LMFDB - Embedded newform 285.2.k.d.77.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(77,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("285.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.k (of order $4$, degree $2$, 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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.11
Character	$\chi$	$=$	285.77
Dual form			285.2.k.d.248.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.538497 - 0.538497i) q^{2} +(-0.777077 - 1.54795i) q^{3} +1.42004i q^{4} +(-1.01787 + 1.99096i) q^{5} +(-1.25202 - 0.415113i) q^{6} +(1.88175 + 1.88175i) q^{7} +(1.84168 + 1.84168i) q^{8} +(-1.79230 + 2.40575i) q^{9} +O(q^{10})$	\(q+(0.538497 - 0.538497i) q^{2} +(-0.777077 - 1.54795i) q^{3} +1.42004i q^{4} +(-1.01787 + 1.99096i) q^{5} +(-1.25202 - 0.415113i) q^{6} +(1.88175 + 1.88175i) q^{7} +(1.84168 + 1.84168i) q^{8} +(-1.79230 + 2.40575i) q^{9} +(0.524007 + 1.62025i) q^{10} +1.35850i q^{11} +(2.19815 - 1.10348i) q^{12} +(1.03932 - 1.03932i) q^{13} +2.02663 q^{14} +(3.87288 + 0.0284829i) q^{15} -0.856600 q^{16} +(1.42628 - 1.42628i) q^{17} +(0.330342 + 2.26064i) q^{18} +1.00000i q^{19} +(-2.82725 - 1.44542i) q^{20} +(1.45059 - 4.37511i) q^{21} +(0.731550 + 0.731550i) q^{22} +(1.15037 + 1.15037i) q^{23} +(1.41970 - 4.28196i) q^{24} +(-2.92787 - 4.05309i) q^{25} -1.11935i q^{26} +(5.11675 + 0.904938i) q^{27} +(-2.67216 + 2.67216i) q^{28} +4.57000 q^{29} +(2.10087 - 2.07020i) q^{30} -4.81716 q^{31} +(-4.14464 + 4.14464i) q^{32} +(2.10290 - 1.05566i) q^{33} -1.53609i q^{34} +(-5.66187 + 1.83111i) q^{35} +(-3.41627 - 2.54514i) q^{36} +(2.99094 + 2.99094i) q^{37} +(0.538497 + 0.538497i) q^{38} +(-2.41645 - 0.801186i) q^{39} +(-5.54132 + 1.79213i) q^{40} -8.00113i q^{41} +(-1.57485 - 3.13713i) q^{42} +(5.08869 - 5.08869i) q^{43} -1.92913 q^{44} +(-2.96544 - 6.01716i) q^{45} +1.23894 q^{46} +(-6.64580 + 6.64580i) q^{47} +(0.665644 + 1.32597i) q^{48} +0.0819438i q^{49} +(-3.75923 - 0.605928i) q^{50} +(-3.31613 - 1.09948i) q^{51} +(1.47588 + 1.47588i) q^{52} +(7.34782 + 7.34782i) q^{53} +(3.24266 - 2.26805i) q^{54} +(-2.70473 - 1.38278i) q^{55} +6.93116i q^{56} +(1.54795 - 0.777077i) q^{57} +(2.46093 - 2.46093i) q^{58} -1.44815 q^{59} +(-0.0404469 + 5.49965i) q^{60} -8.86625 q^{61} +(-2.59403 + 2.59403i) q^{62} +(-7.89968 + 1.15436i) q^{63} +2.75056i q^{64} +(1.01136 + 3.12715i) q^{65} +(0.563933 - 1.70087i) q^{66} +(-2.63849 - 2.63849i) q^{67} +(2.02537 + 2.02537i) q^{68} +(0.886786 - 2.67463i) q^{69} +(-2.06285 + 4.03495i) q^{70} +4.15837i q^{71} +(-7.73149 + 1.12978i) q^{72} +(10.4907 - 10.4907i) q^{73} +3.22123 q^{74} +(-3.99880 + 7.68177i) q^{75} -1.42004 q^{76} +(-2.55636 + 2.55636i) q^{77} +(-1.73269 + 0.869818i) q^{78} -13.1425i q^{79} +(0.871909 - 1.70546i) q^{80} +(-2.57531 - 8.62368i) q^{81} +(-4.30858 - 4.30858i) q^{82} +(-5.76879 - 5.76879i) q^{83} +(6.21284 + 2.05990i) q^{84} +(1.38790 + 4.29143i) q^{85} -5.48049i q^{86} +(-3.55125 - 7.07414i) q^{87} +(-2.50193 + 2.50193i) q^{88} +15.3007 q^{89} +(-4.83710 - 1.64334i) q^{90} +3.91149 q^{91} +(-1.63357 + 1.63357i) q^{92} +(3.74331 + 7.45673i) q^{93} +7.15749i q^{94} +(-1.99096 - 1.01787i) q^{95} +(9.63641 + 3.19499i) q^{96} +(-6.91795 - 6.91795i) q^{97} +(0.0441265 + 0.0441265i) q^{98} +(-3.26823 - 2.43485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) $ 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7	$ 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) $ 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^10 - 18 * q^12 - 8 * q^13 - 8 * q^15 - 84 * q^16 + 8 * q^21 + 40 * q^22 - 20 * q^25 - 14 * q^27 + 36 * q^28 + 28 * q^30 - 28 * q^33 + 92 * q^36 - 4 * q^37 - 20 * q^40 - 100 * q^42 + 16 * q^43 + 28 * q^45 - 24 * q^46 - 58 * q^48 + 32 * q^51 + 148 * q^52 - 72 * q^55 - 2 * q^57 - 12 * q^58 + 58 * q^60 - 112 * q^61 - 64 * q^63 + 92 * q^66 - 8 * q^67 + 8 * q^70 - 88 * q^72 + 76 * q^73 + 80 * q^75 + 36 * q^76 - 36 * q^78 + 4 * q^81 + 20 * q^82 - 28 * q^85 - 4 * q^87 + 140 * q^88 + 76 * q^90 - 24 * q^91 - 48 * q^93 + 32 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	0.538497	−	0.538497i	0.380775	−	0.380775i	−0.490606	−	0.871381i	$-0.663225\pi$
$2$	0.538497	−	0.538497i	0.380775	−	0.380775i	0.871381	+	0.490606i	$0.163225\pi$
$3$	−0.777077	−	1.54795i	−0.448646	−	0.893710i
$3$	−0.777077	−	1.54795i	−0.448646	−	0.893710i
$4$			1.42004i			0.710021i
$5$	−1.01787	+	1.99096i	−0.455206	+	0.890386i
$5$	−1.01787	+	1.99096i	−0.455206	+	0.890386i
$6$	−1.25202	−	0.415113i	−0.511136	−	0.169469i
$7$	1.88175	+	1.88175i	0.711234	+	0.711234i	0.966793	−	0.255560i	$-0.0822597\pi$
$7$	1.88175	+	1.88175i	0.711234	+	0.711234i	−0.255560	+	0.966793i	$0.582260\pi$
$8$	1.84168	+	1.84168i	0.651133	+	0.651133i
$9$	−1.79230	+	2.40575i	−0.597434	+	0.801918i
$10$	0.524007	+	1.62025i	0.165706	+	0.512368i
$11$			1.35850i			0.409604i	0.978803	+	0.204802i	$0.0656551\pi$
$11$			1.35850i			0.409604i	−0.978803	+	0.204802i	$0.934345\pi$
$12$	2.19815	−	1.10348i	0.634552	−	0.318548i
$13$	1.03932	−	1.03932i	0.288256	−	0.288256i	−0.548134	−	0.836390i	$-0.684662\pi$
$13$	1.03932	−	1.03932i	0.288256	−	0.288256i	0.836390	+	0.548134i	$0.184662\pi$
$14$	2.02663			0.541640
$15$	3.87288	+	0.0284829i	0.999973	+	0.00735426i
$16$	−0.856600			−0.214150
$17$	1.42628	−	1.42628i	0.345923	−	0.345923i	−0.512665	−	0.858588i	$-0.671342\pi$
$17$	1.42628	−	1.42628i	0.345923	−	0.345923i	0.858588	+	0.512665i	$0.171342\pi$
$18$	0.330342	+	2.26064i	0.0778625	+	0.532838i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−2.82725	−	1.44542i	−0.632192	−	0.323206i
$21$	1.45059	−	4.37511i	0.316544	−	0.954728i
$22$	0.731550	+	0.731550i	0.155967	+	0.155967i
$23$	1.15037	+	1.15037i	0.239868	+	0.239868i	0.816795	−	0.576928i	$-0.195749\pi$
$23$	1.15037	+	1.15037i	0.239868	+	0.239868i	−0.576928	+	0.816795i	$0.695749\pi$
$24$	1.41970	−	4.28196i	0.289796	−	0.874052i
$25$	−2.92787	−	4.05309i	−0.585575	−	0.810618i
$26$		−	1.11935i		−	0.219522i
$27$	5.11675	+	0.904938i	0.984718	+	0.174155i
$28$	−2.67216	+	2.67216i	−0.504990	+	0.504990i
$29$	4.57000			0.848628			0.424314	−	0.905515i	$-0.360515\pi$
$29$	4.57000			0.848628			0.424314	+	0.905515i	$0.360515\pi$
$30$	2.10087	−	2.07020i	0.383565	−	0.377964i
$31$	−4.81716			−0.865188			−0.432594	−	0.901589i	$-0.642402\pi$
$31$	−4.81716			−0.865188			−0.432594	+	0.901589i	$0.642402\pi$
$32$	−4.14464	+	4.14464i	−0.732676	+	0.732676i
$33$	2.10290	−	1.05566i	0.366067	−	0.183767i
$34$		−	1.53609i		−	0.263438i
$35$	−5.66187	+	1.83111i	−0.957030	+	0.309515i
$36$	−3.41627	−	2.54514i	−0.569378	−	0.424190i
$37$	2.99094	+	2.99094i	0.491708	+	0.491708i	0.908844	−	0.417136i	$-0.136966\pi$
$37$	2.99094	+	2.99094i	0.491708	+	0.491708i	−0.417136	+	0.908844i	$0.636966\pi$
$38$	0.538497	+	0.538497i	0.0873558	+	0.0873558i
$39$	−2.41645	−	0.801186i	−0.386942	−	0.128292i
$40$	−5.54132	+	1.79213i	−0.876160	+	0.283360i
$41$		−	8.00113i		−	1.24957i	−0.780798	−	0.624783i	$-0.785187\pi$
$41$		−	8.00113i		−	1.24957i	0.780798	−	0.624783i	$-0.214813\pi$
$42$	−1.57485	−	3.13713i	−0.243005	−	0.484069i
$43$	5.08869	−	5.08869i	0.776018	−	0.776018i	−0.203133	−	0.979151i	$-0.565113\pi$
$43$	5.08869	−	5.08869i	0.776018	−	0.776018i	0.979151	+	0.203133i	$0.0651125\pi$
$44$	−1.92913			−0.290827
$45$	−2.96544	−	6.01716i	−0.442061	−	0.896985i
$46$	1.23894			0.182671
$47$	−6.64580	+	6.64580i	−0.969389	+	0.969389i	−0.999545	−	0.0301564i	$-0.990399\pi$
$47$	−6.64580	+	6.64580i	−0.969389	+	0.969389i	0.0301564	+	0.999545i	$0.490399\pi$
$48$	0.665644	+	1.32597i	0.0960775	+	0.191388i
$49$			0.0819438i			0.0117063i
$50$	−3.75923	−	0.605928i	−0.531636	−	0.0856911i
$51$	−3.31613	−	1.09948i	−0.464352	−	0.153958i
$52$	1.47588	+	1.47588i	0.204668	+	0.204668i
$53$	7.34782	+	7.34782i	1.00930	+	1.00930i	0.999956	+	0.00934447i	$0.00297448\pi$
$53$	7.34782	+	7.34782i	1.00930	+	1.00930i	0.00934447	+	0.999956i	$0.497026\pi$
$54$	3.24266	−	2.26805i	0.441270	−	0.308642i
$55$	−2.70473	−	1.38278i	−0.364706	−	0.186454i
$56$			6.93116i			0.926216i
$57$	1.54795	−	0.777077i	0.205031	−	0.102926i
$58$	2.46093	−	2.46093i	0.323137	−	0.323137i
$59$	−1.44815			−0.188533			−0.0942667	−	0.995547i	$-0.530051\pi$
$59$	−1.44815			−0.188533			−0.0942667	+	0.995547i	$0.530051\pi$
$60$	−0.0404469	+	5.49965i	−0.00522167	+	0.710001i
$61$	−8.86625			−1.13521			−0.567603	−	0.823302i	$-0.692129\pi$
$61$	−8.86625			−1.13521			−0.567603	+	0.823302i	$0.692129\pi$
$62$	−2.59403	+	2.59403i	−0.329442	+	0.329442i
$63$	−7.89968	+	1.15436i	−0.995266	+	0.145436i
$64$			2.75056i			0.343820i
$65$	1.01136	+	3.12715i	0.125443	+	0.387875i
$66$	0.563933	−	1.70087i	0.0694153	−	0.209363i
$67$	−2.63849	−	2.63849i	−0.322343	−	0.322343i	0.527322	−	0.849665i	$-0.323196\pi$
