LMFDB - Embedded newform 930.2.y.b.29.8

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			29.8
Character	$\chi$	$=$	930.29
Dual form			930.2.y.b.449.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-1.26101 + 1.18737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.72517 + 1.42260i) q^{5} +(-1.71810 + 0.219404i) q^{6} +(0.914445 - 0.297121i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.180286 - 2.99458i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-1.26101 + 1.18737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.72517 + 1.42260i) q^{5} +(-1.71810 + 0.219404i) q^{6} +(0.914445 - 0.297121i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.180286 - 2.99458i) q^{9} +(-2.23187 + 0.136884i) q^{10} +(1.31924 + 4.06020i) q^{11} +(-1.51893 - 0.832372i) q^{12} +(-4.29369 + 3.11955i) q^{13} +(0.914445 + 0.297121i) q^{14} +(0.486285 - 3.84233i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.11281 + 1.33633i) q^{17} +(1.90602 - 2.31670i) q^{18} +(-3.39964 - 2.46998i) q^{19} +(-1.88608 - 1.20112i) q^{20} +(-0.800329 + 1.46046i) q^{21} +(-1.31924 + 4.06020i) q^{22} +(-8.17154 - 2.65510i) q^{23} +(-0.739587 - 1.56621i) q^{24} +(0.952392 - 4.90846i) q^{25} -5.30729 q^{26} +(3.32834 + 3.99026i) q^{27} +(0.565158 + 0.777874i) q^{28} +(-0.531008 - 0.385800i) q^{29} +(2.65188 - 2.82268i) q^{30} +(5.48547 - 0.953751i) q^{31} -1.00000 q^{32} +(-6.48455 - 3.55352i) q^{33} +(2.54186 + 3.49856i) q^{34} +(-1.15488 + 1.81348i) q^{35} +(2.90372 - 0.753914i) q^{36} -11.5866 q^{37} +(-1.29855 - 3.99651i) q^{38} +(1.71031 - 9.03199i) q^{39} +(-0.819872 - 2.08034i) q^{40} +(3.51204 - 4.83391i) q^{41} +(-1.50592 + 0.711116i) q^{42} +(-3.99229 - 2.90057i) q^{43} +(-3.45381 + 2.50934i) q^{44} +(3.94908 + 5.42262i) q^{45} +(-5.05029 - 6.95113i) q^{46} +(1.31333 - 0.954190i) q^{47} +(0.322256 - 1.70181i) q^{48} +(-4.91519 + 3.57109i) q^{49} +(3.65562 - 3.41122i) q^{50} +(-6.77301 + 3.19832i) q^{51} +(-4.29369 - 3.11955i) q^{52} +(9.64977 + 3.13540i) q^{53} +(0.347272 + 5.18453i) q^{54} +(-8.05197 - 5.12776i) q^{55} +0.961505i q^{56} +(7.21976 - 0.921973i) q^{57} +(-0.202827 - 0.624237i) q^{58} +(5.34618 + 7.35839i) q^{59} +(3.80455 - 0.724862i) q^{60} -2.74710i q^{61} +(4.99844 + 2.45268i) q^{62} +(-0.724891 - 2.79194i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.96944 - 11.4900i) q^{65} +(-3.15741 - 6.68638i) q^{66} -6.69091i q^{67} +4.32446i q^{68} +(13.4570 - 6.35458i) q^{69} +(-2.00026 + 0.788311i) q^{70} +(-3.52318 - 1.14475i) q^{71} +(2.79230 + 1.09684i) q^{72} +(1.08376 + 3.33548i) q^{73} +(-9.37376 - 6.81043i) q^{74} +(4.62720 + 7.32045i) q^{75} +(1.29855 - 3.99651i) q^{76} +(2.41274 + 3.32086i) q^{77} +(6.69254 - 6.30174i) q^{78} +(-6.26135 - 2.03444i) q^{79} +(0.559502 - 2.16494i) q^{80} +(-8.93499 - 1.07976i) q^{81} +(5.68261 - 1.84639i) q^{82} +(-4.99843 + 6.87975i) q^{83} +(-1.63630 - 0.309851i) q^{84} +(-8.99635 + 3.54551i) q^{85} +(-1.52492 - 4.69321i) q^{86} +(1.12769 - 0.144008i) q^{87} -4.26915 q^{88} +(2.62990 + 8.09401i) q^{89} +(0.00753618 + 6.70820i) q^{90} +(-2.99946 + 4.12840i) q^{91} -8.59207i q^{92} +(-5.78476 + 7.71599i) q^{93} +1.62336 q^{94} +(9.37874 - 0.575213i) q^{95} +(1.26101 - 1.18737i) q^{96} +(13.1863 - 4.28449i) q^{97} -6.07551 q^{98} +(12.3964 - 3.21857i) 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
$3$	−1.26101	+	1.18737i	−0.728044	+	0.685531i
$3$	−1.26101	+	1.18737i	−0.728044	+	0.685531i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.72517	+	1.42260i	−0.771517	+	0.636208i
$5$	−1.72517	+	1.42260i	−0.771517	+	0.636208i
$6$	−1.71810	+	0.219404i	−0.701411	+	0.0895711i
$7$	0.914445	−	0.297121i	0.345628	−	0.112301i	−0.131059	−	0.991375i	$-0.541838\pi$
$7$	0.914445	−	0.297121i	0.345628	−	0.112301i	0.476687	+	0.879073i	$0.341838\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.180286	−	2.99458i	0.0600952	−	0.998193i
$10$	−2.23187	+	0.136884i	−0.705781	+	0.0432867i
$11$	1.31924	+	4.06020i	0.397766	+	1.22420i	0.926787	+	0.375588i	$0.122559\pi$
$11$	1.31924	+	4.06020i	0.397766	+	1.22420i	−0.529021	+	0.848609i	$0.677441\pi$
$12$	−1.51893	−	0.832372i	−0.438478	−	0.240285i
$13$	−4.29369	+	3.11955i	−1.19086	+	0.865207i	−0.993354	−	0.115096i	$-0.963283\pi$
$13$	−4.29369	+	3.11955i	−1.19086	+	0.865207i	−0.197501	+	0.980303i	$0.563283\pi$
$14$	0.914445	+	0.297121i	0.244396	+	0.0794090i
$15$	0.486285	−	3.84233i	0.125558	−	0.992086i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	4.11281	+	1.33633i	0.997503	+	0.324108i	0.761867	−	0.647733i	$-0.224283\pi$
$17$	4.11281	+	1.33633i	0.997503	+	0.324108i	0.235635	+	0.971842i	$0.424283\pi$
$18$	1.90602	−	2.31670i	0.449254	−	0.546050i
$19$	−3.39964	−	2.46998i	−0.779930	−	0.566652i	0.125028	−	0.992153i	$-0.460098\pi$
$19$	−3.39964	−	2.46998i	−0.779930	−	0.566652i	−0.904958	+	0.425501i	$0.860098\pi$
$20$	−1.88608	−	1.20112i	−0.421741	−	0.268579i
$21$	−0.800329	+	1.46046i	−0.174646	+	0.318699i
$22$	−1.31924	+	4.06020i	−0.281263	+	0.865638i
$23$	−8.17154	−	2.65510i	−1.70388	−	0.553626i	−0.714588	−	0.699545i	$-0.753386\pi$
$23$	−8.17154	−	2.65510i	−1.70388	−	0.553626i	−0.989296	+	0.145920i	$0.953386\pi$
$24$	−0.739587	−	1.56621i	−0.150968	−	0.319701i
$25$	0.952392	−	4.90846i	0.190478	−	0.981691i
$26$	−5.30729			−1.04085
$27$	3.32834	+	3.99026i	0.640540	+	0.767925i
$28$	0.565158	+	0.777874i	0.106805	+	0.147004i
$29$	−0.531008	−	0.385800i	−0.0986056	−	0.0716412i	0.537390	−	0.843334i	$-0.319410\pi$
$29$	−0.531008	−	0.385800i	−0.0986056	−	0.0716412i	−0.635996	+	0.771693i	$0.719410\pi$
$30$	2.65188	−	2.82268i	0.484165	−	0.515349i
$31$	5.48547	−	0.953751i	0.985219	−	0.171299i
$31$	5.48547	−	0.953751i	0.985219	−	0.171299i
$32$	−1.00000			−0.176777
$33$	−6.48455	−	3.55352i	−1.12882	−	0.618588i
$34$	2.54186	+	3.49856i	0.435925	+	0.599999i
$35$	−1.15488	+	1.81348i	−0.195211	+	0.306534i
$36$	2.90372	−	0.753914i	0.483954	−	0.125652i
$37$	−11.5866			−1.90483			−0.952413	−	0.304811i	$-0.901407\pi$
$37$	−11.5866			−1.90483			−0.952413	+	0.304811i	$0.901407\pi$
$38$	−1.29855	−	3.99651i	−0.210652	−	0.648320i
$39$	1.71031	−	9.03199i	0.273869	−	1.44628i
$40$	−0.819872	−	2.08034i	−0.129633	−	0.328930i
$41$	3.51204	−	4.83391i	0.548489	−	0.754930i	−0.441317	−	0.897351i	$-0.645489\pi$
$41$	3.51204	−	4.83391i	0.548489	−	0.754930i	0.989806	+	0.142421i	$0.0454886\pi$
$42$	−1.50592	+	0.711116i	−0.232368	+	0.109728i
$43$	−3.99229	−	2.90057i	−0.608818	−	0.442332i	0.240180	−	0.970728i	$-0.422794\pi$
$43$	−3.99229	−	2.90057i	−0.608818	−	0.442332i	−0.848998	+	0.528396i	$0.822794\pi$
$44$	−3.45381	+	2.50934i	−0.520682	+	0.378298i
$45$	3.94908	+	5.42262i	0.588694	+	0.808356i
$46$	−5.05029	−	6.95113i	−0.744625	−	1.02489i
$47$	1.31333	−	0.954190i	0.191569	−	0.139183i	−0.487867	−	0.872918i	$-0.662225\pi$
$47$	1.31333	−	0.954190i	0.191569	−	0.139183i	0.679435	+	0.733735i	$0.262225\pi$
$48$	0.322256	−	1.70181i	0.0465137	−	0.245635i
$49$	−4.91519	+	3.57109i	−0.702170	+	0.510156i
$50$	3.65562	−	3.41122i	0.516983	−	0.482420i
$51$	−6.77301	+	3.19832i	−0.948412	+	0.447854i
$52$	−4.29369	−	3.11955i	−0.595428	−	0.432604i
$53$	9.64977	+	3.13540i	1.32550	+	0.430681i	0.884380	−	0.466768i	$-0.154582\pi$
$53$	9.64977	+	3.13540i	1.32550	+	0.430681i	0.441119	+	0.897449i	$0.354582\pi$
$54$	0.347272	+	5.18453i	0.0472578	+	0.705526i
$55$	−8.05197	−	5.12776i	−1.08573	−	0.691427i
$56$			0.961505i			0.128486i
$57$	7.21976	−	0.921973i	0.956281	−	0.122118i
$58$	−0.202827	−	0.624237i	−0.0266325	−	0.0819663i
$59$	5.34618	+	7.35839i	0.696014	+	0.957981i	0.999986	+	0.00530000i	$0.00168705\pi$
$59$	5.34618	+	7.35839i	0.696014	+	0.957981i	−0.303972	+	0.952681i	$0.598313\pi$
$60$	3.80455	−	0.724862i	0.491165	−	0.0935793i
$61$		−	2.74710i		−	0.351731i	−0.984414	−	0.175865i	$-0.943728\pi$
$61$		−	2.74710i		−	0.351731i	0.984414	−	0.175865i	$-0.0562723\pi$
$62$	4.99844	+	2.45268i	0.634802	+	0.311490i
$63$	−0.724891	−	2.79194i	−0.0913277	−	0.351752i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	2.96944	−	11.4900i	0.368314	−	1.42515i
$66$	−3.15741	−	6.68638i	−0.388650	−	0.823036i
$67$		−	6.69091i		−	0.817425i	−0.912663	−	0.408712i	$-0.865978\pi$
$67$		−	6.69091i		−	0.817425i	0.912663	−	0.408712i	$-0.134022\pi$
$68$			4.32446i			0.524418i
$69$	13.4570	−	6.35458i	1.62003	−	0.765002i
$70$	−2.00026	+	0.788311i	−0.239076	+	0.0942211i
$71$	−3.52318	−	1.14475i	−0.418124	−	0.135857i	0.0923964	−	0.995722i	$-0.470547\pi$
$71$	−3.52318	−	1.14475i	−0.418124	−	0.135857i	−0.510521	+	0.859866i	$0.670547\pi$
$72$	2.79230	+	1.09684i	0.329076	+	0.129264i
$73$	1.08376	+	3.33548i	0.126845	+	0.390389i	0.994233	−	0.107244i	$-0.0342026\pi$
$73$	1.08376	+	3.33548i	0.126845	+	0.390389i	−0.867388	+	0.497633i	$0.834203\pi$
$74$	−9.37376	−	6.81043i	−1.08968	−	0.791697i
$75$	4.62720	+	7.32045i	0.534303	+	0.845293i
$76$	1.29855	−	3.99651i	0.148953	−	0.458431i
$77$	2.41274	+	3.32086i	0.274958	+	0.378447i
$78$	6.69254	−	6.30174i	0.757781	−	0.713532i
$79$	−6.26135	−	2.03444i	−0.704457	−	0.228892i	−0.0651857	−	0.997873i	$-0.520764\pi$
