LMFDB - Embedded newform 475.2.u.a.74.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(24,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("475.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, degree $6$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			74.2
Root			$0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	475.74
Dual form			475.2.u.a.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32683 + 0.233956i) q^{2} +(1.85083 - 2.20574i) q^{3} +(-0.173648 - 0.0632028i) q^{4} +(2.97178 - 2.49362i) q^{6} +(-0.300767 + 0.173648i) q^{7} +(-2.54920 - 1.47178i) q^{8} +(-0.918748 - 5.21048i) q^{9} +O(q^{10})$	\(q+(1.32683 + 0.233956i) q^{2} +(1.85083 - 2.20574i) q^{3} +(-0.173648 - 0.0632028i) q^{4} +(2.97178 - 2.49362i) q^{6} +(-0.300767 + 0.173648i) q^{7} +(-2.54920 - 1.47178i) q^{8} +(-0.918748 - 5.21048i) q^{9} +(1.11334 - 1.92836i) q^{11} +(-0.460802 + 0.266044i) q^{12} +(1.65452 + 1.97178i) q^{13} +(-0.439693 + 0.160035i) q^{14} +(-2.75490 - 2.31164i) q^{16} +(-0.460802 - 0.0812519i) q^{17} -7.12836i q^{18} +(4.29813 - 0.725293i) q^{19} +(-0.173648 + 0.984808i) q^{21} +(1.92836 - 2.29813i) q^{22} +(-0.921605 + 2.53209i) q^{23} +(-7.96451 + 2.89884i) q^{24} +(1.73396 + 3.00330i) q^{26} +(-5.71253 - 3.29813i) q^{27} +(0.0632028 - 0.0111444i) q^{28} +(1.19459 + 6.77487i) q^{29} +(3.55303 + 6.15403i) q^{31} +(0.669713 + 0.798133i) q^{32} +(-2.19285 - 6.02481i) q^{33} +(-0.592396 - 0.215615i) q^{34} +(-0.169778 + 0.962858i) q^{36} -4.94356i q^{37} +(5.87257 + 0.0432332i) q^{38} +7.41147 q^{39} +(1.89646 + 1.59132i) q^{41} +(-0.460802 + 1.26604i) q^{42} +(-1.33445 - 3.66637i) q^{43} +(-0.315207 + 0.264490i) q^{44} +(-1.81521 + 3.14403i) q^{46} +(-7.18009 + 1.26604i) q^{47} +(-10.1977 + 1.79813i) q^{48} +(-3.43969 + 5.95772i) q^{49} +(-1.03209 + 0.866025i) q^{51} +(-0.162683 - 0.446967i) q^{52} +(-0.970481 + 2.66637i) q^{53} +(-6.80793 - 5.71253i) q^{54} +1.02229 q^{56} +(6.35532 - 10.8229i) q^{57} +9.26857i q^{58} +(1.09492 - 6.20961i) q^{59} +(-8.57785 - 3.12208i) q^{61} +(3.27449 + 8.99660i) q^{62} +(1.18112 + 1.40760i) q^{63} +(4.29813 + 7.44459i) q^{64} +(-1.50000 - 8.50692i) q^{66} +(7.55839 - 1.33275i) q^{67} +(0.0748822 + 0.0432332i) q^{68} +(3.87939 + 6.71929i) q^{69} +(8.74422 - 3.18264i) q^{71} +(-5.32661 + 14.6348i) q^{72} +(-0.892951 + 1.06418i) q^{73} +(1.15657 - 6.55926i) q^{74} +(-0.792204 - 0.145708i) q^{76} +0.773318i q^{77} +(9.83375 + 1.73396i) q^{78} +(9.07398 + 7.61397i) q^{79} +(-2.93242 + 1.06731i) q^{81} +(2.14398 + 2.55509i) q^{82} +(-12.8438 + 7.41534i) q^{83} +(0.0923963 - 0.160035i) q^{84} +(-0.912818 - 5.17685i) q^{86} +(17.1546 + 9.90420i) q^{87} +(-5.67626 + 3.27719i) q^{88} +(7.88326 - 6.61484i) q^{89} +(-0.840022 - 0.305743i) q^{91} +(0.320070 - 0.381445i) q^{92} +(20.1503 + 3.55303i) q^{93} -9.82295 q^{94} +3.00000 q^{96} +(-9.30975 - 1.64156i) q^{97} +(-5.95772 + 7.10014i) q^{98} +(-11.0706 - 4.02936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^6 - 6 * q^9	$ 12 q + 6 q^{6} - 6 q^{9} + 6 q^{14} - 36 q^{16} + 24 q^{19} - 30 q^{24} + 30 q^{26} + 6 q^{29} + 18 q^{31} - 48 q^{36} + 48 q^{39} + 42 q^{41} - 18 q^{44} - 36 q^{46} - 30 q^{49} + 6 q^{51} - 60 q^{54} - 12 q^{56} - 24 q^{59} - 24 q^{61} + 24 q^{64} - 18 q^{66} + 24 q^{69} - 12 q^{71} - 30 q^{74} + 72 q^{76} + 78 q^{79} + 12 q^{81} - 6 q^{84} + 48 q^{86} + 24 q^{89} + 30 q^{91} - 36 q^{94} + 36 q^{96} - 18 q^{99}+O(q^{100}) $ 12 * q + 6 * q^6 - 6 * q^9 + 6 * q^14 - 36 * q^16 + 24 * q^19 - 30 * q^24 + 30 * q^26 + 6 * q^29 + 18 * q^31 - 48 * q^36 + 48 * q^39 + 42 * q^41 - 18 * q^44 - 36 * q^46 - 30 * q^49 + 6 * q^51 - 60 * q^54 - 12 * q^56 - 24 * q^59 - 24 * q^61 + 24 * q^64 - 18 * q^66 + 24 * q^69 - 12 * q^71 - 30 * q^74 + 72 * q^76 + 78 * q^79 + 12 * q^81 - 6 * q^84 + 48 * q^86 + 24 * q^89 + 30 * q^91 - 36 * q^94 + 36 * q^96 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	1.32683	+	0.233956i	0.938209	+	0.165432i	0.621786	−	0.783187i	$-0.286407\pi$
$2$	1.32683	+	0.233956i	0.938209	+	0.165432i	0.316423	+	0.948618i	$0.397518\pi$
$3$	1.85083	−	2.20574i	1.06858	−	1.27348i	0.108397	−	0.994108i	$-0.465428\pi$
$3$	1.85083	−	2.20574i	1.06858	−	1.27348i	0.960182	−	0.279375i	$-0.0901273\pi$
$4$	−0.173648	−	0.0632028i	−0.0868241	−	0.0316014i
$5$		0			0
$5$		0			0
$6$	2.97178	−	2.49362i	1.21322	−	1.01802i
$7$	−0.300767	+	0.173648i	−0.113679	+	0.0656328i	−0.555762	−	0.831342i	$-0.687573\pi$
$7$	−0.300767	+	0.173648i	−0.113679	+	0.0656328i	0.442082	+	0.896975i	$0.354240\pi$
$8$	−2.54920	−	1.47178i	−0.901278	−	0.520353i
$9$	−0.918748	−	5.21048i	−0.306249	−	1.73683i
$10$		0			0
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	−0.647931	−	0.761699i	$-0.724366\pi$
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	0.983616	+	0.180276i	$0.0576989\pi$
$12$	−0.460802	+	0.266044i	−0.133022	+	0.0768004i
$13$	1.65452	+	1.97178i	0.458882	+	0.546874i	0.945022	−	0.327007i	$-0.106040\pi$
$13$	1.65452	+	1.97178i	0.458882	+	0.546874i	−0.486140	+	0.873881i	$0.661596\pi$
$14$	−0.439693	+	0.160035i	−0.117513	+	0.0427712i
$15$		0			0
$16$	−2.75490	−	2.31164i	−0.688725	−	0.577909i
$17$	−0.460802	−	0.0812519i	−0.111761	−	0.0197065i	0.117488	−	0.993074i	$-0.462516\pi$
$17$	−0.460802	−	0.0812519i	−0.111761	−	0.0197065i	−0.229249	+	0.973368i	$0.573627\pi$
$18$		−	7.12836i		−	1.68017i
$19$	4.29813	−	0.725293i	0.986059	−	0.166394i
$19$	4.29813	−	0.725293i	0.986059	−	0.166394i
$20$		0			0
$21$	−0.173648	+	0.984808i	−0.0378931	+	0.214903i
$22$	1.92836	−	2.29813i	0.411128	−	0.489964i
$23$	−0.921605	+	2.53209i	−0.192168	+	0.527977i	−0.997933	−	0.0642578i	$-0.979532\pi$
$23$	−0.921605	+	2.53209i	−0.192168	+	0.527977i	0.805765	+	0.592235i	$0.201754\pi$
$24$	−7.96451	+	2.89884i	−1.62575	+	0.591724i
$25$		0			0
$26$	1.73396	+	3.00330i	0.340057	+	0.588995i
$27$	−5.71253	−	3.29813i	−1.09938	−	0.634726i
$28$	0.0632028	−	0.0111444i	0.0119442	−	0.00210608i
$29$	1.19459	+	6.77487i	0.221830	+	1.25806i	0.868653	+	0.495421i	$0.164986\pi$
$29$	1.19459	+	6.77487i	0.221830	+	1.25806i	−0.646822	+	0.762641i	$0.723903\pi$
$30$		0			0
$31$	3.55303	+	6.15403i	0.638144	+	1.10530i	0.985840	+	0.167690i	$0.0536307\pi$
$31$	3.55303	+	6.15403i	0.638144	+	1.10530i	−0.347696	+	0.937607i	$0.613036\pi$
$32$	0.669713	+	0.798133i	0.118390	+	0.141091i
$33$	−2.19285	−	6.02481i	−0.381727	−	1.04879i
$34$	−0.592396	−	0.215615i	−0.101595	−	0.0369776i
$35$		0			0
$36$	−0.169778	+	0.962858i	−0.0282963	+	0.160476i
$37$		−	4.94356i		−	0.812717i	−0.913714	−	0.406358i	$-0.866798\pi$
$37$		−	4.94356i		−	0.812717i	0.913714	−	0.406358i	$-0.133202\pi$
$38$	5.87257	+	0.0432332i	0.952657	+	0.00701336i
$39$	7.41147			1.18679
$40$		0			0
$41$	1.89646	+	1.59132i	0.296177	+	0.248522i	0.778751	−	0.627333i	$-0.215854\pi$
$41$	1.89646	+	1.59132i	0.296177	+	0.248522i	−0.482574	+	0.875855i	$0.660298\pi$
$42$	−0.460802	+	1.26604i	−0.0711034	+	0.195355i
$43$	−1.33445	−	3.66637i	−0.203502	−	0.559117i	0.795394	−	0.606093i	$-0.207264\pi$
$43$	−1.33445	−	3.66637i	−0.203502	−	0.559117i	−0.998896	+	0.0469757i	$0.985042\pi$
$44$	−0.315207	+	0.264490i	−0.0475193	+	0.0398734i
$45$		0			0
$46$	−1.81521	+	3.14403i	−0.267638	+	0.463562i
$47$	−7.18009	+	1.26604i	−1.04732	+	0.184672i	−0.670726	−	0.741705i	$-0.734017\pi$
$47$	−7.18009	+	1.26604i	−1.04732	+	0.184672i	−0.376598	+	0.926377i	$0.622906\pi$
$48$	−10.1977	+	1.79813i	−1.47191	+	0.259538i
$49$	−3.43969	+	5.95772i	−0.491385	+	0.851103i
$50$		0			0
$51$	−1.03209	+	0.866025i	−0.144521	+	0.121268i
$52$	−0.162683	−	0.446967i	−0.0225600	−	0.0619831i
$53$	−0.970481	+	2.66637i	−0.133306	+	0.366255i	−0.988329	−	0.152335i	$-0.951321\pi$
$53$	−0.970481	+	2.66637i	−0.133306	+	0.366255i	0.855023	+	0.518590i	$0.173543\pi$
$54$	−6.80793	−	5.71253i	−0.926442	−	0.777377i
$55$		0			0
$56$	1.02229			0.136609
$57$	6.35532	−	10.8229i	0.841783	−	1.43353i
$58$			9.26857i			1.21702i
$59$	1.09492	−	6.20961i	0.142547	−	0.808423i	−0.826757	−	0.562559i	$-0.809817\pi$
$59$	1.09492	−	6.20961i	0.142547	−	0.808423i	0.969304	−	0.245864i	$-0.0790718\pi$
$60$		0			0
$61$	−8.57785	−	3.12208i	−1.09828	−	0.399742i	−0.271599	−	0.962411i	$-0.587552\pi$
$61$	−8.57785	−	3.12208i	−1.09828	−	0.399742i	−0.826682	+	0.562669i	$0.809775\pi$
$62$	3.27449	+	8.99660i	0.415861	+	1.14257i
$63$	1.18112	+	1.40760i	0.148807	+	0.177341i
$64$	4.29813	+	7.44459i	0.537267	+	0.930573i
$65$		0			0
$66$	−1.50000	−	8.50692i	−0.184637	−	1.04713i
$67$	7.55839	−	1.33275i	0.923405	−	0.162821i	0.308320	−	0.951283i	$-0.400233\pi$
$67$	7.55839	−	1.33275i	0.923405	−	0.162821i	0.615084	+	0.788461i	$0.289122\pi$
$68$	0.0748822	+	0.0432332i	0.00908080	+	0.00524280i
$69$	3.87939	+	6.71929i	0.467023	+	0.808908i
$70$		0			0
