LMFDB - Embedded newform 273.2.bf.b.152.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(152,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 4]))

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

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

chi := DirichletCharacter("273.152");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			152.12
Character	$\chi$	$=$	273.152
Dual form			273.2.bf.b.185.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.765058 + 0.441707i) q^{2} +(0.162694 - 1.72439i) q^{3} +(-0.609790 + 1.05619i) q^{4} +(-1.72131 + 2.98140i) q^{5} +(0.637205 + 1.39112i) q^{6} +(-0.0494112 - 2.64529i) q^{7} -2.84422i q^{8} +(-2.94706 - 0.561097i) q^{9} +O(q^{10})$	\(q+(-0.765058 + 0.441707i) q^{2} +(0.162694 - 1.72439i) q^{3} +(-0.609790 + 1.05619i) q^{4} +(-1.72131 + 2.98140i) q^{5} +(0.637205 + 1.39112i) q^{6} +(-0.0494112 - 2.64529i) q^{7} -2.84422i q^{8} +(-2.94706 - 0.561097i) q^{9} -3.04126i q^{10} -3.84076i q^{11} +(1.72207 + 1.22335i) q^{12} +(-0.144185 - 3.60267i) q^{13} +(1.20624 + 2.00198i) q^{14} +(4.86105 + 3.45327i) q^{15} +(0.0367306 + 0.0636193i) q^{16} +(0.0809974 - 0.140292i) q^{17} +(2.50251 - 0.872465i) q^{18} -1.63423i q^{19} +(-2.09928 - 3.63606i) q^{20} +(-4.56956 - 0.345169i) q^{21} +(1.69649 + 2.93840i) q^{22} +(-3.93521 + 2.27200i) q^{23} +(-4.90455 - 0.462738i) q^{24} +(-3.42582 - 5.93370i) q^{25} +(1.70163 + 2.69256i) q^{26} +(-1.44702 + 4.99060i) q^{27} +(2.82405 + 1.56088i) q^{28} +(-8.21721 - 4.74421i) q^{29} +(-5.24432 - 0.494795i) q^{30} +(0.139734 - 0.0806754i) q^{31} +(4.87013 + 2.81177i) q^{32} +(-6.62298 - 0.624869i) q^{33} +0.143108i q^{34} +(7.97171 + 4.40605i) q^{35} +(2.38971 - 2.77050i) q^{36} +(1.99228 + 3.45072i) q^{37} +(0.721851 + 1.25028i) q^{38} +(-6.23587 - 0.337501i) q^{39} +(8.47975 + 4.89579i) q^{40} +(2.41336 - 4.18006i) q^{41} +(3.64844 - 1.75433i) q^{42} +(4.32913 + 7.49828i) q^{43} +(4.05656 + 2.34206i) q^{44} +(6.74566 - 7.82054i) q^{45} +(2.00711 - 3.47642i) q^{46} +(3.42471 - 5.93177i) q^{47} +(0.115680 - 0.0529875i) q^{48} +(-6.99512 + 0.261414i) q^{49} +(5.24191 + 3.02642i) q^{50} +(-0.228740 - 0.162496i) q^{51} +(3.89302 + 2.04459i) q^{52} +(-11.2686 + 6.50591i) q^{53} +(-1.09733 - 4.45726i) q^{54} +(11.4508 + 6.61114i) q^{55} +(-7.52379 + 0.140536i) q^{56} +(-2.81806 - 0.265880i) q^{57} +8.38220 q^{58} +(4.45863 - 7.72257i) q^{59} +(-6.61153 + 3.02841i) q^{60} -6.50715i q^{61} +(-0.0712698 + 0.123443i) q^{62} +(-1.33865 + 7.82356i) q^{63} -5.11484 q^{64} +(10.9892 + 5.77144i) q^{65} +(5.34297 - 2.44735i) q^{66} -0.945460 q^{67} +(0.0987829 + 0.171097i) q^{68} +(3.27758 + 7.15549i) q^{69} +(-8.04501 + 0.150272i) q^{70} +(-4.33350 + 2.50195i) q^{71} +(-1.59588 + 8.38209i) q^{72} +(8.62581 - 4.98012i) q^{73} +(-3.04842 - 1.76000i) q^{74} +(-10.7894 + 4.94208i) q^{75} +(1.72606 + 0.996539i) q^{76} +(-10.1599 + 0.189777i) q^{77} +(4.91988 - 2.49622i) q^{78} +(-5.23295 + 9.06373i) q^{79} -0.252899 q^{80} +(8.37034 + 3.30717i) q^{81} +4.26399i q^{82} -1.04892 q^{83} +(3.15104 - 4.61583i) q^{84} +(0.278843 + 0.482971i) q^{85} +(-6.62408 - 3.82441i) q^{86} +(-9.51777 + 13.3978i) q^{87} -10.9240 q^{88} +(3.44435 + 5.96579i) q^{89} +(-1.70644 + 8.96277i) q^{90} +(-9.52297 + 0.559423i) q^{91} -5.54177i q^{92} +(-0.116382 - 0.254082i) q^{93} +6.05087i q^{94} +(4.87230 + 2.81302i) q^{95} +(5.64094 - 7.94056i) q^{96} +(-6.97520 + 4.02713i) q^{97} +(5.23621 - 3.28979i) q^{98} +(-2.15504 + 11.3189i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9	$ 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42} - 20 q^{43} - 3 q^{45} + 6 q^{48} - 10 q^{51} + 30 q^{52} - 27 q^{54} + 18 q^{55} + 4 q^{57} - 60 q^{58} + 55 q^{60} - 74 q^{63} - 84 q^{64} + 75 q^{66} - 88 q^{67} - 33 q^{69} + 20 q^{70} - 34 q^{72} + 84 q^{73} + 33 q^{75} + 18 q^{76} - 71 q^{78} + 20 q^{79} - 32 q^{81} - 6 q^{84} - 2 q^{85} + 3 q^{87} + 92 q^{88} - 76 q^{91} + 28 q^{93} + 30 q^{96} + 24 q^{97} + 22 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9 + 6 * q^12 - 12 * q^13 - 9 * q^15 - 16 * q^16 + 2 * q^18 + 10 * q^21 + 10 * q^22 - 24 * q^25 - 50 * q^28 - 16 * q^30 - 24 * q^31 - 33 * q^39 + 90 * q^40 - 48 * q^42 - 20 * q^43 - 3 * q^45 + 6 * q^48 - 10 * q^51 + 30 * q^52 - 27 * q^54 + 18 * q^55 + 4 * q^57 - 60 * q^58 + 55 * q^60 - 74 * q^63 - 84 * q^64 + 75 * q^66 - 88 * q^67 - 33 * q^69 + 20 * q^70 - 34 * q^72 + 84 * q^73 + 33 * q^75 + 18 * q^76 - 71 * q^78 + 20 * q^79 - 32 * q^81 - 6 * q^84 - 2 * q^85 + 3 * q^87 + 92 * q^88 - 76 * q^91 + 28 * q^93 + 30 * q^96 + 24 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.765058	+	0.441707i	−0.540978	+	0.312334i	−0.745475	−	0.666533i	$-0.767777\pi$
$2$	−0.765058	+	0.441707i	−0.540978	+	0.312334i	0.204497	+	0.978867i	$0.434444\pi$
$3$	0.162694	−	1.72439i	0.0939315	−	0.995579i
$3$	0.162694	−	1.72439i	0.0939315	−	0.995579i
$4$	−0.609790	+	1.05619i	−0.304895	+	0.528094i
$5$	−1.72131	+	2.98140i	−0.769794	+	1.33332i	0.167881	+	0.985807i	$0.446308\pi$
$5$	−1.72131	+	2.98140i	−0.769794	+	1.33332i	−0.937675	+	0.347514i	$0.887026\pi$
$6$	0.637205	+	1.39112i	0.260138	+	0.567924i
$7$	−0.0494112	−	2.64529i	−0.0186757	−	0.999826i
$7$	−0.0494112	−	2.64529i	−0.0186757	−	0.999826i
$8$		−	2.84422i		−	1.00558i
$9$	−2.94706	−	0.561097i	−0.982354	−	0.187032i
$10$		−	3.04126i		−	0.961730i
$11$		−	3.84076i		−	1.15803i	−0.815316	−	0.579016i	$-0.803437\pi$
$11$		−	3.84076i		−	1.15803i	0.815316	−	0.579016i	$-0.196563\pi$
$12$	1.72207	+	1.22335i	0.497120	+	0.353152i
$13$	−0.144185	−	3.60267i	−0.0399897	−	0.999200i
$13$	−0.144185	−	3.60267i	−0.0399897	−	0.999200i
$14$	1.20624	+	2.00198i	0.322382	+	0.535051i
$15$	4.86105	+	3.45327i	1.25512	+	0.891631i
$16$	0.0367306	+	0.0636193i	0.00918265	+	0.0159048i
$17$	0.0809974	−	0.140292i	0.0196448	−	0.0340257i	−0.856036	−	0.516916i	$-0.827080\pi$
$17$	0.0809974	−	0.140292i	0.0196448	−	0.0340257i	0.875681	+	0.482891i	$0.160413\pi$
$18$	2.50251	−	0.872465i	0.589848	−	0.205642i
$19$		−	1.63423i		−	0.374919i	−0.982272	−	0.187459i	$-0.939975\pi$
$19$		−	1.63423i		−	0.374919i	0.982272	−	0.187459i	$-0.0600253\pi$
$20$	−2.09928	−	3.63606i	−0.469413	−	0.813047i
$21$	−4.56956	−	0.345169i	−0.997159	−	0.0753220i
$22$	1.69649	+	2.93840i	0.361693	+	0.626470i
$23$	−3.93521	+	2.27200i	−0.820549	+	0.473744i	−0.850606	−	0.525804i	$-0.823764\pi$
$23$	−3.93521	+	2.27200i	−0.820549	+	0.473744i	0.0300569	+	0.999548i	$0.490431\pi$
$24$	−4.90455	−	0.462738i	−1.00114	−	0.0944560i
$25$	−3.42582	−	5.93370i	−0.685164	−	1.18674i
$26$	1.70163	+	2.69256i	0.333718	+	0.528055i
$27$	−1.44702	+	4.99060i	−0.278479	+	0.960442i
$28$	2.82405	+	1.56088i	0.533696	+	0.294979i
$29$	−8.21721	−	4.74421i	−1.52590	−	0.880978i	−0.999528	−	0.0307223i	$-0.990219\pi$
$29$	−8.21721	−	4.74421i	−1.52590	−	0.880978i	−0.526370	−	0.850255i	$-0.676447\pi$
$30$	−5.24432	−	0.494795i	−0.957478	−	0.0903367i
$31$	0.139734	−	0.0806754i	0.0250970	−	0.0144897i	−0.487399	−	0.873179i	$-0.662054\pi$
$31$	0.139734	−	0.0806754i	0.0250970	−	0.0144897i	0.512496	+	0.858690i	$0.328721\pi$
$32$	4.87013	+	2.81177i	0.860926	+	0.497056i
$33$	−6.62298	−	0.624869i	−1.15291	−	0.108776i
$34$			0.143108i			0.0245429i
$35$	7.97171	+	4.40605i	1.34747	+	0.744759i
$36$	2.38971	−	2.77050i	0.398286	−	0.461750i
$37$	1.99228	+	3.45072i	0.327528	+	0.567296i	0.982021	−	0.188773i	$-0.0604510\pi$
$37$	1.99228	+	3.45072i	0.327528	+	0.567296i	−0.654493	+	0.756068i	$0.727118\pi$
$38$	0.721851	+	1.25028i	0.117100	+	0.202823i
$39$	−6.23587	−	0.337501i	−0.998539	−	0.0540434i
$40$	8.47975	+	4.89579i	1.34077	+	0.774092i
$41$	2.41336	−	4.18006i	0.376904	−	0.652816i	−0.613706	−	0.789534i	$-0.710322\pi$
$41$	2.41336	−	4.18006i	0.376904	−	0.652816i	0.990610	+	0.136718i	$0.0436555\pi$
$42$	3.64844	−	1.75433i	0.562967	−	0.270699i
$43$	4.32913	+	7.49828i	0.660186	+	1.14348i	0.980566	+	0.196187i	$0.0628561\pi$
$43$	4.32913	+	7.49828i	0.660186	+	1.14348i	−0.320380	+	0.947289i	$0.603811\pi$
$44$	4.05656	+	2.34206i	0.611550	+	0.353078i
$45$	6.74566	−	7.82054i	1.00558	−	1.16582i
$46$	2.00711	−	3.47642i	0.295933	−	0.512570i
$47$	3.42471	−	5.93177i	0.499545	−	0.865238i	−0.500455	−	0.865763i	$-0.666834\pi$
$47$	3.42471	−	5.93177i	0.499545	−	0.865238i	1.00000		0.000525066i	$0.000167134\pi$
$48$	0.115680	−	0.0529875i	0.0166970	−	0.00764809i
$49$	−6.99512	+	0.261414i	−0.999302	+	0.0373449i
$50$	5.24191	+	3.02642i	0.741317	+	0.428000i
$51$	−0.228740	−	0.162496i	−0.0320300	−	0.0227540i
$52$	3.89302	+	2.04459i	0.539864	+	0.283533i
$53$	−11.2686	+	6.50591i	−1.54786	+	0.893656i	−0.549552	+	0.835459i	$0.685202\pi$
$53$	−11.2686	+	6.50591i	−1.54786	+	0.893656i	−0.998305	+	0.0581968i	$0.981465\pi$
$54$	−1.09733	−	4.45726i	−0.149327	−	0.606557i
$55$	11.4508	+	6.61114i	1.54403	+	0.891446i
$56$	−7.52379	+	0.140536i	−1.00541	+	0.0187800i
$57$	−2.81806	−	0.265880i	−0.373261	−	0.0352166i
$58$	8.38220			1.10064
$59$	4.45863	−	7.72257i	0.580464	−	1.00539i	−0.414961	−	0.909839i	$-0.636205\pi$
$59$	4.45863	−	7.72257i	0.580464	−	1.00539i	0.995424	−	0.0955531i	$-0.0304620\pi$
$60$	−6.61153	+	3.02841i	−0.853544	+	0.390967i
$61$		−	6.50715i		−	0.833155i	−0.909100	−	0.416577i	$-0.863229\pi$
