LMFDB - Embedded newform 930.2.n.e.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, 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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 16 x^{10} - 6 x^{9} + 161 x^{8} - 180 x^{7} + 1725 x^{6} - 2255 x^{5} + 17635 x^{4} + \cdots + 25 $ x^12 - x^11 + 16x^10 - 6x^9 + 161x^8 - 180x^7 + 1725x^6 - 2255x^5 + 17635x^4 - 18375x^3 + 60975x^2 + 2000x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.3
Root			$-2.70981 + 1.96879i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.e.481.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(0.726038 + 2.23451i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(0.726038 + 2.23451i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(1.22604 + 3.77336i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(3.41341 - 2.47998i) q^{13} +(-0.726038 + 2.23451i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.923830 - 2.84326i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-1.20360 - 0.874465i) q^{19} +(0.309017 + 0.951057i) q^{20} +(-1.90079 - 1.38101i) q^{21} +(-1.22604 + 3.77336i) q^{22} +(-1.98377 + 6.10542i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +4.21920 q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.90079 + 1.38101i) q^{28} +(-1.49479 - 1.08603i) q^{29} -1.00000 q^{30} +(-1.73285 + 5.29124i) q^{31} -1.00000 q^{32} +(-3.20981 - 2.33206i) q^{33} +(2.41862 - 1.75723i) q^{34} +(0.726038 + 2.23451i) q^{35} +1.00000 q^{36} -7.05969 q^{37} +(-0.459733 - 1.41491i) q^{38} +(-1.30381 + 4.01270i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(2.07914 + 1.51058i) q^{41} +(-0.726038 - 2.23451i) q^{42} +(3.23865 + 2.35302i) q^{43} +(-3.20981 + 2.33206i) q^{44} +(0.309017 - 0.951057i) q^{45} +(-5.19358 + 3.77336i) q^{46} +(1.92964 - 1.40196i) q^{47} +(0.309017 - 0.951057i) q^{48} +(1.19719 - 0.869812i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.923830 + 2.84326i) q^{51} +(3.41341 + 2.47998i) q^{52} +(-3.37591 + 10.3900i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.22604 + 3.77336i) q^{55} -2.34951 q^{56} +1.48773 q^{57} +(-0.570958 - 1.75723i) q^{58} +(10.3330 - 7.50738i) q^{59} +(-0.809017 - 0.587785i) q^{60} +0.0596861 q^{61} +(-4.51202 + 3.26216i) q^{62} +2.34951 q^{63} +(-0.809017 - 0.587785i) q^{64} +(3.41341 - 2.47998i) q^{65} +(-1.22604 - 3.77336i) q^{66} -7.69531 q^{67} +2.98958 q^{68} +(-1.98377 - 6.10542i) q^{69} +(-0.726038 + 2.23451i) q^{70} +(-0.930272 + 2.86308i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.45031 + 4.46361i) q^{73} +(-5.71141 - 4.14958i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(0.459733 - 1.41491i) q^{76} +(-7.54147 + 5.47920i) q^{77} +(-3.41341 + 2.47998i) q^{78} +(4.72948 - 14.5559i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.794161 + 2.44418i) q^{82} +(-5.54083 - 4.02565i) q^{83} +(0.726038 - 2.23451i) q^{84} +(0.923830 - 2.84326i) q^{85} +(1.23706 + 3.80726i) q^{86} +1.84766 q^{87} -3.96754 q^{88} +(2.23184 + 6.86891i) q^{89} +(0.809017 - 0.587785i) q^{90} +(8.01982 + 5.82674i) q^{91} -6.41962 q^{92} +(-1.70821 - 5.29925i) q^{93} +2.38516 q^{94} +(-1.20360 - 0.874465i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-4.15049 - 12.7739i) q^{97} +1.47981 q^{98} +3.96754 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{24} + 12 q^{25} + 10 q^{26} - 3 q^{27} + 4 q^{28} + q^{29} - 12 q^{30} - 6 q^{31} - 12 q^{32} - 5 q^{33} + 2 q^{34} - q^{35} + 12 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 3 q^{40} + 15 q^{41} + q^{42} + 10 q^{43} - 5 q^{44} - 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 5 q^{52} - 13 q^{53} + 3 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} + 4 q^{58} + 11 q^{59} - 3 q^{60} - 70 q^{61} - 19 q^{62} - 6 q^{63} - 3 q^{64} - 5 q^{65} - 5 q^{66} + 38 q^{67} - 2 q^{68} + q^{70} + 21 q^{71} + 3 q^{72} - 14 q^{73} - 11 q^{74} - 3 q^{75} + 3 q^{76} - 14 q^{77} + 5 q^{78} + 5 q^{79} - 3 q^{80} - 3 q^{81} - 15 q^{82} - q^{84} + 3 q^{85} + 10 q^{86} + 6 q^{87} + 3 q^{89} + 3 q^{90} + 16 q^{91} - 10 q^{92} - 11 q^{93} - 6 q^{94} - 2 q^{95} + 3 q^{96} - 35 q^{97} - 10 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 - 3 * q^12 - 5 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^24 + 12 * q^25 + 10 * q^26 - 3 * q^27 + 4 * q^28 + q^29 - 12 * q^30 - 6 * q^31 - 12 * q^32 - 5 * q^33 + 2 * q^34 - q^35 + 12 * q^36 - 14 * q^37 - 3 * q^38 + 10 * q^39 + 3 * q^40 + 15 * q^41 + q^42 + 10 * q^43 - 5 * q^44 - 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 3 * q^50 + 3 * q^51 - 5 * q^52 - 13 * q^53 + 3 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 + 4 * q^58 + 11 * q^59 - 3 * q^60 - 70 * q^61 - 19 * q^62 - 6 * q^63 - 3 * q^64 - 5 * q^65 - 5 * q^66 + 38 * q^67 - 2 * q^68 + q^70 + 21 * q^71 + 3 * q^72 - 14 * q^73 - 11 * q^74 - 3 * q^75 + 3 * q^76 - 14 * q^77 + 5 * q^78 + 5 * q^79 - 3 * q^80 - 3 * q^81 - 15 * q^82 - q^84 + 3 * q^85 + 10 * q^86 + 6 * q^87 + 3 * q^89 + 3 * q^90 + 16 * q^91 - 10 * q^92 - 11 * q^93 - 6 * q^94 - 2 * q^95 + 3 * q^96 - 35 * q^97 - 10 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.00000			−0.408248
$7$	0.726038	+	2.23451i	0.274417	+	0.844567i	0.989373	+	0.145398i	$0.0464464\pi$
$7$	0.726038	+	2.23451i	0.274417	+	0.844567i	−0.714957	+	0.699169i	$0.753554\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	1.22604	+	3.77336i	0.369664	+	1.13771i	0.947008	+	0.321209i	$0.104089\pi$
$11$	1.22604	+	3.77336i	0.369664	+	1.13771i	−0.577344	+	0.816501i	$0.695911\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	3.41341	−	2.47998i	0.946709	−	0.687824i	−0.00331751	−	0.999994i	$-0.501056\pi$
$13$	3.41341	−	2.47998i	0.946709	−	0.687824i	0.950026	+	0.312170i	$0.101056\pi$
$14$	−0.726038	+	2.23451i	−0.194042	+	0.597199i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.923830	−	2.84326i	0.224062	−	0.689591i	−0.774324	−	0.632790i	$-0.781910\pi$
$17$	0.923830	−	2.84326i	0.224062	−	0.689591i	0.998385	−	0.0568014i	$-0.0180902\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	−1.20360	−	0.874465i	−0.276124	−	0.200616i	0.441101	−	0.897458i	$-0.354588\pi$
$19$	−1.20360	−	0.874465i	−0.276124	−	0.200616i	−0.717225	+	0.696842i	$0.754588\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	−1.90079	−	1.38101i	−0.414787	−	0.301360i
$22$	−1.22604	+	3.77336i	−0.261392	+	0.804482i
$23$	−1.98377	+	6.10542i	−0.413645	+	1.27307i	0.499813	+	0.866134i	$0.333402\pi$
$23$	−1.98377	+	6.10542i	−0.413645	+	1.27307i	−0.913457	+	0.406934i	$0.866598\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	1.00000			0.200000
$26$	4.21920			0.827454
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−1.90079	+	1.38101i	−0.359216	+	0.260986i
$29$	−1.49479	−	1.08603i	−0.277575	−	0.201670i	0.440284	−	0.897859i	$-0.354878\pi$
$29$	−1.49479	−	1.08603i	−0.277575	−	0.201670i	−0.717859	+	0.696188i	$0.754878\pi$
$30$	−1.00000			−0.182574
$31$	−1.73285	+	5.29124i	−0.311228	+	0.950335i
$31$	−1.73285	+	5.29124i	−0.311228	+	0.950335i
$32$	−1.00000			−0.176777
$33$	−3.20981	−	2.33206i	−0.558756	−	0.405960i
$34$	2.41862	−	1.75723i	0.414790	−	0.301362i
$35$	0.726038	+	2.23451i	0.122723	+	0.377702i
$36$	1.00000			0.166667
$37$	−7.05969			−1.16061			−0.580303	−	0.814401i	$-0.697066\pi$
$37$	−7.05969			−1.16061			−0.580303	+	0.814401i	$0.697066\pi$
$38$	−0.459733	−	1.41491i	−0.0745786	−	0.229529i
$39$	−1.30381	+	4.01270i	−0.208776	+	0.642546i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	2.07914	+	1.51058i	0.324707	+	0.235914i	0.738181	−	0.674602i	$-0.235685\pi$
$41$	2.07914	+	1.51058i	0.324707	+	0.235914i	−0.413474	+	0.910516i	$0.635685\pi$
$42$	−0.726038	−	2.23451i	−0.112030	−	0.344793i
$43$	3.23865	+	2.35302i	0.493890	+	0.358832i	0.806678	−	0.590991i	$-0.201263\pi$
$43$	3.23865	+	2.35302i	0.493890	+	0.358832i	−0.312788	+	0.949823i	$0.601263\pi$
$44$	−3.20981	+	2.33206i	−0.483897	+	0.351572i
$45$	0.309017	−	0.951057i	0.0460655	−	0.141775i
$46$	−5.19358	+	3.77336i	−0.765752	+	0.556351i
$47$	1.92964	−	1.40196i	0.281466	−	0.204497i	−0.438090	−	0.898931i	$-0.644345\pi$
$47$	1.92964	−	1.40196i	0.281466	−	0.204497i	0.719557	+	0.694434i	$0.244345\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	1.19719	−	0.869812i	0.171028	−	0.124259i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	0.923830	+	2.84326i	0.129362	+	0.398136i
$52$	3.41341	+	2.47998i	0.473354	+	0.343912i
$53$	−3.37591	+	10.3900i	−0.463716	+	1.42717i	0.396874	+	0.917873i	$0.370095\pi$
$53$	−3.37591	+	10.3900i	−0.463716	+	1.42717i	−0.860590	+	0.509299i	$0.829905\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	1.22604	+	3.77336i	0.165319	+	0.508799i
$56$	−2.34951			−0.313966
$57$	1.48773			0.197054
$58$	−0.570958	−	1.75723i	−0.0749705	−	0.230735i
$59$	10.3330	−	7.50738i	1.34525	−	0.977378i	0.346012	−	0.938230i	$-0.387536\pi$
$59$	10.3330	−	7.50738i	1.34525	−	0.977378i	0.999233	−	0.0391476i	$-0.0124642\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	0.0596861			0.00764203			0.00382101	−	0.999993i	$-0.498784\pi$
$61$	0.0596861			0.00764203			0.00382101	+	0.999993i	$0.498784\pi$
$62$	−4.51202	+	3.26216i	−0.573027	+	0.414295i
