LMFDB - Embedded newform 475.2.u.a.199.1

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			199.1
Root			$-0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	475.199
Dual form			475.2.u.a.74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32683 + 0.233956i) q^{2} +(-1.85083 - 2.20574i) q^{3} +(-0.173648 + 0.0632028i) q^{4} +(2.97178 + 2.49362i) q^{6} +(0.300767 + 0.173648i) q^{7} +(2.54920 - 1.47178i) q^{8} +(-0.918748 + 5.21048i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$

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	$-0.713593\pi$
$2$	−1.32683	+	0.233956i	−0.938209	+	0.165432i	−0.316423	+	0.948618i	$0.602482\pi$
$3$	−1.85083	−	2.20574i	−1.06858	−	1.27348i	−0.960182	−	0.279375i	$-0.909873\pi$
$3$	−1.85083	−	2.20574i	−1.06858	−	1.27348i	−0.108397	−	0.994108i	$-0.534572\pi$
$4$	−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	$-0.312427\pi$
$7$	0.300767	+	0.173648i	0.113679	+	0.0656328i	−0.442082	+	0.896975i	$0.645760\pi$
$8$	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	0.983616	−	0.180276i	$-0.0576989\pi$
$11$	1.11334	+	1.92836i	0.335685	+	0.581423i	−0.647931	+	0.761699i	$0.724366\pi$
$12$	0.460802	+	0.266044i	0.133022	+	0.0768004i
$13$	−1.65452	+	1.97178i	−0.458882	+	0.546874i	−0.945022	−	0.327007i	$-0.893960\pi$
$13$	−1.65452	+	1.97178i	−0.458882	+	0.546874i	0.486140	+	0.873881i	$0.338404\pi$
$14$	−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	$-0.537484\pi$
$17$	0.460802	−	0.0812519i	0.111761	−	0.0197065i	0.229249	+	0.973368i	$0.426373\pi$
$18$		−	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	$-0.0204680\pi$
$23$	0.921605	+	2.53209i	0.192168	+	0.527977i	−0.805765	+	0.592235i	$0.798246\pi$
$24$	−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	−0.646822	−	0.762641i	$-0.723903\pi$
$29$	1.19459	−	6.77487i	0.221830	−	1.25806i	0.868653	−	0.495421i	$-0.164986\pi$
$30$		0			0
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	−0.347696	−	0.937607i	$-0.613036\pi$
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	0.985840	−	0.167690i	$-0.0536307\pi$
$32$	−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	−0.482574	−	0.875855i	$-0.660298\pi$
$41$	1.89646	−	1.59132i	0.296177	−	0.248522i	0.778751	+	0.627333i	$0.215854\pi$
$42$	0.460802	+	1.26604i	0.0711034	+	0.195355i
$43$	1.33445	−	3.66637i	0.203502	−	0.559117i	−0.795394	−	0.606093i	$-0.792736\pi$
$43$	1.33445	−	3.66637i	0.203502	−	0.559117i	0.998896	+	0.0469757i	$0.0149583\pi$
$44$	−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	$-0.265983\pi$
$47$	7.18009	+	1.26604i	1.04732	+	0.184672i	0.376598	+	0.926377i	$0.377094\pi$
$48$	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	$-0.0486794\pi$
$53$	0.970481	+	2.66637i	0.133306	+	0.366255i	−0.855023	+	0.518590i	$0.826457\pi$
$54$	−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	0.969304	+	0.245864i	$0.0790718\pi$
$59$	1.09492	+	6.20961i	0.142547	+	0.808423i	−0.826757	+	0.562559i	$0.809817\pi$
$60$		0			0
$61$	−8.57785	+	3.12208i	−1.09828	+	0.399742i	−0.826682	−	0.562669i	$-0.809775\pi$
$61$	−8.57785	+	3.12208i	−1.09828	+	0.399742i	−0.271599	+	0.962411i	$0.587552\pi$
$62$	−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	$-0.599767\pi$
$67$	−7.55839	−	1.33275i	−0.923405	−	0.162821i	−0.615084	+	0.788461i	$0.710878\pi$
$68$	−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	0.804026	−	0.594594i	$-0.202687\pi$
$71$	8.74422	+	3.18264i	1.03775	+	0.377709i	0.233722	+	0.972303i	$0.424909\pi$
$72$	5.32661	+	14.6348i	0.627748	+	1.72472i
$73$	0.892951	+	1.06418i	0.104512	+	0.124553i	0.815765	−	0.578384i	$-0.196316\pi$
$73$	0.892951	+	1.06418i	0.104512	+	0.124553i	−0.711253	+	0.702936i	$0.751872\pi$
$74$	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	0.0311616	−	0.999514i	$-0.490079\pi$
