LMFDB - Embedded newform 441.2.g.f.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, not 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$0.247934 + 0.429435i$ of defining polynomial
Character	$\chi$	$=$	441.79
Dual form			441.2.g.f.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.247934 + 0.429435i) q^{2} +(-1.59836 - 0.667278i) q^{3} +(0.877057 - 1.51911i) q^{4} +3.69258 q^{5} +(-0.109735 - 0.851830i) q^{6} +1.86155 q^{8} +(2.10948 + 2.13309i) q^{9} +O(q^{10})$	\(q+(0.247934 + 0.429435i) q^{2} +(-1.59836 - 0.667278i) q^{3} +(0.877057 - 1.51911i) q^{4} +3.69258 q^{5} +(-0.109735 - 0.851830i) q^{6} +1.86155 q^{8} +(2.10948 + 2.13309i) q^{9} +(0.915516 + 1.58572i) q^{10} -0.892568 q^{11} +(-2.41552 + 1.84283i) q^{12} +(-0.598355 - 1.03638i) q^{13} +(-5.90205 - 2.46398i) q^{15} +(-1.29257 - 2.23880i) q^{16} +(0.124991 + 0.216492i) q^{17} +(-0.393012 + 1.43475i) q^{18} +(-1.40414 + 2.43204i) q^{19} +(3.23860 - 5.60943i) q^{20} +(-0.221298 - 0.383300i) q^{22} +2.47772 q^{23} +(-2.97541 - 1.24217i) q^{24} +8.63514 q^{25} +(0.296705 - 0.513909i) q^{26} +(-1.94833 - 4.81705i) q^{27} +(2.07128 - 3.58755i) q^{29} +(-0.405204 - 3.14545i) q^{30} +(1.79257 - 3.10483i) q^{31} +(2.50249 - 4.33444i) q^{32} +(1.42664 + 0.595591i) q^{33} +(-0.0619793 + 0.107351i) q^{34} +(5.09054 - 1.33368i) q^{36} +(-2.36568 + 4.09747i) q^{37} -1.39253 q^{38} +(0.264830 + 2.05578i) q^{39} +6.87391 q^{40} +(2.39093 + 4.14121i) q^{41} +(-4.98928 + 8.64169i) q^{43} +(-0.782834 + 1.35591i) q^{44} +(7.78942 + 7.87662i) q^{45} +(0.614310 + 1.06402i) q^{46} +(-5.08653 - 8.81013i) q^{47} +(0.572088 + 4.44091i) q^{48} +(2.14095 + 3.70823i) q^{50} +(-0.0553208 - 0.429435i) q^{51} -2.09917 q^{52} +(-4.94465 - 8.56438i) q^{53} +(1.58555 - 2.03099i) q^{54} -3.29588 q^{55} +(3.86715 - 2.95031i) q^{57} +2.05416 q^{58} +(0.906186 - 1.56956i) q^{59} +(-8.91949 + 6.80481i) q^{60} +(5.40205 + 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(-2.20948 - 3.82692i) q^{65} +(0.0979457 + 0.760316i) q^{66} +(-0.514685 + 0.891460i) q^{67} +0.438499 q^{68} +(-3.96027 - 1.65332i) q^{69} -4.94533 q^{71} +(3.92690 + 3.97085i) q^{72} +(0.915262 + 1.58528i) q^{73} -2.34613 q^{74} +(-13.8020 - 5.76204i) q^{75} +(2.46302 + 4.26607i) q^{76} +(-0.817161 + 0.623424i) q^{78} +(0.899562 + 1.55809i) q^{79} +(-4.77293 - 8.26696i) q^{80} +(-0.100184 + 8.99944i) q^{81} +(-1.18559 + 2.05350i) q^{82} +(-6.16156 + 10.6721i) q^{83} +(0.461541 + 0.799412i) q^{85} -4.94806 q^{86} +(-5.70453 + 4.35207i) q^{87} -1.66156 q^{88} +(1.20370 - 2.08488i) q^{89} +(-1.45123 + 5.29793i) q^{90} +(2.17310 - 3.76392i) q^{92} +(-4.93695 + 3.76648i) q^{93} +(2.52225 - 4.36867i) q^{94} +(-5.18489 + 8.98049i) q^{95} +(-6.89215 + 5.25813i) q^{96} +(-5.52210 + 9.56456i) q^{97} +(-1.88286 - 1.90393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	$ 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + 7 q^{10} - 8 q^{11} - 22 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} - 12 q^{17} - 2 q^{18} - q^{19} - 5 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 2 q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} - 26 q^{30} + 3 q^{31} - 2 q^{32} + q^{33} - 3 q^{34} + 34 q^{36} + 40 q^{38} + 20 q^{39} - 6 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + q^{45} + 3 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} + 24 q^{51} - 20 q^{52} - 21 q^{53} + 53 q^{54} - 4 q^{55} - 4 q^{57} + 20 q^{58} - 30 q^{59} - 41 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} + 41 q^{66} - 2 q^{67} + 54 q^{68} - 15 q^{69} - 6 q^{71} + 48 q^{72} - 15 q^{73} + 72 q^{74} - 31 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} - 20 q^{80} + 8 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} + 16 q^{86} - 32 q^{87} + 36 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 12 q^{93} + 3 q^{94} - 14 q^{95} + q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + 7 * q^10 - 8 * q^11 - 22 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 - 12 * q^17 - 2 * q^18 - q^19 - 5 * q^20 - q^22 - 6 * q^23 - 3 * q^24 + 2 * q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 - 26 * q^30 + 3 * q^31 - 2 * q^32 + q^33 - 3 * q^34 + 34 * q^36 + 40 * q^38 + 20 * q^39 - 6 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + q^45 + 3 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 + 24 * q^51 - 20 * q^52 - 21 * q^53 + 53 * q^54 - 4 * q^55 - 4 * q^57 + 20 * q^58 - 30 * q^59 - 41 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 + 41 * q^66 - 2 * q^67 + 54 * q^68 - 15 * q^69 - 6 * q^71 + 48 * q^72 - 15 * q^73 + 72 * q^74 - 31 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 - 20 * q^80 + 8 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 + 16 * q^86 - 32 * q^87 + 36 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 12 * q^93 + 3 * q^94 - 14 * q^95 + q^96 + 12 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.247934	+	0.429435i	0.175316	+	0.303656i	0.940271	−	0.340428i	$-0.110572\pi$
$2$	0.247934	+	0.429435i	0.175316	+	0.303656i	−0.764955	+	0.644084i	$0.777239\pi$
$3$	−1.59836	−	0.667278i	−0.922811	−	0.385253i
$3$	−1.59836	−	0.667278i	−0.922811	−	0.385253i
$4$	0.877057	−	1.51911i	0.438529	−	0.759554i
$5$	3.69258			1.65137			0.825686	−	0.564130i	$-0.190788\pi$
$5$	3.69258			1.65137			0.825686	+	0.564130i	$0.190788\pi$
$6$	−0.109735	−	0.851830i	−0.0447990	−	0.347758i
$7$		0			0
$7$		0			0
$8$	1.86155			0.658156
$9$	2.10948	+	2.13309i	0.703160	+	0.711031i
$10$	0.915516	+	1.58572i	0.289512	+	0.501449i
$11$	−0.892568			−0.269119			−0.134560	−	0.990905i	$-0.542962\pi$
$11$	−0.892568			−0.269119			−0.134560	+	0.990905i	$0.542962\pi$
$12$	−2.41552	+	1.84283i	−0.697300	+	0.531980i
$13$	−0.598355	−	1.03638i	−0.165954	−	0.287441i	0.771040	−	0.636787i	$-0.219737\pi$
$13$	−0.598355	−	1.03638i	−0.165954	−	0.287441i	−0.936994	+	0.349346i	$0.886404\pi$
$14$		0			0
$15$	−5.90205	−	2.46398i	−1.52390	−	0.636196i
$16$	−1.29257	−	2.23880i	−0.323143	−	0.559701i
$17$	0.124991	+	0.216492i	0.0303149	+	0.0525069i	0.880785	−	0.473517i	$-0.157016\pi$
$17$	0.124991	+	0.216492i	0.0303149	+	0.0525069i	−0.850470	+	0.526024i	$0.823682\pi$
$18$	−0.393012	+	1.43475i	−0.0926339	+	0.338174i
$19$	−1.40414	+	2.43204i	−0.322131	+	0.557948i	−0.980928	−	0.194374i	$-0.937733\pi$
$19$	−1.40414	+	2.43204i	−0.322131	+	0.557948i	0.658796	+	0.752321i	$0.271066\pi$
$20$	3.23860	−	5.60943i	0.724174	−	1.25431i
$21$		0			0
$22$	−0.221298	−	0.383300i	−0.0471809	−	0.0817198i
$23$	2.47772			0.516639			0.258320	−	0.966059i	$-0.416831\pi$
$23$	2.47772			0.516639			0.258320	+	0.966059i	$0.416831\pi$
$24$	−2.97541	−	1.24217i	−0.607354	−	0.253557i
$25$	8.63514			1.72703
$26$	0.296705	−	0.513909i	0.0581887	−	0.100786i
$27$	−1.94833	−	4.81705i	−0.374957	−	0.927042i
$28$		0			0
$29$	2.07128	−	3.58755i	0.384626	−	0.666192i	−0.607091	−	0.794632i	$-0.707664\pi$
$29$	2.07128	−	3.58755i	0.384626	−	0.666192i	0.991717	+	0.128440i	$0.0409970\pi$
$30$	−0.405204	−	3.14545i	−0.0739798	−	0.574278i
$31$	1.79257	−	3.10483i	0.321956	−	0.557644i	−0.658936	−	0.752199i	$-0.728993\pi$
$31$	1.79257	−	3.10483i	0.321956	−	0.557644i	0.980892	+	0.194555i	$0.0623264\pi$
$32$	2.50249	−	4.33444i	0.442382	−	0.766229i
$33$	1.42664	+	0.595591i	0.248346	+	0.103679i
$34$	−0.0619793	+	0.107351i	−0.0106294	+	0.0184106i
$35$		0			0
$36$	5.09054	−	1.33368i	0.848423	−	0.222280i
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	−0.992304	−	0.123826i	$-0.960483\pi$
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	0.603389	+	0.797447i	$0.293817\pi$
$38$	−1.39253			−0.225899
$39$	0.264830	+	2.05578i	0.0424067	+	0.329188i
$40$	6.87391			1.08686
$41$	2.39093	+	4.14121i	0.373400	+	0.646748i	0.990086	−	0.140461i	$-0.0448584\pi$
$41$	2.39093	+	4.14121i	0.373400	+	0.646748i	−0.616686	+	0.787209i	$0.711525\pi$
$42$		0			0
$43$	−4.98928	+	8.64169i	−0.760859	+	1.31785i	0.181550	+	0.983382i	$0.441889\pi$
$43$	−4.98928	+	8.64169i	−0.760859	+	1.31785i	−0.942408	+	0.334464i	$0.891445\pi$
$44$	−0.782834	+	1.35591i	−0.118017	+	0.204411i
$45$	7.78942	+	7.87662i	1.16118	+	1.17418i
$46$	0.614310	+	1.06402i	0.0905751	+	0.156881i
$47$	−5.08653	−	8.81013i	−0.741947	−	1.28509i	−0.951608	−	0.307316i	$-0.900569\pi$
$47$	−5.08653	−	8.81013i	−0.741947	−	1.28509i	0.209661	−	0.977774i	$-0.432764\pi$
$48$	0.572088	+	4.44091i	0.0825738	+	0.640990i
$49$		0			0
$50$	2.14095	+	3.70823i	0.302776	+	0.524423i
$51$	−0.0553208	−	0.429435i	−0.00774646	−	0.0601329i
$52$	−2.09917			−0.291102
$53$	−4.94465	−	8.56438i	−0.679199	−	1.17641i	−0.975222	−	0.221227i	$-0.928994\pi$
$53$	−4.94465	−	8.56438i	−0.679199	−	1.17641i	0.296023	−	0.955181i	$-0.404339\pi$
$54$	1.58555	−	2.03099i	0.215766	−	0.276383i
$55$	−3.29588			−0.444416
$56$		0			0
$57$	3.86715	−	2.95031i	0.512217	−	0.390778i
$58$	2.05416			0.269724