$63$	2.34951			0.296010
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	3.41341	−	2.47998i	0.423381	−	0.307604i
$66$	−1.22604	−	3.77336i	−0.150915	−	0.464468i
$67$	−7.69531			−0.940132			−0.470066	−	0.882631i	$-0.655770\pi$
$67$	−7.69531			−0.940132			−0.470066	+	0.882631i	$0.655770\pi$
$68$	2.98958			0.362539
$69$	−1.98377	−	6.10542i	−0.238818	−	0.735006i
$70$	−0.726038	+	2.23451i	−0.0867781	+	0.267076i
$71$	−0.930272	+	2.86308i	−0.110403	+	0.339785i	−0.990961	−	0.134154i	$-0.957168\pi$
$71$	−0.930272	+	2.86308i	−0.110403	+	0.339785i	0.880558	+	0.473939i	$0.157168\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	1.45031	+	4.46361i	0.169746	+	0.522426i	0.999355	−	0.0359203i	$-0.0114362\pi$
$73$	1.45031	+	4.46361i	0.169746	+	0.522426i	−0.829608	+	0.558346i	$0.811436\pi$
$74$	−5.71141	−	4.14958i	−0.663937	−	0.482379i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$	0.459733	−	1.41491i	0.0527350	−	0.162302i
$77$	−7.54147	+	5.47920i	−0.859430	+	0.624413i
$78$	−3.41341	+	2.47998i	−0.386492	+	0.280803i
$79$	4.72948	−	14.5559i	0.532108	−	1.63766i	−0.217707	−	0.976014i	$-0.569858\pi$
$79$	4.72948	−	14.5559i	0.532108	−	1.63766i	0.749815	−	0.661647i	$-0.230142\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.794161	+	2.44418i	0.0877004	+	0.269914i
$83$	−5.54083	−	4.02565i	−0.608186	−	0.441873i	0.240589	−	0.970627i	$-0.422659\pi$
$83$	−5.54083	−	4.02565i	−0.608186	−	0.441873i	−0.848775	+	0.528754i	$0.822659\pi$
$84$	0.726038	−	2.23451i	0.0792172	−	0.243806i
$85$	0.923830	−	2.84326i	0.100203	−	0.308394i
$86$	1.23706	+	3.80726i	0.133395	+	0.410548i
$87$	1.84766			0.198090
$88$	−3.96754			−0.422941
$89$	2.23184	+	6.86891i	0.236575	+	0.728103i	0.996909	+	0.0785701i	$0.0250354\pi$
$89$	2.23184	+	6.86891i	0.236575	+	0.728103i	−0.760334	+	0.649533i	$0.774965\pi$
$90$	0.809017	−	0.587785i	0.0852779	−	0.0619580i
$91$	8.01982	+	5.82674i	0.840706	+	0.610809i
$92$	−6.41962			−0.669291
$93$	−1.70821	−	5.29925i	−0.177133	−	0.549506i
$94$	2.38516			0.246011
$95$	−1.20360	−	0.874465i	−0.123487	−	0.0897182i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−4.15049	−	12.7739i	−0.421418	−	1.29699i	−0.906383	−	0.422458i	$-0.861167\pi$
$97$	−4.15049	−	12.7739i	−0.421418	−	1.29699i	0.484964	−	0.874534i	$-0.338833\pi$
$98$	1.47981			0.149484
$99$	3.96754			0.398753
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	0.143063	−	0.440302i	0.0142353	−	0.0438117i	−0.943687	−	0.330841i	$-0.892668\pi$
$101$	0.143063	−	0.440302i	0.0142353	−	0.0438117i	0.957922	+	0.287029i	$0.0926677\pi$
$102$	−0.923830	+	2.84326i	−0.0914728	+	0.281524i
$103$	−9.06128	−	6.58340i	−0.892834	−	0.648682i	0.0437813	−	0.999041i	$-0.486060\pi$
$103$	−9.06128	−	6.58340i	−0.892834	−	0.648682i	−0.936615	+	0.350359i	$0.886060\pi$
$104$	1.30381	+	4.01270i	0.127849	+	0.393478i
$105$	−1.90079	−	1.38101i	−0.185498	−	0.134772i
$106$	−8.83824	+	6.42135i	−0.858445	+	0.623697i
$107$	−4.83427	+	14.8783i	−0.467346	+	1.43834i	0.388662	+	0.921381i	$0.372937\pi$
$107$	−4.83427	+	14.8783i	−0.467346	+	1.43834i	−0.856008	+	0.516963i	$0.827063\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	15.7513	−	11.4440i	1.50870	−	1.09614i	0.541953	−	0.840409i	$-0.317685\pi$
$109$	15.7513	−	11.4440i	1.50870	−	1.09614i	0.966749	−	0.255727i	$-0.0823149\pi$
$110$	−1.22604	+	3.77336i	−0.116898	+	0.359775i
$111$	5.71141	−	4.14958i	0.542103	−	0.393861i
$112$	−1.90079	−	1.38101i	−0.179608	−	0.130493i
$113$	0.302208	+	0.930100i	0.0284293	+	0.0874965i	0.964264	−	0.264942i	$-0.0853527\pi$
$113$	0.302208	+	0.930100i	0.0284293	+	0.0874965i	−0.935835	+	0.352438i	$0.885353\pi$
$114$	1.20360	+	0.874465i	0.112727	+	0.0819011i
$115$	−1.98377	+	6.10542i	−0.184988	+	0.569333i
$116$	0.570958	−	1.75723i	0.0530121	−	0.163155i
$117$	−1.30381	−	4.01270i	−0.120537	−	0.370974i
$118$	12.7723			1.17579
$119$	7.02403			0.643892
$120$	−0.309017	−	0.951057i	−0.0282093	−	0.0868192i
$121$	−3.83586	+	2.78692i	−0.348715	+	0.253356i
$122$	0.0482871	+	0.0350826i	0.00437171	+	0.00317623i
$123$	−2.56996			−0.231725
$124$	−5.56775	−	0.0129517i	−0.499999	−	0.00116310i
$125$	1.00000			0.0894427
$126$	1.90079	+	1.38101i	0.169336	+	0.123030i
$127$	8.54804	−	6.21052i	0.758516	−	0.551094i	−0.139939	−	0.990160i	$-0.544691\pi$
$127$	8.54804	−	6.21052i	0.758516	−	0.551094i	0.898455	+	0.439066i	$0.144691\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−4.00319			−0.352462
$130$	4.21920			0.370049
$131$	−3.50855	−	10.7982i	−0.306543	−	0.943442i	−0.979097	−	0.203394i	$-0.934803\pi$
$131$	−3.50855	−	10.7982i	−0.306543	−	0.943442i	0.672554	−	0.740048i	$-0.265197\pi$
$132$	1.22604	−	3.77336i	0.106713	−	0.328429i
$133$	1.08015	−	3.32435i	0.0936606	−	0.288258i
$134$	−6.22564	−	4.52319i	−0.537813	−	0.390744i
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$	2.41862	+	1.75723i	0.207395	+	0.150681i
$137$	2.36448	−	1.71790i	0.202011	−	0.146770i	−0.482181	−	0.876072i	$-0.660155\pi$
$137$	2.36448	−	1.71790i	0.202011	−	0.146770i	0.684192	+	0.729302i	$0.260155\pi$
$138$	1.98377	−	6.10542i	0.168870	−	0.519728i
$139$	12.9763	−	9.42787i	1.10064	−	0.799661i	0.119475	−	0.992837i	$-0.461879\pi$
$139$	12.9763	−	9.42787i	1.10064	−	0.799661i	0.981164	+	0.193176i	$0.0618787\pi$
$140$	−1.90079	+	1.38101i	−0.160646	+	0.116716i
$141$	−0.737055	+	2.26842i	−0.0620712	+	0.191036i
$142$	−2.43548	+	1.76948i	−0.204381	+	0.148492i
$143$	13.5428	+	9.83944i	1.13251	+	0.822816i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	−1.49479	−	1.08603i	−0.124135	−	0.0901897i
$146$	−1.45031	+	4.46361i	−0.120029	+	0.369411i
$147$	−0.457287	+	1.40739i	−0.0377164	+	0.116079i
$148$	−2.18156	−	6.71416i	−0.179323	−	0.551901i
$149$	−4.77032			−0.390800			−0.195400	−	0.980724i	$-0.562601\pi$
$149$	−4.77032			−0.390800			−0.195400	+	0.980724i	$0.562601\pi$
$150$	−1.00000			−0.0816497
$151$	−3.61013	−	11.1108i	−0.293788	−	0.904186i	−0.983626	−	0.180222i	$-0.942318\pi$
$151$	−3.61013	−	11.1108i	−0.293788	−	0.904186i	0.689838	−	0.723964i	$-0.257682\pi$
$152$	1.20360	−	0.874465i	0.0976247	−	0.0709285i
$153$	−2.41862	−	1.75723i	−0.195534	−	0.142064i
$154$	−9.32177			−0.751170
$155$	−1.73285	+	5.29124i	−0.139186	+	0.425003i
$156$	−4.21920			−0.337807
$157$	1.35410	+	0.983813i	0.108069	+	0.0785168i	0.640507	−	0.767952i	$-0.278724\pi$
$157$	1.35410	+	0.983813i	0.108069	+	0.0785168i	−0.532438	+	0.846469i	$0.678724\pi$
$158$	12.3819	−	8.99601i	0.985055	−	0.715684i
$159$	−3.37591	−	10.3900i	−0.267727	−	0.823978i
$160$	−1.00000			−0.0790569
$161$	−15.0829			−1.18870
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	4.91565	−	15.1288i	0.385023	−	1.18498i	−0.551440	−	0.834214i	$-0.685922\pi$
$163$	4.91565	−	15.1288i	0.385023	−	1.18498i	0.936463	−	0.350765i	$-0.114078\pi$
$164$	−0.794161	+	2.44418i	−0.0620136	+	0.190858i
$165$	−3.20981	−	2.33206i	−0.249883	−	0.181551i
$166$	−2.11641	−	6.51364i	−0.164265	−	0.505557i
$167$	16.3360	+	11.8688i	1.26412	+	0.918435i	0.998952	−	0.0457681i	$-0.0145735\pi$
$167$	16.3360	+	11.8688i	1.26412	+	0.918435i	0.265165	+	0.964203i	$0.414574\pi$
$168$	1.90079	−	1.38101i	0.146649	−	0.106547i
$169$	1.48380	−	4.56666i	0.114138	−	0.351281i
$170$	2.41862	−	1.75723i	0.185500	−	0.134773i
$171$	−1.20360	+	0.874465i	−0.0920414	+	0.0668720i
$172$	−1.23706	+	3.80726i	−0.0943246	+	0.290301i
$173$	13.3845	−	9.72442i	1.01761	−	0.739334i	0.0518150	−	0.998657i	$-0.483499\pi$
$173$	13.3845	−	9.72442i	1.01761	−	0.739334i	0.965791	+	0.259323i	$0.0834994\pi$
$174$	1.49479	+	1.08603i	0.113320	+	0.0823315i
$175$	0.726038	+	2.23451i	0.0548833	+	0.168913i
$176$	−3.20981	−	2.33206i	−0.241948	−	0.175786i
$177$	−3.94686	+	12.1472i	−0.296664	+	0.913039i
$178$	−2.23184	+	6.86891i	−0.167284	+	0.514846i
$179$	−0.525411	−	1.61705i	−0.0392710	−	0.120864i	0.929499	−	0.368824i	$-0.120240\pi$
$179$	−0.525411	−	1.61705i	−0.0392710	−	0.120864i	−0.968770	+	0.247961i	$0.920240\pi$
$180$	1.00000			0.0745356
$181$	14.9106			1.10829			0.554147	−	0.832419i	$-0.313044\pi$
$181$	14.9106			1.10829			0.554147	+	0.832419i	$0.313044\pi$
$182$	3.06330	+	9.42787i	0.227067	+	0.698840i
$183$	−0.0482871	+	0.0350826i	−0.00356949	+	0.00259338i
$184$	−5.19358	−	3.77336i	−0.382876	−	0.278176i
$185$	−7.05969			−0.519038
$186$	1.73285	−	5.29124i	0.127059	−	0.387973i
$187$	11.8613			0.867382
$188$	1.92964	+	1.40196i	0.140733	+	0.102249i
$189$	−1.90079	+	1.38101i	−0.138262	+	0.100453i
$190$	−0.459733	−	1.41491i	−0.0333526	−	0.102649i
$191$	13.3098			0.963065			0.481532	−	0.876428i	$-0.340080\pi$
$191$	13.3098			0.963065			0.481532	+	0.876428i	$0.340080\pi$
$192$	1.00000			0.0721688
$193$	−6.76081	−	20.8076i	−0.486654	−	1.49777i	−0.829571	−	0.558401i	$-0.811415\pi$
$193$	−6.76081	−	20.8076i	−0.486654	−	1.49777i	0.342918	−	0.939365i	$-0.388585\pi$
$194$	4.15049	−	12.7739i	0.297988	−	0.917112i
$195$	−1.30381	+	4.01270i	−0.0933674	+	0.287355i
$196$	1.19719	+	0.869812i	0.0855139	+	0.0621295i
$197$	−1.19986	−	3.69280i	−0.0854868	−	0.263101i	0.899171	−	0.437597i	$-0.144170\pi$
$197$	−1.19986	−	3.69280i	−0.0854868	−	0.263101i	−0.984658	+	0.174496i	$0.944170\pi$
$198$	3.20981	+	2.33206i	0.228111	+	0.165732i