$79$	9.07398	−	7.61397i	1.02090	−	0.856639i	0.989741	+	0.142876i	$0.0456349\pi$
$80$		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	$-0.0306519\pi$
$83$	12.8438	+	7.41534i	1.40979	+	0.813940i	0.414418	+	0.910087i	$0.363985\pi$
$84$	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	0.956575	−	0.291487i	$-0.0941501\pi$
$89$	7.88326	+	6.61484i	0.835623	+	0.701171i	−0.120951	+	0.992658i	$0.538594\pi$
$90$		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	$-0.396221\pi$
$97$	9.30975	−	1.64156i	0.945261	−	0.166675i	0.624974	+	0.780645i	$0.285109\pi$
$98$	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	0.218194	−	0.975905i	$-0.429983\pi$
$101$	−7.08512	−	5.94512i	−0.704996	−	0.591562i	−0.923190	+	0.384343i	$0.874428\pi$
$102$	1.57202	+	0.907604i	0.155653	+	0.0898662i
$103$	−4.77163	+	2.75490i	−0.470162	+	0.271448i	−0.716308	−	0.697785i	$-0.754169\pi$
$103$	−4.77163	+	2.75490i	−0.470162	+	0.271448i	0.246145	+	0.969233i	$0.420836\pi$
$104$	−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	$-0.168611\pi$
$107$	8.86327	+	5.11721i	0.856845	+	0.494699i	−0.00610974	+	0.999981i	$0.501945\pi$
$108$	−0.783520	+	0.933763i	−0.0753943	+	0.0898514i
$109$	−1.71301	−	0.623485i	−0.164077	−	0.0597190i	0.258676	−	0.965964i	$-0.416714\pi$
$109$	−1.71301	−	0.623485i	−0.164077	−	0.0597190i	−0.422753	+	0.906245i	$0.638936\pi$
$110$		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	$-0.605627\pi$
$127$	7.45891	−	8.88919i	0.661871	−	0.788788i	0.987653	+	0.156657i	$0.0500719\pi$
$128$	−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	0.995601	−	0.0936982i	$-0.0298689\pi$
$131$	0.320422	+	1.81720i	0.0279954	+	0.158770i	−0.967605	+	0.252468i	$0.918758\pi$
$132$			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	$-0.107633\pi$
$137$	0.0874810	+	0.240352i	0.00747401	+	0.0205347i	−0.935900	+	0.352267i	$0.885411\pi$
$138$	−3.57526	+	9.82295i	−0.304346	+	0.836185i
$139$	−3.26604	−	2.74054i	−0.277022	−	0.232449i	0.493682	−	0.869643i	$-0.335651\pi$
$139$	−3.26604	−	2.74054i	−0.277022	−	0.232449i	−0.770704	+	0.637193i	$0.780095\pi$
$140$		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	−0.991919	−	0.126874i	$-0.959506\pi$
$149$	−12.6853	+	10.6442i	−1.03922	+	0.872007i	−0.0472981	+	0.998881i	$0.515061\pi$
$150$		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	−0.736444	−	0.676499i	$-0.763496\pi$
$157$	3.28974	−	9.03849i	0.262550	−	0.721350i	0.998994	−	0.0448510i	$-0.0142813\pi$
$158$	−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	$-0.560559\pi$
$163$	7.23567	−	4.17752i	0.566742	−	0.327209i	0.755847	+	0.654748i	$0.227225\pi$
$164$	−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	$-0.0612118\pi$
$167$	1.38008	+	3.79174i	0.106794	+	0.293413i	−0.874773	+	0.484533i	$0.838990\pi$
$168$	−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	$-0.277922\pi$
$173$	19.8378	−	3.49794i	1.50824	−	0.265943i	0.865799	+	0.500391i	$0.166811\pi$
$174$	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	0.566652	−	0.823957i	$-0.308238\pi$
$179$	−5.75624	−	9.97011i	−0.430242	−	0.745201i	−0.996894	+	0.0787564i	$0.974905\pi$
$180$		0			0
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	−0.878829	−	0.477136i	$-0.841675\pi$
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	0.989020	−	0.147784i	$-0.0472141\pi$
$182$	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	$-0.218812\pi$
$193$	0.191336	+	0.228026i	0.0137727	+	0.0164137i	−0.759114	+	0.650958i	$0.774368\pi$
$194$	−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	$-0.178260\pi$
$197$	11.3806	+	6.57057i	0.810832	+	0.468134i	−0.0364128	+	0.999337i	$0.511593\pi$
$198$	13.7461	−	7.93629i	0.976890	−	0.564008i
$199$	0.0445774	−	0.252811i	0.00316001	−	0.0179213i	−0.983187	−	0.182602i	$-0.941548\pi$
