LMFDB - Embedded newform 930.2.y.b.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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([5, 5, 3]))

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (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:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	930.29
Dual form			930.2.y.b.449.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-1.11267 + 1.32739i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.20040 + 0.397802i) q^{5} +(-1.68039 + 0.419865i) q^{6} +(4.23373 - 1.37562i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.523911 - 2.95390i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-1.11267 + 1.32739i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.20040 + 0.397802i) q^{5} +(-1.68039 + 0.419865i) q^{6} +(4.23373 - 1.37562i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.523911 - 2.95390i) q^{9} +(-2.01398 - 0.971534i) q^{10} +(-1.74615 - 5.37411i) q^{11} +(-1.60626 - 0.648031i) q^{12} +(5.38800 - 3.91461i) q^{13} +(4.23373 + 1.37562i) q^{14} +(1.92029 - 3.36340i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.37063 - 0.445344i) q^{17} +(1.31240 - 2.69770i) q^{18} +(-2.24391 - 1.63029i) q^{19} +(-1.05829 - 1.96978i) q^{20} +(-2.88478 + 7.15041i) q^{21} +(1.74615 - 5.37411i) q^{22} +(5.33835 + 1.73454i) q^{23} +(-0.918585 - 1.46840i) q^{24} +(4.68351 - 1.75064i) q^{25} +6.65993 q^{26} +(4.50391 + 2.59129i) q^{27} +(2.61659 + 3.60142i) q^{28} +(-0.775562 - 0.563479i) q^{29} +(3.53051 - 1.59233i) q^{30} +(-5.56474 + 0.183353i) q^{31} -1.00000 q^{32} +(9.07642 + 3.66181i) q^{33} +(-0.847094 - 1.16592i) q^{34} +(-8.76867 + 4.71110i) q^{35} +(2.64743 - 1.41107i) q^{36} -6.77784 q^{37} +(-0.857097 - 2.63787i) q^{38} +(-0.798887 + 11.5076i) q^{39} +(0.301629 - 2.21563i) q^{40} +(2.05639 - 2.83037i) q^{41} +(-6.53674 + 4.08918i) q^{42} +(6.32988 + 4.59893i) q^{43} +(4.57149 - 3.32138i) q^{44} +(2.32788 + 6.29134i) q^{45} +(3.29928 + 4.54108i) q^{46} +(-5.85456 + 4.25358i) q^{47} +(0.119954 - 1.72789i) q^{48} +(10.3690 - 7.53352i) q^{49} +(4.81804 + 1.33660i) q^{50} +(2.11620 - 1.32383i) q^{51} +(5.38800 + 3.91461i) q^{52} +(5.27393 + 1.71360i) q^{53} +(2.12061 + 4.74373i) q^{54} +(5.98006 + 11.1306i) q^{55} +4.45161i q^{56} +(4.66077 - 1.16455i) q^{57} +(-0.296238 - 0.911728i) q^{58} +(-5.35910 - 7.37616i) q^{59} +(3.79219 + 0.786956i) q^{60} -3.02037i q^{61} +(-4.60975 - 3.12254i) q^{62} +(-6.28154 - 11.7853i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-10.2985 + 10.7571i) q^{65} +(5.19062 + 8.29745i) q^{66} -11.2740i q^{67} -1.44116i q^{68} +(-8.24225 + 5.15609i) q^{69} +(-9.86311 - 1.34273i) q^{70} +(11.6189 + 3.77519i) q^{71} +(2.97122 + 0.414536i) q^{72} +(1.62888 + 5.01318i) q^{73} +(-5.48339 - 3.98392i) q^{74} +(-2.88744 + 8.16472i) q^{75} +(0.857097 - 2.63787i) q^{76} +(-14.7855 - 20.3505i) q^{77} +(-7.41034 + 8.84031i) q^{78} +(9.48156 + 3.08075i) q^{79} +(1.54634 - 1.61519i) q^{80} +(-8.45103 + 3.09516i) q^{81} +(3.32730 - 1.08111i) q^{82} +(5.59084 - 7.69513i) q^{83} +(-7.69189 - 0.533989i) q^{84} +(3.19308 + 0.434696i) q^{85} +(2.41780 + 7.44122i) q^{86} +(1.61090 - 0.402502i) q^{87} +5.65067 q^{88} +(1.01650 + 3.12845i) q^{89} +(-1.81466 + 6.45810i) q^{90} +(17.4263 - 23.9853i) q^{91} +5.61308i q^{92} +(5.94837 - 7.59058i) q^{93} -7.23663 q^{94} +(5.58603 + 2.69467i) q^{95} +(1.11267 - 1.32739i) q^{96} +(-2.59765 + 0.844027i) q^{97} +12.8168 q^{98} +(-14.9597 + 7.97352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	$ 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) $ 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−1.11267	+	1.32739i	−0.642403	+	0.766367i
$3$	−1.11267	+	1.32739i	−0.642403	+	0.766367i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.20040	+	0.397802i	−0.984048	+	0.177902i
$5$	−2.20040	+	0.397802i	−0.984048	+	0.177902i
$6$	−1.68039	+	0.419865i	−0.686017	+	0.171409i
$7$	4.23373	−	1.37562i	1.60020	−	0.519936i	0.633042	−	0.774117i	$-0.281806\pi$
$7$	4.23373	−	1.37562i	1.60020	−	0.519936i	0.967157	+	0.254181i	$0.0818059\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.523911	−	2.95390i	−0.174637	−	0.984633i
$10$	−2.01398	−	0.971534i	−0.636877	−	0.307226i
$11$	−1.74615	−	5.37411i	−0.526485	−	1.62035i	−0.761360	−	0.648329i	$-0.775468\pi$
$11$	−1.74615	−	5.37411i	−0.526485	−	1.62035i	0.234875	−	0.972026i	$-0.424532\pi$
$12$	−1.60626	−	0.648031i	−0.463686	−	0.187070i
$13$	5.38800	−	3.91461i	1.49436	−	1.08572i	0.521802	−	0.853066i	$-0.325260\pi$
$13$	5.38800	−	3.91461i	1.49436	−	1.08572i	0.972560	−	0.232651i	$-0.0747401\pi$
$14$	4.23373	+	1.37562i	1.13151	+	0.367650i
$15$	1.92029	−	3.36340i	0.495817	−	0.868427i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.37063	−	0.445344i	−0.332426	−	0.108012i	0.138048	−	0.990425i	$-0.455917\pi$
$17$	−1.37063	−	0.445344i	−0.332426	−	0.108012i	−0.470474	+	0.882414i	$0.655917\pi$
$18$	1.31240	−	2.69770i	0.309337	−	0.635854i
$19$	−2.24391	−	1.63029i	−0.514788	−	0.374015i	0.299849	−	0.953987i	$-0.403064\pi$
$19$	−2.24391	−	1.63029i	−0.514788	−	0.374015i	−0.814637	+	0.579971i	$0.803064\pi$
$20$	−1.05829	−	1.96978i	−0.236641	−	0.440455i
$21$	−2.88478	+	7.15041i	−0.629510	+	1.56035i
$22$	1.74615	−	5.37411i	0.372281	−	1.14576i
$23$	5.33835	+	1.73454i	1.11312	+	0.361676i	0.807140	−	0.590361i	$-0.201015\pi$
$23$	5.33835	+	1.73454i	1.11312	+	0.361676i	0.305984	+	0.952037i	$0.401015\pi$
$24$	−0.918585	−	1.46840i	−0.187505	−	0.299736i
$25$	4.68351	−	1.75064i	0.936702	−	0.350129i
$26$	6.65993			1.30612
$27$	4.50391	+	2.59129i	0.866778	+	0.498695i
$28$	2.61659	+	3.60142i	0.494489	+	0.680605i
$29$	−0.775562	−	0.563479i	−0.144018	−	0.104635i	0.513443	−	0.858124i	$-0.328370\pi$
$29$	−0.775562	−	0.563479i	−0.144018	−	0.104635i	−0.657461	+	0.753488i	$0.728370\pi$
$30$	3.53051	−	1.59233i	0.644579	−	0.290719i
$31$	−5.56474	+	0.183353i	−0.999458	+	0.0329312i
$31$	−5.56474	+	0.183353i	−0.999458	+	0.0329312i
$32$	−1.00000			−0.176777
$33$	9.07642	+	3.66181i	1.58000	+	0.637440i
$34$	−0.847094	−	1.16592i	−0.145275	−	0.199954i
$35$	−8.76867	+	4.71110i	−1.48217	+	0.796321i
$36$	2.64743	−	1.41107i	0.441238	−	0.235179i
$37$	−6.77784			−1.11427			−0.557135	−	0.830422i	$-0.688100\pi$
$37$	−6.77784			−1.11427			−0.557135	+	0.830422i	$0.688100\pi$
$38$	−0.857097	−	2.63787i	−0.139039	−	0.427919i
$39$	−0.798887	+	11.5076i	−0.127924	+	1.84270i
$40$	0.301629	−	2.21563i	0.0476917	−	0.350322i
$41$	2.05639	−	2.83037i	0.321154	−	0.442030i	−0.617665	−	0.786441i	$-0.711921\pi$
$41$	2.05639	−	2.83037i	0.321154	−	0.442030i	0.938819	+	0.344411i	$0.111921\pi$
$42$	−6.53674	+	4.08918i	−1.00864	+	0.630974i
$43$	6.32988	+	4.59893i	0.965297	+	0.701330i	0.954375	−	0.298611i	$-0.0965232\pi$
$43$	6.32988	+	4.59893i	0.965297	+	0.701330i	0.0109224	+	0.999940i	$0.496523\pi$
$44$	4.57149	−	3.32138i	0.689178	−	0.500717i
$45$	2.32788	+	6.29134i	0.347020	+	0.937858i
$46$	3.29928	+	4.54108i	0.486453	+	0.669545i
$47$	−5.85456	+	4.25358i	−0.853975	+	0.620449i	−0.926239	−	0.376937i	$-0.876977\pi$
$47$	−5.85456	+	4.25358i	−0.853975	+	0.620449i	0.0722643	+	0.997386i	$0.476977\pi$
$48$	0.119954	−	1.72789i	0.0173139	−	0.249400i
$49$	10.3690	−	7.53352i	1.48129	−	1.07622i
$50$	4.81804	+	1.33660i	0.681374	+	0.189023i
$51$	2.11620	−	1.32383i	0.296328	−	0.185373i
$52$	5.38800	+	3.91461i	0.747181	+	0.542859i
$53$	5.27393	+	1.71360i	0.724431	+	0.235382i	0.647943	−	0.761689i	$-0.275629\pi$
$53$	5.27393	+	1.71360i	0.724431	+	0.235382i	0.0764875	+	0.997071i	$0.475629\pi$
$54$	2.12061	+	4.74373i	0.288579	+	0.645540i
$55$	5.98006	+	11.1306i	0.806352	+	1.50084i
$56$			4.45161i			0.594871i
$57$	4.66077	−	1.16455i	0.617334	−	0.154248i
$58$	−0.296238	−	0.911728i	−0.0388980	−	0.119716i
$59$	−5.35910	−	7.37616i	−0.697695	−	0.960294i	−0.999975	−	0.00707535i	$-0.997748\pi$
$59$	−5.35910	−	7.37616i	−0.697695	−	0.960294i	0.302280	−	0.953219i	$-0.402252\pi$
$60$	3.79219	+	0.786956i	0.489570	+	0.101596i
$61$		−	3.02037i		−	0.386719i	−0.981128	−	0.193359i	$-0.938062\pi$
$61$		−	3.02037i		−	0.386719i	0.981128	−	0.193359i	$-0.0619383\pi$
$62$	−4.60975	−	3.12254i	−0.585438	−	0.396563i
$63$	−6.28154	−	11.7853i	−0.791400	−	1.48481i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−10.2985	+	10.7571i	−1.27737	+	1.33425i
$66$	5.19062	+	8.29745i	0.638921	+	1.02135i
$67$		−	11.2740i		−	1.37734i	−0.725074	−	0.688671i	$-0.758194\pi$
$67$		−	11.2740i		−	1.37734i	0.725074	−	0.688671i	$-0.241806\pi$
$68$		−	1.44116i		−	0.174767i
$69$	−8.24225	+	5.15609i	−0.992250	+	0.620720i
$70$	−9.86311	−	1.34273i	−1.17887	−	0.160487i
$71$	11.6189	+	3.77519i	1.37890	+	0.448033i	0.902309	−	0.431090i	$-0.141871\pi$
$71$	11.6189	+	3.77519i	1.37890	+	0.448033i	0.476595	+	0.879123i	$0.341871\pi$
$72$	2.97122	+	0.414536i	0.350162	+	0.0488535i
$73$	1.62888	+	5.01318i	0.190646	+	0.586749i	1.00000		0.000572905i	$-0.000182361\pi$
$73$	1.62888	+	5.01318i	0.190646	+	0.586749i	−0.809354	+	0.587322i	$0.800182\pi$
$74$	−5.48339	−	3.98392i	−0.637431	−	0.463121i
$75$	−2.88744	+	8.16472i	−0.333413	+	0.942781i
$76$	0.857097	−	2.63787i	0.0983157	−	0.302585i
$77$	−14.7855	−	20.3505i	−1.68496	−	2.31915i
$78$	−7.41034	+	8.84031i	−0.839056	+	1.00097i
$79$	9.48156	+	3.08075i	1.06676	+	0.346611i	0.789224	−	0.614105i	$-0.210483\pi$
