LMFDB - Embedded newform 504.2.cz.b.187.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(187,504)]

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, 4, 5]))

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

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

chi := DirichletCharacter("504.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cz (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:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			187.5
Character	$\chi$	$=$	504.187
Dual form			504.2.cz.b.283.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38863 - 0.267785i) q^{2} +(-1.73191 - 0.0223461i) q^{3} +(1.85658 + 0.743707i) q^{4} -3.43019 q^{5} +(2.39899 + 0.494808i) q^{6} +(-0.366949 - 2.62018i) q^{7} +(-2.37895 - 1.52990i) q^{8} +(2.99900 + 0.0774026i) q^{9} +O(q^{10})$	\(q+(-1.38863 - 0.267785i) q^{2} +(-1.73191 - 0.0223461i) q^{3} +(1.85658 + 0.743707i) q^{4} -3.43019 q^{5} +(2.39899 + 0.494808i) q^{6} +(-0.366949 - 2.62018i) q^{7} +(-2.37895 - 1.52990i) q^{8} +(2.99900 + 0.0774026i) q^{9} +(4.76327 + 0.918553i) q^{10} +0.474256 q^{11} +(-3.19881 - 1.32952i) q^{12} +(-3.17749 - 5.50357i) q^{13} +(-0.192088 + 3.73672i) q^{14} +(5.94077 + 0.0766513i) q^{15} +(2.89380 + 2.76151i) q^{16} +(-1.34940 + 0.779079i) q^{17} +(-4.14377 - 0.910570i) q^{18} +(1.30211 + 0.751775i) q^{19} +(-6.36844 - 2.55106i) q^{20} +(0.576971 + 4.54611i) q^{21} +(-0.658566 - 0.126999i) q^{22} +5.70347i q^{23} +(4.08594 + 2.70280i) q^{24} +6.76622 q^{25} +(2.93858 + 8.49330i) q^{26} +(-5.19226 - 0.201070i) q^{27} +(1.26738 - 5.13749i) q^{28} +(-2.46022 - 1.42041i) q^{29} +(-8.22901 - 1.69729i) q^{30} +(-3.65531 + 6.33118i) q^{31} +(-3.27892 - 4.60963i) q^{32} +(-0.821368 - 0.0105978i) q^{33} +(2.08245 - 0.720502i) q^{34} +(1.25871 + 8.98772i) q^{35} +(5.51033 + 2.37408i) q^{36} +(5.00540 + 2.88987i) q^{37} +(-1.60684 - 1.39262i) q^{38} +(5.38013 + 9.60267i) q^{39} +(8.16026 + 5.24784i) q^{40} +(6.19109 - 3.57443i) q^{41} +(0.416179 - 6.46736i) q^{42} +(-3.72090 + 6.44479i) q^{43} +(0.880496 + 0.352708i) q^{44} +(-10.2872 - 0.265506i) q^{45} +(1.52730 - 7.92001i) q^{46} +(1.13815 + 1.97134i) q^{47} +(-4.95008 - 4.84734i) q^{48} +(-6.73070 + 1.92295i) q^{49} +(-9.39577 - 1.81189i) q^{50} +(2.35445 - 1.31914i) q^{51} +(-1.80622 - 12.5810i) q^{52} +(0.668616 - 0.386026i) q^{53} +(7.15628 + 1.66962i) q^{54} -1.62679 q^{55} +(-3.13566 + 6.79468i) q^{56} +(-2.23834 - 1.33110i) q^{57} +(3.03597 + 2.63123i) q^{58} +(6.42624 + 3.71019i) q^{59} +(10.9725 + 4.56051i) q^{60} +(5.76297 + 9.98175i) q^{61} +(6.77126 - 7.81283i) q^{62} +(-0.897673 - 7.88633i) q^{63} +(3.31882 + 7.27911i) q^{64} +(10.8994 + 18.8783i) q^{65} +(1.13774 + 0.234666i) q^{66} +(-5.87235 + 10.1712i) q^{67} +(-3.08469 + 0.442863i) q^{68} +(0.127450 - 9.87789i) q^{69} +(0.658898 - 12.8177i) q^{70} -7.46590i q^{71} +(-7.01606 - 4.77230i) q^{72} +(5.82793 - 3.36476i) q^{73} +(-6.17678 - 5.35332i) q^{74} +(-11.7185 - 0.151198i) q^{75} +(1.85838 + 2.36412i) q^{76} +(-0.174028 - 1.24264i) q^{77} +(-4.89956 - 14.7753i) q^{78} +(-1.00749 + 0.581674i) q^{79} +(-9.92629 - 9.47250i) q^{80} +(8.98802 + 0.464261i) q^{81} +(-9.55431 + 3.30568i) q^{82} +(8.86081 + 5.11579i) q^{83} +(-2.30978 + 8.86932i) q^{84} +(4.62872 - 2.67239i) q^{85} +(6.89276 - 7.95302i) q^{86} +(4.22914 + 2.51499i) q^{87} +(-1.12823 - 0.725564i) q^{88} +(-14.1057 - 8.14395i) q^{89} +(14.2139 + 3.12343i) q^{90} +(-13.2544 + 10.3451i) q^{91} +(-4.24172 + 10.5890i) q^{92} +(6.47213 - 10.8833i) q^{93} +(-1.05258 - 3.04224i) q^{94} +(-4.46649 - 2.57873i) q^{95} +(5.57578 + 8.05671i) q^{96} +(-2.29977 - 1.32777i) q^{97} +(9.86138 - 0.867884i) q^{98} +(1.42230 + 0.0367087i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.38863	−	0.267785i	−0.981909	−	0.189352i
$2$	−1.38863	−	0.267785i	−0.981909	−	0.189352i
$3$	−1.73191	−	0.0223461i	−0.999917	−	0.0129015i
$3$	−1.73191	−	0.0223461i	−0.999917	−	0.0129015i
$4$	1.85658	+	0.743707i	0.928291	+	0.371854i
$5$	−3.43019			−1.53403			−0.767014	−	0.641630i	$-0.778258\pi$
$5$	−3.43019			−1.53403			−0.767014	+	0.641630i	$0.778258\pi$
$6$	2.39899	+	0.494808i	0.979385	+	0.202005i
$7$	−0.366949	−	2.62018i	−0.138694	−	0.990335i
$7$	−0.366949	−	2.62018i	−0.138694	−	0.990335i
$8$	−2.37895	−	1.52990i	−0.841086	−	0.540901i
$9$	2.99900	+	0.0774026i	0.999667	+	0.0258009i
$10$	4.76327	+	0.918553i	1.50628	+	0.290472i
$11$	0.474256			0.142994			0.0714968	−	0.997441i	$-0.477222\pi$
$11$	0.474256			0.142994			0.0714968	+	0.997441i	$0.477222\pi$
$12$	−3.19881	−	1.32952i	−0.923417	−	0.383799i
$13$	−3.17749	−	5.50357i	−0.881276	−	1.52642i	−0.849923	−	0.526907i	$-0.823352\pi$
$13$	−3.17749	−	5.50357i	−0.881276	−	1.52642i	−0.0313537	−	0.999508i	$-0.509982\pi$
$14$	−0.192088	+	3.73672i	−0.0513376	+	0.998681i
$15$	5.94077	+	0.0766513i	1.53390	+	0.0197913i
$16$	2.89380	+	2.76151i	0.723450	+	0.690377i
$17$	−1.34940	+	0.779079i	−0.327279	+	0.188954i	−0.654632	−	0.755948i	$-0.727177\pi$
$17$	−1.34940	+	0.779079i	−0.327279	+	0.188954i	0.327354	+	0.944902i	$0.393843\pi$
$18$	−4.14377	−	0.910570i	−0.976697	−	0.214623i
$19$	1.30211	+	0.751775i	0.298725	+	0.172469i	0.641870	−	0.766814i	$-0.278159\pi$
$19$	1.30211	+	0.751775i	0.298725	+	0.172469i	−0.343145	+	0.939282i	$0.611492\pi$
$20$	−6.36844	−	2.55106i	−1.42403	−	0.570434i
$21$	0.576971	+	4.54611i	0.125905	+	0.992042i
$22$	−0.658566	−	0.126999i	−0.140407	−	0.0270762i
$23$			5.70347i			1.18926i	0.804001	+	0.594628i	$0.202701\pi$
$23$			5.70347i			1.18926i	−0.804001	+	0.594628i	$0.797299\pi$
$24$	4.08594	+	2.70280i	0.834038	+	0.551707i
$25$	6.76622			1.35324
$26$	2.93858	+	8.49330i	0.576303	+	1.66567i
$27$	−5.19226	−	0.201070i	−0.999251	−	0.0386959i
$28$	1.26738	−	5.13749i	0.239512	−	0.970894i
$29$	−2.46022	−	1.42041i	−0.456852	−	0.263764i	0.253868	−	0.967239i	$-0.418297\pi$
$29$	−2.46022	−	1.42041i	−0.456852	−	0.263764i	−0.710720	+	0.703475i	$0.751631\pi$
$30$	−8.22901	−	1.69729i	−1.50240	−	0.309881i
$31$	−3.65531	+	6.33118i	−0.656513	+	1.13711i	0.325000	+	0.945714i	$0.394636\pi$
$31$	−3.65531	+	6.33118i	−0.656513	+	1.13711i	−0.981512	+	0.191399i	$0.938697\pi$
$32$	−3.27892	−	4.60963i	−0.579637	−	0.814874i
$33$	−0.821368	−	0.0105978i	−0.142982	−	0.00184483i
$34$	2.08245	−	0.720502i	0.357137	−	0.123565i
$35$	1.25871	+	8.98772i	0.212760	+	1.51920i
$36$	5.51033	+	2.37408i	0.918388	+	0.395681i
$37$	5.00540	+	2.88987i	0.822882	+	0.475091i	0.851409	−	0.524502i	$-0.175748\pi$
$37$	5.00540	+	2.88987i	0.822882	+	0.475091i	−0.0285273	+	0.999593i	$0.509082\pi$
$38$	−1.60684	−	1.39262i	−0.260663	−	0.225913i
$39$	5.38013	+	9.60267i	0.861510	+	1.53766i
$40$	8.16026	+	5.24784i	1.29025	+	0.829757i
$41$	6.19109	−	3.57443i	0.966886	−	0.558232i	0.0686007	−	0.997644i	$-0.478147\pi$
$41$	6.19109	−	3.57443i	0.966886	−	0.558232i	0.898286	+	0.439412i	$0.144813\pi$
$42$	0.416179	−	6.46736i	0.0642178	−	0.997936i
$43$	−3.72090	+	6.44479i	−0.567432	+	0.982821i	0.429387	+	0.903121i	$0.358730\pi$
$43$	−3.72090	+	6.44479i	−0.567432	+	0.982821i	−0.996819	+	0.0797001i	$0.974604\pi$
$44$	0.880496	+	0.352708i	0.132740	+	0.0531727i
$45$	−10.2872	−	0.265506i	−1.53352	−	0.0395793i
$46$	1.52730	−	7.92001i	0.225189	−	1.16774i
$47$	1.13815	+	1.97134i	0.166017	+	0.287550i	0.937016	−	0.349287i	$-0.113576\pi$
$47$	1.13815	+	1.97134i	0.166017	+	0.287550i	−0.770999	+	0.636836i	$0.780243\pi$
$48$	−4.95008	−	4.84734i	−0.714483	−	0.699653i
$49$	−6.73070	+	1.92295i	−0.961528	+	0.274707i
$50$	−9.39577	−	1.81189i	−1.32876	−	0.256240i
$51$	2.35445	−	1.31914i	0.329689	−	0.184716i
$52$	−1.80622	−	12.5810i	−0.250478	−	1.74466i
$53$	0.668616	−	0.386026i	0.0918415	−	0.0530247i	−0.453376	−	0.891319i	$-0.649780\pi$
$53$	0.668616	−	0.386026i	0.0918415	−	0.0530247i	0.545217	+	0.838295i	$0.316447\pi$
$54$	7.15628	+	1.66962i	0.973847	+	0.227206i
$55$	−1.62679			−0.219356
$56$	−3.13566	+	6.79468i	−0.419020	+	0.907977i
$57$	−2.23834	−	1.33110i	−0.296475	−	0.176309i
$58$	3.03597	+	2.63123i	0.398643	+	0.345498i
$59$	6.42624	+	3.71019i	0.836626	+	0.483026i	0.856116	−	0.516784i	$-0.172871\pi$
$59$	6.42624	+	3.71019i	0.836626	+	0.483026i	−0.0194902	+	0.999810i	$0.506204\pi$
$60$	10.9725	+	4.56051i	1.41655	+	0.588759i
$61$	5.76297	+	9.98175i	0.737872	+	1.27803i	0.953452	+	0.301546i	$0.0975027\pi$
$61$	5.76297	+	9.98175i	0.737872	+	1.27803i	−0.215579	+	0.976486i	$0.569164\pi$
$62$	6.77126	−	7.81283i	0.859951	−	0.992230i
$63$	−0.897673	−	7.88633i	−0.113096	−	0.993584i
$64$	3.31882	+	7.27911i	0.414853	+	0.909888i
$65$	10.8994	+	18.8783i	1.35190	+	2.34157i
$66$	1.13774	+	0.234666i	0.140046	+	0.0288854i
$67$	−5.87235	+	10.1712i	−0.717421	+	1.24261i	0.244597	+	0.969625i	$0.421344\pi$
$67$	−5.87235	+	10.1712i	−0.717421	+	1.24261i	−0.962018	+	0.272985i	$0.911989\pi$
$68$	−3.08469	+	0.442863i	−0.374073	+	0.0537050i
$69$	0.127450	−	9.87789i	0.0153432	−	1.18916i
$70$	0.658898	−	12.8177i	0.0787533	−	1.53201i
$71$		−	7.46590i		−	0.886039i	−0.896512	−	0.443020i	$-0.853907\pi$
$71$		−	7.46590i		−	0.886039i	0.896512	−	0.443020i	$-0.146093\pi$
$72$	−7.01606	−	4.77230i	−0.826851	−	0.562421i