$71$	8.74422	−	3.18264i	1.03775	−	0.377709i	0.233722	−	0.972303i	$-0.424909\pi$
$71$	8.74422	−	3.18264i	1.03775	−	0.377709i	0.804026	+	0.594594i	$0.202687\pi$
$72$	−5.32661	+	14.6348i	−0.627748	+	1.72472i
$73$	−0.892951	+	1.06418i	−0.104512	+	0.124553i	−0.815765	−	0.578384i	$-0.803684\pi$
$73$	−0.892951	+	1.06418i	−0.104512	+	0.124553i	0.711253	+	0.702936i	$0.248128\pi$
$74$	1.15657	−	6.55926i	0.134449	−	0.762498i
$75$		0			0
$76$	−0.792204	−	0.145708i	−0.0908720	−	0.0167139i
$77$			0.773318i			0.0881278i
$78$	9.83375	+	1.73396i	1.11345	+	0.196332i
$79$	9.07398	+	7.61397i	1.02090	+	0.856639i	0.989741	−	0.142876i	$-0.0456349\pi$
$79$	9.07398	+	7.61397i	1.02090	+	0.856639i	0.0311616	+	0.999514i	$0.490079\pi$
$80$		0			0
$81$	−2.93242	+	1.06731i	−0.325824	+	0.118590i
$82$	2.14398	+	2.55509i	0.236763	+	0.282163i
$83$	−12.8438	+	7.41534i	−1.40979	+	0.813940i	−0.995367	−	0.0961469i	$-0.969348\pi$
$83$	−12.8438	+	7.41534i	−1.40979	+	0.813940i	−0.414418	+	0.910087i	$0.636015\pi$
$84$	0.0923963	−	0.160035i	0.0100813	−	0.0174613i
$85$		0			0
$86$	−0.912818	−	5.17685i	−0.0984317	−	0.558234i
$87$	17.1546	+	9.90420i	1.83916	+	1.06184i
$88$	−5.67626	+	3.27719i	−0.605091	+	0.349349i
$89$	7.88326	−	6.61484i	0.835623	−	0.701171i	−0.120951	−	0.992658i	$-0.538594\pi$
$89$	7.88326	−	6.61484i	0.835623	−	0.701171i	0.956575	+	0.291487i	$0.0941501\pi$
$90$		0			0
$91$	−0.840022	−	0.305743i	−0.0880583	−	0.0320506i
$92$	0.320070	−	0.381445i	0.0333696	−	0.0397684i
$93$	20.1503	+	3.55303i	2.08948	+	0.368432i
$94$	−9.82295			−1.01316
$95$		0			0
$96$	3.00000			0.306186
$97$	−9.30975	−	1.64156i	−0.945261	−	0.166675i	−0.320287	−	0.947320i	$-0.603779\pi$
$97$	−9.30975	−	1.64156i	−0.945261	−	0.166675i	−0.624974	+	0.780645i	$0.714891\pi$
$98$	−5.95772	+	7.10014i	−0.601821	+	0.717222i
$99$	−11.0706	−	4.02936i	−1.11263	−	0.404966i
$100$		0			0
$101$	−7.08512	+	5.94512i	−0.704996	+	0.591562i	−0.923190	−	0.384343i	$-0.874428\pi$
$101$	−7.08512	+	5.94512i	−0.704996	+	0.591562i	0.218194	+	0.975905i	$0.429983\pi$
$102$	−1.57202	+	0.907604i	−0.155653	+	0.0898662i
$103$	4.77163	+	2.75490i	0.470162	+	0.271448i	0.716308	−	0.697785i	$-0.245831\pi$
$103$	4.77163	+	2.75490i	0.470162	+	0.271448i	−0.246145	+	0.969233i	$0.579164\pi$
$104$	−1.31567	−	7.46156i	−0.129012	−	0.731666i
$105$		0			0
$106$	−1.91147	+	3.31077i	−0.185659	+	0.321570i
$107$	−8.86327	+	5.11721i	−0.856845	+	0.494699i	−0.862954	−	0.505282i	$-0.831389\pi$
$107$	−8.86327	+	5.11721i	−0.856845	+	0.494699i	0.00610974	+	0.999981i	$0.498055\pi$
$108$	0.783520	+	0.933763i	0.0753943	+	0.0898514i
$109$	−1.71301	+	0.623485i	−0.164077	+	0.0597190i	−0.422753	−	0.906245i	$-0.638936\pi$
$109$	−1.71301	+	0.623485i	−0.164077	+	0.0597190i	0.258676	+	0.965964i	$0.416714\pi$
$110$		0			0
$111$	−10.9042	−	9.14971i	−1.03498	−	0.868452i
$112$	1.23000	+	0.216881i	0.116224	+	0.0204934i
$113$		−	17.6878i		−	1.66393i	−0.554830	−	0.831963i	$-0.687217\pi$
$113$		−	17.6878i		−	1.66393i	0.554830	−	0.831963i	$-0.312783\pi$
$114$	10.9645	−	12.8733i	1.02692	−	1.20570i
$115$		0			0
$116$	0.220752	−	1.25195i	0.0204963	−	0.116240i
$117$	8.75384	−	10.4324i	0.809293	−	0.964477i
$118$	2.90555	−	7.98293i	0.267477	−	0.734888i
$119$	0.152704	−	0.0555796i	0.0139983	−	0.00509497i
$120$		0			0
$121$	3.02094	+	5.23243i	0.274631	+	0.475675i
$122$	−10.6509	−	6.14930i	−0.964287	−	0.556731i
$123$	7.02006	−	1.23783i	0.632977	−	0.111611i
$124$	−0.228026	−	1.29320i	−0.0204773	−	0.116133i
$125$		0			0
$126$	1.23783	+	2.14398i	0.110274	+	0.191001i
$127$	−7.45891	−	8.88919i	−0.661871	−	0.788788i	0.325782	−	0.945445i	$-0.394373\pi$
$127$	−7.45891	−	8.88919i	−0.661871	−	0.788788i	−0.987653	+	0.156657i	$0.949928\pi$
$128$	3.24849	+	8.92514i	0.287128	+	0.788879i
$129$	−10.5569	−	3.84240i	−0.929484	−	0.338304i
$130$		0			0
$131$	0.320422	−	1.81720i	0.0279954	−	0.158770i	−0.967605	−	0.252468i	$-0.918758\pi$
$131$	0.320422	−	1.81720i	0.0279954	−	0.158770i	0.995601	+	0.0936982i	$0.0298689\pi$
$132$			1.18479i			0.103123i
$133$	−1.16679	+	0.964508i	−0.101174	+	0.0836334i
$134$	10.3405			0.893282
$135$		0			0
$136$	1.05509	+	0.885328i	0.0904735	+	0.0759162i
$137$	−0.0874810	+	0.240352i	−0.00747401	+	0.0205347i	−0.943374	−	0.331732i	$-0.892367\pi$
$137$	−0.0874810	+	0.240352i	−0.00747401	+	0.0205347i	0.935900	+	0.352267i	$0.114589\pi$
$138$	3.57526	+	9.82295i	0.304346	+	0.836185i
$139$	−3.26604	+	2.74054i	−0.277022	+	0.232449i	−0.770704	−	0.637193i	$-0.780095\pi$
$139$	−3.26604	+	2.74054i	−0.277022	+	0.232449i	0.493682	+	0.869643i	$0.335651\pi$
$140$		0			0
$141$	−10.4966	+	18.1806i	−0.883973	+	1.53109i
$142$	12.3467	−	2.17705i	1.03611	−	0.182694i
$143$	5.64436	−	0.995252i	0.472005	−	0.0832272i
$144$	−9.51367	+	16.4782i	−0.792806	+	1.37318i
$145$		0			0
$146$	−1.43376	+	1.20307i	−0.118659	+	0.0995668i
$147$	6.77487	+	18.6138i	0.558782	+	1.53524i
$148$	−0.312447	+	0.858441i	−0.0256830	+	0.0705634i
$149$	−12.6853	−	10.6442i	−1.03922	−	0.872007i	−0.0472981	−	0.998881i	$-0.515061\pi$
$149$	−12.6853	−	10.6442i	−1.03922	−	0.872007i	−0.991919	+	0.126874i	$0.959506\pi$
$150$		0			0
$151$	−4.36184			−0.354962			−0.177481	−	0.984124i	$-0.556795\pi$
$151$	−4.36184			−0.354962			−0.177481	+	0.984124i	$0.556795\pi$
$152$	−12.0243	−	4.47700i	−0.975298	−	0.363132i
$153$			2.47565i			0.200145i
$154$	−0.180922	+	1.02606i	−0.0145791	+	0.0826823i
$155$		0			0
$156$	−1.28699	−	0.468426i	−0.103042	−	0.0375041i
$157$	−3.28974	−	9.03849i	−0.262550	−	0.721350i	−0.998994	−	0.0448510i	$-0.985719\pi$
$157$	−3.28974	−	9.03849i	−0.262550	−	0.721350i	0.736444	−	0.676499i	$-0.236504\pi$
$158$	10.2583	+	12.2253i	0.816105	+	0.972596i
$159$	4.08512	+	7.07564i	0.323971	+	0.561135i
$160$		0			0
$161$	−0.162504	−	0.921605i	−0.0128071	−	0.0726326i
$162$	−4.14052	+	0.730085i	−0.325310	+	0.0573609i
$163$	−7.23567	−	4.17752i	−0.566742	−	0.327209i	0.189105	−	0.981957i	$-0.439441\pi$
$163$	−7.23567	−	4.17752i	−0.566742	−	0.327209i	−0.755847	+	0.654748i	$0.772775\pi$
$164$	−0.228741	−	0.396191i	−0.0178617	−	0.0309373i
$165$		0			0
$166$	−18.7763	+	6.83402i	−1.45732	+	0.530423i
$167$	−1.38008	+	3.79174i	−0.106794	+	0.293413i	−0.981567	−	0.191120i	$-0.938788\pi$
$167$	−1.38008	+	3.79174i	−0.106794	+	0.293413i	0.874773	+	0.484533i	$0.161010\pi$
$168$	1.89209	−	2.25490i	0.145978	−	0.173969i
$169$	1.10694	−	6.27779i	0.0851496	−	0.482907i
$170$		0			0
$171$	−7.72803	−	21.7290i	−0.590977	−	1.66166i
$172$			0.721000i			0.0549758i
$173$	−19.8378	−	3.49794i	−1.50824	−	0.265943i	−0.642441	−	0.766335i	$-0.722078\pi$
$173$	−19.8378	−	3.49794i	−1.50824	−	0.265943i	−0.865799	+	0.500391i	$0.833189\pi$
$174$	20.4440	+	17.1546i	1.54986	+	1.30049i
$175$		0			0
$176$	−7.52481	+	2.73881i	−0.567204	+	0.206445i
$177$	−11.6703	−	13.9081i	−0.877190	−	1.04539i
$178$	12.0073	−	6.93242i	0.899985	−	0.519607i
$179$	−5.75624	+	9.97011i	−0.430242	+	0.745201i	−0.996894	−	0.0787564i	$-0.974905\pi$
$179$	−5.75624	+	9.97011i	−0.430242	+	0.745201i	0.566652	+	0.823957i	$0.308238\pi$
$180$		0			0
$181$	1.48246	+	8.40744i	0.110190	+	0.624920i	0.989020	+	0.147784i	$0.0472141\pi$
$181$	1.48246	+	8.40744i	0.110190	+	0.624920i	−0.878829	+	0.477136i	$0.841675\pi$
$182$	−1.04303	−	0.602196i	−0.0773149	−	0.0446378i
$183$	−22.7627	+	13.1420i	−1.68266	+	0.971487i
$184$	6.07604	−	5.09840i	0.447931	−	0.375859i
$185$		0			0
$186$	25.9047	+	9.42853i	1.89942	+	0.691333i
$187$	−0.669713	+	0.798133i	−0.0489743	+	0.0583653i
$188$	1.32683	+	0.233956i	0.0967689	+	0.0170630i
$189$	2.29086			0.166635
$190$		0			0
$191$	18.3354			1.32671			0.663353	−	0.748307i	$-0.269133\pi$
$191$	18.3354			1.32671			0.663353	+	0.748307i	$0.269133\pi$
$192$	24.3759	+	4.29813i	1.75918	+	0.310191i
$193$	−0.191336	+	0.228026i	−0.0137727	+	0.0164137i	−0.772887	−	0.634544i	$-0.781188\pi$
$193$	−0.191336	+	0.228026i	−0.0137727	+	0.0164137i	0.759114	+	0.650958i	$0.225632\pi$
$194$	−11.9684	−	4.35613i	−0.859279	−	0.312752i
$195$		0			0
$196$	0.973841	−	0.817150i	0.0695601	−	0.0583678i
$197$	−11.3806	+	6.57057i	−0.810832	+	0.468134i	−0.847245	−	0.531203i	$-0.821740\pi$
$197$	−11.3806	+	6.57057i	−0.810832	+	0.468134i	0.0364128	+	0.999337i	$0.488407\pi$
$198$	−13.7461	−	7.93629i	−0.976890	−	0.564008i
$199$	0.0445774	+	0.252811i	0.00316001	+	0.0179213i	0.986347	−	0.164680i	$-0.0526593\pi$
$199$	0.0445774	+	0.252811i	0.00316001	+	0.0179213i	−0.983187	+	0.182602i	$0.941548\pi$
$200$		0			0
$201$	11.0496	−	19.1385i	0.779381	−	1.34993i
$202$	−10.7916	+	6.23055i	−0.759297	+	0.438380i
$203$	−1.53574	−	1.83022i	−0.107788	−	0.128456i
$204$	0.233956	−	0.0851529i	0.0163802	−	0.00596189i
$205$		0			0
$206$	5.68660	+	4.77163i	0.396204	+	0.332455i
$207$	14.0401	+	2.47565i	0.975856	+	0.172070i
$208$		−	9.25671i		−	0.641837i
$209$	3.38666	−	9.09586i	0.234260	−	0.629174i
$210$		0			0
