LMFDB - Embedded newform 930.2.z.b.349.1

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 44 x^{13} + 63 x^{12} - 46 x^{11} + 110 x^{10} - 120 x^{9} - 79 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 44x^13 + 63x^12 - 46x^11 + 110x^10 - 120x^9 - 79x^8 + 120x^7 + 110x^6 + 46x^5 + 63x^4 + 44x^3 + 18x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.1
Root			$-0.693851 - 1.36176i$ of defining polynomial
Character	$\chi$	$=$	930.349
Dual form			930.2.z.b.469.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.82930 + 1.28594i) q^{5} -1.00000 q^{6} +(0.907165 - 1.24861i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.82930 + 1.28594i) q^{5} -1.00000 q^{6} +(0.907165 - 1.24861i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(2.13715 - 0.657718i) q^{10} +(-0.748606 - 0.543894i) q^{11} +(0.951057 + 0.309017i) q^{12} +(0.363271 - 0.118034i) q^{13} +(-1.24861 + 0.907165i) q^{14} +(-1.34239 + 1.78829i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.98990 + 4.11525i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(1.91279 - 5.88696i) q^{19} +(-2.23580 - 0.0348889i) q^{20} +(0.476925 - 1.46782i) q^{21} +(0.543894 + 0.748606i) q^{22} +(2.62866 + 3.61803i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(1.69271 - 4.70476i) q^{25} -0.381966 q^{26} +(0.587785 - 0.809017i) q^{27} +(1.46782 - 0.476925i) q^{28} +(0.226596 - 0.697391i) q^{29} +(1.82930 - 1.28594i) q^{30} +(-0.474137 - 5.54754i) q^{31} -1.00000i q^{32} +(-0.880039 - 0.285942i) q^{33} +(-1.57188 - 4.83776i) q^{34} +(-0.0538462 + 3.45064i) q^{35} +1.00000 q^{36} +2.46869i q^{37} +(-3.63834 + 5.00775i) q^{38} +(0.309017 - 0.224514i) q^{39} +(2.11559 + 0.724080i) q^{40} +(1.17672 - 3.62158i) q^{41} +(-0.907165 + 1.24861i) q^{42} +(9.18916 + 2.98574i) q^{43} +(-0.285942 - 0.880039i) q^{44} +(-0.724080 + 2.11559i) q^{45} +(-1.38197 - 4.25325i) q^{46} +(9.29221 - 3.01922i) q^{47} +(0.587785 + 0.809017i) q^{48} +(1.42705 + 4.39201i) q^{49} +(-3.06371 + 3.95142i) q^{50} +(4.11525 + 2.98990i) q^{51} +(0.363271 + 0.118034i) q^{52} +(4.20609 + 5.78918i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(2.06884 + 0.0322837i) q^{55} -1.54336 q^{56} -6.18992i q^{57} +(-0.431011 + 0.593236i) q^{58} +(-3.32049 - 10.2194i) q^{59} +(-2.13715 + 0.657718i) q^{60} +11.9176 q^{61} +(-1.26335 + 5.42254i) q^{62} -1.54336i q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.512749 + 0.683066i) q^{65} +(0.748606 + 0.543894i) q^{66} -8.96590i q^{67} +5.08672i q^{68} +(3.61803 + 2.62866i) q^{69} +(1.11752 - 3.26512i) q^{70} +(-2.77340 + 2.01500i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-6.32506 + 8.70569i) q^{73} +(0.762867 - 2.34786i) q^{74} +(0.156009 - 4.99757i) q^{75} +(5.00775 - 3.63834i) q^{76} +(-1.35822 + 0.441312i) q^{77} +(-0.363271 + 0.118034i) q^{78} +(-5.01750 + 3.64543i) q^{79} +(-1.78829 - 1.34239i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-2.23826 + 3.08070i) q^{82} +(-6.10820 - 1.98467i) q^{83} +(1.24861 - 0.907165i) q^{84} +(-10.7614 - 3.68320i) q^{85} +(-7.81677 - 5.67921i) q^{86} -0.733280i q^{87} +0.925328i q^{88} +(6.19594 + 4.50162i) q^{89} +(1.34239 - 1.78829i) q^{90} +(0.182169 - 0.560659i) q^{91} +4.47214i q^{92} +(-2.16522 - 5.12951i) q^{93} -9.77041 q^{94} +(4.07122 + 13.2288i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(10.0015 - 13.7658i) q^{97} -4.61803i q^{98} -0.925328 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{15} - 4 q^{16} + 8 q^{19} - 2 q^{20} - 4 q^{24} + 16 q^{25} - 24 q^{26} + 36 q^{29} - 12 q^{30} + 40 q^{31} + 8 q^{34} + 14 q^{35} + 16 q^{36} - 4 q^{39} + 6 q^{40} + 32 q^{41} + 12 q^{44} - 2 q^{45} - 40 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{54} + 24 q^{55} - 4 q^{60} - 16 q^{61} + 4 q^{64} + 6 q^{65} - 8 q^{66} + 40 q^{69} + 18 q^{70} - 12 q^{71} - 12 q^{74} - 8 q^{75} + 32 q^{76} - 8 q^{79} - 8 q^{80} - 4 q^{81} - 40 q^{85} - 68 q^{86} + 20 q^{89} - 4 q^{90} - 56 q^{94} - 18 q^{95} + 4 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9 + 4 * q^10 + 8 * q^11 + 4 * q^15 - 4 * q^16 + 8 * q^19 - 2 * q^20 - 4 * q^24 + 16 * q^25 - 24 * q^26 + 36 * q^29 - 12 * q^30 + 40 * q^31 + 8 * q^34 + 14 * q^35 + 16 * q^36 - 4 * q^39 + 6 * q^40 + 32 * q^41 + 12 * q^44 - 2 * q^45 - 40 * q^46 - 4 * q^49 - 8 * q^50 + 8 * q^51 - 4 * q^54 + 24 * q^55 - 4 * q^60 - 16 * q^61 + 4 * q^64 + 6 * q^65 - 8 * q^66 + 40 * q^69 + 18 * q^70 - 12 * q^71 - 12 * q^74 - 8 * q^75 + 32 * q^76 - 8 * q^79 - 8 * q^80 - 4 * q^81 - 40 * q^85 - 68 * q^86 + 20 * q^89 - 4 * q^90 - 56 * q^94 - 18 * q^95 + 4 * q^96 - 8 * 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
$5$	−1.82930	+	1.28594i	−0.818090	+	0.575091i
$5$	−1.82930	+	1.28594i	−0.818090	+	0.575091i
$6$	−1.00000			−0.408248
$7$	0.907165	−	1.24861i	0.342876	−	0.471929i	−0.602402	−	0.798192i	$-0.705790\pi$
$7$	0.907165	−	1.24861i	0.342876	−	0.471929i	0.945279	+	0.326264i	$0.105790\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	2.13715	−	0.657718i	0.675826	−	0.207989i
$11$	−0.748606	−	0.543894i	−0.225713	−	0.163990i	0.469181	−	0.883102i	$-0.344549\pi$
$11$	−0.748606	−	0.543894i	−0.225713	−	0.163990i	−0.694895	+	0.719112i	$0.744549\pi$
$12$	0.951057	+	0.309017i	0.274546	+	0.0892055i
$13$	0.363271	−	0.118034i	0.100753	−	0.0327367i	−0.258207	−	0.966090i	$-0.583131\pi$
$13$	0.363271	−	0.118034i	0.100753	−	0.0327367i	0.358960	+	0.933353i	$0.383131\pi$
$14$	−1.24861	+	0.907165i	−0.333704	+	0.242450i
$15$	−1.34239	+	1.78829i	−0.346605	+	0.461734i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.98990	+	4.11525i	0.725158	+	0.998094i	0.999337	+	0.0364151i	$0.0115939\pi$
$17$	2.98990	+	4.11525i	0.725158	+	0.998094i	−0.274179	+	0.961679i	$0.588406\pi$
$18$	−0.951057	+	0.309017i	−0.224166	+	0.0728360i
$19$	1.91279	−	5.88696i	0.438824	−	1.35056i	−0.450293	−	0.892881i	$-0.648680\pi$
$19$	1.91279	−	5.88696i	0.438824	−	1.35056i	0.889117	−	0.457681i	$-0.151320\pi$
$20$	−2.23580	−	0.0348889i	−0.499939	−	0.00780140i
$21$	0.476925	−	1.46782i	0.104074	−	0.320306i
$22$	0.543894	+	0.748606i	0.115959	+	0.159603i
$23$	2.62866	+	3.61803i	0.548113	+	0.754412i	0.989755	−	0.142779i	$-0.0456039\pi$
$23$	2.62866	+	3.61803i	0.548113	+	0.754412i	−0.441642	+	0.897191i	$0.645604\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	1.69271	−	4.70476i	0.338541	−	0.940952i
$26$	−0.381966			−0.0749097
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	1.46782	−	0.476925i	0.277393	−	0.0901304i
$29$	0.226596	−	0.697391i	0.0420778	−	0.129502i	−0.927811	−	0.373051i	$-0.878312\pi$
$29$	0.226596	−	0.697391i	0.0420778	−	0.129502i	0.969889	+	0.243549i	$0.0783116\pi$
$30$	1.82930	−	1.28594i	0.333984	−	0.234780i
$31$	−0.474137	−	5.54754i	−0.0851575	−	0.996367i
$31$	−0.474137	−	5.54754i	−0.0851575	−	0.996367i
$32$		−	1.00000i		−	0.176777i
$33$	−0.880039	−	0.285942i	−0.153195	−	0.0497761i
$34$	−1.57188	−	4.83776i	−0.269576	−	0.829669i
$35$	−0.0538462	+	3.45064i	−0.00910167	+	0.583265i
$36$	1.00000			0.166667
$37$			2.46869i			0.405850i	0.979194	+	0.202925i	$0.0650448\pi$
$37$			2.46869i			0.405850i	−0.979194	+	0.202925i	$0.934955\pi$
$38$	−3.63834	+	5.00775i	−0.590217	+	0.812364i
$39$	0.309017	−	0.224514i	0.0494823	−	0.0359510i
$40$	2.11559	+	0.724080i	0.334504	+	0.114487i
$41$	1.17672	−	3.62158i	0.183773	−	0.565595i	−0.816152	−	0.577837i	$-0.803897\pi$
$41$	1.17672	−	3.62158i	0.183773	−	0.565595i	0.999925	+	0.0122419i	$0.00389681\pi$
$42$	−0.907165	+	1.24861i	−0.139979	+	0.192664i
$43$	9.18916	+	2.98574i	1.40133	+	0.455321i	0.909622	−	0.415437i	$-0.136371\pi$
$43$	9.18916	+	2.98574i	1.40133	+	0.455321i	0.491712	+	0.870758i	$0.336371\pi$
$44$	−0.285942	−	0.880039i	−0.0431074	−	0.132671i
$45$	−0.724080	+	2.11559i	−0.107940	+	0.315373i
$46$	−1.38197	−	4.25325i	−0.203760	−	0.627108i
$47$	9.29221	−	3.01922i	1.35541	−	0.440399i	0.460901	−	0.887452i	$-0.347526\pi$
$47$	9.29221	−	3.01922i	1.35541	−	0.440399i	0.894508	+	0.447053i	$0.147526\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	1.42705	+	4.39201i	0.203864	+	0.627430i
$50$	−3.06371	+	3.95142i	−0.433274	+	0.558815i
$51$	4.11525	+	2.98990i	0.576250	+	0.418670i
$52$	0.363271	+	0.118034i	0.0503767	+	0.0163684i
$53$	4.20609	+	5.78918i	0.577750	+	0.795205i	0.993446	−	0.114299i	$-0.0364620\pi$
$53$	4.20609	+	5.78918i	0.577750	+	0.795205i	−0.415696	+	0.909504i	$0.636462\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	2.06884	+	0.0322837i	0.278963	+	0.00435313i
$56$	−1.54336			−0.206240
$57$		−	6.18992i		−	0.819875i
$58$	−0.431011	+	0.593236i	−0.0565945	+	0.0778957i
$59$	−3.32049	−	10.2194i	−0.432291	−	1.33045i	−0.895837	−	0.444382i	$-0.853423\pi$
$59$	−3.32049	−	10.2194i	−0.432291	−	1.33045i	0.463546	−	0.886073i	$-0.346577\pi$
$60$	−2.13715	+	0.657718i	−0.275905	+	0.0849110i
$61$	11.9176			1.52590			0.762948	−	0.646460i	$-0.223751\pi$
$61$	11.9176			1.52590			0.762948	+	0.646460i	$0.223751\pi$
$62$	−1.26335	+	5.42254i	−0.160446	+	0.688663i
$63$		−	1.54336i		−	0.194445i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−0.512749	+	0.683066i	−0.0635986	+	0.0847239i
$66$	0.748606	+	0.543894i	0.0921470	+	0.0669487i
$67$		−	8.96590i		−	1.09536i	−0.836688	−	0.547680i	$-0.815511\pi$
$67$		−	8.96590i		−	1.09536i	0.836688	−	0.547680i	$-0.184489\pi$
