LMFDB - Embedded newform 330.2.m.b.181.1

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			181.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	330.181
Dual form			330.2.m.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.00000 + 0.726543i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.00000 + 0.726543i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.00000 q^{10} +(-2.54508 + 2.12663i) q^{11} -1.00000 q^{12} +(1.73607 + 5.34307i) q^{13} +(-1.00000 - 0.726543i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.57295 - 4.84104i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(2.61803 + 1.90211i) q^{19} +(-0.309017 - 0.951057i) q^{20} -1.23607 q^{21} +(-2.80902 - 1.76336i) q^{22} +0.145898 q^{23} +(-0.309017 - 0.951057i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.54508 + 3.30220i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.381966 - 1.17557i) q^{28} +(0.309017 - 0.224514i) q^{29} +(-0.809017 - 0.587785i) q^{30} +(-1.11803 - 3.44095i) q^{31} +1.00000 q^{32} +(-3.30902 + 0.224514i) q^{33} +5.09017 q^{34} +(-0.381966 - 1.17557i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(6.97214 - 5.06555i) q^{37} +(-1.00000 + 3.07768i) q^{38} +(-1.73607 + 5.34307i) q^{39} +(0.809017 - 0.587785i) q^{40} +(2.61803 + 1.90211i) q^{41} +(-0.381966 - 1.17557i) q^{42} +11.0902 q^{43} +(0.809017 - 3.21644i) q^{44} -1.00000 q^{45} +(0.0450850 + 0.138757i) q^{46} +(-9.16312 - 6.65740i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-1.69098 + 5.20431i) q^{49} +(0.309017 - 0.951057i) q^{50} +(4.11803 - 2.99193i) q^{51} +(-4.54508 - 3.30220i) q^{52} +(-0.145898 - 0.449028i) q^{53} -1.00000 q^{54} +(-1.23607 - 3.07768i) q^{55} +1.23607 q^{56} +(1.00000 + 3.07768i) q^{57} +(0.309017 + 0.224514i) q^{58} +(-2.35410 + 1.71036i) q^{59} +(0.309017 - 0.951057i) q^{60} +(2.92705 - 2.12663i) q^{62} +(-1.00000 - 0.726543i) q^{63} +(0.309017 + 0.951057i) q^{64} -5.61803 q^{65} +(-1.23607 - 3.07768i) q^{66} +6.09017 q^{67} +(1.57295 + 4.84104i) q^{68} +(0.118034 + 0.0857567i) q^{69} +(1.00000 - 0.726543i) q^{70} +(0.472136 - 1.45309i) q^{71} +(0.309017 - 0.951057i) q^{72} +(10.8541 - 7.88597i) q^{73} +(6.97214 + 5.06555i) q^{74} +(-0.309017 - 0.951057i) q^{75} -3.23607 q^{76} +(1.00000 - 3.97574i) q^{77} -5.61803 q^{78} +(2.19098 + 6.74315i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.00000 + 3.07768i) q^{82} +(1.23607 - 3.80423i) q^{83} +(1.00000 - 0.726543i) q^{84} +(4.11803 + 2.99193i) q^{85} +(3.42705 + 10.5474i) q^{86} +0.381966 q^{87} +(3.30902 - 0.224514i) q^{88} +12.7639 q^{89} +(-0.309017 - 0.951057i) q^{90} +(-5.61803 - 4.08174i) q^{91} +(-0.118034 + 0.0857567i) q^{92} +(1.11803 - 3.44095i) q^{93} +(3.50000 - 10.7719i) q^{94} +(-2.61803 + 1.90211i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-3.90983 - 12.0332i) q^{97} -5.47214 q^{98} +(-2.80902 - 1.76336i) 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 $\left(\mathbb{Z}/330\mathbb{Z}\right)^\times$.

$n$	$67$	$211$	$221$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	−0.309017	+	0.951057i	−0.126156	+	0.388267i
$7$	−1.00000	+	0.726543i	−0.377964	+	0.274607i	−0.760506	−	0.649331i	$-0.775049\pi$
$7$	−1.00000	+	0.726543i	−0.377964	+	0.274607i	0.382541	+	0.923938i	$0.375049\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−1.00000			−0.316228
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$12$	−1.00000			−0.288675
$13$	1.73607	+	5.34307i	0.481499	+	1.48190i	0.836989	+	0.547220i	$0.184314\pi$
$13$	1.73607	+	5.34307i	0.481499	+	1.48190i	−0.355490	+	0.934680i	$0.615686\pi$
$14$	−1.00000	−	0.726543i	−0.267261	−	0.194177i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.57295	−	4.84104i	0.381496	−	1.17412i	−0.557494	−	0.830181i	$-0.688237\pi$
$17$	1.57295	−	4.84104i	0.381496	−	1.17412i	0.938990	−	0.343944i	$-0.111763\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	2.61803	+	1.90211i	0.600618	+	0.436375i	0.846098	−	0.533027i	$-0.178946\pi$
$19$	2.61803	+	1.90211i	0.600618	+	0.436375i	−0.245480	+	0.969402i	$0.578946\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	−1.23607			−0.269732
$22$	−2.80902	−	1.76336i	−0.598884	−	0.375949i
$23$	0.145898			0.0304218			0.0152109	−	0.999884i	$-0.495158\pi$
$23$	0.145898			0.0304218			0.0152109	+	0.999884i	$0.495158\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−4.54508	+	3.30220i	−0.891364	+	0.647614i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	0.381966	−	1.17557i	0.0721848	−	0.222162i
$29$	0.309017	−	0.224514i	0.0573830	−	0.0416912i	−0.558724	−	0.829354i	$-0.688709\pi$
$29$	0.309017	−	0.224514i	0.0573830	−	0.0416912i	0.616107	+	0.787662i	$0.288709\pi$
$30$	−0.809017	−	0.587785i	−0.147706	−	0.107314i
$31$	−1.11803	−	3.44095i	−0.200805	−	0.618014i	−0.999860	−	0.0167555i	$-0.994666\pi$
$31$	−1.11803	−	3.44095i	−0.200805	−	0.618014i	0.799055	−	0.601258i	$-0.205334\pi$
$32$	1.00000			0.176777
$33$	−3.30902	+	0.224514i	−0.576026	+	0.0390829i
$34$	5.09017			0.872957
$35$	−0.381966	−	1.17557i	−0.0645640	−	0.198708i
$36$	−0.809017	−	0.587785i	−0.134836	−	0.0979642i
$37$	6.97214	−	5.06555i	1.14621	−	0.832772i	0.158239	−	0.987401i	$-0.449418\pi$
$37$	6.97214	−	5.06555i	1.14621	−	0.832772i	0.987973	+	0.154629i	$0.0494182\pi$
$38$	−1.00000	+	3.07768i	−0.162221	+	0.499266i
$39$	−1.73607	+	5.34307i	−0.277993	+	0.855576i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	2.61803	+	1.90211i	0.408868	+	0.297060i	0.773143	−	0.634231i	$-0.218683\pi$
$41$	2.61803	+	1.90211i	0.408868	+	0.297060i	−0.364275	+	0.931291i	$0.618683\pi$
$42$	−0.381966	−	1.17557i	−0.0589386	−	0.181394i
$43$	11.0902			1.69124			0.845618	−	0.533789i	$-0.179232\pi$
$43$	11.0902			1.69124			0.845618	+	0.533789i	$0.179232\pi$
$44$	0.809017	−	3.21644i	0.121964	−	0.484897i
$45$	−1.00000			−0.149071
$46$	0.0450850	+	0.138757i	0.00664742	+	0.0204586i
$47$	−9.16312	−	6.65740i	−1.33658	−	0.971081i	−0.999562	−	0.0295820i	$-0.990582\pi$
$47$	−9.16312	−	6.65740i	−1.33658	−	0.971081i	−0.337016	−	0.941499i	$-0.609418\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	−1.69098	+	5.20431i	−0.241569	+	0.743473i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	4.11803	−	2.99193i	0.576640	−	0.418954i
$52$	−4.54508	−	3.30220i	−0.630290	−	0.457932i
$53$	−0.145898	−	0.449028i	−0.0200406	−	0.0616787i	0.940536	−	0.339694i	$-0.110323\pi$
$53$	−0.145898	−	0.449028i	−0.0200406	−	0.0616787i	−0.960577	+	0.278015i	$0.910323\pi$
$54$	−1.00000			−0.136083
$55$	−1.23607	−	3.07768i	−0.166671	−	0.414995i
$56$	1.23607			0.165177
$57$	1.00000	+	3.07768i	0.132453	+	0.407649i
$58$	0.309017	+	0.224514i	0.0405759	+	0.0294801i
$59$	−2.35410	+	1.71036i	−0.306478	+	0.222669i	−0.730384	−	0.683037i	$-0.760659\pi$
$59$	−2.35410	+	1.71036i	−0.306478	+	0.222669i	0.423906	+	0.905706i	$0.360659\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$61$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$62$	2.92705	−	2.12663i	0.371736	−	0.270082i
$63$	−1.00000	−	0.726543i	−0.125988	−	0.0915358i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−5.61803			−0.696831
$66$	−1.23607	−	3.07768i	−0.152149	−	0.378837i
$67$	6.09017			0.744033			0.372016	−	0.928226i	$-0.378667\pi$
$67$	6.09017			0.744033			0.372016	+	0.928226i	$0.378667\pi$
$68$	1.57295	+	4.84104i	0.190748	+	0.587062i
$69$	0.118034	+	0.0857567i	0.0142096	+	0.0103239i
$70$	1.00000	−	0.726543i	0.119523	−	0.0868384i
$71$	0.472136	−	1.45309i	0.0560322	−	0.172449i	−0.919124	−	0.393969i	$-0.871102\pi$
$71$	0.472136	−	1.45309i	0.0560322	−	0.172449i	0.975156	+	0.221520i	$0.0711017\pi$
$72$	0.309017	−	0.951057i	0.0364180	−	0.112083i
$73$	10.8541	−	7.88597i	1.27038	−	0.922983i	0.271159	−	0.962535i	$-0.412593\pi$
$73$	10.8541	−	7.88597i	1.27038	−	0.922983i	0.999218	+	0.0395520i	$0.0125931\pi$
$74$	6.97214	+	5.06555i	0.810494	+	0.588859i
$75$	−0.309017	−	0.951057i	−0.0356822	−	0.109819i
$76$	−3.23607			−0.371202
$77$	1.00000	−	3.97574i	0.113961	−	0.453078i
$78$	−5.61803			−0.636117
$79$	2.19098	+	6.74315i	0.246505	+	0.758664i	0.995385	+	0.0959588i	$0.0305917\pi$
$79$	2.19098	+	6.74315i	0.246505	+	0.758664i	−0.748880	+	0.662705i	$0.769408\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−1.00000	+	3.07768i	−0.110432	+	0.339873i
$83$	1.23607	−	3.80423i	0.135676	−	0.417568i	−0.860018	−	0.510263i	$-0.829548\pi$
$83$	1.23607	−	3.80423i	0.135676	−	0.417568i	0.995695	+	0.0926948i	$0.0295481\pi$
$84$	1.00000	−	0.726543i	0.109109	−	0.0792723i
$85$	4.11803	+	2.99193i	0.446663	+	0.324520i
$86$	3.42705	+	10.5474i	0.369548	+	1.13735i
$87$	0.381966			0.0409511
$88$	3.30902	−	0.224514i	0.352742	−	0.0239333i
$89$	12.7639			1.35297			0.676487	−	0.736455i	$-0.263501\pi$
