LMFDB - Embedded newform 504.2.cy.a.347.4

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			347.4
Character	$\chi$	$=$	504.347
Dual form			504.2.cy.a.443.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40917 - 0.119296i) q^{2} +(-1.11238 + 1.32763i) q^{3} +(1.97154 + 0.336217i) q^{4} -4.38485 q^{5} +(1.72592 - 1.73816i) q^{6} +(-2.42141 + 1.06619i) q^{7} +(-2.73813 - 0.708985i) q^{8} +(-0.525222 - 2.95367i) q^{9} +O(q^{10})$	\(q+(-1.40917 - 0.119296i) q^{2} +(-1.11238 + 1.32763i) q^{3} +(1.97154 + 0.336217i) q^{4} -4.38485 q^{5} +(1.72592 - 1.73816i) q^{6} +(-2.42141 + 1.06619i) q^{7} +(-2.73813 - 0.708985i) q^{8} +(-0.525222 - 2.95367i) q^{9} +(6.17901 + 0.523095i) q^{10} +3.86348i q^{11} +(-2.63947 + 2.24348i) q^{12} +(-1.11772 - 0.645313i) q^{13} +(3.53938 - 1.21358i) q^{14} +(4.87762 - 5.82147i) q^{15} +(3.77392 + 1.32573i) q^{16} +(-2.24544 - 1.29641i) q^{17} +(0.387768 + 4.22488i) q^{18} +(-1.02175 - 1.76971i) q^{19} +(-8.64489 - 1.47426i) q^{20} +(1.27802 - 4.40076i) q^{21} +(0.460898 - 5.44431i) q^{22} +0.834265 q^{23} +(3.98711 - 2.84657i) q^{24} +14.2269 q^{25} +(1.49807 + 1.04270i) q^{26} +(4.50563 + 2.58830i) q^{27} +(-5.13238 + 1.28791i) q^{28} +(1.56877 + 2.71720i) q^{29} +(-7.56789 + 7.62158i) q^{30} +(1.51306 - 0.873564i) q^{31} +(-5.15995 - 2.31840i) q^{32} +(-5.12929 - 4.29766i) q^{33} +(3.00956 + 2.09473i) q^{34} +(10.6175 - 4.67508i) q^{35} +(-0.0424210 - 5.99985i) q^{36} +(-5.79153 + 3.34374i) q^{37} +(1.22870 + 2.61572i) q^{38} +(2.10006 - 0.766083i) q^{39} +(12.0063 + 3.10879i) q^{40} +(-2.42962 - 1.40274i) q^{41} +(-2.32595 + 6.04896i) q^{42} +(4.10614 + 7.11204i) q^{43} +(-1.29897 + 7.61699i) q^{44} +(2.30302 + 12.9514i) q^{45} +(-1.17562 - 0.0995245i) q^{46} +(3.81166 - 6.60200i) q^{47} +(-5.95811 + 3.53566i) q^{48} +(4.72648 - 5.16337i) q^{49} +(-20.0482 - 1.69721i) q^{50} +(4.21894 - 1.53903i) q^{51} +(-1.98665 - 1.64805i) q^{52} +(3.05083 - 5.28419i) q^{53} +(-6.04044 - 4.18486i) q^{54} -16.9408i q^{55} +(7.38605 - 1.20262i) q^{56} +(3.48610 + 0.612091i) q^{57} +(-1.88652 - 4.01615i) q^{58} +(8.75498 - 5.05469i) q^{59} +(11.5737 - 9.83731i) q^{60} +(-4.22260 - 2.43792i) q^{61} +(-2.23637 + 1.05050i) q^{62} +(4.42095 + 6.59206i) q^{63} +(6.99468 + 3.88258i) q^{64} +(4.90102 + 2.82960i) q^{65} +(6.71536 + 6.66805i) q^{66} +(-7.36306 - 12.7532i) q^{67} +(-3.99110 - 3.31087i) q^{68} +(-0.928019 + 1.10760i) q^{69} +(-15.5197 + 5.32137i) q^{70} +10.8381 q^{71} +(-0.655980 + 8.45989i) q^{72} +(-4.73025 + 8.19303i) q^{73} +(8.56016 - 4.02100i) q^{74} +(-15.8257 + 18.8881i) q^{75} +(-1.41940 - 3.83259i) q^{76} +(-4.11920 - 9.35508i) q^{77} +(-3.05074 + 0.829015i) q^{78} +(-2.53771 - 1.46515i) q^{79} +(-16.5481 - 5.81313i) q^{80} +(-8.44828 + 3.10266i) q^{81} +(3.25642 + 2.26655i) q^{82} +(-8.11652 + 4.68608i) q^{83} +(3.99928 - 8.24656i) q^{84} +(9.84592 + 5.68455i) q^{85} +(-4.93782 - 10.5119i) q^{86} +(-5.35251 - 0.939797i) q^{87} +(2.73915 - 10.5787i) q^{88} +(-1.59615 + 0.921536i) q^{89} +(-1.70031 - 18.5255i) q^{90} +(3.39448 + 0.370873i) q^{91} +(1.64478 + 0.280494i) q^{92} +(-0.523321 + 2.98052i) q^{93} +(-6.15889 + 8.84864i) q^{94} +(4.48020 + 7.75993i) q^{95} +(8.81780 - 4.27158i) q^{96} +(-0.0399262 - 0.0691541i) q^{97} +(-7.27640 + 6.71223i) q^{98} +(11.4114 - 2.02919i) 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 $

$2$	−1.40917	−	0.119296i	−0.996436	−	0.0843550i
$2$	−1.40917	−	0.119296i	−0.996436	−	0.0843550i
$3$	−1.11238	+	1.32763i	−0.642233	+	0.766510i
$3$	−1.11238	+	1.32763i	−0.642233	+	0.766510i
$4$	1.97154	+	0.336217i	0.985768	+	0.168109i
$5$	−4.38485			−1.96096			−0.980482	−	0.196607i	$-0.937008\pi$
$5$	−4.38485			−1.96096			−0.980482	+	0.196607i	$0.937008\pi$
$6$	1.72592	−	1.73816i	0.704603	−	0.709602i
$7$	−2.42141	+	1.06619i	−0.915208	+	0.402982i