$79$	−6.26135	−	2.03444i	−0.704457	−	0.228892i	−0.639271	+	0.768981i	$0.720764\pi$
$80$	0.559502	−	2.16494i	0.0625543	−	0.242047i
$81$	−8.93499	−	1.07976i	−0.992777	−	0.119973i
$82$	5.68261	−	1.84639i	0.627539	−	0.203900i
$83$	−4.99843	+	6.87975i	−0.548649	+	0.755151i	−0.989828	−	0.142268i	$-0.954560\pi$
$83$	−4.99843	+	6.87975i	−0.548649	+	0.755151i	0.441179	+	0.897419i	$0.354560\pi$
$84$	−1.63630	−	0.309851i	−0.178535	−	0.0338075i
$85$	−8.99635	+	3.54551i	−0.975791	+	0.384564i
$86$	−1.52492	−	4.69321i	−0.164436	−	0.506082i
$87$	1.12769	−	0.144008i	0.120901	−	0.0154393i
$88$	−4.26915			−0.455093
$89$	2.62990	+	8.09401i	0.278769	+	0.857963i	0.988197	+	0.153185i	$0.0489532\pi$
$89$	2.62990	+	8.09401i	0.278769	+	0.857963i	−0.709428	+	0.704778i	$0.751047\pi$
$90$	0.00753618	+	6.70820i	0.000794383	+	0.707106i
$91$	−2.99946	+	4.12840i	−0.314429	+	0.432774i
$92$		−	8.59207i		−	0.895785i
$93$	−5.78476	+	7.71599i	−0.599852	+	0.800111i
$94$	1.62336			0.167437
$95$	9.37874	−	0.575213i	0.962239	−	0.0590156i
$96$	1.26101	−	1.18737i	0.128701	−	0.121186i
$97$	13.1863	−	4.28449i	1.33887	−	0.435024i	0.449934	−	0.893062i	$-0.351447\pi$
$97$	13.1863	−	4.28449i	1.33887	−	0.435024i	0.888933	+	0.458037i	$0.151447\pi$
$98$	−6.07551			−0.613719
$99$	12.3964	−	3.21857i	1.24589	−	0.323478i
$100$	4.96253	−	0.611018i	0.496253	−	0.0611018i
$101$	−6.25672	−	2.03293i	−0.622567	−	0.202284i	−0.0192872	−	0.999814i	$-0.506140\pi$
$101$	−6.25672	−	2.03293i	−0.622567	−	0.202284i	−0.603280	+	0.797530i	$0.706140\pi$
$102$	−7.35941	−	1.39359i	−0.728690	−	0.137986i
$103$	−5.39534	+	7.42605i	−0.531619	+	0.731710i	−0.987376	−	0.158394i	$-0.949368\pi$
$103$	−5.39534	+	7.42605i	−0.531619	+	0.731710i	0.455757	+	0.890104i	$0.349368\pi$
$104$	−1.64004	−	5.04754i	−0.160820	−	0.494952i
$105$	−0.696958	−	3.65809i	−0.0680162	−	0.356993i
$106$	5.96389	+	8.20859i	0.579264	+	0.797289i
$107$	−5.84901	+	18.0014i	−0.565445	+	1.74026i	0.101181	+	0.994868i	$0.467738\pi$
$107$	−5.84901	+	18.0014i	−0.565445	+	1.74026i	−0.666626	+	0.745392i	$0.732262\pi$
$108$	−2.76644	+	4.39850i	−0.266201	+	0.423246i
$109$	−11.8543	+	8.61265i	−1.13544	+	0.824943i	−0.986477	−	0.163901i	$-0.947592\pi$
$109$	−11.8543	+	8.61265i	−1.13544	+	0.824943i	−0.148959	+	0.988843i	$0.547592\pi$
$110$	−3.50015	−	8.88128i	−0.333727	−	0.846796i
$111$	14.6108	−	13.7576i	1.38680	−	1.30582i
$112$	−0.565158	+	0.777874i	−0.0534024	+	0.0735021i
$113$	4.76120	+	14.6535i	0.447896	+	1.37848i	0.879277	+	0.476311i	$0.158026\pi$
$113$	4.76120	+	14.6535i	0.447896	+	1.37848i	−0.431381	+	0.902170i	$0.641974\pi$
$114$	6.38283	+	3.49778i	0.597807	+	0.327597i
$115$	17.8744	−	7.04440i	1.66680	−	0.656893i
$116$	0.202827	−	0.624237i	0.0188320	−	0.0579589i
$117$	8.56764	+	13.4202i	0.792079	+	1.24070i
$118$			9.09547i			0.837306i
$119$	4.15799			0.381162
$120$	3.50401	+	1.64983i	0.319871	+	0.150608i
$121$	−5.84566	+	4.24712i	−0.531423	+	0.386102i
$122$	1.61471	−	2.22245i	0.146189	−	0.201211i
$123$	1.31095	+	10.2657i	0.118204	+	0.925628i
$124$	2.60217	+	4.92226i	0.233682	+	0.442032i
$125$	5.33976	+	9.82278i	0.477603	+	0.878576i
$126$	1.05461	−	2.68481i	0.0939525	−	0.239182i
$127$	−12.9959	+	9.44210i	−1.15320	+	0.837851i	−0.988904	−	0.148559i	$-0.952536\pi$
$127$	−12.9959	+	9.44210i	−1.15320	+	0.837851i	−0.164300	+	0.986410i	$0.552536\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	8.47836	−	1.08270i	0.746478	−	0.0953263i
$130$	9.15596	−	7.55018i	0.803031	−	0.662195i
$131$	−14.5380	+	4.72367i	−1.27019	+	0.412709i	−0.865114	−	0.501575i	$-0.832754\pi$
$131$	−14.5380	+	4.72367i	−1.27019	+	0.412709i	−0.405073	+	0.914284i	$0.632754\pi$
$132$	1.37576	−	7.26527i	0.119745	−	0.632361i
$133$	−3.84267	−	1.24856i	−0.333201	−	0.108264i
$134$	3.93282	−	5.41306i	0.339744	−	0.467617i
$135$	−11.4185	−	2.14894i	−0.982748	−	0.184951i
$136$	−2.54186	+	3.49856i	−0.217962	+	0.299999i
$137$	8.84006	+	12.1673i	0.755257	+	1.03952i	0.997594	+	0.0693300i	$0.0220861\pi$
$137$	8.84006	+	12.1673i	0.755257	+	1.03952i	−0.242337	+	0.970192i	$0.577914\pi$
$138$	14.6221	+	2.76885i	1.24471	+	0.235700i
$139$	10.8675	+	14.9578i	0.921765	+	1.26870i	0.962986	+	0.269551i	$0.0868753\pi$
$139$	10.8675	+	14.9578i	0.921765	+	1.26870i	−0.0412206	+	0.999150i	$0.513125\pi$
$140$	−2.08160	−	0.537964i	−0.175927	−	0.0454663i
$141$	−0.523140	+	2.76266i	−0.0440563	+	0.232658i
$142$	−2.17744	−	2.99699i	−0.182727	−	0.251502i
$143$	−18.3304	−	13.3178i	−1.53287	−	1.11369i
$144$	1.61431	+	2.52863i	0.134526	+	0.210719i
$145$	1.46492	−	0.0898457i	0.121655	−	0.00746128i
$146$	−1.08376	+	3.33548i	−0.0896930	+	0.276047i
$147$	1.95787	−	10.3393i	0.161483	−	0.852775i
$148$	−3.58046	−	11.0195i	−0.294312	−	0.905798i
$149$		−	3.06406i		−	0.251017i	−0.992093	−	0.125509i	$-0.959944\pi$
$149$		−	3.06406i		−	0.251017i	0.992093	−	0.125509i	$-0.0400563\pi$
$150$	−0.559371	+	8.64217i	−0.0456725	+	0.705630i
$151$	−9.54214	+	3.10043i	−0.776528	+	0.252309i	−0.670357	−	0.742038i	$-0.733859\pi$
$151$	−9.54214	+	3.10043i	−0.776528	+	0.252309i	−0.106171	+	0.994348i	$0.533859\pi$
$152$	3.39964	−	2.46998i	0.275747	−	0.200342i
$153$	4.74323	−	12.0752i	0.383468	−	0.976223i
$154$			4.10481i			0.330775i
$155$	−8.10653	+	9.44903i	−0.651132	+	0.758964i
$156$	9.11845	−	1.16444i	0.730060	−	0.0932297i
$157$	12.3009	−	16.9308i	0.981722	−	1.35122i	0.0458248	−	0.998949i	$-0.485408\pi$
$157$	12.3009	−	16.9308i	0.981722	−	1.35122i	0.935897	−	0.352274i	$-0.114592\pi$
$158$	−3.86973	−	5.32622i	−0.307859	−	0.423732i
$159$	−15.8913	+	7.50412i	−1.26027	+	0.595116i
$160$	1.72517	−	1.42260i	0.136386	−	0.112467i
$161$	−8.26131			−0.651083
$162$	−6.59390	−	6.12540i	−0.518065	−	0.481257i
$163$	5.13641	+	1.66892i	0.402314	+	0.130720i	0.503183	−	0.864180i	$-0.332162\pi$
$163$	5.13641	+	1.66892i	0.402314	+	0.130720i	−0.100869	+	0.994900i	$0.532162\pi$
$164$	5.68261	+	1.84639i	0.443737	+	0.144179i
$165$	16.2422	−	3.09454i	1.26445	−	0.240910i
$166$	−8.08764	+	2.62783i	−0.627722	+	0.203959i
$167$	5.04830	−	6.94839i	0.390649	−	0.537683i	−0.567717	−	0.823224i	$-0.692173\pi$
$167$	5.04830	−	6.94839i	0.390649	−	0.537683i	0.958367	+	0.285541i	$0.0921732\pi$
$168$	−1.14167	−	1.21247i	−0.0880814	−	0.0935438i
$169$	4.68697	−	14.4250i	0.360536	−	1.10962i
$170$	−9.36220	−	2.41955i	−0.718048	−	0.185571i
$171$	−8.00945	+	9.73517i	−0.612498	+	0.744467i
$172$	1.52492	−	4.69321i	0.116274	−	0.357854i
$173$	16.1328	−	11.7212i	1.22656	−	0.891145i	0.229929	−	0.973207i	$-0.426151\pi$
$173$	16.1328	−	11.7212i	1.22656	−	0.891145i	0.996627	+	0.0820619i	$0.0261505\pi$
$174$	0.996969	+	0.546337i	0.0755800	+	0.0414177i
$175$	−0.587496	−	4.77149i	−0.0444105	−	0.360691i
$176$	−3.45381	−	2.50934i	−0.260341	−	0.189149i
$177$	−15.4787	−	2.93107i	−1.16345	−	0.220313i
$178$	−2.62990	+	8.09401i	−0.197120	+	0.606671i
$179$	−1.18900	−	3.65938i	−0.0888703	−	0.273515i	0.896738	−	0.442563i	$-0.145931\pi$
$179$	−1.18900	−	3.65938i	−0.0888703	−	0.273515i	−0.985608	+	0.169048i	$0.945931\pi$
$180$	−3.93688	+	5.43148i	−0.293438	+	0.404838i
$181$			7.10327i			0.527982i	0.964525	+	0.263991i	$0.0850389\pi$
$181$			7.10327i			0.527982i	−0.964525	+	0.263991i	$0.914961\pi$
$182$	−4.85323	+	1.57691i	−0.359745	+	0.116888i
$183$	3.26184	+	3.46412i	0.241122	+	0.256075i
$184$	5.05029	−	6.95113i	0.372312	−	0.512444i
$185$	19.9888	−	16.4832i	1.46961	−	1.21187i
$186$	−9.21532	+	2.84217i	−0.675700	+	0.208398i
$187$			18.4618i			1.35006i
$188$	1.31333	+	0.954190i	0.0957844	+	0.0695914i
$189$	4.22918	+	2.65995i	0.307627	+	0.193483i
$190$	7.92566	+	5.04733i	0.574988	+	0.366172i
$191$			1.07999i			0.0781451i	0.999236	+	0.0390726i	$0.0124404\pi$
$191$			1.07999i			0.0781451i	−0.999236	+	0.0390726i	$0.987560\pi$
$192$	1.71810	−	0.219404i	0.123993	−	0.0158341i
$193$	7.34154	−	2.38541i	0.528455	−	0.171706i	−0.0326238	−	0.999468i	$-0.510386\pi$
$193$	7.34154	−	2.38541i	0.528455	−	0.171706i	0.561079	+	0.827762i	$0.310386\pi$
$194$	13.1863	+	4.28449i	0.946722	+	0.307609i
$195$	9.89839	+	18.0148i	0.708838	+	1.29007i
$196$	−4.91519	−	3.57109i	−0.351085	−	0.255078i
$197$	13.6357	−	4.43051i	0.971504	−	0.315661i	0.220081	−	0.975482i	$-0.429368\pi$
$197$	13.6357	−	4.43051i	0.971504	−	0.315661i	0.751423	+	0.659821i	$0.229368\pi$
$198$	11.9207	+	4.68256i	0.847171	+	0.332775i
$199$	5.76768	+	7.93854i	0.408860	+	0.562748i	0.962940	−	0.269716i	$-0.0869297\pi$
$199$	5.76768	+	7.93854i	0.408860	+	0.562748i	−0.554080	+	0.832464i	$0.686930\pi$
$200$	4.37391	+	2.42258i	0.309282	+	0.171302i
$201$	7.94461	+	8.43729i	0.560370	+	0.595121i
$202$	−3.86687	−	5.32228i	−0.272072	−	0.374475i
$203$	−0.600207	−	0.195019i	−0.0421263	−	0.0136876i
$204$	−5.13476	−	5.45319i	−0.359505	−	0.381799i
$205$	0.817891	+	13.3355i	0.0571240	+	0.931395i
$206$	−8.72984	+	2.83650i	−0.608237	+	0.197628i
$207$	−9.42410	+	23.9916i	−0.655020	+	1.66753i
$208$	1.64004	−	5.04754i	0.113717	−	0.349984i
$209$	5.54368	−	17.0617i	0.383465	−	1.18018i
$210$	1.58632	−	3.36912i	0.109466	−	0.232491i
$211$	−5.34175			−0.367741			−0.183871	−	0.982950i	$-0.558863\pi$
$211$	−5.34175			−0.367741			−0.183871	+	0.982950i	$0.558863\pi$
$212$			10.1464i			0.696856i
