LMFDB - Embedded newform 504.2.cy.a.347.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(347,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("504.347");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cy (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			347.10
Character	$\chi$	$=$	504.347
Dual form			504.2.cy.a.443.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36156 + 0.382313i) q^{2} +(-1.59594 - 0.673028i) q^{3} +(1.70767 - 1.04108i) q^{4} -0.632847 q^{5} +(2.43027 + 0.306217i) q^{6} +(-1.94512 + 1.79346i) q^{7} +(-1.92708 + 2.07036i) q^{8} +(2.09407 + 2.14823i) q^{9} +O(q^{10})$	\(q+(-1.36156 + 0.382313i) q^{2} +(-1.59594 - 0.673028i) q^{3} +(1.70767 - 1.04108i) q^{4} -0.632847 q^{5} +(2.43027 + 0.306217i) q^{6} +(-1.94512 + 1.79346i) q^{7} +(-1.92708 + 2.07036i) q^{8} +(2.09407 + 2.14823i) q^{9} +(0.861657 - 0.241945i) q^{10} -4.02378i q^{11} +(-3.42603 + 0.512193i) q^{12} +(4.91266 + 2.83633i) q^{13} +(1.96272 - 3.18555i) q^{14} +(1.00999 + 0.425924i) q^{15} +(1.83230 - 3.55565i) q^{16} +(-0.471154 - 0.272021i) q^{17} +(-3.67249 - 2.12435i) q^{18} +(-0.489234 - 0.847378i) q^{19} +(-1.08070 + 0.658845i) q^{20} +(4.31135 - 1.55315i) q^{21} +(1.53834 + 5.47861i) q^{22} -2.12080 q^{23} +(4.46891 - 2.00719i) q^{24} -4.59950 q^{25} +(-7.77323 - 1.98365i) q^{26} +(-1.89619 - 4.83781i) q^{27} +(-1.45449 + 5.08768i) q^{28} +(-4.00971 - 6.94503i) q^{29} +(-1.53799 - 0.193788i) q^{30} +(1.51802 - 0.876428i) q^{31} +(-1.13541 + 5.54174i) q^{32} +(-2.70812 + 6.42173i) q^{33} +(0.745500 + 0.190244i) q^{34} +(1.23096 - 1.13499i) q^{35} +(5.81246 + 1.48838i) q^{36} +(5.03405 - 2.90641i) q^{37} +(0.990083 + 0.966713i) q^{38} +(-5.93140 - 7.83297i) q^{39} +(1.21954 - 1.31022i) q^{40} +(-6.25701 - 3.61249i) q^{41} +(-5.27636 + 3.76298i) q^{42} +(-4.96013 - 8.59120i) q^{43} +(-4.18908 - 6.87131i) q^{44} +(-1.32522 - 1.35950i) q^{45} +(2.88759 - 0.810810i) q^{46} +(1.86819 - 3.23581i) q^{47} +(-5.31730 + 4.44143i) q^{48} +(0.566968 - 6.97700i) q^{49} +(6.26249 - 1.75845i) q^{50} +(0.568857 + 0.751229i) q^{51} +(11.3421 - 0.270957i) q^{52} +(-0.176173 + 0.305140i) q^{53} +(4.43133 + 5.86202i) q^{54} +2.54644i q^{55} +(0.0352810 - 7.48323i) q^{56} +(0.210480 + 1.68163i) q^{57} +(8.11463 + 7.92309i) q^{58} +(8.90652 - 5.14218i) q^{59} +(2.16815 - 0.324140i) q^{60} +(6.42814 + 3.71129i) q^{61} +(-1.73180 + 1.77366i) q^{62} +(-7.92598 - 0.422922i) q^{63} +(-0.572750 - 7.97947i) q^{64} +(-3.10896 - 1.79496i) q^{65} +(1.23215 - 9.77889i) q^{66} +(-5.52633 - 9.57189i) q^{67} +(-1.08777 + 0.0259864i) q^{68} +(3.38468 + 1.42736i) q^{69} +(-1.24210 + 2.01596i) q^{70} -4.51619 q^{71} +(-8.48303 + 0.195663i) q^{72} +(4.20833 - 7.28904i) q^{73} +(-5.74299 + 5.88182i) q^{74} +(7.34055 + 3.09560i) q^{75} +(-1.71764 - 0.937713i) q^{76} +(7.21651 + 7.82673i) q^{77} +(11.0706 + 8.39739i) q^{78} +(-4.48487 - 2.58934i) q^{79} +(-1.15957 + 2.25018i) q^{80} +(-0.229769 + 8.99707i) q^{81} +(9.90037 + 2.52647i) q^{82} +(-14.3393 + 8.27879i) q^{83} +(5.74543 - 7.14073i) q^{84} +(0.298168 + 0.172148i) q^{85} +(10.0380 + 9.80108i) q^{86} +(1.72508 + 13.7825i) q^{87} +(8.33066 + 7.75414i) q^{88} +(2.25028 - 1.29920i) q^{89} +(2.32412 + 1.34439i) q^{90} +(-14.6426 + 3.29370i) q^{91} +(-3.62164 + 2.20793i) q^{92} +(-3.01253 + 0.377061i) q^{93} +(-1.30656 + 5.11997i) q^{94} +(0.309610 + 0.536260i) q^{95} +(5.54179 - 8.08013i) q^{96} +(3.33047 + 5.76854i) q^{97} +(1.89544 + 9.71634i) q^{98} +(8.64400 - 8.42607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9	$ 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 5 q^{12} - 3 q^{14} + q^{16} + 5 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} + 148 q^{25} + 6 q^{26} - 8 q^{27} + 24 q^{30} - 33 q^{32} + 22 q^{33} - 4 q^{34} - 30 q^{35} - 38 q^{36} - 12 q^{40} - 12 q^{41} + 7 q^{42} - 4 q^{43} - 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} + 26 q^{51} - 18 q^{52} - 40 q^{54} + 18 q^{56} + 4 q^{57} + 6 q^{58} - 6 q^{59} - 2 q^{60} - 8 q^{64} - 6 q^{65} + 43 q^{66} + 2 q^{67} - 18 q^{70} - 11 q^{72} - 4 q^{73} - 36 q^{75} + 2 q^{76} - 29 q^{78} - 87 q^{80} - 10 q^{81} - 4 q^{82} - 72 q^{83} - 65 q^{84} + 14 q^{88} + 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} + 9 q^{94} - 88 q^{96} - 4 q^{97} - 57 q^{98} + 10 q^{99}+O(q^{100}) $ 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 5 * q^12 - 3 * q^14 + q^16 + 5 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 + 148 * q^25 + 6 * q^26 - 8 * q^27 + 24 * q^30 - 33 * q^32 + 22 * q^33 - 4 * q^34 - 30 * q^35 - 38 * q^36 - 12 * q^40 - 12 * q^41 + 7 * q^42 - 4 * q^43 - 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 + 26 * q^51 - 18 * q^52 - 40 * q^54 + 18 * q^56 + 4 * q^57 + 6 * q^58 - 6 * q^59 - 2 * q^60 - 8 * q^64 - 6 * q^65 + 43 * q^66 + 2 * q^67 - 18 * q^70 - 11 * q^72 - 4 * q^73 - 36 * q^75 + 2 * q^76 - 29 * q^78 - 87 * q^80 - 10 * q^81 - 4 * q^82 - 72 * q^83 - 65 * q^84 + 14 * q^88 + 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 + 9 * q^94 - 88 * q^96 - 4 * q^97 - 57 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.36156	+	0.382313i	−0.962766	+	0.270336i
$2$	−1.36156	+	0.382313i	−0.962766	+	0.270336i
$3$	−1.59594	−	0.673028i	−0.921418	−	0.388573i
$3$	−1.59594	−	0.673028i	−0.921418	−	0.388573i
$4$	1.70767	−	1.04108i	0.853837	−	0.520540i
$5$	−0.632847			−0.283018			−0.141509	−	0.989937i	$-0.545195\pi$
$5$	−0.632847			−0.283018			−0.141509	+	0.989937i	$0.545195\pi$
$6$	2.43027	+	0.306217i	0.992155	+	0.125012i
$7$	−1.94512	+	1.79346i	−0.735186	+	0.677866i
$7$	−1.94512	+	1.79346i	−0.735186	+	0.677866i
$8$	−1.92708	+	2.07036i	−0.681325	+	0.731981i
$9$	2.09407	+	2.14823i	0.698022	+	0.716076i
$10$	0.861657	−	0.241945i	0.272480	−	0.0765098i
$11$		−	4.02378i		−	1.21322i	−0.795001	−	0.606608i	$-0.792530\pi$
$11$		−	4.02378i		−	1.21322i	0.795001	−	0.606608i	$-0.207470\pi$
$12$	−3.42603	+	0.512193i	−0.989009	+	0.147857i
$13$	4.91266	+	2.83633i	1.36253	+	0.786655i	0.989960	−	0.141350i	$-0.0451442\pi$
$13$	4.91266	+	2.83633i	1.36253	+	0.786655i	0.372567	+	0.928005i	$0.378478\pi$
$14$	1.96272	−	3.18555i	0.524560	−	0.851373i
$15$	1.00999	+	0.425924i	0.260778	+	0.109973i
$16$	1.83230	−	3.55565i	0.458075	−	0.888913i
$17$	−0.471154	−	0.272021i	−0.114272	−	0.0659747i	0.441775	−	0.897126i	$-0.354349\pi$
$17$	−0.471154	−	0.272021i	−0.114272	−	0.0659747i	−0.556046	+	0.831151i	$0.687682\pi$
$18$	−3.67249	−	2.12435i	−0.865613	−	0.500713i
$19$	−0.489234	−	0.847378i	−0.112238	−	0.194402i	0.804434	−	0.594042i	$-0.202469\pi$
$19$	−0.489234	−	0.847378i	−0.112238	−	0.194402i	−0.916672	+	0.399640i	$0.869135\pi$
$20$	−1.08070	+	0.658845i	−0.241651	+	0.147322i
$21$	4.31135	−	1.55315i	0.940813	−	0.338925i
$22$	1.53834	+	5.47861i	0.327976	+	1.16804i
$23$	−2.12080			−0.442218			−0.221109	−	0.975249i	$-0.570968\pi$
$23$	−2.12080			−0.442218			−0.221109	+	0.975249i	$0.570968\pi$
$24$	4.46891	−	2.00719i	0.912213	−	0.409717i
$25$	−4.59950			−0.919901
$26$	−7.77323	−	1.98365i	−1.52446	−	0.389025i
$27$	−1.89619	−	4.83781i	−0.364923	−	0.931038i
$28$	−1.45449	+	5.08768i	−0.274872	+	0.961481i
$29$	−4.00971	−	6.94503i	−0.744585	−	1.28966i	−0.950388	−	0.311066i	$-0.899314\pi$
$29$	−4.00971	−	6.94503i	−0.744585	−	1.28966i	0.205803	−	0.978593i	$-0.434019\pi$
$30$	−1.53799	−	0.193788i	−0.280797	−	0.0353807i
$31$	1.51802	−	0.876428i	0.272644	−	0.157411i	−0.357445	−	0.933934i	$-0.616352\pi$
$31$	1.51802	−	0.876428i	0.272644	−	0.157411i	0.630089	+	0.776523i	$0.283019\pi$
$32$	−1.13541	+	5.54174i	−0.200714	+	0.979650i
$33$	−2.70812	+	6.42173i	−0.471423	+	1.11788i
$34$	0.745500	+	0.190244i	0.127852	+	0.0326265i
$35$	1.23096	−	1.13499i	0.208071	−	0.191848i
$36$	5.81246	+	1.48838i	0.968744	+	0.248063i
$37$	5.03405	−	2.90641i	0.827593	−	0.477811i	−0.0254350	−	0.999676i	$-0.508097\pi$
$37$	5.03405	−	2.90641i	0.827593	−	0.477811i	0.853028	+	0.521866i	$0.174764\pi$
$38$	0.990083	+	0.966713i	0.160613	+	0.156821i
$39$	−5.93140	−	7.83297i	−0.949784	−	1.25428i
$40$	1.21954	−	1.31022i	0.192827	−	0.207164i
$41$	−6.25701	−	3.61249i	−0.977181	−	0.564176i	−0.0757629	−	0.997126i	$-0.524139\pi$
$41$	−6.25701	−	3.61249i	−0.977181	−	0.564176i	−0.901418	+	0.432950i	$0.857473\pi$
$42$	−5.27636	+	3.76298i	−0.814160	+	0.580641i
$43$	−4.96013	−	8.59120i	−0.756413	−	1.31015i	−0.944669	−	0.328025i	$-0.893617\pi$
$43$	−4.96013	−	8.59120i	−0.756413	−	1.31015i	0.188256	−	0.982120i	$-0.439717\pi$
$44$	−4.18908	−	6.87131i	−0.631528	−	1.03589i
$45$	−1.32522	−	1.35950i	−0.197553	−	0.202662i
$46$	2.88759	−	0.810810i	0.425752	−	0.119547i
$47$	1.86819	−	3.23581i	0.272504	−	0.471991i	−0.696998	−	0.717073i	$-0.745481\pi$
$47$	1.86819	−	3.23581i	0.272504	−	0.471991i	0.969502	+	0.245082i	$0.0788148\pi$
$48$	−5.31730	+	4.44143i	−0.767486	+	0.641065i
$49$	0.566968	−	6.97700i	0.0809955	−	0.996714i
$50$	6.26249	−	1.75845i	0.885649	−	0.248682i
$51$	0.568857	+	0.751229i	0.0796559	+	0.105193i
$52$	11.3421	−	0.270957i	1.57286	−	0.0375749i
$53$	−0.176173	+	0.305140i	−0.0241992	+	0.0419143i	−0.877871	−	0.478896i	$-0.841037\pi$
$53$	−0.176173	+	0.305140i	−0.0241992	+	0.0419143i	0.853672	+	0.520811i	$0.174370\pi$
$54$	4.43133	+	5.86202i	0.603028	+	0.797720i
$55$			2.54644i			0.343362i
$56$	0.0352810	−	7.48323i	0.00471462	−	0.999989i
$57$	0.210480	+	1.68163i	0.0278788	+	0.222738i
$58$	8.11463	+	7.92309i	1.06550	+	1.04035i
$59$	8.90652	−	5.14218i	1.15953	−	0.669455i	0.208339	−	0.978057i	$-0.433194\pi$