$89$	12.7639			1.35297			0.676487	+	0.736455i	$0.263501\pi$
$90$	−0.309017	−	0.951057i	−0.0325733	−	0.100250i
$91$	−5.61803	−	4.08174i	−0.588930	−	0.427883i
$92$	−0.118034	+	0.0857567i	−0.0123059	+	0.00894076i
$93$	1.11803	−	3.44095i	0.115935	−	0.356810i
$94$	3.50000	−	10.7719i	0.360997	−	1.11104i
$95$	−2.61803	+	1.90211i	−0.268605	+	0.195153i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	−3.90983	−	12.0332i	−0.396983	−	1.22179i	−0.927406	−	0.374055i	$-0.877967\pi$
$97$	−3.90983	−	12.0332i	−0.396983	−	1.22179i	0.530423	−	0.847733i	$-0.322033\pi$
$98$	−5.47214			−0.552769
$99$	−2.80902	−	1.76336i	−0.282317	−	0.177224i
$100$	1.00000			0.100000
$101$	4.13525	+	12.7270i	0.411473	+	1.26638i	0.915368	+	0.402619i	$0.131900\pi$
$101$	4.13525	+	12.7270i	0.411473	+	1.26638i	−0.503894	+	0.863765i	$0.668100\pi$
$102$	4.11803	+	2.99193i	0.407746	+	0.296245i
$103$	−9.09017	+	6.60440i	−0.895681	+	0.650750i	−0.937353	−	0.348381i	$-0.886732\pi$
$103$	−9.09017	+	6.60440i	−0.895681	+	0.650750i	0.0416720	+	0.999131i	$0.486732\pi$
$104$	1.73607	−	5.34307i	0.170235	−	0.523931i
$105$	0.381966	−	1.17557i	0.0372761	−	0.114724i
$106$	0.381966	−	0.277515i	0.0370998	−	0.0269546i
$107$	−15.9443	−	11.5842i	−1.54139	−	1.11989i	−0.949456	−	0.313900i	$-0.898364\pi$
$107$	−15.9443	−	11.5842i	−1.54139	−	1.11989i	−0.591935	−	0.805986i	$-0.701636\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	6.47214			0.619918			0.309959	−	0.950750i	$-0.399685\pi$
$109$	6.47214			0.619918			0.309959	+	0.950750i	$0.399685\pi$
$110$	2.54508	−	2.12663i	0.242664	−	0.202766i
$111$	8.61803			0.817988
$112$	0.381966	+	1.17557i	0.0360924	+	0.111081i
$113$	−0.454915	−	0.330515i	−0.0427948	−	0.0310922i	0.566182	−	0.824280i	$-0.308420\pi$
$113$	−0.454915	−	0.330515i	−0.0427948	−	0.0310922i	−0.608977	+	0.793188i	$0.708420\pi$
$114$	−2.61803	+	1.90211i	−0.245201	+	0.178149i
$115$	−0.0450850	+	0.138757i	−0.00420420	+	0.0129392i
$116$	−0.118034	+	0.363271i	−0.0109592	+	0.0337289i
$117$	−4.54508	+	3.30220i	−0.420193	+	0.305288i
$118$	−2.35410	−	1.71036i	−0.216713	−	0.157451i
$119$	1.94427	+	5.98385i	0.178231	+	0.548539i
$120$	1.00000			0.0912871
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$		0			0
$123$	1.00000	+	3.07768i	0.0901670	+	0.277505i
$124$	2.92705	+	2.12663i	0.262857	+	0.190977i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	0.381966	−	1.17557i	0.0340282	−	0.104728i
$127$	−5.14590	+	15.8374i	−0.456625	+	1.40535i	0.412593	+	0.910916i	$0.364623\pi$
$127$	−5.14590	+	15.8374i	−0.456625	+	1.40535i	−0.869217	+	0.494430i	$0.835377\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	8.97214	+	6.51864i	0.789953	+	0.573934i
$130$	−1.73607	−	5.34307i	−0.152263	−	0.468618i
$131$	−5.61803			−0.490850			−0.245425	−	0.969416i	$-0.578927\pi$
$131$	−5.61803			−0.490850			−0.245425	+	0.969416i	$0.578927\pi$
$132$	2.54508	−	2.12663i	0.221521	−	0.185099i
$133$	−4.00000			−0.346844
$134$	1.88197	+	5.79210i	0.162577	+	0.500361i
$135$	−0.809017	−	0.587785i	−0.0696291	−	0.0505885i
$136$	−4.11803	+	2.99193i	−0.353119	+	0.256556i
$137$	3.64590	−	11.2209i	0.311490	−	0.958668i	−0.665685	−	0.746233i	$-0.731861\pi$
$137$	3.64590	−	11.2209i	0.311490	−	0.958668i	0.977175	−	0.212435i	$-0.0681394\pi$
$138$	−0.0450850	+	0.138757i	−0.00383789	+	0.0118118i
$139$	−10.7082	+	7.77997i	−0.908258	+	0.659888i	−0.940574	−	0.339590i	$-0.889712\pi$
$139$	−10.7082	+	7.77997i	−0.908258	+	0.659888i	0.0323157	+	0.999478i	$0.489712\pi$
$140$	1.00000	+	0.726543i	0.0845154	+	0.0614041i
$141$	−3.50000	−	10.7719i	−0.294753	−	0.907157i
$142$	1.52786			0.128216
$143$	−15.7812	−	9.90659i	−1.31969	−	0.828431i
$144$	1.00000			0.0833333
$145$	0.118034	+	0.363271i	0.00980219	+	0.0301680i
$146$	10.8541	+	7.88597i	0.898292	+	0.652647i
$147$	−4.42705	+	3.21644i	−0.365137	+	0.265288i
$148$	−2.66312	+	8.19624i	−0.218907	+	0.673727i
$149$	−1.66312	+	5.11855i	−0.136248	+	0.419328i	−0.995782	−	0.0917502i	$-0.970754\pi$
$149$	−1.66312	+	5.11855i	−0.136248	+	0.419328i	0.859534	+	0.511079i	$0.170754\pi$
$150$	0.809017	−	0.587785i	0.0660560	−	0.0479925i
$151$	−2.47214	−	1.79611i	−0.201180	−	0.146166i	0.482634	−	0.875822i	$-0.339680\pi$
$151$	−2.47214	−	1.79611i	−0.201180	−	0.146166i	−0.683814	+	0.729656i	$0.739680\pi$
$152$	−1.00000	−	3.07768i	−0.0811107	−	0.249633i
$153$	5.09017			0.411516
$154$	4.09017	−	0.277515i	0.329595	−	0.0223628i
$155$	3.61803			0.290607
$156$	−1.73607	−	5.34307i	−0.138997	−	0.427788i
$157$	−19.6353	−	14.2658i	−1.56706	−	1.13854i	−0.929901	−	0.367809i	$-0.880108\pi$
$157$	−19.6353	−	14.2658i	−1.56706	−	1.13854i	−0.637163	−	0.770729i	$-0.719892\pi$
$158$	−5.73607	+	4.16750i	−0.456337	+	0.331548i
$159$	0.145898	−	0.449028i	0.0115705	−	0.0356102i
$160$	−0.309017	+	0.951057i	−0.0244299	+	0.0751876i
$161$	−0.145898	+	0.106001i	−0.0114984	+	0.00835406i
$162$	−0.809017	−	0.587785i	−0.0635624	−	0.0461808i
$163$	−1.80902	−	5.56758i	−0.141693	−	0.436087i	0.854878	−	0.518829i	$-0.173632\pi$
$163$	−1.80902	−	5.56758i	−0.141693	−	0.436087i	−0.996571	+	0.0827427i	$0.973632\pi$
$164$	−3.23607			−0.252694
$165$	0.809017	−	3.21644i	0.0629819	−	0.250400i
$166$	4.00000			0.310460
$167$	6.26393	+	19.2784i	0.484718	+	1.49181i	0.832389	+	0.554191i	$0.186972\pi$
$167$	6.26393	+	19.2784i	0.484718	+	1.49181i	−0.347672	+	0.937616i	$0.613028\pi$
$168$	1.00000	+	0.726543i	0.0771517	+	0.0560540i
$169$	−15.0172	+	10.9106i	−1.15517	+	0.839281i
$170$	−1.57295	+	4.84104i	−0.120640	+	0.371291i
$171$	−1.00000	+	3.07768i	−0.0764719	+	0.235356i
$172$	−8.97214	+	6.51864i	−0.684119	+	0.497042i
$173$	14.9443	+	10.8576i	1.13619	+	0.825492i	0.986584	−	0.163254i	$-0.0521989\pi$
$173$	14.9443	+	10.8576i	1.13619	+	0.825492i	0.149608	+	0.988745i	$0.452199\pi$
$174$	0.118034	+	0.363271i	0.00894813	+	0.0275395i
$175$	1.23607			0.0934380
$176$	1.23607	+	3.07768i	0.0931721	+	0.231989i
$177$	−2.90983			−0.218716
$178$	3.94427	+	12.1392i	0.295636	+	0.909873i
$179$	−20.1074	−	14.6089i	−1.50290	−	1.09192i	−0.969210	−	0.246237i	$-0.920806\pi$
$179$	−20.1074	−	14.6089i	−1.50290	−	1.09192i	−0.533687	−	0.845682i	$-0.679194\pi$
$180$	0.809017	−	0.587785i	0.0603006	−	0.0438109i
$181$	−4.29180	+	13.2088i	−0.319007	+	0.981802i	0.655067	+	0.755571i	$0.272640\pi$
$181$	−4.29180	+	13.2088i	−0.319007	+	0.981802i	−0.974074	+	0.226231i	$0.927360\pi$
$182$	2.14590	−	6.60440i	0.159065	−	0.489550i
$183$		0			0
$184$	−0.118034	−	0.0857567i	−0.00870158	−	0.00632207i
$185$	2.66312	+	8.19624i	0.195796	+	0.602599i
$186$	3.61803			0.265287
$187$	6.29180	+	15.6659i	0.460102	+	1.14561i
$188$	11.3262			0.826051
$189$	−0.381966	−	1.17557i	−0.0277839	−	0.0855102i
$190$	−2.61803	−	1.90211i	−0.189932	−	0.137994i
$191$	−3.85410	+	2.80017i	−0.278873	+	0.202613i	−0.718426	−	0.695604i	$-0.755137\pi$
$191$	−3.85410	+	2.80017i	−0.278873	+	0.202613i	0.439553	+	0.898217i	$0.355137\pi$
$192$	−0.309017	+	0.951057i	−0.0223014	+	0.0686366i
$193$	−0.944272	+	2.90617i	−0.0679702	+	0.209191i	−0.979273	−	0.202547i	$-0.935078\pi$
$193$	−0.944272	+	2.90617i	−0.0679702	+	0.209191i	0.911302	+	0.411738i	$0.135078\pi$
$194$	10.2361	−	7.43694i	0.734907	−	0.533941i
$195$	−4.54508	−	3.30220i	−0.325480	−	0.236475i
$196$	−1.69098	−	5.20431i	−0.120785	−	0.371736i
$197$	−6.94427			−0.494759			−0.247379	−	0.968919i	$-0.579569\pi$
$197$	−6.94427			−0.494759			−0.247379	+	0.968919i	$0.579569\pi$
$198$	0.809017	−	3.21644i	0.0574943	−	0.228582i
$199$	−20.9787			−1.48714			−0.743571	−	0.668657i	$-0.766869\pi$
$199$	−20.9787			−1.48714			−0.743571	+	0.668657i	$0.766869\pi$
$200$	0.309017	+	0.951057i	0.0218508	+	0.0672499i
$201$	4.92705	+	3.57971i	0.347527	+	0.252493i
$202$	−10.8262	+	7.86572i	−0.761731	+	0.553430i
$203$	−0.145898	+	0.449028i	−0.0102400	+	0.0315156i
$204$	−1.57295	+	4.84104i	−0.110128	+	0.338941i
$205$	−2.61803	+	1.90211i	−0.182851	+	0.132849i
$206$	−9.09017	−	6.60440i	−0.633342	−	0.460150i
$207$	0.0450850	+	0.138757i	0.00313362	+	0.00964430i
$208$	5.61803			0.389541
$209$	−10.7082	+	0.726543i	−0.740702	+	0.0502560i
$210$	1.23607			0.0852968
$211$	−6.41641	−	19.7477i	−0.441724	−	1.35949i	−0.886037	−	0.463614i	$-0.846552\pi$
$211$	−6.41641	−	19.7477i	−0.441724	−	1.35949i	0.444313	−	0.895871i	$-0.353448\pi$
$212$	0.381966	+	0.277515i	0.0262335	+	0.0190598i
$213$	1.23607	−	0.898056i	0.0846940	−	0.0615338i
$214$	6.09017	−	18.7436i	0.416315	−	1.28129i
$215$	−3.42705	+	10.5474i	−0.233723	+	0.719325i
$216$	0.809017	−	0.587785i	0.0550466	−	0.0399937i
$217$	3.61803	+	2.62866i	0.245608	+	0.178445i
$218$	2.00000	+	6.15537i	0.135457	+	0.416894i
$219$	13.4164			0.906597
$220$	2.80902	+	1.76336i	0.189384	+	0.118885i
$221$	28.5967			1.92363