$68$			5.08672i			0.616856i
$69$	3.61803	+	2.62866i	0.435560	+	0.316453i
$70$	1.11752	−	3.26512i	0.133569	−	0.390256i
$71$	−2.77340	+	2.01500i	−0.329143	+	0.239136i	−0.740067	−	0.672533i	$-0.765206\pi$
$71$	−2.77340	+	2.01500i	−0.329143	+	0.239136i	0.410924	+	0.911670i	$0.365206\pi$
$72$	−0.951057	−	0.309017i	−0.112083	−	0.0364180i
$73$	−6.32506	+	8.70569i	−0.740292	+	1.01892i	0.258310	+	0.966062i	$0.416834\pi$
$73$	−6.32506	+	8.70569i	−0.740292	+	1.01892i	−0.998602	+	0.0528623i	$0.983166\pi$
$74$	0.762867	−	2.34786i	0.0886815	−	0.272934i
$75$	0.156009	−	4.99757i	0.0180144	−	0.577069i
$76$	5.00775	−	3.63834i	0.574428	−	0.417347i
$77$	−1.35822	+	0.441312i	−0.154783	+	0.0502922i
$78$	−0.363271	+	0.118034i	−0.0411324	+	0.0133647i
$79$	−5.01750	+	3.64543i	−0.564513	+	0.410143i	−0.833108	−	0.553111i	$-0.813441\pi$
$79$	−5.01750	+	3.64543i	−0.564513	+	0.410143i	0.268595	+	0.963253i	$0.413441\pi$
$80$	−1.78829	−	1.34239i	−0.199937	−	0.150084i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−2.23826	+	3.08070i	−0.247174	+	0.340206i
$83$	−6.10820	−	1.98467i	−0.670462	−	0.217846i	−0.0460472	−	0.998939i	$-0.514662\pi$
$83$	−6.10820	−	1.98467i	−0.670462	−	0.217846i	−0.624415	+	0.781093i	$0.714662\pi$
$84$	1.24861	−	0.907165i	0.136234	−	0.0989799i
$85$	−10.7614	−	3.68320i	−1.16724	−	0.399499i
$86$	−7.81677	−	5.67921i	−0.842904	−	0.612405i
$87$		−	0.733280i		−	0.0786159i
$88$			0.925328i			0.0986403i
$89$	6.19594	+	4.50162i	0.656769	+	0.477170i	0.865570	−	0.500788i	$-0.166956\pi$
$89$	6.19594	+	4.50162i	0.656769	+	0.477170i	−0.208801	+	0.977958i	$0.566956\pi$
$90$	1.34239	−	1.78829i	0.141501	−	0.188502i
$91$	0.182169	−	0.560659i	0.0190965	−	0.0587730i
$92$			4.47214i			0.466252i
$93$	−2.16522	−	5.12951i	−0.224522	−	0.531905i
$94$	−9.77041			−1.00774
$95$	4.07122	+	13.2288i	0.417698	+	1.35724i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	10.0015	−	13.7658i	1.01549	−	1.39771i	0.100179	−	0.994969i	$-0.468058\pi$
$97$	10.0015	−	13.7658i	1.01549	−	1.39771i	0.915315	−	0.402739i	$-0.131942\pi$
$98$		−	4.61803i		−	0.466492i
$99$	−0.925328			−0.0929990
$100$	4.13482	−	2.81128i	0.413482	−	0.281128i
$101$	6.86385	−	4.98688i	0.682979	−	0.496213i	−0.191366	−	0.981519i	$-0.561292\pi$
$101$	6.86385	−	4.98688i	0.682979	−	0.496213i	0.874345	+	0.485306i	$0.161292\pi$
$102$	−2.98990	−	4.11525i	−0.296044	−	0.407470i
$103$	0.0253454	+	0.00823521i	0.00249735	+	0.000811440i	0.310265	−	0.950650i	$-0.399582\pi$
$103$	0.0253454	+	0.00823521i	0.00249735	+	0.000811440i	−0.307768	+	0.951461i	$0.599582\pi$
$104$	−0.309017	−	0.224514i	−0.0303016	−	0.0220154i
$105$	1.01510	+	3.29840i	0.0990632	+	0.321890i
$106$	−2.21127	−	6.80559i	−0.214778	−	0.661017i
$107$	−7.58368	−	10.4380i	−0.733142	−	1.00908i	−0.998984	−	0.0450666i	$-0.985650\pi$
$107$	−7.58368	−	10.4380i	−0.733142	−	1.00908i	0.265842	−	0.964017i	$-0.414350\pi$
$108$	0.951057	−	0.309017i	0.0915155	−	0.0297352i
$109$	1.03348	+	3.18073i	0.0989897	+	0.304659i	0.988273	−	0.152698i	$-0.0487962\pi$
$109$	1.03348	+	3.18073i	0.0989897	+	0.304659i	−0.889283	+	0.457357i	$0.848796\pi$
$110$	−1.95761	−	0.670012i	−0.186651	−	0.0638831i
$111$	0.762867	+	2.34786i	0.0724081	+	0.222849i
$112$	1.46782	+	0.476925i	0.138696	+	0.0450652i
$113$	−3.74154	+	5.14979i	−0.351975	+	0.484452i	−0.947891	−	0.318595i	$-0.896789\pi$
$113$	−3.74154	+	5.14979i	−0.351975	+	0.484452i	0.595916	+	0.803047i	$0.296789\pi$
$114$	−1.91279	+	5.88696i	−0.179149	+	0.551365i
$115$	−9.46119	−	3.23819i	−0.882261	−	0.301962i
$116$	0.593236	−	0.431011i	0.0550806	−	0.0400184i
$117$	0.224514	−	0.309017i	0.0207563	−	0.0285686i
$118$			10.7453i			0.989188i
$119$	7.85066			0.719668
$120$	2.23580	+	0.0348889i	0.204099	+	0.00318491i
$121$	−3.13460	−	9.64730i	−0.284963	−	0.877027i
$122$	−11.3343	−	3.68275i	−1.02616	−	0.333420i
$123$		−	3.80795i		−	0.343351i
$124$	2.87718	−	4.76674i	0.258378	−	0.428066i
$125$	2.95357	+	10.7832i	0.264176	+	0.964475i
$126$	−0.476925	+	1.46782i	−0.0424879	+	0.130764i
$127$	7.36953	−	2.39450i	0.653940	−	0.212478i	0.0367892	−	0.999323i	$-0.488287\pi$
$127$	7.36953	−	2.39450i	0.653940	−	0.212478i	0.617150	+	0.786845i	$0.288287\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	9.66205			0.850696
$130$	0.698732	−	0.491186i	0.0612828	−	0.0430799i
$131$	−1.33582	−	0.970527i	−0.116711	−	0.0847954i	0.527899	−	0.849307i	$-0.322980\pi$
$131$	−1.33582	−	0.970527i	−0.116711	−	0.0847954i	−0.644610	+	0.764512i	$0.722980\pi$
$132$	−0.543894	−	0.748606i	−0.0473399	−	0.0651578i
$133$	−5.61528	−	7.72877i	−0.486906	−	0.670169i
$134$	−2.77062	+	8.52708i	−0.239345	+	0.736627i
$135$	−0.0348889	+	2.23580i	−0.00300276	+	0.192427i
$136$	1.57188	−	4.83776i	0.134788	−	0.414835i
$137$	5.00980	−	1.62778i	0.428016	−	0.139071i	−0.0870836	−	0.996201i	$-0.527755\pi$
$137$	5.00980	−	1.62778i	0.428016	−	0.139071i	0.515100	+	0.857130i	$0.327755\pi$
$138$	−2.62866	−	3.61803i	−0.223766	−	0.307988i
$139$	3.79972	+	11.6943i	0.322288	+	0.991900i	0.972650	+	0.232276i	$0.0746171\pi$
$139$	3.79972	+	11.6943i	0.322288	+	0.991900i	−0.650362	+	0.759624i	$0.725383\pi$
$140$	−2.07180	+	2.75998i	−0.175099	+	0.233261i
$141$	7.90443	−	5.74290i	0.665673	−	0.483640i
$142$	3.26033	−	1.05935i	0.273601	−	0.0888983i
$143$	−0.336145	−	0.109220i	−0.0281099	−	0.00913345i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$	0.482291	+	1.56713i	0.0400521	+	0.130143i
$146$	8.70569	−	6.32506i	0.720488	−	0.523465i
$147$	2.71441	+	3.73607i	0.223881	+	0.308146i
$148$	−1.45106	+	1.99721i	−0.119276	+	0.164170i
$149$	−17.5853			−1.44064			−0.720320	−	0.693642i	$-0.756005\pi$
$149$	−17.5853			−1.44064			−0.720320	+	0.693642i	$0.756005\pi$
$150$	−1.69271	+	4.70476i	−0.138209	+	0.384142i
$151$	4.99766	+	3.63101i	0.406704	+	0.295488i	0.772266	−	0.635299i	$-0.219123\pi$
$151$	4.99766	+	3.63101i	0.406704	+	0.295488i	−0.365562	+	0.930787i	$0.619123\pi$
$152$	−5.88696	+	1.91279i	−0.477496	+	0.155148i
$153$	4.83776	+	1.57188i	0.391110	+	0.127079i
$154$	1.42812			0.115081
$155$	8.00116	+	9.53842i	0.642668	+	0.766145i
$156$	0.381966			0.0305818
$157$	5.05900	+	1.64377i	0.403752	+	0.131187i	0.503851	−	0.863790i	$-0.331916\pi$
$157$	5.05900	+	1.64377i	0.403752	+	0.131187i	−0.100099	+	0.994977i	$0.531916\pi$
$158$	5.89842	−	1.91651i	0.469253	−	0.152470i
$159$	5.78918	+	4.20609i	0.459112	+	0.333564i
$160$	1.28594	+	1.82930i	0.101663	+	0.144619i
$161$	6.90212			0.543964
$162$	−0.587785	+	0.809017i	−0.0461808	+	0.0635624i
$163$	−4.15251	−	5.71544i	−0.325250	−	0.447668i	0.614811	−	0.788674i	$-0.289232\pi$
$163$	−4.15251	−	5.71544i	−0.325250	−	0.447668i	−0.940061	+	0.341006i	$0.889232\pi$
$164$	3.08070	−	2.23826i	0.240562	−	0.174779i
$165$	1.97756	−	0.608604i	0.153953	−	0.0473798i
$166$	5.19594	+	3.77507i	0.403283	+	0.293003i
$167$	7.18452	+	2.33439i	0.555955	+	0.180641i	0.573500	−	0.819205i	$-0.305585\pi$
$167$	7.18452	+	2.33439i	0.555955	+	0.180641i	−0.0175452	+	0.999846i	$0.505585\pi$
$168$	−1.46782	+	0.476925i	−0.113245	+	0.0367956i
$169$	−10.3992	+	7.55545i	−0.799937	+	0.581189i
$170$	9.09654	+	6.82839i	0.697672	+	0.523713i
$171$	−1.91279	−	5.88696i	−0.146275	−	0.450187i
$172$	5.67921	+	7.81677i	0.433036	+	0.596023i
$173$	−16.8936	+	5.48906i	−1.28439	+	0.417325i	−0.870126	−	0.492829i	$-0.835963\pi$
$173$	−16.8936	+	5.48906i	−1.28439	+	0.417325i	−0.414269	+	0.910155i	$0.635963\pi$
$174$	−0.226596	+	0.697391i	−0.0171782	+	0.0528691i
$175$	−4.33882	−	6.38152i	−0.327984	−	0.482397i
$176$	0.285942	−	0.880039i	0.0215537	−	0.0663354i
$177$	−6.31595	−	8.69316i	−0.474736	−	0.653418i
$178$	−4.50162	−	6.19594i	−0.337410	−	0.464406i
$179$	−11.0039	−	7.99480i	−0.822470	−	0.597559i	0.0949491	−	0.995482i	$-0.469731\pi$
$179$	−11.0039	−	7.99480i	−0.822470	−	0.597559i	−0.917419	+	0.397923i	$0.869731\pi$
$180$	−1.82930	+	1.28594i	−0.136348	+	0.0958485i
$181$	−20.4231			−1.51804			−0.759020	−	0.651067i	$-0.774322\pi$
$181$	−20.4231			−1.51804			−0.759020	+	0.651067i	$0.774322\pi$
$182$	−0.346506	+	0.476925i	−0.0256848	+	0.0353520i
$183$	11.3343	−	3.68275i	0.837858	−	0.272237i
$184$	1.38197	−	4.25325i	0.101880	−	0.313554i
$185$	−3.17459	−	4.51598i	−0.233401	−	0.332022i
$186$	0.474137	+	5.54754i	0.0347654	+	0.406765i
$187$		−	4.70689i		−	0.344202i
$188$	9.29221	+	3.01922i	0.677704	+	0.220199i
$189$	−0.476925	−	1.46782i	−0.0346912	−	0.106769i
$190$	0.215960	−	13.8394i	0.0156674	−	1.00402i
$191$	−13.1289			−0.949972			−0.474986	−	0.879993i	$-0.657547\pi$
$191$	−13.1289			−0.949972			−0.474986	+	0.879993i	$0.657547\pi$
$192$			1.00000i			0.0721688i
$193$	−6.21140	+	8.54926i	−0.447106	+	0.615389i	−0.971773	−	0.235919i	$-0.924190\pi$
$193$	−6.21140	+	8.54926i	−0.447106	+	0.615389i	0.524666	+	0.851308i	$0.324190\pi$
$194$	−13.7658	+	10.0015i	−0.988329	+	0.718063i
$195$	−0.276574	+	0.808082i	−0.0198059	+	0.0578680i
$196$	−1.42705	+	4.39201i	−0.101932	+	0.313715i
$197$	−6.80121	+	9.36106i	−0.484566	+	0.666948i	−0.979374	−	0.202054i	$-0.935238\pi$
$197$	−6.80121	+	9.36106i	−0.484566	+	0.666948i	0.494808	+	0.869002i	$0.335238\pi$
$198$	0.880039	+	0.285942i	0.0625417	+	0.0203210i
$199$	4.44983	+	13.6952i	0.315440	+	0.970824i	0.975573	+	0.219675i	$0.0704998\pi$
$199$	4.44983	+	13.6952i	0.315440	+	0.970824i	−0.660133	+	0.751148i	$0.729500\pi$
