LMFDB - Embedded newform 441.2.h.f.373.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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([4, 4]))

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Embedding invariants

Embedding label			373.3
Root			$0.247934 + 0.429435i$ of defining polynomial
Character	$\chi$	$=$	441.373
Dual form			441.2.h.f.214.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.495868 q^{2} +(0.221298 - 1.71786i) q^{3} -1.75411 q^{4} +(-1.84629 - 3.19787i) q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(-2.90205 - 0.760316i) q^{9} +O(q^{10})$	\(q-0.495868 q^{2} +(0.221298 - 1.71786i) q^{3} -1.75411 q^{4} +(-1.84629 - 3.19787i) q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(-2.90205 - 0.760316i) q^{9} +(0.915516 + 1.58572i) q^{10} +(0.446284 - 0.772987i) q^{11} +(-0.388182 + 3.01332i) q^{12} +(-0.598355 + 1.03638i) q^{13} +(-5.90205 + 2.46398i) q^{15} +2.58515 q^{16} +(0.124991 + 0.216492i) q^{17} +(1.43904 + 0.377017i) q^{18} +(-1.40414 + 2.43204i) q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(-1.23886 - 2.14576i) q^{23} +(0.411957 - 3.19787i) q^{24} +(-4.31757 + 7.47825i) q^{25} +(0.296705 - 0.513909i) q^{26} +(-1.94833 + 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} +(2.92664 - 1.22181i) q^{30} -3.58515 q^{31} -5.00499 q^{32} +(-1.22912 - 0.937712i) q^{33} +(-0.0619793 - 0.107351i) q^{34} +(5.09054 + 1.33368i) q^{36} +(-2.36568 + 4.09747i) q^{37} +(0.696267 - 1.20597i) q^{38} +(1.64794 + 1.25724i) q^{39} +(-3.43695 - 5.95298i) q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +(-0.782834 + 1.35591i) q^{44} +(2.92664 + 10.6841i) q^{45} +(0.614310 + 1.06402i) q^{46} +10.1731 q^{47} +(0.572088 - 4.44091i) q^{48} +(2.14095 - 3.70823i) q^{50} +(0.399562 - 0.166808i) q^{51} +(1.04958 - 1.81793i) q^{52} +(-4.94465 - 8.56438i) q^{53} +(0.966116 - 2.38862i) q^{54} -3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} +(-1.02708 - 1.77895i) q^{58} -1.81237 q^{59} +(10.3529 - 4.32210i) q^{60} -10.8041 q^{61} +1.77776 q^{62} -2.68848 q^{64} +4.41895 q^{65} +(0.609480 + 0.464982i) q^{66} +1.02937 q^{67} +(-0.219249 - 0.379751i) q^{68} +(-3.96027 + 1.65332i) q^{69} -4.94533 q^{71} +(-5.40231 - 1.41536i) q^{72} +(0.915262 + 1.58528i) q^{73} +(1.17306 - 2.03181i) q^{74} +(11.8911 + 9.07189i) q^{75} +(2.46302 - 4.26607i) q^{76} +(-0.817161 - 0.623424i) q^{78} -1.79912 q^{79} +(-4.77293 - 8.26696i) q^{80} +(7.84384 + 4.41296i) q^{81} +(-1.18559 + 2.05350i) q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(2.47403 + 4.28514i) q^{86} +(6.62127 - 2.76423i) q^{87} +(0.830779 - 1.43895i) q^{88} +(1.20370 - 2.08488i) q^{89} +(-1.45123 - 5.29793i) q^{90} +(2.17310 + 3.76392i) q^{92} +(-0.793387 + 6.15877i) q^{93} -5.04450 q^{94} +10.3698 q^{95} +(-1.10759 + 8.59784i) q^{96} +(-5.52210 - 9.56456i) q^{97} +(-1.88286 + 1.90393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9	$ 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9} + 7 q^{10} + 4 q^{11} + 20 q^{12} + 8 q^{13} - 19 q^{15} - 4 q^{16} - 12 q^{17} + 4 q^{18} - q^{19} - 5 q^{20} - q^{22} + 3 q^{23} - 6 q^{24} - q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} + 16 q^{30} - 6 q^{31} + 4 q^{32} - 14 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} + 2 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + 16 q^{45} + 3 q^{46} + 54 q^{47} + 5 q^{48} + 19 q^{50} - 9 q^{51} + 10 q^{52} - 21 q^{53} - q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} + 60 q^{59} + 10 q^{60} - 28 q^{61} + 12 q^{62} - 50 q^{64} + 22 q^{65} - 19 q^{66} + 4 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 36 q^{72} - 15 q^{73} - 36 q^{74} + 14 q^{75} - 5 q^{76} - 20 q^{78} + 8 q^{79} - 20 q^{80} + 23 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} - 2 q^{87} - 18 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 6 q^{93} - 6 q^{94} + 28 q^{95} - 59 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) $ 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9 + 7 * q^10 + 4 * q^11 + 20 * q^12 + 8 * q^13 - 19 * q^15 - 4 * q^16 - 12 * q^17 + 4 * q^18 - q^19 - 5 * q^20 - q^22 + 3 * q^23 - 6 * q^24 - q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 + 16 * q^30 - 6 * q^31 + 4 * q^32 - 14 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 + 2 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + 16 * q^45 + 3 * q^46 + 54 * q^47 + 5 * q^48 + 19 * q^50 - 9 * q^51 + 10 * q^52 - 21 * q^53 - q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 + 60 * q^59 + 10 * q^60 - 28 * q^61 + 12 * q^62 - 50 * q^64 + 22 * q^65 - 19 * q^66 + 4 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 36 * q^72 - 15 * q^73 - 36 * q^74 + 14 * q^75 - 5 * q^76 - 20 * q^78 + 8 * q^79 - 20 * q^80 + 23 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 - 2 * q^87 - 18 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 6 * q^93 - 6 * q^94 + 28 * q^95 - 59 * q^96 + 12 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.495868			−0.350632			−0.175316	−	0.984512i	$-0.556095\pi$
$2$	−0.495868			−0.350632			−0.175316	+	0.984512i	$0.556095\pi$
$3$	0.221298	−	1.71786i	0.127767	−	0.991804i
$3$	0.221298	−	1.71786i	0.127767	−	0.991804i
$4$	−1.75411			−0.877057
$5$	−1.84629	−	3.19787i	−0.825686	−	1.43013i	−0.901394	−	0.433000i	$-0.857455\pi$
$5$	−1.84629	−	3.19787i	−0.825686	−	1.43013i	0.0757082	−	0.997130i	$-0.475878\pi$
$6$	−0.109735	+	0.851830i	−0.0447990	+	0.347758i
$7$		0			0
$7$		0			0
$8$	1.86155			0.658156
$9$	−2.90205	−	0.760316i	−0.967351	−	0.253439i
$10$	0.915516	+	1.58572i	0.289512	+	0.501449i
$11$	0.446284	−	0.772987i	0.134560	−	0.233064i	−0.790869	−	0.611985i	$-0.790371\pi$
$11$	0.446284	−	0.772987i	0.134560	−	0.233064i	0.925429	+	0.378921i	$0.123705\pi$
$12$	−0.388182	+	3.01332i	−0.112059	+	0.869869i
$13$	−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
$16$	2.58515			0.646287
$17$	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	$0.823682\pi$
$18$	1.43904	+	0.377017i	0.339184	+	0.0888637i
$19$	−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
$23$	−1.23886	−	2.14576i	−0.258320	−	0.447423i	0.707472	−	0.706741i	$-0.249835\pi$
$23$	−1.23886	−	2.14576i	−0.258320	−	0.447423i	−0.965792	+	0.259318i	$0.916502\pi$
$24$	0.411957	−	3.19787i	0.0840903	−	0.652762i
$25$	−4.31757	+	7.47825i	−0.863514	+	1.49565i
$26$	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	0.991717	−	0.128440i	$-0.0409970\pi$
