LMFDB - Embedded newform 370.2.o.c.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			201.3
Character	$\chi$	$=$	370.201
Dual form			370.2.o.c.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 + 0.342020i) q^{2} +(1.85873 - 0.676523i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} +1.97802 q^{6} +(0.241589 - 1.37012i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.699071 - 0.586590i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.22452 + 3.85299i) q^{11} +(1.85873 + 0.676523i) q^{12} +(-4.31212 - 3.61830i) q^{13} +(0.695629 - 1.20487i) q^{14} +(-0.343480 - 1.94797i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.05466 + 1.72407i) q^{17} +(0.857537 - 0.312118i) q^{18} +(2.46158 - 0.895943i) q^{19} +(0.766044 - 0.642788i) q^{20} +(-0.477869 - 2.71013i) q^{21} +(0.772569 + 4.38145i) q^{22} +(0.731413 - 1.26685i) q^{23} +(1.51525 + 1.27145i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-2.81454 - 4.87492i) q^{26} +(-2.06449 + 3.57580i) q^{27} +(1.06577 - 0.894284i) q^{28} +(1.12599 + 1.95027i) q^{29} +(0.343480 - 1.94797i) q^{30} -3.91173 q^{31} +(-0.173648 + 0.984808i) q^{32} +(6.74143 + 5.65673i) q^{33} +(-2.52042 + 0.917358i) q^{34} +(-1.30736 - 0.475838i) q^{35} +0.912572 q^{36} +(-5.34543 + 2.90283i) q^{37} +2.61956 q^{38} +(-10.4629 - 3.80820i) q^{39} +(0.939693 - 0.342020i) q^{40} +(2.17972 + 1.82900i) q^{41} +(0.477869 - 2.71013i) q^{42} -1.08006 q^{43} +(-0.772569 + 4.38145i) q^{44} +(-0.456286 - 0.790311i) q^{45} +(1.12059 - 0.940287i) q^{46} +(-1.42236 + 2.46360i) q^{47} +(0.989011 + 1.71302i) q^{48} +(4.75898 + 1.73213i) q^{49} +(-0.766044 - 0.642788i) q^{50} +(-2.65270 + 4.59461i) q^{51} +(-0.977478 - 5.54355i) q^{52} +(-1.51336 - 8.58267i) q^{53} +(-3.16298 + 2.65406i) q^{54} +(4.18074 - 1.52166i) q^{55} +(1.30736 - 0.475838i) q^{56} +(3.96930 - 3.33064i) q^{57} +(0.391051 + 2.21776i) q^{58} +(-2.27716 - 12.9144i) q^{59} +(0.989011 - 1.71302i) q^{60} +(4.74529 + 3.98177i) q^{61} +(-3.67582 - 1.33789i) q^{62} +(-0.634812 - 1.09953i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.31212 + 3.61830i) q^{65} +(4.40016 + 7.62129i) q^{66} +(-2.46893 + 14.0020i) q^{67} -2.68217 q^{68} +(0.502452 - 2.84954i) q^{69} +(-1.06577 - 0.894284i) q^{70} +(-1.73713 + 0.632262i) q^{71} +(0.857537 + 0.312118i) q^{72} -8.55998 q^{73} +(-6.01588 + 0.899526i) q^{74} -1.97802 q^{75} +(2.46158 + 0.895943i) q^{76} +(5.81648 - 2.11703i) q^{77} +(-8.52947 - 7.15707i) q^{78} +(-0.519316 + 2.94519i) q^{79} +1.00000 q^{80} +(-1.89362 + 10.7393i) q^{81} +(1.42271 + 2.46420i) q^{82} +(12.5191 - 10.5048i) q^{83} +(1.37597 - 2.38325i) q^{84} +(1.34109 + 2.32283i) q^{85} +(-1.01492 - 0.369401i) q^{86} +(3.41231 + 2.86327i) q^{87} +(-2.22452 + 3.85299i) q^{88} +(-0.948852 - 5.38121i) q^{89} +(-0.158466 - 0.898708i) q^{90} +(-5.99927 + 5.03399i) q^{91} +(1.37461 - 0.500316i) q^{92} +(-7.27086 + 2.64638i) q^{93} +(-2.17918 + 1.82855i) q^{94} +(-0.454882 - 2.57977i) q^{95} +(0.343480 + 1.94797i) q^{96} +(4.62509 - 8.01090i) q^{97} +(3.87956 + 3.25533i) q^{98} +(3.81522 + 1.38863i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9} + 12 q^{10} - 15 q^{11} + 3 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 36 q^{21} + 9 q^{22} + 21 q^{23} - 6 q^{26} - 12 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{31}+ \cdots + 63 q^{99}+O(q^{100}) $ 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9 + 12 * q^10 - 15 * q^11 + 3 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 36 * q^21 + 9 * q^22 + 21 * q^23 - 6 * q^26 - 12 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^31 - 39 * q^33 - 21 * q^34 + 6 * q^35 + 54 * q^36 - 12 * q^37 - 36 * q^38 - 18 * q^39 + 27 * q^41 - 36 * q^42 - 24 * q^43 - 9 * q^44 - 27 * q^45 + 3 * q^46 - 6 * q^47 - 3 * q^48 - 27 * q^49 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 9 * q^54 + 9 * q^55 - 6 * q^56 - 27 * q^57 + 27 * q^58 + 51 * q^59 - 3 * q^60 - 3 * q^62 - 27 * q^63 - 12 * q^64 + 15 * q^66 - 18 * q^69 + 3 * q^70 - 66 * q^71 + 6 * q^72 + 42 * q^73 - 42 * q^74 + 6 * q^75 - 6 * q^76 + 69 * q^77 + 36 * q^78 - 30 * q^79 + 24 * q^80 - 90 * q^81 + 24 * q^82 + 57 * q^83 + 6 * q^84 - 6 * q^86 + 6 * q^87 + 15 * q^88 - 57 * q^89 + 6 * q^90 + 3 * q^91 + 15 * q^92 - 72 * q^93 + 3 * q^94 - 15 * q^95 - 3 * q^97 - 72 * q^98 + 63 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	1.85873	−	0.676523i	1.07314	−	0.390591i	0.255790	−	0.966732i	$-0.417664\pi$
$3$	1.85873	−	0.676523i	1.07314	−	0.390591i	0.817350	+	0.576141i	$0.195442\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$6$	1.97802			0.807524
$7$	0.241589	−	1.37012i	0.0913122	−	0.517857i	−0.904503	−	0.426467i	$-0.859758\pi$
$7$	0.241589	−	1.37012i	0.0913122	−	0.517857i	0.995815	−	0.0913901i	$-0.0291310\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.699071	−	0.586590i	0.233024	−	0.195530i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.22452	+	3.85299i	0.670719	+	1.16172i	0.977701	+	0.210004i	$0.0673476\pi$
$11$	2.22452	+	3.85299i	0.670719	+	1.16172i	−0.306982	+	0.951715i	$0.599319\pi$
$12$	1.85873	+	0.676523i	0.536570	+	0.195296i
$13$	−4.31212	−	3.61830i	−1.19597	−	1.00354i	−0.999736	−	0.0229776i	$-0.992685\pi$
$13$	−4.31212	−	3.61830i	−1.19597	−	1.00354i	−0.196231	−	0.980558i	$-0.562870\pi$
$14$	0.695629	−	1.20487i	0.185915	−	0.322014i
$15$	−0.343480	−	1.94797i	−0.0886861	−	0.502964i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−2.05466	+	1.72407i	−0.498329	+	0.418148i	−0.857000	−	0.515316i	$-0.827675\pi$
$17$	−2.05466	+	1.72407i	−0.498329	+	0.418148i	0.358671	+	0.933464i	$0.383230\pi$
$18$	0.857537	−	0.312118i	0.202123	−	0.0735669i
$19$	2.46158	−	0.895943i	0.564726	−	0.205543i	−0.0438513	−	0.999038i	$-0.513963\pi$
$19$	2.46158	−	0.895943i	0.564726	−	0.205543i	0.608577	+	0.793495i	$0.291741\pi$
$20$	0.766044	−	0.642788i	0.171293	−	0.143732i
$21$	−0.477869	−	2.71013i	−0.104280	−	0.591399i
$22$	0.772569	+	4.38145i	0.164712	+	0.934129i
$23$	0.731413	−	1.26685i	0.152510	−	0.264155i	−0.779639	−	0.626229i	$-0.784598\pi$
$23$	0.731413	−	1.26685i	0.152510	−	0.264155i	0.932150	+	0.362073i	$0.117931\pi$
$24$	1.51525	+	1.27145i	0.309300	+	0.259533i
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	−2.81454	−	4.87492i	−0.551976	−	0.956050i
$27$	−2.06449	+	3.57580i	−0.397311	+	0.688163i
$28$	1.06577	−	0.894284i	0.201411	−	0.169004i
$29$	1.12599	+	1.95027i	0.209091	+	0.362155i	0.951428	−	0.307870i	$-0.0996163\pi$
$29$	1.12599	+	1.95027i	0.209091	+	0.362155i	−0.742338	+	0.670026i	$0.766283\pi$
$30$	0.343480	−	1.94797i	0.0627106	−	0.355649i
$31$	−3.91173			−0.702568			−0.351284	−	0.936269i	$-0.614255\pi$
$31$	−3.91173			−0.702568			−0.351284	+	0.936269i	$0.614255\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	6.74143	+	5.65673i	1.17353	+	0.984710i
$34$	−2.52042	+	0.917358i	−0.432248	+	0.157326i
$35$	−1.30736	−	0.475838i	−0.220983	−	0.0804314i
$36$	0.912572			0.152095
$37$	−5.34543	+	2.90283i	−0.878782	+	0.477223i
$37$	−5.34543	+	2.90283i	−0.878782	+	0.477223i
$38$	2.61956			0.424949
$39$	−10.4629	−	3.80820i	−1.67541	−	0.609800i
$40$	0.939693	−	0.342020i	0.148578	−	0.0540781i
$41$	2.17972	+	1.82900i	0.340414	+	0.285642i	0.796927	−	0.604075i	$-0.206457\pi$
$41$	2.17972	+	1.82900i	0.340414	+	0.285642i	−0.456513	+	0.889717i	$0.650902\pi$
$42$	0.477869	−	2.71013i	0.0737368	−	0.418182i
$43$	−1.08006			−0.164707			−0.0823535	−	0.996603i	$-0.526244\pi$
$43$	−1.08006			−0.164707			−0.0823535	+	0.996603i	$0.526244\pi$
$44$	−0.772569	+	4.38145i	−0.116469	+	0.660529i
$45$	−0.456286	−	0.790311i	−0.0680191	−	0.117813i
$46$	1.12059	−	0.940287i	0.165222	−	0.138638i
$47$	−1.42236	+	2.46360i	−0.207473	+	0.359353i	−0.950918	−	0.309444i	$-0.899857\pi$
$47$	−1.42236	+	2.46360i	−0.207473	+	0.359353i	0.743445	+	0.668797i	$0.233190\pi$
$48$	0.989011	+	1.71302i	0.142751	+	0.247253i
$49$	4.75898	+	1.73213i	0.679854	+	0.247447i
$50$	−0.766044	−	0.642788i	−0.108335	−	0.0909039i
$51$	−2.65270	+	4.59461i	−0.371452	+	0.643374i
$52$	−0.977478	−	5.54355i	−0.135552	−	0.768753i
$53$	−1.51336	−	8.58267i	−0.207876	−	1.17892i	−0.892850	−	0.450354i	$-0.851298\pi$
$53$	−1.51336	−	8.58267i	−0.207876	−	1.17892i	0.684975	−	0.728567i	$-0.259813\pi$
$54$	−3.16298	+	2.65406i	−0.430427	+	0.361171i
$55$	4.18074	−	1.52166i	0.563730	−	0.205181i
$56$	1.30736	−	0.475838i	0.174703	−	0.0635866i
$57$	3.96930	−	3.33064i	0.525747	−	0.441154i
$58$	0.391051	+	2.21776i	0.0513475	+	0.291206i
$59$	−2.27716	−	12.9144i	−0.296461	−	1.68131i	−0.661206	−	0.750204i	$-0.729955\pi$
$59$	−2.27716	−	12.9144i	−0.296461	−	1.68131i	0.364746	−	0.931107i	$-0.381156\pi$
$60$	0.989011	−	1.71302i	0.127681	−	0.221150i
$61$	4.74529	+	3.98177i	0.607572	+	0.509813i	0.893869	−	0.448328i	$-0.147980\pi$
$61$	4.74529	+	3.98177i	0.607572	+	0.509813i	−0.286298	+	0.958141i	$0.592425\pi$
$62$	−3.67582	−	1.33789i	−0.466830	−	0.169912i
$63$	−0.634812	−	1.09953i	−0.0799788	−	0.138527i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−4.31212	+	3.61830i	−0.534853	+	0.448795i
$66$	4.40016	+	7.62129i	0.541622	+	0.938116i
$67$	−2.46893	+	14.0020i	−0.301628	+	1.71062i	0.337339	+	0.941383i	$0.390473\pi$
$67$	−2.46893	+	14.0020i	−0.301628	+	1.71062i	−0.638967	+	0.769234i	$0.720638\pi$
$68$	−2.68217			−0.325261
$69$	0.502452	−	2.84954i	0.0604881	−	0.343045i
