LMFDB - Embedded newform 441.2.f.f.148.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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, 0]))

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

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

chi := DirichletCharacter("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, degree $2$, 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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			148.3
Root			$0.247934 + 0.429435i$ of defining polynomial
Character	$\chi$	$=$	441.148
Dual form			441.2.f.f.295.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.247934 + 0.429435i) q^{2} +(1.37706 + 1.05058i) q^{3} +(0.877057 - 1.51911i) q^{4} +(-1.84629 + 3.19787i) q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(0.792574 + 2.89341i) q^{9} +O(q^{10})$	\(q+(0.247934 + 0.429435i) q^{2} +(1.37706 + 1.05058i) q^{3} +(0.877057 - 1.51911i) q^{4} +(-1.84629 + 3.19787i) q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(0.792574 + 2.89341i) q^{9} -1.83103 q^{10} +(0.446284 + 0.772987i) q^{11} +(2.80370 - 1.17048i) q^{12} +(-0.598355 + 1.03638i) q^{13} +(-5.90205 + 2.46398i) q^{15} +(-1.29257 - 2.23880i) q^{16} -0.249983 q^{17} +(-1.04602 + 1.05773i) q^{18} +2.80827 q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(-1.23886 + 2.14576i) q^{23} +(2.56346 + 1.95570i) q^{24} +(-4.31757 - 7.47825i) q^{25} -0.593411 q^{26} +(-1.94833 + 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} +(-2.52144 - 1.92364i) q^{30} +(1.79257 - 3.10483i) q^{31} +(2.50249 - 4.33444i) q^{32} +(-0.197524 + 1.53330i) q^{33} +(-0.0619793 - 0.107351i) q^{34} +(5.09054 + 1.33368i) q^{36} +4.73136 q^{37} +(0.696267 + 1.20597i) q^{38} +(-1.91277 + 0.798539i) q^{39} +(-3.43695 + 5.95298i) q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +1.56567 q^{44} +(-10.7161 - 2.80753i) q^{45} -1.22862 q^{46} +(-5.08653 - 8.81013i) q^{47} +(0.572088 - 4.44091i) q^{48} +(2.14095 - 3.70823i) q^{50} +(-0.344241 - 0.262626i) q^{51} +(1.04958 + 1.81793i) q^{52} +9.88929 q^{53} +(-2.55167 + 0.357630i) q^{54} -3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} +(-1.02708 + 1.77895i) q^{58} +(0.906186 - 1.56956i) q^{59} +(-1.43339 + 11.1269i) q^{60} +(5.40205 + 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(-2.20948 - 3.82692i) q^{65} +(-0.707426 + 0.295335i) q^{66} +(-0.514685 + 0.891460i) q^{67} +(-0.219249 + 0.379751i) q^{68} +(-3.96027 + 1.65332i) q^{69} -4.94533 q^{71} +(1.47541 + 5.38622i) q^{72} -1.83052 q^{73} +(1.17306 + 2.03181i) q^{74} +(1.91094 - 14.8339i) q^{75} +(2.46302 - 4.26607i) q^{76} +(-0.817161 - 0.623424i) q^{78} +(0.899562 + 1.55809i) q^{79} +9.54586 q^{80} +(-7.74365 + 4.58648i) q^{81} +2.37117 q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(2.47403 - 4.28514i) q^{86} +(-0.916739 + 7.11630i) q^{87} +(0.830779 + 1.43895i) q^{88} -2.40741 q^{89} +(-1.45123 - 5.29793i) q^{90} +(2.17310 + 3.76392i) q^{92} +(5.73034 - 2.39229i) q^{93} +(2.52225 - 4.36867i) q^{94} +(-5.18489 + 8.98049i) q^{95} +(7.99975 - 3.33972i) 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} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9	$ 10 q + 2 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9} - 14 q^{10} + 4 q^{11} + 2 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} + 24 q^{17} - 2 q^{18} + 2 q^{19} - 5 q^{20} - q^{22} + 3 q^{23} + 9 q^{24} - q^{25} + 22 q^{26} + 7 q^{27} + 7 q^{29} + 10 q^{30} + 3 q^{31} - 2 q^{32} + 13 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} - 22 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} + 20 q^{44} - 17 q^{45} - 6 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} - 15 q^{51} + 10 q^{52} + 42 q^{53} - 52 q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} - 30 q^{59} + 31 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} - 22 q^{66} - 2 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 12 q^{72} + 30 q^{73} - 36 q^{74} + 17 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} + 40 q^{80} - 31 q^{81} - 10 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} + 34 q^{87} - 18 q^{88} + 56 q^{89} - 28 q^{90} + 27 q^{92} + 18 q^{93} + 3 q^{94} - 14 q^{95} + 58 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) $ 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9 - 14 * q^10 + 4 * q^11 + 2 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 + 24 * q^17 - 2 * q^18 + 2 * q^19 - 5 * q^20 - q^22 + 3 * q^23 + 9 * q^24 - q^25 + 22 * q^26 + 7 * q^27 + 7 * q^29 + 10 * q^30 + 3 * q^31 - 2 * q^32 + 13 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 - 22 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 + 20 * q^44 - 17 * q^45 - 6 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 - 15 * q^51 + 10 * q^52 + 42 * q^53 - 52 * q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 - 30 * q^59 + 31 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 - 22 * q^66 - 2 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 12 * q^72 + 30 * q^73 - 36 * q^74 + 17 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 + 40 * q^80 - 31 * q^81 - 10 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 + 34 * q^87 - 18 * q^88 + 56 * q^89 - 28 * q^90 + 27 * q^92 + 18 * q^93 + 3 * q^94 - 14 * q^95 + 58 * q^96 + 12 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	$0.777239\pi$
$3$	1.37706	+	1.05058i	0.795044	+	0.606551i
$3$	1.37706	+	1.05058i	0.795044	+	0.606551i
$4$	0.877057	−	1.51911i	0.438529	−	0.759554i
$5$	−1.84629	+	3.19787i	−0.825686	+	1.43013i	0.0757082	+	0.997130i	$0.475878\pi$
$5$	−1.84629	+	3.19787i	−0.825686	+	1.43013i	−0.901394	+	0.433000i	$0.857455\pi$
$6$	−0.109735	+	0.851830i	−0.0447990	+	0.347758i
$7$		0			0
$7$		0			0
$8$	1.86155			0.658156
$9$	0.792574	+	2.89341i	0.264191	+	0.964470i
$10$	−1.83103			−0.579023
$11$	0.446284	+	0.772987i	0.134560	+	0.233064i	0.925429	−	0.378921i	$-0.123705\pi$
$11$	0.446284	+	0.772987i	0.134560	+	0.233064i	−0.790869	+	0.611985i	$0.790371\pi$
$12$	2.80370	−	1.17048i	0.809358	−	0.337889i
$13$	−0.598355	+	1.03638i	−0.165954	+	0.287441i	−0.936994	−	0.349346i	$-0.886404\pi$
$13$	−0.598355	+	1.03638i	−0.165954	+	0.287441i	0.771040	+	0.636787i	$0.219737\pi$
$14$		0			0
$15$	−5.90205	+	2.46398i	−1.52390	+	0.636196i
$16$	−1.29257	−	2.23880i	−0.323143	−	0.559701i
$17$	−0.249983			−0.0606298			−0.0303149	−	0.999540i	$-0.509651\pi$
$17$	−0.249983			−0.0606298			−0.0303149	+	0.999540i	$0.509651\pi$
$18$	−1.04602	+	1.05773i	−0.246550	+	0.249310i
$19$	2.80827			0.644262			0.322131	−	0.946695i	$-0.395601\pi$
$19$	2.80827			0.644262			0.322131	+	0.946695i	$0.395601\pi$
$20$	3.23860	+	5.60943i	0.724174	+	1.25431i
$21$		0			0
$22$	−0.221298	+	0.383300i	−0.0471809	+	0.0817198i
$23$	−1.23886	+	2.14576i	−0.258320	+	0.447423i	−0.965792	−	0.259318i	$-0.916502\pi$
$23$	−1.23886	+	2.14576i	−0.258320	+	0.447423i	0.707472	+	0.706741i	$0.249835\pi$
$24$	2.56346	+	1.95570i	0.523263	+	0.399205i
$25$	−4.31757	−	7.47825i	−0.863514	−	1.49565i
$26$	−0.593411			−0.116377
$27$	−1.94833	+	4.81705i	−0.374957	+	0.927042i
$28$		0			0
$29$	2.07128	+	3.58755i	0.384626	+	0.666192i	0.991717	−	0.128440i	$-0.0409970\pi$
$29$	2.07128	+	3.58755i	0.384626	+	0.666192i	−0.607091	+	0.794632i	$0.707664\pi$
$30$	−2.52144	−	1.92364i	−0.460349	−	0.351207i
$31$	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