$79$	9.48156	+	3.08075i	1.06676	+	0.346611i	0.277534	+	0.960716i	$0.410483\pi$
$80$	1.54634	−	1.61519i	0.172886	−	0.180584i
$81$	−8.45103	+	3.09516i	−0.939004	+	0.343907i
$82$	3.32730	−	1.08111i	0.367439	−	0.119388i
$83$	5.59084	−	7.69513i	0.613674	−	0.844650i	−0.383199	−	0.923666i	$-0.625178\pi$
$83$	5.59084	−	7.69513i	0.613674	−	0.844650i	0.996873	+	0.0790158i	$0.0251778\pi$
$84$	−7.69189	−	0.533989i	−0.839254	−	0.0582629i
$85$	3.19308	+	0.434696i	0.346339	+	0.0471494i
$86$	2.41780	+	7.44122i	0.260718	+	0.802407i
$87$	1.61090	−	0.402502i	0.172707	−	0.0431528i
$88$	5.65067			0.602364
$89$	1.01650	+	3.12845i	0.107748	+	0.331615i	0.990366	−	0.138477i	$-0.0442206\pi$
$89$	1.01650	+	3.12845i	0.107748	+	0.331615i	−0.882617	+	0.470092i	$0.844221\pi$
$90$	−1.81466	+	6.45810i	−0.191282	+	0.680743i
$91$	17.4263	−	23.9853i	1.82677	−	2.51434i
$92$			5.61308i			0.585204i
$93$	5.94837	−	7.59058i	0.616817	−	0.787107i
$94$	−7.23663			−0.746401
$95$	5.58603	+	2.69467i	0.573114	+	0.276467i
$96$	1.11267	−	1.32739i	0.113562	−	0.135476i
$97$	−2.59765	+	0.844027i	−0.263751	+	0.0856979i	−0.437907	−	0.899020i	$-0.644280\pi$
$97$	−2.59765	+	0.844027i	−0.263751	+	0.0856979i	0.174156	+	0.984718i	$0.444280\pi$
$98$	12.8168			1.29469
$99$	−14.9597	+	7.97352i	−1.50351	+	0.801369i
$100$	3.11225	+	3.91330i	0.311225	+	0.391330i
$101$	−8.82368	−	2.86699i	−0.877989	−	0.285276i	−0.164867	−	0.986316i	$-0.552720\pi$
$101$	−8.82368	−	2.86699i	−0.877989	−	0.285276i	−0.713122	+	0.701040i	$0.752720\pi$
$102$	2.49017	+	0.172873i	0.246564	+	0.0171170i
$103$	−0.719470	+	0.990266i	−0.0708915	+	0.0975738i	−0.842990	−	0.537929i	$-0.819207\pi$
$103$	−0.719470	+	0.990266i	−0.0708915	+	0.0975738i	0.772099	+	0.635502i	$0.219207\pi$
$104$	2.05803	+	6.33397i	0.201807	+	0.621097i
$105$	3.50322	−	16.8813i	0.341879	−	1.64745i
$106$	3.25947	+	4.48628i	0.316588	+	0.435746i
$107$	0.369442	−	1.13702i	0.0357153	−	0.109920i	−0.931610	−	0.363461i	$-0.881595\pi$
$107$	0.369442	−	1.13702i	0.0357153	−	0.109920i	0.967325	+	0.253540i	$0.0815951\pi$
$108$	−1.07268	+	5.08423i	−0.103219	+	0.489230i
$109$	−2.38751	+	1.73463i	−0.228682	+	0.166147i	−0.696226	−	0.717823i	$-0.745139\pi$
$109$	−2.38751	+	1.73463i	−0.228682	+	0.166147i	0.467544	+	0.883970i	$0.345139\pi$
$110$	−1.70441	+	12.5198i	−0.162509	+	1.19372i
$111$	7.54153	−	8.99682i	0.715811	−	0.853940i
$112$	−2.61659	+	3.60142i	−0.247244	+	0.340303i
$113$	1.79079	+	5.51149i	0.168463	+	0.518477i	0.999275	−	0.0380769i	$-0.0121232\pi$
$113$	1.79079	+	5.51149i	0.168463	+	0.518477i	−0.830811	+	0.556554i	$0.812123\pi$
$114$	4.45515	+	1.79739i	0.417263	+	0.168341i
$115$	−12.4365	−	1.69307i	−1.15971	−	0.157879i
$116$	0.296238	−	0.911728i	0.0275050	−	0.0846518i
$117$	−14.3862	−	13.8647i	−1.33000	−	1.28179i
$118$		−	9.11744i		−	0.839328i
$119$	−6.41549			−0.588107
$120$	2.60538	+	2.86565i	0.237838	+	0.261597i
$121$	−16.9328	+	12.3024i	−1.53935	+	1.11840i
$122$	1.77533	−	2.44353i	0.160731	−	0.221227i
$123$	1.46891	+	5.87891i	0.132447	+	0.530083i
$124$	−1.89398	−	5.23573i	−0.170084	−	0.470182i
$125$	−9.60917	+	5.71522i	−0.859471	+	0.511185i
$126$	1.84535	−	13.2267i	0.164397	−	1.17833i
$127$	−0.454031	+	0.329873i	−0.0402887	+	0.0292715i	−0.607747	−	0.794130i	$-0.707927\pi$
$127$	−0.454031	+	0.329873i	−0.0402887	+	0.0292715i	0.567459	+	0.823402i	$0.307927\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−13.1476	+	3.28509i	−1.15759	+	0.289236i
$130$	−14.6545	+	2.64933i	−1.28529	+	0.232362i
$131$	10.0862	−	3.27719i	0.881232	−	0.286330i	0.166763	−	0.985997i	$-0.446668\pi$
$131$	10.0862	−	3.27719i	0.881232	−	0.286330i	0.714469	+	0.699667i	$0.246668\pi$
$132$	−0.677822	+	9.76375i	−0.0589968	+	0.849825i
$133$	−11.7428	−	3.81546i	−1.01823	−	0.330842i
$134$	6.62671	−	9.12089i	0.572461	−	0.787925i
$135$	−10.9412	−	3.91022i	−0.941670	−	0.336538i
$136$	0.847094	−	1.16592i	0.0726377	−	0.0999772i
$137$	5.29228	+	7.28420i	0.452150	+	0.622332i	0.972858	−	0.231404i	$-0.0743318\pi$
$137$	5.29228	+	7.28420i	0.452150	+	0.622332i	−0.520707	+	0.853735i	$0.674332\pi$
$138$	−9.69879	−	0.673312i	−0.825616	−	0.0573161i
$139$	2.99755	+	4.12578i	0.254249	+	0.349944i	0.916994	−	0.398902i	$-0.130608\pi$
$139$	2.99755	+	4.12578i	0.254249	+	0.349944i	−0.662745	+	0.748846i	$0.730608\pi$
$140$	−7.19019	−	6.88369i	−0.607682	−	0.581778i
$141$	0.868064	−	12.5041i	0.0731042	−	1.05304i
$142$	7.18085	+	9.88359i	0.602603	+	0.829412i
$143$	−30.4458	−	22.1202i	−2.54601	−	1.84978i
$144$	2.16011	+	2.08181i	0.180009	+	0.173484i
$145$	1.93070	+	0.931358i	0.160336	+	0.0773451i
$146$	−1.62888	+	5.01318i	−0.134807	+	0.414894i
$147$	−1.53743	+	22.1460i	−0.126805	+	1.82657i
$148$	−2.09447	−	6.44611i	−0.172164	−	0.529867i
$149$			4.37794i			0.358655i	0.983789	+	0.179327i	$0.0573921\pi$
$149$			4.37794i			0.358655i	−0.983789	+	0.179327i	$0.942608\pi$
$150$	−7.13509	+	4.90821i	−0.582578	+	0.400753i
$151$	−11.2851	+	3.66674i	−0.918365	+	0.298395i	−0.729796	−	0.683665i	$-0.760385\pi$
$151$	−11.2851	+	3.66674i	−0.918365	+	0.298395i	−0.188569	+	0.982060i	$0.560385\pi$
$152$	2.24391	−	1.63029i	0.182005	−	0.132234i
$153$	−0.597413	+	4.28201i	−0.0482980	+	0.346180i
$154$		−	25.1546i		−	2.02701i
$155$	12.1717	−	2.61711i	0.977656	−	0.210212i
$156$	−11.1913	+	2.79627i	−0.896021	+	0.223881i
$157$	−3.03247	+	4.17384i	−0.242018	+	0.333109i	−0.912696	−	0.408640i	$-0.866003\pi$
$157$	−3.03247	+	4.17384i	−0.242018	+	0.333109i	0.670678	+	0.741748i	$0.266003\pi$
$158$	5.85993	+	8.06550i	0.466191	+	0.641656i
$159$	−8.14279	+	5.09387i	−0.645765	+	0.403970i
$160$	2.20040	−	0.397802i	0.173957	−	0.0314490i
$161$	24.9872			1.96927
$162$	−8.65632	−	2.46336i	−0.680105	−	0.193539i
$163$	−5.29480	−	1.72038i	−0.414721	−	0.134751i	0.0942222	−	0.995551i	$-0.469964\pi$
$163$	−5.29480	−	1.72038i	−0.414721	−	0.134751i	−0.508943	+	0.860800i	$0.669964\pi$
$164$	3.32730	+	1.08111i	0.259819	+	0.0844203i
$165$	−21.4284	−	4.44683i	−1.66820	−	0.346185i
$166$	9.04616	−	2.93928i	0.702118	−	0.228132i
$167$	3.75787	−	5.17226i	0.290793	−	0.400242i	−0.638479	−	0.769640i	$-0.720436\pi$
$167$	3.75787	−	5.17226i	0.290793	−	0.400242i	0.929271	+	0.369398i	$0.120436\pi$
$168$	−5.90900	−	4.95319i	−0.455889	−	0.382147i
$169$	9.68914	−	29.8201i	0.745319	−	2.29386i
$170$	2.32775	+	2.22852i	0.178530	+	0.170920i
$171$	−3.64012	+	7.48241i	−0.278367	+	0.572194i
$172$	−2.41780	+	7.44122i	−0.184355	+	0.567388i
$173$	−4.01164	+	2.91463i	−0.305000	+	0.221595i	−0.729748	−	0.683716i	$-0.760363\pi$
$173$	−4.01164	+	2.91463i	−0.305000	+	0.221595i	0.424748	+	0.905311i	$0.360363\pi$
$174$	1.53983	+	0.621233i	0.116734	+	0.0470956i
$175$	17.4205	−	13.8545i	1.31686	−	1.04730i
$176$	4.57149	+	3.32138i	0.344589	+	0.250359i
$177$	15.7539	+	1.09367i	1.18414	+	0.0822056i
$178$	−1.01650	+	3.12845i	−0.0761896	+	0.234488i
$179$	−3.57442	−	11.0009i	−0.267165	−	0.822249i	−0.991187	−	0.132472i	$-0.957709\pi$
$179$	−3.57442	−	11.0009i	−0.267165	−	0.822249i	0.724022	−	0.689777i	$-0.242291\pi$
$180$	−5.26407	+	4.15808i	−0.392360	+	0.309925i
$181$			17.4586i			1.29769i	0.760921	+	0.648845i	$0.224748\pi$
$181$			17.4586i			1.29769i	−0.760921	+	0.648845i	$0.775252\pi$
$182$	28.1964	−	9.16155i	2.09005	−	0.679099i
$183$	4.00920	+	3.36069i	0.296368	+	0.248429i
$184$	−3.29928	+	4.54108i	−0.243226	+	0.334773i
$185$	14.9140	−	2.69624i	1.09650	−	0.198231i
$186$	9.27396	−	2.64455i	0.680000	−	0.193907i
$187$			8.14353i			0.595514i
$188$	−5.85456	−	4.25358i	−0.426987	−	0.310224i
$189$	22.6330	+	4.77516i	1.64631	+	0.347342i
$190$	2.93530	+	5.46342i	0.212949	+	0.396358i
$191$		−	19.9315i		−	1.44219i	−0.692837	−	0.721095i	$-0.743639\pi$
$191$		−	19.9315i		−	1.44219i	0.692837	−	0.721095i	$-0.256361\pi$
$192$	1.68039	−	0.419865i	0.121272	−	0.0303011i
$193$	3.66952	−	1.19230i	0.264138	−	0.0858237i	−0.173954	−	0.984754i	$-0.555654\pi$
$193$	3.66952	−	1.19230i	0.264138	−	0.0858237i	0.438092	+	0.898930i	$0.355654\pi$
$194$	−2.59765	−	0.844027i	−0.186500	−	0.0605976i
$195$	−2.81989	−	25.6392i	−0.201937	−	1.83606i
$196$	10.3690	+	7.53352i	0.740643	+	0.538109i
$197$	−13.3199	+	4.32788i	−0.949000	+	0.308349i	−0.742309	−	0.670057i	$-0.766269\pi$
$197$	−13.3199	+	4.32788i	−0.949000	+	0.308349i	−0.206691	+	0.978406i	$0.566269\pi$
$198$	−16.7894	−	2.34241i	−1.19317	−	0.166467i
$199$	4.75455	+	6.54407i	0.337041	+	0.463897i	0.943574	−	0.331161i	$-0.107440\pi$
$199$	4.75455	+	6.54407i	0.337041	+	0.463897i	−0.606533	+	0.795058i	$0.707440\pi$
$200$	0.217678	+	4.99526i	0.0153922	+	0.353218i
$201$	14.9650	+	12.5443i	1.05555	+	0.884809i
$202$	−5.45334	−	7.50587i	−0.383695	−	0.528111i
$203$	−4.05865	−	1.31874i	−0.284862	−	0.0925571i
$204$	1.91298	+	1.60354i	0.133935	+	0.112271i
$205$	−3.39894	+	7.04599i	−0.237393	+	0.492113i
$206$	−1.16413	+	0.378248i	−0.0811086	+	0.0263538i
$207$	2.32682	−	16.6777i	0.161725	−	1.15918i
$208$	−2.05803	+	6.33397i	−0.142699	+	0.439182i
$209$	−4.84317	+	14.9058i	−0.335009	+	1.03105i
$210$	12.7568	−	11.5981i	0.880300	−	0.800348i
$211$	27.2090			1.87315			0.936574	−	0.350471i	$-0.113978\pi$
$211$	27.2090			1.87315			0.936574	+	0.350471i	$0.113978\pi$
$212$			5.54534i			0.380856i
$213$	−17.9391	+	11.2222i	−1.22917	+	0.768929i
$214$	0.967211	−	0.702720i	0.0661172	−	0.0480369i
