LMFDB - Embedded newform 336.2.s.d.155.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.6
Character	$\chi$	$=$	336.155
Dual form			336.2.s.d.323.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15900 + 0.810376i) q^{2} +(-1.50282 - 0.861124i) q^{3} +(0.686583 - 1.87846i) q^{4} +(-1.19856 + 1.19856i) q^{5} +(2.43961 - 0.219802i) q^{6} +1.00000 q^{7} +(0.726504 + 2.73353i) q^{8} +(1.51693 + 2.58823i) q^{9} +O(q^{10})$	\(q+(-1.15900 + 0.810376i) q^{2} +(-1.50282 - 0.861124i) q^{3} +(0.686583 - 1.87846i) q^{4} +(-1.19856 + 1.19856i) q^{5} +(2.43961 - 0.219802i) q^{6} +1.00000 q^{7} +(0.726504 + 2.73353i) q^{8} +(1.51693 + 2.58823i) q^{9} +(0.417853 - 2.36042i) q^{10} +(-1.10347 - 1.10347i) q^{11} +(-2.64939 + 2.23175i) q^{12} +(0.418588 - 0.418588i) q^{13} +(-1.15900 + 0.810376i) q^{14} +(2.83333 - 0.769110i) q^{15} +(-3.05721 - 2.57943i) q^{16} -4.01838i q^{17} +(-3.85557 - 1.77048i) q^{18} +(-4.91902 - 4.91902i) q^{19} +(1.42853 + 3.07436i) q^{20} +(-1.50282 - 0.861124i) q^{21} +(2.17316 + 0.384703i) q^{22} -3.26657i q^{23} +(1.26210 - 4.73361i) q^{24} +2.12691i q^{25} +(-0.145932 + 0.824359i) q^{26} +(-0.0508894 - 5.19590i) q^{27} +(0.686583 - 1.87846i) q^{28} +(-4.61925 - 4.61925i) q^{29} +(-2.66057 + 3.18746i) q^{30} -7.31001i q^{31} +(5.63363 + 0.512088i) q^{32} +(0.708095 + 2.60855i) q^{33} +(3.25640 + 4.65733i) q^{34} +(-1.19856 + 1.19856i) q^{35} +(5.90337 - 1.07246i) q^{36} +(2.61222 + 2.61222i) q^{37} +(9.68742 + 1.71491i) q^{38} +(-0.989519 + 0.268606i) q^{39} +(-4.14706 - 2.40554i) q^{40} -8.46457 q^{41} +(2.43961 - 0.219802i) q^{42} +(3.91816 - 3.91816i) q^{43} +(-2.83046 + 1.31520i) q^{44} +(-4.92028 - 1.28401i) q^{45} +(2.64715 + 3.78597i) q^{46} +8.08425 q^{47} +(2.37322 + 6.50906i) q^{48} +1.00000 q^{49} +(-1.72359 - 2.46509i) q^{50} +(-3.46033 + 6.03891i) q^{51} +(-0.498905 - 1.07370i) q^{52} +(-1.78619 + 1.78619i) q^{53} +(4.26961 + 5.98084i) q^{54} +2.64516 q^{55} +(0.726504 + 2.73353i) q^{56} +(3.15651 + 11.6283i) q^{57} +(9.09705 + 1.61040i) q^{58} +(-5.55480 - 5.55480i) q^{59} +(0.500572 - 5.85035i) q^{60} +(0.325351 - 0.325351i) q^{61} +(5.92385 + 8.47233i) q^{62} +(1.51693 + 2.58823i) q^{63} +(-6.94438 + 3.97184i) q^{64} +1.00341i q^{65} +(-2.93459 - 2.44950i) q^{66} +(-1.41837 - 1.41837i) q^{67} +(-7.54837 - 2.75895i) q^{68} +(-2.81292 + 4.90907i) q^{69} +(0.417853 - 2.36042i) q^{70} -11.7001i q^{71} +(-5.97294 + 6.02694i) q^{72} -2.89479i q^{73} +(-5.14445 - 0.910695i) q^{74} +(1.83153 - 3.19636i) q^{75} +(-12.6175 + 5.86286i) q^{76} +(-1.10347 - 1.10347i) q^{77} +(0.929185 - 1.11320i) q^{78} +15.6711i q^{79} +(6.75585 - 0.572642i) q^{80} +(-4.39784 + 7.85233i) q^{81} +(9.81047 - 6.85948i) q^{82} +(-9.34150 + 9.34150i) q^{83} +(-2.64939 + 2.23175i) q^{84} +(4.81628 + 4.81628i) q^{85} +(-1.36598 + 7.71635i) q^{86} +(2.96415 + 10.9196i) q^{87} +(2.21470 - 3.81806i) q^{88} +6.70359 q^{89} +(6.74316 - 2.49910i) q^{90} +(0.418588 - 0.418588i) q^{91} +(-6.13612 - 2.24277i) q^{92} +(-6.29482 + 10.9856i) q^{93} +(-9.36968 + 6.55128i) q^{94} +11.7915 q^{95} +(-8.02535 - 5.62083i) q^{96} -3.43505 q^{97} +(-1.15900 + 0.810376i) q^{98} +(1.18215 - 4.52994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) $ 48 * q + 6 * q^6 + 48 * q^7	$ 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) $ 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

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 $

$2$	−1.15900	+	0.810376i	−0.819540	+	0.573022i
$2$	−1.15900	+	0.810376i	−0.819540	+	0.573022i
$3$	−1.50282	−	0.861124i	−0.867653	−	0.497170i
$3$	−1.50282	−	0.861124i	−0.867653	−	0.497170i
$4$	0.686583	−	1.87846i	0.343291	−	0.939229i
$5$	−1.19856	+	1.19856i	−0.536012	+	0.536012i	−0.922355	−	0.386343i	$-0.873738\pi$
$5$	−1.19856	+	1.19856i	−0.536012	+	0.536012i	0.386343	+	0.922355i	$0.373738\pi$
$6$	2.43961	−	0.219802i	0.995966	−	0.0897336i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	0.726504	+	2.73353i	0.256858	+	0.966449i
$9$	1.51693	+	2.58823i	0.505644	+	0.862742i
$10$	0.417853	−	2.36042i	0.132137	−	0.746430i
$11$	−1.10347	−	1.10347i	−0.332710	−	0.332710i	0.520905	−	0.853615i	$-0.325595\pi$
$11$	−1.10347	−	1.10347i	−0.332710	−	0.332710i	−0.853615	+	0.520905i	$0.825595\pi$
$12$	−2.64939	+	2.23175i	−0.764814	+	0.644251i
$13$	0.418588	−	0.418588i	0.116096	−	0.116096i	−0.646672	−	0.762768i	$-0.723840\pi$
$13$	0.418588	−	0.418588i	0.116096	−	0.116096i	0.762768	+	0.646672i	$0.223840\pi$
$14$	−1.15900	+	0.810376i	−0.309757	+	0.216582i
$15$	2.83333	−	0.769110i	0.731562	−	0.198583i
$16$	−3.05721	−	2.57943i	−0.764302	−	0.644858i
$17$		−	4.01838i		−	0.974601i	−0.873234	−	0.487301i	$-0.837982\pi$
$17$		−	4.01838i		−	0.974601i	0.873234	−	0.487301i	$-0.162018\pi$
$18$	−3.85557	−	1.77048i	−0.908766	−	0.417307i
$19$	−4.91902	−	4.91902i	−1.12850	−	1.12850i	−0.990421	−	0.138080i	$-0.955907\pi$
$19$	−4.91902	−	4.91902i	−1.12850	−	1.12850i	−0.138080	−	0.990421i	$-0.544093\pi$
$20$	1.42853	+	3.07436i	0.319430	+	0.687447i
$21$	−1.50282	−	0.861124i	−0.327942	−	0.187913i
$22$	2.17316	+	0.384703i	0.463320	+	0.0820190i
$23$		−	3.26657i		−	0.681127i	−0.940221	−	0.340564i	$-0.889382\pi$
$23$		−	3.26657i		−	0.681127i	0.940221	−	0.340564i	$-0.110618\pi$
$24$	1.26210	−	4.73361i	0.257626	−	0.966245i
$25$			2.12691i			0.425381i
$26$	−0.145932	+	0.824359i	−0.0286196	+	0.161670i
$27$	−0.0508894	−	5.19590i	−0.00979366	−	0.999952i
$28$	0.686583	−	1.87846i	0.129752	−	0.354995i
$29$	−4.61925	−	4.61925i	−0.857772	−	0.857772i	0.133303	−	0.991075i	$-0.457442\pi$
$29$	−4.61925	−	4.61925i	−0.857772	−	0.857772i	−0.991075	+	0.133303i	$0.957442\pi$
$30$	−2.66057	+	3.18746i	−0.485752	+	0.581948i
$31$		−	7.31001i		−	1.31292i	−0.754363	−	0.656458i	$-0.772054\pi$
$31$		−	7.31001i		−	1.31292i	0.754363	−	0.656458i	$-0.227946\pi$
$32$	5.63363	+	0.512088i	0.995894	+	0.0905252i
$33$	0.708095	+	2.60855i	0.123263	+	0.454091i
$34$	3.25640	+	4.65733i	0.558468	+	0.798725i
$35$	−1.19856	+	1.19856i	−0.202594	+	0.202594i
$36$	5.90337	−	1.07246i	0.983896	−	0.178743i
$37$	2.61222	+	2.61222i	0.429446	+	0.429446i	0.888440	−	0.458994i	$-0.151790\pi$
$37$	2.61222	+	2.61222i	0.429446	+	0.429446i	−0.458994	+	0.888440i	$0.651790\pi$
$38$	9.68742	+	1.71491i	1.57151	+	0.278196i
$39$	−0.989519	+	0.268606i	−0.158450	+	0.0430114i
$40$	−4.14706	−	2.40554i	−0.655708	−	0.380350i
$41$	−8.46457			−1.32194			−0.660972	−	0.750411i	$-0.729856\pi$
$41$	−8.46457			−1.32194			−0.660972	+	0.750411i	$0.729856\pi$
$42$	2.43961	−	0.219802i	0.376440	−	0.0339161i
$43$	3.91816	−	3.91816i	0.597514	−	0.597514i	−0.342136	−	0.939650i	$-0.611150\pi$
$43$	3.91816	−	3.91816i	0.597514	−	0.597514i	0.939650	+	0.342136i	$0.111150\pi$
$44$	−2.83046	+	1.31520i	−0.426708	+	0.198275i
$45$	−4.92028	−	1.28401i	−0.733472	−	0.191409i
$46$	2.64715	+	3.78597i	0.390301	+	0.558211i
$47$	8.08425			1.17921			0.589604	−	0.807692i	$-0.299284\pi$
$47$	8.08425			1.17921			0.589604	+	0.807692i	$0.299284\pi$
$48$	2.37322	+	6.50906i	0.342545	+	0.939502i
$49$	1.00000			0.142857
$50$	−1.72359	−	2.46509i	−0.243753	−	0.348617i
$51$	−3.46033	+	6.03891i	−0.484543	+	0.845616i
$52$	−0.498905	−	1.07370i	−0.0691857	−	0.148895i
$53$	−1.78619	+	1.78619i	−0.245352	+	0.245352i	−0.819060	−	0.573708i	$-0.805504\pi$
$53$	−1.78619	+	1.78619i	−0.245352	+	0.245352i	0.573708	+	0.819060i	$0.305504\pi$
$54$	4.26961	+	5.98084i	0.581021	+	0.813889i
$55$	2.64516			0.356674
$56$	0.726504	+	2.73353i	0.0970832	+	0.365283i
$57$	3.15651	+	11.6283i	0.418090	+	1.54020i
$58$	9.09705	+	1.61040i	1.19450	+	0.211456i
$59$	−5.55480	−	5.55480i	−0.723173	−	0.723173i	0.246077	−	0.969250i	$-0.420858\pi$
$59$	−5.55480	−	5.55480i	−0.723173	−	0.723173i	−0.969250	+	0.246077i	$0.920858\pi$
$60$	0.500572	−	5.85035i	0.0646236	−	0.755276i
$61$	0.325351	−	0.325351i	0.0416569	−	0.0416569i	−0.685972	−	0.727628i	$-0.740623\pi$
$61$	0.325351	−	0.325351i	0.0416569	−	0.0416569i	0.727628	+	0.685972i	$0.240623\pi$
$62$	5.92385	+	8.47233i	0.752330	+	1.07599i
$63$	1.51693	+	2.58823i	0.191115	+	0.326086i
$64$	−6.94438	+	3.97184i	−0.868048	+	0.496480i
$65$			1.00341i			0.124457i
$66$	−2.93459	−	2.44950i	−0.361223	−	0.301513i
$67$	−1.41837	−	1.41837i	−0.173282	−	0.173282i	0.615138	−	0.788420i	$-0.289100\pi$
$67$	−1.41837	−	1.41837i	−0.173282	−	0.173282i	−0.788420	+	0.615138i	$0.789100\pi$
$68$	−7.54837	−	2.75895i	−0.915374	−	0.334572i
$69$	−2.81292	+	4.90907i	−0.338636	+	0.590982i
$70$	0.417853	−	2.36042i	0.0499429	−	0.282124i
$71$		−	11.7001i		−	1.38855i	−0.719712	−	0.694273i	$-0.755726\pi$
$71$		−	11.7001i		−	1.38855i	0.719712	−	0.694273i	$-0.244274\pi$
$72$	−5.97294	+	6.02694i	−0.703918	+	0.710281i
$73$		−	2.89479i		−	0.338809i	−0.985547	−	0.169405i	$-0.945816\pi$
$73$		−	2.89479i		−	0.338809i	0.985547	−	0.169405i	$-0.0541844\pi$
$74$	−5.14445	−	0.910695i	−0.598030	−	0.105866i
$75$	1.83153	−	3.19636i	0.211487	−	0.369084i
$76$	−12.6175	+	5.86286i	−1.44733	+	0.672516i
$77$	−1.10347	−	1.10347i	−0.125753	−	0.125753i