$59$	0.906186	−	1.56956i	0.117975	−	0.204339i	−0.800990	−	0.598678i	$-0.795693\pi$
$59$	0.906186	−	1.56956i	0.117975	−	0.204339i	0.918965	+	0.394339i	$0.129026\pi$
$60$	−8.91949	+	6.80481i	−1.15150	+	0.878497i
$61$	5.40205	+	9.35663i	0.691662	+	1.19799i	0.971293	+	0.237886i	$0.0764546\pi$
$61$	5.40205	+	9.35663i	0.691662	+	1.19799i	−0.279631	+	0.960108i	$0.590212\pi$
$62$	1.77776			0.225776
$63$		0			0
$64$	−2.68848			−0.336060
$65$	−2.20948	−	3.82692i	−0.274052	−	0.474671i
$66$	0.0979457	+	0.760316i	0.0120563	+	0.0935885i
$67$	−0.514685	+	0.891460i	−0.0628787	+	0.108909i	−0.895751	−	0.444556i	$-0.853361\pi$
$67$	−0.514685	+	0.891460i	−0.0628787	+	0.108909i	0.832872	+	0.553465i	$0.186695\pi$
$68$	0.438499			0.0531758
$69$	−3.96027	−	1.65332i	−0.476761	−	0.199037i
$70$		0			0
$71$	−4.94533			−0.586903			−0.293451	−	0.955974i	$-0.594804\pi$
$71$	−4.94533			−0.586903			−0.293451	+	0.955974i	$0.594804\pi$
$72$	3.92690	+	3.97085i	0.462789	+	0.467970i
$73$	0.915262	+	1.58528i	0.107123	+	0.185543i	0.914604	−	0.404351i	$-0.132503\pi$
$73$	0.915262	+	1.58528i	0.107123	+	0.185543i	−0.807480	+	0.589894i	$0.799169\pi$
$74$	−2.34613			−0.272732
$75$	−13.8020	−	5.76204i	−1.59372	−	0.665343i
$76$	2.46302	+	4.26607i	0.282527	+	0.489352i
$77$		0			0
$78$	−0.817161	+	0.623424i	−0.0925253	+	0.0705889i
$79$	0.899562	+	1.55809i	0.101209	+	0.175298i	0.912183	−	0.409783i	$-0.134396\pi$
$79$	0.899562	+	1.55809i	0.101209	+	0.175298i	−0.810974	+	0.585082i	$0.801062\pi$
$80$	−4.77293	−	8.26696i	−0.533630	−	0.924274i
$81$	−0.100184	+	8.99944i	−0.0111316	+	0.999938i
$82$	−1.18559	+	2.05350i	−0.130926	+	0.226771i
$83$	−6.16156	+	10.6721i	−0.676319	+	1.17142i	0.299763	+	0.954014i	$0.403092\pi$
$83$	−6.16156	+	10.6721i	−0.676319	+	1.17142i	−0.976082	+	0.217405i	$0.930241\pi$
$84$		0			0
$85$	0.461541	+	0.799412i	0.0500611	+	0.0867084i
$86$	−4.94806			−0.533563
$87$	−5.70453	+	4.35207i	−0.611590	+	0.466591i
$88$	−1.66156			−0.177123
$89$	1.20370	−	2.08488i	0.127592	−	0.220997i	−0.795151	−	0.606412i	$-0.792608\pi$
$89$	1.20370	−	2.08488i	0.127592	−	0.220997i	0.922743	+	0.385415i	$0.125942\pi$
$90$	−1.45123	+	5.29793i	−0.152973	+	0.558451i
$91$		0			0
$92$	2.17310	−	3.76392i	0.226561	−	0.392416i
$93$	−4.93695	+	3.76648i	−0.511938	+	0.390565i
$94$	2.52225	−	4.36867i	0.260150	−	0.450593i
$95$	−5.18489	+	8.98049i	−0.531958	+	0.921379i
$96$	−6.89215	+	5.25813i	−0.703427	+	0.536655i
$97$	−5.52210	+	9.56456i	−0.560684	+	0.971134i	0.436752	+	0.899582i	$0.356129\pi$
$97$	−5.52210	+	9.56456i	−0.560684	+	0.971134i	−0.997437	+	0.0715522i	$0.977205\pi$
$98$		0			0
$99$	−1.88286	−	1.90393i	−0.189234	−	0.191352i
$100$	7.57351	−	13.1177i	0.757351	−	1.31177i
$101$	2.59964			0.258674			0.129337	−	0.991601i	$-0.458715\pi$
$101$	2.59964			0.258674			0.129337	+	0.991601i	$0.458715\pi$
$102$	0.170698	−	0.130228i	0.0169016	−	0.0128945i
$103$	−9.71155			−0.956908			−0.478454	−	0.878113i	$-0.658803\pi$
$103$	−9.71155			−0.956908			−0.478454	+	0.878113i	$0.658803\pi$
$104$	−1.11387	−	1.92927i	−0.109224	−	0.189181i
$105$		0			0
$106$	2.45189	−	4.24680i	0.238149	−	0.412486i
$107$	−5.45025	+	9.44012i	−0.526896	+	0.912610i	0.472613	+	0.881270i	$0.343311\pi$
$107$	−5.45025	+	9.44012i	−0.526896	+	0.912610i	−0.999509	+	0.0313403i	$0.990022\pi$
$108$	−9.02642	−	1.26510i	−0.868568	−	0.121735i
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	0.810731	−	0.585419i	$-0.199070\pi$
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	−0.912353	+	0.409404i	$0.865737\pi$
$110$	−0.817161	−	1.41536i	−0.0779132	−	0.134950i
$111$	6.51535	−	4.97066i	0.618410	−	0.471794i
$112$		0			0
$113$	7.91318	+	13.7060i	0.744409	+	1.28935i	0.950470	+	0.310816i	$0.100602\pi$
$113$	7.91318	+	13.7060i	0.744409	+	1.28935i	−0.206061	+	0.978539i	$0.566065\pi$
$114$	2.22576	+	0.929207i	0.208462	+	0.0870282i
$115$	9.14916			0.853164
$116$	−3.63325	−	6.29298i	−0.337339	−	0.584289i
$117$	0.948482	−	3.46258i	0.0876872	−	0.320115i
$118$	0.898698			0.0827318
$119$		0			0
$120$	−10.9869	−	4.58681i	−1.00297	−	0.418716i
$121$	−10.2033			−0.927575
$122$	−2.67871	+	4.63966i	−0.242519	+	0.420055i
$123$	−1.05822	−	8.21454i	−0.0954162	−	0.740680i
$124$	−3.14438	−	5.44623i	−0.282374	−	0.489086i
$125$	13.4230			1.20059
$126$		0			0
$127$	−1.26946			−0.112647			−0.0563233	−	0.998413i	$-0.517938\pi$
$127$	−1.26946			−0.112647			−0.0563233	+	0.998413i	$0.517938\pi$
$128$	−5.67155	−	9.82342i	−0.501299	−	0.868275i
$129$	13.7411	−	10.4833i	1.20983	−	0.923000i
$130$	1.09561	−	1.89765i	0.0960912	−	0.166435i
$131$	15.0289			1.31308			0.656540	−	0.754291i	$-0.272019\pi$
$131$	15.0289			1.31308			0.656540	+	0.754291i	$0.272019\pi$
$132$	2.15601	−	1.64485i	0.187657	−	0.143166i
$133$		0			0
$134$	−0.510432			−0.0440946
$135$	−7.19437	−	17.7873i	−0.619193	−	1.53089i
$136$	0.232677	+	0.403009i	0.0199519	+	0.0345577i
$137$	−0.488493			−0.0417347			−0.0208674	−	0.999782i	$-0.506643\pi$
$137$	−0.488493			−0.0417347			−0.0208674	+	0.999782i	$0.506643\pi$
$138$	−0.271891	−	2.11059i	−0.0231449	−	0.179666i
$139$	4.93487	+	8.54745i	0.418570	+	0.724985i	0.995796	−	0.0915997i	$-0.0291980\pi$
$139$	4.93487	+	8.54745i	0.418570	+	0.724985i	−0.577226	+	0.816585i	$0.695865\pi$
$140$		0			0
$141$	2.25128	+	17.4759i	0.189592	+	1.47173i
$142$	−1.22612	−	2.12370i	−0.102893	−	0.178217i
$143$	0.534073	+	0.925042i	0.0446614	+	0.0773559i
$144$	2.04892	−	7.47989i	0.170743	−	0.623325i
$145$	7.64835	−	13.2473i	0.635161	−	1.10013i
$146$	−0.453849	+	0.786090i	−0.0375609	+	0.0650573i
$147$		0			0
$148$	4.14967	+	7.18744i	0.341101	+	0.590804i
$149$	21.0240			1.72235			0.861175	−	0.508309i	$-0.169729\pi$
$149$	21.0240			1.72235			0.861175	+	0.508309i	$0.169729\pi$
$150$	−0.947575	−	7.35567i	−0.0773692	−	0.600588i
$151$	1.49838			0.121937			0.0609683	−	0.998140i	$-0.480581\pi$
$151$	1.49838			0.121937			0.0609683	+	0.998140i	$0.480581\pi$
$152$	−2.61387	+	4.52735i	−0.212013	+	0.367217i
$153$	−0.198130	+	0.723303i	−0.0160179	+	0.0584756i
$154$		0			0
$155$	6.61922	−	11.4648i	0.531669	−	0.920877i
$156$	3.35522	+	1.40073i	0.268632	+	0.112148i
$157$	−8.33982	+	14.4450i	−0.665590	+	1.15284i	0.313535	+	0.949577i	$0.398487\pi$
$157$	−8.33982	+	14.4450i	−0.665590	+	1.15284i	−0.979125	+	0.203259i	$0.934847\pi$
$158$	−0.446064	+	0.772606i	−0.0354870	+	0.0614652i
$159$	2.18848	+	16.9884i	0.173558	+	1.34727i
$160$	9.24065	−	16.0053i	0.730538	−	1.26533i
$161$		0			0
$162$	−3.88951	+	2.18825i	−0.305589	+	0.171925i
$163$	−3.34135	+	5.78738i	−0.261714	+	0.453303i	−0.966698	−	0.255921i	$-0.917621\pi$
$163$	−3.34135	+	5.78738i	−0.261714	+	0.453303i	0.704983	+	0.709224i	$0.250954\pi$
$164$	8.38793			0.654987
$165$	5.26799	+	2.19927i	0.410112	+	0.171213i
$166$	−6.11064			−0.474278
$167$	−8.81549	−	15.2689i	−0.682163	−	1.18154i	−0.974319	−	0.225170i	$-0.927706\pi$
$167$	−8.81549	−	15.2689i	−0.682163	−	1.18154i	0.292156	−	0.956371i	$-0.405627\pi$
$168$		0			0
$169$	5.78394	−	10.0181i	0.444919	−	0.770622i
$170$	−0.228863	+	0.396403i	−0.0175530	+	0.0304027i
$171$	−8.14976	+	2.13518i	−0.623228	+	0.163281i
$172$	8.75178	+	15.1585i	0.667317	+	1.15583i
$173$	−1.94342	−	3.36611i	−0.147756	−	0.255920i	0.782642	−	0.622472i	$-0.213872\pi$
$173$	−1.94342	−	3.36611i	−0.147756	−	0.255920i	−0.930398	+	0.366552i	$0.880538\pi$
$174$	−3.28328	−	1.37070i	−0.248905	−	0.103912i
$175$		0			0
$176$	1.15371	+	1.99829i	0.0869642	+	0.150626i
$177$	−2.49574	+	1.90404i	−0.187591	+	0.143116i
$178$	1.19376			0.0894759
$179$	3.66758	+	6.35244i	0.274128	+	0.474804i	0.969915	−	0.243445i	$-0.0782775\pi$
$179$	3.66758	+	6.35244i	0.274128	+	0.474804i	−0.695787	+	0.718248i	$0.744944\pi$
$180$	18.7972	−	4.92473i	1.40106	−	0.367067i
$181$	−11.2566			−0.836693			−0.418346	−	0.908288i	$-0.637390\pi$
$181$	−11.2566			−0.836693			−0.418346	+	0.908288i	$0.637390\pi$
$182$		0			0
$183$	−2.39093	−	18.5599i	−0.176743	−	1.37199i
$184$	4.61238			0.340029
$185$	−8.73545	+	15.1302i	−0.642243	+	1.11240i
$186$	−2.84149	−	1.18626i	−0.208348	−	0.0869808i
$187$	−0.111563	−	0.193234i	−0.00815833	−	0.0141306i
$188$	−17.8447			−1.30146
$189$		0			0
$190$	−5.14204			−0.373043
$191$	11.9230	+	20.6512i	0.862715	+	1.49427i	0.869298	+	0.494288i	$0.164571\pi$
$191$	11.9230	+	20.6512i	0.862715	+	1.49427i	−0.00658302	+	0.999978i	$0.502095\pi$
$192$	4.29715	+	1.79396i	0.310120	+	0.129468i
$193$	−2.96728	+	5.13948i	−0.213589	+	0.369948i	−0.952835	−	0.303488i	$-0.901849\pi$
$193$	−2.96728	+	5.13948i	−0.213589	+	0.369948i	0.739246	+	0.673436i	$0.235182\pi$
$194$	−5.47647			−0.393188
$195$	0.977905	+	7.59112i	0.0700293	+	0.543611i
$196$		0			0
$197$	−15.4682			−1.10206			−0.551032	−	0.834484i	$-0.685766\pi$
$197$	−15.4682			−1.10206			−0.551032	+	0.834484i	$0.685766\pi$
$198$	0.350790	−	1.28061i	0.0249296	−	0.0910092i
$199$	−7.74818	−	13.4202i	−0.549254	−	0.951336i	−0.998326	−	0.0578402i	$-0.981579\pi$