$199$	−2.46266	+	1.78923i	−0.174573	+	0.126835i	−0.671641	−	0.740877i	$-0.734410\pi$
$199$	−2.46266	+	1.78923i	−0.174573	+	0.126835i	0.497067	+	0.867712i	$0.334410\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$	6.22564	−	4.52319i	0.439123	−	0.319041i
$202$	0.374544	−	0.272122i	0.0263528	−	0.0191464i
$203$	1.34147	−	4.12862i	0.0941528	−	0.289773i
$204$	−2.41862	+	1.75723i	−0.169337	+	0.123031i
$205$	2.07914	+	1.51058i	0.145213	+	0.105504i
$206$	−3.46110	−	10.6522i	−0.241146	−	0.742172i
$207$	5.19358	+	3.77336i	0.360979	+	0.262266i
$208$	−1.30381	+	4.01270i	−0.0904026	+	0.278231i
$209$	1.82401	−	5.61373i	0.126170	−	0.388310i
$210$	−0.726038	−	2.23451i	−0.0501014	−	0.154196i
$211$	17.9955			1.23886			0.619431	−	0.785051i	$-0.287363\pi$
$211$	17.9955			1.23886			0.619431	+	0.785051i	$0.287363\pi$
$212$	−10.9247			−0.750309
$213$	−0.930272	−	2.86308i	−0.0637412	−	0.196175i
$214$	−12.6563	+	9.19532i	−0.865165	+	0.628579i
$215$	3.23865	+	2.35302i	0.220874	+	0.160475i
$216$	−1.00000			−0.0680414
$217$	−13.0815	−	0.0304301i	−0.888028	−	0.00206573i
$218$	19.4697			1.31865
$219$	−3.79697	−	2.75866i	−0.256575	−	0.186413i
$220$	−3.20981	+	2.33206i	−0.216405	+	0.157228i
$221$	−3.89783	−	11.9963i	−0.262196	−	0.806957i
$222$	7.05969			0.473815
$223$	−15.6572			−1.04848			−0.524241	−	0.851570i	$-0.675651\pi$
$223$	−15.6572			−1.04848			−0.524241	+	0.851570i	$0.675651\pi$
$224$	−0.726038	−	2.23451i	−0.0485104	−	0.149300i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−0.302208	+	0.930100i	−0.0201026	+	0.0618693i
$227$	20.1907	+	14.6694i	1.34011	+	0.973644i	0.999440	+	0.0334596i	$0.0106525\pi$
$227$	20.1907	+	14.6694i	1.34011	+	0.973644i	0.340666	+	0.940184i	$0.389347\pi$
$228$	0.459733	+	1.41491i	0.0304466	+	0.0937050i
$229$	−4.56772	−	3.31864i	−0.301843	−	0.219302i	0.426545	−	0.904466i	$-0.359730\pi$
$229$	−4.56772	−	3.31864i	−0.301843	−	0.219302i	−0.728389	+	0.685164i	$0.759730\pi$
$230$	−5.19358	+	3.77336i	−0.342454	+	0.248808i
$231$	2.88059	−	8.86553i	0.189529	−	0.583309i
$232$	1.49479	−	1.08603i	0.0981377	−	0.0713012i
$233$	0.460332	−	0.334450i	0.0301573	−	0.0219106i	−0.572604	−	0.819832i	$-0.694067\pi$
$233$	0.460332	−	0.334450i	0.0301573	−	0.0219106i	0.602762	+	0.797921i	$0.294067\pi$
$234$	1.30381	−	4.01270i	0.0852324	−	0.262318i
$235$	1.92964	−	1.40196i	0.125876	−	0.0914539i
$236$	10.3330	+	7.50738i	0.672623	+	0.488689i
$237$	4.72948	+	14.5559i	0.307213	+	0.945504i
$238$	5.68256	+	4.12862i	0.368346	+	0.267619i
$239$	6.63423	−	20.4181i	0.429133	−	1.32074i	−0.469848	−	0.882747i	$-0.655691\pi$
$239$	6.63423	−	20.4181i	0.429133	−	1.32074i	0.898981	−	0.437988i	$-0.144309\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	1.82932	+	5.63006i	0.117837	+	0.362664i	0.992528	−	0.122016i	$-0.0389360\pi$
$241$	1.82932	+	5.63006i	0.117837	+	0.362664i	−0.874692	+	0.484680i	$0.838936\pi$
$242$	−4.74139			−0.304788
$243$	1.00000			0.0641500
$244$	0.0184440	+	0.0567649i	0.00118076	+	0.00363400i
$245$	1.19719	−	0.869812i	0.0764859	−	0.0555703i
$246$	−2.07914	−	1.51058i	−0.132561	−	0.0963113i
$247$	−6.27703			−0.399398
$248$	−4.49679	−	3.28312i	−0.285547	−	0.208478i
$249$	6.84885			0.434028
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−12.6611	+	9.19881i	−0.799160	+	0.580624i	−0.910668	−	0.413140i	$-0.864432\pi$
$251$	−12.6611	+	9.19881i	−0.799160	+	0.580624i	0.111507	+	0.993764i	$0.464432\pi$
$252$	0.726038	+	2.23451i	0.0457361	+	0.140761i
$253$	−25.4701			−1.60129
$254$	10.5660			0.662968
$255$	0.923830	+	2.84326i	0.0578525	+	0.178052i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−5.80557	+	17.8677i	−0.362142	+	1.11456i	0.589610	+	0.807688i	$0.299281\pi$
$257$	−5.80557	+	17.8677i	−0.362142	+	1.11456i	−0.951752	+	0.306869i	$0.900719\pi$
$258$	−3.23865	−	2.35302i	−0.201630	−	0.146493i
$259$	−5.12560	−	15.7750i	−0.318489	−	0.980209i
$260$	3.41341	+	2.47998i	0.211690	+	0.153802i
$261$	−1.49479	+	1.08603i	−0.0925251	+	0.0672234i
$262$	3.50855	−	10.7982i	0.216759	−	0.667114i
$263$	−22.4430	+	16.3058i	−1.38389	+	1.00546i	−0.387389	+	0.921916i	$0.626623\pi$
$263$	−22.4430	+	16.3058i	−1.38389	+	1.00546i	−0.996504	+	0.0835412i	$0.973377\pi$
$264$	3.20981	−	2.33206i	0.197550	−	0.143529i
$265$	−3.37591	+	10.3900i	−0.207380	+	0.638251i
$266$	2.82786	−	2.05456i	0.173387	−	0.125973i
$267$	−5.84304	−	4.24522i	−0.357588	−	0.259803i
$268$	−2.37798	−	7.31868i	−0.145258	−	0.447059i
$269$	−10.2891	−	7.47550i	−0.627340	−	0.455789i	0.228138	−	0.973629i	$-0.426736\pi$
$269$	−10.2891	−	7.47550i	−0.627340	−	0.455789i	−0.855478	+	0.517840i	$0.826736\pi$
$270$	−0.309017	+	0.951057i	−0.0188062	+	0.0578795i
$271$	−7.56192	+	23.2732i	−0.459354	+	1.41375i	0.406593	+	0.913609i	$0.366717\pi$
$271$	−7.56192	+	23.2732i	−0.459354	+	1.41375i	−0.865947	+	0.500136i	$0.833283\pi$
$272$	0.923830	+	2.84326i	0.0560154	+	0.172398i
$273$	−9.91305			−0.599965
$274$	2.92266			0.176564
$275$	1.22604	+	3.77336i	0.0739329	+	0.227542i
$276$	5.19358	−	3.77336i	0.312617	−	0.227129i
$277$	−9.58794	−	6.96604i	−0.576083	−	0.418549i	0.261227	−	0.965277i	$-0.415873\pi$
$277$	−9.58794	−	6.96604i	−0.576083	−	0.418549i	−0.837310	+	0.546728i	$0.815873\pi$
$278$	16.0396			0.961994
$279$	4.49679	+	3.28312i	0.269216	+	0.196555i
$280$	−2.34951			−0.140410
$281$	1.03562	+	0.752424i	0.0617800	+	0.0448858i	0.618247	−	0.785984i	$-0.287843\pi$
$281$	1.03562	+	0.752424i	0.0617800	+	0.0448858i	−0.556467	+	0.830870i	$0.687843\pi$
$282$	−1.92964	+	1.40196i	−0.114908	+	0.0834856i
$283$	−5.00521	−	15.4045i	−0.297529	−	0.915700i	−0.982360	−	0.186998i	$-0.940124\pi$
$283$	−5.00521	−	15.4045i	−0.297529	−	0.915700i	0.684831	−	0.728702i	$-0.259876\pi$
$284$	−3.01042			−0.178636
$285$	1.48773			0.0881254
$286$	5.17290	+	15.9206i	0.305880	+	0.941402i
$287$	−1.86589	+	5.74261i	−0.110140	+	0.338976i
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	6.52264	+	4.73898i	0.383685	+	0.278763i
$290$	−0.570958	−	1.75723i	−0.0335278	−	0.103188i
$291$	10.8661	+	7.89470i	0.636983	+	0.462795i
$292$	−3.79697	+	2.75866i	−0.222201	+	0.161438i
$293$	4.37537	−	13.4660i	0.255612	−	0.786693i	−0.738096	−	0.674695i	$-0.764275\pi$
$293$	4.37537	−	13.4660i	0.255612	−	0.786693i	0.993708	−	0.111998i	$-0.0357249\pi$
$294$	−1.19719	+	0.869812i	−0.0698218	+	0.0507285i
$295$	10.3330	−	7.50738i	0.601612	−	0.437097i
$296$	2.18156	−	6.71416i	0.126801	−	0.390253i
$297$	−3.20981	+	2.33206i	−0.186252	+	0.135320i
$298$	−3.85927	−	2.80392i	−0.223562	−	0.162427i
$299$	8.36993	+	25.7600i	0.484046	+	1.48974i
$300$	−0.809017	−	0.587785i	−0.0467086	−	0.0339358i
$301$	−2.90647	+	8.94520i	−0.167526	+	0.515593i
$302$	3.61013	−	11.1108i	0.207739	−	0.639356i
$303$	0.143063	+	0.440302i	0.00821875	+	0.0252947i
$304$	1.48773			0.0853271
$305$	0.0596861			0.00341762
$306$	−0.923830	−	2.84326i	−0.0528118	−	0.162538i
$307$	−1.36192	+	0.989491i	−0.0777288	+	0.0564732i	−0.625971	−	0.779846i	$-0.715297\pi$
$307$	−1.36192	+	0.989491i	−0.0777288	+	0.0564732i	0.548242	+	0.836320i	$0.315297\pi$
$308$	−7.54147	−	5.47920i	−0.429715	−	0.312206i
$309$	11.2004			0.637166
$310$	−4.51202	+	3.26216i	−0.256265	+	0.185278i
$311$	3.22201			0.182703			0.0913517	−	0.995819i	$-0.470881\pi$
$311$	3.22201			0.182703			0.0913517	+	0.995819i	$0.470881\pi$
$312$	−3.41341	−	2.47998i	−0.193246	−	0.140401i
$313$	−9.42720	+	6.84926i	−0.532857	+	0.387143i	−0.821425	−	0.570316i	$-0.806821\pi$
$313$	−9.42720	+	6.84926i	−0.532857	+	0.387143i	0.288568	+	0.957459i	$0.406821\pi$
$314$	0.517221	+	1.59184i	0.0291885	+	0.0898329i
$315$	2.34951			0.132380
$316$	15.3049			0.860970
$317$	1.82149	+	5.60596i	0.102305	+	0.314862i	0.989088	−	0.147323i	$-0.0470656\pi$
$317$	1.82149	+	5.60596i	0.102305	+	0.314862i	−0.886784	+	0.462185i	$0.847066\pi$
$318$	3.37591	−	10.3900i	0.189311	−	0.582641i
$319$	2.26530	−	6.97188i	0.126833	−	0.390350i
$320$	−0.809017	−	0.587785i	−0.0452254	−	0.0328582i
$321$	−4.83427	−	14.8783i	−0.269822	−	0.830428i
$322$	−12.2024	−	8.86553i	−0.680011	−	0.494057i
$323$	−3.59825	+	2.61428i	−0.200212	+	0.145462i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	3.41341	−	2.47998i	0.189342	−	0.137565i
$326$	12.8693	−	9.35012i	0.712766	−	0.517855i
$327$	−6.01647	+	18.5168i	−0.332711	+	1.02398i
$328$	−2.07914	+	1.51058i	−0.114801	+	0.0834080i
$329$	4.53369	+	3.29392i	0.249951	+	0.181600i
$330$	−1.22604	−	3.77336i	−0.0674912	−	0.207716i
$331$	1.63782	+	1.18994i	0.0900225	+	0.0654052i	0.631886	−	0.775061i	$-0.282281\pi$
$331$	1.63782	+	1.18994i	0.0900225	+	0.0654052i	−0.541864	+	0.840466i	$0.682281\pi$
$332$	2.11641	−	6.51364i	0.116153	−	0.357482i
$333$	−2.18156	+	6.71416i	−0.119549	+	0.367934i
$334$	6.23979	+	19.2041i	0.341426	+	1.05080i
$335$	−7.69531			−0.420440
$336$	2.34951			0.128176
$337$	3.57479	+	11.0021i	0.194731	+	0.599321i	0.999980	+	0.00638317i	$0.00203184\pi$
$337$	3.57479	+	11.0021i	0.194731	+	0.599321i	−0.805249	+	0.592937i	$0.797968\pi$
$338$	3.88463	−	2.82235i	0.211296	−	0.153516i
$339$	−0.791191	−	0.574834i	−0.0429716	−	0.0312207i
$340$	2.98958			0.162133
$341$	−22.0903	−	0.0513863i	−1.19626	−	0.00278273i
$342$	−1.48773			−0.0804471
$343$	16.1184	+	11.7107i	0.870310	+	0.632317i
$344$	−3.23865	+	2.35302i	−0.174616	+	0.126866i
