LMFDB - Embedded newform 930.2.n.d.901.2

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} - 2 x^{11} + 13 x^{10} - 9 x^{9} + 60 x^{8} + x^{7} + 263 x^{6} + 823 x^{5} + 1931 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 13x^10 - 9x^9 + 60x^8 + x^7 + 263x^6 + 823x^5 + 1931x^4 + 1170x^3 + 1340x^2 + 1000x + 400
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			901.2
Root			$0.270443 + 0.832338i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.d.481.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.167143 + 0.514413i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(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} +(0.167143 + 0.514413i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.529970 - 1.63108i) q^{11} +(0.809017 + 0.587785i) q^{12} +(-3.39847 + 2.46914i) q^{13} +(0.167143 - 0.514413i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.833670 - 2.56577i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-5.35916 - 3.89366i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(0.437586 + 0.317925i) q^{21} +(-0.529970 + 1.63108i) q^{22} +(2.05648 - 6.32920i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +4.20074 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.437586 + 0.317925i) q^{28} +(3.52017 + 2.55755i) q^{29} +1.00000 q^{30} +(-5.41765 - 1.28417i) q^{31} +1.00000 q^{32} +(-1.38748 - 1.00806i) q^{33} +(-2.18258 + 1.58573i) q^{34} +(-0.167143 - 0.514413i) q^{35} +1.00000 q^{36} -0.145898 q^{37} +(2.04702 + 6.30007i) q^{38} +(-1.29810 + 3.99514i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-6.85149 - 4.97790i) q^{41} +(-0.167143 - 0.514413i) q^{42} +(-4.76104 - 3.45910i) q^{43} +(1.38748 - 1.00806i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(-5.38394 + 3.91166i) q^{46} +(-0.782052 + 0.568194i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(5.42643 - 3.94254i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-0.833670 - 2.56577i) q^{51} +(-3.39847 - 2.46914i) q^{52} +(4.10493 - 12.6337i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(0.529970 + 1.63108i) q^{55} +0.540886 q^{56} -6.62428 q^{57} +(-1.34459 - 4.13821i) q^{58} +(-2.57653 + 1.87196i) q^{59} +(-0.809017 - 0.587785i) q^{60} -13.6341 q^{61} +(3.62815 + 4.22333i) q^{62} +0.540886 q^{63} +(-0.809017 - 0.587785i) q^{64} +(3.39847 - 2.46914i) q^{65} +(0.529970 + 1.63108i) q^{66} +13.9954 q^{67} +2.69781 q^{68} +(-2.05648 - 6.32920i) q^{69} +(-0.167143 + 0.514413i) q^{70} +(-2.94315 + 9.05808i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(1.52334 + 4.68835i) q^{73} +(0.118034 + 0.0857567i) q^{74} +(0.809017 - 0.587785i) q^{75} +(2.04702 - 6.30007i) q^{76} +(0.750469 - 0.545247i) q^{77} +(3.39847 - 2.46914i) q^{78} +(-4.09172 + 12.5930i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.61704 + 8.05441i) q^{82} +(-7.08111 - 5.14473i) q^{83} +(-0.167143 + 0.514413i) q^{84} +(-0.833670 + 2.56577i) q^{85} +(1.81855 + 5.59694i) q^{86} +4.35117 q^{87} -1.71502 q^{88} +(-0.291590 - 0.897422i) q^{89} +(0.809017 - 0.587785i) q^{90} +(-1.83819 - 1.33552i) q^{91} +6.65491 q^{92} +(-5.13779 + 2.14549i) q^{93} +0.966670 q^{94} +(5.35916 + 3.89366i) q^{95} +(0.809017 - 0.587785i) q^{96} +(1.98053 + 6.09543i) q^{97} -6.70744 q^{98} -1.71502 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	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 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 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	0.167143	+	0.514413i	0.0631741	+	0.194430i	0.977662	−	0.210183i	$-0.0674061\pi$
$7$	0.167143	+	0.514413i	0.0631741	+	0.194430i	−0.914488	+	0.404613i	$0.867406\pi$
$8$	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
$11$	−0.529970	−	1.63108i	−0.159792	−	0.491789i	0.838823	−	0.544404i	$-0.183244\pi$
$11$	−0.529970	−	1.63108i	−0.159792	−	0.491789i	−0.998615	+	0.0526152i	$0.983244\pi$
$12$	0.809017	+	0.587785i	0.233543	+	0.169679i
$13$	−3.39847	+	2.46914i	−0.942567	+	0.684815i	−0.949037	−	0.315164i	$-0.897940\pi$
$13$	−3.39847	+	2.46914i	−0.942567	+	0.684815i	0.00647039	+	0.999979i	$0.497940\pi$
$14$	0.167143	−	0.514413i	0.0446708	−	0.137483i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.833670	−	2.56577i	0.202195	−	0.622291i	−0.797622	−	0.603157i	$-0.793909\pi$
$17$	0.833670	−	2.56577i	0.202195	−	0.622291i	0.999817	−	0.0191338i	$-0.00609085\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	−5.35916	−	3.89366i	−1.22948	−	0.893266i	−0.232624	−	0.972567i	$-0.574731\pi$
$19$	−5.35916	−	3.89366i	−1.22948	−	0.893266i	−0.996851	+	0.0793006i	$0.974731\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	0.437586	+	0.317925i	0.0954891	+	0.0693769i
$22$	−0.529970	+	1.63108i	−0.112990	+	0.347748i
$23$	2.05648	−	6.32920i	0.428806	−	1.31973i	−0.470497	−	0.882402i	$-0.655925\pi$
$23$	2.05648	−	6.32920i	0.428806	−	1.31973i	0.899303	−	0.437327i	$-0.144075\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	1.00000			0.200000
$26$	4.20074			0.823834
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−0.437586	+	0.317925i	−0.0826960	+	0.0600822i
$29$	3.52017	+	2.55755i	0.653679	+	0.474926i	0.864523	−	0.502594i	$-0.167621\pi$
$29$	3.52017	+	2.55755i	0.653679	+	0.474926i	−0.210843	+	0.977520i	$0.567621\pi$
$30$	1.00000			0.182574
$31$	−5.41765	−	1.28417i	−0.973038	−	0.230645i
$31$	−5.41765	−	1.28417i	−0.973038	−	0.230645i
$32$	1.00000			0.176777
$33$	−1.38748	−	1.00806i	−0.241529	−	0.175481i
$34$	−2.18258	+	1.58573i	−0.374309	+	0.271951i
$35$	−0.167143	−	0.514413i	−0.0282523	−	0.0869517i
$36$	1.00000			0.166667
$37$	−0.145898			−0.0239855			−0.0119927	−	0.999928i	$-0.503818\pi$
$37$	−0.145898			−0.0239855			−0.0119927	+	0.999928i	$0.503818\pi$
$38$	2.04702	+	6.30007i	0.332070	+	1.02201i
$39$	−1.29810	+	3.99514i	−0.207863	+	0.639735i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	−6.85149	−	4.97790i	−1.07002	−	0.777417i	−0.0941068	−	0.995562i	$-0.530000\pi$
$41$	−6.85149	−	4.97790i	−1.07002	−	0.777417i	−0.975916	+	0.218145i	$0.930000\pi$
$42$	−0.167143	−	0.514413i	−0.0257907	−	0.0793757i
$43$	−4.76104	−	3.45910i	−0.726052	−	0.527507i	0.162260	−	0.986748i	$-0.448122\pi$
$43$	−4.76104	−	3.45910i	−0.726052	−	0.527507i	−0.888312	+	0.459241i	$0.848122\pi$
$44$	1.38748	−	1.00806i	0.209170	−	0.151971i
$45$	−0.309017	+	0.951057i	−0.0460655	+	0.141775i
$46$	−5.38394	+	3.91166i	−0.793818	+	0.576743i
$47$	−0.782052	+	0.568194i	−0.114074	+	0.0828796i	−0.643360	−	0.765564i	$-0.722460\pi$
$47$	−0.782052	+	0.568194i	−0.114074	+	0.0828796i	0.529286	+	0.848444i	$0.322460\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	5.42643	−	3.94254i	0.775205	−	0.563219i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	−0.833670	−	2.56577i	−0.116737	−	0.359280i
$52$	−3.39847	−	2.46914i	−0.471283	−	0.342407i
$53$	4.10493	−	12.6337i	0.563855	−	1.73537i	−0.107475	−	0.994208i	$-0.534276\pi$
$53$	4.10493	−	12.6337i	0.563855	−	1.73537i	0.671329	−	0.741159i	$-0.265724\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	0.529970	+	1.63108i	0.0714612	+	0.219935i
$56$	0.540886			0.0722789
$57$	−6.62428			−0.877408
$58$	−1.34459	−	4.13821i	−0.176553	−	0.543373i
$59$	−2.57653	+	1.87196i	−0.335436	+	0.243708i	−0.742734	−	0.669587i	$-0.766471\pi$
$59$	−2.57653	+	1.87196i	−0.335436	+	0.243708i	0.407298	+	0.913295i	$0.366471\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	−13.6341			−1.74566			−0.872832	−	0.488020i	$-0.837719\pi$
$61$	−13.6341			−1.74566			−0.872832	+	0.488020i	$0.837719\pi$
$62$	3.62815	+	4.22333i	0.460775	+	0.536364i
$63$	0.540886			0.0681452
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	3.39847	−	2.46914i	0.421529	−	0.306259i
$66$	0.529970	+	1.63108i	0.0652348	+	0.200772i
$67$	13.9954			1.70982			0.854908	−	0.518780i	$-0.173614\pi$
$67$	13.9954			1.70982			0.854908	+	0.518780i	$0.173614\pi$
$68$	2.69781			0.327158
$69$	−2.05648	−	6.32920i	−0.247571	−	0.761946i
$70$	−0.167143	+	0.514413i	−0.0199774	+	0.0614841i
$71$	−2.94315	+	9.05808i	−0.349287	+	1.07500i	0.609961	+	0.792431i	$0.291185\pi$
$71$	−2.94315	+	9.05808i	−0.349287	+	1.07500i	−0.959248	+	0.282564i	$0.908815\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	1.52334	+	4.68835i	0.178293	+	0.548730i	0.999769	−	0.0215140i	$-0.00684865\pi$
$73$	1.52334	+	4.68835i	0.178293	+	0.548730i	−0.821475	+	0.570244i	$0.806849\pi$
$74$	0.118034	+	0.0857567i	0.0137212	+	0.00996902i
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$	2.04702	−	6.30007i	0.234809	−	0.722667i
$77$	0.750469	−	0.545247i	0.0855238	−	0.0621367i
$78$	3.39847	−	2.46914i	0.384801	−	0.279574i
$79$	−4.09172	+	12.5930i	−0.460355	+	1.41683i	0.404378	+	0.914592i	$0.367488\pi$