$70$	−1.06577	−	0.894284i	−0.127383	−	0.106887i
$71$	−1.73713	+	0.632262i	−0.206159	+	0.0750357i	−0.443036	−	0.896504i	$-0.646098\pi$
$71$	−1.73713	+	0.632262i	−0.206159	+	0.0750357i	0.236877	+	0.971540i	$0.423876\pi$
$72$	0.857537	+	0.312118i	0.101062	+	0.0367835i
$73$	−8.55998			−1.00187			−0.500935	−	0.865485i	$-0.667010\pi$
$73$	−8.55998			−1.00187			−0.500935	+	0.865485i	$0.667010\pi$
$74$	−6.01588	+	0.899526i	−0.699332	+	0.104568i
$75$	−1.97802			−0.228402
$76$	2.46158	+	0.895943i	0.282363	+	0.102772i
$77$	5.81648	−	2.11703i	0.662850	−	0.241258i
$78$	−8.52947	−	7.15707i	−0.965772	−	0.810379i
$79$	−0.519316	+	2.94519i	−0.0584276	+	0.331359i	−0.999985	−	0.00549352i	$-0.998251\pi$
$79$	−0.519316	+	2.94519i	−0.0584276	+	0.331359i	0.941557	+	0.336853i	$0.109362\pi$
$80$	1.00000			0.111803
$81$	−1.89362	+	10.7393i	−0.210402	+	1.19325i
$82$	1.42271	+	2.46420i	0.157112	+	0.272126i
$83$	12.5191	−	10.5048i	1.37415	−	1.15305i	0.402826	−	0.915277i	$-0.368028\pi$
$83$	12.5191	−	10.5048i	1.37415	−	1.15305i	0.971321	−	0.237770i	$-0.0764165\pi$
$84$	1.37597	−	2.38325i	0.150131	−	0.260034i
$85$	1.34109	+	2.32283i	0.145461	+	0.251946i
$86$	−1.01492	−	0.369401i	−0.109442	−	0.0398335i
$87$	3.41231	+	2.86327i	0.365838	+	0.306975i
$88$	−2.22452	+	3.85299i	−0.237135	+	0.410730i
$89$	−0.948852	−	5.38121i	−0.100578	−	0.570407i	−0.992895	−	0.118997i	$-0.962032\pi$
$89$	−0.948852	−	5.38121i	−0.100578	−	0.570407i	0.892317	−	0.451410i	$-0.149079\pi$
$90$	−0.158466	−	0.898708i	−0.0167038	−	0.0947322i
$91$	−5.99927	+	5.03399i	−0.628895	+	0.527705i
$92$	1.37461	−	0.500316i	0.143313	−	0.0521616i
$93$	−7.27086	+	2.64638i	−0.753953	+	0.274417i
$94$	−2.17918	+	1.82855i	−0.224766	+	0.188601i
$95$	−0.454882	−	2.57977i	−0.0466699	−	0.264678i
$96$	0.343480	+	1.94797i	0.0350563	+	0.198814i
$97$	4.62509	−	8.01090i	0.469607	−	0.813383i	−0.529789	−	0.848129i	$-0.677729\pi$
$97$	4.62509	−	8.01090i	0.469607	−	0.813383i	0.999396	+	0.0347460i	$0.0110622\pi$
$98$	3.87956	+	3.25533i	0.391894	+	0.328838i
$99$	3.81522	+	1.38863i	0.383444	+	0.139562i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	0.824232	−	1.42761i	0.0820142	−	0.142053i	−0.822101	−	0.569342i	$-0.807198\pi$
$101$	0.824232	−	1.42761i	0.0820142	−	0.142053i	0.904115	+	0.427289i	$0.140531\pi$
$102$	−4.06417	+	3.41025i	−0.402413	+	0.337665i
$103$	−4.37703	−	7.58124i	−0.431282	−	0.747002i	0.565702	−	0.824610i	$-0.308605\pi$
$103$	−4.37703	−	7.58124i	−0.431282	−	0.747002i	−0.996984	+	0.0776078i	$0.975272\pi$
$104$	0.977478	−	5.54355i	0.0958496	−	0.543590i
$105$	−2.75194			−0.268562
$106$	1.51336	−	8.58267i	0.146990	−	0.833623i
$107$	−8.47684	−	7.11292i	−0.819487	−	0.687632i	0.133365	−	0.991067i	$-0.457422\pi$
$107$	−8.47684	−	7.11292i	−0.819487	−	0.687632i	−0.952852	+	0.303435i	$0.901866\pi$
$108$	−3.87997	+	1.41219i	−0.373350	+	0.135888i
$109$	0.947449	+	0.344843i	0.0907491	+	0.0330300i	0.386996	−	0.922081i	$-0.373513\pi$
$109$	0.947449	+	0.344843i	0.0907491	+	0.0330300i	−0.296247	+	0.955111i	$0.595735\pi$
$110$	4.44905			0.424200
$111$	−7.97188	+	9.01189i	−0.756658	+	0.855371i
$112$	1.39126			0.131462
$113$	2.35368	+	0.856671i	0.221416	+	0.0805888i	0.450346	−	0.892854i	$-0.351301\pi$
$113$	2.35368	+	0.856671i	0.221416	+	0.0805888i	−0.228930	+	0.973443i	$0.573523\pi$
$114$	4.86907	−	1.77220i	0.456030	−	0.165981i
$115$	−1.12059	−	0.940287i	−0.104496	−	0.0876822i
$116$	−0.391051	+	2.21776i	−0.0363082	+	0.205914i
$117$	−5.13693			−0.474910
$118$	2.27716	−	12.9144i	0.209629	−	1.18887i
$119$	1.86580	+	3.23166i	0.171038	+	0.296246i
$120$	1.51525	−	1.27145i	0.138323	−	0.116067i
$121$	−4.39700	+	7.61583i	−0.399727	+	0.692348i
$122$	3.09726	+	5.36462i	0.280413	+	0.485690i
$123$	5.28887	+	1.92499i	0.476881	+	0.173571i
$124$	−2.99656	−	2.51441i	−0.269099	−	0.225801i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$	−0.220468	−	1.25034i	−0.0196408	−	0.111389i
$127$	−3.53961	−	20.0741i	−0.314089	−	1.78129i	−0.577280	−	0.816546i	$-0.695886\pi$
$127$	−3.53961	−	20.0741i	−0.314089	−	1.78129i	0.263191	−	0.964744i	$-0.415225\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−2.00754	+	0.730684i	−0.176754	+	0.0643331i
$130$	−5.28960	+	1.92526i	−0.463928	+	0.168856i
$131$	−11.8599	+	9.95168i	−1.03621	+	0.869482i	−0.991577	−	0.129521i	$-0.958656\pi$
$131$	−11.8599	+	9.95168i	−1.03621	+	0.869482i	−0.0446319	+	0.999004i	$0.514211\pi$
$132$	1.52816	+	8.66661i	0.133009	+	0.754332i
$133$	−0.632859	−	3.58912i	−0.0548758	−	0.311216i
$134$	−7.10900	+	12.3132i	−0.614124	+	1.06369i
$135$	3.16298	+	2.65406i	0.272226	+	0.228425i
$136$	−2.52042	−	0.917358i	−0.216124	−	0.0786628i
$137$	10.2253	+	17.7107i	0.873603	+	1.51312i	0.858244	+	0.513242i	$0.171556\pi$
$137$	10.2253	+	17.7107i	0.873603	+	1.51312i	0.0153586	+	0.999882i	$0.495111\pi$
$138$	1.44675	−	2.50585i	0.123156	−	0.213312i
$139$	−3.22078	+	2.70255i	−0.273183	+	0.229227i	−0.769078	−	0.639155i	$-0.779284\pi$
$139$	−3.22078	+	2.70255i	−0.273183	+	0.229227i	0.495896	+	0.868382i	$0.334840\pi$
$140$	−0.695629	−	1.20487i	−0.0587914	−	0.101830i
$141$	−0.977105	+	5.54144i	−0.0822871	+	0.466673i
$142$	−1.84861			−0.155132
$143$	4.34884	−	24.6635i	0.363669	−	2.06247i
$144$	0.699071	+	0.586590i	0.0582559	+	0.0488825i
$145$	2.11616	−	0.770221i	0.175738	−	0.0639633i
$146$	−8.04375	−	2.92768i	−0.665705	−	0.242297i
$147$	10.0175			0.826229
$148$	−5.96074	−	1.21228i	−0.489970	−	0.0996484i
$149$	19.0560			1.56113			0.780565	−	0.625074i	$-0.214931\pi$
$149$	19.0560			1.56113			0.780565	+	0.625074i	$0.214931\pi$
$150$	−1.85873	−	0.676523i	−0.151765	−	0.0552379i
$151$	1.92626	−	0.701101i	0.156757	−	0.0570548i	−0.262450	−	0.964946i	$-0.584530\pi$
$151$	1.92626	−	0.701101i	0.156757	−	0.0570548i	0.419207	+	0.907891i	$0.362308\pi$
$152$	2.00670	+	1.68382i	0.162765	+	0.136576i
$153$	−0.425035	+	2.41049i	−0.0343620	+	0.194877i
$154$	6.18977			0.498786
$155$	−0.679265	+	3.85230i	−0.0545599	+	0.309424i
$156$	−5.56722	−	9.64270i	−0.445734	−	0.772034i
$157$	3.42849	−	2.87684i	0.273623	−	0.229597i	−0.495642	−	0.868527i	$-0.665067\pi$
$157$	3.42849	−	2.87684i	0.273623	−	0.229597i	0.769265	+	0.638930i	$0.220623\pi$
$158$	−1.49531	+	2.58995i	−0.118960	+	0.206046i
$159$	−8.61931	−	14.9291i	−0.683555	−	1.18395i
$160$	0.939693	+	0.342020i	0.0742892	+	0.0270391i
$161$	−1.55903	−	1.30818i	−0.122869	−	0.103099i
$162$	−5.45246	+	9.44395i	−0.428386	+	0.741986i
$163$	−1.02354	−	5.80478i	−0.0801698	−	0.454665i	−0.998295	−	0.0583744i	$-0.981408\pi$
$163$	−1.02354	−	5.80478i	−0.0801698	−	0.454665i	0.918125	−	0.396291i	$-0.129703\pi$
$164$	0.494101	+	2.80219i	0.0385828	+	0.218814i
$165$	6.74143	−	5.65673i	0.524820	−	0.440376i
$166$	15.3569	−	5.58946i	1.19193	−	0.433826i
$167$	23.0441	−	8.38738i	1.78321	−	0.649035i	0.783595	−	0.621272i	$-0.213384\pi$
$167$	23.0441	−	8.38738i	1.78321	−	0.649035i	0.999615	−	0.0277636i	$-0.00883857\pi$
$168$	2.10811	−	1.76891i	0.162644	−	0.136475i
$169$	3.24487	+	18.4026i	0.249605	+	1.41558i
$170$	0.465755	+	2.64143i	0.0357218	+	0.202588i
$171$	1.19527	−	2.07027i	0.0914046	−	0.158317i
$172$	−0.827371	−	0.694247i	−0.0630865	−	0.0529358i
$173$	1.78838	+	0.650919i	0.135968	+	0.0494884i	0.409108	−	0.912486i	$-0.365840\pi$
$173$	1.78838	+	0.650919i	0.135968	+	0.0494884i	−0.273140	+	0.961974i	$0.588062\pi$
$174$	2.22723	+	3.85767i	0.168846	+	0.292449i
$175$	−0.695629	+	1.20487i	−0.0525846	+	0.0910792i
$176$	−3.40817	+	2.85979i	−0.256900	+	0.215565i
$177$	−12.9695	−	22.4639i	−0.974849	−	1.68849i
$178$	0.948852	−	5.38121i	0.0711195	−	0.403339i
$179$	18.4043			1.37560			0.687800	−	0.725900i	$-0.258576\pi$
$179$	18.4043			1.37560			0.687800	+	0.725900i	$0.258576\pi$
$180$	0.158466	−	0.898708i	0.0118114	−	0.0669857i
$181$	14.2547	+	11.9612i	1.05955	+	0.889066i	0.994065	−	0.108788i	$-0.0346970\pi$
$181$	14.2547	+	11.9612i	1.05955	+	0.889066i	0.0654821	+	0.997854i	$0.479141\pi$
$182$	−7.35920	+	2.67853i	−0.545500	+	0.198546i
$183$	11.5140	+	4.19074i	0.851138	+	0.309789i
$184$	1.46283			0.107841
$185$	1.93051	+	5.76829i	0.141934	+	0.424093i
$186$	−7.73749			−0.567340
$187$	−11.2135	−	4.08137i	−0.820009	−	0.298459i
$188$	−2.67316	+	0.972952i	−0.194960	+	0.0709598i
$189$	4.40052	+	3.69248i	0.320091	+	0.268588i
$190$	0.454882	−	2.57977i	0.0330006	−	0.187156i
$191$	9.31052			0.673686			0.336843	−	0.941561i	$-0.390641\pi$
$191$	9.31052			0.673686			0.336843	+	0.941561i	$0.390641\pi$
$192$	−0.343480	+	1.94797i	−0.0247885	+	0.140583i
$193$	6.68267	+	11.5747i	0.481029	+	0.833167i	0.999763	−	0.0217689i	$-0.00692981\pi$
$193$	6.68267	+	11.5747i	0.481029	+	0.833167i	−0.518734	+	0.854936i	$0.673596\pi$
$194$	7.08606	−	5.94591i	0.508749	−	0.426891i
$195$	−5.56722	+	9.64270i	−0.398677	+	0.690528i
$196$	2.53220	+	4.38590i	0.180871	+	0.313278i
$197$	8.82065	+	3.21046i	0.628446	+	0.228735i	0.636555	−	0.771232i	$-0.280359\pi$
$197$	8.82065	+	3.21046i	0.628446	+	0.228735i	−0.00810906	+	0.999967i	$0.502581\pi$
$198$	3.11020	+	2.60977i	0.221032	+	0.185468i
$199$	−5.94363	+	10.2947i	−0.421333	+	0.729770i	−0.996070	−	0.0885681i	$-0.971771\pi$
$199$	−5.94363	+	10.2947i	−0.421333	+	0.729770i	0.574737	+	0.818338i	$0.305104\pi$
$200$	−0.173648	−	0.984808i	−0.0122788	−	0.0696364i
$201$	4.88360	+	27.6963i	0.344463	+	1.95354i
$202$	1.26280	−	1.05961i	0.0888501	−	0.0745541i
