LMFDB - Embedded newform 930.2.n.a.721.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			721.1
Root			$-0.227943 + 0.701538i$ of defining polynomial
Character	$\chi$	$=$	930.721
Dual form			930.2.n.a.841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(1.15245 + 0.837304i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(1.15245 + 0.837304i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(4.35264 + 3.16238i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(2.13372 + 6.56693i) q^{13} +(1.15245 - 0.837304i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.246670 - 0.179216i) q^{17} +(0.309017 + 0.951057i) q^{18} +(-1.20880 + 3.72032i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(0.440197 - 1.35479i) q^{21} +(4.35264 - 3.16238i) q^{22} +(-0.909897 + 0.661079i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +6.90488 q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.440197 - 1.35479i) q^{28} +(-1.52752 + 4.70122i) q^{29} -1.00000 q^{30} +(-3.97412 - 3.89953i) q^{31} +1.00000 q^{32} +(1.66256 - 5.11683i) q^{33} +(-0.0942195 - 0.289978i) q^{34} +(1.15245 + 0.837304i) q^{35} +1.00000 q^{36} +4.52981 q^{37} +(3.16469 + 2.29928i) q^{38} +(5.58616 - 4.05858i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(0.985882 - 3.03423i) q^{41} +(-1.15245 - 0.837304i) q^{42} +(0.344405 - 1.05997i) q^{43} +(-1.66256 - 5.11683i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(0.347550 + 1.06965i) q^{46} +(-3.46656 - 10.6690i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-1.53606 - 4.72749i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-0.246670 - 0.179216i) q^{51} +(2.13372 - 6.56693i) q^{52} +(-0.509029 + 0.369832i) q^{53} +(0.809017 - 0.587785i) q^{54} +(4.35264 + 3.16238i) q^{55} -1.42451 q^{56} +3.91177 q^{57} +(3.99910 + 2.90551i) q^{58} +(3.93487 + 12.1103i) q^{59} +(-0.309017 + 0.951057i) q^{60} +1.85410 q^{61} +(-4.93675 + 2.57459i) q^{62} -1.42451 q^{63} +(0.309017 - 0.951057i) q^{64} +(2.13372 + 6.56693i) q^{65} +(-4.35264 - 3.16238i) q^{66} -6.25972 q^{67} -0.304901 q^{68} +(0.909897 + 0.661079i) q^{69} +(1.15245 - 0.837304i) q^{70} +(11.5631 - 8.40107i) q^{71} +(0.309017 - 0.951057i) q^{72} +(-13.0127 - 9.45429i) q^{73} +(1.39979 - 4.30810i) q^{74} +(-0.309017 - 0.951057i) q^{75} +(3.16469 - 2.29928i) q^{76} +(2.36833 + 7.28896i) q^{77} +(-2.13372 - 6.56693i) q^{78} +(-12.7802 + 9.28539i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-2.58107 - 1.87526i) q^{82} +(4.31568 - 13.2823i) q^{83} +(-1.15245 + 0.837304i) q^{84} +(0.246670 - 0.179216i) q^{85} +(-0.901664 - 0.655097i) q^{86} +4.94315 q^{87} -5.38016 q^{88} +(10.6525 + 7.73951i) q^{89} +(0.309017 + 0.951057i) q^{90} +(-3.03950 + 9.35463i) q^{91} +1.12469 q^{92} +(-2.48061 + 4.98464i) q^{93} -11.2180 q^{94} +(-1.20880 + 3.72032i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(5.07968 + 3.69060i) q^{97} -4.97078 q^{98} -5.38016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{12} + q^{13} + 9 q^{14} + 2 q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + q^{21} - q^{22} + 8 q^{23} + 2 q^{24} + 8 q^{25} + 16 q^{26} + 2 q^{27} - q^{28} - q^{29} - 8 q^{30} + 3 q^{31} + 8 q^{32} + q^{33} - 12 q^{34} + 9 q^{35} + 8 q^{36} + 8 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} + 29 q^{41} - 9 q^{42} - 25 q^{43} - q^{44} - 2 q^{45} + 3 q^{46} + 13 q^{47} + 2 q^{48} + 25 q^{49} - 2 q^{50} - 13 q^{51} + q^{52} - 19 q^{53} + 2 q^{54} - q^{55} - 16 q^{56} + 12 q^{57} + 4 q^{58} + 23 q^{59} + 2 q^{60} - 12 q^{61} - 27 q^{62} - 16 q^{63} - 2 q^{64} + q^{65} + q^{66} - 24 q^{67} - 2 q^{68} - 8 q^{69} + 9 q^{70} + 3 q^{71} - 2 q^{72} - 14 q^{73} + 8 q^{74} + 2 q^{75} + 8 q^{76} - 24 q^{77} - q^{78} - 34 q^{79} - 2 q^{80} - 2 q^{81} - 21 q^{82} + 8 q^{83} - 9 q^{84} + 13 q^{85} + 6 q^{87} + 4 q^{88} + 25 q^{89} - 2 q^{90} + 3 q^{91} - 22 q^{92} - 18 q^{93} - 42 q^{94} - 2 q^{95} + 2 q^{96} - 28 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^12 + q^13 + 9 * q^14 + 2 * q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + q^21 - q^22 + 8 * q^23 + 2 * q^24 + 8 * q^25 + 16 * q^26 + 2 * q^27 - q^28 - q^29 - 8 * q^30 + 3 * q^31 + 8 * q^32 + q^33 - 12 * q^34 + 9 * q^35 + 8 * q^36 + 8 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 + 29 * q^41 - 9 * q^42 - 25 * q^43 - q^44 - 2 * q^45 + 3 * q^46 + 13 * q^47 + 2 * q^48 + 25 * q^49 - 2 * q^50 - 13 * q^51 + q^52 - 19 * q^53 + 2 * q^54 - q^55 - 16 * q^56 + 12 * q^57 + 4 * q^58 + 23 * q^59 + 2 * q^60 - 12 * q^61 - 27 * q^62 - 16 * q^63 - 2 * q^64 + q^65 + q^66 - 24 * q^67 - 2 * q^68 - 8 * q^69 + 9 * q^70 + 3 * q^71 - 2 * q^72 - 14 * q^73 + 8 * q^74 + 2 * q^75 + 8 * q^76 - 24 * q^77 - q^78 - 34 * q^79 - 2 * q^80 - 2 * q^81 - 21 * q^82 + 8 * q^83 - 9 * q^84 + 13 * q^85 + 6 * q^87 + 4 * q^88 + 25 * q^89 - 2 * q^90 + 3 * q^91 - 22 * q^92 - 18 * q^93 - 42 * q^94 - 2 * q^95 + 2 * q^96 - 28 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.00000			−0.408248
$7$	1.15245	+	0.837304i	0.435585	+	0.316471i	0.783878	−	0.620914i	$-0.213239\pi$
$7$	1.15245	+	0.837304i	0.435585	+	0.316471i	−0.348293	+	0.937386i	$0.613239\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.309017	−	0.951057i	0.0977198	−	0.300750i
$11$	4.35264	+	3.16238i	1.31237	+	0.953492i	0.999994	+	0.00353383i	$0.00112486\pi$
$11$	4.35264	+	3.16238i	1.31237	+	0.953492i	0.312376	+	0.949959i	$0.398875\pi$
$12$	−0.309017	+	0.951057i	−0.0892055	+	0.274546i
$13$	2.13372	+	6.56693i	0.591789	+	1.82134i	0.570103	+	0.821573i	$0.306903\pi$
$13$	2.13372	+	6.56693i	0.591789	+	1.82134i	0.0216852	+	0.999765i	$0.493097\pi$
$14$	1.15245	−	0.837304i	0.308005	−	0.223779i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.246670	−	0.179216i	0.0598262	−	0.0434663i	−0.557470	−	0.830197i	$-0.688228\pi$
$17$	0.246670	−	0.179216i	0.0598262	−	0.0434663i	0.617296	+	0.786731i	$0.288228\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	−1.20880	+	3.72032i	−0.277319	+	0.853499i	0.711278	+	0.702911i	$0.248117\pi$
$19$	−1.20880	+	3.72032i	−0.277319	+	0.853499i	−0.988597	+	0.150588i	$0.951883\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$	0.440197	−	1.35479i	0.0960588	−	0.295639i
$22$	4.35264	−	3.16238i	0.927986	−	0.674221i
$23$	−0.909897	+	0.661079i	−0.189727	+	0.137844i	−0.678594	−	0.734514i	$-0.737410\pi$
$23$	−0.909897	+	0.661079i	−0.189727	+	0.137844i	0.488867	+	0.872358i	$0.337410\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	6.90488			1.35416
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−0.440197	−	1.35479i	−0.0831894	−	0.256031i
$29$	−1.52752	+	4.70122i	−0.283653	+	0.872994i	0.703146	+	0.711045i	$0.251778\pi$
$29$	−1.52752	+	4.70122i	−0.283653	+	0.872994i	−0.986799	+	0.161949i	$0.948222\pi$
$30$	−1.00000			−0.182574
$31$	−3.97412	−	3.89953i	−0.713773	−	0.700377i
$31$	−3.97412	−	3.89953i	−0.713773	−	0.700377i
$32$	1.00000			0.176777
$33$	1.66256	−	5.11683i	0.289414	−	0.890726i
$34$	−0.0942195	−	0.289978i	−0.0161585	−	0.0497308i
$35$	1.15245	+	0.837304i	0.194800	+	0.141530i
$36$	1.00000			0.166667
$37$	4.52981			0.744696			0.372348	−	0.928093i	$-0.378553\pi$
$37$	4.52981			0.744696			0.372348	+	0.928093i	$0.378553\pi$
$38$	3.16469	+	2.29928i	0.513381	+	0.372993i
$39$	5.58616	−	4.05858i	0.894502	−	0.649894i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	0.985882	−	3.03423i	0.153969	−	0.473868i	−0.844086	−	0.536208i	$-0.819856\pi$
$41$	0.985882	−	3.03423i	0.153969	−	0.473868i	0.998055	+	0.0623401i	$0.0198563\pi$
$42$	−1.15245	−	0.837304i	−0.177827	−	0.129199i
$43$	0.344405	−	1.05997i	0.0525213	−	0.161644i	−0.921355	−	0.388721i	$-0.872917\pi$
$43$	0.344405	−	1.05997i	0.0525213	−	0.161644i	0.973877	+	0.227077i	$0.0729170\pi$
$44$	−1.66256	−	5.11683i	−0.250640	−	0.771392i
$45$	−0.809017	+	0.587785i	−0.120601	+	0.0876219i
$46$	0.347550	+	1.06965i	0.0512434	+	0.157711i
$47$	−3.46656	−	10.6690i	−0.505649	−	1.55623i	−0.799677	−	0.600431i	$-0.794996\pi$
$47$	−3.46656	−	10.6690i	−0.505649	−	1.55623i	0.294028	−	0.955797i	$-0.405004\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	−1.53606	−	4.72749i	−0.219437	−	0.675356i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	−0.246670	−	0.179216i	−0.0345407	−	0.0250953i
$52$	2.13372	−	6.56693i	0.295894	−	0.910669i
$53$	−0.509029	+	0.369832i	−0.0699206	+	0.0508003i	−0.622196	−	0.782861i	$-0.713760\pi$
$53$	−0.509029	+	0.369832i	−0.0699206	+	0.0508003i	0.552276	+	0.833661i	$0.313760\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	4.35264	+	3.16238i	0.586910	+	0.426415i
$56$	−1.42451			−0.190358
$57$	3.91177			0.518127
$58$	3.99910	+	2.90551i	0.525107	+	0.381513i
$59$	3.93487	+	12.1103i	0.512277	+	1.57663i	0.788183	+	0.615441i	$0.211022\pi$
$59$	3.93487	+	12.1103i	0.512277	+	1.57663i	−0.275907	+	0.961184i	$0.588978\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	1.85410			0.237393			0.118697	−	0.992931i	$-0.462128\pi$
$61$	1.85410			0.237393			0.118697	+	0.992931i	$0.462128\pi$
$62$	−4.93675	+	2.57459i	−0.626968	+	0.326973i
$63$	−1.42451			−0.179471
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	2.13372	+	6.56693i	0.264656	+	0.814527i