$7$	−2.42141	+	1.06619i	−0.915208	+	0.402982i
$8$	−2.73813	−	0.708985i	−0.968074	−	0.250664i
$9$	−0.525222	−	2.95367i	−0.175074	−	0.984555i
$10$	6.17901	+	0.523095i	1.95398	+	0.165417i
$11$			3.86348i			1.16488i	0.812873	+	0.582441i	$0.197902\pi$
$11$			3.86348i			1.16488i	−0.812873	+	0.582441i	$0.802098\pi$
$12$	−2.63947	+	2.24348i	−0.761950	+	0.647636i
$13$	−1.11772	−	0.645313i	−0.309999	−	0.178978i	0.336927	−	0.941531i	$-0.390612\pi$
$13$	−1.11772	−	0.645313i	−0.309999	−	0.178978i	−0.646926	+	0.762553i	$0.723946\pi$
$14$	3.53938	−	1.21358i	0.945940	−	0.324343i
$15$	4.87762	−	5.82147i	1.25940	−	1.50310i
$16$	3.77392	+	1.32573i	0.943479	+	0.331433i
$17$	−2.24544	−	1.29641i	−0.544600	−	0.314425i	0.202341	−	0.979315i	$-0.435145\pi$
$17$	−2.24544	−	1.29641i	−0.544600	−	0.314425i	−0.746941	+	0.664890i	$0.768478\pi$
$18$	0.387768	+	4.22488i	0.0913979	+	0.995814i
$19$	−1.02175	−	1.76971i	−0.234404	−	0.406000i	0.724695	−	0.689070i	$-0.241981\pi$
$19$	−1.02175	−	1.76971i	−0.234404	−	0.406000i	−0.959099	+	0.283069i	$0.908647\pi$
$20$	−8.64489	−	1.47426i	−1.93306	−	0.329655i
$21$	1.27802	−	4.40076i	0.278887	−	0.960324i
$22$	0.460898	−	5.44431i	0.0982637	−	1.16073i
$23$	0.834265			0.173956			0.0869781	−	0.996210i	$-0.472279\pi$
$23$	0.834265			0.173956			0.0869781	+	0.996210i	$0.472279\pi$
$24$	3.98711	−	2.84657i	0.813865	−	0.581053i
$25$	14.2269			2.84538
$26$	1.49807	+	1.04270i	0.293796	+	0.204490i
$27$	4.50563	+	2.58830i	0.867109	+	0.498118i
$28$	−5.13238	+	1.28791i	−0.969928	+	0.243392i
$29$	1.56877	+	2.71720i	0.291314	+	0.504571i	0.974121	−	0.226028i	$-0.0725742\pi$
$29$	1.56877	+	2.71720i	0.291314	+	0.504571i	−0.682807	+	0.730599i	$0.739241\pi$
$30$	−7.56789	+	7.62158i	−1.38170	+	1.39150i
$31$	1.51306	−	0.873564i	0.271753	−	0.156897i	−0.357931	−	0.933748i	$-0.616518\pi$
$31$	1.51306	−	0.873564i	0.271753	−	0.156897i	0.629684	+	0.776851i	$0.283184\pi$
$32$	−5.15995	−	2.31840i	−0.912158	−	0.409838i
$33$	−5.12929	−	4.29766i	−0.892894	−	0.748126i
$34$	3.00956	+	2.09473i	0.516135	+	0.359244i
$35$	10.6175	−	4.67508i	1.79469	−	0.790233i
$36$	−0.0424210	−	5.99985i	−0.00707016	−	0.999975i
$37$	−5.79153	+	3.34374i	−0.952122	+	0.549708i	−0.893739	−	0.448587i	$-0.851928\pi$
$37$	−5.79153	+	3.34374i	−0.952122	+	0.549708i	−0.0583822	+	0.998294i	$0.518594\pi$
$38$	1.22870	+	2.61572i	0.199321	+	0.424326i
$39$	2.10006	−	0.766083i	0.336279	−	0.122672i
$40$	12.0063	+	3.10879i	1.89836	+	0.491543i
$41$	−2.42962	−	1.40274i	−0.379444	−	0.219072i	0.298133	−	0.954524i	$-0.403636\pi$
$41$	−2.42962	−	1.40274i	−0.379444	−	0.219072i	−0.677576	+	0.735453i	$0.736970\pi$
$42$	−2.32595	+	6.04896i	−0.358901	+	0.933376i
$43$	4.10614	+	7.11204i	0.626180	+	1.08458i	0.988311	+	0.152448i	$0.0487157\pi$
$43$	4.10614	+	7.11204i	0.626180	+	1.08458i	−0.362132	+	0.932127i	$0.617951\pi$
$44$	−1.29897	+	7.61699i	−0.195827	+	1.14830i
$45$	2.30302	+	12.9514i	0.343314	+	1.93068i
$46$	−1.17562	−	0.0995245i	−0.173336	−	0.0146741i
$47$	3.81166	−	6.60200i	0.555988	−	0.963000i	−0.441838	−	0.897095i	$-0.645673\pi$
$47$	3.81166	−	6.60200i	0.555988	−	0.963000i	0.997826	−	0.0659050i	$-0.0209934\pi$
$48$	−5.95811	+	3.53566i	−0.859979	+	0.510329i
$49$	4.72648	−	5.16337i	0.675211	−	0.737624i
$50$	−20.0482	−	1.69721i	−2.83524	−	0.240022i
$51$	4.21894	−	1.53903i	0.590769	−	0.215507i
$52$	−1.98665	−	1.64805i	−0.275499	−	0.228544i
$53$	3.05083	−	5.28419i	0.419063	−	0.725839i	−0.576782	−	0.816898i	$-0.695692\pi$
$53$	3.05083	−	5.28419i	0.419063	−	0.725839i	0.995845	+	0.0910591i	$0.0290252\pi$
$54$	−6.04044	−	4.18486i	−0.822000	−	0.569487i
$55$		−	16.9408i		−	2.28429i
$56$	7.38605	−	1.20262i	0.987002	−	0.160706i
$57$	3.48610	+	0.612091i	0.461745	+	0.0810735i
$58$	−1.88652	−	4.01615i	−0.247713	−	0.527346i
$59$	8.75498	−	5.05469i	1.13980	−	0.658065i	0.193420	−	0.981116i	$-0.438042\pi$