$222$	2.66312	+	8.19624i	0.178737	+	0.550095i
$223$	−2.23607	−	1.62460i	−0.149738	−	0.108791i	0.510394	−	0.859941i	$-0.329500\pi$
$223$	−2.23607	−	1.62460i	−0.149738	−	0.108791i	−0.660132	+	0.751150i	$0.729500\pi$
$224$	−1.00000	+	0.726543i	−0.0668153	+	0.0485442i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	0.173762	−	0.534785i	0.0115585	−	0.0355733i
$227$	19.7082	−	14.3188i	1.30808	−	0.950375i	0.308080	−	0.951360i	$-0.400314\pi$
$227$	19.7082	−	14.3188i	1.30808	−	0.950375i	1.00000		0.000985137i	$0.000313579\pi$
$228$	−2.61803	−	1.90211i	−0.173384	−	0.125971i
$229$	1.61803	+	4.97980i	0.106923	+	0.329074i	0.990177	−	0.139820i	$-0.0446525\pi$
$229$	1.61803	+	4.97980i	0.106923	+	0.329074i	−0.883254	+	0.468894i	$0.844652\pi$
$230$	−0.145898			−0.00962023
$231$	3.14590	−	2.62866i	0.206985	−	0.172953i
$232$	−0.381966			−0.0250773
$233$	−7.59017	−	23.3601i	−0.497249	−	1.53037i	−0.813423	−	0.581673i	$-0.802398\pi$
$233$	−7.59017	−	23.3601i	−0.497249	−	1.53037i	0.316174	−	0.948701i	$-0.397602\pi$
$234$	−4.54508	−	3.30220i	−0.297121	−	0.215871i
$235$	9.16312	−	6.65740i	0.597736	−	0.434281i
$236$	0.899187	−	2.76741i	0.0585321	−	0.180143i
$237$	−2.19098	+	6.74315i	−0.142320	+	0.438015i
$238$	−5.09017	+	3.69822i	−0.329947	+	0.239720i
$239$	−1.00000	−	0.726543i	−0.0646846	−	0.0469961i	0.554973	−	0.831868i	$-0.312729\pi$
$239$	−1.00000	−	0.726543i	−0.0646846	−	0.0469961i	−0.619658	+	0.784872i	$0.712729\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	11.8885			0.765808			0.382904	−	0.923788i	$-0.374924\pi$
$241$	11.8885			0.765808			0.382904	+	0.923788i	$0.374924\pi$
$242$	10.8992	−	1.48584i	0.700626	−	0.0955135i
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−4.42705	−	3.21644i	−0.282834	−	0.205491i
$246$	−2.61803	+	1.90211i	−0.166920	+	0.121274i
$247$	−5.61803	+	17.2905i	−0.357467	+	1.10017i
$248$	−1.11803	+	3.44095i	−0.0709952	+	0.218501i
$249$	3.23607	−	2.35114i	0.205077	−	0.148998i
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	3.28115	+	10.0984i	0.207105	+	0.637402i	0.999620	+	0.0275509i	$0.00877084\pi$
$251$	3.28115	+	10.0984i	0.207105	+	0.637402i	−0.792516	+	0.609851i	$0.791229\pi$
$252$	1.23607			0.0778650
$253$	−0.371323	+	0.310271i	−0.0233449	+	0.0195066i
$254$	−16.6525			−1.04487
$255$	1.57295	+	4.84104i	0.0985019	+	0.303158i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	11.6180	−	8.44100i	0.724713	−	0.526535i	−0.163173	−	0.986597i	$-0.552173\pi$
$257$	11.6180	−	8.44100i	0.724713	−	0.526535i	0.887887	+	0.460063i	$0.152173\pi$
$258$	−3.42705	+	10.5474i	−0.213359	+	0.656651i
$259$	−3.29180	+	10.1311i	−0.204542	+	0.629516i
$260$	4.54508	−	3.30220i	0.281874	−	0.204794i
$261$	0.309017	+	0.224514i	0.0191277	+	0.0138971i
$262$	−1.73607	−	5.34307i	−0.107255	−	0.330096i
$263$	0.145898			0.00899646			0.00449823	−	0.999990i	$-0.498568\pi$
$263$	0.145898			0.00899646			0.00449823	+	0.999990i	$0.498568\pi$
$264$	2.80902	+	1.76336i	0.172883	+	0.108527i
$265$	0.472136			0.0290031
$266$	−1.23607	−	3.80423i	−0.0757882	−	0.233252i
$267$	10.3262	+	7.50245i	0.631955	+	0.459143i
$268$	−4.92705	+	3.57971i	−0.300968	+	0.218666i
$269$	8.59017	−	26.4378i	0.523752	−	1.61194i	−0.243019	−	0.970022i	$-0.578138\pi$
$269$	8.59017	−	26.4378i	0.523752	−	1.61194i	0.766771	−	0.641921i	$-0.221862\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	6.97214	−	5.06555i	0.423527	−	0.307710i	−0.355528	−	0.934666i	$-0.615699\pi$
$271$	6.97214	−	5.06555i	0.423527	−	0.307710i	0.779055	+	0.626955i	$0.215699\pi$
$272$	−4.11803	−	2.99193i	−0.249692	−	0.181412i
$273$	−2.14590	−	6.60440i	−0.129876	−	0.399716i
$274$	11.7984			0.712766
$275$	3.30902	−	0.224514i	0.199541	−	0.0135387i
$276$	−0.145898			−0.00878203
$277$	4.48278	+	13.7966i	0.269344	+	0.828956i	0.990661	+	0.136350i	$0.0435373\pi$
$277$	4.48278	+	13.7966i	0.269344	+	0.828956i	−0.721317	+	0.692606i	$0.756463\pi$
$278$	−10.7082	−	7.77997i	−0.642235	−	0.466611i
$279$	2.92705	−	2.12663i	0.175238	−	0.127318i
$280$	−0.381966	+	1.17557i	−0.0228268	+	0.0702538i
$281$	−5.09017	+	15.6659i	−0.303654	+	0.934551i	0.676522	+	0.736422i	$0.263486\pi$
$281$	−5.09017	+	15.6659i	−0.303654	+	0.934551i	−0.980176	+	0.198129i	$0.936514\pi$
$282$	9.16312	−	6.65740i	0.545656	−	0.396442i
$283$	5.39919	+	3.92274i	0.320948	+	0.233183i	0.736580	−	0.676350i	$-0.236439\pi$
$283$	5.39919	+	3.92274i	0.320948	+	0.233183i	−0.415632	+	0.909533i	$0.636439\pi$
$284$	0.472136	+	1.45309i	0.0280161	+	0.0862247i
$285$	−3.23607			−0.191688
$286$	4.54508	−	18.0701i	0.268757	−	1.06851i
$287$	−4.00000			−0.236113
$288$	0.309017	+	0.951057i	0.0182090	+	0.0560415i
$289$	−7.20820	−	5.23707i	−0.424012	−	0.308063i
$290$	−0.309017	+	0.224514i	−0.0181461	+	0.0131839i
$291$	3.90983	−	12.0332i	0.229198	−	0.705400i
$292$	−4.14590	+	12.7598i	−0.242620	+	0.746709i
$293$	16.1803	−	11.7557i	0.945266	−	0.686776i	−0.00441682	−	0.999990i	$-0.501406\pi$
$293$	16.1803	−	11.7557i	0.945266	−	0.686776i	0.949682	+	0.313215i	$0.101406\pi$
$294$	−4.42705	−	3.21644i	−0.258191	−	0.187587i
$295$	−0.899187	−	2.76741i	−0.0523527	−	0.161125i
$296$	−8.61803			−0.500913
$297$	−1.23607	−	3.07768i	−0.0717239	−	0.178585i
$298$	−5.38197			−0.311769
$299$	0.253289	+	0.779543i	0.0146481	+	0.0450821i
$300$	0.809017	+	0.587785i	0.0467086	+	0.0339358i
$301$	−11.0902	+	8.05748i	−0.639227	+	0.464425i
$302$	0.944272	−	2.90617i	0.0543367	−	0.167231i
$303$	−4.13525	+	12.7270i	−0.237564	+	0.731147i
$304$	2.61803	−	1.90211i	0.150155	−	0.109094i
$305$		0			0
$306$	1.57295	+	4.84104i	0.0899195	+	0.276744i
$307$	22.4508			1.28134			0.640669	−	0.767817i	$-0.278657\pi$
$307$	22.4508			1.28134			0.640669	+	0.767817i	$0.278657\pi$
$308$	1.52786	+	3.80423i	0.0870581	+	0.216766i
$309$	−11.2361			−0.639198
$310$	1.11803	+	3.44095i	0.0635001	+	0.195433i
$311$	−3.85410	−	2.80017i	−0.218546	−	0.158783i	0.473126	−	0.880995i	$-0.343126\pi$
$311$	−3.85410	−	2.80017i	−0.218546	−	0.158783i	−0.691672	+	0.722212i	$0.743126\pi$
$312$	4.54508	−	3.30220i	0.257315	−	0.186950i
$313$	−0.145898	+	0.449028i	−0.00824664	+	0.0253806i	−0.955095	−	0.296299i	$-0.904247\pi$
$313$	−0.145898	+	0.449028i	−0.00824664	+	0.0253806i	0.946849	+	0.321680i	$0.104247\pi$
$314$	7.50000	−	23.0826i	0.423249	−	1.30263i
$315$	1.00000	−	0.726543i	0.0563436	−	0.0409360i
$316$	−5.73607	−	4.16750i	−0.322679	−	0.234440i
$317$	−0.180340	−	0.555029i	−0.0101289	−	0.0311735i	0.945864	−	0.324562i	$-0.105217\pi$
$317$	−0.180340	−	0.555029i	−0.0101289	−	0.0311735i	−0.955993	+	0.293389i	$0.905217\pi$
$318$	0.472136			0.0264761
$319$	−0.309017	+	1.22857i	−0.0173016	+	0.0687868i
$320$	−1.00000			−0.0559017
$321$	−6.09017	−	18.7436i	−0.339920	−	1.04617i
$322$	−0.145898	−	0.106001i	−0.00813058	−	0.00590721i
$323$	13.3262	−	9.68208i	0.741492	−	0.538725i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	1.73607	−	5.34307i	0.0962997	−	0.296380i
$326$	4.73607	−	3.44095i	0.262307	−	0.190577i
$327$	5.23607	+	3.80423i	0.289555	+	0.210374i
$328$	−1.00000	−	3.07768i	−0.0552158	−	0.169937i
$329$	14.0000			0.771845
$330$	3.30902	−	0.224514i	0.182155	−	0.0123591i
$331$	4.76393			0.261849			0.130925	−	0.991392i	$-0.458205\pi$
$331$	4.76393			0.261849			0.130925	+	0.991392i	$0.458205\pi$
$332$	1.23607	+	3.80423i	0.0678380	+	0.208784i
$333$	6.97214	+	5.06555i	0.382071	+	0.277591i
$334$	−16.3992	+	11.9147i	−0.897324	+	0.651944i
$335$	−1.88197	+	5.79210i	−0.102823	+	0.316456i
$336$	−0.381966	+	1.17557i	−0.0208380	+	0.0641326i
$337$	8.70820	−	6.32688i	0.474366	−	0.344647i	−0.324774	−	0.945792i	$-0.605288\pi$
$337$	8.70820	−	6.32688i	0.474366	−	0.344647i	0.799140	+	0.601144i	$0.205288\pi$
$338$	−15.0172	−	10.9106i	−0.816829	−	0.593461i
$339$	−0.173762	−	0.534785i	−0.00943746	−	0.0290455i
$340$	−5.09017			−0.276053
$341$	10.1631	+	6.37988i	0.550364	+	0.345490i
$342$	−3.23607			−0.174987
$343$	−4.76393	−	14.6619i	−0.257228	−	0.791667i
$344$	−8.97214	−	6.51864i	−0.483745	−	0.351461i
$345$	−0.118034	+	0.0857567i	−0.00635474	+	0.00461699i
$346$	−5.70820	+	17.5680i	−0.306875	+	0.944464i
$347$	0.0344419	−	0.106001i	0.00184894	−	0.00569044i	−0.950128	−	0.311861i	$-0.899048\pi$
$347$	0.0344419	−	0.106001i	0.00184894	−	0.00569044i	0.951977	+	0.306170i	$0.0990477\pi$
$348$	−0.309017	+	0.224514i	−0.0165650	+	0.0120352i
$349$	−12.4721	−	9.06154i	−0.667618	−	0.485053i	0.201609	−	0.979466i	$-0.435383\pi$
$349$	−12.4721	−	9.06154i	−0.667618	−	0.485053i	−0.869227	+	0.494413i	$0.835383\pi$
$350$	0.381966	+	1.17557i	0.0204169	+	0.0628369i
$351$	−5.61803			−0.299868
$352$	−2.54508	+	2.12663i	−0.135653	+	0.113350i
$353$	21.3820			1.13805			0.569024	−	0.822321i	$-0.307321\pi$
$353$	21.3820			1.13805			0.569024	+	0.822321i	$0.307321\pi$
