LMFDB - Embedded newform 380.2.k.c.267.5

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			267.5
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34536 + 0.435901i) q^{2} +(-1.82161 - 1.82161i) q^{3} +(1.61998 - 1.17289i) q^{4} +(2.11542 + 0.724569i) q^{5} +(3.24476 + 1.65668i) q^{6} +(-1.36053 + 1.36053i) q^{7} +(-1.66819 + 2.28411i) q^{8} +3.63653i q^{9} +O(q^{10})$	\(q+(-1.34536 + 0.435901i) q^{2} +(-1.82161 - 1.82161i) q^{3} +(1.61998 - 1.17289i) q^{4} +(2.11542 + 0.724569i) q^{5} +(3.24476 + 1.65668i) q^{6} +(-1.36053 + 1.36053i) q^{7} +(-1.66819 + 2.28411i) q^{8} +3.63653i q^{9} +(-3.16184 - 0.0526904i) q^{10} +1.55414i q^{11} +(-5.08752 - 0.814429i) q^{12} +(-2.11246 + 2.11246i) q^{13} +(1.23734 - 2.42345i) q^{14} +(-2.53359 - 5.17335i) q^{15} +(1.24867 - 3.80011i) q^{16} +(0.503748 + 0.503748i) q^{17} +(-1.58517 - 4.89243i) q^{18} +1.00000 q^{19} +(4.27678 - 1.30736i) q^{20} +4.95670 q^{21} +(-0.677450 - 2.09087i) q^{22} +(3.79747 + 3.79747i) q^{23} +(7.19954 - 1.12196i) q^{24} +(3.95000 + 3.06553i) q^{25} +(1.92119 - 3.76283i) q^{26} +(1.15951 - 1.15951i) q^{27} +(-0.608282 + 3.79977i) q^{28} +2.83793i q^{29} +(5.66366 + 5.85562i) q^{30} +4.40335i q^{31} +(-0.0234394 + 5.65681i) q^{32} +(2.83103 - 2.83103i) q^{33} +(-0.897306 - 0.458137i) q^{34} +(-3.86388 + 1.89229i) q^{35} +(4.26524 + 5.89110i) q^{36} +(-2.89859 - 2.89859i) q^{37} +(-1.34536 + 0.435901i) q^{38} +7.69614 q^{39} +(-5.18392 + 3.62312i) q^{40} +5.57983 q^{41} +(-6.66854 + 2.16063i) q^{42} +(5.10385 + 5.10385i) q^{43} +(1.82283 + 2.51767i) q^{44} +(-2.63491 + 7.69278i) q^{45} +(-6.76429 - 3.45364i) q^{46} +(9.15647 - 9.15647i) q^{47} +(-9.19691 + 4.64772i) q^{48} +3.29794i q^{49} +(-6.65044 - 2.40243i) q^{50} -1.83527i q^{51} +(-0.944464 + 5.89981i) q^{52} +(5.52010 - 5.52010i) q^{53} +(-1.05452 + 2.06538i) q^{54} +(-1.12608 + 3.28765i) q^{55} +(-0.837967 - 5.37720i) q^{56} +(-1.82161 - 1.82161i) q^{57} +(-1.23706 - 3.81803i) q^{58} +9.43187 q^{59} +(-10.1721 - 5.40911i) q^{60} -12.6853 q^{61} +(-1.91943 - 5.92409i) q^{62} +(-4.94759 - 4.94759i) q^{63} +(-2.43427 - 7.62065i) q^{64} +(-5.99935 + 2.93811i) q^{65} +(-2.57470 + 5.04280i) q^{66} +(-0.237062 + 0.237062i) q^{67} +(1.40690 + 0.225222i) q^{68} -13.8350i q^{69} +(4.37345 - 4.23008i) q^{70} +11.8257i q^{71} +(-8.30621 - 6.06643i) q^{72} +(-7.73406 + 7.73406i) q^{73} +(5.16314 + 2.63614i) q^{74} +(-1.61116 - 12.7796i) q^{75} +(1.61998 - 1.17289i) q^{76} +(-2.11444 - 2.11444i) q^{77} +(-10.3541 + 3.35476i) q^{78} -12.4310 q^{79} +(5.39490 - 7.13407i) q^{80} +6.68525 q^{81} +(-7.50687 + 2.43225i) q^{82} +(-0.972495 - 0.972495i) q^{83} +(8.02975 - 5.81365i) q^{84} +(0.700639 + 1.43064i) q^{85} +(-9.09128 - 4.64173i) q^{86} +(5.16960 - 5.16960i) q^{87} +(-3.54981 - 2.59260i) q^{88} -4.55517i q^{89} +(0.191610 - 11.4981i) q^{90} -5.74810i q^{91} +(10.6058 + 1.69782i) q^{92} +(8.02119 - 8.02119i) q^{93} +(-8.32742 + 16.3101i) q^{94} +(2.11542 + 0.724569i) q^{95} +(10.3472 - 10.2618i) q^{96} +(13.9158 + 13.9158i) q^{97} +(-1.43757 - 4.43691i) q^{98} -5.65166 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.34536	+	0.435901i	−0.951312	+	0.308229i
$2$	−1.34536	+	0.435901i	−0.951312	+	0.308229i
$3$	−1.82161	−	1.82161i	−1.05171	−	1.05171i	−0.998588	−	0.0531190i	$-0.983084\pi$
$3$	−1.82161	−	1.82161i	−1.05171	−	1.05171i	−0.0531190	−	0.998588i	$-0.516916\pi$
$4$	1.61998	−	1.17289i	0.809990	−	0.586444i
$5$	2.11542	+	0.724569i	0.946044	+	0.324037i
$5$	2.11542	+	0.724569i	0.946044	+	0.324037i
$6$	3.24476	+	1.65668i	1.32467	+	0.676336i
$7$	−1.36053	+	1.36053i	−0.514231	+	0.514231i	−0.915820	−	0.401589i	$-0.868458\pi$
$7$	−1.36053	+	1.36053i	−0.514231	+	0.514231i	0.401589	+	0.915820i	$0.368458\pi$
$8$	−1.66819	+	2.28411i	−0.589795	+	0.807553i
$9$			3.63653i			1.21218i
$10$	−3.16184	−	0.0526904i	−0.999861	−	0.0166622i
$11$			1.55414i			0.468590i	0.972166	+	0.234295i	$0.0752781\pi$
$11$			1.55414i			0.468590i	−0.972166	+	0.234295i	$0.924722\pi$
$12$	−5.08752	−	0.814429i	−1.46864	−	0.235105i
$13$	−2.11246	+	2.11246i	−0.585890	+	0.585890i	−0.936516	−	0.350626i	$-0.885969\pi$
$13$	−2.11246	+	2.11246i	−0.585890	+	0.585890i	0.350626	+	0.936516i	$0.385969\pi$
$14$	1.23734	−	2.42345i	0.330693	−	0.647695i
$15$	−2.53359	−	5.17335i	−0.654170	−	1.33575i
$16$	1.24867	−	3.80011i	0.312168	−	0.950027i
$17$	0.503748	+	0.503748i	0.122177	+	0.122177i	0.765551	−	0.643375i	$-0.222466\pi$
$17$	0.503748	+	0.503748i	0.122177	+	0.122177i	−0.643375	+	0.765551i	$0.722466\pi$
$18$	−1.58517	−	4.89243i	−0.373627	−	1.15316i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	4.27678	−	1.30736i	0.956316	−	0.292335i
$21$	4.95670			1.08164
$22$	−0.677450	−	2.09087i	−0.144433	−	0.445775i
$23$	3.79747	+	3.79747i	0.791828	+	0.791828i	0.981791	−	0.189963i	$-0.0608369\pi$
$23$	3.79747	+	3.79747i	0.791828	+	0.791828i	−0.189963	+	0.981791i	$0.560837\pi$
$24$	7.19954	−	1.12196i	1.46960	−	0.229018i
$25$	3.95000	+	3.06553i	0.790000	+	0.613107i
$26$	1.92119	−	3.76283i	0.376776	−	0.737952i
$27$	1.15951	−	1.15951i	0.223147	−	0.223147i
$28$	−0.608282	+	3.79977i	−0.114954	+	0.718089i
$29$			2.83793i			0.526990i	0.964661	+	0.263495i	$0.0848753\pi$
$29$			2.83793i			0.526990i	−0.964661	+	0.263495i	$0.915125\pi$
$30$	5.66366	+	5.85562i	1.03404	+	1.06908i
$31$			4.40335i			0.790865i	0.918495	+	0.395433i	$0.129405\pi$
$31$			4.40335i			0.790865i	−0.918495	+	0.395433i	$0.870595\pi$
$32$	−0.0234394	+	5.65681i	−0.00414353	+	0.999991i
$33$	2.83103	−	2.83103i	0.492819	−	0.492819i
$34$	−0.897306	−	0.458137i	−0.153887	−	0.0785699i
$35$	−3.86388	+	1.89229i	−0.653115	+	0.319855i
$36$	4.26524	+	5.89110i	0.710873	+	0.981851i
$37$	−2.89859	−	2.89859i	−0.476525	−	0.476525i	0.427494	−	0.904018i	$-0.359397\pi$
$37$	−2.89859	−	2.89859i	−0.476525	−	0.476525i	−0.904018	+	0.427494i	$0.859397\pi$
$38$	−1.34536	+	0.435901i	−0.218246	+	0.0707125i
$39$	7.69614			1.23237
$40$	−5.18392	+	3.62312i	−0.819649	+	0.572866i
$41$	5.57983			0.871422			0.435711	−	0.900087i	$-0.356497\pi$
$41$	5.57983			0.871422			0.435711	+	0.900087i	$0.356497\pi$
$42$	−6.66854	+	2.16063i	−1.02898	+	0.333393i
$43$	5.10385	+	5.10385i	0.778330	+	0.778330i	0.979547	−	0.201217i	$-0.0644896\pi$
$43$	5.10385	+	5.10385i	0.778330	+	0.778330i	−0.201217	+	0.979547i	$0.564490\pi$
$44$	1.82283	+	2.51767i	0.274801	+	0.379553i
$45$	−2.63491	+	7.69278i	−0.392790	+	1.14677i
$46$	−6.76429	−	3.45364i	−0.997340	−	0.509212i
$47$	9.15647	−	9.15647i	1.33561	−	1.33561i	0.435345	−	0.900264i	$-0.356626\pi$
$47$	9.15647	−	9.15647i	1.33561	−	1.33561i	0.900264	−	0.435345i	$-0.143374\pi$
$48$	−9.19691	+	4.64772i	−1.32746	+	0.670841i
$49$			3.29794i			0.471134i
$50$	−6.65044	−	2.40243i	−0.940514	−	0.339755i
$51$		−	1.83527i		−	0.256989i
$52$	−0.944464	+	5.89981i	−0.130974	+	0.818156i
$53$	5.52010	−	5.52010i	0.758244	−	0.758244i	−0.217759	−	0.976003i	$-0.569875\pi$
$53$	5.52010	−	5.52010i	0.758244	−	0.758244i	0.976003	+	0.217759i	$0.0698747\pi$
$54$	−1.05452	+	2.06538i	−0.143502	+	0.281063i
$55$	−1.12608	+	3.28765i	−0.151840	+	0.443307i
$56$	−0.837967	−	5.37720i	−0.111978	−	0.718559i
$57$	−1.82161	−	1.82161i	−0.241278	−	0.241278i
$58$	−1.23706	−	3.81803i	−0.162434	−	0.501332i
$59$	9.43187			1.22793			0.613963	−	0.789335i	$-0.289575\pi$
$59$	9.43187			1.22793			0.613963	+	0.789335i	$0.289575\pi$
$60$	−10.1721	−	5.40911i	−1.31322	−	0.698314i
$61$	−12.6853			−1.62418			−0.812092	−	0.583529i	$-0.801671\pi$
$61$	−12.6853			−1.62418			−0.812092	+	0.583529i	$0.801671\pi$
$62$	−1.91943	−	5.92409i	−0.243767	−	0.752360i
$63$	−4.94759	−	4.94759i	−0.623338	−	0.623338i
$64$	−2.43427	−	7.62065i	−0.304284	−	0.952581i
$65$	−5.99935	+	2.93811i	−0.744128	+	0.364428i
$66$	−2.57470	+	5.04280i	−0.316924	+	0.620726i
$67$	−0.237062	+	0.237062i	−0.0289617	+	0.0289617i	−0.721439	−	0.692478i	$-0.756519\pi$
$67$	−0.237062	+	0.237062i	−0.0289617	+	0.0289617i	0.692478	+	0.721439i	$0.256519\pi$
$68$	1.40690	+	0.225222i	0.170612	+	0.0273122i
$69$		−	13.8350i		−	1.66554i
$70$	4.37345	−	4.23008i	0.522728	−	0.505591i
$71$			11.8257i			1.40345i	0.712446	+	0.701727i	$0.247587\pi$
$71$			11.8257i			1.40345i	−0.712446	+	0.701727i	$0.752413\pi$
$72$	−8.30621	−	6.06643i	−0.978897	−	0.714935i
$73$	−7.73406	+	7.73406i	−0.905203	+	0.905203i	−0.995880	−	0.0906774i	$-0.971097\pi$
$73$	−7.73406	+	7.73406i	−0.905203	+	0.905203i	0.0906774	+	0.995880i	$0.471097\pi$
$74$	5.16314	+	2.63614i	0.600202	+	0.306445i
$75$	−1.61116	−	12.7796i	−0.186040	−	1.47566i
$76$	1.61998	−	1.17289i	0.185824	−	0.134539i
$77$	−2.11444	−	2.11444i	−0.240963	−	0.240963i
$78$	−10.3541	+	3.35476i	−1.17237	+	0.379851i