$213$	5.80200	−	2.73979i	0.397547	−	0.187727i
$214$	−15.3129	+	11.1255i	−1.04677	+	0.760522i
$215$	11.0137	−	0.675489i	0.751129	−	0.0460679i
$216$	−4.82347	+	1.93239i	−0.328196	+	0.131482i
$217$	4.73278	−	2.50200i	0.321282	−	0.169847i
$218$	−14.6527			−0.992407
$219$	−5.32710	−	2.91924i	−0.359972	−	0.197264i
$220$	2.38860	−	9.24244i	0.161039	−	0.623125i
$221$	−21.8279	+	7.09231i	−1.46830	+	0.477080i
$222$	19.9069	−	2.54214i	1.33607	−	0.170617i
$223$	−5.52002			−0.369648			−0.184824	−	0.982772i	$-0.559172\pi$
$223$	−5.52002			−0.369648			−0.184824	+	0.982772i	$0.559172\pi$
$224$	−0.914445	+	0.297121i	−0.0610989	+	0.0198523i
$225$	−14.5271	−	3.73694i	−0.968470	−	0.249129i
$226$	−4.76120	+	14.6535i	−0.316710	+	0.974733i
$227$	−9.32119	−	6.77224i	−0.618669	−	0.449489i	0.233787	−	0.972288i	$-0.424888\pi$
$227$	−9.32119	−	6.77224i	−0.618669	−	0.449489i	−0.852456	+	0.522798i	$0.824888\pi$
$228$	3.10788	+	6.58150i	0.205824	+	0.435870i
$229$	2.80773	−	3.86451i	0.185540	−	0.255374i	−0.706107	−	0.708105i	$-0.749550\pi$
$229$	2.80773	−	3.86451i	0.185540	−	0.255374i	0.891647	+	0.452731i	$0.149550\pi$
$230$	18.6013	+	4.80728i	1.22653	+	0.316983i
$231$	−6.98559	−	1.32280i	−0.459618	−	0.0870339i
$232$	0.531008	−	0.385800i	0.0348624	−	0.0253290i
$233$	−4.86747	+	3.53642i	−0.318879	+	0.231679i	−0.735697	−	0.677311i	$-0.763145\pi$
$233$	−4.86747	+	3.53642i	−0.318879	+	0.231679i	0.416818	+	0.908990i	$0.363145\pi$
$234$	−0.956829	+	15.8931i	−0.0625499	+	1.03896i
$235$	−0.908276	+	3.51448i	−0.0592494	+	0.229260i
$236$	−5.34618	+	7.35839i	−0.348007	+	0.478990i
$237$	10.3113	−	4.86912i	0.669788	−	0.316284i
$238$	3.36389	+	2.44401i	0.218048	+	0.158421i
$239$	−6.75114	+	20.7779i	−0.436695	+	1.34401i	0.454645	+	0.890673i	$0.349766\pi$
$239$	−6.75114	+	20.7779i	−0.436695	+	1.34401i	−0.891340	+	0.453336i	$0.850234\pi$
$240$	1.86505	+	3.39434i	0.120389	+	0.219104i
$241$	21.9440	−	7.13003i	1.41354	−	0.459285i	0.499993	−	0.866029i	$-0.333336\pi$
$241$	21.9440	−	7.13003i	1.41354	−	0.459285i	0.913542	+	0.406744i	$0.133336\pi$
$242$	−7.22563			−0.464481
$243$	12.5492	−	9.24760i	0.805030	−	0.593234i
$244$	2.61265	−	0.848902i	0.167258	−	0.0543454i
$245$	3.39926	−	13.1531i	0.217171	−	0.840321i
$246$	−4.97346	+	9.07569i	−0.317096	+	0.578645i
$247$	22.3022			1.41906
$248$	−0.788032	+	5.51172i	−0.0500401	+	0.349994i
$249$	−1.86577	−	14.6104i	−0.118239	−	0.925899i
$250$	−1.45373	+	11.0854i	−0.0919419	+	0.701104i
$251$	−17.4626	+	12.6873i	−1.10223	+	0.800818i	−0.981423	−	0.191858i	$-0.938549\pi$
$251$	−17.4626	+	12.6873i	−1.10223	+	0.800818i	−0.120809	+	0.992676i	$0.538549\pi$
$252$	2.43129	−	1.55217i	0.153157	−	0.0977776i
$253$		−	36.6808i		−	2.30610i
$254$	−16.0639			−1.00794
$255$	7.13463	−	15.1529i	0.446788	−	0.948914i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	1.35302	−	4.16417i	0.0843992	−	0.259754i	−0.899947	−	0.435999i	$-0.856395\pi$
$257$	1.35302	−	4.16417i	0.0843992	−	0.259754i	0.984346	+	0.176245i	$0.0563951\pi$
$258$	7.49553	+	4.10753i	0.466652	+	0.255724i
$259$	−10.5953	+	3.44263i	−0.658361	+	0.213914i
$260$	11.8452	−	0.726486i	0.734609	−	0.0450547i
$261$	−1.25104	+	1.52059i	−0.0774374	+	0.0941221i
$262$	−14.5380	−	4.72367i	−0.898158	−	0.291829i
$263$	6.33275	+	8.71629i	0.390494	+	0.537469i	0.958327	−	0.285675i	$-0.0922178\pi$
$263$	6.33275	+	8.71629i	0.390494	+	0.537469i	−0.567832	+	0.823144i	$0.692218\pi$
$264$	5.38343	−	5.06908i	0.331327	−	0.311980i
$265$	−21.1079	+	8.31873i	−1.29665	+	0.511015i
$266$	−2.37490	−	3.26877i	−0.145614	−	0.200421i
$267$	−12.9269	−	7.08393i	−0.791116	−	0.433530i
$268$	6.36343	−	2.06760i	0.388708	−	0.126299i
$269$	−5.69593	−	4.13833i	−0.347287	−	0.252319i	0.400443	−	0.916322i	$-0.368856\pi$
$269$	−5.69593	−	4.13833i	−0.347287	−	0.252319i	−0.747730	+	0.664003i	$0.768856\pi$
$270$	−7.97465	−	8.45015i	−0.485321	−	0.514260i
$271$	6.47908	+	2.10518i	0.393576	+	0.127881i	0.499118	−	0.866534i	$-0.333658\pi$
$271$	6.47908	+	2.10518i	0.393576	+	0.127881i	−0.105541	+	0.994415i	$0.533658\pi$
$272$	−4.11281	+	1.33633i	−0.249376	+	0.0810271i
$273$	−1.11961	−	8.76743i	−0.0677621	−	0.530629i
$274$			15.0396i			0.908576i
$275$	21.1858	−	2.60852i	1.27755	−	0.157300i
$276$	10.2020	+	10.8347i	0.614088	+	0.652171i
$277$	15.5890	+	11.3261i	0.936655	+	0.680519i	0.947613	−	0.319420i	$-0.103488\pi$
$277$	15.5890	+	11.3261i	0.936655	+	0.680519i	−0.0109584	+	0.999940i	$0.503488\pi$
$278$			18.4888i			1.10889i
$279$	−1.86713	−	16.5986i	−0.111782	−	0.993733i
$280$	−1.36784	−	1.65875i	−0.0817441	−	0.0991296i
$281$	4.53559	−	6.24270i	0.270570	−	0.372408i	−0.652012	−	0.758209i	$-0.726075\pi$
$281$	4.53559	−	6.24270i	0.270570	−	0.372408i	0.922582	+	0.385801i	$0.126075\pi$
$282$	−2.04708	+	1.92754i	−0.121902	+	0.114783i
$283$	−4.69848	+	1.52663i	−0.279296	+	0.0907486i	−0.445315	−	0.895374i	$-0.646908\pi$
$283$	−4.69848	+	1.52663i	−0.279296	+	0.0907486i	0.166020	+	0.986122i	$0.446908\pi$
$284$		−	3.70449i		−	0.219821i
$285$	−11.1437	+	11.8614i	−0.660095	+	0.702610i
$286$	−7.00159	−	21.5487i	−0.414013	−	1.27420i
$287$	1.77531	−	5.46385i	0.104793	−	0.322521i
$288$	−0.180286	+	2.99458i	−0.0106234	+	0.176457i
$289$	1.37612	+	0.999813i	0.0809485	+	0.0588125i
$290$	1.23795	+	0.788370i	0.0726951	+	0.0462947i
$291$	−11.5408	+	21.0599i	−0.676531	+	1.23455i
$292$	−2.83733	+	2.06144i	−0.166042	+	0.120637i
$293$	−6.58119	+	20.2548i	−0.384477	+	1.18330i	0.552382	+	0.833591i	$0.313719\pi$
$293$	−6.58119	+	20.2548i	−0.384477	+	1.18330i	−0.936859	+	0.349708i	$0.886281\pi$
$294$	7.66127	−	7.21390i	0.446814	−	0.420723i
$295$	−19.6911	−	5.08894i	−1.14646	−	0.296289i
$296$	3.58046	−	11.0195i	0.208110	−	0.640496i
$297$	−11.8104	+	18.7778i	−0.685307	+	1.08960i
$298$	1.80101	−	2.47888i	0.104330	−	0.143597i
$299$	43.3688	−	14.0914i	2.50808	−	0.814925i
$300$	−5.53228	+	6.66287i	−0.319406	+	0.384681i
$301$	−4.51255	−	1.46622i	−0.260099	−	0.0845112i
$302$	−9.54214	−	3.10043i	−0.549089	−	0.178410i
$303$	10.3036	−	4.86552i	0.591928	−	0.279517i
$304$	4.20218			0.241012
$305$	3.90804	+	4.73921i	0.223774	+	0.271366i
$306$	10.9350	−	6.98104i	0.625111	−	0.399080i
$307$	−12.6266	−	17.3790i	−0.720639	−	0.991874i	−0.999502	−	0.0315437i	$-0.989958\pi$
$307$	−12.6266	−	17.3790i	−0.720639	−	0.991874i	0.278863	−	0.960331i	$-0.410042\pi$
$308$	−2.41274	+	3.32086i	−0.137479	+	0.189223i
$309$	−2.01393	−	15.7706i	−0.114568	−	0.897158i
$310$	−12.1123	+	2.87953i	−0.687934	+	0.163546i
$311$			9.94506i			0.563933i	0.959424	+	0.281966i	$0.0909867\pi$
$311$			9.94506i			0.563933i	−0.959424	+	0.281966i	$0.909013\pi$
$312$	8.06142	+	4.41764i	0.456388	+	0.250100i
$313$	14.0891	−	10.2363i	0.796364	−	0.578593i	−0.113481	−	0.993540i	$-0.536200\pi$
$313$	14.0891	−	10.2363i	0.796364	−	0.578593i	0.909845	+	0.414948i	$0.136200\pi$
$314$	19.9033	−	6.46698i	1.12321	−	0.364953i
$315$	5.22239	+	3.78533i	0.294248	+	0.213279i
$316$		−	6.58357i		−	0.370355i
$317$	−9.13474	−	28.1138i	−0.513058	−	1.57903i	−0.786788	−	0.617223i	$-0.788257\pi$
$317$	−9.13474	−	28.1138i	−0.513058	−	1.57903i	0.273730	−	0.961807i	$-0.411743\pi$
$318$	−17.2672	−	3.26973i	−0.968295	−	0.183358i
$319$	0.865898	−	2.66496i	0.0484810	−	0.149209i
$320$	2.23187	−	0.136884i	0.124766	−	0.00765207i
$321$	−13.9987	−	29.6449i	−0.781333	−	1.65462i
$322$	−6.68354	−	4.85588i	−0.372459	−	0.270608i
$323$	−10.6813	−	14.7016i	−0.594326	−	0.818019i
$324$	−1.73415	−	8.83135i	−0.0963419	−	0.490630i
$325$	11.2229	+	24.0464i	0.622534	+	1.33386i
$326$	3.17447	+	4.36929i	0.175818	+	0.241993i
$327$	4.72193	−	24.9361i	0.261124	−	1.37897i
$328$	3.51204	+	4.83391i	0.193920	+	0.266908i
$329$	0.917458	−	1.26277i	0.0505811	−	0.0696189i
$330$	14.9591	+	7.04337i	0.823473	+	0.387725i
$331$	1.79069	−	2.46467i	0.0984250	−	0.135470i	−0.756964	−	0.653457i	$-0.773318\pi$
$331$	1.79069	−	2.46467i	0.0984250	−	0.135470i	0.855389	+	0.517986i	$0.173318\pi$
$332$	−8.08764	−	2.62783i	−0.443867	−	0.144221i
$333$	−2.08890	+	34.6970i	−0.114471	+	1.90138i
$334$	8.16833	−	2.65405i	0.446951	−	0.145223i
$335$	9.51852	+	11.5429i	0.520052	+	0.630657i
$336$	−0.210958	−	1.65196i	−0.0115087	−	0.0901218i
$337$	4.24788	+	13.0736i	0.231397	+	0.712167i	0.997579	+	0.0695430i	$0.0221541\pi$
$337$	4.24788	+	13.0736i	0.231397	+	0.712167i	−0.766182	+	0.642624i	$0.777846\pi$
$338$	12.2707	−	8.91515i	0.667435	−	0.484920i
$339$	−23.4030	−	12.8248i	−1.27108	−	0.696548i
$340$	−6.15200	−	7.46042i	−0.333639	−	0.404598i
$341$	11.1091	+	21.0139i	0.601590	+	1.13797i
$342$	−12.2020	+	3.16808i	−0.659807	+	0.171310i
$343$	−7.38973	+	10.1711i	−0.399008	+	0.549187i
$344$	3.99229	−	2.90057i	0.215250	−	0.156388i
$345$	−14.1755	+	30.1067i	−0.763181	+	1.62089i
$346$	19.9413			1.07205
$347$		−	19.3954i		−	1.04120i	−0.853801	−	0.520600i	$-0.825708\pi$
$347$		−	19.3954i		−	1.04120i	0.853801	−	0.520600i	$-0.174292\pi$
$348$	0.485436	+	1.02800i	0.0260221	+	0.0551066i
$349$	−10.6468	+	32.7675i	−0.569911	+	1.75401i	0.0829779	+	0.996551i	$0.473557\pi$
$349$	−10.6468	+	32.7675i	−0.569911	+	1.75401i	−0.652889	+	0.757454i	$0.726443\pi$
$350$	2.32932	−	4.20554i	0.124507	−	0.224796i