$59$	8.75498	−	5.05469i	1.13980	−	0.658065i	0.946381	+	0.323051i	$0.104709\pi$
$60$	11.5737	−	9.83731i	1.49416	−	1.26999i
$61$	−4.22260	−	2.43792i	−0.540649	−	0.312144i	0.204693	−	0.978826i	$-0.434380\pi$
$61$	−4.22260	−	2.43792i	−0.540649	−	0.312144i	−0.745342	+	0.666682i	$0.767714\pi$
$62$	−2.23637	+	1.05050i	−0.284019	+	0.133414i
$63$	4.42095	+	6.59206i	0.556987	+	0.830521i
$64$	6.99468	+	3.88258i	0.874335	+	0.485323i
$65$	4.90102	+	2.82960i	0.607896	+	0.350969i
$66$	6.71536	+	6.66805i	0.826603	+	0.820780i
$67$	−7.36306	−	12.7532i	−0.899542	−	1.55805i	−0.828081	−	0.560608i	$-0.810567\pi$
$67$	−7.36306	−	12.7532i	−0.899542	−	1.55805i	−0.0714603	−	0.997443i	$-0.522766\pi$
$68$	−3.99110	−	3.31087i	−0.483992	−	0.401502i
$69$	−0.928019	+	1.10760i	−0.111720	+	0.133339i
$70$	−15.5197	+	5.32137i	−1.85495	+	0.636025i
$71$	10.8381			1.28625			0.643123	−	0.765763i	$-0.277639\pi$
$71$	10.8381			1.28625			0.643123	+	0.765763i	$0.277639\pi$
$72$	−0.655980	+	8.45989i	−0.0773080	+	0.997007i
$73$	−4.73025	+	8.19303i	−0.553634	+	0.958922i	0.444375	+	0.895841i	$0.353426\pi$
$73$	−4.73025	+	8.19303i	−0.553634	+	0.958922i	−0.998008	+	0.0630807i	$0.979907\pi$
$74$	8.56016	−	4.02100i	0.995099	−	0.467432i
$75$	−15.8257	+	18.8881i	−1.82740	+	2.18101i
$76$	−1.41940	−	3.83259i	−0.162816	−	0.439628i
$77$	−4.11920	−	9.35508i	−0.469427	−	1.06611i
$78$	−3.05074	+	0.829015i	−0.345429	+	0.0938674i
$79$	−2.53771	−	1.46515i	−0.285515	−	0.164842i	0.350402	−	0.936599i	$-0.386045\pi$
$79$	−2.53771	−	1.46515i	−0.285515	−	0.164842i	−0.635917	+	0.771757i	$0.719378\pi$
$80$	−16.5481	−	5.81313i	−1.85013	−	0.649928i
$81$	−8.44828	+	3.10266i	−0.938698	+	0.344740i
$82$	3.25642	+	2.26655i	0.359611	+	0.250299i
$83$	−8.11652	+	4.68608i	−0.890904	+	0.514364i	−0.874238	−	0.485497i	$-0.838639\pi$
$83$	−8.11652	+	4.68608i	−0.890904	+	0.514364i	−0.0166661	+	0.999861i	$0.505305\pi$
$84$	3.99928	−	8.24656i	0.436357	−	0.899774i
$85$	9.84592	+	5.68455i	1.06794	+	0.616576i
$86$	−4.93782	−	10.5119i	−0.532459	−	1.13353i
$87$	−5.35251	−	0.939797i	−0.573850	−	0.100757i
$88$	2.73915	−	10.5787i	0.291994	−	1.12769i
$89$	−1.59615	+	0.921536i	−0.169191	+	0.0976827i	−0.582204	−	0.813042i	$-0.697810\pi$
$89$	−1.59615	+	0.921536i	−0.169191	+	0.0976827i	0.413013	+	0.910725i	$0.364476\pi$
$90$	−1.70031	−	18.5255i	−0.179228	−	1.95276i
$91$	3.39448	+	0.370873i	0.355838	+	0.0388781i
$92$	1.64478	+	0.280494i	0.171481	+	0.0292436i
$93$	−0.523321	+	2.98052i	−0.0542659	+	0.309066i
$94$	−6.15889	+	8.84864i	−0.635241	+	0.912667i
$95$	4.48020	+	7.75993i	0.459659	+	0.796152i
$96$	8.81780	−	4.27158i	0.899963	−	0.435966i
$97$	−0.0399262	−	0.0691541i	−0.00405389	−	0.00702154i	0.863991	−	0.503507i	$-0.167957\pi$
$97$	−0.0399262	−	0.0691541i	−0.00405389	−	0.00702154i	−0.868045	+	0.496485i	$0.834624\pi$
$98$	−7.27640	+	6.71223i	−0.735027	+	0.678038i
$99$	11.4114	−	2.02919i	1.14689	−	0.203941i
$100$	28.0489	+	4.78334i	2.80489	+	0.478334i
$101$	−3.62440			−0.360642			−0.180321	−	0.983608i	$-0.557714\pi$
$101$	−3.62440			−0.360642			−0.180321	+	0.983608i	$0.557714\pi$
$102$	−6.12881	+	1.66545i	−0.606843	+	0.164904i
$103$			4.78410i			0.471392i	0.971827	+	0.235696i	$0.0757369\pi$
$103$			4.78410i			0.471392i	−0.971827	+	0.235696i	$0.924263\pi$
$104$	2.60293	+	2.55939i	0.255238	+	0.250969i
$105$	−5.60393	+	19.2967i	−0.546888	+	1.88316i
$106$	−4.92952	+	7.08238i	−0.478798	+	0.687902i
$107$	5.37324	−	3.10224i	0.519451	−	0.299905i	−0.217259	−	0.976114i	$-0.569712\pi$
$107$	5.37324	−	3.10224i	0.519451	−	0.299905i	0.736710	+	0.676209i	$0.236378\pi$
$108$	8.01279	+	6.61779i	0.771031	+	0.636797i
$109$	−13.0938	−	7.55971i	−1.25416	−	0.724089i	−0.282226	−	0.959348i	$-0.591073\pi$
$109$	−13.0938	−	7.55971i	−1.25416	−	0.724089i	−0.971933	+	0.235259i	$0.924406\pi$
$110$	−2.02097	+	23.8725i	−0.192692	+	2.27615i
$111$	2.00312	−	11.4085i	0.190127	−	1.08285i