$211$	0.425145	−	2.41112i	0.0292682	−	0.165988i	−0.966670	−	0.256024i	$-0.917587\pi$
$211$	0.425145	−	2.41112i	0.0292682	−	0.165988i	0.995938	+	0.0900364i	$0.0286983\pi$
$212$	0.337044	−	0.401674i	0.0231483	−	0.0275871i
$213$	9.16404	−	25.1780i	0.627909	−	1.72517i
$214$	−12.9572	+	4.71605i	−0.885738	+	0.322382i
$215$		0			0
$216$	9.70826	+	16.8152i	0.660564	+	1.14413i
$217$	−2.13727	−	1.23396i	−0.145088	−	0.0837664i
$218$	−2.41874	+	0.426489i	−0.163818	+	0.0288855i
$219$	0.694593	+	3.93923i	0.0469362	+	0.266189i
$220$		0			0
$221$	−0.602196	−	1.04303i	−0.0405081	−	0.0701621i
$222$	−12.3274	−	14.6912i	−0.827359	−	0.986008i
$223$	2.91052	+	7.99660i	0.194903	+	0.535492i	0.998193	−	0.0600971i	$-0.0191410\pi$
$223$	2.91052	+	7.99660i	0.194903	+	0.535492i	−0.803289	+	0.595589i	$0.796919\pi$
$224$	−0.340022	−	0.123758i	−0.0227187	−	0.00826893i
$225$		0			0
$226$	4.13816	−	23.4686i	0.275266	−	1.56111i
$227$			14.1506i			0.939211i	0.882876	+	0.469606i	$0.155604\pi$
$227$			14.1506i			0.939211i	−0.882876	+	0.469606i	$0.844396\pi$
$228$	−1.78763	+	1.47771i	−0.118389	+	0.0978638i
$229$	20.5330			1.35686			0.678430	−	0.734665i	$-0.262661\pi$
$229$	20.5330			1.35686			0.678430	+	0.734665i	$0.262661\pi$
$230$		0			0
$231$	1.70574	+	1.43128i	0.112229	+	0.0941715i
$232$	6.92588	−	19.0287i	0.454706	−	1.24929i
$233$	−6.03698	−	16.5865i	−0.395496	−	1.08662i	−0.964454	−	0.264249i	$-0.914876\pi$
$233$	−6.03698	−	16.5865i	−0.395496	−	1.08662i	0.568959	−	0.822366i	$-0.307346\pi$
$234$	14.0556	−	11.7940i	0.918841	−	0.770999i
$235$		0			0
$236$	−0.582596	+	1.00909i	−0.0379238	+	0.0656859i
$237$	33.5888	−	5.92262i	2.18183	−	0.384715i
$238$	0.215615	−	0.0380187i	0.0139762	−	0.00246438i
$239$	1.17617	−	2.03719i	0.0760804	−	0.131775i	−0.825475	−	0.564438i	$-0.809093\pi$
$239$	1.17617	−	2.03719i	0.0760804	−	0.131775i	0.901556	+	0.432663i	$0.142426\pi$
$240$		0			0
$241$	10.5719	−	8.87089i	0.680997	−	0.571424i	−0.235300	−	0.971923i	$-0.575607\pi$
$241$	10.5719	−	8.87089i	0.680997	−	0.571424i	0.916298	+	0.400498i	$0.131163\pi$
$242$	2.78412	+	7.64930i	0.178970	+	0.491716i
$243$	3.69496	−	10.1518i	0.237032	−	0.651240i
$244$	1.29220	+	1.08429i	0.0827249	+	0.0694144i
$245$		0			0
$246$	9.60401			0.612329
$247$	8.54147	+	7.27497i	0.543481	+	0.462895i
$248$		−	20.9172i		−	1.32824i
$249$	−7.41534	+	42.0545i	−0.469928	+	2.66510i
$250$		0			0
$251$	3.91400	+	1.42458i	0.247050	+	0.0899187i	0.462577	−	0.886579i	$-0.346925\pi$
$251$	3.91400	+	1.42458i	0.247050	+	0.0899187i	−0.215528	+	0.976498i	$0.569147\pi$
$252$	−0.116135	−	0.319078i	−0.00731581	−	0.0201000i
$253$	3.85673	+	4.59627i	0.242470	+	0.288965i
$254$	−7.81702	−	13.5395i	−0.490483	−	0.849542i
$255$		0			0
$256$	−0.763356	−	4.32921i	−0.0477098	−	0.270575i
$257$	0.657115	−	0.115867i	0.0409897	−	0.00722759i	−0.153116	−	0.988208i	$-0.548931\pi$
$257$	0.657115	−	0.115867i	0.0409897	−	0.00722759i	0.194105	+	0.980981i	$0.437820\pi$
$258$	−13.1082	−	7.56805i	−0.816084	−	0.471166i
$259$	0.858441	+	1.48686i	0.0533409	+	0.0923892i
$260$		0			0
$261$	34.2028	−	12.4488i	2.11710	−	0.770561i
$262$	0.850290	−	2.33615i	0.0525311	−	0.144328i
$263$	−7.32753	+	8.73261i	−0.451835	+	0.538476i	−0.943089	−	0.332540i	$-0.892094\pi$
$263$	−7.32753	+	8.73261i	−0.451835	+	0.538476i	0.491254	+	0.871016i	$0.336539\pi$
$264$	−3.27719	+	18.5859i	−0.201697	+	1.14388i
$265$		0			0
$266$	−1.77379	+	1.00676i	−0.108758	+	0.0617283i
$267$		−	29.6313i		−	1.81341i
$268$	−1.39673	−	0.246282i	−0.0853191	−	0.0150441i
$269$	−14.8537	−	12.4637i	−0.905646	−	0.759927i	0.0656400	−	0.997843i	$-0.479091\pi$
$269$	−14.8537	−	12.4637i	−0.905646	−	0.759927i	−0.971286	+	0.237916i	$0.923536\pi$
$270$		0			0
$271$	12.5865	−	4.58110i	0.764573	−	0.278282i	0.0698486	−	0.997558i	$-0.477748\pi$
$271$	12.5865	−	4.58110i	0.764573	−	0.278282i	0.694725	+	0.719276i	$0.255526\pi$
$272$	1.08164	+	1.28905i	0.0655841	+	0.0781600i
$273$	−2.22913	+	1.28699i	−0.134913	+	0.0778921i
$274$	−0.172304	+	0.298439i	−0.0104093	+	0.0180294i
$275$		0			0
$276$	−0.248970	−	1.41198i	−0.0149863	−	0.0849913i
$277$	15.3693	+	8.87346i	0.923450	+	0.533154i	0.884734	−	0.466096i	$-0.154340\pi$
$277$	15.3693	+	8.87346i	0.923450	+	0.533154i	0.0387161	+	0.999250i	$0.487673\pi$
$278$	−4.97464	+	2.87211i	−0.298359	+	0.172258i
$279$	28.8011	−	24.1670i	1.72428	−	1.44684i
$280$		0			0
$281$	−17.1766	−	6.25179i	−1.02467	−	0.372950i	−0.225622	−	0.974215i	$-0.572442\pi$
$281$	−17.1766	−	6.25179i	−1.02467	−	0.372950i	−0.799050	+	0.601265i	$0.794664\pi$
$282$	−18.1806	+	21.6668i	−1.08264	+	1.29024i
$283$	7.57099	+	1.33497i	0.450049	+	0.0793557i	0.394079	−	0.919077i	$-0.371064\pi$
$283$	7.57099	+	1.33497i	0.450049	+	0.0793557i	0.0559700	+	0.998432i	$0.482175\pi$
$284$	−1.71957			−0.102038
$285$		0			0
$286$	7.72193			0.456608
$287$	−0.846723	−	0.149300i	−0.0499805	−	0.00881290i
$288$	3.54336	−	4.22281i	0.208794	−	0.248832i
$289$	−15.7690	−	5.73946i	−0.927590	−	0.337615i
$290$		0			0
$291$	−20.8516	+	17.4966i	−1.22234	+	1.02567i
$292$	0.222318	−	0.128356i	0.0130102	−	0.00751144i
$293$	9.09586	+	5.25150i	0.531386	+	0.306796i	0.741581	−	0.670864i	$-0.234076\pi$
$293$	9.09586	+	5.25150i	0.531386	+	0.306796i	−0.210195	+	0.977660i	$0.567410\pi$
$294$	4.63429	+	26.2823i	0.270277	+	1.53282i
$295$		0			0
$296$	−7.27584	+	12.6021i	−0.422900	+	0.732484i
$297$	−12.7200	+	7.34389i	−0.738089	+	0.426136i
$298$	−14.3409	−	17.0908i	−0.830745	−	0.990044i
$299$	−6.51754	+	2.37219i	−0.376919	+	0.137187i
$300$		0			0
$301$	1.03802	+	0.871001i	0.0598304	+	0.0502037i
$302$	−5.78742	−	1.02048i	−0.333028	−	0.0587219i
$303$			26.6313i			1.52993i
$304$	−13.5175	−	7.93761i	−0.775284	−	0.455253i
$305$		0			0
$306$	−0.579193	+	3.28476i	−0.0331102	+	0.187777i
$307$	−7.51774	+	8.95929i	−0.429060	+	0.511334i	−0.936651	−	0.350264i	$-0.886092\pi$
$307$	−7.51774	+	8.95929i	−0.429060	+	0.511334i	0.507591	+	0.861598i	$0.330536\pi$
$308$	0.0488759	−	0.134285i	0.00278496	−	0.00765162i
$309$	14.9081	−	5.42609i	0.848091	−	0.308680i
$310$		0			0
$311$	−7.98293	−	13.8268i	−0.452670	−	0.784048i	0.545881	−	0.837863i	$-0.316195\pi$
$311$	−7.98293	−	13.8268i	−0.452670	−	0.784048i	−0.998551	+	0.0538151i	$0.982862\pi$
$312$	−18.8933	−	10.9081i	−1.06962	−	0.617548i
$313$	26.2241	−	4.62402i	1.48227	−	0.261365i	0.626788	−	0.779190i	$-0.284369\pi$
$313$	26.2241	−	4.62402i	1.48227	−	0.261365i	0.855487	+	0.517825i	$0.173258\pi$
$314$	−2.25031	−	12.7622i	−0.126993	−	0.720211i
$315$		0			0
$316$	−1.09446	−	1.89565i	−0.0615679	−	0.106639i
$317$	−18.9829	−	22.6229i	−1.06618	−	1.27063i	−0.961111	−	0.276164i	$-0.910937\pi$
$317$	−18.9829	−	22.6229i	−1.06618	−	1.27063i	−0.105073	−	0.994465i	$-0.533508\pi$
$318$	3.76487	+	10.3439i	0.211123	+	0.580057i
$319$	14.3944	+	5.23913i	0.805932	+	0.293335i
$320$		0			0
$321$	−5.11721	+	29.0211i	−0.285615	+	1.61980i
$322$		−	1.26083i		−	0.0702633i
$323$	−2.03952	−	0.0150147i	−0.113482	−	0.000835443i
$324$	0.576666			0.0320370
$325$		0			0
$326$	−8.62314	−	7.23567i	−0.477592	−	0.400747i
$327$	−1.79525	+	4.93242i	−0.0992777	+	0.272763i
$328$	−2.49238	−	6.84776i	−0.137619	−	0.378104i
$329$	1.93969	−	1.62760i	0.106939	−	0.0897322i
$330$		0			0
$331$	−13.8327	+	23.9590i	−0.760317	+	1.31691i	0.182371	+	0.983230i	$0.441623\pi$
$331$	−13.8327	+	23.9590i	−0.760317	+	1.31691i	−0.942687	+	0.333677i	$0.891710\pi$
$332$	2.69896	−	0.475900i	0.148125	−	0.0261184i
$333$	−25.7583	+	4.54189i	−1.41155	+	0.248894i
$334$	−2.71823	+	4.70810i	−0.148735	+	0.257616i
$335$		0			0
$336$	2.75490	−	2.31164i	0.150292	−	0.126110i
$337$	6.10841	+	16.7827i	0.332746	+	0.914212i	0.987394	+	0.158279i	$0.0505945\pi$
$337$	6.10841	+	16.7827i	0.332746	+	0.914212i	−0.654648	+	0.755934i	$0.727183\pi$
$338$	2.93745	−	8.07057i	0.159776	−	0.438981i
$339$	−39.0146	−	32.7371i	−2.11898	−	1.77804i
$340$		0			0
$341$	15.8229			0.856861
$342$	−5.17015	−	30.6386i	−0.279569	−	1.65675i
$343$		−	4.82026i		−	0.260270i
$344$	−1.99432	+	11.3103i	−0.107526	+	0.609813i
$345$		0			0
$346$	−25.5030	−	9.28233i	−1.37105	−	0.499021i
$347$	−1.98394	−	5.45084i	−0.106504	−	0.292616i	0.874981	−	0.484157i	$-0.160874\pi$
$347$	−1.98394	−	5.45084i	−0.106504	−	0.292616i	−0.981485	+	0.191541i	$0.938652\pi$
$348$	−2.35289	−	2.80406i	−0.126128	−	0.150314i
$349$	2.68614	+	4.65253i	0.143786	+	0.249044i	0.928919	−	0.370282i	$-0.120739\pi$
$349$	2.68614	+	4.65253i	0.143786	+	0.249044i	−0.785134	+	0.619326i	$0.787406\pi$
$350$		0			0
$351$	−2.94831	−	16.7207i	−0.157369	−	0.892485i
$352$	2.28471	−	0.402856i	0.121775	−	0.0214723i
$353$	21.8537	+	12.6172i	1.16315	+	0.671546i	0.952057	−	0.305919i	$-0.0989637\pi$
$353$	21.8537	+	12.6172i	1.16315	+	0.671546i	0.211095	+	0.977466i	$0.432297\pi$
$354$	−12.2306	−	21.1839i	−0.650047	−	1.12591i
$355$		0			0
