LMFDB - Embedded newform 336.2.s.d.155.19

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			155.19
Character	$\chi$	$=$	336.155
Dual form			336.2.s.d.323.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15900 - 0.810376i) q^{2} +(-0.861124 - 1.50282i) q^{3} +(0.686583 - 1.87846i) q^{4} +(1.19856 - 1.19856i) q^{5} +(-2.21589 - 1.04394i) q^{6} +1.00000 q^{7} +(-0.726504 - 2.73353i) q^{8} +(-1.51693 + 2.58823i) q^{9} +O(q^{10})$	\(q+(1.15900 - 0.810376i) q^{2} +(-0.861124 - 1.50282i) q^{3} +(0.686583 - 1.87846i) q^{4} +(1.19856 - 1.19856i) q^{5} +(-2.21589 - 1.04394i) 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} +(-3.41422 + 0.585775i) 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} +(0.339306 + 4.22905i) q^{18} +(-4.91902 - 4.91902i) q^{19} +(-1.42853 - 3.07436i) q^{20} +(-0.861124 - 1.50282i) q^{21} +(2.17316 + 0.384703i) q^{22} +3.26657i q^{23} +(-3.48239 + 3.44571i) q^{24} +2.12691i q^{25} +(0.145932 - 0.824359i) q^{26} +(5.19590 + 0.0508894i) q^{27} +(0.686583 - 1.87846i) q^{28} +(4.61925 + 4.61925i) q^{29} +(-3.90711 + 1.40466i) 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} +(3.82038 + 4.62652i) 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} +(-2.21589 - 1.04394i) q^{42} +(3.91816 - 3.91816i) q^{43} +(2.83046 - 1.31520i) q^{44} +(1.28401 + 4.92028i) q^{45} +(2.64715 + 3.78597i) q^{46} -8.08425 q^{47} +(-1.24379 + 6.81564i) q^{48} +1.00000 q^{49} +(1.72359 + 2.46509i) q^{50} +(6.03891 - 3.46033i) q^{51} +(-0.498905 - 1.07370i) q^{52} +(1.78619 - 1.78619i) q^{53} +(6.06331 - 4.15165i) 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} +(-3.39006 + 4.79423i) 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} +(-1.29322 - 3.59715i) q^{66} +(-1.41837 - 1.41837i) q^{67} +(7.54837 + 2.75895i) q^{68} +(4.90907 - 2.81292i) q^{69} +(0.417853 - 2.36042i) q^{70} +11.7001i q^{71} +(8.17706 + 2.26622i) q^{72} -2.89479i q^{73} +(5.14445 + 0.910695i) q^{74} +(3.19636 - 1.83153i) q^{75} +(-12.6175 + 5.86286i) q^{76} +(1.10347 + 1.10347i) q^{77} +(-1.36453 + 0.490566i) 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} +(-3.41422 + 0.585775i) 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} +(5.47545 + 4.66209i) q^{90} +(0.418588 - 0.418588i) q^{91} +(6.13612 + 2.24277i) q^{92} +(-10.9856 + 6.29482i) q^{93} +(-9.36968 + 6.55128i) q^{94} -11.7915 q^{95} +(4.08168 + 8.90730i) q^{96} -3.43505 q^{97} +(1.15900 - 0.810376i) q^{98} +(-4.52994 + 1.18215i) 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
$3$	−0.861124	−	1.50282i	−0.497170	−	0.867653i
$3$	−0.861124	−	1.50282i	−0.497170	−	0.867653i
$4$	0.686583	−	1.87846i	0.343291	−	0.939229i
$5$	1.19856	−	1.19856i	0.536012	−	0.536012i	−0.386343	−	0.922355i	$-0.626262\pi$
$5$	1.19856	−	1.19856i	0.536012	−	0.536012i	0.922355	+	0.386343i	$0.126262\pi$
$6$	−2.21589	−	1.04394i	−0.904635	−	0.426187i
$7$	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	0.853615	−	0.520905i	$-0.174405\pi$
$11$	1.10347	+	1.10347i	0.332710	+	0.332710i	−0.520905	+	0.853615i	$0.674405\pi$
$12$	−3.41422	+	0.585775i	−0.985599	+	0.169099i
$13$	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	$0.162018\pi$
$17$			4.01838i			0.974601i	−0.873234	+	0.487301i	$0.837982\pi$
$18$	0.339306	+	4.22905i	0.0799752	+	0.996797i
$19$	−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
$21$	−0.861124	−	1.50282i	−0.187913	−	0.327942i
$22$	2.17316	+	0.384703i	0.463320	+	0.0820190i
$23$			3.26657i			0.681127i	0.940221	+	0.340564i	$0.110618\pi$
$23$			3.26657i			0.681127i	−0.940221	+	0.340564i	$0.889382\pi$
$24$	−3.48239	+	3.44571i	−0.710840	+	0.703353i
$25$			2.12691i			0.425381i
$26$	0.145932	−	0.824359i	0.0286196	−	0.161670i
$27$	5.19590	+	0.0508894i	0.999952	+	0.00979366i
$28$	0.686583	−	1.87846i	0.129752	−	0.354995i
$29$	4.61925	+	4.61925i	0.857772	+	0.857772i	0.991075	−	0.133303i	$-0.0425583\pi$
$29$	4.61925	+	4.61925i	0.857772	+	0.857772i	−0.133303	+	0.991075i	$0.542558\pi$
$30$	−3.90711	+	1.40466i	−0.713337	+	0.256454i
$31$		−	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
$36$	3.82038	+	4.62652i	0.636729	+	0.771087i
$37$	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	$-0.270144\pi$
$41$	8.46457			1.32194			0.660972	+	0.750411i	$0.270144\pi$
$42$	−2.21589	−	1.04394i	−0.341920	−	0.161084i
$43$	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
$45$	1.28401	+	4.92028i	0.191409	+	0.733472i
$46$	2.64715	+	3.78597i	0.390301	+	0.558211i
$47$	−8.08425			−1.17921			−0.589604	−	0.807692i	$-0.700716\pi$
$47$	−8.08425			−1.17921			−0.589604	+	0.807692i	$0.700716\pi$
$48$	−1.24379	+	6.81564i	−0.179525	+	0.983753i
$49$	1.00000			0.142857
$50$	1.72359	+	2.46509i	0.243753	+	0.348617i
$51$	6.03891	−	3.46033i	0.845616	−	0.484543i
$52$	−0.498905	−	1.07370i	−0.0691857	−	0.148895i
$53$	1.78619	−	1.78619i	0.245352	−	0.245352i	−0.573708	−	0.819060i	$-0.694496\pi$
$53$	1.78619	−	1.78619i	0.245352	−	0.245352i	0.819060	+	0.573708i	$0.194496\pi$
$54$	6.06331	−	4.15165i	0.825113	−	0.564968i
$55$	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	0.969250	−	0.246077i	$-0.0791417\pi$
$59$	5.55480	+	5.55480i	0.723173	+	0.723173i	−0.246077	+	0.969250i	$0.579142\pi$
$60$	−3.39006	+	4.79423i	−0.437654	+	0.618932i
$61$	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
$66$	−1.29322	−	3.59715i	−0.159185	−	0.442778i
$67$	−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
$69$	4.90907	−	2.81292i	0.590982	−	0.338636i
$70$	0.417853	−	2.36042i	0.0499429	−	0.282124i
$71$			11.7001i			1.38855i	0.719712	+	0.694273i	$0.244274\pi$