$73$	5.82793	−	3.36476i	0.682107	−	0.393815i	−0.118541	−	0.992949i	$-0.537822\pi$
$73$	5.82793	−	3.36476i	0.682107	−	0.393815i	0.800649	+	0.599134i	$0.204488\pi$
$74$	−6.17678	−	5.35332i	−0.718036	−	0.622311i
$75$	−11.7185	−	0.151198i	−1.35313	−	0.0174589i
$76$	1.85838	+	2.36412i	0.213171	+	0.271183i
$77$	−0.174028	−	1.24264i	−0.0198323	−	0.141612i
$78$	−4.89956	−	14.7753i	−0.554765	−	1.67297i
$79$	−1.00749	+	0.581674i	−0.113351	+	0.0654434i	−0.555604	−	0.831447i	$-0.687513\pi$
$79$	−1.00749	+	0.581674i	−0.113351	+	0.0654434i	0.442252	+	0.896891i	$0.354180\pi$
$80$	−9.92629	−	9.47250i	−1.10979	−	1.05906i
$81$	8.98802	+	0.464261i	0.998669	+	0.0515846i
$82$	−9.55431	+	3.30568i	−1.05510	+	0.365051i
$83$	8.86081	+	5.11579i	0.972600	+	0.561531i	0.900028	−	0.435832i	$-0.143546\pi$
$83$	8.86081	+	5.11579i	0.972600	+	0.561531i	0.0725723	+	0.997363i	$0.476879\pi$
$84$	−2.30978	+	8.86932i	−0.252018	+	0.967723i
$85$	4.62872	−	2.67239i	0.502055	−	0.289861i
$86$	6.89276	−	7.95302i	0.743266	−	0.857596i
$87$	4.22914	+	2.51499i	0.453411	+	0.269636i
$88$	−1.12823	−	0.725564i	−0.120270	−	0.0773454i
$89$	−14.1057	−	8.14395i	−1.49520	−	0.863257i	−0.495220	−	0.868768i	$-0.664913\pi$
$89$	−14.1057	−	8.14395i	−1.49520	−	0.863257i	−0.999985	+	0.00551082i	$0.998246\pi$
$90$	14.2139	+	3.12343i	1.49828	+	0.329238i
$91$	−13.2544	+	10.3451i	−1.38944	+	1.08446i
$92$	−4.24172	+	10.5890i	−0.442229	+	1.10398i
$93$	6.47213	−	10.8833i	0.671129	−	1.12855i
$94$	−1.05258	−	3.04224i	−0.108565	−	0.313783i
$95$	−4.46649	−	2.57873i	−0.458253	−	0.264572i
$96$	5.57578	+	8.05671i	0.569076	+	0.822285i
$97$	−2.29977	−	1.32777i	−0.233506	−	0.134815i	0.378682	−	0.925527i	$-0.376377\pi$
$97$	−2.29977	−	1.32777i	−0.233506	−	0.134815i	−0.612189	+	0.790712i	$0.709711\pi$
$98$	9.86138	−	0.867884i	0.996150	−	0.0876695i
$99$	1.42230	+	0.0367087i	0.142946	+	0.00368936i
$100$	12.5620	+	5.03209i	1.25620	+	0.503209i
$101$	−14.9069			−1.48329			−0.741647	−	0.670791i	$-0.765955\pi$
$101$	−14.9069			−1.48329			−0.741647	+	0.670791i	$0.765955\pi$
$102$	−3.62271	+	1.20131i	−0.358701	+	0.118947i
$103$	−2.07757			−0.204710			−0.102355	−	0.994748i	$-0.532638\pi$
$103$	−2.07757			−0.204710			−0.102355	+	0.994748i	$0.532638\pi$
$104$	−0.860811	+	17.9540i	−0.0844095	+	1.76053i
$105$	−1.97912	−	15.5940i	−0.193143	−	1.52182i
$106$	−1.03183	+	0.357001i	−0.100220	+	0.0346750i
$107$	2.42088	−	4.19310i	0.234036	−	0.405362i	−0.724956	−	0.688795i	$-0.758140\pi$
$107$	2.42088	−	4.19310i	0.234036	−	0.405362i	0.958992	+	0.283433i	$0.0914734\pi$
$108$	−9.49032	−	4.23483i	−0.913207	−	0.407496i
$109$	13.0150	−	7.51419i	1.24661	−	0.719729i	0.276176	−	0.961107i	$-0.410933\pi$
$109$	13.0150	−	7.51419i	1.24661	−	0.719729i	0.970431	+	0.241378i	$0.0775995\pi$
$110$	2.25901	+	0.435629i	0.215388	+	0.0415356i
$111$	−8.60430	−	5.11683i	−0.816684	−	0.485668i
$112$	6.17377	−	8.59561i	0.583367	−	0.812209i
$113$	−3.38463	−	5.86236i	−0.318400	−	0.551484i	0.661755	−	0.749720i	$-0.269812\pi$
$113$	−3.38463	−	5.86236i	−0.318400	−	0.551484i	−0.980154	+	0.198236i	$0.936479\pi$
$114$	2.75177	+	2.44780i	0.257727	+	0.229257i
$115$		−	19.5640i		−	1.82435i
$116$	−3.51124	−	4.46680i	−0.326010	−	0.414732i
$117$	−9.10330	−	16.7512i	−0.841600	−	1.54865i
$118$	−7.93014	−	6.87293i	−0.730028	−	0.632705i
$119$	2.53649	+	3.24980i	0.232520	+	0.297909i
$120$	−14.0155	−	9.27113i	−1.27944	−	0.846334i
$121$	−10.7751			−0.979553
$122$	−5.32966	−	15.4042i	−0.482525	−	1.39463i
$123$	−10.8023	+	6.05223i	−0.974008	+	0.545711i
$124$	−11.4949	+	9.03588i	−1.03227	+	0.811446i
$125$	−6.05847			−0.541886
$126$	−0.865303	+	11.1916i	−0.0770873	+	0.997024i
$127$		−	0.737098i		−	0.0654069i	−0.999465	−	0.0327034i	$-0.989588\pi$
$127$		−	0.737098i		−	0.0654069i	0.999465	−	0.0327034i	$-0.0104117\pi$
$128$	−2.65938	−	10.9967i	−0.235058	−	0.971981i
$129$	6.58827	−	11.0786i	0.580064	−	0.975418i
$130$	−10.0799	−	29.1337i	−0.884065	−	2.55519i
$131$			11.2263i			0.980845i	0.871485	+	0.490423i	$0.163158\pi$
$131$			11.2263i			0.980845i	−0.871485	+	0.490423i	$0.836842\pi$
$132$	−1.51706	−	0.630533i	−0.132043	−	0.0548808i
$133$	1.49198	−	3.68763i	0.129371	−	0.319758i
$134$	10.8782	−	12.5515i	0.939734	−	1.08429i
$135$	17.8105	+	0.689709i	1.53288	+	0.0593607i
$136$	4.40208	+	0.211060i	0.377475	+	0.0180982i
$137$	−0.266468			−0.0227659			−0.0113829	−	0.999935i	$-0.503623\pi$
$137$	−0.266468			−0.0227659			−0.0113829	+	0.999935i	$0.503623\pi$
$138$	−2.82213	+	13.6826i	−0.240235	+	1.16474i
$139$	6.51267	−	3.76009i	0.552397	−	0.318927i	−0.197691	−	0.980264i	$-0.563344\pi$
$139$	6.51267	−	3.76009i	0.552397	−	0.318927i	0.750088	+	0.661338i	$0.230011\pi$
$140$	−4.34734	+	17.6226i	−0.367418	+	1.48938i
$141$	−1.92713	−	3.43961i	−0.162293	−	0.289668i
$142$	−1.99925	+	10.3674i	−0.167774	+	0.870010i
$143$	−1.50694	−	2.61010i	−0.126017	−	0.218268i
$144$	8.46476	+	8.50575i	0.705397	+	0.708813i
$145$	8.43904	+	4.87228i	0.700824	+	0.404621i
$146$	−8.99386	+	3.11177i	−0.744337	+	0.257532i
$147$	11.6999	−	3.17996i	0.964992	−	0.262279i
$148$	7.14372	+	9.08783i	0.587210	+	0.747015i
$149$		−	7.08720i		−	0.580606i	−0.956935	−	0.290303i	$-0.906244\pi$
$149$		−	7.08720i		−	0.580606i	0.956935	−	0.290303i	$-0.0937561\pi$
$150$	16.2321	+	3.34798i	1.32535	+	0.273362i
$151$			19.6252i			1.59708i	0.601943	+	0.798539i	$0.294393\pi$
$151$			19.6252i			1.59708i	−0.601943	+	0.798539i	$0.705607\pi$
$152$	−1.94752	−	3.78053i	−0.157965	−	0.306642i
$153$	−4.10717	+	2.23201i	−0.332045	+	0.180447i
$154$	−0.0910988	+	1.77216i	−0.00734095	+	0.142805i
$155$	12.5384	−	21.7172i	1.00711	−	1.74436i
$156$	2.84708	+	21.8294i	0.227948	+	1.74775i
$157$	0.602048	−	1.04278i	0.0480487	−	0.0832228i	−0.841001	−	0.541034i	$-0.818033\pi$
$157$	0.602048	−	1.04278i	0.0480487	−	0.0832228i	0.889049	+	0.457811i	$0.151366\pi$
$158$	1.55479	−	0.537939i	0.123693	−	0.0427961i
$159$	−1.16661	+	0.653619i	−0.0925179	+	0.0518354i
$160$	11.2473	+	15.8119i	0.889180	+	1.25004i
$161$	14.9441	−	2.09289i	1.17776	−	0.164943i
$162$	−12.3567	−	3.05154i	−0.970834	−	0.239752i
$163$	5.10301	−	8.83867i	0.399698	−	0.692298i	−0.593990	−	0.804472i	$-0.702448\pi$
$163$	5.10301	−	8.83867i	0.399698	−	0.692298i	0.993689	+	0.112174i	$0.0357815\pi$
$164$	14.1526	−	2.03186i	1.10513	−	0.158662i
$165$	2.81745	+	0.0363524i	0.219338	+	0.00283003i
$166$	−10.9345	−	9.47673i	−0.848678	−	0.735537i
$167$	6.57039	+	11.3803i	0.508432	+	0.880631i	0.999952	+	0.00976432i	$0.00310813\pi$
$167$	6.57039	+	11.3803i	0.508432	+	0.880631i	−0.491520	+	0.870866i	$0.663559\pi$
$168$	5.58250	−	11.6977i	0.430699	−	0.902496i
$169$	−13.6929	+	23.7167i	−1.05330	+	1.82436i
$170$	−7.14320	+	2.47146i	−0.547858	+	0.189552i
$171$	3.84685	+	2.35536i	0.294176	+	0.180119i
$172$	−11.7012	+	9.19802i	−0.892207	+	0.701342i
$173$	10.6960	+	18.5260i	0.813203	+	1.40851i	0.910611	+	0.413265i	$0.135612\pi$
$173$	10.6960	+	18.5260i	0.813203	+	1.40851i	−0.0974076	+	0.995245i	$0.531055\pi$
$174$	−5.19923	−	4.62489i	−0.394152	−	0.350612i
$175$	−2.48286	−	17.7287i	−0.187687	−	1.34017i
$176$	1.37240	+	1.30966i	0.103449	+	0.0987195i
$177$	−11.0467	−	6.56931i	−0.830324	−	0.493780i
$178$	17.4068	+	15.0862i	1.30470	+	1.13076i
$179$	−2.71351	−	4.69994i	−0.202817	−	0.351290i	0.746618	−	0.665253i	$-0.231676\pi$
$179$	−2.71351	−	4.69994i	−0.202817	−	0.351290i	−0.949435	+	0.313963i	$0.898343\pi$
$180$	−18.9015	−	8.14356i	−1.40883	−	0.606985i
$181$	−2.74212			−0.203820			−0.101910	−	0.994794i	$-0.532495\pi$
$181$	−2.74212			−0.203820			−0.101910	+	0.994794i	$0.532495\pi$
$182$	21.1757	−	10.8162i	1.56965	−	0.801752i
$183$	−9.75787	−	17.4162i	−0.721322	−	1.28745i
$184$	8.72574	−	13.5683i	0.643270	−	1.00027i
$185$	−17.1695	−	9.91280i	−1.26232	−	0.728803i
$186$	−11.9018	+	13.3798i	−0.872681	+	0.981053i
$187$	−0.639963	+	0.369483i	−0.0467988	+	0.0270193i
$188$	0.646977	+	4.50641i	0.0471856	+	0.328664i
$189$	1.37846	+	13.6784i	0.100268	+	0.994960i
$190$	5.51176	+	4.77696i	0.399865	+	0.346557i
$191$	−2.81021	+	1.62247i	−0.203340	+	0.117398i	−0.598212	−	0.801338i	$-0.704122\pi$
$191$	−2.81021	+	1.62247i	−0.203340	+	0.117398i	0.394873	+	0.918736i	$0.370789\pi$
$192$	−5.58523	−	12.6809i	−0.403079	−	0.915165i
$193$	−5.93884	+	10.2864i	−0.427487	+	0.740430i	−0.996649	−	0.0817958i	$-0.973934\pi$
$193$	−5.93884	+	10.2864i	−0.427487	+	0.740430i	0.569162	+	0.822226i	$0.307268\pi$
$194$	2.83797	+	2.45963i	0.203754	+	0.176591i
$195$	−18.4549	−	32.9390i	−1.32158	−	2.35881i
$196$	−13.9262	−	1.43556i	−0.994729	−	0.102540i
$197$			24.8936i			1.77360i	0.462156	+	0.886799i	$0.347076\pi$
$197$			24.8936i			1.77360i	−0.462156	+	0.886799i	$0.652924\pi$
$198$	−1.96521	−	0.431844i	−0.139661	−	0.0306898i
$199$	10.5675	+	18.3035i	0.749111	+	1.29750i	0.948249	+	0.317527i	$0.102852\pi$
$199$	10.5675	+	18.3035i	0.749111	+	1.29750i	−0.199138	+	0.979971i	$0.563814\pi$
$200$	−16.0965	−	10.3516i	−1.13820	−	0.731970i
$201$	10.3976	−	17.4844i	0.733393	−	1.23325i
$202$	20.7002	+	3.99184i	1.45646	+	0.280865i
$203$	−2.81896	+	6.96745i	−0.197852	+	0.489019i
$204$	5.35229	−	0.698066i	0.374735	−	0.0488744i
$205$	−21.2366	+	12.2610i	−1.48323	+	0.856344i