$356$	−1.78699	+	0.650411i	−0.0947102	+	0.0344717i
$357$	0.160035	−	0.439693i	0.00846995	−	0.0232710i
$358$	−9.97011	+	11.8819i	−0.526937	+	0.627979i
$359$	−1.16116	+	6.58526i	−0.0612837	+	0.347557i	0.938712	+	0.344702i	$0.112020\pi$
$359$	−1.16116	+	6.58526i	−0.0612837	+	0.347557i	−0.999996	+	0.00285518i	$0.999091\pi$
$360$		0			0
$361$	17.9479	−	6.23481i	0.944626	−	0.328148i
$362$			11.5021i			0.604535i
$363$	17.1326	+	3.02094i	0.899230	+	0.158558i
$364$	0.126545	+	0.106183i	0.00663274	+	0.00556553i
$365$		0			0
$366$	−33.2768	+	12.1118i	−1.73941	+	0.633092i
$367$	−5.21870	−	6.21941i	−0.272414	−	0.324650i	0.612441	−	0.790516i	$-0.290188\pi$
$367$	−5.21870	−	6.21941i	−0.272414	−	0.324650i	−0.884856	+	0.465865i	$0.845743\pi$
$368$	8.39220	−	4.84524i	0.437473	−	0.252575i
$369$	6.54916	−	11.3435i	0.340936	−	0.590518i
$370$		0			0
$371$	−0.171122	−	0.970481i	−0.00888421	−	0.0503849i
$372$	−3.27449	−	1.89053i	−0.169775	−	0.0980194i
$373$	30.2222	−	17.4488i	1.56484	−	0.903463i	0.568090	−	0.822967i	$-0.307683\pi$
$373$	30.2222	−	17.4488i	1.56484	−	0.903463i	0.996755	−	0.0804968i	$-0.0256507\pi$
$374$	−1.07532	+	0.902302i	−0.0556036	+	0.0466569i
$375$		0			0
$376$	20.1668	+	7.34013i	1.04003	+	0.378538i
$377$	−11.3821	+	13.5646i	−0.586207	+	0.698615i
$378$	3.03958	+	0.535959i	0.156339	+	0.0275668i
$379$	−1.70140			−0.0873950			−0.0436975	−	0.999045i	$-0.513914\pi$
$379$	−1.70140			−0.0873950			−0.0436975	+	0.999045i	$0.513914\pi$
$380$		0			0
$381$	−33.4124			−1.71177
$382$	24.3280	+	4.28968i	1.24473	+	0.219479i
$383$	−1.88771	+	2.24969i	−0.0964575	+	0.114954i	−0.812114	−	0.583499i	$-0.801683\pi$
$383$	−1.88771	+	2.24969i	−0.0964575	+	0.114954i	0.715656	+	0.698453i	$0.246128\pi$
$384$	25.6989	+	9.35365i	1.31144	+	0.477326i
$385$		0			0
$386$	−0.307218	+	0.257787i	−0.0156370	+	0.0131210i
$387$	−17.8775	+	10.3216i	−0.908767	+	0.524677i
$388$	1.51287	+	0.873455i	0.0768043	+	0.0443430i
$389$	4.26604	+	24.1939i	0.216297	+	1.22668i	0.878642	+	0.477482i	$0.158450\pi$
$389$	4.26604	+	24.1939i	0.216297	+	1.22668i	−0.662344	+	0.749199i	$0.730438\pi$
$390$		0			0
$391$	0.630415	−	1.09191i	0.0318815	−	0.0552203i
$392$	17.5369	−	10.1250i	0.885749	−	0.511387i
$393$	−3.41523	−	4.07011i	−0.172275	−	0.205310i
$394$	−16.6373	+	6.05547i	−0.838174	+	0.305070i
$395$		0			0
$396$	1.66772	+	1.39938i	0.0838060	+	0.0703216i
$397$	31.3521	+	5.52822i	1.57352	+	0.277453i	0.891202	−	0.453606i	$-0.149863\pi$
$397$	31.3521	+	5.52822i	1.57352	+	0.277453i	0.682314	+	0.731059i	$0.260974\pi$
$398$			0.345866i			0.0173367i
$399$	−0.0320889	+	4.35878i	−0.00160645	+	0.218212i
$400$		0			0
$401$	−0.0150147	+	0.0851529i	−0.000749801	+	0.00425233i	−0.985180	−	0.171522i	$-0.945132\pi$
$401$	−0.0150147	+	0.0851529i	−0.000749801	+	0.00425233i	0.984431	+	0.175774i	$0.0562428\pi$
$402$	19.1385	−	22.8084i	0.954543	−	1.13758i
$403$	−6.25584	+	17.1878i	−0.311626	+	0.856185i
$404$	1.60607	−	0.584561i	0.0799048	−	0.0290830i
$405$		0			0
$406$	−1.60947	−	2.78768i	−0.0798767	−	0.138350i
$407$	−9.53298	−	5.50387i	−0.472532	−	0.272817i
$408$	3.90560	−	0.688663i	0.193356	−	0.0340939i
$409$	−3.47400	−	19.7021i	−0.171778	−	0.974204i	−0.941797	−	0.336182i	$-0.890864\pi$
$409$	−3.47400	−	19.7021i	−0.171778	−	0.974204i	0.770019	−	0.638021i	$-0.220247\pi$
$410$		0			0
$411$	0.368241	+	0.637812i	0.0181640	+	0.0314609i
$412$	−0.654467	−	0.779963i	−0.0322433	−	0.0384260i
$413$	0.748971	+	2.05778i	0.0368545	+	0.101257i
$414$	18.0496	+	6.56953i	0.887091	+	0.322875i
$415$		0			0
$416$	−0.465690	+	2.64106i	−0.0228323	+	0.129488i
$417$			12.2763i			0.601174i
$418$	6.62154	−	11.2763i	0.323870	−	0.551542i
$419$	−25.4097			−1.24135			−0.620673	−	0.784070i	$-0.713141\pi$
$419$	−25.4097			−1.24135			−0.620673	+	0.784070i	$0.713141\pi$
$420$		0			0
$421$	3.34730	+	2.80872i	0.163137	+	0.136888i	0.720702	−	0.693245i	$-0.243820\pi$
$421$	3.34730	+	2.80872i	0.163137	+	0.136888i	−0.557565	+	0.830134i	$0.688264\pi$
$422$	1.12819	−	3.09967i	0.0549193	−	0.150890i
$423$	13.1934	+	36.2486i	0.641485	+	1.76247i
$424$	6.39827	−	5.36879i	0.310727	−	0.260731i
$425$		0			0
$426$	18.0496	−	31.2629i	0.874507	−	1.51469i
$427$	3.12208	−	0.550507i	0.151088	−	0.0266409i
$428$	1.86251	−	0.328411i	0.0900279	−	0.0158744i
$429$	8.25150	−	14.2920i	0.398386	−	0.690025i
$430$		0			0
$431$	−29.3444	+	24.6228i	−1.41347	+	1.18604i	−0.458736	+	0.888572i	$0.651698\pi$
$431$	−29.3444	+	24.6228i	−1.41347	+	1.18604i	−0.954732	+	0.297468i	$0.903858\pi$
$432$	8.11338	+	22.2913i	0.390355	+	1.07249i
$433$	−6.20118	+	17.0376i	−0.298010	+	0.818775i	0.696823	+	0.717244i	$0.254597\pi$
$433$	−6.20118	+	17.0376i	−0.298010	+	0.818775i	−0.994832	+	0.101532i	$0.967626\pi$
$434$	−2.54710	−	2.13727i	−0.122265	−	0.102592i
$435$		0			0
$436$	0.336867			0.0161330
$437$	−2.12467	+	11.5517i	−0.101637	+	0.552592i
$438$			5.38919i			0.257505i
$439$	1.05762	−	5.99806i	0.0504774	−	0.286272i	−0.949112	−	0.314940i	$-0.898016\pi$
$439$	1.05762	−	5.99806i	0.0504774	−	0.286272i	0.999589	+	0.0286685i	$0.00912670\pi$
$440$		0			0
$441$	34.2028	+	12.4488i	1.62870	+	0.592800i
$442$	−0.554987	−	1.52481i	−0.0263981	−	0.0725280i
$443$	−19.2149	−	22.8995i	−0.912928	−	1.08799i	−0.995812	−	0.0914266i	$-0.970857\pi$
$443$	−19.2149	−	22.8995i	−0.912928	−	1.08799i	0.0828833	−	0.996559i	$-0.473587\pi$
$444$	1.31521	+	2.27801i	0.0624170	+	0.108109i
$445$		0			0
$446$	1.99092	+	11.2910i	0.0942726	+	0.534646i
$447$	−46.9566	+	8.27972i	−2.22097	+	0.391617i
$448$	−2.58548	−	1.49273i	−0.122152	−	0.0705247i
$449$	−5.62495	−	9.74270i	−0.265458	−	0.459787i	0.702226	−	0.711955i	$-0.252190\pi$
$449$	−5.62495	−	9.74270i	−0.265458	−	0.459787i	−0.967683	+	0.252168i	$0.918856\pi$
$450$		0			0
$451$	5.18004	−	1.88538i	0.243919	−	0.0887792i
$452$	−1.11792	+	3.07145i	−0.0525824	+	0.144469i
$453$	−8.07305	+	9.62108i	−0.379305	+	0.452038i
$454$	−3.31062	+	18.7755i	−0.155375	+	0.881176i
$455$		0			0
$456$	−32.1300	+	18.2362i	−1.50463	+	0.853989i
$457$			23.3901i			1.09414i	0.837086	+	0.547072i	$0.184258\pi$
$457$			23.3901i			1.09414i	−0.837086	+	0.547072i	$0.815742\pi$
$458$	27.2438	+	4.80381i	1.27302	+	0.224468i
$459$	2.36437	+	1.98394i	0.110359	+	0.0926025i
$460$		0			0
$461$	34.4149	−	12.5260i	1.60286	−	0.583395i	0.622853	−	0.782339i	$-0.285974\pi$
$461$	34.4149	−	12.5260i	1.60286	−	0.583395i	0.980011	+	0.198945i	$0.0637514\pi$
$462$	1.92836	+	2.29813i	0.0897156	+	0.106919i
$463$	−37.2273	+	21.4932i	−1.73010	+	0.998873i	−0.841322	+	0.540534i	$0.818222\pi$
$463$	−37.2273	+	21.4932i	−1.73010	+	0.998873i	−0.888777	+	0.458340i	$0.848444\pi$
$464$	12.3701	−	21.4256i	0.574265	−	0.994657i
$465$		0			0
$466$	−4.12954	−	23.4198i	−0.191297	−	1.08490i
$467$	22.1670	+	12.7981i	1.02577	+	0.592227i	0.915769	−	0.401705i	$-0.131582\pi$
$467$	22.1670	+	12.7981i	1.02577	+	0.592227i	0.109998	+	0.993932i	$0.464916\pi$
$468$	−2.17945	+	1.25830i	−0.100745	+	0.0581651i
$469$	−2.04189	+	1.71335i	−0.0942857	+	0.0791151i
$470$		0			0
$471$	−26.0253	−	9.47243i	−1.19918	−	0.436466i
$472$	−11.9304	+	14.2181i	−0.549140	+	0.654439i
$473$	−8.55580	−	1.50862i	−0.393396	−	0.0693663i
$474$	45.9522			2.11066
$475$		0			0
$476$	−0.0300295			−0.00137640
$477$	14.7847	+	2.60694i	0.676946	+	0.119364i
$478$	2.03719	−	2.42783i	0.0931791	−	0.111046i
$479$	35.8739	+	13.0570i	1.63912	+	0.596591i	0.986885	−	0.161424i	$-0.0516088\pi$
$479$	35.8739	+	13.0570i	1.63912	+	0.596591i	0.652236	+	0.758016i	$0.273831\pi$
$480$		0			0
$481$	9.74763	−	8.17923i	0.444453	−	0.372941i
$482$	16.1025	−	9.29679i	0.733449	−	0.423457i
$483$	−2.33359	−	1.34730i	−0.106182	−	0.0613041i
$484$	−0.193877	−	1.09953i	−0.00881261	−	0.0499788i
$485$		0			0
$486$	7.27766	−	12.6053i	0.330121	−	0.571787i
$487$	−6.72367	+	3.88191i	−0.304678	+	0.175906i	−0.644543	−	0.764568i	$-0.722952\pi$
$487$	−6.72367	+	3.88191i	−0.304678	+	0.175906i	0.339864	+	0.940475i	$0.389619\pi$
$488$	17.2716	+	20.5835i	0.781850	+	0.931773i
$489$	−22.6065	+	8.22811i	−1.02230	+	0.372088i
$490$		0			0
$491$	−28.1313	−	23.6050i	−1.26955	−	1.06528i	−0.994596	−	0.103822i	$-0.966893\pi$
$491$	−28.1313	−	23.6050i	−1.26955	−	1.06528i	−0.274954	−	0.961457i	$-0.588663\pi$
$492$	−1.29725	−	0.228741i	−0.0584848	−	0.0103124i
$493$		−	3.21894i		−	0.144974i
$494$	9.63104	+	11.6510i	0.433321	+	0.524201i
$495$		0			0
$496$	4.43763	−	25.1671i	0.199256	−	1.13003i
$497$	−2.07732	+	2.47565i	−0.0931805	+	0.111048i
$498$	−19.6778	+	54.0642i	−0.881782	+	2.42268i
$499$	4.62923	−	1.68490i	0.207233	−	0.0754266i	−0.236318	−	0.971676i	$-0.575941\pi$
$499$	4.62923	−	1.68490i	0.207233	−	0.0754266i	0.443551	+	0.896249i	$0.353719\pi$
$500$		0			0
$501$	5.80928	+	10.0620i	0.259539	+	0.449535i
$502$	4.85992	+	2.80587i	0.216909	+	0.125232i