$199$	−7.74818	−	13.4202i	−0.549254	−	0.951336i	0.449072	−	0.893496i	$-0.351755\pi$
$200$	16.0747			1.13665
$201$	1.41750	−	1.08143i	0.0999828	−	0.0762784i
$202$	0.644540	+	1.11638i	0.0453497	+	0.0785480i
$203$		0			0
$204$	−0.700877	−	0.292600i	−0.0490712	−	0.0204861i
$205$	8.82870	+	15.2917i	0.616623	+	1.06802i
$206$	−2.40783	−	4.17048i	−0.167761	−	0.290571i
$207$	5.22669	+	5.28520i	0.363280	+	0.367347i
$208$	−1.54684	+	2.67920i	−0.107254	+	0.185769i
$209$	1.25329	−	2.17076i	0.0866918	−	0.150155i
$210$		0			0
$211$	0.771898	+	1.33697i	0.0531397	+	0.0920406i	0.891372	−	0.453273i	$-0.149744\pi$
$211$	0.771898	+	1.33697i	0.0531397	+	0.0920406i	−0.838232	+	0.545314i	$0.816410\pi$
$212$	−17.3469			−1.19139
$213$	7.90440	+	3.29991i	0.541600	+	0.226106i
$214$	−5.40522			−0.369493
$215$	−18.4233	+	31.9101i	−1.25646	+	2.17625i
$216$	−3.62691	−	8.96717i	−0.246780	−	0.610138i
$217$		0			0
$218$	0.526098	−	0.911229i	0.0356319	−	0.0617162i
$219$	−0.405092	−	3.14458i	−0.0273736	−	0.212491i
$220$	−2.89068	+	5.00680i	−0.194889	+	0.337558i
$221$	0.149579	−	0.259078i	0.0100617	−	0.0174275i
$222$	3.74995	+	1.56552i	0.251680	+	0.105071i
$223$	2.72171	−	4.71414i	0.182259	−	0.315682i	−0.760390	−	0.649466i	$-0.774992\pi$
$223$	2.72171	−	4.71414i	0.182259	−	0.315682i	0.942649	+	0.333784i	$0.108326\pi$
$224$		0			0
$225$	18.2157	+	18.4196i	1.21438	+	1.22797i
$226$	−3.92389	+	6.79638i	−0.261014	+	0.452089i
$227$	16.0764			1.06703			0.533513	−	0.845792i	$-0.320872\pi$
$227$	16.0764			1.06703			0.533513	+	0.845792i	$0.320872\pi$
$228$	−1.09012	−	8.46222i	−0.0721951	−	0.560424i
$229$	9.96840			0.658730			0.329365	−	0.944203i	$-0.393165\pi$
$229$	9.96840			0.658730			0.329365	+	0.944203i	$0.393165\pi$
$230$	2.26839	+	3.92897i	0.149573	+	0.259068i
$231$		0			0
$232$	3.85578	−	6.67840i	0.253144	−	0.438458i
$233$	8.27045	−	14.3248i	0.541815	−	0.938451i	−0.456985	−	0.889474i	$-0.651071\pi$
$233$	8.27045	−	14.3248i	0.541815	−	0.938451i	0.998800	−	0.0489765i	$-0.0155959\pi$
$234$	1.72211	−	0.451180i	0.112578	−	0.0294946i
$235$	−18.7824	−	32.5321i	−1.22523	−	2.12216i
$236$	−1.58955	−	2.75319i	−0.103471	−	0.179217i
$237$	−0.398143	−	3.09063i	−0.0258621	−	0.200758i
$238$		0			0
$239$	−11.0119	−	19.0732i	−0.712303	−	1.23375i	−0.963990	−	0.265937i	$-0.914319\pi$
$239$	−11.0119	−	19.0732i	−0.712303	−	1.23375i	0.251687	−	0.967809i	$-0.419015\pi$
$240$	2.11248	+	16.3984i	0.136360	+	1.05851i
$241$	−16.7201			−1.07703			−0.538517	−	0.842615i	$-0.681015\pi$
$241$	−16.7201			−1.07703			−0.538517	+	0.842615i	$0.681015\pi$
$242$	−2.52975	−	4.38166i	−0.162619	−	0.281664i
$243$	6.16526	−	14.3175i	0.395502	−	0.918465i
$244$	18.9516			1.21325
$245$		0			0
$246$	3.26524	−	2.49110i	0.208184	−	0.158827i
$247$	3.36069			0.213836
$248$	3.33696	−	5.77978i	0.211897	−	0.367017i
$249$	16.9696	−	12.9464i	1.07541	−	0.820444i
$250$	3.32803	+	5.76432i	0.210483	+	0.364568i
$251$	8.53099			0.538471			0.269236	−	0.963074i	$-0.413229\pi$
$251$	8.53099			0.538471			0.269236	+	0.963074i	$0.413229\pi$
$252$		0			0
$253$	−2.21153			−0.139038
$254$	−0.314743	−	0.545151i	−0.0197488	−	0.0342058i
$255$	−0.204276	−	1.58572i	−0.0127923	−	0.0993017i
$256$	0.123861	−	0.214533i	0.00774131	−	0.0134083i
$257$	17.1197			1.06790			0.533950	−	0.845516i	$-0.320707\pi$
$257$	17.1197			1.06790			0.533950	+	0.845516i	$0.320707\pi$
$258$	7.90875	+	3.30173i	0.492377	+	0.205557i
$259$		0			0
$260$	−7.75135			−0.480718
$261$	12.0219	−	3.14965i	0.744137	−	0.194958i
$262$	3.72617	+	6.45392i	0.230204	+	0.398725i
$263$	20.5527			1.26733			0.633666	−	0.773607i	$-0.281549\pi$
$263$	20.5527			1.26733			0.633666	+	0.773607i	$0.281549\pi$
$264$	2.65576	+	1.10872i	0.163451	+	0.0682370i
$265$	−18.2585	−	31.6246i	−1.12161	−	1.94269i
$266$		0			0
$267$	−3.31514	+	2.52917i	−0.202883	+	0.154783i
$268$	0.902816	+	1.56372i	0.0551483	+	0.0955196i
$269$	−9.92267	−	17.1866i	−0.604996	−	1.04788i	−0.992052	−	0.125827i	$-0.959842\pi$
$269$	−9.92267	−	17.1866i	−0.604996	−	1.04788i	0.387057	−	0.922056i	$-0.373492\pi$
$270$	5.85477	−	7.49960i	0.356310	−	0.456411i
$271$	−5.32056	+	9.21548i	−0.323201	+	0.559801i	−0.981147	−	0.193265i	$-0.938092\pi$
$271$	−5.32056	+	9.21548i	−0.323201	+	0.559801i	0.657946	+	0.753065i	$0.271426\pi$
$272$	0.323121	−	0.559663i	0.0195921	−	0.0339345i
$273$		0			0
$274$	−0.121114	−	0.209776i	−0.00731676	−	0.0126730i
$275$	−7.70745			−0.464777
$276$	−5.98496	+	4.56602i	−0.360252	+	0.274842i
$277$	−24.8813			−1.49497			−0.747487	−	0.664276i	$-0.768740\pi$
$277$	−24.8813			−1.49497			−0.747487	+	0.664276i	$0.768740\pi$
$278$	−2.44705	+	4.23841i	−0.146764	+	0.254203i
$279$	10.4043	−	2.72585i	0.622889	−	0.163192i
$280$		0			0
$281$	−6.83733	+	11.8426i	−0.407881	+	0.706470i	−0.994652	−	0.103282i	$-0.967065\pi$
$281$	−6.83733	+	11.8426i	−0.407881	+	0.706470i	0.586771	+	0.809753i	$0.300399\pi$
$282$	−6.94657	+	5.29964i	−0.413662	+	0.315589i
$283$	3.16089	−	5.47483i	0.187896	−	0.325445i	−0.756653	−	0.653817i	$-0.773167\pi$
$283$	3.16089	−	5.47483i	0.187896	−	0.325445i	0.944548	+	0.328372i	$0.106500\pi$
$284$	−4.33734	+	7.51249i	−0.257374	+	0.445784i
$285$	14.2798	−	10.8943i	0.845861	−	0.645320i
$286$	−0.264830	+	0.458699i	−0.0156597	+	0.0271234i
$287$		0			0
$288$	14.5247	−	3.80537i	0.855878	−	0.224234i
$289$	8.46875	−	14.6683i	0.498162	−	0.862842i
$290$	7.58515			0.445415
$291$	15.2085	−	11.6028i	0.891538	−	0.680168i
$292$	3.21095			0.187907
$293$	1.31508	+	2.27778i	0.0768277	+	0.133069i	0.901880	−	0.431987i	$-0.142188\pi$
$293$	1.31508	+	2.27778i	0.0768277	+	0.133069i	−0.825052	+	0.565057i	$0.808854\pi$
$294$		0			0
$295$	3.34616	−	5.79573i	0.194821	−	0.337440i
$296$	−4.40382	+	7.62764i	−0.255967	+	0.443348i
$297$	1.73902	+	4.29955i	0.100908	+	0.249485i
$298$	5.21256	+	9.02841i	0.301955	+	0.523002i
$299$	−1.48255	−	2.56786i	−0.0857384	−	0.148503i
$300$	−20.8583	+	15.9131i	−1.20426	+	0.918745i
$301$		0			0
$302$	0.371500	+	0.643457i	0.0213774	+	0.0370268i
$303$	−4.15515	−	1.73468i	−0.238707	−	0.0996550i
$304$	7.25980			0.416378
$305$	19.9475	+	34.5501i	1.14219	+	1.97833i
$306$	−0.359735	+	0.0942478i	−0.0205647	+	0.00538779i
$307$	2.79496			0.159517			0.0797583	−	0.996814i	$-0.474585\pi$
$307$	2.79496			0.159517			0.0797583	+	0.996814i	$0.474585\pi$
$308$		0			0
$309$	15.5225	+	6.48030i	0.883045	+	0.368652i
$310$	6.56452			0.372840
$311$	−7.55013	+	13.0772i	−0.428129	+	0.741541i	−0.996707	−	0.0810885i	$-0.974160\pi$
$311$	−7.55013	+	13.0772i	−0.428129	+	0.741541i	0.568578	+	0.822629i	$0.307494\pi$
$312$	0.492993	+	3.82692i	0.0279102	+	0.216657i
$313$	−12.7392	−	22.0650i	−0.720064	−	1.24719i	−0.960974	−	0.276640i	$-0.910779\pi$
$313$	−12.7392	−	22.0650i	−0.720064	−	1.24719i	0.240910	−	0.970548i	$-0.422554\pi$
$314$	−8.27090			−0.466754
$315$		0			0
$316$	3.15587			0.177531
$317$	−16.2605	−	28.1639i	−0.913278	−	1.58184i	−0.809403	−	0.587253i	$-0.800209\pi$
$317$	−16.2605	−	28.1639i	−0.913278	−	1.58184i	−0.103875	−	0.994590i	$-0.533124\pi$
$318$	−6.75279	+	5.15181i	−0.378678	+	0.288899i
$319$	−1.84875	+	3.20214i	−0.103510	+	0.179285i
$320$	−9.92743			−0.554960
$321$	15.0106	−	11.4518i	0.837811	−	0.639179i
$322$		0			0
$323$	−0.702021			−0.0390615
$324$	13.5833	+	8.04522i	0.754625	+	0.446957i
$325$	−5.16688	−	8.94931i	−0.286607	−	0.496418i
$326$	−3.31373			−0.183531
$327$	0.469578	+	3.64516i	0.0259677	+	0.201578i
$328$	4.45083	+	7.70906i	0.245756	+	0.425661i
$329$		0			0
$330$	0.361672	+	2.80753i	0.0199094	+	0.154549i
$331$	−9.04741	−	15.6706i	−0.497291	−	0.861333i	0.502704	−	0.864458i	$-0.332338\pi$
$331$	−9.04741	−	15.6706i	−0.497291	−	0.861333i	−0.999995	+	0.00312545i	$0.999005\pi$
$332$	10.8081	+	18.7201i	0.593170	+	1.02740i
$333$	−13.7307	+	3.59733i	−0.752435	+	0.197132i
$334$	4.37132	−	7.57135i	0.239188	−	0.414286i
$335$	−1.90051	+	3.29179i	−0.103836	+	0.179850i
$336$		0			0
$337$	−12.5086	−	21.6656i	−0.681389	−	1.18020i	−0.974557	−	0.224139i	$-0.928043\pi$
$337$	−12.5086	−	21.6656i	−0.681389	−	1.18020i	0.293168	−	0.956061i	$-0.405290\pi$
$338$	5.73615			0.312005
$339$	−3.50234	−	27.1874i	−0.190221	−	1.47662i
$340$	1.61919			0.0878130
$341$	−1.59999	+	2.77127i	−0.0866446	+	0.150073i
$342$	−2.93752	−	2.97041i	−0.158843	−	0.160621i
$343$		0			0
$344$	−9.28778	+	16.0869i	−0.500764	+	0.867348i
$345$	−14.6236	−	6.10503i	−0.787309	−	0.328684i
$346$	0.963682	−	1.66915i	0.0518078	−	0.0897338i
$347$	−5.37444	+	9.30881i	−0.288515	+	0.499723i	−0.973456	−	0.228876i	$-0.926495\pi$
$347$	−5.37444	+	9.30881i	−0.288515	+	0.499723i	0.684940	+	0.728599i	$0.259828\pi$
$348$	1.60807	+	12.4828i	0.0862013	+	0.669149i
$349$	1.64301	−	2.84577i	0.0879482	−	0.152331i	−0.818695	−	0.574228i	$-0.805302\pi$
$349$	1.64301	−	2.84577i	0.0879482	−	0.152331i	0.906644	+	0.421897i	$0.138636\pi$
$350$		0			0
$351$	−3.82651	+	4.90153i	−0.204244	+	0.261624i
