LMFDB - Embedded newform 357.2.p.a.16.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(16,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("357.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.p (of order $6$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			16.11
Character	$\chi$	$=$	357.16
Dual form			357.2.p.a.67.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0460015 - 0.0796769i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.995768 + 1.72472i) q^{4} +(-2.24725 - 1.29745i) q^{5} +0.0920029i q^{6} +(-0.592654 + 2.57852i) q^{7} +0.367233 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.0460015 - 0.0796769i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.995768 + 1.72472i) q^{4} +(-2.24725 - 1.29745i) q^{5} +0.0920029i q^{6} +(-0.592654 + 2.57852i) q^{7} +0.367233 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.206754 + 0.119369i) q^{10} +(0.491425 - 0.283724i) q^{11} +(-1.72472 - 0.995768i) q^{12} -4.02464 q^{13} +(0.178185 + 0.165836i) q^{14} +2.59490 q^{15} +(-1.97464 + 3.42018i) q^{16} +(-4.08417 + 0.565300i) q^{17} +(-0.0460015 - 0.0796769i) q^{18} +(-2.52479 + 4.37306i) q^{19} -5.16784i q^{20} +(-0.776007 - 2.52939i) q^{21} -0.0522069i q^{22} +(-0.789725 - 0.455948i) q^{23} +(-0.318033 + 0.183617i) q^{24} +(0.866760 + 1.50127i) q^{25} +(-0.185140 + 0.320671i) q^{26} +1.00000i q^{27} +(-5.03737 + 1.54544i) q^{28} +3.39629i q^{29} +(0.119369 - 0.206754i) q^{30} +(3.87189 - 2.23544i) q^{31} +(0.548906 + 0.950733i) q^{32} +(-0.283724 + 0.491425i) q^{33} +(-0.142836 + 0.351419i) q^{34} +(4.67734 - 5.02564i) q^{35} +1.99154 q^{36} +(-1.21803 - 0.703231i) q^{37} +(0.232288 + 0.402334i) q^{38} +(3.48544 - 2.01232i) q^{39} +(-0.825265 - 0.476467i) q^{40} +7.36878i q^{41} +(-0.237231 - 0.0545259i) q^{42} +2.56899 q^{43} +(0.978690 + 0.565047i) q^{44} +(-2.24725 + 1.29745i) q^{45} +(-0.0726571 + 0.0419486i) q^{46} +(2.24907 - 3.89551i) q^{47} -3.94928i q^{48} +(-6.29752 - 3.05634i) q^{49} +0.159489 q^{50} +(3.25434 - 2.53165i) q^{51} +(-4.00761 - 6.94139i) q^{52} +(0.854178 + 1.47948i) q^{53} +(0.0796769 + 0.0460015i) q^{54} -1.47247 q^{55} +(-0.217642 + 0.946917i) q^{56} -5.04957i q^{57} +(0.270606 + 0.156234i) q^{58} +(5.95304 + 10.3110i) q^{59} +(2.58392 + 4.47548i) q^{60} +(10.3915 + 5.99952i) q^{61} -0.411334i q^{62} +(1.93674 + 1.80251i) q^{63} -7.79757 q^{64} +(9.04439 + 5.22178i) q^{65} +(0.0261035 + 0.0452125i) q^{66} +(4.74414 + 8.21710i) q^{67} +(-5.04187 - 6.48114i) q^{68} +0.911896 q^{69} +(-0.185263 - 0.603863i) q^{70} -11.4550i q^{71} +(0.183617 - 0.318033i) q^{72} +(7.71523 - 4.45439i) q^{73} +(-0.112062 + 0.0646993i) q^{74} +(-1.50127 - 0.866760i) q^{75} -10.0564 q^{76} +(0.440344 + 1.43530i) q^{77} -0.370279i q^{78} +(6.99091 + 4.03620i) q^{79} +(8.87504 - 5.12400i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.587122 + 0.338975i) q^{82} -17.8951 q^{83} +(3.58977 - 3.85708i) q^{84} +(9.91160 + 4.02864i) q^{85} +(0.118177 - 0.204689i) q^{86} +(-1.69814 - 2.94127i) q^{87} +(0.180467 - 0.104193i) q^{88} +(9.00190 - 15.5918i) q^{89} +0.238739i q^{90} +(2.38522 - 10.3776i) q^{91} -1.81607i q^{92} +(-2.23544 + 3.87189i) q^{93} +(-0.206921 - 0.358398i) q^{94} +(11.3477 - 6.55158i) q^{95} +(-0.950733 - 0.548906i) q^{96} +7.04692i q^{97} +(-0.533215 + 0.361171i) q^{98} -0.567448i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) $ 48 * q - 24 * q^4 + 24 * q^9	$ 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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 $

$2$	0.0460015	−	0.0796769i	0.0325280	−	0.0563401i	−0.849303	−	0.527905i	$-0.822978\pi$
$2$	0.0460015	−	0.0796769i	0.0325280	−	0.0563401i	0.881831	+	0.471565i	$0.156311\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.995768	+	1.72472i	0.497884	+	0.862360i
$5$	−2.24725	−	1.29745i	−1.00500	−	0.580238i	−0.0952772	−	0.995451i	$-0.530374\pi$
$5$	−2.24725	−	1.29745i	−1.00500	−	0.580238i	−0.909724	+	0.415213i	$0.863707\pi$
$6$			0.0920029i			0.0375600i
$7$	−0.592654	+	2.57852i	−0.224002	+	0.974589i
$7$	−0.592654	+	2.57852i	−0.224002	+	0.974589i
$8$	0.367233			0.129836
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.206754	+	0.119369i	−0.0653813	+	0.0377479i
$11$	0.491425	−	0.283724i	0.148170	−	0.0855460i	−0.424082	−	0.905624i	$-0.639403\pi$
$11$	0.491425	−	0.283724i	0.148170	−	0.0855460i	0.572252	+	0.820078i	$0.306070\pi$
$12$	−1.72472	−	0.995768i	−0.497884	−	0.287453i
$13$	−4.02464			−1.11624			−0.558118	−	0.829762i	$-0.688476\pi$
$13$	−4.02464			−1.11624			−0.558118	+	0.829762i	$0.688476\pi$
$14$	0.178185	+	0.165836i	0.0476221	+	0.0443217i
$15$	2.59490			0.670001
$16$	−1.97464	+	3.42018i	−0.493661	+	0.855045i
$17$	−4.08417	+	0.565300i	−0.990556	+	0.137105i
$17$	−4.08417	+	0.565300i	−0.990556	+	0.137105i
$18$	−0.0460015	−	0.0796769i	−0.0108427	−	0.0187800i
$19$	−2.52479	+	4.37306i	−0.579226	+	1.00325i	0.416343	+	0.909208i	$0.363312\pi$
$19$	−2.52479	+	4.37306i	−0.579226	+	1.00325i	−0.995568	+	0.0940407i	$0.970022\pi$
$20$		−	5.16784i		−	1.15556i
$21$	−0.776007	−	2.52939i	−0.169339	−	0.551958i
$22$		−	0.0522069i		−	0.0111306i
$23$	−0.789725	−	0.455948i	−0.164669	−	0.0950718i	0.415401	−	0.909639i	$-0.363641\pi$
$23$	−0.789725	−	0.455948i	−0.164669	−	0.0950718i	−0.580070	+	0.814567i	$0.696975\pi$
$24$	−0.318033	+	0.183617i	−0.0649182	+	0.0374806i
$25$	0.866760	+	1.50127i	0.173352	+	0.300254i
$26$	−0.185140	+	0.320671i	−0.0363089	+	0.0628888i
$27$			1.00000i			0.192450i
$28$	−5.03737	+	1.54544i	−0.951973	+	0.292062i
$29$			3.39629i			0.630675i	0.948980	+	0.315337i	$0.102118\pi$
$29$			3.39629i			0.630675i	−0.948980	+	0.315337i	$0.897882\pi$
$30$	0.119369	−	0.206754i	0.0217938	−	0.0377479i
$31$	3.87189	−	2.23544i	0.695412	−	0.401496i	−0.110224	−	0.993907i	$-0.535157\pi$
$31$	3.87189	−	2.23544i	0.695412	−	0.401496i	0.805636	+	0.592410i	$0.201824\pi$
$32$	0.548906	+	0.950733i	0.0970338	+	0.168067i
$33$	−0.283724	+	0.491425i	−0.0493900	+	0.0855460i
$34$	−0.142836	+	0.351419i	−0.0244962	+	0.0602678i
$35$	4.67734	−	5.02564i	0.790616	−	0.849489i
$36$	1.99154			0.331923
$37$	−1.21803	−	0.703231i	−0.200243	−	0.115610i	0.396526	−	0.918024i	$-0.370216\pi$
$37$	−1.21803	−	0.703231i	−0.200243	−	0.115610i	−0.596769	+	0.802413i	$0.703549\pi$
$38$	0.232288	+	0.402334i	0.0376821	+	0.0652672i
$39$	3.48544	−	2.01232i	0.558118	−	0.322229i
$40$	−0.825265	−	0.476467i	−0.130486	−	0.0753360i
$41$			7.36878i			1.15081i	0.817868	+	0.575405i	$0.195156\pi$
$41$			7.36878i			1.15081i	−0.817868	+	0.575405i	$0.804844\pi$
$42$	−0.237231	−	0.0545259i	−0.0366056	−	0.00841352i
$43$	2.56899			0.391768			0.195884	−	0.980627i	$-0.437242\pi$
$43$	2.56899			0.391768			0.195884	+	0.980627i	$0.437242\pi$
$44$	0.978690	+	0.565047i	0.147543	+	0.0851840i
$45$	−2.24725	+	1.29745i	−0.335000	+	0.193413i
$46$	−0.0726571	+	0.0419486i	−0.0107127	+	0.00618498i
$47$	2.24907	−	3.89551i	0.328061	−	0.568218i	−0.654066	−	0.756437i	$-0.726938\pi$
$47$	2.24907	−	3.89551i	0.328061	−	0.568218i	0.982127	+	0.188219i	$0.0602715\pi$
$48$		−	3.94928i		−	0.570030i
$49$	−6.29752	−	3.05634i	−0.899646	−	0.436620i
$50$	0.159489			0.0225551
$51$	3.25434	−	2.53165i	0.455699	−	0.354502i
$52$	−4.00761	−	6.94139i	−0.555756	−	0.962597i
$53$	0.854178	+	1.47948i	0.117330	+	0.203222i	0.918709	−	0.394935i	$-0.129233\pi$
$53$	0.854178	+	1.47948i	0.117330	+	0.203222i	−0.801379	+	0.598158i	$0.795900\pi$
$54$	0.0796769	+	0.0460015i	0.0108427	+	0.00626001i
$55$	−1.47247			−0.198548
$56$	−0.217642	+	0.946917i	−0.0290836	+	0.126537i
$57$		−	5.04957i		−	0.668832i
$58$	0.270606	+	0.156234i	0.0355323	+	0.0205146i
$59$	5.95304	+	10.3110i	0.775019	+	1.34237i	0.934784	+	0.355218i	$0.115593\pi$
$59$	5.95304	+	10.3110i	0.775019	+	1.34237i	−0.159764	+	0.987155i	$0.551073\pi$
$60$	2.58392	+	4.47548i	0.333583	+	0.577782i
$61$	10.3915	+	5.99952i	1.33049	+	0.768160i	0.985375	−	0.170400i	$-0.0545060\pi$
$61$	10.3915	+	5.99952i	1.33049	+	0.768160i	0.345117	+	0.938560i	$0.387839\pi$
$62$		−	0.411334i		−	0.0522394i
$63$	1.93674	+	1.80251i	0.244006	+	0.227095i
$64$	−7.79757			−0.974696
$65$	9.04439	+	5.22178i	1.12182	+	0.647682i
$66$	0.0261035	+	0.0452125i	0.00321311	+	0.00556528i
$67$	4.74414	+	8.21710i	0.579589	+	1.00388i	0.995526	+	0.0944847i	$0.0301204\pi$
$67$	4.74414	+	8.21710i	0.579589	+	1.00388i	−0.415937	+	0.909393i	$0.636546\pi$
$68$	−5.04187	−	6.48114i	−0.611416	−	0.785954i
$69$	0.911896			0.109779
$70$	−0.185263	−	0.603863i	−0.0221431	−	0.0721755i
$71$		−	11.4550i		−	1.35946i	−0.733461	−	0.679731i	$-0.762096\pi$
$71$		−	11.4550i		−	1.35946i	0.733461	−	0.679731i	$-0.237904\pi$
$72$	0.183617	−	0.318033i	0.0216394	−	0.0374806i
$73$	7.71523	−	4.45439i	0.902999	−	0.521347i	0.0248271	−	0.999692i	$-0.492096\pi$