$78$	0.929185	−	1.11320i	0.105209	−	0.126045i
$79$			15.6711i			1.76313i	0.472059	+	0.881567i	$0.343511\pi$
$79$			15.6711i			1.76313i	−0.472059	+	0.881567i	$0.656489\pi$
$80$	6.75585	−	0.572642i	0.755327	−	0.0640233i
$81$	−4.39784	+	7.85233i	−0.488649	+	0.872481i
$82$	9.81047	−	6.85948i	1.08339	−	0.757503i
$83$	−9.34150	+	9.34150i	−1.02536	+	1.02536i	−0.0256926	+	0.999670i	$0.508179\pi$
$83$	−9.34150	+	9.34150i	−1.02536	+	1.02536i	−0.999670	+	0.0256926i	$0.991821\pi$
$84$	−2.64939	+	2.23175i	−0.289073	+	0.243504i
$85$	4.81628	+	4.81628i	0.522398	+	0.522398i
$86$	−1.36598	+	7.71635i	−0.147298	+	0.832076i
$87$	2.96415	+	10.9196i	0.317790	+	1.17071i
$88$	2.21470	−	3.81806i	0.236088	−	0.407007i
$89$	6.70359			0.710579			0.355289	−	0.934756i	$-0.384382\pi$
$89$	6.70359			0.710579			0.355289	+	0.934756i	$0.384382\pi$
$90$	6.74316	−	2.49910i	0.710791	−	0.263428i
$91$	0.418588	−	0.418588i	0.0438800	−	0.0438800i
$92$	−6.13612	−	2.24277i	−0.639735	−	0.233825i
$93$	−6.29482	+	10.9856i	−0.652742	+	1.13916i
$94$	−9.36968	+	6.55128i	−0.966408	+	0.675713i
$95$	11.7915			1.20978
$96$	−8.02535	−	5.62083i	−0.819084	−	0.573673i
$97$	−3.43505			−0.348777			−0.174388	−	0.984677i	$-0.555795\pi$
$97$	−3.43505			−0.348777			−0.174388	+	0.984677i	$0.555795\pi$
$98$	−1.15900	+	0.810376i	−0.117077	+	0.0818603i
$99$	1.18215	−	4.52994i	0.118810	−	0.455276i
$100$	3.99531	+	1.46030i	0.399531	+	0.146030i
$101$	9.10445	−	9.10445i	0.905926	−	0.905926i	−0.0900140	−	0.995940i	$-0.528691\pi$
$101$	9.10445	−	9.10445i	0.905926	−	0.905926i	0.995940	+	0.0900140i	$0.0286912\pi$
$102$	−0.883247	−	9.80328i	−0.0874545	−	0.970670i
$103$	−8.02126			−0.790358			−0.395179	−	0.918604i	$-0.629317\pi$
$103$	−8.02126			−0.790358			−0.395179	+	0.918604i	$0.629317\pi$
$104$	1.44833	+	0.840118i	0.142020	+	0.0823803i
$105$	2.83333	−	0.769110i	0.276504	−	0.0750575i
$106$	0.622718	−	3.51769i	0.0604837	−	0.341668i
$107$	6.48216	+	6.48216i	0.626654	+	0.626654i	0.947225	−	0.320571i	$-0.103875\pi$
$107$	6.48216	+	6.48216i	0.626654	+	0.626654i	−0.320571	+	0.947225i	$0.603875\pi$
$108$	−9.79523	−	3.47182i	−0.942546	−	0.334076i
$109$	3.96122	−	3.96122i	0.379416	−	0.379416i	−0.491476	−	0.870891i	$-0.663542\pi$
$109$	3.96122	−	3.96122i	0.379416	−	0.379416i	0.870891	+	0.491476i	$0.163542\pi$
$110$	−3.06575	+	2.14357i	−0.292308	+	0.204382i
$111$	−1.67625	−	6.17513i	−0.159102	−	0.586118i
$112$	−3.05721	−	2.57943i	−0.288879	−	0.243734i
$113$			11.3357i			1.06637i	0.845998	+	0.533186i	$0.179005\pi$
$113$			11.3357i			1.06637i	−0.845998	+	0.533186i	$0.820995\pi$
$114$	−13.0817	−	10.9193i	−1.22521	−	1.02268i
$115$	3.91518	+	3.91518i	0.365093	+	0.365093i
$116$	−11.8486	+	5.50556i	−1.10011	+	0.511179i
$117$	1.71837	+	0.448432i	0.158863	+	0.0414575i
$118$	10.9395	+	1.93656i	1.00706	+	0.178275i
$119$		−	4.01838i		−	0.368365i
$120$	4.16081	+	7.18623i	0.379828	+	0.656010i
$121$		−	8.56469i		−	0.778608i
$122$	−0.113427	+	0.640739i	−0.0102692	+	0.0580098i
$123$	12.7207	+	7.28904i	1.14699	+	0.657231i
$124$	−13.7315	−	5.01892i	−1.23313	−	0.450713i
$125$	−8.54203	−	8.54203i	−0.764022	−	0.764022i
$126$	−3.85557	−	1.77048i	−0.343481	−	0.157727i
$127$		−	11.8859i		−	1.05471i	−0.849646	−	0.527353i	$-0.823185\pi$
$127$		−	11.8859i		−	1.05471i	0.849646	−	0.527353i	$-0.176815\pi$
$128$	4.82989	−	10.2309i	0.426906	−	0.904296i
$129$	−9.26231	+	2.51427i	−0.815501	+	0.221369i
$130$	−0.813136	−	1.16295i	−0.0713168	−	0.101998i
$131$	−2.46217	+	2.46217i	−0.215121	+	0.215121i	−0.806439	−	0.591318i	$-0.798608\pi$
$131$	−2.46217	+	2.46217i	−0.215121	+	0.215121i	0.591318	+	0.806439i	$0.298608\pi$
$132$	5.38622	+	0.460861i	0.468810	+	0.0401128i
$133$	−4.91902	−	4.91902i	−0.426533	−	0.426533i
$134$	2.79332	+	0.494486i	0.241306	+	0.0427171i
$135$	6.28860	+	6.16661i	0.541236	+	0.530737i
$136$	10.9844	−	2.91937i	0.941903	−	0.250334i
$137$	18.6319			1.59183			0.795916	−	0.605407i	$-0.206990\pi$
$137$	18.6319			1.59183			0.795916	+	0.605407i	$0.206990\pi$
$138$	−0.717998	−	7.96916i	−0.0611200	−	0.678380i
$139$	−15.8218	+	15.8218i	−1.34199	+	1.34199i	−0.447912	+	0.894078i	$0.647832\pi$
$139$	−15.8218	+	15.8218i	−1.34199	+	1.34199i	−0.894078	+	0.447912i	$0.852168\pi$
$140$	1.42853	+	3.07436i	0.120733	+	0.259830i
$141$	−12.1492	−	6.96154i	−1.02314	−	0.586267i
$142$	9.48148	+	13.5605i	0.795668	+	1.13797i
$143$	−0.923803			−0.0772523
$144$	2.03858	−	11.8256i	0.169882	−	0.985464i
$145$	11.0729			0.919553
$146$	2.34586	+	3.35507i	0.194145	+	0.277668i
$147$	−1.50282	−	0.861124i	−0.123950	−	0.0710243i
$148$	6.70045	−	3.11344i	0.550773	−	0.255923i
$149$	14.7316	−	14.7316i	1.20686	−	1.20686i	0.234819	−	0.972039i	$-0.424550\pi$
$149$	14.7316	−	14.7316i	1.20686	−	1.20686i	0.972039	−	0.234819i	$-0.0754499\pi$
$150$	0.467498	+	5.18882i	0.0381710	+	0.423665i
$151$	7.80033			0.634782			0.317391	−	0.948295i	$-0.397193\pi$
$151$	7.80033			0.634782			0.317391	+	0.948295i	$0.397193\pi$
$152$	9.87261	−	17.0200i	0.800774	−	1.38050i
$153$	10.4005	−	6.09561i	0.840830	−	0.492801i
$154$	2.17316	+	0.384703i	0.175118	+	0.0310003i
$155$	8.76148	+	8.76148i	0.703739	+	0.703739i
$156$	−0.174821	+	2.04319i	−0.0139969	+	0.163586i
$157$	3.31101	−	3.31101i	0.264248	−	0.264248i	−0.562530	−	0.826777i	$-0.690172\pi$
$157$	3.31101	−	3.31101i	0.264248	−	0.264248i	0.826777	+	0.562530i	$0.190172\pi$
$158$	−12.6995	−	18.1628i	−1.01031	−	1.44496i
$159$	4.22245	−	1.14619i	0.334862	−	0.0908988i
$160$	−7.36601	+	6.13847i	−0.582334	+	0.485289i
$161$		−	3.26657i		−	0.257442i
$162$	−1.26622	−	12.6648i	−0.0994835	−	0.995039i
$163$	6.35075	+	6.35075i	0.497429	+	0.497429i	0.910637	−	0.413207i	$-0.135592\pi$
$163$	6.35075	+	6.35075i	0.497429	+	0.497429i	−0.413207	+	0.910637i	$0.635592\pi$
$164$	−5.81163	+	15.9003i	−0.453812	+	1.24161i
$165$	−3.97520	−	2.27781i	−0.309469	−	0.177327i
$166$	3.25672	−	18.3970i	0.252770	−	1.42788i
$167$		−	23.1146i		−	1.78866i	−0.447407	−	0.894331i	$-0.647652\pi$
$167$		−	23.1146i		−	1.78866i	0.447407	−	0.894331i	$-0.352348\pi$
$168$	1.26210	−	4.73361i	0.0973735	−	0.365206i
$169$			12.6496i			0.973044i
$170$	−9.48508	−	1.67909i	−0.727472	−	0.128781i
$171$	5.26973	−	20.1934i	0.402986	−	1.54422i
$172$	−4.66996	−	10.0502i	−0.356081	−	0.766324i
$173$	11.0546	+	11.0546i	0.840464	+	0.840464i	0.988919	−	0.148456i	$-0.0474302\pi$
$173$	11.0546	+	11.0546i	0.840464	+	0.840464i	−0.148456	+	0.988919i	$0.547430\pi$
$174$	−12.2845	−	10.2538i	−0.931283	−	0.777341i
$175$			2.12691i			0.160779i
$176$	0.527213	+	6.21989i	0.0397401	+	0.468842i
$177$	3.56449	+	13.1312i	0.267923	+	0.987003i
$178$	−7.76949	+	5.43242i	−0.582348	+	0.407177i
$179$	−10.1184	+	10.1184i	−0.756287	+	0.756287i	−0.975645	−	0.219357i	$-0.929604\pi$
$179$	−10.1184	+	10.1184i	−0.756287	+	0.756287i	0.219357	+	0.975645i	$0.429604\pi$
$180$	−5.79014	+	8.36096i	−0.431572	+	0.623189i
$181$	4.85885	+	4.85885i	0.361156	+	0.361156i	0.864238	−	0.503083i	$-0.167801\pi$
$181$	4.85885	+	4.85885i	0.361156	+	0.361156i	−0.503083	+	0.864238i	$0.667801\pi$
$182$	−0.145932	+	0.824359i	−0.0108172	+	0.0611056i
$183$	−0.769110	+	0.208776i	−0.0568543	+	0.0154332i
$184$	8.92928	−	2.37318i	0.658275	−	0.174953i
$185$	−6.26180			−0.460377
$186$	−1.60675	−	17.8335i	−0.117813	−	1.30762i
$187$	−4.43419	+	4.43419i	−0.324260	+	0.324260i
$188$	5.55050	−	15.1859i	0.404812	−	1.10755i
$189$	−0.0508894	−	5.19590i	−0.00370166	−	0.377946i
$190$	−13.6664	+	9.55553i	−0.991464	+	0.693231i
$191$	−2.01613			−0.145882			−0.0729409	−	0.997336i	$-0.523238\pi$
$191$	−2.01613			−0.145882			−0.0729409	+	0.997336i	$0.523238\pi$
$192$	13.8564	+	0.0110128i	1.00000	+	0.000794783i
$193$	−19.8255			−1.42707			−0.713534	−	0.700621i	$-0.752906\pi$
$193$	−19.8255			−1.42707			−0.713534	+	0.700621i	$0.752906\pi$
$194$	3.98124	−	2.78368i	0.285836	−	0.199857i
$195$	0.864057	−	1.50794i	0.0618764	−	0.107986i
$196$	0.686583	−	1.87846i	0.0490416	−	0.134176i
$197$	−6.81358	+	6.81358i	−0.485448	+	0.485448i	−0.906866	−	0.421419i	$-0.861532\pi$
$197$	−6.81358	+	6.81358i	−0.485448	+	0.485448i	0.421419	+	0.906866i	$0.361532\pi$
$198$	2.30084	+	6.20820i	0.163513	+	0.441198i
$199$	−19.4422			−1.37822			−0.689110	−	0.724656i	$-0.741999\pi$
$199$	−19.4422			−1.37822			−0.689110	+	0.724656i	$0.741999\pi$
$200$	−5.81397	+	1.54521i	−0.411110	+	0.109263i
$201$	0.910163	+	3.35295i	0.0641980	+	0.236499i
$202$	−3.17407	+	17.9301i	−0.223327	+	1.26156i
$203$	−4.61925	−	4.61925i	−0.324207	−	0.324207i
$204$	8.96803	+	10.6463i	0.627888	+	0.745389i
$205$	10.1453	−	10.1453i	0.708578	−	0.708578i
$206$	9.29668	−	6.50023i	0.647730	−	0.452893i
$207$	8.45463	−	4.95517i	0.587638	−	0.344408i
$208$	−2.35943	+	0.199991i	−0.163597	+	0.0138669i
$209$			10.8560i			0.750927i
$210$	−2.66057	+	3.18746i	−0.183597	+	0.219956i
$211$	−17.4276	−	17.4276i	−1.19977	−	1.19977i	−0.974236	−	0.225530i	$-0.927589\pi$
$211$	−17.4276	−	17.4276i	−1.19977	−	1.19977i	−0.225530	−	0.974236i	$-0.572411\pi$
$212$	2.12892	+	4.58165i	0.146215	+	0.314669i
