LMFDB - Embedded newform 460.2.w.a.167.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			167.48
Character	$\chi$	$=$	460.167
Dual form			460.2.w.a.303.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.863411 - 1.12005i) q^{2} +(0.941428 + 1.72410i) q^{3} +(-0.509042 - 1.93413i) q^{4} +(2.16292 - 0.567244i) q^{5} +(2.74392 + 0.434154i) q^{6} +(-2.47259 - 3.30299i) q^{7} +(-2.60585 - 1.09980i) q^{8} +(-0.464299 + 0.722463i) q^{9} +O(q^{10})$	\(q+(0.863411 - 1.12005i) q^{2} +(0.941428 + 1.72410i) q^{3} +(-0.509042 - 1.93413i) q^{4} +(2.16292 - 0.567244i) q^{5} +(2.74392 + 0.434154i) q^{6} +(-2.47259 - 3.30299i) q^{7} +(-2.60585 - 1.09980i) q^{8} +(-0.464299 + 0.722463i) q^{9} +(1.23215 - 2.91235i) q^{10} +(3.31258 - 1.51280i) q^{11} +(2.85541 - 2.69848i) q^{12} +(0.335508 + 0.251158i) q^{13} +(-5.83440 - 0.0824079i) q^{14} +(3.01422 + 3.19507i) q^{15} +(-3.48175 + 1.96911i) q^{16} +(-4.20183 + 0.300521i) q^{17} +(0.408317 + 1.14382i) q^{18} +(3.04773 + 3.51726i) q^{19} +(-2.19814 - 3.89463i) q^{20} +(3.36692 - 7.37252i) q^{21} +(1.16570 - 5.01644i) q^{22} +(-2.92890 + 3.79757i) q^{23} +(-0.557057 - 5.52811i) q^{24} +(4.35647 - 2.45381i) q^{25} +(0.570992 - 0.158934i) q^{26} +(4.19543 + 0.300063i) q^{27} +(-5.12978 + 6.46369i) q^{28} +(5.59741 + 4.85019i) q^{29} +(6.18116 - 0.617430i) q^{30} +(1.18309 + 4.02924i) q^{31} +(-0.800675 + 5.59990i) q^{32} +(5.72677 + 4.28701i) q^{33} +(-3.29131 + 4.96575i) q^{34} +(-7.22163 - 5.74156i) q^{35} +(1.63369 + 0.530252i) q^{36} +(-1.87055 - 8.59878i) q^{37} +(6.57096 - 0.376772i) q^{38} +(-0.117164 + 0.814895i) q^{39} +(-6.26010 - 0.900630i) q^{40} +(-9.38159 + 6.02918i) q^{41} +(-5.35058 - 10.1366i) q^{42} +(3.26619 + 5.98157i) q^{43} +(-4.61221 - 5.63689i) q^{44} +(-0.594430 + 1.82600i) q^{45} +(1.72463 + 6.55939i) q^{46} +(3.73612 - 3.73612i) q^{47} +(-6.67275 - 4.14910i) q^{48} +(-2.82394 + 9.61746i) q^{49} +(1.01303 - 6.99813i) q^{50} +(-4.47385 - 6.96145i) q^{51} +(0.314986 - 0.776767i) q^{52} +(-2.77472 - 3.70660i) q^{53} +(3.95847 - 4.44003i) q^{54} +(6.30672 - 5.15112i) q^{55} +(2.81056 + 11.3265i) q^{56} +(-3.19489 + 8.56582i) q^{57} +(10.2653 - 2.08170i) q^{58} +(-0.0867511 - 0.603367i) q^{59} +(4.64533 - 7.45633i) q^{60} +(-2.36173 + 0.693466i) q^{61} +(5.53447 + 2.15377i) q^{62} +(3.53431 - 0.252779i) q^{63} +(5.58088 + 5.73182i) q^{64} +(0.868145 + 0.352921i) q^{65} +(9.74624 - 2.71284i) q^{66} +(2.09288 + 5.61123i) q^{67} +(2.72016 + 7.97393i) q^{68} +(-9.30472 - 1.47458i) q^{69} +(-12.6661 + 3.13128i) q^{70} +(-13.5311 - 6.17945i) q^{71} +(2.00446 - 1.37199i) q^{72} +(-10.2317 - 0.731789i) q^{73} +(-11.2462 - 5.32917i) q^{74} +(8.33190 + 5.20089i) q^{75} +(5.25144 - 7.68514i) q^{76} +(-13.1874 - 7.20089i) q^{77} +(0.811565 + 0.834820i) q^{78} +(-0.730992 - 5.08416i) q^{79} +(-6.41380 + 6.23404i) q^{80} +(4.50262 + 9.85937i) q^{81} +(-1.34716 + 15.7136i) q^{82} +(-0.133320 - 0.612861i) q^{83} +(-15.9733 - 2.75915i) q^{84} +(-8.91777 + 3.03347i) q^{85} +(9.51975 + 1.50625i) q^{86} +(-3.09263 + 14.2166i) q^{87} +(-10.2959 + 0.298964i) q^{88} +(-1.94420 + 6.62135i) q^{89} +(1.53198 + 2.24238i) q^{90} -1.72919i q^{91} +(8.83594 + 3.73177i) q^{92} +(-5.83301 + 5.83301i) q^{93} +(-0.958846 - 7.41045i) q^{94} +(8.58714 + 5.87876i) q^{95} +(-10.4085 + 3.89146i) q^{96} +(9.61122 + 2.09079i) q^{97} +(8.33385 + 11.4668i) q^{98} +(-0.445081 + 3.09561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	0.863411	−	1.12005i	0.610524	−	0.791998i
$2$	0.863411	−	1.12005i	0.610524	−	0.791998i
$3$	0.941428	+	1.72410i	0.543534	+	0.995407i	0.994685	+	0.102960i	$0.0328314\pi$
$3$	0.941428	+	1.72410i	0.543534	+	0.995407i	−0.451152	+	0.892447i	$0.648987\pi$
$4$	−0.509042	−	1.93413i	−0.254521	−	0.967067i
$5$	2.16292	−	0.567244i	0.967288	−	0.253679i
$5$	2.16292	−	0.567244i	0.967288	−	0.253679i
$6$	2.74392	+	0.434154i	1.12020	+	0.177243i
$7$	−2.47259	−	3.30299i	−0.934552	−	1.24841i	−0.968506	−	0.248991i	$-0.919901\pi$
$7$	−2.47259	−	3.30299i	−0.934552	−	1.24841i	0.0339541	−	0.999423i	$-0.489190\pi$
$8$	−2.60585	−	1.09980i	−0.921306	−	0.388838i
$9$	−0.464299	+	0.722463i	−0.154766	+	0.240821i
$10$	1.23215	−	2.91235i	0.389639	−	0.920967i
$11$	3.31258	−	1.51280i	0.998780	−	0.456128i	0.152178	−	0.988353i	$-0.451371\pi$
$11$	3.31258	−	1.51280i	0.998780	−	0.456128i	0.846603	+	0.532225i	$0.178644\pi$
$12$	2.85541	−	2.69848i	0.824285	−	0.778985i
$13$	0.335508	+	0.251158i	0.0930531	+	0.0696587i	0.644791	−	0.764359i	$-0.276944\pi$
$13$	0.335508	+	0.251158i	0.0930531	+	0.0696587i	−0.551738	+	0.834017i	$0.686035\pi$
$14$	−5.83440	−	0.0824079i	−1.55931	−	0.0220244i
$15$	3.01422	+	3.19507i	0.778268	+	0.824963i
$16$	−3.48175	+	1.96911i	−0.870438	+	0.492278i
$17$	−4.20183	+	0.300521i	−1.01909	+	0.0728871i	−0.570875	−	0.821037i	$-0.693396\pi$
$17$	−4.20183	+	0.300521i	−1.01909	+	0.0728871i	−0.448219	+	0.893924i	$0.647942\pi$
$18$	0.408317	+	1.14382i	0.0962412	+	0.269602i
$19$	3.04773	+	3.51726i	0.699196	+	0.806915i	0.988644	−	0.150279i	$-0.0480170\pi$
$19$	3.04773	+	3.51726i	0.699196	+	0.806915i	−0.289448	+	0.957194i	$0.593472\pi$
$20$	−2.19814	−	3.89463i	−0.491520	−	0.870866i
$21$	3.36692	−	7.37252i	0.734721	−	1.60881i
$22$	1.16570	−	5.01644i	0.248527	−	1.06951i
$23$	−2.92890	+	3.79757i	−0.610719	+	0.791848i
$23$	−2.92890	+	3.79757i	−0.610719	+	0.791848i
$24$	−0.557057	−	5.52811i	−0.113709	−	1.12842i
$25$	4.35647	−	2.45381i	0.871294	−	0.490762i
$26$	0.570992	−	0.158934i	0.111981	−	0.0311696i
$27$	4.19543	+	0.300063i	0.807411	+	0.0577472i
$28$	−5.12978	+	6.46369i	−0.969438	+	1.22152i
$29$	5.59741	+	4.85019i	1.03941	+	0.900657i	0.995151	−	0.0983627i	$-0.0313605\pi$
$29$	5.59741	+	4.85019i	1.03941	+	0.900657i	0.0442632	+	0.999020i	$0.485906\pi$
$30$	6.18116	−	0.617430i	1.12852	−	0.112727i
$31$	1.18309	+	4.02924i	0.212490	+	0.723674i	0.994896	+	0.100905i	$0.0321739\pi$
$31$	1.18309	+	4.02924i	0.212490	+	0.723674i	−0.782406	+	0.622768i	$0.786008\pi$
$32$	−0.800675	+	5.59990i	−0.141541	+	0.989932i
$33$	5.72677	+	4.28701i	0.996904	+	0.746273i
$34$	−3.29131	+	4.96575i	−0.564455	+	0.851620i
$35$	−7.22163	−	5.74156i	−1.22068	−	0.970501i
$36$	1.63369	+	0.530252i	0.272281	+	0.0883754i
$37$	−1.87055	−	8.59878i	−0.307517	−	1.41363i	−0.828464	−	0.560042i	$-0.810785\pi$
$37$	−1.87055	−	8.59878i	−0.307517	−	1.41363i	0.520947	−	0.853589i	$-0.325579\pi$
$38$	6.57096	−	0.376772i	1.06595	−	0.0611206i
$39$	−0.117164	+	0.814895i	−0.0187613	+	0.130488i
$40$	−6.26010	−	0.900630i	−0.989809	−	0.142402i
$41$	−9.38159	+	6.02918i	−1.46516	+	0.941600i	−0.466798	+	0.884364i	$0.654592\pi$
$41$	−9.38159	+	6.02918i	−1.46516	+	0.941600i	−0.998361	+	0.0572361i	$0.981771\pi$
$42$	−5.35058	−	10.1366i	−0.825613	−	1.56412i
$43$	3.26619	+	5.98157i	0.498089	+	0.912181i	0.998912	+	0.0466319i	$0.0148488\pi$
$43$	3.26619	+	5.98157i	0.498089	+	0.912181i	−0.500823	+	0.865549i	$0.666969\pi$
$44$	−4.61221	−	5.63689i	−0.695317	−	0.849794i
$45$	−0.594430	+	1.82600i	−0.0886123	+	0.272204i
$46$	1.72463	+	6.55939i	0.254283	+	0.967130i
$47$	3.73612	−	3.73612i	0.544968	−	0.544968i	−0.380013	−	0.924981i	$-0.624080\pi$
$47$	3.73612	−	3.73612i	0.544968	−	0.544968i	0.924981	+	0.380013i	$0.124080\pi$
$48$	−6.67275	−	4.14910i	−0.963129	−	0.598871i
$49$	−2.82394	+	9.61746i	−0.403420	+	1.37392i
$50$	1.01303	−	6.99813i	0.143263	−	0.989685i
$51$	−4.47385	−	6.96145i	−0.626464	−	0.974798i
$52$	0.314986	−	0.776767i	0.0436807	−	0.107718i
$53$	−2.77472	−	3.70660i	−0.381138	−	0.509140i	0.568418	−	0.822740i	$-0.307556\pi$
$53$	−2.77472	−	3.70660i	−0.381138	−	0.509140i	−0.949555	+	0.313600i	$0.898465\pi$
$54$	3.95847	−	4.44003i	0.538679	−	0.604211i
$55$	6.30672	−	5.15112i	0.850399	−	0.694577i
$56$	2.81056	+	11.3265i	0.375577	+	1.51356i
$57$	−3.19489	+	8.56582i	−0.423173	+	1.13457i
$58$	10.2653	−	2.08170i	1.34791	−	0.273341i
$59$	−0.0867511	−	0.603367i	−0.0112940	−	0.0785517i	0.983395	−	0.181479i	$-0.0580883\pi$
$59$	−0.0867511	−	0.603367i	−0.0112940	−	0.0785517i	−0.994689	+	0.102927i	$0.967179\pi$
$60$	4.64533	−	7.45633i	0.599709	−	0.962608i
$61$	−2.36173	+	0.693466i	−0.302388	+	0.0887892i	−0.429407	−	0.903111i	$-0.641277\pi$
$61$	−2.36173	+	0.693466i	−0.302388	+	0.0887892i	0.127019	+	0.991900i	$0.459459\pi$
$62$	5.53447	+	2.15377i	0.702878	+	0.273529i
$63$	3.53431	−	0.252779i	0.445282	−	0.0318472i
$64$	5.58088	+	5.73182i	0.697610	+	0.716477i
$65$	0.868145	+	0.352921i	0.107680	+	0.0437744i
$66$	9.74624	−	2.71284i	1.19968	−	0.333928i
$67$	2.09288	+	5.61123i	0.255686	+	0.685521i	0.999847	+	0.0175201i	$0.00557709\pi$
$67$	2.09288	+	5.61123i	0.255686	+	0.685521i	−0.744160	+	0.668001i	$0.767150\pi$
$68$	2.72016	+	7.97393i	0.329868	+	0.966982i
$69$	−9.30472	−	1.47458i	−1.12016	−	0.177518i
$70$	−12.6661	+	3.13128i	−1.51389	+	0.374260i
$71$	−13.5311	−	6.17945i	−1.60585	−	0.733366i	−0.607697	−	0.794169i	$-0.707907\pi$
$71$	−13.5311	−	6.17945i	−1.60585	−	0.733366i	−0.998150	+	0.0608028i	$0.980634\pi$
$72$	2.00446	−	1.37199i	0.236227	−	0.161691i
$73$	−10.2317	−	0.731789i	−1.19753	−	0.0856494i	−0.541712	−	0.840564i	$-0.682224\pi$
$73$	−10.2317	−	0.731789i	−1.19753	−	0.0856494i	−0.655823	+	0.754915i	$0.727678\pi$
$74$	−11.2462	−	5.32917i	−1.30734	−	0.619503i
$75$	8.33190	+	5.20089i	0.962085	+	0.600547i
$76$	5.25144	−	7.68514i	0.602381	−	0.881546i
$77$	−13.1874	−	7.20089i	−1.50285	−	0.820617i
$78$	0.811565	+	0.834820i	0.0918917	+	0.0945247i