$73$	7.71523	−	4.45439i	0.902999	−	0.521347i	0.878172	+	0.478345i	$0.158763\pi$
$74$	−0.112062	+	0.0646993i	−0.0130270	+	0.00752114i
$75$	−1.50127	−	0.866760i	−0.173352	−	0.100085i
$76$	−10.0564			−1.15355
$77$	0.440344	+	1.43530i	0.0501818	+	0.163567i
$78$		−	0.370279i		−	0.0419259i
$79$	6.99091	+	4.03620i	0.786539	+	0.454108i	0.838743	−	0.544528i	$-0.183291\pi$
$79$	6.99091	+	4.03620i	0.786539	+	0.454108i	−0.0522040	+	0.998636i	$0.516625\pi$
$80$	8.87504	−	5.12400i	0.992259	−	0.572881i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.587122	+	0.338975i	0.0648367	+	0.0374335i
$83$	−17.8951			−1.96424			−0.982121	−	0.188252i	$-0.939718\pi$
$83$	−17.8951			−1.96424			−0.982121	+	0.188252i	$0.939718\pi$
$84$	3.58977	−	3.85708i	0.391676	−	0.420842i
$85$	9.91160	+	4.02864i	1.07506	+	0.436967i
$86$	0.118177	−	0.204689i	0.0127434	−	0.0220722i
$87$	−1.69814	−	2.94127i	−0.182060	−	0.315337i
$88$	0.180467	−	0.104193i	0.0192379	−	0.0111070i
$89$	9.00190	−	15.5918i	0.954200	−	1.65272i	0.218012	−	0.975946i	$-0.430043\pi$
$89$	9.00190	−	15.5918i	0.954200	−	1.65272i	0.736188	−	0.676777i	$-0.236624\pi$
$90$			0.238739i			0.0251653i
$91$	2.38522	−	10.3776i	0.250039	−	1.08787i
$92$		−	1.81607i		−	0.189339i
$93$	−2.23544	+	3.87189i	−0.231804	+	0.401496i
$94$	−0.206921	−	0.358398i	−0.0213423	−	0.0369660i
$95$	11.3477	−	6.55158i	1.16425	−	0.672177i
$96$	−0.950733	−	0.548906i	−0.0970338	−	0.0560225i
$97$			7.04692i			0.715506i	0.933816	+	0.357753i	$0.116457\pi$
$97$			7.04692i			0.715506i	−0.933816	+	0.357753i	$0.883543\pi$
$98$	−0.533215	+	0.361171i	−0.0538628	+	0.0364838i
$99$		−	0.567448i		−	0.0570307i
$100$	−1.72618	+	2.98984i	−0.172618	+	0.298984i
$101$	−0.496397	−	0.859785i	−0.0493934	−	0.0855518i	0.840272	−	0.542166i	$-0.182395\pi$
$101$	−0.496397	−	0.859785i	−0.0493934	−	0.0855518i	−0.889665	+	0.456614i	$0.849062\pi$
$102$	−0.0520093	−	0.375756i	−0.00514969	−	0.0372053i
$103$	7.09571	−	12.2901i	0.699161	−	1.21098i	−0.269597	−	0.962973i	$-0.586891\pi$
$103$	7.09571	−	12.2901i	0.699161	−	1.21098i	0.968758	−	0.248009i	$-0.0797762\pi$
$104$	−1.47798			−0.144928
$105$	−1.53788	+	6.69101i	−0.150082	+	0.652975i
$106$	0.157174			0.0152661
$107$	−5.98706	−	3.45663i	−0.578791	−	0.334165i	0.181862	−	0.983324i	$-0.441788\pi$
$107$	−5.98706	−	3.45663i	−0.578791	−	0.334165i	−0.760653	+	0.649159i	$0.775121\pi$
$108$	−1.72472	+	0.995768i	−0.165961	+	0.0958178i
$109$	−7.61859	+	4.39860i	−0.729729	+	0.421309i	−0.818323	−	0.574759i	$-0.805096\pi$
$109$	−7.61859	+	4.39860i	−0.729729	+	0.421309i	0.0885940	+	0.996068i	$0.471763\pi$
$110$	−0.0677359	+	0.117322i	−0.00645837	+	0.0111862i
$111$	1.40646			0.133495
$112$	−7.64872	−	7.11864i	−0.722736	−	0.672648i
$113$			5.17191i			0.486532i	0.969960	+	0.243266i	$0.0782188\pi$
$113$			5.17191i			0.486532i	−0.969960	+	0.243266i	$0.921781\pi$
$114$	−0.402334	−	0.232288i	−0.0376821	−	0.0217557i
$115$	1.18314	+	2.04926i	0.110328	+	0.191095i
$116$	−5.85765	+	3.38191i	−0.543869	+	0.314003i
$117$	−2.01232	+	3.48544i	−0.186039	+	0.322229i
$118$	1.09539			0.100839
$119$	0.962859	−	10.8661i	0.0882651	−	0.996097i
$120$	0.952934			0.0869906
$121$	−5.33900	+	9.24742i	−0.485364	+	0.840675i
$122$	0.956046	−	0.551973i	0.0865563	−	0.0499733i
$123$	−3.68439	−	6.38155i	−0.332210	−	0.575405i
$124$	7.71101	+	4.45195i	0.692469	+	0.399797i
$125$			8.47620i			0.758134i
$126$	0.232711	−	0.0713949i	0.0207316	−	0.00636036i
$127$	−3.02483			−0.268410			−0.134205	−	0.990954i	$-0.542848\pi$
$127$	−3.02483			−0.268410			−0.134205	+	0.990954i	$0.542848\pi$
$128$	−1.45651	+	2.52275i	−0.128739	+	0.222982i
$129$	−2.22481	+	1.28450i	−0.195884	+	0.113094i
$130$	0.832110	−	0.480419i	0.0729809	−	0.0421356i
$131$	−4.05477	−	2.34102i	−0.354267	−	0.204536i	0.312296	−	0.949985i	$-0.398902\pi$
$131$	−4.05477	−	2.34102i	−0.354267	−	0.204536i	−0.666563	+	0.745449i	$0.732235\pi$
$132$	−1.13009			−0.0983620
$133$	−9.77969	−	9.10192i	−0.848007	−	0.789237i
$134$	0.872950			0.0754114
$135$	1.29745	−	2.24725i	0.111667	−	0.193413i
$136$	−1.49984	+	0.207597i	−0.128610	+	0.0178013i
$137$	1.73267	+	3.00108i	0.148032	+	0.256399i	0.930500	−	0.366292i	$-0.119373\pi$
$137$	1.73267	+	3.00108i	0.148032	+	0.256399i	−0.782468	+	0.622691i	$0.786039\pi$
$138$	0.0419486	−	0.0726571i	0.00357090	−	0.00618498i
$139$			16.2881i			1.38153i	0.723077	+	0.690767i	$0.242727\pi$
$139$			16.2881i			1.38153i	−0.723077	+	0.690767i	$0.757273\pi$
$140$	13.3254	+	3.06274i	1.12620	+	0.258849i
$141$			4.49815i			0.378812i
$142$	−0.912702	−	0.526949i	−0.0765922	−	0.0442205i
$143$	−1.97781	+	1.14189i	−0.165393	+	0.0954895i
$144$	1.97464	+	3.42018i	0.164554	+	0.285015i
$145$	4.40652	−	7.63231i	0.365941	−	0.633829i
$146$		−	0.819634i		−	0.0678334i
$147$	6.98198	−	0.501896i	0.575864	−	0.0413957i
$148$		−	2.80102i		−	0.230242i
$149$	−10.0891	+	17.4749i	−0.826535	+	1.43160i	0.0742050	+	0.997243i	$0.476358\pi$
$149$	−10.0891	+	17.4749i	−0.826535	+	1.43160i	−0.900740	+	0.434358i	$0.856975\pi$
$150$	−0.138121	+	0.0797444i	−0.0112776	+	0.00651111i
$151$	5.89907	+	10.2175i	0.480059	+	0.831487i	0.999738	−	0.0228744i	$-0.00728177\pi$
$151$	5.89907	+	10.2175i	0.480059	+	0.831487i	−0.519679	+	0.854362i	$0.673948\pi$
$152$	−0.927185	+	1.60593i	−0.0752046	+	0.130258i
$153$	−1.55252	+	3.81964i	−0.125514	+	0.308800i
$154$	0.134617	+	0.0309406i	0.0108477	+	0.00249327i
$155$	−11.6015			−0.931854
$156$	6.94139	+	4.00761i	0.555756	+	0.320866i
$157$	7.57587	+	13.1218i	0.604620	+	1.04723i	0.992111	+	0.125359i	$0.0400083\pi$
$157$	7.57587	+	13.1218i	0.604620	+	1.04723i	−0.387492	+	0.921873i	$0.626658\pi$
$158$	0.643184	−	0.371342i	0.0511690	−	0.0295424i
$159$	−1.47948	−	0.854178i	−0.117330	−	0.0677407i
$160$		−	2.84871i		−	0.225211i
$161$	1.64370	−	1.76610i	0.129542	−	0.139188i
$162$	−0.0920029			−0.00722843
$163$	−9.99885	−	5.77284i	−0.783171	−	0.452164i	0.0543821	−	0.998520i	$-0.482681\pi$
$163$	−9.99885	−	5.77284i	−0.783171	−	0.452164i	−0.837553	+	0.546356i	$0.816014\pi$
$164$	−12.7091	+	7.33760i	−0.992413	+	0.572970i
$165$	1.27520	−	0.736236i	0.0992741	−	0.0573159i
$166$	−0.823201	+	1.42583i	−0.0638928	+	0.110665i
$167$			2.63261i			0.203717i	0.994799	+	0.101859i	$0.0324790\pi$
$167$			2.63261i			0.203717i	−0.994799	+	0.101859i	$0.967521\pi$
$168$	−0.284975	−	0.928875i	−0.0219863	−	0.0716643i
$169$	3.19777			0.245982
$170$	0.776938	−	0.604403i	0.0595884	−	0.0463556i
$171$	2.52479	+	4.37306i	0.193075	+	0.334416i
$172$	2.55812	+	4.43079i	0.195055	+	0.337845i
$173$	−5.35289	−	3.09049i	−0.406972	−	0.234966i	0.282516	−	0.959263i	$-0.408831\pi$
$173$	−5.35289	−	3.09049i	−0.406972	−	0.234966i	−0.689488	+	0.724297i	$0.742164\pi$
$174$	−0.312468			−0.0236882
$175$	−4.38475	+	1.34522i	−0.331456	+	0.101689i
$176$			2.24101i			0.168923i
$177$	−10.3110	−	5.95304i	−0.775019	−	0.447458i
$178$	−0.828202	−	1.43449i	−0.0620763	−	0.107519i
$179$	0.730702	+	1.26561i	0.0546152	+	0.0945964i	0.892040	−	0.451956i	$-0.149273\pi$
$179$	0.730702	+	1.26561i	0.0546152	+	0.0945964i	−0.837425	+	0.546552i	$0.815940\pi$
$180$	−4.47548	−	2.58392i	−0.333583	−	0.192594i
$181$		−	15.0781i		−	1.12075i	−0.828240	−	0.560374i	$-0.810658\pi$
$181$		−	15.0781i		−	1.12075i	0.828240	−	0.560374i	$-0.189342\pi$
$182$	−0.717133	−	0.667433i	−0.0531574	−	0.0494734i
$183$	−11.9990			−0.886994
$184$	−0.290013	−	0.167439i	−0.0213801	−	0.0123438i
$185$	1.82481	+	3.16067i	0.134163	+	0.232377i
$186$	0.205667	+	0.356225i	0.0150802	+	0.0261197i
$187$	−1.84667	+	1.43658i	−0.135042	+	0.105053i
$188$	8.95822			0.653345
$189$	−2.57852	−	0.592654i	−0.187560	−	0.0431092i
$190$		−	1.20553i		−	0.0874582i
$191$	2.68838	−	4.65641i	0.194525	−	0.336926i	−0.752220	−	0.658912i	$-0.771017\pi$
$191$	2.68838	−	4.65641i	0.194525	−	0.336926i	0.946745	+	0.321986i	$0.104350\pi$
$192$	6.75289	−	3.89878i	0.487348	−	0.281370i
$193$	−10.0785	+	5.81882i	−0.725465	+	0.418848i	−0.816761	−	0.576976i	$-0.804233\pi$
$193$	−10.0785	+	5.81882i	−0.725465	+	0.418848i	0.0912955	+	0.995824i	$0.470899\pi$
$194$	0.561477	+	0.324169i	0.0403117	+	0.0232740i
$195$	−10.4436			−0.747879
$196$	−0.999544	−	13.9049i	−0.0713960	−	0.993205i
$197$			11.9759i			0.853248i	0.904429	+	0.426624i	$0.140297\pi$
$197$			11.9759i			0.853248i	−0.904429	+	0.426624i	$0.859703\pi$
$198$	−0.0452125	−	0.0261035i	−0.00321311	−	0.00185509i
$199$	3.39920	−	1.96253i	0.240963	−	0.139120i	−0.374656	−	0.927164i	$-0.622239\pi$
$199$	3.39920	−	1.96253i	0.240963	−	0.139120i	0.615619	+	0.788044i	$0.288906\pi$
$200$	0.318303	+	0.551317i	0.0225074	+	0.0389840i
$201$	−8.21710	−	4.74414i	−0.579589	−	0.334626i
$202$	−0.0913400			−0.00642666
$203$	−8.75739	−	2.01282i	−0.614648	−	0.141272i
$204$	7.60696	+	3.09190i	0.532594	+	0.216476i
$205$	9.56064	−	16.5595i	0.667744	−	1.15657i
