LMFDB - Embedded newform 930.2.n.g.901.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 31 x^{14} + 20 x^{13} + 474 x^{12} + 463 x^{11} + 6637 x^{10} + 13567 x^{9} + \cdots + 22848400 $ x^16 - x^15 + 31x^14 + 20x^13 + 474x^12 + 463x^11 + 6637x^10 + 13567x^9 + 108596x^8 + 172826x^7 + 917001x^6 + 1583565x^5 + 3229491x^4 - 1732290x^3 + 4672960x^2 - 5544800x + 22848400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.3
Root			$1.03459 - 3.18415i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.g.481.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(1.03459 + 3.18415i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(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} +(1.03459 + 3.18415i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(1.50424 + 4.62958i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(-2.46770 + 1.79289i) q^{13} +(1.03459 - 3.18415i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.99805 + 6.14938i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-6.48532 - 4.71186i) q^{19} +(0.309017 + 0.951057i) q^{20} +(-2.70860 - 1.96791i) q^{21} +(1.50424 - 4.62958i) q^{22} +(2.45267 - 7.54854i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +3.05025 q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.70860 + 1.96791i) q^{28} +(3.26327 + 2.37090i) q^{29} +1.00000 q^{30} +(0.262113 - 5.56159i) q^{31} +1.00000 q^{32} +(-3.93815 - 2.86124i) q^{33} +(5.23097 - 3.80052i) q^{34} +(1.03459 + 3.18415i) q^{35} +1.00000 q^{36} -4.97717 q^{37} +(2.47717 + 7.62395i) q^{38} +(0.942579 - 2.90096i) q^{39} +(0.309017 - 0.951057i) q^{40} +(0.430426 + 0.312723i) q^{41} +(1.03459 + 3.18415i) q^{42} +(1.69577 + 1.23205i) q^{43} +(-3.93815 + 2.86124i) q^{44} +(0.309017 - 0.951057i) q^{45} +(-6.42118 + 4.66526i) q^{46} +(-10.9469 + 7.95340i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-3.40529 + 2.47409i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.99805 - 6.14938i) q^{51} +(-2.46770 - 1.79289i) q^{52} +(-1.98646 + 6.11370i) q^{53} +(0.309017 - 0.951057i) q^{54} +(1.50424 + 4.62958i) q^{55} +3.34801 q^{56} +8.01629 q^{57} +(-1.24646 - 3.83620i) q^{58} +(2.86977 - 2.08501i) q^{59} +(-0.809017 - 0.587785i) q^{60} -12.8491 q^{61} +(-3.48108 + 4.34536i) q^{62} +3.34801 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-2.46770 + 1.79289i) q^{65} +(1.50424 + 4.62958i) q^{66} -1.70715 q^{67} -6.46584 q^{68} +(2.45267 + 7.54854i) q^{69} +(1.03459 - 3.18415i) q^{70} +(2.29986 - 7.07823i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(3.21789 + 9.90364i) q^{73} +(4.02662 + 2.92551i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(2.47717 - 7.62395i) q^{76} +(-13.1850 + 9.57945i) q^{77} +(-2.46770 + 1.79289i) q^{78} +(1.45620 - 4.48172i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.164408 - 0.505996i) q^{82} +(6.03442 + 4.38427i) q^{83} +(1.03459 - 3.18415i) q^{84} +(-1.99805 + 6.14938i) q^{85} +(-0.647726 - 1.99349i) q^{86} -4.03362 q^{87} +4.86783 q^{88} +(2.48197 + 7.63872i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(-8.26189 - 6.00262i) q^{91} +7.93701 q^{92} +(3.05697 + 4.65349i) q^{93} +13.5311 q^{94} +(-6.48532 - 4.71186i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(0.438243 + 1.34877i) q^{97} +4.20917 q^{98} +4.86783 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 16 q^{25} + 4 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 16 q^{30} + 17 q^{31} + 16 q^{32} + 5 q^{33} + 3 q^{34} + q^{35} + 16 q^{36} + 4 q^{37} + 3 q^{38} - 6 q^{39} - 4 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} + 5 q^{44} - 4 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 33 q^{49} - 4 q^{50} + 3 q^{51} + 4 q^{52} + 9 q^{53} - 4 q^{54} + 6 q^{56} + 18 q^{57} - 15 q^{58} - 7 q^{59} - 4 q^{60} + 30 q^{61} + 12 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{65} + 86 q^{67} - 12 q^{68} - 2 q^{69} + q^{70} - 3 q^{71} - 4 q^{72} + 8 q^{73} - q^{74} - 4 q^{75} + 3 q^{76} + 2 q^{77} + 4 q^{78} + 30 q^{79} - 4 q^{80} - 4 q^{81} - 7 q^{82} + 16 q^{83} + q^{84} + 3 q^{85} - 12 q^{86} - 10 q^{88} - 29 q^{89} - 4 q^{90} + 30 q^{91} + 8 q^{92} - 8 q^{93} + 24 q^{94} - 12 q^{95} - 4 q^{96} - 5 q^{97} + 62 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^12 + 4 * q^13 + q^14 - 4 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 16 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 16 * q^30 + 17 * q^31 + 16 * q^32 + 5 * q^33 + 3 * q^34 + q^35 + 16 * q^36 + 4 * q^37 + 3 * q^38 - 6 * q^39 - 4 * q^40 - 7 * q^41 + q^42 - 2 * q^43 + 5 * q^44 - 4 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 33 * q^49 - 4 * q^50 + 3 * q^51 + 4 * q^52 + 9 * q^53 - 4 * q^54 + 6 * q^56 + 18 * q^57 - 15 * q^58 - 7 * q^59 - 4 * q^60 + 30 * q^61 + 12 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^65 + 86 * q^67 - 12 * q^68 - 2 * q^69 + q^70 - 3 * q^71 - 4 * q^72 + 8 * q^73 - q^74 - 4 * q^75 + 3 * q^76 + 2 * q^77 + 4 * q^78 + 30 * q^79 - 4 * q^80 - 4 * q^81 - 7 * q^82 + 16 * q^83 + q^84 + 3 * q^85 - 12 * q^86 - 10 * q^88 - 29 * q^89 - 4 * q^90 + 30 * q^91 + 8 * q^92 - 8 * q^93 + 24 * q^94 - 12 * q^95 - 4 * q^96 - 5 * q^97 + 62 * q^98 - 10 * 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
$7$	1.03459	+	3.18415i	0.391039	+	1.20349i	0.932004	+	0.362449i	$0.118059\pi$
$7$	1.03459	+	3.18415i	0.391039	+	1.20349i	−0.540965	+	0.841045i	$0.681941\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.809017	−	0.587785i	−0.255834	−	0.185874i
$11$	1.50424	+	4.62958i	0.453546	+	1.39587i	0.872834	+	0.488017i	$0.162280\pi$
$11$	1.50424	+	4.62958i	0.453546	+	1.39587i	−0.419288	+	0.907853i	$0.637720\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	−2.46770	+	1.79289i	−0.684418	+	0.497258i	−0.874820	−	0.484448i	$-0.839021\pi$
$13$	−2.46770	+	1.79289i	−0.684418	+	0.497258i	0.190403	+	0.981706i	$0.439021\pi$
$14$	1.03459	−	3.18415i	0.276506	−	0.850999i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.99805	+	6.14938i	−0.484599	+	1.49144i	0.347961	+	0.937509i	$0.386874\pi$
$17$	−1.99805	+	6.14938i	−0.484599	+	1.49144i	−0.832561	+	0.553934i	$0.813126\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	−6.48532	−	4.71186i	−1.48783	−	1.08097i	−0.974926	−	0.222531i	$-0.928568\pi$
$19$	−6.48532	−	4.71186i	−1.48783	−	1.08097i	−0.512908	−	0.858444i	$-0.671432\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	−2.70860	−	1.96791i	−0.591064	−	0.429433i
$22$	1.50424	−	4.62958i	0.320705	−	0.987029i
$23$	2.45267	−	7.54854i	0.511417	−	1.57398i	−0.278290	−	0.960497i	$-0.589768\pi$
$23$	2.45267	−	7.54854i	0.511417	−	1.57398i	0.789708	−	0.613483i	$-0.210232\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	1.00000			0.200000
$26$	3.05025			0.598203
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−2.70860	+	1.96791i	−0.511877	+	0.371900i
$29$	3.26327	+	2.37090i	0.605974	+	0.440266i	0.847994	−	0.530005i	$-0.177810\pi$
$29$	3.26327	+	2.37090i	0.605974	+	0.440266i	−0.242020	+	0.970271i	$0.577810\pi$
$30$	1.00000			0.182574
$31$	0.262113	−	5.56159i	0.0470769	−	0.998891i
$31$	0.262113	−	5.56159i	0.0470769	−	0.998891i
$32$	1.00000			0.176777
$33$	−3.93815	−	2.86124i	−0.685545	−	0.498077i
$34$	5.23097	−	3.80052i	0.897104	−	0.651784i
$35$	1.03459	+	3.18415i	0.174878	+	0.538219i
$36$	1.00000			0.166667
$37$	−4.97717			−0.818242			−0.409121	−	0.912480i	$-0.634165\pi$
$37$	−4.97717			−0.818242			−0.409121	+	0.912480i	$0.634165\pi$
$38$	2.47717	+	7.62395i	0.401850	+	1.23677i
$39$	0.942579	−	2.90096i	0.150933	−	0.464525i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	0.430426	+	0.312723i	0.0672213	+	0.0488391i	0.620888	−	0.783899i	$-0.286772\pi$
$41$	0.430426	+	0.312723i	0.0672213	+	0.0488391i	−0.553667	+	0.832738i	$0.686772\pi$
$42$	1.03459	+	3.18415i	0.159641	+	0.491324i
$43$	1.69577	+	1.23205i	0.258602	+	0.187885i	0.709531	−	0.704675i	$-0.248907\pi$
$43$	1.69577	+	1.23205i	0.258602	+	0.187885i	−0.450928	+	0.892560i	$0.648907\pi$
$44$	−3.93815	+	2.86124i	−0.593699	+	0.431348i
$45$	0.309017	−	0.951057i	0.0460655	−	0.141775i
$46$	−6.42118	+	4.66526i	−0.946751	+	0.687855i
$47$	−10.9469	+	7.95340i	−1.59677	+	1.16012i	−0.703409	+	0.710786i	$0.748340\pi$
$47$	−10.9469	+	7.95340i	−1.59677	+	1.16012i	−0.893362	+	0.449337i	$0.851660\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−3.40529	+	2.47409i	−0.486470	+	0.353441i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	−1.99805	−	6.14938i	−0.279783	−	0.861085i
$52$	−2.46770	−	1.79289i	−0.342209	−	0.248629i
$53$	−1.98646	+	6.11370i	−0.272861	+	0.839781i	0.716916	+	0.697160i	$0.245553\pi$
$53$	−1.98646	+	6.11370i	−0.272861	+	0.839781i	−0.989777	+	0.142621i	$0.954447\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	1.50424	+	4.62958i	0.202832	+	0.624252i
$56$	3.34801			0.447397
$57$	8.01629			1.06178
$58$	−1.24646	−	3.83620i	−0.163668	−	0.503718i
$59$	2.86977	−	2.08501i	0.373613	−	0.271445i	−0.385095	−	0.922877i	$-0.625831\pi$
$59$	2.86977	−	2.08501i	0.373613	−	0.271445i	0.758707	+	0.651432i	$0.225831\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	−12.8491			−1.64516			−0.822578	−	0.568653i	$-0.807465\pi$
