LMFDB - Embedded newform 380.2.k.c.343.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			343.3
Character	$\chi$	$=$	380.343
Dual form			380.2.k.c.267.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38463 + 0.287770i) q^{2} +(1.15541 - 1.15541i) q^{3} +(1.83438 - 0.796907i) q^{4} +(-0.283261 + 2.21805i) q^{5} +(-1.26732 + 1.93230i) q^{6} +(-3.26325 - 3.26325i) q^{7} +(-2.31060 + 1.63130i) q^{8} +0.330062i q^{9} +O(q^{10})$	\(q+(-1.38463 + 0.287770i) q^{2} +(1.15541 - 1.15541i) q^{3} +(1.83438 - 0.796907i) q^{4} +(-0.283261 + 2.21805i) q^{5} +(-1.26732 + 1.93230i) q^{6} +(-3.26325 - 3.26325i) q^{7} +(-2.31060 + 1.63130i) q^{8} +0.330062i q^{9} +(-0.246078 - 3.15269i) q^{10} -4.56912i q^{11} +(1.19870 - 3.04021i) q^{12} +(-3.90789 - 3.90789i) q^{13} +(5.45745 + 3.57932i) q^{14} +(2.23548 + 2.89004i) q^{15} +(2.72988 - 2.92365i) q^{16} +(3.68739 - 3.68739i) q^{17} +(-0.0949818 - 0.457012i) q^{18} +1.00000 q^{19} +(1.24797 + 4.29448i) q^{20} -7.54078 q^{21} +(1.31485 + 6.32652i) q^{22} +(-0.671647 + 0.671647i) q^{23} +(-0.784875 + 4.55450i) q^{24} +(-4.83953 - 1.25658i) q^{25} +(6.53553 + 4.28639i) q^{26} +(3.84758 + 3.84758i) q^{27} +(-8.58655 - 3.38553i) q^{28} -1.43401i q^{29} +(-3.92696 - 3.35832i) q^{30} -2.10503i q^{31} +(-2.93852 + 4.83374i) q^{32} +(-5.27920 - 5.27920i) q^{33} +(-4.04454 + 6.16678i) q^{34} +(8.16243 - 6.31372i) q^{35} +(0.263028 + 0.605458i) q^{36} +(3.01280 - 3.01280i) q^{37} +(-1.38463 + 0.287770i) q^{38} -9.03041 q^{39} +(-2.96380 - 5.58712i) q^{40} +3.51686 q^{41} +(10.4412 - 2.17001i) q^{42} +(-1.49689 + 1.49689i) q^{43} +(-3.64116 - 8.38148i) q^{44} +(-0.732095 - 0.0934937i) q^{45} +(0.736700 - 1.12326i) q^{46} +(-5.49969 - 5.49969i) q^{47} +(-0.223890 - 6.53214i) q^{48} +14.2977i q^{49} +(7.06254 + 0.347220i) q^{50} -8.52089i q^{51} +(-10.2828 - 4.05432i) q^{52} +(5.92537 + 5.92537i) q^{53} +(-6.43468 - 4.22024i) q^{54} +(10.1345 + 1.29425i) q^{55} +(12.8634 + 2.21674i) q^{56} +(1.15541 - 1.15541i) q^{57} +(0.412665 + 1.98557i) q^{58} +1.07843 q^{59} +(6.40380 + 3.51996i) q^{60} -11.0480 q^{61} +(0.605762 + 2.91467i) q^{62} +(1.07708 - 1.07708i) q^{63} +(2.67775 - 7.53855i) q^{64} +(9.77486 - 7.56095i) q^{65} +(8.82890 + 5.79052i) q^{66} +(-1.29688 - 1.29688i) q^{67} +(3.82556 - 9.70258i) q^{68} +1.55205i q^{69} +(-9.48501 + 11.0910i) q^{70} +1.88311i q^{71} +(-0.538428 - 0.762641i) q^{72} +(-3.20108 - 3.20108i) q^{73} +(-3.30461 + 5.03859i) q^{74} +(-7.04349 + 4.13977i) q^{75} +(1.83438 - 0.796907i) q^{76} +(-14.9102 + 14.9102i) q^{77} +(12.5037 - 2.59868i) q^{78} +2.07546 q^{79} +(5.71156 + 6.88318i) q^{80} +7.90087 q^{81} +(-4.86954 + 1.01205i) q^{82} +(-2.08842 + 2.08842i) q^{83} +(-13.8326 + 6.00930i) q^{84} +(7.13434 + 9.22333i) q^{85} +(1.64187 - 2.50339i) q^{86} +(-1.65687 - 1.65687i) q^{87} +(7.45358 + 10.5574i) q^{88} +10.9661i q^{89} +(1.04058 - 0.0812209i) q^{90} +25.5049i q^{91} +(-0.696814 + 1.76729i) q^{92} +(-2.43216 - 2.43216i) q^{93} +(9.19765 + 6.03237i) q^{94} +(-0.283261 + 2.21805i) q^{95} +(2.18976 + 8.98014i) q^{96} +(1.72131 - 1.72131i) q^{97} +(-4.11443 - 19.7969i) q^{98} +1.50809 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.38463	+	0.287770i	−0.979078	+	0.203484i
$2$	−1.38463	+	0.287770i	−0.979078	+	0.203484i
$3$	1.15541	−	1.15541i	0.667075	−	0.667075i	−0.289963	−	0.957038i	$-0.593643\pi$
$3$	1.15541	−	1.15541i	0.667075	−	0.667075i	0.957038	+	0.289963i	$0.0936428\pi$
$4$	1.83438	−	0.796907i	0.917189	−	0.398453i
$5$	−0.283261	+	2.21805i	−0.126678	+	0.991944i
$5$	−0.283261	+	2.21805i	−0.126678	+	0.991944i
$6$	−1.26732	+	1.93230i	−0.517380	+	0.788858i
$7$	−3.26325	−	3.26325i	−1.23339	−	1.23339i	−0.962652	−	0.270742i	$-0.912731\pi$
$7$	−3.26325	−	3.26325i	−1.23339	−	1.23339i	−0.270742	−	0.962652i	$-0.587269\pi$
$8$	−2.31060	+	1.63130i	−0.816921	+	0.576750i
$9$			0.330062i			0.110021i
$10$	−0.246078	−	3.15269i	−0.0778167	−	0.996968i
$11$		−	4.56912i		−	1.37764i	−0.724932	−	0.688820i	$-0.758129\pi$
$11$		−	4.56912i		−	1.37764i	0.724932	−	0.688820i	$-0.241871\pi$
$12$	1.19870	−	3.04021i	0.346036	−	0.877632i
$13$	−3.90789	−	3.90789i	−1.08385	−	1.08385i	−0.996146	−	0.0877064i	$-0.972046\pi$
$13$	−3.90789	−	3.90789i	−1.08385	−	1.08385i	−0.0877064	−	0.996146i	$-0.527954\pi$
$14$	5.45745	+	3.57932i	1.45857	+	0.956613i
$15$	2.23548	+	2.89004i	0.577197	+	0.746205i
$16$	2.72988	−	2.92365i	0.682470	−	0.730914i
$17$	3.68739	−	3.68739i	0.894324	−	0.894324i	−0.100602	−	0.994927i	$-0.532077\pi$
$17$	3.68739	−	3.68739i	0.894324	−	0.894324i	0.994927	+	0.100602i	$0.0320770\pi$
$18$	−0.0949818	−	0.457012i	−0.0223874	−	0.107719i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	1.24797	+	4.29448i	0.279055	+	0.960275i
$21$	−7.54078			−1.64553
$22$	1.31485	+	6.32652i	0.280328	+	1.34882i
$23$	−0.671647	+	0.671647i	−0.140048	+	0.140048i	−0.773655	−	0.633607i	$-0.781574\pi$
$23$	−0.671647	+	0.671647i	−0.140048	+	0.140048i	0.633607	+	0.773655i	$0.281574\pi$
$24$	−0.784875	+	4.55450i	−0.160212	+	0.929684i
$25$	−4.83953	−	1.25658i	−0.967905	−	0.251315i
$26$	6.53553	+	4.28639i	1.28172	+	0.840630i
$27$	3.84758	+	3.84758i	0.740468	+	0.740468i
$28$	−8.58655	−	3.38553i	−1.62270	−	0.639805i
$29$		−	1.43401i		−	0.266289i	−0.991097	−	0.133145i	$-0.957493\pi$
$29$		−	1.43401i		−	0.266289i	0.991097	−	0.133145i	$-0.0425074\pi$
$30$	−3.92696	−	3.35832i	−0.716962	−	0.613143i
$31$		−	2.10503i		−	0.378074i	−0.981970	−	0.189037i	$-0.939463\pi$
$31$		−	2.10503i		−	0.378074i	0.981970	−	0.189037i	$-0.0605366\pi$
$32$	−2.93852	+	4.83374i	−0.519462	+	0.854493i
$33$	−5.27920	−	5.27920i	−0.918990	−	0.918990i
$34$	−4.04454	+	6.16678i	−0.693633	+	1.05759i
$35$	8.16243	−	6.31372i	1.37970	−	1.06721i
$36$	0.263028	+	0.605458i	0.0438381	+	0.100910i
$37$	3.01280	−	3.01280i	0.495301	−	0.495301i	−0.414670	−	0.909972i	$-0.636103\pi$
$37$	3.01280	−	3.01280i	0.495301	−	0.495301i	0.909972	+	0.414670i	$0.136103\pi$
$38$	−1.38463	+	0.287770i	−0.224616	+	0.0466824i
$39$	−9.03041			−1.44602
$40$	−2.96380	−	5.58712i	−0.468618	−	0.883401i
$41$	3.51686			0.549241			0.274621	−	0.961553i	$-0.411448\pi$
$41$	3.51686			0.549241			0.274621	+	0.961553i	$0.411448\pi$
$42$	10.4412	−	2.17001i	1.61111	−	0.334840i
$43$	−1.49689	+	1.49689i	−0.228273	+	0.228273i	−0.811971	−	0.583698i	$-0.801605\pi$
$43$	−1.49689	+	1.49689i	−0.228273	+	0.228273i	0.583698	+	0.811971i	$0.301605\pi$
$44$	−3.64116	−	8.38148i	−0.548925	−	1.26356i
$45$	−0.732095	−	0.0934937i	−0.109134	−	0.0139372i
$46$	0.736700	−	1.12326i	0.108621	−	0.165616i
$47$	−5.49969	−	5.49969i	−0.802212	−	0.802212i	0.181229	−	0.983441i	$-0.441993\pi$
$47$	−5.49969	−	5.49969i	−0.802212	−	0.802212i	−0.983441	+	0.181229i	$0.941993\pi$
$48$	−0.223890	−	6.53214i	−0.0323157	−	0.942834i
$49$			14.2977i			2.04252i
$50$	7.06254	+	0.347220i	0.998794	+	0.0491044i
$51$		−	8.52089i		−	1.19316i
$52$	−10.2828	−	4.05432i	−1.42596	−	0.562233i
$53$	5.92537	+	5.92537i	0.813913	+	0.813913i	0.985218	−	0.171305i	$-0.0547985\pi$
$53$	5.92537	+	5.92537i	0.813913	+	0.813913i	−0.171305	+	0.985218i	$0.554798\pi$
$54$	−6.43468	−	4.22024i	−0.875649	−	0.574302i
$55$	10.1345	+	1.29425i	1.36654	+	0.174517i
$56$	12.8634	+	2.21674i	1.71895	+	0.296225i
$57$	1.15541	−	1.15541i	0.153038	−	0.153038i
$58$	0.412665	+	1.98557i	0.0541855	+	0.260718i
$59$	1.07843			0.140400			0.0702000	−	0.997533i	$-0.477636\pi$
$59$	1.07843			0.140400			0.0702000	+	0.997533i	$0.477636\pi$
$60$	6.40380	+	3.51996i	0.826727	+	0.454425i
$61$	−11.0480			−1.41455			−0.707277	−	0.706936i	$-0.750077\pi$
$61$	−11.0480			−1.41455			−0.707277	+	0.706936i	$0.750077\pi$
$62$	0.605762	+	2.91467i	0.0769319	+	0.370164i
$63$	1.07708	−	1.07708i	0.135699	−	0.135699i
$64$	2.67775	−	7.53855i	0.334719	−	0.942318i
$65$	9.77486	−	7.56095i	1.21242	−	0.937820i
$66$	8.82890	+	5.79052i	1.08676	+	0.712763i
$67$	−1.29688	−	1.29688i	−0.158439	−	0.158439i	0.623436	−	0.781875i	$-0.285736\pi$
$67$	−1.29688	−	1.29688i	−0.158439	−	0.158439i	−0.781875	+	0.623436i	$0.785736\pi$
$68$	3.82556	−	9.70258i	0.463918	−	1.17661i
$69$			1.55205i			0.186845i
$70$	−9.48501	+	11.0910i	−1.13368	+	1.32563i
$71$			1.88311i			0.223484i	0.993737	+	0.111742i	$0.0356430\pi$
$71$			1.88311i			0.223484i	−0.993737	+	0.111742i	$0.964357\pi$
$72$	−0.538428	−	0.762641i	−0.0634544	−	0.0898781i
$73$	−3.20108	−	3.20108i	−0.374659	−	0.374659i	0.494512	−	0.869171i	$-0.335347\pi$
$73$	−3.20108	−	3.20108i	−0.374659	−	0.374659i	−0.869171	+	0.494512i	$0.835347\pi$
$74$	−3.30461	+	5.03859i	−0.384153	+	0.585725i
$75$	−7.04349	+	4.13977i	−0.813312	+	0.478019i
$76$	1.83438	−	0.796907i	0.210417	−	0.0914115i
$77$	−14.9102	+	14.9102i	−1.69917	+	1.69917i