$345$	−1.98377	−	6.10542i	−0.106803	−	0.328705i
$346$	16.5442			0.889420
$347$	−10.3186			−0.553929			−0.276965	−	0.960880i	$-0.589329\pi$
$347$	−10.3186			−0.553929			−0.276965	+	0.960880i	$0.589329\pi$
$348$	0.570958	+	1.75723i	0.0306066	+	0.0941974i
$349$	9.53909	−	29.3583i	0.510616	−	1.57151i	−0.280504	−	0.959853i	$-0.590501\pi$
$349$	9.53909	−	29.3583i	0.510616	−	1.57151i	0.791120	−	0.611661i	$-0.209499\pi$
$350$	−0.726038	+	2.23451i	−0.0388084	+	0.119440i
$351$	3.41341	+	2.47998i	0.182194	+	0.132372i
$352$	−1.22604	−	3.77336i	−0.0653480	−	0.201121i
$353$	−1.21053	−	0.879505i	−0.0644302	−	0.0468113i	0.555104	−	0.831781i	$-0.312678\pi$
$353$	−1.21053	−	0.879505i	−0.0644302	−	0.0468113i	−0.619534	+	0.784970i	$0.712678\pi$
$354$	−10.3330	+	7.50738i	−0.549194	+	0.399013i
$355$	−0.930272	+	2.86308i	−0.0493737	+	0.151957i
$356$	−5.84304	+	4.24522i	−0.309681	+	0.224996i
$357$	−5.68256	+	4.12862i	−0.300753	+	0.218510i
$358$	0.525411	−	1.61705i	0.0277688	−	0.0854636i
$359$	−27.1280	+	19.7097i	−1.43176	+	1.04024i	−0.442077	+	0.896977i	$0.645758\pi$
$359$	−27.1280	+	19.7097i	−1.43176	+	1.04024i	−0.989685	+	0.143259i	$0.954242\pi$
$360$	0.809017	+	0.587785i	0.0426389	+	0.0309790i
$361$	−5.18736	−	15.9651i	−0.273019	−	0.840267i
$362$	12.0629	+	8.76422i	0.634013	+	0.460637i
$363$	1.46517	−	4.50933i	0.0769014	−	0.236678i
$364$	−3.06330	+	9.42787i	−0.160561	+	0.494155i
$365$	1.45031	+	4.46361i	0.0759129	+	0.233636i
$366$	−0.0596861			−0.00311984
$367$	−37.4401			−1.95435			−0.977177	−	0.212425i	$-0.931864\pi$
$367$	−37.4401			−1.95435			−0.977177	+	0.212425i	$0.931864\pi$
$368$	−1.98377	−	6.10542i	−0.103411	−	0.318267i
$369$	2.07914	−	1.51058i	0.108236	−	0.0786379i
$370$	−5.71141	−	4.14958i	−0.296922	−	0.215726i
$371$	−25.6676			−1.33259
$372$	4.51202	−	3.26216i	0.233937	−	0.169135i
$373$	1.07628			0.0557278			0.0278639	−	0.999612i	$-0.491129\pi$
$373$	1.07628			0.0557278			0.0278639	+	0.999612i	$0.491129\pi$
$374$	9.59597	+	6.97188i	0.496196	+	0.360507i
$375$	−0.809017	+	0.587785i	−0.0417775	+	0.0303531i
$376$	0.737055	+	2.26842i	0.0380107	+	0.116985i
$377$	−7.79565			−0.401496
$378$	−2.34951			−0.120846
$379$	−1.38097	−	4.25020i	−0.0709359	−	0.218318i	0.909303	−	0.416134i	$-0.136615\pi$
$379$	−1.38097	−	4.25020i	−0.0709359	−	0.218318i	−0.980239	+	0.197816i	$0.936615\pi$
$380$	0.459733	−	1.41491i	0.0235838	−	0.0725836i
$381$	−3.26506	+	10.0488i	−0.167274	+	0.514817i
$382$	10.7679	+	7.82332i	0.550932	+	0.400276i
$383$	8.09934	+	24.9272i	0.413857	+	1.27372i	0.913269	+	0.407357i	$0.133549\pi$
$383$	8.09934	+	24.9272i	0.413857	+	1.27372i	−0.499412	+	0.866365i	$0.666451\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$	−7.54147	+	5.47920i	−0.384349	+	0.279246i
$386$	6.76081	−	20.8076i	0.344116	−	1.05908i
$387$	3.23865	−	2.35302i	0.164630	−	0.119611i
$388$	10.8661	−	7.89470i	0.551644	−	0.400793i
$389$	−3.20766	+	9.87217i	−0.162635	+	0.500539i	−0.998854	−	0.0478563i	$-0.984761\pi$
$389$	−3.20766	+	9.87217i	−0.162635	+	0.500539i	0.836219	+	0.548395i	$0.184761\pi$
$390$	−3.41341	+	2.47998i	−0.172845	+	0.125579i
$391$	15.5266	+	11.2807i	0.785214	+	0.570491i
$392$	0.457287	+	1.40739i	0.0230965	+	0.0710837i
$393$	9.18549	+	6.67365i	0.463347	+	0.336641i
$394$	1.19986	−	3.69280i	0.0604483	−	0.186041i
$395$	4.72948	−	14.5559i	0.237966	−	0.732384i
$396$	1.22604	+	3.77336i	0.0616107	+	0.189618i
$397$	19.7649			0.991974			0.495987	−	0.868330i	$-0.334806\pi$
$397$	19.7649			0.991974			0.495987	+	0.868330i	$0.334806\pi$
$398$	−3.04402			−0.152583
$399$	1.08015	+	3.32435i	0.0540750	+	0.166426i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−7.38981	−	5.36901i	−0.369029	−	0.268115i	0.387779	−	0.921752i	$-0.373242\pi$
$401$	−7.38981	−	5.36901i	−0.369029	−	0.268115i	−0.756808	+	0.653637i	$0.773242\pi$
$402$	7.69531			0.383807
$403$	7.20729	+	22.3586i	0.359021	+	1.11376i
$404$	0.462961			0.0230332
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	3.51202	−	2.55163i	0.174298	−	0.126635i
$407$	−8.65544	−	26.6387i	−0.429034	−	1.32043i
$408$	−2.98958			−0.148006
$409$	8.55780			0.423156			0.211578	−	0.977361i	$-0.432140\pi$
$409$	8.55780			0.423156			0.211578	+	0.977361i	$0.432140\pi$
$410$	0.794161	+	2.44418i	0.0392208	+	0.120709i
$411$	−0.903152	+	2.77962i	−0.0445492	+	0.137108i
$412$	3.46110	−	10.6522i	0.170516	−	0.524795i
$413$	24.2775	+	17.6387i	1.19462	+	0.867941i
$414$	1.98377	+	6.10542i	0.0974970	+	0.300065i
$415$	−5.54083	−	4.02565i	−0.271989	−	0.197611i
$416$	−3.41341	+	2.47998i	−0.167356	+	0.121591i
$417$	−4.95652	+	15.2546i	−0.242722	+	0.747022i
$418$	4.77532	−	3.46948i	0.233569	−	0.169698i
$419$	17.8849	−	12.9942i	0.873735	−	0.634806i	−0.0578513	−	0.998325i	$-0.518425\pi$
$419$	17.8849	−	12.9942i	0.873735	−	0.634806i	0.931587	+	0.363519i	$0.118425\pi$
$420$	0.726038	−	2.23451i	0.0354270	−	0.109033i
$421$	−8.31677	+	6.04249i	−0.405334	+	0.294493i	−0.771710	−	0.635974i	$-0.780598\pi$
$421$	−8.31677	+	6.04249i	−0.405334	+	0.294493i	0.366376	+	0.930467i	$0.380598\pi$
$422$	14.5587	+	10.5775i	0.708705	+	0.514904i
$423$	−0.737055	−	2.26842i	−0.0358368	−	0.110294i
$424$	−8.83824	−	6.42135i	−0.429223	−	0.311849i
$425$	0.923830	−	2.84326i	0.0448123	−	0.137918i
$426$	0.930272	−	2.86308i	0.0450718	−	0.138717i
$427$	0.0433344	+	0.133370i	0.00209710	+	0.00645421i
$428$	−15.6440			−0.756182
$429$	−16.7399			−0.808208
$430$	1.23706	+	3.80726i	0.0596561	+	0.183603i
$431$	31.4495	−	22.8494i	1.51487	−	1.10062i	0.550912	−	0.834563i	$-0.314280\pi$
$431$	31.4495	−	22.8494i	1.51487	−	1.10062i	0.963958	−	0.266054i	$-0.0857199\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	−17.1038			−0.821954			−0.410977	−	0.911646i	$-0.634812\pi$
$433$	−17.1038			−0.821954			−0.410977	+	0.911646i	$0.634812\pi$
$434$	−10.5652	−	7.71371i	−0.507148	−	0.370270i
$435$	1.84766			0.0885885
$436$	15.7513	+	11.4440i	0.754351	+	0.548068i
$437$	7.72664	−	5.61373i	0.369615	−	0.268541i
$438$	−1.45031	−	4.46361i	−0.0692987	−	0.213279i
$439$	−17.0719			−0.814795			−0.407398	−	0.913251i	$-0.633564\pi$
$439$	−17.0719			−0.814795			−0.407398	+	0.913251i	$0.633564\pi$
$440$	−3.96754			−0.189145
$441$	−0.457287	−	1.40739i	−0.0217756	−	0.0670184i
$442$	3.89783	−	11.9963i	0.185401	−	0.570605i
$443$	5.57798	−	17.1673i	0.265018	−	0.815641i	−0.726671	−	0.686985i	$-0.758934\pi$
$443$	5.57798	−	17.1673i	0.265018	−	0.815641i	0.991689	−	0.128656i	$-0.0410663\pi$
$444$	5.71141	+	4.14958i	0.271051	+	0.196930i
$445$	2.23184	+	6.86891i	0.105800	+	0.325617i
$446$	−12.6669	−	9.20306i	−0.599796	−	0.435778i
$447$	3.85927	−	2.80392i	0.182537	−	0.132621i
$448$	0.726038	−	2.23451i	0.0343021	−	0.105571i
$449$	14.8777	−	10.8093i	0.702120	−	0.510120i	−0.178502	−	0.983940i	$-0.557125\pi$
$449$	14.8777	−	10.8093i	0.702120	−	0.510120i	0.880622	+	0.473819i	$0.157125\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	−3.15087	+	9.69737i	−0.148369	+	0.456631i
$452$	−0.791191	+	0.574834i	−0.0372145	+	0.0270379i
$453$	9.45143	+	6.86687i	0.444067	+	0.322634i
$454$	7.71217	+	23.7356i	0.361950	+	1.11397i
$455$	8.01982	+	5.82674i	0.375975	+	0.273162i
$456$	−0.459733	+	1.41491i	−0.0215290	+	0.0662594i
$457$	5.39598	−	16.6071i	0.252413	−	0.776848i	−0.741915	−	0.670494i	$-0.766082\pi$
$457$	5.39598	−	16.6071i	0.252413	−	0.776848i	0.994328	−	0.106354i	$-0.0339177\pi$
$458$	−1.74471	−	5.36967i	−0.0815251	−	0.250908i
$459$	2.98958			0.139541
$460$	−6.41962			−0.299316
$461$	−5.97546	−	18.3906i	−0.278305	−	0.856535i	−0.988326	−	0.152354i	$-0.951315\pi$
$461$	−5.97546	−	18.3906i	−0.278305	−	0.856535i	0.710021	−	0.704181i	$-0.248685\pi$
$462$	7.54147	−	5.47920i	0.350861	−	0.254915i
$463$	−8.92776	−	6.48640i	−0.414908	−	0.301448i	0.360678	−	0.932690i	$-0.382545\pi$
$463$	−8.92776	−	6.48640i	−0.414908	−	0.301448i	−0.775586	+	0.631242i	$0.782545\pi$
$464$	1.84766			0.0857755
$465$	−1.70821	−	5.29925i	−0.0792164	−	0.245747i
$466$	0.569001			0.0263585
$467$	−9.02821	−	6.55938i	−0.417776	−	0.303532i	0.358967	−	0.933350i	$-0.383129\pi$
$467$	−9.02821	−	6.55938i	−0.417776	−	0.303532i	−0.776742	+	0.629819i	$0.783129\pi$
$468$	3.41341	−	2.47998i	0.157785	−	0.114637i
$469$	−5.58709	−	17.1953i	−0.257988	−	0.794005i
$470$	2.38516			0.110019
$471$	−1.67376			−0.0771229
$472$	3.94686	+	12.1472i	0.181669	+	0.559120i
$473$	−4.90807	+	15.1055i	−0.225673	+	0.694551i
$474$	−4.72948	+	14.5559i	−0.217232	+	0.668572i
$475$	−1.20360	−	0.874465i	−0.0552249	−	0.0401232i
$476$	2.17055	+	6.68025i	0.0994868	+	0.306189i
$477$	8.83824	+	6.42135i	0.404675	+	0.294014i
$478$	17.3686	−	12.6191i	0.794423	−	0.577182i
$479$	2.62339	−	8.07397i	0.119866	−	0.368909i	−0.873065	−	0.487604i	$-0.837871\pi$
$479$	2.62339	−	8.07397i	0.119866	−	0.368909i	0.992931	+	0.118695i	$0.0378710\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	−24.0976	+	17.5079i	−1.09875	+	0.798292i
$482$	−1.82932	+	5.63006i	−0.0833231	+	0.256442i
$483$	12.2024	−	8.86553i	0.555226	−	0.403396i
$484$	−3.83586	−	2.78692i	−0.174357	−	0.126678i
$485$	−4.15049	−	12.7739i	−0.188464	−	0.580032i
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	−7.84496	+	24.1443i	−0.355489	+	1.09408i	0.600236	+	0.799823i	$0.295073\pi$