$61$	−12.8491			−1.64516			−0.822578	+	0.568653i	$0.807465\pi$
$62$	−3.48108	+	4.34536i	−0.442097	+	0.551861i
$63$	3.34801			0.421810
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−2.46770	+	1.79289i	−0.306081	+	0.222381i
$66$	1.50424	+	4.62958i	0.185159	+	0.569862i
$67$	−1.70715			−0.208561			−0.104281	−	0.994548i	$-0.533254\pi$
$67$	−1.70715			−0.208561			−0.104281	+	0.994548i	$0.533254\pi$
$68$	−6.46584			−0.784098
$69$	2.45267	+	7.54854i	0.295267	+	0.908738i
$70$	1.03459	−	3.18415i	0.123657	−	0.380578i
$71$	2.29986	−	7.07823i	0.272943	−	0.840031i	−0.716814	−	0.697265i	$-0.754400\pi$
$71$	2.29986	−	7.07823i	0.272943	−	0.840031i	0.989756	−	0.142766i	$-0.0455998\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	3.21789	+	9.90364i	0.376625	+	1.15913i	0.942376	+	0.334557i	$0.108587\pi$
$73$	3.21789	+	9.90364i	0.376625	+	1.15913i	−0.565751	+	0.824576i	$0.691413\pi$
$74$	4.02662	+	2.92551i	0.468085	+	0.340083i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$	2.47717	−	7.62395i	0.284151	−	0.874527i
$77$	−13.1850	+	9.57945i	−1.50257	+	1.09168i
$78$	−2.46770	+	1.79289i	−0.279412	+	0.203005i
$79$	1.45620	−	4.48172i	0.163835	−	0.504233i	−0.835113	−	0.550078i	$-0.814598\pi$
$79$	1.45620	−	4.48172i	0.163835	−	0.504233i	0.998949	+	0.0458450i	$0.0145980\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.164408	−	0.505996i	−0.0181558	−	0.0558779i
$83$	6.03442	+	4.38427i	0.662364	+	0.481236i	0.867461	−	0.497506i	$-0.165751\pi$
$83$	6.03442	+	4.38427i	0.662364	+	0.481236i	−0.205096	+	0.978742i	$0.565751\pi$
$84$	1.03459	−	3.18415i	0.112883	−	0.347419i
$85$	−1.99805	+	6.14938i	−0.216719	+	0.666994i
$86$	−0.647726	−	1.99349i	−0.0698461	−	0.214964i
$87$	−4.03362			−0.432450
$88$	4.86783			0.518912
$89$	2.48197	+	7.63872i	0.263088	+	0.809703i	0.992128	+	0.125231i	$0.0399672\pi$
$89$	2.48197	+	7.63872i	0.263088	+	0.809703i	−0.729039	+	0.684472i	$0.760033\pi$
$90$	−0.809017	+	0.587785i	−0.0852779	+	0.0619580i
$91$	−8.26189	−	6.00262i	−0.866082	−	0.629245i
$92$	7.93701			0.827490
$93$	3.05697	+	4.65349i	0.316993	+	0.482544i
$94$	13.5311			1.39563
$95$	−6.48532	−	4.71186i	−0.665379	−	0.483426i
$96$	−0.809017	+	0.587785i	−0.0825700	+	0.0599906i
$97$	0.438243	+	1.34877i	0.0444968	+	0.136947i	0.970837	−	0.239741i	$-0.0770627\pi$
$97$	0.438243	+	1.34877i	0.0444968	+	0.136947i	−0.926340	+	0.376689i	$0.877063\pi$
$98$	4.20917			0.425190
$99$	4.86783			0.489235
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−5.25414	+	16.1706i	−0.522806	+	1.60903i	0.245807	+	0.969319i	$0.420947\pi$
$101$	−5.25414	+	16.1706i	−0.522806	+	1.60903i	−0.768613	+	0.639713i	$0.779053\pi$
$102$	−1.99805	+	6.14938i	−0.197837	+	0.608879i
$103$	9.32762	+	6.77691i	0.919077	+	0.667749i	0.943294	−	0.331958i	$-0.107709\pi$
$103$	9.32762	+	6.77691i	0.919077	+	0.667749i	−0.0242167	+	0.999707i	$0.507709\pi$
$104$	0.942579	+	2.90096i	0.0924274	+	0.284462i
$105$	−2.70860	−	1.96791i	−0.264332	−	0.192048i
$106$	5.20062	−	3.77847i	0.505129	−	0.366998i
$107$	−1.77144	+	5.45192i	−0.171251	+	0.527057i	−0.999442	−	0.0333887i	$-0.989370\pi$
$107$	−1.77144	+	5.45192i	−0.171251	+	0.527057i	0.828191	+	0.560445i	$0.189370\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	4.59104	−	3.33559i	0.439742	−	0.319491i	−0.345790	−	0.938312i	$-0.612389\pi$
$109$	4.59104	−	3.33559i	0.439742	−	0.319491i	0.785533	+	0.618820i	$0.212389\pi$
$110$	1.50424	−	4.62958i	0.143424	−	0.441413i
$111$	4.02662	−	2.92551i	0.382190	−	0.277677i
$112$	−2.70860	−	1.96791i	−0.255938	−	0.185950i
$113$	−1.96875	−	6.05920i	−0.185205	−	0.570001i	0.814747	−	0.579816i	$-0.196876\pi$
$113$	−1.96875	−	6.05920i	−0.185205	−	0.570001i	−0.999952	+	0.00981504i	$0.996876\pi$
$114$	−6.48532	−	4.71186i	−0.607406	−	0.441306i
$115$	2.45267	−	7.54854i	0.228713	−	0.703905i
$116$	−1.24646	+	3.83620i	−0.115731	+	0.356183i
$117$	0.942579	+	2.90096i	0.0871414	+	0.268194i
$118$	−3.54723			−0.326549
$119$	−21.6477			−1.98444
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	−10.2711	+	7.46236i	−0.933733	+	0.678397i
$122$	10.3951	+	7.55250i	0.941130	+	0.683771i
$123$	−0.532036			−0.0479721
$124$	5.37038	−	1.46934i	0.482275	−	0.131951i
$125$	1.00000			0.0894427
$126$	−2.70860	−	1.96791i	−0.241301	−	0.175315i
$127$	−11.1390	+	8.09294i	−0.988425	+	0.718133i	−0.959576	−	0.281451i	$-0.909184\pi$
$127$	−11.1390	+	8.09294i	−0.988425	+	0.718133i	−0.0288492	+	0.999584i	$0.509184\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−2.09608			−0.184550
$130$	3.05025			0.267524
$131$	0.0277742	+	0.0854802i	0.00242664	+	0.00746844i	0.952263	−	0.305280i	$-0.0987502\pi$
$131$	0.0277742	+	0.0854802i	0.00242664	+	0.00746844i	−0.949836	+	0.312749i	$0.898750\pi$
$132$	1.50424	−	4.62958i	0.130927	−	0.402953i
$133$	8.29359	−	25.5250i	0.719145	−	2.21330i
$134$	1.38111	+	1.00344i	0.119310	+	0.0866837i
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$	5.23097	+	3.80052i	0.448552	+	0.325892i
$137$	14.6549	−	10.6474i	1.25206	−	0.909672i	0.253716	−	0.967279i	$-0.418347\pi$
$137$	14.6549	−	10.6474i	1.25206	−	0.909672i	0.998339	+	0.0576070i	$0.0183470\pi$
$138$	2.45267	−	7.54854i	0.208785	−	0.642575i
$139$	−0.791701	+	0.575205i	−0.0671512	+	0.0487882i	−0.620854	−	0.783926i	$-0.713214\pi$
$139$	−0.791701	+	0.575205i	−0.0671512	+	0.0487882i	0.553703	+	0.832714i	$0.313214\pi$
$140$	−2.70860	+	1.96791i	−0.228918	+	0.166319i
$141$	4.18135	−	12.8689i	0.352133	−	1.08375i
$142$	−6.02110	+	4.37459i	−0.505280	+	0.367107i
$143$	−12.0123	−	8.72748i	−1.00452	−	0.729829i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	3.26327	+	2.37090i	0.271000	+	0.196893i
$146$	3.21789	−	9.90364i	0.266314	−	0.819631i
$147$	1.30070	−	4.00316i	0.107280	−	0.330175i
$148$	−1.53803	−	4.73357i	−0.126425	−	0.389097i
$149$	19.6302			1.60817			0.804085	−	0.594514i	$-0.202656\pi$
$149$	19.6302			1.60817			0.804085	+	0.594514i	$0.202656\pi$
$150$	1.00000			0.0816497
$151$	−3.65243	−	11.2410i	−0.297231	−	0.914782i	−0.982463	−	0.186458i	$-0.940299\pi$
$151$	−3.65243	−	11.2410i	−0.297231	−	0.914782i	0.685232	−	0.728325i	$-0.259701\pi$
$152$	−6.48532	+	4.71186i	−0.526029	+	0.382182i
$153$	5.23097	+	3.80052i	0.422899	+	0.307254i
$154$	16.2975			1.31329
$155$	0.262113	−	5.56159i	0.0210534	−	0.446718i
$156$	3.05025			0.244215
$157$	4.56771	+	3.31863i	0.364543	+	0.264856i	0.754944	−	0.655789i	$-0.227664\pi$
$157$	4.56771	+	3.31863i	0.364543	+	0.264856i	−0.390402	+	0.920645i	$0.627664\pi$
$158$	−3.81238	+	2.76985i	−0.303296	+	0.220358i
$159$	−1.98646	−	6.11370i	−0.157537	−	0.484848i
$160$	1.00000			0.0790569
$161$	26.5732			2.09426
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−0.185547	+	0.571054i	−0.0145331	+	0.0447284i	−0.958060	−	0.286567i	$-0.907486\pi$
$163$	−0.185547	+	0.571054i	−0.0145331	+	0.0447284i	0.943527	+	0.331296i	$0.107486\pi$
$164$	−0.164408	+	0.505996i	−0.0128381	+	0.0395117i
$165$	−3.93815	−	2.86124i	−0.306585	−	0.222747i
$166$	−2.30495	−	7.09389i	−0.178898	−	0.550593i
$167$	15.5217	+	11.2772i	1.20111	+	0.872656i	0.994393	−	0.105745i	$-0.0337228\pi$
$167$	15.5217	+	11.2772i	1.20111	+	0.872656i	0.206715	+	0.978401i	$0.433723\pi$
$168$	−2.70860	+	1.96791i	−0.208973	+	0.151828i
$169$	−1.14212	+	3.51509i	−0.0878555	+	0.270392i
$170$	5.23097	−	3.80052i	0.401197	−	0.291487i
$171$	−6.48532	+	4.71186i	−0.495945	+	0.360325i
$172$	−0.647726	+	1.99349i	−0.0493886	+	0.152003i
$173$	−8.36359	+	6.07651i	−0.635872	+	0.461988i	−0.858430	−	0.512931i	$-0.828560\pi$
$173$	−8.36359	+	6.07651i	−0.635872	+	0.461988i	0.222557	+	0.974920i	$0.428560\pi$
$174$	3.26327	+	2.37090i	0.247388	+	0.179738i
$175$	1.03459	+	3.18415i	0.0782078	+	0.240699i
$176$	−3.93815	−	2.86124i	−0.296850	−	0.215674i
$177$	−1.09616	+	3.37362i	−0.0823921	+	0.253577i
$178$	2.48197	−	7.63872i	0.186032	−	0.572547i
$179$	−1.55063	−	4.77233i	−0.115899	−	0.356701i	0.876234	−	0.481885i	$-0.160048\pi$
$179$	−1.55063	−	4.77233i	−0.115899	−	0.356701i	−0.992134	+	0.125184i	$0.960048\pi$
$180$	1.00000			0.0745356
$181$	15.3207			1.13878			0.569389	−	0.822068i	$-0.307180\pi$
$181$	15.3207			1.13878			0.569389	+	0.822068i	$0.307180\pi$
$182$	3.15576	+	9.71244i	0.233921	+	0.719934i
$183$	10.3951	−	7.55250i	0.768429	−	0.558297i
$184$	−6.42118	−	4.66526i	−0.473375	−	0.343927i
$185$	−4.97717			−0.365929
$186$	0.262113	−	5.56159i	0.0192191	−	0.407796i
$187$	−31.4746			−2.30165
$188$	−10.9469	−	7.95340i	−0.798386	−	0.580061i
$189$	−2.70860	+	1.96791i	−0.197021	+	0.143144i
$190$	2.47717	+	7.62395i	0.179713	+	0.553099i
$191$	2.99484			0.216699			0.108349	−	0.994113i	$-0.465443\pi$
$191$	2.99484			0.216699			0.108349	+	0.994113i	$0.465443\pi$
$192$	1.00000			0.0721688
$193$	−7.86639	−	24.2103i	−0.566235	−	1.74269i	−0.664252	−	0.747509i	$-0.731250\pi$
$193$	−7.86639	−	24.2103i	−0.566235	−	1.74269i	0.0980165	−	0.995185i	$-0.468750\pi$
$194$	0.438243	−	1.34877i	0.0314640	−	0.0968363i
$195$	0.942579	−	2.90096i	0.0674995	−	0.207742i
$196$	−3.40529	−	2.47409i	−0.243235	−	0.176720i
$197$	7.48006	+	23.0213i	0.532932	+	1.64020i	0.748075	+	0.663614i	$0.230978\pi$
$197$	7.48006	+	23.0213i	0.532932	+	1.64020i	−0.215143	+	0.976583i	$0.569022\pi$