$200$	−4.80118	+	1.39596i	−0.339494	+	0.0987092i
$201$	−2.77062	−	8.52708i	−0.195424	−	0.601454i
$202$	−8.06894	+	2.62176i	−0.567729	+	0.184466i
$203$	−0.665206	−	0.915578i	−0.0466883	−	0.0642610i
$204$	1.57188	+	4.83776i	0.110054	+	0.338711i
$205$	2.50456	+	8.13816i	0.174926	+	0.568394i
$206$	−0.0215601	−	0.0156643i	−0.00150216	−	0.00109138i
$207$	4.25325	+	1.38197i	0.295622	+	0.0960533i
$208$	0.224514	+	0.309017i	0.0155672	+	0.0214265i
$209$	−4.63381	+	3.36666i	−0.320527	+	0.232877i
$210$	0.0538462	−	3.45064i	0.00371574	−	0.238117i
$211$	21.8129			1.50166			0.750829	−	0.660496i	$-0.229654\pi$
$211$	21.8129			1.50166			0.750829	+	0.660496i	$0.229654\pi$
$212$			7.15582i			0.491464i
$213$	−2.01500	+	2.77340i	−0.138065	+	0.190031i
$214$	3.98698	+	12.2706i	0.272544	+	0.838804i
$215$	−20.6493	+	6.35490i	−1.40827	+	0.433401i
$216$	−1.00000			−0.0680414
$217$	−7.35681	−	4.44053i	−0.499413	−	0.301442i
$218$		−	3.34442i		−	0.226513i
$219$	−3.32528	+	10.2342i	−0.224702	+	0.691560i
$220$	1.65475	+	1.24215i	0.111564	+	0.0837460i
$221$	1.57188	+	1.14204i	0.105736	+	0.0768220i
$222$		−	2.46869i		−	0.165688i
$223$			23.4742i			1.57195i	0.618259	+	0.785974i	$0.287838\pi$
$223$			23.4742i			1.57195i	−0.618259	+	0.785974i	$0.712162\pi$
$224$	−1.24861	−	0.907165i	−0.0834260	−	0.0606125i
$225$	−1.39596	−	4.80118i	−0.0930640	−	0.320078i
$226$	5.14979	−	3.74154i	0.342559	−	0.248884i
$227$	−6.27971	−	2.04040i	−0.416799	−	0.135426i	0.0931074	−	0.995656i	$-0.470320\pi$
$227$	−6.27971	−	2.04040i	−0.416799	−	0.135426i	−0.509907	+	0.860230i	$0.670320\pi$
$228$	3.63834	−	5.00775i	0.240955	−	0.331646i
$229$	−3.96036	+	12.1887i	−0.261708	+	0.805455i	0.730725	+	0.682672i	$0.239182\pi$
$229$	−3.96036	+	12.1887i	−0.261708	+	0.805455i	−0.992434	+	0.122783i	$0.960818\pi$
$230$	7.99747	+	6.00337i	0.527338	+	0.395850i
$231$	−1.15537	+	0.839425i	−0.0760178	+	0.0552301i
$232$	−0.697391	+	0.226596i	−0.0457859	+	0.0148768i
$233$	−4.72435	+	1.53503i	−0.309502	+	0.100563i	−0.459650	−	0.888100i	$-0.652025\pi$
$233$	−4.72435	+	1.53503i	−0.309502	+	0.100563i	0.150148	+	0.988664i	$0.452025\pi$
$234$	−0.309017	+	0.224514i	−0.0202011	+	0.0146769i
$235$	−13.1157	+	17.4723i	−0.855576	+	1.13977i
$236$	3.32049	−	10.2194i	0.216145	−	0.665227i
$237$	−3.64543	+	5.01750i	−0.236796	+	0.325922i
$238$	−7.46642	−	2.42599i	−0.483976	−	0.157253i
$239$	−6.77385	+	4.92149i	−0.438164	+	0.318345i	−0.784905	−	0.619616i	$-0.787288\pi$
$239$	−6.77385	+	4.92149i	−0.438164	+	0.318345i	0.346741	+	0.937961i	$0.387288\pi$
$240$	−2.11559	−	0.724080i	−0.136561	−	0.0467392i
$241$	−2.57746	−	1.87263i	−0.166029	−	0.120627i	0.501668	−	0.865060i	$-0.332720\pi$
$241$	−2.57746	−	1.87263i	−0.166029	−	0.120627i	−0.667697	+	0.744433i	$0.732720\pi$
$242$			10.1438i			0.652066i
$243$		−	1.00000i		−	0.0641500i
$244$	9.64156	+	7.00500i	0.617238	+	0.448449i
$245$	−8.25838	−	6.19922i	−0.527609	−	0.396054i
$246$	−1.17672	+	3.62158i	−0.0750250	+	0.230903i
$247$		−	2.36434i		−	0.150439i
$248$	−4.20936	+	3.64435i	−0.267295	+	0.231416i
$249$	−6.42254			−0.407012
$250$	0.523164	−	11.1681i	0.0330878	−	0.706332i
$251$	−1.68110	−	5.17391i	−0.106110	−	0.326574i	0.883879	−	0.467715i	$-0.154923\pi$
$251$	−1.68110	−	5.17391i	−0.106110	−	0.326574i	−0.989989	+	0.141141i	$0.954923\pi$
$252$	0.907165	−	1.24861i	0.0571460	−	0.0786548i
$253$		−	4.13819i		−	0.260166i
$254$	−7.74878			−0.486202
$255$	−11.3729	−	0.177470i	−0.712197	−	0.0111136i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.01990	+	1.40377i	0.0636194	+	0.0875646i	0.839641	−	0.543142i	$-0.182765\pi$
$257$	1.01990	+	1.40377i	0.0636194	+	0.0875646i	−0.776022	+	0.630706i	$0.782765\pi$
$258$	−9.18916	−	2.98574i	−0.572092	−	0.185884i
$259$	3.08242	+	2.23951i	0.191532	+	0.139156i
$260$	−0.816318	+	0.251226i	−0.0506259	+	0.0155804i
$261$	−0.226596	−	0.697391i	−0.0140259	−	0.0431674i
$262$	0.970527	+	1.33582i	0.0599594	+	0.0825270i
$263$	9.17528	−	2.98123i	0.565772	−	0.183830i	−0.0121448	−	0.999926i	$-0.503866\pi$
$263$	9.17528	−	2.98123i	0.565772	−	0.183830i	0.577917	+	0.816096i	$0.303866\pi$
$264$	0.285942	+	0.880039i	0.0175985	+	0.0541627i
$265$	−15.1388	−	5.18139i	−0.929967	−	0.318290i
$266$	2.95213	+	9.08571i	0.181007	+	0.557081i
$267$	7.28377	+	2.36664i	0.445759	+	0.144836i
$268$	5.27002	−	7.25357i	0.321918	−	0.443082i
$269$	8.82160	−	27.1501i	0.537862	−	1.65537i	−0.199519	−	0.979894i	$-0.563938\pi$
$269$	8.82160	−	27.1501i	0.537862	−	1.65537i	0.737382	−	0.675476i	$-0.236062\pi$
$270$	0.724080	−	2.11559i	0.0440661	−	0.128751i
$271$	−9.67087	+	7.02630i	−0.587463	+	0.426817i	−0.841407	−	0.540402i	$-0.818272\pi$
$271$	−9.67087	+	7.02630i	−0.587463	+	0.426817i	0.253944	+	0.967219i	$0.418272\pi$
$272$	−2.98990	+	4.11525i	−0.181289	+	0.249523i
$273$		−	0.589512i		−	0.0356789i
$274$	−5.26762			−0.318229
$275$	−3.82606	+	2.60136i	−0.230720	+	0.156868i
$276$	1.38197	+	4.25325i	0.0831846	+	0.256016i
$277$	−24.9219	−	8.09762i	−1.49741	−	0.486539i	−0.558150	−	0.829740i	$-0.688489\pi$
$277$	−24.9219	−	8.09762i	−1.49741	−	0.486539i	−0.939262	+	0.343201i	$0.888489\pi$
$278$		−	12.2961i		−	0.737474i
$279$	−3.64435	−	4.20936i	−0.218181	−	0.252008i
$280$	2.82328	−	1.98467i	0.168723	−	0.118607i
$281$	−1.31102	+	4.03490i	−0.0782088	+	0.240702i	−0.982515	−	0.186182i	$-0.940389\pi$
$281$	−1.31102	+	4.03490i	−0.0782088	+	0.240702i	0.904307	+	0.426884i	$0.140389\pi$
$282$	−9.29221	+	3.01922i	−0.553343	+	0.179792i
$283$	−12.1375	+	16.7059i	−0.721501	+	0.993061i	0.277972	+	0.960589i	$0.410338\pi$
$283$	−12.1375	+	16.7059i	−0.721501	+	0.993061i	−0.999473	+	0.0324714i	$0.989662\pi$
$284$	−3.42812			−0.203421
$285$	7.95988	+	11.3232i	0.471502	+	0.670731i
$286$	0.285942	+	0.207749i	0.0169081	+	0.0122845i
$287$	−3.45444	−	4.75463i	−0.203909	−	0.280657i
$288$	−0.587785	−	0.809017i	−0.0346356	−	0.0476718i
$289$	−2.74245	+	8.44040i	−0.161321	+	0.496494i
$290$	0.0255833	−	1.63946i	0.00150231	−	0.0962727i
$291$	5.25808	−	16.1827i	0.308234	−	0.948647i
$292$	−10.2342	+	3.32528i	−0.598909	+	0.194597i
$293$	1.75132	+	2.41049i	0.102313	+	0.140822i	0.857104	−	0.515144i	$-0.172261\pi$
$293$	1.75132	+	2.41049i	0.102313	+	0.140822i	−0.754790	+	0.655966i	$0.772261\pi$
$294$	−1.42705	−	4.39201i	−0.0832273	−	0.256147i
$295$	19.2158	+	14.4245i	1.11879	+	0.839825i
$296$	1.99721	−	1.45106i	0.116086	−	0.0843411i
$297$	−0.880039	+	0.285942i	−0.0510651	+	0.0165920i
$298$	16.7246	+	5.43414i	0.968828	+	0.314791i
$299$	1.38197	+	1.00406i	0.0799212	+	0.0580661i
$300$	3.06371	−	3.95142i	0.176883	−	0.228135i
$301$	12.0641	−	8.76508i	0.695363	−	0.505211i
$302$	−3.63101	−	4.99766i	−0.208941	−	0.287583i
$303$	4.98688	−	6.86385i	0.286489	−	0.394318i
$304$	6.18992			0.355016
$305$	−21.8010	+	15.3254i	−1.24832	+	0.877528i
$306$	−4.11525	−	2.98990i	−0.235253	−	0.170921i
$307$	10.3308	−	3.35668i	0.589610	−	0.191576i	0.00100894	−	0.999999i	$-0.499679\pi$
$307$	10.3308	−	3.35668i	0.589610	−	0.191576i	0.588601	+	0.808424i	$0.299679\pi$
$308$	−1.35822	−	0.441312i	−0.0773917	−	0.0251461i
$309$	0.0266497			0.00151605
$310$	−4.66202	−	11.5441i	−0.264785	−	0.655659i
$311$	−12.6656			−0.718203			−0.359101	−	0.933299i	$-0.616917\pi$
$311$	−12.6656			−0.718203			−0.359101	+	0.933299i	$0.616917\pi$
$312$	−0.363271	−	0.118034i	−0.0205662	−	0.00668236i
$313$	−28.6743	+	9.31686i	−1.62077	+	0.526620i	−0.972123	−	0.234470i	$-0.924665\pi$
$313$	−28.6743	+	9.31686i	−1.62077	+	0.526620i	−0.648646	+	0.761090i	$0.724665\pi$
$314$	−4.30344	−	3.12663i	−0.242857	−	0.176446i
$315$	1.98467	+	2.82328i	0.111824	+	0.159074i
$316$	−6.20197			−0.348888
$317$	1.40571	−	1.93480i	0.0789528	−	0.108669i	−0.767714	−	0.640793i	$-0.778606\pi$
$317$	1.40571	−	1.93480i	0.0789528	−	0.108669i	0.846667	+	0.532124i	$0.178606\pi$
$318$	−4.20609	−	5.78918i	−0.235866	−	0.324641i
$319$	−0.548938	+	0.398827i	−0.0307346	+	0.0223300i
$320$	−0.657718	−	2.13715i	−0.0367675	−	0.119470i
$321$	−10.4380	−	7.58368i	−0.582594	−	0.423280i
$322$	−6.56431	−	2.13287i	−0.365815	−	0.118860i
$323$	29.9453	−	9.72983i	1.66620	−	0.541382i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	0.0595901	−	1.90890i	0.00330547	−	0.105887i
$326$	2.18311	+	6.71891i	0.120911	+	0.372126i
$327$	1.96580	+	2.70569i	0.108709	+	0.149625i
$328$	−3.62158	+	1.17672i	−0.199968	+	0.0649736i
$329$	4.65975	−	14.3412i	0.256900	−	0.790658i
$330$	−2.06884	−	0.0322837i	−0.113886	−	0.00177716i
$331$	10.2425	−	31.5233i	0.562981	−	1.73268i	−0.110894	−	0.993832i	$-0.535371\pi$
$331$	10.2425	−	31.5233i	0.562981	−	1.73268i	0.673875	−	0.738845i	$-0.264629\pi$
$332$	−3.77507	−	5.19594i	−0.207184	−	0.285164i
$333$	1.45106	+	1.99721i	0.0795176	+	0.109447i
$334$	−6.11152	−	4.44028i	−0.334408	−	0.242961i
$335$	11.5296	+	16.4014i	0.629931	+	0.896102i
$336$	1.54336			0.0841973
$337$	−7.90961	+	10.8866i	−0.430864	+	0.593034i	−0.968151	−	0.250366i	$-0.919449\pi$
$337$	−7.90961	+	10.8866i	−0.430864	+	0.593034i	0.537287	+	0.843399i	$0.319449\pi$
$338$	12.2250	−	3.97214i	0.664951	−	0.216056i
$339$	−1.96705	+	6.05395i	−0.106835	+	0.328805i
$340$	−6.54123	−	9.30516i	−0.354748	−	0.504643i
$341$	−2.66233	+	4.41080i	−0.144173	+	0.238858i
$342$			6.18992i			0.334712i
$343$	17.0532	+	5.54093i	0.920788	+	0.299182i
