305258i	$0.0987426\pi$
$282$	6.19452	−	2.01272i	0.368878	−	0.119856i
$283$	4.49665	−	6.18911i	0.267298	−	0.367904i	−0.654177	−	0.756341i	$-0.726985\pi$
$283$	4.49665	−	6.18911i	0.267298	−	0.367904i	0.921475	+	0.388437i	$0.126985\pi$
$284$	8.00195			0.474828
$285$	−13.1811	+	6.82640i	−0.780783	+	0.404361i
$286$	−4.01657	−	2.91821i	−0.237505	−	0.172558i
$287$	−0.523330	−	0.720302i	−0.0308912	−	0.0425181i
$288$	−0.587785	−	0.809017i	−0.0346356	−	0.0476718i
$289$	4.72384	−	14.5385i	0.277873	−	0.855206i
$290$	19.0970	+	2.89521i	1.12141	+	0.170013i
$291$	−3.84365	+	11.8295i	−0.225319	+	0.693459i
$292$	0.433404	−	0.140822i	0.0253631	−	0.00824096i
$293$	−9.08435	−	12.5035i	−0.530714	−	0.730464i	0.456525	−	0.889710i	$-0.349094\pi$
$293$	−9.08435	−	12.5035i	−0.530714	−	0.730464i	−0.987239	+	0.159246i	$0.949094\pi$
$294$	2.14108	+	6.58956i	0.124870	+	0.384311i
$295$	−19.7163	+	19.9791i	−1.14793	+	1.16323i
$296$	−6.92869	+	5.03399i	−0.402722	+	0.292595i
$297$	−3.43271	+	1.11535i	−0.199186	+	0.0647194i
$298$	18.0480	+	5.86415i	1.04549	+	0.339701i
$299$	−5.39935	−	3.92286i	−0.312253	−	0.226865i
$300$	4.00582	−	2.99222i	0.231276	−	0.172756i
$301$	0.733096	−	0.532625i	0.0422549	−	0.0307000i
$302$	−1.62127	−	2.23149i	−0.0932938	−	0.128408i
$303$	−3.59462	+	4.94756i	−0.206505	+	0.284230i
$304$	−6.63840			−0.380738
$305$	−7.02225	−	13.5593i	−0.402093	−	0.776403i
$306$	−1.05895	−	0.769375i	−0.0605363	−	0.0439822i
$307$	19.9361	−	6.47765i	1.13782	−	0.369699i	0.321275	−	0.946986i	$-0.395889\pi$
$307$	19.9361	−	6.47765i	1.13782	−	0.369699i	0.816541	+	0.577287i	$0.195889\pi$
$308$	0.916764	+	0.297875i	0.0522375	+	0.0169730i
$309$	12.7326			0.724333
$310$	0.196162	+	12.4484i	0.0111413	+	0.707019i
$311$	23.1203			1.31103			0.655516	−	0.755182i	$-0.272451\pi$
$311$	23.1203			1.31103			0.655516	+	0.755182i	$0.272451\pi$
$312$	1.30820	+	0.425060i	0.0740622	+	0.0240643i
$313$	30.1291	−	9.78952i	1.70300	−	0.553337i	0.713853	−	0.700296i	$-0.246949\pi$
$313$	30.1291	−	9.78952i	1.70300	−	0.553337i	0.989143	+	0.146959i	$0.0469487\pi$
$314$	−12.1688	−	8.84117i	−0.686727	−	0.498936i
$315$	−0.530286	+	0.274631i	−0.0298782	+	0.0154737i
$316$	14.2062			0.799159
$317$	−10.8907	+	14.9898i	−0.611684	+	0.841910i	−0.996715	−	0.0809934i	$-0.974191\pi$
$317$	−10.8907	+	14.9898i	−0.611684	+	0.841910i	0.385031	+	0.922904i	$0.374191\pi$
$318$	0.524377	+	0.721743i	0.0294056	+	0.0404734i
$319$	25.2233	−	18.3258i	1.41223	−	1.02605i
$320$	2.20617	−	0.364410i	0.123329	−	0.0203711i
$321$	−0.663746	−	0.482239i	−0.0370467	−	0.0269160i
$322$	1.23238	+	0.400423i	0.0686776	+	0.0223147i
$323$	−8.26398	+	2.68513i	−0.459820	+	0.149405i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	−2.03852	+	6.56856i	−0.113077	+	0.364358i
$326$	−1.14047	−	3.51001i	−0.0631650	−	0.194402i
$327$	10.7339	+	14.7740i	0.593587	+	0.817003i
$328$	−3.17061	+	1.03019i	−0.175068	+	0.0568829i
$329$	0.537532	−	1.65435i	0.0296351	−	0.0912075i
$330$	1.20975	−	7.97959i	0.0665948	−	0.439262i
$331$	−7.66060	+	23.5769i	−0.421065	+	1.29590i	0.485648	+	0.874155i	$0.338584\pi$
$331$	−7.66060	+	23.5769i	−0.421065	+	1.29590i	−0.906712	+	0.421749i	$0.861416\pi$
$332$	4.85177	+	6.67788i	0.266275	+	0.366496i
$333$	−5.03399	−	6.92869i	−0.275861	−	0.379690i
$334$	−15.8301	−	11.5012i	−0.866183	−	0.629318i
$335$	18.4244	−	9.54183i	1.00663	−	0.521326i
$336$	−0.267067			−0.0145697
$337$	−9.10515	+	12.5322i	−0.495989	+	0.682671i	−0.981479	−	0.191572i	$-0.938641\pi$
$337$	−9.10515	+	12.5322i	−0.495989	+	0.682671i	0.485489	+	0.874243i	$0.338641\pi$
$338$	10.5643	−	3.43254i	0.574621	−	0.186706i
$339$	1.21609	−	3.74275i	0.0660491	−	0.203278i
$340$	2.59901	−	1.34601i	0.140951	−	0.0729975i
$341$	14.3393	+	14.0796i	0.776517	+	0.762455i
$342$		−	6.63840i		−	0.358964i
$343$	3.53783	+	1.14951i	0.191025	+	0.0620677i
$344$	−1.04849	−	3.22692i	−0.0565308	−	0.173984i
$345$	1.62623	−	10.7267i	0.0875534	−	0.577507i
$346$	20.1289			1.08213
$347$			19.0457i			1.02243i	0.859453	+	0.511214i	$0.170804\pi$
$347$			19.0457i			1.02243i	−0.859453	+	0.511214i	$0.829196\pi$
$348$	−5.07729	+	6.98829i	−0.272171	+	0.374612i
$349$	−9.90948	+	7.19966i	−0.530442	+	0.385389i	−0.820523	−	0.571613i	$-0.806318\pi$
$349$	−9.90948	+	7.19966i	−0.530442	+	0.385389i	0.290081	+	0.957002i	$0.406318\pi$
$350$	−0.0176780	−	1.33522i	−0.000944927	−	0.0713705i
$351$	−0.425060	+	1.30820i	−0.0226880	+	0.0698266i
$352$	2.12153	−	2.92003i	0.113078	−	0.155638i
$353$	−0.982831	−	0.319341i	−0.0523108	−	0.0169968i	0.282745	−	0.959195i	$-0.408755\pi$
$353$	−0.982831	−	0.319341i	−0.0523108	−	0.0169968i	−0.335056	+	0.942198i	$0.608755\pi$
$354$	−3.87911	−	11.9387i	−0.206172	−	0.634533i
$355$	−15.9961	−	8.01750i	−0.848986	−	0.425525i
$356$	−0.327081	−	1.00665i	−0.0173352	−	0.0533524i
$357$	−0.332465	+	0.108025i	−0.0175959	+	0.00571726i
$358$	4.62864	+	6.37078i	0.244631	+	0.336706i
$359$	1.36750	+	4.20873i	0.0721739	+	0.222128i	0.980636	−	0.195838i	$-0.0627428\pi$
$359$	1.36750	+	4.20873i	0.0721739	+	0.222128i	−0.908462	+	0.417967i	$0.862743\pi$
$360$	0.364410	+	2.20617i	0.0192061	+	0.116276i
$361$	−20.2807	−	14.7348i	−1.06741	−	0.775517i
$362$	3.19501	+	1.03812i	0.167926	+	0.0545625i
$363$	−1.19173	−	1.64027i	−0.0625495	−	0.0860920i
$364$	0.297198	−	0.215927i	0.0155774	−	0.0113177i
$365$	−1.00748	−	0.152740i	−0.0527341	−	0.00799479i
$366$	6.82886			0.356950
$367$		−	35.4506i		−	1.85051i	−0.379350	−	0.925253i	$-0.623852\pi$
$367$		−	35.4506i		−	1.85051i	0.379350	−	0.925253i	$-0.376148\pi$
$368$	2.85190	−	3.92531i	0.148666	−	0.204621i
$369$	−1.03019	−	3.17061i	−0.0536297	−	0.165055i
$370$	18.8944	−	3.12093i	0.982273	−	0.162249i
$371$	0.238257			0.0123697
$372$	−4.98380	−	2.48228i	−0.258398	−	0.128700i
$373$		−	9.16512i		−	0.474552i	−0.971442	−	0.237276i	$-0.923745\pi$
$373$		−	9.16512i		−	0.474552i	0.971442	−	0.237276i	$-0.0762545\pi$
$374$	1.45993	−	4.49320i	0.0754912	−	0.232338i
$375$	−11.0058	+	1.96792i	−0.568336	+	0.101623i
$376$	−5.26937	−	3.82842i	−0.271747	−	0.197436i
$377$		−	11.8818i		−	0.611943i
$378$		−	0.267067i		−	0.0137365i