$199$	0.0445774	−	0.252811i	0.00316001	−	0.0179213i	0.986347	+	0.164680i	$0.0526593\pi$
$200$		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	0.995938	−	0.0900364i	$-0.0286983\pi$
$211$	0.425145	+	2.41112i	0.0292682	+	0.165988i	−0.966670	+	0.256024i	$0.917587\pi$
$212$	−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	$-0.980859\pi$
$223$	−2.91052	+	7.99660i	−0.194903	+	0.535492i	0.803289	+	0.595589i	$0.203081\pi$
$224$	−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	−0.568959	−	0.822366i	$-0.692654\pi$
$233$	6.03698	−	16.5865i	0.395496	−	1.08662i	0.964454	−	0.264249i	$-0.0851242\pi$
$234$	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	0.901556	−	0.432663i	$-0.142426\pi$
$239$	1.17617	+	2.03719i	0.0760804	+	0.131775i	−0.825475	+	0.564438i	$0.809093\pi$
$240$		0			0
$241$	10.5719	+	8.87089i	0.680997	+	0.571424i	0.916298	−	0.400498i	$-0.131163\pi$
$241$	10.5719	+	8.87089i	0.680997	+	0.571424i	−0.235300	+	0.971923i	$0.575607\pi$
$242$	−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	−0.215528	−	0.976498i	$-0.569147\pi$
$251$	3.91400	−	1.42458i	0.247050	−	0.0899187i	0.462577	+	0.886579i	$0.346925\pi$
$252$	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	$-0.451069\pi$
$257$	−0.657115	−	0.115867i	−0.0409897	−	0.00722759i	−0.194105	+	0.980981i	$0.562180\pi$
$258$	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	$-0.107906\pi$
$263$	7.32753	+	8.73261i	0.451835	+	0.538476i	−0.491254	+	0.871016i	$0.663461\pi$
$264$	−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	−0.971286	−	0.237916i	$-0.923536\pi$
$269$	−14.8537	+	12.4637i	−0.905646	+	0.759927i	0.0656400	+	0.997843i	$0.479091\pi$
$270$		0			0
$271$	12.5865	+	4.58110i	0.764573	+	0.278282i	0.694725	−	0.719276i	$-0.255526\pi$
$271$	12.5865	+	4.58110i	0.764573	+	0.278282i	0.0698486	+	0.997558i	$0.477748\pi$
$272$	−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	$-0.845660\pi$
$277$	−15.3693	+	8.87346i	−0.923450	+	0.533154i	−0.0387161	+	0.999250i	$0.512327\pi$
$278$	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	−0.799050	−	0.601265i	$-0.794664\pi$
$281$	−17.1766	+	6.25179i	−1.02467	+	0.372950i	−0.225622	+	0.974215i	$0.572442\pi$
$282$	18.1806	+	21.6668i	1.08264	+	1.29024i
$283$	−7.57099	+	1.33497i	−0.450049	+	0.0793557i	−0.394079	−	0.919077i	$-0.628936\pi$
$283$	−7.57099	+	1.33497i	−0.450049	+	0.0793557i	−0.0559700	+	0.998432i	$0.517825\pi$
$284$	−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	$-0.765924\pi$
$293$	−9.09586	+	5.25150i	−0.531386	+	0.306796i	0.210195	+	0.977660i	$0.432590\pi$
$294$	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	$-0.113908\pi$
$307$	7.51774	+	8.95929i	0.429060	+	0.511334i	−0.507591	+	0.861598i	$0.669464\pi$
$308$	−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	−0.998551	−	0.0538151i	$-0.982862\pi$
$311$	−7.98293	+	13.8268i	−0.452670	+	0.784048i	0.545881	+	0.837863i	$0.316195\pi$
$312$	18.8933	−	10.9081i	1.06962	−	0.617548i
$313$	−26.2241	−	4.62402i	−1.48227	−	0.261365i	−0.626788	−	0.779190i	$-0.715631\pi$
$313$	−26.2241	−	4.62402i	−1.48227	−	0.261365i	−0.855487	+	0.517825i	$0.826742\pi$
$314$	−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	0.105073	−	0.994465i	$-0.466492\pi$
$317$	18.9829	−	22.6229i	1.06618	−	1.27063i	0.961111	−	0.276164i	$-0.0890632\pi$
$318$	−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	−0.942687	−	0.333677i	$-0.891710\pi$
$331$	−13.8327	−	23.9590i	−0.760317	−	1.31691i	0.182371	−	0.983230i	$-0.441623\pi$
$332$	−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	0.654648	+	0.755934i	$0.272817\pi$
$337$	−6.10841	+	16.7827i	−0.332746	+	0.914212i	−0.987394	+	0.158279i	$0.949406\pi$
$338$	−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	$-0.839126\pi$