$351$	−26.7387	−	6.74999i	−1.42720	−	0.360288i
$352$	−1.31924	−	4.06020i	−0.0703157	−	0.216409i
$353$	−1.22064	+	1.68006i	−0.0649680	+	0.0894207i	−0.840265	−	0.542177i	$-0.817600\pi$
$353$	−1.22064	+	1.68006i	−0.0649680	+	0.0894207i	0.775297	+	0.631597i	$0.217600\pi$
$354$	−10.7997	−	11.4695i	−0.573999	−	0.609595i
$355$	7.70659	−	3.03721i	0.409023	−	0.161198i
$356$	−6.88517	+	5.00237i	−0.364913	+	0.265125i
$357$	−5.24326	+	4.93709i	−0.277503	+	0.261299i
$358$	1.18900	−	3.65938i	0.0628408	−	0.193404i
$359$	−2.68754	−	3.69908i	−0.141843	−	0.195230i	0.732185	−	0.681106i	$-0.238501\pi$
$359$	−2.68754	−	3.69908i	−0.141843	−	0.195230i	−0.874028	+	0.485876i	$0.838501\pi$
$360$	−6.37755	+	2.08012i	−0.336126	+	0.109632i
$361$	−0.414599	−	1.27600i	−0.0218210	−	0.0671581i
$362$	−4.17519	+	5.74666i	−0.219443	+	0.302038i
$363$	2.32851	−	12.2966i	0.122215	−	0.645406i
$364$	−4.85323	−	1.57691i	−0.254378	−	0.0826525i
$365$	−6.61475	−	4.21249i	−0.346232	−	0.220492i
$366$	0.602724	+	4.71979i	0.0315049	+	0.246708i
$367$	15.0062			0.783317			0.391658	−	0.920111i	$-0.371902\pi$
$367$	15.0062			0.783317			0.391658	+	0.920111i	$0.371902\pi$
$368$	8.17154	−	2.65510i	0.425971	−	0.138406i
$369$	−13.8424	−	11.3886i	−0.720604	−	0.592865i
$370$	25.8598	−	1.58603i	1.34439	−	0.0824535i
$371$	9.75578			0.506495
$372$	−9.12593	−	3.11726i	−0.473158	−	0.161623i
$373$		−	14.4077i		−	0.746000i	−0.927831	−	0.373000i	$-0.878329\pi$
$373$		−	14.4077i		−	0.746000i	0.927831	−	0.373000i	$-0.121671\pi$
$374$	−10.8516	+	14.9359i	−0.561121	+	0.772316i
$375$	−18.3968	−	6.04632i	−0.950006	−	0.312230i
$376$	0.501647	+	1.54391i	0.0258705	+	0.0796212i
$377$	3.48350			0.179410
$378$	1.85800	+	4.63779i	0.0955651	+	0.238542i
$379$	−3.17108	−	9.75959i	−0.162888	−	0.501316i	0.835987	−	0.548749i	$-0.184896\pi$
$379$	−3.17108	−	9.75959i	−0.162888	−	0.501316i	−0.998874	+	0.0474332i	$0.984896\pi$
$380$	3.44525	+	8.74196i	0.176738	+	0.448453i
$381$	5.17669	−	27.3376i	0.265210	−	1.40055i
$382$	−0.634801	+	0.873728i	−0.0324792	+	0.0447038i
$383$	−8.83194	+	2.86967i	−0.451291	+	0.146633i	−0.525839	−	0.850584i	$-0.676249\pi$
$383$	−8.83194	+	2.86967i	−0.451291	+	0.146633i	0.0745480	+	0.997217i	$0.476249\pi$
$384$	1.51893	+	0.832372i	0.0775127	+	0.0424768i
$385$	−8.88665	−	2.29665i	−0.452906	−	0.117048i
$386$	7.34154	+	2.38541i	0.373674	+	0.121414i
$387$	−9.40572	+	11.4323i	−0.478120	+	0.581135i
$388$	8.14959	+	11.2169i	0.413733	+	0.569454i
$389$	1.26103	−	3.88104i	0.0639365	−	0.196776i	−0.913985	−	0.405747i	$-0.867011\pi$
$389$	1.26103	−	3.88104i	0.0639365	−	0.196776i	0.977922	+	0.208971i	$0.0670114\pi$
$390$	−2.58086	+	20.3924i	−0.130687	+	1.03261i
$391$	−30.0599	−	21.8398i	−1.52019	−	1.10449i
$392$	−1.87744	−	5.77815i	−0.0948248	−	0.291841i
$393$	12.7237	−	23.2186i	0.641827	−	1.17122i
$394$	13.6357	+	4.43051i	0.686957	+	0.223206i
$395$	13.6961	−	5.39769i	0.689124	−	0.271587i
$396$	6.89175	+	10.7951i	0.346323	+	0.542475i
$397$			32.1109i			1.61160i	0.592188	+	0.805800i	$0.298264\pi$
$397$			32.1109i			1.61160i	−0.592188	+	0.805800i	$0.701736\pi$
$398$			9.81257i			0.491860i
$399$	6.32814	−	2.98824i	0.316803	−	0.149599i
$400$	2.11462	+	4.53083i	0.105731	+	0.226541i
$401$	−2.44803	−	1.77860i	−0.122249	−	0.0888190i	0.524981	−	0.851114i	$-0.324073\pi$
$401$	−2.44803	−	1.77860i	−0.122249	−	0.0888190i	−0.647230	+	0.762295i	$0.724073\pi$
$402$	1.46801	+	11.4956i	0.0732176	+	0.573350i
$403$	−20.5776	+	21.2073i	−1.02504	+	1.05641i
$404$		−	6.57870i		−	0.327303i
$405$	16.9504	−	10.8482i	0.842273	−	0.539051i
$406$	−0.370948	−	0.510566i	−0.0184098	−	0.0253390i
$407$	−15.2855	−	47.0439i	−0.757674	−	2.33188i
$408$	−0.948802	−	7.42985i	−0.0469727	−	0.367833i
$409$			5.95196i			0.294306i	0.989114	+	0.147153i	$0.0470109\pi$
$409$			5.95196i			0.294306i	−0.989114	+	0.147153i	$0.952989\pi$
$410$	−7.17675	+	11.2694i	−0.354434	+	0.556557i
$411$	−25.5945	−	4.84661i	−1.26248	−	0.239066i
$412$	−8.72984	−	2.83650i	−0.430088	−	0.139744i
$413$	7.07513	+	5.14038i	0.348144	+	0.252942i
$414$	−21.7262	+	13.8703i	−1.06778	+	0.681688i
$415$	−1.16404	−	18.9795i	−0.0571407	−	0.931667i
$416$	4.29369	−	3.11955i	0.210515	−	0.152948i
$417$	−31.4644	−	5.95814i	−1.54082	−	0.291771i
$418$	14.5136	−	10.5447i	0.709881	−	0.515759i
$419$	11.6950	+	16.0968i	0.571339	+	0.786381i	0.992713	−	0.120506i	$-0.0384518\pi$
$419$	11.6950	+	16.0968i	0.571339	+	0.786381i	−0.421373	+	0.906887i	$0.638452\pi$
$420$	3.26368	−	1.79326i	0.159251	−	0.0875021i
$421$	25.4987	−	18.5259i	1.24273	−	0.902895i	0.244951	−	0.969535i	$-0.421228\pi$
$421$	25.4987	−	18.5259i	1.24273	−	0.902895i	0.997777	+	0.0666403i	$0.0212280\pi$
$422$	−4.32157	−	3.13980i	−0.210371	−	0.152843i
$423$	−2.62062	−	4.10489i	−0.127419	−	0.199587i
$424$	−5.96389	+	8.20859i	−0.289632	+	0.398644i
$425$	10.4763	−	18.9148i	0.508177	−	0.917504i
$426$	6.30433	+	1.19380i	0.305446	+	0.0578396i
$427$	−0.816223	−	2.51208i	−0.0394998	−	0.121568i
$428$	−18.9278			−0.914909
$429$	38.9280	−	4.97116i	1.87946	−	0.240010i
$430$	9.30732	+	5.92721i	0.448839	+	0.285836i
$431$	−18.7101	−	25.7523i	−0.901235	−	1.24044i	−0.970073	−	0.242815i	$-0.921929\pi$
$431$	−18.7101	−	25.7523i	−0.901235	−	1.24044i	0.0688379	−	0.997628i	$-0.478071\pi$
$432$	−5.03810	−	1.27183i	−0.242396	−	0.0611911i
$433$	−14.9895			−0.720350			−0.360175	−	0.932885i	$-0.617283\pi$
$433$	−14.9895			−0.720350			−0.360175	+	0.932885i	$0.617283\pi$
$434$	5.29954	+	0.757696i	0.254386	+	0.0363706i
$435$	−1.74059	+	1.85270i	−0.0834550	+	0.0888302i
$436$	−11.8543	−	8.61265i	−0.567718	−	0.412471i
$437$	21.2222	+	29.2099i	1.01520	+	1.39730i
$438$	−2.59383	−	5.49291i	−0.123938	−	0.262461i
$439$	0.285040			0.0136042			0.00680210	−	0.999977i	$-0.497835\pi$
$439$	0.285040			0.0136042			0.00680210	+	0.999977i	$0.497835\pi$
$440$	7.36499	−	6.07331i	0.351112	−	0.289534i
$441$	9.80778	+	15.3627i	0.467037	+	0.731559i
$442$	−21.8279	−	7.09231i	−1.03825	−	0.337347i
$443$	−5.39096	+	16.5917i	−0.256132	+	0.788294i	0.737472	+	0.675378i	$0.236019\pi$
$443$	−5.39096	+	16.5917i	−0.256132	+	0.788294i	−0.993604	+	0.112917i	$0.963981\pi$
$444$	17.5993	+	9.64436i	0.835224	+	0.457701i
$445$	−16.0516	−	10.2222i	−0.760918	−	0.484578i
$446$	−4.46579	−	3.24459i	−0.211461	−	0.153636i
$447$	3.63818	+	3.86380i	0.172080	+	0.182752i
$448$	−0.914445	−	0.297121i	−0.0432035	−	0.0140377i
$449$	−20.2707	+	14.7275i	−0.956633	+	0.695034i	−0.952366	−	0.304957i	$-0.901358\pi$
$449$	−20.2707	+	14.7275i	−0.956633	+	0.695034i	−0.00426633	+	0.999991i	$0.501358\pi$
$450$	−9.55612	−	11.5620i	−0.450480	−	0.545040i
$451$	24.2599	+	7.88251i	1.14235	+	0.371173i
$452$	−12.4650	+	9.05633i	−0.586303	+	0.425974i
$453$	8.35135	−	15.2398i	0.392381	−	0.716026i
$454$	−3.56038	−	10.9577i	−0.167097	−	0.514271i
$455$	−0.698519	−	11.3892i	−0.0327471	−	0.533935i
$456$	−1.35418	+	7.15131i	−0.0634153	+	0.334891i
$457$	−8.93825	+	27.5091i	−0.418114	+	1.28682i	0.491323	+	0.870978i	$0.336514\pi$
$457$	−8.93825	+	27.5091i	−0.418114	+	1.28682i	−0.909436	+	0.415844i	$0.863486\pi$
$458$	4.54300	−	1.47611i	0.212281	−	0.0689741i
$459$	8.35653	+	20.8589i	0.390049	+	0.973611i
$460$	12.2231	+	14.8227i	0.569906	+	0.691114i
$461$	−3.24833	−	9.99734i	−0.151290	−	0.465622i	0.846476	−	0.532427i	$-0.178720\pi$
$461$	−3.24833	−	9.99734i	−0.151290	−	0.465622i	−0.997766	+	0.0668041i	$0.978720\pi$
$462$	−4.87394	−	5.17620i	−0.226756	−	0.240818i
$463$	21.1610	+	15.3743i	0.983433	+	0.714506i	0.958473	−	0.285183i	$-0.0920542\pi$
$463$	21.1610	+	15.3743i	0.983433	+	0.714506i	0.0249598	+	0.999688i	$0.492054\pi$
$464$	0.656362			0.0304708
$465$	−0.997130	−	21.5408i	−0.0462408	−	0.998930i
$466$	−6.01652			−0.278710
$467$	9.34027	+	6.78611i	0.432216	+	0.314024i	0.782534	−	0.622607i	$-0.213927\pi$
$467$	9.34027	+	6.78611i	0.432216	+	0.314024i	−0.350318	+	0.936631i	$0.613927\pi$
$468$	−10.1158	+	12.2954i	−0.467604	+	0.568354i
$469$	−1.98801	−	6.11847i	−0.0917978	−	0.282525i
$470$	−2.80057	+	2.30941i	−0.129181	+	0.106525i
$471$	4.59159	+	35.9557i	0.211569	+	1.65675i
$472$	−8.65031	+	2.81066i	−0.398163	+	0.129371i
$473$	6.51010	−	20.0360i	0.299335	−	0.921257i
$474$	11.2040	+	2.12160i	0.514616	+	0.0974483i
$475$	−15.3616	+	14.3346i	−0.704838	+	0.657716i
$476$	1.28489	+	3.95449i	0.0588928	+	0.181254i
$477$	11.1289	−	28.3317i	0.509558	−	1.29722i
$478$	−17.6747	+	12.8414i	−0.808422	+	0.587353i
$479$	−4.15701	−	1.35070i	−0.189939	−	0.0617149i	0.212503	−	0.977160i	$-0.431838\pi$
$479$	−4.15701	−	1.35070i	−0.189939	−	0.0617149i	−0.402442	+	0.915446i	$0.631838\pi$
$480$	−0.486285	+	3.84233i	−0.0221958	+	0.175378i
$481$	49.7493	−	36.1450i	2.26837	−	1.64807i
$482$	21.9440	+	7.13003i	0.999520	+	0.324764i
$483$	10.4176	−	9.80927i	0.474017	−	0.446337i
$484$	−5.84566	−	4.24712i	−0.265712	−	0.193051i
$485$	−16.6534	+	26.1504i	−0.756193	+	1.18743i
$486$	15.5881	−	0.105237i	0.707091	−	0.00477365i
$487$	1.83195	−	5.63815i	0.0830134	−	0.255489i	−0.900932	−	0.433961i	$-0.857115\pi$
$487$	1.83195	−	5.63815i	0.0830134	−	0.255489i	0.983945	+	0.178472i	$0.0571155\pi$
$488$	2.61265	+	0.848902i	0.118269	+	0.0384280i
