LMFDB - Embedded newform 330.2.m.b.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [330,2,Mod(31,330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(330, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("330.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 330 = 2 \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	330.m (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:	$2.63506326670$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	330.91
Dual form			330.2.m.b.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.00000 + 3.07768i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.00000 + 3.07768i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.00000 q^{10} +(3.04508 - 1.31433i) q^{11} -1.00000 q^{12} +(-2.73607 + 1.98787i) q^{13} +(-1.00000 - 3.07768i) q^{14} +(0.309017 - 0.951057i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.92705 + 3.57971i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.381966 + 1.17557i) q^{19} +(0.809017 - 0.587785i) q^{20} +3.23607 q^{21} +(-1.69098 + 2.85317i) q^{22} +6.85410 q^{23} +(0.809017 - 0.587785i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.04508 - 3.21644i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.61803 + 1.90211i) q^{28} +(-0.809017 + 2.48990i) q^{29} +(0.309017 + 0.951057i) q^{30} +(1.11803 - 0.812299i) q^{31} +1.00000 q^{32} +(-2.19098 - 2.48990i) q^{33} -6.09017 q^{34} +(-2.61803 + 1.90211i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-1.97214 + 6.06961i) q^{37} +(-1.00000 - 0.726543i) q^{38} +(2.73607 + 1.98787i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(0.381966 + 1.17557i) q^{41} +(-2.61803 + 1.90211i) q^{42} -0.0901699 q^{43} +(-0.309017 - 3.30220i) q^{44} -1.00000 q^{45} +(-5.54508 + 4.02874i) q^{46} +(-1.33688 - 4.11450i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-2.80902 - 2.04087i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(1.88197 - 5.79210i) q^{51} +(1.04508 + 3.21644i) q^{52} +(-6.85410 + 4.97980i) q^{53} -1.00000 q^{54} +(3.23607 + 0.726543i) q^{55} -3.23607 q^{56} +(1.00000 - 0.726543i) q^{57} +(-0.809017 - 2.48990i) q^{58} +(4.35410 - 13.4005i) q^{59} +(-0.809017 - 0.587785i) q^{60} +(-0.427051 + 1.31433i) q^{62} +(-1.00000 - 3.07768i) q^{63} +(-0.809017 + 0.587785i) q^{64} -3.38197 q^{65} +(3.23607 + 0.726543i) q^{66} -5.09017 q^{67} +(4.92705 - 3.57971i) q^{68} +(-2.11803 - 6.51864i) q^{69} +(1.00000 - 3.07768i) q^{70} +(-8.47214 - 6.15537i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(4.14590 - 12.7598i) q^{73} +(-1.97214 - 6.06961i) q^{74} +(0.809017 - 0.587785i) q^{75} +1.23607 q^{76} +(1.00000 + 10.6861i) q^{77} -3.38197 q^{78} +(3.30902 - 2.40414i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.00000 - 0.726543i) q^{82} +(-3.23607 - 2.35114i) q^{83} +(1.00000 - 3.07768i) q^{84} +(1.88197 + 5.79210i) q^{85} +(0.0729490 - 0.0530006i) q^{86} +2.61803 q^{87} +(2.19098 + 2.48990i) q^{88} +17.2361 q^{89} +(0.809017 - 0.587785i) q^{90} +(-3.38197 - 10.4086i) q^{91} +(2.11803 - 6.51864i) q^{92} +(-1.11803 - 0.812299i) q^{93} +(3.50000 + 2.54290i) q^{94} +(-0.381966 + 1.17557i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-15.0902 + 10.9637i) q^{97} +3.47214 q^{98} +(-1.69098 + 2.85317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 4 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 - q^4 + q^5 + q^6 - 4 * q^7 - q^8 - q^9	$ 4 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 4 q^{7} - q^{8} - q^{9} - 4 q^{10} + q^{11} - 4 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} - q^{16} + 13 q^{17} - q^{18} + 6 q^{19} + q^{20} + 4 q^{21} - 9 q^{22} + 14 q^{23} + q^{24} - q^{25} - 7 q^{26} + q^{27} + 6 q^{28} - q^{29} - q^{30} + 4 q^{32} - 11 q^{33} - 2 q^{34} - 6 q^{35} - q^{36} + 10 q^{37} - 4 q^{38} + 2 q^{39} + q^{40} + 6 q^{41} - 6 q^{42} + 22 q^{43} + q^{44} - 4 q^{45} - 11 q^{46} - 21 q^{47} + q^{48} - 9 q^{49} - q^{50} + 12 q^{51} - 7 q^{52} - 14 q^{53} - 4 q^{54} + 4 q^{55} - 4 q^{56} + 4 q^{57} - q^{58} + 4 q^{59} - q^{60} + 5 q^{62} - 4 q^{63} - q^{64} - 18 q^{65} + 4 q^{66} + 2 q^{67} + 13 q^{68} - 4 q^{69} + 4 q^{70} - 16 q^{71} - q^{72} + 30 q^{73} + 10 q^{74} + q^{75} - 4 q^{76} + 4 q^{77} - 18 q^{78} + 11 q^{79} + q^{80} - q^{81} - 4 q^{82} - 4 q^{83} + 4 q^{84} + 12 q^{85} + 7 q^{86} + 6 q^{87} + 11 q^{88} + 60 q^{89} + q^{90} - 18 q^{91} + 4 q^{92} + 14 q^{94} - 6 q^{95} + q^{96} - 38 q^{97} - 4 q^{98} - 9 q^{99}+O(q^{100}) $ 4 * q - q^2 + q^3 - q^4 + q^5 + q^6 - 4 * q^7 - q^8 - q^9 - 4 * q^10 + q^11 - 4 * q^12 - 2 * q^13 - 4 * q^14 - q^15 - q^16 + 13 * q^17 - q^18 + 6 * q^19 + q^20 + 4 * q^21 - 9 * q^22 + 14 * q^23 + q^24 - q^25 - 7 * q^26 + q^27 + 6 * q^28 - q^29 - q^30 + 4 * q^32 - 11 * q^33 - 2 * q^34 - 6 * q^35 - q^36 + 10 * q^37 - 4 * q^38 + 2 * q^39 + q^40 + 6 * q^41 - 6 * q^42 + 22 * q^43 + q^44 - 4 * q^45 - 11 * q^46 - 21 * q^47 + q^48 - 9 * q^49 - q^50 + 12 * q^51 - 7 * q^52 - 14 * q^53 - 4 * q^54 + 4 * q^55 - 4 * q^56 + 4 * q^57 - q^58 + 4 * q^59 - q^60 + 5 * q^62 - 4 * q^63 - q^64 - 18 * q^65 + 4 * q^66 + 2 * q^67 + 13 * q^68 - 4 * q^69 + 4 * q^70 - 16 * q^71 - q^72 + 30 * q^73 + 10 * q^74 + q^75 - 4 * q^76 + 4 * q^77 - 18 * q^78 + 11 * q^79 + q^80 - q^81 - 4 * q^82 - 4 * q^83 + 4 * q^84 + 12 * q^85 + 7 * q^86 + 6 * q^87 + 11 * q^88 + 60 * q^89 + q^90 - 18 * q^91 + 4 * q^92 + 14 * q^94 - 6 * q^95 + q^96 - 38 * q^97 - 4 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/330\mathbb{Z}\right)^\times$.

$n$	$67$	$211$	$221$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	−1.00000	+	3.07768i	−0.377964	+	1.16326i	0.563492	+	0.826121i	$0.309457\pi$
$7$	−1.00000	+	3.07768i	−0.377964	+	1.16326i	−0.941457	+	0.337134i	$0.890543\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−1.00000			−0.316228
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$12$	−1.00000			−0.288675
$13$	−2.73607	+	1.98787i	−0.758849	+	0.551336i	−0.898557	−	0.438857i	$-0.855384\pi$
$13$	−2.73607	+	1.98787i	−0.758849	+	0.551336i	0.139708	+	0.990193i	$0.455384\pi$
$14$	−1.00000	−	3.07768i	−0.267261	−	0.822546i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	4.92705	+	3.57971i	1.19499	+	0.868208i	0.993782	−	0.111342i	$-0.0355148\pi$
$17$	4.92705	+	3.57971i	1.19499	+	0.868208i	0.201203	+	0.979550i	$0.435515\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	0.381966	+	1.17557i	0.0876290	+	0.269694i	0.985263	−	0.171048i	$-0.0547153\pi$
$19$	0.381966	+	1.17557i	0.0876290	+	0.269694i	−0.897634	+	0.440742i	$0.854715\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	3.23607			0.706168
$22$	−1.69098	+	2.85317i	−0.360519	+	0.608298i
$23$	6.85410			1.42918			0.714590	−	0.699544i	$-0.246614\pi$
$23$	6.85410			1.42918			0.714590	+	0.699544i	$0.246614\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	1.04508	−	3.21644i	0.204958	−	0.630796i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	2.61803	+	1.90211i	0.494762	+	0.359466i
$29$	−0.809017	+	2.48990i	−0.150231	+	0.462363i	−0.997646	−	0.0685673i	$-0.978157\pi$
$29$	−0.809017	+	2.48990i	−0.150231	+	0.462363i	0.847416	+	0.530930i	$0.178157\pi$
$30$	0.309017	+	0.951057i	0.0564185	+	0.173638i
$31$	1.11803	−	0.812299i	0.200805	−	0.145893i	−0.482839	−	0.875709i	$-0.660394\pi$
$31$	1.11803	−	0.812299i	0.200805	−	0.145893i	0.683644	+	0.729816i	$0.260394\pi$
$32$	1.00000			0.176777
$33$	−2.19098	−	2.48990i	−0.381401	−	0.433436i
$34$	−6.09017			−1.04446
$35$	−2.61803	+	1.90211i	−0.442529	+	0.321516i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−1.97214	+	6.06961i	−0.324217	+	0.997838i	0.647576	+	0.762001i	$0.275783\pi$
$37$	−1.97214	+	6.06961i	−0.324217	+	0.997838i	−0.971793	+	0.235837i	$0.924217\pi$
$38$	−1.00000	−	0.726543i	−0.162221	−	0.117861i
$39$	2.73607	+	1.98787i	0.438122	+	0.318314i
$40$	−0.309017	+	0.951057i	−0.0488599	+	0.150375i
$41$	0.381966	+	1.17557i	0.0596531	+	0.183593i	0.976443	−	0.215778i	$-0.0692286\pi$
$41$	0.381966	+	1.17557i	0.0596531	+	0.183593i	−0.916789	+	0.399371i	$0.869229\pi$
$42$	−2.61803	+	1.90211i	−0.403971	+	0.293502i
$43$	−0.0901699			−0.0137508			−0.00687539	−	0.999976i	$-0.502189\pi$
$43$	−0.0901699			−0.0137508			−0.00687539	+	0.999976i	$0.502189\pi$
$44$	−0.309017	−	3.30220i	−0.0465861	−	0.497825i
$45$	−1.00000			−0.149071
$46$	−5.54508	+	4.02874i	−0.817578	+	0.594005i
$47$	−1.33688	−	4.11450i	−0.195004	−	0.600161i	−0.999977	−	0.00684879i	$-0.997820\pi$
$47$	−1.33688	−	4.11450i	−0.195004	−	0.600161i	0.804972	−	0.593312i	$-0.202180\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−2.80902	−	2.04087i	−0.401288	−	0.291553i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	1.88197	−	5.79210i	0.263528	−	0.811056i
$52$	1.04508	+	3.21644i	0.144927	+	0.446040i
$53$	−6.85410	+	4.97980i	−0.941483	+	0.684028i	−0.948777	−	0.315946i	$-0.897678\pi$
$53$	−6.85410	+	4.97980i	−0.941483	+	0.684028i	0.00729395	+	0.999973i	$0.497678\pi$
$54$	−1.00000			−0.136083
$55$	3.23607	+	0.726543i	0.436351	+	0.0979670i
$56$	−3.23607			−0.432438
$57$	1.00000	−	0.726543i	0.132453	−	0.0962329i
$58$	−0.809017	−	2.48990i	−0.106229	−	0.326940i
$59$	4.35410	−	13.4005i	0.566856	−	1.74460i	−0.0955164	−	0.995428i	$-0.530450\pi$