$347$	1.98394	−	5.45084i	0.106504	−	0.292616i	0.981485	+	0.191541i	$0.0613485\pi$
$348$	2.35289	−	2.80406i	0.126128	−	0.150314i
$349$	2.68614	−	4.65253i	0.143786	−	0.249044i	−0.785134	−	0.619326i	$-0.787406\pi$
$349$	2.68614	−	4.65253i	0.143786	−	0.249044i	0.928919	+	0.370282i	$0.120739\pi$
$350$		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	$-0.901036\pi$
$353$	−21.8537	+	12.6172i	−1.16315	+	0.671546i	−0.211095	+	0.977466i	$0.567703\pi$
$354$	−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	−0.999996	−	0.00285518i	$-0.999091\pi$
$359$	−1.16116	−	6.58526i	−0.0612837	−	0.347557i	0.938712	−	0.344702i	$-0.112020\pi$
$360$		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	$-0.709812\pi$
$367$	5.21870	−	6.21941i	0.272414	−	0.324650i	0.884856	+	0.465865i	$0.154257\pi$
$368$	−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	−0.996755	−	0.0804968i	$-0.974349\pi$
$373$	−30.2222	−	17.4488i	−1.56484	−	0.903463i	−0.568090	−	0.822967i	$-0.692317\pi$
$374$	−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	$-0.198317\pi$
$383$	1.88771	+	2.24969i	0.0964575	+	0.114954i	−0.715656	+	0.698453i	$0.753872\pi$
$384$	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	−0.662344	−	0.749199i	$-0.730438\pi$
$389$	4.26604	−	24.1939i	0.216297	−	1.22668i	0.878642	−	0.477482i	$-0.158450\pi$
$390$		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	$-0.850137\pi$
$397$	−31.3521	+	5.52822i	−1.57352	+	0.277453i	−0.682314	+	0.731059i	$0.739026\pi$
$398$			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	0.984431	−	0.175774i	$-0.0562428\pi$
$401$	−0.0150147	−	0.0851529i	−0.000749801	−	0.00425233i	−0.985180	+	0.171522i	$0.945132\pi$
$402$	−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	0.770019	+	0.638021i	$0.220247\pi$
$409$	−3.47400	+	19.7021i	−0.171778	+	0.974204i	−0.941797	+	0.336182i	$0.890864\pi$
$410$		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	−0.557565	−	0.830134i	$-0.688264\pi$
$421$	3.34730	−	2.80872i	0.163137	−	0.136888i	0.720702	+	0.693245i	$0.243820\pi$
$422$	−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	−0.954732	−	0.297468i	$-0.903858\pi$
$431$	−29.3444	−	24.6228i	−1.41347	−	1.18604i	−0.458736	−	0.888572i	$-0.651698\pi$
$432$	−8.11338	+	22.2913i	−0.390355	+	1.07249i
$433$	6.20118	+	17.0376i	0.298010	+	0.818775i	0.994832	+	0.101532i	$0.0323743\pi$
$433$	6.20118	+	17.0376i	0.298010	+	0.818775i	−0.696823	+	0.717244i	$0.745403\pi$
$434$	−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	0.999589	−	0.0286685i	$-0.00912670\pi$
$439$	1.05762	+	5.99806i	0.0504774	+	0.286272i	−0.949112	+	0.314940i	$0.898016\pi$
$440$		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	−0.0828833	−	0.996559i	$-0.526413\pi$
$443$	19.2149	−	22.8995i	0.912928	−	1.08799i	0.995812	−	0.0914266i	$-0.0291427\pi$
$444$	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	−0.967683	−	0.252168i	$-0.918856\pi$
$449$	−5.62495	+	9.74270i	−0.265458	+	0.459787i	0.702226	+	0.711955i	$0.252190\pi$
$450$		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	0.980011	−	0.198945i	$-0.0637514\pi$
$461$	34.4149	+	12.5260i	1.60286	+	0.583395i	0.622853	+	0.782339i	$0.285974\pi$
$462$	−1.92836	+	2.29813i	−0.0897156	+	0.106919i
$463$	37.2273	+	21.4932i	1.73010	+	0.998873i	0.888777	+	0.458340i	$0.151556\pi$
$463$	37.2273	+	21.4932i	1.73010	+	0.998873i	0.841322	+	0.540534i	$0.181778\pi$
$464$	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	$-0.868418\pi$
$467$	−22.1670	+	12.7981i	−1.02577	+	0.592227i	−0.109998	+	0.993932i	$0.535084\pi$
$468$	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	0.652236	−	0.758016i	$-0.273831\pi$
$479$	35.8739	−	13.0570i	1.63912	−	0.596591i	0.986885	+	0.161424i	$0.0516088\pi$
$480$		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	$-0.277048\pi$
