LMFDB - Embedded newform 484.2.g.g.239.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,2,Mod(215,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("484.215");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.g (of order $10$, degree $4$, 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:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.26873856000000000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			239.3
Root			$-1.38331 + 0.294032i$ of defining polynomial
Character	$\chi$	$=$	484.239
Dual form			484.2.g.g.403.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.147826 + 1.40647i) q^{2} +(-1.64728 + 0.535233i) q^{3} +(-1.95630 + 0.415823i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.996297 - 2.23772i) q^{6} +(-0.874032 + 2.68999i) q^{7} +(-0.874032 - 2.68999i) q^{8} +O(q^{10})$	\(q+(0.147826 + 1.40647i) q^{2} +(-1.64728 + 0.535233i) q^{3} +(-1.95630 + 0.415823i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.996297 - 2.23772i) q^{6} +(-0.874032 + 2.68999i) q^{7} +(-0.874032 - 2.68999i) q^{8} +(-0.707107 + 1.22474i) q^{10} +(3.00000 - 1.73205i) q^{12} +(-2.87955 - 3.96336i) q^{13} +(-3.91259 - 0.831647i) q^{14} +(-1.64728 - 0.535233i) q^{15} +(3.65418 - 1.62695i) q^{16} +(-2.87955 + 3.96336i) q^{17} +(0.874032 + 2.68999i) q^{19} +(-1.82709 - 0.813473i) q^{20} -4.89898i q^{21} -5.19615i q^{23} +(2.87955 + 3.96336i) q^{24} +(-1.23607 - 3.80423i) q^{25} +(5.14866 - 4.63587i) q^{26} +(3.05422 - 4.20378i) q^{27} +(0.591302 - 5.62587i) q^{28} +(0.509278 - 2.39596i) q^{30} +(-1.01807 - 1.40126i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-6.00000 - 3.46410i) q^{34} +(-2.28825 + 1.66251i) q^{35} +(0.927051 - 2.85317i) q^{37} +(-3.65418 + 1.62695i) q^{38} +(6.86474 + 4.98752i) q^{39} +(0.874032 - 2.68999i) q^{40} +(-4.65921 + 1.51387i) q^{41} +(6.89025 - 0.724194i) q^{42} -5.65685 q^{43} +(7.30821 - 0.768124i) q^{46} +(-3.29456 + 1.07047i) q^{47} +(-5.14866 + 4.63587i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(5.16779 - 2.30085i) q^{50} +(2.62210 - 8.06998i) q^{51} +(7.28130 + 6.55611i) q^{52} +(1.61803 - 1.17557i) q^{53} +(6.36396 + 3.67423i) q^{54} +8.00000 q^{56} +(-2.87955 - 3.96336i) q^{57} +(1.64728 + 0.535233i) q^{59} +(3.44512 + 0.362097i) q^{60} +(-5.75910 + 7.92672i) q^{61} +(1.82033 - 1.63903i) q^{62} +(-6.47214 + 4.70228i) q^{64} -4.89898i q^{65} +8.66025i q^{67} +(3.98519 - 8.95088i) q^{68} +(2.78115 + 8.55951i) q^{69} +(-2.67652 - 2.97258i) q^{70} +(-7.12652 + 9.80881i) q^{71} +(-4.65921 - 1.51387i) q^{73} +(4.14993 + 0.882095i) q^{74} +(4.07230 + 5.60503i) q^{75} +(-2.82843 - 4.89898i) q^{76} +(-6.00000 + 10.3923i) q^{78} +(-9.15298 + 6.65003i) q^{79} +(3.91259 + 0.831647i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-2.81795 - 6.32923i) q^{82} +(2.03711 + 9.58385i) q^{84} +(-4.65921 + 1.51387i) q^{85} +(-0.836228 - 7.95618i) q^{86} -1.00000 q^{89} +(13.1782 - 4.28187i) q^{91} +(2.16068 + 10.1652i) q^{92} +(2.42705 + 1.76336i) q^{93} +(-1.99259 - 4.47544i) q^{94} +(-0.874032 + 2.68999i) q^{95} +(-7.28130 - 6.55611i) q^{96} +(-5.66312 + 4.11450i) q^{97} +(0.707107 - 1.22474i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^5	$ 16 q + 4 q^{4} + 4 q^{5} + 48 q^{12} + 8 q^{14} + 8 q^{16} - 4 q^{20} + 16 q^{25} - 24 q^{26} - 96 q^{34} - 12 q^{37} - 8 q^{38} + 24 q^{42} + 24 q^{48} - 4 q^{49} + 8 q^{53} + 128 q^{56} + 12 q^{60} - 32 q^{64} - 36 q^{69} - 8 q^{70} - 96 q^{78} - 8 q^{80} + 36 q^{81} - 24 q^{82} + 16 q^{86} - 16 q^{89} + 36 q^{92} + 12 q^{93} - 28 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^5 + 48 * q^12 + 8 * q^14 + 8 * q^16 - 4 * q^20 + 16 * q^25 - 24 * q^26 - 96 * q^34 - 12 * q^37 - 8 * q^38 + 24 * q^42 + 24 * q^48 - 4 * q^49 + 8 * q^53 + 128 * q^56 + 12 * q^60 - 32 * q^64 - 36 * q^69 - 8 * q^70 - 96 * q^78 - 8 * q^80 + 36 * q^81 - 24 * q^82 + 16 * q^86 - 16 * q^89 + 36 * q^92 + 12 * q^93 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	0.147826	+	1.40647i	0.104528	+	0.994522i
$2$	0.147826	+	1.40647i	0.104528	+	0.994522i
$3$	−1.64728	+	0.535233i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$3$	−1.64728	+	0.535233i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$4$	−1.95630	+	0.415823i	−0.978148	+	0.207912i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i	0.753804	−	0.657099i	$-0.228217\pi$
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i	−0.392000	+	0.919965i	$0.628217\pi$
$6$	−0.996297	−	2.23772i	−0.406737	−	0.913545i
$7$	−0.874032	+	2.68999i	−0.330353	+	1.01672i	0.638613	+	0.769528i	$0.279509\pi$
$7$	−0.874032	+	2.68999i	−0.330353	+	1.01672i	−0.968966	+	0.247194i	$0.920491\pi$
$8$	−0.874032	−	2.68999i	−0.309017	−	0.951057i
$9$		0			0
$10$	−0.707107	+	1.22474i	−0.223607	+	0.387298i
$11$		0			0
$11$		0			0
$12$	3.00000	−	1.73205i	0.866025	−	0.500000i
$13$	−2.87955	−	3.96336i	−0.798643	−	1.09924i	−0.992978	−	0.118302i	$-0.962255\pi$
$13$	−2.87955	−	3.96336i	−0.798643	−	1.09924i	0.194335	−	0.980935i	$-0.437745\pi$
$14$	−3.91259	−	0.831647i	−1.04568	−	0.222267i
$15$	−1.64728	−	0.535233i	−0.425325	−	0.138197i
$16$	3.65418	−	1.62695i	0.913545	−	0.406737i
$17$	−2.87955	+	3.96336i	−0.698393	+	0.961255i	0.301577	+	0.953442i	$0.402487\pi$
$17$	−2.87955	+	3.96336i	−0.698393	+	0.961255i	−0.999969	+	0.00781345i	$0.997513\pi$
$18$		0			0
$19$	0.874032	+	2.68999i	0.200517	+	0.617127i	0.999868	+	0.0162627i	$0.00517680\pi$
$19$	0.874032	+	2.68999i	0.200517	+	0.617127i	−0.799351	+	0.600864i	$0.794823\pi$
$20$	−1.82709	−	0.813473i	−0.408550	−	0.181898i
$21$		−	4.89898i		−	1.06904i
$22$		0			0
$23$		−	5.19615i		−	1.08347i	−0.840548	−	0.541736i	$-0.817767\pi$
$23$		−	5.19615i		−	1.08347i	0.840548	−	0.541736i	$-0.182233\pi$
$24$	2.87955	+	3.96336i	0.587785	+	0.809017i
$25$	−1.23607	−	3.80423i	−0.247214	−	0.760845i
$26$	5.14866	−	4.63587i	1.00973	−	0.909169i
$27$	3.05422	−	4.20378i	0.587785	−	0.809017i
$28$	0.591302	−	5.62587i	0.111746	−	1.06319i
$29$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$29$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$30$	0.509278	−	2.39596i	0.0929809	−	0.437441i
$31$	−1.01807	−	1.40126i	−0.182851	−	0.251673i	0.707745	−	0.706468i	$-0.249713\pi$
$31$	−1.01807	−	1.40126i	−0.182851	−	0.251673i	−0.890596	+	0.454795i	$0.849713\pi$
$32$	2.82843	+	4.89898i	0.500000	+	0.866025i
$33$		0			0
$34$	−6.00000	−	3.46410i	−1.02899	−	0.594089i
$35$	−2.28825	+	1.66251i	−0.386784	+	0.281015i
$36$		0			0
$37$	0.927051	−	2.85317i	0.152406	−	0.469058i	−0.845483	−	0.534003i	$-0.820687\pi$
$37$	0.927051	−	2.85317i	0.152406	−	0.469058i	0.997889	+	0.0649448i	$0.0206871\pi$
$38$	−3.65418	+	1.62695i	−0.592787	+	0.263926i
$39$	6.86474	+	4.98752i	1.09924	+	0.798643i
$40$	0.874032	−	2.68999i	0.138197	−	0.425325i
$41$	−4.65921	+	1.51387i	−0.727646	+	0.236426i	−0.649335	−	0.760503i	$-0.724953\pi$
$41$	−4.65921	+	1.51387i	−0.727646	+	0.236426i	−0.0783108	+	0.996929i	$0.524953\pi$
$42$	6.89025	−	0.724194i	1.06319	−	0.111746i
$43$	−5.65685			−0.862662			−0.431331	−	0.902194i	$-0.641956\pi$
$43$	−5.65685			−0.862662			−0.431331	+	0.902194i	$0.641956\pi$
$44$		0			0
$45$		0			0
$46$	7.30821	−	0.768124i	1.07754	−	0.113254i
$47$	−3.29456	+	1.07047i	−0.480560	+	0.156144i	−0.539272	−	0.842131i	$-0.681301\pi$
$47$	−3.29456	+	1.07047i	−0.480560	+	0.156144i	0.0587119	+	0.998275i	$0.481301\pi$
$48$	−5.14866	+	4.63587i	−0.743145	+	0.669131i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	5.16779	−	2.30085i	0.730836	−	0.325389i
$51$	2.62210	−	8.06998i	0.367167	−	1.13002i
$52$	7.28130	+	6.55611i	1.00973	+	0.909169i
$53$	1.61803	−	1.17557i	0.222254	−	0.161477i	−0.471087	−	0.882087i	$-0.656138\pi$
$53$	1.61803	−	1.17557i	0.222254	−	0.161477i	0.693341	+	0.720610i	$0.256138\pi$
$54$	6.36396	+	3.67423i	0.866025	+	0.500000i
$55$		0			0
$56$	8.00000			1.06904
$57$	−2.87955	−	3.96336i	−0.381405	−	0.524960i
$58$		0			0
$59$	1.64728	+	0.535233i	0.214457	+	0.0696814i	0.414275	−	0.910152i	$-0.364035\pi$
$59$	1.64728	+	0.535233i	0.214457	+	0.0696814i	−0.199818	+	0.979833i	$0.564035\pi$
$60$	3.44512	+	0.362097i	0.444764	+	0.0467465i
$61$	−5.75910	+	7.92672i	−0.737377	+	1.01491i	0.261389	+	0.965234i	$0.415820\pi$
$61$	−5.75910	+	7.92672i	−0.737377	+	1.01491i	−0.998765	+	0.0496783i	$0.984180\pi$
$62$	1.82033	−	1.63903i	0.231182	−	0.208157i
$63$		0			0
$64$	−6.47214	+	4.70228i	−0.809017	+	0.587785i
$65$		−	4.89898i		−	0.607644i
$66$		0			0
$67$			8.66025i			1.05802i	0.848616	+	0.529009i	$0.177436\pi$
$67$			8.66025i			1.05802i	−0.848616	+	0.529009i	$0.822564\pi$