$66$	−4.35264	−	3.16238i	−0.535773	−	0.389262i
$67$	−6.25972			−0.764747			−0.382374	−	0.924008i	$-0.624893\pi$
$67$	−6.25972			−0.764747			−0.382374	+	0.924008i	$0.624893\pi$
$68$	−0.304901			−0.0369746
$69$	0.909897	+	0.661079i	0.109539	+	0.0795845i
$70$	1.15245	−	0.837304i	0.137744	−	0.100077i
$71$	11.5631	−	8.40107i	1.37229	−	0.997024i	0.374731	−	0.927134i	$-0.377735\pi$
$71$	11.5631	−	8.40107i	1.37229	−	0.997024i	0.997555	−	0.0698899i	$-0.0222648\pi$
$72$	0.309017	−	0.951057i	0.0364180	−	0.112083i
$73$	−13.0127	−	9.45429i	−1.52302	−	1.10654i	−0.959963	−	0.280126i	$-0.909624\pi$
$73$	−13.0127	−	9.45429i	−1.52302	−	1.10654i	−0.563060	−	0.826416i	$-0.690376\pi$
$74$	1.39979	−	4.30810i	0.162722	−	0.500807i
$75$	−0.309017	−	0.951057i	−0.0356822	−	0.109819i
$76$	3.16469	−	2.29928i	0.363015	−	0.263746i
$77$	2.36833	+	7.28896i	0.269896	+	0.830654i
$78$	−2.13372	−	6.56693i	−0.241597	−	0.743558i
$79$	−12.7802	+	9.28539i	−1.43789	+	1.04469i	−0.449412	+	0.893325i	$0.648367\pi$
$79$	−12.7802	+	9.28539i	−1.43789	+	1.04469i	−0.988478	+	0.151364i	$0.951633\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−2.58107	−	1.87526i	−0.285032	−	0.207088i
$83$	4.31568	−	13.2823i	0.473707	−	1.45792i	−0.373986	−	0.927434i	$-0.622009\pi$
$83$	4.31568	−	13.2823i	0.473707	−	1.45792i	0.847693	−	0.530486i	$-0.177991\pi$
$84$	−1.15245	+	0.837304i	−0.125743	+	0.0913574i
$85$	0.246670	−	0.179216i	0.0267551	−	0.0194387i
$86$	−0.901664	−	0.655097i	−0.0972289	−	0.0706410i
$87$	4.94315			0.529962
$88$	−5.38016			−0.573527
$89$	10.6525	+	7.73951i	1.12916	+	0.820386i	0.985573	−	0.169251i	$-0.0541348\pi$
$89$	10.6525	+	7.73951i	1.12916	+	0.820386i	0.143592	+	0.989637i	$0.454135\pi$
$90$	0.309017	+	0.951057i	0.0325733	+	0.100250i
$91$	−3.03950	+	9.35463i	−0.318627	+	0.980632i
$92$	1.12469			0.117258
$93$	−2.48061	+	4.98464i	−0.257227	+	0.516883i
$94$	−11.2180			−1.15705
$95$	−1.20880	+	3.72032i	−0.124021	+	0.381697i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	5.07968	+	3.69060i	0.515763	+	0.374724i	0.815005	−	0.579453i	$-0.196734\pi$
$97$	5.07968	+	3.69060i	0.515763	+	0.374724i	−0.299242	+	0.954177i	$0.596734\pi$
$98$	−4.97078			−0.502125
$99$	−5.38016			−0.540726
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	−3.07870	+	2.23681i	−0.306343	+	0.222571i	−0.730326	−	0.683099i	$-0.760632\pi$
$101$	−3.07870	+	2.23681i	−0.306343	+	0.222571i	0.423983	+	0.905670i	$0.360632\pi$
$102$	−0.246670	+	0.179216i	−0.0244239	+	0.0177450i
$103$	3.04823	−	9.38149i	0.300351	−	0.924385i	−0.681020	−	0.732265i	$-0.738463\pi$
$103$	3.04823	−	9.38149i	0.300351	−	0.924385i	0.981371	−	0.192121i	$-0.0615365\pi$
$104$	−5.58616	−	4.05858i	−0.547768	−	0.397977i
$105$	0.440197	−	1.35479i	0.0429588	−	0.132214i
$106$	0.194432	+	0.598400i	0.0188849	+	0.0581217i
$107$	15.3837	−	11.1769i	1.48720	−	1.08051i	0.512048	−	0.858957i	$-0.328887\pi$
$107$	15.3837	−	11.1769i	1.48720	−	1.08051i	0.975148	−	0.221554i	$-0.0711129\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	−1.67596	−	5.15808i	−0.160528	−	0.494054i	0.838151	−	0.545438i	$-0.183637\pi$
$109$	−1.67596	−	5.15808i	−0.160528	−	0.494054i	−0.998679	+	0.0513841i	$0.983637\pi$
$110$	4.35264	−	3.16238i	0.415008	−	0.301521i
$111$	−1.39979	−	4.30810i	−0.132862	−	0.408907i
$112$	−0.440197	+	1.35479i	−0.0415947	+	0.128015i
$113$	−6.48793	−	4.71376i	−0.610334	−	0.443433i	0.239198	−	0.970971i	$-0.423115\pi$
$113$	−6.48793	−	4.71376i	−0.610334	−	0.443433i	−0.849532	+	0.527538i	$0.823115\pi$
$114$	1.20880	−	3.72032i	0.113215	−	0.348440i
$115$	−0.909897	+	0.661079i	−0.0848483	+	0.0616459i
$116$	3.99910	−	2.90551i	0.371307	−	0.269770i
$117$	−5.58616	−	4.05858i	−0.516441	−	0.375216i
$118$	12.7335			1.17221
$119$	0.434333			0.0398152
$120$	0.809017	+	0.587785i	0.0738528	+	0.0536572i
$121$	5.54564	+	17.0677i	0.504149	+	1.55161i
$122$	0.572949	−	1.76336i	0.0518724	−	0.159647i
$123$	−3.19038			−0.287667
$124$	0.923043	+	5.49072i	0.0828917	+	0.493081i
$125$	1.00000			0.0894427
$126$	−0.440197	+	1.35479i	−0.0392159	+	0.120694i
$127$	−5.79826	−	17.8452i	−0.514512	−	1.58351i	−0.784168	−	0.620549i	$-0.786910\pi$
$127$	−5.79826	−	17.8452i	−0.514512	−	1.58351i	0.269656	−	0.962957i	$-0.413090\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−1.11452			−0.0981279
$130$	6.90488			0.605598
$131$	8.04655	+	5.84616i	0.703030	+	0.510781i	0.880918	−	0.473269i	$-0.156926\pi$
$131$	8.04655	+	5.84616i	0.703030	+	0.510781i	−0.177887	+	0.984051i	$0.556926\pi$
$132$	−4.35264	+	3.16238i	−0.378848	+	0.275250i
$133$	−4.50812	+	3.27534i	−0.390904	+	0.284008i
$134$	−1.93436	+	5.95335i	−0.167103	+	0.514291i
$135$	0.809017	+	0.587785i	0.0696291	+	0.0505885i
$136$	−0.0942195	+	0.289978i	−0.00807925	+	0.0248654i
$137$	5.22952	+	16.0948i	0.446788	+	1.37507i	0.880511	+	0.474025i	$0.157199\pi$
$137$	5.22952	+	16.0948i	0.446788	+	1.37507i	−0.433724	+	0.901046i	$0.642801\pi$
$138$	0.909897	−	0.661079i	0.0774556	−	0.0562748i
$139$	−5.09602	−	15.6839i	−0.432238	−	1.33029i	−0.895890	−	0.444276i	$-0.853461\pi$
$139$	−5.09602	−	15.6839i	−0.432238	−	1.33029i	0.463652	−	0.886018i	$-0.346539\pi$
$140$	−0.440197	−	1.35479i	−0.0372034	−	0.114500i
$141$	−9.07556	+	6.59378i	−0.764300	+	0.555296i
$142$	−4.41670	−	13.5932i	−0.370642	−	1.14072i
$143$	−11.4798	+	35.3311i	−0.959986	+	2.95453i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	−1.52752	+	4.70122i	−0.126853	+	0.390415i
$146$	−13.0127	+	9.45429i	−1.07694	+	0.782443i
$147$	−4.02145	+	2.92175i	−0.331683	+	0.240982i
$148$	−3.66469	−	2.66255i	−0.301236	−	0.218861i
$149$	−14.3584			−1.17629			−0.588145	−	0.808756i	$-0.700141\pi$
$149$	−14.3584			−1.17629			−0.588145	+	0.808756i	$0.700141\pi$
$150$	−1.00000			−0.0816497
$151$	12.1208	+	8.80624i	0.986373	+	0.716642i	0.959124	−	0.282987i	$-0.0913253\pi$
$151$	12.1208	+	8.80624i	0.986373	+	0.716642i	0.0272491	+	0.999629i	$0.491325\pi$
$152$	−1.20880	−	3.72032i	−0.0980470	−	0.301758i
$153$	−0.0942195	+	0.289978i	−0.00761719	+	0.0234433i
$154$	7.66407			0.617588
$155$	−3.97412	−	3.89953i	−0.319209	−	0.313218i
$156$	−6.90488			−0.552832
$157$	−2.66215	+	8.19325i	−0.212462	+	0.653892i	0.786862	+	0.617130i	$0.211705\pi$
$157$	−2.66215	+	8.19325i	−0.212462	+	0.653892i	−0.999324	+	0.0367627i	$0.988295\pi$
$158$	4.88162	+	15.0241i	0.388361	+	1.19525i
$159$	0.509029	+	0.369832i	0.0403687	+	0.0293295i
$160$	1.00000			0.0790569
$161$	−1.60214			−0.126266
$162$	−0.809017	−	0.587785i	−0.0635624	−	0.0461808i
$163$	−3.19952	+	2.32459i	−0.250606	+	0.182076i	−0.705995	−	0.708217i	$-0.749500\pi$
$163$	−3.19952	+	2.32459i	−0.250606	+	0.182076i	0.455389	+	0.890292i	$0.349500\pi$
$164$	−2.58107	+	1.87526i	−0.201548	+	0.146433i
$165$	1.66256	−	5.11683i	0.129430	−	0.398345i
$166$	−11.2986	−	8.20891i	−0.876941	−	0.637135i
$167$	6.66779	−	20.5214i	0.515969	−	1.58799i	−0.265542	−	0.964099i	$-0.585551\pi$
$167$	6.66779	−	20.5214i	0.515969	−	1.58799i	0.781511	−	0.623891i	$-0.214449\pi$
$168$	0.440197	+	1.35479i	0.0339619	+	0.104524i
$169$	−28.0545	+	20.3828i	−2.15804	+	1.56791i
$170$	−0.0942195	−	0.289978i	−0.00722630	−	0.0222403i
$171$	−1.20880	−	3.72032i	−0.0924396	−	0.284500i
$172$	−0.901664	+	0.655097i	−0.0687512	+	0.0499507i
$173$	0.775827	+	2.38775i	0.0589851	+	0.181537i	0.976208	−	0.216838i	$-0.0695742\pi$
$173$	0.775827	+	2.38775i	0.0589851	+	0.181537i	−0.917223	+	0.398375i	$0.869574\pi$
$174$	1.52752	−	4.70122i	0.115801	−	0.356398i
$175$	1.15245	+	0.837304i	0.0871171	+	0.0632942i
$176$	−1.66256	+	5.11683i	−0.125320	+	0.385696i
$177$	10.3016	−	7.48457i	0.774318	−	0.562575i
$178$	10.6525	−	7.73951i	0.798440	−	0.580101i
$179$	7.93225	+	5.76312i	0.592884	+	0.430755i	0.843346	−	0.537371i	$-0.180583\pi$
$179$	7.93225	+	5.76312i	0.592884	+	0.430755i	−0.250462	+	0.968126i	$0.580583\pi$
$180$	1.00000			0.0745356
$181$	−10.3534			−0.769559			−0.384779	−	0.923009i	$-0.625722\pi$
$181$	−10.3534			−0.769559			−0.384779	+	0.923009i	$0.625722\pi$
$182$	7.95753	+	5.78148i	0.589851	+	0.428552i
$183$	−0.572949	−	1.76336i	−0.0423536	−	0.130351i
$184$	0.347550	−	1.06965i	0.0256217	−	0.0788555i
$185$	4.52981			0.333038
$186$	3.97412	+	3.89953i	0.291397	+	0.285928i
$187$	1.64041			0.119959
$188$	−3.46656	+	10.6690i	−0.252825	+	0.778114i
$189$	0.440197	+	1.35479i	0.0320196	+	0.0985462i
$190$	3.16469	+	2.29928i	0.229591	+	0.166808i
$191$	−8.38572			−0.606769			−0.303385	−	0.952868i	$-0.598117\pi$
$191$	−8.38572			−0.606769			−0.303385	+	0.952868i	$0.598117\pi$
$192$	−1.00000			−0.0721688
$193$	−4.82980	−	3.50905i	−0.347656	−	0.252587i	0.400229	−	0.916415i	$-0.368931\pi$
$193$	−4.82980	−	3.50905i	−0.347656	−	0.252587i	−0.747885	+	0.663828i	$0.768931\pi$
$194$	5.07968	−	3.69060i	0.364700	−	0.264970i
$195$	5.58616	−	4.05858i	0.400033	−	0.290641i
$196$	−1.53606	+	4.72749i	−0.109718	+	0.337678i
$197$	21.1340	+	15.3547i	1.50573	+	1.09398i	0.968027	+	0.250846i	$0.0807089\pi$
$197$	21.1340	+	15.3547i	1.50573	+	1.09398i	0.537706	+	0.843133i	$0.319291\pi$
$198$	−1.66256	+	5.11683i	−0.118153	+	0.363637i
$199$	−1.46072	−	4.49563i	−0.103548	−	0.318687i	0.885839	−	0.463992i	$-0.153584\pi$
