LMFDB - Embedded newform 441.2.s.c.374.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(362,441)]

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([1, 5]))

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

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

chi := DirichletCharacter("441.362");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.s (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			374.1
Root			$-1.82904 - 1.05600i$ of defining polynomial
Character	$\chi$	$=$	441.374
Dual form			441.2.s.c.362.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02704 - 0.592963i) q^{2} +(-1.25233 - 1.19652i) q^{3} +(-0.296790 - 0.514055i) q^{4} -2.83797 q^{5} +(0.576705 + 1.97146i) q^{6} +3.07579i q^{8} +(0.136673 + 2.99689i) q^{9} +O(q^{10})$	\(q+(-1.02704 - 0.592963i) q^{2} +(-1.25233 - 1.19652i) q^{3} +(-0.296790 - 0.514055i) q^{4} -2.83797 q^{5} +(0.576705 + 1.97146i) q^{6} +3.07579i q^{8} +(0.136673 + 2.99689i) q^{9} +(2.91472 + 1.68281i) q^{10} +0.157816i q^{11} +(-0.243398 + 0.998883i) q^{12} +(-3.41468 - 1.97146i) q^{13} +(3.55408 + 3.39569i) q^{15} +(1.23025 - 2.13086i) q^{16} +(-2.07244 + 3.58956i) q^{17} +(1.63667 - 3.15897i) q^{18} +(5.48711 - 3.16799i) q^{19} +(0.842281 + 1.45887i) q^{20} +(0.0935793 - 0.162084i) q^{22} -0.546125i q^{23} +(3.68025 - 3.85192i) q^{24} +3.05408 q^{25} +(2.33801 + 4.04955i) q^{26} +(3.41468 - 3.91663i) q^{27} +(4.02704 - 2.32501i) q^{29} +(-1.63667 - 5.59496i) q^{30} +(-0.112086 + 0.0647129i) q^{31} +(2.80039 - 1.61680i) q^{32} +(0.188831 - 0.197639i) q^{33} +(4.25696 - 2.45776i) q^{34} +(1.50000 - 0.959702i) q^{36} +(1.23025 + 2.13086i) q^{37} -7.51399 q^{38} +(1.91741 + 6.55466i) q^{39} -8.72902i q^{40} +(-1.99569 + 3.45664i) q^{41} +(3.28434 + 5.68864i) q^{43} +(0.0811263 - 0.0468383i) q^{44} +(-0.387874 - 8.50508i) q^{45} +(-0.323832 + 0.560893i) q^{46} +(-4.33370 + 7.50619i) q^{47} +(-4.09030 + 1.19652i) q^{48} +(-3.13667 - 1.81096i) q^{50} +(6.89037 - 2.01561i) q^{51} +2.34044i q^{52} +(2.25370 + 1.30117i) q^{53} +(-5.82943 + 1.99777i) q^{54} -0.447879i q^{55} +(-10.6623 - 2.59808i) q^{57} -5.51459 q^{58} +(1.80686 + 3.12957i) q^{59} +(0.690757 - 2.83480i) q^{60} +(2.91472 + 1.68281i) q^{61} +0.153489 q^{62} -8.75583 q^{64} +(9.69076 + 5.59496i) q^{65} +(-0.311130 + 0.0910136i) q^{66} +(-0.663715 - 1.14959i) q^{67} +2.46031 q^{68} +(-0.653450 + 0.683930i) q^{69} -0.409310i q^{71} +(-9.21780 + 0.420378i) q^{72} +(13.0011 + 7.50619i) q^{73} -2.91798i q^{74} +(-3.82473 - 3.65428i) q^{75} +(-3.25704 - 1.88045i) q^{76} +(1.91741 - 7.86887i) q^{78} +(-2.16372 + 3.74766i) q^{79} +(-3.49142 + 6.04732i) q^{80} +(-8.96264 + 0.819187i) q^{81} +(4.09932 - 2.36674i) q^{82} +(3.22585 + 5.58733i) q^{83} +(5.88151 - 10.1871i) q^{85} -7.78996i q^{86} +(-7.82512 - 1.90675i) q^{87} -0.485411 q^{88} +(-2.52684 - 4.37662i) q^{89} +(-4.64483 + 8.96507i) q^{90} +(-0.280738 + 0.162084i) q^{92} +(0.217799 + 0.0530713i) q^{93} +(8.90179 - 5.13945i) q^{94} +(-15.5723 + 8.99066i) q^{95} +(-5.44156 - 1.32595i) q^{96} +(-2.18452 + 1.26123i) q^{97} +(-0.472958 + 0.0215693i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 2 q^{4}+O(q^{10}) $ 12 * q + 6 * q^2 + 2 * q^4	$ 12 q + 6 q^{2} + 2 q^{4} + 6 q^{15} + 2 q^{16} + 18 q^{18} - 10 q^{22} + 30 q^{29} - 18 q^{30} + 12 q^{32} + 18 q^{36} + 2 q^{37} - 12 q^{39} - 10 q^{43} - 54 q^{44} + 20 q^{46} - 36 q^{50} + 66 q^{51} + 12 q^{53} - 18 q^{57} - 4 q^{58} - 30 q^{60} + 16 q^{64} + 78 q^{65} + 12 q^{67} - 54 q^{72} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 6 q^{85} - 68 q^{88} + 30 q^{92} - 54 q^{93} - 72 q^{95} - 24 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 + 2 * q^4 + 6 * q^15 + 2 * q^16 + 18 * q^18 - 10 * q^22 + 30 * q^29 - 18 * q^30 + 12 * q^32 + 18 * q^36 + 2 * q^37 - 12 * q^39 - 10 * q^43 - 54 * q^44 + 20 * q^46 - 36 * q^50 + 66 * q^51 + 12 * q^53 - 18 * q^57 - 4 * q^58 - 30 * q^60 + 16 * q^64 + 78 * q^65 + 12 * q^67 - 54 * q^72 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 6 * q^85 - 68 * q^88 + 30 * q^92 - 54 * q^93 - 72 * q^95 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.02704	−	0.592963i	−0.726228	−	0.419288i	0.0908124	−	0.995868i	$-0.471054\pi$
$2$	−1.02704	−	0.592963i	−0.726228	−	0.419288i	−0.817041	+	0.576580i	$0.804387\pi$
$3$	−1.25233	−	1.19652i	−0.723034	−	0.690812i
$3$	−1.25233	−	1.19652i	−0.723034	−	0.690812i
$4$	−0.296790	−	0.514055i	−0.148395	−	0.257027i
$5$	−2.83797			−1.26918			−0.634590	−	0.772849i	$-0.718831\pi$
$5$	−2.83797			−1.26918			−0.634590	+	0.772849i	$0.718831\pi$
$6$	0.576705	+	1.97146i	0.235439	+	0.804847i
$7$		0			0
$7$		0			0
$8$			3.07579i			1.08746i
$9$	0.136673	+	2.99689i	0.0455577	+	0.998962i
$10$	2.91472	+	1.68281i	0.921714	+	0.532152i
$11$			0.157816i			0.0475835i	0.999717	+	0.0237917i	$0.00757386\pi$
$11$			0.157816i			0.0475835i	−0.999717	+	0.0237917i	$0.992426\pi$
$12$	−0.243398	+	0.998883i	−0.0702630	+	0.288353i
$13$	−3.41468	−	1.97146i	−0.947061	−	0.546786i	−0.0548943	−	0.998492i	$-0.517482\pi$
$13$	−3.41468	−	1.97146i	−0.947061	−	0.546786i	−0.892167	+	0.451706i	$0.850816\pi$
$14$		0			0
$15$	3.55408	+	3.39569i	0.917661	+	0.876764i
$16$	1.23025	−	2.13086i	0.307563	−	0.532715i
$17$	−2.07244	+	3.58956i	−0.502640	+	0.870597i	0.497356	+	0.867547i	$0.334304\pi$
$17$	−2.07244	+	3.58956i	−0.502640	+	0.870597i	−0.999995	+	0.00305055i	$0.999029\pi$
$18$	1.63667	−	3.15897i	0.385768	−	0.744576i
$19$	5.48711	−	3.16799i	1.25883	−	0.726786i	0.285983	−	0.958235i	$-0.407680\pi$
$19$	5.48711	−	3.16799i	1.25883	−	0.726786i	0.972847	+	0.231449i	$0.0743466\pi$
$20$	0.842281	+	1.45887i	0.188340	+	0.326214i
$21$		0			0
$22$	0.0935793	−	0.162084i	0.0199512	−	0.0345565i
$23$		−	0.546125i		−	0.113875i	−0.998378	−	0.0569374i	$-0.981866\pi$
$23$		−	0.546125i		−	0.113875i	0.998378	−	0.0569374i	$-0.0181336\pi$
$24$	3.68025	−	3.85192i	0.751228	−	0.786269i
$25$	3.05408			0.610817
$26$	2.33801	+	4.04955i	0.458522	+	0.794183i
$27$	3.41468	−	3.91663i	0.657155	−	0.753756i
$28$		0			0
$29$	4.02704	−	2.32501i	0.747803	−	0.431744i	−0.0770966	−	0.997024i	$-0.524565\pi$
$29$	4.02704	−	2.32501i	0.747803	−	0.431744i	0.824900	+	0.565279i	$0.191232\pi$
$30$	−1.63667	−	5.59496i	−0.298814	−	1.02150i
$31$	−0.112086	+	0.0647129i	−0.0201313	+	0.0116228i	−0.510032	−	0.860156i	$-0.670366\pi$
$31$	−0.112086	+	0.0647129i	−0.0201313	+	0.0116228i	0.489901	+	0.871778i	$0.337033\pi$
$32$	2.80039	−	1.61680i	0.495043	−	0.285813i
$33$	0.188831	−	0.197639i	0.0328712	−	0.0344045i
$34$	4.25696	−	2.45776i	0.730062	−	0.421502i
$35$		0			0
$36$	1.50000	−	0.959702i	0.250000	−	0.159950i
$37$	1.23025	+	2.13086i	0.202252	+	0.350311i	0.949254	−	0.314511i	$-0.101841\pi$
$37$	1.23025	+	2.13086i	0.202252	+	0.350311i	−0.747002	+	0.664822i	$0.768507\pi$
$38$	−7.51399			−1.21893
$39$	1.91741	+	6.55466i	0.307032	+	1.04959i
$40$		−	8.72902i		−	1.38018i
$41$	−1.99569	+	3.45664i	−0.311675	+	0.539836i	−0.978725	−	0.205176i	$-0.934223\pi$
$41$	−1.99569	+	3.45664i	−0.311675	+	0.539836i	0.667050	+	0.745013i	$0.267557\pi$
$42$		0			0
$43$	3.28434	+	5.68864i	0.500857	+	0.867509i	1.00000		0.000989450i	$0.000314952\pi$
$43$	3.28434	+	5.68864i	0.500857	+	0.867509i	−0.499143	+	0.866520i	$0.666352\pi$
$44$	0.0811263	−	0.0468383i	0.0122303	−	0.00706114i
$45$	−0.387874	−	8.50508i	−0.0578209	−	1.26786i
$46$	−0.323832	+	0.560893i	−0.0477464	+	0.0826992i
$47$	−4.33370	+	7.50619i	−0.632135	+	1.09489i	0.354979	+	0.934874i	$0.384488\pi$
$47$	−4.33370	+	7.50619i	−0.632135	+	1.09489i	−0.987114	+	0.160016i	$0.948845\pi$
$48$	−4.09030	+	1.19652i	−0.590385	+	0.172703i
$49$		0			0
$50$	−3.13667	−	1.81096i	−0.443593	−	0.256108i
$51$	6.89037	−	2.01561i	0.964845	−	0.282242i
$52$			2.34044i			0.324561i
$53$	2.25370	+	1.30117i	0.309569	+	0.178730i	0.646734	−	0.762716i	$-0.276135\pi$
$53$	2.25370	+	1.30117i	0.309569	+	0.178730i	−0.337165	+	0.941446i	$0.609468\pi$
$54$	−5.82943	+	1.99777i	−0.793285	+	0.271861i
$55$		−	0.447879i		−	0.0603920i
$56$		0			0
$57$	−10.6623	−	2.59808i	−1.41225	−	0.344124i
$58$	−5.51459			−0.724101
$59$	1.80686	+	3.12957i	0.235233	+	0.407436i	0.959340	−	0.282252i	$-0.0910813\pi$
$59$	1.80686	+	3.12957i	0.235233	+	0.407436i	−0.724107	+	0.689687i	$0.757748\pi$
$60$	0.690757	−	2.83480i	0.0891764	−	0.365971i
$61$	2.91472	+	1.68281i	0.373191	+	0.215462i	0.674852	−	0.737953i	$-0.264208\pi$
$61$	2.91472	+	1.68281i	0.373191	+	0.215462i	−0.301660	+	0.953415i	$0.597541\pi$
$62$	0.153489			0.0194932
$63$		0			0
$64$	−8.75583			−1.09448
$65$	9.69076	+	5.59496i	1.20199	+	0.693970i
$66$	−0.311130	+	0.0910136i	−0.0382974	+	0.0112030i