$487$	6.72367	+	3.88191i	0.304678	+	0.175906i	−0.339864	+	0.940475i	$0.610381\pi$
$488$	−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	−0.274954	+	0.961457i	$0.588663\pi$
$491$	−28.1313	+	23.6050i	−1.26955	+	1.06528i	−0.994596	+	0.103822i	$0.966893\pi$
$492$	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	0.443551	−	0.896249i	$-0.353719\pi$
$499$	4.62923	+	1.68490i	0.207233	+	0.0754266i	−0.236318	+	0.971676i	$0.575941\pi$
$500$		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	$-0.181827\pi$
$503$	32.4490	+	5.72163i	1.44683	+	0.255115i	0.605589	+	0.795778i	$0.292938\pi$
$504$	−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	−0.965657	−	0.259819i	$-0.916337\pi$
$509$	−34.7075	+	12.6325i	−1.53839	+	0.559926i	−0.572728	+	0.819746i	$0.694115\pi$
$510$		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	0.746126	−	0.665804i	$-0.231912\pi$
$521$	−4.64590	−	8.04693i	−0.203540	−	0.352542i	−0.949667	+	0.313262i	$0.898578\pi$
$522$	−48.2937	−	8.51548i	−2.11376	−	0.372713i
$523$	−27.9834	−	4.93423i	−1.22363	−	0.215759i	−0.475742	−	0.879585i	$-0.657820\pi$
$523$	−27.9834	−	4.93423i	−1.22363	−	0.215759i	−0.747887	+	0.663826i	$0.768932\pi$
$524$	−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	−0.876372	−	0.481635i	$-0.840043\pi$
$541$	2.60220	−	14.7578i	0.111877	−	0.634487i	0.988249	−	0.152852i	$-0.0488458\pi$
$542$	−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	$-0.137593\pi$
$547$	−1.32948	−	3.65270i	−0.0568443	−	0.156178i	−0.964864	+	0.262748i	$0.915371\pi$
$548$	−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	$-0.687528\pi$
$557$	8.48762	−	10.1152i	0.359632	−	0.428593i	0.915276	+	0.402828i	$0.131973\pi$
$558$	−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	$-0.405815\pi$
$563$	−9.27752	−	5.35638i	−0.391001	−	0.225745i	−0.682594	+	0.730798i	$0.739148\pi$
$564$	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	$-0.403839\pi$
$577$	−9.14036	−	5.27719i	−0.380518	−	0.219692i	−0.678044	+	0.735022i	$0.737172\pi$
$578$	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	$-0.684915\pi$
$587$	−18.8638	+	3.32619i	−0.778591	+	0.137287i	−0.229791	+	0.973240i	$0.573804\pi$
$588$		−	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	$-0.0539795\pi$
$593$	2.97373	+	8.17024i	0.122116	+	0.335512i	−0.863539	+	0.504282i	$0.831757\pi$
$594$	−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	0.830008	+	0.557752i	$0.188336\pi$
$599$	−3.44373	+	19.5303i	−0.140707	+	0.797988i	−0.970715	+	0.240236i	$0.922775\pi$
$600$		0			0
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	−0.283718	−	0.958908i	$-0.591568\pi$
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	0.972298	−	0.233747i	$-0.0750986\pi$
$602$	−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	−0.744546	−	0.667571i	$-0.767334\pi$
$613$	6.31142	−	17.3405i	0.254916	−	0.700376i	0.999462	−	0.0328044i	$-0.0104439\pi$
$614$	−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	$-0.189356\pi$
$617$	35.1433	+	6.19671i	1.41482	+	0.249470i	0.586598	+	0.809878i	$0.300467\pi$
$618$	−21.0499	−	3.71167i	−0.846752	−	0.149305i
$619$	1.82976	+	3.16923i	0.0735441	+	0.127382i	0.900452	−	0.434955i	$-0.143236\pi$
$619$	1.82976	+	3.16923i	0.0735441	+	0.127382i	−0.826908	+	0.562337i	$0.809902\pi$
$620$		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	−0.327129	−	0.944980i	$-0.606081\pi$
$631$	0.745977	−	0.271514i	0.0296969	−	0.0108088i	0.356826	+	0.934171i	$0.383859\pi$
$632$	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	−0.266723	−	0.963773i	$-0.585941\pi$
$641$	−27.6104	−	10.0494i	−1.09055	−	0.396926i	−0.823823	+	0.566847i	$0.808163\pi$
$642$	13.5793	+	37.3089i	0.535933	+	1.47246i
$643$	14.2788	+	17.0168i	0.563101	+	0.671078i	0.970200	−	0.242306i	$-0.0779039\pi$