$59$	8.90652	−	5.14218i	1.15953	−	0.669455i	0.951191	+	0.308602i	$0.0998610\pi$
$60$	2.16815	−	0.324140i	0.279907	−	0.0418463i
$61$	6.42814	+	3.71129i	0.823038	+	0.475181i	0.851463	−	0.524414i	$-0.175716\pi$
$61$	6.42814	+	3.71129i	0.823038	+	0.475181i	−0.0284247	+	0.999596i	$0.509049\pi$
$62$	−1.73180	+	1.77366i	−0.219939	+	0.225256i
$63$	−7.92598	−	0.422922i	−0.998579	−	0.0532832i
$64$	−0.572750	−	7.97947i	−0.0715937	−	0.997434i
$65$	−3.10896	−	1.79496i	−0.385619	−	0.222637i
$66$	1.23215	−	9.77889i	0.151667	−	1.20370i
$67$	−5.52633	−	9.57189i	−0.675149	−	1.16939i	−0.976425	−	0.215856i	$-0.930746\pi$
$67$	−5.52633	−	9.57189i	−0.675149	−	1.16939i	0.301276	−	0.953537i	$-0.402587\pi$
$68$	−1.08777	+	0.0259864i	−0.131912	+	0.00315131i
$69$	3.38468	+	1.42736i	0.407468	+	0.171834i
$70$	−1.24210	+	2.01596i	−0.148460	+	0.240954i
$71$	−4.51619			−0.535973			−0.267987	−	0.963423i	$-0.586358\pi$
$71$	−4.51619			−0.535973			−0.267987	+	0.963423i	$0.586358\pi$
$72$	−8.48303	+	0.195663i	−0.999734	+	0.0230591i
$73$	4.20833	−	7.28904i	0.492547	−	0.853117i	−0.507416	−	0.861701i	$-0.669399\pi$
$73$	4.20833	−	7.28904i	0.492547	−	0.853117i	0.999963	+	0.00858427i	$0.00273249\pi$
$74$	−5.74299	+	5.88182i	−0.667609	+	0.683748i
$75$	7.34055	+	3.09560i	0.847613	+	0.357449i
$76$	−1.71764	−	0.937713i	−0.197027	−	0.107563i
$77$	7.21651	+	7.82673i	0.822398	+	0.891939i
$78$	11.0706	+	8.39739i	1.25350	+	0.950817i
$79$	−4.48487	−	2.58934i	−0.504588	−	0.291324i	0.226018	−	0.974123i	$-0.427429\pi$
$79$	−4.48487	−	2.58934i	−0.504588	−	0.291324i	−0.730606	+	0.682799i	$0.760762\pi$
$80$	−1.15957	+	2.25018i	−0.129643	+	0.251578i
$81$	−0.229769	+	8.99707i	−0.0255299	+	0.999674i
$82$	9.90037	+	2.52647i	1.09331	+	0.279002i
$83$	−14.3393	+	8.27879i	−1.57394	+	0.908716i	−0.578263	+	0.815851i	$0.696269\pi$
$83$	−14.3393	+	8.27879i	−1.57394	+	0.908716i	−0.995679	+	0.0928649i	$0.970398\pi$
$84$	5.74543	−	7.14073i	0.626877	−	0.779118i
$85$	0.298168	+	0.172148i	0.0323409	+	0.0186720i
$86$	10.0380	+	9.80108i	1.08243	+	1.05688i
$87$	1.72508	+	13.7825i	0.184948	+	1.47764i
$88$	8.33066	+	7.75414i	0.888052	+	0.826594i
$89$	2.25028	−	1.29920i	0.238529	−	0.137715i	−0.375971	−	0.926631i	$-0.622691\pi$
$89$	2.25028	−	1.29920i	0.238529	−	0.137715i	0.614500	+	0.788916i	$0.289358\pi$
$90$	2.32412	+	1.34439i	0.244984	+	0.141711i
$91$	−14.6426	+	3.29370i	−1.53496	+	0.345273i
$92$	−3.62164	+	2.20793i	−0.377582	+	0.230192i
$93$	−3.01253	+	0.377061i	−0.312385	+	0.0390994i
$94$	−1.30656	+	5.11997i	−0.134762	+	0.528085i
$95$	0.309610	+	0.536260i	0.0317653	+	0.0550191i
$96$	5.54179	−	8.08013i	0.565607	−	0.824675i
$97$	3.33047	+	5.76854i	0.338158	+	0.585707i	0.984086	−	0.177691i	$-0.0568628\pi$
$97$	3.33047	+	5.76854i	0.338158	+	0.585707i	−0.645928	+	0.763398i	$0.723529\pi$
$98$	1.89544	+	9.71634i	0.191468	+	0.981499i
$99$	8.64400	−	8.42607i	0.868755	−	0.846852i
$100$	−7.85446	+	4.78846i	−0.785446	+	0.478846i
$101$	2.01591			0.200590			0.100295	−	0.994958i	$-0.468021\pi$
$101$	2.01591			0.200590			0.100295	+	0.994958i	$0.468021\pi$
$102$	−1.06174	−	0.805360i	−0.105127	−	0.0797425i
$103$			12.1605i			1.19821i	0.800671	+	0.599105i	$0.204477\pi$
$103$			12.1605i			1.19821i	−0.800671	+	0.599105i	$0.795523\pi$
$104$	−15.3393	+	4.70514i	−1.50414	+	0.461377i
$105$	−2.72842	+	0.982905i	−0.266267	+	0.0959217i
$106$	0.123210	−	0.482819i	0.0119673	−	0.0468955i
$107$	10.0486	−	5.80154i	0.971432	−	0.560856i	0.0717593	−	0.997422i	$-0.477139\pi$
$107$	10.0486	−	5.80154i	0.971432	−	0.560856i	0.899672	+	0.436566i	$0.143805\pi$
$108$	−8.27464	−	6.28732i	−0.796227	−	0.604998i
$109$	−17.5241	−	10.1175i	−1.67850	−	0.969085i	−0.962616	−	0.270869i	$-0.912689\pi$
$109$	−17.5241	−	10.1175i	−1.67850	−	0.969085i	−0.715887	−	0.698216i	$-0.753978\pi$
$110$	−0.973536	−	3.46712i	−0.0928230	−	0.330577i
$111$	−9.99015	+	1.25041i	−0.948223	+	0.118683i
$112$	2.81290	+	10.2023i	0.265794	+	0.964030i
$113$	13.8665	+	8.00581i	1.30445	+	0.753123i	0.981164	−	0.193179i	$-0.0618799\pi$
$113$	13.8665	+	8.00581i	1.30445	+	0.753123i	0.323284	+	0.946302i	$0.395213\pi$
$114$	−0.929491	−	2.20917i	−0.0870548	−	0.206908i
$115$	1.34214			0.125156
$116$	−14.0776	−	7.68541i	−1.30707	−	0.713572i
$117$	4.19436	+	16.4930i	0.387769	+	1.52478i
$118$	−10.1608	+	10.4064i	−0.935379	+	0.957991i
$119$	1.40431	−	0.315885i	0.128733	−	0.0289572i
$120$	−2.82814	+	1.27025i	−0.258172	+	0.115957i
$121$	−5.19083			−0.471893
$122$	−10.1711	−	2.59557i	−0.920852	−	0.234992i
$123$	7.55453	+	9.97646i	0.681169	+	0.899547i
$124$	1.67985	−	3.07703i	0.150855	−	0.276326i
$125$	6.07502			0.543366
$126$	10.9534	−	2.45437i	0.975803	−	0.218653i
$127$		−	2.61169i		−	0.231750i	−0.993264	−	0.115875i	$-0.963033\pi$
$127$		−	2.61169i		−	0.231750i	0.993264	−	0.115875i	$-0.0369672\pi$
$128$	3.83048	+	10.6455i	0.338570	+	0.940941i
$129$	2.13397	+	17.0494i	0.187885	+	1.50111i
$130$	4.91926	+	1.25534i	0.431448	+	0.110101i
$131$		−	4.83044i		−	0.422037i	−0.977482	−	0.211019i	$-0.932322\pi$
$131$		−	4.83044i		−	0.422037i	0.977482	−	0.211019i	$-0.0676781\pi$
$132$	2.06095	+	13.7856i	0.179383	+	1.19988i
$133$	2.47136	+	0.770826i	0.214294	+	0.0668391i
$134$	11.1839	+	10.9199i	0.966139	+	0.943334i
$135$	1.20000	+	3.06160i	0.103280	+	0.263500i
$136$	1.47113	−	0.451251i	0.126148	−	0.0386945i
$137$		−	12.0086i		−	1.02597i	−0.858399	−	0.512983i	$-0.828540\pi$
$137$		−	12.0086i		−	1.02597i	0.858399	−	0.512983i	$-0.171460\pi$
$138$	−5.15413	−	0.649425i	−0.438749	−	0.0552827i
$139$	2.58319	−	4.47421i	0.219103	−	0.379497i	−0.735431	−	0.677600i	$-0.763020\pi$
$139$	2.58319	−	4.47421i	0.219103	−	0.379497i	0.954534	+	0.298102i	$0.0963536\pi$
$140$	0.920467	−	3.21972i	0.0777936	−	0.272116i
$141$	−5.15932	+	3.90682i	−0.434493	+	0.329013i
$142$	6.14905	−	1.72660i	0.516017	−	0.144893i
$143$	11.4128	−	19.7675i	0.954383	−	1.65304i
$144$	11.4753	−	3.50957i	0.956276	−	0.292465i
$145$	2.53754	+	4.39514i	0.210731	+	0.364997i
$146$	−2.94319	+	11.5333i	−0.243580	+	0.954505i
$147$	−5.60057	+	10.7533i	−0.461927	+	0.886918i
$148$	5.57071	−	10.2041i	0.457909	−	0.838768i
$149$	3.30035			0.270375			0.135187	−	0.990820i	$-0.456836\pi$
$149$	3.30035			0.270375			0.135187	+	0.990820i	$0.456836\pi$
$150$	−11.1781	−	1.40845i	−0.912685	−	0.114999i
$151$			2.83998i			0.231115i	0.993301	+	0.115557i	$0.0368654\pi$
$151$			2.83998i			0.231115i	−0.993301	+	0.115557i	$0.963135\pi$
$152$	2.69716	+	0.620074i	0.218769	+	0.0502946i
$153$	−0.402265	−	1.58178i	−0.0325212	−	0.127879i
$154$	−12.8180	−	7.89758i	−1.03290	−	0.636405i
$155$	−0.960673	+	0.554645i	−0.0771631	+	0.0445501i
$156$	−18.2837	−	7.20110i	−1.46386	−	0.576549i
$157$	−3.84161	+	2.21795i	−0.306594	+	0.177012i	−0.645401	−	0.763844i	$-0.723310\pi$
$157$	−3.84161	+	2.21795i	−0.306594	+	0.177012i	0.338808	+	0.940856i	$0.389976\pi$
$158$	7.09635	+	1.81091i	0.564555	+	0.144069i
$159$	0.486530	−	0.368417i	0.0385843	−	0.0292174i
$160$	0.718541	−	3.50707i	0.0568057	−	0.277258i
$161$	4.12521	−	3.80359i	0.325112	−	0.299764i
$162$	−3.12685	−	12.3379i	−0.245668	−	0.969354i
$163$	1.25204	+	2.16860i	0.0980675	+	0.169858i	0.910885	−	0.412661i	$-0.135401\pi$
$163$	1.25204	+	2.16860i	0.0980675	+	0.169858i	−0.812817	+	0.582519i	$0.802067\pi$
$164$	−14.4458	+	0.345104i	−1.12803	+	0.0269481i
$165$	1.71382	−	4.06397i	0.133421	−	0.316380i
$166$	16.3587	−	16.7541i	1.26968	−	1.30037i
$167$	2.03015	−	3.51633i	0.157098	−	0.272102i	−0.776723	−	0.629842i	$-0.783120\pi$
$167$	2.03015	−	3.51633i	0.157098	−	0.272102i	0.933821	+	0.357741i	$0.116453\pi$
$168$	−5.09273	+	11.9191i	−0.392913	+	0.919576i
$169$	9.58949	+	16.6095i	0.737653	+	1.27765i
$170$	−0.471787	−	0.120395i	−0.0361844	−	0.00923388i
$171$	0.795873	−	2.82545i	0.0608619	−	0.216068i
$172$	−17.4144	−	9.50707i	−1.32784	−	0.724907i
$173$	−8.45802	+	14.6497i	−0.643052	+	1.11380i	0.341696	+	0.939810i	$0.388999\pi$
$173$	−8.45802	+	14.6497i	−0.643052	+	1.11380i	−0.984748	+	0.173988i	$0.944335\pi$
$174$	−7.61802	−	18.1062i	−0.577521	−	1.37262i
$175$	8.94658	−	8.24905i	0.676298	−	0.623570i
$176$	−14.3072	−	7.37278i	−1.07844	−	0.555744i
$177$	−17.6751	+	2.21229i	−1.32854	+	0.166286i
$178$	−2.56718	+	2.62924i	−0.192418	+	0.197070i
$179$	19.3338	+	11.1623i	1.44507	+	0.834313i	0.998182	−	0.0602756i	$-0.0191979\pi$
$179$	19.3338	+	11.1623i	1.44507	+	0.834313i	0.446891	+	0.894589i	$0.352531\pi$
$180$	−3.67840	−	0.941917i	−0.274172	−	0.0702063i
$181$		−	21.0730i		−	1.56634i	−0.621807	−	0.783171i	$-0.713601\pi$
$181$		−	21.0730i		−	1.56634i	0.621807	−	0.783171i	$-0.286399\pi$
$182$	18.6775	−	10.0826i	1.38446	−	0.747371i
$183$	−7.76114	−	10.2493i	−0.573720	−	0.757651i
$184$	4.08695	−	4.39082i	0.301294	−	0.323695i
$185$	−3.18578	+	1.83931i	−0.234223	+	0.135229i
$186$	3.95758	−	1.66512i	0.290184	−	0.122092i
$187$	−1.09455	+	1.89582i	−0.0800416	+	0.138636i
$188$	−0.178470	−	7.47065i	−0.0130163	−	0.544853i
$189$	12.3648	+	6.00937i	0.899405	+	0.437117i
$190$	−0.626571	−	0.611781i	−0.0454562	−	0.0443833i
$191$	−7.44013	+	12.8867i	−0.538349	+	0.932448i	0.460644	+	0.887585i	$0.347618\pi$
$191$	−7.44013	+	12.8867i	−0.538349	+	0.932448i	−0.998993	+	0.0448627i	$0.985715\pi$
$192$	−4.45633	+	13.1203i	−0.321608	+	0.946873i
$193$	−7.61026	−	13.1814i	−0.547798	−	0.948815i	−0.998425	−	0.0561021i	$-0.982133\pi$
$193$	−7.61026	−	13.1814i	−0.547798	−	0.948815i	0.450627	−	0.892713i	$-0.351201\pi$
$194$	−6.74001	−	6.58092i	−0.483905	−	0.472482i
$195$	3.75367	+	4.95707i	0.268806	+	0.354983i
$196$	−6.29543	−	12.5047i	−0.449673	−	0.893193i