$487$	−7.84496	+	24.1443i	−0.355489	+	1.09408i	−0.955725	+	0.294260i	$0.904927\pi$
$488$	−0.0184440	+	0.0567649i	−0.000834922	+	0.00256963i
$489$	4.91565	+	15.1288i	0.222293	+	0.684148i
$490$	1.47981			0.0668511
$491$	−11.2980			−0.509870			−0.254935	−	0.966958i	$-0.582054\pi$
$491$	−11.2980			−0.509870			−0.254935	+	0.966958i	$0.582054\pi$
$492$	−0.794161	−	2.44418i	−0.0358035	−	0.110192i
$493$	−4.46878	+	3.24676i	−0.201264	+	0.146227i
$494$	−5.07822	−	3.68954i	−0.228480	−	0.166000i
$495$	3.96754			0.178328
$496$	−1.70821	−	5.29925i	−0.0767010	−	0.237943i
$497$	−7.07301			−0.317268
$498$	5.54083	+	4.02565i	0.248291	+	0.180394i
$499$	−34.6031	+	25.1406i	−1.54905	+	1.12545i	−0.604719	+	0.796439i	$0.706714\pi$
$499$	−34.6031	+	25.1406i	−1.54905	+	1.12545i	−0.944327	+	0.329008i	$0.893286\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	−20.1924			−0.902130
$502$	−15.6500			−0.698492
$503$	3.78519	+	11.6496i	0.168773	+	0.519431i	0.999295	−	0.0375559i	$-0.0119572\pi$
$503$	3.78519	+	11.6496i	0.168773	+	0.519431i	−0.830521	+	0.556987i	$0.811957\pi$
$504$	−0.726038	+	2.23451i	−0.0323403	+	0.0995332i
$505$	0.143063	−	0.440302i	0.00636622	−	0.0195932i
$506$	−20.6057	−	14.9709i	−0.916037	−	0.665540i
$507$	1.48380	+	4.56666i	0.0658977	+	0.202812i
$508$	8.54804	+	6.21052i	0.379258	+	0.275547i
$509$	−18.6813	+	13.5727i	−0.828033	+	0.601601i	−0.919002	−	0.394252i	$-0.871004\pi$
$509$	−18.6813	+	13.5727i	−0.828033	+	0.601601i	0.0909689	+	0.995854i	$0.471004\pi$
$510$	−0.923830	+	2.84326i	−0.0409079	+	0.125902i
$511$	−8.92101	+	6.48149i	−0.394642	+	0.286724i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	0.459733	−	1.41491i	0.0202977	−	0.0624700i
$514$	−15.1992	+	11.0429i	−0.670407	+	0.487079i
$515$	−9.06128	−	6.58340i	−0.399288	−	0.290099i
$516$	−1.23706	−	3.80726i	−0.0544583	−	0.167605i
$517$	7.65591	+	5.56234i	0.336707	+	0.244632i
$518$	5.12560	−	15.7750i	0.225206	−	0.693112i
$519$	−5.11243	+	15.7344i	−0.224411	+	0.690665i
$520$	1.30381	+	4.01270i	0.0571756	+	0.175969i
$521$	−24.2636			−1.06301			−0.531505	−	0.847055i	$-0.678373\pi$
$521$	−24.2636			−1.06301			−0.531505	+	0.847055i	$0.678373\pi$
$522$	−1.84766			−0.0808699
$523$	−4.86792	−	14.9819i	−0.212859	−	0.655114i	−0.999299	−	0.0374461i	$-0.988078\pi$
$523$	−4.86792	−	14.9819i	−0.212859	−	0.655114i	0.786439	−	0.617668i	$-0.211922\pi$
$524$	9.18549	−	6.67365i	0.401270	−	0.291540i
$525$	−1.90079	−	1.38101i	−0.0829574	−	0.0602720i
$526$	−27.7410			−1.20957
$527$	13.4435	+	9.81514i	0.585608	+	0.427554i
$528$	3.96754			0.172665
$529$	−14.7334	−	10.7044i	−0.640583	−	0.465411i
$530$	−8.83824	+	6.42135i	−0.383908	+	0.278926i
$531$	−3.94686	−	12.1472i	−0.171279	−	0.527143i
$532$	3.49543			0.151546
$533$	10.8432			0.469670
$534$	−2.23184	−	6.86891i	−0.0965813	−	0.297247i
$535$	−4.83427	+	14.8783i	−0.209004	+	0.643247i
$536$	2.37798	−	7.31868i	0.102713	−	0.316119i
$537$	1.37554	+	0.999390i	0.0593591	+	0.0431269i
$538$	−3.93010	−	12.0956i	−0.169439	−	0.521479i
$539$	4.74992	+	3.45102i	0.204593	+	0.148646i
$540$	−0.809017	+	0.587785i	−0.0348145	+	0.0252942i
$541$	5.54321	−	17.0602i	0.238321	−	0.733477i	−0.758342	−	0.651856i	$-0.773990\pi$
$541$	5.54321	−	17.0602i	0.238321	−	0.733477i	0.996663	−	0.0816204i	$-0.0260095\pi$
$542$	−19.7974	+	14.3836i	−0.850369	+	0.617829i
$543$	−12.0629	+	8.76422i	−0.517669	+	0.376109i
$544$	−0.923830	+	2.84326i	−0.0396089	+	0.121904i
$545$	15.7513	−	11.4440i	0.674712	−	0.490207i
$546$	−8.01982	−	5.82674i	−0.343217	−	0.249362i
$547$	0.923432	+	2.84203i	0.0394831	+	0.121516i	0.968855	−	0.247628i	$-0.0796509\pi$
$547$	0.923432	+	2.84203i	0.0394831	+	0.121516i	−0.929372	+	0.369144i	$0.879651\pi$
$548$	2.36448	+	1.71790i	0.101006	+	0.0733849i
$549$	0.0184440	−	0.0567649i	0.000787172	−	0.00242267i
$550$	−1.22604	+	3.77336i	−0.0522784	+	0.160896i
$551$	0.849431	+	2.61428i	0.0361870	+	0.111372i
$552$	6.41962			0.273237
$553$	35.9590			1.52913
$554$	−3.66227	−	11.2713i	−0.155595	−	0.478871i
$555$	5.71141	−	4.14958i	0.242436	−	0.176140i
$556$	12.9763	+	9.42787i	0.550320	+	0.399831i
$557$	−34.4255			−1.45866			−0.729329	−	0.684164i	$-0.760167\pi$
$557$	−34.4255			−1.45866			−0.729329	+	0.684164i	$0.760167\pi$
$558$	1.70821	+	5.29925i	0.0723144	+	0.224335i
$559$	16.8903			0.714383
$560$	−1.90079	−	1.38101i	−0.0803231	−	0.0583582i
$561$	−9.59597	+	6.97188i	−0.405142	+	0.294353i
$562$	0.395573	+	1.21745i	0.0166862	+	0.0513549i
$563$	7.48446			0.315432			0.157716	−	0.987484i	$-0.449587\pi$
$563$	7.48446			0.315432			0.157716	+	0.987484i	$0.449587\pi$
$564$	−2.38516			−0.100433
$565$	0.302208	+	0.930100i	0.0127140	+	0.0391296i
$566$	5.00521	−	15.4045i	0.210385	−	0.647498i
$567$	0.726038	−	2.23451i	0.0304907	−	0.0938408i
$568$	−2.43548	−	1.76948i	−0.102191	−	0.0742458i
$569$	2.22283	+	6.84116i	0.0931858	+	0.286796i	0.986777	−	0.162086i	$-0.0518222\pi$
$569$	2.22283	+	6.84116i	0.0931858	+	0.286796i	−0.893591	+	0.448882i	$0.851822\pi$
$570$	1.20360	+	0.874465i	0.0504132	+	0.0366273i
$571$	20.5348	−	14.9194i	0.859356	−	0.624359i	−0.0683538	−	0.997661i	$-0.521775\pi$
$571$	20.5348	−	14.9194i	0.859356	−	0.624359i	0.927710	+	0.373303i	$0.121775\pi$
$572$	−5.17290	+	15.9206i	−0.216290	+	0.665672i
$573$	−10.7679	+	7.82332i	−0.449834	+	0.326824i
$574$	−4.88496	+	3.54913i	−0.203894	+	0.148138i
$575$	−1.98377	+	6.10542i	−0.0827290	+	0.254614i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	31.7859	+	23.0938i	1.32327	+	0.961408i	0.999885	+	0.0151392i	$0.00481916\pi$
$577$	31.7859	+	23.0938i	1.32327	+	0.961408i	0.323380	+	0.946269i	$0.395181\pi$
$578$	2.49143	+	7.66783i	0.103630	+	0.318940i
$579$	17.7000	+	12.8598i	0.735588	+	0.534436i
$580$	0.570958	−	1.75723i	0.0237078	−	0.0729650i
$581$	4.97252	−	15.3039i	0.206295	−	0.634911i
$582$	4.15049	+	12.7739i	0.172043	+	0.529495i
$583$	−43.3440			−1.79513
$584$	−4.69331			−0.194211
$585$	−1.30381	−	4.01270i	−0.0539057	−	0.165905i
$586$	11.4549	−	8.32246i	0.473197	−	0.343797i
$587$	−24.8350	−	18.0437i	−1.02505	−	0.744743i	−0.0577390	−	0.998332i	$-0.518389\pi$
$587$	−24.8350	−	18.0437i	−1.02505	−	0.744743i	−0.967312	+	0.253588i	$0.918389\pi$
$588$	−1.47981			−0.0610265
$589$	6.71266	−	4.85321i	0.276590	−	0.199973i
$590$	12.7723			0.525828
$591$	3.14129	+	2.28228i	0.129215	+	0.0938803i
$592$	5.71141	−	4.14958i	0.234737	−	0.170547i
$593$	5.25502	+	16.1733i	0.215798	+	0.664157i	0.999096	+	0.0425110i	$0.0135358\pi$
$593$	5.25502	+	16.1733i	0.215798	+	0.664157i	−0.783298	+	0.621646i	$0.786464\pi$
$594$	−3.96754			−0.162790
$595$	7.02403			0.287957
$596$	−1.47411	−	4.53685i	−0.0603819	−	0.185836i
$597$	0.940653	−	2.89503i	0.0384984	−	0.118486i
$598$	−8.36993	+	25.7600i	−0.342272	+	1.05340i
$599$	19.2192	+	13.9636i	0.785276	+	0.570537i	0.906558	−	0.422082i	$-0.138700\pi$
$599$	19.2192	+	13.9636i	0.785276	+	0.570537i	−0.121282	+	0.992618i	$0.538700\pi$
$600$	−0.309017	−	0.951057i	−0.0126156	−	0.0388267i
$601$	18.1413	+	13.1804i	0.739998	+	0.537640i	0.892711	−	0.450631i	$-0.148801\pi$
$601$	18.1413	+	13.1804i	0.739998	+	0.537640i	−0.152712	+	0.988271i	$0.548801\pi$
$602$	−7.60924	+	5.52844i	−0.310129	+	0.225322i
$603$	−2.37798	+	7.31868i	−0.0968389	+	0.298040i
$604$	9.45143	−	6.86687i	0.384573	−	0.279409i
$605$	−3.83586	+	2.78692i	−0.155950	+	0.113304i
$606$	−0.143063	+	0.440302i	−0.00581153	+	0.0178861i
$607$	1.90138	−	1.38144i	0.0771748	−	0.0560708i	−0.548529	−	0.836132i	$-0.684812\pi$
$607$	1.90138	−	1.38144i	0.0771748	−	0.0560708i	0.625704	+	0.780061i	$0.284812\pi$
$608$	1.20360	+	0.874465i	0.0488123	+	0.0354642i
$609$	1.34147	+	4.12862i	0.0543591	+	0.167300i
$610$	0.0482871	+	0.0350826i	0.00195509	+	0.00142045i
$611$	3.10979	−	9.57093i	0.125808	−	0.387199i
$612$	0.923830	−	2.84326i	0.0373436	−	0.114932i
$613$	8.17691	+	25.1659i	0.330262	+	1.01644i	0.969009	+	0.247026i	$0.0794532\pi$
$613$	8.17691	+	25.1659i	0.330262	+	1.01644i	−0.638747	+	0.769417i	$0.720547\pi$
$614$	−1.68342			−0.0679374
$615$	−2.56996			−0.103631
$616$	−2.88059	−	8.86553i	−0.116062	−	0.357202i
$617$	−12.0451	+	8.75129i	−0.484918	+	0.352314i	−0.803227	−	0.595673i	$-0.796885\pi$
$617$	−12.0451	+	8.75129i	−0.484918	+	0.352314i	0.318308	+	0.947987i	$0.396885\pi$
$618$	9.06128	+	6.58340i	0.364498	+	0.264823i
$619$	−19.2106			−0.772137			−0.386069	−	0.922470i	$-0.626167\pi$
$619$	−19.2106			−0.772137			−0.386069	+	0.922470i	$0.626167\pi$
$620$	−5.56775	−	0.0129517i	−0.223606	−	0.000520152i
$621$	−6.41962			−0.257610
$622$	2.60666	+	1.89385i	0.104518	+	0.0759365i
$623$	−13.7283	+	9.97417i	−0.550012	+	0.399607i
$624$	−1.30381	−	4.01270i	−0.0521940	−	0.160637i
$625$	1.00000			0.0400000
$626$	−11.6527			−0.465734
$627$	1.82401	+	5.61373i	0.0728440	+	0.224191i
$628$	−0.517221	+	1.59184i	−0.0206394	+	0.0635214i
$629$	−6.52195	+	20.0725i	−0.260047	+	0.800343i
$630$	1.90079	+	1.38101i	0.0757294	+	0.0550206i
$631$	12.4465	+	38.3063i	0.495487	+	1.52495i	0.816197	+	0.577774i	$0.196078\pi$
$631$	12.4465	+	38.3063i	0.495487	+	1.52495i	−0.320711	+	0.947177i	$0.603922\pi$
$632$	12.3819	+	8.99601i	0.492527	+	0.357842i
$633$	−14.5587	+	10.5775i	−0.578655	+	0.420418i