$71$			11.7001i			1.38855i	−0.719712	+	0.694273i	$0.755726\pi$
$72$	8.17706	+	2.26622i	0.963675	+	0.267077i
$73$		−	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
$75$	3.19636	−	1.83153i	0.369084	−	0.211487i
$76$	−12.6175	+	5.86286i	−1.44733	+	0.672516i
$77$	1.10347	+	1.10347i	0.125753	+	0.125753i
$78$	−1.36453	+	0.490566i	−0.154502	+	0.0555457i
$79$			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	$-0.491821\pi$
$83$	9.34150	−	9.34150i	1.02536	−	1.02536i	0.999670	−	0.0256926i	$-0.00817912\pi$
$84$	−3.41422	+	0.585775i	−0.372521	+	0.0639133i
$85$	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	$-0.615618\pi$
$89$	−6.70359			−0.710579			−0.355289	+	0.934756i	$0.615618\pi$
$90$	5.47545	+	4.66209i	0.577163	+	0.491428i
$91$	0.418588	−	0.418588i	0.0438800	−	0.0438800i
$92$	6.13612	+	2.24277i	0.639735	+	0.233825i
$93$	−10.9856	+	6.29482i	−1.13916	+	0.652742i
$94$	−9.36968	+	6.55128i	−0.966408	+	0.675713i
$95$	−11.7915			−1.20978
$96$	4.08168	+	8.90730i	0.416584	+	0.909097i
$97$	−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
$99$	−4.52994	+	1.18215i	−0.455276	+	0.118810i
$100$	3.99531	+	1.46030i	0.399531	+	0.146030i
$101$	−9.10445	+	9.10445i	−0.905926	+	0.905926i	−0.995940	−	0.0900140i	$-0.971309\pi$
$101$	−9.10445	+	9.10445i	−0.905926	+	0.905926i	0.0900140	+	0.995940i	$0.471309\pi$
$102$	4.19495	−	8.90432i	0.415362	−	0.881659i
$103$	−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	0.320571	−	0.947225i	$-0.396125\pi$
$107$	−6.48216	−	6.48216i	−0.626654	−	0.626654i	−0.947225	+	0.320571i	$0.896125\pi$
$108$	3.66301	−	9.72535i	0.352473	−	0.935822i
$109$	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	$-0.820995\pi$
$113$		−	11.3357i		−	1.06637i	0.845998	−	0.533186i	$-0.179005\pi$
$114$	5.76487	+	16.0352i	0.539929	+	1.50183i
$115$	3.91518	+	3.91518i	0.365093	+	0.365093i
$116$	11.8486	−	5.50556i	1.10011	−	0.511179i
$117$	0.448432	+	1.71837i	0.0414575	+	0.158863i
$118$	10.9395	+	1.93656i	1.00706	+	0.178275i
$119$			4.01838i			0.368365i
$120$	−0.0439630	+	8.30375i	−0.00401325	+	0.758025i
$121$		−	8.56469i		−	0.778608i
$122$	0.113427	−	0.640739i	0.0102692	−	0.0580098i
$123$	−7.28904	−	12.7207i	−0.657231	−	1.14699i
$124$	−13.7315	−	5.01892i	−1.23313	−	0.450713i
$125$	8.54203	+	8.54203i	0.764022	+	0.764022i
$126$	0.339306	+	4.22905i	0.0302278	+	0.376754i
$127$		−	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	−0.591318	−	0.806439i	$-0.701392\pi$
$131$	2.46217	−	2.46217i	0.215121	−	0.215121i	0.806439	+	0.591318i	$0.201392\pi$
$132$	−4.41389	−	3.12111i	−0.384180	−	0.271658i
$133$	−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	$-0.793010\pi$
$137$	−18.6319			−1.59183			−0.795916	+	0.605407i	$0.793010\pi$
$138$	3.41011	−	7.23838i	0.290288	−	0.616172i
$139$	−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
$141$	6.96154	+	12.1492i	0.586267	+	1.02314i
$142$	9.48148	+	13.5605i	0.795668	+	1.13797i
$143$	0.923803			0.0772523
$144$	11.3137	−	3.99993i	0.942811	−	0.333327i
$145$	11.0729			0.919553
$146$	−2.34586	−	3.35507i	−0.194145	−	0.277668i
$147$	−0.861124	−	1.50282i	−0.0710243	−	0.123950i
$148$	6.70045	−	3.11344i	0.550773	−	0.255923i
$149$	−14.7316	+	14.7316i	−1.20686	+	1.20686i	−0.234819	+	0.972039i	$0.575450\pi$
$149$	−14.7316	+	14.7316i	−1.20686	+	1.20686i	−0.972039	+	0.234819i	$0.924550\pi$
$150$	2.22036	−	4.71300i	0.181292	−	0.384815i
$151$	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
$156$	−1.18395	+	1.67435i	−0.0947920	+	0.134055i
$157$	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
$162$	−11.4604	−	5.53698i	−0.900418	−	0.435026i
$163$	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
$165$	−2.27781	−	3.97520i	−0.177327	−	0.309469i
$166$	3.25672	−	18.3970i	0.252770	−	1.42788i
$167$			23.1146i			1.78866i	0.447407	+	0.894331i	$0.352348\pi$
$167$			23.1146i			1.78866i	−0.447407	+	0.894331i	$0.647652\pi$
$168$	−3.48239	+	3.44571i	−0.268672	+	0.265843i
$169$			12.6496i			0.973044i
$170$	9.48508	+	1.67909i	0.727472	+	0.128781i
$171$	20.1934	−	5.26973i	1.54422	−	0.402986i
$172$	−4.66996	−	10.0502i	−0.356081	−	0.766324i
$173$	−11.0546	−	11.0546i	−0.840464	−	0.840464i	0.148456	−	0.988919i	$-0.452570\pi$
$173$	−11.0546	−	11.0546i	−0.840464	−	0.840464i	−0.988919	+	0.148456i	$0.952570\pi$
$174$	−5.41354	−	15.0580i	−0.410400	−	1.14154i
$175$			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	−0.219357	−	0.975645i	$-0.570396\pi$
$179$	10.1184	−	10.1184i	0.756287	−	0.756287i	0.975645	+	0.219357i	$0.0703961\pi$
$180$	10.1241	+	0.966215i	0.754607	+	0.0720174i
$181$	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
$186$	−7.63121	+	16.1982i	−0.559547	+	1.18771i
$187$	−4.43419	+	4.43419i	−0.324260	+	0.324260i
$188$	−5.55050	+	15.1859i	−0.404812	+	1.10755i
$189$	5.19590	+	0.0508894i	0.377946	+	0.00370166i
$190$	−13.6664	+	9.55553i	−0.991464	+	0.693231i
$191$	2.01613			0.145882			0.0729409	−	0.997336i	$-0.476762\pi$
$191$	2.01613			0.145882			0.0729409	+	0.997336i	$0.476762\pi$
$192$	11.9489	+	7.01590i	0.862340	+	0.506329i
$193$	−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
$195$	−1.50794	+	0.864057i	−0.107986	+	0.0618764i
$196$	0.686583	−	1.87846i	0.0490416	−	0.134176i
$197$	6.81358	−	6.81358i	0.485448	−	0.485448i	−0.421419	−	0.906866i	$-0.638468\pi$
$197$	6.81358	−	6.81358i	0.485448	−	0.485448i	0.906866	+	0.421419i	$0.138468\pi$
$198$	−4.29224	+	5.04107i	−0.305036	+	0.358253i
$199$	−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
$204$	−2.35387	−	13.7196i	−0.164804	−	0.960566i
$205$	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