$78$	12.5037	−	2.59868i	1.41577	−	0.294242i
$79$	2.07546			0.233507			0.116753	−	0.993161i	$-0.462751\pi$
$79$	2.07546			0.233507			0.116753	+	0.993161i	$0.462751\pi$
$80$	5.71156	+	6.88318i	0.638571	+	0.769563i
$81$	7.90087			0.877875
$82$	−4.86954	+	1.01205i	−0.537750	+	0.111762i
$83$	−2.08842	+	2.08842i	−0.229234	+	0.229234i	−0.812373	−	0.583139i	$-0.801824\pi$
$83$	−2.08842	+	2.08842i	−0.229234	+	0.229234i	0.583139	+	0.812373i	$0.301824\pi$
$84$	−13.8326	+	6.00930i	−1.50926	+	0.655668i
$85$	7.13434	+	9.22333i	0.773828	+	1.00041i
$86$	1.64187	−	2.50339i	0.177048	−	0.269948i
$87$	−1.65687	−	1.65687i	−0.177635	−	0.177635i
$88$	7.45358	+	10.5574i	0.794554	+	1.12542i
$89$			10.9661i			1.16240i	0.813759	+	0.581202i	$0.197417\pi$
$89$			10.9661i			1.16240i	−0.813759	+	0.581202i	$0.802583\pi$
$90$	1.04058	−	0.0812209i	0.109687	−	0.00856144i
$91$			25.5049i			2.67363i
$92$	−0.696814	+	1.76729i	−0.0726479	+	0.184253i
$93$	−2.43216	−	2.43216i	−0.252204	−	0.252204i
$94$	9.19765	+	6.03237i	0.948666	+	0.622191i
$95$	−0.283261	+	2.21805i	−0.0290620	+	0.227568i
$96$	2.18976	+	8.98014i	0.223491	+	0.916532i
$97$	1.72131	−	1.72131i	0.174773	−	0.174773i	−0.614300	−	0.789073i	$-0.710561\pi$
$97$	1.72131	−	1.72131i	0.174773	−	0.174773i	0.789073	+	0.614300i	$0.210561\pi$
$98$	−4.11443	−	19.7969i	−0.415620	−	1.99979i
$99$	1.50809			0.151569
$100$	−9.87889	+	1.55161i	−0.987889	+	0.155161i
$101$	15.3995			1.53231			0.766154	−	0.642658i	$-0.222168\pi$
$101$	15.3995			1.53231			0.766154	+	0.642658i	$0.222168\pi$
$102$	2.45205	+	11.7982i	0.242790	+	1.16820i
$103$	−0.538076	+	0.538076i	−0.0530182	+	0.0530182i	−0.733119	−	0.680101i	$-0.761936\pi$
$103$	−0.538076	+	0.538076i	−0.0530182	+	0.0530182i	0.680101	+	0.733119i	$0.261936\pi$
$104$	15.4045	+	2.65465i	1.51053	+	0.260309i
$105$	2.13601	−	16.7259i	0.208453	−	1.63228i
$106$	−9.90957	−	6.49928i	−0.962502	−	0.631266i
$107$	−2.15177	−	2.15177i	−0.208019	−	0.208019i	0.595406	−	0.803425i	$-0.296991\pi$
$107$	−2.15177	−	2.15177i	−0.208019	−	0.208019i	−0.803425	+	0.595406i	$0.796991\pi$
$108$	10.1241	+	3.99175i	0.974190	+	0.384107i
$109$			12.9951i			1.24471i	0.782737	+	0.622353i	$0.213823\pi$
$109$			12.9951i			1.24471i	−0.782737	+	0.622353i	$0.786177\pi$
$110$	−14.4050	+	1.12436i	−1.37346	+	0.107203i
$111$		−	6.96203i		−	0.660807i
$112$	−18.4489	+	0.632338i	−1.74326	+	0.0597503i
$113$	4.57006	+	4.57006i	0.429915	+	0.429915i	0.888599	−	0.458685i	$-0.151679\pi$
$113$	4.57006	+	4.57006i	0.429915	+	0.429915i	−0.458685	+	0.888599i	$0.651679\pi$
$114$	−1.26732	+	1.93230i	−0.118695	+	0.180976i
$115$	−1.29950	−	1.68000i	−0.121179	−	0.156661i
$116$	−1.14277	−	2.63052i	−0.106104	−	0.244237i
$117$	1.28984	−	1.28984i	0.119246	−	0.119246i
$118$	−1.49323	+	0.310340i	−0.137463	+	0.0285692i
$119$	−24.0658			−2.20611
$120$	−9.87980	−	3.03101i	−0.901899	−	0.276692i
$121$	−9.87682			−0.897892
$122$	15.2974	−	3.17929i	1.38496	−	0.287839i
$123$	4.06341	−	4.06341i	0.366385	−	0.366385i
$124$	−1.67751	−	3.86141i	−0.150645	−	0.346765i
$125$	4.15801	−	10.3784i	0.371903	−	0.928271i
$126$	−1.18140	+	1.80130i	−0.105247	+	0.160472i
$127$	6.46266	+	6.46266i	0.573468	+	0.573468i	0.933096	−	0.359628i	$-0.117096\pi$
$127$	6.46266	+	6.46266i	0.573468	+	0.573468i	−0.359628	+	0.933096i	$0.617096\pi$
$128$	−1.53832	+	11.2086i	−0.135969	+	0.990713i
$129$			3.45904i			0.304551i
$130$	−11.3587	+	13.2820i	−0.996224	+	1.16491i
$131$		−	11.2765i		−	0.985230i	−0.870247	−	0.492615i	$-0.836041\pi$
$131$		−	11.2765i		−	0.985230i	0.870247	−	0.492615i	$-0.163959\pi$
$132$	−13.8911	−	5.47701i	−1.20906	−	0.476713i
$133$	−3.26325	−	3.26325i	−0.282960	−	0.282960i
$134$	2.16889	+	1.42249i	0.187364	+	0.122884i
$135$	−9.62402	+	7.44427i	−0.828303	+	0.640701i
$136$	−2.50486	+	14.5353i	−0.214790	+	1.24639i
$137$	4.91194	−	4.91194i	0.419655	−	0.419655i	−0.465430	−	0.885085i	$-0.654100\pi$
$137$	4.91194	−	4.91194i	0.419655	−	0.419655i	0.885085	+	0.465430i	$0.154100\pi$
$138$	−0.446634	−	2.14901i	−0.0380200	−	0.182936i
$139$	13.9325			1.18174			0.590870	−	0.806767i	$-0.298785\pi$
$139$	13.9325			1.18174			0.590870	+	0.806767i	$0.298785\pi$
$140$	9.94152	−	18.0864i	0.840212	−	1.52858i
$141$	−12.7088			−1.07027
$142$	−0.541902	−	2.60740i	−0.0454754	−	0.218808i
$143$	−17.8556	+	17.8556i	−1.49316	+	1.49316i
$144$	0.964987	+	0.901029i	0.0804156	+	0.0750858i
$145$	3.18071	+	0.406200i	0.264144	+	0.0337330i
$146$	5.35348	+	3.51113i	0.443057	+	0.290583i
$147$	16.5196	+	16.5196i	1.36252	+	1.36252i
$148$	3.12569	−	7.92753i	0.256930	−	0.651639i
$149$		−	16.9391i		−	1.38771i	−0.720116	−	0.693853i	$-0.755912\pi$
$149$		−	16.9391i		−	1.38771i	0.720116	−	0.693853i	$-0.244088\pi$
$150$	8.56130	−	7.75894i	0.699027	−	0.633514i
$151$		−	23.4511i		−	1.90842i	−0.299137	−	0.954210i	$-0.596699\pi$
$151$		−	23.4511i		−	1.90842i	0.299137	−	0.954210i	$-0.403301\pi$
$152$	−2.31060	+	1.63130i	−0.187414	+	0.132316i
$153$	1.21707	+	1.21707i	0.0983941	+	0.0983941i
$154$	16.3543	−	24.9357i	1.31787	−	2.00938i
$155$	4.66906	+	0.596272i	0.375028	+	0.0478937i
$156$	−16.5652	+	7.19640i	−1.32628	+	0.576173i
$157$	14.2678	−	14.2678i	1.13869	−	1.13869i	0.150010	−	0.988684i	$-0.452069\pi$
$157$	14.2678	−	14.2678i	1.13869	−	1.13869i	0.988684	−	0.150010i	$-0.0479307\pi$
$158$	−2.87373	+	0.597253i	−0.228622	+	0.0475149i
$159$	13.6925			1.08588
$160$	−9.88914	−	7.88701i	−0.781805	−	0.623523i
$161$	4.38351			0.345469
$162$	−10.9398	+	2.27363i	−0.859508	+	0.178633i
$163$	9.47832	−	9.47832i	0.742400	−	0.742400i	−0.230640	−	0.973039i	$-0.574082\pi$
$163$	9.47832	−	9.47832i	0.742400	−	0.742400i	0.973039	+	0.230640i	$0.0740818\pi$
$164$	6.45125	−	2.80261i	0.503758	−	0.218847i
$165$	13.2049	−	10.2141i	1.02800	−	0.795170i
$166$	2.29069	−	3.49266i	0.177792	−	0.271083i
$167$	13.9319	+	13.9319i	1.07808	+	1.07808i	0.996681	+	0.0814021i	$0.0259398\pi$
$167$	13.9319	+	13.9319i	1.07808	+	1.07808i	0.0814021	+	0.996681i	$0.474060\pi$
$168$	17.4237	−	12.3012i	1.34427	−	0.949062i
$169$			17.5432i			1.34947i
$170$	−12.5326	−	10.7178i	−0.961206	−	0.822019i
$171$			0.330062i			0.0252405i
$172$	−1.55298	+	3.93874i	−0.118414	+	0.300326i
$173$	1.27870	+	1.27870i	0.0972178	+	0.0972178i	0.754043	−	0.656825i	$-0.228101\pi$
$173$	1.27870	+	1.27870i	0.0972178	+	0.0972178i	−0.656825	+	0.754043i	$0.728101\pi$
$174$	2.77094	+	1.81735i	0.210064	+	0.137773i
$175$	11.6921	+	19.8931i	0.883838	+	1.50378i
$176$	−13.3585	−	12.4731i	−1.00694	−	0.940198i
$177$	1.24603	−	1.24603i	0.0936575	−	0.0936575i
$178$	−3.15571	−	15.1839i	−0.236530	−	1.13808i
$179$	3.98743			0.298034			0.149017	−	0.988835i	$-0.452389\pi$
$179$	3.98743			0.298034			0.149017	+	0.988835i	$0.452389\pi$
$180$	−1.41744	+	0.411909i	−0.105650	+	0.0307019i
$181$	19.3398			1.43752			0.718758	−	0.695261i	$-0.244711\pi$
$181$	19.3398			1.43752			0.718758	+	0.695261i	$0.244711\pi$
$182$	−7.33952	−	35.3147i	−0.544042	−	2.61770i
$183$	−12.7650	+	12.7650i	−0.943615	+	0.943615i
$184$	0.456253	−	2.64756i	0.0336354	−	0.195181i
$185$	5.82914	+	7.53596i	0.428567	+	0.554055i
$186$	4.06754	+	2.66773i	0.298247	+	0.195608i
$187$	−16.8481	−	16.8481i	−1.23206	−	1.23206i
$188$	−14.4712	−	5.70576i	−1.05542	−	0.416136i
$189$		−	25.1113i		−	1.82658i
$190$	−0.246078	−	3.15269i	−0.0178524	−	0.228720i
$191$			1.41454i			0.102352i	0.998690	+	0.0511761i	$0.0162970\pi$
$191$			1.41454i			0.102352i	−0.998690	+	0.0511761i	$0.983703\pi$
$192$	−5.61621	−	11.8040i	−0.405315	−	0.851880i
$193$	−7.89499	−	7.89499i	−0.568294	−	0.568294i	0.363356	−	0.931650i	$-0.381631\pi$
$193$	−7.89499	−	7.89499i	−0.568294	−	0.568294i	−0.931650	+	0.363356i	$0.881631\pi$
$194$	−1.88803	+	2.87871i	−0.135553	+	0.206680i
$195$	2.55797	−	20.0299i	0.183180	−	1.43437i
$196$	11.3939	+	26.2273i	0.813850	+	1.87338i
$197$	−17.3505	+	17.3505i	−1.23617	+	1.23617i	−0.274617	+	0.961554i	$0.588551\pi$
$197$	−17.3505	+	17.3505i	−1.23617	+	1.23617i	−0.961554	+	0.274617i	$0.911449\pi$
$198$	−2.08814	+	0.433983i	−0.148398	+	0.0308418i
$199$	−22.0059			−1.55996			−0.779979	−	0.625805i	$-0.784770\pi$
$199$	−22.0059			−1.55996			−0.779979	+	0.625805i	$0.784770\pi$
$200$	13.2321	−	4.99125i	0.935648	−	0.352935i
$201$	−2.99685			−0.211382
$202$	−21.3225	+	4.43151i	−1.50025	+	0.311800i
$203$	−4.67954	+	4.67954i	−0.328439	+	0.328439i
$204$	−6.79036	−	15.6305i	−0.475420	−	1.09436i
$205$	−0.996190	+	7.80059i	−0.0695769	+	0.544817i
$206$	0.590192	−	0.899876i	0.0411206	−	0.0626974i
$207$	−0.221685	−	0.221685i	−0.0154082	−	0.0154082i
$208$	−22.0934	+	0.757252i	−1.53190	+	0.0525060i
$209$		−	4.56912i		−	0.316052i
$210$	1.85562	+	23.7737i	0.128050	+	1.64054i
$211$		−	13.2621i		−	0.913002i	−0.889723	−	0.456501i	$-0.849102\pi$