$79$	−4.09172	+	12.5930i	−0.460355	+	1.41683i	−0.864732	+	0.502233i	$0.832512\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	2.61704	+	8.05441i	0.289003	+	0.889461i
$83$	−7.08111	−	5.14473i	−0.777253	−	0.564707i	0.126901	−	0.991915i	$-0.459497\pi$
$83$	−7.08111	−	5.14473i	−0.777253	−	0.564707i	−0.904153	+	0.427208i	$0.859497\pi$
$84$	−0.167143	+	0.514413i	−0.0182368	+	0.0561271i
$85$	−0.833670	+	2.56577i	−0.0904242	+	0.278297i
$86$	1.81855	+	5.59694i	0.196100	+	0.603533i
$87$	4.35117			0.466494
$88$	−1.71502			−0.182822
$89$	−0.291590	−	0.897422i	−0.0309085	−	0.0951265i	0.934412	−	0.356194i	$-0.115926\pi$
$89$	−0.291590	−	0.897422i	−0.0309085	−	0.0951265i	−0.965321	+	0.261067i	$0.915926\pi$
$90$	0.809017	−	0.587785i	0.0852779	−	0.0619580i
$91$	−1.83819	−	1.33552i	−0.192694	−	0.140001i
$92$	6.65491			0.693822
$93$	−5.13779	+	2.14549i	−0.532764	+	0.222477i
$94$	0.966670			0.0997044
$95$	5.35916	+	3.89366i	0.549838	+	0.399481i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	1.98053	+	6.09543i	0.201092	+	0.618897i	0.999851	+	0.0172467i	$0.00549006\pi$
$97$	1.98053	+	6.09543i	0.201092	+	0.618897i	−0.798759	+	0.601651i	$0.794510\pi$
$98$	−6.70744			−0.677554
$99$	−1.71502			−0.172366
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−0.246270	+	0.757940i	−0.0245048	+	0.0754179i	−0.962561	−	0.271065i	$-0.912624\pi$
$101$	−0.246270	+	0.757940i	−0.0245048	+	0.0754179i	0.938056	+	0.346483i	$0.112624\pi$
$102$	−0.833670	+	2.56577i	−0.0825456	+	0.254049i
$103$	−13.2760	−	9.64558i	−1.30812	−	0.950407i	−0.308123	−	0.951346i	$-0.599701\pi$
$103$	−13.2760	−	9.64558i	−1.30812	−	0.950407i	−1.00000		0.000939746i	$0.999701\pi$
$104$	1.29810	+	3.99514i	0.127289	+	0.391756i
$105$	−0.437586	−	0.317925i	−0.0427040	−	0.0310263i
$106$	−10.7468	+	7.80803i	−1.04382	+	0.758383i
$107$	3.68948	−	11.3551i	0.356676	−	1.09774i	−0.598356	−	0.801231i	$-0.704179\pi$
$107$	3.68948	−	11.3551i	0.356676	−	1.09774i	0.955031	−	0.296505i	$-0.0958210\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−9.23491	+	6.70956i	−0.884544	+	0.642659i	−0.934450	−	0.356095i	$-0.884108\pi$
$109$	−9.23491	+	6.70956i	−0.884544	+	0.642659i	0.0499056	+	0.998754i	$0.484108\pi$
$110$	0.529970	−	1.63108i	0.0505307	−	0.155517i
$111$	−0.118034	+	0.0857567i	−0.0112033	+	0.00813967i
$112$	−0.437586	−	0.317925i	−0.0413480	−	0.0300411i
$113$	2.39033	+	7.35669i	0.224864	+	0.692059i	0.998305	+	0.0581920i	$0.0185335\pi$
$113$	2.39033	+	7.35669i	0.224864	+	0.692059i	−0.773442	+	0.633867i	$0.781466\pi$
$114$	5.35916	+	3.89366i	0.501931	+	0.364674i
$115$	−2.05648	+	6.32920i	−0.191768	+	0.590201i
$116$	−1.34459	+	4.13821i	−0.124842	+	0.384223i
$117$	1.29810	+	3.99514i	0.120009	+	0.369351i
$118$	3.18477			0.293182
$119$	1.45921			0.133765
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	6.51963	−	4.73679i	0.592694	−	0.430617i
$122$	11.0302	+	8.01391i	0.998628	+	0.725545i
$123$	−8.46891			−0.763616
$124$	−0.452822	−	5.54932i	−0.0406646	−	0.498344i
$125$	−1.00000			−0.0894427
$126$	−0.437586	−	0.317925i	−0.0389833	−	0.0283230i
$127$	17.8570	−	12.9739i	1.58456	−	1.15125i	0.673330	−	0.739342i	$-0.264863\pi$
$127$	17.8570	−	12.9739i	1.58456	−	1.15125i	0.911227	−	0.411905i	$-0.135137\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−5.88497			−0.518143
$130$	−4.20074			−0.368430
$131$	−4.33522	−	13.3424i	−0.378770	−	1.16573i	−0.940900	−	0.338685i	$-0.890018\pi$
$131$	−4.33522	−	13.3424i	−0.378770	−	1.16573i	0.562130	−	0.827049i	$-0.309982\pi$
$132$	0.529970	−	1.63108i	0.0461280	−	0.141967i
$133$	1.10720	−	3.40762i	0.0960066	−	0.295478i
$134$	−11.3226	−	8.22632i	−0.978120	−	0.710646i
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$	−2.18258	−	1.58573i	−0.187154	−	0.135976i
$137$	−5.38600	+	3.91316i	−0.460157	+	0.334324i	−0.793593	−	0.608449i	$-0.791792\pi$
$137$	−5.38600	+	3.91316i	−0.460157	+	0.334324i	0.333436	+	0.942773i	$0.391792\pi$
$138$	−2.05648	+	6.32920i	−0.175059	+	0.538777i
$139$	−6.81824	+	4.95374i	−0.578315	+	0.420171i	−0.838116	−	0.545491i	$-0.816343\pi$
$139$	−6.81824	+	4.95374i	−0.578315	+	0.420171i	0.259801	+	0.965662i	$0.416343\pi$
$140$	0.437586	−	0.317925i	0.0369828	−	0.0268696i
$141$	−0.298717	+	0.919357i	−0.0251565	+	0.0774239i
$142$	7.70526	−	5.59820i	0.646611	−	0.469790i
$143$	5.82845	+	4.23461i	0.487399	+	0.354116i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	−3.52017	−	2.55755i	−0.292334	−	0.212393i
$146$	1.52334	−	4.68835i	0.126072	−	0.388011i
$147$	2.07271	−	6.37916i	0.170955	−	0.526144i
$148$	−0.0450850	−	0.138757i	−0.00370596	−	0.0114058i
$149$	11.5879			0.949316			0.474658	−	0.880170i	$-0.342572\pi$
$149$	11.5879			0.949316			0.474658	+	0.880170i	$0.342572\pi$
$150$	−1.00000			−0.0816497
$151$	2.71869	+	8.36728i	0.221244	+	0.680919i	0.998651	+	0.0519216i	$0.0165346\pi$
$151$	2.71869	+	8.36728i	0.221244	+	0.680919i	−0.777407	+	0.628998i	$0.783465\pi$
$152$	−5.35916	+	3.89366i	−0.434685	+	0.315817i
$153$	−2.18258	−	1.58573i	−0.176451	−	0.128199i
$154$	−0.927630			−0.0747506
$155$	5.41765	+	1.28417i	0.435156	+	0.103147i
$156$	−4.20074			−0.336329
$157$	6.81562	+	4.95184i	0.543946	+	0.395200i	0.825548	−	0.564331i	$-0.190866\pi$
$157$	6.81562	+	4.95184i	0.543946	+	0.395200i	−0.281602	+	0.959531i	$0.590866\pi$
$158$	10.7123	−	7.78291i	0.852222	−	0.619175i
$159$	−4.10493	−	12.6337i	−0.325542	−	1.00191i
$160$	−1.00000			−0.0790569
$161$	3.59955			0.283684
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−0.714291	+	2.19836i	−0.0559476	+	0.172189i	−0.975125	−	0.221654i	$-0.928855\pi$
$163$	−0.714291	+	2.19836i	−0.0559476	+	0.172189i	0.919178	+	0.393843i	$0.128855\pi$
$164$	2.61704	−	8.05441i	0.204356	−	0.628944i
$165$	1.38748	+	1.00806i	0.108015	+	0.0784776i
$166$	2.70474	+	8.32434i	0.209929	+	0.646094i
$167$	14.5424	+	10.5656i	1.12532	+	0.817594i	0.985007	−	0.172514i	$-0.0551889\pi$
$167$	14.5424	+	10.5656i	1.12532	+	0.817594i	0.140314	+	0.990107i	$0.455189\pi$
$168$	0.437586	−	0.317925i	0.0337605	−	0.0245284i
$169$	1.43577	−	4.41884i	0.110444	−	0.339911i
$170$	2.18258	−	1.58573i	0.167396	−	0.121620i
$171$	−5.35916	+	3.89366i	−0.409825	+	0.297755i
$172$	1.81855	−	5.59694i	0.138664	−	0.426762i
$173$	−7.38007	+	5.36193i	−0.561096	+	0.407660i	−0.831860	−	0.554986i	$-0.812724\pi$
$173$	−7.38007	+	5.36193i	−0.561096	+	0.407660i	0.270764	+	0.962646i	$0.412724\pi$
$174$	−3.52017	−	2.55755i	−0.266863	−	0.193888i
$175$	0.167143	+	0.514413i	0.0126348	+	0.0388860i
$176$	1.38748	+	1.00806i	0.104585	+	0.0759856i
$177$	−0.984148	+	3.02889i	−0.0739731	+	0.227666i
$178$	−0.291590	+	0.897422i	−0.0218556	+	0.0672646i
$179$	−7.90920	−	24.3420i	−0.591162	−	1.81941i	−0.572973	−	0.819574i	$-0.694210\pi$
$179$	−7.90920	−	24.3420i	−0.591162	−	1.81941i	−0.0181884	−	0.999835i	$-0.505790\pi$
$180$	−1.00000			−0.0745356
$181$	−8.21209			−0.610400			−0.305200	−	0.952288i	$-0.598723\pi$
$181$	−8.21209			−0.610400			−0.305200	+	0.952288i	$0.598723\pi$
$182$	0.702125	+	2.16092i	0.0520450	+	0.160178i
$183$	−11.0302	+	8.01391i	−0.815376	+	0.592405i
$184$	−5.38394	−	3.91166i	−0.396909	−	0.288371i
$185$	0.145898			0.0107266
$186$	5.41765	+	1.28417i	0.397241	+	0.0941602i
$187$	−4.62680			−0.338345
$188$	−0.782052	−	0.568194i	−0.0570370	−	0.0414398i
$189$	0.437586	−	0.317925i	0.0318297	−	0.0231256i
$190$	−2.04702	−	6.30007i	−0.148506	−	0.457055i
$191$	12.3456			0.893293			0.446646	−	0.894711i	$-0.352618\pi$
$191$	12.3456			0.893293			0.446646	+	0.894711i	$0.352618\pi$
$192$	−1.00000			−0.0721688
$193$	3.85546	+	11.8659i	0.277522	+	0.854126i	0.988541	+	0.150953i	$0.0482341\pi$
$193$	3.85546	+	11.8659i	0.277522	+	0.854126i	−0.711019	+	0.703173i	$0.751766\pi$
$194$	1.98053	−	6.09543i	0.142193	−	0.437627i
$195$	1.29810	−	3.99514i	0.0929590	−	0.286098i
$196$	5.42643	+	3.94254i	0.387602	+	0.281610i
$197$	1.85123	+	5.69751i	0.131895	+	0.405931i	0.995094	−	0.0989328i	$-0.0315429\pi$
$197$	1.85123	+	5.69751i	0.131895	+	0.405931i	−0.863199	+	0.504863i	$0.831543\pi$
$198$	1.38748	+	1.00806i	0.0986039	+	0.0716399i
$199$	14.4980	−	10.5334i	1.02774	−	0.746694i	0.0598814	−	0.998206i	$-0.480928\pi$
$199$	14.4980	−	10.5334i	1.02774	−	0.746694i	0.967854	+	0.251512i	$0.0809278\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	11.3226	−	8.22632i	0.798631	−	0.580240i
$202$	0.644743	−	0.468433i	0.0453639	−	0.0329588i
$203$	−0.727268	+	2.23830i	−0.0510442	+	0.157098i
$204$	2.18258	−	1.58573i	0.152811	−	0.111024i
$205$	6.85149	+	4.97790i	0.478529	+	0.347672i
$206$	5.07098	+	15.6069i	0.353312	+	1.08738i
$207$	−5.38394	−	3.91166i	−0.374209	−	0.271879i
$208$	1.29810	−	3.99514i	0.0900071	−	0.277013i
$209$	−3.51067	+	10.8047i	−0.242838	+	0.747380i
$210$	0.167143	+	0.514413i	0.0115340	+	0.0354979i
$211$	−8.61380			−0.592999			−0.296499	−	0.955033i	$-0.595819\pi$