$210$	−3.90711	+	1.40466i	−0.269616	+	0.0969306i
$211$	−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
$213$	17.5831	−	10.0752i	1.20478	−	0.690344i
$214$	−12.7658	−	2.25987i	−0.872654	−	0.154481i
$215$		−	9.39231i		−	0.640550i
$216$	−3.63574	−	14.2401i	−0.247381	−	0.968918i
$217$		−	7.31001i		−	0.496236i
$218$	1.38099	−	7.80114i	0.0935327	−	0.528360i
$219$	−4.35034	+	2.49277i	−0.293969	+	0.168446i
$220$	1.81612	−	4.96883i	0.122443	−	0.334998i
$221$	1.68205	+	1.68205i	0.113147	+	0.113147i
$222$	−3.06140	−	8.51540i	−0.205468	−	0.571516i
$223$			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	−0.832536	−	0.553970i	$-0.813112\pi$
$227$	−4.19702	+	4.19702i	−0.278566	+	0.278566i	0.553970	+	0.832536i	$0.313112\pi$
$228$	19.6760	+	13.9132i	1.30308	+	0.921421i
$229$	−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	$-0.153720\pi$
$233$	27.0374			1.77128			0.885640	+	0.464372i	$0.153720\pi$
$234$	1.91226	+	1.62820i	0.125008	+	0.106439i
$235$	−9.68946	+	9.68946i	−0.632070	+	0.632070i
$236$	14.2483	−	6.62062i	0.927484	−	0.430966i
$237$	23.5508	−	13.4947i	1.52979	−	0.876577i
$238$	3.25640	+	4.65733i	0.211081	+	0.301890i
$239$	2.75475			0.178190			0.0890950	−	0.996023i	$-0.471603\pi$
$239$	2.75475			0.178190			0.0890950	+	0.996023i	$0.471603\pi$
$240$	6.67820	+	9.65971i	0.431076	+	0.623532i
$241$	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
$243$	−8.01354	+	13.3710i	−0.514069	+	0.857749i
$244$	−0.387777	−	0.834538i	−0.0248249	−	0.0534258i
$245$	1.19856	−	1.19856i	0.0765732	−	0.0765732i
$246$	−18.7566	−	8.83651i	−1.19588	−	0.563395i
$247$	−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	0.659214	−	0.751955i	$-0.270889\pi$
$251$	−1.46929	−	1.46929i	−0.0927408	−	0.0927408i	−0.751955	+	0.659214i	$0.770889\pi$
$252$	3.82038	+	4.62652i	0.240661	+	0.291444i
$253$	−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	$-0.893104\pi$
$257$		−	10.5661i		−	0.659092i	0.944139	−	0.329546i	$-0.106896\pi$
$258$	−12.7726	+	4.59191i	−0.795185	+	0.285880i
$259$	2.61222	+	2.61222i	0.162315	+	0.162315i
$260$	−1.88486	−	0.688922i	−0.116894	−	0.0427251i
$261$	−18.9627	+	4.94858i	−1.17376	+	0.306309i
$262$	0.858383	−	4.84894i	0.0530311	−	0.299569i
$263$		−	3.52053i		−	0.217085i	−0.994092	−	0.108543i	$-0.965382\pi$
$263$		−	3.52053i		−	0.217085i	0.994092	−	0.108543i	$-0.0346184\pi$
$264$	−7.64499	−	0.0404753i	−0.470517	−	0.00249108i
$265$		−	4.28171i		−	0.263024i
$266$	−9.68742	−	1.71491i	−0.593974	−	0.105148i
$267$	5.77262	+	10.0743i	0.353279	+	0.616536i
$268$	−3.63818	+	1.69052i	−0.222237	+	0.103265i
$269$	−2.95588	−	2.95588i	−0.180223	−	0.180223i	0.611230	−	0.791453i	$-0.290675\pi$
$269$	−2.95588	−	2.95588i	−0.180223	−	0.180223i	−0.791453	+	0.611230i	$0.790675\pi$
$270$	2.29124	−	12.2433i	0.139441	−	0.745101i
$271$			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
$276$	−1.91348	−	11.1528i	−0.115178	−	0.671319i
$277$	−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	$-0.265809\pi$
$281$	22.5004			1.34226			0.671130	+	0.741340i	$0.265809\pi$
$282$	17.9138	+	8.43947i	1.06675	+	0.502563i
$283$	−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
$285$	10.1539	+	17.7205i	0.601467	+	1.04967i
$286$	1.07069	−	0.748628i	0.0633114	−	0.0442673i
$287$	8.46457			0.499648
$288$	9.87123	−	13.8043i	0.581668	−	0.813427i
$289$	0.852586			0.0501521
$290$	12.8335	−	8.97320i	0.753611	−	0.526924i
$291$	2.95801	+	5.16226i	0.173401	+	0.302617i
$292$	−5.43773	−	1.98751i	−0.318219	−	0.116310i
$293$	−14.0097	+	14.0097i	−0.818455	+	0.818455i	−0.985884	−	0.167429i	$-0.946454\pi$
$293$	−14.0097	+	14.0097i	−0.818455	+	0.818455i	0.167429	+	0.985884i	$0.446454\pi$
$294$	−2.21589	−	1.04394i	−0.129234	−	0.0608838i
$295$	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
$300$	−1.24589	−	7.26172i	−0.0719315	−	0.419256i
$301$	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
$306$	−16.9940	+	1.36346i	−0.971480	+	0.0779439i
$307$	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
$309$	6.90730	+	12.0545i	0.392942	+	0.685757i
$310$	−17.2547	−	3.05451i	−0.980000	−	0.173484i
$311$		−	6.02505i		−	0.341649i	−0.985301	−	0.170825i	$-0.945357\pi$
$311$		−	6.02505i		−	0.341649i	0.985301	−	0.170825i	$-0.0546431\pi$
$312$	−0.0153537	+	2.90002i	−0.000869235	+	0.164182i
$313$		−	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
$315$	1.28401	+	4.92028i	0.0723459	+	0.277226i
$316$	29.4375	+	10.7595i	1.65599	+	0.605269i
$317$	−12.0141	−	12.0141i	−0.674781	−	0.674781i	0.284034	−	0.958814i	$-0.408327\pi$
$317$	−12.0141	−	12.0141i	−0.674781	−	0.674781i	−0.958814	+	0.284034i	$0.908327\pi$
$318$	−5.82269	+	2.09333i	−0.326520	+	0.117388i
$319$			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
$324$	−17.7697	+	2.86988i	−0.987208	+	0.159438i
$325$	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
$330$	−5.86140	−	2.76139i	−0.322659	−	0.152010i
$331$	−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
$333$	−10.7236	+	2.79846i	−0.587648	+	0.153355i
$334$	18.7315	+	26.7899i	1.02494	+	1.46588i
$335$	−3.40001			−0.185762
$336$	−1.24379	+	6.81564i	−0.0678541	+	0.371824i
$337$	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
$339$	−17.0355	+	9.76143i	−0.925241	+	0.530168i
$340$	12.3539	−	5.74040i	0.669987	−	0.311317i
$341$	8.06641	−	8.06641i	0.436820	−	0.436820i
$342$	19.1337	−	22.4718i	1.03463	−	1.21514i
$343$	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	0.547832	−	0.836588i	$-0.315453\pi$
$347$	−5.37894	−	5.37894i	−0.288756	−	0.288756i	−0.836588	+	0.547832i	$0.815453\pi$
$348$	−18.4769	−	13.0653i	−0.990468	−	0.700371i