$489$	−8.45869	+	3.99431i	−0.382515	+	0.180629i
$490$	10.4813	−	8.64305i	0.473495	−	0.390453i
$491$	9.37732			0.423193			0.211596	−	0.977357i	$-0.432134\pi$
$491$	9.37732			0.423193			0.211596	+	0.977357i	$0.432134\pi$
$492$	−9.35817	+	4.41906i	−0.421899	+	0.199227i
$493$	−1.66838	−	2.29632i	−0.0751399	−	0.103421i
$494$	18.0429	+	13.1089i	0.811787	+	0.589798i
$495$	−16.8071	+	23.1878i	−0.755425	+	1.04221i
$496$	−3.87724	+	3.99588i	−0.174093	+	0.179420i
$497$	−3.56188			−0.159772
$498$	7.07836	−	12.9168i	0.317189	−	0.578814i
$499$	−21.5271	−	29.6295i	−0.963686	−	1.32640i	−0.945172	−	0.326572i	$-0.894106\pi$
$499$	−21.5271	−	29.6295i	−0.963686	−	1.32640i	−0.0185139	−	0.999829i	$-0.505894\pi$
$500$	−7.69194	+	8.11382i	−0.343994	+	0.362861i
$501$	1.88439	+	14.7562i	0.0841882	+	0.659259i
$502$	−21.5850			−0.963386
$503$	0.202641	+	0.623665i	0.00903532	+	0.0278079i	0.955473	−	0.295080i	$-0.0953463\pi$
$503$	0.202641	+	0.623665i	0.00903532	+	0.0278079i	−0.946437	+	0.322888i	$0.895346\pi$
$504$	2.87930	+	0.173345i	0.128254	+	0.00772142i
$505$	13.6859	−	5.39369i	0.609016	−	0.240016i
$506$	21.5604	−	29.6754i	0.958479	−	1.31923i
$507$	11.2176	+	23.7553i	0.498190	+	1.05501i
$508$	−12.9959	−	9.44210i	−0.576602	−	0.418926i
$509$	1.31851	−	0.957955i	0.0584420	−	0.0424606i	−0.558181	−	0.829719i	$-0.688500\pi$
$509$	1.31851	−	0.957955i	0.0584420	−	0.0424606i	0.616623	+	0.787259i	$0.288500\pi$
$510$	14.6787	−	8.06536i	0.649985	−	0.357140i
$511$	1.98209	+	2.72811i	0.0876824	+	0.120684i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−1.45930	−	21.7864i	−0.0644298	−	0.961891i
$514$	3.54226	−	2.57360i	0.156242	−	0.113517i
$515$	−1.25648	−	20.4866i	−0.0553669	−	0.902747i
$516$	3.64967	+	7.72883i	0.160668	+	0.340243i
$517$	5.60680	+	4.07358i	0.246587	+	0.179156i
$518$	−10.5953	−	3.44263i	−0.465531	−	0.151260i
$519$	−6.42621	+	33.9362i	−0.282079	+	1.48963i
$520$	10.0100	+	6.37470i	0.438967	+	0.279549i
$521$		−	7.53834i		−	0.330261i	−0.986272	−	0.165130i	$-0.947195\pi$
$521$		−	7.53834i		−	0.330261i	0.986272	−	0.165130i	$-0.0528045\pi$
$522$	−1.90589	+	0.494840i	−0.0834187	+	0.0216586i
$523$	−6.02873	−	18.5545i	−0.263618	−	0.811333i	−0.992009	−	0.126171i	$-0.959731\pi$
$523$	−6.02873	−	18.5545i	−0.263618	−	0.811333i	0.728390	−	0.685162i	$-0.240269\pi$
$524$	−8.98495	−	12.3667i	−0.392509	−	0.540243i
$525$	6.40638	+	5.31931i	0.279597	+	0.232154i
$526$			10.7739i			0.469765i
$527$	23.8352	+	3.40781i	1.03828	+	0.148447i
$528$	7.33482	−	0.936666i	0.319207	−	0.0407632i
$529$	41.1172	+	29.8734i	1.78770	+	1.29884i
$530$	−21.9663	−	5.67692i	−0.954154	−	0.246590i
$531$	22.9991	−	14.6830i	0.998077	−	0.637186i
$532$		−	4.04042i		−	0.175174i
$533$			31.7113i			1.37357i
$534$	−6.29428	−	13.3293i	−0.272380	−	0.576815i
$535$	−15.5184	−	39.3762i	−0.670917	−	1.70238i
$536$	6.36343	+	2.06760i	0.274858	+	0.0893069i
$537$	5.84439	+	3.20271i	0.252204	+	0.138207i
$538$	−2.17565	−	6.69597i	−0.0937990	−	0.288684i
$539$	−20.9837	−	15.2455i	−0.903831	−	0.656672i
$540$	−1.48475	−	11.5237i	−0.0638935	−	0.495901i
$541$	13.9204	−	42.8425i	0.598483	−	1.84194i	0.0619222	−	0.998081i	$-0.480277\pi$
$541$	13.9204	−	42.8425i	0.598483	−	1.84194i	0.536561	−	0.843861i	$-0.319723\pi$
$542$	4.00429	+	5.51144i	0.171999	+	0.236736i
$543$	−8.43423	−	8.95728i	−0.361948	−	0.384394i
$544$	−4.11281	−	1.33633i	−0.176335	−	0.0572948i
$545$	8.19823	−	31.7222i	0.351174	−	1.35883i
$546$	4.24758	−	7.75110i	0.181780	−	0.331716i
$547$	17.7158	−	5.75623i	0.757475	−	0.246118i	0.0952803	−	0.995450i	$-0.469625\pi$
$547$	17.7158	−	5.75623i	0.757475	−	0.246118i	0.662194	+	0.749332i	$0.269625\pi$
$548$	−8.84006	+	12.1673i	−0.377629	+	0.519761i
$549$	−8.22642	−	0.495263i	−0.351095	−	0.0211373i
$550$	18.6729	+	10.3423i	0.796215	+	0.440999i
$551$	0.852315	+	2.62316i	0.0363099	+	0.111750i
$552$	1.88513	+	14.7620i	0.0802365	+	0.628313i
$553$	−6.33014			−0.269185
$554$	5.95448	+	18.3260i	0.252982	+	0.778598i
$555$	−5.63439	+	44.5196i	−0.239167	+	1.88975i
$556$	−10.8675	+	14.9578i	−0.460883	+	0.634351i
$557$			14.5932i			0.618336i	0.951008	+	0.309168i	$0.100050\pi$
$557$			14.5932i			0.618336i	−0.951008	+	0.309168i	$0.899950\pi$
$558$	8.24588	−	14.5260i	0.349076	−	0.614936i
$559$	26.1901			1.10772
$560$	−0.131615	−	2.14596i	−0.00556175	−	0.0906833i
$561$	−21.9210	−	23.2805i	−0.925507	−	0.982902i
$562$	7.33873	−	2.38450i	0.309566	−	0.100584i
$563$	−13.9891			−0.589571			−0.294786	−	0.955563i	$-0.595248\pi$
$563$	−13.9891			−0.589571			−0.294786	+	0.955563i	$0.595248\pi$
$564$	−2.78910	+	0.356172i	−0.117442	+	0.0149975i
$565$	−29.0599	−	18.5063i	−1.22256	−	0.778567i
$566$	−4.69848	−	1.52663i	−0.197492	−	0.0641690i
$567$	−8.49138	+	1.66740i	−0.356605	+	0.0700241i
$568$	2.17744	−	2.99699i	0.0913635	−	0.125751i
$569$	1.31443	+	4.04540i	0.0551038	+	0.169592i	0.974821	−	0.222990i	$-0.0715818\pi$
$569$	1.31443	+	4.04540i	0.0551038	+	0.169592i	−0.919717	+	0.392582i	$0.871582\pi$
$570$	−15.9874	+	3.04600i	−0.669638	+	0.127583i
$571$	4.80859	+	6.61846i	0.201233	+	0.276974i	0.897692	−	0.440622i	$-0.145242\pi$
$571$	4.80859	+	6.61846i	0.201233	+	0.276974i	−0.696459	+	0.717596i	$0.745242\pi$
$572$	7.00159	−	21.5487i	0.292751	−	0.900995i
$573$	−1.28235	−	1.36187i	−0.0535709	−	0.0568931i
$574$	4.64783	−	3.37685i	0.193997	−	0.140947i
$575$	−20.8149	+	37.5810i	−0.868043	+	1.56724i
$576$	−1.90602	+	2.31670i	−0.0794176	+	0.0965290i
$577$	−8.20262	+	11.2899i	−0.341480	+	0.470007i	−0.944873	−	0.327437i	$-0.893815\pi$
$577$	−8.20262	+	11.2899i	−0.341480	+	0.470007i	0.603393	+	0.797444i	$0.293815\pi$
$578$	0.525633	+	1.61773i	0.0218634	+	0.0672887i
$579$	−6.42537	+	11.7252i	−0.267029	+	0.487282i
$580$	0.538132	+	1.36545i	0.0223447	+	0.0566974i
$581$	−2.52667	+	7.77630i	−0.104824	+	0.322615i
$582$	−21.7153	+	10.2543i	−0.900130	+	0.425054i
$583$			43.3164i			1.79398i
$584$	−3.50714			−0.145126
$585$	−33.8722	−	10.9637i	−1.40044	−	0.453293i
$586$	−17.2298	+	12.5182i	−0.711756	+	0.517121i
$587$	1.47716	−	2.03314i	0.0609690	−	0.0839166i	−0.777444	−	0.628952i	$-0.783484\pi$
$587$	1.47716	−	2.03314i	0.0609690	−	0.0839166i	0.838413	+	0.545036i	$0.183484\pi$
$588$	10.4383	−	1.33299i	0.430469	−	0.0549715i
$589$	−21.0043	−	10.3066i	−0.865469	−	0.424676i
$590$	−12.9393	−	15.6912i	−0.532701	−	0.645996i
$591$	−11.9341	+	21.7776i	−0.490902	+	0.895811i
$592$	9.37376	−	6.81043i	0.385259	−	0.279907i
$593$	6.10403	+	18.7863i	0.250662	+	0.771459i	0.994653	+	0.103270i	$0.0329305\pi$
$593$	6.10403	+	18.7863i	0.250662	+	0.771459i	−0.743991	+	0.668190i	$0.767070\pi$
$594$	−20.5921	+	8.24964i	−0.844905	+	0.338487i
$595$	−7.17322	+	5.91518i	−0.294074	+	0.242499i
$596$	2.91409	−	0.946846i	0.119366	−	0.0387843i
$597$	−16.6991	−	3.16216i	−0.683449	−	0.129419i
$598$	43.3688	+	14.0914i	1.77348	+	0.576239i
$599$	−0.479554	+	0.660049i	−0.0195940	+	0.0269689i	−0.818702	−	0.574219i	$-0.805306\pi$
$599$	−0.479554	+	0.660049i	−0.0195940	+	0.0269689i	0.799108	+	0.601188i	$0.205306\pi$
$600$	−8.39205	+	2.13858i	−0.342604	+	0.0873073i
$601$	−24.7647	+	34.0857i	−1.01017	+	1.39038i	−0.0913037	+	0.995823i	$0.529103\pi$
$601$	−24.7647	+	34.0857i	−1.01017	+	1.39038i	−0.918870	+	0.394561i	$0.870897\pi$
$602$	−2.78891	−	3.83860i	−0.113667	−	0.156450i
$603$	−20.0364	−	1.20627i	−0.815947	−	0.0491233i
$604$	−5.89737	−	8.11703i	−0.239960	−	0.330277i
$605$	4.04275	−	15.6430i	0.164361	−	0.635980i
$606$	11.1957	+	2.12003i	0.454794	+	0.0861203i
$607$	−6.71803	−	9.24658i	−0.272677	−	0.375307i	0.650615	−	0.759408i	$-0.274511\pi$
$607$	−6.71803	−	9.24658i	−0.272677	−	0.375307i	−0.923291	+	0.384101i	$0.874511\pi$
$608$	3.39964	+	2.46998i	0.137873	+	0.100171i
$609$	0.988426	−	0.466749i	0.0400531	−	0.0189136i
$610$	0.376036	+	6.13119i	0.0152252	+	0.248245i
$611$	−2.66239	+	8.19399i	−0.107709	+	0.331493i
$612$	12.9499	+	0.779639i	0.523470	+	0.0315150i
$613$	1.78901	+	5.50600i	0.0722574	+	0.222385i	0.980663	−	0.195705i	$-0.0626995\pi$
$613$	1.78901	+	5.50600i	0.0722574	+	0.222385i	−0.908405	+	0.418090i	$0.862700\pi$
$614$		−	21.4817i		−	0.866930i
$615$	−16.8657	−	15.8451i	−0.680089	−	0.638936i
$616$	−3.90390	+	1.26845i	−0.157293	+	0.0511075i
$617$	−28.1428	+	20.4469i	−1.13299	+	0.823162i	−0.986126	−	0.165996i	$-0.946916\pi$
$617$	−28.1428	+	20.4469i	−1.13299	+	0.823162i	−0.146859	+	0.989157i	$0.546916\pi$
$618$	7.64042	−	13.9424i	0.307343	−	0.560847i
$619$		−	28.4459i		−	1.14334i	−0.820485	−	0.571668i	$-0.806297\pi$
$619$		−	28.4459i		−	1.14334i	0.820485	−	0.571668i	$-0.193703\pi$
$620$	−11.4916	−	4.78986i	−0.461514	−	0.192365i
$621$	−16.6032	−	41.4436i	−0.666263	−	1.66307i
$622$	−5.84556	+	8.04572i	−0.234386	+	0.322604i
$623$	4.80980	+	6.62013i	0.192701	+	0.265230i
$624$	3.92520	+	8.31233i	0.157134	+	0.332760i
$625$	−23.1859	−	9.34955i	−0.927436	−	0.373982i
$626$	17.4151			0.696048
$627$	13.2680	+	28.0974i	0.529873	+	1.12210i
$628$	19.9033	+	6.46698i	0.794229	+	0.258061i
$629$	−47.6535	−	15.4836i	−1.90007	−	0.617370i
$630$	2.00004	+	6.13204i	0.0796835	+	0.244306i
$631$	−44.3316	+	14.4042i	−1.76481	+	0.573423i	−0.997681	−	0.0680663i	$-0.978317\pi$