$33$	−0.197524	+	1.53330i	−0.0343845	+	0.266914i
$34$	−0.0619793	−	0.107351i	−0.0106294	−	0.0184106i
$35$		0			0
$36$	5.09054	+	1.33368i	0.848423	+	0.222280i
$37$	4.73136			0.777830			0.388915	−	0.921274i	$-0.372850\pi$
$37$	4.73136			0.777830			0.388915	+	0.921274i	$0.372850\pi$
$38$	0.696267	+	1.20597i	0.112949	+	0.195634i
$39$	−1.91277	+	0.798539i	−0.306288	+	0.127869i
$40$	−3.43695	+	5.95298i	−0.543430	+	0.941249i
$41$	2.39093	−	4.14121i	0.373400	−	0.646748i	−0.616686	−	0.787209i	$-0.711525\pi$
$41$	2.39093	−	4.14121i	0.373400	−	0.646748i	0.990086	+	0.140461i	$0.0448584\pi$
$42$		0			0
$43$	−4.98928	−	8.64169i	−0.760859	−	1.31785i	−0.942408	−	0.334464i	$-0.891445\pi$
$43$	−4.98928	−	8.64169i	−0.760859	−	1.31785i	0.181550	−	0.983382i	$-0.441889\pi$
$44$	1.56567			0.236033
$45$	−10.7161	−	2.80753i	−1.59746	−	0.418522i
$46$	−1.22862			−0.181150
$47$	−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
$51$	−0.344241	−	0.262626i	−0.0482034	−	0.0367751i
$52$	1.04958	+	1.81793i	0.145551	+	0.252102i
$53$	9.88929			1.35840			0.679199	−	0.733954i	$-0.262327\pi$
$53$	9.88929			1.35840			0.679199	+	0.733954i	$0.262327\pi$
$54$	−2.55167	+	0.357630i	−0.347238	+	0.0486673i
$55$	−3.29588			−0.444416
$56$		0			0
$57$	3.86715	+	2.95031i	0.512217	+	0.390778i
$58$	−1.02708	+	1.77895i	−0.134862	+	0.233588i
$59$	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	$0.129026\pi$
$60$	−1.43339	+	11.1269i	−0.185050	+	1.43648i
$61$	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
$66$	−0.707426	+	0.295335i	−0.0870781	+	0.0363532i
$67$	−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	$0.186695\pi$
$68$	−0.219249	+	0.379751i	−0.0265879	+	0.0460516i
$69$	−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	$0.594804\pi$
$72$	1.47541	+	5.38622i	0.173879	+	0.634772i
$73$	−1.83052			−0.214247			−0.107123	−	0.994246i	$-0.534164\pi$
$73$	−1.83052			−0.214247			−0.107123	+	0.994246i	$0.534164\pi$
$74$	1.17306	+	2.03181i	0.136366	+	0.236193i
$75$	1.91094	−	14.8339i	0.220656	−	1.71287i
$76$	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	$0.801062\pi$
$80$	9.54586			1.06726
$81$	−7.74365	+	4.58648i	−0.860406	+	0.509609i
$82$	2.37117			0.261852
$83$	−6.16156	−	10.6721i	−0.676319	−	1.17142i	−0.976082	−	0.217405i	$-0.930241\pi$
$83$	−6.16156	−	10.6721i	−0.676319	−	1.17142i	0.299763	−	0.954014i	$-0.403092\pi$
$84$		0			0
$85$	0.461541	−	0.799412i	0.0500611	−	0.0867084i
$86$	2.47403	−	4.28514i	0.266781	−	0.462079i
$87$	−0.916739	+	7.11630i	−0.0982847	+	0.762948i
$88$	0.830779	+	1.43895i	0.0885613	+	0.153393i
$89$	−2.40741			−0.255185			−0.127592	−	0.991827i	$-0.540725\pi$
$89$	−2.40741			−0.255185			−0.127592	+	0.991827i	$0.540725\pi$
$90$	−1.45123	−	5.29793i	−0.152973	−	0.558451i
$91$		0			0
$92$	2.17310	+	3.76392i	0.226561	+	0.392416i
$93$	5.73034	−	2.39229i	0.594209	−	0.248069i
$94$	2.52225	−	4.36867i	0.260150	−	0.450593i
$95$	−5.18489	+	8.98049i	−0.531958	+	0.921379i
$96$	7.99975	−	3.33972i	0.816471	−	0.340858i
$97$	−5.52210	−	9.56456i	−0.560684	−	0.971134i	−0.997437	−	0.0715522i	$-0.977205\pi$
$97$	−5.52210	−	9.56456i	−0.560684	−	0.971134i	0.436752	−	0.899582i	$-0.356129\pi$
$98$		0			0
$99$	−1.88286	+	1.90393i	−0.189234	+	0.191352i
$100$	−15.1470			−1.51470
$101$	−1.29982	−	2.25136i	−0.129337	−	0.224018i	0.794083	−	0.607810i	$-0.207952\pi$
$101$	−1.29982	−	2.25136i	−0.129337	−	0.224018i	−0.923420	+	0.383791i	$0.874618\pi$
$102$	0.0274318	−	0.212943i	0.00271615	−	0.0210845i
$103$	4.85578	−	8.41045i	0.478454	−	0.828706i	−0.521241	−	0.853409i	$-0.674531\pi$
$103$	4.85578	−	8.41045i	0.478454	−	0.828706i	0.999695	+	0.0247032i	$0.00786408\pi$
$104$	−1.11387	+	1.92927i	−0.109224	+	0.189181i
$105$		0			0
$106$	2.45189	+	4.24680i	0.238149	+	0.412486i
$107$	10.9005			1.05379			0.526896	−	0.849930i	$-0.323356\pi$
$107$	10.9005			1.05379			0.526896	+	0.849930i	$0.323356\pi$
$108$	5.60882	+	7.18456i	0.539709	+	0.691335i
$109$	2.12193			0.203244			0.101622	−	0.994823i	$-0.467597\pi$
$109$	2.12193			0.203244			0.101622	+	0.994823i	$0.467597\pi$
$110$	−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	−0.206061	−	0.978539i	$-0.566065\pi$
$113$	7.91318	−	13.7060i	0.744409	−	1.28935i	0.950470	−	0.310816i	$-0.100602\pi$
$114$	−0.308165	+	2.39217i	−0.0288623	+	0.224047i
$115$	−4.57458	−	7.92341i	−0.426582	−	0.738861i
$116$	7.26651			0.674679
$117$	−3.47292	−	0.909879i	−0.321072	−	0.0841183i
$118$	0.898698			0.0827318
$119$		0			0
$120$	−10.9869	+	4.58681i	−1.00297	+	0.418716i
$121$	5.10166	−	8.83634i	0.463787	−	0.803303i
$122$	−2.67871	+	4.63966i	−0.242519	+	0.420055i
$123$	7.64311	−	3.19083i	0.689156	−	0.287707i
$124$	−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
$129$	2.20824	−	17.1417i	0.194425	−	1.50925i
$130$	1.09561	−	1.89765i	0.0960912	−	0.166435i
$131$	−7.51444	+	13.0154i	−0.656540	+	1.13716i	0.324965	+	0.945726i	$0.394647\pi$
$131$	−7.51444	+	13.0154i	−0.656540	+	1.13716i	−0.981505	+	0.191435i	$0.938686\pi$
$132$	2.15601	+	1.64485i	0.187657	+	0.143166i
$133$		0			0
$134$	−0.510432			−0.0440946
$135$	−11.8071	−	15.1242i	−1.01619	−	1.30168i
$136$	−0.465355			−0.0399038
$137$	0.244246	+	0.423047i	0.0208674	+	0.0361433i	0.876271	−	0.481819i	$-0.160024\pi$
$137$	0.244246	+	0.423047i	0.0208674	+	0.0361433i	−0.855403	+	0.517963i	$0.826691\pi$
$138$	−1.69188	−	1.29076i	−0.144022	−	0.109877i
$139$	4.93487	−	8.54745i	0.418570	−	0.724985i	−0.577226	−	0.816585i	$-0.695865\pi$
$139$	4.93487	−	8.54745i	0.418570	−	0.724985i	0.995796	+	0.0915997i	$0.0291980\pi$
$140$		0			0
$141$	2.25128	−	17.4759i	0.189592	−	1.47173i
$142$	−1.22612	−	2.12370i	−0.102893	−	0.178217i
$143$	−1.06815			−0.0893229
$144$	5.45332	−	5.51436i	0.454443	−	0.459530i
$145$	−15.2967			−1.27032
$146$	−0.453849	−	0.786090i	−0.0375609	−	0.0650573i
$147$		0			0
$148$	4.14967	−	7.18744i	0.341101	−	0.590804i
$149$	−10.5120	+	18.2073i	−0.861175	+	1.49160i	0.00962096	+	0.999954i	$0.496938\pi$
$149$	−10.5120	+	18.2073i	−0.861175	+	1.49160i	−0.870796	+	0.491645i	$0.836396\pi$
$150$	6.84399	−	2.85721i	0.558809	−	0.233290i
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	0.833930	−	0.551870i	$-0.186086\pi$
$151$	−0.749191	−	1.29764i	−0.0609683	−	0.105600i	−0.894898	+	0.446270i	$0.852752\pi$
$152$	5.22773			0.424025
$153$	−0.198130	−	0.723303i	−0.0160179	−	0.0584756i
$154$		0			0
$155$	6.61922	+	11.4648i	0.531669	+	0.920877i
$156$	−0.464542	+	3.60607i	−0.0371931	+	0.288716i
$157$	−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
$159$	13.6181	+	10.3895i	1.07999	+	0.823938i
$160$	9.24065	+	16.0053i	0.730538	+	1.26533i
$161$		0			0
$162$	−3.88951	−	2.18825i	−0.305589	−	0.171925i
$163$	6.68269			0.523429			0.261714	−	0.965145i	$-0.415712\pi$
$163$	6.68269			0.523429			0.261714	+	0.965145i	$0.415712\pi$
$164$	−4.19396	−	7.26416i	−0.327494	−	0.567236i
$165$	−4.53861	−	3.46258i	−0.353331	−	0.269561i
$166$	3.05532	−	5.29197i	0.237139	−	0.410737i
$167$	−8.81549	+	15.2689i	−0.682163	+	1.18154i	0.292156	+	0.956371i	$0.405627\pi$
$167$	−8.81549	+	15.2689i	−0.682163	+	1.18154i	−0.974319	+	0.225170i	$0.927706\pi$
$168$		0			0
$169$	5.78394	+	10.0181i	0.444919	+	0.770622i
$170$	0.457727			0.0351061
$171$	2.22576	+	8.12549i	0.170208	+	0.621372i
$172$	−17.5036			−1.33463
$173$	−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
$177$	2.89681	−	1.20936i	0.217738	−	0.0909007i