$215$	−15.7577	−	7.60143i	−1.07467	−	0.518414i
$216$	−3.85625	+	3.48272i	−0.262385	+	0.236969i
$217$	−23.3074	+	8.43125i	−1.58221	+	0.572351i
$218$	−2.95113			−0.199875
$219$	−8.46685	−	3.41588i	−0.572137	−	0.230824i
$220$	−8.73785	+	9.12691i	−0.589106	+	0.615336i
$221$	−9.12828	+	2.96596i	−0.614035	+	0.199512i
$222$	11.3894	−	2.84578i	0.764408	−	0.190996i
$223$	−0.364375			−0.0244004			−0.0122002	−	0.999926i	$-0.503884\pi$
$223$	−0.364375			−0.0244004			−0.0122002	+	0.999926i	$0.503884\pi$
$224$	−4.23373	+	1.37562i	−0.282878	+	0.0919126i
$225$	−7.62497	−	12.9174i	−0.508331	−	0.861162i
$226$	−1.79079	+	5.51149i	−0.119122	+	0.366619i
$227$	11.3356	+	8.23581i	0.752372	+	0.546630i	0.896561	−	0.442920i	$-0.146057\pi$
$227$	11.3356	+	8.23581i	0.752372	+	0.546630i	−0.144189	+	0.989550i	$0.546057\pi$
$228$	2.54781	+	4.07279i	0.168733	+	0.269727i
$229$	6.35796	−	8.75098i	0.420146	−	0.578281i	−0.545511	−	0.838104i	$-0.683664\pi$
$229$	6.35796	−	8.75098i	0.420146	−	0.578281i	0.965656	+	0.259823i	$0.0836642\pi$
$230$	−9.06619	−	8.67971i	−0.597807	−	0.572323i
$231$	43.4644	+	3.01739i	2.85975	+	0.198530i
$232$	0.775562	−	0.563479i	0.0509181	−	0.0369942i
$233$	13.2655	−	9.63794i	0.869051	−	0.631402i	−0.0612813	−	0.998121i	$-0.519519\pi$
$233$	13.2655	−	9.63794i	0.869051	−	0.631402i	0.930332	+	0.366718i	$0.119519\pi$
$234$	−3.48921	−	19.6728i	−0.228097	−	1.28605i
$235$	11.1903	−	11.6885i	0.729973	−	0.762476i
$236$	5.35910	−	7.37616i	0.348847	−	0.480147i
$237$	−14.6392	+	9.15783i	−0.950920	+	0.594865i
$238$	−5.19024	−	3.77093i	−0.336433	−	0.244433i
$239$	−1.75540	+	5.40257i	−0.113547	+	0.349463i	−0.991641	−	0.129025i	$-0.958815\pi$
$239$	−1.75540	+	5.40257i	−0.113547	+	0.349463i	0.878094	+	0.478488i	$0.158815\pi$
$240$	0.423411	+	3.84977i	0.0273311	+	0.248502i
$241$	−16.3387	+	5.30876i	−1.05247	+	0.341968i	−0.783636	−	0.621220i	$-0.786637\pi$
$241$	−16.3387	+	5.30876i	−1.05247	+	0.341968i	−0.268831	+	0.963187i	$0.586637\pi$
$242$	−20.9301			−1.34544
$243$	5.29477	−	14.6617i	0.339660	−	0.940548i
$244$	2.87254	−	0.933345i	0.183896	−	0.0597513i
$245$	−19.8191	+	20.7016i	−1.26620	+	1.32257i
$246$	−2.26716	+	5.61954i	−0.144549	+	0.358289i
$247$	−18.4721			−1.17535
$248$	1.54522	−	5.34905i	0.0981217	−	0.339665i
$249$	3.99363	+	15.9834i	0.253086	+	1.01291i
$250$	−11.1333	−	1.02442i	−0.704132	−	0.0647900i
$251$	−11.6246	+	8.44574i	−0.733736	+	0.533090i	−0.890743	−	0.454507i	$-0.849815\pi$
$251$	−11.6246	+	8.44574i	−0.733736	+	0.533090i	0.157007	+	0.987597i	$0.449815\pi$
$252$	9.26738	−	9.61596i	0.583790	−	0.605749i
$253$		−	31.7177i		−	1.99407i
$254$	−0.561213			−0.0352136
$255$	−4.12987	+	3.75478i	−0.258623	+	0.235134i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−9.33501	+	28.7302i	−0.582302	+	1.79214i	0.0275425	+	0.999621i	$0.491232\pi$
$257$	−9.33501	+	28.7302i	−0.582302	+	1.79214i	−0.609845	+	0.792521i	$0.708768\pi$
$258$	−12.5676	−	5.07030i	−0.782424	−	0.315663i
$259$	−28.6955	+	9.32375i	−1.78305	+	0.579349i
$260$	−13.4130	−	6.47035i	−0.831838	−	0.401274i
$261$	−1.25813	+	2.58614i	−0.0778765	+	0.160078i
$262$	10.0862	+	3.27719i	0.623125	+	0.202466i
$263$	18.5302	+	25.5046i	1.14262	+	1.57268i	0.761510	+	0.648153i	$0.224458\pi$
$263$	18.5302	+	25.5046i	1.14262	+	1.57268i	0.381111	+	0.924529i	$0.375542\pi$
$264$	−6.28736	+	7.50063i	−0.386960	+	0.461632i
$265$	−12.2864	−	1.67263i	−0.754749	−	0.102749i
$266$	−7.25743	−	9.98899i	−0.444982	−	0.612465i
$267$	−5.28370	−	2.13167i	−0.323357	−	0.130456i
$268$	10.7222	−	3.48387i	0.654965	−	0.212811i
$269$	0.0764673	+	0.0555568i	0.00466230	+	0.00338736i	0.590114	−	0.807320i	$-0.299083\pi$
$269$	0.0764673	+	0.0555568i	0.00466230	+	0.00338736i	−0.585452	+	0.810707i	$0.699083\pi$
$270$	−6.55326	−	9.59452i	−0.398819	−	0.583904i
$271$	1.46522	+	0.476080i	0.0890060	+	0.0289198i	0.353181	−	0.935555i	$-0.385100\pi$
$271$	1.46522	+	0.476080i	0.0890060	+	0.0289198i	−0.264176	+	0.964475i	$0.585100\pi$
$272$	1.37063	−	0.445344i	0.0831064	−	0.0270029i
$273$	12.4479	+	49.8192i	0.753381	+	3.01520i
$274$			9.00377i			0.543938i
$275$	−17.5863	−	22.1128i	−1.06049	−	1.33345i
$276$	−7.45073	−	6.24553i	−0.448481	−	0.375937i
$277$	13.9719	+	10.1512i	0.839488	+	0.609924i	0.922228	−	0.386647i	$-0.126367\pi$
$277$	13.9719	+	10.1512i	0.839488	+	0.609924i	−0.0827395	+	0.996571i	$0.526367\pi$
$278$			5.09974i			0.305862i
$279$	3.45704	+	16.3416i	0.206967	+	0.978348i
$280$	−1.77086	−	9.79531i	−0.105829	−	0.585382i
$281$	3.79013	−	5.21667i	0.226100	−	0.311200i	−0.680862	−	0.732411i	$-0.738395\pi$
$281$	3.79013	−	5.21667i	0.226100	−	0.311200i	0.906963	+	0.421211i	$0.138395\pi$
$282$	8.05201	−	9.60581i	0.479490	−	0.572017i
$283$	−2.08257	+	0.676669i	−0.123796	+	0.0402238i	−0.370260	−	0.928928i	$-0.620731\pi$
$283$	−2.08257	+	0.676669i	−0.123796	+	0.0402238i	0.246464	+	0.969152i	$0.420731\pi$
$284$			12.2168i			0.724933i
$285$	−9.79229	+	4.41653i	−0.580045	+	0.261613i
$286$	−11.6293	−	35.7912i	−0.687653	−	2.11638i
$287$	4.81266	−	14.8118i	0.284082	−	0.874316i
$288$	0.523911	+	2.95390i	0.0308718	+	0.174060i
$289$	−12.0730	−	8.77155i	−0.710177	−	0.515974i
$290$	1.01453	+	1.88832i	0.0595752	+	0.110886i
$291$	1.76999	−	4.38721i	0.103758	−	0.257183i
$292$	−4.26447	+	3.09832i	−0.249559	+	0.181315i
$293$	−4.43572	+	13.6517i	−0.259138	+	0.797543i	0.733849	+	0.679313i	$0.237722\pi$
$293$	−4.43572	+	13.6517i	−0.259138	+	0.797543i	−0.992986	+	0.118230i	$0.962278\pi$
$294$	−14.2609	+	17.0128i	−0.831713	+	0.992209i
$295$	14.7264	+	14.0986i	0.857404	+	0.820855i
$296$	2.09447	−	6.44611i	0.121739	−	0.374673i
$297$	6.06138	−	28.7293i	0.351717	−	1.66704i
$298$	−2.57329	+	3.54183i	−0.149067	+	0.205172i
$299$	35.5531	−	11.5519i	2.05609	−	0.668064i
$300$	−8.65738	−	0.223078i	−0.499834	−	0.0128794i
$301$	33.1254	+	10.7631i	1.90931	+	0.620374i
$302$	−11.2851	−	3.66674i	−0.649382	−	0.210997i
$303$	13.6235	−	8.52242i	0.782649	−	0.489600i
$304$	2.77362			0.159078
$305$	1.20151	+	6.64601i	0.0687981	+	0.380550i
$306$	−3.00022	+	3.11307i	−0.171511	+	0.177962i
$307$	−11.2237	−	15.4481i	−0.640570	−	0.881670i	0.358075	−	0.933693i	$-0.383433\pi$
$307$	−11.2237	−	15.4481i	−0.640570	−	0.881670i	−0.998646	+	0.0520231i	$0.983433\pi$
$308$	14.7855	−	20.3505i	0.842481	−	1.15958i
$309$	−0.513930	−	2.05686i	−0.0292364	−	0.117011i
$310$	11.3854	+	5.03707i	0.646649	+	0.286086i
$311$		−	29.1782i		−	1.65454i	−0.561802	−	0.827272i	$-0.689892\pi$
$311$		−	29.1782i		−	1.65454i	0.561802	−	0.827272i	$-0.310108\pi$
$312$	−10.6976	−	4.31585i	−0.605630	−	0.244337i
$313$	−22.8245	+	16.5830i	−1.29012	+	0.937326i	−0.999808	−	0.0196063i	$-0.993759\pi$
$313$	−22.8245	+	16.5830i	−1.29012	+	0.937326i	−0.290311	+	0.956932i	$0.593759\pi$
$314$	−4.90664	+	1.59426i	−0.276898	+	0.0899695i
$315$	18.5101	+	23.4335i	1.04293	+	1.32033i
$316$			9.96950i			0.560828i
$317$	−5.10117	−	15.6998i	−0.286510	−	0.881788i	−0.985942	−	0.167088i	$-0.946563\pi$
$317$	−5.10117	−	15.6998i	−0.286510	−	0.881788i	0.699432	−	0.714699i	$-0.253437\pi$
$318$	−9.58175	−	0.665187i	−0.537318	−	0.0373018i
$319$	−1.67395	+	5.15188i	−0.0937230	+	0.288450i
$320$	2.01398	+	0.971534i	0.112585	+	0.0543104i
$321$	1.09820	+	1.75553i	0.0612957	+	0.0979841i
$322$	20.2151	+	14.6871i	1.12654	+	0.818481i
$323$	2.34952	+	3.23384i	0.130731	+	0.179935i
$324$	−5.55519	−	7.08095i	−0.308621	−	0.393386i
$325$	18.3816	−	27.7666i	1.01963	−	1.54021i
$326$	−3.27237	−	4.50402i	−0.181240	−	0.249455i
$327$	0.354000	−	5.09923i	0.0195762	−	0.281988i
$328$	2.05639	+	2.83037i	0.113545	+	0.156281i
$329$	−18.9353	+	26.0622i	−1.04394	+	1.43685i
$330$	−14.7222	−	16.1929i	−0.810429	−	0.891388i
$331$	−0.892592	+	1.22855i	−0.0490613	+	0.0675271i	−0.832843	−	0.553510i	$-0.813288\pi$
$331$	−0.892592	+	1.22855i	−0.0490613	+	0.0675271i	0.783781	+	0.621037i	$0.213288\pi$
$332$	9.04616	+	2.93928i	0.496473	+	0.161314i
$333$	3.55099	+	20.0211i	0.194593	+	1.09715i
$334$	6.08036	−	1.97563i	0.332703	−	0.108102i
$335$	4.48483	+	24.8074i	0.245032	+	1.35537i
$336$	−1.86907	−	7.48044i	−0.101966	−	0.408091i
$337$	2.95041	+	9.08043i	0.160719	+	0.494643i	0.998695	−	0.0510641i	$-0.0162613\pi$
$337$	2.95041	+	9.08043i	0.160719	+	0.494643i	−0.837976	+	0.545707i	$0.816261\pi$
$338$	25.3665	−	18.4298i	1.37976	−	1.00245i
$339$	−9.30845	−	3.75542i	−0.505565	−	0.203966i
$340$	0.573297	+	3.17113i	0.0310914	+	0.171979i
$341$	10.7023	+	29.5854i	0.579560	+	1.60214i
$342$	−7.34296	+	3.91379i	−0.397062	+	0.211633i
$343$	15.2201	−	20.9487i	0.821811	−	1.13113i
$344$	−6.32988	+	4.59893i	−0.341284	+	0.247957i
$345$	16.0851	−	14.6242i	0.865995	−	0.787342i
$346$	−4.95866			−0.266579
$347$			16.5865i			0.890408i	0.895429	+	0.445204i	$0.146869\pi$
$347$			16.5865i			0.890408i	−0.895429	+	0.445204i	$0.853131\pi$
$348$	0.880599	+	1.40768i	0.0472050	+	0.0754595i
$349$	−0.615980	+	1.89579i	−0.0329727	+	0.101479i	−0.966188	−	0.257837i	$-0.916990\pi$
$349$	−0.615980	+	1.89579i	−0.0329727	+	0.101479i	0.933216	+	0.359317i	$0.116990\pi$
$350$	22.2369	−	0.969017i	1.18861	−	0.0517961i
$351$	34.4110	−	3.66916i	1.83672	−	0.195845i
$352$	1.74615	+	5.37411i	0.0930703	+	0.286441i
$353$	−2.67666	+	3.68411i	−0.142464	+	0.196085i	−0.874286	−	0.485410i	$-0.838670\pi$
$353$	−2.67666	+	3.68411i	−0.142464	+	0.196085i	0.731822	+	0.681496i	$0.238670\pi$