$68$	3.98519	−	8.95088i	0.483275	−	1.08545i
$69$	2.78115	+	8.55951i	0.334811	+	1.03044i
$70$	−2.67652	−	2.97258i	−0.319906	−	0.355291i
$71$	−7.12652	+	9.80881i	−0.845762	+	1.16409i	0.139019	+	0.990290i	$0.455605\pi$
$71$	−7.12652	+	9.80881i	−0.845762	+	1.16409i	−0.984781	+	0.173802i	$0.944395\pi$
$72$		0			0
$73$	−4.65921	−	1.51387i	−0.545319	−	0.177185i	0.0233860	−	0.999727i	$-0.492555\pi$
$73$	−4.65921	−	1.51387i	−0.545319	−	0.177185i	−0.568705	+	0.822542i	$0.692555\pi$
$74$	4.14993	+	0.882095i	0.482419	+	0.102541i
$75$	4.07230	+	5.60503i	0.470228	+	0.647214i
$76$	−2.82843	−	4.89898i	−0.324443	−	0.561951i
$77$		0			0
$78$	−6.00000	+	10.3923i	−0.679366	+	1.17670i
$79$	−9.15298	+	6.65003i	−1.02979	+	0.748187i	−0.968267	−	0.249919i	$-0.919596\pi$
$79$	−9.15298	+	6.65003i	−1.02979	+	0.748187i	−0.0615241	+	0.998106i	$0.519596\pi$
$80$	3.91259	+	0.831647i	0.437441	+	0.0929809i
$81$	−2.78115	+	8.55951i	−0.309017	+	0.951057i
$82$	−2.81795	−	6.32923i	−0.311191	−	0.698946i
$83$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$83$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$84$	2.03711	+	9.58385i	0.222267	+	1.04568i
$85$	−4.65921	+	1.51387i	−0.505362	+	0.164202i
$86$	−0.836228	−	7.95618i	−0.0901728	−	0.857936i
$87$		0			0
$88$		0			0
$89$	−1.00000			−0.106000			−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000			−0.106000			−0.0529999	+	0.998595i	$0.516878\pi$
$90$		0			0
$91$	13.1782	−	4.28187i	1.38145	−	0.448861i
$92$	2.16068	+	10.1652i	0.225267	+	1.05980i
$93$	2.42705	+	1.76336i	0.251673	+	0.182851i
$94$	−1.99259	−	4.47544i	−0.205520	−	0.461606i
$95$	−0.874032	+	2.68999i	−0.0896738	+	0.275988i
$96$	−7.28130	−	6.55611i	−0.743145	−	0.669131i
$97$	−5.66312	+	4.11450i	−0.575003	+	0.417764i	−0.836919	−	0.547327i	$-0.815646\pi$
$97$	−5.66312	+	4.11450i	−0.575003	+	0.417764i	0.261916	+	0.965091i	$0.415646\pi$
$98$	0.707107	−	1.22474i	0.0714286	−	0.123718i
$99$		0			0
$100$	4.00000	+	6.92820i	0.400000	+	0.692820i
$101$	2.87955	+	3.96336i	0.286526	+	0.394369i	0.927882	−	0.372875i	$-0.121628\pi$
$101$	2.87955	+	3.96336i	0.286526	+	0.394369i	−0.641356	+	0.767243i	$0.721628\pi$
$102$	11.7378	+	2.49494i	1.16221	+	0.247036i
$103$	3.29456	+	1.07047i	0.324622	+	0.105476i	0.466795	−	0.884366i	$-0.345409\pi$
$103$	3.29456	+	1.07047i	0.324622	+	0.105476i	−0.142172	+	0.989842i	$0.545409\pi$
$104$	−8.14459	+	11.2101i	−0.798643	+	1.09924i
$105$	2.87955	−	3.96336i	0.281015	−	0.386784i
$106$	1.89259	+	2.10193i	0.183824	+	0.204158i
$107$	−2.62210	−	8.06998i	−0.253488	−	0.780155i	−0.994124	−	0.108248i	$-0.965476\pi$
$107$	−2.62210	−	8.06998i	−0.253488	−	0.780155i	0.740636	−	0.671906i	$-0.234524\pi$
$108$	−4.22693	+	9.49384i	−0.406737	+	0.913545i
$109$			9.79796i			0.938474i	0.883072	+	0.469237i	$0.155471\pi$
$109$			9.79796i			0.938474i	−0.883072	+	0.469237i	$0.844529\pi$
$110$		0			0
$111$			5.19615i			0.493197i
$112$	1.18260	+	11.2517i	0.111746	+	1.06319i
$113$	−1.54508	−	4.75528i	−0.145349	−	0.447339i	0.851706	−	0.524019i	$-0.175568\pi$
$113$	−1.54508	−	4.75528i	−0.145349	−	0.447339i	−0.997056	+	0.0766799i	$0.975568\pi$
$114$	5.14866	−	4.63587i	0.482216	−	0.434189i
$115$	3.05422	−	4.20378i	0.284808	−	0.392004i
$116$		0			0
$117$		0			0
$118$	−0.509278	+	2.39596i	−0.0468828	+	0.220566i
$119$	−8.14459	−	11.2101i	−0.746613	−	1.02763i
$120$			4.89898i			0.447214i
$121$		0			0
$122$	−12.0000	−	6.92820i	−1.08643	−	0.627250i
$123$	6.86474	−	4.98752i	0.618972	−	0.449710i
$124$	2.57433	+	2.31794i	0.231182	+	0.208157i
$125$	2.78115	−	8.55951i	0.248754	−	0.765586i
$126$		0			0
$127$	−11.4412	−	8.31254i	−1.01524	−	0.737619i	−0.0499421	−	0.998752i	$-0.515904\pi$
$127$	−11.4412	−	8.31254i	−1.01524	−	0.737619i	−0.965303	+	0.261134i	$0.915904\pi$
$128$	−7.57035	−	8.40772i	−0.669131	−	0.743145i
$129$	9.31841	−	3.02774i	0.820440	−	0.266577i
$130$	6.89025	−	0.724194i	0.604315	−	0.0635161i
$131$	2.82843			0.247121			0.123560	−	0.992337i	$-0.460569\pi$
$131$	2.82843			0.247121			0.123560	+	0.992337i	$0.460569\pi$
$132$		0			0
$133$	−8.00000			−0.693688
$134$	−12.1804	+	1.28021i	−1.05222	+	0.110593i
$135$	4.94183	−	1.60570i	0.425325	−	0.138197i
$136$	13.1782	+	4.28187i	1.13002	+	0.367167i
$137$	−15.3713	−	11.1679i	−1.31326	−	0.954140i	−0.999990	−	0.00447593i	$-0.998575\pi$
$137$	−15.3713	−	11.1679i	−1.31326	−	0.954140i	−0.313271	−	0.949664i	$-0.601425\pi$
$138$	−11.6275	+	5.17691i	−0.989802	+	0.440688i
$139$	−6.11822	+	18.8300i	−0.518941	+	1.59714i	0.257054	+	0.966397i	$0.417248\pi$
$139$	−6.11822	+	18.8300i	−0.518941	+	1.59714i	−0.775995	+	0.630739i	$0.782752\pi$
$140$	3.78517	−	4.20386i	0.319906	−	0.355291i
$141$	4.85410	−	3.52671i	0.408789	−	0.297003i
$142$	−14.8492	−	8.57321i	−1.24612	−	0.719448i
$143$		0			0
$144$		0			0
$145$		0			0
$146$	1.44045	−	6.77681i	0.119213	−	0.560852i
$147$	1.64728	+	0.535233i	0.135865	+	0.0441453i
$148$	−0.627171	+	5.96713i	−0.0515531	+	0.490495i
$149$	8.63864	−	11.8901i	0.707705	−	0.974073i	−0.292138	−	0.956376i	$-0.594367\pi$
$149$	8.63864	−	11.8901i	0.707705	−	0.974073i	0.999843	−	0.0176966i	$-0.00563330\pi$
$150$	−7.28130	+	6.55611i	−0.594516	+	0.535304i
$151$	1.74806	+	5.37999i	0.142255	+	0.437817i	0.996648	−	0.0818111i	$-0.0260704\pi$
$151$	1.74806	+	5.37999i	0.142255	+	0.437817i	−0.854392	+	0.519628i	$0.826070\pi$
$152$	6.47214	−	4.70228i	0.524960	−	0.381405i
$153$		0			0
$154$		0			0
$155$		−	1.73205i		−	0.139122i
$156$	−15.5034	−	6.90255i	−1.24126	−	0.552646i
$157$	3.39919	+	10.4616i	0.271285	+	0.834928i	0.990179	+	0.139808i	$0.0446487\pi$
$157$	3.39919	+	10.4616i	0.271285	+	0.834928i	−0.718894	+	0.695120i	$0.755351\pi$
$158$	−10.7061	−	11.8903i	−0.851731	−	0.945943i
$159$	−2.03615	+	2.80252i	−0.161477	+	0.222254i
$160$	−0.591302	+	5.62587i	−0.0467465	+	0.444764i
$161$	13.9776	+	4.54160i	1.10159	+	0.357929i
$162$	−12.4498	−	2.64628i	−0.978148	−	0.207912i
$163$	10.1807	+	14.0126i	0.797417	+	1.09755i	0.993145	+	0.116892i	$0.0372932\pi$
$163$	10.1807	+	14.0126i	0.797417	+	1.09755i	−0.195728	+	0.980658i	$0.562707\pi$
$164$	8.48528	−	4.89898i	0.662589	−	0.382546i
$165$		0			0
$166$		0			0
$167$	16.0177	−	11.6376i	1.23949	−	0.900541i	0.241924	−	0.970295i	$-0.422221\pi$
$167$	16.0177	−	11.6376i	1.23949	−	0.900541i	0.997564	+	0.0697542i	$0.0222215\pi$
$168$	−13.1782	+	4.28187i	−1.01672	+	0.330353i
$169$	−3.39919	+	10.4616i	−0.261476	+	0.804740i
$170$	−2.81795	−	6.32923i	−0.216127	−	0.485430i
$171$		0			0
$172$	11.0665	−	2.35225i	0.843811	−	0.179358i
$173$	9.31841	−	3.02774i	0.708466	−	0.230194i	0.0674505	−	0.997723i	$-0.478514\pi$
$173$	9.31841	−	3.02774i	0.708466	−	0.230194i	0.641015	+	0.767528i	$0.278514\pi$
$174$		0			0
$175$	11.3137			0.855236
$176$		0			0
$177$	−3.00000			−0.225494
$178$	−0.147826	−	1.40647i	−0.0110800	−	0.105419i
$179$	−8.23639	+	2.67617i	−0.615617	+	0.200026i	−0.600193	−	0.799855i	$-0.704910\pi$
$179$	−8.23639	+	2.67617i	−0.615617	+	0.200026i	−0.0154235	+	0.999881i	$0.504910\pi$
$180$		0			0
$181$	16.9894	+	12.3435i	1.26281	+	0.917484i	0.998892	−	0.0470610i	$-0.0149855\pi$
$181$	16.9894	+	12.3435i	1.26281	+	0.917484i	0.263917	+	0.964545i	$0.414986\pi$
$182$	7.97038	+	17.9018i	0.590804	+	1.32697i
$183$	5.24419	−	16.1400i	0.387662	−	1.19310i
$184$	−13.9776	+	4.54160i	−1.03044	+	0.334811i
$185$	2.42705	−	1.76336i	0.178440	−	0.129644i
$186$	−2.12132	+	3.67423i	−0.155543	+	0.269408i
$187$		0			0
$188$	6.00000	−	3.46410i	0.437595	−	0.252646i
$189$	8.63864	+	11.8901i	0.628369	+	0.864876i
$190$	−3.91259	−	0.831647i	−0.283849	−	0.0603340i
$191$	−4.94183	−	1.60570i	−0.357579	−	0.116184i	0.124718	−	0.992192i	$-0.460197\pi$
$191$	−4.94183	−	1.60570i	−0.357579	−	0.116184i	−0.482297	+	0.876008i	$0.660197\pi$
$192$	8.14459	−	11.2101i	0.587785	−	0.809017i
$193$	5.75910	−	7.92672i	0.414549	−	0.570577i	−0.549772	−	0.835315i	$-0.685285\pi$
$193$	5.75910	−	7.92672i	0.414549	−	0.570577i	0.964321	+	0.264737i	$0.0852853\pi$
$194$	−6.62406	−	7.35676i	−0.475579	−	0.528184i
$195$	2.62210	+	8.06998i	0.187772	+	0.577903i
$196$	1.82709	+	0.813473i	0.130506	+	0.0581052i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		−	10.3923i		−	0.736691i	−0.929689	−	0.368345i	$-0.879924\pi$
$199$		−	10.3923i		−	0.736691i	0.929689	−	0.368345i	$-0.120076\pi$
$200$	−9.15298	+	6.65003i	−0.647214	+	0.470228i
$201$	−4.63525	−	14.2658i	−0.326946	−	1.00624i
$202$	−5.14866	+	4.63587i	−0.362258	+	0.326179i
$203$		0			0
$204$	−1.77391	+	16.8776i	−0.124198	+	1.18167i
$205$	−4.65921	−	1.51387i	−0.325413	−	0.105733i
$206$	−1.01856	+	4.79193i	−0.0709661	+	0.333869i
$207$		0			0
