LMFDB - Embedded newform 930.2.z.b.469.3

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			469.3
Root			$1.36176 + 0.693851i$ of defining polynomial
Character	$\chi$	$=$	930.469
Dual form			930.2.z.b.349.3

$q$-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} +(-1.34239 + 1.78829i) 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} +(2.13715 - 0.657718i) 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} +(-0.724080 + 2.11559i) 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} +(3.26512 + 1.11752i) q^{35} +1.00000 q^{36} +2.46869i q^{37} +(3.63834 + 5.00775i) q^{38} +(0.309017 + 0.224514i) q^{39} +(-0.0348889 + 2.23580i) 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} +(-2.23580 - 0.0348889i) 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} +(0.156009 - 4.99757i) 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} +(0.670012 - 1.95761i) q^{55} -1.54336 q^{56} -6.18992i q^{57} +(0.431011 + 0.593236i) q^{58} +(-3.32049 + 10.2194i) q^{59} +(1.34239 - 1.78829i) q^{60} +11.9176 q^{61} +(1.26335 + 5.42254i) q^{62} -1.54336i q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.816318 - 0.251226i) q^{65} +(0.748606 - 0.543894i) q^{66} -8.96590i q^{67} +5.08672i q^{68} +(3.61803 - 2.62866i) q^{69} +(3.45064 + 0.0538462i) 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} +(-3.06371 + 3.95142i) 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} +(0.657718 + 2.13715i) 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} +(0.177470 - 11.3729i) q^{85} +(-7.81677 + 5.67921i) q^{86} -0.733280i q^{87} +0.925328i q^{88} +(6.19594 - 4.50162i) q^{89} +(-2.13715 + 0.657718i) q^{90} +(0.182169 + 0.560659i) q^{91} +4.47214i q^{92} +(2.16522 - 5.12951i) q^{93} -9.77041 q^{94} +(-11.0694 - 8.30931i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$

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	$-0.294210\pi$
$7$	−0.907165	−	1.24861i	−0.342876	−	0.471929i	−0.945279	+	0.326264i	$0.894210\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−1.34239	+	1.78829i	−0.424502	+	0.565507i
$11$	−0.748606	+	0.543894i	−0.225713	+	0.163990i	−0.694895	−	0.719112i	$-0.744549\pi$
$11$	−0.748606	+	0.543894i	−0.225713	+	0.163990i	0.469181	+	0.883102i	$0.344549\pi$
$12$	−0.951057	+	0.309017i	−0.274546	+	0.0892055i
$13$	−0.363271	−	0.118034i	−0.100753	−	0.0327367i	0.258207	−	0.966090i	$-0.416869\pi$
$13$	−0.363271	−	0.118034i	−0.100753	−	0.0327367i	−0.358960	+	0.933353i	$0.616869\pi$
$14$	−1.24861	−	0.907165i	−0.333704	−	0.242450i
$15$	2.13715	−	0.657718i	0.551810	−	0.169822i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.98990	+	4.11525i	−0.725158	+	0.998094i	0.274179	+	0.961679i	$0.411594\pi$
$17$	−2.98990	+	4.11525i	−0.725158	+	0.998094i	−0.999337	+	0.0364151i	$0.988406\pi$
$18$	0.951057	+	0.309017i	0.224166	+	0.0728360i
$19$	1.91279	+	5.88696i	0.438824	+	1.35056i	0.889117	+	0.457681i	$0.151320\pi$
$19$	1.91279	+	5.88696i	0.438824	+	1.35056i	−0.450293	+	0.892881i	$0.648680\pi$
$20$	−0.724080	+	2.11559i	−0.161909	+	0.473060i
$21$	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	$-0.954396\pi$
$23$	−2.62866	+	3.61803i	−0.548113	+	0.754412i	0.441642	+	0.897191i	$0.354396\pi$
$24$	−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	0.969889	−	0.243549i	$-0.0783116\pi$
$29$	0.226596	+	0.697391i	0.0420778	+	0.129502i	−0.927811	+	0.373051i	$0.878312\pi$
$30$	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
$35$	3.26512	+	1.11752i	0.551905	+	0.188895i
$36$	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
$40$	−0.0348889	+	2.23580i	−0.00551642	+	0.353510i
$41$	1.17672	+	3.62158i	0.183773	+	0.565595i	0.999925	−	0.0122419i	$-0.00389681\pi$
$41$	1.17672	+	3.62158i	0.183773	+	0.565595i	−0.816152	+	0.577837i	$0.803897\pi$
$42$	0.907165	+	1.24861i	0.139979	+	0.192664i
$43$	−9.18916	+	2.98574i	−1.40133	+	0.455321i	−0.909622	−	0.415437i	$-0.863629\pi$
$43$	−9.18916	+	2.98574i	−1.40133	+	0.455321i	−0.491712	+	0.870758i	$0.663629\pi$
$44$	−0.285942	+	0.880039i	−0.0431074	+	0.132671i
$45$	−2.23580	−	0.0348889i	−0.333293	−	0.00520093i
$46$	−1.38197	+	4.25325i	−0.203760	+	0.627108i
$47$	−9.29221	−	3.01922i	−1.35541	−	0.440399i	−0.460901	−	0.887452i	$-0.652474\pi$
$47$	−9.29221	−	3.01922i	−1.35541	−	0.440399i	−0.894508	+	0.447053i	$0.852474\pi$
$48$	−0.587785	+	0.809017i	−0.0848395	+	0.116772i
$49$	1.42705	−	4.39201i	0.203864	−	0.627430i
$50$	0.156009	−	4.99757i	0.0220630	−	0.706762i
$51$	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	$-0.963538\pi$
$53$	−4.20609	+	5.78918i	−0.577750	+	0.795205i	0.415696	+	0.909504i	$0.363538\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	0.670012	−	1.95761i	0.0903444	−	0.263964i
$56$	−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	0.463546	+	0.886073i	$0.346577\pi$
$59$	−3.32049	+	10.2194i	−0.432291	+	1.33045i	−0.895837	+	0.444382i	$0.853423\pi$
$60$	1.34239	−	1.78829i	0.173302	−	0.230867i
$61$	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
$65$	0.816318	−	0.251226i	0.101252	−	0.0311607i
$66$	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
$70$	3.45064	+	0.0538462i	0.412431	+	0.00643586i
$71$	−2.77340	−	2.01500i	−0.329143	−	0.239136i	0.410924	−	0.911670i	$-0.365206\pi$
$71$	−2.77340	−	2.01500i	−0.329143	−	0.239136i	−0.740067	+	0.672533i	$0.765206\pi$
$72$	0.951057	−	0.309017i	0.112083	−	0.0364180i
$73$	6.32506	+	8.70569i	0.740292	+	1.01892i	0.998602	+	0.0528623i	$0.0168344\pi$
$73$	6.32506	+	8.70569i	0.740292	+	1.01892i	−0.258310	+	0.966062i	$0.583166\pi$
$74$	0.762867	+	2.34786i	0.0886815	+	0.272934i
$75$	−3.06371	+	3.95142i	−0.353767	+	0.456270i