$503$	−32.4490	+	5.72163i	−1.44683	+	0.255115i	−0.841239	−	0.540663i	$-0.818173\pi$
$503$	−32.4490	+	5.72163i	−1.44683	+	0.255115i	−0.605589	+	0.795778i	$0.707062\pi$
$504$	−0.939226	−	5.32661i	−0.0418364	−	0.237266i
$505$		0			0
$506$	4.04189	+	7.00076i	0.179684	+	0.311222i
$507$	−11.7984	−	14.0608i	−0.523985	−	0.624461i
$508$	0.733405	+	2.01501i	0.0325396	+	0.0894018i
$509$	−34.7075	−	12.6325i	−1.53839	−	0.559926i	−0.572728	−	0.819746i	$-0.694115\pi$
$509$	−34.7075	−	12.6325i	−1.53839	−	0.559926i	−0.965657	+	0.259819i	$0.916337\pi$
$510$		0			0
$511$	0.0837781	−	0.475129i	0.00370613	−	0.0210185i
$512$		−	24.9186i		−	1.10126i
$513$	−26.9453	−	10.0326i	−1.18967	−	0.442948i
$514$	0.898986			0.0396526
$515$		0			0
$516$	1.59034	+	1.33445i	0.0700107	+	0.0587459i
$517$	−5.55250	+	15.2554i	−0.244199	+	0.670930i
$518$	0.791143	+	2.17365i	0.0347608	+	0.0955046i
$519$	−44.4320	+	37.2829i	−1.95035	+	1.63654i
$520$		0			0
$521$	−4.64590	+	8.04693i	−0.203540	+	0.352542i	−0.949667	−	0.313262i	$-0.898578\pi$
$521$	−4.64590	+	8.04693i	−0.203540	+	0.352542i	0.746126	+	0.665804i	$0.231912\pi$
$522$	48.2937	−	8.51548i	2.11376	−	0.372713i
$523$	27.9834	−	4.93423i	1.22363	−	0.215759i	0.475742	−	0.879585i	$-0.342180\pi$
$523$	27.9834	−	4.93423i	1.22363	−	0.215759i	0.747887	+	0.663826i	$0.231068\pi$
$524$	−0.170493	+	0.295303i	−0.00744802	+	0.0129004i
$525$		0			0
$526$	−11.7654	+	9.87236i	−0.512996	+	0.430455i
$527$	−1.13722	−	3.12449i	−0.0495381	−	0.136105i
$528$	−7.88609	+	21.6668i	−0.343198	+	0.942928i
$529$	12.0569	+	10.1169i	0.524213	+	0.439867i
$530$		0			0
$531$	−33.3610			−1.44775
$532$	0.263571	−	0.0937404i	0.0114273	−	0.00406416i
$533$			6.37227i			0.276014i
$534$	6.93242	−	39.3157i	0.299995	−	1.70136i
$535$		0			0
$536$	−21.2294	−	7.72686i	−0.916969	−	0.333749i
$537$	11.3376	+	31.1498i	0.489253	+	1.34421i
$538$	−16.7923	−	20.0123i	−0.723969	−	0.862793i
$539$	7.65910	+	13.2660i	0.329901	+	0.571405i
$540$		0			0
$541$	2.60220	+	14.7578i	0.111877	+	0.634487i	0.988249	+	0.152852i	$0.0488458\pi$
$541$	2.60220	+	14.7578i	0.111877	+	0.634487i	−0.876372	+	0.481635i	$0.840043\pi$
$542$	17.7718	−	3.13366i	0.763366	−	0.134602i
$543$	21.2884	+	12.2909i	0.913572	+	0.527451i
$544$	−0.243756	−	0.422197i	−0.0104509	−	0.0181016i
$545$		0			0
$546$	−3.25877	+	1.18610i	−0.139463	+	0.0507602i
$547$	1.32948	−	3.65270i	0.0568443	−	0.156178i	−0.908020	−	0.418926i	$-0.862407\pi$
$547$	1.32948	−	3.65270i	0.0568443	−	0.156178i	0.964864	+	0.262748i	$0.0846288\pi$
$548$	0.0303818	−	0.0362077i	0.00129785	−	0.00154672i
$549$	−8.38666	+	47.5631i	−0.357934	+	2.02994i
$550$		0			0
$551$	10.0483	+	28.2529i	0.428071	+	1.20361i
$552$		−	22.8384i		−	0.972068i
$553$	−4.05131	−	0.714355i	−0.172279	−	0.0303775i
$554$	18.3164	+	15.3693i	0.778189	+	0.652978i
$555$		0			0
$556$	0.740352	−	0.269466i	0.0313979	−	0.0114279i
$557$	−8.48762	−	10.1152i	−0.359632	−	0.428593i	0.555644	−	0.831420i	$-0.312472\pi$
$557$	−8.48762	−	10.1152i	−0.359632	−	0.428593i	−0.915276	+	0.402828i	$0.868027\pi$
$558$	43.8681	−	25.3273i	1.85709	−	1.07219i
$559$	5.02141	−	8.69734i	0.212383	−	0.367858i
$560$		0			0
$561$	0.520945	+	2.95442i	0.0219943	+	0.124736i
$562$	−21.3278	−	12.3136i	−0.899659	−	0.519418i
$563$	9.27752	−	5.35638i	0.391001	−	0.225745i	−0.291593	−	0.956543i	$-0.594185\pi$
$563$	9.27752	−	5.35638i	0.391001	−	0.225745i	0.682594	+	0.730798i	$0.260852\pi$
$564$	2.97178	−	2.49362i	0.125135	−	0.105000i
$565$		0			0
$566$	9.73308	+	3.54255i	0.409112	+	0.148905i
$567$	0.696639	−	0.830222i	0.0292561	−	0.0348661i
$568$	−26.9749	−	4.75641i	−1.13184	−	0.199574i
$569$	13.4706			0.564717			0.282358	−	0.959309i	$-0.408883\pi$
$569$	13.4706			0.564717			0.282358	+	0.959309i	$0.408883\pi$
$570$		0			0
$571$	12.6655			0.530035			0.265017	−	0.964244i	$-0.414622\pi$
$571$	12.6655			0.530035			0.265017	+	0.964244i	$0.414622\pi$
$572$	−1.04303	−	0.183915i	−0.0436115	−	0.00768988i
$573$	33.9358	−	40.4432i	1.41769	−	1.68954i
$574$	−1.08853	−	0.396191i	−0.0454342	−	0.0165367i
$575$		0			0
$576$	34.8410	−	29.2350i	1.45171	−	1.21813i
$577$	9.14036	−	5.27719i	0.380518	−	0.219692i	−0.297526	−	0.954714i	$-0.596161\pi$
$577$	9.14036	−	5.27719i	0.380518	−	0.219692i	0.678044	+	0.735022i	$0.262828\pi$
$578$	−19.5800	−	11.3045i	−0.814421	−	0.470206i
$579$	0.148833	+	0.844075i	0.00618530	+	0.0350786i
$580$		0			0
$581$	2.57532	−	4.46059i	0.106842	−	0.185056i
$582$	−31.7600	+	18.3366i	−1.31649	+	0.760077i
$583$	4.06126	+	4.84002i	0.168200	+	0.200453i
$584$	3.84255	−	1.39857i	0.159006	−	0.0578734i
$585$		0			0
$586$	10.8400	+	9.09586i	0.447797	+	0.375746i
$587$	18.8638	+	3.32619i	0.778591	+	0.137287i	0.548800	−	0.835954i	$-0.315085\pi$
$587$	18.8638	+	3.32619i	0.778591	+	0.137287i	0.229791	+	0.973240i	$0.426196\pi$
$588$		−	3.66044i		−	0.150954i
$589$	19.7349	+	23.8739i	0.813162	+	0.983706i
$590$		0			0
$591$	−6.57057	+	37.2636i	−0.270277	+	1.53282i
$592$	−11.4277	+	13.6190i	−0.469676	+	0.559738i
$593$	−2.97373	+	8.17024i	−0.122116	+	0.335512i	−0.985655	−	0.168770i	$-0.946020\pi$
$593$	−2.97373	+	8.17024i	−0.122116	+	0.335512i	0.863539	+	0.504282i	$0.168243\pi$
$594$	−18.5954	+	6.76817i	−0.762978	+	0.277701i
$595$		0			0
$596$	1.53003	+	2.65009i	0.0626724	+	0.108552i
$597$	0.640140	+	0.369585i	0.0261992	+	0.0151261i
$598$	−9.20264	+	1.62267i	−0.376324	+	0.0663561i
$599$	−3.44373	−	19.5303i	−0.140707	−	0.797988i	−0.970715	−	0.240236i	$-0.922775\pi$
$599$	−3.44373	−	19.5303i	−0.140707	−	0.797988i	0.830008	−	0.557752i	$-0.188336\pi$
$600$		0			0
$601$	16.8807	+	29.2383i	0.688579	+	1.19265i	0.972298	+	0.233747i	$0.0750986\pi$
$601$	16.8807	+	29.2383i	0.688579	+	1.19265i	−0.283718	+	0.958908i	$0.591568\pi$
$602$	1.17350	+	1.39852i	0.0478282	+	0.0569994i
$603$	−13.8885	−	38.1584i	−0.565584	−	1.55393i
$604$	0.757426	+	0.275681i	0.0308192	+	0.0112173i
$605$		0			0
$606$	−6.23055	+	35.3352i	−0.253099	+	1.43540i
$607$		−	35.2850i		−	1.43217i	−0.698011	−	0.716087i	$-0.745932\pi$
$607$		−	35.2850i		−	1.43217i	0.698011	−	0.716087i	$-0.254068\pi$
$608$	3.45740	+	2.94475i	0.140216	+	0.119425i
$609$	−6.87939			−0.278767
$610$		0			0
$611$	−14.3760	−	12.0629i	−0.581590	−	0.488012i
$612$	0.156468	−	0.429892i	0.00632485	−	0.0173774i
$613$	−6.31142	−	17.3405i	−0.254916	−	0.700376i	−0.999462	−	0.0328044i	$-0.989556\pi$
$613$	−6.31142	−	17.3405i	−0.254916	−	0.700376i	0.744546	−	0.667571i	$-0.232666\pi$
$614$	−12.0708	+	10.1286i	−0.487139	+	0.408758i
$615$		0			0
$616$	1.13816	−	1.97134i	0.0458576	−	0.0794277i
$617$	−35.1433	+	6.19671i	−1.41482	+	0.249470i	−0.828217	−	0.560408i	$-0.810644\pi$
$617$	−35.1433	+	6.19671i	−1.41482	+	0.249470i	−0.586598	+	0.809878i	$0.699533\pi$
$618$	21.0499	−	3.71167i	0.846752	−	0.149305i
$619$	1.82976	−	3.16923i	0.0735441	−	0.127382i	−0.826908	−	0.562337i	$-0.809902\pi$
$619$	1.82976	−	3.16923i	0.0735441	−	0.127382i	0.900452	+	0.434955i	$0.143236\pi$
$620$		0			0
$621$	13.6159	−	11.4251i	0.546386	−	0.458472i
$622$	−7.35710	−	20.2135i	−0.294993	−	0.810487i
$623$	−1.22237	+	3.35844i	−0.0489733	+	0.134553i
$624$	−20.4179	−	17.1326i	−0.817369	−	0.685854i
$625$		0			0
$626$	35.8767			1.43392
$627$	−13.7949	−	24.3050i	−0.550917	−	0.970648i
$628$			1.77744i			0.0709275i
$629$	−0.401674	+	2.27801i	−0.0160158	+	0.0908301i
$630$		0			0
$631$	0.745977	+	0.271514i	0.0296969	+	0.0108088i	0.356826	−	0.934171i	$-0.383859\pi$
$631$	0.745977	+	0.271514i	0.0296969	+	0.0108088i	−0.327129	+	0.944980i	$0.606081\pi$
$632$	−11.9253	−	32.7645i	−0.474362	−	1.30330i
$633$	−4.53141	−	5.40033i	−0.180108	−	0.214644i
$634$	−19.8942	−	34.4578i	−0.790101	−	1.36850i
$635$		0			0
$636$	−0.262174	−	1.48686i	−0.0103959	−	0.0589579i
$637$	−17.4384	+	3.07486i	−0.690933	+	0.121830i
$638$	17.8732	+	10.3191i	0.707605	+	0.408536i
$639$	−24.6168	−	42.6375i	−0.973826	−	1.68672i
$640$		0			0
$641$	−27.6104	+	10.0494i	−1.09055	+	0.396926i	−0.823823	−	0.566847i	$-0.808163\pi$
$641$	−27.6104	+	10.0494i	−1.09055	+	0.396926i	−0.266723	+	0.963773i	$0.585941\pi$
$642$	−13.5793	+	37.3089i	−0.535933	+	1.47246i
$643$	−14.2788	+	17.0168i	−0.563101	+	0.671078i	−0.970200	−	0.242306i	$-0.922096\pi$
$643$	−14.2788	+	17.0168i	−0.563101	+	0.671078i	0.407098	+	0.913384i	$0.366541\pi$
$644$	−0.0300295	+	0.170306i	−0.00118333	+	0.00671099i
$645$		0			0
$646$	−2.70258	−	0.497079i	−0.106332	−	0.0195573i
$647$		−	11.2591i		−	0.442640i	−0.975201	−	0.221320i	$-0.928963\pi$
$647$		−	11.2591i		−	0.442640i	0.975201	−	0.221320i	$-0.0710365\pi$
$648$	9.04617	+	1.59508i	0.355367	+	0.0626608i
$649$	−10.7554	−	9.02482i	−0.422185	−	0.354255i
$650$		0			0
$651$	−6.67752	+	2.43042i	−0.261713	+	0.0952556i
$652$	0.992431	+	1.18273i	0.0388666	+	0.0463194i
$653$	23.3827	−	13.5000i	0.915035	−	0.528296i	0.0329874	−	0.999456i	$-0.489498\pi$