$61$		−	6.50715i		−	0.833155i	0.909100	−	0.416577i	$-0.136771\pi$
$62$	−0.0712698	+	0.123443i	−0.00905127	+	0.0156773i
$63$	−1.33865	+	7.82356i	−0.168654	+	0.985675i
$64$	−5.11484			−0.639355
$65$	10.9892	+	5.77144i	1.36304	+	0.715859i
$66$	5.34297	−	2.44735i	0.657674	−	0.301248i
$67$	−0.945460			−0.115506			−0.0577532	−	0.998331i	$-0.518394\pi$
$67$	−0.945460			−0.115506			−0.0577532	+	0.998331i	$0.518394\pi$
$68$	0.0987829	+	0.171097i	0.0119792	+	0.0207486i
$69$	3.27758	+	7.15549i	0.394574	+	0.861420i
$70$	−8.04501	+	0.150272i	−0.961562	+	0.0179610i
$71$	−4.33350	+	2.50195i	−0.514292	+	0.296927i	−0.734596	−	0.678505i	$-0.762628\pi$
$71$	−4.33350	+	2.50195i	−0.514292	+	0.296927i	0.220304	+	0.975431i	$0.429295\pi$
$72$	−1.59588	+	8.38209i	−0.188077	+	0.987839i
$73$	8.62581	−	4.98012i	1.00958	−	0.582878i	0.0985078	−	0.995136i	$-0.468593\pi$
$73$	8.62581	−	4.98012i	1.00958	−	0.582878i	0.911067	+	0.412258i	$0.135260\pi$
$74$	−3.04842	−	1.76000i	−0.354371	−	0.204596i
$75$	−10.7894	+	4.94208i	−1.24585	+	0.570663i
$76$	1.72606	+	0.996539i	0.197992	+	0.114311i
$77$	−10.1599	+	0.189777i	−1.15783	+	0.0216270i
$78$	4.91988	−	2.49622i	0.557067	−	0.282641i
$79$	−5.23295	+	9.06373i	−0.588753	+	1.01975i	0.405644	+	0.914031i	$0.367047\pi$
$79$	−5.23295	+	9.06373i	−0.588753	+	1.01975i	−0.994396	+	0.105718i	$0.966286\pi$
$80$	−0.252899			−0.0282750
$81$	8.37034	+	3.30717i	0.930038	+	0.367464i
$82$			4.26399i			0.470879i
$83$	−1.04892			−0.115134			−0.0575672	−	0.998342i	$-0.518334\pi$
$83$	−1.04892			−0.115134			−0.0575672	+	0.998342i	$0.518334\pi$
$84$	3.15104	−	4.61583i	0.343806	−	0.503628i
$85$	0.278843	+	0.482971i	0.0302448	+	0.0523856i
$86$	−6.62408	−	3.82441i	−0.714293	−	0.412397i
$87$	−9.51777	+	13.3978i	−1.02041	+	1.43640i
$88$	−10.9240			−1.16450
$89$	3.44435	+	5.96579i	0.365100	+	0.632372i	0.988792	−	0.149298i	$-0.0477014\pi$
$89$	3.44435	+	5.96579i	0.365100	+	0.632372i	−0.623692	+	0.781670i	$0.714368\pi$
$90$	−1.70644	+	8.96277i	−0.179875	+	0.944759i
$91$	−9.52297	+	0.559423i	−0.998279	+	0.0586435i
$92$		−	5.54177i		−	0.577769i
$93$	−0.116382	−	0.254082i	−0.0120683	−	0.0263470i
$94$			6.05087i			0.624099i
$95$	4.87230	+	2.81302i	0.499887	+	0.288610i
$96$	5.64094	−	7.94056i	0.575726	−	0.810430i
$97$	−6.97520	+	4.02713i	−0.708224	+	0.408893i	−0.810403	−	0.585873i	$-0.800752\pi$
$97$	−6.97520	+	4.02713i	−0.708224	+	0.408893i	0.102179	+	0.994766i	$0.467419\pi$
$98$	5.23621	−	3.28979i	0.528937	−	0.332319i
$99$	−2.15504	+	11.3189i	−0.216589	+	1.13760i
$100$	8.35613			0.835613
$101$	5.09912			0.507381			0.253691	−	0.967285i	$-0.418355\pi$
$101$	5.09912			0.507381			0.253691	+	0.967285i	$0.418355\pi$
$102$	0.246775	+	0.0232829i	0.0244344	+	0.00230535i
$103$	−0.996557	−	0.575362i	−0.0981937	−	0.0566921i	0.450099	−	0.892979i	$-0.351389\pi$
$103$	−0.996557	−	0.575362i	−0.0981937	−	0.0566921i	−0.548293	+	0.836287i	$0.684722\pi$
$104$	−10.2468	+	0.410094i	−1.00478	+	0.0402130i
$105$	8.89471	−	13.0295i	0.868035	−	1.27155i
$106$	5.74741	−	9.95481i	0.558238	−	0.966897i
$107$	16.5672	−	9.56507i	1.60161	−	0.924690i	0.610445	−	0.792058i	$-0.290991\pi$
$107$	16.5672	−	9.56507i	1.60161	−	0.924690i	0.991165	−	0.132632i	$-0.0423428\pi$
$108$	−4.38864	−	4.57155i	−0.422297	−	0.439897i
$109$	−9.89648	−	17.1412i	−0.947911	−	1.64183i	−0.749815	−	0.661647i	$-0.769858\pi$
$109$	−9.89648	−	17.1412i	−0.947911	−	1.64183i	−0.198096	−	0.980183i	$-0.563476\pi$
$110$	−11.6807			−1.11371
$111$	6.27454	−	2.87406i	0.595553	−	0.272793i
$112$	0.166476	−	0.100307i	0.0157305	−	0.00947808i
$113$	0.613946	−	0.354462i	0.0577552	−	0.0333450i	−0.470844	−	0.882216i	$-0.656051\pi$
$113$	0.613946	−	0.354462i	0.0577552	−	0.0333450i	0.528600	+	0.848871i	$0.322717\pi$
$114$	2.27342	−	1.04134i	0.212925	−	0.0975306i
$115$		−	15.6432i		−	1.45874i
$116$	10.0216	−	5.78595i	0.930478	−	0.537212i
$117$	−1.59652	+	10.6982i	−0.147599	+	0.989047i
$118$			7.87762i			0.725194i
$119$	−0.375114	−	0.207330i	−0.0343867	−	0.0190059i
$120$	9.82187	−	13.8259i	0.896610	−	1.26213i
$121$	−3.75142			−0.341038
$122$	2.87425	+	4.97835i	0.260222	+	0.450718i
$123$	−6.81543	−	4.84165i	−0.614527	−	0.436557i
$124$			0.196780i			0.0176714i
$125$	6.37450			0.570153
$126$	−2.43157	−	6.57677i	−0.216622	−	0.585905i
$127$	3.35273	−	5.80710i	0.297507	−	0.515297i	−0.678058	−	0.735008i	$-0.737178\pi$
$127$	3.35273	−	5.80710i	0.297507	−	0.515297i	0.975565	+	0.219711i	$0.0705116\pi$
$128$	−5.82712	+	3.36429i	−0.515049	+	0.297364i
$129$	13.6343	−	6.24520i	1.20043	−	0.549859i
$130$	−10.9566	+	0.438504i	−0.960961	+	0.0384593i
$131$	5.07994	−	8.79871i	0.443836	−	0.768747i	−0.554134	−	0.832427i	$-0.686951\pi$
$131$	5.07994	−	8.79871i	0.443836	−	0.768747i	0.997970	+	0.0636806i	$0.0202839\pi$
$132$	4.69861	−	6.61407i	0.408961	−	0.575681i
$133$	−4.32302	+	0.0807494i	−0.374853	+	0.00700186i
$134$	0.723332	−	0.417616i	0.0624864	−	0.0360765i
$135$	−12.3882	−	12.9045i	−1.06621	−	1.11064i
$136$	−0.399020	−	0.230374i	−0.0342157	−	0.0197544i
$137$	7.99479	+	4.61579i	0.683041	+	0.394354i	0.801000	−	0.598665i	$-0.204302\pi$
$137$	7.99479	+	4.61579i	0.683041	+	0.394354i	−0.117959	+	0.993018i	$0.537635\pi$
$138$	−5.66817	−	4.02664i	−0.482507	−	0.342771i
$139$	−8.92213	+	5.15119i	−0.756765	+	0.436919i	−0.828133	−	0.560532i	$-0.810597\pi$
$139$	−8.92213	+	5.15119i	−0.756765	+	0.436919i	0.0713680	+	0.997450i	$0.477264\pi$
$140$	−9.51469	+	5.73286i	−0.804138	+	0.484515i
$141$	−9.67152	−	6.87061i	−0.814489	−	0.578610i
$142$	2.21026	−	3.82827i	0.185481	−	0.321262i
$143$	−13.8370	+	0.553780i	−1.15711	+	0.0463094i
$144$	−0.0725507	−	0.208099i	−0.00604590	−	0.0173416i
$145$	28.2888	−	16.3325i	2.34925	−	1.35634i
$146$	−4.39950	+	7.62016i	−0.364105	+	0.630649i
$147$	−0.687283	+	12.1049i	−0.0566862	+	0.998392i
$148$	−4.85948			−0.399447
$149$			3.00651i			0.246303i	0.992388	+	0.123151i	$0.0393001\pi$
$149$			3.00651i			0.246303i	−0.992388	+	0.123151i	$0.960700\pi$
$150$	6.07156	−	8.54673i	0.495741	−	0.697837i
$151$	1.79991	+	3.11753i	0.146475	+	0.253701i	0.929922	−	0.367757i	$-0.119874\pi$
$151$	1.79991	+	3.11753i	0.146475	+	0.253701i	−0.783448	+	0.621458i	$0.786541\pi$
$152$	−4.64812			−0.377012
$153$	−0.317422	+	0.368001i	−0.0256620	+	0.0297511i
$154$	7.68911	−	4.63289i	0.619606	−	0.373329i
$155$			0.555470i			0.0446164i
$156$	4.15904	−	6.38045i	0.332990	−	0.510845i
$157$	4.18032	−	2.41351i	0.333626	−	0.192619i	−0.323824	−	0.946117i	$-0.604968\pi$
$157$	4.18032	−	2.41351i	0.333626	−	0.192619i	0.657450	+	0.753498i	$0.271635\pi$
$158$		−	9.24571i		−	0.735549i
$159$	9.38542	+	20.4899i	0.744312	+	1.62496i
$160$	−16.7660	+	9.67987i	−1.32547	+	0.765261i
$161$	6.20453	+	10.2975i	0.488986	+	0.811558i
$162$	−7.86460	+	1.16705i	−0.617901	+	0.0916924i
$163$	−8.42882			−0.660196			−0.330098	−	0.943947i	$-0.607082\pi$
$163$	−8.42882			−0.660196			−0.330098	+	0.943947i	$0.607082\pi$
$164$	2.94329	+	5.09792i	0.229832	+	0.398081i
$165$	13.2632	−	18.6701i	1.03254	−	1.45347i
$166$	0.802488	−	0.463317i	0.0622852	−	0.0359604i
$167$	−0.713480	+	1.23578i	−0.0552108	+	0.0956279i	−0.892310	−	0.451423i	$-0.850916\pi$
$167$	−0.713480	+	1.23578i	−0.0552108	+	0.0956279i	0.837099	+	0.547051i	$0.184250\pi$
$168$	−0.981736	+	12.9968i	−0.0757425	+	1.00273i
$169$	−12.9584	+	1.03890i	−0.996802	+	0.0799155i
$170$	−0.426663	−	0.246334i	−0.0327236	−	0.0188930i
$171$	−0.916963	+	4.81618i	−0.0701219	+	0.368303i
$172$	−10.5595			−0.805151
$173$	16.7089			1.27036			0.635179	−	0.772365i	$-0.280926\pi$
$173$	16.7089			1.27036			0.635179	+	0.772365i	$0.280926\pi$
$174$	1.36373	−	14.4542i	0.103384	−	1.09577i
$175$	−15.5271	+	9.35548i	−1.17374	+	0.707208i
$176$	0.244346	−	0.141073i	0.0184183	−	0.0106338i
$177$	−12.5913	−	8.94484i	−0.946423	−	0.672335i
$178$	−5.27026	−	3.04278i	−0.395022	−	0.228066i
$179$		−	11.0051i		−	0.822561i	−0.911509	−	0.411281i	$-0.865082\pi$
$179$		−	11.0051i		−	0.822561i	0.911509	−	0.411281i	$-0.134918\pi$
$180$	4.14652	+	11.8936i	0.309063	+	0.886495i
$181$			2.82101i			0.209684i	0.994489	+	0.104842i	$0.0334337\pi$
$181$			2.82101i			0.209684i	−0.994489	+	0.104842i	$0.966566\pi$
$182$	7.03853	−	4.63435i	0.521731	−	0.343521i
$183$	−11.2209	−	1.05867i	−0.829471	−	0.0782594i
$184$	6.46206	+	11.1926i	0.476389	+	0.825131i
$185$	−13.7173			−1.00852
$186$	0.201269	+	0.142980i	0.0147577	+	0.0104838i
$187$	−0.538826	−	0.311091i	−0.0394029	−	0.0227493i
$188$	4.17671	+	7.23427i	0.304618	+	0.527614i
$189$	13.2731	+	3.58120i	0.965476	+	0.260494i
$190$	−4.97012			−0.360570
$191$		−	2.53976i		−	0.183771i	−0.995770	−	0.0918854i	$-0.970711\pi$
$191$		−	2.53976i		−	0.183771i	0.995770	−	0.0918854i	$-0.0292893\pi$
$192$	−0.832154	+	8.81999i	−0.0600555	+	0.636528i
$193$	10.7149			0.771275			0.385638	−	0.922650i	$-0.373982\pi$
$193$	10.7149			0.771275			0.385638	+	0.922650i	$0.373982\pi$
$194$	3.55762	−	6.16198i	0.255422	−	0.442405i
$195$	11.7401	−	18.0107i	0.840726	−	1.28977i
$196$	3.98945	−	7.54757i	0.284961	−	0.539112i
$197$	4.30705	+	2.48668i	0.306865	+	0.177168i	0.645523	−	0.763741i	$-0.276640\pi$
$197$	4.30705	+	2.48668i	0.306865	+	0.177168i	−0.338658	+	0.940910i	$0.609973\pi$
$198$	−3.35093	−	9.61155i	−0.238140	−	0.683063i