$354$	−0.899187	−	2.76741i	−0.0477912	−	0.147086i
$355$	1.23607	+	0.898056i	0.0656037	+	0.0476639i
$356$	−10.3262	+	7.50245i	−0.547290	+	0.397629i
$357$	−1.94427	+	5.98385i	−0.102902	+	0.316699i
$358$	7.68034	−	23.6377i	0.405919	−	1.24929i
$359$	−8.23607	+	5.98385i	−0.434683	+	0.315816i	−0.783519	−	0.621368i	$-0.786577\pi$
$359$	−8.23607	+	5.98385i	−0.434683	+	0.315816i	0.348836	+	0.937184i	$0.386577\pi$
$360$	0.809017	+	0.587785i	0.0426389	+	0.0309790i
$361$	−2.63525	−	8.11048i	−0.138698	−	0.426867i
$362$	−13.8885			−0.729966
$363$	7.94427	−	7.60845i	0.416966	−	0.399340i
$364$	6.94427			0.363979
$365$	4.14590	+	12.7598i	0.217006	+	0.667876i
$366$		0			0
$367$	25.2705	−	18.3601i	1.31911	−	0.958389i	0.319167	−	0.947698i	$-0.396597\pi$
$367$	25.2705	−	18.3601i	1.31911	−	0.958389i	0.999943	−	0.0106909i	$-0.00340310\pi$
$368$	0.0450850	−	0.138757i	0.00235022	−	0.00723322i
$369$	−1.00000	+	3.07768i	−0.0520579	+	0.160218i
$370$	−6.97214	+	5.06555i	−0.362464	+	0.263346i
$371$	0.472136	+	0.343027i	0.0245121	+	0.0178091i
$372$	1.11803	+	3.44095i	0.0579674	+	0.178405i
$373$	−20.4721			−1.06001			−0.530004	−	0.847995i	$-0.677809\pi$
$373$	−20.4721			−1.06001			−0.530004	+	0.847995i	$0.677809\pi$
$374$	−12.9549	+	10.8249i	−0.669883	+	0.559742i
$375$	1.00000			0.0516398
$376$	3.50000	+	10.7719i	0.180499	+	0.555518i
$377$	1.73607	+	1.26133i	0.0894120	+	0.0649617i
$378$	1.00000	−	0.726543i	0.0514344	−	0.0373693i
$379$	10.0000	−	30.7768i	0.513665	−	1.58090i	−0.272032	−	0.962288i	$-0.587696\pi$
$379$	10.0000	−	30.7768i	0.513665	−	1.58090i	0.785697	−	0.618612i	$-0.212304\pi$
$380$	1.00000	−	3.07768i	0.0512989	−	0.157882i
$381$	−13.4721	+	9.78808i	−0.690198	+	0.501459i
$382$	−3.85410	−	2.80017i	−0.197193	−	0.143269i
$383$	4.73607	+	14.5761i	0.242002	+	0.744805i	0.996115	+	0.0880606i	$0.0280669\pi$
$383$	4.73607	+	14.5761i	0.242002	+	0.744805i	−0.754113	+	0.656744i	$0.771933\pi$
$384$	−1.00000			−0.0510310
$385$	3.47214	+	2.17963i	0.176956	+	0.111084i
$386$	−3.05573			−0.155532
$387$	3.42705	+	10.5474i	0.174207	+	0.536153i
$388$	10.2361	+	7.43694i	0.519658	+	0.377553i
$389$	−0.118034	+	0.0857567i	−0.00598456	+	0.00434804i	−0.590774	−	0.806837i	$-0.701177\pi$
$389$	−0.118034	+	0.0857567i	−0.00598456	+	0.00434804i	0.584789	+	0.811185i	$0.301177\pi$
$390$	1.73607	−	5.34307i	0.0879092	−	0.270557i
$391$	0.229490	−	0.706298i	0.0116058	−	0.0357190i
$392$	4.42705	−	3.21644i	0.223600	−	0.162455i
$393$	−4.54508	−	3.30220i	−0.229269	−	0.166574i
$394$	−2.14590	−	6.60440i	−0.108109	−	0.332725i
$395$	−7.09017			−0.356745
$396$	3.30902	−	0.224514i	0.166284	−	0.0112823i
$397$	26.7984			1.34497			0.672486	−	0.740110i	$-0.265227\pi$
$397$	26.7984			1.34497			0.672486	+	0.740110i	$0.265227\pi$
$398$	−6.48278	−	19.9519i	−0.324952	−	1.00010i
$399$	−3.23607	−	2.35114i	−0.162006	−	0.117704i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−11.1459	+	34.3035i	−0.556600	+	1.71304i	0.135082	+	0.990834i	$0.456870\pi$
$401$	−11.1459	+	34.3035i	−0.556600	+	1.71304i	−0.691681	+	0.722203i	$0.743130\pi$
$402$	−1.88197	+	5.79210i	−0.0938639	+	0.288883i
$403$	16.4443	−	11.9475i	0.819148	−	0.595146i
$404$	−10.8262	−	7.86572i	−0.538625	−	0.391334i
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	−0.472136			−0.0234317
$407$	−6.97214	+	27.7194i	−0.345596	+	1.37400i
$408$	−5.09017			−0.252001
$409$	−10.5000	−	32.3157i	−0.519192	−	1.59791i	−0.775524	−	0.631319i	$-0.782514\pi$
$409$	−10.5000	−	32.3157i	−0.519192	−	1.59791i	0.256332	−	0.966589i	$-0.417486\pi$
$410$	−2.61803	−	1.90211i	−0.129295	−	0.0939387i
$411$	9.54508	−	6.93491i	0.470824	−	0.342074i
$412$	3.47214	−	10.6861i	0.171060	−	0.526468i
$413$	1.11146	−	3.42071i	0.0546912	−	0.168322i
$414$	−0.118034	+	0.0857567i	−0.00580105	+	0.00421471i
$415$	3.23607	+	2.35114i	0.158852	+	0.115413i
$416$	1.73607	+	5.34307i	0.0851177	+	0.261965i
$417$	−13.2361			−0.648173
$418$	−4.00000	−	9.95959i	−0.195646	−	0.487140i
$419$	16.1459			0.788779			0.394389	−	0.918943i	$-0.370956\pi$
$419$	16.1459			0.788779			0.394389	+	0.918943i	$0.370956\pi$
$420$	0.381966	+	1.17557i	0.0186380	+	0.0573620i
$421$	−5.23607	−	3.80423i	−0.255190	−	0.185407i	0.452834	−	0.891595i	$-0.350413\pi$
$421$	−5.23607	−	3.80423i	−0.255190	−	0.185407i	−0.708024	+	0.706188i	$0.750413\pi$
$422$	16.7984	−	12.2047i	0.817732	−	0.594117i
$423$	3.50000	−	10.7719i	0.170176	−	0.523747i
$424$	−0.145898	+	0.449028i	−0.00708543	+	0.0218067i
$425$	−4.11803	+	2.99193i	−0.199754	+	0.145130i
$426$	1.23607	+	0.898056i	0.0598877	+	0.0435110i
$427$		0			0
$428$	19.7082			0.952632
$429$	−6.94427	−	17.2905i	−0.335273	−	0.834795i
$430$	−11.0902			−0.534815
$431$	−6.90983	−	21.2663i	−0.332835	−	1.02436i	−0.967779	−	0.251802i	$-0.918977\pi$
$431$	−6.90983	−	21.2663i	−0.332835	−	1.02436i	0.634944	−	0.772558i	$-0.281023\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	−24.9443	+	18.1231i	−1.19875	+	0.870939i	−0.994161	−	0.107910i	$-0.965584\pi$
$433$	−24.9443	+	18.1231i	−1.19875	+	0.870939i	−0.204584	+	0.978849i	$0.565584\pi$
$434$	−1.38197	+	4.25325i	−0.0663365	+	0.204163i
$435$	−0.118034	+	0.363271i	−0.00565930	+	0.0174175i
$436$	−5.23607	+	3.80423i	−0.250762	+	0.182189i
$437$	0.381966	+	0.277515i	0.0182719	+	0.0132753i
$438$	4.14590	+	12.7598i	0.198099	+	0.609685i
$439$	17.3262			0.826936			0.413468	−	0.910519i	$-0.364317\pi$
$439$	17.3262			0.826936			0.413468	+	0.910519i	$0.364317\pi$
$440$	−0.809017	+	3.21644i	−0.0385684	+	0.153338i
$441$	−5.47214			−0.260578
$442$	8.83688	+	27.1971i	0.420328	+	1.29364i
$443$	−10.2361	−	7.43694i	−0.486330	−	0.353340i	0.317441	−	0.948278i	$-0.397176\pi$
$443$	−10.2361	−	7.43694i	−0.486330	−	0.353340i	−0.803771	+	0.594938i	$0.797176\pi$
$444$	−6.97214	+	5.06555i	−0.330883	+	0.240401i
$445$	−3.94427	+	12.1392i	−0.186976	+	0.575454i
$446$	0.854102	−	2.62866i	0.0404429	−	0.124470i
$447$	−4.35410	+	3.16344i	−0.205942	+	0.149626i
$448$	−1.00000	−	0.726543i	−0.0472456	−	0.0343259i
$449$	9.00000	+	27.6992i	0.424736	+	1.30720i	0.903247	+	0.429122i	$0.141177\pi$
$449$	9.00000	+	27.6992i	0.424736	+	1.30720i	−0.478510	+	0.878082i	$0.658823\pi$
$450$	1.00000			0.0471405
$451$	−10.7082	+	0.726543i	−0.504230	+	0.0342116i
$452$	0.562306			0.0264486
$453$	−0.944272	−	2.90617i	−0.0443658	−	0.136544i
$454$	19.7082	+	14.3188i	0.924952	+	0.672017i
$455$	5.61803	−	4.08174i	0.263377	−	0.191355i
$456$	1.00000	−	3.07768i	0.0468293	−	0.144126i
$457$	−8.23607	+	25.3480i	−0.385267	+	1.18573i	0.551019	+	0.834492i	$0.314239\pi$
$457$	−8.23607	+	25.3480i	−0.385267	+	1.18573i	−0.936286	+	0.351237i	$0.885761\pi$
$458$	−4.23607	+	3.07768i	−0.197938	+	0.143811i
$459$	4.11803	+	2.99193i	0.192213	+	0.139651i
$460$	−0.0450850	−	0.138757i	−0.00210210	−	0.00646959i
$461$	−28.2148			−1.31409			−0.657047	−	0.753850i	$-0.728195\pi$
$461$	−28.2148			−1.31409			−0.657047	+	0.753850i	$0.728195\pi$
$462$	3.47214	+	2.17963i	0.161538	+	0.101405i
$463$	−23.8885			−1.11019			−0.555097	−	0.831785i	$-0.687319\pi$
$463$	−23.8885			−1.11019			−0.555097	+	0.831785i	$0.687319\pi$
$464$	−0.118034	−	0.363271i	−0.00547959	−	0.0168644i
$465$	2.92705	+	2.12663i	0.135739	+	0.0986200i
$466$	19.8713	−	14.4374i	0.920521	−	0.668798i
$467$	−11.9098	+	36.6547i	−0.551121	+	1.69618i	0.154852	+	0.987938i	$0.450510\pi$
$467$	−11.9098	+	36.6547i	−0.551121	+	1.69618i	−0.705973	+	0.708239i	$0.749490\pi$
$468$	1.73607	−	5.34307i	0.0802498	−	0.246983i
$469$	−6.09017	+	4.42477i	−0.281218	+	0.204317i
$470$	9.16312	+	6.65740i	0.422663	+	0.307083i
$471$	−7.50000	−	23.0826i	−0.345582	−	1.06359i
$472$	2.90983			0.133936
$473$	−28.2254	+	23.5847i	−1.29781	+	1.08442i
$474$	−7.09017			−0.325662
$475$	−1.00000	−	3.07768i	−0.0458831	−	0.141214i
$476$	−5.09017	−	3.69822i	−0.233308	−	0.169508i
$477$	0.381966	−	0.277515i	0.0174890	−	0.0127065i
$478$	0.381966	−	1.17557i	0.0174707	−	0.0537693i
$479$	5.32624	−	16.3925i	0.243362	−	0.748991i	−0.752540	−	0.658547i	$-0.771171\pi$
$479$	5.32624	−	16.3925i	0.243362	−	0.748991i	0.995902	−	0.0904442i	$-0.0288287\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	39.1697	+	28.4585i	1.78598	+	1.29759i
$482$	3.67376	+	11.3067i	0.167335	+	0.515005i
$483$	−0.180340			−0.00820575
$484$	4.78115	+	9.90659i	0.217325	+	0.450300i
$485$	12.6525			0.574519
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	12.4721	+	9.06154i	0.565166	+	0.410617i	0.833346	−	0.552751i	$-0.186422\pi$
$487$	12.4721	+	9.06154i	0.565166	+	0.410617i	−0.268180	+	0.963369i	$0.586422\pi$
$488$		0			0
$489$	1.80902	−	5.56758i	0.0818066	−	0.251775i
$490$	1.69098	−	5.20431i	0.0763908	−	0.235107i
$491$	0.836881	−	0.608030i	0.0377679	−	0.0274400i	−0.568741	−	0.822517i	$-0.692569\pi$