$653$	23.3827	−	13.5000i	0.915035	−	0.528296i	0.882048	+	0.471160i	$0.156165\pi$
$654$	−3.53596	+	6.12446i	−0.138267	+	0.239485i
$655$		0			0
$656$	−1.54601	−	8.76785i	−0.0603615	−	0.342327i
$657$	6.36527	+	3.67499i	0.248333	+	0.143375i
$658$	2.95442	−	1.70574i	0.115175	−	0.0664966i
$659$	−21.4691	+	18.0147i	−0.836317	+	0.701753i	−0.956732	−	0.290970i	$-0.906022\pi$
$659$	−21.4691	+	18.0147i	−0.836317	+	0.701753i	0.120415	+	0.992724i	$0.461577\pi$
$660$		0			0
$661$	−10.6823	−	3.88803i	−0.415492	−	0.151227i	0.125811	−	0.992054i	$-0.459847\pi$
$661$	−10.6823	−	3.88803i	−0.415492	−	0.151227i	−0.541303	+	0.840827i	$0.682069\pi$
$662$	−23.9590	+	28.5533i	−0.931194	+	1.10975i
$663$	−3.41523	−	0.602196i	−0.132636	−	0.0233874i
$664$	43.6551			1.69415
$665$		0			0
$666$	−35.2395			−1.36550
$667$	−18.2555	−	3.21894i	−0.706857	−	0.124638i
$668$	0.479297	−	0.571203i	0.0185445	−	0.0221005i
$669$	23.0253	+	8.38052i	0.890209	+	0.324010i
$670$		0			0
$671$	−15.5706	+	13.0653i	−0.601095	+	0.504379i
$672$	−0.902302	+	0.520945i	−0.0348071	+	0.0200959i
$673$	14.3476	+	8.28359i	0.553059	+	0.319309i	0.750355	−	0.661035i	$-0.229883\pi$
$673$	14.3476	+	8.28359i	0.553059	+	0.319309i	−0.197296	+	0.980344i	$0.563216\pi$
$674$	4.17840	+	23.6969i	0.160946	+	0.912769i
$675$		0			0
$676$	−0.588993	+	1.02017i	−0.0226536	+	0.0392371i
$677$	7.83721	−	4.52481i	0.301208	−	0.173903i	−0.341777	−	0.939781i	$-0.611029\pi$
$677$	7.83721	−	4.52481i	0.301208	−	0.173903i	0.642986	+	0.765878i	$0.277695\pi$
$678$	−44.1066	−	52.5642i	−1.69390	−	2.01872i
$679$	3.08512	−	1.12289i	0.118396	−	0.0430927i
$680$		0			0
$681$	31.2126	+	26.1905i	1.19607	+	1.00362i
$682$	20.9943	+	3.70187i	0.803914	+	0.141752i
$683$			8.73143i			0.334099i	0.985949	+	0.167049i	$0.0534239\pi$
$683$			8.73143i			0.334099i	−0.985949	+	0.167049i	$0.946576\pi$
$684$	−0.0313737	+	4.26163i	−0.00119960	+	0.162947i
$685$		0			0
$686$	1.12773	−	6.39566i	0.0430568	−	0.244187i
$687$	38.0032	−	45.2904i	1.44991	−	1.72794i
$688$	−4.79904	+	13.1853i	−0.182962	+	0.502683i
$689$	−6.86319	+	2.49800i	−0.261467	+	0.0951661i
$690$		0			0
$691$	−17.3601	−	30.0686i	−0.660409	−	1.14386i	−0.980508	−	0.196478i	$-0.937050\pi$
$691$	−17.3601	−	30.0686i	−0.660409	−	1.14386i	0.320099	−	0.947384i	$-0.396284\pi$
$692$	3.22372	+	1.86122i	0.122547	+	0.0707528i
$693$	4.02936	−	0.710485i	0.153063	−	0.0269891i
$694$	−1.35710	−	7.69648i	−0.0515147	−	0.292154i
$695$		0			0
$696$	−29.1536	−	50.4956i	−1.10507	−	1.91403i
$697$	−0.744596	−	0.887374i	−0.0282036	−	0.0336117i
$698$	2.47556	+	6.80154i	0.0937012	+	0.257442i
$699$	−47.7588	−	17.3828i	−1.80640	−	0.657478i
$700$		0			0
$701$	6.84436	−	38.8163i	0.258508	−	1.46607i	−0.528397	−	0.848997i	$-0.677207\pi$
$701$	6.84436	−	38.8163i	0.258508	−	1.46607i	0.786905	−	0.617074i	$-0.211682\pi$
$702$		−	22.8753i		−	0.863371i
$703$	−3.58553	−	21.2481i	−0.135231	−	0.801387i
$704$	19.1411			0.721409
$705$		0			0
$706$	26.0442	+	21.8537i	0.980185	+	0.822473i
$707$	1.09861	−	3.01842i	0.0413176	−	0.113519i
$708$	1.14749	+	3.15270i	0.0431253	+	0.118486i
$709$	31.5009	−	26.4324i	1.18304	−	0.992690i	0.183088	−	0.983096i	$-0.441391\pi$
$709$	31.5009	−	26.4324i	1.18304	−	0.992690i	0.999954	−	0.00959399i	$-0.00305391\pi$
$710$		0			0
$711$	31.3357	−	54.2751i	1.17518	−	2.03548i
$712$	−29.8316	+	5.26011i	−1.11799	+	0.197131i
$713$	−18.8571	+	3.32501i	−0.706202	+	0.124523i
$714$	0.315207	−	0.545955i	0.0117963	−	0.0204319i
$715$		0			0
$716$	1.62970	−	1.36748i	0.0609047	−	0.0511051i
$717$	−2.31661	−	6.36484i	−0.0865154	−	0.237699i
$718$	−3.08132	+	8.46585i	−0.114994	+	0.315943i
$719$	32.4768	+	27.2513i	1.21118	+	1.01630i	0.999238	+	0.0390200i	$0.0124236\pi$
$719$	32.4768	+	27.2513i	1.21118	+	1.01630i	0.211943	+	0.977282i	$0.432021\pi$
$720$		0			0
$721$	−1.91353			−0.0712637
$722$	25.2724	−	4.07351i	0.940543	−	0.151600i
$723$		−	39.7374i		−	1.47785i
$724$	0.273947	−	1.55363i	0.0101812	−	0.0577403i
$725$		0			0
$726$	22.0253	+	8.01655i	0.817435	+	0.297522i
$727$	17.6675	+	48.5411i	0.655251	+	1.80029i	0.597371	+	0.801965i	$0.296212\pi$
$727$	17.6675	+	48.5411i	0.655251	+	1.80029i	0.0578805	+	0.998324i	$0.481566\pi$
$728$	1.69140	+	2.01573i	0.0626874	+	0.0747079i
$729$	−20.2344	−	35.0470i	−0.749423	−	1.29804i
$730$		0			0
$731$	0.317018	+	1.79790i	0.0117254	+	0.0664978i
$732$	4.78331	−	0.843426i	0.176796	−	0.0311739i
$733$	19.8460	+	11.4581i	0.733030	+	0.423215i	0.819530	−	0.573037i	$-0.194235\pi$
$733$	19.8460	+	11.4581i	0.733030	+	0.423215i	−0.0864997	+	0.996252i	$0.527568\pi$
$734$	−5.46926	−	9.47303i	−0.201874	−	0.349656i
$735$		0			0
$736$	−2.63816	+	0.960210i	−0.0972437	+	0.0353938i
$737$	5.84504	−	16.0591i	0.215305	−	0.591545i
$738$	11.3435	−	13.5186i	0.417559	−	0.497628i
$739$	−4.88413	+	27.6993i	−0.179666	+	1.01894i	0.752954	+	0.658074i	$0.228628\pi$
$739$	−4.88413	+	27.6993i	−0.179666	+	1.01894i	−0.932619	+	0.360862i	$0.882483\pi$
$740$		0			0
$741$	31.8555	−	5.37549i	1.17024	−	0.197474i
$742$		−	1.32770i		−	0.0487413i
$743$	6.03931	+	1.06489i	0.221561	+	0.0390671i	0.283326	−	0.959024i	$-0.408562\pi$
$743$	6.03931	+	1.06489i	0.221561	+	0.0390671i	−0.0617657	+	0.998091i	$0.519673\pi$
$744$	−46.1377	−	38.7142i	−1.69149	−	1.41933i
$745$		0			0
$746$	44.1819	−	16.0809i	1.61761	−	0.588763i
$747$	50.4377	+	60.1093i	1.84542	+	2.19928i
$748$	0.166739	−	0.0962667i	0.00609657	−	0.00351986i
$749$	1.77719	−	3.07818i	0.0649371	−	0.112474i
$750$		0			0
$751$	0.979522	+	5.55515i	0.0357433	+	0.202710i	0.997450	−	0.0713710i	$-0.0227374\pi$
$751$	0.979522	+	5.55515i	0.0357433	+	0.202710i	−0.961707	+	0.274081i	$0.911626\pi$
$752$	22.7071	+	13.1099i	0.828042	+	0.478070i
$753$	10.3864	−	5.99660i	0.378502	−	0.218528i
$754$	−18.2756	+	15.3350i	−0.665558	+	0.558469i
$755$		0			0
$756$	−0.397804	−	0.144789i	−0.0144680	−	0.00526591i
$757$	10.0866	−	12.0207i	0.366602	−	0.436900i	−0.550936	−	0.834548i	$-0.685729\pi$
$757$	10.0866	−	12.0207i	0.366602	−	0.436900i	0.917538	+	0.397648i	$0.130173\pi$
$758$	−2.25746	−	0.398052i	−0.0819948	−	0.0144579i
$759$	17.2763			0.627090
$760$		0			0
$761$	4.86484			0.176350			0.0881751	−	0.996105i	$-0.471896\pi$
$761$	4.86484			0.176350			0.0881751	+	0.996105i	$0.471896\pi$
$762$	−44.3325	−	7.81702i	−1.60600	−	0.283181i
$763$	0.406951	−	0.484985i	0.0147326	−	0.0175576i
$764$	−3.18392	−	1.15885i	−0.115190	−	0.0419257i
$765$		0			0
$766$	−3.03099	+	2.54331i	−0.109514	+	0.0918934i
$767$	14.0556	−	8.11499i	0.507517	−	0.293015i
$768$	−10.9619	−	6.32888i	−0.395555	−	0.228374i
$769$	−3.91266	−	22.1898i	−0.141094	−	0.800184i	−0.970421	−	0.241420i	$-0.922387\pi$
$769$	−3.91266	−	22.1898i	−0.141094	−	0.800184i	0.829327	−	0.558764i	$-0.188724\pi$
$770$		0			0
$771$	0.960637	−	1.66387i	0.0345965	−	0.0599229i
$772$	0.0476371	−	0.0275033i	0.00171450	−	0.000989864i
$773$	−16.9902	−	20.2481i	−0.611094	−	0.728273i	0.368418	−	0.929660i	$-0.379900\pi$
$773$	−16.9902	−	20.2481i	−0.611094	−	0.728273i	−0.979512	+	0.201387i	$0.935455\pi$
$774$	−26.1352	+	9.51244i	−0.939411	+	0.341918i
$775$		0			0
$776$	21.3164	+	17.8866i	0.765214	+	0.642091i
$777$	4.86846	+	0.858441i	0.174655	+	0.0307964i
$778$			33.0993i			1.18667i
$779$	9.30541	+	5.46421i	0.333401	+	0.195776i
$780$		0			0
$781$	3.59802	−	20.4054i	0.128747	−	0.730162i
$782$	1.09191	−	1.30129i	0.0390466	−	0.0465340i
$783$	15.5203	−	42.6416i	0.554650	−	1.52389i
$784$	23.2481	−	8.46161i	0.830289	−	0.302200i
$785$		0			0
$786$	−3.57919	−	6.19934i	−0.127666	−	0.221123i
$787$	−13.4733	−	7.77884i	−0.480273	−	0.277286i	0.240257	−	0.970709i	$-0.422768\pi$
$787$	−13.4733	−	7.77884i	−0.480273	−	0.277286i	−0.720530	+	0.693424i	$0.756101\pi$
$788$	2.39149	−	0.421685i	0.0851934	−	0.0150219i
$789$	5.69981	+	32.3252i	0.202919	+	1.15081i
$790$		0			0
$791$	3.07145	+	5.31991i	0.109208	+	0.189154i
$792$	22.2908	+	26.5651i	0.792068	+	0.943950i
$793$	−8.03617	−	22.0792i	−0.285373	−	0.784055i
$794$	40.3055	+	14.6700i	1.43039	+	0.520618i
$795$		0			0
$796$	0.00823757	−	0.0467176i	0.000291973	−	0.00165586i
$797$		−	33.4935i		−	1.18640i	−0.805055	−	0.593200i	$-0.797864\pi$
$797$		−	33.4935i		−	1.18640i	0.805055	−	0.593200i	$-0.202136\pi$
$798$	−1.06234	+	5.77584i	−0.0376063	+	0.204463i
$799$	3.41147			0.120689
$800$		0			0
$801$	−41.7092	−	34.9982i	−1.47372	−	1.23660i
$802$	−0.0398440	+	0.109470i	−0.00140694	+	0.00386553i
$803$	1.05796	+	2.90673i	0.0373347	+	0.102576i
$804$	−3.12836	+	2.62500i	−0.110329	+	0.0925767i
$805$		0			0
$806$	−12.3216	+	21.3416i	−0.434010	+	0.751727i
$807$	−54.9834	+	9.69506i	−1.93551	+	0.341282i
$808$	26.8113	−	4.72756i	0.943219	−	0.166315i
$809$	20.5581	−	35.6076i	0.722784	−	1.25190i	−0.237096	−	0.971486i	$-0.576196\pi$
$809$	20.5581	−	35.6076i	0.722784	−	1.25190i	0.959880	−	0.280412i	$-0.0904711\pi$
$810$		0			0