$76$	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	0.268595	−	0.963253i	$-0.413441\pi$
$79$	−5.01750	−	3.64543i	−0.564513	−	0.410143i	−0.833108	+	0.553111i	$0.813441\pi$
$80$	0.657718	+	2.13715i	0.0735351	+	0.238941i
$81$	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	$-0.485338\pi$
$83$	6.10820	−	1.98467i	0.670462	−	0.217846i	0.624415	+	0.781093i	$0.285338\pi$
$84$	1.24861	+	0.907165i	0.136234	+	0.0989799i
$85$	0.177470	−	11.3729i	0.0192494	−	1.23356i
$86$	−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	−0.208801	−	0.977958i	$-0.566956\pi$
$89$	6.19594	−	4.50162i	0.656769	−	0.477170i	0.865570	+	0.500788i	$0.166956\pi$
$90$	−2.13715	+	0.657718i	−0.225275	+	0.0693295i
$91$	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
$95$	−11.0694	−	8.30931i	−1.13569	−	0.852517i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	−10.0015	−	13.7658i	−1.01549	−	1.39771i	−0.915315	−	0.402739i	$-0.868058\pi$
$97$	−10.0015	−	13.7658i	−1.01549	−	1.39771i	−0.100179	−	0.994969i	$-0.531942\pi$
$98$		−	4.61803i		−	0.466492i
$99$	−0.925328			−0.0929990
$100$	−1.39596	−	4.80118i	−0.139596	−	0.480118i
$101$	6.86385	+	4.98688i	0.682979	+	0.496213i	0.874345	−	0.485306i	$-0.161292\pi$
$101$	6.86385	+	4.98688i	0.682979	+	0.496213i	−0.191366	+	0.981519i	$0.561292\pi$
$102$	2.98990	−	4.11525i	0.296044	−	0.407470i
$103$	−0.0253454	+	0.00823521i	−0.00249735	+	0.000811440i	−0.310265	−	0.950650i	$-0.600418\pi$
$103$	−0.0253454	+	0.00823521i	−0.00249735	+	0.000811440i	0.307768	+	0.951461i	$0.400418\pi$
$104$	−0.309017	+	0.224514i	−0.0303016	+	0.0220154i
$105$	−2.75998	−	2.07180i	−0.269346	−	0.202187i
$106$	−2.21127	+	6.80559i	−0.214778	+	0.661017i
$107$	7.58368	−	10.4380i	0.733142	−	1.00908i	−0.265842	−	0.964017i	$-0.585650\pi$
$107$	7.58368	−	10.4380i	0.733142	−	1.00908i	0.998984	−	0.0450666i	$-0.0143500\pi$
$108$	−0.951057	−	0.309017i	−0.0915155	−	0.0297352i
$109$	1.03348	−	3.18073i	0.0989897	−	0.304659i	−0.889283	−	0.457357i	$-0.848796\pi$
$109$	1.03348	−	3.18073i	0.0989897	−	0.304659i	0.988273	+	0.152698i	$0.0487962\pi$
$110$	0.0322837	−	2.06884i	0.00307813	−	0.197257i
$111$	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	$-0.103211\pi$
$113$	3.74154	+	5.14979i	0.351975	+	0.484452i	−0.595916	+	0.803047i	$0.703211\pi$
$114$	−1.91279	−	5.88696i	−0.179149	−	0.551365i
$115$	0.156028	−	9.99878i	0.0145497	−	0.932391i
$116$	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
$120$	0.724080	−	2.11559i	0.0660992	−	0.193126i
$121$	−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	$-0.511713\pi$
$127$	−7.36953	−	2.39450i	−0.653940	−	0.212478i	−0.617150	+	0.786845i	$0.711713\pi$
$128$	−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	−0.644610	−	0.764512i	$-0.722980\pi$
$131$	−1.33582	+	0.970527i	−0.116711	+	0.0847954i	0.527899	+	0.849307i	$0.322980\pi$
$132$	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
$135$	2.11559	+	0.724080i	0.182081	+	0.0623189i
$136$	1.57188	+	4.83776i	0.134788	+	0.414835i
$137$	−5.00980	−	1.62778i	−0.428016	−	0.139071i	0.0870836	−	0.996201i	$-0.472245\pi$
$137$	−5.00980	−	1.62778i	−0.428016	−	0.139071i	−0.515100	+	0.857130i	$0.672245\pi$
$138$	2.62866	−	3.61803i	0.223766	−	0.307988i
$139$	3.79972	−	11.6943i	0.322288	−	0.991900i	−0.650362	−	0.759624i	$-0.725383\pi$
$139$	3.79972	−	11.6943i	0.322288	−	0.991900i	0.972650	−	0.232276i	$-0.0746171\pi$
$140$	3.29840	−	1.01510i	0.278765	−	0.0857913i
$141$	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
$145$	−1.31132	−	0.984350i	−0.108899	−	0.0817458i
$146$	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	−0.365562	−	0.930787i	$-0.619123\pi$
$151$	4.99766	−	3.63101i	0.406704	−	0.295488i	0.772266	+	0.635299i	$0.219123\pi$
$152$	5.88696	+	1.91279i	0.477496	+	0.155148i
$153$	−4.83776	+	1.57188i	−0.391110	+	0.127079i
$154$	1.42812			0.115081
$155$	−6.26647	−	10.7578i	−0.503335	−	0.864091i
$156$	0.381966			0.0305818
$157$	−5.05900	+	1.64377i	−0.403752	+	0.131187i	−0.503851	−	0.863790i	$-0.668084\pi$
$157$	−5.05900	+	1.64377i	−0.403752	+	0.131187i	0.100099	+	0.994977i	$0.468084\pi$
$158$	−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	$-0.710768\pi$
$163$	4.15251	−	5.71544i	0.325250	−	0.447668i	0.940061	+	0.341006i	$0.110768\pi$
$164$	3.08070	+	2.23826i	0.240562	+	0.174779i
$165$	−1.24215	+	1.65475i	−0.0967016	+	0.128822i
$166$	5.19594	−	3.77507i	0.403283	−	0.293003i
$167$	−7.18452	+	2.33439i	−0.555955	+	0.180641i	−0.573500	−	0.819205i	$-0.694415\pi$
$167$	−7.18452	+	2.33439i	−0.555955	+	0.180641i	0.0175452	+	0.999846i	$0.494415\pi$
$168$	1.46782	+	0.476925i	0.113245	+	0.0367956i
$169$	−10.3992	−	7.55545i	−0.799937	−	0.581189i
$170$	−3.34563	−	10.8711i	−0.256598	−	0.833774i
$171$	−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	$-0.164037\pi$
$173$	16.8936	+	5.48906i	1.28439	+	0.417325i	0.414269	+	0.910155i	$0.364037\pi$
$174$	−0.226596	−	0.697391i	−0.0171782	−	0.0528691i
$175$	−7.40995	+	2.15447i	−0.560140	+	0.162863i
$176$	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	−0.917419	−	0.397923i	$-0.869731\pi$
$179$	−11.0039	+	7.99480i	−0.822470	+	0.597559i	0.0949491	+	0.995482i	$0.469731\pi$
$180$	−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
$190$	−13.0953	−	4.48200i	−0.950034	−	0.325158i
$191$	−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	$-0.0758099\pi$
$193$	6.21140	+	8.54926i	0.447106	+	0.615389i	−0.524666	+	0.851308i	$0.675810\pi$
$194$	−13.7658	−	10.0015i	−0.988329	−	0.718063i
$195$	−0.853998	−	0.0133264i	−0.0611561	−	0.000954322i
$196$	−1.42705	−	4.39201i	−0.101932	−	0.313715i