$197$	−26.2367			−1.86929			−0.934645	−	0.355583i	$-0.884282\pi$
$197$	−26.2367			−1.86929			−0.934645	+	0.355583i	$0.884282\pi$
$198$	−8.54791	+	14.7773i	−0.607473	+	1.05018i
$199$	19.3001	+	11.1429i	1.36815	+	0.789900i	0.990691	−	0.136128i	$-0.0434660\pi$
$199$	19.3001	+	11.1429i	1.36815	+	0.789900i	0.377455	+	0.926028i	$0.376799\pi$
$200$	8.86360	−	9.52261i	0.626751	−	0.673350i
$201$	2.37756	+	18.9956i	0.167700	+	1.33984i
$202$	−2.74478	+	0.770708i	−0.193122	+	0.0542268i
$203$	20.2550	+	6.31762i	1.42162	+	0.443410i
$204$	1.75351	+	0.690629i	0.122770	+	0.0483537i
$205$	3.95973	+	2.28615i	0.276559	+	0.159672i
$206$	−4.64911	−	16.5572i	−0.323919	−	1.15360i
$207$	−4.44110	−	4.55597i	−0.308678	−	0.316662i
$208$	19.0865	−	12.2707i	1.32341	−	0.850821i
$209$	−3.40966	+	1.96857i	−0.235851	+	0.136169i
$210$	3.33913	−	2.38139i	0.230422	−	0.164332i
$211$	−5.90657	+	10.2305i	−0.406625	+	0.704295i	−0.994509	−	0.104650i	$-0.966628\pi$
$211$	−5.90657	+	10.2305i	−0.406625	+	0.704295i	0.587884	+	0.808945i	$0.299961\pi$
$212$	0.0168300	+	0.704491i	0.00115589	+	0.0483846i
$213$	7.20758	+	3.03952i	0.493855	+	0.208265i
$214$	−11.4637	+	11.7408i	−0.783642	+	0.802586i
$215$	3.13900	+	5.43691i	0.214078	+	0.370794i
$216$	13.6701	+	5.39705i	0.930133	+	0.367222i
$217$	−1.38088	+	4.42727i	−0.0937403	+	0.300543i
$218$	27.7281	+	7.07592i	1.87798	+	0.479242i
$219$	−11.6220	+	8.80056i	−0.785340	+	0.594687i
$220$	2.65105	+	4.34849i	0.178734	+	0.293175i
$221$	−1.54308	−	2.67269i	−0.103799	−	0.179785i
$222$	13.1241	−	5.52186i	0.880833	−	0.370603i
$223$	−15.4188	+	8.90206i	−1.03252	+	0.596126i	−0.917706	−	0.397261i	$-0.869961\pi$
$223$	−15.4188	+	8.90206i	−1.03252	+	0.596126i	−0.114815	+	0.993387i	$0.536628\pi$
$224$	−7.73040	−	12.8157i	−0.516509	−	0.856282i
$225$	−9.63167	−	9.88079i	−0.642111	−	0.658719i
$226$	−21.9407	−	5.59904i	−1.45947	−	0.372442i
$227$		−	5.48384i		−	0.363975i	−0.983301	−	0.181988i	$-0.941747\pi$
$227$		−	5.48384i		−	0.363975i	0.983301	−	0.181988i	$-0.0582531\pi$
$228$	2.11015	+	2.65256i	0.139748	+	0.175670i
$229$		−	25.3426i		−	1.67468i	−0.546679	−	0.837342i	$-0.684108\pi$
$229$		−	25.3426i		−	1.67468i	0.546679	−	0.837342i	$-0.315892\pi$
$230$	−1.82740	+	0.513118i	−0.120495	+	0.0338340i
$231$	−6.24953	−	17.3479i	−0.411189	−	1.14141i
$232$	22.1057	+	5.08207i	1.45131	+	0.333654i
$233$	10.4685	−	6.04397i	0.685812	−	0.395954i	−0.116229	−	0.993222i	$-0.537081\pi$
$233$	10.4685	−	6.04397i	0.685812	−	0.395954i	0.802041	+	0.597269i	$0.203747\pi$
$234$	−12.0163	−	20.8526i	−0.785533	−	1.36317i
$235$	−1.18228	+	2.04777i	−0.0771235	+	0.133582i
$236$	9.85601	−	18.0536i	0.641571	−	1.17519i
$237$	5.41490	+	7.15089i	0.351736	+	0.464500i
$238$	−1.79128	+	0.966981i	−0.116111	+	0.0626801i
$239$	8.84354	−	15.3175i	0.572041	−	0.990804i	−0.424315	−	0.905514i	$-0.639485\pi$
$239$	8.84354	−	15.3175i	0.572041	−	0.990804i	0.996356	−	0.0852893i	$-0.0271814\pi$
$240$	3.36504	−	2.81074i	0.217212	−	0.181433i
$241$	4.50895			0.290447			0.145224	−	0.989399i	$-0.453610\pi$
$241$	4.50895			0.290447			0.145224	+	0.989399i	$0.453610\pi$
$242$	7.06760	−	1.98452i	0.454323	−	0.127570i
$243$	6.42198	−	14.2042i	0.411970	−	0.911197i
$244$	14.8409	−	0.354543i	0.950092	−	0.0226973i
$245$	−0.358804	+	4.41537i	−0.0229231	+	0.282088i
$246$	−14.1000	−	10.6953i	−0.898986	−	0.681909i
$247$		−	5.55051i		−	0.353170i
$248$	−1.11082	+	4.83178i	−0.0705371	+	0.306818i
$249$	28.4565	−	3.56174i	1.80336	−	0.225716i
$250$	−8.27148	+	2.32256i	−0.523134	+	0.146891i
$251$			8.50330i			0.536723i	0.963318	+	0.268362i	$0.0864822\pi$
$251$			8.50330i			0.536723i	−0.963318	+	0.268362i	$0.913518\pi$
$252$	−13.9753	+	7.52937i	−0.880360	+	0.474306i
$253$			8.53365i			0.536506i
$254$	0.998482	+	3.55596i	0.0626503	+	0.223121i
$255$	−0.359999	−	0.475413i	−0.0225440	−	0.0297715i
$256$	−9.28534	−	13.0301i	−0.580334	−	0.814379i
$257$		−	17.5378i		−	1.09398i	−0.837141	−	0.546988i	$-0.815774\pi$
$257$		−	17.5378i		−	1.09398i	0.837141	−	0.546988i	$-0.184226\pi$
$258$	−9.42371	−	22.3978i	−0.586694	−	1.39443i
$259$	−4.57928	+	14.6817i	−0.284542	+	0.912277i
$260$	−7.17779	+	0.171474i	−0.445148	+	0.0106344i
$261$	6.52290	−	23.1571i	0.403757	−	1.43339i
$262$	1.84674	+	6.57692i	0.114092	+	0.406323i
$263$	3.91218			0.241235			0.120618	−	0.992699i	$-0.461513\pi$
$263$	3.91218			0.241235			0.120618	+	0.992699i	$0.461513\pi$
$264$	−8.07651	−	17.9819i	−0.497075	−	1.10671i
$265$	0.111490	−	0.193107i	0.00684881	−	0.0118625i
$266$	−3.65959	−	0.104692i	−0.224384	−	0.00641905i
$267$	−4.46571	+	0.558947i	−0.273297	+	0.0342070i
$268$	−19.4023	−	10.5923i	−1.18518	−	0.647028i
$269$	−0.199097	+	0.344847i	−0.0121392	+	0.0210257i	−0.872031	−	0.489450i	$-0.837197\pi$
$269$	−0.199097	+	0.344847i	−0.0121392	+	0.0210257i	0.859892	+	0.510476i	$0.170531\pi$
$270$	−2.80435	−	3.70976i	−0.170668	−	0.225769i
$271$	−8.12965	+	4.69365i	−0.493841	+	0.285119i	−0.726167	−	0.687519i	$-0.758700\pi$
$271$	−8.12965	+	4.69365i	−0.493841	+	0.285119i	0.232326	+	0.972638i	$0.425367\pi$
$272$	−1.83051	+	1.17684i	−0.110991	+	0.0713562i
$273$	25.5854	+	4.59830i	1.54850	+	0.278302i
$274$	4.59105	+	16.3504i	0.277356	+	0.987766i
$275$			18.5074i			1.11604i
$276$	7.26593	−	1.08626i	0.437357	−	0.0653852i
$277$		−	1.43957i		−	0.0864953i	−0.999064	−	0.0432477i	$-0.986230\pi$
$277$		−	1.43957i		−	0.0864953i	0.999064	−	0.0432477i	$-0.0137704\pi$
$278$	−1.80661	+	7.07947i	−0.108353	+	0.424599i
$279$	5.06160	+	1.42575i	0.303030	+	0.0853574i
$280$	−0.0223275	+	4.73574i	−0.00133432	+	0.283015i
$281$	−7.17246	+	4.14102i	−0.427873	+	0.247033i	−0.698440	−	0.715669i	$-0.746122\pi$
$281$	−7.17246	+	4.14102i	−0.427873	+	0.247033i	0.270567	+	0.962701i	$0.412789\pi$
$282$	5.53108	−	7.29183i	0.329371	−	0.434222i
$283$	−7.39055	−	12.8008i	−0.439323	−	0.760929i	0.558315	−	0.829629i	$-0.311448\pi$
$283$	−7.39055	−	12.8008i	−0.439323	−	0.760929i	−0.997637	+	0.0687003i	$0.978115\pi$
$284$	−7.71218	+	4.70172i	−0.457634	+	0.278996i
$285$	−0.133202	−	1.06422i	−0.00789019	−	0.0630388i
$286$	−7.98176	+	31.2778i	−0.471972	+	1.84949i
$287$	18.6495	−	4.19501i	1.10084	−	0.247624i
$288$	−14.2825	+	9.16564i	−0.841607	+	0.540091i
$289$	−8.35201	−	14.4661i	−0.491295	−	0.850947i
$290$	−5.13532	−	5.01410i	−0.301556	−	0.294438i
$291$	−1.43285	−	11.4478i	−0.0839951	−	0.671080i
$292$	−0.402025	−	16.8285i	−0.0235267	−	0.984814i
$293$	−7.69700	+	13.3316i	−0.449663	+	0.778840i	−0.998364	−	0.0571792i	$-0.981789\pi$
$293$	−7.69700	+	13.3316i	−0.449663	+	0.778840i	0.548701	+	0.836019i	$0.315123\pi$
$294$	3.51436	−	16.7824i	0.204962	−	0.978770i
$295$	−5.63646	+	3.25421i	−0.328168	+	0.189468i
$296$	−3.68370	+	16.0232i	−0.214111	+	0.931327i
$297$	−19.4663	+	7.62987i	−1.12955	+	0.442730i
$298$	−4.49361	+	1.26176i	−0.260308	+	0.0730920i
$299$	−10.4188	−	6.01529i	−0.602534	−	0.347873i
$300$	15.7580	−	2.35583i	0.909790	−	0.136014i
$301$	25.0561	+	7.81508i	1.44421	+	0.450453i
$302$	−1.08576	−	3.86680i	−0.0624785	−	0.222509i
$303$	−3.21728	−	1.35676i	−0.184828	−	0.0779440i
$304$	−3.90940	+	0.186894i	−0.224220	+	0.0107191i
$305$	−4.06803	−	2.34868i	−0.232934	−	0.134485i
$306$	1.15244	+	1.99989i	0.0658806	+	0.114326i
$307$	−12.6235			−0.720461			−0.360230	−	0.932863i	$-0.617302\pi$
$307$	−12.6235			−0.720461			−0.360230	+	0.932863i	$0.617302\pi$
$308$	20.4717	+	5.85253i	1.16648	+	0.333479i
$309$	8.18436	−	19.4075i	0.465592	−	1.10405i
$310$	1.09596	−	1.12246i	0.0622465	−	0.0637513i
$311$	3.14409	+	5.44572i	0.178285	+	0.308799i	0.941293	−	0.337590i	$-0.109612\pi$
$311$	3.14409	+	5.44572i	0.178285	+	0.308799i	−0.763008	+	0.646389i	$0.776278\pi$
$312$	27.6473	+	2.81463i	1.56522	+	0.159347i
$313$	−11.1179	+	19.2569i	−0.628424	+	1.08846i	0.359444	+	0.933166i	$0.382966\pi$
$313$	−11.1179	+	19.2569i	−0.628424	+	1.08846i	−0.987868	+	0.155295i	$0.950367\pi$
$314$	4.38261	−	4.48856i	0.247325	−	0.253304i
$315$	5.01593	+	0.267645i	0.282616	+	0.0150801i
$316$	−10.3544	+	0.247362i	−0.582482	+	0.0139152i
$317$	8.81955	−	15.2759i	0.495355	−	0.857981i	−0.504630	−	0.863336i	$-0.668371\pi$
$317$	8.81955	−	15.2759i	0.495355	−	0.857981i	0.999986	+	0.00535475i	$0.00170448\pi$
$318$	−0.521588	+	0.687628i	−0.0292492	+	0.0385603i
$319$	−27.9453	+	16.1342i	−1.56464	+	0.903343i
$320$	0.362463	+	5.04978i	0.0202623	+	0.282291i
$321$	−19.9415	+	2.49596i	−1.11303	+	0.139311i
$322$	−4.16255	+	6.75592i	−0.231970	+	0.376493i
$323$			0.532327i			0.0296195i
$324$	8.97430	+	15.6033i	0.498572	+	0.866848i
$325$	−22.5958	−	13.0457i	−1.25339	−	0.723645i
$326$	−2.53381	−	2.47400i	−0.140335	−	0.137022i
$327$	21.1581	+	27.9412i	1.17004	+	1.54515i
$328$	19.5369	−	5.99270i	1.07874	−	0.330892i
$329$	2.16945	+	9.64457i	0.119606	+	0.531722i
$330$	−0.779762	+	6.18854i	−0.0429245	+	0.340668i
$331$	2.73496	−	4.73709i	0.150327	−	0.260374i	−0.781021	−	0.624505i	$-0.785301\pi$
$331$	2.73496	−	4.73709i	0.150327	−	0.260374i	0.931348	+	0.364131i	$0.118634\pi$
$332$	−15.8679	+	29.0658i	−0.870866	+	1.59520i
$333$	16.7853	+	4.72807i	0.919827	+	0.259097i
$334$	−1.41983	+	5.56383i	−0.0776897	+	0.304439i
$335$	3.49732	+	6.05754i	0.191079	+	0.330959i
$336$	2.37723	−	18.1755i	0.129689	−	0.991555i
$337$	−0.784458	+	1.35872i	−0.0427321	+	0.0740142i	−0.886600	−	0.462536i	$-0.846940\pi$
$337$	−0.784458	+	1.35872i	−0.0427321	+	0.0740142i	0.843868	+	0.536550i	$0.180273\pi$
$338$	−19.4067	−	18.9486i	−1.05558	−	1.03067i
$339$	−16.7420	−	22.1093i	−0.909298	−	1.20081i
$340$	0.688394	−	0.0164454i	0.0373334	−	0.000891877i
$341$	−3.52656	−	6.10817i	−0.190974	−	0.330776i