$199$	8.50598	+	4.91093i	0.602973	+	0.348127i	0.770210	−	0.637790i	$-0.220151\pi$
$199$	8.50598	+	4.91093i	0.602973	+	0.348127i	−0.167237	+	0.985917i	$0.553485\pi$
$200$	−16.8767	+	9.74379i	−1.19337	+	0.688990i
$201$	−0.153821	+	1.63035i	−0.0108497	+	0.114996i
$202$	−3.90112	+	2.25231i	−0.274482	+	0.158472i
$203$	−12.1438	+	21.9713i	−0.852327	+	1.54208i
$204$	0.311110	−	0.142504i	0.0217820	−	0.00997728i
$205$	8.30829	+	14.3904i	0.580276	+	1.00507i
$206$	1.01657			0.0708275
$207$	12.8721	−	4.48768i	0.894675	−	0.311915i
$208$	0.223903	−	0.141501i	0.0155249	−	0.00981133i
$209$	−6.27669			−0.434168
$210$	−1.04975	+	13.8972i	−0.0724394	+	0.958998i
$211$	7.89735	−	13.6786i	0.543676	−	0.941675i	−0.455013	−	0.890485i	$-0.650365\pi$
$211$	7.89735	−	13.6786i	0.543676	−	0.941675i	0.998689	−	0.0511899i	$-0.0163014\pi$
$212$		−	15.8690i		−	1.08989i
$213$	3.60931	+	7.87971i	0.247306	+	0.539909i
$214$	−8.44991	+	14.6357i	−0.577624	+	1.00047i
$215$	−29.8071			−2.03283
$216$	14.1944	+	4.11565i	0.965805	+	0.280034i
$217$	−0.220314	−	0.365651i	−0.0149559	−	0.0248220i
$218$	15.1428	+	8.74268i	1.02560	+	0.592129i
$219$	−7.18431	−	15.6845i	−0.485470	−	1.05986i
$220$	−13.9652	+	8.06282i	−0.941534	+	0.543595i
$221$	−0.517103	−	0.271579i	−0.0347841	−	0.0182684i
$222$	−3.53090	+	4.97032i	−0.236978	+	0.333586i
$223$	−0.772875	−	0.446219i	−0.0517555	−	0.0298811i	0.473899	−	0.880579i	$-0.342846\pi$
$223$	−0.772875	−	0.446219i	−0.0517555	−	0.0298811i	−0.525654	+	0.850698i	$0.676180\pi$
$224$	7.19731	−	13.0218i	0.480891	−	0.870059i
$225$	6.76673	+	19.4092i	0.451115	+	1.29395i
$226$	−0.313136	+	0.542368i	−0.0208295	+	0.0360778i
$227$	1.41048	−	2.44303i	0.0936171	−	0.162150i	−0.815414	−	0.578879i	$-0.803490\pi$
$227$	1.41048	−	2.44303i	0.0936171	−	0.162150i	0.909031	+	0.416729i	$0.136824\pi$
$228$	1.99924	−	2.81427i	0.132403	−	0.186379i
$229$	−15.0847	−	8.70916i	−0.996826	−	0.575518i	−0.0895184	−	0.995985i	$-0.528533\pi$
$229$	−15.0847	−	8.70916i	−0.996826	−	0.575518i	−0.907308	+	0.420467i	$0.861866\pi$
$230$	6.90973	+	11.9680i	0.455614	+	0.789146i
$231$	−1.32571	+	17.5506i	−0.0872252	+	1.15474i
$232$	−13.4936	+	23.3716i	−0.885897	+	1.53442i
$233$	−17.8552	−	10.3087i	−1.16973	−	0.675345i	−0.216115	−	0.976368i	$-0.569338\pi$
$233$	−17.8552	−	10.3087i	−1.16973	−	0.675345i	−0.953617	+	0.301023i	$0.902672\pi$
$234$	−3.50403	−	8.88993i	−0.229065	−	0.581153i
$235$	11.7900	+	20.4208i	0.769093	+	1.33211i
$236$	5.43765	+	9.41829i	0.353961	+	0.613079i
$237$	14.7781	+	10.4983i	0.959938	+	0.681936i
$238$	0.378563	−	0.00707116i	0.0245386	−	0.000458355i
$239$		−	17.5634i		−	1.13608i	−0.823000	−	0.568042i	$-0.807701\pi$
$239$		−	17.5634i		−	1.13608i	0.823000	−	0.568042i	$-0.192299\pi$
$240$	−0.0411452	+	0.436097i	−0.00265591	+	0.0281500i
$241$	1.70847	+	0.986388i	0.110053	+	0.0635389i	0.554016	−	0.832506i	$-0.313095\pi$
$241$	1.70847	+	0.986388i	0.110053	+	0.0635389i	−0.443963	+	0.896045i	$0.646428\pi$
$242$	2.87006	−	1.65703i	0.184494	−	0.106518i
$243$	7.06467	−	13.8957i	0.453199	−	0.891409i
$244$	6.87277	+	3.96800i	0.439984	+	0.254025i
$245$	11.2614	−	21.3052i	0.719464	−	1.36114i
$246$	7.35279	+	0.693726i	0.468797	+	0.0442303i
$247$	−5.88759	+	0.235632i	−0.374619	+	0.0149929i
$248$	−0.229459	−	0.397434i	−0.0145706	−	0.0252371i
$249$	−0.170654	+	1.80876i	−0.0108147	+	0.114625i
$250$	−4.87687	+	2.81566i	−0.308440	+	0.178078i
$251$	0.542545	+	0.939716i	0.0342452	+	0.0593144i	0.882640	−	0.470050i	$-0.155764\pi$
$251$	0.542545	+	0.939716i	0.0342452	+	0.0593144i	−0.848395	+	0.529364i	$0.822431\pi$
$252$	−7.44685	−	6.18459i	−0.469108	−	0.389593i
$253$	8.72619	+	15.1142i	0.548611	+	0.950222i
$254$			5.92370i			0.371686i
$255$	0.878198	−	0.402259i	0.0549949	−	0.0251904i
$256$	8.08689	−	14.0069i	0.505431	−	0.875432i
$257$	−6.98711	−	12.1020i	−0.435844	−	0.754904i	0.561520	−	0.827463i	$-0.310217\pi$
$257$	−6.98711	−	12.1020i	−0.435844	−	0.754904i	−0.997364	+	0.0725593i	$0.976883\pi$
$258$	−7.67249	+	10.8003i	−0.477668	+	0.672397i
$259$	9.02973	−	5.44065i	0.561080	−	0.338066i
$260$	−12.7968	+	8.08726i	−0.793625	+	0.501551i
$261$	21.5547	+	18.5921i	1.33420	+	1.15082i
$262$			8.97537i			0.554500i
$263$			6.24938i			0.385353i	0.981262	+	0.192677i	$0.0617168\pi$
$263$			6.24938i			0.385353i	−0.981262	+	0.192677i	$0.938283\pi$
$264$	−1.77726	+	18.8372i	−0.109383	+	1.15935i
$265$		−	44.7948i		−	2.75172i
$266$	3.27169	−	1.97128i	0.200600	−	0.120867i
$267$	10.8477	−	4.96881i	0.663871	−	0.304086i
$268$	0.576533	−	0.998584i	0.0352173	−	0.0609982i
$269$	5.02185	−	8.69811i	0.306188	−	0.530333i	−0.671337	−	0.741152i	$-0.734280\pi$
$269$	5.02185	−	8.69811i	0.306188	−	0.530333i	0.977525	+	0.210819i	$0.0676131\pi$
$270$	15.1777	+	4.40076i	0.923686	+	0.267822i
$271$	13.2862	−	7.67080i	0.807080	−	0.465968i	−0.0388607	−	0.999245i	$-0.512373\pi$
$271$	13.2862	−	7.67080i	0.807080	−	0.465968i	0.845941	+	0.533277i	$0.179040\pi$
$272$	0.0119003			0.000721564
$273$	−0.584666	+	16.5124i	−0.0353856	+	0.999374i
$274$	−8.15531			−0.492680
$275$	−22.7899	+	13.1577i	−1.37428	+	0.793442i
$276$	−9.55618	−	0.901612i	−0.575215	−	0.0542707i
$277$	−4.72535	+	8.18454i	−0.283919	+	0.491761i	−0.972346	−	0.233544i	$-0.924968\pi$
$277$	−4.72535	+	8.18454i	−0.283919	+	0.491761i	0.688428	+	0.725305i	$0.258301\pi$
$278$	4.55063	−	7.88193i	0.272929	−	0.472727i
$279$	−0.457071	+	0.159351i	−0.0273641	+	0.00954010i
$280$	12.5318	−	22.6733i	0.748917	−	1.35499i
$281$		−	11.6272i		−	0.693622i	−0.937935	−	0.346811i	$-0.887265\pi$
$281$		−	11.6272i		−	0.693622i	0.937935	−	0.346811i	$-0.112735\pi$
$282$	10.4341	+	0.984440i	0.621340	+	0.0586226i
$283$		−	1.62803i		−	0.0967762i	−0.998829	−	0.0483881i	$-0.984592\pi$
$283$		−	1.62803i		−	0.0967762i	0.998829	−	0.0483881i	$-0.0154084\pi$
$284$		−	6.10266i		−	0.362126i
$285$	5.64345	−	7.94409i	0.334289	−	0.470567i
$286$	10.3415	−	6.53556i	0.611505	−	0.386456i
$287$	−11.1767	−	6.17750i	−0.659741	−	0.364646i
$288$	−12.7749	−	11.0191i	−0.752768	−	0.649306i
$289$	8.48688	+	14.6997i	0.499228	+	0.864689i
$290$	−14.4284	+	24.9907i	−0.847263	+	1.46750i
$291$	5.80954	+	12.6832i	0.340561	+	0.743501i
$292$			12.1473i			0.710867i
$293$	−2.80580	−	4.85979i	−0.163917	−	0.283912i	0.772353	−	0.635193i	$-0.219079\pi$
$293$	−2.80580	−	4.85979i	−0.163917	−	0.283912i	−0.936270	+	0.351281i	$0.885746\pi$
$294$	−4.82099	−	9.56450i	−0.281166	−	0.557813i
$295$	15.3494	+	26.5859i	0.893674	+	1.54789i
$296$	9.81462	−	5.66647i	0.570463	−	0.329357i
$297$	19.1677	+	5.55766i	1.11222	+	0.322488i
$298$	−1.32800	−	2.30016i	−0.0769287	−	0.133244i
$299$	8.75265	+	13.8497i	0.506179	+	0.800947i
$300$	1.35949	−	14.4093i	0.0784903	−	0.831918i
$301$	19.6212	−	11.8223i	1.13095	−	0.681426i
$302$	−2.75407	−	1.59006i	−0.158479	−	0.0914979i
$303$	0.829596	−	8.79288i	0.0476591	−	0.505138i
$304$	0.103969	−	0.0600263i	0.00596301	−	0.00344275i
$305$	19.4004	+	11.2008i	1.11086	+	0.641357i
$306$	0.0802977	−	0.421749i	0.00459031	−	0.0241098i
$307$		−	8.81390i		−	0.503036i	−0.967853	−	0.251518i	$-0.919070\pi$
$307$		−	8.81390i		−	0.503036i	0.967853	−	0.251518i	$-0.0809297\pi$
$308$	5.99498	−	10.8465i	0.341596	−	0.618037i
$309$	−1.15428	+	1.62485i	−0.0656650	+	0.0924343i
$310$	−0.245355	−	0.424967i	−0.0139352	−	0.0241365i
$311$	11.9788	+	20.7478i	0.679254	+	1.17650i	0.975206	+	0.221299i	$0.0710297\pi$
$311$	11.9788	+	20.7478i	0.679254	+	1.17650i	−0.295952	+	0.955203i	$0.595637\pi$
$312$	−0.959927	+	17.7362i	−0.0543452	+	1.00411i
$313$	5.88550	+	3.39799i	0.332668	+	0.192066i	0.657025	−	0.753869i	$-0.271815\pi$
$313$	5.88550	+	3.39799i	0.332668	+	0.192066i	−0.324357	+	0.945935i	$0.605148\pi$
$314$	−2.13213	+	3.69295i	−0.120323	+	0.208405i
$315$	−21.0209	−	17.4578i	−1.18439	−	0.983636i
$316$	−6.38200	−	11.0540i	−0.359016	−	0.621833i
$317$	6.84769	+	3.95352i	0.384605	+	0.222052i	0.679820	−	0.733379i	$-0.262058\pi$
$317$	6.84769	+	3.95352i	0.384605	+	0.222052i	−0.295215	+	0.955431i	$0.595391\pi$
$318$	−16.2309	−	11.5304i	−0.910185	−	0.646592i
$319$	−18.2214	+	31.5603i	−1.02020	+	1.76704i
$320$	8.80422	−	15.2494i	0.492171	−	0.852465i
$321$	−13.7986	−	30.1245i	−0.770160	−	1.68139i
$322$	−9.29531	−	5.13762i	−0.518008	−	0.286308i
$323$	−0.229269	−	0.132369i	−0.0127569	−	0.00736518i
$324$	−8.59715	+	6.82397i	−0.477619	+	0.379109i
$325$	−20.8832	+	13.1976i	−1.15839	+	0.732073i
$326$	6.44854	−	3.72307i	0.357151	−	0.206202i
$327$	−31.1683	+	14.2766i	−1.72361	+	0.789500i
$328$	−11.8890	−	6.86413i	−0.656461	−	0.379008i
$329$	−15.8605	−	8.76625i	−0.874416	−	0.483299i
$330$	−1.90039	+	20.1422i	−0.104613	+	1.10879i
$331$	−8.82633			−0.485139			−0.242569	−	0.970134i	$-0.577990\pi$
$331$	−8.82633			−0.485139			−0.242569	+	0.970134i	$0.577990\pi$
$332$	0.639624	−	1.10786i	0.0351039	−	0.0608018i
$333$	−3.93517	−	11.2874i	−0.215646	−	0.618543i
$334$		−	1.26060i		−	0.0689768i
$335$	1.62743	−	2.81879i	0.0889161	−	0.154007i
$336$	−0.145883	−	0.303390i	−0.00795858	−	0.0165513i
$337$	−11.5765			−0.630611			−0.315306	−	0.948990i	$-0.602107\pi$
$337$	−11.5765			−0.630611			−0.315306	+	0.948990i	$0.602107\pi$
$338$	9.45506	−	6.51864i	0.514287	−	0.354567i
$339$	−0.511346	−	1.11635i	−0.0277725	−	0.0606320i