$208$	−16.9706	−	9.79796i	−1.17670	−	0.679366i
$209$		0			0
$210$	6.00000	+	3.46410i	0.414039	+	0.239046i
$211$	4.57649	−	3.32502i	0.315059	−	0.228904i	−0.419005	−	0.907984i	$-0.637621\pi$
$211$	4.57649	−	3.32502i	0.315059	−	0.228904i	0.734064	+	0.679080i	$0.237621\pi$
$212$	−2.67652	+	2.97258i	−0.183824	+	0.204158i
$213$	6.48936	−	19.9722i	0.444643	−	1.36847i
$214$	10.9625	−	4.88084i	0.749384	−	0.333647i
$215$	−4.57649	−	3.32502i	−0.312114	−	0.226764i
$216$	−13.9776	−	4.54160i	−0.951057	−	0.309017i
$217$	4.65921	−	1.51387i	0.316288	−	0.102768i
$218$	−13.7805	+	1.44839i	−0.933333	+	0.0980973i
$219$	8.48528			0.573382
$220$		0			0
$221$	24.0000			1.61441
$222$	−7.30821	+	0.768124i	−0.490495	+	0.0515531i
$223$	−21.4146	+	6.95803i	−1.43403	+	0.465944i	−0.920030	−	0.391847i	$-0.871836\pi$
$223$	−21.4146	+	6.95803i	−1.43403	+	0.465944i	−0.513998	+	0.857791i	$0.671836\pi$
$224$	−15.6504	+	3.32659i	−1.04568	+	0.222267i
$225$		0			0
$226$	6.45974	−	2.87606i	0.429696	−	0.191313i
$227$	2.62210	−	8.06998i	0.174035	−	0.535624i	−0.825553	−	0.564324i	$-0.809137\pi$
$227$	2.62210	−	8.06998i	0.174035	−	0.535624i	0.999588	+	0.0287004i	$0.00913689\pi$
$228$	7.28130	+	6.55611i	0.482216	+	0.434189i
$229$	0.809017	−	0.587785i	0.0534613	−	0.0388419i	−0.560734	−	0.827996i	$-0.689481\pi$
$229$	0.809017	−	0.587785i	0.0534613	−	0.0388419i	0.614195	+	0.789154i	$0.289481\pi$
$230$	6.36396	+	3.67423i	0.419627	+	0.242272i
$231$		0			0
$232$		0			0
$233$	11.5182	+	15.8534i	0.754582	+	1.03859i	0.997645	+	0.0685824i	$0.0218476\pi$
$233$	11.5182	+	15.8534i	0.754582	+	1.03859i	−0.243064	+	0.970010i	$0.578152\pi$
$234$		0			0
$235$	−3.29456	−	1.07047i	−0.214913	−	0.0698295i
$236$	−3.44512	−	0.362097i	−0.224259	−	0.0235705i
$237$	11.5182	−	15.8534i	0.748187	−	1.02979i
$238$	14.5626	−	13.1122i	0.943953	−	0.849940i
$239$	−1.74806	−	5.37999i	−0.113073	−	0.348003i	0.878467	−	0.477802i	$-0.158567\pi$
$239$	−1.74806	−	5.37999i	−0.113073	−	0.348003i	−0.991540	+	0.129800i	$0.958567\pi$
$240$	−6.89025	+	0.724194i	−0.444764	+	0.0467465i
$241$			29.3939i			1.89343i	0.322078	+	0.946713i	$0.395619\pi$
$241$			29.3939i			1.89343i	−0.322078	+	0.946713i	$0.604381\pi$
$242$		0			0
$243$		0			0
$244$	7.97038	−	17.9018i	0.510251	−	1.14604i
$245$	−0.309017	−	0.951057i	−0.0197424	−	0.0607608i
$246$	8.02957	+	8.91774i	0.511947	+	0.568574i
$247$	8.14459	−	11.2101i	0.518228	−	0.713280i
$248$	−2.87955	+	3.96336i	−0.182851	+	0.251673i
$249$		0			0
$250$	12.4498	+	2.64628i	0.787394	+	0.167366i
$251$	−13.2350	−	18.2164i	−0.835383	−	1.14981i	−0.986897	−	0.161351i	$-0.948415\pi$
$251$	−13.2350	−	18.2164i	−0.835383	−	1.14981i	0.151514	−	0.988455i	$-0.451585\pi$
$252$		0			0
$253$		0			0
$254$	10.0000	−	17.3205i	0.627456	−	1.08679i
$255$	6.86474	−	4.98752i	0.429886	−	0.312331i
$256$	10.7061	−	11.8903i	0.669131	−	0.743145i
$257$	−6.79837	+	20.9232i	−0.424071	+	1.30516i	0.479810	+	0.877372i	$0.340706\pi$
$257$	−6.79837	+	20.9232i	−0.424071	+	1.30516i	−0.903881	+	0.427784i	$0.859294\pi$
$258$	5.63591	+	12.6585i	0.350876	+	0.788081i
$259$	6.86474	+	4.98752i	0.426554	+	0.309910i
$260$	2.03711	+	9.58385i	0.126336	+	0.594365i
$261$		0			0
$262$	0.418114	+	3.97809i	0.0258312	+	0.245767i
$263$	−14.1421			−0.872041			−0.436021	−	0.899937i	$-0.643613\pi$
$263$	−14.1421			−0.872041			−0.436021	+	0.899937i	$0.643613\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$	−1.18260	−	11.2517i	−0.0725101	−	0.689888i
$267$	1.64728	−	0.535233i	0.100812	−	0.0327557i
$268$	−3.60114	−	16.9420i	−0.219974	−	1.03490i
$269$	8.09017	+	5.87785i	0.493266	+	0.358379i	0.806439	−	0.591317i	$-0.201392\pi$
$269$	8.09017	+	5.87785i	0.493266	+	0.358379i	−0.313173	+	0.949696i	$0.601392\pi$
$270$	2.98889	+	6.71316i	0.181898	+	0.408550i
$271$	0.874032	−	2.68999i	0.0530937	−	0.163406i	−0.920994	−	0.389577i	$-0.872621\pi$
$271$	0.874032	−	2.68999i	0.0530937	−	0.163406i	0.974087	+	0.226172i	$0.0726211\pi$
$272$	−4.07422	+	19.1677i	−0.247036	+	1.16221i
$273$	−19.4164	+	14.1068i	−1.17513	+	0.853785i
$274$	13.4350	−	23.2702i	0.811640	−	1.40580i
$275$		0			0
$276$	−9.00000	−	15.5885i	−0.541736	−	0.938315i
$277$	−5.75910	−	7.92672i	−0.346031	−	0.476270i	0.600160	−	0.799880i	$-0.295104\pi$
$277$	−5.75910	−	7.92672i	−0.346031	−	0.476270i	−0.946191	+	0.323610i	$0.895104\pi$
$278$	−27.3881	−	5.82153i	−1.64263	−	0.349152i
$279$		0			0
$280$	6.47214	+	4.70228i	0.386784	+	0.281015i
$281$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$281$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$282$	5.67776	+	6.30579i	0.338106	+	0.375505i
$283$	−3.49613	−	10.7600i	−0.207823	−	0.639614i	−0.999586	−	0.0287850i	$-0.990836\pi$
$283$	−3.49613	−	10.7600i	−0.207823	−	0.639614i	0.791762	−	0.610829i	$-0.209164\pi$
$284$	9.86284	−	22.1523i	0.585252	−	1.31450i
$285$		−	4.89898i		−	0.290191i
$286$		0			0
$287$		−	13.8564i		−	0.817918i
$288$		0			0
$289$	−2.16312	−	6.65740i	−0.127242	−	0.391612i
$290$		0			0
$291$	7.12652	−	9.80881i	0.417764	−	0.575003i
$292$	9.74428	+	1.02417i	0.570241	+	0.0599348i
$293$	4.65921	+	1.51387i	0.272194	+	0.0884411i	0.441934	−	0.897048i	$-0.354293\pi$
$293$	4.65921	+	1.51387i	0.272194	+	0.0884411i	−0.169740	+	0.985489i	$0.554293\pi$
$294$	−0.509278	+	2.39596i	−0.0297017	+	0.139735i
$295$	1.01807	+	1.40126i	0.0592746	+	0.0815844i
$296$	−8.48528			−0.493197
$297$		0			0
$298$	18.0000	+	10.3923i	1.04271	+	0.602010i
$299$	−20.5942	+	14.9626i	−1.19099	+	0.865308i
$300$	−10.2973	−	9.27175i	−0.594516	−	0.535304i
$301$	4.94427	−	15.2169i	0.284983	−	0.877088i
$302$	−7.30836	+	3.25389i	−0.420549	+	0.187241i
$303$	−6.86474	−	4.98752i	−0.394369	−	0.286526i
$304$	7.57035	+	8.40772i	0.434189	+	0.482216i
$305$	−9.31841	+	3.02774i	−0.533571	+	0.173368i
$306$		0			0
$307$	19.7990			1.12999			0.564994	−	0.825095i	$-0.308878\pi$
$307$	19.7990			1.12999			0.564994	+	0.825095i	$0.308878\pi$
$308$		0			0
$309$	−6.00000			−0.341328
$310$	2.43607	−	0.256041i	0.138360	−	0.0145422i
$311$	9.88367	−	3.21140i	0.560451	−	0.182102i	−0.0150728	−	0.999886i	$-0.504798\pi$
$311$	9.88367	−	3.21140i	0.560451	−	0.182102i	0.575524	+	0.817785i	$0.304798\pi$
$312$	7.41641	−	22.8254i	0.419871	−	1.29223i
$313$	−21.8435	−	15.8702i	−1.23467	−	0.897037i	−0.237434	−	0.971404i	$-0.576306\pi$
$313$	−21.8435	−	15.8702i	−1.23467	−	0.897037i	−0.997231	+	0.0743667i	$0.976306\pi$
$314$	−14.2114	+	6.32734i	−0.801998	+	0.357072i
$315$		0			0
$316$	15.1407	−	16.8154i	0.851731	−	0.945943i
$317$	20.2254	−	14.6946i	1.13597	−	0.825333i	0.149420	−	0.988774i	$-0.452259\pi$
$317$	20.2254	−	14.6946i	1.13597	−	0.825333i	0.986553	+	0.163441i	$0.0522594\pi$
$318$	−4.24264	−	2.44949i	−0.237915	−	0.137361i
$319$		0			0
$320$	−8.00000			−0.447214
$321$	8.63864	+	11.8901i	0.482162	+	0.663639i
$322$	−4.32136	+	20.3304i	−0.240820	+	1.13297i
$323$	−13.1782	−	4.28187i	−0.733256	−	0.238249i
$324$	1.88151	−	17.9014i	0.104528	−	0.994522i
$325$	−11.5182	+	15.8534i	−0.638914	+	0.879390i
$326$	−18.2033	+	16.3903i	−1.00819	+	0.907774i
$327$	−5.24419	−	16.1400i	−0.290004	−	0.892542i
$328$	8.14459	+	11.2101i	0.449710	+	0.618972i
$329$		−	9.79796i		−	0.540179i
$330$		0			0
$331$		−	5.19615i		−	0.285606i	−0.989751	−	0.142803i	$-0.954388\pi$
$331$		−	5.19615i		−	0.285606i	0.989751	−	0.142803i	$-0.0456116\pi$
$332$		0			0
$333$		0			0
$334$	18.7357	+	20.8081i	1.02517	+	1.13857i
$335$	−5.09037	+	7.00629i	−0.278117	+	0.382795i
$336$	−7.97038	−	17.9018i	−0.434820	−	0.976621i
$337$	−32.6144	−	10.5971i	−1.77662	−	0.577259i	−0.777928	−	0.628353i	$-0.783729\pi$
$337$	−32.6144	−	10.5971i	−1.77662	−	0.577259i	−0.998694	+	0.0510938i	$0.983729\pi$
$338$	−15.2164	−	3.23435i	−0.827663	−	0.175925i
$339$	5.09037	+	7.00629i	0.276471	+	0.380530i
$340$	8.48528	−	4.89898i	0.460179	−	0.265684i
$341$		0			0
$342$		0			0
$343$	−13.7295	+	9.97505i	−0.741322	+	0.538602i
$344$	4.94427	+	15.2169i	0.266577	+	0.820440i
$345$	−2.78115	+	8.55951i	−0.149732	+	0.460828i
$346$	5.63591	+	12.6585i	0.302988	+	0.680523i
$347$	−20.5942	−	14.9626i	−1.10556	−	0.803233i	−0.123597	−	0.992332i	$-0.539443\pi$
$347$	−20.5942	−	14.9626i	−1.10556	−	0.803233i	−0.981958	+	0.189100i	$0.939443\pi$
$348$		0			0
$349$	−4.65921	+	1.51387i	−0.249402	+	0.0810355i	−0.431050	−	0.902328i	$-0.641857\pi$
$349$	−4.65921	+	1.51387i	−0.249402	+	0.0810355i	0.181648	+	0.983364i	$0.441857\pi$
$350$	1.67246	+	15.9124i	0.0893965	+	0.850551i
$351$	−25.4558			−1.35873
$352$		0			0
$353$	−17.0000			−0.904819			−0.452409	−	0.891810i	$-0.649435\pi$
$353$	−17.0000			−0.904819			−0.452409	+	0.891810i	$0.649435\pi$