$342$	−0.00341994	+	4.15128i	−0.000184929	+	0.224476i
$343$	11.4102	+	14.5879i	0.616092	+	0.787674i
$344$	27.3454	+	6.28666i	1.47436	+	0.338954i
$345$	−2.14198	−	0.903300i	−0.115321	−	0.0486320i
$346$	5.91530	−	23.1800i	0.318009	−	1.24617i
$347$	−13.6538	+	7.88304i	−0.732976	+	0.423184i	−0.819510	−	0.573065i	$-0.805754\pi$
$347$	−13.6538	+	7.88304i	−0.732976	+	0.423184i	0.0865341	+	0.996249i	$0.472421\pi$
$348$	17.2946	+	21.7401i	0.927087	+	1.16539i
$349$	−11.3033	+	6.52596i	−0.605051	+	0.349326i	−0.771026	−	0.636804i	$-0.780256\pi$
$349$	−11.3033	+	6.52596i	−0.605051	+	0.349326i	0.165975	+	0.986130i	$0.446923\pi$
$350$	−9.02756	+	14.6519i	−0.482543	+	0.783179i
$351$	4.40627	−	29.1448i	0.235189	−	1.55563i
$352$	22.2987	+	4.56865i	1.18853	+	0.243510i
$353$			9.28559i			0.494222i	0.968987	+	0.247111i	$0.0794813\pi$
$353$			9.28559i			0.494222i	−0.968987	+	0.247111i	$0.920519\pi$
$354$	23.2199	−	9.76959i	1.23412	−	0.519248i
$355$	2.85806			0.151690
$356$	2.49017	−	4.56133i	0.131979	−	0.241750i
$357$	−2.45380	−	0.441005i	−0.129869	−	0.0233404i
$358$	−30.5915	−	7.80663i	−1.61681	−	0.412593i
$359$	15.5018	+	26.8499i	0.818152	+	1.41708i	0.907042	+	0.421040i	$0.138335\pi$
$359$	15.5018	+	26.8499i	0.818152	+	1.41708i	−0.0888902	+	0.996041i	$0.528332\pi$
$360$	5.36846	−	0.123825i	0.282942	−	0.00652614i
$361$	9.02130	−	15.6254i	0.474805	−	0.822387i
$362$	8.05646	+	28.6920i	0.423438	+	1.50802i
$363$	8.28426	+	3.49357i	0.434811	+	0.183365i
$364$	−21.5757	+	20.8686i	−1.13087	+	1.09381i
$365$	−2.66323	+	4.61284i	−0.139400	+	0.241447i
$366$	14.4857	+	10.9878i	0.757178	+	0.574344i
$367$		−	29.6636i		−	1.54843i	−0.632923	−	0.774215i	$-0.718145\pi$
$367$		−	29.6636i		−	1.54843i	0.632923	−	0.774215i	$-0.281855\pi$
$368$	−3.88595	+	7.54084i	−0.202569	+	0.393093i
$369$	−5.34215	−	21.0063i	−0.278101	−	1.09354i
$370$	3.63443	−	3.72229i	0.188945	−	0.193513i
$371$	−0.204582	−	0.909494i	−0.0106213	−	0.0472186i
$372$	−4.75187	+	3.78018i	−0.246373	+	0.195993i
$373$		−	15.2411i		−	0.789152i	−0.918863	−	0.394576i	$-0.870891\pi$
$373$		−	15.2411i		−	0.789152i	0.918863	−	0.394576i	$-0.129109\pi$
$374$	0.765499	−	2.99973i	0.0395830	−	0.155112i
$375$	−9.69538	−	4.08866i	−0.500667	−	0.211137i
$376$	3.09912	+	10.1035i	0.159825	+	0.521047i
$377$		−	45.4914i		−	2.34293i
$378$	−19.1328	−	3.45488i	−0.984085	−	0.177700i
$379$	−5.65608			−0.290533			−0.145267	−	0.989393i	$-0.546404\pi$
$379$	−5.65608			−0.290533			−0.145267	+	0.989393i	$0.546404\pi$
$380$	1.08700	+	0.593429i	0.0557621	+	0.0304422i
$381$	−1.75774	+	4.16811i	−0.0900517	+	0.213539i
$382$	5.20342	−	20.3904i	0.266230	−	1.04326i
$383$	−24.3732			−1.24541			−0.622706	−	0.782456i	$-0.713967\pi$
$383$	−24.3732			−1.24541			−0.622706	+	0.782456i	$0.713967\pi$
$384$	1.05151	−	19.5677i	0.0536596	−	0.998559i
$385$	−4.56695	−	4.95312i	−0.232753	−	0.252434i
$386$	15.4012	+	15.0377i	0.783900	+	0.765397i
$387$	8.06901	−	28.6460i	0.410171	−	1.45616i
$388$	11.6929	+	6.38350i	0.593616	+	0.324073i
$389$	−0.0673875			−0.00341668			−0.00170834	−	0.999999i	$-0.500544\pi$
$389$	−0.0673875			−0.00341668			−0.00170834	+	0.999999i	$0.500544\pi$
$390$	−7.00598	−	5.31426i	−0.354762	−	0.269098i
$391$	0.999224	+	0.576903i	0.0505330	+	0.0291752i
$392$	13.3523	+	14.6190i	0.674392	+	0.738373i
$393$	−3.25102	+	7.70911i	−0.163992	+	0.388873i
$394$	35.7228	−	10.0306i	1.79969	−	0.505336i
$395$	2.83824	+	1.63866i	0.142807	+	0.0824498i
$396$	5.98892	−	23.3881i	0.300955	−	1.17530i
$397$	−32.1509	+	18.5623i	−1.61361	+	0.931615i	−0.625080	+	0.780561i	$0.714934\pi$
$397$	−32.1509	+	18.5623i	−1.61361	+	0.931615i	−0.988525	+	0.151055i	$0.951733\pi$
$398$	−30.5382	−	7.79303i	−1.53074	−	0.390630i
$399$	−3.42536	−	2.89349i	−0.171483	−	0.144856i
$400$	−8.42768	+	16.3542i	−0.421384	+	0.817712i
$401$			10.2198i			0.510352i	0.966895	+	0.255176i	$0.0821333\pi$
$401$			10.2198i			0.510352i	−0.966895	+	0.255176i	$0.917867\pi$
$402$	−10.4994	−	24.9546i	−0.523664	−	1.24462i
$403$	9.94334			0.495313
$404$	3.44252	−	2.09872i	0.171272	−	0.104415i
$405$	0.145409	−	5.69376i	0.00722541	−	0.282925i
$406$	−29.9937	−	0.858043i	−1.48856	−	0.0425839i
$407$	−11.6948	−	20.2559i	−0.579688	−	1.00405i
$408$	−2.65154	−	0.269940i	−0.131271	−	0.0133640i
$409$	16.5119	+	28.5995i	0.816463	+	1.41415i	0.908273	+	0.418378i	$0.137401\pi$
$409$	16.5119	+	28.5995i	0.816463	+	1.41415i	−0.0918104	+	0.995777i	$0.529265\pi$
$410$	−6.26542	−	1.59887i	−0.309427	−	0.0789625i
$411$	−8.08215	+	19.1651i	−0.398663	+	0.945344i
$412$	12.6601	+	20.7662i	0.623717	+	1.02308i
$413$	−8.10191	+	25.9757i	−0.398669	+	1.27818i
$414$	7.78862	+	4.50532i	0.382790	+	0.221424i
$415$	9.07457	−	5.23921i	0.445453	−	0.257183i
$416$	−21.2961	+	24.0043i	−1.04413	+	1.17691i
$417$	−7.13388	+	5.40203i	−0.349348	+	0.264538i
$418$	3.88984	−	3.98388i	0.190258	−	0.194858i
$419$	21.7720	+	12.5700i	1.06363	+	0.614087i	0.926434	−	0.376457i	$-0.122858\pi$
$419$	21.7720	+	12.5700i	1.06363	+	0.614087i	0.137196	+	0.990544i	$0.456191\pi$
$420$	−3.63597	+	4.51899i	−0.177417	+	0.220504i
$421$	−6.20961	+	3.58512i	−0.302638	+	0.174728i	−0.643627	−	0.765339i	$-0.722571\pi$
$421$	−6.20961	+	3.58512i	−0.302638	+	0.174728i	0.340989	+	0.940067i	$0.389238\pi$
$422$	4.13089	−	16.1875i	0.201088	−	0.787997i
$423$	10.8634	−	2.76269i	0.528195	−	0.134327i
$424$	−0.292251	−	0.952770i	−0.0141929	−	0.0462706i
$425$	2.16707	+	1.25116i	0.105119	+	0.0606902i
$426$	−10.9756	−	1.38293i	−0.531769	−	0.0670033i
$427$	−19.1595	+	4.30975i	−0.927195	+	0.208563i
$428$	11.1198	−	20.3685i	0.537496	−	0.984549i
$429$	−31.5182	+	23.8667i	−1.52171	+	1.15229i
$430$	−6.35253	−	6.20258i	−0.306346	−	0.299115i
$431$	−4.90392	+	8.49385i	−0.236214	+	0.409134i	−0.959625	−	0.281283i	$-0.909240\pi$
$431$	−4.90392	+	8.49385i	−0.236214	+	0.409134i	0.723411	+	0.690418i	$0.242573\pi$
$432$	−20.6760	−	2.12213i	−0.994774	−	0.102101i
$433$	32.0519			1.54032			0.770158	−	0.637853i	$-0.220177\pi$
$433$	32.0519			1.54032			0.770158	+	0.637853i	$0.220177\pi$
$434$	0.187548	−	6.55591i	0.00900258	−	0.314694i
$435$	−1.09171	−	8.72222i	−0.0523434	−	0.418199i
$436$	−40.4586	+	0.966538i	−1.93762	+	0.0462888i
$437$	1.03757	+	1.79712i	0.0496336	+	0.0859679i
$438$	12.4594	−	16.4257i	0.595334	−	0.784850i
$439$	1.49359	+	0.862324i	0.0712851	+	0.0411565i	0.535219	−	0.844713i	$-0.320229\pi$
$439$	1.49359	+	0.862324i	0.0712851	+	0.0411565i	−0.463934	+	0.885870i	$0.653562\pi$
$440$	−5.27203	−	4.90718i	−0.251334	−	0.233941i
$441$	16.1755	−	13.3923i	0.770260	−	0.637730i
$442$	3.12279	+	3.04908i	0.148536	+	0.145030i
$443$	16.3215	+	9.42323i	0.775458	+	0.447711i	0.834818	−	0.550526i	$-0.185573\pi$
$443$	16.3215	+	9.42323i	0.775458	+	0.447711i	−0.0593601	+	0.998237i	$0.518906\pi$
$444$	−15.7581	+	12.5358i	−0.747848	+	0.594925i
$445$	−1.42408	+	0.822194i	−0.0675079	+	0.0389757i
$446$	17.5902	−	18.0155i	0.832922	−	0.853058i
$447$	−5.26716	−	2.22122i	−0.249128	−	0.105060i
$448$	15.4250	+	14.4938i	0.728761	+	0.684768i
$449$		−	29.2027i		−	1.37816i	−0.724685	−	0.689080i	$-0.758015\pi$
$449$		−	29.2027i		−	1.37816i	0.724685	−	0.689080i	$-0.241985\pi$
$450$	16.8916	+	9.77094i	0.796278	+	0.460607i
$451$	−14.5359	+	25.1768i	−0.684467	+	1.18553i
$452$	32.0141	−	0.764802i	1.50582	−	0.0359733i
$453$	1.91139	−	4.53245i	0.0898048	−	0.212953i
$454$	2.09654	+	7.46656i	0.0983956	+	0.350423i
$455$	9.26650	−	2.08440i	0.434420	−	0.0977184i
$456$	−3.88719	−	2.80487i	−0.182034	−	0.131350i
$457$	13.6390	−	23.6234i	0.638005	−	1.10506i	−0.347865	−	0.937544i	$-0.613093\pi$
$457$	13.6390	−	23.6234i	0.638005	−	1.10506i	0.985870	−	0.167512i	$-0.0535733\pi$
$458$	9.68879	+	34.5054i	0.452727	+	1.61233i
$459$	−0.422588	+	2.79516i	−0.0197247	+	0.130467i
$460$	2.29194	−	1.39728i	0.106862	−	0.0651485i
$461$	15.5982	+	27.0168i	0.726480	+	1.25830i	0.958362	+	0.285556i	$0.0921781\pi$
$461$	15.5982	+	27.0168i	0.726480	+	1.25830i	−0.231883	+	0.972744i	$0.574489\pi$
$462$	15.1414	+	21.2309i	0.704443	+	0.987752i
$463$	29.0747	+	16.7863i	1.35121	+	0.780124i	0.988420	−	0.151745i	$-0.0484891\pi$
$463$	29.0747	+	16.7863i	1.35121	+	0.780124i	0.362795	+	0.931869i	$0.381822\pi$
$464$	−32.0411	+	1.53177i	−1.48747	+	0.0711106i
$465$	1.90647	−	0.238622i	0.0884104	−	0.0110658i
$466$	−11.9427	+	12.2314i	−0.553236	+	0.566610i
$467$	4.86224	−	2.80722i	0.224998	−	0.129903i	−0.383264	−	0.923639i	$-0.625200\pi$
$467$	4.86224	−	2.80722i	0.224998	−	0.129903i	0.608262	+	0.793736i	$0.291867\pi$
$468$	24.3331	+	23.7979i	1.12480	+	1.10006i
$469$	27.9162	+	8.70717i	1.28905	+	0.402060i
$470$	0.826854	−	3.24016i	0.0381399	−	0.149457i
$471$	7.62373	−	0.954217i	0.351283	−	0.0439680i
$472$	−6.51740	+	28.3491i	−0.299988	+	1.30487i
$473$	−34.5691	+	19.9585i	−1.58949	+	0.917692i
$474$	−10.1066	−	7.66616i	−0.464210	−	0.352118i
$475$	2.25023	+	3.89752i	0.103248	+	0.178830i
$476$	2.06924	−	2.00143i	0.0948435	−	0.0917353i
$477$	−1.02443	+	0.260525i	−0.0469054	+	0.0119286i
$478$	−6.18492	+	24.2366i	−0.282892	+	1.10856i
$479$	20.8943			0.954686			0.477343	−	0.878717i	$-0.341600\pi$
$479$	20.8943			0.954686			0.477343	+	0.878717i	$0.341600\pi$
$480$	−3.50711	+	5.11349i	−0.160077	+	0.233398i
$481$	32.9741			1.50349
$482$	−6.13919	+	1.72383i	−0.279633	+	0.0785183i
$483$	−9.14352	+	3.29392i	−0.416045	+	0.149879i
$484$	−8.86424	+	5.40407i	−0.402920	+	0.245640i
$485$	−2.10768	−	3.65060i	−0.0957047	−	0.165765i
$486$	−3.31345	+	21.7950i	−0.150301	+	0.988640i
$487$	8.81708	+	5.09054i	0.399540	+	0.230674i	0.686285	−	0.727332i	$-0.259240\pi$