$340$	−0.680144			−0.0368860
$341$	−0.309855	−	0.536684i	−0.0167796	−	0.0290631i
$342$	−1.42581	−	4.08969i	−0.0770990	−	0.221145i
$343$	1.03715	+	18.4912i	0.0560010	+	0.998431i
$344$	21.3268	−	12.3130i	1.14986	−	0.663873i
$345$	−26.9751	−	2.54506i	−1.45229	−	0.137022i
$346$	−12.7833	+	7.38045i	−0.687235	+	0.396776i
$347$	−16.1319	−	9.31375i	−0.866005	−	0.499988i	1.36023e−5	−	1.00000i	$-0.499996\pi$
$347$	−16.1319	−	9.31375i	−0.866005	−	0.499988i	−0.866019	+	0.500012i	$0.833329\pi$
$348$	−8.34680	−	18.2224i	−0.447435	−	0.976825i
$349$	−9.48259	−	5.47477i	−0.507591	−	0.293058i	0.224252	−	0.974531i	$-0.428006\pi$
$349$	−9.48259	−	5.47477i	−0.507591	−	0.293058i	−0.731843	+	0.681473i	$0.761340\pi$
$350$	7.74674	−	14.0159i	0.414081	−	0.749181i
$351$	18.1881	+	4.49356i	0.970810	+	0.239849i
$352$	10.7993	−	18.7050i	0.575607	−	0.996980i
$353$	22.8725			1.21738			0.608691	−	0.793408i	$-0.291695\pi$
$353$	22.8725			1.21738			0.608691	+	0.793408i	$0.291695\pi$
$354$	13.5841	+	1.28164i	0.721987	+	0.0681185i
$355$		−	17.2265i		−	0.914289i
$356$	−8.40132			−0.445269
$357$	−0.418547	+	0.613113i	−0.0221518	+	0.0324494i
$358$	4.86104	+	8.41956i	0.256914	+	0.444988i
$359$	29.3954	+	16.9714i	1.55143	+	0.895719i	0.998026	+	0.0628057i	$0.0200048\pi$
$359$	29.3954	+	16.9714i	1.55143	+	0.895719i	0.553404	+	0.832913i	$0.313328\pi$
$360$	−22.2433	−	19.1861i	−1.17233	−	1.01120i
$361$	16.3293			0.859436
$362$	−1.24606	−	2.15824i	−0.0654915	−	0.113435i
$363$	−0.610334	+	6.46893i	−0.0320342	+	0.339531i
$364$	5.21616	−	10.3992i	0.273401	−	0.545065i
$365$			34.2893i			1.79478i
$366$	9.05225	−	4.14639i	0.473169	−	0.216735i
$367$			28.2805i			1.47623i	0.674675	+	0.738115i	$0.264284\pi$
$367$			28.2805i			1.47623i	−0.674675	+	0.738115i	$0.735716\pi$
$368$	−0.289085	−	0.166904i	−0.0150696	−	0.00870045i
$369$	−9.45774	+	10.9648i	−0.492350	+	0.570803i
$370$	10.4945	−	6.05903i	0.545585	−	0.314994i
$371$	17.7668	+	29.4872i	0.922407	+	1.53090i
$372$	0.339327	+	0.0320150i	0.0175933	+	0.00165990i
$373$	4.22220			0.218617			0.109309	−	0.994008i	$-0.465136\pi$
$373$	4.22220			0.218617			0.109309	+	0.994008i	$0.465136\pi$
$374$	0.549645			0.0284215
$375$	1.03709	−	10.9921i	0.0535553	−	0.567632i
$376$	−16.8713	−	9.74063i	−0.870069	−	0.502335i
$377$	−15.9070	+	30.2879i	−0.819253	+	1.55991i
$378$	−11.7365	+	3.12299i	−0.603662	+	0.160629i
$379$	16.6762	−	28.8840i	0.856599	−	1.48367i	−0.0185539	−	0.999828i	$-0.505906\pi$
$379$	16.6762	−	28.8840i	0.856599	−	1.48367i	0.875153	−	0.483846i	$-0.160760\pi$
$380$	−5.94216	+	3.43071i	−0.304826	+	0.175992i
$381$	−9.46826	−	6.72621i	−0.485073	−	0.344594i
$382$	1.12183	+	1.94307i	0.0573978	+	0.0994159i
$383$	17.8717			0.913202			0.456601	−	0.889672i	$-0.349067\pi$
$383$	17.8717			0.913202			0.456601	+	0.889672i	$0.349067\pi$
$384$	4.85332	+	10.5956i	0.247670	+	0.540704i
$385$	16.9226	−	30.6174i	0.862454	−	1.56041i
$386$	−8.19752	+	4.73284i	−0.417243	+	0.240895i
$387$	−8.55096	−	24.5269i	−0.434670	−	1.24677i
$388$		−	9.82283i		−	0.498679i
$389$	−21.4374	+	12.3769i	−1.08692	+	0.627533i	−0.932755	−	0.360512i	$-0.882602\pi$
$389$	−21.4374	+	12.3769i	−1.08692	+	0.627533i	−0.154165	+	0.988045i	$0.549269\pi$
$390$	−1.02643	+	18.9649i	−0.0519752	+	0.960325i
$391$			0.736103i			0.0372263i
$392$	0.743519	+	19.8957i	0.0375534	+	1.00488i
$393$	−14.3460	−	10.1913i	−0.723658	−	0.514083i
$394$	−4.39353			−0.221343
$395$	−18.0151	−	31.2030i	−0.906436	−	1.56999i
$396$	−10.6408	−	9.17831i	−0.534721	−	0.461228i
$397$		−	22.6228i		−	1.13541i	−0.823233	−	0.567704i	$-0.807832\pi$
$397$		−	22.6228i		−	1.13541i	0.823233	−	0.567704i	$-0.192168\pi$
$398$	−8.67676			−0.434927
$399$	−0.564086	+	7.46772i	−0.0282396	+	0.373853i
$400$	0.251665	−	0.435896i	0.0125832	−	0.0217948i
$401$	−21.1382	+	12.2042i	−1.05559	+	0.609446i	−0.924210	−	0.381885i	$-0.875275\pi$
$401$	−21.1382	+	12.2042i	−1.05559	+	0.609446i	−0.131383	+	0.991332i	$0.541942\pi$
$402$	−0.602452	−	1.31525i	−0.0300476	−	0.0655989i
$403$	−0.310794	−	0.491783i	−0.0154818	−	0.0244974i
$404$	−3.10939	+	5.38563i	−0.154698	+	0.267945i
$405$	−24.2680	+	19.2626i	−1.20588	+	0.957168i
$406$	−0.414175	−	22.1733i	−0.0205551	−	1.10044i
$407$	13.2534	−	7.65185i	0.656947	−	0.379288i
$408$	−0.462174	+	0.650587i	−0.0228810	+	0.0322089i
$409$	27.5146	+	15.8856i	1.36051	+	0.785492i	0.989692	−	0.143213i	$-0.0457435\pi$
$409$	27.5146	+	15.8856i	1.36051	+	0.785492i	0.370819	+	0.928705i	$0.379077\pi$
$410$	−12.7126	−	7.33965i	−0.627833	−	0.362480i
$411$	9.26014	−	13.0352i	0.456769	−	0.642979i
$412$	1.21538	−	0.701701i	0.0598775	−	0.0345703i
$413$	−20.6487	−	11.4128i	−1.01606	−	0.561586i
$414$	−7.86569	+	9.11904i	−0.386578	+	0.448176i
$415$	1.80552	−	3.12726i	0.0886297	−	0.153511i
$416$	9.42768	−	17.9509i	0.462230	−	0.880114i
$417$	7.43110	+	16.2233i	0.363903	+	0.794460i
$418$	4.80203	−	2.77246i	0.234875	−	0.135605i
$419$	9.86318	−	17.0835i	0.481848	−	0.834585i	−0.517935	−	0.855420i	$-0.673299\pi$
$419$	9.86318	−	17.0835i	0.481848	−	0.834585i	0.999783	+	0.0208352i	$0.00663253\pi$
$420$	8.33772	+	17.3398i	0.406839	+	0.846094i
$421$	−14.3999			−0.701807			−0.350903	−	0.936412i	$-0.614125\pi$
$421$	−14.3999			−0.701807			−0.350903	+	0.936412i	$0.614125\pi$
$422$			13.9533i			0.679234i
$423$	−13.4211	+	15.5597i	−0.652558	+	0.756538i
$424$	18.5043	+	32.0503i	0.898646	+	1.55650i
$425$	−1.10993			−0.0538395
$426$	−6.24185	−	4.43419i	−0.302419	−	0.214837i
$427$	−17.2133	+	0.321526i	−0.833009	+	0.0155597i
$428$			23.3308i			1.12773i
$429$	−1.29626	+	23.9505i	−0.0625840	+	1.15634i
$430$	22.8042	−	13.1660i	1.09972	−	0.634921i
$431$			5.03575i			0.242564i	0.992618	+	0.121282i	$0.0387005\pi$
$431$			5.03575i			0.242564i	−0.992618	+	0.121282i	$0.961300\pi$
$432$	−0.370648	+	0.0912495i	−0.0178328	+	0.00439024i
$433$	27.2316	−	15.7222i	1.30867	−	0.755561i	0.326795	−	0.945095i	$-0.394031\pi$
$433$	27.2316	−	15.7222i	1.30867	−	0.755561i	0.981874	+	0.189535i	$0.0606979\pi$
$434$	0.330064	+	0.182430i	0.0158436	+	0.00875691i
$435$	−23.5613	−	51.4381i	−1.12968	−	2.46627i
$436$	24.1391			1.15605
$437$	3.71297	+	6.43105i	0.177615	+	0.307639i
$438$	12.4244	+	8.82622i	0.593660	+	0.421733i
$439$	−7.05969	+	4.07592i	−0.336941	+	0.194533i	−0.658918	−	0.752214i	$-0.728986\pi$
$439$	−7.05969	+	4.07592i	−0.336941	+	0.194533i	0.321978	+	0.946747i	$0.395652\pi$
$440$	18.8035	−	32.5687i	0.896423	−	1.55265i
$441$	20.7617	+	3.15454i	0.988653	+	0.150216i
$442$	0.515572	−	0.0206341i	0.0245233	−	0.000981463i
$443$	18.0400	+	10.4154i	0.857106	+	0.494850i	0.863042	−	0.505132i	$-0.168556\pi$
$443$	18.0400	+	10.4154i	0.857106	+	0.494850i	−0.00593636	+	0.999982i	$0.501890\pi$
$444$	−0.790609	+	8.37966i	−0.0375207	+	0.397681i
$445$	−23.7152			−1.12421
$446$	0.788393			0.0373315
$447$	5.18440	+	0.489141i	0.245214	+	0.0231356i
$448$	0.252730	+	13.5302i	0.0119404	+	0.639243i
$449$	2.96108	−	1.70958i	0.139742	−	0.0806801i	−0.428499	−	0.903542i	$-0.640957\pi$
$449$	2.96108	−	1.70958i	0.139742	−	0.0806801i	0.568241	+	0.822862i	$0.307624\pi$
$450$	−13.7501	−	11.8603i	−0.648186	−	0.559098i
$451$	−16.0546	−	9.26913i	−0.755982	−	0.436466i
$452$			0.864590i			0.0406669i
$453$	5.66869	−	2.59655i	0.266338	−	0.121996i
$454$			2.49208i			0.116959i
$455$	14.7241	−	29.3547i	0.690278	−	1.37617i
$456$	−0.756221	+	8.01518i	−0.0354133	+	0.375345i
$457$	−16.2857	−	28.2076i	−0.761812	−	1.31950i	−0.941916	−	0.335849i	$-0.890977\pi$
$457$	−16.2857	−	28.2076i	−0.761812	−	1.31950i	0.180104	−	0.983648i	$-0.442357\pi$
$458$	15.3876			0.719015
$459$	0.582935	+	0.607231i	0.0272091	+	0.0283431i
$460$	16.5222	+	9.53910i	0.770352	+	0.444763i
$461$	−17.7020	−	30.6608i	−0.824467	−	1.42802i	−0.902326	−	0.431054i	$-0.858142\pi$
$461$	−17.7020	−	30.6608i	−0.824467	−	1.42802i	0.0778597	−	0.996964i	$-0.475191\pi$
$462$	−6.73796	−	14.0128i	−0.313478	−	0.651934i
$463$	17.8630			0.830164			0.415082	−	0.909784i	$-0.363753\pi$
$463$	17.8630			0.830164			0.415082	+	0.909784i	$0.363753\pi$
$464$		−	0.697031i		−	0.0323588i
$465$	0.957848	+	0.0903717i	0.0444192	+	0.00419089i
$466$	18.2137			0.843732
$467$	−20.0513	+	34.7299i	−0.927864	+	1.60711i	−0.140976	+	0.990013i	$0.545024\pi$
$467$	−20.0513	+	34.7299i	−0.927864	+	1.60711i	−0.786888	+	0.617095i	$0.788309\pi$
$468$	−10.3257	−	8.20988i	−0.477308	−	0.379502i
$469$	0.0467164	+	2.50102i	0.00215716	+	0.115486i
$470$	−18.0400	−	10.4154i	−0.832125	−	0.480428i
$471$	−3.48173	−	7.60118i	−0.160430	−	0.350244i
$472$	−21.9647	−	12.6813i	−1.01101	−	0.583705i
$473$	28.7991	−	16.6271i	1.32418	−	0.764517i
$474$	−15.9432	−	1.50422i	−0.732297	−	0.0690912i
$475$	−9.69704	+	5.59859i	−0.444930	+	0.256881i
$476$	0.447720	−	0.269763i	0.0205212	−	0.0123646i
$477$	36.8596	−	12.8506i	1.68769	−	0.588387i
$478$	7.75788	+	13.4370i	0.354837	+	0.614596i
$479$	−25.9586			−1.18608			−0.593039	−	0.805174i	$-0.702072\pi$
$479$	−25.9586			−1.18608			−0.593039	+	0.805174i	$0.702072\pi$
$480$	13.9642	+	30.4861i	0.637374	+	1.39149i
$481$	12.1446	−	7.67505i	0.553744	−	0.349952i
$482$	−1.74278			−0.0793813
$483$	18.7664	−	9.02371i	0.853901	−	0.410593i
$484$	2.28758	−	3.96221i	0.103981	−	0.180100i
$485$		−	27.7278i		−	1.25905i
$486$	0.732936	+	13.7515i	0.0332467	+	0.623782i