$349$	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	$0.169158\pi$
$353$			19.0425i			1.01353i	−0.862085	+	0.506764i	$0.830842\pi$
$354$	−6.50997	−	18.1077i	−0.346001	−	0.962414i
$355$	14.0233	+	14.0233i	0.744278	+	0.744278i
$356$	−4.60257	+	12.5924i	−0.243936	+	0.667396i
$357$	6.03891	−	3.46033i	0.319613	−	0.183140i
$358$	3.52758	−	19.9270i	0.186438	−	1.05318i
$359$			28.4851i			1.50338i	0.659514	+	0.751692i	$0.270762\pi$
$359$			28.4851i			1.50338i	−0.659514	+	0.751692i	$0.729238\pi$
$360$	12.5169	−	7.08449i	0.659698	−	0.373385i
$361$			29.3935i			1.54703i
$362$	9.56893	+	1.69394i	0.502932	+	0.0890313i
$363$	−12.8712	+	7.37526i	−0.675562	+	0.387101i
$364$	−0.498905	−	1.07370i	−0.0261497	−	0.0562770i
$365$	−3.46958	−	3.46958i	−0.181606	−	0.181606i
$366$	−1.06059	+	0.381296i	−0.0554379	+	0.0199307i
$367$			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
$372$	4.28202	+	24.9579i	0.222012	+	1.29401i
$373$	−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
$378$	6.06331	−	4.15165i	0.311863	−	0.213538i
$379$	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
$381$	−17.8624	+	10.2353i	−0.915118	+	0.524368i
$382$	2.33670	−	1.63382i	0.119556	−	0.0835935i
$383$	9.38265			0.479431			0.239716	−	0.970843i	$-0.422946\pi$
$383$	9.38265			0.479431			0.239716	+	0.970843i	$0.422946\pi$
$384$	19.5344	−	1.55166i	0.996860	−	0.0791829i
$385$	2.64516			0.134810
$386$	−22.9778	+	16.0661i	−1.16954	+	0.817741i
$387$	4.19751	+	16.0847i	0.213372	+	0.817630i
$388$	−2.35845	+	6.45260i	−0.119732	+	0.327581i
$389$	−1.88977	+	1.88977i	−0.0958149	+	0.0958149i	−0.753389	−	0.657575i	$-0.771582\pi$
$389$	−1.88977	+	1.88977i	−0.0958149	+	0.0958149i	0.657575	+	0.753389i	$0.271582\pi$
$390$	−1.04750	+	2.22344i	−0.0530421	+	0.112588i
$391$	−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
$396$	−0.889563	+	9.32094i	−0.0447022	+	0.468395i
$397$	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	$0.0267887\pi$
$401$			3.36660i			0.168120i	−0.996461	+	0.0840599i	$0.973211\pi$
$402$	1.66227	+	4.62366i	0.0829064	+	0.230607i
$403$	−3.05988	−	3.05988i	−0.152424	−	0.152424i
$404$	10.8514	+	23.3533i	0.539876	+	1.16187i
$405$	−14.6826	−	4.14041i	−0.729582	−	0.205739i
$406$	9.09705	+	1.61040i	0.451479	+	0.0799229i
$407$			5.76503i			0.285762i
$408$	−13.8462	−	13.9936i	−0.685489	−	0.692786i
$409$		−	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
$411$	16.0444	+	28.0004i	0.791411	+	1.38116i
$412$	−5.50726	+	15.0676i	−0.271323	+	0.742327i
$413$	5.55480	+	5.55480i	0.273334	+	0.273334i
$414$	−13.8145	+	1.10837i	−0.678946	+	0.0544733i
$415$		−	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	−0.593676	−	0.804704i	$-0.702324\pi$
$419$	4.31964	−	4.31964i	0.211028	−	0.211028i	0.804704	+	0.593676i	$0.202324\pi$
$420$	−3.39006	+	4.79423i	−0.165418	+	0.233934i
$421$	−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
$426$	12.2142	−	25.9262i	0.591780	−	1.25613i
$427$	0.325351	−	0.325351i	0.0157448	−	0.0157448i
$428$	−16.6270	+	7.72592i	−0.803696	+	0.373446i
$429$	−0.795509	−	1.38831i	−0.0384075	−	0.0670282i
$430$	−7.61130	−	10.8857i	−0.367049	−	0.524956i
$431$	−7.92801			−0.381879			−0.190939	−	0.981602i	$-0.561153\pi$
$431$	−7.92801			−0.381879			−0.190939	+	0.981602i	$0.561153\pi$
$432$	−15.7537	−	13.5581i	−0.757950	−	0.652313i
$433$	−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
$435$	−9.53513	−	16.6405i	−0.457174	−	0.797853i
$436$	−4.72127	−	10.1607i	−0.226108	−	0.486608i
$437$	16.0683	−	16.0683i	0.768653	−	0.768653i
$438$	−3.02198	+	6.41454i	−0.144396	+	0.306499i
$439$	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	0.0614763	−	0.998109i	$-0.480419\pi$
$443$	−19.7138	−	19.7138i	−0.936632	−	0.936632i	−0.998109	+	0.0614763i	$0.980419\pi$
$444$	−10.4488	−	7.38850i	−0.495880	−	0.350643i
$445$	−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	$0.249530\pi$
$449$			29.9224i			1.41212i	−0.708150	+	0.706062i	$0.750470\pi$
$450$	−8.99480	+	0.721672i	−0.424019	+	0.0340200i
$451$	9.34044	+	9.34044i	0.439824	+	0.439824i
$452$	−21.2936	−	7.78289i	−1.00157	−	0.366076i
$453$	−6.71705	−	11.7225i	−0.315594	−	0.550770i
$454$	−1.46320	+	8.26553i	−0.0686715	+	0.387921i
$455$		−	1.00341i		−	0.0470404i
$456$	34.0795	+	0.180429i	1.59592	+	0.00844935i
$457$		−	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
$459$	−0.204493	+	20.8791i	−0.00954492	+	0.974555i
$460$	10.0426	−	4.66641i	0.468239	−	0.217573i
$461$	−24.1724	−	24.1724i	−1.12582	−	1.12582i	−0.990850	−	0.134969i	$-0.956906\pi$
$461$	−24.1724	−	24.1724i	−1.12582	−	1.12582i	−0.134969	−	0.990850i	$-0.543094\pi$
$462$	−1.29322	−	3.59715i	−0.0601661	−	0.167354i
$463$		−	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	−0.574882	−	0.818236i	$-0.694952\pi$
$467$	5.25892	−	5.25892i	0.243354	−	0.243354i	0.818236	+	0.574882i	$0.194952\pi$
$468$	3.53577	+	0.337444i	0.163441	+	0.0155983i
$469$	−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
$474$	16.3597	−	34.7254i	0.751424	−	1.59499i
$475$	10.4623	−	10.4623i	0.480043	−	0.480043i
$476$	7.54837	+	2.75895i	0.345979	+	0.126456i
$477$	1.91354	+	7.33259i	0.0876149	+	0.335736i
$478$	3.19277	−	2.23238i	0.146034	−	0.102107i
$479$	−21.8173			−0.996860			−0.498430	−	0.866930i	$-0.666090\pi$
$479$	−21.8173			−0.996860			−0.498430	+	0.866930i	$0.666090\pi$
$480$	15.5681	+	5.78380i	0.710582	+	0.263993i
$481$	2.18689			0.0997135
$482$	16.7931	−	11.7418i	0.764907	−	0.534822i
$483$	4.90907	−	2.81292i	0.223370	−	0.127992i
$484$	−16.0884	−	5.88037i	−0.731291	−	0.267289i
$485$	−4.11712	+	4.11712i	−0.186949	+	0.186949i