$344$	−2.98574	−	9.18916i	−0.160980	−	0.495446i
$345$	−9.99878	−	0.156028i	−0.538316	−	0.00840027i
$346$	17.7630			0.954943
$347$			28.5542i			1.53287i	0.642323	+	0.766434i	$0.277971\pi$
$347$			28.5542i			1.53287i	−0.642323	+	0.766434i	$0.722029\pi$
$348$	0.431011	−	0.593236i	0.0231046	−	0.0318008i
$349$	10.8420	−	7.87718i	0.580360	−	0.421656i	−0.258494	−	0.966013i	$-0.583226\pi$
$349$	10.8420	−	7.87718i	0.580360	−	0.421656i	0.838854	+	0.544357i	$0.183226\pi$
$350$	2.15447	+	7.40995i	0.115161	+	0.396079i
$351$	0.118034	−	0.363271i	0.00630019	−	0.0193900i
$352$	−0.543894	+	0.748606i	−0.0289897	+	0.0399008i
$353$	−1.32198	−	0.429538i	−0.0703621	−	0.0228620i	0.273624	−	0.961837i	$-0.411777\pi$
$353$	−1.32198	−	0.429538i	−0.0703621	−	0.0228620i	−0.343987	+	0.938975i	$0.611777\pi$
$354$	3.32049	+	10.2194i	0.176482	+	0.543156i
$355$	2.48223	−	7.25248i	0.131743	−	0.384922i
$356$	2.36664	+	7.28377i	0.125432	+	0.386039i
$357$	7.46642	−	2.42599i	0.395165	−	0.128397i
$358$	7.99480	+	11.0039i	0.422538	+	0.581574i
$359$	8.28125	+	25.4871i	0.437067	+	1.34516i	0.890953	+	0.454095i	$0.150037\pi$
$359$	8.28125	+	25.4871i	0.437067	+	1.34516i	−0.453886	+	0.891060i	$0.649963\pi$
$360$	2.13715	−	0.657718i	0.112638	−	0.0346648i
$361$	−15.6262	−	11.3531i	−0.822433	−	0.597533i
$362$	19.4236	+	6.31110i	1.02088	+	0.331704i
$363$	−5.96236	−	8.20648i	−0.312943	−	0.430729i
$364$	0.476925	−	0.346506i	0.0249977	−	0.0181619i
$365$	0.375434	−	24.0590i	0.0196511	−	1.25931i
$366$	−11.9176			−0.622944
$367$			10.5384i			0.550099i	0.961430	+	0.275050i	$0.0886943\pi$
$367$			10.5384i			0.550099i	−0.961430	+	0.275050i	$0.911306\pi$
$368$	−2.62866	+	3.61803i	−0.137028	+	0.188603i
$369$	−1.17672	−	3.62158i	−0.0612577	−	0.188532i
$370$	1.62370	+	5.27596i	0.0844122	+	0.274284i
$371$	11.0440			0.573377
$372$	1.26335	−	5.42254i	0.0655018	−	0.281146i
$373$		−	27.1726i		−	1.40695i	−0.710722	−	0.703473i	$-0.751632\pi$
$373$		−	27.1726i		−	1.40695i	0.710722	−	0.703473i	$-0.248368\pi$
$374$	−1.45451	+	4.47652i	−0.0752108	+	0.231475i
$375$	6.14119	+	9.34269i	0.317130	+	0.482454i
$376$	−7.90443	−	5.74290i	−0.407640	−	0.296168i
$377$		−	0.280088i		−	0.0144253i
$378$			1.54336i			0.0793820i
$379$	26.3569	+	19.1494i	1.35386	+	0.983640i	0.998809	+	0.0487952i	$0.0155382\pi$
$379$	26.3569	+	19.1494i	1.35386	+	0.983640i	0.355056	+	0.934845i	$0.384462\pi$
$380$	−4.48200	+	13.0953i	−0.229922	+	0.671775i
$381$	6.26889	−	4.55462i	0.321165	−	0.233340i
$382$	12.4863	+	4.05704i	0.638855	+	0.207576i
$383$	6.23389	−	8.58021i	0.318537	−	0.438428i	−0.619483	−	0.785010i	$-0.712658\pi$
$383$	6.23389	−	8.58021i	0.318537	−	0.438428i	0.938020	+	0.346582i	$0.112658\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$	1.91709	−	2.55388i	0.0977041	−	0.130158i
$386$	8.54926	−	6.21140i	0.435146	−	0.316152i
$387$	9.18916	−	2.98574i	0.467111	−	0.151774i
$388$	16.1827	−	5.25808i	0.821552	−	0.266938i
$389$	28.1741	−	20.4697i	1.42848	−	1.03785i	0.438185	−	0.898885i	$-0.355621\pi$
$389$	28.1741	−	20.4697i	1.42848	−	1.03785i	0.990297	−	0.138968i	$-0.0443786\pi$
$390$	0.512749	−	0.683066i	0.0259640	−	0.0345884i
$391$	−7.02968	+	21.6351i	−0.355506	+	1.09414i
$392$	2.71441	−	3.73607i	0.137099	−	0.188700i
$393$	−1.57035	−	0.510236i	−0.0792135	−	0.0257380i
$394$	9.36106	−	6.80121i	0.471604	−	0.342640i
$395$	4.49072	−	13.1208i	0.225953	−	0.660179i
$396$	−0.748606	−	0.543894i	−0.0376189	−	0.0273317i
$397$			16.4210i			0.824145i	0.911151	+	0.412072i	$0.135195\pi$
$397$			16.4210i			0.824145i	−0.911151	+	0.412072i	$0.864805\pi$
$398$		−	14.3999i		−	0.721804i
$399$	−7.72877	−	5.61528i	−0.386922	−	0.281116i
$400$	4.99757	+	0.156009i	0.249878	+	0.00780045i
$401$	10.5220	−	32.3834i	0.525444	−	1.61715i	−0.237992	−	0.971267i	$-0.576489\pi$
$401$	10.5220	−	32.3834i	0.525444	−	1.61715i	0.763436	−	0.645884i	$-0.223511\pi$
$402$			8.96590i			0.447179i
$403$	−0.827039	−	1.95930i	−0.0411977	−	0.0975996i
$404$	8.48419			0.422104
$405$	0.657718	+	2.13715i	0.0326822	+	0.106196i
$406$	0.349720	+	1.07633i	0.0173563	+	0.0534172i
$407$	1.34271	−	1.84808i	0.0665555	−	0.0916057i
$408$		−	5.08672i		−	0.251830i
$409$	−4.50739			−0.222876			−0.111438	−	0.993771i	$-0.535546\pi$
$409$	−4.50739			−0.222876			−0.111438	+	0.993771i	$0.535546\pi$
$410$	0.132855	−	8.51380i	0.00656126	−	0.420467i
$411$	4.26159	−	3.09623i	0.210209	−	0.152726i
$412$	0.0156643	+	0.0215601i	0.000771725	+	0.00106219i
$413$	−15.7723	−	5.12472i	−0.776102	−	0.252171i
$414$	−3.61803	−	2.62866i	−0.177817	−	0.129191i
$415$	13.7259	−	4.22422i	0.673779	−	0.207359i
$416$	−0.118034	−	0.363271i	−0.00578709	−	0.0178108i
$417$	7.22749	+	9.94779i	0.353932	+	0.487145i
$418$	5.44737	−	1.76996i	0.266440	−	0.0865715i
$419$	−0.658158	−	2.02560i	−0.0321531	−	0.0989571i	0.933692	−	0.358077i	$-0.116568\pi$
$419$	−0.658158	−	2.02560i	−0.0321531	−	0.0989571i	−0.965845	+	0.259120i	$0.916568\pi$
$420$	−1.11752	+	3.26512i	−0.0545293	+	0.159321i
$421$	−0.888558	−	2.73470i	−0.0433057	−	0.133281i	0.927066	−	0.374898i	$-0.122322\pi$
$421$	−0.888558	−	2.73470i	−0.0433057	−	0.133281i	−0.970372	+	0.241617i	$0.922322\pi$
$422$	−20.7453	−	6.74054i	−1.00986	−	0.328124i
$423$	5.74290	−	7.90443i	0.279229	−	0.384326i
$424$	2.21127	−	6.80559i	0.107389	−	0.330509i
$425$	24.4223	−	7.10086i	1.18465	−	0.344442i
$426$	2.77340	−	2.01500i	0.134372	−	0.0976269i
$427$	10.8113	−	14.8804i	0.523193	−	0.720114i
$428$		−	12.9021i		−	0.623648i
$429$	−0.353444			−0.0170644
$430$	21.6024	+	0.337099i	1.04176	+	0.0162563i
$431$	4.97006	+	15.2963i	0.239399	+	0.736795i	0.996507	+	0.0835053i	$0.0266115\pi$
$431$	4.97006	+	15.2963i	0.239399	+	0.736795i	−0.757108	+	0.653290i	$0.773388\pi$
$432$	0.951057	+	0.309017i	0.0457577	+	0.0148676i
$433$			14.1221i			0.678667i	0.940666	+	0.339333i	$0.110201\pi$
$433$			14.1221i			0.678667i	−0.940666	+	0.339333i	$0.889799\pi$
$434$	5.62455	+	6.49657i	0.269987	+	0.311845i
$435$	0.942956	+	1.34139i	0.0452113	+	0.0643148i
$436$	−1.03348	+	3.18073i	−0.0494949	+	0.152330i
$437$	26.3273	−	8.55426i	1.25941	−	0.409206i
$438$	6.32506	−	8.70569i	0.302223	−	0.415974i
$439$	−22.1050			−1.05501			−0.527507	−	0.849551i	$-0.676873\pi$
$439$	−22.1050			−1.05501			−0.527507	+	0.849551i	$0.676873\pi$
$440$	−1.18992	−	1.69271i	−0.0567271	−	0.0806966i
$441$	3.73607	+	2.71441i	0.177908	+	0.129258i
$442$	−1.14204	−	1.57188i	−0.0543213	−	0.0747669i
$443$	−5.26690	−	7.24926i	−0.250238	−	0.344423i	0.665357	−	0.746526i	$-0.268279\pi$
$443$	−5.26690	−	7.24926i	−0.250238	−	0.344423i	−0.915595	+	0.402103i	$0.868279\pi$
$444$	−0.762867	+	2.34786i	−0.0362041	+	0.111425i
$445$	−17.1231	−	0.267201i	−0.811712	−	0.0126665i
$446$	7.25392	−	22.3253i	0.343483	−	1.05713i
$447$	−16.7246	+	5.43414i	−0.791045	+	0.257026i
$448$	0.907165	+	1.24861i	0.0428595	+	0.0589911i
$449$	−0.339540	−	1.04500i	−0.0160239	−	0.0493165i	0.942725	−	0.333571i	$-0.108254\pi$
$449$	−0.339540	−	1.04500i	−0.0160239	−	0.0493165i	−0.958749	+	0.284255i	$0.908254\pi$
$450$	−0.156009	+	4.99757i	−0.00735434	+	0.235587i
$451$	−2.85066	+	2.07112i	−0.134232	+	0.0975254i
$452$	−6.05395	+	1.96705i	−0.284754	+	0.0925221i
$453$	5.87510	+	1.90894i	0.276036	+	0.0896897i
$454$	5.34184	+	3.88108i	0.250705	+	0.182148i
$455$	0.387732	+	1.25987i	0.0181772	+	0.0590638i
$456$	−5.00775	+	3.63834i	−0.234509	+	0.170381i
$457$	−15.2504	−	20.9904i	−0.713385	−	0.981891i	−0.999718	−	0.0237602i	$-0.992436\pi$
$457$	−15.2504	−	20.9904i	−0.713385	−	0.981891i	0.286332	−	0.958130i	$-0.407564\pi$
$458$	7.53306	−	10.3684i	0.351997	−	0.484482i
$459$	5.08672			0.237428
$460$	−5.75091	−	8.18090i	−0.268137	−	0.381436i
$461$	11.4323	+	8.30604i	0.532455	+	0.386851i	0.821275	−	0.570532i	$-0.193263\pi$
$461$	11.4323	+	8.30604i	0.532455	+	0.386851i	−0.288820	+	0.957383i	$0.593263\pi$
$462$	1.35822	−	0.441312i	0.0631901	−	0.0205317i
$463$	16.6339	+	5.40468i	0.773043	+	0.251177i	0.668867	−	0.743382i	$-0.266779\pi$
$463$	16.6339	+	5.40468i	0.773043	+	0.251177i	0.104176	+	0.994559i	$0.466779\pi$
$464$	0.733280			0.0340417
$465$	10.5571	+	6.59909i	0.489573	+	0.306025i
$466$	4.96748			0.230114
$467$	12.5886	+	4.09028i	0.582530	+	0.189275i	0.585434	−	0.810720i	$-0.300924\pi$
$467$	12.5886	+	4.09028i	0.582530	+	0.189275i	−0.00290377	+	0.999996i	$0.500924\pi$
$468$	0.363271	−	0.118034i	0.0167922	−	0.00545612i
$469$	−11.1949	−	8.13356i	−0.516931	−	0.375573i
$470$	17.8730	−	12.5642i	0.824422	−	0.579542i
$471$	5.31935			0.245103
$472$	−6.31595	+	8.69316i	−0.290715	+	0.400135i
$473$	−5.25513	−	7.23307i	−0.241631	−	0.332577i
$474$	5.01750	−	3.64543i	0.230461	−	0.167440i
$475$	−24.4589	−	18.9641i	−1.12225	−	0.870133i
$476$	6.35131	+	4.61450i	0.291112	+	0.211505i
$477$	6.80559	+	2.21127i	0.311607	+	0.101247i
$478$	7.96314	−	2.58738i	0.364226	−	0.118344i
$479$	−6.29124	+	4.57085i	−0.287454	+	0.208848i	−0.722162	−	0.691724i	$-0.756852\pi$
$479$	−6.29124	+	4.57085i	−0.287454	+	0.208848i	0.434708	+	0.900571i	$0.356852\pi$
$480$	1.78829	+	1.34239i	0.0816239	+	0.0612716i
$481$	0.291389	+	0.896804i	0.0132862	+	0.0408907i
$482$	1.87263	+	2.57746i	0.0852962	+	0.117400i
$483$	6.56431	−	2.13287i	0.298686	−	0.0970491i
$484$	3.13460	−	9.64730i	0.142482	−	0.438513i