$199$	−1.46072	−	4.49563i	−0.103548	−	0.318687i	−0.989387	+	0.145305i	$0.953584\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	1.93436	+	5.95335i	0.136439	+	0.419917i
$202$	1.17596	+	3.61923i	0.0827403	+	0.254648i
$203$	−5.69674	+	4.13892i	−0.399833	+	0.290495i
$204$	0.0942195	+	0.289978i	0.00659668	+	0.0203025i
$205$	0.985882	−	3.03423i	0.0688570	−	0.211920i
$206$	−7.98037	−	5.79808i	−0.556019	−	0.403971i
$207$	0.347550	−	1.06965i	0.0241564	−	0.0743457i
$208$	−5.58616	+	4.05858i	−0.387331	+	0.281412i
$209$	−17.0265	+	12.3705i	−1.17775	+	0.855685i
$210$	−1.15245	−	0.837304i	−0.0795266	−	0.0577795i
$211$	−5.56675			−0.383231			−0.191615	−	0.981470i	$-0.561373\pi$
$211$	−5.56675			−0.383231			−0.191615	+	0.981470i	$0.561373\pi$
$212$	0.629195			0.0432133
$213$	−11.5631	−	8.40107i	−0.792289	−	0.575632i
$214$	−5.87604	−	18.0846i	−0.401678	−	1.23624i
$215$	0.344405	−	1.05997i	0.0234882	−	0.0722893i
$216$	−1.00000			−0.0680414
$217$	−1.31488	−	7.82157i	−0.0892599	−	0.530963i
$218$	−5.42352			−0.367327
$219$	−4.97042	+	15.2974i	−0.335870	+	1.03370i
$220$	−1.66256	−	5.11683i	−0.112090	−	0.344977i
$221$	1.70322	+	1.23746i	0.114571	+	0.0832409i
$222$	−4.52981			−0.304021
$223$	20.6298			1.38148			0.690738	−	0.723105i	$-0.257286\pi$
$223$	20.6298			1.38148			0.690738	+	0.723105i	$0.257286\pi$
$224$	1.15245	+	0.837304i	0.0770013	+	0.0559447i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−6.48793	+	4.71376i	−0.431571	+	0.313555i
$227$	1.49442	−	4.59935i	0.0991881	−	0.305270i	−0.889134	−	0.457646i	$-0.848693\pi$
$227$	1.49442	−	4.59935i	0.0991881	−	0.305270i	0.988323	+	0.152377i	$0.0486927\pi$
$228$	−3.16469	−	2.29928i	−0.209587	−	0.152274i
$229$	1.19318	−	3.67223i	0.0788477	−	0.242668i	−0.903861	−	0.427826i	$-0.859280\pi$
$229$	1.19318	−	3.67223i	0.0788477	−	0.242668i	0.982709	+	0.185158i	$0.0592796\pi$
$230$	0.347550	+	1.06965i	0.0229167	+	0.0705305i
$231$	6.20036	−	4.50483i	0.407954	−	0.296396i
$232$	−1.52752	−	4.70122i	−0.100286	−	0.308650i
$233$	2.51502	+	7.74044i	0.164765	+	0.507093i	0.999019	−	0.0442866i	$-0.0141015\pi$
$233$	2.51502	+	7.74044i	0.164765	+	0.507093i	−0.834254	+	0.551380i	$0.814101\pi$
$234$	−5.58616	+	4.05858i	−0.365179	+	0.265318i
$235$	−3.46656	−	10.6690i	−0.226133	−	0.695966i
$236$	3.93487	−	12.1103i	0.256138	−	0.788313i
$237$	12.7802	+	9.28539i	0.830166	+	0.603151i
$238$	0.134216	−	0.413075i	0.00869995	−	0.0267757i
$239$	15.0062	−	10.9027i	0.970673	−	0.705235i	0.0150679	−	0.999886i	$-0.495204\pi$
$239$	15.0062	−	10.9027i	0.970673	−	0.705235i	0.955605	+	0.294652i	$0.0952036\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	12.3947	+	9.00525i	0.798410	+	0.580079i	0.910447	−	0.413625i	$-0.135738\pi$
$241$	12.3947	+	9.00525i	0.798410	+	0.580079i	−0.112037	+	0.993704i	$0.535738\pi$
$242$	17.9461			1.15362
$243$	−1.00000			−0.0641500
$244$	−1.50000	−	1.08981i	−0.0960277	−	0.0697682i
$245$	−1.53606	−	4.72749i	−0.0981350	−	0.302028i
$246$	−0.985882	+	3.03423i	−0.0628576	+	0.193456i
$247$	−27.0103			−1.71862
$248$	5.50722	+	0.818860i	0.349709	+	0.0519976i
$249$	−13.9658			−0.885048
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	0.608445	+	1.87260i	0.0384047	+	0.118198i	0.968421	−	0.249321i	$-0.0802074\pi$
$251$	0.608445	+	1.87260i	0.0384047	+	0.118198i	−0.930016	+	0.367519i	$0.880207\pi$
$252$	1.15245	+	0.837304i	0.0725975	+	0.0527452i
$253$	−6.05103			−0.380425
$254$	−18.7636			−1.17733
$255$	−0.246670	−	0.179216i	−0.0154471	−	0.0112229i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	3.82380	−	2.77815i	0.238522	−	0.173297i	−0.462102	−	0.886827i	$-0.652905\pi$
$257$	3.82380	−	2.77815i	0.238522	−	0.173297i	0.700625	+	0.713530i	$0.252905\pi$
$258$	−0.344405	+	1.05997i	−0.0214417	+	0.0659908i
$259$	5.22038	+	3.79283i	0.324379	+	0.235675i
$260$	2.13372	−	6.56693i	0.132328	−	0.407264i
$261$	−1.52752	−	4.70122i	−0.0945510	−	0.290998i
$262$	8.04655	−	5.84616i	0.497117	−	0.361177i
$263$	−3.76816	−	11.5972i	−0.232355	−	0.715115i	−0.997461	−	0.0712111i	$-0.977314\pi$
$263$	−3.76816	−	11.5972i	−0.232355	−	0.715115i	0.765106	−	0.643904i	$-0.222686\pi$
$264$	1.66256	+	5.11683i	0.102323	+	0.314919i
$265$	−0.509029	+	0.369832i	−0.0312694	+	0.0227186i
$266$	1.72195	+	5.29962i	0.105580	+	0.324940i
$267$	4.06890	−	12.5228i	0.249013	−	0.766382i
$268$	5.06422	+	3.67937i	0.309347	+	0.224754i
$269$	−4.47757	+	13.7805i	−0.273002	+	0.840215i	0.716739	+	0.697342i	$0.245634\pi$
$269$	−4.47757	+	13.7805i	−0.273002	+	0.840215i	−0.989741	+	0.142873i	$0.954366\pi$
$270$	0.809017	−	0.587785i	0.0492352	−	0.0357715i
$271$	−0.370805	+	0.269406i	−0.0225248	+	0.0163652i	−0.598991	−	0.800756i	$-0.704431\pi$
$271$	−0.370805	+	0.269406i	−0.0225248	+	0.0163652i	0.576466	+	0.817121i	$0.304431\pi$
$272$	0.246670	+	0.179216i	0.0149566	+	0.0108666i
$273$	9.83604			0.595304
$274$	16.9231			1.02236
$275$	4.35264	+	3.16238i	0.262474	+	0.190698i
$276$	−0.347550	−	1.06965i	−0.0209200	−	0.0643852i
$277$	5.76736	−	17.7501i	0.346527	−	1.06650i	−0.614234	−	0.789124i	$-0.710535\pi$
$277$	5.76736	−	17.7501i	0.346527	−	1.06650i	0.960761	−	0.277377i	$-0.0894649\pi$
$278$	−16.4911			−0.989068
$279$	5.50722	+	0.818860i	0.329709	+	0.0490238i
$280$	−1.42451			−0.0851306
$281$	−2.55635	+	7.86765i	−0.152499	+	0.469345i	−0.997899	−	0.0647897i	$-0.979362\pi$
$281$	−2.55635	+	7.86765i	−0.152499	+	0.469345i	0.845400	+	0.534134i	$0.179362\pi$
$282$	3.46656	+	10.6690i	0.206430	+	0.635327i
$283$	−18.7722	−	13.6388i	−1.11589	−	0.810742i	−0.132310	−	0.991208i	$-0.542239\pi$
$283$	−18.7722	−	13.6388i	−1.11589	−	0.810742i	−0.983581	+	0.180466i	$0.942239\pi$
$284$	−14.2928			−0.848119
$285$	3.91177			0.231713
$286$	30.0544	+	21.8358i	1.77716	+	1.29118i
$287$	3.67676	−	2.67132i	0.217032	−	0.157683i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	−5.22456	+	16.0795i	−0.307327	+	0.945856i
$290$	3.99910	+	2.90551i	0.234835	+	0.170618i
$291$	1.94026	−	5.97152i	0.113740	−	0.350057i
$292$	4.97042	+	15.2974i	0.290872	+	0.895211i
$293$	5.56440	−	4.04277i	0.325076	−	0.236181i	−0.413263	−	0.910612i	$-0.635611\pi$
$293$	5.56440	−	4.04277i	0.325076	−	0.236181i	0.738338	+	0.674431i	$0.235611\pi$
$294$	1.53606	+	4.72749i	0.0895846	+	0.275713i
$295$	3.93487	+	12.1103i	0.229097	+	0.705088i
$296$	−3.66469	+	2.66255i	−0.213006	+	0.154758i
$297$	1.66256	+	5.11683i	0.0964715	+	0.296909i
$298$	−4.43700	+	13.6557i	−0.257029	+	0.791053i
$299$	−6.28273	−	4.56467i	−0.363339	−	0.263982i
$300$	−0.309017	+	0.951057i	−0.0178411	+	0.0549093i
$301$	1.28443	−	0.933191i	0.0740331	−	0.0537882i
$302$	12.1208	−	8.80624i	0.697471	−	0.506742i
$303$	3.07870	+	2.23681i	0.176867	+	0.128501i
$304$	−3.91177			−0.224356
$305$	1.85410			0.106166
$306$	0.246670	+	0.179216i	0.0141012	+	0.0102451i
$307$	−0.654649	−	2.01480i	−0.0373628	−	0.114991i	0.930636	−	0.365947i	$-0.119255\pi$
$307$	−0.654649	−	2.01480i	−0.0373628	−	0.114991i	−0.967998	+	0.250956i	$0.919255\pi$
$308$	2.36833	−	7.28896i	0.134948	−	0.415327i
$309$	−9.86428			−0.561159
$310$	−4.93675	+	2.57459i	−0.280388	+	0.146227i
$311$	−23.4416			−1.32925			−0.664625	−	0.747177i	$-0.731409\pi$
$311$	−23.4416			−1.32925			−0.664625	+	0.747177i	$0.731409\pi$
$312$	−2.13372	+	6.56693i	−0.120798	+	0.371779i
$313$	3.90659	+	12.0233i	0.220814	+	0.679595i	0.998690	+	0.0511769i	$0.0162972\pi$
$313$	3.90659	+	12.0233i	0.220814	+	0.679595i	−0.777876	+	0.628418i	$0.783703\pi$
$314$	6.96959	+	5.06370i	0.393317	+	0.285761i
$315$	−1.42451			−0.0802619
$316$	15.7973			0.888665
$317$	4.64512	+	3.37488i	0.260896	+	0.189552i	0.710542	−	0.703655i	$-0.248450\pi$
$317$	4.64512	+	3.37488i	0.260896	+	0.189552i	−0.449646	+	0.893207i	$0.648450\pi$
$318$	0.509029	−	0.369832i	0.0285450	−	0.0207391i
$319$	−21.5158	+	15.6321i	−1.20465	+	0.875230i
$320$	0.309017	−	0.951057i	0.0172746	−	0.0531657i
$321$	−15.3837	−	11.1769i	−0.858633	−	0.623833i
$322$	−0.495087	+	1.52372i	−0.0275901	+	0.0849137i
$323$	0.368565	+	1.13433i	0.0205075	+	0.0631156i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	2.13372	+	6.56693i	0.118358	+	0.364268i
$326$	1.22211	+	3.76126i	0.0676863	+	0.208317i
$327$	−4.38772	+	3.18787i	−0.242642	+	0.176289i
$328$	0.985882	+	3.03423i	0.0544362	+	0.167538i
$329$	4.93813	−	15.1980i	0.272248	−	0.837893i
$330$	−4.35264	−	3.16238i	−0.239605	−	0.174083i
$331$	7.39069	−	22.7462i	0.406229	−	1.25024i	−0.513635	−	0.858009i	$-0.671702\pi$
$331$	7.39069	−	22.7462i	0.406229	−	1.25024i	0.919865	−	0.392236i	$-0.128298\pi$
$332$	−11.2986	+	8.20891i	−0.620091	+	0.450522i
$333$	−3.66469	+	2.66255i	−0.200824	+	0.145907i
$334$	−17.4565	−	12.6829i	−0.955178	−	0.693977i
$335$	−6.25972			−0.342005
$336$	1.42451			0.0777132
$337$	−1.29932	−	0.944011i	−0.0707785	−	0.0514236i	0.551833	−	0.833954i	$-0.313928\pi$
$337$	−1.29932	−	0.944011i	−0.0707785	−	0.0514236i	−0.622612	+	0.782531i	$0.713928\pi$
$338$	10.7159	+	32.9801i	0.582867	+	1.79388i
$339$	−2.47817	+	7.62702i	−0.134596	+	0.414243i
$340$	−0.304901			−0.0165356
$341$	−4.96611	−	29.5409i	−0.268930	−	1.59973i
$342$	−3.91177			−0.211524
$343$	5.26950	−	16.2179i	0.284526	−	0.875682i
$344$	0.344405	+	1.05997i	0.0185691	+	0.0571497i
$345$	0.909897	+	0.661079i	0.0489872	+	0.0355913i