$634$	−1.82149	+	5.60596i	−0.0723405	+	0.222641i
$635$	8.54804	−	6.21052i	0.339219	−	0.246457i
$636$	8.83824	−	6.42135i	0.350459	−	0.254623i
$637$	1.92939	−	5.93805i	0.0764451	−	0.235274i
$638$	5.93063	−	4.30886i	0.234796	−	0.170589i
$639$	2.43548	+	1.76948i	0.0963462	+	0.0699996i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	4.83295	+	3.51135i	0.190890	+	0.138690i	0.679125	−	0.734022i	$-0.262359\pi$
$641$	4.83295	+	3.51135i	0.190890	+	0.138690i	−0.488235	+	0.872712i	$0.662359\pi$
$642$	4.83427	−	14.8783i	0.190793	−	0.587201i
$643$	8.25175	−	25.3963i	0.325417	−	1.00153i	−0.645834	−	0.763477i	$-0.723490\pi$
$643$	8.25175	−	25.3963i	0.325417	−	1.00153i	0.971252	−	0.238054i	$-0.0765096\pi$
$644$	−4.66089	−	14.3447i	−0.183665	−	0.565262i
$645$	−4.00319			−0.157626
$646$	−4.44768			−0.174992
$647$	7.47574	+	23.0079i	0.293901	+	0.904536i	0.983588	+	0.180428i	$0.0577483\pi$
$647$	7.47574	+	23.0079i	0.293901	+	0.904536i	−0.689687	+	0.724108i	$0.742252\pi$
$648$	0.809017	−	0.587785i	0.0317812	−	0.0230904i
$649$	40.9967	+	29.7858i	1.60926	+	1.16920i
$650$	4.21920			0.165491
$651$	10.6010	−	7.66448i	0.415487	−	0.300395i
$652$	15.9074			0.622981
$653$	−18.6887	−	13.5782i	−0.731347	−	0.531355i	0.158642	−	0.987336i	$-0.449288\pi$
$653$	−18.6887	−	13.5782i	−0.731347	−	0.531355i	−0.889989	+	0.455982i	$0.849288\pi$
$654$	−15.7513	+	11.4440i	−0.615925	+	0.447496i
$655$	−3.50855	−	10.7982i	−0.137090	−	0.421920i
$656$	−2.56996			−0.100340
$657$	4.69331			0.183104
$658$	1.73172	+	5.32968i	0.0675094	+	0.207772i
$659$	11.5274	−	35.4777i	0.449044	−	1.38202i	−0.428943	−	0.903332i	$-0.641114\pi$
$659$	11.5274	−	35.4777i	0.449044	−	1.38202i	0.877987	−	0.478684i	$-0.158886\pi$
$660$	1.22604	−	3.77336i	0.0477235	−	0.146878i
$661$	8.29776	+	6.02867i	0.322745	+	0.234488i	0.737346	−	0.675515i	$-0.236079\pi$
$661$	8.29776	+	6.02867i	0.322745	+	0.234488i	−0.414601	+	0.910003i	$0.636079\pi$
$662$	0.625590	+	1.92537i	0.0243142	+	0.0748315i
$663$	10.2046	+	7.41410i	0.396315	+	0.287940i
$664$	5.54083	−	4.02565i	0.215026	−	0.156226i
$665$	1.08015	−	3.32435i	0.0418863	−	0.128913i
$666$	−5.71141	+	4.14958i	−0.221312	+	0.160793i
$667$	9.59597	−	6.97188i	0.371557	−	0.269952i
$668$	−6.23979	+	19.2041i	−0.241425	+	0.743029i
$669$	12.6669	−	9.20306i	0.489732	−	0.355811i
$670$	−6.22564	−	4.52319i	−0.240517	−	0.174746i
$671$	0.0731775	+	0.225217i	0.00282498	+	0.00869441i
$672$	1.90079	+	1.38101i	0.0733246	+	0.0532735i
$673$	−2.73174	+	8.40742i	−0.105301	+	0.324082i	−0.989801	−	0.142457i	$-0.954500\pi$
$673$	−2.73174	+	8.40742i	−0.105301	+	0.324082i	0.884500	+	0.466540i	$0.154500\pi$
$674$	−3.57479	+	11.0021i	−0.137696	+	0.423784i
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$	4.80167			0.184680
$677$	39.7616			1.52816			0.764080	−	0.645121i	$-0.223193\pi$
$677$	39.7616			1.52816			0.764080	+	0.645121i	$0.223193\pi$
$678$	−0.302208	−	0.930100i	−0.0116062	−	0.0357203i
$679$	25.5300	−	18.5487i	0.979753	−	0.711832i
$680$	2.41862	+	1.75723i	0.0927498	+	0.0673867i
$681$	−24.9571			−0.956359
$682$	−17.8412	−	13.0259i	−0.683175	−	0.498788i
$683$	25.9336			0.992322			0.496161	−	0.868231i	$-0.334743\pi$
$683$	25.9336			0.992322			0.496161	+	0.868231i	$0.334743\pi$
$684$	−1.20360	−	0.874465i	−0.0460207	−	0.0334360i
$685$	2.36448	−	1.71790i	0.0903422	−	0.0656375i
$686$	6.15667	+	18.9483i	0.235063	+	0.723448i
$687$	5.64601			0.215409
$688$	−4.00319			−0.152620
$689$	14.2436	+	43.8374i	0.542639	+	1.67007i
$690$	1.98377	−	6.10542i	0.0755209	−	0.232429i
$691$	−8.80282	+	27.0923i	−0.334875	+	1.03064i	0.631909	+	0.775043i	$0.282272\pi$
$691$	−8.80282	+	27.0923i	−0.334875	+	1.03064i	−0.966784	+	0.255596i	$0.917728\pi$
$692$	13.3845	+	9.72442i	0.508803	+	0.369667i
$693$	2.88059	+	8.86553i	0.109424	+	0.336774i
$694$	−8.34789	−	6.06510i	−0.316882	−	0.230228i
$695$	12.9763	−	9.42787i	0.492221	−	0.357619i
$696$	−0.570958	+	1.75723i	−0.0216421	+	0.0666076i
$697$	6.21575	−	4.51601i	0.235438	−	0.171056i
$698$	24.9737	−	18.1444i	0.945267	−	0.686777i
$699$	−0.175831	+	0.541152i	−0.00665054	+	0.0204683i
$700$	−1.90079	+	1.38101i	−0.0718432	+	0.0521971i
$701$	−38.7919	−	28.1840i	−1.46515	−	1.06449i	−0.981984	−	0.188965i	$-0.939487\pi$
$701$	−38.7919	−	28.1840i	−1.46515	−	1.06449i	−0.483166	−	0.875529i	$-0.660513\pi$
$702$	1.30381	+	4.01270i	0.0492090	+	0.151450i
$703$	8.49702	+	6.17345i	0.320471	+	0.232836i
$704$	1.22604	−	3.77336i	0.0462080	−	0.142214i
$705$	−0.737055	+	2.26842i	−0.0277591	+	0.0854337i
$706$	−0.462383	−	1.42307i	−0.0174020	−	0.0535579i
$707$	1.08773			0.0409083
$708$	−12.7723			−0.480013
$709$	4.58365	+	14.1070i	0.172142	+	0.529800i	0.999491	−	0.0318882i	$-0.0101520\pi$
$709$	4.58365	+	14.1070i	0.172142	+	0.529800i	−0.827349	+	0.561688i	$0.810152\pi$
$710$	−2.43548	+	1.76948i	−0.0914021	+	0.0664075i
$711$	−12.3819	−	8.99601i	−0.464359	−	0.337377i
$712$	−7.22240			−0.270671
$713$	−28.8677	−	21.0764i	−1.08110	−	0.789316i
$714$	−7.02403			−0.262868
$715$	13.5428	+	9.83944i	0.506473	+	0.367974i
$716$	1.37554	−	0.999390i	0.0514064	−	0.0373490i
$717$	6.63423	+	20.4181i	0.247760	+	0.762527i
$718$	−33.5321			−1.25141
$719$	−33.6559			−1.25516			−0.627578	−	0.778554i	$-0.715953\pi$
$719$	−33.6559			−1.25516			−0.627578	+	0.778554i	$0.715953\pi$
$720$	0.309017	+	0.951057i	0.0115164	+	0.0354438i
$721$	8.13188	−	25.0274i	0.302847	−	0.932067i
$722$	5.18736	−	15.9651i	0.193054	−	0.594158i
$723$	−4.78921	−	3.47957i	−0.178113	−	0.129406i
$724$	4.60762	+	14.1808i	0.171241	+	0.527025i
$725$	−1.49479	−	1.08603i	−0.0555150	−	0.0403340i
$726$	3.83586	−	2.78692i	0.142362	−	0.103432i
$727$	−6.93133	+	21.3325i	−0.257069	+	0.791177i	0.736346	+	0.676605i	$0.236550\pi$
$727$	−6.93133	+	21.3325i	−0.257069	+	0.791177i	−0.993415	+	0.114572i	$0.963450\pi$
$728$	−8.01982	+	5.82674i	−0.297234	+	0.215953i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−1.45031	+	4.46361i	−0.0536785	+	0.165205i
$731$	9.68220	−	7.03453i	0.358109	−	0.260181i
$732$	−0.0482871	−	0.0350826i	−0.00178474	−	0.00129669i
$733$	12.8153	+	39.4414i	0.473344	+	1.45680i	0.848179	+	0.529710i	$0.177699\pi$
$733$	12.8153	+	39.4414i	0.473344	+	1.45680i	−0.374835	+	0.927091i	$0.622301\pi$
$734$	−30.2896	−	22.0067i	−1.11801	−	0.812282i
$735$	−0.457287	+	1.40739i	−0.0168673	+	0.0519122i
$736$	1.98377	−	6.10542i	0.0731228	−	0.225049i
$737$	−9.43474	−	29.0372i	−0.347533	−	1.06960i
$738$	2.56996			0.0946015
$739$	19.9113			0.732448			0.366224	−	0.930527i	$-0.380650\pi$
$739$	19.9113			0.732448			0.366224	+	0.930527i	$0.380650\pi$
$740$	−2.18156	−	6.71416i	−0.0801959	−	0.246817i
$741$	5.07822	−	3.68954i	0.186553	−	0.135539i
$742$	−20.7655	−	15.0870i	−0.762326	−	0.553862i
$743$	−40.5561			−1.48786			−0.743930	−	0.668258i	$-0.767040\pi$
$743$	−40.5561			−1.48786			−0.743930	+	0.668258i	$0.767040\pi$
$744$	5.56775	+	0.0129517i	0.204124	+	0.000474832i
$745$	−4.77032			−0.174771
$746$	0.870731	+	0.632623i	0.0318797	+	0.0231620i
$747$	−5.54083	+	4.02565i	−0.202729	+	0.147291i
$748$	3.66533	+	11.2807i	0.134018	+	0.412465i
$749$	−36.7557			−1.34303
$750$	−1.00000			−0.0365148
$751$	10.2072	+	31.4146i	0.372467	+	1.14633i	0.945172	+	0.326573i	$0.105894\pi$
$751$	10.2072	+	31.4146i	0.372467	+	1.14633i	−0.572705	+	0.819761i	$0.694106\pi$
$752$	−0.737055	+	2.26842i	−0.0268776	+	0.0827209i
$753$	4.83610	−	14.8840i	0.176237	−	0.542403i
$754$	−6.30681	−	4.58217i	−0.229681	−	0.166873i
$755$	−3.61013	−	11.1108i	−0.131386	−	0.404364i
$756$	−1.90079	−	1.38101i	−0.0691311	−	0.0502267i
$757$	37.5333	−	27.2695i	1.36417	−	0.991127i	0.366002	−	0.930614i	$-0.380726\pi$
$757$	37.5333	−	27.2695i	1.36417	−	0.991127i	0.998167	−	0.0605128i	$-0.0192736\pi$
$758$	1.38097	−	4.25020i	0.0501593	−	0.154374i
$759$	20.6057	−	14.9709i	0.747941	−	0.543411i
$760$	1.20360	−	0.874465i	0.0436591	−	0.0317202i
$761$	2.82150	−	8.68369i	0.102279	−	0.314784i	−0.886803	−	0.462148i	$-0.847079\pi$
$761$	2.82150	−	8.68369i	0.102279	−	0.314784i	0.989082	+	0.147364i	$0.0470789\pi$
$762$	−8.54804	+	6.21052i	−0.309663	+	0.224983i
$763$	37.0078	+	26.8878i	1.33977	+	0.973402i
$764$	4.11296	+	12.6584i	0.148802	+	0.457965i
$765$	−2.41862	−	1.75723i	−0.0874453	−	0.0635327i
$766$	−8.09934	+	24.9272i	−0.292641	+	0.900657i
$767$	16.6526	−	51.2515i	0.601291	−	1.85058i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	−31.5277			−1.13692			−0.568459	−	0.822712i	$-0.692460\pi$
$769$	−31.5277			−1.13692			−0.568459	+	0.822712i	$0.692460\pi$
$770$	−9.32177			−0.335933
$771$	−5.80557	−	17.8677i	−0.209083	−	0.643490i
$772$	17.7000	−	12.8598i	0.637038	−	0.462835i
$773$	−44.9301	−	32.6437i	−1.61603	−	1.17411i	−0.837294	−	0.546753i	$-0.815864\pi$
$773$	−44.9301	−	32.6437i	−1.61603	−	1.17411i	−0.778731	−	0.627358i	$-0.784136\pi$
$774$	4.00319			0.143892
$775$	−1.73285	+	5.29124i	−0.0622457	+	0.190067i
$776$	13.4313			0.482154
$777$	13.4190	+	9.74947i	0.481404	+	0.349760i
$778$	−8.39777	+	6.10134i	−0.301075	+	0.218744i
$779$	−1.18150	−	3.63627i	−0.0423315	−	0.130283i
$780$	−4.21920			−0.151072
$781$	−11.9440			−0.427389
$782$	5.93063	+	18.2526i	0.212079	+	0.652712i
$783$	0.570958	−	1.75723i	0.0204044	−	0.0627982i