$67$	−0.663715	−	1.14959i	−0.0810857	−	0.140445i	0.822631	−	0.568576i	$-0.192505\pi$
$67$	−0.663715	−	1.14959i	−0.0810857	−	0.140445i	−0.903717	+	0.428131i	$0.859172\pi$
$68$	2.46031			0.298356
$69$	−0.653450	+	0.683930i	−0.0786661	+	0.0823355i
$70$		0			0
$71$		−	0.409310i		−	0.0485761i	−0.999705	−	0.0242881i	$-0.992268\pi$
$71$		−	0.409310i		−	0.0485761i	0.999705	−	0.0242881i	$-0.00773189\pi$
$72$	−9.21780	+	0.420378i	−1.08633	+	0.0495420i
$73$	13.0011	+	7.50619i	1.52166	+	0.878533i	0.999673	+	0.0255830i	$0.00814420\pi$
$73$	13.0011	+	7.50619i	1.52166	+	0.878533i	0.521992	+	0.852950i	$0.325189\pi$
$74$		−	2.91798i		−	0.339208i
$75$	−3.82473	−	3.65428i	−0.441642	−	0.421960i
$76$	−3.25704	−	1.88045i	−0.373608	−	0.215703i
$77$		0			0
$78$	1.91741	−	7.86887i	0.217104	−	0.890974i
$79$	−2.16372	+	3.74766i	−0.243437	+	0.421645i	−0.961691	−	0.274136i	$-0.911608\pi$
$79$	−2.16372	+	3.74766i	−0.243437	+	0.421645i	0.718254	+	0.695781i	$0.244942\pi$
$80$	−3.49142	+	6.04732i	−0.390353	+	0.676111i
$81$	−8.96264	+	0.819187i	−0.995849	+	0.0910208i
$82$	4.09932	−	2.36674i	0.452694	−	0.261363i
$83$	3.22585	+	5.58733i	0.354083	+	0.613289i	0.986961	−	0.160963i	$-0.0514598\pi$
$83$	3.22585	+	5.58733i	0.354083	+	0.613289i	−0.632878	+	0.774252i	$0.718126\pi$
$84$		0			0
$85$	5.88151	−	10.1871i	0.637940	−	1.10494i
$86$		−	7.78996i		−	0.840013i
$87$	−7.82512	−	1.90675i	−0.838941	−	0.204425i
$88$	−0.485411			−0.0517450
$89$	−2.52684	−	4.37662i	−0.267845	−	0.463921i	0.700460	−	0.713691i	$-0.252978\pi$
$89$	−2.52684	−	4.37662i	−0.267845	−	0.463921i	−0.968305	+	0.249771i	$0.919645\pi$
$90$	−4.64483	+	8.96507i	−0.489608	+	0.945001i
$91$		0			0
$92$	−0.280738	+	0.162084i	−0.0292690	+	0.0168984i
$93$	0.217799	+	0.0530713i	0.0225847	+	0.00550324i
$94$	8.90179	−	5.13945i	0.918150	−	0.530094i
$95$	−15.5723	+	8.99066i	−1.59768	+	0.922422i
$96$	−5.44156	−	1.32595i	−0.555377	−	0.135329i
$97$	−2.18452	+	1.26123i	−0.221805	+	0.128059i	−0.606786	−	0.794866i	$-0.707541\pi$
$97$	−2.18452	+	1.26123i	−0.221805	+	0.128059i	0.384981	+	0.922925i	$0.374208\pi$
$98$		0			0
$99$	−0.472958	+	0.0215693i	−0.0475341	+	0.00216779i
$100$	−0.906421	−	1.56997i	−0.0906421	−	0.156997i
$101$	−2.99146			−0.297662			−0.148831	−	0.988863i	$-0.547551\pi$
$101$	−2.99146			−0.297662			−0.148831	+	0.988863i	$0.547551\pi$
$102$	−8.27188	−	2.01561i	−0.819039	−	0.199576i
$103$			13.1966i			1.30030i	0.759804	+	0.650152i	$0.225295\pi$
$103$			13.1966i			1.30030i	−0.759804	+	0.650152i	$0.774705\pi$
$104$	6.06382	−	10.5028i	0.594606	−	1.02989i
$105$		0			0
$106$	−1.54309	−	2.67272i	−0.149879	−	0.259597i
$107$	−16.9356	+	9.77777i	−1.63723	+	0.945253i	−0.655444	+	0.755244i	$0.727518\pi$
$107$	−16.9356	+	9.77777i	−1.63723	+	0.945253i	−0.981782	+	0.190009i	$0.939148\pi$
$108$	−3.02680	−	0.592916i	−0.291254	−	0.0570534i
$109$	−6.62422	+	11.4735i	−0.634485	+	1.09896i	0.352139	+	0.935948i	$0.385455\pi$
$109$	−6.62422	+	11.4735i	−0.634485	+	1.09896i	−0.986624	+	0.163013i	$0.947879\pi$
$110$	−0.265576	+	0.459990i	−0.0253216	+	0.0438584i
$111$	1.00893	−	4.14057i	0.0957638	−	0.393005i
$112$		0			0
$113$	−8.72665	−	5.03834i	−0.820935	−	0.473967i	0.0298041	−	0.999556i	$-0.490512\pi$
$113$	−8.72665	−	5.03834i	−0.820935	−	0.473967i	−0.850739	+	0.525589i	$0.823845\pi$
$114$	9.41002	+	8.99066i	0.881329	+	0.842052i
$115$			1.54989i			0.144528i
$116$	−2.39037	−	1.38008i	−0.221940	−	0.128137i
$117$	5.44156	−	10.5028i	0.503072	−	0.970988i
$118$		−	4.28561i		−	0.394522i
$119$		0			0
$120$	−10.4445	+	10.9316i	−0.953444	+	0.997917i
$121$	10.9751			0.997736
$122$	−1.99569	−	3.45664i	−0.180681	−	0.312949i
$123$	6.63521	−	1.94097i	0.598277	−	0.175012i
$124$	0.0665320	+	0.0384123i	0.00597475	+	0.00344952i
$125$	5.52245			0.493943
$126$		0			0
$127$	−12.4897			−1.10828			−0.554140	−	0.832423i	$-0.686953\pi$
$127$	−12.4897			−1.10828			−0.554140	+	0.832423i	$0.686953\pi$
$128$	3.39183	+	1.95827i	0.299798	+	0.173089i
$129$	2.69350	−	11.0538i	0.237149	−	0.973237i
$130$	−6.63521	−	11.4925i	−0.581946	−	1.00796i
$131$	10.0450			0.877635			0.438817	−	0.898576i	$-0.355398\pi$
$131$	10.0450			0.877635			0.438817	+	0.898576i	$0.355398\pi$
$132$	−0.157640	−	0.0384123i	−0.0137208	−	0.00334336i
$133$		0			0
$134$			1.57423i			0.135993i
$135$	−9.69076	+	11.1153i	−0.834048	+	0.956651i
$136$	−11.0408	−	6.37438i	−0.946737	−	0.546599i
$137$		−	8.04145i		−	0.687028i	−0.939148	−	0.343514i	$-0.888383\pi$
$137$		−	8.04145i		−	0.687028i	0.939148	−	0.343514i	$-0.111617\pi$
$138$	1.07667	−	0.314953i	0.0916519	−	0.0268106i
$139$	16.3702	+	9.45136i	1.38850	+	0.801654i	0.993147	−	0.116873i	$-0.0372872\pi$
$139$	16.3702	+	9.45136i	1.38850	+	0.801654i	0.395358	+	0.918527i	$0.370621\pi$
$140$		0			0
$141$	14.4086	−	4.21488i	1.21342	−	0.354957i
$142$	−0.242705	+	0.420378i	−0.0203674	+	0.0352774i
$143$	0.311130	−	0.538892i	0.0260180	−	0.0450644i
$144$	6.55408	+	3.39569i	0.546174	+	0.282975i
$145$	−11.4286	+	6.59832i	−0.949096	+	0.547961i
$146$	−8.90179	−	15.4184i	−0.736717	−	1.27603i
$147$		0			0
$148$	0.730252	−	1.26483i	0.0600264	−	0.103969i
$149$		−	19.4063i		−	1.58982i	−0.606725	−	0.794912i	$-0.707517\pi$
$149$		−	19.4063i		−	1.58982i	0.606725	−	0.794912i	$-0.292483\pi$
$150$	1.76131	+	6.02102i	0.143810	+	0.491614i
$151$	−1.78794			−0.145500			−0.0727501	−	0.997350i	$-0.523178\pi$
$151$	−1.78794			−0.145500			−0.0727501	+	0.997350i	$0.523178\pi$
$152$	9.74407	+	16.8772i	0.790348	+	1.36892i
$153$	−11.0408	−	5.72026i	−0.892592	−	0.462455i
$154$		0			0
$155$	0.318097	−	0.183653i	0.0255502	−	0.0147514i
$156$	2.80039	−	2.93101i	0.224211	−	0.234669i
$157$	−3.80255	+	2.19540i	−0.303477	+	0.175212i	−0.644004	−	0.765022i	$-0.722728\pi$
$157$	−3.80255	+	2.19540i	−0.303477	+	0.175212i	0.340527	+	0.940235i	$0.389395\pi$
$158$	4.44445	−	2.56601i	0.353582	−	0.204140i
$159$	−1.26550	−	4.32610i	−0.100360	−	0.343082i
$160$	−7.94742	+	4.58845i	−0.628299	+	0.362749i
$161$		0			0
$162$	9.69076	+	4.47318i	0.761378	+	0.351446i
$163$	−2.71780	−	4.70737i	−0.212874	−	0.368709i	0.739738	−	0.672894i	$-0.234949\pi$
$163$	−2.71780	−	4.70737i	−0.212874	−	0.368709i	−0.952613	+	0.304185i	$0.901616\pi$
$164$	2.36920			0.185004
$165$	−0.535897	+	0.560893i	−0.0417195	+	0.0436655i
$166$		−	7.65123i		−	0.593851i
$167$	−5.25273	+	9.09799i	−0.406468	+	0.704024i	−0.994491	−	0.104821i	$-0.966573\pi$
$167$	−5.25273	+	9.09799i	−0.406468	+	0.704024i	0.588023	+	0.808844i	$0.299907\pi$
$168$		0			0
$169$	1.27335	+	2.20550i	0.0979497	+	0.169654i
$170$	−12.0811	+	6.97504i	−0.926580	+	0.534961i
$171$	10.2440	+	16.0113i	0.783381	+	1.22441i
$172$	1.94951	−	3.37666i	0.148649	−	0.257468i
$173$	8.77949	−	15.2065i	0.667492	−	1.15613i	−0.311111	−	0.950374i	$-0.600701\pi$
$173$	8.77949	−	15.2065i	0.667492	−	1.15613i	0.978603	−	0.205757i	$-0.0659656\pi$
$174$	6.90610	+	6.59832i	0.523550	+	0.500218i
$175$		0			0
$176$	0.336285	+	0.194154i	0.0253484	+	0.0146349i
$177$	1.48181	−	6.08121i	0.111380	−	0.457092i
$178$			5.99330i			0.449217i
$179$	15.7645	+	9.10163i	1.17829	+	0.680288i	0.955619	−	0.294605i	$-0.0951880\pi$
$179$	15.7645	+	9.10163i	1.17829	+	0.680288i	0.222674	+	0.974893i	$0.428521\pi$
$180$	−4.25696	+	2.72361i	−0.317295	+	0.203006i
$181$			6.60182i			0.490710i	0.969433	+	0.245355i	$0.0789045\pi$
$181$			6.60182i			0.490710i	−0.969433	+	0.245355i	$0.921096\pi$
$182$		0			0
$183$	−1.63667	−	5.59496i	−0.120986	−	0.413591i
$184$	1.67977			0.123834
$185$	−3.49142	−	6.04732i	−0.256694	−	0.444608i
$186$	−0.192220	−	0.183653i	−0.0140942	−	0.0134661i
$187$	−0.566492	−	0.327065i	−0.0414260	−	0.0239173i
$188$	5.14479			0.375223
$189$		0			0
$190$	21.3245			1.54704
$191$	12.3063	+	7.10506i	0.890454	+	0.514104i	0.874091	−	0.485762i	$-0.161458\pi$
$191$	12.3063	+	7.10506i	0.890454	+	0.514104i	0.0163630	+	0.999866i	$0.494791\pi$
$192$	10.9652	+	10.4765i	0.791346	+	0.756079i
$193$	5.00214	+	8.66395i	0.360062	+	0.623645i	0.987971	−	0.154642i	$-0.0494223\pi$
$193$	5.00214	+	8.66395i	0.360062	+	0.623645i	−0.627909	+	0.778287i	$0.716089\pi$
$194$	2.99146			0.214774
$195$	−5.44156	−	18.6020i	−0.389678	−	1.33211i
$196$		0			0
$197$			20.1017i			1.43218i	0.698006	+	0.716092i	$0.254071\pi$
$197$			20.1017i			1.43218i	−0.698006	+	0.716092i	$0.745929\pi$
$198$	0.498537	+	0.258294i	0.0354295	+	0.0183562i
$199$	−11.2045	−	6.46890i	−0.794263	−	0.458568i	0.0471981	−	0.998886i	$-0.484971\pi$
$199$	−11.2045	−	6.46890i	−0.794263	−	0.458568i	−0.841461	+	0.540318i	$0.818304\pi$
$200$			9.39373i			0.664237i
$201$	−0.544315	+	2.23382i	−0.0383930	+	0.157561i
$202$	3.07236	+	1.77383i	0.216170	+	0.124806i
$203$		0			0
$204$	−3.08113	−	2.94381i	−0.215722	−	0.206108i