$211$		−	13.2621i		−	0.913002i	0.889723	−	0.456501i	$-0.150898\pi$
$212$	15.5913	+	6.14740i	1.07082	+	0.422205i
$213$	2.17576	+	2.17576i	0.149081	+	0.149081i
$214$	3.59860	+	2.36018i	0.245995	+	0.161338i
$215$	−2.89617	−	3.74419i	−0.197517	−	0.255352i
$216$	−15.1668	−	2.61368i	−1.03197	−	0.177838i
$217$	−6.86923	+	6.86923i	−0.466314	+	0.466314i
$218$	−3.73960	−	17.9934i	−0.253278	−	1.21866i
$219$	−7.39712			−0.499851
$220$	19.6220	−	5.70214i	1.32291	−	0.384438i
$221$	−28.8198			−1.93863
$222$	2.00346	+	9.63981i	0.134464	+	0.646981i
$223$	−6.10795	+	6.10795i	−0.409019	+	0.409019i	−0.881396	−	0.472378i	$-0.843396\pi$
$223$	−6.10795	+	6.10795i	−0.409019	+	0.409019i	0.472378	+	0.881396i	$0.343396\pi$
$224$	25.3629	−	6.18459i	1.69463	−	0.413225i
$225$	0.414748	−	1.59734i	0.0276499	−	0.106490i
$226$	−7.64294	−	5.01269i	−0.508401	−	0.333439i
$227$	14.8986	+	14.8986i	0.988853	+	0.988853i	0.999939	−	0.0110855i	$-0.00352868\pi$
$227$	14.8986	+	14.8986i	0.988853	+	0.988853i	−0.0110855	+	0.999939i	$0.503529\pi$
$228$	1.19870	−	3.04021i	0.0793860	−	0.201343i
$229$		−	25.6102i		−	1.69237i	−0.532888	−	0.846186i	$-0.678893\pi$
$229$		−	25.6102i		−	1.69237i	0.532888	−	0.846186i	$-0.321107\pi$
$230$	2.28277	+	1.95222i	0.150521	+	0.128725i
$231$			34.4547i			2.26695i
$232$	2.33930	+	3.31343i	0.153582	+	0.217537i
$233$	10.2855	+	10.2855i	0.673827	+	0.673827i	0.958596	−	0.284769i	$-0.0919169\pi$
$233$	10.2855	+	10.2855i	0.673827	+	0.673827i	−0.284769	+	0.958596i	$0.591917\pi$
$234$	−1.41477	+	2.15713i	−0.0924866	+	0.141016i
$235$	13.7565	−	10.6408i	0.897372	−	0.694126i
$236$	1.97825	−	0.859411i	0.128773	−	0.0559429i
$237$	2.39800	−	2.39800i	0.155767	−	0.155767i
$238$	33.3221	−	6.92541i	2.15995	−	0.448908i
$239$	−3.19293			−0.206534			−0.103267	−	0.994654i	$-0.532930\pi$
$239$	−3.19293			−0.206534			−0.103267	+	0.994654i	$0.532930\pi$
$240$	14.5521	+	1.35370i	0.939332	+	0.0873812i
$241$	−11.7591			−0.757470			−0.378735	−	0.925505i	$-0.623641\pi$
$241$	−11.7591			−0.757470			−0.378735	+	0.925505i	$0.623641\pi$
$242$	13.6757	−	2.84225i	0.879107	−	0.182707i
$243$	−2.41401	+	2.41401i	−0.154859	+	0.154859i
$244$	−20.2662	+	8.80425i	−1.29741	+	0.563634i
$245$	−31.7130	−	4.04997i	−2.02607	−	0.258743i
$246$	−4.45698	+	6.79563i	−0.284167	+	0.433274i
$247$	−3.90789	−	3.90789i	−0.248653	−	0.248653i
$248$	3.43392	+	4.86387i	0.218054	+	0.308856i
$249$			4.82595i			0.305832i
$250$	−2.77070	+	15.5667i	−0.175234	+	0.984527i
$251$		−	14.5530i		−	0.918575i	−0.888288	−	0.459287i	$-0.848105\pi$
$251$		−	14.5530i		−	0.918575i	0.888288	−	0.459287i	$-0.151895\pi$
$252$	1.11743	−	2.83409i	0.0703917	−	0.178531i
$253$	3.06883	+	3.06883i	0.192936	+	0.192936i
$254$	−10.8081	−	7.08861i	−0.678162	−	0.444779i
$255$	18.8998	+	2.41364i	1.18355	+	0.151148i
$256$	−1.09552	−	15.9625i	−0.0684697	−	0.997653i
$257$	−11.5648	+	11.5648i	−0.721392	+	0.721392i	−0.968889	−	0.247496i	$-0.920392\pi$
$257$	−11.5648	+	11.5648i	−0.721392	+	0.721392i	0.247496	+	0.968889i	$0.420392\pi$
$258$	−0.995406	−	4.78947i	−0.0619713	−	0.298180i
$259$	−19.6631			−1.22180
$260$	11.9054	−	21.6593i	0.738342	−	1.34325i
$261$	0.473312			0.0292973
$262$	3.24503	+	15.6137i	0.200478	+	0.964618i
$263$	−0.240407	+	0.240407i	−0.0148241	+	0.0148241i	−0.714480	−	0.699656i	$-0.753337\pi$
$263$	−0.240407	+	0.240407i	−0.0148241	+	0.0148241i	0.699656	+	0.714480i	$0.253337\pi$
$264$	20.8100	+	3.58618i	1.28077	+	0.220714i
$265$	−14.8212	+	11.4644i	−0.910461	+	0.704251i
$266$	5.45745	+	3.57932i	0.334618	+	0.219462i
$267$	12.6703	+	12.6703i	0.775411	+	0.775411i
$268$	−3.41246	−	1.34547i	−0.208449	−	0.0821879i
$269$		−	5.22590i		−	0.318629i	−0.987228	−	0.159314i	$-0.949072\pi$
$269$		−	5.22590i		−	0.318629i	0.987228	−	0.159314i	$-0.0509283\pi$
$270$	11.1834	−	13.0770i	0.680601	−	0.795843i
$271$			10.0441i			0.610137i	0.952330	+	0.305069i	$0.0986794\pi$
$271$			10.0441i			0.610137i	−0.952330	+	0.305069i	$0.901321\pi$
$272$	−0.714526	−	20.8468i	−0.0433245	−	1.26402i
$273$	29.4685	+	29.4685i	1.78352	+	1.78352i
$274$	−5.38769	+	8.21471i	−0.325482	+	0.496269i
$275$	−5.74145	+	22.1124i	−0.346222	+	1.33343i
$276$	1.23684	+	2.84705i	0.0744491	+	0.171372i
$277$	−1.69900	+	1.69900i	−0.102083	+	0.102083i	−0.756304	−	0.654221i	$-0.772997\pi$
$277$	−1.69900	+	1.69900i	−0.102083	+	0.102083i	0.654221	+	0.756304i	$0.272997\pi$
$278$	−19.2913	+	4.00935i	−1.15702	+	0.240465i
$279$	0.694788			0.0415959
$280$	−8.56056	+	27.9038i	−0.511591	+	1.66757i
$281$	−8.96932			−0.535065			−0.267532	−	0.963549i	$-0.586208\pi$
$281$	−8.96932			−0.535065			−0.267532	+	0.963549i	$0.586208\pi$
$282$	17.5969	−	3.65720i	1.04788	−	0.217783i
$283$	10.6254	−	10.6254i	0.631617	−	0.631617i	−0.316856	−	0.948474i	$-0.602627\pi$
$283$	10.6254	−	10.6254i	0.631617	−	0.631617i	0.948474	+	0.316856i	$0.102627\pi$
$284$	1.50066	+	3.45434i	0.0890480	+	0.204977i
$285$	2.23548	+	2.89004i	0.132418	+	0.171191i
$286$	19.5850	−	29.8616i	1.15809	−	1.76575i
$287$	−11.4764	−	11.4764i	−0.677431	−	0.677431i
$288$	−1.59543	−	0.969894i	−0.0940119	−	0.0571516i
$289$		−	10.1937i		−	0.599632i
$290$	−4.52099	+	0.352878i	−0.265482	+	0.0207217i
$291$		−	3.97764i		−	0.233173i
$292$	−8.42296	−	3.32103i	−0.492917	−	0.194349i
$293$	21.8787	+	21.8787i	1.27817	+	1.27817i	0.941692	+	0.336476i	$0.109235\pi$
$293$	21.8787	+	21.8787i	1.27817	+	1.27817i	0.336476	+	0.941692i	$0.390765\pi$
$294$	−27.6274	−	18.1197i	−1.61126	−	1.05676i
$295$	−0.305478	+	2.39202i	−0.0177856	+	0.139269i
$296$	−2.04661	+	11.8761i	−0.118957	+	0.690287i
$297$	17.5800	−	17.5800i	1.02010	−	1.02010i
$298$	4.87457	+	23.4543i	0.282376	+	1.35867i
$299$	5.24944			0.303583
$300$	−9.62141	+	13.2069i	−0.555492	+	0.762501i
$301$	9.76946			0.563102
$302$	6.74850	+	32.4709i	0.388333	+	1.86849i
$303$	17.7927	−	17.7927i	1.02216	−	1.02216i
$304$	2.72988	−	2.92365i	0.156569	−	0.167683i
$305$	3.12948	−	24.5051i	0.179193	−	1.40316i
$306$	−2.03542	−	1.33495i	−0.116357	−	0.0763139i
$307$	−16.5064	−	16.5064i	−0.942071	−	0.942071i	0.0563407	−	0.998412i	$-0.482057\pi$
$307$	−16.5064	−	16.5064i	−0.942071	−	0.942071i	−0.998412	+	0.0563407i	$0.982057\pi$
$308$	−15.4689	+	39.2329i	−0.881421	+	2.23550i
$309$			1.24340i			0.0707343i
$310$	−6.63649	+	0.518000i	−0.376927	+	0.0294204i
$311$			19.4406i			1.10238i	0.834381	+	0.551188i	$0.185825\pi$
$311$			19.4406i			1.10238i	−0.834381	+	0.551188i	$0.814175\pi$
$312$	20.8657	−	14.7313i	1.18129	−	0.833994i
$313$	−8.63499	−	8.63499i	−0.488079	−	0.488079i	0.419621	−	0.907699i	$-0.362163\pi$
$313$	−8.63499	−	8.63499i	−0.488079	−	0.488079i	−0.907699	+	0.419621i	$0.862163\pi$
$314$	−15.6497	+	23.8614i	−0.883165	+	1.34658i
$315$	2.08392	+	2.69411i	0.117415	+	0.151796i
$316$	3.80717	−	1.65394i	0.214170	−	0.0930416i
$317$	13.6017	−	13.6017i	0.763949	−	0.763949i	−0.213085	−	0.977034i	$-0.568351\pi$
$317$	13.6017	−	13.6017i	0.763949	−	0.763949i	0.977034	+	0.213085i	$0.0683510\pi$
$318$	−18.9589	+	3.94027i	−1.06316	+	0.220960i
$319$	−6.55216			−0.366850
$320$	15.9624	+	8.07477i	0.892325	+	0.451393i
$321$	−4.97234			−0.277529
$322$	−6.06952	+	1.26144i	−0.338241	+	0.0702974i
$323$	3.68739	−	3.68739i	0.205172	−	0.205172i
$324$	14.4932	−	6.29626i	0.805177	−	0.349792i
$325$	14.0018	+	23.8229i	0.776678	+	1.32146i
$326$	−10.3964	+	15.8515i	−0.575801	+	0.877934i
$327$	15.0147	+	15.0147i	0.830313	+	0.830313i
$328$	−8.12606	+	5.73704i	−0.448687	+	0.316775i
$329$			35.8938i			1.97889i
$330$	−15.3446	+	17.9428i	−0.844691	+	0.987716i
$331$		−	21.6643i		−	1.19078i	−0.803437	−	0.595390i	$-0.796998\pi$
$331$		−	21.6643i		−	1.19078i	0.803437	−	0.595390i	$-0.203002\pi$
$332$	−2.16667	+	5.49522i	−0.118912	+	0.301589i
$333$	0.994410	+	0.994410i	0.0544934	+	0.0544934i
$334$	−23.2997	−	15.2813i	−1.27490	−	0.836155i
$335$	3.24390	−	2.50919i	0.177233	−	0.137092i
$336$	−20.5854	+	22.0466i	−1.12303	+	1.20274i
$337$	0.169255	−	0.169255i	0.00921991	−	0.00921991i	−0.702482	−	0.711702i	$-0.747925\pi$
$337$	0.169255	−	0.169255i	0.00921991	−	0.00921991i	0.711702	+	0.702482i	$0.247925\pi$
$338$	−5.04839	−	24.2907i	−0.274596	−	1.32124i
$339$	10.5606			0.573571
$340$	20.4372	+	11.2337i	1.10836	+	0.609231i
$341$	−9.61810			−0.520849
$342$	−0.0949818	−	0.457012i	−0.00513603	−	0.0247124i
$343$	23.8141	−	23.8141i	1.28584	−	1.28584i
$344$	1.01684	−	5.90058i	0.0548246	−	0.318138i
$345$	−3.44254	−	0.439637i	−0.185340	−	0.0236692i
$346$	−2.13849	−	1.40255i	−0.114966	−	0.0754016i
$347$	−22.3067	−	22.3067i	−1.19749	−	1.19749i	−0.974917	−	0.222569i	$-0.928556\pi$
$347$	−22.3067	−	22.3067i	−1.19749	−	1.19749i	−0.222569	−	0.974917i	$-0.571444\pi$
$348$	−4.35969	−	1.71895i	−0.233704	−	0.0921455i