$59$	4.35410	−	13.4005i	0.566856	−	1.74460i	0.662372	−	0.749175i	$-0.269550\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$61$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$62$	−0.427051	+	1.31433i	−0.0542355	+	0.166920i
$63$	−1.00000	−	3.07768i	−0.125988	−	0.387752i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−3.38197			−0.419481
$66$	3.23607	+	0.726543i	0.398332	+	0.0894312i
$67$	−5.09017			−0.621863			−0.310932	−	0.950432i	$-0.600641\pi$
$67$	−5.09017			−0.621863			−0.310932	+	0.950432i	$0.600641\pi$
$68$	4.92705	−	3.57971i	0.597493	−	0.434104i
$69$	−2.11803	−	6.51864i	−0.254981	−	0.784752i
$70$	1.00000	−	3.07768i	0.119523	−	0.367854i
$71$	−8.47214	−	6.15537i	−1.00546	−	0.730508i	−0.0422061	−	0.999109i	$-0.513439\pi$
$71$	−8.47214	−	6.15537i	−1.00546	−	0.730508i	−0.963251	+	0.268601i	$0.913439\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	4.14590	−	12.7598i	0.485241	−	1.49342i	−0.346391	−	0.938090i	$-0.612593\pi$
$73$	4.14590	−	12.7598i	0.485241	−	1.49342i	0.831632	−	0.555327i	$-0.187407\pi$
$74$	−1.97214	−	6.06961i	−0.229256	−	0.705578i
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$	1.23607			0.141787
$77$	1.00000	+	10.6861i	0.113961	+	1.21780i
$78$	−3.38197			−0.382932
$79$	3.30902	−	2.40414i	0.372293	−	0.270487i	−0.385868	−	0.922554i	$-0.626098\pi$
$79$	3.30902	−	2.40414i	0.372293	−	0.270487i	0.758161	+	0.652067i	$0.226098\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−1.00000	−	0.726543i	−0.110432	−	0.0802332i
$83$	−3.23607	−	2.35114i	−0.355205	−	0.258071i	0.395845	−	0.918318i	$-0.370452\pi$
$83$	−3.23607	−	2.35114i	−0.355205	−	0.258071i	−0.751049	+	0.660246i	$0.770452\pi$
$84$	1.00000	−	3.07768i	0.109109	−	0.335803i
$85$	1.88197	+	5.79210i	0.204128	+	0.628241i
$86$	0.0729490	−	0.0530006i	0.00786629	−	0.00571520i
$87$	2.61803			0.280683
$88$	2.19098	+	2.48990i	0.233560	+	0.265424i
$89$	17.2361			1.82702			0.913510	−	0.406817i	$-0.133361\pi$
$89$	17.2361			1.82702			0.913510	+	0.406817i	$0.133361\pi$
$90$	0.809017	−	0.587785i	0.0852779	−	0.0619580i
$91$	−3.38197	−	10.4086i	−0.354526	−	1.09112i
$92$	2.11803	−	6.51864i	0.220820	−	0.679615i
$93$	−1.11803	−	0.812299i	−0.115935	−	0.0842315i
$94$	3.50000	+	2.54290i	0.360997	+	0.262280i
$95$	−0.381966	+	1.17557i	−0.0391889	+	0.120611i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	−15.0902	+	10.9637i	−1.53217	+	1.11319i	−0.577160	+	0.816631i	$0.695839\pi$
$97$	−15.0902	+	10.9637i	−1.53217	+	1.11319i	−0.955015	+	0.296559i	$0.904161\pi$
$98$	3.47214			0.350739
$99$	−1.69098	+	2.85317i	−0.169950	+	0.286754i
$100$	1.00000			0.100000
$101$	−12.6353	+	9.18005i	−1.25725	+	0.913449i	−0.998620	−	0.0525259i	$-0.983273\pi$
$101$	−12.6353	+	9.18005i	−1.25725	+	0.913449i	−0.258635	+	0.965975i	$0.583273\pi$
$102$	1.88197	+	5.79210i	0.186342	+	0.573503i
$103$	2.09017	−	6.43288i	0.205951	−	0.633851i	−0.793722	−	0.608280i	$-0.791860\pi$
$103$	2.09017	−	6.43288i	0.205951	−	0.633851i	0.999673	−	0.0255706i	$-0.00814025\pi$
$104$	−2.73607	−	1.98787i	−0.268294	−	0.194927i
$105$	2.61803	+	1.90211i	0.255494	+	0.185627i
$106$	2.61803	−	8.05748i	0.254286	−	0.782612i
$107$	1.94427	+	5.98385i	0.187960	+	0.578481i	0.999987	−	0.00513899i	$-0.00163580\pi$
$107$	1.94427	+	5.98385i	0.187960	+	0.578481i	−0.812027	+	0.583620i	$0.801636\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−2.47214			−0.236788			−0.118394	−	0.992967i	$-0.537775\pi$
$109$	−2.47214			−0.236788			−0.118394	+	0.992967i	$0.537775\pi$
$110$	−3.04508	+	1.31433i	−0.290337	+	0.125316i
$111$	6.38197			0.605749
$112$	2.61803	−	1.90211i	0.247381	−	0.179733i
$113$	−6.04508	−	18.6049i	−0.568674	−	1.75020i	−0.656775	−	0.754086i	$-0.728080\pi$
$113$	−6.04508	−	18.6049i	−0.568674	−	1.75020i	0.0881015	−	0.996112i	$-0.471920\pi$
$114$	−0.381966	+	1.17557i	−0.0357744	+	0.110102i
$115$	5.54508	+	4.02874i	0.517082	+	0.375682i
$116$	2.11803	+	1.53884i	0.196655	+	0.142878i
$117$	1.04508	−	3.21644i	0.0966181	−	0.297360i
$118$	4.35410	+	13.4005i	0.400828	+	1.23362i
$119$	−15.9443	+	11.5842i	−1.46161	+	1.06192i
$120$	1.00000			0.0912871
$121$	7.54508	−	8.00448i	0.685917	−	0.727680i
$122$		0			0
$123$	1.00000	−	0.726543i	0.0901670	−	0.0655101i
$124$	−0.427051	−	1.31433i	−0.0383503	−	0.118030i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	2.61803	+	1.90211i	0.233233	+	0.169454i
$127$	−11.8541	−	8.61251i	−1.05188	−	0.764237i	−0.0793121	−	0.996850i	$-0.525272\pi$
$127$	−11.8541	−	8.61251i	−1.05188	−	0.764237i	−0.972569	+	0.232613i	$0.925272\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	0.0278640	+	0.0857567i	0.00245329	+	0.00755046i
$130$	2.73607	−	1.98787i	0.239969	−	0.174348i
$131$	−3.38197			−0.295484			−0.147742	−	0.989026i	$-0.547200\pi$
$131$	−3.38197			−0.295484			−0.147742	+	0.989026i	$0.547200\pi$
$132$	−3.04508	+	1.31433i	−0.265041	+	0.114398i
$133$	−4.00000			−0.346844
$134$	4.11803	−	2.99193i	0.355744	−	0.258463i
$135$	0.309017	+	0.951057i	0.0265959	+	0.0818539i
$136$	−1.88197	+	5.79210i	−0.161377	+	0.496668i
$137$	10.3541	+	7.52270i	0.884611	+	0.642707i	0.934467	−	0.356049i	$-0.115876\pi$
$137$	10.3541	+	7.52270i	0.884611	+	0.642707i	−0.0498566	+	0.998756i	$0.515876\pi$
$138$	5.54508	+	4.02874i	0.472029	+	0.342949i
$139$	2.70820	−	8.33499i	0.229707	−	0.706965i	−0.768073	−	0.640363i	$-0.778784\pi$
$139$	2.70820	−	8.33499i	0.229707	−	0.706965i	0.997780	−	0.0666024i	$-0.0212159\pi$
$140$	1.00000	+	3.07768i	0.0845154	+	0.260112i
$141$	−3.50000	+	2.54290i	−0.294753	+	0.214151i
$142$	10.4721			0.878802
$143$	−5.71885	+	9.64932i	−0.478234	+	0.806917i
$144$	1.00000			0.0833333
$145$	−2.11803	+	1.53884i	−0.175893	+	0.127794i
$146$	4.14590	+	12.7598i	0.343117	+	1.05601i
$147$	−1.07295	+	3.30220i	−0.0884953	+	0.272361i
$148$	5.16312	+	3.75123i	0.424406	+	0.308349i
$149$	6.16312	+	4.47777i	0.504902	+	0.366833i	0.810886	−	0.585204i	$-0.198985\pi$
$149$	6.16312	+	4.47777i	0.504902	+	0.366833i	−0.305984	+	0.952037i	$0.598985\pi$
$150$	−0.309017	+	0.951057i	−0.0252311	+	0.0776534i
$151$	6.47214	+	19.9192i	0.526695	+	1.62100i	0.760940	+	0.648823i	$0.224738\pi$
$151$	6.47214	+	19.9192i	0.526695	+	1.62100i	−0.234245	+	0.972178i	$0.575262\pi$
$152$	−1.00000	+	0.726543i	−0.0811107	+	0.0589304i
$153$	−6.09017			−0.492361
$154$	−7.09017	−	8.05748i	−0.571342	−	0.649290i
$155$	1.38197			0.111002
$156$	2.73607	−	1.98787i	0.219061	−	0.159157i
$157$	−2.86475	−	8.81678i	−0.228632	−	0.703656i	−0.997903	−	0.0647330i	$-0.979380\pi$
$157$	−2.86475	−	8.81678i	−0.228632	−	0.703656i	0.769271	−	0.638923i	$-0.220620\pi$
$158$	−1.26393	+	3.88998i	−0.100553	+	0.309470i
$159$	6.85410	+	4.97980i	0.543566	+	0.394924i
$160$	0.809017	+	0.587785i	0.0639584	+	0.0464685i
$161$	−6.85410	+	21.0948i	−0.540179	+	1.66250i
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−0.690983	+	0.502029i	−0.0541220	+	0.0393219i	−0.614517	−	0.788903i	$-0.710649\pi$
$163$	−0.690983	+	0.502029i	−0.0541220	+	0.0393219i	0.560395	+	0.828225i	$0.310649\pi$
$164$	1.23607			0.0965207
$165$	−0.309017	−	3.30220i	−0.0240569	−	0.257076i
$166$	4.00000			0.310460
$167$	10.7361	−	7.80021i	0.830782	−	0.603598i	−0.0889985	−	0.996032i	$-0.528367\pi$
$167$	10.7361	−	7.80021i	0.830782	−	0.603598i	0.919780	+	0.392433i	$0.128367\pi$
$168$	1.00000	+	3.07768i	0.0771517	+	0.237448i
$169$	−0.482779	+	1.48584i	−0.0371369	+	0.114295i
$170$	−4.92705	−	3.57971i	−0.377888	−	0.274551i
$171$	−1.00000	−	0.726543i	−0.0764719	−	0.0555601i
$172$	−0.0278640	+	0.0857567i	−0.00212461	+	0.00653889i
$173$	−2.94427	−	9.06154i	−0.223849	−	0.688936i	−0.998406	−	0.0564325i	$-0.982027\pi$
$173$	−2.94427	−	9.06154i	−0.223849	−	0.688936i	0.774558	−	0.632503i	$-0.217973\pi$
$174$	−2.11803	+	1.53884i	−0.160568	+	0.116659i
$175$	−3.23607			−0.244624
$176$	−3.23607	−	0.726543i	−0.243928	−	0.0547652i
$177$	−14.0902			−1.05908
$178$	−13.9443	+	10.1311i	−1.04517	+	0.759359i
$179$	5.60739	+	17.2578i	0.419116	+	1.28991i	0.908517	+	0.417848i	$0.137215\pi$
$179$	5.60739	+	17.2578i	0.419116	+	1.28991i	−0.489401	+	0.872059i	$0.662785\pi$
$180$	−0.309017	+	0.951057i	−0.0230328	+	0.0708876i
$181$	−17.7082	−	12.8658i	−1.31624	−	0.956305i	−0.999971	−	0.00763529i	$-0.997570\pi$
$181$	−17.7082	−	12.8658i	−1.31624	−	0.956305i	−0.316270	−	0.948669i	$-0.602430\pi$
$182$	8.85410	+	6.43288i	0.656310	+	0.476837i
$183$		0			0
$184$	2.11803	+	6.51864i	0.156144	+	0.480560i
$185$	−5.16312	+	3.75123i	−0.379600	+	0.275796i
$186$	1.38197			0.101331
$187$	19.7082	+	4.42477i	1.44121	+	0.323571i
$188$	−4.32624			−0.315523
$189$	−2.61803	+	1.90211i	−0.190434	+	0.138358i
$190$	−0.381966	−	1.17557i	−0.0277107	−	0.0852848i
$191$	2.85410	−	8.78402i	0.206516	−	0.635590i	−0.793132	−	0.609050i	$-0.791551\pi$
$191$	2.85410	−	8.78402i	0.206516	−	0.635590i	0.999648	−	0.0265400i	$-0.00844895\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	16.9443	+	12.3107i	1.21968	+	0.886146i	0.996073	−	0.0885344i	$-0.0282183\pi$
$193$	16.9443	+	12.3107i	1.21968	+	0.886146i	0.223602	+	0.974680i	$0.428218\pi$
$194$	5.76393	−	17.7396i	0.413826	−	1.27363i
$195$	1.04508	+	3.21644i	0.0748401	+	0.230334i
$196$	−2.80902	+	2.04087i	−0.200644	+	0.145776i
$197$	10.9443			0.779747			0.389874	−	0.920868i	$-0.372519\pi$