$178$	−0.596879	−	1.03382i	−0.0447380	−	0.0774884i
$179$	−7.33516			−0.548256			−0.274128	−	0.961693i	$-0.588389\pi$
$179$	−7.33516			−0.548256			−0.274128	+	0.961693i	$0.588389\pi$
$180$	−13.6635	+	13.8165i	−1.01842	+	1.02982i
$181$	−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
$184$	−2.30619	+	3.99444i	−0.170015	+	0.294474i
$185$	−8.73545	+	15.1302i	−0.642243	+	1.11240i
$186$	2.44808	+	1.86768i	0.179502	+	0.136945i
$187$	−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	$0.502095\pi$
$192$	−3.70219	−	2.82446i	−0.267183	−	0.203838i
$193$	−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	$0.235182\pi$
$194$	2.73823	−	4.74276i	0.196594	−	0.340510i
$195$	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	$0.685766\pi$
$198$	−1.28444	−	0.336513i	−0.0912811	−	0.0239150i
$199$	15.4964			1.09851			0.549254	−	0.835655i	$-0.314912\pi$
$199$	15.4964			1.09851			0.549254	+	0.835655i	$0.314912\pi$
$200$	−8.03736	−	13.9211i	−0.568327	−	0.984371i
$201$	−1.64530	+	0.686875i	−0.116050	+	0.0484485i
$202$	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
$206$	4.81565			0.335522
$207$	−7.19047	−	1.88385i	−0.499772	−	0.130936i
$208$	3.09367			0.214508
$209$	1.25329	+	2.17076i	0.0866918	+	0.150155i
$210$		0			0
$211$	0.771898	−	1.33697i	0.0531397	−	0.0920406i	−0.838232	−	0.545314i	$-0.816410\pi$
$211$	0.771898	−	1.33697i	0.0531397	−	0.0920406i	0.891372	+	0.453273i	$0.149744\pi$
$212$	8.67347	−	15.0229i	0.595697	−	1.03178i
$213$	−6.81001	−	5.19545i	−0.466614	−	0.355987i
$214$	2.70261	+	4.68105i	0.184746	+	0.319990i
$215$	36.8467			2.51292
$216$	−3.62691	+	8.96717i	−0.246780	+	0.610138i
$217$		0			0
$218$	0.526098	+	0.911229i	0.0356319	+	0.0617162i
$219$	−2.52074	−	1.92311i	−0.170336	−	0.129952i
$220$	−2.89068	+	5.00680i	−0.194889	+	0.337558i
$221$	0.149579	−	0.259078i	0.0100617	−	0.0174275i
$222$	−0.519194	+	4.03031i	−0.0348460	+	0.270497i
$223$	2.72171	+	4.71414i	0.182259	+	0.315682i	0.942649	−	0.333784i	$-0.108326\pi$
$223$	2.72171	+	4.71414i	0.182259	+	0.315682i	−0.760390	+	0.649466i	$0.774992\pi$
$224$		0			0
$225$	18.2157	−	18.4196i	1.21438	−	1.22797i
$226$	7.84779			0.522027
$227$	−8.03818	−	13.9225i	−0.533513	−	0.924072i	−0.999234	−	0.0391399i	$-0.987538\pi$
$227$	−8.03818	−	13.9225i	−0.533513	−	0.924072i	0.465721	−	0.884932i	$-0.345795\pi$
$228$	7.87356	−	3.28703i	0.521439	−	0.217689i
$229$	−4.98420	+	8.63289i	−0.329365	+	0.570477i	−0.982386	−	0.186863i	$-0.940168\pi$
$229$	−4.98420	+	8.63289i	−0.329365	+	0.570477i	0.653021	+	0.757340i	$0.273501\pi$
$230$	2.26839	−	3.92897i	0.149573	−	0.259068i
$231$		0			0
$232$	3.85578	+	6.67840i	0.253144	+	0.438458i
$233$	−16.5409			−1.08363			−0.541815	−	0.840498i	$-0.682263\pi$
$233$	−16.5409			−1.08363			−0.541815	+	0.840498i	$0.682263\pi$
$234$	−0.470322	−	1.71698i	−0.0307459	−	0.112243i
$235$	37.5648			2.45046
$236$	−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	0.251687	+	0.967809i	$0.419015\pi$
$239$	−11.0119	+	19.0732i	−0.712303	+	1.23375i	−0.963990	+	0.265937i	$0.914319\pi$
$240$	13.1452	+	10.0287i	0.848519	+	0.647348i
$241$	8.36004	+	14.4800i	0.538517	+	0.932739i	0.998984	+	0.0450623i	$0.0143486\pi$
$241$	8.36004	+	14.4800i	0.538517	+	0.932739i	−0.460467	+	0.887677i	$0.652318\pi$
$242$	5.05950			0.325237
$243$	−15.4819	−	1.81946i	−0.993165	−	0.116718i
$244$	18.9516			1.21325
$245$		0			0
$246$	3.26524	+	2.49110i	0.208184	+	0.158827i
$247$	−1.68035	+	2.91045i	−0.106918	+	0.185187i
$248$	3.33696	−	5.77978i	0.211897	−	0.367017i
$249$	2.72708	−	21.1693i	0.172822	−	1.34155i
$250$	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
$255$	1.47541	−	0.615952i	0.0923939	−	0.0385724i
$256$	0.123861	−	0.214533i	0.00774131	−	0.0134083i
$257$	−8.55986	+	14.8261i	−0.533950	+	0.924828i	0.465264	+	0.885172i	$0.345959\pi$
$257$	−8.55986	+	14.8261i	−0.533950	+	0.924828i	−0.999213	+	0.0396557i	$0.987374\pi$
$258$	7.90875	−	3.30173i	0.492377	−	0.205557i
$259$		0			0
$260$	−7.75135			−0.480718
$261$	−8.73863	+	8.83645i	−0.540908	+	0.546963i
$262$	−7.45235			−0.460408
$263$	−10.2763	−	17.7991i	−0.633666	−	1.09754i	−0.986796	−	0.161967i	$-0.948216\pi$
$263$	−10.2763	−	17.7991i	−0.633666	−	1.09754i	0.353130	−	0.935574i	$-0.385117\pi$
$264$	−0.367700	+	2.85432i	−0.0226303	+	0.175671i
$265$	−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
$269$	19.8453			1.20999			0.604996	−	0.796229i	$-0.293175\pi$
$269$	19.8453			1.20999			0.604996	+	0.796229i	$0.293175\pi$
$270$	3.56746	−	8.82018i	0.217109	−	0.536779i
$271$	10.6411			0.646402			0.323201	−	0.946330i	$-0.395241\pi$
$271$	10.6411			0.646402			0.323201	+	0.946330i	$0.395241\pi$
$272$	0.323121	+	0.559663i	0.0195921	+	0.0339345i
$273$		0			0
$274$	−0.121114	+	0.209776i	−0.00731676	+	0.0126730i
$275$	3.85373	−	6.67485i	0.232388	−	0.402509i
$276$	−0.961806	+	7.46614i	−0.0578939	+	0.449409i
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	0.949024	+	0.315205i	$0.102073\pi$
$277$	12.4407	+	21.5479i	0.747487	+	1.29469i	−0.201536	+	0.979481i	$0.564593\pi$
$278$	4.89409			0.293528
$279$	10.4043	+	2.72585i	0.622889	+	0.163192i
$280$		0			0
$281$	−6.83733	−	11.8426i	−0.407881	−	0.706470i	0.586771	−	0.809753i	$-0.300399\pi$
$281$	−6.83733	−	11.8426i	−0.407881	−	0.706470i	−0.994652	+	0.103282i	$0.967065\pi$
$282$	8.06290	−	3.36608i	0.480139	−	0.200447i
$283$	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
$285$	−16.5746	+	6.91952i	−0.981794	+	0.409877i
$286$	−0.264830	−	0.458699i	−0.0156597	−	0.0271234i
$287$		0			0
$288$	14.5247	+	3.80537i	0.855878	+	0.224234i
$289$	−16.9375			−0.996324
$290$	−3.79257	−	6.56893i	−0.222708	−	0.385741i
$291$	2.44406	−	18.9723i	0.143273	−	1.11218i
$292$	−1.60547	+	2.78076i	−0.0939533	+	0.162732i
$293$	1.31508	−	2.27778i	0.0768277	−	0.133069i	−0.825052	−	0.565057i	$-0.808854\pi$
$293$	1.31508	−	2.27778i	0.0768277	−	0.133069i	0.901880	+	0.431987i	$0.142188\pi$
$294$		0			0
$295$	3.34616	+	5.79573i	0.194821	+	0.337440i
$296$	8.80764			0.511934
$297$	−4.59303	+	0.643739i	−0.266515	+	0.0373535i
$298$	−10.4251			−0.603911
$299$	−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
$303$	0.575296	−	4.46581i	0.0330499	−	0.256554i
$304$	−3.62990	−	6.28717i	−0.208189	−	0.360594i
$305$	−39.8950			−2.28438
$306$	0.261488	−	0.264415i	0.0149483	−	0.0151156i
$307$	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
$310$	−3.28226	+	5.68504i	−0.186420	+	0.322889i
$311$	−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	$0.307494\pi$
$312$	−3.56071	+	1.48652i	−0.201585	+	0.0841574i
$313$	−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	$-0.533124\pi$
$318$	−1.08520	+	8.42399i	−0.0608549	+	0.472394i
$319$	−1.84875	+	3.20214i	−0.103510	+	0.179285i
$320$	4.96372	−	8.59741i	0.277480	−	0.480610i
$321$	15.0106	+	11.4518i	0.837811	+	0.639179i
$322$		0			0
$323$	−0.702021			−0.0390615
$324$	0.175735	+	15.7861i	0.00976303	+	0.877003i
$325$	10.3338			0.573214
$326$	1.65687	+	2.86978i	0.0917654	+	0.158942i
$327$	2.92201	+	2.22925i	0.161588	+	0.123278i
$328$	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	$0.999005\pi$
$332$	−21.6162			−1.18634
$333$	3.74995	+	13.6898i	0.205496	+	0.750194i
$334$	−8.74264			−0.478376
$335$	−1.90051	−	3.29179i	−0.103836	−	0.179850i
$336$		0			0
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	0.293168	+	0.956061i	$0.405290\pi$
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	−0.974557	+	0.224139i	$0.928043\pi$
