LMFDB - Embedded newform 760.2.w.d.267.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(267,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("760.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.w (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:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.12
Character	$\chi$	$=$	760.267
Dual form			760.2.w.d.723.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07153 + 0.922945i) q^{2} +(0.0817665 - 0.0817665i) q^{3} +(0.296346 - 1.97792i) q^{4} +(1.80920 - 1.31408i) q^{5} +(-0.0121492 + 0.163081i) q^{6} +(1.71397 - 1.71397i) q^{7} +(1.50797 + 2.39291i) q^{8} +2.98663i q^{9} +O(q^{10})$	\(q+(-1.07153 + 0.922945i) q^{2} +(0.0817665 - 0.0817665i) q^{3} +(0.296346 - 1.97792i) q^{4} +(1.80920 - 1.31408i) q^{5} +(-0.0121492 + 0.163081i) q^{6} +(1.71397 - 1.71397i) q^{7} +(1.50797 + 2.39291i) q^{8} +2.98663i q^{9} +(-0.725784 + 3.07786i) q^{10} +1.68163 q^{11} +(-0.137497 - 0.185959i) q^{12} +(-1.43476 - 1.43476i) q^{13} +(-0.254668 + 3.41847i) q^{14} +(0.0404841 - 0.255379i) q^{15} +(-3.82436 - 1.17230i) q^{16} +(4.55456 + 4.55456i) q^{17} +(-2.75649 - 3.20026i) q^{18} +1.00000i q^{19} +(-2.06300 - 3.96788i) q^{20} -0.280291i q^{21} +(-1.80192 + 1.55205i) q^{22} +(-0.291416 - 0.291416i) q^{23} +(0.318961 + 0.0723585i) q^{24} +(1.54639 - 4.75486i) q^{25} +(2.86160 + 0.213182i) q^{26} +(0.489506 + 0.489506i) q^{27} +(-2.88218 - 3.89803i) q^{28} -0.499068 q^{29} +(0.192321 + 0.311011i) q^{30} -2.05973i q^{31} +(5.17988 - 2.27352i) q^{32} +(0.137501 - 0.137501i) q^{33} +(-9.08395 - 0.676733i) q^{34} +(0.848619 - 5.35321i) q^{35} +(5.90732 + 0.885075i) q^{36} +(4.25853 - 4.25853i) q^{37} +(-0.922945 - 1.07153i) q^{38} -0.234631 q^{39} +(5.87269 + 2.34766i) q^{40} -5.19926 q^{41} +(0.258693 + 0.300340i) q^{42} +(2.30445 - 2.30445i) q^{43} +(0.498345 - 3.32614i) q^{44} +(3.92467 + 5.40340i) q^{45} +(0.581222 + 0.0432997i) q^{46} +(8.59240 - 8.59240i) q^{47} +(-0.408559 + 0.216850i) q^{48} +1.12460i q^{49} +(2.73147 + 6.52220i) q^{50} +0.744821 q^{51} +(-3.26304 + 2.41267i) q^{52} +(-2.04150 - 2.04150i) q^{53} +(-0.976306 - 0.0727325i) q^{54} +(3.04240 - 2.20980i) q^{55} +(6.68600 + 1.51676i) q^{56} +(0.0817665 + 0.0817665i) q^{57} +(0.534766 - 0.460613i) q^{58} -5.44632i q^{59} +(-0.493123 - 0.155755i) q^{60} +6.54656i q^{61} +(1.90102 + 2.20706i) q^{62} +(5.11900 + 5.11900i) q^{63} +(-3.45205 + 7.21688i) q^{64} +(-4.48117 - 0.710378i) q^{65} +(-0.0204304 + 0.274242i) q^{66} +(2.56407 + 2.56407i) q^{67} +(10.3583 - 7.65884i) q^{68} -0.0476562 q^{69} +(4.03140 + 6.51935i) q^{70} +8.51554i q^{71} +(-7.14674 + 4.50375i) q^{72} +(-8.77306 + 8.77306i) q^{73} +(-0.632748 + 8.49352i) q^{74} +(-0.262345 - 0.515231i) q^{75} +(1.97792 + 0.296346i) q^{76} +(2.88227 - 2.88227i) q^{77} +(0.251414 - 0.216552i) q^{78} +0.712885 q^{79} +(-8.45951 + 2.90459i) q^{80} -8.87984 q^{81} +(5.57116 - 4.79863i) q^{82} +(12.4110 - 12.4110i) q^{83} +(-0.554394 - 0.0830631i) q^{84} +(14.2251 + 2.25505i) q^{85} +(-0.342403 + 4.59615i) q^{86} +(-0.0408071 + 0.0408071i) q^{87} +(2.53585 + 4.02399i) q^{88} +11.2344i q^{89} +(-9.19243 - 2.16765i) q^{90} -4.91829 q^{91} +(-0.662759 + 0.490039i) q^{92} +(-0.168417 - 0.168417i) q^{93} +(-1.27669 + 17.1373i) q^{94} +(1.31408 + 1.80920i) q^{95} +(0.237642 - 0.609438i) q^{96} +(9.74041 + 9.74041i) q^{97} +(-1.03794 - 1.20504i) q^{98} +5.02241i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 8 q^{6}+O(q^{10}) $ 108 * q + 8 * q^6	$ 108 q + 8 q^{6} + 8 q^{10} + 18 q^{12} + 16 q^{16} + 4 q^{17} - 36 q^{22} - 4 q^{25} - 40 q^{26} + 16 q^{28} - 12 q^{30} - 10 q^{32} + 24 q^{35} - 80 q^{36} + 28 q^{40} + 108 q^{42} - 32 q^{43} + 64 q^{46} - 26 q^{48} - 28 q^{50} + 34 q^{52} - 12 q^{56} - 58 q^{60} - 92 q^{62} - 4 q^{65} - 92 q^{66} + 40 q^{68} + 28 q^{70} - 68 q^{72} - 20 q^{73} + 12 q^{78} + 56 q^{80} - 92 q^{81} + 44 q^{82} + 72 q^{83} + 40 q^{86} - 40 q^{88} + 4 q^{90} + 32 q^{91} + 24 q^{92} + 124 q^{96} - 84 q^{97} + 76 q^{98}+O(q^{100}) $ 108 * q + 8 * q^6 + 8 * q^10 + 18 * q^12 + 16 * q^16 + 4 * q^17 - 36 * q^22 - 4 * q^25 - 40 * q^26 + 16 * q^28 - 12 * q^30 - 10 * q^32 + 24 * q^35 - 80 * q^36 + 28 * q^40 + 108 * q^42 - 32 * q^43 + 64 * q^46 - 26 * q^48 - 28 * q^50 + 34 * q^52 - 12 * q^56 - 58 * q^60 - 92 * q^62 - 4 * q^65 - 92 * q^66 + 40 * q^68 + 28 * q^70 - 68 * q^72 - 20 * q^73 + 12 * q^78 + 56 * q^80 - 92 * q^81 + 44 * q^82 + 72 * q^83 + 40 * q^86 - 40 * q^88 + 4 * q^90 + 32 * q^91 + 24 * q^92 + 124 * q^96 - 84 * q^97 + 76 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.07153	+	0.922945i	−0.757685	+	0.652620i
$2$	−1.07153	+	0.922945i	−0.757685	+	0.652620i
$3$	0.0817665	−	0.0817665i	0.0472079	−	0.0472079i	−0.683109	−	0.730317i	$-0.739373\pi$
$3$	0.0817665	−	0.0817665i	0.0472079	−	0.0472079i	0.730317	+	0.683109i	$0.239373\pi$
$4$	0.296346	−	1.97792i	0.148173	−	0.988961i
$5$	1.80920	−	1.31408i	0.809098	−	0.587674i
$5$	1.80920	−	1.31408i	0.809098	−	0.587674i
$6$	−0.0121492	+	0.163081i	−0.00495987	+	0.0665776i
$7$	1.71397	−	1.71397i	0.647821	−	0.647821i	−0.304645	−	0.952466i	$-0.598538\pi$
$7$	1.71397	−	1.71397i	0.647821	−	0.647821i	0.952466	+	0.304645i	$0.0985379\pi$
$8$	1.50797	+	2.39291i	0.533148	+	0.846022i
$9$			2.98663i			0.995543i
$10$	−0.725784	+	3.07786i	−0.229513	+	0.973306i
$11$	1.68163			0.507031			0.253515	−	0.967331i	$-0.418413\pi$
$11$	1.68163			0.507031			0.253515	+	0.967331i	$0.418413\pi$
$12$	−0.137497	−	0.185959i	−0.0396919	−	0.0536817i
$13$	−1.43476	−	1.43476i	−0.397932	−	0.397932i	0.479571	−	0.877503i	$-0.340792\pi$
$13$	−1.43476	−	1.43476i	−0.397932	−	0.397932i	−0.877503	+	0.479571i	$0.840792\pi$
$14$	−0.254668	+	3.41847i	−0.0680629	+	0.913625i
$15$	0.0404841	−	0.255379i	0.0104529	−	0.0659387i
$16$	−3.82436	−	1.17230i	−0.956090	−	0.293075i
$17$	4.55456	+	4.55456i	1.10464	+	1.10464i	0.993843	+	0.110800i	$0.0353413\pi$
$17$	4.55456	+	4.55456i	1.10464	+	1.10464i	0.110800	+	0.993843i	$0.464659\pi$
$18$	−2.75649	−	3.20026i	−0.649712	−	0.754308i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−2.06300	−	3.96788i	−0.461301	−	0.887244i
$21$		−	0.280291i		−	0.0611645i
$22$	−1.80192	+	1.55205i	−0.384170	+	0.330899i
$23$	−0.291416	−	0.291416i	−0.0607645	−	0.0607645i	0.676071	−	0.736836i	$-0.263681\pi$
$23$	−0.291416	−	0.291416i	−0.0607645	−	0.0607645i	−0.736836	+	0.676071i	$0.763681\pi$
$24$	0.318961	+	0.0723585i	0.0651077	+	0.0147701i
$25$	1.54639	−	4.75486i	0.309278	−	0.950972i
$26$	2.86160	+	0.213182i	0.561206	+	0.0418085i
$27$	0.489506	+	0.489506i	0.0942054	+	0.0942054i
$28$	−2.88218	−	3.89803i	−0.544680	−	0.736659i
$29$	−0.499068			−0.0926747			−0.0463373	−	0.998926i	$-0.514755\pi$
$29$	−0.499068			−0.0926747			−0.0463373	+	0.998926i	$0.514755\pi$
$30$	0.192321	+	0.311011i	0.0351129	+	0.0567825i
$31$		−	2.05973i		−	0.369938i	−0.982744	−	0.184969i	$-0.940781\pi$
$31$		−	2.05973i		−	0.369938i	0.982744	−	0.184969i	$-0.0592185\pi$
$32$	5.17988	−	2.27352i	0.915681	−	0.401905i
$33$	0.137501	−	0.137501i	0.0239359	−	0.0239359i
$34$	−9.08395	−	0.676733i	−1.55788	−	0.116059i
$35$	0.848619	−	5.35321i	0.143443	−	0.904858i
$36$	5.90732	+	0.885075i	0.984553	+	0.147513i
$37$	4.25853	−	4.25853i	0.700098	−	0.700098i	−0.264333	−	0.964431i	$-0.585152\pi$
$37$	4.25853	−	4.25853i	0.700098	−	0.700098i	0.964431	+	0.264333i	$0.0851519\pi$
$38$	−0.922945	−	1.07153i	−0.149721	−	0.173825i
$39$	−0.234631			−0.0375711
$40$	5.87269	+	2.34766i	0.928554	+	0.371197i
$41$	−5.19926			−0.811989			−0.405994	−	0.913876i	$-0.633075\pi$
$41$	−5.19926			−0.811989			−0.405994	+	0.913876i	$0.633075\pi$
$42$	0.258693	+	0.300340i	0.0399172	+	0.0463434i
$43$	2.30445	−	2.30445i	0.351425	−	0.351425i	−0.509215	−	0.860639i	$-0.670064\pi$
$43$	2.30445	−	2.30445i	0.351425	−	0.351425i	0.860639	+	0.509215i	$0.170064\pi$
$44$	0.498345	−	3.32614i	0.0751283	−	0.501434i
$45$	3.92467	+	5.40340i	0.585055	+	0.805491i
$46$	0.581222	+	0.0432997i	0.0856966	+	0.00638419i
$47$	8.59240	−	8.59240i	1.25333	−	1.25333i	0.299113	−	0.954218i	$-0.403309\pi$
$47$	8.59240	−	8.59240i	1.25333	−	1.25333i	0.954218	−	0.299113i	$-0.0966907\pi$
$48$	−0.408559	+	0.216850i	−0.0589704	+	0.0312995i
$49$			1.12460i			0.160656i
$50$	2.73147	+	6.52220i	0.386288	+	0.922378i
$51$	0.744821			0.104296
$52$	−3.26304	+	2.41267i	−0.452502	+	0.334577i
$53$	−2.04150	−	2.04150i	−0.280421	−	0.280421i	0.552856	−	0.833277i	$-0.313538\pi$
$53$	−2.04150	−	2.04150i	−0.280421	−	0.280421i	−0.833277	+	0.552856i	$0.813538\pi$
$54$	−0.976306	−	0.0727325i	−0.132858	−	0.00989764i
$55$	3.04240	−	2.20980i	0.410237	−	0.297969i
$56$	6.68600	+	1.51676i	0.893455	+	0.202686i
$57$	0.0817665	+	0.0817665i	0.0108302	+	0.0108302i
$58$	0.534766	−	0.460613i	0.0702182	−	0.0604814i
$59$		−	5.44632i		−	0.709051i	−0.935046	−	0.354525i	$-0.884642\pi$
$59$		−	5.44632i		−	0.709051i	0.935046	−	0.354525i	$-0.115358\pi$
$60$	−0.493123	−	0.155755i	−0.0636620	−	0.0201079i
$61$			6.54656i			0.838201i	0.907940	+	0.419101i	$0.137655\pi$
$61$			6.54656i			0.838201i	−0.907940	+	0.419101i	$0.862345\pi$
$62$	1.90102	+	2.20706i	0.241429	+	0.280297i