$354$	−0.443477	−	4.21940i	−0.0235705	−	0.224259i
$355$	−11.5309	+	3.74663i	−0.611999	+	0.198851i
$356$	1.95630	−	0.415823i	0.103683	−	0.0220386i
$357$	19.4164	+	14.1068i	1.02763	+	0.746613i
$358$	−4.98149	−	11.1886i	−0.263280	−	0.591336i
$359$	−2.62210	+	8.06998i	−0.138389	+	0.425917i	−0.996102	−	0.0882117i	$-0.971885\pi$
$359$	−2.62210	+	8.06998i	−0.138389	+	0.425917i	0.857713	+	0.514129i	$0.171885\pi$
$360$		0			0
$361$	8.89919	−	6.46564i	0.468378	−	0.340297i
$362$	−14.8492	+	25.7196i	−0.780459	+	1.35179i
$363$		0			0
$364$	−24.0000	+	13.8564i	−1.25794	+	0.726273i
$365$	−2.87955	−	3.96336i	−0.150722	−	0.207452i
$366$	23.4755	+	4.98988i	1.22709	+	0.260825i
$367$	1.64728	+	0.535233i	0.0859872	+	0.0279389i	0.351695	−	0.936115i	$-0.385606\pi$
$367$	1.64728	+	0.535233i	0.0859872	+	0.0279389i	−0.265707	+	0.964054i	$0.585606\pi$
$368$	−8.45386	−	18.9877i	−0.440688	−	0.989802i
$369$		0			0
$370$	2.83888	+	3.15290i	0.147586	+	0.163911i
$371$	1.74806	+	5.37999i	0.0907550	+	0.279315i
$372$	−5.48127	−	2.44042i	−0.284191	−	0.126530i
$373$			14.6969i			0.760979i	0.924785	+	0.380489i	$0.124244\pi$
$373$			14.6969i			0.760979i	−0.924785	+	0.380489i	$0.875756\pi$
$374$		0			0
$375$			15.5885i			0.804984i
$376$	5.75910	+	7.92672i	0.297003	+	0.408789i
$377$		0			0
$378$	−15.4460	+	13.9076i	−0.794455	+	0.715331i
$379$	−7.12652	+	9.80881i	−0.366065	+	0.503845i	−0.951826	−	0.306639i	$-0.900796\pi$
$379$	−7.12652	+	9.80881i	−0.366065	+	0.503845i	0.585761	+	0.810484i	$0.300796\pi$
$380$	0.591302	−	5.62587i	0.0303332	−	0.288601i
$381$	23.2960	+	7.56934i	1.19349	+	0.387789i
$382$	1.52783	−	7.18789i	0.0781707	−	0.367764i
$383$	19.3434	+	26.6239i	0.988402	+	1.36042i	0.932178	+	0.362000i	$0.117906\pi$
$383$	19.3434	+	26.6239i	0.988402	+	1.36042i	0.0562238	+	0.998418i	$0.482094\pi$
$384$	16.9706	+	9.79796i	0.866025	+	0.500000i
$385$		0			0
$386$	12.0000	+	6.92820i	0.610784	+	0.352636i
$387$		0			0
$388$	9.36783	−	10.4040i	0.475579	−	0.528184i
$389$	5.87132	−	18.0701i	0.297688	−	0.916189i	−0.684617	−	0.728903i	$-0.740031\pi$
$389$	5.87132	−	18.0701i	0.297688	−	0.916189i	0.982305	−	0.187287i	$-0.0599693\pi$
$390$	−10.9625	+	4.88084i	−0.555110	+	0.247151i
$391$	20.5942	+	14.9626i	1.04149	+	0.756690i
$392$	−0.874032	+	2.68999i	−0.0441453	+	0.135865i
$393$	−4.65921	+	1.51387i	−0.235026	+	0.0763645i
$394$		0			0
$395$	−11.3137			−0.569254
$396$		0			0
$397$	6.00000			0.301131			0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000			0.301131			0.150566	+	0.988600i	$0.451890\pi$
$398$	14.6164	−	1.53625i	0.732655	−	0.0770052i
$399$	13.1782	−	4.28187i	0.659736	−	0.214361i
$400$	−10.7061	−	11.8903i	−0.535304	−	0.594516i
$401$	−8.09017	−	5.87785i	−0.404004	−	0.293526i	0.367166	−	0.930155i	$-0.380328\pi$
$401$	−8.09017	−	5.87785i	−0.404004	−	0.293526i	−0.771170	+	0.636629i	$0.780328\pi$
$402$	19.3792	−	8.62819i	0.966548	−	0.430335i
$403$	−2.62210	+	8.06998i	−0.130616	+	0.401994i
$404$	−7.28130	−	6.55611i	−0.362258	−	0.326179i
$405$	−7.28115	+	5.29007i	−0.361803	+	0.262866i
$406$		0			0
$407$		0			0
$408$	−24.0000			−1.18818
$409$	−17.2773	−	23.7801i	−0.854307	−	1.17585i	−0.982897	−	0.184155i	$-0.941045\pi$
$409$	−17.2773	−	23.7801i	−0.854307	−	1.17585i	0.128590	−	0.991698i	$-0.458955\pi$
$410$	1.44045	−	6.77681i	0.0711390	−	0.334683i
$411$	31.2983	+	10.1694i	1.54383	+	0.501621i
$412$	−6.89025	−	0.724194i	−0.339458	−	0.0356785i
$413$	−2.87955	+	3.96336i	−0.141693	+	0.195024i
$414$		0			0
$415$		0			0
$416$	11.2718	−	25.3169i	0.552646	−	1.24126i
$417$		−	34.2929i		−	1.67933i
$418$		0			0
$419$			10.3923i			0.507697i	0.967244	+	0.253849i	$0.0816965\pi$
$419$			10.3923i			0.507697i	−0.967244	+	0.253849i	$0.918303\pi$
$420$	−3.98519	+	8.95088i	−0.194457	+	0.436758i
$421$	9.27051	+	28.5317i	0.451817	+	1.39055i	0.874832	+	0.484427i	$0.160972\pi$
$421$	9.27051	+	28.5317i	0.451817	+	1.39055i	−0.423015	+	0.906123i	$0.639028\pi$
$422$	5.35304	+	5.94516i	0.260582	+	0.289406i
$423$		0			0
$424$	−4.57649	−	3.32502i	−0.222254	−	0.161477i
$425$	18.6368	+	6.05547i	0.904019	+	0.293734i
$426$	29.0495	+	6.17466i	1.40745	+	0.299163i
$427$	−16.2892	−	22.4201i	−0.788289	−	1.08499i
$428$	8.48528	+	14.6969i	0.410152	+	0.710403i
$429$		0			0
$430$	4.00000	−	6.92820i	0.192897	−	0.334108i
$431$	11.4412	−	8.31254i	0.551105	−	0.400401i	−0.277088	−	0.960845i	$-0.589369\pi$
$431$	11.4412	−	8.31254i	0.551105	−	0.400401i	0.828193	+	0.560444i	$0.189369\pi$
$432$	4.32136	−	20.3304i	0.207912	−	0.978148i
$433$	−6.48936	+	19.9722i	−0.311859	+	0.959802i	0.665170	+	0.746692i	$0.268359\pi$
$433$	−6.48936	+	19.9722i	−0.311859	+	0.959802i	−0.977028	+	0.213110i	$0.931641\pi$
$434$	2.81795	+	6.32923i	0.135266	+	0.303813i
$435$		0			0
$436$	−4.07422	−	19.1677i	−0.195120	−	0.917966i
$437$	13.9776	−	4.54160i	0.668640	−	0.217254i
$438$	1.25434	+	11.9343i	0.0599348	+	0.570241i
$439$	22.6274			1.07995			0.539974	−	0.841682i	$-0.318434\pi$
$439$	22.6274			1.07995			0.539974	+	0.841682i	$0.318434\pi$
$440$		0			0
$441$		0			0
$442$	3.54781	+	33.7552i	0.168752	+	1.60557i
$443$	4.94183	−	1.60570i	0.234794	−	0.0762891i	−0.189257	−	0.981928i	$-0.560608\pi$
$443$	4.94183	−	1.60570i	0.234794	−	0.0762891i	0.424051	+	0.905639i	$0.360608\pi$
$444$	−2.16068	−	10.1652i	−0.102541	−	0.482419i
$445$	−0.809017	−	0.587785i	−0.0383511	−	0.0278637i
$446$	−12.9519	−	29.0904i	−0.613289	−	1.37747i
$447$	−7.86629	+	24.2099i	−0.372063	+	1.14509i
$448$	−6.99226	−	21.5200i	−0.330353	−	1.01672i
$449$	−18.6074	+	13.5191i	−0.878137	+	0.638004i	−0.932758	−	0.360503i	$-0.882605\pi$
$449$	−18.6074	+	13.5191i	−0.878137	+	0.638004i	0.0546209	+	0.998507i	$0.482605\pi$
$450$		0			0
$451$		0			0
$452$	5.00000	+	8.66025i	0.235180	+	0.407344i
$453$	−5.75910	−	7.92672i	−0.270586	−	0.372430i
$454$	11.7378	+	2.49494i	0.550881	+	0.117093i
$455$	13.1782	+	4.28187i	0.617805	+	0.200737i
$456$	−8.14459	+	11.2101i	−0.381405	+	0.524960i
$457$	−11.5182	+	15.8534i	−0.538798	+	0.741592i	−0.988439	−	0.151617i	$-0.951552\pi$
$457$	−11.5182	+	15.8534i	−0.538798	+	0.741592i	0.449641	+	0.893209i	$0.351552\pi$
$458$	0.946294	+	1.05097i	0.0442174	+	0.0491084i
$459$	7.86629	+	24.2099i	0.367167	+	1.13002i
$460$	−4.22693	+	9.49384i	−0.197082	+	0.442653i
$461$		−	29.3939i		−	1.36901i	−0.729008	−	0.684505i	$-0.760019\pi$
$461$		−	29.3939i		−	1.36901i	0.729008	−	0.684505i	$-0.239981\pi$
$462$		0			0
$463$			36.3731i			1.69040i	0.534450	+	0.845200i	$0.320519\pi$
$463$			36.3731i			1.69040i	−0.534450	+	0.845200i	$0.679481\pi$
$464$		0			0
$465$	0.927051	+	2.85317i	0.0429910	+	0.132313i
$466$	−20.5946	+	18.5435i	−0.954028	+	0.859011i
$467$	−19.3434	+	26.6239i	−0.895106	+	1.23201i	0.0768969	+	0.997039i	$0.475499\pi$
$467$	−19.3434	+	26.6239i	−0.895106	+	1.23201i	−0.972003	+	0.234969i	$0.924501\pi$
$468$		0			0
$469$	−23.2960	−	7.56934i	−1.07571	−	0.349520i
$470$	1.01856	−	4.79193i	0.0469824	−	0.221035i
$471$	−11.1988	−	15.4138i	−0.516014	−	0.710232i
$472$		−	4.89898i		−	0.225494i
$473$		0			0
$474$	24.0000	+	13.8564i	1.10236	+	0.636446i
$475$	9.15298	−	6.65003i	0.419968	−	0.305124i
$476$	20.5946	+	18.5435i	0.943953	+	0.849940i
$477$		0			0
$478$	7.30836	−	3.25389i	0.334277	−	0.148830i
$479$	25.1707	+	18.2876i	1.15008	+	0.835581i	0.988491	−	0.151277i	$-0.0483386\pi$
$479$	25.1707	+	18.2876i	1.15008	+	0.835581i	0.161587	+	0.986858i	$0.448339\pi$
$480$	−2.03711	−	9.58385i	−0.0929809	−	0.437441i
$481$	−13.9776	+	4.54160i	−0.637325	+	0.207079i
$482$	−41.3415	+	4.34517i	−1.88305	+	0.197917i
$483$	−25.4558			−1.15828
$484$		0			0
$485$	−7.00000			−0.317854
$486$		0			0
$487$	37.8874	−	12.3104i	1.71684	−	0.557836i	0.725393	−	0.688334i	$-0.241658\pi$
$487$	37.8874	−	12.3104i	1.71684	−	0.557836i	0.991448	+	0.130499i	$0.0416578\pi$
$488$	26.3565	+	8.56373i	1.19310	+	0.387662i
$489$	−24.2705	−	17.6336i	−1.09755	−	0.797417i
$490$	1.29195	−	0.575212i	0.0583643	−	0.0259855i
$491$	10.4884	−	32.2799i	0.473334	−	1.45677i	−0.374857	−	0.927083i	$-0.622308\pi$
$491$	10.4884	−	32.2799i	0.473334	−	1.45677i	0.848191	−	0.529690i	$-0.177692\pi$
$492$	−11.3555	+	12.6116i	−0.511947	+	0.568574i
$493$		0			0
$494$	16.9706	+	9.79796i	0.763542	+	0.440831i
$495$		0			0
$496$	−6.00000	−	3.46410i	−0.269408	−	0.155543i
$497$	−20.1568	−	27.7435i	−0.904158	−	1.24447i
$498$		0			0
$499$	−16.4728	−	5.35233i	−0.737423	−	0.239603i	−0.0838623	−	0.996477i	$-0.526726\pi$
$499$	−16.4728	−	5.35233i	−0.737423	−	0.239603i	−0.653561	+	0.756874i	$0.726726\pi$
$500$	−1.88151	+	17.9014i	−0.0841438	+	0.800575i
$501$	−20.1568	+	27.7435i	−0.900541	+	1.23949i
