LMFDB - Embedded newform 441.2.s.c.374.2

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			374.2
Root			$1.82904 + 1.05600i$ of defining polynomial
Character	$\chi$	$=$	441.374
Dual form			441.2.s.c.362.2

$q$-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	$-0.281169\pi$
$5$	2.83797			1.26918			0.634590	+	0.772849i	$0.281169\pi$
$6$	−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	0.892167	−	0.451706i	$-0.149184\pi$
$13$	3.41468	+	1.97146i	0.947061	+	0.546786i	0.0548943	+	0.998492i	$0.482518\pi$
$14$		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	$-0.665696\pi$
$17$	2.07244	−	3.58956i	0.502640	−	0.870597i	0.999995	−	0.00305055i	$-0.000971021\pi$
$18$	1.63667	−	3.15897i	0.385768	−	0.744576i
$19$	−5.48711	+	3.16799i	−1.25883	+	0.726786i	−0.972847	−	0.231449i	$-0.925653\pi$
$19$	−5.48711	+	3.16799i	−1.25883	+	0.726786i	−0.285983	+	0.958235i	$0.592320\pi$
$20$	−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	−0.489901	−	0.871778i	$-0.662967\pi$
$31$	0.112086	−	0.0647129i	0.0201313	−	0.0116228i	0.510032	+	0.860156i	$0.329634\pi$
$32$	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	−0.667050	−	0.745013i	$-0.732443\pi$
$41$	1.99569	−	3.45664i	0.311675	−	0.539836i	0.978725	+	0.205176i	$0.0657768\pi$
$42$		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	$-0.615512\pi$
$47$	4.33370	−	7.50619i	0.632135	−	1.09489i	0.987114	−	0.160016i	$-0.0511547\pi$
$48$	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	0.724107	−	0.689687i	$-0.242252\pi$
$59$	−1.80686	−	3.12957i	−0.235233	−	0.407436i	−0.959340	+	0.282252i	$0.908919\pi$
$60$	0.690757	−	2.83480i	0.0891764	−	0.365971i
$61$	−2.91472	−	1.68281i	−0.373191	−	0.215462i	0.301660	−	0.953415i	$-0.402459\pi$
$61$	−2.91472	−	1.68281i	−0.373191	−	0.215462i	−0.674852	+	0.737953i	$0.735792\pi$
$62$	−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	$-0.991856\pi$
$73$	−13.0011	−	7.50619i	−1.52166	−	0.878533i	−0.521992	−	0.852950i	$-0.674811\pi$
$74$		−	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	0.632878	−	0.774252i	$-0.281874\pi$
$83$	−3.22585	−	5.58733i	−0.354083	−	0.613289i	−0.986961	+	0.160963i	$0.948540\pi$
$84$		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	0.968305	−	0.249771i	$-0.0803552\pi$
$89$	2.52684	+	4.37662i	0.267845	+	0.463921i	−0.700460	+	0.713691i	$0.747022\pi$
$90$	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	−0.384981	−	0.922925i	$-0.625792\pi$
$97$	2.18452	−	1.26123i	0.221805	−	0.128059i	0.606786	+	0.794866i	$0.292459\pi$
$98$		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	$-0.452449\pi$
$101$	2.99146			0.297662			0.148831	+	0.988863i	$0.452449\pi$
$102$	−8.27188	−	2.01561i	−0.819039	−	0.199576i
$103$		−	13.1966i		−	1.30030i	−0.759804	−	0.650152i	$-0.774705\pi$
$103$		−	13.1966i		−	1.30030i	0.759804	−	0.650152i	$-0.225295\pi$
$104$	−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	$-0.644602\pi$
$131$	−10.0450			−0.877635			−0.438817	+	0.898576i	$0.644602\pi$
$132$	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	−0.395358	−	0.918527i	$-0.629379\pi$
$139$	−16.3702	−	9.45136i	−1.38850	−	0.801654i	−0.993147	+	0.116873i	$0.962713\pi$
$140$		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	−0.340527	−	0.940235i	$-0.610605\pi$
$157$	3.80255	−	2.19540i	0.303477	−	0.175212i	0.644004	+	0.765022i	$0.277272\pi$
$158$	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	−0.588023	−	0.808844i	$-0.700093\pi$
$167$	5.25273	−	9.09799i	0.406468	−	0.704024i	0.994491	+	0.104821i	$0.0334268\pi$
$168$		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	$0.399299\pi$
$173$	−8.77949	+	15.2065i	−0.667492	+	1.15613i	−0.978603	+	0.205757i	$0.934034\pi$
$174$	−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	$-0.921096\pi$
$181$		−	6.60182i		−	0.490710i	0.969433	−	0.245355i	$-0.0789045\pi$
$182$		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	0.841461	−	0.540318i	$-0.181696\pi$