$63$	5.11900	+	5.11900i	0.644933	+	0.644933i
$64$	−3.45205	+	7.21688i	−0.431506	+	0.902110i
$65$	−4.48117	−	0.710378i	−0.555820	−	0.0881115i
$66$	−0.0204304	+	0.274242i	−0.00251481	+	0.0337569i
$67$	2.56407	+	2.56407i	0.313252	+	0.313252i	0.846168	−	0.532916i	$-0.178904\pi$
$67$	2.56407	+	2.56407i	0.313252	+	0.313252i	−0.532916	+	0.846168i	$0.678904\pi$
$68$	10.3583	−	7.65884i	1.25613	−	0.928771i
$69$	−0.0476562			−0.00573713
$70$	4.03140	+	6.51935i	0.481844	+	0.779211i
$71$			8.51554i			1.01061i	0.862941	+	0.505304i	$0.168620\pi$
$71$			8.51554i			1.01061i	−0.862941	+	0.505304i	$0.831380\pi$
$72$	−7.14674	+	4.50375i	−0.842251	+	0.530772i
$73$	−8.77306	+	8.77306i	−1.02681	+	1.02681i	−0.0271788	+	0.999631i	$0.508652\pi$
$73$	−8.77306	+	8.77306i	−1.02681	+	1.02681i	−0.999631	+	0.0271788i	$0.991348\pi$
$74$	−0.632748	+	8.49352i	−0.0735554	+	0.987352i
$75$	−0.262345	−	0.515231i	−0.0302930	−	0.0594937i
$76$	1.97792	+	0.296346i	0.226883	+	0.0339932i
$77$	2.88227	−	2.88227i	0.328465	−	0.328465i
$78$	0.251414	−	0.216552i	0.0284670	−	0.0245196i
$79$	0.712885			0.0802058			0.0401029	−	0.999196i	$-0.487231\pi$
$79$	0.712885			0.0802058			0.0401029	+	0.999196i	$0.487231\pi$
$80$	−8.45951	+	2.90459i	−0.945802	+	0.324743i
$81$	−8.87984			−0.986648
$82$	5.57116	−	4.79863i	0.615232	−	0.529920i
$83$	12.4110	−	12.4110i	1.36228	−	1.36228i	0.491276	−	0.871004i	$-0.336531\pi$
$83$	12.4110	−	12.4110i	1.36228	−	1.36228i	0.871004	−	0.491276i	$-0.163469\pi$
$84$	−0.554394	−	0.0830631i	−0.0604894	−	0.00906293i
$85$	14.2251	+	2.25505i	1.54293	+	0.244594i
$86$	−0.342403	+	4.59615i	−0.0369222	+	0.495616i
$87$	−0.0408071	+	0.0408071i	−0.00437498	+	0.00437498i
$88$	2.53585	+	4.02399i	0.270322	+	0.428959i
$89$			11.2344i			1.19085i	0.803411	+	0.595424i	$0.203016\pi$
$89$			11.2344i			1.19085i	−0.803411	+	0.595424i	$0.796984\pi$
$90$	−9.19243	−	2.16765i	−0.968967	−	0.228490i
$91$	−4.91829			−0.515577
$92$	−0.662759	+	0.490039i	−0.0690974	+	0.0510901i
$93$	−0.168417	−	0.168417i	−0.0174640	−	0.0174640i
$94$	−1.27669	+	17.1373i	−0.131681	+	1.76758i
$95$	1.31408	+	1.80920i	0.134822	+	0.185620i
$96$	0.237642	−	0.609438i	0.0242543	−	0.0622005i
$97$	9.74041	+	9.74041i	0.988989	+	0.988989i	0.999940	−	0.0109510i	$-0.00348589\pi$
$97$	9.74041	+	9.74041i	0.988989	+	0.988989i	−0.0109510	+	0.999940i	$0.503486\pi$
$98$	−1.03794	−	1.20504i	−0.104848	−	0.121727i
$99$			5.02241i			0.504771i
$100$	−8.94648	−	4.46773i	−0.894648	−	0.446773i
$101$			1.46784i			0.146056i	0.997330	+	0.0730280i	$0.0232662\pi$
$101$			1.46784i			0.146056i	−0.997330	+	0.0730280i	$0.976734\pi$
$102$	−0.798096	+	0.687428i	−0.0790233	+	0.0680655i
$103$	−8.41368	−	8.41368i	−0.829024	−	0.829024i	0.158357	−	0.987382i	$-0.449380\pi$
$103$	−8.41368	−	8.41368i	−0.829024	−	0.829024i	−0.987382	+	0.158357i	$0.949380\pi$
$104$	1.26968	−	5.59685i	0.124503	−	0.548816i
$105$	−0.368325	−	0.507102i	−0.0359448	−	0.0494881i
$106$	4.07171	+	0.303333i	0.395479	+	0.0294623i
$107$	−9.42506	−	9.42506i	−0.911155	−	0.911155i	0.0852081	−	0.996363i	$-0.472844\pi$
$107$	−9.42506	−	9.42506i	−0.911155	−	0.911155i	−0.996363	+	0.0852081i	$0.972844\pi$
$108$	1.11327	−	0.823141i	0.107124	−	0.0792068i
$109$	−11.3511			−1.08724			−0.543618	−	0.839333i	$-0.682946\pi$
$109$	−11.3511			−1.08724			−0.543618	+	0.839333i	$0.682946\pi$
$110$	−1.22050	+	5.17583i	−0.116370	+	0.493496i
$111$		−	0.696410i		−	0.0661003i
$112$	−8.56413	+	4.54556i	−0.809235	+	0.429515i
$113$	11.3207	−	11.3207i	1.06497	−	1.06497i	0.0672281	−	0.997738i	$-0.478584\pi$
$113$	11.3207	−	11.3207i	1.06497	−	1.06497i	0.997738	−	0.0672281i	$-0.0214155\pi$
$114$	−0.163081	−	0.0121492i	−0.0152739	−	0.00113787i
$115$	−0.910174	−	0.144286i	−0.0848742	−	0.0134547i
$116$	−0.147897	+	0.987119i	−0.0137319	+	0.0916517i
$117$	4.28511	−	4.28511i	0.396158	−	0.396158i
$118$	5.02665	+	5.83589i	0.462741	+	0.537237i
$119$	15.6128			1.43122
$120$	0.672149	−	0.288230i	0.0613585	−	0.0263117i
$121$	−8.17212			−0.742920
$122$	−6.04212	−	7.01483i	−0.547027	−	0.635093i
$123$	−0.425126	+	0.425126i	−0.0383323	+	0.0383323i
$124$	−4.07399	−	0.610393i	−0.365855	−	0.0548149i
$125$	−3.45053	−	10.6346i	−0.308625	−	0.951184i
$126$	−10.2097	−	0.760599i	−0.909553	−	0.0677596i
$127$	−7.06753	+	7.06753i	−0.627142	+	0.627142i	−0.947348	−	0.320206i	$-0.896248\pi$
$127$	−7.06753	+	7.06753i	−0.627142	+	0.627142i	0.320206	+	0.947348i	$0.396248\pi$
$128$	−2.96181	−	10.9191i	−0.261790	−	0.965125i
$129$		−	0.376853i		−	0.0331800i
$130$	5.45733	−	3.37468i	0.478640	−	0.295979i
$131$	9.57540			0.836607			0.418303	−	0.908307i	$-0.362625\pi$
$131$	9.57540			0.836607			0.418303	+	0.908307i	$0.362625\pi$
$132$	−0.231219	−	0.312714i	−0.0201250	−	0.0272183i
$133$	1.71397	+	1.71397i	0.148620	+	0.148620i
$134$	−5.11398	−	0.380979i	−0.441780	−	0.0329116i
$135$	1.52886	+	0.242363i	0.131583	+	0.0208593i
$136$	−4.03052	+	17.7668i	−0.345614	+	1.52349i
$137$	4.06617	+	4.06617i	0.347397	+	0.347397i	0.859139	−	0.511742i	$-0.171000\pi$
$137$	4.06617	+	4.06617i	0.347397	+	0.347397i	−0.511742	+	0.859139i	$0.671000\pi$
$138$	0.0510650	−	0.0439840i	0.00434694	−	0.00374417i
$139$		−	12.6520i		−	1.07313i	−0.843860	−	0.536564i	$-0.819722\pi$
$139$		−	12.6520i		−	1.07313i	0.843860	−	0.536564i	$-0.180278\pi$
$140$	−10.3368	−	3.26491i	−0.873615	−	0.275935i
$141$		−	1.40514i		−	0.118334i
$142$	−7.85937	−	9.12464i	−0.659544	−	0.765723i
$143$	−2.41274	−	2.41274i	−0.201764	−	0.201764i
$144$	3.50122	−	11.4219i	0.291768	−	0.951828i
$145$	−0.902913	+	0.655816i	−0.0749829	+	0.0544625i
$146$	1.30353	−	17.4976i	0.107881	−	1.44811i
$147$	0.0919542	+	0.0919542i	0.00758426	+	0.00758426i
$148$	−7.16105	−	9.68504i	−0.588634	−	0.796106i
$149$	6.93839			0.568415			0.284207	−	0.958763i	$-0.408270\pi$
$149$	6.93839			0.568415			0.284207	+	0.958763i	$0.408270\pi$
$150$	0.756640	+	0.309955i	0.0617794	+	0.0253077i
$151$		−	4.74419i		−	0.386076i	−0.981191	−	0.193038i	$-0.938166\pi$
$151$		−	4.74419i		−	0.386076i	0.981191	−	0.193038i	$-0.0618341\pi$
$152$	−2.39291	+	1.50797i	−0.194091	+	0.122313i
$153$	−13.6028	+	13.6028i	−1.09972	+	1.09972i
$154$	−0.428258	+	5.74861i	−0.0345100	+	0.463236i
$155$	−2.70665	−	3.72646i	−0.217403	−	0.299316i
$156$	−0.0695320	+	0.464082i	−0.00556702	+	0.0371563i
$157$	7.78145	−	7.78145i	0.621027	−	0.621027i	−0.324767	−	0.945794i	$-0.605286\pi$
$157$	7.78145	−	7.78145i	0.621027	−	0.621027i	0.945794	+	0.324767i	$0.105286\pi$
$158$	−0.763876	+	0.657953i	−0.0607707	+	0.0523439i
$159$	−0.333852			−0.0264762
$160$	6.38383	−	10.9200i	0.504686	−	0.863303i
$161$	−0.998960			−0.0787291
$162$	9.51500	−	8.19560i	0.747569	−	0.643907i
$163$	−4.91686	+	4.91686i	−0.385118	+	0.385118i	−0.872942	−	0.487824i	$-0.837791\pi$
$163$	−4.91686	+	4.91686i	−0.385118	+	0.385118i	0.487824	+	0.872942i	$0.337791\pi$
$164$	−1.54078	+	10.2837i	−0.120315	+	0.803025i
$165$	0.0680793	−	0.429454i	0.00529996	−	0.0334329i
$166$	−1.84407	+	24.7533i	−0.143127	+	1.92123i
$167$	−14.3698	+	14.3698i	−1.11197	+	1.11197i	−0.119088	+	0.992884i	$0.537997\pi$
$167$	−14.3698	+	14.3698i	−1.11197	+	1.11197i	−0.992884	+	0.119088i	$0.962003\pi$
$168$	0.670712	−	0.422671i	0.0517465	−	0.0326097i
$169$		−	8.88290i		−	0.683300i
$170$	−17.3239	+	10.7127i	−1.32868	+	0.821625i
$171$	−2.98663			−0.228393
$172$	−3.87510	−	5.24093i	−0.295474	−	0.399617i
$173$	−1.79071	−	1.79071i	−0.136145	−	0.136145i	0.635750	−	0.771895i	$-0.280691\pi$
$173$	−1.79071	−	1.79071i	−0.136145	−	0.136145i	−0.771895	+	0.635750i	$0.780691\pi$
$174$	0.00606326	−	0.0813886i	0.000459655	−	0.00617005i
$175$	−5.49922	−	10.8002i	−0.415702	−	0.816416i
$176$	−6.43116	−	1.97137i	−0.484767	−	0.148598i
$177$	−0.445326	−	0.445326i	−0.0334728	−	0.0334728i
$178$	−10.3688	−	12.0380i	−0.777172	−	0.902288i
$179$		−	10.4499i		−	0.781061i	−0.920590	−	0.390530i	$-0.872292\pi$
$179$		−	10.4499i		−	0.781061i	0.920590	−	0.390530i	$-0.127708\pi$
$180$	11.8506	−	6.16141i	0.883289	−	0.459245i
$181$			18.8451i			1.40074i	0.713778	+	0.700372i	$0.246983\pi$
$181$			18.8451i			1.40074i	−0.713778	+	0.700372i	$0.753017\pi$
$182$	5.27009	−	4.53931i	0.390645	−	0.336476i
$183$	0.535289	+	0.535289i	0.0395697	+	0.0395697i
$184$	0.257886	−	1.13678i	0.0190116	−	0.0838046i
$185$	2.10848	−	13.3006i	0.155018	−	0.977877i
$186$	0.335903	+	0.0250240i	0.0246296	+	0.00183485i
$187$	7.65909	+	7.65909i	0.560088	+	0.560088i
$188$	−14.4488	−	19.5414i	−1.05379	−	1.42521i
$189$	1.67800			0.122056
$190$	−3.07786	−	0.725784i	−0.223292	−	0.0526539i
$191$			20.8497i			1.50863i	0.656512	+	0.754316i	$0.272031\pi$
$191$			20.8497i			1.50863i	−0.656512	+	0.754316i	$0.727969\pi$
$192$	0.307837	+	0.872361i	0.0222162	+	0.0629572i
$193$	−15.9285	+	15.9285i	−1.14656	+	1.14656i	−0.159334	+	0.987225i	$0.550935\pi$
$193$	−15.9285	+	15.9285i	−1.14656	+	1.14656i	−0.987225	+	0.159334i	$0.949065\pi$
$194$	−19.4270	−	1.44727i	−1.39478	−	0.103908i
$195$	−0.424494	+	0.308324i	−0.0303987	+	0.0220795i
$196$	2.22436	+	0.333269i	0.158883	+	0.0238050i
$197$	2.47527	−	2.47527i	0.176356	−	0.176356i	−0.613409	−	0.789765i	$-0.710202\pi$