$502$	23.6642	−	21.3074i	1.05619	−	0.950995i
$503$	12.2364	+	37.6599i	0.545596	+	1.67917i	0.719568	+	0.694422i	$0.244340\pi$
$503$	12.2364	+	37.6599i	0.545596	+	1.67917i	−0.173972	+	0.984751i	$0.555660\pi$
$504$		0			0
$505$			4.89898i			0.218002i
$506$		0			0
$507$		−	19.0526i		−	0.846154i
$508$	25.8390	+	11.5042i	1.14642	+	0.510419i
$509$	−0.309017	−	0.951057i	−0.0136969	−	0.0421548i	0.943974	−	0.330019i	$-0.107055\pi$
$509$	−0.309017	−	0.951057i	−0.0136969	−	0.0421548i	−0.957671	+	0.287864i	$0.907055\pi$
$510$	8.02957	+	8.91774i	0.355555	+	0.394884i
$511$	8.14459	−	11.2101i	0.360296	−	0.495904i
$512$	18.3060	+	13.3001i	0.809017	+	0.587785i
$513$	13.9776	+	4.54160i	0.617127	+	0.200517i
$514$	−30.4328	−	6.46869i	−1.34233	−	0.285322i
$515$	2.03615	+	2.80252i	0.0897234	+	0.123494i
$516$	−16.9706	+	9.79796i	−0.747087	+	0.431331i
$517$		0			0
$518$	−6.00000	+	10.3923i	−0.263625	+	0.456612i
$519$	−13.7295	+	9.97505i	−0.602657	+	0.437856i
$520$	−13.1782	+	4.28187i	−0.577903	+	0.187772i
$521$	−5.25329	+	16.1680i	−0.230151	+	0.708331i	0.767577	+	0.640957i	$0.221462\pi$
$521$	−5.25329	+	16.1680i	−0.230151	+	0.708331i	−0.997728	+	0.0673745i	$0.978538\pi$
$522$		0			0
$523$	29.7472	+	21.6126i	1.30075	+	0.945053i	0.999963	−	0.00863696i	$-0.00274927\pi$
$523$	29.7472	+	21.6126i	1.30075	+	0.945053i	0.300791	+	0.953690i	$0.402749\pi$
$524$	−5.53324	+	1.17613i	−0.241721	+	0.0513793i
$525$	−18.6368	+	6.05547i	−0.813378	+	0.264282i
$526$	−2.09057	−	19.8904i	−0.0911532	−	0.867264i
$527$	8.48528			0.369625
$528$		0			0
$529$	−4.00000			−0.173913
$530$	0.295651	+	2.81293i	0.0128423	+	0.122186i
$531$		0			0
$532$	15.6504	−	3.32659i	0.678529	−	0.144226i
$533$	19.4164	+	14.1068i	0.841018	+	0.611035i
$534$	0.996297	+	2.23772i	0.0431140	+	0.0968356i
$535$	2.62210	−	8.06998i	0.113363	−	0.348896i
$536$	23.2960	−	7.56934i	1.00624	−	0.326946i
$537$	12.1353	−	8.81678i	0.523675	−	0.380472i
$538$	−7.07107	+	12.2474i	−0.304855	+	0.528025i
$539$		0			0
$540$	−9.00000	+	5.19615i	−0.387298	+	0.223607i
$541$	−8.63864	−	11.8901i	−0.371404	−	0.511194i	0.581878	−	0.813276i	$-0.302318\pi$
$541$	−8.63864	−	11.8901i	−0.371404	−	0.511194i	−0.953282	+	0.302082i	$0.902318\pi$
$542$	3.91259	+	0.831647i	0.168060	+	0.0357223i
$543$	−34.5928	−	11.2399i	−1.48452	−	0.482350i
$544$	−27.5610	−	2.89678i	−1.18167	−	0.124198i
$545$	−5.75910	+	7.92672i	−0.246693	+	0.339543i
$546$	−22.7110	−	25.2232i	−0.971943	−	1.07945i
$547$	−1.74806	−	5.37999i	−0.0747418	−	0.230032i	0.906705	−	0.421765i	$-0.138589\pi$
$547$	−1.74806	−	5.37999i	−0.0747418	−	0.230032i	−0.981447	+	0.191733i	$0.938589\pi$
$548$	34.7147	+	15.4560i	1.48294	+	0.660247i
$549$		0			0
$550$		0			0
$551$		0			0
$552$	20.5942	−	14.9626i	0.876548	−	0.636849i
$553$	−9.88854	−	30.4338i	−0.420504	−	1.29418i
$554$	10.2973	−	9.27175i	0.437491	−	0.393919i
$555$	−3.05422	+	4.20378i	−0.129644	+	0.178440i
$556$	4.13912	−	39.3811i	0.175538	−	1.67013i
$557$	−23.2960	−	7.56934i	−0.987085	−	0.320723i	−0.229391	−	0.973334i	$-0.573674\pi$
$557$	−23.2960	−	7.56934i	−0.987085	−	0.320723i	−0.757693	+	0.652611i	$0.773674\pi$
$558$		0			0
$559$	16.2892	+	22.4201i	0.688959	+	0.948271i
$560$	−5.65685	+	9.79796i	−0.239046	+	0.414039i
$561$		0			0
$562$		0			0
$563$	9.15298	−	6.65003i	0.385752	−	0.280265i	−0.377960	−	0.925822i	$-0.623374\pi$
$563$	9.15298	−	6.65003i	0.385752	−	0.280265i	0.763713	+	0.645556i	$0.223374\pi$
$564$	−8.02957	+	8.91774i	−0.338106	+	0.375505i
$565$	1.54508	−	4.75528i	0.0650022	−	0.200056i
$566$	14.6167	−	6.50779i	0.614387	−	0.273543i
$567$	−20.5942	−	14.9626i	−0.864876	−	0.628369i
$568$	32.6144	+	10.5971i	1.36847	+	0.444643i
$569$	18.6368	−	6.05547i	0.781296	−	0.253859i	0.108903	−	0.994052i	$-0.465266\pi$
$569$	18.6368	−	6.05547i	0.781296	−	0.253859i	0.672394	+	0.740194i	$0.265266\pi$
$570$	6.89025	−	0.724194i	0.288601	−	0.0303332i
$571$	5.65685			0.236732			0.118366	−	0.992970i	$-0.462234\pi$
$571$	5.65685			0.236732			0.118366	+	0.992970i	$0.462234\pi$
$572$		0			0
$573$	9.00000			0.375980
$574$	19.4886	−	2.04833i	0.813437	−	0.0854957i
$575$	−19.7673	+	6.42280i	−0.824355	+	0.267849i
$576$		0			0
$577$	13.7533	+	9.99235i	0.572557	+	0.415987i	0.836033	−	0.548679i	$-0.184869\pi$
$577$	13.7533	+	9.99235i	0.572557	+	0.415987i	−0.263476	+	0.964666i	$0.584869\pi$
$578$	9.04364	−	4.02649i	0.376166	−	0.167480i
$579$	−5.24419	+	16.1400i	−0.217941	+	0.670754i
$580$		0			0
$581$		0			0
$582$	14.8492	+	8.57321i	0.615521	+	0.355371i
$583$		0			0
$584$			13.8564i			0.573382i
$585$		0			0
$586$	−1.44045	+	6.77681i	−0.0595046	+	0.279947i
$587$	9.88367	+	3.21140i	0.407943	+	0.132549i	0.505798	−	0.862652i	$-0.331198\pi$
$587$	9.88367	+	3.21140i	0.407943	+	0.132549i	−0.0978551	+	0.995201i	$0.531198\pi$
$588$	−3.44512	−	0.362097i	−0.142075	−	0.0149326i
$589$	2.87955	−	3.96336i	0.118650	−	0.163307i
$590$	−1.82033	+	1.63903i	−0.0749416	+	0.0674777i
$591$		0			0
$592$	−1.25434	−	11.9343i	−0.0515531	−	0.490495i
$593$		−	9.79796i		−	0.402354i	−0.979555	−	0.201177i	$-0.935523\pi$
$593$		−	9.79796i		−	0.402354i	0.979555	−	0.201177i	$-0.0644766\pi$
$594$		0			0
$595$		−	13.8564i		−	0.568057i
$596$	−11.9556	+	26.8526i	−0.489719	+	1.09993i
$597$	5.56231	+	17.1190i	0.227650	+	0.700635i
$598$	−24.0887	−	26.7532i	−0.985060	−	1.09402i
$599$	26.4699	−	36.4327i	1.08153	−	1.48860i	0.223708	−	0.974656i	$-0.428184\pi$
$599$	26.4699	−	36.4327i	1.08153	−	1.48860i	0.857823	−	0.513945i	$-0.171816\pi$
$600$	11.5182	−	15.8534i	0.470228	−	0.647214i
$601$	4.65921	+	1.51387i	0.190053	+	0.0617520i	0.402497	−	0.915421i	$-0.368142\pi$
$601$	4.65921	+	1.51387i	0.190053	+	0.0617520i	−0.212444	+	0.977173i	$0.568142\pi$
$602$	22.1330	+	4.70450i	0.902072	+	0.191741i
$603$		0			0
$604$	−5.65685	−	9.79796i	−0.230174	−	0.398673i
$605$		0			0
$606$	6.00000	−	10.3923i	0.243733	−	0.422159i
$607$	−18.3060	+	13.3001i	−0.743016	+	0.539833i	−0.893654	−	0.448756i	$-0.851867\pi$
$607$	−18.3060	+	13.3001i	−0.743016	+	0.539833i	0.150638	+	0.988589i	$0.451867\pi$
$608$	−10.7061	+	11.8903i	−0.434189	+	0.482216i
$609$		0			0
$610$	−5.63591	−	12.6585i	−0.228191	−	0.512526i
$611$	13.7295	+	9.97505i	0.555435	+	0.403547i
$612$		0			0
$613$	−9.31841	+	3.02774i	−0.376367	+	0.122289i	−0.491091	−	0.871108i	$-0.663402\pi$
$613$	−9.31841	+	3.02774i	−0.376367	+	0.122289i	0.114724	+	0.993397i	$0.463402\pi$
$614$	2.92680	+	27.8466i	0.118116	+	1.12380i
$615$	8.48528			0.342160
$616$		0			0
$617$	2.00000			0.0805170			0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000			0.0805170			0.0402585	+	0.999189i	$0.487182\pi$
$618$	−0.886953	−	8.43880i	−0.0356785	−	0.339458i
$619$	−1.64728	+	0.535233i	−0.0662097	+	0.0215128i	−0.341935	−	0.939724i	$-0.611082\pi$
$619$	−1.64728	+	0.535233i	−0.0662097	+	0.0215128i	0.275725	+	0.961237i	$0.411082\pi$
$620$	0.720227	+	3.38840i	0.0289250	+	0.136082i
$621$	−21.8435	−	15.8702i	−0.876548	−	0.636849i
$622$	5.97778	+	13.4263i	0.239687	+	0.538346i
$623$	0.874032	−	2.68999i	0.0350174	−	0.107772i
$624$	33.1994	+	7.05676i	1.32904	+	0.282496i
$625$	−8.89919	+	6.46564i	−0.355967	+	0.258626i
$626$	19.0919	−	33.0681i	0.763065	−	1.32167i
$627$		0			0
$628$	−11.0000	−	19.0526i	−0.438948	−	0.760280i
$629$	8.63864	+	11.8901i	0.344445	+	0.474088i
$630$		0			0
$631$	34.5928	+	11.2399i	1.37712	+	0.447453i	0.901721	−	0.432318i	$-0.142304\pi$
$631$	34.5928	+	11.2399i	1.37712	+	0.447453i	0.475398	+	0.879771i	$0.342304\pi$
$632$	25.8885	+	18.8091i	1.02979	+	0.748187i
$633$	−5.75910	+	7.92672i	−0.228904	+	0.315059i
$634$	23.6573	+	26.2741i	0.939553	+	1.04348i
$635$	−4.37016	−	13.4500i	−0.173425	−	0.533746i
$636$	2.81795	−	6.32923i	0.111739	−	0.250970i
$637$			4.89898i			0.194105i
$638$		0			0
$639$		0			0
$640$	−1.18260	−	11.2517i	−0.0467465	−	0.444764i
$641$	5.87132	+	18.0701i	0.231903	+	0.713725i	0.997517	+	0.0704245i	$0.0224354\pi$
$641$	5.87132	+	18.0701i	0.231903	+	0.713725i	−0.765614	+	0.643300i	$0.777565\pi$
$642$	−15.4460	+	13.9076i	−0.609604	+	0.548890i
$643$	−15.2711	+	21.0189i	−0.602234	+	0.828904i	−0.995911	−	0.0903453i	$-0.971203\pi$
$643$	−15.2711	+	21.0189i	−0.602234	+	0.828904i	0.393677	+	0.919249i	$0.371203\pi$
$644$	−29.2329	−	3.07250i	−1.15194	−	0.121073i
$645$	9.31841	+	3.02774i	0.366912	+	0.119217i
$646$	4.07422	−	19.1677i	0.160298	−	0.754143i
$647$	−1.01807	−	1.40126i	−0.0400246	−	0.0550892i	0.788536	−	0.614989i	$-0.210840\pi$
$647$	−1.01807	−	1.40126i	−0.0400246	−	0.0550892i	−0.828560	+	0.559900i	$0.810840\pi$
$648$	25.4558			1.00000
$649$		0			0
$650$	−24.0000	−	13.8564i	−0.941357	−	0.543493i