$346$	2.51063			0.134972
$347$	−1.91508			−0.102807			−0.0514034	−	0.998678i	$-0.516369\pi$
$347$	−1.91508			−0.102807			−0.0514034	+	0.998678i	$0.516369\pi$
$348$	−3.99910	−	2.90551i	−0.214374	−	0.155752i
$349$	22.7011	−	16.4933i	1.21516	−	0.882865i	0.219470	−	0.975619i	$-0.429567\pi$
$349$	22.7011	−	16.4933i	1.21516	−	0.882865i	0.995689	+	0.0927542i	$0.0295671\pi$
$350$	1.15245	−	0.837304i	0.0616011	−	0.0447558i
$351$	−2.13372	+	6.56693i	−0.113890	+	0.350517i
$352$	4.35264	+	3.16238i	0.231996	+	0.168555i
$353$	6.91914	−	21.2949i	0.368269	−	1.13341i	−0.579640	−	0.814873i	$-0.696807\pi$
$353$	6.91914	−	21.2949i	0.368269	−	1.13341i	0.947909	−	0.318542i	$-0.103193\pi$
$354$	−3.93487	−	12.1103i	−0.209136	−	0.643655i
$355$	11.5631	−	8.40107i	0.613705	−	0.445883i
$356$	−4.06890	−	12.5228i	−0.215651	−	0.663706i
$357$	−0.134216	−	0.413075i	−0.00710348	−	0.0218623i
$358$	7.93225	−	5.76312i	0.419232	−	0.304590i
$359$	1.22165	+	3.75984i	0.0644760	+	0.198437i	0.978105	−	0.208112i	$-0.0667320\pi$
$359$	1.22165	+	3.75984i	0.0644760	+	0.198437i	−0.913629	+	0.406549i	$0.866732\pi$
$360$	0.309017	−	0.951057i	0.0162866	−	0.0501251i
$361$	2.99177	+	2.17365i	0.157461	+	0.114402i
$362$	−3.19936	+	9.84663i	−0.168155	+	0.517527i
$363$	14.5187	−	10.5484i	0.762033	−	0.553650i
$364$	7.95753	−	5.78148i	0.417088	−	0.303032i
$365$	−13.0127	−	9.45429i	−0.681117	−	0.494860i
$366$	−1.85410			−0.0969155
$367$	8.69606			0.453931			0.226965	−	0.973903i	$-0.427120\pi$
$367$	8.69606			0.453931			0.226965	+	0.973903i	$0.427120\pi$
$368$	−0.909897	−	0.661079i	−0.0474317	−	0.0344611i
$369$	0.985882	+	3.03423i	0.0513230	+	0.157956i
$370$	1.39979	−	4.30810i	0.0727715	−	0.223968i
$371$	−0.896293			−0.0465332
$372$	4.93675	−	2.57459i	0.255958	−	0.133486i
$373$	−15.8745			−0.821948			−0.410974	−	0.911647i	$-0.634811\pi$
$373$	−15.8745			−0.821948			−0.410974	+	0.911647i	$0.634811\pi$
$374$	0.506915	−	1.56013i	0.0262120	−	0.0806722i
$375$	−0.309017	−	0.951057i	−0.0159576	−	0.0491123i
$376$	9.07556	+	6.59378i	0.468036	+	0.340048i
$377$	−34.1319			−1.75788
$378$	1.42451			0.0732687
$379$	−6.56664	−	4.77094i	−0.337306	−	0.245067i	0.406219	−	0.913776i	$-0.366847\pi$
$379$	−6.56664	−	4.77094i	−0.337306	−	0.245067i	−0.743524	+	0.668709i	$0.766847\pi$
$380$	3.16469	−	2.29928i	0.162345	−	0.117951i
$381$	−15.1800	+	11.0289i	−0.777697	+	0.565030i
$382$	−2.59133	+	7.97529i	−0.132584	+	0.408051i
$383$	−20.2333	−	14.7003i	−1.03387	−	0.751152i	−0.0647920	−	0.997899i	$-0.520638\pi$
$383$	−20.2333	−	14.7003i	−1.03387	−	0.751152i	−0.969080	+	0.246747i	$0.920638\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	2.36833	+	7.28896i	0.120701	+	0.371480i
$386$	−4.82980	+	3.50905i	−0.245830	+	0.178606i
$387$	0.344405	+	1.05997i	0.0175071	+	0.0538813i
$388$	−1.94026	−	5.97152i	−0.0985020	−	0.303158i
$389$	21.5339	−	15.6453i	1.09181	−	0.793246i	0.112106	−	0.993696i	$-0.464240\pi$
$389$	21.5339	−	15.6453i	1.09181	−	0.793246i	0.979704	+	0.200450i	$0.0642403\pi$
$390$	−2.13372	−	6.56693i	−0.108045	−	0.332529i
$391$	−0.105968	+	0.326136i	−0.00535904	+	0.0164934i
$392$	4.02145	+	2.92175i	0.203114	+	0.147571i
$393$	3.07351	−	9.45929i	0.155038	−	0.477158i
$394$	21.1340	−	15.3547i	1.06471	−	0.773560i
$395$	−12.7802	+	9.28539i	−0.643044	+	0.467199i
$396$	4.35264	+	3.16238i	0.218728	+	0.158915i
$397$	−11.4176			−0.573033			−0.286517	−	0.958075i	$-0.592497\pi$
$397$	−11.4176			−0.573033			−0.286517	+	0.958075i	$0.592497\pi$
$398$	−4.72699			−0.236943
$399$	4.50812	+	3.27534i	0.225689	+	0.163972i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	6.15233	−	18.9349i	0.307233	−	0.945565i	−0.671602	−	0.740912i	$-0.734393\pi$
$401$	6.15233	−	18.9349i	0.307233	−	0.945565i	0.978835	−	0.204653i	$-0.0656065\pi$
$402$	6.25972			0.312207
$403$	17.1283	−	34.4183i	0.853220	−	1.71450i
$404$	3.80549			0.189330
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	2.17596	+	6.69692i	0.107991	+	0.332362i
$407$	19.7166	+	14.3250i	0.977316	+	0.710062i
$408$	0.304901			0.0150948
$409$	1.02216			0.0505427			0.0252713	−	0.999681i	$-0.491955\pi$
$409$	1.02216			0.0505427			0.0252713	+	0.999681i	$0.491955\pi$
$410$	−2.58107	−	1.87526i	−0.127470	−	0.0926125i
$411$	13.6910	−	9.94713i	0.675330	−	0.490656i
$412$	−7.98037	+	5.79808i	−0.393165	+	0.285651i
$413$	−5.60525	+	17.2512i	−0.275816	+	0.848876i
$414$	−0.909897	−	0.661079i	−0.0447190	−	0.0324903i
$415$	4.31568	−	13.2823i	0.211848	−	0.652002i
$416$	2.13372	+	6.56693i	0.104614	+	0.321970i
$417$	−13.3415	+	9.69320i	−0.653338	+	0.474678i
$418$	6.50356	+	20.0159i	0.318099	+	0.979009i
$419$	6.52595	+	20.0848i	0.318813	+	0.981207i	0.974156	+	0.225875i	$0.0725241\pi$
$419$	6.52595	+	20.0848i	0.318813	+	0.981207i	−0.655343	+	0.755331i	$0.727476\pi$
$420$	−1.15245	+	0.837304i	−0.0562338	+	0.0408563i
$421$	2.83732	+	8.73237i	0.138282	+	0.425590i	0.996086	−	0.0883878i	$-0.0281715\pi$
$421$	2.83732	+	8.73237i	0.138282	+	0.425590i	−0.857804	+	0.513977i	$0.828171\pi$
$422$	−1.72022	+	5.29429i	−0.0837390	+	0.257722i
$423$	9.07556	+	6.59378i	0.441269	+	0.320601i
$424$	0.194432	−	0.598400i	0.00944245	−	0.0290609i
$425$	0.246670	−	0.179216i	0.0119652	−	0.00869326i
$426$	−11.5631	+	8.40107i	−0.560233	+	0.407033i
$427$	2.13676	+	1.55245i	0.103405	+	0.0751282i
$428$	−19.0153			−0.919138
$429$	37.1493			1.79359
$430$	−0.901664	−	0.655097i	−0.0434821	−	0.0315916i
$431$	−11.3364	−	34.8899i	−0.546056	−	1.68059i	−0.718466	−	0.695562i	$-0.755155\pi$
$431$	−11.3364	−	34.8899i	−0.546056	−	1.68059i	0.172410	−	0.985025i	$-0.444845\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	7.29374			0.350515			0.175257	−	0.984523i	$-0.443924\pi$
$433$	7.29374			0.350515			0.175257	+	0.984523i	$0.443924\pi$
$434$	−7.84507	−	1.16647i	−0.376576	−	0.0559924i
$435$	4.94315			0.237006
$436$	−1.67596	+	5.15808i	−0.0802640	+	0.247027i
$437$	−1.35954	−	4.18422i	−0.0650354	−	0.200158i
$438$	13.0127	+	9.45429i	0.621772	+	0.451744i
$439$	−1.89448			−0.0904187			−0.0452094	−	0.998978i	$-0.514395\pi$
$439$	−1.89448			−0.0904187			−0.0452094	+	0.998978i	$0.514395\pi$
$440$	−5.38016			−0.256489
$441$	4.02145	+	2.92175i	0.191497	+	0.139131i
$442$	1.70322	−	1.23746i	0.0810141	−	0.0588602i
$443$	8.62549	−	6.26679i	0.409809	−	0.297744i	−0.363715	−	0.931510i	$-0.618492\pi$
$443$	8.62549	−	6.26679i	0.409809	−	0.297744i	0.773525	+	0.633766i	$0.218492\pi$
$444$	−1.39979	+	4.30810i	−0.0664310	+	0.204454i
$445$	10.6525	+	7.73951i	0.504978	+	0.366888i
$446$	6.37497	−	19.6201i	0.301864	−	0.929041i
$447$	4.43700	+	13.6557i	0.209863	+	0.645892i
$448$	1.15245	−	0.837304i	0.0544482	−	0.0395589i
$449$	−1.00174	−	3.08303i	−0.0472749	−	0.145497i	0.924633	−	0.380860i	$-0.124372\pi$
$449$	−1.00174	−	3.08303i	−0.0472749	−	0.145497i	−0.971908	+	0.235363i	$0.924372\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	13.8866	−	10.0892i	0.653893	−	0.475081i
$452$	2.47817	+	7.62702i	0.116563	+	0.358745i
$453$	4.62972	−	14.2488i	0.217523	−	0.669467i
$454$	−3.91244	−	2.84255i	−0.183620	−	0.133408i
$455$	−3.03950	+	9.35463i	−0.142494	+	0.438552i
$456$	−3.16469	+	2.29928i	−0.148200	+	0.107674i
$457$	25.3334	−	18.4058i	1.18505	−	0.860986i	0.192314	−	0.981334i	$-0.438401\pi$
$457$	25.3334	−	18.4058i	1.18505	−	0.860986i	0.992732	+	0.120348i	$0.0384009\pi$
$458$	−3.12379	−	2.26957i	−0.145965	−	0.106050i
$459$	0.304901			0.0142315
$460$	1.12469			0.0524392
$461$	−25.1595	−	18.2795i	−1.17180	−	0.851360i	−0.180573	−	0.983562i	$-0.557795\pi$
$461$	−25.1595	−	18.2795i	−1.17180	−	0.851360i	−0.991223	+	0.132202i	$0.957795\pi$
$462$	−2.36833	−	7.28896i	−0.110185	−	0.339113i
$463$	−12.8674	+	39.6019i	−0.598000	+	1.84045i	−0.0588115	+	0.998269i	$0.518731\pi$
$463$	−12.8674	+	39.6019i	−0.598000	+	1.84045i	−0.539188	+	0.842185i	$0.681269\pi$
$464$	−4.94315			−0.229480
$465$	−2.48061	+	4.98464i	−0.115035	+	0.231157i
$466$	8.13878			0.377022
$467$	−3.32756	+	10.2412i	−0.153981	+	0.473904i	−0.998056	−	0.0623202i	$-0.980150\pi$
$467$	−3.32756	+	10.2412i	−0.153981	+	0.473904i	0.844075	+	0.536225i	$0.180150\pi$
$468$	2.13372	+	6.56693i	0.0986314	+	0.303556i
$469$	−7.21402	−	5.24129i	−0.333113	−	0.242020i
$470$	−11.2180			−0.517448
$471$	8.61489			0.396953
$472$	−10.3016	−	7.48457i	−0.474171	−	0.344505i
$473$	4.85109	−	3.52453i	0.223054	−	0.162058i
$474$	12.7802	−	9.28539i	0.587016	−	0.426492i
$475$	−1.20880	+	3.72032i	−0.0554638	+	0.170700i
$476$	−0.351383	−	0.255295i	−0.0161056	−	0.0117014i
$477$	0.194432	−	0.598400i	0.00890243	−	0.0273989i
$478$	−5.73187	−	17.6409i	−0.262170	−	0.806875i
$479$	10.1436	−	7.36972i	0.463471	−	0.336731i	−0.331421	−	0.943483i	$-0.607528\pi$
$479$	10.1436	−	7.36972i	0.463471	−	0.336731i	0.794891	+	0.606752i	$0.207528\pi$
$480$	−0.309017	−	0.951057i	−0.0141046	−	0.0434096i
$481$	9.66536	+	29.7469i	0.440702	+	1.35634i
$482$	12.3947	−	9.00525i	0.564561	−	0.410178i
$483$	0.495087	+	1.52372i	0.0225272	+	0.0693317i
$484$	5.54564	−	17.0677i	0.252075	−	0.775806i
$485$	5.07968	+	3.69060i	0.230656	+	0.167582i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−11.2642	+	8.18390i	−0.510428	+	0.370848i	−0.812986	−	0.582283i	$-0.802160\pi$