$197$	2.47527	−	2.47527i	0.176356	−	0.176356i	0.789765	+	0.613409i	$0.210202\pi$
$198$	−4.63540	−	5.38165i	−0.329424	−	0.382457i
$199$	−14.9416			−1.05918			−0.529591	−	0.848253i	$-0.677655\pi$
$199$	−14.9416			−1.05918			−0.529591	+	0.848253i	$0.677655\pi$
$200$	13.7099	−	3.46981i	0.969434	−	0.245353i
$201$	0.419311			0.0295759
$202$	−1.35474	−	1.57284i	−0.0953191	−	0.110664i
$203$	−0.855390	+	0.855390i	−0.0600366	+	0.0600366i
$204$	0.220725	−	1.47320i	0.0154538	−	0.103144i
$205$	−9.40650	+	6.83225i	−0.656978	+	0.477185i
$206$	16.7809	+	1.25013i	1.16918	+	0.0871010i
$207$	0.870353	−	0.870353i	0.0604937	−	0.0604937i
$208$	3.80508	+	7.16902i	0.263835	+	0.497082i
$209$			1.68163i			0.116321i
$210$	0.862697	+	0.203431i	0.0595318	+	0.0140381i
$211$	−2.53428			−0.174467			−0.0872337	−	0.996188i	$-0.527803\pi$
$211$	−2.53428			−0.174467			−0.0872337	+	0.996188i	$0.527803\pi$
$212$	−4.64291	+	3.43293i	−0.318876	+	0.235775i
$213$	0.696286	+	0.696286i	0.0477087	+	0.0477087i
$214$	18.7980	+	1.40041i	1.28501	+	0.0957300i
$215$	1.14097	−	7.19742i	0.0778137	−	0.490860i
$216$	−0.433184	+	1.90950i	−0.0294744	+	0.129925i
$217$	−3.53032	−	3.53032i	−0.239654	−	0.239654i
$218$	12.1630	−	10.4764i	0.823783	−	0.709553i
$219$			1.43469i			0.0969470i
$220$	−3.46920	−	6.67250i	−0.233894	−	0.449860i
$221$		−	13.0694i		−	0.879145i
$222$	0.642748	+	0.746223i	0.0431384	+	0.0500832i
$223$	−16.3266	−	16.3266i	−1.09331	−	1.09331i	−0.995173	−	0.0981371i	$-0.968712\pi$
$223$	−16.3266	−	16.3266i	−1.09331	−	1.09331i	−0.0981371	−	0.995173i	$-0.531288\pi$
$224$	4.98141	−	12.7749i	0.332835	−	0.853560i
$225$	14.2010	+	4.61850i	0.946733	+	0.307900i
$226$	−1.68208	+	22.5789i	−0.111890	+	1.50193i
$227$	−6.11132	−	6.11132i	−0.405623	−	0.405623i	0.474586	−	0.880209i	$-0.342598\pi$
$227$	−6.11132	−	6.11132i	−0.405623	−	0.405623i	−0.880209	+	0.474586i	$0.842598\pi$
$228$	0.185959	−	0.137497i	0.0123154	−	0.00910594i
$229$	−9.79993			−0.647597			−0.323799	−	0.946126i	$-0.604960\pi$
$229$	−9.79993			−0.647597			−0.323799	+	0.946126i	$0.604960\pi$
$230$	1.10845	−	0.685434i	0.0730887	−	0.0451962i
$231$		−	0.471346i		−	0.0310123i
$232$	−0.752581	−	1.19423i	−0.0494093	−	0.0784048i
$233$	−8.84565	+	8.84565i	−0.579498	+	0.579498i	−0.934765	−	0.355267i	$-0.884390\pi$
$233$	−8.84565	+	8.84565i	−0.579498	+	0.579498i	0.355267	+	0.934765i	$0.384390\pi$
$234$	−0.636697	+	8.54653i	−0.0416222	+	0.558704i
$235$	4.25425	−	26.8364i	0.277517	−	1.75062i
$236$	−10.7724	−	1.61400i	−0.701224	−	0.105062i
$237$	0.0582901	−	0.0582901i	0.00378635	−	0.00378635i
$238$	−16.7295	+	14.4097i	−1.08441	+	0.934044i
$239$	14.0518			0.908938			0.454469	−	0.890762i	$-0.349829\pi$
$239$	14.0518			0.908938			0.454469	+	0.890762i	$0.349829\pi$
$240$	−0.454207	+	0.929203i	−0.0293189	+	0.0599798i
$241$	−5.93439			−0.382268			−0.191134	−	0.981564i	$-0.561216\pi$
$241$	−5.93439			−0.382268			−0.191134	+	0.981564i	$0.561216\pi$
$242$	8.75666	−	7.54241i	0.562899	−	0.484845i
$243$	−2.19459	+	2.19459i	−0.140783	+	0.140783i
$244$	12.9486	+	1.94005i	0.828949	+	0.124199i
$245$	1.47781	+	2.03462i	0.0944137	+	0.129987i
$246$	0.0631667	−	0.847901i	0.00402736	−	0.0540602i
$247$	1.43476	−	1.43476i	0.0912918	−	0.0912918i
$248$	4.92875	−	3.10601i	0.312976	−	0.197232i
$249$		−	2.02960i		−	0.128621i
$250$	13.5125	+	8.21058i	0.854603	+	0.519283i
$251$	−14.3718			−0.907143			−0.453572	−	0.891220i	$-0.649850\pi$
$251$	−14.3718			−0.907143			−0.453572	+	0.891220i	$0.649850\pi$
$252$	11.6420	−	8.60799i	0.733376	−	0.542253i
$253$	−0.490055	−	0.490055i	−0.0308095	−	0.0308095i
$254$	1.05012	−	14.0960i	0.0658903	−	0.884462i
$255$	1.34753	−	0.978753i	0.0843854	−	0.0612919i
$256$	13.2514	+	8.96658i	0.828214	+	0.560411i
$257$	0.519722	+	0.519722i	0.0324193	+	0.0324193i	0.723131	−	0.690711i	$-0.242702\pi$
$257$	0.519722	+	0.519722i	0.0324193	+	0.0324193i	−0.690711	+	0.723131i	$0.742702\pi$
$258$	0.347814	+	0.403808i	0.0216540	+	0.0251400i
$259$		−	14.5980i		−	0.907076i
$260$	−2.73305	+	8.65288i	−0.169496	+	0.536629i
$261$		−	1.49053i		−	0.0922616i
$262$	−10.2603	+	8.83757i	−0.633884	+	0.545987i
$263$	−7.30132	−	7.30132i	−0.450219	−	0.450219i	0.445208	−	0.895427i	$-0.353130\pi$
$263$	−7.30132	−	7.30132i	−0.450219	−	0.450219i	−0.895427	+	0.445208i	$0.853130\pi$
$264$	0.536375	+	0.121680i	0.0330116	+	0.00748891i
$265$	−6.37616	−	1.01078i	−0.391684	−	0.0620918i
$266$	−3.41847	−	0.254668i	−0.209600	−	0.0156147i
$267$	0.918601	+	0.918601i	0.0562175	+	0.0562175i
$268$	5.83140	−	4.31169i	0.356209	−	0.263378i
$269$	−31.3080			−1.90888			−0.954441	−	0.298399i	$-0.903548\pi$
$269$	−31.3080			−1.90888			−0.954441	+	0.298399i	$0.903548\pi$
$270$	−1.86191	+	1.15136i	−0.113312	+	0.0700693i
$271$			5.69225i			0.345779i	0.984941	+	0.172890i	$0.0553104\pi$
$271$			5.69225i			0.345779i	−0.984941	+	0.172890i	$0.944690\pi$
$272$	−12.0790	−	22.7576i	−0.732395	−	1.37988i
$273$	−0.402151	+	0.402151i	−0.0243393	+	0.0243393i
$274$	−8.10987	−	0.604167i	−0.489935	−	0.0364990i
$275$	2.60046	−	7.99592i	0.156814	−	0.482172i
$276$	−0.0141227	+	0.0942603i	−0.000850088	+	0.00567380i
$277$	2.91549	−	2.91549i	0.175175	−	0.175175i	−0.614074	−	0.789249i	$-0.710470\pi$
$277$	2.91549	−	2.91549i	0.175175	−	0.175175i	0.789249	+	0.614074i	$0.210470\pi$
$278$	11.6771	+	13.5570i	0.700345	+	0.813092i
$279$	6.15165			0.368289
$280$	14.0895	−	6.04181i	0.842006	−	0.361067i
$281$	4.42798			0.264151			0.132076	−	0.991240i	$-0.457836\pi$
$281$	4.42798			0.264151			0.132076	+	0.991240i	$0.457836\pi$
$282$	1.29687	+	1.50565i	0.0772273	+	0.0896600i
$283$	−13.5718	+	13.5718i	−0.806757	+	0.806757i	−0.984142	−	0.177385i	$-0.943236\pi$
$283$	−13.5718	+	13.5718i	−0.806757	+	0.806757i	0.177385	+	0.984142i	$0.443236\pi$
$284$	16.8431	+	2.52355i	0.999453	+	0.149745i
$285$	0.255379	+	0.0404841i	0.0151274	+	0.00239807i
$286$	4.81215	+	0.358494i	0.284549	+	0.0211982i
$287$	−8.91140	+	8.91140i	−0.526023	+	0.526023i
$288$	6.79016	+	15.4704i	0.400114	+	0.911600i
$289$			24.4880i			1.44047i
$290$	0.362216	−	1.53606i	0.0212700	−	0.0902008i
$291$	1.59288			0.0933762
$292$	14.7526	+	19.9523i	0.863330	+	1.16762i
$293$	19.6405	+	19.6405i	1.14741	+	1.14741i	0.987060	+	0.160349i	$0.0512620\pi$
$293$	19.6405	+	19.6405i	1.14741	+	1.14741i	0.160349	+	0.987060i	$0.448738\pi$
$294$	−0.183400	−	0.0136629i	−0.0106961	−	0.000796836i
$295$	−7.15690	−	9.85347i	−0.416691	−	0.573691i
$296$	16.6120	+	3.76855i	0.965554	+	0.219042i
$297$	0.823168	+	0.823168i	0.0477650	+	0.0477650i
$298$	−7.43468	+	6.40375i	−0.430679	+	0.370959i
$299$			0.836228i			0.0483603i
$300$	−1.09683	+	0.366212i	−0.0633256	+	0.0211432i
$301$		−	7.89951i		−	0.455320i
$302$	4.37862	+	5.08353i	0.251961	+	0.292524i
$303$	0.120020	+	0.120020i	0.00689500	+	0.00689500i
$304$	1.17230	−	3.82436i	0.0672360	−	0.219342i
$305$	8.60270	+	11.8440i	0.492589	+	0.678187i
$306$	2.02115	−	27.1304i	0.115541	−	1.55094i
$307$	24.5418	+	24.5418i	1.40068	+	1.40068i	0.797944	+	0.602731i	$0.205921\pi$
$307$	24.5418	+	24.5418i	1.40068	+	1.40068i	0.602731	+	0.797944i	$0.294079\pi$
$308$	−4.84676	−	6.55506i	−0.276170	−	0.373509i
$309$	−1.37591			−0.0782730
$310$	6.33956	+	1.49492i	0.360063	+	0.0849056i
$311$			21.7682i			1.23436i	0.786821	+	0.617181i	$0.211725\pi$
$311$			21.7682i			1.23436i	−0.786821	+	0.617181i	$0.788275\pi$
$312$	−0.353817	−	0.561452i	−0.0200309	−	0.0317859i
$313$	−14.2831	+	14.2831i	−0.807326	+	0.807326i	−0.984228	−	0.176902i	$-0.943392\pi$
$313$	−14.2831	+	14.2831i	−0.807326	+	0.807326i	0.176902	+	0.984228i	$0.443392\pi$
$314$	−1.15620	+	15.5199i	−0.0652479	+	0.875838i
$315$	15.9881	+	2.53451i	0.900825	+	0.142803i
$316$	0.211261	−	1.41003i	0.0118843	−	0.0793204i
$317$	−14.6113	+	14.6113i	−0.820651	+	0.820651i	−0.986201	−	0.165550i	$-0.947060\pi$
$317$	−14.6113	+	14.6113i	−0.820651	+	0.820651i	0.165550	+	0.986201i	$0.447060\pi$
$318$	0.357732	−	0.308127i	0.0200606	−	0.0172789i
$319$	−0.839249			−0.0469889
$320$	3.23811	+	17.5930i	0.181016	+	0.983480i
$321$	−1.54131			−0.0860274
$322$	1.07041	−	0.921985i	0.0596518	−	0.0513802i
$323$	−4.55456	+	4.55456i	−0.253422	+	0.253422i
$324$	−2.63150	+	17.5636i	−0.146195	+	0.975757i
$325$	−9.04081	+	4.60339i	−0.501494	+	0.255350i
$326$	0.730564	−	9.80654i	0.0404622	−	0.543134i
$327$	−0.928138	+	0.928138i	−0.0513261	+	0.0513261i
$328$	−7.84034	−	12.4414i	−0.432910	−	0.686960i
$329$		−	29.4543i		−	1.62387i
$330$	0.323413	+	0.523005i	0.0178033	+	0.0287905i
$331$	14.0460			0.772037			0.386019	−	0.922491i	$-0.373850\pi$
$331$	14.0460			0.772037			0.386019	+	0.922491i	$0.373850\pi$
$332$	−20.8700	−	28.2259i	−1.14539	−	1.54910i
$333$	12.7186	+	12.7186i	0.696978	+	0.696978i
$334$	2.13512	−	28.6603i	0.116829	−	1.56822i
$335$	8.00832	+	1.26952i	0.437541	+	0.0693613i
$336$	−0.328585	+	1.07193i	−0.0179258	+	0.0584788i
$337$	7.29058	+	7.29058i	0.397143	+	0.397143i	0.877224	−	0.480081i	$-0.159393\pi$
$337$	7.29058	+	7.29058i	0.397143	+	0.397143i	−0.480081	+	0.877224i	$0.659393\pi$
$338$	8.19843	+	9.51828i	0.445936	+	0.517726i
$339$		−	1.85131i		−	0.100550i
$340$	8.67587	−	27.4680i	0.470515	−	1.48966i
$341$		−	3.46370i		−	0.187570i
