LMFDB - Embedded newform 930.2.z.d.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	930.109
Dual form			930.2.z.d.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.90693 + 1.16774i) q^{5} +1.00000 q^{6} +(0.507889 + 0.165023i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.90693 + 1.16774i) q^{5} +1.00000 q^{6} +(0.507889 + 0.165023i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(2.06559 + 0.856357i) q^{10} +(-1.80117 + 5.54343i) q^{11} +(-0.587785 - 0.809017i) q^{12} +(2.51984 - 3.46826i) q^{13} +(-0.165023 - 0.507889i) q^{14} +(0.176142 - 2.22912i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.85867 + 1.90360i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-2.96683 + 2.15553i) q^{19} +(-0.521315 - 2.17445i) q^{20} +(-0.432036 + 0.313892i) q^{21} +(5.54343 - 1.80117i) q^{22} +(5.75478 - 1.86984i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(2.27276 - 4.45360i) q^{25} -4.28701 q^{26} +(0.951057 + 0.309017i) q^{27} +(-0.313892 + 0.432036i) q^{28} +(5.74196 - 4.17178i) q^{29} +(-1.90693 + 1.16774i) q^{30} +(-5.04314 + 2.35939i) q^{31} +1.00000i q^{32} +(-3.42603 - 4.71552i) q^{33} +(4.98369 + 3.62086i) q^{34} +(-1.16121 + 0.278396i) q^{35} +1.00000 q^{36} -8.35251i q^{37} +(3.48772 + 1.13323i) q^{38} +(1.32476 + 4.07719i) q^{39} +(-1.45275 + 1.69986i) q^{40} +(-7.07462 + 5.14001i) q^{41} +(0.507889 + 0.165023i) q^{42} +(-6.45965 - 8.89095i) q^{43} +(-4.71552 - 3.42603i) q^{44} +(1.69986 + 1.45275i) q^{45} +(-4.89531 - 3.55665i) q^{46} +(-1.32241 + 1.82014i) q^{47} +(0.951057 - 0.309017i) q^{48} +(-5.43240 - 3.94687i) q^{49} +(-4.93893 + 0.779062i) q^{50} +(1.90360 - 5.85867i) q^{51} +(2.51984 + 3.46826i) q^{52} +(-2.11076 + 0.685828i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-3.03859 - 12.6742i) q^{55} +0.534026 q^{56} -3.66721i q^{57} +(-6.75008 - 2.19323i) q^{58} +(-0.622219 - 0.452069i) q^{59} +(2.06559 + 0.856357i) q^{60} -6.01014 q^{61} +(4.87307 + 2.69317i) q^{62} -0.534026i q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.755122 + 9.55626i) q^{65} +(-1.80117 + 5.54343i) q^{66} +2.67417i q^{67} -6.16017i q^{68} +(-1.86984 + 5.75478i) q^{69} +(0.907770 + 0.775803i) q^{70} +(-4.16751 - 12.8263i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(0.0284296 + 0.00923734i) q^{73} +(-6.75733 + 4.90948i) q^{74} +(2.26715 + 4.45646i) q^{75} +(-1.13323 - 3.48772i) q^{76} +(-1.82959 + 2.51821i) q^{77} +(2.51984 - 3.46826i) q^{78} +(-0.640695 - 1.97185i) q^{79} +(2.22912 + 0.176142i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(8.31672 + 2.70226i) q^{82} +(-0.00859472 - 0.0118296i) q^{83} +(-0.165023 - 0.507889i) q^{84} +(8.94916 - 10.4714i) q^{85} +(-3.39604 + 10.4519i) q^{86} +7.09745i q^{87} +5.82870i q^{88} +(-1.01110 + 3.11184i) q^{89} +(0.176142 - 2.22912i) q^{90} +(1.85214 - 1.34566i) q^{91} +6.05093i q^{92} +(1.05550 - 5.46680i) q^{93} +2.24981 q^{94} +(3.14044 - 7.57494i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-0.413510 - 0.134358i) q^{97} +6.71482i q^{98} +5.82870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$3$	−0.587785	+	0.809017i	−0.339358	+	0.467086i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−1.90693	+	1.16774i	−0.852805	+	0.522230i
$5$	−1.90693	+	1.16774i	−0.852805	+	0.522230i
$6$	1.00000			0.408248
$7$	0.507889	+	0.165023i	0.191964	+	0.0623728i	0.403421	−	0.915014i	$-0.367821\pi$
$7$	0.507889	+	0.165023i	0.191964	+	0.0623728i	−0.211457	+	0.977387i	$0.567821\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	2.06559	+	0.856357i	0.653196	+	0.270804i
$11$	−1.80117	+	5.54343i	−0.543073	+	1.67141i	0.182456	+	0.983214i	$0.441595\pi$
$11$	−1.80117	+	5.54343i	−0.543073	+	1.67141i	−0.725529	+	0.688192i	$0.758405\pi$
$12$	−0.587785	−	0.809017i	−0.169679	−	0.233543i
$13$	2.51984	−	3.46826i	0.698878	−	0.961923i	−0.301087	−	0.953597i	$-0.597350\pi$
$13$	2.51984	−	3.46826i	0.698878	−	0.961923i	0.999965	−	0.00832662i	$-0.00265047\pi$
$14$	−0.165023	−	0.507889i	−0.0441042	−	0.135739i
$15$	0.176142	−	2.22912i	0.0454796	−	0.575556i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.85867	+	1.90360i	−1.42094	+	0.461690i	−0.915900	−	0.401407i	$-0.868521\pi$
$17$	−5.85867	+	1.90360i	−1.42094	+	0.461690i	−0.505037	+	0.863098i	$0.668521\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	−2.96683	+	2.15553i	−0.680638	+	0.494513i	−0.873569	−	0.486700i	$-0.838201\pi$
$19$	−2.96683	+	2.15553i	−0.680638	+	0.494513i	0.192931	+	0.981212i	$0.438201\pi$
$20$	−0.521315	−	2.17445i	−0.116570	−	0.486222i
$21$	−0.432036	+	0.313892i	−0.0942779	+	0.0684969i
$22$	5.54343	−	1.80117i	1.18186	−	0.384010i
$23$	5.75478	−	1.86984i	1.19995	−	0.389889i	0.360210	−	0.932871i	$-0.382705\pi$
$23$	5.75478	−	1.86984i	1.19995	−	0.389889i	0.839744	+	0.542983i	$0.182705\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	2.27276	−	4.45360i	0.454552	−	0.890720i
$26$	−4.28701			−0.840752
$27$	0.951057	+	0.309017i	0.183031	+	0.0594703i
$28$	−0.313892	+	0.432036i	−0.0593201	+	0.0816471i
$29$	5.74196	−	4.17178i	1.06625	−	0.774680i	0.0910195	−	0.995849i	$-0.470987\pi$
$29$	5.74196	−	4.17178i	1.06625	−	0.774680i	0.975235	+	0.221170i	$0.0709874\pi$
$30$	−1.90693	+	1.16774i	−0.348156	+	0.213200i
$31$	−5.04314	+	2.35939i	−0.905775	+	0.423759i
$31$	−5.04314	+	2.35939i	−0.905775	+	0.423759i
$32$			1.00000i			0.176777i
$33$	−3.42603	−	4.71552i	−0.596394	−	0.820867i
$34$	4.98369	+	3.62086i	0.854695	+	0.620972i
$35$	−1.16121	+	0.278396i	−0.196281	+	0.0470574i
$36$	1.00000			0.166667
$37$		−	8.35251i		−	1.37314i	−0.727061	−	0.686572i	$-0.759114\pi$
$37$		−	8.35251i		−	1.37314i	0.727061	−	0.686572i	$-0.240886\pi$
$38$	3.48772	+	1.13323i	0.565783	+	0.183834i
$39$	1.32476	+	4.07719i	0.212131	+	0.652873i
$40$	−1.45275	+	1.69986i	−0.229699	+	0.268772i
$41$	−7.07462	+	5.14001i	−1.10487	+	0.802735i	−0.981848	−	0.189669i	$-0.939259\pi$
$41$	−7.07462	+	5.14001i	−1.10487	+	0.802735i	−0.123022	+	0.992404i	$0.539259\pi$
$42$	0.507889	+	0.165023i	0.0783689	+	0.0254636i
$43$	−6.45965	−	8.89095i	−0.985088	−	1.35586i	−0.934043	−	0.357161i	$-0.883745\pi$
$43$	−6.45965	−	8.89095i	−0.985088	−	1.35586i	−0.0510452	−	0.998696i	$-0.516255\pi$
$44$	−4.71552	−	3.42603i	−0.710891	−	0.516493i
$45$	1.69986	+	1.45275i	0.253400	+	0.216562i
$46$	−4.89531	−	3.55665i	−0.721773	−	0.524399i
$47$	−1.32241	+	1.82014i	−0.192893	+	0.265494i	−0.894498	−	0.447072i	$-0.852467\pi$
$47$	−1.32241	+	1.82014i	−0.192893	+	0.265494i	0.701605	+	0.712566i	$0.252467\pi$
$48$	0.951057	−	0.309017i	0.137273	−	0.0446028i
$49$	−5.43240	−	3.94687i	−0.776057	−	0.563839i
$50$	−4.93893	+	0.779062i	−0.698471	+	0.110176i
$51$	1.90360	−	5.85867i	0.266557	−	0.820378i
$52$	2.51984	+	3.46826i	0.349439	+	0.480962i
$53$	−2.11076	+	0.685828i	−0.289935	+	0.0942057i	−0.450374	−	0.892840i	$-0.648709\pi$
$53$	−2.11076	+	0.685828i	−0.289935	+	0.0942057i	0.160438	+	0.987046i	$0.448709\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	−3.03859	−	12.6742i	−0.409723	−	1.70899i
$56$	0.534026			0.0713622
$57$		−	3.66721i		−	0.485733i
$58$	−6.75008	−	2.19323i	−0.886329	−	0.287986i
$59$	−0.622219	−	0.452069i	−0.0810060	−	0.0588543i	0.546545	−	0.837430i	$-0.315943\pi$
$59$	−0.622219	−	0.452069i	−0.0810060	−	0.0588543i	−0.627551	+	0.778575i	$0.715943\pi$
$60$	2.06559	+	0.856357i	0.266666	+	0.110555i
$61$	−6.01014			−0.769520			−0.384760	−	0.923017i	$-0.625716\pi$
$61$	−6.01014			−0.769520			−0.384760	+	0.923017i	$0.625716\pi$
$62$	4.87307	+	2.69317i	0.618881	+	0.342033i
$63$		−	0.534026i		−	0.0672809i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−0.755122	+	9.55626i	−0.0936613	+	1.18531i
$66$	−1.80117	+	5.54343i	−0.221708	+	0.682349i
$67$			2.67417i			0.326702i	0.986568	+	0.163351i	$0.0522303\pi$
$67$			2.67417i			0.326702i	−0.986568	+	0.163351i	$0.947770\pi$
$68$		−	6.16017i		−	0.747031i
$69$	−1.86984	+	5.75478i	−0.225102	+	0.692794i
$70$	0.907770	+	0.775803i	0.108499	+	0.0927262i
$71$	−4.16751	−	12.8263i	−0.494593	−	1.52220i	−0.817590	−	0.575800i	$-0.804691\pi$
$71$	−4.16751	−	12.8263i	−0.494593	−	1.52220i	0.322998	−	0.946400i	$-0.395309\pi$
$72$	−0.587785	−	0.809017i	−0.0692712	−	0.0953436i
$73$	0.0284296	+	0.00923734i	0.00332743	+	0.00108115i	0.310680	−	0.950514i	$-0.399443\pi$
$73$	0.0284296	+	0.00923734i	0.00332743	+	0.00108115i	−0.307353	+	0.951596i	$0.599443\pi$
$74$	−6.75733	+	4.90948i	−0.785523	+	0.570716i
$75$	2.26715	+	4.45646i	0.261787	+	0.514588i
$76$	−1.13323	−	3.48772i	−0.129990	−	0.400069i
$77$	−1.82959	+	2.51821i	−0.208501	+	0.286976i
$78$	2.51984	−	3.46826i	0.285316	−	0.392704i
$79$	−0.640695	−	1.97185i	−0.0720838	−	0.221851i	0.908524	−	0.417833i	$-0.137210\pi$
$79$	−0.640695	−	1.97185i	−0.0720838	−	0.221851i	−0.980607	+	0.195982i	$0.937210\pi$
$80$	2.22912	+	0.176142i	0.249223	+	0.0196933i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	8.31672	+	2.70226i	0.918428	+	0.298415i