$79$	−12.4310			−1.39860			−0.699300	−	0.714828i	$-0.746505\pi$
$79$	−12.4310			−1.39860			−0.699300	+	0.714828i	$0.746505\pi$
$80$	5.39490	−	7.13407i	0.603168	−	0.797614i
$81$	6.68525			0.742805
$82$	−7.50687	+	2.43225i	−0.828995	+	0.268597i
$83$	−0.972495	−	0.972495i	−0.106745	−	0.106745i	0.651717	−	0.758462i	$-0.274049\pi$
$83$	−0.972495	−	0.972495i	−0.106745	−	0.106745i	−0.758462	+	0.651717i	$0.774049\pi$
$84$	8.02975	−	5.81365i	0.876118	−	0.634321i
$85$	0.700639	+	1.43064i	0.0759949	+	0.155175i
$86$	−9.09128	−	4.64173i	−0.980338	−	0.500531i
$87$	5.16960	−	5.16960i	0.554239	−	0.554239i
$88$	−3.54981	−	2.59260i	−0.378411	−	0.276372i
$89$		−	4.55517i		−	0.482847i	−0.970420	−	0.241423i	$-0.922386\pi$
$89$		−	4.55517i		−	0.482847i	0.970420	−	0.241423i	$-0.0776142\pi$
$90$	0.191610	−	11.4981i	0.0201975	−	1.21201i
$91$		−	5.74810i		−	0.602565i
$92$	10.6058	+	1.69782i	1.10574	+	0.177010i
$93$	8.02119	−	8.02119i	0.831758	−	0.831758i
$94$	−8.32742	+	16.3101i	−0.858908	+	1.68225i
$95$	2.11542	+	0.724569i	0.217037	+	0.0743392i
$96$	10.3472	−	10.2618i	1.05606	−	1.04734i
$97$	13.9158	+	13.9158i	1.41294	+	1.41294i	0.736503	+	0.676434i	$0.236476\pi$
$97$	13.9158	+	13.9158i	1.41294	+	1.41294i	0.676434	+	0.736503i	$0.263524\pi$
$98$	−1.43757	−	4.43691i	−0.145217	−	0.448195i
$99$	−5.65166			−0.568013
$100$	9.99445	+	0.333197i	0.999445	+	0.0333197i
$101$	−19.2521			−1.91565			−0.957826	−	0.287350i	$-0.907226\pi$
$101$	−19.2521			−1.91565			−0.957826	+	0.287350i	$0.907226\pi$
$102$	0.799994	+	2.46909i	0.0792112	+	0.244476i
$103$	−10.7447	−	10.7447i	−1.05871	−	1.05871i	−0.998166	−	0.0605401i	$-0.980718\pi$
$103$	−10.7447	−	10.7447i	−1.05871	−	1.05871i	−0.0605401	−	0.998166i	$-0.519282\pi$
$104$	−1.30109	−	8.34905i	−0.127582	−	0.818692i
$105$	10.4855	+	3.59147i	1.02328	+	0.350491i
$106$	−5.02029	+	9.83273i	−0.487614	+	0.955039i
$107$	6.30131	−	6.30131i	0.609171	−	0.609171i	−0.333558	−	0.942729i	$-0.608249\pi$
$107$	6.30131	−	6.30131i	0.609171	−	0.609171i	0.942729	+	0.333558i	$0.108249\pi$
$108$	0.518407	−	3.23835i	0.0498837	−	0.311610i
$109$		−	12.1283i		−	1.16168i	−0.814018	−	0.580840i	$-0.802724\pi$
$109$		−	12.1283i		−	1.16168i	0.814018	−	0.580840i	$-0.197276\pi$
$110$	0.0818881	−	4.91393i	0.00780772	−	0.468525i
$111$			10.5602i			1.00233i
$112$	3.47130	+	6.86900i	0.328007	+	0.649059i
$113$	−9.96634	+	9.96634i	−0.937554	+	0.937554i	−0.998162	−	0.0606075i	$-0.980696\pi$
$113$	−9.96634	+	9.96634i	−0.937554	+	0.937554i	0.0606075	+	0.998162i	$0.480696\pi$
$114$	3.24476	+	1.65668i	0.303900	+	0.155162i
$115$	5.28172	+	10.7848i	0.492523	+	1.00569i
$116$	3.32857	+	4.59739i	0.309050	+	0.426857i
$117$	−7.68200	−	7.68200i	−0.710201	−	0.710201i
$118$	−12.6893	+	4.11136i	−1.16814	+	0.378482i
$119$	−1.37073			−0.125654
$120$	16.0430	+	2.84316i	1.46452	+	0.259544i
$121$	8.58466			0.780424
$122$	17.0663	−	5.52953i	1.54511	−	0.500620i
$123$	−10.1643	−	10.1643i	−0.916481	−	0.916481i
$124$	5.16463	+	7.13334i	0.463798	+	0.640593i
$125$	6.13472	+	9.34694i	0.548706	+	0.836015i
$126$	8.81295	+	4.49963i	0.785120	+	0.400858i
$127$	−3.63230	+	3.63230i	−0.322315	+	0.322315i	−0.849655	−	0.527340i	$-0.823190\pi$
$127$	−3.63230	+	3.63230i	−0.322315	+	0.322315i	0.527340	+	0.849655i	$0.323190\pi$
$128$	6.59682	+	9.19140i	0.583082	+	0.812413i
$129$		−	18.5944i		−	1.63715i
$130$	6.79055	−	6.56794i	0.595571	−	0.576046i
$131$			5.60922i			0.490080i	0.969513	+	0.245040i	$0.0788010\pi$
$131$			5.60922i			0.490080i	−0.969513	+	0.245040i	$0.921199\pi$
$132$	1.26573	−	7.90669i	0.110168	−	0.688189i
$133$	−1.36053	+	1.36053i	−0.117973	+	0.117973i
$134$	0.215598	−	0.422269i	0.0186248	−	0.0364785i
$135$	3.29298	−	1.61270i	0.283415	−	0.138799i
$136$	−1.99096	+	0.310265i	−0.170724	+	0.0266050i
$137$	1.49575	+	1.49575i	0.127790	+	0.127790i	0.768109	−	0.640319i	$-0.221198\pi$
$137$	1.49575	+	1.49575i	0.127790	+	0.127790i	−0.640319	+	0.768109i	$0.721198\pi$
$138$	6.03071	+	18.6131i	0.513368	+	1.58445i
$139$	−10.3913			−0.881381			−0.440691	−	0.897659i	$-0.645266\pi$
$139$	−10.3913			−0.881381			−0.440691	+	0.897659i	$0.645266\pi$
$140$	−4.03997	+	7.59737i	−0.341439	+	0.642095i
$141$	−33.3590			−2.80934
$142$	−5.15484	−	15.9098i	−0.432585	−	1.33512i
$143$	−3.28304	−	3.28304i	−0.274542	−	0.274542i
$144$	13.8192	+	4.54083i	1.15160	+	0.378402i
$145$	−2.05627	+	6.00341i	−0.170764	+	0.498556i
$146$	7.03380	−	13.7764i	0.582121	−	1.14014i
$147$	6.00755	−	6.00755i	0.495495	−	0.495495i
$148$	−8.09537	−	1.29594i	−0.665435	−	0.106525i
$149$		−	5.86771i		−	0.480701i	−0.970686	−	0.240351i	$-0.922738\pi$
$149$		−	5.86771i		−	0.480701i	0.970686	−	0.240351i	$-0.0772624\pi$
$150$	7.73821	+	16.4908i	0.631822	+	1.34647i
$151$			8.00365i			0.651327i	0.945486	+	0.325664i	$0.105588\pi$
$151$			8.00365i			0.651327i	−0.945486	+	0.325664i	$0.894412\pi$
$152$	−1.66819	+	2.28411i	−0.135308	+	0.185265i
$153$	−1.83189	+	1.83189i	−0.148100	+	0.148100i
$154$	3.76637	+	1.92300i	0.303503	+	0.154959i
$155$	−3.19053	+	9.31493i	−0.256269	+	0.748193i
$156$	12.4676	−	9.02670i	0.998206	−	0.722715i
$157$	3.64795	+	3.64795i	0.291138	+	0.291138i	0.837530	−	0.546392i	$-0.183999\pi$
$157$	3.64795	+	3.64795i	0.291138	+	0.291138i	−0.546392	+	0.837530i	$0.683999\pi$
$158$	16.7242	−	5.41870i	1.33051	−	0.431089i
$159$	−20.1109			−1.59490
$160$	−4.14833	+	11.9495i	−0.327954	+	0.944694i
$161$	−10.3331			−0.814365
$162$	−8.99406	+	2.91411i	−0.706640	+	0.228954i
$163$	−7.67574	−	7.67574i	−0.601210	−	0.601210i	0.339424	−	0.940634i	$-0.389768\pi$
$163$	−7.67574	−	7.67574i	−0.601210	−	0.601210i	−0.940634	+	0.339424i	$0.889768\pi$
$164$	9.03921	−	6.54451i	0.705844	−	0.511040i
$165$	8.04009	−	3.93754i	0.625920	−	0.306537i
$166$	1.73227	+	0.884443i	0.134450	+	0.0686461i
$167$	−2.56389	+	2.56389i	−0.198400	+	0.198400i	−0.799314	−	0.600914i	$-0.794803\pi$
$167$	−2.56389	+	2.56389i	−0.198400	+	0.198400i	0.600914	+	0.799314i	$0.294803\pi$
$168$	−8.26872	+	11.3216i	−0.637946	+	0.873482i
$169$			4.07507i			0.313467i
$170$	−1.56623	−	1.61931i	−0.120124	−	0.124196i
$171$			3.63653i			0.278092i
$172$	14.2544	+	2.28190i	1.08689	+	0.173993i
$173$	3.14197	−	3.14197i	0.238879	−	0.238879i	−0.577507	−	0.816386i	$-0.695974\pi$
$173$	3.14197	−	3.14197i	0.238879	−	0.238879i	0.816386	+	0.577507i	$0.195974\pi$
$174$	−4.70153	+	9.20840i	−0.356422	+	0.698087i
$175$	−9.54482	+	1.20334i	−0.721521	+	0.0909641i
$176$	5.90588	+	1.94061i	0.445173	+	0.146279i
$177$	−17.1812	−	17.1812i	−1.29142	−	1.29142i
$178$	1.98560	+	6.12833i	0.148827	+	0.459338i
$179$	−0.307021			−0.0229478			−0.0114739	−	0.999934i	$-0.503652\pi$
$179$	−0.307021			−0.0229478			−0.0114739	+	0.999934i	$0.503652\pi$
$180$	4.75426	+	15.5526i	0.354361	+	1.15922i
$181$	21.5665			1.60303			0.801514	−	0.597976i	$-0.204028\pi$
$181$	21.5665			1.60303			0.801514	+	0.597976i	$0.204028\pi$
$182$	2.50561	+	7.73326i	0.185728	+	0.573227i
$183$	23.1076	+	23.1076i	1.70817	+	1.70817i
$184$	−15.0087	+	2.33892i	−1.10646	+	0.172427i
$185$	−4.03150	−	8.23195i	−0.296402	−	0.605225i
$186$	−7.29493	+	14.2878i	−0.534890	+	1.04763i
$187$	−0.782893	+	0.782893i	−0.0572508	+	0.0572508i
$188$	4.09380	−	25.5728i	0.298571	−	1.86509i
$189$			3.15508i			0.229498i
$190$	−3.16184	−	0.0526904i	−0.229384	−	0.00382257i
$191$			16.5890i			1.20033i	0.799874	+	0.600167i	$0.204899\pi$
$191$			16.5890i			1.20033i	−0.799874	+	0.600167i	$0.795101\pi$
$192$	−9.44756	+	18.3162i	−0.681819	+	1.32185i
$193$	3.14132	−	3.14132i	0.226117	−	0.226117i	−0.584951	−	0.811068i	$-0.698886\pi$
$193$	3.14132	−	3.14132i	0.226117	−	0.226117i	0.811068	+	0.584951i	$0.198886\pi$
$194$	−24.7877	−	12.6558i	−1.77965	−	0.908637i
$195$	16.2806	+	5.57638i	1.16588	+	0.399333i
$196$	3.86811	+	5.34259i	0.276293	+	0.381614i
$197$	−3.04631	−	3.04631i	−0.217041	−	0.217041i	0.590209	−	0.807250i	$-0.299045\pi$
$197$	−3.04631	−	3.04631i	−0.217041	−	0.217041i	−0.807250	+	0.590209i	$0.799045\pi$
$198$	7.60351	−	2.46357i	0.540358	−	0.175078i
$199$	−4.50587			−0.319413			−0.159706	−	0.987165i	$-0.551055\pi$
$199$	−4.50587			−0.319413			−0.159706	+	0.987165i	$0.551055\pi$
$200$	−13.5914	+	3.90832i	−0.961054	+	0.276360i
$201$	0.863669			0.0609185
$202$	25.9009	−	8.39200i	1.82238	−	0.590459i
$203$	−3.86108	−	3.86108i	−0.270995	−	0.270995i
$204$	−2.15256	−	2.97309i	−0.150709	−	0.208158i
$205$	11.8037	+	4.04297i	0.824404	+	0.282373i
$206$	19.1391	+	9.77184i	1.33348	+	0.680836i
$207$	−13.8096	+	13.8096i	−0.959835	+	0.959835i
$208$	5.38979	+	10.6653i	0.373715	+	0.739507i
$209$			1.55414i			0.107502i
$210$	−15.6723	−	0.261171i	−1.08149	−	0.0180225i
$211$		−	5.66687i		−	0.390123i	−0.980791	−	0.195062i	$-0.937509\pi$