$487$	−11.2642	+	8.18390i	−0.510428	+	0.370848i	0.302558	+	0.953131i	$0.402160\pi$
$488$	−1.50000	+	1.08981i	−0.0679018	+	0.0493336i
$489$	3.19952	+	2.32459i	0.144687	+	0.105121i
$490$	−4.97078			−0.224557
$491$	15.0493			0.679164			0.339582	−	0.940576i	$-0.389714\pi$
$491$	15.0493			0.679164			0.339582	+	0.940576i	$0.389714\pi$
$492$	2.58107	+	1.87526i	0.116364	+	0.0845432i
$493$	0.465741	+	1.43340i	0.0209759	+	0.0645573i
$494$	−8.34664	+	25.6883i	−0.375533	+	1.15577i
$495$	−5.38016			−0.241820
$496$	2.48061	−	4.98464i	0.111383	−	0.223817i
$497$	20.3601			0.913277
$498$	−4.31568	+	13.2823i	−0.193390	+	0.595194i
$499$	4.03111	+	12.4065i	0.180457	+	0.555391i	0.999841	−	0.0178553i	$-0.00568384\pi$
$499$	4.03111	+	12.4065i	0.180457	+	0.555391i	−0.819383	+	0.573246i	$0.805684\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	−21.5774			−0.964009
$502$	1.96897			0.0878794
$503$	17.9086	+	13.0113i	0.798504	+	0.580147i	0.910475	−	0.413565i	$-0.135716\pi$
$503$	17.9086	+	13.0113i	0.798504	+	0.580147i	−0.111971	+	0.993711i	$0.535716\pi$
$504$	1.15245	−	0.837304i	0.0513342	−	0.0372965i
$505$	−3.07870	+	2.23681i	−0.137001	+	0.0995367i
$506$	−1.86987	+	5.75487i	−0.0831259	+	0.255835i
$507$	28.0545	+	20.3828i	1.24595	+	0.905232i
$508$	−5.79826	+	17.8452i	−0.257256	+	0.791753i
$509$	−8.44348	−	25.9863i	−0.374250	−	1.15182i	−0.943983	−	0.329994i	$-0.892953\pi$
$509$	−8.44348	−	25.9863i	−0.374250	−	1.15182i	0.569732	−	0.821830i	$-0.307047\pi$
$510$	−0.246670	+	0.179216i	−0.0109227	+	0.00793582i
$511$	−7.08039	−	21.7912i	−0.313218	−	0.963986i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−3.16469	+	2.29928i	−0.139725	+	0.101516i
$514$	−1.46056	−	4.49515i	−0.0644226	−	0.198273i
$515$	3.04823	−	9.38149i	0.134321	−	0.413398i
$516$	0.901664	+	0.655097i	0.0396936	+	0.0288391i
$517$	18.6506	−	57.4007i	0.820253	−	2.52448i
$518$	5.22038	−	3.79283i	0.229370	−	0.166647i
$519$	2.03114	−	1.47571i	0.0891573	−	0.0647765i
$520$	−5.58616	−	4.05858i	−0.244969	−	0.177981i
$521$	−28.8518			−1.26402			−0.632009	−	0.774961i	$-0.717770\pi$
$521$	−28.8518			−1.26402			−0.632009	+	0.774961i	$0.717770\pi$
$522$	−4.94315			−0.216356
$523$	2.60185	+	1.89036i	0.113771	+	0.0826595i	0.643216	−	0.765685i	$-0.277600\pi$
$523$	2.60185	+	1.89036i	0.113771	+	0.0826595i	−0.529445	+	0.848344i	$0.677600\pi$
$524$	−3.07351	−	9.45929i	−0.134267	−	0.413231i
$525$	0.440197	−	1.35479i	0.0192118	−	0.0591277i
$526$	−12.1940			−0.531685
$527$	−1.67915	−	0.249671i	−0.0731451	−	0.0108758i
$528$	5.38016			0.234141
$529$	−6.71650	+	20.6713i	−0.292022	+	0.898751i
$530$	0.194432	+	0.598400i	0.00844558	+	0.0259928i
$531$	−10.3016	−	7.48457i	−0.447053	−	0.324803i
$532$	5.57235			0.241592
$533$	22.0292			0.954190
$534$	−10.6525	−	7.73951i	−0.460980	−	0.334921i
$535$	15.3837	−	11.1769i	0.665094	−	0.483219i
$536$	5.06422	−	3.67937i	0.218741	−	0.158925i
$537$	3.02985	−	9.32492i	0.130748	−	0.402400i
$538$	11.7224	+	8.51684i	0.505390	+	0.367187i
$539$	8.26422	−	25.4347i	0.355965	−	1.09555i
$540$	−0.309017	−	0.951057i	−0.0132980	−	0.0409270i
$541$	−13.7126	+	9.96277i	−0.589550	+	0.428333i	−0.842154	−	0.539237i	$-0.818713\pi$
$541$	−13.7126	+	9.96277i	−0.589550	+	0.428333i	0.252605	+	0.967570i	$0.418713\pi$
$542$	0.141635	+	0.435907i	0.00608374	+	0.0187238i
$543$	3.19936	+	9.84663i	0.137298	+	0.422559i
$544$	0.246670	−	0.179216i	0.0105759	−	0.00768383i
$545$	−1.67596	−	5.15808i	−0.0717903	−	0.220948i
$546$	3.03950	−	9.35463i	0.130079	−	0.400341i
$547$	−2.96248	−	2.15237i	−0.126667	−	0.0920286i	0.522648	−	0.852548i	$-0.324944\pi$
$547$	−2.96248	−	2.15237i	−0.126667	−	0.0920286i	−0.649315	+	0.760520i	$0.724944\pi$
$548$	5.22952	−	16.0948i	0.223394	−	0.687536i
$549$	−1.50000	+	1.08981i	−0.0640184	+	0.0465121i
$550$	4.35264	−	3.16238i	0.185597	−	0.134844i
$551$	−15.6436	−	11.3657i	−0.666438	−	0.484195i
$552$	−1.12469			−0.0478702
$553$	−22.5033			−0.956938
$554$	−15.0991	−	10.9702i	−0.641501	−	0.466078i
$555$	−1.39979	−	4.30810i	−0.0594177	−	0.182869i
$556$	−5.09602	+	15.6839i	−0.216119	+	0.665147i
$557$	−36.9213			−1.56441			−0.782203	−	0.623023i	$-0.785904\pi$
$557$	−36.9213			−1.56441			−0.782203	+	0.623023i	$0.785904\pi$
$558$	2.48061	−	4.98464i	0.105012	−	0.211016i
$559$	7.69561			0.325490
$560$	−0.440197	+	1.35479i	−0.0186017	+	0.0572502i
$561$	−0.506915	−	1.56013i	−0.0214020	−	0.0658685i
$562$	6.69262	+	4.86247i	0.282311	+	0.205111i
$563$	15.4103			0.649468			0.324734	−	0.945805i	$-0.394725\pi$
$563$	15.4103			0.649468			0.324734	+	0.945805i	$0.394725\pi$
$564$	11.2180			0.472363
$565$	−6.48793	−	4.71376i	−0.272949	−	0.198309i
$566$	−18.7722	+	13.6388i	−0.789054	+	0.573281i
$567$	1.15245	−	0.837304i	0.0483984	−	0.0351635i
$568$	−4.41670	+	13.5932i	−0.185321	+	0.570359i
$569$	14.2717	+	10.3690i	0.598299	+	0.434690i	0.845275	−	0.534332i	$-0.179437\pi$
$569$	14.2717	+	10.3690i	0.598299	+	0.434690i	−0.246976	+	0.969022i	$0.579437\pi$
$570$	1.20880	−	3.72032i	0.0506312	−	0.155827i
$571$	3.79658	+	11.6847i	0.158882	+	0.488988i	0.998534	−	0.0541371i	$-0.0172408\pi$
$571$	3.79658	+	11.6847i	0.158882	+	0.488988i	−0.839652	+	0.543125i	$0.817241\pi$
$572$	30.0544	−	21.8358i	1.25664	−	0.913001i
$573$	2.59133	+	7.97529i	0.108254	+	0.333173i
$574$	−1.40440	−	4.32229i	−0.0586184	−	0.180409i
$575$	−0.909897	+	0.661079i	−0.0379453	+	0.0275689i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−3.87192	+	11.9166i	−0.161190	+	0.496093i	−0.998735	−	0.0502755i	$-0.983990\pi$
$577$	−3.87192	+	11.9166i	−0.161190	+	0.496093i	0.837545	+	0.546368i	$0.183990\pi$
$578$	13.6781	+	9.93771i	0.568933	+	0.413354i
$579$	−1.84482	+	5.67776i	−0.0766680	+	0.235960i
$580$	3.99910	−	2.90551i	0.166053	−	0.120645i
$581$	16.0949	−	11.6936i	0.667730	−	0.485134i
$582$	−5.07968	−	3.69060i	−0.210559	−	0.152980i
$583$	−3.38517			−0.140199
$584$	16.0846			0.665586
$585$	−5.58616	−	4.05858i	−0.230959	−	0.167802i
$586$	−2.12541	−	6.54134i	−0.0877999	−	0.270220i
$587$	0.0727008	−	0.223750i	0.00300068	−	0.00923515i	−0.949545	−	0.313631i	$-0.898455\pi$
$587$	0.0727008	−	0.223750i	0.00300068	−	0.00923515i	0.952546	+	0.304396i	$0.0984545\pi$
$588$	4.97078			0.204992
$589$	19.3114	−	10.0712i	0.795714	−	0.414977i
$590$	12.7335			0.524230
$591$	8.07246	−	24.8445i	0.332056	−	1.02196i
$592$	1.39979	+	4.30810i	0.0575309	+	0.177062i
$593$	−16.8678	−	12.2552i	−0.692678	−	0.503260i	0.184862	−	0.982765i	$-0.440816\pi$
$593$	−16.8678	−	12.2552i	−0.692678	−	0.503260i	−0.877539	+	0.479505i	$0.840816\pi$
$594$	5.38016			0.220750
$595$	0.434333			0.0178059
$596$	11.6162	+	8.43968i	0.475819	+	0.345703i
$597$	−3.82421	+	2.77845i	−0.156515	+	0.113715i
$598$	−6.28273	+	4.56467i	−0.256920	+	0.186663i
$599$	−6.81471	+	20.9735i	−0.278441	+	0.856954i	0.709847	+	0.704356i	$0.248764\pi$
$599$	−6.81471	+	20.9735i	−0.278441	+	0.856954i	−0.988288	+	0.152598i	$0.951236\pi$
$600$	0.809017	+	0.587785i	0.0330280	+	0.0239962i
$601$	−5.83684	+	17.9640i	−0.238090	+	0.732765i	0.758607	+	0.651549i	$0.225880\pi$
$601$	−5.83684	+	17.9640i	−0.238090	+	0.732765i	−0.996697	+	0.0812162i	$0.974120\pi$
$602$	−0.490607	−	1.50993i	−0.0199957	−	0.0615403i
$603$	5.06422	−	3.67937i	0.206231	−	0.149836i
$604$	−4.62972	−	14.2488i	−0.188380	−	0.579775i
$605$	5.54564	+	17.0677i	0.225462	+	0.693902i
$606$	3.07870	−	2.23681i	0.125064	−	0.0908642i
$607$	0.868382	+	2.67261i	0.0352465	+	0.108478i	0.967132	−	0.254275i	$-0.0818369\pi$
$607$	0.868382	+	2.67261i	0.0352465	+	0.108478i	−0.931885	+	0.362753i	$0.881837\pi$
$608$	−1.20880	+	3.72032i	−0.0490235	+	0.150879i
$609$	5.69674	+	4.13892i	0.230843	+	0.167718i
$610$	0.572949	−	1.76336i	0.0231980	−	0.0713962i
$611$	62.6656	−	45.5292i	2.53518	−	1.84192i
$612$	0.246670	−	0.179216i	0.00997103	−	0.00724438i
$613$	−33.2314	−	24.1440i	−1.34220	−	0.975167i	−0.999360	−	0.0357736i	$-0.988610\pi$
$613$	−33.2314	−	24.1440i	−1.34220	−	0.975167i	−0.342842	−	0.939393i	$-0.611390\pi$
$614$	−2.11849			−0.0854952
$615$	−3.19038			−0.128649
$616$	−6.20036	−	4.50483i	−0.249820	−	0.181505i
$617$	0.775869	+	2.38788i	0.0312353	+	0.0961324i	0.965459	−	0.260556i	$-0.0839058\pi$
$617$	0.775869	+	2.38788i	0.0312353	+	0.0961324i	−0.934223	+	0.356688i	$0.883906\pi$
$618$	−3.04823	+	9.38149i	−0.122618	+	0.377379i
$619$	−19.4110			−0.780194			−0.390097	−	0.920774i	$-0.627559\pi$
$619$	−19.4110			−0.780194			−0.390097	+	0.920774i	$0.627559\pi$
$620$	0.923043	+	5.49072i	0.0370703	+	0.220513i
$621$	−1.12469			−0.0451324
$622$	−7.24385	+	22.2943i	−0.290452	+	0.893919i
$623$	5.79618	+	17.8388i	0.232219	+	0.714696i
$624$	5.58616	+	4.05858i	0.223625	+	0.162473i
$625$	1.00000			0.0400000
$626$	12.6420			0.505276
$627$	17.0265	+	12.3705i	0.679974	+	0.494030i
$628$	6.96959	−	5.06370i	0.278117	−	0.202064i
$629$	1.11737	−	0.811814i	0.0445523	−	0.0323692i
$630$	−0.440197	+	1.35479i	−0.0175379	+	0.0539760i
$631$	−1.04338	−	0.758062i	−0.0415364	−	0.0301780i	0.566823	−	0.823839i	$-0.308172\pi$
$631$	−1.04338	−	0.758062i	−0.0415364	−	0.0301780i	−0.608360	+	0.793661i	$0.708172\pi$
$632$	4.88162	−	15.0241i	0.194180	−	0.597626i
$633$	1.72022	+	5.29429i	0.0683726	+	0.210429i