$487$	12.8783	−	22.3058i	0.583570	−	1.01077i	−0.411482	−	0.911418i	$-0.634989\pi$
$487$	12.8783	−	22.3058i	0.583570	−	1.01077i	0.995052	−	0.0993553i	$-0.0316780\pi$
$488$	−18.5078			−0.837807
$489$	−1.37132	+	14.5346i	−0.0620132	+	0.657277i
$490$	0.795028	+	21.2740i	0.0359157	+	0.961059i
$491$	−3.64975	−	2.10719i	−0.164711	−	0.0950959i	0.415379	−	0.909649i	$-0.363649\pi$
$491$	−3.64975	−	2.10719i	−0.164711	−	0.0950959i	−0.580090	+	0.814553i	$0.696982\pi$
$492$	9.26968	−	4.24598i	0.417909	−	0.191424i
$493$	−1.33115	+	0.768537i	−0.0599518	+	0.0346132i
$494$	4.40027	−	2.78086i	0.197978	−	0.125117i
$495$	−30.0368	−	25.9085i	−1.35005	−	1.16450i
$496$	0.0102650	+	0.00592651i	0.000460913	+	0.000266108i
$497$	6.83250	+	11.3397i	0.306480	+	0.508657i
$498$	−0.668380	−	1.45918i	−0.0299508	−	0.0653876i
$499$	4.79919	−	8.31244i	0.214841	−	0.372116i	−0.738382	−	0.674383i	$-0.764410\pi$
$499$	4.79919	−	8.31244i	0.214841	−	0.372116i	0.953223	+	0.302266i	$0.0977432\pi$
$500$	−3.88711	+	6.73267i	−0.173837	+	0.301094i
$501$	2.01490	+	1.43138i	0.0900190	+	0.0639491i
$502$	−0.830158	−	0.479292i	−0.0370518	−	0.0213918i
$503$	2.79256	+	4.83685i	0.124514	+	0.215664i	0.921543	−	0.388277i	$-0.126930\pi$
$503$	2.79256	+	4.83685i	0.124514	+	0.215664i	−0.797029	+	0.603941i	$0.793596\pi$
$504$	22.2519	+	3.80740i	0.991179	+	0.169595i
$505$	−8.77717	+	15.2025i	−0.390579	+	0.676502i
$506$	−13.3521	−	7.70883i	−0.593573	−	0.342699i
$507$	−0.316785	+	22.5144i	−0.0140689	+	0.999901i
$508$	4.08893	+	7.08223i	0.181417	+	0.314223i
$509$	−16.3326	−	28.2889i	−0.723929	−	1.25388i	−0.959413	−	0.282003i	$-0.909001\pi$
$509$	−16.3326	−	28.2889i	−0.723929	−	1.25388i	0.235485	−	0.971878i	$-0.424332\pi$
$510$	−0.494192	+	0.695657i	−0.0218832	+	0.0308042i
$511$	−13.6001	−	22.5717i	−0.601631	−	0.998513i
$512$			0.830992i			0.0367250i
$513$	8.15581	+	2.36477i	0.360088	+	0.104407i
$514$	10.6911	+	6.17250i	0.471564	+	0.272258i
$515$	3.43077	−	1.98075i	0.151178	−	0.0872825i
$516$	−1.71796	+	18.2086i	−0.0756290	+	0.801591i
$517$	−22.7825	−	13.1535i	−1.00197	−	0.578489i
$518$	−4.50509	+	8.15091i	−0.197942	+	0.358130i
$519$	2.71845	−	28.8128i	0.119327	−	1.26474i
$520$	16.4152	−	31.2556i	0.719856	−	1.37065i
$521$	−11.5944	−	20.0821i	−0.507961	−	0.879815i	−0.999958	−	0.00921756i	$-0.997066\pi$
$521$	−11.5944	−	20.0821i	−0.507961	−	0.879815i	0.491996	−	0.870597i	$-0.336267\pi$
$522$	−24.7029	−	4.70323i	−1.08121	−	0.205855i
$523$	−22.1779	+	12.8044i	−0.969771	+	0.559897i	−0.899166	−	0.437607i	$-0.855826\pi$
$523$	−22.1779	+	12.8044i	−0.969771	+	0.559897i	−0.0706045	+	0.997504i	$0.522493\pi$
$524$	6.19539	+	10.7307i	0.270647	+	0.468774i
$525$	13.6064	+	28.2969i	0.593830	+	1.23498i
$526$	−2.76039	−	4.78114i	−0.120359	−	0.208468i
$527$		−	0.0261380i		−	0.00113859i
$528$	−0.203512	−	0.444301i	−0.00885673	−	0.0193357i
$529$	−1.17606	+	2.03700i	−0.0511332	+	0.0885652i
$530$	19.7862	+	34.2706i	0.859456	+	1.48862i
$531$	−17.4730	+	20.2572i	−0.758261	+	0.879086i
$532$	2.55085	−	4.61516i	0.110593	−	0.200093i
$533$	−15.4073	−	8.09183i	−0.667366	−	0.350496i
$534$	−6.10439	+	8.59295i	−0.264163	+	0.371853i
$535$			65.8578i			2.84728i
$536$			2.68910i			0.116151i
$537$	−18.9772	−	1.79047i	−0.818924	−	0.0772644i
$538$			8.87275i			0.382531i
$539$	1.00403	+	26.8666i	0.0432466	+	1.15722i
$540$	21.1838	−	5.21522i	0.911606	−	0.224427i
$541$	−20.3485	+	35.2447i	−0.874851	+	1.51529i	−0.0179303	+	0.999839i	$0.505708\pi$
$541$	−20.3485	+	35.2447i	−0.874851	+	1.51529i	−0.856921	+	0.515448i	$0.827626\pi$
$542$	−6.77649	+	11.7372i	−0.291075	+	0.504157i
$543$	4.86453	+	0.458962i	0.208757	+	0.0196959i
$544$	0.788936	−	0.455493i	0.0338254	−	0.0195291i
$545$	68.1397			2.91878
$546$	−6.84632	−	12.8912i	−0.292995	−	0.551691i
$547$	−24.1727			−1.03355			−0.516776	−	0.856121i	$-0.672868\pi$
$547$	−24.1727			−1.03355			−0.516776	+	0.856121i	$0.672868\pi$
$548$	−9.75029	+	5.62933i	−0.416512	+	0.240473i
$549$	−3.65114	+	19.1770i	−0.155827	+	0.818453i
$550$	11.6237	−	20.1329i	0.495638	−	0.858469i
$551$	−7.75314	+	13.4288i	−0.330295	+	0.572088i
$552$	20.3518	−	9.32216i	0.866230	−	0.396777i
$553$	24.2348	+	13.3948i	1.03057	+	0.569605i
$554$		−	8.34887i		−	0.354709i
$555$	−2.23172	+	23.6540i	−0.0947314	+	1.00406i
$556$		−	12.5646i		−	0.532857i
$557$			6.69804i			0.283805i	0.989881	+	0.141903i	$0.0453220\pi$
$557$			6.69804i			0.283805i	−0.989881	+	0.141903i	$0.954678\pi$
$558$	0.279300	−	0.323804i	0.0118237	−	0.0137077i
$559$	26.3896	−	16.6776i	1.11616	−	0.705386i
$560$	0.0124961	+	0.668991i	0.000528055	+	0.0282700i
$561$	−0.624108	+	0.878535i	−0.0263498	+	0.0370918i
$562$	5.13582	+	8.89550i	0.216642	+	0.375234i
$563$	6.04230	−	10.4656i	0.254653	−	0.441072i	−0.710148	−	0.704052i	$-0.751372\pi$
$563$	6.04230	−	10.4656i	0.254653	−	0.441072i	0.964801	+	0.262981i	$0.0847055\pi$
$564$	13.1543	−	6.02532i	0.553894	−	0.253712i
$565$			2.44056i			0.102675i
$566$	0.719110	+	1.24554i	0.0302265	+	0.0523538i
$567$	8.33485	−	22.3054i	0.350031	−	0.936738i
$568$	7.11610	+	12.3254i	0.298585	+	0.517164i
$569$	−10.1564	+	5.86379i	−0.425778	+	0.245823i	−0.697546	−	0.716540i	$-0.745725\pi$
$569$	−10.1564	+	5.86379i	−0.425778	+	0.245823i	0.271768	+	0.962363i	$0.412392\pi$
$570$	−0.808609	+	8.57044i	−0.0338689	+	0.358976i
$571$	−15.1381	−	26.2200i	−0.633511	−	1.09727i	−0.986829	−	0.161770i	$-0.948280\pi$
$571$	−15.1381	−	26.2200i	−0.633511	−	1.09727i	0.353318	−	0.935503i	$-0.385053\pi$
$572$	7.85276	−	14.9521i	0.328340	−	0.625180i
$573$	−4.37955	−	0.413204i	−0.182958	−	0.0172619i
$574$	11.2795	−	0.210689i	0.470797	−	0.00879399i
$575$	26.9627	+	15.5669i	1.12442	+	0.649185i
$576$	15.0737	+	2.86992i	0.628072	+	0.119580i
$577$	−27.0888	+	15.6397i	−1.12772	+	0.651089i	−0.943360	−	0.331770i	$-0.892354\pi$
$577$	−27.0888	+	15.6397i	−1.12772	+	0.651089i	−0.184359	+	0.982859i	$0.559021\pi$
$578$	−12.9859	−	7.49742i	−0.540143	−	0.311852i
$579$	1.74325	−	18.4767i	0.0724470	−	0.767865i
$580$			39.8377i			1.65417i
$581$	0.0518286	+	2.77471i	0.00215021	+	0.115114i
$582$	−10.0469	−	7.13726i	−0.416456	−	0.295849i
$583$	24.9876	+	43.2799i	1.03488	+	1.79247i
$584$	−14.1645	−	24.5337i	−0.586133	−	1.01521i
$585$	−29.1474	−	23.1748i	−1.20510	−	0.958159i
$586$	4.29320	+	2.47868i	0.177351	+	0.102393i
$587$	0.348443	−	0.603522i	0.0143818	−	0.0249100i	−0.858745	−	0.512403i	$-0.828755\pi$
$587$	0.348443	−	0.603522i	0.0143818	−	0.0249100i	0.873127	+	0.487493i	$0.162089\pi$
$588$	−12.3659	−	8.10733i	−0.509961	−	0.334341i
$589$	−0.131842	−	0.228358i	−0.00543247	−	0.00940931i
$590$	−23.4863	−	13.5598i	−0.966916	−	0.558249i
$591$	4.98874	−	7.02248i	0.205209	−	0.288866i
$592$	−0.146355	+	0.253494i	−0.00601515	+	0.0104186i
$593$	−14.0745	+	24.3778i	−0.577972	+	1.00108i	0.417740	+	0.908567i	$0.362822\pi$
$593$	−14.0745	+	24.3778i	−0.577972	+	1.00108i	−0.995712	+	0.0925098i	$0.970511\pi$
$594$	−17.1193	+	4.21457i	−0.702412	+	0.172926i
$595$	1.26382	−	0.761486i	0.0518116	−	0.0312179i
$596$	−3.17544	−	1.83334i	−0.130071	−	0.0750966i
$597$	9.85224	−	13.8687i	0.403225	−	0.567607i
$598$	−12.8138	−	6.72971i	−0.523994	−	0.275198i
$599$	5.29808	−	3.05885i	0.216474	−	0.124981i	−0.387843	−	0.921726i	$-0.626780\pi$
$599$	5.29808	−	3.05885i	0.216474	−	0.124981i	0.604316	+	0.796744i	$0.293446\pi$
$600$	14.0564	+	30.6874i	0.573849	+	1.25281i
$601$	−4.63482	−	2.67591i	−0.189058	−	0.109153i	0.402483	−	0.915427i	$-0.368147\pi$
$601$	−4.63482	−	2.67591i	−0.189058	−	0.109153i	−0.591542	+	0.806275i	$0.701480\pi$
$602$	−9.78938	+	17.7116i	−0.398985	+	0.721870i
$603$	2.78633	+	0.530495i	0.113468	+	0.0216034i
$604$	−4.39027			−0.178638
$605$	6.45737	−	11.1845i	0.262529	−	0.454714i
$606$	3.24919	+	7.09351i	0.131989	+	0.288154i
$607$			21.7643i			0.883386i	0.897166	+	0.441693i	$0.145622\pi$
$607$			21.7643i			0.883386i	−0.897166	+	0.441693i	$0.854378\pi$
$608$	4.59509	−	7.95893i	0.186355	−	0.322777i
$609$	35.9115	+	24.5153i	1.45521	+	0.993409i
$610$	−19.7899			−0.801270
$611$	−21.8640	−	11.4828i	−0.884522	−	0.464545i
$612$	−0.195117	−	0.559660i	−0.00788715	−	0.0226229i
$613$	−20.7209			−0.836908			−0.418454	−	0.908238i	$-0.637428\pi$
$613$	−20.7209			−0.836908			−0.418454	+	0.908238i	$0.637428\pi$
$614$	3.89316	+	6.74315i	0.157115	+	0.272131i
$615$	26.1664	−	11.9855i	1.05513	−	0.483303i
$616$	0.539767	+	28.8971i	0.0217478	+	1.16430i
$617$	−23.0797	+	13.3251i	−0.929153	+	0.536447i	−0.886544	−	0.462645i	$-0.846900\pi$
$617$	−23.0797	+	13.3251i	−0.929153	+	0.536447i	−0.0426095	+	0.999092i	$0.513567\pi$
$618$	0.165389	−	1.75296i	0.00665293	−	0.0705143i
$619$	29.5414	−	17.0557i	1.18737	−	0.685527i	0.229660	−	0.973271i	$-0.426239\pi$
$619$	29.5414	−	17.0557i	1.18737	−	0.685527i	0.957707	+	0.287744i	$0.0929052\pi$
$620$	−0.586681	−	0.338720i	−0.0235617	−	0.0136033i
$621$	−5.64430	−	22.9267i	−0.226498	−	0.920018i
$622$	−18.3289	−	10.5822i	−0.734923	−	0.424308i
$623$	15.6110	−	9.40608i	0.625443	−	0.376847i
$624$	−0.207576	−	0.409118i	−0.00830968	−	0.0163778i
$625$	6.15661	−	10.6636i	0.246264	−	0.426542i
$626$	−6.00367			−0.239955
$627$	−1.02118	+	10.8235i	−0.0407820	+	0.432248i
$628$			5.88694i			0.234915i
$629$	0.645477			0.0257368