$198$	−3.93815	−	2.86124i	−0.279872	−	0.203339i
$199$	12.6754	−	9.20920i	0.898534	−	0.652823i	−0.0395552	−	0.999217i	$-0.512594\pi$
$199$	12.6754	−	9.20920i	0.898534	−	0.652823i	0.938089	+	0.346394i	$0.112594\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	1.38111	−	1.00344i	0.0974161	−	0.0707769i
$202$	13.7555	−	9.99396i	0.967834	−	0.703173i
$203$	−4.17315	+	12.8436i	−0.292898	+	0.901447i
$204$	5.23097	−	3.80052i	0.366241	−	0.266090i
$205$	0.430426	+	0.312723i	0.0300623	+	0.0218415i
$206$	−3.56283	−	10.9653i	−0.248234	−	0.763987i
$207$	−6.42118	−	4.66526i	−0.446303	−	0.324258i
$208$	0.942579	−	2.90096i	0.0653561	−	0.201145i
$209$	12.0584	−	37.1120i	0.834099	−	2.56709i
$210$	1.03459	+	3.18415i	0.0713936	+	0.219727i
$211$	−8.39359			−0.577838			−0.288919	−	0.957353i	$-0.593296\pi$
$211$	−8.39359			−0.577838			−0.288919	+	0.957353i	$0.593296\pi$
$212$	−6.42832			−0.441499
$213$	2.29986	+	7.07823i	0.157584	+	0.484992i
$214$	4.63768	−	3.36947i	0.317025	−	0.230332i
$215$	1.69577	+	1.23205i	0.115650	+	0.0840249i
$216$	1.00000			0.0680414
$217$	17.9801	−	4.91937i	1.22057	−	0.333949i
$218$	−5.67484			−0.384349
$219$	−8.42454	−	6.12078i	−0.569277	−	0.413604i
$220$	−3.93815	+	2.86124i	−0.265510	+	0.192905i
$221$	−6.09456	−	18.7571i	−0.409964	−	1.26174i
$222$	−4.97717			−0.334046
$223$	−26.5441			−1.77753			−0.888763	−	0.458367i	$-0.848435\pi$
$223$	−26.5441			−1.77753			−0.888763	+	0.458367i	$0.848435\pi$
$224$	1.03459	+	3.18415i	0.0691266	+	0.212750i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−1.96875	+	6.05920i	−0.130959	+	0.403052i
$227$	−6.71530	−	4.87895i	−0.445710	−	0.323827i	0.342190	−	0.939631i	$-0.388831\pi$
$227$	−6.71530	−	4.87895i	−0.445710	−	0.323827i	−0.787900	+	0.615804i	$0.788831\pi$
$228$	2.47717	+	7.62395i	0.164055	+	0.504908i
$229$	4.16080	+	3.02300i	0.274953	+	0.199765i	0.716713	−	0.697368i	$-0.245646\pi$
$229$	4.16080	+	3.02300i	0.274953	+	0.199765i	−0.441760	+	0.897133i	$0.645646\pi$
$230$	−6.42118	+	4.66526i	−0.423400	+	0.307618i
$231$	5.03621	−	15.4999i	0.331358	−	1.01982i
$232$	3.26327	−	2.37090i	0.214244	−	0.155657i
$233$	−2.09838	+	1.52456i	−0.137469	+	0.0998774i	−0.654395	−	0.756153i	$-0.727077\pi$
$233$	−2.09838	+	1.52456i	−0.137469	+	0.0998774i	0.516925	+	0.856031i	$0.327077\pi$
$234$	0.942579	−	2.90096i	0.0616183	−	0.189642i
$235$	−10.9469	+	7.95340i	−0.714098	+	0.518822i
$236$	2.86977	+	2.08501i	0.186806	+	0.135723i
$237$	1.45620	+	4.48172i	0.0945903	+	0.291119i
$238$	17.5133	+	12.7242i	1.13522	+	0.824787i
$239$	−1.82378	+	5.61300i	−0.117970	+	0.363075i	−0.992555	−	0.121798i	$-0.961134\pi$
$239$	−1.82378	+	5.61300i	−0.117970	+	0.363075i	0.874585	+	0.484873i	$0.161134\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	4.67464	+	14.3871i	0.301120	+	0.926752i	0.981097	+	0.193519i	$0.0619900\pi$
$241$	4.67464	+	14.3871i	0.301120	+	0.926752i	−0.679977	+	0.733234i	$0.738010\pi$
$242$	12.6957			0.816113
$243$	1.00000			0.0641500
$244$	−3.97058	−	12.2202i	−0.254190	−	0.782318i
$245$	−3.40529	+	2.47409i	−0.217556	+	0.158064i
$246$	0.430426	+	0.312723i	0.0274430	+	0.0199385i
$247$	24.4517			1.55582
$248$	−5.20839	−	1.96791i	−0.330733	−	0.124962i
$249$	−7.45896			−0.472692
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	15.2517	−	11.0810i	0.962676	−	0.699425i	0.00890553	−	0.999960i	$-0.497165\pi$
$251$	15.2517	−	11.0810i	0.962676	−	0.699425i	0.953771	+	0.300535i	$0.0971652\pi$
$252$	1.03459	+	3.18415i	0.0651732	+	0.200582i
$253$	38.6360			2.42902
$254$	13.7685			0.863915
$255$	−1.99805	−	6.14938i	−0.125123	−	0.385089i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.29966	+	7.07764i	−0.143449	+	0.441491i	−0.996808	−	0.0798324i	$-0.974561\pi$
$257$	−2.29966	+	7.07764i	−0.143449	+	0.441491i	0.853359	+	0.521323i	$0.174561\pi$
$258$	1.69577	+	1.23205i	0.105574	+	0.0767039i
$259$	−5.14934	−	15.8480i	−0.319964	−	0.984749i
$260$	−2.46770	−	1.79289i	−0.153040	−	0.111190i
$261$	3.26327	−	2.37090i	0.201991	−	0.146755i
$262$	0.0277742	−	0.0854802i	0.00171590	−	0.00528098i
$263$	21.7135	−	15.7758i	1.33891	−	0.972775i	0.339426	−	0.940633i	$-0.389767\pi$
$263$	21.7135	−	15.7758i	1.33891	−	0.972775i	0.999483	−	0.0321420i	$-0.0102329\pi$
$264$	−3.93815	+	2.86124i	−0.242377	+	0.176097i
$265$	−1.98646	+	6.11370i	−0.122027	+	0.375561i
$266$	−21.7129	+	15.7753i	−1.33130	+	0.967248i
$267$	−6.49789	−	4.72099i	−0.397664	−	0.288920i
$268$	−0.527538	−	1.62359i	−0.0322245	−	0.0991768i
$269$	1.59428	+	1.15831i	0.0972050	+	0.0706236i	0.635326	−	0.772244i	$-0.280866\pi$
$269$	1.59428	+	1.15831i	0.0972050	+	0.0706236i	−0.538121	+	0.842868i	$0.680866\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	1.47408	−	4.53675i	0.0895439	−	0.275588i	−0.896250	−	0.443550i	$-0.853719\pi$
$271$	1.47408	−	4.53675i	0.0895439	−	0.275588i	0.985793	+	0.167963i	$0.0537188\pi$
$272$	−1.99805	−	6.14938i	−0.121150	−	0.372861i
$273$	10.2123			0.618074
$274$	−18.1145			−1.09434
$275$	1.50424	+	4.62958i	0.0907091	+	0.279174i
$276$	−6.42118	+	4.66526i	−0.386509	+	0.280815i
$277$	−10.0908	−	7.33140i	−0.606297	−	0.440501i	0.241811	−	0.970323i	$-0.422259\pi$
$277$	−10.0908	−	7.33140i	−0.606297	−	0.440501i	−0.848109	+	0.529822i	$0.822259\pi$
$278$	0.978596			0.0586923
$279$	−5.20839	−	1.96791i	−0.311818	−	0.117816i
$280$	3.34801			0.200082
$281$	3.64008	+	2.64467i	0.217149	+	0.157768i	0.691042	−	0.722814i	$-0.257152\pi$
$281$	3.64008	+	2.64467i	0.217149	+	0.157768i	−0.473894	+	0.880582i	$0.657152\pi$
$282$	−10.9469	+	7.95340i	−0.651879	+	0.473618i
$283$	2.41871	+	7.44402i	0.143777	+	0.442501i	0.996852	−	0.0792881i	$-0.0252647\pi$
$283$	2.41871	+	7.44402i	0.143777	+	0.442501i	−0.853074	+	0.521789i	$0.825265\pi$
$284$	7.44249			0.441631
$285$	8.01629			0.474844
$286$	4.58831	+	14.1214i	0.271312	+	0.835014i
$287$	−0.550440	+	1.69408i	−0.0324914	+	0.0999984i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	−20.0693	−	14.5812i	−1.18055	−	0.857719i
$290$	−1.24646	−	3.83620i	−0.0731945	−	0.225270i
$291$	−1.14734	−	0.833588i	−0.0672580	−	0.0488658i
$292$	−8.42454	+	6.12078i	−0.493009	+	0.358192i
$293$	4.59578	−	14.1444i	0.268489	−	0.826323i	−0.722381	−	0.691496i	$-0.756952\pi$
$293$	4.59578	−	14.1444i	0.268489	−	0.826323i	0.990869	−	0.134827i	$-0.0430479\pi$
$294$	−3.40529	+	2.47409i	−0.198600	+	0.144292i
$295$	2.86977	−	2.08501i	0.167085	−	0.121394i
$296$	−1.53803	+	4.73357i	−0.0893962	+	0.275133i
$297$	−3.93815	+	2.86124i	−0.228515	+	0.166026i
$298$	−15.8812	−	11.5384i	−0.919972	−	0.668399i
$299$	7.48126	+	23.0249i	0.432652	+	1.33157i
$300$	−0.809017	−	0.587785i	−0.0467086	−	0.0339358i
$301$	−2.16859	+	6.67424i	−0.124996	+	0.384697i
$302$	−3.65243	+	11.2410i	−0.210174	+	0.646849i
$303$	−5.25414	−	16.1706i	−0.301842	−	0.928975i
$304$	8.01629			0.459766
$305$	−12.8491			−0.735736
$306$	−1.99805	−	6.14938i	−0.114221	−	0.351536i
$307$	−16.8265	+	12.2252i	−0.960340	+	0.697728i	−0.953230	−	0.302247i	$-0.902263\pi$
$307$	−16.8265	+	12.2252i	−0.960340	+	0.697728i	−0.00711065	+	0.999975i	$0.502263\pi$
$308$	−13.1850	−	9.57945i	−0.751284	−	0.545840i
$309$	−11.5296			−0.655894
$310$	−3.48108	+	4.34536i	−0.197712	+	0.246800i
$311$	−21.2493			−1.20494			−0.602470	−	0.798142i	$-0.705817\pi$
$311$	−21.2493			−1.20494			−0.602470	+	0.798142i	$0.705817\pi$
$312$	−2.46770	−	1.79289i	−0.139706	−	0.101502i
$313$	−12.5839	+	9.14275i	−0.711285	+	0.516779i	−0.883588	−	0.468265i	$-0.844879\pi$
$313$	−12.5839	+	9.14275i	−0.711285	+	0.516779i	0.172303	+	0.985044i	$0.444879\pi$
$314$	−1.74471	−	5.36966i	−0.0984597	−	0.303028i
$315$	3.34801			0.188639
$316$	4.71236			0.265091
$317$	−5.69864	−	17.5386i	−0.320067	−	0.985066i	−0.973618	−	0.228183i	$-0.926721\pi$
$317$	−5.69864	−	17.5386i	−0.320067	−	0.985066i	0.653551	−	0.756883i	$-0.273279\pi$
$318$	−1.98646	+	6.11370i	−0.111395	+	0.342839i
$319$	−6.06754	+	18.6740i	−0.339717	+	1.04554i
$320$	−0.809017	−	0.587785i	−0.0452254	−	0.0328582i
$321$	−1.77144	−	5.45192i	−0.0988719	−	0.304296i
$322$	−21.4982	−	15.6193i	−1.19805	−	0.870431i
$323$	41.9330	−	30.4661i	2.33321	−	1.69518i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	−2.46770	+	1.79289i	−0.136884	+	0.0994517i
$326$	0.485768	−	0.352931i	0.0269042	−	0.0195470i
$327$	−1.75362	+	5.39710i	−0.0969756	+	0.298460i
$328$	0.430426	−	0.312723i	0.0237663	−	0.0172672i
$329$	−36.6504	−	26.6280i	−2.02060	−	1.46805i
$330$	1.50424	+	4.62958i	0.0828057	+	0.254850i
$331$	16.6662	+	12.1087i	0.916059	+	0.665556i	0.942540	−	0.334093i	$-0.108430\pi$
$331$	16.6662	+	12.1087i	0.916059	+	0.665556i	−0.0264806	+	0.999649i	$0.508430\pi$
$332$	−2.30495	+	7.09389i	−0.126500	+	0.389328i
$333$	−1.53803	+	4.73357i	−0.0842836	+	0.259398i
$334$	−5.92878	−	18.2469i	−0.324408	−	0.998426i
$335$	−1.70715			−0.0932714
$336$	3.34801			0.182649
$337$	−2.40631	−	7.40587i	−0.131080	−	0.403423i	0.863880	−	0.503698i	$-0.168028\pi$
$337$	−2.40631	−	7.40587i	−0.131080	−	0.403423i	−0.994960	+	0.100275i	$0.968028\pi$
$338$	2.99011	−	2.17245i	0.162641	−	0.118165i
$339$	5.15426	+	3.74479i	0.279941	+	0.203389i
$340$	−6.46584			−0.350659
$341$	26.1421	−	7.15250i	1.41567	−	0.387330i