$112$	−10.5517	+	0.813569i	−0.997041	+	0.0768751i
$113$	−10.8240	−	6.24924i	−1.01824	−	0.587880i	−0.104644	−	0.994510i	$-0.533370\pi$
$113$	−10.8240	−	6.24924i	−1.01824	−	0.587880i	−0.913593	+	0.406630i	$0.866704\pi$
$114$	−4.83950	−	1.27842i	−0.453261	−	0.119735i
$115$	−3.65813			−0.341122
$116$	2.17933	+	5.88450i	0.202345	+	0.546362i
$117$	−1.31899	+	3.64029i	−0.121941	+	0.336545i
$118$	−12.9403	+	6.07850i	−1.19125	+	0.559571i
$119$	6.81936	+	0.745068i	0.625129	+	0.0683003i
$120$	−17.4829	+	12.4818i	−1.59596	+	1.13943i
$121$	−3.92648			−0.356952
$122$	5.65955	+	3.93919i	0.512391	+	0.356638i
$123$	4.56500	−	1.66527i	0.411612	−	0.150152i
$124$	3.27676	−	1.21355i	0.294261	−	0.108980i
$125$	−40.4586			−3.61873
$126$	−5.44347	−	9.81675i	−0.484943	−	0.874546i
$127$			12.8724i			1.14224i	0.820867	+	0.571120i	$0.193491\pi$
$127$			12.8724i			1.14224i	−0.820867	+	0.571120i	$0.806509\pi$
$128$	−9.39354	−	6.30567i	−0.830279	−	0.557348i
$129$	−14.0098	−	2.45984i	−1.23349	−	0.216577i
$130$	−6.56882	−	4.57207i	−0.576123	−	0.400997i
$131$			12.1139i			1.05839i	0.848499	+	0.529197i	$0.177507\pi$
$131$			12.1139i			1.05839i	−0.848499	+	0.529197i	$0.822493\pi$
$132$	−8.66763	−	10.1975i	−0.754420	−	0.887582i
$133$	4.36092	+	3.19584i	0.378140	+	0.277114i
$134$	8.85443	+	18.8499i	0.764906	+	1.62838i
$135$	−19.7565	−	11.3493i	−1.70037	−	0.976791i
$136$	5.22917	+	5.14171i	0.448398	+	0.440898i
$137$			5.93944i			0.507441i	0.967278	+	0.253720i	$0.0816543\pi$
$137$			5.93944i			0.507441i	−0.967278	+	0.253720i	$0.918346\pi$
$138$	1.43987	−	1.45009i	0.122570	−	0.123440i
$139$	8.16906	−	14.1492i	0.692891	−	1.20012i	−0.277995	−	0.960582i	$-0.589670\pi$
$139$	8.16906	−	14.1492i	0.692891	−	1.20012i	0.970886	−	0.239540i	$-0.0769966\pi$
$140$	22.5047	−	5.64730i	1.90199	−	0.477284i
$141$	4.52501	+	12.4044i	0.381075	+	1.04464i
$142$	−15.2727	−	1.29294i	−1.28166	−	0.108501i
$143$	2.49316	−	4.31827i	0.208488	−	0.361112i
$144$	1.93362	−	11.8432i	0.161135	−	0.986932i
$145$	−6.87884	−	11.9145i	−0.571257	−	0.989445i
$146$	7.64313	−	10.9811i	0.632550	−	0.908802i
$147$	1.59742	+	12.0187i	0.131753	+	0.991283i
$148$	−12.5424	+	4.64510i	−1.03098	+	0.381824i
$149$	19.4122			1.59031			0.795156	−	0.606405i	$-0.207389\pi$
$149$	19.4122			1.59031			0.795156	+	0.606405i	$0.207389\pi$
$150$	24.5545	−	24.7287i	2.00486	−	2.01909i
$151$			2.68876i			0.218808i	0.993997	+	0.109404i	$0.0348942\pi$
$151$			2.68876i			0.218808i	−0.993997	+	0.109404i	$0.965106\pi$
$152$	1.54297	+	5.57011i	0.125151	+	0.451795i
$153$	−2.64979	+	7.31319i	−0.214223	+	0.591236i
$154$	4.68864	+	13.6743i	0.377822	+	1.10191i
$155$	−6.63453	+	3.83045i	−0.532898	+	0.307669i
$156$	4.39792	−	0.804283i	0.352116	−	0.0643942i
$157$	19.0937	−	11.0238i	1.52384	−	0.879792i	0.524243	−	0.851569i	$-0.324349\pi$
$157$	19.0937	−	11.0238i	1.52384	−	0.879792i	0.999602	−	0.0282229i	$-0.00898482\pi$
$158$	3.40129	+	2.36739i	0.270592	+	0.188339i
$159$	3.62179	+	9.92840i	0.287226	+	0.787374i
$160$	22.6256	+	10.1658i	1.78871	+	0.803679i
$161$	−2.02010	+	0.889484i	−0.159206	+	0.0701012i
$162$	12.2752	−	3.36434i	0.964433	−	0.264328i
$163$	−9.21628	−	15.9631i	−0.721875	−	1.25032i	−0.960247	−	0.279150i	$-0.909947\pi$
$163$	−9.21628	−	15.9631i	−0.721875	−	1.25032i	0.238372	−	0.971174i	$-0.423386\pi$
$164$	−4.31847	−	3.58244i	−0.337216	−	0.279742i
$165$	22.4911	+	18.8446i	1.75093	+	1.46705i
$166$	11.9966	−	5.63522i	0.931118	−	0.437378i
$167$	2.13103	−	3.69105i	0.164904	−	0.285622i	−0.771717	−	0.635966i	$-0.780602\pi$
$167$	2.13103	−	3.69105i	0.164904	−	0.285622i	0.936621	+	0.350344i	$0.113935\pi$
$168$	−6.61946	+	11.1437i	−0.510702	+	0.859758i
$169$	−5.66714	−	9.81578i	−0.435934	−	0.755060i
$170$	−13.1965	−	9.18509i	−1.01212	−	0.704464i
$171$	−4.69050	+	3.94739i	−0.358692	+	0.301864i
$172$	5.70421	+	15.4022i	0.434942	+	1.17441i