$67$	−2.63849	−	2.63849i	−0.322343	−	0.322343i	−0.849665	+	0.527322i	$0.823196\pi$
$68$	2.02537	+	2.02537i	0.245612	+	0.245612i
$69$	0.886786	−	2.67463i	0.106756	−	0.321988i
$70$	−2.06285	+	4.03495i	−0.246558	+	0.482269i
$71$			4.15837i			0.493508i	0.969078	+	0.246754i	$0.0793639\pi$
$71$			4.15837i			0.493508i	−0.969078	+	0.246754i	$0.920636\pi$
$72$	−7.73149	+	1.12978i	−0.911165	+	0.133146i
$73$	10.4907	−	10.4907i	1.22785	−	1.22785i	0.263068	−	0.964777i	$-0.415266\pi$
$73$	10.4907	−	10.4907i	1.22785	−	1.22785i	0.964777	−	0.263068i	$-0.0847344\pi$
$74$	3.22123			0.374460
$75$	−3.99880	+	7.68177i	−0.461742	+	0.887014i
$76$	−1.42004			−0.162890
$77$	−2.55636	+	2.55636i	−0.291324	+	0.291324i
$78$	−1.73269	+	0.869818i	−0.196189	+	0.0984875i
$79$		−	13.1425i		−	1.47865i	−0.673349	−	0.739325i	$-0.735145\pi$
$79$		−	13.1425i		−	1.47865i	0.673349	−	0.739325i	$-0.264855\pi$
$80$	0.871909	−	1.70546i	0.0974824	−	0.190676i
$81$	−2.57531	−	8.62368i	−0.286145	−	0.958186i
$82$	−4.30858	−	4.30858i	−0.475804	−	0.475804i
$83$	−5.76879	−	5.76879i	−0.633207	−	0.633207i	0.315664	−	0.948871i	$-0.397773\pi$
$83$	−5.76879	−	5.76879i	−0.633207	−	0.633207i	−0.948871	+	0.315664i	$0.897773\pi$
$84$	6.21284	+	2.05990i	0.677877	+	0.224753i
$85$	1.38790	+	4.29143i	0.150539	+	0.465471i
$86$		−	5.48049i		−	0.590976i
$87$	−3.55125	−	7.07414i	−0.380734	−	0.758427i
$88$	−2.50193	+	2.50193i	−0.266707	+	0.266707i
$89$	15.3007			1.62187			0.810935	−	0.585137i	$-0.198959\pi$
$89$	15.3007			1.62187			0.810935	+	0.585137i	$0.198959\pi$
$90$	−4.83710	−	1.64334i	−0.509875	−	0.173224i
$91$	3.91149			0.410035
$92$	−1.63357	+	1.63357i	−0.170311	+	0.170311i
$93$	3.74331	+	7.45673i	0.388163	+	0.773227i
$94$			7.15749i			0.738238i
$95$	−1.99096	−	1.01787i	−0.204269	−	0.104431i
$96$	9.63641	+	3.19499i	0.983512	+	0.326088i
$97$	−6.91795	−	6.91795i	−0.702412	−	0.702412i	0.262516	−	0.964928i	$-0.415448\pi$
$97$	−6.91795	−	6.91795i	−0.702412	−	0.702412i	−0.964928	+	0.262516i	$0.915448\pi$
$98$	0.0441265	+	0.0441265i	0.00445745	+	0.00445745i
$99$	−3.26823	−	2.43485i	−0.328469	−	0.244711i
$100$	5.75556	−	4.15770i	0.575556	−	0.415770i
$101$		−	10.3771i		−	1.03256i	−0.856420	−	0.516280i	$-0.827316\pi$
$101$		−	10.3771i		−	1.03256i	0.856420	−	0.516280i	$-0.172684\pi$
$102$	−2.37780	+	1.19366i	−0.235437	+	0.118190i
$103$	12.0754	−	12.0754i	1.18983	−	1.18983i	0.212711	−	0.977115i	$-0.431771\pi$
$103$	12.0754	−	12.0754i	1.18983	−	1.18983i	0.977115	−	0.212711i	$-0.0682292\pi$
$104$	3.82821			0.375387
$105$	7.23418	+	7.34138i	0.705984	+	0.716445i
$106$	7.91356			0.768633
$107$	2.52880	−	2.52880i	0.244468	−	0.244468i	−0.574227	−	0.818696i	$-0.694697\pi$
$107$	2.52880	−	2.52880i	0.244468	−	0.244468i	0.818696	+	0.574227i	$0.194697\pi$
$108$	−1.28505	+	7.26599i	−0.123654	+	0.699170i
$109$			16.1197i			1.54399i	0.635631	+	0.771993i	$0.280740\pi$
$109$			16.1197i			1.54399i	−0.635631	+	0.771993i	$0.719260\pi$
$110$	−2.20111	+	0.711866i	−0.209868	+	0.0678737i
$111$	2.30564	−	6.95402i	0.218841	−	0.660046i
$112$	−1.61190	−	1.61190i	−0.152311	−	0.152311i
$113$	−3.45958	−	3.45958i	−0.325449	−	0.325449i	0.525404	−	0.850853i	$-0.323914\pi$
$113$	−3.45958	−	3.45958i	−0.325449	−	0.325449i	−0.850853	+	0.525404i	$0.823914\pi$
$114$	0.415113	−	1.25202i	0.0388789	−	0.117263i
$115$	−3.46126	+	1.11941i	−0.322764	+	0.104386i
$116$			6.48959i			0.602544i
$117$	0.637575	+	4.36314i	0.0589438	+	0.403372i
$118$	−0.779826	+	0.779826i	−0.0717888	+	0.0717888i
$119$	5.36779			0.492064
$120$	7.08016	+	7.18507i	0.646327	+	0.655904i
$121$	9.15447			0.832224
$122$	−4.77445	+	4.77445i	−0.432258	+	0.432258i
$123$	−12.3853	+	6.21749i	−1.11675	+	0.560612i
$124$		−	6.84057i		−	0.614301i
$125$	11.0498	−	1.70376i	0.988321	−	0.152389i
$126$	−3.63234	+	4.87558i	−0.323594	+	0.434351i
$127$	5.66599	+	5.66599i	0.502775	+	0.502775i	0.912299	−	0.409524i	$-0.134305\pi$
$127$	5.66599	+	5.66599i	0.502775	+	0.502775i	−0.409524	+	0.912299i	$0.634305\pi$
$128$	−6.80812	−	6.80812i	−0.601758	−	0.601758i
$129$	−11.8313	−	3.92273i	−1.04169	−	0.345377i
$130$	2.22858	+	1.13935i	0.195459	+	0.0999276i
$131$		−	2.41624i		−	0.211108i	−0.994414	−	0.105554i	$-0.966338\pi$
$131$		−	2.41624i		−	0.211108i	0.994414	−	0.105554i	$-0.0336616\pi$
$132$	1.49908	+	2.98620i	0.130478	+	0.259915i
$133$	−1.88175	+	1.88175i	−0.163168	+	0.163168i
$134$	−2.84164			−0.245480
$135$	−7.00989	+	9.26614i	−0.603315	+	0.797503i
$136$	5.25350			0.450484
$137$	8.01837	−	8.01837i	0.685056	−	0.685056i	−0.276079	−	0.961135i	$-0.589035\pi$
$137$	8.01837	−	8.01837i	0.685056	−	0.685056i	0.961135	+	0.276079i	$0.0890352\pi$
$138$	−0.962750	−	1.91781i	−0.0819547	−	0.163255i
$139$			12.9146i			1.09540i	0.836673	+	0.547702i	$0.184497\pi$
$139$			12.9146i			1.09540i	−0.836673	+	0.547702i	$0.815503\pi$
$140$	−2.60026	−	8.04009i	−0.219762	−	0.679511i
$141$	15.4517	+	5.12307i	1.30126	+	0.431440i
$142$	2.23927	+	2.23927i	0.187915	+	0.187915i
$143$	1.41192	+	1.41192i	0.118071	+	0.118071i
$144$	1.53529	−	2.06077i	0.127940	−	0.171731i
$145$	−4.65168	+	9.09871i	−0.386301	+	0.755607i
$146$		−	11.2984i		−	0.935066i
$147$	0.126845	−	0.0636766i	0.0104620	−	0.00525196i
$148$	−4.24726	+	4.24726i	−0.349123	+	0.349123i
$149$	−20.4717			−1.67711			−0.838553	−	0.544820i	$-0.816598\pi$
$149$	−20.4717			−1.67711			−0.838553	+	0.544820i	$0.816598\pi$
$150$	1.98327	+	6.28996i	0.161933	+	0.513573i
$151$	−20.5637			−1.67345			−0.836727	−	0.547620i	$-0.815534\pi$
$151$	−20.5637			−1.67345			−0.836727	+	0.547620i	$0.815534\pi$
$152$	−1.84168	+	1.84168i	−0.149380	+	0.149380i
$153$	0.874953	+	5.98759i	0.0707358	+	0.484068i
$154$			2.75319i			0.221858i
$155$	4.90325	−	9.59080i	0.393839	−	0.770351i
$156$	1.13772	−	3.43147i	0.0910903	−	0.274737i
$157$	13.4944	+	13.4944i	1.07697	+	1.07697i	0.996779	+	0.0801951i	$0.0255543\pi$
$157$	13.4944	+	13.4944i	1.07697	+	1.07697i	0.0801951	+	0.996779i	$0.474446\pi$
$158$	−7.07722	−	7.07722i	−0.563033	−	0.563033i
$159$	5.66424	−	17.0839i	0.449203	−	1.35484i
$160$	−4.03312	−	12.4705i	−0.318846	−	0.985883i
$161$			4.32939i			0.341204i
$162$	−6.03062	−	3.25703i	−0.473810	−	0.255896i
$163$	−17.7892	+	17.7892i	−1.39336	+	1.39336i	−0.575692	+	0.817667i	$0.695267\pi$
$163$	−17.7892	+	17.7892i	−1.39336	+	1.39336i	−0.817667	+	0.575692i	$0.804733\pi$
$164$	11.3619			0.887218
$165$	−0.0386941	+	5.26132i	−0.00301233	+	0.409593i
$166$	−6.21295			−0.482219
$167$	11.9087	−	11.9087i	0.921524	−	0.921524i	−0.0756134	−	0.997137i	$-0.524091\pi$
$167$	11.9087	−	11.9087i	0.921524	−	0.921524i	0.997137	+	0.0756134i	$0.0240915\pi$
$168$	10.7291	−	5.38605i	0.827768	−	0.415543i
$169$			10.8396i			0.833817i
$170$	3.05830	+	1.56355i	0.234561	+	0.119918i
$171$	−2.40575	−	1.79230i	−0.183973	−	0.137061i
$172$	7.22615	+	7.22615i	0.550989	+	0.550989i
$173$	11.4812	+	11.4812i	0.872902	+	0.872902i	0.992788	−	0.119886i	$-0.0382528\pi$
$173$	11.4812	+	11.4812i	0.872902	+	0.872902i	−0.119886	+	0.992788i	$0.538253\pi$
$174$	−5.72174	−	1.89707i	−0.433764	−	0.143816i
$175$	2.11738	−	13.1364i	0.160059	−	0.993019i
$176$		−	1.16369i		−	0.0877167i
$177$	1.12533	+	2.24167i	0.0845847	+	0.168494i
$178$	8.23938	−	8.23938i	0.617567	−	0.617567i
$179$	0.0965741			0.00721829			0.00360914	−	0.999993i	$-0.498851\pi$
$179$	0.0965741			0.00721829			0.00360914	+	0.999993i	$0.498851\pi$
$180$	8.54461	−	4.21104i	0.636878	−	0.313872i
$181$	5.94681			0.442023			0.221011	−	0.975271i	$-0.429064\pi$
$181$	5.94681			0.442023			0.221011	+	0.975271i	$0.429064\pi$
$182$	2.10632	−	2.10632i	0.156131	−	0.156131i
$183$	6.88976	+	13.7245i	0.509306	+	1.01455i
$184$			4.23722i			0.312372i
$185$	−8.99925	+	2.91046i	−0.661638	+	0.213981i
$186$	6.03119	+	1.99967i	0.442228	+	0.146623i
$187$	1.93760	+	1.93760i	0.141691	+	0.141691i
$188$	−9.43730	−	9.43730i	−0.688286	−	0.688286i
$189$	7.92556	+	11.3313i	0.576499	+	0.824230i
$190$	−1.62025	+	0.524007i	−0.117545	+	0.0380155i
$191$			14.8626i			1.07542i	0.843130	+	0.537710i	$0.180710\pi$
$191$			14.8626i			1.07542i	−0.843130	+	0.537710i	$0.819290\pi$
$192$	4.25773	−	2.13740i	0.307275	−	0.154253i
$193$	6.65613	−	6.65613i	0.479119	−	0.479119i	−0.425731	−	0.904850i	$-0.639983\pi$
$193$	6.65613	−	6.65613i	0.479119	−	0.479119i	0.904850	+	0.425731i	$0.139983\pi$
$194$	−7.45060			−0.534922
$195$	4.05477	−	3.99557i	0.290368	−	0.286129i
$196$	−0.116364			−0.00831168
$197$	8.57331	−	8.57331i	0.610823	−	0.610823i	−0.332338	−	0.943161i	$-0.607837\pi$
$197$	8.57331	−	8.57331i	0.610823	−	0.610823i	0.943161	+	0.332338i	$0.107837\pi$
$198$	−3.07109	+	0.448771i	−0.218253	+	0.0318928i
$199$		−	11.7684i		−	0.834236i	−0.908852	−	0.417118i	$-0.863040\pi$
$199$		−	11.7684i		−	0.834236i	0.908852	−	0.417118i	$-0.136960\pi$