$199$	11.2045	+	6.46890i	0.794263	+	0.458568i	−0.0471981	+	0.998886i	$0.515029\pi$
$200$			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	−0.433136	−	0.901328i	$-0.642593\pi$
$223$	1.95429	−	1.12831i	0.130869	−	0.0755571i	0.564005	+	0.825771i	$0.309260\pi$
$224$		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	$-0.712319\pi$
$227$	−18.6417			−1.23729			−0.618647	+	0.785669i	$0.712319\pi$
$228$	1.82889	+	6.25206i	0.121121	+	0.414053i
$229$		−	14.3057i		−	0.945344i	−0.881238	−	0.472672i	$-0.843289\pi$
$229$		−	14.3057i		−	0.945344i	0.881238	−	0.472672i	$-0.156711\pi$
$230$	−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	$0.0465070\pi$
$241$			4.52023i			0.291174i	−0.989345	+	0.145587i	$0.953493\pi$
$242$	−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	$-0.267063\pi$
$251$	21.1727			1.33641			0.668205	+	0.743978i	$0.267063\pi$
$252$		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	$-0.0695331\pi$
$257$	31.3005			1.95247			0.976236	+	0.216712i	$0.0695331\pi$
$258$	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	−0.981501	−	0.191457i	$-0.938679\pi$
$269$	−5.32947	+	9.23092i	−0.324944	+	0.562819i	0.656557	+	0.754276i	$0.272012\pi$
$270$	16.5438	−	5.66960i	1.00682	−	0.345041i
$271$	6.44754	−	3.72249i	0.391660	−	0.226125i	−0.291219	−	0.956656i	$-0.594061\pi$
$271$	6.44754	−	3.72249i	0.391660	−	0.226125i	0.682879	+	0.730531i	$0.260727\pi$
$272$	−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	−0.260478	−	0.965480i	$-0.583880\pi$
$283$	7.49302	−	4.32610i	0.445414	−	0.257160i	0.705891	+	0.708320i	$0.250547\pi$
$284$	−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	−0.965454	−	0.260573i	$-0.916089\pi$
$293$	−4.40023	+	7.62143i	−0.257064	+	0.445249i	0.708390	+	0.705821i	$0.249422\pi$
$294$		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	$0.103309\pi$
$307$			11.1747i			0.637771i	−0.947793	+	0.318886i	$0.896691\pi$
$308$		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	0.534070	−	0.845440i	$-0.320662\pi$
$311$	−8.20279	−	14.2076i	−0.465137	−	0.805641i	−0.999208	+	0.0397985i	$0.987328\pi$
$312$	−20.1608	+	5.89756i	−1.14138	+	0.333884i
$313$	−7.10514	−	4.10216i	−0.401606	−	0.231868i	0.285570	−	0.958358i	$-0.407817\pi$
$313$	−7.10514	−	4.10216i	−0.401606	−	0.231868i	−0.687177	+	0.726490i	$0.741150\pi$
$314$	−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	−0.694689	−	0.719311i	$-0.744458\pi$
$349$	−7.82927	+	4.52023i	−0.419091	+	0.241963i	0.275597	+	0.961273i	$0.411124\pi$
$350$		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	$-0.489699\pi$
$353$	1.21579			0.0647101			0.0323550	+	0.999476i	$0.489699\pi$
$354$	−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	$0.263405\pi$
$367$			28.2090i			1.47250i	−0.676710	+	0.736250i	$0.736595\pi$
$368$	−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	$-0.281715\pi$
$383$	24.7864			1.26653			0.633264	+	0.773936i	$0.281715\pi$
$384$	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	−0.541165	−	0.840916i	$-0.682017\pi$
$397$	−1.66358	+	0.960470i	−0.0834929	+	0.0482046i	0.457672	+	0.889121i	$0.348683\pi$
$398$	−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	−0.277090	−	0.960844i	$-0.589370\pi$
$409$	8.42281	−	4.86291i	0.416481	−	0.240455i	0.693571	+	0.720389i	$0.256037\pi$
$410$	−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	$-0.572660\pi$
$419$	14.9512	−	25.8963i	0.730416	−	1.26512i	0.956706	−	0.291058i	$-0.0940072\pi$
$420$		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	$-0.706316\pi$
$433$		−	33.1771i		−	1.59439i	0.603721	−	0.797196i	$-0.293684\pi$
$434$		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	0.664601	−	0.747198i	$-0.268601\pi$
$439$	7.32931	+	4.23158i	0.349809	+	0.201962i	−0.314792	+	0.949161i	$0.601935\pi$
$440$	−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	$0.195822\pi$
$461$	19.4984	+	33.7721i	0.908129	+	1.57293i	0.0914676	+	0.995808i	$0.470844\pi$