$211$	−8.61380			−0.592999			−0.296499	+	0.955033i	$0.595819\pi$
$212$	13.2838			0.912336
$213$	2.94315	+	9.05808i	0.201661	+	0.620649i
$214$	−9.65919	+	7.01781i	−0.660289	+	0.479728i
$215$	4.76104	+	3.45910i	0.324700	+	0.235908i
$216$	−1.00000			−0.0680414
$217$	−0.244925	−	3.00155i	−0.0166266	−	0.203758i
$218$	11.4150			0.773120
$219$	3.98815	+	2.89756i	0.269494	+	0.195799i
$220$	−1.38748	+	1.00806i	−0.0935439	+	0.0679636i
$221$	3.50203	+	10.7781i	0.235572	+	0.725017i
$222$	0.145898			0.00979203
$223$	26.2708			1.75922			0.879612	−	0.475691i	$-0.157802\pi$
$223$	26.2708			1.75922			0.879612	+	0.475691i	$0.157802\pi$
$224$	0.167143	+	0.514413i	0.0111677	+	0.0343707i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	2.39033	−	7.35669i	0.159003	−	0.489360i
$227$	19.2270	+	13.9692i	1.27614	+	0.927170i	0.999429	−	0.0337839i	$-0.0107558\pi$
$227$	19.2270	+	13.9692i	1.27614	+	0.927170i	0.276710	+	0.960953i	$0.410756\pi$
$228$	−2.04702	−	6.30007i	−0.135567	−	0.417232i
$229$	19.8312	+	14.4082i	1.31048	+	0.952122i	0.999999	+	0.00154352i	$0.000491319\pi$
$229$	19.8312	+	14.4082i	1.31048	+	0.952122i	0.310485	+	0.950578i	$0.399509\pi$
$230$	5.38394	−	3.91166i	0.355006	−	0.257927i
$231$	0.286654	−	0.882229i	0.0188604	−	0.0580464i
$232$	3.52017	−	2.55755i	0.231111	−	0.167912i
$233$	10.8550	−	7.88662i	0.711135	−	0.516669i	−0.172405	−	0.985026i	$-0.555154\pi$
$233$	10.8550	−	7.88662i	0.711135	−	0.516669i	0.883539	+	0.468357i	$0.155154\pi$
$234$	1.29810	−	3.99514i	0.0848595	−	0.261171i
$235$	0.782052	−	0.568194i	0.0510155	−	0.0370649i
$236$	−2.57653	−	1.87196i	−0.167718	−	0.121854i
$237$	4.09172	+	12.5930i	0.265786	+	0.818005i
$238$	−1.18052	−	0.857702i	−0.0765221	−	0.0555965i
$239$	−0.00619940	+	0.0190798i	−0.000401006	+	0.00123417i	−0.951257	−	0.308400i	$-0.900207\pi$
$239$	−0.00619940	+	0.0190798i	−0.000401006	+	0.00123417i	0.950856	+	0.309634i	$0.100207\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	−5.92887	−	18.2472i	−0.381912	−	1.17541i	−0.938695	−	0.344747i	$-0.887965\pi$
$241$	−5.92887	−	18.2472i	−0.381912	−	1.17541i	0.556783	−	0.830658i	$-0.312035\pi$
$242$	−8.05871			−0.518033
$243$	−1.00000			−0.0641500
$244$	−4.21316	−	12.9668i	−0.269720	−	0.830113i
$245$	−5.42643	+	3.94254i	−0.346682	+	0.251879i
$246$	6.85149	+	4.97790i	0.436835	+	0.317379i
$247$	27.8269			1.77058
$248$	−2.89547	+	4.75566i	−0.183862	+	0.301984i
$249$	−8.75273			−0.554682
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	2.41877	−	1.75734i	0.152671	−	0.110922i	−0.508827	−	0.860869i	$-0.669921\pi$
$251$	2.41877	−	1.75734i	0.152671	−	0.110922i	0.661499	+	0.749946i	$0.269921\pi$
$252$	0.167143	+	0.514413i	0.0105290	+	0.0324050i
$253$	−11.4133			−0.717548
$254$	−22.0725			−1.38495
$255$	0.833670	+	2.56577i	0.0522064	+	0.160675i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	1.71261	−	5.27086i	0.106830	−	0.328787i	−0.883326	−	0.468759i	$-0.844701\pi$
$257$	1.71261	−	5.27086i	0.106830	−	0.328787i	0.990155	+	0.139972i	$0.0447012\pi$
$258$	4.76104	+	3.45910i	0.296409	+	0.215354i
$259$	−0.0243858	−	0.0750519i	−0.00151526	−	0.00466350i
$260$	3.39847	+	2.46914i	0.210764	+	0.153129i
$261$	3.52017	−	2.55755i	0.217893	−	0.158309i
$262$	−4.33522	+	13.3424i	−0.267831	+	0.824298i
$263$	6.85948	−	4.98371i	0.422974	−	0.307309i	−0.355859	−	0.934540i	$-0.615812\pi$
$263$	6.85948	−	4.98371i	0.422974	−	0.307309i	0.778833	+	0.627231i	$0.215812\pi$
$264$	−1.38748	+	1.00806i	−0.0853935	+	0.0620420i
$265$	−4.10493	+	12.6337i	−0.252164	+	0.776080i
$266$	−2.89869	+	2.10602i	−0.177730	+	0.129129i
$267$	−0.763393	−	0.554637i	−0.0467189	−	0.0339433i
$268$	4.32483	+	13.3105i	0.264181	+	0.813066i
$269$	0.174790	+	0.126992i	0.0106571	+	0.00774284i	0.593101	−	0.805128i	$-0.297903\pi$
$269$	0.174790	+	0.126992i	0.0106571	+	0.00774284i	−0.582444	+	0.812871i	$0.697903\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	6.85325	−	21.0921i	0.416305	−	1.28126i	−0.494773	−	0.869022i	$-0.664749\pi$
$271$	6.85325	−	21.0921i	0.416305	−	1.28126i	0.911078	−	0.412234i	$-0.135251\pi$
$272$	0.833670	+	2.56577i	0.0505487	+	0.155573i
$273$	−2.27212			−0.137515
$274$	6.65747			0.402192
$275$	−0.529970	−	1.63108i	−0.0319584	−	0.0983579i
$276$	5.38394	−	3.91166i	0.324075	−	0.235454i
$277$	13.8697	+	10.0770i	0.833352	+	0.605465i	0.920506	−	0.390729i	$-0.127777\pi$
$277$	13.8697	+	10.0770i	0.833352	+	0.605465i	−0.0871539	+	0.996195i	$0.527777\pi$
$278$	8.42781			0.505466
$279$	−2.89547	+	4.75566i	−0.173347	+	0.284714i
$280$	−0.540886			−0.0323241
$281$	−7.30218	−	5.30535i	−0.435612	−	0.316490i	0.348277	−	0.937392i	$-0.386767\pi$
$281$	−7.30218	−	5.30535i	−0.435612	−	0.316490i	−0.783889	+	0.620901i	$0.786767\pi$
$282$	0.782052	−	0.568194i	0.0465705	−	0.0338355i
$283$	−6.10257	−	18.7818i	−0.362760	−	1.11646i	−0.951372	−	0.308045i	$-0.900325\pi$
$283$	−6.10257	−	18.7818i	−0.362760	−	1.11646i	0.588612	−	0.808416i	$-0.299675\pi$
$284$	−9.52423			−0.565159
$285$	6.62428			0.392389
$286$	−2.22627	−	6.85175i	−0.131642	−	0.405153i
$287$	1.41552	−	4.35652i	0.0835554	−	0.257157i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	7.86511	+	5.71434i	0.462654	+	0.336137i
$290$	1.34459	+	4.13821i	0.0789568	+	0.243004i
$291$	5.18508	+	3.76718i	0.303955	+	0.220836i
$292$	−3.98815	+	2.89756i	−0.233389	+	0.169567i
$293$	2.82995	−	8.70970i	0.165328	−	0.508826i	−0.833733	−	0.552168i	$-0.813801\pi$
$293$	2.82995	−	8.70970i	0.165328	−	0.508826i	0.999060	+	0.0433424i	$0.0138006\pi$
$294$	−5.42643	+	3.94254i	−0.316476	+	0.229933i
$295$	2.57653	−	1.87196i	0.150011	−	0.108990i
$296$	−0.0450850	+	0.138757i	−0.00262051	+	0.00806510i
$297$	−1.38748	+	1.00806i	−0.0805098	+	0.0584938i
$298$	−9.37479	−	6.81119i	−0.543067	−	0.394561i
$299$	8.63875	+	26.5873i	0.499592	+	1.53758i
$300$	0.809017	+	0.587785i	0.0467086	+	0.0339358i
$301$	0.983631	−	3.02731i	0.0566956	−	0.174491i
$302$	2.71869	−	8.36728i	0.156443	−	0.481483i
$303$	0.246270	+	0.757940i	0.0141478	+	0.0435425i
$304$	6.62428			0.379929
$305$	13.6341			0.780685
$306$	0.833670	+	2.56577i	0.0476577	+	0.146675i
$307$	10.9939	−	7.98756i	0.627457	−	0.455874i	−0.228061	−	0.973647i	$-0.573239\pi$
$307$	10.9939	−	7.98756i	0.627457	−	0.455874i	0.855518	+	0.517772i	$0.173239\pi$
$308$	0.750469	+	0.545247i	0.0427619	+	0.0310684i
$309$	−16.4100			−0.933534
$310$	−3.62815	−	4.22333i	−0.206065	−	0.239869i
$311$	2.05628			0.116601			0.0583003	−	0.998299i	$-0.481432\pi$
$311$	2.05628			0.116601			0.0583003	+	0.998299i	$0.481432\pi$
$312$	3.39847	+	2.46914i	0.192401	+	0.139787i
$313$	−7.03045	+	5.10792i	−0.397385	+	0.288717i	−0.768475	−	0.639880i	$-0.778984\pi$
$313$	−7.03045	+	5.10792i	−0.397385	+	0.288717i	0.371090	+	0.928597i	$0.378984\pi$
$314$	−2.60334	−	8.01225i	−0.146915	−	0.452157i
$315$	−0.540886			−0.0304755
$316$	−13.2411			−0.744869
$317$	−2.59962	−	8.00080i	−0.146009	−	0.449370i	0.851130	−	0.524954i	$-0.175918\pi$
$317$	−2.59962	−	8.00080i	−0.146009	−	0.449370i	−0.997139	+	0.0755848i	$0.975918\pi$
$318$	−4.10493	+	12.6337i	−0.230193	+	0.708461i
$319$	2.30599	−	7.09711i	0.129111	−	0.397362i
$320$	0.809017	+	0.587785i	0.0452254	+	0.0328582i
$321$	−3.68948	−	11.3551i	−0.205927	−	0.633778i
$322$	−2.91210	−	2.11576i	−0.162285	−	0.117907i
$323$	−14.4580	+	10.5044i	−0.804465	+	0.584478i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	−3.39847	+	2.46914i	−0.188513	+	0.136963i
$326$	1.87004	−	1.35866i	0.103572	−	0.0752494i
$327$	−3.52742	+	10.8563i	−0.195067	+	0.600354i
$328$	−6.85149	+	4.97790i	−0.378310	+	0.274859i
$329$	−0.423001	−	0.307328i	−0.0233208	−	0.0169436i
$330$	−0.529970	−	1.63108i	−0.0291739	−	0.0897880i
$331$	13.9045	+	10.1022i	0.764259	+	0.555267i	0.900214	−	0.435448i	$-0.143410\pi$
$331$	13.9045	+	10.1022i	0.764259	+	0.555267i	−0.135955	+	0.990715i	$0.543410\pi$
$332$	2.70474	−	8.32434i	0.148442	−	0.456858i
$333$	−0.0450850	+	0.138757i	−0.00247064	+	0.00760385i
$334$	−5.55468	−	17.0956i	−0.303939	−	0.935427i
$335$	−13.9954			−0.764653
$336$	−0.540886			−0.0295078
$337$	4.82888	+	14.8618i	0.263046	+	0.809572i	0.992137	+	0.125156i	$0.0399430\pi$
$337$	4.82888	+	14.8618i	0.263046	+	0.809572i	−0.729091	+	0.684417i	$0.760057\pi$
$338$	−3.75889	+	2.73099i	−0.204457	+	0.148547i
$339$	6.25798	+	4.54669i	0.339887	+	0.246942i
$340$	−2.69781			−0.146309
$341$	0.776599	+	9.51719i	0.0420552	+	0.515385i
$342$	6.62428			0.358200
$343$	5.99819	+	4.35794i	0.323872	+	0.235306i
$344$	−4.76104	+	3.45910i	−0.256698	+	0.186502i
$345$	2.05648	+	6.32920i	0.110717	+	0.340752i
$346$	9.12227			0.490416
$347$	−25.9126			−1.39106			−0.695530	−	0.718497i	$-0.744830\pi$
$347$	−25.9126			−1.39106			−0.695530	+	0.718497i	$0.744830\pi$
$348$	1.34459	+	4.13821i	0.0720774	+	0.221831i
$349$	−6.27038	+	19.2983i	−0.335646	+	1.03301i	0.630757	+	0.775980i	$0.282744\pi$