$200$	2.07230	−	12.8567i	0.146534	−	0.909108i
$201$	−2.03394	+	6.13456i	−0.143463	+	0.432699i
$202$	−5.58804	−	5.58804i	−0.393173	−	0.393173i
$203$	8.59959	+	8.59959i	0.603573	+	0.603573i
$204$	1.56131	−	4.70905i	0.109313	−	0.329699i
$205$	15.9300	+	8.14412i	1.11260	+	0.568810i
$206$		−	13.0052i		−	0.906112i
$207$	−4.82930	+	0.705694i	−0.335659	+	0.0490491i
$208$	−0.890284	+	0.890284i	−0.0617301	+	0.0617301i
$209$	−1.35850			−0.0939696
$210$	7.84890	+	0.0577244i	0.541625	+	0.00398336i
$211$	−7.35863			−0.506589			−0.253295	−	0.967389i	$-0.581514\pi$
$211$	−7.35863			−0.506589			−0.253295	+	0.967389i	$0.581514\pi$
$212$	−10.4342	+	10.4342i	−0.716624	+	0.716624i
$213$	6.43695	−	3.23137i	0.441053	−	0.221410i
$214$		−	2.72350i		−	0.186175i
$215$	4.95176	+	15.3110i	0.337707	+	1.04420i
$216$	7.75682	+	11.0900i	0.527784	+	0.754581i
$217$	−9.06468	−	9.06468i	−0.615351	−	0.615351i
$218$	8.68041	+	8.68041i	0.587911	+	0.587911i
$219$	−24.3912	−	8.08701i	−1.64820	−	0.546470i
$220$	1.96361	−	3.84083i	0.132386	−	0.258949i
$221$		−	2.96472i		−	0.199429i
$222$	−2.50314	−	4.98630i	−0.168000	−	0.334659i
$223$	3.88777	−	3.88777i	0.260344	−	0.260344i	−0.564850	−	0.825194i	$-0.691066\pi$
$223$	3.88777	−	3.88777i	0.260344	−	0.260344i	0.825194	+	0.564850i	$0.191066\pi$
$224$	−15.5983			−1.04221
$225$	14.9984	+	0.220622i	0.999892	+	0.0147081i
$226$	−3.72594			−0.247846
$227$	4.24472	−	4.24472i	0.281732	−	0.281732i	−0.552068	−	0.833799i	$-0.686161\pi$
$227$	4.24472	−	4.24472i	0.281732	−	0.281732i	0.833799	+	0.552068i	$0.186161\pi$
$228$	1.10348	+	2.19815i	0.0730799	+	0.145576i
$229$		−	0.797154i		−	0.0526774i	−0.999653	−	0.0263387i	$-0.991615\pi$
$229$		−	0.797154i		−	0.0526774i	0.999653	−	0.0263387i	$-0.00838484\pi$
$230$	−1.26108	+	2.46668i	−0.0831531	+	0.162648i
$231$	5.94361	+	1.97063i	0.391061	+	0.129658i
$232$	8.41650	+	8.41650i	0.552570	+	0.552570i
$233$	−4.73483	−	4.73483i	−0.310189	−	0.310189i	0.534794	−	0.844983i	$-0.320389\pi$
$233$	−4.73483	−	4.73483i	−0.310189	−	0.310189i	−0.844983	+	0.534794i	$0.820389\pi$
$234$	2.69287	+	2.00620i	0.176038	+	0.131150i
$235$	−6.46697	−	19.9961i	−0.421858	−	1.30440i
$236$		−	2.05644i		−	0.133863i
$237$	−20.3440	+	10.2128i	−1.32148	+	0.663390i
$238$	2.89054	−	2.89054i	0.187366	−	0.187366i
$239$	−19.0557			−1.23261			−0.616305	−	0.787508i	$-0.711371\pi$
$239$	−19.0557			−1.23261			−0.616305	+	0.787508i	$0.711371\pi$
$240$	−3.31751	−	0.0243985i	−0.214144	−	0.00157491i
$241$	−22.0109			−1.41785			−0.708923	−	0.705286i	$-0.750818\pi$
$241$	−22.0109			−1.41785			−0.708923	+	0.705286i	$0.750818\pi$
$242$	4.92966	−	4.92966i	0.316890	−	0.316890i
$243$	−11.3478	+	10.6877i	−0.727962	+	0.685617i
$244$		−	12.5904i		−	0.806020i
$245$	−0.163147	−	0.0834083i	−0.0104231	−	0.00532876i
$246$	−3.32137	+	10.0176i	−0.211763	+	0.638698i
$247$	1.03932	+	1.03932i	0.0661305	+	0.0661305i
$248$	−8.87169	−	8.87169i	−0.563353	−	0.563353i
$249$	−4.44700	+	13.4126i	−0.281817	+	0.849988i
$250$	5.03280	−	6.86774i	0.318302	−	0.434354i
$251$			16.8840i			1.06571i	0.846206	+	0.532856i	$0.178881\pi$
$251$			16.8840i			1.06571i	−0.846206	+	0.532856i	$0.821119\pi$
$252$	−1.63924	−	11.2179i	−0.103263	−	0.706659i
$253$	−1.56277	+	1.56277i	−0.0982508	+	0.0982508i
$254$	6.10224			0.382889
$255$	5.56442	−	5.48317i	0.348458	−	0.343370i
$256$	−12.8334			−0.802089
$257$	2.37821	−	2.37821i	0.148349	−	0.148349i	−0.629031	−	0.777380i	$-0.716548\pi$
$257$	2.37821	−	2.37821i	0.148349	−	0.148349i	0.777380	+	0.629031i	$0.216548\pi$
$258$	−8.48353	+	4.25876i	−0.528161	+	0.265139i
$259$			11.2564i			0.699438i
$260$	−4.44069	+	1.43617i	−0.275400	+	0.0890674i
$261$	−8.19083	+	10.9943i	−0.506999	+	0.680531i
$262$	−1.30114	−	1.30114i	−0.0803846	−	0.0803846i
$263$	−7.09700	−	7.09700i	−0.437620	−	0.437620i	0.453590	−	0.891210i	$-0.350143\pi$
$263$	−7.09700	−	7.09700i	−0.437620	−	0.437620i	−0.891210	+	0.453590i	$0.850143\pi$
$264$	5.81706	+	1.92867i	0.358015	+	0.118702i
$265$	−22.1084	+	7.15010i	−1.35811	+	0.439227i
$266$			2.02663i			0.124261i
$267$	−11.8898	−	23.6847i	−0.727645	−	1.44948i
$268$	3.74676	−	3.74676i	0.228870	−	0.228870i
$269$	13.1757			0.803338			0.401669	−	0.915785i	$-0.368430\pi$
$269$	13.1757			0.803338			0.401669	+	0.915785i	$0.368430\pi$
$270$	1.21499	+	8.76460i	0.0739417	+	0.533397i
$271$	4.75635			0.288927			0.144464	−	0.989510i	$-0.453854\pi$
$271$	4.75635			0.288927			0.144464	+	0.989510i	$0.453854\pi$
$272$	−1.22175	+	1.22175i	−0.0740794	+	0.0740794i
$273$	−3.03953	−	6.05479i	−0.183961	−	0.366452i
$274$		−	8.63574i		−	0.521704i
$275$	5.50614	−	3.97753i	0.332033	−	0.239854i
$276$	3.79809	+	1.25927i	0.228618	+	0.0757993i
$277$	3.20574	+	3.20574i	0.192614	+	0.192614i	0.796825	−	0.604210i	$-0.206511\pi$
$277$	3.20574	+	3.20574i	0.192614	+	0.192614i	−0.604210	+	0.796825i	$0.706511\pi$
$278$	6.95449	+	6.95449i	0.417103	+	0.417103i
$279$	8.63381	−	11.5889i	0.516893	−	0.693810i
$280$	−13.7997	−	7.05504i	−0.824689	−	0.421619i
$281$		−	22.4973i		−	1.34208i	−0.741422	−	0.671039i	$-0.765848\pi$
$281$		−	22.4973i		−	1.34208i	0.741422	−	0.671039i	$-0.234152\pi$
$282$	11.0794	−	5.56192i	0.659771	−	0.331207i
$283$	1.27507	−	1.27507i	0.0757948	−	0.0757948i	−0.668193	−	0.743988i	$-0.732932\pi$
$283$	1.27507	−	1.27507i	0.0757948	−	0.0757948i	0.743988	+	0.668193i	$0.232932\pi$
$284$	−5.90506			−0.350401
$285$	−0.0284829	+	3.87288i	−0.00168718	+	0.229410i
$286$	1.52063			0.0899170
$287$	15.0561	−	15.0561i	0.888733	−	0.888733i
$288$	−2.54254	−	17.3994i	−0.149821	−	1.02527i
$289$			12.9315i			0.760675i
$290$	2.39472	+	7.40455i	0.140623	+	0.434810i
$291$	−5.33286	+	16.0844i	−0.312618	+	0.942886i
$292$	14.8972	+	14.8972i	0.871796	+	0.871796i
$293$	−22.3002	−	22.3002i	−1.30279	−	1.30279i	−0.926504	−	0.376285i	$-0.877201\pi$
$293$	−22.3002	−	22.3002i	−1.30279	−	1.30279i	−0.376285	−	0.926504i	$-0.622799\pi$
$294$	0.0340159	−	0.102595i	0.00198385	−	0.00598348i
$295$	1.47403	−	2.88322i	0.0858216	−	0.167868i
$296$			11.0167i			0.640334i
$297$	−1.22936	+	6.95112i	−0.0713348	+	0.403345i
$298$	−11.0239	+	11.0239i	−0.638600	+	0.638600i
$299$	2.39120			0.138287
$300$	−10.9084	−	5.67847i	−0.629798	−	0.327846i
$301$	19.1512			1.10386
$302$	−11.0735	+	11.0735i	−0.637210	+	0.637210i
$303$	−16.0632	+	8.06381i	−0.922809	+	0.463254i
$304$		−	0.856600i		−	0.0491294i
$305$	9.02471	−	17.6524i	0.516753	−	1.01077i
$306$	3.69546	+	2.75314i	0.211255	+	0.157387i
$307$	−16.7879	−	16.7879i	−0.958136	−	0.958136i	0.0410218	−	0.999158i	$-0.486939\pi$
$307$	−16.7879	−	16.7879i	−0.958136	−	0.958136i	−0.999158	+	0.0410218i	$0.986939\pi$
$308$	−3.63014	−	3.63014i	−0.206846	−	0.206846i
$309$	−28.0757	−	9.30862i	−1.59717	−	0.529549i
$310$	−2.52423	−	7.80501i	−0.143367	−	0.443295i
$311$			18.7091i			1.06090i	0.847717	+	0.530449i	$0.177977\pi$
$311$			18.7091i			1.06090i	−0.847717	+	0.530449i	$0.822023\pi$
$312$	−2.97481	−	5.92588i	−0.168416	−	0.335487i
$313$	−19.9866	+	19.9866i	−1.12971	+	1.12971i	−0.139485	+	0.990224i	$0.544545\pi$
$313$	−19.9866	+	19.9866i	−1.12971	+	1.12971i	−0.990224	+	0.139485i	$0.955455\pi$
$314$	14.5334			0.820170
$315$	5.74257	−	16.9030i	0.323557	−	0.952374i
$316$	18.6629			1.04987
$317$	−15.6450	+	15.6450i	−0.878712	+	0.878712i	−0.993401	−	0.114690i	$-0.963413\pi$
$317$	−15.6450	+	15.6450i	−0.878712	+	0.878712i	0.114690	+	0.993401i	$0.463413\pi$
$318$	−6.14945	−	12.2498i	−0.344844	−	0.686935i
$319$			6.20837i			0.347602i
$320$	−5.47626	−	2.79972i	−0.306132	−	0.156509i
$321$	−5.87953	−	1.94938i	−0.328163	−	0.108804i
$322$	2.33137	+	2.33137i	0.129922	+	0.129922i
$323$	1.42628	+	1.42628i	0.0793602	+	0.0793602i
$324$	12.2460	−	3.65704i	0.680332	−	0.203169i
$325$	−7.25548	−	1.16947i	−0.402461	−	0.0648703i
$326$			19.1589i			1.06111i
$327$	24.9525	−	12.5262i	1.37988	−	0.692703i
$328$	14.7355	−	14.7355i	0.813634	−	0.813634i
$329$	−25.0114			−1.37892
$330$	2.81237	+	2.85404i	0.154816	+	0.157110i
$331$	−7.58564			−0.416944			−0.208472	−	0.978028i	$-0.566849\pi$
$331$	−7.58564			−0.416944			−0.208472	+	0.978028i	$0.566849\pi$
$332$	8.19192	−	8.19192i	0.449590	−	0.449590i
$333$	−12.5561	+	1.83480i	−0.688072	+	0.100546i
$334$		−	12.8256i		−	0.701787i
$335$	7.93878	−	2.56749i	0.433742	−	0.140277i
$336$	−1.24257	+	3.74772i	−0.0677880	+	0.204455i
$337$	12.6842	+	12.6842i	0.690954	+	0.690954i	0.962442	−	0.271488i	$-0.0875157\pi$
$337$	12.6842	+	12.6842i	0.690954	+	0.690954i	−0.271488	+	0.962442i	$0.587516\pi$
$338$	5.83710	+	5.83710i	0.317497	+	0.317497i
$339$	−2.66689	+	8.04361i	−0.144846	+	0.436869i
$340$	−6.09401	+	1.97087i	−0.330494	+	0.106886i
$341$		−	6.54413i		−	0.354385i
$342$	−2.26064	+	0.330342i	−0.122242	+	0.0178629i
$343$	13.0180	−	13.0180i	0.702908	−	0.702908i