$197$	10.9443			0.779747			0.389874	+	0.920868i	$0.372519\pi$
$198$	−0.309017	−	3.30220i	−0.0219609	−	0.234677i
$199$	25.9787			1.84158			0.920791	−	0.390056i	$-0.127544\pi$
$199$	25.9787			1.84158			0.920791	+	0.390056i	$0.127544\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	1.57295	+	4.84104i	0.110947	+	0.341461i
$202$	4.82624	−	14.8536i	0.339573	−	1.04510i
$203$	−6.85410	−	4.97980i	−0.481064	−	0.349513i
$204$	−4.92705	−	3.57971i	−0.344963	−	0.250630i
$205$	−0.381966	+	1.17557i	−0.0266777	+	0.0821054i
$206$	2.09017	+	6.43288i	0.145629	+	0.448200i
$207$	−5.54508	+	4.02874i	−0.385410	+	0.280017i
$208$	3.38197			0.234497
$209$	2.70820	+	3.07768i	0.187330	+	0.212888i
$210$	−3.23607			−0.223310
$211$	20.4164	−	14.8334i	1.40552	−	1.02117i	0.411569	−	0.911379i	$-0.364981\pi$
$211$	20.4164	−	14.8334i	1.40552	−	1.02117i	0.993954	−	0.109794i	$-0.0350191\pi$
$212$	2.61803	+	8.05748i	0.179807	+	0.553390i
$213$	−3.23607	+	9.95959i	−0.221732	+	0.682420i
$214$	−5.09017	−	3.69822i	−0.347957	−	0.252805i
$215$	−0.0729490	−	0.0530006i	−0.00497508	−	0.00361461i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	1.38197	+	4.25325i	0.0938140	+	0.288730i
$218$	2.00000	−	1.45309i	0.135457	−	0.0984153i
$219$	−13.4164			−0.906597
$220$	1.69098	−	2.85317i	0.114006	−	0.192361i
$221$	−20.5967			−1.38549
$222$	−5.16312	+	3.75123i	−0.346526	+	0.251766i
$223$	2.23607	+	6.88191i	0.149738	+	0.460847i	0.997590	−	0.0693868i	$-0.0221043\pi$
$223$	2.23607	+	6.88191i	0.149738	+	0.460847i	−0.847852	+	0.530234i	$0.822104\pi$
$224$	−1.00000	+	3.07768i	−0.0668153	+	0.205636i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	15.8262	+	11.4984i	1.05275	+	0.764865i
$227$	6.29180	−	19.3642i	0.417601	−	1.28524i	−0.492302	−	0.870424i	$-0.663845\pi$
$227$	6.29180	−	19.3642i	0.417601	−	1.28524i	0.909904	−	0.414820i	$-0.136155\pi$
$228$	−0.381966	−	1.17557i	−0.0252963	−	0.0778541i
$229$	−0.618034	+	0.449028i	−0.0408408	+	0.0296726i	−0.608018	−	0.793923i	$-0.708035\pi$
$229$	−0.618034	+	0.449028i	−0.0408408	+	0.0296726i	0.567178	+	0.823596i	$0.308035\pi$
$230$	−6.85410			−0.451946
$231$	9.85410	−	4.25325i	0.648352	−	0.279844i
$232$	−2.61803			−0.171882
$233$	3.59017	−	2.60841i	0.235200	−	0.170883i	−0.463942	−	0.885865i	$-0.653565\pi$
$233$	3.59017	−	2.60841i	0.235200	−	0.170883i	0.699142	+	0.714983i	$0.253565\pi$
$234$	1.04508	+	3.21644i	0.0683193	+	0.210265i
$235$	1.33688	−	4.11450i	0.0872085	−	0.268400i
$236$	−11.3992	−	8.28199i	−0.742024	−	0.539112i
$237$	−3.30902	−	2.40414i	−0.214944	−	0.156166i
$238$	6.09017	−	18.7436i	0.394767	−	1.21497i
$239$	−1.00000	−	3.07768i	−0.0646846	−	0.199079i	0.913491	−	0.406859i	$-0.133376\pi$
$239$	−1.00000	−	3.07768i	−0.0646846	−	0.199079i	−0.978175	+	0.207780i	$0.933376\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	−23.8885			−1.53880			−0.769398	−	0.638769i	$-0.779444\pi$
$241$	−23.8885			−1.53880			−0.769398	+	0.638769i	$0.779444\pi$
$242$	−1.39919	+	10.9106i	−0.0899431	+	0.701363i
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−1.07295	−	3.30220i	−0.0685482	−	0.210970i
$246$	−0.381966	+	1.17557i	−0.0243533	+	0.0749516i
$247$	−3.38197	−	2.45714i	−0.215189	−	0.156344i
$248$	1.11803	+	0.812299i	0.0709952	+	0.0515811i
$249$	−1.23607	+	3.80423i	−0.0783326	+	0.241083i
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−6.78115	+	4.92680i	−0.428023	+	0.310977i	−0.780858	−	0.624709i	$-0.785218\pi$
$251$	−6.78115	+	4.92680i	−0.428023	+	0.310977i	0.352835	+	0.935685i	$0.385218\pi$
$252$	−3.23607			−0.203853
$253$	20.8713	−	9.00854i	1.31217	−	0.566362i
$254$	14.6525			0.919378
$255$	4.92705	−	3.57971i	0.308544	−	0.224170i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	9.38197	−	28.8747i	0.585231	−	1.80116i	−0.0131100	−	0.999914i	$-0.504173\pi$
$257$	9.38197	−	28.8747i	0.585231	−	1.80116i	0.598341	−	0.801242i	$-0.295827\pi$
$258$	−0.0729490	−	0.0530006i	−0.00454161	−	0.00329967i
$259$	−16.7082	−	12.1392i	−1.03820	−	0.754294i
$260$	−1.04508	+	3.21644i	−0.0648134	+	0.199475i
$261$	−0.809017	−	2.48990i	−0.0500769	−	0.154121i
$262$	2.73607	−	1.98787i	0.169035	−	0.122811i
$263$	6.85410			0.422642			0.211321	−	0.977417i	$-0.432223\pi$
$263$	6.85410			0.422642			0.211321	+	0.977417i	$0.432223\pi$
$264$	1.69098	−	2.85317i	0.104073	−	0.175600i
$265$	−8.47214			−0.520439
$266$	3.23607	−	2.35114i	0.198416	−	0.144158i
$267$	−5.32624	−	16.3925i	−0.325960	−	1.00320i
$268$	−1.57295	+	4.84104i	−0.0960832	+	0.295714i
$269$	−2.59017	−	1.88187i	−0.157925	−	0.114740i	0.506016	−	0.862524i	$-0.331118\pi$
$269$	−2.59017	−	1.88187i	−0.157925	−	0.114740i	−0.663942	+	0.747784i	$0.731118\pi$
$270$	−0.809017	−	0.587785i	−0.0492352	−	0.0357715i
$271$	−1.97214	+	6.06961i	−0.119799	+	0.368703i	−0.992918	−	0.118805i	$-0.962094\pi$
$271$	−1.97214	+	6.06961i	−0.119799	+	0.368703i	0.873119	+	0.487507i	$0.162094\pi$
$272$	−1.88197	−	5.79210i	−0.114111	−	0.351197i
$273$	−8.85410	+	6.43288i	−0.535875	+	0.389336i
$274$	−12.7984			−0.773178
$275$	2.19098	+	2.48990i	0.132121	+	0.150147i
$276$	−6.85410			−0.412568
$277$	19.0172	−	13.8168i	1.14263	−	0.830172i	0.155150	−	0.987891i	$-0.450414\pi$
$277$	19.0172	−	13.8168i	1.14263	−	0.830172i	0.987484	+	0.157719i	$0.0504139\pi$
$278$	2.70820	+	8.33499i	0.162427	+	0.499900i
$279$	−0.427051	+	1.31433i	−0.0255669	+	0.0786867i
$280$	−2.61803	−	1.90211i	−0.156457	−	0.113673i
$281$	6.09017	+	4.42477i	0.363309	+	0.263959i	0.754431	−	0.656379i	$-0.227913\pi$
$281$	6.09017	+	4.42477i	0.363309	+	0.263959i	−0.391122	+	0.920339i	$0.627913\pi$
$282$	1.33688	−	4.11450i	0.0796101	−	0.245015i
$283$	−6.89919	−	21.2335i	−0.410114	−	1.26220i	−0.916549	−	0.399923i	$-0.869037\pi$
$283$	−6.89919	−	21.2335i	−0.410114	−	1.26220i	0.506435	−	0.862278i	$-0.330963\pi$
$284$	−8.47214	+	6.15537i	−0.502729	+	0.365254i
$285$	1.23607			0.0732183
$286$	−1.04508	−	11.1679i	−0.0617972	−	0.660373i
$287$	−4.00000			−0.236113
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	6.20820	+	19.1069i	0.365188	+	1.12393i
$290$	0.809017	−	2.48990i	0.0475071	−	0.146212i
$291$	15.0902	+	10.9637i	0.884601	+	0.642701i
$292$	−10.8541	−	7.88597i	−0.635188	−	0.461491i
$293$	−6.18034	+	19.0211i	−0.361059	+	1.11123i	0.591353	+	0.806413i	$0.298594\pi$
$293$	−6.18034	+	19.0211i	−0.361059	+	1.11123i	−0.952412	+	0.304813i	$0.901406\pi$
$294$	−1.07295	−	3.30220i	−0.0625757	−	0.192588i
$295$	11.3992	−	8.28199i	0.663686	−	0.482196i
$296$	−6.38197			−0.370944
$297$	3.23607	+	0.726543i	0.187776	+	0.0421583i
$298$	−7.61803			−0.441301
$299$	−18.7533	+	13.6251i	−1.08453	+	0.787958i
$300$	−0.309017	−	0.951057i	−0.0178411	−	0.0549093i
$301$	0.0901699	−	0.277515i	0.00519731	−	0.0159957i
$302$	−16.9443	−	12.3107i	−0.975033	−	0.708403i
$303$	12.6353	+	9.18005i	0.725876	+	0.527380i
$304$	0.381966	−	1.17557i	0.0219073	−	0.0674236i
$305$		0			0
$306$	4.92705	−	3.57971i	0.281661	−	0.204639i
$307$	−33.4508			−1.90914			−0.954570	−	0.297985i	$-0.903685\pi$
$307$	−33.4508			−1.90914			−0.954570	+	0.297985i	$0.903685\pi$
$308$	10.4721	+	2.35114i	0.596705	+	0.133969i
$309$	−6.76393			−0.384787
$310$	−1.11803	+	0.812299i	−0.0635001	+	0.0461355i
$311$	2.85410	+	8.78402i	0.161841	+	0.498096i	0.998790	−	0.0491856i	$-0.0156626\pi$
$311$	2.85410	+	8.78402i	0.161841	+	0.498096i	−0.836948	+	0.547282i	$0.815663\pi$
$312$	−1.04508	+	3.21644i	−0.0591663	+	0.182095i
$313$	−6.85410	−	4.97980i	−0.387417	−	0.281475i	0.376979	−	0.926222i	$-0.376963\pi$
$313$	−6.85410	−	4.97980i	−0.387417	−	0.281475i	−0.764396	+	0.644747i	$0.776963\pi$
$314$	7.50000	+	5.44907i	0.423249	+	0.307509i
$315$	1.00000	−	3.07768i	0.0563436	−	0.173408i
$316$	−1.26393	−	3.88998i	−0.0711017	−	0.218829i
$317$	22.1803	−	16.1150i	1.24577	−	0.905106i	0.247803	−	0.968810i	$-0.420291\pi$
$317$	22.1803	−	16.1150i	1.24577	−	0.905106i	0.997969	+	0.0637041i	$0.0202914\pi$
$318$	−8.47214			−0.475094
$319$	0.809017	+	8.64527i	0.0452963	+	0.484042i
$320$	−1.00000			−0.0559017
$321$	5.09017	−	3.69822i	0.284106	−	0.206415i
$322$	−6.85410	−	21.0948i	−0.381964	−	1.17556i
$323$	−2.32624	+	7.15942i	−0.129435	+	0.398361i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−2.73607	−	1.98787i	−0.151770	−	0.110267i
$326$	0.263932	−	0.812299i	0.0146178	−	0.0449891i
$327$	0.763932	+	2.35114i	0.0422455	+	0.130018i
$328$	−1.00000	+	0.726543i	−0.0552158	+	0.0401166i
$329$	14.0000			0.771845
$330$	2.19098	+	2.48990i	0.120610	+	0.137064i
$331$	9.23607			0.507660			0.253830	−	0.967249i	$-0.418310\pi$
$331$	9.23607			0.507660			0.253830	+	0.967249i	$0.418310\pi$
$332$	−3.23607	+	2.35114i	−0.177602	+	0.129036i
$333$	−1.97214	−	6.06961i	−0.108072	−	0.332613i
$334$	−4.10081	+	12.6210i	−0.224387	+	0.690591i
$335$	−4.11803	−	2.99193i	−0.224992	−	0.163466i
$336$	−2.61803	−	1.90211i	−0.142825	−	0.103769i
$337$	−4.70820	+	14.4904i	−0.256472	+	0.789340i	0.737064	+	0.675823i	$0.236212\pi$
$337$	−4.70820	+	14.4904i	−0.256472	+	0.789340i	−0.993536	+	0.113517i	$0.963788\pi$
$338$	−0.482779	−	1.48584i	−0.0262597	−	0.0808191i
$339$	−15.8262	+	11.4984i	−0.859563	+	0.624509i
$340$	6.09017			0.330286
$341$	2.33688	−	3.94298i	0.126549	−	0.213525i
$342$	1.23607			0.0668389
$343$	−9.23607	+	6.71040i	−0.498701	+	0.362327i