$197$	6.80121	+	9.36106i	0.484566	+	0.666948i	0.979374	−	0.202054i	$-0.0647617\pi$
$197$	6.80121	+	9.36106i	0.484566	+	0.666948i	−0.494808	+	0.869002i	$0.664762\pi$
$198$	−0.880039	+	0.285942i	−0.0625417	+	0.0203210i
$199$	4.44983	−	13.6952i	0.315440	−	0.970824i	−0.660133	−	0.751148i	$-0.729500\pi$
$199$	4.44983	−	13.6952i	0.315440	−	0.970824i	0.975573	−	0.219675i	$-0.0704998\pi$
$200$	−2.81128	−	4.13482i	−0.198788	−	0.292376i
$201$	−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
$205$	−6.80972	−	5.11177i	−0.475612	−	0.357022i
$206$	−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
$210$	−3.26512	−	1.11752i	−0.225314	−	0.0771161i
$211$	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
$215$	12.9703	−	17.2786i	0.884566	−	1.17839i
$216$	−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
$220$	−0.608604	−	1.97756i	−0.0410321	−	0.133327i
$221$	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
$225$	4.13482	−	2.81128i	0.275654	−	0.187419i
$226$	5.14979	+	3.74154i	0.342559	+	0.248884i
$227$	6.27971	−	2.04040i	0.416799	−	0.135426i	−0.0931074	−	0.995656i	$-0.529680\pi$
$227$	6.27971	−	2.04040i	0.416799	−	0.135426i	0.509907	+	0.860230i	$0.329680\pi$
$228$	−3.63834	−	5.00775i	−0.240955	−	0.331646i
$229$	−3.96036	−	12.1887i	−0.261708	−	0.805455i	−0.992434	−	0.122783i	$-0.960818\pi$
$229$	−3.96036	−	12.1887i	−0.261708	−	0.805455i	0.730725	−	0.682672i	$-0.239182\pi$
$230$	−2.94140	−	9.55762i	−0.193950	−	0.630211i
$231$	−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	$-0.347975\pi$
$233$	4.72435	+	1.53503i	0.309502	+	0.100563i	−0.150148	+	0.988664i	$0.547975\pi$
$234$	−0.309017	−	0.224514i	−0.0202011	−	0.0146769i
$235$	20.8808	−	6.42617i	1.36211	−	0.419197i
$236$	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	0.346741	−	0.937961i	$-0.387288\pi$
$239$	−6.77385	−	4.92149i	−0.438164	−	0.318345i	−0.784905	+	0.619616i	$0.787288\pi$
$240$	0.0348889	−	2.23580i	0.00225207	−	0.144320i
$241$	−2.57746	+	1.87263i	−0.166029	+	0.120627i	−0.667697	−	0.744433i	$-0.732720\pi$
$241$	−2.57746	+	1.87263i	−0.166029	+	0.120627i	0.501668	+	0.865060i	$0.332720\pi$
$242$			10.1438i			0.652066i
$243$		−	1.00000i		−	0.0641500i
$244$	9.64156	−	7.00500i	0.617238	−	0.448449i
$245$	3.03736	+	9.86943i	0.194050	+	0.630535i
$246$	−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
$250$	6.14119	+	9.34269i	0.388403	+	0.590883i
$251$	−1.68110	+	5.17391i	−0.106110	+	0.326574i	−0.989989	−	0.141141i	$-0.954923\pi$
$251$	−1.68110	+	5.17391i	−0.106110	+	0.326574i	0.883879	+	0.467715i	$0.154923\pi$
$252$	−0.907165	−	1.24861i	−0.0571460	−	0.0786548i
$253$		−	4.13819i		−	0.260166i
$254$	−7.74878			−0.486202
$255$	−3.68320	+	10.7614i	−0.230651	+	0.673905i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.01990	+	1.40377i	−0.0636194	+	0.0875646i	−0.839641	−	0.543142i	$-0.817235\pi$
$257$	−1.01990	+	1.40377i	−0.0636194	+	0.0875646i	0.776022	+	0.630706i	$0.217235\pi$
$258$	9.18916	−	2.98574i	0.572092	−	0.185884i
$259$	3.08242	−	2.23951i	0.191532	−	0.139156i
$260$	0.512749	−	0.683066i	0.0317993	−	0.0423619i
$261$	−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	$-0.496134\pi$
$263$	−9.17528	−	2.98123i	−0.565772	−	0.183830i	−0.577917	+	0.816096i	$0.696134\pi$
$264$	0.285942	−	0.880039i	0.0175985	−	0.0541627i
$265$	0.249659	−	15.9990i	0.0153364	−	0.982808i
$266$	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	0.737382	+	0.675476i	$0.236062\pi$
$269$	8.82160	+	27.1501i	0.537862	+	1.65537i	−0.199519	+	0.979894i	$0.563938\pi$
$270$	2.23580	+	0.0348889i	0.136066	+	0.00212327i
$271$	−9.67087	−	7.02630i	−0.587463	−	0.426817i	0.253944	−	0.967219i	$-0.418272\pi$
$271$	−9.67087	−	7.02630i	−0.587463	−	0.426817i	−0.841407	+	0.540402i	$0.818272\pi$
$272$	2.98990	+	4.11525i	0.181289	+	0.249523i
$273$		−	0.589512i		−	0.0356789i
$274$	−5.26762			−0.318229
$275$	1.29172	+	4.44266i	0.0778937	+	0.267903i
$276$	1.38197	−	4.25325i	0.0831846	−	0.256016i
$277$	24.9219	−	8.09762i	1.49741	−	0.486539i	0.558150	−	0.829740i	$-0.311511\pi$
$277$	24.9219	−	8.09762i	1.49741	−	0.486539i	0.939262	+	0.343201i	$0.111511\pi$
$278$		−	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	0.904307	−	0.426884i	$-0.140389\pi$
$281$	−1.31102	−	4.03490i	−0.0782088	−	0.240702i	−0.982515	+	0.186182i	$0.940389\pi$
$282$	9.29221	+	3.01922i	0.553343	+	0.179792i
$283$	12.1375	+	16.7059i	0.721501	+	0.993061i	0.999473	+	0.0324714i	$0.0103378\pi$
$283$	12.1375	+	16.7059i	0.721501	+	0.993061i	−0.277972	+	0.960589i	$0.589662\pi$
$284$	−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
$290$	−1.55132	−	0.530954i	−0.0910965	−	0.0311787i
$291$	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	$-0.827739\pi$
$293$	−1.75132	+	2.41049i	−0.102313	+	0.140822i	0.754790	+	0.655966i	$0.227739\pi$
$294$	−1.42705	+	4.39201i	−0.0832273	+	0.256147i
$295$	−7.06739	−	22.9644i	−0.411480	−	1.33704i
$296$	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
$300$	−0.156009	+	4.99757i	−0.00900718	+	0.288535i
$301$	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	$-0.500321\pi$
$307$	−10.3308	−	3.35668i	−0.589610	−	0.191576i	−0.588601	+	0.808424i	$0.700321\pi$
$308$	1.35822	−	0.441312i	0.0773917	−	0.0251461i
$309$	0.0266497			0.00151605
$310$	−9.28413	−	8.29488i	−0.527303	−	0.471117i
$311$	−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	$-0.0753355\pi$
$313$	28.6743	+	9.31686i	1.62077	+	0.526620i	0.648646	+	0.761090i	$0.275335\pi$
$314$	−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	$-0.221394\pi$
$317$	−1.40571	−	1.93480i	−0.0789528	−	0.108669i	−0.846667	+	0.532124i	$0.821394\pi$