$379$	−17.1669	−	12.4725i	−0.881806	−	0.640669i	0.0519229	−	0.998651i	$-0.483465\pi$
$379$	−17.1669	−	12.4725i	−0.881806	−	0.640669i	−0.933729	+	0.357982i	$0.883465\pi$
$380$	13.2703	+	6.65130i	0.680754	+	0.341205i
$381$	4.77079	−	3.46618i	0.244415	−	0.177578i
$382$	−16.8743	−	5.48280i	−0.863366	−	0.280525i
$383$	−7.96840	+	10.9676i	−0.407166	+	0.560416i	−0.962524	−	0.271195i	$-0.912581\pi$
$383$	−7.96840	+	10.9676i	−0.407166	+	0.560416i	0.555358	+	0.831611i	$0.312581\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	−1.53418	−	1.51400i	−0.0781892	−	0.0771608i
$386$	−10.9881	+	7.98331i	−0.559278	+	0.406340i
$387$	3.22692	−	1.04849i	0.164034	−	0.0532978i
$388$	11.8295	−	3.84365i	0.600553	−	0.195132i
$389$	−20.8934	+	15.1800i	−1.05934	+	0.769654i	−0.973966	−	0.226695i	$-0.927208\pi$
$389$	−20.8934	+	15.1800i	−1.05934	+	0.769654i	−0.0853724	+	0.996349i	$0.527208\pi$
$390$	−2.18924	−	2.16045i	−0.110857	−	0.109399i
$391$	1.96254	−	6.04007i	0.0992497	−	0.305459i
$392$	4.07257	−	5.60542i	0.205696	−	0.283116i
$393$	−2.56779	−	0.834324i	−0.129528	−	0.0420861i
$394$	4.30704	−	3.12925i	0.216986	−	0.157649i
$395$	−28.3985	−	14.2338i	−1.42888	−	0.716178i
$396$	2.92003	+	2.12153i	0.146737	+	0.106611i
$397$		−	17.9258i		−	0.899668i	−0.893112	−	0.449834i	$-0.851483\pi$
$397$		−	17.9258i		−	0.899668i	0.893112	−	0.449834i	$-0.148517\pi$
$398$		−	24.2461i		−	1.21535i
$399$	−1.43431	−	1.04208i	−0.0718051	−	0.0521695i
$400$	−4.77532	−	1.48200i	−0.238766	−	0.0740998i
$401$	−6.45007	+	19.8513i	−0.322101	+	0.991325i	0.650631	+	0.759394i	$0.274504\pi$
$401$	−6.45007	+	19.8513i	−0.322101	+	0.991325i	−0.972732	+	0.231931i	$0.925496\pi$
$402$			9.27905i			0.462797i
$403$	7.55304	−	1.26713i	0.376243	−	0.0631204i
$404$	6.11553			0.304259
$405$	−2.20617	+	0.364410i	−0.109626	+	0.0181077i
$406$	0.712881	+	2.19402i	0.0353797	+	0.108887i
$407$	18.1695	−	25.0081i	0.900628	−	1.23961i
$408$			1.30894i			0.0648021i
$409$	4.15471			0.205437			0.102719	−	0.994710i	$-0.467246\pi$
$409$	4.15471			0.205437			0.102719	+	0.994710i	$0.467246\pi$
$410$	7.37033	+	1.11738i	0.363994	+	0.0551837i
$411$	5.49372	−	3.99142i	0.270985	−	0.196882i
$412$	−7.48405	−	10.3009i	−0.368712	−	0.507489i
$413$	−3.18843	−	1.03598i	−0.156892	−	0.0509774i
$414$	3.92531	+	2.85190i	0.192918	+	0.140163i
$415$	−3.00795	−	18.2105i	−0.147655	−	0.893916i
$416$	−0.425060	−	1.30820i	−0.0208403	−	0.0641398i
$417$	9.00505	+	12.3944i	0.440979	+	0.606956i
$418$	22.7877	−	7.40417i	1.11458	−	0.362150i
$419$	−1.93446	−	5.95367i	−0.0945047	−	0.290856i	0.892620	−	0.450811i	$-0.148865\pi$
$419$	−1.93446	−	5.95367i	−0.0945047	−	0.290856i	−0.987124	+	0.159955i	$0.948865\pi$
$420$	0.533875	+	0.267586i	0.0260504	+	0.0130569i
$421$	3.91879	+	12.0608i	0.190990	+	0.587807i	1.00000		1.21940e-5i	$3.88146e-6\pi$
$421$	3.91879	+	12.0608i	0.190990	+	0.587807i	−0.809010	+	0.587795i	$0.799996\pi$
$422$	−22.1040	−	7.18202i	−1.07601	−	0.349615i
$423$	3.82842	−	5.26937i	0.186144	−	0.256206i
$424$	0.275681	−	0.848460i	0.0133883	−	0.0412049i
$425$	−6.54412	+	0.0866424i	−0.317436	+	0.00420277i
$426$	6.47371	−	4.70343i	0.313652	−	0.227882i
$427$	1.07198	−	1.47546i	0.0518769	−	0.0714024i
$428$			0.820435i			0.0396572i
$429$	−4.96476			−0.239701
$430$	−1.13723	+	7.50123i	−0.0548422	+	0.361742i
$431$	−0.0364745	−	0.112257i	−0.00175692	−	0.00540723i	0.950174	−	0.311719i	$-0.100905\pi$
$431$	−0.0364745	−	0.112257i	−0.00175692	−	0.00540723i	−0.951931	+	0.306312i	$0.900905\pi$
$432$	−0.951057	−	0.309017i	−0.0457577	−	0.0148676i
$433$		−	26.6588i		−	1.28114i	−0.767900	−	0.640570i	$-0.778698\pi$
$433$		−	26.6588i		−	1.28114i	0.767900	−	0.640570i	$-0.221302\pi$
$434$	−1.31867	+	0.687147i	−0.0632984	+	0.0329841i
$435$	17.1515	−	8.88263i	0.822352	−	0.425890i
$436$	5.64316	−	17.3679i	0.270258	−	0.831769i
$437$	30.6327	−	9.95318i	1.46536	−	0.476125i
$438$	0.267859	−	0.368676i	0.0127988	−	0.0176160i
$439$	33.9358			1.61967			0.809834	−	0.586659i	$-0.199557\pi$
$439$	33.9358			1.61967			0.809834	+	0.586659i	$0.199557\pi$
$440$	−7.16670	+	3.71158i	−0.341659	+	0.176942i
$441$	5.60542	+	4.07257i	0.266925	+	0.193932i
$442$	−1.05829	−	1.45661i	−0.0503378	−	0.0692841i
$443$	−1.35803	−	1.86917i	−0.0645220	−	0.0888069i	0.775537	−	0.631303i	$-0.217479\pi$
$443$	−1.35803	−	1.86917i	−0.0645220	−	0.0888069i	−0.840059	+	0.542496i	$0.817479\pi$
$444$	−2.64652	+	8.14516i	−0.125598	+	0.386552i
$445$	−0.354764	+	2.34004i	−0.0168174	+	0.110928i
$446$	4.89232	−	15.0570i	0.231658	−	0.712970i
$447$	18.0480	−	5.86415i	0.853642	−	0.277365i
$448$	0.156978	+	0.216062i	0.00741653	+	0.0102080i
$449$	6.43831	+	19.8151i	0.303843	+	0.935132i	0.980107	+	0.198472i	$0.0635979\pi$
$449$	6.43831	+	19.8151i	0.303843	+	0.935132i	−0.676264	+	0.736659i	$0.736402\pi$
$450$	1.48200	−	4.77532i	0.0698620	−	0.225111i
$451$	9.73474	−	7.07270i	0.458391	−	0.333040i
$452$	−3.74275	+	1.21609i	−0.176044	+	0.0572002i
$453$	−2.62328	−	0.852354i	−0.123252	−	0.0400471i
$454$	−5.72633	−	4.16042i	−0.268750	−	0.195258i
$455$	−0.810454	+	0.133869i	−0.0379947	+	0.00627586i
$456$	−5.37058	+	3.90195i	−0.251500	+	0.182726i
$457$	3.78029	+	5.20313i	0.176835	+	0.243392i	0.888229	−	0.459401i	$-0.151936\pi$
$457$	3.78029	+	5.20313i	0.176835	+	0.243392i	−0.711394	+	0.702793i	$0.751936\pi$
$458$	13.5481	−	18.6474i	0.633062	−	0.871335i
$459$	−1.30894			−0.0610960
$460$	−9.63397	+	4.98935i	−0.449186	+	0.232630i
$461$	−10.4708	−	7.60751i	−0.487675	−	0.354317i	0.316614	−	0.948554i	$-0.397454\pi$
$461$	−10.4708	−	7.60751i	−0.487675	−	0.354317i	−0.804290	+	0.594237i	$0.797454\pi$
$462$	0.916764	−	0.297875i	0.0426517	−	0.0138584i
$463$	10.2909	+	3.34372i	0.478259	+	0.155396i	0.538219	−	0.842805i	$-0.319097\pi$
$463$	10.2909	+	3.34372i	0.478259	+	0.155396i	−0.0599599	+	0.998201i	$0.519097\pi$
$464$	8.63801			0.401009
$465$	7.47566	+	9.95563i	0.346675	+	0.461681i
$466$	7.29299			0.337841
$467$	−27.1019	−	8.80594i	−1.25413	−	0.407490i	−0.394729	−	0.918798i	$-0.629161\pi$
$467$	−27.1019	−	8.80594i	−1.25413	−	0.407490i	−0.859398	+	0.511307i	$0.829161\pi$
$468$	1.30820	−	0.425060i	0.0604716	−	0.0196484i
$469$	2.00485	+	1.45661i	0.0925754	+	0.0672600i