$79$	−0.730992	−	5.08416i	−0.0822430	−	0.572013i	−0.988722	−	0.149762i	$-0.952149\pi$
$79$	−0.730992	−	5.08416i	−0.0822430	−	0.572013i	0.906479	−	0.422251i	$-0.138760\pi$
$80$	−6.41380	+	6.23404i	−0.717084	+	0.696987i
$81$	4.50262	+	9.85937i	0.500291	+	1.09549i
$82$	−1.34716	+	15.7136i	−0.148769	+	1.73527i
$83$	−0.133320	−	0.612861i	−0.0146337	−	0.0672702i	0.969251	−	0.246074i	$-0.0791408\pi$
$83$	−0.133320	−	0.612861i	−0.0146337	−	0.0672702i	−0.983885	+	0.178804i	$0.942777\pi$
$84$	−15.9733	−	2.75915i	−1.74283	−	0.301048i
$85$	−8.91777	+	3.03347i	−0.967268	+	0.329026i
$86$	9.51975	+	1.50625i	1.02654	+	0.162423i
$87$	−3.09263	+	14.2166i	−0.331565	+	1.52418i
$88$	−10.2959	+	0.298964i	−1.09754	+	0.0318697i
$89$	−1.94420	+	6.62135i	−0.206085	+	0.701862i	0.789972	+	0.613144i	$0.210095\pi$
$89$	−1.94420	+	6.62135i	−0.206085	+	0.701862i	−0.996057	+	0.0887183i	$0.971723\pi$
$90$	1.53198	+	2.24238i	0.161485	+	0.236368i
$91$		−	1.72919i		−	0.181269i
$92$	8.83594	+	3.73177i	0.921211	+	0.389064i
$93$	−5.83301	+	5.83301i	−0.604855	+	0.604855i
$94$	−0.958846	−	7.41045i	−0.0988975	−	0.764330i
$95$	8.58714	+	5.87876i	0.881022	+	0.603148i
$96$	−10.4085	+	3.89146i	−1.06232	+	0.397171i
$97$	9.61122	+	2.09079i	0.975871	+	0.212288i	0.672103	−	0.740458i	$-0.265391\pi$
$97$	9.61122	+	2.09079i	0.975871	+	0.212288i	0.303769	+	0.952746i	$0.401755\pi$
$98$	8.33385	+	11.4668i	0.841846	+	1.15832i
$99$	−0.445081	+	3.09561i	−0.0447324	+	0.311120i
$100$	−6.96362	−	7.17690i	−0.696362	−	0.717690i
$101$	16.7078	+	10.7375i	1.66249	+	1.06842i	0.914395	+	0.404823i	$0.132667\pi$
$101$	16.7078	+	10.7375i	1.66249	+	1.06842i	0.748094	+	0.663593i	$0.230969\pi$
$102$	−11.6600	−	0.999638i	−1.15451	−	0.0989790i
$103$	2.03306	−	5.45085i	0.200324	−	0.537088i	−0.797479	−	0.603347i	$-0.793834\pi$
$103$	2.03306	−	5.45085i	0.200324	−	0.537088i	0.997802	+	0.0662586i	$0.0211062\pi$
$104$	−0.598059	−	1.02347i	−0.0586445	−	0.100360i
$105$	3.10036	−	17.8560i	0.302564	−	1.74257i
$106$	−6.54732	−	0.0924775i	−0.635932	−	0.00898221i
$107$	−0.607469	+	1.11250i	−0.0587262	+	0.107549i	−0.905393	−	0.424574i	$-0.860424\pi$
$107$	−0.607469	+	1.11250i	−0.0587262	+	0.107549i	0.846667	+	0.532123i	$0.178606\pi$
$108$	−1.55529	−	8.26727i	−0.149657	−	0.795518i
$109$	−2.76730	−	2.39788i	−0.265059	−	0.229675i	0.512183	−	0.858876i	$-0.328837\pi$
$109$	−2.76730	−	2.39788i	−0.265059	−	0.229675i	−0.777243	+	0.629201i	$0.783382\pi$
$110$	−0.324235	−	11.5114i	−0.0309146	−	1.09757i
$111$	13.0641	−	11.3201i	1.23999	−	1.07446i
$112$	15.1129	+	6.63141i	1.42804	+	0.626609i
$113$	0.427518	+	1.14622i	0.0402175	+	0.107827i	0.955506	−	0.294971i	$-0.0953102\pi$
$113$	0.427518	+	1.14622i	0.0402175	+	0.107827i	−0.915289	+	0.402799i	$0.868037\pi$
$114$	6.83568	+	10.9743i	0.640220	+	1.02783i
$115$	−4.18085	+	9.87525i	−0.389866	+	0.920872i
$116$	6.53160	−	13.2951i	0.606444	−	1.23442i
$117$	−0.337228	+	0.125780i	−0.0311768	+	0.0116283i
$118$	−0.750706	−	0.423788i	−0.0691080	−	0.0390129i
$119$	11.3820	+	13.1356i	1.04339	+	1.20414i
$120$	−4.34066	−	11.6409i	−0.396246	−	1.06266i
$121$	1.48114	−	1.70933i	0.134649	−	0.155393i
$122$	−1.26242	+	3.24401i	−0.114294	+	0.293699i
$123$	−19.2270	−	10.4987i	−1.73364	−	0.946638i
$124$	7.19086	−	4.33931i	0.645758	−	0.389682i
$125$	8.03080	−	7.77858i	0.718296	−	0.695737i
$126$	2.76844	−	4.17687i	0.246632	−	0.372105i
$127$	−9.62146	−	3.58862i	−0.853767	−	0.318438i	−0.115797	−	0.993273i	$-0.536942\pi$
$127$	−9.62146	−	3.58862i	−0.853767	−	0.318438i	−0.737969	+	0.674834i	$0.764215\pi$
$128$	11.2385	−	1.30197i	0.993356	−	0.115079i
$129$	−7.23793	+	11.2624i	−0.637264	+	0.991602i
$130$	1.14486	−	0.667654i	0.100411	−	0.0585571i
$131$	13.7597	+	1.97834i	1.20219	+	0.172849i	0.714163	−	0.699980i	$-0.246808\pi$
$131$	13.7597	+	1.97834i	1.20219	+	0.172849i	0.488027	+	0.872829i	$0.337717\pi$
$132$	5.37649	−	13.2586i	0.467963	−	1.15401i
$133$	4.08172	−	18.7634i	0.353930	−	1.62699i
$134$	8.09190	+	2.50066i	0.699034	+	0.216024i
$135$	9.24460	−	1.73082i	0.795648	−	0.148965i
$136$	11.2799	+	3.83806i	0.967239	+	0.329111i
$137$	−5.20509	−	5.20509i	−0.444701	−	0.444701i	0.448887	−	0.893588i	$-0.351820\pi$
$137$	−5.20509	−	5.20509i	−0.444701	−	0.444701i	−0.893588	+	0.448887i	$0.851820\pi$
$138$	−9.68541	+	9.14863i	−0.824477	+	0.778783i
$139$	−3.62888			−0.307797			−0.153899	−	0.988087i	$-0.549183\pi$
$139$	−3.62888			−0.307797			−0.153899	+	0.988087i	$0.549183\pi$
$140$	−7.42884	+	16.8903i	−0.627852	+	1.42749i
$141$	9.95870	+	2.92414i	0.838674	+	0.246257i
$142$	−18.6042	+	9.82016i	−1.56123	+	0.824090i
$143$	1.49135	+	0.324423i	0.124713	+	0.0271296i
$144$	0.193964	−	3.42969i	0.0161637	−	0.285808i
$145$	14.8580	+	7.31548i	1.23389	+	0.607518i
$146$	−9.65384	+	10.8283i	−0.798958	+	0.896154i
$147$	−19.2400	+	4.18540i	−1.58689	+	0.345206i
$148$	−15.6790	+	7.99503i	−1.28881	+	0.657188i
$149$	14.5535	−	6.64636i	1.19227	−	0.544491i	0.282363	−	0.959307i	$-0.408882\pi$
$149$	14.5535	−	6.64636i	1.19227	−	0.544491i	0.909905	+	0.414817i	$0.136154\pi$
$150$	13.0191	−	4.84168i	1.06301	−	0.395321i
$151$	−9.43892	+	1.35711i	−0.768129	+	0.110440i	−0.515229	−	0.857052i	$-0.672293\pi$
$151$	−9.43892	+	1.35711i	−0.768129	+	0.110440i	−0.252899	+	0.967493i	$0.581384\pi$
$152$	−4.07362	−	12.5173i	−0.330415	−	1.01529i
$153$	1.73379	−	3.17520i	0.140169	−	0.256700i
$154$	−19.4516	+	8.55332i	−1.56745	+	0.689246i
$155$	4.84450	+	8.04384i	0.389120	+	0.646097i
$156$	1.63576	−	0.188204i	0.130965	−	0.0150684i
$157$	0.695256	−	9.72095i	0.0554875	−	0.775816i	−0.891189	−	0.453632i	$-0.850128\pi$
$157$	0.695256	−	9.72095i	0.0554875	−	0.775816i	0.946677	−	0.322185i	$-0.104417\pi$
$158$	−6.32568	−	3.57097i	−0.503244	−	0.284091i
$159$	3.77833	−	8.27338i	0.299641	−	0.656122i
$160$	1.44471	+	12.5663i	0.114215	+	0.993456i
$161$	19.7853	+	0.284323i	1.55930	+	0.0224078i
$162$	14.9306	+	3.46951i	1.17306	+	0.272590i
$163$	−11.2442	+	4.19388i	−0.880715	+	0.328490i	−0.748820	−	0.662774i	$-0.769379\pi$
$163$	−11.2442	+	4.19388i	−0.880715	+	0.328490i	−0.131896	+	0.991264i	$0.542106\pi$
$164$	16.4369	+	15.0762i	1.28350	+	1.17725i
$165$	14.8184	+	6.02399i	1.15361	+	0.468967i
$166$	−0.801547	−	0.379826i	−0.0622121	−	0.0294802i
$167$	0.367773	+	5.14214i	0.0284591	+	0.397910i	0.991638	+	0.129050i	$0.0411926\pi$
$167$	0.367773	+	5.14214i	0.0284591	+	0.397910i	−0.963179	+	0.268861i	$0.913353\pi$
$168$	−16.8820	+	15.5087i	−1.30247	+	1.19652i
$169$	−3.61304	−	12.3049i	−0.277926	−	0.946529i
$170$	−4.30206	+	12.6075i	−0.329953	+	0.966953i
$171$	−3.95615	+	0.568808i	−0.302534	+	0.0434978i
$172$	9.90654	−	9.36211i	0.755367	−	0.713854i
$173$	0.520239	+	0.194039i	0.0395530	+	0.0147525i	0.369163	−	0.929365i	$-0.379644\pi$
$173$	0.520239	+	0.194039i	0.0395530	+	0.0147525i	−0.329610	+	0.944117i	$0.606917\pi$
$174$	13.2531	+	15.7387i	1.00472	+	1.19315i
$175$	−18.8767	−	8.32213i	−1.42694	−	0.629094i
$176$	−8.55471	+	11.7900i	−0.644835	+	0.888708i
$177$	0.958593	−	0.717594i	0.0720523	−	0.0539376i
$178$	5.73762	+	7.89456i	0.430053	+	0.591723i
$179$	4.80915	−	3.09065i	0.359453	−	0.231006i	−0.348432	−	0.937334i	$-0.613286\pi$
$179$	4.80915	−	3.09065i	0.359453	−	0.231006i	0.707885	+	0.706328i	$0.249650\pi$
$180$	3.83432	+	0.220195i	0.285794	+	0.0164124i
$181$	−8.10400	−	2.37955i	−0.602366	−	0.176871i	−0.0336900	−	0.999432i	$-0.510726\pi$
$181$	−8.10400	−	2.37955i	−0.602366	−	0.176871i	−0.568676	+	0.822562i	$0.692544\pi$
$182$	−1.93679	−	1.49300i	−0.143564	−	0.110669i
$183$	−3.41900	−	3.41900i	−0.252740	−	0.252740i
$184$	11.8088	−	6.67468i	0.870559	−	0.492064i
$185$	−8.92346	−	17.5374i	−0.656066	−	1.28938i
$186$	1.49700	+	11.5696i	0.109765	+	0.848322i
$187$	−13.4643	+	7.35205i	−0.984606	+	0.537635i
$188$	−9.12799	−	5.32431i	−0.665727	−	0.388315i
$189$	−9.38247	−	14.5994i	−0.682475	−	1.06195i
$190$	13.9988	−	4.54227i	1.01558	−	0.329531i
$191$	3.77186	+	0.542312i	0.272922	+	0.0392403i	0.277417	−	0.960750i	$-0.410522\pi$
$191$	3.77186	+	0.542312i	0.272922	+	0.0392403i	−0.00449480	+	0.999990i	$0.501431\pi$
$192$	−4.62821	+	15.0181i	−0.334012	+	1.08384i
$193$	−1.47404	+	0.320657i	−0.106104	+	0.0230814i	−0.265304	−	0.964165i	$-0.585472\pi$
$193$	−1.47404	+	0.320657i	−0.106104	+	0.0230814i	0.159200	+	0.987246i	$0.449109\pi$
$194$	10.6402	−	8.95987i	0.763924	−	0.643281i
$195$	0.208827	+	1.82901i	0.0149544	+	0.130978i
$196$	20.0390	+	0.566193i	1.43135	+	0.0404424i
$197$	−13.1348	+	17.5460i	−0.935814	+	1.25010i	0.0322707	+	0.999479i	$0.489726\pi$
$197$	−13.1348	+	17.5460i	−0.935814	+	1.25010i	−0.968085	+	0.250622i	$0.919365\pi$
$198$	3.08296	+	3.17130i	0.219097	+	0.225374i
$199$	14.6220	−	4.29339i	1.03652	−	0.304351i	0.281162	−	0.959660i	$-0.409280\pi$
$199$	14.6220	−	4.29339i	1.03652	−	0.304351i	0.755360	+	0.655310i	$0.227462\pi$
$200$	−14.0510	+	1.60301i	−0.993555	+	0.113350i
$201$	−7.70401	+	8.89090i	−0.543399	+	0.627116i
$202$	26.4522	−	9.44280i	1.86117	−	0.664393i
$203$	2.18003	−	30.4808i	0.153008	−	2.13933i
$204$	−11.1870	+	12.1967i	−0.783247	+	0.853939i
$205$	−16.8716	+	18.3623i	−1.17837	+	1.28248i
$206$	−4.34988	−	6.98346i	−0.303070	−	0.486561i
$207$	−1.38372	−	3.87923i	−0.0961749	−	0.269625i
$208$	−1.66271	−	0.213818i	−0.115288	−	0.0148256i
$209$	15.4168	+	7.04060i	1.06640	+	0.487008i
$210$	−17.3228	−	18.8897i	−1.19539	−	1.30351i
$211$	−0.432572	+	0.374826i	−0.0297795	+	0.0258041i	−0.669623	−	0.742701i	$-0.733544\pi$