$29$	2.07128	+	3.58755i	0.384626	+	0.666192i	−0.607091	+	0.794632i	$0.707664\pi$
$30$	2.92664	−	1.22181i	0.534329	−	0.223071i
$31$	−3.58515			−0.643912			−0.321956	−	0.946755i	$-0.604340\pi$
$31$	−3.58515			−0.643912			−0.321956	+	0.946755i	$0.604340\pi$
$32$	−5.00499			−0.884765
$33$	−1.22912	−	0.937712i	−0.213962	−	0.163235i
$34$	−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	$0.293817\pi$
$38$	0.696267	−	1.20597i	0.112949	−	0.195634i
$39$	1.64794	+	1.25724i	0.263882	+	0.201319i
$40$	−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	$-0.441889\pi$
$44$	−0.782834	+	1.35591i	−0.118017	+	0.204411i
$45$	2.92664	+	10.6841i	0.436278	+	1.59270i
$46$	0.614310	+	1.06402i	0.0905751	+	0.156881i
$47$	10.1731			1.48389			0.741947	−	0.670459i	$-0.233903\pi$
$47$	10.1731			1.48389			0.741947	+	0.670459i	$0.233903\pi$
$48$	0.572088	−	4.44091i	0.0825738	−	0.640990i
$49$		0			0
$50$	2.14095	−	3.70823i	0.302776	−	0.524423i
$51$	0.399562	−	0.166808i	0.0559498	−	0.0233578i
$52$	1.04958	−	1.81793i	0.145551	−	0.252102i
$53$	−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	$-0.404339\pi$
$54$	0.966116	−	2.38862i	0.131472	−	0.325051i
$55$	−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
$59$	−1.81237			−0.235951			−0.117975	−	0.993017i	$-0.537640\pi$
$59$	−1.81237			−0.235951			−0.117975	+	0.993017i	$0.537640\pi$
$60$	10.3529	−	4.32210i	1.33655	−	0.557980i
$61$	−10.8041			−1.38332			−0.691662	−	0.722221i	$-0.743121\pi$
$61$	−10.8041			−1.38332			−0.691662	+	0.722221i	$0.743121\pi$
$62$	1.77776			0.225776
$63$		0			0
$64$	−2.68848			−0.336060
$65$	4.41895			0.548103
$66$	0.609480	+	0.464982i	0.0750219	+	0.0572353i
$67$	1.02937			0.125757			0.0628787	−	0.998021i	$-0.479972\pi$
$67$	1.02937			0.125757			0.0628787	+	0.998021i	$0.479972\pi$
$68$	−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	$0.594804\pi$
$72$	−5.40231	−	1.41536i	−0.636668	−	0.166802i
$73$	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	$0.799169\pi$
$74$	1.17306	−	2.03181i	0.136366	−	0.236193i
$75$	11.8911	+	9.07189i	1.37306	+	1.04753i
$76$	2.46302	−	4.26607i	0.282527	−	0.489352i
$77$		0			0
$78$	−0.817161	−	0.623424i	−0.0925253	−	0.0705889i
$79$	−1.79912			−0.202417			−0.101209	−	0.994865i	$-0.532271\pi$
$79$	−1.79912			−0.202417			−0.101209	+	0.994865i	$0.532271\pi$
$80$	−4.77293	−	8.26696i	−0.533630	−	0.924274i
$81$	7.84384	+	4.41296i	0.871538	+	0.490329i
$82$	−1.18559	+	2.05350i	−0.130926	+	0.226771i
$83$	−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
$87$	6.62127	−	2.76423i	0.709875	−	0.296357i
$88$	0.830779	−	1.43895i	0.0885613	−	0.153393i
$89$	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
$93$	−0.793387	+	6.15877i	−0.0822704	+	0.638634i
$94$	−5.04450			−0.520300
$95$	10.3698			1.06392
$96$	−1.10759	+	8.59784i	−0.113043	+	0.877513i
$97$	−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
$100$	7.57351	−	13.1177i	0.757351	−	1.31177i
$101$	−1.29982	+	2.25136i	−0.129337	+	0.224018i	−0.923420	−	0.383791i	$-0.874618\pi$
$101$	−1.29982	+	2.25136i	−0.129337	+	0.224018i	0.794083	+	0.607810i	$0.207952\pi$
$102$	−0.198130	+	0.0827148i	−0.0196178	+	0.00818999i
$103$	4.85578	+	8.41045i	0.478454	+	0.828706i	0.999695	−	0.0247032i	$-0.00786408\pi$
$103$	4.85578	+	8.41045i	0.478454	+	0.828706i	−0.521241	+	0.853409i	$0.674531\pi$
$104$	−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	$0.990022\pi$
$108$	3.41760	−	8.44966i	0.328859	−	0.813069i
$109$	−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	$0.865737\pi$
$110$	1.63432			0.155826
$111$	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	$-0.100602\pi$
$114$	−1.91760	−	1.46297i	−0.179600	−	0.137019i
$115$	−4.57458	+	7.92341i	−0.426582	+	0.738861i
$116$	−3.63325	−	6.29298i	−0.337339	−	0.584289i
$117$	2.52444	−	2.55270i	0.233384	−	0.235997i
$118$	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
$122$	5.35741			0.485038
$123$	−6.58489	−	5.02371i	−0.593740	−	0.452973i
$124$	6.28876			0.564747
$125$	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	$0.517938\pi$
$128$	11.3431			1.00260
$129$	−15.9493	+	6.65848i	−1.40426	+	0.586246i
$130$	−2.19122			−0.192182
$131$	−7.51444	−	13.0154i	−0.656540	−	1.13716i	−0.981505	−	0.191435i	$-0.938686\pi$
$131$	−7.51444	−	13.0154i	−0.656540	−	1.13716i	0.324965	−	0.945726i	$-0.394647\pi$
$132$	2.15601	+	1.64485i	0.187657	+	0.143166i
$133$		0			0
$134$	−0.510432			−0.0440946
$135$	19.0015	−	2.66316i	1.63539	−	0.229209i
$136$	0.232677	+	0.403009i	0.0199519	+	0.0345577i
$137$	0.244246	−	0.423047i	0.0208674	−	0.0361433i	−0.855403	−	0.517963i	$-0.826691\pi$
$137$	0.244246	−	0.423047i	0.0208674	−	0.0361433i	0.876271	+	0.481819i	$0.160024\pi$
$138$	1.96377	−	0.819831i	0.167167	−	0.0697887i
$139$	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
$142$	2.45223			0.205787
$143$	0.534073	+	0.925042i	0.0446614	+	0.0773559i
$144$	−7.50224	−	1.96553i	−0.625187	−	0.163794i
$145$	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
$149$	−10.5120	−	18.2073i	−0.861175	−	1.49160i	−0.870796	−	0.491645i	$-0.836396\pi$
$149$	−10.5120	−	18.2073i	−0.861175	−	1.49160i	0.00962096	−	0.999954i	$-0.496938\pi$
$150$	−5.89641	−	4.49846i	−0.481440	−	0.367298i
$151$	−0.749191	+	1.29764i	−0.0609683	+	0.105600i	−0.894898	−	0.446270i	$-0.852752\pi$
$151$	−0.749191	+	1.29764i	−0.0609683	+	0.105600i	0.833930	+	0.551870i	$0.186086\pi$
$152$	−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
$156$	−2.89068	−	2.20534i	−0.231439	−	0.176568i
$157$	16.6796			1.33118			0.665590	−	0.746317i	$-0.268180\pi$
$157$	16.6796			1.33118			0.665590	+	0.746317i	$0.268180\pi$
$158$	0.892128			0.0709739
$159$	−15.8066	+	6.59890i	−1.25355	+	0.523327i
$160$	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	$0.250954\pi$
$164$	−4.19396	+	7.26416i	−0.327494	+	0.567236i
$165$	−0.729372	+	5.66184i	−0.0567815	+	0.440774i
$166$	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
$170$	−0.228863	+	0.396403i	−0.0175530	+	0.0304027i
$171$	5.92400	−	5.99031i	0.453020	−	0.458091i
$172$	8.75178	+	15.1585i	0.667317	+	1.15583i
$173$	3.88685			0.295511			0.147756	−	0.989024i	$-0.452795\pi$
$173$	3.88685			0.295511			0.147756	+	0.989024i	$0.452795\pi$
$174$	−3.28328	+	1.37070i	−0.248905	+	0.103912i
$175$		0			0
$176$	1.15371	−	1.99829i	0.0869642	−	0.150626i
$177$	−0.401075	+	3.11339i	−0.0301466	+	0.234017i
$178$	−0.596879	+	1.03382i	−0.0447380	+	0.0774884i
$179$	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	$0.744944\pi$