$470$	6.69776	+	12.9327i	0.308945	+	0.596543i
$471$	−15.0415			−0.693076
$472$	−7.37851	+	10.1556i	−0.339623	+	0.467451i
$473$	7.19832	+	9.90764i	0.330979	+	0.455554i
$474$	11.4930	−	8.35017i	0.527892	−	0.383536i
$475$	−19.8636	−	26.5923i	−0.911402	−	1.22014i
$476$	0.282812	+	0.205475i	0.0129627	+	0.00941793i
$477$	0.848460	+	0.275681i	0.0388483	+	0.0126226i
$478$	13.2610	−	4.30877i	0.606545	−	0.197078i
$479$	−11.2322	+	8.16069i	−0.513213	+	0.372871i	−0.814041	−	0.580807i	$-0.802737\pi$
$479$	−11.2322	+	8.16069i	−0.513213	+	0.372871i	0.300828	+	0.953678i	$0.402737\pi$
$480$	1.57064	−	1.59157i	0.0716895	−	0.0726449i
$481$	−3.64035	−	11.2039i	−0.165986	−	0.510852i
$482$	−11.0249	−	15.1745i	−0.502170	−	0.691177i
$483$	1.23238	−	0.400423i	0.0560751	−	0.0182199i
$484$	−0.626528	+	1.92826i	−0.0284786	+	0.0876480i
$485$	−27.4987	−	4.16896i	−1.24865	−	0.189303i
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	1.29932	+	1.78836i	0.0588777	+	0.0810382i	0.837441	−	0.546528i	$-0.184051\pi$
$487$	1.29932	+	1.78836i	0.0588777	+	0.0810382i	−0.778563	+	0.627567i	$0.784051\pi$
$488$	−4.01390	−	5.52467i	−0.181701	−	0.250090i
$489$	−2.98580	−	2.16931i	−0.135022	−	0.0980995i
$490$	−13.7575	+	7.12489i	−0.621500	+	0.321870i
$491$	−2.56656			−0.115827			−0.0579136	−	0.998322i	$-0.518445\pi$
$491$	−2.56656			−0.115827			−0.0579136	+	0.998322i	$0.518445\pi$
$492$	−1.95954	+	2.69708i	−0.0883430	+	0.121594i
$493$	10.7532	−	3.49394i	0.484301	−	0.157359i
$494$	2.82172	−	8.68436i	0.126955	−	0.390728i
$495$	−3.71158	−	7.16670i	−0.166823	−	0.322119i
$496$	0.921201	+	5.49103i	0.0413632	+	0.246554i
$497$		−	2.13706i		−	0.0958602i
$498$	7.85032	+	2.55072i	0.351781	+	0.114301i
$499$	0.557092	+	1.71455i	0.0249388	+	0.0767539i	0.962751	−	0.270388i	$-0.0871521\pi$
$499$	0.557092	+	1.71455i	0.0249388	+	0.0767539i	−0.937812	+	0.347142i	$0.887152\pi$
$500$	8.06112	+	7.74715i	0.360504	+	0.346463i
$501$	−19.5670			−0.874191
$502$			16.2075i			0.723376i
$503$	5.34883	−	7.36203i	0.238492	−	0.328257i	−0.672947	−	0.739691i	$-0.734972\pi$
$503$	5.34883	−	7.36203i	0.238492	−	0.328257i	0.911440	+	0.411434i	$0.134972\pi$
$504$	−0.216062	+	0.156978i	−0.00962417	+	0.00699237i
$505$	−12.2251	−	6.12741i	−0.544010	−	0.272666i
$506$	−5.41164	+	16.6553i	−0.240577	+	0.740419i
$507$	6.52908	−	8.98651i	0.289967	−	0.399105i
$508$	−5.60840	−	1.82228i	−0.248833	−	0.0808506i
$509$	−0.509387	−	1.56773i	−0.0225782	−	0.0694884i	0.939133	−	0.343555i	$-0.111631\pi$
$509$	−0.509387	−	1.56773i	−0.0225782	−	0.0694884i	−0.961711	+	0.274066i	$0.911631\pi$
$510$	1.31148	−	2.61660i	0.0580734	−	0.115865i
$511$	−0.0376089	−	0.115748i	−0.00166372	−	0.00512040i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−3.90195	−	5.37058i	−0.172275	−	0.237117i
$514$	−6.93075	−	21.3307i	−0.305702	−	0.940855i
$515$	4.63989	+	28.0904i	0.204458	+	1.23781i
$516$	−2.74498	−	1.99435i	−0.120841	−	0.0877963i
$517$	22.3583	+	7.26464i	0.983315	+	0.319499i
$518$	1.34441	+	1.85043i	0.0590701	+	0.0813031i
$519$	16.2846	−	11.8314i	0.714814	−	0.519343i
$520$	−0.461036	+	3.04101i	−0.0202178	+	0.133357i
$521$	17.0761			0.748118			0.374059	−	0.927405i	$-0.377966\pi$
$521$	17.0761			0.748118			0.374059	+	0.927405i	$0.377966\pi$
$522$			8.63801i			0.378075i
$523$	0.187013	−	0.257401i	0.00817749	−	0.0112553i	−0.804909	−	0.593399i	$-0.797786\pi$
$523$	0.187013	−	0.257401i	0.00817749	−	0.0112553i	0.813086	+	0.582143i	$0.197786\pi$
$524$	0.834324	+	2.56779i	0.0364476	+	0.112174i
$525$	−0.799124	−	1.06982i	−0.0348766	−	0.0466910i
$526$	7.51535			0.327685
$527$	3.36781	+	6.46303i	0.146704	+	0.281534i
$528$		−	3.60936i		−	0.157077i
$529$	−0.167302	+	0.514902i	−0.00727399	+	0.0223870i
$530$	−1.40120	+	1.41988i	−0.0608644	+	0.0616756i
$531$	−10.1556	−	7.37851i	−0.440717	−	0.320200i
$532$			1.77290i			0.0768650i
$533$		−	4.58568i		−	0.198628i
$534$	−0.856308	−	0.622145i	−0.0370561	−	0.0269228i
$535$	0.822029	−	1.64007i	0.0355394	−	0.0709065i
$536$	7.50691	−	5.45409i	0.324249	−	0.235581i
$537$	7.48930	+	2.43342i	0.323187	+	0.105010i
$538$	−1.77422	+	2.44200i	−0.0764919	+	0.105282i
$539$	−7.72792	+	23.7841i	−0.332865	+	1.02445i
$540$	1.59157	+	1.57064i	0.0684903	+	0.0675895i
$541$	−18.5863	+	13.5037i	−0.799087	+	0.580570i	−0.910646	−	0.413187i	$-0.864415\pi$
$541$	−18.5863	+	13.5037i	−0.799087	+	0.580570i	0.111559	+	0.993758i	$0.464415\pi$
$542$	0.622623	−	0.202302i	0.0267439	−	0.00868964i
$543$	3.19501	−	1.03812i	0.137111	−	0.0445501i
$544$	1.05895	−	0.769375i	0.0454023	−	0.0329867i
$545$	−28.6824	+	29.0647i	−1.22862	+	1.24499i
$546$	0.113520	−	0.349378i	0.00485819	−	0.0149520i
$547$	−10.8953	+	14.9961i	−0.465848	+	0.641185i	−0.975709	−	0.219072i	$-0.929697\pi$
$547$	−10.8953	+	14.9961i	−0.465848	+	0.641185i	0.509860	+	0.860257i	$0.329697\pi$
$548$	−6.45825	−	2.09841i	−0.275883	−	0.0896398i
$549$	5.52467	−	4.01390i	0.235787	−	0.171309i
$550$	18.0452	−	0.238914i	0.769451	−	0.0101873i
$551$	46.3911	+	33.7051i	1.97633	+	1.43589i
$552$		−	4.85195i		−	0.206513i
$553$		−	3.79400i		−	0.161337i
$554$	18.9180	+	13.7447i	0.803747	+	0.583957i
$555$	13.4515	−	13.6307i	0.570983	−	0.578592i
$556$	4.73424	−	14.5705i	0.200776	−	0.617926i
$557$		−	25.7758i		−	1.09215i	−0.837735	−	0.546077i	$-0.816121\pi$
$557$		−	25.7758i		−	1.09215i	0.837735	−	0.546077i	$-0.183879\pi$
$558$	−5.49103	+	0.921201i	−0.232454	+	0.0389976i
$559$	4.66713			0.197399
$560$	−0.0973219	−	0.589197i	−0.00411260	−	0.0248981i
$561$	−1.45993	−	4.49320i	−0.0616383	−	0.189703i
$562$	−0.0778462	+	0.107146i	−0.00328374	+	0.00451968i
$563$			38.3271i			1.61529i	0.589667	+	0.807647i	$0.299259\pi$
$563$			38.3271i			1.61529i	−0.589667	+	0.807647i	$0.700741\pi$
$564$	−6.51331			−0.274260
$565$	8.70031	+	1.31902i	0.366025	+	0.0554915i
$566$	−6.18911	+	4.49665i	−0.260148	+	0.189008i
$567$	−0.156978	−	0.216062i	−0.00659247	−	0.00907375i
$568$	−7.61031	−	2.47274i	−0.319321	−	0.103754i
$569$	32.5238	+	23.6299i	1.36347	+	0.990617i	0.998216	+	0.0597073i	$0.0190167\pi$
$569$	32.5238	+	23.6299i	1.36347	+	0.990617i	0.365251	+	0.930909i	$0.380983\pi$