$206$	−0.652826	−	1.13073i	−0.0454845	−	0.0787815i
$207$	−0.789725	+	0.455948i	−0.0548897	+	0.0316906i
$208$	7.94723	−	13.7650i	0.551042	−	0.954432i
$209$			2.86537i			0.198202i
$210$	0.462374	+	0.430329i	0.0319068	+	0.0296956i
$211$		−	24.8315i		−	1.70947i	−0.519063	−	0.854736i	$-0.673719\pi$
$211$		−	24.8315i		−	1.70947i	0.519063	−	0.854736i	$-0.326281\pi$
$212$	−1.70113	+	2.94644i	−0.116834	+	0.202362i
$213$	5.72752	+	9.92035i	0.392443	+	0.679731i
$214$	−0.550827	+	0.318020i	−0.0376537	+	0.0217394i
$215$	−5.77317	−	3.33314i	−0.393727	−	0.227318i
$216$			0.367233i			0.0249870i
$217$	3.46943	+	11.3086i	0.235520	+	0.767677i
$218$			0.809368i			0.0548173i
$219$	−4.45439	+	7.71523i	−0.301000	+	0.521347i
$220$	−1.46624	−	2.53960i	−0.0988540	−	0.171220i
$221$	16.4373	−	2.27513i	1.10569	−	0.153042i
$222$	0.0646993	−	0.112062i	0.00434233	−	0.00752114i
$223$	3.36437			0.225295			0.112647	−	0.993635i	$-0.464067\pi$
$223$	3.36437			0.225295			0.112647	+	0.993635i	$0.464067\pi$
$224$	−2.77679	+	0.851909i	−0.185532	+	0.0569206i
$225$	1.73352			0.115568
$226$	0.412081	+	0.237915i	0.0274112	+	0.0158259i
$227$	−14.7815	+	8.53413i	−0.981086	+	0.566430i	−0.902598	−	0.430485i	$-0.858343\pi$
$227$	−14.7815	+	8.53413i	−0.981086	+	0.566430i	−0.0784879	+	0.996915i	$0.525009\pi$
$228$	8.70910	−	5.02820i	0.576774	−	0.333001i
$229$	12.3043	−	21.3116i	0.813089	−	1.40831i	−0.0976035	−	0.995225i	$-0.531118\pi$
$229$	12.3043	−	21.3116i	0.813089	−	1.40831i	0.910692	−	0.413086i	$-0.135549\pi$
$230$	0.217705			0.0143550
$231$	−1.09900	−	1.02283i	−0.0723087	−	0.0672974i
$232$			1.24723i			0.0818846i
$233$	−15.3132	−	8.84109i	−1.00320	−	0.579199i	−0.0940081	−	0.995571i	$-0.529968\pi$
$233$	−15.3132	−	8.84109i	−1.00320	−	0.579199i	−0.909194	+	0.416372i	$0.863301\pi$
$234$	0.185140	+	0.320671i	0.0121030	+	0.0209629i
$235$	−10.1085	+	5.83612i	−0.659403	+	0.380707i
$236$	−11.8557	+	20.5346i	−0.771739	+	1.33669i
$237$	−8.07240			−0.524359
$238$	−0.821487	−	0.576576i	−0.0532491	−	0.0373739i
$239$	15.9412			1.03115			0.515576	−	0.856844i	$-0.327578\pi$
$239$	15.9412			1.03115			0.515576	+	0.856844i	$0.327578\pi$
$240$	−5.12400	+	8.87504i	−0.330753	+	0.572881i
$241$	−8.63027	+	4.98269i	−0.555925	+	0.320963i	−0.751508	−	0.659724i	$-0.770673\pi$
$241$	−8.63027	+	4.98269i	−0.555925	+	0.320963i	0.195583	+	0.980687i	$0.437340\pi$
$242$	0.491204	+	0.850790i	0.0315758	+	0.0546909i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$			23.8965i			1.52982i
$245$	10.1867	+	15.0391i	0.650803	+	0.960812i
$246$	−0.677950			−0.0432245
$247$	10.1614	−	17.6000i	0.646552	−	1.11986i
$248$	1.42189	−	0.820927i	0.0902899	−	0.0521289i
$249$	15.4976	−	8.94755i	0.982121	−	0.567028i
$250$	0.675357	+	0.389918i	0.0427133	+	0.0246606i
$251$	−23.2503			−1.46755			−0.733773	−	0.679395i	$-0.762242\pi$
$251$	−23.2503			−1.46755			−0.733773	+	0.679395i	$0.762242\pi$
$252$	−1.18029	+	5.13521i	−0.0743513	+	0.323488i
$253$	−0.517454			−0.0325321
$254$	−0.139146	+	0.241009i	−0.00873082	+	0.0151222i
$255$	−10.5980	+	1.46690i	−0.663674	+	0.0918608i
$256$	−7.66356	−	13.2737i	−0.478973	−	0.829605i
$257$	−13.0027	+	22.5214i	−0.811088	+	1.40485i	0.101015	+	0.994885i	$0.467791\pi$
$257$	−13.0027	+	22.5214i	−0.811088	+	1.40485i	−0.912103	+	0.409961i	$0.865542\pi$
$258$			0.236355i			0.0147148i
$259$	2.53516	−	2.72394i	0.157527	−	0.169258i
$260$			20.7987i			1.28988i
$261$	2.94127	+	1.69814i	0.182060	+	0.105112i
$262$	−0.373051	+	0.215381i	−0.0230472	+	0.0133063i
$263$	−1.34207	−	2.32453i	−0.0827553	−	0.143336i	0.821677	−	0.569953i	$-0.193039\pi$
$263$	−1.34207	−	2.32453i	−0.0827553	−	0.143336i	−0.904432	+	0.426617i	$0.859705\pi$
$264$	−0.104193	+	0.180467i	−0.00641263	+	0.0111070i
$265$		−	4.43302i		−	0.272318i
$266$	−1.17509	+	0.360514i	−0.0720496	+	0.0221045i
$267$			18.0038i			1.10182i
$268$	−9.44813	+	16.3646i	−0.577136	+	0.999629i
$269$	9.93923	−	5.73842i	0.606006	−	0.349878i	−0.165395	−	0.986227i	$-0.552890\pi$
$269$	9.93923	−	5.73842i	0.606006	−	0.349878i	0.771401	+	0.636350i	$0.219557\pi$
$270$	−0.119369	−	0.206754i	−0.00726459	−	0.0125826i
$271$	−3.18239	+	5.51206i	−0.193316	+	0.334834i	−0.946347	−	0.323151i	$-0.895258\pi$
$271$	−3.18239	+	5.51206i	−0.193316	+	0.334834i	0.753031	+	0.657985i	$0.228591\pi$
$272$	6.13134	−	15.0849i	0.371767	−	0.914654i
$273$	3.12315	+	10.1799i	0.189022	+	0.616115i
$274$	0.318822			0.0192607
$275$	0.851894	+	0.491841i	0.0513711	+	0.0296591i
$276$	0.908037	+	1.57277i	0.0546574	+	0.0946694i
$277$	−5.51132	+	3.18196i	−0.331143	+	0.191186i	−0.656349	−	0.754458i	$-0.727900\pi$
$277$	−5.51132	+	3.18196i	−0.331143	+	0.191186i	0.325205	+	0.945643i	$0.394567\pi$
$278$	1.29778	+	0.749275i	0.0778358	+	0.0449385i
$279$		−	4.47088i		−	0.267664i
$280$	1.71768	−	1.84558i	0.102651	−	0.110295i
$281$	26.8735			1.60314			0.801569	−	0.597902i	$-0.203999\pi$
$281$	26.8735			1.60314			0.801569	+	0.597902i	$0.203999\pi$
$282$	0.358398	+	0.206921i	0.0213423	+	0.0123220i
$283$	14.9714	−	8.64375i	0.889958	−	0.513817i	0.0160292	−	0.999872i	$-0.494898\pi$
$283$	14.9714	−	8.64375i	0.889958	−	0.513817i	0.873929	+	0.486054i	$0.161564\pi$
$284$	19.7567	−	11.4066i	1.17235	−	0.676855i
$285$	−6.55158	+	11.3477i	−0.388082	+	0.672177i
$286$			0.210114i			0.0124243i
$287$	−19.0005	−	4.36713i	−1.12157	−	0.257784i
$288$	1.09781			0.0646892
$289$	16.3609	−	4.61756i	0.962404	−	0.271621i
$290$	−0.405413	−	0.702195i	−0.0238066	−	0.0412343i
$291$	−3.52346	−	6.10281i	−0.206549	−	0.357753i
$292$	15.3651	+	8.87107i	0.899177	+	0.519140i
$293$	−9.80679			−0.572919			−0.286459	−	0.958092i	$-0.592478\pi$
$293$	−9.80679			−0.572919			−0.286459	+	0.958092i	$0.592478\pi$
$294$	0.281192	−	0.579391i	0.0163995	−	0.0337908i
$295$		−	30.8951i		−	1.79878i
$296$	−0.447301	−	0.258249i	−0.0259989	−	0.0150104i
$297$	0.283724	+	0.491425i	0.0164633	+	0.0285153i
$298$	0.928231	+	1.60774i	0.0537710	+	0.0931341i
$299$	3.17836	+	1.83503i	0.183810	+	0.106123i
$300$		−	3.45237i		−	0.199322i
$301$	−1.52252	+	6.62419i	−0.0877567	+	0.381812i
$302$	1.08546			0.0624614
$303$	0.859785	+	0.496397i	0.0493934	+	0.0285173i
$304$	−9.97110	−	17.2705i	−0.571882	−	0.990528i
$305$	−15.5682	−	26.9649i	−0.891431	−	1.54400i
$306$	0.232919	+	0.299409i	0.0133151	+	0.0171161i
$307$	20.8056			1.18744			0.593719	−	0.804673i	$-0.297659\pi$
$307$	20.8056			1.18744			0.593719	+	0.804673i	$0.297659\pi$
$308$	−2.03701	+	2.18869i	−0.116069	+	0.124712i
$309$			14.1914i			0.807321i
$310$	−0.533685	+	0.924370i	−0.0303113	+	0.0525007i
$311$	0.743711	−	0.429382i	0.0421720	−	0.0243480i	−0.478766	−	0.877943i	$-0.658916\pi$
$311$	0.743711	−	0.429382i	0.0421720	−	0.0243480i	0.520938	+	0.853595i	$0.325582\pi$
$312$	1.27997	−	0.738991i	0.0724641	−	0.0418371i
$313$	−22.6964	−	13.1038i	−1.28288	−	0.740668i	−0.305502	−	0.952191i	$-0.598824\pi$
$313$	−22.6964	−	13.1038i	−1.28288	−	0.740668i	−0.977373	+	0.211523i	$0.932158\pi$
$314$	1.39400			0.0786682
$315$	−2.01366	−	6.56352i	−0.113457	−	0.369812i
$316$			16.0765i			0.904373i
$317$	0.284138	+	0.164047i	0.0159588	+	0.00921382i	0.507958	−	0.861382i	$-0.330400\pi$
$317$	0.284138	+	0.164047i	0.0159588	+	0.00921382i	−0.491999	+	0.870596i	$0.663734\pi$
$318$	−0.136116	+	0.0785869i	−0.00763303	+	0.00440693i
$319$	0.963609	+	1.66902i	0.0539517	+	0.0934471i
$320$	17.5231	+	10.1170i	0.979571	+	0.565555i
$321$	6.91326			0.385860
$322$	−0.0651047	−	0.212209i	−0.00362815	−	0.0118259i
$323$	7.83956	−	19.2876i	0.436205	−	1.07319i
$324$	0.995768	−	1.72472i	0.0553204	−	0.0958178i
$325$	−3.48840	−	6.04209i	−0.193502	−	0.335155i
$326$	−0.919924	+	0.531118i	−0.0509499	+	0.0294159i
$327$	4.39860	−	7.61859i	0.243243	−	0.421309i
$328$			2.70606i			0.149417i
$329$	8.71172	+	8.10796i	0.480293	+	0.447007i
$330$		−	0.135472i		−	0.00745748i
$331$	−6.69774	+	11.6008i	−0.368141	+	0.637639i	−0.989275	−	0.146065i	$-0.953339\pi$
$331$	−6.69774	+	11.6008i	−0.368141	+	0.637639i	0.621134	+	0.783705i	$0.286672\pi$
$332$	−17.8194	−	30.8640i	−0.977964	−	1.69388i
$333$	−1.21803	+	0.703231i	−0.0667477	+	0.0385368i
$334$	0.209758	+	0.121104i	0.0114775	+	0.00662651i
$335$		−	24.6212i		−	1.34520i
$336$	10.1833	+	2.34056i	0.555545	+	0.127688i
$337$		−	1.96127i		−	0.106837i	−0.998572	−	0.0534186i	$-0.982988\pi$
$337$		−	1.96127i		−	0.106837i	0.998572	−	0.0534186i	$-0.0170117\pi$
$338$	0.147102	−	0.254788i	0.00800129	−	0.0138586i
$339$	−2.58595	−	4.47900i	−0.140450	−	0.243266i
$340$	2.92138	+	21.1063i	0.158434	+	1.14465i
$341$	1.26850	−	2.19710i	0.0686929	−	0.118980i
$342$	0.464576			0.0251214
$343$	11.6131	−	14.4269i	0.627047	−	0.778981i
$344$	0.943419			0.0508657
$345$	−2.04926	−	1.18314i	−0.110328	−	0.0636982i
$346$	−0.492481	+	0.284334i	−0.0264760	+	0.0152859i