$342$	3.20026	−	2.75649i	0.173050	−	0.149054i
$343$	13.9253	+	13.9253i	0.751897	+	0.751897i
$344$	8.98937	+	2.03930i	0.484674	+	0.109952i
$345$	−0.0862195	+	0.0626240i	−0.00464190	+	0.00337156i
$346$	3.57152	+	0.266070i	0.192006	+	0.0143040i
$347$	10.3952	+	10.3952i	0.558042	+	0.558042i	0.928749	−	0.370708i	$-0.120885\pi$
$347$	10.3952	+	10.3952i	0.558042	+	0.558042i	−0.370708	+	0.928749i	$0.620885\pi$
$348$	0.0686202	+	0.0928063i	0.00367843	+	0.00497494i
$349$	−27.2478			−1.45854			−0.729269	−	0.684227i	$-0.760140\pi$
$349$	−27.2478			−1.45854			−0.729269	+	0.684227i	$0.760140\pi$
$350$	15.8605	+	6.49721i	0.847781	+	0.347290i
$351$		−	1.40465i		−	0.0749747i
$352$	8.71064	−	3.82322i	0.464279	−	0.203778i
$353$	14.4723	−	14.4723i	0.770280	−	0.770280i	−0.207875	−	0.978155i	$-0.566655\pi$
$353$	14.4723	−	14.4723i	0.770280	−	0.770280i	0.978155	+	0.207875i	$0.0666548\pi$
$354$	0.888192	+	0.0661682i	0.0472069	+	0.00351680i
$355$	11.1901	+	15.4063i	0.593908	+	0.817681i
$356$	22.2209	+	3.32928i	1.17770	+	0.176452i
$357$	1.27660	−	1.27660i	0.0675649	−	0.0675649i
$358$	9.64466	+	11.1973i	0.509736	+	0.591798i
$359$	−0.139983			−0.00738804			−0.00369402	−	0.999993i	$-0.501176\pi$
$359$	−0.139983			−0.00738804			−0.00369402	+	0.999993i	$0.501176\pi$
$360$	−7.01158	+	17.5395i	−0.369543	+	0.924415i
$361$	−1.00000			−0.0526316
$362$	−17.3930	−	20.1931i	−0.914155	−	1.06132i
$363$	−0.668205	+	0.668205i	−0.0350717	+	0.0350717i
$364$	−1.45752	+	9.72800i	−0.0763946	+	0.509886i
$365$	−4.34370	+	27.4007i	−0.227360	+	1.43422i
$366$	−1.06762	−	0.0795352i	−0.0558054	−	0.00415737i
$367$	−6.97245	+	6.97245i	−0.363959	+	0.363959i	−0.865268	−	0.501309i	$-0.832852\pi$
$367$	−6.97245	+	6.97245i	−0.363959	+	0.363959i	0.501309	+	0.865268i	$0.332852\pi$
$368$	0.772854	+	1.45611i	0.0402878	+	0.0759049i
$369$		−	15.5283i		−	0.808369i
$370$	10.0164	+	16.1979i	0.520728	+	0.842091i
$371$	−6.99814			−0.363325
$372$	−0.383025	+	0.283206i	−0.0198589	+	0.0146835i
$373$	−9.67996	−	9.67996i	−0.501209	−	0.501209i	0.410604	−	0.911814i	$-0.365318\pi$
$373$	−9.67996	−	9.67996i	−0.501209	−	0.501209i	−0.911814	+	0.410604i	$0.865318\pi$
$374$	−15.2758	−	1.13801i	−0.789895	−	0.0588453i
$375$	−1.15169	−	0.587412i	−0.0594729	−	0.0303338i
$376$	33.5179	+	7.60377i	1.72856	+	0.392134i
$377$	0.716045	+	0.716045i	0.0368782	+	0.0368782i
$378$	−1.79802	+	1.54870i	−0.0924803	+	0.0796565i
$379$			8.50054i			0.436643i	0.975877	+	0.218322i	$0.0700582\pi$
$379$			8.50054i			0.436643i	−0.975877	+	0.218322i	$0.929942\pi$
$380$	3.96788	−	2.06300i	0.203548	−	0.105830i
$381$			1.15577i			0.0592121i
$382$	−19.2431	−	22.3410i	−0.984564	−	1.14307i
$383$	−8.55363	−	8.55363i	−0.437070	−	0.437070i	0.453955	−	0.891025i	$-0.350013\pi$
$383$	−8.55363	−	8.55363i	−0.437070	−	0.437070i	−0.891025	+	0.453955i	$0.850013\pi$
$384$	−1.13500	−	0.650643i	−0.0579201	−	0.0332030i
$385$	1.42706	−	9.00213i	0.0727299	−	0.458791i
$386$	2.36671	−	31.7690i	0.120463	−	1.61700i
$387$	6.88252	+	6.88252i	0.349858	+	0.349858i
$388$	22.1523	−	16.3793i	1.12461	−	0.831531i
$389$	−11.0464			−0.560072			−0.280036	−	0.959989i	$-0.590346\pi$
$389$	−11.0464			−0.560072			−0.280036	+	0.959989i	$0.590346\pi$
$390$	0.170292	−	0.722163i	0.00862305	−	0.0365681i
$391$		−	2.65455i		−	0.134246i
$392$	−2.69106	+	1.69586i	−0.135919	+	0.0856537i
$393$	0.782947	−	0.782947i	0.0394945	−	0.0394945i
$394$	−0.367785	+	4.93686i	−0.0185287	+	0.248715i
$395$	1.28975	−	0.936787i	0.0648943	−	0.0471349i
$396$	9.93393	+	1.48837i	0.499199	+	0.0747934i
$397$	−5.91962	+	5.91962i	−0.297097	+	0.297097i	−0.839876	−	0.542779i	$-0.817372\pi$
$397$	−5.91962	+	5.91962i	−0.297097	+	0.297097i	0.542779	+	0.839876i	$0.317372\pi$
$398$	16.0103	−	13.7903i	0.802526	−	0.691244i
$399$	0.280291			0.0140321
$400$	−11.4881	+	16.3714i	−0.574403	+	0.818572i
$401$	12.0790			0.603197			0.301599	−	0.953435i	$-0.402480\pi$
$401$	12.0790			0.603197			0.301599	+	0.953435i	$0.402480\pi$
$402$	−0.449303	+	0.387001i	−0.0224092	+	0.0193018i
$403$	−2.95523	+	2.95523i	−0.147210	+	0.147210i
$404$	2.90328	+	0.434990i	0.144444	+	0.0216415i
$405$	−16.0654	+	11.6688i	−0.798295	+	0.579828i
$406$	0.127097	−	1.70605i	0.00630771	−	0.0846699i
$407$	7.16128	−	7.16128i	0.354971	−	0.354971i
$408$	1.12317	+	1.78229i	0.0556051	+	0.0882365i
$409$			4.33801i			0.214501i	0.994232	+	0.107250i	$0.0342047\pi$
$409$			4.33801i			0.214501i	−0.994232	+	0.107250i	$0.965795\pi$
$410$	3.77354	−	16.0026i	0.186362	−	0.790313i
$411$	0.664953			0.0327997
$412$	−19.1350	+	14.1482i	−0.942712	+	0.697034i
$413$	−9.33484	−	9.33484i	−0.459338	−	0.459338i
$414$	−0.129320	+	1.73590i	−0.00635574	+	0.0853146i
$415$	6.14489	−	38.7629i	0.301641	−	1.90279i
$416$	−10.6939	−	4.16993i	−0.524310	−	0.204448i
$417$	−1.03451	−	1.03451i	−0.0506601	−	0.0506601i
$418$	−1.55205	−	1.80192i	−0.0759134	−	0.0881346i
$419$		−	10.9004i		−	0.532519i	−0.963901	−	0.266260i	$-0.914212\pi$
$419$		−	10.9004i		−	0.532519i	0.963901	−	0.266260i	$-0.0857879\pi$
$420$	−1.11216	+	0.578240i	−0.0542678	+	0.0282152i
$421$		−	27.0805i		−	1.31982i	−0.751343	−	0.659912i	$-0.770594\pi$
$421$		−	27.0805i		−	1.31982i	0.751343	−	0.659912i	$-0.229406\pi$
$422$	2.71556	−	2.33900i	0.132191	−	0.113861i
$423$	25.6623	+	25.6623i	1.24774	+	1.24774i
$424$	1.80660	−	7.96364i	0.0877364	−	0.386748i
$425$	28.6994	−	14.6132i	1.39213	−	0.708842i
$426$	−1.38872	−	0.103457i	−0.0672838	−	0.00501249i
$427$	11.2206	+	11.2206i	0.543004	+	0.543004i
$428$	−21.4351	+	15.8490i	−1.03611	+	0.766089i
$429$	−0.394563			−0.0190497
$430$	5.42024	+	8.76530i	0.261387	+	0.422700i
$431$			23.8909i			1.15078i	0.817878	+	0.575392i	$0.195151\pi$
$431$			23.8909i			1.15078i	−0.817878	+	0.575392i	$0.804849\pi$
$432$	−1.29820	−	2.44589i	−0.0624596	−	0.117678i
$433$	23.7413	−	23.7413i	1.14093	−	1.14093i	0.152653	−	0.988280i	$-0.451218\pi$
$433$	23.7413	−	23.7413i	1.14093	−	1.14093i	0.988280	−	0.152653i	$-0.0487818\pi$
$434$	7.04113	+	0.524548i	0.337985	+	0.0251791i
$435$	−0.0202043	+	0.127452i	−0.000968723	+	0.00611085i
$436$	−3.36385	+	22.4516i	−0.161099	+	1.07523i
$437$	0.291416	−	0.291416i	0.0139403	−	0.0139403i
$438$	−1.32414	−	1.53731i	−0.0632696	−	0.0734553i
$439$	15.6214			0.745570			0.372785	−	0.927918i	$-0.378403\pi$
$439$	15.6214			0.745570			0.372785	+	0.927918i	$0.378403\pi$
$440$	9.87570	+	3.94789i	0.470806	+	0.188208i
$441$	−3.35875			−0.159940
$442$	12.0624	+	14.0043i	0.573748	+	0.666115i
$443$	6.06453	−	6.06453i	0.288135	−	0.288135i	−0.548208	−	0.836342i	$-0.684690\pi$
$443$	6.06453	−	6.06453i	0.288135	−	0.288135i	0.836342	+	0.548208i	$0.184690\pi$
$444$	−1.37745	−	0.206378i	−0.0653707	−	0.00979428i
$445$	14.7630	+	20.3253i	0.699831	+	0.963513i
$446$	32.5630	+	2.42586i	1.54190	+	0.114868i
$447$	0.567327	−	0.567327i	0.0268337	−	0.0268337i
$448$	6.45281	+	18.2863i	0.304867	+	0.863944i
$449$			6.33217i			0.298833i	0.988774	+	0.149417i	$0.0477396\pi$
$449$			6.33217i			0.298833i	−0.988774	+	0.149417i	$0.952260\pi$
$450$	−19.4794	+	8.15788i	−0.918267	+	0.384566i
$451$	−8.74324			−0.411703
$452$	−19.0367	−	25.7464i	−0.895411	−	1.21101i
$453$	−0.387915	−	0.387915i	−0.0182259	−	0.0182259i
$454$	12.1889	+	0.908042i	0.572052	+	0.0426165i
$455$	−8.89816	+	6.46303i	−0.417152	+	0.302991i
$456$	−0.0723585	+	0.318961i	−0.00338850	+	0.0149367i
$457$	6.32435	+	6.32435i	0.295840	+	0.295840i	0.839382	−	0.543542i	$-0.182917\pi$
$457$	6.32435	+	6.32435i	0.295840	+	0.295840i	−0.543542	+	0.839382i	$0.682917\pi$
$458$	10.5009	−	9.04479i	0.490675	−	0.422635i
$459$			4.45896i			0.208127i
$460$	−0.555112	+	1.75750i	−0.0258822	+	0.0819437i
$461$		−	23.1523i		−	1.07831i	−0.842207	−	0.539154i	$-0.818744\pi$
$461$		−	23.1523i		−	1.07831i	0.842207	−	0.539154i	$-0.181256\pi$
$462$	0.435026	+	0.505061i	0.0202393	+	0.0234975i
$463$	−19.9330	−	19.9330i	−0.926363	−	0.926363i	0.0711059	−	0.997469i	$-0.477347\pi$
$463$	−19.9330	−	19.9330i	−0.926363	−	0.926363i	−0.997469	+	0.0711059i	$0.977347\pi$
$464$	1.90862	+	0.585057i	0.0886053	+	0.0271606i
$465$	−0.526012	−	0.0833862i	−0.0243932	−	0.00386694i
$466$	1.31432	−	17.6424i	0.0608846	−	0.817269i
$467$	−11.5957	−	11.5957i	−0.536585	−	0.536585i	0.385939	−	0.922524i	$-0.373878\pi$
$467$	−11.5957	−	11.5957i	−0.536585	−	0.536585i	−0.922524	+	0.385939i	$0.873878\pi$
$468$	−7.20574	−	9.74549i	−0.333085	−	0.450485i
$469$	8.78951			0.405862
$470$	20.2100	+	32.6825i	0.932218	+	1.50753i
$471$		−	1.27252i		−	0.0586348i
$472$	13.0326	−	8.21289i	0.599872	−	0.378029i
$473$	3.87523	−	3.87523i	0.178183	−	0.178183i
$474$	−0.00866095	+	0.116258i	−0.000397811	+	0.00533991i
$475$	4.75486	+	1.54639i	0.218168	+	0.0709533i
$476$	4.62678	−	30.8809i	0.212068	−	1.41542i
$477$	6.09719	−	6.09719i	0.279171	−	0.279171i
$478$	−15.0570	+	12.9691i	−0.688689	+	0.593192i
$479$	−25.2035			−1.15158			−0.575788	−	0.817599i	$-0.695305\pi$
$479$	−25.2035			−1.15158			−0.575788	+	0.817599i	$0.695305\pi$
$480$	−0.370908	−	1.41487i	−0.0169295	−	0.0645799i
$481$	−12.2200			−0.557183
$482$	6.35887	−	5.47711i	0.289638	−	0.249476i
$483$	−0.0816814	+	0.0816814i	−0.00371663	+	0.00371663i