$173$	3.28193	−	5.68447i	0.249521	−	0.432183i	−0.713872	−	0.700276i	$-0.753060\pi$
$173$	3.28193	−	5.68447i	0.249521	−	0.432183i	0.963393	+	0.268093i	$0.0863936\pi$
$174$	7.43050	+	1.96287i	0.563305	+	0.148805i
$175$	−34.4492	+	15.1686i	−2.60412	+	1.14664i
$176$	−5.12193	+	14.5804i	−0.386080	+	1.09904i
$177$	−3.02809	+	17.2461i	−0.227605	+	1.29630i
$178$	2.35918	−	1.10819i	0.176828	−	0.0830624i
$179$	−12.2099	−	7.04939i	−0.912611	−	0.526896i	−0.0313407	−	0.999509i	$-0.509978\pi$
$179$	−12.2099	−	7.04939i	−0.912611	−	0.526896i	−0.881270	+	0.472613i	$0.843311\pi$
$180$	0.186010	+	26.3084i	0.0138643	+	1.96092i
$181$			16.6663i			1.23880i	0.785077	+	0.619398i	$0.212623\pi$
$181$			16.6663i			1.23880i	−0.785077	+	0.619398i	$0.787377\pi$
$182$	−4.73916	−	0.927572i	−0.351290	−	0.0687562i
$183$	7.93381	−	2.89418i	0.586484	−	0.213944i
$184$	−2.28432	−	0.591481i	−0.168403	−	0.0436046i
$185$	25.3950	−	14.6618i	1.86708	−	1.07796i
$186$	1.09301	−	4.13764i	0.0801437	−	0.303386i
$187$	5.00864	−	8.67522i	0.366268	−	0.634395i
$188$	9.73454	−	11.7345i	0.709964	−	0.855829i
$189$	−13.6696	−	1.46347i	−0.994318	−	0.106452i
$190$	−5.38765	−	11.4696i	−0.390861	−	0.832089i
$191$	−0.317338	+	0.549645i	−0.0229617	+	0.0397709i	−0.877278	−	0.479983i	$-0.840643\pi$
$191$	−0.317338	+	0.549645i	−0.0229617	+	0.0397709i	0.854316	+	0.519754i	$0.173976\pi$
$192$	−12.9354	+	4.96747i	−0.933531	+	0.358496i
$193$	−8.15739	−	14.1290i	−0.587182	−	1.01703i	−0.994600	−	0.103787i	$-0.966904\pi$
$193$	−8.15739	−	14.1290i	−0.587182	−	1.01703i	0.407418	−	0.913242i	$-0.366429\pi$
$194$	0.0480131	+	0.102213i	0.00344714	+	0.00733848i
$195$	−9.20847	+	3.35916i	−0.659432	+	0.240554i
$196$	11.0544	−	8.59065i	0.789603	−	0.613618i
$197$	12.7073			0.905358			0.452679	−	0.891674i	$-0.350468\pi$
$197$	12.7073			0.905358			0.452679	+	0.891674i	$0.350468\pi$
$198$	−16.3227	+	1.49814i	−1.16001	+	0.106468i
$199$	9.19588	+	5.30925i	0.651879	+	0.376363i	0.789176	−	0.614167i	$-0.210508\pi$
$199$	9.19588	+	5.30925i	0.651879	+	0.376363i	−0.137297	+	0.990530i	$0.543841\pi$
$200$	−38.9551	−	10.0867i	−2.75454	−	0.713235i
$201$	25.1221	+	4.41095i	1.77198	+	0.311125i
$202$	5.10741	+	0.432377i	0.359356	+	0.0304219i
$203$	−6.69570	−	4.90684i	−0.469946	−	0.344393i
$204$	8.83524	−	1.61577i	0.618590	−	0.113126i
$205$	10.6535	+	6.15082i	0.744075	+	0.429592i
$206$	0.570725	−	6.74163i	0.0397643	−	0.469712i
$207$	−0.438174	−	2.46414i	−0.0304552	−	0.171270i
$208$	−3.36265	−	3.91715i	−0.233158	−	0.271605i
$209$	6.83726	−	3.94749i	0.472943	−	0.273054i
$210$	10.1989	−	26.5238i	0.703793	−	1.83032i
$211$	0.286716	−	0.496606i	0.0197383	−	0.0341878i	−0.855988	−	0.516996i	$-0.827050\pi$
$211$	0.286716	−	0.496606i	0.0197383	−	0.0341878i	0.875726	+	0.482809i	$0.160383\pi$
$212$	7.79145	−	9.39223i	0.535119	−	0.645061i
$213$	−12.0561	+	14.3890i	−0.826069	+	0.985919i
$214$	−7.94191	+	3.73059i	−0.542898	+	0.255018i
$215$	−18.0048	−	31.1852i	−1.22792	−	2.12681i
$216$	−10.5019	−	10.2815i	−0.714566	−	0.699568i
$217$	−2.73235	+	3.72846i	−0.185484	+	0.253105i
$218$	17.5496	+	12.2150i	1.18861	+	0.827303i
$219$	−5.61551	−	15.3938i	−0.379461	−	1.04022i
$220$	5.69579	−	33.3994i	0.384010	−	2.25179i
$221$	1.67318	+	2.89803i	0.112550	+	0.194942i
$222$	−4.18373	+	15.8376i	−0.280794	+	1.06295i
$223$	12.6300	−	7.29191i	0.845765	−	0.488303i	−0.0134546	−	0.999909i	$-0.504283\pi$
$223$	12.6300	−	7.29191i	0.845765	−	0.488303i	0.859220	+	0.511607i	$0.170950\pi$
$224$	14.9662	+	0.112315i	0.999972	+	0.00750434i
$225$	−7.47229	−	42.0215i	−0.498153	−	2.80144i
$226$	14.5074	+	10.0975i	0.965017	+	0.671678i
$227$			11.5987i			0.769832i	0.922952	+	0.384916i	$0.125770\pi$
$227$			11.5987i			0.769832i	−0.922952	+	0.384916i	$0.874230\pi$
$228$	6.66718	+	2.37885i	0.441545	+	0.157543i
$229$		−	9.45067i		−	0.624518i	−0.949997	−	0.312259i	$-0.898914\pi$