$349$	−6.27038	+	19.2983i	−0.335646	+	1.03301i	−0.966403	+	0.257032i	$0.917256\pi$
$350$	0.167143	−	0.514413i	0.00893417	−	0.0274965i
$351$	3.39847	+	2.46914i	0.181397	+	0.131793i
$352$	−0.529970	−	1.63108i	−0.0282475	−	0.0869369i
$353$	−22.8055	−	16.5692i	−1.21381	−	0.881887i	−0.218242	−	0.975895i	$-0.570032\pi$
$353$	−22.8055	−	16.5692i	−1.21381	−	0.881887i	−0.995571	+	0.0940077i	$0.970032\pi$
$354$	2.57653	−	1.87196i	0.136941	−	0.0994935i
$355$	2.94315	−	9.05808i	0.156206	−	0.480753i
$356$	0.763393	−	0.554637i	0.0404597	−	0.0293957i
$357$	1.18052	−	0.857702i	0.0624800	−	0.0453944i
$358$	−7.90920	+	24.3420i	−0.418014	+	1.28652i
$359$	−5.97670	+	4.34233i	−0.315438	+	0.229179i	−0.734226	−	0.678905i	$-0.762455\pi$
$359$	−5.97670	+	4.34233i	−0.315438	+	0.229179i	0.418788	+	0.908084i	$0.362455\pi$
$360$	0.809017	+	0.587785i	0.0426389	+	0.0309790i
$361$	7.68869	+	23.6634i	0.404668	+	1.24544i
$362$	6.64372	+	4.82695i	0.349186	+	0.253699i
$363$	2.49028	−	7.66429i	0.130706	−	0.402271i
$364$	0.702125	−	2.16092i	0.0368013	−	0.113263i
$365$	−1.52334	−	4.68835i	−0.0797351	−	0.245400i
$366$	13.6341			0.712665
$367$	−17.8739			−0.933010			−0.466505	−	0.884519i	$-0.654487\pi$
$367$	−17.8739			−0.933010			−0.466505	+	0.884519i	$0.654487\pi$
$368$	2.05648	+	6.32920i	0.107201	+	0.329932i
$369$	−6.85149	+	4.97790i	−0.356674	+	0.259139i
$370$	−0.118034	−	0.0857567i	−0.00613629	−	0.00445828i
$371$	7.18503			0.373028
$372$	−3.62815	−	4.22333i	−0.188111	−	0.218970i
$373$	−14.3523			−0.743135			−0.371568	−	0.928406i	$-0.621180\pi$
$373$	−14.3523			−0.743135			−0.371568	+	0.928406i	$0.621180\pi$
$374$	3.74316	+	2.71957i	0.193554	+	0.140625i
$375$	−0.809017	+	0.587785i	−0.0417775	+	0.0303531i
$376$	0.298717	+	0.919357i	0.0154052	+	0.0474122i
$377$	−18.2782			−0.941373
$378$	−0.540886			−0.0278202
$379$	−7.55097	−	23.2395i	−0.387867	−	1.19373i	−0.934379	−	0.356281i	$-0.884045\pi$
$379$	−7.55097	−	23.2395i	−0.387867	−	1.19373i	0.546512	−	0.837452i	$-0.315955\pi$
$380$	−2.04702	+	6.30007i	−0.105010	+	0.323187i
$381$	6.82078	−	20.9922i	0.349439	−	1.07546i
$382$	−9.98776	−	7.25653i	−0.511018	−	0.371277i
$383$	−4.09969	−	12.6175i	−0.209484	−	0.644726i	−0.999499	−	0.0316390i	$-0.989927\pi$
$383$	−4.09969	−	12.6175i	−0.209484	−	0.644726i	0.790015	−	0.613087i	$-0.210073\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$	−0.750469	+	0.545247i	−0.0382474	+	0.0277884i
$386$	3.85546	−	11.8659i	0.196238	−	0.603958i
$387$	−4.76104	+	3.45910i	−0.242017	+	0.175836i
$388$	−5.18508	+	3.76718i	−0.263233	+	0.191250i
$389$	4.63289	−	14.2586i	0.234897	−	0.722939i	−0.762238	−	0.647297i	$-0.775899\pi$
$389$	4.63289	−	14.2586i	0.234897	−	0.722939i	0.997135	−	0.0756419i	$-0.0241006\pi$
$390$	−3.39847	+	2.46914i	−0.172088	+	0.125030i
$391$	−14.5248	−	10.5529i	−0.734553	−	0.533684i
$392$	−2.07271	−	6.37916i	−0.104688	−	0.322196i
$393$	−11.3498	−	8.24608i	−0.572519	−	0.415960i
$394$	1.85123	−	5.69751i	0.0932637	−	0.287036i
$395$	4.09172	−	12.5930i	0.205877	−	0.633624i
$396$	−0.529970	−	1.63108i	−0.0266320	−	0.0819649i
$397$	23.5930			1.18410			0.592050	−	0.805902i	$-0.298319\pi$
$397$	23.5930			1.18410			0.592050	+	0.805902i	$0.298319\pi$
$398$	−17.9205			−0.898274
$399$	−1.10720	−	3.40762i	−0.0554295	−	0.170594i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	12.8514	+	9.33712i	0.641770	+	0.466274i	0.860458	−	0.509521i	$-0.170178\pi$
$401$	12.8514	+	9.33712i	0.641770	+	0.466274i	−0.218687	+	0.975795i	$0.570178\pi$
$402$	−13.9954			−0.698029
$403$	21.5825	−	9.01267i	1.07510	−	0.448953i
$404$	−0.796946			−0.0396495
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	1.90401	−	1.38335i	0.0944945	−	0.0686543i
$407$	0.0773216	+	0.237971i	0.00383269	+	0.0117958i
$408$	−2.69781			−0.133562
$409$	−17.5666			−0.868611			−0.434306	−	0.900766i	$-0.643006\pi$
$409$	−17.5666			−0.868611			−0.434306	+	0.900766i	$0.643006\pi$
$410$	−2.61704	−	8.05441i	−0.129246	−	0.397779i
$411$	−2.05727	+	6.33163i	−0.101478	+	0.312316i
$412$	5.07098	−	15.6069i	0.249829	−	0.768895i
$413$	−1.39361	−	1.01252i	−0.0685751	−	0.0498227i
$414$	2.05648	+	6.32920i	0.101070	+	0.311063i
$415$	7.08111	+	5.14473i	0.347598	+	0.252545i
$416$	−3.39847	+	2.46914i	−0.166624	+	0.121059i
$417$	−2.60434	+	8.01532i	−0.127535	+	0.392512i
$418$	9.19106	−	6.67770i	0.449549	−	0.326617i
$419$	−17.2384	+	12.5245i	−0.842152	+	0.611860i	−0.922971	−	0.384869i	$-0.874247\pi$
$419$	−17.2384	+	12.5245i	−0.842152	+	0.611860i	0.0808187	+	0.996729i	$0.474247\pi$
$420$	0.167143	−	0.514413i	0.00815574	−	0.0251008i
$421$	−32.3228	+	23.4839i	−1.57532	+	1.14454i	−0.653492	+	0.756933i	$0.726697\pi$
$421$	−32.3228	+	23.4839i	−1.57532	+	1.14454i	−0.921826	+	0.387603i	$0.873303\pi$
$422$	6.96871	+	5.06307i	0.339232	+	0.246466i
$423$	0.298717	+	0.919357i	0.0145241	+	0.0447007i
$424$	−10.7468	−	7.80803i	−0.521912	−	0.379192i
$425$	0.833670	−	2.56577i	0.0404389	−	0.124458i
$426$	2.94315	−	9.05808i	0.142596	−	0.438865i
$427$	−2.27884	−	7.01355i	−0.110281	−	0.339410i
$428$	11.9394			0.577114
$429$	7.20436			0.347830
$430$	−1.81855	−	5.59694i	−0.0876985	−	0.269908i
$431$	−20.6534	+	15.0055i	−0.994837	+	0.722792i	−0.960975	−	0.276635i	$-0.910781\pi$
$431$	−20.6534	+	15.0055i	−0.994837	+	0.722792i	−0.0338623	+	0.999427i	$0.510781\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	−20.1718			−0.969394			−0.484697	−	0.874682i	$-0.661070\pi$
$433$	−20.1718			−0.969394			−0.484697	+	0.874682i	$0.661070\pi$
$434$	−1.56612	+	2.57227i	−0.0751761	+	0.123473i
$435$	−4.35117			−0.208623
$436$	−9.23491	−	6.70956i	−0.442272	−	0.321329i
$437$	−35.6647	+	25.9119i	−1.70607	+	1.23954i
$438$	−1.52334	−	4.68835i	−0.0727879	−	0.224018i
$439$	10.6624			0.508887			0.254443	−	0.967088i	$-0.418108\pi$
$439$	10.6624			0.508887			0.254443	+	0.967088i	$0.418108\pi$
$440$	1.71502			0.0817603
$441$	−2.07271	−	6.37916i	−0.0987006	−	0.303769i
$442$	3.50203	−	10.7781i	0.166575	−	0.512664i
$443$	−0.335653	+	1.03303i	−0.0159474	+	0.0490810i	−0.958714	−	0.284374i	$-0.908214\pi$
$443$	−0.335653	+	1.03303i	−0.0159474	+	0.0490810i	0.942766	+	0.333455i	$0.108214\pi$
$444$	−0.118034	−	0.0857567i	−0.00560165	−	0.00406983i
$445$	0.291590	+	0.897422i	0.0138227	+	0.0425419i
$446$	−21.2535	−	15.4416i	−1.00638	−	0.731181i
$447$	9.37479	−	6.81119i	0.443412	−	0.322158i
$448$	0.167143	−	0.514413i	0.00789676	−	0.0243037i
$449$	−25.3918	+	18.4482i	−1.19831	+	0.870625i	−0.994118	−	0.108306i	$-0.965457\pi$
$449$	−25.3918	+	18.4482i	−1.19831	+	0.870625i	−0.204194	+	0.978930i	$0.565457\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	−4.48827	+	13.8135i	−0.211344	+	0.650451i
$452$	−6.25798	+	4.54669i	−0.294350	+	0.213858i
$453$	7.11763	+	5.17126i	0.334415	+	0.242967i
$454$	−7.34405	−	22.6027i	−0.344673	−	1.06080i
$455$	1.83819	+	1.33552i	0.0861755	+	0.0626102i
$456$	−2.04702	+	6.30007i	−0.0958603	+	0.295028i
$457$	0.167154	−	0.514446i	0.00781912	−	0.0240648i	−0.947071	−	0.321025i	$-0.895973\pi$
$457$	0.167154	−	0.514446i	0.00781912	−	0.0240648i	0.954890	+	0.296960i	$0.0959728\pi$
$458$	−7.57485	−	23.3130i	−0.353949	−	1.08934i
$459$	−2.69781			−0.125923
$460$	−6.65491			−0.310287
$461$	1.45203	+	4.46890i	0.0676279	+	0.208137i	0.979160	−	0.203093i	$-0.0650993\pi$
$461$	1.45203	+	4.46890i	0.0676279	+	0.208137i	−0.911532	+	0.411230i	$0.865099\pi$
$462$	−0.750469	+	0.545247i	−0.0349150	+	0.0253672i
$463$	14.2941	+	10.3853i	0.664305	+	0.482646i	0.868114	−	0.496365i	$-0.165332\pi$
$463$	14.2941	+	10.3853i	0.664305	+	0.482646i	−0.203809	+	0.979011i	$0.565332\pi$
$464$	−4.35117			−0.201998
$465$	5.13779	−	2.14549i	0.238259	−	0.0994949i
$466$	−13.4175			−0.621554
$467$	−26.0610	−	18.9344i	−1.20596	−	0.876179i	−0.211100	−	0.977464i	$-0.567705\pi$
$467$	−26.0610	−	18.9344i	−1.20596	−	0.876179i	−0.994857	+	0.101285i	$0.967705\pi$
$468$	−3.39847	+	2.46914i	−0.157094	+	0.114136i
$469$	2.33924	+	7.19944i	0.108016	+	0.332439i
$470$	−0.966670			−0.0445891
$471$	8.42458			0.388184
$472$	0.984148	+	3.02889i	0.0452991	+	0.139416i
$473$	−3.11886	+	9.59886i	−0.143405	+	0.441356i
$474$	4.09172	−	12.5930i	0.187939	−	0.578417i
$475$	−5.35916	−	3.89366i	−0.245895	−	0.178653i
$476$	0.450920	+	1.38779i	0.0206679	+	0.0636093i
$477$	−10.7468	−	7.80803i	−0.492064	−	0.357505i
$478$	0.0162302	−	0.0117920i	0.000742354	−	0.000539352i
$479$	10.8258	−	33.3185i	0.494645	−	1.52236i	−0.322863	−	0.946446i	$-0.604645\pi$
$479$	10.8258	−	33.3185i	0.494645	−	1.52236i	0.817509	−	0.575916i	$-0.195355\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	0.495830	−	0.360242i	0.0226079	−	0.0164256i
$482$	−5.92887	+	18.2472i	−0.270053	+	0.831137i
$483$	2.91210	−	2.11576i	0.132505	−	0.0962705i
$484$	6.51963	+	4.73679i	0.296347	+	0.215309i