$630$	23.7935	+	4.07117i	0.947954	+	0.162199i
$631$	−2.85221	−	4.94018i	−0.113545	−	0.196665i	0.803652	−	0.595099i	$-0.202887\pi$
$631$	−2.85221	−	4.94018i	−0.113545	−	0.196665i	−0.917197	+	0.398434i	$0.869554\pi$
$632$	25.7793	+	14.8837i	1.02544	+	0.592040i
$633$	−22.3025	−	15.8436i	−0.886443	−	0.629725i
$634$	−6.98518			−0.277417
$635$	11.5422	+	19.9917i	0.458038	+	0.793345i
$636$	−27.3643	−	2.58179i	−1.08507	−	0.102375i
$637$	1.95038	+	25.1634i	0.0772768	+	0.997010i
$638$		−	32.1940i		−	1.27457i
$639$	14.1749	−	4.94188i	0.560752	−	0.195498i
$640$		−	23.1639i		−	0.915635i
$641$	−2.36730	−	1.36676i	−0.0935029	−	0.0539839i	0.452519	−	0.891755i	$-0.350525\pi$
$641$	−2.36730	−	1.36676i	−0.0935029	−	0.0539839i	−0.546022	+	0.837771i	$0.683859\pi$
$642$	23.8629	+	16.9521i	0.941794	+	0.669046i
$643$	1.97815	−	1.14209i	0.0780108	−	0.0450395i	−0.460487	−	0.887666i	$-0.652325\pi$
$643$	1.97815	−	1.14209i	0.0780108	−	0.0450395i	0.538498	+	0.842627i	$0.318992\pi$
$644$	−14.6596	+	0.273826i	−0.577668	+	0.0107902i
$645$	−4.84944	+	51.3992i	−0.190947	+	2.02384i
$646$	0.233872			0.00920158
$647$	34.3748			1.35141			0.675707	−	0.737170i	$-0.263838\pi$
$647$	34.3748			1.35141			0.675707	+	0.737170i	$0.263838\pi$
$648$	9.40633	−	23.8071i	0.369516	−	0.935231i
$649$	−29.6605	−	17.1245i	−1.16428	−	0.672196i
$650$	10.1474	−	19.3212i	0.398012	−	0.757840i
$651$	−0.666369	+	0.320419i	−0.0261171	+	0.0125582i
$652$	5.13981	−	8.90242i	0.201291	−	0.348645i
$653$	−3.81525	+	2.20274i	−0.149302	+	0.0861998i	−0.572790	−	0.819702i	$-0.694139\pi$
$653$	−3.81525	+	2.20274i	−0.149302	+	0.0861998i	0.423488	+	0.905902i	$0.360806\pi$
$654$	17.5395	−	24.6897i	0.685847	−	0.965444i
$655$	17.4883	+	30.2906i	0.683324	+	1.18355i
$656$	0.354577			0.0138439
$657$	−28.2151	+	9.83679i	−1.10078	+	0.383770i
$658$	16.0063	−	0.298981i	0.623991	−	0.0116555i
$659$	−40.5474	+	23.4100i	−1.57950	+	0.911926i	−0.584573	+	0.811341i	$0.698738\pi$
$659$	−40.5474	+	23.4100i	−1.57950	+	0.911926i	−0.994928	+	0.100585i	$0.967929\pi$
$660$	11.6314	+	25.3933i	0.452752	+	0.988432i
$661$		−	26.9642i		−	1.04879i	−0.851476	−	0.524393i	$-0.824292\pi$
$661$		−	26.9642i		−	1.04879i	0.851476	−	0.524393i	$-0.175708\pi$
$662$	6.75266	−	3.89865i	0.262449	−	0.151525i
$663$	−0.552438	+	0.847504i	−0.0214549	+	0.0329143i
$664$			2.98337i			0.115777i
$665$	7.20051	−	13.0276i	0.279224	−	0.505190i
$666$	7.99634	+	6.89730i	0.309852	+	0.267265i
$667$	43.1153			1.66943
$668$	−0.870147	−	1.50714i	−0.0336670	−	0.0583129i
$669$	−0.895200	+	1.26014i	−0.0346104	+	0.0487199i
$670$			2.87539i			0.111086i
$671$	−24.9924			−0.964820
$672$	−21.2838	−	14.5296i	−0.821041	−	0.560490i
$673$	−7.16313	+	12.4069i	−0.276118	+	0.478251i	−0.970417	−	0.241436i	$-0.922381\pi$
$673$	−7.16313	+	12.4069i	−0.276118	+	0.478251i	0.694298	+	0.719687i	$0.255715\pi$
$674$	8.85668	−	5.11341i	0.341147	−	0.196961i
$675$	34.5700	−	8.51073i	1.33060	−	0.327578i
$676$	6.80465	−	14.3200i	0.261717	−	0.550771i
$677$	19.8879	−	34.4468i	0.764353	−	1.32390i	−0.176235	−	0.984348i	$-0.556392\pi$
$677$	19.8879	−	34.4468i	0.764353	−	1.32390i	0.940588	−	0.339550i	$-0.110275\pi$
$678$	0.884310	+	0.628210i	0.0339617	+	0.0241263i
$679$	10.9976	+	18.2524i	0.422049	+	0.700464i
$680$	1.37368	−	0.793092i	0.0526781	−	0.0304137i
$681$	−3.98326	−	2.82969i	−0.152639	−	0.108434i
$682$	0.474114	+	0.273730i	0.0181548	+	0.0104817i
$683$	21.6231	+	12.4841i	0.827386	+	0.477692i	0.852957	−	0.521981i	$-0.174807\pi$
$683$	21.6231	+	12.4841i	0.827386	+	0.477692i	−0.0255707	+	0.999673i	$0.508140\pi$
$684$	−4.52764	−	3.90535i	−0.173119	−	0.149325i
$685$	−27.5230	+	15.8904i	−1.05160	+	0.607142i
$686$	−8.96117	−	13.6887i	−0.342139	−	0.522638i
$687$	−17.4722	+	24.5950i	−0.666607	+	0.938360i
$688$	−0.318023	+	0.550832i	−0.0121245	+	0.0210003i
$689$	25.0634	+	39.6589i	0.954840	+	1.51088i
$690$	21.7617	−	9.96796i	0.828454	−	0.379474i
$691$	−19.8811	+	11.4784i	−0.756313	+	0.436657i	−0.827970	−	0.560772i	$-0.810504\pi$
$691$	−19.8811	+	11.4784i	−0.756313	+	0.436657i	0.0716575	+	0.997429i	$0.477171\pi$
$692$	−10.1890	+	17.6478i	−0.387326	+	0.670868i
$693$	30.0484	+	5.14142i	1.14144	+	0.195306i
$694$	16.4558			0.624653
$695$		−	35.4672i		−	1.34535i
$696$	38.1064	+	27.0707i	1.44442	+	1.02611i
$697$	−0.390952	−	0.677149i	−0.0148084	−	0.0256488i
$698$	9.67298			0.366128
$699$	−20.6812	+	29.1122i	−0.782233	+	1.10112i
$700$	−0.412887	−	22.1044i	−0.0156056	−	0.835467i
$701$		−	12.8742i		−	0.486253i	−0.969995	−	0.243126i	$-0.921827\pi$
$701$		−	12.8742i		−	0.486253i	0.969995	−	0.243126i	$-0.0781730\pi$
$702$	−15.8998	+	4.59598i	−0.600100	+	0.173464i
$703$	5.63928	−	3.25584i	0.212690	−	0.122796i
$704$			19.6449i			0.740393i
$705$	37.1317	−	17.0082i	1.39846	−	0.640566i
$706$	−17.4988	+	10.1029i	−0.658576	+	0.380229i
$707$	−0.251954	−	13.4886i	−0.00947569	−	0.507293i
$708$	17.1255	−	7.84435i	0.643616	−	0.294809i
$709$	−37.2273			−1.39810			−0.699050	−	0.715073i	$-0.746393\pi$
$709$	−37.2273			−1.39810			−0.699050	+	0.715073i	$0.746393\pi$
$710$	7.60907	+	13.1793i	0.285563	+	0.494610i
$711$	20.5074	−	23.7752i	0.769089	−	0.891639i
$712$	16.9680	−	9.79649i	0.635903	−	0.367139i
$713$	−0.366589	+	0.634950i	−0.0137289	+	0.0237791i
$714$	0.0493965	−	0.653942i	0.00184862	−	0.0244732i
$715$	22.1667	−	42.2067i	0.828987	−	1.57844i
$716$	11.6235	+	6.71082i	0.434390	+	0.250795i
$717$	−30.2862	−	2.85747i	−1.13106	−	0.106714i
$718$	−29.9856			−1.11905
$719$	−47.8697			−1.78524			−0.892619	−	0.450811i	$-0.851135\pi$
$719$	−47.8697			−1.78524			−0.892619	+	0.450811i	$0.851135\pi$
$720$	0.745309	+	0.141901i	0.0277760	+	0.00528833i
$721$	−1.47276	+	2.66461i	−0.0548484	+	0.0992353i
$722$	−12.4929	+	7.21275i	−0.464936	+	0.268431i
$723$	1.97888	−	2.78560i	0.0735953	−	0.103598i
$724$	−2.97952	−	1.72023i	−0.110733	−	0.0639317i
$725$			65.0113i			2.41446i
$726$	−2.39043	−	5.21870i	−0.0887171	−	0.193684i
$727$			10.2075i			0.378574i	0.981922	+	0.189287i	$0.0606176\pi$
$727$			10.2075i			0.378574i	−0.981922	+	0.189287i	$0.939382\pi$
$728$	1.59112	+	27.0854i	0.0589710	+	1.00385i
$729$	−22.8123	−	14.4430i	−0.844899	−	0.534927i
$730$	−15.1458	−	26.2333i	−0.560572	−	0.970939i
$731$	1.40259			0.0518768
$732$	7.96054	−	11.2058i	0.294230	−	0.414178i
$733$	36.4929	+	21.0692i	1.34789	+	0.778208i	0.987951	−	0.154766i	$-0.0494625\pi$
$733$	36.4929	+	21.0692i	1.34789	+	0.778208i	0.359944	+	0.932974i	$0.382796\pi$
$734$	−12.4917	−	21.6362i	−0.461076	−	0.798608i
$735$	−34.9064	−	22.8853i	−1.28754	−	0.844137i
$736$	−25.5534			−0.941909
$737$			3.63128i			0.133760i
$738$	2.39251	−	12.5662i	0.0880696	−	0.462570i
$739$	7.12014			0.261919			0.130959	−	0.991388i	$-0.458194\pi$
$739$	7.12014			0.261919			0.130959	+	0.991388i	$0.458194\pi$
$740$	8.36468	−	14.4881i	0.307492	−	0.532591i
$741$	−0.551555	+	10.1909i	−0.0202619	+	0.374371i
$742$	−26.6173	−	14.7117i	−0.977153	−	0.540083i
$743$	19.3136	+	11.1507i	0.708546	+	0.409079i	0.810522	−	0.585708i	$-0.199183\pi$
$743$	19.3136	+	11.1507i	0.708546	+	0.409079i	−0.101976	+	0.994787i	$0.532517\pi$
$744$	−0.722664	+	0.331017i	−0.0264942	+	0.0121357i
$745$	−8.96360	−	5.17514i	−0.328401	−	0.189602i
$746$	−3.23023	+	1.86497i	−0.118267	+	0.0682815i
$747$	3.09124	+	0.588548i	0.113103	+	0.0215338i
$748$	0.657142	−	0.379401i	0.0240275	−	0.0138723i
$749$	−26.1210	−	43.3524i	−0.954440	−	1.58406i
$750$	4.06187	+	8.86772i	0.148318	+	0.323803i
$751$	−11.7813	−	20.4059i	−0.429908	−	0.744622i	0.566957	−	0.823747i	$-0.308121\pi$
$751$	−11.7813	−	20.4059i	−0.429908	−	0.744622i	−0.996865	+	0.0791256i	$0.974787\pi$
$752$	0.503166			0.0183486
$753$	1.70871	−	0.782675i	0.0622688	−	0.0285223i
$754$	−1.20859	−	30.1983i	−0.0440141	−	1.09976i
$755$	−12.3928			−0.451021
$756$	−11.8762	+	11.8351i	−0.431934	+	0.430438i
$757$	−3.94895	+	6.83979i	−0.143527	+	0.248596i	−0.928822	−	0.370525i	$-0.879178\pi$
$757$	−3.94895	+	6.83979i	−0.143527	+	0.248596i	0.785295	+	0.619121i	$0.212511\pi$
$758$			29.4640i			1.07018i
$759$	27.4825	−	12.5884i	0.997552	−	0.456930i
$760$	8.00085	−	13.8579i	0.290221	−	0.502678i
$761$	42.8464			1.55318			0.776590	−	0.630007i	$-0.216948\pi$
$761$	42.8464			1.55318			0.776590	+	0.630007i	$0.216948\pi$
$762$	10.2148	+	0.963750i	0.370042	+	0.0349130i
$763$	−44.8545	+	27.0260i	−1.62384	+	0.978408i
$764$	2.68247	+	1.54872i	0.0970482	+	0.0560308i
$765$	−0.550775	−	1.57980i	−0.0199133	−	0.0571179i
$766$	−13.6729	+	7.89405i	−0.494022	+	0.285224i
$767$	−28.4647	−	14.9495i	−1.02780	−	0.539794i
$768$	−22.8377	−	16.2238i	−0.824085	−	0.585427i
$769$	−28.1847	−	16.2725i	−1.01637	−	0.586800i	−0.103318	−	0.994648i	$-0.532946\pi$
$769$	−28.1847	−	16.2725i	−1.01637	−	0.586800i	−0.913050	+	0.407848i	$0.866279\pi$
$770$	0.577160	+	30.8989i	0.0207994	+	1.11352i
$771$	−22.0054	+	10.0796i	−0.792505	+	0.363008i
$772$	−6.53384	+	11.3169i	−0.235158	+	0.407306i
$773$	−22.8515	+	39.5799i	−0.821910	+	1.42359i	0.0823488	+	0.996604i	$0.473758\pi$
$773$	−22.8515	+	39.5799i	−0.821910	+	1.42359i	−0.904258	+	0.426986i	$0.859575\pi$
$774$	17.3757	+	14.9875i	0.624557	+	0.538716i
$775$	−0.957407	−	0.552759i	−0.0343911	−	0.0198557i
$776$	11.4541	+	19.8390i	0.411177	+	0.712179i