$211$	−0.432572	+	0.374826i	−0.0297795	+	0.0258041i	0.639844	+	0.768505i	$0.278999\pi$
$212$	−5.75661	+	7.25350i	−0.395365	+	0.498173i
$213$	−2.08459	−	29.1464i	−0.142834	−	1.99708i
$214$	0.721560	+	1.64094i	0.0493248	+	0.112172i
$215$	10.4575	+	11.0850i	0.713197	+	0.755988i
$216$	−10.6026	−	5.39605i	−0.721418	−	0.367155i
$217$	10.3833	−	13.8704i	0.704862	−	0.941586i
$218$	−5.07507	+	1.02917i	−0.343727	+	0.0697041i
$219$	−8.37077	−	18.3294i	−0.565644	−	1.23859i
$220$	−13.1733	−	9.57592i	−0.888147	−	0.645608i
$221$	−1.48523	−	0.954497i	−0.0999071	−	0.0642064i
$222$	−1.39944	−	24.4065i	−0.0939245	−	1.63806i
$223$	−7.63539	+	5.71578i	−0.511303	+	0.382757i	−0.823550	−	0.567244i	$-0.808010\pi$
$223$	−7.63539	+	5.71578i	−0.511303	+	0.382757i	0.312246	+	0.950001i	$0.398919\pi$
$224$	20.4762	−	11.2016i	1.36812	−	0.748441i
$225$	−0.249916	+	4.28669i	−0.0166611	+	0.285779i
$226$	1.65295	+	0.510816i	0.109953	+	0.0339790i
$227$	−9.79405	+	5.34796i	−0.650054	+	0.354956i	−0.770202	−	0.637800i	$-0.779845\pi$
$227$	−9.79405	+	5.34796i	−0.650054	+	0.354956i	0.120148	+	0.992756i	$0.461663\pi$
$228$	18.1938	+	1.81898i	1.20491	+	0.120465i
$229$			7.09649i			0.468949i	0.972122	+	0.234475i	$0.0753369\pi$
$229$			7.09649i			0.468949i	−0.972122	+	0.234475i	$0.924663\pi$
$230$	7.45102	+	13.2092i	0.491306	+	0.870987i
$231$		−	29.5155i		−	1.94198i
$232$	−9.25178	−	18.7949i	−0.607409	−	1.23394i
$233$	−6.22453	+	3.39885i	−0.407783	+	0.222666i	−0.670029	−	0.742335i	$-0.733718\pi$
$233$	−6.22453	+	3.39885i	−0.407783	+	0.222666i	0.262247	+	0.965001i	$0.415537\pi$
$234$	−0.150287	+	0.486313i	−0.00982455	+	0.0317913i
$235$	5.96164	−	10.2002i	0.388894	−	0.665389i
$236$	−1.12283	+	0.474927i	−0.0730902	+	0.0309151i
$237$	8.07740	−	6.04667i	0.524684	−	0.392773i
$238$	24.5399	−	1.40709i	1.59069	−	0.0912084i
$239$	−17.8672	−	11.4826i	−1.15573	−	0.742745i	−0.184961	−	0.982746i	$-0.559216\pi$
$239$	−17.8672	−	11.4826i	−1.15573	−	0.742745i	−0.970773	+	0.240001i	$0.922852\pi$
$240$	−16.7862	−	5.18911i	−1.08354	−	0.334955i
$241$	−9.63882	−	21.1061i	−0.620891	−	1.35956i	−0.914870	−	0.403749i	$-0.867707\pi$
$241$	−9.63882	−	21.1061i	−0.620891	−	1.35956i	0.293979	−	0.955812i	$-0.405021\pi$
$242$	−0.635705	−	3.13481i	−0.0408646	−	0.201513i
$243$	−5.19766	+	6.94326i	−0.333430	+	0.445410i
$244$	2.54347	+	4.21490i	0.162829	+	0.269831i
$245$	−0.652520	+	22.4037i	−0.0416880	+	1.43132i
$246$	−28.3599	+	12.4705i	−1.80816	+	0.795092i
$247$	0.139147	+	1.94553i	0.00885371	+	0.123791i
$248$	1.34840	−	11.8008i	0.0856236	−	0.749349i
$249$	0.931120	−	0.806820i	0.0590073	−	0.0511301i
$250$	−1.77855	−	15.7110i	−0.112485	−	0.993653i
$251$	6.22264	+	2.84179i	0.392770	+	0.179372i	0.602003	−	0.798494i	$-0.294370\pi$
$251$	6.22264	+	2.84179i	0.392770	+	0.179372i	−0.209233	+	0.977866i	$0.567097\pi$
$252$	−2.28802	−	6.70716i	−0.144132	−	0.422511i
$253$	−3.95725	+	17.0106i	−0.248790	+	1.06945i
$254$	−12.3267	+	7.67810i	−0.773448	+	0.481767i
$255$	−13.6254	−	12.5193i	−0.853258	−	0.783989i
$256$	8.24521	−	13.7119i	0.515325	−	0.856995i
$257$	0.500302	−	6.99514i	0.0312080	−	0.436345i	−0.957695	−	0.287784i	$-0.907081\pi$
$257$	0.500302	−	6.99514i	0.0312080	−	0.436345i	0.988903	−	0.148561i	$-0.0474641\pi$
$258$	6.36523	+	17.8310i	0.396282	+	1.11011i
$259$	−23.7766	+	27.4397i	−1.47741	+	1.70502i
$260$	0.240674	−	1.85876i	0.0149259	−	0.115275i
$261$	−6.10295	+	1.79199i	−0.377763	+	0.110921i
$262$	14.0961	−	13.7035i	0.870861	−	0.846603i
$263$	15.1429	−	20.2286i	0.933752	−	1.24735i	−0.0350178	−	0.999387i	$-0.511149\pi$
$263$	15.1429	−	20.2286i	0.933752	−	1.24735i	0.968770	−	0.247960i	$-0.0797603\pi$
$264$	−10.2083	−	17.4696i	−0.628274	−	1.07518i
$265$	−8.10406	−	6.44314i	−0.497828	−	0.395799i
$266$	−17.4918	−	20.7723i	−1.07249	−	1.27363i
$267$	−13.2462	+	2.88153i	−0.810653	+	0.176347i
$268$	9.78751	−	6.90427i	0.597868	−	0.421745i
$269$	30.2631	+	4.35118i	1.84517	+	0.265296i	0.974143	−	0.225931i	$-0.0725425\pi$
$269$	30.2631	+	4.35118i	1.84517	+	0.265296i	0.871031	+	0.491227i	$0.163452\pi$
$270$	6.04328	−	11.8489i	0.367782	−	0.721098i
$271$	−14.6859	−	22.8518i	−0.892107	−	1.38815i	−0.921417	−	0.388575i	$-0.872967\pi$
$271$	−14.6859	−	22.8518i	−0.892107	−	1.38815i	0.0293102	−	0.999570i	$-0.490669\pi$
$272$	14.0380	−	9.32022i	0.851178	−	0.565121i
$273$	2.98129	−	1.62791i	0.180436	−	0.0985255i
$274$	−10.3241	+	1.33585i	−0.623703	+	0.0807016i
$275$	10.7190	−	14.7189i	0.646381	−	0.887585i
$276$	1.88446	+	18.7472i	0.113431	+	1.12845i
$277$	−14.3814	−	14.3814i	−0.864097	−	0.864097i	0.127714	−	0.991811i	$-0.459236\pi$
$277$	−14.3814	−	14.3814i	−0.864097	−	0.864097i	−0.991811	+	0.127714i	$0.959236\pi$
$278$	−3.13321	+	4.06454i	−0.187918	+	0.243775i
$279$	−3.46029	−	1.01603i	−0.207162	−	0.0608283i
$280$	12.5039	+	22.9040i	0.747251	+	1.36877i
$281$	−1.79983	+	1.15668i	−0.107369	+	0.0690018i	−0.593223	−	0.805038i	$-0.702145\pi$
$281$	−1.79983	+	1.15668i	−0.107369	+	0.0690018i	0.485854	+	0.874040i	$0.338509\pi$
$282$	11.8737	−	8.62955i	0.707066	−	0.513882i
$283$	−1.28435	+	0.961455i	−0.0763469	+	0.0571526i	−0.636769	−	0.771054i	$-0.719730\pi$
$283$	−1.28435	+	0.961455i	−0.0763469	+	0.0571526i	0.560423	+	0.828207i	$0.310639\pi$
$284$	−5.06399	+	29.3166i	−0.300492	+	1.73962i
$285$	−2.05138	+	20.3395i	−0.121513	+	1.20481i
$286$	1.65102	−	1.39028i	0.0976268	−	0.0822090i
$287$	43.1112	+	16.0796i	2.54477	+	0.949152i
$288$	−3.67397	−	3.17849i	−0.216491	−	0.187294i
$289$	0.738132	−	0.106127i	0.0434195	−	0.00624278i
$290$	21.0223	−	10.3255i	1.23447	−	0.606335i
$291$	5.44354	+	18.5390i	0.319106	+	1.08677i
$292$	3.79301	+	20.1621i	0.221969	+	1.17990i
$293$	−0.130747	−	1.82808i	−0.00763833	−	0.106798i	0.992203	−	0.124636i	$-0.0397762\pi$
$293$	−0.130747	−	1.82808i	−0.00763833	−	0.106798i	−0.999841	+	0.0178380i	$0.994322\pi$
$294$	−11.9241	+	25.1635i	−0.695429	+	1.46757i
$295$	−0.529892	−	1.25583i	−0.0308515	−	0.0731171i
$296$	−4.58257	+	24.4643i	−0.266356	+	1.42196i
$297$	14.3516	−	5.35288i	0.832766	−	0.310606i
$298$	5.12137	−	22.0392i	0.296673	−	1.27670i
$299$	−1.93646	+	0.538496i	−0.111988	+	0.0311420i
$300$	5.81793	−	18.7625i	0.335898	−	1.08325i
$301$	11.6812	−	25.5782i	0.673291	−	1.47430i
$302$	−6.62963	+	11.7438i	−0.381493	+	0.675783i
$303$	−2.78321	+	38.9144i	−0.159891	+	2.23557i
$304$	−17.5373	−	6.24493i	−1.00583	−	0.358171i
$305$	−4.71487	+	2.83959i	−0.269973	+	0.162594i
$306$	−2.05942	−	4.68344i	−0.117729	−	0.267735i
$307$	−6.89957	+	12.6356i	−0.393779	+	0.721153i	−0.997080	−	0.0763609i	$-0.975670\pi$
$307$	−6.89957	+	12.6356i	−0.393779	+	0.721153i	0.603301	+	0.797513i	$0.293852\pi$
$308$	−7.21453	+	29.1718i	−0.411086	+	1.66222i
$309$	11.3118	−	1.62639i	0.643504	−	0.0925219i
$310$	13.1923	+	1.51904i	0.749274	+	0.0862756i
$311$	3.26893	−	1.49287i	0.185364	−	0.0846529i	−0.320571	−	0.947224i	$-0.603875\pi$
$311$	3.26893	−	1.49287i	0.185364	−	0.0846529i	0.505935	+	0.862572i	$0.331148\pi$
$312$	1.20153	−	1.99463i	0.0680234	−	0.112924i
$313$	26.4004	−	5.74306i	1.49224	−	0.324617i	0.608861	−	0.793277i	$-0.291627\pi$
$313$	26.4004	−	5.74306i	1.49224	−	0.324617i	0.883378	+	0.468661i	$0.155263\pi$
$314$	−10.2877	−	9.17191i	−0.580568	−	0.517601i
$315$	7.50106	−	2.55156i	0.422637	−	0.143764i
$316$	−9.46134	+	4.00189i	−0.532242	+	0.225124i
$317$	−0.754305	−	0.164089i	−0.0423660	−	0.00921615i	0.191332	−	0.981525i	$-0.438719\pi$
$317$	−0.754305	−	0.164089i	−0.0423660	−	0.00921615i	−0.233698	+	0.972309i	$0.575083\pi$
$318$	−6.00438	−	11.3753i	−0.336709	−	0.637893i
$319$	25.8793	+	7.59884i	1.44896	+	0.425453i
$320$	15.3224	+	9.23176i	0.856546	+	0.516071i
$321$	−2.48994			−0.138975
$322$	17.4013	−	21.9151i	0.969738	−	1.22128i
$323$	−13.8630	−	13.8630i	−0.771361	−	0.771361i
$324$	16.7773	−	13.7275i	0.932073	−	0.762639i
$325$	2.07792	+	0.270890i	0.115262	+	0.0150263i
$326$	−5.01102	+	16.2152i	−0.277535	+	0.898076i
$327$	1.52896	−	7.02852i	0.0845517	−	0.388678i
$328$	31.0779	−	5.39326i	1.71599	−	0.297793i
$329$	−21.5783	−	3.10248i	−1.18965	−	0.171046i
$330$	19.5415	−	11.3962i	1.07573	−	0.627338i
$331$	−12.8916	+	20.0597i	−0.708585	+	1.10258i	0.281149	+	0.959664i	$0.409284\pi$
$331$	−12.8916	+	20.0597i	−0.708585	+	1.10258i	−0.989735	+	0.142916i	$0.954352\pi$
$332$	−1.11749	+	0.569830i	−0.0613302	+	0.0312735i
$333$	7.08080	+	2.64100i	0.388025	+	0.144726i
$334$	6.07701	+	4.02785i	0.332519	+	0.220394i
$335$	7.70968	+	10.9495i	0.421225	+	0.598234i
$336$	2.79453	+	32.2991i	0.152454	+	1.76206i
$337$	14.4972	+	7.91605i	0.789711	+	0.431215i	0.822866	−	0.568235i	$-0.192374\pi$
$337$	14.4972	+	7.91605i	0.789711	+	0.431215i	−0.0331551	+	0.999450i	$0.510556\pi$
$338$	−16.9017	−	6.57737i	−0.919329	−	0.357762i
$339$	−1.57372	+	1.81617i	−0.0854726	+	0.0986406i
$340$	10.4067	+	15.7040i	0.564380	+	0.851670i
$341$	10.0145	+	11.5574i	0.542318	+	0.625869i
$342$	−2.77869	+	4.92221i	−0.150254	+	0.266163i
$343$	11.6882	−	4.35948i	0.631104	−	0.235390i
$344$	−1.93265	−	19.1792i	−0.104202	−	1.03407i
$345$	−20.9618	+	2.08865i	−1.12855	+	0.112449i
$346$	0.666514	−	0.415160i	0.0358320	−	0.0223191i
$347$	3.76536	+	10.0953i	0.202135	+	0.541945i	0.997978	−	0.0635578i	$-0.0202447\pi$
$347$	3.76536	+	10.0953i	0.202135	+	0.541945i	−0.795843	+	0.605503i	$0.792972\pi$
$348$	29.0711	−	1.25527i	1.55837	−	0.0672898i
$349$	−8.40577	+	7.28364i	−0.449951	+	0.389884i	−0.850147	−	0.526545i	$-0.823487\pi$
$349$	−8.40577	+	7.28364i	−0.449951	+	0.389884i	0.400197	+	0.916429i	$0.368942\pi$