$484$	−2.42177	+	16.1638i	−0.110081	+	0.734719i
$485$	30.4220	+	4.82266i	1.38139	+	0.218985i
$486$	0.326080	−	4.37705i	0.0147913	−	0.198547i
$487$	11.7968	−	11.7968i	0.534566	−	0.534566i	−0.387362	−	0.921928i	$-0.626614\pi$
$487$	11.7968	−	11.7968i	0.534566	−	0.534566i	0.921928	+	0.387362i	$0.126614\pi$
$488$	−15.6653	+	9.87202i	−0.709137	+	0.446885i
$489$			0.804068i			0.0363612i
$490$	−3.46135	−	0.816213i	−0.156368	−	0.0368727i
$491$	−26.2767			−1.18585			−0.592926	−	0.805257i	$-0.702027\pi$
$491$	−26.2767			−1.18585			−0.592926	+	0.805257i	$0.702027\pi$
$492$	0.714881	+	0.966850i	0.0322293	+	0.0435890i
$493$	−2.27304	−	2.27304i	−0.102372	−	0.102372i
$494$	−0.213182	+	2.86160i	−0.00959153	+	0.128749i
$495$	6.59984	+	9.08653i	0.296641	+	0.408409i
$496$	−2.41462	+	7.87714i	−0.108420	+	0.353694i
$497$	14.5954	+	14.5954i	0.654693	+	0.654693i
$498$	1.87321	+	2.17478i	0.0839405	+	0.0974540i
$499$			28.6015i			1.28038i	0.768217	+	0.640190i	$0.221144\pi$
$499$			28.6015i			1.28038i	−0.768217	+	0.640190i	$0.778856\pi$
$500$	−22.0569	+	3.67338i	−0.986414	+	0.164279i
$501$			2.34994i			0.104988i
$502$	15.3998	−	13.2644i	0.687329	−	0.592020i
$503$	−26.7711	−	26.7711i	−1.19366	−	1.19366i	−0.976031	−	0.217632i	$-0.930167\pi$
$503$	−26.7711	−	26.7711i	−1.19366	−	1.19366i	−0.217632	−	0.976031i	$-0.569833\pi$
$504$	−4.53001	+	19.9686i	−0.201783	+	0.889473i
$505$	1.92886	+	2.65562i	0.0858333	+	0.118174i
$506$	0.977401	+	0.0728141i	0.0434508	+	0.00323698i
$507$	−0.726324	−	0.726324i	−0.0322572	−	0.0322572i
$508$	11.8846	+	16.0735i	0.527294	+	0.713145i
$509$	−10.8890			−0.482645			−0.241323	−	0.970445i	$-0.577581\pi$
$509$	−10.8890			−0.482645			−0.241323	+	0.970445i	$0.577581\pi$
$510$	−0.540579	+	2.29246i	−0.0239372	+	0.101512i
$511$			30.0736i			1.33038i
$512$	−22.4749	+	2.62239i	−0.993262	+	0.115894i
$513$	−0.489506	+	0.489506i	−0.0216122	+	0.0216122i
$514$	−1.03657	−	0.0772221i	−0.0457212	−	0.00340612i
$515$	−26.2783	−	4.16577i	−1.15796	−	0.183566i
$516$	−0.745386	−	0.111679i	−0.0328138	−	0.00491639i
$517$	14.4492	−	14.4492i	0.635477	−	0.635477i
$518$	13.4732	+	15.6422i	0.591976	+	0.687278i
$519$	−0.292840			−0.0128543
$520$	−5.05759	−	11.7943i	−0.221790	−	0.517213i
$521$	18.3820			0.805332			0.402666	−	0.915347i	$-0.368084\pi$
$521$	18.3820			0.805332			0.402666	+	0.915347i	$0.368084\pi$
$522$	1.37568	+	1.59715i	0.0602118	+	0.0699052i
$523$	−25.6420	+	25.6420i	−1.12125	+	1.12125i	−0.129691	+	0.991555i	$0.541398\pi$
$523$	−25.6420	+	25.6420i	−1.12125	+	1.12125i	−0.991555	+	0.129691i	$0.958602\pi$
$524$	2.83763	−	18.9394i	0.123963	−	0.827372i
$525$	−1.33274	−	0.433440i	−0.0581657	−	0.0189169i
$526$	14.5623	+	1.08486i	0.634946	+	0.0473020i
$527$	9.38116	−	9.38116i	0.408650	−	0.408650i
$528$	−0.687046	+	0.364661i	−0.0298998	+	0.0158698i
$529$		−	22.8302i		−	0.992615i
$530$	7.76513	−	4.80176i	0.337296	−	0.208575i
$531$	16.2661			0.705890
$532$	3.89803	−	2.88218i	0.169001	−	0.124958i
$533$	7.45972	+	7.45972i	0.323116	+	0.323116i
$534$	−1.83213	−	0.136489i	−0.0792838	−	0.00590646i
$535$	−29.4371	−	4.66652i	−1.27268	−	0.201751i
$536$	−2.26905	+	10.0022i	−0.0980082	+	0.432027i
$537$	−0.854450	−	0.854450i	−0.0368722	−	0.0368722i
$538$	33.5474	−	28.8956i	1.44633	−	1.24578i
$539$			1.89115i			0.0814578i
$540$	0.932447	−	2.95215i	0.0401261	−	0.127040i
$541$			28.0784i			1.20719i	0.797293	+	0.603593i	$0.206265\pi$
$541$			28.0784i			1.20719i	−0.797293	+	0.603593i	$0.793735\pi$
$542$	−5.25363	−	6.09941i	−0.225663	−	0.261992i
$543$	1.54090	+	1.54090i	0.0661262	+	0.0661262i
$544$	33.9469	+	13.2372i	1.45546	+	0.567539i
$545$	−20.5363	+	14.9162i	−0.879680	+	0.638941i
$546$	0.0597531	−	0.802080i	0.00255720	−	0.0343259i
$547$	−1.79355	−	1.79355i	−0.0766867	−	0.0766867i	0.667723	−	0.744410i	$-0.267269\pi$
$547$	−1.79355	−	1.79355i	−0.0766867	−	0.0766867i	−0.744410	+	0.667723i	$0.767269\pi$
$548$	9.24757	−	6.83758i	0.395037	−	0.292087i
$549$	−19.5521			−0.834465
$550$	4.59332	+	10.9679i	0.195860	+	0.467674i
$551$		−	0.499068i		−	0.0212610i
$552$	−0.0718641	−	0.114037i	−0.00305874	−	0.00485374i
$553$	1.22186	−	1.22186i	0.0519590	−	0.0519590i
$554$	−0.433194	+	5.81486i	−0.0184046	+	0.247050i
$555$	−0.915138	−	1.25994i	−0.0388454	−	0.0534816i
$556$	−25.0246	−	3.74936i	−1.06128	−	0.159008i
$557$	0.959844	−	0.959844i	0.0406699	−	0.0406699i	−0.686479	−	0.727149i	$-0.740845\pi$
$557$	0.959844	−	0.959844i	0.0406699	−	0.0406699i	0.727149	+	0.686479i	$0.240845\pi$
$558$	−6.59166	+	5.67763i	−0.279047	+	0.240353i
$559$	−6.61267			−0.279686
$560$	−9.52099	+	19.4778i	−0.402335	+	0.823086i
$561$	1.25251			0.0528812
$562$	−4.74471	+	4.08678i	−0.200143	+	0.172390i
$563$	−6.16317	+	6.16317i	−0.259747	+	0.259747i	−0.824951	−	0.565204i	$-0.808797\pi$
$563$	−6.16317	+	6.16317i	−0.259747	+	0.259747i	0.565204	+	0.824951i	$0.308797\pi$
$564$	−2.77926	−	0.416408i	−0.117028	−	0.0175339i
$565$	5.60510	−	35.3578i	0.235809	−	1.48751i
$566$	2.01654	−	27.0685i	0.0847615	−	1.13777i
$567$	−15.2198	+	15.2198i	−0.639171	+	0.639171i
$568$	−20.3769	+	12.8412i	−0.854997	+	0.538804i
$569$			10.4809i			0.439382i	0.975570	+	0.219691i	$0.0705049\pi$
$569$			10.4809i			0.439382i	−0.975570	+	0.219691i	$0.929495\pi$
$570$	−0.311011	+	0.192321i	−0.0130268	+	0.00805545i
$571$	−10.5243			−0.440429			−0.220214	−	0.975451i	$-0.570676\pi$
$571$	−10.5243			−0.440429			−0.220214	+	0.975451i	$0.570676\pi$
$572$	−5.48723	+	4.05721i	−0.229433	+	0.169641i
$573$	1.70481	+	1.70481i	0.0712193	+	0.0712193i
$574$	1.32409	−	17.7735i	0.0552663	−	0.741853i
$575$	−1.83629	+	0.935000i	−0.0765785	+	0.0389922i
$576$	−21.5541	−	10.3100i	−0.898089	−	0.429583i
$577$	1.18895	+	1.18895i	0.0494965	+	0.0494965i	0.731422	−	0.681925i	$-0.238857\pi$
$577$	1.18895	+	1.18895i	0.0494965	+	0.0494965i	−0.681925	+	0.731422i	$0.738857\pi$
$578$	−22.6011	−	26.2396i	−0.940081	−	1.09142i
$579$			2.60484i			0.108253i
$580$	1.02958	+	1.98024i	0.0427509	+	0.0822251i
$581$		−	42.5441i		−	1.76503i
$582$	−1.70681	+	1.47014i	−0.0707497	+	0.0609392i
$583$	−3.43304	−	3.43304i	−0.142182	−	0.142182i
$584$	−34.2227	−	7.76364i	−1.41614	−	0.321262i
$585$	2.12163	−	13.3836i	0.0877188	−	0.553343i
$586$	−39.1724	−	2.91825i	−1.61820	−	0.120552i
$587$	13.0363	+	13.0363i	0.538067	+	0.538067i	0.922961	−	0.384894i	$-0.125762\pi$
$587$	13.0363	+	13.0363i	0.538067	+	0.538067i	−0.384894	+	0.922961i	$0.625762\pi$
$588$	0.209129	−	0.154628i	0.00862432	−	0.00637675i
$589$	2.05973			0.0848697
$590$	16.7630	+	3.95285i	0.690123	+	0.162736i
$591$		−	0.404788i		−	0.0166508i
$592$	−21.2784	+	11.2939i	−0.874537	+	0.464175i
$593$	−1.09556	+	1.09556i	−0.0449894	+	0.0449894i	−0.729244	−	0.684254i	$-0.760128\pi$
$593$	−1.09556	+	1.09556i	−0.0449894	+	0.0449894i	0.684254	+	0.729244i	$0.260128\pi$
$594$	−1.64179	−	0.122309i	−0.0673633	−	0.00501841i
$595$	28.2466	−	20.5164i	1.15800	−	0.841092i
$596$	2.05616	−	13.7236i	0.0842237	−	0.562140i
$597$	−1.22172	+	1.22172i	−0.0500018	+	0.0500018i
$598$	−0.771792	−	0.896042i	−0.0315609	−	0.0366419i
$599$	38.0368			1.55414			0.777072	−	0.629412i	$-0.216704\pi$
$599$	38.0368			1.55414			0.777072	+	0.629412i	$0.216704\pi$
$600$	0.837294	−	1.40472i	0.0341824	−	0.0573475i
$601$	8.12072			0.331251			0.165626	−	0.986189i	$-0.447036\pi$
$601$	8.12072			0.331251			0.165626	+	0.986189i	$0.447036\pi$
$602$	7.29081	+	8.46455i	0.297151	+	0.344989i
$603$	−7.65794	+	7.65794i	−0.311855	+	0.311855i
$604$	−9.38363	−	1.40592i	−0.381815	−	0.0572061i
$605$	−14.7850	+	10.7388i	−0.601095	+	0.436595i
$606$	−0.239378	−	0.0178331i	−0.00972405	−	0.000724419i
$607$	−1.42181	+	1.42181i	−0.0577096	+	0.0577096i	−0.735373	−	0.677663i	$-0.762993\pi$
$607$	−1.42181	+	1.42181i	−0.0577096	+	0.0577096i	0.677663	+	0.735373i	$0.262993\pi$
$608$	2.27352	+	5.17988i	0.0922034	+	0.210072i
$609$			0.139884i			0.00566840i
$610$	−20.1494	−	4.75139i	−0.815826	−	0.192378i
$611$	−24.6561			−0.997480
$612$	22.8741	+	30.9364i	0.924631	+	1.25053i
$613$	−7.70428	−	7.70428i	−0.311173	−	0.311173i	0.534191	−	0.845364i	$-0.320616\pi$
$613$	−7.70428	−	7.70428i	−0.311173	−	0.311173i	−0.845364	+	0.534191i	$0.820616\pi$
$614$	−48.9480	−	3.64651i	−1.97538	−	0.147161i
$615$	−0.210487	+	1.32778i	−0.00848767	+	0.0535415i
$616$	11.2434	+	2.55064i	0.453009	+	0.102768i
$617$	−21.5196	−	21.5196i	−0.866345	−	0.866345i	0.125721	−	0.992066i	$-0.459876\pi$
$617$	−21.5196	−	21.5196i	−0.866345	−	0.866345i	−0.992066	+	0.125721i	$0.959876\pi$
$618$	1.47433	−	1.26989i	0.0593063	−	0.0510826i
$619$		−	38.7238i		−	1.55644i	−0.627990	−	0.778221i	$-0.716122\pi$
$619$		−	38.7238i		−	1.55644i	0.627990	−	0.778221i	$-0.283878\pi$
$620$	−8.17275	+	4.24922i	−0.328226	+	0.170653i
$621$		−	0.285300i		−	0.0114487i
$622$	−20.0909	−	23.3253i	−0.805570	−	0.935257i
$623$	19.2555	+	19.2555i	0.771457	+	0.771457i
$624$	0.897314	+	0.275058i	0.0359213	+	0.0110111i
$625$	−20.2173	−	14.7057i	−0.808694	−	0.588230i
$626$	2.12223	−	28.4872i	0.0848213	−	1.13858i
$627$	0.137501	+	0.137501i	0.00549126	+	0.00549126i
$628$	−13.0851	−	17.6971i	−0.522153	−	0.706192i
$629$	38.7915			1.54672
$630$	−19.4709	+	12.0403i	−0.775738	+	0.479697i