$570$	14.6455	−	2.41910i	0.613431	−	0.101325i
$571$	−4.50853	−	13.8758i	−0.188676	−	0.580685i	0.811316	−	0.584608i	$-0.198752\pi$
$571$	−4.50853	−	13.8758i	−0.188676	−	0.580685i	−0.999992	+	0.00392218i	$0.998752\pi$
$572$	2.91821	+	4.01657i	0.122017	+	0.167941i
$573$	−16.8743	+	5.48280i	−0.704935	+	0.229047i
$574$	0.275131	+	0.846766i	0.0114837	+	0.0353433i
$575$	24.2576	−	0.321164i	1.01161	−	0.0133935i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	35.7946	+	11.6304i	1.49015	+	0.484179i	0.937128	−	0.348987i	$-0.113474\pi$
$577$	35.7946	+	11.6304i	1.49015	+	0.484179i	0.553023	+	0.833166i	$0.313474\pi$
$578$	−8.98529	+	12.3672i	−0.373739	+	0.514407i
$579$	−4.19707	+	12.9173i	−0.174424	+	0.536823i
$580$	−17.2676	−	8.65479i	−0.716999	−	0.359371i
$581$	1.78344	−	1.29575i	0.0739897	−	0.0537567i
$582$	7.31105	−	10.0628i	0.303053	−	0.417116i
$583$			3.22000i			0.133359i
$584$	−0.455708			−0.0188573
$585$	−3.04101	−	0.461036i	−0.125730	−	0.0190615i
$586$	4.77593	+	14.6988i	0.197292	+	0.607201i
$587$	24.9490	+	8.10641i	1.02975	+	0.334587i	0.774693	−	0.632337i	$-0.217904\pi$
$587$	24.9490	+	8.10641i	1.02975	+	0.334587i	0.255061	+	0.966925i	$0.417904\pi$
$588$		−	6.92868i		−	0.285734i
$589$	−16.4784	+	33.0845i	−0.678979	+	1.36322i
$590$	24.9252	−	12.9086i	1.02615	−	0.531437i
$591$	1.64514	−	5.06323i	0.0676721	−	0.208273i
$592$	8.14516	−	2.64652i	0.334764	−	0.108771i
$593$	16.1919	−	22.2862i	0.664921	−	0.915185i	−0.334711	−	0.942321i	$-0.608639\pi$
$593$	16.1919	−	22.2862i	0.664921	−	0.915185i	0.999632	+	0.0271359i	$0.00863867\pi$
$594$	3.60936			0.148094
$595$	−0.359475	−	0.694111i	−0.0147370	−	0.0284558i
$596$	−15.3526	−	11.1543i	−0.628865	−	0.456897i
$597$	−14.2515	−	19.6155i	−0.583274	−	0.802808i
$598$	3.92286	+	5.39935i	0.160418	+	0.220796i
$599$	−2.34791	+	7.22611i	−0.0959329	+	0.295251i	−0.987496	−	0.157646i	$-0.949609\pi$
$599$	−2.34791	+	7.22611i	−0.0959329	+	0.295251i	0.891563	+	0.452897i	$0.149609\pi$
$600$	−4.73441	+	1.60790i	−0.193282	+	0.0656424i
$601$	−8.09073	+	24.9007i	−0.330028	+	1.01572i	0.639092	+	0.769131i	$0.279310\pi$
$601$	−8.09073	+	24.9007i	−0.330028	+	1.01572i	−0.969120	+	0.246591i	$0.920690\pi$
$602$	−0.861806	+	0.280018i	−0.0351246	+	0.0114127i
$603$	5.45409	+	7.50691i	0.222108	+	0.305705i
$604$	0.852354	+	2.62328i	0.0346818	+	0.106740i
$605$	3.18445	−	3.22689i	0.129466	−	0.131192i
$606$	4.94756	−	3.59462i	0.200981	−	0.146021i
$607$	−41.1106	+	13.3576i	−1.66863	+	0.542170i	−0.982653	−	0.185456i	$-0.940624\pi$
$607$	−41.1106	+	13.3576i	−1.66863	+	0.542170i	−0.685974	+	0.727626i	$0.740624\pi$
$608$	6.31349	+	2.05138i	0.256046	+	0.0831944i
$609$	1.86635	+	1.35598i	0.0756281	+	0.0549471i
$610$	2.48850	+	15.0657i	0.100757	+	0.609991i
$611$	7.24815	−	5.26609i	0.293229	−	0.213043i
$612$	0.769375	+	1.05895i	0.0311001	+	0.0428057i
$613$	17.4308	−	23.9914i	0.704022	−	0.969003i	−0.295883	−	0.955224i	$-0.595614\pi$
$613$	17.4308	−	23.9914i	0.704022	−	0.969003i	0.999905	−	0.0137792i	$-0.00438618\pi$
$614$	−20.9621			−0.845962
$615$	6.61950	−	3.42819i	0.266924	−	0.138238i
$616$	−0.779846	−	0.566591i	−0.0314209	−	0.0228286i
$617$	−19.3110	+	6.27452i	−0.777431	+	0.252603i	−0.670743	−	0.741690i	$-0.734025\pi$
$617$	−19.3110	+	6.27452i	−0.777431	+	0.252603i	−0.106688	+	0.994293i	$0.534025\pi$
$618$	−12.1094	−	3.93460i	−0.487113	−	0.158273i
$619$	16.2454			0.652958			0.326479	−	0.945204i	$-0.394138\pi$
$619$	16.2454			0.652958			0.326479	+	0.945204i	$0.394138\pi$
$620$	3.66019	−	11.8997i	0.146997	−	0.477904i
$621$	4.85195			0.194702
$622$	−21.9887	−	7.14456i	−0.881667	−	0.286471i
$623$	−0.268844	+	0.0873526i	−0.0107710	+	0.00349971i
$624$	−1.11282	−	0.808512i	−0.0445485	−	0.0323664i
$625$	−8.35219	−	23.5635i	−0.334088	−	0.942542i
$626$	−31.6796			−1.26617
$627$	14.0836	−	19.3844i	0.562443	−	0.774137i
$628$	8.84117	+	12.1688i	0.352801	+	0.485589i
$629$	9.06923	−	6.58918i	0.361614	−	0.262728i
$630$	0.589197	−	0.0973219i	0.0234742	−	0.00387740i
$631$	−38.5038	−	27.9746i	−1.53281	−	1.11365i	−0.954650	−	0.297730i	$-0.903771\pi$
$631$	−38.5038	−	27.9746i	−1.53281	−	1.11365i	−0.578161	−	0.815923i	$-0.696229\pi$
$632$	−13.5109	−	4.38995i	−0.537433	−	0.174623i
$633$	−22.1040	+	7.18202i	−0.878555	+	0.285460i
$634$	14.9898	−	10.8907i	0.595320	−	0.432526i
$635$	9.38553	+	9.26209i	0.372453	+	0.367555i
$636$	−0.275681	−	0.848460i	−0.0109315	−	0.0336436i
$637$	5.60192	+	7.71038i	0.221956	+	0.305496i
$638$	−29.6517	+	9.63444i	−1.17392	+	0.381431i
$639$	2.47274	−	7.61031i	0.0978200	−	0.301059i
$640$	−2.21081	−	0.335171i	−0.0873898	−	0.0132488i
$641$	−0.798376	+	2.45715i	−0.0315340	+	0.0970516i	−0.965585	−	0.260089i	$-0.916248\pi$
$641$	−0.798376	+	2.45715i	−0.0315340	+	0.0970516i	0.934051	+	0.357140i	$0.116248\pi$
$642$	0.482239	+	0.663746i	0.0190325	+	0.0261960i
$643$	16.8451	+	23.1853i	0.664307	+	0.914340i	0.999614	−	0.0277685i	$-0.00884014\pi$
$643$	16.8451	+	23.1853i	0.664307	+	0.914340i	−0.335307	+	0.942109i	$0.608840\pi$
$644$	−1.04832	−	0.761650i	−0.0413097	−	0.0300132i
$645$	3.48908	+	6.73707i	0.137382	+	0.265272i
$646$	8.68926			0.341874
$647$	−24.0195	+	33.0599i	−0.944302	+	1.29972i	0.00970986	+	0.999953i	$0.496909\pi$
$647$	−24.0195	+	33.0599i	−0.944302	+	1.29972i	−0.954012	+	0.299768i	$0.903091\pi$
$648$	−0.951057	+	0.309017i	−0.0373610	+	0.0121393i
$649$	14.0011	−	43.0910i	0.549592	−	1.69147i
$650$	3.96855	−	5.61714i	0.155659	−	0.220322i
$651$	−0.662935	+	1.33101i	−0.0259825	+	0.0521664i
$652$			3.69065i			0.144537i
$653$	−32.2601	−	10.4819i	−1.26244	−	0.410190i	−0.400074	−	0.916483i	$-0.631016\pi$
$653$	−32.2601	−	10.4819i	−1.26244	−	0.410190i	−0.862362	+	0.506292i	$0.831016\pi$
$654$	−5.64316	−	17.3679i	−0.220665	−	0.679137i
$655$	0.904938	−	5.96902i	0.0353589	−	0.233229i
$656$	3.33377			0.130162
$657$		−	0.455708i		−	0.0177789i
$658$	−1.02245	+	1.40728i	−0.0398591	+	0.0548614i
$659$	20.8672	−	15.1609i	0.812871	−	0.590586i	−0.101790	−	0.994806i	$-0.532457\pi$
$659$	20.8672	−	15.1609i	0.812871	−	0.590586i	0.914662	+	0.404220i	$0.132457\pi$
$660$	−3.61637	+	7.21521i	−0.140767	+	0.280852i