$349$		−	19.1551i		−	1.02535i	−0.858583	−	0.512674i	$-0.828655\pi$
$349$		−	19.1551i		−	1.02535i	0.858583	−	0.512674i	$-0.171345\pi$
$350$	−21.9138	−	24.1799i	−1.17134	−	1.29247i
$351$		−	30.0718i		−	1.60512i
$352$	22.0859	+	13.4264i	1.17718	+	0.715632i
$353$	0.692765	+	0.692765i	0.0368721	+	0.0368721i	0.725302	−	0.688430i	$-0.241700\pi$
$353$	0.692765	+	0.692765i	0.0368721	+	0.0368721i	−0.688430	+	0.725302i	$0.741700\pi$
$354$	−1.36672	+	2.08386i	−0.0726402	+	0.110756i
$355$	−4.17684	−	0.533412i	−0.221684	−	0.0283106i
$356$	8.73896	+	20.1160i	0.463164	+	1.06614i
$357$	−27.8058	+	27.8058i	−1.47164	+	1.47164i
$358$	−5.52109	+	1.14746i	−0.291799	+	0.0606452i
$359$	−13.0487			−0.688684			−0.344342	−	0.938844i	$-0.611898\pi$
$359$	−13.0487			−0.688684			−0.344342	+	0.938844i	$0.611898\pi$
$360$	1.84409	−	0.978237i	0.0971923	−	0.0515576i
$361$	1.00000			0.0526316
$362$	−26.7784	+	5.56541i	−1.40744	+	0.292511i
$363$	−11.4118	+	11.4118i	−0.598962	+	0.598962i
$364$	20.3250	+	46.7855i	1.06532	+	2.45223i
$365$	8.00692	−	6.19343i	0.419101	−	0.324179i
$366$	14.0014	−	21.3481i	0.731862	−	1.11588i
$367$	12.7436	+	12.7436i	0.665208	+	0.665208i	0.956603	−	0.291395i	$-0.0941193\pi$
$367$	12.7436	+	12.7436i	0.665208	+	0.665208i	−0.291395	+	0.956603i	$0.594119\pi$
$368$	0.130149	+	3.79718i	0.00678447	+	0.197942i
$369$			1.16078i			0.0604279i
$370$	−10.2398	−	8.75704i	−0.532342	−	0.455257i
$371$		−	38.6720i		−	2.00775i
$372$	−6.39971	−	2.52330i	−0.331810	−	0.130827i
$373$	15.6699	+	15.6699i	0.811354	+	0.811354i	0.984837	−	0.173483i	$-0.0555021\pi$
$373$	15.6699	+	15.6699i	0.811354	+	0.811354i	−0.173483	+	0.984837i	$0.555502\pi$
$374$	28.1767	+	18.4800i	1.45698	+	0.955576i
$375$	−7.18709	−	16.7955i	−0.371139	−	0.867315i
$376$	21.6792	+	3.73596i	1.11802	+	0.192668i
$377$	−5.60395	+	5.60395i	−0.288618	+	0.288618i
$378$	7.22626	+	34.7697i	0.371679	+	1.78836i
$379$	4.20942			0.216223			0.108112	−	0.994139i	$-0.465520\pi$
$379$	4.20942			0.216223			0.108112	+	0.994139i	$0.465520\pi$
$380$	1.24797	+	4.29448i	0.0640197	+	0.220302i
$381$	14.9340			0.765093
$382$	−0.407061	−	1.95860i	−0.0208270	−	0.100211i
$383$	−23.3914	+	23.3914i	−1.19524	+	1.19524i	−0.219671	+	0.975574i	$0.570498\pi$
$383$	−23.3914	+	23.3914i	−1.19524	+	1.19524i	−0.975574	+	0.219671i	$0.929502\pi$
$384$	11.1732	+	14.7279i	0.570179	+	0.751582i
$385$	−28.8481	−	37.2951i	−1.47024	−	1.90073i
$386$	13.2036	+	8.65967i	0.672043	+	0.440766i
$387$	−0.494066	−	0.494066i	−0.0251148	−	0.0251148i
$388$	1.78581	−	4.52926i	0.0906608	−	0.229938i
$389$			12.7135i			0.644603i	0.946637	+	0.322301i	$0.104456\pi$
$389$			12.7135i			0.644603i	−0.946637	+	0.322301i	$0.895544\pi$
$390$	2.22218	+	28.4701i	0.112525	+	1.44164i
$391$			4.95325i			0.250497i
$392$	−23.3237	−	33.0362i	−1.17802	−	1.66858i
$393$	−13.0289	−	13.0289i	−0.657223	−	0.657223i
$394$	19.0310	−	29.0169i	0.958767	−	1.46185i
$395$	−0.587896	+	4.60347i	−0.0295803	+	0.231626i
$396$	2.76641	−	1.20181i	0.139017	−	0.0603931i
$397$	25.9638	−	25.9638i	1.30308	−	1.30308i	0.376783	−	0.926302i	$-0.377030\pi$
$397$	25.9638	−	25.9638i	1.30308	−	1.30308i	0.926302	−	0.376783i	$-0.122970\pi$
$398$	30.4700	−	6.33264i	1.52732	−	0.317426i
$399$	−7.54078			−0.377511
$400$	−16.8851	+	10.7188i	−0.844256	+	0.535940i
$401$	11.2570			0.562146			0.281073	−	0.959686i	$-0.409310\pi$
$401$	11.2570			0.562146			0.281073	+	0.959686i	$0.409310\pi$
$402$	4.14952	−	0.862403i	0.206959	−	0.0430127i
$403$	−8.22620	+	8.22620i	−0.409776	+	0.409776i
$404$	28.2485	−	12.2720i	1.40541	−	0.610553i
$405$	−2.23801	+	17.5246i	−0.111208	+	0.870803i
$406$	5.13278	−	7.82604i	0.254736	−	0.388400i
$407$	−13.7658	−	13.7658i	−0.682347	−	0.682347i
$408$	13.9001	+	19.6884i	0.688157	+	0.974720i
$409$		−	31.3473i		−	1.55003i	−0.631945	−	0.775013i	$-0.717743\pi$
$409$		−	31.3473i		−	1.55003i	0.631945	−	0.775013i	$-0.282257\pi$
$410$	−0.865422	−	11.0876i	−0.0427401	−	0.547576i
$411$		−	11.3506i		−	0.559884i
$412$	−0.558238	+	1.41583i	−0.0275024	+	0.0697530i
$413$	−3.51920	−	3.51920i	−0.173169	−	0.173169i
$414$	0.370745	+	0.243157i	0.0182211	+	0.0119505i
$415$	−4.04066	−	5.22379i	−0.198348	−	0.256426i
$416$	30.3731	−	7.40631i	1.48917	−	0.363124i
$417$	16.0977	−	16.0977i	0.788310	−	0.788310i
$418$	1.31485	+	6.32652i	0.0643116	+	0.309440i
$419$	14.6694			0.716648			0.358324	−	0.933597i	$-0.383348\pi$
$419$	14.6694			0.716648			0.358324	+	0.933597i	$0.383348\pi$
$420$	−9.41070	−	32.3837i	−0.459195	−	1.58016i
$421$	−2.62268			−0.127822			−0.0639108	−	0.997956i	$-0.520357\pi$
$421$	−2.62268			−0.127822			−0.0639108	+	0.997956i	$0.520357\pi$
$422$	3.81644	+	18.3631i	0.185781	+	0.893901i
$423$	1.81524	−	1.81524i	0.0882599	−	0.0882599i
$424$	−23.3572	−	4.02513i	−1.13433	−	0.195478i
$425$	−22.4787	+	13.2117i	−1.09038	+	0.640864i
$426$	−3.63874	−	2.38650i	−0.176297	−	0.115626i
$427$	36.0525	+	36.0525i	1.74470	+	1.74470i
$428$	−5.66191	−	2.23239i	−0.273679	−	0.107907i
$429$			41.2610i			1.99210i
$430$	5.08758	+	4.35087i	0.245345	+	0.209818i
$431$			16.4900i			0.794295i	0.917755	+	0.397148i	$0.130000\pi$
$431$			16.4900i			0.794295i	−0.917755	+	0.397148i	$0.870000\pi$
$432$	21.7524	−	0.745567i	1.04656	−	0.0358711i
$433$	−2.04849	−	2.04849i	−0.0984443	−	0.0984443i	0.656169	−	0.754614i	$-0.272176\pi$
$433$	−2.04849	−	2.04849i	−0.0984443	−	0.0984443i	−0.754614	+	0.656169i	$0.772176\pi$
$434$	7.53456	−	11.4881i	0.361670	−	0.551445i
$435$	4.14435	−	3.20570i	0.198706	−	0.153701i
$436$	10.3559	+	23.8379i	0.495957	+	1.14163i
$437$	−0.671647	+	0.671647i	−0.0321292	+	0.0321292i
$438$	10.2422	−	2.12867i	0.489393	−	0.101712i
$439$	21.5207			1.02712			0.513562	−	0.858052i	$-0.328325\pi$
$439$	21.5207			1.02712			0.513562	+	0.858052i	$0.328325\pi$
$440$	−25.5282	+	13.5419i	−1.21701	+	0.645587i
$441$	−4.71911			−0.224719
$442$	39.9047	−	8.29347i	1.89807	−	0.394480i
$443$	−3.24964	+	3.24964i	−0.154395	+	0.154395i	−0.780078	−	0.625683i	$-0.784820\pi$
$443$	−3.24964	+	3.24964i	−0.154395	+	0.154395i	0.625683	+	0.780078i	$0.284820\pi$
$444$	−5.54809	−	12.7710i	−0.263301	−	0.606084i
$445$	−24.3234	−	3.10627i	−1.15304	−	0.147251i
$446$	6.69954	−	10.2149i	0.317233	−	0.483690i
$447$	−19.5716	−	19.5716i	−0.925705	−	0.925705i
$448$	−33.3384	+	15.8620i	−1.57509	+	0.749410i
$449$		−	37.4922i		−	1.76937i	−0.466193	−	0.884683i	$-0.654375\pi$
$449$		−	37.4922i		−	1.76937i	0.466193	−	0.884683i	$-0.345625\pi$
$450$	−0.114604	+	2.33107i	−0.00540249	+	0.109888i
$451$		−	16.0689i		−	0.756657i
$452$	12.0251	+	4.74130i	0.565614	+	0.223012i
$453$	−27.0956	−	27.0956i	−1.27306	−	1.27306i
$454$	−24.9163	−	16.3416i	−1.16938	−	0.766949i
$455$	−56.5711	−	7.22454i	−2.65210	−	0.338691i
$456$	−0.784875	+	4.55450i	−0.0367551	+	0.213284i
$457$	4.61218	−	4.61218i	0.215749	−	0.215749i	−0.590956	−	0.806704i	$-0.701249\pi$
$457$	4.61218	−	4.61218i	0.215749	−	0.215749i	0.806704	+	0.590956i	$0.201249\pi$
$458$	7.36985	+	35.4606i	0.344370	+	1.65696i
$459$	28.3751			1.32444
$460$	−3.72257	−	2.04618i	−0.173566	−	0.0954035i
$461$	15.1656			0.706330			0.353165	−	0.935561i	$-0.385105\pi$
$461$	15.1656			0.706330			0.353165	+	0.935561i	$0.385105\pi$
$462$	−9.91502	−	47.7069i	−0.461289	−	2.21952i
$463$	−23.1697	+	23.1697i	−1.07679	+	1.07679i	−0.0799921	+	0.996795i	$0.525490\pi$
$463$	−23.1697	+	23.1697i	−1.07679	+	1.07679i	−0.996795	+	0.0799921i	$0.974510\pi$
$464$	−4.19255	−	3.91468i	−0.194634	−	0.181734i
$465$	6.08361	−	4.70573i	0.282121	−	0.218223i
$466$	−17.2015	−	11.2817i	−0.796842	−	0.522616i
$467$	−20.1047	−	20.1047i	−0.930336	−	0.930336i	0.0673906	−	0.997727i	$-0.478533\pi$
$467$	−20.1047	−	20.1047i	−0.930336	−	0.930336i	−0.997727	+	0.0673906i	$0.978533\pi$
$468$	1.33818	−	3.39395i	0.0618572	−	0.156885i
$469$			8.46409i			0.390835i
$470$	−15.9855	+	18.6922i	−0.737354	+	0.862205i
$471$		−	32.9703i		−	1.51919i
$472$	−2.49183	+	1.75924i	−0.114696	+	0.0809758i
$473$	6.83946	+	6.83946i	0.314479	+	0.314479i
$474$	−2.63026	+	4.01040i	−0.120812	+	0.184204i
$475$	−4.83953	−	1.25658i	−0.222053	−	0.0576557i
$476$	−44.1458	+	19.1782i	−2.02342	+	0.879031i
$477$	−1.95574	+	1.95574i	−0.0895472	+	0.0895472i
$478$	4.42102	−	0.918829i	0.202213	−	0.0420263i
$479$	−10.8855			−0.497370			−0.248685	−	0.968584i	$-0.579998\pi$
$479$	−10.8855			−0.497370			−0.248685	+	0.968584i	$0.579998\pi$
$480$	−20.5387	+	2.31327i	−0.937460	+	0.105586i
$481$	−23.5474			−1.07367
$482$	16.2820	−	3.38391i	0.741623	−	0.154133i
$483$	5.06474	−	5.06474i	0.230454	−	0.230454i
$484$	−18.1178	+	7.87090i	−0.823537	+	0.357768i
$485$	3.33038	+	4.30554i	0.151225	+	0.195505i
$486$	2.64782	−	4.03718i	0.120108	−	0.183130i