$347$	20.1607	−	11.6398i	1.08228	−	0.624856i	0.150772	−	0.988569i	$-0.451824\pi$
$347$	20.1607	−	11.6398i	1.08228	−	0.624856i	0.931511	+	0.363712i	$0.118491\pi$
$348$	3.38191	−	5.85765i	0.181290	−	0.314003i
$349$	4.10104			0.219524			0.109762	−	0.993958i	$-0.464991\pi$
$349$	4.10104			0.219524			0.109762	+	0.993958i	$0.464991\pi$
$350$	−0.0945216	+	0.411245i	−0.00505239	+	0.0219820i
$351$		−	4.02464i		−	0.214820i
$352$	0.539492	+	0.311476i	0.0287550	+	0.0166017i
$353$	14.1007	+	24.4231i	0.750503	+	1.29991i	0.947579	+	0.319522i	$0.103522\pi$
$353$	14.1007	+	24.4231i	0.750503	+	1.29991i	−0.197076	+	0.980388i	$0.563144\pi$
$354$	−0.948639	+	0.547697i	−0.0504196	+	0.0291098i
$355$	−14.8624	+	25.7423i	−0.788812	+	1.36626i
$356$	35.8552			1.90032
$357$	4.59921	+	9.89178i	0.243416	+	0.523528i
$358$	0.134453			0.00710609
$359$	15.8565	−	27.4643i	0.836875	−	1.44951i	−0.0556204	−	0.998452i	$-0.517714\pi$
$359$	15.8565	−	27.4643i	0.836875	−	1.44951i	0.892495	−	0.451057i	$-0.148953\pi$
$360$	−0.825265	+	0.476467i	−0.0434953	+	0.0251120i
$361$	−3.24910	−	5.62760i	−0.171005	−	0.296189i
$362$	−1.20138	−	0.693615i	−0.0631430	−	0.0364556i
$363$		−	10.6780i		−	0.560450i
$364$	20.2736	−	6.21987i	1.06263	−	0.326010i
$365$	−23.1174			−1.21002
$366$	−0.551973	+	0.956046i	−0.0288521	+	0.0499733i
$367$	14.7978	−	8.54351i	0.772439	−	0.445968i	−0.0613053	−	0.998119i	$-0.519526\pi$
$367$	14.7978	−	8.54351i	0.772439	−	0.445968i	0.833744	+	0.552151i	$0.186193\pi$
$368$	3.11885	−	1.80067i	0.162581	−	0.0938664i
$369$	6.38155	+	3.68439i	0.332210	+	0.191802i
$370$	0.335777			0.0174562
$371$	−4.32110	+	1.32570i	−0.224340	+	0.0688267i
$372$	−8.90391			−0.461646
$373$	14.2321	−	24.6507i	0.736909	−	1.27636i	−0.216972	−	0.976178i	$-0.569618\pi$
$373$	14.2321	−	24.6507i	0.736909	−	1.27636i	0.953881	−	0.300186i	$-0.0970487\pi$
$374$	0.0295126	+	0.213222i	0.00152606	+	0.0110254i
$375$	−4.23810	−	7.34060i	−0.218855	−	0.379067i
$376$	0.825934	−	1.43056i	0.0425943	−	0.0737755i
$377$		−	13.6689i		−	0.703982i
$378$	−0.165836	+	0.178185i	−0.00852971	+	0.00916487i
$379$		−	25.2307i		−	1.29601i	−0.761634	−	0.648007i	$-0.775603\pi$
$379$		−	25.2307i		−	1.29601i	0.761634	−	0.648007i	$-0.224397\pi$
$380$	22.5993	+	13.0477i	1.15932	+	0.669333i
$381$	2.61958	−	1.51241i	0.134205	−	0.0774833i
$382$	−0.247339	−	0.428404i	−0.0126550	−	0.0219190i
$383$	−11.7646	+	20.3769i	−0.601143	+	1.04121i	0.391505	+	0.920176i	$0.371955\pi$
$383$	−11.7646	+	20.3769i	−0.601143	+	1.04121i	−0.992648	+	0.121035i	$0.961379\pi$
$384$		−	2.91302i		−	0.148655i
$385$	0.872666	−	3.79680i	0.0444752	−	0.193503i
$386$			1.07070i			0.0544970i
$387$	1.28450	−	2.22481i	0.0652946	−	0.113094i
$388$	−12.1540	+	7.01710i	−0.617024	+	0.356239i
$389$	11.9154	+	20.6382i	0.604137	+	1.04640i	0.992187	+	0.124758i	$0.0398154\pi$
$389$	11.9154	+	20.6382i	0.604137	+	1.04640i	−0.388050	+	0.921638i	$0.626851\pi$
$390$	−0.480419	+	0.832110i	−0.0243270	+	0.0421356i
$391$	3.48312	+	1.41574i	0.176149	+	0.0715969i
$392$	−2.31266	−	1.12239i	−0.116807	−	0.0566891i
$393$	4.68205			0.236178
$394$	0.954203	+	0.550909i	0.0480721	+	0.0277544i
$395$	−10.4736	−	18.1407i	−0.526982	−	0.912759i
$396$	0.978690	−	0.565047i	0.0491810	−	0.0283947i
$397$	24.1298	+	13.9313i	1.21104	+	0.699194i	0.962986	−	0.269552i	$-0.0868756\pi$
$397$	24.1298	+	13.9313i	1.21104	+	0.699194i	0.248054	+	0.968746i	$0.420209\pi$
$398$		−	0.361117i		−	0.0181012i
$399$	13.0204	+	2.99265i	0.651836	+	0.149820i
$400$	−6.84616			−0.342308
$401$	−11.0085	−	6.35575i	−0.549737	−	0.317391i	0.199279	−	0.979943i	$-0.436140\pi$
$401$	−11.0085	−	6.35575i	−0.549737	−	0.317391i	−0.749016	+	0.662552i	$0.769473\pi$
$402$	−0.755997	+	0.436475i	−0.0377057	+	0.0217694i
$403$	−15.5830	+	8.99684i	−0.776244	+	0.448165i
$404$	0.988593	−	1.71229i	0.0491843	−	0.0851897i
$405$			2.59490i			0.128942i
$406$	−0.563228	+	0.605169i	−0.0279526	+	0.0300340i
$407$	−0.798094			−0.0395601
$408$	1.19510	−	0.929705i	0.0591664	−	0.0460273i
$409$	10.1224	+	17.5326i	0.500523	+	0.866931i	1.00000		0.000603908i	$0.000192230\pi$
$409$	10.1224	+	17.5326i	0.500523	+	0.866931i	−0.499477	+	0.866327i	$0.666474\pi$
$410$	−0.879607	−	1.52352i	−0.0434407	−	0.0752415i
$411$	−3.00108	−	1.73267i	−0.148032	−	0.0854664i
$412$	28.2627			1.39240
$413$	−30.1151	+	9.23919i	−1.48187	+	0.454631i
$414$			0.0838972i			0.00412332i
$415$	40.2148	+	23.2180i	1.97407	+	1.13973i
$416$	−2.20915	−	3.82636i	−0.108313	−	0.187603i
$417$	−8.14403	−	14.1059i	−0.398815	−	0.690767i
$418$	0.228304	+	0.131811i	0.0111667	+	0.00644710i
$419$			26.9981i			1.31894i	0.751730	+	0.659471i	$0.229220\pi$
$419$			26.9981i			1.31894i	−0.751730	+	0.659471i	$0.770780\pi$
$420$	−13.0715	+	4.01028i	−0.637823	+	0.195682i
$421$	−31.6894			−1.54445			−0.772223	−	0.635352i	$-0.780855\pi$
$421$	−31.6894			−1.54445			−0.772223	+	0.635352i	$0.780855\pi$
$422$	−1.97850	−	1.14229i	−0.0963117	−	0.0556056i
$423$	−2.24907	−	3.89551i	−0.109354	−	0.189406i
$424$	0.313682	+	0.543314i	0.0152338	+	0.0263856i
$425$	−4.38866	−	5.64147i	−0.212881	−	0.273651i
$426$	1.05390			0.0510615
$427$	−21.6284	+	23.2390i	−1.04667	+	1.12461i
$428$		−	13.7680i		−	0.665501i
$429$	1.14189	−	1.97781i	0.0551309	−	0.0954895i
$430$	−0.531149	+	0.306659i	−0.0256143	+	0.0147884i
$431$	−27.0299	+	15.6057i	−1.30199	+	0.751702i	−0.980744	−	0.195296i	$-0.937433\pi$
$431$	−27.0299	+	15.6057i	−1.30199	+	0.751702i	−0.321241	+	0.946997i	$0.604100\pi$
$432$	−3.42018	−	1.97464i	−0.164554	−	0.0950050i
$433$	−6.19141			−0.297540			−0.148770	−	0.988872i	$-0.547531\pi$
$433$	−6.19141			−0.297540			−0.148770	+	0.988872i	$0.547531\pi$
$434$	1.06063	+	0.243778i	0.0509120	+	0.0117017i
$435$			8.81303i			0.422553i
$436$	−15.1727	−	8.75996i	−0.726641	−	0.419526i
$437$	3.98778	−	2.30234i	0.190761	−	0.110136i
$438$	0.409817	+	0.709824i	0.0195818	+	0.0339167i
$439$	23.9969	+	13.8546i	1.14531	+	0.661245i	0.947740	−	0.319044i	$-0.103362\pi$
$439$	23.9969	+	13.8546i	1.14531	+	0.661245i	0.197570	+	0.980289i	$0.436695\pi$
$440$	−0.540741			−0.0257788
$441$	−5.79563	+	3.92565i	−0.275982	+	0.186936i
$442$	0.574866	−	1.41433i	0.0273436	−	0.0672730i
$443$	4.27859	−	7.41073i	0.203282	−	0.352094i	−0.746302	−	0.665607i	$-0.768173\pi$
$443$	4.27859	−	7.41073i	0.203282	−	0.352094i	0.949584	+	0.313513i	$0.101506\pi$
$444$	1.40051	+	2.42575i	0.0664652	+	0.115121i
$445$	−40.4591	+	23.3591i	−1.91794	+	1.10733i
$446$	0.154766	−	0.268063i	0.00732838	−	0.0126931i
$447$		−	20.1783i		−	0.954401i
$448$	4.62126	−	20.1062i	0.218334	−	0.949928i
$449$			38.1356i			1.79973i	0.436168	+	0.899865i	$0.356335\pi$
$449$			38.1356i			1.79973i	−0.436168	+	0.899865i	$0.643665\pi$
$450$	0.0797444	−	0.138121i	0.00375919	−	0.00651111i
$451$	2.09070	+	3.62120i	0.0984473	+	0.170516i
$452$	−8.92009	+	5.15002i	−0.419566	+	0.242236i
$453$	−10.2175	−	5.89907i	−0.480059	−	0.277162i
$454$			1.57033i			0.0736992i
$455$	−18.8247	+	20.2264i	−0.882513	+	0.948229i
$456$		−	1.85437i		−	0.0868388i
$457$	−10.3381	+	17.9062i	−0.483598	+	0.837616i	−0.999823	−	0.0188369i	$-0.994004\pi$
$457$	−10.3381	+	17.9062i	−0.483598	+	0.837616i	0.516225	+	0.856453i	$0.327337\pi$
$458$	−1.13203	−	1.96073i	−0.0528962	−	0.0916189i
$459$	−0.565300	−	4.08417i	−0.0263860	−	0.190633i
$460$	−2.35627	+	4.08118i	−0.109862	+	0.190286i
$461$	−6.58358			−0.306628			−0.153314	−	0.988178i	$-0.548995\pi$
$461$	−6.58358			−0.306628			−0.153314	+	0.988178i	$0.548995\pi$
$462$	−0.132052	+	0.0405129i	−0.00614360	+	0.00188483i
$463$	−10.9099			−0.507027			−0.253514	−	0.967332i	$-0.581586\pi$
$463$	−10.9099			−0.507027			−0.253514	+	0.967332i	$0.581586\pi$
$464$	−11.6159	−	6.70645i	−0.539255	−	0.311339i
$465$	10.0472	−	5.80074i	0.465927	−	0.269003i
$466$	−1.40886	+	0.813406i	−0.0652642	+	0.0376803i
$467$	2.47680	−	4.28994i	0.114613	−	0.198515i	−0.803012	−	0.595962i	$-0.796771\pi$
$467$	2.47680	−	4.28994i	0.114613	−	0.198515i	0.917625	+	0.397448i	$0.130104\pi$
$468$	−8.01522			−0.370504
$469$	−23.9996	+	7.36297i	−1.10820	+	0.339991i
$470$			1.07388i			0.0495344i
$471$	−13.1218	−	7.57587i	−0.604620	−	0.349077i
$472$	2.18615	+	3.78653i	0.100626	+	0.174289i
$473$	1.26247	−	0.728885i	0.0580482	−	0.0335142i
$474$	−0.371342	+	0.643184i	−0.0170563	+	0.0295424i
$475$	−8.75353			−0.401640
$476$	19.6998	−	9.15948i	0.902940	−	0.419824i
$477$	1.70836			0.0782202
$478$	0.733320	−	1.27015i	0.0335413	−	0.0580952i
$479$	25.4454	−	14.6909i	1.16263	−	0.671244i	0.210696	−	0.977552i	$-0.432427\pi$
$479$	25.4454	−	14.6909i	1.16263	−	0.671244i	0.951932	+	0.306308i	$0.0990938\pi$
$480$	1.42436	+	2.46706i	0.0650127	+	0.112605i
$481$	4.90214	+	2.83025i	0.223518	+	0.129048i
$482$			0.916845i			0.0417611i
$483$	−0.540439	+	2.35134i	−0.0245908	+	0.106990i