$213$	−10.0752	+	17.5831i	−0.690344	+	1.20478i
$214$	−12.7658	−	2.25987i	−0.872654	−	0.154481i
$215$			9.39231i			0.640550i
$216$	14.1662	−	3.91395i	0.963887	−	0.266311i
$217$		−	7.31001i		−	0.496236i
$218$	−1.38099	+	7.80114i	−0.0935327	+	0.528360i
$219$	−2.49277	+	4.35034i	−0.168446	+	0.293969i
$220$	1.81612	−	4.96883i	0.122443	−	0.334998i
$221$	−1.68205	−	1.68205i	−0.113147	−	0.113147i
$222$	6.94696	+	5.79862i	0.466249	+	0.389178i
$223$			11.5112i			0.770849i	0.922739	+	0.385425i	$0.125945\pi$
$223$			11.5112i			0.770849i	−0.922739	+	0.385425i	$0.874055\pi$
$224$	5.63363	+	0.512088i	0.376413	+	0.0342153i
$225$	−5.50492	+	3.22637i	−0.366995	+	0.215091i
$226$	−9.18617	−	13.1381i	−0.611055	−	0.873934i
$227$	4.19702	−	4.19702i	0.278566	−	0.278566i	−0.553970	−	0.832536i	$-0.686888\pi$
$227$	4.19702	−	4.19702i	0.278566	−	0.278566i	0.832536	+	0.553970i	$0.186888\pi$
$228$	24.0105	+	2.05440i	1.59013	+	0.136056i
$229$	−5.34847	−	5.34847i	−0.353437	−	0.353437i	0.507950	−	0.861387i	$-0.330404\pi$
$229$	−5.34847	−	5.34847i	−0.353437	−	0.353437i	−0.861387	+	0.507950i	$0.830404\pi$
$230$	−7.71048	−	1.36495i	−0.508414	−	0.0900019i
$231$	0.708095	+	2.60855i	0.0465892	+	0.171630i
$232$	9.27095	−	15.9828i	0.608668	−	1.04932i
$233$	−27.0374			−1.77128			−0.885640	−	0.464372i	$-0.846280\pi$
$233$	−27.0374			−1.77128			−0.885640	+	0.464372i	$0.846280\pi$
$234$	−2.35500	+	0.872792i	−0.153951	+	0.0570562i
$235$	−9.68946	+	9.68946i	−0.632070	+	0.632070i
$236$	−14.2483	+	6.62062i	−0.927484	+	0.430966i
$237$	13.4947	−	23.5508i	0.876577	−	1.52979i
$238$	3.25640	+	4.65733i	0.211081	+	0.301890i
$239$	−2.75475			−0.178190			−0.0890950	−	0.996023i	$-0.528397\pi$
$239$	−2.75475			−0.178190			−0.0890950	+	0.996023i	$0.528397\pi$
$240$	−10.6459	−	4.95705i	−0.687193	−	0.319976i
$241$	14.4893			0.933336			0.466668	−	0.884432i	$-0.345454\pi$
$241$	14.4893			0.933336			0.466668	+	0.884432i	$0.345454\pi$
$242$	6.94061	+	9.92651i	0.446160	+	0.638100i
$243$	13.3710	−	8.01354i	0.857749	−	0.514069i
$244$	−0.387777	−	0.834538i	−0.0248249	−	0.0534258i
$245$	−1.19856	+	1.19856i	−0.0765732	+	0.0765732i
$246$	−20.6502	+	1.86053i	−1.31661	+	0.118623i
$247$	−4.11809			−0.262028
$248$	19.9821	−	5.31075i	1.26887	−	0.337233i
$249$	22.0828	−	5.99440i	1.39944	−	0.379879i
$250$	16.8225	+	2.97800i	1.06395	+	0.188345i
$251$	1.46929	+	1.46929i	0.0927408	+	0.0927408i	0.751955	−	0.659214i	$-0.229111\pi$
$251$	1.46929	+	1.46929i	0.0927408	+	0.0927408i	−0.659214	+	0.751955i	$0.729111\pi$
$252$	5.90337	−	1.07246i	0.371878	−	0.0675586i
$253$	−3.60458	+	3.60458i	−0.226618	+	0.226618i
$254$	9.63206	+	13.7758i	0.604369	+	0.864373i
$255$	−3.09058	−	11.3854i	−0.193540	−	0.712981i
$256$	2.69305	+	15.7717i	0.168315	+	0.985733i
$257$			10.5661i			0.659092i	0.944139	+	0.329546i	$0.106896\pi$
$257$			10.5661i			0.659092i	−0.944139	+	0.329546i	$0.893104\pi$
$258$	8.69756	−	10.4200i	0.541487	−	0.648721i
$259$	2.61222	+	2.61222i	0.162315	+	0.162315i
$260$	1.88486	+	0.688922i	0.116894	+	0.0427251i
$261$	4.94858	−	18.9627i	0.306309	−	1.17376i
$262$	0.858383	−	4.84894i	0.0530311	−	0.299569i
$263$			3.52053i			0.217085i	0.994092	+	0.108543i	$0.0346184\pi$
$263$			3.52053i			0.217085i	−0.994092	+	0.108543i	$0.965382\pi$
$264$	−6.61612	+	3.83072i	−0.407194	+	0.235765i
$265$		−	4.28171i		−	0.263024i
$266$	9.68742	+	1.71491i	0.593974	+	0.105148i
$267$	−10.0743	−	5.77262i	−0.616536	−	0.353279i
$268$	−3.63818	+	1.69052i	−0.222237	+	0.103265i
$269$	2.95588	+	2.95588i	0.180223	+	0.180223i	0.791453	−	0.611230i	$-0.209325\pi$
$269$	2.95588	+	2.95588i	0.180223	+	0.180223i	−0.611230	+	0.791453i	$0.709325\pi$
$270$	−12.2858	−	2.05100i	−0.747689	−	0.124820i
$271$			26.4875i			1.60900i	0.593953	+	0.804500i	$0.297566\pi$
$271$			26.4875i			1.60900i	−0.593953	+	0.804500i	$0.702434\pi$
$272$	−10.3652	+	12.2850i	−0.628480	+	0.744890i
$273$	−0.989519	+	0.268606i	−0.0598884	+	0.0162568i
$274$	−21.5945	+	15.0989i	−1.30457	+	0.912155i
$275$	2.34699	−	2.34699i	0.141529	−	0.141529i
$276$	7.29017	+	8.65444i	0.438817	+	0.520936i
$277$	−0.907324	−	0.907324i	−0.0545158	−	0.0545158i	0.679323	−	0.733839i	$-0.262273\pi$
$277$	−0.907324	−	0.907324i	−0.0545158	−	0.0545158i	−0.733839	+	0.679323i	$0.762273\pi$
$278$	5.51594	−	31.1592i	0.330824	−	1.86880i
$279$	18.9200	−	11.0888i	1.13271	−	0.663868i
$280$	−4.14706	−	2.40554i	−0.247834	−	0.143759i
$281$	−22.5004			−1.34226			−0.671130	−	0.741340i	$-0.734191\pi$
$281$	−22.5004			−1.34226			−0.671130	+	0.741340i	$0.734191\pi$
$282$	19.7224	−	1.77693i	1.17445	−	0.105815i
$283$	−0.463851	+	0.463851i	−0.0275731	+	0.0275731i	−0.720759	−	0.693186i	$-0.756207\pi$
$283$	−0.463851	+	0.463851i	−0.0275731	+	0.0275731i	0.693186	+	0.720759i	$0.256207\pi$
$284$	−21.9781	−	8.03309i	−1.30416	−	0.476676i
$285$	−17.7205	−	10.1539i	−1.04967	−	0.601467i
$286$	1.07069	−	0.748628i	0.0633114	−	0.0442673i
$287$	−8.46457			−0.499648
$288$	7.22043	+	15.3579i	0.425468	+	0.904974i
$289$	0.852586			0.0501521
$290$	−12.8335	+	8.97320i	−0.753611	+	0.526924i
$291$	5.16226	+	2.95801i	0.302617	+	0.173401i
$292$	−5.43773	−	1.98751i	−0.318219	−	0.116310i
$293$	14.0097	−	14.0097i	0.818455	−	0.818455i	−0.167429	−	0.985884i	$-0.553546\pi$
$293$	14.0097	−	14.0097i	0.818455	−	0.818455i	0.985884	+	0.167429i	$0.0535464\pi$
$294$	2.43961	−	0.219802i	0.142281	−	0.0128191i
$295$	13.3155			0.775259
$296$	−5.24279	+	9.03837i	−0.304731	+	0.525344i
$297$	−5.67739	+	5.78970i	−0.329436	+	0.335953i
$298$	−5.13586	+	29.0121i	−0.297512	+	1.68063i
$299$	−1.36735	−	1.36735i	−0.0790758	−	0.0790758i
$300$	−4.74673	−	5.63502i	−0.274052	−	0.325338i
$301$	3.91816	−	3.91816i	0.225839	−	0.225839i
$302$	−9.04062	+	6.32120i	−0.520229	+	0.363744i
$303$	−21.5224	+	5.84228i	−1.23643	+	0.335630i
$304$	2.35018	+	27.7268i	0.134792	+	1.59024i
$305$			0.779905i			0.0446572i
$306$	−7.11448	+	15.4931i	−0.406708	+	0.885684i
$307$	13.0226	+	13.0226i	0.743236	+	0.743236i	0.973199	−	0.229963i	$-0.0738605\pi$
$307$	13.0226	+	13.0226i	0.743236	+	0.743236i	−0.229963	+	0.973199i	$0.573861\pi$
$308$	−2.83046	+	1.31520i	−0.161280	+	0.0749407i
$309$	12.0545	+	6.90730i	0.685757	+	0.392942i
$310$	−17.2547	−	3.05451i	−0.980000	−	0.173484i
$311$			6.02505i			0.341649i	0.985301	+	0.170825i	$0.0546431\pi$
$311$			6.02505i			0.341649i	−0.985301	+	0.170825i	$0.945357\pi$
$312$	−1.45313	−	2.50974i	−0.0822674	−	0.142086i
$313$		−	23.2145i		−	1.31216i	−0.754691	−	0.656080i	$-0.772213\pi$
$313$		−	23.2145i		−	1.31216i	0.754691	−	0.656080i	$-0.227787\pi$
$314$	−1.15431	+	6.52064i	−0.0651417	+	0.367981i
$315$	−4.92028	−	1.28401i	−0.277226	−	0.0723459i
$316$	29.4375	+	10.7595i	1.65599	+	0.605269i
$317$	12.0141	+	12.0141i	0.674781	+	0.674781i	0.958814	−	0.284034i	$-0.0916727\pi$
$317$	12.0141	+	12.0141i	0.674781	+	0.674781i	−0.284034	+	0.958814i	$0.591673\pi$
$318$	−3.96500	+	4.75021i	−0.222346	+	0.266379i
$319$			10.1944i			0.570779i
$320$	3.56277	−	13.0838i	0.199165	−	0.731404i
$321$	−4.15957	−	15.3234i	−0.232165	−	0.855271i
$322$	2.64715	+	3.78597i	0.147520	+	0.210984i
$323$	−19.7665	+	19.7665i	−1.09984	+	1.09984i
$324$	11.7308	+	13.6524i	0.651710	+	0.758468i
$325$	0.890298	+	0.890298i	0.0493849	+	0.0493849i
$326$	−12.5070	−	2.21406i	−0.692701	−	0.122625i
$327$	−9.36409	+	2.54189i	−0.517835	+	0.140567i
$328$	−6.14954	−	23.1382i	−0.339552	−	1.27759i
$329$	8.08425			0.445699
$330$	6.45316	−	0.581411i	0.355235	−	0.0320056i
$331$	−6.71058	+	6.71058i	−0.368847	+	0.368847i	−0.867057	−	0.498210i	$-0.833991\pi$
$331$	−6.71058	+	6.71058i	−0.368847	+	0.368847i	0.498210	+	0.867057i	$0.333991\pi$
$332$	11.1339	+	23.9613i	0.611052	+	1.31505i
$333$	−2.79846	+	10.7236i	−0.153355	+	0.587648i
$334$	18.7315	+	26.7899i	1.02494	+	1.46588i
$335$	3.40001			0.185762
$336$	2.37322	+	6.50906i	0.129470	+	0.355098i
$337$	12.9404			0.704908			0.352454	−	0.935829i	$-0.385347\pi$
$337$	12.9404			0.704908			0.352454	+	0.935829i	$0.385347\pi$
$338$	−10.2509	−	14.6609i	−0.557576	−	0.797448i
$339$	9.76143	−	17.0355i	0.530168	−	0.925241i
$340$	12.3539	−	5.74040i	0.669987	−	0.311317i
$341$	−8.06641	+	8.06641i	−0.436820	+	0.436820i
$342$	10.2566	+	27.6747i	0.554612	+	1.49647i
$343$	1.00000			0.0539949
$344$	13.5570	+	7.86386i	0.730943	+	0.423991i
$345$	−2.51236	−	9.25527i	−0.135261	−	0.498287i
$346$	−21.7707	−	3.85394i	−1.17040	−	0.207189i
$347$	5.37894	+	5.37894i	0.288756	+	0.288756i	0.836588	−	0.547832i	$-0.184547\pi$
$347$	5.37894	+	5.37894i	0.288756	+	0.288756i	−0.547832	+	0.836588i	$0.684547\pi$
$348$	22.5472	+	1.92920i	1.20866	+	0.103416i
$349$	1.76640	−	1.76640i	0.0945535	−	0.0945535i	−0.658248	−	0.752801i	$-0.728702\pi$
$349$	1.76640	−	1.76640i	0.0945535	−	0.0945535i	0.752801	+	0.658248i	$0.228702\pi$
$350$	−1.72359	−	2.46509i	−0.0921300	−	0.131765i
$351$	−2.19625	−	2.15364i	−0.117227	−	0.114953i
$352$	−5.65149	−	6.78164i	−0.301225	−	0.361463i
$353$		−	19.0425i		−	1.01353i	−0.862085	−	0.506764i	$-0.830842\pi$
$353$		−	19.0425i		−	1.01353i	0.862085	−	0.506764i	$-0.169158\pi$