$180$	−5.13366	−	18.7412i	−0.382641	−	1.39689i
$181$	−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
$185$	17.4709			1.28449
$186$	0.393415	−	3.05394i	0.0288466	−	0.223925i
$187$	0.223127			0.0163167
$188$	−17.8447			−1.30146
$189$		0			0
$190$	−5.14204			−0.373043
$191$	−23.8459			−1.72543			−0.862715	−	0.505690i	$-0.831238\pi$
$191$	−23.8459			−1.72543			−0.862715	+	0.505690i	$0.831238\pi$
$192$	−0.594956	+	4.61842i	−0.0429373	+	0.333306i
$193$	5.93456			0.427179			0.213589	−	0.976924i	$-0.431485\pi$
$193$	5.93456			0.427179			0.213589	+	0.976924i	$0.431485\pi$
$194$	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	$0.685766\pi$
$198$	0.933648	−	0.944100i	0.0663515	−	0.0670942i
$199$	−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	$-0.351755\pi$
$200$	−8.03736	+	13.9211i	−0.568327	+	0.984371i
$201$	0.227798	−	1.76831i	0.0160676	−	0.124727i
$202$	0.644540	−	1.11638i	0.0453497	−	0.0785480i
$203$		0			0
$204$	−0.700877	+	0.292600i	−0.0490712	+	0.0204861i
$205$	−17.6574			−1.23325
$206$	−2.40783	−	4.17048i	−0.167761	−	0.290571i
$207$	1.96377	+	7.16905i	0.136492	+	0.498283i
$208$	−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	−0.838232	−	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
$213$	−1.09439	+	8.49536i	−0.0749866	+	0.582093i
$214$	2.70261	−	4.68105i	0.184746	−	0.319990i
$215$	−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
$219$	2.92583	−	1.22147i	0.197709	−	0.0825392i
$220$	5.78135			0.389779
$221$	−0.299157			−0.0201235
$222$	−3.23075	−	2.46479i	−0.216834	−	0.165426i
$223$	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
$226$	−3.92389	+	6.79638i	−0.261014	+	0.452089i
$227$	−8.03818	+	13.9225i	−0.533513	+	0.924072i	0.465721	+	0.884932i	$0.345795\pi$
$227$	−8.03818	+	13.9225i	−0.533513	+	0.924072i	−0.999234	+	0.0391399i	$0.987538\pi$
$228$	−6.78343	−	5.17518i	−0.449244	−	0.342735i
$229$	−4.98420	−	8.63289i	−0.329365	−	0.570477i	0.653021	−	0.757340i	$-0.273501\pi$
$229$	−4.98420	−	8.63289i	−0.329365	−	0.570477i	−0.982386	+	0.186863i	$0.940168\pi$
$230$	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	$-0.0155959\pi$
$234$	−1.25179	+	1.26580i	−0.0818320	+	0.0827480i
$235$	−18.7824	−	32.5321i	−1.22523	−	2.12216i
$236$	3.17911			0.206942
$237$	−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	$0.914319\pi$
$240$	−15.2577	+	6.36974i	−0.984879	+	0.411165i
$241$	8.36004	−	14.4800i	0.538517	−	0.932739i	−0.460467	−	0.887677i	$-0.652318\pi$
$241$	8.36004	−	14.4800i	0.538517	−	0.932739i	0.998984	−	0.0450623i	$-0.0143486\pi$
$242$	−2.52975	−	4.38166i	−0.162619	−	0.281664i
$243$	9.31665	−	12.4980i	0.597664	−	0.801747i
$244$	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
$248$	−6.67392			−0.423794
$249$	−19.6967	+	8.22294i	−1.24823	+	0.521108i
$250$	−6.65606			−0.420966
$251$	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
$254$	0.629487			0.0394975
$255$	−1.27114	−	0.969769i	−0.0796017	−	0.0607293i
$256$	−0.247722			−0.0154826
$257$	−8.55986	−	14.8261i	−0.533950	−	0.924828i	−0.999213	−	0.0396557i	$-0.987374\pi$
$257$	−8.55986	−	14.8261i	−0.533950	−	0.924828i	0.465264	−	0.885172i	$-0.345959\pi$
$258$	7.90875	−	3.30173i	0.492377	−	0.205557i
$259$		0			0
$260$	−7.75135			−0.480718
$261$	−3.28328	−	11.9861i	−0.203230	−	0.741921i
$262$	3.72617	+	6.45392i	0.230204	+	0.398725i
$263$	−10.2763	+	17.7991i	−0.633666	+	1.09754i	0.353130	+	0.935574i	$0.385117\pi$
$263$	−10.2763	+	17.7991i	−0.633666	+	1.09754i	−0.986796	+	0.161967i	$0.948216\pi$
$264$	−2.28806	−	1.74559i	−0.140820	−	0.107434i
$265$	−18.2585	+	31.6246i	−1.12161	+	1.94269i
$266$		0			0
$267$	−3.31514	−	2.52917i	−0.202883	−	0.154783i
$268$	−1.80563			−0.110297
$269$	−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	$-0.373492\pi$
$270$	−9.42223	+	1.32058i	−0.573419	+	0.0803679i
$271$	−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
$275$	3.85373	+	6.67485i	0.232388	+	0.402509i
$276$	6.94677	−	2.90012i	0.418146	−	0.174567i
$277$	12.4407	−	21.5479i	0.747487	−	1.29469i	−0.201536	−	0.979481i	$-0.564593\pi$
$277$	12.4407	−	21.5479i	0.747487	−	1.29469i	0.949024	−	0.315205i	$-0.102073\pi$
$278$	−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	0.586771	−	0.809753i	$-0.300399\pi$
$281$	−6.83733	−	11.8426i	−0.407881	−	0.706470i	−0.994652	+	0.103282i	$0.967065\pi$
$282$	−1.11634	+	8.66572i	−0.0664770	+	0.516036i
$283$	−6.32179			−0.375791			−0.187896	−	0.982189i	$-0.560167\pi$
$283$	−6.32179			−0.375791			−0.187896	+	0.982189i	$0.560167\pi$
$284$	8.67468			0.514747
$285$	2.29481	−	17.8138i	0.135933	−	1.05520i
$286$	−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
$290$	−3.79257	+	6.56893i	−0.222708	+	0.385741i
$291$	−17.6526	+	7.36955i	−1.03481	+	0.432011i
$292$	−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
$296$	−4.40382	+	7.62764i	−0.255967	+	0.443348i
$297$	2.85401	+	3.65581i	0.165606	+	0.212132i
$298$	5.21256	+	9.02841i	0.301955	+	0.523002i
$299$	2.96511			0.171477
$300$	−20.8583	−	15.9131i	−1.20426	−	0.918745i
$301$		0			0
$302$	0.371500	−	0.643457i	0.0213774	−	0.0370268i
$303$	3.57986	+	2.73113i	0.205657	+	0.156899i
$304$	−3.62990	+	6.28717i	−0.208189	+	0.360594i
$305$	19.9475	+	34.5501i	1.14219	+	1.97833i
$306$	0.0982463	+	0.358663i	0.00561637	+	0.0205034i
$307$	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
$311$	15.1003			0.856258			0.428129	−	0.903718i	$-0.359173\pi$
$311$	15.1003			0.856258			0.428129	+	0.903718i	$0.359173\pi$
$312$	3.06772	+	2.34041i	0.173675	+	0.132499i
$313$	25.4785			1.44013			0.720064	−	0.693908i	$-0.244112\pi$
$313$	25.4785			1.44013			0.720064	+	0.693908i	$0.244112\pi$
$314$	−8.27090			−0.466754
$315$		0			0
$316$	3.15587			0.177531
$317$	32.5209			1.82656			0.913278	−	0.407337i	$-0.133543\pi$
$317$	32.5209			1.82656			0.913278	+	0.407337i	$0.133543\pi$
$318$	7.83799	−	3.27219i	0.439533	−	0.183495i
$319$	3.69751			0.207021
$320$	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
$324$	−13.7590	−	7.74084i	−0.764388	−	0.430046i
$325$	−5.16688	−	8.94931i	−0.286607	−	0.496418i
$326$	1.65687	−	2.86978i	0.0917654	−	0.158942i
$327$	−3.39159	+	1.41591i	−0.187556	+	0.0783003i
$328$	4.45083	−	7.70906i	0.245756	−	0.425661i
$329$		0			0
$330$	0.361672	−	2.80753i	0.0199094	−	0.154549i
$331$	18.0948			0.994582			0.497291	−	0.867584i	$-0.334328\pi$
$331$	18.0948			0.994582			0.497291	+	0.867584i	$0.334328\pi$
$332$	10.8081	+	18.7201i	0.593170	+	1.02740i
$333$	9.98070	−	10.0924i	0.546939	−	0.553062i