$350$	−25.6196	+	13.9575i	−1.36942	+	0.746059i
$351$	1.33224	+	1.15439i	0.0711095	+	0.0616167i
$352$	5.81926	+	19.7614i	0.310168	+	1.05329i
$353$	12.9986	−	23.8051i	0.691843	−	1.26702i	−0.261522	−	0.965197i	$-0.584224\pi$
$353$	12.9986	−	23.8051i	0.691843	−	1.26702i	0.953365	−	0.301819i	$-0.0975937\pi$
$354$	0.0239164	−	1.69325i	0.00127114	−	0.0899954i
$355$	−32.7720	−	5.69023i	−1.73936	−	0.302006i
$356$	13.7963	+	0.389808i	0.731201	+	0.0206598i
$357$	−11.9316	+	31.9899i	−0.631488	+	1.69309i
$358$	0.690576	−	8.05501i	0.0364981	−	0.425720i
$359$	20.0894	+	12.9107i	1.06028	+	0.681400i	0.949920	−	0.312492i	$-0.101164\pi$
$359$	20.0894	+	12.9107i	1.06028	+	0.681400i	0.110358	+	0.993892i	$0.464800\pi$
$360$	3.55723	−	4.10453i	0.187482	−	0.216328i
$361$	−0.378524	+	2.63269i	−0.0199223	+	0.138563i
$362$	−9.66231	+	7.02239i	−0.507840	+	0.369089i
$363$	4.34143	+	0.944420i	0.227866	+	0.0495692i
$364$	−3.34449	+	0.880231i	−0.175299	+	0.0461366i
$365$	−22.5456	+	4.22109i	−1.18009	+	0.220942i
$366$	−6.78146	+	0.877460i	−0.354473	+	0.0458656i
$367$	0.465233	−	0.465233i	0.0242850	−	0.0242850i	−0.694860	−	0.719145i	$-0.744534\pi$
$367$	0.465233	−	0.465233i	0.0242850	−	0.0242850i	0.719145	+	0.694860i	$0.244534\pi$
$368$	2.71989	−	18.9895i	0.141784	−	0.989898i
$369$		−	9.57719i		−	0.498569i
$370$	−27.3475	−	5.14726i	−1.42173	−	0.267594i
$371$	−5.38211	+	18.3298i	−0.279425	+	0.951636i
$372$	14.2511	+	8.31258i	0.738883	+	0.430987i
$373$	−5.53835	+	25.4594i	−0.286765	+	1.31824i	0.577990	+	0.816044i	$0.303837\pi$
$373$	−5.53835	+	25.4594i	−0.286765	+	1.31824i	−0.864755	+	0.502194i	$0.832526\pi$
$374$	−3.39052	+	21.4286i	−0.175319	+	1.10804i
$375$	20.9714	+	6.52289i	1.08296	+	0.336841i
$376$	−13.8447	+	5.62677i	−0.713987	+	0.290178i
$377$	0.659813	+	3.03311i	0.0339821	+	0.156213i
$378$	−24.4531	−	2.09642i	−1.25773	−	0.107828i
$379$	−12.6826	−	27.7710i	−0.651461	−	1.42650i	−0.890270	−	0.455434i	$-0.849484\pi$
$379$	−12.6826	−	27.7710i	−0.651461	−	1.42650i	0.238809	−	0.971067i	$-0.423243\pi$
$380$	6.99911	−	19.6012i	0.359047	−	1.00552i
$381$	−2.87079	−	19.9667i	−0.147075	−	1.02293i
$382$	3.86408	−	3.75645i	0.197704	−	0.192197i
$383$	−12.7895	−	6.98360i	−0.653513	−	0.356845i	0.118041	−	0.993009i	$-0.462339\pi$
$383$	−12.7895	−	6.98360i	−0.653513	−	0.356845i	−0.771554	+	0.636164i	$0.780520\pi$
$384$	12.8250	+	18.1506i	0.654473	+	0.926245i
$385$	−32.6081	−	8.09447i	−1.66186	−	0.412532i
$386$	−0.913548	+	1.92786i	−0.0464984	+	0.0981256i
$387$	−5.83795	−	0.417539i	−0.296760	−	0.0212247i
$388$	−0.848637	−	19.6537i	−0.0430830	−	0.997765i
$389$	8.87372	+	4.05249i	0.449915	+	0.205469i	0.627469	−	0.778642i	$-0.284091\pi$
$389$	8.87372	+	4.05249i	0.449915	+	0.205469i	−0.177553	+	0.984111i	$0.556818\pi$
$390$	2.22890	+	1.34529i	0.112865	+	0.0681216i
$391$	11.1655	−	16.8369i	0.564665	−	0.851481i
$392$	17.9360	−	21.9559i	0.905907	−	1.10894i
$393$	9.54289	+	25.5855i	0.481375	+	1.29062i
$394$	8.31176	+	29.8611i	0.418741	+	1.50438i
$395$	−4.46504	−	10.5820i	−0.224660	−	0.532438i
$396$	6.21389	−	0.714947i	0.312260	−	0.0359274i
$397$	14.7466	−	1.05470i	0.740110	−	0.0529337i	0.303807	−	0.952734i	$-0.401742\pi$
$397$	14.7466	−	1.05470i	0.740110	−	0.0529337i	0.436303	+	0.899800i	$0.356288\pi$
$398$	7.81593	−	20.0843i	0.391777	−	1.00674i
$399$	36.1925	−	10.6271i	1.81189	−	0.532019i
$400$	−10.3363	+	17.1219i	−0.516816	+	0.856096i
$401$	0.806568	+	5.60980i	0.0402781	+	0.280140i	1.00000		0.000812638i	$-0.000258671\pi$
$401$	0.806568	+	5.60980i	0.0402781	+	0.280140i	−0.959722	+	0.280953i	$0.909350\pi$
$402$	3.30656	+	16.3054i	0.164916	+	0.813240i
$403$	−0.615040	+	1.64899i	−0.0306373	+	0.0821419i
$404$	12.2627	−	37.7810i	0.610093	−	1.87967i
$405$	15.3315	+	18.7710i	0.761828	+	0.932737i
$406$	−32.2578	−	28.7592i	−1.60093	−	1.42729i
$407$	−19.2046	−	25.6544i	−0.951938	−	1.27164i
$408$	4.00198	+	23.0608i	0.198127	+	1.14168i
$409$	−10.0418	−	15.6254i	−0.496537	−	0.772626i	0.499040	−	0.866579i	$-0.333686\pi$
$409$	−10.0418	−	15.6254i	−0.496537	−	0.772626i	−0.995577	+	0.0939530i	$0.970050\pi$
$410$	5.99961	+	34.7514i	0.296300	+	1.71625i
$411$	4.07386	−	13.8743i	0.200949	−	0.684369i
$412$	−11.5776	−	1.15750i	−0.570387	−	0.0570262i
$413$	−1.77842	+	1.77842i	−0.0875102	+	0.0875102i
$414$	−5.53966	−	1.79954i	−0.272260	−	0.0884424i
$415$	−0.636002	−	1.24995i	−0.0312201	−	0.0613574i
$416$	−1.67509	+	1.67772i	−0.0821282	+	0.0822568i
$417$	−3.41633	−	6.25653i	−0.167298	−	0.306384i
$418$	21.1969	−	11.1887i	1.03677	−	0.547256i
$419$	23.0054	−	14.7847i	1.12389	−	0.722278i	0.159612	−	0.987180i	$-0.448976\pi$
$419$	23.0054	−	14.7847i	1.12389	−	0.722278i	0.964275	+	0.264902i	$0.0853395\pi$
$420$	−36.1142	+	3.09295i	−1.76219	+	0.150921i
$421$	2.06650	−	14.3728i	0.100715	−	0.700488i	−0.875426	−	0.483352i	$-0.839419\pi$
$421$	2.06650	−	14.3728i	0.100715	−	0.700488i	0.976141	−	0.217136i	$-0.0696716\pi$
$422$	0.0463375	+	0.808133i	0.00225568	+	0.0393393i
$423$	0.964531	+	4.43388i	0.0468971	+	0.215583i
$424$	3.15399	+	12.7105i	0.153171	+	0.617275i
$425$	−17.5677	+	11.6197i	−0.852160	+	0.563639i
$426$	−34.4454	−	22.8305i	−1.66889	−	1.10614i
$427$	8.13010	+	6.08612i	0.393443	+	0.294528i
$428$	2.46094	+	0.608619i	0.118954	+	0.0294187i
$429$	0.844661	+	2.87665i	0.0407806	+	0.138886i
$430$	21.4449	−	2.14211i	1.03416	−	0.103302i
$431$	−18.1550	−	15.7314i	−0.874494	−	0.757753i	0.0968835	−	0.995296i	$-0.469113\pi$
$431$	−18.1550	−	15.7314i	−0.874494	−	0.757753i	−0.971377	+	0.237543i	$0.923658\pi$
$432$	−15.1983	+	7.21652i	−0.731229	+	0.347205i
$433$	2.98262	+	0.213321i	0.143335	+	0.0102515i	0.142822	−	0.989748i	$-0.454382\pi$
$433$	2.98262	+	0.213321i	0.143335	+	0.0102515i	0.000512896		1.00000i	$0.499837\pi$
$434$	−6.57059	−	23.6057i	−0.315398	−	1.13311i
$435$	1.37516	+	32.5036i	0.0659336	+	1.55843i
$436$	−3.22915	+	6.57295i	−0.154648	+	0.314787i
$437$	−22.2835	+	1.27222i	−1.06597	+	0.0608585i
$438$	−27.7574	−	6.45012i	−1.32630	−	0.308199i
$439$	−4.16576	+	9.12175i	−0.198821	+	0.435357i	−0.982613	−	0.185666i	$-0.940556\pi$
$439$	−4.16576	+	9.12175i	−0.198821	+	0.435357i	0.783792	+	0.621024i	$0.213283\pi$
$440$	−22.0996	+	6.48690i	−1.05356	+	0.309251i
$441$	−5.63711	−	6.50557i	−0.268434	−	0.309789i
$442$	−2.35145	+	0.839410i	−0.111847	+	0.0399267i
$443$	−6.59671	+	0.471806i	−0.313419	+	0.0224162i	−0.227163	−	0.973857i	$-0.572945\pi$
$443$	−6.59671	+	0.471806i	−0.313419	+	0.0224162i	−0.0862563	+	0.996273i	$0.527490\pi$
$444$	−28.5449	−	19.5054i	−1.35468	−	0.925684i
$445$	−0.449242	+	15.4243i	−0.0212961	+	0.731182i
$446$	−0.190499	+	13.4871i	−0.00902037	+	0.638633i
$447$	25.1600	+	18.8346i	1.19003	+	0.890844i
$448$	5.13293	−	32.6061i	0.242508	−	1.54049i
$449$	−32.9401	+	15.0432i	−1.55454	+	0.709934i	−0.993066	−	0.117562i	$-0.962492\pi$
$449$	−32.9401	+	15.0432i	−1.55454	+	0.709934i	−0.561473	+	0.827495i	$0.689765\pi$
$450$	4.58554	+	3.98109i	0.216164	+	0.187671i
$451$	−21.9563	+	34.1647i	−1.03388	+	1.60875i
$452$	1.99932	−	1.41035i	0.0940401	−	0.0663374i
$453$	−11.2259	−	14.9960i	−0.527437	−	0.704573i
$454$	−2.46629	+	15.5874i	−0.115749	+	0.731551i
$455$	−0.980873	−	3.74011i	−0.0459841	−	0.175339i
$456$	17.7461	−	18.8075i	0.831036	−	0.880741i
$457$	−1.49216	−	2.73269i	−0.0698003	−	0.127830i	0.840449	−	0.541891i	$-0.182292\pi$
$457$	−1.49216	−	2.73269i	−0.0698003	−	0.127830i	−0.910249	+	0.414062i	$0.864110\pi$
$458$	7.94845	+	6.12719i	0.371407	+	0.286305i
$459$	−17.7187			−0.827037
$460$	21.2283	+	3.05940i	0.989774	+	0.142645i
$461$	12.8946			0.600562			0.300281	−	0.953851i	$-0.402920\pi$
$461$	12.8946			0.600562			0.300281	+	0.953851i	$0.402920\pi$
$462$	−33.0590	−	25.4840i	−1.53804	−	1.18562i
$463$	17.4077	+	31.8797i	0.809002	+	1.48158i	0.875195	+	0.483770i	$0.160733\pi$
$463$	17.4077	+	31.8797i	0.809002	+	1.48158i	−0.0661926	+	0.997807i	$0.521085\pi$
$464$	−29.0394	−	5.86523i	−1.34812	−	0.272286i
$465$	−9.30761	+	15.9251i	−0.431630	+	0.738508i
$466$	−1.56743	+	9.90642i	−0.0726100	+	0.458906i
$467$	14.1044	+	18.8413i	0.652676	+	0.871873i	0.997773	−	0.0666939i	$-0.0212451\pi$
$467$	14.1044	+	18.8413i	0.652676	+	0.871873i	−0.345098	+	0.938567i	$0.612154\pi$
$468$	0.414938	+	0.588218i	0.0191805	+	0.0271904i
$469$	13.3590	−	20.7871i	0.616863	−	0.959857i
$470$	−6.27745	−	15.4843i	−0.289557	−	0.714239i
$471$	17.4144	−	7.95289i	0.802413	−	0.366450i
$472$	−0.437523	+	1.66769i	−0.0201386	+	0.0767617i
$473$	19.8685	+	14.8733i	0.913552	+	0.683877i
$474$	0.201527	−	14.2679i	0.00925643	−	0.655346i
$475$	21.9080	+	7.84431i	1.00521	+	0.359921i
$476$	19.6120	−	28.7009i	0.898916	−	1.31551i
$477$	3.96618	−	0.283667i	0.181599	−	0.0129882i
$478$	−28.2878	+	10.0981i	−1.29385	+	0.461875i
$479$	−1.73508	−	2.00239i	−0.0792779	−	0.0914915i	0.714725	−	0.699406i	$-0.246552\pi$
$479$	−1.73508	−	2.00239i	−0.0792779	−	0.0914915i	−0.794003	+	0.607914i	$0.792006\pi$
$480$	−20.3055	+	14.3211i	−0.926814	+	0.653667i
$481$	1.53207	−	3.35476i	0.0698563	−	0.152964i
$482$	−31.9622	−	7.42722i	−1.45584	−	0.338301i
$483$	18.1363	+	34.3795i	0.825228	+	1.56432i
$484$	−4.06003	−	1.99460i	−0.184547	−	0.0906638i
$485$	21.9743	−	0.929683i	0.997802	−	0.0422147i
$486$	3.28911	+	11.8165i	0.149197	+	0.536009i
$487$	4.73558	+	0.338695i	0.214590	+	0.0153478i	0.178220	−	0.983991i	$-0.442966\pi$
$487$	4.73558	+	0.338695i	0.214590	+	0.0153478i	0.0363696	+	0.999338i	$0.488421\pi$