$205$	5.66372	−	9.80984i	0.395571	−	0.685149i
$206$	7.82512	−	13.5535i	0.545202	−	0.944318i
$207$	1.63667	−	0.0746406i	0.113757	−	0.00518788i
$208$	−8.40183	+	4.85080i	−0.582562	+	0.336342i
$209$	0.499960	+	0.865957i	0.0345830	+	0.0598995i
$210$		0			0
$211$	−4.50720	+	7.80669i	−0.310288	+	0.537435i	−0.978425	−	0.206604i	$-0.933759\pi$
$211$	−4.50720	+	7.80669i	−0.310288	+	0.537435i	0.668136	+	0.744039i	$0.267092\pi$
$212$		−	1.54470i		−	0.106090i
$213$	−0.489748	+	0.512592i	−0.0335570	+	0.0351222i
$214$	23.1914			1.58533
$215$	−9.32085	−	16.1442i	−0.635677	−	1.10102i
$216$	12.0467	+	10.5028i	0.819677	+	0.714628i
$217$		0			0
$218$	13.6067	−	7.85584i	0.921562	−	0.532064i
$219$	−7.30039	−	24.9564i	−0.493315	−	1.68639i
$220$	−0.230234	+	0.132926i	−0.0155224	+	0.00896185i
$221$	14.1534	−	8.17147i	0.952061	−	0.549672i
$222$	−3.49142	+	3.65428i	−0.234329	+	0.245259i
$223$	−1.95429	+	1.12831i	−0.130869	+	0.0755571i	−0.564005	−	0.825771i	$-0.690740\pi$
$223$	−1.95429	+	1.12831i	−0.130869	+	0.0755571i	0.433136	+	0.901328i	$0.357407\pi$
$224$		0			0
$225$	0.417411	+	9.15274i	0.0278274	+	0.610183i
$226$	5.97509	+	10.3492i	0.397457	+	0.688416i
$227$	18.6417			1.23729			0.618647	−	0.785669i	$-0.287681\pi$
$227$	18.6417			1.23729			0.618647	+	0.785669i	$0.287681\pi$
$228$	1.82889	+	6.25206i	0.121121	+	0.414053i
$229$			14.3057i			0.945344i	0.881238	+	0.472672i	$0.156711\pi$
$229$			14.3057i			0.945344i	−0.881238	+	0.472672i	$0.843289\pi$
$230$	0.919025	−	1.59180i	0.0605987	−	0.104960i
$231$		0			0
$232$	7.15126	+	12.3863i	0.469503	+	0.813204i
$233$	14.7812	−	8.53394i	0.968350	−	0.559077i	0.0696170	−	0.997574i	$-0.477822\pi$
$233$	14.7812	−	8.53394i	0.968350	−	0.559077i	0.898733	+	0.438497i	$0.144489\pi$
$234$	−11.8165	+	7.56022i	−0.772469	+	0.494227i
$235$	12.2989	−	21.3024i	0.802293	−	1.38961i
$236$	1.07251	−	1.85765i	0.0698148	−	0.120923i
$237$	7.19385	−	2.10439i	0.467291	−	0.136695i
$238$		0			0
$239$	1.93560	+	1.11752i	0.125203	+	0.0722863i	0.561294	−	0.827617i	$-0.310304\pi$
$239$	1.93560	+	1.11752i	0.125203	+	0.0722863i	−0.436090	+	0.899903i	$0.643637\pi$
$240$	11.6082	−	3.39569i	0.749304	−	0.219191i
$241$		−	4.52023i		−	0.291174i	−0.989345	−	0.145587i	$-0.953493\pi$
$241$		−	4.52023i		−	0.291174i	0.989345	−	0.145587i	$-0.0465070\pi$
$242$	−11.2719	−	6.50783i	−0.724584	−	0.418339i
$243$	12.2044	+	9.69810i	0.782911	+	0.622133i
$244$		−	1.99777i		−	0.127894i
$245$		0			0
$246$	−7.96557	−	1.94097i	−0.507866	−	0.123752i
$247$	−24.9823			−1.58959
$248$	−0.199044	−	0.344754i	−0.0126393	−	0.0218919i
$249$	2.64553	−	10.8570i	0.167653	−	0.688034i
$250$	−5.67179	−	3.27461i	−0.358716	−	0.207105i
$251$	−21.1727			−1.33641			−0.668205	−	0.743978i	$-0.732937\pi$
$251$	−21.1727			−1.33641			−0.668205	+	0.743978i	$0.732937\pi$
$252$		0			0
$253$	0.0861875			0.00541856
$254$	12.8274	+	7.40592i	0.804865	+	0.464689i
$255$	−19.5547	+	5.72026i	−1.22456	+	0.358216i
$256$	6.43346	+	11.1431i	0.402091	+	0.696443i
$257$	−31.3005			−1.95247			−0.976236	−	0.216712i	$-0.930467\pi$
$257$	−31.3005			−1.95247			−0.976236	+	0.216712i	$0.930467\pi$
$258$	−9.32085	+	9.75562i	−0.580291	+	0.607358i
$259$		0			0
$260$		−	6.64211i		−	0.411926i
$261$	7.51819	+	11.7508i	0.465364	+	0.727357i
$262$	−10.3166	−	5.95631i	−0.637363	−	0.367982i
$263$		−	6.67671i		−	0.411704i	−0.978583	−	0.205852i	$-0.934004\pi$
$263$		−	6.67671i		−	0.411704i	0.978583	−	0.205852i	$-0.0659965\pi$
$264$	0.607896	+	0.580805i	0.0374134	+	0.0357460i
$265$	−6.39593	−	3.69269i	−0.392899	−	0.226840i
$266$		0			0
$267$	−2.07227	+	8.50440i	−0.126821	+	0.520461i
$268$	−0.393968	+	0.682372i	−0.0240654	+	0.0416825i
$269$	5.32947	−	9.23092i	0.324944	−	0.562819i	−0.656557	−	0.754276i	$-0.727988\pi$
$269$	5.32947	−	9.23092i	0.324944	−	0.562819i	0.981501	+	0.191457i	$0.0613213\pi$
$270$	16.5438	−	5.66960i	1.00682	−	0.345041i
$271$	−6.44754	+	3.72249i	−0.391660	+	0.226125i	−0.682879	−	0.730531i	$-0.739273\pi$
$271$	−6.44754	+	3.72249i	−0.391660	+	0.226125i	0.291219	+	0.956656i	$0.405939\pi$
$272$	5.09924	+	8.83214i	0.309187	+	0.535527i
$273$		0			0
$274$	−4.76829	+	8.25891i	−0.288063	+	0.498939i
$275$			0.481985i			0.0290648i
$276$	0.545515	+	0.132926i	0.0328361	+	0.00800119i
$277$	−26.5586			−1.59575			−0.797874	−	0.602824i	$-0.794042\pi$
$277$	−26.5586			−1.59575			−0.797874	+	0.602824i	$0.794042\pi$
$278$	−11.2086	−	19.4139i	−0.672248	−	1.16437i
$279$	−0.209256	−	0.327065i	−0.0125278	−	0.0195808i
$280$		0			0
$281$	21.0993	−	12.1817i	1.25868	−	0.726699i	0.285862	−	0.958271i	$-0.407720\pi$
$281$	21.0993	−	12.1817i	1.25868	−	0.726699i	0.972818	+	0.231572i	$0.0743869\pi$
$282$	−17.2975	−	4.21488i	−1.03005	−	0.250993i
$283$	−7.49302	+	4.32610i	−0.445414	+	0.257160i	−0.705891	−	0.708320i	$-0.749453\pi$
$283$	−7.49302	+	4.32610i	−0.445414	+	0.257160i	0.260478	+	0.965480i	$0.416120\pi$
$284$	−0.210408	+	0.121479i	−0.0124854	+	0.00720844i
$285$	30.2592	+	7.37327i	1.79240	+	0.436755i
$286$	−0.639086	+	0.368977i	−0.0377900	+	0.0218181i
$287$		0			0
$288$	5.22812	+	8.17147i	0.308070	+	0.481508i
$289$	−0.0899807	−	0.155851i	−0.00529298	−	0.00916772i
$290$	15.6502			0.919014
$291$	4.24484	+	1.03434i	0.248837	+	0.0606342i
$292$		−	8.91104i		−	0.521479i
$293$	4.40023	−	7.62143i	0.257064	−	0.445249i	−0.708390	−	0.705821i	$-0.750578\pi$
$293$	4.40023	−	7.62143i	0.257064	−	0.445249i	0.965454	+	0.260573i	$0.0839114\pi$
$294$		0			0
$295$	−5.12782	−	8.88164i	−0.298553	−	0.517109i
$296$	−6.55408	+	3.78400i	−0.380948	+	0.219941i
$297$	0.618109	+	0.538892i	0.0358663	+	0.0312697i
$298$	−11.5072	+	19.9311i	−0.666594	+	1.15457i
$299$	−1.07667	+	1.86484i	−0.0622652	+	0.107846i
$300$	−0.743359	+	3.05067i	−0.0429178	+	0.176131i
$301$		0			0
$302$	1.83628	+	1.06018i	0.105666	+	0.0610065i
$303$	3.74630	+	3.57935i	0.215220	+	0.205628i
$304$		−	15.5897i		−	0.894130i
$305$	−8.27188	−	4.77577i	−0.473647	−	0.273460i
$306$	7.94742	+	12.4217i	0.454324	+	0.710102i
$307$		−	11.1747i		−	0.637771i	−0.947793	−	0.318886i	$-0.896691\pi$
$307$		−	11.1747i		−	0.637771i	0.947793	−	0.318886i	$-0.103309\pi$
$308$		0			0
$309$	15.7901	−	16.5266i	0.898266	−	0.940165i
$310$	−0.435599			−0.0247404
$311$	8.20279	+	14.2076i	0.465137	+	0.805641i	0.999208	−	0.0397985i	$-0.0126716\pi$
$311$	8.20279	+	14.2076i	0.465137	+	0.805641i	−0.534070	+	0.845440i	$0.679338\pi$
$312$	−20.1608	+	5.89756i	−1.14138	+	0.333884i
$313$	7.10514	+	4.10216i	0.401606	+	0.231868i	0.687177	−	0.726490i	$-0.258850\pi$
$313$	7.10514	+	4.10216i	0.401606	+	0.231868i	−0.285570	+	0.958358i	$0.592183\pi$
$314$	5.20717			0.293858
$315$		0			0
$316$	2.56867			0.144499
$317$	−19.8427	−	11.4562i	−1.11448	−	0.643443i	−0.174491	−	0.984659i	$-0.555828\pi$
$317$	−19.8427	−	11.4562i	−1.11448	−	0.643443i	−0.939985	+	0.341215i	$0.889161\pi$
$318$	−1.26550	+	5.19347i	−0.0709655	+	0.291236i
$319$	0.366926	+	0.635534i	0.0205439	+	0.0355831i
$320$	24.8488			1.38909
$321$	32.9083	+	8.01878i	1.83676	+	0.447565i
$322$		0			0
$323$			26.2618i			1.46125i
$324$	3.08113	+	4.36416i	0.171174	+	0.242453i
$325$	−10.4287	−	6.02102i	−0.578481	−	0.333986i
$326$			6.44622i			0.357023i
$327$	22.0240	−	6.44260i	1.21793	−	0.356276i
$328$	−10.6319	−	6.13833i	−0.587049	−	0.338933i
$329$		0			0
$330$	0.882977	−	0.258294i	0.0486063	−	0.0142186i
$331$	−9.63161	+	16.6824i	−0.529401	+	0.916950i	0.470011	+	0.882661i	$0.344250\pi$
$331$	−9.63161	+	16.6824i	−0.529401	+	0.916950i	−0.999412	+	0.0342892i	$0.989083\pi$
$332$	1.91480	−	3.31652i	0.105088	−	0.182018i
$333$	−6.21780	+	3.97816i	−0.340733	+	0.218002i
$334$	10.7895	−	6.22935i	0.590378	−	0.340855i
$335$	1.88361	+	3.26250i	0.102912	+	0.178249i
$336$		0			0
$337$	−2.26829	+	3.92878i	−0.123561	+	0.214015i	−0.921170	−	0.389161i	$-0.872765\pi$
$337$	−2.26829	+	3.92878i	−0.123561	+	0.214015i	0.797608	+	0.603176i	$0.206098\pi$
$338$		−	3.02019i		−	0.164277i
$339$	4.90019	+	16.7513i	0.266142	+	0.909806i
$340$	−6.98229			−0.378668
$341$	−0.0102128	−	0.0176890i	−0.000553052	−	0.000957915i
$342$	−1.02696	−	22.5186i	−0.0555317	−	1.21767i
$343$		0			0
$344$	−17.4971	+	10.1019i	−0.943379	+	0.544660i
$345$	1.85447	−	1.94097i	0.0998414	−	0.104498i
$346$	−18.0338	+	10.4118i	−0.969504	+	0.559743i
$347$	−7.56294	+	4.36646i	−0.406000	+	0.234404i	−0.689070	−	0.724695i	$-0.741981\pi$
$347$	−7.56294	+	4.36646i	−0.406000	+	0.234404i	0.283070	+	0.959099i	$0.408647\pi$
$348$	1.34224	+	4.58845i	0.0719517	+	0.245967i
$349$	7.82927	−	4.52023i	0.419091	−	0.241963i	−0.275597	−	0.961273i	$-0.588876\pi$
$349$	7.82927	−	4.52023i	0.419091	−	0.241963i	0.694689	+	0.719311i	$0.255542\pi$
$350$		0			0
$351$	−19.3815	+	6.64211i	−1.03451	+	0.354529i