$354$	12.1024	+	10.1447i	0.643233	+	0.539187i
$355$	−27.0679	−	3.68493i	−1.43661	−	0.195576i
$356$	−2.66122	+	1.93349i	−0.141044	+	0.102475i
$357$	7.13835	−	8.51583i	0.377801	−	0.450706i
$358$	3.57442	−	11.0009i	0.188914	−	0.581418i
$359$	−13.5789	−	18.6897i	−0.716666	−	0.986406i	−0.999628	−	0.0272753i	$-0.991317\pi$
$359$	−13.5789	−	18.6897i	−0.716666	−	0.986406i	0.282962	−	0.959131i	$-0.408683\pi$
$360$	−6.70278	+	0.269813i	−0.353267	+	0.0142204i
$361$	−3.49406	−	10.7536i	−0.183898	−	0.565980i
$362$	−10.2619	+	14.1243i	−0.539355	+	0.742358i
$363$	2.51065	−	36.1649i	0.131775	−	1.89817i
$364$	28.1964	+	9.16155i	1.47789	+	0.480196i
$365$	−5.57844	−	10.3830i	−0.291989	−	0.543473i
$366$	1.26815	+	5.07540i	0.0662871	+	0.265295i
$367$	1.39911			0.0730328			0.0365164	−	0.999333i	$-0.488374\pi$
$367$	1.39911			0.0730328			0.0365164	+	0.999333i	$0.488374\pi$
$368$	−5.33835	+	1.73454i	−0.278281	+	0.0904190i
$369$	−9.43800	−	4.59150i	−0.491323	−	0.239024i
$370$	13.6505	+	6.58490i	0.709653	+	0.342333i
$371$	24.6857			1.28162
$372$	9.05722	+	3.31162i	0.469595	+	0.171699i
$373$			27.1642i			1.40651i	0.710938	+	0.703255i	$0.248271\pi$
$373$			27.1642i			1.40651i	−0.710938	+	0.703255i	$0.751729\pi$
$374$	−4.78665	+	6.58826i	−0.247512	+	0.340671i
$375$	3.10557	−	19.1143i	0.160371	−	0.987057i
$376$	−2.23624	−	6.88244i	−0.115325	−	0.354935i
$377$	−6.38453			−0.328820
$378$	15.5037	+	17.1665i	0.797423	+	0.882950i
$379$	−6.70098	−	20.6235i	−0.344206	−	1.05936i	−0.962007	−	0.273024i	$-0.911976\pi$
$379$	−6.70098	−	20.6235i	−0.344206	−	1.05936i	0.617801	−	0.786335i	$-0.288024\pi$
$380$	−0.836604	+	6.14532i	−0.0429169	+	0.315249i
$381$	0.0673198	−	0.969716i	0.00344890	−	0.0496800i
$382$	11.7154	−	16.1249i	0.599413	−	0.825021i
$383$	31.3851	−	10.1976i	1.60370	−	0.521075i	0.635684	−	0.771950i	$-0.280718\pi$
$383$	31.3851	−	10.1976i	1.60370	−	0.521075i	0.968019	+	0.250875i	$0.0807183\pi$
$384$	1.60626	+	0.648031i	0.0819689	+	0.0330697i
$385$	40.6294	+	38.8975i	2.07067	+	1.98240i
$386$	3.66952	+	1.19230i	0.186774	+	0.0606865i
$387$	10.2685	−	21.1072i	0.521975	−	1.07294i
$388$	−1.60543	−	2.20969i	−0.0815036	−	0.112180i
$389$	−9.90695	+	30.4905i	−0.502302	+	1.54593i	0.302957	+	0.953004i	$0.402026\pi$
$389$	−9.90695	+	30.4905i	−0.502302	+	1.54593i	−0.805259	+	0.592923i	$0.797974\pi$
$390$	12.7890	−	22.4000i	0.647597	−	1.13427i
$391$	−6.54443	−	4.75480i	−0.330966	−	0.240461i
$392$	3.96061	+	12.1895i	0.200041	+	0.615662i
$393$	−6.87251	+	17.0347i	−0.346672	+	0.859286i
$394$	−13.3199	−	4.32788i	−0.671045	−	0.218036i
$395$	−22.0887	−	3.00709i	−1.11140	−	0.151303i
$396$	−12.2061	−	11.7636i	−0.613379	−	0.591144i
$397$		−	6.31579i		−	0.316980i	−0.987361	−	0.158490i	$-0.949337\pi$
$397$		−	6.31579i		−	0.316980i	0.987361	−	0.158490i	$-0.0506626\pi$
$398$			8.08892i			0.405461i
$399$	18.1305	−	11.3418i	0.907658	−	0.567802i
$400$	−2.76003	+	4.16920i	−0.138002	+	0.208460i
$401$	11.2973	+	8.20797i	0.564160	+	0.409887i	0.832979	−	0.553304i	$-0.186633\pi$
$401$	11.2973	+	8.20797i	0.564160	+	0.409887i	−0.268819	+	0.963191i	$0.586633\pi$
$402$	4.73357	+	18.9448i	0.236089	+	0.944880i
$403$	−29.2651	+	22.7717i	−1.45780	+	1.13434i
$404$		−	9.27777i		−	0.461586i
$405$	17.3644	−	10.1724i	0.862843	−	0.505472i
$406$	−2.50839	−	3.45250i	−0.124489	−	0.171345i
$407$	11.8352	+	36.4249i	0.586647	+	1.80551i
$408$	0.605093	+	2.42172i	0.0299566	+	0.119893i
$409$			20.0159i			0.989720i	0.868973	+	0.494860i	$0.164781\pi$
$409$			20.0159i			0.989720i	−0.868973	+	0.494860i	$0.835219\pi$
$410$	−6.89133	+	3.70247i	−0.340339	+	0.182852i
$411$	−15.5575	−	1.08004i	−0.767397	−	0.0532744i
$412$	−1.16413	−	0.378248i	−0.0573524	−	0.0186349i
$413$	−32.8358	−	23.8566i	−1.61574	−	1.17391i
$414$	11.6853	−	12.1249i	0.574303	−	0.595905i
$415$	−9.24094	+	19.1564i	−0.453620	+	0.940350i
$416$	−5.38800	+	3.91461i	−0.264168	+	0.191930i
$417$	−8.81181	−	0.611735i	−0.431516	−	0.0299568i
$418$	−12.6796	+	9.21226i	−0.620179	+	0.450586i
$419$	5.21803	+	7.18200i	0.254917	+	0.350864i	0.917226	−	0.398368i	$-0.130423\pi$
$419$	5.21803	+	7.18200i	0.254917	+	0.350864i	−0.662308	+	0.749231i	$0.730423\pi$
$420$	17.1377	−	1.88486i	0.836232	−	0.0919717i
$421$	−22.8495	+	16.6012i	−1.11362	+	0.809091i	−0.983230	−	0.182372i	$-0.941623\pi$
$421$	−22.8495	+	16.6012i	−1.11362	+	0.809091i	−0.130389	+	0.991463i	$0.541623\pi$
$422$	22.0126	+	15.9931i	1.07156	+	0.778530i
$423$	15.6319	+	15.0653i	0.760050	+	0.732498i
$424$	−3.25947	+	4.48628i	−0.158294	+	0.217873i
$425$	−7.19898	+	0.313709i	−0.349202	+	0.0152171i
$426$	−21.1093	−	1.46545i	−1.02275	−	0.0710015i
$427$	−4.15488	−	12.7874i	−0.201069	−	0.618827i
$428$	1.19554			0.0577885
$429$	63.2383	−	15.8008i	3.05318	−	0.762871i
$430$	−8.28025	−	15.4118i	−0.399309	−	0.743225i
$431$	1.40838	+	1.93846i	0.0678391	+	0.0933725i	0.841588	−	0.540119i	$-0.181621\pi$
$431$	1.40838	+	1.93846i	0.0678391	+	0.0933725i	−0.773749	+	0.633492i	$0.781621\pi$
$432$	−5.16686	+	0.550930i	−0.248591	+	0.0265066i
$433$	7.95312			0.382203			0.191101	−	0.981570i	$-0.438794\pi$
$433$	7.95312			0.382203			0.191101	+	0.981570i	$0.438794\pi$
$434$	−23.8118	−	6.87872i	−1.14300	−	0.330189i
$435$	−3.38451	+	1.52649i	−0.162275	+	0.0731894i
$436$	−2.38751	−	1.73463i	−0.114341	−	0.0830736i
$437$	−9.15097	−	12.5952i	−0.437750	−	0.602512i
$438$	−4.84202	−	7.74020i	−0.231361	−	0.369841i
$439$	−9.19317			−0.438766			−0.219383	−	0.975639i	$-0.570404\pi$
$439$	−9.19317			−0.438766			−0.219383	+	0.975639i	$0.570404\pi$
$440$	−12.4337	+	2.24785i	−0.592755	+	0.107162i
$441$	−27.6857	−	26.6821i	−1.31837	−	1.27058i
$442$	−9.12828	−	2.96596i	−0.434188	−	0.141076i
$443$	0.880278	−	2.70922i	0.0418233	−	0.128719i	−0.927965	−	0.372668i	$-0.878443\pi$
$443$	0.880278	−	2.70922i	0.0418233	−	0.128719i	0.969788	+	0.243949i	$0.0784430\pi$
$444$	10.8869	+	4.39225i	0.516672	+	0.208447i
$445$	−3.48120	−	6.47948i	−0.165025	−	0.307157i
$446$	−0.294786	−	0.214174i	−0.0139585	−	0.0101414i
$447$	−5.81122	−	4.87122i	−0.274861	−	0.230401i
$448$	−4.23373	−	1.37562i	−0.200025	−	0.0649920i
$449$	0.992443	−	0.721052i	0.0468363	−	0.0340286i	−0.564121	−	0.825692i	$-0.690785\pi$
$449$	0.992443	−	0.721052i	0.0468363	−	0.0340286i	0.610957	+	0.791664i	$0.290785\pi$
$450$	1.42394	−	14.9323i	0.0671253	−	0.703913i
$451$	−18.8015	−	6.10898i	−0.885328	−	0.287661i
$452$	−4.68835	+	3.40629i	−0.220522	+	0.160218i
$453$	7.68941	−	19.0595i	0.361280	−	0.895494i
$454$	4.32982	+	13.3258i	0.203209	+	0.625412i
$455$	−28.8034	+	59.7093i	−1.35033	+	2.79922i
$456$	−0.332708	+	4.79252i	−0.0155805	+	0.224430i
$457$	7.62272	−	23.4603i	0.356576	−	1.09743i	−0.598514	−	0.801112i	$-0.704242\pi$
$457$	7.62272	−	23.4603i	0.356576	−	1.09743i	0.955090	−	0.296315i	$-0.0957580\pi$
$458$	10.2874	−	3.34258i	0.480698	−	0.156188i
$459$	−5.01916	−	5.55748i	−0.234274	−	0.259401i
$460$	−2.23289	−	12.3510i	−0.104109	−	0.575869i
$461$	2.89750	+	8.91760i	0.134950	+	0.415334i	0.995582	−	0.0938933i	$-0.0299313\pi$
$461$	2.89750	+	8.91760i	0.134950	+	0.415334i	−0.860632	+	0.509227i	$0.829931\pi$
$462$	33.3898	+	27.9888i	1.55344	+	1.30216i
$463$	21.1198	+	15.3444i	0.981518	+	0.713115i	0.958047	−	0.286610i	$-0.0925283\pi$
$463$	21.1198	+	15.3444i	0.981518	+	0.713115i	0.0234709	+	0.999725i	$0.492528\pi$
$464$	0.958648			0.0445041
$465$	−10.0692	+	19.0686i	−0.466950	+	0.884284i
$466$	16.3970			0.759578
$467$	−6.73232	−	4.89132i	−0.311535	−	0.226343i	0.421020	−	0.907051i	$-0.361672\pi$
$467$	−6.73232	−	4.89132i	−0.311535	−	0.226343i	−0.732555	+	0.680708i	$0.761672\pi$
$468$	8.74053	−	17.9665i	0.404031	−	0.830502i
$469$	−15.5088	−	47.7312i	−0.716130	−	2.20402i
$470$	15.9235	−	2.87874i	0.734495	−	0.132787i
$471$	−2.16614	−	8.66939i	−0.0998107	−	0.399464i
$472$	8.67120	−	2.81744i	0.399124	−	0.129683i
$473$	13.6622	−	42.0479i	0.628188	−	1.93336i
$474$	−17.2262	−	1.19588i	−0.791227	−	0.0549287i
$475$	−13.3634	−	3.70721i	−0.613156	−	0.170099i
$476$	−1.98249	−	6.10149i	−0.0908675	−	0.279661i
$477$	2.29874	−	16.4764i	0.105252	−	0.754404i
$478$	−4.59570	+	3.33897i	−0.210202	+	0.152721i
$479$	23.0507	+	7.48963i	1.05321	+	0.342210i	0.783929	−	0.620851i	$-0.213213\pi$
$479$	23.0507	+	7.48963i	1.05321	+	0.342210i	0.269285	+	0.963061i	$0.413213\pi$
$480$	−1.92029	+	3.36340i	−0.0876489	+	0.153518i
$481$	−36.5190	+	26.5326i	−1.66512	+	1.20978i
$482$	−16.3387	−	5.30876i	−0.744207	−	0.241808i
$483$	−27.8026	+	33.1677i	−1.26506	+	1.50918i
$484$	−16.9328	−	12.3024i	−0.769673	−	0.559200i
$485$	5.38010	−	2.89054i	0.244298	−	0.131253i
$486$	12.9015	−	8.74937i	0.585224	−	0.396880i
$487$	3.37085	−	10.3744i	0.152748	−	0.470110i	−0.845178	−	0.534485i	$-0.820506\pi$
$487$	3.37085	−	10.3744i	0.152748	−	0.470110i	0.997926	+	0.0643755i	$0.0205055\pi$
$488$	2.87254	+	0.933345i	0.130034	+	0.0422506i
$489$	8.17500	−	5.11402i	0.369686	−	0.231264i
$490$	−28.2020	+	5.09854i	−1.27404	+	0.230329i
$491$	3.78940			0.171013			0.0855066	−	0.996338i	$-0.472749\pi$
$491$	3.78940			0.171013			0.0855066	+	0.996338i	$0.472749\pi$
$492$	−5.13725	+	3.21370i	−0.231605	+	0.144885i
$493$	0.812064	+	1.11771i	0.0365735	+	0.0503392i
$494$	−14.9443	−	10.8577i	−0.672375	−	0.488509i
$495$	29.7455	−	23.4959i	1.33696	−	1.05606i
$496$	4.39420	−	3.41921i	0.197305	−	0.153527i
$497$	54.3843			2.43947