$491$	0.836881	−	0.608030i	0.0377679	−	0.0274400i	0.606509	+	0.795077i	$0.292569\pi$
$492$	−2.61803	−	1.90211i	−0.118030	−	0.0857539i
$493$	−0.600813	−	1.84911i	−0.0270593	−	0.0832798i
$494$	−18.1803			−0.817972
$495$	2.54508	−	2.12663i	0.114393	−	0.0955848i
$496$	−3.61803			−0.162455
$497$	0.583592	+	1.79611i	0.0261777	+	0.0805666i
$498$	3.23607	+	2.35114i	0.145012	+	0.105357i
$499$	19.0344	−	13.8293i	0.852099	−	0.619086i	−0.0736252	−	0.997286i	$-0.523457\pi$
$499$	19.0344	−	13.8293i	0.852099	−	0.619086i	0.925724	+	0.378200i	$0.123457\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−6.26393	+	19.2784i	−0.279852	+	0.861295i
$502$	−8.59017	+	6.24112i	−0.383398	+	0.278555i
$503$	7.01722	+	5.09831i	0.312882	+	0.227322i	0.733132	−	0.680086i	$-0.238058\pi$
$503$	7.01722	+	5.09831i	0.312882	+	0.227322i	−0.420250	+	0.907408i	$0.638058\pi$
$504$	0.381966	+	1.17557i	0.0170141	+	0.0523641i
$505$	−13.3820			−0.595490
$506$	−0.409830	−	0.257270i	−0.0182192	−	0.0114371i
$507$	−18.5623			−0.824381
$508$	−5.14590	−	15.8374i	−0.228312	−	0.702673i
$509$	12.7812	+	9.28605i	0.566515	+	0.411597i	0.833837	−	0.552010i	$-0.186139\pi$
$509$	12.7812	+	9.28605i	0.566515	+	0.411597i	−0.267323	+	0.963607i	$0.586139\pi$
$510$	−4.11803	+	2.99193i	−0.182350	+	0.132485i
$511$	−5.12461	+	15.7719i	−0.226699	+	0.697709i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−2.61803	+	1.90211i	−0.115589	+	0.0839803i
$514$	11.6180	+	8.44100i	0.512450	+	0.372316i
$515$	−3.47214	−	10.6861i	−0.153001	−	0.470887i
$516$	−11.0902			−0.488218
$517$	37.4787	−	2.54290i	1.64831	−	0.111837i
$518$	−10.6525			−0.468043
$519$	5.70820	+	17.5680i	0.250562	+	0.771152i
$520$	4.54508	+	3.30220i	0.199315	+	0.144811i
$521$	−34.2705	+	24.8990i	−1.50142	+	1.09084i	−0.531606	+	0.846992i	$0.678411\pi$
$521$	−34.2705	+	24.8990i	−1.50142	+	1.09084i	−0.969812	+	0.243852i	$0.921589\pi$
$522$	−0.118034	+	0.363271i	−0.00516621	+	0.0159000i
$523$	−4.58359	+	14.1068i	−0.200426	+	0.616849i	0.799444	+	0.600741i	$0.205128\pi$
$523$	−4.58359	+	14.1068i	−0.200426	+	0.616849i	−0.999870	+	0.0161084i	$0.994872\pi$
$524$	4.54508	−	3.30220i	0.198553	−	0.144257i
$525$	1.00000	+	0.726543i	0.0436436	+	0.0317089i
$526$	0.0450850	+	0.138757i	0.00196580	+	0.00605010i
$527$	−18.4164			−0.802231
$528$	−0.809017	+	3.21644i	−0.0352079	+	0.139978i
$529$	−22.9787			−0.999075
$530$	0.145898	+	0.449028i	0.00633741	+	0.0195045i
$531$	−2.35410	−	1.71036i	−0.102159	−	0.0742231i
$532$	3.23607	−	2.35114i	0.140301	−	0.101935i
$533$	−5.61803	+	17.2905i	−0.243344	+	0.748936i
$534$	−3.94427	+	12.1392i	−0.170685	+	0.525315i
$535$	15.9443	−	11.5842i	0.689331	−	0.500828i
$536$	−4.92705	−	3.57971i	−0.212816	−	0.154620i
$537$	−7.68034	−	23.6377i	−0.331431	−	1.02004i
$538$	27.7984			1.19847
$539$	−6.76393	−	16.8415i	−0.291343	−	0.725415i
$540$	1.00000			0.0430331
$541$	−9.90983	−	30.4993i	−0.426057	−	1.31127i	−0.901979	−	0.431781i	$-0.857885\pi$
$541$	−9.90983	−	30.4993i	−0.426057	−	1.31127i	0.475922	−	0.879488i	$-0.342115\pi$
$542$	6.97214	+	5.06555i	0.299479	+	0.217584i
$543$	−11.2361	+	8.16348i	−0.482186	+	0.350329i
$544$	1.57295	−	4.84104i	0.0674396	−	0.207558i
$545$	−2.00000	+	6.15537i	−0.0856706	+	0.263667i
$546$	5.61803	−	4.08174i	0.240430	−	0.174682i
$547$	−15.1074	−	10.9762i	−0.645945	−	0.469307i	0.215942	−	0.976406i	$-0.430718\pi$
$547$	−15.1074	−	10.9762i	−0.645945	−	0.469307i	−0.861888	+	0.507099i	$0.830718\pi$
$548$	3.64590	+	11.2209i	0.155745	+	0.479334i
$549$		0			0
$550$	1.23607	+	3.07768i	0.0527061	+	0.131233i
$551$	1.23607			0.0526583
$552$	−0.0450850	−	0.138757i	−0.00191894	−	0.00590590i
$553$	−7.09017	−	5.15131i	−0.301505	−	0.219056i
$554$	−11.7361	+	8.52675i	−0.498618	+	0.362267i
$555$	−2.66312	+	8.19624i	−0.113043	+	0.347911i
$556$	4.09017	−	12.5882i	0.173462	−	0.533861i
$557$	−4.14590	+	3.01217i	−0.175667	+	0.127630i	−0.672145	−	0.740420i	$-0.734627\pi$
$557$	−4.14590	+	3.01217i	−0.175667	+	0.127630i	0.496477	+	0.868050i	$0.334627\pi$
$558$	2.92705	+	2.12663i	0.123912	+	0.0900273i
$559$	19.2533	+	59.2555i	0.814327	+	2.50624i
$560$	−1.23607			−0.0522334
$561$	−4.11803	+	16.3722i	−0.173864	+	0.691236i
$562$	−16.4721			−0.694835
$563$	10.7984	+	33.2340i	0.455097	+	1.40065i	0.871021	+	0.491246i	$0.163458\pi$
$563$	10.7984	+	33.2340i	0.455097	+	1.40065i	−0.415924	+	0.909399i	$0.636542\pi$
$564$	9.16312	+	6.65740i	0.385837	+	0.280327i
$565$	0.454915	−	0.330515i	0.0191384	−	0.0139049i
$566$	−2.06231	+	6.34712i	−0.0866852	+	0.266790i
$567$	0.381966	−	1.17557i	0.0160411	−	0.0493693i
$568$	−1.23607	+	0.898056i	−0.0518643	+	0.0376816i
$569$	−1.14590	−	0.832544i	−0.0480385	−	0.0349020i	0.563507	−	0.826111i	$-0.309452\pi$
$569$	−1.14590	−	0.832544i	−0.0480385	−	0.0349020i	−0.611545	+	0.791209i	$0.709452\pi$
$570$	−1.00000	−	3.07768i	−0.0418854	−	0.128910i
$571$	16.3607			0.684673			0.342337	−	0.939577i	$-0.388782\pi$
$571$	16.3607			0.684673			0.342337	+	0.939577i	$0.388782\pi$
$572$	18.5902	−	1.26133i	0.777294	−	0.0527387i
$573$	−4.76393			−0.199016
$574$	−1.23607	−	3.80423i	−0.0515925	−	0.158785i
$575$	−0.118034	−	0.0857567i	−0.00492236	−	0.00357630i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	10.7984	−	33.2340i	0.449542	−	1.38355i	−0.427883	−	0.903834i	$-0.640740\pi$
$577$	10.7984	−	33.2340i	0.449542	−	1.38355i	0.877425	−	0.479714i	$-0.159260\pi$
$578$	2.75329	−	8.47375i	0.114522	−	0.352462i
$579$	−2.47214	+	1.79611i	−0.102738	+	0.0746439i
$580$	−0.309017	−	0.224514i	−0.0128312	−	0.00932244i
$581$	1.52786	+	4.70228i	0.0633865	+	0.195084i
$582$	12.6525			0.524462
$583$	1.32624	+	0.832544i	0.0549272	+	0.0344804i
$584$	−13.4164			−0.555175
$585$	−1.73607	−	5.34307i	−0.0717776	−	0.220909i
$586$	16.1803	+	11.7557i	0.668404	+	0.485624i
$587$	32.1246	−	23.3399i	1.32592	−	0.963341i	0.326087	−	0.945340i	$-0.394270\pi$
$587$	32.1246	−	23.3399i	1.32592	−	0.963341i	0.999838	−	0.0180007i	$-0.00573013\pi$
$588$	1.69098	−	5.20431i	0.0697350	−	0.214622i
$589$	3.61803	−	11.1352i	0.149078	−	0.458816i
$590$	2.35410	−	1.71036i	0.0969168	−	0.0704142i
$591$	−5.61803	−	4.08174i	−0.231095	−	0.167900i
$592$	−2.66312	−	8.19624i	−0.109454	−	0.336863i
$593$	−33.3262			−1.36854			−0.684272	−	0.729227i	$-0.739880\pi$
$593$	−33.3262			−1.36854			−0.684272	+	0.729227i	$0.739880\pi$
$594$	2.54508	−	2.12663i	0.104426	−	0.0872566i
$595$	−6.29180			−0.257938
$596$	−1.66312	−	5.11855i	−0.0681240	−	0.209664i
$597$	−16.9721	−	12.3310i	−0.694623	−	0.504673i
$598$	−0.663119	+	0.481784i	−0.0271170	+	0.0197016i
$599$	−1.29180	+	3.97574i	−0.0527814	+	0.162444i	−0.973973	−	0.226666i	$-0.927217\pi$
$599$	−1.29180	+	3.97574i	−0.0527814	+	0.162444i	0.921191	+	0.389110i	$0.127217\pi$
$600$	−0.309017	+	0.951057i	−0.0126156	+	0.0388267i
$601$	0.854102	−	0.620541i	0.0348395	−	0.0253124i	−0.570229	−	0.821486i	$-0.693146\pi$
$601$	0.854102	−	0.620541i	0.0348395	−	0.0253124i	0.605069	+	0.796173i	$0.293146\pi$
$602$	−11.0902	−	8.05748i	−0.452002	−	0.328398i
$603$	1.88197	+	5.79210i	0.0766396	+	0.235872i
$604$	3.05573			0.124336
$605$	9.69098	+	5.20431i	0.393994	+	0.211585i
$606$	−13.3820			−0.543605
$607$	1.38197	+	4.25325i	0.0560923	+	0.172634i	0.975178	−	0.221425i	$-0.0710706\pi$
$607$	1.38197	+	4.25325i	0.0560923	+	0.172634i	−0.919085	+	0.394059i	$0.871071\pi$
$608$	2.61803	+	1.90211i	0.106175	+	0.0771409i
$609$	−0.381966	+	0.277515i	−0.0154780	+	0.0112455i
$610$		0			0
$611$	19.6631	−	60.5169i	0.795485	−	2.44825i
$612$	−4.11803	+	2.99193i	−0.166462	+	0.120941i
$613$	−4.85410	−	3.52671i	−0.196055	−	0.142443i	0.485427	−	0.874277i	$-0.338664\pi$
$613$	−4.85410	−	3.52671i	−0.196055	−	0.142443i	−0.681482	+	0.731835i	$0.738664\pi$
$614$	6.93769	+	21.3520i	0.279983	+	0.861698i
$615$	−3.23607			−0.130491
$616$	−3.14590	+	2.62866i	−0.126752	+	0.105912i
$617$	−18.3607			−0.739173			−0.369587	−	0.929196i	$-0.620501\pi$
$617$	−18.3607			−0.739173			−0.369587	+	0.929196i	$0.620501\pi$
$618$	−3.47214	−	10.6861i	−0.139670	−	0.429859i
$619$	−14.9443	−	10.8576i	−0.600661	−	0.436406i	0.245452	−	0.969409i	$-0.421063\pi$
$619$	−14.9443	−	10.8576i	−0.600661	−	0.436406i	−0.846113	+	0.533003i	$0.821063\pi$
$620$	−2.92705	+	2.12663i	−0.117553	+	0.0854074i
$621$	−0.0450850	+	0.138757i	−0.00180920	+	0.00556814i
$622$	1.47214	−	4.53077i	0.0590273	−	0.181667i
$623$	−12.7639	+	9.27354i	−0.511376	+	0.371537i
$624$	4.54508	+	3.30220i	0.181949	+	0.132194i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−0.472136			−0.0188703
$627$	−9.09017	−	5.70634i	−0.363026	−	0.227889i
$628$	24.2705			0.968499
$629$	−13.5557	−	41.7202i	−0.540502	−	1.66349i
$630$	1.00000	+	0.726543i	0.0398410	+	0.0289461i