$354$	−14.7725	−	12.3306i	−0.785148	−	0.655363i
$355$	14.0233	+	14.0233i	0.744278	+	0.744278i
$356$	4.60257	−	12.5924i	0.243936	−	0.667396i
$357$	−3.46033	+	6.03891i	−0.183140	+	0.319613i
$358$	3.52758	−	19.9270i	0.186438	−	1.05318i
$359$		−	28.4851i		−	1.50338i	−0.659514	−	0.751692i	$-0.729238\pi$
$359$		−	28.4851i		−	1.50338i	0.659514	−	0.751692i	$-0.270762\pi$
$360$	−0.0647151	−	14.3826i	−0.00341079	−	0.758028i
$361$			29.3935i			1.54703i
$362$	−9.56893	−	1.69394i	−0.502932	−	0.0890313i
$363$	−7.37526	+	12.8712i	−0.387101	+	0.675562i
$364$	−0.498905	−	1.07370i	−0.0261497	−	0.0562770i
$365$	3.46958	+	3.46958i	0.181606	+	0.181606i
$366$	0.722215	−	0.865241i	0.0377508	−	0.0452269i
$367$			18.2398i			0.952112i	0.879415	+	0.476056i	$0.157934\pi$
$367$			18.2398i			0.952112i	−0.879415	+	0.476056i	$0.842066\pi$
$368$	−8.42591	+	9.98659i	−0.439231	+	0.520587i
$369$	−12.8402	−	21.9082i	−0.668433	−	1.14050i
$370$	7.25745	−	5.07441i	0.377297	−	0.263806i
$371$	−1.78619	+	1.78619i	−0.0927344	+	0.0927344i
$372$	16.3141	+	19.3671i	0.845847	+	1.00414i
$373$	−13.6888	−	13.6888i	−0.708779	−	0.708779i	0.257499	−	0.966278i	$-0.417101\pi$
$373$	−13.6888	−	13.6888i	−0.708779	−	0.708779i	−0.966278	+	0.257499i	$0.917101\pi$
$374$	1.54589	−	8.73260i	0.0799358	−	0.451552i
$375$	5.48138	+	20.1929i	0.283057	+	1.04276i
$376$	5.87324	+	22.0985i	0.302889	+	1.13965i
$377$	−3.86712			−0.199167
$378$	4.26961	+	5.98084i	0.219605	+	0.307621i
$379$	21.2201	−	21.2201i	1.09000	−	1.09000i	0.0944749	−	0.995527i	$-0.469883\pi$
$379$	21.2201	−	21.2201i	1.09000	−	1.09000i	0.995527	−	0.0944749i	$-0.0301172\pi$
$380$	8.09583	−	22.1498i	0.415307	−	1.13626i
$381$	−10.2353	+	17.8624i	−0.524368	+	0.915118i
$382$	2.33670	−	1.63382i	0.119556	−	0.0835935i
$383$	−9.38265			−0.479431			−0.239716	−	0.970843i	$-0.577054\pi$
$383$	−9.38265			−0.479431			−0.239716	+	0.970843i	$0.577054\pi$
$384$	−16.0686	+	11.2161i	−0.819995	+	0.572371i
$385$	2.64516			0.134810
$386$	22.9778	−	16.0661i	1.16954	−	0.817741i
$387$	16.0847	+	4.19751i	0.817630	+	0.213372i
$388$	−2.35845	+	6.45260i	−0.119732	+	0.327581i
$389$	1.88977	−	1.88977i	0.0958149	−	0.0958149i	−0.657575	−	0.753389i	$-0.728418\pi$
$389$	1.88977	−	1.88977i	0.0958149	−	0.0958149i	0.753389	+	0.657575i	$0.228418\pi$
$390$	0.220550	+	2.44792i	0.0111680	+	0.123955i
$391$	−13.1263			−0.663828
$392$	0.726504	+	2.73353i	0.0366940	+	0.138064i
$393$	5.82042	−	1.57996i	0.293602	−	0.0796985i
$394$	2.37541	−	13.4185i	0.119671	−	0.676016i
$395$	−18.7827	−	18.7827i	−0.945061	−	0.945061i
$396$	−7.69766	−	5.33079i	−0.386822	−	0.267882i
$397$	22.5436	−	22.5436i	1.13143	−	1.13143i	0.141494	−	0.989939i	$-0.454810\pi$
$397$	22.5436	−	22.5436i	1.13143	−	1.13143i	0.989939	−	0.141494i	$-0.0451905\pi$
$398$	22.5336	−	15.7555i	1.12951	−	0.789751i
$399$	3.15651	+	11.6283i	0.158023	+	0.582142i
$400$	5.48622	−	6.50240i	0.274311	−	0.325120i
$401$		−	3.36660i		−	0.168120i	−0.996461	−	0.0840599i	$-0.973211\pi$
$401$		−	3.36660i		−	0.168120i	0.996461	−	0.0840599i	$-0.0267887\pi$
$402$	−3.77203	−	3.14851i	−0.188132	−	0.157034i
$403$	−3.05988	−	3.05988i	−0.152424	−	0.152424i
$404$	−10.8514	−	23.3533i	−0.539876	−	1.16187i
$405$	−4.14041	−	14.6826i	−0.205739	−	0.729582i
$406$	9.09705	+	1.61040i	0.451479	+	0.0799229i
$407$		−	5.76503i		−	0.285762i
$408$	−19.0215	−	5.07162i	−0.941703	−	0.251083i
$409$		−	13.1993i		−	0.652662i	−0.945256	−	0.326331i	$-0.894188\pi$
$409$		−	13.1993i		−	0.652662i	0.945256	−	0.326331i	$-0.105812\pi$
$410$	−3.53694	+	19.9799i	−0.174677	+	0.986739i
$411$	−28.0004	−	16.0444i	−1.38116	−	0.791411i
$412$	−5.50726	+	15.0676i	−0.271323	+	0.742327i
$413$	−5.55480	−	5.55480i	−0.273334	−	0.273334i
$414$	−5.78341	+	12.5945i	−0.284239	+	0.618985i
$415$		−	22.3927i		−	1.09921i
$416$	2.57252	−	2.14382i	0.126128	−	0.105109i
$417$	37.4019	−	10.1528i	1.83158	−	0.497184i
$418$	−8.79746	−	12.5822i	−0.430298	−	0.615415i
$419$	−4.31964	+	4.31964i	−0.211028	+	0.211028i	−0.804704	−	0.593676i	$-0.797676\pi$
$419$	−4.31964	+	4.31964i	−0.211028	+	0.211028i	0.593676	+	0.804704i	$0.297676\pi$
$420$	0.500572	−	5.85035i	0.0244254	−	0.285468i
$421$	−3.88545	−	3.88545i	−0.189365	−	0.189365i	0.606056	−	0.795422i	$-0.292751\pi$
$421$	−3.88545	−	3.88545i	−0.189365	−	0.189365i	−0.795422	+	0.606056i	$0.792751\pi$
$422$	34.3216	+	6.07577i	1.67075	+	0.295764i
$423$	12.2632	+	20.9239i	0.596259	+	1.01735i
$424$	−6.18028	−	3.58493i	−0.300141	−	0.174100i
$425$	8.54673			0.414577
$426$	−2.57170	−	28.5437i	−0.124599	−	1.38294i
$427$	0.325351	−	0.325351i	0.0157448	−	0.0157448i
$428$	16.6270	−	7.72592i	0.803696	−	0.373446i
$429$	1.38831	+	0.795509i	0.0670282	+	0.0384075i
$430$	−7.61130	−	10.8857i	−0.367049	−	0.524956i
$431$	7.92801			0.381879			0.190939	−	0.981602i	$-0.438847\pi$
$431$	7.92801			0.381879			0.190939	+	0.981602i	$0.438847\pi$
$432$	−13.2469	+	16.0162i	−0.637342	+	0.770581i
$433$	−7.10644			−0.341514			−0.170757	−	0.985313i	$-0.554621\pi$
$433$	−7.10644			−0.341514			−0.170757	+	0.985313i	$0.554621\pi$
$434$	5.92385	+	8.47233i	0.284354	+	0.406685i
$435$	−16.6405	−	9.53513i	−0.797853	−	0.457174i
$436$	−4.72127	−	10.1607i	−0.226108	−	0.486608i
$437$	−16.0683	+	16.0683i	−0.768653	+	0.768653i
$438$	−0.636279	−	7.06214i	−0.0304026	−	0.337442i
$439$	5.48850			0.261952			0.130976	−	0.991386i	$-0.458189\pi$
$439$	5.48850			0.261952			0.130976	+	0.991386i	$0.458189\pi$
$440$	1.92172	+	7.23063i	0.0916145	+	0.344707i
$441$	1.51693	+	2.58823i	0.0722348	+	0.123249i
$442$	3.31259	+	0.586411i	0.157564	+	0.0278927i
$443$	19.7138	+	19.7138i	0.936632	+	0.936632i	0.998109	−	0.0614763i	$-0.0195809\pi$
$443$	19.7138	+	19.7138i	0.936632	+	0.936632i	−0.0614763	+	0.998109i	$0.519581\pi$
$444$	−12.7506	−	1.09098i	−0.605117	−	0.0517756i
$445$	−8.03465	+	8.03465i	−0.380879	+	0.380879i
$446$	−9.32842	−	13.3416i	−0.441714	−	0.631742i
$447$	−34.8246	+	9.45319i	−1.64715	+	0.447120i
$448$	−6.94438	+	3.97184i	−0.328091	+	0.187652i
$449$		−	29.9224i		−	1.41212i	−0.708150	−	0.706062i	$-0.750470\pi$
$449$		−	29.9224i		−	1.41212i	0.708150	−	0.706062i	$-0.249530\pi$
$450$	3.76565	−	8.20043i	0.177515	−	0.386572i
$451$	9.34044	+	9.34044i	0.439824	+	0.439824i
$452$	21.2936	+	7.78289i	1.00157	+	0.366076i
$453$	−11.7225	−	6.71705i	−0.550770	−	0.315594i
$454$	−1.46320	+	8.26553i	−0.0686715	+	0.387921i
$455$			1.00341i			0.0470404i
$456$	−29.4931	+	17.0764i	−1.38114	+	0.799677i
$457$		−	35.9554i		−	1.68192i	−0.541097	−	0.840960i	$-0.681991\pi$
$457$		−	35.9554i		−	1.68192i	0.541097	−	0.840960i	$-0.318009\pi$
$458$	10.5332	+	1.86463i	0.492183	+	0.0871286i
$459$	−20.8791	+	0.204493i	−0.974555	+	0.00954492i
$460$	10.0426	−	4.66641i	0.468239	−	0.217573i
$461$	24.1724	+	24.1724i	1.12582	+	1.12582i	0.990850	+	0.134969i	$0.0430936\pi$
$461$	24.1724	+	24.1724i	1.12582	+	1.12582i	0.134969	+	0.990850i	$0.456906\pi$
$462$	−2.93459	−	2.44950i	−0.136530	−	0.113961i
$463$		−	32.0117i		−	1.48771i	−0.668341	−	0.743855i	$-0.732995\pi$
$463$		−	32.0117i		−	1.48771i	0.668341	−	0.743855i	$-0.267005\pi$
$464$	2.20696	+	26.0370i	0.102456	+	1.20874i
$465$	−5.62220	−	20.7116i	−0.260723	−	0.960479i
$466$	31.3365	−	21.9105i	1.45164	−	1.01498i
$467$	−5.25892	+	5.25892i	−0.243354	+	0.243354i	−0.818236	−	0.574882i	$-0.805048\pi$
$467$	−5.25892	+	5.25892i	−0.243354	+	0.243354i	0.574882	+	0.818236i	$0.305048\pi$
$468$	2.02216	−	2.92000i	0.0934746	−	0.134977i
$469$	−1.41837	−	1.41837i	−0.0654944	−	0.0654944i
$470$	3.37802	−	19.0822i	0.155817	−	0.880197i
$471$	−7.82705	+	2.12466i	−0.360651	+	0.0978992i
$472$	11.1486	−	19.2198i	0.513157	−	0.884663i
$473$	−8.64719			−0.397598
$474$	3.44453	+	38.2313i	0.158212	+	1.75602i
$475$	10.4623	−	10.4623i	0.480043	−	0.480043i
$476$	−7.54837	−	2.75895i	−0.345979	−	0.126456i
$477$	−7.33259	−	1.91354i	−0.335736	−	0.0876149i
$478$	3.19277	−	2.23238i	0.146034	−	0.102107i
$479$	21.8173			0.996860			0.498430	−	0.866930i	$-0.333910\pi$
$479$	21.8173			0.996860			0.498430	+	0.866930i	$0.333910\pi$
$480$	16.3558	−	2.88197i	0.746535	−	0.131543i
$481$	2.18689			0.0997135
$482$	−16.7931	+	11.7418i	−0.764907	+	0.534822i
$483$	−2.81292	+	4.90907i	−0.127992	+	0.223370i
$484$	−16.0884	−	5.88037i	−0.731291	−	0.267289i
$485$	4.11712	−	4.11712i	0.186949	−	0.186949i
$486$	−9.00305	+	20.1232i	−0.408387	+	0.912809i
$487$	−12.5140			−0.567064			−0.283532	−	0.958963i	$-0.591506\pi$
$487$	−12.5140			−0.567064			−0.283532	+	0.958963i	$0.591506\pi$
$488$	1.12572	+	0.652988i	0.0509592	+	0.0295594i
$489$	−4.07525	−	15.0128i	−0.184289	−	0.678903i
$490$	0.417853	−	2.36042i	0.0188767	−	0.106633i
$491$	23.5407	+	23.5407i	1.06238	+	1.06238i	0.997920	+	0.0644581i	$0.0205319\pi$
$491$	23.5407	+	23.5407i	1.06238	+	1.06238i	0.0644581	+	0.997920i	$0.479468\pi$
$492$	22.4260	−	18.8908i	1.01104	−	0.851663i
$493$	−18.5619	+	18.5619i	−0.835986	+	0.835986i
$494$	4.77288	−	3.33720i	0.214742	−	0.150148i
$495$	4.01253	+	6.84628i	0.180350	+	0.307717i
$496$	−18.8557	+	22.3482i	−0.846645	+	1.00346i