$344$	18.7435			1.01058
$345$	4.42246	+	4.48799i	0.238097	+	0.241625i
$346$	12.3652			0.664759
$347$	1.73182	−	1.73182i	0.0929691	−	0.0929691i	−0.659093	−	0.752062i	$-0.729060\pi$
$347$	1.73182	−	1.73182i	0.0929691	−	0.0929691i	0.752062	+	0.659093i	$0.229060\pi$
$348$	10.0456	−	5.04292i	0.538499	−	0.270329i
$349$		−	21.0315i		−	1.12579i	−0.826529	−	0.562894i	$-0.809688\pi$
$349$		−	21.0315i		−	1.12579i	0.826529	−	0.562894i	$-0.190312\pi$
$350$	−5.93372	−	8.21412i	−0.317171	−	0.439063i
$351$	6.25847	−	4.37743i	0.334053	−	0.233650i
$352$	−5.63051	−	5.63051i	−0.300107	−	0.300107i
$353$	10.4959	+	10.4959i	0.558642	+	0.558642i	0.928921	−	0.370279i	$-0.120738\pi$
$353$	10.4959	+	10.4959i	0.558642	+	0.558642i	−0.370279	+	0.928921i	$0.620738\pi$
$354$	1.81312	+	0.601147i	0.0963662	+	0.0319506i
$355$	−8.27916	−	4.23269i	−0.439412	−	0.224648i
$356$			21.7276i			1.15156i
$357$	−4.17118	−	8.30907i	−0.220762	−	0.439762i
$358$	0.0520049	−	0.0520049i	0.00274854	−	0.00274854i
$359$	−9.49391			−0.501070			−0.250535	−	0.968108i	$-0.580606\pi$
$359$	−9.49391			−0.501070			−0.250535	+	0.968108i	$0.580606\pi$
$360$	5.62031	−	16.5431i	0.296216	−	0.871897i
$361$	−1.00000			−0.0526316
$362$	3.20234	−	3.20234i	0.168311	−	0.168311i
$363$	−7.11373	−	14.1707i	−0.373374	−	0.743767i
$364$			5.55447i			0.291133i
$365$	10.2084	+	31.5648i	0.534334	+	1.65218i
$366$	11.1007	+	3.68050i	0.580244	+	0.192383i
$367$	6.92348	+	6.92348i	0.361403	+	0.361403i	0.864329	−	0.502927i	$-0.167743\pi$
$367$	6.92348	+	6.92348i	0.361403	+	0.361403i	−0.502927	+	0.864329i	$0.667743\pi$
$368$	−0.985402	−	0.985402i	−0.0513677	−	0.0513677i
$369$	19.2487	+	14.3404i	1.00205	+	0.746533i
$370$	−3.27880	+	6.41335i	−0.170457	+	0.333414i
$371$			27.6535i			1.43570i
$372$	−10.5889	+	5.31565i	−0.549007	+	0.275604i
$373$	−1.99286	+	1.99286i	−0.103186	+	0.103186i	−0.756815	−	0.653629i	$-0.773246\pi$
$373$	−1.99286	+	1.99286i	−0.103186	+	0.103186i	0.653629	+	0.756815i	$0.273246\pi$
$374$	2.08679			0.107905
$375$	−11.2239	−	15.7805i	−0.579597	−	0.814903i
$376$	−24.4789			−1.26240
$377$	4.74971	−	4.74971i	0.244623	−	0.244623i
$378$	10.3698	+	1.83398i	0.533363	+	0.0943295i
$379$			15.8461i			0.813957i	0.913438	+	0.406979i	$0.133418\pi$
$379$			15.8461i			0.813957i	−0.913438	+	0.406979i	$0.866582\pi$
$380$	1.44542	−	2.82725i	0.0741485	−	0.145035i
$381$	4.36776	−	13.1736i	0.223767	−	0.674903i
$382$	8.00347	+	8.00347i	0.409493	+	0.409493i
$383$	−8.84581	−	8.84581i	−0.452000	−	0.452000i	0.444018	−	0.896018i	$-0.353553\pi$
$383$	−8.84581	−	8.84581i	−0.452000	−	0.452000i	−0.896018	+	0.444018i	$0.853553\pi$
$384$	−5.24820	+	15.8291i	−0.267821	+	0.807773i
$385$	−2.48757	−	7.69167i	−0.126778	−	0.392004i
$386$		−	7.16862i		−	0.364873i
$387$	3.12167	+	21.3626i	0.158683	+	1.08592i
$388$	9.82378	−	9.82378i	0.498727	−	0.498727i
$389$	23.6010			1.19662			0.598310	−	0.801265i	$-0.295839\pi$
$389$	23.6010			1.19662			0.598310	+	0.801265i	$0.295839\pi$
$390$	0.0318822	−	4.33509i	0.00161442	−	0.219516i
$391$	3.28148			0.165952
$392$	−0.150914	+	0.150914i	−0.00762233	+	0.00762233i
$393$	−3.74022	+	1.87760i	−0.188669	+	0.0947126i
$394$		−	9.23341i		−	0.465172i
$395$	26.1663	+	13.3774i	1.31657	+	0.673091i
$396$	3.45758	−	4.64101i	0.173750	−	0.233220i
$397$	1.76659	+	1.76659i	0.0886627	+	0.0886627i	0.750047	−	0.661384i	$-0.230031\pi$
$397$	1.76659	+	1.76659i	0.0886627	+	0.0886627i	−0.661384	+	0.750047i	$0.730031\pi$
$398$	−6.33723	−	6.33723i	−0.317656	−	0.317656i
$399$	4.37511	+	1.45059i	0.219030	+	0.0726203i
$400$	2.50802	+	3.47188i	0.125401	+	0.173594i
$401$		−	9.59474i		−	0.479139i	−0.970879	−	0.239569i	$-0.922994\pi$
$401$		−	9.59474i		−	0.479139i	0.970879	−	0.239569i	$-0.0770062\pi$
$402$	2.20817	+	4.39872i	0.110134	+	0.219388i
$403$	−5.00659	+	5.00659i	−0.249396	+	0.249396i
$404$	14.7359			0.733139
$405$	19.7908	+	3.65045i	0.983411	+	0.181393i
$406$	9.26171			0.459651
$407$	−4.06320	+	4.06320i	−0.201405	+	0.201405i
$408$	−4.08238	−	8.13216i	−0.202108	−	0.402602i
$409$			8.72806i			0.431575i	0.976440	+	0.215787i	$0.0692318\pi$
$409$			8.72806i			0.431575i	−0.976440	+	0.215787i	$0.930768\pi$
$410$	12.9638	−	4.19265i	0.640238	−	0.207060i
$411$	−18.6429	−	6.18115i	−0.919588	−	0.304894i
$412$	17.1476	+	17.1476i	0.844801	+	0.844801i
$413$	−2.72506	−	2.72506i	−0.134091	−	0.134091i
$414$	−2.22055	+	2.98058i	−0.109134	+	0.146487i
$415$	17.3573	−	5.61356i	0.852038	−	0.275559i
$416$			8.61524i			0.422397i
$417$	19.9912	−	10.0357i	0.978973	−	0.491448i
$418$	−0.731550	+	0.731550i	−0.0357813	+	0.0357813i
$419$	−29.4005			−1.43631			−0.718153	−	0.695885i	$-0.755012\pi$
$419$	−29.4005			−1.43631			−0.718153	+	0.695885i	$0.755012\pi$
$420$	−10.4251	+	10.2728i	−0.508691	+	0.501263i
$421$	36.5632			1.78198			0.890991	−	0.454021i	$-0.150011\pi$
$421$	36.5632			1.78198			0.890991	+	0.454021i	$0.150011\pi$
$422$	−3.96260	+	3.96260i	−0.192897	+	0.192897i
$423$	−4.07688	−	27.8994i	−0.198225	−	1.35652i
$424$			27.0647i			1.31438i
$425$	−9.95679	−	1.60487i	−0.482975	−	0.0778478i
$426$	1.72619	−	5.20637i	0.0836344	−	0.252249i
$427$	−16.6840	−	16.6840i	−0.807397	−	0.807397i
$428$	3.59100	+	3.59100i	0.173578	+	0.173578i
$429$	1.08841	−	3.28276i	0.0525491	−	0.158493i
$430$	10.9115	+	5.57844i	0.526197	+	0.269016i
$431$			8.93679i			0.430470i	0.976562	+	0.215235i	$0.0690518\pi$
$431$			8.93679i			0.430470i	−0.976562	+	0.215235i	$0.930948\pi$
$432$	−4.38300	−	0.775170i	−0.210877	−	0.0372954i
$433$	17.0999	−	17.0999i	0.821769	−	0.821769i	−0.164592	−	0.986362i	$-0.552631\pi$
$433$	17.0999	−	17.0999i	0.821769	−	0.821769i	0.986362	+	0.164592i	$0.0526309\pi$
$434$	−9.76261			−0.468620
$435$	17.6991	+	0.130167i	0.848606	+	0.00624103i
$436$	−22.8906			−1.09626
$437$	−1.15037	+	1.15037i	−0.0550294	+	0.0550294i
$438$	−17.4894	+	8.77976i	−0.835677	+	0.419513i
$439$			25.4047i			1.21250i	0.795273	+	0.606251i	$0.207327\pi$
$439$			25.4047i			1.21250i	−0.795273	+	0.606251i	$0.792673\pi$
$440$	−2.43461	−	7.52790i	−0.116065	−	0.358879i
$441$	−0.197137	−	0.146868i	−0.00938746	−	0.00699371i
$442$	−1.59650	−	1.59650i	−0.0759376	−	0.0759376i
$443$	24.4950	+	24.4950i	1.16379	+	1.16379i	0.983638	+	0.180157i	$0.0576606\pi$
$443$	24.4950	+	24.4950i	1.16379	+	1.16379i	0.180157	+	0.983638i	$0.442339\pi$
$444$	9.87499	+	3.27410i	0.468646	+	0.155382i
$445$	−15.5741	+	30.4631i	−0.738285	+	1.44409i
$446$		−	4.18711i		−	0.198265i
$447$	15.9081	+	31.6892i	0.752426	+	1.49885i
$448$	−5.17585	+	5.17585i	−0.244536	+	0.244536i
$449$	−35.4891			−1.67483			−0.837417	−	0.546564i	$-0.815935\pi$
$449$	−35.4891			−1.67483			−0.837417	+	0.546564i	$0.815935\pi$
$450$	8.19539	−	7.95778i	0.386334	−	0.375133i
$451$	10.8696			0.511827
$452$	4.91274	−	4.91274i	0.231076	−	0.231076i
$453$	15.9796	+	31.8317i	0.750788	+	1.49558i
$454$		−	4.57154i		−	0.214553i
$455$	−3.98139	+	7.78763i	−0.186651	+	0.365090i
$456$	4.28196	+	1.41970i	0.200521	+	0.0664837i
$457$	−11.0478	−	11.0478i	−0.516797	−	0.516797i	0.399804	−	0.916601i	$-0.369078\pi$
$457$	−11.0478	−	11.0478i	−0.516797	−	0.516797i	−0.916601	+	0.399804i	$0.869078\pi$
$458$	−0.429265	−	0.429265i	−0.0200582	−	0.0200582i
$459$	8.58859	−	6.00721i	0.400881	−	0.280392i
$460$	−1.58961	−	4.91513i	−0.0741159	−	0.229169i
$461$		−	12.3684i		−	0.576055i	−0.957622	−	0.288028i	$-0.907001\pi$
$461$		−	12.3684i		−	0.576055i	0.957622	−	0.288028i	$-0.0929995\pi$
$462$	4.26180	−	2.13944i	0.198277	−	0.0995357i
$463$	13.1567	−	13.1567i	0.611444	−	0.611444i	−0.331878	−	0.943322i	$-0.607682\pi$
$463$	13.1567	−	13.1567i	0.611444	−	0.611444i	0.943322	+	0.331878i	$0.107682\pi$
$464$	−3.91466			−0.181734
$465$	−18.6563	−	0.137207i	−0.865165	−	0.00636281i
$466$	−5.09938			−0.236224
$467$	−4.49454	+	4.49454i	−0.207982	+	0.207982i	−0.803409	−	0.595427i	$-0.796983\pi$
$467$	−4.49454	+	4.49454i	−0.207982	+	0.207982i	0.595427	+	0.803409i	$0.296983\pi$
$468$	−6.19583	+	0.905383i	−0.286403	+	0.0418513i
$469$		−	9.92994i		−	0.458522i
$470$	−14.2503	−	7.28540i	−0.657317	−	0.336051i
$471$	10.4025	−	31.3750i	0.479322	−	1.44568i
$472$	−2.66704	−	2.66704i	−0.122760	−	0.122760i
$473$	6.91300	+	6.91300i	0.317860	+	0.317860i
$474$	−5.45564	+	16.4547i	−0.250586	+	0.755791i
$475$	4.05309	−	2.92787i	0.185969	−	0.134340i
$476$			7.62248i			0.349376i
$477$	−30.8466	+	4.50754i	−1.41237	+	0.206386i
$478$	−10.2614	+	10.2614i	−0.469347	+	0.469347i
$479$	−36.0986			−1.64939			−0.824693	−	0.565580i	$-0.808652\pi$
$479$	−36.0986			−1.64939			−0.824693	+	0.565580i	$0.808652\pi$
$480$	−16.1697	+	15.9336i	−0.738045	+	0.727268i
$481$	6.21711			0.283476
$482$	−11.8528	+	11.8528i	−0.539880	+	0.539880i
$483$	6.70168	−	3.36427i	0.304937	−	0.153080i
$484$			12.9997i			0.590897i