$352$	−2.23365	+	3.86879i	−0.119054	+	0.206207i
$353$	−16.8192			−0.895195			−0.447598	−	0.894235i	$-0.647720\pi$
$353$	−16.8192			−0.895195			−0.447598	+	0.894235i	$0.647720\pi$
$354$	−1.43644	−	0.599681i	−0.0763458	−	0.0318727i
$355$	−18.2610			−0.969195
$356$	−2.11144	−	3.65711i	−0.111906	−	0.193827i
$357$		0			0
$358$	−1.81864	+	3.14997i	−0.0961180	+	0.166481i
$359$	11.8921	−	20.5978i	0.627642	−	1.08711i	−0.360382	−	0.932805i	$-0.617354\pi$
$359$	11.8921	−	20.5978i	0.627642	−	1.08711i	0.988024	−	0.154303i	$-0.0493131\pi$
$360$	14.5004	+	14.6627i	0.764237	+	0.772792i
$361$	5.55680	+	9.62466i	0.292463	+	0.506561i
$362$	−2.79088	−	4.83395i	−0.146686	−	0.254067i
$363$	16.3085	+	6.80845i	0.855976	+	0.357351i
$364$		0			0
$365$	3.37968	+	5.85377i	0.176900	+	0.306401i
$366$	7.37747	−	5.62838i	0.385626	−	0.294200i
$367$	0.689984			0.0360169			0.0180084	−	0.999838i	$-0.494267\pi$
$367$	0.689984			0.0360169			0.0180084	+	0.999838i	$0.494267\pi$
$368$	−3.20263	−	5.54712i	−0.166949	−	0.289164i
$369$	−3.78998	+	13.8359i	−0.197298	+	0.720267i
$370$	−8.66327			−0.450382
$371$		0			0
$372$	1.39169	+	10.8032i	0.0721558	+	0.560119i
$373$	−3.76012			−0.194691			−0.0973457	−	0.995251i	$-0.531035\pi$
$373$	−3.76012			−0.194691			−0.0973457	+	0.995251i	$0.531035\pi$
$374$	0.0553208	−	0.0958184i	0.00286057	−	0.00495465i
$375$	−21.4548	−	8.95690i	−1.10792	−	0.462532i
$376$	−9.46882	−	16.4005i	−0.488317	−	0.845790i
$377$	−4.95744			−0.255321
$378$		0			0
$379$	32.8735			1.68860			0.844300	−	0.535872i	$-0.180017\pi$
$379$	32.8735			1.68860			0.844300	+	0.535872i	$0.180017\pi$
$380$	9.09489	+	15.7528i	0.466558	+	0.808102i
$381$	2.02905	+	0.847085i	0.103952	+	0.0433975i
$382$	−5.91222	+	10.2403i	−0.302495	+	0.523937i
$383$	1.07267			0.0548109			0.0274055	−	0.999624i	$-0.491275\pi$
$383$	1.07267			0.0548109			0.0274055	+	0.999624i	$0.491275\pi$
$384$	2.51021	+	19.4858i	0.128099	+	0.994381i
$385$		0			0
$386$	−2.94276			−0.149782
$387$	−28.9583	+	7.58687i	−1.47204	+	0.385662i
$388$	9.68640	+	16.7773i	0.491752	+	0.851740i
$389$	−23.7436			−1.20385			−0.601925	−	0.798553i	$-0.705599\pi$
$389$	−23.7436			−1.20385			−0.601925	+	0.798553i	$0.705599\pi$
$390$	−3.01743	+	2.30204i	−0.152794	+	0.116569i
$391$	0.309693	+	0.536405i	0.0156619	+	0.0271271i
$392$		0			0
$393$	−24.0215	−	10.0284i	−1.21172	−	0.505868i
$394$	−3.83510	−	6.64258i	−0.193209	−	0.334648i
$395$	3.32170	+	5.75336i	0.167133	+	0.289483i
$396$	−4.54365	+	1.19040i	−0.228327	+	0.0598200i
$397$	0.0160489	−	0.0277975i	0.000805471	−	0.00139512i	−0.865622	−	0.500697i	$-0.833077\pi$
$397$	0.0160489	−	0.0277975i	0.000805471	−	0.00139512i	0.866428	+	0.499302i	$0.166410\pi$
$398$	3.84208	−	6.65467i	0.192586	−	0.333569i
$399$		0			0
$400$	−11.1616	−	19.3324i	−0.558078	−	0.966619i
$401$	24.5256			1.22475			0.612374	−	0.790568i	$-0.290215\pi$
$401$	24.5256			1.22475			0.612374	+	0.790568i	$0.290215\pi$
$402$	0.815851	+	0.340600i	0.0406910	+	0.0169876i
$403$	−4.29039			−0.213719
$404$	2.28004	−	3.94914i	0.113436	−	0.196477i
$405$	−0.369938	+	33.2312i	−0.0183824	+	1.65127i
$406$		0			0
$407$	2.11153	−	3.65728i	0.104665	−	0.181284i
$408$	−0.102982	−	0.799412i	−0.00509838	−	0.0395768i
$409$	13.3948	−	23.2006i	0.662333	−	1.14719i	−0.317669	−	0.948202i	$-0.602900\pi$
$409$	13.3948	−	23.2006i	0.662333	−	1.14719i	0.980001	−	0.198992i	$-0.0637667\pi$
$410$	−4.37787	+	7.58269i	−0.216208	+	0.374483i
$411$	0.780785	+	0.325960i	0.0385133	+	0.0160784i
$412$	−8.51759	+	14.7529i	−0.419631	+	0.726823i
$413$		0			0
$414$	−0.973773	+	3.55490i	−0.0478583	+	0.174714i
$415$	−22.7520	+	39.4077i	−1.11685	+	1.93445i
$416$	−5.98952			−0.293660
$417$	−2.18416	−	16.9548i	−0.106959	−	0.830280i
$418$	1.24293			0.0607938
$419$	10.5262	+	18.2320i	0.514240	+	0.890689i	0.999864	+	0.0165215i	$0.00525920\pi$
$419$	10.5262	+	18.2320i	0.514240	+	0.890689i	−0.485624	+	0.874168i	$0.661407\pi$
$420$		0			0
$421$	−7.44533	+	12.8957i	−0.362863	+	0.628498i	−0.988431	−	0.151672i	$-0.951534\pi$
$421$	−7.44533	+	12.8957i	−0.362863	+	0.628498i	0.625568	+	0.780170i	$0.284867\pi$
$422$	−0.382760	+	0.662959i	−0.0186325	+	0.0322724i
$423$	8.06290	−	29.4349i	0.392032	−	1.43117i
$424$	−9.20469	−	15.9430i	−0.447019	−	0.774260i
$425$	1.07932	+	1.86944i	0.0523547	+	0.0906809i
$426$	0.542675	+	4.21258i	0.0262927	+	0.204100i
$427$		0			0
$428$	9.56037	+	16.5590i	0.462118	+	0.800412i
$429$	−0.236379	−	1.83492i	−0.0114125	−	0.0885908i
$430$	−18.2711			−0.881110
$431$	−7.95192	−	13.7731i	−0.383031	−	0.663428i	0.608463	−	0.793582i	$-0.291786\pi$
$431$	−7.95192	−	13.7731i	−0.383031	−	0.663428i	−0.991494	+	0.130154i	$0.958453\pi$
$432$	−8.26607	+	10.5883i	−0.397702	+	0.509431i
$433$	16.3658			0.786490			0.393245	−	0.919434i	$-0.371352\pi$
$433$	16.3658			0.786490			0.393245	+	0.919434i	$0.371352\pi$
$434$		0			0
$435$	−21.0644	+	16.0704i	−1.00996	+	0.770515i
$436$	−3.72210			−0.178256
$437$	−3.47905	+	6.02590i	−0.166426	+	0.288258i
$438$	1.24995	−	0.953608i	0.0597251	−	0.0455652i
$439$	−7.77236	−	13.4621i	−0.370954	−	0.642512i	0.618758	−	0.785582i	$-0.287636\pi$
$439$	−7.77236	−	13.4621i	−0.370954	−	0.642512i	−0.989713	+	0.143070i	$0.954303\pi$
$440$	−6.13543			−0.292495
$441$		0			0
$442$	0.148343			0.00705594
$443$	−0.895027	−	1.55023i	−0.0425240	−	0.0736537i	0.843980	−	0.536375i	$-0.180207\pi$
$443$	−0.895027	−	1.55023i	−0.0425240	−	0.0736537i	−0.886504	+	0.462721i	$0.846873\pi$
$444$	−1.83663	−	14.2571i	−0.0871625	−	0.676611i
$445$	4.44477	−	7.69857i	0.210702	−	0.364947i
$446$	2.69922			0.127812
$447$	−33.6038	−	14.0288i	−1.58940	−	0.663540i
$448$		0			0
$449$	13.5666			0.640250			0.320125	−	0.947375i	$-0.396275\pi$
$449$	13.5666			0.640250			0.320125	+	0.947375i	$0.396275\pi$
$450$	−3.39372	+	12.3893i	−0.159981	+	0.584036i
$451$	−2.13407	−	3.69631i	−0.100489	−	0.174053i
$452$	27.7612			1.30578
$453$	−2.39495	−	0.999837i	−0.112524	−	0.0469764i
$454$	3.98588	+	6.90375i	0.187067	+	0.324009i
$455$		0			0
$456$	7.19889	−	5.49214i	0.337119	−	0.257193i
$457$	−1.28459	−	2.22497i	−0.0600905	−	0.104080i	0.834415	−	0.551136i	$-0.185806\pi$
$457$	−1.28459	−	2.22497i	−0.0600905	−	0.104080i	−0.894506	+	0.447057i	$0.852472\pi$
$458$	2.47151	+	4.28078i	0.115486	+	0.200028i
$459$	0.799326	−	1.02389i	0.0373094	−	0.0477910i
$460$	8.02434	−	13.8986i	0.374137	−	0.648024i
$461$	−18.0934	+	31.3388i	−0.842695	+	1.45959i	0.0449122	+	0.998991i	$0.485699\pi$
$461$	−18.0934	+	31.3388i	−0.842695	+	1.45959i	−0.887608	+	0.460600i	$0.847634\pi$
$462$		0			0
$463$	8.19224	+	14.1894i	0.380726	+	0.659436i	0.991166	−	0.132626i	$-0.0423409\pi$
$463$	8.19224	+	14.1894i	0.380726	+	0.659436i	−0.610440	+	0.792062i	$0.709008\pi$
$464$	−10.7091			−0.497158
$465$	−18.2301	+	13.9080i	−0.845400	+	0.644968i
$466$	8.20210			0.379955
$467$	4.35022	−	7.53480i	0.201304	−	0.348669i	−0.747645	−	0.664099i	$-0.768815\pi$
$467$	4.35022	−	7.53480i	0.201304	−	0.348669i	0.948949	+	0.315430i	$0.102149\pi$
$468$	−4.42815	−	4.47772i	−0.204692	−	0.206983i
$469$		0			0
$470$	9.31361	−	16.1316i	0.429605	−	0.744097i
$471$	22.9688	−	17.5233i	1.05835	−	0.807429i
$472$	1.68691	−	2.92181i	0.0776462	−	0.134487i
$473$	4.45328	−	7.71330i	0.204762	−	0.354658i
$474$	1.22851	−	0.937250i	0.0564274	−	0.0430493i
$475$	−12.1249	+	21.0010i	−0.556330	+	0.963591i
$476$		0			0
$477$	7.83799	−	28.6138i	0.358877	−	1.31014i
$478$	5.46047	−	9.45782i	0.249756	−	0.432591i
$479$	17.7674			0.811813			0.405907	−	0.913915i	$-0.366956\pi$
$479$	17.7674			0.811813			0.405907	+	0.913915i	$0.366956\pi$
$480$	−25.4498	+	19.4160i	−1.16162	+	0.886217i
$481$	5.66207			0.258168
$482$	−4.14548	−	7.18018i	−0.188821	−	0.327048i
$483$		0			0
$484$	−8.94890	+	15.4999i	−0.406768	+	0.704543i
$485$	−20.3908	+	35.3179i	−0.925898	+	1.60370i
$486$	7.67699	−	0.902212i	0.348235	−	0.0409251i
$487$	8.32763	+	14.4239i	0.377361	+	0.653608i	0.990677	−	0.136229i	$-0.0434983\pi$
$487$	8.32763	+	14.4239i	0.377361	+	0.653608i	−0.613316	+	0.789837i	$0.710165\pi$
$488$	10.0562	+	17.4178i	0.455222	+	0.788467i
$489$	9.20245	−	7.02068i	0.416149	−	0.317486i
$490$		0			0
$491$	−3.21021	−	5.56025i	−0.144875	−	0.250930i	0.784451	−	0.620190i	$-0.212945\pi$
$491$	−3.21021	−	5.56025i	−0.144875	−	0.250930i	−0.929326	+	0.369260i	$0.879611\pi$
$492$	−13.4069	−	5.59708i	−0.604429	−	0.252336i
$493$	1.03557			0.0466396
$494$	0.833230	+	1.44320i	0.0374888	+	0.0649325i
$495$	−6.95259	−	7.03042i	−0.312496	−	0.315994i
$496$	−9.26814			−0.416152
$497$		0			0
$498$	9.76698	+	4.07750i	0.437669	+	0.182717i
$499$	11.1459			0.498960			0.249480	−	0.968380i	$-0.419740\pi$
$499$	11.1459			0.498960			0.249480	+	0.968380i	$0.419740\pi$
$500$	11.7728	−	20.3911i	0.526495	−	0.911916i
$501$	3.90170	+	30.2875i	0.174315	+	1.35314i
$502$	2.11512	+	3.66350i	0.0944026	+	0.163510i
$503$	17.7223			0.790200			0.395100	−	0.918638i	$-0.370710\pi$