$342$	8.01629			0.433471
$343$	7.55924	+	5.49211i	0.408161	+	0.296546i
$344$	1.69577	−	1.23205i	0.0914297	−	0.0664276i
$345$	2.45267	+	7.54854i	0.132047	+	0.406400i
$346$	10.3380			0.555773
$347$	2.01796			0.108330			0.0541649	−	0.998532i	$-0.482750\pi$
$347$	2.01796			0.108330			0.0541649	+	0.998532i	$0.482750\pi$
$348$	−1.24646	−	3.83620i	−0.0668172	−	0.205642i
$349$	−7.17791	+	22.0913i	−0.384225	+	1.18252i	0.552816	+	0.833303i	$0.313553\pi$
$349$	−7.17791	+	22.0913i	−0.384225	+	1.18252i	−0.937041	+	0.349219i	$0.886447\pi$
$350$	1.03459	−	3.18415i	0.0553013	−	0.170200i
$351$	−2.46770	−	1.79289i	−0.131716	−	0.0956974i
$352$	1.50424	+	4.62958i	0.0801763	+	0.246757i
$353$	18.1377	+	13.1778i	0.965371	+	0.701383i	0.954392	−	0.298557i	$-0.0965052\pi$
$353$	18.1377	+	13.1778i	0.965371	+	0.701383i	0.0109789	+	0.999940i	$0.496505\pi$
$354$	2.86977	−	2.08501i	0.152527	−	0.110817i
$355$	2.29986	−	7.07823i	0.122064	−	0.375673i
$356$	−6.49789	+	4.72099i	−0.344387	+	0.250212i
$357$	17.5133	−	12.7242i	0.926904	−	0.673435i
$358$	−1.55063	+	4.77233i	−0.0819531	+	0.252226i
$359$	−8.84747	+	6.42806i	−0.466952	+	0.339260i	−0.796252	−	0.604965i	$-0.793187\pi$
$359$	−8.84747	+	6.42806i	−0.466952	+	0.339260i	0.329300	+	0.944225i	$0.393187\pi$
$360$	−0.809017	−	0.587785i	−0.0426389	−	0.0309790i
$361$	13.9864	+	43.0457i	0.736126	+	2.26556i
$362$	−12.3947	−	9.00528i	−0.651451	−	0.473307i
$363$	3.92320	−	12.0744i	0.205914	−	0.633739i
$364$	3.15576	−	9.71244i	0.165407	−	0.509070i
$365$	3.21789	+	9.90364i	0.168432	+	0.518380i
$366$	−12.8491			−0.671632
$367$	35.7485			1.86606			0.933029	−	0.359802i	$-0.117156\pi$
$367$	35.7485			1.86606			0.933029	+	0.359802i	$0.117156\pi$
$368$	2.45267	+	7.54854i	0.127854	+	0.393495i
$369$	0.430426	−	0.312723i	0.0224071	−	0.0162797i
$370$	4.02662	+	2.92551i	0.209334	+	0.152090i
$371$	−21.5221			−1.11737
$372$	−3.48108	+	4.34536i	−0.180485	+	0.225296i
$373$	−1.01571			−0.0525915			−0.0262957	−	0.999654i	$-0.508371\pi$
$373$	−1.01571			−0.0525915			−0.0262957	+	0.999654i	$0.508371\pi$
$374$	25.4635	+	18.5003i	1.31668	+	0.956627i
$375$	−0.809017	+	0.587785i	−0.0417775	+	0.0303531i
$376$	4.18135	+	12.8689i	0.215637	+	0.663661i
$377$	−12.3036			−0.633665
$378$	3.34801			0.172203
$379$	2.43032	+	7.47976i	0.124837	+	0.384210i	0.993871	−	0.110543i	$-0.0352588\pi$
$379$	2.43032	+	7.47976i	0.124837	+	0.384210i	−0.869034	+	0.494752i	$0.835259\pi$
$380$	2.47717	−	7.62395i	0.127076	−	0.391100i
$381$	4.25471	−	13.0947i	0.217976	−	0.670860i
$382$	−2.42287	−	1.76032i	−0.123965	−	0.0900658i
$383$	−9.13368	−	28.1106i	−0.466709	−	1.43638i	−0.856820	−	0.515616i	$-0.827563\pi$
$383$	−9.13368	−	28.1106i	−0.466709	−	1.43638i	0.390110	−	0.920768i	$-0.372437\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	−13.1850	+	9.57945i	−0.671969	+	0.488214i
$386$	−7.86639	+	24.2103i	−0.400389	+	1.23227i
$387$	1.69577	−	1.23205i	0.0862007	−	0.0626285i
$388$	−1.14734	+	0.833588i	−0.0582471	+	0.0423190i
$389$	−7.69448	+	23.6812i	−0.390125	+	1.20068i	0.542568	+	0.840012i	$0.317452\pi$
$389$	−7.69448	+	23.6812i	−0.390125	+	1.20068i	−0.932693	+	0.360671i	$0.882548\pi$
$390$	−2.46770	+	1.79289i	−0.124957	+	0.0907866i
$391$	41.5183	+	30.1648i	2.09967	+	1.52550i
$392$	1.30070	+	4.00316i	0.0656955	+	0.202190i
$393$	−0.0727138	−	0.0528297i	−0.00366793	−	0.00266490i
$394$	7.48006	−	23.0213i	0.376840	−	1.15979i
$395$	1.45620	−	4.48172i	0.0732693	−	0.225500i
$396$	1.50424	+	4.62958i	0.0755910	+	0.232645i
$397$	4.64449			0.233100			0.116550	−	0.993185i	$-0.462816\pi$
$397$	4.64449			0.233100			0.116550	+	0.993185i	$0.462816\pi$
$398$	−15.6676			−0.785347
$399$	8.29359	+	25.5250i	0.415199	+	1.27785i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	23.2615	+	16.9005i	1.16162	+	0.843970i	0.989983	−	0.141190i	$-0.0450927\pi$
$401$	23.2615	+	16.9005i	1.16162	+	0.843970i	0.171642	+	0.985159i	$0.445093\pi$
$402$	−1.70715			−0.0851448
$403$	9.32451	+	14.1943i	0.464487	+	0.707068i
$404$	−17.0027			−0.845918
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	10.9255	−	7.93781i	0.542221	−	0.393947i
$407$	−7.48687	−	23.0422i	−0.371110	−	1.14216i
$408$	−6.46584			−0.320107
$409$	13.2932			0.657307			0.328654	−	0.944451i	$-0.393405\pi$
$409$	13.2932			0.657307			0.328654	+	0.944451i	$0.393405\pi$
$410$	−0.164408	−	0.505996i	−0.00811954	−	0.0249894i
$411$	−5.59769	+	17.2279i	−0.276114	+	0.849790i
$412$	−3.56283	+	10.9653i	−0.175528	+	0.540220i
$413$	9.60803	+	6.98064i	0.472780	+	0.343495i
$414$	2.45267	+	7.54854i	0.120542	+	0.370991i
$415$	6.03442	+	4.38427i	0.296218	+	0.215215i
$416$	−2.46770	+	1.79289i	−0.120989	+	0.0879037i
$417$	0.302403	−	0.930700i	0.0148087	−	0.0455766i
$418$	−31.5694	+	22.9365i	−1.54411	+	1.12186i
$419$	16.3138	−	11.8527i	0.796982	−	0.579042i	−0.113045	−	0.993590i	$-0.536060\pi$
$419$	16.3138	−	11.8527i	0.796982	−	0.579042i	0.910027	+	0.414548i	$0.136060\pi$
$420$	1.03459	−	3.18415i	0.0504829	−	0.155370i
$421$	1.33048	−	0.966649i	0.0648435	−	0.0471116i	−0.554891	−	0.831923i	$-0.687240\pi$
$421$	1.33048	−	0.966649i	0.0648435	−	0.0471116i	0.619735	+	0.784811i	$0.287240\pi$
$422$	6.79055	+	4.93363i	0.330559	+	0.240165i
$423$	4.18135	+	12.8689i	0.203304	+	0.625706i
$424$	5.20062	+	3.77847i	0.252564	+	0.183499i
$425$	−1.99805	+	6.14938i	−0.0969198	+	0.298289i
$426$	2.29986	−	7.07823i	0.111428	−	0.342941i
$427$	−13.2935	−	40.9133i	−0.643320	−	1.97993i
$428$	−5.73249			−0.277090
$429$	14.8481			0.716872
$430$	−0.647726	−	1.99349i	−0.0312361	−	0.0961349i
$431$	−13.1918	+	9.58437i	−0.635424	+	0.461663i	−0.858275	−	0.513190i	$-0.828464\pi$
$431$	−13.1918	+	9.58437i	−0.635424	+	0.461663i	0.222851	+	0.974853i	$0.428464\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	−5.73601			−0.275655			−0.137827	−	0.990456i	$-0.544012\pi$
$433$	−5.73601			−0.275655			−0.137827	+	0.990456i	$0.544012\pi$
$434$	−17.4377	−	6.58858i	−0.837038	−	0.316262i
$435$	−4.03362			−0.193397
$436$	4.59104	+	3.33559i	0.219871	+	0.159746i
$437$	−51.4740	+	37.3981i	−2.46234	+	1.78899i
$438$	3.21789	+	9.90364i	0.153757	+	0.473214i
$439$	27.8364			1.32856			0.664278	−	0.747485i	$-0.268739\pi$
$439$	27.8364			1.32856			0.664278	+	0.747485i	$0.268739\pi$
$440$	4.86783			0.232065
$441$	1.30070	+	4.00316i	0.0619383	+	0.190626i
$442$	−6.09456	+	18.7571i	−0.289889	+	0.892185i
$443$	3.62311	−	11.1508i	0.172139	−	0.529790i	−0.827352	−	0.561684i	$-0.810154\pi$
$443$	3.62311	−	11.1508i	0.172139	−	0.529790i	0.999491	+	0.0318937i	$0.0101538\pi$
$444$	4.02662	+	2.92551i	0.191095	+	0.138838i
$445$	2.48197	+	7.63872i	0.117657	+	0.362110i
$446$	21.4747	+	15.6022i	1.01685	+	0.738788i
$447$	−15.8812	+	11.5384i	−0.751154	+	0.545746i
$448$	1.03459	−	3.18415i	0.0488799	−	0.150437i
$449$	15.1191	−	10.9847i	0.713514	−	0.518398i	−0.170791	−	0.985307i	$-0.554632\pi$
$449$	15.1191	−	10.9847i	0.713514	−	0.518398i	0.884305	+	0.466909i	$0.154632\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	−0.800310	+	2.46310i	−0.0376851	+	0.115983i
$452$	5.15426	−	3.74479i	0.242436	−	0.176140i
$453$	9.56220	+	6.94734i	0.449271	+	0.326415i
$454$	2.56502	+	7.89430i	0.120382	+	0.370498i
$455$	−8.26189	−	6.00262i	−0.387323	−	0.281407i
$456$	2.47717	−	7.62395i	0.116004	−	0.357024i
$457$	−4.98305	+	15.3362i	−0.233097	+	0.717399i	0.764271	+	0.644895i	$0.223099\pi$
$457$	−4.98305	+	15.3362i	−0.233097	+	0.717399i	−0.997368	+	0.0725039i	$0.976901\pi$
$458$	−1.58928	−	4.89131i	−0.0742623	−	0.228556i
$459$	−6.46584			−0.301799
$460$	7.93701			0.370065
$461$	−4.98160	−	15.3318i	−0.232016	−	0.714073i	−0.997503	−	0.0706215i	$-0.977502\pi$
$461$	−4.98160	−	15.3318i	−0.232016	−	0.714073i	0.765487	−	0.643452i	$-0.222498\pi$
$462$	−13.1850	+	9.57945i	−0.613421	+	0.445676i
$463$	23.0582	+	16.7527i	1.07160	+	0.778566i	0.976200	−	0.216873i	$-0.0695858\pi$
$463$	23.0582	+	16.7527i	1.07160	+	0.778566i	0.0954037	+	0.995439i	$0.469586\pi$
$464$	−4.03362			−0.187256
$465$	3.05697	+	4.65349i	0.141763	+	0.215800i
$466$	2.59374			0.120153
$467$	−8.73242	−	6.34447i	−0.404088	−	0.293587i	0.367116	−	0.930175i	$-0.380345\pi$
$467$	−8.73242	−	6.34447i	−0.404088	−	0.293587i	−0.771204	+	0.636588i	$0.780345\pi$
$468$	−2.46770	+	1.79289i	−0.114070	+	0.0828764i
$469$	−1.76620	−	5.43581i	−0.0815556	−	0.251002i
$470$	13.5311			0.624144
$471$	−5.64600			−0.260154
$472$	−1.09616	−	3.37362i	−0.0504547	−	0.155283i
$473$	−3.15302	+	9.70399i	−0.144976	+	0.446190i
$474$	1.45620	−	4.48172i	0.0668854	−	0.205852i
$475$	−6.48532	−	4.71186i	−0.297567	−	0.216195i
$476$	−6.68950	−	20.5882i	−0.306613	−	0.943657i
$477$	5.20062	+	3.77847i	0.238120	+	0.173004i
$478$	4.77471	−	3.46903i	0.218390	−	0.158670i
$479$	−7.75867	+	23.8787i	−0.354503	+	1.09105i	0.601795	+	0.798651i	$0.294453\pi$
$479$	−7.75867	+	23.8787i	−0.354503	+	1.09105i	−0.956297	+	0.292396i	$0.905547\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	12.2822	−	8.92353i	0.560019	−	0.406878i
$482$	4.67464	−	14.3871i	0.212924	−	0.655313i
$483$	−21.4982	+	15.6193i	−0.978200	+	0.710704i
$484$	−10.2711	−	7.46236i	−0.466867	−	0.339198i
$485$	0.438243	+	1.34877i	0.0198996	+	0.0612447i