$318$	4.20609	−	5.78918i	0.235866	−	0.324641i
$319$	−0.548938	−	0.398827i	−0.0307346	−	0.0223300i
$320$	1.78829	+	1.34239i	0.0999684	+	0.0750421i
$321$	−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
$325$	−1.17023	+	1.50931i	−0.0649128	+	0.0837213i
$326$	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
$330$	−0.670012	+	1.95761i	−0.0368829	+	0.107763i
$331$	10.2425	+	31.5233i	0.562981	+	1.73268i	0.673875	+	0.738845i	$0.264629\pi$
$331$	10.2425	+	31.5233i	0.562981	+	1.73268i	−0.110894	+	0.993832i	$0.535371\pi$
$332$	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	$-0.0805509\pi$
$337$	7.90961	+	10.8866i	0.430864	+	0.593034i	−0.537287	+	0.843399i	$0.680551\pi$
$338$	−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
$345$	−3.23819	+	9.46119i	−0.174338	+	0.509373i
$346$	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	0.838854	−	0.544357i	$-0.183226\pi$
$349$	10.8420	+	7.87718i	0.580360	+	0.421656i	−0.258494	+	0.966013i	$0.583226\pi$
$350$	−6.38152	+	4.33882i	−0.341106	+	0.231920i
$351$	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	$-0.588223\pi$
$353$	1.32198	−	0.429538i	0.0703621	−	0.0228620i	0.343987	+	0.938975i	$0.388223\pi$
$354$	3.32049	−	10.2194i	0.176482	−	0.543156i
$355$	7.66457	+	0.119603i	0.406793	+	0.00634788i
$356$	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	−0.453886	−	0.891060i	$-0.649963\pi$
$359$	8.28125	−	25.4871i	0.437067	−	1.34516i	0.890953	−	0.454095i	$-0.150037\pi$
$360$	−1.34239	+	1.78829i	−0.0707504	+	0.0942511i
$361$	−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
$365$	−22.7655	−	7.79170i	−1.19160	−	0.407836i
$366$	−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
$370$	−4.41473	−	3.31395i	−0.229511	−	0.172284i
$371$	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
$375$	0.523164	−	11.1681i	0.0270161	−	0.576718i
$376$	−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	0.355056	−	0.934845i	$-0.384462\pi$
$379$	26.3569	−	19.1494i	1.35386	−	0.983640i	0.998809	−	0.0487952i	$-0.0155382\pi$
$380$	−13.8394	−	0.215960i	−0.709946	−	0.0110785i
$381$	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	$-0.287342\pi$
$383$	−6.23389	−	8.58021i	−0.318537	−	0.438428i	−0.938020	+	0.346582i	$0.887342\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$	−3.05210	+	0.939297i	−0.155549	+	0.0478710i
$386$	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	0.990297	+	0.138968i	$0.0443786\pi$
$389$	28.1741	+	20.4697i	1.42848	+	1.03785i	0.438185	+	0.898885i	$0.355621\pi$
$390$	−0.816318	+	0.251226i	−0.0413359	+	0.0127213i
$391$	−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
$395$	13.8663	+	0.216380i	0.697691	+	0.0108873i
$396$	−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
$400$	−3.95142	−	3.06371i	−0.197571	−	0.153185i
$401$	10.5220	+	32.3834i	0.525444	+	1.61715i	0.763436	+	0.645884i	$0.223511\pi$
$401$	10.5220	+	32.3834i	0.525444	+	1.61715i	−0.237992	+	0.971267i	$0.576489\pi$
$402$			8.96590i			0.447179i
$403$	0.827039	−	1.95930i	0.0411977	−	0.0975996i
$404$	8.48419			0.422104
$405$	−1.78829	−	1.34239i	−0.0888608	−	0.0667041i
$406$	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	$0.535546\pi$
$410$	−8.05605	−	2.75726i	−0.397860	−	0.136172i
$411$	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
$415$	−8.62158	+	11.4854i	−0.423217	+	0.563794i
$416$	−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	−0.965845	−	0.259120i	$-0.916568\pi$
$419$	−0.658158	+	2.02560i	−0.0321531	+	0.0989571i	0.933692	+	0.358077i	$0.116568\pi$
$420$	−3.45064	−	0.0538462i	−0.168374	−	0.00262743i
$421$	−0.888558	+	2.73470i	−0.0433057	+	0.133281i	−0.970372	−	0.241617i	$-0.922322\pi$
$421$	−0.888558	+	2.73470i	−0.0433057	+	0.133281i	0.927066	+	0.374898i	$0.122322\pi$
$422$	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
$425$	14.3002	+	21.0327i	0.693662	+	1.02023i
$426$	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
$430$	6.99610	−	20.4409i	0.337382	−	0.985748i
$431$	4.97006	−	15.2963i	0.239399	−	0.736795i	−0.757108	−	0.653290i	$-0.773388\pi$
$431$	4.97006	−	15.2963i	0.239399	−	0.736795i	0.996507	−	0.0835053i	$-0.0266115\pi$
$432$	−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	$-0.731721\pi$
$443$	5.26690	−	7.24926i	0.250238	−	0.344423i	0.915595	+	0.402103i	$0.131721\pi$
$444$	−0.762867	−	2.34786i	−0.0362041	−	0.111425i
$445$	−5.54545	+	16.2025i	−0.262879	+	0.768070i
$446$	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	−0.958749	−	0.284255i	$-0.908254\pi$
$449$	−0.339540	+	1.04500i	−0.0160239	+	0.0493165i	0.942725	+	0.333571i	$0.108254\pi$
$450$	3.06371	−	3.95142i	0.144425	−	0.186272i
$451$	−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
$455$	−1.05422	−	0.791357i	−0.0494225	−	0.0370994i
$456$	−5.00775	−	3.63834i	−0.234509	−	0.170381i
$457$	15.2504	−	20.9904i	0.713385	−	0.981891i	−0.286332	−	0.958130i	$-0.592436\pi$
$457$	15.2504	−	20.9904i	0.713385	−	0.981891i	0.999718	−	0.0237602i	$-0.00756382\pi$
$458$	−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	−0.288820	−	0.957383i	$-0.593263\pi$
$461$	11.4323	−	8.30604i	0.532455	−	0.386851i	0.821275	+	0.570532i	$0.193263\pi$
$462$	−1.35822	−	0.441312i	−0.0631901	−	0.0205317i
$463$	−16.6339	+	5.40468i	−0.773043	+	0.251177i	−0.668867	−	0.743382i	$-0.733221\pi$
$463$	−16.6339	+	5.40468i	−0.773043	+	0.251177i	−0.104176	+	0.994559i	$0.533221\pi$
$464$	0.733280			0.0340417
$465$	2.63541	+	12.1678i	0.122214	+	0.564267i
$466$	4.96748			0.230114
$467$	−12.5886	+	4.09028i	−0.582530	+	0.189275i	−0.585434	−	0.810720i	$-0.699076\pi$