$485$	−0.593652	+	38.0432i	−0.0269564	+	1.72745i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	9.21924	+	12.6892i	0.417763	+	0.575002i	0.965090	−	0.261917i	$-0.0843546\pi$
$487$	9.21924	+	12.6892i	0.417763	+	0.575002i	−0.547327	+	0.836919i	$0.684355\pi$
$488$	−7.00500	−	9.64156i	−0.317102	−	0.436453i
$489$	−5.71544	−	4.15251i	−0.258461	−	0.187783i
$490$	5.93852	+	8.44779i	0.268275	+	0.381632i
$491$	−13.9699			−0.630453			−0.315226	−	0.949016i	$-0.602080\pi$
$491$	−13.9699			−0.630453			−0.315226	+	0.949016i	$0.602080\pi$
$492$	2.23826	−	3.08070i	0.100908	−	0.138889i
$493$	3.54743	−	1.15263i	0.159768	−	0.0519119i
$494$	−0.730621	+	2.24862i	−0.0328722	+	0.101170i
$495$	1.69271	−	1.18992i	0.0760815	−	0.0534828i
$496$	5.12951	−	2.16522i	0.230322	−	0.0972210i
$497$			5.29082i			0.237326i
$498$	6.10820	+	1.98467i	0.273715	+	0.0889354i
$499$	−12.5671	−	38.6777i	−0.562582	−	1.73145i	−0.675028	−	0.737793i	$-0.735868\pi$
$499$	−12.5671	−	38.6777i	−0.562582	−	1.73145i	0.112445	−	0.993658i	$-0.464132\pi$
$500$	−3.94869	+	10.4598i	−0.176591	+	0.467777i
$501$	7.55426			0.337499
$502$			5.44017i			0.242807i
$503$	9.12070	−	12.5536i	0.406672	−	0.559736i	−0.555731	−	0.831362i	$-0.687562\pi$
$503$	9.12070	−	12.5536i	0.406672	−	0.559736i	0.962403	+	0.271627i	$0.0875615\pi$
$504$	−1.24861	+	0.907165i	−0.0556173	+	0.0404084i
$505$	−6.14323	+	17.9490i	−0.273370	+	0.798722i
$506$	−1.27877	+	3.93565i	−0.0568483	+	0.174961i
$507$	−7.55545	+	10.3992i	−0.335549	+	0.461844i
$508$	7.36953	+	2.39450i	0.326970	+	0.106239i
$509$	1.87802	+	5.77995i	0.0832418	+	0.256192i	0.984011	−	0.178105i	$-0.0569968\pi$
$509$	1.87802	+	5.77995i	0.0832418	+	0.256192i	−0.900770	+	0.434297i	$0.856997\pi$
$510$	10.7614	+	3.68320i	0.476523	+	0.163095i
$511$	5.13211	+	15.7950i	0.227031	+	0.698730i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	−3.63834	−	5.00775i	−0.160637	−	0.221098i
$514$	−0.536192	−	1.65023i	−0.0236504	−	0.0727884i
$515$	−0.0569544	+	0.0175280i	−0.00250971	+	0.000772375i
$516$	7.81677	+	5.67921i	0.344114	+	0.250013i
$517$	−8.59834	−	2.79377i	−0.378155	−	0.122870i
$518$	−2.23951	−	3.08242i	−0.0983984	−	0.135434i
$519$	−14.3705	+	10.4408i	−0.630797	+	0.458301i
$520$	0.853998	+	0.0133264i	0.0374503	+	0.000584401i
$521$	28.2494			1.23763			0.618815	−	0.785537i	$-0.287613\pi$
$521$	28.2494			1.23763			0.618815	+	0.785537i	$0.287613\pi$
$522$			0.733280i			0.0320948i
$523$	−17.4607	+	24.0327i	−0.763505	+	1.05087i	0.233409	+	0.972379i	$0.425012\pi$
$523$	−17.4607	+	24.0327i	−0.763505	+	1.05087i	−0.996914	+	0.0784962i	$0.974988\pi$
$524$	−0.510236	−	1.57035i	−0.0222898	−	0.0686009i
$525$	−6.09846	−	4.72841i	−0.266159	−	0.206365i
$526$	−9.64746			−0.420649
$527$	21.4119	−	18.5378i	0.932716	−	0.807519i
$528$		−	0.925328i		−	0.0402697i
$529$	0.927051	−	2.85317i	0.0403066	−	0.124051i
$530$	12.7967	+	9.60593i	0.555852	+	0.417255i
$531$	−8.69316	−	6.31595i	−0.377251	−	0.274089i
$532$		−	9.55328i		−	0.414187i
$533$		−	1.45451i		−	0.0630017i
$534$	−6.19594	−	4.50162i	−0.268125	−	0.194804i
$535$	27.2956	+	9.34217i	1.18009	+	0.403897i
$536$	−7.25357	+	5.27002i	−0.313306	+	0.227630i
$537$	−12.9359	−	4.20311i	−0.558223	−	0.181378i
$538$	−16.7797	+	23.0952i	−0.723423	+	0.995707i
$539$	1.32049	−	4.06405i	0.0568775	−	0.175051i
$540$	−1.34239	+	1.78829i	−0.0577674	+	0.0769557i
$541$	−5.19450	+	3.77402i	−0.223329	+	0.162258i	−0.693824	−	0.720145i	$-0.744075\pi$
$541$	−5.19450	+	3.77402i	−0.223329	+	0.162258i	0.470495	+	0.882403i	$0.344075\pi$
$542$	11.3688	−	3.69394i	0.488331	−	0.158668i
$543$	−19.4236	+	6.31110i	−0.833545	+	0.270835i
$544$	4.11525	−	2.98990i	0.176440	−	0.128191i
$545$	−5.98079	−	4.48953i	−0.256189	−	0.192310i
$546$	−0.182169	+	0.560659i	−0.00779612	+	0.0239940i
$547$	5.52462	−	7.60398i	0.236216	−	0.325123i	−0.674409	−	0.738358i	$-0.735601\pi$
$547$	5.52462	−	7.60398i	0.236216	−	0.325123i	0.910624	+	0.413236i	$0.135601\pi$
$548$	5.00980	+	1.62778i	0.214008	+	0.0695355i
$549$	9.64156	−	7.00500i	0.411492	−	0.298966i
$550$	4.44266	−	1.29172i	0.189436	−	0.0550791i
$551$	−3.67208	−	2.66792i	−0.156436	−	0.113657i
$552$		−	4.47214i		−	0.190347i
$553$			9.57188i			0.407038i
$554$	21.1998	+	15.4026i	0.900695	+	0.654393i
$555$	−4.41473	−	3.31395i	−0.187395	−	0.140669i
$556$	−3.79972	+	11.6943i	−0.161144	+	0.495950i
$557$		−	27.6438i		−	1.17130i	−0.810563	−	0.585652i	$-0.800839\pi$
$557$		−	27.6438i		−	1.17130i	0.810563	−	0.585652i	$-0.199161\pi$
$558$	2.16522	+	5.12951i	0.0916609	+	0.217149i
$559$	3.69058			0.156095
$560$	−3.29840	+	1.01510i	−0.139383	+	0.0428956i
$561$	−1.45451	−	4.47652i	−0.0614094	−	0.188999i
$562$	2.49370	−	3.43229i	0.105191	−	0.144782i
$563$		−	39.1376i		−	1.64945i	−0.565533	−	0.824726i	$-0.691329\pi$
$563$		−	39.1376i		−	1.64945i	0.565533	−	0.824726i	$-0.308671\pi$
$564$	9.77041			0.411408
$565$	0.222085	−	14.2319i	0.00934320	−	0.598743i
$566$	16.7059	−	12.1375i	0.702200	−	0.510178i
$567$	−0.907165	−	1.24861i	−0.0380974	−	0.0524365i
$568$	3.26033	+	1.05935i	0.136800	+	0.0444492i
$569$	−36.9479	−	26.8442i	−1.54894	−	1.12537i	−0.944403	−	0.328790i	$-0.893359\pi$
$569$	−36.9479	−	26.8442i	−1.54894	−	1.12537i	−0.604534	−	0.796579i	$-0.706641\pi$
$570$	−4.07122	−	13.2288i	−0.170525	−	0.554093i
$571$	−1.57649	−	4.85193i	−0.0659739	−	0.203047i	0.912635	−	0.408775i	$-0.134044\pi$
$571$	−1.57649	−	4.85193i	−0.0659739	−	0.203047i	−0.978609	+	0.205728i	$0.934044\pi$
$572$	−0.207749	−	0.285942i	−0.00868642	−	0.0119558i
$573$	−12.4863	+	4.05704i	−0.521623	+	0.169485i
$574$	1.81611	+	5.58941i	0.0758029	+	0.233297i
$575$	21.4715	−	6.24292i	0.895424	−	0.260348i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−14.6855	−	4.77162i	−0.611367	−	0.198645i	−0.0130636	−	0.999915i	$-0.504158\pi$
$577$	−14.6855	−	4.77162i	−0.611367	−	0.198645i	−0.598304	+	0.801269i	$0.704158\pi$
$578$	5.21645	−	7.17983i	0.216976	−	0.298642i
$579$	−3.26553	+	10.0503i	−0.135711	+	0.417674i
$580$	−0.530954	+	1.55132i	−0.0220466	+	0.0644150i
$581$	−8.01922	+	5.82631i	−0.332693	+	0.241716i
$582$	−10.0015	+	13.7658i	−0.414574	+	0.570612i
$583$		−	6.62148i		−	0.274234i
$584$	10.7608			0.445286
$585$	−0.0133264	+	0.853998i	−0.000550978	+	0.0353085i
$586$	−0.920725	−	2.83370i	−0.0380348	−	0.117059i
$587$	−21.1340	−	6.86687i	−0.872296	−	0.283426i	−0.161541	−	0.986866i	$-0.551646\pi$
$587$	−21.1340	−	6.86687i	−0.872296	−	0.283426i	−0.710755	+	0.703440i	$0.751646\pi$
$588$			4.61803i			0.190445i
$589$	−33.5651	−	7.82005i	−1.38302	−	0.322220i
$590$	−13.8179	−	19.6565i	−0.568873	−	0.809244i
$591$	−3.57561	+	11.0046i	−0.147081	+	0.452668i
$592$	−2.34786	+	0.762867i	−0.0964966	+	0.0313536i
$593$	−4.75218	+	6.54082i	−0.195149	+	0.268599i	−0.895366	−	0.445330i	$-0.853086\pi$
$593$	−4.75218	+	6.54082i	−0.195149	+	0.268599i	0.700218	+	0.713929i	$0.253086\pi$
$594$	0.925328			0.0379667
$595$	−14.3612	+	10.0955i	−0.588753	+	0.413875i
$596$	−14.2268	−	10.3364i	−0.582751	−	0.423393i
$597$	8.46407	+	11.6498i	0.346411	+	0.476794i
$598$	−1.00406	−	1.38197i	−0.0410589	−	0.0565128i
$599$	6.94640	−	21.3788i	0.283822	−	0.873515i	−0.702927	−	0.711262i	$-0.748124\pi$
$599$	6.94640	−	21.3788i	0.283822	−	0.873515i	0.986749	−	0.162253i	$-0.0518761\pi$
$600$	−4.13482	+	2.81128i	−0.168803	+	0.114770i
$601$	9.91124	−	30.5037i	0.404288	−	1.24427i	−0.517201	−	0.855864i	$-0.673026\pi$
$601$	9.91124	−	30.5037i	0.404288	−	1.24427i	0.921488	−	0.388406i	$-0.126974\pi$
$602$	−14.1822	+	4.60808i	−0.578023	+	0.187811i
$603$	−5.27002	−	7.25357i	−0.214612	−	0.295388i
$604$	1.90894	+	5.87510i	0.0776735	+	0.239055i
$605$	18.1400	+	13.6169i	0.737496	+	0.553607i
$606$	−6.86385	+	4.98688i	−0.278825	+	0.202578i
$607$	14.8483	−	4.82449i	0.602672	−	0.195820i	0.00824040	−	0.999966i	$-0.497377\pi$
$607$	14.8483	−	4.82449i	0.602672	−	0.195820i	0.594432	+	0.804146i	$0.297377\pi$
$608$	−5.88696	−	1.91279i	−0.238748	−	0.0775739i
$609$	−0.915578	−	0.665206i	−0.0371011	−	0.0269555i
$610$	25.4697	−	7.83843i	1.03124	−	0.317369i
$611$	3.01922	−	2.19359i	0.122145	−	0.0887433i
$612$	2.98990	+	4.11525i	0.120860	+	0.166349i
$613$	−22.8972	+	31.5153i	−0.924810	+	1.27289i	0.0370393	+	0.999314i	$0.488207\pi$
$613$	−22.8972	+	31.5153i	−0.924810	+	1.27289i	−0.961850	+	0.273578i	$0.911793\pi$
$614$	−10.8625			−0.438373
$615$	4.89681	+	6.96590i	0.197458	+	0.280892i
$616$	1.15537	+	0.839425i	0.0465512	+	0.0338214i
$617$	19.1458	−	6.22085i	0.770781	−	0.250442i	0.102882	−	0.994694i	$-0.467194\pi$
$617$	19.1458	−	6.22085i	0.770781	−	0.250442i	0.667899	+	0.744252i	$0.267194\pi$
$618$	−0.0253454	−	0.00823521i	−0.00101954	−	0.000331269i
$619$	−0.512710			−0.0206076			−0.0103038	−	0.999947i	$-0.503280\pi$
$619$	−0.512710			−0.0206076			−0.0103038	+	0.999947i	$0.503280\pi$
$620$	0.866526	+	12.4197i	0.0348005	+	0.498787i
$621$	4.47214			0.179461
$622$	12.0457	+	3.91390i	0.482990	+	0.156933i
$623$	11.2415	−	3.65258i	0.450381	−	0.146338i
$624$	0.309017	+	0.224514i	0.0123706	+	0.00898775i
$625$	−19.2695	−	15.9275i	−0.770780	−	0.637102i
$626$	30.1500			1.20504
$627$	−3.36666	+	4.63381i	−0.134451	+	0.185057i
$628$	3.12663	+	4.30344i	0.124766	+	0.171726i
$629$	−10.1593	+	7.38114i	−0.405076	+	0.294305i
$630$	−1.01510	−	3.29840i	−0.0404424	−	0.131411i
$631$	−17.6615	−	12.8318i	−0.703094	−	0.510827i	0.177845	−	0.984059i	$-0.443088\pi$