$487$	21.7783	+	21.7783i	0.986867	+	0.986867i	0.999915	−	0.0130478i	$-0.00415338\pi$
$487$	21.7783	+	21.7783i	0.986867	+	0.986867i	−0.0130478	+	0.999915i	$0.504153\pi$
$488$	25.5276	−	18.0226i	1.15558	−	0.815845i
$489$		−	21.9027i		−	0.990473i
$490$	45.0760	−	3.51834i	2.03633	−	0.158942i
$491$		−	2.46368i		−	0.111185i	−0.998454	−	0.0555923i	$-0.982295\pi$
$491$		−	2.46368i		−	0.111185i	0.998454	−	0.0555923i	$-0.0177047\pi$
$492$	4.21567	−	10.6920i	0.190057	−	0.482032i
$493$	−5.28776	−	5.28776i	−0.238149	−	0.238149i
$494$	6.53553	+	4.28639i	0.294047	+	0.192854i
$495$	−0.427184	+	3.34503i	−0.0192005	+	0.150348i
$496$	−6.15437	−	5.74647i	−0.276339	−	0.258024i
$497$	6.14507	−	6.14507i	0.275644	−	0.275644i
$498$	−1.38876	−	6.68214i	−0.0622320	−	0.299434i
$499$	−23.3731			−1.04632			−0.523161	−	0.852234i	$-0.675247\pi$
$499$	−23.3731			−1.04632			−0.523161	+	0.852234i	$0.675247\pi$
$500$	−0.643257	−	22.3514i	−0.0287673	−	0.999586i
$501$	32.1941			1.43833
$502$	4.18790	+	20.1504i	0.186915	+	0.899357i
$503$	10.6038	−	10.6038i	0.472800	−	0.472800i	−0.430019	−	0.902820i	$-0.641493\pi$
$503$	10.6038	−	10.6038i	0.472800	−	0.472800i	0.902820	+	0.430019i	$0.141493\pi$
$504$	−0.731663	+	4.24572i	−0.0325908	+	0.189119i
$505$	−4.36208	+	34.1569i	−0.194110	+	1.51996i
$506$	−5.13230	−	3.36607i	−0.228159	−	0.149640i
$507$	20.2695	+	20.2695i	0.900201	+	0.900201i
$508$	17.0051	+	6.70482i	0.754479	+	0.297478i
$509$			17.1016i			0.758015i	0.925394	+	0.379007i	$0.123734\pi$
$509$			17.1016i			0.758015i	−0.925394	+	0.379007i	$0.876266\pi$
$510$	−26.8637	+	2.09680i	−1.18955	+	0.0928480i
$511$			20.8919i			0.924203i
$512$	6.11039	+	21.7868i	0.270044	+	0.962848i
$513$	3.84758	+	3.84758i	0.169875	+	0.169875i
$514$	12.6849	−	19.3409i	0.559508	−	0.853091i
$515$	−1.04107	−	1.34590i	−0.0458748	−	0.0593074i
$516$	2.75653	+	6.34518i	0.121349	+	0.279331i
$517$	−25.1287	+	25.1287i	−1.10516	+	1.10516i
$518$	27.2260	−	5.65843i	1.19624	−	0.248617i
$519$	2.95484			0.129703
$520$	−10.2516	+	33.4160i	−0.449564	+	1.46539i
$521$	−4.34873			−0.190521			−0.0952606	−	0.995452i	$-0.530368\pi$
$521$	−4.34873			−0.190521			−0.0952606	+	0.995452i	$0.530368\pi$
$522$	−0.655360	+	0.136205i	−0.0286843	+	0.00596153i
$523$	−27.4034	+	27.4034i	−1.19827	+	1.19827i	−0.223581	+	0.974685i	$0.571775\pi$
$523$	−27.4034	+	27.4034i	−1.19827	+	1.19827i	−0.974685	+	0.223581i	$0.928225\pi$
$524$	−8.98630	−	20.6853i	−0.392568	−	0.903642i
$525$	36.4938	+	9.47558i	1.59272	+	0.413548i
$526$	0.263692	−	0.402056i	0.0114975	−	0.0175305i
$527$	−7.76206	−	7.76206i	−0.338120	−	0.338120i
$528$	−29.8461	+	1.02298i	−1.29889	+	0.0445194i
$529$			22.0978i			0.960773i
$530$	17.2228	−	20.1390i	0.748109	−	0.874781i
$531$			0.355950i			0.0154469i
$532$	−8.58655	−	3.38553i	−0.372274	−	0.146781i
$533$	−13.7435	−	13.7435i	−0.595297	−	0.595297i
$534$	−21.1898	−	13.8975i	−0.916972	−	0.601405i
$535$	5.38224	−	4.16322i	0.232695	−	0.179992i
$536$	5.11216	+	0.880976i	0.220812	+	0.0380524i
$537$	4.60711	−	4.60711i	0.198811	−	0.198811i
$538$	1.50386	+	7.23591i	0.0648358	+	0.311962i
$539$	65.3276			2.81386
$540$	−11.7217	+	21.3250i	−0.504421	+	0.917684i
$541$	15.7990			0.679254			0.339627	−	0.940560i	$-0.389699\pi$
$541$	15.7990			0.679254			0.339627	+	0.940560i	$0.389699\pi$
$542$	−2.89040	−	13.9074i	−0.124153	−	0.597372i
$543$	22.3454	−	22.3454i	0.958931	−	0.958931i
$544$	6.98843	+	28.6594i	0.299626	+	1.22876i
$545$	−28.8239	−	3.68101i	−1.23468	−	0.157677i
$546$	−49.2830	−	32.3227i	−2.10912	−	1.38329i
$547$	15.7388	+	15.7388i	0.672943	+	0.672943i	0.958394	−	0.285450i	$-0.0921432\pi$
$547$	15.7388	+	15.7388i	0.672943	+	0.672943i	−0.285450	+	0.958394i	$0.592143\pi$
$548$	5.09599	−	12.9247i	0.217690	−	0.552116i
$549$		−	3.64653i		−	0.155630i
$550$	1.58649	−	32.2695i	0.0676482	−	1.37598i
$551$		−	1.43401i		−	0.0610909i
$552$	−2.53186	−	3.58618i	−0.107763	−	0.152638i
$553$	−6.77274	−	6.77274i	−0.288006	−	0.288006i
$554$	1.86356	−	2.84140i	0.0791749	−	0.120719i
$555$	15.4422	+	1.97207i	0.655483	+	0.0837098i
$556$	25.5575	−	11.1029i	1.08388	−	0.470868i
$557$	−17.9451	+	17.9451i	−0.760359	+	0.760359i	−0.976387	−	0.216029i	$-0.930690\pi$
$557$	−17.9451	+	17.9451i	−0.760359	+	0.760359i	0.216029	+	0.976387i	$0.430690\pi$
$558$	−0.962022	+	0.199939i	−0.0407256	+	0.00846410i
$559$	11.6993			0.494830
$560$	3.82330	−	41.0998i	0.161564	−	1.73678i
$561$	−38.9329			−1.64375
$562$	12.4192	−	2.58110i	0.523870	−	0.108877i
$563$	20.3784	−	20.3784i	0.858847	−	0.858847i	−0.132355	−	0.991202i	$-0.542254\pi$
$563$	20.3784	−	20.3784i	0.858847	−	0.858847i	0.991202	+	0.132355i	$0.0422540\pi$
$564$	−23.3127	+	10.1277i	−0.981641	+	0.426453i
$565$	−11.4311	+	8.84211i	−0.480912	+	0.371990i
$566$	−11.6546	+	17.7699i	−0.489879	+	0.746927i
$567$	−25.7826	−	25.7826i	−1.08277	−	1.08277i
$568$	−3.07191	−	4.35112i	−0.128895	−	0.182569i
$569$			15.5685i			0.652665i	0.945255	+	0.326333i	$0.105813\pi$
$569$			15.5685i			0.652665i	−0.945255	+	0.326333i	$0.894187\pi$
$570$	−3.92696	−	3.35832i	−0.164482	−	0.140665i
$571$			21.2800i			0.890540i	0.895396	+	0.445270i	$0.146892\pi$
$571$			21.2800i			0.890540i	−0.895396	+	0.445270i	$0.853108\pi$
$572$	−18.5246	+	46.9831i	−0.774554	+	1.96446i
$573$	1.63437	+	1.63437i	0.0682767	+	0.0682767i
$574$	19.1931	+	12.5880i	0.801104	+	0.525412i
$575$	4.09443	−	2.40648i	0.170750	−	0.100357i
$576$	2.48819	+	0.883823i	0.103674	+	0.0368259i
$577$	7.89632	−	7.89632i	0.328728	−	0.328728i	−0.523375	−	0.852103i	$-0.675327\pi$
$577$	7.89632	−	7.89632i	0.328728	−	0.328728i	0.852103	+	0.523375i	$0.175327\pi$
$578$	2.93345	+	14.1145i	0.122015	+	0.587086i
$579$	−18.2439			−0.758190
$580$	6.15833	−	1.78961i	0.255711	−	0.0743094i
$581$	13.6301			0.565471
$582$	1.14464	+	5.50754i	0.0474470	+	0.228295i
$583$	27.0737	−	27.0737i	1.12128	−	1.12128i
$584$	12.6183	+	2.17451i	0.522151	+	0.0899819i
$585$	2.49558	+	3.22631i	0.103180	+	0.133391i
$586$	−36.5899	−	23.9978i	−1.51151	−	0.991340i
$587$	20.8805	+	20.8805i	0.861831	+	0.861831i	0.991551	−	0.129720i	$-0.0414079\pi$
$587$	20.8805	+	20.8805i	0.861831	+	0.861831i	−0.129720	+	0.991551i	$0.541408\pi$
$588$	43.4678	+	17.1386i	1.79258	+	0.706785i
$589$		−	2.10503i		−	0.0867361i
$590$	−0.265379	−	3.39997i	−0.0109255	−	0.139974i
$591$			40.0938i			1.64924i
$592$	−0.583806	−	17.0330i	−0.0239943	−	0.700051i
$593$	4.40488	+	4.40488i	0.180887	+	0.180887i	0.791742	−	0.610855i	$-0.209174\pi$
$593$	4.40488	+	4.40488i	0.180887	+	0.180887i	−0.610855	+	0.791742i	$0.709174\pi$
$594$	−19.2828	+	29.4008i	−0.791182	+	1.20633i
$595$	6.81691	−	53.3792i	0.279466	−	2.18834i
$596$	−13.4989	−	31.0727i	−0.552936	−	1.27279i
$597$	−25.4258	+	25.4258i	−1.04061	+	1.04061i
$598$	−7.26851	+	1.51063i	−0.297232	+	0.0617743i
$599$	−22.4494			−0.917256			−0.458628	−	0.888628i	$-0.651659\pi$
$599$	−22.4494			−0.917256			−0.458628	+	0.888628i	$0.651659\pi$
$600$	9.52150	−	21.0554i	0.388714	−	0.859582i
$601$	−2.44752			−0.0998364			−0.0499182	−	0.998753i	$-0.515896\pi$
$601$	−2.44752			−0.0998364			−0.0499182	+	0.998753i	$0.515896\pi$
$602$	−13.5270	+	2.81135i	−0.551321	+	0.114582i
$603$	0.428050	−	0.428050i	0.0174316	−	0.0174316i
$604$	−18.6883	−	43.0181i	−0.760416	−	1.75038i
$605$	2.79772	−	21.9073i	0.113743	−	0.890659i
$606$	−19.5160	+	29.7564i	−0.792785	+	1.20877i
$607$	8.33475	+	8.33475i	0.338297	+	0.338297i	0.855726	−	0.517429i	$-0.173111\pi$
$607$	8.33475	+	8.33475i	0.338297	+	0.338297i	−0.517429	+	0.855726i	$0.673111\pi$
$608$	−2.93852	+	4.83374i	−0.119173	+	0.196034i
$609$			10.8136i			0.438188i
$610$	2.71868	+	34.8310i	0.110076	+	1.41027i
$611$			42.9843i			1.73896i
$612$	3.20245	+	1.26267i	0.129451	+	0.0510405i
$613$	−24.6735	−	24.6735i	−0.996555	−	0.996555i	0.00343930	−	0.999994i	$-0.498905\pi$
$613$	−24.6735	−	24.6735i	−0.996555	−	0.996555i	−0.999994	+	0.00343930i	$0.998905\pi$
$614$	27.6053	+	18.1052i	1.11406	+	0.730665i
$615$	7.86186	+	10.1639i	0.317021	+	0.409847i
$616$	10.1286	−	58.7744i	0.408091	−	2.36809i
$617$	−2.72052	+	2.72052i	−0.109524	+	0.109524i	−0.759745	−	0.650221i	$-0.774676\pi$
$617$	−2.72052	+	2.72052i	−0.109524	+	0.109524i	0.650221	+	0.759745i	$0.274676\pi$
$618$	−0.357812	−	1.72164i	−0.0143933	−	0.0692544i
$619$	21.6528			0.870300			0.435150	−	0.900358i	$-0.356695\pi$
$619$	21.6528			0.870300			0.435150	+	0.900358i	$0.356695\pi$
$620$	9.03999	−	2.62702i	0.363055	−	0.105504i
$621$	−5.16843			−0.207402
$622$	−5.59441	−	26.9179i	−0.224316	−	1.07931i
$623$	35.7852	−	35.7852i	1.43370	−	1.43370i
$624$	−24.6519	+	26.4018i	−0.986867	+	1.05692i
$625$	21.8420	+	12.1625i	0.873681	+	0.486499i
$626$	14.4411	+	9.47134i	0.577183	+	0.378551i