$487$	8.81708	+	5.09054i	0.399540	+	0.230674i	−0.286746	+	0.958007i	$0.592573\pi$
$488$	−20.0712	+	6.15660i	−0.908580	+	0.278696i
$489$	−0.538659	−	4.30362i	−0.0243590	−	0.194617i
$490$	−1.19952	−	6.14896i	−0.0541888	−	0.277782i
$491$	7.21514	+	4.16566i	0.325615	+	0.187994i	0.653892	−	0.756588i	$-0.273135\pi$
$491$	7.21514	+	4.16566i	0.325615	+	0.187994i	−0.328278	+	0.944581i	$0.606468\pi$
$492$	23.2870	+	9.17168i	1.04986	+	0.413491i
$493$			4.36290i			0.196495i
$494$	2.12203	+	7.55733i	0.0954746	+	0.340020i
$495$	−5.47033	+	5.33241i	−0.245873	+	0.239674i
$496$	−0.334808	−	7.00343i	−0.0150333	−	0.314463i
$497$	8.78453	−	8.09963i	0.394040	−	0.363318i
$498$	−37.3835	+	15.7288i	−1.67519	+	0.704825i
$499$	3.85280			0.172475			0.0862375	−	0.996275i	$-0.472516\pi$
$499$	3.85280			0.172475			0.0862375	+	0.996275i	$0.472516\pi$
$500$	10.3741	−	6.32458i	0.463946	−	0.282844i
$501$	−5.60659	+	4.24551i	−0.250484	+	0.189675i
$502$	−3.25092	−	11.5777i	−0.145096	−	0.516739i
$503$	−22.0278			−0.982172			−0.491086	−	0.871111i	$-0.663400\pi$
$503$	−22.0278			−0.982172			−0.491086	+	0.871111i	$0.663400\pi$
$504$	16.1496	−	15.5946i	0.719359	−	0.694638i
$505$	−1.27576			−0.0567707
$506$	−3.26252	−	11.6190i	−0.145037	−	0.516530i
$507$	−4.12563	−	32.9618i	−0.183226	−	1.46388i
$508$	−2.71898	−	4.45991i	−0.120635	−	0.197877i
$509$	−29.2386			−1.29598			−0.647988	−	0.761650i	$-0.724390\pi$
$509$	−29.2386			−1.29598			−0.647988	+	0.761650i	$0.724390\pi$
$510$	0.671916	+	0.509670i	0.0297529	+	0.0225686i
$511$	4.88694	+	21.7255i	0.216185	+	0.961080i
$512$	17.6241	+	14.1913i	0.778882	+	0.627171i
$513$	−3.17177	+	3.97361i	−0.140037	+	0.175439i
$514$	6.70491	+	23.8787i	0.295741	+	1.05324i
$515$		−	7.69573i		−	0.339115i
$516$	21.3939	+	26.8931i	0.941814	+	1.18390i
$517$	−13.0202	−	7.51721i	−0.572627	−	0.330606i
$518$	0.621945	−	21.7407i	0.0273267	−	0.955231i
$519$	23.3582	−	17.6876i	1.02531	−	0.776401i
$520$	9.70742	−	2.97763i	0.425698	−	0.130578i
$521$	8.24862	+	4.76234i	0.361378	+	0.208642i	0.669685	−	0.742645i	$-0.266429\pi$
$521$	8.24862	+	4.76234i	0.361378	+	0.208642i	−0.308307	+	0.951287i	$0.599762\pi$
$522$	−0.0280295	+	34.0235i	−0.00122682	+	1.48917i
$523$	16.1411	+	27.9572i	0.705800	+	1.22248i	0.966402	+	0.257035i	$0.0827455\pi$
$523$	16.1411	+	27.9572i	0.705800	+	1.22248i	−0.260603	+	0.965446i	$0.583921\pi$
$524$	−5.02888	−	8.24882i	−0.219688	−	0.360351i
$525$	−19.8301	+	7.14371i	−0.865455	+	0.311777i
$526$	−5.32665	+	1.49568i	−0.232253	+	0.0652145i
$527$	−0.953627			−0.0415406
$528$	17.8713	+	21.3957i	0.777751	+	0.931127i
$529$	−18.5022			−0.804443
$530$	−0.0779733	+	0.305551i	−0.00338694	+	0.0132723i
$531$	29.6974	+	8.36517i	1.28876	+	0.363017i
$532$	5.02277	−	1.25657i	0.217765	−	0.0544790i
$533$	−20.4924	−	35.4938i	−0.887623	−	1.53741i
$534$	5.86663	−	2.46834i	0.253874	−	0.106815i
$535$	−6.35920	+	3.67149i	−0.274932	+	0.158732i
$536$	30.4669	+	7.00429i	1.31597	+	0.302539i
$537$	−23.3430	−	30.8266i	−1.00732	−	1.33027i
$538$	0.139243	−	0.545646i	0.00600320	−	0.0235245i
$539$	−28.0739	−	2.28136i	−1.20923	−	0.0982650i
$540$	5.23658	+	3.97891i	0.225346	+	0.171225i
$541$	21.7810	−	12.5753i	0.936439	−	0.540653i	0.0475967	−	0.998867i	$-0.484844\pi$
$541$	21.7810	−	12.5753i	0.936439	−	0.540653i	0.888842	+	0.458213i	$0.151510\pi$
$542$	9.27453	−	9.49875i	0.398375	−	0.408006i
$543$	−14.1827	+	33.6313i	−0.608638	+	1.44326i
$544$	2.04242	−	2.30216i	0.0875681	−	0.0987041i
$545$	11.0901	+	6.40285i	0.475046	+	0.274268i
$546$	−36.5940	+	3.52079i	−1.56608	+	0.150676i
$547$	−7.03386	−	12.1830i	−0.300746	−	0.520908i	0.675559	−	0.737306i	$-0.263902\pi$
$547$	−7.03386	−	12.1830i	−0.300746	−	0.520908i	−0.976305	+	0.216398i	$0.930569\pi$
$548$	−12.5020	−	20.5068i	−0.534057	−	0.876008i
$549$	5.48826	+	21.5808i	0.234233	+	0.921045i
$550$	−7.07562	−	25.1989i	−0.301705	−	1.07448i
$551$	−3.92338	+	6.79549i	−0.167141	+	0.289497i
$552$	−9.47768	+	4.25686i	−0.403397	+	0.181184i
$553$	13.3675	−	3.00689i	0.568444	−	0.127866i
$554$	0.550365	+	1.96005i	0.0233828	+	0.0832747i
$555$	6.32224	−	0.791317i	0.268364	−	0.0335895i
$556$	−0.246774	−	10.3298i	−0.0104656	−	0.438081i
$557$	−8.15764	+	14.1294i	−0.345650	+	0.598684i	−0.985472	−	0.169840i	$-0.945675\pi$
$557$	−8.15764	+	14.1294i	−0.345650	+	0.598684i	0.639822	+	0.768524i	$0.279008\pi$
$558$	−7.43674	−	0.00612659i	−0.314822	−	0.000259359i
$559$		−	56.2742i		−	2.38014i
$560$	−1.78013	−	6.45651i	−0.0752244	−	0.272838i
$561$	3.02278	−	2.28896i	0.127622	−	0.0966398i
$562$	8.18254	−	8.38036i	0.345160	−	0.353504i
$563$	−24.8088	+	14.3234i	−1.04557	+	0.603659i	−0.921405	−	0.388603i	$-0.872958\pi$
$563$	−24.8088	+	14.3234i	−1.04557	+	0.603659i	−0.124162	+	0.992262i	$0.539624\pi$
$564$	−4.74313	+	12.0428i	−0.199722	+	0.507095i
$565$	−8.77535	−	5.06645i	−0.369182	−	0.213147i
$566$	14.9566	+	14.6035i	0.628671	+	0.613832i
$567$	−15.6890	−	17.9124i	−0.658876	−	0.752252i
$568$	8.70305	−	9.35012i	0.365172	−	0.392323i
$569$	−38.6880	−	22.3365i	−1.62189	−	0.936396i	−0.986415	−	0.164271i	$-0.947473\pi$
$569$	−38.6880	−	22.3365i	−1.62189	−	0.936396i	−0.635470	−	0.772125i	$-0.719194\pi$
$570$	0.588225	+	1.39807i	0.0246380	+	0.0585586i
$571$	7.26658	+	12.5861i	0.304097	+	0.526711i	0.977060	−	0.212965i	$-0.0683120\pi$
$571$	7.26658	+	12.5861i	0.304097	+	0.526711i	−0.672963	+	0.739676i	$0.734979\pi$
$572$	−1.09027	−	45.6380i	−0.0455865	−	1.90822i
$573$	20.5471	−	15.5590i	0.858368	−	0.649986i
$574$	−23.7885	+	12.8417i	−0.992914	+	0.536002i
$575$	9.75464			0.406797
$576$	15.9423	−	17.9399i	0.664265	−	0.747498i
$577$	0.306786	−	0.531369i	0.0127717	−	0.0221212i	−0.859569	−	0.511020i	$-0.829268\pi$
$577$	0.306786	−	0.531369i	0.0127717	−	0.0221212i	0.872341	+	0.488899i	$0.162601\pi$
$578$	16.9023	+	16.5033i	0.703043	+	0.686449i
$579$	3.27412	+	26.1586i	0.136068	+	1.08711i
$580$	8.90898	+	4.86369i	0.369925	+	0.201954i
$581$	13.0439	−	41.8202i	0.541152	−	1.73500i
$582$	6.32753	+	15.0390i	0.262285	+	0.623386i
$583$	1.22782	+	0.708882i	0.0508511	+	0.0293589i
$584$	6.98113	+	22.7593i	0.288881	+	0.941785i
$585$	−2.65439	−	10.4375i	−0.109746	−	0.431539i
$586$	5.38306	−	21.0944i	0.222372	−	0.871401i
$587$	−34.5667	+	19.9571i	−1.42672	+	0.823718i	−0.996861	−	0.0791778i	$-0.974771\pi$
$587$	−34.5667	+	19.9571i	−1.42672	+	0.823718i	−0.429860	+	0.902895i	$0.641437\pi$
$588$	1.63112	+	24.1938i	0.0672664	+	0.997735i
$589$	−1.48533	−	0.857556i	−0.0612020	−	0.0353350i
$590$	6.43024	−	6.58569i	0.264729	−	0.271129i
$591$	41.8723	+	17.6580i	1.72240	+	0.726355i
$592$	−1.11029	−	23.2248i	−0.0456327	−	0.954532i
$593$	−13.9936	+	8.07922i	−0.574649	+	0.331774i	−0.759004	−	0.651086i	$-0.774314\pi$
$593$	−13.9936	+	8.07922i	−0.574649	+	0.331774i	0.184355	+	0.982860i	$0.440980\pi$
$594$	23.5875	−	17.8307i	0.967807	−	0.731603i
$595$	−0.888713	+	0.199907i	−0.0364337	+	0.00819539i
$596$	5.63591	−	3.43593i	0.230856	−	0.140741i
$597$	−23.3023	−	30.7729i	−0.953701	−	1.25945i
$598$	16.4855	+	4.20692i	0.674142	+	0.172034i
$599$	2.58011	+	4.46888i	0.105420	+	0.182593i	0.913910	−	0.405917i	$-0.133048\pi$
$599$	2.58011	+	4.46888i	0.105420	+	0.182593i	−0.808489	+	0.588511i	$0.799715\pi$
$600$	−20.5548	+	9.23210i	−0.839145	+	0.376899i
$601$	−6.51033	−	11.2762i	−0.265562	−	0.459967i	0.702149	−	0.712030i	$-0.252224\pi$
$601$	−6.51033	−	11.2762i	−0.265562	−	0.459967i	−0.967711	+	0.252064i	$0.918891\pi$
$602$	−37.1030	−	1.06142i	−1.51221	−	0.0432604i
$603$	8.99009	−	31.9160i	0.366105	−	1.29972i
$604$	2.95665	+	4.84976i	0.120304	+	0.197334i
$605$	3.28500			0.133554
$606$	4.89921	+	0.617305i	0.199017	+	0.0250763i
$607$		−	5.98062i		−	0.242746i	−0.992607	−	0.121373i	$-0.961270\pi$
$607$		−	5.98062i		−	0.242746i	0.992607	−	0.121373i	$-0.0387297\pi$
$608$	5.25142	−	1.74908i	0.212973	−	0.0709347i
$609$	−28.0739	−	23.7148i	−1.13761	−	0.960971i
$610$	6.43678	+	1.64260i	0.260617	+	0.0665068i
$611$	18.3556	−	10.5976i	0.742589	−	0.428734i
$612$	−2.33369	−	2.28237i	−0.0943340	−	0.0922592i
$613$	−15.2390	−	8.79826i	−0.615499	−	0.355358i	0.159616	−	0.987179i	$-0.448974\pi$
$613$	−15.2390	−	8.79826i	−0.615499	−	0.355358i	−0.775114	+	0.631821i	$0.782308\pi$
$614$	17.1876	−	4.82612i	0.693635	−	0.194766i
$615$	−4.78086	−	6.31357i	−0.192783	−	0.254588i
$616$	−30.1109	−	0.141963i	−1.21320	−	0.00571986i
$617$	−7.74226	−	4.46999i	−0.311692	−	0.179955i	0.335992	−	0.941865i	$-0.390929\pi$
$617$	−7.74226	−	4.46999i	−0.311692	−	0.179955i	−0.647683	+	0.761910i	$0.724262\pi$
$618$	−3.72375	+	29.5533i	−0.149791	+	1.18881i
$619$	14.4561			0.581038			0.290519	−	0.956869i	$-0.406172\pi$
$619$	14.4561			0.581038			0.290519	+	0.956869i	$0.406172\pi$
$620$	−1.06309	+	1.94729i	−0.0426946	+	0.0782051i
$621$	4.02145	+	10.2601i	0.161375	+	0.411722i
$622$	−6.36283	−	6.21264i	−0.255126	−	0.249104i
$623$	−2.04699	+	6.56289i	−0.0820109	+	0.262937i
$624$	−38.7194	+	6.73763i	−1.55002	+	0.269721i
$625$	19.1530			0.766119
$626$	7.77558	−	30.4698i	0.310775	−	1.21782i
$627$	6.76653	−	0.846926i	0.270229	−	0.0338230i
$628$	−4.25114	+	7.78696i	−0.169639	+	0.310734i
$629$	−3.16242			−0.126094
$630$	−6.93180	+	1.55324i	−0.276169	+	0.0618826i
$631$			49.1971i			1.95851i	0.202639	+	0.979254i	$0.435048\pi$
$631$			49.1971i			1.95851i	−0.202639	+	0.979254i	$0.564952\pi$
$632$	14.0036	−	4.29542i	0.557032	−	0.170863i
$633$	16.3119	−	12.3520i	0.648341	−	0.490947i
$634$	−6.16815	+	24.1709i	−0.244968	+	0.959947i
$635$			1.65280i			0.0655893i
$636$	0.447282	−	1.13565i	0.0177359	−	0.0450316i