$498$	−6.16388	+	15.2782i	−0.276210	+	0.684633i
$499$	9.82917	+	13.5287i	0.440014	+	0.605627i	0.970215	−	0.242244i	$-0.0778836\pi$
$499$	9.82917	+	13.5287i	0.440014	+	0.605627i	−0.530201	+	0.847872i	$0.677884\pi$
$500$	−8.40490	−	7.37277i	−0.375878	−	0.329720i
$501$	2.68431	+	10.7432i	0.119926	+	0.479971i
$502$	−14.3687			−0.641309
$503$	7.59199	+	23.3658i	0.338510	+	1.04183i	0.964967	+	0.262371i	$0.0845045\pi$
$503$	7.59199	+	23.3658i	0.338510	+	1.04183i	−0.626457	+	0.779456i	$0.715495\pi$
$504$	13.1496	−	2.33225i	0.585729	−	0.103886i
$505$	20.5561	+	2.79844i	0.914735	+	0.124529i
$506$	18.6432	−	25.6601i	0.828790	−	1.14073i
$507$	28.8020	+	46.0413i	1.27914	+	2.04477i
$508$	−0.454031	−	0.329873i	−0.0201444	−	0.0146357i
$509$	−7.31081	+	5.31162i	−0.324046	+	0.235433i	−0.737900	−	0.674910i	$-0.764182\pi$
$509$	−7.31081	+	5.31162i	−0.324046	+	0.235433i	0.413854	+	0.910343i	$0.364182\pi$
$510$	−5.54814	+	0.610204i	−0.245676	+	0.0270203i
$511$	13.7925	+	18.9837i	0.610144	+	0.839791i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−5.88178	−	13.1573i	−0.259687	−	0.580910i
$514$	−24.4394	+	17.7563i	−1.07797	+	0.783195i
$515$	1.18919	−	2.46519i	0.0524021	−	0.108629i
$516$	−7.18715	−	11.4890i	−0.316397	−	0.505775i
$517$	33.0822	+	24.0356i	1.45495	+	1.05708i
$518$	−28.6955	−	9.32375i	−1.26081	−	0.409662i
$519$	0.594812	−	8.56803i	0.0261094	−	0.376095i
$520$	−7.04816	−	13.1186i	−0.309082	−	0.575288i
$521$			3.66527i			0.160579i	0.996772	+	0.0802893i	$0.0255844\pi$
$521$			3.66527i			0.160579i	−0.996772	+	0.0802893i	$0.974416\pi$
$522$	−2.53795	+	1.35272i	−0.111083	+	0.0592071i
$523$	−3.52719	−	10.8556i	−0.154233	−	0.474681i	0.843849	−	0.536581i	$-0.180284\pi$
$523$	−3.52719	−	10.8556i	−0.154233	−	0.474681i	−0.998082	+	0.0618992i	$0.980284\pi$
$524$	6.23359	+	8.57980i	0.272316	+	0.374810i
$525$	−0.993055	+	38.5392i	−0.0433405	+	1.68199i
$526$			31.5255i			1.37458i
$527$	7.70884	+	2.22691i	0.335802	+	0.0970059i
$528$	−9.49534	+	2.37252i	−0.413232	+	0.103251i
$529$	6.88202	+	5.00008i	0.299218	+	0.217395i
$530$	−8.95678	−	8.57497i	−0.389058	−	0.372473i
$531$	−18.9807	+	19.6947i	−0.823694	+	0.854676i
$532$		−	12.3471i		−	0.535314i
$533$		−	23.3000i		−	1.00924i
$534$	−3.02164	−	4.83023i	−0.130759	−	0.209025i
$535$	−0.360609	+	2.64887i	−0.0155905	+	0.114521i
$536$	10.7222	+	3.48387i	0.463130	+	0.150480i
$537$	18.5797	+	7.49582i	0.801772	+	0.323469i
$538$	0.0292079	+	0.0898927i	0.00125924	+	0.00387555i
$539$	−58.5918	−	42.5695i	−2.52373	−	1.83360i
$540$	0.337818	−	11.6140i	0.0145374	−	0.499789i
$541$	0.410241	−	1.26259i	0.0176377	−	0.0542831i	−0.941850	−	0.336033i	$-0.890915\pi$
$541$	0.410241	−	1.26259i	0.0176377	−	0.0542831i	0.959488	+	0.281750i	$0.0909147\pi$
$542$	0.905558	+	1.24639i	0.0388970	+	0.0535372i
$543$	−23.1744	−	19.4258i	−0.994507	−	0.833640i
$544$	1.37063	+	0.445344i	0.0587651	+	0.0190939i
$545$	4.56344	−	4.76663i	0.195476	−	0.204180i
$546$	−19.2124	+	47.6213i	−0.822217	+	2.03800i
$547$	19.7891	−	6.42988i	0.846122	−	0.274922i	0.146301	−	0.989240i	$-0.453263\pi$
$547$	19.7891	−	6.42988i	0.846122	−	0.274922i	0.699821	+	0.714318i	$0.253263\pi$
$548$	−5.29228	+	7.28420i	−0.226075	+	0.311166i
$549$	−8.92186	+	1.58240i	−0.380776	+	0.0675354i
$550$	−1.23003	−	28.2266i	−0.0524485	−	1.20359i
$551$	0.821654	+	2.52879i	0.0350036	+	0.107730i
$552$	−2.35673	−	9.43216i	−0.100309	−	0.401460i
$553$	44.3803			1.88724
$554$	5.33678	+	16.4249i	0.226738	+	0.697828i
$555$	−13.0154	+	22.7966i	−0.552474	+	0.967663i
$556$	−2.99755	+	4.12578i	−0.127125	+	0.174972i
$557$		−	45.4143i		−	1.92427i	−0.272577	−	0.962134i	$-0.587876\pi$
$557$		−	45.4143i		−	1.92427i	0.272577	−	0.962134i	$-0.412124\pi$
$558$	−6.80857	+	15.2527i	−0.288230	+	0.645696i
$559$	52.1084			2.20395
$560$	4.32488	−	8.96545i	0.182760	−	0.378859i
$561$	−10.8096	−	9.06110i	−0.456383	−	0.382560i
$562$	6.13256	−	1.99259i	0.258686	−	0.0840523i
$563$	−37.4431			−1.57804			−0.789019	−	0.614369i	$-0.789411\pi$
$563$	−37.4431			−1.57804			−0.789019	+	0.614369i	$0.789411\pi$
$564$	12.1604	−	3.03841i	0.512044	−	0.127940i
$565$	−6.13293	−	11.4151i	−0.258014	−	0.480237i
$566$	−2.08257	−	0.676669i	−0.0875370	−	0.0284425i
$567$	−31.5216	+	24.7295i	−1.32378	+	1.03854i
$568$	−7.18085	+	9.88359i	−0.301302	+	0.414706i
$569$	−12.8254	−	39.4726i	−0.537670	−	1.65478i	−0.737808	−	0.675010i	$-0.764139\pi$
$569$	−12.8254	−	39.4726i	−0.537670	−	1.65478i	0.200139	−	0.979768i	$-0.435861\pi$
$570$	−10.5181	−	2.18272i	−0.440555	−	0.0914241i
$571$	−3.38564	−	4.65993i	−0.141684	−	0.195012i	0.732277	−	0.681007i	$-0.238457\pi$
$571$	−3.38564	−	4.65993i	−0.141684	−	0.195012i	−0.873962	+	0.485995i	$0.838457\pi$
$572$	11.6293	−	35.7912i	0.486244	−	1.49651i
$573$	26.4567	+	22.1772i	1.10525	+	0.926467i
$574$	12.5997	−	9.15423i	0.525902	−	0.382090i
$575$	28.0388	−	1.22184i	1.16930	−	0.0509544i
$576$	−1.31240	+	2.69770i	−0.0546835	+	0.112404i
$577$	−25.2255	+	34.7200i	−1.05015	+	1.44541i	−0.161476	+	0.986877i	$0.551625\pi$
$577$	−25.2255	+	34.7200i	−1.05015	+	1.44541i	−0.888677	+	0.458534i	$0.848375\pi$
$578$	−4.61148	−	14.1927i	−0.191812	−	0.590337i
$579$	−2.50034	+	6.19752i	−0.103911	+	0.257560i
$580$	−0.289156	+	2.12401i	−0.0120065	+	0.0881947i
$581$	13.0845	−	40.2700i	0.542837	−	1.67068i
$582$	4.01068	−	2.50896i	0.166248	−	0.104000i
$583$		−	31.3349i		−	1.29776i
$584$	−5.27117			−0.218123
$585$	37.1708	+	24.7850i	1.53682	+	1.02473i
$586$	−11.6129	+	8.43724i	−0.479723	+	0.348539i
$587$	−22.9929	+	31.6470i	−0.949018	+	1.30621i	0.00294410	+	0.999996i	$0.499063\pi$
$587$	−22.9929	+	31.6470i	−0.949018	+	1.30621i	−0.951962	+	0.306216i	$0.900937\pi$
$588$	−21.5372	+	5.38132i	−0.888180	+	0.221922i
$589$	12.7857	+	8.66075i	0.526825	+	0.356860i
$590$	3.62693	+	20.0620i	0.149318	+	0.825939i
$591$	9.07589	−	22.4961i	0.373332	−	0.925367i
$592$	5.48339	−	3.98392i	0.225366	−	0.163738i
$593$	−4.70492	−	14.4803i	−0.193208	−	0.594633i	−0.999993	−	0.00378775i	$-0.998794\pi$
$593$	−4.70492	−	14.4803i	−0.193208	−	0.594633i	0.806785	−	0.590845i	$-0.201206\pi$
$594$	21.7904	−	19.6797i	0.894072	−	0.807468i
$595$	14.1166	−	2.55209i	0.578725	−	0.104626i
$596$	−4.16367	+	1.35286i	−0.170550	+	0.0554152i
$597$	−13.9768	−	0.970299i	−0.572031	−	0.0397117i
$598$	35.5531	+	11.5519i	1.45387	+	0.472392i
$599$	−14.1248	+	19.4412i	−0.577125	+	0.794345i	−0.993376	−	0.114905i	$-0.963344\pi$
$599$	−14.1248	+	19.4412i	−0.577125	+	0.794345i	0.416251	+	0.909250i	$0.363344\pi$
$600$	−6.87285	−	5.26915i	−0.280583	−	0.215112i
$601$	−15.9947	+	22.0148i	−0.652438	+	0.898003i	−0.999202	−	0.0399489i	$-0.987280\pi$
$601$	−15.9947	+	22.0148i	−0.652438	+	0.898003i	0.346764	+	0.937952i	$0.387280\pi$
$602$	20.4726	+	28.1781i	0.834401	+	1.14845i
$603$	−33.3024	+	5.90659i	−1.35618	+	0.240535i
$604$	−6.97455	−	9.59964i	−0.283790	−	0.390604i
$605$	32.3650	−	33.8061i	1.31582	−	1.37441i
$606$	16.0310	+	1.11291i	0.651214	+	0.0452088i
$607$	6.20209	+	8.53645i	0.251735	+	0.346484i	0.916118	−	0.400909i	$-0.131306\pi$
$607$	6.20209	+	8.53645i	0.251735	+	0.346484i	−0.664383	+	0.747392i	$0.731306\pi$
$608$	2.24391	+	1.63029i	0.0910025	+	0.0661172i
$609$	6.26643	−	3.92008i	0.253929	−	0.158850i
$610$	−2.93439	+	6.08297i	−0.118810	+	0.246292i
$611$	−14.8932	+	45.8366i	−0.602515	+	1.85435i
$612$	−4.25705	+	0.755041i	−0.172081	+	0.0305207i
$613$	10.3306	+	31.7944i	0.417250	+	1.28416i	0.910223	+	0.414119i	$0.135910\pi$
$613$	10.3306	+	31.7944i	0.417250	+	1.28416i	−0.492973	+	0.870045i	$0.664090\pi$
$614$		−	19.0949i		−	0.770607i
$615$	−5.57083	−	12.3516i	−0.224638	−	0.498065i
$616$	23.9234	−	7.77319i	0.963902	−	0.313191i
$617$	1.03239	−	0.750072i	0.0415623	−	0.0301967i	−0.566810	−	0.823848i	$-0.691823\pi$
$617$	1.03239	−	0.750072i	0.0415623	−	0.0301967i	0.608372	+	0.793652i	$0.291823\pi$
$618$	0.793214	−	1.96611i	0.0319077	−	0.0790887i
$619$			1.52113i			0.0611394i	0.999533	+	0.0305697i	$0.00973215\pi$
$619$			1.52113i			0.0611394i	−0.999533	+	0.0305697i	$0.990268\pi$
$620$	6.25029	+	10.7673i	0.251018	+	0.432424i
$621$	19.5488	+	21.6454i	0.784465	+	0.868602i
$622$	17.1505	−	23.6057i	0.687673	−	0.946500i
$623$	8.60714	+	11.8467i	0.344838	+	0.474628i
$624$	−6.11771	−	9.77946i	−0.244905	−	0.391492i
$625$	18.8705	−	16.3983i	0.754820	−	0.655932i
$626$	−28.2127			−1.12761
$627$	−14.3968	−	23.0140i	−0.574954	−	0.919091i
$628$	−4.90664	−	1.59426i	−0.195796	−	0.0636181i
$629$	9.28989	+	3.01847i	0.370412	+	0.120354i
$630$	1.20110	+	29.8381i	0.0478530	+	1.18878i
$631$	−0.154916	+	0.0503352i	−0.00616711	+	0.00200381i	−0.312099	−	0.950050i	$-0.601032\pi$
$631$	−0.154916	+	0.0503352i	−0.00616711	+	0.00200381i	0.305932	+	0.952053i	$0.401032\pi$
$632$	−5.85993	+	8.06550i	−0.233095	+	0.320828i
$633$	−30.2748	+	36.1169i	−1.20332	+	1.43552i
$634$	5.10117	−	15.6998i	0.202593	−	0.623518i
$635$	0.867825	−	0.906466i	0.0344386	−	0.0359720i
$636$	−7.36081	−	6.17016i	−0.291875	−	0.244663i
$637$	26.3774	−	81.1812i	1.04511	−	3.21652i
$638$	−4.38245	+	3.18403i	−0.173503	+	0.126057i
$639$	5.06429	−	36.2988i	0.200340	−	1.43596i
$640$	1.05829	+	1.96978i	0.0418327	+	0.0778622i
$641$	−1.35330	−	0.983233i	−0.0534523	−	0.0388354i	0.560738	−	0.827993i	$-0.310517\pi$
$641$	−1.35330	−	0.983233i	−0.0534523	−	0.0388354i	−0.614191	+	0.789158i	$0.710517\pi$