$811$	12.7836	−	10.7267i	0.448892	−	0.376665i	−0.390132	−	0.920759i	$-0.627571\pi$
$811$	12.7836	−	10.7267i	0.448892	−	0.376665i	0.839025	+	0.544093i	$0.183126\pi$
$812$	0.151003	+	0.414878i	0.00529917	+	0.0145594i
$813$	13.1907	−	36.2413i	0.462620	−	1.27104i
$814$	−11.3610	−	9.53298i	−0.398202	−	0.334131i
$815$		0			0
$816$	4.84524			0.169617
$817$	−8.39484	−	14.7907i	−0.293698	−	0.517461i
$818$		−	26.9540i		−	0.942424i
$819$	−0.821299	+	4.65782i	−0.0286985	+	0.162757i
$820$		0			0
$821$	29.4971	+	10.7361i	1.02945	+	0.374691i	0.800873	−	0.598834i	$-0.204369\pi$
$821$	29.4971	+	10.7361i	1.02945	+	0.374691i	0.228581	+	0.973525i	$0.426591\pi$
$822$	0.339373	+	0.932419i	0.0118370	+	0.0325218i
$823$	29.7777	+	35.4877i	1.03799	+	1.23702i	0.970952	+	0.239274i	$0.0769094\pi$
$823$	29.7777	+	35.4877i	1.03799	+	1.23702i	0.0670347	+	0.997751i	$0.478646\pi$
$824$	−8.10922	−	14.0456i	−0.282498	−	0.489301i
$825$		0			0
$826$	0.512326	+	2.90555i	0.0178261	+	0.101097i
$827$	40.1396	−	7.07769i	1.39579	−	0.246115i	0.575377	−	0.817888i	$-0.304855\pi$
$827$	40.1396	−	7.07769i	1.39579	−	0.246115i	0.820412	+	0.571773i	$0.193744\pi$
$828$	−2.28157	−	1.31727i	−0.0792901	−	0.0457782i
$829$	−17.7417	−	30.7295i	−0.616195	−	1.06728i	−0.990174	−	0.139843i	$-0.955340\pi$
$829$	−17.7417	−	30.7295i	−0.616195	−	1.06728i	0.373979	−	0.927437i	$-0.377993\pi$
$830$		0			0
$831$	48.0185	−	17.4773i	1.66574	−	0.606281i
$832$	−7.56774	+	20.7922i	−0.262364	+	0.720840i
$833$	2.06910	−	2.46585i	0.0716899	−	0.0854367i
$834$	−2.87211	+	16.2886i	−0.0994531	+	0.564026i
$835$		0			0
$836$	−1.16297	+	1.36543i	−0.0402222	+	0.0472245i
$837$		−	46.8735i		−	1.62019i
$838$	−33.7143	−	5.94475i	−1.16464	−	0.205358i
$839$	29.2649	+	24.5562i	1.01034	+	0.847774i	0.988383	−	0.151985i	$-0.0485667\pi$
$839$	29.2649	+	24.5562i	1.01034	+	0.847774i	0.0219545	+	0.999759i	$0.493011\pi$
$840$		0			0
$841$	−17.2208	+	6.26784i	−0.593819	+	0.216132i
$842$	3.78417	+	4.50980i	0.130411	+	0.155418i
$843$	−45.5809	+	26.3161i	−1.56989	+	0.906376i
$844$	−0.226215	+	0.391815i	−0.00778663	+	0.0134868i
$845$		0			0
$846$	9.02481	+	51.1823i	0.310280	+	1.75968i
$847$	−1.81720	−	1.04916i	−0.0624399	−	0.0360497i
$848$	8.83726	−	5.10220i	0.303473	−	0.175210i
$849$	16.9572	−	14.2288i	0.581971	−	0.488331i
$850$		0			0
$851$	12.5175	+	4.55601i	0.429096	+	0.156178i
$852$	−3.18264	+	3.79292i	−0.109035	+	0.129943i
$853$	−25.2127	−	4.44568i	−0.863266	−	0.152217i	−0.275552	−	0.961286i	$-0.588861\pi$
$853$	−25.2127	−	4.44568i	−0.863266	−	0.152217i	−0.587714	+	0.809069i	$0.699972\pi$
$854$	4.27126			0.146159
$855$		0			0
$856$	30.1257			1.02967
$857$	20.7661	+	3.66163i	0.709357	+	0.125079i	0.516674	−	0.856182i	$-0.327170\pi$
$857$	20.7661	+	3.66163i	0.709357	+	0.125079i	0.192683	+	0.981261i	$0.438281\pi$
$858$	14.2920	−	17.0326i	0.487921	−	0.581482i
$859$	−18.3871	−	6.69237i	−0.627361	−	0.228341i	0.00872148	−	0.999962i	$-0.497224\pi$
$859$	−18.3871	−	6.69237i	−0.627361	−	0.228341i	−0.636082	+	0.771621i	$0.719446\pi$
$860$		0			0
$861$	−1.89646	+	1.59132i	−0.0646312	+	0.0542320i
$862$	−44.6956	+	25.8050i	−1.52234	+	0.878922i
$863$	−4.28591	−	2.47447i	−0.145894	−	0.0842319i	0.425276	−	0.905064i	$-0.360177\pi$
$863$	−4.28591	−	2.47447i	−0.145894	−	0.0842319i	−0.571170	+	0.820832i	$0.693510\pi$
$864$	−1.19341	−	6.76817i	−0.0406007	−	0.230258i
$865$		0			0
$866$	−12.2139	+	21.1552i	−0.415047	+	0.718882i
$867$	−41.8456	+	24.1596i	−1.42115	+	0.820502i
$868$	0.293144	+	0.349356i	0.00994997	+	0.0118579i
$869$	24.7849	−	9.02098i	0.840771	−	0.306016i
$870$		0			0
$871$	15.1334	+	12.6984i	0.512776	+	0.430270i
$872$	5.28444	+	0.931790i	0.178954	+	0.0315544i
$873$			50.0164i			1.69280i
$874$	−5.52166	+	14.8300i	−0.186773	+	0.501633i
$875$		0			0
$876$	0.128356	−	0.727940i	0.00433673	−	0.0245948i
$877$	0.784120	−	0.934478i	0.0264779	−	0.0315551i	−0.752643	−	0.658429i	$-0.771221\pi$
$877$	0.784120	−	0.934478i	0.0264779	−	0.0315551i	0.779121	+	0.626874i	$0.215666\pi$
$878$	2.80656	−	7.71095i	0.0947167	−	0.260232i
$879$	28.4183	−	10.3434i	0.958527	−	0.348875i
$880$		0			0
$881$	−23.2515	−	40.2728i	−0.783363	−	1.35682i	−0.929972	−	0.367630i	$-0.880169\pi$
$881$	−23.2515	−	40.2728i	−0.783363	−	1.35682i	0.146609	−	0.989194i	$-0.453164\pi$
$882$	42.4688	+	24.5194i	1.43000	+	0.825610i
$883$	−12.7285	+	2.24438i	−0.428349	+	0.0755296i	−0.383667	−	0.923472i	$-0.625339\pi$
$883$	−12.7285	+	2.24438i	−0.428349	+	0.0755296i	−0.0446828	+	0.999001i	$0.514228\pi$
$884$	0.0386476	+	0.219182i	0.00129986	+	0.00737187i
$885$		0			0
$886$	−20.1374	−	34.8791i	−0.676531	−	1.17179i
$887$	14.9283	+	17.7909i	0.501243	+	0.597359i	0.956040	−	0.293237i	$-0.0947324\pi$
$887$	14.9283	+	17.7909i	0.501243	+	0.597359i	−0.454796	+	0.890595i	$0.650288\pi$
$888$	14.3306	+	39.3730i	0.480904	+	1.32127i
$889$	3.78699	+	1.37835i	0.127012	+	0.0462284i
$890$		0			0
$891$	−1.20661	+	6.84305i	−0.0404231	+	0.229251i
$892$		−	1.57255i		−	0.0526528i
$893$	−29.9428	+	10.6493i	−1.00200	+	0.356365i
$894$	−64.2404			−2.14852
$895$		0			0
$896$	−2.52687	−	2.12030i	−0.0844169	−	0.0708342i
$897$	−6.83045	+	18.7665i	−0.228062	+	0.626596i
$898$	−5.18398	−	14.2429i	−0.172992	−	0.475291i
$899$	−37.4484	+	31.4229i	−1.24897	+	1.04801i
$900$		0			0
$901$	0.663848	−	1.14982i	0.0221160	−	0.0383060i
$902$	7.31412	−	1.28968i	0.243534	−	0.0429416i
$903$	3.84240	−	0.677519i	0.127867	−	0.0225464i
$904$	−26.0326	+	45.0897i	−0.865830	+	1.49966i
$905$		0			0
$906$	−12.9624	+	10.8768i	−0.430648	+	0.361357i
$907$	−13.6797	−	37.5847i	−0.454228	−	1.24798i	−0.929722	−	0.368261i	$-0.879953\pi$
$907$	−13.6797	−	37.5847i	−0.454228	−	1.24798i	0.475495	−	0.879719i	$-0.342269\pi$
$908$	0.894360	−	2.45723i	0.0296804	−	0.0815462i
$909$	37.4864	+	31.4548i	1.24334	+	1.04329i
$910$		0			0
$911$	−18.7997			−0.622863			−0.311431	−	0.950269i	$-0.600808\pi$
$911$	−18.7997			−0.622863			−0.311431	+	0.950269i	$0.600808\pi$
$912$	−42.5270	+	15.1250i	−1.40821	+	0.500837i
$913$			33.0232i			1.09291i
$914$	−5.47225	+	31.0347i	−0.181006	+	1.02654i
$915$		0			0
$916$	−3.56552	−	1.29774i	−0.117808	−	0.0428787i
$917$	0.219182	+	0.602196i	0.00723801	+	0.0198863i
$918$	2.67296	+	3.18551i	0.0882208	+	0.105137i
$919$	19.9158	+	34.4952i	0.656962	+	1.13789i	0.981398	+	0.191984i	$0.0614921\pi$
$919$	19.9158	+	34.4952i	0.656962	+	1.13789i	−0.324436	+	0.945908i	$0.605175\pi$
$920$		0			0
$921$	5.84776	+	33.1643i	0.192690	+	1.09280i
$922$	48.5932	−	8.56830i	1.60033	−	0.282182i
$923$	20.7430	+	11.9760i	0.682763	+	0.394193i
$924$	−0.205737	−	0.356347i	−0.00676825	−	0.0117230i
$925$		0			0
$926$	−54.4227	+	19.8082i	−1.78844	+	0.650939i
$927$	9.97043	−	27.3935i	0.327472	−	0.899721i
$928$	−4.60722	+	5.49067i	−0.151239	+	0.180240i
$929$	−4.68051	+	26.5445i	−0.153563	+	0.870897i	0.806526	+	0.591199i	$0.201345\pi$
$929$	−4.68051	+	26.5445i	−0.153563	+	0.870897i	−0.960088	+	0.279698i	$0.909766\pi$
$930$		0			0
$931$	−10.4632	+	28.1019i	−0.342916	+	0.921002i
$932$			3.26176i			0.106843i
$933$	−45.2734	−	7.98293i	−1.48219	−	0.261349i
$934$	26.4176	+	22.1670i	0.864411	+	0.725327i
$935$		0			0
$936$	−37.6695	+	13.7106i	−1.23127	+	0.448145i
$937$	−1.68642	−	2.00980i	−0.0550930	−	0.0656573i	0.737794	−	0.675026i	$-0.235867\pi$
$937$	−1.68642	−	2.00980i	−0.0550930	−	0.0656573i	−0.792887	+	0.609368i	$0.791423\pi$
$938$	−3.11008	+	1.79561i	−0.101548	+	0.0586287i
$939$	38.3371	−	66.4018i	1.25108	−	2.16694i
$940$		0			0
$941$	−3.24194	−	18.3860i	−0.105684	−	0.599366i	−0.990945	−	0.134270i	$-0.957131\pi$
$941$	−3.24194	−	18.3860i	−0.105684	−	0.599366i	0.885260	−	0.465096i	$-0.153980\pi$
$942$	−32.3149	−	18.6570i	−1.05288	−	0.607879i
$943$	−5.77715	+	3.33544i	−0.188130	+	0.108617i
$944$	−17.3708	+	14.5758i	−0.565370	+	0.474402i
$945$		0			0
$946$	−10.9991	−	4.00335i	−0.357612	−	0.130160i
$947$	5.39917	−	6.43448i	0.175449	−	0.209092i	−0.671152	−	0.741320i	$-0.734200\pi$
$947$	5.39917	−	6.43448i	0.175449	−	0.209092i	0.846602	+	0.532227i	$0.178645\pi$
$948$	−6.20697	−	1.09446i	−0.201593	−	0.0355463i
$949$	−3.57573			−0.116073
$950$		0			0
$951$	−85.0343			−2.75742
$952$	−0.471073	−	0.0830629i	−0.0152676	−	0.00269208i
$953$	−21.6573	+	25.8102i	−0.701550	+	0.836075i	−0.992701	−	0.120602i	$-0.961517\pi$
$953$	−21.6573	+	25.8102i	−0.701550	+	0.836075i	0.291151	+	0.956677i	$0.405962\pi$
$954$	19.0069	+	6.91793i	0.615370	+	0.223976i
$955$		0			0
$956$	−0.332997	+	0.279418i	−0.0107699	+	0.00903701i
$957$	38.1978	−	22.0535i	1.23476	−	0.712888i
$958$	44.5438	+	25.7173i	1.43914	+	0.830890i
$959$	−0.0154253	−	0.0874810i	−0.000498108	−	0.00282491i
$960$		0			0
$961$	−9.74809	+	16.8842i	−0.314455	+	0.544651i
$962$	14.8470	−	8.57192i	0.478686	−	0.276370i
$963$	34.8062	+	41.4805i	1.12162	+	1.33669i