$634$	4.64512	−	3.37488i	0.184481	−	0.134034i
$635$	−5.79826	−	17.8452i	−0.230097	−	0.708165i
$636$	−0.194432	−	0.598400i	−0.00770973	−	0.0237281i
$637$	27.7676	−	20.1743i	1.10019	−	0.799336i
$638$	8.21829	+	25.2933i	0.325365	+	1.00137i
$639$	−4.41670	+	13.5932i	−0.174722	+	0.537739i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	2.91529	−	8.97234i	0.115147	−	0.354386i	−0.876831	−	0.480799i	$-0.840347\pi$
$641$	2.91529	−	8.97234i	0.115147	−	0.354386i	0.991978	+	0.126413i	$0.0403465\pi$
$642$	−15.3837	+	11.1769i	−0.607145	+	0.441117i
$643$	25.8061	−	18.7492i	1.01769	−	0.739396i	0.0518830	−	0.998653i	$-0.483478\pi$
$643$	25.8061	−	18.7492i	1.01769	−	0.739396i	0.965808	+	0.259257i	$0.0834777\pi$
$644$	1.29615	+	0.941711i	0.0510756	+	0.0371086i
$645$	−1.11452			−0.0438841
$646$	1.19270			0.0469262
$647$	12.2925	+	8.93102i	0.483268	+	0.351114i	0.802589	−	0.596532i	$-0.203455\pi$
$647$	12.2925	+	8.93102i	0.483268	+	0.351114i	−0.319322	+	0.947646i	$0.603455\pi$
$648$	0.309017	+	0.951057i	0.0121393	+	0.0373610i
$649$	−21.1702	+	65.1552i	−0.831004	+	2.55757i
$650$	6.90488			0.270832
$651$	−7.03243	+	3.66752i	−0.275623	+	0.143742i
$652$	3.95482			0.154883
$653$	2.23048	−	6.86470i	0.0872853	−	0.268637i	−0.897881	−	0.440238i	$-0.854894\pi$
$653$	2.23048	−	6.86470i	0.0872853	−	0.268637i	0.985166	+	0.171601i	$0.0548941\pi$
$654$	1.67596	+	5.15808i	0.0655352	+	0.201697i
$655$	8.04655	+	5.84616i	0.314405	+	0.228428i
$656$	3.19038			0.124564
$657$	16.0846			0.627520
$658$	−12.9282	−	9.39289i	−0.503994	−	0.366173i
$659$	30.9486	−	22.4855i	1.20559	−	0.875911i	0.210765	−	0.977537i	$-0.432405\pi$
$659$	30.9486	−	22.4855i	1.20559	−	0.875911i	0.994823	+	0.101626i	$0.0324046\pi$
$660$	−4.35264	+	3.16238i	−0.169426	+	0.123095i
$661$	−7.62171	+	23.4572i	−0.296450	+	0.912379i	0.686280	+	0.727337i	$0.259242\pi$
$661$	−7.62171	+	23.4572i	−0.296450	+	0.912379i	−0.982731	+	0.185042i	$0.940758\pi$
$662$	−19.3491	−	14.0579i	−0.752023	−	0.546377i
$663$	0.650574	−	2.00226i	0.0252662	−	0.0777613i
$664$	4.31568	+	13.2823i	0.167481	+	0.515453i
$665$	−4.50812	+	3.27534i	−0.174818	+	0.127012i
$666$	1.39979	+	4.30810i	0.0542407	+	0.166936i
$667$	−1.71799	−	5.28743i	−0.0665209	−	0.204730i
$668$	−17.4565	+	12.6829i	−0.675413	+	0.490716i
$669$	−6.37497	−	19.6201i	−0.246471	−	0.758559i
$670$	−1.93436	+	5.95335i	−0.0747309	+	0.229998i
$671$	8.07023	+	5.86337i	0.311548	+	0.226353i
$672$	0.440197	−	1.35479i	0.0169810	−	0.0522620i
$673$	19.2207	−	13.9647i	0.740905	−	0.538299i	−0.152089	−	0.988367i	$-0.548600\pi$
$673$	19.2207	−	13.9647i	0.740905	−	0.538299i	0.892995	+	0.450067i	$0.148600\pi$
$674$	−1.29932	+	0.944011i	−0.0500479	+	0.0363620i
$675$	0.809017	+	0.587785i	0.0311391	+	0.0226239i
$676$	34.6773			1.33374
$677$	−19.0509			−0.732187			−0.366093	−	0.930578i	$-0.619305\pi$
$677$	−19.0509			−0.732187			−0.366093	+	0.930578i	$0.619305\pi$
$678$	6.48793	+	4.71376i	0.249168	+	0.181031i
$679$	2.76392	+	8.50647i	0.106069	+	0.326448i
$680$	−0.0942195	+	0.289978i	−0.00361315	+	0.0111201i
$681$	−4.83604			−0.185318
$682$	−29.6297	−	4.40559i	−1.13458	−	0.168699i
$683$	−20.7287			−0.793162			−0.396581	−	0.918000i	$-0.629803\pi$
$683$	−20.7287			−0.793162			−0.396581	+	0.918000i	$0.629803\pi$
$684$	−1.20880	+	3.72032i	−0.0462198	+	0.142250i
$685$	5.22952	+	16.0948i	0.199810	+	0.614950i
$686$	−13.7957	−	10.0232i	−0.526723	−	0.382687i
$687$	−3.86122			−0.147315
$688$	1.11452			0.0424906
$689$	−3.51479	−	2.55364i	−0.133903	−	0.0972860i
$690$	0.909897	−	0.661079i	0.0346392	−	0.0251668i
$691$	−18.4448	+	13.4009i	−0.701673	+	0.509795i	−0.880477	−	0.474090i	$-0.842777\pi$
$691$	−18.4448	+	13.4009i	−0.701673	+	0.509795i	0.178804	+	0.983885i	$0.442777\pi$
$692$	0.775827	−	2.38775i	0.0294925	−	0.0907687i
$693$	−6.20036	−	4.50483i	−0.235532	−	0.171124i
$694$	−0.591792	+	1.82135i	−0.0224641	+	0.0691374i
$695$	−5.09602	−	15.6839i	−0.193303	−	0.594925i
$696$	−3.99910	+	2.90551i	−0.151585	+	0.110133i
$697$	−0.300596	−	0.925140i	−0.0113859	−	0.0350422i
$698$	−8.67103	−	26.6867i	−0.328203	−	1.01011i
$699$	6.58441	−	4.78386i	0.249045	−	0.180942i
$700$	−0.440197	−	1.35479i	−0.0166379	−	0.0512061i
$701$	−9.22711	+	28.3981i	−0.348503	+	1.07258i	0.611179	+	0.791493i	$0.290696\pi$
$701$	−9.22711	+	28.3981i	−0.348503	+	1.07258i	−0.959682	+	0.281089i	$0.909304\pi$
$702$	5.58616	+	4.05858i	0.210836	+	0.153181i
$703$	−5.47565	+	16.8523i	−0.206518	+	0.635597i
$704$	4.35264	−	3.16238i	0.164046	−	0.119187i
$705$	−9.07556	+	6.59378i	−0.341805	+	0.248336i
$706$	−18.1145	−	13.1610i	−0.681750	−	0.495320i
$707$	−5.42094			−0.203876
$708$	−12.7335			−0.478555
$709$	20.5787	+	14.9513i	0.772848	+	0.561507i	0.902824	−	0.430010i	$-0.141490\pi$
$709$	20.5787	+	14.9513i	0.772848	+	0.561507i	−0.129976	+	0.991517i	$0.541490\pi$
$710$	−4.41670	−	13.5932i	−0.165756	−	0.510144i
$711$	4.88162	−	15.0241i	0.183075	−	0.563447i
$712$	−13.1672			−0.493463
$713$	6.19394	+	0.920967i	0.231965	+	0.0344905i
$714$	−0.434333			−0.0162545
$715$	−11.4798	+	35.3311i	−0.429319	+	1.32131i
$716$	−3.02985	−	9.32492i	−0.113231	−	0.348488i
$717$	−15.0062	−	10.9027i	−0.560418	−	0.407168i
$718$	3.95333			0.147537
$719$	−28.8237			−1.07494			−0.537471	−	0.843282i	$-0.680620\pi$
$719$	−28.8237			−1.07494			−0.537471	+	0.843282i	$0.680620\pi$
$720$	−0.809017	−	0.587785i	−0.0301503	−	0.0219055i
$721$	11.3681	−	8.25940i	0.423370	−	0.307596i
$722$	2.99177	−	2.17365i	0.111342	−	0.0808947i
$723$	4.73434	−	14.5708i	0.176072	−	0.541894i
$724$	8.37604	+	6.08555i	0.311293	+	0.226168i
$725$	−1.52752	+	4.70122i	−0.0567306	+	0.174599i
$726$	−5.54564	−	17.0677i	−0.205818	−	0.633443i
$727$	23.6462	−	17.1799i	0.876988	−	0.637169i	−0.0554651	−	0.998461i	$-0.517664\pi$
$727$	23.6462	−	17.1799i	0.876988	−	0.637169i	0.932453	+	0.361292i	$0.117664\pi$
$728$	−3.03950	−	9.35463i	−0.112652	−	0.346706i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−13.0127	+	9.45429i	−0.481622	+	0.349919i
$731$	−0.105009	−	0.323185i	−0.00388391	−	0.0119534i
$732$	−0.572949	+	1.76336i	−0.0211768	+	0.0651755i
$733$	−11.5939	−	8.42343i	−0.428229	−	0.311126i	0.352711	−	0.935732i	$-0.385260\pi$
$733$	−11.5939	−	8.42343i	−0.428229	−	0.311126i	−0.780940	+	0.624606i	$0.785260\pi$
$734$	2.68723	−	8.27044i	0.0991875	−	0.305268i
$735$	−4.02145	+	2.92175i	−0.148333	+	0.107770i
$736$	−0.909897	+	0.661079i	−0.0335392	+	0.0243677i
$737$	−27.2463	−	19.7956i	−1.00363	−	0.729181i
$738$	3.19038			0.117440
$739$	−20.5370			−0.755466			−0.377733	−	0.925915i	$-0.623296\pi$
$739$	−20.5370			−0.755466			−0.377733	+	0.925915i	$0.623296\pi$
$740$	−3.66469	−	2.66255i	−0.134717	−	0.0978774i
$741$	8.34664	+	25.6883i	0.306622	+	0.943684i
$742$	−0.276970	+	0.852425i	−0.0101679	+	0.0312935i
$743$	−14.1909			−0.520612			−0.260306	−	0.965526i	$-0.583823\pi$
$743$	−14.1909			−0.520612			−0.260306	+	0.965526i	$0.583823\pi$
$744$	−0.923043	−	5.49072i	−0.0338404	−	0.201300i
$745$	−14.3584			−0.526053
$746$	−4.90548	+	15.0975i	−0.179602	+	0.552759i
$747$	4.31568	+	13.2823i	0.157902	+	0.485974i
$748$	−1.32712	−	0.964210i	−0.0485244	−	0.0352550i
$749$	27.0874			0.989751
$750$	−1.00000			−0.0365148
$751$	11.0273	+	8.01178i	0.402391	+	0.292354i	0.770514	−	0.637423i	$-0.220000\pi$
$751$	11.0273	+	8.01178i	0.402391	+	0.292354i	−0.368123	+	0.929777i	$0.620000\pi$
$752$	9.07556	−	6.59378i	0.330952	−	0.240450i
$753$	1.59293	−	1.15733i	0.0580496	−	0.0421755i
$754$	−10.5473	+	32.4613i	−0.384111	+	1.18217i
$755$	12.1208	+	8.80624i	0.441119	+	0.320492i
$756$	0.440197	−	1.35479i	0.0160098	−	0.0492731i
$757$	15.4692	+	47.6092i	0.562236	+	1.73039i	0.676023	+	0.736881i	$0.263702\pi$
$757$	15.4692	+	47.6092i	0.562236	+	1.73039i	−0.113787	+	0.993505i	$0.536298\pi$
$758$	−6.56664	+	4.77094i	−0.238511	+	0.173288i
$759$	1.86987	+	5.75487i	0.0678720	+	0.208889i
$760$	−1.20880	−	3.72032i	−0.0438479	−	0.134950i
$761$	−8.68652	+	6.31113i	−0.314886	+	0.228778i	−0.733990	−	0.679160i	$-0.762344\pi$
$761$	−8.68652	+	6.31113i	−0.314886	+	0.228778i	0.419104	+	0.907938i	$0.362344\pi$
$762$	5.79826	+	17.8452i	0.210049	+	0.646463i
$763$	2.38742	−	7.34772i	0.0864303	−	0.266005i
$764$	6.78419	+	4.92900i	0.245443	+	0.178325i
$765$	−0.0942195	+	0.289978i	−0.00340651	+	0.0104842i
$766$	−20.2333	+	14.7003i	−0.731058	+	0.531145i
$767$	−71.1315	+	51.6800i	−2.56841	+	1.86606i
$768$	0.809017	+	0.587785i	0.0291929	+	0.0212099i
$769$	37.7586			1.36161			0.680806	−	0.732464i	$-0.261630\pi$
$769$	37.7586			1.36161			0.680806	+	0.732464i	$0.261630\pi$
$770$	7.66407			0.276194
$771$	−3.82380	−	2.77815i	−0.137711	−	0.100053i
$772$	1.84482	+	5.67776i	0.0663964	+	0.204347i
$773$	−7.37496	+	22.6978i	−0.265259	+	0.816383i	0.726375	+	0.687299i	$0.241204\pi$
$773$	−7.37496	+	22.6978i	−0.265259	+	0.816383i	−0.991634	+	0.129084i	$0.958796\pi$
$774$	1.11452			0.0400605
$775$	−3.97412	−	3.89953i	−0.142755	−	0.140075i
$776$	−6.27883			−0.225397
$777$	1.99401	−	6.13692i	0.0715346	−	0.220161i
$778$	−8.22520	−	25.3146i	−0.294888	−	0.907571i
$779$	10.0966	+	7.33559i	0.361747	+	0.262825i
$780$	−6.90488			−0.247234
$781$	76.8973			2.75160
$782$	0.277428	+	0.201563i	0.00992081	+	0.00720789i