$334$	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	0.293168	+	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
$339$	−21.7938	−	16.6268i	−1.18368	−	0.903045i
$340$	−0.809596	+	1.40226i	−0.0439065	+	0.0760483i
$341$	−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
$345$	12.5989	+	9.61190i	0.678303	+	0.517488i
$346$	−1.92736			−0.103616
$347$	10.7489			0.577030			0.288515	−	0.957475i	$-0.406838\pi$
$347$	10.7489			0.577030			0.288515	+	0.957475i	$0.406838\pi$
$348$	−11.6145	+	4.84878i	−0.622601	+	0.259922i
$349$	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
$352$	−2.23365	+	3.86879i	−0.119054	+	0.206207i
$353$	8.40960	−	14.5658i	0.447598	−	0.775262i	−0.550631	−	0.834748i	$-0.685613\pi$
$353$	8.40960	−	14.5658i	0.447598	−	0.775262i	0.998229	+	0.0594866i	$0.0189463\pi$
$354$	0.198880	−	1.54383i	0.0105704	−	0.0820538i
$355$	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
$359$	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	$-0.0493131\pi$
$360$	5.44808	+	19.8890i	0.287139	+	1.04824i
$361$	5.55680	+	9.62466i	0.292463	+	0.506561i
$362$	5.58177			0.293371
$363$	16.3085	−	6.80845i	0.855976	−	0.357351i
$364$		0			0
$365$	3.37968	−	5.85377i	0.176900	−	0.306401i
$366$	1.18559	−	9.20326i	0.0619716	−	0.481062i
$367$	−0.344992	+	0.597544i	−0.0180084	+	0.0311915i	−0.874889	−	0.484323i	$-0.839066\pi$
$367$	−0.344992	+	0.597544i	−0.0180084	+	0.0311915i	0.856881	+	0.515515i	$0.172399\pi$
$368$	−3.20263	−	5.54712i	−0.166949	−	0.289164i
$369$	−10.0872	+	10.2002i	−0.525121	+	0.530999i
$370$	−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	0.910585	−	0.413321i	$-0.135631\pi$
$373$	1.88006	+	3.25636i	0.0973457	+	0.168608i	−0.813239	+	0.581929i	$0.802298\pi$
$374$	−0.110642			−0.00572114
$375$	2.97050	−	23.0589i	0.153396	−	1.19075i
$376$	18.9376			0.976634
$377$	−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	$0.180017\pi$
$380$	−18.1898			−0.933116
$381$	−0.280930	+	2.18075i	−0.0143925	+	0.111723i
$382$	11.8244			0.604991
$383$	−0.536335	−	0.928960i	−0.0274055	−	0.0474676i	0.851997	−	0.523546i	$-0.175391\pi$
$383$	−0.536335	−	0.928960i	−0.0274055	−	0.0474676i	−0.879403	+	0.476078i	$0.842058\pi$
$384$	2.51021	−	19.4858i	0.128099	−	0.994381i
$385$		0			0
$386$	−2.94276			−0.149782
$387$	7.90875	+	28.8721i	0.402024	+	1.46765i
$388$	9.68640	+	16.7773i	0.491752	+	0.851740i
$389$	11.8718	−	20.5626i	0.601925	−	1.04256i	−0.390605	−	0.920559i	$-0.627734\pi$
$389$	11.8718	−	20.5626i	0.601925	−	1.04256i	0.992529	−	0.122006i	$-0.0389326\pi$
$390$	−0.484912	+	3.76419i	−0.0245545	+	0.190607i
$391$	0.309693	−	0.536405i	0.0156619	−	0.0271271i
$392$		0			0
$393$	−24.0215	+	10.0284i	−1.21172	+	0.505868i
$394$	7.67019			0.386419
$395$	3.32170	+	5.75336i	0.167133	+	0.289483i
$396$	3.30274	−	3.33972i	0.165969	−	0.167827i
$397$	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
$401$	−12.2628	−	21.2398i	−0.612374	−	1.06066i	−0.990839	−	0.135048i	$-0.956881\pi$
$401$	−12.2628	−	21.2398i	−0.612374	−	1.06066i	0.378465	−	0.925616i	$-0.376452\pi$
$402$	−0.112958	+	0.876848i	−0.00563381	+	0.0437332i
$403$	2.14519	−	3.71558i	0.106860	−	0.185086i
$404$	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
$408$	0.743802	−	0.310521i	0.0368237	−	0.0153731i
$409$	−26.7897			−1.32467			−0.662333	−	0.749210i	$-0.730433\pi$
$409$	−26.7897			−1.32467			−0.662333	+	0.749210i	$0.730433\pi$
$410$	8.75574			0.432415
$411$	−0.672682	−	0.513199i	−0.0331810	−	0.0253143i
$412$	−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
$416$	2.99476	−	5.18708i	0.146830	−	0.254317i
$417$	−13.5912	−	10.3689i	−0.665564	−	0.507769i
$418$	−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	$0.951534\pi$
$422$	−0.382760	+	0.662959i	−0.0186325	+	0.0322724i
$423$	−29.5228	−	7.73475i	−1.43545	−	0.376076i
$424$	−9.20469	−	15.9430i	−0.447019	−	0.774260i
$425$	−2.15864			−0.104709
$426$	0.542675	−	4.21258i	0.0262927	−	0.204100i
$427$		0			0
$428$	9.56037	−	16.5590i	0.462118	−	0.800412i
$429$	1.70728	−	0.712750i	0.0824281	−	0.0344119i
$430$	9.13554	−	15.8232i	0.440555	−	0.763064i
$431$	−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	$0.958453\pi$
$432$	−5.03673	+	12.4528i	−0.242330	+	0.599135i
$433$	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
$437$	6.95811			0.332851
$438$	−1.45083	+	0.605687i	−0.0693231	+	0.0289409i
$439$	15.5447			0.741909			0.370954	−	0.928651i	$-0.379031\pi$
$439$	15.5447			0.741909			0.370954	+	0.928651i	$0.379031\pi$
$440$	−6.13543			−0.292495
$441$		0			0
$442$	0.148343			0.00705594
$443$	1.79005			0.0850480			0.0425240	−	0.999095i	$-0.486460\pi$
$443$	1.79005			0.0850480			0.0425240	+	0.999095i	$0.486460\pi$
$444$	−11.4287	−	8.71910i	−0.542381	−	0.413790i
$445$	−8.88955			−0.421405
$446$	−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	$0.396275\pi$
$450$	−9.03257	+	9.13368i	−0.425799	+	0.430566i
$451$	−2.13407	−	3.69631i	−0.100489	−	0.174053i
$452$	−13.8806	+	24.0419i	−0.652890	+	1.13084i
$453$	2.06336	+	1.57417i	0.0969450	+	0.0739608i
$454$	3.98588	−	6.90375i	0.187067	−	0.324009i
$455$		0			0
$456$	7.19889	+	5.49214i	0.337119	+	0.257193i
$457$	2.56917			0.120181			0.0600905	−	0.998193i	$-0.480861\pi$
$457$	2.56917			0.120181			0.0600905	+	0.998193i	$0.480861\pi$
$458$	2.47151	+	4.28078i	0.115486	+	0.200028i
$459$	−1.28638	+	0.180293i	−0.0600429	+	0.00841535i
$460$	8.02434	−	13.8986i	0.374137	−	0.648024i
$461$	−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
$465$	21.1597	−	8.83372i	0.981259	−	0.409654i
$466$	−4.10105	+	7.10323i	−0.189978	+	0.329051i
$467$	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
$471$	3.69117	−	28.6532i	0.170080	−	1.32027i
$472$	−3.37381			−0.155292
$473$	−8.90655			−0.409524
$474$	0.197426	−	1.53255i	0.00906809	−	0.0703922i
$475$	−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
$479$	−8.88370	+	15.3870i	−0.405907	+	0.703051i	−0.994427	−	0.105432i	$-0.966378\pi$
$479$	−8.88370	+	15.3870i	−0.405907	+	0.703051i	0.588520	+	0.808483i	$0.299711\pi$
$480$	29.5397	−	12.3322i	1.34830	−	0.562884i
$481$	−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
$485$	−20.3908	+	35.3179i	−0.925898	+	1.60370i
$486$	−4.61983	+	6.19736i	−0.209560	+	0.281118i
$487$	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	$0.710165\pi$
$488$	−20.1123			−0.910443
$489$	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	$0.212945\pi$
$492$	11.5507	+	8.81217i	0.520744	+	0.397283i
$493$	−0.517784	+	0.896827i	−0.0233198	+	0.0403911i