$661$	7.70304	−	23.7075i	0.299613	−	0.922115i	−0.682019	−	0.731334i	$-0.738898\pi$
$661$	7.70304	−	23.7075i	0.299613	−	0.922115i	0.981633	−	0.190781i	$-0.0611021\pi$
$662$	14.5713	−	20.0557i	0.566331	−	0.779487i
$663$	−1.71235	−	0.556377i	−0.0665023	−	0.0216079i
$664$	−2.55072	−	7.85032i	−0.0989873	−	0.304652i
$665$	1.77635	−	3.54408i	0.0688837	−	0.137433i
$666$	2.64652	+	8.14516i	0.102551	+	0.315619i
$667$	−39.8599	+	12.9513i	−1.54338	+	0.501475i
$668$	11.5012	+	15.8301i	0.444995	+	0.612484i
$669$	−4.89232	−	15.0570i	−0.189148	−	0.582137i
$670$	−20.4712	+	3.38138i	−0.790871	+	0.130634i
$671$	19.9405	+	14.4876i	0.769795	+	0.559289i
$672$	0.253996	+	0.0825284i	0.00979811	+	0.00318360i
$673$	13.0874	+	18.0133i	0.504483	+	0.694361i	0.982977	−	0.183730i	$-0.0588172\pi$
$673$	13.0874	+	18.0133i	0.504483	+	0.694361i	−0.478494	+	0.878091i	$0.658817\pi$
$674$	12.5322	−	9.10515i	0.482721	−	0.350717i
$675$	−1.60790	−	4.73441i	−0.0618882	−	0.182228i
$676$	−11.1079			−0.427228
$677$		−	10.8573i		−	0.417281i	−0.977992	−	0.208641i	$-0.933096\pi$
$677$		−	10.8573i		−	0.417281i	0.977992	−	0.208641i	$-0.0669039\pi$
$678$	−2.31315	+	3.18377i	−0.0888358	+	0.122272i
$679$	−1.02651	−	3.15928i	−0.0393939	−	0.121242i
$680$	−2.88775	+	0.476990i	−0.110740	+	0.0182917i
$681$	−7.07813			−0.271235
$682$	−9.28665	−	17.8216i	−0.355604	−	0.682425i
$683$		−	33.6782i		−	1.28866i	−0.764748	−	0.644330i	$-0.777136\pi$
$683$		−	33.6782i		−	1.28866i	0.764748	−	0.644330i	$-0.222864\pi$
$684$	−2.05138	+	6.31349i	−0.0784364	+	0.241402i
$685$	10.8077	+	10.6656i	0.412942	+	0.407511i
$686$	−3.00946	−	2.18650i	−0.114902	−	0.0834809i
$687$		−	23.0494i		−	0.879390i
$688$			3.39299i			0.129356i
$689$	0.992775	+	0.721293i	0.0378217	+	0.0274791i
$690$	−4.86138	+	9.69918i	−0.185069	+	0.369241i
$691$	−24.3461	+	17.6885i	−0.926169	+	0.672901i	−0.945052	−	0.326920i	$-0.893989\pi$
$691$	−24.3461	+	17.6885i	−0.926169	+	0.672901i	0.0188827	+	0.999822i	$0.493989\pi$
$692$	−19.1437	−	6.22016i	−0.727734	−	0.236455i
$693$	0.566591	−	0.779846i	0.0215230	−	0.0296239i
$694$	5.88545	−	18.1136i	0.223409	−	0.687581i
$695$	−24.0627	+	24.3834i	−0.912749	+	0.924914i
$696$	6.98829	−	5.07729i	0.264891	−	0.192454i
$697$	4.15013	−	1.34846i	0.157197	−	0.0510765i
$698$	11.6493	−	3.78508i	0.440932	−	0.143268i
$699$	5.90016	−	4.28671i	0.223164	−	0.162138i
$700$	−0.395793	+	1.27533i	−0.0149596	+	0.0482030i
$701$	−2.04944	+	6.30754i	−0.0774064	+	0.238232i	−0.982271	−	0.187468i	$-0.939972\pi$
$701$	−2.04944	+	6.30754i	−0.0774064	+	0.238232i	0.904864	+	0.425700i	$0.139972\pi$
$702$	0.808512	−	1.11282i	0.0305153	−	0.0420007i
$703$	54.0709	+	17.5687i	2.03932	+	0.662616i
$704$	−2.92003	+	2.12153i	−0.110053	+	0.0799581i
$705$	13.0203	+	6.52596i	0.490372	+	0.245782i
$706$	0.836046	+	0.607423i	0.0314650	+	0.0228607i
$707$		−	1.63326i		−	0.0614250i
$708$			12.5531i			0.471773i
$709$	0.951946	+	0.691630i	0.0357511	+	0.0259747i	0.605517	−	0.795832i	$-0.292966\pi$
$709$	0.951946	+	0.691630i	0.0357511	+	0.0259747i	−0.569766	+	0.821807i	$0.692966\pi$
$710$	12.7357	+	12.5682i	0.477961	+	0.471675i
$711$	4.38995	−	13.5109i	0.164636	−	0.506697i
$712$			1.05846i			0.0396673i
$713$	−12.4837	−	23.9570i	−0.467520	−	0.897198i
$714$	0.349575			0.0130825
$715$	−1.80921	−	10.9531i	−0.0676605	−	0.409624i
$716$	−2.43342	−	7.48930i	−0.0909413	−	0.279888i
$717$	8.19576	−	11.2805i	0.306076	−	0.421278i
$718$		−	4.42532i		−	0.165152i
$719$	−39.0808			−1.45747			−0.728734	−	0.684797i	$-0.759891\pi$
$719$	−39.0808			−1.45747			−0.728734	+	0.684797i	$0.759891\pi$
$720$	0.335171	−	2.21081i	0.0124911	−	0.0823919i
$721$	−2.75104	+	1.99874i	−0.102454	+	0.0744371i
$722$	14.7348	+	20.2807i	0.548373	+	0.754771i
$723$	−17.8386	−	5.79612i	−0.663426	−	0.215560i
$724$	−2.71784	−	1.97463i	−0.101008	−	0.0733864i
$725$	25.8468	+	34.6023i	0.959927	+	1.28510i
$726$	0.626528	+	1.92826i	0.0232526	+	0.0715643i
$727$	1.81266	+	2.49491i	0.0672278	+	0.0925311i	0.841307	−	0.540558i	$-0.181787\pi$
$727$	1.81266	+	2.49491i	0.0672278	+	0.0925311i	−0.774079	+	0.633089i	$0.781787\pi$
$728$	−0.349378	+	0.113520i	−0.0129488	+	0.00420732i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	0.910974	+	0.456594i	0.0337166	+	0.0168993i
$731$	1.37241	+	4.22384i	0.0507604	+	0.156224i
$732$	−6.49463	−	2.11023i	−0.240049	−	0.0779965i
$733$	21.8906	−	30.1299i	0.808549	−	1.11287i	−0.182997	−	0.983114i	$-0.558580\pi$
$733$	21.8906	−	30.1299i	0.808549	−	1.11287i	0.991546	−	0.129759i	$-0.0414202\pi$
$734$	−10.9548	+	33.7155i	−0.404350	+	1.24446i
$735$	−6.94214	+	13.8506i	−0.256065	+	0.510887i
$736$	−3.92531	+	2.85190i	−0.144689	+	0.105123i
$737$	−19.6858	+	27.0951i	−0.725135	+	0.998062i
$738$			3.33377i			0.122718i
$739$	−10.0610			−0.370100			−0.185050	−	0.982729i	$-0.559245\pi$
$739$	−10.0610			−0.370100			−0.185050	+	0.982729i	$0.559245\pi$
$740$	−18.9341	−	2.87052i	−0.696030	−	0.105522i
$741$	−2.82172	−	8.68436i	−0.103658	−	0.319028i
$742$	−0.226596	−	0.0736255i	−0.00831860	−	0.00270288i
$743$		−	21.3046i		−	0.781589i	−0.920478	−	0.390794i	$-0.872200\pi$
$743$		−	21.3046i		−	0.781589i	0.920478	−	0.390794i	$-0.127800\pi$
$744$	3.97281	+	3.90087i	0.145650	+	0.143013i
$745$	19.5142	+	37.6801i	0.714946	+	1.38049i
$746$	−2.83218	+	8.71654i	−0.103693	+	0.319135i
$747$	7.85032	−	2.55072i	0.287228	−	0.0933261i
$748$	−2.77695	+	3.82215i	−0.101535	+	0.139751i
$749$	0.219111			0.00800615
$750$	11.0752	+	1.52937i	0.404411	+	0.0558447i
$751$	−28.9531	−	21.0357i	−1.05651	−	0.767603i	−0.0830741	−	0.996543i	$-0.526474\pi$
$751$	−28.9531	−	21.0357i	−1.05651	−	0.767603i	−0.973440	+	0.228941i	$0.926474\pi$
$752$	3.82842	+	5.26937i	0.139608	+	0.192154i
$753$	9.52653	+	13.1121i	0.347166	+	0.477833i
$754$	−3.67167	+	11.3002i	−0.133714	+	0.411531i
$755$	0.924495	−	6.09801i	0.0336458	−	0.221929i
$756$	−0.0825284	+	0.253996i	−0.00300153	+	0.00923775i
$757$	−3.08020	+	1.00082i	−0.111952	+	0.0363754i	−0.364457	−	0.931220i	$-0.618745\pi$
$757$	−3.08020	+	1.00082i	−0.111952	+	0.0363754i	0.252505	+	0.967595i	$0.418745\pi$
$758$	12.4725	+	17.1669i	0.453022	+	0.623531i
$759$	5.41164	+	16.6553i	0.196430	+	0.604550i