$485$	−1.98053	−	6.09543i	−0.0899311	−	0.276779i
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	10.3460	−	31.8418i	0.468823	−	1.44289i	−0.385287	−	0.922797i	$-0.625898\pi$
$487$	10.3460	−	31.8418i	0.468823	−	1.44289i	0.854110	−	0.520092i	$-0.174102\pi$
$488$	−4.21316	+	12.9668i	−0.190721	+	0.586979i
$489$	0.714291	+	2.19836i	0.0323014	+	0.0994134i
$490$	6.70744			0.303011
$491$	21.7438			0.981283			0.490641	−	0.871362i	$-0.336763\pi$
$491$	21.7438			0.981283			0.490641	+	0.871362i	$0.336763\pi$
$492$	−2.61704	−	8.05441i	−0.117985	−	0.363121i
$493$	9.49676	−	6.89980i	0.427713	−	0.310751i
$494$	−22.5124	−	16.3563i	−1.01288	−	0.735903i
$495$	1.71502			0.0770844
$496$	5.13779	−	2.14549i	0.230693	−	0.0963355i
$497$	−5.15152			−0.231077
$498$	7.08111	+	5.14473i	0.317312	+	0.230541i
$499$	12.3725	−	8.98914i	0.553869	−	0.402409i	−0.275341	−	0.961347i	$-0.588791\pi$
$499$	12.3725	−	8.98914i	0.553869	−	0.402409i	0.829210	+	0.558937i	$0.188791\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	17.9753			0.803079
$502$	−2.98976			−0.133440
$503$	4.42055	+	13.6051i	0.197103	+	0.606619i	0.999946	+	0.0104289i	$0.00331968\pi$
$503$	4.42055	+	13.6051i	0.197103	+	0.606619i	−0.802843	+	0.596190i	$0.796680\pi$
$504$	0.167143	−	0.514413i	0.00744514	−	0.0229138i
$505$	0.246270	−	0.757940i	0.0109589	−	0.0337279i
$506$	9.23355	+	6.70857i	0.410482	+	0.298232i
$507$	−1.43577	−	4.41884i	−0.0637647	−	0.196248i
$508$	17.8570	+	12.9739i	0.792278	+	0.575624i
$509$	−24.9731	+	18.1440i	−1.10691	+	0.804218i	−0.982174	−	0.187972i	$-0.939809\pi$
$509$	−24.9731	+	18.1440i	−1.10691	+	0.804218i	−0.124737	+	0.992190i	$0.539809\pi$
$510$	0.833670	−	2.56577i	0.0369155	−	0.113614i
$511$	−2.15713	+	1.56725i	−0.0954260	+	0.0693311i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−2.04702	+	6.30007i	−0.0903780	+	0.278155i
$514$	−4.48367	+	3.25757i	−0.197766	+	0.143685i
$515$	13.2760	+	9.64558i	0.585010	+	0.425035i
$516$	−1.81855	−	5.59694i	−0.0800574	−	0.246391i
$517$	1.34123	+	0.974464i	0.0589874	+	0.0428569i
$518$	−0.0243858	+	0.0750519i	−0.00107145	+	0.00329759i
$519$	−2.81894	+	8.67579i	−0.123738	+	0.380825i
$520$	−1.29810	−	3.99514i	−0.0569255	−	0.175199i
$521$	12.0910			0.529718			0.264859	−	0.964287i	$-0.414675\pi$
$521$	12.0910			0.529718			0.264859	+	0.964287i	$0.414675\pi$
$522$	−4.35117			−0.190446
$523$	−3.58856	−	11.0444i	−0.156917	−	0.482940i	0.841433	−	0.540361i	$-0.181712\pi$
$523$	−3.58856	−	11.0444i	−0.156917	−	0.482940i	−0.998350	+	0.0574211i	$0.981712\pi$
$524$	11.3498	−	8.24608i	0.495816	−	0.360232i
$525$	0.437586	+	0.317925i	0.0190978	+	0.0138754i
$526$	−8.47879			−0.369693
$527$	−7.81143	+	12.8299i	−0.340271	+	0.558878i
$528$	1.71502			0.0746366
$529$	−17.2222	−	12.5127i	−0.748792	−	0.544029i
$530$	10.7468	−	7.80803i	0.466813	−	0.339159i
$531$	0.984148	+	3.02889i	0.0427084	+	0.131443i
$532$	3.58298			0.155342
$533$	35.5757			1.54096
$534$	0.291590	+	0.897422i	0.0126183	+	0.0388352i
$535$	−3.68948	+	11.3551i	−0.159510	+	0.490922i
$536$	4.32483	−	13.3105i	0.186804	−	0.574924i
$537$	−20.7066	−	15.0442i	−0.893554	−	0.649205i
$538$	−0.0667637	−	0.205478i	−0.00287839	−	0.00885877i
$539$	−9.30644	−	6.76153i	−0.400857	−	0.291240i
$540$	−0.809017	+	0.587785i	−0.0348145	+	0.0252942i
$541$	4.40834	−	13.5675i	0.189529	−	0.583312i	−0.810467	−	0.585784i	$-0.800787\pi$
$541$	4.40834	−	13.5675i	0.189529	−	0.583312i	0.999997	+	0.00247188i	$0.000786825\pi$
$542$	−17.9420	+	13.0357i	−0.770677	+	0.559929i
$543$	−6.64372	+	4.82695i	−0.285109	+	0.207144i
$544$	0.833670	−	2.56577i	0.0357433	−	0.110007i
$545$	9.23491	−	6.70956i	0.395580	−	0.287406i
$546$	1.83819	+	1.33552i	0.0786671	+	0.0571550i
$547$	5.04060	+	15.5134i	0.215520	+	0.663303i	0.999116	+	0.0420326i	$0.0133833\pi$
$547$	5.04060	+	15.5134i	0.215520	+	0.663303i	−0.783596	+	0.621271i	$0.786617\pi$
$548$	−5.38600	−	3.91316i	−0.230079	−	0.167162i
$549$	−4.21316	+	12.9668i	−0.179813	+	0.553409i
$550$	−0.529970	+	1.63108i	−0.0225980	+	0.0695495i
$551$	−8.90692	−	27.4127i	−0.379447	−	1.16782i
$552$	−6.65491			−0.283252
$553$	−7.16192			−0.304556
$554$	−5.29777	−	16.3049i	−0.225081	−	0.692727i
$555$	0.118034	−	0.0857567i	0.00501026	−	0.00364017i
$556$	−6.81824	−	4.95374i	−0.289158	−	0.210085i
$557$	−34.0059			−1.44088			−0.720439	−	0.693518i	$-0.756060\pi$
$557$	−34.0059			−1.44088			−0.720439	+	0.693518i	$0.756060\pi$
$558$	5.13779	−	2.14549i	0.217500	−	0.0908260i
$559$	24.7212			1.04560
$560$	0.437586	+	0.317925i	0.0184914	+	0.0134348i
$561$	−3.74316	+	2.71957i	−0.158036	+	0.114820i
$562$	2.78919	+	8.58423i	0.117655	+	0.362104i
$563$	−4.19941			−0.176984			−0.0884921	−	0.996077i	$-0.528205\pi$
$563$	−4.19941			−0.176984			−0.0884921	+	0.996077i	$0.528205\pi$
$564$	−0.966670			−0.0407041
$565$	−2.39033	−	7.35669i	−0.100562	−	0.309498i
$566$	−6.10257	+	18.7818i	−0.256510	+	0.789457i
$567$	0.167143	−	0.514413i	0.00701935	−	0.0216033i
$568$	7.70526	+	5.59820i	0.323306	+	0.234895i
$569$	−3.56820	−	10.9818i	−0.149587	−	0.460380i	0.847986	−	0.530019i	$-0.177815\pi$
$569$	−3.56820	−	10.9818i	−0.149587	−	0.460380i	−0.997572	+	0.0696391i	$0.977815\pi$
$570$	−5.35916	−	3.89366i	−0.224470	−	0.163087i
$571$	−19.8021	+	14.3870i	−0.828690	+	0.602079i	−0.919189	−	0.393818i	$-0.871154\pi$
$571$	−19.8021	+	14.3870i	−0.828690	+	0.602079i	0.0904981	+	0.995897i	$0.471154\pi$
$572$	−2.22627	+	6.85175i	−0.0930850	+	0.286486i
$573$	9.98776	−	7.25653i	0.417245	−	0.303146i
$574$	−3.70588	+	2.69248i	−0.154680	+	0.112382i
$575$	2.05648	−	6.32920i	0.0857612	−	0.263946i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	14.8951	+	10.8219i	0.620090	+	0.450522i	0.852953	−	0.521988i	$-0.174809\pi$
$577$	14.8951	+	10.8219i	0.620090	+	0.450522i	−0.232863	+	0.972510i	$0.574809\pi$
$578$	−3.00420	−	9.24599i	−0.124958	−	0.384583i
$579$	10.0937	+	7.33353i	0.419481	+	0.304771i
$580$	1.34459	−	4.13821i	0.0558309	−	0.171830i
$581$	1.46296	−	4.50252i	0.0606937	−	0.186796i
$582$	−1.98053	−	6.09543i	−0.0820954	−	0.252664i
$583$	−22.7820			−0.943534
$584$	4.92962			0.203989
$585$	−1.29810	−	3.99514i	−0.0536699	−	0.165179i
$586$	−7.40891	+	5.38289i	−0.306059	+	0.222365i
$587$	18.0056	+	13.0818i	0.743170	+	0.539944i	0.893702	−	0.448661i	$-0.148099\pi$
$587$	18.0056	+	13.0818i	0.743170	+	0.539944i	−0.150532	+	0.988605i	$0.548099\pi$
$588$	6.70744			0.276610
$589$	24.0339	+	27.9765i	0.990299	+	1.15275i
$590$	−3.18477			−0.131115
$591$	4.84659	+	3.52125i	0.199362	+	0.144845i
$592$	0.118034	−	0.0857567i	0.00485117	−	0.00352458i
$593$	−12.8278	−	39.4798i	−0.526773	−	1.62124i	−0.760783	−	0.649006i	$-0.775185\pi$
$593$	−12.8278	−	39.4798i	−0.526773	−	1.62124i	0.234011	−	0.972234i	$-0.424815\pi$
$594$	1.71502			0.0703681
$595$	−1.45921			−0.0598217
$596$	3.58085	+	11.0207i	0.146677	+	0.451427i
$597$	5.53774	−	17.0434i	0.226645	−	0.697541i
$598$	8.63875	−	26.5873i	0.353265	−	1.08724i
$599$	0.802290	+	0.582897i	0.0327807	+	0.0238165i	0.604055	−	0.796943i	$-0.293551\pi$
$599$	0.802290	+	0.582897i	0.0327807	+	0.0238165i	−0.571274	+	0.820759i	$0.693551\pi$
$600$	−0.309017	−	0.951057i	−0.0126156	−	0.0388267i
$601$	29.6673	+	21.5545i	1.21015	+	0.879228i	0.995245	−	0.0974057i	$-0.0310544\pi$
$601$	29.6673	+	21.5545i	1.21015	+	0.879228i	0.214909	+	0.976634i	$0.431054\pi$
$602$	−2.57518	+	1.87098i	−0.104956	+	0.0762554i
$603$	4.32483	−	13.3105i	0.176121	−	0.542044i
$604$	−7.11763	+	5.17126i	−0.289612	+	0.210416i
$605$	−6.51963	+	4.73679i	−0.265061	+	0.192578i
$606$	0.246270	−	0.757940i	0.0100040	−	0.0307892i
$607$	6.79636	−	4.93785i	0.275856	−	0.200421i	−0.441252	−	0.897383i	$-0.645465\pi$
$607$	6.79636	−	4.93785i	0.275856	−	0.200421i	0.717108	+	0.696962i	$0.245465\pi$
$608$	−5.35916	−	3.89366i	−0.217343	−	0.157909i
$609$	0.727268	+	2.23830i	0.0294704	+	0.0907005i
$610$	−11.0302	−	8.01391i	−0.446600	−	0.324474i
$611$	1.25483	−	3.86198i	0.0507652	−	0.156239i
$612$	0.833670	−	2.56577i	0.0336991	−	0.103715i
$613$	−6.21203	−	19.1187i	−0.250902	−	0.772196i	−0.994610	−	0.103691i	$-0.966935\pi$
$613$	−6.21203	−	19.1187i	−0.250902	−	0.772196i	0.743708	−	0.668505i	$-0.233065\pi$
$614$	−13.5893			−0.548418
$615$	8.46891			0.341499
$616$	−0.286654	−	0.882229i	−0.0115496	−	0.0355460i
$617$	−16.0709	+	11.6762i	−0.646992	+	0.470067i	−0.862245	−	0.506491i	$-0.830942\pi$
$617$	−16.0709	+	11.6762i	−0.646992	+	0.470067i	0.215253	+	0.976558i	$0.430942\pi$
$618$	13.2760	+	9.64558i	0.534039	+	0.388002i
$619$	10.5525			0.424140			0.212070	−	0.977254i	$-0.431980\pi$
$619$	10.5525			0.424140			0.212070	+	0.977254i	$0.431980\pi$
$620$	0.452822	+	5.54932i	0.0181858	+	0.222866i
$621$	−6.65491			−0.267052
$622$	−1.66356	−	1.20865i	−0.0667027	−	0.0484624i
$623$	0.412909	−	0.299996i	0.0165428	−	0.0120191i