$494$	0.833230	+	1.44320i	0.0374888	+	0.0649325i
$495$	9.56482	+	2.50591i	0.429907	+	0.112632i
$496$	−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	0.713902	−	0.700246i	$-0.246926\pi$
$499$	−5.57296	−	9.65264i	−0.249480	−	0.432112i	−0.963382	+	0.268134i	$0.913593\pi$
$500$	−23.5456			−1.05299
$501$	24.2789	+	18.5227i	1.08470	+	0.827533i
$502$	−4.23025			−0.188805
$503$	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
$506$	1.09663			0.0487511
$507$	18.4896	−	7.71899i	0.821151	−	0.342812i
$508$	2.22678			0.0987976
$509$	15.5411	+	26.9180i	0.688848	+	1.19312i	0.972211	+	0.234107i	$0.0752167\pi$
$509$	15.5411	+	26.9180i	0.688848	+	1.19312i	−0.283362	+	0.959013i	$0.591450\pi$
$510$	0.630316	+	0.480878i	0.0279109	+	0.0212936i
$511$		0			0
$512$	−22.5634			−0.997169
$513$	−8.97952	−	11.5022i	−0.396456	−	0.507835i
$514$	4.24456	+	7.35180i	0.187220	+	0.324274i
$515$	17.9303	−	31.0563i	0.790105	−	1.36850i
$516$	27.9769	−	11.6797i	1.23161	−	0.514172i
$517$	4.54008	−	7.86365i	0.199672	−	0.345843i
$518$		0			0
$519$	0.860152	−	6.67704i	0.0377565	−	0.293089i
$520$	8.22608			0.360737
$521$	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	$0.800085\pi$
$522$	1.62807	+	5.94353i	0.0712588	+	0.260141i
$523$	−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
$527$	−0.448113	−	0.776154i	−0.0195201	−	0.0338098i
$528$	−3.17745	−	2.42412i	−0.138281	−	0.105496i
$529$	8.43046	−	14.6020i	0.366542	−	0.634869i
$530$	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
$534$	1.64387	+	1.25413i	0.0711373	+	0.0542717i
$535$	40.2510			1.74020
$536$	1.91622			0.0827680
$537$	11.7242	−	4.89459i	0.505937	−	0.211217i
$538$	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	$-0.00675826\pi$
$542$	2.63830	−	4.56966i	0.113325	−	0.196284i
$543$	−2.49105	+	19.3371i	−0.106901	+	0.829836i
$544$	−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	$0.918419\pi$
$548$	−0.428436	+	0.742073i	−0.0183019	+	0.0316998i
$549$	31.3541	+	8.21454i	1.33816	+	0.350588i
$550$	−1.91094	−	3.30985i	−0.0814828	−	0.141132i
$551$	−11.6334			−0.495600
$552$	−7.37223	+	3.07774i	−0.313783	+	0.130997i
$553$		0			0
$554$	−6.16893	+	10.6849i	−0.262093	+	0.453958i
$555$	3.86628	−	30.0125i	0.164114	−	1.27396i
$556$	−8.65633	+	14.9932i	−0.367110	+	0.635853i
$557$	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	$0.778597\pi$
$558$	−5.15916	−	1.35166i	−0.218405	−	0.0572204i
$559$	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
$563$	−45.2127			−1.90549			−0.952744	−	0.303774i	$-0.901753\pi$
$563$	−45.2127			−1.90549			−0.952744	+	0.303774i	$0.901753\pi$
$564$	−3.94900	+	30.6547i	−0.166283	+	1.29079i
$565$	−58.4401			−2.45859
$566$	3.13477			0.131764
$567$		0			0
$568$	−9.20596			−0.386274
$569$	22.4299			0.940309			0.470155	−	0.882584i	$-0.344198\pi$
$569$	22.4299			0.940309			0.470155	+	0.882584i	$0.344198\pi$
$570$	−1.13792	+	8.83329i	−0.0476624	+	0.369986i
$571$	−21.8269			−0.913426			−0.456713	−	0.889614i	$-0.650973\pi$
$571$	−21.8269			−0.913426			−0.456713	+	0.889614i	$0.650973\pi$
$572$	−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
$576$	7.80212	+	2.04410i	0.325088	+	0.0851707i
$577$	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	$0.599481\pi$
$578$	−4.19939	+	7.27355i	−0.174671	+	0.302540i
$579$	1.31331	−	10.1947i	0.0545791	−	0.423678i
$580$	−13.4161	+	23.2373i	−0.557072	+	0.964878i
$581$		0			0
$582$	8.75335	−	3.65433i	0.362838	−	0.151477i
$583$	−8.82687			−0.365571
$584$	1.70380	+	2.95107i	0.0705039	+	0.122116i
$585$	−12.8240	−	3.35980i	−0.530209	−	0.138911i
$586$	−0.652105	+	1.12948i	−0.0269382	+	0.0466584i
$587$	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
$591$	−3.42309	+	26.5721i	−0.140807	+	1.09303i
$592$	−6.11563	+	10.5926i	−0.251351	+	0.435352i
$593$	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
$597$	−24.7687	+	10.3404i	−1.01372	+	0.423204i
$598$	−1.47030			−0.0601252
$599$	−46.9989			−1.92032			−0.960161	−	0.279447i	$-0.909849\pi$
$599$	−46.9989			−1.92032			−0.960161	+	0.279447i	$0.909849\pi$
$600$	22.1358	+	16.8877i	0.903690	+	0.689439i
$601$	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
$604$	1.31417	−	2.27620i	0.0534727	−	0.0926174i
$605$	18.8383	−	32.6289i	0.765885	−	1.32655i
$606$	−1.77514	−	1.35428i	−0.0721100	−	0.0550138i
$607$	−14.3266	−	24.8144i	−0.581500	−	1.00719i	−0.995302	−	0.0968200i	$-0.969133\pi$
$607$	−14.3266	−	24.8144i	−0.581500	−	1.00719i	0.413802	−	0.910367i	$-0.364200\pi$
$608$	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
$612$	0.347543	+	1.26876i	0.0140486	+	0.0512865i
$613$	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	$0.631414\pi$
$614$	−1.38593			−0.0559316
$615$	−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	$0.140187\pi$
$618$	−7.69712	+	3.21338i	−0.309624	+	0.129261i
$619$	11.3565	−	19.6700i	0.456456	−	0.790605i	−0.542315	−	0.840175i	$-0.682452\pi$
$619$	11.3565	−	19.6700i	0.456456	−	0.790605i	0.998771	+	0.0495708i	$0.0157853\pi$
$620$	−11.6109	−	20.1106i	−0.466304	−	0.807662i
$621$	12.7500	−	1.78698i	0.511639	−	0.0717090i
$622$	−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
$626$	−12.6340			−0.504955
$627$	4.00640	−	1.67258i	0.160000	−	0.0667965i
$628$	−29.2580			−1.16752
$629$	−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	$0.779314\pi$
$632$	−3.34915			−0.133222
$633$	−2.12590	−	1.62188i	−0.0844968	−	0.0644639i
$634$	−16.1261			−0.640449
$635$	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
$639$	14.3516	+	3.76002i	0.567741	+	0.148744i
$640$	−20.9427	−	36.2737i	−0.827831	−	1.43385i
$641$	14.2363	−	24.6580i	0.562301	−	0.973933i	−0.434995	−	0.900433i	$-0.643250\pi$
$641$	14.2363	−	24.6580i	0.562301	−	0.973933i	0.997295	−	0.0735002i	$-0.0234169\pi$
$642$	−7.44329	−	5.67860i	−0.293763	−	0.224116i
$643$	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
$646$	0.348110			0.0136962
$647$	−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	$0.854474\pi$
$648$	14.6017	+	8.21493i	0.573608	+	0.322713i
$649$	−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
$653$	9.17255	+	15.8873i	0.358950	+	0.621719i	0.987786	−	0.155819i	$-0.0498017\pi$
$653$	9.17255	+	15.8873i	0.358950	+	0.621719i	−0.628836	+	0.777538i	$0.716468\pi$
$654$	1.68178	−	0.702107i	0.0657629	−	0.0274546i
$655$	−27.7477	+	48.0604i	−1.08419	+	1.87787i
$656$	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	−0.998764	−	0.0497098i	$-0.984170\pi$