$642$	−0.143410	+	2.06576i	−0.00565993	+	0.0815291i
$643$	−4.49377	+	13.8304i	−0.177217	+	0.545418i	−0.999728	−	0.0233317i	$-0.992573\pi$
$643$	−4.49377	+	13.8304i	−0.177217	+	0.545418i	0.822511	+	0.568750i	$0.192573\pi$
$644$	7.72147	+	23.7642i	0.304269	+	0.936442i
$645$	27.6233	−	12.4587i	1.08766	−	0.490559i
$646$			3.99724i			0.157269i
$647$	18.1098	−	5.88424i	0.711970	−	0.231333i	0.0694319	−	0.997587i	$-0.477881\pi$
$647$	18.1098	−	5.88424i	0.711970	−	0.231333i	0.642538	+	0.766254i	$0.277881\pi$
$648$	−0.332160	−	8.99387i	−0.0130485	−	0.353313i
$649$	−30.2825	+	41.6803i	−1.18869	+	1.63609i
$650$	31.1919	−	11.6592i	1.22345	−	0.457311i
$651$	14.7420	−	40.3192i	0.577785	−	1.58023i
$652$		−	5.56728i		−	0.218032i
$653$	−0.233244	−	0.169461i	−0.00912753	−	0.00663154i	0.583212	−	0.812320i	$-0.301796\pi$
$653$	−0.233244	−	0.169461i	−0.00912753	−	0.00663154i	−0.592340	+	0.805688i	$0.701796\pi$
$654$	3.28364	−	3.91729i	0.128401	−	0.153178i
$655$	−20.8899	+	11.2234i	−0.816236	+	0.438535i
$656$			3.49854i			0.136595i
$657$	13.9550	−	7.43802i	0.544438	−	0.290185i
$658$	−30.6379	+	9.95486i	−1.19439	+	0.388081i
$659$	27.6182	+	8.97368i	1.07585	+	0.349565i	0.792764	−	0.609529i	$-0.208641\pi$
$659$	27.6182	+	8.97368i	1.07585	+	0.349565i	0.283087	+	0.959094i	$0.408641\pi$
$660$	−2.39256	−	21.7538i	−0.0931302	−	0.846765i
$661$	21.7423	+	15.7967i	0.845679	+	0.614422i	0.923951	−	0.382510i	$-0.124940\pi$
$661$	21.7423	+	15.7967i	0.845679	+	0.614422i	−0.0782723	+	0.996932i	$0.524940\pi$
$662$	−1.44424	+	0.469263i	−0.0561321	+	0.0182384i
$663$	6.21983	−	15.4169i	0.241558	−	0.598743i
$664$	5.59084	+	7.69513i	0.216967	+	0.298629i
$665$	27.3566	+	3.72423i	1.06084	+	0.144420i
$666$	−8.89527	+	18.2846i	−0.344685	+	0.708514i
$667$	−3.16285	−	4.35329i	−0.122466	−	0.168560i
$668$	6.08036	+	1.97563i	0.235256	+	0.0764394i
$669$	0.405431	−	0.483667i	0.0156749	−	0.0186996i
$670$	−10.9531	+	22.7057i	−0.423155	+	0.877198i
$671$	−16.2318	+	5.27403i	−0.626621	+	0.203602i
$672$	2.88478	−	7.15041i	0.111283	−	0.275833i
$673$	7.29718	−	22.4584i	0.281286	−	0.865708i	−0.706202	−	0.708011i	$-0.749593\pi$
$673$	7.29718	−	22.4584i	0.281286	−	0.865708i	0.987487	−	0.157698i	$-0.0504071\pi$
$674$	−2.95041	+	9.08043i	−0.113646	+	0.349765i
$675$	25.6305	+	4.25161i	0.986519	+	0.163644i
$676$	31.3547			1.20595
$677$			7.70536i			0.296141i	0.988977	+	0.148070i	$0.0473062\pi$
$677$			7.70536i			0.296141i	−0.988977	+	0.148070i	$0.952694\pi$
$678$	−5.32331	−	8.50957i	−0.204441	−	0.326808i
$679$	−9.83667	+	7.14676i	−0.377497	+	0.274267i
$680$	−1.40014	+	2.90247i	−0.0536928	+	0.111305i
$681$	−23.5450	+	5.88298i	−0.902245	+	0.225436i
$682$	−8.73154	+	30.2257i	−0.334348	+	1.15740i
$683$	49.0392			1.87643			0.938217	−	0.346049i	$-0.112477\pi$
$683$	49.0392			1.87643			0.938217	+	0.346049i	$0.112477\pi$
$684$	−8.24105	−	1.14977i	−0.315104	−	0.0439624i
$685$	−14.5428	−	13.9229i	−0.555652	−	0.531966i
$686$	24.6267	−	8.00170i	0.940252	−	0.305506i
$687$	4.54160	+	18.1765i	0.173273	+	0.693475i
$688$	−7.82416			−0.298293
$689$	35.1241	−	11.4125i	1.33812	−	0.434782i
$690$	21.6091	−	2.37664i	0.822643	−	0.0904772i
$691$	−3.94944	+	12.1551i	−0.150244	+	0.462402i	−0.997648	−	0.0685457i	$-0.978164\pi$
$691$	−3.94944	+	12.1551i	−0.150244	+	0.462402i	0.847404	+	0.530948i	$0.178164\pi$
$692$	−4.01164	−	2.91463i	−0.152500	−	0.110798i
$693$	−52.3669	+	54.3367i	−1.98926	+	2.06408i
$694$	−9.74927	+	13.4187i	−0.370077	+	0.509368i
$695$	−8.23705	−	7.88593i	−0.312449	−	0.299130i
$696$	−0.114994	+	1.65644i	−0.00435883	+	0.0627872i
$697$	−4.07903	+	2.96359i	−0.154504	+	0.112254i
$698$	−1.61266	+	1.17166i	−0.0610400	+	0.0443481i
$699$	−1.96689	+	28.3323i	−0.0743947	+	1.07163i
$700$	18.5596	+	12.2866i	0.701488	+	0.464389i
$701$	1.62799	−	2.24073i	0.0614882	−	0.0846313i	−0.777165	−	0.629296i	$-0.783343\pi$
$701$	1.62799	−	2.24073i	0.0614882	−	0.0846313i	0.838654	+	0.544665i	$0.183343\pi$
$702$	29.9957	+	17.2579i	1.13212	+	0.651356i
$703$	15.2089	+	11.0499i	0.573613	+	0.416754i
$704$	−1.74615	+	5.37411i	−0.0658106	+	0.202544i
$705$	3.06407	+	27.8594i	0.115400	+	1.04924i
$706$	−4.33093	+	1.40720i	−0.162997	+	0.0529608i
$707$	−41.3010			−1.55328
$708$	3.82809	+	15.3209i	0.143868	+	0.575793i
$709$	18.2438	−	5.92778i	0.685161	−	0.222622i	0.0543076	−	0.998524i	$-0.482705\pi$
$709$	18.2438	−	5.92778i	0.685161	−	0.222622i	0.630854	+	0.775902i	$0.282705\pi$
$710$	−19.7324	−	18.8913i	−0.740545	−	0.708977i
$711$	4.13271	−	29.6216i	0.154989	−	1.11090i
$712$	−3.28945			−0.123277
$713$	−30.0246	−	8.67345i	−1.12443	−	0.324823i
$714$	10.7805	−	2.69364i	0.403451	−	0.100807i
$715$	75.7924	+	36.5618i	2.83447	+	1.36733i
$716$	9.35795	−	6.79895i	0.349723	−	0.254089i
$717$	−5.21811	−	8.34140i	−0.194874	−	0.311515i
$718$		−	23.1018i		−	0.862151i
$719$	43.9505			1.63908			0.819539	−	0.573024i	$-0.194230\pi$
$719$	43.9505			1.63908			0.819539	+	0.573024i	$0.194230\pi$
$720$	−5.58125	−	3.72151i	−0.208001	−	0.138692i
$721$	−1.68381	+	5.18224i	−0.0627084	+	0.192997i
$722$	3.49406	−	10.7536i	0.130035	−	0.400208i
$723$	11.1329	−	27.5947i	0.414036	−	1.02626i
$724$	−16.6041	+	5.39501i	−0.617088	+	0.200504i
$725$	−4.61880	−	1.28132i	−0.171538	−	0.0475872i
$726$	23.2884	−	27.7823i	0.864313	−	1.03110i
$727$	−31.8816	−	10.3589i	−1.18242	−	0.384192i	−0.349156	−	0.937065i	$-0.613532\pi$
$727$	−31.8816	−	10.3589i	−1.18242	−	0.384192i	−0.833266	+	0.552873i	$0.813532\pi$
$728$	17.4263	+	23.9853i	0.645862	+	0.888953i
$729$	13.5704	+	23.3419i	0.502607	+	0.864515i
$730$	1.58994	−	11.6790i	0.0588462	−	0.432258i
$731$	−6.62780	−	9.12238i	−0.245138	−	0.337403i
$732$	−1.95729	+	4.85148i	−0.0723436	+	0.179316i
$733$	−32.4797	+	10.5533i	−1.19967	+	0.389795i	−0.839638	−	0.543146i	$-0.817233\pi$
$733$	−32.4797	+	10.5533i	−1.19967	+	0.389795i	−0.360029	+	0.932941i	$0.617233\pi$
$734$	1.13190	+	0.822374i	0.0417792	+	0.0303544i
$735$	−5.42677	−	49.3417i	−0.200170	−	1.82000i
$736$	−5.33835	−	1.73454i	−0.196774	−	0.0639359i
$737$	−60.5879	+	19.6862i	−2.23178	+	0.725150i
$738$	−4.93669	−	9.26212i	−0.181722	−	0.340943i
$739$		−	1.57918i		−	0.0580912i	−0.999578	−	0.0290456i	$-0.990753\pi$
$739$		−	1.57918i		−	0.0580912i	0.999578	−	0.0290456i	$-0.00924680\pi$
$740$	7.17294	+	13.3508i	0.263682	+	0.490786i
$741$	20.5535	−	24.5197i	0.755051	−	0.900753i
$742$	19.9711	+	14.5099i	0.733163	+	0.532674i
$743$		−	4.24878i		−	0.155873i	−0.996958	−	0.0779363i	$-0.975167\pi$
$743$		−	4.24878i		−	0.155873i	0.996958	−	0.0779363i	$-0.0248331\pi$
$744$	5.38092	+	8.00285i	0.197274	+	0.293399i
$745$	−1.74155	−	9.63321i	−0.0638055	−	0.352933i
$746$	−15.9667	+	21.9763i	−0.584583	+	0.804610i
$747$	−25.6597	−	12.4832i	−0.938840	−	0.456736i
$748$	−7.74496	+	2.51649i	−0.283184	+	0.0920120i
$749$		−	5.32206i		−	0.194464i
$750$	13.7475	−	13.6384i	0.501990	−	0.498003i
$751$	9.69838	+	29.8485i	0.353899	+	1.08919i	0.956645	+	0.291256i	$0.0940730\pi$
$751$	9.69838	+	29.8485i	0.353899	+	1.08919i	−0.602747	+	0.797933i	$0.705927\pi$
$752$	2.23624	−	6.88244i	0.0815473	−	0.250977i
$753$	1.72359	−	24.8276i	0.0628111	−	0.904770i
$754$	−5.16519	−	3.75273i	−0.188105	−	0.136666i
$755$	23.3730	−	12.5575i	0.850630	−	0.457014i
$756$	2.45252	+	23.0008i	0.0891973	+	0.836532i
$757$	−21.4747	+	15.6022i	−0.780510	+	0.567073i	−0.905132	−	0.425131i	$-0.860228\pi$
$757$	−21.4747	+	15.6022i	−0.780510	+	0.567073i	0.124622	+	0.992204i	$0.460228\pi$
$758$	6.70098	−	20.6235i	0.243391	−	0.749079i
$759$	42.1016	+	35.2914i	1.52819	+	1.28100i
$760$	−4.28896	+	4.47993i	−0.155577	+	0.162504i
$761$	−0.554515	+	1.70662i	−0.0201012	+	0.0618650i	−0.960604	−	0.277921i	$-0.910355\pi$
$761$	−0.554515	+	1.70662i	−0.0201012	+	0.0618650i	0.940503	+	0.339786i	$0.110355\pi$
$762$	0.624447	−	0.744947i	0.0226213	−	0.0269866i
$763$	−7.72188	+	10.6283i	−0.279551	+	0.384769i
$764$	18.9559	−	6.15916i	0.685802	−	0.222830i
$765$	−0.388845	−	9.65979i	−0.0140587	−	0.349250i
$766$	31.3851	+	10.1976i	1.13399	+	0.368455i
$767$	−57.7496	−	18.7640i	−2.08522	−	0.677528i
$768$	0.918585	+	1.46840i	0.0331466	+	0.0529864i
$769$	−8.64890			−0.311887			−0.155944	−	0.987766i	$-0.549842\pi$
$769$	−8.64890			−0.311887			−0.155944	+	0.987766i	$0.549842\pi$
$770$	10.0065	+	55.3501i	0.360610	+	1.99468i
$771$	−27.7493	−	44.3586i	−0.999366	−	1.59753i
$772$	2.26789	+	3.12148i	0.0816232	+	0.112345i
$773$	20.0481	−	27.5938i	0.721079	−	0.992480i	−0.278408	−	0.960463i	$-0.589807\pi$
$773$	20.0481	−	27.5938i	0.721079	−	0.992480i	0.999487	−	0.0320175i	$-0.0101932\pi$
$774$	20.7139	−	11.0405i	0.744546	−	0.396841i
$775$	−25.7415	+	10.6006i	−0.924663	+	0.380786i
$776$		−	2.73133i		−	0.0980489i
$777$	19.5526	−	48.4644i	0.701445	−	1.73865i
$778$	−25.9367	+	18.8441i	−0.929877	+	0.675595i
$779$	−9.22869	+	2.99858i	−0.330652	+	0.107435i
$780$	23.5129	−	10.6048i	0.841898	−	0.379714i
$781$		−	69.0331i		−	2.47020i
$782$	−2.49975	−	7.69343i	−0.0893908	−	0.275117i
$783$	−2.03292	−	4.54757i	−0.0726507	−	0.162517i
$784$	−3.96061	+	12.1895i	−0.141450	+	0.435339i
$785$	5.01229	−	10.3904i	0.178896	−	0.370850i
$786$	−15.5727	+	9.74179i	−0.555460	+	0.347478i
$787$	−44.4181	−	32.2716i	−1.58333	−	1.15036i	−0.912745	−	0.408531i	$-0.866041\pi$
$787$	−44.4181	−	32.2716i	−1.58333	−	1.15036i	−0.670589	−	0.741829i	$-0.733959\pi$