$211$		−	5.66687i		−	0.390123i	0.980791	−	0.195062i	$-0.0624907\pi$
$212$	2.46800	−	15.4169i	0.169503	−	1.05884i
$213$	21.5418	−	21.5418i	1.47602	−	1.47602i
$214$	−5.73078	+	11.2243i	−0.391748	+	0.767276i
$215$	7.09869	+	14.4949i	0.484127	+	0.988542i
$216$	0.714156	+	4.58271i	0.0485921	+	0.311814i
$217$	−5.99087	−	5.99087i	−0.406687	−	0.406687i
$218$	5.28674	+	16.3169i	0.358063	+	1.10512i
$219$	28.1769			1.90402
$220$	2.03182	+	6.64669i	0.136985	+	0.448120i
$221$	−2.12829			−0.143164
$222$	−4.60320	−	14.2072i	−0.308947	−	0.953528i
$223$	−4.78190	−	4.78190i	−0.320220	−	0.320220i	0.528632	−	0.848851i	$-0.322705\pi$
$223$	−4.78190	−	4.78190i	−0.320220	−	0.320220i	−0.848851	+	0.528632i	$0.822705\pi$
$224$	−7.66434	−	7.72812i	−0.512096	−	0.516357i
$225$	−11.1479	+	14.3643i	−0.743193	+	0.957619i
$226$	9.06396	−	17.7526i	0.602926	−	1.18089i
$227$	−4.16223	+	4.16223i	−0.276257	+	0.276257i	−0.831613	−	0.555356i	$-0.812582\pi$
$227$	−4.16223	+	4.16223i	−0.276257	+	0.276257i	0.555356	+	0.831613i	$0.312582\pi$
$228$	−5.08752	−	0.814429i	−0.336929	−	0.0539369i
$229$		−	23.9738i		−	1.58423i	−0.610369	−	0.792117i	$-0.708979\pi$
$229$		−	23.9738i		−	1.58423i	0.610369	−	0.792117i	$-0.291021\pi$
$230$	−11.8069	−	12.2071i	−0.778525	−	0.804912i
$231$			7.70338i			0.506845i
$232$	−6.48213	−	4.73421i	−0.425573	−	0.310816i
$233$	15.2827	−	15.2827i	1.00120	−	1.00120i	0.00120416	−	0.999999i	$-0.499617\pi$
$233$	15.2827	−	15.2827i	1.00120	−	1.00120i	0.999999	−	0.00120416i	$-0.000383296\pi$
$234$	13.6836	+	6.98645i	0.894528	+	0.456719i
$235$	26.0043	−	12.7353i	1.69633	−	0.830759i
$236$	15.2794	−	11.0625i	0.994607	−	0.720109i
$237$	22.6445	+	22.6445i	1.47092	+	1.47092i
$238$	1.84412	−	0.597501i	0.119536	−	0.0387302i
$239$	3.86042			0.249710			0.124855	−	0.992175i	$-0.460153\pi$
$239$	3.86042			0.249710			0.124855	+	0.992175i	$0.460153\pi$
$240$	−22.8229	+	3.16809i	−1.47321	+	0.204500i
$241$	−6.43756			−0.414679			−0.207340	−	0.978269i	$-0.566481\pi$
$241$	−6.43756			−0.414679			−0.207340	+	0.978269i	$0.566481\pi$
$242$	−11.5494	+	3.74206i	−0.742427	+	0.240549i
$243$	−15.6564	−	15.6564i	−1.00436	−	1.00436i
$244$	−20.5499	+	14.8784i	−1.31557	+	0.952493i
$245$	−2.38958	+	6.97652i	−0.152665	+	0.445713i
$246$	18.1052	+	9.24397i	1.15435	+	0.589374i
$247$	−2.11246	+	2.11246i	−0.134412	+	0.134412i
$248$	−10.0577	−	7.34563i	−0.638666	−	0.466448i
$249$			3.54301i			0.224529i
$250$	−12.3277	−	9.90085i	−0.779675	−	0.626185i
$251$		−	21.2078i		−	1.33862i	−0.742982	−	0.669311i	$-0.766589\pi$
$251$		−	21.2078i		−	1.33862i	0.742982	−	0.669311i	$-0.233411\pi$
$252$	−13.8180	−	2.21203i	−0.870450	−	0.139345i
$253$	−5.90179	+	5.90179i	−0.371042	+	0.371042i
$254$	3.30343	−	6.47008i	0.207275	−	0.405969i
$255$	1.32978	−	3.88236i	0.0832738	−	0.243123i
$256$	−12.8816	−	9.49017i	−0.805102	−	0.593136i
$257$	4.01904	+	4.01904i	0.250701	+	0.250701i	0.821258	−	0.570557i	$-0.193273\pi$
$257$	4.01904	+	4.01904i	0.250701	+	0.250701i	−0.570557	+	0.821258i	$0.693273\pi$
$258$	8.10534	+	25.0162i	0.504617	+	1.55744i
$259$	7.88721			0.490087
$260$	−6.27275	+	11.7962i	−0.389020	+	0.731572i
$261$	−10.3202			−0.638805
$262$	−2.44507	−	7.54641i	−0.151057	−	0.466219i
$263$	17.8228	+	17.8228i	1.09900	+	1.09900i	0.994528	+	0.104471i	$0.0333150\pi$
$263$	17.8228	+	17.8228i	1.09900	+	1.09900i	0.104471	+	0.994528i	$0.466685\pi$
$264$	1.74367	+	11.1891i	0.107316	+	0.688640i
$265$	15.6770	−	7.67763i	0.963031	−	0.471633i
$266$	1.23734	−	2.42345i	0.0758662	−	0.148591i
$267$	−8.29774	+	8.29774i	−0.507813	+	0.507813i
$268$	−0.105989	+	0.662082i	−0.00647429	+	0.0404431i
$269$			13.5261i			0.824704i	0.911025	+	0.412352i	$0.135293\pi$
$269$			13.5261i			0.824704i	−0.911025	+	0.412352i	$0.864707\pi$
$270$	−3.72727	+	3.60508i	−0.226834	+	0.219398i
$271$		−	16.0044i		−	0.972195i	−0.873905	−	0.486098i	$-0.838420\pi$
$271$		−	16.0044i		−	0.972195i	0.873905	−	0.486098i	$-0.161580\pi$
$272$	2.54331	−	1.28528i	0.154211	−	0.0779316i
$273$	−10.4708	+	10.4708i	−0.633722	+	0.633722i
$274$	−2.66432	−	1.36032i	−0.160957	−	0.0821800i
$275$	−4.76425	+	6.13884i	−0.287295	+	0.370186i
$276$	−16.2269	−	22.4125i	−0.976747	−	1.34907i
$277$	16.3659	+	16.3659i	0.983333	+	0.983333i	0.999863	−	0.0165304i	$-0.00526202\pi$
$277$	16.3659	+	16.3659i	0.983333	+	0.983333i	−0.0165304	+	0.999863i	$0.505262\pi$
$278$	13.9801	−	4.52959i	0.838469	−	0.271667i
$279$	−16.0129			−0.958668
$280$	2.12350	−	11.9822i	0.126903	−	0.716074i
$281$	8.82028			0.526174			0.263087	−	0.964772i	$-0.415259\pi$
$281$	8.82028			0.526174			0.263087	+	0.964772i	$0.415259\pi$
$282$	44.8799	−	14.5413i	2.67256	−	0.865919i
$283$	−10.7184	−	10.7184i	−0.637141	−	0.637141i	0.312708	−	0.949849i	$-0.398764\pi$
$283$	−10.7184	−	10.7184i	−0.637141	−	0.637141i	−0.949849	+	0.312708i	$0.898764\pi$
$284$	13.8702	+	19.1574i	0.823046	+	1.13678i
$285$	−2.53359	−	5.17335i	−0.150077	−	0.306443i
$286$	5.84795	+	2.98579i	0.345797	+	0.176553i
$287$	−7.59150	+	7.59150i	−0.448112	+	0.448112i
$288$	−20.5711	−	0.0852379i	−1.21217	−	0.00502269i
$289$		−	16.4925i		−	0.970146i
$290$	0.149532	−	8.97307i	0.00878081	−	0.526917i
$291$		−	50.6984i		−	2.97199i
$292$	−3.45784	+	21.6002i	−0.202355	+	1.26406i
$293$	4.73427	−	4.73427i	0.276579	−	0.276579i	−0.555163	−	0.831742i	$-0.687344\pi$
$293$	4.73427	−	4.73427i	0.276579	−	0.276579i	0.831742	+	0.555163i	$0.187344\pi$
$294$	−5.46361	+	10.7010i	−0.318644	+	0.624096i
$295$	19.9524	+	6.83404i	1.16167	+	0.397893i
$296$	11.4561	−	1.78528i	0.665871	−	0.103767i
$297$	1.80203	+	1.80203i	0.104564	+	0.104564i
$298$	2.55774	+	7.89417i	0.148166	+	0.457297i
$299$	−16.0440			−0.927848
$300$	−17.5990	−	18.8129i	−1.01608	−	1.08617i
$301$	−13.8878			−0.800482
$302$	−3.48880	−	10.7678i	−0.200758	−	0.619616i
$303$	35.0697	+	35.0697i	2.01470	+	2.01470i
$304$	1.24867	−	3.80011i	0.0716162	−	0.217951i
$305$	−26.8347	−	9.19136i	−1.53655	−	0.526296i
$306$	1.66603	−	3.26308i	0.0952406	−	0.186538i
$307$	20.1802	−	20.1802i	1.15174	−	1.15174i	0.165541	−	0.986203i	$-0.447063\pi$
$307$	20.1802	−	20.1802i	1.15174	−	1.15174i	0.986203	−	0.165541i	$-0.0529370\pi$
$308$	−5.90536	−	0.945353i	−0.336489	−	0.0538665i
$309$			39.1453i			2.22690i
$310$	0.232014	−	13.9227i	0.0131775	−	0.790755i
$311$		−	33.6583i		−	1.90859i	−0.298869	−	0.954294i	$-0.596609\pi$
$311$		−	33.6583i		−	1.90859i	0.298869	−	0.954294i	$-0.403391\pi$
$312$	−12.8386	+	17.5788i	−0.726845	+	0.995203i
$313$	13.2867	−	13.2867i	0.751008	−	0.751008i	−0.223660	−	0.974667i	$-0.571800\pi$
$313$	13.2867	−	13.2867i	0.751008	−	0.751008i	0.974667	+	0.223660i	$0.0718004\pi$
$314$	−6.49795	−	3.31766i	−0.366700	−	0.187226i
$315$	−6.88137	−	14.0511i	−0.387721	−	0.791690i
$316$	−20.1380	+	14.5802i	−1.13285	+	0.820200i
$317$	−6.21355	−	6.21355i	−0.348988	−	0.348988i	0.510745	−	0.859733i	$-0.329370\pi$
$317$	−6.21355	−	6.21355i	−0.348988	−	0.348988i	−0.859733	+	0.510745i	$0.829370\pi$
$318$	27.0564	−	8.76638i	1.51725	−	0.491594i
$319$	−4.41053			−0.246942
$320$	0.372171	−	17.8847i	0.0208050	−	0.999784i
$321$	−22.9571			−1.28134
$322$	13.9018	−	4.50422i	0.774715	−	0.251011i
$323$	0.503748	+	0.503748i	0.0280293	+	0.0280293i
$324$	10.8300	−	7.84104i	0.601665	−	0.435613i
$325$	−14.8200	+	1.86840i	−0.822066	+	0.103640i
$326$	13.6725	+	6.98076i	0.757249	+	0.386628i
$327$	−22.0930	+	22.0930i	−1.22175	+	1.22175i
$328$	−9.30822	+	12.7449i	−0.513960	+	0.703720i
$329$			24.9152i			1.37362i
$330$	−9.10043	+	8.80209i	−0.500962	+	0.484539i
$331$			8.91952i			0.490261i	0.969490	+	0.245131i	$0.0788309\pi$
$331$			8.91952i			0.490261i	−0.969490	+	0.245131i	$0.921169\pi$
$332$	−2.71605	−	0.434796i	−0.149063	−	0.0238625i
$333$	10.5408	−	10.5408i	0.577632	−	0.577632i
$334$	2.33175	−	4.56695i	0.127588	−	0.249893i
$335$	−0.673253	+	0.329718i	−0.0367837	+	0.0180144i
$336$	6.18929	−	18.8360i	0.337653	−	1.02759i
$337$	8.92479	+	8.92479i	0.486164	+	0.486164i	0.907094	−	0.420929i	$-0.138296\pi$
$337$	8.92479	+	8.92479i	0.486164	+	0.486164i	−0.420929	+	0.907094i	$0.638296\pi$
$338$	−1.77633	−	5.48243i	−0.0966194	−	0.298205i
$339$	36.3096			1.97206
$340$	2.81300	+	1.49584i	0.152556	+	0.0811231i
$341$	−6.84340			−0.370591
$342$	−1.58517	−	4.89243i	−0.0857160	−	0.264553i
$343$	−14.0106	−	14.0106i	−0.756502	−	0.756502i
$344$	−20.1719	+	3.14353i	−1.08760	+	0.169488i
$345$	10.0244	−	29.2669i	0.539697	−	1.57568i
$346$	−2.85748	+	5.59666i	−0.153619	+	0.300878i
$347$	5.26345	−	5.26345i	0.282557	−	0.282557i	−0.551571	−	0.834128i	$-0.685971\pi$
$347$	5.26345	−	5.26345i	0.282557	−	0.282557i	0.834128	+	0.551571i	$0.185971\pi$
$348$	2.31129	−	14.4380i	0.123898	−	0.773958i