$659$	−13.9248	−	24.1184i	−0.542432	−	0.939519i	0.456332	−	0.889810i	$-0.349163\pi$
$660$	1.27940	−	9.93152i	0.0498007	−	0.386584i
$661$	−39.0141			−1.51747			−0.758737	−	0.651397i	$-0.774183\pi$
$661$	−39.0141			−1.51747			−0.758737	+	0.651397i	$0.774183\pi$
$662$	−8.97265			−0.348732
$663$	−0.0662030	+	0.513909i	−0.00257111	+	0.0199586i
$664$	−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
$668$	15.4634	−	26.7834i	0.598296	−	1.03628i
$669$	8.70051	−	3.63227i	0.336381	−	0.140432i
$670$	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	$0.435576\pi$
$674$	6.20264	−	10.7433i	0.238917	−	0.413816i
$675$	−27.6111	−	35.3681i	−1.06275	−	1.36132i
$676$	−10.1457	−	17.5729i	−0.390219	−	0.675879i
$677$	23.3915			0.899010			0.449505	−	0.893278i	$-0.351600\pi$
$677$	23.3915			0.899010			0.449505	+	0.893278i	$0.351600\pi$
$678$	10.8069	+	8.24471i	0.415035	+	0.316636i
$679$		0			0
$680$	0.859180	−	1.48814i	0.0329480	−	0.0570677i
$681$	22.1381	+	16.8895i	0.848333	+	0.647206i
$682$	0.793387	−	1.37419i	0.0303803	−	0.0526203i
$683$	−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	$-0.363694\pi$
$684$	−10.3914	+	10.5077i	−0.397324	+	0.401772i
$685$	−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
$689$	11.8346			0.450863
$690$	−6.24741	−	4.76624i	−0.237835	−	0.181448i
$691$	4.11330			0.156477			0.0782387	−	0.996935i	$-0.475070\pi$
$691$	4.11330			0.156477			0.0782387	+	0.996935i	$0.475070\pi$
$692$	−6.81797			−0.259180
$693$		0			0
$694$	−5.33003			−0.202325
$695$	−36.4448			−1.38243
$696$	12.3258	−	5.14575i	0.467208	−	0.195049i
$697$	1.19538			0.0452784
$698$	−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	$0.314200\pi$
$702$	1.89745	+	2.43051i	0.0716145	+	0.0917338i
$703$	−6.64347	−	11.5068i	−0.250563	−	0.433988i
$704$	−1.19983	+	2.07816i	−0.0452202	+	0.0783236i
$705$	−60.0420	+	25.0662i	−2.26131	+	0.944047i
$706$	−4.17005	+	7.22274i	−0.156942	+	0.271831i
$707$		0			0
$708$	0.703531	−	5.46125i	0.0264403	−	0.205246i
$709$	−42.4617			−1.59468			−0.797342	−	0.603528i	$-0.793761\pi$
$709$	−42.4617			−1.59468			−0.797342	+	0.603528i	$0.793761\pi$
$710$	−4.52753	−	7.84192i	−0.169915	−	0.294302i
$711$	5.22115	+	1.36790i	0.195809	+	0.0513004i
$712$	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
$716$	−6.43336	−	11.1429i	−0.240426	−	0.416430i
$717$	30.3282	+	23.1378i	1.13263	+	0.864097i
$718$	−5.89692	+	10.2138i	−0.220071	+	0.381175i
$719$	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
$723$	−23.0245	−	17.5657i	−0.856290	−	0.653277i
$724$	19.7453			0.733828
$725$	−35.7715			−1.32852
$726$	−8.08689	+	3.37609i	−0.300132	+	0.125299i
$727$	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
$730$	−1.67588	+	2.90270i	−0.0620269	+	0.107434i
$731$	1.24724	−	2.16028i	0.0461307	−	0.0799007i
$732$	4.19396	−	32.5562i	0.155013	−	1.20331i
$733$	−12.5264	−	21.6964i	−0.462674	−	0.801375i	0.536419	−	0.843952i	$-0.319777\pi$
$733$	−12.5264	−	21.6964i	−0.462674	−	0.801375i	−0.999093	+	0.0425768i	$0.986443\pi$
$734$	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
$738$	5.00194	−	5.05793i	0.184124	−	0.186185i
$739$	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	$0.664384\pi$
$740$	−30.6460			−1.12657
$741$	−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	$0.249410\pi$
$744$	−1.47693	+	11.4648i	−0.0541467	+	0.420321i
$745$	−38.8163	+	67.2318i	−1.42212	+	2.46318i
$746$	−0.932261	−	1.61472i	−0.0341325	−	0.0591192i
$747$	9.76698	+	35.6558i	0.357355	+	1.30458i
$748$	−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	0.737795	+	0.675025i	$0.235867\pi$
$751$	26.1297	+	45.2580i	0.953486	+	1.65149i	0.215692	+	0.976461i	$0.430799\pi$
$752$	26.2989			0.959021
$753$	1.88789	−	14.6550i	0.0687986	−	0.534058i
$754$	2.45824			0.0895237
$755$	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	$0.788725\pi$
$758$	−16.3009			−0.592077
$759$	−0.489408	+	3.79909i	−0.0177644	+	0.137898i
$760$	19.3038			0.700223
$761$	−8.62550	−	14.9398i	−0.312674	−	0.541568i	0.666266	−	0.745714i	$-0.267891\pi$
$761$	−8.62550	−	14.9398i	−0.312674	−	0.541568i	−0.978940	+	0.204146i	$0.934558\pi$
$762$	0.139304	−	1.08137i	0.00504646	−	0.0391738i
$763$		0			0
$764$	41.8285			1.51330
$765$	−1.94722	+	1.96902i	−0.0704020	+	0.0711901i
$766$	0.265952	+	0.460642i	0.00960922	+	0.0166437i
$767$	1.08444	−	1.87831i	0.0391570	−	0.0678218i
$768$	−0.0548204	+	0.425550i	−0.00197816	+	0.0153557i
$769$	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
$772$	−10.4099			−0.374660
$773$	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	$0.757354\pi$
$774$	−3.92170	−	14.3168i	−0.140963	−	0.514605i
$775$	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
$779$	6.71439	+	11.6297i	0.240568	+	0.416676i
$780$	−1.71536	+	13.3157i	−0.0614197	+	0.476778i
$781$	−2.20702	+	3.82268i	−0.0789735	+	0.136786i
$782$	−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
$786$	11.9115	−	4.97279i	0.424869	−	0.177373i
$787$	28.1301			1.00273			0.501364	−	0.865236i	$-0.332832\pi$
$787$	28.1301			1.00273			0.501364	+	0.865236i	$0.332832\pi$
$788$	27.1330			0.966573
$789$	28.3022	+	21.5922i	1.00758	+	0.768701i
$790$	−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
$794$	−0.00795814	+	0.0137839i	−0.000282424	+	0.000489172i
$795$	50.2860	+	38.3639i	1.78346	+	1.36063i
$796$	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
$800$	21.6094	−	37.4285i	0.764007	−	1.32330i
$801$	−5.07838	+	5.13523i	−0.179436	+	0.181444i
$802$	6.08073	+	10.5321i	0.214718	+	0.371902i
$803$	1.63387			0.0576580
$804$	−0.399583	+	3.10181i	−0.0140922	+	0.109393i
$805$		0			0
$806$	−1.06373	+	1.84244i	−0.0374684	+	0.0648972i
$807$	−31.7199	+	13.2423i	−1.11659	+	0.466153i
$808$	−2.41968	+	4.19100i	−0.0851240	+	0.147439i
$809$	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	$0.644037\pi$
$810$	0.183441	+	16.4783i	0.00644544	+	0.578988i
$811$	−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
$815$	24.6764			0.864375
$816$	1.03293	−	0.431223i	0.0361596	−	0.0150958i
$817$	28.0226			0.980385
$818$	13.2842			0.464470
$819$		0			0
$820$	30.9731			1.08163
$821$	−16.3935			−0.572139			−0.286069	−	0.958209i	$-0.592349\pi$
$821$	−16.3935			−0.572139			−0.286069	+	0.958209i	$0.592349\pi$
$822$	0.333562	+	0.254479i	0.0116343	+	0.00887598i
$823$	−26.3780			−0.919478			−0.459739	−	0.888054i	$-0.652057\pi$
$823$	−26.3780			−0.919478			−0.459739	+	0.888054i	$0.652057\pi$
$824$	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	$0.279562\pi$