$503$	17.7223			0.790200			0.395100	+	0.918638i	$0.370710\pi$
$504$		0			0
$505$	9.59939			0.427167
$506$	−0.548314	−	0.949708i	−0.0243755	−	0.0422197i
$507$	−15.9296	+	12.1530i	−0.707460	+	0.539732i
$508$	−1.11339	+	1.92845i	−0.0493988	+	0.0855612i
$509$	−31.0823			−1.37770			−0.688848	−	0.724906i	$-0.741883\pi$
$509$	−31.0823			−1.37770			−0.688848	+	0.724906i	$0.741883\pi$
$510$	0.630316	−	0.480878i	0.0279109	−	0.0212936i
$511$		0			0
$512$	−22.5634			−0.997169
$513$	14.4510	+	2.02539i	0.638026	+	0.0894230i
$514$	4.24456	+	7.35180i	0.187220	+	0.324274i
$515$	−35.8607			−1.58021
$516$	−3.87350	−	30.0686i	−0.170522	−	1.32370i
$517$	4.54008	+	7.86365i	0.199672	+	0.345843i
$518$		0			0
$519$	0.860152	+	6.67704i	0.0377565	+	0.293089i
$520$	−4.11304	−	7.12399i	−0.180369	−	0.312408i
$521$	2.37986	+	4.12203i	0.104263	+	0.180590i	0.913437	−	0.406980i	$-0.133418\pi$
$521$	2.37986	+	4.12203i	0.104263	+	0.180590i	−0.809174	+	0.587570i	$0.800085\pi$
$522$	4.33321	+	4.38172i	0.189659	+	0.191783i
$523$	−20.1258	+	34.8588i	−0.880038	+	1.52427i	−0.0287402	+	0.999587i	$0.509150\pi$
$523$	−20.1258	+	34.8588i	−0.880038	+	1.52427i	−0.851298	+	0.524683i	$0.824184\pi$
$524$	13.1812	−	22.8305i	0.575823	−	0.997355i
$525$		0			0
$526$	5.09571	+	8.82602i	0.222183	+	0.384833i
$527$	0.896226			0.0390402
$528$	−0.510628	−	3.96382i	−0.0222222	−	0.172503i
$529$	−16.8609			−0.733084
$530$	9.05381	−	15.6817i	0.393272	−	0.681168i
$531$	5.25960	−	1.37798i	0.228247	−	0.0597991i
$532$		0			0
$533$	2.86125	−	4.95583i	0.123935	−	0.214661i
$534$	−1.90805	−	0.796568i	−0.0825693	−	0.0344709i
$535$	−20.1255	+	34.8584i	−0.870101	+	1.50706i
$536$	−0.958109	+	1.65949i	−0.0413840	+	0.0716792i
$537$	−1.62326	−	12.6008i	−0.0700488	−	0.543763i
$538$	4.92033	−	8.52227i	0.212131	−	0.367421i
$539$		0			0
$540$	−33.3308	−	4.67150i	−1.43433	−	0.201029i
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	−0.481502	−	0.876445i	$-0.659908\pi$
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	0.999775	−	0.0212301i	$-0.00675826\pi$
$542$	−5.27659			−0.226649
$543$	17.9920	+	7.51125i	0.772109	+	0.322339i
$544$	1.25116			0.0536431
$545$	−3.91769	−	6.78564i	−0.167815	−	0.290665i
$546$		0			0
$547$	−6.17751	+	10.6998i	−0.264131	+	0.457489i	−0.967336	−	0.253499i	$-0.918419\pi$
$547$	−6.17751	+	10.6998i	−0.264131	+	0.457489i	0.703204	+	0.710988i	$0.251752\pi$
$548$	−0.428436	+	0.742073i	−0.0183019	+	0.0316998i
$549$	−8.56305	+	31.2607i	−0.365462	+	1.33418i
$550$	−1.91094	−	3.30985i	−0.0814828	−	0.141132i
$551$	5.81671	+	10.0748i	0.247800	+	0.429203i
$552$	−7.37223	−	3.07774i	−0.313783	−	0.130997i
$553$		0			0
$554$	−6.16893	−	10.6849i	−0.262093	−	0.453958i
$555$	24.0584	−	18.3545i	1.02122	−	0.779107i
$556$	17.3127			0.734220
$557$	4.03845	+	6.99479i	0.171114	+	0.296379i	0.938810	−	0.344436i	$-0.111930\pi$
$557$	4.03845	+	6.99479i	0.171114	+	0.296379i	−0.767695	+	0.640815i	$0.778597\pi$
$558$	3.75015	+	3.79213i	0.158757	+	0.160534i
$559$	11.9415			0.505070
$560$		0			0
$561$	0.0493776	+	0.383300i	0.00208472	+	0.0161829i
$562$	−6.78083			−0.286032
$563$	22.6064	−	39.1554i	0.952744	−	1.65020i	0.213296	−	0.976988i	$-0.431580\pi$
$563$	22.6064	−	39.1554i	0.952744	−	1.65020i	0.739448	−	0.673214i	$-0.235087\pi$
$564$	28.5222	+	11.9074i	1.20100	+	0.501391i
$565$	29.2200	+	50.6106i	1.22930	+	2.12920i
$566$	3.13477			0.131764
$567$		0			0
$568$	−9.20596			−0.386274
$569$	−11.2149	−	19.4248i	−0.470155	−	0.814332i	0.529263	−	0.848458i	$-0.322468\pi$
$569$	−11.2149	−	19.4248i	−0.470155	−	0.814332i	−0.999418	+	0.0341263i	$0.989135\pi$
$570$	8.21881	+	3.43117i	0.344248	+	0.143716i
$571$	10.9134	−	18.9026i	0.456713	−	0.791050i	−0.542072	−	0.840332i	$-0.682360\pi$
$571$	10.9134	−	18.9026i	0.456713	−	0.791050i	0.998785	+	0.0492820i	$0.0156933\pi$
$572$	1.87365			0.0783413
$573$	−5.27706	−	40.9638i	−0.220452	−	1.71129i
$574$		0			0
$575$	21.3954			0.892251
$576$	−5.67130	−	5.73479i	−0.236304	−	0.238949i
$577$	16.1022	+	27.8898i	0.670342	+	1.16107i	0.977807	+	0.209508i	$0.0671861\pi$
$577$	16.1022	+	27.8898i	0.670342	+	1.16107i	−0.307465	+	0.951559i	$0.599481\pi$
$578$	8.39877			0.349343
$579$	8.17222	−	6.23471i	0.339626	−	0.259106i
$580$	−13.4161	−	23.2373i	−0.557072	−	0.964878i
$581$		0			0
$582$	8.75335	+	3.65433i	0.362838	+	0.151477i
$583$	4.41343	+	7.64429i	0.182786	+	0.316594i
$584$	1.70380	+	2.95107i	0.0705039	+	0.122116i
$585$	3.50234	−	12.7858i	0.144804	−	0.528629i
$586$	−0.652105	+	1.12948i	−0.0269382	+	0.0466584i
$587$	9.72304	−	16.8408i	0.401313	−	0.695094i	−0.592572	−	0.805518i	$-0.701887\pi$
$587$	9.72304	−	16.8408i	0.401313	−	0.695094i	0.993885	+	0.110424i	$0.0352208\pi$
$588$		0			0
$589$	5.03404	+	8.71921i	0.207424	+	0.359269i
$590$	3.31851			0.136621
$591$	24.7237	+	10.3216i	1.01700	+	0.424574i
$592$	12.2313			0.502701
$593$	14.4202	−	24.9766i	0.592168	−	1.02566i	−0.401772	−	0.915740i	$-0.631606\pi$
$593$	14.4202	−	24.9766i	0.592168	−	1.02566i	0.993940	−	0.109925i	$-0.0350611\pi$
$594$	−1.41521	+	1.81280i	−0.0580669	+	0.0743801i
$595$		0			0
$596$	18.4392	−	31.9377i	0.755300	−	1.30822i
$597$	3.42932	+	26.6205i	0.140353	+	1.08950i
$598$	0.735152	−	1.27332i	0.0300626	−	0.0520699i
$599$	23.4994	−	40.7022i	0.960161	−	1.66305i	0.238072	−	0.971247i	$-0.423484\pi$
$599$	23.4994	−	40.7022i	0.960161	−	1.66305i	0.722089	−	0.691800i	$-0.243182\pi$
$600$	−25.6931	−	10.7263i	−1.04892	−	0.437899i
$601$	7.80843	−	13.5246i	0.318512	−	0.551680i	−0.661665	−	0.749799i	$-0.730150\pi$
$601$	7.80843	−	13.5246i	0.318512	−	0.551680i	0.980178	+	0.198119i	$0.0634834\pi$
$602$		0			0
$603$	−2.98729	+	0.782646i	−0.121652	+	0.0318718i
$604$	1.31417	−	2.27620i	0.0534727	−	0.0926174i
$605$	−37.6766			−1.53177
$606$	−0.285271	−	2.21445i	−0.0115883	−	0.0899560i
$607$	28.6532			1.16300			0.581500	−	0.813547i	$-0.302466\pi$
$607$	28.6532			1.16300			0.581500	+	0.813547i	$0.302466\pi$
$608$	7.02769	+	12.1723i	0.285010	+	0.493652i
$609$		0			0
$610$	−9.89134	+	17.1323i	−0.400489	+	0.693667i
$611$	−6.08711	+	10.5432i	−0.246258	+	0.426531i
$612$	0.925004	+	0.935359i	0.0373911	+	0.0378097i
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	0.993873	+	0.110524i	$0.0352529\pi$
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	−0.401220	+	0.915982i	$0.631414\pi$
$614$	0.692965	+	1.20025i	0.0279658	+	0.0484382i
$615$	−3.90755	−	30.3328i	−0.157568	−	1.22314i
$616$		0			0
$617$	2.06401	+	3.57497i	0.0830938	+	0.143923i	0.904577	−	0.426310i	$-0.140187\pi$
$617$	2.06401	+	3.57497i	0.0830938	+	0.143923i	−0.821484	+	0.570232i	$0.806853\pi$
$618$	1.06569	+	8.27259i	0.0428685	+	0.332772i
$619$	−22.7130			−0.912912			−0.456456	−	0.889746i	$-0.650881\pi$
$619$	−22.7130			−0.912912			−0.456456	+	0.889746i	$0.650881\pi$
$620$	−11.6109	−	20.1106i	−0.466304	−	0.807662i
$621$	−4.82742	−	11.9353i	−0.193718	−	0.478947i
$622$	−7.48774			−0.300231
$623$		0			0
$624$	4.26017	−	3.25014i	0.170543	−	0.130110i
$625$	6.38996			0.255598
$626$	6.31698	−	10.9413i	0.252477	−	0.437304i
$627$	−3.45170	+	2.63335i	−0.137848	+	0.105166i
$628$	14.6290	+	25.3382i	0.583761	+	1.01110i
$629$	−1.18276			−0.0471597
$630$		0			0
$631$	−38.6411			−1.53828			−0.769138	−	0.639082i	$-0.779314\pi$
$631$	−38.6411			−1.53828			−0.769138	+	0.639082i	$0.779314\pi$
$632$	1.67458	+	2.90045i	0.0666110	+	0.115374i
$633$	−0.341639	−	2.65202i	−0.0135789	−	0.105408i
$634$	8.06304	−	13.9656i	0.320224	−	0.554645i
$635$	−4.68759			−0.186021
$636$	27.7266	+	11.5752i	1.09943	+	0.458988i
$637$		0			0
$638$	−1.83348			−0.0725881
$639$	−10.4321	−	10.5489i	−0.412687	−	0.417306i
$640$	−20.9427	−	36.2737i	−0.827831	−	1.43385i
$641$	−28.4726			−1.12460			−0.562301	−	0.826933i	$-0.690084\pi$
$641$	−28.4726			−1.12460			−0.562301	+	0.826933i	$0.690084\pi$
$642$	8.63946	+	3.60678i	0.340972	+	0.142348i
$643$	8.52125	+	14.7592i	0.336045	+	0.582048i	0.983685	−	0.179899i	$-0.0575771\pi$
$643$	8.52125	+	14.7592i	0.336045	+	0.582048i	−0.647640	+	0.761947i	$0.724244\pi$
$644$		0			0
$645$	50.7400	−	38.7103i	1.99788	−	1.52422i
$646$	−0.174055	−	0.301472i	−0.00684810	−	0.0118613i
$647$	−1.68809	−	2.92386i	−0.0663657	−	0.114949i	0.830933	−	0.556372i	$-0.187807\pi$
$647$	−1.68809	−	2.92386i	−0.0663657	−	0.114949i	−0.897299	+	0.441423i	$0.854474\pi$
$648$	−0.186497	+	16.7529i	−0.00732631	+	0.658115i
$649$	−0.808833	+	1.40094i	−0.0317495	+	0.0549917i
$650$	2.56209	−	4.43768i	0.100494	−	0.174060i
$651$		0			0
$652$	5.86110	+	10.1517i	0.229538	+	0.397572i
$653$	−18.3451			−0.717899			−0.358950	−	0.933357i	$-0.616865\pi$
$653$	−18.3451			−0.717899			−0.358950	+	0.933357i	$0.616865\pi$
$654$	−1.44893	+	1.10541i	−0.0566578	+	0.0432251i
$655$	55.4954			2.16838
$656$	6.18090	−	10.7056i	0.241324	−	0.417985i
$657$	−1.45083	+	5.29646i	−0.0566021	+	0.206635i
$658$		0			0
$659$	−13.9248	+	24.1184i	−0.542432	+	0.939519i	0.456332	+	0.889810i	$0.349163\pi$