$206$	2.88498	+	0.556343i	0.201006	+	0.0387622i
$207$	−0.441464	+	17.1047i	−0.0306839	+	1.18886i
$208$	6.00314	−	24.7009i	0.416243	−	1.71270i
$209$	0.617535	+	0.356534i	0.0427158	+	0.0246620i
$210$	−1.42757	+	22.1843i	−0.0985120	+	1.53086i
$211$	−10.7741	−	18.6613i	−0.741719	−	1.28469i	−0.951712	−	0.306992i	$-0.900678\pi$
$211$	−10.7741	−	18.6613i	−0.741719	−	1.28469i	0.209993	−	0.977703i	$-0.432656\pi$
$212$	1.52843	−	0.219434i	0.104973	−	0.0150708i
$213$	−0.166833	+	12.9302i	−0.0114312	+	0.885965i
$214$	−4.48456	+	5.17438i	−0.306558	+	0.353713i
$215$	12.7634	−	22.1069i	0.870457	−	1.50768i
$216$	12.0445	+	8.42197i	0.819526	+	0.573042i
$217$	17.9301	+	7.25435i	1.21718	+	0.492457i
$218$	−20.0851	+	6.94922i	−1.36034	+	0.470660i
$219$	−10.1686	+	5.69721i	−0.687131	+	0.384982i
$220$	−3.02027	−	1.20986i	−0.203627	−	0.0815685i
$221$	8.57543	+	4.95103i	0.576846	+	0.333042i
$222$	10.5780	+	9.40948i	0.709947	+	0.631523i
$223$	9.18301	−	15.9054i	0.614940	−	1.06511i	−0.375455	−	0.926840i	$-0.622514\pi$
$223$	9.18301	−	15.9054i	0.614940	−	1.06511i	0.990395	−	0.138266i	$-0.0441530\pi$
$224$	−10.8749	+	10.2829i	−0.726607	+	0.687053i
$225$	20.2919	+	0.523723i	1.35279	+	0.0349149i
$226$	3.13015	+	9.04700i	0.208215	+	0.601797i
$227$			25.5327i			1.69466i	0.531064	+	0.847332i	$0.321793\pi$
$227$			25.5327i			1.69466i	−0.531064	+	0.847332i	$0.678207\pi$
$228$	−3.16571	−	4.13597i	−0.209654	−	0.273911i
$229$	−16.4395			−1.08635			−0.543177	−	0.839618i	$-0.682779\pi$
$229$	−16.4395			−1.08635			−0.543177	+	0.839618i	$0.682779\pi$
$230$	−5.23894	+	27.1672i	−0.345446	+	1.79135i
$231$	0.273632	+	2.15602i	0.0180037	+	0.141856i
$232$	3.67967	+	7.14298i	0.241582	+	0.468960i
$233$	4.13335	−	7.15918i	0.270785	−	0.469014i	−0.698278	−	0.715827i	$-0.746050\pi$
$233$	4.13335	−	7.15918i	0.270785	−	0.469014i	0.969063	+	0.246813i	$0.0793834\pi$
$234$	8.15540	+	25.6989i	0.533135	+	1.67999i
$235$	−3.90409	−	6.76208i	−0.254675	−	0.441109i
$236$	9.17155	+	11.6675i	0.597017	+	0.759491i
$237$	1.75787	−	0.984891i	0.114186	−	0.0639756i
$238$	−2.65200	−	5.19200i	−0.171904	−	0.336548i
$239$	1.93666	−	1.11813i	0.125272	−	0.0723259i	−0.436055	−	0.899920i	$-0.643625\pi$
$239$	1.93666	−	1.11813i	0.125272	−	0.0723259i	0.561327	+	0.827594i	$0.310291\pi$
$240$	16.9797	+	16.6273i	1.09604	+	1.07329i
$241$		−	6.44268i		−	0.415009i	−0.978234	−	0.207505i	$-0.933466\pi$
$241$		−	6.44268i		−	0.415009i	0.978234	−	0.207505i	$-0.0665342\pi$
$242$	14.9626	+	2.88540i	0.961832	+	0.185481i
$243$	−15.5560	−	1.00490i	−0.997920	−	0.0644646i
$244$	3.27592	+	22.8179i	0.209720	+	1.46077i
$245$	23.0876	−	6.59608i	1.47501	−	0.421408i
$246$	16.6210	−	5.51162i	1.05972	−	0.351408i
$247$		−	9.55502i		−	0.607971i
$248$	18.3819	−	9.46932i	1.16725	−	0.601303i
$249$	−15.2318	−	9.05808i	−0.965275	−	0.574032i
$250$	8.41297	+	1.62237i	0.532083	+	0.102607i
$251$			0.693436i			0.0437693i	0.999761	+	0.0218847i	$0.00696666\pi$
$251$			0.693436i			0.0437693i	−0.999761	+	0.0218847i	$0.993033\pi$
$252$	4.19852	−	15.3092i	0.264482	−	0.964391i
$253$			2.70491i			0.170056i
$254$	−0.197384	+	1.02356i	−0.0123849	+	0.0642236i
$255$	−8.07622	+	4.52490i	−0.505753	+	0.283360i
$256$	0.748145	+	15.9825i	0.0467591	+	0.998906i
$257$			25.0796i			1.56442i	0.623014	+	0.782211i	$0.285908\pi$
$257$			25.0796i			1.56442i	−0.623014	+	0.782211i	$0.714092\pi$
$258$	−12.1153	+	13.6199i	−0.754268	+	0.847935i
$259$	5.73525	−	14.1755i	0.356371	−	0.880821i
$260$	6.19569	+	43.1551i	0.384241	+	2.67637i
$261$	−7.26827	−	4.45024i	−0.449895	−	0.275463i
$262$	3.00623	−	15.5892i	0.185725	−	0.963101i
$263$		−	2.09298i		−	0.129059i	−0.997916	−	0.0645295i	$-0.979445\pi$
$263$		−	2.09298i		−	0.129059i	0.997916	−	0.0645295i	$-0.0205546\pi$
$264$	1.93778	+	1.28182i	0.119262	+	0.0788906i
$265$	−2.29348	+	1.32414i	−0.140887	+	0.0813414i
$266$	−3.05929	+	4.72122i	−0.187577	+	0.289477i
$267$	24.2478	+	14.4198i	1.48394	+	0.882475i
$268$	−18.4669	+	14.5164i	−1.12805	+	0.886729i
$269$	4.38390	+	7.59313i	0.267291	+	0.462962i	0.968161	−	0.250327i	$-0.0805382\pi$
$269$	4.38390	+	7.59313i	0.267291	+	0.462962i	−0.700870	+	0.713289i	$0.747205\pi$
$270$	−24.5474	−	5.72712i	−1.49391	−	0.348541i
$271$	−6.89166	+	11.9367i	−0.418638	+	0.725103i	−0.995803	−	0.0915250i	$-0.970826\pi$
$271$	−6.89166	+	11.9367i	−0.418638	+	0.725103i	0.577164	+	0.816628i	$0.304159\pi$
$272$	−6.05634	−	1.47189i	−0.367219	−	0.0892466i
$273$	23.1865	−	17.6206i	1.40331	−	1.06645i
$274$	0.370025	+	0.0713560i	0.0223540	+	0.00431078i
$275$	3.20892			0.193505
$276$	7.58288	−	18.2443i	0.456436	−	1.09818i
$277$		−	6.97710i		−	0.419213i	−0.977786	−	0.209607i	$-0.932782\pi$
$277$		−	6.97710i		−	0.419213i	0.977786	−	0.209607i	$-0.0672183\pi$
$278$	−10.0506	+	3.47738i	−0.602794	+	0.208559i
$279$	−11.4523	+	18.7043i	−0.685633	+	1.11980i
$280$	10.7559	−	23.3071i	0.642788	−	1.39286i
$281$	8.15000	−	14.1162i	0.486188	−	0.842103i	−0.513686	−	0.857978i	$-0.671720\pi$
$281$	8.15000	−	14.1162i	0.486188	−	0.842103i	0.999874	+	0.0158755i	$0.00505356\pi$
$282$	1.75499	+	5.29240i	0.104508	+	0.315158i
$283$	−16.3518	−	9.44071i	−0.972013	−	0.561192i	−0.0721638	−	0.997393i	$-0.522990\pi$
$283$	−16.3518	−	9.44071i	−0.972013	−	0.561192i	−0.899849	+	0.436201i	$0.856324\pi$
$284$	5.55244	−	13.8611i	0.329477	−	0.822502i
$285$	7.67793	+	4.56593i	0.454801	+	0.270462i
$286$	1.39364	+	4.02800i	0.0824077	+	0.238181i
$287$	−11.6375	−	14.9101i	−0.686938	−	0.880118i
$288$	−9.47670	−	14.0781i	−0.558420	−	0.829558i
$289$	−7.28607	+	12.6198i	−0.428592	+	0.742344i
$290$	−10.4140	−	9.02564i	−0.611530	−	0.530004i
$291$	3.95332	+	2.35097i	0.231748	+	0.137816i
$292$	13.3224	−	1.91268i	0.779636	−	0.111931i
$293$	−9.06611	−	15.7030i	−0.529648	−	0.917377i	−0.999402	−	0.0345796i	$-0.988991\pi$
$293$	−9.06611	−	15.7030i	−0.529648	−	0.917377i	0.469754	−	0.882797i	$-0.344343\pi$
$294$	−17.0984	+	1.28273i	−0.997198	+	0.0748104i
$295$	−22.0433	−	12.7267i	−1.28341	−	0.740976i
$296$	−7.48639	−	14.5326i	−0.435138	−	0.844690i
$297$	−2.46246	−	0.0953587i	−0.142887	−	0.00553327i
$298$	−1.89784	+	9.84150i	−0.109939	+	0.570103i
$299$	31.3895	−	18.1227i	1.81530	−	1.04806i
$300$	−21.6438	−	8.99582i	−1.24961	−	0.519374i
$301$	18.2519	+	7.38452i	1.05202	+	0.425637i
$302$	5.25533	−	27.2522i	0.302410	−	1.56819i
$303$	25.8174	+	0.333111i	1.48317	+	0.0191367i
$304$	1.69202	+	5.77128i	0.0970439	+	0.331005i
$305$	−19.7681	−	34.2393i	−1.13192	−	1.96054i
$306$	6.30103	−	1.99960i	0.360206	−	0.114310i
$307$		−	4.93979i		−	0.281929i	−0.990015	−	0.140964i	$-0.954980\pi$
$307$		−	4.93979i		−	0.281929i	0.990015	−	0.140964i	$-0.0450203\pi$
$308$	0.601061	−	2.43648i	0.0342486	−	0.138832i
$309$	3.59817	+	0.0464256i	0.204692	+	0.00264106i
$310$	−23.2267	+	26.7995i	−1.31919	+	1.52211i
$311$	−2.91832	+	5.05468i	−0.165483	+	0.286625i	−0.936827	−	0.349794i	$-0.886252\pi$
$311$	−2.91832	+	5.05468i	−0.165483	+	0.286625i	0.771344	+	0.636419i	$0.219585\pi$
$312$	1.89205	−	31.0753i	0.107116	−	1.75930i
$313$	−19.7435	+	11.3989i	−1.11597	+	0.644305i	−0.940369	−	0.340157i	$-0.889520\pi$
$313$	−19.7435	+	11.3989i	−1.11597	+	0.644305i	−0.175600	+	0.984462i	$0.556186\pi$
$314$	−1.11526	+	1.28681i	−0.0629379	+	0.0726191i
$315$	3.07919	+	27.0516i	0.173493	+	1.52419i
$316$	−2.30308	+	0.330649i	−0.129558	+	0.0186005i
$317$	4.21039	−	2.43087i	0.236479	−	0.136531i	−0.377078	−	0.926181i	$-0.623071\pi$
$317$	4.21039	−	2.43087i	0.236479	−	0.136531i	0.613557	+	0.789650i	$0.289738\pi$
$318$	1.79501	−	0.595236i	0.100659	−	0.0333792i
$319$	−1.16678	−	0.673639i	−0.0653269	−	0.0377165i
$320$	−11.3842	−	24.9687i	−0.636396	−	1.39579i
$321$	−4.28645	+	7.20795i	−0.239246	+	0.402309i
$322$	−21.3123	−	1.09557i	−1.18769	−	0.0610536i
$323$	−2.34277			−0.130355
$324$	16.3417	+	7.54639i	0.907874	+	0.419244i
$325$	−21.4996	−	37.2384i	−1.19258	−	2.06561i
$326$	−9.45305	+	10.9071i	−0.523556	+	0.604090i
$327$	−22.7086	+	12.7230i	−1.25579	+	0.703586i
$328$	−20.1968	−	0.968347i	−1.11518	−	0.0534680i
$329$	4.74762	−	3.70555i	0.261745	−	0.204294i
$330$	−3.90266	−	0.804950i	−0.214834	−	0.0443110i
$331$	5.07643	+	8.79263i	0.279026	+	0.483287i	0.971143	−	0.238498i	$-0.0766552\pi$
$331$	5.07643	+	8.79263i	0.279026	+	0.483287i	−0.692117	+	0.721785i	$0.743322\pi$
$332$	12.6462	+	16.0877i	0.694049	+	0.882929i
$333$	14.7875	+	9.05415i	0.810350	+	0.496164i
$334$	−6.07638	−	17.5624i	−0.332485	−	0.960972i
$335$	20.1433	−	34.8892i	1.10054	−	1.90620i
$336$	−10.8845	+	14.7488i	−0.593797	+	0.804615i
$337$	10.2774	+	17.8010i	0.559847	+	0.969683i	0.997509	+	0.0705433i	$0.0224733\pi$
$337$	10.2774	+	17.8010i	0.559847	+	0.969683i	−0.437662	+	0.899140i	$0.644193\pi$
$338$	25.3653	−	29.2670i	1.37969	−	1.59191i
$339$	5.73087	+	10.2287i	0.311258	+	0.555546i
$340$	10.5811	−	1.51910i	0.573839	−	0.0823850i
$341$	−1.73355	+	3.00260i	−0.0938771	+	0.162600i
$342$	−4.71111	−	4.30085i	−0.254748	−	0.232563i
$343$	7.50829	+	16.9300i	0.405410	+	0.914135i
$344$	18.7117	−	9.63924i	1.00887	−	0.519713i
$345$	−0.437179	+	33.8830i	−0.0235369	+	1.82420i
$346$	−9.89181	−	28.5900i	−0.531787	−	1.53701i
$347$	−0.0772354	+	0.133776i	−0.00414621	+	0.00718145i	−0.868091	−	0.496405i	$-0.834653\pi$