$828$	−3.44468	−	12.5753i	−0.119711	−	0.437023i
$829$	−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	$0.972097\pi$
$830$	11.2820	−	19.5410i	0.391604	−	0.678279i
$831$	−34.2630	−	26.1398i	−1.18857	−	0.906779i
$832$	1.60867	−	2.78629i	0.0557705	−	0.0965974i
$833$		0			0
$834$	6.73944	+	5.14162i	0.233368	+	0.178040i
$835$	65.1038			2.25301
$836$	−2.19841	−	3.80776i	−0.0760337	−	0.131694i
$837$	6.98506	−	17.2698i	0.241439	−	0.596933i
$838$	−5.21962	+	9.04065i	−0.180309	+	0.312304i
$839$	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
$843$	−21.8570	+	9.12480i	−0.752794	+	0.314275i
$844$	−1.35400	+	2.34519i	−0.0466065	+	0.0807249i
$845$	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
$849$	−1.39900	+	10.8599i	−0.0480135	+	0.372711i
$850$	1.07040			0.0367144
$851$	11.7230			0.401858
$852$	1.91969	−	14.9018i	0.0657675	−	0.510529i
$853$	−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
$856$	−10.1459	+	17.5732i	−0.346780	+	0.600640i
$857$	−12.6934	+	21.9856i	−0.433598	+	0.751015i	−0.997180	−	0.0750458i	$-0.976090\pi$
$857$	−12.6934	+	21.9856i	−0.433598	+	0.751015i	0.563582	+	0.826060i	$0.309423\pi$
$858$	−0.846585	+	0.353430i	−0.0289019	+	0.0120659i
$859$	−2.97891	−	5.15963i	−0.101639	−	0.176044i	0.810721	−	0.585433i	$-0.199075\pi$
$859$	−2.97891	−	5.15963i	−0.101639	−	0.176044i	−0.912360	+	0.409388i	$0.865742\pi$
$860$	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	$0.0766715\pi$
$864$	9.75138	−	24.1093i	0.331749	−	0.820214i
$865$	−7.17624	−	12.4296i	−0.244000	−	0.422620i
$866$	−8.11528			−0.275768
$867$	−23.3239	−	17.7942i	−0.792122	−	0.604322i
$868$		0			0
$869$	−0.802920	+	1.39070i	−0.0272372	+	0.0471762i
$870$	10.4452	+	7.96879i	0.354125	+	0.270167i
$871$	−0.615929	+	1.06682i	−0.0208700	+	0.0361478i
$872$	−1.97503	−	3.42086i	−0.0668830	−	0.115845i
$873$	8.75335	+	31.9554i	0.296256	+	1.08153i
$874$	−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	−0.993516	−	0.113695i	$-0.963731\pi$
$877$	−17.6270	−	30.5308i	−0.595220	−	1.03095i	0.398295	−	0.917257i	$-0.369602\pi$
$878$	−7.70813			−0.260137
$879$	−3.62188	−	2.76318i	−0.122163	−	0.0931998i
$880$	−8.52033			−0.287220
$881$	−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	$0.446137\pi$
$884$	0.524756			0.0176495
$885$	10.6967	−	4.46564i	0.359566	−	0.150111i
$886$	−0.887631			−0.0298205
$887$	−7.95282	−	13.7747i	−0.267030	−	0.462509i	0.701064	−	0.713099i	$-0.252709\pi$
$887$	−7.95282	−	13.7747i	−0.267030	−	0.462509i	−0.968093	+	0.250590i	$0.919376\pi$
$888$	12.1286	+	9.25311i	0.407010	+	0.310514i
$889$		0			0
$890$	4.40804			0.147758
$891$	6.91174	−	4.09375i	0.231552	−	0.137146i
$892$	−4.77419	−	8.26914i	−0.159852	−	0.276871i
$893$	−14.2844	+	24.7413i	−0.478009	+	0.827935i
$894$	16.6630	−	6.95645i	0.557295	−	0.232658i
$895$	13.5428	−	23.4569i	0.452687	−	0.784077i
$896$		0			0
$897$	0.656173	−	5.09363i	0.0219090	−	0.170071i
$898$	−6.72727			−0.224492
$899$	−7.42583	−	12.8619i	−0.247665	−	0.428969i
$900$	−31.9524	+	32.3100i	−1.06508	+	1.07700i
$901$	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
$905$	20.7829	+	35.9970i	0.690846	+	1.19658i
$906$	−1.02315	−	0.780579i	−0.0339920	−	0.0259330i
$907$	8.54624	−	14.8025i	0.283773	−	0.491510i	−0.688538	−	0.725201i	$-0.741747\pi$
$907$	8.54624	−	14.8025i	0.283773	−	0.491510i	0.972311	+	0.233691i	$0.0750804\pi$
$908$	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	0.999984	−	0.00564955i	$-0.00179832\pi$
$911$	14.9435	+	25.8829i	0.495099	+	0.857537i	−0.504885	+	0.863187i	$0.668465\pi$
$912$	9.99717	+	7.62699i	0.331039	+	0.252555i
$913$	−10.9992			−0.364021
$914$	−1.27397			−0.0421393
$915$	63.7664	−	26.6211i	2.10805	−	0.880065i
$916$	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	$0.0390791\pi$
$920$	−8.51579	+	14.7498i	−0.280757	+	0.486286i
$921$	0.618519	−	4.80133i	0.0203809	−	0.158209i
$922$	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
$926$	−4.06227	+	7.03606i	−0.133495	+	0.231219i
$927$	−7.69712	−	28.0995i	−0.252807	−	0.922909i
$928$	−10.3667	−	17.9557i	−0.340304	−	0.589423i
$929$	−12.6176			−0.413970			−0.206985	−	0.978344i	$-0.566365\pi$
$929$	−12.6176			−0.413970			−0.206985	+	0.978344i	$0.566365\pi$
$930$	−10.4924	+	4.38036i	−0.344061	+	0.143638i
$931$		0			0
$932$	−14.5073	+	25.1274i	−0.475203	+	0.823075i
$933$	3.34166	−	25.9401i	0.109401	−	0.849240i
$934$	−2.15714	+	3.73627i	−0.0705836	+	0.122254i
$935$	−0.411957	−	0.713530i	−0.0134724	−	0.0233349i
$936$	4.69936	−	4.75196i	0.153603	−	0.155323i
$937$	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
$941$	−50.9397			−1.66059			−0.830294	−	0.557326i	$-0.811827\pi$
$941$	−50.9397			−1.66059			−0.830294	+	0.557326i	$0.811827\pi$
$942$	−1.83034	+	14.2082i	−0.0596356	+	0.462929i
$943$	−11.8481			−0.385827
$944$	−4.68525			−0.152492
$945$		0			0
$946$	4.41648			0.143592
$947$	27.6798			0.899474			0.449737	−	0.893161i	$-0.351518\pi$
$947$	27.6798			0.899474			0.449737	+	0.893161i	$0.351518\pi$
$948$	0.698388	−	5.42133i	0.0226826	−	0.176076i
$949$	−2.19061			−0.0711102
$950$	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	$0.646375\pi$
$954$	−3.88661	−	14.1887i	−0.125834	−	0.459375i
$955$	44.0265	+	76.2561i	1.42466	+	2.46759i
$956$	19.3162	−	33.4567i	0.624731	−	1.08207i
$957$	0.818252	−	6.35179i	0.0264503	−	0.205324i
$958$	4.40515	−	7.62994i	0.142324	−	0.246512i
$959$		0			0
$960$	15.8676	−	6.62436i	0.512123	−	0.213800i
$961$	−18.1467			−0.585378
$962$	1.40382	+	2.43149i	0.0452610	+	0.0783943i
$963$	22.9944	−	23.2518i	0.740984	−	0.749279i
$964$	−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	−0.682025	−	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
$969$	−0.155356	+	1.20597i	−0.00499075	+	0.0387413i
$970$	10.1111	−	17.5130i	0.324649	−	0.562309i
$971$	−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
$975$	−16.5170	+	6.89549i	−0.528968	+	0.220833i
$976$	−27.9302			−0.894024
$977$	11.9156			0.381215			0.190608	−	0.981666i	$-0.438954\pi$
$977$	11.9156			0.381215			0.190608	+	0.981666i	$0.438954\pi$
$978$	−4.56320	−	3.48133i	−0.145915	−	0.111321i
$979$	−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
$983$	−9.23896	+	16.0024i	−0.294677	+	0.510396i	−0.974910	−	0.222601i	$-0.928545\pi$
$983$	−9.23896	+	16.0024i	−0.294677	+	0.510396i	0.680233	+	0.732996i	$0.261879\pi$
$984$	−12.2581	−	9.35187i	−0.390773	−	0.298127i
$985$	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
$989$	−12.3620	+	21.4117i	−0.393090	+	0.680851i