$203$	2.94413	−	1.07158i	0.206637	−	0.0752099i
$204$	−4.98545	+	1.81455i	−0.349051	+	0.127044i
$205$	2.17972	−	1.82900i	0.152238	−	0.127743i
$206$	−1.52013	−	8.62107i	−0.105912	−	0.600658i
$207$	−0.231809	−	1.31465i	−0.0161118	−	0.0913748i
$208$	2.81454	−	4.87492i	0.195153	−	0.338015i
$209$	8.92790	+	7.49140i	0.617556	+	0.518191i
$210$	−2.58598	−	0.941219i	−0.178449	−	0.0649503i
$211$	−1.98769	−	3.44279i	−0.136839	−	0.237011i	0.789460	−	0.613802i	$-0.210361\pi$
$211$	−1.98769	−	3.44279i	−0.136839	−	0.237011i	−0.926298	+	0.376791i	$0.877027\pi$
$212$	4.35754	−	7.54748i	0.299277	−	0.518363i
$213$	−2.80111	+	2.35041i	−0.191929	+	0.161048i
$214$	−5.53287	−	9.58321i	−0.378219	−	0.655094i
$215$	−0.187550	+	1.06365i	−0.0127908	+	0.0725402i
$216$	−4.12898			−0.280941
$217$	−0.945033	+	5.35955i	−0.0641530	+	0.363830i
$218$	0.772367	+	0.648093i	0.0523113	+	0.0438944i
$219$	−15.9107	+	5.79102i	−1.07515	+	0.391321i
$220$	4.18074	+	1.52166i	0.281865	+	0.102591i
$221$	15.0982			1.01561
$222$	−10.5734	+	5.74186i	−0.709638	+	0.385369i
$223$	−10.5978			−0.709681			−0.354841	−	0.934927i	$-0.615465\pi$
$223$	−10.5978			−0.709681			−0.354841	+	0.934927i	$0.615465\pi$
$224$	1.30736	+	0.475838i	0.0873514	+	0.0317933i
$225$	−0.857537	+	0.312118i	−0.0571692	+	0.0208079i
$226$	1.91874	+	1.61001i	0.127633	+	0.107097i
$227$	3.26639	−	18.5246i	0.216798	−	1.22952i	−0.660961	−	0.750421i	$-0.729851\pi$
$227$	3.26639	−	18.5246i	0.216798	−	1.22952i	0.877759	−	0.479103i	$-0.159038\pi$
$228$	5.18155			0.343157
$229$	2.56743	−	14.5606i	0.169660	−	0.962191i	−0.774468	−	0.632613i	$-0.781982\pi$
$229$	2.56743	−	14.5606i	0.169660	−	0.962191i	0.944128	−	0.329578i	$-0.106907\pi$
$230$	−0.731413	−	1.26685i	−0.0482280	−	0.0835333i
$231$	9.37907	−	7.86997i	0.617098	−	0.517806i
$232$	−1.12599	+	1.95027i	−0.0739247	+	0.128041i
$233$	−10.6405	−	18.4298i	−0.697080	−	1.20738i	−0.969475	−	0.245192i	$-0.921149\pi$
$233$	−10.6405	−	18.4298i	−0.697080	−	1.20738i	0.272395	−	0.962186i	$-0.412184\pi$
$234$	−4.82714	−	1.75694i	−0.315560	−	0.114854i
$235$	2.17918	+	1.82855i	0.142154	+	0.119282i
$236$	6.55681	−	11.3567i	0.426812	−	0.739260i
$237$	1.02722	+	5.82564i	0.0667250	+	0.378416i
$238$	0.647985	+	3.67491i	0.0420026	+	0.238209i
$239$	−12.8656	+	10.7955i	−0.832205	+	0.698303i	−0.955796	−	0.294031i	$-0.905003\pi$
$239$	−12.8656	+	10.7955i	−0.832205	+	0.698303i	0.123591	+	0.992333i	$0.460559\pi$
$240$	1.85873	−	0.676523i	0.119981	−	0.0436694i
$241$	4.56212	−	1.66048i	0.293872	−	0.106961i	−0.190877	−	0.981614i	$-0.561133\pi$
$241$	4.56212	−	1.66048i	0.293872	−	0.106961i	0.484749	+	0.874653i	$0.338911\pi$
$242$	−6.73660	+	5.65268i	−0.433045	+	0.363368i
$243$	1.59466	+	9.04374i	0.102297	+	0.580156i
$244$	1.07567	+	6.10042i	0.0688626	+	0.390539i
$245$	2.53220	−	4.38590i	0.161776	−	0.280205i
$246$	4.31153	+	3.61780i	0.274893	+	0.230663i
$247$	−13.8564	−	5.04333i	−0.881664	−	0.320899i
$248$	−1.95587	−	3.38766i	−0.124198	−	0.215116i
$249$	16.1629	−	27.9950i	1.02428	−	1.77411i
$250$	−0.766044	+	0.642788i	−0.0484489	+	0.0406535i
$251$	−10.5602	−	18.2908i	−0.666553	−	1.15450i	−0.978862	−	0.204523i	$-0.934436\pi$
$251$	−10.5602	−	18.2908i	−0.666553	−	1.15450i	0.312309	−	0.949981i	$-0.398898\pi$
$252$	0.220468	−	1.25034i	0.0138882	−	0.0787637i
$253$	6.50818			0.409166
$254$	3.53961	−	20.0741i	0.222095	−	1.25956i
$255$	4.06417	+	3.41025i	0.254508	+	0.213558i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	23.6257	+	8.59906i	1.47373	+	0.536395i	0.949111	−	0.314941i	$-0.101985\pi$
$257$	23.6257	+	8.59906i	1.47373	+	0.536395i	0.524621	+	0.851336i	$0.324207\pi$
$258$	−2.13638			−0.133005
$259$	2.68583	+	8.02518i	0.166890	+	0.498660i
$260$	−5.62907			−0.349100
$261$	1.93115	+	0.702882i	0.119535	+	0.0435073i
$262$	−14.5484	+	5.29518i	−0.898802	+	0.327137i
$263$	5.75111	+	4.82576i	0.354629	+	0.297569i	0.802646	−	0.596456i	$-0.203425\pi$
$263$	5.75111	+	4.82576i	0.354629	+	0.297569i	−0.448017	+	0.894025i	$0.647870\pi$
$264$	−1.52816	+	8.66661i	−0.0940516	+	0.533393i
$265$	−8.71508			−0.535363
$266$	0.632859	−	3.58912i	0.0388031	−	0.220063i
$267$	−5.40418	−	9.36031i	−0.330730	−	0.572842i
$268$	−10.8916	+	9.13916i	−0.665312	+	0.558263i
$269$	−8.27886	+	14.3394i	−0.504771	+	0.874289i	0.495214	+	0.868771i	$0.335090\pi$
$269$	−8.27886	+	14.3394i	−0.504771	+	0.874289i	−0.999985	+	0.00551803i	$0.998244\pi$
$270$	2.06449	+	3.57580i	0.125641	+	0.217616i
$271$	−12.7036	−	4.62374i	−0.771689	−	0.280872i	−0.0739865	−	0.997259i	$-0.523572\pi$
$271$	−12.7036	−	4.62374i	−0.771689	−	0.280872i	−0.697703	+	0.716387i	$0.745794\pi$
$272$	−2.05466	−	1.72407i	−0.124582	−	0.104537i
$273$	−7.74544	+	13.4155i	−0.468775	+	0.811942i
$274$	3.55119	+	20.1398i	0.214535	+	1.21669i
$275$	−0.772569	−	4.38145i	−0.0465876	−	0.264212i
$276$	2.21655	−	1.85991i	0.133421	−	0.111953i
$277$	23.7458	−	8.64278i	1.42675	−	0.519294i	0.490751	−	0.871300i	$-0.336722\pi$
$277$	23.7458	−	8.64278i	1.42675	−	0.519294i	0.935998	+	0.352006i	$0.114500\pi$
$278$	−3.95087	+	1.43800i	−0.236957	+	0.0862454i
$279$	−2.73458	+	2.29458i	−0.163715	+	0.137373i
$280$	−0.241589	−	1.37012i	−0.0144377	−	0.0818805i
$281$	−3.09595	−	17.5580i	−0.184689	−	1.04742i	−0.926354	−	0.376653i	$-0.877075\pi$
$281$	−3.09595	−	17.5580i	−0.184689	−	1.04742i	0.741665	−	0.670770i	$-0.234036\pi$
$282$	−2.81346	+	4.87306i	−0.167539	+	0.290186i
$283$	13.8452	+	11.6175i	0.823009	+	0.690587i	0.953675	−	0.300840i	$-0.0972670\pi$
$283$	13.8452	+	11.6175i	0.823009	+	0.690587i	−0.130666	+	0.991426i	$0.541711\pi$
$284$	−1.73713	−	0.632262i	−0.103079	−	0.0375179i
$285$	−2.59078	−	4.48736i	−0.153464	−	0.265808i
$286$	12.5220	−	21.6887i	0.740441	−	1.28248i
$287$	3.03255	−	2.54461i	0.179006	−	0.150204i
$288$	0.456286	+	0.790311i	0.0268869	+	0.0465695i
$289$	−1.70278	+	9.65697i	−0.100164	+	0.568057i
$290$	2.25197			0.132240
$291$	3.17725	−	18.0191i	0.186254	−	1.05630i
$292$	−6.55732	−	5.50225i	−0.383738	−	0.321995i
$293$	−17.2999	+	6.29665i	−1.01067	+	0.367854i	−0.793690	−	0.608322i	$-0.791843\pi$
$293$	−17.2999	+	6.29665i	−1.01067	+	0.367854i	−0.216980	+	0.976176i	$0.569621\pi$
$294$	9.41337	+	3.42619i	0.548999	+	0.199819i
$295$	−13.1136			−0.763505
$296$	−5.18664	−	3.17786i	−0.301467	−	0.184709i
$297$	−18.3700			−1.06594
$298$	17.9068	+	6.51755i	1.03731	+	0.377551i
$299$	−7.73776	+	2.81632i	−0.447486	+	0.162872i
$300$	−1.51525	−	1.27145i	−0.0874832	−	0.0734071i
$301$	−0.260930	+	1.47981i	−0.0150398	+	0.0852948i
$302$	2.04988			0.117957
$303$	0.566215	−	3.21116i	0.0325282	−	0.184476i
$304$	1.30978	+	2.26861i	0.0751211	+	0.130114i
$305$	4.74529	−	3.98177i	0.271714	−	0.227995i
$306$	−1.22384	+	2.11975i	−0.0699622	+	0.121178i
$307$	6.71192	+	11.6254i	0.383070	+	0.663496i	0.991499	−	0.130112i	$-0.0415336\pi$
$307$	6.71192	+	11.6254i	0.383070	+	0.663496i	−0.608430	+	0.793608i	$0.708200\pi$
$308$	5.81648	+	2.11703i	0.331425	+	0.120629i
$309$	−13.2646	−	11.1303i	−0.754598	−	0.633183i
$310$	−1.95587	+	3.38766i	−0.111086	+	0.192406i
$311$	−5.26923	−	29.8833i	−0.298791	−	1.69453i	−0.651383	−	0.758749i	$-0.725811\pi$
$311$	−5.26923	−	29.8833i	−0.298791	−	1.69453i	0.352592	−	0.935777i	$-0.385300\pi$
$312$	−1.93347	−	10.9653i	−0.109461	−	0.620786i
$313$	−19.9752	+	16.7612i	−1.12907	+	0.947400i	−0.999027	−	0.0441089i	$-0.985955\pi$
$313$	−19.9752	+	16.7612i	−1.12907	+	0.947400i	−0.130040	+	0.991509i	$0.541511\pi$
$314$	4.20566	−	1.53074i	0.237339	−	0.0863844i
$315$	−1.19306	+	0.434237i	−0.0672211	+	0.0244665i
$316$	−2.29095	+	1.92233i	−0.128876	+	0.108140i
$317$	4.75846	+	26.9866i	0.267262	+	1.51572i	0.762516	+	0.646969i	$0.223964\pi$
$317$	4.75846	+	26.9866i	0.267262	+	1.51572i	−0.495254	+	0.868748i	$0.664925\pi$
$318$	−2.99345	−	16.9767i	−0.167865	−	0.952007i
$319$	−5.00957	+	8.67683i	−0.280482	+	0.485809i
$320$	0.766044	+	0.642788i	0.0428232	+	0.0359329i
$321$	−20.5682	−	7.48623i	−1.14801	−	0.417841i
$322$	−1.01758	−	1.76251i	−0.0567078	−	0.0982208i
$323$	−3.51306	+	6.08480i	−0.195472	+	0.338567i
$324$	−8.35366	+	7.00955i	−0.464092	+	0.389420i
$325$	2.81454	+	4.87492i	0.156122	+	0.270412i
$326$	1.02354	−	5.80478i	0.0566886	−	0.321497i
$327$	1.99435			0.110288
$328$	−0.494101	+	2.80219i	−0.0272822	+	0.154725i
$329$	3.03181	+	2.54399i	0.167149	+	0.140255i
$330$	8.26959	−	3.00988i	0.455226	−	0.165689i
$331$	−3.32053	−	1.20857i	−0.182513	−	0.0664292i	0.249147	−	0.968466i	$-0.419850\pi$
$331$	−3.32053	−	1.20857i	−0.182513	−	0.0664292i	−0.431660	+	0.902036i	$0.642072\pi$
$332$	16.3425			0.896911
$333$	−2.03406	+	5.16486i	−0.111466	+	0.283032i
$334$	24.5231			1.34184
$335$	13.3606	+	4.86285i	0.729965	+	0.265686i
$336$	2.58598	−	0.941219i	0.141077	−	0.0513477i
$337$	−22.3027	−	18.7142i	−1.21491	−	1.01943i	−0.999075	−	0.0429981i	$-0.986309\pi$
$337$	−22.3027	−	18.7142i	−1.21491	−	1.01943i	−0.215832	−	0.976430i	$-0.569246\pi$
$338$	−3.24487	+	18.4026i	−0.176498	+	1.00097i
$339$	4.95443			0.269088
$340$	−0.465755	+	2.64143i	−0.0252591	+	0.143251i
$341$	−8.70173	−	15.0718i	−0.471225	−	0.816186i
$342$	1.83126	−	1.53661i	0.0990232	−	0.0830903i
$343$	8.39235	−	14.5360i	0.453144	−	0.784869i
$344$	−0.540028	−	0.935356i	−0.0291164	−	0.0504310i
$345$	−2.71900	−	0.989637i	−0.146386	−	0.0532802i
$346$	1.45790	+	1.22333i	0.0783774	+	0.0657665i