$344$	−0.0278640	−	0.0857567i	−0.00150233	−	0.00462369i
$345$	2.11803	−	6.51864i	0.114031	−	0.350952i
$346$	7.70820	+	5.60034i	0.414396	+	0.301076i
$347$	−29.0344	−	21.0948i	−1.55865	−	1.13243i	−0.937105	−	0.349048i	$-0.886505\pi$
$347$	−29.0344	−	21.0948i	−1.55865	−	1.13243i	−0.621546	−	0.783378i	$-0.713495\pi$
$348$	0.809017	−	2.48990i	0.0433679	−	0.133473i
$349$	−3.52786	−	10.8576i	−0.188842	−	0.581197i	0.811151	−	0.584837i	$-0.198841\pi$
$349$	−3.52786	−	10.8576i	−0.188842	−	0.581197i	−0.999993	+	0.00363995i	$0.998841\pi$
$350$	2.61803	−	1.90211i	0.139940	−	0.101672i
$351$	−3.38197			−0.180516
$352$	3.04508	−	1.31433i	0.162304	−	0.0700539i
$353$	23.6180			1.25706			0.628531	−	0.777785i	$-0.283657\pi$
$353$	23.6180			1.25706			0.628531	+	0.777785i	$0.283657\pi$
$354$	11.3992	−	8.28199i	0.605860	−	0.440183i
$355$	−3.23607	−	9.95959i	−0.171753	−	0.528600i
$356$	5.32624	−	16.3925i	0.282290	−	0.868799i
$357$	15.9443	+	11.5842i	0.843860	+	0.613100i
$358$	−14.6803	−	10.6659i	−0.775880	−	0.563710i
$359$	−3.76393	+	11.5842i	−0.198653	+	0.611390i	0.801262	+	0.598314i	$0.204162\pi$
$359$	−3.76393	+	11.5842i	−0.198653	+	0.611390i	−0.999915	+	0.0130763i	$0.995838\pi$
$360$	−0.309017	−	0.951057i	−0.0162866	−	0.0501251i
$361$	14.1353	−	10.2699i	0.743961	−	0.540519i
$362$	21.8885			1.15044
$363$	−9.94427	−	4.70228i	−0.521939	−	0.246806i
$364$	−10.9443			−0.573636
$365$	10.8541	−	7.88597i	0.568130	−	0.412770i
$366$		0			0
$367$	−8.27051	+	25.4540i	−0.431717	+	1.32869i	0.464696	+	0.885470i	$0.346163\pi$
$367$	−8.27051	+	25.4540i	−0.431717	+	1.32869i	−0.896414	+	0.443219i	$0.853837\pi$
$368$	−5.54508	−	4.02874i	−0.289058	−	0.210013i
$369$	−1.00000	−	0.726543i	−0.0520579	−	0.0378223i
$370$	1.97214	−	6.06961i	0.102526	−	0.315544i
$371$	−8.47214	−	26.0746i	−0.439851	−	1.35372i
$372$	−1.11803	+	0.812299i	−0.0579674	+	0.0421158i
$373$	−11.5279			−0.596890			−0.298445	−	0.954427i	$-0.596468\pi$
$373$	−11.5279			−0.596890			−0.298445	+	0.954427i	$0.596468\pi$
$374$	−18.5451	+	8.00448i	−0.958944	+	0.413902i
$375$	1.00000			0.0516398
$376$	3.50000	−	2.54290i	0.180499	−	0.131140i
$377$	−2.73607	−	8.42075i	−0.140915	−	0.433691i
$378$	1.00000	−	3.07768i	0.0514344	−	0.158299i
$379$	10.0000	+	7.26543i	0.513665	+	0.373200i	0.814212	−	0.580567i	$-0.197169\pi$
$379$	10.0000	+	7.26543i	0.513665	+	0.373200i	−0.300547	+	0.953767i	$0.597169\pi$
$380$	1.00000	+	0.726543i	0.0512989	+	0.0372708i
$381$	−4.52786	+	13.9353i	−0.231970	+	0.713929i
$382$	2.85410	+	8.78402i	0.146029	+	0.449430i
$383$	0.263932	−	0.191758i	0.0134863	−	0.00979837i	−0.581022	−	0.813888i	$-0.697347\pi$
$383$	0.263932	−	0.191758i	0.0134863	−	0.00979837i	0.594508	+	0.804090i	$0.297347\pi$
$384$	−1.00000			−0.0510310
$385$	−5.47214	+	9.23305i	−0.278886	+	0.470560i
$386$	−20.9443			−1.06604
$387$	0.0729490	−	0.0530006i	0.00370821	−	0.00269417i
$388$	5.76393	+	17.7396i	0.292619	+	0.900590i
$389$	2.11803	−	6.51864i	0.107389	−	0.330508i	−0.882895	−	0.469570i	$-0.844409\pi$
$389$	2.11803	−	6.51864i	0.107389	−	0.330508i	0.990284	+	0.139062i	$0.0444088\pi$
$390$	−2.73607	−	1.98787i	−0.138546	−	0.100660i
$391$	33.7705	+	24.5357i	1.70785	+	1.24082i
$392$	1.07295	−	3.30220i	0.0541921	−	0.166786i
$393$	1.04508	+	3.21644i	0.0527176	+	0.162248i
$394$	−8.85410	+	6.43288i	−0.446063	+	0.324084i
$395$	4.09017			0.205799
$396$	2.19098	+	2.48990i	0.110101	+	0.125122i
$397$	2.20163			0.110496			0.0552482	−	0.998473i	$-0.482405\pi$
$397$	2.20163			0.110496			0.0552482	+	0.998473i	$0.482405\pi$
$398$	−21.0172	+	15.2699i	−1.05350	+	0.765411i
$399$	1.23607	+	3.80423i	0.0618808	+	0.190450i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−17.8541	−	12.9718i	−0.891591	−	0.647779i	0.0447011	−	0.999000i	$-0.485766\pi$
$401$	−17.8541	−	12.9718i	−0.891591	−	0.647779i	−0.936292	+	0.351221i	$0.885766\pi$
$402$	−4.11803	−	2.99193i	−0.205389	−	0.149224i
$403$	−1.44427	+	4.44501i	−0.0719443	+	0.221422i
$404$	4.82624	+	14.8536i	0.240114	+	0.738996i
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	8.47214			0.420465
$407$	1.97214	+	21.0745i	0.0977551	+	1.04462i
$408$	6.09017			0.301508
$409$	−10.5000	+	7.62870i	−0.519192	+	0.377215i	−0.816299	−	0.577629i	$-0.803978\pi$
$409$	−10.5000	+	7.62870i	−0.519192	+	0.377215i	0.297108	+	0.954844i	$0.403978\pi$
$410$	−0.381966	−	1.17557i	−0.0188640	−	0.0580573i
$411$	3.95492	−	12.1720i	0.195082	−	0.600399i
$412$	−5.47214	−	3.97574i	−0.269593	−	0.195871i
$413$	36.8885	+	26.8011i	1.81517	+	1.31880i
$414$	2.11803	−	6.51864i	0.104096	−	0.320374i
$415$	−1.23607	−	3.80423i	−0.0606762	−	0.186742i
$416$	−2.73607	+	1.98787i	−0.134147	+	0.0974633i
$417$	−8.76393			−0.429172
$418$	−4.00000	−	0.898056i	−0.195646	−	0.0439254i
$419$	22.8541			1.11650			0.558248	−	0.829674i	$-0.311474\pi$
$419$	22.8541			1.11650			0.558248	+	0.829674i	$0.311474\pi$
$420$	2.61803	−	1.90211i	0.127747	−	0.0928136i
$421$	−0.763932	−	2.35114i	−0.0372318	−	0.114588i	0.930713	−	0.365750i	$-0.119187\pi$
$421$	−0.763932	−	2.35114i	−0.0372318	−	0.114588i	−0.967945	+	0.251162i	$0.919187\pi$
$422$	−7.79837	+	24.0009i	−0.379619	+	1.16835i
$423$	3.50000	+	2.54290i	0.170176	+	0.123640i
$424$	−6.85410	−	4.97980i	−0.332865	−	0.241840i
$425$	−1.88197	+	5.79210i	−0.0912888	+	0.280958i
$426$	−3.23607	−	9.95959i	−0.156788	−	0.482544i
$427$		0			0
$428$	6.29180			0.304125
$429$	10.9443	+	2.45714i	0.528394	+	0.118632i
$430$	0.0901699			0.00434838
$431$	−18.0902	+	13.1433i	−0.871373	+	0.633089i	−0.930955	−	0.365134i	$-0.881023\pi$
$431$	−18.0902	+	13.1433i	−0.871373	+	0.633089i	0.0595822	+	0.998223i	$0.481023\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	−7.05573	+	21.7153i	−0.339077	+	1.04357i	0.625602	+	0.780142i	$0.284853\pi$
$433$	−7.05573	+	21.7153i	−0.339077	+	1.04357i	−0.964679	+	0.263428i	$0.915147\pi$
$434$	−3.61803	−	2.62866i	−0.173671	−	0.126180i
$435$	2.11803	+	1.53884i	0.101552	+	0.0737818i
$436$	−0.763932	+	2.35114i	−0.0365857	+	0.112599i
$437$	2.61803	+	8.05748i	0.125238	+	0.385442i
$438$	10.8541	−	7.88597i	0.518629	−	0.376806i
$439$	1.67376			0.0798843			0.0399422	−	0.999202i	$-0.487283\pi$
$439$	1.67376			0.0798843			0.0399422	+	0.999202i	$0.487283\pi$
$440$	0.309017	+	3.30220i	0.0147318	+	0.157426i
$441$	3.47214			0.165340
$442$	16.6631	−	12.1065i	0.792584	−	0.575846i
$443$	−5.76393	−	17.7396i	−0.273853	−	0.842832i	−0.989521	−	0.144391i	$-0.953878\pi$
$443$	−5.76393	−	17.7396i	−0.273853	−	0.842832i	0.715668	−	0.698441i	$-0.246122\pi$
$444$	1.97214	−	6.06961i	0.0935934	−	0.288051i
$445$	13.9443	+	10.1311i	0.661022	+	0.480261i
$446$	−5.85410	−	4.25325i	−0.277200	−	0.201397i
$447$	2.35410	−	7.24518i	0.111345	−	0.342685i
$448$	−1.00000	−	3.07768i	−0.0472456	−	0.145407i
$449$	9.00000	−	6.53888i	0.424736	−	0.308589i	−0.354804	−	0.934941i	$-0.615453\pi$
$449$	9.00000	−	6.53888i	0.424736	−	0.308589i	0.779541	+	0.626352i	$0.215453\pi$
$450$	1.00000			0.0471405
$451$	2.70820	+	3.07768i	0.127524	+	0.144922i
$452$	−19.5623			−0.920133
$453$	16.9443	−	12.3107i	0.796111	−	0.578409i
$454$	6.29180	+	19.3642i	0.295289	+	0.908805i
$455$	3.38197	−	10.4086i	0.158549	−	0.487964i
$456$	1.00000	+	0.726543i	0.0468293	+	0.0340235i
$457$	−3.76393	−	2.73466i	−0.176069	−	0.127922i	0.496260	−	0.868174i	$-0.334706\pi$
$457$	−3.76393	−	2.73466i	−0.176069	−	0.127922i	−0.672330	+	0.740252i	$0.734706\pi$
$458$	0.236068	−	0.726543i	0.0110307	−	0.0339491i
$459$	1.88197	+	5.79210i	0.0878427	+	0.270352i
$460$	5.54508	−	4.02874i	0.258541	−	0.187841i
$461$	23.2148			1.08122			0.540610	−	0.841273i	$-0.318193\pi$
$461$	23.2148			1.08122			0.540610	+	0.841273i	$0.318193\pi$
$462$	−5.47214	+	9.23305i	−0.254587	+	0.429560i
$463$	11.8885			0.552507			0.276254	−	0.961085i	$-0.410907\pi$
$463$	11.8885			0.552507			0.276254	+	0.961085i	$0.410907\pi$
$464$	2.11803	−	1.53884i	0.0983273	−	0.0714389i
$465$	−0.427051	−	1.31433i	−0.0198040	−	0.0609505i
$466$	−1.37132	+	4.22050i	−0.0635253	+	0.195511i
$467$	−23.0902	−	16.7760i	−1.06849	−	0.776300i	−0.0928462	−	0.995680i	$-0.529596\pi$
$467$	−23.0902	−	16.7760i	−1.06849	−	0.776300i	−0.975639	+	0.219380i	$0.929596\pi$
$468$	−2.73607	−	1.98787i	−0.126475	−	0.0918893i
$469$	5.09017	−	15.6659i	0.235042	−	0.723386i
$470$	1.33688	+	4.11450i	0.0616657	+	0.189788i
$471$	−7.50000	+	5.44907i	−0.345582	+	0.251080i
$472$	14.0902			0.648553
$473$	−0.274575	+	0.118513i	−0.0126250	+	0.00544923i
$474$	4.09017			0.187868
$475$	−1.00000	+	0.726543i	−0.0458831	+	0.0333361i
$476$	6.09017	+	18.7436i	0.279142	+	0.859112i
$477$	2.61803	−	8.05748i	0.119872	−	0.368927i
$478$	2.61803	+	1.90211i	0.119746	+	0.0870006i
$479$	−10.3262	−	7.50245i	−0.471818	−	0.342796i	0.326331	−	0.945255i	$-0.394187\pi$
$479$	−10.3262	−	7.50245i	−0.471818	−	0.342796i	−0.798149	+	0.602460i	$0.794187\pi$
$480$	0.309017	−	0.951057i	0.0141046	−	0.0434096i
$481$	−6.66970	−	20.5272i	−0.304112	−	0.935960i
$482$	19.3262	−	14.0413i	0.880286	−	0.639565i
$483$	22.1803			1.00924
$484$	−5.28115	−	9.64932i	−0.240052	−	0.438606i
$485$	−18.6525			−0.846965
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	3.52786	+	10.8576i	0.159863	+	0.492007i	0.998621	−	0.0524969i	$-0.0167180\pi$
$487$	3.52786	+	10.8576i	0.159863	+	0.492007i	−0.838758	+	0.544504i	$0.816718\pi$