$651$	−6.86474	+	4.98752i	−0.269050	+	0.195476i
$652$	−25.7433	−	23.1794i	−1.00819	−	0.907774i
$653$	9.57953	−	29.4828i	0.374876	−	1.15375i	−0.568687	−	0.822554i	$-0.692548\pi$
$653$	9.57953	−	29.4828i	0.374876	−	1.15375i	0.943562	−	0.331195i	$-0.107452\pi$
$654$	21.9251	−	9.76168i	0.857339	−	0.381712i
$655$	2.28825	+	1.66251i	0.0894092	+	0.0649596i
$656$	−14.5626	+	13.1122i	−0.568574	+	0.511947i
$657$		0			0
$658$	13.7805	−	1.44839i	0.537220	−	0.0564641i
$659$	−45.2548			−1.76288			−0.881439	−	0.472298i	$-0.843425\pi$
$659$	−45.2548			−1.76288			−0.881439	+	0.472298i	$0.843425\pi$
$660$		0			0
$661$	−17.0000			−0.661223			−0.330612	−	0.943767i	$-0.607255\pi$
$661$	−17.0000			−0.661223			−0.330612	+	0.943767i	$0.607255\pi$
$662$	7.30821	−	0.768124i	0.284042	−	0.0298540i
$663$	−39.5347	+	12.8456i	−1.53540	+	0.498882i
$664$		0			0
$665$	−6.47214	−	4.70228i	−0.250979	−	0.182347i
$666$		0			0
$667$		0			0
$668$	−26.4962	+	29.4270i	−1.02517	+	1.13857i
$669$	31.5517	−	22.9236i	1.21986	−	0.886279i
$670$	−10.6066	−	6.12372i	−0.409769	−	0.236580i
$671$		0			0
$672$	24.0000	−	13.8564i	0.925820	−	0.534522i
$673$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$673$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$674$	10.0832	−	47.4376i	0.388390	−	1.82723i
$675$	−19.7673	−	6.42280i	−0.760845	−	0.247214i
$676$	2.29963	−	21.8795i	0.0884472	−	0.841519i
$677$	14.3977	−	19.8168i	0.553350	−	0.761621i	−0.437112	−	0.899407i	$-0.643999\pi$
$677$	14.3977	−	19.8168i	0.553350	−	0.761621i	0.990462	+	0.137786i	$0.0439986\pi$
$678$	−9.10163	+	8.19514i	−0.349546	+	0.314733i
$679$	−6.11822	−	18.8300i	−0.234796	−	0.722627i
$680$	8.14459	+	11.2101i	0.312331	+	0.429886i
$681$			14.6969i			0.563188i
$682$		0			0
$683$		−	3.46410i		−	0.132550i	−0.997801	−	0.0662751i	$-0.978889\pi$
$683$		−	3.46410i		−	0.132550i	0.997801	−	0.0662751i	$-0.0211115\pi$
$684$		0			0
$685$	−5.87132	−	18.0701i	−0.224332	−	0.690422i
$686$	−16.0591	−	17.8355i	−0.613141	−	0.680962i
$687$	−1.01807	+	1.40126i	−0.0388419	+	0.0534613i
$688$	−20.6712	+	9.20340i	−0.788081	+	0.350876i
$689$	−9.31841	−	3.02774i	−0.355003	−	0.115348i
$690$	−12.4498	−	2.64628i	−0.473955	−	0.100742i
$691$	−9.16267	−	12.6113i	−0.348564	−	0.479757i	0.598354	−	0.801232i	$-0.295822\pi$
$691$	−9.16267	−	12.6113i	−0.348564	−	0.479757i	−0.946918	+	0.321474i	$0.895822\pi$
$692$	−16.9706	+	9.79796i	−0.645124	+	0.372463i
$693$		0			0
$694$	18.0000	−	31.1769i	0.683271	−	1.18346i
$695$	−16.0177	+	11.6376i	−0.607587	+	0.441438i
$696$		0			0
$697$	7.41641	−	22.8254i	0.280916	−	0.864572i
$698$	−2.81795	−	6.32923i	−0.106661	−	0.239565i
$699$	−27.4589	−	19.9501i	−1.03859	−	0.754582i
$700$	−22.1330	+	4.70450i	−0.836547	+	0.177814i
$701$	−32.6144	+	10.5971i	−1.23183	+	0.400246i	−0.851377	−	0.524554i	$-0.824232\pi$
$701$	−32.6144	+	10.5971i	−1.23183	+	0.400246i	−0.380453	+	0.924800i	$0.624232\pi$
$702$	−3.76302	−	35.8028i	−0.142026	−	1.35129i
$703$	8.48528			0.320028
$704$		0			0
$705$	6.00000			0.225973
$706$	−2.51303	−	23.9099i	−0.0945793	−	0.899862i
$707$	−13.1782	+	4.28187i	−0.495618	+	0.161036i
$708$	5.86889	−	1.24747i	0.220566	−	0.0468828i
$709$	20.2254	+	14.6946i	0.759582	+	0.551868i	0.898782	−	0.438396i	$-0.144453\pi$
$709$	20.2254	+	14.6946i	0.759582	+	0.551868i	−0.139200	+	0.990264i	$0.544453\pi$
$710$	−6.97408	−	15.6640i	−0.261733	−	0.587861i
$711$		0			0
$712$	0.874032	+	2.68999i	0.0327557	+	0.100812i
$713$	−7.28115	+	5.29007i	−0.272681	+	0.198115i
$714$	−16.9706	+	29.3939i	−0.635107	+	1.10004i
$715$		0			0
$716$	15.0000	−	8.66025i	0.560576	−	0.323649i
$717$	5.75910	+	7.92672i	0.215077	+	0.296029i
$718$	−11.7378	−	2.49494i	−0.438050	−	0.0931103i
$719$	14.8255	+	4.81710i	0.552898	+	0.179647i	0.572123	−	0.820168i	$-0.306120\pi$
$719$	14.8255	+	4.81710i	0.552898	+	0.179647i	−0.0192251	+	0.999815i	$0.506120\pi$
$720$		0			0
$721$	−5.75910	+	7.92672i	−0.214480	+	0.295206i
$722$	10.4092	+	11.5606i	0.387391	+	0.430242i
$723$	−15.7326	−	48.4199i	−0.585101	−	1.80076i
$724$	−38.3689	−	17.0829i	−1.42597	−	0.634882i
$725$		0			0
$726$		0			0
$727$		−	25.9808i		−	0.963573i	−0.876289	−	0.481787i	$-0.839988\pi$
$727$		−	25.9808i		−	0.963573i	0.876289	−	0.481787i	$-0.160012\pi$
$728$	−23.0364	−	31.7069i	−0.853785	−	1.17513i
$729$	−8.34346	−	25.6785i	−0.309017	−	0.951057i
$730$	5.14866	−	4.63587i	0.190560	−	0.171581i
$731$	16.2892	−	22.4201i	0.602477	−	0.829239i
$732$	−3.54781	+	33.7552i	−0.131131	+	1.24763i
$733$	−9.31841	−	3.02774i	−0.344183	−	0.111832i	0.131824	−	0.991273i	$-0.457917\pi$
$733$	−9.31841	−	3.02774i	−0.344183	−	0.111832i	−0.476008	+	0.879441i	$0.657917\pi$
$734$	−0.509278	+	2.39596i	−0.0187978	+	0.0884366i
$735$	1.01807	+	1.40126i	0.0375522	+	0.0516862i
$736$	25.4558	−	14.6969i	0.938315	−	0.541736i
$737$		0			0
$738$		0			0
$739$	−4.57649	+	3.32502i	−0.168349	+	0.122313i	−0.668770	−	0.743470i	$-0.733179\pi$
$739$	−4.57649	+	3.32502i	−0.168349	+	0.122313i	0.500421	+	0.865782i	$0.333179\pi$
$740$	−4.01478	+	4.45887i	−0.147586	+	0.163911i
$741$	−7.41641	+	22.8254i	−0.272449	+	0.838510i
$742$	−7.30836	+	3.25389i	−0.268298	+	0.119454i
$743$	−27.4589	−	19.9501i	−1.00737	−	0.731898i	−0.0437150	−	0.999044i	$-0.513919\pi$
$743$	−27.4589	−	19.9501i	−1.00737	−	0.731898i	−0.963656	+	0.267146i	$0.913919\pi$
$744$	2.62210	−	8.06998i	0.0961307	−	0.295860i
$745$	13.9776	−	4.54160i	0.512100	−	0.166391i
$746$	−20.6707	+	2.17258i	−0.756810	+	0.0795439i
$747$		0			0
$748$		0			0
$749$	24.0000			0.876941
$750$	−21.9246	+	2.30437i	−0.800575	+	0.0841438i
$751$	4.94183	−	1.60570i	0.180330	−	0.0585928i	−0.217460	−	0.976069i	$-0.569777\pi$
$751$	4.94183	−	1.60570i	0.180330	−	0.0585928i	0.397790	+	0.917476i	$0.369777\pi$
$752$	−10.2973	+	9.27175i	−0.375505	+	0.338106i
$753$	31.5517	+	22.9236i	1.14981	+	0.835383i
$754$		0			0
$755$	−1.74806	+	5.37999i	−0.0636186	+	0.195798i
$756$	−21.8439	−	19.6683i	−0.794455	−	0.715331i
$757$	−24.2705	+	17.6336i	−0.882127	+	0.640903i	−0.933813	−	0.357761i	$-0.883540\pi$
$757$	−24.2705	+	17.6336i	−0.882127	+	0.640903i	0.0516866	+	0.998663i	$0.483540\pi$
$758$	−14.8492	−	8.57321i	−0.539349	−	0.311393i
$759$		0			0
$760$	8.00000			0.290191
$761$	25.9159	+	35.6702i	0.939452	+	1.29304i	0.956057	+	0.293182i	$0.0947143\pi$
$761$	25.9159	+	35.6702i	0.939452	+	1.29304i	−0.0166048	+	0.999862i	$0.505286\pi$
$762$	−7.20227	+	33.8840i	−0.260911	+	1.22749i
$763$	−26.3565	−	8.56373i	−0.954168	−	0.310028i
$764$	10.3354	+	1.08629i	0.373921	+	0.0393007i
$765$		0			0
$766$	−34.5862	+	31.1415i	−1.24965	+	1.12519i
$767$	−2.62210	−	8.06998i	−0.0946784	−	0.291390i
$768$	−11.2718	+	25.3169i	−0.406737	+	0.913545i
$769$			4.89898i			0.176662i	0.996091	+	0.0883309i	$0.0281533\pi$
$769$			4.89898i			0.176662i	−0.996091	+	0.0883309i	$0.971847\pi$
$770$		0			0
$771$		−	38.1051i		−	1.37232i
$772$	−7.97038	+	17.9018i	−0.286860	+	0.644299i
$773$	−3.09017	−	9.51057i	−0.111146	−	0.342071i	0.879978	−	0.475015i	$-0.157557\pi$
$773$	−3.09017	−	9.51057i	−0.111146	−	0.342071i	−0.991124	+	0.132943i	$0.957557\pi$
$774$		0			0
$775$	−4.07230	+	5.60503i	−0.146281	+	0.201339i
$776$	16.0177	+	11.6376i	0.575003	+	0.417764i
$777$	−13.9776	−	4.54160i	−0.501444	−	0.162929i
$778$	26.2829	+	5.58660i	0.942287	+	0.200289i
$779$	−8.14459	−	11.2101i	−0.291810	−	0.401642i
$780$	−8.48528	−	14.6969i	−0.303822	−	0.526235i
$781$		0			0
$782$	−18.0000	+	31.1769i	−0.643679	+	1.11488i
$783$		0			0
$784$	−3.91259	−	0.831647i	−0.139735	−	0.0297017i
$785$	−3.39919	+	10.4616i	−0.121322	+	0.373391i
$786$	−2.81795	−	6.32923i	−0.100513	−	0.225756i
$787$	−22.8825	−	16.6251i	−0.815671	−	0.592620i	0.0997979	−	0.995008i	$-0.468180\pi$
$787$	−22.8825	−	16.6251i	−0.815671	−	0.592620i	−0.915469	+	0.402388i	$0.868180\pi$
$788$		0			0
$789$	23.2960	−	7.56934i	0.829361	−	0.269476i
$790$	−1.67246	−	15.9124i	−0.0595033	−	0.566136i
$791$	14.1421			0.502836
$792$		0			0
$793$	48.0000			1.70453
$794$	0.886953	+	8.43880i	0.0314768	+	0.299482i
$795$	−3.29456	+	1.07047i	−0.116846	+	0.0379655i
$796$	4.32136	+	20.3304i	0.153167	+	0.720592i
$797$	−5.66312	−	4.11450i	−0.200598	−	0.145743i	0.482952	−	0.875647i	$-0.339565\pi$
$797$	−5.66312	−	4.11450i	−0.200598	−	0.145743i	−0.683550	+	0.729904i	$0.739565\pi$
$798$	7.97038	+	17.9018i	0.282148	+	0.633715i
$799$	5.24419	−	16.1400i	0.185526	−	0.570991i
$800$	15.1407	−	16.8154i	0.535304	−	0.594516i
$801$		0			0
$802$	7.07107	−	12.2474i	0.249688	−	0.432472i
$803$		0			0
$804$	15.0000	+	25.9808i	0.529009	+	0.916271i
$805$	8.63864	+	11.8901i	0.304472	+	0.419070i
$806$	−11.7378	−	2.49494i	−0.413445	−	0.0878805i