$347$	−0.0772354	+	0.133776i	−0.00414621	+	0.00718145i	0.863945	+	0.503586i	$0.167986\pi$
$348$	5.98132	+	7.81454i	0.320633	+	0.418903i
$349$	8.03155	−	13.9111i	0.429919	−	0.744642i	−0.566947	−	0.823755i	$-0.691875\pi$
$349$	8.03155	−	13.9111i	0.429919	−	0.744642i	0.996866	+	0.0791128i	$0.0252087\pi$
$350$	−1.29971	+	25.2835i	−0.0694723	+	1.35146i
$351$	15.3917	+	29.2149i	0.821550	+	1.55937i
$352$	−1.55505	−	2.18614i	−0.0828845	−	0.116522i
$353$			2.69911i			0.143659i	0.997417	+	0.0718294i	$0.0228837\pi$
$353$			2.69911i			0.143659i	−0.997417	+	0.0718294i	$0.977116\pi$
$354$	13.5807	+	12.0805i	0.721805	+	0.642071i
$355$			25.6095i			1.35921i
$356$	−20.1317	−	25.6105i	−1.06698	−	1.35735i
$357$	−4.32035	−	5.68503i	−0.228657	−	0.300884i
$358$	2.50949	+	7.25311i	0.132631	+	0.383339i
$359$	15.6674	+	9.04556i	0.826892	+	0.477406i	0.852787	−	0.522259i	$-0.174910\pi$
$359$	15.6674	+	9.04556i	0.826892	+	0.477406i	−0.0258955	+	0.999665i	$0.508244\pi$
$360$	24.0664	+	16.3699i	1.26841	+	0.862770i
$361$	−8.36967	−	14.4967i	−0.440509	−	0.762984i
$362$	3.80779	+	0.734298i	0.200133	+	0.0385939i
$363$	18.6614	+	0.240781i	0.979471	+	0.0126377i
$364$	−32.3016	+	9.34921i	−1.69306	+	0.490032i
$365$	−19.9909	+	11.5418i	−1.04637	+	0.604123i
$366$	8.88626	+	26.7977i	0.464492	+	1.40074i
$367$	−29.9203			−1.56183			−0.780913	−	0.624640i	$-0.785246\pi$
$367$	−29.9203			−1.56183			−0.780913	+	0.624640i	$0.785246\pi$
$368$	−15.7502	+	16.5047i	−0.821036	+	0.860367i
$369$	18.8438	−	10.2405i	0.980967	−	0.533100i
$370$	21.1875	+	18.3629i	1.10149	+	0.954643i
$371$	−1.25681	−	1.61024i	−0.0652501	−	0.0835997i
$372$	20.1101	−	15.3924i	1.04266	−	0.798060i
$373$		−	14.5179i		−	0.751710i	−0.926678	−	0.375855i	$-0.877349\pi$
$373$		−	14.5179i		−	0.751710i	0.926678	−	0.375855i	$-0.122651\pi$
$374$	0.987614	−	0.341703i	0.0510683	−	0.0176690i
$375$	10.4927	+	0.135383i	0.541841	+	0.00699115i
$376$	0.308337	−	6.43099i	0.0159013	−	0.331653i
$377$			18.0533i			0.929795i
$378$	1.74871	−	19.3634i	0.0899440	−	0.995947i
$379$	−29.4138			−1.51088			−0.755442	−	0.655215i	$-0.772578\pi$
$379$	−29.4138			−1.51088			−0.755442	+	0.655215i	$0.772578\pi$
$380$	−6.37459	−	8.10939i	−0.327010	−	0.416003i
$381$	−0.0164712	+	1.27659i	−0.000843847	+	0.0654014i
$382$	4.33681	−	1.50049i	0.221891	−	0.0767715i
$383$	−29.0678			−1.48530			−0.742649	−	0.669681i	$-0.766431\pi$
$383$	−29.0678			−1.48530			−0.742649	+	0.669681i	$0.766431\pi$
$384$	4.36007	+	19.1047i	0.222499	+	0.974933i
$385$	0.596950	+	4.26248i	0.0304234	+	0.217236i
$386$	11.0014	−	12.6936i	0.559956	−	0.646089i
$387$	−11.6578	+	19.0399i	−0.592600	+	0.967853i
$388$	−3.28224	−	4.17548i	−0.166630	−	0.211978i
$389$			19.1450i			0.970689i	0.874323	+	0.485345i	$0.161306\pi$
$389$			19.1450i			0.970689i	−0.874323	+	0.485345i	$0.838694\pi$
$390$	16.8064	+	50.6820i	0.851026	+	2.56638i
$391$	−4.44346	−	7.69629i	−0.224715	−	0.389218i
$392$	18.9539	+	5.72268i	0.957317	+	0.289039i
$393$	0.250863	−	19.4429i	0.0126544	−	0.980764i
$394$	6.66613	−	34.5680i	0.335835	−	1.74151i
$395$	3.45588	−	1.99525i	0.173884	−	0.100392i
$396$	2.61331	+	1.12592i	0.131324	+	0.0565798i
$397$	−0.464152	+	0.803935i	−0.0232951	+	0.0403483i	−0.877438	−	0.479690i	$-0.840749\pi$
$397$	−0.464152	+	0.803935i	−0.0232951	+	0.0403483i	0.854143	+	0.520038i	$0.174082\pi$
$398$	−9.77297	−	28.2465i	−0.489875	−	1.41587i
$399$	−2.66637	+	6.35329i	−0.133485	+	0.318062i
$400$	19.5801	+	18.6850i	0.979004	+	0.934248i
$401$	5.92017			0.295639			0.147820	−	0.989014i	$-0.452774\pi$
$401$	5.92017			0.295639			0.147820	+	0.989014i	$0.452774\pi$
$402$	−19.1205	+	21.4950i	−0.953645	+	1.07207i
$403$	46.4588			2.31428
$404$	−27.6759	−	11.0864i	−1.37693	−	0.551568i
$405$	−30.8306	−	1.59250i	−1.53199	−	0.0791322i
$406$	5.78026	−	8.92033i	0.286869	−	0.442709i
$407$	2.37384	+	1.37054i	0.117667	+	0.0679350i
$408$	−7.61927	−	0.463905i	−0.377210	−	0.0229667i
$409$	3.60648	+	2.08220i	0.178329	+	0.102958i	0.586507	−	0.809944i	$-0.300503\pi$
$409$	3.60648	+	2.08220i	0.178329	+	0.102958i	−0.408178	+	0.912902i	$0.633836\pi$
$410$	32.7731	−	11.3391i	1.61855	−	0.559999i
$411$	0.461498	+	0.00595451i	0.0227640	+	0.000293714i
$412$	−3.85719	−	1.54511i	−0.190030	−	0.0761220i
$413$	7.36327	−	18.1994i	0.362323	−	0.895533i
$414$	5.19341	−	23.6339i	0.255242	−	1.16154i
$415$	−30.3943	−	17.5481i	−1.49200	−	0.861405i
$416$	−14.9507	+	32.6928i	−0.733016	+	1.60290i
$417$	−11.3634	+	6.36660i	−0.556466	+	0.311774i
$418$	−0.762052	−	0.660460i	−0.0372732	−	0.0323041i
$419$	−17.3206	+	10.0001i	−0.846167	+	0.488535i	−0.859356	−	0.511378i	$-0.829135\pi$
$419$	−17.3206	+	10.0001i	−0.846167	+	0.488535i	0.0131886	+	0.999913i	$0.495802\pi$
$420$	7.92299	−	30.4235i	0.386602	−	1.48451i
$421$	8.32808	+	4.80822i	0.405886	+	0.234338i	0.689021	−	0.724742i	$-0.258041\pi$
$421$	8.32808	+	4.80822i	0.405886	+	0.234338i	−0.283135	+	0.959080i	$0.591374\pi$
$422$	9.96401	+	28.7987i	0.485041	+	1.40190i
$423$	3.26074	+	6.00015i	0.158543	+	0.291737i
$424$	−2.18119	−	0.104578i	−0.105928	−	0.00507876i
$425$	−9.13037	+	5.27142i	−0.442888	+	0.255701i
$426$	3.69419	−	17.9106i	0.178984	−	0.867773i
$427$	24.0393	−	18.7628i	1.16334	−	0.907996i
$428$	7.61301	−	5.98440i	0.367989	−	0.289267i
$429$	2.55156	+	4.55413i	0.123190	+	0.219875i
$430$	−23.6435	+	27.2804i	−1.14019	+	1.31558i
$431$	0.0488960	−	0.0282301i	0.00235524	−	0.00135980i	−0.498822	−	0.866705i	$-0.666234\pi$
$431$	0.0488960	−	0.0282301i	0.00235524	−	0.00135980i	0.501177	+	0.865345i	$0.332900\pi$
$432$	−14.4701	−	14.9203i	−0.696193	−	0.717855i
$433$			2.83084i			0.136041i	0.997684	+	0.0680207i	$0.0216684\pi$
$433$			2.83084i			0.136041i	−0.997684	+	0.0680207i	$0.978332\pi$
$434$	−22.9557	−	14.8750i	−1.10191	−	0.714024i
$435$	−14.5068	−	8.62692i	−0.695545	−	0.413629i
$436$	29.7517	−	4.27139i	1.42485	−	0.204563i
$437$	−4.28773	+	7.42656i	−0.205110	+	0.355261i
$438$	15.6461	−	5.18832i	0.747598	−	0.247907i
$439$	−2.07387	−	3.59205i	−0.0989805	−	0.171439i	0.812282	−	0.583264i	$-0.198225\pi$
$439$	−2.07387	−	3.59205i	−0.0989805	−	0.171439i	−0.911263	+	0.411825i	$0.864891\pi$
$440$	3.87006	+	2.48882i	0.184498	+	0.118650i
$441$	−20.3342	+	5.24595i	−0.968296	+	0.249807i
$442$	−10.5823	−	9.17151i	−0.503348	−	0.436244i
$443$	−15.1638	−	26.2645i	−0.720455	−	1.24786i	−0.960818	−	0.277181i	$-0.910600\pi$
$443$	−15.1638	−	26.2645i	−0.720455	−	1.24786i	0.240363	−	0.970683i	$-0.422734\pi$
$444$	−12.1692	−	15.8989i	−0.577523	−	0.754528i
$445$	48.3854	+	27.9353i	2.29369	+	1.32426i
$446$	−17.0110	+	19.6277i	−0.805495	+	0.929398i
$447$	−0.158371	+	12.2744i	−0.00749069	+	0.580558i
$448$	17.8547	−	11.3670i	0.843557	−	0.537039i
$449$	−19.3070			−0.911152			−0.455576	−	0.890197i	$-0.650567\pi$
$449$	−19.3070			−0.911152			−0.455576	+	0.890197i	$0.650567\pi$
$450$	−28.0377	−	6.16112i	−1.32171	−	0.290438i
$451$	2.93616	−	1.69520i	0.138259	−	0.0798236i
$452$	−1.92397	−	13.4011i	−0.0904962	−	0.630336i
$453$	0.438547	−	33.9891i	0.0206047	−	1.59695i
$454$	6.83726	−	35.4554i	0.320889	−	1.66401i
$455$	45.4650	−	35.4858i	2.13143	−	1.66360i
$456$	3.28845	+	6.59105i	0.153996	+	0.308654i
$457$	−5.68534	−	9.84729i	−0.265949	−	0.460637i	0.701863	−	0.712312i	$-0.252352\pi$
$457$	−5.68534	−	9.84729i	−0.265949	−	0.460637i	−0.967812	+	0.251675i	$0.919019\pi$
$458$	22.8284	+	4.40225i	1.06670	+	0.205704i
$459$	7.16311	−	3.77386i	0.334345	−	0.176149i
$460$	14.5499	−	36.3222i	0.678393	−	1.69353i
$461$	−12.7030	+	22.0023i	−0.591638	+	1.02475i	0.402374	+	0.915475i	$0.368185\pi$
$461$	−12.7030	+	22.0023i	−0.591638	+	1.02475i	−0.994012	+	0.109272i	$0.965148\pi$
$462$	0.197375	−	3.06719i	0.00918274	−	0.142698i
$463$	23.1697	−	13.3771i	1.07679	−	0.621684i	0.146761	−	0.989172i	$-0.453115\pi$
$463$	23.1697	−	13.3771i	1.07679	−	0.621684i	0.930028	+	0.367488i	$0.119782\pi$
$464$	−3.19692	−	10.9043i	−0.148413	−	0.506220i
$465$	−22.2006	+	37.3319i	−1.02953	+	1.73123i
$466$	−7.65682	+	8.83460i	−0.354695	+	0.409255i
$467$	2.12077	+	1.22443i	0.0981375	+	0.0566597i	0.548266	−	0.836304i	$-0.315288\pi$
$467$	2.12077	+	1.22443i	0.0981375	+	0.0566597i	−0.450128	+	0.892964i	$0.648622\pi$
$468$	−4.44307	−	37.8701i	−0.205381	−	1.75055i
$469$	28.8052	+	11.6543i	1.33010	+	0.538145i
$470$	3.61055	+	10.4355i	0.166542	+	0.481353i
$471$	−1.06599	+	1.79254i	−0.0491184	+	0.0825960i
$472$	−9.61151	−	18.6579i	−0.442405	−	0.858798i
$473$	−1.76466	+	3.05648i	−0.0811391	+	0.140537i
$474$	−2.70477	+	0.896917i	−0.124234	+	0.0411968i
$475$	8.81037	+	5.08667i	0.404248	+	0.233392i
$476$	2.29230	+	7.91993i	0.105068	+	0.363009i
$477$	2.03506	−	1.10594i	0.0931790	−	0.0506375i
$478$	−2.98872	+	1.03406i	−0.136701	+	0.0472969i
$479$	−25.4847			−1.16442			−0.582212	−	0.813037i	$-0.697813\pi$
$479$	−25.4847			−1.16442			−0.582212	+	0.813037i	$0.697813\pi$
$480$	−19.1260	−	27.6361i	−0.872979	−	1.26141i
$481$		−	36.7301i		−	1.67475i
$482$	−1.72525	+	8.94649i	−0.0785830	+	0.407501i
$483$	−25.9286	+	3.29074i	−1.17979	+	0.149734i
$484$	−20.0048	−	8.01351i	−0.909310	−	0.364250i
$485$	7.88865	+	4.55452i	0.358205	+	0.206810i