$467$	−12.5886	+	4.09028i	−0.582530	+	0.189275i	0.00290377	+	0.999996i	$0.499076\pi$
$468$	−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
$475$	30.9345	+	0.965683i	1.41937	+	0.0443086i
$476$	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	0.434708	−	0.900571i	$-0.356852\pi$
$479$	−6.29124	−	4.57085i	−0.287454	−	0.208848i	−0.722162	+	0.691724i	$0.756852\pi$
$480$	−0.657718	−	2.13715i	−0.0300206	−	0.0975471i
$481$	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
$485$	35.9978	+	12.3206i	1.63457	+	0.559449i
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	−9.21924	+	12.6892i	−0.417763	+	0.575002i	−0.965090	−	0.261917i	$-0.915645\pi$
$487$	−9.21924	+	12.6892i	−0.417763	+	0.575002i	0.547327	+	0.836919i	$0.315645\pi$
$488$	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	0.112445	+	0.993658i	$0.464132\pi$
$499$	−12.5671	+	38.6777i	−0.562582	+	1.73145i	−0.675028	+	0.737793i	$0.735868\pi$
$500$	8.72767	+	6.98769i	0.390313	+	0.312499i
$501$	7.55426			0.337499
$502$			5.44017i			0.242807i
$503$	−9.12070	−	12.5536i	−0.406672	−	0.559736i	0.555731	−	0.831362i	$-0.312438\pi$
$503$	−9.12070	−	12.5536i	−0.406672	−	0.559736i	−0.962403	+	0.271627i	$0.912438\pi$
$504$	−1.24861	−	0.907165i	−0.0556173	−	0.0404084i
$505$	−18.9689	−	0.296004i	−0.844105	−	0.0131720i
$506$	−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	−0.900770	−	0.434297i	$-0.856997\pi$
$509$	1.87802	−	5.77995i	0.0832418	−	0.256192i	0.984011	+	0.178105i	$0.0569968\pi$
$510$	−0.177470	+	11.3729i	−0.00785852	+	0.503599i
$511$	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
$515$	0.0357744	−	0.0476574i	0.00157641	−	0.00210004i
$516$	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
$520$	0.276574	−	0.808082i	0.0121286	−	0.0354368i
$521$	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	0.996914	+	0.0784962i	$0.0250119\pi$
$523$	17.4607	+	24.0327i	0.763505	+	1.05087i	−0.233409	+	0.972379i	$0.574988\pi$
$524$	−0.510236	+	1.57035i	−0.0222898	+	0.0686009i
$525$	7.71305	+	0.240778i	0.336625	+	0.0105084i
$526$	−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
$530$	−4.70651	−	15.2931i	−0.204438	−	0.664288i
$531$	−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
$535$	−0.450141	+	28.8465i	−0.0194613	+	1.24714i
$536$	−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
$540$	2.13715	−	0.657718i	0.0919683	−	0.0283037i
$541$	−5.19450	−	3.77402i	−0.223329	−	0.162258i	0.470495	−	0.882403i	$-0.344075\pi$
$541$	−5.19450	−	3.77402i	−0.223329	−	0.162258i	−0.693824	+	0.720145i	$0.744075\pi$
$542$	−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
$545$	2.19968	+	7.14753i	0.0942241	+	0.306167i
$546$	−0.182169	−	0.560659i	−0.00779612	−	0.0239940i
$547$	−5.52462	−	7.60398i	−0.236216	−	0.325123i	0.674409	−	0.738358i	$-0.264399\pi$
$547$	−5.52462	−	7.60398i	−0.236216	−	0.325123i	−0.910624	+	0.413236i	$0.864399\pi$
$548$	−5.00980	+	1.62778i	−0.214008	+	0.0695355i
$549$	9.64156	+	7.00500i	0.411492	+	0.298966i
$550$	2.60136	+	3.82606i	0.110922	+	0.163144i
$551$	−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
$555$	1.62370	+	5.27596i	0.0689223	+	0.223952i
$556$	−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
$560$	2.07180	−	2.75998i	0.0875495	−	0.116630i
$561$	−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
$565$	−13.4668	−	4.60913i	−0.566551	−	0.193908i
$566$	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	−0.604534	+	0.796579i	$0.706641\pi$
$569$	−36.9479	+	26.8442i	−1.54894	+	1.12537i	−0.944403	+	0.328790i	$0.893359\pi$
$570$	11.0694	+	8.30931i	0.463645	+	0.348039i
$571$	−1.57649	+	4.85193i	−0.0659739	+	0.203047i	−0.978609	−	0.205728i	$-0.934044\pi$
$571$	−1.57649	+	4.85193i	−0.0659739	+	0.203047i	0.912635	+	0.408775i	$0.134044\pi$
$572$	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
$575$	12.5724	+	18.4915i	0.524307	+	0.771147i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	14.6855	−	4.77162i	0.611367	−	0.198645i	0.0130636	−	0.999915i	$-0.495842\pi$
$577$	14.6855	−	4.77162i	0.611367	−	0.198645i	0.598304	+	0.801269i	$0.295842\pi$
$578$	−5.21645	−	7.17983i	−0.216976	−	0.298642i
$579$	−3.26553	−	10.0503i	−0.135711	−	0.417674i
$580$	−1.63946	−	0.0255833i	−0.0680751	−	0.00106229i
$581$	−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
$585$	0.808082	+	0.276574i	0.0334101	+	0.0114349i
$586$	−0.920725	+	2.83370i	−0.0380348	+	0.117059i
$587$	21.1340	−	6.86687i	0.872296	−	0.283426i	0.161541	−	0.986866i	$-0.448354\pi$
$587$	21.1340	−	6.86687i	0.872296	−	0.283426i	0.710755	+	0.703440i	$0.248354\pi$
$588$			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	$-0.146914\pi$
$593$	4.75218	+	6.54082i	0.195149	+	0.268599i	−0.700218	+	0.713929i	$0.746914\pi$
$594$	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	0.986749	+	0.162253i	$0.0518761\pi$
$599$	6.94640	+	21.3788i	0.283822	+	0.873515i	−0.702927	+	0.711262i	$0.748124\pi$
$600$	1.39596	+	4.80118i	0.0569898	+	0.196007i
$601$	9.91124	+	30.5037i	0.404288	+	1.24427i	0.921488	+	0.388406i	$0.126974\pi$
$601$	9.91124	+	30.5037i	0.404288	+	1.24427i	−0.517201	+	0.855864i	$0.673026\pi$
$602$	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
$605$	−6.67173	−	21.6787i	−0.271245	−	0.881366i
$606$	−6.86385	−	4.98688i	−0.278825	−	0.202578i
$607$	−14.8483	−	4.82449i	−0.602672	−	0.195820i	−0.00824040	−	0.999966i	$-0.502623\pi$
$607$	−14.8483	−	4.82449i	−0.602672	−	0.195820i	−0.594432	+	0.804146i	$0.702623\pi$
$608$	5.88696	−	1.91279i	0.238748	−	0.0775739i
$609$	−0.915578	+	0.665206i	−0.0371011	+	0.0269555i
$610$	−15.9981	+	21.3122i	−0.647746	+	0.862904i