$643$	14.2788	+	17.0168i	0.563101	+	0.671078i	−0.407098	+	0.913384i	$0.633459\pi$
$644$	−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	$-0.510502\pi$
$653$	−23.3827	−	13.5000i	−0.915035	−	0.528296i	−0.882048	+	0.471160i	$0.843835\pi$
$654$	−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	0.120415	−	0.992724i	$-0.461577\pi$
$659$	−21.4691	−	18.0147i	−0.836317	−	0.701753i	−0.956732	+	0.290970i	$0.906022\pi$
$660$		0			0
$661$	−10.6823	+	3.88803i	−0.415492	+	0.151227i	−0.541303	−	0.840827i	$-0.682069\pi$
$661$	−10.6823	+	3.88803i	−0.415492	+	0.151227i	0.125811	+	0.992054i	$0.459847\pi$
$662$	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	$-0.770117\pi$
$673$	−14.3476	+	8.28359i	−0.553059	+	0.319309i	0.197296	+	0.980344i	$0.436784\pi$
$674$	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	$-0.388971\pi$
$677$	−7.83721	−	4.52481i	−0.301208	−	0.173903i	−0.642986	+	0.765878i	$0.722305\pi$
$678$	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	0.320099	+	0.947384i	$0.396284\pi$
$691$	−17.3601	+	30.0686i	−0.660409	+	1.14386i	−0.980508	+	0.196478i	$0.937050\pi$
$692$	−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	0.786905	+	0.617074i	$0.211682\pi$
$701$	6.84436	+	38.8163i	0.258508	+	1.46607i	−0.528397	+	0.848997i	$0.677207\pi$
$702$		−	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	0.999954	+	0.00959399i	$0.00305391\pi$
$709$	31.5009	+	26.4324i	1.18304	+	0.992690i	0.183088	+	0.983096i	$0.441391\pi$
$710$		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	0.211943	−	0.977282i	$-0.432021\pi$
$719$	32.4768	−	27.2513i	1.21118	−	1.01630i	0.999238	−	0.0390200i	$-0.0124236\pi$
$720$		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	−0.0578805	+	0.998324i	$0.518434\pi$
$727$	−17.6675	+	48.5411i	−0.655251	+	1.80029i	−0.597371	+	0.801965i	$0.703788\pi$
$728$	−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	$-0.805765\pi$
$733$	−19.8460	+	11.4581i	−0.733030	+	0.423215i	0.0864997	+	0.996252i	$0.472432\pi$
$734$	−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	−0.932619	−	0.360862i	$-0.882483\pi$
$739$	−4.88413	−	27.6993i	−0.179666	−	1.01894i	0.752954	−	0.658074i	$-0.228628\pi$
$740$		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	$-0.591438\pi$
$743$	−6.03931	+	1.06489i	−0.221561	+	0.0390671i	0.0617657	+	0.998091i	$0.480327\pi$
$744$	−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	−0.961707	−	0.274081i	$-0.911626\pi$
$751$	0.979522	−	5.55515i	0.0357433	−	0.202710i	0.997450	+	0.0713710i	$0.0227374\pi$
$752$	−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	$-0.314271\pi$
$757$	−10.0866	−	12.0207i	−0.366602	−	0.436900i	−0.917538	+	0.397648i	$0.869827\pi$
$758$	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	0.829327	+	0.558764i	$0.188724\pi$
$769$	−3.91266	+	22.1898i	−0.141094	+	0.800184i	−0.970421	+	0.241420i	$0.922387\pi$
$770$		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	$-0.620100\pi$
$773$	16.9902	−	20.2481i	0.611094	−	0.728273i	0.979512	+	0.201387i	$0.0645449\pi$
$774$	−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	$-0.577232\pi$
$787$	13.4733	−	7.77884i	0.480273	−	0.277286i	0.720530	+	0.693424i	$0.243899\pi$
$788$	−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	0.959880	+	0.280412i	$0.0904711\pi$
$809$	20.5581	+	35.6076i	0.722784	+	1.25190i	−0.237096	+	0.971486i	$0.576196\pi$
$810$		0			0
$811$	12.7836	+	10.7267i	0.448892	+	0.376665i	0.839025	−	0.544093i	$-0.183126\pi$
$811$	12.7836	+	10.7267i	0.448892	+	0.376665i	−0.390132	+	0.920759i	$0.627571\pi$
$812$	−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	0.228581	−	0.973525i	$-0.426591\pi$
$821$	29.4971	−	10.7361i	1.02945	−	0.374691i	0.800873	+	0.598834i	$0.204369\pi$