$631$		−	39.3146i		−	1.56509i	−0.622595	−	0.782545i	$-0.713921\pi$
$631$		−	39.3146i		−	1.56509i	0.622595	−	0.782545i	$-0.286079\pi$
$632$	1.07501	+	1.70587i	0.0427616	+	0.0678559i
$633$	−0.207220	+	0.207220i	−0.00823624	+	0.00823624i
$634$	2.17100	−	29.1418i	0.0862213	−	1.15737i
$635$	−3.49926	+	22.0739i	−0.138864	+	0.875974i
$636$	−0.0989357	+	0.660333i	−0.00392305	+	0.0261839i
$637$	1.61353	−	1.61353i	0.0639303	−	0.0639303i
$638$	0.899279	−	0.774580i	0.0356028	−	0.0306659i
$639$	−25.4327			−1.00610
$640$	−19.7071	−	15.8628i	−0.778992	−	0.627033i
$641$	−6.95367			−0.274653			−0.137327	−	0.990526i	$-0.543851\pi$
$641$	−6.95367			−0.274653			−0.137327	+	0.990526i	$0.543851\pi$
$642$	1.65156	−	1.42254i	0.0651817	−	0.0561433i
$643$	−29.8072	+	29.8072i	−1.17548	+	1.17548i	−0.194600	+	0.980883i	$0.562341\pi$
$643$	−29.8072	+	29.8072i	−1.17548	+	1.17548i	−0.980883	+	0.194600i	$0.937659\pi$
$644$	−0.296038	+	1.97587i	−0.0116655	+	0.0778600i
$645$	−0.495215	−	0.681801i	−0.0194991	−	0.0268459i
$646$	0.676733	−	9.08395i	0.0266257	−	0.357403i
$647$	−26.6464	+	26.6464i	−1.04758	+	1.04758i	−0.0487659	+	0.998810i	$0.515529\pi$
$647$	−26.6464	+	26.6464i	−1.04758	+	1.04758i	−0.998810	+	0.0487659i	$0.984471\pi$
$648$	−13.3905	−	21.2487i	−0.526030	−	0.834726i
$649$		−	9.15870i		−	0.359510i
$650$	5.43880	−	13.2768i	0.213327	−	0.520760i
$651$	−0.577324			−0.0226271
$652$	8.26807	+	11.1823i	0.323803	+	0.437931i
$653$	32.3188	+	32.3188i	1.26473	+	1.26473i	0.948773	+	0.315958i	$0.102326\pi$
$653$	32.3188	+	32.3188i	1.26473	+	1.26473i	0.315958	+	0.948773i	$0.397674\pi$
$654$	0.137906	−	1.85115i	0.00539255	−	0.0723855i
$655$	17.3238	−	12.5828i	0.676897	−	0.491652i
$656$	19.8838	+	6.09509i	0.776334	+	0.237973i
$657$	−26.2019	−	26.2019i	−1.02223	−	1.02223i
$658$	27.1847	+	31.5611i	1.05977	+	1.23038i
$659$			38.2660i			1.49063i	0.666711	+	0.745316i	$0.267702\pi$
$659$			38.2660i			1.49063i	−0.666711	+	0.745316i	$0.732298\pi$
$660$	−0.829252	−	0.261922i	−0.0322786	−	0.0101953i
$661$		−	39.1924i		−	1.52441i	−0.647336	−	0.762204i	$-0.724117\pi$
$661$		−	39.1924i		−	1.52441i	0.647336	−	0.762204i	$-0.275883\pi$
$662$	−15.0507	+	12.9637i	−0.584961	+	0.503847i
$663$	−1.06864	−	1.06864i	−0.0415026	−	0.0415026i
$664$	48.4137	+	10.9830i	1.87882	+	0.426222i
$665$	5.35321	+	0.848619i	0.207589	+	0.0329080i
$666$	−25.3670	−	1.88978i	−0.982951	−	0.0732276i
$667$	0.145437	+	0.145437i	0.00563133	+	0.00563133i
$668$	24.1640	+	32.6809i	0.934933	+	1.26446i
$669$	−2.66994			−0.103226
$670$	−9.75283	+	6.03091i	−0.376785	+	0.232994i
$671$			11.0089i			0.424994i
$672$	−0.637247	−	1.45187i	−0.0245823	−	0.0560072i
$673$	23.4605	−	23.4605i	0.904336	−	0.904336i	−0.0914717	−	0.995808i	$-0.529157\pi$
$673$	23.4605	−	23.4605i	0.904336	−	0.904336i	0.995808	+	0.0914717i	$0.0291571\pi$
$674$	−14.5409	−	1.08326i	−0.560093	−	0.0417256i
$675$	3.08450	−	1.57056i	0.118722	−	0.0604510i
$676$	−17.5697	−	2.63241i	−0.675758	−	0.101247i
$677$	29.4622	−	29.4622i	1.13232	−	1.13232i	0.142533	−	0.989790i	$-0.454475\pi$
$677$	29.4622	−	29.4622i	1.13232	−	1.13232i	0.989790	−	0.142533i	$-0.0455246\pi$
$678$	1.70866	+	1.98374i	0.0656207	+	0.0761849i
$679$	33.3896			1.28138
$680$	16.0550	+	37.4401i	0.615680	+	1.43576i
$681$	−0.999403			−0.0382972
$682$	3.19681	+	3.71146i	0.122412	+	0.142119i
$683$	8.73981	−	8.73981i	0.334419	−	0.334419i	−0.519843	−	0.854262i	$-0.674009\pi$
$683$	8.73981	−	8.73981i	0.334419	−	0.334419i	0.854262	+	0.519843i	$0.174009\pi$
$684$	−0.885075	+	5.90732i	−0.0338417	+	0.225872i
$685$	12.6998	+	2.01324i	0.485234	+	0.0769218i
$686$	−27.7737	−	2.06908i	−1.06040	−	0.0789977i
$687$	−0.801306	+	0.801306i	−0.0305717	+	0.0305717i
$688$	−11.5145	+	6.11153i	−0.438987	+	0.233000i
$689$			5.85813i			0.223177i
$690$	0.0345881	−	0.146679i	0.00131675	−	0.00558398i
$691$	−33.2858			−1.26625			−0.633126	−	0.774049i	$-0.718229\pi$
$691$	−33.2858			−1.26625			−0.633126	+	0.774049i	$0.718229\pi$
$692$	−4.07256	+	3.01122i	−0.154815	+	0.114469i
$693$	8.60827	+	8.60827i	0.327001	+	0.327001i
$694$	−20.7329	−	1.54455i	−0.787009	−	0.0586303i
$695$	−16.6257	−	22.8899i	−0.630649	−	0.868265i
$696$	−0.159184	−	0.0361119i	−0.00603384	−	0.00136882i
$697$	−23.6804	−	23.6804i	−0.896957	−	0.896957i
$698$	29.1967	−	25.1482i	1.10511	−	0.951872i
$699$			1.44655i			0.0547137i
$700$	−22.9916	+	7.67646i	−0.869000	+	0.290143i
$701$			16.1577i			0.610268i	0.952309	+	0.305134i	$0.0987012\pi$
$701$			16.1577i			0.610268i	−0.952309	+	0.305134i	$0.901299\pi$
$702$	1.29641	+	1.50512i	0.0489300	+	0.0568072i
$703$	4.25853	+	4.25853i	0.160613	+	0.160613i
$704$	−5.80507	+	12.1361i	−0.218787	+	0.457398i
$705$	−1.84647	−	2.54218i	−0.0695420	−	0.0957439i
$706$	−2.15034	+	28.8645i	−0.0809291	+	1.08633i
$707$	2.51584	+	2.51584i	0.0946181	+	0.0946181i
$708$	−1.01279	+	0.748851i	−0.0380631	+	0.0281435i
$709$	34.4178			1.29259			0.646294	−	0.763089i	$-0.276318\pi$
$709$	34.4178			1.29259			0.646294	+	0.763089i	$0.276318\pi$
$710$	−26.2097	−	6.18044i	−0.983631	−	0.231948i
$711$			2.12912i			0.0798483i
$712$	−26.8830	+	16.9412i	−1.00748	+	0.634899i
$713$	−0.600239	+	0.600239i	−0.0224791	+	0.0224791i
$714$	−0.189682	+	2.54615i	−0.00709868	+	0.0952872i
$715$	−7.53567	−	1.19459i	−0.281818	−	0.0446753i
$716$	−20.6691	−	3.09678i	−0.772439	−	0.115732i
$717$	1.14897	−	1.14897i	0.0429091	−	0.0429091i
$718$	0.149996	−	0.129197i	0.00559781	−	0.00482159i
$719$	24.1031			0.898893			0.449446	−	0.893307i	$-0.351621\pi$
$719$	24.1031			0.898893			0.449446	+	0.893307i	$0.351621\pi$
$720$	−8.67493	−	25.2654i	−0.323296	−	0.941587i
$721$	−28.8416			−1.07412
$722$	1.07153	−	0.922945i	0.0398782	−	0.0343484i
$723$	−0.485234	+	0.485234i	−0.0180461	+	0.0180461i
$724$	37.2741	+	5.58467i	1.38528	+	0.207553i
$725$	−0.771755	+	2.37300i	−0.0286623	+	0.0881310i
$726$	0.0992843	−	1.33272i	0.00368479	−	0.0494618i
$727$	−8.09087	+	8.09087i	−0.300074	+	0.300074i	−0.841043	−	0.540969i	$-0.818058\pi$
$727$	−8.09087	+	8.09087i	−0.300074	+	0.300074i	0.540969	+	0.841043i	$0.318058\pi$
$728$	−7.41664	−	11.7690i	−0.274879	−	0.436190i
$729$		−	26.2806i		−	0.973356i
$730$	−20.6349	−	33.3696i	−0.763733	−	1.23507i
$731$	20.9915			0.776398
$732$	1.21739	−	0.900130i	0.0449961	−	0.0332698i
$733$	−15.1974	−	15.1974i	−0.561330	−	0.561330i	0.368355	−	0.929685i	$-0.379921\pi$
$733$	−15.1974	−	15.1974i	−0.561330	−	0.561330i	−0.929685	+	0.368355i	$0.879921\pi$
$734$	1.03599	−	13.9064i	0.0382391	−	0.513293i
$735$	0.287198	+	0.0455282i	0.0105935	+	0.00167933i
$736$	−2.17204	−	0.846960i	−0.0800625	−	0.0312194i
$737$	4.31183	+	4.31183i	0.158828	+	0.158828i
$738$	14.3317	+	16.6390i	0.527558	+	0.612489i
$739$		−	21.5559i		−	0.792948i	−0.918046	−	0.396474i	$-0.870234\pi$
$739$		−	21.5559i		−	0.792948i	0.918046	−	0.396474i	$-0.129766\pi$
$740$	−25.6827	−	8.11197i	−0.944113	−	0.298202i
$741$		−	0.234631i		−	0.00861939i
$742$	7.49870	−	6.45889i	0.275286	−	0.237113i
$743$	24.2464	+	24.2464i	0.889515	+	0.889515i	0.994476	−	0.104961i	$-0.0334718\pi$
$743$	24.2464	+	24.2464i	0.889515	+	0.889515i	−0.104961	+	0.994476i	$0.533472\pi$
$744$	0.149039	−	0.656974i	0.00546403	−	0.0240858i
$745$	12.5529	−	9.11759i	0.459903	−	0.334043i
$746$	19.3064	+	1.43828i	0.706858	+	0.0526593i
$747$	37.0669	+	37.0669i	1.35621	+	1.35621i
$748$	17.4188	−	12.8793i	0.636895	−	0.470915i
$749$	−32.3086			−1.18053
$750$	1.77622	−	0.433516i	0.0648582	−	0.0158298i
$751$			10.2768i			0.375007i	0.982264	+	0.187504i	$0.0600396\pi$
$751$			10.2768i			0.375007i	−0.982264	+	0.187504i	$0.939960\pi$
$752$	−42.9333	+	22.7876i	−1.56562	+	0.830977i
$753$	−1.17514	+	1.17514i	−0.0428243	+	0.0428243i
$754$	−1.42813	−	0.106393i	−0.0520096	−	0.00387459i
$755$	−6.23424	−	8.58317i	−0.226887	−	0.312373i
$756$	0.497268	−	3.31895i	0.0180855	−	0.120709i
$757$	28.3840	−	28.3840i	1.03163	−	1.03163i	0.0321496	−	0.999483i	$-0.489765\pi$
$757$	28.3840	−	28.3840i	1.03163	−	1.03163i	0.999483	−	0.0321496i	$-0.0102353\pi$
$758$	−7.84553	−	9.10857i	−0.284962	−	0.330838i
$759$	−0.0801401			−0.00290890
$760$	−2.34766	+	5.87269i	−0.0851585	+	0.213025i
$761$	39.8010			1.44279			0.721393	−	0.692526i	$-0.243502\pi$
$761$	39.8010			1.44279			0.721393	+	0.692526i	$0.243502\pi$
$762$	−1.06672	−	1.23844i	−0.0386430	−	0.0448641i
$763$	−19.4554	+	19.4554i	−0.704334	+	0.704334i
$764$	41.2391	+	6.17872i	1.49198	+	0.223538i
$765$	−6.73498	+	42.4852i	−0.243504	+	1.53606i
$766$	17.0600	+	1.27093i	0.616403	+	0.0459206i
$767$	−7.81418	+	7.81418i	−0.282154	+	0.282154i
$768$	1.81669	−	0.350357i	0.0655541	−	0.0126424i
$769$		−	33.1667i		−	1.19602i	−0.801488	−	0.598011i	$-0.795958\pi$
$769$		−	33.1667i		−	1.19602i	0.801488	−	0.598011i	$-0.204042\pi$
$770$	6.77932	+	10.9631i	0.244310	+	0.395084i
$771$	0.0849916			0.00306090
$772$	26.7850	+	36.2257i	0.964013	+	1.30379i
$773$	8.28210	+	8.28210i	0.297886	+	0.297886i	0.840186	−	0.542299i	$-0.182446\pi$
$773$	8.28210	+	8.28210i	0.297886	+	0.297886i	−0.542299	+	0.840186i	$0.682446\pi$
$774$	−13.7270	−	1.02263i	−0.493407	−	0.0367577i
$775$	−9.79372	−	3.18515i	−0.351801	−	0.114414i