$83$	−0.00859472	−	0.0118296i	−0.000943393	−	0.00129847i	0.808545	−	0.588434i	$-0.200255\pi$
$83$	−0.00859472	−	0.0118296i	−0.000943393	−	0.00129847i	−0.809488	+	0.587136i	$0.800255\pi$
$84$	−0.165023	−	0.507889i	−0.0180055	−	0.0554152i
$85$	8.94916	−	10.4714i	0.970673	−	1.13579i
$86$	−3.39604	+	10.4519i	−0.366205	+	1.12706i
$87$			7.09745i			0.760927i
$88$			5.82870i			0.621342i
$89$	−1.01110	+	3.11184i	−0.107176	+	0.329854i	−0.990235	−	0.139408i	$-0.955480\pi$
$89$	−1.01110	+	3.11184i	−0.107176	+	0.329854i	0.883059	+	0.469262i	$0.155480\pi$
$90$	0.176142	−	2.22912i	0.0185670	−	0.234970i
$91$	1.85214	−	1.34566i	0.194157	−	0.141063i
$92$			6.05093i			0.630853i
$93$	1.05550	−	5.46680i	0.109450	−	0.566881i
$94$	2.24981			0.232050
$95$	3.14044	−	7.57494i	0.322202	−	0.777172i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	−0.413510	−	0.134358i	−0.0419856	−	0.0136420i	0.287949	−	0.957646i	$-0.407027\pi$
$97$	−0.413510	−	0.134358i	−0.0419856	−	0.0136420i	−0.329935	+	0.944004i	$0.607027\pi$
$98$			6.71482i			0.678299i
$99$	5.82870			0.585807
$100$	3.53331	+	3.53776i	0.353331	+	0.353776i
$101$	−5.98275	−	18.4130i	−0.595305	−	1.83216i	−0.553200	−	0.833048i	$-0.686593\pi$
$101$	−5.98275	−	18.4130i	−0.595305	−	1.83216i	−0.0421054	−	0.999113i	$-0.513407\pi$
$102$	−5.85867	+	1.90360i	−0.580095	+	0.188484i
$103$	3.75062	+	5.16228i	0.369559	+	0.508655i	0.952781	−	0.303658i	$-0.0982081\pi$
$103$	3.75062	+	5.16228i	0.369559	+	0.508655i	−0.583222	+	0.812313i	$0.698208\pi$
$104$	1.32476	−	4.07719i	0.129903	−	0.399801i
$105$	0.457316	−	1.10308i	0.0446295	−	0.107649i
$106$	1.79552	+	1.30452i	0.174396	+	0.126706i
$107$	−2.75216	+	0.894232i	−0.266062	+	0.0864486i	−0.439010	−	0.898482i	$-0.644671\pi$
$107$	−2.75216	+	0.894232i	−0.266062	+	0.0864486i	0.172948	+	0.984931i	$0.444671\pi$
$108$	−0.587785	+	0.809017i	−0.0565597	+	0.0778477i
$109$	16.7148	+	12.1440i	1.60099	+	1.16319i	0.885581	+	0.464484i	$0.153760\pi$
$109$	16.7148	+	12.1440i	1.60099	+	1.16319i	0.715411	+	0.698704i	$0.246240\pi$
$110$	−8.46762	+	9.90799i	−0.807356	+	0.944690i
$111$	6.75733	+	4.90948i	0.641377	+	0.465988i
$112$	−0.313892	−	0.432036i	−0.0296600	−	0.0408235i
$113$	−15.9225	−	5.17352i	−1.49786	−	0.486684i	−0.558466	−	0.829527i	$-0.688610\pi$
$113$	−15.9225	−	5.17352i	−1.49786	−	0.486684i	−0.939393	+	0.342843i	$0.888610\pi$
$114$	−2.96683	+	2.15553i	−0.277869	+	0.201884i
$115$	−8.79046	+	10.2857i	−0.819715	+	0.959151i
$116$	2.19323	+	6.75008i	0.203637	+	0.626729i
$117$	−4.07719	−	1.32476i	−0.376936	−	0.122474i
$118$			0.769105i			0.0708018i
$119$	−3.28969			−0.301565
$120$	−0.521315	−	2.17445i	−0.0475893	−	0.198499i
$121$	−18.5862	−	13.5036i	−1.68965	−	1.22760i
$122$	3.53267	+	4.86231i	0.319833	+	0.440212i
$123$		−	8.74471i		−	0.788484i
$124$	−0.685496	−	5.52540i	−0.0615594	−	0.496196i
$125$	0.866669	+	11.1467i	0.0775172	+	0.996991i
$126$	−0.432036	+	0.313892i	−0.0384888	+	0.0279638i
$127$	2.72033	−	3.74421i	0.241390	−	0.332245i	−0.671083	−	0.741383i	$-0.734170\pi$
$127$	2.72033	−	3.74421i	0.241390	−	0.332245i	0.912473	+	0.409138i	$0.134170\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	10.9898			0.967600
$130$	8.17502	−	5.00612i	0.716997	−	0.439066i
$131$	−1.16405	+	3.58256i	−0.101703	+	0.313010i	−0.988943	−	0.148299i	$-0.952620\pi$
$131$	−1.16405	+	3.58256i	−0.101703	+	0.313010i	0.887239	+	0.461309i	$0.152620\pi$
$132$	5.54343	−	1.80117i	0.482493	−	0.156772i
$133$	−1.86253	+	0.605173i	−0.161502	+	0.0524752i
$134$	2.16345	−	1.57184i	0.186894	−	0.135786i
$135$	−2.17445	+	0.521315i	−0.187147	+	0.0448676i
$136$	−4.98369	+	3.62086i	−0.427347	+	0.310486i
$137$	−8.31204	+	11.4405i	−0.710145	+	0.977431i	0.289649	+	0.957133i	$0.406462\pi$
$137$	−8.31204	+	11.4405i	−0.710145	+	0.977431i	−0.999794	+	0.0202982i	$0.993538\pi$
$138$	5.75478	−	1.86984i	0.489879	−	0.159171i
$139$	7.12795	+	5.17876i	0.604585	+	0.439256i	0.847503	−	0.530790i	$-0.178105\pi$
$139$	7.12795	+	5.17876i	0.604585	+	0.439256i	−0.242919	+	0.970047i	$0.578105\pi$
$140$	0.0940643	−	1.19041i	0.00794988	−	0.100608i
$141$	−0.695230	−	2.13970i	−0.0585489	−	0.180195i
$142$	−7.92708	+	10.9107i	−0.665226	+	0.915605i
$143$	14.6874	+	20.2155i	1.22822	+	1.69050i
$144$	−0.309017	+	0.951057i	−0.0257514	+	0.0792547i
$145$	−6.07795	+	14.6604i	−0.504746	+	1.21748i
$146$	−0.00923734	−	0.0284296i	−0.000764487	−	0.00235285i
$147$	6.38617	−	2.07499i	0.526722	−	0.171142i
$148$	7.94371	+	2.58107i	0.652969	+	0.212163i
$149$	5.44619			0.446169			0.223085	−	0.974799i	$-0.428387\pi$
$149$	5.44619			0.446169			0.223085	+	0.974799i	$0.428387\pi$
$150$	2.27276	−	4.45360i	0.185570	−	0.363635i
$151$	−5.58587	+	17.1915i	−0.454572	+	1.39903i	0.417065	+	0.908877i	$0.363059\pi$
$151$	−5.58587	+	17.1915i	−0.454572	+	1.39903i	−0.871637	+	0.490152i	$0.836941\pi$
$152$	−2.15553	+	2.96683i	−0.174837	+	0.240642i
$153$	3.62086	+	4.98369i	0.292729	+	0.402907i
$154$	3.11268			0.250827
$155$	6.86176	−	10.3883i	0.551150	−	0.834406i
$156$	−4.28701			−0.343235
$157$	7.97293	+	10.9738i	0.636309	+	0.875804i	0.998412	−	0.0563338i	$-0.0179411\pi$
$157$	7.97293	+	10.9738i	0.636309	+	0.875804i	−0.362103	+	0.932138i	$0.617941\pi$
$158$	−1.21867	+	1.67736i	−0.0969524	+	0.133444i
$159$	0.685828	−	2.11076i	0.0543897	−	0.167394i
$160$	−1.16774	−	1.90693i	−0.0923181	−	0.150756i
$161$	3.23135			0.254666
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	21.4518	−	6.97010i	1.68023	−	0.545941i	0.695276	−	0.718743i	$-0.255282\pi$
$163$	21.4518	−	6.97010i	1.68023	−	0.545941i	0.984957	+	0.172802i	$0.0552821\pi$
$164$	−2.70226	−	8.31672i	−0.211011	−	0.649426i
$165$	12.0397	+	4.99145i	0.937289	+	0.388584i
$166$	−0.00451851	+	0.0139065i	−0.000350705	+	0.00107936i
$167$	−7.53711	−	10.3739i	−0.583239	−	0.802760i	0.410807	−	0.911722i	$-0.365247\pi$
$167$	−7.53711	−	10.3739i	−0.583239	−	0.802760i	−0.994046	+	0.108963i	$0.965247\pi$
$168$	−0.313892	+	0.432036i	−0.0242173	+	0.0333323i
$169$	−1.66203	−	5.11521i	−0.127849	−	0.393478i
$170$	−13.7318	−	1.08506i	−1.05318	−	0.0832206i
$171$	2.96683	+	2.15553i	0.226879	+	0.164838i
$172$	10.4519	−	3.39604i	0.796953	−	0.258946i
$173$	5.04622	−	6.94553i	0.383657	−	0.528059i	−0.572892	−	0.819631i	$-0.694178\pi$
$173$	5.04622	−	6.94553i	0.383657	−	0.528059i	0.956549	+	0.291572i	$0.0941784\pi$
$174$	5.74196	−	4.17178i	0.435297	−	0.316262i
$175$	1.88925	−	1.88688i	0.142814	−	0.142634i
$176$	4.71552	−	3.42603i	0.355446	−	0.258246i
$177$	0.731462	−	0.237666i	0.0549801	−	0.0178641i
$178$	3.11184	−	1.01110i	0.233242	−	0.0757849i
$179$	−2.09342	+	6.44289i	−0.156470	+	0.481564i	−0.998307	−	0.0581675i	$-0.981474\pi$
$179$	−2.09342	+	6.44289i	−0.156470	+	0.481564i	0.841837	+	0.539732i	$0.181474\pi$
$180$	−1.90693	+	1.16774i	−0.142134	+	0.0870383i
$181$	2.73840			0.203544			0.101772	−	0.994808i	$-0.467549\pi$
$181$	2.73840			0.203544			0.101772	+	0.994808i	$0.467549\pi$
$182$	−2.17732	−	0.707455i	−0.161394	−	0.0524401i
$183$	3.53267	−	4.86231i	0.261143	−	0.359432i
$184$	4.89531	−	3.55665i	0.360887	−	0.262200i
$185$	9.75358	+	15.9277i	0.717097	+	1.17102i
$186$	−5.04314	+	2.35939i	−0.369781	+	0.172999i
$187$		−	35.9058i		−	2.62569i
$188$	−1.32241	−	1.82014i	−0.0964464	−	0.132747i
$189$	0.432036	+	0.313892i	0.0314260	+	0.0228323i
$190$	−7.97416	+	1.91177i	−0.578506	+	0.138694i
$191$	−4.08299			−0.295434			−0.147717	−	0.989030i	$-0.547193\pi$
$191$	−4.08299			−0.295434			−0.147717	+	0.989030i	$0.547193\pi$
$192$			1.00000i			0.0721688i
$193$	−24.4833	−	7.95512i	−1.76235	−	0.572622i	−0.764910	−	0.644138i	$-0.777216\pi$
$193$	−24.4833	−	7.95512i	−1.76235	−	0.572622i	−0.997439	+	0.0715156i	$0.977216\pi$
$194$	0.134358	+	0.413510i	0.00964632	+	0.0296883i
$195$	−7.28732	−	6.22793i	−0.521856	−	0.445992i
$196$	5.43240	−	3.94687i	0.388029	−	0.281919i
$197$	−0.340781	−	0.110727i	−0.0242797	−	0.00788894i	0.296852	−	0.954924i	$-0.404063\pi$
$197$	−0.340781	−	0.110727i	−0.0242797	−	0.00788894i	−0.321132	+	0.947035i	$0.604063\pi$
$198$	−3.42603	−	4.71552i	−0.243477	−	0.335117i
$199$	−9.74540	−	7.08045i	−0.690833	−	0.501920i	0.186101	−	0.982531i	$-0.440415\pi$
$199$	−9.74540	−	7.08045i	−0.690833	−	0.501920i	−0.876934	+	0.480611i	$0.840415\pi$
$200$	0.785282	−	4.93795i	0.0555279	−	0.349166i
$201$	−2.16345	−	1.57184i	−0.152598	−	0.110869i
$202$	−11.3799	+	15.6630i	−0.800684	+	1.10205i
$203$	3.60471	−	1.17124i	0.253001	−	0.0822051i
$204$	4.98369	+	3.62086i	0.348928	+	0.253511i
$205$	7.48859	−	18.0630i	0.523026	−	1.26157i
$206$	1.97182	−	6.06863i	0.137383	−	0.422821i
$207$	−3.55665	−	4.89531i	−0.247204	−	0.340247i
$208$	−4.07719	+	1.32476i	−0.282702	+	0.0918555i
$209$	−6.60526	−	20.3289i	−0.456895	−	1.40618i
$210$	−1.16121	+	0.278396i	−0.0801312	+	0.0192111i
$211$	26.1281			1.79874			0.899368	−	0.437193i	$-0.144027\pi$
$211$	26.1281			1.79874			0.899368	+	0.437193i	$0.144027\pi$
$212$		−	2.21938i		−	0.152428i
$213$	12.8263	+	4.16751i	0.878843	+	0.285553i