$486$	21.3325	+	5.56111i	0.967660	+	0.252257i
$487$	−13.8547	+	7.99900i	−0.627816	+	0.362469i	−0.779906	−	0.625897i	$-0.784733\pi$
$487$	−13.8547	+	7.99900i	−0.627816	+	0.362469i	0.152090	+	0.988367i	$0.451400\pi$
$488$	1.56124	−	32.5629i	0.0706741	−	1.47405i
$489$	−9.03544	+	15.1937i	−0.408597	+	0.687084i
$490$	−33.8264	+	2.97701i	−1.52812	+	0.134488i
$491$	−12.7631	−	22.1064i	−0.575992	−	0.997647i	−0.995933	−	0.0900958i	$-0.971283\pi$
$491$	−12.7631	−	22.1064i	−0.575992	−	0.997647i	0.419941	−	0.907551i	$-0.362051\pi$
$492$	−24.5564	+	3.20274i	−1.10709	+	0.144391i
$493$	4.42645			0.199357
$494$	−2.55869	+	13.2684i	−0.115121	+	0.596972i
$495$	−4.87875	−	0.125918i	−0.219283	−	0.00565958i
$496$	−28.0613	+	8.22700i	−1.25999	+	0.369403i
$497$	−19.5620	+	2.73961i	−0.877476	+	0.122888i
$498$	18.7257	+	16.6571i	0.839118	+	0.746425i
$499$	16.7856			0.751425			0.375713	−	0.926736i	$-0.377398\pi$
$499$	16.7856			0.751425			0.375713	+	0.926736i	$0.377398\pi$
$500$	−11.2481	−	4.50573i	−0.503028	−	0.201502i
$501$	−11.1250	−	19.8564i	−0.497029	−	0.887117i
$502$	0.185692	−	0.962926i	0.00828782	−	0.0429775i
$503$	−5.59428			−0.249437			−0.124718	−	0.992192i	$-0.539803\pi$
$503$	−5.59428			−0.249437			−0.124718	+	0.992192i	$0.539803\pi$
$504$	−9.92976	+	20.1345i	−0.442307	+	0.896864i
$505$	51.1336			2.27541
$506$	0.724333	−	3.75612i	0.0322005	−	0.166980i
$507$	24.2447	−	40.7692i	1.07675	−	1.81062i
$508$	0.548185	−	1.36848i	0.0243218	−	0.0607166i
$509$	36.7745			1.63000			0.815002	−	0.579459i	$-0.196736\pi$
$509$	36.7745			1.63000			0.815002	+	0.579459i	$0.196736\pi$
$510$	12.4266	−	4.12072i	0.550258	−	0.182468i
$511$	−10.9548	−	14.0355i	−0.484613	−	0.620895i
$512$	3.24097	−	22.3941i	0.143232	−	0.989689i
$513$	−6.60974	−	4.16522i	−0.291827	−	0.183899i
$514$	6.71593	−	34.8263i	0.296227	−	1.53612i
$515$	7.12648			0.314030
$516$	20.4709	−	15.6686i	0.901182	−	0.689773i
$517$	0.539777	+	0.934921i	0.0237394	+	0.0411178i
$518$	−11.7601	+	18.1487i	−0.516709	+	0.797407i
$519$	−18.1105	−	32.3244i	−0.794964	−	1.41888i
$520$	2.95275	−	61.5855i	0.129487	−	2.70070i
$521$	5.19390	−	2.99870i	0.227549	−	0.131375i	−0.381892	−	0.924207i	$-0.624727\pi$
$521$	5.19390	−	2.99870i	0.227549	−	0.131375i	0.609441	+	0.792832i	$0.291394\pi$
$522$	8.90123	+	8.12607i	0.389596	+	0.355668i
$523$	−22.6114	−	13.0547i	−0.988727	−	0.570842i	−0.0838338	−	0.996480i	$-0.526716\pi$
$523$	−22.6114	−	13.0547i	−0.988727	−	0.570842i	−0.904894	+	0.425638i	$0.860050\pi$
$524$	−8.34907	+	20.8425i	−0.364731	+	0.910510i
$525$	3.90391	+	30.7600i	0.170381	+	1.34248i
$526$	−0.560469	+	2.90638i	−0.0244376	+	0.126724i
$527$		−	11.3911i		−	0.496204i
$528$	−2.34761	−	2.29888i	−0.102166	−	0.100046i
$529$	−9.52962			−0.414331
$530$	3.53938	−	1.22458i	0.153741	−	0.0531925i
$531$	18.9851	+	11.6243i	0.823885	+	0.504451i
$532$	5.51250	−	5.73680i	0.238997	−	0.248722i
$533$	−39.3442	−	22.7154i	−1.70419	−	0.983914i
$534$	−29.8099	−	26.5169i	−1.29000	−	1.14750i
$535$	−8.30410	+	14.3831i	−0.359018	+	0.621837i
$536$	29.5309	−	15.2127i	1.27554	−	0.657089i
$537$	4.59452	+	8.20049i	0.198268	+	0.353877i
$538$	−4.05428	−	11.7180i	−0.174793	−	0.505198i
$539$	−3.19207	+	0.911970i	−0.137492	+	0.0392813i
$540$	32.5536	+	14.5263i	1.40089	+	0.625111i
$541$	−14.9651	−	8.64011i	−0.643400	−	0.371467i	0.142523	−	0.989791i	$-0.454479\pi$
$541$	−14.9651	−	8.64011i	−0.643400	−	0.371467i	−0.785923	+	0.618324i	$0.787812\pi$
$542$	12.7664	−	14.7302i	0.548365	−	0.632715i
$543$	4.74910	+	0.0612756i	0.203803	+	0.00262959i
$544$	8.01586	+	3.66571i	0.343677	+	0.157166i
$545$	−44.6438	+	25.7751i	−1.91233	+	1.10408i
$546$	−36.9160	+	18.2595i	−1.57986	+	0.781434i
$547$	−19.8968	+	34.4623i	−0.850726	+	1.47350i	0.0298274	+	0.999555i	$0.490504\pi$
$547$	−19.8968	+	34.4623i	−0.850726	+	1.47350i	−0.880554	+	0.473946i	$0.842829\pi$
$548$	−0.494720	−	0.198174i	−0.0211334	−	0.00846558i
$549$	16.5105	+	30.3814i	0.704652	+	1.29664i
$550$	−4.45600	−	0.859300i	−0.190005	−	0.0366407i
$551$	−2.13566	−	3.69907i	−0.0909820	−	0.157586i
$552$	−15.4154	+	23.3040i	−0.656121	+	0.991885i
$553$	1.89379	+	2.42636i	0.0805320	+	0.103179i
$554$	−1.86836	+	9.68860i	−0.0793790	+	0.411629i
$555$	29.5144	+	17.5517i	1.25282	+	0.745029i
$556$	14.8877	−	2.13740i	0.631380	−	0.0906460i
$557$	−23.2480	+	13.4223i	−0.985051	+	0.568719i	−0.903791	−	0.427973i	$-0.859228\pi$
$557$	−23.2480	+	13.4223i	−0.985051	+	0.568719i	−0.0812598	+	0.996693i	$0.525894\pi$
$558$	20.9118	−	22.9066i	0.885265	−	0.969712i
$559$	47.2924			2.00026
$560$	−21.1772	+	29.4846i	−0.894901	+	1.24595i
$561$	1.11661	−	0.625609i	0.0471435	−	0.0264133i
$562$	−15.0974	+	17.4197i	−0.636847	+	0.734808i
$563$	3.18023	+	1.83611i	0.134031	+	0.0773827i	0.565516	−	0.824737i	$-0.308677\pi$
$563$	3.18023	+	1.83611i	0.134031	+	0.0773827i	−0.431485	+	0.902120i	$0.642010\pi$
$564$	−1.01980	−	7.81914i	−0.0429415	−	0.329245i
$565$	11.6099	+	20.1090i	0.488434	+	0.845993i
$566$	20.1785	+	17.4884i	0.848166	+	0.735093i
$567$	−2.08170	−	23.7206i	−0.0874232	−	0.996171i
$568$	−11.4221	+	17.7610i	−0.479259	+	0.745235i
$569$	−2.23920	−	3.87840i	−0.0938721	−	0.162591i	0.815265	−	0.579088i	$-0.196591\pi$
$569$	−2.23920	−	3.87840i	−0.0938721	−	0.162591i	−0.909137	+	0.416497i	$0.863258\pi$
$570$	−9.43911	−	8.39642i	−0.395361	−	0.351687i
$571$	−2.80826	+	4.86404i	−0.117522	+	0.203554i	−0.918785	−	0.394758i	$-0.870828\pi$
$571$	−2.80826	+	4.86404i	−0.117522	+	0.203554i	0.801263	+	0.598312i	$0.204162\pi$
$572$	−0.856613	−	5.96660i	−0.0358168	−	0.249476i
$573$	4.90327	−	2.74718i	0.204837	−	0.114765i
$574$	12.1674	+	23.8210i	0.507858	+	0.994270i
$575$			38.5910i			1.60935i
$576$	9.38973	+	22.0869i	0.391239	+	0.920289i
$577$	−25.2928	+	14.6028i	−1.05295	+	0.607923i	−0.923475	−	0.383659i	$-0.874664\pi$
$577$	−25.2928	+	14.6028i	−1.05295	+	0.607923i	−0.129479	+	0.991582i	$0.541330\pi$
$578$	13.4971	−	15.5732i	0.561403	−	0.647759i
$579$	10.5154	−	17.6823i	0.437004	−	0.734853i
$580$	12.0442	+	15.3220i	0.500109	+	0.636210i
$581$	10.1528	−	25.0942i	0.421210	−	1.04108i
$582$	−4.86014	−	4.32326i	−0.201459	−	0.179205i
$583$	0.317095	−	0.183075i	0.0131327	−	0.00758220i
$584$	−19.0121	−	0.911544i	−0.786726	−	0.0377200i
$585$	31.2261	+	57.4597i	1.29104	+	2.37567i
$586$	8.38445	+	24.2334i	0.346359	+	1.00107i
$587$	20.9295	+	12.0837i	0.863855	+	0.498747i	0.865301	−	0.501252i	$-0.167127\pi$
$587$	20.9295	+	12.0837i	0.863855	+	0.498747i	−0.00144654	+	0.999999i	$0.500460\pi$
$588$	24.0868	+	2.79745i	0.993323	+	0.115365i
$589$	−9.51924	+	5.49594i	−0.392233	+	0.226456i
$590$	27.2019	+	23.5755i	1.11988	+	0.970587i
$591$	0.556275	−	43.1134i	0.0228821	−	1.77345i
$592$	6.50422	+	22.1851i	0.267322	+	0.911803i
$593$	−32.6384	−	18.8438i	−1.34030	−	0.773822i	−0.353448	−	0.935454i	$-0.614991\pi$
$593$	−32.6384	−	18.8438i	−1.34030	−	0.773822i	−0.986851	+	0.161632i	$0.948324\pi$
$594$	3.39391	+	0.791827i	0.139254	+	0.0324891i
$595$	−8.70065	−	11.1474i	−0.356692	−	0.457001i
$596$	5.27080	−	13.1580i	0.215901	−	0.538972i
$597$	−17.8929	−	31.9360i	−0.732309	−	1.30706i
$598$	−48.4413	+	16.7601i	−1.98091	+	0.685372i
$599$	−19.2247	−	11.0994i	−0.785499	−	0.453508i	0.0528767	−	0.998601i	$-0.483161\pi$
$599$	−19.2247	−	11.0994i	−0.785499	−	0.453508i	−0.838376	+	0.545093i	$0.816494\pi$
$600$	27.6463	+	18.2877i	1.12866	+	0.746594i
$601$	30.9546	+	17.8716i	1.26266	+	0.728999i	0.973589	−	0.228307i	$-0.0733190\pi$
$601$	30.9546	+	17.8716i	1.26266	+	0.728999i	0.289075	+	0.957306i	$0.406652\pi$
$602$	−23.3676	−	15.1419i	−0.952394	−	0.617139i
$603$	−18.3985	+	30.0489i	−0.749243	+	1.22369i
$604$	−14.5954	+	36.4359i	−0.593879	+	1.48255i
$605$	36.9606			1.50266
$606$	−35.7616	−	7.37607i	−1.45271	−	0.299632i
$607$	−1.07359			−0.0435755			−0.0217877	−	0.999763i	$-0.506936\pi$
$607$	−1.07359			−0.0435755			−0.0217877	+	0.999763i	$0.506936\pi$
$608$	−0.804126	−	8.46726i	−0.0326116	−	0.343393i
$609$	5.03786	−	12.0040i	0.204144	−	0.486426i
$610$	18.2818	+	52.8393i	0.740207	+	2.13940i
$611$	7.23294	−	12.5278i	0.292613	−	0.506821i
$612$	−9.28526	+	1.08938i	−0.375334	+	0.0440357i
$613$	4.73198	−	2.73201i	0.191123	−	0.110345i	−0.401385	−	0.915909i	$-0.631471\pi$
$613$	4.73198	−	2.73201i	0.191123	−	0.110345i	0.592508	+	0.805565i	$0.298138\pi$
$614$	−1.32280	+	6.85954i	−0.0533839	+	0.276829i
$615$	37.0539	−	20.7603i	1.49416	−	0.837137i
$616$	−1.48710	+	3.22242i	−0.0599171	+	0.129835i
$617$	19.0173	+	32.9389i	0.765606	+	1.32607i	0.939926	+	0.341379i	$0.110894\pi$
$617$	19.0173	+	32.9389i	0.765606	+	1.32607i	−0.174320	+	0.984689i	$0.555773\pi$
$618$	−4.98409	−	1.02800i	−0.200489	−	0.0413523i
$619$		−	9.34753i		−	0.375709i	−0.982197	−	0.187855i	$-0.939847\pi$
$619$		−	9.34753i		−	0.375709i	0.982197	−	0.187855i	$-0.0601533\pi$
$620$	39.4298	−	30.9948i	1.58354	−	1.24478i
$621$	1.14680	−	29.6139i	0.0460194	−	1.18837i
$622$	5.40603	−	6.23760i	0.216762	−	0.250105i
$623$	−16.1625	+	39.9480i	−0.647538	+	1.60048i
$624$	−10.9489	+	42.6455i	−0.438305	+	1.70719i
$625$	−13.0494			−0.521975
$626$	30.4689	−	10.5419i	1.21778	−	0.421337i
$627$	−1.06155	−	0.631283i	−0.0423940	−	0.0252110i
$628$	1.89327	−	1.48826i	0.0755499	−	0.0593879i