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	11.1104	−	34.1943i	0.503461	−	1.54949i	−0.299882	−	0.953976i	$-0.596947\pi$
$487$	11.1104	−	34.1943i	0.503461	−	1.54949i	0.803343	−	0.595517i	$-0.203053\pi$
$488$	−3.97058	+	12.2202i	−0.179740	+	0.553182i
$489$	−0.185547	−	0.571054i	−0.00839071	−	0.0258240i
$490$	4.20917			0.190151
$491$	−24.8343			−1.12076			−0.560379	−	0.828237i	$-0.689344\pi$
$491$	−24.8343			−1.12076			−0.560379	+	0.828237i	$0.689344\pi$
$492$	−0.164408	−	0.505996i	−0.00741209	−	0.0228121i
$493$	−21.0998	+	15.3299i	−0.950286	+	0.690423i
$494$	−19.7818	−	14.3723i	−0.890026	−	0.646642i
$495$	4.86783			0.218793
$496$	3.05697	+	4.65349i	0.137262	+	0.208948i
$497$	24.9175			1.11770
$498$	6.03442	+	4.38427i	0.270409	+	0.196464i
$499$	−6.88283	+	5.00067i	−0.308118	+	0.223861i	−0.731088	−	0.682283i	$-0.760987\pi$
$499$	−6.88283	+	5.00067i	−0.308118	+	0.223861i	0.422971	+	0.906143i	$0.360987\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	−19.1859			−0.857164
$502$	−18.8521			−0.841410
$503$	−9.36832	−	28.8327i	−0.417713	−	1.28559i	−0.909802	−	0.415043i	$-0.863767\pi$
$503$	−9.36832	−	28.8327i	−0.417713	−	1.28559i	0.492089	−	0.870545i	$-0.336233\pi$
$504$	1.03459	−	3.18415i	0.0460844	−	0.141833i
$505$	−5.25414	+	16.1706i	−0.233806	+	0.719581i
$506$	−31.2572	−	22.7097i	−1.38955	−	1.00957i
$507$	−1.14212	−	3.51509i	−0.0507234	−	0.156111i
$508$	−11.1390	−	8.09294i	−0.494212	−	0.359066i
$509$	4.73269	−	3.43850i	0.209773	−	0.152409i	−0.477938	−	0.878394i	$-0.658616\pi$
$509$	4.73269	−	3.43850i	0.209773	−	0.152409i	0.687711	+	0.725985i	$0.258616\pi$
$510$	−1.99805	+	6.14938i	−0.0884753	+	0.272299i
$511$	−28.2054	+	20.4924i	−1.24773	+	0.906532i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	2.47717	−	7.62395i	0.109370	−	0.336605i
$514$	6.02060	−	4.37422i	0.265557	−	0.192939i
$515$	9.32762	+	6.77691i	0.411024	+	0.298626i
$516$	−0.647726	−	1.99349i	−0.0285145	−	0.0877587i
$517$	−53.2877	−	38.7158i	−2.34359	−	1.70272i
$518$	−5.14934	+	15.8480i	−0.226249	+	0.696323i
$519$	3.19461	−	9.83199i	0.140228	−	0.431577i
$520$	0.942579	+	2.90096i	0.0413348	+	0.127215i
$521$	36.2425			1.58781			0.793907	−	0.608040i	$-0.208044\pi$
$521$	36.2425			1.58781			0.793907	+	0.608040i	$0.208044\pi$
$522$	−4.03362			−0.176547
$523$	−3.05056	−	9.38866i	−0.133392	−	0.410538i	0.861945	−	0.507002i	$-0.169246\pi$
$523$	−3.05056	−	9.38866i	−0.133392	−	0.410538i	−0.995336	+	0.0964648i	$0.969246\pi$
$524$	−0.0727138	+	0.0528297i	−0.00317652	+	0.00230787i
$525$	−2.70860	−	1.96791i	−0.118213	−	0.0858867i
$526$	−26.8393			−1.17025
$527$	33.6766	+	12.7242i	1.46698	+	0.554274i
$528$	4.86783			0.211845
$529$	−32.3575	−	23.5091i	−1.40685	−	1.02214i
$530$	5.20062	−	3.77847i	0.225901	−	0.164126i
$531$	−1.09616	−	3.37362i	−0.0475691	−	0.146403i
$532$	26.8386			1.16360
$533$	−1.62284			−0.0702931
$534$	2.48197	+	7.63872i	0.107405	+	0.330560i
$535$	−1.77144	+	5.45192i	−0.0765858	+	0.235707i
$536$	−0.527538	+	1.62359i	−0.0227861	+	0.0701286i
$537$	4.05959	+	2.94946i	0.175184	+	0.127279i
$538$	−0.608961	−	1.87419i	−0.0262542	−	0.0808021i
$539$	−16.5763	−	12.0434i	−0.713994	−	0.518747i
$540$	−0.809017	+	0.587785i	−0.0348145	+	0.0252942i
$541$	−2.96782	+	9.13400i	−0.127596	+	0.392701i	−0.994365	−	0.106009i	$-0.966193\pi$
$541$	−2.96782	+	9.13400i	−0.127596	+	0.392701i	0.866769	+	0.498710i	$0.166193\pi$
$542$	−3.85919	+	2.80386i	−0.165766	+	0.120436i
$543$	−12.3947	+	9.00528i	−0.531908	+	0.386453i
$544$	−1.99805	+	6.14938i	−0.0856658	+	0.263652i
$545$	4.59104	−	3.33559i	0.196659	−	0.142881i
$546$	−8.26189	−	6.00262i	−0.353576	−	0.256888i
$547$	12.4926	+	38.4483i	0.534145	+	1.64393i	0.745489	+	0.666518i	$0.232216\pi$
$547$	12.4926	+	38.4483i	0.534145	+	1.64393i	−0.211344	+	0.977412i	$0.567784\pi$
$548$	14.6549	+	10.6474i	0.626028	+	0.454836i
$549$	−3.97058	+	12.2202i	−0.169460	+	0.521545i
$550$	1.50424	−	4.62958i	0.0641411	−	0.197406i
$551$	−9.99197	−	30.7521i	−0.425672	−	1.31008i
$552$	7.93701			0.337822
$553$	15.7770			0.670907
$554$	3.85434	+	11.8624i	0.163755	+	0.503987i
$555$	4.02662	−	2.92551i	0.170920	−	0.124181i
$556$	−0.791701	−	0.575205i	−0.0335756	−	0.0243941i
$557$	18.0048			0.762886			0.381443	−	0.924392i	$-0.375427\pi$
$557$	18.0048			0.762886			0.381443	+	0.924392i	$0.375427\pi$
$558$	3.05697	+	4.65349i	0.129412	+	0.196998i
$559$	−6.39358			−0.270420
$560$	−2.70860	−	1.96791i	−0.114459	−	0.0831594i
$561$	25.4635	−	18.5003i	1.07507	−	0.781083i
$562$	−1.39039	−	4.27917i	−0.0586499	−	0.180506i
$563$	18.8061			0.792582			0.396291	−	0.918125i	$-0.370297\pi$
$563$	18.8061			0.792582			0.396291	+	0.918125i	$0.370297\pi$
$564$	13.5311			0.569763
$565$	−1.96875	−	6.05920i	−0.0828260	−	0.254912i
$566$	2.41871	−	7.44402i	0.101666	−	0.312896i
$567$	1.03459	−	3.18415i	0.0434488	−	0.133722i
$568$	−6.02110	−	4.37459i	−0.252640	−	0.183554i
$569$	0.0660906	+	0.203406i	0.00277066	+	0.00852722i	0.952432	−	0.304750i	$-0.0985730\pi$
$569$	0.0660906	+	0.203406i	0.00277066	+	0.00852722i	−0.949662	+	0.313278i	$0.898573\pi$
$570$	−6.48532	−	4.71186i	−0.271640	−	0.197358i
$571$	−29.1726	+	21.1951i	−1.22083	+	0.886987i	−0.996169	−	0.0874487i	$-0.972129\pi$
$571$	−29.1726	+	21.1951i	−1.22083	+	0.886987i	−0.224664	+	0.974436i	$0.572129\pi$
$572$	4.58831	−	14.1214i	0.191847	−	0.590444i
$573$	−2.42287	+	1.76032i	−0.101217	+	0.0735385i
$574$	1.44107	−	1.04700i	0.0601491	−	0.0437009i
$575$	2.45267	−	7.54854i	0.102283	−	0.314796i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	6.81900	+	4.95429i	0.283879	+	0.206250i	0.720607	−	0.693343i	$-0.243863\pi$
$577$	6.81900	+	4.95429i	0.283879	+	0.206250i	−0.436729	+	0.899593i	$0.643863\pi$
$578$	7.66580	+	23.5929i	0.318855	+	0.981335i
$579$	20.5945	+	14.9628i	0.855878	+	0.621832i
$580$	−1.24646	+	3.83620i	−0.0517563	+	0.159290i
$581$	−7.71698	+	23.7504i	−0.320154	+	0.985333i
$582$	0.438243	+	1.34877i	0.0181658	+	0.0559085i
$583$	−31.2920			−1.29598
$584$	10.4133			0.430905
$585$	0.942579	+	2.90096i	0.0389708	+	0.119940i
$586$	−12.0319	+	8.74170i	−0.497034	+	0.361116i
$587$	28.8300	+	20.9462i	1.18994	+	0.864542i	0.993258	−	0.115926i	$-0.0369834\pi$
$587$	28.8300	+	20.9462i	1.18994	+	0.864542i	0.196682	+	0.980467i	$0.436983\pi$
$588$	4.20917			0.173583
$589$	−27.9053	+	34.8336i	−1.14982	+	1.43530i
$590$	−3.54723			−0.146037
$591$	−19.5831	−	14.2279i	−0.805539	−	0.585258i
$592$	4.02662	−	2.92551i	0.165493	−	0.120238i
$593$	5.42487	+	16.6960i	0.222773	+	0.685624i	0.998510	+	0.0545682i	$0.0173782\pi$
$593$	5.42487	+	16.6960i	0.222773	+	0.685624i	−0.775737	+	0.631056i	$0.782622\pi$
$594$	4.86783			0.199729
$595$	−21.6477			−0.887468
$596$	6.06607	+	18.6695i	0.248476	+	0.764731i
$597$	−4.84156	+	14.9008i	−0.198152	+	0.609849i
$598$	7.48126	−	23.0249i	0.305931	−	0.941560i
$599$	−16.2501	−	11.8064i	−0.663959	−	0.482395i	0.204039	−	0.978963i	$-0.434593\pi$
$599$	−16.2501	−	11.8064i	−0.663959	−	0.482395i	−0.867998	+	0.496568i	$0.834593\pi$
$600$	0.309017	+	0.951057i	0.0126156	+	0.0388267i
$601$	−21.7372	−	15.7930i	−0.886679	−	0.644210i	0.0483311	−	0.998831i	$-0.484610\pi$
$601$	−21.7372	−	15.7930i	−0.886679	−	0.644210i	−0.935010	+	0.354621i	$0.884610\pi$
$602$	5.67745	−	4.12491i	0.231395	−	0.168119i
$603$	−0.527538	+	1.62359i	−0.0214830	+	0.0661178i
$604$	9.56220	−	6.94734i	0.389080	−	0.282683i
$605$	−10.2711	+	7.46236i	−0.417578	+	0.303388i
$606$	−5.25414	+	16.1706i	−0.213435	+	0.656885i
$607$	35.1745	−	25.5558i	1.42769	−	1.03728i	0.437248	−	0.899341i	$-0.355953\pi$
$607$	35.1745	−	25.5558i	1.42769	−	1.03728i	0.990441	−	0.137935i	$-0.0440467\pi$
$608$	−6.48532	−	4.71186i	−0.263014	−	0.191091i
$609$	−4.17315	−	12.8436i	−0.169105	−	0.520451i
$610$	10.3951	+	7.55250i	0.420886	+	0.305792i
$611$	12.7542	−	39.2532i	0.515978	−	1.58802i
$612$	−1.99805	+	6.14938i	−0.0807665	+	0.248574i
$613$	−9.83532	−	30.2700i	−0.397245	−	1.22259i	−0.927199	−	0.374568i	$-0.877791\pi$
$613$	−9.83532	−	30.2700i	−0.397245	−	1.22259i	0.529954	−	0.848026i	$-0.322209\pi$
$614$	20.7987			0.839368
$615$	−0.532036			−0.0214538
$616$	5.03621	+	15.4999i	0.202915	+	0.624508i
$617$	−14.0071	+	10.1767i	−0.563904	+	0.409700i	−0.832886	−	0.553445i	$-0.813313\pi$
$617$	−14.0071	+	10.1767i	−0.563904	+	0.409700i	0.268982	+	0.963145i	$0.413313\pi$
$618$	9.32762	+	6.77691i	0.375212	+	0.272607i
$619$	−4.30193			−0.172909			−0.0864546	−	0.996256i	$-0.527554\pi$
$619$	−4.30193			−0.172909			−0.0864546	+	0.996256i	$0.527554\pi$
$620$	5.37038	−	1.46934i	0.215680	−	0.0590102i
$621$	7.93701			0.318501
$622$	17.1911	+	12.4901i	0.689300	+	0.500806i
$623$	−21.7550	+	15.8059i	−0.871595	+	0.633251i
$624$	0.942579	+	2.90096i	0.0377333	+	0.116131i
$625$	1.00000			0.0400000
$626$	15.5546			0.621686
$627$	12.0584	+	37.1120i	0.481568	+	1.48211i
$628$	−1.74471	+	5.36966i	−0.0696215	+	0.214273i
$629$	9.94466	−	30.6065i	0.396519	−	1.22036i
$630$	−2.70860	−	1.96791i	−0.107913	−	0.0784034i
$631$	−4.06098	−	12.4984i	−0.161665	−	0.497554i	0.837110	−	0.547035i	$-0.184243\pi$
$631$	−4.06098	−	12.4984i	−0.161665	−	0.497554i	−0.998775	+	0.0494806i	$0.984243\pi$