$760$	−10.5655	−	10.4265i	−0.383250	−	0.378210i
$761$	−27.8664	+	20.2462i	−1.01016	+	0.733923i	−0.964242	−	0.265023i	$-0.914621\pi$
$761$	−27.8664	+	20.2462i	−1.01016	+	0.733923i	−0.0459157	+	0.998945i	$0.514621\pi$
$762$	−5.60840	+	1.82228i	−0.203171	+	0.0660143i
$763$	−4.63839	−	1.50710i	−0.167921	−	0.0545608i
$764$	14.3542	+	10.4289i	0.519315	+	0.377305i
$765$	−0.476990	−	2.88775i	−0.0172456	−	0.104407i
$766$	10.9676	−	7.96840i	0.396274	−	0.287910i
$767$	−10.1493	−	13.9693i	−0.366470	−	0.504403i
$768$	0.587785	−	0.809017i	0.0212099	−	0.0291929i
$769$	22.4424			0.809295			0.404648	−	0.914473i	$-0.367394\pi$
$769$	22.4424			0.809295			0.404648	+	0.914473i	$0.367394\pi$
$770$	0.991241	+	1.91399i	0.0357218	+	0.0689755i
$771$	−18.1449	−	13.1831i	−0.653474	−	0.474777i
$772$	12.9173	−	4.19707i	0.464902	−	0.151056i
$773$	−34.1756	−	11.1043i	−1.22921	−	0.399394i	−0.378781	−	0.925486i	$-0.623657\pi$
$773$	−34.1756	−	11.1043i	−1.22921	−	0.399394i	−0.850428	+	0.526092i	$0.823657\pi$
$774$	−3.39299			−0.121958
$775$	−19.2397	+	20.1205i	−0.691109	+	0.722751i
$776$	−12.4383			−0.446509
$777$	2.17531	+	0.706800i	0.0780387	+	0.0253563i
$778$	24.5617	−	7.98057i	0.880579	−	0.286117i
$779$	17.9043	+	13.0082i	0.641488	+	0.466068i
$780$	1.41448	+	2.73122i	0.0506464	+	0.0977934i
$781$	28.8819			1.03348
$782$	−3.73297	+	5.13799i	−0.133491	+	0.183734i
$783$	5.07729	+	6.98829i	0.181448	+	0.249741i
$784$	−5.60542	+	4.07257i	−0.200193	+	0.145449i
$785$	−5.48127	−	33.1842i	−0.195635	−	1.18439i
$786$	2.18429	+	1.58698i	0.0779110	+	0.0566057i
$787$	−14.0556	−	4.56695i	−0.501029	−	0.162794i	0.0475895	−	0.998867i	$-0.484846\pi$
$787$	−14.0556	−	4.56695i	−0.501029	−	0.162794i	−0.548619	+	0.836073i	$0.684846\pi$
$788$	−5.06323	+	1.64514i	−0.180370	+	0.0586058i
$789$	6.08005	−	4.41741i	0.216455	−	0.157264i
$790$	22.6101	+	22.3127i	0.804431	+	0.793852i
$791$	0.324779	+	0.999566i	0.0115478	+	0.0355405i
$792$	−2.12153	−	2.92003i	−0.0753853	−	0.103759i
$793$	8.93352	−	2.90268i	0.317239	−	0.103077i
$794$	−5.53936	+	17.0484i	−0.196585	+	0.605025i
$795$	−0.299014	+	1.97231i	−0.0106049	+	0.0699507i
$796$	−7.49245	+	23.0594i	−0.265563	+	0.817318i
$797$	8.43326	+	11.6074i	0.298721	+	0.411155i	0.931822	−	0.362914i	$-0.118218\pi$
$797$	8.43326	+	11.6074i	0.298721	+	0.411155i	−0.633101	+	0.774069i	$0.718218\pi$
$798$	1.04208	+	1.43431i	0.0368894	+	0.0507739i
$799$	6.89729	+	5.01117i	0.244008	+	0.177283i
$800$	4.08364	+	2.88512i	0.144378	+	0.102004i
$801$	−1.05846			−0.0373987
$802$	12.2688	−	16.8865i	0.433225	−	0.596283i
$803$	1.56431	−	0.508276i	0.0552034	−	0.0179367i
$804$	2.86738	−	8.82490i	0.101125	−	0.311230i
$805$	1.33249	+	2.57292i	0.0469642	+	0.0906835i
$806$	−7.57493	−	1.12890i	−0.266815	−	0.0397638i
$807$			3.01848i			0.106255i
$808$	−5.81621	−	1.88980i	−0.204614	−	0.0664830i
$809$	−0.646721	−	1.99040i	−0.0227375	−	0.0699788i	0.939044	−	0.343797i	$-0.111713\pi$
$809$	−0.646721	−	1.99040i	−0.0227375	−	0.0699788i	−0.961781	+	0.273818i	$0.911713\pi$
$810$	2.21081	+	0.335171i	0.0776798	+	0.0117767i
$811$	−30.9639			−1.08729			−0.543644	−	0.839316i	$-0.682956\pi$
$811$	−30.9639			−1.08729			−0.543644	+	0.839316i	$0.682956\pi$
$812$		−	2.30693i		−	0.0809574i
$813$	0.384802	−	0.529635i	0.0134956	−	0.0185751i
$814$	−25.0081	+	18.1695i	−0.876535	+	0.636840i
$815$	3.69782	−	7.37771i	0.129529	−	0.258430i
$816$	0.404484	−	1.24487i	0.0141598	−	0.0435793i
$817$	−13.2393	+	18.2223i	−0.463184	+	0.637518i
$818$	−3.95136	−	1.28388i	−0.138156	−	0.0448897i
$819$	−0.113520	−	0.349378i	−0.00396670	−	0.0122082i
$820$	−6.66431	−	3.34025i	−0.232728	−	0.116647i
$821$	−13.6416	−	41.9844i	−0.476093	−	1.46526i	−0.844477	−	0.535591i	$-0.820089\pi$
$821$	−13.6416	−	41.9844i	−0.476093	−	1.46526i	0.368384	−	0.929674i	$-0.379911\pi$
$822$	−6.45825	+	2.09841i	−0.225257	+	0.0731906i
$823$	30.6992	+	42.2538i	1.07011	+	1.47287i	0.869969	+	0.493107i	$0.164139\pi$
$823$	30.6992	+	42.2538i	1.07011	+	1.47287i	0.200137	+	0.979768i	$0.435861\pi$
$824$	3.93460	+	12.1094i	0.137068	+	0.421852i
$825$	14.4585	−	10.8000i	0.503379	−	0.376008i
$826$	2.71224	+	1.97056i	0.0943709	+	0.0685645i
$827$	−5.00823	−	1.62727i	−0.174153	−	0.0565858i	0.220642	−	0.975355i	$-0.429185\pi$
$827$	−5.00823	−	1.62727i	−0.174153	−	0.0565858i	−0.394796	+	0.918769i	$0.629185\pi$
$828$	−2.85190	−	3.92531i	−0.0991105	−	0.136414i
$829$	−11.5817	+	8.41462i	−0.402250	+	0.292252i	−0.770457	−	0.637492i	$-0.779972\pi$
$829$	−11.5817	+	8.41462i	−0.402250	+	0.292252i	0.368207	+	0.929744i	$0.379972\pi$
$830$	−2.76661	+	18.2487i	−0.0960304	+	0.633421i
$831$	23.3839			0.811178
$832$			1.37552i			0.0476877i
$833$	−5.33075	+	7.33714i	−0.184699	+	0.254217i
$834$	−4.73424	−	14.5705i	−0.163933	−	0.504535i
$835$	−7.13042	−	43.1683i	−0.246758	−	1.49390i
$836$	−23.9604			−0.828687
$837$	−3.90087	+	3.97281i	−0.134834	+	0.137320i
$838$			6.26006i			0.216250i
$839$	4.69316	−	14.4441i	0.162026	−	0.498664i	−0.836779	−	0.547541i	$-0.815564\pi$
$839$	4.69316	−	14.4441i	0.162026	−	0.498664i	0.998805	+	0.0488765i	$0.0155641\pi$
$840$	−0.425057	−	0.419466i	−0.0146658	−	0.0144730i
$841$	−36.9034	−	26.8119i	−1.27253	−	0.924549i
$842$		−	12.6815i		−	0.437032i
$843$			0.132440i			0.00456147i
$844$	18.8028	+	13.6610i	0.647218	+	0.470232i
$845$	22.2051	+	11.1295i	0.763878	+	0.382867i
$846$	−5.26937	+	3.82842i	−0.181165	+	0.131624i
$847$	0.514974	+	0.167325i	0.0176947	+	0.00574936i
$848$	−0.524377	+	0.721743i	−0.0180072	+	0.0247848i
$849$	−2.36403	+	7.27573i	−0.0811332	+	0.249702i
$850$	6.25060	+	1.93984i	0.214394	+	0.0665360i
$851$	−33.6176	+	24.4246i	−1.15240	+	0.837266i
$852$	−7.61031	+	2.47274i	−0.260725	+	0.0847146i
$853$	−43.2756	+	14.0611i	−1.48173	+	0.481443i	−0.934629	−	0.355625i	$-0.884268\pi$
$853$	−43.2756	+	14.0611i	−1.48173	+	0.481443i	−0.547099	+	0.837068i	$0.684268\pi$
$854$	−1.47546	+	1.07198i	−0.0504891	+	0.0366825i
$855$	10.4265	−	10.5655i	0.356580	−	0.361332i
$856$	0.253528	−	0.780280i	0.00866542	−	0.0266694i
$857$	5.66591	−	7.79846i	0.193544	−	0.266390i	−0.701205	−	0.712959i	$-0.747354\pi$