$629$	−9.00574			−0.359082
$630$	2.96816	−	38.3892i	0.118254	−	1.52946i
$631$			3.40904i			0.135712i	0.997695	+	0.0678559i	$0.0216158\pi$
$631$			3.40904i			0.135712i	−0.997695	+	0.0678559i	$0.978384\pi$
$632$	3.28667	+	0.157581i	0.130737	+	0.00626823i
$633$	18.2427	+	32.5603i	0.725083	+	1.29416i
$634$	−6.49762	+	2.24810i	−0.258053	+	0.0892834i
$635$			2.52839i			0.100336i
$636$	−2.65200	+	0.345885i	−0.105159	+	0.0137152i
$637$	31.9698	+	30.9327i	1.26669	+	1.22560i
$638$	1.43983	+	1.24788i	0.0570034	+	0.0494040i
$639$	0.577880	−	22.3902i	0.0228606	−	0.885744i
$640$	9.12219	+	37.7208i	0.360586	+	1.49105i
$641$	30.7529			1.21467			0.607333	−	0.794447i	$-0.292239\pi$
$641$	30.7529			1.21467			0.607333	+	0.794447i	$0.292239\pi$
$642$	7.88246	−	8.86133i	0.311096	−	0.349729i
$643$	29.5363	−	17.0528i	1.16480	−	0.672495i	0.212348	−	0.977194i	$-0.431889\pi$
$643$	29.5363	−	17.0528i	1.16480	−	0.672495i	0.952449	+	0.304699i	$0.0985558\pi$
$644$	29.3015	+	7.22845i	1.15464	+	0.284841i
$645$	−22.5990	+	38.0018i	−0.889835	+	1.49632i
$646$	3.25323	+	0.627357i	0.127997	+	0.0246830i
$647$	11.9440	+	20.6875i	0.469565	+	0.813311i	0.999395	−	0.0347933i	$-0.0110773\pi$
$647$	11.9440	+	20.6875i	0.469565	+	0.813311i	−0.529829	+	0.848104i	$0.677744\pi$
$648$	−20.6718	−	14.8552i	−0.812065	−	0.583568i
$649$	3.04769	+	1.75958i	0.119632	+	0.0690696i
$650$	19.8831	+	57.4675i	0.779879	+	2.25406i
$651$	−30.8912	−	12.9645i	−1.21072	−	0.508120i
$652$	16.0475	−	12.6146i	0.628470	−	0.494025i
$653$			25.2300i			0.987325i	0.869654	+	0.493663i	$0.164342\pi$
$653$			25.2300i			0.987325i	−0.869654	+	0.493663i	$0.835658\pi$
$654$	34.9409	−	11.5866i	1.36630	−	0.453071i
$655$		−	38.5083i		−	1.50464i
$656$	27.7866	+	6.75307i	1.08488	+	0.263663i
$657$	17.7384	−	9.63981i	0.692041	−	0.376085i
$658$	−7.58498	+	3.87430i	−0.295693	+	0.151036i
$659$	−20.3164	+	35.1890i	−0.791414	+	1.37077i	0.133677	+	0.991025i	$0.457322\pi$
$659$	−20.3164	+	35.1890i	−0.791414	+	1.37077i	−0.925091	+	0.379745i	$0.876012\pi$
$660$	5.20379	+	2.16285i	0.202557	+	0.0841888i
$661$	−7.24959	+	12.5567i	−0.281976	+	0.488398i	−0.971871	−	0.235512i	$-0.924323\pi$
$661$	−7.24959	+	12.5567i	−0.281976	+	0.488398i	0.689895	+	0.723909i	$0.257657\pi$
$662$	−4.69475	−	13.5691i	−0.182466	−	0.527378i
$663$	−14.7412	−	8.76634i	−0.572501	−	0.340457i
$664$	−13.2528	−	25.7264i	−0.514308	−	0.998376i
$665$	−5.11777	+	12.6493i	−0.198458	+	0.490518i
$666$	−18.1098	−	16.5327i	−0.701741	−	0.640630i
$667$	8.10128	−	14.0318i	0.313683	−	0.543314i
$668$	3.73490	+	26.0148i	0.144508	+	1.00654i
$669$	−16.2595	+	27.3415i	−0.628630	+	1.05708i
$670$	−37.3143	+	43.0541i	−1.44158	+	1.66332i
$671$	2.73312	+	4.73391i	0.105511	+	0.182750i
$672$	19.0640	−	17.5660i	0.735410	−	0.677622i
$673$	10.1333	−	17.5513i	0.390608	−	0.676554i	−0.601922	−	0.798555i	$-0.705598\pi$
$673$	10.1333	−	17.5513i	0.390608	−	0.676554i	0.992530	+	0.122002i	$0.0389313\pi$
$674$	−9.50469	−	27.4711i	−0.366107	−	1.05815i
$675$	−35.1320	−	1.36048i	−1.35223	−	0.0523650i
$676$	−43.0602	+	33.8486i	−1.65616	+	1.30187i
$677$	−10.7474	−	18.6151i	−0.413057	−	0.715435i	0.582166	−	0.813070i	$-0.302206\pi$
$677$	−10.7474	−	18.6151i	−0.413057	−	0.715435i	−0.995222	+	0.0976352i	$0.968872\pi$
$678$	−5.21897	−	15.7385i	−0.200433	−	0.604433i
$679$	−2.63511	+	6.51304i	−0.101126	+	0.249947i
$680$	−15.1000	−	0.723976i	−0.579058	−	0.0277632i
$681$	0.570555	−	44.2202i	0.0218637	−	1.69452i
$682$	3.21131	−	3.70528i	0.122968	−	0.141883i
$683$	7.49070	+	12.9743i	0.286624	+	0.496447i	0.973002	−	0.230798i	$-0.0741337\pi$
$683$	7.49070	+	12.9743i	0.286624	+	0.496447i	−0.686378	+	0.727245i	$0.740800\pi$
$684$	5.39029	+	7.23385i	0.206103	+	0.276593i
$685$	0.914036			0.0349235
$686$	−5.89264	−	25.5201i	−0.224982	−	0.974363i
$687$	28.4717	+	0.367359i	1.08626	+	0.0140156i
$688$	−28.5649	+	8.37462i	−1.08903	+	0.319279i
$689$	−4.24904	−	2.45318i	−0.161875	−	0.0934588i
$690$	9.68044	−	46.9339i	0.368528	−	1.78674i
$691$	22.7409	−	13.1294i	0.865103	−	0.499468i	−0.000614602	−	1.00000i	$-0.500196\pi$
$691$	22.7409	−	13.1294i	0.865103	−	0.499468i	0.865718	+	0.500532i	$0.166862\pi$
$692$	6.08009	+	42.3499i	0.231130	+	1.60990i
$693$	−0.425727	−	3.74014i	−0.0161720	−	0.142076i
$694$	0.143074	−	0.165082i	0.00543103	−	0.00626644i
$695$	−22.3397	+	12.8978i	−0.847394	+	0.489243i
$696$	−6.21323	−	12.4532i	−0.235512	−	0.472037i
$697$	−5.56952	+	9.64670i	−0.210961	+	0.365395i
$698$	−14.8780	+	17.1666i	−0.563141	+	0.649764i
$699$	−7.31856	+	12.3067i	−0.276814	+	0.465481i
$700$	8.57534	−	34.7614i	0.324117	−	1.31386i
$701$			29.8710i			1.12821i	0.825702	+	0.564107i	$0.190779\pi$
$701$			29.8710i			1.12821i	−0.825702	+	0.564107i	$0.809221\pi$
$702$	−13.5501	−	44.6903i	−0.511417	−	1.68673i
$703$	4.34506	+	7.52586i	0.163877	+	0.283843i
$704$	1.57397	+	3.45216i	0.0593213	+	0.130108i
$705$	6.61041	+	11.7985i	0.248962	+	0.444358i
$706$	0.722779	−	3.74806i	0.0272021	−	0.141060i
$707$	5.47008	+	39.0588i	0.205724	+	1.46896i
$708$	−15.6236	−	20.4120i	−0.587169	−	0.767130i
$709$	1.43291	−	0.827290i	0.0538140	−	0.0310695i	−0.472852	−	0.881142i	$-0.656775\pi$
$709$	1.43291	−	0.827290i	0.0538140	−	0.0310695i	0.526666	+	0.850073i	$0.323442\pi$
$710$	6.85782	−	35.5621i	0.257369	−	1.33462i
$711$	−3.06648	+	1.66646i	−0.115002	+	0.0624971i
$712$	21.0974	+	40.9544i	0.790660	+	1.53483i
$713$	−36.1097	−	20.8480i	−1.35232	−	0.780762i
$714$	4.47699	+	9.05132i	0.167547	+	0.338737i
$715$	5.16911	+	8.95315i	0.193314	+	0.334829i
$716$	−1.54248	−	10.7439i	−0.0576452	−	0.401518i
$717$	−3.37910	+	1.89322i	−0.126195	+	0.0707036i
$718$	−19.3339	−	16.7564i	−0.721535	−	0.625343i
$719$	−0.288134	+	0.499063i	−0.0107456	+	0.0186119i	−0.871348	−	0.490665i	$-0.836754\pi$
$719$	−0.288134	+	0.499063i	−0.0107456	+	0.0186119i	0.860603	+	0.509277i	$0.170087\pi$
$720$	−29.0358	−	29.1764i	−1.08210	−	1.08734i
$721$	0.762365	+	5.44362i	0.0283919	+	0.202731i
$722$	7.74038	+	22.3718i	0.288067	+	0.832592i
$723$	−0.143968	+	11.1581i	−0.00535425	+	0.414975i
$724$	−5.09098	−	2.03934i	−0.189205	−	0.0757913i
$725$	−16.6464	−	9.61081i	−0.618232	−	0.356936i
$726$	−25.8493	−	5.33160i	−0.959359	−	0.197874i
$727$	−15.5406	+	26.9170i	−0.576367	+	0.998298i	0.419524	+	0.907744i	$0.362197\pi$
$727$	−15.5406	+	26.9170i	−0.576367	+	0.998298i	−0.995892	+	0.0905536i	$0.971136\pi$
$728$	47.3585	−	4.33271i	1.75522	−	0.160581i
$729$	26.9191	+	2.08802i	0.997005	+	0.0773339i
$730$	30.8507	−	10.6740i	1.14183	−	0.395061i
$731$		−	11.5955i		−	0.428875i
$732$	−5.16370	−	39.5917i	−0.190856	−	1.46335i
$733$	−28.7598			−1.06227			−0.531134	−	0.847288i	$-0.678234\pi$
$733$	−28.7598			−1.06227			−0.531134	+	0.847288i	$0.678234\pi$
$734$	41.5482	+	8.01219i	1.53357	+	0.295735i
$735$	−40.1329	+	10.9079i	−1.48033	+	0.402343i
$736$	26.2909	−	18.7013i	0.969095	−	0.689338i
$737$	−2.78500	+	4.82376i	−0.102587	+	0.177685i
$738$	−28.9093	+	9.17420i	−1.06416	+	0.337707i
$739$	5.45227	+	9.44362i	0.200565	+	0.347389i	0.948711	−	0.316146i	$-0.102389\pi$
$739$	5.45227	+	9.44362i	0.200565	+	0.347389i	−0.748146	+	0.663535i	$0.769056\pi$
$740$	−24.5043	−	31.1730i	−0.900797	−	1.14594i
$741$	−0.213517	+	16.5484i	−0.00784374	+	0.607921i
$742$	1.31404	+	2.57258i	0.0482399	+	0.0944425i
$743$	0.928514	−	0.536078i	0.0340639	−	0.0196668i	−0.482871	−	0.875691i	$-0.660406\pi$
$743$	0.928514	−	0.536078i	0.0340639	−	0.0196668i	0.516935	+	0.856025i	$0.327073\pi$
$744$	−32.0473	+	15.9892i	−1.17491	+	0.586193i
$745$			24.3105i			0.890666i
$746$	−3.88768	+	20.1600i	−0.142338	+	0.738111i
$747$	26.1776	+	16.0281i	0.957789	+	0.586438i
$748$	−1.46293	+	0.210030i	−0.0534901	+	0.00767947i
$749$	−11.8750	−	4.80450i	−0.433903	−	0.175553i
$750$	−14.5342	−	2.99778i	−0.530715	−	0.109464i
$751$			6.92894i			0.252841i	0.991977	+	0.126420i	$0.0403488\pi$
$751$			6.92894i			0.252841i	−0.991977	+	0.126420i	$0.959651\pi$
$752$	−2.15028	+	8.84769i	−0.0784128	+	0.322642i
$753$	0.0154956	−	1.20097i	0.000564690	−	0.0437657i
$754$	4.83441	−	25.0694i	0.176059	−	0.912974i
$755$		−	67.3183i		−	2.44996i
$756$	−7.61354	+	26.4203i	−0.276902	+	0.960898i
$757$			11.3209i			0.411464i	0.978608	+	0.205732i	$0.0659576\pi$
$757$			11.3209i			0.411464i	−0.978608	+	0.205732i	$0.934042\pi$
$758$	40.8448	+	7.87656i	1.48355	+	0.286090i
$759$	0.0604441	−	4.68465i	0.00219398	−	0.170042i
$760$	6.68038	+	12.9680i	0.242323	+	0.470397i
$761$		−	3.75950i		−	0.136282i	−0.997676	−	0.0681409i	$-0.978293\pi$
$761$		−	3.75950i		−	0.136282i	0.997676	−	0.0681409i	$-0.0217068\pi$
$762$	0.364722	−	1.76829i	0.0132125	−	0.0640585i
$763$	−24.4644	−	31.3442i	−0.885669	−	1.13474i
$764$	−6.42403	+	0.922286i	−0.232413	+	0.0333671i
$765$	14.0884	−	7.65623i	0.509366	−	0.276812i
$766$	40.3645	+	7.78392i	1.45843	+	0.281245i
$767$		−	47.1564i		−	1.70272i
$768$	−0.938571	−	27.6969i	−0.0338678	−	0.999426i
$769$	37.0942	−	21.4163i	1.33765	−	0.772293i	0.351192	−	0.936304i	$-0.385777\pi$
$769$	37.0942	−	21.4163i	1.33765	−	0.772293i	0.986459	+	0.164011i	$0.0524432\pi$
$770$	0.312486	−	6.07886i	0.0112612	−	0.219067i
$771$	0.560430	−	43.4355i	0.0201834	−	1.56429i