$485$	20.8150	−	6.73180i	0.945160	−	0.305675i
$486$	−0.355462	+	11.8661i	−0.0161241	+	0.538256i
$487$	−17.2732	−	17.2732i	−0.782724	−	0.782724i	0.197565	−	0.980290i	$-0.436697\pi$
$487$	−17.2732	−	17.2732i	−0.782724	−	0.782724i	−0.980290	+	0.197565i	$0.936697\pi$
$488$	−16.3288	−	16.3288i	−0.739171	−	0.739171i
$489$	41.3604	+	13.7132i	1.87038	+	0.620134i
$490$	−0.132769	+	0.0429391i	−0.00599791	+	0.00193979i
$491$		−	15.1161i		−	0.682178i	−0.940031	−	0.341089i	$-0.889204\pi$
$491$		−	15.1161i		−	0.682178i	0.940031	−	0.341089i	$-0.110796\pi$
$492$	−8.82910	−	17.5877i	−0.398046	−	0.792915i
$493$	6.51809	−	6.51809i	0.293560	−	0.293560i
$494$	1.11935			0.0503617
$495$	8.17433	−	4.02855i	0.367409	−	0.181070i
$496$	4.12638			0.185280
$497$	−7.82500	+	7.82500i	−0.350999	+	0.350999i
$498$	4.82794	+	9.61734i	0.216345	+	0.430963i
$499$			23.4062i			1.04781i	0.851778	+	0.523903i	$0.175524\pi$
$499$			23.4062i			1.04781i	−0.851778	+	0.523903i	$0.824476\pi$
$500$	2.41941	+	15.6911i	0.108199	+	0.701728i
$501$	−27.6881	−	9.18011i	−1.23701	−	0.410137i
$502$	9.09201	+	9.09201i	0.405796	+	0.405796i
$503$	9.30918	+	9.30918i	0.415076	+	0.415076i	0.883502	−	0.468427i	$-0.155179\pi$
$503$	9.30918	+	9.30918i	0.415076	+	0.415076i	−0.468427	+	0.883502i	$0.655179\pi$
$504$	−16.6747	−	12.4227i	−0.742749	−	0.553353i
$505$	20.6604	+	10.5626i	0.919378	+	0.470028i
$506$			1.68310i			0.0748229i
$507$	16.7792	−	8.42322i	0.745190	−	0.374088i
$508$	−8.04594	+	8.04594i	−0.356981	+	0.356981i
$509$	−0.204055			−0.00904456			−0.00452228	−	0.999990i	$-0.501439\pi$
$509$	−0.204055			−0.00904456			−0.00452228	+	0.999990i	$0.501439\pi$
$510$	0.0437524	−	5.94910i	0.00193739	−	0.263431i
$511$	39.4817			1.74657
$512$	6.70547	−	6.70547i	0.296343	−	0.296343i
$513$	−0.904938	+	5.11675i	−0.0399540	+	0.225910i
$514$		−	2.56132i		−	0.112975i
$515$	11.7505	+	36.3329i	0.517788	+	1.60102i
$516$	5.57044	−	16.8010i	0.245225	−	0.739622i
$517$	−9.02833	−	9.02833i	−0.397066	−	0.397066i
$518$	6.06153	+	6.06153i	0.266328	+	0.266328i
$519$	8.85058	−	26.6942i	0.388497	−	1.17174i
$520$	−3.89662	+	7.62182i	−0.170878	+	0.334239i
$521$		−	10.4402i		−	0.457391i	−0.973498	−	0.228696i	$-0.926554\pi$
$521$		−	10.4402i		−	0.457391i	0.973498	−	0.228696i	$-0.0734461\pi$
$522$	1.50967	+	10.3311i	0.0660763	+	0.452182i
$523$	0.714367	−	0.714367i	0.0312371	−	0.0312371i	−0.691316	−	0.722553i	$-0.742969\pi$
$523$	0.714367	−	0.714367i	0.0312371	−	0.0312371i	0.722553	+	0.691316i	$0.242969\pi$
$524$	3.43116			0.149891
$525$	−21.9799	+	6.93041i	−0.959281	+	0.302468i
$526$	−7.64344			−0.333270
$527$	−6.87061	+	6.87061i	−0.299288	+	0.299288i
$528$	−1.80134	+	0.904280i	−0.0783933	+	0.0393537i
$529$		−	20.3533i		−	0.884927i
$530$	−8.05499	+	15.7556i	−0.349887	+	0.684380i
$531$	2.59553	−	3.48390i	0.112636	−	0.151188i
$532$	−2.67216	−	2.67216i	−0.115853	−	0.115853i
$533$	−8.31575	−	8.31575i	−0.360195	−	0.360195i
$534$	−19.1568	−	6.35152i	−0.828995	−	0.274857i
$535$	2.46076	+	7.60875i	0.106388	+	0.328955i
$536$		−	9.71852i		−	0.419776i
$537$	−0.0750455	−	0.149492i	−0.00323845	−	0.00645105i
$538$	7.09509	−	7.09509i	0.305891	−	0.305891i
$539$	−0.111321			−0.00479493
$540$	−13.1583	−	9.95433i	−0.566243	−	0.428366i
$541$	0.689057			0.0296249			0.0148124	−	0.999890i	$-0.495285\pi$
$541$	0.689057			0.0296249			0.0148124	+	0.999890i	$0.495285\pi$
$542$	2.56128	−	2.56128i	0.110016	−	0.110016i
$543$	−4.62113	−	9.20537i	−0.198312	−	0.395040i
$544$			11.8228i			0.506899i
$545$	−32.0937	−	16.4078i	−1.37474	−	0.702832i
$546$	−4.89726	−	1.62371i	−0.209584	−	0.0694883i
$547$	−3.45744	−	3.45744i	−0.147829	−	0.147829i	0.629318	−	0.777148i	$-0.283334\pi$
$547$	−3.45744	−	3.45744i	−0.147829	−	0.147829i	−0.777148	+	0.629318i	$0.783334\pi$
$548$	11.3864	+	11.3864i	0.486404	+	0.486404i
$549$	15.8910	−	21.3300i	0.678211	−	0.910343i
$550$	0.823155	−	5.10693i	0.0350994	−	0.217760i
$551$			4.57000i			0.194689i
$552$	6.55900	−	3.29264i	0.279170	−	0.140144i
$553$	24.7309	−	24.7309i	1.05167	−	1.05167i
$554$	3.45257			0.146686
$555$	11.4984	+	11.6687i	0.488078	+	0.495310i
$556$	−18.3393			−0.777760
$557$	16.2110	−	16.2110i	0.686881	−	0.686881i	−0.274660	−	0.961541i	$-0.588565\pi$
$557$	16.2110	−	16.2110i	0.686881	−	0.686881i	0.961541	+	0.274660i	$0.0885654\pi$
$558$	−1.59131	−	10.8899i	−0.0673657	−	0.461005i
$559$		−	10.5776i		−	0.447384i
$560$	4.84995	−	1.56853i	0.204948	−	0.0662825i
$561$	1.49365	−	4.50498i	0.0630618	−	0.190200i
$562$	−12.1147	−	12.1147i	−0.511030	−	0.511030i
$563$	−12.6620	−	12.6620i	−0.533639	−	0.533639i	0.388014	−	0.921653i	$-0.373161\pi$
$563$	−12.6620	−	12.6620i	−0.533639	−	0.533639i	−0.921653	+	0.388014i	$0.873161\pi$
$564$	−7.27497	+	21.9420i	−0.306331	+	0.923925i
$565$	10.4093	−	3.36648i	0.437922	−	0.141629i
$566$		−	1.37324i		−	0.0577215i
$567$	11.3815	−	21.0737i	0.477978	−	0.885010i
$568$	−7.65840	+	7.65840i	−0.321339	+	0.321339i
$569$	16.6123			0.696424			0.348212	−	0.937416i	$-0.386789\pi$
$569$	16.6123			0.696424			0.348212	+	0.937416i	$0.386789\pi$
$570$	2.07020	+	2.10087i	0.0867110	+	0.0879959i
$571$	8.75730			0.366482			0.183241	−	0.983068i	$-0.441341\pi$
$571$	8.75730			0.366482			0.183241	+	0.983068i	$0.441341\pi$
$572$	−2.00499	+	2.00499i	−0.0838328	+	0.0838328i
$573$	23.0066	−	11.5494i	0.961113	−	0.482482i
$574$		−	16.2153i		−	0.676815i
$575$	1.29441	−	8.03066i	0.0539807	−	0.334902i
$576$	−6.61717	−	4.92983i	−0.275715	−	0.205410i
$577$	−8.00995	−	8.00995i	−0.333459	−	0.333459i	0.520440	−	0.853898i	$-0.325768\pi$
$577$	−8.00995	−	8.00995i	−0.333459	−	0.333459i	−0.853898	+	0.520440i	$0.825768\pi$
$578$	6.96356	+	6.96356i	0.289646	+	0.289646i
$579$	−15.4757	−	5.13104i	−0.643148	−	0.213239i
$580$	−12.9205	−	6.60558i	−0.536497	−	0.274282i
$581$		−	21.7108i		−	0.900716i
$582$	5.78969	+	11.5332i	0.239990	+	0.478065i
$583$	−9.98204	+	9.98204i	−0.413414	+	0.413414i
$584$	38.6411			1.59898
$585$	−9.33582	−	3.17173i	−0.385988	−	0.131135i
$586$	−24.0171			−0.992139
$587$	−6.86560	+	6.86560i	−0.283373	+	0.283373i	−0.834453	−	0.551079i	$-0.814216\pi$
$587$	−6.86560	+	6.86560i	−0.283373	+	0.283373i	0.551079	+	0.834453i	$0.314216\pi$
$588$	0.0904235	+	0.180125i	0.00372900	+	0.00742823i
$589$		−	4.81716i		−	0.198488i
$590$	−0.758843	−	2.34637i	−0.0312411	−	0.0965985i
$591$	−19.9332	−	6.60894i	−0.819942	−	0.271855i
$592$	−2.56204	−	2.56204i	−0.105299	−	0.105299i
$593$	−14.3489	−	14.3489i	−0.589237	−	0.589237i	0.348188	−	0.937425i	$-0.386797\pi$
$593$	−14.3489	−	14.3489i	−0.589237	−	0.589237i	−0.937425	+	0.348188i	$0.886797\pi$
$594$	3.08115	+	4.40516i	0.126421	+	0.180746i
$595$	−5.46372	+	10.6871i	−0.223991	+	0.438127i
$596$		−	29.0706i		−	1.19078i
$597$	−18.2168	+	9.14492i	−0.745565	+	0.374277i
$598$	1.28766	−	1.28766i	0.0526562	−	0.0526562i
$599$	39.2061			1.60192			0.800959	−	0.598719i	$-0.204323\pi$
$599$	39.2061			1.60192			0.800959	+	0.598719i	$0.204323\pi$
$600$	−21.5119	+	6.78286i	−0.878220	+	0.276909i
$601$	3.96904			0.161900			0.0809502	−	0.996718i	$-0.474205\pi$
$601$	3.96904			0.161900			0.0809502	+	0.996718i	$0.474205\pi$
$602$	10.3129	−	10.3129i	0.420322	−	0.420322i
$603$	11.0765	−	1.61859i	0.451071	−	0.0659140i
$604$		−	29.2014i		−	1.18819i
$605$	−9.31808	+	18.2262i	−0.378834	+	0.741001i
$606$	−4.30767	+	12.9924i	−0.174987	+	0.527778i
$607$	−18.3365	−	18.3365i	−0.744254	−	0.744254i	0.229139	−	0.973394i	$-0.426409\pi$
$607$	−18.3365	−	18.3365i	−0.744254	−	0.744254i	−0.973394	+	0.229139i	$0.926409\pi$
$608$	−4.14464	−	4.14464i	−0.168087	−	0.168087i
$609$	6.62920	−	19.9943i	0.268629	−	0.810210i
$610$	−4.64598	−	14.3655i	−0.188110	−	0.581644i
$611$			13.8143i			0.558865i
$612$	−8.50263	+	1.24247i	−0.343698	+	0.0502239i
$613$	−4.77647	+	4.77647i	−0.192920	+	0.192920i	−0.796956	−	0.604037i	$-0.793558\pi$
$613$	−4.77647	+	4.77647i	−0.192920	+	0.192920i	0.604037	+	0.796956i	$0.293558\pi$
$614$	−18.0805			−0.729669
$615$	0.227895	−	30.9874i	0.00918963	−	1.24953i
$616$	−9.41601			−0.379382
$617$	9.18925	−	9.18925i	0.369945	−	0.369945i	−0.497512	−	0.867457i	$-0.665753\pi$
$617$	9.18925	−	9.18925i	0.369945	−	0.369945i	0.867457	+	0.497512i	$0.165753\pi$
$618$	−20.1313	+	10.1060i	−0.809801	+	0.406523i
$619$		−	8.76775i		−	0.352406i	−0.984354	−	0.176203i	$-0.943619\pi$
$619$		−	8.76775i		−	0.352406i	0.984354	−	0.176203i	$-0.0563815\pi$
$620$	13.6193	+	6.96282i	0.546965	+	0.279634i
$621$	4.84512	+	6.92713i	0.194428	+	0.277976i
$622$	10.0748	+	10.0748i	0.403964	+	0.403964i
$623$	28.7920	+	28.7920i	1.15353	+	1.15353i
$624$	2.06993	+	0.686296i	0.0828637	+	0.0274738i
$625$	−7.85512	+	23.7339i	−0.314205	+	0.949355i
$626$			21.5255i			0.860331i
$627$	1.05566	+	2.10290i	0.0421591	+	0.0839816i
$628$	−19.1627	+	19.1627i	−0.764674	+	0.764674i