$497$		−	11.7001i		−	0.524821i
$498$	−20.7363	+	24.8429i	−0.929217	+	1.11324i
$499$	−19.9809	−	19.9809i	−0.894466	−	0.894466i	0.100474	−	0.994940i	$-0.467964\pi$
$499$	−19.9809	−	19.9809i	−0.894466	−	0.894466i	−0.994940	+	0.100474i	$0.967964\pi$
$500$	−21.9106	+	10.1810i	−0.979874	+	0.455310i
$501$	−19.9045	+	34.7371i	−0.889269	+	1.55194i
$502$	−2.89359	−	0.512237i	−0.129147	−	0.0228623i
$503$			22.8810i			1.02021i	0.860111	+	0.510107i	$0.170394\pi$
$503$			22.8810i			1.02021i	−0.860111	+	0.510107i	$0.829606\pi$
$504$	−5.97294	+	6.02694i	−0.266056	+	0.268461i
$505$			21.8245i			0.971176i
$506$	1.25666	−	7.09879i	0.0558654	−	0.315580i
$507$	10.8928	−	19.0100i	0.483768	−	0.844264i
$508$	−22.3272	−	8.16067i	−0.990610	−	0.362071i
$509$	23.7478	+	23.7478i	1.05260	+	1.05260i	0.998537	+	0.0540652i	$0.0172179\pi$
$509$	23.7478	+	23.7478i	1.05260	+	1.05260i	0.0540652	+	0.998537i	$0.482782\pi$
$510$	12.8084	+	10.6912i	0.567168	+	0.473414i
$511$		−	2.89479i		−	0.128058i
$512$	−15.9023	−	16.0971i	−0.702788	−	0.711399i
$513$	−25.3084	+	25.8091i	−1.11739	+	1.13950i
$514$	−8.56247	−	12.2461i	−0.377675	−	0.540153i
$515$	9.61396	−	9.61396i	0.423642	−	0.423642i
$516$	−1.63640	+	19.1251i	−0.0720385	+	0.841936i
$517$	−8.92076	−	8.92076i	−0.392335	−	0.392335i
$518$	−5.14445	−	0.910695i	−0.226034	−	0.0400136i
$519$	−7.09367	−	26.1324i	−0.311377	−	1.14708i
$520$	−2.74284	+	0.728979i	−0.120282	+	0.0319678i
$521$	−22.7881			−0.998365			−0.499182	−	0.866497i	$-0.666366\pi$
$521$	−22.7881			−0.998365			−0.499182	+	0.866497i	$0.666366\pi$
$522$	9.63151	+	25.9881i	0.421560	+	1.13747i
$523$	−1.58537	+	1.58537i	−0.0693235	+	0.0693235i	−0.740918	−	0.671595i	$-0.765610\pi$
$523$	−1.58537	+	1.58537i	−0.0693235	+	0.0693235i	0.671595	+	0.740918i	$0.265610\pi$
$524$	2.93460	+	6.31556i	0.128198	+	0.275897i
$525$	1.83153	−	3.19636i	0.0799345	−	0.139500i
$526$	−2.85296	−	4.08032i	−0.124395	−	0.177910i
$527$	−29.3744			−1.27957
$528$	4.56379	−	9.80137i	0.198614	−	0.426550i
$529$	12.3295			0.536065
$530$	3.46980	+	4.96253i	0.150718	+	0.215558i
$531$	5.95083	−	22.8033i	0.258244	−	0.989580i
$532$	−12.6175	+	5.86286i	−0.547037	+	0.254187i
$533$	−3.54317	+	3.54317i	−0.153472	+	0.153472i
$534$	16.3541	−	1.47346i	0.707712	−	0.0637628i
$535$	−15.5385			−0.671788
$536$	2.84671	−	4.90762i	0.122959	−	0.211977i
$537$	23.9194	−	6.49295i	1.03220	−	0.280192i
$538$	−5.82125	−	1.03050i	−0.250972	−	0.0444282i
$539$	−1.10347	−	1.10347i	−0.0475300	−	0.0475300i
$540$	15.9014	−	7.57898i	0.684285	−	0.326147i
$541$	6.57208	−	6.57208i	0.282556	−	0.282556i	−0.551572	−	0.834128i	$-0.685972\pi$
$541$	6.57208	−	6.57208i	0.282556	−	0.282556i	0.834128	+	0.551572i	$0.185972\pi$
$542$	−21.4648	−	30.6991i	−0.921992	−	1.31864i
$543$	−3.11790	−	11.4861i	−0.133802	−	0.492914i
$544$	2.05777	−	22.6381i	0.0882260	−	0.970600i
$545$			9.49551i			0.406743i
$546$	0.929185	−	1.11320i	0.0397654	−	0.0476405i
$547$	−1.65996	−	1.65996i	−0.0709749	−	0.0709749i	0.670728	−	0.741703i	$-0.265982\pi$
$547$	−1.65996	−	1.65996i	−0.0709749	−	0.0709749i	−0.741703	+	0.670728i	$0.765982\pi$
$548$	12.7924	−	34.9993i	0.546462	−	1.49509i
$549$	1.33562	+	0.348547i	0.0570027	+	0.0148756i
$550$	−0.818228	+	4.62211i	−0.0348894	+	0.197088i
$551$			45.4443i			1.93599i
$552$	−15.4627	−	4.12276i	−0.658136	−	0.175476i
$553$			15.6711i			0.666402i
$554$	1.78687	+	0.316319i	0.0759166	+	0.0134391i
$555$	9.41035	+	5.39219i	0.399447	+	0.228886i
$556$	18.8576	+	40.5836i	0.799742	+	1.72113i
$557$	9.02242	+	9.02242i	0.382292	+	0.382292i	0.871927	−	0.489635i	$-0.162870\pi$
$557$	9.02242	+	9.02242i	0.382292	+	0.382292i	−0.489635	+	0.871927i	$0.662870\pi$
$558$	−12.9422	+	28.1842i	−0.547889	+	1.19313i
$559$		−	3.28019i		−	0.138737i
$560$	6.75585	−	0.572642i	0.285487	−	0.0241985i
$561$	10.4822	−	2.84540i	0.442557	−	0.120133i
$562$	26.0780	−	18.2338i	1.10004	−	0.769145i
$563$	20.0512	−	20.0512i	0.845057	−	0.845057i	−0.144454	−	0.989511i	$-0.546143\pi$
$563$	20.0512	−	20.0512i	0.845057	−	0.845057i	0.989511	+	0.144454i	$0.0461427\pi$
$564$	−21.4184	+	18.0420i	−0.901876	+	0.759706i
$565$	−13.5865	−	13.5865i	−0.571589	−	0.571589i
$566$	0.161712	−	0.913499i	0.00679726	−	0.0383972i
$567$	−4.39784	+	7.85233i	−0.184692	+	0.329767i
$568$	31.9826	−	8.50017i	1.34196	−	0.356659i
$569$	−33.2100			−1.39224			−0.696118	−	0.717928i	$-0.745091\pi$
$569$	−33.2100			−1.39224			−0.696118	+	0.717928i	$0.745091\pi$
$570$	28.7666	−	2.59179i	1.20490	−	0.108558i
$571$	32.5442	−	32.5442i	1.36193	−	1.36193i	0.490478	−	0.871454i	$-0.336822\pi$
$571$	32.5442	−	32.5442i	1.36193	−	1.36193i	0.871454	−	0.490478i	$-0.163178\pi$
$572$	−0.634267	+	1.73533i	−0.0265201	+	0.0725576i
$573$	3.02988	+	1.73614i	0.126575	+	0.0725281i
$574$	9.81047	−	6.85948i	0.409481	−	0.286309i
$575$	6.94770			0.289739
$576$	−20.8142	−	11.9486i	−0.867258	−	0.497860i
$577$	13.4111			0.558311			0.279156	−	0.960246i	$-0.409945\pi$
$577$	13.4111			0.558311			0.279156	+	0.960246i	$0.409945\pi$
$578$	−0.988151	+	0.690915i	−0.0411017	+	0.0287383i
$579$	29.7941	+	17.0722i	1.23820	+	0.709495i
$580$	7.60245	−	20.8000i	0.315675	−	0.863671i
$581$	−9.34150	+	9.34150i	−0.387551	+	0.387551i
$582$	−8.38018	+	0.755030i	−0.347370	+	0.0312970i
$583$	3.94203			0.163262
$584$	7.91299	−	2.10307i	0.327442	−	0.0870258i
$585$	−2.59704	+	1.52210i	−0.107375	+	0.0629310i
$586$	−4.88419	+	27.5904i	−0.201764	+	1.13975i
$587$	9.20109	+	9.20109i	0.379770	+	0.379770i	0.871019	−	0.491249i	$-0.163460\pi$
$587$	9.20109	+	9.20109i	0.379770	+	0.379770i	−0.491249	+	0.871019i	$0.663460\pi$
$588$	−2.64939	+	2.23175i	−0.109259	+	0.0920358i
$589$	−35.9581	+	35.9581i	−1.48163	+	1.48163i
$590$	−15.4327	+	10.7906i	−0.635356	+	0.444241i
$591$	16.1069	−	4.37224i	0.662550	−	0.179850i
$592$	−1.24805	−	14.7241i	−0.0512946	−	0.605158i
$593$		−	8.75371i		−	0.359472i	−0.983715	−	0.179736i	$-0.942476\pi$
$593$		−	8.75371i		−	0.359472i	0.983715	−	0.179736i	$-0.0575243\pi$
$594$	1.88829	−	11.3111i	0.0774775	−	0.464101i
$595$	4.81628	+	4.81628i	0.197448	+	0.197448i
$596$	−17.5582	−	37.7871i	−0.719212	−	1.54782i
$597$	29.2181	+	16.7421i	1.19582	+	0.685210i
$598$	2.69283	+	0.476697i	0.110118	+	0.0194936i
$599$		−	29.7166i		−	1.21419i	−0.794630	−	0.607094i	$-0.792335\pi$
$599$		−	29.7166i		−	1.21419i	0.794630	−	0.607094i	$-0.207665\pi$
$600$	10.0680	+	2.68438i	0.411023	+	0.109589i
$601$		−	16.8927i		−	0.689069i	−0.938774	−	0.344535i	$-0.888037\pi$
$601$		−	16.8927i		−	0.689069i	0.938774	−	0.344535i	$-0.111963\pi$
$602$	−1.36598	+	7.71635i	−0.0556734	+	0.314495i
$603$	1.51950	−	5.82264i	0.0618787	−	0.237116i
$604$	5.35557	−	14.6526i	0.217915	−	0.596205i
$605$	10.2653	+	10.2653i	0.417343	+	0.417343i
$606$	20.2101	−	24.2125i	0.820980	−	0.983564i
$607$		−	2.55183i		−	0.103576i	−0.998658	−	0.0517878i	$-0.983508\pi$
$607$		−	2.55183i		−	0.103576i	0.998658	−	0.0517878i	$-0.0164919\pi$
$608$	−25.1930	−	30.2309i	−1.02171	−	1.22603i
$609$	2.96415	+	10.9196i	0.120113	+	0.442486i
$610$	−0.632016	−	0.903913i	−0.0255896	−	0.0365984i
$611$	3.38397	−	3.38397i	0.136901	−	0.136901i
$612$	−4.30956	−	23.7220i	−0.174203	−	0.958906i
$613$	10.4070	+	10.4070i	0.420336	+	0.420336i	0.885320	−	0.464983i	$-0.153940\pi$
$613$	10.4070	+	10.4070i	0.420336	+	0.420336i	−0.464983	+	0.885320i	$0.653940\pi$
$614$	−25.6464	−	4.54004i	−1.03500	−	0.183221i
$615$	−23.9829	+	6.51019i	−0.967084	+	0.262516i
$616$	2.21470	−	3.81806i	0.0892330	−	0.153834i
$617$	20.4380			0.822803			0.411402	−	0.911454i	$-0.365039\pi$
$617$	20.4380			0.822803			0.411402	+	0.911454i	$0.365039\pi$
$618$	−19.5687	+	1.76309i	−0.787170	+	0.0709217i
$619$	−8.09052	+	8.09052i	−0.325185	+	0.325185i	−0.850752	−	0.525567i	$-0.823853\pi$
$619$	−8.09052	+	8.09052i	−0.325185	+	0.325185i	0.525567	+	0.850752i	$0.323853\pi$
$620$	22.4736	−	10.4426i	0.902560	−	0.419385i
$621$	−16.9728	+	0.166234i	−0.681095	+	0.00667073i
$622$	−4.88255	−	6.98306i	−0.195772	−	0.279995i
$623$	6.70359			0.268574
$624$	3.71802	+	1.73121i	0.148840	+	0.0693040i
$625$	9.84173			0.393669
$626$	18.8125	+	26.9057i	0.751897	+	1.07537i
$627$	9.34839	−	16.3147i	0.373339	−	0.651544i
$628$	−3.94631	−	8.49288i	−0.157475	−	0.338903i
$629$	10.4969	−	10.4969i	0.418539	−	0.418539i
$630$	6.74316	−	2.49910i	0.268654	−	0.0995665i
$631$	18.0532			0.718685			0.359342	−	0.933206i	$-0.383001\pi$
$631$	18.0532			0.718685			0.359342	+	0.933206i	$0.383001\pi$
$632$	−42.8374	+	11.3851i	−1.70398	+	0.452875i
$633$	11.1832	+	41.1979i	0.444493	+	1.63747i
$634$	−23.6604	−	4.18847i	−0.939674	−	0.166345i
$635$	14.2460	+	14.2460i	0.565335	+	0.565335i
$636$	0.745993	−	8.71865i	0.0295806	−	0.345717i
$637$	0.418588	−	0.418588i	0.0165851	−	0.0165851i
$638$	−8.26133	−	11.8154i	−0.327069	−	0.467776i
$639$	30.2825	−	17.7482i	1.19796	−	0.702110i
$640$	6.47349	+	18.0513i	0.255887	+	0.713541i
$641$		−	16.0485i		−	0.633879i	−0.948446	−	0.316939i	$-0.897345\pi$
$641$		−	16.0485i		−	0.633879i	0.948446	−	0.316939i	$-0.102655\pi$