$788$	−8.23212	−	11.3305i	−0.293257	−	0.403634i
$789$	−54.4726	−	3.78161i	−1.93928	−	0.134629i
$790$	−16.1026	−	15.4162i	−0.572906	−	0.548484i
$791$	15.1634	+	20.8707i	0.539150	+	0.742077i
$792$	−2.96045	−	16.6915i	−0.105195	−	0.593107i
$793$	−11.8236	−	16.2737i	−0.419867	−	0.577898i
$794$	3.71233	−	5.10958i	0.131746	−	0.181332i
$795$	15.8910	−	14.4477i	0.563597	−	0.512409i
$796$	−4.75455	+	6.54407i	−0.168520	+	0.231948i
$797$	31.4728	+	10.2261i	1.11482	+	0.362228i	0.807789	−	0.589471i	$-0.200664\pi$
$797$	31.4728	+	10.2261i	1.11482	+	0.362228i	0.307033	+	0.951699i	$0.400664\pi$
$798$	21.3344	+	1.48108i	0.755230	+	0.0524298i
$799$	9.91872	−	3.22279i	0.350899	−	0.114014i
$800$	−4.68351	+	1.75064i	−0.165587	+	0.0618946i
$801$	8.70858	−	4.64166i	0.307703	−	0.164005i
$802$	4.31519	+	13.2808i	0.152375	+	0.468961i
$803$	24.0971	−	17.5076i	0.850369	−	0.617829i
$804$	−7.30593	+	18.1090i	−0.257660	+	0.638654i
$805$	−54.9818	+	9.93995i	−1.93785	+	0.350337i
$806$	−37.0608	+	1.22112i	−1.30541	+	0.0430121i
$807$	−0.158829	+	0.0396851i	−0.00559103	+	0.00139698i
$808$	5.45334	−	7.50587i	0.191848	−	0.264056i
$809$	9.37538	−	6.81161i	0.329621	−	0.239484i	−0.410649	−	0.911794i	$-0.634698\pi$
$809$	9.37538	−	6.81161i	0.329621	−	0.239484i	0.740270	+	0.672310i	$0.234698\pi$
$810$	20.0273	+	1.97686i	0.703687	+	0.0694599i
$811$	−35.0738			−1.23161			−0.615804	−	0.787899i	$-0.711169\pi$
$811$	−35.0738			−1.23161			−0.615804	+	0.787899i	$0.711169\pi$
$812$		−	4.26752i		−	0.149761i
$813$	−2.26226	+	1.41520i	−0.0793409	+	0.0496331i
$814$	−11.8352	+	36.4249i	−0.414822	+	1.27669i
$815$	12.3350	+	1.67925i	0.432078	+	0.0588216i
$816$	−0.933918	+	2.31487i	−0.0326937	+	0.0810368i
$817$	−6.70606	−	20.6391i	−0.234615	−	0.722072i
$818$	−11.7650	+	16.1932i	−0.411354	+	0.566181i
$819$	−79.9798	−	38.9094i	−2.79472	−	1.35960i
$820$	−7.75146	−	1.05526i	−0.270693	−	0.0368512i
$821$	−46.2737	+	33.6198i	−1.61496	+	1.17334i	−0.771288	+	0.636486i	$0.780387\pi$
$821$	−46.2737	+	33.6198i	−1.61496	+	1.17334i	−0.843675	+	0.536854i	$0.819613\pi$
$822$	−11.9515	−	10.0183i	−0.416856	−	0.349427i
$823$	−12.7635	+	39.2821i	−0.444909	+	1.36929i	0.437675	+	0.899133i	$0.355802\pi$
$823$	−12.7635	+	39.2821i	−0.444909	+	1.36929i	−0.882584	+	0.470155i	$0.844198\pi$
$824$	−0.719470	−	0.990266i	−0.0250639	−	0.0344976i
$825$	48.9200	+	1.26054i	1.70318	+	0.0438864i
$826$	−12.5421	−	38.6008i	−0.436397	−	1.34309i
$827$	11.3507	−	15.6228i	0.394701	−	0.543259i	−0.564703	−	0.825294i	$-0.691009\pi$
$827$	11.3507	−	15.6228i	0.394701	−	0.543259i	0.959404	+	0.282035i	$0.0910094\pi$
$828$	16.5805	−	2.94075i	0.576211	−	0.102198i
$829$	−22.0052	−	7.14993i	−0.764273	−	0.248327i	−0.0991615	−	0.995071i	$-0.531616\pi$
$829$	−22.0052	−	7.14993i	−0.764273	−	0.248327i	−0.665112	+	0.746744i	$0.731616\pi$
$830$	−18.7359	+	10.0662i	−0.650333	+	0.349401i
$831$	−29.0206	+	7.25114i	−1.00672	+	0.251539i
$832$	−6.65993			−0.230892
$833$	−17.5670	+	5.70788i	−0.608662	+	0.197766i
$834$	−6.76933	−	5.67435i	−0.234403	−	0.196487i
$835$	−6.21128	+	12.8759i	−0.214950	+	0.445590i
$836$	−15.6728			−0.542056
$837$	−25.5382	−	13.5941i	−0.882730	−	0.469880i
$838$			8.87744i			0.306666i
$839$	3.15289	−	4.33958i	0.108850	−	0.149819i	−0.751117	−	0.660170i	$-0.770484\pi$
$839$	3.15289	−	4.33958i	0.108850	−	0.149819i	0.859966	+	0.510351i	$0.170484\pi$
$840$	14.9725	+	8.54838i	0.516602	+	0.294947i
$841$	−8.67750	−	26.7066i	−0.299224	−	0.920918i
$842$	−28.2436			−0.973338
$843$	2.70735	+	10.8354i	0.0932462	+	0.373192i
$844$	8.40805	+	25.8773i	0.289417	+	0.890734i
$845$	−9.45749	+	69.4705i	−0.325347	+	2.38986i
$846$	3.79135	+	21.3763i	0.130349	+	0.734931i
$847$	−54.7654	+	75.3782i	−1.88176	+	2.59002i
$848$	−5.27393	+	1.71360i	−0.181108	+	0.0588454i
$849$	1.41902	−	3.51729i	0.0487008	−	0.120713i
$850$	−6.00849	−	3.97766i	−0.206090	−	0.136433i
$851$	−36.1825	−	11.7564i	−1.24032	−	0.403005i
$852$	−16.2164	−	13.5933i	−0.555565	−	0.465699i
$853$	13.9891	+	19.2544i	0.478978	+	0.659257i	0.978308	−	0.207155i	$-0.0664205\pi$
$853$	13.9891	+	19.2544i	0.478978	+	0.659257i	−0.499330	+	0.866412i	$0.666421\pi$
$854$	4.15488	−	12.7874i	0.142177	−	0.437576i
$855$	5.03319	−	17.9123i	0.172132	−	0.612588i
$856$	0.967211	+	0.702720i	0.0330586	+	0.0240185i
$857$	9.61131	+	29.5806i	0.328316	+	1.01045i	0.969921	+	0.243418i	$0.0782688\pi$
$857$	9.61131	+	29.5806i	0.328316	+	1.01045i	−0.641605	+	0.767035i	$0.721731\pi$
$858$	60.4484	+	24.3874i	2.06367	+	0.832573i
$859$	−42.3312	−	13.7542i	−1.44432	−	0.469288i	−0.521079	−	0.853508i	$-0.674470\pi$
$859$	−42.3312	−	13.7542i	−1.44432	−	0.469288i	−0.923242	+	0.384220i	$0.874470\pi$
$860$	2.35999	−	17.3355i	0.0804750	−	0.591134i
$861$	14.3061	+	22.8690i	0.487551	+	0.779374i
$862$			2.39607i			0.0816106i
$863$		−	14.3195i		−	0.487441i	−0.969845	−	0.243721i	$-0.921632\pi$
$863$		−	14.3195i		−	0.487441i	0.969845	−	0.243721i	$-0.0783680\pi$
$864$	−4.50391	−	2.59129i	−0.153226	−	0.0881576i
$865$	7.66777	−	8.00918i	0.260712	−	0.272320i
$866$	6.43421	+	4.67473i	0.218643	+	0.158854i
$867$	25.0766	−	6.26566i	0.851645	−	0.212793i
$868$	−15.2210	−	19.5612i	−0.516634	−	0.663952i
$869$		−	56.3344i		−	1.91101i
$870$	−3.63537	−	0.754413i	−0.123251	−	0.0255770i
$871$	−44.1335	−	60.7445i	−1.49541	−	2.05825i
$872$	−0.911948	−	2.80669i	−0.0308825	−	0.0950464i
$873$	3.85411	+	7.23099i	0.130442	+	0.244732i
$874$		−	15.5686i		−	0.526614i
$875$	−32.8207	+	37.4153i	−1.10954	+	1.26487i
$876$	0.632299	−	9.10802i	0.0213634	−	0.307731i
$877$	7.08822	+	2.30310i	0.239352	+	0.0777703i	0.426237	−	0.904612i	$-0.359839\pi$
$877$	7.08822	+	2.30310i	0.239352	+	0.0777703i	−0.186885	+	0.982382i	$0.559839\pi$
$878$	−7.43743	−	5.40361i	−0.251001	−	0.182363i
$879$	−13.1856	−	21.0779i	−0.444740	−	0.710939i
$880$	−11.3804	−	5.48982i	−0.383632	−	0.185062i
$881$	5.78354	−	4.20199i	0.194852	−	0.141569i	−0.486081	−	0.873914i	$-0.661574\pi$
$881$	5.78354	−	4.20199i	0.194852	−	0.141569i	0.680934	+	0.732345i	$0.261574\pi$
$882$	−6.71486	−	37.8595i	−0.226101	−	1.27480i
$883$	38.2653	−	27.8013i	1.28773	−	0.935590i	0.287972	−	0.957639i	$-0.407019\pi$
$883$	38.2653	−	27.8013i	1.28773	−	0.935590i	0.999757	+	0.0220491i	$0.00701900\pi$
$884$	−5.64159	−	7.76498i	−0.189747	−	0.261165i
$885$	−35.1000	+	3.86043i	−1.17987	+	0.129767i
$886$	2.30460	−	1.67439i	0.0774245	−	0.0562522i
$887$	−24.5371	−	17.8272i	−0.823875	−	0.598580i	0.0939448	−	0.995577i	$-0.470052\pi$
$887$	−24.5371	−	17.8272i	−0.823875	−	0.598580i	−0.917820	+	0.396997i	$0.870052\pi$
$888$	6.22602	+	9.95259i	0.208932	+	0.333987i
$889$	−1.46846	+	2.02117i	−0.0492507	+	0.0677877i
$890$	0.992193	−	7.28821i	0.0332584	−	0.244301i
$891$	31.3905	+	40.0121i	1.05162	+	1.34046i
$892$	−0.112598	−	0.346541i	−0.00377006	−	0.0116031i
$893$	20.0717			0.671673
$894$	−1.83814	−	7.35665i	−0.0614767	−	0.246043i
$895$	12.2413	+	22.7845i	0.409183	+	0.761603i
$896$	−2.61659	−	3.60142i	−0.0874141	−	0.120315i
$897$	−24.2252	+	60.0462i	−0.808855	+	2.00488i
$898$	1.22673			0.0409364
$899$	4.41912	+	2.99341i	0.147386	+	0.0998360i
$900$	9.92896	−	11.2435i	0.330965	−	0.374783i
$901$	−6.46545	−	4.69743i	−0.215395	−	0.156494i
$902$	−11.6200	−	15.9935i	−0.386903	−	0.532526i
$903$	−51.1445	+	31.9944i	−1.70198	+	1.06471i
$904$	−5.79512			−0.192743
$905$	−6.94507	−	38.4160i	−0.230862	−	1.27699i
$906$	17.4238	−	10.8997i	0.578866	−	0.362120i
$907$	−14.9471	−	4.85661i	−0.496310	−	0.161261i	0.0501572	−	0.998741i	$-0.484028\pi$
$907$	−14.9471	−	4.85661i	−0.496310	−	0.161261i	−0.546467	+	0.837480i	$0.684028\pi$
$908$	−4.32982	+	13.3258i	−0.143690	+	0.442233i
$909$	−3.84597	+	27.5663i	−0.127563	+	0.914317i
$910$	−58.3987	+	31.3756i	−1.93590	+	1.04009i
$911$	33.5335	+	24.3635i	1.11101	+	0.807199i	0.982823	−	0.184551i	$-0.0590831\pi$
$911$	33.5335	+	24.3635i	1.11101	+	0.807199i	0.128191	+	0.991750i	$0.459083\pi$
$912$	−3.08614	+	3.68167i	−0.102192	+	0.121912i
$913$	−51.1169	−	16.6089i	−1.69172	−	0.549674i
$914$	19.9565	−	14.4993i	0.660104	−	0.479593i
$915$	−10.1587	−	5.79999i	−0.335837	−	0.191742i
$916$	10.2874	+	3.34258i	0.339905	+	0.110442i
$917$	38.1939	−	27.7495i	1.26127	−	0.916368i
$918$	−0.793979	−	7.44629i	−0.0262052	−	0.245764i
$919$	−0.370374	−	1.13989i	−0.0122175	−	0.0376016i	0.944762	−	0.327757i	$-0.106293\pi$
$919$	−0.370374	−	1.13989i	−0.0122175	−	0.0376016i	−0.956979	+	0.290156i	$0.906293\pi$
$920$	5.45329	−	11.3046i	0.179790	−	0.372703i
$921$	32.9939	+	2.29051i	1.08719	+	0.0754750i
$922$	−2.89750	+	8.91760i	−0.0954242	+	0.293685i
$923$	77.3808	−	25.1426i	2.54702	−	0.827577i
$924$	10.5615	+	42.2695i	0.347448	+	1.39056i
$925$	−31.7441	+	11.8656i	−1.04374	+	0.390138i
$926$	8.06703	+	24.8278i	0.265099	+	0.815891i
$927$	3.30208	+	1.60643i	0.108455	+	0.0527621i
$928$	0.775562	+	0.563479i	0.0254591	+	0.0184971i
$929$	−19.2509			−0.631601			−0.315800	−	0.948826i	$-0.602273\pi$
$929$	−19.2509			−0.631601			−0.315800	+	0.948826i	$0.602273\pi$
$930$	−19.3544	+	9.50825i	−0.634656	+	0.311788i
$931$	−35.5489			−1.16507
$932$	13.2655	+	9.63794i	0.434525	+	0.315701i
$933$	38.7307	+	32.4658i	1.26799	+	1.06288i
$934$	−2.57152	−	7.91432i	−0.0841427	−	0.258964i
$935$	−3.23951	−	17.9190i	−0.105943	−	0.586015i
$936$	17.6317	−	9.39766i	0.576310	−	0.307172i