$484$	−21.2656			−0.966619
$485$	9.14304	−	15.8362i	0.415164	−	0.719085i
$486$	0.0796769	−	0.0460015i	0.00361422	−	0.00208667i
$487$	−2.84746	+	1.64398i	−0.129031	+	0.0744960i	−0.563126	−	0.826371i	$-0.690401\pi$
$487$	−2.84746	+	1.64398i	−0.129031	+	0.0744960i	0.434095	+	0.900867i	$0.357068\pi$
$488$	3.81609	+	2.20322i	0.172746	+	0.0997351i
$489$	11.5457			0.522114
$490$	1.66687	−	0.119822i	0.0753015	−	0.00541301i
$491$	28.1092			1.26855			0.634276	−	0.773107i	$-0.281298\pi$
$491$	28.1092			1.26855			0.634276	+	0.773107i	$0.281298\pi$
$492$	7.33760	−	12.7091i	0.330804	−	0.572970i
$493$	−1.91992	−	13.8710i	−0.0864690	−	0.624719i
$494$	−0.934876	−	1.61925i	−0.0420621	−	0.0728536i
$495$	−0.736236	+	1.27520i	−0.0330914	+	0.0573159i
$496$			17.6568i			0.792812i
$497$	29.5370	+	6.78887i	1.32492	+	0.304522i
$498$		−	1.64640i		−	0.0737770i
$499$	10.8306	+	6.25303i	0.484843	+	0.279924i	0.722433	−	0.691441i	$-0.243024\pi$
$499$	10.8306	+	6.25303i	0.484843	+	0.279924i	−0.237590	+	0.971366i	$0.576357\pi$
$500$	−14.6191	+	8.44033i	−0.653785	+	0.377463i
$501$	−1.31630	−	2.27991i	−0.0588081	−	0.101859i
$502$	−1.06955	+	1.85251i	−0.0477363	+	0.0826816i
$503$		−	19.2020i		−	0.856173i	−0.903738	−	0.428087i	$-0.859188\pi$
$503$		−	19.2020i		−	0.856173i	0.903738	−	0.428087i	$-0.140812\pi$
$504$	0.711234	+	0.661942i	0.0316809	+	0.0294852i
$505$			2.57620i			0.114640i
$506$	−0.0238036	+	0.0412291i	−0.00105820	+	0.00183286i
$507$	−2.76935	+	1.59888i	−0.122991	+	0.0710089i
$508$	−3.01202	−	5.21698i	−0.133637	−	0.231466i
$509$	−0.593291	+	1.02761i	−0.0262972	+	0.0455480i	−0.878874	−	0.477053i	$-0.841705\pi$
$509$	−0.593291	+	1.02761i	−0.0262972	+	0.0455480i	0.852577	+	0.522601i	$0.175038\pi$
$510$	−0.370647	+	0.911897i	−0.0164125	+	0.0403795i
$511$	6.91327	+	22.5338i	0.305825	+	0.996835i
$512$	−7.23619			−0.319797
$513$	−4.37306	−	2.52479i	−0.193075	−	0.111472i
$514$	1.19629	+	2.07203i	0.0527661	+	0.0913935i
$515$	−31.8917	+	18.4127i	−1.40532	+	0.811359i
$516$	−4.43079	−	2.55812i	−0.195055	−	0.112615i
$517$		−	2.55246i		−	0.112257i
$518$	−0.100414	−	0.327299i	−0.00441194	−	0.0143807i
$519$	6.18098			0.271315
$520$	3.32140	+	1.91761i	0.145653	+	0.0840928i
$521$	−23.4431	+	13.5349i	−1.02706	+	0.592973i	−0.916141	−	0.400857i	$-0.868712\pi$
$521$	−23.4431	+	13.5349i	−1.02706	+	0.592973i	−0.110918	+	0.993830i	$0.535379\pi$
$522$	0.270606	−	0.156234i	0.0118441	−	0.00683819i
$523$	−6.97354	+	12.0785i	−0.304931	+	0.528157i	−0.977246	−	0.212109i	$-0.931967\pi$
$523$	−6.97354	+	12.0785i	−0.304931	+	0.528157i	0.672315	+	0.740266i	$0.265300\pi$
$524$		−	9.32447i		−	0.407341i
$525$	3.12469	−	3.35737i	0.136373	−	0.146528i
$526$	−0.246948			−0.0107674
$527$	−14.5498	+	11.3187i	−0.633798	+	0.493050i
$528$	−1.12051	−	1.94078i	−0.0487638	−	0.0844614i
$529$	−11.0842	−	19.1984i	−0.481923	−	0.834715i
$530$	−0.353209	−	0.203925i	−0.0153424	−	0.00885795i
$531$	11.9061			0.516680
$532$	5.95996	−	25.9306i	0.258397	−	1.12424i
$533$		−	29.6567i		−	1.28458i
$534$	1.43449	+	0.828202i	0.0620763	+	0.0358398i
$535$	8.96962	+	15.5358i	0.387790	+	0.671672i
$536$	1.74221	+	3.01759i	0.0752518	+	0.130340i
$537$	−1.26561	−	0.730702i	−0.0546152	−	0.0315321i
$538$		−	1.05590i		−	0.0455232i
$539$	−3.96191	+	0.284800i	−0.170652	+	0.0122672i
$540$	5.16784			0.222388
$541$	−18.9861	−	10.9617i	−0.816278	−	0.471278i	0.0328532	−	0.999460i	$-0.489541\pi$
$541$	−18.9861	−	10.9617i	−0.816278	−	0.471278i	−0.849131	+	0.528182i	$0.822874\pi$
$542$	0.292789	+	0.507125i	0.0125764	+	0.0217829i
$543$	7.53906	+	13.0580i	0.323532	+	0.560374i
$544$	−2.77927	−	3.57266i	−0.119160	−	0.153176i
$545$	22.8279			0.977838
$546$	0.954772	+	0.219447i	0.0408605	+	0.00939148i
$547$		−	25.8872i		−	1.10686i	−0.832897	−	0.553428i	$-0.813319\pi$
$547$		−	25.8872i		−	1.10686i	0.832897	−	0.553428i	$-0.186681\pi$
$548$	−3.45068	+	5.97675i	−0.147406	+	0.255314i
$549$	10.3915	−	5.99952i	0.443497	−	0.256053i
$550$	0.0783768	−	0.0452508i	0.00334200	−	0.00192950i
$551$	−14.8522	−	8.57490i	−0.632723	−	0.365303i
$552$	0.334878			0.0142534
$553$	−14.5506	+	15.6341i	−0.618755	+	0.664830i
$554$			0.585500i			0.0248755i
$555$	−3.16067	−	1.82481i	−0.134163	−	0.0774591i
$556$	−28.0923	+	16.2191i	−1.19138	+	0.687844i
$557$	−18.3209	−	31.7328i	−0.776283	−	1.34456i	−0.934071	−	0.357088i	$-0.883770\pi$
$557$	−18.3209	−	31.7328i	−0.776283	−	1.34456i	0.157788	−	0.987473i	$-0.449564\pi$
$558$	−0.356225	−	0.205667i	−0.0150802	−	0.00870657i
$559$	−10.3393			−0.437305
$560$	7.95252	+	25.9212i	0.336055	+	1.09537i
$561$	0.880975	−	2.16745i	0.0371948	−	0.0915098i
$562$	1.23622	−	2.14120i	0.0521468	−	0.0903209i
$563$	13.9584	+	24.1767i	0.588277	+	1.01893i	0.994458	+	0.105134i	$0.0335270\pi$
$563$	13.9584	+	24.1767i	0.588277	+	1.01893i	−0.406181	+	0.913793i	$0.633140\pi$
$564$	−7.75804	+	4.47911i	−0.326673	+	0.188604i
$565$	6.71030	−	11.6226i	0.282304	−	0.488965i
$566$		−	1.59050i		−	0.0668537i
$567$	2.52939	−	0.776007i	0.106224	−	0.0325892i
$568$		−	4.20667i		−	0.176508i
$569$	−3.76429	+	6.51995i	−0.157807	+	0.273330i	−0.934078	−	0.357070i	$-0.883776\pi$
$569$	−3.76429	+	6.51995i	−0.157807	+	0.273330i	0.776270	+	0.630400i	$0.217109\pi$
$570$	0.602764	+	1.04402i	0.0252470	+	0.0437291i
$571$	−10.2196	+	5.90031i	−0.427679	+	0.246920i	−0.698357	−	0.715749i	$-0.746085\pi$
$571$	−10.2196	+	5.90031i	−0.427679	+	0.246920i	0.270679	+	0.962670i	$0.412752\pi$
$572$	−3.93888	−	2.27411i	−0.164693	−	0.0950854i
$573$			5.37676i			0.224618i
$574$	−1.22201	+	1.31301i	−0.0510058	+	0.0548040i
$575$		−	1.58079i		−	0.0659235i
$576$	−3.89878	+	6.75289i	−0.162449	+	0.281370i
$577$	−7.32167	−	12.6815i	−0.304805	−	0.527938i	0.672413	−	0.740176i	$-0.265258\pi$
$577$	−7.32167	−	12.6815i	−0.304805	−	0.527938i	−0.977218	+	0.212238i	$0.931925\pi$
$578$	0.384711	−	1.51600i	0.0160019	−	0.0630572i
$579$	5.81882	−	10.0785i	0.241822	−	0.418848i
$580$	17.5515			0.728785
$581$	10.6056	−	46.1428i	0.439994	−	1.91433i
$582$	−0.648337			−0.0268745
$583$	0.839528	+	0.484702i	0.0347697	+	0.0200743i
$584$	2.83329	−	1.63580i	0.117242	−	0.0676898i
$585$	9.04439	−	5.22178i	0.373939	−	0.215894i
$586$	−0.451127	+	0.781374i	−0.0186359	+	0.0322783i
$587$	44.7544			1.84721			0.923606	−	0.383342i	$-0.125227\pi$
$587$	44.7544			1.84721			0.923606	+	0.383342i	$0.125227\pi$
$588$	7.81807	+	11.5422i	0.322412	+	0.475992i
$589$			22.5760i			0.930228i
$590$	−2.46163	−	1.42122i	−0.101344	−	0.0585107i
$591$	−5.98795	−	10.3714i	−0.246312	−	0.426624i
$592$	4.81035	−	2.77726i	0.197704	−	0.114145i
$593$	6.77991	−	11.7432i	0.278418	−	0.482234i	−0.692574	−	0.721347i	$-0.743523\pi$
$593$	6.77991	−	11.7432i	0.278418	−	0.482234i	0.970992	+	0.239113i	$0.0768567\pi$
$594$	0.0522069			0.00214208
$595$	−16.2621	+	23.1697i	−0.666680	+	0.949864i
$596$	−40.1858			−1.64607
$597$	−1.96253	+	3.39920i	−0.0803210	+	0.139120i
$598$	0.292419	−	0.168828i	0.0119579	−	0.00690390i
$599$	−4.20027	−	7.27508i	−0.171618	−	0.297252i	0.767367	−	0.641208i	$-0.221566\pi$
$599$	−4.20027	−	7.27508i	−0.171618	−	0.297252i	−0.938986	+	0.343956i	$0.888233\pi$
$600$	−0.551317	−	0.318303i	−0.0225074	−	0.0129947i
$601$		−	18.4312i		−	0.751822i	−0.926656	−	0.375911i	$-0.877330\pi$
$601$		−	18.4312i		−	0.751822i	0.926656	−	0.375911i	$-0.122670\pi$
$602$	0.457757	+	0.426032i	0.0186568	+	0.0173638i
$603$	9.48829			0.386393
$604$	−11.7482	+	20.3485i	−0.478028	+	0.827968i
$605$	23.9962	−	13.8542i	0.975583	−	0.563253i
$606$	0.0791028	−	0.0456700i	0.00321333	−	0.00185522i
$607$	2.04732	+	1.18202i	0.0830982	+	0.0479768i	0.540973	−	0.841040i	$-0.318056\pi$
$607$	2.04732	+	1.18202i	0.0830982	+	0.0479768i	−0.457875	+	0.889017i	$0.651389\pi$
$608$	−5.54348			−0.224818
$609$	8.59054	−	2.63554i	0.348106	−	0.106798i
$610$	−2.86463			−0.115986
$611$	−9.05172	+	15.6780i	−0.366193	+	0.634265i
$612$	−8.13377	+	1.12582i	−0.328788	+	0.0455084i
$613$	−3.94814	−	6.83837i	−0.159464	−	0.276199i	0.775212	−	0.631702i	$-0.217643\pi$
$613$	−3.94814	−	6.83837i	−0.159464	−	0.276199i	−0.934675	+	0.355502i	$0.884310\pi$
$614$	0.957087	−	1.65772i	0.0386249	−	0.0669003i
$615$			19.1213i			0.771044i
$616$	0.161709	+	0.527089i	0.00651543	+	0.0212370i
$617$			45.8056i			1.84407i	0.387112	+	0.922033i	$0.373473\pi$
$617$			45.8056i			1.84407i	−0.387112	+	0.922033i	$0.626527\pi$
$618$	1.13073	+	0.652826i	0.0454845	+	0.0262605i
$619$	−41.2023	+	23.7881i	−1.65606	+	0.956126i	−0.681552	+	0.731770i	$0.738695\pi$
$619$	−41.2023	+	23.7881i	−1.65606	+	0.956126i	−0.974507	+	0.224356i	$0.927972\pi$
$620$	−11.5524	−	20.0093i	−0.463955	−	0.803594i
$621$	0.455948	−	0.789725i	0.0182966	−	0.0316906i
$622$		−	0.0790088i		−	0.00316796i
$623$	34.8686	+	32.4521i	1.39698	+	1.30017i
$624$			15.8945i			0.636288i
$625$	15.3313	−	26.5545i	0.613250	−	1.06218i