$777$	−7.91274	−	16.4560i	−0.283868	−	0.590354i
$778$	10.9339	−	18.9381i	0.392000	−	0.678963i
$779$	−6.83119	−	3.94399i	−0.244753	−	0.141308i
$780$	11.8637	+	23.3825i	0.424787	+	0.837227i
$781$	9.60938	+	16.6439i	0.343851	+	0.595567i
$782$	−0.325142	−	0.563162i	−0.0116270	−	0.0201386i
$783$	35.5670	−	34.1439i	1.27106	−	1.22020i
$784$	−0.273566	−	0.435422i	−0.00977021	−	0.0155508i
$785$			16.6176i			0.593108i
$786$	15.4771	+	1.46024i	0.552049	+	0.0520850i
$787$	−10.7291	−	6.19444i	−0.382451	−	0.220808i	0.296433	−	0.955054i	$-0.404203\pi$
$787$	−10.7291	−	6.19444i	−0.382451	−	0.220808i	−0.678884	+	0.734246i	$0.737536\pi$
$788$	−5.25280	+	3.03270i	−0.187123	+	0.108036i
$789$	10.7764	+	1.01674i	0.383649	+	0.0361968i
$790$	27.5651	+	15.9147i	0.980724	+	0.566221i
$791$	−0.967990	−	1.60655i	−0.0344178	−	0.0571224i
$792$	32.1936	+	6.12940i	1.14395	+	0.217799i
$793$	−23.4431	+	0.938233i	−0.832488	+	0.0333176i
$794$	9.99266	+	17.3078i	0.354626	+	0.614230i
$795$	−77.2438	−	7.28785i	−2.73956	−	0.258473i
$796$	−10.3737	+	5.98927i	−0.367687	+	0.212284i
$797$	10.3478	+	17.9229i	0.366537	+	0.634861i	0.989022	−	0.147771i	$-0.0472099\pi$
$797$	10.3478	+	17.9229i	0.366537	+	0.634861i	−0.622484	+	0.782632i	$0.713877\pi$
$798$	−2.86698	−	5.96240i	−0.101490	−	0.211067i
$799$	−0.554785	−	0.960916i	−0.0196269	−	0.0339948i
$800$		−	38.5305i		−	1.36226i
$801$	−6.80332	−	19.5142i	−0.240384	−	0.689499i
$802$	10.7813	−	18.6738i	0.380701	−	0.659394i
$803$	−19.1274	−	33.1297i	−0.674992	−	1.16912i
$804$	−1.62815	−	1.15663i	−0.0574205	−	0.0407913i
$805$	−41.3809	+	0.772952i	−1.45849	+	0.0272430i
$806$	0.454999	+	0.238963i	0.0160267	+	0.00841710i
$807$	−14.1819	−	10.0748i	−0.499227	−	0.354649i
$808$		−	14.5030i		−	0.510214i
$809$		−	37.9266i		−	1.33343i	−0.745314	−	0.666714i	$-0.767700\pi$
$809$		−	37.9266i		−	1.33343i	0.745314	−	0.666714i	$-0.232300\pi$
$810$	10.0580	−	25.4564i	0.353401	−	0.894445i
$811$			29.8342i			1.04762i	0.851835	+	0.523811i	$0.175490\pi$
$811$			29.8342i			1.04762i	−0.851835	+	0.523811i	$0.824510\pi$
$812$	−15.8007	−	26.2240i	−0.554495	−	0.920283i
$813$	−11.0659	−	24.1587i	−0.388098	−	0.847281i
$814$	−6.75975	+	11.7082i	−0.236929	+	0.410373i
$815$	14.5086	−	25.1297i	0.508215	−	0.880253i
$816$	0.00193611	−	0.0205208i	6.77775e−5	−	0.000718373i
$817$	12.2539	−	7.07481i	0.428711	−	0.247516i
$818$	−28.0671			−0.981342
$819$	28.3787	+	3.69466i	0.991631	+	0.129102i
$820$	−20.2653			−0.707693
$821$	18.4843	−	10.6719i	0.645105	−	0.372452i	−0.141473	−	0.989942i	$-0.545184\pi$
$821$	18.4843	−	10.6719i	0.645105	−	0.372452i	0.786578	+	0.617490i	$0.211851\pi$
$822$	−1.32682	+	14.0630i	−0.0462782	+	0.490502i
$823$	24.7403	−	42.8515i	0.862394	−	1.49371i	−0.00721793	−	0.999974i	$-0.502298\pi$
$823$	24.7403	−	42.8515i	0.862394	−	1.49371i	0.869612	−	0.493736i	$-0.164369\pi$
$824$	−1.63646	+	2.83443i	−0.0570087	+	0.0987420i
$825$	18.9813	+	41.4394i	0.660846	+	1.44274i
$826$	20.8386	−	0.389243i	0.725067	−	0.0135435i
$827$		−	32.7958i		−	1.14042i	−0.821498	−	0.570211i	$-0.806861\pi$
$827$		−	32.7958i		−	1.14042i	0.821498	−	0.570211i	$-0.193139\pi$
$828$	−3.10947	+	16.3319i	−0.108061	+	0.567574i
$829$		−	29.1184i		−	1.01132i	−0.862731	−	0.505662i	$-0.831248\pi$
$829$		−	29.1184i		−	1.01132i	0.862731	−	0.505662i	$-0.168752\pi$
$830$			3.19005i			0.110728i
$831$	13.3446	+	9.47993i	0.462918	+	0.328855i
$832$	0.737483	+	18.4271i	0.0255676	+	0.638843i
$833$	−0.529912	+	1.00253i	−0.0183604	+	0.0347356i
$834$	−12.8512	−	9.12942i	−0.445000	−	0.316126i
$835$	−2.45624	−	4.25434i	−0.0850018	−	0.147227i
$836$	3.82747	−	6.62936i	0.132376	−	0.229281i
$837$	0.200421	+	0.814096i	0.00692757	+	0.0281393i
$838$			17.4265i			0.601989i
$839$	5.75458	+	9.96723i	0.198670	+	0.344107i	0.948098	−	0.317980i	$-0.103004\pi$
$839$	5.75458	+	9.96723i	0.198670	+	0.344107i	−0.749427	+	0.662087i	$0.769671\pi$
$840$	−37.0588	−	25.2985i	−1.27865	−	0.872882i
$841$	30.5151	+	52.8536i	1.05224	+	1.82254i
$842$	11.0167	−	6.36052i	0.379662	−	0.219198i
$843$	−20.0499	−	1.89168i	−0.690555	−	0.0651529i
$844$	9.63146	+	16.6822i	0.331529	+	0.574224i
$845$	19.2081	−	40.4225i	0.660778	−	1.39058i
$846$	3.39512	−	17.8323i	0.116727	−	0.613086i
$847$	0.185362	+	9.92360i	0.00636913	+	0.340979i
$848$	−0.827803	−	0.477932i	−0.0284269	−	0.0164123i
$849$	−2.80736	−	0.264870i	−0.0963483	−	0.00909032i
$850$	0.849162	−	0.490264i	0.0291260	−	0.0168159i
$851$	−15.6801	−	9.05289i	−0.537506	−	0.310329i
$852$	−10.5234	−	0.992866i	−0.360525	−	0.0340150i
$853$		−	29.7525i		−	1.01870i	−0.860558	−	0.509352i	$-0.829885\pi$
$853$		−	29.7525i		−	1.01870i	0.860558	−	0.509352i	$-0.170115\pi$
$854$	13.0272	−	7.84921i	0.445780	−	0.268594i
$855$	−12.7806	−	11.0240i	−0.437086	−	0.377012i
$856$	−27.2052	−	47.1207i	−0.929854	−	1.61055i
$857$	−19.5077	−	33.7884i	−0.666371	−	1.15419i	−0.978912	−	0.204285i	$-0.934513\pi$
$857$	−19.5077	−	33.7884i	−0.666371	−	1.15419i	0.312540	−	0.949905i	$-0.398820\pi$
$858$	−9.58737	−	18.8961i	−0.327307	−	0.645102i
$859$	−13.9082	−	8.02991i	−0.474542	−	0.273977i	0.243597	−	0.969877i	$-0.421673\pi$
$859$	−13.9082	−	8.02991i	−0.474542	−	0.273977i	−0.718139	+	0.695899i	$0.755006\pi$
$860$	18.1761	−	31.4819i	0.619800	−	1.07352i
$861$	−12.4708	+	18.2680i	−0.425004	+	0.622573i
$862$	−2.22433	−	3.85264i	−0.0757608	−	0.131222i
$863$	42.9178	+	24.7786i	1.46094	+	0.843474i	0.999055	−	0.0434667i	$-0.0138402\pi$
$863$	42.9178	+	24.7786i	1.46094	+	0.843474i	0.461884	+	0.886940i	$0.347174\pi$
$864$	−21.0796	+	20.2362i	−0.717143	+	0.688450i
$865$	−28.7613	+	49.8160i	−0.977913	+	1.69379i
$866$	−13.8892	+	24.0568i	−0.471974	+	0.817483i
$867$	26.7288	−	12.2432i	0.907759	−	0.415799i
$868$	0.520541	−	0.00972316i	0.0176683	−	0.000330026i
$869$	34.8116	+	20.0985i	1.18090	+	0.681794i
$870$	40.7463	+	28.9460i	1.38143	+	0.981361i
$871$	0.136321	+	3.40618i	0.00461907	+	0.115414i
$872$	−48.7534	+	28.1478i	−1.65100	+	0.953204i
$873$	22.8160	−	7.95445i	0.772203	−	0.269217i
$874$	−5.68128	−	3.28009i	−0.192172	−	0.110951i
$875$	−0.314972	−	16.8624i	−0.0106480	−	0.570053i
$876$	20.9467	+	1.97629i	0.707724	+	0.0667728i
$877$	−22.6958			−0.766384			−0.383192	−	0.923669i	$-0.625175\pi$
$877$	−22.6958			−0.766384			−0.383192	+	0.923669i	$0.625175\pi$
$878$	3.60072	−	6.23663i	0.121518	−	0.210476i
$879$	−8.83667	+	4.04764i	−0.298054	+	0.136524i
$880$			0.971324i			0.0327433i
$881$	4.12034	−	7.13665i	0.138818	−	0.240440i	−0.788232	−	0.615379i	$-0.789003\pi$
$881$	4.12034	−	7.13665i	0.138818	−	0.240440i	0.927049	+	0.374939i	$0.122336\pi$
$882$	−17.2773	+	6.75719i	−0.581757	+	0.227526i
$883$	36.7826			1.23783			0.618917	−	0.785456i	$-0.287572\pi$
$883$	36.7826			1.23783			0.618917	+	0.785456i	$0.287572\pi$
$884$	0.602162	−	0.380551i	0.0202529	−	0.0127993i
$885$	48.3417	−	22.1430i	1.62499	−	0.744328i
$886$	−18.4022			−0.618234
$887$	−16.4394	−	28.4739i	−0.551981	−	0.956059i	−0.998132	−	0.0611011i	$-0.980539\pi$
$887$	−16.4394	−	28.4739i	−0.551981	−	0.956059i	0.446151	−	0.894958i	$-0.352795\pi$
$888$	−8.17445	−	17.8462i	−0.274316	−	0.598878i
$889$	−15.5271	−	8.58201i	−0.520763	−	0.287831i
$890$	18.1435	−	10.4752i	0.608171	−	0.351128i
$891$	12.7021	−	32.1485i	0.425535	−	1.07701i
$892$	0.942583	−	0.544201i	0.0315600	−	0.0182212i
$893$	−9.69389	−	5.59677i	−0.324394	−	0.187289i
$894$	−4.18243	+	1.91576i	−0.139881	+	0.0640728i
$895$	32.8106	+	18.9432i	1.09674	+	0.633202i
$896$	9.18744	+	15.2482i	0.306931	+	0.509406i
$897$	25.3063	−	12.8397i	0.844952	−	0.428706i
$898$	−1.51027	+	2.61586i	−0.0503982	+	0.0872923i
$899$	−1.53096			−0.0510605
$900$	−24.6260	−	4.68860i	−0.820868	−	0.156287i
$901$			2.10785i			0.0702226i
$902$	16.3770			0.545293
$903$	−17.1940	−	35.7581i	−0.572182	−	1.18995i
$904$	−1.00817	−	1.74620i	−0.0335312	−	0.0580777i
$905$	−8.41056	−	4.85584i	−0.279577	−	0.161414i
$906$	−3.18997	+	4.49041i	−0.105980	+	0.149184i
$907$	45.9316			1.52513			0.762567	−	0.646909i	$-0.223939\pi$
$907$	45.9316			1.52513			0.762567	+	0.646909i	$0.223939\pi$
$908$	1.72020	+	2.97947i	0.0570868	+	0.0988772i
$909$	−15.0274	−	2.86110i	−0.498428	−	0.0948967i
$910$	1.70135	+	28.9618i	0.0563992	+	0.960075i
$911$			41.6510i			1.37996i	0.723829	+	0.689979i	$0.242380\pi$
$911$			41.6510i			1.37996i	−0.723829	+	0.689979i	$0.757620\pi$
$912$	−0.0865939	−	0.189049i	−0.00286741	−	0.00626003i
$913$			4.02866i			0.133329i
$914$	24.9190	+	14.3870i	0.824247	+	0.475879i
$915$	22.4709	−	31.6316i	0.742867	−	1.04571i
$916$	18.3970	−	10.6215i	0.607855	−	0.350945i
$917$	−23.5261	−	13.0032i	−0.776902	−	0.429402i
$918$	−0.714197	−	0.207081i	−0.0235720	−	0.00683469i
$919$	−9.16673			−0.302382			−0.151191	−	0.988505i	$-0.548311\pi$
$919$	−9.16673			−0.302382			−0.151191	+	0.988505i	$0.548311\pi$
$920$	−44.4929			−1.46689
$921$	−15.1986	−	1.43397i	−0.500812	−	0.0472509i
$922$	27.0862	+	15.6382i	0.892037	+	0.515018i
$923$	9.63852	+	15.2514i	0.317256	+	0.502007i
$924$	−17.7283	−	12.1024i	−0.583218	−	0.398139i
$925$	13.6504	−	23.6431i	0.448821	−	0.777381i
$926$	−13.6662	+	7.89021i	−0.449101	+	0.259288i
$927$	2.61408	+	2.25479i	0.0858576	+	0.0740571i
$928$	−26.6793	−	46.2099i	−0.875790	−	1.51691i
$929$	29.7764			0.976931			0.488466	−	0.872583i	$-0.337557\pi$