$352$	0.255158	+	0.441947i	0.0136000	+	0.0235559i
$353$	−1.21579			−0.0647101			−0.0323550	−	0.999476i	$-0.510301\pi$
$353$	−1.21579			−0.0647101			−0.0323550	+	0.999476i	$0.510301\pi$
$354$	−5.12782	+	5.36700i	−0.272540	+	0.285253i
$355$			1.16161i			0.0616518i
$356$	−1.49988	+	2.59787i	−0.0794936	+	0.137687i
$357$		0			0
$358$	−10.7939	−	18.6955i	−0.570473	−	0.988089i
$359$	−14.9882	+	8.65345i	−0.791048	+	0.456712i	−0.840331	−	0.542073i	$-0.817640\pi$
$359$	−14.9882	+	8.65345i	−0.791048	+	0.456712i	0.0492833	+	0.998785i	$0.484306\pi$
$360$	26.1599	−	1.19302i	1.37875	−	0.0628778i
$361$	10.5723	−	18.3117i	0.556435	−	0.963774i
$362$	3.91464	−	6.78035i	0.205749	−	0.356367i
$363$	−13.7445	−	13.1319i	−0.721397	−	0.689248i
$364$		0			0
$365$	−36.8968	−	21.3024i	−1.93127	−	1.11502i
$366$	−1.63667	+	6.71675i	−0.0855503	+	0.351090i
$367$		−	28.2090i		−	1.47250i	−0.676710	−	0.736250i	$-0.736595\pi$
$367$		−	28.2090i		−	1.47250i	0.676710	−	0.736250i	$-0.263405\pi$
$368$	−1.16372	−	0.671871i	−0.0606628	−	0.0350237i
$369$	−10.6319	−	5.50843i	−0.553475	−	0.286757i
$370$			8.28114i			0.430516i
$371$		0			0
$372$	−0.0373591	−	0.127712i	−0.00193698	−	0.00662155i
$373$	28.2527			1.46287			0.731435	−	0.681911i	$-0.238851\pi$
$373$	28.2527			1.46287			0.731435	+	0.681911i	$0.238851\pi$
$374$	0.387874	+	0.671818i	0.0200565	+	0.0347389i
$375$	−6.91595	−	6.60773i	−0.357138	−	0.341222i
$376$	−23.0875	−	13.3296i	−1.19065	−	0.687420i
$377$	−18.3347			−0.944287
$378$		0			0
$379$	14.6447			0.752250			0.376125	−	0.926569i	$-0.377256\pi$
$379$	14.6447			0.752250			0.376125	+	0.926569i	$0.377256\pi$
$380$	9.24338	+	5.33667i	0.474175	+	0.273765i
$381$	15.6412	+	14.9442i	0.801325	+	0.765613i
$382$	−8.42607	−	14.5944i	−0.431115	−	0.746714i
$383$	−24.7864			−1.26653			−0.633264	−	0.773936i	$-0.718285\pi$
$383$	−24.7864			−1.26653			−0.633264	+	0.773936i	$0.718285\pi$
$384$	−1.90458	−	6.51081i	−0.0971928	−	0.332253i
$385$		0			0
$386$		−	11.8643i		−	0.603878i
$387$	−16.5993	+	10.6203i	−0.843791	+	0.539858i
$388$	1.29669	+	0.748643i	0.0658293	+	0.0380066i
$389$			5.12348i			0.259771i	0.991529	+	0.129885i	$0.0414609\pi$
$389$			5.12348i			0.259771i	−0.991529	+	0.129885i	$0.958539\pi$
$390$	−5.44156	+	22.3316i	−0.275544	+	1.13081i
$391$	1.96035	+	1.13181i	0.0991391	+	0.0572380i
$392$		0			0
$393$	−12.5797	−	12.0190i	−0.634560	−	0.606280i
$394$	11.9195	−	20.6453i	0.600498	−	1.04009i
$395$	6.14056	−	10.6358i	0.308965	−	0.535144i
$396$	0.151457	+	0.236725i	0.00761099	+	0.0118959i
$397$	1.66358	−	0.960470i	0.0834929	−	0.0482046i	−0.457672	−	0.889121i	$-0.651317\pi$
$397$	1.66358	−	0.960470i	0.0834929	−	0.0482046i	0.541165	+	0.840916i	$0.317983\pi$
$398$	7.67163	+	13.2877i	0.384544	+	0.666050i
$399$		0			0
$400$	3.75729	−	6.50783i	0.187865	−	0.325391i
$401$			14.3889i			0.718549i	0.933232	+	0.359274i	$0.116976\pi$
$401$			14.3889i			0.718549i	−0.933232	+	0.359274i	$0.883024\pi$
$402$	1.88361	−	1.97146i	0.0939457	−	0.0983277i
$403$	0.510317			0.0254207
$404$	0.887835	+	1.53778i	0.0441714	+	0.0765072i
$405$	25.4357	−	2.32483i	1.26391	−	0.115522i
$406$		0			0
$407$	−0.336285	+	0.194154i	−0.0166690	+	0.00962386i
$408$	6.19961	+	21.1934i	0.306927	+	1.04923i
$409$	−8.42281	+	4.86291i	−0.416481	+	0.240455i	−0.693571	−	0.720389i	$-0.743963\pi$
$409$	−8.42281	+	4.86291i	−0.416481	+	0.240455i	0.277090	+	0.960844i	$0.410630\pi$
$410$	−11.6337	+	6.71675i	−0.574550	+	0.331717i
$411$	−9.62177	+	10.0706i	−0.474607	+	0.496745i
$412$	6.78380	−	3.91663i	0.334214	−	0.192958i
$413$		0			0
$414$	−1.72519	−	0.893828i	−0.0847885	−	0.0439292i
$415$	−9.15486	−	15.8567i	−0.449394	−	0.778374i
$416$	−12.7499			−0.625115
$417$	−9.19222	−	31.4236i	−0.450145	−	1.53882i
$418$		−	1.18583i		−	0.0580010i
$419$	−14.9512	+	25.8963i	−0.730416	+	1.26512i	0.226289	+	0.974060i	$0.427340\pi$
$419$	−14.9512	+	25.8963i	−0.730416	+	1.26512i	−0.956706	+	0.291058i	$0.905993\pi$
$420$		0			0
$421$	−12.5452	−	21.7290i	−0.611417	−	1.05901i	−0.991002	−	0.133848i	$-0.957266\pi$
$421$	−12.5452	−	21.7290i	−0.611417	−	1.05901i	0.379585	−	0.925157i	$-0.376067\pi$
$422$	9.25816	−	5.34520i	0.450680	−	0.260200i
$423$	−23.0875	−	11.9617i	−1.12255	−	0.581598i
$424$	−4.00214	+	6.93190i	−0.194361	+	0.336643i
$425$	−6.32939	+	10.9628i	−0.307021	+	0.531775i
$426$	0.806939	−	0.236051i	0.0390963	−	0.0114367i
$427$		0			0
$428$	10.0526	+	5.80388i	0.485912	+	0.280541i
$429$	−1.03443	+	0.302599i	−0.0499429	+	0.0146096i
$430$			22.1077i			1.06613i
$431$	5.53443	+	3.19531i	0.266584	+	0.153913i	0.627334	−	0.778750i	$-0.284146\pi$
$431$	5.53443	+	3.19531i	0.266584	+	0.153913i	−0.360750	+	0.932663i	$0.617479\pi$
$432$	−4.14487	−	12.0946i	−0.199420	−	0.581904i
$433$			33.1771i			1.59439i	0.603721	+	0.797196i	$0.293684\pi$
$433$			33.1771i			1.59439i	−0.603721	+	0.797196i	$0.706316\pi$
$434$		0			0
$435$	22.2075	+	5.41131i	1.06477	+	0.259452i
$436$	7.86400			0.376617
$437$	−1.73012	−	2.99665i	−0.0827627	−	0.143349i
$438$	−7.30039	+	29.9601i	−0.348826	+	1.43155i
$439$	−7.32931	−	4.23158i	−0.349809	−	0.201962i	0.314792	−	0.949161i	$-0.398065\pi$
$439$	−7.32931	−	4.23158i	−0.349809	−	0.201962i	−0.664601	+	0.747198i	$0.731399\pi$
$440$	1.37758			0.0656737
$441$		0			0
$442$	−19.3815			−0.921885
$443$	−16.1082	−	9.30006i	−0.765322	−	0.441859i	0.0658812	−	0.997827i	$-0.479014\pi$
$443$	−16.1082	−	9.30006i	−0.765322	−	0.441859i	−0.831203	+	0.555969i	$0.812348\pi$
$444$	−2.42792	+	0.710230i	−0.115224	+	0.0337060i
$445$	7.17111	+	12.4207i	0.339943	+	0.588799i
$446$	2.67618			0.126721
$447$	−23.2200	+	24.3031i	−1.09827	+	1.14950i
$448$		0			0
$449$		−	20.3100i		−	0.958489i	−0.877681	−	0.479245i	$-0.840911\pi$
$449$		−	20.3100i		−	0.958489i	0.877681	−	0.479245i	$-0.159089\pi$
$450$	4.99854	−	9.64776i	0.235633	−	0.454800i
$451$	−0.545515	−	0.314953i	−0.0256873	−	0.0148306i
$452$			5.98130i			0.281337i
$453$	2.23909	+	2.13930i	0.105202	+	0.100513i
$454$	−19.1458	−	11.0538i	−0.898558	−	0.518783i
$455$		0			0
$456$	7.99115	−	32.7949i	0.374220	−	1.53576i
$457$	−5.67830	+	9.83511i	−0.265620	+	0.460067i	−0.967726	−	0.252005i	$-0.918910\pi$
$457$	−5.67830	+	9.83511i	−0.265620	+	0.460067i	0.702106	+	0.712072i	$0.252243\pi$
$458$	8.48272	−	14.6925i	0.396372	−	0.686536i
$459$	6.98229	+	20.3742i	0.325905	+	0.950985i
$460$	0.796727	−	0.459990i	0.0371476	−	0.0214472i
$461$	−19.4984	−	33.7721i	−0.908129	−	1.57293i	−0.816661	−	0.577117i	$-0.804178\pi$
$461$	−19.4984	−	33.7721i	−0.908129	−	1.57293i	−0.0914676	−	0.995808i	$-0.529156\pi$
$462$		0			0
$463$	−5.03443	+	8.71990i	−0.233970	+	0.405248i	−0.958973	−	0.283498i	$-0.908505\pi$
$463$	−5.03443	+	8.71990i	−0.233970	+	0.405248i	0.725003	+	0.688746i	$0.241838\pi$
$464$		−	11.4414i		−	0.531154i
$465$	−0.618109	−	0.150615i	−0.0286641	−	0.00698459i
$466$	−20.2412			−0.937657
$467$	−1.79665	−	3.11188i	−0.0831389	−	0.144001i	0.821458	−	0.570269i	$-0.193161\pi$
$467$	−1.79665	−	3.11188i	−0.0831389	−	0.144001i	−0.904597	+	0.426269i	$0.859828\pi$
$468$	−7.01403	+	0.319875i	−0.324224	+	0.0147862i
$469$		0			0
$470$	−25.2630	+	14.5856i	−1.16530	+	0.672784i
$471$	7.38891	+	1.80046i	0.340463	+	0.0829607i
$472$	−9.62592	+	5.55753i	−0.443069	+	0.255806i
$473$	−0.897761	+	0.518322i	−0.0412791	+	0.0238325i
$474$	−8.63621	−	2.10439i	−0.396674	−	0.0966579i
$475$	16.7581	−	9.67530i	0.768915	−	0.443933i
$476$		0			0
$477$	−3.59144	+	6.93190i	−0.164441	+	0.317390i
$478$	−1.32529	−	2.29548i	−0.0606176	−	0.104993i
$479$	−1.62218			−0.0741193			−0.0370597	−	0.999313i	$-0.511799\pi$
$479$	−1.62218			−0.0741193			−0.0370597	+	0.999313i	$0.511799\pi$
$480$	15.4430	+	3.76300i	0.704873	+	0.171757i
$481$		−	9.70160i		−	0.442355i
$482$	−2.68033	+	4.64247i	−0.122086	+	0.211459i
$483$		0			0
$484$	−3.25729	−	5.64180i	−0.148059	−	0.256445i
$485$	6.19961	−	3.57935i	0.281510	−	0.162530i
$486$	−6.78380	−	17.1971i	−0.307719	−	0.780076i
$487$	−3.99786	+	6.92450i	−0.181161	+	0.313779i	−0.942276	−	0.334837i	$-0.891319\pi$
$487$	−3.99786	+	6.92450i	−0.181161	+	0.313779i	0.761115	+	0.648616i	$0.224652\pi$
$488$	−5.17598	+	8.96507i	−0.234306	+	0.405829i
$489$	−2.22888	+	9.14709i	−0.100793	+	0.413646i
$490$		0			0
$491$	9.30632	+	5.37300i	0.419988	+	0.242480i	0.695072	−	0.718940i	$-0.255372\pi$
$491$	9.30632	+	5.37300i	0.419988	+	0.242480i	−0.275084	+	0.961420i	$0.588706\pi$
$492$	−2.96703	−	2.83480i	−0.133764	−	0.127803i
$493$			19.2738i			0.868047i
$494$	25.6579	+	14.8136i	1.15440	+	0.666494i
$495$	1.34224	−	0.0612130i	0.0603293	−	0.00275132i
$496$			0.318453i			0.0142990i
$497$		0			0
$498$	−9.15486	+	9.58188i	−0.410239	+	0.429374i