$637$	22.5744	−	32.6675i	0.894429	−	1.29433i
$638$	31.8808	−	32.6515i	1.26217	−	1.29269i
$639$	−9.45721	−	9.70181i	−0.374121	−	0.383798i
$640$	−2.42411	−	6.73699i	−0.0958213	−	0.266303i
$641$			29.2765i			1.15635i	0.815912	+	0.578176i	$0.196235\pi$
$641$			29.2765i			1.15635i	−0.815912	+	0.578176i	$0.803765\pi$
$642$	26.1973	−	11.0223i	1.03392	−	0.435015i
$643$	7.39938	−	12.8161i	0.291803	−	0.505418i	−0.682433	−	0.730948i	$-0.739078\pi$
$643$	7.39938	−	12.8161i	0.291803	−	0.505418i	0.974236	+	0.225530i	$0.0724114\pi$
$644$	3.08468	−	10.7900i	0.121553	−	0.425184i
$645$	−1.35047	−	10.7896i	−0.0531749	−	0.424842i
$646$	−0.203515	−	0.724793i	−0.00800720	−	0.0285166i
$647$	19.4269	−	33.6484i	0.763751	−	1.32286i	−0.177154	−	0.984183i	$-0.556689\pi$
$647$	19.4269	−	33.6484i	0.763751	−	1.32286i	0.940905	−	0.338672i	$-0.109978\pi$
$648$	−18.1844	−	17.8137i	−0.714349	−	0.699790i
$649$	−20.6910	−	35.8379i	−0.812194	−	1.40676i
$650$	35.7530	+	9.12379i	1.40235	+	0.357865i
$651$	5.18348	−	6.13629i	0.203157	−	0.240500i
$652$	4.39577	+	2.39979i	0.172152	+	0.0939829i
$653$	−27.8055			−1.08811			−0.544057	−	0.839049i	$-0.683112\pi$
$653$	−27.8055			−1.08811			−0.544057	+	0.839049i	$0.683112\pi$
$654$	−39.4902	−	29.9546i	−1.54419	−	1.17132i
$655$			3.05693i			0.119444i
$656$	−24.3095	+	15.6286i	−0.949126	+	0.610194i
$657$	24.4710	−	6.22328i	0.954706	−	0.242793i
$658$	−6.64107	−	12.3022i	−0.258896	−	0.479591i
$659$	17.2830	−	9.97832i	0.673248	−	0.388700i	−0.124058	−	0.992275i	$-0.539591\pi$
$659$	17.2830	−	9.97832i	0.673248	−	0.388700i	0.797306	+	0.603575i	$0.206258\pi$
$660$	−1.30427	−	8.72416i	−0.0507686	−	0.339588i
$661$	−16.2007	+	9.35349i	−0.630135	+	0.363808i	−0.780804	−	0.624776i	$-0.785190\pi$
$661$	−16.2007	+	9.35349i	−0.630135	+	0.363808i	0.150670	+	0.988584i	$0.451857\pi$
$662$	−1.91275	+	7.49543i	−0.0743413	+	0.291318i
$663$	0.663870	+	5.30400i	0.0257826	+	0.205990i
$664$	10.4929	−	45.6413i	0.407202	−	1.77123i
$665$	−1.56399	−	0.487815i	−0.0606490	−	0.0189166i
$666$	−24.6617	−	0.0203170i	−0.955621	−	0.000787267i
$667$	8.50381	+	14.7290i	0.329269	+	0.570311i
$668$	−0.193942	−	8.11829i	−0.00750385	−	0.314106i
$669$	30.5989	−	3.82988i	1.18302	−	0.148072i
$670$	−7.07768	−	6.91062i	−0.273435	−	0.266980i
$671$	14.9334	−	25.8654i	0.576498	−	0.998524i
$672$	3.71199	+	25.6558i	0.143193	+	0.989695i
$673$	−5.48980	−	9.50862i	−0.211616	−	0.366530i	0.740604	−	0.671942i	$-0.234539\pi$
$673$	−5.48980	−	9.50862i	−0.211616	−	0.366530i	−0.952221	+	0.305411i	$0.901206\pi$
$674$	0.548628	−	2.14988i	0.0211323	−	0.0828104i
$675$	8.72155	+	22.2516i	0.335693	+	0.856463i
$676$	33.6675	+	18.3802i	1.29491	+	0.706929i
$677$	8.35248	−	14.4669i	0.321012	−	0.556009i	−0.659685	−	0.751542i	$-0.729310\pi$
$677$	8.35248	−	14.4669i	0.321012	−	0.556009i	0.980697	+	0.195533i	$0.0626437\pi$
$678$	31.2478	+	23.7024i	1.20006	+	0.910287i
$679$	−16.8238	−	5.24742i	−0.645640	−	0.201377i
$680$	−0.931000	+	0.285573i	−0.0357022	+	0.0109512i
$681$	−3.69078	+	8.75190i	−0.141431	+	0.335373i
$682$	7.13684	+	6.96838i	0.273284	+	0.266833i
$683$	−40.6504	−	23.4695i	−1.55544	−	0.898035i	−0.997683	−	0.0680329i	$-0.978328\pi$
$683$	−40.6504	−	23.4695i	−1.55544	−	0.898035i	−0.557760	−	0.830002i	$-0.688339\pi$
$684$	−1.58243	−	5.65352i	−0.0605058	−	0.216168i
$685$			7.59963i			0.290367i
$686$	−21.1128	−	15.5000i	−0.806089	−	0.591794i
$687$	−17.0563	+	40.4453i	−0.650737	+	1.54308i
$688$	−39.6358	+	1.89484i	−1.51110	+	0.0722402i
$689$	−1.73096	+	0.999368i	−0.0659442	+	0.0380729i
$690$	3.26178	+	0.410987i	0.124174	+	0.0156460i
$691$	23.3701	−	40.4781i	0.889039	−	1.53986i	0.0480254	−	0.998846i	$-0.484707\pi$
$691$	23.3701	−	40.4781i	0.889039	−	1.53986i	0.841013	−	0.541014i	$-0.181959\pi$
$692$	0.808003	+	33.8224i	0.0307157	+	1.28574i
$693$	−1.70175	+	31.8924i	−0.0646441	+	1.21149i
$694$	15.5767	−	15.9532i	0.591282	−	0.605577i
$695$	−1.63476	+	2.83149i	−0.0620100	+	0.107404i
$696$	−31.8591	−	22.9885i	−1.20762	−	0.871375i
$697$	1.96534	+	3.40407i	0.0744427	+	0.128938i
$698$	12.8951	−	13.2069i	0.488087	−	0.499887i
$699$	−20.7748	+	2.60026i	−0.785776	+	0.0983509i
$700$	6.68991	−	23.4008i	0.252855	−	0.884467i
$701$	18.7728			0.709037			0.354519	−	0.935049i	$-0.384645\pi$
$701$	18.7728			0.709037			0.354519	+	0.935049i	$0.384645\pi$
$702$	5.14303	+	41.3668i	0.194111	+	1.56129i
$703$	−4.92565	−	2.84383i	−0.185775	−	0.107257i
$704$	−32.1077	+	2.30462i	−1.21010	+	0.0868586i
$705$	3.26506	−	2.47242i	0.122969	−	0.0931166i
$706$	−3.55000	−	12.6429i	−0.133606	−	0.475820i
$707$	−3.92118	+	3.61546i	−0.147471	+	0.135973i
$708$	−27.8802	+	22.1791i	−1.04780	+	0.833542i
$709$	23.2730	+	13.4367i	0.874035	+	0.504624i	0.868687	−	0.495361i	$-0.164964\pi$
$709$	23.2730	+	13.4367i	0.874035	+	0.504624i	0.00534803	+	0.999986i	$0.498298\pi$
$710$	−3.89141	+	1.09267i	−0.146042	+	0.0410072i
$711$	−3.82913	−	15.0568i	−0.143603	−	0.564674i
$712$	−1.64665	+	7.16253i	−0.0617110	+	0.268427i
$713$	−3.21942	+	1.85873i	−0.120568	+	0.0696100i
$714$	3.50959	−	0.337665i	0.131343	−	0.0126368i
$715$	−7.22253	+	12.5098i	−0.270107	+	0.467839i
$716$	44.6367	−	1.06635i	1.66815	−	0.0398513i
$717$	−24.4229	+	18.4938i	−0.912088	+	0.690665i
$718$	−31.3716	−	30.6311i	−1.17078	−	1.14314i
$719$	−4.77591	−	8.27211i	−0.178111	−	0.308498i	0.763122	−	0.646254i	$-0.223665\pi$
$719$	−4.77591	−	8.27211i	−0.178111	−	0.308498i	−0.941234	+	0.337756i	$0.890332\pi$
$720$	−7.26212	+	2.22102i	−0.270643	+	0.0827726i
$721$	−21.8094	−	23.6536i	−0.812225	−	0.880906i
$722$	−6.30924	+	24.7238i	−0.234806	+	0.920123i
$723$	−7.19603	−	3.03465i	−0.267623	−	0.112860i
$724$	−21.9387	−	35.9858i	−0.815344	−	1.33740i
$725$	18.4427	+	31.9437i	0.684945	+	1.18636i
$726$	−12.6151	−	1.58952i	−0.468191	−	0.0589925i
$727$	18.8834	−	10.9023i	0.700345	−	0.404345i	−0.107131	−	0.994245i	$-0.534166\pi$
$727$	18.8834	−	10.9023i	0.700345	−	0.404345i	0.807476	+	0.589900i	$0.200833\pi$
$728$	21.3982	−	36.6625i	0.793070	−	1.35880i
$729$	−19.8089	+	18.3469i	−0.733663	+	0.679513i
$730$	1.86259	−	7.29883i	0.0689374	−	0.270142i
$731$			5.39704i			0.199617i
$732$	−23.9239	−	9.42252i	−0.884251	−	0.348266i
$733$			33.3949i			1.23347i	0.787172	+	0.616734i	$0.211545\pi$
$733$			33.3949i			1.23347i	−0.787172	+	0.616734i	$0.788455\pi$
$734$	11.3408	+	40.3887i	0.418596	+	1.49078i
$735$	3.54430	−	6.80520i	0.130733	−	0.251013i
$736$	2.40798	−	11.7529i	0.0887594	−	0.433219i
$737$	−38.5152	+	22.2368i	−1.41873	+	0.819102i
$738$	15.3046	+	26.5589i	0.563370	+	0.977645i
$739$	−10.6745	+	18.4887i	−0.392667	+	0.680119i	−0.992800	−	0.119781i	$-0.961781\pi$
$739$	−10.6745	+	18.4887i	−0.392667	+	0.680119i	0.600133	+	0.799900i	$0.295114\pi$
$740$	−3.52541	+	6.45760i	−0.129596	+	0.237386i
$741$	−3.73565	+	8.85829i	−0.137232	+	0.325417i
$742$	0.626260	+	1.16011i	0.0229907	+	0.0425891i
$743$	−3.14863	+	5.45358i	−0.115512	+	0.200072i	−0.917984	−	0.396617i	$-0.870184\pi$
$743$	−3.14863	+	5.45358i	−0.115512	+	0.200072i	0.802472	+	0.596689i	$0.203517\pi$
$744$	5.02473	−	6.96364i	0.184215	−	0.255299i
$745$	−2.08861			−0.0765209
$746$	5.82685	+	20.7516i	0.213336	+	0.759769i
$747$	−47.8122	−	13.4677i	−1.74936	−	0.492758i
$748$	0.104564	+	4.37696i	0.00382322	+	0.160038i
$749$	−9.14079	+	29.3064i	−0.333997	+	1.07083i
$750$	14.7640	+	1.86027i	0.539103	+	0.0679275i
$751$		−	9.22009i		−	0.336446i	−0.985749	−	0.168223i	$-0.946197\pi$
$751$		−	9.22009i		−	0.336446i	0.985749	−	0.168223i	$-0.0538029\pi$
$752$	−8.08232	−	12.5716i	−0.294732	−	0.458440i
$753$	5.72296	−	13.5708i	0.208556	−	0.494547i
$754$	17.3920	+	61.9392i	0.633378	+	2.25569i
$755$		−	1.79727i		−	0.0654095i
$756$	27.3712	−	2.61069i	0.995482	−	0.0949498i
$757$			6.05173i			0.219954i	0.993934	+	0.109977i	$0.0350777\pi$
$757$			6.05173i			0.219954i	−0.993934	+	0.109977i	$0.964922\pi$
$758$	7.70107	−	2.16239i	0.279715	−	0.0785415i
$759$	5.74338	−	13.6192i	0.208472	−	0.494346i
$760$	−1.70689	−	0.392412i	−0.0619155	−	0.0142343i
$761$			15.7869i			0.572274i	0.958189	+	0.286137i	$0.0923713\pi$
$761$			15.7869i			0.572274i	−0.958189	+	0.286137i	$0.907629\pi$
$762$	0.799743	−	6.34712i	0.0289716	−	0.229932i
$763$	52.2319	−	11.7490i	1.89092	−	0.425344i
$764$	0.710762	+	29.7520i	0.0257145	+	1.07639i
$765$	0.254572	+	1.00102i	0.00920407	+	0.0361920i
$766$	33.1855	−	9.31818i	1.19904	−	0.336679i
$767$	58.3396			2.10652
$768$	6.04929	+	27.0445i	0.218285	+	0.975885i
$769$	−10.6781	+	18.4950i	−0.385063	+	0.666949i	−0.991778	−	0.127971i	$-0.959154\pi$
$769$	−10.6781	+	18.4950i	−0.385063	+	0.666949i	0.606715	+	0.794919i	$0.292487\pi$
$770$	8.11180	+	4.99796i	0.292329	+	0.180114i
$771$	−11.8034	+	27.9893i	−0.425089	+	1.00801i
$772$	−26.7187	−	14.5866i	−0.961627	−	0.524982i
$773$	20.3413	−	35.2321i	0.731625	−	1.26721i	−0.224564	−	0.974459i	$-0.572096\pi$
$773$	20.3413	−	35.2321i	0.731625	−	1.26721i	0.956188	−	0.292752i	$-0.0945710\pi$
$774$	−0.0346733	+	42.0881i	−0.00124631	+	1.51283i
$775$	−6.98213	+	4.03114i	−0.250806	+	0.144803i
$776$	−18.3610	−	4.22117i	−0.659122	−	0.151531i
$777$	17.1895	−	20.3492i	0.616668	−	0.730023i
$778$	0.0917519	−	0.0257631i	0.00328947	−	0.000923652i
$779$			7.06940i			0.253288i
$780$	11.5708	+	4.55719i	0.414299	+	0.163174i
$781$			18.1722i			0.650251i
$782$	−1.58106	−	0.403469i	−0.0565385	−	0.0144280i
$783$	−25.9956	+	32.5674i	−0.929006	+	1.16386i
$784$	−23.7689	−	14.7999i	−0.848891	−	0.528568i
$785$	2.43115	−	1.40362i	0.0867714	−	0.0500975i
$786$	1.47916	−	11.7393i	0.0527599	−	0.418727i