$229$		−	9.45067i		−	0.624518i	0.949997	−	0.312259i	$-0.101086\pi$
$230$	5.15493	+	0.436400i	0.339906	+	0.0287754i
$231$	17.0022	+	4.93761i	1.11866	+	0.324871i
$232$	−2.36905	−	8.55227i	−0.155536	−	0.561484i
$233$	8.17106	−	4.71757i	0.535304	−	0.309058i	−0.207870	−	0.978157i	$-0.566653\pi$
$233$	8.17106	−	4.71757i	0.535304	−	0.309058i	0.743174	+	0.669099i	$0.233320\pi$
$234$	2.29296	−	4.97245i	0.149895	−	0.325059i
$235$	−16.7136	+	28.9488i	−1.09027	+	1.88841i
$236$	18.9602	−	7.02193i	1.23421	−	0.457089i
$237$	4.76808	−	1.73935i	0.309720	−	0.112983i
$238$	−9.52077	−	1.86345i	−0.617140	−	0.120790i
$239$	−2.79444	+	4.84011i	−0.180757	+	0.313081i	−0.942139	−	0.335223i	$-0.891188\pi$
$239$	−2.79444	+	4.84011i	−0.180757	+	0.313081i	0.761381	+	0.648304i	$0.224522\pi$
$240$	26.1254	−	15.5033i	1.68639	−	1.00074i
$241$	3.98960			0.256993			0.128496	−	0.991710i	$-0.458985\pi$
$241$	3.98960			0.256993			0.128496	+	0.991710i	$0.458985\pi$
$242$	5.53308	+	0.468413i	0.355680	+	0.0301107i
$243$	5.27850	−	14.6676i	0.338616	−	0.940925i
$244$	−7.50535	−	6.22617i	−0.480481	−	0.398589i
$245$	−20.7249	+	22.6406i	−1.32407	+	1.44646i
$246$	−6.63153	+	1.80206i	−0.422811	+	0.114895i
$247$			2.63738i			0.167813i
$248$	−4.76229	+	1.31919i	−0.302405	+	0.0837689i
$249$	2.80726	−	15.9885i	0.177903	−	1.01323i
$250$	57.0132	+	4.82655i	3.60583	+	0.305258i
$251$		−	16.5643i		−	1.04553i	−0.852478	−	0.522764i	$-0.824901\pi$
$251$		−	16.5643i		−	1.04553i	0.852478	−	0.522764i	$-0.175099\pi$
$252$	6.49970	+	14.4829i	0.409442	+	0.912336i
$253$			3.22316i			0.202639i
$254$	1.53563	−	18.1394i	0.0963537	−	1.13817i
$255$	−18.4994	+	6.74841i	−1.15848	+	0.422602i
$256$	12.4849	+	10.0064i	0.780305	+	0.625399i
$257$		−	1.73195i		−	0.108036i	−0.998540	−	0.0540179i	$-0.982797\pi$
$257$		−	1.73195i		−	0.108036i	0.998540	−	0.0540179i	$-0.0172028\pi$
$258$	19.4487	+	5.13765i	1.21082	+	0.319856i
$259$	10.4586	−	14.2714i	0.649867	−	0.886784i
$260$	8.71117	+	7.22647i	0.540244	+	0.448167i
$261$	7.20174	−	6.06077i	0.445776	−	0.375152i
$262$	1.44514	−	17.0706i	0.0892809	−	1.05462i
$263$	11.6050			0.715593			0.357796	−	0.933800i	$-0.383528\pi$
$263$	11.6050			0.715593			0.357796	+	0.933800i	$0.383528\pi$
$264$	10.9977	+	15.4041i	0.676859	+	0.948058i
$265$	−13.3774	+	23.1704i	−0.821768	+	1.42334i
$266$	−5.76404	−	5.02372i	−0.353416	−	0.308024i
$267$	0.552060	−	3.14420i	0.0337855	−	0.192422i
$268$	−10.2287	−	27.6190i	−0.624818	−	1.68710i
$269$	2.54655	−	4.41076i	0.155266	−	0.268929i	−0.777890	−	0.628401i	$-0.783710\pi$
$269$	2.54655	−	4.41076i	0.155266	−	0.268929i	0.933156	+	0.359472i	$0.117043\pi$
$270$	26.4864	+	18.3500i	1.61191	+	1.11674i
$271$	−8.89568	+	5.13592i	−0.540374	+	0.311985i	−0.745231	−	0.666807i	$-0.767661\pi$
$271$	−8.89568	+	5.13592i	−0.540374	+	0.311985i	0.204856	+	0.978792i	$0.434327\pi$
$272$	−6.75542	−	7.86938i	−0.409608	−	0.477151i
$273$	−4.26833	+	4.09407i	−0.258331	+	0.247784i
$274$	0.708552	−	8.36970i	0.0428052	−	0.505632i
$275$			54.9654i			3.31454i
$276$	−2.20202	+	1.87165i	−0.132546	+	0.112660i
$277$		−	32.4017i		−	1.94683i	−0.229052	−	0.973414i	$-0.573562\pi$
$277$		−	32.4017i		−	1.94683i	0.229052	−	0.973414i	$-0.426438\pi$
$278$	−13.1996	+	18.9642i	−0.791658	+	1.13740i
$279$	−3.37491	−	4.01025i	−0.202050	−	0.240087i
$280$	−32.3867	+	5.27330i	−1.93548	+	0.315140i
$281$	24.2964	−	14.0275i	1.44940	−	0.836813i	0.450956	−	0.892546i	$-0.351083\pi$
$281$	24.2964	−	14.0275i	1.44940	−	0.836813i	0.998446	+	0.0557336i	$0.0177498\pi$
$282$	−4.89673	−	18.0198i	−0.291596	−	1.07306i
$283$	10.9028	+	18.8843i	0.648107	+	1.12255i	0.983575	+	0.180502i	$0.0577723\pi$
$283$	10.9028	+	18.8843i	0.648107	+	1.12255i	−0.335468	+	0.942052i	$0.608894\pi$
$284$	21.3677	+	3.64396i	1.26794	+	0.216229i
$285$	−15.2860	−	2.68393i	−0.905466	−	0.158982i
$286$	−4.02844	+	5.78777i	−0.238207	+	0.342238i