$624$	−1.29810	−	3.99514i	−0.0519656	−	0.159934i
$625$	1.00000			0.0400000
$626$	8.69012			0.347327
$627$	3.51067	+	10.8047i	0.140203	+	0.431500i
$628$	−2.60334	+	8.01225i	−0.103884	+	0.319723i
$629$	−0.121631	+	0.374341i	−0.00484974	+	0.0149260i
$630$	0.437586	+	0.317925i	0.0174338	+	0.0126664i
$631$	−6.98828	−	21.5077i	−0.278199	−	0.856208i	−0.988355	−	0.152164i	$-0.951376\pi$
$631$	−6.98828	−	21.5077i	−0.278199	−	0.856208i	0.710156	−	0.704044i	$-0.248624\pi$
$632$	10.7123	+	7.78291i	0.426111	+	0.309588i
$633$	−6.96871	+	5.06307i	−0.276981	+	0.201239i
$634$	−2.59962	+	8.00080i	−0.103244	+	0.317752i
$635$	−17.8570	+	12.9739i	−0.708635	+	0.514854i
$636$	10.7468	−	7.80803i	0.426140	−	0.309609i
$637$	−8.70694	+	26.7972i	−0.344981	+	1.06174i
$638$	−6.03716	+	4.38625i	−0.239014	+	0.173653i
$639$	7.70526	+	5.59820i	0.304815	+	0.221461i
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	−31.6401	−	22.9879i	−1.24971	−	0.907966i	−0.251503	−	0.967856i	$-0.580925\pi$
$641$	−31.6401	−	22.9879i	−1.24971	−	0.907966i	−0.998205	+	0.0598903i	$0.980925\pi$
$642$	−3.68948	+	11.3551i	−0.145612	+	0.448149i
$643$	4.19808	−	12.9204i	0.165556	−	0.509529i	−0.833521	−	0.552488i	$-0.813678\pi$
$643$	4.19808	−	12.9204i	0.165556	−	0.509529i	0.999077	+	0.0429589i	$0.0136784\pi$
$644$	1.11232	+	3.42337i	0.0438316	+	0.134900i
$645$	5.88497			0.231720
$646$	17.8711			0.703128
$647$	6.33719	+	19.5039i	0.249141	+	0.766777i	0.994928	+	0.100592i	$0.0320737\pi$
$647$	6.33719	+	19.5039i	0.249141	+	0.766777i	−0.745787	+	0.666185i	$0.767926\pi$
$648$	−0.809017	+	0.587785i	−0.0317812	+	0.0230904i
$649$	4.41880	+	3.21045i	0.173453	+	0.126021i
$650$	4.20074			0.164767
$651$	−1.96242	−	2.28434i	−0.0769131	−	0.0895304i
$652$	−2.31150			−0.0905251
$653$	−10.0035	−	7.26799i	−0.391468	−	0.284418i	0.374589	−	0.927191i	$-0.377784\pi$
$653$	−10.0035	−	7.26799i	−0.391468	−	0.284418i	−0.766057	+	0.642773i	$0.777784\pi$
$654$	9.23491	−	6.70956i	0.361114	−	0.262364i
$655$	4.33522	+	13.3424i	0.169391	+	0.521332i
$656$	8.46891			0.330655
$657$	4.92962			0.192323
$658$	0.161572	+	0.497268i	0.00629873	+	0.0193855i
$659$	−9.65374	+	29.7111i	−0.376056	+	1.15738i	0.566707	+	0.823919i	$0.308217\pi$
$659$	−9.65374	+	29.7111i	−0.376056	+	1.15738i	−0.942763	+	0.333463i	$0.891783\pi$
$660$	−0.529970	+	1.63108i	−0.0206291	+	0.0634897i
$661$	−9.76997	−	7.09830i	−0.380008	−	0.276092i	0.381341	−	0.924434i	$-0.375462\pi$
$661$	−9.76997	−	7.09830i	−0.380008	−	0.276092i	−0.761349	+	0.648343i	$0.775462\pi$
$662$	−5.31104	−	16.3457i	−0.206419	−	0.635293i
$663$	9.16844	+	6.66126i	0.356073	+	0.258702i
$664$	−7.08111	+	5.14473i	−0.274800	+	0.199654i
$665$	−1.10720	+	3.40762i	−0.0429355	+	0.132142i
$666$	0.118034	−	0.0857567i	0.00457372	−	0.00332301i
$667$	23.4264	−	17.0203i	0.907075	−	0.659028i
$668$	−5.55468	+	17.0956i	−0.214917	+	0.661447i
$669$	21.2535	−	15.4416i	0.821710	−	0.597007i
$670$	11.3226	+	8.22632i	0.437428	+	0.317810i
$671$	7.22566	+	22.2383i	0.278943	+	0.858499i
$672$	0.437586	+	0.317925i	0.0168802	+	0.0122642i
$673$	−9.39090	+	28.9022i	−0.361993	+	1.11410i	0.589850	+	0.807513i	$0.299187\pi$
$673$	−9.39090	+	28.9022i	−0.361993	+	1.11410i	−0.951843	+	0.306586i	$0.900813\pi$
$674$	4.82888	−	14.8618i	0.186002	−	0.572454i
$675$	−0.309017	−	0.951057i	−0.0118941	−	0.0366062i
$676$	4.64624			0.178702
$677$	−23.9945			−0.922184			−0.461092	−	0.887352i	$-0.652542\pi$
$677$	−23.9945			−0.922184			−0.461092	+	0.887352i	$0.652542\pi$
$678$	−2.39033	−	7.35669i	−0.0918002	−	0.282532i
$679$	−2.80454	+	2.03762i	−0.107628	+	0.0781966i
$680$	2.18258	+	1.58573i	0.0836980	+	0.0608101i
$681$	23.7659			0.910709
$682$	4.96578	−	8.15604i	0.190150	−	0.312311i
$683$	−1.90585			−0.0729254			−0.0364627	−	0.999335i	$-0.511609\pi$
$683$	−1.90585			−0.0729254			−0.0364627	+	0.999335i	$0.511609\pi$
$684$	−5.35916	−	3.89366i	−0.204913	−	0.148878i
$685$	5.38600	−	3.91316i	0.205789	−	0.149514i
$686$	−2.29110	−	7.05129i	−0.0874747	−	0.269219i
$687$	24.5127			0.935219
$688$	5.88497			0.224362
$689$	17.2437	+	53.0708i	0.656934	+	2.02184i
$690$	2.05648	−	6.32920i	0.0782889	−	0.240948i
$691$	0.876532	−	2.69769i	0.0333448	−	0.102625i	−0.932999	−	0.359879i	$-0.882818\pi$
$691$	0.876532	−	2.69769i	0.0333448	−	0.102625i	0.966344	+	0.257254i	$0.0828179\pi$
$692$	−7.38007	−	5.36193i	−0.280548	−	0.203830i
$693$	−0.286654	−	0.882229i	−0.0108891	−	0.0335131i
$694$	20.9637	+	15.2310i	0.795772	+	0.578162i
$695$	6.81824	−	4.95374i	0.258631	−	0.187906i
$696$	1.34459	−	4.13821i	0.0509664	−	0.156858i
$697$	−18.4840	+	13.4294i	−0.700133	+	0.508676i
$698$	16.4161	−	11.9270i	0.621358	−	0.451443i
$699$	4.14624	−	12.7608i	0.156825	−	0.482658i
$700$	−0.437586	+	0.317925i	−0.0165392	+	0.0120164i
$701$	−8.61100	−	6.25626i	−0.325233	−	0.236296i	0.413172	−	0.910653i	$-0.364421\pi$
$701$	−8.61100	−	6.25626i	−0.325233	−	0.236296i	−0.738405	+	0.674357i	$0.764421\pi$
$702$	−1.29810	−	3.99514i	−0.0489937	−	0.150787i
$703$	0.781891	+	0.568077i	0.0294896	+	0.0214254i
$704$	−0.529970	+	1.63108i	−0.0199740	+	0.0614737i
$705$	0.298717	−	0.919357i	0.0112503	−	0.0346250i
$706$	8.71092	+	26.8095i	0.327840	+	1.00899i
$707$	−0.431057			−0.0162116
$708$	−3.18477			−0.119691
$709$	−7.79317	−	23.9849i	−0.292679	−	0.900772i	−0.983991	−	0.178217i	$-0.942967\pi$
$709$	−7.79317	−	23.9849i	−0.292679	−	0.900772i	0.691313	−	0.722556i	$-0.257033\pi$
$710$	−7.70526	+	5.59820i	−0.289173	+	0.210097i
$711$	10.7123	+	7.78291i	0.401741	+	0.291882i
$712$	−0.943605			−0.0353631
$713$	−19.2691	+	31.6485i	−0.721633	+	1.18524i
$714$	−1.45921			−0.0546095
$715$	−5.82845	−	4.23461i	−0.217972	−	0.158366i
$716$	20.7066	−	15.0442i	0.773841	−	0.562228i
$717$	0.00619940	+	0.0190798i	0.000231521	+	0.000712548i
$718$	7.38761			0.275703
$719$	40.0904			1.49512			0.747559	−	0.664195i	$-0.231226\pi$
$719$	40.0904			1.49512			0.747559	+	0.664195i	$0.231226\pi$
$720$	−0.309017	−	0.951057i	−0.0115164	−	0.0354438i
$721$	2.74282	−	8.44154i	0.102148	−	0.314379i
$722$	7.68869	−	23.6634i	0.286144	−	0.880659i
$723$	−15.5220	−	11.2774i	−0.577269	−	0.419411i
$724$	−2.53768	−	7.81017i	−0.0943120	−	0.290263i
$725$	3.52017	+	2.55755i	0.130736	+	0.0949852i
$726$	−6.51963	+	4.73679i	−0.241966	+	0.175799i
$727$	12.9655	−	39.9036i	0.480863	−	1.47994i	−0.357022	−	0.934096i	$-0.616208\pi$
$727$	12.9655	−	39.9036i	0.480863	−	1.47994i	0.837885	−	0.545847i	$-0.183792\pi$
$728$	−1.83819	+	1.33552i	−0.0681277	+	0.0494977i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−1.52334	+	4.68835i	−0.0563813	+	0.173524i
$731$	−12.8444	+	9.33199i	−0.475067	+	0.345156i
$732$	−11.0302	−	8.01391i	−0.407688	−	0.296203i
$733$	8.88031	+	27.3308i	0.328002	+	1.00949i	0.970067	+	0.242836i	$0.0780776\pi$
$733$	8.88031	+	27.3308i	0.328002	+	1.00949i	−0.642066	+	0.766649i	$0.721922\pi$
$734$	14.4603	+	10.5060i	0.533739	+	0.387784i
$735$	−2.07271	+	6.37916i	−0.0764532	+	0.235299i
$736$	2.05648	−	6.32920i	0.0758029	−	0.233297i
$737$	−7.41717	−	22.8277i	−0.273215	−	0.840869i
$738$	8.46891			0.311745
$739$	−17.1082			−0.629335			−0.314668	−	0.949202i	$-0.601893\pi$
$739$	−17.1082			−0.629335			−0.314668	+	0.949202i	$0.601893\pi$
$740$	0.0450850	+	0.138757i	0.00165736	+	0.00510082i
$741$	22.5124	−	16.3563i	0.827015	−	0.600862i
$742$	−5.81281	−	4.22326i	−0.213395	−	0.155041i
$743$	30.1293			1.10534			0.552669	−	0.833401i	$-0.313609\pi$
$743$	30.1293			1.10534			0.552669	+	0.833401i	$0.313609\pi$
$744$	0.452822	+	5.54932i	0.0166013	+	0.203448i
$745$	−11.5879			−0.424547
$746$	11.6113	+	8.43609i	0.425119	+	0.308867i
$747$	−7.08111	+	5.14473i	−0.259084	+	0.188236i
$748$	−1.42976	−	4.40035i	−0.0522772	−	0.160893i
$749$	6.45787			0.235965
$750$	1.00000			0.0365148
$751$	1.61408	+	4.96764i	0.0588988	+	0.181272i	0.976177	−	0.216975i	$-0.0696189\pi$
$751$	1.61408	+	4.96764i	0.0588988	+	0.181272i	−0.917278	+	0.398246i	$0.869619\pi$
$752$	0.298717	−	0.919357i	0.0108931	−	0.0335255i
$753$	0.923887	−	2.84343i	0.0336683	−	0.103620i
$754$	14.7873	+	10.7436i	0.538523	+	0.391260i
$755$	−2.71869	−	8.36728i	−0.0989434	−	0.304516i
$756$	0.437586	+	0.317925i	0.0159149	+	0.0115628i
$757$	−33.5525	+	24.3773i	−1.21949	+	0.886010i	−0.996057	−	0.0887102i	$-0.971726\pi$
$757$	−33.5525	+	24.3773i	−1.21949	+	0.886010i	−0.223430	+	0.974720i	$0.571726\pi$
$758$	−7.55097	+	23.2395i	−0.274264	+	0.844096i
$759$	−9.23355	+	6.70857i	−0.335157	+	0.243506i
$760$	5.35916	−	3.89366i	0.194397	−	0.141238i
$761$	−6.50864	+	20.0315i	−0.235938	+	0.726142i	0.761058	+	0.648684i	$0.224680\pi$
$761$	−6.50864	+	20.0315i	−0.235938	+	0.726142i	−0.996996	+	0.0774581i	$0.975320\pi$
$762$	−17.8570	+	12.9739i	−0.646892	+	0.469995i
$763$	−4.99504	−	3.62911i	−0.180832	−	0.131382i
$764$	3.81499	+	11.7413i	0.138021	+	0.424786i