$787$	−21.5452	−	37.3175i	−0.768005	−	1.33022i	−0.938643	−	0.344890i	$-0.887916\pi$
$787$	−21.5452	−	37.3175i	−0.768005	−	1.33022i	0.170638	−	0.985334i	$-0.445417\pi$
$788$	−44.8038	+	27.3146i	−1.59607	+	0.973041i
$789$	−6.24361	−	2.63301i	−0.222279	−	0.0937375i
$790$	−4.49090	−	1.14603i	−0.159779	−	0.0407740i
$791$	−41.3300	+	9.29678i	−1.46953	+	0.330555i
$792$	0.787306	+	34.1338i	0.0279757	+	1.21289i
$793$	21.0528	+	36.4646i	0.747608	+	1.29490i
$794$	36.6786	−	37.5653i	1.30168	−	1.33314i
$795$	−0.307899	+	0.233152i	−0.0109200	+	0.00826904i
$796$	44.5589	−	1.06449i	1.57935	−	0.0377299i
$797$	6.61383	−	11.4555i	0.234274	−	0.405774i	−0.724788	−	0.688972i	$-0.758062\pi$
$797$	6.61383	−	11.4555i	0.234274	−	0.405774i	0.959061	+	0.283198i	$0.0913955\pi$
$798$	5.77004	+	2.63009i	0.204257	+	0.0931042i
$799$	−1.76041	+	1.01638i	−0.0622790	+	0.0359568i
$800$	5.22233	−	25.4892i	0.184637	−	0.901181i
$801$	7.50321	+	2.11350i	0.265113	+	0.0746769i
$802$	−3.90715	−	13.9148i	−0.137966	−	0.491349i
$803$	−29.3295	−	16.9334i	−1.03502	−	0.597566i
$804$	23.8360	+	29.9630i	0.840632	+	1.05671i
$805$	−2.61063	+	2.40709i	−0.0920125	+	0.0848387i
$806$	−13.5384	+	3.80147i	−0.476871	+	0.133901i
$807$	0.549840	−	0.416358i	0.0193553	−	0.0146565i
$808$	−3.88481	+	4.17365i	−0.136667	+	0.146829i
$809$	26.4300	+	15.2593i	0.929228	+	0.536490i	0.886567	−	0.462600i	$-0.153083\pi$
$809$	26.4300	+	15.2593i	0.929228	+	0.536490i	0.0426605	+	0.999090i	$0.486417\pi$
$810$	1.97882	+	7.80798i	0.0695285	+	0.274344i
$811$	−4.41909			−0.155175			−0.0775875	−	0.996986i	$-0.524722\pi$
$811$	−4.41909			−0.155175			−0.0775875	+	0.996986i	$0.524722\pi$
$812$	41.1662	−	10.2987i	1.44465	−	0.361413i
$813$	16.1334	−	2.01932i	0.565824	−	0.0708208i
$814$	23.6672	+	23.1085i	0.829534	+	0.809954i
$815$	−0.792351	−	1.37239i	−0.0277548	−	0.0480728i
$816$	3.71343	−	0.646180i	0.129996	−	0.0226208i
$817$	−4.85333	+	8.40621i	−0.169796	+	0.294096i
$818$	−33.4159	−	32.6271i	−1.16836	−	1.14078i
$819$	−37.7381	−	24.5583i	−1.31868	−	0.858138i
$820$	9.14199	−	0.218398i	0.319252	−	0.00762679i
$821$	16.8483	−	29.1820i	0.588008	−	1.01846i	−0.406485	−	0.913658i	$-0.633245\pi$
$821$	16.8483	−	29.1820i	0.588008	−	1.01846i	0.994493	−	0.104803i	$-0.0334212\pi$
$822$	3.67724	−	29.1843i	0.128259	−	1.01792i
$823$	−16.5778	+	9.57122i	−0.577867	+	0.333632i	−0.760285	−	0.649589i	$-0.774941\pi$
$823$	−16.5778	+	9.57122i	−0.577867	+	0.333632i	0.182418	+	0.983221i	$0.441608\pi$
$824$	−25.1766	−	23.4342i	−0.877067	−	0.816370i
$825$	12.4560	−	29.5368i	0.433662	−	1.02834i
$826$	1.10038	−	38.4648i	0.0382871	−	1.33836i
$827$			21.7716i			0.757074i	0.925586	+	0.378537i	$0.123573\pi$
$827$			21.7716i			0.757074i	−0.925586	+	0.378537i	$0.876427\pi$
$828$	−12.3271	−	3.15656i	−0.428396	−	0.109698i
$829$	−5.22064	−	3.01414i	−0.181320	−	0.104685i	0.406592	−	0.913610i	$-0.366717\pi$
$829$	−5.22064	−	3.01414i	−0.181320	−	0.104685i	−0.587913	+	0.808924i	$0.700050\pi$
$830$	−10.3525	+	10.6028i	−0.359342	+	0.368029i
$831$	−0.968870	+	2.29747i	−0.0336097	+	0.0796983i
$832$	19.8187	−	40.8249i	0.687088	−	1.41535i
$833$	−2.16502	+	3.13301i	−0.0750135	+	0.108553i
$834$	7.64793	−	10.0825i	0.264826	−	0.349130i
$835$	−1.28478	+	2.22530i	−0.0444615	+	0.0770096i
$836$	−3.77315	+	6.91141i	−0.130497	+	0.239036i
$837$	−7.11845	−	5.68201i	−0.246050	−	0.196399i
$838$	−34.4495	−	8.79114i	−1.19004	−	0.303685i
$839$	−13.4681	−	23.3275i	−0.464972	−	0.805355i	0.534228	−	0.845340i	$-0.320602\pi$
$839$	−13.4681	−	23.3275i	−0.464972	−	0.805355i	−0.999200	+	0.0399853i	$0.987269\pi$
$840$	3.22292	−	7.54294i	0.111201	−	0.260256i
$841$	−17.6556	+	30.5804i	−0.608815	+	1.05450i
$842$	7.08410	−	7.25536i	0.244134	−	0.250036i
$843$	14.2339	−	1.78157i	0.490240	−	0.0613604i
$844$	0.564260	+	23.6195i	0.0194226	+	0.813018i
$845$	−6.06868	−	10.5113i	−0.208769	−	0.361598i
$846$	−13.7349	+	7.91477i	−0.472215	+	0.272115i
$847$	10.0968	−	9.30956i	0.346929	−	0.319880i
$848$	0.762172	+	1.18552i	0.0261731	+	0.0407109i
$849$	3.17959	+	25.4034i	0.109123	+	0.871842i
$850$	−3.42893	−	0.875027i	−0.117611	−	0.0300132i
$851$	−10.6762	+	6.16392i	−0.365976	+	0.211297i
$852$	15.4726	−	2.31316i	0.530082	−	0.0792476i
$853$	21.2026	−	12.2414i	0.725965	−	0.419136i	−0.0909793	−	0.995853i	$-0.529000\pi$
$853$	21.2026	−	12.2414i	0.725965	−	0.419136i	0.816944	+	0.576717i	$0.195666\pi$
$854$	24.4391	−	13.1929i	0.836290	−	0.451452i
$855$	−0.503665	+	1.78808i	−0.0172250	+	0.0611510i
$856$	−7.35310	+	31.9841i	−0.251324	+	1.09320i
$857$		−	45.6585i		−	1.55966i	−0.625989	−	0.779832i	$-0.715305\pi$
$857$		−	45.6585i		−	1.55966i	0.625989	−	0.779832i	$-0.284695\pi$
$858$	33.7893	−	44.5456i	1.15355	−	1.52076i
$859$	21.3605			0.728812			0.364406	−	0.931240i	$-0.381272\pi$
$859$	21.3605			0.728812			0.364406	+	0.931240i	$0.381272\pi$
$860$	11.0207	+	6.01652i	0.375801	+	0.205162i
$861$	−32.5869	−	5.85662i	−1.11056	−	0.199593i
$862$	3.42967	−	13.4397i	0.116815	−	0.457758i
$863$	17.0148	+	29.4704i	0.579189	+	1.00318i	0.995573	+	0.0939957i	$0.0299640\pi$
$863$	17.0148	+	29.4704i	0.579189	+	1.00318i	−0.416384	+	0.909189i	$0.636703\pi$
$864$	28.9629	−	5.01529i	0.985336	−	0.170624i
$865$	5.35263	−	9.27103i	0.181995	−	0.315225i
$866$	−43.6405	+	12.2538i	−1.48296	+	0.416403i
$867$	3.59324	+	28.7082i	0.122033	+	0.974982i
$868$	2.25105	+	8.99794i	0.0764056	+	0.305410i
$869$	−10.4190	+	18.0462i	−0.353439	+	0.612174i
$870$	4.82104	+	11.4584i	0.163449	+	0.388477i
$871$		−	62.6979i		−	2.12444i
$872$	54.7172	−	16.7838i	1.85296	−	0.568372i
$873$	−5.41792	+	19.2343i	−0.183369	+	0.650983i
$874$	−2.09977	−	2.05021i	−0.0710258	−	0.0693493i
$875$	−11.8166	+	10.8953i	−0.399475	+	0.368329i
$876$	−10.6844	+	27.1279i	−0.360994	+	0.916567i
$877$		−	23.3842i		−	0.789627i	−0.918761	−	0.394814i	$-0.870809\pi$
$877$		−	23.3842i		−	0.789627i	0.918761	−	0.394814i	$-0.129191\pi$
$878$	−2.36328	−	0.603085i	−0.0797570	−	0.0203531i
$879$	21.2565	−	16.0962i	0.716964	−	0.542910i
$880$	9.05425	+	4.66584i	0.305219	+	0.157285i
$881$		−	9.35930i		−	0.315323i	−0.987493	−	0.157661i	$-0.949605\pi$
$881$		−	9.35930i		−	0.315323i	0.987493	−	0.157661i	$-0.0503955\pi$
$882$	−16.9038	+	24.4185i	−0.569179	+	0.822214i
$883$	48.0947			1.61851			0.809257	−	0.587454i	$-0.199870\pi$
$883$	48.0947			1.61851			0.809257	+	0.587454i	$0.199870\pi$
$884$	−5.41757	−	2.95762i	−0.182212	−	0.0994754i
$885$	11.1857	−	1.40004i	0.376002	−	0.0470619i
$886$	−25.8253	−	6.59034i	−0.867617	−	0.221407i
$887$	−13.5654			−0.455483			−0.227741	−	0.973722i	$-0.573134\pi$
$887$	−13.5654			−0.455483			−0.227741	+	0.973722i	$0.573134\pi$
$888$	16.6630	−	23.0928i	0.559174	−	0.774944i
$889$	4.68397	+	5.08004i	0.157095	+	0.170379i
$890$	1.62463	−	1.66391i	0.0544578	−	0.0557743i
$891$	36.2022	+	0.924540i	1.21282	+	0.0309733i
$892$	−17.0626	+	31.2541i	−0.571297	+	1.04646i
$893$	−3.65593			−0.122341
$894$	8.02074	+	1.01062i	0.268254	+	0.0338002i
$895$	−12.2353	−	7.06406i	−0.408981	−	0.236125i
$896$	−26.5431	−	13.8370i	−0.886744	−	0.462261i
$897$	12.5793	+	16.6122i	0.420012	+	0.554665i
$898$	11.1646	+	39.7611i	0.372566	+	1.32685i
$899$	−12.1736	−	7.02845i	−0.406014	−	0.234412i
$900$	−26.7345	−	6.84581i	−0.891148	−	0.228194i
$901$	0.166009	−	0.0958454i	0.00553057	−	0.00319307i
$902$	10.1660	−	39.8370i	0.338490	−	1.32643i
$903$	−34.7283	−	29.3358i	−1.15568	−	0.976235i
$904$	−43.2966	+	13.2807i	−1.44002	+	0.441710i
$905$			13.3360i			0.443302i
$906$	−0.869650	+	6.90194i	−0.0288922	+	0.229301i
$907$	19.8279			0.658375			0.329188	−	0.944265i	$-0.393225\pi$
$907$	19.8279			0.658375			0.329188	+	0.944265i	$0.393225\pi$
$908$	−5.70912	−	9.36462i	−0.189464	−	0.310776i
$909$	4.22145	+	4.33063i	0.140017	+	0.143638i
$910$	−11.8200	+	6.38073i	−0.391828	+	0.211519i
$911$	−14.1294	−	24.4729i	−0.468129	−	0.810823i	0.531208	−	0.847242i	$-0.321738\pi$
$911$	−14.1294	−	24.4729i	−0.468129	−	0.810823i	−0.999337	+	0.0364187i	$0.988405\pi$
$912$	6.36497	+	2.33287i	0.210765	+	0.0772489i
$913$	33.3121	+	57.6982i	1.10247	+	1.90953i
$914$	−9.53872	+	37.3790i	−0.315513	+	1.23639i
$915$	4.91161	+	6.48625i	0.162373	+	0.214429i
$916$	−26.3837	−	43.2769i	−0.871741	−	1.42991i
$917$	8.66322	+	9.39578i	0.286085	+	0.310276i
$918$	−0.493248	−	3.96733i	−0.0162796	−	0.130941i
$919$	18.3029	−	10.5672i	0.603759	−	0.348580i	−0.166760	−	0.985997i	$-0.553331\pi$
$919$	18.3029	−	10.5672i	0.603759	−	0.348580i	0.770519	+	0.637417i	$0.219997\pi$
$920$	−2.58641	+	2.77871i	−0.0852715	+	0.0916115i
$921$	20.1464	+	8.49597i	0.663846	+	0.279952i
$922$	−31.5667	−	30.8216i	−1.03959	−	1.01505i
$923$	−22.1865	−	12.8094i	−0.730278	−	0.421626i
$924$	−28.7328	−	23.1183i	−0.945238	−	0.760538i
$925$	−23.1541	+	13.3680i	−0.761303	+	0.439539i
$926$	−46.0044	−	11.7398i	−1.51180	−	0.385795i
$927$	−26.1235	+	25.4649i	−0.858009	+	0.836377i
$928$	43.0402	−	14.3353i	1.41286	−	0.470580i
$929$	14.1962	+	8.19617i	0.465761	+	0.268907i	0.714464	−	0.699672i	$-0.246671\pi$
$929$	14.1962	+	8.19617i	0.465761	+	0.268907i	−0.248702	+	0.968580i	$0.580004\pi$
$930$	−2.50454	+	1.05376i	−0.0821271	+	0.0345543i
$931$	−6.18953	+	2.93295i	−0.202854	+	0.0961235i
$932$	11.5845	−	21.2196i	0.379462	−	0.695073i
$933$	−1.35266	−	10.8071i	−0.0442842	−	0.353809i
$934$	−5.54699	+	5.68108i	−0.181503	+	0.185891i
$935$	0.692684	−	1.19976i	0.0226532	−	0.0392365i
$936$	−42.2292	−	23.0994i	−1.38030	−	0.755027i
$937$	16.6946			0.545389			0.272695	−	0.962101i	$-0.412085\pi$
$937$	16.6946			0.545389			0.272695	+	0.962101i	$0.412085\pi$