$659$	−13.9248	+	24.1184i	−0.542432	+	0.939519i	−0.998764	+	0.0497098i	$0.984170\pi$
$660$	7.96125	−	6.07376i	0.309891	−	0.236421i
$661$	19.5071	−	33.7872i	0.758737	−	1.31417i	−0.184758	−	0.982784i	$-0.559150\pi$
$661$	19.5071	−	33.7872i	0.758737	−	1.31417i	0.943495	−	0.331387i	$-0.107516\pi$
$662$	4.48633	−	7.77054i	0.174366	−	0.302011i
$663$	−0.411957	+	0.314288i	−0.0159991	+	0.0122059i
$664$	−11.4700	+	19.8667i	−0.445123	+	0.770976i
$665$		0			0
$666$	−4.94911	−	5.00452i	−0.191774	−	0.193921i
$667$	5.13203	−	8.88894i	0.198713	−	0.344181i
$668$	−30.9268			−1.19659
$669$	−7.49590	+	5.71873i	−0.289808	+	0.221099i
$670$	−1.88481			−0.0728165
$671$	−4.82170	−	8.35143i	−0.186140	−	0.322404i
$672$		0			0
$673$	24.6154	−	42.6352i	0.948856	−	1.64347i	0.201014	−	0.979588i	$-0.435576\pi$
$673$	24.6154	−	42.6352i	0.948856	−	1.64347i	0.747841	−	0.663878i	$-0.231090\pi$
$674$	6.20264	−	10.7433i	0.238917	−	0.413816i
$675$	−16.8241	−	41.5959i	−0.647561	−	1.60103i
$676$	−10.1457	−	17.5729i	−0.390219	−	0.675879i
$677$	−11.6958	−	20.2577i	−0.449505	−	0.778565i	0.548849	−	0.835922i	$-0.315066\pi$
$677$	−11.6958	−	20.2577i	−0.449505	−	0.778565i	−0.998354	+	0.0573564i	$0.981733\pi$
$678$	10.8069	−	8.24471i	0.415035	−	0.316636i
$679$		0			0
$680$	0.859180	+	1.48814i	0.0329480	+	0.0570677i
$681$	−25.6958	−	10.7274i	−0.984663	−	0.411075i
$682$	−1.58677			−0.0607607
$683$	−15.1632	−	26.2634i	−0.580204	−	1.00494i	−0.995455	−	0.0952356i	$-0.969640\pi$
$683$	−15.1632	−	26.2634i	−0.580204	−	1.00494i	0.415251	−	0.909707i	$-0.363694\pi$
$684$	−3.90425	+	14.2530i	−0.149283	+	0.544979i
$685$	−1.80380			−0.0689196
$686$		0			0
$687$	−15.9330	−	6.65169i	−0.607884	−	0.253778i
$688$	25.7961			0.983466
$689$	−5.91731	+	10.2491i	−0.225432	+	0.390459i
$690$	−1.00398	−	7.79353i	−0.0382209	−	0.296695i
$691$	−2.05665	−	3.56223i	−0.0782387	−	0.135513i	0.824251	−	0.566224i	$-0.191596\pi$
$691$	−2.05665	−	3.56223i	−0.0782387	−	0.135513i	−0.902490	+	0.430711i	$0.858263\pi$
$692$	−6.81797			−0.259180
$693$		0			0
$694$	−5.33003			−0.202325
$695$	18.2224	+	31.5621i	0.691215	+	1.19722i
$696$	−10.6192	+	8.10158i	−0.402522	+	0.307090i
$697$	−0.597691	+	1.03523i	−0.0226392	+	0.0392122i
$698$	1.62943			0.0616749
$699$	−22.7778	+	17.3775i	−0.861534	+	0.657277i
$700$		0			0
$701$	29.1835			1.10225			0.551123	−	0.834424i	$-0.314200\pi$
$701$	29.1835			1.10225			0.551123	+	0.834424i	$0.314200\pi$
$702$	−3.05361	−	0.427980i	−0.115251	−	0.0161531i
$703$	−6.64347	−	11.5068i	−0.250563	−	0.433988i
$704$	2.39965			0.0904403
$705$	8.31303	+	64.5310i	0.313087	+	2.43038i
$706$	−4.17005	−	7.22274i	−0.156942	−	0.271831i
$707$		0			0
$708$	0.703531	+	5.46125i	0.0264403	+	0.205246i
$709$	21.2309	+	36.7729i	0.797342	+	1.38104i	0.921341	+	0.388755i	$0.127095\pi$
$709$	21.2309	+	36.7729i	0.797342	+	1.38104i	−0.123999	+	0.992282i	$0.539572\pi$
$710$	−4.52753	−	7.84192i	−0.169915	−	0.294302i
$711$	−1.42594	+	5.20560i	−0.0534768	+	0.195225i
$712$	2.24075	−	3.88109i	0.0839757	−	0.145450i
$713$	4.44149	−	7.69288i	0.166335	−	0.288101i
$714$		0			0
$715$	1.97211	+	3.41579i	0.0737526	+	0.127743i
$716$	12.8667			0.480852
$717$	4.87385	+	37.8339i	0.182017	+	1.41293i
$718$	11.7938			0.440142
$719$	5.57126	−	9.64970i	0.207773	−	0.359873i	−0.743240	−	0.669025i	$-0.766712\pi$
$719$	5.57126	−	9.64970i	0.207773	−	0.359873i	0.951013	+	0.309152i	$0.100045\pi$
$720$	7.56580	−	27.6201i	0.281961	−	1.02934i
$721$		0			0
$722$	−2.75544	+	4.77256i	−0.102547	+	0.177616i
$723$	26.7246	+	11.1569i	0.993899	+	0.414931i
$724$	−9.87264	+	17.0999i	−0.366914	+	0.635513i
$725$	17.8858	−	30.9790i	0.664260	−	1.15053i
$726$	1.11966	+	8.69150i	0.0415544	+	0.322572i
$727$	14.3410	−	24.8393i	0.531878	−	0.921239i	−0.467430	−	0.884030i	$-0.654820\pi$
$727$	14.3410	−	24.8393i	0.531878	−	0.921239i	0.999308	−	0.0372089i	$-0.0118467\pi$
$728$		0			0
$729$	−19.4080	+	18.7704i	−0.718815	+	0.695202i
$730$	−1.67588	+	2.90270i	−0.0620269	+	0.107434i
$731$	−2.49447			−0.0922614
$732$	−30.2915	−	12.6460i	−1.11960	−	0.467410i
$733$	25.0528			0.925348			0.462674	−	0.886529i	$-0.346890\pi$
$733$	25.0528			0.925348			0.462674	+	0.886529i	$0.346890\pi$
$734$	0.171071	+	0.296303i	0.00631433	+	0.0109367i
$735$		0			0
$736$	6.20047	−	10.7395i	0.228552	−	0.395864i
$737$	0.459391	−	0.795689i	0.0169219	−	0.0293096i
$738$	−6.88127	+	1.80284i	−0.253303	+	0.0663635i
$739$	13.7608	+	23.8344i	0.506198	+	0.876761i	0.999974	+	0.00717223i	$0.00228301\pi$
$739$	13.7608	+	23.8344i	0.506198	+	0.876761i	−0.493776	+	0.869589i	$0.664384\pi$
$740$	15.3230	+	26.5402i	0.563284	+	0.975637i
$741$	−5.37158	−	2.24252i	−0.197330	−	0.0823809i
$742$		0			0
$743$	−7.00608	−	12.1349i	−0.257028	−	0.445186i	0.708416	−	0.705795i	$-0.249410\pi$
$743$	−7.00608	−	12.1349i	−0.257028	−	0.445186i	−0.965444	+	0.260609i	$0.916077\pi$
$744$	−9.19037	+	7.01147i	−0.336935	+	0.257053i
$745$	77.6326			2.84424
$746$	−0.932261	−	1.61472i	−0.0341325	−	0.0591192i
$747$	−35.7623	+	9.36947i	−1.30848	+	0.342811i
$748$	−0.391390			−0.0143106
$749$		0			0
$750$	−1.47297	−	11.4342i	−0.0537854	−	0.417516i
$751$	−52.2594			−1.90697			−0.953486	−	0.301436i	$-0.902534\pi$
$751$	−52.2594			−1.90697			−0.953486	+	0.301436i	$0.902534\pi$
$752$	−13.1494	+	22.7755i	−0.479511	+	0.830537i
$753$	−13.6356	−	5.69254i	−0.496907	−	0.207448i
$754$	−1.22912	−	2.12889i	−0.0447618	−	0.0775298i
$755$	5.53289			0.201363
$756$		0			0
$757$	−43.3447			−1.57539			−0.787694	−	0.616066i	$-0.788725\pi$
$757$	−43.3447			−1.57539			−0.787694	+	0.616066i	$0.788725\pi$
$758$	8.15047	+	14.1170i	0.296038	+	0.512753i
$759$	3.53481	+	1.47571i	0.128306	+	0.0535647i
$760$	−9.65191	+	16.7176i	−0.350112	+	0.606411i
$761$	17.2510			0.625348			0.312674	−	0.949860i	$-0.398775\pi$
$761$	17.2510			0.625348			0.312674	+	0.949860i	$0.398775\pi$
$762$	0.139304	+	1.08137i	0.00504646	+	0.0391738i
$763$		0			0
$764$	41.8285			1.51330
$765$	−0.731610	+	2.67085i	−0.0264514	+	0.0965650i
$766$	0.265952	+	0.460642i	0.00960922	+	0.0166437i
$767$	−2.16889			−0.0783139
$768$	−0.341127	+	0.260251i	−0.0123094	+	0.00939100i
$769$	10.6727	+	18.4856i	0.384867	+	0.666609i	0.991751	−	0.128182i	$-0.0409141\pi$
$769$	10.6727	+	18.4856i	0.384867	+	0.666609i	−0.606884	+	0.794790i	$0.707581\pi$
$770$		0			0
$771$	−27.3634	−	11.4236i	−0.985469	−	0.411411i
$772$	5.20495	+	9.01523i	0.187330	+	0.324465i
$773$	6.57357	+	11.3858i	0.236435	+	0.409517i	0.959689	−	0.281065i	$-0.0906877\pi$
$773$	6.57357	+	11.3858i	0.236435	+	0.409517i	−0.723254	+	0.690582i	$0.757354\pi$
$774$	−10.4378	−	10.5547i	−0.375180	−	0.379380i
$775$	15.4791	−	26.8106i	0.556027	−	0.963066i
$776$	−10.2796	+	17.8049i	−0.369018	+	0.639158i
$777$		0			0
$778$	−5.88685	−	10.1963i	−0.211054	−	0.365556i
$779$	−13.4288			−0.481136
$780$	12.3894	+	5.17230i	0.443612	+	0.185198i
$781$	4.41405			0.157947
$782$	−0.153567	+	0.265986i	−0.00549155	+	0.00951164i
$783$	−21.3170	−	2.98769i	−0.761807	−	0.106771i
$784$		0			0
$785$	−30.7954	+	53.3393i	−1.09914	+	1.90376i
$786$	−1.64919	−	12.8021i	−0.0588247	−	0.456634i
$787$	−14.0650	+	24.3614i	−0.501364	+	0.868389i	0.498634	+	0.866812i	$0.333835\pi$
$787$	−14.0650	+	24.3614i	−0.501364	+	0.868389i	−0.999999	+	0.00157623i	$0.999498\pi$
$788$	−13.5665	+	23.4979i	−0.483287	+	0.837077i
$789$	−32.8505	−	13.7143i	−1.16951	−	0.488243i
$790$	−1.64713	+	2.85291i	−0.0586021	+	0.101502i
$791$		0			0
$792$	−3.50502	−	3.54426i	−0.124546	−	0.125940i
$793$	6.46470	−	11.1972i	0.229568	−	0.397624i
$794$	0.0159163			0.000564847
$795$	8.08114	+	62.7309i	0.286609	+	2.22484i
$796$	−27.1824			−0.963455
$797$	−12.8683	−	22.2885i	−0.455817	−	0.789499i	0.542917	−	0.839786i	$-0.317320\pi$
$797$	−12.8683	−	22.2885i	−0.455817	−	0.789499i	−0.998735	+	0.0502873i	$0.983986\pi$
$798$		0			0
$799$	1.27155	−	2.20238i	0.0449841	−	0.0779147i
$800$	21.6094	−	37.4285i	0.764007	−	1.32330i
$801$	6.98643	−	1.83039i	0.246853	−	0.0646737i
$802$	6.08073	+	10.5321i	0.214718	+	0.371902i
$803$	−0.816934	−	1.41497i	−0.0288290	−	0.0499333i
$804$	−0.399583	−	3.10181i	−0.0140922	−	0.109393i
$805$		0			0
$806$	−1.06373	−	1.84244i	−0.0374684	−	0.0648972i
$807$	4.39173	+	34.0914i	0.154596	+	1.20007i
$808$	4.83936			0.170248
$809$	15.9353	+	27.6007i	0.560254	+	0.970388i	0.997474	+	0.0710338i	$0.0226298\pi$
$809$	15.9353	+	27.6007i	0.560254	+	0.970388i	−0.437220	+	0.899355i	$0.644037\pi$
$810$	−14.3623	+	8.08027i	−0.504641	+	0.283912i
$811$	−43.3860			−1.52349			−0.761744	−	0.647878i	$-0.775657\pi$
$811$	−43.3860			−1.52349			−0.761744	+	0.647878i	$0.775657\pi$
$812$		0			0
$813$	14.6534	−	11.1793i	0.513918	−	0.392076i
$814$	2.09408			0.0733975
$815$	−12.3382	+	21.3704i	−0.432188	+	0.748571i
$816$	−0.889913	+	0.678928i	−0.0311532	+	0.0237672i
$817$	−14.0113	−	24.2682i	−0.490193	−	0.849039i
$818$	13.2842			0.464470
$819$		0			0