$486$	1.54779	+	21.9910i	0.0702091	+	0.997532i
$487$	−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	$-0.979468\pi$
$491$	−23.5407	−	23.5407i	−1.06238	−	1.06238i	−0.0644581	−	0.997920i	$-0.520532\pi$
$492$	−28.8999	+	4.95834i	−1.30291	+	0.223539i
$493$	−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
$498$	−30.4517	+	10.9478i	−1.36458	+	0.490583i
$499$	−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
$501$	34.7371	−	19.9045i	1.55194	−	0.889269i
$502$	−2.89359	−	0.512237i	−0.129147	−	0.0228623i
$503$		−	22.8810i		−	1.02021i	−0.860111	−	0.510107i	$-0.829606\pi$
$503$		−	22.8810i		−	1.02021i	0.860111	−	0.510107i	$-0.170394\pi$
$504$	8.17706	+	2.26622i	0.364235	+	0.100946i
$505$			21.8245i			0.971176i
$506$	−1.25666	+	7.09879i	−0.0558654	+	0.315580i
$507$	19.0100	−	10.8928i	0.844264	−	0.483768i
$508$	−22.3272	−	8.16067i	−0.990610	−	0.362071i
$509$	−23.7478	−	23.7478i	−1.05260	−	1.05260i	−0.998537	−	0.0540652i	$-0.982782\pi$
$509$	−23.7478	−	23.7478i	−1.05260	−	1.05260i	−0.0540652	−	0.998537i	$-0.517218\pi$
$510$	−5.64445	−	15.7003i	−0.249941	−	0.695219i
$511$		−	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
$516$	−11.0823	+	15.6726i	−0.487871	+	0.689948i
$517$	−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	$-0.333634\pi$
$521$	22.7881			0.998365			0.499182	+	0.866497i	$0.333634\pi$
$522$	−17.9677	+	21.1024i	−0.786424	+	0.923625i
$523$	−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
$525$	3.19636	−	1.83153i	0.139500	−	0.0799345i
$526$	−2.85296	−	4.08032i	−0.124395	−	0.177910i
$527$	29.3744			1.27957
$528$	−8.89338	+	6.14840i	−0.387035	+	0.267575i
$529$	12.3295			0.536065
$530$	−3.46980	−	4.96253i	−0.150718	−	0.215558i
$531$	−22.8033	+	5.95083i	−0.989580	+	0.258244i
$532$	−12.6175	+	5.86286i	−0.547037	+	0.254187i
$533$	3.54317	−	3.54317i	0.153472	−	0.153472i
$534$	14.8544	+	6.99815i	0.642815	+	0.302839i
$535$	−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
$540$	−7.26607	−	16.0468i	−0.312682	−	0.690542i
$541$	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
$546$	−1.36453	+	0.490566i	−0.0583964	+	0.0209943i
$547$	−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
$549$	0.348547	+	1.33562i	0.0148756	+	0.0570027i
$550$	−0.818228	+	4.62211i	−0.0348894	+	0.197088i
$551$		−	45.4443i		−	1.93599i
$552$	−11.2557	−	11.3755i	−0.479073	−	0.484173i
$553$			15.6711i			0.666402i
$554$	−1.78687	−	0.316319i	−0.0759166	−	0.0134391i
$555$	−5.39219	−	9.41035i	−0.228886	−	0.399447i
$556$	18.8576	+	40.5836i	0.799742	+	1.72113i
$557$	−9.02242	−	9.02242i	−0.382292	−	0.382292i	0.489635	−	0.871927i	$-0.337130\pi$
$557$	−9.02242	−	9.02242i	−0.382292	−	0.382292i	−0.871927	+	0.489635i	$0.837130\pi$
$558$	30.9144	−	2.48033i	1.30871	−	0.105001i
$559$		−	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	−0.989511	−	0.144454i	$-0.953857\pi$
$563$	−20.0512	+	20.0512i	−0.845057	+	0.845057i	0.144454	+	0.989511i	$0.453857\pi$
$564$	27.6014	−	4.73555i	1.16223	−	0.199403i
$565$	−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	$-0.254909\pi$
$569$	33.2100			1.39224			0.696118	+	0.717928i	$0.254909\pi$
$570$	26.1287	+	12.3096i	1.09441	+	0.515593i
$571$	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
$573$	−1.73614	−	3.02988i	−0.0725281	−	0.126575i
$574$	9.81047	−	6.85948i	0.409481	−	0.286309i
$575$	−6.94770			−0.289739
$576$	0.254122	−	23.9987i	0.0105884	−	0.999944i
$577$	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
$579$	17.0722	+	29.7941i	0.709495	+	1.23820i
$580$	7.60245	−	20.8000i	0.315675	−	0.863671i
$581$	9.34150	−	9.34150i	0.387551	−	0.387551i
$582$	7.61171	+	3.58599i	0.315516	+	0.148644i
$583$	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	0.491249	−	0.871019i	$-0.336540\pi$
$587$	−9.20109	−	9.20109i	−0.379770	−	0.379770i	−0.871019	+	0.491249i	$0.836540\pi$
$588$	−3.41422	+	0.585775i	−0.140800	+	0.0241570i
$589$	−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	$0.0575243\pi$
$593$			8.75371i			0.359472i	−0.983715	+	0.179736i	$0.942476\pi$
$594$	11.2720	+	2.10947i	0.462494	+	0.0865527i
$595$	4.81628	+	4.81628i	0.197448	+	0.197448i
$596$	17.5582	+	37.7871i	0.719212	+	1.54782i
$597$	16.7421	+	29.2181i	0.685210	+	1.19582i
$598$	2.69283	+	0.476697i	0.110118	+	0.0194936i
$599$			29.7166i			1.21419i	0.794630	+	0.607094i	$0.207665\pi$
$599$			29.7166i			1.21419i	−0.794630	+	0.607094i	$0.792335\pi$
$600$	−7.32871	−	7.40673i	−0.299193	−	0.302378i
$601$		−	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
$603$	5.82264	−	1.51950i	0.237116	−	0.0618787i
$604$	5.35557	−	14.6526i	0.217915	−	0.596205i
$605$	−10.2653	−	10.2653i	−0.417343	−	0.417343i
$606$	29.6790	−	10.6700i	1.20563	−	0.433439i
$607$		−	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
$612$	−18.5912	+	15.3517i	−0.751503	+	0.620557i
$613$	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	$-0.634961\pi$
$617$	−20.4380			−0.822803			−0.411402	+	0.911454i	$0.634961\pi$
$618$	17.7743	+	8.37372i	0.714986	+	0.336840i
$619$	−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
$621$	−0.166234	+	16.9728i	−0.00667073	+	0.681095i
$622$	−4.88255	−	6.98306i	−0.195772	−	0.279995i
$623$	−6.70359			−0.268574
$624$	2.33231	+	3.37358i	0.0933673	+	0.135051i
$625$	9.84173			0.393669
$626$	−18.8125	−	26.9057i	−0.751897	−	1.07537i
$627$	−16.3147	+	9.34839i	−0.651544	+	0.373339i
$628$	−3.94631	−	8.49288i	−0.157475	−	0.338903i
$629$	−10.4969	+	10.4969i	−0.418539	+	0.418539i
$630$	5.47545	+	4.66209i	0.218147	+	0.185742i
$631$	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
$636$	−5.05213	+	7.14475i	−0.200330	+	0.283308i