$488$	6.91697	+	0.790361i	0.313117	+	0.0357779i
$489$	−17.8163	−	15.4379i	−0.805680	−	0.698125i
$490$	24.5299	+	20.0745i	1.10815	+	0.906871i
$491$	1.28472	+	4.37534i	0.0579784	+	0.197456i	0.983389	−	0.181509i	$-0.0580982\pi$
$491$	1.28472	+	4.37534i	0.0579784	+	0.197456i	−0.925411	+	0.378965i	$0.876280\pi$
$492$	−10.5186	+	42.5319i	−0.474216	+	1.91748i
$493$	−24.9770	−	18.6975i	−1.12491	−	0.842095i
$494$	2.29924	+	1.52394i	0.103448	+	0.0685653i
$495$	0.793289	+	6.94803i	0.0356557	+	0.312291i
$496$	−12.0533	−	11.6992i	−0.541208	−	0.525309i
$497$	13.0462	+	59.9724i	0.585202	+	2.69013i
$498$	−0.0997424	−	1.73952i	−0.00446957	−	0.0779498i
$499$	2.34453	−	16.3066i	0.104956	−	0.729982i	−0.867592	−	0.497277i	$-0.834333\pi$
$499$	2.34453	−	16.3066i	0.104956	−	0.729982i	0.972547	−	0.232705i	$-0.0747577\pi$
$500$	−19.1328	−	11.5730i	−0.855646	−	0.517561i
$501$	−8.51931	+	5.47503i	−0.380615	+	0.244606i
$502$	8.55565	−	4.51607i	0.381857	−	0.201562i
$503$	−10.5879	−	19.3903i	−0.472092	−	0.864572i	−0.999884	−	0.0151989i	$-0.995162\pi$
$503$	−10.5879	−	19.3903i	−0.472092	−	0.864572i	0.527792	−	0.849373i	$-0.323020\pi$
$504$	−9.48789	−	3.22833i	−0.422624	−	0.143801i
$505$	42.2284	+	13.7469i	1.87914	+	0.611728i
$506$	15.6361	+	19.1195i	0.695108	+	0.849965i
$507$	17.8134	−	17.8134i	0.791120	−	0.791120i
$508$	−2.04315	+	20.4360i	−0.0906500	+	0.906699i
$509$	−3.18108	+	10.8337i	−0.140999	+	0.480198i	−0.999466	−	0.0326705i	$-0.989599\pi$
$509$	−3.18108	+	10.8337i	−0.140999	+	0.480198i	0.858467	+	0.512868i	$0.171417\pi$
$510$	−25.7866	+	4.45191i	−1.14185	+	0.197134i
$511$	22.8818	+	35.6048i	1.01223	+	1.57506i
$512$	−8.23908	−	21.0741i	−0.364119	−	0.931352i
$513$	11.7311	+	15.6709i	0.517941	+	0.691889i
$514$	−7.40297	−	6.60005i	−0.326531	−	0.291116i
$515$	1.30539	−	12.9430i	0.0575225	−	0.570337i
$516$	25.4675	+	8.26608i	1.12114	+	0.363894i
$517$	6.72417	−	18.0282i	0.295729	−	0.792879i
$518$	10.2049	+	50.3228i	0.448379	+	2.21106i
$519$	0.155225	+	1.07962i	0.00681363	+	0.0473899i
$520$	−1.87411	−	1.87444i	−0.0821853	−	0.0821998i
$521$	−22.0497	+	6.47437i	−0.966013	+	0.283647i	−0.726439	−	0.687231i	$-0.758826\pi$
$521$	−22.0497	+	6.47437i	−0.966013	+	0.283647i	−0.239574	+	0.970878i	$0.577008\pi$
$522$	−3.26224	+	8.38286i	−0.142784	+	0.366908i
$523$	2.35431	−	0.168384i	0.102947	−	0.00736292i	−0.0197706	−	0.999805i	$-0.506294\pi$
$523$	2.35431	−	0.168384i	0.102947	−	0.00736292i	0.122718	+	0.992442i	$0.460839\pi$
$524$	−3.17787	−	27.6201i	−0.138826	−	1.20659i
$525$	−3.42289	−	40.3799i	−0.149387	−	1.76232i
$526$	−9.58252	−	34.4265i	−0.417818	−	1.50107i
$527$	−6.18203	−	16.5747i	−0.269294	−	0.722004i
$528$	−28.3808	−	3.64966i	−1.23512	−	0.158831i
$529$	−5.84304	−	22.2454i	−0.254045	−	0.967192i
$530$	−14.2138	+	3.51390i	−0.617408	+	0.152634i
$531$	0.476189	+	0.217468i	0.0206648	+	0.00943731i
$532$	−38.3687	+	1.65674i	−1.66349	+	0.0718288i
$533$	−4.66187	−	0.333424i	−0.201928	−	0.0144422i
$534$	−8.20943	+	17.3244i	−0.355257	+	0.749699i
$535$	−0.682851	+	2.75082i	−0.0295222	+	0.118929i
$536$	0.717500	−	16.9238i	0.0309913	−	0.730995i
$537$	9.85605	+	5.38181i	0.425320	+	0.232242i
$538$	31.0031	−	30.1395i	1.33664	−	1.29940i
$539$	5.19481	+	36.1307i	0.223756	+	1.55626i
$540$	−8.05352	−	16.9992i	−0.346568	−	0.731531i
$541$	4.40447	+	9.64445i	0.189363	+	0.414647i	0.980372	−	0.197158i	$-0.0631711\pi$
$541$	4.40447	+	9.64445i	0.189363	+	0.414647i	−0.791009	+	0.611805i	$0.790444\pi$
$542$	−38.2752	−	3.28143i	−1.64406	−	0.140949i
$543$	−3.52676	−	16.2123i	−0.151348	−	0.695734i
$544$	1.68141	−	23.7705i	0.0720900	−	1.01915i
$545$	−7.34564	−	3.61669i	−0.314652	−	0.154922i
$546$	0.750736	−	4.74476i	0.0321285	−	0.203057i
$547$	3.86061	−	17.7469i	0.165068	−	0.758805i	−0.817949	−	0.575290i	$-0.804889\pi$
$547$	3.86061	−	17.7469i	0.165068	−	0.758805i	0.983017	−	0.183514i	$-0.0587473\pi$
$548$	−7.41774	+	12.7170i	−0.316870	+	0.543241i
$549$	0.595544	−	2.02824i	0.0254172	−	0.0865630i
$550$	−7.23107	−	24.7144i	−0.308334	−	1.05382i
$551$			34.4696i			1.46845i
$552$	22.6250	+	14.0759i	0.962982	+	0.599108i
$553$	−14.9855	+	14.9855i	−0.637249	+	0.637249i
$554$	−28.5251	+	3.69089i	−1.21192	+	0.156811i
$555$	21.8354	−	31.8951i	0.926863	−	1.35387i
$556$	1.84725	+	7.01874i	0.0783409	+	0.297661i
$557$	−29.3368	−	6.38183i	−1.24304	−	0.270407i	−0.457496	−	0.889212i	$-0.651254\pi$
$557$	−29.3368	−	6.38183i	−1.24304	−	0.270407i	−0.785545	+	0.618805i	$0.787617\pi$
$558$	−4.12566	+	2.99846i	−0.174653	+	0.126935i
$559$	−0.406489	+	2.82719i	−0.0171927	+	0.119578i
$560$	36.4497	+	5.77051i	1.54028	+	0.243849i
$561$	−25.3513	−	16.2923i	−1.07033	−	0.687861i
$562$	−0.258449	+	3.01460i	−0.0109020	+	0.127163i
$563$	−8.70485	+	23.3386i	−0.366866	+	0.983605i	0.614067	+	0.789254i	$0.289533\pi$
$563$	−8.70485	+	23.3386i	−0.366866	+	0.983605i	−0.980932	+	0.194351i	$0.937740\pi$
$564$	0.586283	−	20.7500i	0.0246870	−	0.873732i
$565$	1.57488	+	2.23668i	0.0662555	+	0.0940978i
$566$	−0.0320439	+	2.26868i	−0.00134691	+	0.0953596i
$567$	21.4323	−	39.2503i	0.900072	−	1.64836i
$568$	28.4639	+	30.9842i	1.19432	+	1.30007i
$569$	9.14796	+	7.92675i	0.383502	+	0.332307i	0.825183	−	0.564866i	$-0.191072\pi$
$569$	9.14796	+	7.92675i	0.383502	+	0.332307i	−0.441680	+	0.897172i	$0.645617\pi$
$570$	21.0101	+	19.8590i	0.880018	+	0.831802i
$571$	5.18331	−	4.49136i	0.216915	−	0.187958i	−0.539625	−	0.841906i	$-0.681434\pi$
$571$	5.18331	−	4.49136i	0.216915	−	0.187958i	0.756540	+	0.653948i	$0.226888\pi$
$572$	−0.131681	−	3.04962i	−0.00550586	−	0.127511i
$573$	2.61594	+	7.01360i	0.109282	+	0.292997i
$574$	55.2328	−	34.4035i	2.30537	−	1.43598i
$575$	−3.44117	+	23.7310i	−0.143507	+	0.989649i
$576$	−6.73222	+	1.37070i	−0.280509	+	0.0571127i
$577$	−33.5716	+	12.5216i	−1.39760	+	0.521279i	−0.931594	−	0.363501i	$-0.881581\pi$
$577$	−33.5716	+	12.5216i	−1.39760	+	0.521279i	−0.466009	+	0.884780i	$0.654309\pi$
$578$	0.518443	−	0.918379i	0.0215644	−	0.0381995i
$579$	−1.94055	−	2.23951i	−0.0806463	−	0.0930708i
$580$	6.58577	−	32.4613i	0.273459	−	1.34788i
$581$	−1.69463	+	1.95571i	−0.0703051	+	0.0811364i
$582$	25.4647	+	9.90972i	1.05554	+	0.410771i
$583$	−14.7989	−	8.08078i	−0.612906	−	0.334672i
$584$	25.8575	+	13.1598i	1.06999	+	0.544556i
$585$	−0.658051	+	0.463342i	−0.0272071	+	0.0191568i
$586$	−2.16044	−	1.43194i	−0.0892470	−	0.0591531i
$587$	14.6415	+	5.46099i	0.604319	+	0.225399i	0.632952	−	0.774191i	$-0.281843\pi$
$587$	14.6415	+	5.46099i	0.604319	+	0.225399i	−0.0286337	+	0.999590i	$0.509116\pi$
$588$	17.8891	+	35.0821i	0.737733	+	1.44676i
$589$	−10.5662	+	16.4413i	−0.435371	+	0.677451i
$590$	−1.86411	−	0.490788i	−0.0767442	−	0.0202054i
$591$	−42.6165	−	6.12732i	−1.75301	−	0.252044i
$592$	23.4447	+	26.2555i	0.963573	+	1.07909i
$593$	0.324977	−	1.49390i	0.0133452	−	0.0613470i	−0.969993	−	0.243134i	$-0.921825\pi$
$593$	0.324977	−	1.49390i	0.0133452	−	0.0613470i	0.983338	+	0.181787i	$0.0581882\pi$
$594$	6.39584	−	20.6963i	0.262425	−	0.849181i
$595$	32.0695	+	21.9548i	1.31472	+	0.900060i
$596$	−20.2633	−	24.7651i	−0.830016	−	1.01442i
$597$	21.1677	+	21.1677i	0.866338	+	0.866338i
$598$	−1.06882	+	2.63388i	−0.0437072	+	0.107707i
$599$	36.3784			1.48638			0.743191	−	0.669080i	$-0.233311\pi$
$599$	36.3784			1.48638			0.743191	+	0.669080i	$0.233311\pi$
$600$	−15.9917	−	22.7161i	−0.652860	−	0.927382i
$601$	11.8859	+	3.49001i	0.484835	+	0.142360i	0.515010	−	0.857184i	$-0.327788\pi$
$601$	11.8859	+	3.49001i	0.484835	+	0.142360i	−0.0301751	+	0.999545i	$0.509606\pi$
$602$	−18.5633	−	35.1680i	−0.756583	−	1.43334i
$603$	−5.02563	−	1.09326i	−0.204659	−	0.0445209i
$604$	7.42964	+	17.5653i	0.302308	+	0.714723i
$605$	2.23398	−	4.53731i	0.0908244	−	0.184468i
$606$	41.1832	+	36.7165i	1.67295	+	1.49150i
$607$	−32.0146	+	6.96435i	−1.29943	+	0.282674i	−0.808486	−	0.588515i	$-0.799713\pi$
$607$	−32.0146	+	6.96435i	−1.29943	+	0.282674i	−0.490947	+	0.871190i	$0.663349\pi$
$608$	−22.1366	+	14.2508i	−0.897756	+	0.577946i
$609$	54.6041	−	24.9369i	2.21267	−	1.01049i
$610$	−0.890379	+	7.73264i	−0.0360504	+	0.313085i
$611$	2.19185	−	0.315141i	0.0886728	−	0.0127492i
$612$	−7.02384	−	1.73708i	−0.283922	−	0.0702171i
$613$	−7.10343	+	13.0090i	−0.286905	+	0.525427i	−0.980890	−	0.194562i	$-0.937671\pi$
$613$	−7.10343	+	13.0090i	−0.286905	+	0.525427i	0.693985	+	0.719989i	$0.255853\pi$
$614$	8.19540	+	18.6376i	0.330740	+	0.752153i
$615$	−47.5418	−	11.8015i	−1.91707	−	0.475884i
$616$	26.4449	+	33.2680i	1.06550	+	1.34040i
$617$	2.35726	−	32.9588i	0.0948998	−	1.32687i	−0.697374	−	0.716707i	$-0.745648\pi$
$617$	2.35726	−	32.9588i	0.0948998	−	1.32687i	0.792274	−	0.610166i	$-0.208897\pi$
$618$	7.94507	−	14.0740i	0.319597	−	0.566141i
$619$	−12.8245	+	28.0817i	−0.515459	+	1.12870i	0.455671	+	0.890148i	$0.349399\pi$
$619$	−12.8245	+	28.0817i	−0.515459	+	1.12870i	−0.971130	+	0.238550i	$0.923328\pi$
$620$	13.0918	−	13.4646i	0.525780	−	0.540750i
$621$	−13.4275	+	15.0536i	−0.538828	+	0.604079i
$622$	1.15034	−	4.95034i	0.0461242	−	0.198490i
$623$	26.6775	−	9.95020i	1.06881	−	0.398646i
$624$	−1.19668	−	3.06797i	−0.0479056	−	0.122817i
$625$	12.9576	−	21.3799i	0.518305	−	0.855196i
$626$	16.3619	−	34.5285i	0.653952	−	1.38004i
$627$	2.37510	+	33.2082i	0.0948522	+	1.32621i
$628$	−19.1555	+	3.60365i	−0.764389	+	0.143801i
$629$	10.4439	+	35.5685i	0.416424	+	1.41821i
$630$	3.61861	−	10.6046i	0.144169	−	0.422499i