$611$	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	0.961850	+	0.273578i	$0.0882073\pi$
$613$	22.8972	+	31.5153i	0.924810	+	1.27289i	−0.0370393	+	0.999314i	$0.511793\pi$
$614$	−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	$-0.532806\pi$
$617$	−19.1458	−	6.22085i	−0.770781	−	0.250442i	−0.667899	+	0.744252i	$0.732806\pi$
$618$	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	$0.503280\pi$
$620$	−11.3930	−	5.01994i	−0.457553	−	0.201606i
$621$	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
$630$	2.75998	+	2.07180i	0.109960	+	0.0825424i
$631$	−17.6615	+	12.8318i	−0.703094	+	0.510827i	−0.880938	−	0.473231i	$-0.843088\pi$
$631$	−17.6615	+	12.8318i	−0.703094	+	0.510827i	0.177845	+	0.984059i	$0.443088\pi$
$632$	−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
$635$	16.5603	−	5.09651i	0.657175	−	0.202249i
$636$	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
$640$	2.11559	+	0.724080i	0.0836259	+	0.0286218i
$641$	−13.7525	−	42.3258i	−0.543191	−	1.67177i	−0.725252	−	0.688483i	$-0.758277\pi$
$641$	−13.7525	−	42.3258i	−0.543191	−	1.67177i	0.182061	−	0.983287i	$-0.441723\pi$
$642$	−7.58368	+	10.4380i	−0.299304	+	0.411956i
$643$	−28.2974	+	38.9481i	−1.11594	+	1.53596i	−0.303582	+	0.952805i	$0.598183\pi$
$643$	−28.2974	+	38.9481i	−1.11594	+	1.53596i	−0.812360	+	0.583157i	$0.801817\pi$
$644$	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	$-0.0270296\pi$
$647$	15.4609	+	21.2801i	0.607830	+	0.836607i	−0.388567	+	0.921421i	$0.627030\pi$
$648$	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	$-0.520158\pi$
$653$	12.0645	−	3.92001i	0.472122	−	0.153402i	0.535408	+	0.844594i	$0.320158\pi$
$654$	−1.03348	+	3.18073i	−0.0404124	+	0.124377i
$655$	1.19557	−	3.49317i	0.0467149	−	0.136490i
$656$	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	0.998777	+	0.0494355i	$0.0157422\pi$
$659$	34.7696	+	25.2616i	1.35443	+	0.984053i	0.355655	+	0.934617i	$0.384258\pi$
$660$	−0.0322837	+	2.06884i	−0.00125664	+	0.0805297i
$661$	−14.7566	−	45.4161i	−0.573965	−	1.76648i	−0.639678	−	0.768643i	$-0.720932\pi$
$661$	−14.7566	−	45.4161i	−0.573965	−	1.76648i	0.0657136	−	0.997839i	$-0.479068\pi$
$662$	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
$665$	−0.333304	+	21.3592i	−0.0129250	+	0.828274i
$666$	−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
$670$	16.0336	+	12.0358i	0.619433	+	0.464982i
$671$	−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	$-0.739793\pi$
$673$	5.73399	−	7.89217i	0.221029	−	0.304221i	0.905103	+	0.425192i	$0.139793\pi$
$674$	10.8866	+	7.90961i	0.419338	+	0.304667i
$675$	−4.80118	+	1.39596i	−0.184797	+	0.0537305i
$676$	−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
$680$	−9.09654	−	6.82839i	−0.348836	−	0.261857i
$681$	−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
$685$	11.2577	−	3.46461i	0.430134	−	0.132376i
$686$	−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
$690$	−0.156028	+	9.99878i	−0.00593988	+	0.380647i
$691$	36.9659	+	26.8573i	1.40625	+	1.02170i	0.993854	+	0.110697i	$0.0353082\pi$
$691$	36.9659	+	26.8573i	1.40625	+	1.02170i	0.412397	+	0.911004i	$0.364692\pi$
$692$	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
$695$	8.08739	+	26.2787i	0.306772	+	0.996808i
$696$	−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
$700$	−4.72841	+	6.09846i	−0.178717	+	0.230500i
$701$	−6.65390	−	20.4786i	−0.251314	−	0.773466i	−0.994534	−	0.104418i	$-0.966702\pi$
$701$	−6.65390	−	20.4786i	−0.251314	−	0.773466i	0.743219	−	0.669048i	$-0.233298\pi$
$702$	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
$705$	−21.8446	−	0.340879i	−0.822717	−	0.0128382i
$706$	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	−0.376372	−	0.926469i	$-0.622829\pi$
$709$	10.3432	−	7.51477i	0.388447	−	0.282223i	0.764819	+	0.644246i	$0.222829\pi$
$710$	7.32640	−	2.25473i	0.274955	−	0.0846186i
$711$	−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
$715$	−0.474461	+	0.632060i	−0.0177438	+	0.0236377i
$716$	−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	$0.332326\pi$
$720$	−0.724080	+	2.11559i	−0.0269849	+	0.0788433i
$721$	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
$725$	3.66461	+	0.114398i	0.136100	+	0.00424865i
$726$	3.13460	−	9.64730i	0.116336	−	0.358045i
$727$	−10.6614	+	14.6741i	−0.395408	+	0.544232i	−0.959584	−	0.281422i	$-0.909194\pi$
$727$	−10.6614	+	14.6741i	−0.395408	+	0.544232i	0.564176	+	0.825655i	$0.309194\pi$
$728$	0.560659	+	0.182169i	0.0207794	+	0.00675164i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−24.0590	−	0.375434i	−0.890464	−	0.0138954i
$731$	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	0.980190	+	0.198058i	$0.0634635\pi$
$733$	23.4368	+	32.2580i	0.865659	+	1.19148i	−0.114531	+	0.993420i	$0.536536\pi$
$734$	3.25654	+	10.0226i	0.120201	+	0.369941i
$735$	0.161118	−	10.3250i	0.00594294	−	0.380843i
$736$	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	$0.558440\pi$
$740$	−5.22273	−	1.78753i	−0.191991	−	0.0657109i
$741$	−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	−0.634781	−	0.772692i	$-0.718910\pi$
$751$	−2.63263	+	1.91272i	−0.0960661	+	0.0697961i	0.538715	+	0.842488i	$0.318910\pi$
$752$	−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
$755$	−4.47297	+	13.0689i	−0.162788	+	0.475627i
$756$	0.476925	+	1.46782i	0.0173456	+	0.0533843i
$757$	−33.9201	−	11.0213i	−1.23285	−	0.400577i	−0.381103	−	0.924533i	$-0.624456\pi$
$757$	−33.9201	−	11.0213i	−1.23285	−	0.400577i	−0.851745	+	0.523956i	$0.824456\pi$
$758$	19.1494	−	26.3569i	0.695539	−	0.957327i
$759$	−1.27877	+	3.93565i	−0.0464165	+	0.142855i
$760$	−13.2288	+	4.07122i	−0.479858	+	0.147679i