$822$	−0.339373	+	0.932419i	−0.0118370	+	0.0325218i
$823$	−29.7777	+	35.4877i	−1.03799	+	1.23702i	−0.0670347	+	0.997751i	$0.521354\pi$
$823$	−29.7777	+	35.4877i	−1.03799	+	1.23702i	−0.970952	+	0.239274i	$0.923091\pi$
$824$	−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	$-0.695145\pi$
$827$	−40.1396	−	7.07769i	−1.39579	−	0.246115i	−0.820412	+	0.571773i	$0.806256\pi$
$828$	2.28157	−	1.31727i	0.0792901	−	0.0457782i
$829$	−17.7417	+	30.7295i	−0.616195	+	1.06728i	0.373979	+	0.927437i	$0.377993\pi$
$829$	−17.7417	+	30.7295i	−0.616195	+	1.06728i	−0.990174	+	0.139843i	$0.955340\pi$
$830$		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	0.0219545	−	0.999759i	$-0.493011\pi$
$839$	29.2649	−	24.5562i	1.01034	−	0.847774i	0.988383	+	0.151985i	$0.0485667\pi$
$840$		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	$-0.411139\pi$
$853$	25.2127	−	4.44568i	0.863266	−	0.152217i	0.587714	+	0.809069i	$0.300028\pi$
$854$	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	$-0.672830\pi$
$857$	−20.7661	+	3.66163i	−0.709357	+	0.125079i	−0.192683	+	0.981261i	$0.561719\pi$
$858$	−14.2920	−	17.0326i	−0.487921	−	0.581482i
$859$	−18.3871	+	6.69237i	−0.627361	+	0.228341i	−0.636082	−	0.771621i	$-0.719446\pi$
$859$	−18.3871	+	6.69237i	−0.627361	+	0.228341i	0.00872148	+	0.999962i	$0.497224\pi$
$860$		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	$-0.639823\pi$
$863$	4.28591	−	2.47447i	0.145894	−	0.0842319i	0.571170	+	0.820832i	$0.306490\pi$
$864$	−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	$-0.228779\pi$
$877$	−0.784120	−	0.934478i	−0.0264779	−	0.0315551i	−0.779121	+	0.626874i	$0.784334\pi$
$878$	−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	0.146609	+	0.989194i	$0.453164\pi$
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	−0.929972	+	0.367630i	$0.880169\pi$
$882$	−42.4688	+	24.5194i	−1.43000	+	0.825610i
$883$	12.7285	+	2.24438i	0.428349	+	0.0755296i	0.383667	−	0.923472i	$-0.374661\pi$
$883$	12.7285	+	2.24438i	0.428349	+	0.0755296i	0.0446828	+	0.999001i	$0.485772\pi$
$884$	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	$-0.905268\pi$
$887$	−14.9283	+	17.7909i	−0.501243	+	0.597359i	0.454796	+	0.890595i	$0.349712\pi$
$888$	−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	−0.475495	−	0.879719i	$-0.657731\pi$
$907$	13.6797	−	37.5847i	0.454228	−	1.24798i	0.929722	−	0.368261i	$-0.120047\pi$
$908$	−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	−0.324436	−	0.945908i	$-0.605175\pi$
$919$	19.9158	−	34.4952i	0.656962	−	1.13789i	0.981398	−	0.191984i	$-0.0614921\pi$
$920$		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	−0.960088	−	0.279698i	$-0.909766\pi$
$929$	−4.68051	−	26.5445i	−0.153563	−	0.870897i	0.806526	−	0.591199i	$-0.201345\pi$
$930$		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	$-0.764133\pi$
$937$	1.68642	−	2.00980i	0.0550930	−	0.0656573i	0.792887	+	0.609368i	$0.208577\pi$
$938$	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	0.885260	+	0.465096i	$0.153980\pi$
$941$	−3.24194	+	18.3860i	−0.105684	+	0.599366i	−0.990945	+	0.134270i	$0.957131\pi$
$942$	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	$-0.265800\pi$
$947$	−5.39917	−	6.43448i	−0.175449	−	0.209092i	−0.846602	+	0.532227i	$0.821355\pi$
$948$	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	$-0.0384826\pi$
$953$	21.6573	+	25.8102i	0.701550	+	0.836075i	−0.291151	+	0.956677i	$0.594038\pi$
$954$	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	$-0.495089\pi$
$967$	11.5649	−	2.03920i	0.371902	−	0.0655763i	0.356475	+	0.934305i	$0.383978\pi$
$968$		−	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	0.999473	+	0.0324723i	$0.0103381\pi$
$971$	2.22432	+	12.6147i	0.0713817	+	0.404826i	−0.928091	+	0.372354i	$0.878551\pi$