$626$	−2.08813	+	1.20558i	−0.0834586	+	0.0481848i
$627$	−1.43269	−	2.48148i	−0.0572160	−	0.0991009i
$628$	−15.0876	+	26.1325i	−0.602061	+	1.04280i
$629$	5.37218	+	2.18356i	0.214203	+	0.0870642i
$630$	−0.615592	−	0.141489i	−0.0245258	−	0.00563707i
$631$	−25.2685			−1.00592			−0.502961	−	0.864309i	$-0.667756\pi$
$631$	−25.2685			−1.00592			−0.502961	+	0.864309i	$0.667756\pi$
$632$	2.56729	+	1.48223i	0.102121	+	0.0589598i
$633$	12.4158	+	21.5047i	0.493482	+	0.854736i
$634$	0.0261416	−	0.0150928i	0.00103821	−	0.000599413i
$635$	6.79754	+	3.92456i	0.269752	+	0.155742i
$636$		−	3.40225i		−	0.134908i
$637$	25.3453	+	12.3007i	1.00422	+	0.487370i
$638$	0.177310			0.00701976
$639$	−9.92035	−	5.72752i	−0.392443	−	0.226577i
$640$	6.54629	−	3.77951i	0.258765	−	0.149398i
$641$	24.6611	−	14.2381i	0.974055	−	0.562371i	0.0735848	−	0.997289i	$-0.476556\pi$
$641$	24.6611	−	14.2381i	0.974055	−	0.562371i	0.900470	+	0.434918i	$0.143223\pi$
$642$	0.318020	−	0.550827i	0.0125512	−	0.0217394i
$643$			11.7016i			0.461465i	0.973017	+	0.230732i	$0.0741122\pi$
$643$			11.7016i			0.461465i	−0.973017	+	0.230732i	$0.925888\pi$
$644$	4.68278	+	1.07630i	0.184527	+	0.0424123i
$645$	6.66628			0.262485
$646$	−1.17614	−	1.51189i	−0.0462747	−	0.0594845i
$647$	−12.8849	−	22.3174i	−0.506559	−	0.877386i	−0.999971	−	0.00759043i	$-0.997584\pi$
$647$	−12.8849	−	22.3174i	−0.506559	−	0.877386i	0.493412	−	0.869796i	$-0.335749\pi$
$648$	−0.183617	−	0.318033i	−0.00721314	−	0.0124935i
$649$	5.85094	+	3.37804i	0.229669	+	0.132600i
$650$	−0.641886			−0.0251768
$651$	−8.65891	−	8.05881i	−0.339369	−	0.315850i
$652$		−	22.9936i		−	0.900500i
$653$	−8.52373	−	4.92118i	−0.333559	−	0.192581i	0.323861	−	0.946105i	$-0.395019\pi$
$653$	−8.52373	−	4.92118i	−0.333559	−	0.192581i	−0.657420	+	0.753524i	$0.728352\pi$
$654$	−0.404684	−	0.700933i	−0.0158244	−	0.0274087i
$655$	6.07473	+	10.5217i	0.237359	+	0.411118i
$656$	−25.2026	−	14.5507i	−0.983995	−	0.568110i
$657$		−	8.90878i		−	0.347565i
$658$	1.04677	−	0.321145i	0.0408073	−	0.0125195i
$659$	8.21723			0.320098			0.160049	−	0.987109i	$-0.448835\pi$
$659$	8.21723			0.320098			0.160049	+	0.987109i	$0.448835\pi$
$660$	2.53960	+	1.46624i	0.0988540	+	0.0570734i
$661$	3.42953	+	5.94012i	0.133393	+	0.231044i	0.924983	−	0.380010i	$-0.124079\pi$
$661$	3.42953	+	5.94012i	0.133393	+	0.231044i	−0.791589	+	0.611054i	$0.790746\pi$
$662$	0.616212	+	1.06731i	0.0239498	+	0.0414822i
$663$	−13.0976	+	10.1890i	−0.508668	+	0.395708i
$664$	−6.57167			−0.255030
$665$	10.1681	+	33.1430i	0.394303	+	1.28523i
$666$			0.129399i			0.00501409i
$667$	1.54853	−	2.68213i	0.0599594	−	0.103853i
$668$	−4.54051	+	2.62147i	−0.175678	+	0.101428i
$669$	−2.91363	+	1.68218i	−0.112647	+	0.0650370i
$670$	−1.96174	−	1.13261i	−0.0757886	−	0.0437566i
$671$	6.80883			0.262852
$672$	1.97882	−	2.12617i	0.0763346	−	0.0820189i
$673$			45.8169i			1.76611i	0.469267	+	0.883056i	$0.344518\pi$
$673$			45.8169i			1.76611i	−0.469267	+	0.883056i	$0.655482\pi$
$674$	−0.156268	−	0.0902212i	−0.00601921	−	0.00347519i
$675$	−1.50127	+	0.866760i	−0.0577840	+	0.0333616i
$676$	3.18423	+	5.51525i	0.122471	+	0.212125i
$677$	−21.4581	−	12.3888i	−0.824700	−	0.476141i	0.0273344	−	0.999626i	$-0.491298\pi$
$677$	−21.4581	−	12.3888i	−0.824700	−	0.476141i	−0.852035	+	0.523485i	$0.824631\pi$
$678$	−0.475831			−0.0182742
$679$	−18.1706	−	4.17638i	−0.697324	−	0.160275i
$680$	3.63987	+	1.47945i	0.139583	+	0.0567343i
$681$	8.53413	−	14.7815i	0.327029	−	0.566430i
$682$	−0.116705	−	0.202140i	−0.00446888	−	0.00774032i
$683$	22.0453	−	12.7279i	0.843540	−	0.487018i	−0.0149262	−	0.999889i	$-0.504751\pi$
$683$	22.0453	−	12.7279i	0.843540	−	0.487018i	0.858466	+	0.512871i	$0.171418\pi$
$684$	−5.02820	+	8.70910i	−0.192258	+	0.333001i
$685$		−	8.99223i		−	0.343575i
$686$	−0.615275	−	1.58895i	−0.0234913	−	0.0606665i
$687$			24.6085i			0.938874i
$688$	−5.07284	+	8.78642i	−0.193400	+	0.334979i
$689$	−3.43776	−	5.95438i	−0.130968	−	0.226844i
$690$	−0.188538	+	0.108852i	−0.00717752	+	0.00414394i
$691$	4.38623	+	2.53239i	0.166860	+	0.0963367i	0.581104	−	0.813829i	$-0.302621\pi$
$691$	4.38623	+	2.53239i	0.166860	+	0.0963367i	−0.414244	+	0.910166i	$0.635954\pi$
$692$		−	12.3096i		−	0.467942i
$693$	1.46318	+	0.336300i	0.0555815	+	0.0127750i
$694$		−	2.14179i		−	0.0813012i
$695$	21.1330	−	36.6034i	0.801619	−	1.38844i
$696$	−0.623614	−	1.08013i	−0.0236380	−	0.0409423i
$697$	−4.16558	−	30.0954i	−0.157782	−	1.13994i
$698$	0.188654	−	0.326758i	0.00714065	−	0.0123680i
$699$	17.6822			0.668801
$700$	−6.68632	−	6.22293i	−0.252719	−	0.235205i
$701$	−44.5560			−1.68286			−0.841429	−	0.540367i	$-0.818285\pi$
$701$	−44.5560			−1.68286			−0.841429	+	0.540367i	$0.818285\pi$
$702$	−0.320671	−	0.185140i	−0.0121030	−	0.00698764i
$703$	6.15054	−	3.55101i	0.231972	−	0.133929i
$704$	−3.83192	+	2.21236i	−0.144421	+	0.0833814i
$705$	5.83612	−	10.1085i	0.219801	−	0.380707i
$706$	2.59461			0.0976494
$707$	2.51116	−	0.770415i	0.0944420	−	0.0289744i
$708$		−	23.7114i		−	0.891128i
$709$	25.6607	+	14.8152i	0.963708	+	0.556397i	0.897312	−	0.441396i	$-0.145517\pi$
$709$	25.6607	+	14.8152i	0.963708	+	0.556397i	0.0663956	+	0.997793i	$0.478850\pi$
$710$	1.36738	+	2.36837i	0.0513169	+	0.0888834i
$711$	6.99091	−	4.03620i	0.262180	−	0.151369i
$712$	3.30580	−	5.72581i	0.123890	−	0.214584i
$713$	−4.07698			−0.152684
$714$	0.999716	+	0.0885859i	0.0374134	+	0.00331524i
$715$	5.92618			0.221627
$716$	−1.45522	+	2.52051i	−0.0543841	+	0.0941960i
$717$	−13.8055	+	7.97061i	−0.515576	+	0.297668i
$718$	−1.45885	−	2.52679i	−0.0544436	−	0.0942991i
$719$	40.1048	+	23.1545i	1.49566	+	0.863518i	0.999988	−	0.00499240i	$-0.00158914\pi$
$719$	40.1048	+	23.1545i	1.49566	+	0.863518i	0.495670	+	0.868511i	$0.334922\pi$
$720$		−	10.2480i		−	0.381921i
$721$	27.4850	+	25.5802i	1.02360	+	0.952656i
$722$	−0.597853			−0.0222498
$723$	4.98269	−	8.63027i	0.185308	−	0.320963i
$724$	26.0055	−	15.0143i	0.966488	−	0.558002i
$725$	−5.09875	+	2.94376i	−0.189363	+	0.109329i
$726$	−0.850790	−	0.491204i	−0.0315758	−	0.0182303i
$727$	32.3898			1.20127			0.600635	−	0.799523i	$-0.294915\pi$
$727$	32.3898			1.20127			0.600635	+	0.799523i	$0.294915\pi$
$728$	0.875931	−	3.81101i	0.0324642	−	0.141245i
$729$	−1.00000			−0.0370370
$730$	−1.06343	+	1.84192i	−0.0393595	+	0.0681726i
$731$	−10.4922	+	1.45225i	−0.388068	+	0.0537135i
$732$	−11.9483	−	20.6950i	−0.441620	−	0.764909i
$733$	−4.29420	+	7.43778i	−0.158610	+	0.274721i	−0.934368	−	0.356310i	$-0.884035\pi$
$733$	−4.29420	+	7.43778i	−0.158610	+	0.274721i	0.775758	+	0.631031i	$0.217368\pi$
$734$		−	1.57206i		−	0.0580257i
$735$	−16.3415	−	7.93090i	−0.602764	−	0.292536i
$736$		−	1.00109i		−	0.0369007i
$737$	4.66278	+	2.69206i	0.171756	+	0.0991632i
$738$	0.587122	−	0.338975i	0.0216122	−	0.0124778i
$739$	11.6739	+	20.2198i	0.429432	+	0.743799i	0.996823	−	0.0796502i	$-0.0253803\pi$
$739$	11.6739	+	20.2198i	0.429432	+	0.743799i	−0.567391	+	0.823449i	$0.692047\pi$
$740$	−3.63418	+	6.29459i	−0.133595	+	0.231394i
$741$			20.3227i			0.746574i
$742$	−0.0931496	+	0.405276i	−0.00341963	+	0.0148781i
$743$			17.3283i			0.635715i	0.948138	+	0.317858i	$0.102963\pi$
$743$			17.3283i			0.635715i	−0.948138	+	0.317858i	$0.897037\pi$
$744$	−0.820927	+	1.42189i	−0.0300966	+	0.0521289i
$745$	45.3457	−	26.1804i	1.66134	−	0.959174i
$746$	−1.30939	−	2.26793i	−0.0479403	−	0.0830350i
$747$	−8.94755	+	15.4976i	−0.327374	+	0.567028i
$748$	−4.31655	−	1.75449i	−0.157829	−	0.0641506i
$749$	12.4612	−	13.3892i	0.455324	−	0.489229i
$750$	−0.779835			−0.0284756
$751$	25.4332	+	14.6839i	0.928071	+	0.535822i	0.886201	−	0.463301i	$-0.153335\pi$
$751$	25.4332	+	14.6839i	0.928071	+	0.535822i	0.0418699	+	0.999123i	$0.486669\pi$
$752$	8.88223	+	15.3845i	0.323902	+	0.561014i
$753$	20.1353	−	11.6251i	0.733773	−	0.423644i
$754$	−1.08909	−	0.628787i	−0.0396624	−	0.0228991i
$755$		−	30.6150i		−	1.11419i
$756$	−1.54544	−	5.03737i	−0.0562073	−	0.183207i
$757$	17.3116			0.629200			0.314600	−	0.949224i	$-0.398130\pi$
$757$	17.3116			0.629200			0.314600	+	0.949224i	$0.398130\pi$
$758$	−2.01030	−	1.16065i	−0.0730175	−	0.0421567i
$759$	0.448128	−	0.258727i	0.0162660	−	0.00939120i
$760$	4.16724	−	2.40595i	0.151162	−	0.0872732i
$761$	10.3527	−	17.9314i	0.375284	−	0.650011i	−0.615085	−	0.788460i	$-0.710879\pi$
$761$	10.3527	−	17.9314i	0.375284	−	0.650011i	0.990370	+	0.138449i	$0.0442118\pi$
$762$		−	0.278293i		−	0.0100815i
$763$	−6.82668	−	22.2515i	−0.247142	−	0.805560i
$764$	10.7080			0.387402
$765$	8.44471	−	6.56938i	0.305319	−	0.237517i
$766$	1.08238	+	1.87473i	0.0391079	+	0.0677369i
$767$	−23.9589	−	41.4980i	−0.865104	−	1.49840i
$768$	13.2737	+	7.66356i	0.478973	+	0.276535i
$769$	−47.9099			−1.72767			−0.863837	−	0.503771i	$-0.831945\pi$