$349$		−	20.6928i		−	1.10766i	−0.832629	−	0.553831i	$-0.813165\pi$
$349$		−	20.6928i		−	1.10766i	0.832629	−	0.553831i	$-0.186835\pi$
$350$	12.3167	−	5.77953i	0.658354	−	0.308929i
$351$			4.89881i			0.261479i
$352$	−8.79144	−	0.0364279i	−0.468586	−	0.00194162i
$353$	−21.2548	+	21.2548i	−1.13128	+	1.13128i	−0.141312	+	0.989965i	$0.545132\pi$
$353$	−21.2548	+	21.2548i	−1.13128	+	1.13128i	−0.989965	+	0.141312i	$0.954868\pi$
$354$	30.6042	+	15.6256i	1.62659	+	0.830489i
$355$	−8.56854	+	25.0163i	−0.454771	+	1.32773i
$356$	−5.34270	−	7.37928i	−0.283162	−	0.391101i
$357$	2.49693	+	2.49693i	0.132151	+	0.132151i
$358$	0.413053	−	0.133831i	0.0218305	−	0.00707317i
$359$	−3.46265			−0.182752			−0.0913758	−	0.995816i	$-0.529126\pi$
$359$	−3.46265			−0.182752			−0.0913758	+	0.995816i	$0.529126\pi$
$360$	−13.1756	−	18.8515i	−0.694414	−	0.993559i
$361$	1.00000			0.0526316
$362$	−29.0147	+	9.40088i	−1.52498	+	0.494099i
$363$	−15.6379	−	15.6379i	−0.820777	−	0.820777i
$364$	−6.74188	−	9.31181i	−0.353370	−	0.488072i
$365$	−21.9646	+	10.7569i	−1.14968	+	0.563043i
$366$	−41.1607	−	21.0154i	−2.15151	−	1.09849i
$367$	−3.64892	+	3.64892i	−0.190472	+	0.190472i	−0.795900	−	0.605428i	$-0.793002\pi$
$367$	−3.64892	+	3.64892i	−0.190472	+	0.190472i	0.605428	+	0.795900i	$0.293002\pi$
$368$	19.1726	−	9.68901i	0.999441	−	0.505075i
$369$			20.2912i			1.05632i
$370$	9.01213	+	9.31759i	0.468519	+	0.484398i
$371$			15.0205i			0.779824i
$372$	3.58622	−	22.4021i	0.185937	−	1.16150i
$373$	−17.0960	+	17.0960i	−0.885197	+	0.885197i	−0.994057	−	0.108860i	$-0.965280\pi$
$373$	−17.0960	+	17.0960i	−0.885197	+	0.885197i	0.108860	+	0.994057i	$0.465280\pi$
$374$	0.712008	−	1.39454i	0.0368170	−	0.0721097i
$375$	5.85140	−	28.2015i	0.302165	−	1.45632i
$376$	5.63960	+	36.1891i	0.290840	+	1.86631i
$377$	−5.99500	−	5.99500i	−0.308758	−	0.308758i
$378$	−1.37530	−	4.24471i	−0.0707379	−	0.218324i
$379$	−30.1318			−1.54777			−0.773883	−	0.633329i	$-0.781688\pi$
$379$	−30.1318			−1.54777			−0.773883	+	0.633329i	$0.781688\pi$
$380$	4.27678	−	1.30736i	0.219394	−	0.0670663i
$381$	13.2333			0.677962
$382$	−7.23115	−	22.3181i	−0.369978	−	1.14189i
$383$	−4.04584	−	4.04584i	−0.206733	−	0.206733i	0.596144	−	0.802877i	$-0.296699\pi$
$383$	−4.04584	−	4.04584i	−0.206733	−	0.206733i	−0.802877	+	0.596144i	$0.796699\pi$
$384$	4.72632	−	28.7600i	0.241189	−	1.46765i
$385$	−2.94088	−	6.00499i	−0.149881	−	0.306043i
$386$	−2.85689	+	5.59550i	−0.145412	+	0.284803i
$387$	−18.5603	+	18.5603i	−0.943473	+	0.943473i
$388$	38.8650	+	6.22167i	1.97307	+	0.315857i
$389$			15.7511i			0.798612i	0.916818	+	0.399306i	$0.130749\pi$
$389$			15.7511i			0.798612i	−0.916818	+	0.399306i	$0.869251\pi$
$390$	−24.3340	−	0.405513i	−1.23220	−	0.0205340i
$391$			3.82594i			0.193486i
$392$	−7.53283	−	5.50159i	−0.380465	−	0.277872i
$393$	10.2178	−	10.2178i	0.515420	−	0.515420i
$394$	5.42628	+	2.77049i	0.273372	+	0.139575i
$395$	−26.2969	−	9.00714i	−1.32314	−	0.453198i
$396$	−9.15557	+	6.62876i	−0.460085	+	0.333108i
$397$	−0.149984	−	0.149984i	−0.00752749	−	0.00752749i	0.703333	−	0.710861i	$-0.251694\pi$
$397$	−0.149984	−	0.149984i	−0.00752749	−	0.00752749i	−0.710861	+	0.703333i	$0.751694\pi$
$398$	6.06201	−	1.96412i	0.303861	−	0.0984522i
$399$	4.95670			0.248145
$400$	16.5816	−	11.1826i	0.829080	−	0.559129i
$401$	22.0930			1.10327			0.551637	−	0.834085i	$-0.314004\pi$
$401$	22.0930			1.10327			0.551637	+	0.834085i	$0.314004\pi$
$402$	−1.16194	+	0.376474i	−0.0579525	+	0.0187768i
$403$	−9.30188	−	9.30188i	−0.463360	−	0.463360i
$404$	−31.1880	+	22.5805i	−1.55166	+	1.12342i
$405$	14.1421	+	4.84392i	0.702727	+	0.240696i
$406$	6.87758	+	3.51149i	0.341329	+	0.174272i
$407$	4.50480	−	4.50480i	0.223294	−	0.223294i
$408$	4.19194	+	3.06157i	0.207532	+	0.151570i
$409$		−	27.0421i		−	1.33714i	−0.743647	−	0.668572i	$-0.766906\pi$
$409$		−	27.0421i		−	1.33714i	0.743647	−	0.668572i	$-0.233094\pi$
$410$	−17.6425	−	0.294003i	−0.871301	−	0.0145198i
$411$		−	5.44934i		−	0.268796i
$412$	−30.0085	−	4.80388i	−1.47841	−	0.236670i
$413$	−12.8323	+	12.8323i	−0.631437	+	0.631437i
$414$	12.5593	−	24.5985i	0.617254	−	1.20895i
$415$	−1.35260	−	2.76188i	−0.0663963	−	0.135575i
$416$	−11.9002	−	11.9993i	−0.583457	−	0.588312i
$417$	18.9290	+	18.9290i	0.926955	+	0.926955i
$418$	−0.677450	−	2.09087i	−0.0331352	−	0.102268i
$419$	−2.29890			−0.112309			−0.0561543	−	0.998422i	$-0.517884\pi$
$419$	−2.29890			−0.112309			−0.0561543	+	0.998422i	$0.517884\pi$
$420$	21.1987	−	6.48020i	1.03439	−	0.316201i
$421$	31.3358			1.52721			0.763607	−	0.645682i	$-0.223427\pi$
$421$	31.3358			1.52721			0.763607	+	0.645682i	$0.223427\pi$
$422$	2.47019	+	7.62397i	0.120247	+	0.371129i
$423$	33.2978	+	33.2978i	1.61899	+	1.61899i
$424$	3.39990	+	21.8171i	0.165114	+	1.05953i
$425$	0.445549	+	3.53406i	0.0216123	+	0.171427i
$426$	−19.5914	+	38.3716i	−0.949206	+	1.85911i
$427$	17.2587	−	17.2587i	0.835206	−	0.835206i
$428$	2.81727	−	17.5987i	0.136178	−	0.850667i
$429$			11.9608i			0.577475i
$430$	−15.8686	−	16.4065i	−0.765253	−	0.791190i
$431$			23.9910i			1.15561i	0.816176	+	0.577803i	$0.196090\pi$
$431$			23.9910i			1.15561i	−0.816176	+	0.577803i	$0.803910\pi$
$432$	−2.95841	−	5.85409i	−0.142336	−	0.281655i
$433$	−14.4453	+	14.4453i	−0.694195	+	0.694195i	−0.963152	−	0.268957i	$-0.913321\pi$
$433$	−14.4453	+	14.4453i	−0.694195	+	0.694195i	0.268957	+	0.963152i	$0.413321\pi$
$434$	10.6713	+	5.44845i	0.512239	+	0.261534i
$435$	14.6816	−	7.19014i	0.703929	−	0.344741i
$436$	−14.2251	−	19.6476i	−0.681259	−	0.940949i
$437$	3.79747	+	3.79747i	0.181658	+	0.181658i
$438$	−37.9080	+	12.2823i	−1.81131	+	0.586873i
$439$	21.8570			1.04318			0.521590	−	0.853197i	$-0.325339\pi$
$439$	21.8570			1.04318			0.521590	+	0.853197i	$0.325339\pi$
$440$	−5.63082	−	8.05651i	−0.268439	−	0.384079i
$441$	−11.9930			−0.571097
$442$	2.86331	−	0.927724i	0.136194	−	0.0441274i
$443$	−1.78277	−	1.78277i	−0.0847021	−	0.0847021i	0.663486	−	0.748188i	$-0.269076\pi$
$443$	−1.78277	−	1.78277i	−0.0847021	−	0.0847021i	−0.748188	+	0.663486i	$0.769076\pi$
$444$	12.3859	+	17.1073i	0.587809	+	0.811876i
$445$	3.30053	−	9.63609i	0.156460	−	0.456795i
$446$	8.51781	+	4.34894i	0.403330	+	0.205928i
$447$	−10.6887	+	10.6887i	−0.505557	+	0.505557i
$448$	13.6800	+	7.05620i	0.646319	+	0.333374i
$449$		−	9.43772i		−	0.445394i	−0.974888	−	0.222697i	$-0.928514\pi$
$449$		−	9.43772i		−	0.445394i	0.974888	−	0.222697i	$-0.0714860\pi$
$450$	8.73651	−	24.1845i	0.411843	−	1.14007i
$451$			8.67181i			0.408339i
$452$	−4.45588	+	27.8347i	−0.209587	+	1.30923i
$453$	14.5795	−	14.5795i	0.685006	−	0.685006i
$454$	3.78537	−	7.41401i	0.177656	−	0.347957i
$455$	4.16489	−	12.1597i	0.195253	−	0.570053i
$456$	7.19954	−	1.12196i	0.337150	−	0.0525404i
$457$	14.1913	+	14.1913i	0.663842	+	0.663842i	0.956283	−	0.292441i	$-0.0944676\pi$
$457$	14.1913	+	14.1913i	0.663842	+	0.663842i	−0.292441	+	0.956283i	$0.594468\pi$
$458$	10.4502	+	32.2534i	0.488306	+	1.50710i
$459$	1.16820			0.0545268
$460$	21.2056	+	11.2763i	0.988717	+	0.525759i
$461$	−30.7713			−1.43316			−0.716582	−	0.697503i	$-0.754294\pi$
$461$	−30.7713			−1.43316			−0.716582	+	0.697503i	$0.754294\pi$
$462$	−3.35791	−	10.3638i	−0.156224	−	0.482168i
$463$	−19.8356	−	19.8356i	−0.921839	−	0.921839i	0.0753202	−	0.997159i	$-0.476002\pi$
$463$	−19.8356	−	19.8356i	−0.921839	−	0.921839i	−0.997159	+	0.0753202i	$0.976002\pi$
$464$	10.7844	+	3.54364i	0.500655	+	0.164509i
$465$	22.7801	−	11.1563i	1.05640	−	0.517360i
$466$	−13.8990	+	27.2225i	−0.643857	+	1.26106i
$467$	15.9671	−	15.9671i	0.738868	−	0.738868i	−0.233491	−	0.972359i	$-0.575015\pi$
$467$	15.9671	−	15.9671i	0.738868	−	0.738868i	0.972359	+	0.233491i	$0.0750150\pi$
$468$	−21.4548	−	3.43457i	−0.991749	−	0.158763i
$469$		−	0.645058i		−	0.0297860i
$470$	−29.4337	+	28.4688i	−1.35768	+	1.31317i
$471$		−	13.2903i		−	0.612384i
$472$	−15.7342	+	21.5434i	−0.724224	+	0.991615i
$473$	−7.93207	+	7.93207i	−0.364717	+	0.364717i
$474$	−40.3357	−	20.5942i	−1.85268	−	0.945923i
$475$	3.95000	+	3.06553i	0.181238	+	0.140656i
$476$	−2.22055	+	1.60771i	−0.101779	+	0.0736891i
$477$	20.0740	+	20.0740i	0.919125	+	0.919125i
$478$	−5.19365	+	1.68276i	−0.237552	+	0.0769678i
$479$	36.8494			1.68369			0.841845	−	0.539720i	$-0.181470\pi$
$479$	36.8494			1.68369			0.841845	+	0.539720i	$0.181470\pi$
$480$	29.3240	−	14.2108i	1.33845	−	0.648629i
$481$	12.2463			0.558382
$482$	8.66082	−	2.80614i	0.394490	−	0.127816i
$483$	18.8229	+	18.8229i	0.856473	+	0.856473i
$484$	13.9070	−	10.0688i	0.632136	−	0.457675i
$485$	19.3548	+	39.5208i	0.878858	+	1.79455i
$486$	27.8882	+	14.2389i	1.26503	+	0.645888i