$488$		0			0
$489$	0.690983	+	0.502029i	0.0312473	+	0.0227025i
$490$	2.80902	+	2.04087i	0.126898	+	0.0921971i
$491$	8.66312	−	26.6623i	0.390961	−	1.20325i	−0.541102	−	0.840957i	$-0.681993\pi$
$491$	8.66312	−	26.6623i	0.390961	−	1.20325i	0.932063	−	0.362297i	$-0.118007\pi$
$492$	−0.381966	−	1.17557i	−0.0172204	−	0.0529988i
$493$	−12.8992	+	9.37181i	−0.580950	+	0.422085i
$494$	4.18034			0.188082
$495$	−3.04508	+	1.31433i	−0.136866	+	0.0590746i
$496$	−1.38197			−0.0620521
$497$	27.4164	−	19.9192i	1.22979	−	0.893498i
$498$	−1.23607	−	3.80423i	−0.0553895	−	0.170471i
$499$	−10.0344	+	30.8828i	−0.449203	+	1.38251i	0.428604	+	0.903492i	$0.359005\pi$
$499$	−10.0344	+	30.8828i	−0.449203	+	1.38251i	−0.877808	+	0.479013i	$0.840995\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−10.7361	−	7.80021i	−0.479652	−	0.348488i
$502$	2.59017	−	7.97172i	0.115605	−	0.355795i
$503$	−7.51722	−	23.1356i	−0.335176	−	1.03157i	−0.966635	−	0.256157i	$-0.917544\pi$
$503$	−7.51722	−	23.1356i	−0.335176	−	1.03157i	0.631459	−	0.775409i	$-0.282456\pi$
$504$	2.61803	−	1.90211i	0.116617	−	0.0847268i
$505$	−15.6180			−0.694993
$506$	−11.5902	+	19.5559i	−0.515246	+	0.869366i
$507$	1.56231			0.0693844
$508$	−11.8541	+	8.61251i	−0.525941	+	0.382118i
$509$	2.71885	+	8.36775i	0.120511	+	0.370894i	0.993056	−	0.117638i	$-0.0375324\pi$
$509$	2.71885	+	8.36775i	0.120511	+	0.370894i	−0.872546	+	0.488532i	$0.837532\pi$
$510$	−1.88197	+	5.79210i	−0.0833349	+	0.256478i
$511$	35.1246	+	25.5195i	1.55382	+	1.12892i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−0.381966	+	1.17557i	−0.0168642	+	0.0519027i
$514$	9.38197	+	28.8747i	0.413821	+	1.27361i
$515$	5.47214	−	3.97574i	0.241131	−	0.175192i
$516$	0.0901699			0.00396951
$517$	−9.47871	−	10.7719i	−0.416873	−	0.473747i
$518$	20.6525			0.907418
$519$	−7.70820	+	5.60034i	−0.338353	+	0.245828i
$520$	−1.04508	−	3.21644i	−0.0458300	−	0.141050i
$521$	−0.729490	+	2.24514i	−0.0319595	+	0.0983614i	−0.965764	−	0.259423i	$-0.916468\pi$
$521$	−0.729490	+	2.24514i	−0.0319595	+	0.0983614i	0.933804	+	0.357784i	$0.116468\pi$
$522$	2.11803	+	1.53884i	0.0927038	+	0.0673533i
$523$	−31.4164	−	22.8254i	−1.37374	−	0.998083i	−0.997434	−	0.0715891i	$-0.977193\pi$
$523$	−31.4164	−	22.8254i	−1.37374	−	0.998083i	−0.376309	−	0.926494i	$-0.622807\pi$
$524$	−1.04508	+	3.21644i	−0.0456547	+	0.140511i
$525$	1.00000	+	3.07768i	0.0436436	+	0.134321i
$526$	−5.54508	+	4.02874i	−0.241777	+	0.175661i
$527$	8.41641			0.366624
$528$	0.309017	+	3.30220i	0.0134482	+	0.143710i
$529$	23.9787			1.04255
$530$	6.85410	−	4.97980i	0.297723	−	0.216309i
$531$	4.35410	+	13.4005i	0.188952	+	0.581534i
$532$	−1.23607	+	3.80423i	−0.0535903	+	0.164934i
$533$	−3.38197	−	2.45714i	−0.146489	−	0.106431i
$534$	13.9443	+	10.1311i	0.603428	+	0.438416i
$535$	−1.94427	+	5.98385i	−0.0840582	+	0.258705i
$536$	−1.57295	−	4.84104i	−0.0679410	−	0.209101i
$537$	14.6803	−	10.6659i	0.633503	−	0.460267i
$538$	3.20163			0.138032
$539$	−11.2361	−	2.52265i	−0.483972	−	0.108658i
$540$	1.00000			0.0430331
$541$	−21.0902	+	15.3229i	−0.906737	+	0.658783i	−0.940188	−	0.340657i	$-0.889350\pi$
$541$	−21.0902	+	15.3229i	−0.906737	+	0.658783i	0.0334503	+	0.999440i	$0.489350\pi$
$542$	−1.97214	−	6.06961i	−0.0847105	−	0.260712i
$543$	−6.76393	+	20.8172i	−0.290268	+	0.893353i
$544$	4.92705	+	3.57971i	0.211246	+	0.153479i
$545$	−2.00000	−	1.45309i	−0.0856706	−	0.0622433i
$546$	3.38197	−	10.4086i	0.144735	−	0.445448i
$547$	10.6074	+	32.6462i	0.453539	+	1.39585i	0.872842	+	0.488004i	$0.162275\pi$
$547$	10.6074	+	32.6462i	0.453539	+	1.39585i	−0.419302	+	0.907847i	$0.637725\pi$
$548$	10.3541	−	7.52270i	0.442305	−	0.321354i
$549$		0			0
$550$	−3.23607	−	0.726543i	−0.137986	−	0.0309799i
$551$	−3.23607			−0.137861
$552$	5.54508	−	4.02874i	0.236014	−	0.171475i
$553$	4.09017	+	12.5882i	0.173932	+	0.535307i
$554$	−7.26393	+	22.3561i	−0.308615	+	0.949819i
$555$	5.16312	+	3.75123i	0.219162	+	0.159231i
$556$	−7.09017	−	5.15131i	−0.300690	−	0.218464i
$557$	−10.8541	+	33.4055i	−0.459903	+	1.41544i	0.405378	+	0.914149i	$0.367140\pi$
$557$	−10.8541	+	33.4055i	−0.459903	+	1.41544i	−0.865281	+	0.501287i	$0.832860\pi$
$558$	−0.427051	−	1.31433i	−0.0180785	−	0.0556399i
$559$	0.246711	−	0.179246i	0.0104348	−	0.00758130i
$560$	3.23607			0.136749
$561$	−1.88197	−	20.1109i	−0.0794567	−	0.849085i
$562$	−7.52786			−0.317544
$563$	−13.7984	+	10.0251i	−0.581532	+	0.422508i	−0.839276	−	0.543705i	$-0.817021\pi$
$563$	−13.7984	+	10.0251i	−0.581532	+	0.422508i	0.257744	+	0.966213i	$0.417021\pi$
$564$	1.33688	+	4.11450i	0.0562928	+	0.173252i
$565$	6.04508	−	18.6049i	0.254319	−	0.782712i
$566$	18.0623	+	13.1230i	0.759215	+	0.551602i
$567$	2.61803	+	1.90211i	0.109947	+	0.0798812i
$568$	3.23607	−	9.95959i	0.135782	−	0.417895i
$569$	−7.85410	−	24.1724i	−0.329261	−	1.01336i	−0.969480	−	0.245169i	$-0.921156\pi$
$569$	−7.85410	−	24.1724i	−0.329261	−	1.01336i	0.640219	−	0.768192i	$-0.278844\pi$
$570$	−1.00000	+	0.726543i	−0.0418854	+	0.0304315i
$571$	−28.3607			−1.18686			−0.593429	−	0.804887i	$-0.702226\pi$
$571$	−28.3607			−1.18686			−0.593429	+	0.804887i	$0.702226\pi$
$572$	7.40983	+	8.42075i	0.309821	+	0.352089i
$573$	−9.23607			−0.385842
$574$	3.23607	−	2.35114i	0.135071	−	0.0981347i
$575$	2.11803	+	6.51864i	0.0883281	+	0.271846i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−13.7984	−	10.0251i	−0.574434	−	0.417351i	0.262279	−	0.964992i	$-0.415526\pi$
$577$	−13.7984	−	10.0251i	−0.574434	−	0.417351i	−0.836713	+	0.547641i	$0.815526\pi$
$578$	−16.2533	−	11.8087i	−0.676048	−	0.491177i
$579$	6.47214	−	19.9192i	0.268973	−	0.827813i
$580$	0.809017	+	2.48990i	0.0335926	+	0.103387i
$581$	10.4721	−	7.60845i	0.434457	−	0.315652i
$582$	−18.6525			−0.773170
$583$	−14.3262	+	24.1724i	−0.593332	+	1.00112i
$584$	13.4164			0.555175
$585$	2.73607	−	1.98787i	0.113122	−	0.0821883i
$586$	−6.18034	−	19.0211i	−0.255307	−	0.785756i
$587$	−8.12461	+	25.0050i	−0.335339	+	1.03207i	0.631216	+	0.775607i	$0.282556\pi$
$587$	−8.12461	+	25.0050i	−0.335339	+	1.03207i	−0.966555	+	0.256459i	$0.917444\pi$
$588$	2.80902	+	2.04087i	0.115842	+	0.0841641i
$589$	1.38197	+	1.00406i	0.0569429	+	0.0413715i
$590$	−4.35410	+	13.4005i	−0.179256	+	0.551692i
$591$	−3.38197	−	10.4086i	−0.139115	−	0.428153i
$592$	5.16312	−	3.75123i	0.212203	−	0.154174i
$593$	−17.6738			−0.725774			−0.362887	−	0.931833i	$-0.618209\pi$
$593$	−17.6738			−0.725774			−0.362887	+	0.931833i	$0.618209\pi$
$594$	−3.04508	+	1.31433i	−0.124941	+	0.0539275i
$595$	−19.7082			−0.807958
$596$	6.16312	−	4.47777i	0.252451	−	0.183417i
$597$	−8.02786	−	24.7072i	−0.328559	−	1.01120i
$598$	7.16312	−	22.0458i	0.292922	−	0.901520i
$599$	−14.7082	−	10.6861i	−0.600961	−	0.436624i	0.245259	−	0.969458i	$-0.421127\pi$
$599$	−14.7082	−	10.6861i	−0.600961	−	0.436624i	−0.846220	+	0.532834i	$0.821127\pi$
$600$	0.809017	+	0.587785i	0.0330280	+	0.0239962i
$601$	−5.85410	+	18.0171i	−0.238794	+	0.734932i	0.757802	+	0.652485i	$0.226273\pi$
$601$	−5.85410	+	18.0171i	−0.238794	+	0.734932i	−0.996595	+	0.0824468i	$0.973727\pi$
$602$	0.0901699	+	0.277515i	0.00367505	+	0.0113106i
$603$	4.11803	−	2.99193i	0.167699	−	0.121841i
$604$	20.9443			0.852210
$605$	10.8090	−	2.04087i	0.439449	−	0.0829732i
$606$	−15.6180			−0.634439
$607$	3.61803	−	2.62866i	0.146851	−	0.106694i	−0.511934	−	0.859025i	$-0.671071\pi$
$607$	3.61803	−	2.62866i	0.146851	−	0.106694i	0.658785	+	0.752331i	$0.271071\pi$
$608$	0.381966	+	1.17557i	0.0154908	+	0.0476757i
$609$	−2.61803	+	8.05748i	−0.106088	+	0.326506i
$610$		0			0
$611$	11.8369	+	8.60000i	0.478869	+	0.347919i
$612$	−1.88197	+	5.79210i	−0.0760740	+	0.234132i
$613$	1.85410	+	5.70634i	0.0748865	+	0.230477i	0.981492	−	0.191502i	$-0.0613357\pi$
$613$	1.85410	+	5.70634i	0.0748865	+	0.230477i	−0.906606	+	0.421979i	$0.861336\pi$
$614$	27.0623	−	19.6619i	1.09215	−	0.793490i
$615$	1.23607			0.0498431
$616$	−9.85410	+	4.25325i	−0.397033	+	0.171368i
$617$	26.3607			1.06124			0.530621	−	0.847610i	$-0.321959\pi$
$617$	26.3607			1.06124			0.530621	+	0.847610i	$0.321959\pi$
$618$	5.47214	−	3.97574i	0.220122	−	0.159928i
$619$	2.94427	+	9.06154i	0.118340	+	0.364214i	0.992629	−	0.121192i	$-0.0386717\pi$
$619$	2.94427	+	9.06154i	0.118340	+	0.364214i	−0.874289	+	0.485406i	$0.838672\pi$
$620$	0.427051	−	1.31433i	0.0171508	−	0.0527847i
$621$	5.54508	+	4.02874i	0.222517	+	0.161668i
$622$	−7.47214	−	5.42882i	−0.299605	−	0.217676i
$623$	−17.2361	+	53.0472i	−0.690548	+	2.12529i
$624$	−1.04508	−	3.21644i	−0.0418369	−	0.128761i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	8.47214			0.338615
$627$	2.09017	−	3.52671i	0.0834733	−	0.140843i
$628$	−9.27051			−0.369934
$629$	−31.4443	+	22.8456i	−1.25377	+	0.910914i
$630$	1.00000	+	3.07768i	0.0398410	+	0.122618i
$631$	−1.75329	+	5.39607i	−0.0697973	+	0.214814i	−0.979871	−	0.199633i	$-0.936025\pi$
$631$	−1.75329	+	5.39607i	−0.0697973	+	0.214814i	0.910073	+	0.414447i	$0.136025\pi$
$632$	3.30902	+	2.40414i	0.131626	+	0.0956316i
$633$	−20.4164	−	14.8334i	−0.811479	−	0.589574i
$634$	−8.47214	+	26.0746i	−0.336472	+	1.03555i
$635$	−4.52786	−	13.9353i	−0.179683	−	0.553007i
$636$	6.85410	−	4.97980i	0.271783	−	0.197462i
$637$	11.7426			0.465261