$338$	−2.86807	+	4.96765i	−0.156003	+	0.270204i
$339$	25.2961	−	10.5606i	1.37390	−	0.573572i
$340$	−0.809596	−	1.40226i	−0.0439065	−	0.0760483i
$341$	3.19999			0.173289
$342$	−2.93752	+	2.97041i	−0.158843	+	0.160621i
$343$		0			0
$344$	−9.28778	−	16.0869i	−0.500764	−	0.867348i
$345$	2.02469	−	15.7169i	0.109006	−	0.846171i
$346$	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	$0.259828\pi$
$348$	10.0064	+	7.63403i	0.536399	+	0.409227i
$349$	1.64301	+	2.84577i	0.0879482	+	0.152331i	0.906644	−	0.421897i	$-0.138636\pi$
$349$	1.64301	+	2.84577i	0.0879482	+	0.152331i	−0.818695	+	0.574228i	$0.805302\pi$
$350$		0			0
$351$	−3.82651	−	4.90153i	−0.204244	−	0.261624i
$352$	4.46729			0.238107
$353$	8.40960	+	14.5658i	0.447598	+	0.775262i	0.998229	−	0.0594866i	$-0.0189463\pi$
$353$	8.40960	+	14.5658i	0.447598	+	0.775262i	−0.550631	+	0.834748i	$0.685613\pi$
$354$	1.23756	+	0.944152i	0.0657755	+	0.0501811i
$355$	9.13051	−	15.8145i	0.484597	−	0.839347i
$356$	−2.11144	+	3.65711i	−0.111906	+	0.193827i
$357$		0			0
$358$	−1.81864	−	3.14997i	−0.0961180	−	0.166481i
$359$	−23.7842			−1.25528			−0.627642	−	0.778502i	$-0.715980\pi$
$359$	−23.7842			−1.25528			−0.627642	+	0.778502i	$0.715980\pi$
$360$	−19.9485	−	5.22634i	−1.05138	−	0.275453i
$361$	−11.1136			−0.584926
$362$	−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
$366$	−8.56305	+	3.57488i	−0.447598	+	0.186862i
$367$	−0.344992	−	0.597544i	−0.0180084	−	0.0311915i	0.856881	−	0.515515i	$-0.172399\pi$
$367$	−0.344992	−	0.597544i	−0.0180084	−	0.0311915i	−0.874889	+	0.484323i	$0.839066\pi$
$368$	6.40526			0.333897
$369$	13.8772	+	3.63573i	0.722419	+	0.189268i
$370$	−8.66327			−0.450382
$371$		0			0
$372$	1.39169	−	10.8032i	0.0721558	−	0.560119i
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	−0.813239	−	0.581929i	$-0.802298\pi$
$373$	1.88006	−	3.25636i	0.0973457	−	0.168608i	0.910585	+	0.413321i	$0.135631\pi$
$374$	0.0553208	−	0.0958184i	0.00286057	−	0.00495465i
$375$	18.4843	+	14.1020i	0.954525	+	0.728222i
$376$	−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
$381$	−1.74812	−	1.33367i	−0.0895591	−	0.0683260i
$382$	−5.91222	+	10.2403i	−0.302495	+	0.523937i
$383$	−0.536335	+	0.928960i	−0.0274055	+	0.0474676i	−0.879403	−	0.476078i	$-0.842058\pi$
$383$	−0.536335	+	0.928960i	−0.0274055	+	0.0474676i	0.851997	+	0.523546i	$0.175391\pi$
$384$	2.51021	−	19.4858i	0.128099	−	0.994381i
$385$		0			0
$386$	−2.94276			−0.149782
$387$	21.0496	−	21.2852i	1.07001	−	1.08199i
$388$	−19.3728			−0.983505
$389$	11.8718	+	20.5626i	0.601925	+	1.04256i	0.992529	+	0.122006i	$0.0389326\pi$
$389$	11.8718	+	20.5626i	0.601925	+	1.04256i	−0.390605	+	0.920559i	$0.627734\pi$
$390$	3.50234	−	1.46215i	0.177348	−	0.0740389i
$391$	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
$395$	−6.64340			−0.334266
$396$	1.24091	+	4.53012i	0.0623579	+	0.227647i
$397$	−0.0320978			−0.00161094			−0.000805471	−	1.00000i	$-0.500256\pi$
$397$	−0.0320978			−0.00161094			−0.000805471		1.00000i	$0.500256\pi$
$398$	3.84208	+	6.65467i	0.192586	+	0.333569i
$399$		0			0
$400$	−11.1616	+	19.3324i	−0.558078	+	0.966619i
$401$	−12.2628	+	21.2398i	−0.612374	+	1.06066i	0.378465	+	0.925616i	$0.376452\pi$
$401$	−12.2628	+	21.2398i	−0.612374	+	1.06066i	−0.990839	+	0.135048i	$0.956881\pi$
$402$	−0.702894	−	0.536248i	−0.0350571	−	0.0267456i
$403$	2.14519	+	3.71558i	0.106860	+	0.185086i
$404$	−4.56007			−0.226872
$405$	−0.369938	−	33.2312i	−0.0183824	−	1.65127i
$406$		0			0
$407$	2.11153	+	3.65728i	0.104665	+	0.181284i
$408$	−0.640820	−	0.488891i	−0.0317253	−	0.0242037i
$409$	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
$411$	−0.108103	+	0.839160i	−0.00533230	+	0.0413927i
$412$	−8.51759	−	14.7529i	−0.419631	−	0.726823i
$413$		0			0
$414$	−0.973773	−	3.55490i	−0.0478583	−	0.174714i
$415$	45.5041			2.23371
$416$	2.99476	+	5.18708i	0.146830	+	0.254317i
$417$	15.7754	−	6.58586i	0.772522	−	0.322511i
$418$	−0.621466	+	1.07641i	−0.0303969	+	0.0526490i
$419$	10.5262	−	18.2320i	0.514240	−	0.890689i	−0.485624	−	0.874168i	$-0.661407\pi$
$419$	10.5262	−	18.2320i	0.514240	−	0.890689i	0.999864	−	0.0165215i	$-0.00525920\pi$
$420$		0			0
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	0.625568	−	0.780170i	$-0.284867\pi$
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	−0.988431	+	0.151672i	$0.951534\pi$
$422$	0.765520			0.0372649
$423$	21.4599	−	21.7001i	1.04342	−	1.05510i
$424$	18.4094			0.894038
$425$	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
$429$	−1.47090	−	1.12217i	−0.0710157	−	0.0541789i
$430$	9.13554	+	15.8232i	0.440555	+	0.763064i
$431$	15.9038			0.766061			0.383031	−	0.923736i	$-0.374880\pi$
$431$	15.9038			0.766061			0.383031	+	0.923736i	$0.374880\pi$
$432$	13.3028	−	1.86446i	0.640031	−	0.0897040i
$433$	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
$436$	1.86105	−	3.22344i	0.0891282	−	0.154375i
$437$	−3.47905	+	6.02590i	−0.166426	+	0.288258i
$438$	0.200872	−	1.55930i	0.00959804	−	0.0745060i
$439$	−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	$0.846873\pi$
$444$	13.2653	−	5.53797i	0.629543	−	0.262820i
$445$	4.44477	−	7.69857i	0.210702	−	0.364947i
$446$	−1.34961	+	2.33759i	−0.0639058	+	0.110688i
$447$	−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	$0.396275\pi$
$450$	12.4263	+	3.25559i	0.585781	+	0.153470i
$451$	4.26814			0.200979
$452$	−13.8806	−	24.0419i	−0.652890	−	1.13084i
$453$	0.331589	−	2.57400i	0.0155794	−	0.120937i
$454$	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	$0.852472\pi$
$458$	−4.94301			−0.230972
$459$	0.487050	−	1.20418i	0.0227335	−	0.0562064i
$460$	−16.0487			−0.748274
$461$	−18.0934	−	31.3388i	−0.842695	−	1.45959i	−0.887608	−	0.460600i	$-0.847634\pi$
$461$	−18.0934	−	31.3388i	−0.842695	−	1.45959i	0.0449122	−	0.998991i	$-0.485699\pi$
$462$		0			0
$463$	8.19224	−	14.1894i	0.380726	−	0.659436i	−0.610440	−	0.792062i	$-0.709008\pi$
$463$	8.19224	−	14.1894i	0.380726	−	0.659436i	0.991166	+	0.132626i	$0.0423409\pi$
$464$	5.35455	−	9.27436i	0.248579	−	0.430551i
$465$	−2.92964	+	22.7417i	−0.135859	+	1.05462i
$466$	−4.10105	−	7.10323i	−0.189978	−	0.329051i
$467$	−8.70044			−0.402608			−0.201304	−	0.979529i	$-0.564518\pi$
$467$	−8.70044			−0.402608			−0.201304	+	0.979529i	$0.564518\pi$
$468$	−4.42815	+	4.47772i	−0.204692	+	0.206983i
$469$		0			0
$470$	9.31361	+	16.1316i	0.429605	+	0.744097i
$471$	−26.6600	+	11.1300i	−1.22843	+	0.512841i
$472$	1.68691	−	2.92181i	0.0776462	−	0.134487i
$473$	4.45328	−	7.71330i	0.204762	−	0.354658i
$474$	−1.42594	+	0.595297i	−0.0654955	+	0.0273429i
$475$	−12.1249	−	21.0010i	−0.556330	−	0.963591i
$476$		0			0
$477$	7.83799	+	28.6138i	0.358877	+	1.31014i
$478$	−10.9209			−0.499513
$479$	−8.88370	−	15.3870i	−0.405907	−	0.703051i	0.588520	−	0.808483i	$-0.299711\pi$
$479$	−8.88370	−	15.3870i	−0.405907	−	0.703051i	−0.994427	+	0.105432i	$0.966378\pi$
$480$	−4.08988	+	31.7482i	−0.186677	+	1.44910i
$481$	−2.83103	+	4.90349i	−0.129084	+	0.223580i
$482$	−4.14548	+	7.18018i	−0.188821	+	0.327048i
$483$		0			0
$484$	−8.94890	−	15.4999i	−0.406768	−	0.704543i
$485$	40.7816			1.85180
$486$	−3.05716	−	7.09957i	−0.138675	−	0.322043i
$487$	−16.6553			−0.754722			−0.377361	−	0.926066i	$-0.623168\pi$
$487$	−16.6553			−0.754722			−0.377361	+	0.926066i	$0.623168\pi$
$488$	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	−0.929326	−	0.369260i	$-0.879611\pi$