$772$	−18.6760	+	14.6808i	−0.672164	+	0.528372i
$773$	−20.9662	−	36.3146i	−0.754103	−	1.30614i	−0.945819	−	0.324694i	$-0.894739\pi$
$773$	−20.9662	−	36.3146i	−0.754103	−	1.30614i	0.191716	−	0.981450i	$-0.438595\pi$
$774$	21.2870	−	23.3176i	0.765145	−	0.838134i
$775$	−24.7326	+	42.8381i	−0.888422	+	1.53879i
$776$	3.43968	+	6.67712i	0.123477	+	0.239695i
$777$	−10.2497	+	24.4224i	−0.367705	+	0.876150i
$778$	5.12673	−	26.5853i	0.183802	−	0.953129i
$779$	10.7487			0.385111
$780$	−9.76602	−	74.8790i	−0.349680	−	2.68110i
$781$		−	3.54075i		−	0.126698i
$782$	4.10937	+	11.8772i	0.146951	+	0.424727i
$783$	12.4885	+	7.86982i	0.446303	+	0.281244i
$784$	−24.7875	−	13.0222i	−0.885268	−	0.465080i
$785$	−2.06514	+	3.57693i	−0.0737081	+	0.127666i
$786$	−5.55486	+	26.9318i	−0.198135	+	0.960625i
$787$	46.2706	+	26.7143i	1.64937	+	0.952263i	0.977324	+	0.211751i	$0.0679167\pi$
$787$	46.2706	+	26.7143i	1.64937	+	0.952263i	0.672044	+	0.740511i	$0.265417\pi$
$788$	−18.5136	+	46.2171i	−0.659519	+	1.64642i
$789$	−0.0467700	+	3.62485i	−0.00166505	+	0.129048i
$790$	−5.33323	+	1.84524i	−0.189748	+	0.0656505i
$791$	−14.1185	+	11.0195i	−0.501994	+	0.391810i
$792$	−3.32741	−	2.26329i	−0.118234	−	0.0804227i
$793$	36.6235	−	63.4338i	1.30054	−	2.25260i
$794$	0.859817	−	0.992075i	0.0305138	−	0.0352074i
$795$	4.00169	−	2.24204i	0.141925	−	0.0795170i
$796$	6.00704	+	41.8410i	0.212914	+	1.48302i
$797$	15.2010	+	26.3288i	0.538445	+	0.932615i	0.998988	+	0.0449772i	$0.0143215\pi$
$797$	15.2010	+	26.3288i	0.538445	+	0.932615i	−0.460543	+	0.887638i	$0.652345\pi$
$798$	5.40391	−	8.10836i	0.191296	−	0.287033i
$799$	−3.07166	−	1.77342i	−0.108668	−	0.0627392i
$800$	−22.1859	−	31.1897i	−0.784391	−	1.10272i
$801$	−41.6727	−	25.5155i	−1.47243	−	0.901547i
$802$	−8.22092	−	1.58533i	−0.290291	−	0.0559800i
$803$	2.76393	−	1.59576i	0.0975370	−	0.0563130i
$804$	32.3073	−	24.7283i	1.13939	−	0.872101i
$805$	−51.2613	+	7.17900i	−1.80672	+	0.253027i
$806$	−64.5140	−	12.4410i	−2.27241	−	0.438214i
$807$	−7.42283	−	13.2486i	−0.261296	−	0.466371i
$808$	35.4628	+	22.8061i	1.24758	+	0.802314i
$809$	1.93967	+	3.35961i	0.0681952	+	0.118118i	0.898107	−	0.439777i	$-0.144943\pi$
$809$	1.93967	+	3.35961i	0.0681952	+	0.118118i	−0.829912	+	0.557895i	$0.811609\pi$
$810$	42.3859	+	10.4674i	1.48929	+	0.367786i
$811$			23.3384i			0.819521i	0.912193	+	0.409760i	$0.134388\pi$
$811$			23.3384i			0.819521i	−0.912193	+	0.409760i	$0.865612\pi$
$812$	−10.4154	+	10.8392i	−0.365508	+	0.380380i
$813$	12.2024	−	20.5193i	0.427958	−	0.719642i
$814$	−2.92938	−	2.53885i	−0.102675	−	0.0889865i
$815$	−17.5043	+	30.3183i	−0.613149	+	1.06201i
$816$	10.4561	+	2.68452i	0.366037	+	0.0939769i
$817$	−9.69005	+	5.59455i	−0.339012	+	0.195729i
$818$	−4.45048	−	3.85717i	−0.155607	−	0.134863i
$819$	−40.5506	+	29.9991i	−1.41695	+	1.04825i
$820$	−48.5462	+	6.96968i	−1.69531	+	0.243392i
$821$	8.87710	−	5.12520i	0.309813	−	0.178871i	−0.337030	−	0.941494i	$-0.609422\pi$
$821$	8.87710	−	5.12520i	0.309813	−	0.178871i	0.646843	+	0.762623i	$0.276089\pi$
$822$	−0.639255	−	0.131851i	−0.0222966	−	0.00459882i
$823$	14.5526	+	8.40197i	0.507273	+	0.292874i	0.731712	−	0.681614i	$-0.238722\pi$
$823$	14.5526	+	8.40197i	0.507273	+	0.292874i	−0.224439	+	0.974488i	$0.572055\pi$
$824$	4.94245	+	3.17848i	0.172178	+	0.110728i
$825$	−5.55755	−	0.0717068i	−0.193489	−	0.00249651i
$826$	−15.0984	+	23.3004i	−0.525339	+	0.810725i
$827$	−5.02789			−0.174837			−0.0874185	−	0.996172i	$-0.527862\pi$
$827$	−5.02789			−0.174837			−0.0874185	+	0.996172i	$0.527862\pi$
$828$	−13.5405	+	31.4280i	−0.470566	+	1.09220i
$829$	−13.7881	−	23.8816i	−0.478879	−	0.829442i	0.520828	−	0.853662i	$-0.325623\pi$
$829$	−13.7881	−	23.8816i	−0.478879	−	0.829442i	−0.999707	+	0.0242193i	$0.992290\pi$
$830$	37.5073	+	32.5070i	1.30190	+	1.12833i
$831$	−0.155911	+	12.0837i	−0.00540848	+	0.419178i
$832$	29.5156	−	41.3947i	1.02327	−	1.43510i
$833$	7.58430	−	7.83858i	0.262781	−	0.271591i
$834$	17.4844	−	5.79791i	0.605434	−	0.200765i
$835$	−22.5377	−	39.0365i	−0.779950	−	1.35091i
$836$	0.881347	+	1.12120i	0.0304820	+	0.0387775i
$837$	20.2523	−	32.1382i	0.700023	−	1.11086i
$838$	26.7298	−	9.24818i	0.923365	−	0.319473i
$839$	−3.00315	+	5.20161i	−0.103680	+	0.179579i	−0.913198	−	0.407516i	$-0.866395\pi$
$839$	−3.00315	+	5.20161i	−0.103680	+	0.179579i	0.809518	+	0.587095i	$0.199729\pi$
$840$	−19.1490	+	40.1253i	−0.660704	+	1.38445i
$841$	−10.4649	−	18.1257i	−0.360858	−	0.625024i
$842$	−10.2771	−	8.90697i	−0.354171	−	0.306954i
$843$	−14.4305	+	24.2659i	−0.497012	+	0.835760i
$844$	−6.12447	−	42.6590i	−0.210813	−	1.46838i
$845$	46.9691	−	81.3529i	1.61579	−	2.79863i
$846$	−2.92121	−	9.20516i	−0.100433	−	0.316480i
$847$	3.95391	+	28.2327i	0.135858	+	0.970086i
$848$	3.00085	+	0.729308i	0.103050	+	0.0250445i
$849$	28.1088	+	16.7158i	0.964692	+	0.573686i
$850$	14.0903	−	4.87507i	0.483293	−	0.167214i
$851$	−16.4823	+	28.5482i	−0.565005	+	0.978618i
$852$	−9.92605	+	23.8820i	−0.340061	+	0.818183i
$853$	13.6201	−	23.5908i	0.466345	−	0.807732i	−0.532917	−	0.846168i	$-0.678904\pi$
$853$	13.6201	−	23.5908i	0.466345	−	0.807732i	0.999261	+	0.0384354i	$0.0122374\pi$
$854$	−38.4060	+	19.6172i	−1.31423	+	0.671288i
$855$	−13.1954	−	8.07934i	−0.451274	−	0.276307i
$856$	−12.1742	+	6.27147i	−0.416105	+	0.214354i
$857$		−	22.0436i		−	0.752995i	−0.926418	−	0.376498i	$-0.877128\pi$
$857$		−	22.0436i		−	0.752995i	0.926418	−	0.376498i	$-0.122872\pi$
$858$	−2.32364	−	7.00726i	−0.0793279	−	0.239224i
$859$			22.9536i			0.783168i	0.920142	+	0.391584i	$0.128073\pi$
$859$			22.9536i			0.783168i	−0.920142	+	0.391584i	$0.871927\pi$
$860$	40.1373	−	31.5510i	1.36867	−	1.07588i
$861$	19.8218	+	26.0830i	0.675526	+	0.888908i
$862$	−0.0754580	+	0.0261076i	−0.00257011	+	0.000889227i
$863$	18.2603	+	10.5426i	0.621589	+	0.358874i	0.777487	−	0.628899i	$-0.216494\pi$
$863$	18.2603	+	10.5426i	0.621589	+	0.358874i	−0.155899	+	0.987773i	$0.549827\pi$
$864$	16.0982	+	24.5937i	0.547671	+	0.836694i
$865$	−36.6894	−	63.5479i	−1.24748	−	2.16069i
$866$	0.758055	−	3.93099i	0.0257598	−	0.133580i
$867$	12.9008	−	21.6936i	0.438134	−	0.736753i
$868$	27.8937	+	26.8031i	0.946774	+	0.909756i
$869$	−0.477808	+	0.275862i	−0.0162085	+	0.00935799i
$870$	17.8343	+	15.8643i	0.604641	+	0.537849i
$871$	74.6372			2.52899
$872$	−42.4579	−	2.03566i	−1.43781	−	0.0689363i
$873$	−6.79424	−	4.16000i	−0.229950	−	0.140795i
$874$	7.94278	−	9.16455i	0.268669	−	0.309996i
$875$	2.22315	+	15.8743i	0.0751563	+	0.536649i
$876$	−23.1159	+	3.01487i	−0.781015	+	0.101863i
$877$			35.8012i			1.20892i	0.796636	+	0.604460i	$0.206611\pi$
$877$			35.8012i			1.20892i	−0.796636	+	0.604460i	$0.793389\pi$
$878$	1.91794	+	5.54338i	0.0647274	+	0.187080i
$879$	15.3508	+	27.3987i	0.517768	+	0.924134i
$880$	−4.70760	−	4.49239i	−0.158693	−	0.151439i
$881$			3.49385i			0.117711i	0.998267	+	0.0588554i	$0.0187451\pi$
$881$			3.49385i			0.117711i	−0.998267	+	0.0588554i	$0.981255\pi$
$882$	29.6415	−	1.83949i	0.998080	−	0.0619388i
$883$	6.79486			0.228665			0.114333	−	0.993443i	$-0.463527\pi$
$883$	6.79486			0.228665			0.114333	+	0.993443i	$0.463527\pi$
$884$	12.2389	+	15.5696i	0.411638	+	0.523662i
$885$	37.8925	+	22.5340i	1.27374	+	0.757472i
$886$	14.0237	+	40.5323i	0.471135	+	1.36171i
$887$	51.9796			1.74531			0.872653	−	0.488341i	$-0.162398\pi$
$887$	51.9796			1.74531			0.872653	+	0.488341i	$0.162398\pi$
$888$	12.6410	+	25.3364i	0.424204	+	0.850234i
$889$	−1.93133	+	0.270478i	−0.0647747	+	0.00907153i
$890$	−59.7087	−	51.7487i	−2.00144	−	1.73462i
$891$	4.26262	+	0.220179i	0.142803	+	0.00737626i
$892$	28.8780	−	22.7003i	0.966907	−	0.760062i
$893$			3.42254i			0.114531i
$894$	3.50681	−	17.0021i	0.117285	−	0.568637i
$895$	9.30787	+	16.1217i	0.311128	+	0.538889i
$896$	−27.8375	+	11.0033i	−0.929986	+	0.367594i
$897$	−54.7686	+	30.6854i	−1.82867	+	1.02456i
$898$	26.8102	+	5.17011i	0.894669	+	0.172529i
$899$	17.9857	−	10.3841i	0.599858	−	0.346328i
$900$	37.2841	+	16.0636i	1.24280	+	0.535452i
$901$	−0.601489	+	1.04181i	−0.0200385	+	0.0347077i
$902$	−4.53119	+	1.56774i	−0.150872	+	0.0522000i
$903$	−31.4455	−	13.1972i	−1.04644	−	0.439174i
$904$	−0.916929	+	19.1244i	−0.0304966	+	0.636069i
$905$	9.40600			0.312666
$906$	−9.71073	+	47.0808i	−0.322617	+	1.56415i
$907$	−11.7382			−0.389759			−0.194880	−	0.980827i	$-0.562432\pi$
$907$	−11.7382			−0.389759			−0.194880	+	0.980827i	$0.562432\pi$
$908$	−18.9888	+	47.4035i	−0.630167	+	1.57314i
$909$	−44.7059	−	1.15383i	−1.48280	−	0.0382703i
$910$	−72.6366	+	37.1017i	−2.40788	+	1.22991i
$911$	−6.82136	−	3.93831i	−0.226002	−	0.130482i	0.382724	−	0.923863i	$-0.374986\pi$
$911$	−6.82136	−	3.93831i	−0.226002	−	0.130482i	−0.608726	+	0.793380i	$0.708319\pi$
$912$	−2.80145	−	10.0331i	−0.0927653	−	0.332230i
$913$	4.20229	+	2.42620i	0.139076	+	0.0802954i
$914$	5.25787	+	15.1967i	0.173915	+	0.502662i
$915$	33.4714	+	59.7411i	1.10653	+	1.97498i
$916$	−30.5213	−	12.2262i	−1.00845	−	0.403965i
$917$	29.4149	−	4.11948i	0.971366	−	0.136037i
$918$	−10.9575	+	3.32232i	−0.361651	+	0.109653i
$919$	−49.6843	−	28.6853i	−1.63893	−	0.946240i	−0.981201	−	0.192989i	$-0.938182\pi$