$214$	2.34113	+	1.70093i	0.160036	+	0.116273i
$215$	22.7004	+	9.41121i	1.54816	+	0.641839i
$216$	1.00000			0.0680414
$217$	−2.95071	+	0.366072i	−0.200307	+	0.0248506i
$218$		−	20.6607i		−	1.39932i
$219$	−0.0241837	+	0.0175705i	−0.00163418	+	0.00118730i
$220$	12.9929	+	1.02668i	0.875979	+	0.0692186i
$221$	−8.16074	+	25.1162i	−0.548951	+	1.68950i
$222$		−	8.35251i		−	0.560584i
$223$			10.5278i			0.704996i	0.935813	+	0.352498i	$0.114668\pi$
$223$			10.5278i			0.704996i	−0.935813	+	0.352498i	$0.885332\pi$
$224$	−0.165023	+	0.507889i	−0.0110261	+	0.0339347i
$225$	−4.93795	−	0.785282i	−0.329197	−	0.0523522i
$226$	5.17352	+	15.9225i	0.344137	+	1.05915i
$227$	−2.13442	−	2.93778i	−0.141667	−	0.194988i	0.732288	−	0.680995i	$-0.238453\pi$
$227$	−2.13442	−	2.93778i	−0.141667	−	0.194988i	−0.873954	+	0.486008i	$0.838453\pi$
$228$	3.48772	+	1.13323i	0.230980	+	0.0750499i
$229$	−6.26364	+	4.55080i	−0.413913	+	0.300726i	−0.775184	−	0.631735i	$-0.782343\pi$
$229$	−6.26364	+	4.55080i	−0.413913	+	0.300726i	0.361271	+	0.932461i	$0.382343\pi$
$230$	13.4882	+	1.06582i	0.889389	+	0.0702782i
$231$	−0.961870	−	2.96033i	−0.0632864	−	0.194775i
$232$	4.17178	−	5.74196i	0.273891	−	0.376978i
$233$	0.754045	−	1.03785i	0.0493991	−	0.0679921i	−0.783603	−	0.621262i	$-0.786620\pi$
$233$	0.754045	−	1.03785i	0.0493991	−	0.0679921i	0.833002	+	0.553270i	$0.186620\pi$
$234$	1.32476	+	4.07719i	0.0866022	+	0.266534i
$235$	0.396286	−	5.01510i	0.0258508	−	0.327149i
$236$	0.622219	−	0.452069i	0.0405030	−	0.0294272i
$237$	1.97185	+	0.640695i	0.128086	+	0.0416176i
$238$	1.93363	+	2.66142i	0.125339	+	0.172514i
$239$	−2.40186	−	7.39217i	−0.155364	−	0.478160i	0.842834	−	0.538174i	$-0.180886\pi$
$239$	−2.40186	−	7.39217i	−0.155364	−	0.478160i	−0.998198	+	0.0600138i	$0.980886\pi$
$240$	−1.45275	+	1.69986i	−0.0937743	+	0.109726i
$241$	0.479173	−	1.47474i	0.0308662	−	0.0949965i	−0.934437	−	0.356130i	$-0.884096\pi$
$241$	0.479173	−	1.47474i	0.0308662	−	0.0949965i	0.965303	+	0.261133i	$0.0840961\pi$
$242$			22.9738i			1.47681i
$243$		−	1.00000i		−	0.0641500i
$244$	1.85724	−	5.71598i	0.118897	−	0.365928i
$245$	14.9681	+	1.18276i	0.956279	+	0.0755638i
$246$	−7.07462	+	5.14001i	−0.451061	+	0.327715i
$247$			15.7214i			1.00033i
$248$	−4.06722	+	3.80233i	−0.258269	+	0.241448i
$249$	0.0146222			0.000926645
$250$	8.50845	−	7.25302i	0.538122	−	0.458721i
$251$	13.0441	+	9.47711i	0.823338	+	0.598190i	0.917667	−	0.397351i	$-0.130070\pi$
$251$	13.0441	+	9.47711i	0.823338	+	0.598190i	−0.0943286	+	0.995541i	$0.530070\pi$
$252$	0.507889	+	0.165023i	0.0319940	+	0.0103955i
$253$			35.2691i			2.21735i
$254$	−4.62810			−0.290393
$255$	3.21139	+	13.3950i	0.201105	+	0.838827i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	16.4064	−	5.33078i	1.02341	−	0.332525i	0.251226	−	0.967929i	$-0.419166\pi$
$257$	16.4064	−	5.33078i	1.02341	−	0.332525i	0.772180	+	0.635404i	$0.219166\pi$
$258$	−6.45965	−	8.89095i	−0.402160	−	0.553526i
$259$	1.37836	−	4.24215i	0.0856469	−	0.263594i
$260$	−8.85519	−	3.67121i	−0.549176	−	0.227679i
$261$	−5.74196	−	4.17178i	−0.355418	−	0.258227i
$262$	3.58256	−	1.16405i	0.221331	−	0.0719149i
$263$	−4.37308	+	6.01902i	−0.269655	+	0.371149i	−0.922273	−	0.386538i	$-0.873671\pi$
$263$	−4.37308	+	6.01902i	−0.269655	+	0.371149i	0.652618	+	0.757687i	$0.273671\pi$
$264$	−4.71552	−	3.42603i	−0.290220	−	0.210857i
$265$	3.22420	−	3.77265i	0.198061	−	0.231752i
$266$	1.58436	+	1.15111i	0.0971436	+	0.0705790i
$267$	−1.92322	−	2.64709i	−0.117699	−	0.161999i
$268$	−2.54329	−	0.826365i	−0.155356	−	0.0504782i
$269$	1.59346	−	1.15771i	0.0971547	−	0.0705870i	−0.538147	−	0.842851i	$-0.680876\pi$
$269$	1.59346	−	1.15771i	0.0971547	−	0.0705870i	0.635302	+	0.772264i	$0.280876\pi$
$270$	1.69986	+	1.45275i	0.103450	+	0.0884113i
$271$	9.15481	+	28.1756i	0.556115	+	1.71155i	0.692980	+	0.720957i	$0.256297\pi$
$271$	9.15481	+	28.1756i	0.556115	+	1.71155i	−0.136865	+	0.990590i	$0.543703\pi$
$272$	5.85867	+	1.90360i	0.355234	+	0.115423i
$273$			2.28937i			0.138559i
$274$	14.1413			0.854306
$275$	20.5946	+	20.6206i	1.24190	+	1.24347i
$276$	−4.89531	−	3.55665i	−0.294663	−	0.214085i
$277$	−16.5705	−	22.8074i	−0.995627	−	1.37036i	−0.927970	−	0.372654i	$-0.878448\pi$
$277$	−16.5705	−	22.8074i	−0.995627	−	1.37036i	−0.0676565	−	0.997709i	$-0.521552\pi$
$278$		−	8.81063i		−	0.528426i
$279$	3.80233	+	4.06722i	0.227639	+	0.243498i
$280$	−1.01835	+	0.623604i	−0.0608580	+	0.0372675i
$281$	−20.6971	+	15.0373i	−1.23469	+	0.897052i	−0.997232	−	0.0743472i	$-0.976313\pi$
$281$	−20.6971	+	15.0373i	−1.23469	+	0.897052i	−0.237453	+	0.971399i	$0.576313\pi$
$282$	−1.32241	+	1.82014i	−0.0787481	+	0.108388i
$283$	4.09614	+	1.33092i	0.243490	+	0.0791147i	0.428220	−	0.903675i	$-0.359141\pi$
$283$	4.09614	+	1.33092i	0.243490	+	0.0791147i	−0.184730	+	0.982789i	$0.559141\pi$
$284$	13.4864			0.800268
$285$	4.28235	+	6.99310i	0.253665	+	0.414236i
$286$	7.72163	−	23.7647i	0.456589	−	1.40524i
$287$	−4.44134	+	1.44308i	−0.262164	+	0.0851822i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	16.9471	−	12.3128i	0.996887	−	0.724281i
$290$	15.4330	−	3.70001i	0.906260	−	0.217272i
$291$	0.351753	−	0.255563i	0.0206201	−	0.0149814i
$292$	−0.0175705	+	0.0241837i	−0.00102823	+	0.00141524i
$293$	−25.4166	+	8.25836i	−1.48485	+	0.482458i	−0.935559	−	0.353170i	$-0.885104\pi$
$293$	−25.4166	+	8.25836i	−1.48485	+	0.482458i	−0.549295	+	0.835628i	$0.685104\pi$
$294$	−5.43240	−	3.94687i	−0.316824	−	0.230186i
$295$	1.71443	+	0.135472i	0.0998178	+	0.00788746i
$296$	−2.58107	−	7.94371i	−0.150022	−	0.461719i
$297$	−3.42603	+	4.71552i	−0.198798	+	0.273622i
$298$	−3.20119	−	4.40606i	−0.185440	−	0.255236i
$299$	8.01602	−	24.6708i	0.463579	−	1.42675i
$300$	−4.93893	+	0.779062i	−0.285149	+	0.0449792i
$301$	−1.81357	−	5.58160i	−0.104533	−	0.321718i
$302$	17.1915	−	5.58587i	0.989263	−	0.321431i
$303$	18.4130	+	5.98275i	1.05780	+	0.343700i
$304$	3.66721			0.210329
$305$	11.4609	−	7.01829i	0.656250	−	0.401866i
$306$	1.90360	−	5.85867i	0.108821	−	0.334918i
$307$	1.07392	−	1.47813i	0.0612921	−	0.0843613i	−0.777271	−	0.629166i	$-0.783396\pi$
$307$	1.07392	−	1.47813i	0.0612921	−	0.0843613i	0.838563	+	0.544805i	$0.183396\pi$
$308$	−1.82959	−	2.51821i	−0.104250	−	0.143488i
$309$	−6.38093			−0.362999
$310$	−12.4375	+	0.554798i	−0.706404	+	0.0315104i
$311$	−17.5010			−0.992393			−0.496197	−	0.868210i	$-0.665271\pi$
$311$	−17.5010			−0.992393			−0.496197	+	0.868210i	$0.665271\pi$
$312$	2.51984	+	3.46826i	0.142658	+	0.196352i
$313$	−11.4601	+	15.7734i	−0.647761	+	0.891567i	−0.999000	−	0.0447191i	$-0.985761\pi$
$313$	−11.4601	+	15.7734i	−0.647761	+	0.891567i	0.351238	+	0.936286i	$0.385761\pi$
$314$	4.19162	−	12.9005i	0.236547	−	0.728016i
$315$	0.623604	+	1.01835i	0.0351361	+	0.0573775i
$316$	2.07333			0.116634
$317$	−31.1014	−	10.1055i	−1.74683	−	0.567579i	−0.751123	−	0.660162i	$-0.770487\pi$
$317$	−31.1014	−	10.1055i	−1.74683	−	0.567579i	−0.995705	+	0.0925837i	$0.970487\pi$
$318$	−2.11076	+	0.685828i	−0.118366	+	0.0384593i
$319$	12.7837	+	39.3442i	0.715750	+	2.20285i
$320$	−0.856357	+	2.06559i	−0.0478718	+	0.115470i
$321$	0.894232	−	2.75216i	0.0499111	−	0.153611i
$322$	−1.89934	−	2.61422i	−0.105846	−	0.145685i
$323$	13.2784	−	18.2762i	0.738832	−	1.01692i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	−9.71928	−	19.1049i	−0.539128	−	1.05975i
$326$	−18.2480	−	13.2579i	−1.01066	−	0.734289i
$327$	−19.6495	+	6.38450i	−1.08662	+	0.353064i
$328$	−5.14001	+	7.07462i	−0.283810	+	0.390631i
$329$	−0.971999	+	0.706199i	−0.0535880	+	0.0389340i
$330$	−3.03859	−	12.6742i	−0.167269	−	0.697693i
$331$	−0.517988	+	0.376340i	−0.0284712	+	0.0206855i	−0.601930	−	0.798549i	$-0.705601\pi$
$331$	−0.517988	+	0.376340i	−0.0284712	+	0.0206855i	0.573459	+	0.819235i	$0.305601\pi$
$332$	0.0139065	−	0.00451851i	0.000763221	−	0.000247986i
$333$	−7.94371	+	2.58107i	−0.435313	+	0.141442i
$334$	−3.96249	+	12.1953i	−0.216818	+	0.667297i
$335$	−3.12274	−	5.09946i	−0.170614	−	0.278613i
$336$	0.534026			0.0291335
$337$	15.3703	+	4.99411i	0.837273	+	0.272047i	0.696106	−	0.717939i	$-0.254914\pi$
$337$	15.3703	+	4.99411i	0.837273	+	0.272047i	0.141167	+	0.989986i	$0.454914\pi$
$338$	−3.16137	+	4.35126i	−0.171956	+	0.236677i
$339$	13.5445	−	9.84062i	0.735634	−	0.534469i
$340$	7.19349	+	11.7470i	0.390122	+	0.637071i
$341$	−3.99555	−	32.2059i	−0.216371	−	1.74405i
$342$		−	3.66721i		−	0.198300i
$343$	−4.30498	−	5.92529i	−0.232447	−	0.319936i
$344$	−8.89095	−	6.45965i	−0.479368	−	0.348281i
$345$	−3.15444	−	13.1574i	−0.169829	−	0.708373i
$346$	−8.58515			−0.461540
$347$			27.0378i			1.45146i	0.687978	+	0.725732i	$0.258499\pi$
$347$			27.0378i			1.45146i	−0.687978	+	0.725732i	$0.741501\pi$
$348$	−6.75008	−	2.19323i	−0.361842	−	0.117570i
$349$	−1.95362	−	6.01263i	−0.104575	−	0.321849i	0.885055	−	0.465486i	$-0.154120\pi$
$349$	−1.95362	−	6.01263i	−0.104575	−	0.321849i	−0.989630	+	0.143637i	$0.954120\pi$