$776$	−8.61969	+	37.9962i	−0.309429	+	1.36398i
$777$	−1.19363	−	1.19363i	−0.0428212	−	0.0428212i
$778$	11.8365	−	10.1952i	0.424358	−	0.365515i
$779$		−	5.19926i		−	0.186283i
$780$	0.484044	+	0.930987i	0.0173316	+	0.0333347i
$781$			14.3200i			0.512410i
$782$	2.45000	+	2.84442i	0.0876118	+	0.101716i
$783$	−0.244297	−	0.244297i	−0.00873046	−	0.00873046i
$784$	1.31836	−	4.30086i	0.0470844	−	0.153602i
$785$	3.85274	−	24.3036i	0.137510	−	0.867433i
$786$	−0.116333	+	1.56157i	−0.00414946	+	0.0556992i
$787$	−31.5765	−	31.5765i	−1.12558	−	1.12558i	−0.990887	−	0.134694i	$-0.956995\pi$
$787$	−31.5765	−	31.5765i	−1.12558	−	1.12558i	−0.134694	−	0.990887i	$-0.543005\pi$
$788$	−4.16236	−	5.62943i	−0.148278	−	0.200540i
$789$	−1.19401			−0.0425078
$790$	−0.517400	+	2.19416i	−0.0184083	+	0.0780647i
$791$		−	38.8069i		−	1.37981i
$792$	−12.0182	+	7.57364i	−0.427047	+	0.269118i
$793$	9.39277	−	9.39277i	0.333547	−	0.333547i
$794$	0.879558	−	11.8065i	0.0312143	−	0.418998i
$795$	−0.604004	+	0.438708i	−0.0214218	+	0.0155594i
$796$	−4.42788	+	29.5533i	−0.156942	+	1.04749i
$797$	−24.0274	+	24.0274i	−0.851096	+	0.851096i	−0.990268	−	0.139172i	$-0.955556\pi$
$797$	−24.0274	+	24.0274i	−0.851096	+	0.851096i	0.139172	+	0.990268i	$0.455556\pi$
$798$	−0.300340	+	0.258693i	−0.0106319	+	0.00915764i
$799$	78.2692			2.76897
$800$	−2.80015	−	28.1453i	−0.0990002	−	0.995087i
$801$	−33.5531			−1.18554
$802$	−12.9430	+	11.1483i	−0.457034	+	0.393659i
$803$	−14.7531	+	14.7531i	−0.520624	+	0.520624i
$804$	0.124261	−	0.829364i	0.00438235	−	0.0292494i
$805$	−1.80732	+	1.31271i	−0.0636995	+	0.0462670i
$806$	0.439098	−	5.89412i	0.0154666	−	0.207611i
$807$	−2.55995	+	2.55995i	−0.0901143	+	0.0901143i
$808$	−3.51242	+	2.21347i	−0.123567	+	0.0778694i
$809$		−	28.8766i		−	1.01525i	−0.861579	−	0.507624i	$-0.830524\pi$
$809$		−	28.8766i		−	1.01525i	0.861579	−	0.507624i	$-0.169476\pi$
$810$	6.44484	−	27.3309i	0.226449	−	0.960310i
$811$	38.5975			1.35534			0.677670	−	0.735366i	$-0.262990\pi$
$811$	38.5975			1.35534			0.677670	+	0.735366i	$0.262990\pi$
$812$	1.43840	+	1.94539i	0.0504781	+	0.0682697i
$813$	0.465435	+	0.465435i	0.0163235	+	0.0163235i
$814$	−1.06405	+	14.2830i	−0.0372949	+	0.500618i
$815$	−2.43442	+	15.3567i	−0.0852742	+	0.537922i
$816$	−2.84846	−	0.873152i	−0.0997161	−	0.0305664i
$817$	2.30445	+	2.30445i	0.0806223	+	0.0806223i
$818$	−4.00375	−	4.64830i	−0.139988	−	0.162524i
$819$		−	14.6891i		−	0.513279i
$820$	10.7261	+	20.6300i	0.374571	+	0.720432i
$821$			26.9264i			0.939739i	0.882736	+	0.469870i	$0.155699\pi$
$821$			26.9264i			0.939739i	−0.882736	+	0.469870i	$0.844301\pi$
$822$	−0.712516	+	0.613715i	−0.0248519	+	0.0214058i
$823$	27.4545	+	27.4545i	0.957005	+	0.957005i	0.999113	−	0.0421084i	$-0.0134075\pi$
$823$	27.4545	+	27.4545i	0.957005	+	0.957005i	−0.0421084	+	0.999113i	$0.513407\pi$
$824$	7.44561	−	32.8208i	0.259380	−	1.14337i
$825$	−0.441168	−	0.866428i	−0.0153595	−	0.0301652i
$826$	18.6181	+	1.38700i	0.647806	+	0.0482601i
$827$	−5.55262	−	5.55262i	−0.193083	−	0.193083i	0.603944	−	0.797027i	$-0.293595\pi$
$827$	−5.55262	−	5.55262i	−0.193083	−	0.193083i	−0.797027	+	0.603944i	$0.793595\pi$
$828$	−1.46357	−	1.97942i	−0.0508624	−	0.0687895i
$829$	−38.8189			−1.34824			−0.674118	−	0.738624i	$-0.735476\pi$
$829$	−38.8189			−1.34824			−0.674118	+	0.738624i	$0.735476\pi$
$830$	29.1916	+	47.2069i	1.01325	+	1.63858i
$831$		−	0.476778i		−	0.0165393i
$832$	15.3074	−	5.40164i	0.530688	−	0.187268i
$833$	−5.12204	+	5.12204i	−0.177468	+	0.177468i
$834$	2.06330	+	0.153711i	0.0714462	+	0.00532257i
$835$	−7.11477	+	44.8810i	−0.246217	+	1.55317i
$836$	3.32614	+	0.498345i	0.115037	+	0.0172356i
$837$	1.00825	−	1.00825i	0.0348502	−	0.0348502i
$838$	10.0605	+	11.6801i	0.347533	+	0.403482i
$839$	26.9953			0.931982			0.465991	−	0.884789i	$-0.345698\pi$
$839$	26.9953			0.931982			0.465991	+	0.884789i	$0.345698\pi$
$840$	0.658027	−	1.64606i	0.0227041	−	0.0567946i
$841$	−28.7509			−0.991411
$842$	24.9938	+	29.0175i	0.861344	+	1.00001i
$843$	0.362060	−	0.362060i	0.0124700	−	0.0124700i
$844$	−0.751025	+	5.01262i	−0.0258513	+	0.172541i
$845$	−11.6728	−	16.0709i	−0.401558	−	0.552857i
$846$	−51.1828	−	3.81300i	−1.75970	−	0.131094i
$847$	−14.0068	+	14.0068i	−0.481279	+	0.481279i
$848$	5.41417	+	10.2007i	0.185923	+	0.350292i
$849$			2.21943i			0.0761706i
$850$	−17.2651	+	42.1464i	−0.592188	+	1.44561i
$851$	−2.48201			−0.0850823
$852$	1.58354	−	1.17086i	0.0542512	−	0.0401129i
$853$	10.6243	+	10.6243i	0.363770	+	0.363770i	0.865199	−	0.501429i	$-0.167192\pi$
$853$	10.6243	+	10.6243i	0.363770	+	0.363770i	−0.501429	+	0.865199i	$0.667192\pi$
$854$	−22.3792	−	1.66720i	−0.765802	−	0.0570505i
$855$	−5.40340	+	3.92467i	−0.184792	+	0.134221i
$856$	8.34062	−	36.7661i	0.285077	−	1.25664i
$857$	26.6560	+	26.6560i	0.910552	+	0.910552i	0.996315	−	0.0857639i	$-0.0273331\pi$
$857$	26.6560	+	26.6560i	0.910552	+	0.910552i	−0.0857639	+	0.996315i	$0.527333\pi$
$858$	0.422786	−	0.364160i	0.0144337	−	0.0124322i
$859$			18.8892i			0.644491i	0.946656	+	0.322246i	$0.104438\pi$
$859$			18.8892i			0.644491i	−0.946656	+	0.322246i	$0.895562\pi$
$860$	−13.8978	−	4.38968i	−0.473912	−	0.149687i
$861$			1.45731i			0.0496649i
$862$	−22.0500	−	25.5998i	−0.751026	−	0.871932i
$863$	−25.1352	−	25.1352i	−0.855611	−	0.855611i	0.135207	−	0.990817i	$-0.456830\pi$
$863$	−25.1352	−	25.1352i	−0.855611	−	0.855611i	−0.990817	+	0.135207i	$0.956830\pi$
$864$	3.64848	+	1.42268i	0.124124	+	0.0484005i
$865$	−5.59288	−	0.886613i	−0.190164	−	0.0301457i
$866$	−3.52757	+	47.3513i	−0.119872	+	1.60906i
$867$	2.00230	+	2.00230i	0.0680016	+	0.0680016i
$868$	−8.02890	+	5.93650i	−0.272519	+	0.201498i
$869$	1.19881			0.0406668
$870$	−0.0959815	−	0.155216i	−0.00325408	−	0.00526230i
$871$		−	7.35768i		−	0.249306i
$872$	−17.1171	−	27.1621i	−0.579658	−	0.919826i
$873$	−29.0910	+	29.0910i	−0.984581	+	0.984581i
$874$	−0.0432997	+	0.581222i	−0.00146463	+	0.0196601i
$875$	−24.1415	−	12.3132i	−0.816130	−	0.416263i
$876$	2.83770	+	0.425163i	0.0958769	+	0.0143649i
$877$	9.15127	−	9.15127i	0.309016	−	0.309016i	−0.535512	−	0.844528i	$-0.679881\pi$
$877$	9.15127	−	9.15127i	0.309016	−	0.309016i	0.844528	+	0.535512i	$0.179881\pi$
$878$	−16.7388	+	14.4177i	−0.564908	+	0.486575i
$879$	3.21187			0.108334
$880$	−14.2258	+	4.88445i	−0.479551	+	0.164655i
$881$	22.3071			0.751545			0.375773	−	0.926712i	$-0.377377\pi$
$881$	22.3071			0.751545			0.375773	+	0.926712i	$0.377377\pi$
$882$	3.59899	−	3.09994i	0.121184	−	0.104380i
$883$	23.4882	−	23.4882i	0.790440	−	0.790440i	−0.191125	−	0.981566i	$-0.561214\pi$
$883$	23.4882	−	23.4882i	0.790440	−	0.790440i	0.981566	+	0.191125i	$0.0612137\pi$
$884$	−25.8503	−	3.87307i	−0.869441	−	0.130266i
$885$	−1.39088	−	0.220489i	−0.0467538	−	0.00741166i
$886$	−0.901090	+	12.0955i	−0.0302727	+	0.406358i
$887$	5.01730	−	5.01730i	0.168464	−	0.168464i	−0.617840	−	0.786304i	$-0.711992\pi$
$887$	5.01730	−	5.01730i	0.168464	−	0.168464i	0.786304	+	0.617840i	$0.211992\pi$
$888$	1.66645	−	1.05017i	0.0559223	−	0.0352413i
$889$			24.2271i			0.812551i
$890$	−34.5781	−	8.15378i	−1.15906	−	0.273315i
$891$	−14.9326			−0.500261
$892$	−37.1311	+	27.4544i	−1.24324	+	0.919242i
$893$	8.59240	+	8.59240i	0.287534	+	0.287534i
$894$	−0.0842955	+	1.13152i	−0.00281926	+	0.0378437i
$895$	−13.7320	−	18.9059i	−0.459009	−	0.631955i
$896$	−23.7916	−	13.6386i	−0.794821	−	0.455635i
$897$	0.0683754	+	0.0683754i	0.00228299	+	0.00228299i
$898$	−5.84424	−	6.78510i	−0.195025	−	0.226422i
$899$			1.02795i			0.0342839i
$900$	13.3434	−	26.7198i	0.444781	−	0.890660i
$901$		−	18.5962i		−	0.619530i
$902$	9.36863	−	8.06953i	0.311941	−	0.268686i
$903$	−0.645915	−	0.645915i	−0.0214947	−	0.0214947i
$904$	44.1609	+	10.0182i	1.46877	+	0.333200i
$905$	24.7639	+	34.0945i	0.823181	+	1.13334i
$906$	0.773687	+	0.0576379i	0.0257040	+	0.00191489i
$907$	−15.1970	−	15.1970i	−0.504608	−	0.504608i	0.408259	−	0.912866i	$-0.366136\pi$
$907$	−15.1970	−	15.1970i	−0.504608	−	0.504608i	−0.912866	+	0.408259i	$0.866136\pi$
$908$	−13.8988	+	10.2767i	−0.461248	+	0.341043i
$909$	−4.38391			−0.145405
$910$	3.56962	−	15.1378i	0.118332	−	0.501814i
$911$		−	60.0386i		−	1.98917i	−0.103942	−	0.994583i	$-0.533145\pi$
$911$		−	60.0386i		−	1.98917i	0.103942	−	0.994583i	$-0.466855\pi$
$912$	−0.216850	−	0.408559i	−0.00718061	−	0.0135287i
$913$	20.8707	−	20.8707i	0.690718	−	0.690718i
$914$	−12.6137	−	0.939694i	−0.417225	−	0.0310823i
$915$	1.67186	+	0.265031i	0.0552699	+	0.00876167i
$916$	−2.90417	+	19.3835i	−0.0959565	+	0.640449i
$917$	16.4120	−	16.4120i	0.541971	−	0.541971i
$918$	−4.11538	−	4.77791i	−0.135828	−	0.157694i
$919$	35.6594			1.17630			0.588148	−	0.808753i	$-0.299857\pi$
$919$	35.6594			1.17630			0.588148	+	0.808753i	$0.299857\pi$
$920$	−1.02725	−	2.39554i	−0.0338675	−	0.0789788i
$921$	4.01340			0.132246
$922$	21.3683	+	24.8083i	0.703726	+	0.817018i
$923$	12.2178	−	12.2178i	0.402153	−	0.402153i
$924$	−0.932286	−	0.139682i	−0.0306700	−	0.00459518i
$925$	−13.6634	−	26.8341i	−0.449248	−	0.882298i
$926$	39.7557	+	2.96171i	1.30645	+	0.0973278i
$927$	25.1285	−	25.1285i	0.825329	−	0.825329i