$627$	−5.27920	−	5.27920i	−0.210831	−	0.210831i
$628$	14.8024	−	37.5426i	0.590681	−	1.49811i
$629$		−	22.2188i		−	0.885920i
$630$	−3.66073	−	3.13064i	−0.145847	−	0.124728i
$631$			31.3301i			1.24723i	0.781731	+	0.623616i	$0.214337\pi$
$631$			31.3301i			1.24723i	−0.781731	+	0.623616i	$0.785663\pi$
$632$	−4.79555	+	3.38568i	−0.190757	+	0.134675i
$633$	−15.3232	−	15.3232i	−0.609041	−	0.609041i
$634$	−14.9191	+	22.7475i	−0.592515	+	0.903417i
$635$	−16.1652	+	12.5039i	−0.641494	+	0.496202i
$636$	25.1171	−	10.9116i	0.995959	−	0.432673i
$637$	55.8736	−	55.8736i	2.21379	−	2.21379i
$638$	9.07229	−	1.88551i	0.359175	−	0.0746482i
$639$	−0.621543			−0.0245879
$640$	−24.4256	−	6.58704i	−0.965507	−	0.260376i
$641$	−38.8191			−1.53326			−0.766631	−	0.642088i	$-0.778068\pi$
$641$	−38.8191			−1.53326			−0.766631	+	0.642088i	$0.778068\pi$
$642$	6.88483	−	1.43089i	0.271722	−	0.0564727i
$643$	−30.5752	+	30.5752i	−1.20577	+	1.20577i	−0.233384	+	0.972385i	$0.574980\pi$
$643$	−30.5752	+	30.5752i	−1.20577	+	1.20577i	−0.972385	+	0.233384i	$0.925020\pi$
$644$	8.04101	−	3.49325i	0.316860	−	0.137653i
$645$	−7.67233	−	0.979811i	−0.302098	−	0.0385800i
$646$	−4.04454	+	6.16678i	−0.159130	+	0.242629i
$647$	−21.3825	−	21.3825i	−0.840632	−	0.840632i	0.148309	−	0.988941i	$-0.452617\pi$
$647$	−21.3825	−	21.3825i	−0.840632	−	0.840632i	−0.988941	+	0.148309i	$0.952617\pi$
$648$	−18.2558	+	12.8887i	−0.717154	+	0.506314i
$649$		−	4.92749i		−	0.193421i
$650$	−26.2427	−	28.9565i	−1.02932	−	1.13577i
$651$			15.8735i			0.622133i
$652$	9.83348	−	24.9402i	0.385109	−	0.976732i
$653$	9.46388	+	9.46388i	0.370350	+	0.370350i	0.867605	−	0.497255i	$-0.165658\pi$
$653$	9.46388	+	9.46388i	0.370350	+	0.370350i	−0.497255	+	0.867605i	$0.665658\pi$
$654$	−25.1105	−	16.4689i	−0.981897	−	0.643986i
$655$	25.0118	+	3.19419i	0.977293	+	0.124807i
$656$	9.60061	−	10.2821i	0.374841	−	0.401448i
$657$	1.05656	−	1.05656i	0.0412202	−	0.0412202i
$658$	−10.3291	−	49.6994i	−0.402672	−	1.93749i
$659$	−14.8386			−0.578029			−0.289014	−	0.957325i	$-0.593328\pi$
$659$	−14.8386			−0.578029			−0.289014	+	0.957325i	$0.593328\pi$
$660$	16.0831	−	29.2597i	0.626034	−	1.13893i
$661$	31.5760			1.22817			0.614083	−	0.789242i	$-0.289526\pi$
$661$	31.5760			1.22817			0.614083	+	0.789242i	$0.289526\pi$
$662$	6.23434	+	29.9970i	0.242305	+	1.16587i
$663$	−33.2987	+	33.2987i	−1.29321	+	1.29321i
$664$	1.41867	−	8.23233i	0.0550552	−	0.319476i
$665$	8.16243	−	6.31372i	0.316525	−	0.244836i
$666$	−1.66305	−	1.09073i	−0.0644418	−	0.0422647i
$667$	0.963149	+	0.963149i	0.0372933	+	0.0372933i
$668$	36.6588	+	14.4539i	1.41837	+	0.559240i
$669$			14.1144i			0.545693i
$670$	−3.76952	+	4.40779i	−0.145629	+	0.170288i
$671$			50.4797i			1.94875i
$672$	22.1588	−	36.4502i	0.854793	−	1.40610i
$673$	18.0004	+	18.0004i	0.693866	+	0.693866i	0.963080	−	0.269215i	$-0.0867641\pi$
$673$	18.0004	+	18.0004i	0.693866	+	0.693866i	−0.269215	+	0.963080i	$0.586764\pi$
$674$	−0.185648	+	0.283061i	−0.00715091	+	0.0109031i
$675$	−13.7857	−	23.4553i	−0.530611	−	0.902793i
$676$	13.9803	+	32.1808i	0.537702	+	1.23772i
$677$	20.3423	−	20.3423i	0.781819	−	0.781819i	−0.198319	−	0.980138i	$-0.563548\pi$
$677$	20.3423	−	20.3423i	0.781819	−	0.781819i	0.980138	+	0.198319i	$0.0635481\pi$
$678$	−14.6224	+	3.03901i	−0.561571	+	0.116712i
$679$	−11.2342			−0.431127
$680$	−31.5306	−	9.67322i	−1.20914	−	0.370951i
$681$	34.4279			1.31928
$682$	13.3175	−	2.76780i	0.509952	−	0.105984i
$683$	−31.7484	+	31.7484i	−1.21482	+	1.21482i	−0.245396	+	0.969423i	$0.578918\pi$
$683$	−31.7484	+	31.7484i	−1.21482	+	1.21482i	−0.969423	+	0.245396i	$0.921082\pi$
$684$	0.263028	+	0.605458i	0.0100571	+	0.0231503i
$685$	9.50359	+	12.2863i	0.363113	+	0.469436i
$686$	−26.1206	+	39.8266i	−0.997290	+	1.52059i
$687$	−29.5903	−	29.5903i	−1.12894	−	1.12894i
$688$	0.290060	+	8.46272i	0.0110584	+	0.322638i
$689$		−	46.3114i		−	1.76432i
$690$	4.89314	−	0.381926i	0.186279	−	0.0145397i
$691$		−	2.26449i		−	0.0861453i	−0.999072	−	0.0430727i	$-0.986285\pi$
$691$		−	2.26449i		−	0.0861453i	0.999072	−	0.0430727i	$-0.0137147\pi$
$692$	3.36463	+	1.32661i	0.127904	+	0.0504303i
$693$	−4.92128	−	4.92128i	−0.186944	−	0.186944i
$694$	37.3056	+	24.4672i	1.41610	+	0.928763i
$695$	−3.94654	+	30.9031i	−0.149701	+	1.17222i
$696$	6.53120	+	1.12552i	0.247565	+	0.0426627i
$697$	12.9680	−	12.9680i	0.491200	−	0.491200i
$698$	5.51225	+	26.5226i	0.208642	+	1.00390i
$699$	23.7680			0.898987
$700$	37.3006	+	27.1740i	1.40983	+	1.02708i
$701$	1.89491			0.0715697			0.0357849	−	0.999360i	$-0.488607\pi$
$701$	1.89491			0.0715697			0.0357849	+	0.999360i	$0.488607\pi$
$702$	8.65376	+	41.6382i	0.326615	+	1.57153i
$703$	3.01280	−	3.01280i	0.113630	−	0.113630i
$704$	−34.4445	−	12.2349i	−1.29818	−	0.461122i
$705$	3.59990	−	28.1887i	0.135580	−	1.06165i
$706$	−1.15858	−	0.759863i	−0.0436036	−	0.0285978i
$707$	−50.2525	−	50.2525i	−1.88994	−	1.88994i
$708$	1.29272	−	3.27866i	0.0485834	−	0.123220i
$709$		−	6.93479i		−	0.260442i	−0.991485	−	0.130221i	$-0.958431\pi$
$709$		−	6.93479i		−	0.260442i	0.991485	−	0.130221i	$-0.0415686\pi$
$710$	5.93686	−	0.463392i	0.222806	−	0.0173908i
$711$			0.685029i			0.0256906i
$712$	−17.8889	−	25.3383i	−0.670417	−	0.949592i
$713$	1.41383	+	1.41383i	0.0529485	+	0.0529485i
$714$	30.4990	−	46.5024i	1.14140	−	1.74031i
$715$	−34.5469	−	44.6624i	−1.29198	−	1.67028i
$716$	7.31444	−	3.17761i	0.273354	−	0.118753i
$717$	−3.68914	+	3.68914i	−0.137773	+	0.137773i
$718$	18.0676	−	3.75502i	0.674276	−	0.140136i
$719$	37.3420			1.39262			0.696311	−	0.717740i	$-0.254823\pi$
$719$	37.3420			1.39262			0.696311	+	0.717740i	$0.254823\pi$
$720$	−2.27187	+	1.88517i	−0.0846678	+	0.0702560i
$721$	3.51176			0.130785
$722$	−1.38463	+	0.287770i	−0.0515304	+	0.0107097i
$723$	−13.5866	+	13.5866i	−0.505290	+	0.505290i
$724$	35.4765	−	15.4120i	1.31847	−	0.572783i
$725$	−1.80194	+	6.93993i	−0.0669226	+	0.257743i
$726$	12.5171	−	19.0850i	0.464552	−	0.708310i
$727$	−17.4875	−	17.4875i	−0.648575	−	0.648575i	0.304074	−	0.952649i	$-0.401653\pi$
$727$	−17.4875	−	17.4875i	−0.648575	−	0.648575i	−0.952649	+	0.304074i	$0.901653\pi$
$728$	−41.6060	−	58.9315i	−1.54202	−	2.18415i
$729$			29.2810i			1.08448i
$730$	−9.30431	+	10.8797i	−0.344368	+	0.402677i
$731$			11.0392i			0.408301i
$732$	−13.2433	+	33.5883i	−0.489486	+	1.24146i
$733$	−0.838043	−	0.838043i	−0.0309538	−	0.0309538i	0.691460	−	0.722414i	$-0.256968\pi$
$733$	−0.838043	−	0.838043i	−0.0309538	−	0.0309538i	−0.722414	+	0.691460i	$0.756968\pi$
$734$	−21.3123	−	13.9778i	−0.786650	−	0.515932i
$735$	−41.3208	+	31.9621i	−1.52414	+	1.17894i
$736$	−1.27292	−	5.22022i	−0.0469205	−	0.192420i
$737$	−5.92559	+	5.92559i	−0.218272	+	0.218272i
$738$	−0.334038	−	1.60725i	−0.0122961	−	0.0591636i
$739$	2.99968			0.110345			0.0551725	−	0.998477i	$-0.482429\pi$
$739$	2.99968			0.110345			0.0551725	+	0.998477i	$0.482429\pi$
$740$	16.6983	+	9.17851i	0.613842	+	0.337409i
$741$	−9.03041			−0.331740
$742$	11.1286	+	53.5462i	0.408545	+	1.96574i
$743$	29.6466	−	29.6466i	1.08763	−	1.08763i	0.0918551	−	0.995772i	$-0.470720\pi$
$743$	29.6466	−	29.6466i	1.08763	−	1.08763i	0.995772	−	0.0918551i	$-0.0292796\pi$
$744$	9.58734	+	1.65218i	0.351489	+	0.0605719i
$745$	37.5719	+	4.79820i	1.37653	+	0.175792i
$746$	−26.2062	−	17.1876i	−0.959477	−	0.629282i
$747$	−0.689307	−	0.689307i	−0.0252204	−	0.0252204i
$748$	−44.3322	−	17.4794i	−1.62095	−	0.639111i
$749$			14.0435i			0.513139i
$750$	14.7847	+	21.1872i	0.539859	+	0.773648i
$751$			17.4677i			0.637406i	0.947855	+	0.318703i	$0.103247\pi$
$751$			17.4677i			0.637406i	−0.947855	+	0.318703i	$0.896753\pi$
$752$	−31.0927	+	1.06570i	−1.13383	+	0.0388622i
$753$	−16.8146	−	16.8146i	−0.612759	−	0.612759i
$754$	6.14673	−	9.37202i	0.223851	−	0.341309i
$755$	52.0157	+	6.64278i	1.89305	+	0.241755i
$756$	−20.0113	−	46.0635i	−0.727805	−	1.67532i
$757$	8.92826	−	8.92826i	0.324503	−	0.324503i	−0.525988	−	0.850492i	$-0.676305\pi$
$757$	8.92826	−	8.92826i	0.324503	−	0.324503i	0.850492	+	0.525988i	$0.176305\pi$
$758$	−5.82847	+	1.21134i	−0.211699	+	0.0439979i
$759$	7.09151			0.257406
$760$	−2.96380	−	5.58712i	−0.107508	−	0.202666i
$761$	21.6485			0.784756			0.392378	−	0.919804i	$-0.371653\pi$
$761$	21.6485			0.784756			0.392378	+	0.919804i	$0.371653\pi$
$762$	−20.6780	+	4.29756i	−0.749086	+	0.155684i
$763$	42.4064	−	42.4064i	1.53521	−	1.53521i
$764$	1.12725	+	2.59479i	0.0407826	+	0.0938763i
$765$	−3.04427	+	2.35477i	−0.110066	+	0.0851370i
$766$	25.6570	−	39.1197i	0.927025	−	1.41345i
$767$	−4.21440	−	4.21440i	−0.152173	−	0.152173i
$768$	−19.7089	−	17.1774i	−0.711184	−	0.619835i
$769$			28.9274i			1.04315i	0.853206	+	0.521574i	$0.174655\pi$