$350$	−2.63699	−	0.419361i	−0.140953	−	0.0224158i
$351$	3.46826	−	2.51984i	0.185122	−	0.134499i
$352$	−5.54343	−	1.80117i	−0.295466	−	0.0960026i
$353$	−4.43905	−	6.10983i	−0.236267	−	0.325193i	0.674376	−	0.738388i	$-0.264413\pi$
$353$	−4.43905	−	6.10983i	−0.236267	−	0.325193i	−0.910643	+	0.413195i	$0.864413\pi$
$354$	−0.622219	−	0.452069i	−0.0330706	−	0.0240272i
$355$	22.9249	+	19.5922i	1.21673	+	1.03985i
$356$	−2.64709	−	1.92322i	−0.140295	−	0.101930i
$357$	1.93363	−	2.66142i	0.102339	−	0.140857i
$358$	6.44289	−	2.09342i	0.340517	−	0.110641i
$359$	11.6794	+	8.48559i	0.616416	+	0.447852i	0.851668	−	0.524082i	$-0.175592\pi$
$359$	11.6794	+	8.48559i	0.616416	+	0.447852i	−0.235252	+	0.971934i	$0.575592\pi$
$360$	2.06559	+	0.856357i	0.108866	+	0.0451340i
$361$	−1.71554	+	5.27988i	−0.0902914	+	0.277888i
$362$	−1.60959	−	2.21541i	−0.0845982	−	0.116439i
$363$	21.8494	−	7.09929i	1.14679	−	0.372616i
$364$	0.707455	+	2.17732i	0.0370807	+	0.114123i
$365$	−0.0650001	+	0.0155835i	−0.00340226	+	0.000815677i
$366$	−6.01014			−0.314155
$367$		−	36.2330i		−	1.89135i	−0.325120	−	0.945673i	$-0.605405\pi$
$367$		−	36.2330i		−	1.89135i	0.325120	−	0.945673i	$-0.394595\pi$
$368$	−5.75478	−	1.86984i	−0.299988	−	0.0974722i
$369$	7.07462	+	5.14001i	0.368290	+	0.267578i
$370$	7.15273	−	17.2529i	0.371853	−	0.896933i
$371$	−1.18521			−0.0615329
$372$	4.87307	+	2.69317i	0.252657	+	0.139635i
$373$		−	5.71402i		−	0.295861i	−0.988998	−	0.147930i	$-0.952739\pi$
$373$		−	5.71402i		−	0.295861i	0.988998	−	0.147930i	$-0.0472612\pi$
$374$	−29.0484	+	21.1049i	−1.50206	+	1.09131i
$375$	−9.52728	−	5.85071i	−0.491987	−	0.302130i
$376$	−0.695230	+	2.13970i	−0.0358538	+	0.110346i
$377$		−	30.4268i		−	1.56706i
$378$		−	0.534026i		−	0.0274673i
$379$	−9.43295	+	29.0316i	−0.484538	+	1.49125i	0.348111	+	0.937453i	$0.386823\pi$
$379$	−9.43295	+	29.0316i	−0.484538	+	1.49125i	−0.832649	+	0.553801i	$0.813177\pi$
$380$	6.23375	+	5.32752i	0.319784	+	0.273296i
$381$	1.43016	+	4.40158i	0.0732693	+	0.225500i
$382$	2.39992	+	3.30320i	0.122791	+	0.169007i
$383$	−6.66519	−	2.16565i	−0.340575	−	0.110660i	0.133736	−	0.991017i	$-0.457303\pi$
$383$	−6.66519	−	2.16565i	−0.340575	−	0.110660i	−0.474311	+	0.880357i	$0.657303\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	0.548273	−	6.93853i	0.0279426	−	0.353620i
$386$	7.95512	+	24.4833i	0.404905	+	1.24617i
$387$	−6.45965	+	8.89095i	−0.328363	+	0.451952i
$388$	0.255563	−	0.351753i	0.0129743	−	0.0178575i
$389$	−3.17110	−	9.75963i	−0.160781	−	0.494833i	0.837920	−	0.545794i	$-0.183772\pi$
$389$	−3.17110	−	9.75963i	−0.160781	−	0.494833i	−0.998701	+	0.0509605i	$0.983772\pi$
$390$	−0.755122	+	9.55626i	−0.0382371	+	0.483900i
$391$	−30.1559	+	21.9096i	−1.52505	+	1.10801i
$392$	−6.38617	−	2.07499i	−0.322550	−	0.104803i
$393$	−2.21415	−	3.04751i	−0.111689	−	0.153727i
$394$	0.110727	+	0.340781i	0.00557832	+	0.0171683i
$395$	3.52438	+	3.01202i	0.177331	+	0.151551i
$396$	−1.80117	+	5.54343i	−0.0905121	+	0.278568i
$397$			11.6833i			0.586366i	0.956056	+	0.293183i	$0.0947145\pi$
$397$			11.6833i			0.586366i	−0.956056	+	0.293183i	$0.905286\pi$
$398$			12.0460i			0.603810i
$399$	0.605173	−	1.86253i	0.0302966	−	0.0932432i
$400$	−4.45646	+	2.26715i	−0.222823	+	0.113357i
$401$	−17.6227	+	12.8036i	−0.880033	+	0.639382i	−0.933260	−	0.359201i	$-0.883049\pi$
$401$	−17.6227	+	12.8036i	−0.880033	+	0.639382i	0.0532269	+	0.998582i	$0.483049\pi$
$402$			2.67417i			0.133376i
$403$	−4.52493	+	23.4362i	−0.225403	+	1.16744i
$404$	19.3606			0.963224
$405$	0.856357	−	2.06559i	0.0425527	−	0.102640i
$406$	−3.06635	−	2.22784i	−0.152181	−	0.110566i
$407$	46.3015	+	15.0443i	2.29508	+	0.745717i
$408$		−	6.16017i		−	0.304974i
$409$	−0.442555			−0.0218829			−0.0109415	−	0.999940i	$-0.503483\pi$
$409$	−0.442555			−0.0218829			−0.0109415	+	0.999940i	$0.503483\pi$
$410$	−19.0149	+	4.55875i	−0.939081	+	0.225141i
$411$	−4.36990	−	13.4492i	−0.215551	−	0.663398i
$412$	−6.06863	+	1.97182i	−0.298980	+	0.0971444i
$413$	−0.241416	−	0.332281i	−0.0118793	−	0.0163505i
$414$	−1.86984	+	5.75478i	−0.0918976	+	0.282832i
$415$	0.0302035	+	0.0125218i	0.00148263	+	0.000614672i
$416$	3.46826	+	2.51984i	0.170046	+	0.123545i
$417$	−8.37940	+	2.72263i	−0.410341	+	0.133328i
$418$	−12.5639	+	17.2928i	−0.614523	+	0.845818i
$419$	13.9516	+	10.1364i	0.681580	+	0.495197i	0.873881	−	0.486139i	$-0.161595\pi$
$419$	13.9516	+	10.1364i	0.681580	+	0.495197i	−0.192302	+	0.981336i	$0.561595\pi$
$420$	0.907770	+	0.775803i	0.0442946	+	0.0378553i
$421$	−27.8290	−	20.2189i	−1.35630	−	0.985411i	−0.998670	−	0.0515486i	$-0.983584\pi$
$421$	−27.8290	−	20.2189i	−1.35630	−	0.985411i	−0.357632	−	0.933863i	$-0.616416\pi$
$422$	−15.3577	−	21.1381i	−0.747603	−	1.02899i
$423$	2.13970	+	0.695230i	0.104036	+	0.0338032i
$424$	−1.79552	+	1.30452i	−0.0871982	+	0.0633532i
$425$	−4.83748	+	30.4186i	−0.234652	+	1.47552i
$426$	−4.16751	−	12.8263i	−0.201917	−	0.621436i
$427$	−3.05248	−	0.991811i	−0.147720	−	0.0479971i
$428$		−	2.89379i		−	0.139877i
$429$	−24.9877			−1.20642
$430$	−5.72916	−	23.8968i	−0.276285	−	1.15241i
$431$	4.87554	+	3.54229i	0.234846	+	0.170626i	0.698984	−	0.715137i	$-0.253636\pi$
$431$	4.87554	+	3.54229i	0.234846	+	0.170626i	−0.464138	+	0.885763i	$0.653636\pi$
$432$	−0.587785	−	0.809017i	−0.0282798	−	0.0389238i
$433$			28.9949i			1.39341i	0.717359	+	0.696704i	$0.245351\pi$
$433$			28.9949i			1.39341i	−0.717359	+	0.696704i	$0.754649\pi$
$434$	2.03054	+	2.17200i	0.0974691	+	0.104259i
$435$	−8.28799	−	13.5343i	−0.397379	−	0.648922i
$436$	−16.7148	+	12.1440i	−0.800496	+	0.581594i
$437$	−13.0430	+	17.9521i	−0.623929	+	0.858765i
$438$	0.0284296	+	0.00923734i	0.00135842	+	0.000441377i
$439$	−37.7552			−1.80196			−0.900978	−	0.433864i	$-0.857150\pi$
$439$	−37.7552			−1.80196			−0.900978	+	0.433864i	$0.857150\pi$
$440$	−6.80642	−	11.1149i	−0.324483	−	0.529883i
$441$	−2.07499	+	6.38617i	−0.0988092	+	0.304103i
$442$	25.1162	−	8.16074i	1.19466	−	0.388167i
$443$	11.8564	−	3.85239i	0.563316	−	0.183033i	−0.0134966	−	0.999909i	$-0.504296\pi$
$443$	11.8564	−	3.85239i	0.563316	−	0.183033i	0.576813	+	0.816876i	$0.304296\pi$
$444$	−6.75733	+	4.90948i	−0.320688	+	0.232994i
$445$	−1.70573	−	7.11475i	−0.0808594	−	0.337272i
$446$	8.51720	−	6.18811i	0.403301	−	0.293015i
$447$	−3.20119	+	4.40606i	−0.151411	+	0.208399i
$448$	0.507889	−	0.165023i	0.0239955	−	0.00779660i
$449$	−19.5736	−	14.2211i	−0.923737	−	0.671135i	0.0207140	−	0.999785i	$-0.493406\pi$
$449$	−19.5736	−	14.2211i	−0.923737	−	0.671135i	−0.944451	+	0.328651i	$0.893406\pi$
$450$	2.26715	+	4.45646i	0.106874	+	0.210080i
$451$	−15.7507	−	48.4757i	−0.741671	−	2.28263i
$452$	9.84062	−	13.5445i	0.462864	−	0.637077i
$453$	−10.6250	−	14.6240i	−0.499204	−	0.687096i
$454$	−1.12213	+	3.45357i	−0.0526643	+	0.162084i
$455$	−1.96052	+	4.72890i	−0.0919106	+	0.221694i
$456$	−1.13323	−	3.48772i	−0.0530683	−	0.163328i
$457$	−6.93382	+	2.25294i	−0.324351	+	0.105388i	−0.466666	−	0.884433i	$-0.654545\pi$
$457$	−6.93382	+	2.25294i	−0.324351	+	0.105388i	0.142316	+	0.989821i	$0.454545\pi$
$458$	7.36336	+	2.39250i	0.344067	+	0.111794i
$459$	−6.16017			−0.287532
$460$	−7.06592	−	11.5387i	−0.329450	−	0.537994i
$461$	−3.86172	+	11.8851i	−0.179858	+	0.553546i	−0.999822	−	0.0188690i	$-0.993993\pi$
$461$	−3.86172	+	11.8851i	−0.179858	+	0.553546i	0.819964	+	0.572415i	$0.193993\pi$
$462$	−1.82959	+	2.51821i	−0.0851200	+	0.117158i
$463$	3.89601	+	5.36239i	0.181063	+	0.249211i	0.889895	−	0.456166i	$-0.150778\pi$
$463$	3.89601	+	5.36239i	0.181063	+	0.249211i	−0.708832	+	0.705377i	$0.750778\pi$
$464$	−7.09745			−0.329491
$465$	4.37105	+	11.6574i	0.202703	+	0.540597i
$466$	−1.28286			−0.0594272
$467$	−12.6397	−	17.3971i	−0.584897	−	0.805042i	0.409324	−	0.912389i	$-0.365764\pi$
$467$	−12.6397	−	17.3971i	−0.584897	−	0.805042i	−0.994222	+	0.107347i	$0.965764\pi$
$468$	2.51984	−	3.46826i	0.116480	−	0.160321i
$469$	−0.441300	+	1.35818i	−0.0203773	+	0.0627150i
$470$	−4.29023	+	2.62720i	−0.197894	+	0.121184i
$471$	−13.5644			−0.625013
$472$	−0.731462	−	0.237666i	−0.0336683	−	0.0109395i
$473$	60.9213	−	19.7945i	2.80116	−	0.910153i
$474$	−0.640695	−	1.97185i	−0.0294281	−	0.0905703i
$475$	2.85698	+	18.1121i	0.131087	+	0.831040i
$476$	1.01657	−	3.12868i	0.0465944	−	0.143403i
$477$	1.30452	+	1.79552i	0.0597299	+	0.0822112i
$478$	−4.56861	+	6.28816i	−0.208963	+	0.287614i
$479$	1.74525	+	5.37134i	0.0797427	+	0.245423i	0.982978	−	0.183723i	$-0.0588148\pi$
$479$	1.74525	+	5.37134i	0.0797427	+	0.245423i	−0.903235	+	0.429145i	$0.858815\pi$
$480$	2.22912	+	0.176142i	0.101745	+	0.00803974i
$481$	−28.9687	−	21.0470i	−1.32086	−	0.959661i
$482$	−1.47474	+	0.479173i	−0.0671727	+	0.0218257i
$483$	−1.89934	+	2.61422i	−0.0864230	+	0.118951i
$484$	18.5862	−	13.5036i	0.844826	−	0.613802i
$485$	0.945430	−	0.226663i	0.0429298	−	0.0102922i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−13.7317	+	4.46171i	−0.622244	+	0.202179i	−0.603136	−	0.797638i	$-0.706082\pi$