$964$	−2.39646	+	0.872240i	−0.0771848	+	0.0280930i
$965$		0			0
$966$	−2.78106	−	2.33359i	−0.0894791	−	0.0750819i
$967$	−11.5649	−	2.03920i	−0.371902	−	0.0655763i	−0.0154262	−	0.999881i	$-0.504911\pi$
$967$	−11.5649	−	2.03920i	−0.371902	−	0.0655763i	−0.356475	+	0.934305i	$0.616022\pi$
$968$		−	17.7847i		−	0.571621i
$969$	−3.80793	+	4.47086i	−0.122328	+	0.143625i
$970$		0			0
$971$	2.22432	−	12.6147i	0.0713817	−	0.404826i	−0.928091	−	0.372354i	$-0.878551\pi$
$971$	2.22432	−	12.6147i	0.0713817	−	0.404826i	0.999473	−	0.0324723i	$-0.0103381\pi$
$972$	−1.28325	+	1.52931i	−0.0411602	+	0.0490528i
$973$	0.506431	−	1.39141i	0.0162354	−	0.0446065i
$974$	−9.82934	+	3.57759i	−0.314953	+	0.114633i
$975$		0			0
$976$	16.4140	+	28.4299i	0.525399	+	0.910018i
$977$	12.5813	+	7.26382i	0.402512	+	0.232390i	0.687567	−	0.726121i	$-0.258679\pi$
$977$	12.5813	+	7.26382i	0.402512	+	0.232390i	−0.285055	+	0.958511i	$0.592012\pi$
$978$	−31.9200	+	5.62836i	−1.02069	+	0.179975i
$979$	−3.97906	−	22.5663i	−0.127171	−	0.721224i
$980$		0			0
$981$	4.82248	+	8.35278i	0.153970	+	0.266684i
$982$	−31.8029	−	37.9013i	−1.01487	−	1.20948i
$983$	12.6719	+	34.8158i	0.404172	+	1.11045i	0.960206	+	0.279293i	$0.0901002\pi$
$983$	12.6719	+	34.8158i	0.404172	+	1.11045i	−0.556034	+	0.831159i	$0.687678\pi$
$984$	−19.7173	−	7.17653i	−0.628566	−	0.228779i
$985$		0			0
$986$	0.753089	−	4.27098i	0.0239832	−	0.136016i
$987$		−	7.29086i		−	0.232071i
$988$	−1.02341	−	1.80313i	−0.0325591	−	0.0573652i
$989$	10.5134			0.334307
$990$		0			0
$991$	2.62860	+	2.20566i	0.0835004	+	0.0700651i	0.683582	−	0.729873i	$-0.260421\pi$
$991$	2.62860	+	2.20566i	0.0835004	+	0.0700651i	−0.600082	+	0.799938i	$0.704865\pi$
$992$	−2.53223	+	6.95723i	−0.0803983	+	0.220892i
$993$	27.2452	+	74.8556i	0.864600	+	2.37547i
$994$	−3.33544	+	2.79876i	−0.105794	+	0.0887714i
$995$		0			0
$996$	3.94562	−	6.83402i	0.125022	−	0.216544i
$997$	12.5819	−	2.21853i	0.398473	−	0.0702616i	0.0291792	−	0.999574i	$-0.490711\pi$
$997$	12.5819	−	2.21853i	0.398473	−	0.0702616i	0.369294	+	0.929313i	$0.379600\pi$
$998$	6.53639	−	1.15254i	0.206906	−	0.0364831i
$999$	−16.3045	+	28.2403i	−0.515852	+	0.893483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.a.74.2		12
5.2	odd	4		19.2.e.a.17.1	yes	6
5.3	odd	4		475.2.l.a.226.1		6
5.4	even	2	inner	475.2.u.a.74.1		12
15.2	even	4		171.2.u.c.55.1		6
19.9	even	9	inner	475.2.u.a.199.1		12
20.7	even	4		304.2.u.b.17.1		6
35.2	odd	12		931.2.v.b.606.1		6
35.12	even	12		931.2.v.a.606.1		6
35.17	even	12		931.2.x.b.226.1		6
35.27	even	4		931.2.w.a.834.1		6
35.32	odd	12		931.2.x.a.226.1		6
95.2	even	36		361.2.c.h.68.2		6
95.3	even	36		9025.2.a.x.1.2		3
95.7	odd	12		361.2.e.g.54.1		6
95.9	even	18	inner	475.2.u.a.199.2		12
95.12	even	12		361.2.e.a.54.1		6
95.17	odd	36		361.2.c.i.68.2		6
95.22	even	36		361.2.a.h.1.2		3
95.27	even	12		361.2.e.b.62.1		6
95.28	odd	36		475.2.l.a.351.1		6
95.32	even	36		361.2.e.b.99.1		6
95.37	even	4		361.2.e.h.245.1		6
95.42	odd	36		361.2.e.g.234.1		6
95.47	odd	36		19.2.e.a.9.1	✓	6
95.52	even	36		361.2.c.h.292.2		6
95.62	odd	36		361.2.c.i.292.2		6
95.67	even	36		361.2.e.h.28.1		6
95.72	even	36		361.2.e.a.234.1		6
95.73	odd	36		9025.2.a.bd.1.2		3
95.82	odd	36		361.2.e.f.99.1		6
95.87	odd	12		361.2.e.f.62.1		6
95.92	odd	36		361.2.a.g.1.2		3
285.47	even	36		171.2.u.c.28.1		6
285.92	even	36		3249.2.a.z.1.2		3
285.212	odd	36		3249.2.a.s.1.2		3
380.47	even	36		304.2.u.b.161.1		6
380.187	even	36		5776.2.a.br.1.3		3
380.307	odd	36		5776.2.a.bi.1.1		3
665.47	even	36		931.2.x.b.655.1		6
665.142	odd	36		931.2.x.a.655.1		6
665.237	even	36		931.2.w.a.883.1		6
665.332	even	36		931.2.v.a.275.1		6
665.522	odd	36		931.2.v.b.275.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	95.47	odd	36
19.2.e.a.17.1	yes	6	5.2	odd	4
171.2.u.c.28.1		6	285.47	even	36
171.2.u.c.55.1		6	15.2	even	4
304.2.u.b.17.1		6	20.7	even	4
304.2.u.b.161.1		6	380.47	even	36
361.2.a.g.1.2		3	95.92	odd	36
361.2.a.h.1.2		3	95.22	even	36
361.2.c.h.68.2		6	95.2	even	36
361.2.c.h.292.2		6	95.52	even	36
361.2.c.i.68.2		6	95.17	odd	36
361.2.c.i.292.2		6	95.62	odd	36
361.2.e.a.54.1		6	95.12	even	12
361.2.e.a.234.1		6	95.72	even	36
361.2.e.b.62.1		6	95.27	even	12
361.2.e.b.99.1		6	95.32	even	36
361.2.e.f.62.1		6	95.87	odd	12
361.2.e.f.99.1		6	95.82	odd	36
361.2.e.g.54.1		6	95.7	odd	12
361.2.e.g.234.1		6	95.42	odd	36
361.2.e.h.28.1		6	95.67	even	36
361.2.e.h.245.1		6	95.37	even	4
475.2.l.a.226.1		6	5.3	odd	4
475.2.l.a.351.1		6	95.28	odd	36
475.2.u.a.74.1		12	5.4	even	2	inner
475.2.u.a.74.2		12	1.1	even	1	trivial
475.2.u.a.199.1		12	19.9	even	9	inner
475.2.u.a.199.2		12	95.9	even	18	inner
931.2.v.a.275.1		6	665.332	even	36
931.2.v.a.606.1		6	35.12	even	12
931.2.v.b.275.1		6	665.522	odd	36
931.2.v.b.606.1		6	35.2	odd	12
931.2.w.a.834.1		6	35.27	even	4
931.2.w.a.883.1		6	665.237	even	36
931.2.x.a.226.1		6	35.32	odd	12
931.2.x.a.655.1		6	665.142	odd	36
931.2.x.b.226.1		6	35.17	even	12
931.2.x.b.655.1		6	665.47	even	36
3249.2.a.s.1.2		3	285.212	odd	36
3249.2.a.z.1.2		3	285.92	even	36
5776.2.a.bi.1.1		3	380.307	odd	36
5776.2.a.br.1.3		3	380.187	even	36
9025.2.a.x.1.2		3	95.3	even	36
9025.2.a.bd.1.2		3	95.73	odd	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32683 + 0.233956i) q^{2} +(1.85083 - 2.20574i) q^{3} +(-0.173648 - 0.0632028i) q^{4} +(2.97178 - 2.49362i) q^{6} +(-0.300767 + 0.173648i) q^{7} +(-2.54920 - 1.47178i) q^{8} +(-0.918748 - 5.21048i) q^{9} +O(q^{10})\)	\(q+(1.32683 + 0.233956i) q^{2} +(1.85083 - 2.20574i) q^{3} +(-0.173648 - 0.0632028i) q^{4} +(2.97178 - 2.49362i) q^{6} +(-0.300767 + 0.173648i) q^{7} +(-2.54920 - 1.47178i) q^{8} +(-0.918748 - 5.21048i) q^{9} +(1.11334 - 1.92836i) q^{11} +(-0.460802 + 0.266044i) q^{12} +(1.65452 + 1.97178i) q^{13} +(-0.439693 + 0.160035i) q^{14} +(-2.75490 - 2.31164i) q^{16} +(-0.460802 - 0.0812519i) q^{17} -7.12836i q^{18} +(4.29813 - 0.725293i) q^{19} +(-0.173648 + 0.984808i) q^{21} +(1.92836 - 2.29813i) q^{22} +(-0.921605 + 2.53209i) q^{23} +(-7.96451 + 2.89884i) q^{24} +(1.73396 + 3.00330i) q^{26} +(-5.71253 - 3.29813i) q^{27} +(0.0632028 - 0.0111444i) q^{28} +(1.19459 + 6.77487i) q^{29} +(3.55303 + 6.15403i) q^{31} +(0.669713 + 0.798133i) q^{32} +(-2.19285 - 6.02481i) q^{33} +(-0.592396 - 0.215615i) q^{34} +(-0.169778 + 0.962858i) q^{36} -4.94356i q^{37} +(5.87257 + 0.0432332i) q^{38} +7.41147 q^{39} +(1.89646 + 1.59132i) q^{41} +(-0.460802 + 1.26604i) q^{42} +(-1.33445 - 3.66637i) q^{43} +(-0.315207 + 0.264490i) q^{44} +(-1.81521 + 3.14403i) q^{46} +(-7.18009 + 1.26604i) q^{47} +(-10.1977 + 1.79813i) q^{48} +(-3.43969 + 5.95772i) q^{49} +(-1.03209 + 0.866025i) q^{51} +(-0.162683 - 0.446967i) q^{52} +(-0.970481 + 2.66637i) q^{53} +(-6.80793 - 5.71253i) q^{54} +1.02229 q^{56} +(6.35532 - 10.8229i) q^{57} +9.26857i q^{58} +(1.09492 - 6.20961i) q^{59} +(-8.57785 - 3.12208i) q^{61} +(3.27449 + 8.99660i) q^{62} +(1.18112 + 1.40760i) q^{63} +(4.29813 + 7.44459i) q^{64} +(-1.50000 - 8.50692i) q^{66} +(7.55839 - 1.33275i) q^{67} +(0.0748822 + 0.0432332i) q^{68} +(3.87939 + 6.71929i) q^{69} +(8.74422 - 3.18264i) q^{71} +(-5.32661 + 14.6348i) q^{72} +(-0.892951 + 1.06418i) q^{73} +(1.15657 - 6.55926i) q^{74} +(-0.792204 - 0.145708i) q^{76} +0.773318i q^{77} +(9.83375 + 1.73396i) q^{78} +(9.07398 + 7.61397i) q^{79} +(-2.93242 + 1.06731i) q^{81} +(2.14398 + 2.55509i) q^{82} +(-12.8438 + 7.41534i) q^{83} +(0.0923963 - 0.160035i) q^{84} +(-0.912818 - 5.17685i) q^{86} +(17.1546 + 9.90420i) q^{87} +(-5.67626 + 3.27719i) q^{88} +(7.88326 - 6.61484i) q^{89} +(-0.840022 - 0.305743i) q^{91} +(0.320070 - 0.381445i) q^{92} +(20.1503 + 3.55303i) q^{93} -9.82295 q^{94} +3.00000 q^{96} +(-9.30975 - 1.64156i) q^{97} +(-5.95772 + 7.10014i) q^{98} +(-11.0706 - 4.02936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^6 - 6 * q^9	\( 12 q + 6 q^{6} - 6 q^{9} + 6 q^{14} - 36 q^{16} + 24 q^{19} - 30 q^{24} + 30 q^{26} + 6 q^{29} + 18 q^{31} - 48 q^{36} + 48 q^{39} + 42 q^{41} - 18 q^{44} - 36 q^{46} - 30 q^{49} + 6 q^{51} - 60 q^{54} - 12 q^{56} - 24 q^{59} - 24 q^{61} + 24 q^{64} - 18 q^{66} + 24 q^{69} - 12 q^{71} - 30 q^{74} + 72 q^{76} + 78 q^{79} + 12 q^{81} - 6 q^{84} + 48 q^{86} + 24 q^{89} + 30 q^{91} - 36 q^{94} + 36 q^{96} - 18 q^{99}+O(q^{100}) \) 12 * q + 6 * q^6 - 6 * q^9 + 6 * q^14 - 36 * q^16 + 24 * q^19 - 30 * q^24 + 30 * q^26 + 6 * q^29 + 18 * q^31 - 48 * q^36 + 48 * q^39 + 42 * q^41 - 18 * q^44 - 36 * q^46 - 30 * q^49 + 6 * q^51 - 60 * q^54 - 12 * q^56 - 24 * q^59 - 24 * q^61 + 24 * q^64 - 18 * q^66 + 24 * q^69 - 12 * q^71 - 30 * q^74 + 72 * q^76 + 78 * q^79 + 12 * q^81 - 6 * q^84 + 48 * q^86 + 24 * q^89 + 30 * q^91 - 36 * q^94 + 36 * q^96 - 18 * q^99

Introduction

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