$631$	−24.2459	+	3.48603i	−0.965214	+	0.138777i	−0.606860	−	0.794809i	$-0.707571\pi$
$631$	−24.2459	+	3.48603i	−0.965214	+	0.138777i	−0.358354	+	0.933586i	$0.616662\pi$
$632$	−3.68670	+	14.0525i	−0.146649	+	0.558978i
$633$	−1.05347	−	0.392924i	−0.0418717	−	0.0156173i
$634$	−0.835064	+	0.703186i	−0.0331646	+	0.0279271i
$635$	−22.8461	−	2.30419i	−0.906620	−	0.0914390i
$636$	−17.9252	−	3.09630i	−0.710779	−	0.122776i
$637$	−3.36296	+	2.51748i	−0.133245	+	0.0997461i
$638$	30.8556	−	22.4253i	1.22158	−	0.887824i
$639$	10.7469	−	6.90661i	0.425141	−	0.273221i
$640$	23.5696	−	9.19106i	0.931669	−	0.363309i
$641$	40.8918	+	12.0069i	1.61513	+	0.474245i	0.959704	−	0.281014i	$-0.0906707\pi$
$641$	40.8918	+	12.0069i	1.61513	+	0.474245i	0.655426	+	0.755259i	$0.272489\pi$
$642$	−2.14984	+	2.78886i	−0.0848474	+	0.110068i
$643$	−26.4181	−	26.4181i	−1.04183	−	1.04183i	−0.999086	−	0.0427411i	$-0.986391\pi$
$643$	−26.4181	−	26.4181i	−1.04183	−	1.04183i	−0.0427411	−	0.999086i	$-0.513609\pi$
$644$	−9.52164	−	38.4122i	−0.375205	−	1.51365i
$645$	−9.26653	+	28.4655i	−0.364869	+	1.12083i
$646$	−27.4969	+	3.55785i	−1.08185	+	0.139982i
$647$	−10.3738	+	5.66452i	−0.407836	+	0.222695i	−0.670052	−	0.742314i	$-0.733728\pi$
$647$	−10.3738	+	5.66452i	−0.407836	+	0.222695i	0.262217	+	0.965009i	$0.415547\pi$
$648$	−0.889820	−	30.6440i	−0.0349554	−	1.20381i
$649$	−1.20015	−	1.86746i	−0.0471099	−	0.0733044i
$650$	2.09751	−	2.09350i	0.0822712	−	0.0821137i
$651$	33.6890	+	4.84375i	1.32038	+	0.189842i
$652$	13.8353	+	19.6130i	0.541832	+	0.768103i
$653$	15.4973	−	3.37124i	0.606458	−	0.131927i	0.101158	−	0.994870i	$-0.467745\pi$
$653$	15.4973	−	3.37124i	0.606458	−	0.131927i	0.505300	+	0.862944i	$0.331382\pi$
$654$	−6.55220	−	7.78102i	−0.256211	−	0.304262i
$655$	30.8833	−	3.52609i	1.20671	−	0.137776i
$656$	20.7923	−	39.4655i	0.811801	−	1.54087i
$657$	5.27928	−	7.05229i	0.205964	−	0.275136i
$658$	−22.1059	+	21.4901i	−0.861776	+	0.837771i
$659$	−46.8825	+	13.7659i	−1.82628	+	0.536245i	−0.999649	−	0.0264976i	$-0.991565\pi$
$659$	−46.8825	+	13.7659i	−1.82628	+	0.536245i	−0.826632	+	0.562742i	$0.809746\pi$
$660$	4.10805	−	31.7271i	0.159906	−	1.23498i
$661$	20.1181	−	23.2176i	0.782505	−	0.903059i	−0.214783	−	0.976662i	$-0.568904\pi$
$661$	20.1181	−	23.2176i	0.782505	−	0.903059i	0.997288	+	0.0736030i	$0.0234498\pi$
$662$	11.3372	+	31.7590i	0.440633	+	1.23435i
$663$	0.247411	−	3.45926i	0.00960866	−	0.134347i
$664$	−0.326613	+	1.74365i	−0.0126750	+	0.0676666i
$665$	−1.81496	−	42.8991i	−0.0703812	−	1.66355i
$666$	9.07170	−	5.65060i	0.351521	−	0.218956i
$667$	−34.8132	+	7.05083i	−1.34797	+	0.273009i
$668$	9.75837	−	3.32888i	0.377563	−	0.128798i
$669$	−17.0427	−	7.78315i	−0.658909	−	0.300914i
$670$	18.9206	+	0.818655i	0.730968	+	0.0316274i
$671$	−6.77433	+	5.86999i	−0.261520	+	0.226609i
$672$	38.5896	+	24.7574i	1.48863	+	0.955037i
$673$	1.42305	+	19.8968i	0.0548546	+	0.766967i	0.948216	+	0.317627i	$0.102886\pi$
$673$	1.42305	+	19.8968i	0.0548546	+	0.766967i	−0.893361	+	0.449340i	$0.851659\pi$
$674$	21.3834	−	9.40280i	0.823659	−	0.362182i
$675$	19.0136	−	8.98757i	0.731832	−	0.345932i
$676$	−21.9601	+	13.2518i	−0.844619	+	0.509685i
$677$	−19.9955	+	26.7109i	−0.768490	+	1.02658i	0.230083	+	0.973171i	$0.426100\pi$
$677$	−19.9955	+	26.7109i	−0.768490	+	1.02658i	−0.998573	+	0.0534109i	$0.982991\pi$
$678$	0.675439	+	3.33075i	0.0259401	+	0.127917i
$679$	−16.8587	−	36.9155i	−0.646979	−	1.41669i
$680$	26.5746	+	1.90300i	1.01909	+	0.0729769i
$681$	−18.4408	−	11.8512i	−0.706652	−	0.454138i
$682$	21.5916	−	1.23804i	0.826785	−	0.0474070i
$683$	29.8216	−	22.3242i	1.14109	−	0.854211i	0.150171	−	0.988660i	$-0.452017\pi$
$683$	29.8216	−	22.3242i	1.14109	−	0.854211i	0.990920	+	0.134449i	$0.0429266\pi$
$684$	3.11400	+	7.36217i	0.119067	+	0.281500i
$685$	−14.2108	−	8.30565i	−0.542966	−	0.317343i
$686$	5.20888	−	16.8554i	0.198876	−	0.643544i
$687$	−12.2350	+	6.68083i	−0.466795	+	0.254890i
$688$	−23.1504	−	14.3949i	−0.882602	−	0.548800i
$689$		−	1.94049i		−	0.0739266i
$690$	−15.7593	+	25.2818i	−0.599946	+	0.962460i
$691$		−	11.4837i		−	0.436861i	−0.975853	−	0.218430i	$-0.929906\pi$
$691$		−	11.4837i		−	0.436861i	0.975853	−	0.218430i	$-0.0700936\pi$
$692$	0.110474	−	1.10499i	0.00419961	−	0.0420053i
$693$	11.3253	−	6.18407i	0.430212	−	0.234914i
$694$	14.5584	+	4.49901i	0.552628	+	0.170780i
$695$	−7.84898	+	2.05846i	−0.297729	+	0.0780818i
$696$	23.6943	−	33.6450i	0.898130	−	1.27531i
$697$	37.6080	−	28.1530i	1.42450	−	1.06637i
$698$	0.900434	+	15.7037i	0.0340819	+	0.594394i
$699$	−11.7199	−	7.53192i	−0.443287	−	0.284883i
$700$	−6.48709	+	40.7464i	−0.245189	+	1.54007i
$701$	−20.8473	−	45.6492i	−0.787392	−	1.72415i	−0.683971	−	0.729510i	$-0.739748\pi$
$701$	−20.8473	−	45.6492i	−0.787392	−	1.72415i	−0.103421	−	0.994638i	$-0.532979\pi$
$702$	2.44325	−	0.495464i	0.0922144	−	0.0187001i
$703$	24.5432	−	32.7859i	0.925666	−	1.23655i
$704$	27.1582	+	10.5443i	1.02356	+	0.397404i
$705$	23.1986	+	0.675672i	0.873710	+	0.0254473i
$706$	−15.4399	−	35.1126i	−0.581087	−	1.32148i
$707$	−5.84581	−	81.7351i	−0.219854	−	3.07397i
$708$	−1.87589	−	1.48876i	−0.0705001	−	0.0559511i
$709$	−29.7952	+	25.8177i	−1.11898	+	0.969602i	−0.999729	−	0.0232619i	$-0.992595\pi$
$709$	−29.7952	+	25.8177i	−1.11898	+	0.969602i	−0.119251	+	0.992864i	$0.538049\pi$
$710$	−34.6691	+	31.7934i	−1.30111	+	1.19318i
$711$	4.01251	+	1.83245i	0.150481	+	0.0687224i
$712$	12.3485	−	15.1160i	0.462778	−	0.566496i
$713$	−18.7665	−	7.30840i	−0.702811	−	0.273702i
$714$	25.5285	+	40.9845i	0.955381	+	1.53381i
$715$	3.40970	−	0.144257i	0.127516	−	0.00539489i
$716$	−8.42579	−	7.72827i	−0.314887	−	0.288819i
$717$	2.97635	−	41.6148i	0.111154	−	1.55413i
$718$	31.8061	−	11.3540i	1.18699	−	0.423727i
$719$	8.61404	−	9.94113i	0.321249	−	0.370742i	−0.572038	−	0.820227i	$-0.693847\pi$
$719$	8.61404	−	9.94113i	0.321249	−	0.370742i	0.893288	+	0.449485i	$0.148393\pi$
$720$	−1.52594	−	7.52819i	−0.0568685	−	0.280559i
$721$	−23.0311	+	6.76253i	−0.857721	+	0.251850i
$722$	2.62193	+	2.69706i	0.0975783	+	0.100374i
$723$	27.3146	−	36.4881i	1.01584	−	1.35701i
$724$	−0.477094	+	16.8855i	−0.0177311	+	0.627545i
$725$	36.2864	+	7.39470i	1.34764	+	0.274632i
$726$	4.80624	−	4.04721i	0.178376	−	0.150206i
$727$	−9.20700	+	2.00286i	−0.341469	+	0.0742820i	−0.380030	−	0.924974i	$-0.624086\pi$
$727$	−9.20700	+	2.00286i	−0.341469	+	0.0742820i	0.0385610	+	0.999256i	$0.487723\pi$
$728$	−1.90176	+	4.50601i	−0.0704841	+	0.167004i
$729$	15.3215	+	2.20290i	0.567464	+	0.0815890i
$730$	−14.7382	+	28.8968i	−0.545487	+	1.06952i
$731$	−15.5216	−	24.1520i	−0.574086	−	0.893295i
$732$	−4.87239	+	8.35321i	−0.180089	+	0.308744i
$733$	18.5007	−	10.1021i	0.683339	−	0.373131i	−0.0997748	−	0.995010i	$-0.531812\pi$
$733$	18.5007	−	10.1021i	0.683339	−	0.373131i	0.783113	+	0.621879i	$0.213630\pi$
$734$	−0.119399	−	0.922773i	−0.00440708	−	0.0340602i
$735$	−39.2404	+	19.9664i	−1.44740	+	0.736473i
$736$	−18.9209	−	19.4422i	−0.697434	−	0.716649i
$737$	15.4215	+	15.4215i	0.568059	+	0.568059i
$738$	−10.7270	−	8.26906i	−0.394865	−	0.304388i
$739$	−3.87542	−	1.13793i	−0.142560	−	0.0418593i	0.209674	−	0.977771i	$-0.432760\pi$
$739$	−3.87542	−	1.13793i	−0.142560	−	0.0418593i	−0.352234	+	0.935912i	$0.614578\pi$
$740$	−29.3774	+	26.1865i	−1.07993	+	0.962634i
$741$	−3.22328	+	2.07148i	−0.118410	+	0.0760977i
$742$	15.8834	+	21.8544i	0.583097	+	0.802301i
$743$	−9.80302	+	7.33845i	−0.359638	+	0.269222i	−0.763783	−	0.645473i	$-0.776660\pi$
$743$	−9.80302	+	7.33845i	−0.359638	+	0.269222i	0.404145	+	0.914695i	$0.367569\pi$
$744$	21.6151	−	8.78479i	0.792447	−	0.322066i
$745$	27.7080	−	22.6309i	1.01514	−	0.829133i
$746$	23.7340	+	28.1852i	0.868964	+	1.03193i
$747$	0.504669	+	0.188232i	0.0184649	+	0.00688705i
$748$	21.0737	+	22.2992i	0.770532	+	0.815341i
$749$	5.17659	−	0.744281i	0.189148	−	0.0271954i
$750$	25.4130	−	17.8572i	0.927950	−	0.652053i
$751$	−8.83163	−	30.0778i	−0.322271	−	1.09755i	−0.948200	−	0.317674i	$-0.897098\pi$
$751$	−8.83163	−	30.0778i	−0.322271	−	1.09755i	0.625929	−	0.779880i	$-0.284720\pi$
$752$	−5.65141	+	20.3651i	−0.206086	+	0.742637i
$753$	0.958656	+	13.4038i	0.0349354	+	0.488460i
$754$	3.96694	+	1.87980i	0.144467	+	0.0684581i
$755$	−19.6458	+	8.28950i	−0.714986	+	0.301686i
$756$	−23.4612	+	25.5787i	−0.853274	+	0.930288i
$757$	13.0409	−	4.86402i	0.473981	−	0.176786i	−0.101110	−	0.994875i	$-0.532239\pi$
$757$	13.0409	−	4.86402i	0.473981	−	0.176786i	0.575091	+	0.818089i	$0.304967\pi$
$758$	−42.0553	−	9.77261i	−1.52752	−	0.354957i
$759$	−33.0534	+	9.19157i	−1.19976	+	0.333633i
$760$	−15.9113	−	24.7633i	−0.577164	−	0.898259i
$761$	−2.88592	+	6.31928i	−0.104614	+	0.229074i	−0.954699	−	0.297572i	$-0.903823\pi$
$761$	−2.88592	+	6.31928i	−0.104614	+	0.229074i	0.850085	+	0.526646i	$0.176550\pi$
$762$	−24.8425	−	14.0241i	−0.899949	−	0.508039i
$763$	−1.07778	+	15.0693i	−0.0390183	+	0.545547i
$764$	−0.871131	−	7.57134i	−0.0315164	−	0.273922i
$765$	1.94894	−	7.85120i	0.0704641	−	0.283861i
$766$	−18.8646	+	8.29522i	−0.681606	+	0.299718i
$767$	0.122435	−	0.224223i	0.00442086	−	0.00809621i
$768$	31.4029	+	1.30676i	1.13316	+	0.0471535i
$769$	−24.6419	+	3.54297i	−0.888610	+	0.127763i	−0.571477	−	0.820618i	$-0.693629\pi$
$769$	−24.6419	+	3.54297i	−0.888610	+	0.127763i	−0.317133	+	0.948381i	$0.602720\pi$
$770$	−37.2204	+	29.5339i	−1.34133	+	1.06433i
$771$	12.5313	−	5.72285i	0.451304	−	0.206103i
$772$	1.37054	+	2.68776i	0.0493269	+	0.0967346i