$487$	2.71997	−	2.71997i	0.123253	−	0.123253i	−0.642789	−	0.766043i	$-0.722223\pi$
$487$	2.71997	−	2.71997i	0.123253	−	0.123253i	0.766043	+	0.642789i	$0.222223\pi$
$488$	21.1615	−	28.9745i	0.957936	−	1.31162i
$489$			27.9644i			1.26459i
$490$	0.173770	−	10.4275i	0.00785011	−	0.471068i
$491$			13.3446i			0.602234i	0.953587	+	0.301117i	$0.0973594\pi$
$491$			13.3446i			0.602234i	−0.953587	+	0.301117i	$0.902641\pi$
$492$	−28.3875	−	4.54437i	−1.27981	−	0.204876i
$493$	−1.42960	+	1.42960i	−0.0643860	+	0.0643860i
$494$	1.92119	−	3.76283i	0.0864383	−	0.169298i
$495$	−11.9556	−	4.09501i	−0.537366	−	0.184057i
$496$	16.7332	+	5.49834i	0.751343	+	0.246883i
$497$	−16.0892	−	16.0892i	−0.721699	−	0.721699i
$498$	−1.54440	−	4.76663i	−0.0692064	−	0.213598i
$499$	22.8419			1.02255			0.511273	−	0.859418i	$-0.329174\pi$
$499$	22.8419			1.02255			0.511273	+	0.859418i	$0.329174\pi$
$500$	20.9010	+	7.94651i	0.934722	+	0.355379i
$501$	9.34081			0.417317
$502$	9.24449	+	28.5320i	0.412602	+	1.27345i
$503$	18.6666	+	18.6666i	0.832302	+	0.832302i	0.987831	−	0.155529i	$-0.0497082\pi$
$503$	18.6666	+	18.6666i	0.832302	+	0.832302i	−0.155529	+	0.987831i	$0.549708\pi$
$504$	19.5544	−	3.04729i	0.871020	−	0.135737i
$505$	−40.7262	−	13.9494i	−1.81229	−	0.620742i
$506$	5.36743	−	10.5126i	0.238611	−	0.467343i
$507$	7.42318	−	7.42318i	0.329675	−	0.329675i
$508$	−1.62398	+	10.1445i	−0.0720524	+	0.450091i
$509$			19.4380i			0.861575i	0.902453	+	0.430787i	$0.141764\pi$
$509$			19.4380i			0.861575i	−0.902453	+	0.430787i	$0.858236\pi$
$510$	−0.0967009	+	5.80281i	−0.00428199	+	0.256953i
$511$		−	21.0448i		−	0.930966i
$512$	21.4672	+	7.15256i	0.948725	+	0.316102i
$513$	1.15951	−	1.15951i	0.0511934	−	0.0511934i
$514$	−7.15895	−	3.65514i	−0.315768	−	0.161222i
$515$	−14.9443	−	30.5148i	−0.658523	−	1.34464i
$516$	−21.8092	−	30.1226i	−0.960096	−	1.32608i
$517$	14.2304	+	14.2304i	0.625852	+	0.625852i
$518$	−10.6111	+	3.43804i	−0.466226	+	0.151059i
$519$	−11.4469			−0.502462
$520$	3.29711	−	18.6045i	0.144588	−	0.815860i
$521$	22.4977			0.985643			0.492821	−	0.870130i	$-0.335966\pi$
$521$	22.4977			0.985643			0.492821	+	0.870130i	$0.335966\pi$
$522$	13.8844	−	4.49859i	0.607703	−	0.196898i
$523$	28.0028	+	28.0028i	1.22448	+	1.22448i	0.966023	+	0.258455i	$0.0832134\pi$
$523$	28.0028	+	28.0028i	1.22448	+	1.22448i	0.258455	+	0.966023i	$0.416787\pi$
$524$	6.57898	+	9.08682i	0.287404	+	0.396960i
$525$	19.5790	+	15.1949i	0.854496	+	0.663161i
$526$	−31.7470	−	16.2091i	−1.38423	−	0.706748i
$527$	−2.21818	+	2.21818i	−0.0966254	+	0.0966254i
$528$	−7.22319	−	14.2932i	−0.314349	−	0.622034i
$529$			5.84161i			0.253983i
$530$	−17.7445	+	17.1628i	−0.770772	+	0.745504i
$531$			34.2993i			1.48846i
$532$	−0.608282	+	3.79977i	−0.0263724	+	0.164741i
$533$	−11.7871	+	11.7871i	−0.510557	+	0.510557i
$534$	7.54644	−	14.7804i	0.326566	−	0.639612i
$535$	17.8957	−	8.76419i	0.773697	−	0.378909i
$536$	−0.146010	−	0.936939i	−0.00630666	−	0.0404696i
$537$	0.559272	+	0.559272i	0.0241344	+	0.0241344i
$538$	−5.89607	−	18.1975i	−0.254197	−	0.784551i
$539$	−5.12544			−0.220768
$540$	3.44305	−	6.47484i	0.148165	−	0.278633i
$541$	−26.0323			−1.11922			−0.559609	−	0.828757i	$-0.689049\pi$
$541$	−26.0323			−1.11922			−0.559609	+	0.828757i	$0.689049\pi$
$542$	6.97632	+	21.5316i	0.299658	+	0.924861i
$543$	−39.2858	−	39.2858i	−1.68592	−	1.68592i
$544$	−2.86141	+	2.83780i	−0.122682	+	0.121670i
$545$	8.78778	−	25.6564i	0.376427	−	1.09900i
$546$	9.52275	−	18.6512i	0.407536	−	0.798199i
$547$	10.1318	−	10.1318i	0.433205	−	0.433205i	−0.456512	−	0.889717i	$-0.650902\pi$
$547$	10.1318	−	10.1318i	0.433205	−	0.433205i	0.889717	+	0.456512i	$0.150902\pi$
$548$	4.17743	+	0.668739i	0.178451	+	0.0285671i
$549$		−	46.1304i		−	1.96880i
$550$	3.73370	−	10.3357i	0.159206	−	0.440715i
$551$			2.83793i			0.120900i
$552$	31.6007	+	23.0795i	1.34501	+	0.982328i
$553$	16.9128	−	16.9128i	0.719203	−	0.719203i
$554$	−29.1520	−	14.8841i	−1.23855	−	0.632365i
$555$	−7.65158	+	22.3392i	−0.324791	+	0.948248i
$556$	−16.8337	+	12.1879i	−0.713910	+	0.516880i
$557$	−24.1253	−	24.1253i	−1.02222	−	1.02222i	−0.999747	−	0.0224738i	$-0.992846\pi$
$557$	−24.1253	−	24.1253i	−1.02222	−	1.02222i	−0.0224738	−	0.999747i	$-0.507154\pi$
$558$	21.5431	−	6.98005i	0.911992	−	0.295489i
$559$	−21.5633			−0.912031
$560$	2.36619	+	17.0460i	0.0999898	+	0.720325i
$561$	2.85225			0.120422
$562$	−11.8664	+	3.84477i	−0.500555	+	0.162182i
$563$	−8.87395	−	8.87395i	−0.373992	−	0.373992i	0.494937	−	0.868929i	$-0.335191\pi$
$563$	−8.87395	−	8.87395i	−0.373992	−	0.373992i	−0.868929	+	0.494937i	$0.835191\pi$
$564$	−54.0410	+	39.1264i	−2.27554	+	1.64752i
$565$	−28.3043	+	13.8617i	−1.19077	+	0.583166i
$566$	19.0922	+	9.74790i	0.802505	+	0.409735i
$567$	−9.09546	+	9.09546i	−0.381973	+	0.381973i
$568$	−27.0112	−	19.7275i	−1.13336	−	0.827750i
$569$		−	26.0482i		−	1.09200i	−0.837785	−	0.546000i	$-0.816150\pi$
$569$		−	26.0482i		−	1.09200i	0.837785	−	0.546000i	$-0.183850\pi$
$570$	5.66366	+	5.85562i	0.237224	+	0.245265i
$571$		−	6.33339i		−	0.265044i	−0.991180	−	0.132522i	$-0.957692\pi$
$571$		−	6.33339i		−	0.265044i	0.991180	−	0.132522i	$-0.0423076\pi$
$572$	−9.16910	−	1.46783i	−0.383379	−	0.0613729i
$573$	30.2186	−	30.2186i	1.26240	−	1.26240i
$574$	6.90415	−	13.5224i	0.288174	−	0.564416i
$575$	3.35874	+	26.6413i	0.140069	+	1.11102i
$576$	27.7127	−	8.85231i	1.15470	−	0.368846i
$577$	−30.3721	−	30.3721i	−1.26441	−	1.26441i	−0.948934	−	0.315474i	$-0.897836\pi$
$577$	−30.3721	−	30.3721i	−1.26441	−	1.26441i	−0.315474	−	0.948934i	$-0.602164\pi$
$578$	7.18909	+	22.1883i	0.299027	+	0.922911i
$579$	−11.4445			−0.475617
$580$	3.71020	+	12.1372i	0.154058	+	0.503969i
$581$	2.64621			0.109783
$582$	22.0995	+	68.2075i	0.916054	+	2.82729i
$583$	8.57898	+	8.57898i	0.355305	+	0.355305i
$584$	−4.76351	−	30.5673i	−0.197116	−	1.26488i
$585$	−10.6845	−	21.8168i	−0.441751	−	0.902014i
$586$	−4.30562	+	8.43296i	−0.177863	+	0.348362i
$587$	−5.54610	+	5.54610i	−0.228912	+	0.228912i	−0.812238	−	0.583326i	$-0.801751\pi$
$587$	−5.54610	+	5.54610i	−0.228912	+	0.228912i	0.583326	+	0.812238i	$0.301751\pi$
$588$	2.68593	−	16.7783i	0.110766	−	0.691925i
$589$			4.40335i			0.181437i
$590$	−29.8221	−	0.496969i	−1.22775	−	0.0204599i
$591$			11.0984i			0.456527i
$592$	−14.6343	+	7.39556i	−0.601467	+	0.303956i
$593$	33.0633	−	33.0633i	1.35775	−	1.35775i	0.481057	−	0.876689i	$-0.340253\pi$
$593$	33.0633	−	33.0633i	1.35775	−	1.35775i	0.876689	−	0.481057i	$-0.159747\pi$
$594$	−3.20988	−	1.63887i	−0.131703	−	0.0672436i
$595$	−2.89966	−	0.993184i	−0.118874	−	0.0407166i
$596$	−6.88216	−	9.50557i	−0.281904	−	0.389363i
$597$	8.20794	+	8.20794i	0.335929	+	0.335929i
$598$	21.5849	−	6.99359i	0.882673	−	0.285989i
$599$	−7.71075			−0.315053			−0.157526	−	0.987515i	$-0.550352\pi$
$599$	−7.71075			−0.315053			−0.157526	+	0.987515i	$0.550352\pi$
$600$	31.8776	+	17.6387i	1.30140	+	0.720098i
$601$	10.0646			0.410543			0.205272	−	0.978705i	$-0.434192\pi$
$601$	10.0646			0.410543			0.205272	+	0.978705i	$0.434192\pi$
$602$	18.6841	−	6.05373i	0.761508	−	0.246732i
$603$	−0.862082	−	0.862082i	−0.0351067	−	0.0351067i
$604$	9.38737	+	12.9657i	0.381967	+	0.527569i
$605$	18.1602	+	6.22018i	0.738316	+	0.252886i
$606$	−62.4683	−	31.8944i	−2.53760	−	1.29562i
$607$	2.42796	−	2.42796i	0.0985480	−	0.0985480i	−0.656114	−	0.754662i	$-0.727801\pi$
$607$	2.42796	−	2.42796i	0.0985480	−	0.0985480i	0.754662	+	0.656114i	$0.227801\pi$
$608$	−0.0234394	+	5.65681i	−0.000950591	+	0.229414i
$609$			14.0668i			0.570014i
$610$	40.1088	+	0.668393i	1.62396	+	0.0270625i
$611$			38.6853i			1.56504i
$612$	−0.819027	+	5.11624i	−0.0331072	+	0.206812i
$613$	14.7300	−	14.7300i	0.594939	−	0.594939i	−0.344022	−	0.938961i	$-0.611790\pi$
$613$	14.7300	−	14.7300i	0.594939	−	0.594939i	0.938961	+	0.344022i	$0.111790\pi$
$614$	−18.3530	+	35.9462i	−0.740668	+	1.45067i
$615$	−14.1370	−	28.8664i	−0.570058	−	1.16401i
$616$	8.35691	−	1.30231i	0.336709	−	0.0524718i
$617$	−24.8801	−	24.8801i	−1.00163	−	1.00163i	−0.999999	−	0.00163535i	$-0.999479\pi$
$617$	−24.8801	−	24.8801i	−1.00163	−	1.00163i	−0.00163535	−	0.999999i	$-0.500521\pi$
$618$	−17.0635	−	52.6644i	−0.686394	−	2.11847i
$619$	33.6028			1.35061			0.675306	−	0.737537i	$-0.264011\pi$
$619$	33.6028			1.35061			0.675306	+	0.737537i	$0.264011\pi$
$620$	5.75677	+	18.8321i	0.231198	+	0.756317i
$621$	8.80639			0.353388
$622$	14.6717	+	45.2825i	0.588282	+	1.81566i
$623$	6.19743	+	6.19743i	0.248295	+	0.248295i
$624$	9.60995	−	29.2462i	0.384706	−	1.17078i
$625$	6.20502	+	24.2177i	0.248201	+	0.968709i
$626$	−12.0837	+	23.6670i	−0.482961	+	0.945925i
$627$	2.83103	−	2.83103i	0.113060	−	0.113060i