$631$	−17.6615	−	12.8318i	−0.703094	−	0.510827i	−0.880938	+	0.473231i	$0.843088\pi$
$632$	5.89842	+	1.91651i	0.234627	+	0.0762348i
$633$	20.7453	−	6.74054i	0.824550	−	0.267913i
$634$	−1.93480	+	1.40571i	−0.0768407	+	0.0558281i
$635$	−10.4019	+	13.8571i	−0.412787	+	0.549901i
$636$	2.21127	+	6.80559i	0.0876826	+	0.269859i
$637$	1.03681	+	1.42705i	0.0410800	+	0.0565418i
$638$	0.645315	−	0.209676i	0.0255483	−	0.00830114i
$639$	−1.05935	+	3.26033i	−0.0419071	+	0.128977i
$640$	−0.0348889	+	2.23580i	−0.00137911	+	0.0883776i
$641$	−13.7525	+	42.3258i	−0.543191	+	1.67177i	0.182061	+	0.983287i	$0.441723\pi$
$641$	−13.7525	+	42.3258i	−0.543191	+	1.67177i	−0.725252	+	0.688483i	$0.758277\pi$
$642$	7.58368	+	10.4380i	0.299304	+	0.411956i
$643$	28.2974	+	38.9481i	1.11594	+	1.53596i	0.812360	+	0.583157i	$0.198183\pi$
$643$	28.2974	+	38.9481i	1.11594	+	1.53596i	0.303582	+	0.952805i	$0.401817\pi$
$644$	5.58394	+	4.05697i	0.220038	+	0.159867i
$645$	−17.6748	+	12.4248i	−0.695946	+	0.489228i
$646$	−31.4864			−1.23882
$647$	−15.4609	+	21.2801i	−0.607830	+	0.836607i	−0.996397	−	0.0848141i	$-0.972970\pi$
$647$	−15.4609	+	21.2801i	−0.607830	+	0.836607i	0.388567	+	0.921421i	$0.372970\pi$
$648$	−0.951057	+	0.309017i	−0.0373610	+	0.0121393i
$649$	−3.07254	+	9.45631i	−0.120608	+	0.371193i
$650$	−0.646556	+	1.79706i	−0.0253600	+	0.0704864i
$651$	−8.36894	−	1.94981i	−0.328005	−	0.0764191i
$652$		−	7.06468i		−	0.276674i
$653$	−12.0645	−	3.92001i	−0.472122	−	0.153402i	0.0632856	−	0.997995i	$-0.479842\pi$
$653$	−12.0645	−	3.92001i	−0.472122	−	0.153402i	−0.535408	+	0.844594i	$0.679842\pi$
$654$	−1.03348	−	3.18073i	−0.0404124	−	0.124377i
$655$	3.69166	+	0.0576072i	0.144245	+	0.00225090i
$656$	3.80795			0.148676
$657$			10.7608i			0.419820i
$658$	−8.86338	+	12.1994i	−0.345530	+	0.475582i
$659$	34.7696	−	25.2616i	1.35443	−	0.984053i	0.355655	−	0.934617i	$-0.384258\pi$
$659$	34.7696	−	25.2616i	1.35443	−	0.984053i	0.998777	−	0.0494355i	$-0.0157422\pi$
$660$	1.95761	+	0.670012i	0.0761999	+	0.0260802i
$661$	−14.7566	+	45.4161i	−0.573965	+	1.76648i	0.0657136	+	0.997839i	$0.479068\pi$
$661$	−14.7566	+	45.4161i	−0.573965	+	1.76648i	−0.639678	+	0.768643i	$0.720932\pi$
$662$	−19.4825	+	26.8153i	−0.757208	+	1.04221i
$663$	1.84786	+	0.600406i	0.0717650	+	0.0233178i
$664$	1.98467	+	6.10820i	0.0770203	+	0.237044i
$665$	20.2108	+	6.91734i	0.783741	+	0.268243i
$666$	−0.762867	−	2.34786i	−0.0295605	−	0.0909779i
$667$	3.11883	−	1.01337i	0.120761	−	0.0392378i
$668$	4.44028	+	6.11152i	0.171800	+	0.236462i
$669$	7.25392	+	22.3253i	0.280453	+	0.863145i
$670$	−5.89703	−	19.1615i	−0.227822	−	0.740272i
$671$	−8.92160	−	6.48192i	−0.344415	−	0.250232i
$672$	−1.46782	−	0.476925i	−0.0566226	−	0.0183978i
$673$	−5.73399	−	7.89217i	−0.221029	−	0.304221i	0.684074	−	0.729413i	$-0.260207\pi$
$673$	−5.73399	−	7.89217i	−0.221029	−	0.304221i	−0.905103	+	0.425192i	$0.860207\pi$
$674$	10.8866	−	7.90961i	0.419338	−	0.304667i
$675$	−2.81128	−	4.13482i	−0.108206	−	0.159149i
$676$	−12.8541			−0.494389
$677$		−	30.4716i		−	1.17112i	−0.810630	−	0.585559i	$-0.800875\pi$
$677$		−	30.4716i		−	1.17112i	0.810630	−	0.585559i	$-0.199125\pi$
$678$	3.74154	−	5.14979i	0.143693	−	0.197777i
$679$	−8.11512	−	24.9758i	−0.311430	−	0.958482i
$680$	3.34563	+	10.8711i	0.128299	+	0.416887i
$681$	−6.60288			−0.253023
$682$	3.89504	−	3.37222i	0.149149	−	0.129129i
$683$			3.88079i			0.148494i	0.997240	+	0.0742472i	$0.0236554\pi$
$683$			3.88079i			0.148494i	−0.997240	+	0.0742472i	$0.976345\pi$
$684$	1.91279	−	5.88696i	0.0731373	−	0.225094i
$685$	−7.07122	+	9.42003i	−0.270177	+	0.359921i
$686$	−14.5063	−	10.5395i	−0.553855	−	0.402399i
$687$			12.8160i			0.488961i
$688$			9.66205i			0.368362i
$689$	2.21127	+	1.60658i	0.0842427	+	0.0612059i
$690$	9.46119	+	3.23819i	0.360181	+	0.123276i
$691$	36.9659	−	26.8573i	1.40625	−	1.02170i	0.412397	−	0.911004i	$-0.364692\pi$
$691$	36.9659	−	26.8573i	1.40625	−	1.02170i	0.993854	−	0.110697i	$-0.0353082\pi$
$692$	−16.8936	−	5.48906i	−0.642197	−	0.208663i
$693$	−0.839425	+	1.15537i	−0.0318871	+	0.0438889i
$694$	8.82373	−	27.1566i	0.334944	−	1.03085i
$695$	−21.9891	−	16.5063i	−0.834093	−	0.626118i
$696$	−0.593236	+	0.431011i	−0.0224866	+	0.0163374i
$697$	18.4220	−	5.98566i	0.697782	−	0.226723i
$698$	−12.7456	+	4.14128i	−0.482426	+	0.156750i
$699$	−4.01877	+	2.91981i	−0.152004	+	0.110437i
$700$	0.240778	−	7.71305i	0.00910057	−	0.291526i
$701$	−6.65390	+	20.4786i	−0.251314	+	0.773466i	0.743219	+	0.669048i	$0.233298\pi$
$701$	−6.65390	+	20.4786i	−0.251314	+	0.773466i	−0.994534	+	0.104418i	$0.966702\pi$
$702$	−0.224514	+	0.309017i	−0.00847373	+	0.0116631i
$703$	14.5331	+	4.72208i	0.548126	+	0.178097i
$704$	0.748606	−	0.543894i	0.0282142	−	0.0204988i
$705$	−7.07456	+	20.6701i	−0.266443	+	0.778483i
$706$	1.12455	+	0.817031i	0.0423229	+	0.0307494i
$707$		−	13.0942i		−	0.492457i
$708$		−	10.7453i		−	0.403834i
$709$	10.3432	+	7.51477i	0.388447	+	0.282223i	0.764819	−	0.644246i	$-0.222829\pi$
$709$	10.3432	+	7.51477i	0.388447	+	0.282223i	−0.376372	+	0.926469i	$0.622829\pi$
$710$	−4.60188	+	6.13046i	−0.172705	+	0.230072i
$711$	−1.91651	+	5.89842i	−0.0718749	+	0.221208i
$712$		−	7.65861i		−	0.287018i
$713$	18.8248	−	16.2980i	0.704996	−	0.610365i
$714$	−7.85066			−0.293803
$715$	0.755362	−	0.232466i	0.0282489	−	0.00869374i
$716$	−4.20311	−	12.9359i	−0.157078	−	0.483436i
$717$	−4.92149	+	6.77385i	−0.183797	+	0.252974i
$718$		−	26.7987i		−	1.00012i
$719$	26.9610			1.00547			0.502737	−	0.864439i	$-0.332326\pi$
$719$	26.9610			1.00547			0.502737	+	0.864439i	$0.332326\pi$
$720$	−2.23580	−	0.0348889i	−0.0833232	−	0.00130023i
$721$	0.0332750	−	0.0241757i	0.00123923	−	0.000900350i
$722$	11.3531	+	15.6262i	0.422519	+	0.581548i
$723$	−3.02999	−	0.984502i	−0.112686	−	0.0366140i
$724$	−16.5227	−	12.0044i	−0.614060	−	0.446141i
$725$	−2.89749	−	2.24656i	−0.107610	−	0.0834350i
$726$	3.13460	+	9.64730i	0.116336	+	0.358045i
$727$	10.6614	+	14.6741i	0.395408	+	0.544232i	0.959584	−	0.281422i	$-0.0908061\pi$
$727$	10.6614	+	14.6741i	0.395408	+	0.544232i	−0.564176	+	0.825655i	$0.690806\pi$
$728$	−0.560659	+	0.182169i	−0.0207794	+	0.00675164i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	−7.79170	+	22.7655i	−0.288384	+	0.842588i
$731$	15.1876	+	46.7427i	0.561735	+	1.72884i
$732$	11.3343	+	3.68275i	0.418929	+	0.136118i
$733$	−23.4368	+	32.2580i	−0.865659	+	1.19148i	0.114531	+	0.993420i	$0.463464\pi$
$733$	−23.4368	+	32.2580i	−0.865659	+	1.19148i	−0.980190	+	0.198058i	$0.936536\pi$
$734$	3.25654	−	10.0226i	0.120201	−	0.369941i
$735$	−9.76985	−	3.34383i	−0.360366	−	0.123339i
$736$	3.61803	−	2.62866i	0.133363	−	0.0968935i
$737$	−4.87650	+	6.71193i	−0.179628	+	0.247237i
$738$			3.80795i			0.140173i
$739$	−9.92597			−0.365133			−0.182566	−	0.983194i	$-0.558440\pi$
$739$	−9.92597			−0.365133			−0.182566	+	0.983194i	$0.558440\pi$
$740$	0.0861299	−	5.51949i	0.00316620	−	0.202900i
$741$	−0.730621	−	2.24862i	−0.0268400	−	0.0826051i
$742$	−10.5035	−	3.41279i	−0.385595	−	0.125287i
$743$		−	33.4067i		−	1.22557i	−0.790248	−	0.612787i	$-0.790048\pi$
$743$		−	33.4067i		−	1.22557i	0.790248	−	0.612787i	$-0.209952\pi$
$744$	−2.87718	+	4.76674i	−0.105482	+	0.174757i
$745$	32.1688	−	22.6136i	1.17857	−	0.828499i
$746$	−8.39681	+	25.8427i	−0.307429	+	0.946169i
$747$	−6.10820	+	1.98467i	−0.223487	+	0.0726154i
$748$	2.76664	−	3.80795i	0.101158	−	0.139233i
$749$	−19.9126			−0.727592
$750$	−2.95357	−	10.7832i	−0.107849	−	0.393745i
$751$	−2.63263	−	1.91272i	−0.0960661	−	0.0697961i	0.538715	−	0.842488i	$-0.318910\pi$
$751$	−2.63263	−	1.91272i	−0.0960661	−	0.0697961i	−0.634781	+	0.772692i	$0.718910\pi$
$752$	5.74290	+	7.90443i	0.209422	+	0.288245i
$753$	−3.19765	−	4.40119i	−0.116529	−	0.160388i
$754$	−0.0865520	+	0.266380i	−0.00315204	+	0.00970097i
$755$	−13.8115	−	0.215525i	−0.502653	−	0.00784374i
$756$	0.476925	−	1.46782i	0.0173456	−	0.0533843i
$757$	33.9201	−	11.0213i	1.23285	−	0.400577i	0.381103	−	0.924533i	$-0.375544\pi$
$757$	33.9201	−	11.0213i	1.23285	−	0.400577i	0.851745	+	0.523956i	$0.175544\pi$
$758$	−19.1494	−	26.3569i	−0.695539	−	0.957327i
$759$	−1.27877	−	3.93565i	−0.0464165	−	0.142855i
$760$	8.30931	−	11.0694i	0.301410	−	0.401528i
$761$	3.74460	−	2.72061i	0.135742	−	0.0986222i	−0.517842	−	0.855476i	$-0.673265\pi$
$761$	3.74460	−	2.72061i	0.135742	−	0.0986222i	0.653584	+	0.756854i	$0.273265\pi$
$762$	−7.36953	+	2.39450i	−0.266970	+	0.0867437i
$763$	4.90902	+	1.59504i	0.177719	+	0.0577443i
$764$	−10.6215	−	7.71696i	−0.384272	−	0.279190i
$765$	−10.8711	+	3.34563i	−0.393045	+	0.120961i
$766$	−8.58021	+	6.23389i	−0.310016	+	0.225240i
$767$	−2.41248	−	3.32049i	−0.0871095	−	0.119896i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	34.1764			1.23243			0.616216	−	0.787577i	$-0.288665\pi$
$769$	34.1764			1.23243			0.616216	+	0.787577i	$0.288665\pi$
$770$	−2.61246	+	1.83647i	−0.0941465	+	0.0661819i
$771$	1.40377	+	1.01990i	0.0505555	+	0.0367307i
$772$	−10.0503	+	3.26553i	−0.361717	+	0.117529i
$773$	−12.7023	−	4.12723i	−0.456870	−	0.148446i	0.0715355	−	0.997438i	$-0.477210\pi$
$773$	−12.7023	−	4.12723i	−0.456870	−	0.148446i	−0.528406	+	0.848992i	$0.677210\pi$
$774$	−9.66205			−0.347295
$775$	−26.9024	−	7.15965i	−0.966363	−	0.257182i