$487$	−13.7317	+	4.46171i	−0.622244	+	0.202179i	−0.0191076	+	0.999817i	$0.506082\pi$
$488$	−5.71598	+	1.85724i	−0.258750	+	0.0840731i
$489$	−6.97010	+	21.4518i	−0.315199	+	0.970083i
$490$	−7.84117	−	12.8047i	−0.354228	−	0.578456i
$491$	−6.09370			−0.275005			−0.137502	−	0.990501i	$-0.543908\pi$
$491$	−6.09370			−0.275005			−0.137502	+	0.990501i	$0.543908\pi$
$492$	8.31672	+	2.70226i	0.374946	+	0.121827i
$493$	−25.6989	+	35.3715i	−1.15742	+	1.59305i
$494$	12.7188	−	9.24078i	0.572248	−	0.415762i
$495$	−11.1149	+	6.80642i	−0.499579	+	0.305926i
$496$	5.46680	+	1.05550i	0.245467	+	0.0473933i
$497$		−	7.20206i		−	0.323056i
$498$	−0.00859472	−	0.0118296i	−0.000385139	−	0.000530098i
$499$	−14.5645	−	10.5817i	−0.651998	−	0.473704i	0.211953	−	0.977280i	$-0.432017\pi$
$499$	−14.5645	−	10.5817i	−0.651998	−	0.473704i	−0.863951	+	0.503576i	$0.832017\pi$
$500$	−10.8690	−	2.62027i	−0.486074	−	0.117182i
$501$	12.8229			0.572885
$502$		−	16.1234i		−	0.719624i
$503$	24.0206	+	7.80476i	1.07102	+	0.347997i	0.790886	−	0.611963i	$-0.209620\pi$
$503$	24.0206	+	7.80476i	1.07102	+	0.347997i	0.280138	+	0.959960i	$0.409620\pi$
$504$	−0.165023	−	0.507889i	−0.00735071	−	0.0226232i
$505$	32.9103	+	28.1260i	1.46449	+	1.25159i
$506$	28.5333	−	20.7306i	1.26846	−	0.921589i
$507$	5.11521	+	1.66203i	0.227174	+	0.0738135i
$508$	2.72033	+	3.74421i	0.120695	+	0.166122i
$509$	−20.7932	−	15.1071i	−0.921643	−	0.669613i	0.0222896	−	0.999752i	$-0.492904\pi$
$509$	−20.7932	−	15.1071i	−0.921643	−	0.669613i	−0.943932	+	0.330139i	$0.892904\pi$
$510$	8.94916	−	10.4714i	0.396276	−	0.463683i
$511$	0.0129147	+	0.00938307i	0.000571312	+	0.000415083i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−3.48772	+	1.13323i	−0.153987	+	0.0500333i
$514$	−13.9562	−	10.1397i	−0.615579	−	0.447245i
$515$	−13.1804	−	5.46435i	−0.580797	−	0.240788i
$516$	−3.39604	+	10.4519i	−0.149502	+	0.460121i
$517$	−7.70791	−	10.6090i	−0.338994	−	0.466585i
$518$	−4.24215	+	1.37836i	−0.186389	+	0.0605615i
$519$	2.65296	+	8.16496i	0.116452	+	0.358402i
$520$	2.23488	+	9.32189i	0.0980061	+	0.408792i
$521$	32.6477			1.43032			0.715162	−	0.698959i	$-0.246353\pi$
$521$	32.6477			1.43032			0.715162	+	0.698959i	$0.246353\pi$
$522$			7.09745i			0.310647i
$523$	−20.1318	−	6.54122i	−0.880302	−	0.286028i	−0.166220	−	0.986089i	$-0.553156\pi$
$523$	−20.1318	−	6.54122i	−0.880302	−	0.286028i	−0.714083	+	0.700061i	$0.753156\pi$
$524$	−3.04751	−	2.21415i	−0.133131	−	0.0967254i
$525$	0.416039	+	2.63752i	0.0181574	+	0.115111i
$526$	7.43992			0.324396
$527$	25.0548	−	23.4230i	1.09140	−	1.02032i
$528$			5.82870i			0.253662i
$529$	11.0138	−	8.00196i	0.478859	−	0.347911i
$530$	−4.94727	−	0.390926i	−0.214896	−	0.0169808i
$531$	−0.237666	+	0.731462i	−0.0103138	+	0.0317428i
$532$		−	1.95838i		−	0.0849066i
$533$			37.4887i			1.62381i
$534$	−1.01110	+	3.11184i	−0.0437544	+	0.134662i
$535$	4.20395	−	4.91905i	0.181752	−	0.212669i
$536$	0.826365	+	2.54329i	0.0356935	+	0.109853i
$537$	−3.98192	−	5.48065i	−0.171833	−	0.236507i
$538$	−1.87322	−	0.608646i	−0.0807602	−	0.0262406i
$539$	31.6638	−	23.0051i	1.36386	−	0.990901i
$540$	0.176142	−	2.22912i	0.00757994	−	0.0959260i
$541$	5.75311	+	17.7063i	0.247346	+	0.761252i	0.995242	+	0.0974359i	$0.0310641\pi$
$541$	5.75311	+	17.7063i	0.247346	+	0.761252i	−0.747896	+	0.663816i	$0.768936\pi$
$542$	17.4135	−	23.9676i	0.747973	−	1.02950i
$543$	−1.60959	+	2.21541i	−0.0690741	+	0.0950724i
$544$	−1.90360	−	5.85867i	−0.0816161	−	0.251189i
$545$	−46.0551	−	3.63921i	−1.97279	−	0.155887i
$546$	1.85214	−	1.34566i	0.0792643	−	0.0575889i
$547$	−18.0565	−	5.86691i	−0.772040	−	0.250851i	−0.103602	−	0.994619i	$-0.533037\pi$
$547$	−18.0565	−	5.86691i	−0.772040	−	0.250851i	−0.668438	+	0.743768i	$0.733037\pi$
$548$	−8.31204	−	11.4405i	−0.355073	−	0.488716i
$549$	1.85724	+	5.71598i	0.0792649	+	0.243952i
$550$	4.57718	−	28.7818i	0.195172	−	1.22726i
$551$	−8.04304	+	24.7539i	−0.342645	+	1.05455i
$552$			6.05093i			0.257545i
$553$		−	1.10721i		−	0.0470834i
$554$	−8.71164	+	26.8117i	−0.370122	+	1.13912i
$555$	−18.6188	−	1.47123i	−0.790322	−	0.0624501i
$556$	−7.12795	+	5.17876i	−0.302292	+	0.219628i
$557$			24.6080i			1.04268i	0.853350	+	0.521338i	$0.174567\pi$
$557$			24.6080i			1.04268i	−0.853350	+	0.521338i	$0.825433\pi$
$558$	1.05550	−	5.46680i	0.0446828	−	0.231428i
$559$	−47.1135			−1.99269
$560$	1.10308	+	0.457316i	0.0466135	+	0.0193251i
$561$	29.0484	+	21.1049i	1.22643	+	0.891050i
$562$	24.3309	+	7.90559i	1.02634	+	0.333477i
$563$		−	30.9535i		−	1.30453i	−0.757989	−	0.652267i	$-0.773818\pi$
$563$		−	30.9535i		−	1.30453i	0.757989	−	0.652267i	$-0.226182\pi$
$564$	2.24981			0.0947342
$565$	36.4043	−	8.72778i	1.53154	−	0.367181i
$566$	−1.33092	−	4.09614i	−0.0559425	−	0.172173i
$567$	−0.507889	+	0.165023i	−0.0213293	+	0.00693031i
$568$	−7.92708	−	10.9107i	−0.332613	−	0.457802i
$569$	−7.93069	+	24.4081i	−0.332472	+	1.02324i	0.635482	+	0.772115i	$0.280801\pi$
$569$	−7.93069	+	24.4081i	−0.332472	+	1.02324i	−0.967954	+	0.251127i	$0.919199\pi$
$570$	3.14044	−	7.57494i	0.131538	−	0.317279i
$571$	2.07000	+	1.50394i	0.0866268	+	0.0629381i	0.630256	−	0.776388i	$-0.282950\pi$
$571$	2.07000	+	1.50394i	0.0866268	+	0.0629381i	−0.543629	+	0.839326i	$0.682950\pi$
$572$	−23.7647	+	7.72163i	−0.993653	+	0.322857i
$573$	2.39992	−	3.30320i	0.100258	−	0.137993i
$574$	3.77803	+	2.74490i	0.157692	+	0.114570i
$575$	4.75169	−	29.8792i	0.198159	−	1.24605i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	1.66675	+	2.29409i	0.0693877	+	0.0955040i	0.842300	−	0.539008i	$-0.181201\pi$
$577$	1.66675	+	2.29409i	0.0693877	+	0.0955040i	−0.772913	+	0.634512i	$0.781201\pi$
$578$	−19.9225	−	6.47321i	−0.828666	−	0.269250i
$579$	20.8268	−	15.1315i	0.865531	−	0.628845i
$580$	−12.0647	−	10.3108i	−0.500959	−	0.428132i
$581$	−0.00241300	−	0.00742645i	−0.000100108	−	0.000308101i
$582$	−0.413510	−	0.134358i	−0.0171406	−	0.00556930i
$583$		−	12.9361i		−	0.535760i
$584$	0.0298926			0.00123697
$585$	9.32189	−	2.23488i	0.385413	−	0.0924010i
$586$	21.6207	+	15.7083i	0.893141	+	0.648905i
$587$	−10.6441	−	14.6504i	−0.439331	−	0.604687i	0.530732	−	0.847540i	$-0.321917\pi$
$587$	−10.6441	−	14.6504i	−0.439331	−	0.604687i	−0.970063	+	0.242852i	$0.921917\pi$
$588$			6.71482i			0.276914i
$589$	9.87642	−	17.8706i	0.406951	−	0.736344i
$590$	−0.898116	−	1.46663i	−0.0369748	−	0.0603801i
$591$	0.289886	−	0.210614i	0.0119243	−	0.00866352i
$592$	−4.90948	+	6.75733i	−0.201779	+	0.277724i
$593$	−8.23555	−	2.67589i	−0.338193	−	0.109886i	0.134997	−	0.990846i	$-0.456898\pi$
$593$	−8.23555	−	2.67589i	−0.338193	−	0.109886i	−0.473190	+	0.880960i	$0.656898\pi$
$594$	5.82870			0.239155
$595$	6.27321	−	3.84151i	0.257176	−	0.157487i
$596$	−1.68296	+	5.17963i	−0.0689369	+	0.212166i
$597$	11.4564	−	3.72241i	0.468879	−	0.152348i
$598$	−24.6708	+	8.01602i	−1.00886	+	0.327800i
$599$	−12.3802	+	8.99475i	−0.505842	+	0.367516i	−0.811244	−	0.584708i	$-0.801209\pi$
$599$	−12.3802	+	8.99475i	−0.505842	+	0.367516i	0.305402	+	0.952223i	$0.401209\pi$
$600$	3.53331	+	3.53776i	0.144247	+	0.144428i
$601$	−12.5859	+	9.14420i	−0.513390	+	0.373000i	−0.814108	−	0.580714i	$-0.802774\pi$
$601$	−12.5859	+	9.14420i	−0.513390	+	0.373000i	0.300718	+	0.953713i	$0.402774\pi$
$602$	−3.44962	+	4.74800i	−0.140596	+	0.193514i
$603$	2.54329	−	0.826365i	0.103571	−	0.0336522i
$604$	−14.6240	−	10.6250i	−0.595042	−	0.432324i
$605$	51.2113	+	4.04664i	2.08204	+	0.164519i
$606$	−5.98275	−	18.4130i	−0.243032	−	0.747977i
$607$	−17.6813	+	24.3362i	−0.717660	+	0.987775i	0.281938	+	0.959433i	$0.409023\pi$
$607$	−17.6813	+	24.3362i	−0.717660	+	0.987775i	−0.999598	+	0.0283420i	$0.990977\pi$
$608$	−2.15553	−	2.96683i	−0.0874183	−	0.120321i
$609$	−1.17124	+	3.60471i	−0.0474611	+	0.146070i
$610$	−12.4145	−	5.14682i	−0.502647	−	0.208389i
$611$	2.98046	+	9.17291i	0.120576	+	0.371096i
$612$	−5.85867	+	1.90360i	−0.236823	+	0.0769484i
$613$	5.33239	+	1.73260i	0.215373	+	0.0699790i	0.414716	−	0.909951i	$-0.363881\pi$
$613$	5.33239	+	1.73260i	0.215373	+	0.0699790i	−0.199343	+	0.979930i	$0.563881\pi$
$614$	−1.82707			−0.0737345
$615$	10.2116	+	16.6755i	0.411770	+	0.672423i
$616$	−0.961870	+	2.96033i	−0.0387548	+	0.119275i
$617$	22.4730	−	30.9315i	0.904730	−	1.24525i	−0.0642041	−	0.997937i	$-0.520451\pi$
$617$	22.4730	−	30.9315i	0.904730	−	1.24525i	0.968934	−	0.247318i	$-0.0795491\pi$
$618$	3.75062	+	5.16228i	0.150872	+	0.207657i
$619$	35.2739			1.41778			0.708889	−	0.705320i	$-0.249197\pi$
$619$	35.2739			1.41778			0.708889	+	0.705320i	$0.249197\pi$
$620$	7.75944	+	9.73607i	0.311627	+	0.391010i
$621$	6.05093			0.242815
$622$	10.2869	+	14.1586i	0.412465	+	0.567710i
$623$	−1.02705	+	1.41361i	−0.0411478	+	0.0566352i
$624$	1.32476	−	4.07719i	0.0530328	−	0.163218i
$625$	−14.6691	−	20.2439i	−0.586766	−	0.809757i
$626$	19.4970			0.779258
$627$	20.3289	+	6.60526i	0.811858	+	0.263789i
$628$	−12.9005	+	4.19162i	−0.514785	+	0.167264i