$347$	−3.65616	+	6.33265i	−0.196273	+	0.339954i	−0.947317	−	0.320297i	$-0.896217\pi$
$347$	−3.65616	+	6.33265i	−0.196273	+	0.339954i	0.751044	+	0.660252i	$0.229550\pi$
$348$	0.773508	+	4.38678i	0.0414644	+	0.235156i
$349$	−2.00692	−	11.3818i	−0.107428	−	0.609255i	−0.990223	−	0.139496i	$-0.955452\pi$
$349$	−2.00692	−	11.3818i	−0.107428	−	0.609255i	0.882795	−	0.469759i	$-0.155659\pi$
$350$	−1.06577	+	0.894284i	−0.0569676	+	0.0478015i
$351$	21.8406	−	7.94934i	1.16577	−	0.424304i
$352$	−4.18074	+	1.52166i	−0.222834	+	0.0811049i
$353$	−8.40255	+	7.05058i	−0.447223	+	0.375264i	−0.838404	−	0.545049i	$-0.816511\pi$
$353$	−8.40255	+	7.05058i	−0.447223	+	0.375264i	0.391181	+	0.920314i	$0.372066\pi$
$354$	−4.50427	−	25.5450i	−0.239399	−	1.35770i
$355$	0.321008	+	1.82053i	0.0170373	+	0.0966235i
$356$	2.73211	−	4.73215i	0.144802	−	0.250804i
$357$	5.65431	+	4.74453i	0.299258	+	0.251107i
$358$	17.2944	+	6.29464i	0.914036	+	0.332682i
$359$	1.44815	+	2.50827i	0.0764305	+	0.132382i	0.901707	−	0.432347i	$-0.142314\pi$
$359$	1.44815	+	2.50827i	0.0764305	+	0.132382i	−0.825277	+	0.564728i	$0.808981\pi$
$360$	0.456286	−	0.790311i	0.0240484	−	0.0416530i
$361$	−9.29817	+	7.80209i	−0.489377	+	0.410636i
$362$	9.30413	+	16.1152i	0.489014	+	0.846997i
$363$	−3.02056	+	17.1305i	−0.158539	+	0.899117i
$364$	−7.83149			−0.410482
$365$	−1.48642	+	8.42993i	−0.0778030	+	0.441243i
$366$	9.38628	+	7.87602i	0.490629	+	0.411686i
$367$	−29.2777	+	10.6562i	−1.52828	+	0.556250i	−0.963200	−	0.268784i	$-0.913378\pi$
$367$	−29.2777	+	10.6562i	−1.52828	+	0.556250i	−0.565083	+	0.825034i	$0.691156\pi$
$368$	1.37461	+	0.500316i	0.0716564	+	0.0260808i
$369$	2.59665			0.135176
$370$	−0.158787	+	6.08069i	−0.00825495	+	0.316120i
$371$	−12.1249			−0.629495
$372$	−7.27086	−	2.64638i	−0.376977	−	0.137208i
$373$	−8.93473	+	3.25198i	−0.462623	+	0.168381i	−0.562808	−	0.826588i	$-0.690279\pi$
$373$	−8.93473	+	3.25198i	−0.462623	+	0.168381i	0.100185	+	0.994969i	$0.468057\pi$
$374$	−9.14130	−	7.67046i	−0.472685	−	0.396630i
$375$	−0.343480	+	1.94797i	−0.0177372	+	0.100593i
$376$	−2.84472			−0.146705
$377$	2.20126	−	12.4839i	0.113370	−	0.642956i
$378$	2.87224	+	4.97486i	0.147732	+	0.255879i
$379$	−28.3857	+	23.8185i	−1.45808	+	1.22347i	−0.531669	+	0.846952i	$0.678435\pi$
$379$	−28.3857	+	23.8185i	−1.45808	+	1.22347i	−0.926409	+	0.376520i	$0.877121\pi$
$380$	1.30978	−	2.26861i	0.0671904	−	0.116377i
$381$	−20.1598	−	34.9178i	−1.03282	−	1.78889i
$382$	8.74903	+	3.18439i	0.447639	+	0.162927i
$383$	−1.03892	−	0.871760i	−0.0530865	−	0.0445448i	0.615858	−	0.787857i	$-0.288809\pi$
$383$	−1.03892	−	0.871760i	−0.0530865	−	0.0445448i	−0.668945	+	0.743312i	$0.733254\pi$
$384$	−0.989011	+	1.71302i	−0.0504703	+	0.0874171i
$385$	−1.07484	−	6.09574i	−0.0547791	−	0.310667i
$386$	2.32087	+	13.1623i	0.118129	+	0.669943i
$387$	−0.755036	+	0.633550i	−0.0383806	+	0.0322052i
$388$	8.69233	−	3.16375i	0.441286	−	0.160615i
$389$	−28.1186	+	10.2343i	−1.42567	+	0.518901i	−0.935687	−	0.352832i	$-0.885219\pi$
$389$	−28.1186	+	10.2343i	−1.42567	+	0.518901i	−0.489981	+	0.871733i	$0.662996\pi$
$390$	−8.52947	+	7.15707i	−0.431906	+	0.362413i
$391$	0.681318	+	3.86395i	0.0344558	+	0.195408i
$392$	0.879424	+	4.98746i	0.0444176	+	0.251905i
$393$	−15.3119	+	26.5210i	−0.772385	+	1.33781i
$394$	7.19066	+	6.03368i	0.362260	+	0.303973i
$395$	2.81026	+	1.02285i	0.141400	+	0.0514653i
$396$	2.03004	+	3.51613i	0.102013	+	0.176692i
$397$	1.08970	−	1.88741i	0.0546903	−	0.0947263i	−0.837384	−	0.546615i	$-0.815916\pi$
$397$	1.08970	−	1.88741i	0.0546903	−	0.0947263i	0.892074	+	0.451889i	$0.149250\pi$
$398$	−9.10617	+	7.64098i	−0.456451	+	0.383008i
$399$	−3.60444	−	6.24307i	−0.180448	−	0.312545i
$400$	0.173648	−	0.984808i	0.00868241	−	0.0492404i
$401$	−29.4120			−1.46876			−0.734382	−	0.678737i	$-0.762528\pi$
$401$	−29.4120			−1.46876			−0.734382	+	0.678737i	$0.762528\pi$
$402$	−4.88360	+	27.6963i	−0.243572	+	1.38136i
$403$	16.8678	+	14.1538i	0.840247	+	0.705051i
$404$	1.54905	−	0.563808i	0.0770681	−	0.0280505i
$405$	10.2473	+	3.72971i	0.509191	+	0.185331i
$406$	3.13308			0.155492
$407$	−23.0756	−	14.1384i	−1.14381	−	0.700816i
$408$	−5.30540			−0.262656
$409$	23.5327	+	8.56521i	1.16362	+	0.423522i	0.850389	−	0.526155i	$-0.176367\pi$
$409$	23.5327	+	8.56521i	1.16362	+	0.423522i	0.313230	+	0.949677i	$0.398589\pi$
$410$	2.67382	−	0.973190i	0.132050	−	0.0480624i
$411$	30.9877	+	26.0018i	1.52851	+	1.28257i
$412$	1.52013	−	8.62107i	0.0748913	−	0.424730i
$413$	−18.2444			−0.897750
$414$	0.231809	−	1.31465i	0.0113928	−	0.0646117i
$415$	−8.17125	−	14.1530i	−0.401111	−	0.694744i
$416$	4.31212	−	3.61830i	0.211419	−	0.177402i
$417$	−4.15822	+	7.20225i	−0.203629	+	0.352696i
$418$	5.82728	+	10.0931i	0.285021	+	0.493671i
$419$	4.36493	+	1.58870i	0.213241	+	0.0776133i	0.446432	−	0.894818i	$-0.352695\pi$
$419$	4.36493	+	1.58870i	0.213241	+	0.0776133i	−0.233191	+	0.972431i	$0.574917\pi$
$420$	−2.10811	−	1.76891i	−0.102865	−	0.0863141i
$421$	−2.46924	+	4.27685i	−0.120344	+	0.208441i	−0.919903	−	0.392146i	$-0.871733\pi$
$421$	−2.46924	+	4.27685i	−0.120344	+	0.208441i	0.799560	+	0.600587i	$0.205066\pi$
$422$	−0.690319	−	3.91499i	−0.0336042	−	0.190579i
$423$	0.450793	+	2.55657i	0.0219183	+	0.124305i
$424$	6.67614	−	5.60194i	0.324222	−	0.272054i
$425$	2.52042	−	0.917358i	0.122258	−	0.0444984i
$426$	−3.43607	+	1.25063i	−0.166478	+	0.0605932i
$427$	6.60192	−	5.53967i	0.319489	−	0.268083i
$428$	−1.92154	−	10.8976i	−0.0928814	−	0.526756i
$429$	−8.60211	−	48.7850i	−0.415314	−	2.35536i
$430$	−0.540028	+	0.935356i	−0.0260425	+	0.0451069i
$431$	7.19472	+	6.03709i	0.346558	+	0.290796i	0.799406	−	0.600791i	$-0.205148\pi$
$431$	7.19472	+	6.03709i	0.346558	+	0.290796i	−0.452848	+	0.891588i	$0.649592\pi$
$432$	−3.87997	−	1.41219i	−0.186675	−	0.0679442i
$433$	7.23747	+	12.5357i	0.347811	+	0.602426i	0.985860	−	0.167570i	$-0.0535919\pi$
$433$	7.23747	+	12.5357i	0.347811	+	0.602426i	−0.638050	+	0.769995i	$0.720259\pi$
$434$	−2.72111	+	4.71311i	−0.130618	+	0.226236i
$435$	3.41231	−	2.86327i	0.163608	−	0.137283i
$436$	0.504127	+	0.873173i	0.0241433	+	0.0418174i
$437$	0.665414	−	3.77375i	0.0318311	−	0.180523i
$438$	−16.9318			−0.809034
$439$	6.04535	−	34.2849i	0.288529	−	1.63633i	−0.403873	−	0.914815i	$-0.632336\pi$
$439$	6.04535	−	34.2849i	0.288529	−	1.63633i	0.692402	−	0.721512i	$-0.256553\pi$
$440$	3.40817	+	2.85979i	0.162478	+	0.136335i
$441$	4.34291	−	1.58069i	0.206805	−	0.0752710i
$442$	14.1876	+	5.16387i	0.674836	+	0.245620i
$443$	26.6621			1.26675			0.633377	−	0.773843i	$-0.281668\pi$
$443$	26.6621			1.26675			0.633377	+	0.773843i	$0.281668\pi$
$444$	−11.8996	+	1.77928i	−0.564728	+	0.0844410i
$445$	−5.46422			−0.259029
$446$	−9.95868	−	3.62466i	−0.471557	−	0.171633i
$447$	35.4201	−	12.8918i	1.67531	−	0.609764i
$448$	1.06577	+	0.894284i	0.0503527	+	0.0422509i
$449$	5.14706	−	29.1904i	0.242905	−	1.37758i	−0.582404	−	0.812899i	$-0.697888\pi$
$449$	5.14706	−	29.1904i	0.242905	−	1.37758i	0.825309	−	0.564681i	$-0.191001\pi$
$450$	−0.912572			−0.0430191
$451$	−2.19828	+	12.4671i	−0.103513	+	0.587051i
$452$	1.25237	+	2.16917i	0.0589065	+	0.102029i
$453$	3.10609	−	2.60632i	0.145937	−	0.122455i
$454$	9.40521	−	16.2903i	0.441408	−	0.764541i
$455$	3.91575	+	6.78227i	0.183573	+	0.317958i
$456$	4.86907	+	1.77220i	0.228015	+	0.0829907i
$457$	−29.7493	−	24.9626i	−1.39161	−	1.16770i	−0.964682	−	0.263416i	$-0.915151\pi$
$457$	−29.7493	−	24.9626i	−1.39161	−	1.16770i	−0.426930	−	0.904285i	$-0.640405\pi$
$458$	7.39261	−	12.8044i	0.345434	−	0.598309i
$459$	−1.92309	−	10.9064i	−0.0897622	−	0.509067i
$460$	−0.254017	−	1.44060i	−0.0118436	−	0.0671685i
$461$	−10.2492	+	8.60009i	−0.477352	+	0.400546i	−0.849468	−	0.527640i	$-0.823077\pi$
$461$	−10.2492	+	8.60009i	−0.477352	+	0.400546i	0.372116	+	0.928186i	$0.378633\pi$
$462$	11.5051	−	4.18753i	0.535267	−	0.194821i
$463$	−20.3741	+	7.41557i	−0.946866	+	0.344631i	−0.768873	−	0.639401i	$-0.779182\pi$
$463$	−20.3741	+	7.41557i	−0.946866	+	0.344631i	−0.177992	+	0.984032i	$0.556960\pi$
$464$	−1.72511	+	1.44754i	−0.0800863	+	0.0672004i
$465$	1.34360	+	7.61994i	0.0623080	+	0.353366i
$466$	−3.69539	−	20.9576i	−0.171186	−	0.970843i
$467$	−4.98349	+	8.63165i	−0.230608	+	0.399425i	−0.957987	−	0.286811i	$-0.907405\pi$
$467$	−4.98349	+	8.63165i	−0.230608	+	0.399425i	0.727379	+	0.686236i	$0.240738\pi$
$468$	−3.93512	−	3.30196i	−0.181901	−	0.152633i
$469$	18.5880	+	6.76547i	0.858314	+	0.312401i
$470$	1.42236	+	2.46360i	0.0656086	+	0.113637i
$471$	4.42639	−	7.66673i	0.203957	−	0.353264i
$472$	10.0456	−	8.42928i	0.462387	−	0.387989i
$473$	−2.40261	−	4.16144i	−0.110472	−	0.191343i
$474$	−1.02722	+	5.82564i	−0.0471817	+	0.267581i
$475$	−2.61956			−0.120194
$476$	−0.647985	+	3.67491i	−0.0297004	+	0.168439i
$477$	−6.09245	−	5.11218i	−0.278954	−	0.234070i
$478$	−15.7820	+	5.74416i	−0.721850	+	0.262732i
$479$	−3.20931	−	1.16809i	−0.146637	−	0.0533715i	0.267659	−	0.963514i	$-0.413750\pi$
$479$	−3.20931	−	1.16809i	−0.146637	−	0.0533715i	−0.414296	+	0.910142i	$0.635972\pi$
$480$	1.97802			0.0902840
$481$	33.5534	+	6.82399i	1.52990	+	0.311147i
$482$	4.85491			0.221135
$483$	−3.78284	−	1.37684i	−0.172125	−	0.0626484i
$484$	−8.26366	+	3.00773i	−0.375621	+	0.136715i
$485$	−7.08606	−	5.94591i	−0.321761	−	0.269990i
$486$	−1.59466	+	9.04374i	−0.0723350	+	0.410232i