$629$	8.53182			0.340186
$630$	−6.00985	−	12.1946i	−0.239438	−	0.485843i
$631$	−32.6847			−1.30116			−0.650578	−	0.759440i	$-0.725473\pi$
$631$	−32.6847			−1.30116			−0.650578	+	0.759440i	$0.725473\pi$
$632$	24.2044	−	24.2044i	0.962798	−	0.962798i
$633$	5.71823	+	11.3908i	0.227279	+	0.452744i
$634$			16.8496i			0.669183i
$635$	−17.0480	+	5.51353i	−0.676530	+	0.218798i
$636$	24.2598	+	8.04345i	0.961965	+	0.318944i
$637$	0.0851661	+	0.0851661i	0.00337440	+	0.00337440i
$638$	3.34319	+	3.34319i	0.132358	+	0.132358i
$639$	−10.0040	−	7.45305i	−0.395753	−	0.294838i
$640$	20.4845	−	6.62492i	0.809721	−	0.261873i
$641$			20.3444i			0.803555i	0.915737	+	0.401777i	$0.131607\pi$
$641$			20.3444i			0.803555i	−0.915737	+	0.401777i	$0.868393\pi$
$642$	−4.21585	+	2.11637i	−0.166386	+	0.0835266i
$643$	−19.2371	+	19.2371i	−0.758637	+	0.758637i	−0.976074	−	0.217438i	$-0.930230\pi$
$643$	−19.2371	+	19.2371i	−0.758637	+	0.758637i	0.217438	+	0.976074i	$0.430230\pi$
$644$	−6.14792			−0.242262
$645$	19.8528	−	19.5629i	0.781704	−	0.770290i
$646$	1.53609			0.0604368
$647$	−24.0469	+	24.0469i	−0.945381	+	0.945381i	−0.998584	−	0.0532024i	$-0.983057\pi$
$647$	−24.0469	+	24.0469i	−0.945381	+	0.945381i	0.0532024	+	0.998584i	$0.483057\pi$
$648$	11.1392	−	20.6250i	0.437588	−	0.810226i
$649$		−	1.96732i		−	0.0772241i
$650$	−4.53681	+	3.27730i	−0.177948	+	0.128546i
$651$	−6.98772	+	21.0756i	−0.273870	+	0.826019i
$652$	−25.2614	−	25.2614i	−0.989313	−	0.989313i
$653$	7.09109	+	7.09109i	0.277496	+	0.277496i	0.832109	−	0.554613i	$-0.187134\pi$
$653$	7.09109	+	7.09109i	0.277496	+	0.277496i	−0.554613	+	0.832109i	$0.687134\pi$
$654$	6.69149	−	20.1822i	0.261658	−	0.789186i
$655$	4.81064	+	2.45942i	0.187967	+	0.0960976i
$656$			6.85376i			0.267594i
$657$	6.43556	+	44.0406i	0.251075	+	1.71819i
$658$	−13.4686	+	13.4686i	−0.525060	+	0.525060i
$659$	−22.9119			−0.892523			−0.446261	−	0.894903i	$-0.647245\pi$
$659$	−22.9119			−0.892523			−0.446261	+	0.894903i	$0.647245\pi$
$660$	−7.47129	−	0.0549473i	−0.290820	−	0.00213882i
$661$	−13.9390			−0.542164			−0.271082	−	0.962556i	$-0.587382\pi$
$661$	−13.9390			−0.542164			−0.271082	+	0.962556i	$0.587382\pi$
$662$	−4.08485	+	4.08485i	−0.158762	+	0.158762i
$663$	−4.58925	+	2.30382i	−0.178232	+	0.0894730i
$664$		−	21.2486i		−	0.824604i
$665$	−1.83111	−	5.66187i	−0.0710075	−	0.219558i
$666$	−5.77341	+	7.74948i	−0.223715	+	0.300286i
$667$	5.25717	+	5.25717i	0.203559	+	0.203559i
$668$	16.9109	+	16.9109i	0.654301	+	0.654301i
$669$	−9.03917	−	2.99698i	−0.349475	−	0.115870i
$670$	2.89242	−	5.65760i	0.111744	−	0.218572i
$671$		−	12.0448i		−	0.464985i
$672$	12.1211	+	24.1455i	0.467582	+	0.931431i
$673$	−6.98423	+	6.98423i	−0.269222	+	0.269222i	−0.828787	−	0.559565i	$-0.810968\pi$
$673$	−6.98423	+	6.98423i	−0.269222	+	0.269222i	0.559565	+	0.828787i	$0.310968\pi$
$674$	13.6608			0.526196
$675$	−11.3134	−	23.3882i	−0.435452	−	0.900212i
$676$	−15.3927			−0.592027
$677$	−16.3797	+	16.3797i	−0.629521	+	0.629521i	−0.947948	−	0.318426i	$-0.896846\pi$
$677$	−16.3797	+	16.3797i	−0.629521	+	0.629521i	0.318426	+	0.947948i	$0.396846\pi$
$678$	2.89535	+	5.76758i	0.111195	+	0.221502i
$679$		−	26.0357i		−	0.999157i
$680$	−5.34739	+	10.4595i	−0.205063	+	0.401105i
$681$	−9.86909	−	3.27214i	−0.378184	−	0.125389i
$682$	−3.52400	−	3.52400i	−0.134941	−	0.134941i
$683$	−10.2786	−	10.2786i	−0.393299	−	0.393299i	0.482563	−	0.875861i	$-0.339706\pi$
$683$	−10.2786	−	10.2786i	−0.393299	−	0.393299i	−0.875861	+	0.482563i	$0.839706\pi$
$684$	2.54514	−	3.41627i	0.0973160	−	0.130624i
$685$	7.80261	+	24.1260i	0.298122	+	0.921806i
$686$		−	14.0204i		−	0.535299i
$687$	−1.23395	+	0.619450i	−0.0470783	+	0.0236335i
$688$	−4.35897	+	4.35897i	−0.166184	+	0.166184i
$689$	15.2735			0.581875
$690$	4.79825	+	0.0352885i	0.182666	+	0.00134341i
$691$	−39.3216			−1.49586			−0.747931	−	0.663776i	$-0.768953\pi$
$691$	−39.3216			−1.49586			−0.747931	+	0.663776i	$0.768953\pi$
$692$	−16.3038	+	16.3038i	−0.619778	+	0.619778i
$693$	−1.56820	−	10.7317i	−0.0595712	−	0.407665i
$694$		−	1.86516i		−	0.0708006i
$695$	−25.7125	−	13.1454i	−0.975333	−	0.498635i
$696$	6.48805	−	19.5686i	0.245929	−	0.741746i
$697$	−11.4118	−	11.4118i	−0.432254	−	0.432254i
$698$	−11.3254	−	11.3254i	−0.428672	−	0.428672i
$699$	−3.64995	+	11.0086i	−0.138054	+	0.416383i
$700$	18.6542	+	3.00676i	0.705064	+	0.113645i
$701$		−	23.9242i		−	0.903606i	−0.892118	−	0.451803i	$-0.850781\pi$
$701$		−	23.9242i		−	0.903606i	0.892118	−	0.451803i	$-0.149219\pi$
$702$	1.01294	−	5.72741i	0.0382309	−	0.216167i
$703$	−2.99094	+	2.99094i	−0.112805	+	0.112805i
$704$	−3.73664			−0.140830
$705$	−25.9276	+	25.5491i	−0.976492	+	0.962233i
$706$	11.3041			0.425434
$707$	19.5271	−	19.5271i	0.734392	−	0.734392i
$708$	−3.18326	+	1.59801i	−0.119634	+	0.0600569i
$709$		−	16.8818i		−	0.634008i	−0.948424	−	0.317004i	$-0.897323\pi$
$709$		−	16.8818i		−	0.634008i	0.948424	−	0.317004i	$-0.102677\pi$
$710$	−6.73760	+	2.17902i	−0.252858	+	0.0817770i
$711$	31.6177	+	23.5554i	1.18576	+	0.883396i
$712$	28.1790	+	28.1790i	1.05605	+	1.05605i
$713$	−5.54150	−	5.54150i	−0.207531	−	0.207531i
$714$	−6.72058	−	2.22824i	−0.251511	−	0.0833897i
$715$	−4.24825	+	1.37393i	−0.158875	+	0.0513821i
$716$			0.137139i			0.00512513i
$717$	14.8077	+	29.4973i	0.553005	+	1.10160i
$718$	−5.11245	+	5.11245i	−0.190795	+	0.190795i
$719$	−50.5823			−1.88640			−0.943200	−	0.332225i	$-0.892201\pi$
$719$	−50.5823			−1.88640			−0.943200	+	0.332225i	$0.892201\pi$
$720$	2.54019	+	5.15430i	0.0946674	+	0.192089i
$721$	45.4458			1.69249
$722$	−0.538497	+	0.538497i	−0.0200408	+	0.0200408i
$723$	17.1041	+	34.0717i	0.636110	+	1.26714i
$724$			8.44472i			0.313845i
$725$	−13.3804	−	18.5226i	−0.496935	−	0.687914i
$726$	−11.4616	−	3.80014i	−0.425379	−	0.141036i
$727$	19.8082	+	19.8082i	0.734647	+	0.734647i	0.971537	−	0.236889i	$-0.0761279\pi$
$727$	19.8082	+	19.8082i	0.734647	+	0.734647i	−0.236889	+	0.971537i	$0.576128\pi$
$728$	7.20372	+	7.20372i	0.266988	+	0.266988i
$729$	25.3622	+	9.26067i	0.939340	+	0.342988i
$730$	22.4948	+	11.5004i	0.832570	+	0.425648i
$731$		−	14.5158i		−	0.536885i
$732$	−19.4894	+	9.78374i	−0.720348	+	0.361618i
$733$	−5.94719	+	5.94719i	−0.219664	+	0.219664i	−0.808357	−	0.588693i	$-0.799643\pi$
$733$	−5.94719	+	5.94719i	−0.219664	+	0.219664i	0.588693	+	0.808357i	$0.299643\pi$
$734$	7.45655			0.275226
$735$	−0.00233400	+	0.317358i	−8.60908e−5	+	0.0117059i
$736$	−9.53570			−0.351491
$737$	3.58440	−	3.58440i	0.132033	−	0.132033i
$738$	18.0877	−	2.64311i	0.665817	−	0.0972943i
$739$			28.2435i			1.03895i	0.854485	+	0.519476i	$0.173873\pi$
$739$			28.2435i			1.03895i	−0.854485	+	0.519476i	$0.826127\pi$
$740$	−4.13297	−	12.7793i	−0.151931	−	0.469777i
$741$	0.801186	−	2.41645i	0.0294323	−	0.0887707i
$742$	14.8913	+	14.8913i	0.546678	+	0.546678i
$743$	−8.64350	−	8.64350i	−0.317099	−	0.317099i	0.530553	−	0.847652i	$-0.321984\pi$
$743$	−8.64350	−	8.64350i	−0.317099	−	0.317099i	−0.847652	+	0.530553i	$0.821984\pi$
$744$	−6.83895	+	20.6269i	−0.250728	+	0.756220i
$745$	20.8376	−	40.7584i	0.763429	−	1.49327i
$746$			2.14630i			0.0785816i
$747$	24.2177	−	3.53888i	0.886079	−	0.129481i
$748$	−2.75147	+	2.75147i	−0.100604	+	0.100604i
$749$	9.51713			0.347748
$750$	−14.5418	−	2.45376i	−0.530991	−	0.0895986i
$751$	37.9688			1.38550			0.692751	−	0.721177i	$-0.256398\pi$
$751$	37.9688			1.38550			0.692751	+	0.721177i	$0.256398\pi$
$752$	5.69279	−	5.69279i	0.207595	−	0.207595i
$753$	26.1357	−	13.1202i	0.952437	−	0.478127i
$754$		−	5.11541i		−	0.186292i
$755$	20.9313	−	40.9417i	0.761767	−	1.49002i
$756$	−16.0909	+	11.2546i	−0.585220	+	0.409327i
$757$	−30.3088	−	30.3088i	−1.10159	−	1.10159i	−0.994219	−	0.107374i	$-0.965756\pi$
$757$	−30.3088	−	30.3088i	−1.10159	−	1.10159i	−0.107374	−	0.994219i	$-0.534244\pi$
$758$	8.53306	+	8.53306i	0.309935	+	0.309935i
$759$	3.63349	+	1.20470i	0.131887	+	0.0437279i
$760$	−1.79213	−	5.54132i	−0.0650073	−	0.201005i
$761$		−	32.4282i		−	1.17552i	−0.809035	−	0.587760i	$-0.800010\pi$
$761$		−	32.4282i		−	1.17552i	0.809035	−	0.587760i	$-0.199990\pi$
$762$	−4.74191	−	9.44597i	−0.171781	−	0.342191i
$763$	−30.3332	+	30.3332i	−1.09813	+	1.09813i
$764$	−21.1055			−0.763570
$765$	−12.8117	−	4.35260i	−0.463207	−	0.157369i
$766$	−9.52689			−0.344221
$767$	−1.50510	+	1.50510i	−0.0543460	+	0.0543460i
$768$	9.97256	+	19.8655i	0.359854	+	0.716835i
$769$		−	44.0280i		−	1.58769i	−0.608121	−	0.793844i	$-0.708077\pi$
$769$		−	44.0280i		−	1.58769i	0.608121	−	0.793844i	$-0.291923\pi$
$770$	−5.48149	−	2.80239i	−0.197539	−	0.100991i
$771$	−5.52940	−	1.83330i	−0.199137	−	0.0660246i
$772$	9.45199	+	9.45199i	0.340184	+	0.340184i
$773$	14.9315	+	14.9315i	0.537048	+	0.537048i	0.922661	−	0.385613i	$-0.126010\pi$