$776$	−17.0155			−0.610821
$777$	3.62360	+	1.17738i	0.129996	+	0.0422383i
$778$	−33.1206	+	10.7615i	−1.18743	+	0.385820i
$779$	−19.0693	−	13.8546i	−0.683227	−	0.496394i
$780$	−0.698732	+	0.491186i	−0.0250186	+	0.0175873i
$781$	3.17213			0.113508
$782$	13.3712	−	18.4039i	0.478155	−	0.658124i
$783$	−0.431011	−	0.593236i	−0.0154031	−	0.0212005i
$784$	−3.73607	+	2.71441i	−0.133431	+	0.0969433i
$785$	−11.3682	+	3.49863i	−0.405750	+	0.124871i
$786$	1.33582	+	0.970527i	0.0476470	+	0.0346176i
$787$	13.9451	+	4.53105i	0.497091	+	0.161515i	0.546823	−	0.837248i	$-0.315837\pi$
$787$	13.9451	+	4.53105i	0.497091	+	0.161515i	−0.0497326	+	0.998763i	$0.515837\pi$
$788$	−11.0046	+	3.57561i	−0.392022	+	0.127376i
$789$	7.80496	−	5.67063i	0.277864	−	0.201880i
$790$	−8.32548	+	11.0909i	−0.296207	+	0.394597i
$791$	3.03586	+	9.34343i	0.107943	+	0.332214i
$792$	0.543894	+	0.748606i	0.0193264	+	0.0266006i
$793$	4.32933	−	1.40668i	0.153739	−	0.0499528i
$794$	5.07436	−	15.6173i	0.180082	−	0.554236i
$795$	−15.9990	−	0.249659i	−0.567424	−	0.00885449i
$796$	−4.44983	+	13.6952i	−0.157720	+	0.485412i
$797$	12.6221	+	17.3728i	0.447098	+	0.615377i	0.971771	−	0.235926i	$-0.0758124\pi$
$797$	12.6221	+	17.3728i	0.447098	+	0.615377i	−0.524673	+	0.851304i	$0.675812\pi$
$798$	5.61528	+	7.72877i	0.198779	+	0.273595i
$799$	40.2076	+	29.2126i	1.42244	+	1.03347i
$800$	−4.70476	−	1.69271i	−0.166338	−	0.0598462i
$801$	7.65861			0.270604
$802$	−20.0141	+	27.5470i	−0.706721	+	0.972718i
$803$	9.46995	−	3.07697i	0.334187	−	0.108584i
$804$	2.77062	−	8.52708i	0.0977121	−	0.300727i
$805$	−12.6261	+	8.87573i	−0.445011	+	0.312828i
$806$	0.181104	+	2.11897i	0.00637913	+	0.0746376i
$807$		−	28.5473i		−	1.00491i
$808$	−8.06894	−	2.62176i	−0.283864	−	0.0922331i
$809$	8.78617	+	27.0411i	0.308905	+	0.950713i	0.978191	+	0.207708i	$0.0666003\pi$
$809$	8.78617	+	27.0411i	0.308905	+	0.950713i	−0.669286	+	0.743005i	$0.733400\pi$
$810$	0.0348889	−	2.23580i	0.00122587	−	0.0785579i
$811$	−44.8166			−1.57372			−0.786861	−	0.617130i	$-0.788295\pi$
$811$	−44.8166			−1.57372			−0.786861	+	0.617130i	$0.788295\pi$
$812$		−	1.13172i		−	0.0397155i
$813$	−7.02630	+	9.67087i	−0.246423	+	0.339172i
$814$	−1.84808	+	1.34271i	−0.0647750	+	0.0470618i
$815$	14.9459	+	5.11539i	0.523533	+	0.179184i
$816$	−1.57188	+	4.83776i	−0.0550270	+	0.169356i
$817$	35.1539	−	48.3851i	1.22988	−	1.69278i
$818$	4.28678	+	1.39286i	0.149884	+	0.0487002i
$819$	−0.182169	−	0.560659i	−0.00636551	−	0.0195910i
$820$	−2.75726	+	8.05605i	−0.0962878	+	0.281330i
$821$	−4.06662	−	12.5158i	−0.141926	−	0.436804i	0.854677	−	0.519160i	$-0.173755\pi$
$821$	−4.06662	−	12.5158i	−0.141926	−	0.436804i	−0.996603	+	0.0823568i	$0.973755\pi$
$822$	−5.00980	+	1.62778i	−0.174737	+	0.0567755i
$823$	4.01297	+	5.52338i	0.139883	+	0.192533i	0.873211	−	0.487343i	$-0.162034\pi$
$823$	4.01297	+	5.52338i	0.139883	+	0.192533i	−0.733327	+	0.679876i	$0.762034\pi$
$824$	−0.00823521	−	0.0253454i	−0.000286887	−	0.000882948i
$825$	−2.83494	+	3.65636i	−0.0986998	+	0.127298i
$826$	13.4167	+	9.74779i	0.466826	+	0.339169i
$827$	2.27126	+	0.737977i	0.0789794	+	0.0256620i	0.348240	−	0.937405i	$-0.386779\pi$
$827$	2.27126	+	0.737977i	0.0789794	+	0.0256620i	−0.269261	+	0.963067i	$0.586779\pi$
$828$	2.62866	+	3.61803i	0.0913521	+	0.125735i
$829$	−19.0300	+	13.8261i	−0.660939	+	0.480200i	−0.866980	−	0.498343i	$-0.833942\pi$
$829$	−19.0300	+	13.8261i	−0.660939	+	0.480200i	0.206041	+	0.978543i	$0.433942\pi$
$830$	−14.3595	−	0.224075i	−0.498425	−	0.00777777i
$831$	−26.2044			−0.909022
$832$			0.381966i			0.0132423i
$833$	−13.8075	+	19.0043i	−0.478400	+	0.658462i
$834$	−3.79972	−	11.6943i	−0.131573	−	0.404941i
$835$	−16.1446	+	4.96857i	−0.558706	+	0.171944i
$836$	−5.72770			−0.198097
$837$	−4.76674	−	2.87718i	−0.164763	−	0.0994498i
$838$			2.12984i			0.0735742i
$839$	−15.0374	+	46.2804i	−0.519149	+	1.59778i	0.256455	+	0.966556i	$0.417445\pi$
$839$	−15.0374	+	46.2804i	−0.519149	+	1.59778i	−0.775604	+	0.631220i	$0.782555\pi$
$840$	2.07180	−	2.75998i	0.0714839	−	0.0952283i
$841$	23.0265	+	16.7297i	0.794017	+	0.576887i
$842$			2.87543i			0.0990940i
$843$			4.24254i			0.146121i
$844$	17.6470	+	12.8213i	0.607434	+	0.441326i
$845$	9.30740	−	27.1940i	0.320184	−	0.935501i
$846$	−7.90443	+	5.74290i	−0.271760	+	0.197445i
$847$	−14.8893	−	4.83782i	−0.511601	−	0.166229i
$848$	−4.20609	+	5.78918i	−0.144438	+	0.198801i
$849$	−6.38107	+	19.6389i	−0.218998	+	0.674006i
$850$	−25.4212	−	0.793575i	−0.871941	−	0.0272194i
$851$	−8.93180	+	6.48934i	−0.306178	+	0.222452i
$852$	−3.26033	+	1.05935i	−0.111697	+	0.0362926i
$853$	−14.1810	+	4.60770i	−0.485549	+	0.157764i	−0.541554	−	0.840666i	$-0.682164\pi$
$853$	−14.1810	+	4.60770i	−0.485549	+	0.157764i	0.0560047	+	0.998431i	$0.482164\pi$
$854$	−14.8804	+	10.8113i	−0.509197	+	0.369954i
$855$	11.0694	+	8.30931i	0.378564	+	0.284172i
$856$	−3.98698	+	12.2706i	−0.136272	+	0.419402i
$857$	−22.6554	+	31.1824i	−0.773892	+	1.06517i	0.222038	+	0.975038i	$0.428729\pi$
$857$	−22.6554	+	31.1824i	−0.773892	+	1.06517i	−0.995930	+	0.0901330i	$0.971271\pi$
$858$	0.336145	+	0.109220i	0.0114758	+	0.00372871i
$859$	5.40285	−	3.92540i	0.184343	−	0.133933i	−0.491787	−	0.870716i	$-0.663656\pi$
$859$	5.40285	−	3.92540i	0.184343	−	0.133933i	0.676130	+	0.736783i	$0.263656\pi$
$860$	−20.4409	−	6.99610i	−0.697029	−	0.238565i
$861$	−4.75463	−	3.45444i	−0.162037	−	0.117727i
$862$		−	16.0834i		−	0.547804i
$863$			18.9760i			0.645952i	0.946407	+	0.322976i	$0.104683\pi$
$863$			18.9760i			0.645952i	−0.946407	+	0.322976i	$0.895317\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	23.8449	−	31.7653i	0.810750	−	1.08005i
$866$	4.36398	−	13.4310i	0.148294	−	0.456402i
$867$			8.87476i			0.301403i
$868$	−3.34171	−	7.91669i	−0.113425	−	0.268710i
$869$	5.73886			0.194677
$870$	−0.482291	−	1.56713i	−0.0163512	−	0.0531306i
$871$	−1.05828	−	3.25705i	−0.0358585	−	0.110361i
$872$	1.96580	−	2.70569i	0.0665704	−	0.0916264i
$873$		−	17.0155i		−	0.575887i
$874$	−27.6822			−0.936363
$875$	16.1433	+	6.09426i	0.545743	+	0.206023i
$876$	−8.70569	+	6.32506i	−0.294138	+	0.213704i
$877$	0.613333	+	0.844180i	0.0207108	+	0.0285059i	0.819247	−	0.573441i	$-0.194392\pi$
$877$	0.613333	+	0.844180i	0.0207108	+	0.0285059i	−0.798536	+	0.601947i	$0.794392\pi$
$878$	21.0231	+	6.83082i	0.709495	+	0.230529i
$879$	2.41049	+	1.75132i	0.0813037	+	0.0590706i
$880$	0.608604	+	1.97756i	0.0205161	+	0.0666637i
$881$	3.79564	+	11.6818i	0.127878	+	0.393569i	0.994414	−	0.105545i	$-0.0336589\pi$
$881$	3.79564	+	11.6818i	0.127878	+	0.393569i	−0.866536	+	0.499114i	$0.833659\pi$
$882$	−2.71441	−	3.73607i	−0.0913990	−	0.125800i
$883$	−33.7122	+	10.9538i	−1.13451	+	0.368624i	−0.815287	−	0.579057i	$-0.803421\pi$
$883$	−33.7122	+	10.9538i	−1.13451	+	0.368624i	−0.319220	+	0.947681i	$0.603421\pi$
$884$	0.600406	+	1.84786i	0.0201938	+	0.0621503i
$885$	22.7327	+	7.78048i	0.764151	+	0.261538i
$886$	2.76897	+	8.52202i	0.0930255	+	0.286303i
$887$	−24.4107	−	7.93153i	−0.819632	−	0.266315i	−0.130960	−	0.991388i	$-0.541806\pi$
$887$	−24.4107	−	7.93153i	−0.819632	−	0.266315i	−0.688672	+	0.725073i	$0.741806\pi$
$888$	1.45106	−	1.99721i	0.0486944	−	0.0670220i
$889$	3.69559	−	11.3738i	0.123946	−	0.381467i
$890$	16.2025	+	5.54545i	0.543107	+	0.185884i
$891$	−0.748606	+	0.543894i	−0.0250792	+	0.0182211i
$892$	−13.7978	+	18.9910i	−0.461984	+	0.635866i
$893$		−	60.4780i		−	2.02382i
$894$	17.5853			0.588139
$895$	30.4103	+	0.474544i	1.01650	+	0.0158623i
$896$	−0.476925	−	1.46782i	−0.0159329	−	0.0490366i
$897$	1.62460	+	0.527864i	0.0542438	+	0.0176249i
$898$			1.09878i			0.0366666i
$899$	−3.97624	−	0.926391i	−0.132615	−	0.0308969i
$900$	1.69271	−	4.70476i	0.0564235	−	0.156825i
$901$	−11.2481	+	34.6182i	−0.374729	+	1.15330i
$902$	3.35115	−	1.08885i	0.111581	−	0.0362549i
$903$	8.76508	−	12.0641i	0.291684	−	0.401468i
$904$	6.36550			0.211713
$905$	37.3601	−	26.2630i	1.24189	−	0.873011i
$906$	−4.99766	−	3.63101i	−0.166036	−	0.120632i
$907$	−29.8795	−	41.1256i	−0.992133	−	1.36555i	−0.930030	−	0.367485i	$-0.880219\pi$
$907$	−29.8795	−	41.1256i	−0.992133	−	1.36555i	−0.0621039	−	0.998070i	$-0.519781\pi$
$908$	−3.88108	−	5.34184i	−0.128798	−	0.177275i
$909$	2.62176	−	8.06894i	0.0869582	−	0.267630i
$910$	0.0205674	−	1.31803i	0.000681804	−	0.0436922i
$911$	−15.0398	+	46.2876i	−0.498289	+	1.53358i	0.313477	+	0.949596i	$0.398506\pi$
$911$	−15.0398	+	46.2876i	−0.498289	+	1.53358i	−0.811767	+	0.583982i	$0.801494\pi$
$912$	5.88696	−	1.91279i	0.194937	−	0.0633388i
$913$	3.49318	+	4.80795i	0.115607	+	0.159120i
$914$	8.01763	+	24.6757i	0.265200	+	0.816200i
$915$	−15.9981	+	21.3122i	−0.528882	+	0.704558i
$916$	−10.3684	+	7.53306i	−0.342580	+	0.248899i
$917$	−2.42361	+	0.787479i	−0.0800347	+	0.0260049i
$918$	−4.83776	−	1.57188i	−0.159670	−	0.0518799i
$919$	4.09060	+	2.97199i	0.134936	+	0.0980370i	0.653206	−	0.757180i	$-0.273424\pi$
$919$	4.09060	+	2.97199i	0.134936	+	0.0980370i	−0.518270	+	0.855217i	$0.673424\pi$
$920$	2.94140	+	9.55762i	0.0969752	+	0.315105i
$921$	8.78791	−	6.38479i	0.289571	−	0.210386i
$922$	−8.30604	−	11.4323i	−0.273545	−	0.376502i
$923$	−0.769660	+	1.05935i	−0.0253337	+	0.0348688i
$924$	−1.42812			−0.0469816