$487$	−17.9827			−0.814872			−0.407436	−	0.913234i	$-0.633577\pi$
$487$	−17.9827			−0.814872			−0.407436	+	0.913234i	$0.633577\pi$
$488$	−1.07567	+	6.10042i	−0.0486932	+	0.276153i
$489$	−5.82955	−	10.0971i	−0.263622	−	0.456606i
$490$	3.87956	−	3.25533i	0.175260	−	0.147061i
$491$	−14.4466	+	25.0223i	−0.651967	+	1.12924i	0.330678	+	0.943744i	$0.392723\pi$
$491$	−14.4466	+	25.0223i	−0.651967	+	1.12924i	−0.982645	+	0.185497i	$0.940611\pi$
$492$	2.81415	+	4.87425i	0.126872	+	0.219748i
$493$	−5.67592	−	2.06587i	−0.255631	−	0.0930419i
$494$	−11.2959	−	9.47836i	−0.508225	−	0.426451i
$495$	2.03004	−	3.51613i	0.0912434	−	0.158038i
$496$	−0.679265	−	3.85230i	−0.0304999	−	0.172973i
$497$	0.446605	+	2.53282i	0.0200330	+	0.113613i
$498$	24.7630	−	20.7786i	1.10966	−	0.931113i
$499$	−31.2100	+	11.3595i	−1.39715	+	0.508521i	−0.927331	−	0.374242i	$-0.877903\pi$
$499$	−31.2100	+	11.3595i	−1.39715	+	0.508521i	−0.469818	+	0.882763i	$0.655681\pi$
$500$	−0.939693	+	0.342020i	−0.0420243	+	0.0152956i
$501$	37.1587	−	31.1798i	1.66013	−	1.39301i
$502$	−3.66751	−	20.7995i	−0.163689	−	0.928327i
$503$	1.67462	+	9.49727i	0.0746678	+	0.423462i	0.999112	+	0.0421437i	$0.0134187\pi$
$503$	1.67462	+	9.49727i	0.0746678	+	0.423462i	−0.924444	+	0.381318i	$0.875470\pi$
$504$	0.634812	−	1.09953i	0.0282768	−	0.0489768i
$505$	−1.26280	−	1.05961i	−0.0561937	−	0.0471521i
$506$	6.11569	+	2.22593i	0.271876	+	0.0989546i
$507$	18.4811	+	32.0102i	0.820775	+	1.42162i
$508$	10.1919	−	17.6529i	0.452192	−	0.783220i
$509$	11.1698	−	9.37261i	0.495095	−	0.415434i	−0.360753	−	0.932661i	$-0.617480\pi$
$509$	11.1698	−	9.37261i	0.495095	−	0.415434i	0.855848	+	0.517227i	$0.173036\pi$
$510$	2.65270	+	4.59461i	0.117464	+	0.203453i
$511$	−2.06800	+	11.7282i	−0.0914829	+	0.518826i
$512$	−1.00000			−0.0441942
$513$	−1.87820	+	10.6518i	−0.0829245	+	0.470288i
$514$	19.2599	+	16.1609i	0.849516	+	0.712829i
$515$	−8.22613	+	2.99407i	−0.362486	+	0.131934i
$516$	−2.00754	−	0.730684i	−0.0883769	−	0.0321665i
$517$	−12.6563			−0.556623
$518$	−0.220914	+	8.45981i	−0.00970640	+	0.371703i
$519$	3.76449			0.165243
$520$	−5.28960	−	1.92526i	−0.231964	−	0.0844281i
$521$	31.6056	−	11.5035i	1.38467	−	0.503977i	0.461077	−	0.887360i	$-0.347463\pi$
$521$	31.6056	−	11.5035i	1.38467	−	0.503977i	0.923590	+	0.383383i	$0.125241\pi$
$522$	1.57429	+	1.32099i	0.0689048	+	0.0578180i
$523$	3.80585	−	21.5841i	0.166418	−	0.943805i	−0.781172	−	0.624316i	$-0.785378\pi$
$523$	3.80585	−	21.5841i	0.166418	−	0.943805i	0.947590	−	0.319489i	$-0.103511\pi$
$524$	−15.4821			−0.676337
$525$	−0.477869	+	2.71013i	−0.0208559	+	0.118280i
$526$	3.75377	+	6.50173i	0.163672	+	0.283489i
$527$	8.03729	−	6.74409i	0.350110	−	0.293777i
$528$	−4.40016	+	7.62129i	−0.191492	+	0.331674i
$529$	10.4301	+	18.0654i	0.453481	+	0.785453i
$530$	−8.18949	−	2.98073i	−0.355729	−	0.129475i
$531$	−9.16735	−	7.69232i	−0.397829	−	0.333818i
$532$	1.82224	−	3.15622i	0.0790043	−	0.136839i
$533$	−2.78133	−	15.7737i	−0.120473	−	0.683236i
$534$	−1.87685	−	10.6441i	−0.0812193	−	0.460617i
$535$	−8.47684	+	7.11292i	−0.366486	+	0.307518i
$536$	−13.3606	+	4.86285i	−0.577088	+	0.210043i
$537$	34.2087	−	12.4509i	1.47621	−	0.537297i
$538$	−12.6840	+	10.6431i	−0.546844	+	0.458857i
$539$	3.91260	+	22.1894i	0.168527	+	0.955767i
$540$	0.716990	+	4.06625i	0.0308543	+	0.174984i
$541$	−12.2203	+	21.1662i	−0.525391	+	0.910005i	0.474171	+	0.880433i	$0.342748\pi$
$541$	−12.2203	+	21.1662i	−0.525391	+	0.910005i	−0.999563	+	0.0295720i	$0.990586\pi$
$542$	−10.3561	−	8.68978i	−0.444832	−	0.373258i
$543$	34.5878	+	12.5889i	1.48430	+	0.540242i
$544$	−1.34109	−	2.32283i	−0.0574986	−	0.0995906i
$545$	0.504127	−	0.873173i	0.0215944	−	0.0374026i
$546$	−11.8667	+	9.95734i	−0.507848	+	0.426135i
$547$	17.3115	+	29.9844i	0.740187	+	1.28204i	0.952410	+	0.304820i	$0.0985962\pi$
$547$	17.3115	+	29.9844i	0.740187	+	1.28204i	−0.212223	+	0.977221i	$0.568070\pi$
$548$	−3.55119	+	20.1398i	−0.151699	+	0.860331i
$549$	5.65296			0.241262
$550$	0.772569	−	4.38145i	0.0329424	−	0.186826i
$551$	4.51904	+	3.79192i	0.192518	+	0.161541i
$552$	2.71900	−	0.989637i	0.115728	−	0.0421217i
$553$	3.90980	+	1.42305i	0.166262	+	0.0605143i
$554$	25.2698			1.07361
$555$	7.49068	+	9.41567i	0.317962	+	0.399673i
$556$	−4.20442			−0.178307
$557$	16.3616	+	5.95514i	0.693263	+	0.252327i	0.664532	−	0.747260i	$-0.268631\pi$
$557$	16.3616	+	5.95514i	0.693263	+	0.252327i	0.0287316	+	0.999587i	$0.490853\pi$
$558$	−3.35445	+	1.22092i	−0.142005	+	0.0516857i
$559$	4.65733	+	3.90797i	0.196984	+	0.165289i
$560$	0.241589	−	1.37012i	0.0102090	−	0.0578982i
$561$	−23.6040			−0.996560
$562$	3.09595	−	17.5580i	0.130595	−	0.740640i
$563$	4.75156	+	8.22995i	0.200255	+	0.346851i	0.948610	−	0.316446i	$-0.102490\pi$
$563$	4.75156	+	8.22995i	0.200255	+	0.346851i	−0.748356	+	0.663297i	$0.769156\pi$
$564$	−4.31047	+	3.61692i	−0.181504	+	0.152300i
$565$	1.25237	−	2.16917i	0.0526875	−	0.0912575i
$566$	9.03678	+	15.6522i	0.379844	+	0.657910i
$567$	14.2566	+	5.18898i	0.598722	+	0.217917i
$568$	−1.41612	−	1.18826i	−0.0594190	−	0.0498585i
$569$	17.6101	−	30.5016i	0.738253	−	1.27869i	−0.215028	−	0.976608i	$-0.568984\pi$
$569$	17.6101	−	30.5016i	0.738253	−	1.27869i	0.953281	−	0.302084i	$-0.0976824\pi$
$570$	−0.899767	−	5.10283i	−0.0376871	−	0.213734i
$571$	−3.00261	−	17.0287i	−0.125656	−	0.712628i	−0.980916	−	0.194430i	$-0.937714\pi$
$571$	−3.00261	−	17.0287i	−0.125656	−	0.712628i	0.855261	−	0.518198i	$-0.173397\pi$
$572$	19.1848	−	16.0980i	0.802157	−	0.673090i
$573$	17.3058	−	6.29879i	0.722959	−	0.263136i
$574$	3.71997	−	1.35396i	0.155269	−	0.0565131i
$575$	−1.12059	+	0.940287i	−0.0467318	+	0.0392127i
$576$	0.158466	+	0.898708i	0.00660277	+	0.0374462i
$577$	−3.30657	−	18.7525i	−0.137654	−	0.780677i	−0.972974	−	0.230913i	$-0.925829\pi$
$577$	−3.30657	−	18.7525i	−0.137654	−	0.780677i	0.835320	−	0.549764i	$-0.185282\pi$
$578$	−4.90297	+	8.49219i	−0.203937	+	0.353229i
$579$	20.2519	+	16.9933i	0.841639	+	0.706219i
$580$	2.11616	+	0.770221i	0.0878689	+	0.0319817i
$581$	−11.3683	−	19.6905i	−0.471637	−	0.816900i
$582$	9.14854	−	15.8457i	0.379219	−	0.656827i
$583$	29.7024	−	24.9233i	1.23015	−	1.03222i
$584$	−4.27999	−	7.41316i	−0.177107	−	0.306759i
$585$	−0.892019	+	5.05889i	−0.0368805	+	0.209159i
$586$	−18.4102			−0.760517
$587$	−3.82980	+	21.7199i	−0.158073	+	0.896474i	0.797850	+	0.602856i	$0.205971\pi$
$587$	−3.82980	+	21.7199i	−0.158073	+	0.896474i	−0.955923	+	0.293618i	$0.905141\pi$
$588$	7.67385	+	6.43912i	0.316464	+	0.265545i
$589$	−9.62905	+	3.50469i	−0.396758	+	0.144408i
$590$	−12.3228	−	4.48512i	−0.507321	−	0.184650i
$591$	18.5672			0.763752
$592$	−3.78695	−	4.76014i	−0.155643	−	0.195641i
$593$	29.5544			1.21366			0.606828	−	0.794833i	$-0.292442\pi$
$593$	29.5544			1.21366			0.606828	+	0.794833i	$0.292442\pi$
$594$	−17.2622	−	6.28291i	−0.708275	−	0.257791i
$595$	3.50655	−	1.27628i	0.143755	−	0.0523224i
$596$	14.5978	+	12.2490i	0.597948	+	0.501738i
$597$	−4.08304	+	23.1561i	−0.167108	+	0.947714i
$598$	−8.23436			−0.336728
$599$	2.88289	−	16.3497i	0.117792	−	0.668030i	−0.867538	−	0.497370i	$-0.834299\pi$
$599$	2.88289	−	16.3497i	0.117792	−	0.668030i	0.985330	−	0.170660i	$-0.0545899\pi$
$600$	−0.989011	−	1.71302i	−0.0403762	−	0.0699336i
$601$	29.6421	−	24.8726i	1.20913	−	1.01458i	0.209804	−	0.977744i	$-0.432717\pi$
$601$	29.6421	−	24.8726i	1.20913	−	1.01458i	0.999321	−	0.0368330i	$-0.0117270\pi$
$602$	−0.751319	+	1.30132i	−0.0306215	+	0.0530379i
$603$	6.48748	+	11.2366i	0.264191	+	0.457591i
$604$	1.92626	+	0.701101i	0.0783783	+	0.0285274i
$605$	6.73660	+	5.65268i	0.273882	+	0.229814i
$606$	1.63035	−	2.82385i	0.0662284	−	0.114711i
$607$	−2.15042	−	12.1957i	−0.0872830	−	0.495006i	−0.996841	−	0.0794284i	$-0.974690\pi$
$607$	−2.15042	−	12.1957i	−0.0872830	−	0.495006i	0.909558	−	0.415578i	$-0.136421\pi$
$608$	0.454882	+	2.57977i	0.0184479	+	0.104623i
$609$	4.74741	−	3.98355i	0.192375	−	0.161421i
$610$	5.82095	−	2.11865i	0.235684	−	0.0857818i
$611$	15.0474	−	5.47682i	0.608754	−	0.221568i
$612$	−1.87503	+	1.57334i	−0.0757936	+	0.0635984i
$613$	4.46669	+	25.3319i	0.180408	+	1.02315i	0.931714	+	0.363192i	$0.118313\pi$
$613$	4.46669	+	25.3319i	0.180408	+	1.02315i	−0.751306	+	0.659954i	$0.770576\pi$
$614$	2.33103	+	13.2199i	0.0940725	+	0.533512i
$615$	2.81415	−	4.87425i	0.113477	−	0.196549i
$616$	4.74164	+	3.97871i	0.191046	+	0.160307i
$617$	−8.34624	−	3.03778i	−0.336007	−	0.122297i	0.168506	−	0.985701i	$-0.446106\pi$
$617$	−8.34624	−	3.03778i	−0.336007	−	0.122297i	−0.504513	+	0.863404i	$0.668328\pi$
$618$	−8.65786	−	14.9959i	−0.348270	−	0.603222i
$619$	−0.465216	+	0.805778i	−0.0186986	+	0.0323869i	−0.875223	−	0.483719i	$-0.839286\pi$
$619$	−0.465216	+	0.805778i	−0.0186986	+	0.0323869i	0.856525	+	0.516106i	$0.172619\pi$
$620$	−2.99656	+	2.51441i	−0.120345	+	0.100981i
$621$	3.01999	+	5.23078i	0.121188	+	0.209904i
$622$	5.26923	−	29.8833i	0.211277	−	1.19821i
$623$	−7.60214			−0.304573
$624$	1.93347	−	10.9653i	0.0774009	−	0.438962i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	−24.5033	+	8.91846i	−0.979347	+	0.356453i
$627$	21.6627	+	7.88458i	0.865125	+	0.314880i
$628$	4.47557			0.178595
$629$	5.97838	−	15.1802i	0.238374	−	0.605275i
$630$	−1.26962			−0.0505830