$820$	30.9731			1.08163
$821$	8.19677	+	14.1972i	0.286069	+	0.495487i	0.972868	−	0.231361i	$-0.0743179\pi$
$821$	8.19677	+	14.1972i	0.286069	+	0.495487i	−0.686799	+	0.726848i	$0.740985\pi$
$822$	0.0536046	+	0.416113i	0.00186968	+	0.0145136i
$823$	13.1890	−	22.8440i	0.459739	−	0.796292i	−0.539208	−	0.842173i	$-0.681276\pi$
$823$	13.1890	−	22.8440i	0.459739	−	0.796292i	0.998947	+	0.0458812i	$0.0146096\pi$
$824$	−18.0785			−0.629794
$825$	12.3193	+	5.14301i	0.428901	+	0.179057i
$826$		0			0
$827$	36.7225			1.27697			0.638484	−	0.769635i	$-0.279562\pi$
$827$	36.7225			1.27697			0.638484	+	0.769635i	$0.279562\pi$
$828$	12.6129	−	3.30449i	0.438329	−	0.114839i
$829$	−12.1579	−	21.0581i	−0.422261	−	0.731377i	0.573899	−	0.818926i	$-0.305430\pi$
$829$	−12.1579	−	21.0581i	−0.422261	−	0.731377i	−0.996160	+	0.0875485i	$0.972097\pi$
$830$	−22.5640			−0.783209
$831$	39.7692	+	16.6028i	1.37958	+	0.575944i
$832$	1.60867	+	2.78629i	0.0557705	+	0.0965974i
$833$		0			0
$834$	6.73944	−	5.14162i	0.233368	−	0.178040i
$835$	−32.5519	−	56.3815i	−1.12650	−	1.95116i
$836$	−2.19841	−	3.80776i	−0.0760337	−	0.131694i
$837$	−18.4487	−	2.58568i	−0.637679	−	0.0893743i
$838$	−5.21962	+	9.04065i	−0.180309	+	0.312304i
$839$	12.8405	−	22.2404i	0.443303	−	0.767824i	−0.554629	−	0.832098i	$-0.687140\pi$
$839$	12.8405	−	22.2404i	0.443303	−	0.767824i	0.997932	+	0.0642741i	$0.0204732\pi$
$840$		0			0
$841$	5.91963	+	10.2531i	0.204125	+	0.353555i
$842$	−7.38381			−0.254463
$843$	18.8308	−	14.3663i	0.648567	−	0.494801i
$844$	2.70800			0.0932131
$845$	21.3577	−	36.9926i	0.734726	−	1.27258i
$846$	14.6394	−	3.83542i	0.503313	−	0.131864i
$847$		0			0
$848$	−12.7826	+	22.1402i	−0.438958	+	0.760297i
$849$	−8.70546	+	6.64153i	−0.298771	+	0.227937i
$850$	−0.535200	+	0.926994i	−0.0183572	+	0.0317956i
$851$	−5.86148	+	10.1524i	−0.200929	+	0.348019i
$852$	11.9455	−	9.11342i	0.409247	−	0.312221i
$853$	−14.4872	+	25.0925i	−0.496031	+	0.859150i	−0.999990	−	0.00457743i	$-0.998543\pi$
$853$	−14.4872	+	25.0925i	−0.496031	+	0.859150i	0.503959	+	0.863728i	$0.331876\pi$
$854$		0			0
$855$	−30.0937	+	7.88431i	−1.02918	+	0.269638i
$856$	−10.1459	+	17.5732i	−0.346780	+	0.600640i
$857$	25.3868			0.867197			0.433598	−	0.901106i	$-0.357244\pi$
$857$	25.3868			0.867197			0.433598	+	0.901106i	$0.357244\pi$
$858$	0.729372	−	0.556449i	0.0249003	−	0.0189968i
$859$	5.95783			0.203279			0.101639	−	0.994821i	$-0.467591\pi$
$859$	5.95783			0.203279			0.101639	+	0.994821i	$0.467591\pi$
$860$	32.3166	+	55.9740i	1.10199	+	1.90870i
$861$		0			0
$862$	3.94310	−	6.82966i	0.134303	−	0.232619i
$863$	8.19545	−	14.1949i	0.278977	−	0.483201i	−0.692154	−	0.721750i	$-0.743338\pi$
$863$	8.19545	−	14.1949i	0.278977	−	0.483201i	0.971131	+	0.238548i	$0.0766715\pi$
$864$	−25.7549	−	3.60970i	−0.876201	−	0.122804i
$865$	−7.17624	−	12.4296i	−0.244000	−	0.422620i
$866$	4.05764	+	7.02804i	0.137884	+	0.238822i
$867$	−23.3239	+	17.7942i	−0.792122	+	0.604322i
$868$		0			0
$869$	−0.802920	−	1.39070i	−0.0272372	−	0.0471762i
$870$	−12.1238	−	5.06140i	−0.411034	−	0.171598i
$871$	1.23186			0.0417399
$872$	−1.97503	−	3.42086i	−0.0668830	−	0.115845i
$873$	−32.0509	+	8.39709i	−1.08476	+	0.284198i
$874$	−3.45030			−0.116708
$875$		0			0
$876$	−5.13224	−	2.14260i	−0.173402	−	0.0723916i
$877$	35.2539			1.19044			0.595220	−	0.803563i	$-0.297065\pi$
$877$	35.2539			1.19044			0.595220	+	0.803563i	$0.297065\pi$
$878$	3.85407	−	6.67544i	0.130068	−	0.225285i
$879$	−0.582049	−	4.51823i	−0.0196320	−	0.152396i
$880$	4.26017	+	7.37883i	0.143610	+	0.248740i
$881$	−26.2582			−0.884661			−0.442331	−	0.896852i	$-0.645848\pi$
$881$	−26.2582			−0.884661			−0.442331	+	0.896852i	$0.645848\pi$
$882$		0			0
$883$	10.0087			0.336821			0.168410	−	0.985717i	$-0.446137\pi$
$883$	10.0087			0.336821			0.168410	+	0.985717i	$0.446137\pi$
$884$	−0.262378	−	0.454452i	−0.00882473	−	0.0152849i
$885$	−9.21572	+	7.03081i	−0.309783	+	0.236338i
$886$	0.443815	−	0.768711i	0.0149103	−	0.0258253i
$887$	15.9056			0.534059			0.267030	−	0.963688i	$-0.413958\pi$
$887$	15.9056			0.534059			0.267030	+	0.963688i	$0.413958\pi$
$888$	12.1286	−	9.25311i	0.407010	−	0.310514i
$889$		0			0
$890$	4.40804			0.147758
$891$	0.0894212	−	8.03262i	0.00299572	−	0.269103i
$892$	−4.77419	−	8.26914i	−0.159852	−	0.276871i
$893$	28.5688			0.956017
$894$	−2.30706	−	17.9088i	−0.0771596	−	0.598961i
$895$	13.5428	+	23.4569i	0.452687	+	0.784077i
$896$		0			0
$897$	0.656173	+	5.09363i	0.0219090	+	0.170071i
$898$	3.36364	+	5.82599i	0.112246	+	0.194416i
$899$	−7.42583	−	12.8619i	−0.247665	−	0.428969i
$900$	43.9575	−	11.5165i	1.46525	−	0.383884i
$901$	1.23608	−	2.14095i	0.0411797	−	0.0713253i
$902$	1.05822	−	1.83288i	0.0352348	−	0.0610284i
$903$		0			0
$904$	14.7307	+	25.5144i	0.489937	+	0.848597i
$905$	−41.5657			−1.38169
$906$	−0.164424	−	1.27637i	−0.00546264	−	0.0424044i
$907$	−17.0925			−0.567547			−0.283773	−	0.958891i	$-0.591586\pi$
$907$	−17.0925			−0.567547			−0.283773	+	0.958891i	$0.591586\pi$
$908$	14.0999	−	24.4217i	0.467922	−	0.810464i
$909$	5.48390	+	5.54528i	0.181889	+	0.183925i
$910$		0			0
$911$	14.9435	−	25.8829i	0.495099	−	0.857537i	−0.504885	−	0.863187i	$-0.668465\pi$
$911$	14.9435	−	25.8829i	0.495099	−	0.857537i	0.999984	+	0.00564955i	$0.00179832\pi$
$912$	−11.6037	−	4.84431i	−0.384238	−	0.160411i
$913$	5.49961	−	9.52561i	0.182011	−	0.315252i
$914$	0.636986	−	1.10329i	0.0210696	−	0.0364937i
$915$	−8.82870	−	68.5339i	−0.291868	−	2.26566i
$916$	8.74286	−	15.1431i	0.288872	−	0.500341i
$917$		0			0
$918$	0.637873	+	0.0894015i	0.0210530	+	0.00295069i
$919$	11.8283	−	20.4873i	0.390181	−	0.675813i	−0.602292	−	0.798276i	$-0.705746\pi$
$919$	11.8283	−	20.4873i	0.390181	−	0.675813i	0.992473	+	0.122462i	$0.0390791\pi$
$920$	17.0316			0.561515
$921$	−4.46734	−	1.86501i	−0.147204	−	0.0614543i
$922$	−17.9439			−0.590952
$923$	2.95907	+	5.12525i	0.0973989	+	0.168700i
$924$		0			0
$925$	−20.4280	+	35.3823i	−0.671667	+	1.16336i
$926$	−4.06227	+	7.03606i	−0.133495	+	0.231219i
$927$	−20.4863	−	20.7157i	−0.672859	−	0.680391i
$928$	−10.3667	−	17.9557i	−0.340304	−	0.589423i
$929$	6.30880	+	10.9272i	0.206985	+	0.358509i	0.950763	−	0.309918i	$-0.100302\pi$
$929$	6.30880	+	10.9272i	0.206985	+	0.358509i	−0.743778	+	0.668426i	$0.766968\pi$
$930$	−10.4924	−	4.38036i	−0.344061	−	0.143638i
$931$		0			0
$932$	−14.5073	−	25.1274i	−0.475203	−	0.823075i
$933$	20.7939	−	15.8640i	0.680763	−	0.519364i
$934$	4.31427			0.141167
$935$	−0.411957	−	0.713530i	−0.0134724	−	0.0233349i
$936$	1.76564	−	6.44575i	0.0577118	−	0.210686i
$937$	26.3440			0.860622			0.430311	−	0.902681i	$-0.358404\pi$
$937$	26.3440			0.860622			0.430311	+	0.902681i	$0.358404\pi$
$938$		0			0
$939$	5.63834	+	43.7683i	0.184000	+	1.42833i
$940$	−65.8930			−2.14919
$941$	25.4699	−	44.1151i	0.830294	−	1.43811i	−0.0675118	−	0.997718i	$-0.521506\pi$
$941$	25.4699	−	44.1151i	0.830294	−	1.43811i	0.897805	−	0.440392i	$-0.145161\pi$
$942$	13.2198	+	5.51899i	0.430726	+	0.179818i
$943$	5.92404	+	10.2607i	0.192913	+	0.334136i
$944$	−4.68525			−0.152492
$945$		0			0
$946$	4.41648			0.143592
$947$	−13.8399	−	23.9714i	−0.449737	−	0.778967i	0.548632	−	0.836064i	$-0.315149\pi$
$947$	−13.8399	−	23.9714i	−0.449737	−	0.778967i	−0.998369	+	0.0570968i	$0.981816\pi$
$948$	−5.04420	−	2.10584i	−0.163828	−	0.0683945i
$949$	1.09530	−	1.89712i	0.0355551	−	0.0615832i
$950$	−12.0247			−0.390134
$951$	7.19682	+	55.8662i	0.233373	+	1.81159i
$952$		0			0
$953$	−27.4017			−0.887628			−0.443814	−	0.896119i	$-0.646375\pi$
$953$	−27.4017			−0.887628			−0.443814	+	0.896119i	$0.646375\pi$
$954$	14.2311	−	3.72843i	0.460747	−	0.120712i
$955$	44.0265	+	76.2561i	1.42466	+	2.46759i
$956$	−38.6324			−1.24946
$957$	5.09168	−	3.88452i	0.164591	−	0.125569i
$958$	4.40515	+	7.62994i	0.142324	+	0.246512i
$959$		0			0
$960$	15.8676	+	6.62436i	0.512123	+	0.213800i
$961$	9.07336	+	15.7155i	0.292689	+	0.506952i
$962$	1.40382	+	2.43149i	0.0452610	+	0.0783943i
$963$	−31.6339	+	8.28783i	−1.01939	+	0.267072i
$964$	−14.6645	+	25.3996i	−0.472310	+	0.818066i
$965$	−10.9569	+	18.9779i	−0.352715	+	0.610921i
$966$		0			0
$967$	9.09069	+	15.7455i	0.292337	+	0.506342i	0.974362	−	0.224986i	$-0.0722338\pi$
$967$	9.09069	+	15.7455i	0.292337	+	0.506342i	−0.682025	+	0.731329i	$0.738900\pi$
$968$	−18.9940			−0.610489
$969$	1.12208	+	0.468443i	0.0360464	+	0.0150486i
$970$	−20.2223			−0.649299
$971$	−19.7416	+	34.1935i	−0.633538	+	1.09732i	0.353285	+	0.935516i	$0.385065\pi$
$971$	−19.7416	+	34.1935i	−0.633538	+	1.09732i	−0.986823	+	0.161804i	$0.948269\pi$
$972$	−16.3425	−	21.9229i	−0.524185	−	0.703178i
$973$		0			0
$974$	−4.12941	+	7.15234i	−0.132315	+	0.229176i
$975$	2.28684	+	17.7519i	0.0732376	+	0.568516i
$976$	13.9651	−	24.1883i	0.447012	−	0.774248i
$977$	−5.95782	+	10.3193i	−0.190608	+	0.330142i	−0.945452	−	0.325762i	$-0.894379\pi$