$642$	17.2387	+	14.3891i	0.680358	+	0.567894i
$643$	3.36193	+	3.36193i	0.132582	+	0.132582i	0.770283	−	0.637702i	$-0.220115\pi$
$643$	3.36193	+	3.36193i	0.132582	+	0.132582i	−0.637702	+	0.770283i	$0.720115\pi$
$644$	−6.13612	−	2.24277i	−0.241797	−	0.0883776i
$645$	8.08794	−	14.1149i	0.318462	−	0.555775i
$646$	6.89118	−	38.9278i	0.271130	−	1.53159i
$647$			33.9767i			1.33576i	0.744267	+	0.667882i	$0.232799\pi$
$647$			33.9767i			1.33576i	−0.744267	+	0.667882i	$0.767201\pi$
$648$	−24.6596	−	6.31688i	−0.968721	−	0.248151i
$649$			12.2592i			0.481214i
$650$	−1.75334	−	0.310384i	−0.0687715	−	0.0121743i
$651$	−6.29482	+	10.9856i	−0.246713	+	0.430560i
$652$	16.2899	−	7.56931i	0.637963	−	0.296437i
$653$	12.5270	+	12.5270i	0.490219	+	0.490219i	0.908375	−	0.418156i	$-0.137323\pi$
$653$	12.5270	+	12.5270i	0.490219	+	0.490219i	−0.418156	+	0.908375i	$0.637323\pi$
$654$	8.79313	−	10.5345i	0.343839	−	0.411931i
$655$		−	5.90211i		−	0.230615i
$656$	25.8780	+	21.8338i	1.01036	+	0.852467i
$657$	7.49236	−	4.39119i	0.292305	−	0.171317i
$658$	−9.36968	+	6.55128i	−0.365268	+	0.255395i
$659$	21.1739	−	21.1739i	0.824816	−	0.824816i	−0.161978	−	0.986794i	$-0.551787\pi$
$659$	21.1739	−	21.1739i	0.824816	−	0.824816i	0.986794	+	0.161978i	$0.0517873\pi$
$660$	−7.00808	+	5.90334i	−0.272789	+	0.229787i
$661$	28.3104	+	28.3104i	1.10115	+	1.10115i	0.994273	+	0.106874i	$0.0340840\pi$
$661$	28.3104	+	28.3104i	1.10115	+	1.10115i	0.106874	+	0.994273i	$0.465916\pi$
$662$	2.33950	−	13.2157i	0.0909273	−	0.513642i
$663$	1.07936	+	3.97627i	0.0419190	+	0.154425i
$664$	−32.3219	−	18.7486i	−1.25433	−	0.727588i
$665$	11.7915			0.457254
$666$	−5.44669	−	14.6965i	−0.211055	−	0.569476i
$667$	−15.0891	+	15.0891i	−0.584252	+	0.584252i
$668$	−43.4198	−	15.8701i	−1.67996	−	0.614032i
$669$	9.91260	−	17.2993i	0.383243	−	0.668830i
$670$	−3.94063	+	2.75529i	−0.152240	+	0.106446i
$671$	−0.718033			−0.0277193
$672$	−8.02535	−	5.62083i	−0.309585	−	0.216828i
$673$	−37.1776			−1.43309			−0.716546	−	0.697540i	$-0.754278\pi$
$673$	−37.1776			−1.43309			−0.716546	+	0.697540i	$0.754278\pi$
$674$	−14.9980	+	10.4866i	−0.577700	+	0.403928i
$675$	11.0512	−	0.108237i	0.425361	−	0.00416604i
$676$	23.7617	+	8.68497i	0.913911	+	0.334037i
$677$	−18.3210	+	18.3210i	−0.704133	+	0.704133i	−0.965295	−	0.261162i	$-0.915894\pi$
$677$	−18.3210	+	18.3210i	−0.704133	+	0.704133i	0.261162	+	0.965295i	$0.415894\pi$
$678$	2.49160	+	27.6546i	0.0956894	+	1.06207i
$679$	−3.43505			−0.131825
$680$	−9.66639	+	16.6645i	−0.370689	+	0.639054i
$681$	−9.92152	+	2.69321i	−0.380193	+	0.103204i
$682$	2.81218	−	15.8858i	0.107684	−	0.608300i
$683$	−22.2865	−	22.2865i	−0.852769	−	0.852769i	0.137704	−	0.990473i	$-0.456028\pi$
$683$	−22.2865	−	22.2865i	−0.852769	−	0.852769i	−0.990473	+	0.137704i	$0.956028\pi$
$684$	−34.3143	−	23.7634i	−1.31204	−	0.908615i
$685$	−22.3315	+	22.3315i	−0.853242	+	0.853242i
$686$	−1.15900	+	0.810376i	−0.0442510	+	0.0309403i
$687$	3.43209	+	12.6435i	0.130942	+	0.482379i
$688$	−22.0853	+	1.87200i	−0.841993	+	0.0713693i
$689$			1.49536i			0.0569686i
$690$	10.4121	+	8.69095i	0.396381	+	0.330859i
$691$	3.15522	+	3.15522i	0.120030	+	0.120030i	0.764570	−	0.644540i	$-0.222951\pi$
$691$	3.15522	+	3.15522i	0.120030	+	0.120030i	−0.644540	+	0.764570i	$0.722951\pi$
$692$	28.3554	−	13.1757i	1.07791	−	0.500864i
$693$	1.18215	−	4.52994i	0.0449061	−	0.172078i
$694$	−10.5932	−	1.87525i	−0.402111	−	0.0711836i
$695$		−	37.9268i		−	1.43865i
$696$	−27.6957	+	16.0358i	−1.04980	+	0.607834i
$697$			34.0139i			1.28837i
$698$	−0.615820	+	3.47872i	−0.0233091	+	0.131672i
$699$	40.6324	+	23.2826i	1.53686	+	0.880628i
$700$	3.99531	+	1.46030i	0.151008	+	0.0551941i
$701$	28.0109	+	28.0109i	1.05796	+	1.05796i	0.998214	+	0.0597418i	$0.0190277\pi$
$701$	28.0109	+	28.0109i	1.05796	+	1.05796i	0.0597418	+	0.998214i	$0.480972\pi$
$702$	4.29072	+	0.716297i	0.161943	+	0.0270349i
$703$		−	25.6991i		−	0.969260i
$704$	12.0458	+	3.28012i	0.453992	+	0.123624i
$705$	22.9053	−	6.21768i	0.862664	−	0.234171i
$706$	15.4315	+	22.0703i	0.580774	+	0.830626i
$707$	9.10445	−	9.10445i	0.342408	−	0.342408i
$708$	27.1138	+	2.31993i	1.01900	+	0.0871884i
$709$	30.7888	+	30.7888i	1.15630	+	1.15630i	0.985265	+	0.171034i	$0.0547107\pi$
$709$	30.7888	+	30.7888i	1.15630	+	1.15630i	0.171034	+	0.985265i	$0.445289\pi$
$710$	−27.6172	−	4.88892i	−1.03645	−	0.183478i
$711$	−40.5603	+	23.7719i	−1.52113	+	0.891517i
$712$	4.87018	+	18.3245i	0.182518	+	0.686738i
$713$	−23.8787			−0.894263
$714$	−0.883247	−	9.80328i	−0.0330547	−	0.366879i
$715$	1.10723	−	1.10723i	0.0414082	−	0.0414082i
$716$	12.0599	+	25.9542i	0.450700	+	0.969954i
$717$	4.13989	+	2.37218i	0.154607	+	0.0885907i
$718$	23.0836	+	33.0143i	0.861472	+	1.23208i
$719$	−22.9619			−0.856333			−0.428166	−	0.903700i	$-0.640840\pi$
$719$	−22.9619			−0.856333			−0.428166	+	0.903700i	$0.640840\pi$
$720$	11.7303	+	16.6170i	0.437162	+	0.619280i
$721$	−8.02126			−0.298727
$722$	−23.8198	−	34.0672i	−0.886481	−	1.26785i
$723$	−21.7748	−	12.4771i	−0.809812	−	0.464027i
$724$	12.4632	−	5.79115i	0.463190	−	0.215226i
$725$	9.82471	−	9.82471i	0.364880	−	0.364880i
$726$	−1.88253	−	20.8945i	−0.0698673	−	0.775467i
$727$	25.4722			0.944711			0.472355	−	0.881408i	$-0.343404\pi$
$727$	25.4722			0.944711			0.472355	+	0.881408i	$0.343404\pi$
$728$	1.44833	+	0.840118i	0.0536787	+	0.0311368i
$729$	−26.9948	+	0.528832i	−0.999808	+	0.0195864i
$730$	−6.83291	−	1.20959i	−0.252897	−	0.0447691i
$731$	−15.7447	−	15.7447i	−0.582338	−	0.582338i
$732$	−0.135881	+	1.58808i	−0.00502231	+	0.0586973i
$733$	−2.60179	+	2.60179i	−0.0960992	+	0.0960992i	−0.753522	−	0.657423i	$-0.771647\pi$
$733$	−2.60179	+	2.60179i	−0.0960992	+	0.0960992i	0.657423	+	0.753522i	$0.271647\pi$
$734$	−14.7811	−	21.1401i	−0.545581	−	0.780294i
$735$	2.83333	−	0.769110i	0.104509	−	0.0283691i
$736$	1.67277	−	18.4027i	0.0616592	−	0.678331i
$737$			3.13028i			0.115305i
$738$	32.6357	+	14.9864i	1.20134	+	0.551656i
$739$	−27.8272	−	27.8272i	−1.02364	−	1.02364i	−0.999714	−	0.0239281i	$-0.992383\pi$
$739$	−27.8272	−	27.8272i	−1.02364	−	1.02364i	−0.0239281	−	0.999714i	$-0.507617\pi$
$740$	−4.29924	+	11.7625i	−0.158043	+	0.432399i
$741$	6.18874	+	3.54618i	0.227349	+	0.130272i
$742$	0.622718	−	3.51769i	0.0228607	−	0.129138i
$743$			10.6048i			0.389051i	0.980897	+	0.194525i	$0.0623167\pi$
$743$			10.6048i			0.389051i	−0.980897	+	0.194525i	$0.937683\pi$
$744$	−34.6027	−	9.22599i	−1.26860	−	0.338241i
$745$			35.3134i			1.29378i
$746$	26.9584	+	4.77231i	0.987019	+	0.174727i
$747$	−38.3483	−	10.0075i	−1.40309	−	0.366156i
$748$	5.28500	+	11.3739i	0.193239	+	0.415870i
$749$	6.48216	+	6.48216i	0.236853	+	0.236853i
$750$	−22.7167	−	18.9616i	−0.829498	−	0.692381i
$751$		−	15.4515i		−	0.563833i	−0.959439	−	0.281917i	$-0.909030\pi$
$751$		−	15.4515i		−	0.563833i	0.959439	−	0.281917i	$-0.0909701\pi$
$752$	−24.7152	−	20.8528i	−0.901272	−	0.760423i
$753$	−0.942837	−	3.47332i	−0.0343589	−	0.126575i
$754$	4.48201	−	3.13382i	0.163225	−	0.114127i
$755$	−9.34916	+	9.34916i	−0.340251	+	0.340251i
$756$	−9.79523	−	3.47182i	−0.356249	−	0.126269i
$757$	20.2941	+	20.2941i	0.737602	+	0.737602i	0.972113	−	0.234512i	$-0.0753491\pi$
$757$	20.2941	+	20.2941i	0.737602	+	0.737602i	−0.234512	+	0.972113i	$0.575349\pi$
$758$	−7.39793	+	41.7904i	−0.268705	+	1.51790i
$759$	8.52102	−	2.31304i	0.309294	−	0.0839581i
$760$	8.56656	+	32.2324i	0.310742	+	1.16919i
$761$	−0.679283			−0.0246240			−0.0123120	−	0.999924i	$-0.503919\pi$
$761$	−0.679283			−0.0246240			−0.0123120	+	0.999924i	$0.503919\pi$
$762$	−2.61255	−	28.9970i	−0.0946426	−	1.05045i
$763$	3.96122	−	3.96122i	0.143406	−	0.143406i
$764$	−1.38424	+	3.78721i	−0.0500800	+	0.137016i
$765$	−5.15966	+	19.7716i	−0.186548	+	0.714843i
$766$	10.8745	−	7.60347i	0.392913	−	0.274725i
$767$	−4.65035			−0.167914
$768$	9.53425	−	26.0211i	0.344038	−	0.938956i
$769$	12.5414			0.452255			0.226128	−	0.974098i	$-0.427393\pi$
$769$	12.5414			0.452255			0.226128	+	0.974098i	$0.427393\pi$
$770$	−3.06575	+	2.14357i	−0.110482	+	0.0772491i
$771$	9.09868	−	15.8789i	0.327681	−	0.571864i
$772$	−13.6118	+	37.2413i	−0.489900	+	1.34034i
$773$	−23.3063	+	23.3063i	−0.838269	+	0.838269i	−0.988631	−	0.150362i	$-0.951956\pi$
$773$	−23.3063	+	23.3063i	−0.838269	+	0.838269i	0.150362	+	0.988631i	$0.451956\pi$
$774$	−22.0438	+	8.16970i	−0.792347	+	0.293654i
$775$	15.5477			0.558490
$776$	−2.49558	−	9.38982i	−0.0895861	−	0.337075i
$777$	−1.67625	−	6.17513i	−0.0601351	−	0.221532i
$778$	−0.658827	+	3.72167i	−0.0236201	+	0.133428i
$779$	41.6374	+	41.6374i	1.49181	+	1.49181i
$780$	−2.23935	−	2.65842i	−0.0801817	−	0.0951867i
$781$	−12.9108	+	12.9108i	−0.461984	+	0.461984i
$782$	15.2135	−	10.6373i	0.544033	−	0.380388i
$783$	−23.7661	+	24.2362i	−0.849331	+	0.866132i
$784$	−3.05721	−	2.57943i	−0.109186	−	0.0921226i
$785$			7.93690i			0.283280i
$786$	−5.46554	+	6.54791i	−0.194949	+	0.233556i
$787$	−33.1497	−	33.1497i	−1.18166	−	1.18166i	−0.979314	−	0.202345i	$-0.935144\pi$