$928$	−2.58511	+	1.13464i	−0.0848605	+	0.0372464i
$929$			33.2135i			1.08970i	0.838533	+	0.544850i	$0.183414\pi$
$929$			33.2135i			1.08970i	−0.838533	+	0.544850i	$0.816586\pi$
$930$	0.640598	−	0.396130i	0.0210060	−	0.0129896i
$931$	−1.12460			−0.0368571
$932$	14.8746	+	20.1174i	0.487235	+	0.658967i
$933$	1.77991	+	1.77991i	0.0582716	+	0.0582716i
$934$	23.1273	+	1.72293i	0.756749	+	0.0563760i
$935$	23.9215	+	3.79215i	0.782315	+	0.124017i
$936$	16.7157	+	3.79207i	0.546370	+	0.123948i
$937$	0.950228	+	0.950228i	0.0310426	+	0.0310426i	0.722458	−	0.691415i	$-0.243012\pi$
$937$	0.950228	+	0.950228i	0.0310426	+	0.0310426i	−0.691415	+	0.722458i	$0.743012\pi$
$938$	−9.41821	+	8.11223i	−0.307515	+	0.264874i
$939$			2.33575i			0.0762243i
$940$	−51.8197	−	16.3675i	−1.69017	−	0.533848i
$941$			35.6587i			1.16244i	0.813746	+	0.581221i	$0.197425\pi$
$941$			35.6587i			1.16244i	−0.813746	+	0.581221i	$0.802575\pi$
$942$	1.17447	+	1.36355i	0.0382663	+	0.0444267i
$943$	1.51515	+	1.51515i	0.0493401	+	0.0493401i
$944$	−6.38472	+	20.8287i	−0.207805	+	0.677916i
$945$	3.03583	−	2.20502i	0.0987556	−	0.0717294i
$946$	−0.575795	+	7.72904i	−0.0187207	+	0.251293i
$947$	−15.3043	−	15.3043i	−0.497321	−	0.497321i	0.413282	−	0.910603i	$-0.364382\pi$
$947$	−15.3043	−	15.3043i	−0.497321	−	0.497321i	−0.910603	+	0.413282i	$0.864382\pi$
$948$	−0.0980192	−	0.132567i	−0.00318352	−	0.00430559i
$949$	25.1746			0.817201
$950$	−6.52220	+	2.73147i	−0.211608	+	0.0886206i
$951$			2.38943i			0.0774825i
$952$	23.5436	+	37.3600i	0.763053	+	1.21084i
$953$	17.6358	−	17.6358i	0.571280	−	0.571280i	−0.361206	−	0.932486i	$-0.617635\pi$
$953$	17.6358	−	17.6358i	0.571280	−	0.571280i	0.932486	+	0.361206i	$0.117635\pi$
$954$	−0.905943	+	12.1607i	−0.0293310	+	0.393717i
$955$	27.3982	+	37.7212i	0.886584	+	1.22063i
$956$	4.16421	−	27.7935i	0.134680	−	0.898905i
$957$	−0.0686224	+	0.0686224i	−0.00221825	+	0.00221825i
$958$	27.0062	−	23.2614i	0.872532	−	0.751542i
$959$	13.9386			0.450102
$960$	1.70329	+	1.17375i	0.0549734	+	0.0378827i
$961$	26.7575			0.863146
$962$	13.0940	−	11.2784i	0.422169	−	0.363629i
$963$	28.1492	−	28.1492i	0.907094	−	0.907094i
$964$	−1.75863	+	11.7378i	−0.0566417	+	0.378048i
$965$	−7.88649	+	49.7491i	−0.253875	+	1.60148i
$966$	0.0121365	−	0.162911i	0.000390486	−	0.00524159i
$967$	−5.06230	+	5.06230i	−0.162793	+	0.162793i	−0.783803	−	0.621010i	$-0.786723\pi$
$967$	−5.06230	+	5.06230i	−0.162793	+	0.162793i	0.621010	+	0.783803i	$0.286723\pi$
$968$	−12.3233	−	19.5552i	−0.396086	−	0.628526i
$969$			0.744821i			0.0239271i
$970$	−37.0491	+	22.9102i	−1.18957	+	0.735603i
$971$	−47.9083			−1.53745			−0.768725	−	0.639579i	$-0.779109\pi$
$971$	−47.9083			−1.53745			−0.768725	+	0.639579i	$0.779109\pi$
$972$	3.69037	+	4.99109i	0.118369	+	0.160089i
$973$	−21.6851	−	21.6851i	−0.695194	−	0.695194i
$974$	−1.75282	+	23.5285i	−0.0561638	+	0.753901i
$975$	−0.362832	+	1.11564i	−0.0116199	+	0.0357290i
$976$	7.67453	−	25.0364i	0.245656	−	0.801396i
$977$	−8.23886	−	8.23886i	−0.263584	−	0.263584i	0.562924	−	0.826509i	$-0.309676\pi$
$977$	−8.23886	−	8.23886i	−0.263584	−	0.263584i	−0.826509	+	0.562924i	$0.809676\pi$
$978$	−0.742110	−	0.861582i	−0.0237301	−	0.0275503i
$979$			18.8922i			0.603797i
$980$	4.46225	−	2.32004i	0.142541	−	0.0741109i
$981$		−	33.9015i		−	1.08239i
$982$	28.1562	−	24.2520i	0.898502	−	0.773911i
$983$	−17.5737	−	17.5737i	−0.560513	−	0.560513i	0.368940	−	0.929453i	$-0.379721\pi$
$983$	−17.5737	−	17.5737i	−0.560513	−	0.560513i	−0.929453	+	0.368940i	$0.879721\pi$
$984$	−1.65836	−	0.376211i	−0.0528667	−	0.0119932i
$985$	1.22555	−	7.73095i	0.0390493	−	0.246329i
$986$	4.53351	+	0.337736i	0.144376	+	0.0107557i
$987$	−2.40837	−	2.40837i	−0.0766594	−	0.0766594i
$988$	−2.41267	−	3.26304i	−0.0767571	−	0.103811i
$989$	−1.34311			−0.0427083
$990$	−15.4583	−	3.64518i	−0.491296	−	0.115851i
$991$		−	37.6241i		−	1.19517i	−0.801806	−	0.597585i	$-0.796127\pi$
$991$		−	37.6241i		−	1.19517i	0.801806	−	0.597585i	$-0.203873\pi$
$992$	−4.68284	−	10.6691i	−0.148680	−	0.338746i
$993$	1.14849	−	1.14849i	0.0364463	−	0.0364463i
$994$	−29.1101	−	2.16864i	−0.923317	−	0.0687850i
$995$	−27.0323	+	19.6344i	−0.856982	+	0.622454i
$996$	−4.01439	−	0.601464i	−0.127201	−	0.0190581i
$997$	1.69631	−	1.69631i	0.0537228	−	0.0537228i	−0.679735	−	0.733458i	$-0.737905\pi$
$997$	1.69631	−	1.69631i	0.0537228	−	0.0537228i	0.733458	+	0.679735i	$0.237905\pi$
$998$	−26.3976	−	30.6473i	−0.835602	−	0.970125i
$999$	4.16915			0.131906

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.w.d.267.12	✓	108
5.3	odd	4	inner	760.2.w.d.723.40	yes	108
8.3	odd	2	inner	760.2.w.d.267.40	yes	108
40.3	even	4	inner	760.2.w.d.723.12	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.w.d.267.12	✓	108	1.1	even	1	trivial
760.2.w.d.267.40	yes	108	8.3	odd	2	inner
760.2.w.d.723.12	yes	108	40.3	even	4	inner
760.2.w.d.723.40	yes	108	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07153 + 0.922945i) q^{2} +(0.0817665 - 0.0817665i) q^{3} +(0.296346 - 1.97792i) q^{4} +(1.80920 - 1.31408i) q^{5} +(-0.0121492 + 0.163081i) q^{6} +(1.71397 - 1.71397i) q^{7} +(1.50797 + 2.39291i) q^{8} +2.98663i q^{9} +O(q^{10})\)	\(q+(-1.07153 + 0.922945i) q^{2} +(0.0817665 - 0.0817665i) q^{3} +(0.296346 - 1.97792i) q^{4} +(1.80920 - 1.31408i) q^{5} +(-0.0121492 + 0.163081i) q^{6} +(1.71397 - 1.71397i) q^{7} +(1.50797 + 2.39291i) q^{8} +2.98663i q^{9} +(-0.725784 + 3.07786i) q^{10} +1.68163 q^{11} +(-0.137497 - 0.185959i) q^{12} +(-1.43476 - 1.43476i) q^{13} +(-0.254668 + 3.41847i) q^{14} +(0.0404841 - 0.255379i) q^{15} +(-3.82436 - 1.17230i) q^{16} +(4.55456 + 4.55456i) q^{17} +(-2.75649 - 3.20026i) q^{18} +1.00000i q^{19} +(-2.06300 - 3.96788i) q^{20} -0.280291i q^{21} +(-1.80192 + 1.55205i) q^{22} +(-0.291416 - 0.291416i) q^{23} +(0.318961 + 0.0723585i) q^{24} +(1.54639 - 4.75486i) q^{25} +(2.86160 + 0.213182i) q^{26} +(0.489506 + 0.489506i) q^{27} +(-2.88218 - 3.89803i) q^{28} -0.499068 q^{29} +(0.192321 + 0.311011i) q^{30} -2.05973i q^{31} +(5.17988 - 2.27352i) q^{32} +(0.137501 - 0.137501i) q^{33} +(-9.08395 - 0.676733i) q^{34} +(0.848619 - 5.35321i) q^{35} +(5.90732 + 0.885075i) q^{36} +(4.25853 - 4.25853i) q^{37} +(-0.922945 - 1.07153i) q^{38} -0.234631 q^{39} +(5.87269 + 2.34766i) q^{40} -5.19926 q^{41} +(0.258693 + 0.300340i) q^{42} +(2.30445 - 2.30445i) q^{43} +(0.498345 - 3.32614i) q^{44} +(3.92467 + 5.40340i) q^{45} +(0.581222 + 0.0432997i) q^{46} +(8.59240 - 8.59240i) q^{47} +(-0.408559 + 0.216850i) q^{48} +1.12460i q^{49} +(2.73147 + 6.52220i) q^{50} +0.744821 q^{51} +(-3.26304 + 2.41267i) q^{52} +(-2.04150 - 2.04150i) q^{53} +(-0.976306 - 0.0727325i) q^{54} +(3.04240 - 2.20980i) q^{55} +(6.68600 + 1.51676i) q^{56} +(0.0817665 + 0.0817665i) q^{57} +(0.534766 - 0.460613i) q^{58} -5.44632i q^{59} +(-0.493123 - 0.155755i) q^{60} +6.54656i q^{61} +(1.90102 + 2.20706i) q^{62} +(5.11900 + 5.11900i) q^{63} +(-3.45205 + 7.21688i) q^{64} +(-4.48117 - 0.710378i) q^{65} +(-0.0204304 + 0.274242i) q^{66} +(2.56407 + 2.56407i) q^{67} +(10.3583 - 7.65884i) q^{68} -0.0476562 q^{69} +(4.03140 + 6.51935i) q^{70} +8.51554i q^{71} +(-7.14674 + 4.50375i) q^{72} +(-8.77306 + 8.77306i) q^{73} +(-0.632748 + 8.49352i) q^{74} +(-0.262345 - 0.515231i) q^{75} +(1.97792 + 0.296346i) q^{76} +(2.88227 - 2.88227i) q^{77} +(0.251414 - 0.216552i) q^{78} +0.712885 q^{79} +(-8.45951 + 2.90459i) q^{80} -8.87984 q^{81} +(5.57116 - 4.79863i) q^{82} +(12.4110 - 12.4110i) q^{83} +(-0.554394 - 0.0830631i) q^{84} +(14.2251 + 2.25505i) q^{85} +(-0.342403 + 4.59615i) q^{86} +(-0.0408071 + 0.0408071i) q^{87} +(2.53585 + 4.02399i) q^{88} +11.2344i q^{89} +(-9.19243 - 2.16765i) q^{90} -4.91829 q^{91} +(-0.662759 + 0.490039i) q^{92} +(-0.168417 - 0.168417i) q^{93} +(-1.27669 + 17.1373i) q^{94} +(1.31408 + 1.80920i) q^{95} +(0.237642 - 0.609438i) q^{96} +(9.74041 + 9.74041i) q^{97} +(-1.03794 - 1.20504i) q^{98} +5.02241i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 8 q^{6}+O(q^{10}) \) 108 * q + 8 * q^6	\( 108 q + 8 q^{6} + 8 q^{10} + 18 q^{12} + 16 q^{16} + 4 q^{17} - 36 q^{22} - 4 q^{25} - 40 q^{26} + 16 q^{28} - 12 q^{30} - 10 q^{32} + 24 q^{35} - 80 q^{36} + 28 q^{40} + 108 q^{42} - 32 q^{43} + 64 q^{46} - 26 q^{48} - 28 q^{50} + 34 q^{52} - 12 q^{56} - 58 q^{60} - 92 q^{62} - 4 q^{65} - 92 q^{66} + 40 q^{68} + 28 q^{70} - 68 q^{72} - 20 q^{73} + 12 q^{78} + 56 q^{80} - 92 q^{81} + 44 q^{82} + 72 q^{83} + 40 q^{86} - 40 q^{88} + 4 q^{90} + 32 q^{91} + 24 q^{92} + 124 q^{96} - 84 q^{97} + 76 q^{98}+O(q^{100}) \) 108 * q + 8 * q^6 + 8 * q^10 + 18 * q^12 + 16 * q^16 + 4 * q^17 - 36 * q^22 - 4 * q^25 - 40 * q^26 + 16 * q^28 - 12 * q^30 - 10 * q^32 + 24 * q^35 - 80 * q^36 + 28 * q^40 + 108 * q^42 - 32 * q^43 + 64 * q^46 - 26 * q^48 - 28 * q^50 + 34 * q^52 - 12 * q^56 - 58 * q^60 - 92 * q^62 - 4 * q^65 - 92 * q^66 + 40 * q^68 + 28 * q^70 - 68 * q^72 - 20 * q^73 + 12 * q^78 + 56 * q^80 - 92 * q^81 + 44 * q^82 + 72 * q^83 + 40 * q^86 - 40 * q^88 + 4 * q^90 + 32 * q^91 + 24 * q^92 + 124 * q^96 - 84 * q^97 + 76 * q^98

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