$637$	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	$0.102655\pi$
$641$			16.0485i			0.633879i	−0.948446	+	0.316939i	$0.897345\pi$
$642$	7.59679	+	21.1308i	0.299821	+	0.833965i
$643$	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
$645$	−14.1149	+	8.08794i	−0.555775	+	0.318462i
$646$	6.89118	−	38.9278i	0.271130	−	1.53159i
$647$		−	33.9767i		−	1.33576i	−0.744267	−	0.667882i	$-0.767201\pi$
$647$		−	33.9767i		−	1.33576i	0.744267	−	0.667882i	$-0.232799\pi$
$648$	−18.2695	+	17.7264i	−0.717695	+	0.696358i
$649$			12.2592i			0.481214i
$650$	1.75334	+	0.310384i	0.0687715	+	0.0121743i
$651$	−10.9856	+	6.29482i	−0.430560	+	0.246713i
$652$	16.2899	−	7.56931i	0.637963	−	0.296437i
$653$	−12.5270	−	12.5270i	−0.490219	−	0.490219i	0.418156	−	0.908375i	$-0.362677\pi$
$653$	−12.5270	−	12.5270i	−0.490219	−	0.490219i	−0.908375	+	0.418156i	$0.862677\pi$
$654$	−12.9129	+	4.64236i	−0.504935	+	0.181531i
$655$		−	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	−0.986794	−	0.161978i	$-0.948213\pi$
$659$	−21.1739	+	21.1739i	−0.824816	+	0.824816i	0.161978	+	0.986794i	$0.448213\pi$
$660$	−9.03115	+	1.54947i	−0.351537	+	0.0603131i
$661$	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
$666$	−10.1609	+	11.9335i	−0.393725	+	0.462415i
$667$	−15.0891	+	15.0891i	−0.584252	+	0.584252i
$668$	43.4198	+	15.8701i	1.67996	+	0.614032i
$669$	17.2993	−	9.91260i	0.668830	−	0.383243i
$670$	−3.94063	+	2.75529i	−0.152240	+	0.106446i
$671$	0.718033			0.0277193
$672$	4.08168	+	8.90730i	0.157454	+	0.343606i
$673$	−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
$675$	−0.108237	+	11.0512i	−0.00416604	+	0.425361i
$676$	23.7617	+	8.68497i	0.913911	+	0.334037i
$677$	18.3210	−	18.3210i	0.704133	−	0.704133i	−0.261162	−	0.965295i	$-0.584106\pi$
$677$	18.3210	−	18.3210i	0.704133	−	0.704133i	0.965295	+	0.261162i	$0.0841057\pi$
$678$	−11.8338	+	25.1187i	−0.454474	+	0.964678i
$679$	−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	0.990473	−	0.137704i	$-0.0439724\pi$
$683$	22.2865	+	22.2865i	0.852769	+	0.852769i	−0.137704	+	0.990473i	$0.543972\pi$
$684$	3.96545	−	41.5505i	0.151623	−	1.58872i
$685$	−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
$690$	−4.58842	−	12.7629i	−0.174678	−	0.485873i
$691$	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
$693$	−4.52994	+	1.18215i	−0.172078	+	0.0449061i
$694$	−10.5932	−	1.87525i	−0.402111	−	0.0711836i
$695$			37.9268i			1.43865i
$696$	−32.0026	−	0.169433i	−1.21306	−	0.00642235i
$697$			34.0139i			1.28837i
$698$	0.615820	−	3.47872i	0.0233091	−	0.131672i
$699$	−23.2826	−	40.6324i	−0.880628	−	1.53686i
$700$	3.99531	+	1.46030i	0.151008	+	0.0551941i
$701$	−28.0109	−	28.0109i	−1.05796	−	1.05796i	−0.998214	−	0.0597418i	$-0.980972\pi$
$701$	−28.0109	−	28.0109i	−1.05796	−	1.05796i	−0.0597418	−	0.998214i	$-0.519028\pi$
$702$	0.800199	−	4.27587i	0.0302016	−	0.161382i
$703$		−	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
$708$	−22.2191	−	15.7114i	−0.835046	−	0.590471i
$709$	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
$714$	4.19495	−	8.90432i	0.156992	−	0.333236i
$715$	1.10723	−	1.10723i	0.0414082	−	0.0414082i
$716$	−12.0599	−	25.9542i	−0.450700	−	0.969954i
$717$	−2.37218	−	4.13989i	−0.0885907	−	0.154607i
$718$	23.0836	+	33.0143i	0.861472	+	1.23208i
$719$	22.9619			0.856333			0.428166	−	0.903700i	$-0.359160\pi$
$719$	22.9619			0.856333			0.428166	+	0.903700i	$0.359160\pi$
$720$	8.76604	−	18.3543i	0.326691	−	0.684026i
$721$	−8.02126			−0.298727
$722$	23.8198	+	34.0672i	0.886481	+	1.26785i
$723$	−12.4771	−	21.7748i	−0.464027	−	0.809812i
$724$	12.4632	−	5.79115i	0.463190	−	0.215226i
$725$	−9.82471	+	9.82471i	−0.364880	+	0.364880i
$726$	−8.94102	+	18.9784i	−0.331832	+	0.704356i
$727$	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
$732$	−0.920235	+	1.30140i	−0.0340129	+	0.0481011i
$733$	−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
$738$	2.87208	+	35.7971i	0.105723	+	1.31771i
$739$	−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
$741$	3.54618	+	6.18874i	0.130272	+	0.227349i
$742$	0.622718	−	3.51769i	0.0228607	−	0.129138i
$743$		−	10.6048i		−	0.389051i	−0.980897	−	0.194525i	$-0.937683\pi$
$743$		−	10.6048i		−	0.389051i	0.980897	−	0.194525i	$-0.0623167\pi$
$744$	25.1882	+	25.4563i	0.923444	+	0.933274i
$745$			35.3134i			1.29378i
$746$	−26.9584	−	4.77231i	−0.987019	−	0.174727i
$747$	10.0075	+	38.3483i	0.366156	+	1.40309i
$748$	5.28500	+	11.3739i	0.193239	+	0.415870i
$749$	−6.48216	−	6.48216i	−0.236853	−	0.236853i
$750$	−10.0109	−	27.8456i	−0.365545	−	1.01678i
$751$		−	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
$756$	3.66301	−	9.72535i	0.133222	−	0.353707i
$757$	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	$-0.496081\pi$
$761$	0.679283			0.0246240			0.0123120	+	0.999924i	$0.496081\pi$
$762$	−12.4082	+	26.3380i	−0.449502	+	0.954124i
$763$	3.96122	−	3.96122i	0.143406	−	0.143406i
$764$	1.38424	−	3.78721i	0.0500800	−	0.137016i
$765$	−19.7716	+	5.15966i	−0.714843	+	0.186548i
$766$	10.8745	−	7.60347i	0.392913	−	0.274725i
$767$	4.65035			0.167914
$768$	21.3830	−	17.6286i	0.771593	−	0.636116i
$769$	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
$771$	−15.8789	+	9.09868i	−0.571864	+	0.327681i
$772$	−13.6118	+	37.2413i	−0.489900	+	1.34034i
$773$	23.3063	−	23.3063i	0.838269	−	0.838269i	−0.150362	−	0.988631i	$-0.548044\pi$
$773$	23.3063	−	23.3063i	0.838269	−	0.838269i	0.988631	+	0.150362i	$0.0480439\pi$
$774$	17.8996	+	15.2407i	0.643387	+	0.547814i
$775$	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