$919$	−49.6843	−	28.6853i	−1.63893	−	0.946240i	−0.657734	−	0.753250i	$-0.728485\pi$
$920$	−29.9309	+	46.5418i	−0.986794	+	1.53444i
$921$	−0.110385	+	8.55526i	−0.00363731	+	0.281905i
$922$	23.5316	−	27.1513i	0.774973	−	0.894181i
$923$	−41.0891	+	23.7228i	−1.35246	+	0.780845i
$924$	−1.09543	+	4.20633i	−0.0360369	+	0.138378i
$925$	33.8676	+	19.5535i	1.11356	+	0.642914i
$926$	−35.7563	+	12.3713i	−1.17503	+	0.406545i
$927$	−6.23065	−	0.160810i	−0.204641	−	0.00528168i
$928$	1.51932	+	15.9981i	0.0498743	+	0.525164i
$929$	33.1880	−	19.1611i	1.08886	−	0.628656i	0.155590	−	0.987822i	$-0.450272\pi$
$929$	33.1880	−	19.1611i	1.08886	−	0.628656i	0.933274	+	0.359166i	$0.116939\pi$
$930$	40.8254	−	45.8952i	1.33872	−	1.50496i
$931$	−10.2097	−	2.55607i	−0.334611	−	0.0837719i
$932$	12.9983	−	10.2176i	0.425772	−	0.334689i
$933$	5.16721	−	8.68902i	0.169167	−	0.284466i
$934$	−2.61708	−	2.26818i	−0.0856335	−	0.0742173i
$935$	2.19520	−	1.26740i	0.0717906	−	0.0414483i
$936$	−3.97126	+	53.7773i	−0.129805	+	1.75777i
$937$			56.2069i			1.83620i	0.396350	+	0.918099i	$0.370277\pi$
$937$			56.2069i			1.83620i	−0.396350	+	0.918099i	$0.629723\pi$
$938$	−36.8790	−	23.8971i	−1.20414	−	0.780268i
$939$	34.4486	−	19.3007i	1.12419	−	0.629853i
$940$	−2.21926	−	15.4579i	−0.0723841	−	0.504180i
$941$	1.73652	−	3.00774i	0.0566089	−	0.0980496i	−0.836332	−	0.548223i	$-0.815305\pi$
$941$	1.73652	−	3.00774i	0.0566089	−	0.0980496i	0.892941	+	0.450173i	$0.148638\pi$
$942$	1.96029	−	2.20372i	0.0638696	−	0.0718011i
$943$	20.3867	+	35.3107i	0.663881	+	1.14988i
$944$	8.35053	+	28.4827i	0.271787	+	0.927032i
$945$	−4.72837	−	46.9197i	−0.153814	−	1.52630i
$946$	3.26894	−	3.77177i	0.106282	−	0.122631i
$947$	−11.0809	−	19.1927i	−0.360081	−	0.623678i	0.627893	−	0.778300i	$-0.283917\pi$
$947$	−11.0809	−	19.1927i	−0.360081	−	0.623678i	−0.987974	+	0.154622i	$0.950584\pi$
$948$	3.99611	−	0.521188i	0.129788	−	0.0169274i
$949$	−37.0363	−	21.3829i	−1.20225	−	0.694120i
$950$	−10.8722	−	9.42278i	−0.352741	−	0.305715i
$951$	−7.34632	+	4.11595i	−0.238221	+	0.133469i
$952$	−1.06233	−	11.6117i	−0.0344302	−	0.376337i
$953$	−0.928372			−0.0300729			−0.0150365	−	0.999887i	$-0.504786\pi$
$953$	−0.928372			−0.0300729			−0.0150365	+	0.999887i	$0.504786\pi$
$954$	−3.12210	+	0.990781i	−0.101082	+	0.0320777i
$955$	9.63956	−	5.56540i	0.311929	−	0.180092i
$956$	4.42713	−	0.635595i	0.143184	−	0.0205566i
$957$	2.00569	+	1.19275i	0.0648349	+	0.0385562i
$958$	35.3888	+	6.82441i	1.14336	+	0.220487i
$959$	0.0977802	+	0.698194i	0.00315749	+	0.0225459i
$960$	19.1584	+	43.4979i	0.618335	+	1.40389i
$961$	−11.2226	−	19.4380i	−0.362018	−	0.627033i
$962$	−9.83575	+	51.0044i	−0.317117	+	1.64445i
$963$	7.58479	−	12.3877i	0.244417	−	0.399189i
$964$	4.79147	−	11.9614i	0.154323	−	0.385250i
$965$	20.3714	−	35.2843i	0.655778	−	1.13584i
$966$	36.8864	+	2.37367i	1.18680	+	0.0763715i
$967$	32.4918	−	18.7591i	1.04487	−	0.603254i	0.123658	−	0.992325i	$-0.460537\pi$
$967$	32.4918	−	18.7591i	1.04487	−	0.603254i	0.921208	+	0.389071i	$0.127204\pi$
$968$	25.6334	+	16.4848i	0.823889	+	0.529841i
$969$	4.05745	+	0.0523516i	0.130344	+	0.00168178i
$970$	−9.73479	−	8.43699i	−0.312565	−	0.270896i
$971$	−0.424402	−	0.245028i	−0.0136197	−	0.00786334i	0.493175	−	0.869930i	$-0.335836\pi$
$971$	−0.424402	−	0.245028i	−0.0136197	−	0.00786334i	−0.506794	+	0.862067i	$0.669170\pi$
$972$	−28.1337	−	13.4348i	−0.902389	−	0.430922i
$973$	−12.2419	−	15.6846i	−0.392459	−	0.502826i
$974$	21.3810	−	7.39758i	0.685092	−	0.237034i
$975$	36.4031	+	64.9738i	1.16583	+	2.08083i
$976$	−10.8878	+	44.7997i	−0.348511	+	1.43400i
$977$	8.05716	−	13.9554i	0.257771	−	0.446473i	−0.707873	−	0.706339i	$-0.750345\pi$
$977$	8.05716	−	13.9554i	0.257771	−	0.446473i	0.965645	+	0.259867i	$0.0836786\pi$
$978$	16.6155	−	18.6789i	0.531306	−	0.597285i
$979$	−6.68973	−	3.86232i	−0.213805	−	0.123440i
$980$	47.7696	+	4.92424i	1.52594	+	0.157299i
$981$	39.6135	−	21.5277i	1.26476	−	0.687326i
$982$	11.8035	+	34.1153i	0.376665	+	1.08866i
$983$	8.53643			0.272270			0.136135	−	0.990690i	$-0.456532\pi$
$983$	8.53643			0.272270			0.136135	+	0.990690i	$0.456532\pi$
$984$	34.9574	+	2.12841i	1.11440	+	0.0678511i
$985$		−	85.3899i		−	2.72075i
$986$	−6.14670	−	1.18533i	−0.195751	−	0.0377488i
$987$	−8.30525	+	6.31158i	−0.264359	+	0.200900i
$988$	7.10614	−	17.7397i	0.226076	−	0.564374i
$989$	−36.7577	−	21.2221i	−1.16883	−	0.674822i
$990$	6.74105	+	1.48131i	0.214245	+	0.0470790i
$991$	45.8550	−	26.4744i	1.45663	−	0.840986i	0.457787	−	0.889062i	$-0.348642\pi$
$991$	45.8550	−	26.4744i	1.45663	−	0.840986i	0.998844	+	0.0480755i	$0.0153088\pi$
$992$	41.1699	−	3.90986i	1.30714	−	0.124138i
$993$	−8.59542	−	15.3415i	−0.272767	−	0.486846i
$994$	27.8980	+	1.43411i	0.884871	+	0.0454871i
$995$	−36.2486	−	62.7844i	−1.14916	−	1.99040i
$996$	−21.5425	−	28.1451i	−0.682600	−	0.891810i
$997$	4.74803			0.150372			0.0751858	−	0.997170i	$-0.476045\pi$
$997$	4.74803			0.150372			0.0751858	+	0.997170i	$0.476045\pi$
$998$	−23.3089	−	4.49492i	−0.737831	−	0.142284i
$999$	−25.4083	−	16.0114i	−0.803882	−	0.506578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cz.b.187.5	yes	180
7.3	odd	6		504.2.bf.b.115.67	✓	180
8.3	odd	2	inner	504.2.cz.b.187.54	yes	180
9.4	even	3		504.2.bf.b.355.67	yes	180
56.3	even	6		504.2.bf.b.115.68	yes	180
63.31	odd	6	inner	504.2.cz.b.283.54	yes	180
72.67	odd	6		504.2.bf.b.355.68	yes	180
504.283	even	6	inner	504.2.cz.b.283.5	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.67	✓	180	7.3	odd	6
504.2.bf.b.115.68	yes	180	56.3	even	6
504.2.bf.b.355.67	yes	180	9.4	even	3
504.2.bf.b.355.68	yes	180	72.67	odd	6
504.2.cz.b.187.5	yes	180	1.1	even	1	trivial
504.2.cz.b.187.54	yes	180	8.3	odd	2	inner
504.2.cz.b.283.5	yes	180	504.283	even	6	inner
504.2.cz.b.283.54	yes	180	63.31	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.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38863 - 0.267785i) q^{2} +(-1.73191 - 0.0223461i) q^{3} +(1.85658 + 0.743707i) q^{4} -3.43019 q^{5} +(2.39899 + 0.494808i) q^{6} +(-0.366949 - 2.62018i) q^{7} +(-2.37895 - 1.52990i) q^{8} +(2.99900 + 0.0774026i) q^{9} +O(q^{10})\)	\(q+(-1.38863 - 0.267785i) q^{2} +(-1.73191 - 0.0223461i) q^{3} +(1.85658 + 0.743707i) q^{4} -3.43019 q^{5} +(2.39899 + 0.494808i) q^{6} +(-0.366949 - 2.62018i) q^{7} +(-2.37895 - 1.52990i) q^{8} +(2.99900 + 0.0774026i) q^{9} +(4.76327 + 0.918553i) q^{10} +0.474256 q^{11} +(-3.19881 - 1.32952i) q^{12} +(-3.17749 - 5.50357i) q^{13} +(-0.192088 + 3.73672i) q^{14} +(5.94077 + 0.0766513i) q^{15} +(2.89380 + 2.76151i) q^{16} +(-1.34940 + 0.779079i) q^{17} +(-4.14377 - 0.910570i) q^{18} +(1.30211 + 0.751775i) q^{19} +(-6.36844 - 2.55106i) q^{20} +(0.576971 + 4.54611i) q^{21} +(-0.658566 - 0.126999i) q^{22} +5.70347i q^{23} +(4.08594 + 2.70280i) q^{24} +6.76622 q^{25} +(2.93858 + 8.49330i) q^{26} +(-5.19226 - 0.201070i) q^{27} +(1.26738 - 5.13749i) q^{28} +(-2.46022 - 1.42041i) q^{29} +(-8.22901 - 1.69729i) q^{30} +(-3.65531 + 6.33118i) q^{31} +(-3.27892 - 4.60963i) q^{32} +(-0.821368 - 0.0105978i) q^{33} +(2.08245 - 0.720502i) q^{34} +(1.25871 + 8.98772i) q^{35} +(5.51033 + 2.37408i) q^{36} +(5.00540 + 2.88987i) q^{37} +(-1.60684 - 1.39262i) q^{38} +(5.38013 + 9.60267i) q^{39} +(8.16026 + 5.24784i) q^{40} +(6.19109 - 3.57443i) q^{41} +(0.416179 - 6.46736i) q^{42} +(-3.72090 + 6.44479i) q^{43} +(0.880496 + 0.352708i) q^{44} +(-10.2872 - 0.265506i) q^{45} +(1.52730 - 7.92001i) q^{46} +(1.13815 + 1.97134i) q^{47} +(-4.95008 - 4.84734i) q^{48} +(-6.73070 + 1.92295i) q^{49} +(-9.39577 - 1.81189i) q^{50} +(2.35445 - 1.31914i) q^{51} +(-1.80622 - 12.5810i) q^{52} +(0.668616 - 0.386026i) q^{53} +(7.15628 + 1.66962i) q^{54} -1.62679 q^{55} +(-3.13566 + 6.79468i) q^{56} +(-2.23834 - 1.33110i) q^{57} +(3.03597 + 2.63123i) q^{58} +(6.42624 + 3.71019i) q^{59} +(10.9725 + 4.56051i) q^{60} +(5.76297 + 9.98175i) q^{61} +(6.77126 - 7.81283i) q^{62} +(-0.897673 - 7.88633i) q^{63} +(3.31882 + 7.27911i) q^{64} +(10.8994 + 18.8783i) q^{65} +(1.13774 + 0.234666i) q^{66} +(-5.87235 + 10.1712i) q^{67} +(-3.08469 + 0.442863i) q^{68} +(0.127450 - 9.87789i) q^{69} +(0.658898 - 12.8177i) q^{70} -7.46590i q^{71} +(-7.01606 - 4.77230i) q^{72} +(5.82793 - 3.36476i) q^{73} +(-6.17678 - 5.35332i) q^{74} +(-11.7185 - 0.151198i) q^{75} +(1.85838 + 2.36412i) q^{76} +(-0.174028 - 1.24264i) q^{77} +(-4.89956 - 14.7753i) q^{78} +(-1.00749 + 0.581674i) q^{79} +(-9.92629 - 9.47250i) q^{80} +(8.98802 + 0.464261i) q^{81} +(-9.55431 + 3.30568i) q^{82} +(8.86081 + 5.11579i) q^{83} +(-2.30978 + 8.86932i) q^{84} +(4.62872 - 2.67239i) q^{85} +(6.89276 - 7.95302i) q^{86} +(4.22914 + 2.51499i) q^{87} +(-1.12823 - 0.725564i) q^{88} +(-14.1057 - 8.14395i) q^{89} +(14.2139 + 3.12343i) q^{90} +(-13.2544 + 10.3451i) q^{91} +(-4.24172 + 10.5890i) q^{92} +(6.47213 - 10.8833i) q^{93} +(-1.05258 - 3.04224i) q^{94} +(-4.46649 - 2.57873i) q^{95} +(5.57578 + 8.05671i) q^{96} +(-2.29977 - 1.32777i) q^{97} +(9.86138 - 0.867884i) q^{98} +(1.42230 + 0.0367087i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

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