$977$	−5.95782	+	10.3193i	−0.190608	+	0.330142i	0.754844	+	0.655904i	$0.227712\pi$
$978$	5.29653	+	2.21118i	0.169364	+	0.0707058i
$979$	−1.07439	+	1.86090i	−0.0343376	+	0.0594745i
$980$		0			0
$981$	1.68178	−	6.13961i	0.0536952	−	0.196023i
$982$	1.59184	−	2.75715i	0.0507977	−	0.0879842i
$983$	18.4779			0.589354			0.294677	−	0.955597i	$-0.404788\pi$
$983$	18.4779			0.589354			0.294677	+	0.955597i	$0.404788\pi$
$984$	−1.96992	−	15.2917i	−0.0627987	−	0.487483i
$985$	−57.1176			−1.81992
$986$	0.256752	+	0.444708i	0.00817666	+	0.0141624i
$987$		0			0
$988$	2.94752	−	5.10525i	0.0937731	−	0.162420i
$989$	−12.3620	+	21.4117i	−0.393090	+	0.680851i
$990$	1.29532	−	4.72876i	0.0411680	−	0.150290i
$991$	−6.34850	−	10.9959i	−0.201667	−	0.349297i	0.747399	−	0.664376i	$-0.231302\pi$
$991$	−6.34850	−	10.9959i	−0.201667	−	0.349297i	−0.949066	+	0.315079i	$0.897969\pi$
$992$	−8.97181	−	15.5396i	−0.284855	−	0.493384i
$993$	4.00435	+	31.0843i	0.127074	+	0.986430i
$994$		0			0
$995$	−28.6108	−	49.5553i	−0.907023	−	1.57101i
$996$	−4.78362	−	37.1334i	−0.151575	−	1.17662i
$997$	−41.9533			−1.32868			−0.664338	−	0.747432i	$-0.731286\pi$
$997$	−41.9533			−1.32868			−0.664338	+	0.747432i	$0.731286\pi$
$998$	2.76345	+	4.78644i	0.0874755	+	0.151512i
$999$	24.3469	+	3.41235i	0.770301	+	0.107962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.f.79.3		10
3.2	odd	2		1323.2.g.f.667.3		10
7.2	even	3		441.2.f.f.295.3		10
7.3	odd	6		63.2.h.b.25.3	yes	10
7.4	even	3		441.2.h.f.214.3		10
7.5	odd	6		441.2.f.e.295.3		10
7.6	odd	2		63.2.g.b.16.3	yes	10
9.4	even	3		441.2.h.f.373.3		10
9.5	odd	6		1323.2.h.f.226.3		10
21.2	odd	6		1323.2.f.f.883.3		10
21.5	even	6		1323.2.f.e.883.3		10
21.11	odd	6		1323.2.h.f.802.3		10
21.17	even	6		189.2.h.b.46.3		10
21.20	even	2		189.2.g.b.100.3		10
28.3	even	6		1008.2.q.i.529.3		10
28.27	even	2		1008.2.t.i.961.1		10
63.2	odd	6		3969.2.a.bb.1.3		5
63.4	even	3	inner	441.2.g.f.67.3		10
63.5	even	6		1323.2.f.e.442.3		10
63.13	odd	6		63.2.h.b.58.3	yes	10
63.16	even	3		3969.2.a.ba.1.3		5
63.20	even	6		567.2.e.e.163.3		10
63.23	odd	6		1323.2.f.f.442.3		10
63.31	odd	6		63.2.g.b.4.3	✓	10
63.32	odd	6		1323.2.g.f.361.3		10
63.34	odd	6		567.2.e.f.163.3		10
63.38	even	6		567.2.e.e.487.3		10
63.40	odd	6		441.2.f.e.148.3		10
63.41	even	6		189.2.h.b.37.3		10
63.47	even	6		3969.2.a.bc.1.3		5
63.52	odd	6		567.2.e.f.487.3		10
63.58	even	3		441.2.f.f.148.3		10
63.59	even	6		189.2.g.b.172.3		10
63.61	odd	6		3969.2.a.z.1.3		5
84.59	odd	6		3024.2.q.i.2881.1		10
84.83	odd	2		3024.2.t.i.289.5		10
252.31	even	6		1008.2.t.i.193.1		10
252.59	odd	6		3024.2.t.i.1873.5		10
252.139	even	6		1008.2.q.i.625.3		10
252.167	odd	6		3024.2.q.i.2305.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	63.31	odd	6
63.2.g.b.16.3	yes	10	7.6	odd	2
63.2.h.b.25.3	yes	10	7.3	odd	6
63.2.h.b.58.3	yes	10	63.13	odd	6
189.2.g.b.100.3		10	21.20	even	2
189.2.g.b.172.3		10	63.59	even	6
189.2.h.b.37.3		10	63.41	even	6
189.2.h.b.46.3		10	21.17	even	6
441.2.f.e.148.3		10	63.40	odd	6
441.2.f.e.295.3		10	7.5	odd	6
441.2.f.f.148.3		10	63.58	even	3
441.2.f.f.295.3		10	7.2	even	3
441.2.g.f.67.3		10	63.4	even	3	inner
441.2.g.f.79.3		10	1.1	even	1	trivial
441.2.h.f.214.3		10	7.4	even	3
441.2.h.f.373.3		10	9.4	even	3
567.2.e.e.163.3		10	63.20	even	6
567.2.e.e.487.3		10	63.38	even	6
567.2.e.f.163.3		10	63.34	odd	6
567.2.e.f.487.3		10	63.52	odd	6
1008.2.q.i.529.3		10	28.3	even	6
1008.2.q.i.625.3		10	252.139	even	6
1008.2.t.i.193.1		10	252.31	even	6
1008.2.t.i.961.1		10	28.27	even	2
1323.2.f.e.442.3		10	63.5	even	6
1323.2.f.e.883.3		10	21.5	even	6
1323.2.f.f.442.3		10	63.23	odd	6
1323.2.f.f.883.3		10	21.2	odd	6
1323.2.g.f.361.3		10	63.32	odd	6
1323.2.g.f.667.3		10	3.2	odd	2
1323.2.h.f.226.3		10	9.5	odd	6
1323.2.h.f.802.3		10	21.11	odd	6
3024.2.q.i.2305.1		10	252.167	odd	6
3024.2.q.i.2881.1		10	84.59	odd	6
3024.2.t.i.289.5		10	84.83	odd	2
3024.2.t.i.1873.5		10	252.59	odd	6
3969.2.a.z.1.3		5	63.61	odd	6
3969.2.a.ba.1.3		5	63.16	even	3
3969.2.a.bb.1.3		5	63.2	odd	6
3969.2.a.bc.1.3		5	63.47	even	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.247934 + 0.429435i) q^{2} +(-1.59836 - 0.667278i) q^{3} +(0.877057 - 1.51911i) q^{4} +3.69258 q^{5} +(-0.109735 - 0.851830i) q^{6} +1.86155 q^{8} +(2.10948 + 2.13309i) q^{9} +O(q^{10})\)	\(q+(0.247934 + 0.429435i) q^{2} +(-1.59836 - 0.667278i) q^{3} +(0.877057 - 1.51911i) q^{4} +3.69258 q^{5} +(-0.109735 - 0.851830i) q^{6} +1.86155 q^{8} +(2.10948 + 2.13309i) q^{9} +(0.915516 + 1.58572i) q^{10} -0.892568 q^{11} +(-2.41552 + 1.84283i) q^{12} +(-0.598355 - 1.03638i) q^{13} +(-5.90205 - 2.46398i) q^{15} +(-1.29257 - 2.23880i) q^{16} +(0.124991 + 0.216492i) q^{17} +(-0.393012 + 1.43475i) q^{18} +(-1.40414 + 2.43204i) q^{19} +(3.23860 - 5.60943i) q^{20} +(-0.221298 - 0.383300i) q^{22} +2.47772 q^{23} +(-2.97541 - 1.24217i) q^{24} +8.63514 q^{25} +(0.296705 - 0.513909i) q^{26} +(-1.94833 - 4.81705i) q^{27} +(2.07128 - 3.58755i) q^{29} +(-0.405204 - 3.14545i) q^{30} +(1.79257 - 3.10483i) q^{31} +(2.50249 - 4.33444i) q^{32} +(1.42664 + 0.595591i) q^{33} +(-0.0619793 + 0.107351i) q^{34} +(5.09054 - 1.33368i) q^{36} +(-2.36568 + 4.09747i) q^{37} -1.39253 q^{38} +(0.264830 + 2.05578i) q^{39} +6.87391 q^{40} +(2.39093 + 4.14121i) q^{41} +(-4.98928 + 8.64169i) q^{43} +(-0.782834 + 1.35591i) q^{44} +(7.78942 + 7.87662i) q^{45} +(0.614310 + 1.06402i) q^{46} +(-5.08653 - 8.81013i) q^{47} +(0.572088 + 4.44091i) q^{48} +(2.14095 + 3.70823i) q^{50} +(-0.0553208 - 0.429435i) q^{51} -2.09917 q^{52} +(-4.94465 - 8.56438i) q^{53} +(1.58555 - 2.03099i) q^{54} -3.29588 q^{55} +(3.86715 - 2.95031i) q^{57} +2.05416 q^{58} +(0.906186 - 1.56956i) q^{59} +(-8.91949 + 6.80481i) q^{60} +(5.40205 + 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(-2.20948 - 3.82692i) q^{65} +(0.0979457 + 0.760316i) q^{66} +(-0.514685 + 0.891460i) q^{67} +0.438499 q^{68} +(-3.96027 - 1.65332i) q^{69} -4.94533 q^{71} +(3.92690 + 3.97085i) q^{72} +(0.915262 + 1.58528i) q^{73} -2.34613 q^{74} +(-13.8020 - 5.76204i) q^{75} +(2.46302 + 4.26607i) q^{76} +(-0.817161 + 0.623424i) q^{78} +(0.899562 + 1.55809i) q^{79} +(-4.77293 - 8.26696i) q^{80} +(-0.100184 + 8.99944i) q^{81} +(-1.18559 + 2.05350i) q^{82} +(-6.16156 + 10.6721i) q^{83} +(0.461541 + 0.799412i) q^{85} -4.94806 q^{86} +(-5.70453 + 4.35207i) q^{87} -1.66156 q^{88} +(1.20370 - 2.08488i) q^{89} +(-1.45123 + 5.29793i) q^{90} +(2.17310 - 3.76392i) q^{92} +(-4.93695 + 3.76648i) q^{93} +(2.52225 - 4.36867i) q^{94} +(-5.18489 + 8.98049i) q^{95} +(-6.89215 + 5.25813i) q^{96} +(-5.52210 + 9.56456i) q^{97} +(-1.88286 - 1.90393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9	\( 10 q + 2 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 2 q^{6} - 6 q^{8} - 4 q^{9} + 7 q^{10} - 8 q^{11} - 22 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} - 12 q^{17} - 2 q^{18} - q^{19} - 5 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 2 q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} - 26 q^{30} + 3 q^{31} - 2 q^{32} + q^{33} - 3 q^{34} + 34 q^{36} + 40 q^{38} + 20 q^{39} - 6 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + q^{45} + 3 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} + 24 q^{51} - 20 q^{52} - 21 q^{53} + 53 q^{54} - 4 q^{55} - 4 q^{57} + 20 q^{58} - 30 q^{59} - 41 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} + 41 q^{66} - 2 q^{67} + 54 q^{68} - 15 q^{69} - 6 q^{71} + 48 q^{72} - 15 q^{73} + 72 q^{74} - 31 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} - 20 q^{80} + 8 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} + 16 q^{86} - 32 q^{87} + 36 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 12 q^{93} + 3 q^{94} - 14 q^{95} + q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 - 2 * q^3 - 4 * q^4 + 8 * q^5 + 2 * q^6 - 6 * q^8 - 4 * q^9 + 7 * q^10 - 8 * q^11 - 22 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 - 12 * q^17 - 2 * q^18 - q^19 - 5 * q^20 - q^22 - 6 * q^23 - 3 * q^24 + 2 * q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 - 26 * q^30 + 3 * q^31 - 2 * q^32 + q^33 - 3 * q^34 + 34 * q^36 + 40 * q^38 + 20 * q^39 - 6 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + q^45 + 3 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 + 24 * q^51 - 20 * q^52 - 21 * q^53 + 53 * q^54 - 4 * q^55 - 4 * q^57 + 20 * q^58 - 30 * q^59 - 41 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 + 41 * q^66 - 2 * q^67 + 54 * q^68 - 15 * q^69 - 6 * q^71 + 48 * q^72 - 15 * q^73 + 72 * q^74 - 31 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 - 20 * q^80 + 8 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 + 16 * q^86 - 32 * q^87 + 36 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 12 * q^93 + 3 * q^94 - 14 * q^95 + q^96 + 12 * q^97 + 35 * q^99

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