$780$	0.587771	+	3.42585i	0.0210456	+	0.122665i
$781$	−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
$786$	−8.02626	+	2.88555i	−0.286287	+	0.102924i
$787$	−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
$789$	−5.29073	+	3.03162i	−0.188355	+	0.107928i
$790$	36.9903	+	6.54820i	1.31606	+	0.232974i
$791$		−	11.3357i		−	0.403051i
$792$	6.52246	+	11.5239i	0.231765	+	0.409484i
$793$		−	0.272376i		−	0.00967235i
$794$	7.85936	−	44.3970i	0.278918	−	1.57559i
$795$	−6.43464	+	3.68709i	−0.228213	+	0.130767i
$796$	−13.3487	+	36.5214i	−0.473131	+	1.29447i
$797$	21.5577	+	21.5577i	0.763613	+	0.763613i	0.976974	−	0.213360i	$-0.0684408\pi$
$797$	21.5577	+	21.5577i	0.763613	+	0.763613i	−0.213360	+	0.976974i	$0.568441\pi$
$798$	5.76487	+	16.0352i	0.204074	+	0.567640i
$799$		−	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
$804$	5.67348	+	4.01178i	0.200088	+	0.141485i
$805$	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	$-0.274597\pi$
$809$	36.9991			1.30082			0.650410	+	0.759583i	$0.274597\pi$
$810$	−20.3724	+	7.09963i	−0.715815	+	0.249456i
$811$	−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
$813$	39.8059	−	22.8090i	1.39605	−	0.799946i
$814$	4.67184	+	6.68170i	0.163748	+	0.234193i
$815$	15.2235			0.533257
$816$	−27.3879	−	4.99801i	−0.958767	−	0.174966i
$817$	−38.5471			−1.34859
$818$	−10.6964	−	15.2980i	−0.373990	−	0.534883i
$819$	0.448432	+	1.71837i	0.0156695	+	0.0600448i
$820$	−12.0919	−	26.0231i	−0.422268	−	0.908766i
$821$	−38.2753	+	38.2753i	−1.33582	+	1.33582i	−0.435752	+	0.900067i	$0.643517\pi$
$821$	−38.2753	+	38.2753i	−1.33582	+	1.33582i	−0.900067	+	0.435752i	$0.856483\pi$
$822$	41.2864	+	19.4506i	1.44003	+	0.678418i
$823$	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	0.510869	−	0.859659i	$-0.329324\pi$
$827$	−10.0304	−	10.0304i	−0.348790	−	0.348790i	−0.859659	+	0.510869i	$0.829324\pi$
$828$	−15.1129	+	12.4795i	−0.525209	+	0.433694i
$829$	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
$834$	51.5765	−	18.5425i	1.78595	−	0.642073i
$835$	27.7042	+	27.7042i	0.958745	+	0.958745i
$836$	−20.3926	−	7.45356i	−0.705293	−	0.257787i
$837$	0.372002	−	37.9821i	0.0128583	−	1.31285i
$838$	1.50595	−	8.50702i	0.0520223	−	0.293870i
$839$			29.3275i			1.01250i	0.862387	+	0.506249i	$0.168968\pi$
$839$			29.3275i			1.01250i	−0.862387	+	0.506249i	$0.831032\pi$
$840$	−0.0439630	+	8.30375i	−0.00151687	+	0.286507i
$841$			13.6749i			0.471547i
$842$	−7.65192	−	1.35458i	−0.263703	−	0.0466819i
$843$	−19.3756	−	33.8140i	−0.667332	−	1.16462i
$844$	−44.7025	+	20.7715i	−1.53872	+	0.714986i
$845$	15.1613	+	15.1613i	0.521563	+	0.521563i
$846$	−2.74303	−	34.1887i	−0.0943074	−	1.17543i
$847$		−	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
$852$	−6.85363	−	39.9467i	−0.234801	−	1.36855i
$853$	−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	$-0.865705\pi$
$857$	−53.4151			−1.82462			−0.912312	+	0.409495i	$0.865705\pi$
$858$	−2.04705	−	0.964396i	−0.0698852	−	0.0329239i
$859$	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
$861$	−7.28904	−	12.7207i	−0.248410	−	0.433521i
$862$	−9.18860	+	6.42467i	−0.312965	+	0.218825i
$863$	56.4885			1.92289			0.961445	−	0.274999i	$-0.0886774\pi$
$863$	56.4885			1.92289			0.961445	+	0.274999i	$0.0886774\pi$
$864$	−29.2457	−	2.94745i	−0.994960	−	0.100274i
$865$	−26.4991			−0.900998
$866$	−8.23640	+	5.75889i	−0.279884	+	0.195695i
$867$	−0.734182	−	1.28128i	−0.0249341	−	0.0435147i
$868$	−13.7315	−	5.01892i	−0.466079	−	0.170353i
$869$	−17.2926	+	17.2926i	−0.586612	+	0.586612i
$870$	−24.5364	−	11.5594i	−0.831860	−	0.391902i
$871$	−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
$876$	1.69569	+	9.88342i	0.0572922	+	0.333930i
$877$	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	$-0.620118\pi$
$881$		−	55.1865i		−	1.85928i	0.368470	−	0.929640i	$-0.379882\pi$
$882$	0.339306	+	4.22905i	0.0114250	+	0.142400i
$883$	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
$885$	−11.4663	−	20.0108i	−0.385436	−	0.672656i
$886$	−38.8240	−	6.87281i	−1.30432	−	0.230897i
$887$		−	2.82548i		−	0.0948702i	−0.998874	−	0.0474351i	$-0.984895\pi$
$887$		−	2.82548i		−	0.0948702i	0.998874	−	0.0474351i	$-0.0151047\pi$
$888$	−18.0977	−	0.0958157i	−0.607320	−	0.00321536i
$889$		−	11.8859i		−	0.398641i
$890$	−2.80111	+	15.8233i	−0.0938935	+	0.530398i
$891$	3.81194	−	13.5177i	0.127705	−	0.452862i
$892$	21.6234	+	7.90341i	0.724004	+	0.264626i
$893$	39.7666	+	39.7666i	1.33074	+	1.33074i
$894$	48.0225	−	17.2647i	1.60611	−	0.577419i
$895$		−	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
$900$	−9.84019	+	8.12559i	−0.328006	+	0.270853i
$901$	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
$906$	−17.2847	−	8.14308i	−0.574246	−	0.270536i
$907$	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
$909$	−9.75356	−	37.3752i	−0.323505	−	1.23966i
$910$	−0.813136	−	1.16295i	−0.0269552	−	0.0385515i
$911$	17.7959			0.589603			0.294801	−	0.955559i	$-0.404747\pi$
$911$	17.7959			0.589603			0.294801	+	0.955559i	$0.404747\pi$
$912$	39.6445	−	27.4081i	1.31276	−	0.907572i
$913$	20.6162			0.682297
$914$	−29.1373	−	41.6724i	−0.963778	−	1.37840i
$915$	−1.17206	+	0.671595i	−0.0387470	+	0.0222022i
$916$	−13.7191	+	6.37471i	−0.453290	+	0.210626i
$917$	2.46217	−	2.46217i	0.0813079	−	0.0813079i
$918$	16.6829	+	24.3647i	0.550619	+	0.804156i
$919$	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
$924$	−4.41389	−	3.12111i	−0.145206	−	0.102677i
$925$	−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	$0.216350\pi$
$929$			38.3156i			1.25709i	−0.777772	+	0.628547i	$0.783650\pi$