$632$	−3.81238	−	2.76985i	−0.151648	−	0.110179i
$633$	6.79055	−	4.93363i	0.269900	−	0.196094i
$634$	−5.69864	+	17.5386i	−0.226322	+	0.696547i
$635$	−11.1390	+	8.09294i	−0.442037	+	0.321159i
$636$	5.20062	−	3.77847i	0.206218	−	0.149826i
$637$	3.96747	−	12.2106i	0.157197	−	0.483802i
$638$	15.8850	−	11.5411i	0.628894	−	0.456918i
$639$	−6.02110	−	4.37459i	−0.238191	−	0.173056i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	22.5747	+	16.4015i	0.891647	+	0.647819i	0.936307	−	0.351183i	$-0.114220\pi$
$641$	22.5747	+	16.4015i	0.891647	+	0.647819i	−0.0446601	+	0.999002i	$0.514220\pi$
$642$	−1.77144	+	5.45192i	−0.0699130	+	0.215170i
$643$	0.443852	−	1.36604i	0.0175038	−	0.0538712i	−0.941923	−	0.335829i	$-0.890984\pi$
$643$	0.443852	−	1.36604i	0.0175038	−	0.0538712i	0.959427	+	0.281957i	$0.0909837\pi$
$644$	8.21157	+	25.2726i	0.323581	+	0.995880i
$645$	−2.09608			−0.0825332
$646$	−51.8320			−2.03930
$647$	0.768219	+	2.36434i	0.0302018	+	0.0929516i	0.965021	−	0.262172i	$-0.0844388\pi$
$647$	0.768219	+	2.36434i	0.0302018	+	0.0929516i	−0.934819	+	0.355124i	$0.884439\pi$
$648$	−0.809017	+	0.587785i	−0.0317812	+	0.0230904i
$649$	13.9696	+	10.1495i	0.548353	+	0.398402i
$650$	3.05025			0.119641
$651$	−11.6547	+	14.5483i	−0.456783	+	0.570192i
$652$	−0.600442			−0.0235151
$653$	−37.4509	−	27.2097i	−1.46557	−	1.06480i	−0.981868	−	0.189564i	$-0.939292\pi$
$653$	−37.4509	−	27.2097i	−1.46557	−	1.06480i	−0.483700	−	0.875234i	$-0.660708\pi$
$654$	4.59104	−	3.33559i	0.179524	−	0.130432i
$655$	0.0277742	+	0.0854802i	0.00108523	+	0.00333999i
$656$	−0.532036			−0.0207725
$657$	10.4133			0.406262
$658$	13.9992	+	43.0851i	0.545745	+	1.67963i
$659$	−12.2031	+	37.5571i	−0.475363	+	1.46302i	0.370104	+	0.928990i	$0.379322\pi$
$659$	−12.2031	+	37.5571i	−0.475363	+	1.46302i	−0.845467	+	0.534028i	$0.820678\pi$
$660$	1.50424	−	4.62958i	0.0585525	−	0.180206i
$661$	−5.02382	−	3.65002i	−0.195404	−	0.141969i	0.485781	−	0.874080i	$-0.338535\pi$
$661$	−5.02382	−	3.65002i	−0.195404	−	0.141969i	−0.681185	+	0.732111i	$0.738535\pi$
$662$	−6.36594	−	19.5923i	−0.247419	−	0.761478i
$663$	15.9558	+	11.5925i	0.619671	+	0.450217i
$664$	6.03442	−	4.38427i	0.234181	−	0.170143i
$665$	8.29359	−	25.5250i	0.321612	−	0.989819i
$666$	4.02662	−	2.92551i	0.156028	−	0.113361i
$667$	25.9006	−	18.8179i	1.00288	−	0.728632i
$668$	−5.92878	+	18.2469i	−0.229391	+	0.705994i
$669$	21.4747	−	15.6022i	0.830258	−	0.603218i
$670$	1.38111	+	1.00344i	0.0533570	+	0.0387661i
$671$	−19.3281	−	59.4858i	−0.746153	−	2.29642i
$672$	−2.70860	−	1.96791i	−0.104486	−	0.0759138i
$673$	2.37604	−	7.31271i	0.0915897	−	0.281884i	−0.894760	−	0.446547i	$-0.852654\pi$
$673$	2.37604	−	7.31271i	0.0915897	−	0.281884i	0.986350	+	0.164663i	$0.0526536\pi$
$674$	−2.40631	+	7.40587i	−0.0926877	+	0.285263i
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$	−3.69598			−0.142153
$677$	42.1972			1.62177			0.810885	−	0.585206i	$-0.198986\pi$
$677$	42.1972			1.62177			0.810885	+	0.585206i	$0.198986\pi$
$678$	−1.96875	−	6.05920i	−0.0756095	−	0.232702i
$679$	−3.84129	+	2.79086i	−0.147415	+	0.107103i
$680$	5.23097	+	3.80052i	0.200599	+	0.145743i
$681$	8.30056			0.318078
$682$	−25.3535	−	9.57945i	−0.970837	−	0.366816i
$683$	−3.61794			−0.138437			−0.0692183	−	0.997602i	$-0.522050\pi$
$683$	−3.61794			−0.138437			−0.0692183	+	0.997602i	$0.522050\pi$
$684$	−6.48532	−	4.71186i	−0.247972	−	0.180162i
$685$	14.6549	−	10.6474i	0.559936	−	0.406818i
$686$	−2.88737	−	8.88642i	−0.110240	−	0.339285i
$687$	−5.14303			−0.196219
$688$	−2.09608			−0.0799125
$689$	−6.05920	−	18.6483i	−0.230837	−	0.710443i
$690$	2.45267	−	7.54854i	0.0933716	−	0.287368i
$691$	1.48377	−	4.56658i	0.0564454	−	0.173721i	−0.918859	−	0.394586i	$-0.870888\pi$
$691$	1.48377	−	4.56658i	0.0564454	−	0.173721i	0.975304	+	0.220865i	$0.0708880\pi$
$692$	−8.36359	−	6.07651i	−0.317936	−	0.230994i
$693$	5.03621	+	15.4999i	0.191310	+	0.588791i
$694$	−1.63256	−	1.18613i	−0.0619713	−	0.0450248i
$695$	−0.791701	+	0.575205i	−0.0300309	+	0.0218188i
$696$	−1.24646	+	3.83620i	−0.0472469	+	0.145411i
$697$	−2.78306	+	2.02201i	−0.105416	+	0.0765893i
$698$	18.7920	−	13.6532i	0.711288	−	0.516781i
$699$	0.801510	−	2.46679i	0.0303159	−	0.0933027i
$700$	−2.70860	+	1.96791i	−0.102375	+	0.0743800i
$701$	33.9503	+	24.6664i	1.28229	+	0.931636i	0.999620	−	0.0275824i	$-0.00878086\pi$
$701$	33.9503	+	24.6664i	1.28229	+	0.931636i	0.282667	+	0.959218i	$0.408781\pi$
$702$	0.942579	+	2.90096i	0.0355753	+	0.109490i
$703$	32.2785	+	23.4517i	1.21741	+	0.884499i
$704$	1.50424	−	4.62958i	0.0566932	−	0.174484i
$705$	4.18135	−	12.8689i	0.157479	−	0.484670i
$706$	−6.92797	−	21.3221i	−0.260738	−	0.802468i
$707$	−56.9254			−2.14090
$708$	−3.54723			−0.133313
$709$	2.17840	+	6.70444i	0.0818117	+	0.251791i	0.983593	−	0.180402i	$-0.0577400\pi$
$709$	2.17840	+	6.70444i	0.0818117	+	0.251791i	−0.901781	+	0.432193i	$0.857740\pi$
$710$	−6.02110	+	4.37459i	−0.225968	+	0.164175i
$711$	−3.81238	−	2.76985i	−0.142975	−	0.103878i
$712$	8.03183			0.301006
$713$	−41.3390	−	15.6193i	−1.54816	−	0.584948i
$714$	−21.6477			−0.810144
$715$	−12.0123	−	8.72748i	−0.449236	−	0.326389i
$716$	4.05959	−	2.94946i	0.151714	−	0.110227i
$717$	−1.82378	−	5.61300i	−0.0681101	−	0.209621i
$718$	10.9361			0.408131
$719$	−7.99953			−0.298332			−0.149166	−	0.988812i	$-0.547659\pi$
$719$	−7.99953			−0.298332			−0.149166	+	0.988812i	$0.547659\pi$
$720$	0.309017	+	0.951057i	0.0115164	+	0.0354438i
$721$	−11.9284	+	36.7118i	−0.444237	+	1.36722i
$722$	13.9864	−	43.0457i	0.520520	−	1.60200i
$723$	−12.2384	−	8.89170i	−0.455150	−	0.330686i
$724$	4.73435	+	14.5708i	0.175951	+	0.541521i
$725$	3.26327	+	2.37090i	0.121195	+	0.0880532i
$726$	−10.2711	+	7.46236i	−0.381195	+	0.276954i
$727$	9.96556	−	30.6709i	0.369602	−	1.13752i	−0.577446	−	0.816429i	$-0.695951\pi$
$727$	9.96556	−	30.6709i	0.369602	−	1.13752i	0.947049	−	0.321090i	$-0.104049\pi$
$728$	−8.26189	+	6.00262i	−0.306206	+	0.222472i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	3.21789	−	9.90364i	0.119099	−	0.366550i
$731$	−10.9646	+	7.96622i	−0.405539	+	0.294641i
$732$	10.3951	+	7.55250i	0.384215	+	0.279148i
$733$	−5.52404	−	17.0012i	−0.204035	−	0.627955i	−0.999752	−	0.0222861i	$-0.992906\pi$
$733$	−5.52404	−	17.0012i	−0.204035	−	0.627955i	0.795717	−	0.605669i	$-0.207094\pi$
$734$	−28.9212	−	21.0125i	−1.06750	−	0.775584i
$735$	1.30070	−	4.00316i	0.0479772	−	0.147659i
$736$	2.45267	−	7.54854i	0.0904067	−	0.278243i
$737$	−2.56796	−	7.90337i	−0.0945921	−	0.291124i
$738$	−0.532036			−0.0195845
$739$	46.7782			1.72077			0.860383	−	0.509649i	$-0.170225\pi$
$739$	46.7782			1.72077			0.860383	+	0.509649i	$0.170225\pi$
$740$	−1.53803	−	4.73357i	−0.0565391	−	0.174010i
$741$	−19.7818	+	14.3723i	−0.726704	+	0.527981i
$742$	17.4117	+	12.6504i	0.639205	+	0.464409i
$743$	27.9986			1.02717			0.513585	−	0.858039i	$-0.328317\pi$
$743$	27.9986			1.02717			0.513585	+	0.858039i	$0.328317\pi$
$744$	5.37038	−	1.46934i	0.196888	−	0.0538687i
$745$	19.6302			0.719196
$746$	0.821727	+	0.597019i	0.0300856	+	0.0218584i
$747$	6.03442	−	4.38427i	0.220788	−	0.160412i
$748$	−9.72618	−	29.9341i	−0.355624	−	1.09450i
$749$	−19.1924			−0.701276
$750$	1.00000			0.0365148
$751$	9.05206	+	27.8594i	0.330314	+	1.01660i	0.968984	+	0.247122i	$0.0794850\pi$
$751$	9.05206	+	27.8594i	0.330314	+	1.01660i	−0.638670	+	0.769481i	$0.720515\pi$
$752$	4.18135	−	12.8689i	0.152478	−	0.469279i
$753$	−5.82562	+	17.9294i	−0.212297	+	0.653384i
$754$	9.95378	+	7.23185i	0.362495	+	0.263368i
$755$	−3.65243	−	11.2410i	−0.132926	−	0.409103i
$756$	−2.70860	−	1.96791i	−0.0985107	−	0.0715722i
$757$	−0.240414	+	0.174671i	−0.00873801	+	0.00634854i	−0.592146	−	0.805831i	$-0.701719\pi$
$757$	−0.240414	+	0.174671i	−0.00873801	+	0.00634854i	0.583408	+	0.812179i	$0.301719\pi$
$758$	2.43032	−	7.47976i	0.0882733	−	0.271677i
$759$	−31.2572	+	22.7097i	−1.13456	+	0.824309i
$760$	−6.48532	+	4.71186i	−0.235247	+	0.170917i
$761$	14.4088	−	44.3456i	0.522318	−	1.60753i	−0.247242	−	0.968954i	$-0.579524\pi$
$761$	14.4088	−	44.3456i	0.522318	−	1.60753i	0.769560	−	0.638575i	$-0.220476\pi$
$762$	−11.1390	+	8.09294i	−0.403523	+	0.293176i
$763$	15.3709	+	11.1676i	0.556462	+	0.404294i
$764$	0.925455	+	2.84826i	0.0334818	+	0.103046i
$765$	5.23097	+	3.80052i	0.189126	+	0.137408i
$766$	−9.13368	+	28.1106i	−0.330013	+	1.01568i
$767$	−3.34355	+	10.2904i	−0.120728	+	0.371564i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	−15.4979			−0.558870			−0.279435	−	0.960165i	$-0.590147\pi$
$769$	−15.4979			−0.558870			−0.279435	+	0.960165i	$0.590147\pi$
$770$	16.2975			0.587322
$771$	−2.29966	−	7.07764i	−0.0828204	−	0.254895i
$772$	20.5945	−	14.9628i	0.741212	−	0.538522i
$773$	−9.37464	−	6.81108i	−0.337182	−	0.244977i	0.406290	−	0.913744i	$-0.366822\pi$
$773$	−9.37464	−	6.81108i	−0.337182	−	0.244977i	−0.743472	+	0.668767i	$0.766822\pi$
$774$	−2.09608			−0.0753422
$775$	0.262113	−	5.56159i	0.00941538	−	0.199778i
$776$	1.41818			0.0509099
$777$	13.4812	+	9.79463i	0.483634	+	0.351380i
$778$	20.1444	−	14.6358i	0.722212	−	0.524718i
$779$	−1.31794	−	4.05621i	−0.0472202	−	0.145329i
$780$	3.05025			0.109216