$972$	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	$-0.741321\pi$
$977$	−12.5813	+	7.26382i	−0.402512	+	0.232390i	0.285055	+	0.958511i	$0.407988\pi$
$978$	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	0.556034	+	0.831159i	$0.312322\pi$
$983$	−12.6719	+	34.8158i	−0.404172	+	1.11045i	−0.960206	+	0.279293i	$0.909900\pi$
$984$	−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	−0.600082	−	0.799938i	$-0.704865\pi$
$991$	2.62860	−	2.20566i	0.0835004	−	0.0700651i	0.683582	+	0.729873i	$0.260421\pi$
$992$	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	$-0.509289\pi$
$997$	−12.5819	−	2.21853i	−0.398473	−	0.0702616i	−0.369294	+	0.929313i	$0.620400\pi$
$998$	−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.199.1		12
5.2	odd	4		19.2.e.a.9.1	✓	6
5.3	odd	4		475.2.l.a.351.1		6
5.4	even	2	inner	475.2.u.a.199.2		12
15.2	even	4		171.2.u.c.28.1		6
19.17	even	9	inner	475.2.u.a.74.2		12
20.7	even	4		304.2.u.b.161.1		6
35.2	odd	12		931.2.x.a.655.1		6
35.12	even	12		931.2.x.b.655.1		6
35.17	even	12		931.2.v.a.275.1		6
35.27	even	4		931.2.w.a.883.1		6
35.32	odd	12		931.2.v.b.275.1		6
95.2	even	36		361.2.e.h.245.1		6
95.7	odd	12		361.2.e.f.99.1		6
95.12	even	12		361.2.e.b.99.1		6
95.13	even	36		9025.2.a.x.1.2		3
95.17	odd	36		19.2.e.a.17.1	yes	6
95.22	even	36		361.2.e.b.62.1		6
95.27	even	12		361.2.e.a.234.1		6
95.32	even	36		361.2.a.h.1.2		3
95.37	even	4		361.2.e.h.28.1		6
95.42	odd	36		361.2.c.i.68.2		6
95.47	odd	36		361.2.c.i.292.2		6
95.52	even	36		361.2.e.a.54.1		6
95.62	odd	36		361.2.e.g.54.1		6
95.63	odd	36		9025.2.a.bd.1.2		3
95.67	even	36		361.2.c.h.292.2		6
95.72	even	36		361.2.c.h.68.2		6
95.74	even	18	inner	475.2.u.a.74.1		12
95.82	odd	36		361.2.a.g.1.2		3
95.87	odd	12		361.2.e.g.234.1		6
95.92	odd	36		361.2.e.f.62.1		6
95.93	odd	36		475.2.l.a.226.1		6
285.17	even	36		171.2.u.c.55.1		6
285.32	odd	36		3249.2.a.s.1.2		3
285.272	even	36		3249.2.a.z.1.2		3
380.127	odd	36		5776.2.a.bi.1.1		3
380.207	even	36		304.2.u.b.17.1		6
380.367	even	36		5776.2.a.br.1.3		3
665.17	even	36		931.2.x.b.226.1		6
665.207	odd	36		931.2.x.a.226.1		6
665.397	even	36		931.2.v.a.606.1		6
665.492	odd	36		931.2.v.b.606.1		6
665.587	even	36		931.2.w.a.834.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	5.2	odd	4
19.2.e.a.17.1	yes	6	95.17	odd	36
171.2.u.c.28.1		6	15.2	even	4
171.2.u.c.55.1		6	285.17	even	36
304.2.u.b.17.1		6	380.207	even	36
304.2.u.b.161.1		6	20.7	even	4
361.2.a.g.1.2		3	95.82	odd	36
361.2.a.h.1.2		3	95.32	even	36
361.2.c.h.68.2		6	95.72	even	36
361.2.c.h.292.2		6	95.67	even	36
361.2.c.i.68.2		6	95.42	odd	36
361.2.c.i.292.2		6	95.47	odd	36
361.2.e.a.54.1		6	95.52	even	36
361.2.e.a.234.1		6	95.27	even	12
361.2.e.b.62.1		6	95.22	even	36
361.2.e.b.99.1		6	95.12	even	12
361.2.e.f.62.1		6	95.92	odd	36
361.2.e.f.99.1		6	95.7	odd	12
361.2.e.g.54.1		6	95.62	odd	36
361.2.e.g.234.1		6	95.87	odd	12
361.2.e.h.28.1		6	95.37	even	4
361.2.e.h.245.1		6	95.2	even	36
475.2.l.a.226.1		6	95.93	odd	36
475.2.l.a.351.1		6	5.3	odd	4
475.2.u.a.74.1		12	95.74	even	18	inner
475.2.u.a.74.2		12	19.17	even	9	inner
475.2.u.a.199.1		12	1.1	even	1	trivial
475.2.u.a.199.2		12	5.4	even	2	inner
931.2.v.a.275.1		6	35.17	even	12
931.2.v.a.606.1		6	665.397	even	36
931.2.v.b.275.1		6	35.32	odd	12
931.2.v.b.606.1		6	665.492	odd	36
931.2.w.a.834.1		6	665.587	even	36
931.2.w.a.883.1		6	35.27	even	4
931.2.x.a.226.1		6	665.207	odd	36
931.2.x.a.655.1		6	35.2	odd	12
931.2.x.b.226.1		6	665.17	even	36
931.2.x.b.655.1		6	35.12	even	12
3249.2.a.s.1.2		3	285.32	odd	36
3249.2.a.z.1.2		3	285.272	even	36
5776.2.a.bi.1.1		3	380.127	odd	36
5776.2.a.br.1.3		3	380.367	even	36
9025.2.a.x.1.2		3	95.13	even	36
9025.2.a.bd.1.2		3	95.63	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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