$499$	16.9210			0.757488			0.378744	−	0.925501i	$-0.376356\pi$
$499$	16.9210			0.757488			0.378744	+	0.925501i	$0.376356\pi$
$500$	−1.63901	−	2.83884i	−0.0732986	−	0.126957i
$501$	17.4641	−	5.10871i	0.780239	−	0.228240i
$502$	21.7453	+	12.5546i	0.970538	+	0.560341i
$503$	33.9226			1.51253			0.756267	−	0.654263i	$-0.227021\pi$
$503$	33.9226			1.51253			0.756267	+	0.654263i	$0.227021\pi$
$504$		0			0
$505$	8.48968			0.377786
$506$	−0.0885182	−	0.0511060i	−0.00393511	−	0.00227194i
$507$	1.04428	−	4.28561i	0.0463779	−	0.190330i
$508$	3.70681	+	6.42038i	0.164463	+	0.284858i
$509$	10.1361			0.449275			0.224637	−	0.974442i	$-0.427880\pi$
$509$	10.1361			0.449275			0.224637	+	0.974442i	$0.427880\pi$
$510$	23.4754	+	5.72026i	1.03951	+	0.253297i
$511$		0			0
$512$		−	23.0923i		−	1.02055i
$513$	6.32889	−	32.3086i	0.279427	−	1.42646i
$514$	32.1469	+	18.5600i	1.41794	+	0.818648i
$515$		−	37.4517i		−	1.65032i
$516$	−6.48168	+	1.89606i	−0.285340	+	0.0834695i
$517$	−1.18460	−	0.683930i	−0.0520987	−	0.0300792i
$518$		0			0
$519$	−29.1898	+	8.53878i	−1.28129	+	0.374811i
$520$	−17.2089	+	29.8068i	−0.754662	+	1.30711i
$521$	−15.8493	+	27.4518i	−0.694370	+	1.20268i	0.276022	+	0.961151i	$0.410984\pi$
$521$	−15.8493	+	27.4518i	−0.694370	+	1.20268i	−0.970393	+	0.241533i	$0.922350\pi$
$522$	−0.753696	−	16.5266i	−0.0329884	−	0.723349i
$523$	7.01403	−	4.04955i	0.306702	−	0.177075i	−0.338748	−	0.940877i	$-0.610003\pi$
$523$	7.01403	−	4.04955i	0.306702	−	0.177075i	0.645450	+	0.763803i	$0.276670\pi$
$524$	−2.98125	−	5.16367i	−0.130236	−	0.225576i
$525$		0			0
$526$	−3.95904	+	6.85726i	−0.172622	+	0.298991i
$527$		−	0.536454i		−	0.0233683i
$528$	−0.188831	−	0.645517i	−0.00821781	−	0.0280925i
$529$	22.7017			0.987033
$530$	4.37926	+	7.58509i	0.190223	+	0.329475i
$531$	−9.13202	+	5.84268i	−0.396296	+	0.253551i
$532$		0			0
$533$	13.6293	−	7.86887i	0.590350	−	0.340839i
$534$	7.17111	−	7.50560i	0.310324	−	0.324799i
$535$	48.0628	−	27.7490i	2.07793	−	1.19970i
$536$	3.53590	−	2.04145i	0.152727	−	0.0881772i
$537$	−8.85209	−	30.2608i	−0.381996	−	1.30585i
$538$	−10.9472	+	6.32036i	−0.471967	+	0.272490i
$539$		0			0
$540$	8.58998	+	1.68268i	0.369654	+	0.0724110i
$541$	−0.608168	−	1.05338i	−0.0261472	−	0.0452883i	0.852656	−	0.522473i	$-0.174991\pi$
$541$	−0.608168	−	1.05338i	−0.0261472	−	0.0452883i	−0.878803	+	0.477185i	$0.841657\pi$
$542$	8.82920			0.379246
$543$	7.89922	−	8.26768i	0.338988	−	0.354800i
$544$			13.4029i			0.574645i
$545$	18.7994	−	32.5614i	0.805276	−	1.39478i
$546$		0			0
$547$	13.1278	+	22.7380i	0.561305	+	0.972209i	0.997383	+	0.0722999i	$0.0230339\pi$
$547$	13.1278	+	22.7380i	0.561305	+	0.972209i	−0.436078	+	0.899909i	$0.643633\pi$
$548$	−4.13375	+	2.38662i	−0.176585	+	0.101951i
$549$	−4.64483	+	8.96507i	−0.198237	+	0.382620i
$550$	0.285799	−	0.495019i	0.0121865	−	0.0211077i
$551$	14.7312	−	25.5152i	0.627571	−	1.08699i
$552$	−2.10363	−	2.00988i	−0.0895363	−	0.0855460i
$553$		0			0
$554$	27.2768	+	15.7482i	1.15888	+	0.669079i
$555$	−2.86333	+	11.7508i	−0.121541	+	0.498794i
$556$		−	11.2203i		−	0.475845i
$557$	−23.5708	−	13.6086i	−0.998727	−	0.576615i	−0.0908558	−	0.995864i	$-0.528960\pi$
$557$	−23.5708	−	13.6086i	−0.998727	−	0.576615i	−0.907871	+	0.419249i	$0.862294\pi$
$558$	0.0209779	+	0.459990i	0.000888065	+	0.0194729i
$559$		−	25.8998i		−	1.09545i
$560$		0			0
$561$	0.318097	+	1.08741i	0.0134301	+	0.0459106i
$562$	−28.8932			−1.21879
$563$	−4.68017	−	8.10630i	−0.197246	−	0.341640i	0.750389	−	0.660997i	$-0.229866\pi$
$563$	−4.68017	−	8.10630i	−0.197246	−	0.341640i	−0.947634	+	0.319357i	$0.896533\pi$
$564$	−6.44299	−	6.15585i	−0.271299	−	0.259208i
$565$	24.7660	+	14.2987i	1.04191	+	0.601549i
$566$	10.2609			0.431296
$567$		0			0
$568$	1.25895			0.0528244
$569$	30.2424	+	17.4605i	1.26783	+	0.731980i	0.974576	−	0.224055i	$-0.0719296\pi$
$569$	30.2424	+	17.4605i	1.26783	+	0.731980i	0.293251	+	0.956036i	$0.405263\pi$
$570$	−26.7054	−	25.5152i	−1.11856	−	1.06872i
$571$	0.735987	+	1.27477i	0.0308001	+	0.0533473i	0.881015	−	0.473089i	$-0.156861\pi$
$571$	0.735987	+	1.27477i	0.0308001	+	0.0533473i	−0.850214	+	0.526436i	$0.823528\pi$
$572$	−0.369360			−0.0154437
$573$	−6.91025	−	23.6227i	−0.288680	−	0.986851i
$574$		0			0
$575$		−	1.66791i		−	0.0695567i
$576$	−1.19669	−	26.2402i	−0.0498619	−	1.09334i
$577$	16.1251	+	9.30982i	0.671296	+	0.387573i	0.796567	−	0.604550i	$-0.206647\pi$
$577$	16.1251	+	9.30982i	0.671296	+	0.387573i	−0.125272	+	0.992122i	$0.539980\pi$
$578$			0.213421i			0.00887714i
$579$	4.10227	−	16.8353i	0.170484	−	0.699652i
$580$	6.78380	+	3.91663i	0.281682	+	0.162629i
$581$		0			0
$582$	−3.74630	−	3.57935i	−0.155289	−	0.148369i
$583$	−0.205346	+	0.355670i	−0.00850458	+	0.0147304i
$584$	−23.0875	+	39.9887i	−0.955367	+	1.65475i
$585$	−15.4430	+	29.8068i	−0.638489	+	1.23236i
$586$	−9.03845	+	5.21835i	−0.373375	+	0.215568i
$587$	9.28551	+	16.0830i	0.383254	+	0.663816i	0.991525	−	0.129914i	$-0.0414700\pi$
$587$	9.28551	+	16.0830i	0.383254	+	0.663816i	−0.608271	+	0.793729i	$0.708137\pi$
$588$		0			0
$589$	−0.410019	+	0.710174i	−0.0168945	+	0.0292622i
$590$			12.1624i			0.500719i
$591$	24.0521	−	25.1740i	0.989370	−	1.03552i
$592$	6.05408			0.248821
$593$	15.4614	+	26.7800i	0.634924	+	1.09972i	0.986531	+	0.163573i	$0.0523021\pi$
$593$	15.4614	+	26.7800i	0.634924	+	1.09972i	−0.351607	+	0.936148i	$0.614365\pi$
$594$	−0.315280	−	0.919981i	−0.0129361	−	0.0377473i
$595$		0			0
$596$	−9.97588	+	5.75958i	−0.408628	+	0.235922i
$597$	6.29153	+	21.5076i	0.257495	+	0.880247i
$598$	2.21156	−	1.27685i	0.0904375	−	0.0522141i
$599$	−11.8741	+	6.85553i	−0.485164	+	0.280109i	−0.722566	−	0.691302i	$-0.757037\pi$
$599$	−11.8741	+	6.85553i	−0.485164	+	0.280109i	0.237402	+	0.971411i	$0.423704\pi$
$600$	11.2398	−	11.7641i	0.458863	−	0.480266i
$601$	−17.1065	+	9.87644i	−0.697788	+	0.402868i	−0.806523	−	0.591203i	$-0.798653\pi$
$601$	−17.1065	+	9.87644i	−0.697788	+	0.402868i	0.108735	+	0.994071i	$0.465320\pi$
$602$		0			0
$603$	3.35447	−	2.14620i	0.136605	−	0.0873999i
$604$	0.530641	+	0.919097i	0.0215915	+	0.0373975i
$605$	−31.1470			−1.26631
$606$	−1.72519	−	5.89756i	−0.0700811	−	0.239572i
$607$			17.9231i			0.727477i	0.931501	+	0.363739i	$0.118500\pi$
$607$			17.9231i			0.727477i	−0.931501	+	0.363739i	$0.881500\pi$
$608$	10.2440	−	17.7432i	0.415450	−	0.719581i
$609$		0			0
$610$	5.66372	+	9.80984i	0.229317	+	0.397189i
$611$	29.5964	−	17.0875i	1.19734	−	0.691286i
$612$	0.336258	+	7.37327i	0.0135924	+	0.298047i
$613$	20.7163	−	35.8817i	0.836725	−	1.44925i	−0.0558932	−	0.998437i	$-0.517801\pi$
$613$	20.7163	−	35.8817i	0.836725	−	1.44925i	0.892618	−	0.450813i	$-0.148866\pi$
$614$	−6.62616	+	11.4768i	−0.267410	+	0.463168i
$615$	−18.8305	+	5.50843i	−0.759321	+	0.222121i
$616$		0			0
$617$	19.9686	+	11.5289i	0.803904	+	0.464134i	0.844835	−	0.535028i	$-0.179699\pi$
$617$	19.9686	+	11.5289i	0.803904	+	0.464134i	−0.0409302	+	0.999162i	$0.513032\pi$
$618$	−26.0167	+	7.61058i	−1.04655	+	0.306142i
$619$			1.93816i			0.0779014i	0.999241	+	0.0389507i	$0.0124015\pi$
$619$			1.93816i			0.0779014i	−0.999241	+	0.0389507i	$0.987598\pi$
$620$	−0.188816	−	0.109013i	−0.00758303	−	0.00437806i
$621$	−2.13897	−	1.86484i	−0.0858338	−	0.0748334i
$622$		−	19.4558i		−	0.780106i
$623$		0			0
$624$	16.3260	+	3.97816i	0.653562	+	0.159254i
$625$	−30.9430			−1.23772
$626$	−4.86485	−	8.42617i	−0.194439	−	0.336778i
$627$	0.410019	−	1.68268i	0.0163746	−	0.0671997i
$628$	2.25712	+	1.30315i	0.0900687	+	0.0520012i
$629$	−10.1985			−0.406640
$630$		0			0
$631$	23.5831			0.938827			0.469414	−	0.882978i	$-0.344465\pi$
$631$	23.5831			0.938827			0.469414	+	0.882978i	$0.344465\pi$
$632$	−11.5270	−	6.65514i	−0.458521	−	0.264727i
$633$	14.9854	−	4.38362i	0.595616	−	0.174233i
$634$	13.5862	+	23.5320i	0.539576	+	0.934574i
$635$	35.4454			1.40661
$636$	−1.84826	+	1.93447i	−0.0732884	+	0.0767069i
$637$		0			0
$638$		−	0.870293i		−	0.0344552i
$639$	1.22665	−	0.0559416i	0.0485257	−	0.00221302i
$640$	−9.62592	−	5.55753i	−0.380498	−	0.219681i
$641$			24.8368i			0.980996i	0.871442	+	0.490498i	$0.163185\pi$
$641$			24.8368i			0.980996i	−0.871442	+	0.490498i	$0.836815\pi$
$642$	−29.0434	−	27.7490i	−1.14625	−	1.09517i
$643$	37.9247	+	21.8959i	1.49561	+	0.863489i	0.999987	−	0.00505169i	$-0.00160801\pi$
$643$	37.9247	+	21.8959i	1.49561	+	0.863489i	0.495619	+	0.868540i	$0.334941\pi$
$644$		0			0
$645$	−7.64406	+	31.3705i	−0.300985	+	1.23521i
$646$	15.5723	−	26.9720i	0.612683	−	1.06120i
$647$	−14.6857	+	25.4363i	−0.577353	+	1.00001i	0.418428	+	0.908250i	$0.362581\pi$
$647$	−14.6857	+	25.4363i	−0.577353	+	1.00001i	−0.995782	+	0.0917553i	$0.970752\pi$