$807$	−16.4728	−	5.35233i	−0.579869	−	0.188411i
$808$	8.14459	−	11.2101i	0.286526	−	0.394369i
$809$	25.9159	−	35.6702i	0.911156	−	1.25410i	−0.0556149	−	0.998452i	$-0.517712\pi$
$809$	25.9159	−	35.6702i	0.911156	−	1.25410i	0.966771	−	0.255646i	$-0.0822881\pi$
$810$	−8.51664	−	9.45869i	−0.299244	−	0.332344i
$811$	12.2364	+	37.6599i	0.429680	+	1.32242i	0.898441	+	0.439094i	$0.144700\pi$
$811$	12.2364	+	37.6599i	0.429680	+	1.32242i	−0.468761	+	0.883325i	$0.655300\pi$
$812$		0			0
$813$			4.89898i			0.171815i
$814$		0			0
$815$			17.3205i			0.606711i
$816$	−3.54781	−	33.7552i	−0.124198	−	1.18167i
$817$	−4.94427	−	15.2169i	−0.172978	−	0.532372i
$818$	30.8920	−	27.8152i	1.08011	−	0.972537i
$819$		0			0
$820$	9.74428	+	1.02417i	0.340285	+	0.0357654i
$821$	46.5921	+	15.1387i	1.62607	+	0.528344i	0.973364	−	0.229264i	$-0.0736320\pi$
$821$	46.5921	+	15.1387i	1.62607	+	0.528344i	0.652710	+	0.757608i	$0.273632\pi$
$822$	−9.67627	+	45.5233i	−0.337499	+	1.58781i
$823$	−5.09037	−	7.00629i	−0.177439	−	0.244224i	0.711029	−	0.703163i	$-0.248230\pi$
$823$	−5.09037	−	7.00629i	−0.177439	−	0.244224i	−0.888468	+	0.458939i	$0.848230\pi$
$824$		−	9.79796i		−	0.341328i
$825$		0			0
$826$	−6.00000	−	3.46410i	−0.208767	−	0.120532i
$827$	20.5942	−	14.9626i	0.716131	−	0.520300i	−0.169015	−	0.985614i	$-0.554059\pi$
$827$	20.5942	−	14.9626i	0.716131	−	0.520300i	0.885146	+	0.465314i	$0.154059\pi$
$828$		0			0
$829$	−5.25329	+	16.1680i	−0.182454	+	0.561536i	−0.999895	−	0.0144759i	$-0.995392\pi$
$829$	−5.25329	+	16.1680i	−0.182454	+	0.561536i	0.817441	+	0.576012i	$0.195392\pi$
$830$		0			0
$831$	13.7295	+	9.97505i	0.476270	+	0.346031i
$832$	37.2737	+	12.1109i	1.29223	+	0.419871i
$833$	4.65921	−	1.51387i	0.161432	−	0.0524524i
$834$	48.2317	−	5.06936i	1.67013	−	0.175538i
$835$	19.7990			0.685172
$836$		0			0
$837$	−9.00000			−0.311086
$838$	−14.6164	+	1.53625i	−0.504916	+	0.0530688i
$839$	24.7092	−	8.02850i	0.853055	−	0.277174i	0.150330	−	0.988636i	$-0.451966\pi$
$839$	24.7092	−	8.02850i	0.853055	−	0.277174i	0.702725	+	0.711461i	$0.251966\pi$
$840$	−13.1782	−	4.28187i	−0.454692	−	0.147738i
$841$	−23.4615	−	17.0458i	−0.809017	−	0.587785i
$842$	−38.7585	+	17.2564i	−1.33570	+	0.594694i
$843$		0			0
$844$	−7.57035	+	8.40772i	−0.260582	+	0.289406i
$845$	−8.89919	+	6.46564i	−0.306141	+	0.222425i
$846$		0			0
$847$		0			0
$848$	4.00000	−	6.92820i	0.137361	−	0.237915i
$849$	11.5182	+	15.8534i	0.395303	+	0.544088i
$850$	−5.76182	+	27.1072i	−0.197629	+	0.929770i
$851$	−14.8255	−	4.81710i	−0.508212	−	0.165128i
$852$	−4.39020	+	41.7699i	−0.150406	+	1.43101i
$853$	23.0364	−	31.7069i	0.788751	−	1.08562i	−0.205512	−	0.978655i	$-0.565886\pi$
$853$	23.0364	−	31.7069i	0.788751	−	1.08562i	0.994263	−	0.106968i	$-0.0341141\pi$
$854$	29.1252	−	26.2245i	0.996644	−	0.897382i
$855$		0			0
$856$	−19.4164	+	14.1068i	−0.663639	+	0.482162i
$857$			29.3939i			1.00408i	0.864846	+	0.502038i	$0.167416\pi$
$857$			29.3939i			1.00408i	−0.864846	+	0.502038i	$0.832584\pi$
$858$		0			0
$859$			15.5885i			0.531871i	0.963991	+	0.265936i	$0.0856809\pi$
$859$			15.5885i			0.531871i	−0.963991	+	0.265936i	$0.914319\pi$
$860$	10.3356	+	4.60170i	0.352441	+	0.156917i
$861$	7.41641	+	22.8254i	0.252751	+	0.777886i
$862$	13.3826	+	14.8629i	0.455814	+	0.506232i
$863$	18.3253	−	25.2227i	0.623802	−	0.858589i	−0.373821	−	0.927501i	$-0.621953\pi$
$863$	18.3253	−	25.2227i	0.623802	−	0.858589i	0.997623	+	0.0689116i	$0.0219527\pi$
$864$	29.2329	+	3.07250i	0.994522	+	0.104528i
$865$	9.31841	+	3.02774i	0.316836	+	0.102946i
$866$	−29.0495	−	6.17466i	−0.987142	−	0.209824i
$867$	7.12652	+	9.80881i	0.242029	+	0.333125i
$868$	−8.48528	+	4.89898i	−0.288009	+	0.166282i
$869$		0			0
$870$		0			0
$871$	34.3237	−	24.9376i	1.16301	−	0.844979i
$872$	26.3565	−	8.56373i	0.892542	−	0.290004i
$873$		0			0
$874$	8.45386	+	18.9877i	0.285956	+	0.642268i
$875$	20.5942	+	14.9626i	0.696211	+	0.505827i
$876$	−16.5997	+	3.52838i	−0.560852	+	0.119213i
$877$	51.2513	−	16.6525i	1.73063	−	0.562317i	0.737092	−	0.675793i	$-0.236199\pi$
$877$	51.2513	−	16.6525i	1.73063	−	0.562317i	0.993541	+	0.113476i	$0.0361986\pi$
$878$	3.34491	+	31.8247i	0.112885	+	1.07403i
$879$	−8.48528			−0.286201
$880$		0			0
$881$	−49.0000			−1.65085			−0.825426	−	0.564510i	$-0.809065\pi$
$881$	−49.0000			−1.65085			−0.825426	+	0.564510i	$0.809065\pi$
$882$		0			0
$883$	−23.0619	+	7.49326i	−0.776095	+	0.252168i	−0.670172	−	0.742206i	$-0.733780\pi$
$883$	−23.0619	+	7.49326i	−0.776095	+	0.252168i	−0.105923	+	0.994374i	$0.533780\pi$
$884$	−46.9511	+	9.97976i	−1.57914	+	0.335656i
$885$	−2.42705	−	1.76336i	−0.0815844	−	0.0592746i
$886$	2.98889	+	6.71316i	0.100414	+	0.225533i
$887$	−5.24419	+	16.1400i	−0.176083	+	0.541927i	−0.999681	−	0.0252463i	$-0.991963\pi$
$887$	−5.24419	+	16.1400i	−0.176083	+	0.541927i	0.823599	+	0.567173i	$0.191963\pi$
$888$	13.9776	−	4.54160i	0.469058	−	0.152406i
$889$	32.3607	−	23.5114i	1.08534	−	0.788547i
$890$	0.707107	−	1.22474i	0.0237023	−	0.0410535i
$891$		0			0
$892$	39.0000	−	22.5167i	1.30582	−	0.753914i
$893$	−5.75910	−	7.92672i	−0.192721	−	0.265257i
$894$	−35.2133	−	7.48482i	−1.17771	−	0.250330i
$895$	−8.23639	−	2.67617i	−0.275312	−	0.0894544i
$896$	29.2335	−	13.0156i	0.976621	−	0.434820i
$897$	25.9159	−	35.6702i	0.865308	−	1.19099i
$898$	−21.7648	−	24.1722i	−0.726299	−	0.806637i
$899$		0			0
$900$		0			0
$901$			9.79796i			0.326417i
$902$		0			0
$903$			27.7128i			0.922225i
$904$	−11.4412	+	8.31254i	−0.380530	+	0.276471i
$905$	6.48936	+	19.9722i	0.215714	+	0.663898i
$906$	10.2973	−	9.27175i	0.342105	−	0.308033i
$907$	−2.03615	+	2.80252i	−0.0676092	+	0.0930561i	−0.841483	−	0.540284i	$-0.818317\pi$
$907$	−2.03615	+	2.80252i	−0.0676092	+	0.0930561i	0.773873	+	0.633340i	$0.218317\pi$
$908$	−1.77391	+	16.8776i	−0.0588692	+	0.560103i
$909$		0			0
$910$	−4.07422	+	19.1677i	−0.135059	+	0.635403i
$911$	14.2530	+	19.6176i	0.472224	+	0.649961i	0.976987	−	0.213297i	$-0.0684202\pi$
$911$	14.2530	+	19.6176i	0.472224	+	0.649961i	−0.504763	+	0.863258i	$0.668420\pi$
$912$	−16.9706	−	9.79796i	−0.561951	−	0.324443i
$913$		0			0
$914$	−24.0000	−	13.8564i	−0.793849	−	0.458329i
$915$	13.7295	−	9.97505i	0.453882	−	0.329765i
$916$	−1.33826	+	1.48629i	−0.0442174	+	0.0491084i
$917$	−2.47214	+	7.60845i	−0.0816371	+	0.251253i
$918$	−32.8876	+	14.6425i	−1.08545	+	0.483275i
$919$	−9.15298	−	6.65003i	−0.301929	−	0.219364i	0.426497	−	0.904489i	$-0.359748\pi$
$919$	−9.15298	−	6.65003i	−0.301929	−	0.219364i	−0.728426	+	0.685125i	$0.759748\pi$
$920$	−13.9776	−	4.54160i	−0.460828	−	0.149732i
$921$	−32.6144	+	10.5971i	−1.07468	+	0.349186i
$922$	41.3415	−	4.34517i	1.36151	−	0.143100i
$923$	59.3970			1.95508
$924$		0			0
$925$	−12.0000			−0.394558
$926$	−51.1575	+	5.37687i	−1.68114	+	0.176695i
$927$		0			0
$928$		0			0
$929$	17.7984	+	12.9313i	0.583946	+	0.424261i	0.840144	−	0.542363i	$-0.182470\pi$
$929$	17.7984	+	12.9313i	0.583946	+	0.424261i	−0.256199	+	0.966624i	$0.582470\pi$
$930$	−3.87585	+	1.72564i	−0.127094	+	0.0565859i
$931$	0.874032	−	2.68999i	0.0286452	−	0.0881610i
$932$	−29.1252	−	26.2245i	−0.954028	−	0.859011i
$933$	−14.5623	+	10.5801i	−0.476748	+	0.346378i
$934$	−40.3051	−	23.2702i	−1.31882	−	0.761423i
$935$		0			0
$936$		0			0
$937$	−2.87955	−	3.96336i	−0.0940707	−	0.129477i	0.759387	−	0.650639i	$-0.225499\pi$
$937$	−2.87955	−	3.96336i	−0.0940707	−	0.129477i	−0.853458	+	0.521162i	$0.825499\pi$
$938$	7.20227	−	33.8840i	0.235163	−	1.10635i
$939$	44.4765	+	14.4513i	1.45144	+	0.471600i
$940$	6.89025	+	0.724194i	0.224735	+	0.0236206i
$941$	−23.0364	+	31.7069i	−0.750965	+	1.03361i	0.246948	+	0.969029i	$0.420572\pi$
$941$	−23.0364	+	31.7069i	−0.750965	+	1.03361i	−0.997912	+	0.0645853i	$0.979428\pi$
$942$	20.0236	−	18.0293i	0.652404	−	0.587427i
$943$	7.86629	+	24.2099i	0.256162	+	0.788384i
$944$	6.89025	−	0.724194i	0.224259	−	0.0235705i
$945$			14.6969i			0.478091i
$946$		0			0
$947$			43.3013i			1.40710i	0.710645	+	0.703551i	$0.248403\pi$
$947$			43.3013i			1.40710i	−0.710645	+	0.703551i	$0.751597\pi$
$948$	−15.9408	+	35.8035i	−0.517732	+	1.16284i
$949$	7.41641	+	22.8254i	0.240747	+	0.740942i
$950$	10.7061	+	11.8903i	0.347351	+	0.385773i
$951$	−25.4518	+	35.0315i	−0.825333	+	1.13597i
$952$	−23.0364	+	31.7069i	−0.746613	+	1.02763i
$953$	−32.6144	−	10.5971i	−1.05649	−	0.343273i	−0.271275	−	0.962502i	$-0.587445\pi$
$953$	−32.6144	−	10.5971i	−1.05649	−	0.343273i	−0.785210	+	0.619229i	$0.787445\pi$
$954$		0			0
$955$	−3.05422	−	4.20378i	−0.0988323	−	0.136031i
$956$	5.65685	+	9.79796i	0.182956	+	0.316889i