$631$	17.2533	−	12.5352i	0.686843	−	0.499020i	−0.188778	−	0.982020i	$-0.560453\pi$
$631$	17.2533	−	12.5352i	0.686843	−	0.499020i	0.875621	+	0.482999i	$0.160453\pi$
$632$	2.19098	−	6.74315i	0.0871526	−	0.268228i
$633$	6.41641	−	19.7477i	0.255029	−	0.784900i
$634$	0.472136	−	0.343027i	0.0187509	−	0.0136233i
$635$	−13.4721	−	9.78808i	−0.534625	−	0.388428i
$636$	0.145898	+	0.449028i	0.00578523	+	0.0178051i
$637$	−30.7426			−1.21807
$638$	−1.26393	+	0.0857567i	−0.0500395	+	0.00339514i
$639$	1.52786			0.0604414
$640$	−0.309017	−	0.951057i	−0.0122150	−	0.0375938i
$641$	8.23607	+	5.98385i	0.325305	+	0.236348i	0.738436	−	0.674324i	$-0.235565\pi$
$641$	8.23607	+	5.98385i	0.325305	+	0.236348i	−0.413131	+	0.910672i	$0.635565\pi$
$642$	15.9443	−	11.5842i	0.629270	−	0.457192i
$643$	6.11803	−	18.8294i	0.241272	−	0.742558i	−0.754956	−	0.655776i	$-0.772342\pi$
$643$	6.11803	−	18.8294i	0.241272	−	0.742558i	0.996227	−	0.0867821i	$-0.0276584\pi$
$644$	0.0557281	−	0.171513i	0.00219599	−	0.00675858i
$645$	−8.97214	+	6.51864i	−0.353278	+	0.256671i
$646$	13.3262	+	9.68208i	0.524314	+	0.380936i
$647$	−4.51722	−	13.9026i	−0.177590	−	0.546567i	0.822152	−	0.569268i	$-0.192773\pi$
$647$	−4.51722	−	13.9026i	−0.177590	−	0.546567i	−0.999742	+	0.0227013i	$0.992773\pi$
$648$	1.00000			0.0392837
$649$	2.35410	−	9.35930i	0.0924066	−	0.367385i
$650$	5.61803			0.220357
$651$	1.38197	+	4.25325i	0.0541635	+	0.166698i
$652$	4.73607	+	3.44095i	0.185479	+	0.134758i
$653$	34.4164	−	25.0050i	1.34682	−	0.978521i	0.347655	−	0.937623i	$-0.386978\pi$
$653$	34.4164	−	25.0050i	1.34682	−	0.978521i	0.999163	−	0.0408980i	$-0.0130219\pi$
$654$	−2.00000	+	6.15537i	−0.0782062	+	0.240694i
$655$	1.73607	−	5.34307i	0.0678338	−	0.208771i
$656$	2.61803	−	1.90211i	0.102217	−	0.0742650i
$657$	10.8541	+	7.88597i	0.423459	+	0.307661i
$658$	4.32624	+	13.3148i	0.168654	+	0.519065i
$659$	11.4164			0.444720			0.222360	−	0.974965i	$-0.428624\pi$
$659$	11.4164			0.444720			0.222360	+	0.974965i	$0.428624\pi$
$660$	1.23607	+	3.07768i	0.0481139	+	0.119799i
$661$	−36.3607			−1.41427			−0.707133	−	0.707080i	$-0.750012\pi$
$661$	−36.3607			−1.41427			−0.707133	+	0.707080i	$0.750012\pi$
$662$	1.47214	+	4.53077i	0.0572162	+	0.176093i
$663$	23.1353	+	16.8087i	0.898499	+	0.652798i
$664$	−3.23607	+	2.35114i	−0.125584	+	0.0912420i
$665$	1.23607	−	3.80423i	0.0479327	−	0.147522i
$666$	−2.66312	+	8.19624i	−0.103194	+	0.317598i
$667$	0.0450850	−	0.0327561i	0.00174570	−	0.00126832i
$668$	−16.3992	−	11.9147i	−0.634504	−	0.460994i
$669$	−0.854102	−	2.62866i	−0.0330215	−	0.101630i
$670$	−6.09017			−0.235284
$671$		0			0
$672$	−1.23607			−0.0476824
$673$	−0.708204	−	2.17963i	−0.0272993	−	0.0840185i	0.936479	−	0.350725i	$-0.114065\pi$
$673$	−0.708204	−	2.17963i	−0.0272993	−	0.0840185i	−0.963778	+	0.266706i	$0.914065\pi$
$674$	8.70820	+	6.32688i	0.335427	+	0.243702i
$675$	0.809017	−	0.587785i	0.0311391	−	0.0226239i
$676$	5.73607	−	17.6538i	0.220618	−	0.678992i
$677$	7.03444	−	21.6498i	0.270356	−	0.832069i	−0.720055	−	0.693917i	$-0.755884\pi$
$677$	7.03444	−	21.6498i	0.270356	−	0.832069i	0.990411	−	0.138152i	$-0.0441163\pi$
$678$	0.454915	−	0.330515i	0.0174709	−	0.0126934i
$679$	12.6525	+	9.19256i	0.485557	+	0.352778i
$680$	−1.57295	−	4.84104i	−0.0603198	−	0.185645i
$681$	24.3607			0.933503
$682$	−2.92705	+	11.6372i	−0.112083	+	0.445611i
$683$	−19.1246			−0.731783			−0.365891	−	0.930658i	$-0.619236\pi$
$683$	−19.1246			−0.731783			−0.365891	+	0.930658i	$0.619236\pi$
$684$	−1.00000	−	3.07768i	−0.0382360	−	0.117678i
$685$	9.54508	+	6.93491i	0.364699	+	0.264969i
$686$	12.4721	−	9.06154i	0.476188	−	0.345971i
$687$	−1.61803	+	4.97980i	−0.0617318	+	0.189991i
$688$	3.42705	−	10.5474i	0.130655	−	0.402115i
$689$	2.14590	−	1.55909i	0.0817522	−	0.0593965i
$690$	−0.118034	−	0.0857567i	−0.00449348	−	0.00326470i
$691$	3.29180	+	10.1311i	0.125226	+	0.385405i	0.993942	−	0.109904i	$-0.0350545\pi$
$691$	3.29180	+	10.1311i	0.125226	+	0.385405i	−0.868716	+	0.495310i	$0.835054\pi$
$692$	−18.4721			−0.702205
$693$	4.09017	−	0.277515i	0.155373	−	0.0105419i
$694$	0.111456			0.00423082
$695$	−4.09017	−	12.5882i	−0.155149	−	0.477499i
$696$	−0.309017	−	0.224514i	−0.0117133	−	0.00851018i
$697$	13.3262	−	9.68208i	0.504767	−	0.366735i
$698$	4.76393	−	14.6619i	0.180317	−	0.554960i
$699$	7.59017	−	23.3601i	0.287087	−	0.883562i
$700$	−1.00000	+	0.726543i	−0.0377964	+	0.0274607i
$701$	10.0902	+	7.33094i	0.381100	+	0.276886i	0.761799	−	0.647814i	$-0.224316\pi$
$701$	10.0902	+	7.33094i	0.381100	+	0.276886i	−0.380698	+	0.924699i	$0.624316\pi$
$702$	−1.73607	−	5.34307i	−0.0655237	−	0.201661i
$703$	27.8885			1.05184
$704$	−2.80902	−	1.76336i	−0.105869	−	0.0664590i
$705$	11.3262			0.426571
$706$	6.60739	+	20.3355i	0.248672	+	0.765335i
$707$	−13.3820	−	9.72257i	−0.503281	−	0.365655i
$708$	2.35410	−	1.71036i	0.0884726	−	0.0642791i
$709$	−11.5623	+	35.5851i	−0.434232	+	1.33643i	0.459641	+	0.888105i	$0.347978\pi$
$709$	−11.5623	+	35.5851i	−0.434232	+	1.33643i	−0.893872	+	0.448322i	$0.852022\pi$
$710$	−0.472136	+	1.45309i	−0.0177189	+	0.0545333i
$711$	−5.73607	+	4.16750i	−0.215119	+	0.156293i
$712$	−10.3262	−	7.50245i	−0.386992	−	0.281166i
$713$	−0.163119	−	0.502029i	−0.00610885	−	0.0188011i
$714$	−6.29180			−0.235465
$715$	14.2984	−	11.9475i	0.534729	−	0.446810i
$716$	24.8541			0.928841
$717$	−0.381966	−	1.17557i	−0.0142648	−	0.0439025i
$718$	−8.23607	−	5.98385i	−0.307367	−	0.223315i
$719$	−7.56231	+	5.49434i	−0.282026	+	0.204904i	−0.719801	−	0.694181i	$-0.755767\pi$
$719$	−7.56231	+	5.49434i	−0.282026	+	0.204904i	0.437774	+	0.899085i	$0.355767\pi$
$720$	−0.309017	+	0.951057i	−0.0115164	+	0.0354438i
$721$	4.29180	−	13.2088i	0.159835	−	0.491921i
$722$	6.89919	−	5.01255i	0.256761	−	0.186548i
$723$	9.61803	+	6.98791i	0.357699	+	0.259883i
$724$	−4.29180	−	13.2088i	−0.159503	−	0.490901i
$725$	−0.381966			−0.0141859
$726$	9.69098	+	5.20431i	0.359666	+	0.193150i
$727$	−27.8197			−1.03177			−0.515887	−	0.856657i	$-0.672538\pi$
$727$	−27.8197			−1.03177			−0.515887	+	0.856657i	$0.672538\pi$
$728$	2.14590	+	6.60440i	0.0795323	+	0.244775i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−10.8541	+	7.88597i	−0.401728	+	0.291873i
$731$	17.4443	−	53.6879i	0.645200	−	1.98572i
$732$		0			0
$733$	−28.8607	+	20.9685i	−1.06599	+	0.774490i	−0.975188	−	0.221379i	$-0.928944\pi$
$733$	−28.8607	+	20.9685i	−1.06599	+	0.774490i	−0.0908057	+	0.995869i	$0.528944\pi$
$734$	25.2705	+	18.3601i	0.932752	+	0.677684i
$735$	−1.69098	−	5.20431i	−0.0623728	−	0.191964i
$736$	0.145898			0.00537787
$737$	−15.5000	+	12.9515i	−0.570950	+	0.477075i
$738$	−3.23607			−0.119121
$739$	−15.1459	−	46.6143i	−0.557151	−	1.71473i	−0.690195	−	0.723624i	$-0.742475\pi$
$739$	−15.1459	−	46.6143i	−0.557151	−	1.71473i	0.133044	−	0.991110i	$-0.457525\pi$
$740$	−6.97214	−	5.06555i	−0.256301	−	0.186213i
$741$	−14.7082	+	10.6861i	−0.540319	+	0.392565i
$742$	−0.180340	+	0.555029i	−0.00662049	+	0.0203758i
$743$	−4.26393	+	13.1230i	−0.156428	+	0.481437i	−0.998303	−	0.0582362i	$-0.981452\pi$
$743$	−4.26393	+	13.1230i	−0.156428	+	0.481437i	0.841874	+	0.539674i	$0.181452\pi$
$744$	−2.92705	+	2.12663i	−0.107311	+	0.0779659i
$745$	−4.35410	−	3.16344i	−0.159522	−	0.115899i
$746$	−6.32624	−	19.4702i	−0.231620	−	0.712853i
$747$	4.00000			0.146352
$748$	−14.2984	−	8.97578i	−0.522800	−	0.328187i
$749$	24.3607			0.890120
$750$	0.309017	+	0.951057i	0.0112837	+	0.0347277i
$751$	−0.0278640	−	0.0202444i	−0.00101677	−	0.000738729i	0.587277	−	0.809386i	$-0.300200\pi$
$751$	−0.0278640	−	0.0202444i	−0.00101677	−	0.000738729i	−0.588294	+	0.808647i	$0.700200\pi$
$752$	−9.16312	+	6.65740i	−0.334145	+	0.242770i
$753$	−3.28115	+	10.0984i	−0.119572	+	0.368004i
$754$	−0.663119	+	2.04087i	−0.0241494	+	0.0743241i
$755$	2.47214	−	1.79611i	0.0899702	−	0.0653672i
$756$	1.00000	+	0.726543i	0.0363696	+	0.0264241i
$757$	−14.5689	−	44.8384i	−0.529515	−	1.62968i	−0.755211	−	0.655482i	$-0.772466\pi$
$757$	−14.5689	−	44.8384i	−0.529515	−	1.62968i	0.225696	−	0.974198i	$-0.427534\pi$
$758$	32.3607			1.17539
$759$	−0.482779	+	0.0327561i	−0.0175238	+	0.00118897i
$760$	3.23607			0.117385
$761$	−3.09017	−	9.51057i	−0.112019	−	0.344758i	0.879295	−	0.476278i	$-0.158014\pi$
$761$	−3.09017	−	9.51057i	−0.112019	−	0.344758i	−0.991314	+	0.131520i	$0.958014\pi$
$762$	−13.4721	−	9.78808i	−0.488044	−	0.354585i
$763$	−6.47214	+	4.70228i	−0.234307	+	0.170234i
$764$	1.47214	−	4.53077i	0.0532600	−	0.163917i
$765$	−1.57295	+	4.84104i	−0.0568701	+	0.175028i
$766$	−12.3992	+	9.00854i	−0.448001	+	0.325492i
$767$	−13.2254	−	9.60883i	−0.477542	−	0.346955i
$768$	−0.309017	−	0.951057i	−0.0111507	−	0.0343183i