$769$			28.9274i			1.04315i	−0.853206	+	0.521574i	$0.825345\pi$
$770$	50.6762	+	43.3381i	1.82624	+	1.56180i
$771$			26.7241i			0.962446i
$772$	−20.7740	−	8.19082i	−0.747672	−	0.294794i
$773$	−21.1402	−	21.1402i	−0.760359	−	0.760359i	0.216028	−	0.976387i	$-0.430690\pi$
$773$	−21.1402	−	21.1402i	−0.760359	−	0.760359i	−0.976387	+	0.216028i	$0.930690\pi$
$774$	0.826274	+	0.541919i	0.0296998	+	0.0194789i
$775$	−2.64513	+	10.1873i	−0.0950158	+	0.365939i
$776$	−1.16930	+	6.78523i	−0.0419752	+	0.243576i
$777$	−22.7189	+	22.7189i	−0.815035	+	0.815035i
$778$	−3.65857	−	17.6035i	−0.131166	−	0.631116i
$779$	3.51686			0.126005
$780$	−11.2697	−	38.7809i	−0.403521	−	1.38858i
$781$	8.60415			0.307881
$782$	−1.42540	−	6.85840i	−0.0509721	−	0.245256i
$783$	5.51747	−	5.51747i	0.197178	−	0.197178i
$784$	41.8014	+	39.0309i	1.49291	+	1.39396i
$785$	27.6052	+	35.6883i	0.985273	+	1.27377i
$786$	21.7895	+	14.2909i	0.777207	+	0.509738i
$787$	26.2023	+	26.2023i	0.934011	+	0.934011i	0.997954	−	0.0639423i	$-0.0203674\pi$
$787$	26.2023	+	26.2023i	0.934011	+	0.934011i	−0.0639423	+	0.997954i	$0.520367\pi$
$788$	−18.0006	+	45.6541i	−0.641245	+	1.62636i
$789$			0.555537i			0.0197776i
$790$	−0.510724	−	6.54326i	−0.0181707	−	0.232799i
$791$		−	29.8265i		−	1.06051i
$792$	−3.48459	+	2.46014i	−0.123820	+	0.0874173i
$793$	43.1744	+	43.1744i	1.53317	+	1.53317i
$794$	−28.4785	+	43.4217i	−1.01067	+	1.54098i
$795$	−3.87854	+	30.3706i	−0.137558	+	1.07713i
$796$	−40.3672	+	17.5367i	−1.43078	+	0.621571i
$797$	27.6055	−	27.6055i	0.977839	−	0.977839i	−0.0219210	−	0.999760i	$-0.506978\pi$
$797$	27.6055	−	27.6055i	0.977839	−	0.977839i	0.999760	+	0.0219210i	$0.00697824\pi$
$798$	10.4412	−	2.17001i	0.369613	−	0.0768175i
$799$	−40.5590			−1.43488
$800$	20.2950	−	19.7006i	0.717538	−	0.696520i
$801$	−3.61949			−0.127888
$802$	−15.5867	+	3.23941i	−0.550384	+	0.114388i
$803$	−14.6261	+	14.6261i	−0.516145	+	0.516145i
$804$	−5.49735	+	2.38821i	−0.193877	+	0.0842257i
$805$	−1.24168	+	9.72286i	−0.0437634	+	0.342686i
$806$	9.02296	−	13.7575i	0.317820	−	0.484586i
$807$	−6.03805	−	6.03805i	−0.212549	−	0.212549i
$808$	−35.5821	+	25.1211i	−1.25177	+	0.883758i
$809$			14.9939i			0.527158i	0.964638	+	0.263579i	$0.0849030\pi$
$809$			14.9939i			0.527158i	−0.964638	+	0.263579i	$0.915097\pi$
$810$	−1.94423	−	24.9090i	−0.0683133	−	0.875213i
$811$			32.4492i			1.13945i	0.821837	+	0.569723i	$0.192950\pi$
$811$			32.4492i			1.13945i	−0.821837	+	0.569723i	$0.807050\pi$
$812$	−4.85488	+	12.3132i	−0.170373	+	0.432109i
$813$	11.6051	+	11.6051i	0.407008	+	0.407008i
$814$	23.0219	+	15.0991i	0.806918	+	0.529224i
$815$	18.3386	+	23.7083i	0.642373	+	0.830465i
$816$	−24.9121	−	23.2610i	−0.872100	−	0.814298i
$817$	−1.49689	+	1.49689i	−0.0523695	+	0.0523695i
$818$	9.02081	+	43.4043i	0.315405	+	1.51760i
$819$	−8.41818			−0.294155
$820$	4.38895	+	15.1031i	0.153269	+	0.527423i
$821$	0.233561			0.00815135			0.00407567	−	0.999992i	$-0.498703\pi$
$821$	0.233561			0.00815135			0.00407567	+	0.999992i	$0.498703\pi$
$822$	3.26636	+	15.7163i	0.113927	+	0.548170i
$823$	2.78654	−	2.78654i	0.0971327	−	0.0971327i	−0.656871	−	0.754003i	$-0.728120\pi$
$823$	2.78654	−	2.78654i	0.0971327	−	0.0971327i	0.754003	+	0.656871i	$0.228120\pi$
$824$	0.365518	−	2.12104i	0.0127334	−	0.0738900i
$825$	18.9151	+	32.1825i	0.658539	+	1.12045i
$826$	5.88550	+	3.86006i	0.204783	+	0.134309i
$827$	5.93917	+	5.93917i	0.206525	+	0.206525i	0.802789	−	0.596264i	$-0.203349\pi$
$827$	5.93917	+	5.93917i	0.206525	+	0.206525i	−0.596264	+	0.802789i	$0.703349\pi$
$828$	−0.583316	−	0.229992i	−0.0202716	−	0.00799276i
$829$		−	35.4726i		−	1.23201i	−0.787741	−	0.616007i	$-0.788749\pi$
$829$		−	35.4726i		−	1.23201i	0.787741	−	0.616007i	$-0.211251\pi$
$830$	7.09805	+	6.07022i	0.246377	+	0.210700i
$831$			3.92607i			0.136194i
$832$	−39.9241	+	18.9954i	−1.38412	+	0.658548i
$833$	52.7211	+	52.7211i	1.82668	+	1.82668i
$834$	−17.6569	+	26.9218i	−0.611409	+	0.932226i
$835$	−34.8481	+	26.9554i	−1.20597	+	0.932828i
$836$	−3.64116	−	8.38148i	−0.125932	−	0.289880i
$837$	8.09926	−	8.09926i	0.279951	−	0.279951i
$838$	−20.3116	+	4.22141i	−0.701654	+	0.145826i
$839$	−15.2189			−0.525415			−0.262707	−	0.964876i	$-0.584615\pi$
$839$	−15.2189			−0.525415			−0.262707	+	0.964876i	$0.584615\pi$
$840$	22.3494	+	42.1313i	0.771126	+	1.45367i
$841$	26.9436			0.929090
$842$	3.63143	−	0.754728i	0.125147	−	0.0260096i
$843$	−10.3632	+	10.3632i	−0.356929	+	0.356929i
$844$	−10.5687	−	24.3277i	−0.363789	−	0.837395i
$845$	−38.9117	−	4.96930i	−1.33860	−	0.170949i
$846$	−1.99105	+	3.03579i	−0.0684539	+	0.104373i
$847$	32.2306	+	32.2306i	1.10746	+	1.10746i
$848$	33.4993	−	1.14819i	1.15037	−	0.0394291i
$849$		−	24.5535i		−	0.842673i
$850$	27.3227	−	24.7620i	0.937161	−	0.849330i
$851$			4.04708i			0.138732i
$852$	5.72505	+	2.25729i	0.196137	+	0.0773335i
$853$	−33.9767	−	33.9767i	−1.16334	−	1.16334i	−0.983740	−	0.179600i	$-0.942520\pi$
$853$	−33.9767	−	33.9767i	−1.16334	−	1.16334i	−0.179600	−	0.983740i	$-0.557480\pi$
$854$	−60.2941	−	39.5444i	−2.06322	−	1.35318i
$855$	−0.732095	−	0.0934937i	−0.0250371	−	0.00319742i
$856$	8.48204	+	1.46170i	0.289910	+	0.0499600i
$857$	−11.0752	+	11.0752i	−0.378320	+	0.378320i	−0.870496	−	0.492176i	$-0.836202\pi$
$857$	−11.0752	+	11.0752i	−0.378320	+	0.378320i	0.492176	+	0.870496i	$0.336202\pi$
$858$	−11.8737	−	57.1310i	−0.405360	−	1.95042i
$859$	−24.2535			−0.827518			−0.413759	−	0.910386i	$-0.635784\pi$
$859$	−24.2535			−0.827518			−0.413759	+	0.910386i	$0.635784\pi$
$860$	−8.29644	−	4.56028i	−0.282906	−	0.155504i
$861$	−26.5199			−0.903795
$862$	−4.74532	−	22.8325i	−0.161626	−	0.777677i
$863$	14.6557	−	14.6557i	0.498886	−	0.498886i	−0.412205	−	0.911091i	$-0.635241\pi$
$863$	14.6557	−	14.6557i	0.498886	−	0.498886i	0.911091	+	0.412205i	$0.135241\pi$
$864$	−29.9044	+	7.29202i	−1.01737	+	0.248080i
$865$	−3.19843	+	2.47402i	−0.108750	+	0.0841192i
$866$	3.42589	+	2.24690i	0.116416	+	0.0763528i
$867$	−11.7779	−	11.7779i	−0.400000	−	0.400000i
$868$	−7.12663	+	18.0749i	−0.241893	+	0.613502i
$869$		−	9.48300i		−	0.321689i
$870$	−4.81587	+	5.63131i	−0.163273	+	0.190919i
$871$			10.1361i			0.343449i
$872$	−21.1989	−	30.0265i	−0.717884	−	1.01683i
$873$	0.568139	+	0.568139i	0.0192286	+	0.0192286i
$874$	0.736700	−	1.12326i	0.0249193	−	0.0379948i
$875$	−47.4360	+	20.2987i	−1.60363	+	0.686221i
$876$	−13.5691	+	5.89481i	−0.458458	+	0.199167i
$877$	−10.9822	+	10.9822i	−0.370843	+	0.370843i	−0.867784	−	0.496941i	$-0.834457\pi$
$877$	−10.9822	+	10.9822i	−0.370843	+	0.370843i	0.496941	+	0.867784i	$0.334457\pi$
$878$	−29.7981	+	6.19299i	−1.00564	+	0.209003i
$879$	50.5577			1.70527
$880$	31.4500	−	26.0968i	1.06018	−	0.879721i
$881$	−40.1533			−1.35280			−0.676400	−	0.736535i	$-0.736461\pi$
$881$	−40.1533			−1.35280			−0.676400	+	0.736535i	$0.736461\pi$
$882$	6.53420	−	1.35802i	0.220018	−	0.0457268i
$883$	15.2673	−	15.2673i	0.513786	−	0.513786i	−0.401898	−	0.915684i	$-0.631649\pi$
$883$	15.2673	−	15.2673i	0.513786	−	0.513786i	0.915684	+	0.401898i	$0.131649\pi$
$884$	−52.8664	+	22.9667i	−1.77809	+	0.772454i
$885$	2.41081	+	3.11672i	0.0810386	+	0.104767i
$886$	3.56438	−	5.43468i	0.119748	−	0.182582i
$887$	−1.75836	−	1.75836i	−0.0590401	−	0.0590401i	0.676970	−	0.736010i	$-0.263293\pi$
$887$	−1.75836	−	1.75836i	−0.0590401	−	0.0590401i	−0.736010	+	0.676970i	$0.763293\pi$
$888$	11.3571	+	16.0865i	0.381120	+	0.539827i
$889$		−	42.1786i		−	1.41463i
$890$	34.5727	−	2.69851i	1.15888	−	0.0904544i
$891$		−	36.1000i		−	1.20940i
$892$	−6.33682	+	16.0717i	−0.212172	+	0.538122i
$893$	−5.49969	−	5.49969i	−0.184040	−	0.184040i
$894$	32.7315	+	21.4672i	1.09470	+	0.717972i
$895$	−1.12948	+	8.84433i	−0.0377545	+	0.295633i
$896$	41.5965	−	31.5567i	1.38964	−	1.05424i
$897$	6.06525	−	6.06525i	0.202513	−	0.202513i
$898$	10.7891	+	51.9127i	0.360038	+	1.73235i
$899$	−3.01863			−0.100677
$900$	−0.512129	−	3.26065i	−0.0170710	−	0.108688i
$901$	43.6984			1.45580
$902$	4.62415	+	22.2495i	0.153968	+	0.740826i
$903$	11.2877	−	11.2877i	0.375632	−	0.375632i
$904$	−18.0147	−	3.10446i	−0.599160	−	0.103253i
$905$	−5.47821	+	42.8967i	−0.182102	+	1.42593i
$906$	45.3145	+	29.7199i	1.50547	+	0.987379i
$907$	4.12392	+	4.12392i	0.136933	+	0.136933i	0.772251	−	0.635318i	$-0.219131\pi$
$907$	4.12392	+	4.12392i	0.136933	+	0.136933i	−0.635318	+	0.772251i	$0.719131\pi$
$908$	39.2024	+	15.4568i	1.30098	+	0.512953i
$909$			5.08279i			0.168585i
$910$	80.4089	−	6.27618i	2.66553	−	0.208053i
$911$		−	15.3291i		−	0.507875i	−0.967221	−	0.253938i	$-0.918274\pi$
$911$		−	15.3291i		−	0.507875i	0.967221	−	0.253938i	$-0.0817258\pi$
$912$	−0.223890	−	6.53214i	−0.00741373	−	0.216301i