$925$	11.6146	+	4.17877i	0.381885	+	0.137397i
$926$	−14.1496	−	10.2803i	−0.464986	−	0.337832i
$927$	0.0253454	−	0.00823521i	0.000832451	−	0.000270480i
$928$	−0.697391	−	0.226596i	−0.0228930	−	0.00743838i
$929$	−31.3342			−1.02804			−0.514021	−	0.857778i	$-0.671845\pi$
$929$	−31.3342			−1.02804			−0.514021	+	0.857778i	$0.671845\pi$
$930$	−8.00116	−	9.53842i	−0.262368	−	0.312777i
$931$	28.5853			0.936844
$932$	−4.72435	−	1.53503i	−0.154751	−	0.0502817i
$933$	−12.0457	+	3.91390i	−0.394360	+	0.128135i
$934$	−10.7085	−	7.78017i	−0.350392	−	0.254575i
$935$	6.05278	+	8.61033i	0.197947	+	0.281588i
$936$	−0.381966			−0.0124849
$937$	10.1198	−	13.9287i	0.330600	−	0.455032i	−0.611066	−	0.791579i	$-0.709259\pi$
$937$	10.1198	−	13.9287i	0.330600	−	0.455032i	0.941667	+	0.336547i	$0.109259\pi$
$938$	8.13356	+	11.1949i	0.265570	+	0.365526i
$939$	−24.3919	+	17.7217i	−0.795998	+	0.578326i
$940$	−20.8808	+	6.42617i	−0.681057	+	0.209599i
$941$	17.3656	+	12.6169i	0.566103	+	0.411298i	0.833688	−	0.552236i	$-0.186225\pi$
$941$	17.3656	+	12.6169i	0.566103	+	0.411298i	−0.267584	+	0.963534i	$0.586225\pi$
$942$	−5.05900	−	1.64377i	−0.164831	−	0.0535569i
$943$	16.1962	−	5.26246i	0.527420	−	0.171369i
$944$	8.69316	−	6.31595i	0.282938	−	0.205567i
$945$	2.75998	+	2.07180i	0.0897821	+	0.0673956i
$946$	2.76279	+	8.50299i	0.0898260	+	0.276456i
$947$	−32.3720	−	44.5562i	−1.05195	−	1.44788i	−0.887108	−	0.461562i	$-0.847289\pi$
$947$	−32.3720	−	44.5562i	−1.05195	−	1.44788i	−0.164840	−	0.986320i	$-0.552711\pi$
$948$	−5.89842	+	1.91651i	−0.191572	+	0.0622455i
$949$	−1.27014	+	3.90910i	−0.0412306	+	0.126895i
$950$	17.4016	+	25.5942i	0.564583	+	0.830384i
$951$	0.739028	−	2.27449i	0.0239646	−	0.0737555i
$952$	−4.61450	−	6.35131i	−0.149557	−	0.205847i
$953$	−14.1418	−	19.4645i	−0.458097	−	0.630516i	0.516016	−	0.856579i	$-0.327414\pi$
$953$	−14.1418	−	19.4645i	−0.458097	−	0.630516i	−0.974113	+	0.226063i	$0.927414\pi$
$954$	−5.78918	−	4.20609i	−0.187432	−	0.136177i
$955$	24.0167	−	16.8830i	0.777162	−	0.546320i
$956$	−8.37294			−0.270800
$957$	−0.398827	+	0.548938i	−0.0128922	+	0.0177446i
$958$	7.39580	−	2.40304i	0.238947	−	0.0776387i
$959$	2.51226	−	7.73194i	0.0811251	−	0.249677i
$960$	−1.28594	−	1.82930i	−0.0415036	−	0.0590405i
$961$	−30.5504	+	5.26059i	−0.985496	+	0.169696i
$962$		−	0.942956i		−	0.0304021i
$963$	−12.2706	−	3.98698i	−0.395416	−	0.128478i
$964$	−0.984502	−	3.02999i	−0.0317087	−	0.0975893i
$965$	0.368687	−	23.6267i	0.0118685	−	0.760570i
$966$	−6.90212			−0.222072
$967$			7.89109i			0.253760i	0.991918	+	0.126880i	$0.0404964\pi$
$967$			7.89109i			0.253760i	−0.991918	+	0.126880i	$0.959504\pi$
$968$	−5.96236	+	8.20648i	−0.191637	+	0.263766i
$969$	25.4730	−	18.5072i	0.818312	−	0.594538i
$970$	12.3206	−	35.9978i	0.395590	−	1.15582i
$971$	−16.0270	+	49.3261i	−0.514331	+	1.58295i	0.270164	+	0.962814i	$0.412922\pi$
$971$	−16.0270	+	49.3261i	−0.514331	+	1.58295i	−0.784495	+	0.620135i	$0.787078\pi$
$972$	0.587785	−	0.809017i	0.0188532	−	0.0259492i
$973$	18.0486	+	5.86434i	0.578611	+	0.188002i
$974$	−4.84684	−	14.9170i	−0.155303	−	0.477973i
$975$	−0.533209	−	1.83389i	−0.0170764	−	0.0587314i
$976$	3.68275	+	11.3343i	0.117882	+	0.362803i
$977$	25.8077	−	8.38542i	0.825661	−	0.268274i	0.134444	−	0.990921i	$-0.457075\pi$
$977$	25.8077	−	8.38542i	0.825661	−	0.268274i	0.691217	+	0.722648i	$0.257075\pi$
$978$	4.15251	+	5.71544i	0.132783	+	0.182760i
$979$	−2.18992	−	6.73987i	−0.0699901	−	0.215407i
$980$	−3.03736	−	9.86943i	−0.0970250	−	0.315267i
$981$	2.70569	+	1.96580i	0.0863862	+	0.0627632i
$982$	13.2862	+	4.31694i	0.423979	+	0.137759i
$983$	14.8440	+	20.4310i	0.473451	+	0.651649i	0.977230	−	0.212184i	$-0.0680575\pi$
$983$	14.8440	+	20.4310i	0.473451	+	0.651649i	−0.503779	+	0.863832i	$0.668057\pi$
$984$	−3.08070	+	2.23826i	−0.0982091	+	0.0713531i
$985$	0.403697	−	25.8702i	0.0128628	−	0.824293i
$986$	−3.72999			−0.118787
$987$		−	15.0793i		−	0.479979i
$988$	1.38972	−	1.91279i	0.0442130	−	0.0608540i
$989$	13.3526	+	41.0952i	0.424589	+	1.30675i
$990$	−1.97756	+	0.608604i	−0.0628511	+	0.0193427i
$991$	26.3625			0.837431			0.418716	−	0.908117i	$-0.362480\pi$
$991$	26.3625			0.837431			0.418716	+	0.908117i	$0.362480\pi$
$992$	−5.54754	+	0.474137i	−0.176135	+	0.0150539i
$993$		−	33.1456i		−	1.05184i
$994$	1.63495	−	5.03187i	0.0518576	−	0.159601i
$995$	−25.7513	−	19.3304i	−0.816370	−	0.612814i
$996$	−5.19594	−	3.77507i	−0.164640	−	0.119618i
$997$		−	11.0128i		−	0.348778i	−0.984677	−	0.174389i	$-0.944205\pi$
$997$		−	11.0128i		−	0.348778i	0.984677	−	0.174389i	$-0.0557950\pi$
$998$			40.6681i			1.28733i
$999$	1.99721	+	1.45106i	0.0631890	+	0.0459095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.b.349.1	✓	16
5.4	even	2	inner	930.2.z.b.349.3	yes	16
31.4	even	5	inner	930.2.z.b.469.3	yes	16
155.4	even	10	inner	930.2.z.b.469.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.b.349.1	✓	16	1.1	even	1	trivial
930.2.z.b.349.3	yes	16	5.4	even	2	inner
930.2.z.b.469.1	yes	16	155.4	even	10	inner
930.2.z.b.469.3	yes	16	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)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.82930 + 1.28594i) q^{5} -1.00000 q^{6} +(0.907165 - 1.24861i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.82930 + 1.28594i) q^{5} -1.00000 q^{6} +(0.907165 - 1.24861i) q^{7} +(-0.587785 - 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(2.13715 - 0.657718i) q^{10} +(-0.748606 - 0.543894i) q^{11} +(0.951057 + 0.309017i) q^{12} +(0.363271 - 0.118034i) q^{13} +(-1.24861 + 0.907165i) q^{14} +(-1.34239 + 1.78829i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.98990 + 4.11525i) q^{17} +(-0.951057 + 0.309017i) q^{18} +(1.91279 - 5.88696i) q^{19} +(-2.23580 - 0.0348889i) q^{20} +(0.476925 - 1.46782i) q^{21} +(0.543894 + 0.748606i) q^{22} +(2.62866 + 3.61803i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(1.69271 - 4.70476i) q^{25} -0.381966 q^{26} +(0.587785 - 0.809017i) q^{27} +(1.46782 - 0.476925i) q^{28} +(0.226596 - 0.697391i) q^{29} +(1.82930 - 1.28594i) q^{30} +(-0.474137 - 5.54754i) q^{31} -1.00000i q^{32} +(-0.880039 - 0.285942i) q^{33} +(-1.57188 - 4.83776i) q^{34} +(-0.0538462 + 3.45064i) q^{35} +1.00000 q^{36} +2.46869i q^{37} +(-3.63834 + 5.00775i) q^{38} +(0.309017 - 0.224514i) q^{39} +(2.11559 + 0.724080i) q^{40} +(1.17672 - 3.62158i) q^{41} +(-0.907165 + 1.24861i) q^{42} +(9.18916 + 2.98574i) q^{43} +(-0.285942 - 0.880039i) q^{44} +(-0.724080 + 2.11559i) q^{45} +(-1.38197 - 4.25325i) q^{46} +(9.29221 - 3.01922i) q^{47} +(0.587785 + 0.809017i) q^{48} +(1.42705 + 4.39201i) q^{49} +(-3.06371 + 3.95142i) q^{50} +(4.11525 + 2.98990i) q^{51} +(0.363271 + 0.118034i) q^{52} +(4.20609 + 5.78918i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(2.06884 + 0.0322837i) q^{55} -1.54336 q^{56} -6.18992i q^{57} +(-0.431011 + 0.593236i) q^{58} +(-3.32049 - 10.2194i) q^{59} +(-2.13715 + 0.657718i) q^{60} +11.9176 q^{61} +(-1.26335 + 5.42254i) q^{62} -1.54336i q^{63} +(-0.309017 + 0.951057i) q^{64} +(-0.512749 + 0.683066i) q^{65} +(0.748606 + 0.543894i) q^{66} -8.96590i q^{67} +5.08672i q^{68} +(3.61803 + 2.62866i) q^{69} +(1.11752 - 3.26512i) q^{70} +(-2.77340 + 2.01500i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-6.32506 + 8.70569i) q^{73} +(0.762867 - 2.34786i) q^{74} +(0.156009 - 4.99757i) q^{75} +(5.00775 - 3.63834i) q^{76} +(-1.35822 + 0.441312i) q^{77} +(-0.363271 + 0.118034i) q^{78} +(-5.01750 + 3.64543i) q^{79} +(-1.78829 - 1.34239i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-2.23826 + 3.08070i) q^{82} +(-6.10820 - 1.98467i) q^{83} +(1.24861 - 0.907165i) q^{84} +(-10.7614 - 3.68320i) q^{85} +(-7.81677 - 5.67921i) q^{86} -0.733280i q^{87} +0.925328i q^{88} +(6.19594 + 4.50162i) q^{89} +(1.34239 - 1.78829i) q^{90} +(0.182169 - 0.560659i) q^{91} +4.47214i q^{92} +(-2.16522 - 5.12951i) q^{93} -9.77041 q^{94} +(4.07122 + 13.2288i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(10.0015 - 13.7658i) q^{97} -4.61803i q^{98} -0.925328 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{15} - 4 q^{16} + 8 q^{19} - 2 q^{20} - 4 q^{24} + 16 q^{25} - 24 q^{26} + 36 q^{29} - 12 q^{30} + 40 q^{31} + 8 q^{34} + 14 q^{35} + 16 q^{36} - 4 q^{39} + 6 q^{40} + 32 q^{41} + 12 q^{44} - 2 q^{45} - 40 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{54} + 24 q^{55} - 4 q^{60} - 16 q^{61} + 4 q^{64} + 6 q^{65} - 8 q^{66} + 40 q^{69} + 18 q^{70} - 12 q^{71} - 12 q^{74} - 8 q^{75} + 32 q^{76} - 8 q^{79} - 8 q^{80} - 4 q^{81} - 40 q^{85} - 68 q^{86} + 20 q^{89} - 4 q^{90} - 56 q^{94} - 18 q^{95} + 4 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9 + 4 * q^10 + 8 * q^11 + 4 * q^15 - 4 * q^16 + 8 * q^19 - 2 * q^20 - 4 * q^24 + 16 * q^25 - 24 * q^26 + 36 * q^29 - 12 * q^30 + 40 * q^31 + 8 * q^34 + 14 * q^35 + 16 * q^36 - 4 * q^39 + 6 * q^40 + 32 * q^41 + 12 * q^44 - 2 * q^45 - 40 * q^46 - 4 * q^49 - 8 * q^50 + 8 * q^51 - 4 * q^54 + 24 * q^55 - 4 * q^60 - 16 * q^61 + 4 * q^64 + 6 * q^65 - 8 * q^66 + 40 * q^69 + 18 * q^70 - 12 * q^71 - 12 * q^74 - 8 * q^75 + 32 * q^76 - 8 * q^79 - 8 * q^80 - 4 * q^81 - 40 * q^85 - 68 * q^86 + 20 * q^89 - 4 * q^90 - 56 * q^94 - 18 * q^95 + 4 * q^96 - 8 * q^99

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