$638$	−5.73607	−	6.51864i	−0.227093	−	0.258075i
$639$	10.4721			0.414271
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	3.76393	+	11.5842i	0.148666	+	0.457548i	0.997464	−	0.0711694i	$-0.0226731\pi$
$641$	3.76393	+	11.5842i	0.148666	+	0.457548i	−0.848798	+	0.528717i	$0.822673\pi$
$642$	−1.94427	+	5.98385i	−0.0767343	+	0.236164i
$643$	3.88197	+	2.82041i	0.153090	+	0.111226i	0.661693	−	0.749775i	$-0.269838\pi$
$643$	3.88197	+	2.82041i	0.153090	+	0.111226i	−0.508604	+	0.861001i	$0.669838\pi$
$644$	17.9443	+	13.0373i	0.707103	+	0.513741i
$645$	−0.0278640	+	0.0857567i	−0.00109715	+	0.00337667i
$646$	−2.32624	−	7.15942i	−0.0915246	−	0.281684i
$647$	10.0172	−	7.27794i	0.393818	−	0.286125i	−0.373200	−	0.927751i	$-0.621740\pi$
$647$	10.0172	−	7.27794i	0.393818	−	0.286125i	0.767018	+	0.641625i	$0.221740\pi$
$648$	1.00000			0.0392837
$649$	−4.35410	−	46.5285i	−0.170913	−	1.82640i
$650$	3.38197			0.132652
$651$	3.61803	−	2.62866i	0.141802	−	0.103025i
$652$	0.263932	+	0.812299i	0.0103364	+	0.0318121i
$653$	7.58359	−	23.3399i	0.296769	−	0.913361i	−0.685853	−	0.727740i	$-0.740571\pi$
$653$	7.58359	−	23.3399i	0.296769	−	0.913361i	0.982622	−	0.185620i	$-0.0594294\pi$
$654$	−2.00000	−	1.45309i	−0.0782062	−	0.0568201i
$655$	−2.73607	−	1.98787i	−0.106907	−	0.0776725i
$656$	0.381966	−	1.17557i	0.0149133	−	0.0458983i
$657$	4.14590	+	12.7598i	0.161747	+	0.497806i
$658$	−11.3262	+	8.22899i	−0.441543	+	0.320800i
$659$	−15.4164			−0.600538			−0.300269	−	0.953855i	$-0.597076\pi$
$659$	−15.4164			−0.600538			−0.300269	+	0.953855i	$0.597076\pi$
$660$	−3.23607	−	0.726543i	−0.125964	−	0.0282806i
$661$	8.36068			0.325193			0.162596	−	0.986693i	$-0.448013\pi$
$661$	8.36068			0.325193			0.162596	+	0.986693i	$0.448013\pi$
$662$	−7.47214	+	5.42882i	−0.290413	+	0.210997i
$663$	6.36475	+	19.5887i	0.247186	+	0.760761i
$664$	1.23607	−	3.80423i	0.0479687	−	0.147633i
$665$	−3.23607	−	2.35114i	−0.125489	−	0.0911733i
$666$	5.16312	+	3.75123i	0.200067	+	0.145357i
$667$	−5.54508	+	17.0660i	−0.214707	+	0.660799i
$668$	−4.10081	−	12.6210i	−0.158665	−	0.488321i
$669$	5.85410	−	4.25325i	0.226333	−	0.164440i
$670$	5.09017			0.196650
$671$		0			0
$672$	3.23607			0.124834
$673$	12.7082	−	9.23305i	0.489865	−	0.355908i	−0.315267	−	0.949003i	$-0.602094\pi$
$673$	12.7082	−	9.23305i	0.489865	−	0.355908i	0.805132	+	0.593095i	$0.202094\pi$
$674$	−4.70820	−	14.4904i	−0.181353	−	0.558148i
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$	1.26393	+	0.918300i	0.0486128	+	0.0353192i
$677$	−22.0344	−	16.0090i	−0.846852	−	0.615274i	0.0774240	−	0.996998i	$-0.475330\pi$
$677$	−22.0344	−	16.0090i	−0.846852	−	0.615274i	−0.924276	+	0.381724i	$0.875330\pi$
$678$	6.04508	−	18.6049i	0.232160	−	0.714515i
$679$	−18.6525	−	57.4064i	−0.715816	−	2.20306i
$680$	−4.92705	+	3.57971i	−0.188944	+	0.137276i
$681$	−20.3607			−0.780223
$682$	0.427051	+	4.56352i	0.0163526	+	0.174746i
$683$	21.1246			0.808311			0.404155	−	0.914690i	$-0.367565\pi$
$683$	21.1246			0.808311			0.404155	+	0.914690i	$0.367565\pi$
$684$	−1.00000	+	0.726543i	−0.0382360	+	0.0277800i
$685$	3.95492	+	12.1720i	0.151110	+	0.465067i
$686$	3.52786	−	10.8576i	0.134694	−	0.414547i
$687$	0.618034	+	0.449028i	0.0235795	+	0.0171315i
$688$	0.0729490	+	0.0530006i	0.00278116	+	0.00202063i
$689$	8.85410	−	27.2501i	0.337314	−	1.03815i
$690$	2.11803	+	6.51864i	0.0806322	+	0.248160i
$691$	16.7082	−	12.1392i	0.635610	−	0.461798i	−0.222729	−	0.974880i	$-0.571497\pi$
$691$	16.7082	−	12.1392i	0.635610	−	0.461798i	0.858339	+	0.513083i	$0.171497\pi$
$692$	−9.52786			−0.362195
$693$	−7.09017	−	8.05748i	−0.269333	−	0.306078i
$694$	35.8885			1.36231
$695$	7.09017	−	5.15131i	0.268945	−	0.195400i
$696$	0.809017	+	2.48990i	0.0306657	+	0.0943794i
$697$	−2.32624	+	7.15942i	−0.0881125	+	0.271183i
$698$	9.23607	+	6.71040i	0.349590	+	0.253992i
$699$	−3.59017	−	2.60841i	−0.135793	−	0.0986592i
$700$	−1.00000	+	3.07768i	−0.0377964	+	0.116326i
$701$	−1.09017	−	3.35520i	−0.0411752	−	0.126724i	0.928356	−	0.371692i	$-0.121222\pi$
$701$	−1.09017	−	3.35520i	−0.0411752	−	0.126724i	−0.969531	+	0.244968i	$0.921222\pi$
$702$	2.73607	−	1.98787i	0.103266	−	0.0750273i
$703$	−7.88854			−0.297522
$704$	−1.69098	+	2.85317i	−0.0637313	+	0.107533i
$705$	−4.32624			−0.162936
$706$	−19.1074	+	13.8823i	−0.719116	+	0.522468i
$707$	−15.6180	−	48.0674i	−0.587377	−	1.80776i
$708$	−4.35410	+	13.4005i	−0.163637	+	0.503623i
$709$	8.56231	+	6.22088i	0.321564	+	0.233630i	0.736843	−	0.676064i	$-0.236316\pi$
$709$	8.56231	+	6.22088i	0.321564	+	0.233630i	−0.415278	+	0.909694i	$0.636316\pi$
$710$	8.47214	+	6.15537i	0.317954	+	0.231007i
$711$	−1.26393	+	3.88998i	−0.0474012	+	0.145886i
$712$	5.32624	+	16.3925i	0.199609	+	0.614334i
$713$	7.66312	−	5.56758i	0.286986	−	0.208508i
$714$	−19.7082			−0.737561
$715$	−10.2984	+	4.44501i	−0.385137	+	0.166234i
$716$	18.1459			0.678144
$717$	−2.61803	+	1.90211i	−0.0977723	+	0.0710357i
$718$	−3.76393	−	11.5842i	−0.140469	−	0.432318i
$719$	12.5623	−	38.6628i	0.468495	−	1.44188i	−0.386038	−	0.922483i	$-0.626157\pi$
$719$	12.5623	−	38.6628i	0.468495	−	1.44188i	0.854533	−	0.519397i	$-0.173843\pi$
$720$	0.809017	+	0.587785i	0.0301503	+	0.0219055i
$721$	17.7082	+	12.8658i	0.659488	+	0.479146i
$722$	−5.39919	+	16.6170i	−0.200937	+	0.618420i
$723$	7.38197	+	22.7194i	0.274538	+	0.844942i
$724$	−17.7082	+	12.8658i	−0.658120	+	0.478152i
$725$	−2.61803			−0.0972313
$726$	10.8090	−	2.04087i	0.401160	−	0.0757438i
$727$	−50.1803			−1.86109			−0.930543	−	0.366183i	$-0.880664\pi$
$727$	−50.1803			−1.86109			−0.930543	+	0.366183i	$0.880664\pi$
$728$	8.85410	−	6.43288i	0.328155	−	0.238418i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−4.14590	+	12.7598i	−0.153447	+	0.472260i
$731$	−0.444272	−	0.322782i	−0.0164320	−	0.0119385i
$732$		0			0
$733$	15.8607	−	48.8142i	0.585828	−	1.80299i	−0.0100937	−	0.999949i	$-0.503213\pi$
$733$	15.8607	−	48.8142i	0.585828	−	1.80299i	0.595921	−	0.803043i	$-0.296787\pi$
$734$	−8.27051	−	25.4540i	−0.305270	−	0.939525i
$735$	−2.80902	+	2.04087i	−0.103612	+	0.0752786i
$736$	6.85410			0.252646
$737$	−15.5000	+	6.69015i	−0.570950	+	0.246435i
$738$	1.23607			0.0455003
$739$	−21.8541	+	15.8779i	−0.803916	+	0.584079i	−0.912060	−	0.410056i	$-0.865509\pi$
$739$	−21.8541	+	15.8779i	−0.803916	+	0.584079i	0.108144	+	0.994135i	$0.465509\pi$
$740$	1.97214	+	6.06961i	0.0724972	+	0.223123i
$741$	−1.29180	+	3.97574i	−0.0474553	+	0.146052i
$742$	22.1803	+	16.1150i	0.814266	+	0.591599i
$743$	−8.73607	−	6.34712i	−0.320495	−	0.232853i	0.415892	−	0.909414i	$-0.363470\pi$
$743$	−8.73607	−	6.34712i	−0.320495	−	0.232853i	−0.736387	+	0.676561i	$0.763470\pi$
$744$	0.427051	−	1.31433i	0.0156564	−	0.0481856i
$745$	2.35410	+	7.24518i	0.0862476	+	0.265443i
$746$	9.32624	−	6.77591i	0.341458	−	0.248084i
$747$	4.00000			0.146352
$748$	10.2984	−	17.3763i	0.376546	−	0.635340i
$749$	−20.3607			−0.743963
$750$	−0.809017	+	0.587785i	−0.0295411	+	0.0214629i
$751$	−8.97214	−	27.6134i	−0.327398	−	1.00763i	−0.970347	−	0.241718i	$-0.922289\pi$
$751$	−8.97214	−	27.6134i	−0.327398	−	1.00763i	0.642949	−	0.765909i	$-0.277711\pi$
$752$	−1.33688	+	4.11450i	−0.0487510	+	0.150040i
$753$	6.78115	+	4.92680i	0.247119	+	0.179542i
$754$	7.16312	+	5.20431i	0.260865	+	0.189530i
$755$	−6.47214	+	19.9192i	−0.235545	+	0.724933i
$756$	1.00000	+	3.07768i	0.0363696	+	0.111934i
$757$	43.5689	−	31.6546i	1.58354	−	1.15051i	0.671044	−	0.741417i	$-0.265846\pi$
$757$	43.5689	−	31.6546i	1.58354	−	1.15051i	0.912494	−	0.409090i	$-0.134154\pi$
$758$	−12.3607			−0.448960
$759$	−15.0172	−	17.0660i	−0.545091	−	0.619457i
$760$	−1.23607			−0.0448369
$761$	8.09017	−	5.87785i	0.293268	−	0.213072i	−0.431416	−	0.902153i	$-0.641986\pi$
$761$	8.09017	−	5.87785i	0.293268	−	0.213072i	0.724684	+	0.689081i	$0.241986\pi$
$762$	−4.52786	−	13.9353i	−0.164027	−	0.504824i
$763$	2.47214	−	7.60845i	0.0894973	−	0.275444i
$764$	−7.47214	−	5.42882i	−0.270332	−	0.196408i
$765$	−4.92705	−	3.57971i	−0.178138	−	0.129425i
$766$	−0.100813	+	0.310271i	−0.00364252	+	0.0112105i
$767$	14.7254	+	45.3202i	0.531704	+	1.63642i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	−24.4508			−0.881720			−0.440860	−	0.897576i	$-0.645327\pi$
$769$	−24.4508			−0.881720			−0.440860	+	0.897576i	$0.645327\pi$
$770$	−1.00000	−	10.6861i	−0.0360375	−	0.385102i
$771$	−30.3607			−1.09341
$772$	16.9443	−	12.3107i	0.609838	−	0.443073i
$773$	6.05573	+	18.6376i	0.217809	+	0.670348i	0.998942	+	0.0459835i	$0.0146422\pi$
$773$	6.05573	+	18.6376i	0.217809	+	0.670348i	−0.781133	+	0.624365i	$0.785358\pi$
$774$	−0.0278640	+	0.0857567i	−0.00100155	+	0.00308246i
$775$	1.11803	+	0.812299i	0.0401610	+	0.0291787i
$776$	−15.0902	−	10.9637i	−0.541706	−	0.393572i
$777$	−6.38197	+	19.6417i	−0.228952	+	0.704641i
$778$	2.11803	+	6.51864i	0.0759352	+	0.233705i
$779$	−1.23607	+	0.898056i	−0.0442867	+	0.0321762i
$780$	3.38197			0.121094
$781$	−33.8885	−	7.60845i	−1.21263	−	0.272252i
$782$	−41.7426			−1.49271
$783$	−2.11803	+	1.53884i	−0.0756924	+	0.0549937i
$784$	1.07295	+	3.30220i	0.0383196	+	0.117936i
$785$	2.86475	−	8.81678i	0.102247	−	0.314684i
$786$	−2.73607	−	1.98787i	−0.0975923	−	0.0709050i
$787$	−17.0172	−	12.3637i	−0.606598	−	0.440720i	0.241616	−	0.970372i	$-0.422322\pi$