$287$	7.37872	+	0.806183i	0.435552	+	0.0475875i
$288$	−4.13765	+	16.4584i	−0.243813	+	0.969822i
$289$	−5.13866	−	8.90042i	−0.302274	−	0.523554i
$290$	8.27212	+	17.6102i	0.485756	+	1.03411i
$291$	0.136224	+	0.0239184i	0.00798562	+	0.00140212i
$292$	−12.0805	+	14.5625i	−0.706958	+	0.852204i
$293$	0.162130	−	0.280818i	0.00947174	−	0.0164055i	−0.861251	−	0.508180i	$-0.830318\pi$
$293$	0.162130	−	0.280818i	0.00947174	−	0.0164055i	0.870722	+	0.491775i	$0.163652\pi$
$294$	−0.817268	−	17.1269i	−0.0476640	−	0.998863i
$295$	−38.3893	+	22.1641i	−2.23511	+	1.29044i
$296$	18.2286	−	5.04948i	1.05952	−	0.293495i
$297$	−9.99983	+	17.4074i	−0.580249	+	1.01008i
$298$	−27.3552	−	2.31580i	−1.58464	−	0.134151i
$299$	−0.932471	−	0.538362i	−0.0539262	−	0.0311343i
$300$	−37.5515	+	31.9177i	−2.16804	+	1.84277i
$301$	−17.5254	−	12.8433i	−1.01015	−	0.740273i
$302$	0.320758	−	3.78893i	0.0184576	−	0.218028i
$303$	4.03171	−	4.81188i	0.231616	−	0.276435i
$304$	−1.50982	−	8.03331i	−0.0865939	−	0.460742i
$305$	18.5155	+	10.6899i	1.06019	+	0.612103i
$306$	4.60645	−	9.98943i	0.263333	−	0.571058i
$307$	13.3950			0.764491			0.382245	−	0.924061i	$-0.375151\pi$
$307$	13.3950			0.764491			0.382245	+	0.924061i	$0.375151\pi$
$308$	−4.97582	−	19.8288i	−0.283524	−	1.12985i
$309$	−6.35154	−	5.32174i	−0.361326	−	0.302743i
$310$	9.80615	−	4.60629i	0.556952	−	0.261620i
$311$	2.07778	+	3.59882i	0.117820	+	0.204070i	0.918904	−	0.394482i	$-0.129076\pi$
$311$	2.07778	+	3.59882i	0.117820	+	0.204070i	−0.801084	+	0.598553i	$0.795743\pi$
$312$	−6.29338	+	0.608719i	−0.356293	+	0.0344619i
$313$	−10.2417	+	17.7391i	−0.578895	+	1.00267i	0.416712	+	0.909039i	$0.363182\pi$
$313$	−10.2417	+	17.7391i	−0.578895	+	1.00267i	−0.995606	+	0.0936363i	$0.970151\pi$
$314$	−28.2214	+	13.2566i	−1.59263	+	0.748112i
$315$	−19.3852	−	28.9052i	−1.09223	−	1.62862i
$316$	−4.51059	−	3.74182i	−0.253740	−	0.210494i
$317$	2.79892	−	4.84787i	0.157203	−	0.272284i	−0.776656	−	0.629925i	$-0.783086\pi$
$317$	2.79892	−	4.84787i	0.157203	−	0.272284i	0.933859	+	0.357641i	$0.116419\pi$
$318$	−3.91930	−	14.4229i	−0.219784	−	0.808796i
$319$	−10.4978	+	6.06093i	−0.587766	+	0.339347i
$320$	−30.6706	−	17.0245i	−1.71454	−	0.951701i
$321$	−1.85844	+	10.5846i	−0.103728	+	0.590773i
$322$	2.95278	−	1.01245i	0.164552	−	0.0564215i
$323$			5.29839i			0.294810i
$324$	−17.6993	+	3.27655i	−0.983293	+	0.182031i
$325$	−15.9016	−	9.18082i	−0.882064	−	0.509260i
$326$	11.0830	+	23.5942i	0.613831	+	1.30676i
$327$	24.6018	−	8.97450i	1.36048	−	0.496291i
$328$	5.65810	+	5.56346i	0.312416	+	0.307191i
$329$	−2.19063	+	20.0501i	−0.120773	+	1.10540i
$330$	−29.4458	−	29.2384i	−1.62094	−	1.60952i
$331$	−4.04772	+	7.01085i	−0.222483	+	0.385351i	−0.955561	−	0.294793i	$-0.904749\pi$
$331$	−4.04772	+	7.01085i	−0.222483	+	0.385351i	0.733079	+	0.680144i	$0.238083\pi$
$332$	−17.5776	+	6.50986i	−0.964694	+	0.357275i
$333$	12.9181	+	15.3500i	0.707909	+	0.841177i
$334$	−3.44331	+	4.94710i	−0.188410	+	0.270693i
$335$	32.2859	+	55.9209i	1.76397	+	3.05528i
$336$	10.6574	−	14.9138i	0.581407	−	0.813613i
$337$	−2.09329	+	3.62568i	−0.114029	+	0.197503i	−0.917391	−	0.397987i	$-0.869709\pi$
$337$	−2.09329	+	3.62568i	−0.114029	+	0.197503i	0.803362	+	0.595490i	$0.203042\pi$
$338$	6.81500	+	14.5082i	0.370687	+	0.789142i
$339$	20.3371	−	7.41879i	1.10456	−	0.402933i
$340$	17.5004	+	14.5177i	0.949090	+	0.787331i
$341$	3.37500	+	5.84566i	0.182766	+	0.316560i
$342$	7.08064	−	5.00299i	0.382877	−	0.270531i
$343$	−5.93963	+	17.5420i	−0.320710	+	0.947178i
$344$	−6.20079	−	22.3848i	−0.334324	−	1.20691i
$345$	4.06923	−	4.85665i	0.219080	−	0.261473i
$346$	−5.30295	+	7.61889i	−0.285088	+	0.409594i
$347$	23.0332	−	13.2982i	1.23649	−	0.713886i	0.268113	−	0.963387i	$-0.413600\pi$
$347$	23.0332	−	13.2982i	1.23649	−	0.713886i	0.968375	+	0.249501i	$0.0802666\pi$
$348$	−10.2367	−	3.65245i	−0.548745	−	0.195792i