$629$	15.8998	+	48.9346i	0.633968	+	1.95115i
$630$	0.457316	−	1.10308i	0.0182199	−	0.0439476i
$631$	−8.65950	+	26.6512i	−0.344729	+	1.06097i	0.616999	+	0.786964i	$0.288348\pi$
$631$	−8.65950	+	26.6512i	−0.344729	+	1.06097i	−0.961729	+	0.274004i	$0.911652\pi$
$632$	−1.21867	−	1.67736i	−0.0484762	−	0.0667218i
$633$	−15.3577	+	21.1381i	−0.610415	+	0.840164i
$634$	10.1055	+	31.1014i	0.401339	+	1.23519i
$635$	−0.815201	+	10.3166i	−0.0323503	+	0.409401i
$636$	1.79552	+	1.30452i	0.0711970	+	0.0517276i
$637$	−27.3776	+	8.89551i	−1.08474	+	0.352453i
$638$	24.3160	−	33.4682i	0.962682	−	1.32502i
$639$	−10.9107	+	7.92708i	−0.431620	+	0.313590i
$640$	2.17445	−	0.521315i	0.0859527	−	0.0206068i
$641$	26.6418	−	19.3564i	1.05229	−	0.764533i	0.0796425	−	0.996823i	$-0.474622\pi$
$641$	26.6418	−	19.3564i	1.05229	−	0.764533i	0.972646	+	0.232291i	$0.0746221\pi$
$642$	−2.75216	+	0.894232i	−0.108619	+	0.0352925i
$643$	4.95652	−	1.61047i	0.195466	−	0.0635107i	−0.209648	−	0.977777i	$-0.567232\pi$
$643$	4.95652	−	1.61047i	0.195466	−	0.0635107i	0.405114	+	0.914266i	$0.367232\pi$
$644$	−0.998542	+	3.07320i	−0.0393481	+	0.121101i
$645$	−20.9568	+	12.8333i	−0.825174	+	0.505310i
$646$	−22.5906			−0.888817
$647$	−19.2758	−	6.26308i	−0.757809	−	0.246227i	−0.0954711	−	0.995432i	$-0.530436\pi$
$647$	−19.2758	−	6.26308i	−0.757809	−	0.246227i	−0.662338	+	0.749205i	$0.730436\pi$
$648$	−0.587785	+	0.809017i	−0.0230904	+	0.0317812i
$649$	3.62673	−	2.63497i	0.142362	−	0.103432i
$650$	−9.74333	+	19.0926i	−0.382165	+	0.748875i
$651$	1.43822	−	2.60234i	0.0563684	−	0.101994i
$652$			22.5557i			0.883351i
$653$	−6.57615	−	9.05129i	−0.257345	−	0.354205i	0.660722	−	0.750631i	$-0.270250\pi$
$653$	−6.57615	−	9.05129i	−0.257345	−	0.354205i	−0.918067	+	0.396426i	$0.870250\pi$
$654$	16.7148	+	12.1440i	0.653602	+	0.474870i
$655$	−1.96376	−	8.19100i	−0.0767303	−	0.320049i
$656$	8.74471			0.341424
$657$		−	0.0298926i		−	0.00116622i
$658$	1.14265	+	0.371271i	0.0445453	+	0.0144736i
$659$	0.602380	+	1.85394i	0.0234654	+	0.0722191i	0.962103	−	0.272685i	$-0.0879116\pi$
$659$	0.602380	+	1.85394i	0.0234654	+	0.0722191i	−0.938638	+	0.344904i	$0.887912\pi$
$660$	−8.46762	+	9.90799i	−0.329602	+	0.385668i
$661$	25.5420	−	18.5573i	0.993468	−	0.721797i	0.0327901	−	0.999462i	$-0.489561\pi$
$661$	25.5420	−	18.5573i	0.993468	−	0.721797i	0.960678	+	0.277666i	$0.0895607\pi$
$662$	0.608931	+	0.197854i	0.0236668	+	0.00768981i
$663$	−15.5227	−	21.3651i	−0.602850	−	0.829752i
$664$	−0.0118296	−	0.00859472i	−0.000459078	−	0.000333540i
$665$	2.84503	−	3.32898i	0.110326	−	0.129092i
$666$	6.75733	+	4.90948i	0.261841	+	0.190239i
$667$	25.2431	−	34.7442i	0.977418	−	1.34530i
$668$	12.1953	−	3.96249i	0.471850	−	0.153313i
$669$	−8.51720	−	6.18811i	−0.329294	−	0.239246i
$670$	−2.29004	+	5.52374i	−0.0884721	+	0.213401i
$671$	10.8253	−	33.3168i	0.417905	−	1.28618i
$672$	−0.313892	−	0.432036i	−0.0121087	−	0.0166661i
$673$	−23.9780	+	7.79091i	−0.924283	+	0.300318i	−0.732223	−	0.681065i	$-0.761517\pi$
$673$	−23.9780	+	7.79091i	−0.924283	+	0.300318i	−0.192060	+	0.981383i	$0.561517\pi$
$674$	−4.99411	−	15.3703i	−0.192366	−	0.592042i
$675$	3.53776	−	3.53331i	0.136168	−	0.135997i
$676$	5.37845			0.206863
$677$			31.0011i			1.19147i	0.803182	+	0.595734i	$0.203139\pi$
$677$			31.0011i			1.19147i	−0.803182	+	0.595734i	$0.796861\pi$
$678$	−15.9225	−	5.17352i	−0.611498	−	0.198688i
$679$	−0.187845	−	0.136477i	−0.00720883	−	0.00523752i
$680$	5.27531	−	12.7244i	0.202299	−	0.487958i
$681$	3.63130			0.139152
$682$	−23.7066	+	22.1626i	−0.907774	+	0.848652i
$683$		−	41.7635i		−	1.59804i	−0.601307	−	0.799018i	$-0.705353\pi$
$683$		−	41.7635i		−	1.59804i	0.601307	−	0.799018i	$-0.294647\pi$
$684$	−2.96683	+	2.15553i	−0.113440	+	0.0824188i
$685$	2.49087	−	31.5226i	0.0951713	−	1.20442i
$686$	−2.26326	+	6.96560i	−0.0864117	+	0.265948i
$687$		−	7.74229i		−	0.295387i
$688$			10.9898i			0.418983i
$689$	−2.94015	+	9.04885i	−0.112011	+	0.344734i
$690$	−8.79046	+	10.2857i	−0.334647	+	0.391572i
$691$	−3.11303	−	9.58093i	−0.118425	−	0.364476i	0.874221	−	0.485529i	$-0.161373\pi$
$691$	−3.11303	−	9.58093i	−0.118425	−	0.364476i	−0.992646	+	0.121053i	$0.961373\pi$
$692$	5.04622	+	6.94553i	0.191829	+	0.264029i
$693$	2.96033	+	0.961870i	0.112454	+	0.0365384i
$694$	21.8740	−	15.8924i	0.830326	−	0.603267i
$695$	−19.6399	−	1.55192i	−0.744985	−	0.0588677i
$696$	2.19323	+	6.75008i	0.0831343	+	0.255861i
$697$	31.6634	−	43.5809i	1.19934	−	1.65074i
$698$	−3.71601	+	5.11465i	−0.140653	+	0.193592i
$699$	0.396425	+	1.22007i	0.0149942	+	0.0461473i
$700$	1.21071	+	2.37986i	0.0457607	+	0.0899504i
$701$	−5.87723	+	4.27006i	−0.221980	+	0.161278i	−0.693218	−	0.720728i	$-0.743807\pi$
$701$	−5.87723	+	4.27006i	−0.221980	+	0.161278i	0.471237	+	0.882006i	$0.343807\pi$
$702$	−4.07719	−	1.32476i	−0.153884	−	0.0499998i
$703$	18.0041	+	24.7805i	0.679037	+	0.934615i
$704$	1.80117	+	5.54343i	0.0678841	+	0.208926i
$705$	3.82437	+	3.26840i	0.144034	+	0.123095i
$706$	−2.33375	+	7.18253i	−0.0878317	+	0.270318i
$707$		−	10.3390i		−	0.388840i
$708$			0.769105i			0.0289047i
$709$	13.0380	−	40.1269i	0.489653	−	1.50700i	−0.335474	−	0.942049i	$-0.608897\pi$
$709$	13.0380	−	40.1269i	0.489653	−	1.50700i	0.825127	−	0.564947i	$-0.191103\pi$
$710$	2.37551	−	30.0627i	0.0891514	−	1.12823i
$711$	−1.67736	+	1.21867i	−0.0629059	+	0.0457038i
$712$			3.27198i			0.122623i
$713$	−24.6105	+	23.0076i	−0.921669	+	0.861642i
$714$	−3.28969			−0.123114
$715$	−51.6143	−	21.3984i	−1.93027	−	0.800254i
$716$	−5.48065	−	3.98192i	−0.204821	−	0.148812i
$717$	7.39217	+	2.40186i	0.276066	+	0.0896992i
$718$		−	14.4365i		−	0.538767i
$719$	20.8935			0.779197			0.389599	−	0.920985i	$-0.372614\pi$
$719$	20.8935			0.779197			0.389599	+	0.920985i	$0.372614\pi$
$720$	−0.521315	−	2.17445i	−0.0194283	−	0.0810369i
$721$	1.05300	+	3.24080i	0.0392158	+	0.120694i
$722$	5.27988	−	1.71554i	0.196497	−	0.0638457i
$723$	0.911441	+	1.25449i	0.0338969	+	0.0466550i
$724$	−0.846212	+	2.60437i	−0.0314492	+	0.0967907i
$725$	−5.52935	−	35.0538i	−0.205355	−	1.30187i
$726$	−18.5862	−	13.5036i	−0.689798	−	0.501167i
$727$	10.0887	−	3.27803i	0.374171	−	0.121575i	−0.115894	−	0.993262i	$-0.536973\pi$
$727$	10.0887	−	3.27803i	0.374171	−	0.121575i	0.490064	+	0.871686i	$0.336973\pi$
$728$	1.34566	−	1.85214i	0.0498735	−	0.0686449i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	0.0508134	+	0.0434264i	0.00188069	+	0.00160728i
$731$	54.7698	+	39.7926i	2.02573	+	1.47178i
$732$	3.53267	+	4.86231i	0.130571	+	0.179716i
$733$	29.1990	+	9.48732i	1.07849	+	0.350422i	0.793788	−	0.608194i	$-0.208106\pi$
$733$	29.1990	+	9.48732i	1.07849	+	0.350422i	0.284701	+	0.958617i	$0.408106\pi$
$734$	−29.3131	+	21.2972i	−1.08197	+	0.786094i
$735$	−9.75492	+	11.4143i	−0.359816	+	0.421021i
$736$	1.86984	+	5.75478i	0.0689232	+	0.212124i
$737$	−14.8241	−	4.81663i	−0.546052	−	0.177423i
$738$		−	8.74471i		−	0.321897i
$739$	−7.83873			−0.288352			−0.144176	−	0.989552i	$-0.546053\pi$
$739$	−7.83873			−0.288352			−0.144176	+	0.989552i	$0.546053\pi$
$740$	−18.1621	+	4.35429i	−0.667653	+	0.160067i
$741$	−12.7188	−	9.24078i	−0.467238	−	0.339468i
$742$	0.696648	+	0.958854i	0.0255747	+	0.0352006i
$743$		−	19.3413i		−	0.709563i	−0.934949	−	0.354782i	$-0.884555\pi$
$743$		−	19.3413i		−	0.709563i	0.934949	−	0.354782i	$-0.115445\pi$
$744$	−0.685496	−	5.52540i	−0.0251315	−	0.202571i
$745$	−10.3855	+	6.35974i	−0.380495	+	0.233003i
$746$	−4.62274	+	3.35862i	−0.169251	+	0.122968i
$747$	−0.00859472	+	0.0118296i	−0.000314464	+	0.000432823i
$748$	34.1485	+	11.0955i	1.24859	+	0.405692i
$749$	−1.54536			−0.0564662
$750$	0.866669	+	11.1467i	0.0316463	+	0.407020i
$751$	12.1971	−	37.5387i	0.445077	−	1.36981i	−0.437322	−	0.899305i	$-0.644073\pi$
$751$	12.1971	−	37.5387i	0.445077	−	1.36981i	0.882399	−	0.470502i	$-0.155927\pi$
$752$	2.13970	−	0.695230i	0.0780268	−	0.0253524i
$753$	−15.3343	+	4.98241i	−0.558813	+	0.181569i
$754$	−24.6158	+	17.8844i	−0.896456	+	0.651313i
$755$	−9.42343	−	39.3059i	−0.342954	−	1.43049i
$756$	−0.432036	+	0.313892i	−0.0157130	+	0.0114162i
$757$	8.02445	−	11.0447i	0.291654	−	0.401427i	−0.637897	−	0.770122i	$-0.720195\pi$
$757$	8.02445	−	11.0447i	0.291654	−	0.401427i	0.929550	+	0.368695i	$0.120195\pi$
$758$	29.0316	−	9.43295i	1.05448	−	0.342620i
$759$	−28.5333	−	20.7306i	−1.03569	−	0.752475i
$760$	0.645949	−	8.17464i	0.0234310	−	0.296525i
$761$	4.42062	+	13.6053i	0.160248	+	0.493191i	0.998655	−	0.0518532i	$-0.0165128\pi$
$761$	4.42062	+	13.6053i	0.160248	+	0.493191i	−0.838407	+	0.545044i	$0.816513\pi$
$762$	2.72033	−	3.74421i	0.0985470	−	0.135638i
$763$	6.48523	+	8.92616i	0.234781	+	0.323149i
$764$	1.26171	−	3.88315i	0.0456471	−	0.140487i
$765$	−12.7244	−	5.27531i	−0.460051	−	0.190729i
$766$	2.16565	+	6.66519i	0.0782481	+	0.240823i
$767$	−3.13579	+	1.01888i	−0.113227	+	0.0367896i
$768$	−0.951057	−	0.309017i	−0.0343183	−	0.0111507i