$783$	−3.99910	+	2.90551i	−0.142916	+	0.103835i
$784$	4.02145	−	2.92175i	0.143623	−	0.104348i
$785$	−2.66215	+	8.19325i	−0.0950161	+	0.292430i
$786$	−8.04655	−	5.84616i	−0.287011	−	0.208526i
$787$	−0.420529	+	1.29426i	−0.0149902	+	0.0461352i	−0.958272	−	0.285858i	$-0.907721\pi$
$787$	−0.420529	+	1.29426i	−0.0149902	+	0.0461352i	0.943282	+	0.331994i	$0.107721\pi$
$788$	−8.07246	−	24.8445i	−0.287569	−	0.885047i
$789$	−9.86518	+	7.16748i	−0.351210	+	0.255169i
$790$	4.88162	+	15.0241i	0.173680	+	0.534533i
$791$	−3.53017	−	10.8647i	−0.125518	−	0.386306i
$792$	4.35264	−	3.16238i	0.154664	−	0.112370i
$793$	3.95614	+	12.1758i	0.140487	+	0.432374i
$794$	−3.52824	+	10.8588i	−0.125212	+	0.385364i
$795$	0.509029	+	0.369832i	0.0180534	+	0.0131166i
$796$	−1.46072	+	4.49563i	−0.0517738	+	0.159344i
$797$	−7.12306	+	5.17520i	−0.252312	+	0.183315i	−0.706751	−	0.707463i	$-0.749840\pi$
$797$	−7.12306	+	5.17520i	−0.252312	+	0.183315i	0.454439	+	0.890778i	$0.349840\pi$
$798$	4.50812	−	3.27534i	0.159586	−	0.115946i
$799$	−2.76714	−	2.01045i	−0.0978945	−	0.0711245i
$800$	1.00000			0.0353553
$801$	−13.1672			−0.465241
$802$	−16.1070	−	11.7024i	−0.568758	−	0.413227i
$803$	−26.7416	−	82.3022i	−0.943691	−	2.90438i
$804$	1.93436	−	5.95335i	0.0682197	−	0.209959i
$805$	−1.60214			−0.0564678
$806$	−27.4408	−	26.9258i	−0.966561	−	0.948421i
$807$	14.4897			0.510062
$808$	1.17596	−	3.61923i	0.0413701	−	0.127324i
$809$	8.69809	+	26.7700i	0.305809	+	0.941182i	0.979374	+	0.202055i	$0.0647619\pi$
$809$	8.69809	+	26.7700i	0.305809	+	0.941182i	−0.673565	+	0.739128i	$0.735238\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	−44.1248			−1.54943			−0.774716	−	0.632310i	$-0.782107\pi$
$811$	−44.1248			−1.54943			−0.774716	+	0.632310i	$0.782107\pi$
$812$	7.04156			0.247110
$813$	0.370805	+	0.269406i	0.0130047	+	0.00944847i
$814$	19.7166	−	14.3250i	0.691067	−	0.502089i
$815$	−3.19952	+	2.32459i	−0.112074	+	0.0814267i
$816$	0.0942195	−	0.289978i	0.00329834	−	0.0101512i
$817$	3.52711	+	2.56259i	0.123398	+	0.0896538i
$818$	0.315866	−	0.972134i	0.0110440	−	0.0339899i
$819$	−3.03950	−	9.35463i	−0.106209	−	0.326877i
$820$	−2.58107	+	1.87526i	−0.0901350	+	0.0654869i
$821$	6.11589	+	18.8228i	0.213446	+	0.656920i	0.999260	+	0.0384570i	$0.0122443\pi$
$821$	6.11589	+	18.8228i	0.213446	+	0.656920i	−0.785814	+	0.618463i	$0.787756\pi$
$822$	−5.22952	−	16.0948i	−0.182400	−	0.561370i
$823$	−36.1479	+	26.2630i	−1.26004	+	0.915470i	−0.998760	−	0.0497932i	$-0.984144\pi$
$823$	−36.1479	+	26.2630i	−1.26004	+	0.915470i	−0.261277	+	0.965264i	$0.584144\pi$
$824$	3.04823	+	9.38149i	0.106190	+	0.326820i
$825$	1.66256	−	5.11683i	0.0578829	−	0.178145i
$826$	14.6747	+	10.6618i	0.510599	+	0.370972i
$827$	−6.85175	+	21.0875i	−0.238259	+	0.733284i	0.758414	+	0.651773i	$0.225975\pi$
$827$	−6.85175	+	21.0875i	−0.238259	+	0.733284i	−0.996672	+	0.0815112i	$0.974025\pi$
$828$	−0.909897	+	0.661079i	−0.0316211	+	0.0229741i
$829$	−11.4266	+	8.30188i	−0.396861	+	0.288336i	−0.768261	−	0.640137i	$-0.778878\pi$
$829$	−11.4266	+	8.30188i	−0.396861	+	0.288336i	0.371400	+	0.928473i	$0.378878\pi$
$830$	−11.2986	−	8.20891i	−0.392180	−	0.284935i
$831$	−18.6636			−0.647432
$832$	6.90488			0.239383
$833$	−1.22614	−	0.890844i	−0.0424833	−	0.0308659i
$834$	5.09602	+	15.6839i	0.176461	+	0.543090i
$835$	6.66779	−	20.5214i	0.230749	−	0.710171i
$836$	21.0460			0.727890
$837$	−0.923043	−	5.49072i	−0.0319050	−	0.189787i
$838$	21.1184			0.729523
$839$	0.916352	−	2.82024i	0.0316360	−	0.0973655i	−0.933992	−	0.357295i	$-0.883699\pi$
$839$	0.916352	−	2.82024i	0.0316360	−	0.0973655i	0.965628	+	0.259929i	$0.0836992\pi$
$840$	0.440197	+	1.35479i	0.0151882	+	0.0467446i
$841$	3.69335	+	2.68338i	0.127357	+	0.0925303i
$842$	9.18176			0.316424
$843$	8.27254			0.284921
$844$	4.50360	+	3.27205i	0.155020	+	0.112629i
$845$	−28.0545	+	20.3828i	−0.965105	+	0.701190i
$846$	9.07556	−	6.59378i	0.312024	−	0.226699i
$847$	−7.89981	+	24.3131i	−0.271441	+	0.835408i
$848$	−0.509029	−	0.369832i	−0.0174801	−	0.0127001i
$849$	−7.17034	+	22.0680i	−0.246085	+	0.757373i
$850$	−0.0942195	−	0.289978i	−0.00323170	−	0.00994615i
$851$	−4.12166	+	2.99456i	−0.141289	+	0.102652i
$852$	4.41670	+	13.5932i	0.151314	+	0.465696i
$853$	14.8612	+	45.7380i	0.508837	+	1.56604i	0.794222	+	0.607627i	$0.207879\pi$
$853$	14.8612	+	45.7380i	0.508837	+	1.56604i	−0.285385	+	0.958413i	$0.592121\pi$
$854$	2.13676	−	1.55245i	0.0731184	−	0.0531237i
$855$	−1.20880	−	3.72032i	−0.0413402	−	0.127232i
$856$	−5.87604	+	18.0846i	−0.200839	+	0.618119i
$857$	−35.3419	−	25.6774i	−1.20726	−	0.877122i	−0.212276	−	0.977210i	$-0.568088\pi$
$857$	−35.3419	−	25.6774i	−1.20726	−	0.877122i	−0.994979	+	0.100087i	$0.968088\pi$
$858$	11.4798	−	35.3311i	0.391913	−	1.20618i
$859$	−7.32185	+	5.31963i	−0.249818	+	0.181504i	−0.705646	−	0.708564i	$-0.749343\pi$
$859$	−7.32185	+	5.31963i	−0.249818	+	0.181504i	0.455828	+	0.890068i	$0.349343\pi$
$860$	−0.901664	+	0.655097i	−0.0307465	+	0.0223386i
$861$	−3.67676	−	2.67132i	−0.125304	−	0.0910384i
$862$	−36.6854			−1.24951
$863$	−34.1604			−1.16283			−0.581417	−	0.813605i	$-0.697502\pi$
$863$	−34.1604			−1.16283			−0.581417	+	0.813605i	$0.697502\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	0.775827	+	2.38775i	0.0263789	+	0.0811860i
$866$	2.25389	−	6.93676i	0.0765903	−	0.235721i
$867$	16.9070			0.574193
$868$	−3.53364	+	7.10065i	−0.119940	+	0.241012i
$869$	−84.9917			−2.88315
$870$	1.52752	−	4.70122i	0.0517877	−	0.159386i
$871$	−13.3565	−	41.1072i	−0.452569	−	1.39286i
$872$	4.38772	+	3.18787i	0.148587	+	0.107955i
$873$	−6.27883			−0.212506
$874$	−4.39955			−0.148817
$875$	1.15245	+	0.837304i	0.0389599	+	0.0283060i
$876$	13.0127	−	9.45429i	0.439659	−	0.319431i
$877$	−6.20420	+	4.50761i	−0.209501	+	0.152211i	−0.687588	−	0.726101i	$-0.741330\pi$
$877$	−6.20420	+	4.50761i	−0.209501	+	0.152211i	0.478087	+	0.878312i	$0.341330\pi$
$878$	−0.585427	+	1.80176i	−0.0197572	+	0.0608065i
$879$	−5.56440	−	4.04277i	−0.187683	−	0.136359i
$880$	−1.66256	+	5.11683i	−0.0560449	+	0.172488i
$881$	6.02944	+	18.5567i	0.203137	+	0.625191i	0.999785	+	0.0207473i	$0.00660455\pi$
$881$	6.02944	+	18.5567i	0.203137	+	0.625191i	−0.796648	+	0.604444i	$0.793395\pi$
$882$	4.02145	−	2.92175i	0.135409	−	0.0983805i
$883$	−2.96920	−	9.13827i	−0.0999217	−	0.307527i	0.888583	−	0.458715i	$-0.151690\pi$
$883$	−2.96920	−	9.13827i	−0.0999217	−	0.307527i	−0.988505	+	0.151188i	$0.951690\pi$
$884$	−0.650574	−	2.00226i	−0.0218812	−	0.0673433i
$885$	10.3016	−	7.48457i	0.346285	−	0.251591i
$886$	−3.29464	−	10.1399i	−0.110686	−	0.340656i
$887$	−8.18068	+	25.1775i	−0.274680	+	0.845379i	0.714623	+	0.699509i	$0.246598\pi$
$887$	−8.18068	+	25.1775i	−0.274680	+	0.845379i	−0.989304	+	0.145870i	$0.953402\pi$
$888$	3.66469	+	2.66255i	0.122979	+	0.0893495i
$889$	8.25966	−	25.4206i	0.277020	−	0.852580i
$890$	10.6525	−	7.73951i	0.357073	−	0.259429i
$891$	4.35264	−	3.16238i	0.145819	−	0.105944i
$892$	−16.6899	−	12.1259i	−0.558819	−	0.406006i
$893$	43.8823			1.46847
$894$	14.3584			0.480218
$895$	7.93225	+	5.76312i	0.265146	+	0.192640i
$896$	−0.440197	−	1.35479i	−0.0147059	−	0.0452602i
$897$	−2.39979	+	7.38579i	−0.0801266	+	0.246604i
$898$	−3.24169			−0.108177
$899$	24.4031	−	12.7266i	0.813889	−	0.424456i
$900$	1.00000			0.0333333
$901$	−0.0592824	+	0.182453i	−0.00197498	+	0.00607837i
$902$	−5.30420	−	16.3247i	−0.176611	−	0.543551i
$903$	−1.28443	−	0.933191i	−0.0427430	−	0.0310546i
$904$	8.01953			0.266726
$905$	−10.3534			−0.344157
$906$	−12.1208	−	8.80624i	−0.402685	−	0.292568i
$907$	−37.5717	+	27.2974i	−1.24755	+	0.906396i	−0.998077	−	0.0619861i	$-0.980257\pi$
$907$	−37.5717	+	27.2974i	−1.24755	+	0.906396i	−0.249470	+	0.968382i	$0.580257\pi$
$908$	−3.91244	+	2.84255i	−0.129839	+	0.0943335i
$909$	1.17596	−	3.61923i	0.0390041	−	0.120042i
$910$	7.95753	+	5.78148i	0.263789	+	0.191654i
$911$	−1.14388	+	3.52051i	−0.0378985	+	0.116640i	−0.968216	−	0.250116i	$-0.919531\pi$
$911$	−1.14388	+	3.52051i	−0.0378985	+	0.116640i	0.930317	+	0.366755i	$0.119531\pi$
$912$	1.20880	+	3.72032i	0.0400275	+	0.123192i
$913$	60.7882	−	44.1652i	2.01180	−	1.46165i
$914$	−9.67649	−	29.7812i	−0.320070	−	0.985074i
$915$	−0.572949	−	1.76336i	−0.0189411	−	0.0582947i
$916$	−3.12379	+	2.26957i	−0.103213	+	0.0749886i
$917$	4.37823	+	13.4748i	0.144582	+	0.444978i
$918$	0.0942195	−	0.289978i	0.00310971	−	0.00957069i
$919$	−1.76357	−	1.28131i	−0.0581747	−	0.0422664i	0.558318	−	0.829627i	$-0.311447\pi$
$919$	−1.76357	−	1.28131i	−0.0581747	−	0.0422664i	−0.616493	+	0.787361i	$0.711447\pi$
$920$	0.347550	−	1.06965i	0.0114584	−	0.0352653i
$921$	−1.71389	+	1.24522i	−0.0564747	+	0.0410313i
$922$	−25.1595	+	18.2795i	−0.828585	+	0.602002i
$923$	79.8416	+	58.0083i	2.62802	+	1.90937i
$924$	−7.66407			−0.252129
$925$	4.52981			0.148939
$926$	33.6874	+	24.4753i	1.10704	+	0.804308i
$927$	3.04823	+	9.38149i	0.100117	+	0.308128i
$928$	−1.52752	+	4.70122i	−0.0501432	+	0.154325i
$929$	−29.5263			−0.968725			−0.484363	−	0.874867i	$-0.660948\pi$
$929$	−29.5263			−0.968725			−0.484363	+	0.874867i	$0.660948\pi$
$930$	3.97412	+	3.89953i	0.130317	+	0.127871i