$648$	−2.51965	−	27.5672i	−0.0989812	−	1.08294i
$649$	−0.493898	+	0.285152i	−0.0193872	+	0.0111932i
$650$	7.14048	+	12.3677i	0.280073	+	0.485100i
$651$		0			0
$652$	−1.61323	+	2.79420i	−0.0631789	+	0.109429i
$653$			32.4258i			1.26892i	0.772955	+	0.634461i	$0.218778\pi$
$653$			32.4258i			1.26892i	−0.772955	+	0.634461i	$0.781222\pi$
$654$	−26.4398	−	6.44260i	−1.03388	−	0.251925i
$655$	−28.5074			−1.11388
$656$	4.91041	+	8.50508i	0.191719	+	0.332067i
$657$	−20.7183	+	39.9887i	−0.808298	+	1.56011i
$658$		0			0
$659$	−0.203016	+	0.117211i	−0.00790837	+	0.00456590i	−0.503949	−	0.863733i	$-0.668120\pi$
$659$	−0.203016	+	0.117211i	−0.00790837	+	0.00456590i	0.496041	+	0.868299i	$0.334787\pi$
$660$	0.447378	+	0.109013i	0.0174142	+	0.00424332i
$661$	3.05138	−	1.76171i	0.118685	−	0.0685227i	−0.439482	−	0.898251i	$-0.644838\pi$
$661$	3.05138	−	1.76171i	0.118685	−	0.0685227i	0.558167	+	0.829728i	$0.311505\pi$
$662$	19.7841	−	11.4224i	0.768933	−	0.443943i
$663$	−27.5021	−	6.70145i	−1.06809	−	0.260263i
$664$	−17.1855	+	9.92204i	−0.666926	+	0.385050i
$665$		0			0
$666$	8.74484	−	0.398809i	0.338856	−	0.0154535i
$667$	−1.26975	−	2.19927i	−0.0491648	−	0.0851560i
$668$	6.23582			0.241271
$669$	3.79746	+	0.925330i	0.146818	+	0.0357753i
$670$		−	4.46763i		−	0.172600i
$671$	−0.265576	+	0.459990i	−0.0102524	+	0.0177577i
$672$		0			0
$673$	9.16585	+	15.8757i	0.353318	+	0.611964i	0.986829	−	0.161770i	$-0.0517202\pi$
$673$	9.16585	+	15.8757i	0.353318	+	0.611964i	−0.633511	+	0.773734i	$0.718387\pi$
$674$	4.65925	−	2.69002i	0.179468	−	0.103616i
$675$	10.4287	−	11.9617i	0.401401	−	0.460407i
$676$	0.755832	−	1.30914i	0.0290705	−	0.0503515i
$677$	−16.9260	+	29.3166i	−0.650517	+	1.12673i	0.332480	+	0.943110i	$0.392115\pi$
$677$	−16.9260	+	29.3166i	−0.650517	+	1.12673i	−0.982998	+	0.183619i	$0.941219\pi$
$678$	4.90019	−	20.1099i	0.188191	−	0.772317i
$679$		0			0
$680$	31.3334	+	18.0903i	1.20158	+	0.693732i
$681$	−23.3456	−	22.3052i	−0.894606	−	0.854737i
$682$			0.0242232i			0.000927553i
$683$	24.2733	+	14.0142i	0.928794	+	0.536239i	0.886430	−	0.462863i	$-0.153178\pi$
$683$	24.2733	+	14.0142i	0.928794	+	0.536239i	0.0423639	+	0.999102i	$0.486511\pi$
$684$	5.19035	−	10.0180i	0.198458	−	0.383047i
$685$			22.8214i			0.871962i
$686$		0			0
$687$	17.1170	−	17.9154i	0.653055	−	0.683517i
$688$	16.1623			0.616180
$689$	−5.13043	−	8.88616i	−0.195454	−	0.338536i
$690$	−3.05555	+	0.893828i	−0.116323	+	0.0340274i
$691$	−42.7393	−	24.6756i	−1.62588	−	0.938703i	−0.985304	−	0.170809i	$-0.945362\pi$
$691$	−42.7393	−	24.6756i	−1.62588	−	0.938703i	−0.640577	−	0.767894i	$-0.721305\pi$
$692$	−10.4226			−0.396210
$693$		0			0
$694$	10.3566			0.393131
$695$	−46.4583	−	26.8227i	−1.76226	−	1.01744i
$696$	5.86477	−	24.0685i	0.222304	−	0.912313i
$697$	−8.27188	−	14.3273i	−0.313320	−	0.542686i
$698$	−10.7213			−0.405808
$699$	−28.7220	−	6.99871i	−1.08637	−	0.264716i
$700$		0			0
$701$			26.3889i			0.996696i	0.866977	+	0.498348i	$0.166060\pi$
$701$			26.3889i			0.996696i	−0.866977	+	0.498348i	$0.833940\pi$
$702$	23.8442	+	4.67080i	0.899940	+	0.176288i
$703$	13.5011	+	7.79485i	0.509202	+	0.293988i
$704$		−	1.38181i		−	0.0520791i
$705$	−40.8911	+	11.9617i	−1.54005	+	0.450504i
$706$	1.24867	+	0.720920i	0.0469943	+	0.0271322i
$707$		0			0
$708$	−3.56586	+	1.04311i	−0.134013	+	0.0392024i
$709$	5.35661	−	9.27792i	0.201172	−	0.348440i	−0.747735	−	0.663998i	$-0.768858\pi$
$709$	5.35661	−	9.27792i	0.201172	−	0.348440i	0.948906	+	0.315558i	$0.102192\pi$
$710$	0.688791	−	1.19302i	0.0258499	−	0.0447733i
$711$	−11.5270	−	5.97220i	−0.432298	−	0.223975i
$712$	13.4616	−	7.77204i	0.504494	−	0.291270i
$713$	0.0353413	+	0.0612130i	0.00132354	+	0.00229244i
$714$		0			0
$715$	−0.882977	+	1.52936i	−0.0330215	+	0.0571949i
$716$		−	10.8051i		−	0.403805i
$717$	−1.08688	−	3.71549i	−0.0405902	−	0.138758i
$718$	20.5247			0.765975
$719$	8.78970	+	15.2242i	0.327801	+	0.567767i	0.982075	−	0.188490i	$-0.0603592\pi$
$719$	8.78970	+	15.2242i	0.327801	+	0.567767i	−0.654275	+	0.756257i	$0.727026\pi$
$720$	−18.6003	−	9.63688i	−0.693192	−	0.359145i
$721$		0			0
$722$	−21.7163	+	12.5379i	−0.808198	+	0.466614i
$723$	−5.40856	+	5.66084i	−0.201146	+	0.210529i
$724$	3.39370	−	1.95935i	0.126126	−	0.0728188i
$725$	12.2989	−	7.10079i	0.456771	−	0.263717i
$726$	6.32939	+	21.6370i	0.234906	+	0.803025i
$727$	43.4695	−	25.0971i	1.61220	−	0.930802i	0.623336	−	0.781954i	$-0.285777\pi$
$727$	43.4695	−	25.0971i	1.61220	−	0.930802i	0.988860	−	0.148847i	$-0.0475563\pi$
$728$		0			0
$729$	−3.67996	−	26.7480i	−0.136295	−	0.990668i
$730$	25.2630	+	43.7569i	0.935027	+	1.61951i
$731$	−27.2263			−1.00700
$732$	−2.39037	+	2.50187i	−0.0883506	+	0.0924716i
$733$		−	39.9084i		−	1.47405i	−0.675865	−	0.737025i	$-0.736230\pi$
$733$		−	39.9084i		−	1.47405i	0.675865	−	0.737025i	$-0.263770\pi$
$734$	−16.7269	+	28.9719i	−0.617402	+	1.06937i
$735$		0			0
$736$	−0.882977	−	1.52936i	−0.0325470	−	0.0563730i
$737$	0.181424	−	0.104745i	0.00668284	−	0.00385834i
$738$	7.65312	+	11.9617i	0.281715	+	0.440317i
$739$	−15.1716	+	26.2780i	−0.558096	+	0.966650i	0.439560	+	0.898213i	$0.355135\pi$
$739$	−15.1716	+	26.2780i	−0.558096	+	0.966650i	−0.997655	+	0.0684369i	$0.978199\pi$
$740$	−2.07244	+	3.58956i	−0.0761843	+	0.131955i
$741$	31.2861	+	29.8918i	1.14932	+	1.09810i
$742$		0			0
$743$	−39.5861	−	22.8550i	−1.45227	−	0.838470i	−0.453662	−	0.891174i	$-0.649883\pi$
$743$	−39.5861	−	22.8550i	−1.45227	−	0.838470i	−0.998610	+	0.0527041i	$0.983216\pi$
$744$	−0.163236	+	0.669906i	−0.00598453	+	0.0245599i
$745$			55.0744i			2.01777i
$746$	−29.0167	−	16.7528i	−1.06238	−	0.613364i
$747$	−16.3037	+	10.4311i	−0.596521	+	0.381655i
$748$			0.388278i			0.0141968i
$749$		0			0
$750$	3.18483	+	10.8873i	0.116293	+	0.397549i
$751$	12.1551			0.443544			0.221772	−	0.975099i	$-0.428816\pi$
$751$	12.1551			0.443544			0.221772	+	0.975099i	$0.428816\pi$
$752$	10.6631	+	18.4690i	0.388843	+	0.673496i
$753$	26.5153	+	25.3336i	0.966270	+	0.923207i
$754$	18.8305	+	10.8718i	0.685768	+	0.395928i
$755$	5.07411			0.184666
$756$		0			0
$757$	−9.71614			−0.353139			−0.176570	−	0.984288i	$-0.556500\pi$
$757$	−9.71614			−0.353139			−0.176570	+	0.984288i	$0.556500\pi$
$758$	−15.0408	−	8.68379i	−0.546305	−	0.315409i
$759$	−0.107935	−	0.103125i	−0.00391781	−	0.00374321i
$760$	−27.6534	−	47.8971i	−1.00309	−	1.73741i
$761$	38.8349			1.40776			0.703882	−	0.710317i	$-0.251448\pi$
$761$	38.8349			1.40776			0.703882	+	0.710317i	$0.251448\pi$
$762$	−7.20287	−	24.6230i	−0.260932	−	0.891996i
$763$		0			0
$764$		−	8.43483i		−	0.305161i
$765$	31.3334	+	16.2339i	1.13286	+	0.586939i
$766$	25.4567	+	14.6974i	0.919788	+	0.531040i
$767$		−	14.2486i		−	0.514489i
$768$	5.27610	−	21.6526i	0.190385	−	0.781322i
$769$	−9.42879	−	5.44371i	−0.340011	−	0.196305i	0.320266	−	0.947328i	$-0.396228\pi$
$769$	−9.42879	−	5.44371i	−0.340011	−	0.196305i	−0.660277	+	0.751022i	$0.729561\pi$
$770$		0			0
$771$	39.1986	+	37.4517i	1.41170	+	1.34879i
$772$	2.96916	−	5.14274i	0.106863	−	0.185091i
$773$	18.6668	−	32.3319i	0.671400	−	1.16290i	−0.306108	−	0.951997i	$-0.599027\pi$
$773$	18.6668	−	32.3319i	0.671400	−	1.16290i	0.977507	−	0.210901i	$-0.0676398\pi$
$774$	23.3456	−	1.06468i	0.839141	−	0.0382691i
$775$	−0.342320	+	0.197639i	−0.0122965	+	0.00709939i
$776$	−3.87930	−	6.71914i	−0.139259	−	0.241203i
$777$		0			0
$778$	3.03803	−	5.26203i	0.108919	−	0.188653i
$779$			25.2893i			0.906083i
$780$	−7.94742	+	8.31813i	−0.284563	+	0.297837i
$781$	0.0645958			0.00231142
$782$	−1.34224	−	2.32483i	−0.0479984	−	0.0831357i
$783$	4.64483	−	23.7116i	0.165993	−	0.847383i
$784$		0			0
$785$	10.7915	−	6.23049i	0.385166	−	0.222376i
$786$	5.79300	+	19.8033i	0.206629	+	0.706362i
$787$	15.4554	−	8.92315i	0.550924	−	0.318076i	−0.198571	−	0.980087i	$-0.563630\pi$
$787$	15.4554	−	8.92315i	0.550924	−	0.318076i	0.749495	+	0.662011i	$0.230297\pi$
$788$	10.3334	−	5.96597i	0.368111	−	0.212529i
$789$	−7.98883	+	8.36146i	−0.284410	+	0.297676i
$790$	−12.6132	+	7.28225i	−0.448759	+	0.259091i
$791$		0			0
$792$	−0.0663426	−	1.45472i	−0.00235738	−	0.0516913i
$793$	−6.63521	−	11.4925i	−0.235623	−	0.408111i
$794$	−2.27809			−0.0808465
$795$	3.59144	+	12.2773i	0.127375	+	0.435432i
$796$			7.67961i			0.272197i
$797$	5.74854	−	9.95676i	0.203624	−	0.352687i	−0.746070	−	0.665868i	$-0.768061\pi$
$797$	5.74854	−	9.95676i	0.203624	−	0.352687i	0.949693	+	0.313181i	$0.101395\pi$
$798$		0			0
$799$	−17.9626	−	31.1122i	−0.635473	−	1.10067i
$800$	8.55262	−	4.93786i	0.302381	−	0.174580i
$801$	12.7709	−	8.17082i	0.451237	−	0.288702i
$802$	8.53210	−	14.7780i	0.301279	−	0.521831i
$803$	−1.18460	+	2.05179i	−0.0418037	+	0.0724061i