$631$	−44.3316	+	14.4042i	−1.76481	+	0.573423i	−0.767132	+	0.641489i	$0.778317\pi$
$632$	3.86973	−	5.32622i	0.153930	−	0.211866i
$633$	6.73599	−	6.34265i	0.267732	−	0.252098i
$634$	9.13474	−	28.1138i	0.362787	−	1.11654i
$635$	8.98777	−	34.7773i	0.356669	−	1.38009i
$636$	−12.0475	−	12.7947i	−0.477716	−	0.507341i
$637$	9.96410	−	30.6663i	0.394792	−	1.21504i
$638$	2.26695	−	1.64704i	0.0897494	−	0.0652068i
$639$	−4.06322	+	10.3440i	−0.160739	+	0.409204i
$640$	1.88608	+	1.20112i	0.0745540	+	0.0474785i
$641$	20.1426	+	14.6345i	0.795586	+	0.578027i	0.909616	−	0.415450i	$-0.136376\pi$
$641$	20.1426	+	14.6345i	0.795586	+	0.578027i	−0.114030	+	0.993477i	$0.536376\pi$
$642$	6.09960	−	32.2115i	0.240732	−	1.27128i
$643$	7.74948	−	23.8505i	0.305610	−	0.940570i	−0.673839	−	0.738878i	$-0.735356\pi$
$643$	7.74948	−	23.8505i	0.305610	−	0.940570i	0.979449	−	0.201692i	$-0.0646440\pi$
$644$	−2.55289	−	7.85698i	−0.100598	−	0.309608i
$645$	−13.0863	+	13.9292i	−0.515274	+	0.548461i
$646$		−	18.1722i		−	0.714975i
$647$	−4.82110	+	1.56647i	−0.189537	+	0.0615842i	−0.402247	−	0.915531i	$-0.631771\pi$
$647$	−4.82110	+	1.56647i	−0.189537	+	0.0615842i	0.212711	+	0.977115i	$0.431771\pi$
$648$	3.78798	−	8.16402i	0.148806	−	0.320713i
$649$	−22.8237	+	31.4141i	−0.895907	+	1.23311i
$650$	−5.05463	+	26.0506i	−0.198259	+	1.02179i
$651$	−2.99726	+	8.77463i	−0.117472	+	0.343905i
$652$			5.40074i			0.211509i
$653$	−14.0873	−	10.2350i	−0.551277	−	0.400526i	0.276979	−	0.960876i	$-0.410667\pi$
$653$	−14.0873	−	10.2350i	−0.551277	−	0.400526i	−0.828256	+	0.560350i	$0.810667\pi$
$654$	18.4772	−	17.3983i	0.722516	−	0.680326i
$655$	18.3605	−	28.8309i	0.717403	−	1.12652i
$656$			5.97504i			0.233286i
$657$	10.1838	−	2.64408i	0.397306	−	0.103155i
$658$	1.48448	−	0.482336i	0.0578710	−	0.0188034i
$659$	19.4698	+	6.32611i	0.758435	+	0.246430i	0.662607	−	0.748968i	$-0.269450\pi$
$659$	19.4698	+	6.32611i	0.758435	+	0.246430i	0.0958279	+	0.995398i	$0.469450\pi$
$660$	7.96219	+	14.4910i	0.309928	+	0.564060i
$661$	−0.389522	−	0.283005i	−0.0151507	−	0.0110076i	0.580184	−	0.814485i	$-0.302981\pi$
$661$	−0.389522	−	0.283005i	−0.0151507	−	0.0110076i	−0.595335	+	0.803478i	$0.702981\pi$
$662$	2.89739	−	0.941419i	0.112610	−	0.0365893i
$663$	19.1039	−	34.8613i	0.741935	−	1.35390i
$664$	−4.99843	−	6.87975i	−0.193977	−	0.266986i
$665$	8.40544	−	3.31262i	0.325949	−	0.128458i
$666$	−22.0843	+	26.8426i	−0.855750	+	1.04013i
$667$	3.31482	+	4.56245i	0.128350	+	0.176659i
$668$	8.16833	+	2.65405i	0.316042	+	0.102688i
$669$	6.96080	−	6.55433i	0.269120	−	0.253405i
$670$	0.915881	+	14.9333i	0.0353836	+	0.576922i
$671$	11.1538	−	3.62409i	0.430587	−	0.139906i
$672$	0.800329	−	1.46046i	0.0308734	−	0.0563385i
$673$	12.3435	−	37.9894i	0.475807	−	1.46438i	−0.369059	−	0.929406i	$-0.620320\pi$
$673$	12.3435	−	37.9894i	0.475807	−	1.46438i	0.844866	−	0.534978i	$-0.179680\pi$
$674$	−4.24788	+	13.0736i	−0.163622	+	0.503578i
$675$	22.7559	−	12.5367i	0.875874	−	0.482539i
$676$	15.1674			0.583360
$677$		−	0.922234i		−	0.0354443i	−0.999843	−	0.0177222i	$-0.994359\pi$
$677$		−	0.922234i		−	0.0354443i	0.999843	−	0.0177222i	$-0.00564143\pi$
$678$	−11.3952	−	24.1315i	−0.437631	−	0.926763i
$679$	10.7851	−	7.83587i	0.413896	−	0.300713i
$680$	−0.591952	−	9.65166i	−0.0227003	−	0.370124i
$681$	19.7953	−	2.52789i	0.758557	−	0.0968688i
$682$	−3.36422	+	23.5303i	−0.128823	+	0.901023i
$683$	30.1894			1.15517			0.577583	−	0.816332i	$-0.303996\pi$
$683$	30.1894			1.15517			0.577583	+	0.816332i	$0.303996\pi$
$684$	−11.7338	−	4.60911i	−0.448651	−	0.176234i
$685$	−32.5598	−	8.41469i	−1.24405	−	0.321509i
$686$	−11.9568	+	3.88501i	−0.456514	+	0.148330i
$687$	1.04805	+	8.20701i	0.0399854	+	0.313117i
$688$	4.93474			0.188135
$689$	−51.2142	+	16.6405i	−1.95110	+	0.633952i
$690$	−29.1644	+	16.0247i	−1.11027	+	0.610049i
$691$	−4.81974	+	14.8336i	−0.183351	+	0.564298i	−0.999916	−	0.0129564i	$-0.995876\pi$
$691$	−4.81974	+	14.8336i	−0.183351	+	0.564298i	0.816565	+	0.577254i	$0.195876\pi$
$692$	16.1328	+	11.7212i	0.613278	+	0.445573i
$693$	10.3796	−	6.62645i	0.394287	−	0.251718i
$694$	11.4003	−	15.6912i	0.432751	−	0.595630i
$695$	−40.0271	−	10.3445i	−1.51832	−	0.392391i
$696$	−0.211517	+	1.11700i	−0.00801752	+	0.0423398i
$697$	20.9041	−	15.1877i	0.791798	−	0.575275i
$698$	−27.8737	+	20.2514i	−1.05504	+	0.766528i
$699$	1.93886	−	10.2390i	0.0733346	−	0.387273i
$700$	4.35641	−	2.03321i	0.164657	−	0.0768483i
$701$	8.30223	−	11.4270i	0.313571	−	0.431593i	−0.622920	−	0.782286i	$-0.714054\pi$
$701$	8.30223	−	11.4270i	0.313571	−	0.431593i	0.936491	+	0.350692i	$0.114054\pi$
$702$	−17.6645	−	21.1775i	−0.666703	−	0.799291i
$703$	39.3902	+	28.6187i	1.48563	+	1.07937i
$704$	1.31924	−	4.06020i	0.0497207	−	0.153025i
$705$	−3.02766	−	5.51026i	−0.114028	−	0.207528i
$706$	−1.97503	+	0.641727i	−0.0743313	+	0.0241517i
$707$	−6.32545			−0.237893
$708$	−1.99558	−	15.6269i	−0.0749984	−	0.587295i
$709$	5.25985	−	1.70903i	0.197538	−	0.0641839i	−0.208577	−	0.978006i	$-0.566883\pi$
$709$	5.25985	−	1.70903i	0.197538	−	0.0641839i	0.406115	+	0.913822i	$0.366883\pi$
$710$	8.01999	+	2.07267i	0.300985	+	0.0777859i
$711$	−7.22111	+	18.3833i	−0.270813	+	0.689429i
$712$	−8.51054			−0.318946
$713$	−47.3570	−	6.77082i	−1.77354	−	0.253569i
$714$	−7.14384	+	0.912278i	−0.267351	+	0.0341411i
$715$	50.5690	−	3.10148i	1.89117	−	0.115989i
$716$	3.11285	−	2.26162i	0.116333	−	0.0845207i
$717$	−16.1579	−	34.2172i	−0.603426	−	1.27786i
$718$		−	4.57232i		−	0.170637i
$719$	24.3545			0.908271			0.454136	−	0.890933i	$-0.349948\pi$
$719$	24.3545			0.908271			0.454136	+	0.890933i	$0.349948\pi$
$720$	−6.38221	−	2.06578i	−0.237851	−	0.0769871i
$721$	−2.72731	+	8.39378i	−0.101570	+	0.312601i
$722$	0.414599	−	1.27600i	0.0154298	−	0.0474879i
$723$	−19.2055	+	35.0467i	−0.714261	+	1.30340i
$724$	−6.75561	+	2.19503i	−0.251070	+	0.0815776i
$725$	−2.39941	+	2.23900i	−0.0891118	+	0.0831542i
$726$	9.11158	−	8.57952i	0.338162	−	0.318416i
$727$	14.5149	+	4.71617i	0.538327	+	0.174913i	0.565547	−	0.824716i	$-0.308665\pi$
$727$	14.5149	+	4.71617i	0.538327	+	0.174913i	−0.0272193	+	0.999629i	$0.508665\pi$
$728$	−2.99946	−	4.12840i	−0.111167	−	0.153009i
$729$	−4.84427	+	26.5619i	−0.179418	+	0.983773i
$730$	−2.87540	−	7.29603i	−0.106423	−	0.270038i
$731$	−12.5434	−	17.2645i	−0.463934	−	0.638550i
$732$	−2.28661	+	4.17267i	−0.0845156	+	0.154226i
$733$	18.1023	−	5.88179i	0.668624	−	0.217249i	0.0450158	−	0.998986i	$-0.485666\pi$
$733$	18.1023	−	5.88179i	0.668624	−	0.217249i	0.623608	+	0.781737i	$0.285666\pi$
$734$	12.1403	+	8.82042i	0.448105	+	0.325567i
$735$	11.3312	+	20.6224i	0.417956	+	0.760668i
$736$	8.17154	+	2.65510i	0.301207	+	0.0978681i
$737$	27.1664	−	8.82691i	1.00069	−	0.325143i
$738$	−4.50467	−	17.3499i	−0.165819	−	0.638658i
$739$			14.9941i			0.551565i	0.961220	+	0.275783i	$0.0889370\pi$
$739$			14.9941i			0.551565i	−0.961220	+	0.275783i	$0.911063\pi$
$740$	21.8533	+	13.9169i	0.803343	+	0.511596i
$741$	−28.1233	+	26.4811i	−1.03313	+	0.972806i
$742$	7.89260	+	5.73431i	0.289746	+	0.210513i
$743$		−	25.6531i		−	0.941122i	−0.882367	−	0.470561i	$-0.844052\pi$
$743$		−	25.6531i		−	0.941122i	0.882367	−	0.470561i	$-0.155948\pi$
$744$	−5.55075	−	7.88601i	−0.203500	−	0.289115i
$745$	4.35894	+	5.28601i	0.159699	+	0.193664i
$746$	8.46861	−	11.6560i	0.310058	−	0.426758i
$747$	19.7008	+	16.2085i	0.720815	+	0.593039i
$748$	−17.5582	+	5.70500i	−0.641991	+	0.208596i
$749$			18.1992i			0.664983i
$750$	−11.3294	−	15.7049i	−0.413691	−	0.573463i
$751$	−0.275193	−	0.846957i	−0.0100419	−	0.0309059i	0.945910	−	0.324429i	$-0.105172\pi$
$751$	−0.275193	−	0.846957i	−0.0100419	−	0.0309059i	−0.955952	+	0.293523i	$0.905172\pi$
$752$	−0.501647	+	1.54391i	−0.0182932	+	0.0563007i
$753$	6.95591	−	36.7335i	0.253487	−	1.33864i
$754$	2.81821	+	2.04755i	0.102633	+	0.0745674i
$755$	12.0511	−	18.9234i	0.438584	−	0.688695i
$756$	−1.22287	+	4.84416i	−0.0444755	+	0.176180i
$757$	−27.8590	+	20.2407i	−1.01255	+	0.735662i	−0.964743	−	0.263195i	$-0.915224\pi$
$757$	−27.8590	+	20.2407i	−1.01255	+	0.735662i	−0.0478088	+	0.998857i	$0.515224\pi$
$758$	3.17108	−	9.75959i	0.115179	−	0.354484i
$759$	43.5539	+	46.2548i	1.58090	+	1.67894i
$760$	−2.35113	+	9.09746i	−0.0852845	+	0.330000i
$761$	−1.92686	+	5.93028i	−0.0698488	+	0.214972i	−0.979887	−	0.199551i	$-0.936052\pi$
$761$	−1.92686	+	5.93028i	−0.0698488	+	0.214972i	0.910039	+	0.414523i	$0.136052\pi$
$762$	20.2567	−	19.0738i	0.733822	−	0.690972i
$763$	−8.28111	+	11.3980i	−0.299796	+	0.412634i
$764$	−1.02713	+	0.333734i	−0.0371602	+	0.0120741i
$765$	8.99538	+	27.5795i	0.325229	+	0.997138i
$766$	−8.83194	−	2.86967i	−0.319111	−	0.103685i
$767$	−45.9097	−	14.9170i	−1.65770	−	0.538621i
$768$	0.739587	+	1.56621i	0.0266875	+	0.0565157i
$769$	21.5484			0.777055			0.388527	−	0.921437i	$-0.372984\pi$
$769$	21.5484			0.777055			0.388527	+	0.921437i	$0.372984\pi$
$770$	−5.83952	−	7.08147i	−0.210442	−	0.255198i
$771$	3.23826	+	6.85760i	0.116623	+	0.246970i
$772$	4.53732	+	6.24509i	0.163302	+	0.224766i
$773$	−23.6274	+	32.5203i	−0.849818	+	1.16967i	0.134085	+	0.990970i	$0.457190\pi$