$631$	15.7277	+	5.72442i	0.626110	+	0.227886i	0.635537	−	0.772070i	$-0.280779\pi$
$631$	15.7277	+	5.72442i	0.626110	+	0.227886i	−0.00942715	+	0.999956i	$0.503001\pi$
$632$	−2.81026	+	1.02285i	−0.111786	+	0.0406869i
$633$	−6.02372	−	5.05450i	−0.239421	−	0.200898i
$634$	−4.75846	+	26.9866i	−0.188983	+	1.07177i
$635$	−20.3838			−0.808906
$636$	2.99345	−	16.9767i	0.118698	−	0.673171i
$637$	−14.2539	−	24.6885i	−0.564762	−	0.978196i
$638$	−7.67510	+	6.44018i	−0.303860	+	0.254969i
$639$	−0.843496	+	1.46098i	−0.0333682	+	0.0577954i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−11.5608	−	4.20780i	−0.456625	−	0.166198i	0.103459	−	0.994634i	$-0.467009\pi$
$641$	−11.5608	−	4.20780i	−0.456625	−	0.166198i	−0.560084	+	0.828436i	$0.689231\pi$
$642$	−16.7674	−	14.0695i	−0.661756	−	0.555279i
$643$	−14.7887	+	25.6148i	−0.583210	+	1.01015i	0.411886	+	0.911235i	$0.364870\pi$
$643$	−14.7887	+	25.6148i	−0.583210	+	1.01015i	−0.995096	+	0.0989139i	$0.968463\pi$
$644$	−0.353404	−	2.00425i	−0.0139261	−	0.0789786i
$645$	0.370978	+	2.10392i	0.0146072	+	0.0828417i
$646$	−5.38232	+	4.51630i	−0.211765	+	0.177692i
$647$	3.26780	−	1.18938i	0.128470	−	0.0467594i	−0.276985	−	0.960874i	$-0.589335\pi$
$647$	3.26780	−	1.18938i	0.128470	−	0.0467594i	0.405455	+	0.914115i	$0.367113\pi$
$648$	−10.2473	+	3.72971i	−0.402551	+	0.146517i
$649$	44.6934	−	37.5022i	1.75437	−	1.47209i
$650$	0.977478	+	5.54355i	0.0383398	+	0.217436i
$651$	1.86930	+	10.6013i	0.0732635	+	0.415498i
$652$	2.94716	−	5.10464i	0.115420	−	0.199913i
$653$	−8.32421	−	6.98484i	−0.325751	−	0.273338i	0.465215	−	0.885198i	$-0.345977\pi$
$653$	−8.32421	−	6.98484i	−0.325751	−	0.273338i	−0.790966	+	0.611860i	$0.790422\pi$
$654$	1.87407	+	0.682107i	0.0732821	+	0.0266725i
$655$	7.74103	+	13.4079i	0.302467	+	0.523888i
$656$	−1.42271	+	2.46420i	−0.0555474	+	0.0962110i
$657$	−5.98403	+	5.02120i	−0.233459	+	0.195896i
$658$	1.97887	+	3.42751i	0.0771444	+	0.133618i
$659$	−4.84851	+	27.4973i	−0.188871	+	1.07114i	0.732009	+	0.681295i	$0.238583\pi$
$659$	−4.84851	+	27.4973i	−0.188871	+	1.07114i	−0.920880	+	0.389846i	$0.872528\pi$
$660$	8.80031			0.342552
$661$	−4.87777	+	27.6632i	−0.189723	+	1.07597i	0.730012	+	0.683435i	$0.239515\pi$
$661$	−4.87777	+	27.6632i	−0.189723	+	1.07597i	−0.919735	+	0.392540i	$0.871596\pi$
$662$	−2.70692	−	2.27138i	−0.105207	−	0.0882795i
$663$	28.0634	−	10.2143i	1.08989	−	0.396689i
$664$	15.3569	+	5.58946i	0.595964	+	0.216913i
$665$	−3.64449			−0.141327
$666$	−3.67788	+	4.15769i	−0.142515	+	0.161107i
$667$	3.29425			0.127554
$668$	23.0441	+	8.38738i	0.891605	+	0.324518i
$669$	−19.6985	+	7.16966i	−0.761587	+	0.277195i
$670$	10.8916	+	9.13916i	0.420780	+	0.353077i
$671$	−4.78570	+	27.1411i	−0.184750	+	1.04777i
$672$	2.75194			0.106158
$673$	6.27996	−	35.6154i	0.242075	−	1.37287i	−0.585115	−	0.810950i	$-0.698951\pi$
$673$	6.27996	−	35.6154i	0.242075	−	1.37287i	0.827190	−	0.561923i	$-0.189938\pi$
$674$	−14.5571	−	25.2136i	−0.560718	−	0.971192i
$675$	3.16298	−	2.65406i	0.121743	−	0.102155i
$676$	−9.34323	+	16.1829i	−0.359355	+	0.622421i
$677$	6.28200	+	10.8807i	0.241437	+	0.418181i	0.961124	−	0.276118i	$-0.0890480\pi$
$677$	6.28200	+	10.8807i	0.241437	+	0.418181i	−0.719687	+	0.694299i	$0.755715\pi$
$678$	4.65564	+	1.69451i	0.178799	+	0.0650774i
$679$	−9.85853	−	8.27229i	−0.378336	−	0.317461i
$680$	−1.34109	+	2.32283i	−0.0514283	+	0.0890765i
$681$	−6.46100	−	36.6421i	−0.247586	−	1.40413i
$682$	−3.02208	−	17.1391i	−0.115721	−	0.656289i
$683$	−20.3012	+	17.0348i	−0.776805	+	0.651817i	−0.942442	−	0.334370i	$-0.891477\pi$
$683$	−20.3012	+	17.0348i	−0.776805	+	0.651817i	0.165637	+	0.986187i	$0.447032\pi$
$684$	2.24637	−	0.817613i	0.0858922	−	0.0312622i
$685$	19.2172	−	6.99449i	0.734251	−	0.267246i
$686$	12.8578	−	10.7890i	0.490914	−	0.411926i
$687$	−5.07843	−	28.8012i	−0.193754	−	1.09883i
$688$	−0.187550	−	1.06365i	−0.00715027	−	0.0405512i
$689$	−24.5289	+	42.4853i	−0.934477	+	1.61856i
$690$	−2.21655	−	1.85991i	−0.0843827	−	0.0708055i
$691$	−3.51319	−	1.27870i	−0.133648	−	0.0486440i	0.274330	−	0.961636i	$-0.411544\pi$
$691$	−3.51319	−	1.27870i	−0.133648	−	0.0486440i	−0.407978	+	0.912992i	$0.633766\pi$
$692$	0.951579	+	1.64818i	0.0361736	+	0.0626545i
$693$	2.82431	−	4.89184i	0.107287	−	0.185826i
$694$	−5.60156	+	4.70026i	−0.212632	+	0.178420i
$695$	2.10221	+	3.64114i	0.0797414	+	0.138116i
$696$	−0.773508	+	4.38678i	−0.0293197	+	0.166281i
$697$	−7.63190			−0.289079
$698$	2.00692	−	11.3818i	0.0759631	−	0.430808i
$699$	−32.2460	−	27.0576i	−1.21965	−	1.02341i
$700$	−1.30736	+	0.475838i	−0.0494134	+	0.0179850i
$701$	−37.4723	−	13.6388i	−1.41531	−	0.515130i	−0.482626	−	0.875827i	$-0.660317\pi$
$701$	−37.4723	−	13.6388i	−1.41531	−	0.515130i	−0.932683	+	0.360696i	$0.882539\pi$
$702$	23.2423			0.877225
$703$	−10.5574	+	11.9348i	−0.398181	+	0.450128i
$704$	−4.44905			−0.167680
$705$	5.28758	+	1.92452i	0.199142	+	0.0724816i
$706$	−10.3073	+	3.75153i	−0.387919	+	0.141191i
$707$	−1.75688	−	1.47420i	−0.0660742	−	0.0554428i
$708$	4.50427	−	25.5450i	0.169281	−	0.960039i
$709$	1.86813			0.0701593			0.0350796	−	0.999385i	$-0.488832\pi$
$709$	1.86813			0.0701593			0.0350796	+	0.999385i	$0.488832\pi$
$710$	−0.321008	+	1.82053i	−0.0120472	+	0.0683232i
$711$	1.36458	+	2.36352i	0.0511757	+	0.0886389i
$712$	4.18584	−	3.51233i	0.156871	−	0.131630i
$713$	−2.86109	+	4.95556i	−0.107149	+	0.185587i
$714$	3.69059	+	6.39229i	0.138117	+	0.239226i
$715$	−23.5337	−	8.56555i	−0.880109	−	0.320333i
$716$	14.0985	+	11.8300i	0.526886	+	0.442110i
$717$	−16.6103	+	28.7698i	−0.620321	+	1.07443i
$718$	0.502938	+	2.85230i	0.0187695	+	0.106447i
$719$	7.05412	+	40.0059i	0.263074	+	1.49197i	0.774464	+	0.632619i	$0.218020\pi$
$719$	7.05412	+	40.0059i	0.263074	+	1.49197i	−0.511389	+	0.859349i	$0.670869\pi$
$720$	0.699071	−	0.586590i	0.0260528	−	0.0218609i
$721$	−11.4447	+	4.16552i	−0.426222	+	0.155132i
$722$	−11.4059	+	4.15140i	−0.424483	+	0.154499i
$723$	7.35642	−	6.17277i	0.273588	−	0.229568i
$724$	3.23129	+	18.3256i	0.120090	+	0.681064i
$725$	−0.391051	−	2.21776i	−0.0145233	−	0.0823656i
$726$	−8.69737	+	15.0643i	−0.322790	+	0.559088i
$727$	−28.1349	−	23.6080i	−1.04346	−	0.875570i	−0.0510730	−	0.998695i	$-0.516264\pi$
$727$	−28.1349	−	23.6080i	−1.04346	−	0.875570i	−0.992391	+	0.123124i	$0.960709\pi$
$728$	−7.35920	−	2.67853i	−0.272750	−	0.0992729i
$729$	−7.27505	−	12.6008i	−0.269446	−	0.466695i
$730$	−4.27999	+	7.41316i	−0.158409	+	0.274373i
$731$	2.21915	−	1.86209i	0.0820784	−	0.0688719i
$732$	6.12646	+	10.6113i	0.226440	+	0.392206i
$733$	−7.73793	+	43.8840i	−0.285807	+	1.62089i	0.416582	+	0.909098i	$0.363228\pi$
$733$	−7.73793	+	43.8840i	−0.285807	+	1.62089i	−0.702389	+	0.711793i	$0.747883\pi$
$734$	−31.1567			−1.15001
$735$	1.73952	−	9.86531i	0.0641632	−	0.363887i
$736$	1.12059	+	0.940287i	0.0413055	+	0.0346594i
$737$	−59.4417	+	21.6350i	−2.18956	+	0.796936i
$738$	2.44005	+	0.888106i	0.0898195	+	0.0326916i
$739$	37.4898			1.37909			0.689543	−	0.724245i	$-0.257812\pi$
$739$	37.4898			1.37909			0.689543	+	0.724245i	$0.257812\pi$
$740$	−2.22893	+	5.65967i	−0.0819371	+	0.208054i
$741$	−29.1673			−1.07149
$742$	−11.3937	−	4.14697i	−0.418276	−	0.152240i
$743$	22.6220	−	8.23372i	0.829919	−	0.302066i	0.108094	−	0.994141i	$-0.465525\pi$
$743$	22.6220	−	8.23372i	0.829919	−	0.302066i	0.721826	+	0.692075i	$0.243303\pi$
$744$	−5.92726	−	4.97356i	−0.217304	−	0.182340i
$745$	3.30904	−	18.7665i	0.121234	−	0.687552i
$746$	−9.50815			−0.348118
$747$	2.58974	−	14.6871i	0.0947536	−	0.537374i
$748$	−5.96656	−	10.3344i	−0.218159	−	0.377862i
$749$	−11.7935	+	9.89590i	−0.430924	+	0.361588i
$750$	−0.989011	+	1.71302i	−0.0361136	+	0.0625506i
$751$	−16.3078	−	28.2459i	−0.595079	−	1.03071i	−0.993536	−	0.113520i	$-0.963788\pi$
$751$	−16.3078	−	28.2459i	−0.595079	−	1.03071i	0.398457	−	0.917187i	$-0.369546\pi$
$752$	−2.67316	−	0.972952i	−0.0974802	−	0.0354799i
$753$	−32.0027	−	26.8535i	−1.16624	−	0.978594i
$754$	6.33826	−	10.9782i	0.230826	−	0.399802i
$755$	−0.355958	−	2.01874i	−0.0129546	−	0.0734694i
$756$	0.997518	+	5.65721i	0.0362794	+	0.205751i
$757$	22.8989	−	19.2145i	0.832276	−	0.698362i	−0.123537	−	0.992340i	$-0.539424\pi$
$757$	22.8989	−	19.2145i	0.832276	−	0.698362i	0.955812	+	0.293978i	$0.0949792\pi$
$758$	−34.8203	+	12.6735i	−1.26473	+	0.460324i
$759$	12.0970	−	4.40294i	0.439092	−	0.159817i
$760$	2.00670	−	1.68382i	0.0727907	−	0.0610786i
$761$	4.44235	+	25.1938i	0.161035	+	0.913275i	0.953059	+	0.302785i	$0.0979163\pi$
$761$	4.44235	+	25.1938i	0.161035	+	0.913275i	−0.792024	+	0.610490i	$0.790973\pi$
$762$	−7.00142	−	39.7071i	−0.253635	−	1.43843i
$763$	0.701371	−	1.21481i	0.0253913	−	0.0439791i
$764$	7.13227	+	5.98469i	0.258037	+	0.216518i
$765$	2.30006	+	0.837155i	0.0831590	+	0.0302674i
$766$	−0.678109	−	1.17452i	−0.0245011	−	0.0424371i
$767$	−36.9088	+	63.9279i	−1.33270	+	2.30830i
$768$	−1.51525	+	1.27145i	−0.0546770	+	0.0458794i
$769$	6.33779	+	10.9774i	0.228546	+	0.395854i	0.957378	−	0.288839i	$-0.0932694\pi$
$769$	6.33779	+	10.9774i	0.228546	+	0.395854i	−0.728831	+	0.684694i	$0.759936\pi$
$770$	1.07484	−	6.09574i	0.0387346	−	0.219675i
$771$	49.7314			1.79103
$772$	−2.32087	+	13.1623i	−0.0835298	+	0.473721i
$773$	−28.9035	−	24.2529i	−1.03959	−	0.872317i	−0.0476264	−	0.998865i	$-0.515166\pi$
$773$	−28.9035	−	24.2529i	−1.03959	−	0.872317i	−0.991960	+	0.126548i	$0.959610\pi$