$857$	5.66591	−	7.79846i	0.193544	−	0.266390i	0.894749	+	0.446569i	$0.147354\pi$
$858$	4.72177	+	1.53419i	0.161198	+	0.0523766i
$859$	−14.2929	+	10.3844i	−0.487668	+	0.354312i	−0.804287	−	0.594241i	$-0.797452\pi$
$859$	−14.2929	+	10.3844i	−0.487668	+	0.354312i	0.316619	+	0.948553i	$0.397452\pi$
$860$	3.39958	−	6.78267i	0.115925	−	0.231287i
$861$	0.720302	+	0.523330i	0.0245478	+	0.0178350i
$862$			0.118034i			0.00402026i
$863$			47.2130i			1.60715i	0.595204	+	0.803575i	$0.297071\pi$
$863$			47.2130i			1.60715i	−0.595204	+	0.803575i	$0.702929\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	32.0365	+	31.6151i	1.08927	+	1.07495i
$866$	−8.23802	+	25.3540i	−0.279939	+	0.861564i
$867$			15.2867i			0.519163i
$868$	1.46647	−	0.246023i	0.0497754	−	0.00835056i
$869$	51.2752			1.73939
$870$	−19.0570	+	3.14777i	−0.646091	+	0.106720i
$871$	3.94415	+	12.1389i	0.133643	+	0.411309i
$872$	−10.7339	+	14.7740i	−0.363497	+	0.500310i
$873$		−	12.4383i		−	0.420973i
$874$	−32.2092			−1.08949
$875$	2.06901	−	2.15286i	0.0699453	−	0.0727800i
$876$	−0.368676	+	0.267859i	−0.0124564	+	0.00905011i
$877$	−3.47604	−	4.78436i	−0.117378	−	0.161556i	0.746285	−	0.665626i	$-0.231835\pi$
$877$	−3.47604	−	4.78436i	−0.117378	−	0.161556i	−0.863663	+	0.504070i	$0.831835\pi$
$878$	−32.2749	−	10.4867i	−1.08922	−	0.353911i
$879$	12.5035	+	9.08435i	0.421734	+	0.306408i
$880$	7.96288	−	1.31529i	0.268429	−	0.0443383i
$881$	−8.77526	−	27.0075i	−0.295646	−	0.909905i	−0.983004	−	0.183586i	$-0.941229\pi$
$881$	−8.77526	−	27.0075i	−0.295646	−	0.909905i	0.687358	−	0.726319i	$-0.258771\pi$
$882$	−4.07257	−	5.60542i	−0.137131	−	0.188744i
$883$	−5.61852	+	1.82557i	−0.189078	+	0.0614353i	−0.402026	−	0.915628i	$-0.631694\pi$
$883$	−5.61852	+	1.82557i	−0.189078	+	0.0614353i	0.212947	+	0.977064i	$0.431694\pi$
$884$	0.556377	+	1.71235i	0.0187130	+	0.0575927i
$885$	12.5775	−	25.0939i	0.422787	−	0.843523i
$886$	0.713959	+	2.19734i	0.0239859	+	0.0738211i
$887$	−5.30354	−	1.72322i	−0.178075	−	0.0578602i	0.218622	−	0.975810i	$-0.429844\pi$
$887$	−5.30354	−	1.72322i	−0.178075	−	0.0578602i	−0.396698	+	0.917949i	$0.629844\pi$
$888$	5.03399	−	6.92869i	0.168930	−	0.232512i
$889$	−0.486672	+	1.49782i	−0.0163224	+	0.0502353i
$890$	1.06051	−	2.11588i	0.0355484	−	0.0709245i
$891$	2.92003	−	2.12153i	0.0978248	−	0.0710739i
$892$	−9.30574	+	12.8083i	−0.311579	+	0.428852i
$893$			43.2379i			1.44690i
$894$	−18.9768			−0.634679
$895$	−2.63938	+	17.4095i	−0.0882247	+	0.581934i
$896$	−0.0825284	−	0.253996i	−0.00275708	−	0.00848542i
$897$	6.34732	+	2.06237i	0.211931	+	0.0688605i
$898$		−	20.8348i		−	0.695267i
$899$	21.4419	−	43.0501i	0.715129	−	1.43580i
$900$	−2.88512	+	4.08364i	−0.0961706	+	0.136121i
$901$	−0.360850	+	1.11058i	−0.0120217	+	0.0369989i
$902$	−11.4439	+	3.71834i	−0.381039	+	0.123807i
$903$	−0.532625	+	0.733096i	−0.0177247	+	0.0243959i
$904$	3.93536			0.130888
$905$	3.45457	+	6.67045i	0.114834	+	0.221733i
$906$	2.23149	+	1.62127i	0.0741364	+	0.0538632i
$907$	23.6439	+	32.5430i	0.785082	+	1.08057i	0.994703	+	0.102790i	$0.0327771\pi$
$907$	23.6439	+	32.5430i	0.785082	+	1.08057i	−0.209621	+	0.977783i	$0.567223\pi$
$908$	4.16042	+	5.72633i	0.138068	+	0.190035i
$909$	1.88980	−	5.81621i	0.0626807	−	0.192912i
$910$	0.812156	+	0.123128i	0.0269227	+	0.00408164i
$911$	−6.73355	+	20.7237i	−0.223092	+	0.686608i	0.775387	+	0.631486i	$0.217555\pi$
$911$	−6.73355	+	20.7237i	−0.223092	+	0.686608i	−0.998480	+	0.0551217i	$0.982445\pi$
$912$	6.31349	−	2.05138i	0.209061	−	0.0679279i
$913$	17.5118	+	24.1029i	0.579555	+	0.797689i
$914$	−1.98742	−	6.11664i	−0.0657379	−	0.202321i
$915$	10.8686	+	10.7257i	0.359305	+	0.354580i
$916$	−18.6474	+	13.5481i	−0.616127	+	0.447642i
$917$	0.685772	−	0.222821i	0.0226462	−	0.00735819i
$918$	1.24487	+	0.404484i	0.0410870	+	0.0133500i
$919$	−18.3696	−	13.3463i	−0.605956	−	0.440253i	0.242032	−	0.970268i	$-0.422186\pi$
$919$	−18.3696	−	13.3463i	−0.605956	−	0.440253i	−0.847988	+	0.530016i	$0.822186\pi$
$920$	10.7042	−	1.76810i	0.352908	−	0.0582924i
$921$	−16.9587	+	12.3212i	−0.558808	+	0.405998i
$922$	7.60751	+	10.4708i	0.250540	+	0.344839i
$923$	6.46967	−	8.90474i	0.212952	−	0.293103i
$924$	−0.963943			−0.0317114
$925$	34.9736	+	24.7091i	1.14993	+	0.812430i
$926$	−8.75397	−	6.36013i	−0.287673	−	0.209007i
$927$	−12.1094	+	3.93460i	−0.397726	+	0.129229i
$928$	−8.21523	−	2.66929i	−0.269678	−	0.0876238i
$929$	−3.89798			−0.127889			−0.0639443	−	0.997953i	$-0.520368\pi$
$929$	−3.89798			−0.127889			−0.0639443	+	0.997953i	$0.520368\pi$
$930$	−4.03331	−	11.7785i	−0.132258	−	0.386231i
$931$	−45.9953			−1.50744
$932$	−6.93605	−	2.25366i	−0.227198	−	0.0738211i
$933$	−21.9887	+	7.14456i	−0.719878	+	0.233902i
$934$	23.0543	+	16.7499i	0.754358	+	0.548073i
$935$	9.38077	−	4.85823i	0.306784	−	0.158881i
$936$	−1.37552			−0.0449604
$937$	−26.8656	+	36.9774i	−0.877662	+	1.20800i	0.0994010	+	0.995047i	$0.468307\pi$
$937$	−26.8656	+	36.9774i	−0.877662	+	1.20800i	−0.977063	+	0.212951i	$0.931693\pi$
$938$	−1.45661	−	2.00485i	−0.0475600	−	0.0654607i
$939$	−25.6293	+	18.6208i	−0.836381	+	0.607666i
$940$	−2.37351	−	14.3695i	−0.0774154	−	0.468681i
$941$	−38.1220	−	27.6973i	−1.24274	−	0.902905i	−0.244964	−	0.969532i	$-0.578776\pi$
$941$	−38.1220	−	27.6973i	−1.24274	−	0.902905i	−0.997778	+	0.0666272i	$0.978776\pi$
$942$	14.3053	+	4.64808i	0.466092	+	0.151443i
$943$	−15.3836	+	4.99844i	−0.500960	+	0.162772i
$944$	10.1556	−	7.37851i	0.330538	−	0.240150i
$945$	0.419466	−	0.425057i	0.0136452	−	0.0138271i
$946$	−3.78438	−	11.6471i	−0.123041	−	0.378681i
$947$	−15.1742	−	20.8855i	−0.493095	−	0.678687i	0.487860	−	0.872922i	$-0.337778\pi$
$947$	−15.1742	−	20.8855i	−0.493095	−	0.678687i	−0.980955	+	0.194235i	$0.937778\pi$
$948$	−13.5109	+	4.38995i	−0.438812	+	0.142579i
$949$	0.193703	−	0.596158i	0.00628788	−	0.0193521i
$950$	10.6739	+	31.4289i	0.346307	+	1.01969i
$951$	5.72559	−	17.6216i	0.185665	−	0.571418i
$952$	−0.205475	−	0.282812i	−0.00665948	−	0.00916599i
$953$	−3.00466	−	4.13556i	−0.0973304	−	0.133964i	0.757574	−	0.652749i	$-0.226384\pi$
$953$	−3.00466	−	4.13556i	−0.0973304	−	0.133964i	−0.854905	+	0.518785i	$0.826384\pi$