$491$	−3.21021	+	5.56025i	−0.144875	+	0.250930i	0.784451	+	0.620190i	$0.212945\pi$
$492$	1.85623	−	14.4092i	0.0836854	−	0.649619i
$493$	−0.517784	−	0.896827i	−0.0233198	−	0.0403911i
$494$	−1.66646			−0.0749776
$495$	−2.61223	−	9.53633i	−0.117411	−	0.428626i
$496$	−9.26814			−0.416152
$497$		0			0
$498$	9.76698	−	4.07750i	0.437669	−	0.182717i
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	−0.963382	−	0.268134i	$-0.913593\pi$
$499$	−5.57296	+	9.65264i	−0.249480	+	0.432112i	0.713902	+	0.700246i	$0.246926\pi$
$500$	11.7728	−	20.3911i	0.526495	−	0.911916i
$501$	−28.1806	+	11.7648i	−1.25901	+	0.525611i
$502$	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
$507$	−2.55995	+	19.8719i	−0.113691	+	0.882544i
$508$	−1.11339	+	1.92845i	−0.0493988	+	0.0855612i
$509$	15.5411	−	26.9180i	0.688848	−	1.19312i	−0.283362	−	0.959013i	$-0.591450\pi$
$509$	15.5411	−	26.9180i	0.688848	−	1.19312i	0.972211	−	0.234107i	$-0.0752167\pi$
$510$	0.630316	+	0.480878i	0.0279109	+	0.0212936i
$511$		0			0
$512$	−22.5634			−0.997169
$513$	−5.47145	+	13.5276i	−0.241571	+	0.597258i
$514$	−8.48913			−0.374439
$515$	17.9303	+	31.0563i	0.790105	+	1.36850i
$516$	−24.1034	−	18.3888i	−1.06109	−	0.809524i
$517$	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
$521$	−4.75971			−0.208527			−0.104263	−	0.994550i	$-0.533249\pi$
$521$	−4.75971			−0.208527			−0.104263	+	0.994550i	$0.533249\pi$
$522$	−5.96128	−	1.56181i	−0.260918	−	0.0683586i
$523$	40.2515			1.76008			0.880038	−	0.474904i	$-0.157517\pi$
$523$	40.2515			1.76008			0.880038	+	0.474904i	$0.157517\pi$
$524$	13.1812	+	22.8305i	0.575823	+	0.997355i
$525$		0			0
$526$	5.09571	−	8.82602i	0.222183	−	0.384833i
$527$	−0.448113	+	0.776154i	−0.0195201	+	0.0338098i
$528$	3.68808	−	1.53969i	0.160503	−	0.0670064i
$529$	8.43046	+	14.6020i	0.366542	+	0.634869i
$530$	−18.1076			−0.786545
$531$	5.25960	+	1.37798i	0.228247	+	0.0597991i
$532$		0			0
$533$	2.86125	+	4.95583i	0.123935	+	0.214661i
$534$	0.264176	−	2.05070i	0.0114320	−	0.0887426i
$535$	−20.1255	+	34.8584i	−0.870101	+	1.50706i
$536$	−0.958109	+	1.65949i	−0.0413840	+	0.0716792i
$537$	−10.1009	−	7.70616i	−0.435888	−	0.332545i
$538$	4.92033	+	8.52227i	0.212131	+	0.367421i
$539$		0			0
$540$	−33.3308	+	4.67150i	−1.43433	+	0.201029i
$541$	−24.1094			−1.03655			−0.518273	−	0.855215i	$-0.673425\pi$
$541$	−24.1094			−1.03655			−0.518273	+	0.855215i	$0.673425\pi$
$542$	2.63830	+	4.56966i	0.113325	+	0.196284i
$543$	−15.5009	−	11.8259i	−0.665208	−	0.507497i
$544$	−0.625580	+	1.08354i	−0.0268215	+	0.0464563i
$545$	−3.91769	+	6.78564i	−0.167815	+	0.290665i
$546$		0			0
$547$	−6.17751	−	10.6998i	−0.264131	−	0.457489i	0.703204	−	0.710988i	$-0.251752\pi$
$547$	−6.17751	−	10.6998i	−0.264131	−	0.457489i	−0.967336	+	0.253499i	$0.918419\pi$
$548$	0.856872			0.0366038
$549$	−22.7911	+	23.0462i	−0.972699	+	0.983587i
$550$	3.82188			0.162966
$551$	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
$555$	−27.9247	+	11.6579i	−1.18534	+	0.494852i
$556$	−8.65633	−	14.9932i	−0.367110	−	0.635853i
$557$	−8.07689			−0.342229			−0.171114	−	0.985251i	$-0.554737\pi$
$557$	−8.07689			−0.342229			−0.171114	+	0.985251i	$0.554737\pi$
$558$	1.40901	+	5.14379i	0.0596480	+	0.217754i
$559$	11.9415			0.505070
$560$		0			0
$561$	0.0493776	−	0.383300i	0.00208472	−	0.0161829i
$562$	3.39041	−	5.87237i	0.143016	−	0.247711i
$563$	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	$-0.235087\pi$
$564$	−24.5732	−	18.7473i	−1.03472	−	0.789402i
$565$	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	$0.989135\pi$
$570$	−7.08089	−	5.40211i	−0.296586	−	0.226270i
$571$	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	$0.0156933\pi$
$572$	−0.936826	+	1.62263i	−0.0391706	+	0.0678455i
$573$	−5.27706	+	40.9638i	−0.220452	+	1.71129i
$574$		0			0
$575$	21.3954			0.892251
$576$	−2.13082	−	7.77888i	−0.0887842	−	0.324120i
$577$	−32.2044			−1.34068			−0.670342	−	0.742052i	$-0.733853\pi$
$577$	−32.2044			−1.34068			−0.670342	+	0.742052i	$0.733853\pi$
$578$	−4.19939	−	7.27355i	−0.174671	−	0.302540i
$579$	−9.48553	+	3.96000i	−0.394205	+	0.164572i
$580$	−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
$584$	−3.40761			−0.141008
$585$	9.32169	−	9.42604i	0.385404	−	0.389719i
$586$	1.30421			0.0538765
$587$	9.72304	+	16.8408i	0.401313	+	0.695094i	0.993885	−	0.110424i	$-0.0352208\pi$
$587$	9.72304	+	16.8408i	0.401313	+	0.695094i	−0.592572	+	0.805518i	$0.701887\pi$
$588$		0			0
$589$	5.03404	−	8.71921i	0.207424	−	0.359269i
$590$	−1.65926	+	2.87392i	−0.0683105	+	0.118317i
$591$	−21.3006	−	16.2505i	−0.876190	−	0.668458i
$592$	−6.11563	−	10.5926i	−0.251351	−	0.435352i
$593$	−28.8405			−1.18434			−0.592168	−	0.805815i	$-0.701728\pi$
$593$	−28.8405			−1.18434			−0.592168	+	0.805815i	$0.701728\pi$
$594$	−1.41521	−	1.81280i	−0.0580669	−	0.0743801i
$595$		0			0
$596$	18.4392	+	31.9377i	0.755300	+	1.30822i
$597$	21.3394	+	16.2801i	0.873363	+	0.666301i
$598$	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	$-0.243182\pi$
$600$	3.55730	−	27.6140i	0.145226	−	1.12734i
$601$	7.80843	+	13.5246i	0.318512	+	0.551680i	0.980178	−	0.198119i	$-0.0634834\pi$
$601$	7.80843	+	13.5246i	0.318512	+	0.551680i	−0.661665	+	0.749799i	$0.730150\pi$
$602$		0			0
$603$	−2.98729	−	0.782646i	−0.121652	−	0.0318718i
$604$	−2.62833			−0.106945
$605$	18.8383	+	32.6289i	0.765885	+	1.32655i
$606$	2.06041	−	0.860175i	0.0836984	−	0.0349422i
$607$	−14.3266	+	24.8144i	−0.581500	+	1.00719i	0.413802	+	0.910367i	$0.364200\pi$
$607$	−14.3266	+	24.8144i	−0.581500	+	1.00719i	−0.995302	+	0.0968200i	$0.969133\pi$
$608$	7.02769	−	12.1723i	0.285010	−	0.493652i
$609$		0			0
$610$	−9.89134	−	17.1323i	−0.400489	−	0.693667i
$611$	12.1742			0.492516
$612$	−1.27255	−	0.333398i	−0.0514397	−	0.0134768i
$613$	−29.3468			−1.18531			−0.592653	−	0.805458i	$-0.701920\pi$
$613$	−29.3468			−1.18531			−0.592653	+	0.805458i	$0.701920\pi$
$614$	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	−0.821484	−	0.570232i	$-0.806853\pi$
$617$	2.06401	−	3.57497i	0.0830938	−	0.143923i	0.904577	+	0.426310i	$0.140187\pi$
$618$	6.63143	+	5.05921i	0.266755	+	0.203511i
$619$	11.3565	+	19.6700i	0.456456	+	0.790605i	0.998771	−	0.0495708i	$-0.0157853\pi$
$619$	11.3565	+	19.6700i	0.456456	+	0.790605i	−0.542315	+	0.840175i	$0.682452\pi$
$620$	23.2217			0.932608
$621$	−7.92256	−	10.1483i	−0.317921	−	0.407238i
$622$	−7.48774			−0.300231
$623$		0			0
$624$	4.26017	+	3.25014i	0.170543	+	0.130110i
$625$	−3.19498	+	5.53387i	−0.127799	+	0.221355i
$626$	6.31698	−	10.9413i	0.252477	−	0.437304i
$627$	−0.554701	+	4.30594i	−0.0221526	+	0.171963i
$628$	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
$633$	2.46754	−	1.03014i	0.0980757	−	0.0409444i
$634$	8.06304	−	13.9656i	0.320224	−	0.554645i
$635$	2.34380	−	4.05958i	0.0930107	−	0.161099i
$636$	27.7266	−	11.5752i	1.09943	−	0.458988i
$637$		0			0
$638$	−1.83348			−0.0725881
$639$	−3.91954	−	14.3089i	−0.155055	−	0.566050i
$640$	41.8853			1.65566
$641$	14.2363	+	24.6580i	0.562301	+	0.973933i	0.997295	+	0.0735002i	$0.0234169\pi$
$641$	14.2363	+	24.6580i	0.562301	+	0.973933i	−0.434995	+	0.900433i	$0.643250\pi$
$642$	−1.19616	+	9.28538i	−0.0472088	+	0.366465i
$643$	8.52125	−	14.7592i	0.336045	−	0.582048i	−0.647640	−	0.761947i	$-0.724244\pi$
$643$	8.52125	−	14.7592i	0.336045	−	0.582048i	0.983685	+	0.179899i	$0.0575771\pi$
$644$		0			0