$769$	3.01662			0.108782			0.0543910	−	0.998520i	$-0.482678\pi$
$769$	3.01662			0.108782			0.0543910	+	0.998520i	$0.482678\pi$
$770$	−5.93565	+	3.63480i	−0.213906	+	0.130989i
$771$	−5.33078	+	16.4064i	−0.191983	+	0.590864i
$772$	15.1315	−	20.8268i	0.544596	−	0.749572i
$773$	10.6586	+	14.6704i	0.383364	+	0.527656i	0.956472	−	0.291824i	$-0.0942623\pi$
$773$	10.6586	+	14.6704i	0.383364	+	0.527656i	−0.573107	+	0.819480i	$0.694262\pi$
$774$	10.9898			0.395021
$775$	−0.954059	+	27.8225i	−0.0342708	+	0.999413i
$776$	−0.434790			−0.0156081
$777$	2.62179	+	3.60858i	0.0940562	+	0.129457i
$778$	−6.03179	+	8.30204i	−0.216250	+	0.297643i
$779$	9.90976	−	30.4991i	0.355054	−	1.09274i
$780$	8.17502	−	5.00612i	0.292713	−	0.179248i
$781$	78.6080			2.81281
$782$	35.4504	+	11.5185i	1.26770	+	0.411902i
$783$	6.75008	−	2.19323i	0.241228	−	0.0783798i
$784$	2.07499	+	6.38617i	0.0741069	+	0.228078i
$785$	−28.0184	−	11.6159i	−1.00002	−	0.414590i
$786$	−1.16405	+	3.58256i	−0.0415201	+	0.127786i
$787$	5.28461	+	7.27364i	0.188376	+	0.259277i	0.892751	−	0.450551i	$-0.148772\pi$
$787$	5.28461	+	7.27364i	0.188376	+	0.259277i	−0.704375	+	0.709828i	$0.748772\pi$
$788$	0.210614	−	0.289886i	0.00750283	−	0.0103268i
$789$	−2.29906	−	7.07578i	−0.0818488	−	0.251905i
$790$	0.365200	−	4.62170i	0.0129932	−	0.164433i
$791$	−7.23308	−	5.25514i	−0.257179	−	0.186851i
$792$	5.54343	−	1.80117i	0.196977	−	0.0640017i
$793$	−15.1446	+	20.8448i	−0.537800	+	0.740219i
$794$	9.45195	−	6.86724i	0.335437	−	0.243709i
$795$	1.15700	+	4.82594i	0.0410345	+	0.171158i
$796$	9.74540	−	7.08045i	0.345416	−	0.250960i
$797$	−7.85622	+	2.55264i	−0.278282	+	0.0904192i	−0.444833	−	0.895614i	$-0.646737\pi$
$797$	−7.85622	+	2.55264i	−0.278282	+	0.0904192i	0.166551	+	0.986033i	$0.446737\pi$
$798$	−1.86253	+	0.605173i	−0.0659329	+	0.0214229i
$799$	4.28274	−	13.1809i	0.151512	−	0.466307i
$800$	4.45360	+	2.27276i	0.157459	+	0.0803541i
$801$	3.27198			0.115610
$802$	20.7167	+	6.73126i	0.731531	+	0.237689i
$803$	−0.102413	+	0.140959i	−0.00361408	+	0.00497435i
$804$	2.16345	−	1.57184i	0.0762990	−	0.0554345i
$805$	−6.16196	+	3.77338i	−0.217180	+	0.132994i
$806$	21.6200	−	10.1147i	0.761532	−	0.356276i
$807$			1.96962i			0.0693339i
$808$	−11.3799	−	15.6630i	−0.400342	−	0.551023i
$809$	−9.32293	−	6.77350i	−0.327777	−	0.238144i	0.411710	−	0.911315i	$-0.364932\pi$
$809$	−9.32293	−	6.77350i	−0.327777	−	0.238144i	−0.739487	+	0.673171i	$0.764932\pi$
$810$	−2.17445	+	0.521315i	−0.0764024	+	0.0183171i
$811$	41.7882			1.46738			0.733690	−	0.679484i	$-0.237796\pi$
$811$	41.7882			1.46738			0.733690	+	0.679484i	$0.237796\pi$
$812$			3.79022i			0.133011i
$813$	−28.1756	−	9.15481i	−0.988162	−	0.321073i
$814$	−15.0443	−	46.3015i	−0.527302	−	1.62287i
$815$	−32.7677	+	38.3416i	−1.14780	+	1.34305i
$816$	−4.98369	+	3.62086i	−0.174464	+	0.126755i
$817$	38.3294	+	12.4540i	1.34098	+	0.435710i
$818$	0.260127	+	0.358035i	0.00909514	+	0.0125184i
$819$	−1.85214	−	1.34566i	−0.0647191	−	0.0470212i
$820$	14.8648	+	12.7038i	0.519101	+	0.443637i
$821$	20.3995	+	14.8211i	0.711946	+	0.517259i	0.883801	−	0.467863i	$-0.154976\pi$
$821$	20.3995	+	14.8211i	0.711946	+	0.517259i	−0.171855	+	0.985122i	$0.554976\pi$
$822$	−8.31204	+	11.4405i	−0.289916	+	0.399035i
$823$	12.7276	−	4.13546i	0.443658	−	0.144153i	−0.0786649	−	0.996901i	$-0.525066\pi$
$823$	12.7276	−	4.13546i	0.443658	−	0.144153i	0.522323	+	0.852748i	$0.325066\pi$
$824$	5.16228	+	3.75062i	0.179837	+	0.130659i
$825$	−28.7876	+	4.54092i	−1.00225	+	0.158095i
$826$	−0.126920	+	0.390620i	−0.00441611	+	0.0135914i
$827$	9.68152	+	13.3255i	0.336660	+	0.463372i	0.943462	−	0.331480i	$-0.107548\pi$
$827$	9.68152	+	13.3255i	0.336660	+	0.463372i	−0.606802	+	0.794853i	$0.707548\pi$
$828$	5.75478	−	1.86984i	0.199992	−	0.0649814i
$829$	15.8713	+	48.8468i	0.551232	+	1.69652i	0.705691	+	0.708520i	$0.250637\pi$
$829$	15.8713	+	48.8468i	0.551232	+	1.69652i	−0.154459	+	0.987999i	$0.549363\pi$
$830$	−0.00762278	−	0.0317953i	−0.000264590	−	0.00110363i
$831$	28.1915			0.977951
$832$		−	4.28701i		−	0.148625i
$833$	39.3399	+	12.7823i	1.36305	+	0.442881i
$834$	7.12795	+	5.17876i	0.246821	+	0.179326i
$835$	26.4868	+	10.9810i	0.916614	+	0.380012i
$836$	21.3751			0.739272
$837$	−5.52540	+	0.685496i	−0.190986	+	0.0236942i
$838$		−	17.2451i		−	0.595722i
$839$	7.44266	−	5.40741i	0.256949	−	0.186685i	−0.451852	−	0.892093i	$-0.649236\pi$
$839$	7.44266	−	5.40741i	0.256949	−	0.186685i	0.708801	+	0.705408i	$0.249236\pi$
$840$	0.0940643	−	1.19041i	0.00324553	−	0.0410729i
$841$	6.60487	−	20.3277i	0.227754	−	0.700955i
$842$			34.3985i			1.18545i
$843$		−	25.5830i		−	0.881126i
$844$	−8.07404	+	24.8493i	−0.277920	+	0.855349i
$845$	9.14262	+	7.81352i	0.314516	+	0.268793i
$846$	−0.695230	−	2.13970i	−0.0239025	−	0.0735643i
$847$	−7.21129	−	9.92549i	−0.247783	−	0.341044i
$848$	2.11076	+	0.685828i	0.0724838	+	0.0235514i
$849$	−3.48438	+	2.53155i	−0.119584	+	0.0868826i
$850$	27.4526	−	13.9660i	0.941616	−	0.479030i
$851$	−15.6179	−	48.0668i	−0.535374	−	1.64771i
$852$	−7.92708	+	10.9107i	−0.271577	+	0.373794i
$853$	9.18302	−	12.6393i	0.314421	−	0.432763i	−0.622333	−	0.782753i	$-0.713815\pi$
$853$	9.18302	−	12.6393i	0.314421	−	0.432763i	0.936753	+	0.349990i	$0.113815\pi$
$854$	0.991811	+	3.05248i	0.0339391	+	0.104454i
$855$	−8.17464	−	0.645949i	−0.279567	−	0.0220910i
$856$	−2.34113	+	1.70093i	−0.0800181	+	0.0581366i
$857$	−39.1013	−	12.7048i	−1.33568	−	0.433987i	−0.447826	−	0.894121i	$-0.647801\pi$
$857$	−39.1013	−	12.7048i	−1.33568	−	0.433987i	−0.887850	+	0.460134i	$0.847801\pi$
$858$	14.6874	+	20.2155i	0.501420	+	0.690145i
$859$	8.91476	+	27.4368i	0.304168	+	0.936132i	0.979986	+	0.199064i	$0.0637902\pi$
$859$	8.91476	+	27.4368i	0.304168	+	0.936132i	−0.675819	+	0.737068i	$0.736210\pi$
$860$	−15.9654	+	18.6812i	−0.544416	+	0.637023i
$861$	1.44308	−	4.44134i	0.0491800	−	0.151360i
$862$		−	6.02650i		−	0.205263i
$863$			7.33664i			0.249742i	0.992173	+	0.124871i	$0.0398517\pi$
$863$			7.33664i			0.249742i	−0.992173	+	0.124871i	$0.960148\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−1.51220	+	19.1373i	−0.0514165	+	0.650688i
$866$	23.4574	−	17.0428i	0.797114	−	0.579138i
$867$			20.9477i			0.711423i
$868$	0.563663	−	2.91941i	0.0191320	−	0.0990913i
$869$	12.0848			0.409950
$870$	−6.07795	+	14.6604i	−0.206062	+	0.497034i
$871$	9.27473	+	6.73849i	0.314262	+	0.228325i
$872$	19.6495	+	6.38450i	0.665415	+	0.216207i
$873$			0.434790i			0.0147154i
$874$	22.1900			0.750588
$875$	−1.39929	+	5.80430i	−0.0473046	+	0.196221i
$876$	−0.00923734	−	0.0284296i	−0.000312101	−	0.000960547i
$877$	−24.3188	+	7.90165i	−0.821187	+	0.266820i	−0.689328	−	0.724449i	$-0.742094\pi$
$877$	−24.3188	+	7.90165i	−0.821187	+	0.266820i	−0.131858	+	0.991269i	$0.542094\pi$
$878$	22.1919	+	30.5446i	0.748942	+	1.03083i
$879$	8.25836	−	25.4166i	0.278548	−	0.857281i
$880$	−4.99145	+	12.0397i	−0.168262	+	0.405858i
$881$	−28.7408	−	20.8814i	−0.968303	−	0.703513i	−0.0132387	−	0.999912i	$-0.504214\pi$
$881$	−28.7408	−	20.8814i	−0.968303	−	0.703513i	−0.955064	+	0.296399i	$0.904214\pi$
$882$	6.38617	−	2.07499i	0.215034	−	0.0698686i
$883$	−16.9401	+	23.3160i	−0.570079	+	0.784647i	−0.992564	−	0.121723i	$-0.961158\pi$
$883$	−16.9401	+	23.3160i	−0.570079	+	0.784647i	0.422485	+	0.906370i	$0.361158\pi$
$884$	−21.3651	−	15.5227i	−0.718586	−	0.522083i
$885$	−1.11731	+	1.30737i	−0.0375581	+	0.0439468i
$886$	−10.0857	−	7.32768i	−0.338835	−	0.246178i
$887$	18.7187	+	25.7641i	0.628512	+	0.865073i	0.997938	−	0.0641876i	$-0.0204456\pi$
$887$	18.7187	+	25.7641i	0.628512	+	0.865073i	−0.369426	+	0.929260i	$0.620446\pi$
$888$	7.94371	+	2.58107i	0.266574	+	0.0866150i
$889$	1.99950	−	1.45272i	0.0670612	−	0.0487228i
$890$	−4.75335	+	5.56191i	−0.159333	+	0.186436i
$891$	−1.80117	−	5.54343i	−0.0603414	−	0.185712i
$892$	−10.0126	−	3.25328i	−0.335246	−	0.108928i
$893$		−	8.25052i		−	0.276093i
$894$	5.44619			0.182148
$895$	−3.53162	−	14.7307i	−0.118049	−	0.492393i
$896$	−0.432036	−	0.313892i	−0.0144333	−	0.0104864i
$897$	15.2474	+	20.9862i	0.509095	+	0.700709i
$898$			24.1944i			0.807376i
$899$	−19.1147	+	34.5864i	−0.637510	+	1.15352i
$900$	2.27276	−	4.45360i	0.0757586	−	0.148453i
$901$	11.0607	−	8.03608i	0.368486	−	0.267721i
$902$	−29.9596	+	41.2359i	−0.997546	+	1.37300i
$903$	5.58160	+	1.81357i	0.185744	+	0.0603519i
$904$	−16.7419			−0.556826
$905$	−5.22193	+	3.19774i	−0.173583	+	0.106297i
$906$	−5.58587	+	17.1915i	−0.185578	+	0.571151i
$907$	−54.4510	+	17.6922i	−1.80802	+	0.587460i	−0.999999	−	0.00169738i	$-0.999460\pi$
$907$	−54.4510	+	17.6922i	−1.80802	+	0.587460i	−0.808018	+	0.589158i	$0.799460\pi$
$908$	3.45357	−	1.12213i	0.114611	−	0.0372393i
$909$	−15.6630	+	11.3799i	−0.519510	+	0.377446i
$910$	4.97813	−	1.19348i	0.165023	−	0.0395636i
$911$	−14.7520	+	10.7180i	−0.488756	+	0.355102i	−0.804706	−	0.593674i	$-0.797677\pi$
$911$	−14.7520	+	10.7180i	−0.488756	+	0.355102i	0.315950	+	0.948776i	$0.397677\pi$