$761$	3.74460	+	2.72061i	0.135742	+	0.0986222i	0.653584	−	0.756854i	$-0.273265\pi$
$761$	3.74460	+	2.72061i	0.135742	+	0.0986222i	−0.517842	+	0.855476i	$0.673265\pi$
$762$	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
$765$	6.82839	−	9.09654i	0.246881	−	0.328886i
$766$	−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	$-0.522790\pi$
$773$	12.7023	−	4.12723i	0.456870	−	0.148446i	0.528406	+	0.848992i	$0.322790\pi$
$774$	−9.66205			−0.347295
$775$	25.2973	+	11.6211i	0.908704	+	0.417441i
$776$	−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
$785$	7.14066	−	9.51253i	0.254861	−	0.339517i
$786$	1.33582	−	0.970527i	0.0476470	−	0.0346176i
$787$	−13.9451	+	4.53105i	−0.497091	+	0.161515i	−0.546823	−	0.837248i	$-0.684163\pi$
$787$	−13.9451	+	4.53105i	−0.497091	+	0.161515i	0.0497326	+	0.998763i	$0.484163\pi$
$788$	11.0046	+	3.57561i	0.392022	+	0.127376i
$789$	7.80496	+	5.67063i	0.277864	+	0.201880i
$790$	13.2545	−	4.07914i	0.471575	−	0.145129i
$791$	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
$795$	−5.18139	+	15.1388i	−0.183765	+	0.536916i
$796$	−4.44983	−	13.6952i	−0.157720	−	0.485412i
$797$	−12.6221	+	17.3728i	−0.447098	+	0.615377i	−0.971771	−	0.235926i	$-0.924188\pi$
$797$	−12.6221	+	17.3728i	−0.447098	+	0.615377i	0.524673	+	0.851304i	$0.324188\pi$
$798$	−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	−0.669286	−	0.743005i	$-0.733400\pi$
$809$	8.78617	−	27.0411i	0.308905	−	0.950713i	0.978191	−	0.207708i	$-0.0666003\pi$
$810$	−2.11559	−	0.724080i	−0.0743341	−	0.0254416i
$811$	−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
$815$	−0.246479	+	15.7952i	−0.00863378	+	0.553281i
$816$	−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
$820$	−8.51380	−	0.132855i	−0.297315	−	0.00463951i
$821$	−4.06662	+	12.5158i	−0.141926	+	0.436804i	−0.996603	−	0.0823568i	$-0.973755\pi$
$821$	−4.06662	+	12.5158i	−0.141926	+	0.436804i	0.854677	+	0.519160i	$0.173755\pi$
$822$	5.00980	+	1.62778i	0.174737	+	0.0567755i
$823$	−4.01297	+	5.52338i	−0.139883	+	0.192533i	−0.873211	−	0.487343i	$-0.837966\pi$
$823$	−4.01297	+	5.52338i	−0.139883	+	0.192533i	0.733327	+	0.679876i	$0.237966\pi$
$824$	−0.00823521	+	0.0253454i	−0.000286887	+	0.000882948i
$825$	0.144359	−	4.62439i	0.00502595	−	0.161000i
$826$	13.4167	−	9.74779i	0.466826	−	0.339169i
$827$	−2.27126	+	0.737977i	−0.0789794	+	0.0256620i	−0.348240	−	0.937405i	$-0.613221\pi$
$827$	−2.27126	+	0.737977i	−0.0789794	+	0.0256620i	0.269261	+	0.963067i	$0.413221\pi$
$828$	−2.62866	+	3.61803i	−0.0913521	+	0.125735i
$829$	−19.0300	−	13.8261i	−0.660939	−	0.480200i	0.206041	−	0.978543i	$-0.433942\pi$
$829$	−19.0300	−	13.8261i	−0.660939	−	0.480200i	−0.866980	+	0.498343i	$0.833942\pi$
$830$	−4.65043	+	13.5874i	−0.161419	+	0.471627i
$831$	−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
$835$	10.1408	−	13.5092i	0.350936	−	0.467505i
$836$	−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	−0.775604	−	0.631220i	$-0.782555\pi$
$839$	−15.0374	−	46.2804i	−0.519149	−	1.59778i	0.256455	−	0.966556i	$-0.417445\pi$
$840$	−3.29840	+	1.01510i	−0.113805	+	0.0350241i
$841$	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
$845$	28.7391	+	0.448466i	0.988657	+	0.0154277i
$846$	−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
$850$	20.0998	+	15.5842i	0.689416	+	0.534535i
$851$	−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	$-0.317836\pi$
$853$	14.1810	+	4.60770i	0.485549	+	0.157764i	−0.0560047	+	0.998431i	$0.517836\pi$
$854$	−14.8804	−	10.8113i	−0.509197	−	0.369954i
$855$	−4.07122	−	13.2288i	−0.139233	−	0.452415i
$856$	−3.98698	−	12.2706i	−0.136272	−	0.419402i
$857$	22.6554	+	31.1824i	0.773892	+	1.06517i	0.995930	+	0.0901330i	$0.0287292\pi$
$857$	22.6554	+	31.1824i	0.773892	+	1.06517i	−0.222038	+	0.975038i	$0.571271\pi$
$858$	−0.336145	+	0.109220i	−0.0114758	+	0.00372871i
$859$	5.40285	+	3.92540i	0.184343	+	0.133933i	0.676130	−	0.736783i	$-0.263656\pi$
$859$	5.40285	+	3.92540i	0.184343	+	0.133933i	−0.491787	+	0.870716i	$0.663656\pi$
$860$	0.337099	−	21.6024i	0.0114950	−	0.736635i
$861$	−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
$865$	−37.9621	+	11.6830i	−1.29075	+	0.397234i
$866$	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
$870$	1.31132	+	0.984350i	0.0444578	+	0.0333726i
$871$	−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
$875$	10.7845	−	13.4700i	0.364584	−	0.455367i
$876$	−8.70569	−	6.32506i	−0.294138	−	0.213704i
$877$	−0.613333	+	0.844180i	−0.0207108	+	0.0285059i	−0.819247	−	0.573441i	$-0.805608\pi$
$877$	−0.613333	+	0.844180i	−0.0207108	+	0.0285059i	0.798536	+	0.601947i	$0.205608\pi$
$878$	−21.0231	+	6.83082i	−0.709495	+	0.230529i
$879$	2.41049	−	1.75132i	0.0813037	−	0.0590706i
$880$	−1.65475	−	1.24215i	−0.0557818	−	0.0418730i
$881$	3.79564	−	11.6818i	0.127878	−	0.393569i	−0.866536	−	0.499114i	$-0.833659\pi$
$881$	3.79564	−	11.6818i	0.127878	−	0.393569i	0.994414	+	0.105545i	$0.0336589\pi$
$882$	2.71441	−	3.73607i	0.0913990	−	0.125800i
$883$	33.7122	+	10.9538i	1.13451	+	0.368624i	0.815287	−	0.579057i	$-0.196579\pi$
$883$	33.7122	+	10.9538i	1.13451	+	0.368624i	0.319220	+	0.947681i	$0.396579\pi$
$884$	0.600406	−	1.84786i	0.0201938	−	0.0621503i
$885$	−0.374893	+	24.0244i	−0.0126019	+	0.807570i
$886$	2.76897	−	8.52202i	0.0930255	−	0.286303i
$887$	24.4107	−	7.93153i	0.819632	−	0.266315i	0.130960	−	0.991388i	$-0.458194\pi$
$887$	24.4107	−	7.93153i	0.819632	−	0.266315i	0.688672	+	0.725073i	$0.258194\pi$
$888$	−1.45106	−	1.99721i	−0.0486944	−	0.0670220i
$889$	3.69559	+	11.3738i	0.123946	+	0.381467i
$890$	−0.267201	+	17.1231i	−0.00895658	+	0.573967i