$913$	9.54223	+	9.54223i	0.315802	+	0.315802i
$914$	−5.05890	+	7.71339i	−0.167333	+	0.255136i
$915$	−24.6976	−	31.9293i	−0.816477	−	1.05555i
$916$	−20.4090	−	46.9788i	−0.674331	−	1.55222i
$917$	−36.7980	+	36.7980i	−1.21518	+	1.21518i
$918$	−39.2889	+	8.16549i	−1.29673	+	0.269501i
$919$	−14.4491			−0.476633			−0.238317	−	0.971187i	$-0.576596\pi$
$919$	−14.4491			−0.476633			−0.238317	+	0.971187i	$0.576596\pi$
$920$	5.74320	+	1.76195i	0.189348	+	0.0580896i
$921$	−38.1433			−1.25686
$922$	−20.9986	+	4.36419i	−0.691552	+	0.143727i
$923$	7.35898	−	7.35898i	0.242224	−	0.242224i
$924$	27.4572	+	63.2029i	0.903275	+	2.07922i
$925$	−18.3663	+	10.7947i	−0.603882	+	0.354928i
$926$	25.4138	−	38.7489i	0.835150	−	1.27337i
$927$	−0.177598	−	0.177598i	−0.00583310	−	0.00583310i
$928$	6.93164	+	4.21387i	0.227542	+	0.138327i
$929$			1.92626i			0.0631987i	0.999501	+	0.0315993i	$0.0100601\pi$
$929$			1.92626i			0.0631987i	−0.999501	+	0.0315993i	$0.989940\pi$
$930$	−7.06935	+	8.26636i	−0.231813	+	0.271065i
$931$			14.2977i			0.468587i
$932$	27.0641	+	10.6709i	0.886515	+	0.349538i
$933$	22.4618	+	22.4618i	0.735367	+	0.735367i
$934$	33.6231	+	22.0520i	1.10018	+	0.721563i
$935$	42.1425	−	32.5976i	1.37821	−	1.06606i
$936$	−0.876197	+	5.08443i	−0.0286394	+	0.166190i
$937$	12.4587	−	12.4587i	0.407006	−	0.407006i	−0.473687	−	0.880693i	$-0.657077\pi$
$937$	12.4587	−	12.4587i	0.407006	−	0.407006i	0.880693	+	0.473687i	$0.157077\pi$
$938$	−2.43571	−	11.7196i	−0.0795287	−	0.382658i
$939$	−19.9539			−0.651170
$940$	16.7548	−	30.4818i	0.546482	−	0.994206i
$941$	−13.8082			−0.450135			−0.225068	−	0.974343i	$-0.572260\pi$
$941$	−13.8082			−0.450135			−0.225068	+	0.974343i	$0.572260\pi$
$942$	9.48785	+	45.6515i	0.309131	+	1.48741i
$943$	−2.36209	+	2.36209i	−0.0769202	+	0.0769202i
$944$	2.94399	−	3.15297i	0.0958188	−	0.102620i
$945$	55.6982	+	7.11305i	1.81186	+	0.231388i
$946$	−11.4383	−	7.50190i	−0.371891	−	0.243908i
$947$	18.9464	+	18.9464i	0.615675	+	0.615675i	0.944419	−	0.328744i	$-0.106625\pi$
$947$	18.9464	+	18.9464i	0.615675	+	0.615675i	−0.328744	+	0.944419i	$0.606625\pi$
$948$	2.48785	−	6.30982i	0.0808017	−	0.204933i
$949$			25.0189i			0.812149i
$950$	7.06254	+	0.347220i	0.229139	+	0.0112653i
$951$		−	31.4311i		−	1.01922i
$952$	55.6064	−	39.2584i	1.80222	−	1.27237i
$953$	−26.3798	−	26.3798i	−0.854526	−	0.854526i	0.136161	−	0.990687i	$-0.456524\pi$
$953$	−26.3798	−	26.3798i	−0.854526	−	0.854526i	−0.990687	+	0.136161i	$0.956524\pi$
$954$	2.14517	−	3.27077i	0.0694523	−	0.105895i
$955$	−3.13752	−	0.400683i	−0.101528	−	0.0129658i
$956$	−5.85704	+	2.54447i	−0.189430	+	0.0822940i
$957$	−7.57042	+	7.57042i	−0.244717	+	0.244717i
$958$	15.0723	−	3.13251i	0.486964	−	0.101207i
$959$	−32.0578			−1.03520
$960$	27.7727	−	9.11343i	0.896362	−	0.294135i
$961$	26.5689			0.857060
$962$	32.6043	−	6.77622i	1.05120	−	0.218474i
$963$	0.710216	−	0.710216i	0.0228864	−	0.0228864i
$964$	−21.5706	+	9.37091i	−0.694743	+	0.301817i
$965$	19.7479	−	15.2752i	0.635706	−	0.491725i
$966$	−5.55530	+	8.47026i	−0.178739	+	0.272526i
$967$	−15.0189	−	15.0189i	−0.482974	−	0.482974i	0.423106	−	0.906080i	$-0.360940\pi$
$967$	−15.0189	−	15.0189i	−0.482974	−	0.482974i	−0.906080	+	0.423106i	$0.860940\pi$
$968$	22.8214	−	16.1120i	0.733507	−	0.517860i
$969$		−	8.52089i		−	0.273730i
$970$	−5.85034	−	5.00318i	−0.187843	−	0.160643i
$971$		−	32.2254i		−	1.03416i	−0.855937	−	0.517081i	$-0.827019\pi$
$971$		−	32.2254i		−	1.03416i	0.855937	−	0.517081i	$-0.172981\pi$
$972$	−2.50446	+	6.35194i	−0.0803307	+	0.203739i
$973$	−45.4653	−	45.4653i	−1.45755	−	1.45755i
$974$	−36.4219	−	23.8876i	−1.16703	−	0.765409i
$975$	43.7029	+	11.3474i	1.39961	+	0.363408i
$976$	−30.1598	+	32.3006i	−0.965391	+	1.03392i
$977$	−31.7593	+	31.7593i	−1.01607	+	1.01607i	−0.0162011	+	0.999869i	$0.505157\pi$
$977$	−31.7593	+	31.7593i	−1.01607	+	1.01607i	−0.999869	+	0.0162011i	$0.994843\pi$
$978$	6.30293	+	30.3270i	0.201545	+	0.969751i
$979$	50.1054			1.60137
$980$	−61.4010	+	17.8431i	−1.96138	+	0.569977i
$981$	−4.28919			−0.136943
$982$	0.708974	+	3.41128i	0.0226243	+	0.108858i
$983$	15.5304	−	15.5304i	0.495343	−	0.495343i	−0.414641	−	0.909985i	$-0.636093\pi$
$983$	15.5304	−	15.5304i	0.495343	−	0.495343i	0.909985	+	0.414641i	$0.136093\pi$
$984$	−2.76029	+	16.0175i	−0.0879950	+	0.510621i
$985$	−33.5696	−	43.3990i	−1.06962	−	1.38281i
$986$	8.84323	+	5.79991i	0.281626	+	0.184707i
$987$	41.4720	+	41.4720i	1.32007	+	1.32007i
$988$	−10.2828	−	4.05432i	−0.327138	−	0.128985i
$989$		−	2.01076i		−	0.0639385i
$990$	−0.371108	−	4.75454i	−0.0117946	−	0.151109i
$991$			9.29836i			0.295372i	0.989034	+	0.147686i	$0.0471825\pi$
$991$			9.29836i			0.295372i	−0.989034	+	0.147686i	$0.952817\pi$
$992$	10.1752	+	6.18566i	0.323061	+	0.196395i
$993$	−25.0312	−	25.0312i	−0.794340	−	0.794340i
$994$	−6.74026	+	10.2770i	−0.213788	+	0.325966i
$995$	6.23342	−	48.8103i	0.197613	−	1.54739i
$996$	3.84583	+	8.85262i	0.121860	+	0.280506i
$997$	−12.3741	+	12.3741i	−0.391893	+	0.391893i	−0.875362	−	0.483469i	$-0.839377\pi$
$997$	−12.3741	+	12.3741i	−0.391893	+	0.391893i	0.483469	+	0.875362i	$0.339377\pi$
$998$	32.3630	−	6.72606i	1.02443	−	0.212910i
$999$	23.1840			0.733509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.c.343.3	yes	52
4.3	odd	2		380.2.k.d.343.10	yes	52
5.2	odd	4		380.2.k.d.267.10	yes	52
20.7	even	4	inner	380.2.k.c.267.3	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.3	✓	52	20.7	even	4	inner
380.2.k.c.343.3	yes	52	1.1	even	1	trivial
380.2.k.d.267.10	yes	52	5.2	odd	4
380.2.k.d.343.10	yes	52	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38463 + 0.287770i) q^{2} +(1.15541 - 1.15541i) q^{3} +(1.83438 - 0.796907i) q^{4} +(-0.283261 + 2.21805i) q^{5} +(-1.26732 + 1.93230i) q^{6} +(-3.26325 - 3.26325i) q^{7} +(-2.31060 + 1.63130i) q^{8} +0.330062i q^{9} +O(q^{10})\)	\(q+(-1.38463 + 0.287770i) q^{2} +(1.15541 - 1.15541i) q^{3} +(1.83438 - 0.796907i) q^{4} +(-0.283261 + 2.21805i) q^{5} +(-1.26732 + 1.93230i) q^{6} +(-3.26325 - 3.26325i) q^{7} +(-2.31060 + 1.63130i) q^{8} +0.330062i q^{9} +(-0.246078 - 3.15269i) q^{10} -4.56912i q^{11} +(1.19870 - 3.04021i) q^{12} +(-3.90789 - 3.90789i) q^{13} +(5.45745 + 3.57932i) q^{14} +(2.23548 + 2.89004i) q^{15} +(2.72988 - 2.92365i) q^{16} +(3.68739 - 3.68739i) q^{17} +(-0.0949818 - 0.457012i) q^{18} +1.00000 q^{19} +(1.24797 + 4.29448i) q^{20} -7.54078 q^{21} +(1.31485 + 6.32652i) q^{22} +(-0.671647 + 0.671647i) q^{23} +(-0.784875 + 4.55450i) q^{24} +(-4.83953 - 1.25658i) q^{25} +(6.53553 + 4.28639i) q^{26} +(3.84758 + 3.84758i) q^{27} +(-8.58655 - 3.38553i) q^{28} -1.43401i q^{29} +(-3.92696 - 3.35832i) q^{30} -2.10503i q^{31} +(-2.93852 + 4.83374i) q^{32} +(-5.27920 - 5.27920i) q^{33} +(-4.04454 + 6.16678i) q^{34} +(8.16243 - 6.31372i) q^{35} +(0.263028 + 0.605458i) q^{36} +(3.01280 - 3.01280i) q^{37} +(-1.38463 + 0.287770i) q^{38} -9.03041 q^{39} +(-2.96380 - 5.58712i) q^{40} +3.51686 q^{41} +(10.4412 - 2.17001i) q^{42} +(-1.49689 + 1.49689i) q^{43} +(-3.64116 - 8.38148i) q^{44} +(-0.732095 - 0.0934937i) q^{45} +(0.736700 - 1.12326i) q^{46} +(-5.49969 - 5.49969i) q^{47} +(-0.223890 - 6.53214i) q^{48} +14.2977i q^{49} +(7.06254 + 0.347220i) q^{50} -8.52089i q^{51} +(-10.2828 - 4.05432i) q^{52} +(5.92537 + 5.92537i) q^{53} +(-6.43468 - 4.22024i) q^{54} +(10.1345 + 1.29425i) q^{55} +(12.8634 + 2.21674i) q^{56} +(1.15541 - 1.15541i) q^{57} +(0.412665 + 1.98557i) q^{58} +1.07843 q^{59} +(6.40380 + 3.51996i) q^{60} -11.0480 q^{61} +(0.605762 + 2.91467i) q^{62} +(1.07708 - 1.07708i) q^{63} +(2.67775 - 7.53855i) q^{64} +(9.77486 - 7.56095i) q^{65} +(8.82890 + 5.79052i) q^{66} +(-1.29688 - 1.29688i) q^{67} +(3.82556 - 9.70258i) q^{68} +1.55205i q^{69} +(-9.48501 + 11.0910i) q^{70} +1.88311i q^{71} +(-0.538428 - 0.762641i) q^{72} +(-3.20108 - 3.20108i) q^{73} +(-3.30461 + 5.03859i) q^{74} +(-7.04349 + 4.13977i) q^{75} +(1.83438 - 0.796907i) q^{76} +(-14.9102 + 14.9102i) q^{77} +(12.5037 - 2.59868i) q^{78} +2.07546 q^{79} +(5.71156 + 6.88318i) q^{80} +7.90087 q^{81} +(-4.86954 + 1.01205i) q^{82} +(-2.08842 + 2.08842i) q^{83} +(-13.8326 + 6.00930i) q^{84} +(7.13434 + 9.22333i) q^{85} +(1.64187 - 2.50339i) q^{86} +(-1.65687 - 1.65687i) q^{87} +(7.45358 + 10.5574i) q^{88} +10.9661i q^{89} +(1.04058 - 0.0812209i) q^{90} +25.5049i q^{91} +(-0.696814 + 1.76729i) q^{92} +(-2.43216 - 2.43216i) q^{93} +(9.19765 + 6.03237i) q^{94} +(-0.283261 + 2.21805i) q^{95} +(2.18976 + 8.98014i) q^{96} +(1.72131 - 1.72131i) q^{97} +(-4.11443 - 19.7969i) q^{98} +1.50809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

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