$787$	−17.0172	−	12.3637i	−0.606598	−	0.440720i	−0.848215	+	0.529652i	$0.822322\pi$
$788$	3.38197	−	10.4086i	0.120478	−	0.370792i
$789$	−2.11803	−	6.51864i	−0.0754040	−	0.232070i
$790$	−3.30902	+	2.40414i	−0.117730	+	0.0855355i
$791$	63.3050			2.25086
$792$	−3.23607	−	0.726543i	−0.114989	−	0.0258166i
$793$		0			0
$794$	−1.78115	+	1.29408i	−0.0632108	+	0.0459253i
$795$	2.61803	+	8.05748i	0.0928521	+	0.285769i
$796$	8.02786	−	24.7072i	0.284540	−	0.875724i
$797$	17.5623	+	12.7598i	0.622089	+	0.451974i	0.853651	−	0.520846i	$-0.174384\pi$
$797$	17.5623	+	12.7598i	0.622089	+	0.451974i	−0.231562	+	0.972820i	$0.574384\pi$
$798$	−3.23607	−	2.35114i	−0.114556	−	0.0832295i
$799$	8.14183	−	25.0580i	0.288037	−	0.886488i
$800$	0.309017	+	0.951057i	0.0109254	+	0.0336249i
$801$	−13.9443	+	10.1311i	−0.492697	+	0.357965i
$802$	22.0689			0.779279
$803$	−4.14590	−	44.3036i	−0.146306	−	1.56344i
$804$	5.09017			0.179516
$805$	−17.9443	+	13.0373i	−0.632452	+	0.459504i
$806$	−1.44427	−	4.44501i	−0.0508723	−	0.156569i
$807$	−0.989357	+	3.04493i	−0.0348270	+	0.107187i
$808$	−12.6353	−	9.18005i	−0.444507	−	0.322953i
$809$	2.14590	+	1.55909i	0.0754458	+	0.0548146i	0.624869	−	0.780730i	$-0.285152\pi$
$809$	2.14590	+	1.55909i	0.0754458	+	0.0548146i	−0.549423	+	0.835544i	$0.685152\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	−1.41641	−	4.35926i	−0.0497368	−	0.153074i	0.923103	−	0.384552i	$-0.125644\pi$
$811$	−1.41641	−	4.35926i	−0.0497368	−	0.153074i	−0.972840	+	0.231478i	$0.925644\pi$
$812$	−6.85410	+	4.97980i	−0.240532	+	0.174757i
$813$	6.38197			0.223825
$814$	−13.9828	−	15.8904i	−0.490096	−	0.556960i
$815$	−0.854102			−0.0299179
$816$	−4.92705	+	3.57971i	−0.172481	+	0.125315i
$817$	−0.0344419	−	0.106001i	−0.00120497	−	0.00370851i
$818$	4.01064	−	12.3435i	0.140229	−	0.431580i
$819$	8.85410	+	6.43288i	0.309387	+	0.224783i
$820$	1.00000	+	0.726543i	0.0349215	+	0.0253720i
$821$	−13.3820	+	41.1855i	−0.467034	+	1.43738i	0.389373	+	0.921080i	$0.372692\pi$
$821$	−13.3820	+	41.1855i	−0.467034	+	1.43738i	−0.856407	+	0.516302i	$0.827308\pi$
$822$	3.95492	+	12.1720i	0.137944	+	0.424546i
$823$	10.3262	−	7.50245i	0.359950	−	0.261519i	−0.393081	−	0.919504i	$-0.628591\pi$
$823$	10.3262	−	7.50245i	0.359950	−	0.261519i	0.753031	+	0.657985i	$0.228591\pi$
$824$	6.76393			0.235633
$825$	1.69098	−	2.85317i	0.0588725	−	0.0993346i
$826$	−45.5967			−1.58651
$827$	−24.5066	+	17.8051i	−0.852177	+	0.619143i	−0.925745	−	0.378147i	$-0.876561\pi$
$827$	−24.5066	+	17.8051i	−0.852177	+	0.619143i	0.0735683	+	0.997290i	$0.476561\pi$
$828$	2.11803	+	6.51864i	0.0736068	+	0.226538i
$829$	11.0000	−	33.8545i	0.382046	−	1.17582i	−0.556555	−	0.830811i	$-0.687877\pi$
$829$	11.0000	−	33.8545i	0.382046	−	1.17582i	0.938601	−	0.345005i	$-0.112123\pi$
$830$	3.23607	+	2.35114i	0.112326	+	0.0816093i
$831$	−19.0172	−	13.8168i	−0.659700	−	0.479300i
$832$	1.04508	−	3.21644i	0.0362318	−	0.111510i
$833$	−6.53444	−	20.1109i	−0.226405	−	0.696803i
$834$	7.09017	−	5.15131i	0.245513	−	0.178375i
$835$	13.2705			0.459245
$836$	3.76393	−	1.62460i	0.130178	−	0.0561879i
$837$	1.38197			0.0477677
$838$	−18.4894	+	13.4333i	−0.638704	+	0.464046i
$839$	−7.21478	−	22.2048i	−0.249082	−	0.766595i	−0.994938	−	0.100488i	$-0.967959\pi$
$839$	−7.21478	−	22.2048i	−0.249082	−	0.766595i	0.745856	−	0.666107i	$-0.232041\pi$
$840$	−1.00000	+	3.07768i	−0.0345033	+	0.106190i
$841$	17.9164	+	13.0170i	0.617807	+	0.448863i
$842$	2.00000	+	1.45309i	0.0689246	+	0.0500766i
$843$	2.32624	−	7.15942i	0.0801199	−	0.246584i
$844$	−7.79837	−	24.0009i	−0.268431	−	0.826146i
$845$	−1.26393	+	0.918300i	−0.0434806	+	0.0315905i
$846$	−4.32624			−0.148739
$847$	17.0902	+	31.2259i	0.587225	+	1.07293i
$848$	8.47214			0.290934
$849$	−18.0623	+	13.1230i	−0.619897	+	0.450381i
$850$	−1.88197	−	5.79210i	−0.0645509	−	0.198667i
$851$	−13.5172	+	41.6017i	−0.463364	+	1.42609i
$852$	8.47214	+	6.15537i	0.290251	+	0.210879i
$853$	22.2705	+	16.1805i	0.762528	+	0.554009i	0.899685	−	0.436541i	$-0.143796\pi$
$853$	22.2705	+	16.1805i	0.762528	+	0.554009i	−0.137157	+	0.990549i	$0.543796\pi$
$854$		0			0
$855$	−0.381966	−	1.17557i	−0.0130630	−	0.0402037i
$856$	−5.09017	+	3.69822i	−0.173978	+	0.126403i
$857$	24.1591			0.825258			0.412629	−	0.910899i	$-0.364611\pi$
$857$	24.1591			0.825258			0.412629	+	0.910899i	$0.364611\pi$
$858$	−10.2984	+	4.44501i	−0.351581	+	0.151750i
$859$	−19.1246			−0.652523			−0.326262	−	0.945279i	$-0.605789\pi$
$859$	−19.1246			−0.652523			−0.326262	+	0.945279i	$0.605789\pi$
$860$	−0.0729490	+	0.0530006i	−0.00248754	+	0.00180730i
$861$	1.23607	+	3.80423i	0.0421251	+	0.129648i
$862$	6.90983	−	21.2663i	0.235350	−	0.724332i
$863$	35.8713	+	26.0620i	1.22107	+	0.887162i	0.996189	−	0.0872230i	$-0.0277993\pi$
$863$	35.8713	+	26.0620i	1.22107	+	0.887162i	0.224885	+	0.974385i	$0.427799\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	2.94427	−	9.06154i	0.100108	−	0.308102i
$866$	−7.05573	−	21.7153i	−0.239763	−	0.737916i
$867$	16.2533	−	11.8087i	0.551991	−	0.401045i
$868$	4.47214			0.151794
$869$	6.91641	−	11.6699i	0.234623	−	0.395876i
$870$	−2.61803			−0.0887597
$871$	13.9271	−	10.1186i	0.471900	−	0.342856i
$872$	−0.763932	−	2.35114i	−0.0258700	−	0.0796197i
$873$	5.76393	−	17.7396i	0.195080	−	0.600393i
$874$	−6.85410	−	4.97980i	−0.231843	−	0.168444i
$875$	−2.61803	−	1.90211i	−0.0885057	−	0.0643032i
$876$	−4.14590	+	12.7598i	−0.140077	+	0.431112i
$877$	5.86068	+	18.0373i	0.197901	+	0.609077i	0.999930	+	0.0117923i	$0.00375371\pi$
$877$	5.86068	+	18.0373i	0.197901	+	0.609077i	−0.802029	+	0.597285i	$0.796246\pi$
$878$	−1.35410	+	0.983813i	−0.0456987	+	0.0332021i
$879$	20.0000			0.674583
$880$	−2.19098	−	2.48990i	−0.0738580	−	0.0839345i
$881$	8.00000			0.269527			0.134763	−	0.990878i	$-0.456973\pi$
$881$	8.00000			0.269527			0.134763	+	0.990878i	$0.456973\pi$
$882$	−2.80902	+	2.04087i	−0.0945845	+	0.0687197i
$883$	−1.44427	−	4.44501i	−0.0486036	−	0.149587i	0.923809	−	0.382853i	$-0.125058\pi$
$883$	−1.44427	−	4.44501i	−0.0486036	−	0.149587i	−0.972413	+	0.233267i	$0.925058\pi$
$884$	−6.36475	+	19.5887i	−0.214070	+	0.658838i
$885$	−11.3992	−	8.28199i	−0.383179	−	0.278396i
$886$	15.0902	+	10.9637i	0.506964	+	0.368331i
$887$	−13.1180	+	40.3732i	−0.440460	+	1.35560i	0.446926	+	0.894571i	$0.352519\pi$
$887$	−13.1180	+	40.3732i	−0.440460	+	1.35560i	−0.887386	+	0.461027i	$0.847481\pi$
$888$	1.97214	+	6.06961i	0.0661805	+	0.203683i
$889$	38.3607	−	27.8707i	1.28658	−	0.934752i
$890$	−17.2361			−0.577754
$891$	−0.309017	−	3.30220i	−0.0103525	−	0.110628i
$892$	7.23607			0.242281
$893$	4.32624	−	3.14320i	0.144772	−	0.105183i
$894$	2.35410	+	7.24518i	0.0787329	+	0.242315i
$895$	−5.60739	+	17.2578i	−0.187434	+	0.576864i
$896$	2.61803	+	1.90211i	0.0874624	+	0.0635451i
$897$	18.7533	+	13.6251i	0.626154	+	0.454928i
$898$	−3.43769	+	10.5801i	−0.114717	+	0.353064i
$899$	1.11803	+	3.44095i	0.0372885	+	0.114762i
$900$	−0.809017	+	0.587785i	−0.0269672	+	0.0195928i
$901$	−51.5967			−1.71894
$902$	−4.00000	−	0.898056i	−0.133185	−	0.0299020i
$903$	−0.291796			−0.00971037
$904$	15.8262	−	11.4984i	0.526373	−	0.382432i
$905$	−6.76393	−	20.8172i	−0.224841	−	0.691989i
$906$	−6.47214	+	19.9192i	−0.215022	+	0.661771i
$907$	19.0172	+	13.8168i	0.631456	+	0.458780i	0.856904	−	0.515475i	$-0.172385\pi$
$907$	19.0172	+	13.8168i	0.631456	+	0.458780i	−0.225448	+	0.974255i	$0.572385\pi$
$908$	−16.4721	−	11.9677i	−0.546647	−	0.397162i
$909$	4.82624	−	14.8536i	0.160076	−	0.492664i
$910$	3.38197	+	10.4086i	0.112111	+	0.345042i
$911$	−2.85410	+	2.07363i	−0.0945606	+	0.0687023i	−0.634061	−	0.773283i	$-0.718613\pi$
$911$	−2.85410	+	2.07363i	−0.0945606	+	0.0687023i	0.539500	+	0.841985i	$0.318613\pi$
$912$	−1.23607			−0.0409303
$913$	−12.9443	−	2.90617i	−0.428393	−	0.0961802i
$914$	4.65248			0.153890
$915$		0			0
$916$	0.236068	+	0.726543i	0.00779991	+	0.0240056i
$917$	3.38197	−	10.4086i	0.111682	−	0.343723i
$918$	−4.92705	−	3.57971i	−0.162617	−	0.118148i
$919$	−37.4894	−	27.2376i	−1.23666	−	0.898486i	−0.239289	−	0.970948i	$-0.576914\pi$
$919$	−37.4894	−	27.2376i	−1.23666	−	0.898486i	−0.997371	+	0.0724626i	$0.976914\pi$
$920$	−2.11803	+	6.51864i	−0.0698295	+	0.214913i
$921$	10.3369	+	31.8136i	0.340612	+	1.04830i
$922$	−18.7812	+	13.6453i	−0.618524	+	0.449384i
$923$	35.4164			1.16575
$924$	−1.00000	−	10.6861i	−0.0328976	−	0.351548i
$925$	−6.38197			−0.209838
$926$	−9.61803	+	6.98791i	−0.316068	+	0.229637i
$927$	2.09017	+	6.43288i	0.0686502	+	0.211284i
$928$	−0.809017	+	2.48990i	−0.0265573	+	0.0817349i
$929$	24.6525	+	17.9111i	0.808821	+	0.587643i	0.913489	−	0.406864i	$-0.133378\pi$
$929$	24.6525	+	17.9111i	0.808821	+	0.587643i	−0.104667	+	0.994507i	$0.533378\pi$
$930$	1.11803	+	0.812299i	0.0366618	+	0.0266363i
$931$	1.32624	−	4.08174i	0.0434657	−	0.133774i
$932$	−1.37132	−	4.22050i	−0.0449192	−	0.138247i
$933$	7.47214	−	5.42882i	0.244627	−	0.177732i
$934$	28.5410			0.933891
$935$	13.3435	+	15.1639i	0.436378	+	0.495913i
$936$	3.38197			0.110543
$937$	34.5066	−	25.0705i	1.12728	−	0.819017i	0.141984	−	0.989869i	$-0.454652\pi$
$937$	34.5066	−	25.0705i	1.12728	−	0.819017i	0.985297	+	0.170852i	$0.0546519\pi$
$938$	5.09017	+	15.6659i	0.166200	+	0.511511i