$765$	2.18258	+	1.58573i	0.0789112	+	0.0573323i
$766$	−4.09969	+	12.6175i	−0.148128	+	0.455890i
$767$	4.13415	−	12.7236i	0.149276	−	0.459423i
$768$	−0.309017	−	0.951057i	−0.0111507	−	0.0343183i
$769$	29.7118			1.07144			0.535718	−	0.844397i	$-0.320041\pi$
$769$	29.7118			1.07144			0.535718	+	0.844397i	$0.320041\pi$
$770$	0.927630			0.0334295
$771$	−1.71261	−	5.27086i	−0.0616781	−	0.189826i
$772$	−10.0937	+	7.33353i	−0.363281	+	0.263939i
$773$	10.9836	+	7.98009i	0.395054	+	0.287024i	0.767524	−	0.641021i	$-0.221489\pi$
$773$	10.9836	+	7.98009i	0.395054	+	0.287024i	−0.372469	+	0.928045i	$0.621489\pi$
$774$	5.88497			0.211531
$775$	−5.41765	−	1.28417i	−0.194608	−	0.0461289i
$776$	6.40912			0.230074
$777$	−0.0638429	−	0.0463846i	−0.00229035	−	0.00166404i
$778$	−12.1291	+	8.81229i	−0.434848	+	0.315936i
$779$	17.3360	+	53.3547i	0.621126	+	1.91163i
$780$	4.20074			0.150411
$781$	16.3342			0.584485
$782$	5.54800	+	17.0750i	0.198396	+	0.610600i
$783$	1.34459	−	4.13821i	0.0480516	−	0.147888i
$784$	−2.07271	+	6.37916i	−0.0740255	+	0.227827i
$785$	−6.81562	−	4.95184i	−0.243260	−	0.176739i
$786$	4.33522	+	13.3424i	0.154632	+	0.475909i
$787$	2.85684	+	2.07562i	0.101836	+	0.0739878i	0.637538	−	0.770419i	$-0.279953\pi$
$787$	2.85684	+	2.07562i	0.101836	+	0.0739878i	−0.535702	+	0.844407i	$0.679953\pi$
$788$	−4.84659	+	3.52125i	−0.172653	+	0.125439i
$789$	2.62009	−	8.06381i	0.0932777	−	0.287079i
$790$	−10.7123	+	7.78291i	−0.381125	+	0.276904i
$791$	−3.38485	+	2.45924i	−0.120352	+	0.0874405i
$792$	−0.529970	+	1.63108i	−0.0188317	+	0.0579579i
$793$	46.3350	−	33.6644i	1.64541	−	1.19546i
$794$	−19.0871	−	13.8676i	−0.677377	−	0.492143i
$795$	4.10493	+	12.6337i	0.145587	+	0.448070i
$796$	14.4980	+	10.5334i	0.513868	+	0.373347i
$797$	9.09639	−	27.9958i	0.322211	−	0.991662i	−0.650473	−	0.759529i	$-0.725429\pi$
$797$	9.09639	−	27.9958i	0.322211	−	0.991662i	0.972684	−	0.232133i	$-0.0745705\pi$
$798$	−1.10720	+	3.40762i	−0.0391945	+	0.120628i
$799$	0.805883	+	2.48025i	0.0285101	+	0.0877451i
$800$	1.00000			0.0353553
$801$	−0.943605			−0.0333407
$802$	−4.90881	−	15.1078i	−0.173336	−	0.533474i
$803$	6.83976	−	4.96937i	0.241370	−	0.175365i
$804$	11.3226	+	8.22632i	0.399316	+	0.290120i
$805$	−3.59955			−0.126867
$806$	−22.7581	−	5.39449i	−0.801621	−	0.190013i
$807$	0.216052			0.00760539
$808$	0.644743	+	0.468433i	0.0226820	+	0.0164794i
$809$	35.9673	−	26.1317i	1.26454	−	0.918743i	0.265570	−	0.964092i	$-0.414440\pi$
$809$	35.9673	−	26.1317i	1.26454	−	0.918743i	0.998971	+	0.0453483i	$0.0144398\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	−43.7065			−1.53474			−0.767371	−	0.641203i	$-0.778436\pi$
$811$	−43.7065			−1.53474			−0.767371	+	0.641203i	$0.778436\pi$
$812$	−2.35349			−0.0825912
$813$	−6.85325	−	21.0921i	−0.240354	−	0.739733i
$814$	0.0773216	−	0.237971i	0.00271012	−	0.00834089i
$815$	0.714291	−	2.19836i	0.0250205	−	0.0770053i
$816$	2.18258	+	1.58573i	0.0764054	+	0.0555118i
$817$	12.0466	+	37.0757i	0.421458	+	1.29711i
$818$	14.2117	+	10.3254i	0.496899	+	0.361018i
$819$	−1.83819	+	1.33552i	−0.0642314	+	0.0466669i
$820$	−2.61704	+	8.05441i	−0.0913909	+	0.281272i
$821$	31.1021	−	22.5970i	1.08547	−	0.788642i	0.106843	−	0.994276i	$-0.465926\pi$
$821$	31.1021	−	22.5970i	1.08547	−	0.788642i	0.978629	+	0.205634i	$0.0659257\pi$
$822$	5.38600	−	3.91316i	0.187858	−	0.136487i
$823$	9.91722	−	30.5221i	0.345692	−	1.06393i	−0.615520	−	0.788122i	$-0.711054\pi$
$823$	9.91722	−	30.5221i	0.345692	−	1.06393i	0.961212	−	0.275810i	$-0.0889462\pi$
$824$	−13.2760	+	9.64558i	−0.462491	+	0.336020i
$825$	−1.38748	−	1.00806i	−0.0483059	−	0.0350963i
$826$	0.532312	+	1.63829i	0.0185215	+	0.0570033i
$827$	−43.2384	−	31.4145i	−1.50354	−	1.09239i	−0.968943	−	0.247286i	$-0.920461\pi$
$827$	−43.2384	−	31.4145i	−1.50354	−	1.09239i	−0.534602	−	0.845104i	$-0.679539\pi$
$828$	2.05648	−	6.32920i	0.0714676	−	0.219955i
$829$	−5.50845	+	16.9533i	−0.191316	+	0.588811i	0.808683	+	0.588244i	$0.200181\pi$
$829$	−5.50845	+	16.9533i	−0.191316	+	0.588811i	−1.00000		0.000567279i	$0.999819\pi$
$830$	−2.70474	−	8.32434i	−0.0938830	−	0.288942i
$831$	17.1439			0.594717
$832$	4.20074			0.145635
$833$	−5.59179	−	17.2098i	−0.193744	−	0.596283i
$834$	6.81824	−	4.95374i	0.236096	−	0.171534i
$835$	−14.5424	−	10.5656i	−0.503259	−	0.365639i
$836$	−11.3608			−0.392921
$837$	0.452822	+	5.54932i	0.0156518	+	0.191813i
$838$	21.3079			0.736068
$839$	29.4897	+	21.4255i	1.01810	+	0.739691i	0.965892	−	0.258946i	$-0.0833751\pi$
$839$	29.4897	+	21.4255i	1.01810	+	0.739691i	0.0522049	+	0.998636i	$0.483375\pi$
$840$	−0.437586	+	0.317925i	−0.0150982	+	0.0109695i
$841$	−3.11097	−	9.57458i	−0.107275	−	0.330158i
$842$	39.9532			1.37688
$843$	−9.02599			−0.310872
$844$	−2.66181	−	8.19221i	−0.0916233	−	0.281988i
$845$	−1.43577	+	4.41884i	−0.0493919	+	0.152013i
$846$	0.298717	−	0.919357i	0.0102701	−	0.0316082i
$847$	3.52638	+	2.56206i	0.121168	+	0.0880335i
$848$	4.10493	+	12.6337i	0.140964	+	0.433842i
$849$	−15.9767	−	11.6078i	−0.548320	−	0.398378i
$850$	−2.18258	+	1.58573i	−0.0748617	+	0.0543902i
$851$	−0.300036	+	0.923417i	−0.0102851	+	0.0316543i
$852$	−7.70526	+	5.59820i	−0.263978	+	0.191791i
$853$	−1.98294	+	1.44069i	−0.0678947	+	0.0493284i	−0.621215	−	0.783640i	$-0.713361\pi$
$853$	−1.98294	+	1.44069i	−0.0678947	+	0.0493284i	0.553320	+	0.832969i	$0.313361\pi$
$854$	−2.27884	+	7.01355i	−0.0779803	+	0.239999i
$855$	5.35916	−	3.89366i	0.183279	−	0.133160i
$856$	−9.65919	−	7.01781i	−0.330144	−	0.239864i
$857$	−6.21725	−	19.1347i	−0.212377	−	0.653630i	−0.999329	−	0.0366159i	$-0.988342\pi$
$857$	−6.21725	−	19.1347i	−0.212377	−	0.653630i	0.786952	−	0.617014i	$-0.211658\pi$
$858$	−5.82845	−	4.23461i	−0.198980	−	0.144567i
$859$	12.7332	−	39.1887i	0.434450	−	1.33710i	−0.459199	−	0.888334i	$-0.651863\pi$
$859$	12.7332	−	39.1887i	0.434450	−	1.33710i	0.893649	−	0.448767i	$-0.148137\pi$
$860$	−1.81855	+	5.59694i	−0.0620122	+	0.190854i
$861$	−1.41552	−	4.35652i	−0.0482408	−	0.148470i
$862$	25.5290			0.869520
$863$	11.1598			0.379884			0.189942	−	0.981795i	$-0.439170\pi$
$863$	11.1598			0.379884			0.189942	+	0.981795i	$0.439170\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	7.38007	−	5.36193i	0.250930	−	0.182311i
$866$	16.3193	+	11.8567i	0.554553	+	0.402906i
$867$	9.72181			0.330170
$868$	2.77896	−	1.16047i	0.0943240	−	0.0393888i
$869$	22.7087			0.770341
$870$	3.52017	+	2.55755i	0.119345	+	0.0867092i
$871$	−47.5631	+	34.5566i	−1.61162	+	1.17091i
$872$	3.52742	+	10.8563i	0.119454	+	0.367640i
$873$	6.40912			0.216916
$874$	44.0840			1.49116
$875$	−0.167143	−	0.514413i	−0.00565046	−	0.0173903i
$876$	−1.52334	+	4.68835i	−0.0514688	+	0.158405i
$877$	15.3742	−	47.3169i	0.519150	−	1.59778i	−0.256453	−	0.966557i	$-0.582554\pi$
$877$	15.3742	−	47.3169i	0.519150	−	1.59778i	0.775602	−	0.631222i	$-0.217446\pi$
$878$	−8.62603	−	6.26718i	−0.291114	−	0.211507i
$879$	−2.82995	−	8.70970i	−0.0954519	−	0.293771i
$880$	−1.38748	−	1.00806i	−0.0467719	−	0.0339818i
$881$	33.6224	−	24.4281i	1.13277	−	0.823003i	0.146671	−	0.989185i	$-0.453144\pi$
$881$	33.6224	−	24.4281i	1.13277	−	0.823003i	0.986095	+	0.166183i	$0.0531441\pi$
$882$	−2.07271	+	6.37916i	−0.0697919	+	0.214797i
$883$	−7.57717	+	5.50513i	−0.254992	+	0.185262i	−0.707936	−	0.706276i	$-0.750374\pi$
$883$	−7.57717	+	5.50513i	−0.254992	+	0.185262i	0.452944	+	0.891539i	$0.350374\pi$
$884$	−9.16844	+	6.66126i	−0.308368	+	0.224042i
$885$	0.984148	−	3.02889i	0.0330818	−	0.101815i
$886$	0.878752	−	0.638451i	0.0295222	−	0.0214492i
$887$	−29.1957	−	21.2119i	−0.980295	−	0.712226i	−0.0225208	−	0.999746i	$-0.507169\pi$
$887$	−29.1957	−	21.2119i	−0.980295	−	0.712226i	−0.957775	+	0.287520i	$0.907169\pi$
$888$	0.0450850	+	0.138757i	0.00151295	+	0.00465639i
$889$	9.65863	+	7.01740i	0.323940	+	0.235356i
$890$	0.291590	−	0.897422i	0.00977412	−	0.0300817i
$891$	−0.529970	+	1.63108i	−0.0177547	+	0.0546433i
$892$	8.11813	+	24.9850i	0.271815	+	0.836561i
$893$	6.40349			0.214285
$894$	−11.5879			−0.387557
$895$	7.90920	+	24.3420i	0.264376	+	0.813664i
$896$	−0.437586	+	0.317925i	−0.0146187	+	0.0106211i
$897$	22.6165	+	16.4319i	0.755144	+	0.548644i
$898$	31.3860			1.04736
$899$	−15.7867	−	18.3764i	−0.526516	−	0.612889i
$900$	1.00000			0.0333333
$901$	−28.9929	−	21.0646i	−0.965895	−	0.701764i
$902$	11.7504	−	8.53720i	0.391247	−	0.284258i
$903$	−0.983631	−	3.02731i	−0.0327332	−	0.100742i
$904$	7.73528			0.257272
$905$	8.21209			0.272979
$906$	−2.71869	−	8.36728i	−0.0903225	−	0.277984i
$907$	−10.1767	+	31.3208i	−0.337913	+	1.03999i	0.627356	+	0.778732i	$0.284137\pi$
$907$	−10.1767	+	31.3208i	−0.337913	+	1.03999i	−0.965269	+	0.261257i	$0.915863\pi$
$908$	−7.34405	+	22.6027i	−0.243721	+	0.750096i
$909$	0.644743	+	0.468433i	0.0213848	+	0.0155369i