$787$	−33.1497	−	33.1497i	−1.18166	−	1.18166i	−0.202345	−	0.979314i	$-0.564856\pi$
$788$	8.12094	+	17.4771i	0.289297	+	0.622596i
$789$	3.03162	−	5.29073i	0.107928	−	0.188355i
$790$	36.9903	+	6.54820i	1.31606	+	0.232974i
$791$			11.3357i			0.403051i
$792$	13.2416	−	0.0595811i	0.470519	−	0.00211712i
$793$		−	0.272376i		−	0.00967235i
$794$	−7.85936	+	44.3970i	−0.278918	+	1.57559i
$795$	−3.68709	+	6.43464i	−0.130767	+	0.228213i
$796$	−13.3487	+	36.5214i	−0.473131	+	1.29447i
$797$	−21.5577	−	21.5577i	−0.763613	−	0.763613i	0.213360	−	0.976974i	$-0.431559\pi$
$797$	−21.5577	−	21.5577i	−0.763613	−	0.763613i	−0.976974	+	0.213360i	$0.931559\pi$
$798$	−13.0817	−	10.9193i	−0.463087	−	0.386538i
$799$		−	32.4856i		−	1.14926i
$800$	−1.08916	+	11.9822i	−0.0385077	+	0.423635i
$801$	10.1689	+	17.3504i	0.359300	+	0.613047i
$802$	2.72821	+	3.90190i	0.0963364	+	0.137781i
$803$	−3.19432	+	3.19432i	−0.112725	+	0.112725i
$804$	6.92328	+	0.592376i	0.244165	+	0.0208915i
$805$	3.91518	+	3.91518i	0.137992	+	0.137992i
$806$	6.02607	+	1.06676i	0.212259	+	0.0375751i
$807$	−1.89677	−	6.98753i	−0.0667696	−	0.245973i
$808$	31.5017	+	18.2729i	1.10823	+	0.642837i
$809$	−36.9991			−1.30082			−0.650410	−	0.759583i	$-0.725403\pi$
$809$	−36.9991			−1.30082			−0.650410	+	0.759583i	$0.725403\pi$
$810$	16.6971	+	13.6619i	0.586678	+	0.480029i
$811$	−8.02236	+	8.02236i	−0.281703	+	0.281703i	−0.833788	−	0.552085i	$-0.813832\pi$
$811$	−8.02236	+	8.02236i	−0.281703	+	0.281703i	0.552085	+	0.833788i	$0.313832\pi$
$812$	−11.8486	+	5.50556i	−0.415803	+	0.193207i
$813$	22.8090	−	39.8059i	0.799946	−	1.39605i
$814$	4.67184	+	6.68170i	0.163748	+	0.234193i
$815$	−15.2235			−0.533257
$816$	26.1559	−	9.53651i	0.915639	−	0.333845i
$817$	−38.5471			−1.34859
$818$	10.6964	+	15.2980i	0.373990	+	0.534883i
$819$	1.71837	+	0.448432i	0.0600448	+	0.0156695i
$820$	−12.0919	−	26.0231i	−0.422268	−	0.908766i
$821$	38.2753	−	38.2753i	1.33582	−	1.33582i	0.435752	−	0.900067i	$-0.356483\pi$
$821$	38.2753	−	38.2753i	1.33582	−	1.33582i	0.900067	−	0.435752i	$-0.143517\pi$
$822$	45.4546	−	4.09533i	1.58541	−	0.142841i
$823$	38.8930			1.35573			0.677863	−	0.735188i	$-0.262906\pi$
$823$	38.8930			1.35573			0.677863	+	0.735188i	$0.262906\pi$
$824$	−5.82748	−	21.9264i	−0.203010	−	0.763841i
$825$	−5.54815	+	1.50605i	−0.193162	+	0.0524340i
$826$	10.9395	+	1.93656i	0.380634	+	0.0673816i
$827$	10.0304	+	10.0304i	0.348790	+	0.348790i	0.859659	−	0.510869i	$-0.170676\pi$
$827$	10.0304	+	10.0304i	0.348790	+	0.348790i	−0.510869	+	0.859659i	$0.670676\pi$
$828$	−3.50327	−	19.2838i	−0.121747	−	0.670158i
$829$	14.7744	−	14.7744i	0.513137	−	0.513137i	−0.402350	−	0.915486i	$-0.631806\pi$
$829$	14.7744	−	14.7744i	0.513137	−	0.513137i	0.915486	+	0.402350i	$0.131806\pi$
$830$	18.1465	+	25.9532i	0.629874	+	0.900850i
$831$	0.582226	+	2.14486i	0.0201972	+	0.0744044i
$832$	−1.24427	+	4.56940i	−0.0431373	+	0.158416i
$833$		−	4.01838i		−	0.139229i
$834$	−35.1214	+	42.0767i	−1.21615	+	1.45700i
$835$	27.7042	+	27.7042i	0.958745	+	0.958745i
$836$	20.3926	+	7.45356i	0.705293	+	0.257787i
$837$	−37.9821	+	0.372002i	−1.31285	+	0.0128583i
$838$	1.50595	−	8.50702i	0.0520223	−	0.293870i
$839$		−	29.3275i		−	1.01250i	−0.862387	−	0.506249i	$-0.831032\pi$
$839$		−	29.3275i		−	1.01250i	0.862387	−	0.506249i	$-0.168968\pi$
$840$	4.16081	+	7.18623i	0.143562	+	0.247948i
$841$			13.6749i			0.471547i
$842$	7.65192	+	1.35458i	0.263703	+	0.0466819i
$843$	33.8140	+	19.3756i	1.16462	+	0.667332i
$844$	−44.7025	+	20.7715i	−1.53872	+	0.714986i
$845$	−15.1613	−	15.1613i	−0.521563	−	0.521563i
$846$	−31.1693	−	14.3130i	−1.07162	−	0.492092i
$847$		−	8.56469i		−	0.294286i
$848$	10.0681	−	0.853397i	0.345741	−	0.0293058i
$849$	1.09652	−	0.297651i	0.0376324	−	0.0102154i
$850$	−9.90570	+	6.92606i	−0.339763	+	0.237562i
$851$	8.53300	−	8.53300i	0.292507	−	0.292507i
$852$	26.1117	+	30.9982i	0.894572	+	1.06198i
$853$	−32.1800	−	32.1800i	−1.10182	−	1.10182i	−0.994191	−	0.107630i	$-0.965674\pi$
$853$	−32.1800	−	32.1800i	−1.10182	−	1.10182i	−0.107630	−	0.994191i	$-0.534326\pi$
$854$	−0.113427	+	0.640739i	−0.00388138	+	0.0219256i
$855$	17.8869	+	30.5190i	0.611718	+	1.04373i
$856$	−13.0099	+	22.4285i	−0.444668	+	0.766590i
$857$	53.4151			1.82462			0.912312	−	0.409495i	$-0.134295\pi$
$857$	53.4151			1.82462			0.912312	+	0.409495i	$0.134295\pi$
$858$	−2.25372	+	0.203053i	−0.0769407	+	0.00693213i
$859$	3.62080	−	3.62080i	0.123540	−	0.123540i	−0.642634	−	0.766174i	$-0.722158\pi$
$859$	3.62080	−	3.62080i	0.123540	−	0.123540i	0.766174	+	0.642634i	$0.222158\pi$
$860$	17.6431	+	6.44860i	0.601623	+	0.219895i
$861$	12.7207	+	7.28904i	0.433521	+	0.248410i
$862$	−9.18860	+	6.42467i	−0.312965	+	0.218825i
$863$	−56.4885			−1.92289			−0.961445	−	0.274999i	$-0.911323\pi$
$863$	−56.4885			−1.92289			−0.961445	+	0.274999i	$0.911323\pi$
$864$	2.37407	−	29.2978i	0.0807674	−	0.996733i
$865$	−26.4991			−0.900998
$866$	8.23640	−	5.75889i	0.279884	−	0.195695i
$867$	−1.28128	−	0.734182i	−0.0435147	−	0.0249341i
$868$	−13.7315	−	5.01892i	−0.466079	−	0.170353i
$869$	17.2926	−	17.2926i	0.586612	−	0.586612i
$870$	27.0135	−	2.43384i	0.915844	−	0.0825149i
$871$	−1.18743			−0.0402345
$872$	13.7059	+	7.95027i	0.464142	+	0.269230i
$873$	−5.21074	−	8.89070i	−0.176357	−	0.300904i
$874$	5.60189	−	31.6447i	0.189487	−	1.07040i
$875$	−8.54203	−	8.54203i	−0.288773	−	0.288773i
$876$	6.46044	+	7.66943i	0.218278	+	0.259126i
$877$	7.39009	−	7.39009i	0.249546	−	0.249546i	−0.571239	−	0.820784i	$-0.693537\pi$
$877$	7.39009	−	7.39009i	0.249546	−	0.249546i	0.820784	+	0.571239i	$0.193537\pi$
$878$	−6.36120	+	4.44775i	−0.214680	+	0.150104i
$879$	−33.1181	+	8.98996i	−1.11705	+	0.303224i
$880$	−8.08681	−	6.82302i	−0.272606	−	0.230004i
$881$			55.1865i			1.85928i	0.368470	+	0.929640i	$0.379882\pi$
$881$			55.1865i			1.85928i	−0.368470	+	0.929640i	$0.620118\pi$
$882$	−3.85557	−	1.77048i	−0.129824	−	0.0596153i
$883$	28.4851	+	28.4851i	0.958600	+	0.958600i	0.999176	−	0.0405766i	$-0.0129195\pi$
$883$	28.4851	+	28.4851i	0.958600	+	0.958600i	−0.0405766	+	0.999176i	$0.512919\pi$
$884$	−4.31452	+	2.00479i	−0.145113	+	0.0674285i
$885$	−20.0108	−	11.4663i	−0.672656	−	0.385436i
$886$	−38.8240	−	6.87281i	−1.30432	−	0.230897i
$887$			2.82548i			0.0948702i	0.998874	+	0.0474351i	$0.0151047\pi$
$887$			2.82548i			0.0948702i	−0.998874	+	0.0474351i	$0.984895\pi$
$888$	15.6621	−	9.06834i	0.525586	−	0.304313i
$889$		−	11.8859i		−	0.398641i
$890$	2.80111	−	15.8233i	0.0938935	−	0.530398i
$891$	13.5177	−	3.81194i	0.452862	−	0.127705i
$892$	21.6234	+	7.90341i	0.724004	+	0.264626i
$893$	−39.7666	−	39.7666i	−1.33074	−	1.33074i
$894$	32.7013	−	39.1773i	1.09369	−	1.31029i
$895$		−	24.2551i		−	0.810759i
$896$	4.82989	−	10.2309i	0.161355	−	0.341792i
$897$	0.877422	+	3.23234i	0.0292963	+	0.107925i
$898$	24.2484	+	34.6802i	0.809179	+	1.15729i
$899$	−33.7667	+	33.7667i	−1.12618	+	1.12618i
$900$	2.28102	+	12.5559i	0.0760341	+	0.418531i
$901$	7.17760	+	7.17760i	0.239121	+	0.239121i
$902$	−18.3949	−	3.25635i	−0.612482	−	0.108424i
$903$	−9.26231	+	2.51427i	−0.308231	+	0.0836696i
$904$	−30.9865	+	8.23542i	−1.03059	+	0.273906i
$905$	−11.6473			−0.387168
$906$	19.0297	−	1.71452i	0.632221	−	0.0569613i
$907$	19.6410	−	19.6410i	0.652169	−	0.652169i	−0.301346	−	0.953515i	$-0.597436\pi$
$907$	19.6410	−	19.6410i	0.652169	−	0.652169i	0.953515	+	0.301346i	$0.0974359\pi$
$908$	−5.00233	−	10.7655i	−0.166008	−	0.357267i
$909$	37.3752	+	9.75356i	1.23966	+	0.323505i
$910$	−0.813136	−	1.16295i	−0.0269552	−	0.0385515i
$911$	−17.7959			−0.589603			−0.294801	−	0.955559i	$-0.595253\pi$
$911$	−17.7959			−0.589603			−0.294801	+	0.955559i	$0.595253\pi$
$912$	20.3443	−	43.6921i	0.673666	−	1.44679i
$913$	20.6162			0.682297
$914$	29.1373	+	41.6724i	0.963778	+	1.37840i
$915$	0.671595	−	1.17206i	0.0222022	−	0.0387470i
$916$	−13.7191	+	6.37471i	−0.453290	+	0.210626i
$917$	−2.46217	+	2.46217i	−0.0813079	+	0.0813079i
$918$	24.0333	−	17.1570i	0.793217	−	0.566264i
$919$	17.7656			0.586032			0.293016	−	0.956108i	$-0.405341\pi$
$919$	17.7656			0.586032			0.293016	+	0.956108i	$0.405341\pi$
$920$	−7.85788	+	13.5467i	−0.259067	+	0.446621i
$921$	−8.35651	−	30.7846i	−0.275356	−	1.01439i
$922$	−47.6046	−	8.42718i	−1.56777	−	0.277534i
$923$	−4.89753	−	4.89753i	−0.161204	−	0.161204i
$924$	5.38622	+	0.460861i	0.177194	+	0.0151612i
$925$	−5.55595	+	5.55595i	−0.182678	+	0.182678i
$926$	25.9415	+	37.1017i	0.852491	+	1.21924i
$927$	−12.1677	−	20.7608i	−0.399640	−	0.681875i
$928$	−23.6577	−	28.3886i	−0.776601	−	0.931901i
$929$		−	38.3156i		−	1.25709i	−0.777772	−	0.628547i	$-0.783650\pi$
$929$		−	38.3156i		−	1.25709i	0.777772	−	0.628547i	$-0.216350\pi$
$930$	23.3004	+	19.4488i	0.764049	+	0.637751i
$931$	−4.91902	−	4.91902i	−0.161214	−	0.161214i
$932$	−18.5634	+	50.7887i	−0.608065	+	1.66364i
$933$	5.18831	−	9.05456i	0.169858	−	0.296433i
$934$	1.83341	−	10.3568i	0.0599910	−	0.338885i
$935$		−	10.6293i		−	0.347615i
$936$	0.0226013	+	5.02301i	0.000738746	+	0.164182i