$990$	−4.74289	−	1.24260i	−0.150739	−	0.0394925i
$991$	−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	$0.897969\pi$
$992$	17.9436			0.569710
$993$	4.00435	−	31.0843i	0.127074	−	0.986430i
$994$		0			0
$995$	−28.6108	+	49.5553i	−0.907023	+	1.57101i
$996$	34.5503	−	14.4240i	1.09477	−	0.457041i
$997$	20.9767	−	36.3327i	0.664338	−	1.15067i	−0.315127	−	0.949050i	$-0.602047\pi$
$997$	20.9767	−	36.3327i	0.664338	−	1.15067i	0.979464	−	0.201617i	$-0.0646197\pi$
$998$	2.76345	+	4.78644i	0.0874755	+	0.151512i
$999$	−15.1286	−	19.3788i	−0.478648	−	0.613119i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	7.3	odd	6
63.2.g.b.16.3	yes	10	63.34	odd	6
63.2.h.b.25.3	yes	10	63.52	odd	6
63.2.h.b.58.3	yes	10	7.6	odd	2
189.2.g.b.100.3		10	63.20	even	6
189.2.g.b.172.3		10	21.17	even	6
189.2.h.b.37.3		10	21.20	even	2
189.2.h.b.46.3		10	63.38	even	6
441.2.f.e.148.3		10	7.5	odd	6
441.2.f.e.295.3		10	63.61	odd	6
441.2.f.f.148.3		10	7.2	even	3
441.2.f.f.295.3		10	63.16	even	3
441.2.g.f.67.3		10	7.4	even	3
441.2.g.f.79.3		10	9.7	even	3
441.2.h.f.214.3		10	63.25	even	3	inner
441.2.h.f.373.3		10	1.1	even	1	trivial
567.2.e.e.163.3		10	63.41	even	6
567.2.e.e.487.3		10	63.59	even	6
567.2.e.f.163.3		10	63.13	odd	6
567.2.e.f.487.3		10	63.31	odd	6
1008.2.q.i.529.3		10	252.115	even	6
1008.2.q.i.625.3		10	28.27	even	2
1008.2.t.i.193.1		10	28.3	even	6
1008.2.t.i.961.1		10	252.223	even	6
1323.2.f.e.442.3		10	21.5	even	6
1323.2.f.e.883.3		10	63.47	even	6
1323.2.f.f.442.3		10	21.2	odd	6
1323.2.f.f.883.3		10	63.2	odd	6
1323.2.g.f.361.3		10	21.11	odd	6
1323.2.g.f.667.3		10	9.2	odd	6
1323.2.h.f.226.3		10	3.2	odd	2
1323.2.h.f.802.3		10	63.11	odd	6
3024.2.q.i.2305.1		10	84.83	odd	2
3024.2.q.i.2881.1		10	252.227	odd	6
3024.2.t.i.289.5		10	252.83	odd	6
3024.2.t.i.1873.5		10	84.59	odd	6
3969.2.a.z.1.3		5	63.40	odd	6
3969.2.a.ba.1.3		5	63.58	even	3
3969.2.a.bb.1.3		5	63.23	odd	6
3969.2.a.bc.1.3		5	63.5	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.495868 q^{2} +(0.221298 - 1.71786i) q^{3} -1.75411 q^{4} +(-1.84629 - 3.19787i) q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(-2.90205 - 0.760316i) q^{9} +O(q^{10})\)	\(q-0.495868 q^{2} +(0.221298 - 1.71786i) q^{3} -1.75411 q^{4} +(-1.84629 - 3.19787i) q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(-2.90205 - 0.760316i) q^{9} +(0.915516 + 1.58572i) q^{10} +(0.446284 - 0.772987i) q^{11} +(-0.388182 + 3.01332i) q^{12} +(-0.598355 + 1.03638i) q^{13} +(-5.90205 + 2.46398i) q^{15} +2.58515 q^{16} +(0.124991 + 0.216492i) q^{17} +(1.43904 + 0.377017i) q^{18} +(-1.40414 + 2.43204i) q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(-1.23886 - 2.14576i) q^{23} +(0.411957 - 3.19787i) q^{24} +(-4.31757 + 7.47825i) q^{25} +(0.296705 - 0.513909i) q^{26} +(-1.94833 + 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} +(2.92664 - 1.22181i) q^{30} -3.58515 q^{31} -5.00499 q^{32} +(-1.22912 - 0.937712i) q^{33} +(-0.0619793 - 0.107351i) q^{34} +(5.09054 + 1.33368i) q^{36} +(-2.36568 + 4.09747i) q^{37} +(0.696267 - 1.20597i) q^{38} +(1.64794 + 1.25724i) q^{39} +(-3.43695 - 5.95298i) q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +(-0.782834 + 1.35591i) q^{44} +(2.92664 + 10.6841i) q^{45} +(0.614310 + 1.06402i) q^{46} +10.1731 q^{47} +(0.572088 - 4.44091i) q^{48} +(2.14095 - 3.70823i) q^{50} +(0.399562 - 0.166808i) q^{51} +(1.04958 - 1.81793i) q^{52} +(-4.94465 - 8.56438i) q^{53} +(0.966116 - 2.38862i) q^{54} -3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} +(-1.02708 - 1.77895i) q^{58} -1.81237 q^{59} +(10.3529 - 4.32210i) q^{60} -10.8041 q^{61} +1.77776 q^{62} -2.68848 q^{64} +4.41895 q^{65} +(0.609480 + 0.464982i) q^{66} +1.02937 q^{67} +(-0.219249 - 0.379751i) q^{68} +(-3.96027 + 1.65332i) q^{69} -4.94533 q^{71} +(-5.40231 - 1.41536i) q^{72} +(0.915262 + 1.58528i) q^{73} +(1.17306 - 2.03181i) q^{74} +(11.8911 + 9.07189i) q^{75} +(2.46302 - 4.26607i) q^{76} +(-0.817161 - 0.623424i) q^{78} -1.79912 q^{79} +(-4.77293 - 8.26696i) q^{80} +(7.84384 + 4.41296i) q^{81} +(-1.18559 + 2.05350i) q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(2.47403 + 4.28514i) q^{86} +(6.62127 - 2.76423i) q^{87} +(0.830779 - 1.43895i) q^{88} +(1.20370 - 2.08488i) q^{89} +(-1.45123 - 5.29793i) q^{90} +(2.17310 + 3.76392i) q^{92} +(-0.793387 + 6.15877i) q^{93} -5.04450 q^{94} +10.3698 q^{95} +(-1.10759 + 8.59784i) q^{96} +(-5.52210 - 9.56456i) q^{97} +(-1.88286 + 1.90393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9	\( 10 q - 4 q^{2} + q^{3} + 8 q^{4} - 4 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9} + 7 q^{10} + 4 q^{11} + 20 q^{12} + 8 q^{13} - 19 q^{15} - 4 q^{16} - 12 q^{17} + 4 q^{18} - q^{19} - 5 q^{20} - q^{22} + 3 q^{23} - 6 q^{24} - q^{25} - 11 q^{26} + 7 q^{27} + 7 q^{29} + 16 q^{30} - 6 q^{31} + 4 q^{32} - 14 q^{33} - 3 q^{34} + 34 q^{36} - 20 q^{38} + 2 q^{39} + 3 q^{40} - 5 q^{41} - 7 q^{43} - 10 q^{44} + 16 q^{45} + 3 q^{46} + 54 q^{47} + 5 q^{48} + 19 q^{50} - 9 q^{51} + 10 q^{52} - 21 q^{53} - q^{54} - 4 q^{55} - 4 q^{57} - 10 q^{58} + 60 q^{59} + 10 q^{60} - 28 q^{61} + 12 q^{62} - 50 q^{64} + 22 q^{65} - 19 q^{66} + 4 q^{67} - 27 q^{68} - 15 q^{69} - 6 q^{71} - 36 q^{72} - 15 q^{73} - 36 q^{74} + 14 q^{75} - 5 q^{76} - 20 q^{78} + 8 q^{79} - 20 q^{80} + 23 q^{81} + 5 q^{82} - 9 q^{83} - 6 q^{85} - 8 q^{86} - 2 q^{87} - 18 q^{88} - 28 q^{89} - 28 q^{90} + 27 q^{92} - 6 q^{93} - 6 q^{94} + 28 q^{95} - 59 q^{96} + 12 q^{97} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + q^3 + 8 * q^4 - 4 * q^5 + 2 * q^6 - 6 * q^8 + 11 * q^9 + 7 * q^10 + 4 * q^11 + 20 * q^12 + 8 * q^13 - 19 * q^15 - 4 * q^16 - 12 * q^17 + 4 * q^18 - q^19 - 5 * q^20 - q^22 + 3 * q^23 - 6 * q^24 - q^25 - 11 * q^26 + 7 * q^27 + 7 * q^29 + 16 * q^30 - 6 * q^31 + 4 * q^32 - 14 * q^33 - 3 * q^34 + 34 * q^36 - 20 * q^38 + 2 * q^39 + 3 * q^40 - 5 * q^41 - 7 * q^43 - 10 * q^44 + 16 * q^45 + 3 * q^46 + 54 * q^47 + 5 * q^48 + 19 * q^50 - 9 * q^51 + 10 * q^52 - 21 * q^53 - q^54 - 4 * q^55 - 4 * q^57 - 10 * q^58 + 60 * q^59 + 10 * q^60 - 28 * q^61 + 12 * q^62 - 50 * q^64 + 22 * q^65 - 19 * q^66 + 4 * q^67 - 27 * q^68 - 15 * q^69 - 6 * q^71 - 36 * q^72 - 15 * q^73 - 36 * q^74 + 14 * q^75 - 5 * q^76 - 20 * q^78 + 8 * q^79 - 20 * q^80 + 23 * q^81 + 5 * q^82 - 9 * q^83 - 6 * q^85 - 8 * q^86 - 2 * q^87 - 18 * q^88 - 28 * q^89 - 28 * q^90 + 27 * q^92 - 6 * q^93 - 6 * q^94 + 28 * q^95 - 59 * q^96 + 12 * q^97 + 35 * q^99

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