$804$	1.30985	−	0.383166i	0.0461949	−	0.0135132i
$805$		0			0
$806$	−0.524117	−	0.302599i	−0.0184612	−	0.0106586i
$807$	−17.7193	+	5.18335i	−0.623748	+	0.182463i
$808$		−	9.20112i		−	0.323694i
$809$	11.4267	+	6.59723i	0.401743	+	0.231946i	0.687236	−	0.726434i	$-0.258824\pi$
$809$	11.4267	+	6.59723i	0.401743	+	0.231946i	−0.285493	+	0.958381i	$0.592157\pi$
$810$	−27.5021	−	12.6947i	−0.966325	−	0.446048i
$811$		−	46.5800i		−	1.63565i	−0.575469	−	0.817823i	$-0.695181\pi$
$811$		−	46.5800i		−	1.63565i	0.575469	−	0.817823i	$-0.304819\pi$
$812$		0			0
$813$	12.5285	+	3.05283i	0.439394	+	0.107067i
$814$	0.460505			0.0161407
$815$	7.71304	+	13.3594i	0.270176	+	0.467958i
$816$	4.18190	−	17.1621i	0.146396	−	0.600794i
$817$	36.0431	+	20.8095i	1.26099	+	0.728031i
$818$	11.5341			0.403280
$819$		0			0
$820$	−6.72373			−0.234803
$821$	−34.3623	−	19.8391i	−1.19925	−	0.692390i	−0.238865	−	0.971053i	$-0.576775\pi$
$821$	−34.3623	−	19.8391i	−1.19925	−	0.692390i	−0.960389	+	0.278663i	$0.910109\pi$
$822$	15.8534	−	4.63755i	0.552952	−	0.161753i
$823$	19.6156	+	33.9751i	0.683755	+	1.18430i	0.973826	+	0.227294i	$0.0729878\pi$
$823$	19.6156	+	33.9751i	0.683755	+	1.18430i	−0.290071	+	0.957005i	$0.593679\pi$
$824$	−40.5902			−1.41403
$825$	0.576705	−	0.603605i	0.0200783	−	0.0210148i
$826$		0			0
$827$		−	21.0827i		−	0.733118i	−0.930395	−	0.366559i	$-0.880536\pi$
$827$		−	21.0827i		−	0.733118i	0.930395	−	0.366559i	$-0.119464\pi$
$828$	−0.524117	−	0.819187i	−0.0182143	−	0.0284687i
$829$	−11.5407	−	6.66304i	−0.400826	−	0.231417i	0.286014	−	0.958225i	$-0.407669\pi$
$829$	−11.5407	−	6.66304i	−0.400826	−	0.231417i	−0.686840	+	0.726808i	$0.741003\pi$
$830$			21.7140i			0.753703i
$831$	33.2601	+	31.7779i	1.15378	+	1.10236i
$832$	29.8983	+	17.2618i	1.03654	+	0.598446i
$833$		0			0
$834$	−9.19222	+	37.7240i	−0.318301	+	1.30627i
$835$	14.9071	−	25.8198i	0.515881	−	0.893533i
$836$	0.296766	−	0.514014i	0.0102639	−	0.0177776i
$837$	−0.129281	+	0.659973i	−0.00446861	+	0.0228120i
$838$	30.7111	−	17.7311i	1.06090	−	0.612510i
$839$	8.39768	+	14.5452i	0.289920	+	0.502156i	0.973790	−	0.227447i	$-0.0730379\pi$
$839$	8.39768	+	14.5452i	0.289920	+	0.502156i	−0.683870	+	0.729604i	$0.739705\pi$
$840$		0			0
$841$	−3.68862	+	6.38888i	−0.127194	+	0.220306i
$842$			29.7554i			1.02544i
$843$	−40.9990	−	9.99025i	−1.41208	−	0.344082i
$844$	5.35076			0.184181
$845$	−3.61372	−	6.25915i	−0.124316	−	0.215321i
$846$	16.6190	+	25.9752i	0.571372	+	0.893046i
$847$		0			0
$848$	5.54523	−	3.20154i	0.190424	−	0.109941i
$849$	14.5600	+	3.54785i	0.499698	+	0.121762i
$850$	13.0011	−	7.50619i	0.445934	−	0.257460i
$851$	1.16372	−	0.671871i	0.0398916	−	0.0230315i
$852$	0.408852	+	0.0996252i	0.0140070	+	0.00341310i
$853$	−35.5011	+	20.4966i	−1.21554	+	0.701790i	−0.963960	−	0.266048i	$-0.914282\pi$
$853$	−35.5011	+	20.4966i	−1.21554	+	0.701790i	−0.251576	+	0.967838i	$0.580949\pi$
$854$		0			0
$855$	−29.0723	−	45.4395i	−0.994251	−	1.55400i
$856$	−30.0744	−	52.0904i	−1.02792	−	1.78041i
$857$	−41.7436			−1.42593			−0.712967	−	0.701198i	$-0.752649\pi$
$857$	−41.7436			−1.42593			−0.712967	+	0.701198i	$0.752649\pi$
$858$	1.24184	+	0.302599i	0.0423956	+	0.0103306i
$859$		−	27.7682i		−	0.947437i	−0.880676	−	0.473719i	$-0.842911\pi$
$859$		−	27.7682i		−	0.947437i	0.880676	−	0.473719i	$-0.157089\pi$
$860$	−5.53267	+	9.58286i	−0.188662	+	0.326773i
$861$		0			0
$862$	−3.78940	−	6.56343i	−0.129067	−	0.223551i
$863$	39.4985	−	22.8045i	1.34455	−	0.776274i	0.357075	−	0.934076i	$-0.383774\pi$
$863$	39.4985	−	22.8045i	1.34455	−	0.776274i	0.987471	+	0.157802i	$0.0504407\pi$
$864$	3.23000	−	16.4889i	0.109887	−	0.560965i
$865$	−24.9159	+	43.1557i	−0.847168	+	1.46734i
$866$	19.6728	−	34.0743i	0.668510	−	1.15789i
$867$	−0.0737935	+	0.302841i	−0.00250616	+	0.0102850i
$868$		0			0
$869$	−0.591443	−	0.341470i	−0.0200633	−	0.0115836i
$870$	−19.5993	−	18.7259i	−0.664479	−	0.634866i
$871$			5.23396i			0.177346i
$872$	−35.2901	−	20.3747i	−1.19507	−	0.689975i
$873$	−4.07834	−	6.37438i	−0.138031	−	0.215740i
$874$			4.10358i			0.138806i
$875$		0			0
$876$	−10.6623	+	11.1596i	−0.360244	+	0.377048i
$877$	17.6874			0.597259			0.298630	−	0.954369i	$-0.403470\pi$
$877$	17.6874			0.597259			0.298630	+	0.954369i	$0.403470\pi$
$878$	5.01834	+	8.69203i	0.169361	+	0.293342i
$879$	−14.6298	+	4.27959i	−0.493450	+	0.144347i
$880$	−0.954367	−	0.551004i	−0.0321717	−	0.0185743i
$881$	−11.6169			−0.391384			−0.195692	−	0.980665i	$-0.562695\pi$
$881$	−11.6169			−0.391384			−0.195692	+	0.980665i	$0.562695\pi$
$882$		0			0
$883$	−35.5480			−1.19629			−0.598143	−	0.801389i	$-0.704095\pi$
$883$	−35.5480			−1.19629			−0.598143	+	0.801389i	$0.704095\pi$
$884$	−8.40116	−	4.85041i	−0.282562	−	0.163137i
$885$	−4.20534	+	17.2583i	−0.141361	+	0.580132i
$886$	11.0292	+	19.1031i	0.370532	+	0.641781i
$887$	−24.5501			−0.824313			−0.412156	−	0.911113i	$-0.635224\pi$
$887$	−24.5501			−0.824313			−0.412156	+	0.911113i	$0.635224\pi$
$888$	12.7355	+	3.10327i	0.427376	+	0.104139i
$889$		0			0
$890$		−	17.0088i		−	0.570136i
$891$	−0.129281	−	1.41445i	−0.00433108	−	0.0473859i
$892$	1.16002	+	0.669741i	0.0388405	+	0.0224246i
$893$			54.9164i			1.83771i
$894$	38.2588	−	11.1917i	1.27956	−	0.374306i
$895$	−44.7392	−	25.8302i	−1.49547	−	0.863408i
$896$		0			0
$897$	3.57966	−	1.04715i	0.119521	−	0.0349632i
$898$	−12.0431	+	20.8593i	−0.401883	+	0.696082i
$899$	−0.300917	+	0.521203i	−0.0100361	+	0.0173831i
$900$	4.58113	−	2.93101i	0.152704	−	0.0977004i
$901$	−9.34128	+	5.39319i	−0.311203	+	0.179673i
$902$	0.373511	+	0.646940i	0.0124366	+	0.0215407i
$903$		0			0
$904$	15.4969	−	26.8414i	0.515419	−	0.892731i
$905$		−	18.7358i		−	0.622799i
$906$	−1.03111	−	3.52485i	−0.0342564	−	0.117105i
$907$	36.9004			1.22526			0.612628	−	0.790371i	$-0.290112\pi$
$907$	36.9004			1.22526			0.612628	+	0.790371i	$0.290112\pi$
$908$	−5.53267	−	9.58286i	−0.183608	−	0.318018i
$909$	−0.408852	−	8.96507i	−0.0135608	−	0.297352i
$910$		0			0
$911$	−34.4774	+	19.9056i	−1.14229	+	0.659500i	−0.946996	−	0.321245i	$-0.895899\pi$
$911$	−34.4774	+	19.9056i	−1.14229	+	0.659500i	−0.195292	+	0.980745i	$0.562565\pi$
$912$	−18.6534	+	19.5235i	−0.617676	+	0.646487i
$913$	−0.881773	+	0.509092i	−0.0291824	+	0.0168485i
$914$	11.6637	−	6.73405i	0.385801	−	0.222743i
$915$	4.64483	+	15.8783i	0.153553	+	0.524922i
$916$	7.35389	−	4.24577i	0.242979	−	0.140284i
$917$		0			0
$918$	4.91002	−	25.0654i	0.162055	−	0.827280i
$919$	28.4363	+	49.2531i	0.938026	+	1.62471i	0.769147	+	0.639072i	$0.220681\pi$
$919$	28.4363	+	49.2531i	0.938026	+	1.62471i	0.168879	+	0.985637i	$0.445985\pi$
$920$	−4.76713			−0.157168
$921$	−13.3707	+	13.9944i	−0.440580	+	0.461131i
$922$			46.2472i			1.52307i
$923$	−0.806939	+	1.39766i	−0.0265607	+	0.0460045i
$924$		0			0
$925$	3.75729	+	6.50783i	0.123539	+	0.213976i
$926$	10.3412	−	5.97047i	0.339831	−	0.196202i
$927$	−39.5488	+	1.80363i	−1.29895	+	0.0592389i
$928$	7.51819	−	13.0219i	0.246797	−	0.427464i
$929$	−22.8885	+	39.6440i	−0.750946	+	1.30068i	0.196419	+	0.980520i	$0.437069\pi$
$929$	−22.8885	+	39.6440i	−0.750946	+	1.30068i	−0.947365	+	0.320156i	$0.896265\pi$
$930$	0.545515	+	0.521203i	0.0178881	+	0.0170909i
$931$		0			0
$932$	−8.77383	−	5.06557i	−0.287396	−	0.165928i
$933$	6.72713	−	27.6075i	0.220236	−	0.903829i
$934$			4.26138i			0.139437i
$935$	1.60769	+	0.928200i	0.0525771	+	0.0303554i
$936$	32.3046	+	16.7371i	1.05591	+	0.547070i
$937$		−	24.0003i		−	0.784054i	−0.919954	−	0.392027i	$-0.871774\pi$
$937$		−	24.0003i		−	0.784054i	0.919954	−	0.392027i	$-0.128226\pi$
$938$		0			0
$939$	−3.98968	−	13.6387i	−0.130198	−	0.445083i
$940$	−14.6008			−0.476225
$941$	1.64316	+	2.84603i	0.0535654	+	0.0927780i	0.891565	−	0.452893i	$-0.149608\pi$
$941$	1.64316	+	2.84603i	0.0535654	+	0.0927780i	−0.837999	+	0.545671i	$0.816275\pi$
$942$	−6.52111	−	6.23049i	−0.212469	−	0.203000i
$943$	1.88776	+	1.08990i	0.0614738	+	0.0354919i
$944$	8.89158			0.289396
$945$		0			0
$946$	1.22938			0.0399707
$947$	25.9420	+	14.9776i	0.843002	+	0.486707i	0.858284	−	0.513176i	$-0.171531\pi$
$947$	25.9420	+	14.9776i	0.843002	+	0.486707i	−0.0152815	+	0.999883i	$0.504864\pi$
$948$	−3.21683	−	3.07347i	−0.104478	−	0.0998217i
$949$	−29.5964	−	51.2624i	−0.960739	−	1.66405i
$950$	−22.9484			−0.744544
$951$	11.1421	+	38.0892i	0.361307	+	1.23513i
$952$		0			0
$953$			16.0580i			0.520169i	0.965586	+	0.260084i	$0.0837504\pi$
$953$			16.0580i			0.520169i	−0.965586	+	0.260084i	$0.916250\pi$
$954$	7.79893	−	4.98976i	0.252500	−	0.161550i
$955$	−34.9250	−	20.1639i	−1.13015	−	0.652490i
$956$		−	1.32667i		−	0.0429076i
$957$	0.300917	−	1.23493i	0.00972726	−	0.0399197i