$773$	14.9315	+	14.9315i	0.537048	+	0.537048i	−0.385613	+	0.922661i	$0.626010\pi$
$774$	13.1847	+	9.82269i	0.473915	+	0.353069i
$775$	14.1040	+	19.5244i	0.506632	+	0.701337i
$776$		−	25.4813i		−	0.914727i
$777$	17.4243	−	8.74708i	0.625094	−	0.313800i
$778$	12.7091	−	12.7091i	0.455643	−	0.455643i
$779$	8.00113			0.286670
$780$	5.67387	+	5.75795i	0.203157	+	0.206168i
$781$	−5.64916			−0.202143
$782$	1.76707	−	1.76707i	0.0631902	−	0.0631902i
$783$	23.3835	+	4.13557i	0.835660	+	0.147793i
$784$		−	0.0701930i		−	0.00250689i
$785$	−40.6026	+	13.1313i	−1.44917	+	0.468678i
$786$	−1.00301	+	3.02518i	−0.0357763	+	0.107905i
$787$	9.84039	+	9.84039i	0.350772	+	0.350772i	0.860397	−	0.509625i	$-0.170216\pi$
$787$	9.84039	+	9.84039i	0.350772	+	0.350772i	−0.509625	+	0.860397i	$0.670216\pi$
$788$	12.1745	+	12.1745i	0.433697	+	0.433697i
$789$	−5.47089	+	16.5007i	−0.194769	+	0.587442i
$790$	21.2942	−	6.88678i	0.757613	−	0.245021i
$791$		−	13.0201i		−	0.462941i
$792$	−1.53482	−	10.5033i	−0.0545373	−	0.373217i
$793$	−9.21489	+	9.21489i	−0.327231	+	0.327231i
$794$	1.90261			0.0675211
$795$	28.2479	+	28.6665i	1.00185	+	1.01670i
$796$	16.7115			0.592325
$797$	−20.2793	+	20.2793i	−0.718331	+	0.718331i	−0.968263	−	0.249933i	$-0.919592\pi$
$797$	−20.2793	+	20.2793i	−0.718331	+	0.718331i	0.249933	+	0.968263i	$0.419592\pi$
$798$	3.13713	−	1.57485i	0.111053	−	0.0557491i
$799$			18.9575i			0.670668i
$800$	28.9336	+	4.66363i	1.02296	+	0.164884i
$801$	−27.4234	+	36.8097i	−0.968960	+	1.30061i
$802$	−5.16674	−	5.16674i	−0.182444	−	0.182444i
$803$	14.2517	+	14.2517i	0.502931	+	0.502931i
$804$	−8.71133	−	2.88828i	−0.307225	−	0.101862i
$805$	−8.61966	−	4.40677i	−0.303803	−	0.155318i
$806$			5.39207i			0.189927i
$807$	−10.2386	−	20.3954i	−0.360414	−	0.717951i
$808$	19.1113	−	19.1113i	0.672335	−	0.672335i
$809$	37.2896			1.31103			0.655517	−	0.755180i	$-0.272451\pi$
$809$	37.2896			1.31103			0.655517	+	0.755180i	$0.272451\pi$
$810$	12.6230	−	8.69151i	0.443528	−	0.305389i
$811$	14.9637			0.525448			0.262724	−	0.964871i	$-0.415379\pi$
$811$	14.9637			0.525448			0.262724	+	0.964871i	$0.415379\pi$
$812$	−12.2118	+	12.2118i	−0.428549	+	0.428549i
$813$	−3.69605	−	7.36259i	−0.129626	−	0.258217i
$814$			4.37605i			0.153380i
$815$	−17.3105	−	53.5248i	−0.606362	−	1.87489i
$816$	2.84060	+	0.941813i	0.0994409	+	0.0329701i
$817$	5.08869	+	5.08869i	0.178031	+	0.178031i
$818$	4.70004	+	4.70004i	0.164333	+	0.164333i
$819$	−7.01056	+	9.41007i	−0.244969	+	0.328815i
$820$	−11.5650	+	22.6212i	−0.403867	+	0.789966i
$821$		−	46.8115i		−	1.63373i	−0.576826	−	0.816867i	$-0.695709\pi$
$821$		−	46.8115i		−	1.63373i	0.576826	−	0.816867i	$-0.304291\pi$
$822$	−13.3677	+	6.71064i	−0.466252	+	0.234060i
$823$	13.2385	−	13.2385i	0.461466	−	0.461466i	−0.437670	−	0.899136i	$-0.644196\pi$
$823$	13.2385	−	13.2385i	0.461466	−	0.461466i	0.899136	+	0.437670i	$0.144196\pi$
$824$	44.4782			1.54947
$825$	−10.4357	−	5.43239i	−0.363325	−	0.189131i
$826$	−2.93487			−0.102117
$827$	6.42878	−	6.42878i	0.223550	−	0.223550i	−0.586441	−	0.809992i	$-0.699472\pi$
$827$	6.42878	−	6.42878i	0.223550	−	0.223550i	0.809992	+	0.586441i	$0.199472\pi$
$828$	−1.00211	−	6.85780i	−0.0348259	−	0.238325i
$829$		−	12.7014i		−	0.441138i	−0.975371	−	0.220569i	$-0.929209\pi$
$829$		−	12.7014i		−	0.441138i	0.975371	−	0.220569i	$-0.0707913\pi$
$830$	6.32399	−	12.3698i	0.219509	−	0.429361i
$831$	2.47122	−	7.45344i	0.0857257	−	0.258557i
$832$	2.85872	+	2.85872i	0.0991082	+	0.0991082i
$833$	0.116875	+	0.116875i	0.00404946	+	0.00404946i
$834$	5.36103	−	16.1694i	0.185637	−	0.559900i
$835$	11.5883	+	35.8314i	0.401029	+	1.24000i
$836$		−	1.92913i		−	0.0667204i
$837$	−24.6482	−	4.35923i	−0.851966	−	0.150677i
$838$	−15.8321	+	15.8321i	−0.546910	+	0.546910i
$839$	42.3502			1.46209			0.731046	−	0.682328i	$-0.239032\pi$
$839$	42.3502			1.46209			0.731046	+	0.682328i	$0.239032\pi$
$840$	−0.197420	+	26.8436i	−0.00681163	+	0.926191i
$841$	−8.11506			−0.279830
$842$	19.6892	−	19.6892i	0.678534	−	0.678534i
$843$	−34.8247	+	17.4822i	−1.19943	+	0.602117i
$844$		−	10.4496i		−	0.359689i
$845$	−21.5813	−	11.0333i	−0.742419	−	0.379558i
$846$	−17.2192	−	12.8284i	−0.592007	−	0.441049i
$847$	17.2264	+	17.2264i	0.591906	+	0.591906i
$848$	−6.29414	−	6.29414i	−0.216142	−	0.216142i
$849$	−2.96456	−	0.982914i	−0.101744	−	0.0337335i
$850$	−6.22593	+	4.49748i	−0.213547	+	0.154262i
$851$			6.88135i			0.235890i
$852$	4.58869	+	9.14074i	0.157206	+	0.313156i
$853$	0.925735	−	0.925735i	0.0316966	−	0.0316966i	−0.691081	−	0.722777i	$-0.742865\pi$
$853$	0.925735	−	0.925735i	0.0316966	−	0.0316966i	0.722777	+	0.691081i	$0.242865\pi$
$854$	−17.9686			−0.614873
$855$	6.01716	−	2.96544i	0.205782	−	0.101416i
$856$	9.31450			0.318363
$857$	30.2649	−	30.2649i	1.03383	−	1.03383i	0.0344228	−	0.999407i	$-0.489041\pi$
$857$	30.2649	−	30.2649i	1.03383	−	1.03383i	0.999407	−	0.0344228i	$-0.0109593\pi$
$858$	−1.18165	−	2.35387i	−0.0403409	−	0.0803597i
$859$		−	4.89025i		−	0.166853i	−0.996514	−	0.0834267i	$-0.973414\pi$
$859$		−	4.89025i		−	0.166853i	0.996514	−	0.0834267i	$-0.0265864\pi$
$860$	−21.7423	+	7.03170i	−0.741406	+	0.239779i
$861$	−35.0058	−	11.6063i	−1.19300	−	0.395543i
$862$	4.81244	+	4.81244i	0.163912	+	0.163912i
$863$	−30.2719	−	30.2719i	−1.03047	−	1.03047i	−0.999521	−	0.0309455i	$-0.990148\pi$
$863$	−30.2719	−	30.2719i	−1.03047	−	1.03047i	−0.0309455	−	0.999521i	$-0.509852\pi$
$864$	−24.9577	+	17.4564i	−0.849079	+	0.593880i
$865$	−34.5451	+	11.1723i	−1.17457	+	0.379869i
$866$		−	18.4165i		−	0.625818i
$867$	20.0173	−	10.0487i	0.679822	−	0.341273i
$868$	12.8722	−	12.8722i	0.436912	−	0.436912i
$869$	17.8542			0.605661
$870$	9.60100	−	9.46081i	0.325504	−	0.320751i
$871$	−5.48449			−0.185835
$872$	−29.6874	+	29.6874i	−1.00534	+	1.00534i
$873$	29.0420	−	4.24383i	0.982921	−	0.143632i
$874$			1.23894i			0.0419077i
$875$	23.9989	+	17.5868i	0.811311	+	0.594543i
$876$	11.4839	−	34.6365i	0.388005	−	1.17026i
$877$	−0.591402	−	0.591402i	−0.0199702	−	0.0199702i	0.697051	−	0.717021i	$-0.254495\pi$
$877$	−0.591402	−	0.591402i	−0.0199702	−	0.0199702i	−0.717021	+	0.697051i	$0.754495\pi$
$878$	13.6804	+	13.6804i	0.461690	+	0.461690i
$879$	−17.1906	+	51.8485i	−0.579824	+	1.74881i
$880$	2.31687	+	1.18449i	0.0781017	+	0.0399292i
$881$			45.5735i			1.53541i	0.640804	+	0.767705i	$0.278601\pi$
$881$			45.5735i			1.53541i	−0.640804	+	0.767705i	$0.721399\pi$
$882$	−0.185246	+	0.0270695i	−0.00623754	+	0.000911478i
$883$	40.7570	−	40.7570i	1.37158	−	1.37158i	0.513480	−	0.858102i	$-0.328356\pi$
$883$	40.7570	−	40.7570i	1.37158	−	1.37158i	0.858102	−	0.513480i	$-0.171644\pi$
$884$	4.21003			0.141599
$885$	−5.60852	−	0.0412476i	−0.188528	−	0.00138652i
$886$	26.3810			0.886288
$887$	−28.5224	+	28.5224i	−0.957688	+	0.957688i	−0.999140	−	0.0414522i	$-0.986802\pi$
$887$	−28.5224	+	28.5224i	−0.957688	+	0.957688i	0.0414522	+	0.999140i	$0.486802\pi$
$888$	17.0534	−	8.56085i	0.572273	−	0.287283i
$889$			21.3239i			0.715181i
$890$	8.01767	+	24.7909i	0.268753	+	0.830994i
$891$	11.7153	−	3.49856i	0.392477	−	0.117206i
$892$	5.52079	+	5.52079i	0.184850	+	0.184850i
$893$	−6.64580	−	6.64580i	−0.222393	−	0.222393i
$894$	25.6310	+	8.49807i	0.857228	+	0.284218i
$895$	−0.0983001	+	0.192275i	−0.00328581	+	0.00642706i
$896$		−	25.6223i		−	0.855981i
$897$	−1.85815	−	3.70146i	−0.0620418	−	0.123588i
$898$	−19.1108	+	19.1108i	−0.637735	+	0.637735i
$899$	−22.0145			−0.734223
$900$	−0.313292	+	21.2983i	−0.0104431	+	0.709944i
$901$	20.9601			0.698281
$902$	5.85323	−	5.85323i	0.194891	−	0.194891i
$903$	−14.8820	−	29.6452i	−0.495242	−	0.986530i
$904$		−	12.7429i		−	0.423822i
$905$	−6.05309	+	11.8399i	−0.201212	+	0.393571i
$906$	25.7462	+	8.53628i	0.855362	+	0.283599i
$907$	21.1348	+	21.1348i	0.701769	+	0.701769i	0.964790	−	0.263021i	$-0.0847188\pi$
$907$	21.1348	+	21.1348i	0.701769	+	0.701769i	−0.263021	+	0.964790i	$0.584719\pi$
$908$	6.02768	+	6.02768i	0.200035	+	0.200035i
$909$	24.9648	+	18.5989i	0.828029	+	0.616887i
$910$	2.04965	+	6.33758i	0.0679451	+	0.210089i
$911$		−	8.88487i		−	0.294369i	−0.989109	−	0.147184i	$-0.952979\pi$
$911$		−	8.88487i		−	0.294369i	0.989109	−	0.147184i	$-0.0470211\pi$
$912$	−1.32597	+	0.665644i	−0.0439074	+	0.0220417i
$913$	7.83692	−	7.83692i	0.259364	−	0.259364i
$914$	−11.8985			−0.393567
$915$	−34.3379	−	0.252537i	−1.13518	−	0.00834860i
$916$	1.13199			0.0374020
$917$	4.54675	−	4.54675i	0.150147	−	0.150147i
$918$	1.39007	−	7.85980i	0.0458791	−	0.259412i
$919$		−	7.64869i		−	0.252307i	−0.992011	−	0.126154i	$-0.959737\pi$
$919$		−	7.64869i		−	0.252307i	0.992011	−	0.126154i	$-0.0402632\pi$
$920$	−8.43614	−	4.31294i	−0.278131	−	0.142194i
$921$	−12.9413	+	39.0324i	−0.426432	+	1.28616i