$645$	50.7400	+	38.7103i	1.99788	+	1.52422i
$646$	−0.174055	−	0.301472i	−0.00684810	−	0.0118613i
$647$	3.37618			0.132731			0.0663657	−	0.997795i	$-0.478860\pi$
$647$	3.37618			0.132731			0.0663657	+	0.997795i	$0.478860\pi$
$648$	−14.4152	+	8.53795i	−0.566281	+	0.335402i
$649$	1.61767			0.0634989
$650$	2.56209	+	4.43768i	0.100494	+	0.174060i
$651$		0			0
$652$	5.86110	−	10.1517i	0.229538	−	0.397572i
$653$	9.17255	−	15.8873i	0.358950	−	0.621719i	−0.628836	−	0.777538i	$-0.716468\pi$
$653$	9.17255	−	15.8873i	0.358950	−	0.621719i	0.987786	+	0.155819i	$0.0498017\pi$
$654$	−0.232849	+	1.80752i	−0.00910512	+	0.0706797i
$655$	−27.7477	−	48.0604i	−1.08419	−	1.87787i
$656$	−12.3618			−0.482648
$657$	−1.45083	−	5.29646i	−0.0566021	−	0.206635i
$658$		0			0
$659$	−13.9248	−	24.1184i	−0.542432	−	0.939519i	−0.998764	−	0.0497098i	$-0.984170\pi$
$659$	−13.9248	−	24.1184i	−0.542432	−	0.939519i	0.456332	−	0.889810i	$-0.349163\pi$
$660$	−9.24065	+	3.85777i	−0.359692	+	0.150163i
$661$	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
$663$	0.478160	−	0.199621i	0.0185702	−	0.00775264i
$664$	−11.4700	−	19.8667i	−0.445123	−	0.770976i
$665$		0			0
$666$	−4.94911	+	5.00452i	−0.191774	+	0.193921i
$667$	−10.2641			−0.397426
$668$	15.4634	+	26.7834i	0.598296	+	1.03628i
$669$	−1.20462	+	9.35100i	−0.0465732	+	0.361531i
$670$	0.942405	−	1.63229i	0.0364083	−	0.0630610i
$671$	−4.82170	+	8.35143i	−0.186140	+	0.322404i
$672$		0			0
$673$	24.6154	+	42.6352i	0.948856	+	1.64347i	0.747841	+	0.663878i	$0.231090\pi$
$673$	24.6154	+	42.6352i	0.948856	+	1.64347i	0.201014	+	0.979588i	$0.435576\pi$
$674$	−12.4053			−0.477833
$675$	44.4352	−	6.22784i	1.71031	−	0.239710i
$676$	20.2914			0.780438
$677$	−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
$681$	3.55767	−	27.6169i	0.136330	−	1.05828i
$682$	0.793387	+	1.37419i	0.0303803	+	0.0526203i
$683$	30.3264			1.16041			0.580204	−	0.814471i	$-0.302973\pi$
$683$	30.3264			1.16041			0.580204	+	0.814471i	$0.302973\pi$
$684$	14.2956	+	3.74535i	0.546607	+	0.143207i
$685$	−1.80380			−0.0689196
$686$		0			0
$687$	−15.9330	+	6.65169i	−0.607884	+	0.253778i
$688$	−12.8980	+	22.3401i	−0.491733	+	0.851707i
$689$	−5.91731	+	10.2491i	−0.225432	+	0.390459i
$690$	7.25139	−	3.02729i	0.276056	−	0.115247i
$691$	−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
$696$	−1.70655	+	13.2473i	−0.0646867	+	0.502139i
$697$	−0.597691	+	1.03523i	−0.0226392	+	0.0392122i
$698$	−0.814716	+	1.41113i	−0.0308375	+	0.0534120i
$699$	−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	$0.314200\pi$
$702$	1.15616	−	2.85849i	0.0436365	−	0.107887i
$703$	13.2869			0.501127
$704$	−1.19983	−	2.07816i	−0.0452202	−	0.0783236i
$705$	51.7289	+	39.4648i	1.94822	+	1.48633i
$706$	−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	$0.539572\pi$
$710$	9.05507			0.339831
$711$	−3.79522	+	3.83770i	−0.142332	+	0.143925i
$712$	−4.48150			−0.167951
$713$	4.44149	+	7.69288i	0.166335	+	0.288101i
$714$		0			0
$715$	1.97211	−	3.41579i	0.0737526	−	0.127743i
$716$	−6.43336	+	11.1429i	−0.240426	+	0.416430i
$717$	−35.2020	+	14.6961i	−1.31464	+	0.548834i
$718$	−5.89692	−	10.2138i	−0.220071	−	0.381175i
$719$	−11.1425			−0.415546			−0.207773	−	0.978177i	$-0.566621\pi$
$719$	−11.1425			−0.415546			−0.207773	+	0.978177i	$0.566621\pi$
$720$	7.56580	+	27.6201i	0.281961	+	1.02934i
$721$		0			0
$722$	−2.75544	−	4.77256i	−0.102547	−	0.177616i
$723$	−3.70012	+	28.7227i	−0.137609	+	1.06821i
$724$	−9.87264	+	17.0999i	−0.366914	+	0.635513i
$725$	17.8858	−	30.9790i	0.664260	−	1.15053i
$726$	6.96723	+	5.31540i	0.258578	+	0.197273i
$727$	14.3410	+	24.8393i	0.531878	+	0.921239i	0.999308	+	0.0372089i	$0.0118467\pi$
$727$	14.3410	+	24.8393i	0.531878	+	0.921239i	−0.467430	+	0.884030i	$0.654820\pi$
$728$		0			0
$729$	−19.4080	−	18.7704i	−0.718815	−	0.695202i
$730$	3.35175			0.124054
$731$	1.24724	+	2.16028i	0.0461307	+	0.0799007i
$732$	26.0975	+	19.9102i	0.964591	+	0.735901i
$733$	−12.5264	+	21.6964i	−0.462674	+	0.801375i	−0.999093	−	0.0425768i	$-0.986443\pi$
$733$	−12.5264	+	21.6964i	−0.462674	+	0.801375i	0.536419	+	0.843952i	$0.319777\pi$
$734$	0.171071	−	0.296303i	0.00631433	−	0.0109367i
$735$		0			0
$736$	6.20047	+	10.7395i	0.228552	+	0.395864i
$737$	−0.918782			−0.0338438
$738$	1.87933	+	6.86077i	0.0691790	+	0.252549i
$739$	−27.5216			−1.01240			−0.506198	−	0.862417i	$-0.668950\pi$
$739$	−27.5216			−1.01240			−0.506198	+	0.862417i	$0.668950\pi$
$740$	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	−0.965444	−	0.260609i	$-0.916077\pi$
$743$	−7.00608	+	12.1349i	−0.257028	+	0.445186i	0.708416	+	0.705795i	$0.249410\pi$
$744$	10.6673	−	4.45336i	0.391082	−	0.163268i
$745$	−38.8163	−	67.2318i	−1.42212	−	2.46318i
$746$	1.86452			0.0682650
$747$	25.9954	−	26.2864i	0.951121	−	0.961768i
$748$	−0.391390			−0.0143106
$749$		0			0
$750$	−1.47297	+	11.4342i	−0.0537854	+	0.417516i
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.215692	−	0.976461i	$-0.430799\pi$
$751$	26.1297	−	45.2580i	0.953486	−	1.65149i	0.737795	−	0.675025i	$-0.235867\pi$
$752$	−13.1494	+	22.7755i	−0.479511	+	0.830537i
$753$	11.7477	+	8.96246i	0.428109	+	0.326610i
$754$	−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
$759$	−3.04540	−	2.32338i	−0.110541	−	0.0843335i
$760$	−9.65191	+	16.7176i	−0.350112	+	0.606411i
$761$	−8.62550	+	14.9398i	−0.312674	+	0.541568i	−0.978940	−	0.204146i	$-0.934558\pi$
$761$	−8.62550	+	14.9398i	−0.312674	+	0.541568i	0.666266	+	0.745714i	$0.267891\pi$
$762$	0.139304	−	1.08137i	0.00504646	−	0.0391738i
$763$		0			0
$764$	41.8285			1.51330
$765$	2.67883	+	0.701834i	0.0968534	+	0.0253749i
$766$	−0.531903			−0.0192184
$767$	1.08444	+	1.87831i	0.0391570	+	0.0678218i
$768$	0.395948	−	0.165299i	0.0142875	−	0.00596472i
$769$	10.6727	−	18.4856i	0.384867	−	0.666609i	−0.606884	−	0.794790i	$-0.707581\pi$
$769$	10.6727	−	18.4856i	0.384867	−	0.666609i	0.991751	+	0.128182i	$0.0409141\pi$
$770$		0			0
$771$	−27.3634	+	11.4236i	−0.985469	+	0.411411i
$772$	5.20495	+	9.01523i	0.187330	+	0.324465i
$773$	−13.1471			−0.472870			−0.236435	−	0.971647i	$-0.575979\pi$
$773$	−13.1471			−0.472870			−0.236435	+	0.971647i	$0.575979\pi$
$774$	14.3595	+	3.76209i	0.516143	+	0.135225i
$775$	−30.9583			−1.11205
$776$	−10.2796	−	17.8049i	−0.369018	−	0.639158i
$777$		0			0
$778$	−5.88685	+	10.1963i	−0.211054	+	0.365556i
$779$	6.71439	−	11.6297i	0.240568	−	0.416676i
$780$	−10.6740	−	8.14339i	−0.382192	−	0.291580i
$781$	−2.20702	−	3.82268i	−0.0789735	−	0.136786i
$782$	0.307134			0.0109831
$783$	−21.3170	+	2.98769i	−0.761807	+	0.106771i
$784$		0			0
$785$	−30.7954	−	53.3393i	−1.09914	−	1.90376i
$786$	−10.2623	−	7.82927i	−0.366045	−	0.279261i
$787$	−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
$789$	4.54827	−	35.3065i	0.161923	−	1.25694i
$790$	−1.64713	−	2.85291i	−0.0586021	−	0.101502i
$791$		0			0
$792$	−3.50502	+	3.54426i	−0.124546	+	0.125940i
$793$	−12.9294			−0.459136
$794$	−0.00795814	−	0.0137839i	−0.000282424	−	0.000489172i
$795$	−58.3671	+	24.3670i	−2.07007	+	0.864208i
$796$	13.5912	−	23.5406i	0.481727	−	0.834376i
$797$	−12.8683	+	22.2885i	−0.455817	+	0.789499i	−0.998735	−	0.0502873i	$-0.983986\pi$
$797$	−12.8683	+	22.2885i	−0.455817	+	0.789499i	0.542917	+	0.839786i	$0.317320\pi$
$798$		0			0
$799$	1.27155	+	2.20238i	0.0449841	+	0.0779147i
$800$	−43.2188			−1.52801
$801$	−1.90805	−	6.96562i	−0.0674176	−	0.246118i