$774$	−0.926189	+	0.337105i	−0.0332912	+	0.0121170i
$775$	3.67582	+	1.33789i	0.132040	+	0.0480584i
$776$	9.25019			0.332062
$777$	10.4215	+	13.0996i	0.373868	+	0.469947i
$778$	−29.9232			−1.07280
$779$	7.00423	+	2.54933i	0.250953	+	0.0913393i
$780$	−10.4629	+	3.80820i	−0.374633	+	0.136355i
$781$	−6.30038	−	5.28664i	−0.225445	−	0.189171i
$782$	−0.681318	+	3.86395i	−0.0243639	+	0.138175i
$783$	−9.29835			−0.332296
$784$	−0.879424	+	4.98746i	−0.0314080	+	0.178124i
$785$	−2.23779	−	3.87596i	−0.0798700	−	0.138339i
$786$	−23.4592	+	19.6846i	−0.836763	+	0.702128i
$787$	0.160040	−	0.277197i	0.00570480	−	0.00988100i	−0.863159	−	0.504932i	$-0.831517\pi$
$787$	0.160040	−	0.277197i	0.00570480	−	0.00988100i	0.868864	+	0.495051i	$0.164851\pi$
$788$	4.69337	+	8.12916i	0.167194	+	0.289589i
$789$	13.9545	+	5.07903i	0.496794	+	0.180818i
$790$	2.29095	+	1.92233i	0.0815083	+	0.0683935i
$791$	1.74237	−	3.01787i	0.0619515	−	0.107303i
$792$	0.705025	+	3.99839i	0.0250520	+	0.142077i
$793$	−6.05502	−	34.3397i	−0.215020	−	1.21944i
$794$	1.66951	−	1.40089i	0.0592487	−	0.0497156i
$795$	−16.1990	+	5.89595i	−0.574519	+	0.209108i
$796$	−11.1704	+	4.06568i	−0.395923	+	0.144104i
$797$	−25.2853	+	21.2169i	−0.895652	+	0.751541i	−0.969336	−	0.245740i	$-0.920969\pi$
$797$	−25.2853	+	21.2169i	−0.895652	+	0.751541i	0.0736835	+	0.997282i	$0.476525\pi$
$798$	−1.25181	−	7.09936i	−0.0443135	−	0.251315i
$799$	−1.32494	−	7.51412i	−0.0468731	−	0.265830i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−3.81988	−	3.20526i	−0.134969	−	0.113252i
$802$	−27.6382	−	10.0595i	−0.975939	−	0.355213i
$803$	−19.0419	−	32.9815i	−0.671973	−	1.16389i
$804$	−14.0618	+	24.3557i	−0.495920	+	0.858959i
$805$	−1.55903	+	1.30818i	−0.0549486	+	0.0461074i
$806$	11.0097	+	19.0694i	0.387800	+	0.671690i
$807$	−5.68725	+	32.2540i	−0.200201	+	1.13539i
$808$	1.64846			0.0579928
$809$	−5.75193	+	32.6208i	−0.202227	+	1.14689i	0.699517	+	0.714616i	$0.253399\pi$
$809$	−5.75193	+	32.6208i	−0.202227	+	1.14689i	−0.901744	+	0.432271i	$0.857712\pi$
$810$	8.35366	+	7.00955i	0.293518	+	0.246291i
$811$	−21.3466	+	7.76951i	−0.749579	+	0.272824i	−0.688429	−	0.725304i	$-0.741699\pi$
$811$	−21.3466	+	7.76951i	−0.749579	+	0.272824i	−0.0611504	+	0.998129i	$0.519477\pi$
$812$	2.94413	+	1.07158i	0.103319	+	0.0376049i
$813$	−26.7407			−0.937837
$814$	−16.8483	−	21.1781i	−0.590534	−	0.742292i
$815$	−5.89433			−0.206469
$816$	−4.98545	−	1.81455i	−0.174526	−	0.0635221i
$817$	−2.65865	+	0.967669i	−0.0930144	+	0.0338545i
$818$	19.1841	+	16.0973i	0.670755	+	0.562830i
$819$	−1.24103	+	7.03823i	−0.0433651	+	0.245936i
$820$	2.84542			0.0993663
$821$	−2.57942	+	14.6286i	−0.0900224	+	0.510543i	0.906137	+	0.422984i	$0.139017\pi$
$821$	−2.57942	+	14.6286i	−0.0900224	+	0.510543i	−0.996159	+	0.0875582i	$0.972094\pi$
$822$	20.2258	+	35.0321i	0.705455	+	1.22188i
$823$	6.24003	−	5.23601i	0.217514	−	0.182516i	−0.527520	−	0.849543i	$-0.676878\pi$
$823$	6.24003	−	5.23601i	0.217514	−	0.182516i	0.745034	+	0.667027i	$0.232433\pi$
$824$	4.37703	−	7.58124i	0.152481	−	0.264105i
$825$	−4.40016	−	7.62129i	−0.153194	−	0.265339i
$826$	−17.1442	−	6.23997i	−0.596522	−	0.217116i
$827$	15.7808	+	13.2416i	0.548751	+	0.460457i	0.874518	−	0.484993i	$-0.161178\pi$
$827$	15.7808	+	13.2416i	0.548751	+	0.460457i	−0.325767	+	0.945450i	$0.605622\pi$
$828$	0.667467	−	1.15609i	0.0231961	−	0.0401768i
$829$	−1.31492	−	7.45727i	−0.0456690	−	0.259002i	0.953422	−	0.301641i	$-0.0975345\pi$
$829$	−1.31492	−	7.45727i	−0.0456690	−	0.259002i	−0.999091	+	0.0426394i	$0.986423\pi$
$830$	−2.83784	−	16.0942i	−0.0985030	−	0.558638i
$831$	38.2901	−	32.1292i	1.32827	−	1.11455i
$832$	5.28960	−	1.92526i	0.183384	−	0.0667462i
$833$	−12.7644	+	4.64587i	−0.442261	+	0.160970i
$834$	−6.37077	+	5.34571i	−0.220602	+	0.185107i
$835$	−4.25839	−	24.1505i	−0.147368	−	0.835763i
$836$	2.02379	+	11.4775i	0.0699943	+	0.396957i
$837$	8.07573	−	13.9876i	0.279138	−	0.483481i
$838$	3.55832	+	2.98579i	0.122920	+	0.103142i
$839$	1.18435	+	0.431068i	0.0408883	+	0.0148821i	0.362383	−	0.932029i	$-0.381963\pi$
$839$	1.18435	+	0.431068i	0.0408883	+	0.0148821i	−0.321495	+	0.946911i	$0.604185\pi$
$840$	−1.37597	−	2.38325i	−0.0474755	−	0.0822299i
$841$	11.9643	−	20.7228i	0.412562	−	0.714579i
$842$	−3.78310	+	3.17440i	−0.130374	+	0.109397i
$843$	−17.6330	−	30.5412i	−0.607311	−	1.05189i
$844$	0.690319	−	3.91499i	0.0237618	−	0.134760i
$845$	18.6865			0.642834
$846$	−0.450793	+	2.55657i	−0.0154986	+	0.0878968i
$847$	9.37235	+	7.86434i	0.322038	+	0.270222i
$848$	8.18949	−	2.98073i	0.281228	−	0.102359i
$849$	33.5939	+	12.2272i	1.15294	+	0.419636i
$850$	2.68217			0.0919978
$851$	−0.232278	+	8.89499i	−0.00796238	+	0.304916i
$852$	−3.65659			−0.125273
$853$	7.52212	+	2.73783i	0.257553	+	0.0937415i	0.467570	−	0.883956i	$-0.345130\pi$
$853$	7.52212	+	2.73783i	0.257553	+	0.0937415i	−0.210017	+	0.977698i	$0.567352\pi$
$854$	8.09845	−	2.94760i	0.277123	−	0.100865i
$855$	−1.83126	−	1.53661i	−0.0626278	−	0.0525509i
$856$	1.92154	−	10.8976i	0.0656770	−	0.372473i
$857$	30.0913			1.02790			0.513949	−	0.857821i	$-0.328182\pi$
$857$	30.0913			1.02790			0.513949	+	0.857821i	$0.328182\pi$
$858$	8.60211	−	48.7850i	0.293671	−	1.66549i
$859$	10.8825	+	18.8490i	0.371306	+	0.643121i	0.989767	−	0.142695i	$-0.0455768\pi$
$859$	10.8825	+	18.8490i	0.371306	+	0.643121i	−0.618461	+	0.785816i	$0.712243\pi$
$860$	−0.827371	+	0.694247i	−0.0282131	+	0.0236736i
$861$	3.91521	−	6.78134i	0.133430	−	0.231107i
$862$	4.69602	+	8.13375i	0.159947	+	0.277037i
$863$	−29.0933	−	10.5891i	−0.990346	−	0.360457i	−0.204492	−	0.978868i	$-0.565554\pi$
$863$	−29.0933	−	10.5891i	−0.990346	−	0.360457i	−0.785854	+	0.618412i	$0.787776\pi$
$864$	−3.16298	−	2.65406i	−0.107607	−	0.0902928i
$865$	0.951579	−	1.64818i	0.0323547	−	0.0560399i
$866$	2.51355	+	14.2550i	0.0854138	+	0.484406i
$867$	3.36814	+	19.1017i	0.114388	+	0.648728i
$868$	−4.16899	+	3.49820i	−0.141505	+	0.118737i
$869$	−12.5030	+	4.55072i	−0.424135	+	0.154372i
$870$	4.18582	−	1.52351i	0.141913	−	0.0516519i
$871$	61.3098	−	51.4450i	2.07740	−	1.74315i
$872$	0.175081	+	0.992936i	0.00592901	+	0.0336251i
$873$	−1.46584	−	8.31322i	−0.0496113	−	0.281360i
$874$	1.91598	−	3.31858i	0.0648091	−	0.112253i
$875$	1.06577	+	0.894284i	0.0360295	+	0.0302323i
$876$	−15.9107	−	5.79102i	−0.537573	−	0.195661i
$877$	18.3573	+	31.7957i	0.619880	+	1.07366i	0.989507	+	0.144484i	$0.0461523\pi$
$877$	18.3573	+	31.7957i	0.619880	+	1.07366i	−0.369627	+	0.929180i	$0.620514\pi$
$878$	17.4069	−	30.1496i	0.587454	−	1.01750i
$879$	−27.8961	+	23.4076i	−0.940911	+	0.789518i
$880$	2.22452	+	3.85299i	0.0749886	+	0.129884i
$881$	1.49247	−	8.46424i	0.0502827	−	0.285167i	−0.949290	−	0.314402i	$-0.898196\pi$
$881$	1.49247	−	8.46424i	0.0502827	−	0.285167i	0.999573	+	0.0292348i	$0.00930705\pi$
$882$	4.62163			0.155618
$883$	8.01033	−	45.4288i	0.269569	−	1.52880i	−0.486132	−	0.873885i	$-0.661593\pi$
$883$	8.01033	−	45.4288i	0.269569	−	1.52880i	0.755701	−	0.654916i	$-0.227296\pi$
$884$	11.5659	+	9.70491i	0.389002	+	0.326411i
$885$	−24.3747	+	8.87167i	−0.819347	+	0.298218i
$886$	25.0542	+	9.11898i	0.841712	+	0.306358i
$887$	24.2177			0.813149			0.406575	−	0.913618i	$-0.366723\pi$
$887$	24.2177			0.813149			0.406575	+	0.913618i	$0.366723\pi$
$888$	−11.7905	−	2.39791i	−0.395662	−	0.0804685i
$889$	−28.3591			−0.951134
$890$	−5.13469	−	1.86887i	−0.172115	−	0.0626448i
$891$	−45.5906	+	16.5936i	−1.52734	+	0.555907i
$892$	−8.11839	−	6.81213i	−0.271824	−	0.228087i
$893$	−1.29401	+	7.33871i	−0.0433025	+	0.245581i
$894$	37.6932			1.26065
$895$	3.19587	−	18.1247i	0.106826	−	0.605841i
$896$	0.695629	+	1.20487i	0.0232393	+	0.0402517i
$897$	−12.4771	+	10.4696i	−0.416599	+	0.349568i
$898$	14.8204	−	25.6696i	0.494562	−	0.856606i
$899$	−4.40456	−	7.62892i	−0.146900	−	0.254439i
$900$	−0.857537	−	0.312118i	−0.0285846	−	0.0104039i
$901$	17.9066	+	15.0254i	0.596554	+	0.500568i
$902$	−6.32969	+	10.9634i	−0.210756	+	0.365040i
$903$	0.516126	+	2.92710i	0.0171756	+	0.0974076i
$904$	0.434943	+	2.46668i	0.0144660	+	0.0820407i
$905$	14.2547	−	11.9612i	0.473844	−	0.397602i
$906$	3.81018	−	1.38679i	0.126585	−	0.0460731i
$907$	−11.4012	+	4.14968i	−0.378569	+	0.137788i	−0.524294	−	0.851537i	$-0.675671\pi$
$907$	−11.4012	+	4.14968i	−0.378569	+	0.137788i	0.145725	+	0.989325i	$0.453449\pi$
$908$	14.4096	−	12.0911i	0.478200	−	0.401257i
$909$	−0.261226	−	1.48149i	−0.00866433	−	0.0491379i
$910$	1.35992	+	7.71252i	0.0450811	+	0.255667i
$911$	−8.58188	+	14.8643i	−0.284331	+	0.492475i	−0.972447	−	0.233126i	$-0.925105\pi$
$911$	−8.58188	+	14.8643i	−0.284331	+	0.492475i	0.688116	+	0.725601i	$0.258438\pi$
$912$	3.96930	+	3.33064i	0.131437	+	0.110288i
$913$	68.3237	+	24.8678i	2.26118	+	0.823003i
$914$	−19.4175	−	33.6320i	−0.642272	−	1.11245i
$915$	6.12646	−	10.6113i	0.202534	−	0.350800i
$916$	11.3261	−	9.50375i	0.374226	−	0.314013i
$917$	10.7698	+	18.6538i	0.355649	+	0.616003i
$918$	1.92309	−	10.9064i	0.0634715	−	0.359965i
$919$	−28.5502			−0.941783			−0.470891	−	0.882191i	$-0.656068\pi$
$919$	−28.5502			−0.941783			−0.470891	+	0.882191i	$0.656068\pi$
$920$	0.254017	−	1.44060i	0.00837470	−	0.0474953i
$921$	20.3405	+	17.0677i	0.670243	+	0.562400i
$922$	−12.5725	+	4.57601i	−0.414053	+	0.150703i