$939$	−2.61803	+	8.05748i	−0.0854363	+	0.262946i
$940$	−3.50000	−	2.54290i	−0.114157	−	0.0829402i
$941$	−0.826238	−	0.600297i	−0.0269346	−	0.0195691i	0.574237	−	0.818689i	$-0.305299\pi$
$941$	−0.826238	−	0.600297i	−0.0269346	−	0.0195691i	−0.601171	+	0.799120i	$0.705299\pi$
$942$	2.86475	−	8.81678i	0.0933384	−	0.287266i
$943$	2.61803	+	8.05748i	0.0852549	+	0.262388i
$944$	−11.3992	+	8.28199i	−0.371012	+	0.269556i
$945$	−3.23607			−0.105269
$946$	0.152476	−	0.257270i	0.00495742	−	0.00836457i
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	−3.30902	+	2.40414i	−0.107472	+	0.0780829i
$949$	14.0213	+	43.1531i	0.455150	+	1.40081i
$950$	0.381966	−	1.17557i	0.0123926	−	0.0381405i
$951$	−22.1803	−	16.1150i	−0.719247	−	0.522563i
$952$	−15.9443	−	11.5842i	−0.516757	−	0.375446i
$953$	−18.2984	+	56.3166i	−0.592742	+	1.82427i	−0.0270855	+	0.999633i	$0.508623\pi$
$953$	−18.2984	+	56.3166i	−0.592742	+	1.82427i	−0.565657	+	0.824641i	$0.691377\pi$
$954$	2.61803	+	8.05748i	0.0847620	+	0.260871i
$955$	7.47214	−	5.42882i	0.241793	−	0.175673i
$956$	−3.23607			−0.104662
$957$	7.97214	−	3.44095i	0.257703	−	0.111230i
$958$	12.7639			0.412384
$959$	−33.5066	+	24.3440i	−1.08198	+	0.786107i
$960$	0.309017	+	0.951057i	0.00997348	+	0.0306952i
$961$	−8.98936	+	27.6664i	−0.289979	+	0.892464i
$962$	17.4615	+	12.6865i	0.562981	+	0.409030i
$963$	−5.09017	−	3.69822i	−0.164028	−	0.119174i
$964$	−7.38197	+	22.7194i	−0.237757	+	0.731741i
$965$	6.47214	+	19.9192i	0.208345	+	0.641221i
$966$	−17.9443	+	13.0373i	−0.577347	+	0.419468i
$967$	53.3050			1.71417			0.857086	−	0.515174i	$-0.172273\pi$
$967$	53.3050			1.71417			0.857086	+	0.515174i	$0.172273\pi$
$968$	9.94427	+	4.70228i	0.319621	+	0.151137i
$969$	7.52786			0.241830
$970$	15.0902	−	10.9637i	0.484516	−	0.352022i
$971$	2.58359	+	7.95148i	0.0829114	+	0.255175i	0.983915	−	0.178636i	$-0.0571685\pi$
$971$	2.58359	+	7.95148i	0.0829114	+	0.255175i	−0.901004	+	0.433811i	$0.857168\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	22.9443	+	16.6700i	0.735560	+	0.534415i
$974$	−9.23607	−	6.71040i	−0.295943	−	0.215015i
$975$	−1.04508	+	3.21644i	−0.0334695	+	0.103009i
$976$		0			0
$977$	−23.3262	+	16.9475i	−0.746272	+	0.542199i	−0.894669	−	0.446729i	$-0.852589\pi$
$977$	−23.3262	+	16.9475i	−0.746272	+	0.542199i	0.148397	+	0.988928i	$0.452589\pi$
$978$	−0.854102			−0.0273112
$979$	52.4853	−	22.6538i	1.67744	−	0.724020i
$980$	−3.47214			−0.110913
$981$	2.00000	−	1.45309i	0.0638551	−	0.0463934i
$982$	8.66312	+	26.6623i	0.276451	+	0.850829i
$983$	−15.8197	+	48.6879i	−0.504569	+	1.55290i	0.296925	+	0.954901i	$0.404039\pi$
$983$	−15.8197	+	48.6879i	−0.504569	+	1.55290i	−0.801494	+	0.598002i	$0.795961\pi$
$984$	1.00000	+	0.726543i	0.0318788	+	0.0231613i
$985$	8.85410	+	6.43288i	0.282115	+	0.204969i
$986$	4.92705	−	15.1639i	0.156909	−	0.482917i
$987$	−4.32624	−	13.3148i	−0.137706	−	0.423814i
$988$	−3.38197	+	2.45714i	−0.107595	+	0.0781721i
$989$	−0.618034			−0.0196523
$990$	1.69098	−	2.85317i	0.0537430	−	0.0906797i
$991$	54.5197			1.73188			0.865938	−	0.500151i	$-0.166722\pi$
$991$	54.5197			1.73188			0.865938	+	0.500151i	$0.166722\pi$
$992$	1.11803	−	0.812299i	0.0354976	−	0.0257905i
$993$	−2.85410	−	8.78402i	−0.0905722	−	0.278753i
$994$	−10.4721	+	32.2299i	−0.332156	+	1.02227i
$995$	21.0172	+	15.2699i	0.666291	+	0.484089i
$996$	3.23607	+	2.35114i	0.102539	+	0.0744988i
$997$	−7.73607	+	23.8092i	−0.245004	+	0.754044i	0.750632	+	0.660720i	$0.229749\pi$
$997$	−7.73607	+	23.8092i	−0.245004	+	0.754044i	−0.995636	+	0.0933236i	$0.970251\pi$
$998$	−10.0344	−	30.8828i	−0.317635	−	0.977579i
$999$	−5.16312	+	3.75123i	−0.163354	+	0.118684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	330.2.m.b.91.1	✓	4
3.2	odd	2		990.2.n.e.91.1		4
11.2	odd	10		3630.2.a.bb.1.2		2
11.4	even	5	inner	330.2.m.b.301.1	yes	4
11.9	even	5		3630.2.a.bj.1.1		2
33.26	odd	10		990.2.n.e.631.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.b.91.1	✓	4	1.1	even	1	trivial
330.2.m.b.301.1	yes	4	11.4	even	5	inner
990.2.n.e.91.1		4	3.2	odd	2
990.2.n.e.631.1		4	33.26	odd	10
3630.2.a.bb.1.2		2	11.2	odd	10
3630.2.a.bj.1.1		2	11.9	even	5

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:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.00000 + 3.07768i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.00000 + 3.07768i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.00000 q^{10} +(3.04508 - 1.31433i) q^{11} -1.00000 q^{12} +(-2.73607 + 1.98787i) q^{13} +(-1.00000 - 3.07768i) q^{14} +(0.309017 - 0.951057i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.92705 + 3.57971i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.381966 + 1.17557i) q^{19} +(0.809017 - 0.587785i) q^{20} +3.23607 q^{21} +(-1.69098 + 2.85317i) q^{22} +6.85410 q^{23} +(0.809017 - 0.587785i) q^{24} +(0.309017 + 0.951057i) q^{25} +(1.04508 - 3.21644i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.61803 + 1.90211i) q^{28} +(-0.809017 + 2.48990i) q^{29} +(0.309017 + 0.951057i) q^{30} +(1.11803 - 0.812299i) q^{31} +1.00000 q^{32} +(-2.19098 - 2.48990i) q^{33} -6.09017 q^{34} +(-2.61803 + 1.90211i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-1.97214 + 6.06961i) q^{37} +(-1.00000 - 0.726543i) q^{38} +(2.73607 + 1.98787i) q^{39} +(-0.309017 + 0.951057i) q^{40} +(0.381966 + 1.17557i) q^{41} +(-2.61803 + 1.90211i) q^{42} -0.0901699 q^{43} +(-0.309017 - 3.30220i) q^{44} -1.00000 q^{45} +(-5.54508 + 4.02874i) q^{46} +(-1.33688 - 4.11450i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-2.80902 - 2.04087i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(1.88197 - 5.79210i) q^{51} +(1.04508 + 3.21644i) q^{52} +(-6.85410 + 4.97980i) q^{53} -1.00000 q^{54} +(3.23607 + 0.726543i) q^{55} -3.23607 q^{56} +(1.00000 - 0.726543i) q^{57} +(-0.809017 - 2.48990i) q^{58} +(4.35410 - 13.4005i) q^{59} +(-0.809017 - 0.587785i) q^{60} +(-0.427051 + 1.31433i) q^{62} +(-1.00000 - 3.07768i) q^{63} +(-0.809017 + 0.587785i) q^{64} -3.38197 q^{65} +(3.23607 + 0.726543i) q^{66} -5.09017 q^{67} +(4.92705 - 3.57971i) q^{68} +(-2.11803 - 6.51864i) q^{69} +(1.00000 - 3.07768i) q^{70} +(-8.47214 - 6.15537i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(4.14590 - 12.7598i) q^{73} +(-1.97214 - 6.06961i) q^{74} +(0.809017 - 0.587785i) q^{75} +1.23607 q^{76} +(1.00000 + 10.6861i) q^{77} -3.38197 q^{78} +(3.30902 - 2.40414i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.00000 - 0.726543i) q^{82} +(-3.23607 - 2.35114i) q^{83} +(1.00000 - 3.07768i) q^{84} +(1.88197 + 5.79210i) q^{85} +(0.0729490 - 0.0530006i) q^{86} +2.61803 q^{87} +(2.19098 + 2.48990i) q^{88} +17.2361 q^{89} +(0.809017 - 0.587785i) q^{90} +(-3.38197 - 10.4086i) q^{91} +(2.11803 - 6.51864i) q^{92} +(-1.11803 - 0.812299i) q^{93} +(3.50000 + 2.54290i) q^{94} +(-0.381966 + 1.17557i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-15.0902 + 10.9637i) q^{97} +3.47214 q^{98} +(-1.69098 + 2.85317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 4 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 - q^4 + q^5 + q^6 - 4 * q^7 - q^8 - q^9	\( 4 q - q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 4 q^{7} - q^{8} - q^{9} - 4 q^{10} + q^{11} - 4 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} - q^{16} + 13 q^{17} - q^{18} + 6 q^{19} + q^{20} + 4 q^{21} - 9 q^{22} + 14 q^{23} + q^{24} - q^{25} - 7 q^{26} + q^{27} + 6 q^{28} - q^{29} - q^{30} + 4 q^{32} - 11 q^{33} - 2 q^{34} - 6 q^{35} - q^{36} + 10 q^{37} - 4 q^{38} + 2 q^{39} + q^{40} + 6 q^{41} - 6 q^{42} + 22 q^{43} + q^{44} - 4 q^{45} - 11 q^{46} - 21 q^{47} + q^{48} - 9 q^{49} - q^{50} + 12 q^{51} - 7 q^{52} - 14 q^{53} - 4 q^{54} + 4 q^{55} - 4 q^{56} + 4 q^{57} - q^{58} + 4 q^{59} - q^{60} + 5 q^{62} - 4 q^{63} - q^{64} - 18 q^{65} + 4 q^{66} + 2 q^{67} + 13 q^{68} - 4 q^{69} + 4 q^{70} - 16 q^{71} - q^{72} + 30 q^{73} + 10 q^{74} + q^{75} - 4 q^{76} + 4 q^{77} - 18 q^{78} + 11 q^{79} + q^{80} - q^{81} - 4 q^{82} - 4 q^{83} + 4 q^{84} + 12 q^{85} + 7 q^{86} + 6 q^{87} + 11 q^{88} + 60 q^{89} + q^{90} - 18 q^{91} + 4 q^{92} + 14 q^{94} - 6 q^{95} + q^{96} - 38 q^{97} - 4 q^{98} - 9 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 + q^5 + q^6 - 4 * q^7 - q^8 - q^9 - 4 * q^10 + q^11 - 4 * q^12 - 2 * q^13 - 4 * q^14 - q^15 - q^16 + 13 * q^17 - q^18 + 6 * q^19 + q^20 + 4 * q^21 - 9 * q^22 + 14 * q^23 + q^24 - q^25 - 7 * q^26 + q^27 + 6 * q^28 - q^29 - q^30 + 4 * q^32 - 11 * q^33 - 2 * q^34 - 6 * q^35 - q^36 + 10 * q^37 - 4 * q^38 + 2 * q^39 + q^40 + 6 * q^41 - 6 * q^42 + 22 * q^43 + q^44 - 4 * q^45 - 11 * q^46 - 21 * q^47 + q^48 - 9 * q^49 - q^50 + 12 * q^51 - 7 * q^52 - 14 * q^53 - 4 * q^54 + 4 * q^55 - 4 * q^56 + 4 * q^57 - q^58 + 4 * q^59 - q^60 + 5 * q^62 - 4 * q^63 - q^64 - 18 * q^65 + 4 * q^66 + 2 * q^67 + 13 * q^68 - 4 * q^69 + 4 * q^70 - 16 * q^71 - q^72 + 30 * q^73 + 10 * q^74 + q^75 - 4 * q^76 + 4 * q^77 - 18 * q^78 + 11 * q^79 + q^80 - q^81 - 4 * q^82 - 4 * q^83 + 4 * q^84 + 12 * q^85 + 7 * q^86 + 6 * q^87 + 11 * q^88 + 60 * q^89 + q^90 - 18 * q^91 + 4 * q^92 + 14 * q^94 - 6 * q^95 + q^96 - 38 * q^97 - 4 * q^98 - 9 * q^99

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