$802$	−12.1615			−0.429436
$803$	−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
$807$	27.3282	+	20.8491i	0.961997	+	0.733922i
$808$	−2.41968	−	4.19100i	−0.0851240	−	0.147439i
$809$	−31.8705			−1.12051			−0.560254	−	0.828321i	$-0.689296\pi$
$809$	−31.8705			−1.12051			−0.560254	+	0.828321i	$0.689296\pi$
$810$	14.1789	−	8.39800i	0.498195	−	0.295076i
$811$	−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
$814$	−1.04704	+	1.81353i	−0.0366987	+	0.0635641i
$815$	−12.3382	+	21.3704i	−0.432188	+	0.748571i
$816$	−0.143012	+	1.11015i	−0.00500643	+	0.0388631i
$817$	−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	$0.740985\pi$
$822$	−0.387166	+	0.161633i	−0.0135040	+	0.00563761i
$823$	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	$0.0146096\pi$
$824$	9.03925	−	15.6564i	0.314897	−	0.545418i
$825$	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	$0.279562\pi$
$828$	−9.16822	+	9.27085i	−0.318618	+	0.322184i
$829$	24.3158			0.844522			0.422261	−	0.906474i	$-0.361237\pi$
$829$	24.3158			0.844522			0.422261	+	0.906474i	$0.361237\pi$
$830$	11.2820	+	19.5410i	0.391604	+	0.678279i
$831$	−5.50619	+	42.7425i	−0.191008	+	1.48272i
$832$	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
$836$	4.39682			0.152067
$837$	11.4636	+	14.6842i	0.396240	+	0.507559i
$838$	10.4392			0.360618
$839$	12.8405	+	22.2404i	0.443303	+	0.767824i	0.997932	−	0.0642741i	$-0.0204732\pi$
$839$	12.8405	+	22.2404i	0.443303	+	0.767824i	−0.554629	+	0.832098i	$0.687140\pi$
$840$		0			0
$841$	5.91963	−	10.2531i	0.204125	−	0.353555i
$842$	3.69190	−	6.39456i	0.127231	−	0.220371i
$843$	3.02618	−	23.4911i	0.104227	−	0.809076i
$844$	−1.35400	−	2.34519i	−0.0466065	−	0.0807249i
$845$	−42.7153			−1.46945
$846$	14.6394	+	3.83542i	0.503313	+	0.131864i
$847$		0			0
$848$	−12.7826	−	22.1402i	−0.438958	−	0.760297i
$849$	10.1045	−	4.21839i	0.346784	−	0.144775i
$850$	−0.535200	+	0.926994i	−0.0183572	+	0.0317956i
$851$	−5.86148	+	10.1524i	−0.200929	+	0.348019i
$852$	−13.8652	+	5.78842i	−0.475015	+	0.198308i
$853$	−14.4872	−	25.0925i	−0.496031	−	0.859150i	0.503959	−	0.863728i	$-0.331876\pi$
$853$	−14.4872	−	25.0925i	−0.496031	−	0.859150i	−0.999990	+	0.00457743i	$0.998543\pi$
$854$		0			0
$855$	−30.0937	−	7.88431i	−1.02918	−	0.269638i
$856$	20.2918			0.693559
$857$	−12.6934	−	21.9856i	−0.433598	−	0.751015i	0.563582	−	0.826060i	$-0.309423\pi$
$857$	−12.6934	−	21.9856i	−0.433598	−	0.751015i	−0.997180	+	0.0750458i	$0.976090\pi$
$858$	0.117213	−	0.909879i	0.00400158	−	0.0310628i
$859$	−2.97891	+	5.15963i	−0.101639	+	0.176044i	−0.912360	−	0.409388i	$-0.865742\pi$
$859$	−2.97891	+	5.15963i	−0.101639	+	0.176044i	0.810721	+	0.585433i	$0.199075\pi$
$860$	32.3166	−	55.9740i	1.10199	−	1.90870i
$861$		0			0
$862$	3.94310	+	6.82966i	0.134303	+	0.232619i
$863$	−16.3909			−0.557953			−0.278977	−	0.960298i	$-0.589995\pi$
$863$	−16.3909			−0.557953			−0.278977	+	0.960298i	$0.589995\pi$
$864$	16.0036	+	20.4996i	0.544452	+	0.697410i
$865$	14.3525			0.487999
$866$	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
$870$	1.67858	−	13.0302i	0.0569092	−	0.441765i
$871$	−0.615929	−	1.06682i	−0.0208700	−	0.0361478i
$872$	3.95006			0.133766
$873$	23.2975	−	23.5583i	0.788502	−	0.797329i
$874$	−3.45030			−0.116708
$875$		0			0
$876$	−5.13224	+	2.14260i	−0.173402	+	0.0723916i
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	0.398295	+	0.917257i	$0.369602\pi$
$877$	−17.6270	+	30.5308i	−0.595220	+	1.03095i	−0.993516	+	0.113695i	$0.963731\pi$
$878$	3.85407	−	6.67544i	0.130068	−	0.225285i
$879$	4.20392	−	1.75504i	0.141795	−	0.0591962i
$880$	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
$885$	−1.48100	+	11.4965i	−0.0497833	+	0.386449i
$886$	0.443815	−	0.768711i	0.0149103	−	0.0258253i
$887$	−7.95282	+	13.7747i	−0.267030	+	0.462509i	−0.968093	−	0.250590i	$-0.919376\pi$
$887$	−7.95282	+	13.7747i	−0.267030	+	0.462509i	0.701064	+	0.713099i	$0.252709\pi$
$888$	12.1286	+	9.25311i	0.407010	+	0.310514i
$889$		0			0
$890$	4.40804			0.147758
$891$	−7.00116	−	3.93887i	−0.234548	−	0.131957i
$892$	9.54838			0.319703
$893$	−14.2844	−	24.7413i	−0.478009	−	0.827935i
$894$	−14.3560	−	10.9524i	−0.480136	−	0.366303i
$895$	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
$899$	14.8517			0.495331
$900$	−12.0051	−	43.8266i	−0.400171	−	1.46089i
$901$	−2.47215			−0.0823594
$902$	1.05822	+	1.83288i	0.0352348	+	0.0610284i
$903$		0			0
$904$	14.7307	−	25.5144i	0.489937	−	0.848597i
$905$	20.7829	−	35.9970i	0.690846	−	1.19658i
$906$	1.18758	−	0.495787i	0.0394546	−	0.0164714i
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	0.972311	−	0.233691i	$-0.0750804\pi$
$907$	8.54624	+	14.8025i	0.283773	+	0.491510i	−0.688538	+	0.725201i	$0.741747\pi$
$908$	−28.1998			−0.935843
$909$	5.48390	−	5.54528i	0.181889	−	0.183925i
$910$		0			0
$911$	14.9435	+	25.8829i	0.495099	+	0.857537i	0.999984	−	0.00564955i	$-0.00179832\pi$
$911$	14.9435	+	25.8829i	0.495099	+	0.857537i	−0.504885	+	0.863187i	$0.668465\pi$
$912$	1.60658	−	12.4713i	0.0531992	−	0.412966i
$913$	5.49961	−	9.52561i	0.182011	−	0.315252i
$914$	0.636986	−	1.10329i	0.0210696	−	0.0364937i
$915$	−54.9377	−	41.9128i	−1.81619	−	1.38560i
$916$	8.74286	+	15.1431i	0.288872	+	0.500341i
$917$		0			0
$918$	0.637873	−	0.0894015i	0.0210530	−	0.00295069i
$919$	−23.6567			−0.780362			−0.390181	−	0.920738i	$-0.627588\pi$
$919$	−23.6567			−0.780362			−0.390181	+	0.920738i	$0.627588\pi$
$920$	−8.51579	−	14.7498i	−0.280757	−	0.486286i
$921$	3.84882	+	2.93632i	0.126823	+	0.0967550i
$922$	8.97196	−	15.5399i	0.295476	−	0.511779i
$923$	2.95907	−	5.12525i	0.0973989	−	0.168700i
$924$		0			0
$925$	−20.4280	−	35.3823i	−0.671667	−	1.16336i
$926$	8.12454			0.266989
$927$	28.1834	+	7.38385i	0.925666	+	0.242518i
$928$	20.7334			0.680607
$929$	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
$933$	−24.1356	+	10.0761i	−0.790164	+	0.329876i
$934$	−2.15714	−	3.73627i	−0.0705836	−	0.122254i
$935$	0.823914			0.0269449
$936$	−6.46500	−	1.69378i	−0.211315	−	0.0553630i
$937$	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
$940$	32.9465	−	57.0651i	1.07460	−	1.86126i
$941$	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	$-0.145161\pi$
$942$	−11.3895	−	8.68923i	−0.371090	−	0.283110i
$943$	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	$0.981816\pi$
$948$	4.34581	+	3.31548i	0.141145	+	0.107682i
$949$	1.09530	−	1.89712i	0.0355551	−	0.0615832i
$950$	6.01236	−	10.4137i	0.195067	−	0.337866i
$951$	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	$0.646375\pi$
$954$	−10.3444	+	10.4602i	−0.334914	+	0.338663i
$955$	−88.0530			−2.84933
$956$	19.3162	+	33.4567i	0.624731	+	1.08207i
$957$	−5.90994	+	2.46727i	−0.191041	+	0.0797554i
$958$	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
$962$	−2.80764			−0.0905219
$963$	8.63946	+	31.5396i	0.278403	+	1.01635i
$964$	29.3289			0.944621
$965$	−10.9569	−	18.9779i	−0.352715	−	0.610921i
$966$		0			0
$967$	9.09069	−	15.7455i	0.292337	−	0.506342i	−0.682025	−	0.731329i	$-0.738900\pi$
$967$	9.09069	−	15.7455i	0.292337	−	0.506342i	0.974362	+	0.224986i	$0.0722338\pi$
$968$	9.49698	−	16.4492i	0.305244	−	0.528699i
$969$	−0.966723	−	0.737527i	−0.0310556	−	0.0236928i
$970$	10.1111	+	17.5130i	0.324649	+	0.562309i
$971$	39.4832			1.26708			0.633538	−	0.773712i	$-0.281602\pi$
$971$	39.4832			1.26708			0.633538	+	0.773712i	$0.281602\pi$