$628$	10.1882	+	1.63097i	0.406555	+	0.0650829i
$629$		−	2.92031i		−	0.116441i
$630$	15.3828	+	15.9042i	0.612865	+	0.633638i
$631$			30.0536i			1.19642i	0.801341	+	0.598208i	$0.204120\pi$
$631$			30.0536i			1.19642i	−0.801341	+	0.598208i	$0.795880\pi$
$632$	20.7373	−	28.3938i	0.824887	−	1.12944i
$633$	−10.3228	+	10.3228i	−0.410295	+	0.410295i
$634$	11.0680	+	5.65096i	0.439565	+	0.224428i
$635$	−10.3157	+	5.05199i	−0.409366	+	0.200482i
$636$	−32.5793	+	23.5879i	−1.29185	+	0.935319i
$637$	−6.96674	−	6.96674i	−0.276032	−	0.276032i
$638$	5.93374	−	1.92255i	0.234919	−	0.0761147i
$639$	−43.0045			−1.70123
$640$	7.29525	+	24.2235i	0.288370	+	0.957519i
$641$	9.06116			0.357894			0.178947	−	0.983859i	$-0.442731\pi$
$641$	9.06116			0.357894			0.178947	+	0.983859i	$0.442731\pi$
$642$	30.8855	−	10.0070i	1.21895	−	0.394946i
$643$	−16.3493	−	16.3493i	−0.644754	−	0.644754i	0.306966	−	0.951720i	$-0.400686\pi$
$643$	−16.3493	−	16.3493i	−0.644754	−	0.644754i	−0.951720	+	0.306966i	$0.900686\pi$
$644$	−16.7395	+	12.1196i	−0.659627	+	0.477579i
$645$	13.4730	−	39.3351i	0.530497	−	1.54882i
$646$	−0.897306	−	0.458137i	−0.0353040	−	0.0180252i
$647$	19.2785	−	19.2785i	0.757918	−	0.757918i	−0.218025	−	0.975943i	$-0.569962\pi$
$647$	19.2785	−	19.2785i	0.757918	−	0.757918i	0.975943	+	0.218025i	$0.0699616\pi$
$648$	−11.1523	+	15.2698i	−0.438103	+	0.599855i
$649$			14.6584i			0.575393i
$650$	19.1238	−	8.97372i	0.750096	−	0.351978i
$651$			21.8261i			0.855431i
$652$	−21.4373	−	3.43177i	−0.839550	−	0.134398i
$653$	−11.7195	+	11.7195i	−0.458618	+	0.458618i	−0.898202	−	0.439584i	$-0.855126\pi$
$653$	−11.7195	+	11.7195i	−0.458618	+	0.458618i	0.439584	+	0.898202i	$0.355126\pi$
$654$	20.0927	−	39.3534i	0.785685	−	1.53884i
$655$	−4.06426	+	11.8659i	−0.158804	+	0.463637i
$656$	6.96737	−	21.2039i	0.272030	−	0.827875i
$657$	−28.1251	−	28.1251i	−1.09727	−	1.09727i
$658$	−10.8606	−	33.5199i	−0.423390	−	1.30674i
$659$	14.1085			0.549589			0.274795	−	0.961503i	$-0.411390\pi$
$659$	14.1085			0.549589			0.274795	+	0.961503i	$0.411390\pi$
$660$	8.40650	−	15.8089i	0.327222	−	0.615359i
$661$	−16.3969			−0.637767			−0.318883	−	0.947794i	$-0.603308\pi$
$661$	−16.3969			−0.637767			−0.318883	+	0.947794i	$0.603308\pi$
$662$	−3.88803	−	12.0000i	−0.151113	−	0.466392i
$663$	3.87692	+	3.87692i	0.150567	+	0.150567i
$664$	3.84359	−	0.598973i	0.149160	−	0.0232447i
$665$	−3.86388	+	1.89229i	−0.149835	+	0.0733799i
$666$	−9.58640	+	18.7759i	−0.371465	+	0.727551i
$667$	−10.7770	+	10.7770i	−0.417286	+	0.417286i
$668$	−1.14630	+	7.16060i	−0.0443516	+	0.277052i
$669$			17.4215i			0.673555i
$670$	0.762042	−	0.737060i	0.0294403	−	0.0284751i
$671$		−	19.7147i		−	0.761076i
$672$	−0.116182	+	28.0391i	−0.00448181	+	1.08163i
$673$	−6.64730	+	6.64730i	−0.256235	+	0.256235i	−0.823521	−	0.567286i	$-0.807993\pi$
$673$	−6.64730	+	6.64730i	−0.256235	+	0.256235i	0.567286	+	0.823521i	$0.307993\pi$
$674$	−15.8974	−	8.11672i	−0.612344	−	0.312644i
$675$	8.13455	−	1.02555i	0.313099	−	0.0394733i
$676$	4.77959	+	6.60153i	0.183830	+	0.253905i
$677$	−3.20710	−	3.20710i	−0.123259	−	0.123259i	0.642787	−	0.766045i	$-0.277778\pi$
$677$	−3.20710	−	3.20710i	−0.123259	−	0.123259i	−0.766045	+	0.642787i	$0.777778\pi$
$678$	−48.8494	+	15.8274i	−1.87605	+	0.607847i
$679$	−37.8657			−1.45315
$680$	−4.43653	−	0.786247i	−0.170133	−	0.0301512i
$681$	15.1639			0.581082
$682$	9.20683	−	2.98305i	0.352548	−	0.114227i
$683$	10.8321	+	10.8321i	0.414479	+	0.414479i	0.883296	−	0.468817i	$-0.155319\pi$
$683$	10.8321	+	10.8321i	0.414479	+	0.414479i	−0.468817	+	0.883296i	$0.655319\pi$
$684$	4.26524	+	5.89110i	0.163085	+	0.225252i
$685$	2.08036	+	4.24791i	0.0794866	+	0.162304i
$686$	24.9565	+	12.7421i	0.952845	+	0.486494i
$687$	−43.6709	+	43.6709i	−1.66615	+	1.66615i
$688$	25.7682	−	13.0221i	0.982404	−	0.496465i
$689$			23.3219i			0.888494i
$690$	−0.728974	+	43.7441i	−0.0277516	+	1.66531i
$691$			6.63308i			0.252334i	0.992009	+	0.126167i	$0.0402676\pi$
$691$			6.63308i			0.252334i	−0.992009	+	0.126167i	$0.959732\pi$
$692$	1.40475	−	8.77509i	0.0534006	−	0.333579i
$693$	7.68923	−	7.68923i	0.292090	−	0.292090i
$694$	−4.78688	+	9.37557i	−0.181708	+	0.355892i
$695$	−21.9820	−	7.52923i	−0.833826	−	0.285600i
$696$	3.18403	+	20.4318i	0.120690	+	0.774465i
$697$	2.81083	+	2.81083i	0.106468	+	0.106468i
$698$	9.02003	+	27.8393i	0.341413	+	1.05373i
$699$	−55.6783			−2.10595
$700$	−14.0510	+	13.1444i	−0.531079	+	0.496811i
$701$	7.90872			0.298708			0.149354	−	0.988784i	$-0.452281\pi$
$701$	7.90872			0.298708			0.149354	+	0.988784i	$0.452281\pi$
$702$	−2.13540	−	6.59066i	−0.0805954	−	0.248748i
$703$	−2.89859	−	2.89859i	−0.109322	−	0.109322i
$704$	11.8435	−	3.78319i	0.446370	−	0.142584i
$705$	−70.5684	−	24.1709i	−2.65776	−	0.910329i
$706$	19.3303	−	37.8603i	0.727506	−	1.42489i
$707$	26.1929	−	26.1929i	0.985087	−	0.985087i
$708$	−47.9848	−	7.68159i	−1.80338	−	0.288692i
$709$			19.6967i			0.739724i	0.929087	+	0.369862i	$0.120595\pi$
$709$			19.6967i			0.739724i	−0.929087	+	0.369862i	$0.879405\pi$
$710$	0.623102	−	37.3910i	0.0233846	−	1.40326i
$711$		−	45.2058i		−	1.69535i
$712$	10.4045	+	7.59889i	0.389924	+	0.284780i
$713$	−16.7216	+	16.7216i	−0.626229	+	0.626229i
$714$	−4.44768	−	2.27085i	−0.166450	−	0.0849844i
$715$	−4.56622	−	9.32380i	−0.170767	−	0.348690i
$716$	−0.497367	+	0.360101i	−0.0185875	+	0.0134576i
$717$	−7.03219	−	7.03219i	−0.262622	−	0.262622i
$718$	4.65850	−	1.50937i	0.173854	−	0.0563293i
$719$	18.8983			0.704788			0.352394	−	0.935852i	$-0.385368\pi$
$719$	18.8983			0.704788			0.352394	+	0.935852i	$0.385368\pi$
$720$	25.9433	+	19.6187i	0.966848	+	0.731146i
$721$	29.2369			1.08884
$722$	−1.34536	+	0.435901i	−0.0500691	+	0.0162226i
$723$	11.7267	+	11.7267i	0.436121	+	0.436121i
$724$	34.9374	−	25.2951i	1.29844	−	0.940086i
$725$	−8.69976	+	11.2098i	−0.323101	+	0.416322i
$726$	27.8552	+	14.2220i	1.03380	+	0.527828i
$727$	8.62977	−	8.62977i	0.320060	−	0.320060i	−0.528730	−	0.848790i	$-0.677332\pi$
$727$	8.62977	−	8.62977i	0.320060	−	0.320060i	0.848790	+	0.528730i	$0.177332\pi$
$728$	13.1293	+	9.58894i	0.486603	+	0.355390i
$729$			36.9841i			1.36978i
$730$	24.8614	−	24.0463i	0.920160	−	0.889995i
$731$			5.14211i			0.190188i
$732$	64.5366	+	10.3313i	2.38534	+	0.381855i
$733$	−11.4060	+	11.4060i	−0.421292	+	0.421292i	−0.885648	−	0.464357i	$-0.846286\pi$
$733$	−11.4060	+	11.4060i	−0.421292	+	0.421292i	0.464357	+	0.885648i	$0.346286\pi$
$734$	3.31854	−	6.49968i	0.122490	−	0.239908i
$735$	17.0614	−	8.35561i	0.629318	−	0.308201i
$736$	−21.5706	+	21.3926i	−0.795102	+	0.788540i
$737$	−0.368426	−	0.368426i	−0.0135712	−	0.0135712i
$738$	−8.84496	−	27.2989i	−0.325587	−	1.00489i
$739$	17.0455			0.627028			0.313514	−	0.949584i	$-0.398494\pi$
$739$	17.0455			0.627028			0.313514	+	0.949584i	$0.398494\pi$
$740$	−16.1861	−	8.60710i	−0.595013	−	0.316403i
$741$	7.69614			0.282725
$742$	−6.54744	−	20.2079i	−0.240364	−	0.741856i
$743$	9.28212	+	9.28212i	0.340528	+	0.340528i	0.856566	−	0.516038i	$-0.172594\pi$
$743$	9.28212	+	9.28212i	0.340528	+	0.340528i	−0.516038	+	0.856566i	$0.672594\pi$
$744$	4.94036	+	31.7021i	0.181122	+	1.16226i
$745$	4.25156	−	12.4127i	0.155765	−	0.454765i
$746$	15.5481	−	30.4524i	0.569256	−	1.11494i
$747$	3.53651	−	3.53651i	0.129394	−	0.129394i
$748$	−0.350026	+	2.18652i	−0.0127982	+	0.0799469i
$749$			17.1462i			0.626509i
$750$	4.42085	+	40.4918i	0.161427	+	1.47855i
$751$			17.9990i			0.656793i	0.944540	+	0.328397i	$0.106508\pi$
$751$			17.9990i			0.656793i	−0.944540	+	0.328397i	$0.893492\pi$
$752$	−23.3622	−	46.2290i	−0.851930	−	1.68580i
$753$	−38.6323	+	38.6323i	−1.40784	+	1.40784i
$754$	10.6786	+	5.45220i	0.388893	+	0.198557i
$755$	−5.79919	+	16.9311i	−0.211054	+	0.616185i
$756$	3.70055	+	5.11116i	0.134588	+	0.185891i
$757$	0.425732	+	0.425732i	0.0154735	+	0.0154735i	0.714801	−	0.699328i	$-0.246517\pi$
$757$	0.425732	+	0.425732i	0.0154735	+	0.0154735i	−0.699328	+	0.714801i	$0.746517\pi$
$758$	40.5381	−	13.1345i	1.47241	−	0.477066i
$759$	21.5015			0.780456
$760$	−5.18392	+	3.62312i	−0.188040	+	0.131424i
$761$	−6.38301			−0.231384			−0.115692	−	0.993285i	$-0.536909\pi$
$761$	−6.38301			−0.231384			−0.115692	+	0.993285i	$0.536909\pi$
$762$	−17.8035	+	5.76840i	−0.644953	+	0.208967i
$763$	16.5009	+	16.5009i	0.597371	+	0.597371i
$764$	19.4570	+	26.8738i	0.703929	+	0.972259i
$765$	−5.20256	+	2.54789i	−0.188099	+	0.0921192i
$766$	7.20669	+	3.67952i	0.260388	+	0.132946i
$767$	−19.9244	+	19.9244i	−0.719429	+	0.719429i
$768$	6.17793	+	40.7527i	0.222927	+	1.47054i
$769$		−	7.71179i		−	0.278094i	−0.990286	−	0.139047i	$-0.955596\pi$
$769$		−	7.71179i		−	0.278094i	0.990286	−	0.139047i	$-0.0444039\pi$