$781$	36.2287			1.29637
$782$	−15.8586	−	48.8077i	−0.567101	−	1.74536i
$783$	−1.24646	+	3.83620i	−0.0445448	+	0.137095i
$784$	1.30070	−	4.00316i	0.0464537	−	0.142970i
$785$	4.56771	+	3.31863i	0.163029	+	0.118447i
$786$	0.0277742	+	0.0854802i	0.000990673	+	0.00304898i
$787$	−13.2914	−	9.65678i	−0.473788	−	0.344227i	0.325128	−	0.945670i	$-0.394593\pi$
$787$	−13.2914	−	9.65678i	−0.473788	−	0.344227i	−0.798916	+	0.601443i	$0.794593\pi$
$788$	−19.5831	+	14.2279i	−0.697617	+	0.506849i
$789$	−8.29380	+	25.5257i	−0.295267	+	0.908739i
$790$	−3.81238	+	2.76985i	−0.135638	+	0.0985470i
$791$	17.2565	−	12.5376i	0.613571	−	0.445785i
$792$	1.50424	−	4.62958i	0.0534509	−	0.164505i
$793$	31.7077	−	23.0370i	1.12597	−	0.818067i
$794$	−3.75747	−	2.72996i	−0.133348	−	0.0968828i
$795$	−1.98646	−	6.11370i	−0.0704525	−	0.216830i
$796$	12.6754	+	9.20920i	0.449267	+	0.326412i
$797$	−5.14855	+	15.8456i	−0.182371	+	0.561280i	−0.999893	−	0.0146170i	$-0.995347\pi$
$797$	−5.14855	+	15.8456i	−0.182371	+	0.561280i	0.817522	+	0.575897i	$0.195347\pi$
$798$	8.29359	−	25.5250i	0.293590	−	0.903577i
$799$	−27.0359	−	83.2080i	−0.956462	−	2.94369i
$800$	1.00000			0.0353553
$801$	8.03183			0.283791
$802$	−8.88511	−	27.3456i	−0.313744	−	0.965605i
$803$	−41.0092	+	29.7949i	−1.44718	+	1.05144i
$804$	1.38111	+	1.00344i	0.0487080	+	0.0353885i
$805$	26.5732			0.936582
$806$	0.799510	−	16.9642i	0.0281615	−	0.597540i
$807$	−1.97064			−0.0693698
$808$	13.7555	+	9.99396i	0.483917	+	0.351586i
$809$	30.5437	−	22.1913i	1.07386	−	0.780204i	0.0972563	−	0.995259i	$-0.468993\pi$
$809$	30.5437	−	22.1913i	1.07386	−	0.780204i	0.976602	+	0.215056i	$0.0689933\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	50.7577			1.78234			0.891172	−	0.453666i	$-0.149884\pi$
$811$	50.7577			1.78234			0.891172	+	0.453666i	$0.149884\pi$
$812$	−13.5046			−0.473919
$813$	1.47408	+	4.53675i	0.0516982	+	0.159111i
$814$	−7.48687	+	23.0422i	−0.262415	+	0.807629i
$815$	−0.185547	+	0.571054i	−0.00649942	+	0.0200032i
$816$	5.23097	+	3.80052i	0.183121	+	0.133045i
$817$	−5.19236	−	15.9804i	−0.181658	−	0.559085i
$818$	−10.7544	−	7.81355i	−0.376020	−	0.273195i
$819$	−8.26189	+	6.00262i	−0.288694	+	0.209748i
$820$	−0.164408	+	0.505996i	−0.00574138	+	0.0176702i
$821$	−27.8784	+	20.2548i	−0.972961	+	0.706898i	−0.956125	−	0.292960i	$-0.905360\pi$
$821$	−27.8784	+	20.2548i	−0.972961	+	0.706898i	−0.0168368	+	0.999858i	$0.505360\pi$
$822$	14.6549	−	10.6474i	0.511150	−	0.371372i
$823$	6.04676	−	18.6100i	0.210777	−	0.648704i	−0.788650	−	0.614843i	$-0.789219\pi$
$823$	6.04676	−	18.6100i	0.210777	−	0.648704i	0.999427	−	0.0338615i	$-0.0107805\pi$
$824$	9.32762	−	6.77691i	0.324943	−	0.236085i
$825$	−3.93815	−	2.86124i	−0.137109	−	0.0996155i
$826$	−3.66994	−	11.2949i	−0.127694	−	0.393000i
$827$	−5.45893	−	3.96615i	−0.189826	−	0.137916i	0.488813	−	0.872388i	$-0.337430\pi$
$827$	−5.45893	−	3.96615i	−0.189826	−	0.137916i	−0.678639	+	0.734472i	$0.737430\pi$
$828$	2.45267	−	7.54854i	0.0852362	−	0.262330i
$829$	−9.99093	+	30.7489i	−0.346999	+	1.06795i	0.613506	+	0.789690i	$0.289759\pi$
$829$	−9.99093	+	30.7489i	−0.346999	+	1.06795i	−0.960505	+	0.278263i	$0.910241\pi$
$830$	−2.30495	−	7.09389i	−0.0800058	−	0.246233i
$831$	12.4729			0.432681
$832$	3.05025			0.105748
$833$	−8.41014	−	25.8838i	−0.291394	−	0.896819i
$834$	−0.791701	+	0.575205i	−0.0274144	+	0.0199177i
$835$	15.5217	+	11.2772i	0.537152	+	0.390264i
$836$	39.0219			1.34960
$837$	5.37038	−	1.46934i	0.185628	−	0.0507879i
$838$	−20.1650			−0.696588
$839$	17.2667	+	12.5450i	0.596113	+	0.433102i	0.844497	−	0.535560i	$-0.179899\pi$
$839$	17.2667	+	12.5450i	0.596113	+	0.433102i	−0.248384	+	0.968662i	$0.579899\pi$
$840$	−2.70860	+	1.96791i	−0.0934555	+	0.0678994i
$841$	−3.93375	−	12.1068i	−0.135647	−	0.417477i
$842$	−1.64456			−0.0566753
$843$	−4.49938			−0.154967
$844$	−2.59376	−	7.98278i	−0.0892809	−	0.274778i
$845$	−1.14212	+	3.51509i	−0.0392902	+	0.120923i
$846$	4.18135	−	12.8689i	0.143758	−	0.442441i
$847$	−34.3876	−	24.9841i	−1.18157	−	0.858463i
$848$	−1.98646	−	6.11370i	−0.0682153	−	0.209945i
$849$	−6.33226	−	4.60066i	−0.217323	−	0.157894i
$850$	5.23097	−	3.80052i	0.179421	−	0.130357i
$851$	−12.2074	+	37.5704i	−0.418463	+	1.28790i
$852$	−6.02110	+	4.37459i	−0.206280	+	0.149871i
$853$	−45.4589	+	33.0278i	−1.55648	+	1.13085i	−0.617664	+	0.786442i	$0.711921\pi$
$853$	−45.4589	+	33.0278i	−1.55648	+	1.13085i	−0.938819	+	0.344410i	$0.888079\pi$
$854$	−13.2935	+	40.9133i	−0.454896	+	1.40003i
$855$	−6.48532	+	4.71186i	−0.221793	+	0.161142i
$856$	4.63768	+	3.36947i	0.158513	+	0.115166i
$857$	−3.03393	−	9.33748i	−0.103637	−	0.318962i	0.885771	−	0.464122i	$-0.153630\pi$
$857$	−3.03393	−	9.33748i	−0.103637	−	0.318962i	−0.989408	+	0.145160i	$0.953630\pi$
$858$	−12.0123	−	8.72748i	−0.410095	−	0.297951i
$859$	−12.3332	+	37.9576i	−0.420802	+	1.29510i	0.486155	+	0.873872i	$0.338399\pi$
$859$	−12.3332	+	37.9576i	−0.420802	+	1.29510i	−0.906957	+	0.421223i	$0.861601\pi$
$860$	−0.647726	+	1.99349i	−0.0220873	+	0.0679776i
$861$	−0.550440	−	1.69408i	−0.0187589	−	0.0577341i
$862$	16.3059			0.555381
$863$	−26.7862			−0.911812			−0.455906	−	0.890028i	$-0.650685\pi$
$863$	−26.7862			−0.911812			−0.455906	+	0.890028i	$0.650685\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−8.36359	+	6.07651i	−0.284371	+	0.206607i
$866$	4.64053	+	3.37154i	0.157691	+	0.114570i
$867$	24.8070			0.842492
$868$	10.2348	+	15.5799i	0.347390	+	0.528817i
$869$	22.9389			0.778150
$870$	3.26327	+	2.37090i	0.110635	+	0.0803812i
$871$	4.21273	−	3.06073i	0.142743	−	0.103709i
$872$	−1.75362	−	5.39710i	−0.0593852	−	0.182769i
$873$	1.41818			0.0479983
$874$	63.6254			2.15216
$875$	1.03459	+	3.18415i	0.0349756	+	0.107644i
$876$	3.21789	−	9.90364i	0.108722	−	0.334613i
$877$	6.05680	−	18.6409i	0.204524	−	0.629459i	−0.795209	−	0.606336i	$-0.792639\pi$
$877$	6.05680	−	18.6409i	0.204524	−	0.629459i	0.999733	−	0.0231237i	$-0.00736115\pi$
$878$	−22.5201	−	16.3618i	−0.760016	−	0.552184i
$879$	4.59578	+	14.1444i	0.155012	+	0.477078i
$880$	−3.93815	−	2.86124i	−0.132755	−	0.0964523i
$881$	−36.8123	+	26.7457i	−1.24024	+	0.901085i	−0.997614	−	0.0690358i	$-0.978008\pi$
$881$	−36.8123	+	26.7457i	−1.24024	+	0.901085i	−0.242623	+	0.970121i	$0.578008\pi$
$882$	1.30070	−	4.00316i	0.0437970	−	0.134793i
$883$	−24.9962	+	18.1608i	−0.841190	+	0.611160i	−0.922703	−	0.385512i	$-0.874025\pi$
$883$	−24.9962	+	18.1608i	−0.841190	+	0.611160i	0.0815128	+	0.996672i	$0.474025\pi$
$884$	15.9558	−	11.5925i	0.536650	−	0.389899i
$885$	−1.09616	+	3.37362i	−0.0368469	+	0.113403i
$886$	−9.48543	+	6.89157i	−0.318669	+	0.231527i
$887$	6.82072	+	4.95555i	0.229017	+	0.166391i	0.696376	−	0.717677i	$-0.254794\pi$
$887$	6.82072	+	4.95555i	0.229017	+	0.166391i	−0.467359	+	0.884068i	$0.654794\pi$
$888$	−1.53803	−	4.73357i	−0.0516129	−	0.158848i
$889$	−37.2934	−	27.0953i	−1.25078	−	0.908746i
$890$	2.48197	−	7.63872i	0.0831959	−	0.256051i
$891$	1.50424	−	4.62958i	0.0503940	−	0.155097i
$892$	−8.20259	−	25.2450i	−0.274643	−	0.845264i
$893$	108.469			3.62979
$894$	19.6302			0.656533
$895$	−1.55063	−	4.77233i	−0.0518317	−	0.159522i
$896$	−2.70860	+	1.96791i	−0.0904879	+	0.0657433i
$897$	−19.5862	−	14.2302i	−0.653964	−	0.475132i
$898$	−18.6882			−0.623634
$899$	14.0413	−	17.5275i	0.468305	−	0.584576i
$900$	1.00000			0.0333333
$901$	−33.6264	−	24.4310i	−1.12026	−	0.813914i
$902$	2.09524	−	1.52228i	0.0697638	−	0.0506864i
$903$	−2.16859	−	6.67424i	−0.0721662	−	0.222105i
$904$	−6.37102			−0.211897
$905$	15.3207			0.509277
$906$	−3.65243	−	11.2410i	−0.121344	−	0.373458i
$907$	11.6139	−	35.7440i	0.385634	−	1.18686i	−0.550386	−	0.834911i	$-0.685519\pi$
$907$	11.6139	−	35.7440i	0.385634	−	1.18686i	0.936019	−	0.351948i	$-0.114481\pi$
$908$	2.56502	−	7.89430i	0.0851230	−	0.261982i
$909$	13.7555	+	9.99396i	0.456242	+	0.331479i
$910$	3.15576	+	9.71244i	0.104612	+	0.321964i
$911$	17.0480	+	12.3861i	0.564827	+	0.410371i	0.833222	−	0.552938i	$-0.186493\pi$
$911$	17.0480	+	12.3861i	0.564827	+	0.410371i	−0.268395	+	0.963309i	$0.586493\pi$
$912$	−6.48532	+	4.71186i	−0.214750	+	0.156025i
$913$	−11.2201	+	34.5318i	−0.371330	+	1.14284i
$914$	13.0458	−	9.47832i	0.431516	−	0.313515i
$915$	10.3951	−	7.55250i	0.343652	−	0.249678i
$916$	−1.58928	+	4.89131i	−0.0525114	+	0.161613i
$917$	−0.243447	+	0.176874i	−0.00803931	+	0.00584090i
$918$	5.23097	+	3.80052i	0.172648	+	0.125436i
$919$	−12.7611	−	39.2745i	−0.420949	−	1.29555i	−0.906821	−	0.421516i	$-0.861498\pi$
$919$	−12.7611	−	39.2745i	−0.420949	−	1.29555i	0.485872	−	0.874030i	$-0.338502\pi$
$920$	−6.42118	−	4.66526i	−0.211700	−	0.153809i
$921$	6.42716	−	19.7808i	0.211782	−	0.651798i
$922$	−4.98160	+	15.3318i	−0.164060	+	0.504926i
$923$	7.01513	+	21.5904i	0.230906	+	0.710655i
$924$	16.2975			0.536149
$925$	−4.97717			−0.163648
$926$	−8.80743	−	27.1065i	−0.289430	−	0.890775i
$927$	9.32762	−	6.77691i	0.306359	−	0.222583i
$928$	3.26327	+	2.37090i	0.107122	+	0.0778287i
$929$	−0.193237			−0.00633990			−0.00316995	−	0.999995i	$-0.501009\pi$
$929$	−0.193237			−0.00633990			−0.00316995	+	0.999995i	$0.501009\pi$