$972$	−16.3425	+	21.9229i	−0.524185	+	0.703178i
$973$		0			0
$974$	−4.12941	−	7.15234i	−0.132315	−	0.229176i
$975$	14.2302	+	10.8564i	0.455731	+	0.347684i
$976$	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	$0.227712\pi$
$978$	−0.733323	+	5.69252i	−0.0234491	+	0.182027i
$979$	−1.07439	−	1.86090i	−0.0343376	−	0.0594745i
$980$		0			0
$981$	1.68178	+	6.13961i	0.0536952	+	0.196023i
$982$	−3.18368			−0.101595
$983$	−9.23896	−	16.0024i	−0.294677	−	0.510396i	0.680233	−	0.732996i	$-0.261879\pi$
$983$	−9.23896	−	16.0024i	−0.294677	−	0.510396i	−0.974910	+	0.222601i	$0.928545\pi$
$984$	14.2280	−	5.93987i	0.453572	−	0.189356i
$985$	28.5588	−	49.4653i	0.909959	−	1.57609i
$986$	0.256752	−	0.444708i	0.00817666	−	0.0141624i
$987$		0			0
$988$	2.94752	+	5.10525i	0.0937731	+	0.162420i
$989$	24.7241			0.786179
$990$	3.44757	−	3.48616i	0.109571	−	0.110798i
$991$	12.6970			0.403334			0.201667	−	0.979454i	$-0.435364\pi$
$991$	12.6970			0.403334			0.201667	+	0.979454i	$0.435364\pi$
$992$	−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
$996$	−29.7667	−	22.7094i	−0.943194	−	0.719576i
$997$	20.9767	+	36.3327i	0.664338	+	1.15067i	0.979464	+	0.201617i	$0.0646197\pi$
$997$	20.9767	+	36.3327i	0.664338	+	1.15067i	−0.315127	+	0.949050i	$0.602047\pi$
$998$	−5.52690			−0.174951
$999$	−9.21826	+	22.7912i	−0.291653	+	0.721081i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	7.5	odd	6
63.2.g.b.16.3	yes	10	63.52	odd	6
63.2.h.b.25.3	yes	10	63.61	odd	6
63.2.h.b.58.3	yes	10	7.3	odd	6
189.2.g.b.100.3		10	63.38	even	6
189.2.g.b.172.3		10	21.5	even	6
189.2.h.b.37.3		10	21.17	even	6
189.2.h.b.46.3		10	63.47	even	6
441.2.f.e.148.3		10	7.6	odd	2
441.2.f.e.295.3		10	63.34	odd	6
441.2.f.f.148.3		10	1.1	even	1	trivial
441.2.f.f.295.3		10	9.7	even	3	inner
441.2.g.f.67.3		10	7.2	even	3
441.2.g.f.79.3		10	63.25	even	3
441.2.h.f.214.3		10	63.16	even	3
441.2.h.f.373.3		10	7.4	even	3
567.2.e.e.163.3		10	63.59	even	6
567.2.e.e.487.3		10	63.5	even	6
567.2.e.f.163.3		10	63.31	odd	6
567.2.e.f.487.3		10	63.40	odd	6
1008.2.q.i.529.3		10	252.187	even	6
1008.2.q.i.625.3		10	28.3	even	6
1008.2.t.i.193.1		10	28.19	even	6
1008.2.t.i.961.1		10	252.115	even	6
1323.2.f.e.442.3		10	21.20	even	2
1323.2.f.e.883.3		10	63.20	even	6
1323.2.f.f.442.3		10	3.2	odd	2
1323.2.f.f.883.3		10	9.2	odd	6
1323.2.g.f.361.3		10	21.2	odd	6
1323.2.g.f.667.3		10	63.11	odd	6
1323.2.h.f.226.3		10	21.11	odd	6
1323.2.h.f.802.3		10	63.2	odd	6
3024.2.q.i.2305.1		10	84.59	odd	6
3024.2.q.i.2881.1		10	252.47	odd	6
3024.2.t.i.289.5		10	252.227	odd	6
3024.2.t.i.1873.5		10	84.47	odd	6
3969.2.a.z.1.3		5	63.13	odd	6
3969.2.a.ba.1.3		5	9.4	even	3
3969.2.a.bb.1.3		5	9.5	odd	6
3969.2.a.bc.1.3		5	63.41	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.247934 + 0.429435i) q^{2} +(1.37706 + 1.05058i) q^{3} +(0.877057 - 1.51911i) q^{4} +(-1.84629 + 3.19787i) q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(0.792574 + 2.89341i) q^{9} +O(q^{10})\)	\(q+(0.247934 + 0.429435i) q^{2} +(1.37706 + 1.05058i) q^{3} +(0.877057 - 1.51911i) q^{4} +(-1.84629 + 3.19787i) q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(0.792574 + 2.89341i) q^{9} -1.83103 q^{10} +(0.446284 + 0.772987i) q^{11} +(2.80370 - 1.17048i) q^{12} +(-0.598355 + 1.03638i) q^{13} +(-5.90205 + 2.46398i) q^{15} +(-1.29257 - 2.23880i) q^{16} -0.249983 q^{17} +(-1.04602 + 1.05773i) q^{18} +2.80827 q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(-1.23886 + 2.14576i) q^{23} +(2.56346 + 1.95570i) q^{24} +(-4.31757 - 7.47825i) q^{25} -0.593411 q^{26} +(-1.94833 + 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} +(-2.52144 - 1.92364i) q^{30} +(1.79257 - 3.10483i) q^{31} +(2.50249 - 4.33444i) q^{32} +(-0.197524 + 1.53330i) q^{33} +(-0.0619793 - 0.107351i) q^{34} +(5.09054 + 1.33368i) q^{36} +4.73136 q^{37} +(0.696267 + 1.20597i) q^{38} +(-1.91277 + 0.798539i) q^{39} +(-3.43695 + 5.95298i) q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +1.56567 q^{44} +(-10.7161 - 2.80753i) q^{45} -1.22862 q^{46} +(-5.08653 - 8.81013i) q^{47} +(0.572088 - 4.44091i) q^{48} +(2.14095 - 3.70823i) q^{50} +(-0.344241 - 0.262626i) q^{51} +(1.04958 + 1.81793i) q^{52} +9.88929 q^{53} +(-2.55167 + 0.357630i) q^{54} -3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} +(-1.02708 + 1.77895i) q^{58} +(0.906186 - 1.56956i) q^{59} +(-1.43339 + 11.1269i) q^{60} +(5.40205 + 9.35663i) q^{61} +1.77776 q^{62} -2.68848 q^{64} +(-2.20948 - 3.82692i) q^{65} +(-0.707426 + 0.295335i) q^{66} +(-0.514685 + 0.891460i) q^{67} +(-0.219249 + 0.379751i) q^{68} +(-3.96027 + 1.65332i) q^{69} -4.94533 q^{71} +(1.47541 + 5.38622i) q^{72} -1.83052 q^{73} +(1.17306 + 2.03181i) q^{74} +(1.91094 - 14.8339i) q^{75} +(2.46302 - 4.26607i) q^{76} +(-0.817161 - 0.623424i) q^{78} +(0.899562 + 1.55809i) q^{79} +9.54586 q^{80} +(-7.74365 + 4.58648i) q^{81} +2.37117 q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(2.47403 - 4.28514i) q^{86} +(-0.916739 + 7.11630i) q^{87} +(0.830779 + 1.43895i) q^{88} -2.40741 q^{89} +(-1.45123 - 5.29793i) q^{90} +(2.17310 + 3.76392i) q^{92} +(5.73034 - 2.39229i) q^{93} +(2.52225 - 4.36867i) q^{94} +(-5.18489 + 8.98049i) q^{95} +(7.99975 - 3.33972i) q^{96} +(-5.52210 - 9.56456i) q^{97} +(-1.88286 + 1.90393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9	\( 10 q + 2 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} - 7 q^{9} - 14 q^{10} + 4 q^{11} + 2 q^{12} + 8 q^{13} - 19 q^{15} + 2 q^{16} + 24 q^{17} - 2 q^{18} + 2 q^{19} - 5 q^{20} - q^{22} + 3 q^{23} + 9 q^{24} - q^{25} + 22 q^{26} + 7 q^{27} + 7 q^{29} + 10 q^{30} + 3 q^{31} - 2 q^{32} + 13 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} - 22 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} + 20 q^{44} - 17 q^{45} - 6 q^{46} - 27 q^{47} + 5 q^{48} + 19 q^{50} - 15 q^{51} + 10 q^{52} + 42 q^{53} - 52 q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} - 30 q^{59} + 31 q^{60} + 14 q^{61} + 12 q^{62} - 50 q^{64} - 11 q^{65} - 22 q^{66} - 2 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 12 q^{72} + 30 q^{73} - 36 q^{74} + 17 q^{75} - 5 q^{76} - 20 q^{78} - 4 q^{79} + 40 q^{80} - 31 q^{81} - 10 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} + 34 q^{87} - 18 q^{88} + 56 q^{89} - 28 q^{90} + 27 q^{92} + 18 q^{93} + 3 q^{94} - 14 q^{95} + 58 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 - 7 * q^9 - 14 * q^10 + 4 * q^11 + 2 * q^12 + 8 * q^13 - 19 * q^15 + 2 * q^16 + 24 * q^17 - 2 * q^18 + 2 * q^19 - 5 * q^20 - q^22 + 3 * q^23 + 9 * q^24 - q^25 + 22 * q^26 + 7 * q^27 + 7 * q^29 + 10 * q^30 + 3 * q^31 - 2 * q^32 + 13 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 - 22 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 + 20 * q^44 - 17 * q^45 - 6 * q^46 - 27 * q^47 + 5 * q^48 + 19 * q^50 - 15 * q^51 + 10 * q^52 + 42 * q^53 - 52 * q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 - 30 * q^59 + 31 * q^60 + 14 * q^61 + 12 * q^62 - 50 * q^64 - 11 * q^65 - 22 * q^66 - 2 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 12 * q^72 + 30 * q^73 - 36 * q^74 + 17 * q^75 - 5 * q^76 - 20 * q^78 - 4 * q^79 + 40 * q^80 - 31 * q^81 - 10 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 + 34 * q^87 - 18 * q^88 + 56 * q^89 - 28 * q^90 + 27 * q^92 + 18 * q^93 + 3 * q^94 - 14 * q^95 + 58 * q^96 + 12 * q^97 + 35 * q^99

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