$770$	6.57412	+	6.79694i	0.236915	+	0.244945i
$771$		−	14.6422i		−	0.527328i
$772$	1.40446	−	8.77328i	0.0505476	−	0.315757i
$773$	22.4912	−	22.4912i	0.808951	−	0.808951i	−0.175524	−	0.984475i	$-0.556162\pi$
$773$	22.4912	−	22.4912i	0.808951	−	0.808951i	0.984475	+	0.175524i	$0.0561619\pi$
$774$	16.8798	−	33.0607i	0.606732	−	1.18834i
$775$	−13.4986	+	17.3932i	−0.484885	+	0.624784i
$776$	−54.9994	+	8.57095i	−1.97437	+	0.307679i
$777$	−14.3674	−	14.3674i	−0.515428	−	0.515428i
$778$	−6.86592	−	21.1909i	−0.246155	−	0.759729i
$779$	5.57983			0.199918
$780$	32.9147	−	10.0616i	1.17853	−	0.360265i
$781$	−18.3788			−0.657644
$782$	−1.66773	−	5.14726i	−0.0596380	−	0.184066i
$783$	3.29060	+	3.29060i	0.117596	+	0.117596i
$784$	12.5325	+	4.11804i	0.447590	+	0.147073i
$785$	5.07376	+	10.3601i	0.181090	+	0.369769i
$786$	−9.29266	+	18.2006i	−0.331458	+	0.649193i
$787$	33.4301	−	33.4301i	1.19166	−	1.19166i	0.215054	−	0.976602i	$-0.431007\pi$
$787$	33.4301	−	33.4301i	1.19166	−	1.19166i	0.976602	−	0.215054i	$-0.0689926\pi$
$788$	−8.50795	−	1.36199i	−0.303083	−	0.0485187i
$789$		−	64.9323i		−	2.31165i
$790$	39.3049	+	0.654997i	1.39841	+	0.0233037i
$791$		−	27.1189i		−	0.964238i
$792$	9.42805	−	12.9090i	0.335011	−	0.458701i
$793$	26.7971	−	26.7971i	0.951593	−	0.951593i
$794$	0.267161	+	0.136404i	0.00948119	+	0.00484081i
$795$	−42.5431	−	14.5717i	−1.50885	−	0.516807i
$796$	−7.29942	+	5.28488i	−0.258721	+	0.187318i
$797$	−25.0586	−	25.0586i	−0.887621	−	0.887621i	0.106674	−	0.994294i	$-0.465980\pi$
$797$	−25.0586	−	25.0586i	−0.887621	−	0.887621i	−0.994294	+	0.106674i	$0.965980\pi$
$798$	−6.66854	+	2.16063i	−0.236064	+	0.0764855i
$799$	9.22511			0.326361
$800$	−17.4337	+	22.2725i	−0.616375	+	0.787453i
$801$	16.5650			0.585295
$802$	−29.7231	+	9.63038i	−1.04956	+	0.340061i
$803$	−12.0198	−	12.0198i	−0.424169	−	0.424169i
$804$	1.39913	−	1.01299i	0.0493434	−	0.0357253i
$805$	−21.8589	−	7.48706i	−0.770425	−	0.263884i
$806$	16.5691	+	8.45966i	0.583621	+	0.297979i
$807$	24.6394	−	24.6394i	0.867347	−	0.867347i
$808$	32.1161	−	43.9737i	1.12984	−	1.54699i
$809$			21.0772i			0.741034i	0.928826	+	0.370517i	$0.120819\pi$
$809$			21.0772i			0.741034i	−0.928826	+	0.370517i	$0.879181\pi$
$810$	−21.1377	−	0.352249i	−0.742702	−	0.0123768i
$811$			13.1083i			0.460295i	0.973156	+	0.230148i	$0.0739209\pi$
$811$			13.1083i			0.460295i	−0.973156	+	0.230148i	$0.926079\pi$
$812$	−10.7835	−	1.72626i	−0.378426	−	0.0605799i
$813$	−29.1537	+	29.1537i	−1.02246	+	1.02246i
$814$	−4.09692	+	8.02421i	−0.143597	+	0.281249i
$815$	−10.6758	−	21.7990i	−0.373957	−	0.763586i
$816$	−6.97421	−	2.29164i	−0.244146	−	0.0802236i
$817$	5.10385	+	5.10385i	0.178561	+	0.178561i
$818$	11.7877	+	36.3813i	0.412146	+	1.27204i
$819$	20.9031			0.730415
$820$	23.8637	−	7.29485i	0.833355	−	0.254747i
$821$	−7.43302			−0.259414			−0.129707	−	0.991552i	$-0.541404\pi$
$821$	−7.43302			−0.259414			−0.129707	+	0.991552i	$0.541404\pi$
$822$	2.37538	+	7.33132i	0.0828508	+	0.255709i
$823$	11.5081	+	11.5081i	0.401147	+	0.401147i	0.878637	−	0.477490i	$-0.158453\pi$
$823$	11.5081	+	11.5081i	0.401147	+	0.401147i	−0.477490	+	0.878637i	$0.658453\pi$
$824$	42.4662	−	6.61780i	1.47938	−	0.230542i
$825$	19.8612	−	2.50396i	0.691478	−	0.0871765i
$826$	11.6704	−	22.8577i	0.406067	−	0.795320i
$827$	−29.4735	+	29.4735i	−1.02489	+	1.02489i	−0.0252107	+	0.999682i	$0.508026\pi$
$827$	−29.4735	+	29.4735i	−1.02489	+	1.02489i	−0.999682	+	0.0252107i	$0.991974\pi$
$828$	−6.17418	+	38.5684i	−0.214568	+	1.34035i
$829$		−	28.2563i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$829$		−	28.2563i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$830$	3.02363	+	3.12611i	0.104952	+	0.108509i
$831$		−	59.6247i		−	2.06836i
$832$	21.2406	+	10.9560i	0.736385	+	0.379830i
$833$	−1.66133	+	1.66133i	−0.0575616	+	0.0575616i
$834$	−33.7174	−	17.2151i	−1.16754	−	0.596109i
$835$	−7.28141	+	3.56599i	−0.251984	+	0.123406i
$836$	1.82283	+	2.51767i	0.0630438	+	0.0870754i
$837$	5.10571	+	5.10571i	0.176479	+	0.176479i
$838$	3.09284	−	1.00209i	0.106840	−	0.0346167i
$839$	2.63772			0.0910641			0.0455320	−	0.998963i	$-0.485502\pi$
$839$	2.63772			0.0910641			0.0455320	+	0.998963i	$0.485502\pi$
$840$	−25.6951	+	17.9587i	−0.886565	+	0.619635i
$841$	20.9462			0.722281
$842$	−42.1579	+	13.6593i	−1.45286	+	0.470731i
$843$	−16.0671	−	16.0671i	−0.553381	−	0.553381i
$844$	−6.64659	−	9.18021i	−0.228785	−	0.315996i
$845$	−2.95266	+	8.62047i	−0.101575	+	0.296553i
$846$	−59.3120	−	30.2829i	−2.03919	−	1.04115i
$847$	−11.6797	+	11.6797i	−0.401318	+	0.401318i
$848$	−14.0842	−	27.8698i	−0.483653	−	0.957051i
$849$			39.0494i			1.34017i
$850$	−2.13993	−	4.56036i	−0.0733988	−	0.156419i
$851$		−	22.0146i		−	0.754651i
$852$	9.63120	−	60.1635i	0.329960	−	2.06117i
$853$	2.38585	−	2.38585i	0.0816900	−	0.0816900i	−0.665081	−	0.746771i	$-0.731603\pi$
$853$	2.38585	−	2.38585i	0.0816900	−	0.0816900i	0.746771	+	0.665081i	$0.231603\pi$
$854$	−15.6960	+	30.7422i	−0.537107	+	1.05198i
$855$	−2.63491	+	7.69278i	−0.0901121	+	0.263088i
$856$	3.88107	+	24.9047i	0.132652	+	0.851224i
$857$	−31.3170	−	31.3170i	−1.06977	−	1.06977i	−0.997376	−	0.0723910i	$-0.976937\pi$
$857$	−31.3170	−	31.3170i	−1.06977	−	1.06977i	−0.0723910	−	0.997376i	$-0.523063\pi$
$858$	−5.21375	−	16.0916i	−0.177994	−	0.549359i
$859$	−15.2480			−0.520255			−0.260128	−	0.965574i	$-0.583765\pi$
$859$	−15.2480			−0.520255			−0.260128	+	0.965574i	$0.583765\pi$
$860$	28.5006	+	15.1554i	0.971862	+	0.516796i
$861$	27.6575			0.942566
$862$	−10.4577	−	32.2765i	−0.356191	−	1.09934i
$863$	−20.5774	−	20.5774i	−0.700463	−	0.700463i	0.264047	−	0.964510i	$-0.414943\pi$
$863$	−20.5774	−	20.5774i	−0.700463	−	0.700463i	−0.964510	+	0.264047i	$0.914943\pi$
$864$	6.53192	+	6.58628i	0.222221	+	0.224070i
$865$	8.92314	−	4.37001i	0.303396	−	0.148585i
$866$	13.1374	−	25.7308i	0.446425	−	0.874367i
$867$	−30.0429	+	30.0429i	−1.02031	+	1.02031i
$868$	−16.7317	−	2.67848i	−0.567912	−	0.0909135i
$869$		−	19.3195i		−	0.655370i
$870$	−16.6178	+	16.0731i	−0.563397	+	0.544928i
$871$		−	1.00157i		−	0.0339367i
$872$	27.7023	+	20.2323i	0.938118	+	0.685152i
$873$	−50.6053	+	50.6053i	−1.71273	+	1.71273i
$874$	−6.76429	−	3.45364i	−0.228805	−	0.116821i
$875$	−21.0632	−	4.37030i	−0.712066	−	0.147743i
$876$	45.6460	−	33.0483i	1.54223	−	1.11660i
$877$	−23.8806	−	23.8806i	−0.806391	−	0.806391i	0.177694	−	0.984086i	$-0.443136\pi$
$877$	−23.8806	−	23.8806i	−0.806391	−	0.806391i	−0.984086	+	0.177694i	$0.943136\pi$
$878$	−29.4055	+	9.52751i	−0.992389	+	0.321538i
$879$	−17.2480			−0.581760
$880$	11.0873	+	8.38441i	0.373754	+	0.282638i
$881$	47.3330			1.59469			0.797345	−	0.603524i	$-0.206237\pi$
$881$	47.3330			1.59469			0.797345	+	0.603524i	$0.206237\pi$
$882$	16.1349	−	5.22778i	0.543291	−	0.176028i
$883$	10.3674	+	10.3674i	0.348891	+	0.348891i	0.859696	−	0.510806i	$-0.170653\pi$
$883$	10.3674	+	10.3674i	0.348891	+	0.348891i	−0.510806	+	0.859696i	$0.670653\pi$
$884$	−3.44779	+	2.49624i	−0.115962	+	0.0839578i
$885$	−23.8965	−	48.7944i	−0.803272	−	1.64021i
$886$	3.17558	+	1.62136i	0.106686	+	0.0544706i
$887$	33.1947	−	33.1947i	1.11457	−	1.11457i	0.122043	−	0.992525i	$-0.461055\pi$
$887$	33.1947	−	33.1947i	1.11457	−	1.11457i	0.992525	−	0.122043i	$-0.0389447\pi$
$888$	−24.1206	−	17.6164i	−0.809434	−	0.591168i
$889$		−	9.88369i		−	0.331488i
$890$	−0.240014	+	14.4027i	−0.00804528	+	0.482780i
$891$			10.3898i			0.348071i
$892$	−13.3552	−	2.13795i	−0.447166	−	0.0715840i
$893$	9.15647	−	9.15647i	0.306410	−	0.306410i
$894$	9.72090	−	19.0393i	0.325115	−	0.636770i
$895$	−0.649478	−	0.222458i	−0.0217096	−	0.00743594i
$896$	−21.4803	−	3.53000i	−0.717607	−	0.117929i
$897$	29.2259	+	29.2259i	0.975824	+	0.975824i
$898$	4.11392	+	12.6971i	0.137283	+	0.423708i
$899$	−12.4964			−0.416778
$900$	−1.21168	+	36.3451i	−0.0403894	+	1.21150i
$901$	5.56148			0.185280
$902$	−3.78005	−	11.6667i	−0.125862	−	0.388458i
$903$	25.2982	+	25.2982i	0.841873	+	0.841873i
$904$	−6.13841	−	39.3899i	−0.204160	−	1.31009i
$905$	45.6223	+	15.6264i	1.51654	+	0.519440i
$906$	−13.2595	+	25.9699i	−0.440516	+	0.862793i
$907$	−10.5021	+	10.5021i	−0.348718	+	0.348718i	−0.859632	−	0.510914i	$-0.829307\pi$
$907$	−10.5021	+	10.5021i	−0.348718	+	0.348718i	0.510914	+	0.859632i	$0.329307\pi$
$908$	−1.86090	+	11.6246i	−0.0617562	+	0.385774i
$909$		−	70.0106i		−	2.32211i
$910$	−0.302870	+	18.1746i	−0.0100400	+	0.602481i
$911$		−	43.2726i		−	1.43369i	−0.697235	−	0.716843i	$-0.745586\pi$
$911$		−	43.2726i		−	1.43369i	0.697235	−	0.716843i	$-0.254414\pi$
$912$	−9.19691	+	4.64772i	−0.304540	+	0.153901i
$913$	1.51139	−	1.51139i	0.0500197	−	0.0500197i