$462$		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	0.904597	−	0.426269i	$-0.140172\pi$
$467$	1.79665	+	3.11188i	0.0831389	+	0.144001i	−0.821458	+	0.570269i	$0.806839\pi$
$468$	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	$-0.488201\pi$
$479$	1.62218			0.0741193			0.0370597	+	0.999313i	$0.488201\pi$
$480$	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	$-0.772979\pi$
$503$	−33.9226			−1.51253			−0.756267	+	0.654263i	$0.772979\pi$
$504$		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	$-0.572120\pi$
$509$	−10.1361			−0.449275			−0.224637	+	0.974442i	$0.572120\pi$
$510$	−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	$-0.589016\pi$
$521$	15.8493	−	27.4518i	0.694370	−	1.20268i	0.970393	−	0.241533i	$-0.0776502\pi$
$522$	−0.753696	−	16.5266i	−0.0329884	−	0.723349i
$523$	−7.01403	+	4.04955i	−0.306702	+	0.177075i	−0.645450	−	0.763803i	$-0.723330\pi$
$523$	−7.01403	+	4.04955i	−0.306702	+	0.177075i	0.338748	+	0.940877i	$0.389997\pi$
$524$	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	0.947634	−	0.319357i	$-0.103467\pi$
$563$	4.68017	+	8.10630i	0.197246	+	0.341640i	−0.750389	+	0.660997i	$0.770134\pi$
$564$	−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	0.125272	−	0.992122i	$-0.460020\pi$
$577$	−16.1251	−	9.30982i	−0.671296	−	0.387573i	−0.796567	+	0.604550i	$0.793353\pi$
$578$			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	0.608271	−	0.793729i	$-0.291863\pi$
$587$	−9.28551	−	16.0830i	−0.383254	−	0.663816i	−0.991525	+	0.129914i	$0.958530\pi$
$588$		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	$-0.947698\pi$
$593$	−15.4614	−	26.7800i	−0.634924	−	1.09972i	0.351607	−	0.936148i	$-0.385635\pi$
$594$	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	−0.108735	−	0.994071i	$-0.534680\pi$
$601$	17.1065	−	9.87644i	0.697788	−	0.402868i	0.806523	+	0.591203i	$0.201347\pi$
$602$		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	$-0.881500\pi$
$607$		−	17.9231i		−	0.727477i	0.931501	−	0.363739i	$-0.118500\pi$
$608$	−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	$-0.987598\pi$
$619$		−	1.93816i		−	0.0779014i	0.999241	−	0.0389507i	$-0.0124015\pi$
$620$	−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	−0.495619	−	0.868540i	$-0.665059\pi$
$643$	−37.9247	−	21.8959i	−1.49561	−	0.863489i	−0.999987	+	0.00505169i	$0.998392\pi$
$644$		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	$-0.637419\pi$
$647$	14.6857	−	25.4363i	0.577353	−	1.00001i	0.995782	−	0.0917553i	$-0.0292478\pi$
$648$	−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	−0.558167	−	0.829728i	$-0.688495\pi$
$661$	−3.05138	+	1.76171i	−0.118685	+	0.0685227i	0.439482	+	0.898251i	$0.355162\pi$
$662$	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	$-0.607885\pi$
$677$	16.9260	−	29.3166i	0.650517	−	1.12673i	0.982998	−	0.183619i	$-0.0587812\pi$
$678$	−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	$0.0546381\pi$
$691$	42.7393	+	24.6756i	1.62588	+	0.938703i	0.640577	+	0.767894i	$0.278695\pi$
$692$	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	0.654275	−	0.756257i	$-0.272974\pi$
$719$	−8.78970	−	15.2242i	−0.327801	−	0.567767i	−0.982075	+	0.188490i	$0.939641\pi$
$720$	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	$0.714223\pi$
$727$	−43.4695	+	25.0971i	−1.61220	+	0.930802i	−0.988860	+	0.148847i	$0.952444\pi$
$728$		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	$0.263770\pi$
$733$			39.9084i			1.47405i	−0.675865	+	0.737025i	$0.736230\pi$
$734$	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	$-0.748552\pi$
$761$	−38.8349			−1.40776			−0.703882	+	0.710317i	$0.748552\pi$
$762$	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	0.660277	−	0.751022i	$-0.270439\pi$
$769$	9.42879	+	5.44371i	0.340011	+	0.196305i	−0.320266	+	0.947328i	$0.603772\pi$
$770$		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	$0.400973\pi$
$773$	−18.6668	+	32.3319i	−0.671400	+	1.16290i	−0.977507	+	0.210901i	$0.932360\pi$