$931$	19.4446			0.637270
$932$	2.51502	−	7.74044i	0.0823823	−	0.253547i
$933$	7.24385	+	22.2943i	0.237153	+	0.729882i
$934$	8.71165	+	6.32939i	0.285054	+	0.207104i
$935$	1.64041			0.0536472
$936$	6.90488			0.225693
$937$	−34.4537	−	25.0321i	−1.12555	−	0.817762i	−0.140511	−	0.990079i	$-0.544875\pi$
$937$	−34.4537	−	25.0321i	−1.12555	−	0.817762i	−0.985042	+	0.172317i	$0.944875\pi$
$938$	−7.21402	+	5.24129i	−0.235546	+	0.171134i
$939$	10.2276	−	7.43078i	0.333765	−	0.242494i
$940$	−3.46656	+	10.6690i	−0.113067	+	0.347983i
$941$	−19.4838	−	14.1558i	−0.635152	−	0.461465i	0.223029	−	0.974812i	$-0.428406\pi$
$941$	−19.4838	−	14.1558i	−0.635152	−	0.461465i	−0.858181	+	0.513347i	$0.828406\pi$
$942$	2.66215	−	8.19325i	0.0867374	−	0.266950i
$943$	1.10882	+	3.41259i	0.0361080	+	0.111129i
$944$	−10.3016	+	7.48457i	−0.335289	+	0.243602i
$945$	0.440197	+	1.35479i	0.0143196	+	0.0440712i
$946$	−1.85295	−	5.70280i	−0.0602447	−	0.185414i
$947$	3.73572	−	2.71416i	0.121395	−	0.0881984i	−0.525431	−	0.850836i	$-0.676096\pi$
$947$	3.73572	−	2.71416i	0.121395	−	0.0881984i	0.646826	+	0.762638i	$0.276096\pi$
$948$	−4.88162	−	15.0241i	−0.158548	−	0.487960i
$949$	34.3201	−	105.626i	1.11408	−	3.42878i
$950$	3.16469	+	2.29928i	0.102676	+	0.0745986i
$951$	1.77428	−	5.46067i	0.0575349	−	0.177074i
$952$	−0.351383	+	0.255295i	−0.0113884	+	0.00827414i
$953$	0.371619	−	0.269997i	0.0120379	−	0.00874607i	−0.581750	−	0.813368i	$-0.697632\pi$
$953$	0.371619	−	0.269997i	0.0120379	−	0.00874607i	0.593788	+	0.804622i	$0.297632\pi$
$954$	−0.509029	−	0.369832i	−0.0164804	−	0.0119737i
$955$	−8.38572			−0.271356
$956$	−18.5487			−0.599909
$957$	21.5158	+	15.6321i	0.695506	+	0.505314i
$958$	−3.87449	−	11.9245i	−0.125179	−	0.385262i
$959$	−7.44948	+	22.9271i	−0.240556	+	0.740356i
$960$	−1.00000			−0.0322749
$961$	0.587272	+	30.9944i	0.0189443	+	0.999821i
$962$	31.2778			1.00844
$963$	−5.87604	+	18.0846i	−0.189353	+	0.582768i
$964$	−4.73434	−	14.5708i	−0.152483	−	0.469294i
$965$	−4.82980	−	3.50905i	−0.155477	−	0.112960i
$966$	1.60214			0.0515479
$967$	−49.4124			−1.58900			−0.794498	−	0.607267i	$-0.792266\pi$
$967$	−49.4124			−1.58900			−0.794498	+	0.607267i	$0.792266\pi$
$968$	−14.5187	−	10.5484i	−0.466648	−	0.339040i
$969$	0.964916	−	0.701053i	0.0309976	−	0.0225211i
$970$	5.07968	−	3.69060i	0.163099	−	0.118498i
$971$	13.8892	−	42.7467i	0.445727	−	1.37181i	−0.435957	−	0.899967i	$-0.643590\pi$
$971$	13.8892	−	42.7467i	0.445727	−	1.37181i	0.881684	−	0.471840i	$-0.156410\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	7.25931	−	22.3419i	0.232723	−	0.716247i
$974$	4.30253	+	13.2418i	0.137862	+	0.424296i
$975$	5.58616	−	4.05858i	0.178900	−	0.129979i
$976$	0.572949	+	1.76336i	0.0183397	+	0.0564436i
$977$	−2.68087	−	8.25086i	−0.0857685	−	0.263968i	0.898970	−	0.438011i	$-0.144317\pi$
$977$	−2.68087	−	8.25086i	−0.0857685	−	0.263968i	−0.984738	+	0.174043i	$0.944317\pi$
$978$	3.19952	−	2.32459i	0.102309	−	0.0743321i
$979$	21.8913	+	67.3745i	0.699649	+	2.15330i
$980$	−1.53606	+	4.72749i	−0.0490675	+	0.151014i
$981$	4.38772	+	3.18787i	0.140089	+	0.101781i
$982$	4.65048	−	14.3127i	0.148403	−	0.456737i
$983$	30.9805	−	22.5086i	0.988123	−	0.717914i	0.0286140	−	0.999591i	$-0.490891\pi$
$983$	30.9805	−	22.5086i	0.988123	−	0.717914i	0.959509	+	0.281677i	$0.0908907\pi$
$984$	2.58107	−	1.87526i	0.0822816	−	0.0597811i
$985$	21.1340	+	15.3547i	0.673384	+	0.489242i
$986$	1.50717			0.0479981
$987$	−15.9801			−0.508653
$988$	21.8518	+	15.8763i	0.695198	+	0.505091i
$989$	0.387350	+	1.19214i	0.0123170	+	0.0379079i
$990$	−1.66256	+	5.11683i	−0.0528396	+	0.162624i
$991$	−8.53753			−0.271204			−0.135602	−	0.990763i	$-0.543297\pi$
$991$	−8.53753			−0.271204			−0.135602	+	0.990763i	$0.543297\pi$
$992$	−3.97412	−	3.89953i	−0.126178	−	0.123810i
$993$	−23.9168			−0.758976
$994$	6.29163	−	19.3636i	0.199558	−	0.614177i
$995$	−1.46072	−	4.49563i	−0.0463079	−	0.142521i
$996$	11.2986	+	8.20891i	0.358010	+	0.260109i
$997$	−55.3703			−1.75359			−0.876797	−	0.480860i	$-0.840325\pi$
$997$	−55.3703			−1.75359			−0.876797	+	0.480860i	$0.840325\pi$
$998$	13.0450			0.412931
$999$	3.66469	+	2.66255i	0.115946	+	0.0842395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.a.721.1	✓	8
31.4	even	5	inner	930.2.n.a.841.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.a.721.1	✓	8	1.1	even	1	trivial
930.2.n.a.841.1	yes	8	31.4	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(1.15245 + 0.837304i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(1.15245 + 0.837304i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(4.35264 + 3.16238i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(2.13372 + 6.56693i) q^{13} +(1.15245 - 0.837304i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.246670 - 0.179216i) q^{17} +(0.309017 + 0.951057i) q^{18} +(-1.20880 + 3.72032i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(0.440197 - 1.35479i) q^{21} +(4.35264 - 3.16238i) q^{22} +(-0.909897 + 0.661079i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +6.90488 q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.440197 - 1.35479i) q^{28} +(-1.52752 + 4.70122i) q^{29} -1.00000 q^{30} +(-3.97412 - 3.89953i) q^{31} +1.00000 q^{32} +(1.66256 - 5.11683i) q^{33} +(-0.0942195 - 0.289978i) q^{34} +(1.15245 + 0.837304i) q^{35} +1.00000 q^{36} +4.52981 q^{37} +(3.16469 + 2.29928i) q^{38} +(5.58616 - 4.05858i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(0.985882 - 3.03423i) q^{41} +(-1.15245 - 0.837304i) q^{42} +(0.344405 - 1.05997i) q^{43} +(-1.66256 - 5.11683i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(0.347550 + 1.06965i) q^{46} +(-3.46656 - 10.6690i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-1.53606 - 4.72749i) q^{49} +(0.309017 - 0.951057i) q^{50} +(-0.246670 - 0.179216i) q^{51} +(2.13372 - 6.56693i) q^{52} +(-0.509029 + 0.369832i) q^{53} +(0.809017 - 0.587785i) q^{54} +(4.35264 + 3.16238i) q^{55} -1.42451 q^{56} +3.91177 q^{57} +(3.99910 + 2.90551i) q^{58} +(3.93487 + 12.1103i) q^{59} +(-0.309017 + 0.951057i) q^{60} +1.85410 q^{61} +(-4.93675 + 2.57459i) q^{62} -1.42451 q^{63} +(0.309017 - 0.951057i) q^{64} +(2.13372 + 6.56693i) q^{65} +(-4.35264 - 3.16238i) q^{66} -6.25972 q^{67} -0.304901 q^{68} +(0.909897 + 0.661079i) q^{69} +(1.15245 - 0.837304i) q^{70} +(11.5631 - 8.40107i) q^{71} +(0.309017 - 0.951057i) q^{72} +(-13.0127 - 9.45429i) q^{73} +(1.39979 - 4.30810i) q^{74} +(-0.309017 - 0.951057i) q^{75} +(3.16469 - 2.29928i) q^{76} +(2.36833 + 7.28896i) q^{77} +(-2.13372 - 6.56693i) q^{78} +(-12.7802 + 9.28539i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-2.58107 - 1.87526i) q^{82} +(4.31568 - 13.2823i) q^{83} +(-1.15245 + 0.837304i) q^{84} +(0.246670 - 0.179216i) q^{85} +(-0.901664 - 0.655097i) q^{86} +4.94315 q^{87} -5.38016 q^{88} +(10.6525 + 7.73951i) q^{89} +(0.309017 + 0.951057i) q^{90} +(-3.03950 + 9.35463i) q^{91} +1.12469 q^{92} +(-2.48061 + 4.98464i) q^{93} -11.2180 q^{94} +(-1.20880 + 3.72032i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(5.07968 + 3.69060i) q^{97} -4.97078 q^{98} -5.38016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{12} + q^{13} + 9 q^{14} + 2 q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + q^{21} - q^{22} + 8 q^{23} + 2 q^{24} + 8 q^{25} + 16 q^{26} + 2 q^{27} - q^{28} - q^{29} - 8 q^{30} + 3 q^{31} + 8 q^{32} + q^{33} - 12 q^{34} + 9 q^{35} + 8 q^{36} + 8 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} + 29 q^{41} - 9 q^{42} - 25 q^{43} - q^{44} - 2 q^{45} + 3 q^{46} + 13 q^{47} + 2 q^{48} + 25 q^{49} - 2 q^{50} - 13 q^{51} + q^{52} - 19 q^{53} + 2 q^{54} - q^{55} - 16 q^{56} + 12 q^{57} + 4 q^{58} + 23 q^{59} + 2 q^{60} - 12 q^{61} - 27 q^{62} - 16 q^{63} - 2 q^{64} + q^{65} + q^{66} - 24 q^{67} - 2 q^{68} - 8 q^{69} + 9 q^{70} + 3 q^{71} - 2 q^{72} - 14 q^{73} + 8 q^{74} + 2 q^{75} + 8 q^{76} - 24 q^{77} - q^{78} - 34 q^{79} - 2 q^{80} - 2 q^{81} - 21 q^{82} + 8 q^{83} - 9 q^{84} + 13 q^{85} + 6 q^{87} + 4 q^{88} + 25 q^{89} - 2 q^{90} + 3 q^{91} - 22 q^{92} - 18 q^{93} - 42 q^{94} - 2 q^{95} + 2 q^{96} - 28 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^12 + q^13 + 9 * q^14 + 2 * q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + q^21 - q^22 + 8 * q^23 + 2 * q^24 + 8 * q^25 + 16 * q^26 + 2 * q^27 - q^28 - q^29 - 8 * q^30 + 3 * q^31 + 8 * q^32 + q^33 - 12 * q^34 + 9 * q^35 + 8 * q^36 + 8 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 + 29 * q^41 - 9 * q^42 - 25 * q^43 - q^44 - 2 * q^45 + 3 * q^46 + 13 * q^47 + 2 * q^48 + 25 * q^49 - 2 * q^50 - 13 * q^51 + q^52 - 19 * q^53 + 2 * q^54 - q^55 - 16 * q^56 + 12 * q^57 + 4 * q^58 + 23 * q^59 + 2 * q^60 - 12 * q^61 - 27 * q^62 - 16 * q^63 - 2 * q^64 + q^65 + q^66 - 24 * q^67 - 2 * q^68 - 8 * q^69 + 9 * q^70 + 3 * q^71 - 2 * q^72 - 14 * q^73 + 8 * q^74 + 2 * q^75 + 8 * q^76 - 24 * q^77 - q^78 - 34 * q^79 - 2 * q^80 - 2 * q^81 - 21 * q^82 + 8 * q^83 - 9 * q^84 + 13 * q^85 + 6 * q^87 + 4 * q^88 + 25 * q^89 - 2 * q^90 + 3 * q^91 - 22 * q^92 - 18 * q^93 - 42 * q^94 - 2 * q^95 + 2 * q^96 - 28 * q^97 + 4 * q^99

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