$773$	−23.6274	+	32.5203i	−0.849818	+	1.16967i	−0.983903	+	0.178704i	$0.942810\pi$
$774$	−14.3291	+	3.72036i	−0.515049	+	0.133726i
$775$	0.542871	−	27.8335i	0.0195005	−	0.999810i
$776$			13.8649i			0.497721i
$777$	9.27310	−	16.9218i	0.332671	−	0.607066i
$778$	3.30141	−	2.39861i	0.118361	−	0.0859944i
$779$	−23.8793	+	7.75887i	−0.855566	+	0.277990i
$780$	−14.0743	+	14.9808i	−0.503941	+	0.536399i
$781$		−	15.8150i		−	0.565905i
$782$	−11.4819	−	35.3375i	−0.410591	−	1.26367i
$783$	−0.227936	−	3.40293i	−0.00814578	−	0.121611i
$784$	1.87744	−	5.77815i	0.0670513	−	0.206363i
$785$	2.86466	+	46.7078i	0.102244	+	1.66707i
$786$	23.9413	−	11.3054i	0.853956	−	0.403251i
$787$	4.51852	+	3.28289i	0.161068	+	0.117023i	0.665400	−	0.746487i	$-0.268261\pi$
$787$	4.51852	+	3.28289i	0.161068	+	0.117023i	−0.504332	+	0.863510i	$0.668261\pi$
$788$	8.42733	+	11.5992i	0.300211	+	0.413205i
$789$	−18.3352	−	3.47197i	−0.652749	−	0.123605i
$790$	14.2530	+	3.68352i	0.507100	+	0.131054i
$791$	8.70771	+	11.9851i	0.309610	+	0.426142i
$792$	−0.769666	+	12.7843i	−0.0273489	+	0.454270i
$793$	8.56972	+	11.7952i	0.304320	+	0.418860i
$794$	−18.8743	+	25.9783i	−0.669824	+	0.921934i
$795$	16.7398	−	35.5530i	0.593699	−	1.26093i
$796$	−5.76768	+	7.93854i	−0.204430	+	0.281374i
$797$	43.5038	+	14.1352i	1.54098	+	0.500696i	0.951647	−	0.307193i	$-0.0993898\pi$
$797$	43.5038	+	14.1352i	1.54098	+	0.500696i	0.589335	+	0.807889i	$0.299390\pi$
$798$	6.87601	+	1.30205i	0.243408	+	0.0460921i
$799$	6.67659	−	2.16936i	0.236201	−	0.0767463i
$800$	−0.952392	+	4.90846i	−0.0336722	+	0.173540i
$801$	24.7123	−	6.41621i	0.873165	−	0.226706i
$802$	−0.935065	−	2.87783i	−0.0330183	−	0.101620i
$803$	−12.1130	+	8.80060i	−0.427458	+	0.310567i
$804$	−5.56932	+	10.1630i	−0.196415	+	0.358423i
$805$	14.2521	−	11.7526i	0.502322	−	0.414224i
$806$	−29.1130	+	5.06184i	−1.02546	+	0.178296i
$807$	12.0964	−	1.54472i	0.425812	−	0.0543768i
$808$	3.86687	−	5.32228i	0.136036	−	0.187237i
$809$	34.6959	−	25.2081i	1.21984	−	0.886269i	0.223757	−	0.974645i	$-0.428168\pi$
$809$	34.6959	−	25.2081i	1.21984	−	0.886269i	0.996087	+	0.0883759i	$0.0281677\pi$
$810$	20.0896	+	1.18682i	0.705876	+	0.0417008i
$811$	35.0509			1.23080			0.615401	−	0.788214i	$-0.288994\pi$
$811$	35.0509			1.23080			0.615401	+	0.788214i	$0.288994\pi$
$812$		−	0.631095i		−	0.0221471i
$813$	−10.6698	+	5.03844i	−0.374207	+	0.176706i
$814$	15.2855	−	47.0439i	0.535757	−	1.64889i
$815$	−11.2354	+	4.42791i	−0.393558	+	0.155103i
$816$	3.59956	−	6.56857i	0.126010	−	0.229946i
$817$	6.40798	+	19.7217i	0.224187	+	0.689976i
$818$	−3.49848	+	4.81524i	−0.122321	+	0.168361i
$819$	11.8221	+	9.72641i	0.413096	+	0.339868i
$820$	−12.4301	+	4.89877i	−0.434079	+	0.171073i
$821$	12.9316	−	9.39534i	0.451315	−	0.327900i	−0.338800	−	0.940859i	$-0.610021\pi$
$821$	12.9316	−	9.39534i	0.451315	−	0.327900i	0.790115	+	0.612959i	$0.210021\pi$
$822$	−17.8576	−	18.9651i	−0.622857	−	0.661483i
$823$	7.02093	−	21.6082i	0.244734	−	0.753214i	−0.750946	−	0.660364i	$-0.770402\pi$
$823$	7.02093	−	21.6082i	0.244734	−	0.753214i	0.995680	−	0.0928505i	$-0.0295979\pi$
$824$	−5.39534	−	7.42605i	−0.187956	−	0.258699i
$825$	−23.6181	+	28.4448i	−0.822278	+	0.990320i
$826$	2.70246	+	8.31731i	0.0940306	+	0.289396i
$827$	−18.4208	+	25.3541i	−0.640554	+	0.881647i	−0.998645	−	0.0520398i	$-0.983428\pi$
$827$	−18.4208	+	25.3541i	−0.640554	+	0.881647i	0.358091	+	0.933687i	$0.383428\pi$
$828$	−25.7296	−	1.54903i	−0.894166	−	0.0538324i
$829$	2.56408	+	0.833120i	0.0890542	+	0.0289355i	0.353205	−	0.935546i	$-0.385092\pi$
$829$	2.56408	+	0.833120i	0.0890542	+	0.0289355i	−0.264151	+	0.964481i	$0.585092\pi$
$830$	10.2141	−	16.0390i	0.354538	−	0.556720i
$831$	−33.1062	+	4.22771i	−1.14844	+	0.146658i
$832$	5.30729			0.183997
$833$	−24.9874	+	8.11890i	−0.865762	+	0.281303i
$834$	−21.9531	−	23.3146i	−0.760175	−	0.807317i
$835$	1.17566	+	19.1689i	0.0406853	+	0.663366i
$836$	17.9397			0.620459
$837$	22.0632	+	18.7140i	0.762617	+	0.646851i
$838$			19.8968i			0.687322i
$839$	−7.36279	+	10.1340i	−0.254192	+	0.349865i	−0.916974	−	0.398947i	$-0.869376\pi$
$839$	−7.36279	+	10.1340i	−0.254192	+	0.349865i	0.662782	+	0.748812i	$0.269376\pi$
$840$	3.69442	+	0.467565i	0.127470	+	0.0161325i
$841$	−8.82837	−	27.1709i	−0.304426	−	0.936928i
$842$	31.5181			1.08618
$843$	1.69300	+	13.2575i	0.0583102	+	0.456614i
$844$	−1.65069	−	5.08031i	−0.0568191	−	0.174871i
$845$	12.4353	+	31.5532i	0.427787	+	1.08546i
$846$	0.292669	−	4.86129i	0.0100622	−	0.167135i
$847$	−4.08362	+	5.62062i	−0.140315	+	0.193127i
$848$	−9.64977	+	3.13540i	−0.331375	+	0.107670i
$849$	4.11214	−	7.50394i	0.141128	−	0.257535i
$850$	19.5934	−	9.14458i	0.672048	−	0.313657i
$851$	94.6804	+	30.7635i	3.24560	+	1.05456i
$852$	4.39861	+	4.67139i	0.150694	+	0.160039i
$853$	−0.531537	−	0.731597i	−0.0181995	−	0.0250494i	0.799820	−	0.600240i	$-0.204928\pi$
$853$	−0.531537	−	0.731597i	−0.0181995	−	0.0250494i	−0.818020	+	0.575190i	$0.804928\pi$
$854$	0.816223	−	2.51208i	0.0279306	−	0.0859615i
$855$	−0.0316684	−	28.1891i	−0.00108304	−	0.964046i
$856$	−15.3129	−	11.1255i	−0.523384	−	0.380261i
$857$	−0.342159	−	1.05306i	−0.0116879	−	0.0359718i	0.945042	−	0.326948i	$-0.106020\pi$
$857$	−0.342159	−	1.05306i	−0.0116879	−	0.0359718i	−0.956730	+	0.290976i	$0.906020\pi$
$858$	34.4154	+	18.8596i	1.17492	+	0.643855i
$859$	19.2126	+	6.24255i	0.655525	+	0.212993i	0.617849	−	0.786297i	$-0.288004\pi$
$859$	19.2126	+	6.24255i	0.655525	+	0.212993i	0.0376763	+	0.999290i	$0.488004\pi$
$860$	4.04585	+	10.2659i	0.137962	+	0.350065i
$861$	4.24895	+	8.99792i	0.144804	+	0.306648i
$862$		−	31.8316i		−	1.08419i
$863$			46.0925i			1.56901i	0.620123	+	0.784504i	$0.287082\pi$
$863$			46.0925i			1.56901i	−0.620123	+	0.784504i	$0.712918\pi$
$864$	−3.32834	−	3.99026i	−0.113233	−	0.135751i
$865$	−11.1572	+	43.1716i	−0.379356	+	1.46788i
$866$	−12.1268	−	8.81062i	−0.412084	−	0.299397i
$867$	−2.92246	+	0.373202i	−0.0992518	+	0.0126746i
$868$	3.84206	+	3.72798i	0.130408	+	0.126536i
$869$		−	28.1063i		−	0.953439i
$870$	−2.49716	+	0.475772i	−0.0846616	+	0.0161302i
$871$	20.8726	+	28.7287i	0.707242	+	0.973434i
$872$	−4.52794	−	13.9356i	−0.153335	−	0.471918i
$873$	−10.4529	−	40.2599i	−0.353779	−	1.36259i
$874$			36.1054i			1.22128i
$875$	7.80147	+	7.39584i	0.263738	+	0.250025i
$876$	1.13020	−	5.96847i	0.0381858	−	0.201656i
$877$	23.4256	+	7.61143i	0.791025	+	0.257020i	0.676541	−	0.736405i	$-0.263478\pi$
$877$	23.4256	+	7.61143i	0.791025	+	0.257020i	0.114485	+	0.993425i	$0.463478\pi$
$878$	0.230602	+	0.167542i	0.00778244	+	0.00565427i
$879$	−15.7511	−	33.3558i	−0.531272	−	1.12506i
$880$	9.52820	−	0.584380i	0.321196	−	0.0196994i
$881$	8.66707	−	6.29700i	0.292001	−	0.212151i	−0.432134	−	0.901809i	$-0.642239\pi$
$881$	8.66707	−	6.29700i	0.292001	−	0.212151i	0.724135	+	0.689658i	$0.242239\pi$
$882$	−1.09533	+	18.1936i	−0.0368816	+	0.612610i
$883$	30.3409	−	22.0439i	1.02105	−	0.741837i	0.0545532	−	0.998511i	$-0.482627\pi$
$883$	30.3409	−	22.0439i	1.02105	−	0.741837i	0.966498	+	0.256674i	$0.0826265\pi$
$884$	−13.4904	−	18.5679i	−0.453730	−	0.624506i
$885$	30.8732	−	16.9635i	1.03779	−	0.570223i
$886$	−14.1137	+	10.2542i	−0.474160	+	0.344497i
$887$	22.7701	+	16.5435i	0.764547	+	0.555476i	0.900302	−	0.435267i	$-0.143346\pi$
$887$	22.7701	+	16.5435i	0.764547	+	0.555476i	−0.135755	+	0.990742i	$0.543346\pi$
$888$	8.56930	+	18.1470i	0.287567	+	0.608975i
$889$	−9.07863	+	12.4957i	−0.304487	+	0.419091i
$890$	−6.97755	−	17.7048i	−0.233888	−	0.593467i
$891$	−7.40336	−	37.7023i	−0.248022	−	1.26308i
$892$	−1.70578	−	5.24985i	−0.0571138	−	0.175778i
$893$	−6.82167			−0.228279
$894$	0.672265	+	5.26435i	0.0224839	+	0.176066i
$895$	7.25707	+	4.62155i	0.242577	+	0.154481i
$896$	−0.565158	−	0.777874i	−0.0188806	−	0.0259869i
$897$	−37.9567	+	69.2643i	−1.26734	+	2.31267i
$898$	−25.0559			−0.836128
$899$	−3.28078	−	1.60984i	−0.109420	−	0.0536912i
$900$	−0.935068	−	14.9708i	−0.0311689	−	0.499028i
$901$	35.4977	+	25.7906i	1.18260	+	0.859210i
$902$	14.9934	+	20.6367i	0.499227	+	0.687127i
$903$	7.43131	−	3.50917i	0.247298	−	0.116778i
$904$	−15.4076			−0.512448
$905$	−10.1051	−	12.2543i	−0.335906	−	0.407347i
$906$	15.7141	−	7.42042i	0.522066	−	0.246527i
$907$	−10.0397	−	3.26209i	−0.333362	−	0.108316i	0.137553	−	0.990494i	$-0.456076\pi$
$907$	−10.0397	−	3.26209i	−0.333362	−	0.108316i	−0.470915	+	0.882178i	$0.656076\pi$
$908$	3.56038	−	10.9577i	0.118155	−	0.363645i
$909$	−7.21577	+	18.3697i	−0.239332	+	0.609285i
$910$	6.12930	−	9.62466i	0.203184	−	0.319054i
$911$	−12.8753	−	9.35445i	−0.426577	−	0.309927i	0.353701	−	0.935358i	$-0.384923\pi$
$911$	−12.8753	−	9.35445i	−0.426577	−	0.309927i	−0.780279	+	0.625432i	$0.784923\pi$
$912$	−5.29899	+	4.98956i	−0.175467	+	0.165221i
$913$	−34.5273	−	11.2186i	−1.14269	−	0.371282i
$914$	−23.4006	+	17.0016i	−0.774024	+	0.562362i
$915$	−10.5553	−	1.33587i	−0.348947	−	0.0441627i
$916$	4.54300	+	1.47611i	0.150105	+	0.0487721i
$917$	−11.8907	+	8.63907i	−0.392664	+	0.285287i
$918$	−5.50000	+	21.7871i	−0.181527	+	0.719081i