$914$	−25.2784	−	12.9064i	−0.836137	−	0.426906i
$915$	32.1393	+	65.6254i	1.06249	+	2.16951i
$916$	−28.1186	−	38.8371i	−0.929064	−	1.28321i
$917$	−7.63149	−	7.63149i	−0.252014	−	0.252014i
$918$	−1.57164	+	0.509219i	−0.0518720	+	0.0168067i
$919$	24.4807			0.807543			0.403772	−	0.914860i	$-0.367699\pi$
$919$	24.4807			0.807543			0.403772	+	0.914860i	$0.367699\pi$
$920$	−33.4445	−	5.92707i	−1.10263	−	0.195410i
$921$	−73.5209			−2.42259
$922$	41.3985	−	13.4133i	1.36339	−	0.441742i
$923$	−24.9813	−	24.9813i	−0.822269	−	0.822269i
$924$	9.03520	+	12.4793i	0.297236	+	0.410540i
$925$	−2.56371	−	20.3351i	−0.0842942	−	0.668615i
$926$	35.3324	+	18.0396i	1.16109	+	0.592820i
$927$	39.0734	−	39.0734i	1.28334	−	1.28334i
$928$	−16.0536	−	0.0665192i	−0.526986	−	0.00218360i
$929$		−	28.5706i		−	0.937372i	−0.883365	−	0.468686i	$-0.844728\pi$
$929$		−	28.5706i		−	0.937372i	0.883365	−	0.468686i	$-0.155272\pi$
$930$	−25.7843	+	24.9391i	−0.845502	+	0.817784i
$931$			3.29794i			0.108085i
$932$	6.83279	−	42.6826i	0.223816	−	1.39811i
$933$	−61.3124	+	61.3124i	−2.00728	+	2.00728i
$934$	−14.5214	+	28.4415i	−0.475154	+	0.930634i
$935$	−2.22341	+	1.08889i	−0.0727132	+	0.0356104i
$936$	30.3616	−	4.73145i	0.992398	−	0.154652i
$937$	14.5279	+	14.5279i	0.474607	+	0.474607i	0.903402	−	0.428795i	$-0.141062\pi$
$937$	14.5279	+	14.5279i	0.474607	+	0.474607i	−0.428795	+	0.903402i	$0.641062\pi$
$938$	0.281182	+	0.867834i	0.00918090	+	0.0283358i
$939$	−48.4063			−1.57968
$940$	27.1893	−	51.1310i	0.886819	−	1.66771i
$941$	−6.06628			−0.197755			−0.0988775	−	0.995100i	$-0.531525\pi$
$941$	−6.06628			−0.197755			−0.0988775	+	0.995100i	$0.531525\pi$
$942$	5.79325	+	17.8802i	0.188754	+	0.582568i
$943$	21.1892	+	21.1892i	0.690017	+	0.690017i
$944$	11.7773	−	35.8421i	0.383319	−	1.16656i
$945$	−2.28607	+	6.67431i	−0.0743659	+	0.217115i
$946$	7.21388	−	14.1291i	0.234544	−	0.459376i
$947$	0.579007	−	0.579007i	0.0188152	−	0.0188152i	−0.697637	−	0.716452i	$-0.745765\pi$
$947$	0.579007	−	0.579007i	0.0188152	−	0.0188152i	0.716452	+	0.697637i	$0.245765\pi$
$948$	63.2431	+	10.1242i	2.05404	+	0.328819i
$949$		−	32.6757i		−	1.06070i
$950$	−6.65044	−	2.40243i	−0.215769	−	0.0779452i
$951$			22.6374i			0.734066i
$952$	2.28663	−	3.13088i	0.0741102	−	0.101472i
$953$	−25.9886	+	25.9886i	−0.841852	+	0.841852i	−0.989100	−	0.147248i	$-0.952959\pi$
$953$	−25.9886	+	25.9886i	−0.841852	+	0.841852i	0.147248	+	0.989100i	$0.452959\pi$
$954$	−35.7570	−	18.2564i	−1.15768	−	0.591074i
$955$	−12.0198	+	35.0926i	−0.388953	+	1.13557i
$956$	6.25381	−	4.52784i	0.202263	−	0.146441i
$957$	8.03426	+	8.03426i	0.259711	+	0.259711i
$958$	−49.5756	+	16.0627i	−1.60171	+	0.518962i
$959$	−4.07001			−0.131428
$960$	−33.2569	+	31.9010i	−1.07336	+	1.02960i
$961$	11.6105			0.374532
$962$	−16.4756	+	5.33816i	−0.531195	+	0.172109i
$963$	22.9149	+	22.9149i	0.738423	+	0.738423i
$964$	−10.4287	+	7.55053i	−0.335886	+	0.243186i
$965$	8.92130	−	4.36910i	0.287187	−	0.140646i
$966$	−33.5285	−	17.1187i	−1.07876	−	0.550784i
$967$	−18.1554	+	18.1554i	−0.583839	+	0.583839i	−0.935956	−	0.352117i	$-0.885462\pi$
$967$	−18.1554	+	18.1554i	−0.583839	+	0.583839i	0.352117	+	0.935956i	$0.385462\pi$
$968$	−14.3209	+	19.6083i	−0.460290	+	0.630234i
$969$		−	1.83527i		−	0.0589572i
$970$	−43.2663	−	44.7328i	−1.38920	−	1.43628i
$971$			18.2580i			0.585927i	0.956124	+	0.292964i	$0.0946415\pi$
$971$			18.2580i			0.585927i	−0.956124	+	0.292964i	$0.905358\pi$
$972$	−43.7263	−	6.99988i	−1.40252	−	0.224521i
$973$	14.1377	−	14.1377i	0.453233	−	0.453233i
$974$	−2.47369	+	4.84497i	−0.0792623	+	0.155243i
$975$	30.3998	+	23.5928i	0.973572	+	0.755573i
$976$	−15.8398	+	48.2055i	−0.507018	+	1.54302i
$977$	10.0901	+	10.0901i	0.322812	+	0.322812i	0.849845	−	0.527033i	$-0.176696\pi$
$977$	10.0901	+	10.0901i	0.322812	+	0.322812i	−0.527033	+	0.849845i	$0.676696\pi$
$978$	−12.1897	−	37.6221i	−0.389784	−	1.20302i
$979$	7.07935			0.226257
$980$	4.31159	+	14.1045i	0.137729	+	0.450553i
$981$	44.1049			1.40816
$982$	−5.81693	−	17.9533i	−0.185626	−	0.572912i
$983$	−16.8216	−	16.8216i	−0.536524	−	0.536524i	0.385982	−	0.922506i	$-0.373863\pi$
$983$	−16.8216	−	16.8216i	−0.536524	−	0.536524i	−0.922506	+	0.385982i	$0.873863\pi$
$984$	40.1722	−	6.26031i	1.28064	−	0.199572i
$985$	−4.23697	−	8.65150i	−0.135001	−	0.275660i
$986$	1.30016	−	2.54649i	0.0414056	−	0.0810968i
$987$	45.3859	−	45.3859i	1.44465	−	1.44465i
$988$	−0.944464	+	5.89981i	−0.0300474	+	0.187698i
$989$			38.7635i			1.23261i
$990$	17.8696	+	0.297788i	0.567934	+	0.00946434i
$991$		−	52.8671i		−	1.67938i	−0.543066	−	0.839690i	$-0.682737\pi$
$991$		−	52.8671i		−	1.67938i	0.543066	−	0.839690i	$-0.317263\pi$
$992$	−24.9089	−	0.103212i	−0.790858	−	0.00327697i
$993$	16.2479	−	16.2479i	0.515611	−	0.515611i
$994$	28.6590	+	14.6324i	0.909009	+	0.464113i
$995$	−9.53181	−	3.26481i	−0.302179	−	0.103502i
$996$	4.15556	+	5.73961i	0.131674	+	0.181867i
$997$	22.7763	+	22.7763i	0.721333	+	0.721333i	0.968877	−	0.247544i	$-0.0796234\pi$
$997$	22.7763	+	22.7763i	0.721333	+	0.721333i	−0.247544	+	0.968877i	$0.579623\pi$
$998$	−30.7306	+	9.95683i	−0.972760	+	0.315178i
$999$	−6.72186			−0.212670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.c.267.5	✓	52
4.3	odd	2		380.2.k.d.267.16	yes	52
5.3	odd	4		380.2.k.d.343.16	yes	52
20.3	even	4	inner	380.2.k.c.343.5	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.5	✓	52	1.1	even	1	trivial
380.2.k.c.343.5	yes	52	20.3	even	4	inner
380.2.k.d.267.16	yes	52	4.3	odd	2
380.2.k.d.343.16	yes	52	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-1.34536 + 0.435901i) q^{2} +(-1.82161 - 1.82161i) q^{3} +(1.61998 - 1.17289i) q^{4} +(2.11542 + 0.724569i) q^{5} +(3.24476 + 1.65668i) q^{6} +(-1.36053 + 1.36053i) q^{7} +(-1.66819 + 2.28411i) q^{8} +3.63653i q^{9} +O(q^{10})\)	\(q+(-1.34536 + 0.435901i) q^{2} +(-1.82161 - 1.82161i) q^{3} +(1.61998 - 1.17289i) q^{4} +(2.11542 + 0.724569i) q^{5} +(3.24476 + 1.65668i) q^{6} +(-1.36053 + 1.36053i) q^{7} +(-1.66819 + 2.28411i) q^{8} +3.63653i q^{9} +(-3.16184 - 0.0526904i) q^{10} +1.55414i q^{11} +(-5.08752 - 0.814429i) q^{12} +(-2.11246 + 2.11246i) q^{13} +(1.23734 - 2.42345i) q^{14} +(-2.53359 - 5.17335i) q^{15} +(1.24867 - 3.80011i) q^{16} +(0.503748 + 0.503748i) q^{17} +(-1.58517 - 4.89243i) q^{18} +1.00000 q^{19} +(4.27678 - 1.30736i) q^{20} +4.95670 q^{21} +(-0.677450 - 2.09087i) q^{22} +(3.79747 + 3.79747i) q^{23} +(7.19954 - 1.12196i) q^{24} +(3.95000 + 3.06553i) q^{25} +(1.92119 - 3.76283i) q^{26} +(1.15951 - 1.15951i) q^{27} +(-0.608282 + 3.79977i) q^{28} +2.83793i q^{29} +(5.66366 + 5.85562i) q^{30} +4.40335i q^{31} +(-0.0234394 + 5.65681i) q^{32} +(2.83103 - 2.83103i) q^{33} +(-0.897306 - 0.458137i) q^{34} +(-3.86388 + 1.89229i) q^{35} +(4.26524 + 5.89110i) q^{36} +(-2.89859 - 2.89859i) q^{37} +(-1.34536 + 0.435901i) q^{38} +7.69614 q^{39} +(-5.18392 + 3.62312i) q^{40} +5.57983 q^{41} +(-6.66854 + 2.16063i) q^{42} +(5.10385 + 5.10385i) q^{43} +(1.82283 + 2.51767i) q^{44} +(-2.63491 + 7.69278i) q^{45} +(-6.76429 - 3.45364i) q^{46} +(9.15647 - 9.15647i) q^{47} +(-9.19691 + 4.64772i) q^{48} +3.29794i q^{49} +(-6.65044 - 2.40243i) q^{50} -1.83527i q^{51} +(-0.944464 + 5.89981i) q^{52} +(5.52010 - 5.52010i) q^{53} +(-1.05452 + 2.06538i) q^{54} +(-1.12608 + 3.28765i) q^{55} +(-0.837967 - 5.37720i) q^{56} +(-1.82161 - 1.82161i) q^{57} +(-1.23706 - 3.81803i) q^{58} +9.43187 q^{59} +(-10.1721 - 5.40911i) q^{60} -12.6853 q^{61} +(-1.91943 - 5.92409i) q^{62} +(-4.94759 - 4.94759i) q^{63} +(-2.43427 - 7.62065i) q^{64} +(-5.99935 + 2.93811i) q^{65} +(-2.57470 + 5.04280i) q^{66} +(-0.237062 + 0.237062i) q^{67} +(1.40690 + 0.225222i) q^{68} -13.8350i q^{69} +(4.37345 - 4.23008i) q^{70} +11.8257i q^{71} +(-8.30621 - 6.06643i) q^{72} +(-7.73406 + 7.73406i) q^{73} +(5.16314 + 2.63614i) q^{74} +(-1.61116 - 12.7796i) q^{75} +(1.61998 - 1.17289i) q^{76} +(-2.11444 - 2.11444i) q^{77} +(-10.3541 + 3.35476i) q^{78} -12.4310 q^{79} +(5.39490 - 7.13407i) q^{80} +6.68525 q^{81} +(-7.50687 + 2.43225i) q^{82} +(-0.972495 - 0.972495i) q^{83} +(8.02975 - 5.81365i) q^{84} +(0.700639 + 1.43064i) q^{85} +(-9.09128 - 4.64173i) q^{86} +(5.16960 - 5.16960i) q^{87} +(-3.54981 - 2.59260i) q^{88} -4.55517i q^{89} +(0.191610 - 11.4981i) q^{90} -5.74810i q^{91} +(10.6058 + 1.69782i) q^{92} +(8.02119 - 8.02119i) q^{93} +(-8.32742 + 16.3101i) q^{94} +(2.11542 + 0.724569i) q^{95} +(10.3472 - 10.2618i) q^{96} +(13.9158 + 13.9158i) q^{97} +(-1.43757 - 4.43691i) q^{98} -5.65166 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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