$957$		0			0
$958$	−22.0000	+	38.1051i	−0.710788	+	1.23112i
$959$	43.4767	−	31.5876i	1.40393	−	1.02002i
$960$	13.1782	−	4.28187i	0.425325	−	0.138197i
$961$	8.65248	−	26.6296i	0.279112	−	0.859019i
$962$	−8.45386	−	18.9877i	−0.272563	−	0.612188i
$963$		0			0
$964$	−12.2227	−	57.5031i	−0.393665	−	1.85205i
$965$	9.31841	−	3.02774i	0.299970	−	0.0974663i
$966$	−3.76302	−	35.8028i	−0.121073	−	1.15194i
$967$	−45.2548			−1.45530			−0.727649	−	0.685950i	$-0.759387\pi$
$967$	−45.2548			−1.45530			−0.727649	+	0.685950i	$0.759387\pi$
$968$		0			0
$969$	24.0000			0.770991
$970$	−1.03478	−	9.84526i	−0.0332248	−	0.316112i
$971$	31.2983	−	10.1694i	1.00441	−	0.326353i	0.239783	−	0.970826i	$-0.422924\pi$
$971$	31.2983	−	10.1694i	1.00441	−	0.326353i	0.764626	+	0.644474i	$0.222924\pi$
$972$		0			0
$973$	−45.3050	−	32.9160i	−1.45241	−	1.05524i
$974$	22.9148	+	51.4676i	0.734239	+	1.64913i
$975$	10.4884	−	32.2799i	0.335897	−	1.03379i
$976$	−8.14844	+	38.3354i	−0.260825	+	1.22709i
$977$	−15.3713	+	11.1679i	−0.491772	+	0.357293i	−0.805865	−	0.592099i	$-0.798300\pi$
$977$	−15.3713	+	11.1679i	−0.491772	+	0.357293i	0.314093	+	0.949392i	$0.398300\pi$
$978$	21.2132	−	36.7423i	0.678323	−	1.17489i
$979$		0			0
$980$	1.00000	+	1.73205i	0.0319438	+	0.0553283i
$981$		0			0
$982$	46.9511	+	9.97976i	1.49827	+	0.318467i
$983$	1.64728	+	0.535233i	0.0525400	+	0.0170713i	0.335169	−	0.942158i	$-0.391207\pi$
$983$	1.64728	+	0.535233i	0.0525400	+	0.0170713i	−0.282629	+	0.959229i	$0.591207\pi$
$984$	−19.4164	−	14.1068i	−0.618972	−	0.449710i
$985$		0			0
$986$		0			0
$987$	5.24419	+	16.1400i	0.166924	+	0.513741i
$988$	−11.2718	+	25.3169i	−0.358604	+	0.805438i
$989$			29.3939i			0.934671i
$990$		0			0
$991$		−	51.9615i		−	1.65061i	−0.564686	−	0.825306i	$-0.691003\pi$
$991$		−	51.9615i		−	1.65061i	0.564686	−	0.825306i	$-0.308997\pi$
$992$	3.98519	−	8.95088i	0.126530	−	0.284191i
$993$	2.78115	+	8.55951i	0.0882572	+	0.271628i
$994$	36.0406	−	32.4511i	1.14314	−	1.02929i
$995$	6.10844	−	8.40755i	0.193651	−	0.266537i
$996$		0			0
$997$	−4.65921	−	1.51387i	−0.147559	−	0.0479447i	0.234306	−	0.972163i	$-0.424718\pi$
$997$	−4.65921	−	1.51387i	−0.147559	−	0.0479447i	−0.381865	+	0.924218i	$0.624718\pi$
$998$	5.09278	−	23.9596i	0.161209	−	0.758429i
$999$	−9.16267	−	12.6113i	−0.289894	−	0.399005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.g.g.239.3		16
4.3	odd	2	inner	484.2.g.g.239.4		16
11.2	odd	10		44.2.c.a.43.2	yes	4
11.3	even	5	inner	484.2.g.g.215.4		16
11.4	even	5	inner	484.2.g.g.403.1		16
11.5	even	5	inner	484.2.g.g.475.2		16
11.6	odd	10	inner	484.2.g.g.475.3		16
11.7	odd	10	inner	484.2.g.g.403.4		16
11.8	odd	10	inner	484.2.g.g.215.1		16
11.9	even	5		44.2.c.a.43.3	yes	4
11.10	odd	2	inner	484.2.g.g.239.2		16
33.2	even	10		396.2.h.b.307.3		4
33.20	odd	10		396.2.h.b.307.2		4
44.3	odd	10	inner	484.2.g.g.215.3		16
44.7	even	10	inner	484.2.g.g.403.3		16
44.15	odd	10	inner	484.2.g.g.403.2		16
44.19	even	10	inner	484.2.g.g.215.2		16
44.27	odd	10	inner	484.2.g.g.475.1		16
44.31	odd	10		44.2.c.a.43.1	✓	4
44.35	even	10		44.2.c.a.43.4	yes	4
44.39	even	10	inner	484.2.g.g.475.4		16
44.43	even	2	inner	484.2.g.g.239.1		16
88.13	odd	10		704.2.e.b.703.2		4
88.35	even	10		704.2.e.b.703.3		4
88.53	even	10		704.2.e.b.703.1		4
88.75	odd	10		704.2.e.b.703.4		4
132.35	odd	10		396.2.h.b.307.1		4
132.119	even	10		396.2.h.b.307.4		4
176.13	odd	20		2816.2.g.b.1407.3		8
176.35	even	20		2816.2.g.b.1407.8		8
176.53	even	20		2816.2.g.b.1407.6		8
176.75	odd	20		2816.2.g.b.1407.1		8
176.101	odd	20		2816.2.g.b.1407.5		8
176.123	even	20		2816.2.g.b.1407.2		8
176.141	even	20		2816.2.g.b.1407.4		8
176.163	odd	20		2816.2.g.b.1407.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.c.a.43.1	✓	4	44.31	odd	10
44.2.c.a.43.2	yes	4	11.2	odd	10
44.2.c.a.43.3	yes	4	11.9	even	5
44.2.c.a.43.4	yes	4	44.35	even	10
396.2.h.b.307.1		4	132.35	odd	10
396.2.h.b.307.2		4	33.20	odd	10
396.2.h.b.307.3		4	33.2	even	10
396.2.h.b.307.4		4	132.119	even	10
484.2.g.g.215.1		16	11.8	odd	10	inner
484.2.g.g.215.2		16	44.19	even	10	inner
484.2.g.g.215.3		16	44.3	odd	10	inner
484.2.g.g.215.4		16	11.3	even	5	inner
484.2.g.g.239.1		16	44.43	even	2	inner
484.2.g.g.239.2		16	11.10	odd	2	inner
484.2.g.g.239.3		16	1.1	even	1	trivial
484.2.g.g.239.4		16	4.3	odd	2	inner
484.2.g.g.403.1		16	11.4	even	5	inner
484.2.g.g.403.2		16	44.15	odd	10	inner
484.2.g.g.403.3		16	44.7	even	10	inner
484.2.g.g.403.4		16	11.7	odd	10	inner
484.2.g.g.475.1		16	44.27	odd	10	inner
484.2.g.g.475.2		16	11.5	even	5	inner
484.2.g.g.475.3		16	11.6	odd	10	inner
484.2.g.g.475.4		16	44.39	even	10	inner
704.2.e.b.703.1		4	88.53	even	10
704.2.e.b.703.2		4	88.13	odd	10
704.2.e.b.703.3		4	88.35	even	10
704.2.e.b.703.4		4	88.75	odd	10
2816.2.g.b.1407.1		8	176.75	odd	20
2816.2.g.b.1407.2		8	176.123	even	20
2816.2.g.b.1407.3		8	176.13	odd	20
2816.2.g.b.1407.4		8	176.141	even	20
2816.2.g.b.1407.5		8	176.101	odd	20
2816.2.g.b.1407.6		8	176.53	even	20
2816.2.g.b.1407.7		8	176.163	odd	20
2816.2.g.b.1407.8		8	176.35	even	20

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.g (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.147826 + 1.40647i) q^{2} +(-1.64728 + 0.535233i) q^{3} +(-1.95630 + 0.415823i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.996297 - 2.23772i) q^{6} +(-0.874032 + 2.68999i) q^{7} +(-0.874032 - 2.68999i) q^{8} +O(q^{10})\)	\(q+(0.147826 + 1.40647i) q^{2} +(-1.64728 + 0.535233i) q^{3} +(-1.95630 + 0.415823i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-0.996297 - 2.23772i) q^{6} +(-0.874032 + 2.68999i) q^{7} +(-0.874032 - 2.68999i) q^{8} +(-0.707107 + 1.22474i) q^{10} +(3.00000 - 1.73205i) q^{12} +(-2.87955 - 3.96336i) q^{13} +(-3.91259 - 0.831647i) q^{14} +(-1.64728 - 0.535233i) q^{15} +(3.65418 - 1.62695i) q^{16} +(-2.87955 + 3.96336i) q^{17} +(0.874032 + 2.68999i) q^{19} +(-1.82709 - 0.813473i) q^{20} -4.89898i q^{21} -5.19615i q^{23} +(2.87955 + 3.96336i) q^{24} +(-1.23607 - 3.80423i) q^{25} +(5.14866 - 4.63587i) q^{26} +(3.05422 - 4.20378i) q^{27} +(0.591302 - 5.62587i) q^{28} +(0.509278 - 2.39596i) q^{30} +(-1.01807 - 1.40126i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-6.00000 - 3.46410i) q^{34} +(-2.28825 + 1.66251i) q^{35} +(0.927051 - 2.85317i) q^{37} +(-3.65418 + 1.62695i) q^{38} +(6.86474 + 4.98752i) q^{39} +(0.874032 - 2.68999i) q^{40} +(-4.65921 + 1.51387i) q^{41} +(6.89025 - 0.724194i) q^{42} -5.65685 q^{43} +(7.30821 - 0.768124i) q^{46} +(-3.29456 + 1.07047i) q^{47} +(-5.14866 + 4.63587i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(5.16779 - 2.30085i) q^{50} +(2.62210 - 8.06998i) q^{51} +(7.28130 + 6.55611i) q^{52} +(1.61803 - 1.17557i) q^{53} +(6.36396 + 3.67423i) q^{54} +8.00000 q^{56} +(-2.87955 - 3.96336i) q^{57} +(1.64728 + 0.535233i) q^{59} +(3.44512 + 0.362097i) q^{60} +(-5.75910 + 7.92672i) q^{61} +(1.82033 - 1.63903i) q^{62} +(-6.47214 + 4.70228i) q^{64} -4.89898i q^{65} +8.66025i q^{67} +(3.98519 - 8.95088i) q^{68} +(2.78115 + 8.55951i) q^{69} +(-2.67652 - 2.97258i) q^{70} +(-7.12652 + 9.80881i) q^{71} +(-4.65921 - 1.51387i) q^{73} +(4.14993 + 0.882095i) q^{74} +(4.07230 + 5.60503i) q^{75} +(-2.82843 - 4.89898i) q^{76} +(-6.00000 + 10.3923i) q^{78} +(-9.15298 + 6.65003i) q^{79} +(3.91259 + 0.831647i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-2.81795 - 6.32923i) q^{82} +(2.03711 + 9.58385i) q^{84} +(-4.65921 + 1.51387i) q^{85} +(-0.836228 - 7.95618i) q^{86} -1.00000 q^{89} +(13.1782 - 4.28187i) q^{91} +(2.16068 + 10.1652i) q^{92} +(2.42705 + 1.76336i) q^{93} +(-1.99259 - 4.47544i) q^{94} +(-0.874032 + 2.68999i) q^{95} +(-7.28130 - 6.55611i) q^{96} +(-5.66312 + 4.11450i) q^{97} +(0.707107 - 1.22474i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^5	\( 16 q + 4 q^{4} + 4 q^{5} + 48 q^{12} + 8 q^{14} + 8 q^{16} - 4 q^{20} + 16 q^{25} - 24 q^{26} - 96 q^{34} - 12 q^{37} - 8 q^{38} + 24 q^{42} + 24 q^{48} - 4 q^{49} + 8 q^{53} + 128 q^{56} + 12 q^{60} - 32 q^{64} - 36 q^{69} - 8 q^{70} - 96 q^{78} - 8 q^{80} + 36 q^{81} - 24 q^{82} + 16 q^{86} - 16 q^{89} + 36 q^{92} + 12 q^{93} - 28 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^5 + 48 * q^12 + 8 * q^14 + 8 * q^16 - 4 * q^20 + 16 * q^25 - 24 * q^26 - 96 * q^34 - 12 * q^37 - 8 * q^38 + 24 * q^42 + 24 * q^48 - 4 * q^49 + 8 * q^53 + 128 * q^56 + 12 * q^60 - 32 * q^64 - 36 * q^69 - 8 * q^70 - 96 * q^78 - 8 * q^80 + 36 * q^81 - 24 * q^82 + 16 * q^86 - 16 * q^89 + 36 * q^92 + 12 * q^93 - 28 * q^97

Introduction

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