$912$	−2.15553	+	2.96683i	−0.0713767	+	0.0982417i
$913$	0.0810571	−	0.0263371i	0.00268260	−	0.000871630i
$914$	5.89826	+	4.28534i	0.195097	+	0.141746i
$915$	−1.05864	+	13.3973i	−0.0349975	+	0.442902i
$916$	−2.39250	−	7.36336i	−0.0790504	−	0.243292i
$917$	−1.18241	+	1.62745i	−0.0390466	+	0.0537431i
$918$	3.62086	+	4.98369i	0.119506	+	0.164486i
$919$	2.00903	−	6.18316i	0.0662718	−	0.203964i	−0.912437	−	0.409217i	$-0.865802\pi$
$919$	2.00903	−	6.18316i	0.0662718	−	0.203964i	0.978709	+	0.205253i	$0.0658019\pi$
$920$	−5.18175	+	12.4987i	−0.170837	+	0.412071i
$921$	0.564595	+	1.73765i	0.0186041	+	0.0572574i
$922$	11.8851	−	3.86172i	0.391416	−	0.127179i
$923$	−54.9864	−	17.8662i	−1.80990	−	0.588072i
$924$	3.11268			0.102400
$925$	−37.1988	−	18.9832i	−1.22309	−	0.624165i
$926$	2.04825	−	6.30387i	0.0673097	−	0.207158i
$927$	3.75062	−	5.16228i	0.123186	−	0.169552i
$928$	4.17178	+	5.74196i	0.136945	+	0.188489i
$929$	57.5346			1.88765			0.943825	−	0.330446i	$-0.107199\pi$
$929$	57.5346			1.88765			0.943825	+	0.330446i	$0.107199\pi$
$930$	6.86176	−	10.3883i	0.225006	−	0.340645i
$931$	24.6246			0.807039
$932$	0.754045	+	1.03785i	0.0246996	+	0.0339960i
$933$	10.2869	−	14.1586i	0.336777	−	0.463533i
$934$	−6.64510	+	20.4515i	−0.217434	+	0.669194i
$935$	41.9287	+	68.4699i	1.37122	+	2.23920i
$936$	−4.28701			−0.140125
$937$	11.1861	+	3.63457i	0.365432	+	0.118736i	0.485977	−	0.873972i	$-0.338464\pi$
$937$	11.1861	+	3.63457i	0.365432	+	0.118736i	−0.120544	+	0.992708i	$0.538464\pi$
$938$	1.35818	−	0.441300i	0.0443462	−	0.0144089i
$939$	−6.02491	−	18.5428i	−0.196616	−	0.605121i
$940$	4.64718	+	1.92664i	0.151574	+	0.0628401i
$941$	−4.26103	+	13.1141i	−0.138906	+	0.427508i	−0.996177	−	0.0873571i	$-0.972158\pi$
$941$	−4.26103	+	13.1141i	−0.138906	+	0.427508i	0.857271	+	0.514865i	$0.172158\pi$
$942$	7.97293	+	10.9738i	0.259772	+	0.357546i
$943$	−31.1019	+	42.8080i	−1.01282	+	1.39402i
$944$	0.237666	+	0.731462i	0.00773538	+	0.0238071i
$945$	−1.19041	−	0.0940643i	−0.0387239	−	0.00305991i
$946$	−51.8227	−	37.6514i	−1.68490	−	1.22415i
$947$	8.67441	−	2.81849i	0.281880	−	0.0915885i	−0.164665	−	0.986350i	$-0.552654\pi$
$947$	8.67441	−	2.81849i	0.281880	−	0.0915885i	0.446545	+	0.894761i	$0.352654\pi$
$948$	−1.21867	+	1.67736i	−0.0395807	+	0.0544781i
$949$	0.103676	−	0.0753247i	0.00336545	−	0.00244514i
$950$	12.9737	−	12.9574i	0.420922	−	0.420392i
$951$	26.4564	−	19.2217i	0.857908	−	0.623307i
$952$	−3.12868	+	1.01657i	−0.101401	+	0.0329472i
$953$	22.2728	−	7.23688i	0.721487	−	0.234425i	0.0748194	−	0.997197i	$-0.476162\pi$
$953$	22.2728	−	7.23688i	0.721487	−	0.234425i	0.646668	+	0.762772i	$0.276162\pi$
$954$	0.685828	−	2.11076i	0.0222045	−	0.0683384i
$955$	7.78596	−	4.76787i	0.251948	−	0.154285i
$956$	7.77259			0.251383
$957$	−39.3442	−	12.7837i	−1.27182	−	0.413238i
$958$	3.31967	−	4.56913i	0.107254	−	0.147622i
$959$	−6.10954	+	4.43884i	−0.197287	+	0.143338i
$960$	−1.16774	−	1.90693i	−0.0376887	−	0.0615459i
$961$	19.8666	−	23.7975i	0.640857	−	0.767660i
$962$			35.8073i			1.15447i
$963$	1.70093	+	2.34113i	0.0548117	+	0.0754418i
$964$	1.25449	+	0.911441i	0.0404044	+	0.0293555i
$965$	55.9775	−	13.4204i	1.80198	−	0.432017i
$966$	3.23135			0.103967
$967$			33.4583i			1.07595i	0.842962	+	0.537973i	$0.180810\pi$
$967$			33.4583i			1.07595i	−0.842962	+	0.537973i	$0.819190\pi$
$968$	−21.8494	−	7.09929i	−0.702265	−	0.228180i
$969$	6.98089	+	21.4850i	0.224258	+	0.690197i
$970$	−0.739084	−	0.631640i	−0.0237306	−	0.0202807i
$971$	−46.2753	+	33.6210i	−1.48504	+	1.07895i	−0.509157	+	0.860674i	$0.670043\pi$
$971$	−46.2753	+	33.6210i	−1.48504	+	1.07895i	−0.975888	+	0.218274i	$0.929957\pi$
$972$	0.951057	+	0.309017i	0.0305052	+	0.00991172i
$973$	2.76559	+	3.80651i	0.0886607	+	0.122031i
$974$	11.6809	+	8.48667i	0.374280	+	0.271931i
$975$	21.1690	+	3.36651i	0.677952	+	0.107815i
$976$	4.86231	+	3.53267i	0.155639	+	0.113078i
$977$	24.6286	−	33.8984i	0.787940	−	1.08451i	−0.206422	−	0.978463i	$-0.566182\pi$
$977$	24.6286	−	33.8984i	0.787940	−	1.08451i	0.994362	−	0.106043i	$-0.0338181\pi$
$978$	21.4518	−	6.97010i	0.685952	−	0.222879i
$979$	−15.4291	−	11.2099i	−0.493115	−	0.358269i
$980$	−5.75028	+	13.8700i	−0.183686	+	0.443062i
$981$	6.38450	−	19.6495i	0.203841	−	0.627360i
$982$	3.58179	+	4.92991i	0.114299	+	0.157320i
$983$	29.5116	−	9.58888i	0.941272	−	0.305838i	0.202108	−	0.979363i	$-0.435221\pi$
$983$	29.5116	−	9.58888i	0.941272	−	0.305838i	0.739164	+	0.673525i	$0.235221\pi$
$984$	−2.70226	−	8.31672i	−0.0861450	−	0.265127i
$985$	0.779146	−	0.186797i	0.0248257	−	0.00595184i
$986$	43.7215			1.39238
$987$		−	1.20146i		−	0.0382428i
$988$	−14.9519	−	4.85816i	−0.475683	−	0.154559i
$989$	−53.7985	−	39.0869i	−1.71069	−	1.24289i
$990$	12.0397	+	4.99145i	0.382647	+	0.158639i
$991$	42.9410			1.36407			0.682033	−	0.731322i	$-0.261096\pi$
$991$	42.9410			1.36407			0.682033	+	0.731322i	$0.261096\pi$
$992$	−2.35939	−	5.04314i	−0.0749107	−	0.160120i
$993$		−	0.640268i		−	0.0203183i
$994$	−5.82659	+	4.23326i	−0.184808	+	0.134271i
$995$	26.8519	+	2.12180i	0.851263	+	0.0672656i
$996$	−0.00451851	+	0.0139065i	−0.000143175	+	0.000440646i
$997$			12.6895i			0.401881i	0.979603	+	0.200941i	$0.0643998\pi$
$997$			12.6895i			0.401881i	−0.979603	+	0.200941i	$0.935600\pi$
$998$			18.0027i			0.569867i
$999$	2.58107	−	7.94371i	0.0816614	−	0.251328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.d.109.2	✓	72
5.4	even	2	inner	930.2.z.d.109.11	yes	72
31.2	even	5	inner	930.2.z.d.529.11	yes	72
155.64	even	10	inner	930.2.z.d.529.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.109.2	✓	72	1.1	even	1	trivial
930.2.z.d.109.11	yes	72	5.4	even	2	inner
930.2.z.d.529.2	yes	72	155.64	even	10	inner
930.2.z.d.529.11	yes	72	31.2	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)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.90693 + 1.16774i) q^{5} +1.00000 q^{6} +(0.507889 + 0.165023i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.587785 + 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.90693 + 1.16774i) q^{5} +1.00000 q^{6} +(0.507889 + 0.165023i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(2.06559 + 0.856357i) q^{10} +(-1.80117 + 5.54343i) q^{11} +(-0.587785 - 0.809017i) q^{12} +(2.51984 - 3.46826i) q^{13} +(-0.165023 - 0.507889i) q^{14} +(0.176142 - 2.22912i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.85867 + 1.90360i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(-2.96683 + 2.15553i) q^{19} +(-0.521315 - 2.17445i) q^{20} +(-0.432036 + 0.313892i) q^{21} +(5.54343 - 1.80117i) q^{22} +(5.75478 - 1.86984i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(2.27276 - 4.45360i) q^{25} -4.28701 q^{26} +(0.951057 + 0.309017i) q^{27} +(-0.313892 + 0.432036i) q^{28} +(5.74196 - 4.17178i) q^{29} +(-1.90693 + 1.16774i) q^{30} +(-5.04314 + 2.35939i) q^{31} +1.00000i q^{32} +(-3.42603 - 4.71552i) q^{33} +(4.98369 + 3.62086i) q^{34} +(-1.16121 + 0.278396i) q^{35} +1.00000 q^{36} -8.35251i q^{37} +(3.48772 + 1.13323i) q^{38} +(1.32476 + 4.07719i) q^{39} +(-1.45275 + 1.69986i) q^{40} +(-7.07462 + 5.14001i) q^{41} +(0.507889 + 0.165023i) q^{42} +(-6.45965 - 8.89095i) q^{43} +(-4.71552 - 3.42603i) q^{44} +(1.69986 + 1.45275i) q^{45} +(-4.89531 - 3.55665i) q^{46} +(-1.32241 + 1.82014i) q^{47} +(0.951057 - 0.309017i) q^{48} +(-5.43240 - 3.94687i) q^{49} +(-4.93893 + 0.779062i) q^{50} +(1.90360 - 5.85867i) q^{51} +(2.51984 + 3.46826i) q^{52} +(-2.11076 + 0.685828i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(-3.03859 - 12.6742i) q^{55} +0.534026 q^{56} -3.66721i q^{57} +(-6.75008 - 2.19323i) q^{58} +(-0.622219 - 0.452069i) q^{59} +(2.06559 + 0.856357i) q^{60} -6.01014 q^{61} +(4.87307 + 2.69317i) q^{62} -0.534026i q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.755122 + 9.55626i) q^{65} +(-1.80117 + 5.54343i) q^{66} +2.67417i q^{67} -6.16017i q^{68} +(-1.86984 + 5.75478i) q^{69} +(0.907770 + 0.775803i) q^{70} +(-4.16751 - 12.8263i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(0.0284296 + 0.00923734i) q^{73} +(-6.75733 + 4.90948i) q^{74} +(2.26715 + 4.45646i) q^{75} +(-1.13323 - 3.48772i) q^{76} +(-1.82959 + 2.51821i) q^{77} +(2.51984 - 3.46826i) q^{78} +(-0.640695 - 1.97185i) q^{79} +(2.22912 + 0.176142i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(8.31672 + 2.70226i) q^{82} +(-0.00859472 - 0.0118296i) q^{83} +(-0.165023 - 0.507889i) q^{84} +(8.94916 - 10.4714i) q^{85} +(-3.39604 + 10.4519i) q^{86} +7.09745i q^{87} +5.82870i q^{88} +(-1.01110 + 3.11184i) q^{89} +(0.176142 - 2.22912i) q^{90} +(1.85214 - 1.34566i) q^{91} +6.05093i q^{92} +(1.05550 - 5.46680i) q^{93} +2.24981 q^{94} +(3.14044 - 7.57494i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-0.413510 - 0.134358i) q^{97} +6.71482i q^{98} +5.82870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

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