$937$	−22.6399	+	7.35614i	−0.739613	+	0.240315i	−0.654506	−	0.756057i	$-0.727123\pi$
$937$	−22.6399	+	7.35614i	−0.739613	+	0.240315i	−0.0851070	+	0.996372i	$0.527123\pi$
$938$	15.5088	−	47.7312i	0.506381	−	1.55848i
$939$	3.38423	−	48.7484i	0.110440	−	1.59085i
$940$	14.5744	+	7.03063i	0.475366	+	0.229314i
$941$	−11.6048	−	35.7158i	−0.378304	−	1.16430i	−0.941222	−	0.337788i	$-0.890321\pi$
$941$	−11.6048	−	35.7158i	−0.378304	−	1.16430i	0.562918	−	0.826513i	$-0.309679\pi$
$942$	3.34329	−	8.28691i	0.108930	−	0.270002i
$943$	15.8871	−	11.5427i	0.517356	−	0.375881i
$944$	8.67120	+	2.81744i	0.282223	+	0.0917000i
$945$	−51.7011	−	1.50383i	−1.68184	−	0.0489196i
$946$	35.7681	−	25.9870i	1.16292	−	0.844911i
$947$	42.2500	+	13.7278i	1.37294	+	0.446095i	0.900342	−	0.435183i	$-0.143316\pi$
$947$	42.2500	+	13.7278i	1.37294	+	0.446095i	0.472598	+	0.881278i	$0.343316\pi$
$948$	−13.2334	−	11.0928i	−0.429800	−	0.360278i
$949$	28.4011	+	20.6346i	0.921938	+	0.669827i
$950$	−8.63219	−	10.8540i	−0.280065	−	0.352151i
$951$	26.5156	+	10.6975i	0.859828	+	0.346891i
$952$	1.98249	−	6.10149i	0.0642530	−	0.197750i
$953$	−14.1703	−	4.60420i	−0.459020	−	0.149145i	0.0703739	−	0.997521i	$-0.477581\pi$
$953$	−14.1703	−	4.60420i	−0.459020	−	0.149145i	−0.529394	+	0.848376i	$0.677581\pi$
$954$	11.5443	−	11.9786i	0.373762	−	0.387820i
$955$	7.92876	+	43.8571i	0.256569	+	1.41918i
$956$	−5.68060			−0.183724
$957$	−4.97597	−	7.95433i	−0.160850	−	0.257127i
$958$	14.2461	+	19.6081i	0.460271	+	0.633509i
$959$	32.4264	+	23.5592i	1.04710	+	0.760765i
$960$	−3.53051	+	1.59233i	−0.113947	+	0.0513923i
$961$	30.9328	−	2.04062i	0.997831	−	0.0658266i
$962$	−45.1400			−1.45537
$963$	−3.55221	−	0.495593i	−0.114468	−	0.0159703i
$964$	−10.0979	−	13.8985i	−0.325230	−	0.447641i
$965$	−7.60012	+	4.08328i	−0.244656	+	0.131445i
$966$	−41.9883	+	10.4912i	−1.35095	+	0.337550i
$967$	−20.5520			−0.660908			−0.330454	−	0.943822i	$-0.607202\pi$
$967$	−20.5520			−0.660908			−0.330454	+	0.943822i	$0.607202\pi$
$968$	−6.46775	−	19.9057i	−0.207882	−	0.639794i
$969$	−6.90680	−	0.479486i	−0.221878	−	0.0154033i
$970$	6.05161	+	0.823847i	0.194306	+	0.0264521i
$971$	−25.8186	+	35.5362i	−0.828557	+	1.14041i	0.159632	+	0.987177i	$0.448969\pi$
$971$	−25.8186	+	35.5362i	−0.828557	+	1.14041i	−0.988190	+	0.153235i	$0.951031\pi$
$972$	15.5803	+	0.504915i	0.499738	+	0.0161952i
$973$	18.3663	+	13.3439i	0.588798	+	0.427787i
$974$	8.82500	−	6.41174i	0.282771	−	0.205445i
$975$	16.4042	+	55.2947i	0.525355	+	1.77085i
$976$	1.77533	+	2.44353i	0.0568269	+	0.0782155i
$977$	−23.0319	+	16.7337i	−0.736856	+	0.535357i	−0.891725	−	0.452578i	$-0.850505\pi$
$977$	−23.0319	+	16.7337i	−0.736856	+	0.535357i	0.154869	+	0.987935i	$0.450505\pi$
$978$	9.61966	+	0.667819i	0.307603	+	0.0213545i
$979$	15.0377	−	10.9255i	0.480607	−	0.349181i
$980$	−25.8128	−	12.4519i	−0.824559	−	0.397763i
$981$	6.37476	+	6.14367i	0.203530	+	0.196152i
$982$	3.06569	+	2.22735i	0.0978301	+	0.0710777i
$983$	32.1155	+	10.4350i	1.02433	+	0.332824i	0.772545	−	0.634961i	$-0.218984\pi$
$983$	32.1155	+	10.4350i	1.02433	+	0.332824i	0.251781	+	0.967784i	$0.418984\pi$
$984$	−6.04509	−	0.419664i	−0.192710	−	0.0133784i
$985$	27.5873	−	14.8217i	0.879006	−	0.472259i
$986$			1.38157i			0.0439980i
$987$	−13.5258	−	54.1332i	−0.430530	−	1.72308i
$988$	−5.70821	−	17.5681i	−0.181602	−	0.558914i
$989$	25.8141	+	35.5301i	0.820842	+	1.12979i
$990$	37.8752	−	1.52463i	1.20375	−	0.0484558i
$991$		−	15.1711i		−	0.481926i	−0.970534	−	0.240963i	$-0.922537\pi$
$991$		−	15.1711i		−	0.481926i	0.970534	−	0.240963i	$-0.0774632\pi$
$992$	5.56474	−	0.183353i	0.176681	−	0.00582146i
$993$	−0.637593	−	2.55179i	−0.0202334	−	0.0809786i
$994$	43.9978	+	31.9663i	1.39553	+	1.01391i
$995$	−13.0651	−	12.5082i	−0.414193	−	0.396537i
$996$	−13.9670	+	8.73730i	−0.442561	+	0.276852i
$997$		−	6.21320i		−	0.196774i	−0.995148	−	0.0983870i	$-0.968632\pi$
$997$		−	6.21320i		−	0.196774i	0.995148	−	0.0983870i	$-0.0313683\pi$
$998$			16.7224i			0.529338i
$999$	−30.5268	−	17.5634i	−0.965825	−	0.555681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.b.29.9	yes	128
3.2	odd	2		930.2.y.a.29.5	✓	128
5.4	even	2		930.2.y.a.29.24	yes	128
15.14	odd	2	inner	930.2.y.b.29.28	yes	128
31.15	odd	10	inner	930.2.y.b.449.28	yes	128
93.77	even	10		930.2.y.a.449.24	yes	128
155.139	odd	10		930.2.y.a.449.5	yes	128
465.449	even	10	inner	930.2.y.b.449.9	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.5	✓	128	3.2	odd	2
930.2.y.a.29.24	yes	128	5.4	even	2
930.2.y.a.449.5	yes	128	155.139	odd	10
930.2.y.a.449.24	yes	128	93.77	even	10
930.2.y.b.29.9	yes	128	1.1	even	1	trivial
930.2.y.b.29.28	yes	128	15.14	odd	2	inner
930.2.y.b.449.9	yes	128	465.449	even	10	inner
930.2.y.b.449.28	yes	128	31.15	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.11267 + 1.32739i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.20040 + 0.397802i) q^{5} +(-1.68039 + 0.419865i) q^{6} +(4.23373 - 1.37562i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.523911 - 2.95390i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.11267 + 1.32739i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.20040 + 0.397802i) q^{5} +(-1.68039 + 0.419865i) q^{6} +(4.23373 - 1.37562i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.523911 - 2.95390i) q^{9} +(-2.01398 - 0.971534i) q^{10} +(-1.74615 - 5.37411i) q^{11} +(-1.60626 - 0.648031i) q^{12} +(5.38800 - 3.91461i) q^{13} +(4.23373 + 1.37562i) q^{14} +(1.92029 - 3.36340i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.37063 - 0.445344i) q^{17} +(1.31240 - 2.69770i) q^{18} +(-2.24391 - 1.63029i) q^{19} +(-1.05829 - 1.96978i) q^{20} +(-2.88478 + 7.15041i) q^{21} +(1.74615 - 5.37411i) q^{22} +(5.33835 + 1.73454i) q^{23} +(-0.918585 - 1.46840i) q^{24} +(4.68351 - 1.75064i) q^{25} +6.65993 q^{26} +(4.50391 + 2.59129i) q^{27} +(2.61659 + 3.60142i) q^{28} +(-0.775562 - 0.563479i) q^{29} +(3.53051 - 1.59233i) q^{30} +(-5.56474 + 0.183353i) q^{31} -1.00000 q^{32} +(9.07642 + 3.66181i) q^{33} +(-0.847094 - 1.16592i) q^{34} +(-8.76867 + 4.71110i) q^{35} +(2.64743 - 1.41107i) q^{36} -6.77784 q^{37} +(-0.857097 - 2.63787i) q^{38} +(-0.798887 + 11.5076i) q^{39} +(0.301629 - 2.21563i) q^{40} +(2.05639 - 2.83037i) q^{41} +(-6.53674 + 4.08918i) q^{42} +(6.32988 + 4.59893i) q^{43} +(4.57149 - 3.32138i) q^{44} +(2.32788 + 6.29134i) q^{45} +(3.29928 + 4.54108i) q^{46} +(-5.85456 + 4.25358i) q^{47} +(0.119954 - 1.72789i) q^{48} +(10.3690 - 7.53352i) q^{49} +(4.81804 + 1.33660i) q^{50} +(2.11620 - 1.32383i) q^{51} +(5.38800 + 3.91461i) q^{52} +(5.27393 + 1.71360i) q^{53} +(2.12061 + 4.74373i) q^{54} +(5.98006 + 11.1306i) q^{55} +4.45161i q^{56} +(4.66077 - 1.16455i) q^{57} +(-0.296238 - 0.911728i) q^{58} +(-5.35910 - 7.37616i) q^{59} +(3.79219 + 0.786956i) q^{60} -3.02037i q^{61} +(-4.60975 - 3.12254i) q^{62} +(-6.28154 - 11.7853i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-10.2985 + 10.7571i) q^{65} +(5.19062 + 8.29745i) q^{66} -11.2740i q^{67} -1.44116i q^{68} +(-8.24225 + 5.15609i) q^{69} +(-9.86311 - 1.34273i) q^{70} +(11.6189 + 3.77519i) q^{71} +(2.97122 + 0.414536i) q^{72} +(1.62888 + 5.01318i) q^{73} +(-5.48339 - 3.98392i) q^{74} +(-2.88744 + 8.16472i) q^{75} +(0.857097 - 2.63787i) q^{76} +(-14.7855 - 20.3505i) q^{77} +(-7.41034 + 8.84031i) q^{78} +(9.48156 + 3.08075i) q^{79} +(1.54634 - 1.61519i) q^{80} +(-8.45103 + 3.09516i) q^{81} +(3.32730 - 1.08111i) q^{82} +(5.59084 - 7.69513i) q^{83} +(-7.69189 - 0.533989i) q^{84} +(3.19308 + 0.434696i) q^{85} +(2.41780 + 7.44122i) q^{86} +(1.61090 - 0.402502i) q^{87} +5.65067 q^{88} +(1.01650 + 3.12845i) q^{89} +(-1.81466 + 6.45810i) q^{90} +(17.4263 - 23.9853i) q^{91} +5.61308i q^{92} +(5.94837 - 7.59058i) q^{93} -7.23663 q^{94} +(5.58603 + 2.69467i) q^{95} +(1.11267 - 1.32739i) q^{96} +(-2.59765 + 0.844027i) q^{97} +12.8168 q^{98} +(-14.9597 + 7.97352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9	\( 128 q + 32 q^{2} - 32 q^{4} - 2 q^{5} + 32 q^{8} - 4 q^{9} + 2 q^{10} - 35 q^{15} - 32 q^{16} - 6 q^{18} - 8 q^{19} + 3 q^{20} + 20 q^{23} - 10 q^{25} - 48 q^{31} - 128 q^{32} + 8 q^{33} + 10 q^{34} - 16 q^{35} - 4 q^{36} - 12 q^{38} + 4 q^{39} - 3 q^{40} + 5 q^{45} + 10 q^{46} - 6 q^{47} + 46 q^{49} + 5 q^{50} + 34 q^{51} + 20 q^{53} + 35 q^{60} + 8 q^{62} - 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} - 6 q^{72} + 5 q^{75} + 12 q^{76} - 50 q^{77} - 4 q^{78} - 10 q^{79} - 2 q^{80} - 24 q^{81} + 40 q^{83} - 30 q^{85} + 4 q^{87} - 5 q^{90} + 20 q^{91} + 26 q^{93} - 4 q^{94} + 26 q^{95} + 124 q^{98}+O(q^{100}) \) 128 * q + 32 * q^2 - 32 * q^4 - 2 * q^5 + 32 * q^8 - 4 * q^9 + 2 * q^10 - 35 * q^15 - 32 * q^16 - 6 * q^18 - 8 * q^19 + 3 * q^20 + 20 * q^23 - 10 * q^25 - 48 * q^31 - 128 * q^32 + 8 * q^33 + 10 * q^34 - 16 * q^35 - 4 * q^36 - 12 * q^38 + 4 * q^39 - 3 * q^40 + 5 * q^45 + 10 * q^46 - 6 * q^47 + 46 * q^49 + 5 * q^50 + 34 * q^51 + 20 * q^53 + 35 * q^60 + 8 * q^62 - 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 - 6 * q^72 + 5 * q^75 + 12 * q^76 - 50 * q^77 - 4 * q^78 - 10 * q^79 - 2 * q^80 - 24 * q^81 + 40 * q^83 - 30 * q^85 + 4 * q^87 - 5 * q^90 + 20 * q^91 + 26 * q^93 - 4 * q^94 + 26 * q^95 + 124 * q^98

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