$958$	1.66605	+	0.961893i	0.0538275	+	0.0310773i
$959$		0			0
$960$	−31.1190	−	29.7321i	−1.00436	−	0.959600i
$961$	−15.4916	+	26.8323i	−0.499730	+	0.865557i
$962$	−5.75269	+	9.96395i	−0.185474	+	0.321251i
$963$	−31.6175	−	49.4177i	−1.01886	−	1.59246i
$964$	−2.32365	+	1.34156i	−0.0748397	+	0.0432087i
$965$	−14.1959	−	24.5881i	−0.456983	−	0.791518i
$966$		0			0
$967$	25.0275	−	43.3489i	0.804831	−	1.39401i	−0.111574	−	0.993756i	$-0.535589\pi$
$967$	25.0275	−	43.3489i	0.804831	−	1.39401i	0.916405	−	0.400252i	$-0.131077\pi$
$968$			33.7571i			1.08499i
$969$	31.4228	−	32.8885i	1.00945	−	1.05653i
$970$	−8.48968			−0.272587
$971$	0.520938	+	0.902292i	0.0167177	+	0.0289559i	0.874263	−	0.485452i	$-0.161345\pi$
$971$	0.520938	+	0.902292i	0.0167177	+	0.0289559i	−0.857546	+	0.514408i	$0.828012\pi$
$972$	1.36322	−	9.15202i	0.0437253	−	0.293551i
$973$		0			0
$974$	8.21195	−	4.74117i	0.263128	−	0.151917i
$975$	5.85594	+	20.0185i	0.187540	+	0.641105i
$976$	7.17167	−	4.14057i	0.229560	−	0.132536i
$977$	−21.1765	+	12.2262i	−0.677495	+	0.391152i	−0.798910	−	0.601450i	$-0.794590\pi$
$977$	−21.1765	+	12.2262i	−0.677495	+	0.391152i	0.121416	+	0.992602i	$0.461257\pi$
$978$	7.71304	−	8.07281i	0.246636	−	0.258140i
$979$	0.690703	−	0.398777i	0.0220750	−	0.0127450i
$980$		0			0
$981$	−35.2901	−	18.2839i	−1.12673	−	0.583760i
$982$	−6.37199	−	11.0366i	−0.203338	−	0.352192i
$983$	56.1576			1.79115			0.895575	−	0.444911i	$-0.146765\pi$
$983$	56.1576			1.79115			0.895575	+	0.444911i	$0.146765\pi$
$984$	5.97003	+	20.4085i	0.190318	+	0.650600i
$985$		−	57.0480i		−	1.81770i
$986$	11.4286	−	19.7950i	0.363962	−	0.630400i
$987$		0			0
$988$	7.41449	+	12.8423i	0.235886	+	0.408567i
$989$	3.10671	−	1.79366i	0.0987875	−	0.0570350i
$990$	−1.41484	−	0.733031i	−0.0449664	−	0.0232973i
$991$	−9.11390	+	15.7857i	−0.289513	+	0.501451i	−0.973693	−	0.227862i	$-0.926827\pi$
$991$	−9.11390	+	15.7857i	−0.289513	+	0.501451i	0.684181	+	0.729312i	$0.260160\pi$
$992$	−0.209256	+	0.362443i	−0.00664390	+	0.0115076i
$993$	32.0229	−	9.36753i	1.01622	−	0.297270i
$994$		0			0
$995$	31.7979	+	18.3586i	1.00806	+	0.582005i
$996$	−6.36625	+	1.86230i	−0.201722	+	0.0590091i
$997$		−	34.4328i		−	1.09050i	−0.838274	−	0.545249i	$-0.816435\pi$
$997$		−	34.4328i		−	1.09050i	0.838274	−	0.545249i	$-0.183565\pi$
$998$	−17.3786	−	10.0335i	−0.550110	−	0.317606i
$999$	12.5467	+	2.45776i	0.396960	+	0.0777599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.s.c.374.1		12
3.2	odd	2		1323.2.s.c.962.6		12
7.2	even	3		441.2.i.c.68.6		12
7.3	odd	6		63.2.o.a.41.6	yes	12
7.4	even	3		63.2.o.a.41.5	yes	12
7.5	odd	6		441.2.i.c.68.5		12
7.6	odd	2	inner	441.2.s.c.374.2		12
9.2	odd	6		441.2.i.c.227.1		12
9.7	even	3		1323.2.i.c.521.6		12
21.2	odd	6		1323.2.i.c.1097.1		12
21.5	even	6		1323.2.i.c.1097.2		12
21.11	odd	6		189.2.o.a.125.1		12
21.17	even	6		189.2.o.a.125.2		12
21.20	even	2		1323.2.s.c.962.5		12
28.3	even	6		1008.2.cc.a.545.3		12
28.11	odd	6		1008.2.cc.a.545.4		12
63.2	odd	6	inner	441.2.s.c.362.2		12
63.4	even	3		567.2.c.c.566.9		12
63.11	odd	6		63.2.o.a.20.6	yes	12
63.16	even	3		1323.2.s.c.656.5		12
63.20	even	6		441.2.i.c.227.2		12
63.25	even	3		189.2.o.a.62.2		12
63.31	odd	6		567.2.c.c.566.10		12
63.32	odd	6		567.2.c.c.566.4		12
63.34	odd	6		1323.2.i.c.521.5		12
63.38	even	6		63.2.o.a.20.5	✓	12
63.47	even	6	inner	441.2.s.c.362.1		12
63.52	odd	6		189.2.o.a.62.1		12
63.59	even	6		567.2.c.c.566.3		12
63.61	odd	6		1323.2.s.c.656.6		12
84.11	even	6		3024.2.cc.a.881.1		12
84.59	odd	6		3024.2.cc.a.881.6		12
252.11	even	6		1008.2.cc.a.209.3		12
252.115	even	6		3024.2.cc.a.2897.1		12
252.151	odd	6		3024.2.cc.a.2897.6		12
252.227	odd	6		1008.2.cc.a.209.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.5	✓	12	63.38	even	6
63.2.o.a.20.6	yes	12	63.11	odd	6
63.2.o.a.41.5	yes	12	7.4	even	3
63.2.o.a.41.6	yes	12	7.3	odd	6
189.2.o.a.62.1		12	63.52	odd	6
189.2.o.a.62.2		12	63.25	even	3
189.2.o.a.125.1		12	21.11	odd	6
189.2.o.a.125.2		12	21.17	even	6
441.2.i.c.68.5		12	7.5	odd	6
441.2.i.c.68.6		12	7.2	even	3
441.2.i.c.227.1		12	9.2	odd	6
441.2.i.c.227.2		12	63.20	even	6
441.2.s.c.362.1		12	63.47	even	6	inner
441.2.s.c.362.2		12	63.2	odd	6	inner
441.2.s.c.374.1		12	1.1	even	1	trivial
441.2.s.c.374.2		12	7.6	odd	2	inner
567.2.c.c.566.3		12	63.59	even	6
567.2.c.c.566.4		12	63.32	odd	6
567.2.c.c.566.9		12	63.4	even	3
567.2.c.c.566.10		12	63.31	odd	6
1008.2.cc.a.209.3		12	252.11	even	6
1008.2.cc.a.209.4		12	252.227	odd	6
1008.2.cc.a.545.3		12	28.3	even	6
1008.2.cc.a.545.4		12	28.11	odd	6
1323.2.i.c.521.5		12	63.34	odd	6
1323.2.i.c.521.6		12	9.7	even	3
1323.2.i.c.1097.1		12	21.2	odd	6
1323.2.i.c.1097.2		12	21.5	even	6
1323.2.s.c.656.5		12	63.16	even	3
1323.2.s.c.656.6		12	63.61	odd	6
1323.2.s.c.962.5		12	21.20	even	2
1323.2.s.c.962.6		12	3.2	odd	2
3024.2.cc.a.881.1		12	84.11	even	6
3024.2.cc.a.881.6		12	84.59	odd	6
3024.2.cc.a.2897.1		12	252.115	even	6
3024.2.cc.a.2897.6		12	252.151	odd	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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.02704 - 0.592963i) q^{2} +(-1.25233 - 1.19652i) q^{3} +(-0.296790 - 0.514055i) q^{4} -2.83797 q^{5} +(0.576705 + 1.97146i) q^{6} +3.07579i q^{8} +(0.136673 + 2.99689i) q^{9} +O(q^{10})\)	\(q+(-1.02704 - 0.592963i) q^{2} +(-1.25233 - 1.19652i) q^{3} +(-0.296790 - 0.514055i) q^{4} -2.83797 q^{5} +(0.576705 + 1.97146i) q^{6} +3.07579i q^{8} +(0.136673 + 2.99689i) q^{9} +(2.91472 + 1.68281i) q^{10} +0.157816i q^{11} +(-0.243398 + 0.998883i) q^{12} +(-3.41468 - 1.97146i) q^{13} +(3.55408 + 3.39569i) q^{15} +(1.23025 - 2.13086i) q^{16} +(-2.07244 + 3.58956i) q^{17} +(1.63667 - 3.15897i) q^{18} +(5.48711 - 3.16799i) q^{19} +(0.842281 + 1.45887i) q^{20} +(0.0935793 - 0.162084i) q^{22} -0.546125i q^{23} +(3.68025 - 3.85192i) q^{24} +3.05408 q^{25} +(2.33801 + 4.04955i) q^{26} +(3.41468 - 3.91663i) q^{27} +(4.02704 - 2.32501i) q^{29} +(-1.63667 - 5.59496i) q^{30} +(-0.112086 + 0.0647129i) q^{31} +(2.80039 - 1.61680i) q^{32} +(0.188831 - 0.197639i) q^{33} +(4.25696 - 2.45776i) q^{34} +(1.50000 - 0.959702i) q^{36} +(1.23025 + 2.13086i) q^{37} -7.51399 q^{38} +(1.91741 + 6.55466i) q^{39} -8.72902i q^{40} +(-1.99569 + 3.45664i) q^{41} +(3.28434 + 5.68864i) q^{43} +(0.0811263 - 0.0468383i) q^{44} +(-0.387874 - 8.50508i) q^{45} +(-0.323832 + 0.560893i) q^{46} +(-4.33370 + 7.50619i) q^{47} +(-4.09030 + 1.19652i) q^{48} +(-3.13667 - 1.81096i) q^{50} +(6.89037 - 2.01561i) q^{51} +2.34044i q^{52} +(2.25370 + 1.30117i) q^{53} +(-5.82943 + 1.99777i) q^{54} -0.447879i q^{55} +(-10.6623 - 2.59808i) q^{57} -5.51459 q^{58} +(1.80686 + 3.12957i) q^{59} +(0.690757 - 2.83480i) q^{60} +(2.91472 + 1.68281i) q^{61} +0.153489 q^{62} -8.75583 q^{64} +(9.69076 + 5.59496i) q^{65} +(-0.311130 + 0.0910136i) q^{66} +(-0.663715 - 1.14959i) q^{67} +2.46031 q^{68} +(-0.653450 + 0.683930i) q^{69} -0.409310i q^{71} +(-9.21780 + 0.420378i) q^{72} +(13.0011 + 7.50619i) q^{73} -2.91798i q^{74} +(-3.82473 - 3.65428i) q^{75} +(-3.25704 - 1.88045i) q^{76} +(1.91741 - 7.86887i) q^{78} +(-2.16372 + 3.74766i) q^{79} +(-3.49142 + 6.04732i) q^{80} +(-8.96264 + 0.819187i) q^{81} +(4.09932 - 2.36674i) q^{82} +(3.22585 + 5.58733i) q^{83} +(5.88151 - 10.1871i) q^{85} -7.78996i q^{86} +(-7.82512 - 1.90675i) q^{87} -0.485411 q^{88} +(-2.52684 - 4.37662i) q^{89} +(-4.64483 + 8.96507i) q^{90} +(-0.280738 + 0.162084i) q^{92} +(0.217799 + 0.0530713i) q^{93} +(8.90179 - 5.13945i) q^{94} +(-15.5723 + 8.99066i) q^{95} +(-5.44156 - 1.32595i) q^{96} +(-2.18452 + 1.26123i) q^{97} +(-0.472958 + 0.0215693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 2 q^{4}+O(q^{10}) \) 12 * q + 6 * q^2 + 2 * q^4	\( 12 q + 6 q^{2} + 2 q^{4} + 6 q^{15} + 2 q^{16} + 18 q^{18} - 10 q^{22} + 30 q^{29} - 18 q^{30} + 12 q^{32} + 18 q^{36} + 2 q^{37} - 12 q^{39} - 10 q^{43} - 54 q^{44} + 20 q^{46} - 36 q^{50} + 66 q^{51} + 12 q^{53} - 18 q^{57} - 4 q^{58} - 30 q^{60} + 16 q^{64} + 78 q^{65} + 12 q^{67} - 54 q^{72} - 12 q^{78} - 6 q^{79} + 24 q^{81} - 6 q^{85} - 68 q^{88} + 30 q^{92} - 54 q^{93} - 72 q^{95} - 24 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 2 * q^4 + 6 * q^15 + 2 * q^16 + 18 * q^18 - 10 * q^22 + 30 * q^29 - 18 * q^30 + 12 * q^32 + 18 * q^36 + 2 * q^37 - 12 * q^39 - 10 * q^43 - 54 * q^44 + 20 * q^46 - 36 * q^50 + 66 * q^51 + 12 * q^53 - 18 * q^57 - 4 * q^58 - 30 * q^60 + 16 * q^64 + 78 * q^65 + 12 * q^67 - 54 * q^72 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 6 * q^85 - 68 * q^88 + 30 * q^92 - 54 * q^93 - 72 * q^95 - 24 * q^99

Introduction

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