$773$	−48.1516	+	10.4747i	−1.73189	+	0.376750i	−0.964429	−	0.264341i	$-0.914846\pi$
$773$	−48.1516	+	10.4747i	−1.73189	+	0.376750i	−0.767465	+	0.641091i	$0.778482\pi$
$774$	−5.50822	+	6.17831i	−0.197989	+	0.222075i
$775$	15.0411	+	14.6502i	0.540293	+	0.526250i
$776$	−22.7459	−	16.0187i	−0.816531	−	0.575038i
$777$	−69.6926	−	15.1607i	−2.50021	−	0.543887i
$778$	12.2007	−	6.44008i	0.437415	−	0.230888i
$779$	−49.7987	−	14.6222i	−1.78422	−	0.523896i
$780$	3.43126	−	1.33494i	0.122859	−	0.0477987i
$781$	−54.1712			−1.93840
$782$	−9.21785	−	27.0432i	−0.329630	−	0.967063i
$783$	22.0282	+	22.0282i	0.787223	+	0.787223i
$784$	−9.10558	−	39.0463i	−0.325199	−	1.39451i
$785$	−4.01037	−	21.4200i	−0.143136	−	0.764514i
$786$	36.8966	+	11.4022i	1.31606	+	0.406705i
$787$	8.40490	−	38.6367i	0.299602	−	1.37725i	−0.543461	−	0.839435i	$-0.682886\pi$
$787$	8.40490	−	38.6367i	0.299602	−	1.37725i	0.843063	−	0.537815i	$-0.180750\pi$
$788$	40.6225	+	16.4728i	1.44712	+	0.586818i
$789$	49.1320	+	7.06411i	1.74914	+	0.251489i
$790$	−15.7076	−	4.13553i	−0.558850	−	0.147136i
$791$	2.72888	−	4.24622i	0.0970279	−	0.150978i
$792$	4.56436	−	7.57719i	0.162188	−	0.269244i
$793$	−0.966547	−	0.360504i	−0.0343231	−	0.0128019i
$794$	11.5510	−	17.4276i	0.409931	−	0.618483i
$795$	3.47920	−	20.0379i	0.123395	−	0.710672i
$796$	−15.7472	−	26.0953i	−0.558144	−	0.924924i
$797$	35.8793	+	19.5916i	1.27091	+	0.693969i	0.966032	−	0.258423i	$-0.0832027\pi$
$797$	35.8793	+	19.5916i	1.27091	+	0.693969i	0.304877	+	0.952392i	$0.401385\pi$
$798$	19.3461	−	49.7131i	0.684845	−	1.75982i
$799$	−14.5758	+	16.8213i	−0.515653	+	0.595095i
$800$	10.2530	+	26.3605i	0.362498	+	0.931985i
$801$	−3.88099	−	4.47890i	−0.137128	−	0.158254i
$802$	6.97968	+	3.94017i	0.246461	+	0.139132i
$803$	−35.0005	+	13.0545i	−1.23514	+	0.460684i
$804$	21.1179	+	10.3747i	0.744769	+	0.365889i
$805$	42.9554	−	10.6081i	1.51398	−	0.373888i
$806$	1.31592	+	2.11263i	0.0463513	+	0.0744143i
$807$	20.9887	+	56.2728i	0.738837	+	1.98090i
$808$	−31.7289	−	46.3554i	−1.11622	−	1.63078i
$809$	34.3737	−	29.7850i	1.20852	−	1.04718i	0.210947	−	0.977498i	$-0.432345\pi$
$809$	34.3737	−	29.7850i	1.20852	−	1.04718i	0.997569	−	0.0696872i	$-0.0222001\pi$
$810$	34.2619	−	0.965034i	1.20384	−	0.0339078i
$811$	−5.08328	−	4.40468i	−0.178498	−	0.154669i	0.561029	−	0.827796i	$-0.310405\pi$
$811$	−5.08328	−	4.40468i	−0.178498	−	0.154669i	−0.739527	+	0.673127i	$0.764951\pi$
$812$	−60.0636	+	11.2995i	−2.10782	+	0.396535i
$813$	25.5729	−	46.8332i	0.896880	−	1.64251i
$814$	−45.3158	−	0.640062i	−1.58832	−	0.0224342i
$815$	−21.9414	+	15.4492i	−0.768575	+	0.541164i
$816$	29.2847	+	15.4285i	1.02517	+	0.540107i
$817$	−11.0843	+	29.7182i	−0.387791	+	1.03971i
$818$	−26.1715	−	2.24375i	−0.915065	−	0.0784509i
$819$	1.24928	+	0.802862i	0.0436533	+	0.0280543i
$820$	44.1035	+	23.2848i	1.54016	+	0.813142i
$821$	−1.81817	+	12.6457i	−0.0634546	+	0.441337i	0.933183	+	0.359401i	$0.117019\pi$
$821$	−1.81817	+	12.6457i	−0.0634546	+	0.441337i	−0.996638	+	0.0819351i	$0.973890\pi$
$822$	−12.0225	−	16.5422i	−0.419334	−	0.576974i
$823$	19.4683	+	4.23506i	0.678622	+	0.147625i	0.538649	−	0.842530i	$-0.318935\pi$
$823$	19.4683	+	4.23506i	0.678622	+	0.147625i	0.139973	+	0.990155i	$0.455299\pi$
$824$	−11.2927	+	11.9681i	−0.393399	+	0.416929i
$825$	35.4680	+	4.62381i	1.23484	+	0.160980i
$826$	0.456418	+	3.52743i	0.0158808	+	0.122735i
$827$	22.3074	−	22.3074i	0.775703	−	0.775703i	−0.203394	−	0.979097i	$-0.565197\pi$
$827$	22.3074	−	22.3074i	0.775703	−	0.775703i	0.979097	+	0.203394i	$0.0651971\pi$
$828$	−6.79859	+	4.65098i	−0.236267	+	0.161633i
$829$		−	28.7699i		−	0.999220i	−0.866251	−	0.499610i	$-0.833477\pi$
$829$		−	28.7699i		−	0.999220i	0.866251	−	0.499610i	$-0.166523\pi$
$830$	−1.94914	−	0.366861i	−0.0676555	−	0.0127339i
$831$	11.2559	−	38.3341i	0.390463	−	1.32979i
$832$	0.432837	+	3.32475i	0.0150059	+	0.115265i
$833$	8.97548	−	41.2596i	0.310982	−	1.42956i
$834$	−9.95735	−	1.57549i	−0.344795	−	0.0545549i
$835$	3.71231	+	10.9134i	0.128470	+	0.377675i
$836$	5.76969	−	33.4021i	0.199549	−	1.15523i
$837$	3.75456	+	17.2594i	0.129776	+	0.596573i
$838$	3.30349	−	38.5325i	0.114117	−	1.33108i
$839$	−9.07119	−	19.8631i	−0.313172	−	0.685752i	0.685950	−	0.727649i	$-0.259387\pi$
$839$	−9.07119	−	19.8631i	−0.313172	−	0.685752i	−0.999122	+	0.0418973i	$0.986660\pi$
$840$	−27.7171	+	43.1203i	−0.956332	+	1.48779i
$841$	3.67960	+	25.5922i	0.126883	+	0.882490i
$842$	−14.3141	−	14.7242i	−0.493296	−	0.507431i
$843$	−3.68864	−	2.01415i	−0.127044	−	0.0693710i
$844$	0.945161	+	0.645851i	0.0325338	+	0.0222311i
$845$	−14.7946	−	24.5650i	−0.508949	−	0.845063i
$846$	5.79897	+	2.74793i	0.199373	+	0.0944759i
$847$	−9.30815	−	0.665732i	−0.319832	−	0.0228748i
$848$	16.9596	+	7.44172i	0.582395	+	0.255550i
$849$	−2.86677	−	1.30921i	−0.0983872	−	0.0449319i
$850$	−2.15348	+	29.7094i	−0.0738637	+	1.01902i
$851$	38.1331	+	18.0815i	1.30719	+	0.619825i
$852$	−55.3120	+	18.8686i	−1.89496	+	0.646429i
$853$	14.9323	+	40.0350i	0.511272	+	1.37077i	0.894479	+	0.447110i	$0.147547\pi$
$853$	14.9323	+	40.0350i	0.511272	+	1.37077i	−0.383207	+	0.923663i	$0.625180\pi$
$854$	13.8364	−	3.85133i	0.473472	−	0.131790i
$855$	−8.23419	+	3.47439i	−0.281603	+	0.118822i
$856$	2.80649	−	2.23090i	0.0959239	−	0.0762506i
$857$	16.0463	−	1.14765i	0.548131	−	0.0392031i	0.205472	−	0.978663i	$-0.434127\pi$
$857$	16.0463	−	1.14765i	0.548131	−	0.0392031i	0.342659	+	0.939460i	$0.388673\pi$
$858$	3.95129	+	1.53767i	0.134895	+	0.0524951i
$859$	23.5095	−	6.90300i	0.802133	−	0.235527i	0.145127	−	0.989413i	$-0.453641\pi$
$859$	23.5095	−	6.90300i	0.802133	−	0.235527i	0.657006	+	0.753886i	$0.271823\pi$
$860$	16.1165	−	25.8690i	0.549567	−	0.882124i
$861$	12.8632	+	89.4657i	0.438377	+	3.04898i
$862$	−33.2952	+	6.75190i	−1.13404	+	0.229971i
$863$	−18.5755	+	49.8028i	−0.632317	+	1.69531i	0.0830385	+	0.996546i	$0.473538\pi$
$863$	−18.5755	+	49.8028i	−0.632317	+	1.69531i	−0.715355	+	0.698761i	$0.753735\pi$
$864$	−5.03950	+	23.2537i	−0.171447	+	0.791108i
$865$	1.23530	+	0.124589i	0.0420016	+	0.00423616i
$866$	2.81416	−	3.15651i	0.0956289	−	0.107262i
$867$	0.877871	+	1.17270i	0.0298141	+	0.0398269i
$868$	−32.1128	−	13.0220i	−1.08998	−	0.441996i
$869$	−10.1128	−	15.7358i	−0.343053	−	0.533802i
$870$	37.5932	+	26.5238i	1.27453	+	0.899240i
$871$	−0.707128	+	2.40826i	−0.0239601	+	0.0816006i
$872$	4.57397	+	9.29198i	0.154894	+	0.314666i
$873$	−5.97300	+	5.97300i	−0.202155	+	0.202155i
$874$	−17.8149	+	26.0572i	−0.602598	+	0.881398i
$875$	−45.5495	−	7.29243i	−1.53985	−	0.246529i
$876$	−31.1905	+	25.5206i	−1.05383	+	0.862263i
$877$	0.000915862		0.00167728i	3.09265e−5		5.66376e-5i	0.877694	−	0.479221i	$-0.159081\pi$
$877$	0.000915862		0.00167728i	3.09265e−5		5.66376e-5i	−0.877664	+	0.479277i	$0.840899\pi$
$878$	6.62008	+	12.5417i	0.223417	+	0.423262i
$879$	3.02870	−	1.94643i	0.102156	−	0.0656514i
$880$	−11.8153	+	30.3536i	−0.398295	+	1.02322i
$881$	5.81664	−	40.4556i	0.195967	−	1.36298i	−0.619871	−	0.784704i	$-0.712815\pi$
$881$	5.81664	−	40.4556i	0.195967	−	1.36298i	0.815838	−	0.578280i	$-0.196276\pi$
$882$	−12.1537	+	0.696883i	−0.409237	+	0.0234653i
$883$	8.45845	+	38.8829i	0.284649	+	1.30851i	0.868110	+	0.496371i	$0.165334\pi$
$883$	8.45845	+	38.8829i	0.284649	+	1.30851i	−0.583461	+	0.812141i	$0.698302\pi$
$884$	−1.09008	+	3.35851i	−0.0366635	+	0.112959i
$885$	1.66631	−	2.09586i	0.0560124	−	0.0704514i
$886$	−5.16722	+	7.79603i	−0.173596	+	0.261913i
$887$	12.0044	+	8.98637i	0.403068	+	0.301733i	0.781511	−	0.623892i	$-0.214449\pi$
$887$	12.0044	+	8.98637i	0.403068	+	0.301733i	−0.378443	+	0.925625i	$0.623540\pi$
$888$	−46.4930	+	15.1306i	−1.56020	+	0.507751i
$889$	11.9367	+	40.6528i	0.400346	+	1.36345i
$890$	16.8882	+	13.8207i	0.566093	+	0.463271i
$891$	29.8306	+	25.8484i	0.999363	+	0.865953i
$892$	14.9418	+	11.8583i	0.500289	+	0.397045i
$893$	24.5275	+	1.75424i	0.820783	+	0.0587036i
$894$	42.8192	−	11.9186i	1.43209	−	0.398618i
$895$	8.64866	−	9.41280i	0.289093	−	0.314635i
$896$	−32.0887	−	33.9016i	−1.07201	−	1.13257i
$897$	−2.75146	−	2.83169i	−0.0918684	−	0.0945473i
$898$	−11.5916	+	49.8832i	−0.386817	+	1.66462i
$899$	−12.9203	+	28.2916i	−0.430917	+	0.943577i
$900$	8.41825	−	1.69873i	0.280608	−	0.0566244i
$901$	12.7728	+	14.7406i	0.425525	+	0.491082i
$902$	19.3090	+	54.0904i	0.642918	+	1.80101i
$903$	55.0962	−	3.94056i	1.83349	−	0.131134i
$904$	0.146566	−	3.45706i	0.00487470	−	0.114980i
$905$	−18.8781	−	0.549836i	−0.627530	−	0.0182772i
$906$	−26.4888	−	0.374141i	−0.880033	−	0.0124300i
$907$	−0.410636	−	0.307398i	−0.0136350	−	0.0102070i	0.592438	−	0.805616i	$-0.298165\pi$
$907$	−0.410636	−	0.307398i	−0.0136350	−	0.0102070i	−0.606073	+	0.795409i	$0.707256\pi$
$908$	15.3292	+	16.2207i	0.508719	+	0.538302i
$909$	−15.5148	+	7.08538i	−0.514594	+	0.235007i
$910$	−5.03602	−	2.13062i	−0.166942	−	0.0706294i
$911$	−19.6368	+	30.5554i	−0.650596	+	1.01235i	0.346636	+	0.938000i	$0.387324\pi$
$911$	−19.6368	+	30.5554i	−0.650596	+	1.01235i	−0.997232	+	0.0743475i	$0.976313\pi$
$912$	−5.74324	−	36.1151i	−0.190178	−	1.19589i
$913$	−1.36877	−	1.82846i	−0.0452997	−	0.0605133i
$914$	−4.34910	−	0.688133i	−0.143856	−	0.0227614i
$915$	−9.33443	−	5.45562i	−0.308587	−	0.180357i
$916$	13.7256	−	3.61241i	0.453505	−	0.119357i
$917$	−27.4876	−	50.3398i	−0.907721	−	1.66237i
$918$	−15.2985	+	19.8459i	−0.504926	+	0.655011i