$784$	−0.457287	+	1.40739i	−0.0163317	+	0.0502638i
$785$	1.35410	+	0.983813i	0.0483300	+	0.0351138i
$786$	3.50855	+	10.7982i	0.125146	+	0.385159i
$787$	−29.3203	−	21.3025i	−1.04516	−	0.759351i	−0.0738718	−	0.997268i	$-0.523536\pi$
$787$	−29.3203	−	21.3025i	−1.04516	−	0.759351i	−0.971286	+	0.237916i	$0.923536\pi$
$788$	3.14129	−	2.28228i	0.111904	−	0.0813028i
$789$	8.57246	−	26.3833i	0.305188	−	0.939271i
$790$	12.3819	−	8.99601i	0.440530	−	0.320064i
$791$	−1.85891	+	1.35058i	−0.0660952	+	0.0480210i
$792$	−1.22604	+	3.77336i	−0.0435654	+	0.134080i
$793$	0.203733	−	0.148021i	0.00723477	−	0.00525637i
$794$	15.9902	+	11.6175i	0.567470	+	0.412291i
$795$	−3.37591	−	10.3900i	−0.119731	−	0.368494i
$796$	−2.46266	−	1.78923i	−0.0872867	−	0.0634175i
$797$	15.7631	−	48.5138i	0.558357	−	1.71845i	−0.128551	−	0.991703i	$-0.541033\pi$
$797$	15.7631	−	48.5138i	0.558357	−	1.71845i	0.686909	−	0.726744i	$-0.258967\pi$
$798$	−1.08015	+	3.32435i	−0.0382368	+	0.117681i
$799$	−2.20348	−	6.78162i	−0.0779536	−	0.239917i
$800$	−1.00000			−0.0353553
$801$	7.22240			0.255191
$802$	−2.82265	−	8.68724i	−0.0996714	−	0.306757i
$803$	−15.0646	+	10.9451i	−0.531619	+	0.386244i
$804$	6.22564	+	4.52319i	0.219561	+	0.159521i
$805$	−15.0829			−0.531604
$806$	−7.31123	+	22.3248i	−0.257527	+	0.786358i
$807$	12.7181			0.447698
$808$	0.374544	+	0.272122i	0.0131764	+	0.00957321i
$809$	11.0298	−	8.01359i	0.387786	−	0.281743i	−0.376762	−	0.926310i	$-0.622962\pi$
$809$	11.0298	−	8.01359i	0.387786	−	0.281743i	0.764548	+	0.644567i	$0.222962\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	−5.95132			−0.208979			−0.104490	−	0.994526i	$-0.533321\pi$
$811$	−5.95132			−0.208979			−0.104490	+	0.994526i	$0.533321\pi$
$812$	4.34109			0.152342
$813$	−7.56192	−	23.2732i	−0.265208	−	0.816226i
$814$	8.65544	−	26.6387i	0.303373	−	0.933686i
$815$	4.91565	−	15.1288i	0.172188	−	0.529939i
$816$	−2.41862	−	1.75723i	−0.0846686	−	0.0615153i
$817$	−1.84040	−	5.66418i	−0.0643875	−	0.198164i
$818$	6.92341	+	5.03015i	0.242071	+	0.175875i
$819$	8.01982	−	5.82674i	0.280235	−	0.203603i
$820$	−0.794161	+	2.44418i	−0.0277333	+	0.0853543i
$821$	−22.0483	+	16.0190i	−0.769490	+	0.559067i	−0.901806	−	0.432140i	$-0.857759\pi$
$821$	−22.0483	+	16.0190i	−0.769490	+	0.559067i	0.132316	+	0.991208i	$0.457759\pi$
$822$	−2.36448	+	1.71790i	−0.0824708	+	0.0599186i
$823$	2.45199	−	7.54645i	0.0854711	−	0.263053i	−0.899182	−	0.437574i	$-0.855838\pi$
$823$	2.45199	−	7.54645i	0.0854711	−	0.263053i	0.984653	+	0.174521i	$0.0558378\pi$
$824$	9.06128	−	6.58340i	0.315665	−	0.229344i
$825$	−3.20981	−	2.33206i	−0.111751	−	0.0811920i
$826$	9.27319	+	28.5399i	0.322655	+	0.993031i
$827$	−21.9915	−	15.9778i	−0.764721	−	0.555602i	0.135634	−	0.990759i	$-0.456693\pi$
$827$	−21.9915	−	15.9778i	−0.764721	−	0.555602i	−0.900355	+	0.435157i	$0.856693\pi$
$828$	−1.98377	+	6.10542i	−0.0689408	+	0.212178i
$829$	6.25262	−	19.2436i	0.217163	−	0.668358i	−0.781830	−	0.623491i	$-0.785714\pi$
$829$	6.25262	−	19.2436i	0.217163	−	0.668358i	0.998993	−	0.0448664i	$-0.0142862\pi$
$830$	−2.11641	−	6.51364i	−0.0734617	−	0.226092i
$831$	11.8513			0.411118
$832$	−4.21920			−0.146275
$833$	−1.36710	−	4.20749i	−0.0473671	−	0.145781i
$834$	−12.9763	+	9.42787i	−0.449334	+	0.326460i
$835$	16.3360	+	11.8688i	0.565330	+	0.410737i
$836$	5.90263			0.204147
$837$	−5.56775	−	0.0129517i	−0.192450	−	0.000447676i
$838$	22.1070			0.763673
$839$	−17.1550	−	12.4639i	−0.592257	−	0.430300i	0.250865	−	0.968022i	$-0.419285\pi$
$839$	−17.1550	−	12.4639i	−0.592257	−	0.430300i	−0.843122	+	0.537722i	$0.819285\pi$
$840$	1.90079	−	1.38101i	0.0655835	−	0.0476492i
$841$	−7.90656	−	24.3339i	−0.272640	−	0.839099i
$842$	−10.2801			−0.354275
$843$	−1.28010			−0.0440890
$844$	5.56092	+	17.1147i	0.191415	+	0.589114i
$845$	1.48380	−	4.56666i	0.0510442	−	0.157098i
$846$	0.737055	−	2.26842i	0.0253405	−	0.0779900i
$847$	−9.01239	−	6.54788i	−0.309669	−	0.224988i
$848$	−3.37591	−	10.3900i	−0.115929	−	0.356793i
$849$	13.1038	+	9.52048i	0.449722	+	0.326742i
$850$	2.41862	−	1.75723i	0.0829579	−	0.0602725i
$851$	14.0048	−	43.1023i	0.480078	−	1.47753i
$852$	2.43548	−	1.76948i	0.0834383	−	0.0606215i
$853$	−3.11926	+	2.26628i	−0.106802	+	0.0775959i	−0.639904	−	0.768455i	$-0.721026\pi$
$853$	−3.11926	+	2.26628i	−0.106802	+	0.0775959i	0.533103	+	0.846051i	$0.321026\pi$
$854$	−0.0433344	+	0.133370i	−0.00148287	+	0.00456381i
$855$	−1.20360	+	0.874465i	−0.0411622	+	0.0299061i
$856$	−12.6563	−	9.19532i	−0.432582	−	0.314290i
$857$	−12.1230	−	37.3107i	−0.414113	−	1.27451i	−0.913042	−	0.407865i	$-0.866273\pi$
$857$	−12.1230	−	37.3107i	−0.414113	−	1.27451i	0.498929	−	0.866643i	$-0.333727\pi$
$858$	−13.5428	−	9.83944i	−0.462345	−	0.335913i
$859$	−4.71757	+	14.5192i	−0.160962	+	0.495389i	−0.998716	−	0.0506584i	$-0.983868\pi$
$859$	−4.71757	+	14.5192i	−0.160962	+	0.495389i	0.837754	+	0.546047i	$0.183868\pi$
$860$	−1.23706	+	3.80726i	−0.0421832	+	0.129827i
$861$	−1.86589	−	5.74261i	−0.0635893	−	0.195708i
$862$	38.8737			1.32404
$863$	29.0535			0.988992			0.494496	−	0.869180i	$-0.335353\pi$
$863$	29.0535			0.988992			0.494496	+	0.869180i	$0.335353\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	13.3845	−	9.72442i	0.455087	−	0.330640i
$866$	−13.8372	−	10.0533i	−0.470208	−	0.341626i
$867$	−8.06243			−0.273815
$868$	−4.01346	−	12.4506i	−0.136226	−	0.422602i
$869$	60.7229			2.05988
$870$	1.49479	+	1.08603i	0.0506781	+	0.0368198i
$871$	−26.2672	+	19.0843i	−0.890031	+	0.646645i
$872$	6.01647	+	18.5168i	0.203743	+	0.627057i
$873$	−13.4313			−0.454579
$874$	9.55065			0.323056
$875$	0.726038	+	2.23451i	0.0245446	+	0.0755404i
$876$	1.45031	−	4.46361i	0.0490015	−	0.150811i
$877$	−6.23212	+	19.1805i	−0.210444	+	0.647679i	0.789002	+	0.614390i	$0.210598\pi$
$877$	−6.23212	+	19.1805i	−0.210444	+	0.647679i	−0.999446	+	0.0332885i	$0.989402\pi$
$878$	−13.8114	−	10.0346i	−0.466113	−	0.338651i
$879$	4.37537	+	13.4660i	0.147578	+	0.454197i
$880$	−3.20981	−	2.33206i	−0.108203	−	0.0786138i
$881$	5.23858	−	3.80605i	0.176492	−	0.128229i	−0.496032	−	0.868304i	$-0.665210\pi$
$881$	5.23858	−	3.80605i	0.176492	−	0.128229i	0.672524	+	0.740075i	$0.265210\pi$
$882$	0.457287	−	1.40739i	0.0153977	−	0.0473892i
$883$	20.9861	−	15.2473i	0.706239	−	0.513113i	−0.175719	−	0.984440i	$-0.556225\pi$
$883$	20.9861	−	15.2473i	0.706239	−	0.513113i	0.881958	+	0.471327i	$0.156225\pi$
$884$	10.2046	−	7.41410i	0.343219	−	0.249363i
$885$	−3.94686	+	12.1472i	−0.132672	+	0.408324i
$886$	14.6033	−	10.6099i	0.490609	−	0.356448i
$887$	18.8205	+	13.6739i	0.631930	+	0.459124i	0.857068	−	0.515203i	$-0.172283\pi$
$887$	18.8205	+	13.6739i	0.631930	+	0.459124i	−0.225138	+	0.974327i	$0.572283\pi$
$888$	2.18156	+	6.71416i	0.0732085	+	0.225312i
$889$	20.0837	+	14.5917i	0.673586	+	0.489389i
$890$	−2.23184	+	6.86891i	−0.0748116	+	0.230246i
$891$	1.22604	−	3.77336i	0.0410738	−	0.126412i
$892$	−4.83834	−	14.8909i	−0.161999	−	0.498583i
$893$	−3.54847			−0.118745
$894$	4.77032			0.159543
$895$	−0.525411	−	1.61705i	−0.0175625	−	0.0540519i
$896$	1.90079	−	1.38101i	0.0635010	−	0.0461362i
$897$	−21.9128	−	15.9206i	−0.731646	−	0.531572i
$898$	18.3898			0.613676
$899$	8.33667	−	6.02737i	0.278044	−	0.201024i
$900$	1.00000			0.0333333
$901$	26.4226	+	19.1971i	0.880264	+	0.639549i
$902$	−8.24908	+	5.99331i	−0.274664	+	0.199555i
$903$	−2.90647	−	8.94520i	−0.0967213	−	0.297678i
$904$	−0.977965			−0.0325266
$905$	14.9106			0.495644
$906$	3.61013	+	11.1108i	0.119938	+	0.369132i
$907$	5.19367	−	15.9845i	0.172453	−	0.530756i	−0.827055	−	0.562121i	$-0.809986\pi$
$907$	5.19367	−	15.9845i	0.172453	−	0.530756i	0.999508	+	0.0313652i	$0.00998550\pi$
$908$	−7.71217	+	23.7356i	−0.255937	+	0.787695i
$909$	−0.374544	−	0.272122i	−0.0124228	−	0.00902571i
$910$	3.06330	+	9.42787i	0.101547	+	0.312531i
$911$	22.3952	+	16.2711i	0.741986	+	0.539085i	0.893333	−	0.449396i	$-0.148361\pi$
$911$	22.3952	+	16.2711i	0.741986	+	0.539085i	−0.151346	+	0.988481i	$0.548361\pi$
$912$	−1.20360	+	0.874465i	−0.0398551	+	0.0289564i
$913$	8.39695	−	25.8431i	0.277898	−	0.855283i
$914$	14.1269	−	10.2638i	0.467275	−	0.339495i
$915$	−0.0482871	+	0.0350826i	−0.00159632	+	0.00115980i
$916$	1.74471	−	5.36967i	0.0576469	−	0.177419i
$917$	21.5814	−	15.6798i	0.712680	−	0.517792i
$918$	2.41862	+	1.75723i	0.0798263	+	0.0579972i
$919$	−9.57171	−	29.4587i	−0.315741	−	0.971752i	−0.975448	−	0.220229i	$-0.929319\pi$
$919$	−9.57171	−	29.4587i	−0.315741	−	0.971752i	0.659707	−	0.751523i	$-0.270681\pi$
$920$	−5.19358	−	3.77336i	−0.171227	−	0.124404i
$921$	0.520206	−	1.60103i	0.0171414	−	0.0527557i
$922$	5.97546	−	18.3906i	0.196791	−	0.605662i
$923$	3.92501	+	12.0799i	0.129193	+	0.397616i
$924$	9.32177			0.306664
$925$	−7.05969			−0.232121
$926$	−3.41010	−	10.4952i	−0.112063	−	0.344894i
$927$	−9.06128	+	6.58340i	−0.297611	+	0.216227i
$928$	1.49479	+	1.08603i	0.0490688	+	0.0356506i
$929$	−18.1894			−0.596775			−0.298388	−	0.954445i	$-0.596449\pi$
$929$	−18.1894			−0.596775			−0.298388	+	0.954445i	$0.596449\pi$
$930$	1.73285	−	5.29124i	0.0568223	−	0.173507i
$931$	−2.20156			−0.0721532
$932$	0.460332	+	0.334450i	0.0150787	+	0.0109553i