$923$	9.77841	+	3.55905i	0.321860	+	0.117148i
$924$	12.2435			0.402782
$925$	6.01588	−	0.899526i	0.197801	−	0.0295762i
$926$	−21.6817			−0.712504
$927$	−7.50693	−	2.73230i	−0.246560	−	0.0897405i
$928$	−2.11616	+	0.770221i	−0.0694665	+	0.0252837i
$929$	25.1659	+	21.1167i	0.825666	+	0.692816i	0.954292	−	0.298877i	$-0.0966121\pi$
$929$	25.1659	+	21.1167i	0.825666	+	0.692816i	−0.128626	+	0.991693i	$0.541057\pi$
$930$	−1.34360	+	7.61994i	−0.0440584	+	0.249868i
$931$	13.2665			0.434792
$932$	3.69539	−	20.9576i	0.121047	−	0.686490i
$933$	−30.0109	−	51.9803i	−0.982511	−	1.70176i
$934$	−7.63514	+	6.40665i	−0.249829	+	0.209632i
$935$	−5.96656	+	10.3344i	−0.195127	+	0.337970i
$936$	−2.56847	−	4.44872i	−0.0839530	−	0.145411i
$937$	−50.0551	−	18.2186i	−1.63523	−	0.595174i	−0.649032	−	0.760761i	$-0.724826\pi$
$937$	−50.0551	−	18.2186i	−1.63523	−	0.595174i	−0.986195	+	0.165587i	$0.947048\pi$
$938$	15.1531	+	12.7149i	0.494765	+	0.415157i
$939$	−25.7893	+	44.6683i	−0.841601	+	1.45770i
$940$	0.493981	+	2.80150i	0.0161119	+	0.0913750i
$941$	1.75298	+	9.94166i	0.0571456	+	0.324089i	0.999957	−	0.00923682i	$-0.00294021\pi$
$941$	1.75298	+	9.94166i	0.0571456	+	0.324089i	−0.942812	+	0.333326i	$0.891829\pi$
$942$	6.78162	−	5.69046i	0.220957	−	0.185405i
$943$	3.91133	−	1.42361i	0.127370	−	0.0463591i
$944$	12.3228	−	4.48512i	0.401072	−	0.145978i
$945$	4.40052	−	3.69248i	0.143149	−	0.120116i
$946$	−0.834418	−	4.73222i	−0.0271293	−	0.153858i
$947$	−1.26965	−	7.20055i	−0.0412581	−	0.233986i	0.957205	−	0.289412i	$-0.0934597\pi$
$947$	−1.26965	−	7.20055i	−0.0412581	−	0.233986i	−0.998463	+	0.0554253i	$0.982349\pi$
$948$	−2.95776	+	5.12298i	−0.0960635	+	0.166387i
$949$	36.9116	+	30.9725i	1.19820	+	1.00541i
$950$	−2.46158	−	0.895943i	−0.0798643	−	0.0290682i
$951$	27.1018	+	46.9416i	0.878835	+	1.52219i
$952$	−1.86580	+	3.23166i	−0.0604709	+	0.104739i
$953$	32.2885	−	27.0932i	1.04593	−	0.877636i	0.0532663	−	0.998580i	$-0.483037\pi$
$953$	32.2885	−	27.0932i	1.04593	−	0.877636i	0.992659	+	0.120945i	$0.0385923\pi$
$954$	−3.97657	−	6.88762i	−0.128746	−	0.222995i
$955$	1.61676	−	9.16907i	0.0523170	−	0.296704i
$956$	−16.7948			−0.543183
$957$	−3.44137	+	19.5170i	−0.111244	+	0.630895i
$958$	−2.61625	−	2.19529i	−0.0845272	−	0.0709267i
$959$	26.7361	−	9.73114i	0.863353	−	0.314235i
$960$	1.85873	+	0.676523i	0.0599903	+	0.0218347i
$961$	−15.6984			−0.506399
$962$	29.1960	+	17.8884i	0.941316	+	0.576745i
$963$	−10.0983			−0.325413
$964$	4.56212	+	1.66048i	0.146936	+	0.0534804i
$965$	12.5593	−	4.57122i	0.404299	−	0.147153i
$966$	−3.08380	−	2.58761i	−0.0992196	−	0.0832551i
$967$	−0.415824	+	2.35826i	−0.0133720	+	0.0758364i	−0.990763	−	0.135601i	$-0.956703\pi$
$967$	−0.415824	+	2.35826i	−0.0133720	+	0.0758364i	0.977391	+	0.211438i	$0.0678145\pi$
$968$	−8.79400			−0.282650
$969$	−2.41333	+	13.6867i	−0.0775274	+	0.439680i
$970$	−4.62509	−	8.01090i	−0.148503	−	0.257214i
$971$	19.7832	−	16.6000i	0.634872	−	0.532721i	−0.267567	−	0.963539i	$-0.586220\pi$
$971$	19.7832	−	16.6000i	0.634872	−	0.532721i	0.902438	+	0.430819i	$0.141775\pi$
$972$	−4.59163	+	7.95293i	−0.147277	+	0.255090i
$973$	2.92472	+	5.06576i	0.0937622	+	0.162401i
$974$	−16.8982	−	6.15043i	−0.541452	−	0.197073i
$975$	8.52947	+	7.15707i	0.273162	+	0.229210i
$976$	−3.09726	+	5.36462i	−0.0991410	+	0.171717i
$977$	0.841553	+	4.77268i	0.0269237	+	0.152692i	0.995306	−	0.0967797i	$-0.0308542\pi$
$977$	0.841553	+	4.77268i	0.0269237	+	0.152692i	−0.968382	+	0.249471i	$0.919743\pi$
$978$	−2.02458	−	11.4820i	−0.0647390	−	0.367153i
$979$	18.6230	−	15.6265i	0.595193	−	0.499426i
$980$	4.75898	−	1.73213i	0.152020	−	0.0553308i
$981$	0.864615	−	0.314694i	0.0276050	−	0.0100474i
$982$	−22.1335	+	18.5722i	−0.706309	+	0.592664i
$983$	−2.19683	−	12.4589i	−0.0700681	−	0.397376i	−0.999591	−	0.0286106i	$-0.990892\pi$
$983$	−2.19683	−	12.4589i	−0.0700681	−	0.397376i	0.929523	−	0.368765i	$-0.120219\pi$
$984$	0.977344	+	5.54279i	0.0311566	+	0.176698i
$985$	4.69337	−	8.12916i	0.149543	−	0.259017i
$986$	−4.62705	−	3.88256i	−0.147355	−	0.123646i
$987$	7.35639	+	2.67751i	0.234156	+	0.0852259i
$988$	−7.37285	−	12.7702i	−0.234562	−	0.406273i
$989$	−0.789968	+	1.36826i	−0.0251195	+	0.0435083i
$990$	3.11020	−	2.60977i	0.0988486	−	0.0829438i
$991$	−17.2588	−	29.8930i	−0.548242	−	0.949584i	−0.998395	−	0.0566322i	$-0.981964\pi$
$991$	−17.2588	−	29.8930i	−0.548242	−	0.949584i	0.450153	−	0.892952i	$-0.351370\pi$
$992$	0.679265	−	3.85230i	0.0215667	−	0.122311i
$993$	−6.98960			−0.221808
$994$	−0.446605	+	2.53282i	−0.0141655	+	0.0803363i
$995$	9.10617	+	7.64098i	0.288685	+	0.242236i
$996$	30.3763	−	11.0561i	0.962511	−	0.350325i
$997$	34.5685	+	12.5819i	1.09480	+	0.398473i	0.825395	−	0.564555i	$-0.190952\pi$
$997$	34.5685	+	12.5819i	1.09480	+	0.398473i	0.269400	+	0.963028i	$0.413174\pi$
$998$	−33.2129			−1.05134
$999$	0.655628	−	25.1070i	0.0207432	−	0.794352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.c.201.3	yes	24
37.7	even	9	inner	370.2.o.c.81.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.c.81.3	✓	24	37.7	even	9	inner
370.2.o.c.201.3	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(1.85873 - 0.676523i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} +1.97802 q^{6} +(0.241589 - 1.37012i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.699071 - 0.586590i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.22452 + 3.85299i) q^{11} +(1.85873 + 0.676523i) q^{12} +(-4.31212 - 3.61830i) q^{13} +(0.695629 - 1.20487i) q^{14} +(-0.343480 - 1.94797i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.05466 + 1.72407i) q^{17} +(0.857537 - 0.312118i) q^{18} +(2.46158 - 0.895943i) q^{19} +(0.766044 - 0.642788i) q^{20} +(-0.477869 - 2.71013i) q^{21} +(0.772569 + 4.38145i) q^{22} +(0.731413 - 1.26685i) q^{23} +(1.51525 + 1.27145i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-2.81454 - 4.87492i) q^{26} +(-2.06449 + 3.57580i) q^{27} +(1.06577 - 0.894284i) q^{28} +(1.12599 + 1.95027i) q^{29} +(0.343480 - 1.94797i) q^{30} -3.91173 q^{31} +(-0.173648 + 0.984808i) q^{32} +(6.74143 + 5.65673i) q^{33} +(-2.52042 + 0.917358i) q^{34} +(-1.30736 - 0.475838i) q^{35} +0.912572 q^{36} +(-5.34543 + 2.90283i) q^{37} +2.61956 q^{38} +(-10.4629 - 3.80820i) q^{39} +(0.939693 - 0.342020i) q^{40} +(2.17972 + 1.82900i) q^{41} +(0.477869 - 2.71013i) q^{42} -1.08006 q^{43} +(-0.772569 + 4.38145i) q^{44} +(-0.456286 - 0.790311i) q^{45} +(1.12059 - 0.940287i) q^{46} +(-1.42236 + 2.46360i) q^{47} +(0.989011 + 1.71302i) q^{48} +(4.75898 + 1.73213i) q^{49} +(-0.766044 - 0.642788i) q^{50} +(-2.65270 + 4.59461i) q^{51} +(-0.977478 - 5.54355i) q^{52} +(-1.51336 - 8.58267i) q^{53} +(-3.16298 + 2.65406i) q^{54} +(4.18074 - 1.52166i) q^{55} +(1.30736 - 0.475838i) q^{56} +(3.96930 - 3.33064i) q^{57} +(0.391051 + 2.21776i) q^{58} +(-2.27716 - 12.9144i) q^{59} +(0.989011 - 1.71302i) q^{60} +(4.74529 + 3.98177i) q^{61} +(-3.67582 - 1.33789i) q^{62} +(-0.634812 - 1.09953i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-4.31212 + 3.61830i) q^{65} +(4.40016 + 7.62129i) q^{66} +(-2.46893 + 14.0020i) q^{67} -2.68217 q^{68} +(0.502452 - 2.84954i) q^{69} +(-1.06577 - 0.894284i) q^{70} +(-1.73713 + 0.632262i) q^{71} +(0.857537 + 0.312118i) q^{72} -8.55998 q^{73} +(-6.01588 + 0.899526i) q^{74} -1.97802 q^{75} +(2.46158 + 0.895943i) q^{76} +(5.81648 - 2.11703i) q^{77} +(-8.52947 - 7.15707i) q^{78} +(-0.519316 + 2.94519i) q^{79} +1.00000 q^{80} +(-1.89362 + 10.7393i) q^{81} +(1.42271 + 2.46420i) q^{82} +(12.5191 - 10.5048i) q^{83} +(1.37597 - 2.38325i) q^{84} +(1.34109 + 2.32283i) q^{85} +(-1.01492 - 0.369401i) q^{86} +(3.41231 + 2.86327i) q^{87} +(-2.22452 + 3.85299i) q^{88} +(-0.948852 - 5.38121i) q^{89} +(-0.158466 - 0.898708i) q^{90} +(-5.99927 + 5.03399i) q^{91} +(1.37461 - 0.500316i) q^{92} +(-7.27086 + 2.64638i) q^{93} +(-2.17918 + 1.82855i) q^{94} +(-0.454882 - 2.57977i) q^{95} +(0.343480 + 1.94797i) q^{96} +(4.62509 - 8.01090i) q^{97} +(3.87956 + 3.25533i) q^{98} +(3.81522 + 1.38863i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9} + 12 q^{10} - 15 q^{11} + 3 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 36 q^{21} + 9 q^{22} + 21 q^{23} - 6 q^{26} - 12 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{31}+ \cdots + 63 q^{99}+O(q^{100}) \) 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9 + 12 * q^10 - 15 * q^11 + 3 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 36 * q^21 + 9 * q^22 + 21 * q^23 - 6 * q^26 - 12 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^31 - 39 * q^33 - 21 * q^34 + 6 * q^35 + 54 * q^36 - 12 * q^37 - 36 * q^38 - 18 * q^39 + 27 * q^41 - 36 * q^42 - 24 * q^43 - 9 * q^44 - 27 * q^45 + 3 * q^46 - 6 * q^47 - 3 * q^48 - 27 * q^49 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 9 * q^54 + 9 * q^55 - 6 * q^56 - 27 * q^57 + 27 * q^58 + 51 * q^59 - 3 * q^60 - 3 * q^62 - 27 * q^63 - 12 * q^64 + 15 * q^66 - 18 * q^69 + 3 * q^70 - 66 * q^71 + 6 * q^72 + 42 * q^73 - 42 * q^74 + 6 * q^75 - 6 * q^76 + 69 * q^77 + 36 * q^78 - 30 * q^79 + 24 * q^80 - 90 * q^81 + 24 * q^82 + 57 * q^83 + 6 * q^84 - 6 * q^86 + 6 * q^87 + 15 * q^88 - 57 * q^89 + 6 * q^90 + 3 * q^91 + 15 * q^92 - 72 * q^93 + 3 * q^94 - 15 * q^95 - 3 * q^97 - 72 * q^98 + 63 * q^99

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