$938$	−41.3384	−	1.18259i	−1.34975	−	0.0386128i
$939$	30.7040	−	23.2501i	1.00199	−	0.758740i
$940$	0.112944	+	4.72777i	0.00368384	+	0.154203i
$941$	4.80038	+	8.31451i	0.156488	+	0.271045i	0.933600	−	0.358317i	$-0.116649\pi$
$941$	4.80038	+	8.31451i	0.156488	+	0.271045i	−0.777112	+	0.629363i	$0.783316\pi$
$942$	−10.0153	+	4.21387i	−0.326317	+	0.137295i
$943$	13.2699	+	7.66137i	0.432127	+	0.249489i
$944$	−1.96439	−	41.0905i	−0.0639354	−	1.33738i
$945$	−7.82501	−	3.80301i	−0.254547	−	0.123712i
$946$	39.4374	−	40.3908i	1.28222	−	1.31322i
$947$	4.19680	+	2.42302i	0.136378	+	0.0787376i	0.566636	−	0.823968i	$-0.308244\pi$
$947$	4.19680	+	2.42302i	0.136378	+	0.0787376i	−0.430259	+	0.902706i	$0.641578\pi$
$948$	16.6915	+	6.57404i	0.542116	+	0.213515i
$949$	41.3482	−	23.8724i	1.34222	−	0.774930i
$950$	−4.55389	−	4.44640i	−0.147748	−	0.144260i
$951$	−24.3566	+	18.4437i	−0.789818	+	0.598077i
$952$	−2.05222	+	3.51616i	−0.0665128	+	0.113959i
$953$			52.3563i			1.69599i	0.530008	+	0.847993i	$0.322189\pi$
$953$			52.3563i			1.69599i	−0.530008	+	0.847993i	$0.677811\pi$
$954$	1.29522	−	0.746372i	0.0419342	−	0.0241647i
$955$	4.70846	−	8.15530i	0.152362	−	0.263899i
$956$	−0.844831	−	35.3641i	−0.0273238	−	1.14376i
$957$	55.4579	−	6.94133i	1.79270	−	0.224381i
$958$	−28.4488	+	7.98816i	−0.919139	+	0.258086i
$959$	21.5371	+	23.3582i	0.695468	+	0.754276i
$960$	2.82018	−	8.30311i	0.0910208	−	0.267982i
$961$	−13.9637	+	24.1859i	−0.450443	+	0.780191i
$962$	−44.8961	+	12.6064i	−1.44751	+	0.406447i
$963$	33.5054	+	9.43780i	1.07970	+	0.304129i
$964$	7.69982	−	4.69418i	0.247995	−	0.151189i
$965$	4.81613	+	8.34178i	0.155037	+	0.268531i
$966$	11.1901	−	7.98055i	0.360036	−	0.256770i
$967$	49.4020	+	28.5222i	1.58866	+	0.917213i	0.993528	+	0.113585i	$0.0362334\pi$
$967$	49.4020	+	28.5222i	1.58866	+	0.917213i	0.595131	+	0.803628i	$0.297100\pi$
$968$	10.0031	−	10.7469i	0.321512	−	0.345417i
$969$	0.358271	−	0.849563i	0.0115093	−	0.0272919i
$970$	4.26540	+	4.16471i	0.136954	+	0.133721i
$971$	31.7729	−	18.3441i	1.01964	−	0.588689i	0.105640	−	0.994404i	$-0.466311\pi$
$971$	31.7729	−	18.3441i	1.01964	−	0.588689i	0.914000	+	0.405715i	$0.132978\pi$
$972$	−3.82104	−	30.9419i	−0.122560	−	0.992461i
$973$	2.99973	+	13.3357i	0.0961671	+	0.427523i
$974$	−13.9511	−	3.56018i	−0.447023	−	0.114076i
$975$	27.2815	+	36.0278i	0.873707	+	1.15381i
$976$	24.9743	−	16.0560i	0.799409	−	0.513941i
$977$	5.05493	−	2.91847i	0.161722	−	0.0933700i	−0.416955	−	0.908927i	$-0.636903\pi$
$977$	5.05493	−	2.91847i	0.161722	−	0.0933700i	0.578677	+	0.815557i	$0.303569\pi$
$978$	2.37874	+	5.65369i	0.0760638	+	0.180785i
$979$	−5.22769	−	9.05463i	−0.167078	−	0.289387i
$980$	3.98404	+	7.91356i	0.127265	+	0.252789i
$981$	−14.9618	−	58.8326i	−0.477695	−	1.87838i
$982$	−11.4164	−	2.91335i	−0.364312	−	0.0929686i
$983$	−46.9649			−1.49795			−0.748974	−	0.662599i	$-0.769453\pi$
$983$	−46.9649			−1.49795			−0.748974	+	0.662599i	$0.769453\pi$
$984$	−35.2130	−	3.58485i	−1.12255	−	0.114281i
$985$	16.6038			0.529042
$986$	−1.66799	−	5.94034i	−0.0531197	−	0.189179i
$987$	3.02875	−	16.8523i	0.0964061	−	0.536414i
$988$	−5.77852	−	9.47845i	−0.183839	−	0.301550i
$989$	10.5195	+	18.2202i	0.334499	+	0.579370i
$990$	5.40952	−	9.35176i	0.171926	−	0.297218i
$991$	−17.6219	−	10.1740i	−0.559780	−	0.323189i	0.193277	−	0.981144i	$-0.438088\pi$
$991$	−17.6219	−	10.1740i	−0.559780	−	0.323189i	−0.753057	+	0.657955i	$0.771422\pi$
$992$	3.13336	+	9.40756i	0.0994843	+	0.298690i
$993$	−7.55303	+	5.71942i	−0.239688	+	0.181500i
$994$	−8.86404	+	14.3865i	−0.281150	+	0.456313i
$995$	−12.2140	−	7.05175i	−0.387210	−	0.223556i
$996$	44.8864	−	35.7078i	1.42228	−	1.13145i
$997$			47.8951i			1.51685i	0.651759	+	0.758426i	$0.274031\pi$
$997$			47.8951i			1.51685i	−0.651759	+	0.758426i	$0.725969\pi$
$998$	−5.24580	+	1.47297i	−0.166053	+	0.0466262i
$999$	−23.6062	−	18.8427i	−0.746867	−	0.596156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cy.a.347.10	yes	184
7.2	even	3		504.2.bt.a.275.70	yes	184
8.3	odd	2	inner	504.2.cy.a.347.40	yes	184
9.2	odd	6		504.2.bt.a.11.23	✓	184
56.51	odd	6		504.2.bt.a.275.23	yes	184
63.2	odd	6	inner	504.2.cy.a.443.40	yes	184
72.11	even	6		504.2.bt.a.11.70	yes	184
504.443	even	6	inner	504.2.cy.a.443.10	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bt.a.11.23	✓	184	9.2	odd	6
504.2.bt.a.11.70	yes	184	72.11	even	6
504.2.bt.a.275.23	yes	184	56.51	odd	6
504.2.bt.a.275.70	yes	184	7.2	even	3
504.2.cy.a.347.10	yes	184	1.1	even	1	trivial
504.2.cy.a.347.40	yes	184	8.3	odd	2	inner
504.2.cy.a.443.10	yes	184	504.443	even	6	inner
504.2.cy.a.443.40	yes	184	63.2	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cy (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36156 + 0.382313i) q^{2} +(-1.59594 - 0.673028i) q^{3} +(1.70767 - 1.04108i) q^{4} -0.632847 q^{5} +(2.43027 + 0.306217i) q^{6} +(-1.94512 + 1.79346i) q^{7} +(-1.92708 + 2.07036i) q^{8} +(2.09407 + 2.14823i) q^{9} +O(q^{10})\)	\(q+(-1.36156 + 0.382313i) q^{2} +(-1.59594 - 0.673028i) q^{3} +(1.70767 - 1.04108i) q^{4} -0.632847 q^{5} +(2.43027 + 0.306217i) q^{6} +(-1.94512 + 1.79346i) q^{7} +(-1.92708 + 2.07036i) q^{8} +(2.09407 + 2.14823i) q^{9} +(0.861657 - 0.241945i) q^{10} -4.02378i q^{11} +(-3.42603 + 0.512193i) q^{12} +(4.91266 + 2.83633i) q^{13} +(1.96272 - 3.18555i) q^{14} +(1.00999 + 0.425924i) q^{15} +(1.83230 - 3.55565i) q^{16} +(-0.471154 - 0.272021i) q^{17} +(-3.67249 - 2.12435i) q^{18} +(-0.489234 - 0.847378i) q^{19} +(-1.08070 + 0.658845i) q^{20} +(4.31135 - 1.55315i) q^{21} +(1.53834 + 5.47861i) q^{22} -2.12080 q^{23} +(4.46891 - 2.00719i) q^{24} -4.59950 q^{25} +(-7.77323 - 1.98365i) q^{26} +(-1.89619 - 4.83781i) q^{27} +(-1.45449 + 5.08768i) q^{28} +(-4.00971 - 6.94503i) q^{29} +(-1.53799 - 0.193788i) q^{30} +(1.51802 - 0.876428i) q^{31} +(-1.13541 + 5.54174i) q^{32} +(-2.70812 + 6.42173i) q^{33} +(0.745500 + 0.190244i) q^{34} +(1.23096 - 1.13499i) q^{35} +(5.81246 + 1.48838i) q^{36} +(5.03405 - 2.90641i) q^{37} +(0.990083 + 0.966713i) q^{38} +(-5.93140 - 7.83297i) q^{39} +(1.21954 - 1.31022i) q^{40} +(-6.25701 - 3.61249i) q^{41} +(-5.27636 + 3.76298i) q^{42} +(-4.96013 - 8.59120i) q^{43} +(-4.18908 - 6.87131i) q^{44} +(-1.32522 - 1.35950i) q^{45} +(2.88759 - 0.810810i) q^{46} +(1.86819 - 3.23581i) q^{47} +(-5.31730 + 4.44143i) q^{48} +(0.566968 - 6.97700i) q^{49} +(6.26249 - 1.75845i) q^{50} +(0.568857 + 0.751229i) q^{51} +(11.3421 - 0.270957i) q^{52} +(-0.176173 + 0.305140i) q^{53} +(4.43133 + 5.86202i) q^{54} +2.54644i q^{55} +(0.0352810 - 7.48323i) q^{56} +(0.210480 + 1.68163i) q^{57} +(8.11463 + 7.92309i) q^{58} +(8.90652 - 5.14218i) q^{59} +(2.16815 - 0.324140i) q^{60} +(6.42814 + 3.71129i) q^{61} +(-1.73180 + 1.77366i) q^{62} +(-7.92598 - 0.422922i) q^{63} +(-0.572750 - 7.97947i) q^{64} +(-3.10896 - 1.79496i) q^{65} +(1.23215 - 9.77889i) q^{66} +(-5.52633 - 9.57189i) q^{67} +(-1.08777 + 0.0259864i) q^{68} +(3.38468 + 1.42736i) q^{69} +(-1.24210 + 2.01596i) q^{70} -4.51619 q^{71} +(-8.48303 + 0.195663i) q^{72} +(4.20833 - 7.28904i) q^{73} +(-5.74299 + 5.88182i) q^{74} +(7.34055 + 3.09560i) q^{75} +(-1.71764 - 0.937713i) q^{76} +(7.21651 + 7.82673i) q^{77} +(11.0706 + 8.39739i) q^{78} +(-4.48487 - 2.58934i) q^{79} +(-1.15957 + 2.25018i) q^{80} +(-0.229769 + 8.99707i) q^{81} +(9.90037 + 2.52647i) q^{82} +(-14.3393 + 8.27879i) q^{83} +(5.74543 - 7.14073i) q^{84} +(0.298168 + 0.172148i) q^{85} +(10.0380 + 9.80108i) q^{86} +(1.72508 + 13.7825i) q^{87} +(8.33066 + 7.75414i) q^{88} +(2.25028 - 1.29920i) q^{89} +(2.32412 + 1.34439i) q^{90} +(-14.6426 + 3.29370i) q^{91} +(-3.62164 + 2.20793i) q^{92} +(-3.01253 + 0.377061i) q^{93} +(-1.30656 + 5.11997i) q^{94} +(0.309610 + 0.536260i) q^{95} +(5.54179 - 8.08013i) q^{96} +(3.33047 + 5.76854i) q^{97} +(1.89544 + 9.71634i) q^{98} +(8.64400 - 8.42607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9	\( 184 q - 3 q^{2} - 2 q^{3} + q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{10} - 5 q^{12} - 3 q^{14} + q^{16} + 5 q^{18} - 4 q^{19} - 6 q^{20} + 2 q^{22} - 8 q^{24} + 148 q^{25} + 6 q^{26} - 8 q^{27} + 24 q^{30} - 33 q^{32} + 22 q^{33} - 4 q^{34} - 30 q^{35} - 38 q^{36} - 12 q^{40} - 12 q^{41} + 7 q^{42} - 4 q^{43} - 9 q^{44} - 6 q^{46} - 5 q^{48} - 2 q^{49} - 21 q^{50} + 26 q^{51} - 18 q^{52} - 40 q^{54} + 18 q^{56} + 4 q^{57} + 6 q^{58} - 6 q^{59} - 2 q^{60} - 8 q^{64} - 6 q^{65} + 43 q^{66} + 2 q^{67} - 18 q^{70} - 11 q^{72} - 4 q^{73} - 36 q^{75} + 2 q^{76} - 29 q^{78} - 87 q^{80} - 10 q^{81} - 4 q^{82} - 72 q^{83} - 65 q^{84} + 14 q^{88} + 24 q^{89} - 49 q^{90} - 36 q^{91} - 36 q^{92} + 9 q^{94} - 88 q^{96} - 4 q^{97} - 57 q^{98} + 10 q^{99}+O(q^{100}) \) 184 * q - 3 * q^2 - 2 * q^3 + q^4 - 2 * q^6 - 2 * q^9 - 6 * q^10 - 5 * q^12 - 3 * q^14 + q^16 + 5 * q^18 - 4 * q^19 - 6 * q^20 + 2 * q^22 - 8 * q^24 + 148 * q^25 + 6 * q^26 - 8 * q^27 + 24 * q^30 - 33 * q^32 + 22 * q^33 - 4 * q^34 - 30 * q^35 - 38 * q^36 - 12 * q^40 - 12 * q^41 + 7 * q^42 - 4 * q^43 - 9 * q^44 - 6 * q^46 - 5 * q^48 - 2 * q^49 - 21 * q^50 + 26 * q^51 - 18 * q^52 - 40 * q^54 + 18 * q^56 + 4 * q^57 + 6 * q^58 - 6 * q^59 - 2 * q^60 - 8 * q^64 - 6 * q^65 + 43 * q^66 + 2 * q^67 - 18 * q^70 - 11 * q^72 - 4 * q^73 - 36 * q^75 + 2 * q^76 - 29 * q^78 - 87 * q^80 - 10 * q^81 - 4 * q^82 - 72 * q^83 - 65 * q^84 + 14 * q^88 + 24 * q^89 - 49 * q^90 - 36 * q^91 - 36 * q^92 + 9 * q^94 - 88 * q^96 - 4 * q^97 - 57 * q^98 + 10 * q^99

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