$937$			14.6294i			0.477922i	0.971029	+	0.238961i	$0.0768067\pi$
$937$			14.6294i			0.477922i	−0.971029	+	0.238961i	$0.923193\pi$
$938$	2.79332	+	0.494486i	0.0912050	+	0.0161455i
$939$	−19.9906	+	34.8872i	−0.652367	+	1.13850i
$940$	11.5486	+	24.8538i	0.376675	+	0.810643i
$941$	−31.9860	−	31.9860i	−1.04271	−	1.04271i	−0.999046	−	0.0436675i	$-0.986096\pi$
$941$	−31.9860	−	31.9860i	−1.04271	−	1.04271i	−0.0436675	−	0.999046i	$-0.513904\pi$
$942$	7.34981	−	8.80534i	0.239470	−	0.286893i
$943$			27.6501i			0.900412i
$944$	2.65394	+	31.3104i	0.0863785	+	1.01907i
$945$	6.28860	+	6.16661i	0.204568	+	0.200600i
$946$	10.0221	−	7.00747i	0.325848	−	0.227833i
$947$	7.81766	−	7.81766i	0.254040	−	0.254040i	−0.568585	−	0.822625i	$-0.692509\pi$
$947$	7.81766	−	7.81766i	0.254040	−	0.254040i	0.822625	+	0.568585i	$0.192509\pi$
$948$	−34.9739	−	41.5189i	−1.13590	−	1.34847i
$949$	−1.21172	−	1.21172i	−0.0393342	−	0.0393342i
$950$	−3.64746	+	20.6042i	−0.118339	+	0.668490i
$951$	−7.70941	−	28.4007i	−0.249995	−	0.920956i
$952$	10.9844	−	2.91937i	0.356006	−	0.0946174i
$953$	−21.9696			−0.711667			−0.355833	−	0.934549i	$-0.615803\pi$
$953$	−21.9696			−0.711667			−0.355833	+	0.934549i	$0.615803\pi$
$954$	10.0492	−	3.72436i	0.325355	−	0.120580i
$955$	2.41645	−	2.41645i	0.0781945	−	0.0781945i
$956$	−1.89136	+	5.17468i	−0.0611711	+	0.167361i
$957$	8.77868	−	15.3204i	0.283774	−	0.495238i
$958$	−25.2864	+	17.6802i	−0.816966	+	0.571223i
$959$	18.6319			0.601656
$960$	−16.6209	+	16.5945i	−0.536438	+	0.535586i
$961$	−22.4362			−0.723748
$962$	−2.53461	+	1.77220i	−0.0817192	+	0.0571380i
$963$	−6.94431	+	26.6103i	−0.223777	+	0.857504i
$964$	9.94809	−	27.2175i	0.320406	−	0.876617i
$965$	23.7620	−	23.7620i	0.764926	−	0.764926i
$966$	−0.717998	−	7.96916i	−0.0231012	−	0.256403i
$967$	−35.5604			−1.14355			−0.571773	−	0.820412i	$-0.693744\pi$
$967$	−35.5604			−1.14355			−0.571773	+	0.820412i	$0.693744\pi$
$968$	23.4118	−	6.22228i	0.752485	−	0.199992i
$969$	46.7269	−	12.6841i	1.50108	−	0.407471i
$970$	−1.43535	+	8.10817i	−0.0460862	+	0.260338i
$971$	−25.1898	−	25.1898i	−0.808380	−	0.808380i	0.176008	−	0.984389i	$-0.443681\pi$
$971$	−25.1898	−	25.1898i	−0.808380	−	0.808380i	−0.984389	+	0.176008i	$0.943681\pi$
$972$	−5.87282	−	30.6188i	−0.188371	−	0.982098i
$973$	−15.8218	+	15.8218i	−0.507224	+	0.507224i
$974$	14.5038	−	10.1411i	0.464732	−	0.324940i
$975$	−0.571300	−	2.10461i	−0.0182963	−	0.0674016i
$976$	−1.83389	+	0.155444i	−0.0587012	+	0.00497565i
$977$		−	9.13611i		−	0.292290i	−0.989263	−	0.146145i	$-0.953313\pi$
$977$		−	9.13611i		−	0.292290i	0.989263	−	0.146145i	$-0.0466866\pi$
$978$	16.8893	+	14.0974i	0.540059	+	0.450787i
$979$	−7.39724	−	7.39724i	−0.236417	−	0.236417i
$980$	1.42853	+	3.07436i	0.0456328	+	0.0982067i
$981$	16.2614	+	4.24363i	0.519187	+	0.135489i
$982$	−46.3607	−	8.20698i	−1.47943	−	0.261895i
$983$		−	4.41394i		−	0.140783i	−0.997519	−	0.0703914i	$-0.977575\pi$
$983$		−	4.41394i		−	0.140783i	0.997519	−	0.0703914i	$-0.0224248\pi$
$984$	−10.6832	+	40.0680i	−0.340567	+	1.27732i
$985$		−	16.3330i		−	0.520412i
$986$	6.47122	−	36.5554i	0.206085	−	1.16416i
$987$	−12.1492	−	6.96154i	−0.386712	−	0.221588i
$988$	−2.82741	+	7.73566i	−0.0899519	+	0.246104i
$989$	−12.7990	−	12.7990i	−0.406983	−	0.406983i
$990$	−10.1986	−	4.68321i	−0.324133	−	0.148842i
$991$		−	27.8849i		−	0.885793i	−0.896573	−	0.442896i	$-0.853951\pi$
$991$		−	27.8849i		−	0.885793i	0.896573	−	0.442896i	$-0.146049\pi$
$992$	3.74336	−	41.1819i	0.118852	−	1.30753i
$993$	15.8634	−	4.30615i	0.503411	−	0.136651i
$994$	9.48148	+	13.5605i	0.300734	+	0.430112i
$995$	23.3026	−	23.3026i	0.738743	−	0.738743i
$996$	3.90143	−	45.5972i	0.123621	−	1.44480i
$997$	−39.6685	−	39.6685i	−1.25631	−	1.25631i	−0.952839	−	0.303476i	$-0.901853\pi$
$997$	−39.6685	−	39.6685i	−1.25631	−	1.25631i	−0.303476	−	0.952839i	$-0.598147\pi$
$998$	39.3499	+	6.96590i	1.24560	+	0.220502i
$999$	13.4399	−	13.7058i	0.425220	−	0.433631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.d.155.6	✓	48
3.2	odd	2	inner	336.2.s.d.155.19	yes	48
4.3	odd	2		1344.2.s.d.911.20		48
12.11	even	2		1344.2.s.d.911.16		48
16.3	odd	4	inner	336.2.s.d.323.19	yes	48
16.13	even	4		1344.2.s.d.239.16		48
48.29	odd	4		1344.2.s.d.239.20		48
48.35	even	4	inner	336.2.s.d.323.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.6	✓	48	1.1	even	1	trivial
336.2.s.d.155.19	yes	48	3.2	odd	2	inner
336.2.s.d.323.6	yes	48	48.35	even	4	inner
336.2.s.d.323.19	yes	48	16.3	odd	4	inner
1344.2.s.d.239.16		48	16.13	even	4
1344.2.s.d.239.20		48	48.29	odd	4
1344.2.s.d.911.16		48	12.11	even	2
1344.2.s.d.911.20		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15900 + 0.810376i) q^{2} +(-1.50282 - 0.861124i) q^{3} +(0.686583 - 1.87846i) q^{4} +(-1.19856 + 1.19856i) q^{5} +(2.43961 - 0.219802i) q^{6} +1.00000 q^{7} +(0.726504 + 2.73353i) q^{8} +(1.51693 + 2.58823i) q^{9} +O(q^{10})\)	\(q+(-1.15900 + 0.810376i) q^{2} +(-1.50282 - 0.861124i) q^{3} +(0.686583 - 1.87846i) q^{4} +(-1.19856 + 1.19856i) q^{5} +(2.43961 - 0.219802i) q^{6} +1.00000 q^{7} +(0.726504 + 2.73353i) q^{8} +(1.51693 + 2.58823i) q^{9} +(0.417853 - 2.36042i) q^{10} +(-1.10347 - 1.10347i) q^{11} +(-2.64939 + 2.23175i) q^{12} +(0.418588 - 0.418588i) q^{13} +(-1.15900 + 0.810376i) q^{14} +(2.83333 - 0.769110i) q^{15} +(-3.05721 - 2.57943i) q^{16} -4.01838i q^{17} +(-3.85557 - 1.77048i) q^{18} +(-4.91902 - 4.91902i) q^{19} +(1.42853 + 3.07436i) q^{20} +(-1.50282 - 0.861124i) q^{21} +(2.17316 + 0.384703i) q^{22} -3.26657i q^{23} +(1.26210 - 4.73361i) q^{24} +2.12691i q^{25} +(-0.145932 + 0.824359i) q^{26} +(-0.0508894 - 5.19590i) q^{27} +(0.686583 - 1.87846i) q^{28} +(-4.61925 - 4.61925i) q^{29} +(-2.66057 + 3.18746i) q^{30} -7.31001i q^{31} +(5.63363 + 0.512088i) q^{32} +(0.708095 + 2.60855i) q^{33} +(3.25640 + 4.65733i) q^{34} +(-1.19856 + 1.19856i) q^{35} +(5.90337 - 1.07246i) q^{36} +(2.61222 + 2.61222i) q^{37} +(9.68742 + 1.71491i) q^{38} +(-0.989519 + 0.268606i) q^{39} +(-4.14706 - 2.40554i) q^{40} -8.46457 q^{41} +(2.43961 - 0.219802i) q^{42} +(3.91816 - 3.91816i) q^{43} +(-2.83046 + 1.31520i) q^{44} +(-4.92028 - 1.28401i) q^{45} +(2.64715 + 3.78597i) q^{46} +8.08425 q^{47} +(2.37322 + 6.50906i) q^{48} +1.00000 q^{49} +(-1.72359 - 2.46509i) q^{50} +(-3.46033 + 6.03891i) q^{51} +(-0.498905 - 1.07370i) q^{52} +(-1.78619 + 1.78619i) q^{53} +(4.26961 + 5.98084i) q^{54} +2.64516 q^{55} +(0.726504 + 2.73353i) q^{56} +(3.15651 + 11.6283i) q^{57} +(9.09705 + 1.61040i) q^{58} +(-5.55480 - 5.55480i) q^{59} +(0.500572 - 5.85035i) q^{60} +(0.325351 - 0.325351i) q^{61} +(5.92385 + 8.47233i) q^{62} +(1.51693 + 2.58823i) q^{63} +(-6.94438 + 3.97184i) q^{64} +1.00341i q^{65} +(-2.93459 - 2.44950i) q^{66} +(-1.41837 - 1.41837i) q^{67} +(-7.54837 - 2.75895i) q^{68} +(-2.81292 + 4.90907i) q^{69} +(0.417853 - 2.36042i) q^{70} -11.7001i q^{71} +(-5.97294 + 6.02694i) q^{72} -2.89479i q^{73} +(-5.14445 - 0.910695i) q^{74} +(1.83153 - 3.19636i) q^{75} +(-12.6175 + 5.86286i) q^{76} +(-1.10347 - 1.10347i) q^{77} +(0.929185 - 1.11320i) q^{78} +15.6711i q^{79} +(6.75585 - 0.572642i) q^{80} +(-4.39784 + 7.85233i) q^{81} +(9.81047 - 6.85948i) q^{82} +(-9.34150 + 9.34150i) q^{83} +(-2.64939 + 2.23175i) q^{84} +(4.81628 + 4.81628i) q^{85} +(-1.36598 + 7.71635i) q^{86} +(2.96415 + 10.9196i) q^{87} +(2.21470 - 3.81806i) q^{88} +6.70359 q^{89} +(6.74316 - 2.49910i) q^{90} +(0.418588 - 0.418588i) q^{91} +(-6.13612 - 2.24277i) q^{92} +(-6.29482 + 10.9856i) q^{93} +(-9.36968 + 6.55128i) q^{94} +11.7915 q^{95} +(-8.02535 - 5.62083i) q^{96} -3.43505 q^{97} +(-1.15900 + 0.810376i) q^{98} +(1.18215 - 4.52994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 48 q^{7}+O(q^{10}) \) 48 * q + 6 * q^6 + 48 * q^7	\( 48 q + 6 q^{6} + 48 q^{7} - 16 q^{10} + 6 q^{12} - 28 q^{16} - 20 q^{18} + 8 q^{19} - 8 q^{22} - 38 q^{24} - 12 q^{27} - 24 q^{30} + 12 q^{34} - 4 q^{36} + 16 q^{37} - 24 q^{39} + 60 q^{40} + 6 q^{42} - 48 q^{43} + 20 q^{45} + 52 q^{46} + 62 q^{48} + 48 q^{49} + 12 q^{52} + 14 q^{54} - 32 q^{55} - 100 q^{58} - 16 q^{60} + 8 q^{61} - 60 q^{64} - 96 q^{66} - 16 q^{67} - 28 q^{69} - 16 q^{70} - 80 q^{72} - 12 q^{75} + 4 q^{76} - 56 q^{78} + 4 q^{82} + 6 q^{84} - 48 q^{85} + 56 q^{87} + 116 q^{88} + 68 q^{90} - 64 q^{93} + 48 q^{94} + 62 q^{96} + 32 q^{99}+O(q^{100}) \) 48 * q + 6 * q^6 + 48 * q^7 - 16 * q^10 + 6 * q^12 - 28 * q^16 - 20 * q^18 + 8 * q^19 - 8 * q^22 - 38 * q^24 - 12 * q^27 - 24 * q^30 + 12 * q^34 - 4 * q^36 + 16 * q^37 - 24 * q^39 + 60 * q^40 + 6 * q^42 - 48 * q^43 + 20 * q^45 + 52 * q^46 + 62 * q^48 + 48 * q^49 + 12 * q^52 + 14 * q^54 - 32 * q^55 - 100 * q^58 - 16 * q^60 + 8 * q^61 - 60 * q^64 - 96 * q^66 - 16 * q^67 - 28 * q^69 - 16 * q^70 - 80 * q^72 - 12 * q^75 + 4 * q^76 - 56 * q^78 + 4 * q^82 + 6 * q^84 - 48 * q^85 + 56 * q^87 + 116 * q^88 + 68 * q^90 - 64 * q^93 + 48 * q^94 + 62 * q^96 + 32 * q^99

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