$930$	10.2681	+	28.5610i	0.336703	+	0.936552i
$931$	−4.91902	−	4.91902i	−0.161214	−	0.161214i
$932$	18.5634	−	50.7887i	0.608065	−	1.66364i
$933$	−9.05456	+	5.18831i	−0.296433	+	0.169858i
$934$	1.83341	−	10.3568i	0.0599910	−	0.338885i
$935$			10.6293i			0.347615i
$936$	4.37143	−	2.47421i	0.142885	−	0.0808720i
$937$			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
$939$	−34.8872	+	19.9906i	−1.13850	+	0.652367i
$940$	11.5486	+	24.8538i	0.376675	+	0.810643i
$941$	31.9860	+	31.9860i	1.04271	+	1.04271i	0.999046	+	0.0436675i	$0.0139042\pi$
$941$	31.9860	+	31.9860i	1.04271	+	1.04271i	0.0436675	+	0.999046i	$0.486096\pi$
$942$	−10.7934	+	3.88036i	−0.351667	+	0.126429i
$943$			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	−0.822625	−	0.568585i	$-0.807491\pi$
$947$	−7.81766	+	7.81766i	−0.254040	+	0.254040i	0.568585	+	0.822625i	$0.307491\pi$
$948$	−9.17973	−	53.5044i	−0.298144	−	1.73774i
$949$	−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	$-0.384197\pi$
$953$	21.9696			0.711667			0.355833	+	0.934549i	$0.384197\pi$
$954$	8.15996	+	6.94783i	0.264188	+	0.224944i
$955$	2.41645	−	2.41645i	0.0781945	−	0.0781945i
$956$	1.89136	−	5.17468i	0.0611711	−	0.167361i
$957$	15.3204	−	8.77868i	0.495238	−	0.283774i
$958$	−25.2864	+	17.6802i	−0.816966	+	0.571223i
$959$	−18.6319			−0.601656
$960$	22.7305	−	5.91254i	0.733624	−	0.190826i
$961$	−22.4362			−0.723748
$962$	2.53461	−	1.77220i	0.0817192	−	0.0571380i
$963$	26.6103	−	6.94431i	0.857504	−	0.223777i
$964$	9.94809	−	27.2175i	0.320406	−	0.876617i
$965$	−23.7620	+	23.7620i	−0.764926	+	0.764926i
$966$	3.41011	−	7.23838i	0.109718	−	0.232891i
$967$	−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	0.984389	−	0.176008i	$-0.0563186\pi$
$971$	25.1898	+	25.1898i	0.808380	+	0.808380i	−0.176008	+	0.984389i	$0.556319\pi$
$972$	19.6149	+	24.2334i	0.629147	+	0.777286i
$973$	−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	$0.0466866\pi$
$977$			9.13611i			0.292290i	−0.989263	+	0.146145i	$0.953313\pi$
$978$	−7.44279	−	20.7024i	−0.237994	−	0.661990i
$979$	−7.39724	−	7.39724i	−0.236417	−	0.236417i
$980$	−1.42853	−	3.07436i	−0.0456328	−	0.0982067i
$981$	4.24363	+	16.2614i	0.135489	+	0.519187i
$982$	−46.3607	−	8.20698i	−1.47943	−	0.261895i
$983$			4.41394i			0.140783i	0.997519	+	0.0703914i	$0.0224248\pi$
$983$			4.41394i			0.140783i	−0.997519	+	0.0703914i	$0.977575\pi$
$984$	−29.4770	+	29.1665i	−0.939691	+	0.929793i
$985$		−	16.3330i		−	0.520412i
$986$	−6.47122	+	36.5554i	−0.206085	+	1.16416i
$987$	6.96154	+	12.1492i	0.221588	+	0.386712i
$988$	−2.82741	+	7.73566i	−0.0899519	+	0.246104i
$989$	12.7990	+	12.7990i	0.406983	+	0.406983i
$990$	0.897519	+	11.1865i	0.0285250	+	0.355531i
$991$		−	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
$996$	−26.4219	+	37.3659i	−0.837209	+	1.18398i
$997$	−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.155.19	yes	48
3.2	odd	2	inner	336.2.s.d.155.6	✓	48
4.3	odd	2		1344.2.s.d.911.16		48
12.11	even	2		1344.2.s.d.911.20		48
16.3	odd	4	inner	336.2.s.d.323.6	yes	48
16.13	even	4		1344.2.s.d.239.20		48
48.29	odd	4		1344.2.s.d.239.16		48
48.35	even	4	inner	336.2.s.d.323.19	yes	48

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

\(f(q)\)	\(=\)	\(q+(1.15900 - 0.810376i) q^{2} +(-0.861124 - 1.50282i) q^{3} +(0.686583 - 1.87846i) q^{4} +(1.19856 - 1.19856i) q^{5} +(-2.21589 - 1.04394i) q^{6} +1.00000 q^{7} +(-0.726504 - 2.73353i) q^{8} +(-1.51693 + 2.58823i) q^{9} +O(q^{10})\)	\(q+(1.15900 - 0.810376i) q^{2} +(-0.861124 - 1.50282i) q^{3} +(0.686583 - 1.87846i) q^{4} +(1.19856 - 1.19856i) q^{5} +(-2.21589 - 1.04394i) 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} +(-3.41422 + 0.585775i) 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} +(0.339306 + 4.22905i) q^{18} +(-4.91902 - 4.91902i) q^{19} +(-1.42853 - 3.07436i) q^{20} +(-0.861124 - 1.50282i) q^{21} +(2.17316 + 0.384703i) q^{22} +3.26657i q^{23} +(-3.48239 + 3.44571i) q^{24} +2.12691i q^{25} +(0.145932 - 0.824359i) q^{26} +(5.19590 + 0.0508894i) q^{27} +(0.686583 - 1.87846i) q^{28} +(4.61925 + 4.61925i) q^{29} +(-3.90711 + 1.40466i) 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} +(3.82038 + 4.62652i) 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} +(-2.21589 - 1.04394i) q^{42} +(3.91816 - 3.91816i) q^{43} +(2.83046 - 1.31520i) q^{44} +(1.28401 + 4.92028i) q^{45} +(2.64715 + 3.78597i) q^{46} -8.08425 q^{47} +(-1.24379 + 6.81564i) q^{48} +1.00000 q^{49} +(1.72359 + 2.46509i) q^{50} +(6.03891 - 3.46033i) q^{51} +(-0.498905 - 1.07370i) q^{52} +(1.78619 - 1.78619i) q^{53} +(6.06331 - 4.15165i) 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} +(-3.39006 + 4.79423i) 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} +(-1.29322 - 3.59715i) q^{66} +(-1.41837 - 1.41837i) q^{67} +(7.54837 + 2.75895i) q^{68} +(4.90907 - 2.81292i) q^{69} +(0.417853 - 2.36042i) q^{70} +11.7001i q^{71} +(8.17706 + 2.26622i) q^{72} -2.89479i q^{73} +(5.14445 + 0.910695i) q^{74} +(3.19636 - 1.83153i) q^{75} +(-12.6175 + 5.86286i) q^{76} +(1.10347 + 1.10347i) q^{77} +(-1.36453 + 0.490566i) 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} +(-3.41422 + 0.585775i) 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} +(5.47545 + 4.66209i) q^{90} +(0.418588 - 0.418588i) q^{91} +(6.13612 + 2.24277i) q^{92} +(-10.9856 + 6.29482i) q^{93} +(-9.36968 + 6.55128i) q^{94} -11.7915 q^{95} +(4.08168 + 8.90730i) q^{96} -3.43505 q^{97} +(1.15900 - 0.810376i) q^{98} +(-4.52994 + 1.18215i) 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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