$919$	6.94746	+	21.3821i	0.229176	+	0.705330i	0.997841	+	0.0656786i	$0.0209212\pi$
$919$	6.94746	+	21.3821i	0.229176	+	0.705330i	−0.768665	+	0.639651i	$0.779079\pi$
$920$	1.17612	+	19.1764i	0.0387755	+	0.632228i
$921$	36.5577	+	6.92261i	1.20462	+	0.228108i
$922$	3.24833	−	9.99734i	0.106978	−	0.329245i
$923$	18.6985	−	6.07552i	0.615470	−	0.199978i
$924$	−0.900609	−	7.05246i	−0.0296279	−	0.232009i
$925$	−11.0350	+	56.8723i	−0.362828	+	1.86995i
$926$	8.08277	+	24.8762i	0.265616	+	0.817482i
$927$	21.2652	+	17.4956i	0.698440	+	0.574630i
$928$	0.531008	+	0.385800i	0.0174312	+	0.0126645i
$929$	−12.2647			−0.402390			−0.201195	−	0.979551i	$-0.564483\pi$
$929$	−12.2647			−0.402390			−0.201195	+	0.979551i	$0.564483\pi$
$930$	11.8547	−	18.0130i	0.388730	−	0.590668i
$931$	25.5304			0.836725
$932$	−4.86747	−	3.53642i	−0.159439	−	0.115839i
$933$	−11.8085	−	12.5408i	−0.386593	−	0.410568i
$934$	3.56767	+	10.9801i	0.116738	+	0.359281i
$935$	−26.2638	−	31.8496i	−0.858918	−	1.04159i
$936$	−15.4109	+	4.00124i	−0.503722	+	0.130785i
$937$	−27.4779	+	8.92810i	−0.897662	+	0.291668i	−0.721272	−	0.692652i	$-0.756442\pi$
$937$	−27.4779	+	8.92810i	−0.897662	+	0.291668i	−0.176391	+	0.984320i	$0.556442\pi$
$938$	1.98801	−	6.11847i	0.0649109	−	0.199775i
$939$	−5.61213	+	29.6372i	−0.183145	+	0.967173i
$940$	−3.62315	+	0.222213i	−0.118174	+	0.00724780i
$941$	−2.40301	−	7.39569i	−0.0783358	−	0.241093i	0.904218	−	0.427071i	$-0.140455\pi$
$941$	−2.40301	−	7.39569i	−0.0783358	−	0.241093i	−0.982554	+	0.185978i	$0.940455\pi$
$942$	−17.4195	+	31.7876i	−0.567559	+	1.03570i
$943$	−41.5333	+	30.1757i	−1.35251	+	0.982657i
$944$	−8.65031	−	2.81066i	−0.281544	−	0.0914790i
$945$	−11.0801	+	1.42759i	−0.360435	+	0.0464397i
$946$	17.0437	−	12.3829i	0.554137	−	0.402604i
$947$	−7.90649	−	2.56897i	−0.256926	−	0.0834804i	0.177722	−	0.984081i	$-0.443127\pi$
$947$	−7.90649	−	2.56897i	−0.256926	−	0.0834804i	−0.434648	+	0.900600i	$0.643127\pi$
$948$	7.81717	+	8.30194i	0.253890	+	0.269635i
$949$	−15.0586	−	10.9407i	−0.488821	−	0.355149i
$950$	−20.8534	+	2.56761i	−0.676575	+	0.0833042i
$951$	44.9006	+	24.6054i	1.45600	+	0.797886i
$952$	−1.28489	+	3.95449i	−0.0416435	+	0.128166i
$953$	25.7067	+	8.35260i	0.832720	+	0.270567i	0.694191	−	0.719791i	$-0.255762\pi$
$953$	25.7067	+	8.35260i	0.832720	+	0.270567i	0.138529	+	0.990358i	$0.455762\pi$
$954$	25.6565	−	16.3794i	0.830659	−	0.530304i
$955$	−1.53639	−	1.86316i	−0.0497166	−	0.0602903i
$956$	−21.8471			−0.706587
$957$	2.07240	+	4.38868i	0.0669912	+	0.141866i
$958$	−2.56918	−	3.53617i	−0.0830063	−	0.114248i
$959$	11.6989	+	8.49976i	0.377778	+	0.274471i
$960$	−2.65188	+	2.82268i	−0.0855891	+	0.0911017i
$961$	29.1807	−	10.4635i	0.941313	−	0.337534i
$962$	61.4935			1.98263
$963$	52.8521	+	20.7607i	1.70313	+	0.669004i
$964$	13.5621	+	18.6667i	0.436806	+	0.601212i
$965$	−9.27187	+	14.5593i	−0.298472	+	0.468682i
$966$	14.1938	−	1.81256i	0.456676	−	0.0583182i
$967$	58.7213			1.88835			0.944175	−	0.329445i	$-0.106862\pi$
$967$	58.7213			1.88835			0.944175	+	0.329445i	$0.106862\pi$
$968$	−2.23284	−	6.87198i	−0.0717662	−	0.220874i
$969$	30.9256	+	5.85610i	0.993472	+	0.188125i
$970$	−28.8437	+	11.3674i	−0.926116	+	0.364987i
$971$	14.9202	−	20.5360i	0.478813	−	0.659030i	−0.499463	−	0.866335i	$-0.666469\pi$
$971$	14.9202	−	20.5360i	0.478813	−	0.659030i	0.978276	+	0.207305i	$0.0664693\pi$
$972$	12.6729	+	9.07732i	0.406483	+	0.291155i
$973$	14.3820	+	10.4491i	0.461065	+	0.334983i
$974$	4.79609	−	3.48457i	0.153677	−	0.111653i
$975$	−42.7043	−	16.9970i	−1.36763	−	0.544339i
$976$	1.61471	+	2.22245i	0.0516855	+	0.0711390i
$977$	9.53806	−	6.92981i	0.305150	−	0.221704i	−0.424663	−	0.905352i	$-0.639607\pi$
$977$	9.53806	−	6.92981i	0.305150	−	0.221704i	0.729812	+	0.683647i	$0.239607\pi$
$978$	−9.19102	−	1.74042i	−0.293896	−	0.0556526i
$979$	−29.3938	+	21.3559i	−0.939431	+	0.682536i
$980$	13.5598	−	0.831643i	0.433151	−	0.0265658i
$981$	23.6541	+	37.0514i	0.755217	+	1.18296i
$982$	7.58641	+	5.51185i	0.242092	+	0.175890i
$983$	−33.9872	−	11.0431i	−1.08402	−	0.352220i	−0.288088	−	0.957604i	$-0.593020\pi$
$983$	−33.9872	−	11.0431i	−1.08402	−	0.352220i	−0.795934	+	0.605384i	$0.793020\pi$
$984$	−10.1684	−	1.92550i	−0.324156	−	0.0613826i
$985$	−17.2210	+	27.0416i	−0.548706	+	0.861617i
$986$		−	2.83841i		−	0.0903934i
$987$	0.342461	+	2.68173i	0.0109007	+	0.0853605i
$988$	6.89176	+	21.2107i	0.219256	+	0.674801i
$989$	24.9219	+	34.3020i	0.792469	+	1.09074i
$990$	−27.2267	+	8.88032i	−0.865321	+	0.282235i
$991$			14.7675i			0.469105i	0.972103	+	0.234553i	$0.0753625\pi$
$991$			14.7675i			0.469105i	−0.972103	+	0.234553i	$0.924637\pi$
$992$	−5.48547	+	0.953751i	−0.174164	+	0.0302816i
$993$	0.668412	+	5.23418i	0.0212114	+	0.166102i
$994$	−2.88162	−	2.09362i	−0.0913995	−	0.0664057i
$995$	−21.2436	−	5.49016i	−0.673468	−	0.174050i
$996$	13.3188	−	6.28933i	0.422022	−	0.199285i
$997$		−	17.3326i		−	0.548929i	−0.961597	−	0.274464i	$-0.911499\pi$
$997$		−	17.3326i		−	0.548929i	0.961597	−	0.274464i	$-0.0885005\pi$
$998$		−	36.6241i		−	1.15932i
$999$	−38.5642	−	46.2335i	−1.22012	−	1.46276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.b.29.8	yes	128
3.2	odd	2		930.2.y.a.29.6	✓	128
5.4	even	2		930.2.y.a.29.25	yes	128
15.14	odd	2	inner	930.2.y.b.29.27	yes	128
31.15	odd	10	inner	930.2.y.b.449.27	yes	128
93.77	even	10		930.2.y.a.449.25	yes	128
155.139	odd	10		930.2.y.a.449.6	yes	128
465.449	even	10	inner	930.2.y.b.449.8	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.6	✓	128	3.2	odd	2
930.2.y.a.29.25	yes	128	5.4	even	2
930.2.y.a.449.6	yes	128	155.139	odd	10
930.2.y.a.449.25	yes	128	93.77	even	10
930.2.y.b.29.8	yes	128	1.1	even	1	trivial
930.2.y.b.29.27	yes	128	15.14	odd	2	inner
930.2.y.b.449.8	yes	128	465.449	even	10	inner
930.2.y.b.449.27	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)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.26101 + 1.18737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.72517 + 1.42260i) q^{5} +(-1.71810 + 0.219404i) q^{6} +(0.914445 - 0.297121i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.180286 - 2.99458i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.26101 + 1.18737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.72517 + 1.42260i) q^{5} +(-1.71810 + 0.219404i) q^{6} +(0.914445 - 0.297121i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.180286 - 2.99458i) q^{9} +(-2.23187 + 0.136884i) q^{10} +(1.31924 + 4.06020i) q^{11} +(-1.51893 - 0.832372i) q^{12} +(-4.29369 + 3.11955i) q^{13} +(0.914445 + 0.297121i) q^{14} +(0.486285 - 3.84233i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.11281 + 1.33633i) q^{17} +(1.90602 - 2.31670i) q^{18} +(-3.39964 - 2.46998i) q^{19} +(-1.88608 - 1.20112i) q^{20} +(-0.800329 + 1.46046i) q^{21} +(-1.31924 + 4.06020i) q^{22} +(-8.17154 - 2.65510i) q^{23} +(-0.739587 - 1.56621i) q^{24} +(0.952392 - 4.90846i) q^{25} -5.30729 q^{26} +(3.32834 + 3.99026i) q^{27} +(0.565158 + 0.777874i) q^{28} +(-0.531008 - 0.385800i) q^{29} +(2.65188 - 2.82268i) q^{30} +(5.48547 - 0.953751i) q^{31} -1.00000 q^{32} +(-6.48455 - 3.55352i) q^{33} +(2.54186 + 3.49856i) q^{34} +(-1.15488 + 1.81348i) q^{35} +(2.90372 - 0.753914i) q^{36} -11.5866 q^{37} +(-1.29855 - 3.99651i) q^{38} +(1.71031 - 9.03199i) q^{39} +(-0.819872 - 2.08034i) q^{40} +(3.51204 - 4.83391i) q^{41} +(-1.50592 + 0.711116i) q^{42} +(-3.99229 - 2.90057i) q^{43} +(-3.45381 + 2.50934i) q^{44} +(3.94908 + 5.42262i) q^{45} +(-5.05029 - 6.95113i) q^{46} +(1.31333 - 0.954190i) q^{47} +(0.322256 - 1.70181i) q^{48} +(-4.91519 + 3.57109i) q^{49} +(3.65562 - 3.41122i) q^{50} +(-6.77301 + 3.19832i) q^{51} +(-4.29369 - 3.11955i) q^{52} +(9.64977 + 3.13540i) q^{53} +(0.347272 + 5.18453i) q^{54} +(-8.05197 - 5.12776i) q^{55} +0.961505i q^{56} +(7.21976 - 0.921973i) q^{57} +(-0.202827 - 0.624237i) q^{58} +(5.34618 + 7.35839i) q^{59} +(3.80455 - 0.724862i) q^{60} -2.74710i q^{61} +(4.99844 + 2.45268i) q^{62} +(-0.724891 - 2.79194i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(2.96944 - 11.4900i) q^{65} +(-3.15741 - 6.68638i) q^{66} -6.69091i q^{67} +4.32446i q^{68} +(13.4570 - 6.35458i) q^{69} +(-2.00026 + 0.788311i) q^{70} +(-3.52318 - 1.14475i) q^{71} +(2.79230 + 1.09684i) q^{72} +(1.08376 + 3.33548i) q^{73} +(-9.37376 - 6.81043i) q^{74} +(4.62720 + 7.32045i) q^{75} +(1.29855 - 3.99651i) q^{76} +(2.41274 + 3.32086i) q^{77} +(6.69254 - 6.30174i) q^{78} +(-6.26135 - 2.03444i) q^{79} +(0.559502 - 2.16494i) q^{80} +(-8.93499 - 1.07976i) q^{81} +(5.68261 - 1.84639i) q^{82} +(-4.99843 + 6.87975i) q^{83} +(-1.63630 - 0.309851i) q^{84} +(-8.99635 + 3.54551i) q^{85} +(-1.52492 - 4.69321i) q^{86} +(1.12769 - 0.144008i) q^{87} -4.26915 q^{88} +(2.62990 + 8.09401i) q^{89} +(0.00753618 + 6.70820i) q^{90} +(-2.99946 + 4.12840i) q^{91} -8.59207i q^{92} +(-5.78476 + 7.71599i) q^{93} +1.62336 q^{94} +(9.37874 - 0.575213i) q^{95} +(1.26101 - 1.18737i) q^{96} +(13.1863 - 4.28449i) q^{97} -6.07551 q^{98} +(12.3964 - 3.21857i) 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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