$954$	−0.721743	−	0.524377i	−0.0233673	−	0.0169773i
$955$	−18.2452	−	35.2297i	−0.590401	−	1.14001i
$956$	−13.9435			−0.450964
$957$	−18.3258	+	25.2233i	−0.592388	+	0.815353i
$958$	13.2043	−	4.29033i	0.426611	−	0.138614i
$959$	−0.560418	+	1.72479i	−0.0180968	+	0.0556963i
$960$	−1.98559	+	1.02832i	−0.0640846	+	0.0331889i
$961$	29.6529	+	9.03917i	0.956545	+	0.291586i
$962$			11.7804i			0.379816i
$963$	0.780280	+	0.253528i	0.0251442	+	0.00816983i
$964$	5.79612	+	17.8386i	0.186681	+	0.574544i
$965$	−30.0272	−	4.55230i	−0.966609	−	0.146544i
$966$	−1.29580			−0.0416916
$967$			47.5316i			1.52851i	0.644912	+	0.764256i	$0.276894\pi$
$967$			47.5316i			1.52851i	−0.644912	+	0.764256i	$0.723106\pi$
$968$	1.19173	−	1.64027i	0.0383036	−	0.0527203i
$969$	7.02976	−	5.10742i	0.225828	−	0.164074i
$970$	24.8645	+	12.4625i	0.798351	+	0.400146i
$971$	2.09404	−	6.44480i	0.0672010	−	0.206823i	−0.911817	−	0.410597i	$-0.865320\pi$
$971$	2.09404	−	6.44480i	0.0672010	−	0.206823i	0.979018	+	0.203773i	$0.0653205\pi$
$972$	−0.587785	+	0.809017i	−0.0188532	+	0.0259492i
$973$	−3.89130	−	1.26436i	−0.124749	−	0.0405335i
$974$	−0.683091	−	2.10234i	−0.0218877	−	0.0673633i
$975$	−0.0910499	−	6.87701i	−0.00291593	−	0.220241i
$976$	2.11023	+	6.49463i	0.0675470	+	0.207888i
$977$	37.4286	−	12.1613i	1.19745	−	0.389074i	0.358625	−	0.933482i	$-0.383246\pi$
$977$	37.4286	−	12.1613i	1.19745	−	0.389074i	0.838821	+	0.544408i	$0.183246\pi$
$978$	2.16931	+	2.98580i	0.0693668	+	0.0954753i
$979$	−1.18055	−	3.63337i	−0.0377306	−	0.116123i
$980$	15.2859	−	2.52488i	0.488289	−	0.0806542i
$981$	−14.7740	−	10.7339i	−0.471697	−	0.342708i
$982$	2.44094	+	0.793111i	0.0778936	+	0.0253092i
$983$	29.4567	+	40.5437i	0.939523	+	1.29314i	0.956027	+	0.293279i	$0.0947465\pi$
$983$	29.4567	+	40.5437i	0.939523	+	1.29314i	−0.0165036	+	0.999864i	$0.505254\pi$
$984$	2.69708	−	1.95954i	0.0859798	−	0.0624680i
$985$	11.7699	+	1.78438i	0.375019	+	0.0568551i
$986$	−11.3066			−0.360076
$987$			1.73949i			0.0553686i
$988$	−5.36723	+	7.38736i	−0.170754	+	0.235023i
$989$	−5.08722	−	15.6569i	−0.161764	−	0.497859i
$990$	1.31529	+	7.96288i	0.0418025	+	0.253077i
$991$	8.73761			0.277559			0.138780	−	0.990323i	$-0.455682\pi$
$991$	8.73761			0.277559			0.138780	+	0.990323i	$0.455682\pi$
$992$	0.820707	−	5.50694i	0.0260575	−	0.174846i
$993$		−	24.7902i		−	0.786694i
$994$	−0.660388	+	2.03246i	−0.0209462	+	0.0644659i
$995$	38.0818	−	38.5893i	1.20727	−	1.22336i
$996$	−6.67788	−	4.85177i	−0.211597	−	0.153734i
$997$			8.81160i			0.279066i	0.990217	+	0.139533i	$0.0445601\pi$
$997$			8.81160i			0.279066i	−0.990217	+	0.139533i	$0.955440\pi$
$998$		−	1.80279i		−	0.0570662i
$999$	6.92869	+	5.03399i	0.219214	+	0.159268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.d.349.4	✓	72
5.4	even	2	inner	930.2.z.d.349.13	yes	72
31.4	even	5	inner	930.2.z.d.469.13	yes	72
155.4	even	10	inner	930.2.z.d.469.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.349.4	✓	72	1.1	even	1	trivial
930.2.z.d.349.13	yes	72	5.4	even	2	inner
930.2.z.d.469.4	yes	72	155.4	even	10	inner
930.2.z.d.469.13	yes	72	31.4	even	5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.02832 - 1.98559i) q^{5} +1.00000 q^{6} +(0.156978 - 0.216062i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.02832 - 1.98559i) q^{5} +1.00000 q^{6} +(0.156978 - 0.216062i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.364410 + 2.20617i) q^{10} +(2.92003 + 2.12153i) q^{11} +(-0.951057 - 0.309017i) q^{12} +(1.30820 - 0.425060i) q^{13} +(-0.216062 + 0.156978i) q^{14} +(1.59157 + 1.57064i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.769375 + 1.05895i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(-2.05138 + 6.31349i) q^{19} +(0.335171 - 2.21081i) q^{20} +(-0.0825284 + 0.253996i) q^{21} +(-2.12153 - 2.92003i) q^{22} +(-2.85190 - 3.92531i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-2.88512 + 4.08364i) q^{25} -1.37552 q^{26} +(-0.587785 + 0.809017i) q^{27} +(0.253996 - 0.0825284i) q^{28} +(2.66929 - 8.21523i) q^{29} +(-1.02832 - 1.98559i) q^{30} +(5.50694 + 0.820707i) q^{31} -1.00000i q^{32} +(-3.43271 - 1.11535i) q^{33} +(-0.404484 - 1.24487i) q^{34} +(-0.590434 - 0.0895133i) q^{35} +1.00000 q^{36} -8.56433i q^{37} +(3.90195 - 5.37058i) q^{38} +(-1.11282 + 0.808512i) q^{39} +(-1.00194 + 1.99903i) q^{40} +(1.03019 - 3.17061i) q^{41} +(0.156978 - 0.216062i) q^{42} +(3.22692 + 1.04849i) q^{43} +(1.11535 + 3.43271i) q^{44} +(-1.99903 - 1.00194i) q^{45} +(1.49933 + 4.61448i) q^{46} +(6.19452 - 2.01272i) q^{47} +(-0.587785 - 0.809017i) q^{48} +(2.14108 + 6.58956i) q^{49} +(4.00582 - 2.99222i) q^{50} +(-1.05895 - 0.769375i) q^{51} +(1.30820 + 0.425060i) q^{52} +(0.524377 + 0.721743i) q^{53} +(0.809017 - 0.587785i) q^{54} +(1.20975 - 7.97959i) q^{55} -0.267067 q^{56} -6.63840i q^{57} +(-5.07729 + 6.98829i) q^{58} +(-3.87911 - 11.9387i) q^{59} +(0.364410 + 2.20617i) q^{60} +6.82886 q^{61} +(-4.98380 - 2.48228i) q^{62} -0.267067i q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.18924 - 2.16045i) q^{65} +(2.92003 + 2.12153i) q^{66} +9.27905i q^{67} +1.30894i q^{68} +(3.92531 + 2.85190i) q^{69} +(0.533875 + 0.267586i) q^{70} +(6.47371 - 4.70343i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(0.267859 - 0.368676i) q^{73} +(-2.64652 + 8.14516i) q^{74} +(1.48200 - 4.77532i) q^{75} +(-5.37058 + 3.90195i) q^{76} +(0.916764 - 0.297875i) q^{77} +(1.30820 - 0.425060i) q^{78} +(11.4930 - 8.35017i) q^{79} +(1.57064 - 1.59157i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.95954 + 2.69708i) q^{82} +(7.85032 + 2.55072i) q^{83} +(-0.216062 + 0.156978i) q^{84} +(1.31148 - 2.61660i) q^{85} +(-2.74498 - 1.99435i) q^{86} +8.63801i q^{87} -3.60936i q^{88} +(-0.856308 - 0.622145i) q^{89} +(1.59157 + 1.57064i) q^{90} +(0.113520 - 0.349378i) q^{91} -4.85195i q^{92} +(-5.49103 + 0.921201i) q^{93} -6.51331 q^{94} +(14.6455 - 2.41910i) q^{95} +(0.309017 + 0.951057i) q^{96} +(7.31105 - 10.0628i) q^{97} -6.92868i q^{98} +3.60936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

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