$933$	−2.60666	+	1.89385i	−0.0853382	+	0.0620019i
$934$	−3.44847	−	10.6133i	−0.112837	−	0.347278i
$935$	11.8613			0.387905
$936$	4.21920			0.137909
$937$	−17.2058	−	52.9541i	−0.562090	−	1.72994i	−0.676442	−	0.736496i	$-0.736479\pi$
$937$	−17.2058	−	52.9541i	−0.562090	−	1.72994i	0.114352	−	0.993440i	$-0.463521\pi$
$938$	5.58709	−	17.1953i	0.182425	−	0.561446i
$939$	3.60087	−	11.0823i	0.117510	−	0.361659i
$940$	1.92964	+	1.40196i	0.0629378	+	0.0457270i
$941$	10.7935	+	33.2191i	0.351859	+	1.08291i	0.957808	+	0.287408i	$0.0927935\pi$
$941$	10.7935	+	33.2191i	0.351859	+	1.08291i	−0.605949	+	0.795503i	$0.707207\pi$
$942$	−1.35410	−	0.983813i	−0.0441190	−	0.0320543i
$943$	−13.3473	+	9.69737i	−0.434647	+	0.315790i
$944$	−3.94686	+	12.1472i	−0.128459	+	0.395358i
$945$	−1.90079	+	1.38101i	−0.0618328	+	0.0449241i
$946$	−12.8495	+	9.33570i	−0.417773	+	0.303530i
$947$	15.1616	−	46.6627i	0.492687	−	1.51633i	−0.327845	−	0.944732i	$-0.606322\pi$
$947$	15.1616	−	46.6627i	0.492687	−	1.51633i	0.820531	−	0.571602i	$-0.193678\pi$
$948$	−12.3819	+	8.99601i	−0.402147	+	0.292177i
$949$	16.0202	+	11.6393i	0.520037	+	0.377829i
$950$	−0.459733	−	1.41491i	−0.0149157	−	0.0459059i
$951$	−4.76871	−	3.46467i	−0.154636	−	0.112350i
$952$	−2.17055	+	6.68025i	−0.0703478	+	0.216508i
$953$	−3.57782	+	11.0114i	−0.115897	+	0.356694i	−0.992133	−	0.125188i	$-0.960047\pi$
$953$	−3.57782	+	11.0114i	−0.115897	+	0.356694i	0.876236	+	0.481882i	$0.160047\pi$
$954$	3.37591	+	10.3900i	0.109299	+	0.336388i
$955$	13.3098			0.430696
$956$	21.4688			0.694351
$957$	2.26530	+	6.97188i	0.0732268	+	0.225369i
$958$	6.86813	−	4.98999i	0.221899	−	0.161219i
$959$	5.55537	+	4.03621i	0.179392	+	0.130336i
$960$	1.00000			0.0322749
$961$	−24.9945	−	18.3378i	−0.806274	−	0.591543i
$962$	−29.7862			−0.960347
$963$	12.6563	+	9.19532i	0.407843	+	0.296315i
$964$	−4.78921	+	3.47957i	−0.154250	+	0.112069i
$965$	−6.76081	−	20.8076i	−0.217638	−	0.669821i
$966$	15.0829			0.485286
$967$	−57.8903			−1.86163			−0.930813	−	0.365496i	$-0.880899\pi$
$967$	−57.8903			−1.86163			−0.930813	+	0.365496i	$0.880899\pi$
$968$	−1.46517	−	4.50933i	−0.0470923	−	0.144935i
$969$	1.37441	−	4.22999i	0.0441524	−	0.135887i
$970$	4.15049	−	12.7739i	0.133264	−	0.410145i
$971$	32.6436	+	23.7170i	1.04758	+	0.761114i	0.971752	−	0.236006i	$-0.0758385\pi$
$971$	32.6436	+	23.7170i	1.04758	+	0.761114i	0.0758326	+	0.997121i	$0.475839\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	30.4880	+	22.1509i	0.977401	+	0.710124i
$974$	−20.5384	+	14.9220i	−0.658092	+	0.478132i
$975$	−1.30381	+	4.01270i	−0.0417552	+	0.128509i
$976$	−0.0482871	+	0.0350826i	−0.00154563	+	0.00112297i
$977$	−23.6042	+	17.1494i	−0.755165	+	0.548659i	−0.897423	−	0.441170i	$-0.854564\pi$
$977$	−23.6042	+	17.1494i	−0.755165	+	0.548659i	0.142259	+	0.989830i	$0.454564\pi$
$978$	−4.91565	+	15.1288i	−0.157185	+	0.483766i
$979$	−23.1825	+	16.8431i	−0.740916	+	0.538307i
$980$	1.19719	+	0.869812i	0.0382430	+	0.0277851i
$981$	−6.01647	−	18.5168i	−0.192091	−	0.591195i
$982$	−9.14025	−	6.64078i	−0.291677	−	0.211916i
$983$	−3.28583	+	10.1127i	−0.104802	+	0.322546i	−0.989684	−	0.143269i	$-0.954239\pi$
$983$	−3.28583	+	10.1127i	−0.104802	+	0.322546i	0.884882	+	0.465815i	$0.154239\pi$
$984$	0.794161	−	2.44418i	0.0253169	−	0.0779175i
$985$	−1.19986	−	3.69280i	−0.0382309	−	0.117662i
$986$	−5.52372			−0.175911
$987$	−5.60395			−0.178376
$988$	−1.93971	−	5.96981i	−0.0617103	−	0.189925i
$989$	−20.7909	+	15.1055i	−0.661112	+	0.480326i
$990$	3.20981	+	2.33206i	0.102014	+	0.0741178i
$991$	0.906546			0.0287974			0.0143987	−	0.999896i	$-0.495417\pi$
$991$	0.906546			0.0287974			0.0143987	+	0.999896i	$0.495417\pi$
$992$	1.73285	−	5.29124i	0.0550179	−	0.167997i
$993$	−2.02445			−0.0642440
$994$	−5.72219	−	4.15741i	−0.181497	−	0.131865i
$995$	−2.46266	+	1.78923i	−0.0780716	+	0.0567223i
$996$	2.11641	+	6.51364i	0.0670610	+	0.206393i
$997$	34.9707			1.10753			0.553767	−	0.832672i	$-0.313190\pi$
$997$	34.9707			1.10753			0.553767	+	0.832672i	$0.313190\pi$
$998$	−42.7717			−1.35392
$999$	−2.18156	−	6.71416i	−0.0690216	−	0.212427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.e.901.3	yes	12
31.16	even	5	inner	930.2.n.e.481.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.e.481.3	✓	12	31.16	even	5	inner
930.2.n.e.901.3	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(0.726038 + 2.23451i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(0.726038 + 2.23451i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(1.22604 + 3.77336i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(3.41341 - 2.47998i) q^{13} +(-0.726038 + 2.23451i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.923830 - 2.84326i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-1.20360 - 0.874465i) q^{19} +(0.309017 + 0.951057i) q^{20} +(-1.90079 - 1.38101i) q^{21} +(-1.22604 + 3.77336i) q^{22} +(-1.98377 + 6.10542i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +4.21920 q^{26} +(0.309017 + 0.951057i) q^{27} +(-1.90079 + 1.38101i) q^{28} +(-1.49479 - 1.08603i) q^{29} -1.00000 q^{30} +(-1.73285 + 5.29124i) q^{31} -1.00000 q^{32} +(-3.20981 - 2.33206i) q^{33} +(2.41862 - 1.75723i) q^{34} +(0.726038 + 2.23451i) q^{35} +1.00000 q^{36} -7.05969 q^{37} +(-0.459733 - 1.41491i) q^{38} +(-1.30381 + 4.01270i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(2.07914 + 1.51058i) q^{41} +(-0.726038 - 2.23451i) q^{42} +(3.23865 + 2.35302i) q^{43} +(-3.20981 + 2.33206i) q^{44} +(0.309017 - 0.951057i) q^{45} +(-5.19358 + 3.77336i) q^{46} +(1.92964 - 1.40196i) q^{47} +(0.309017 - 0.951057i) q^{48} +(1.19719 - 0.869812i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.923830 + 2.84326i) q^{51} +(3.41341 + 2.47998i) q^{52} +(-3.37591 + 10.3900i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.22604 + 3.77336i) q^{55} -2.34951 q^{56} +1.48773 q^{57} +(-0.570958 - 1.75723i) q^{58} +(10.3330 - 7.50738i) q^{59} +(-0.809017 - 0.587785i) q^{60} +0.0596861 q^{61} +(-4.51202 + 3.26216i) q^{62} +2.34951 q^{63} +(-0.809017 - 0.587785i) q^{64} +(3.41341 - 2.47998i) q^{65} +(-1.22604 - 3.77336i) q^{66} -7.69531 q^{67} +2.98958 q^{68} +(-1.98377 - 6.10542i) q^{69} +(-0.726038 + 2.23451i) q^{70} +(-0.930272 + 2.86308i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.45031 + 4.46361i) q^{73} +(-5.71141 - 4.14958i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(0.459733 - 1.41491i) q^{76} +(-7.54147 + 5.47920i) q^{77} +(-3.41341 + 2.47998i) q^{78} +(4.72948 - 14.5559i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.794161 + 2.44418i) q^{82} +(-5.54083 - 4.02565i) q^{83} +(0.726038 - 2.23451i) q^{84} +(0.923830 - 2.84326i) q^{85} +(1.23706 + 3.80726i) q^{86} +1.84766 q^{87} -3.96754 q^{88} +(2.23184 + 6.86891i) q^{89} +(0.809017 - 0.587785i) q^{90} +(8.01982 + 5.82674i) q^{91} -6.41962 q^{92} +(-1.70821 - 5.29925i) q^{93} +2.38516 q^{94} +(-1.20360 - 0.874465i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-4.15049 - 12.7739i) q^{97} +1.47981 q^{98} +3.96754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 12 q^{5} - 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} - 3 q^{12} - 5 q^{13} + q^{14} - 3 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 3 q^{24} + 12 q^{25} + 10 q^{26} - 3 q^{27} + 4 q^{28} + q^{29} - 12 q^{30} - 6 q^{31} - 12 q^{32} - 5 q^{33} + 2 q^{34} - q^{35} + 12 q^{36} - 14 q^{37} - 3 q^{38} + 10 q^{39} + 3 q^{40} + 15 q^{41} + q^{42} + 10 q^{43} - 5 q^{44} - 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 3 q^{50} + 3 q^{51} - 5 q^{52} - 13 q^{53} + 3 q^{54} + 5 q^{55} + 6 q^{56} - 2 q^{57} + 4 q^{58} + 11 q^{59} - 3 q^{60} - 70 q^{61} - 19 q^{62} - 6 q^{63} - 3 q^{64} - 5 q^{65} - 5 q^{66} + 38 q^{67} - 2 q^{68} + q^{70} + 21 q^{71} + 3 q^{72} - 14 q^{73} - 11 q^{74} - 3 q^{75} + 3 q^{76} - 14 q^{77} + 5 q^{78} + 5 q^{79} - 3 q^{80} - 3 q^{81} - 15 q^{82} - q^{84} + 3 q^{85} + 10 q^{86} + 6 q^{87} + 3 q^{89} + 3 q^{90} + 16 q^{91} - 10 q^{92} - 11 q^{93} - 6 q^{94} - 2 q^{95} + 3 q^{96} - 35 q^{97} - 10 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 12 * q^5 - 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 5 * q^11 - 3 * q^12 - 5 * q^13 + q^14 - 3 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 2 * q^19 - 3 * q^20 + 4 * q^21 - 5 * q^22 + 3 * q^24 + 12 * q^25 + 10 * q^26 - 3 * q^27 + 4 * q^28 + q^29 - 12 * q^30 - 6 * q^31 - 12 * q^32 - 5 * q^33 + 2 * q^34 - q^35 + 12 * q^36 - 14 * q^37 - 3 * q^38 + 10 * q^39 + 3 * q^40 + 15 * q^41 + q^42 + 10 * q^43 - 5 * q^44 - 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 3 * q^50 + 3 * q^51 - 5 * q^52 - 13 * q^53 + 3 * q^54 + 5 * q^55 + 6 * q^56 - 2 * q^57 + 4 * q^58 + 11 * q^59 - 3 * q^60 - 70 * q^61 - 19 * q^62 - 6 * q^63 - 3 * q^64 - 5 * q^65 - 5 * q^66 + 38 * q^67 - 2 * q^68 + q^70 + 21 * q^71 + 3 * q^72 - 14 * q^73 - 11 * q^74 - 3 * q^75 + 3 * q^76 - 14 * q^77 + 5 * q^78 + 5 * q^79 - 3 * q^80 - 3 * q^81 - 15 * q^82 - q^84 + 3 * q^85 + 10 * q^86 + 6 * q^87 + 3 * q^89 + 3 * q^90 + 16 * q^91 - 10 * q^92 - 11 * q^93 - 6 * q^94 - 2 * q^95 + 3 * q^96 - 35 * q^97 - 10 * q^98

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