$769$	−47.9099			−1.72767			−0.863837	+	0.503771i	$0.831945\pi$
$770$	−0.262373	−	0.244190i	−0.00945528	−	0.00879999i
$771$		−	26.0055i		−	0.936564i
$772$	−20.0717	−	11.5884i	−0.722395	−	0.417075i
$773$	8.02513	+	13.8999i	0.288644	+	0.499946i	0.973486	−	0.228745i	$-0.0734623\pi$
$773$	8.02513	+	13.8999i	0.288644	+	0.499946i	−0.684842	+	0.728691i	$0.740129\pi$
$774$	−0.118177	−	0.204689i	−0.00424780	−	0.00735740i
$775$	6.71200	+	3.87517i	0.241102	+	0.139200i
$776$			2.58786i			0.0928988i
$777$	−0.833544	+	3.62659i	−0.0299032	+	0.130103i
$778$	2.19251			0.0786054
$779$	−32.2241	−	18.6046i	−1.15455	−	0.666579i
$780$	−10.3994	−	18.0122i	−0.372357	−	0.644941i
$781$	−3.25007	−	5.62929i	−0.116297	−	0.201432i
$782$	0.273030	−	0.212398i	0.00976354	−	0.00759534i
$783$	−3.39629			−0.121373
$784$	22.8886	−	15.5035i	0.817449	−	0.553696i
$785$		−	39.3173i		−	1.40329i
$786$	0.215381	−	0.373051i	0.00768239	−	0.0133063i
$787$	16.2223	−	9.36597i	0.578264	−	0.333861i	−0.182179	−	0.983265i	$-0.558315\pi$
$787$	16.2223	−	9.36597i	0.578264	−	0.333861i	0.760443	+	0.649405i	$0.224982\pi$
$788$	−20.6551	+	11.9252i	−0.735807	+	0.424819i
$789$	2.32453	+	1.34207i	0.0827553	+	0.0477788i
$790$	−1.92720			−0.0685665
$791$	−13.3359	−	3.06515i	−0.474169	−	0.108984i
$792$		−	0.208386i		−	0.00740466i
$793$	−41.8220	−	24.1459i	−1.48514	−	0.857447i
$794$	2.22001	−	1.28172i	0.0787853	−	0.0454867i
$795$	2.21651	+	3.83910i	0.0786114	+	0.136159i
$796$	6.76963	+	3.90845i	0.239943	+	0.138531i
$797$	−29.0471			−1.02890			−0.514451	−	0.857520i	$-0.672004\pi$
$797$	−29.0471			−1.02890			−0.514451	+	0.857520i	$0.672004\pi$
$798$	0.837403	−	0.899761i	0.0296438	−	0.0318512i
$799$	−6.98346	+	17.1813i	−0.247057	+	0.607831i
$800$	−0.951539	+	1.64811i	−0.0336420	+	0.0582696i
$801$	−9.00190	−	15.5918i	−0.318067	−	0.550908i
$802$	−1.01281	+	0.584747i	−0.0357636	+	0.0206482i
$803$	2.52764	−	4.37799i	0.0891983	−	0.154496i
$804$		−	18.8963i		−	0.666420i
$805$	−5.98525	+	1.83625i	−0.210952	+	0.0647193i
$806$			1.65547i			0.0583115i
$807$	−5.73842	+	9.93923i	−0.202002	+	0.349878i
$808$	−0.182293	−	0.315741i	−0.00641306	−	0.0111077i
$809$	24.8285	−	14.3347i	0.872923	−	0.503982i	0.00460447	−	0.999989i	$-0.498534\pi$
$809$	24.8285	−	14.3347i	0.872923	−	0.503982i	0.868318	+	0.496007i	$0.165201\pi$
$810$	0.206754	+	0.119369i	0.00726459	+	0.00419421i
$811$		−	18.7955i		−	0.659998i	−0.943981	−	0.329999i	$-0.892952\pi$
$811$		−	18.7955i		−	0.659998i	0.943981	−	0.329999i	$-0.107048\pi$
$812$	−5.24877	−	17.1084i	−0.184196	−	0.600386i
$813$		−	6.36477i		−	0.223222i
$814$	−0.0367135	+	0.0635896i	−0.00128681	+	0.00222882i
$815$	14.9800	+	25.9461i	0.524725	+	0.908851i
$816$	2.23253	+	16.1295i	0.0781543	+	0.564647i
$817$	−6.48616	+	11.2344i	−0.226922	+	0.393040i
$818$	1.86259			0.0651239
$819$	−7.79468	−	7.25447i	−0.272368	−	0.253492i
$820$	38.0807			1.32984
$821$	36.9697	+	21.3445i	1.29025	+	0.744927i	0.978699	−	0.205301i	$-0.0658174\pi$
$821$	36.9697	+	21.3445i	1.29025	+	0.744927i	0.311553	+	0.950229i	$0.399151\pi$
$822$	−0.276108	+	0.159411i	−0.00963037	+	0.00556009i
$823$	41.8731	−	24.1754i	1.45960	−	0.842702i	0.460612	−	0.887602i	$-0.347630\pi$
$823$	41.8731	−	24.1754i	1.45960	−	0.842702i	0.998992	+	0.0448992i	$0.0142967\pi$
$824$	2.60578	−	4.51334i	0.0907766	−	0.157230i
$825$	−0.983682			−0.0342474
$826$	−0.649189	+	2.82449i	−0.0225882	+	0.0982767i
$827$			54.4938i			1.89494i	0.319850	+	0.947468i	$0.396368\pi$
$827$			54.4938i			1.89494i	−0.319850	+	0.947468i	$0.603632\pi$
$828$	−1.57277	−	0.908037i	−0.0546574	−	0.0315565i
$829$	−19.5473	−	33.8568i	−0.678904	−	1.17590i	−0.975311	−	0.220835i	$-0.929122\pi$
$829$	−19.5473	−	33.8568i	−0.678904	−	1.17590i	0.296407	−	0.955062i	$-0.404212\pi$
$830$	3.69988	−	2.13613i	0.128425	−	0.0741460i
$831$	3.18196	−	5.51132i	0.110381	−	0.191186i
$832$	31.3824			1.08799
$833$	27.4479	+	8.92260i	0.951013	+	0.309150i
$834$	−1.49855			−0.0518905
$835$	3.41568	−	5.91613i	0.118205	−	0.204736i
$836$	−4.94196	+	2.85324i	−0.170921	+	0.0986815i
$837$	2.23544	+	3.87189i	0.0772680	+	0.133832i
$838$	2.15112	+	1.24195i	0.0743093	+	0.0429025i
$839$			50.9230i			1.75806i	0.476770	+	0.879028i	$0.341808\pi$
$839$			50.9230i			1.75806i	−0.476770	+	0.879028i	$0.658192\pi$
$840$	−0.564760	+	2.45716i	−0.0194861	+	0.0847800i
$841$	17.4652			0.602249
$842$	−1.45776	+	2.52491i	−0.0502376	+	0.0870142i
$843$	−23.2731	+	13.4368i	−0.801569	+	0.462786i
$844$	42.8274	−	24.7264i	1.47418	−	0.851118i
$845$	−7.18619	−	4.14895i	−0.247212	−	0.142728i
$846$	−0.413843			−0.0142282
$847$	−20.6805	−	19.2472i	−0.710590	−	0.661343i
$848$	−6.74678			−0.231685
$849$	−8.64375	+	14.9714i	−0.296653	+	0.513817i
$850$	−0.651379	+	0.0901591i	−0.0223421	+	0.00309243i
$851$	0.641273	+	1.11072i	0.0219826	+	0.0380749i
$852$	−11.4066	+	19.7567i	−0.390782	+	0.676855i
$853$			17.5328i			0.600311i	0.953890	+	0.300155i	$0.0970385\pi$
$853$			17.5328i			0.600311i	−0.953890	+	0.300155i	$0.902962\pi$
$854$	0.856670	+	2.79231i	0.0293146	+	0.0955509i
$855$		−	13.1032i		−	0.448118i
$856$	−2.19864	−	1.26939i	−0.0751481	−	0.0433868i
$857$	−10.2337	+	5.90842i	−0.349576	+	0.201828i	−0.664499	−	0.747289i	$-0.731355\pi$
$857$	−10.2337	+	5.90842i	−0.349576	+	0.201828i	0.314922	+	0.949117i	$0.398022\pi$
$858$	−0.105057	−	0.181964i	−0.00358659	−	0.00621216i
$859$	−14.0187	+	24.2811i	−0.478312	+	0.828460i	−0.999691	−	0.0248649i	$-0.992084\pi$
$859$	−14.0187	+	24.2811i	−0.478312	+	0.828460i	0.521379	+	0.853325i	$0.325418\pi$
$860$		−	13.2761i		−	0.452713i
$861$	18.6385	−	5.71822i	0.635199	−	0.194877i
$862$			2.87155i			0.0978053i
$863$	10.1455	−	17.5726i	0.345358	−	0.598178i	−0.640061	−	0.768324i	$-0.721091\pi$
$863$	10.1455	−	17.5726i	0.345358	−	0.598178i	0.985419	+	0.170147i	$0.0544241\pi$
$864$	−0.950733	+	0.548906i	−0.0323446	+	0.0186742i
$865$	8.01952	+	13.8902i	0.272672	+	0.472282i
$866$	−0.284814	+	0.493313i	−0.00967838	+	0.0167634i
$867$	−11.8601	+	12.1794i	−0.402792	+	0.413633i
$868$	−16.0494	+	17.2445i	−0.544752	+	0.585317i
$869$	4.58067			0.155389
$870$	0.702195	+	0.405413i	0.0238066	+	0.0137448i
$871$	−19.0935	−	33.0709i	−0.646958	−	1.12056i
$872$	−2.79780	+	1.61531i	−0.0947454	+	0.0547013i
$873$	6.10281	+	3.52346i	0.206549	+	0.119251i
$874$		−	0.423645i		−	0.0143300i
$875$	−21.8560	−	5.02345i	−0.738869	−	0.169824i
$876$	−17.7421			−0.599452
$877$	−27.7819	−	16.0399i	−0.938129	−	0.541629i	−0.0487553	−	0.998811i	$-0.515525\pi$
$877$	−27.7819	−	16.0399i	−0.938129	−	0.541629i	−0.889373	+	0.457182i	$0.848859\pi$
$878$	2.20779	−	1.27467i	0.0745092	−	0.0430179i
$879$	8.49293	−	4.90339i	0.286459	−	0.165387i
$880$	2.90761	−	5.03612i	0.0980154	−	0.169768i
$881$			18.1229i			0.610577i	0.952260	+	0.305288i	$0.0987529\pi$
$881$			18.1229i			0.610577i	−0.952260	+	0.305288i	$0.901247\pi$
$882$	0.0461759	+	0.642363i	0.00155482	+	0.0216295i
$883$	10.7261			0.360962			0.180481	−	0.983578i	$-0.442235\pi$
$883$	10.7261			0.360962			0.180481	+	0.983578i	$0.442235\pi$
$884$	20.2917	+	26.0843i	0.682485	+	0.877310i
$885$	15.4476	+	26.7559i	0.519264	+	0.899391i
$886$	−0.393643	−	0.681809i	−0.0132247	−	0.0229058i
$887$	45.0302	+	25.9982i	1.51197	+	0.872935i	0.999902	+	0.0139878i	$0.00445259\pi$
$887$	45.0302	+	25.9982i	1.51197	+	0.872935i	0.512065	+	0.858947i	$0.328881\pi$
$888$	0.516499			0.0173326
$889$	1.79267	−	7.79957i	0.0601243	−	0.261589i
$890$			4.29821i			0.144076i
$891$	−0.491425	−	0.283724i	−0.0164633	−	0.00950512i
$892$	3.35013	+	5.80260i	0.112171	+	0.194285i
$893$	11.3569	+	19.6707i	0.380043	+	0.658253i
$894$	−1.60774	−	0.928231i	−0.0537710	−	0.0310447i
$895$		−	3.79220i		−	0.126759i
$896$	−5.64176	−	5.25076i	−0.188478	−	0.175416i
$897$	−3.67006			−0.122540
$898$	3.03853	+	1.75429i	0.101397	+	0.0585415i
$899$	7.59219	+	13.1501i	0.253214	+	0.438579i
$900$	1.72618	+	2.98984i	0.0575394	+	0.0996612i
$901$	−4.32496	−	5.55958i	−0.144085	−	0.185216i
$902$	0.384701			0.0128092
$903$	−1.99355	−	6.49798i	−0.0663413	−	0.216239i
$904$			1.89929i			0.0631696i
$905$	−19.5631	+	33.8843i	−0.650300	+	1.12635i
$906$	−0.940039	+	0.542732i	−0.0312307	+	0.0180311i
$907$	−28.2657	+	16.3192i	−0.938549	+	0.541871i	−0.889505	−	0.456925i	$-0.848951\pi$
$907$	−28.2657	+	16.3192i	−0.938549	+	0.541871i	−0.0490436	+	0.998797i	$0.515617\pi$
$908$	−29.4380	−	16.9960i	−0.976933	−	0.564033i
$909$	−0.992794			−0.0329289
$910$	0.745617	+	2.43033i	0.0247170	+	0.0805648i
$911$		−	53.2213i		−	1.76330i	−0.471904	−	0.881650i	$-0.656433\pi$
$911$		−	53.2213i		−	1.76330i	0.471904	−	0.881650i	$-0.343567\pi$
$912$	17.2705	+	9.97110i	0.571882	+	0.330176i
$913$	−8.79409	+	5.07727i	−0.291042	+	0.168033i
$914$	0.951140	+	1.64742i	0.0314609	+	0.0544919i