$922$	−6.66037	−	6.66037i	−0.219347	−	0.219347i
$923$	4.32189	+	4.32189i	0.142257	+	0.142257i
$924$	−2.79838	+	8.44017i	−0.0920598	+	0.277661i
$925$	3.36546	−	20.8797i	0.110656	−	0.686519i
$926$		−	14.1697i		−	0.465645i
$927$	7.40769	+	50.6933i	0.243301	+	1.66499i
$928$	−18.9410	+	18.9410i	−0.621770	+	0.621770i
$929$	16.9586			0.556394			0.278197	−	0.960524i	$-0.410263\pi$
$929$	16.9586			0.556394			0.278197	+	0.960524i	$0.410263\pi$
$930$	−10.1202	+	9.97247i	−0.331856	+	0.327010i
$931$	−0.0819438			−0.00268560
$932$	6.72365	−	6.72365i	0.220240	−	0.220240i
$933$	28.9608	−	14.5384i	0.948135	−	0.475967i
$934$			4.84059i			0.158389i
$935$	−5.82993	+	1.88546i	−0.190659	+	0.0616613i
$936$	−6.86130	+	9.20973i	−0.224269	+	0.301029i
$937$	−17.1226	−	17.1226i	−0.559370	−	0.559370i	0.369758	−	0.929128i	$-0.379441\pi$
$937$	−17.1226	−	17.1226i	−0.559370	−	0.559370i	−0.929128	+	0.369758i	$0.879441\pi$
$938$	−5.34725	−	5.34725i	−0.174594	−	0.174594i
$939$	46.4694	+	15.4071i	1.51647	+	0.502793i
$940$	28.3953	−	9.18336i	0.926152	−	0.299528i
$941$			14.2585i			0.464815i	0.972618	+	0.232408i	$0.0746603\pi$
$941$			14.2585i			0.464815i	−0.972618	+	0.232408i	$0.925340\pi$
$942$	−11.2936	−	22.4971i	−0.367966	−	0.732994i
$943$	9.20422	−	9.20422i	0.299730	−	0.299730i
$944$	1.24049			0.0403744
$945$	−30.6274	+	4.24570i	−0.996309	+	0.138113i
$946$	7.44526			0.242066
$947$	2.09590	−	2.09590i	0.0681075	−	0.0681075i	−0.672233	−	0.740340i	$-0.734664\pi$
$947$	2.09590	−	2.09590i	0.0681075	−	0.0681075i	0.740340	+	0.672233i	$0.234664\pi$
$948$	−14.5025	−	28.8893i	−0.471021	−	0.938281i
$949$		−	21.8065i		−	0.707868i
$950$	0.605928	−	3.75923i	0.0196589	−	0.121966i
$951$	36.3751	+	12.0603i	1.17954	+	0.391083i
$952$	9.88576	+	9.88576i	0.320399	+	0.320399i
$953$	−11.9741	−	11.9741i	−0.387880	−	0.387880i	0.486051	−	0.873931i	$-0.338437\pi$
$953$	−11.9741	−	11.9741i	−0.387880	−	0.387880i	−0.873931	+	0.486051i	$0.838437\pi$
$954$	−14.1835	+	19.0381i	−0.459208	+	0.616381i
$955$	−29.5909	−	15.1282i	−0.957539	−	0.489538i
$956$		−	27.0599i		−	0.875178i
$957$	9.61024	−	4.82438i	0.310655	−	0.155950i
$958$	−19.4390	+	19.4390i	−0.628045	+	0.628045i
$959$	30.1771			0.974469
$960$	−0.0783439	+	10.6526i	−0.00252854	+	0.343810i
$961$	−7.79494			−0.251450
$962$	3.34789	−	3.34789i	0.107940	−	0.107940i
$963$	1.55130	+	10.6160i	0.0499899	+	0.342097i
$964$		−	31.2563i		−	1.00670i
$965$	6.47703	+	20.0272i	0.208503	+	0.644699i
$966$	1.79719	−	5.42049i	0.0578236	−	0.174401i
$967$	−13.0776	−	13.0776i	−0.420546	−	0.420546i	0.464846	−	0.885392i	$-0.346110\pi$
$967$	−13.0776	−	13.0776i	−0.420546	−	0.420546i	−0.885392	+	0.464846i	$0.846110\pi$
$968$	16.8596	+	16.8596i	0.541889	+	0.541889i
$969$	1.09948	−	3.31613i	0.0353204	−	0.106530i
$970$	7.58375	−	14.8339i	0.243500	−	0.476287i
$971$		−	18.7656i		−	0.602216i	−0.953590	−	0.301108i	$-0.902644\pi$
$971$		−	18.7656i		−	0.602216i	0.953590	−	0.301108i	$-0.0973564\pi$
$972$	−15.1770	−	16.1144i	−0.486802	−	0.516868i
$973$	−24.3021	+	24.3021i	−0.779088	+	0.779088i
$974$	−18.6032			−0.596084
$975$	3.82779	+	12.1399i	0.122587	+	0.388788i
$976$	7.59483			0.243104
$977$	−18.1924	+	18.1924i	−0.582025	+	0.582025i	−0.935459	−	0.353434i	$-0.885014\pi$
$977$	−18.1924	+	18.1924i	−0.582025	+	0.582025i	0.353434	+	0.935459i	$0.385014\pi$
$978$	29.6570	−	14.8879i	0.948327	−	0.476064i
$979$			20.7860i			0.664324i
$980$	0.118443	−	0.231676i	0.00378353	−	0.00740061i
$981$	−38.7800	−	28.8913i	−1.23815	−	0.922430i
$982$	−8.13996	−	8.13996i	−0.259756	−	0.259756i
$983$	−37.5256	−	37.5256i	−1.19688	−	1.19688i	−0.975096	−	0.221785i	$-0.928812\pi$
$983$	−37.5256	−	37.5256i	−1.19688	−	1.19688i	−0.221785	−	0.975096i	$-0.571188\pi$
$984$	−34.2605	−	11.3592i	−1.09219	−	0.362119i
$985$	8.34262	+	25.7957i	0.265818	+	0.821919i
$986$		−	7.01995i		−	0.223561i
$987$	19.4358	+	38.7164i	0.618648	+	1.23236i
$988$	−1.47588	+	1.47588i	−0.0469540	+	0.0469540i
$989$	11.7077			0.372283
$990$	2.23249	−	6.57122i	0.0709531	−	0.208847i
$991$	−29.6760			−0.942688			−0.471344	−	0.881949i	$-0.656231\pi$
$991$	−29.6760			−0.942688			−0.471344	+	0.881949i	$0.656231\pi$
$992$	19.9654	−	19.9654i	0.633903	−	0.633903i
$993$	5.89463	+	11.7422i	0.187060	+	0.372627i
$994$			8.42748i			0.267304i
$995$	23.4304	+	11.9787i	0.742793	+	0.379750i
$996$	−19.0464	−	6.31493i	−0.603509	−	0.200096i
$997$	−4.05287	−	4.05287i	−0.128356	−	0.128356i	0.640011	−	0.768366i	$-0.278930\pi$
$997$	−4.05287	−	4.05287i	−0.128356	−	0.128356i	−0.768366	+	0.640011i	$0.778930\pi$
$998$	12.6042	+	12.6042i	0.398978	+	0.398978i
$999$	12.5973	+	18.0105i	0.398560	+	0.569827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.k.d.77.11	yes	36
3.2	odd	2	inner	285.2.k.d.77.8	✓	36
5.3	odd	4	inner	285.2.k.d.248.8	yes	36
15.8	even	4	inner	285.2.k.d.248.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.k.d.77.8	✓	36	3.2	odd	2	inner
285.2.k.d.77.11	yes	36	1.1	even	1	trivial
285.2.k.d.248.8	yes	36	5.3	odd	4	inner
285.2.k.d.248.11	yes	36	15.8	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.538497 - 0.538497i) q^{2} +(-0.777077 - 1.54795i) q^{3} +1.42004i q^{4} +(-1.01787 + 1.99096i) q^{5} +(-1.25202 - 0.415113i) q^{6} +(1.88175 + 1.88175i) q^{7} +(1.84168 + 1.84168i) q^{8} +(-1.79230 + 2.40575i) q^{9} +O(q^{10})\)	\(q+(0.538497 - 0.538497i) q^{2} +(-0.777077 - 1.54795i) q^{3} +1.42004i q^{4} +(-1.01787 + 1.99096i) q^{5} +(-1.25202 - 0.415113i) q^{6} +(1.88175 + 1.88175i) q^{7} +(1.84168 + 1.84168i) q^{8} +(-1.79230 + 2.40575i) q^{9} +(0.524007 + 1.62025i) q^{10} +1.35850i q^{11} +(2.19815 - 1.10348i) q^{12} +(1.03932 - 1.03932i) q^{13} +2.02663 q^{14} +(3.87288 + 0.0284829i) q^{15} -0.856600 q^{16} +(1.42628 - 1.42628i) q^{17} +(0.330342 + 2.26064i) q^{18} +1.00000i q^{19} +(-2.82725 - 1.44542i) q^{20} +(1.45059 - 4.37511i) q^{21} +(0.731550 + 0.731550i) q^{22} +(1.15037 + 1.15037i) q^{23} +(1.41970 - 4.28196i) q^{24} +(-2.92787 - 4.05309i) q^{25} -1.11935i q^{26} +(5.11675 + 0.904938i) q^{27} +(-2.67216 + 2.67216i) q^{28} +4.57000 q^{29} +(2.10087 - 2.07020i) q^{30} -4.81716 q^{31} +(-4.14464 + 4.14464i) q^{32} +(2.10290 - 1.05566i) q^{33} -1.53609i q^{34} +(-5.66187 + 1.83111i) q^{35} +(-3.41627 - 2.54514i) q^{36} +(2.99094 + 2.99094i) q^{37} +(0.538497 + 0.538497i) q^{38} +(-2.41645 - 0.801186i) q^{39} +(-5.54132 + 1.79213i) q^{40} -8.00113i q^{41} +(-1.57485 - 3.13713i) q^{42} +(5.08869 - 5.08869i) q^{43} -1.92913 q^{44} +(-2.96544 - 6.01716i) q^{45} +1.23894 q^{46} +(-6.64580 + 6.64580i) q^{47} +(0.665644 + 1.32597i) q^{48} +0.0819438i q^{49} +(-3.75923 - 0.605928i) q^{50} +(-3.31613 - 1.09948i) q^{51} +(1.47588 + 1.47588i) q^{52} +(7.34782 + 7.34782i) q^{53} +(3.24266 - 2.26805i) q^{54} +(-2.70473 - 1.38278i) q^{55} +6.93116i q^{56} +(1.54795 - 0.777077i) q^{57} +(2.46093 - 2.46093i) q^{58} -1.44815 q^{59} +(-0.0404469 + 5.49965i) q^{60} -8.86625 q^{61} +(-2.59403 + 2.59403i) q^{62} +(-7.89968 + 1.15436i) q^{63} +2.75056i q^{64} +(1.01136 + 3.12715i) q^{65} +(0.563933 - 1.70087i) q^{66} +(-2.63849 - 2.63849i) q^{67} +(2.02537 + 2.02537i) q^{68} +(0.886786 - 2.67463i) q^{69} +(-2.06285 + 4.03495i) q^{70} +4.15837i q^{71} +(-7.73149 + 1.12978i) q^{72} +(10.4907 - 10.4907i) q^{73} +3.22123 q^{74} +(-3.99880 + 7.68177i) q^{75} -1.42004 q^{76} +(-2.55636 + 2.55636i) q^{77} +(-1.73269 + 0.869818i) q^{78} -13.1425i q^{79} +(0.871909 - 1.70546i) q^{80} +(-2.57531 - 8.62368i) q^{81} +(-4.30858 - 4.30858i) q^{82} +(-5.76879 - 5.76879i) q^{83} +(6.21284 + 2.05990i) q^{84} +(1.38790 + 4.29143i) q^{85} -5.48049i q^{86} +(-3.55125 - 7.07414i) q^{87} +(-2.50193 + 2.50193i) q^{88} +15.3007 q^{89} +(-4.83710 - 1.64334i) q^{90} +3.91149 q^{91} +(-1.63357 + 1.63357i) q^{92} +(3.74331 + 7.45673i) q^{93} +7.15749i q^{94} +(-1.99096 - 1.01787i) q^{95} +(9.63641 + 3.19499i) q^{96} +(-6.91795 - 6.91795i) q^{97} +(0.0441265 + 0.0441265i) q^{98} +(-3.26823 - 2.43485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7	\( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) \) 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^10 - 18 * q^12 - 8 * q^13 - 8 * q^15 - 84 * q^16 + 8 * q^21 + 40 * q^22 - 20 * q^25 - 14 * q^27 + 36 * q^28 + 28 * q^30 - 28 * q^33 + 92 * q^36 - 4 * q^37 - 20 * q^40 - 100 * q^42 + 16 * q^43 + 28 * q^45 - 24 * q^46 - 58 * q^48 + 32 * q^51 + 148 * q^52 - 72 * q^55 - 2 * q^57 - 12 * q^58 + 58 * q^60 - 112 * q^61 - 64 * q^63 + 92 * q^66 - 8 * q^67 + 8 * q^70 - 88 * q^72 + 76 * q^73 + 80 * q^75 + 36 * q^76 - 36 * q^78 + 4 * q^81 + 20 * q^82 - 28 * q^85 - 4 * q^87 + 140 * q^88 + 76 * q^90 - 24 * q^91 - 48 * q^93 + 32 * q^96 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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