$919$	−34.6122			−1.14175			−0.570876	−	0.821036i	$-0.693396\pi$
$919$	−34.6122			−1.14175			−0.570876	+	0.821036i	$0.693396\pi$
$920$	21.7554	−	21.1353i	0.717256	−	0.696810i
$921$	−28.2805			−0.931873
$922$	11.1333	−	14.4427i	0.366657	−	0.475643i
$923$	−2.98777	−	5.47170i	−0.0983438	−	0.180103i
$924$	−57.0870	+	15.0246i	−1.87802	+	0.494274i
$925$	−29.2488	−	32.8703i	−0.961694	−	1.08077i
$926$	50.7370	+	8.02782i	1.66732	+	0.263810i
$927$	2.99409	+	3.99963i	0.0983388	+	0.131365i
$928$	−31.6423	+	27.4616i	−1.03871	+	0.901470i
$929$	−12.5491	+	19.5267i	−0.411721	+	0.640651i	−0.983742	−	0.179588i	$-0.942523\pi$
$929$	−12.5491	+	19.5267i	−0.411721	+	0.640651i	0.572020	+	0.820239i	$0.306160\pi$
$930$	9.80066	+	24.1749i	0.321376	+	0.792727i
$931$	−42.4337	+	19.3788i	−1.39071	+	0.635116i
$932$	9.74238	+	10.3089i	0.319122	+	0.337680i
$933$	5.65131	+	4.23052i	0.185016	+	0.138501i
$934$	33.2812	+	0.470081i	1.08900	+	0.0153815i
$935$	−24.9518	+	23.5395i	−0.816011	+	0.769822i
$936$	1.01710	+	0.0431209i	0.0332449	+	0.00140945i
$937$	4.70185	−	0.336283i	0.153603	−	0.0109859i	0.00567400	−	0.999984i	$-0.498194\pi$
$937$	4.70185	−	0.336283i	0.153603	−	0.0109859i	0.147929	+	0.988998i	$0.452739\pi$
$938$	−11.7483	−	32.9106i	−0.383595	−	1.07457i
$939$	34.7556	+	40.1102i	1.13421	+	1.30895i
$940$	−22.7633	−	6.33828i	−0.742457	−	0.206732i
$941$	7.13602	−	15.6257i	0.232628	−	0.509383i	−0.756935	−	0.653491i	$-0.773304\pi$
$941$	7.13602	−	15.6257i	0.232628	−	0.509383i	0.989562	+	0.144108i	$0.0460311\pi$
$942$	6.12812	−	26.3717i	0.199665	−	0.859235i
$943$	4.58155	−	53.2861i	0.149196	−	1.73524i
$944$	1.49014	+	1.92995i	0.0485000	+	0.0628146i
$945$	−28.5750	−	26.2553i	−0.929545	−	0.854083i
$946$	33.8136	−	9.41193i	1.09937	−	0.306008i
$947$	22.5028	+	1.60943i	0.731243	+	0.0522995i	0.431995	−	0.901876i	$-0.357810\pi$
$947$	22.5028	+	1.60943i	0.731243	+	0.0522995i	0.299248	+	0.954175i	$0.403264\pi$
$948$	−15.8068	−	12.5448i	−0.513381	−	0.407435i
$949$	−3.24903	−	2.81530i	−0.105468	−	0.0913886i
$950$	27.7017	−	17.7653i	0.898761	−	0.576382i
$951$	−0.427218	−	1.45497i	−0.0138535	−	0.0471807i
$952$	−15.2134	−	46.7473i	−0.493068	−	1.51509i
$953$	−9.68988	−	7.25375i	−0.313886	−	0.234972i	0.430706	−	0.902493i	$-0.358265\pi$
$953$	−9.68988	−	7.25375i	−0.313886	−	0.234972i	−0.744591	+	0.667520i	$0.767356\pi$
$954$	3.10672	−	4.68726i	0.100584	−	0.151756i
$955$	8.46586	−	0.966587i	0.273949	−	0.0312780i
$956$	−13.1137	+	40.4027i	−0.424126	+	1.30672i
$957$	11.2623	+	51.7721i	0.364059	+	1.67355i
$958$	−3.74087	+	0.214498i	−0.120862	+	0.00693011i
$959$	−4.32233	+	30.0625i	−0.139575	+	0.970767i
$960$	−1.49155	+	35.1082i	−0.0481396	+	1.13311i
$961$	11.2438	−	7.22592i	0.362702	−	0.233094i
$962$	−2.43471	−	4.61254i	−0.0784982	−	0.148714i
$963$	−0.521690	−	0.955404i	−0.0168112	−	0.0307875i
$964$	−35.9154	+	29.3866i	−1.15676	+	0.946480i
$965$	−3.00634	+	1.52970i	−0.0967775	+	0.0492427i
$966$	54.1659	+	9.37005i	1.74276	+	0.301476i
$967$	4.97438	−	4.97438i	0.159965	−	0.159965i	−0.622586	−	0.782551i	$-0.713918\pi$
$967$	4.97438	−	4.97438i	0.159965	−	0.159965i	0.782551	+	0.622586i	$0.213918\pi$
$968$	−5.73954	+	2.82529i	−0.184476	+	0.0908081i
$969$	10.8502	−	36.9523i	0.348558	−	1.18708i
$970$	17.9316	−	25.4151i	0.575748	−	0.816030i
$971$	−3.21328	−	4.99996i	−0.103119	−	0.160456i	0.785860	−	0.618405i	$-0.212221\pi$
$971$	−3.21328	−	4.99996i	−0.103119	−	0.160456i	−0.888979	+	0.457948i	$0.848584\pi$
$972$	16.0750	+	6.51856i	0.515606	+	0.209083i
$973$	8.97273	+	11.9862i	0.287653	+	0.384259i
$974$	4.46811	−	5.01167i	0.143168	−	0.160584i
$975$	1.48917	+	3.83756i	0.0476918	+	0.122900i
$976$	6.85744	−	7.06498i	0.219501	−	0.226144i
$977$	2.90383	−	7.78546i	0.0929017	−	0.249079i	−0.882185	−	0.470903i	$-0.843928\pi$
$977$	2.90383	−	7.78546i	0.0929017	−	0.249079i	0.975087	+	0.221824i	$0.0712010\pi$
$978$	−32.6740	+	6.62594i	−1.04480	+	0.211874i
$979$	3.57648	+	24.8750i	0.114305	+	0.795007i
$980$	43.6639	−	10.1424i	1.39479	−	0.323986i
$981$	3.01723	−	0.885939i	0.0963328	−	0.0282859i
$982$	6.00985	+	2.33877i	0.191782	+	0.0746330i
$983$	−21.3953	+	1.53022i	−0.682404	+	0.0488065i	−0.408238	−	0.912876i	$-0.633857\pi$
$983$	−21.3953	+	1.53022i	−0.682404	+	0.0488065i	−0.274167	+	0.961682i	$0.588402\pi$
$984$	38.5561	+	48.5039i	1.22912	+	1.54625i
$985$	−18.4566	+	45.4013i	−0.588078	+	1.44661i
$986$	−42.5077	+	11.8319i	−1.35372	+	0.376805i
$987$	−14.9654	−	40.1237i	−0.476353	−	1.27715i
$988$	3.69208	−	1.25948i	0.117461	−	0.0400695i
$989$	−32.2818	−	5.11589i	−1.02650	−	0.162676i
$990$	8.46711	+	5.11048i	0.269102	+	0.162422i
$991$	−30.7791	−	14.0563i	−0.977729	−	0.446514i	−0.138542	−	0.990357i	$-0.544242\pi$
$991$	−30.7791	−	14.0563i	−0.977729	−	0.446514i	−0.839187	+	0.543843i	$0.816969\pi$
$992$	−23.5107	+	3.39909i	−0.746464	+	0.107921i
$993$	−46.7213	−	3.34158i	−1.48266	−	0.106042i
$994$	78.4366	+	37.1684i	2.48786	+	1.17891i
$995$	29.1908	−	17.5805i	0.925409	−	0.557339i
$996$	−2.03448	−	1.39021i	−0.0644649	−	0.0440504i
$997$	−52.4355	−	28.6319i	−1.66065	−	0.906783i	−0.985617	−	0.168994i	$-0.945948\pi$
$997$	−52.4355	−	28.6319i	−1.66065	−	0.906783i	−0.675031	−	0.737789i	$-0.735870\pi$
$998$	−16.2399	−	16.7053i	−0.514067	−	0.528796i
$999$	−5.26759	−	36.6369i	−0.166659	−	1.15914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.167.48	yes	1360
4.3	odd	2	inner	460.2.w.a.167.64	yes	1360
5.3	odd	4	inner	460.2.w.a.443.13	yes	1360
20.3	even	4	inner	460.2.w.a.443.38	yes	1360
23.4	even	11	inner	460.2.w.a.27.38	yes	1360
92.27	odd	22	inner	460.2.w.a.27.13	✓	1360
115.73	odd	44	inner	460.2.w.a.303.64	yes	1360
460.303	even	44	inner	460.2.w.a.303.48	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.27.13	✓	1360	92.27	odd	22	inner
460.2.w.a.27.38	yes	1360	23.4	even	11	inner
460.2.w.a.167.48	yes	1360	1.1	even	1	trivial
460.2.w.a.167.64	yes	1360	4.3	odd	2	inner
460.2.w.a.303.48	yes	1360	460.303	even	44	inner
460.2.w.a.303.64	yes	1360	115.73	odd	44	inner
460.2.w.a.443.13	yes	1360	5.3	odd	4	inner
460.2.w.a.443.38	yes	1360	20.3	even	4	inner

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.863411 - 1.12005i) q^{2} +(0.941428 + 1.72410i) q^{3} +(-0.509042 - 1.93413i) q^{4} +(2.16292 - 0.567244i) q^{5} +(2.74392 + 0.434154i) q^{6} +(-2.47259 - 3.30299i) q^{7} +(-2.60585 - 1.09980i) q^{8} +(-0.464299 + 0.722463i) q^{9} +O(q^{10})\)	\(q+(0.863411 - 1.12005i) q^{2} +(0.941428 + 1.72410i) q^{3} +(-0.509042 - 1.93413i) q^{4} +(2.16292 - 0.567244i) q^{5} +(2.74392 + 0.434154i) q^{6} +(-2.47259 - 3.30299i) q^{7} +(-2.60585 - 1.09980i) q^{8} +(-0.464299 + 0.722463i) q^{9} +(1.23215 - 2.91235i) q^{10} +(3.31258 - 1.51280i) q^{11} +(2.85541 - 2.69848i) q^{12} +(0.335508 + 0.251158i) q^{13} +(-5.83440 - 0.0824079i) q^{14} +(3.01422 + 3.19507i) q^{15} +(-3.48175 + 1.96911i) q^{16} +(-4.20183 + 0.300521i) q^{17} +(0.408317 + 1.14382i) q^{18} +(3.04773 + 3.51726i) q^{19} +(-2.19814 - 3.89463i) q^{20} +(3.36692 - 7.37252i) q^{21} +(1.16570 - 5.01644i) q^{22} +(-2.92890 + 3.79757i) q^{23} +(-0.557057 - 5.52811i) q^{24} +(4.35647 - 2.45381i) q^{25} +(0.570992 - 0.158934i) q^{26} +(4.19543 + 0.300063i) q^{27} +(-5.12978 + 6.46369i) q^{28} +(5.59741 + 4.85019i) q^{29} +(6.18116 - 0.617430i) q^{30} +(1.18309 + 4.02924i) q^{31} +(-0.800675 + 5.59990i) q^{32} +(5.72677 + 4.28701i) q^{33} +(-3.29131 + 4.96575i) q^{34} +(-7.22163 - 5.74156i) q^{35} +(1.63369 + 0.530252i) q^{36} +(-1.87055 - 8.59878i) q^{37} +(6.57096 - 0.376772i) q^{38} +(-0.117164 + 0.814895i) q^{39} +(-6.26010 - 0.900630i) q^{40} +(-9.38159 + 6.02918i) q^{41} +(-5.35058 - 10.1366i) q^{42} +(3.26619 + 5.98157i) q^{43} +(-4.61221 - 5.63689i) q^{44} +(-0.594430 + 1.82600i) q^{45} +(1.72463 + 6.55939i) q^{46} +(3.73612 - 3.73612i) q^{47} +(-6.67275 - 4.14910i) q^{48} +(-2.82394 + 9.61746i) q^{49} +(1.01303 - 6.99813i) q^{50} +(-4.47385 - 6.96145i) q^{51} +(0.314986 - 0.776767i) q^{52} +(-2.77472 - 3.70660i) q^{53} +(3.95847 - 4.44003i) q^{54} +(6.30672 - 5.15112i) q^{55} +(2.81056 + 11.3265i) q^{56} +(-3.19489 + 8.56582i) q^{57} +(10.2653 - 2.08170i) q^{58} +(-0.0867511 - 0.603367i) q^{59} +(4.64533 - 7.45633i) q^{60} +(-2.36173 + 0.693466i) q^{61} +(5.53447 + 2.15377i) q^{62} +(3.53431 - 0.252779i) q^{63} +(5.58088 + 5.73182i) q^{64} +(0.868145 + 0.352921i) q^{65} +(9.74624 - 2.71284i) q^{66} +(2.09288 + 5.61123i) q^{67} +(2.72016 + 7.97393i) q^{68} +(-9.30472 - 1.47458i) q^{69} +(-12.6661 + 3.13128i) q^{70} +(-13.5311 - 6.17945i) q^{71} +(2.00446 - 1.37199i) q^{72} +(-10.2317 - 0.731789i) q^{73} +(-11.2462 - 5.32917i) q^{74} +(8.33190 + 5.20089i) q^{75} +(5.25144 - 7.68514i) q^{76} +(-13.1874 - 7.20089i) q^{77} +(0.811565 + 0.834820i) q^{78} +(-0.730992 - 5.08416i) q^{79} +(-6.41380 + 6.23404i) q^{80} +(4.50262 + 9.85937i) q^{81} +(-1.34716 + 15.7136i) q^{82} +(-0.133320 - 0.612861i) q^{83} +(-15.9733 - 2.75915i) q^{84} +(-8.91777 + 3.03347i) q^{85} +(9.51975 + 1.50625i) q^{86} +(-3.09263 + 14.2166i) q^{87} +(-10.2959 + 0.298964i) q^{88} +(-1.94420 + 6.62135i) q^{89} +(1.53198 + 2.24238i) q^{90} -1.72919i q^{91} +(8.83594 + 3.73177i) q^{92} +(-5.83301 + 5.83301i) q^{93} +(-0.958846 - 7.41045i) q^{94} +(8.58714 + 5.87876i) q^{95} +(-10.4085 + 3.89146i) q^{96} +(9.61122 + 2.09079i) q^{97} +(8.33385 + 11.4668i) q^{98} +(-0.445081 + 3.09561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

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