$774$	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	−0.749495	−	0.662011i	$-0.769703\pi$
$787$	−15.4554	+	8.92315i	−0.550924	+	0.318076i	0.198571	+	0.980087i	$0.436370\pi$
$788$	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	−0.949693	−	0.313181i	$-0.898605\pi$
$797$	−5.74854	+	9.95676i	−0.203624	+	0.352687i	0.746070	+	0.665868i	$0.231939\pi$
$798$		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	$0.304819\pi$
$811$			46.5800i			1.63565i	−0.575469	+	0.817823i	$0.695181\pi$
$812$		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	0.686840	−	0.726808i	$-0.258997\pi$
$829$	11.5407	+	6.66304i	0.400826	+	0.231417i	−0.286014	+	0.958225i	$0.592331\pi$
$830$			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	0.683870	−	0.729604i	$-0.260295\pi$
$839$	−8.39768	−	14.5452i	−0.289920	−	0.502156i	−0.973790	+	0.227447i	$0.926962\pi$
$840$		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	0.251576	−	0.967838i	$-0.419051\pi$
$853$	35.5011	−	20.4966i	1.21554	−	0.701790i	0.963960	+	0.266048i	$0.0857179\pi$
$854$		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	$-0.247351\pi$
$857$	41.7436			1.42593			0.712967	+	0.701198i	$0.247351\pi$
$858$	1.24184	+	0.302599i	0.0423956	+	0.0103306i
$859$			27.7682i			0.947437i	0.880676	+	0.473719i	$0.157089\pi$
$859$			27.7682i			0.947437i	−0.880676	+	0.473719i	$0.842911\pi$
$860$	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	$-0.437305\pi$
$881$	11.6169			0.391384			0.195692	+	0.980665i	$0.437305\pi$
$882$		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	$-0.364776\pi$
$887$	24.5501			0.824313			0.412156	+	0.911113i	$0.364776\pi$
$888$	−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	$-0.562931\pi$
$929$	22.8885	−	39.6440i	0.750946	−	1.30068i	0.947365	−	0.320156i	$-0.103735\pi$
$930$	−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	$0.128226\pi$
$937$			24.0003i			0.784054i	−0.919954	+	0.392027i	$0.871774\pi$
$938$		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	0.837999	−	0.545671i	$-0.183725\pi$
$941$	−1.64316	−	2.84603i	−0.0535654	−	0.0927780i	−0.891565	+	0.452893i	$0.850392\pi$
$942$	−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	0.857546	−	0.514408i	$-0.171988\pi$
$971$	−0.520938	−	0.902292i	−0.0167177	−	0.0289559i	−0.874263	+	0.485452i	$0.838655\pi$
$972$	−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	$-0.853235\pi$
$983$	−56.1576			−1.79115			−0.895575	+	0.444911i	$0.853235\pi$
$984$	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	$0.183565\pi$
$997$			34.4328i			1.09050i	−0.838274	+	0.545249i	$0.816435\pi$
$998$	−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.374.2		12
3.2	odd	2		1323.2.s.c.962.5		12
7.2	even	3		441.2.i.c.68.5		12
7.3	odd	6		63.2.o.a.41.5	yes	12
7.4	even	3		63.2.o.a.41.6	yes	12
7.5	odd	6		441.2.i.c.68.6		12
7.6	odd	2	inner	441.2.s.c.374.1		12
9.2	odd	6		441.2.i.c.227.2		12
9.7	even	3		1323.2.i.c.521.5		12
21.2	odd	6		1323.2.i.c.1097.2		12
21.5	even	6		1323.2.i.c.1097.1		12
21.11	odd	6		189.2.o.a.125.2		12
21.17	even	6		189.2.o.a.125.1		12
21.20	even	2		1323.2.s.c.962.6		12
28.3	even	6		1008.2.cc.a.545.4		12
28.11	odd	6		1008.2.cc.a.545.3		12
63.2	odd	6	inner	441.2.s.c.362.1		12
63.4	even	3		567.2.c.c.566.10		12
63.11	odd	6		63.2.o.a.20.5	✓	12
63.16	even	3		1323.2.s.c.656.6		12
63.20	even	6		441.2.i.c.227.1		12
63.25	even	3		189.2.o.a.62.1		12
63.31	odd	6		567.2.c.c.566.9		12
63.32	odd	6		567.2.c.c.566.3		12
63.34	odd	6		1323.2.i.c.521.6		12
63.38	even	6		63.2.o.a.20.6	yes	12
63.47	even	6	inner	441.2.s.c.362.2		12
63.52	odd	6		189.2.o.a.62.2		12
63.59	even	6		567.2.c.c.566.4		12
63.61	odd	6		1323.2.s.c.656.5		12
84.11	even	6		3024.2.cc.a.881.6		12
84.59	odd	6		3024.2.cc.a.881.1		12
252.11	even	6		1008.2.cc.a.209.4		12
252.115	even	6		3024.2.cc.a.2897.6		12
252.151	odd	6		3024.2.cc.a.2897.1		12
252.227	odd	6		1008.2.cc.a.209.3		12

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