$910$	−0.702125	−	2.16092i	−0.0232752	−	0.0716337i
$911$	−15.2375	−	11.0707i	−0.504840	−	0.366788i	0.306023	−	0.952024i	$-0.401002\pi$
$911$	−15.2375	−	11.0707i	−0.504840	−	0.366788i	−0.810863	+	0.585236i	$0.801002\pi$
$912$	5.35916	−	3.89366i	0.177459	−	0.128932i
$913$	−4.63869	+	14.2764i	−0.153518	+	0.472480i
$914$	−0.437614	+	0.317945i	−0.0144750	+	0.0105167i
$915$	11.0302	−	8.01391i	0.364647	−	0.264932i
$916$	−7.57485	+	23.3130i	−0.250280	+	0.770283i
$917$	6.13892	−	4.46019i	0.202725	−	0.147288i
$918$	2.18258	+	1.58573i	0.0720357	+	0.0523370i
$919$	10.1574	+	31.2611i	0.335060	+	1.03121i	0.966692	+	0.255941i	$0.0823852\pi$
$919$	10.1574	+	31.2611i	0.335060	+	1.03121i	−0.631632	+	0.775268i	$0.717615\pi$
$920$	5.38394	+	3.91166i	0.177503	+	0.128964i
$921$	4.19931	−	12.9242i	0.138372	−	0.425865i
$922$	1.45203	−	4.46890i	0.0478202	−	0.147175i
$923$	−12.3634	−	38.0507i	−0.406947	−	1.25245i
$924$	0.927630			0.0305168
$925$	−0.145898			−0.00479710
$926$	−5.45988	−	16.8038i	−0.179423	−	0.552206i
$927$	−13.2760	+	9.64558i	−0.436041	+	0.316802i
$928$	3.52017	+	2.55755i	0.115555	+	0.0839558i
$929$	43.3861			1.42345			0.711725	−	0.702458i	$-0.247914\pi$
$929$	43.3861			1.42345			0.711725	+	0.702458i	$0.247914\pi$
$930$	−5.41765	−	1.28417i	−0.177652	−	0.0421097i
$931$	−44.4320			−1.45620
$932$	10.8550	+	7.88662i	0.355567	+	0.258335i
$933$	1.66356	−	1.20865i	0.0544626	−	0.0395694i
$934$	9.95440	+	30.6365i	0.325718	+	1.00246i
$935$	4.62680			0.151313
$936$	4.20074			0.137306
$937$	−14.7518	−	45.4014i	−0.481920	−	1.48320i	−0.836392	−	0.548132i	$-0.815339\pi$
$937$	−14.7518	−	45.4014i	−0.481920	−	1.48320i	0.354471	−	0.935067i	$-0.384661\pi$
$938$	2.33924	−	7.19944i	0.0763789	−	0.235070i
$939$	−2.68539	+	8.26479i	−0.0876345	+	0.269711i
$940$	0.782052	+	0.568194i	0.0255077	+	0.0185324i
$941$	5.22879	+	16.0926i	0.170454	+	0.524602i	0.999397	−	0.0347306i	$-0.0110573\pi$
$941$	5.22879	+	16.0926i	0.170454	+	0.524602i	−0.828943	+	0.559333i	$0.811057\pi$
$942$	−6.81562	−	4.95184i	−0.222065	−	0.161340i
$943$	−45.5961	+	33.1275i	−1.48481	+	1.07878i
$944$	0.984148	−	3.02889i	0.0320313	−	0.0985821i
$945$	−0.437586	+	0.317925i	−0.0142347	+	0.0103421i
$946$	8.16527	−	5.93242i	0.265476	−	0.192880i
$947$	12.7010	−	39.0897i	0.412728	−	1.27025i	−0.501540	−	0.865135i	$-0.667233\pi$
$947$	12.7010	−	39.0897i	0.412728	−	1.27025i	0.914268	−	0.405111i	$-0.132767\pi$
$948$	−10.7123	+	7.78291i	−0.347918	+	0.252777i
$949$	−16.7532	−	12.1719i	−0.543832	−	0.395117i
$950$	2.04702	+	6.30007i	0.0664140	+	0.204401i
$951$	−6.80589	−	4.94477i	−0.220696	−	0.160345i
$952$	0.450920	−	1.38779i	0.0146144	−	0.0449785i
$953$	7.88471	−	24.2667i	0.255411	−	0.786074i	−0.738337	−	0.674431i	$-0.764389\pi$
$953$	7.88471	−	24.2667i	0.255411	−	0.786074i	0.993748	−	0.111643i	$-0.0356112\pi$
$954$	4.10493	+	12.6337i	0.132902	+	0.409030i
$955$	−12.3456			−0.399493
$956$	−0.0200617			−0.000648841
$957$	−2.30599	−	7.09711i	−0.0745421	−	0.229417i
$958$	−28.3424	+	20.5920i	−0.915702	+	0.665297i
$959$	−2.91321	−	2.11657i	−0.0940726	−	0.0683477i
$960$	1.00000			0.0322749
$961$	27.7018	+	13.9144i	0.893606	+	0.448852i
$962$	−0.612880			−0.0197601
$963$	−9.65919	−	7.01781i	−0.311263	−	0.226146i
$964$	15.5220	−	11.2774i	0.499930	−	0.363220i
$965$	−3.85546	−	11.8659i	−0.124112	−	0.381977i
$966$	−3.59955			−0.115814
$967$	38.2981			1.23158			0.615791	−	0.787909i	$-0.288836\pi$
$967$	38.2981			1.23158			0.615791	+	0.787909i	$0.288836\pi$
$968$	−2.49028	−	7.66429i	−0.0800406	−	0.246340i
$969$	−5.52247	+	16.9964i	−0.177407	+	0.546003i
$970$	−1.98053	+	6.09543i	−0.0635909	+	0.195713i
$971$	32.6772	+	23.7414i	1.04866	+	0.761897i	0.971957	−	0.235157i	$-0.0755603\pi$
$971$	32.6772	+	23.7414i	1.04866	+	0.761897i	0.0767041	+	0.997054i	$0.475560\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	−3.68789	−	2.67941i	−0.118228	−	0.0858979i
$974$	−27.0862	+	19.6793i	−0.867899	+	0.630566i
$975$	−1.29810	+	3.99514i	−0.0415725	+	0.127947i
$976$	11.0302	−	8.01391i	0.353068	−	0.256519i
$977$	−23.1079	+	16.7889i	−0.739288	+	0.537124i	−0.892488	−	0.451071i	$-0.851042\pi$
$977$	−23.1079	+	16.7889i	−0.739288	+	0.537124i	0.153200	+	0.988195i	$0.451042\pi$
$978$	0.714291	−	2.19836i	0.0228405	−	0.0702959i
$979$	−1.30923	+	0.951214i	−0.0418433	+	0.0304009i
$980$	−5.42643	−	3.94254i	−0.173341	−	0.125940i
$981$	3.52742	+	10.8563i	0.112622	+	0.346615i
$982$	−17.5911	−	12.7807i	−0.561354	−	0.407847i
$983$	1.63345	−	5.02725i	0.0520990	−	0.160344i	−0.921622	−	0.388089i	$-0.873135\pi$
$983$	1.63345	−	5.02725i	0.0520990	−	0.160344i	0.973721	+	0.227745i	$0.0731352\pi$
$984$	−2.61704	+	8.05441i	−0.0834281	+	0.256765i
$985$	−1.85123	−	5.69751i	−0.0589852	−	0.181538i
$986$	−11.7386			−0.373834
$987$	−0.522858			−0.0166428
$988$	8.59899	+	26.4650i	0.273570	+	0.841963i
$989$	−31.6843	+	23.0200i	−1.00750	+	0.731993i
$990$	−1.38748	−	1.00806i	−0.0440970	−	0.0320384i
$991$	−5.76809			−0.183229			−0.0916147	−	0.995795i	$-0.529203\pi$
$991$	−5.76809			−0.183229			−0.0916147	+	0.995795i	$0.529203\pi$
$992$	−5.41765	−	1.28417i	−0.172010	−	0.0407726i
$993$	17.1869			0.545409
$994$	4.16767	+	3.02799i	0.132190	+	0.0960420i
$995$	−14.4980	+	10.5334i	−0.459617	+	0.333932i
$996$	−2.70474	−	8.32434i	−0.0857031	−	0.263767i
$997$	1.10685			0.0350543			0.0175272	−	0.999846i	$-0.494421\pi$
$997$	1.10685			0.0350543			0.0175272	+	0.999846i	$0.494421\pi$
$998$	−15.2932			−0.484099
$999$	0.0450850	+	0.138757i	0.00142643	+	0.00439009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.d.901.2	yes	12
31.16	even	5	inner	930.2.n.d.481.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.d.481.2	✓	12	31.16	even	5	inner
930.2.n.d.901.2	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(0.167143 + 0.514413i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(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} +(0.167143 + 0.514413i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.529970 - 1.63108i) q^{11} +(0.809017 + 0.587785i) q^{12} +(-3.39847 + 2.46914i) q^{13} +(0.167143 - 0.514413i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.833670 - 2.56577i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-5.35916 - 3.89366i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(0.437586 + 0.317925i) q^{21} +(-0.529970 + 1.63108i) q^{22} +(2.05648 - 6.32920i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +4.20074 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.437586 + 0.317925i) q^{28} +(3.52017 + 2.55755i) q^{29} +1.00000 q^{30} +(-5.41765 - 1.28417i) q^{31} +1.00000 q^{32} +(-1.38748 - 1.00806i) q^{33} +(-2.18258 + 1.58573i) q^{34} +(-0.167143 - 0.514413i) q^{35} +1.00000 q^{36} -0.145898 q^{37} +(2.04702 + 6.30007i) q^{38} +(-1.29810 + 3.99514i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(-6.85149 - 4.97790i) q^{41} +(-0.167143 - 0.514413i) q^{42} +(-4.76104 - 3.45910i) q^{43} +(1.38748 - 1.00806i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(-5.38394 + 3.91166i) q^{46} +(-0.782052 + 0.568194i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(5.42643 - 3.94254i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-0.833670 - 2.56577i) q^{51} +(-3.39847 - 2.46914i) q^{52} +(4.10493 - 12.6337i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(0.529970 + 1.63108i) q^{55} +0.540886 q^{56} -6.62428 q^{57} +(-1.34459 - 4.13821i) q^{58} +(-2.57653 + 1.87196i) q^{59} +(-0.809017 - 0.587785i) q^{60} -13.6341 q^{61} +(3.62815 + 4.22333i) q^{62} +0.540886 q^{63} +(-0.809017 - 0.587785i) q^{64} +(3.39847 - 2.46914i) q^{65} +(0.529970 + 1.63108i) q^{66} +13.9954 q^{67} +2.69781 q^{68} +(-2.05648 - 6.32920i) q^{69} +(-0.167143 + 0.514413i) q^{70} +(-2.94315 + 9.05808i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(1.52334 + 4.68835i) q^{73} +(0.118034 + 0.0857567i) q^{74} +(0.809017 - 0.587785i) q^{75} +(2.04702 - 6.30007i) q^{76} +(0.750469 - 0.545247i) q^{77} +(3.39847 - 2.46914i) q^{78} +(-4.09172 + 12.5930i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.61704 + 8.05441i) q^{82} +(-7.08111 - 5.14473i) q^{83} +(-0.167143 + 0.514413i) q^{84} +(-0.833670 + 2.56577i) q^{85} +(1.81855 + 5.59694i) q^{86} +4.35117 q^{87} -1.71502 q^{88} +(-0.291590 - 0.897422i) q^{89} +(0.809017 - 0.587785i) q^{90} +(-1.83819 - 1.33552i) q^{91} +6.65491 q^{92} +(-5.13779 + 2.14549i) q^{93} +0.966670 q^{94} +(5.35916 + 3.89366i) q^{95} +(0.809017 - 0.587785i) q^{96} +(1.98053 + 6.09543i) q^{97} -6.70744 q^{98} -1.71502 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	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 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 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more