$769$	31.4508			1.13415			0.567073	−	0.823667i	$-0.308076\pi$
$769$	31.4508			1.13415			0.567073	+	0.823667i	$0.308076\pi$
$770$	−1.00000	+	3.97574i	−0.0360375	+	0.143276i
$771$	14.3607			0.517187
$772$	−0.944272	−	2.90617i	−0.0339851	−	0.104595i
$773$	23.9443	+	17.3965i	0.861216	+	0.625710i	0.928215	−	0.372043i	$-0.121343\pi$
$773$	23.9443	+	17.3965i	0.861216	+	0.625710i	−0.0669998	+	0.997753i	$0.521343\pi$
$774$	−8.97214	+	6.51864i	−0.322497	+	0.234308i
$775$	−1.11803	+	3.44095i	−0.0401610	+	0.123603i
$776$	−3.90983	+	12.0332i	−0.140355	+	0.431967i
$777$	−8.61803	+	6.26137i	−0.309170	+	0.224625i
$778$	−0.118034	−	0.0857567i	−0.00423172	−	0.00307453i
$779$	3.23607	+	9.95959i	0.115944	+	0.356839i
$780$	5.61803			0.201158
$781$	1.88854	+	4.70228i	0.0675774	+	0.168261i
$782$	0.742646			0.0265570
$783$	0.118034	+	0.363271i	0.00421819	+	0.0129823i
$784$	4.42705	+	3.21644i	0.158109	+	0.114873i
$785$	19.6353	−	14.2658i	0.700812	−	0.509170i
$786$	1.73607	−	5.34307i	0.0619235	−	0.190581i
$787$	−2.48278	+	7.64121i	−0.0885015	+	0.272380i	−0.985506	−	0.169642i	$-0.945739\pi$
$787$	−2.48278	+	7.64121i	−0.0885015	+	0.272380i	0.897004	+	0.442022i	$0.145739\pi$
$788$	5.61803	−	4.08174i	0.200134	−	0.145406i
$789$	0.118034	+	0.0857567i	0.00420212	+	0.00305302i
$790$	−2.19098	−	6.74315i	−0.0779517	−	0.239911i
$791$	0.695048			0.0247131
$792$	1.23607	+	3.07768i	0.0439218	+	0.109361i
$793$		0			0
$794$	8.28115	+	25.4868i	0.293887	+	0.904492i
$795$	0.381966	+	0.277515i	0.0135469	+	0.00984243i
$796$	16.9721	−	12.3310i	0.601561	−	0.437060i
$797$	−2.56231	+	7.88597i	−0.0907615	+	0.279335i	−0.986126	−	0.165999i	$-0.946915\pi$
$797$	−2.56231	+	7.88597i	−0.0907615	+	0.279335i	0.895364	+	0.445334i	$0.146915\pi$
$798$	1.23607	−	3.80423i	0.0437563	−	0.134668i
$799$	−46.6418	+	33.8873i	−1.65007	+	1.19885i
$800$	−0.809017	−	0.587785i	−0.0286031	−	0.0207813i
$801$	3.94427	+	12.1392i	0.139364	+	0.428918i
$802$	−36.0689			−1.27364
$803$	−10.8541	+	43.1531i	−0.383033	+	1.52284i
$804$	−6.09017			−0.214784
$805$	−0.0557281	−	0.171513i	−0.00196416	−	0.00604505i
$806$	16.4443	+	11.9475i	0.579225	+	0.420831i
$807$	22.4894	−	16.3395i	0.791663	−	0.575177i
$808$	4.13525	−	12.7270i	0.145478	−	0.447735i
$809$	8.85410	−	27.2501i	0.311294	−	0.958063i	−0.665960	−	0.745988i	$-0.731978\pi$
$809$	8.85410	−	27.2501i	0.311294	−	0.958063i	0.977253	−	0.212076i	$-0.0680223\pi$
$810$	0.809017	−	0.587785i	0.0284260	−	0.0206527i
$811$	25.4164	+	18.4661i	0.892491	+	0.648433i	0.936526	−	0.350597i	$-0.114021\pi$
$811$	25.4164	+	18.4661i	0.892491	+	0.648433i	−0.0440355	+	0.999030i	$0.514021\pi$
$812$	−0.145898	−	0.449028i	−0.00512002	−	0.0157578i
$813$	8.61803			0.302248
$814$	−28.5172	+	1.93487i	−0.999528	+	0.0678171i
$815$	5.85410			0.205060
$816$	−1.57295	−	4.84104i	−0.0550642	−	0.169470i
$817$	29.0344	+	21.0948i	1.01579	+	0.738012i
$818$	27.4894	−	19.9722i	0.961143	−	0.698311i
$819$	2.14590	−	6.60440i	0.0749837	−	0.230776i
$820$	1.00000	−	3.07768i	0.0349215	−	0.107477i
$821$	−15.6180	+	11.3472i	−0.545073	+	0.396019i	−0.825966	−	0.563720i	$-0.809370\pi$
$821$	−15.6180	+	11.3472i	−0.545073	+	0.396019i	0.280893	+	0.959739i	$0.409370\pi$
$822$	9.54508	+	6.93491i	0.332923	+	0.241883i
$823$	−5.32624	−	16.3925i	−0.185661	−	0.571406i	0.814298	−	0.580447i	$-0.197122\pi$
$823$	−5.32624	−	16.3925i	−0.185661	−	0.571406i	−0.999959	+	0.00904109i	$0.997122\pi$
$824$	11.2361			0.391427
$825$	2.80902	+	1.76336i	0.0977974	+	0.0613922i
$826$	3.59675			0.125147
$827$	13.5066	+	41.5690i	0.469670	+	1.44549i	0.853013	+	0.521889i	$0.174772\pi$
$827$	13.5066	+	41.5690i	0.469670	+	1.44549i	−0.383344	+	0.923606i	$0.625228\pi$
$828$	−0.118034	−	0.0857567i	−0.00410196	−	0.00298025i
$829$	11.0000	−	7.99197i	0.382046	−	0.277573i	−0.380142	−	0.924928i	$-0.624125\pi$
$829$	11.0000	−	7.99197i	0.382046	−	0.277573i	0.762188	+	0.647355i	$0.224125\pi$
$830$	−1.23607	+	3.80423i	−0.0429045	+	0.132047i
$831$	−4.48278	+	13.7966i	−0.155506	+	0.478598i
$832$	−4.54508	+	3.30220i	−0.157572	+	0.114483i
$833$	22.5344	+	16.3722i	0.780772	+	0.567264i
$834$	−4.09017	−	12.5882i	−0.141631	−	0.435895i
$835$	−20.2705			−0.701490
$836$	8.23607	−	6.88191i	0.284850	−	0.238016i
$837$	3.61803			0.125058
$838$	4.98936	+	15.3557i	0.172354	+	0.530453i
$839$	44.2148	+	32.1239i	1.52646	+	1.10904i	0.958164	+	0.286219i	$0.0923985\pi$
$839$	44.2148	+	32.1239i	1.52646	+	1.10904i	0.568300	+	0.822822i	$0.307601\pi$
$840$	−1.00000	+	0.726543i	−0.0345033	+	0.0250681i
$841$	−8.91641	+	27.4419i	−0.307462	+	0.946272i
$842$	2.00000	−	6.15537i	0.0689246	−	0.212128i
$843$	−13.3262	+	9.68208i	−0.458980	+	0.333469i
$844$	16.7984	+	12.2047i	0.578224	+	0.420104i
$845$	−5.73607	−	17.6538i	−0.197327	−	0.607309i
$846$	11.3262			0.389404
$847$	5.90983	+	12.2452i	0.203064	+	0.420751i
$848$	−0.472136			−0.0162132
$849$	2.06231	+	6.34712i	0.0707782	+	0.217833i
$850$	−4.11803	−	2.99193i	−0.141247	−	0.102622i
$851$	1.01722	−	0.739054i	0.0348699	−	0.0253345i
$852$	−0.472136	+	1.45309i	−0.0161751	+	0.0497819i
$853$	−11.2705	+	34.6871i	−0.385895	+	1.18766i	0.549934	+	0.835208i	$0.314653\pi$
$853$	−11.2705	+	34.6871i	−0.385895	+	1.18766i	−0.935829	+	0.352454i	$0.885347\pi$
$854$		0			0
$855$	−2.61803	−	1.90211i	−0.0895349	−	0.0650509i
$856$	6.09017	+	18.7436i	0.208158	+	0.640644i
$857$	−45.1591			−1.54260			−0.771302	−	0.636469i	$-0.780394\pi$
$857$	−45.1591			−1.54260			−0.771302	+	0.636469i	$0.780394\pi$
$858$	14.2984	−	11.9475i	0.488138	−	0.407880i
$859$	21.1246			0.720762			0.360381	−	0.932805i	$-0.382647\pi$
$859$	21.1246			0.720762			0.360381	+	0.932805i	$0.382647\pi$
$860$	−3.42705	−	10.5474i	−0.116861	−	0.359663i
$861$	−3.23607	−	2.35114i	−0.110285	−	0.0801267i
$862$	18.0902	−	13.1433i	0.616154	−	0.447662i
$863$	14.6287	−	45.0224i	0.497966	−	1.53258i	−0.314317	−	0.949318i	$-0.601775\pi$
$863$	14.6287	−	45.0224i	0.497966	−	1.53258i	0.812283	−	0.583264i	$-0.198225\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−14.9443	+	10.8576i	−0.508120	+	0.369171i
$866$	−24.9443	−	18.1231i	−0.847641	−	0.615847i
$867$	−2.75329	−	8.47375i	−0.0935066	−	0.287784i
$868$	−4.47214			−0.151794
$869$	−19.9164	−	12.5025i	−0.675618	−	0.424118i
$870$	−0.381966			−0.0129499
$871$	10.5729	+	32.5402i	0.358251	+	1.10258i
$872$	−5.23607	−	3.80423i	−0.177316	−	0.128827i
$873$	10.2361	−	7.43694i	0.346438	−	0.251702i
$874$	−0.145898	+	0.449028i	−0.00493507	+	0.0151886i
$875$	−0.381966	+	1.17557i	−0.0129128	+	0.0397415i
$876$	−10.8541	+	7.88597i	−0.366726	+	0.266442i
$877$	−38.8607	−	28.2339i	−1.31223	−	0.953392i	−0.999994	−	0.00338827i	$-0.998921\pi$
$877$	−38.8607	−	28.2339i	−1.31223	−	0.953392i	−0.312238	−	0.950004i	$-0.601079\pi$
$878$	5.35410	+	16.4782i	0.180692	+	0.556113i
$879$	20.0000			0.674583
$880$	−3.30902	+	0.224514i	−0.111547	+	0.00756837i
$881$	8.00000			0.269527			0.134763	−	0.990878i	$-0.456973\pi$
$881$	8.00000			0.269527			0.134763	+	0.990878i	$0.456973\pi$
$882$	−1.69098	−	5.20431i	−0.0569384	−	0.175238i
$883$	16.4443	+	11.9475i	0.553394	+	0.402064i	0.829035	−	0.559196i	$-0.188890\pi$
$883$	16.4443	+	11.9475i	0.553394	+	0.402064i	−0.275641	+	0.961261i	$0.588890\pi$
$884$	−23.1353	+	16.8087i	−0.778123	+	0.565339i
$885$	0.899187	−	2.76741i	0.0302258	−	0.0930256i
$886$	3.90983	−	12.0332i	0.131353	−	0.404264i
$887$	−10.8820	+	7.90621i	−0.365381	+	0.265465i	−0.755293	−	0.655387i	$-0.772505\pi$
$887$	−10.8820	+	7.90621i	−0.365381	+	0.265465i	0.389912	+	0.920852i	$0.372505\pi$
$888$	−6.97214	−	5.06555i	−0.233970	−	0.169989i
$889$	−6.36068	−	19.5762i	−0.213330	−	0.656563i
$890$	−12.7639			−0.427848
$891$	0.809017	−	3.21644i	0.0271031	−	0.107755i
$892$	2.76393			0.0925433
$893$	−11.3262	−	34.8586i	−0.379018	−	1.16650i
$894$	−4.35410	−	3.16344i	−0.145623	−	0.105801i
$895$	20.1074	−	14.6089i	0.672116	−	0.488321i
$896$	0.381966	−	1.17557i	0.0127606	−	0.0392731i
$897$	−0.253289	+	0.779543i	−0.00845707	+	0.0260282i
$898$	−23.5623	+	17.1190i	−0.786284	+	0.571269i
$899$	−1.11803	−	0.812299i	−0.0372885	−	0.0270917i
$900$	0.309017	+	0.951057i	0.0103006	+	0.0317019i
$901$	−2.40325			−0.0800639
$902$	−4.00000	−	9.95959i	−0.133185	−	0.331618i
$903$	−13.7082			−0.456180
$904$	0.173762	+	0.534785i	0.00577924	+	0.0177867i
$905$	−11.2361	−	8.16348i	−0.373500	−	0.271363i
$906$	2.47214	−	1.79611i	0.0821312	−	0.0596718i
$907$	4.48278	−	13.7966i	0.148848	−	0.458108i	−0.848638	−	0.528975i	$-0.822577\pi$
$907$	4.48278	−	13.7966i	0.148848	−	0.458108i	0.997486	+	0.0708670i	$0.0225766\pi$
$908$	−7.52786	+	23.1684i	−0.249821	+	0.768870i
$909$	−10.8262	+	7.86572i	−0.359084	+	0.260890i
$910$	5.61803	+	4.08174i	0.186236	+	0.135308i
$911$	3.85410	+	11.8617i	0.127692	+	0.392996i	0.994382	−	0.105852i	$-0.0337568\pi$