$930$	0.262113	−	5.56159i	0.00859503	−	0.182372i
$931$	33.7419			1.10585
$932$	−2.09838	−	1.52456i	−0.0687347	−	0.0499387i
$933$	17.1911	−	12.4901i	0.562811	−	0.408906i
$934$	3.33549	+	10.2656i	0.109140	+	0.335900i
$935$	−31.4746			−1.02933
$936$	3.05025			0.0997005
$937$	−5.54922	−	17.0788i	−0.181285	−	0.557938i	0.818579	−	0.574393i	$-0.194762\pi$
$937$	−5.54922	−	17.0788i	−0.181285	−	0.557938i	−0.999865	+	0.0164549i	$0.994762\pi$
$938$	−1.76620	+	5.43581i	−0.0576685	+	0.177485i
$939$	4.80663	−	14.7933i	0.156858	−	0.482761i
$940$	−10.9469	−	7.95340i	−0.357049	−	0.259411i
$941$	3.95946	+	12.1860i	0.129075	+	0.397251i	0.994621	−	0.103577i	$-0.0330289\pi$
$941$	3.95946	+	12.1860i	0.129075	+	0.397251i	−0.865547	+	0.500828i	$0.833029\pi$
$942$	4.56771	+	3.31863i	0.148824	+	0.108127i
$943$	3.41630	−	2.48208i	0.111250	−	0.0808278i
$944$	−1.09616	+	3.37362i	−0.0356768	+	0.109802i
$945$	−2.70860	+	1.96791i	−0.0881107	+	0.0640161i
$946$	8.25470	−	5.99739i	0.268384	−	0.194992i
$947$	−17.0612	+	52.5090i	−0.554415	+	1.70631i	0.143069	+	0.989713i	$0.454303\pi$
$947$	−17.0612	+	52.5090i	−0.554415	+	1.70631i	−0.697484	+	0.716601i	$0.745697\pi$
$948$	−3.81238	+	2.76985i	−0.123820	+	0.0899607i
$949$	−25.6969	−	18.6699i	−0.834158	−	0.606051i
$950$	2.47717	+	7.62395i	0.0803700	+	0.247353i
$951$	14.9192	+	10.8395i	0.483789	+	0.351493i
$952$	−6.68950	+	20.5882i	−0.216808	+	0.667266i
$953$	−9.63480	+	29.6529i	−0.312102	+	0.960550i	0.664829	+	0.746995i	$0.268504\pi$
$953$	−9.63480	+	29.6529i	−0.312102	+	0.960550i	−0.976931	+	0.213555i	$0.931496\pi$
$954$	−1.98646	−	6.11370i	−0.0643140	−	0.197938i
$955$	2.99484			0.0969106
$956$	−5.90186			−0.190880
$957$	−6.06754	−	18.6740i	−0.196136	−	0.603644i
$958$	20.3125	−	14.7579i	0.656266	−	0.476805i
$959$	49.0649	+	35.6477i	1.58439	+	1.15112i
$960$	1.00000			0.0322749
$961$	−30.8626	−	2.91553i	−0.995568	−	0.0940494i
$962$	−15.1816			−0.489475
$963$	4.63768	+	3.36947i	0.149447	+	0.108580i
$964$	−12.2384	+	8.89170i	−0.394171	+	0.286382i
$965$	−7.86639	−	24.2103i	−0.253228	−	0.779356i
$966$	26.5732			0.854978
$967$	49.4672			1.59076			0.795379	−	0.606113i	$-0.207272\pi$
$967$	49.4672			1.59076			0.795379	+	0.606113i	$0.207272\pi$
$968$	3.92320	+	12.0744i	0.126096	+	0.388085i
$969$	−16.0170	+	49.2952i	−0.514540	+	1.58359i
$970$	0.438243	−	1.34877i	0.0140711	−	0.0433065i
$971$	−7.93732	−	5.76680i	−0.254721	−	0.185065i	0.453096	−	0.891462i	$-0.350320\pi$
$971$	−7.93732	−	5.76680i	−0.254721	−	0.185065i	−0.707816	+	0.706396i	$0.750320\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	−2.65062	−	1.92579i	−0.0849751	−	0.0617380i
$974$	−29.0874	+	21.1333i	−0.932022	+	0.677154i
$975$	0.942579	−	2.90096i	0.0301867	−	0.0929050i
$976$	10.3951	−	7.55250i	0.332740	−	0.241750i
$977$	−9.47124	+	6.88126i	−0.303012	+	0.220151i	−0.728892	−	0.684629i	$-0.759964\pi$
$977$	−9.47124	+	6.88126i	−0.303012	+	0.220151i	0.425880	+	0.904780i	$0.359964\pi$
$978$	−0.185547	+	0.571054i	−0.00593313	+	0.0182603i
$979$	−31.6306	+	22.9810i	−1.01092	+	0.734475i
$980$	−3.40529	−	2.47409i	−0.108778	−	0.0790318i
$981$	−1.75362	−	5.39710i	−0.0559889	−	0.172316i
$982$	20.0914	+	14.5973i	0.641142	+	0.465817i
$983$	15.1417	−	46.6013i	0.482945	−	1.48635i	−0.351990	−	0.936004i	$-0.614495\pi$
$983$	15.1417	−	46.6013i	0.482945	−	1.48635i	0.834935	−	0.550348i	$-0.185505\pi$
$984$	−0.164408	+	0.505996i	−0.00524114	+	0.0161306i
$985$	7.48006	+	23.0213i	0.238335	+	0.733518i
$986$	26.0807			0.830580
$987$	45.3023			1.44199
$988$	7.55598	+	23.2549i	0.240388	+	0.739838i
$989$	13.4593	−	9.77877i	0.427982	−	0.310947i
$990$	−3.93815	−	2.86124i	−0.125163	−	0.0909361i
$991$	34.2843			1.08908			0.544539	−	0.838735i	$-0.316705\pi$
$991$	34.2843			1.08908			0.544539	+	0.838735i	$0.316705\pi$
$992$	0.262113	−	5.56159i	0.00832210	−	0.176581i
$993$	−20.6006			−0.653740
$994$	−20.1587	−	14.6462i	−0.639395	−	0.464548i
$995$	12.6754	−	9.20920i	0.401837	−	0.291951i
$996$	−2.30495	−	7.09389i	−0.0730350	−	0.224779i
$997$	−38.7609			−1.22757			−0.613785	−	0.789473i	$-0.710354\pi$
$997$	−38.7609			−1.22757			−0.613785	+	0.789473i	$0.710354\pi$
$998$	8.50764			0.269305
$999$	−1.53803	−	4.73357i	−0.0486611	−	0.149764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.g.901.3	yes	16
31.16	even	5	inner	930.2.n.g.481.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.g.481.3	✓	16	31.16	even	5	inner
930.2.n.g.901.3	yes	16	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(1.03459 + 3.18415i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(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} +(1.03459 + 3.18415i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(1.50424 + 4.62958i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(-2.46770 + 1.79289i) q^{13} +(1.03459 - 3.18415i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.99805 + 6.14938i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(-6.48532 - 4.71186i) q^{19} +(0.309017 + 0.951057i) q^{20} +(-2.70860 - 1.96791i) q^{21} +(1.50424 - 4.62958i) q^{22} +(2.45267 - 7.54854i) q^{23} +(0.309017 + 0.951057i) q^{24} +1.00000 q^{25} +3.05025 q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.70860 + 1.96791i) q^{28} +(3.26327 + 2.37090i) q^{29} +1.00000 q^{30} +(0.262113 - 5.56159i) q^{31} +1.00000 q^{32} +(-3.93815 - 2.86124i) q^{33} +(5.23097 - 3.80052i) q^{34} +(1.03459 + 3.18415i) q^{35} +1.00000 q^{36} -4.97717 q^{37} +(2.47717 + 7.62395i) q^{38} +(0.942579 - 2.90096i) q^{39} +(0.309017 - 0.951057i) q^{40} +(0.430426 + 0.312723i) q^{41} +(1.03459 + 3.18415i) q^{42} +(1.69577 + 1.23205i) q^{43} +(-3.93815 + 2.86124i) q^{44} +(0.309017 - 0.951057i) q^{45} +(-6.42118 + 4.66526i) q^{46} +(-10.9469 + 7.95340i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-3.40529 + 2.47409i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-1.99805 - 6.14938i) q^{51} +(-2.46770 - 1.79289i) q^{52} +(-1.98646 + 6.11370i) q^{53} +(0.309017 - 0.951057i) q^{54} +(1.50424 + 4.62958i) q^{55} +3.34801 q^{56} +8.01629 q^{57} +(-1.24646 - 3.83620i) q^{58} +(2.86977 - 2.08501i) q^{59} +(-0.809017 - 0.587785i) q^{60} -12.8491 q^{61} +(-3.48108 + 4.34536i) q^{62} +3.34801 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-2.46770 + 1.79289i) q^{65} +(1.50424 + 4.62958i) q^{66} -1.70715 q^{67} -6.46584 q^{68} +(2.45267 + 7.54854i) q^{69} +(1.03459 - 3.18415i) q^{70} +(2.29986 - 7.07823i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(3.21789 + 9.90364i) q^{73} +(4.02662 + 2.92551i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(2.47717 - 7.62395i) q^{76} +(-13.1850 + 9.57945i) q^{77} +(-2.46770 + 1.79289i) q^{78} +(1.45620 - 4.48172i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.164408 - 0.505996i) q^{82} +(6.03442 + 4.38427i) q^{83} +(1.03459 - 3.18415i) q^{84} +(-1.99805 + 6.14938i) q^{85} +(-0.647726 - 1.99349i) q^{86} -4.03362 q^{87} +4.86783 q^{88} +(2.48197 + 7.63872i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(-8.26189 - 6.00262i) q^{91} +7.93701 q^{92} +(3.05697 + 4.65349i) q^{93} +13.5311 q^{94} +(-6.48532 - 4.71186i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(0.438243 + 1.34877i) q^{97} +4.20917 q^{98} +4.86783 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 16 q^{25} + 4 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 16 q^{30} + 17 q^{31} + 16 q^{32} + 5 q^{33} + 3 q^{34} + q^{35} + 16 q^{36} + 4 q^{37} + 3 q^{38} - 6 q^{39} - 4 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} + 5 q^{44} - 4 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 33 q^{49} - 4 q^{50} + 3 q^{51} + 4 q^{52} + 9 q^{53} - 4 q^{54} + 6 q^{56} + 18 q^{57} - 15 q^{58} - 7 q^{59} - 4 q^{60} + 30 q^{61} + 12 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{65} + 86 q^{67} - 12 q^{68} - 2 q^{69} + q^{70} - 3 q^{71} - 4 q^{72} + 8 q^{73} - q^{74} - 4 q^{75} + 3 q^{76} + 2 q^{77} + 4 q^{78} + 30 q^{79} - 4 q^{80} - 4 q^{81} - 7 q^{82} + 16 q^{83} + q^{84} + 3 q^{85} - 12 q^{86} - 10 q^{88} - 29 q^{89} - 4 q^{90} + 30 q^{91} + 8 q^{92} - 8 q^{93} + 24 q^{94} - 12 q^{95} - 4 q^{96} - 5 q^{97} + 62 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^12 + 4 * q^13 + q^14 - 4 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 16 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 16 * q^30 + 17 * q^31 + 16 * q^32 + 5 * q^33 + 3 * q^34 + q^35 + 16 * q^36 + 4 * q^37 + 3 * q^38 - 6 * q^39 - 4 * q^40 - 7 * q^41 + q^42 - 2 * q^43 + 5 * q^44 - 4 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 33 * q^49 - 4 * q^50 + 3 * q^51 + 4 * q^52 + 9 * q^53 - 4 * q^54 + 6 * q^56 + 18 * q^57 - 15 * q^58 - 7 * q^59 - 4 * q^60 + 30 * q^61 + 12 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^65 + 86 * q^67 - 12 * q^68 - 2 * q^69 + q^70 - 3 * q^71 - 4 * q^72 + 8 * q^73 - q^74 - 4 * q^75 + 3 * q^76 + 2 * q^77 + 4 * q^78 + 30 * q^79 - 4 * q^80 - 4 * q^81 - 7 * q^82 + 16 * q^83 + q^84 + 3 * q^85 - 12 * q^86 - 10 * q^88 - 29 * q^89 - 4 * q^90 + 30 * q^91 + 8 * q^92 - 8 * q^93 + 24 * q^94 - 12 * q^95 - 4 * q^96 - 5 * q^97 + 62 * q^98 - 10 * q^99

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