$915$	26.9649	+	15.5682i	0.891431	+	0.514668i
$916$	49.0088			1.61930
$917$	8.43945	−	9.06790i	0.278695	−	0.299448i
$918$	−0.351419	−	0.142836i	−0.0115985	−	0.00471430i
$919$	−9.04683	+	15.6696i	−0.298427	+	0.516892i	−0.975776	−	0.218770i	$-0.929795\pi$
$919$	−9.04683	+	15.6696i	−0.298427	+	0.516892i	0.677349	+	0.735662i	$0.263129\pi$
$920$	0.434488	+	0.752556i	0.0143247	+	0.0248110i
$921$	−18.0182	+	10.4028i	−0.593719	+	0.342784i
$922$	−0.302854	+	0.524559i	−0.00997397	+	0.0172754i
$923$			46.1025i			1.51748i
$924$	0.669754	−	2.91397i	0.0220333	−	0.0958625i
$925$		−	2.43813i		−	0.0801651i
$926$	−0.501873	+	0.869269i	−0.0164926	+	0.0285659i
$927$	−7.09571	−	12.2901i	−0.233054	−	0.403661i
$928$	−3.22896	+	1.86424i	−0.105996	+	0.0611967i
$929$	−34.1980	−	19.7442i	−1.12200	−	0.647788i	−0.180090	−	0.983650i	$-0.557639\pi$
$929$	−34.1980	−	19.7442i	−1.12200	−	0.647788i	−0.941911	+	0.335862i	$0.890972\pi$
$930$		−	1.06737i		−	0.0350005i
$931$	29.2654	−	19.8228i	0.959136	−	0.649667i
$932$		−	35.2147i		−	1.15350i
$933$	−0.429382	+	0.743711i	−0.0140573	+	0.0243480i
$934$	−0.227873	−	0.394687i	−0.00745622	−	0.0129146i
$935$	6.01383	−	0.832390i	0.196673	−	0.0272220i
$936$	−0.738991	+	1.27997i	−0.0241547	+	0.0418371i
$937$	22.1391			0.723253			0.361626	−	0.932323i	$-0.382222\pi$
$937$	22.1391			0.723253			0.361626	+	0.932323i	$0.382222\pi$
$938$	−0.517357	+	2.25092i	−0.0168923	+	0.0734951i
$939$	26.2075			0.855250
$940$	−20.1314	−	11.6228i	−0.656613	−	0.379096i
$941$	−8.53723	+	4.92897i	−0.278306	+	0.160680i	−0.632656	−	0.774433i	$-0.718035\pi$
$941$	−8.53723	+	4.92897i	−0.278306	+	0.160680i	0.354350	+	0.935113i	$0.384702\pi$
$942$	−1.20724	+	0.697002i	−0.0393341	+	0.0227095i
$943$	3.35978	−	5.81931i	0.109410	−	0.189503i
$944$	−47.0205			−1.53039
$945$	5.02564	+	4.67734i	0.163484	+	0.152154i
$946$		−	0.134119i		−	0.00436059i
$947$	0.598034	+	0.345275i	0.0194335	+	0.0112199i	0.509685	−	0.860361i	$-0.329762\pi$
$947$	0.598034	+	0.345275i	0.0194335	+	0.0112199i	−0.490252	+	0.871581i	$0.663095\pi$
$948$	−8.03824	−	13.9226i	−0.261070	−	0.452186i
$949$	−31.0511	+	17.9273i	−1.00796	+	0.581946i
$950$	−0.402675	+	0.697454i	−0.0130645	+	0.0226284i
$951$	−0.328095			−0.0106392
$952$	0.353594	−	3.99040i	0.0114600	−	0.129330i
$953$	20.6438			0.668719			0.334360	−	0.942446i	$-0.391480\pi$
$953$	20.6438			0.668719			0.334360	+	0.942446i	$0.391480\pi$
$954$	0.0785869	−	0.136116i	0.00254434	−	0.00440693i
$955$	−12.0829	+	6.97609i	−0.390995	+	0.225741i
$956$	15.8738	+	27.4942i	0.513394	+	0.889225i
$957$	−1.66902	−	0.963609i	−0.0539517	−	0.0311490i
$958$		−	2.70321i		−	0.0873367i
$959$	−8.76521	+	2.68913i	−0.283043	+	0.0868365i
$960$	−20.2339			−0.653047
$961$	−5.50564	+	9.53604i	−0.177601	+	0.307614i
$962$	0.451012	−	0.260392i	0.0145412	−	0.00839536i
$963$	−5.98706	+	3.45663i	−0.192930	+	0.111388i
$964$	−17.1875	−	9.92321i	−0.553572	−	0.319605i
$965$	30.1985			0.972125
$966$	0.162487	+	0.151226i	0.00522792	+	0.00486561i
$967$	32.7879			1.05439			0.527194	−	0.849745i	$-0.323244\pi$
$967$	32.7879			1.05439			0.527194	+	0.849745i	$0.323244\pi$
$968$	−1.96066	+	3.39596i	−0.0630179	+	0.109150i
$969$	2.85453	+	20.6233i	0.0917006	+	0.662516i
$970$	−0.841186	−	1.45698i	−0.0270089	−	0.0467807i
$971$	14.0555	−	24.3449i	0.451063	−	0.781264i	−0.547389	−	0.836878i	$-0.684378\pi$
$971$	14.0555	−	24.3449i	0.451063	−	0.781264i	0.998452	+	0.0556140i	$0.0177116\pi$
$972$			1.99154i			0.0638785i
$973$	−41.9991	−	9.65317i	−1.34643	−	0.309467i
$974$			0.302503i			0.00969281i
$975$	6.04209	+	3.48840i	0.193502	+	0.111718i
$976$	−41.0389	+	23.6938i	−1.31362	+	0.758420i
$977$	16.6775	+	28.8862i	0.533560	+	0.924152i	0.999232	+	0.0391949i	$0.0124793\pi$
$977$	16.6775	+	28.8862i	0.533560	+	0.924152i	−0.465672	+	0.884957i	$0.654187\pi$
$978$	0.531118	−	0.919924i	0.0169833	−	0.0294159i
$979$		−	10.2162i		−	0.326512i
$980$	−15.7947	+	32.5446i	−0.504542	+	1.03960i
$981$			8.79720i			0.280873i
$982$	1.29307	−	2.23966i	0.0412634	−	0.0714703i
$983$	−17.7940	+	10.2733i	−0.567539	+	0.327669i	−0.756166	−	0.654380i	$-0.772930\pi$
$983$	−17.7940	+	10.2733i	−0.567539	+	0.327669i	0.188627	+	0.982049i	$0.439596\pi$
$984$	−1.35303	−	2.34352i	−0.0431330	−	0.0747086i
$985$	15.5382	−	26.9129i	0.495087	−	0.857516i
$986$	−1.19352	−	0.485113i	−0.0380094	−	0.0154492i
$987$	−11.5986	−	2.66584i	−0.369186	−	0.0848547i
$988$	40.4735			1.28763
$989$	−2.02880	−	1.17133i	−0.0645120	−	0.0372460i
$990$	0.0677359	+	0.117322i	0.00215279	+	0.00372874i
$991$	12.0731	−	6.97041i	0.383515	−	0.221422i	−0.295832	−	0.955240i	$-0.595597\pi$
$991$	12.0731	−	6.97041i	0.383515	−	0.221422i	0.679346	+	0.733818i	$0.262263\pi$
$992$	4.25061	+	2.45409i	0.134957	+	0.0779174i
$993$		−	13.3955i		−	0.425093i
$994$	1.89966	−	2.04112i	0.0602536	−	0.0647404i
$995$	−10.1852			−0.322891
$996$	30.8640	+	17.8194i	0.977964	+	0.564628i
$997$	28.1809	−	16.2702i	0.892498	−	0.515284i	0.0177393	−	0.999843i	$-0.494353\pi$
$997$	28.1809	−	16.2702i	0.892498	−	0.515284i	0.874759	+	0.484559i	$0.161020\pi$
$998$	0.996445	−	0.575298i	0.0315419	−	0.0182107i
$999$	0.703231	−	1.21803i	0.0222492	−	0.0385368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.p.a.16.11	✓	48
7.4	even	3	inner	357.2.p.a.67.12	yes	48
17.16	even	2	inner	357.2.p.a.16.12	yes	48
119.67	even	6	inner	357.2.p.a.67.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.p.a.16.11	✓	48	1.1	even	1	trivial
357.2.p.a.16.12	yes	48	17.16	even	2	inner
357.2.p.a.67.11	yes	48	119.67	even	6	inner
357.2.p.a.67.12	yes	48	7.4	even	3	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0460015 - 0.0796769i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.995768 + 1.72472i) q^{4} +(-2.24725 - 1.29745i) q^{5} +0.0920029i q^{6} +(-0.592654 + 2.57852i) q^{7} +0.367233 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.0460015 - 0.0796769i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.995768 + 1.72472i) q^{4} +(-2.24725 - 1.29745i) q^{5} +0.0920029i q^{6} +(-0.592654 + 2.57852i) q^{7} +0.367233 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.206754 + 0.119369i) q^{10} +(0.491425 - 0.283724i) q^{11} +(-1.72472 - 0.995768i) q^{12} -4.02464 q^{13} +(0.178185 + 0.165836i) q^{14} +2.59490 q^{15} +(-1.97464 + 3.42018i) q^{16} +(-4.08417 + 0.565300i) q^{17} +(-0.0460015 - 0.0796769i) q^{18} +(-2.52479 + 4.37306i) q^{19} -5.16784i q^{20} +(-0.776007 - 2.52939i) q^{21} -0.0522069i q^{22} +(-0.789725 - 0.455948i) q^{23} +(-0.318033 + 0.183617i) q^{24} +(0.866760 + 1.50127i) q^{25} +(-0.185140 + 0.320671i) q^{26} +1.00000i q^{27} +(-5.03737 + 1.54544i) q^{28} +3.39629i q^{29} +(0.119369 - 0.206754i) q^{30} +(3.87189 - 2.23544i) q^{31} +(0.548906 + 0.950733i) q^{32} +(-0.283724 + 0.491425i) q^{33} +(-0.142836 + 0.351419i) q^{34} +(4.67734 - 5.02564i) q^{35} +1.99154 q^{36} +(-1.21803 - 0.703231i) q^{37} +(0.232288 + 0.402334i) q^{38} +(3.48544 - 2.01232i) q^{39} +(-0.825265 - 0.476467i) q^{40} +7.36878i q^{41} +(-0.237231 - 0.0545259i) q^{42} +2.56899 q^{43} +(0.978690 + 0.565047i) q^{44} +(-2.24725 + 1.29745i) q^{45} +(-0.0726571 + 0.0419486i) q^{46} +(2.24907 - 3.89551i) q^{47} -3.94928i q^{48} +(-6.29752 - 3.05634i) q^{49} +0.159489 q^{50} +(3.25434 - 2.53165i) q^{51} +(-4.00761 - 6.94139i) q^{52} +(0.854178 + 1.47948i) q^{53} +(0.0796769 + 0.0460015i) q^{54} -1.47247 q^{55} +(-0.217642 + 0.946917i) q^{56} -5.04957i q^{57} +(0.270606 + 0.156234i) q^{58} +(5.95304 + 10.3110i) q^{59} +(2.58392 + 4.47548i) q^{60} +(10.3915 + 5.99952i) q^{61} -0.411334i q^{62} +(1.93674 + 1.80251i) q^{63} -7.79757 q^{64} +(9.04439 + 5.22178i) q^{65} +(0.0261035 + 0.0452125i) q^{66} +(4.74414 + 8.21710i) q^{67} +(-5.04187 - 6.48114i) q^{68} +0.911896 q^{69} +(-0.185263 - 0.603863i) q^{70} -11.4550i q^{71} +(0.183617 - 0.318033i) q^{72} +(7.71523 - 4.45439i) q^{73} +(-0.112062 + 0.0646993i) q^{74} +(-1.50127 - 0.866760i) q^{75} -10.0564 q^{76} +(0.440344 + 1.43530i) q^{77} -0.370279i q^{78} +(6.99091 + 4.03620i) q^{79} +(8.87504 - 5.12400i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.587122 + 0.338975i) q^{82} -17.8951 q^{83} +(3.58977 - 3.85708i) q^{84} +(9.91160 + 4.02864i) q^{85} +(0.118177 - 0.204689i) q^{86} +(-1.69814 - 2.94127i) q^{87} +(0.180467 - 0.104193i) q^{88} +(9.00190 - 15.5918i) q^{89} +0.238739i q^{90} +(2.38522 - 10.3776i) q^{91} -1.81607i q^{92} +(-2.23544 + 3.87189i) q^{93} +(-0.206921 - 0.358398i) q^{94} +(11.3477 - 6.55158i) q^{95} +(-0.950733 - 0.548906i) q^{96} +7.04692i q^{97} +(-0.533215 + 0.361171i) q^{98} -0.567448i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) \) 48 * q - 24 * q^4 + 24 * q^9	\( 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

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