$911$	3.85410	+	11.8617i	0.127692	+	0.392996i	−0.866690	+	0.498847i	$0.833757\pi$
$912$	3.23607			0.107157
$913$	4.94427	+	12.3107i	0.163632	+	0.407426i
$914$	−26.6525			−0.881586
$915$		0			0
$916$	−4.23607	−	3.07768i	−0.139964	−	0.101690i
$917$	5.61803	−	4.08174i	0.185524	−	0.134791i
$918$	−1.57295	+	4.84104i	−0.0519151	+	0.159778i
$919$	−14.0106	+	43.1203i	−0.462168	+	1.42241i	0.400340	+	0.916366i	$0.368892\pi$
$919$	−14.0106	+	43.1203i	−0.462168	+	1.42241i	−0.862509	+	0.506042i	$0.831108\pi$
$920$	0.118034	−	0.0857567i	0.00389147	−	0.00282732i
$921$	18.1631	+	13.1963i	0.598495	+	0.434832i
$922$	−8.71885	−	26.8339i	−0.287140	−	0.883726i
$923$	8.58359			0.282532
$924$	−1.00000	+	3.97574i	−0.0328976	+	0.130792i
$925$	−8.61803			−0.283359
$926$	−7.38197	−	22.7194i	−0.242586	−	0.746604i
$927$	−9.09017	−	6.60440i	−0.298560	−	0.216917i
$928$	0.309017	−	0.224514i	0.0101440	−	0.00737003i
$929$	−6.65248	+	20.4742i	−0.218261	+	0.671737i	0.780645	+	0.624974i	$0.214891\pi$
$929$	−6.65248	+	20.4742i	−0.218261	+	0.671737i	−0.998906	+	0.0467630i	$0.985109\pi$
$930$	−1.11803	+	3.44095i	−0.0366618	+	0.112833i
$931$	−14.3262	+	10.4086i	−0.469523	+	0.341129i
$932$	19.8713	+	14.4374i	0.650907	+	0.472911i
$933$	−1.47214	−	4.53077i	−0.0481956	−	0.148331i
$934$	−38.5410			−1.26110
$935$	−16.8435	+	1.14281i	−0.550840	+	0.0373740i
$936$	5.61803			0.183631
$937$	−3.50658	−	10.7921i	−0.114555	−	0.352564i	0.877299	−	0.479944i	$-0.159343\pi$
$937$	−3.50658	−	10.7921i	−0.114555	−	0.352564i	−0.991854	+	0.127380i	$0.959343\pi$
$938$	−6.09017	−	4.42477i	−0.198851	−	0.144474i
$939$	−0.381966	+	0.277515i	−0.0124650	+	0.00905635i
$940$	−3.50000	+	10.7719i	−0.114157	+	0.351340i
$941$	14.8262	−	45.6305i	0.483322	−	1.48751i	−0.351076	−	0.936347i	$-0.614184\pi$
$941$	14.8262	−	45.6305i	0.483322	−	1.48751i	0.834397	−	0.551164i	$-0.185816\pi$
$942$	19.6353	−	14.2658i	0.639751	−	0.464806i
$943$	0.381966	+	0.277515i	0.0124385	+	0.00903712i
$944$	0.899187	+	2.76741i	0.0292660	+	0.0900716i
$945$	1.23607			0.0402093
$946$	−31.1525	−	19.5559i	−1.01285	−	0.635818i
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	−2.19098	−	6.74315i	−0.0711598	−	0.219007i
$949$	60.9787	+	44.3036i	1.97945	+	1.43816i
$950$	2.61803	−	1.90211i	0.0849402	−	0.0617127i
$951$	0.180340	−	0.555029i	0.00584792	−	0.0179981i
$952$	1.94427	−	5.98385i	0.0630142	−	0.193938i
$953$	6.29837	−	4.57604i	0.204024	−	0.148232i	−0.481082	−	0.876676i	$-0.659756\pi$
$953$	6.29837	−	4.57604i	0.204024	−	0.148232i	0.685106	+	0.728443i	$0.259756\pi$
$954$	0.381966	+	0.277515i	0.0123666	+	0.00898487i
$955$	−1.47214	−	4.53077i	−0.0476372	−	0.146612i
$956$	1.23607			0.0399773
$957$	−0.972136	+	0.812299i	−0.0314247	+	0.0262579i
$958$	17.2361			0.556872
$959$	4.50658	+	13.8698i	0.145525	+	0.447880i
$960$	−0.809017	−	0.587785i	−0.0261109	−	0.0189707i
$961$	14.4894	−	10.5271i	0.467399	−	0.339585i
$962$	−14.9615	+	46.0467i	−0.482378	+	1.48461i
$963$	6.09017	−	18.7436i	0.196253	−	0.604005i
$964$	−9.61803	+	6.98791i	−0.309776	+	0.225065i
$965$	−2.47214	−	1.79611i	−0.0795809	−	0.0578189i
$966$	−0.0557281	−	0.171513i	−0.00179302	−	0.00551835i
$967$	−9.30495			−0.299227			−0.149614	−	0.988745i	$-0.547803\pi$
$967$	−9.30495			−0.299227			−0.149614	+	0.988745i	$0.547803\pi$
$968$	−7.94427	+	7.60845i	−0.255339	+	0.244545i
$969$	16.4721			0.529161
$970$	3.90983	+	12.0332i	0.125537	+	0.386363i
$971$	29.4164	+	21.3723i	0.944017	+	0.685869i	0.949384	−	0.314117i	$-0.101708\pi$
$971$	29.4164	+	21.3723i	0.944017	+	0.685869i	−0.00536690	+	0.999986i	$0.501708\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	5.05573	−	15.5599i	0.162079	−	0.498828i
$974$	−4.76393	+	14.6619i	−0.152646	+	0.469797i
$975$	4.54508	−	3.30220i	0.145559	−	0.105755i
$976$		0			0
$977$	−7.67376	−	23.6174i	−0.245505	−	0.755588i	−0.995553	−	0.0942040i	$-0.969969\pi$
$977$	−7.67376	−	23.6174i	−0.245505	−	0.755588i	0.750048	−	0.661384i	$-0.230031\pi$
$978$	5.85410			0.187194
$979$	−32.4853	+	27.1441i	−1.03823	+	0.867530i
$980$	5.47214			0.174801
$981$	2.00000	+	6.15537i	0.0638551	+	0.196526i
$982$	0.836881	+	0.608030i	0.0267059	+	0.0194030i
$983$	−38.1803	+	27.7396i	−1.21776	+	0.884757i	−0.995912	−	0.0903234i	$-0.971210\pi$
$983$	−38.1803	+	27.7396i	−1.21776	+	0.884757i	−0.221851	+	0.975081i	$0.571210\pi$
$984$	1.00000	−	3.07768i	0.0318788	−	0.0981130i
$985$	2.14590	−	6.60440i	0.0683740	−	0.210434i
$986$	1.57295	−	1.14281i	0.0500929	−	0.0363946i
$987$	11.3262	+	8.22899i	0.360518	+	0.261932i
$988$	−5.61803	−	17.2905i	−0.178733	−	0.550085i
$989$	1.61803			0.0514505
$990$	2.80902	+	1.76336i	0.0892764	+	0.0560431i
$991$	−59.5197			−1.89071			−0.945353	−	0.326048i	$-0.894283\pi$
$991$	−59.5197			−1.89071			−0.945353	+	0.326048i	$0.894283\pi$
$992$	−1.11803	−	3.44095i	−0.0354976	−	0.109250i
$993$	3.85410	+	2.80017i	0.122306	+	0.0888607i
$994$	−1.52786	+	1.11006i	−0.0484609	+	0.0352089i
$995$	6.48278	−	19.9519i	0.205518	−	0.632519i
$996$	−1.23607	+	3.80423i	−0.0391663	+	0.120542i
$997$	−3.26393	+	2.37139i	−0.103370	+	0.0751025i	−0.638269	−	0.769813i	$-0.720349\pi$
$997$	−3.26393	+	2.37139i	−0.103370	+	0.0751025i	0.534900	+	0.844916i	$0.320349\pi$
$998$	19.0344	+	13.8293i	0.602525	+	0.437760i
$999$	2.66312	+	8.19624i	0.0842574	+	0.259317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	330.2.m.b.181.1	yes	4
3.2	odd	2		990.2.n.e.181.1		4
11.3	even	5		3630.2.a.bj.1.2		2
11.8	odd	10		3630.2.a.bb.1.1		2
11.9	even	5	inner	330.2.m.b.31.1	✓	4
33.20	odd	10		990.2.n.e.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.b.31.1	✓	4	11.9	even	5	inner
330.2.m.b.181.1	yes	4	1.1	even	1	trivial
990.2.n.e.181.1		4	3.2	odd	2
990.2.n.e.361.1		4	33.20	odd	10
3630.2.a.bb.1.1		2	11.8	odd	10
3630.2.a.bj.1.2		2	11.3	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)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.00000 + 0.726543i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.309017 + 0.951057i) q^{6} +(-1.00000 + 0.726543i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.00000 q^{10} +(-2.54508 + 2.12663i) q^{11} -1.00000 q^{12} +(1.73607 + 5.34307i) q^{13} +(-1.00000 - 0.726543i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.57295 - 4.84104i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(2.61803 + 1.90211i) q^{19} +(-0.309017 - 0.951057i) q^{20} -1.23607 q^{21} +(-2.80902 - 1.76336i) q^{22} +0.145898 q^{23} +(-0.309017 - 0.951057i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.54508 + 3.30220i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(0.381966 - 1.17557i) q^{28} +(0.309017 - 0.224514i) q^{29} +(-0.809017 - 0.587785i) q^{30} +(-1.11803 - 3.44095i) q^{31} +1.00000 q^{32} +(-3.30902 + 0.224514i) q^{33} +5.09017 q^{34} +(-0.381966 - 1.17557i) q^{35} +(-0.809017 - 0.587785i) q^{36} +(6.97214 - 5.06555i) q^{37} +(-1.00000 + 3.07768i) q^{38} +(-1.73607 + 5.34307i) q^{39} +(0.809017 - 0.587785i) q^{40} +(2.61803 + 1.90211i) q^{41} +(-0.381966 - 1.17557i) q^{42} +11.0902 q^{43} +(0.809017 - 3.21644i) q^{44} -1.00000 q^{45} +(0.0450850 + 0.138757i) q^{46} +(-9.16312 - 6.65740i) q^{47} +(0.809017 - 0.587785i) q^{48} +(-1.69098 + 5.20431i) q^{49} +(0.309017 - 0.951057i) q^{50} +(4.11803 - 2.99193i) q^{51} +(-4.54508 - 3.30220i) q^{52} +(-0.145898 - 0.449028i) q^{53} -1.00000 q^{54} +(-1.23607 - 3.07768i) q^{55} +1.23607 q^{56} +(1.00000 + 3.07768i) q^{57} +(0.309017 + 0.224514i) q^{58} +(-2.35410 + 1.71036i) q^{59} +(0.309017 - 0.951057i) q^{60} +(2.92705 - 2.12663i) q^{62} +(-1.00000 - 0.726543i) q^{63} +(0.309017 + 0.951057i) q^{64} -5.61803 q^{65} +(-1.23607 - 3.07768i) q^{66} +6.09017 q^{67} +(1.57295 + 4.84104i) q^{68} +(0.118034 + 0.0857567i) q^{69} +(1.00000 - 0.726543i) q^{70} +(0.472136 - 1.45309i) q^{71} +(0.309017 - 0.951057i) q^{72} +(10.8541 - 7.88597i) q^{73} +(6.97214 + 5.06555i) q^{74} +(-0.309017 - 0.951057i) q^{75} -3.23607 q^{76} +(1.00000 - 3.97574i) q^{77} -5.61803 q^{78} +(2.19098 + 6.74315i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-1.00000 + 3.07768i) q^{82} +(1.23607 - 3.80423i) q^{83} +(1.00000 - 0.726543i) q^{84} +(4.11803 + 2.99193i) q^{85} +(3.42705 + 10.5474i) q^{86} +0.381966 q^{87} +(3.30902 - 0.224514i) q^{88} +12.7639 q^{89} +(-0.309017 - 0.951057i) q^{90} +(-5.61803 - 4.08174i) q^{91} +(-0.118034 + 0.0857567i) q^{92} +(1.11803 - 3.44095i) q^{93} +(3.50000 - 10.7719i) q^{94} +(-2.61803 + 1.90211i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-3.90983 - 12.0332i) q^{97} -5.47214 q^{98} +(-2.80902 - 1.76336i) 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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