$891$	−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
$895$	9.84862	−	28.7753i	0.329203	−	0.961852i
$896$	−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	0.0621039	−	0.998070i	$-0.480219\pi$
$907$	29.8795	−	41.1256i	0.992133	−	1.36555i	0.930030	−	0.367485i	$-0.119781\pi$
$908$	3.88108	−	5.34184i	0.128798	−	0.177275i
$909$	2.62176	+	8.06894i	0.0869582	+	0.267630i
$910$	−1.24716	−	0.426854i	−0.0413431	−	0.0141501i
$911$	−15.0398	−	46.2876i	−0.498289	−	1.53358i	−0.811767	−	0.583982i	$-0.801494\pi$
$911$	−15.0398	−	46.2876i	−0.498289	−	1.53358i	0.313477	−	0.949596i	$-0.398506\pi$
$912$	−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
$915$	25.4697	−	7.83843i	0.842004	−	0.259130i
$916$	−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	−0.518270	−	0.855217i	$-0.673424\pi$
$919$	4.09060	−	2.97199i	0.134936	−	0.0980370i	0.653206	+	0.757180i	$0.273424\pi$
$920$	−7.99747	−	6.00337i	−0.263669	−	0.197925i
$921$	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	$0.671845\pi$
$930$	6.26647	+	10.7578i	0.205486	+	0.352764i
$931$	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	$-0.290741\pi$
$937$	−10.1198	−	13.9287i	−0.330600	−	0.455032i	−0.941667	+	0.336547i	$0.890741\pi$
$938$	−8.13356	+	11.1949i	−0.265570	+	0.365526i
$939$	−24.3919	−	17.7217i	−0.795998	−	0.578326i
$940$	13.1157	−	17.4723i	0.427788	−	0.569884i
$941$	17.3656	−	12.6169i	0.566103	−	0.411298i	−0.267584	−	0.963534i	$-0.586225\pi$
$941$	17.3656	−	12.6169i	0.566103	−	0.411298i	0.833688	+	0.552236i	$0.186225\pi$
$942$	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
$945$	−1.01510	−	3.29840i	−0.0330211	−	0.107297i
$946$	2.76279	−	8.50299i	0.0898260	−	0.276456i
$947$	32.3720	−	44.5562i	1.05195	−	1.44788i	0.164840	−	0.986320i	$-0.447289\pi$
$947$	32.3720	−	44.5562i	1.05195	−	1.44788i	0.887108	−	0.461562i	$-0.152711\pi$
$948$	5.89842	+	1.91651i	0.191572	+	0.0622455i
$949$	−1.27014	−	3.90910i	−0.0412306	−	0.126895i
$950$	29.7189	−	8.64087i	0.964208	−	0.280347i
$951$	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	$-0.672586\pi$
$953$	14.1418	−	19.4645i	0.458097	−	0.630516i	0.974113	+	0.226063i	$0.0725855\pi$
$954$	−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
$965$	−22.3564	−	7.65169i	−0.719678	−	0.246317i
$966$	−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
$970$	38.0432	+	0.593652i	1.22149	+	0.0190610i
$971$	−16.0270	−	49.3261i	−0.514331	−	1.58295i	−0.784495	−	0.620135i	$-0.787078\pi$
$971$	−16.0270	−	49.3261i	−0.514331	−	1.58295i	0.270164	−	0.962814i	$-0.412922\pi$
$972$	−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
$975$	1.57936	−	1.07381i	0.0505800	−	0.0343896i
$976$	3.68275	−	11.3343i	0.117882	−	0.362803i
$977$	−25.8077	−	8.38542i	−0.825661	−	0.268274i	−0.134444	−	0.990921i	$-0.542925\pi$
$977$	−25.8077	−	8.38542i	−0.825661	−	0.268274i	−0.691217	+	0.722648i	$0.742925\pi$
$978$	−4.15251	+	5.71544i	−0.132783	+	0.182760i
$979$	−2.18992	+	6.73987i	−0.0699901	+	0.215407i
$980$	8.25838	+	6.19922i	0.263804	+	0.198027i
$981$	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	$-0.931943\pi$
$983$	−14.8440	+	20.4310i	−0.473451	+	0.651649i	0.503779	+	0.863832i	$0.331943\pi$
$984$	−3.08070	−	2.23826i	−0.0982091	−	0.0713531i
$985$	−24.4793	−	8.37827i	−0.779974	−	0.266954i
$986$	−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
$990$	1.24215	−	1.65475i	0.0394783	−	0.0525915i
$991$	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
$995$	9.47109	+	30.7748i	0.300254	+	0.975627i
$996$	−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.469.3	yes	16
5.4	even	2	inner	930.2.z.b.469.1	yes	16
31.8	even	5	inner	930.2.z.b.349.1	✓	16
155.39	even	10	inner	930.2.z.b.349.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.b.349.1	✓	16	31.8	even	5	inner
930.2.z.b.349.3	yes	16	155.39	even	10	inner
930.2.z.b.469.1	yes	16	5.4	even	2	inner
930.2.z.b.469.3	yes	16	1.1	even	1	trivial

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} +(-1.34239 + 1.78829i) 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} +(2.13715 - 0.657718i) 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} +(-0.724080 + 2.11559i) 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} +(3.26512 + 1.11752i) q^{35} +1.00000 q^{36} +2.46869i q^{37} +(3.63834 + 5.00775i) q^{38} +(0.309017 + 0.224514i) q^{39} +(-0.0348889 + 2.23580i) 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} +(-2.23580 - 0.0348889i) 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} +(0.156009 - 4.99757i) 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} +(0.670012 - 1.95761i) q^{55} -1.54336 q^{56} -6.18992i q^{57} +(0.431011 + 0.593236i) q^{58} +(-3.32049 + 10.2194i) q^{59} +(1.34239 - 1.78829i) q^{60} +11.9176 q^{61} +(1.26335 + 5.42254i) q^{62} -1.54336i q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.816318 - 0.251226i) q^{65} +(0.748606 - 0.543894i) q^{66} -8.96590i q^{67} +5.08672i q^{68} +(3.61803 - 2.62866i) q^{69} +(3.45064 + 0.0538462i) 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} +(-3.06371 + 3.95142i) 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} +(0.657718 + 2.13715i) 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} +(0.177470 - 11.3729i) q^{85} +(-7.81677 + 5.67921i) q^{86} -0.733280i q^{87} +0.925328i q^{88} +(6.19594 - 4.50162i) q^{89} +(-2.13715 + 0.657718i) q^{90} +(0.182169 + 0.560659i) q^{91} +4.47214i q^{92} +(2.16522 - 5.12951i) q^{93} -9.77041 q^{94} +(-11.0694 - 8.30931i) 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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