$929$	29.7764			0.976931			0.488466	+	0.872583i	$0.337557\pi$
$930$	−0.772728	+	0.353948i	−0.0253387	+	0.0116064i
$931$	0.427211	+	11.4316i	0.0140013	+	0.374657i
$932$	21.7758	−	12.5723i	0.713291	−	0.411819i
$933$	37.7263	−	17.2806i	1.23510	−	0.565740i
$934$		−	35.4272i		−	1.15921i
$935$	1.85497	−	1.07097i	0.0606642	−	0.0350245i
$936$	30.4280	+	4.54087i	0.994570	+	0.148423i
$937$			13.4476i			0.439314i	0.975577	+	0.219657i	$0.0704939\pi$
$937$			13.4476i			0.439314i	−0.975577	+	0.219657i	$0.929506\pi$
$938$	−1.14046	−	1.89279i	−0.0372372	−	0.0618018i
$939$	6.81701	−	9.59608i	0.222465	−	0.313156i
$940$	−28.7577			−0.937971
$941$	19.4524	+	33.6926i	0.634130	+	1.09835i	0.986699	+	0.162560i	$0.0519751\pi$
$941$	19.4524	+	33.6926i	0.634130	+	1.09835i	−0.352568	+	0.935786i	$0.614692\pi$
$942$	6.02122	+	4.27745i	0.196182	+	0.139367i
$943$			21.9326i			0.714223i
$944$	0.655072			0.0213208
$945$	−33.5241	+	33.4080i	−1.09054	+	1.08676i
$946$	−14.6886	+	25.4415i	−0.477569	+	0.827174i
$947$	−34.2756	+	19.7890i	−1.11381	+	0.643057i	−0.939813	−	0.341689i	$-0.889001\pi$
$947$	−34.2756	+	19.7890i	−1.11381	+	0.643057i	−0.173995	+	0.984747i	$0.555668\pi$
$948$	−20.0997	+	9.20667i	−0.652807	+	0.299019i
$949$	−19.1854	−	30.3579i	−0.622785	−	0.985458i
$950$	4.94587	−	8.56649i	0.160465	−	0.277934i
$951$	7.93149	−	11.1649i	0.257196	−	0.362046i
$952$	−0.589691	+	1.06691i	−0.0191120	+	0.0345787i
$953$	33.8841	−	19.5630i	1.09761	−	0.633707i	0.162020	−	0.986787i	$-0.448199\pi$
$953$	33.8841	−	19.5630i	1.09761	−	0.633707i	0.935593	+	0.353080i	$0.114866\pi$
$954$	−22.5236	+	26.1126i	−0.729228	+	0.845426i
$955$	7.57204	+	4.37172i	0.245026	+	0.141466i
$956$	18.5503	+	10.7100i	0.599959	+	0.346386i
$957$	51.4579	+	36.5555i	1.66340	+	1.18167i
$958$	19.8598	−	11.4661i	0.641642	−	0.370452i
$959$	11.8151	−	21.3766i	0.381529	−	0.690286i
$960$	−24.8635	−	17.6629i	−0.802466	−	0.570068i
$961$	−15.4870	+	26.8242i	−0.499580	+	0.865298i
$962$	−5.90117	+	11.2362i	−0.190261	+	0.362269i
$963$	−54.1915	+	18.8931i	−1.74630	+	0.608820i
$964$	−2.08362	+	1.20298i	−0.0671090	+	0.0387454i
$965$	−18.4437	+	31.9454i	−0.593723	+	1.02836i
$966$	−10.3716	+	15.1929i	−0.333700	+	0.488824i
$967$	32.9048			1.05815			0.529073	−	0.848576i	$-0.322540\pi$
$967$	32.9048			1.05815			0.529073	+	0.848576i	$0.322540\pi$
$968$			10.6699i			0.342943i
$969$	−0.265556	+	0.373814i	−0.00853089	+	0.0120086i
$970$	12.2476	+	21.2134i	0.393245	+	0.681121i
$971$	21.1816			0.679749			0.339875	−	0.940471i	$-0.389615\pi$
$971$	21.1816			0.679749			0.339875	+	0.940471i	$0.389615\pi$
$972$	10.3685	+	15.9351i	0.332570	+	0.511118i
$973$	14.0673	+	23.3471i	0.450975	+	0.748473i
$974$			22.7537i			0.729075i
$975$	19.3603	+	38.1580i	0.620027	+	1.22203i
$976$	0.413980	−	0.239011i	0.0132512	−	0.00765057i
$977$		−	20.4243i		−	0.653432i	−0.945123	−	0.326716i	$-0.894058\pi$
$977$		−	20.4243i		−	0.653432i	0.945123	−	0.326716i	$-0.105942\pi$
$978$	−5.37089	−	11.7255i	−0.171742	−	0.374941i
$979$	22.9131	−	13.2289i	0.732307	−	0.422798i
$980$	15.6352	+	24.8859i	0.499448	+	0.794949i
$981$	19.5477	+	56.0691i	0.624109	+	1.79015i
$982$	3.72303			0.118807
$983$	−17.3835	−	30.1091i	−0.554448	−	0.960332i	−0.997946	−	0.0640565i	$-0.979596\pi$
$983$	−17.3835	−	30.1091i	−0.554448	−	0.960332i	0.443499	−	0.896275i	$-0.353737\pi$
$984$	−13.7707	+	19.3846i	−0.438995	+	0.617958i
$985$	−14.8276	+	8.56069i	−0.472445	+	0.272766i
$986$	0.678936	−	1.17595i	0.0216217	−	0.0374499i
$987$	−17.6969	+	25.9235i	−0.563298	+	0.825153i
$988$	3.34133	−	6.36209i	0.106302	−	0.202405i
$989$	−34.0721	−	19.6715i	−1.08343	−	0.625519i
$990$	34.4238	+	6.55402i	1.09406	+	0.208301i
$991$	−31.8594			−1.01205			−0.506023	−	0.862520i	$-0.668885\pi$
$991$	−31.8594			−1.01205			−0.506023	+	0.862520i	$0.668885\pi$
$992$	0.907364			0.0288088
$993$	−1.43599	+	15.2201i	−0.0455698	+	0.482994i
$994$	−10.2361	−	5.65761i	−0.324670	−	0.179448i
$995$	−29.2829	+	16.9065i	−0.928329	+	0.535971i
$996$	−1.80632	−	1.28321i	−0.0572356	−	0.0406599i
$997$	−20.8568	−	12.0417i	−0.660543	−	0.381365i	0.131941	−	0.991258i	$-0.457879\pi$
$997$	−20.8568	−	12.0417i	−0.660543	−	0.381365i	−0.792484	+	0.609893i	$0.791212\pi$
$998$			8.47934i			0.268409i
$999$	−20.1041	+	4.94939i	−0.636064	+	0.156592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bf.b.152.12	yes	64
3.2	odd	2	inner	273.2.bf.b.152.21	yes	64
7.3	odd	6		273.2.r.b.269.12	yes	64
13.3	even	3		273.2.r.b.68.12	✓	64
21.17	even	6		273.2.r.b.269.21	yes	64
39.29	odd	6		273.2.r.b.68.21	yes	64
91.3	odd	6	inner	273.2.bf.b.185.21	yes	64
273.185	even	6	inner	273.2.bf.b.185.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.12	✓	64	13.3	even	3
273.2.r.b.68.21	yes	64	39.29	odd	6
273.2.r.b.269.12	yes	64	7.3	odd	6
273.2.r.b.269.21	yes	64	21.17	even	6
273.2.bf.b.152.12	yes	64	1.1	even	1	trivial
273.2.bf.b.152.21	yes	64	3.2	odd	2	inner
273.2.bf.b.185.12	yes	64	273.185	even	6	inner
273.2.bf.b.185.21	yes	64	91.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.765058 + 0.441707i) q^{2} +(0.162694 - 1.72439i) q^{3} +(-0.609790 + 1.05619i) q^{4} +(-1.72131 + 2.98140i) q^{5} +(0.637205 + 1.39112i) q^{6} +(-0.0494112 - 2.64529i) q^{7} -2.84422i q^{8} +(-2.94706 - 0.561097i) q^{9} +O(q^{10})\)	\(q+(-0.765058 + 0.441707i) q^{2} +(0.162694 - 1.72439i) q^{3} +(-0.609790 + 1.05619i) q^{4} +(-1.72131 + 2.98140i) q^{5} +(0.637205 + 1.39112i) q^{6} +(-0.0494112 - 2.64529i) q^{7} -2.84422i q^{8} +(-2.94706 - 0.561097i) q^{9} -3.04126i q^{10} -3.84076i q^{11} +(1.72207 + 1.22335i) q^{12} +(-0.144185 - 3.60267i) q^{13} +(1.20624 + 2.00198i) q^{14} +(4.86105 + 3.45327i) q^{15} +(0.0367306 + 0.0636193i) q^{16} +(0.0809974 - 0.140292i) q^{17} +(2.50251 - 0.872465i) q^{18} -1.63423i q^{19} +(-2.09928 - 3.63606i) q^{20} +(-4.56956 - 0.345169i) q^{21} +(1.69649 + 2.93840i) q^{22} +(-3.93521 + 2.27200i) q^{23} +(-4.90455 - 0.462738i) q^{24} +(-3.42582 - 5.93370i) q^{25} +(1.70163 + 2.69256i) q^{26} +(-1.44702 + 4.99060i) q^{27} +(2.82405 + 1.56088i) q^{28} +(-8.21721 - 4.74421i) q^{29} +(-5.24432 - 0.494795i) q^{30} +(0.139734 - 0.0806754i) q^{31} +(4.87013 + 2.81177i) q^{32} +(-6.62298 - 0.624869i) q^{33} +0.143108i q^{34} +(7.97171 + 4.40605i) q^{35} +(2.38971 - 2.77050i) q^{36} +(1.99228 + 3.45072i) q^{37} +(0.721851 + 1.25028i) q^{38} +(-6.23587 - 0.337501i) q^{39} +(8.47975 + 4.89579i) q^{40} +(2.41336 - 4.18006i) q^{41} +(3.64844 - 1.75433i) q^{42} +(4.32913 + 7.49828i) q^{43} +(4.05656 + 2.34206i) q^{44} +(6.74566 - 7.82054i) q^{45} +(2.00711 - 3.47642i) q^{46} +(3.42471 - 5.93177i) q^{47} +(0.115680 - 0.0529875i) q^{48} +(-6.99512 + 0.261414i) q^{49} +(5.24191 + 3.02642i) q^{50} +(-0.228740 - 0.162496i) q^{51} +(3.89302 + 2.04459i) q^{52} +(-11.2686 + 6.50591i) q^{53} +(-1.09733 - 4.45726i) q^{54} +(11.4508 + 6.61114i) q^{55} +(-7.52379 + 0.140536i) q^{56} +(-2.81806 - 0.265880i) q^{57} +8.38220 q^{58} +(4.45863 - 7.72257i) q^{59} +(-6.61153 + 3.02841i) q^{60} -6.50715i q^{61} +(-0.0712698 + 0.123443i) q^{62} +(-1.33865 + 7.82356i) q^{63} -5.11484 q^{64} +(10.9892 + 5.77144i) q^{65} +(5.34297 - 2.44735i) q^{66} -0.945460 q^{67} +(0.0987829 + 0.171097i) q^{68} +(3.27758 + 7.15549i) q^{69} +(-8.04501 + 0.150272i) q^{70} +(-4.33350 + 2.50195i) q^{71} +(-1.59588 + 8.38209i) q^{72} +(8.62581 - 4.98012i) q^{73} +(-3.04842 - 1.76000i) q^{74} +(-10.7894 + 4.94208i) q^{75} +(1.72606 + 0.996539i) q^{76} +(-10.1599 + 0.189777i) q^{77} +(4.91988 - 2.49622i) q^{78} +(-5.23295 + 9.06373i) q^{79} -0.252899 q^{80} +(8.37034 + 3.30717i) q^{81} +4.26399i q^{82} -1.04892 q^{83} +(3.15104 - 4.61583i) q^{84} +(0.278843 + 0.482971i) q^{85} +(-6.62408 - 3.82441i) q^{86} +(-9.51777 + 13.3978i) q^{87} -10.9240 q^{88} +(3.44435 + 5.96579i) q^{89} +(-1.70644 + 8.96277i) q^{90} +(-9.52297 + 0.559423i) q^{91} -5.54177i q^{92} +(-0.116382 - 0.254082i) q^{93} +6.05087i q^{94} +(4.87230 + 2.81302i) q^{95} +(5.64094 - 7.94056i) q^{96} +(-6.97520 + 4.02713i) q^{97} +(5.23621 - 3.28979i) q^{98} +(-2.15504 + 11.3189i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9	\( 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42} - 20 q^{43} - 3 q^{45} + 6 q^{48} - 10 q^{51} + 30 q^{52} - 27 q^{54} + 18 q^{55} + 4 q^{57} - 60 q^{58} + 55 q^{60} - 74 q^{63} - 84 q^{64} + 75 q^{66} - 88 q^{67} - 33 q^{69} + 20 q^{70} - 34 q^{72} + 84 q^{73} + 33 q^{75} + 18 q^{76} - 71 q^{78} + 20 q^{79} - 32 q^{81} - 6 q^{84} - 2 q^{85} + 3 q^{87} + 92 q^{88} - 76 q^{91} + 28 q^{93} + 30 q^{96} + 24 q^{97} + 22 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9 + 6 * q^12 - 12 * q^13 - 9 * q^15 - 16 * q^16 + 2 * q^18 + 10 * q^21 + 10 * q^22 - 24 * q^25 - 50 * q^28 - 16 * q^30 - 24 * q^31 - 33 * q^39 + 90 * q^40 - 48 * q^42 - 20 * q^43 - 3 * q^45 + 6 * q^48 - 10 * q^51 + 30 * q^52 - 27 * q^54 + 18 * q^55 + 4 * q^57 - 60 * q^58 + 55 * q^60 - 74 * q^63 - 84 * q^64 + 75 * q^66 - 88 * q^67 - 33 * q^69 + 20 * q^70 - 34 * q^72 + 84 * q^73 + 33 * q^75 + 18 * q^76 - 71 * q^78 + 20 * q^79 - 32 * q^81 - 6 * q^84 - 2 * q^85 + 3 * q^87 + 92 * q^88 - 76 * q^91 + 28 * q^93 + 30 * q^96 + 24 * q^97 + 22 * q^99

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