$349$	12.7348	−	7.35246i	0.681680	−	0.393568i	−0.118808	−	0.992917i	$-0.537907\pi$
$349$	12.7348	−	7.35246i	0.681680	−	0.393568i	0.800488	+	0.599349i	$0.204574\pi$
$350$	50.3545	−	17.2655i	2.69156	−	0.922880i
$351$	−3.36575	−	5.80052i	−0.179651	−	0.309609i
$352$	8.95708	−	19.9353i	0.477414	−	1.06256i
$353$			1.24265i			0.0661396i	0.999453	+	0.0330698i	$0.0105284\pi$
$353$			1.24265i			0.0661396i	−0.999453	+	0.0330698i	$0.989472\pi$
$354$	6.32449	−	23.9416i	0.336143	−	1.27248i
$355$	−47.5234			−2.52228
$356$	−3.45670	+	1.28019i	−0.183205	+	0.0678499i
$357$	−8.57489	+	8.22481i	−0.453831	+	0.435303i
$358$	16.3649	+	11.3904i	0.864912	+	0.602002i
$359$	4.77766	+	8.27515i	0.252155	+	0.436746i	0.964119	−	0.265471i	$-0.0855273\pi$
$359$	4.77766	+	8.27515i	0.252155	+	0.436746i	−0.711964	+	0.702216i	$0.752194\pi$
$360$	2.87637	−	37.0953i	0.151598	−	1.95510i
$361$	7.41207	−	12.8381i	0.390109	−	0.675689i
$362$	1.98822	−	23.4857i	0.104499	−	1.23438i
$363$	4.36773	−	5.21292i	0.229247	−	0.273607i
$364$	6.56764	+	1.87247i	0.344238	+	0.0981443i
$365$	20.7414	−	35.9252i	1.08566	−	1.88041i
$366$	−11.5254	+	3.13192i	−0.602441	+	0.163708i
$367$			4.26534i			0.222649i	0.993784	+	0.111325i	$0.0355093\pi$
$367$			4.26534i			0.222649i	−0.993784	+	0.111325i	$0.964491\pi$
$368$	3.14844	+	1.10601i	0.164124	+	0.0576548i
$369$	−2.86715	+	7.91305i	−0.149258	+	0.411937i
$370$	−37.5350	+	17.6315i	−1.95135	+	0.916618i
$371$	−1.75337	+	16.0480i	−0.0910302	+	0.833168i
$372$	−2.03385	+	5.70026i	−0.105450	+	0.295544i
$373$			0.134332i			0.00695545i	0.999994	+	0.00347773i	$0.00110700\pi$
$373$			0.134332i			0.00695545i	−0.999994	+	0.00347773i	$0.998893\pi$
$374$	−8.09296	+	11.6274i	−0.418477	+	0.601237i
$375$	45.0054	−	53.7142i	2.32407	−	2.77379i
$376$	−15.1175	+	15.3747i	−0.779627	+	0.792889i
$377$		−	4.04940i		−	0.208555i
$378$	19.0883	+	3.69302i	0.981794	+	0.189948i
$379$	0.388772			0.0199699			0.00998495	−	0.999950i	$-0.496822\pi$
$379$	0.388772			0.0199699			0.00998495	+	0.999950i	$0.496822\pi$
$380$	6.22385	+	16.8053i	0.319277	+	0.862094i
$381$	−17.0898	−	14.3190i	−0.875538	−	0.733584i
$382$	0.512754	−	0.736688i	0.0262348	−	0.0376922i
$383$	8.88045			0.453770			0.226885	−	0.973922i	$-0.427146\pi$
$383$	8.88045			0.453770			0.226885	+	0.973922i	$0.427146\pi$
$384$	18.8208	−	5.45688i	0.960445	−	0.278470i
$385$	18.0621	+	41.0206i	0.920529	+	2.09060i
$386$	9.80964	+	20.8834i	0.499297	+	1.06294i
$387$	18.8499	−	15.8636i	0.958196	−	0.806390i
$388$	−0.0554651	−	0.149764i	−0.00281581	−	0.00760311i
$389$	−17.1393			−0.868999			−0.434499	−	0.900672i	$-0.643075\pi$
$389$	−17.1393			−0.868999			−0.434499	+	0.900672i	$0.643075\pi$
$390$	13.3771	−	3.63510i	0.677374	−	0.184071i
$391$	−1.87329	−	1.08155i	−0.0947365	−	0.0546961i
$392$	−16.6025	+	10.7870i	−0.838551	+	0.544824i
$393$	−16.0828	−	13.4752i	−0.811270	−	0.679736i
$394$	−17.9068	−	1.51593i	−0.902131	−	0.0763715i
$395$	11.1275	+	6.42446i	0.559885	+	0.323250i
$396$	23.1803	−	0.163893i	1.16485	−	0.00823591i
$397$	23.0330	−	13.2981i	1.15599	−	0.667412i	0.205652	−	0.978625i	$-0.434069\pi$
$397$	23.0330	−	13.2981i	1.15599	−	0.667412i	0.950340	+	0.311213i	$0.100735\pi$
$398$	−12.3252	−	8.57868i	−0.617807	−	0.430010i
$399$	−9.09390	+	2.23472i	−0.455264	+	0.111876i
$400$	53.6912	+	18.8610i	2.68456	+	0.943052i
$401$			7.53690i			0.376375i	0.982133	+	0.188187i	$0.0602612\pi$
$401$			7.53690i			0.376375i	−0.982133	+	0.188187i	$0.939739\pi$
$402$	−34.8752	−	9.21276i	−1.73942	−	0.459491i
$403$	−2.25489			−0.112324
$404$	−7.14564	−	1.21859i	−0.355509	−	0.0606270i
$405$	37.0445	−	13.6047i	1.84075	−	0.676023i
$406$	8.85003	+	7.71336i	0.439219	+	0.382808i
$407$	−12.9185	−	22.3755i	−0.640345	−	1.10911i
$408$	−12.6431	+	1.22289i	−0.625928	+	0.0605421i
$409$	8.11573	+	14.0569i	0.401297	+	0.695067i	0.993883	−	0.110441i	$-0.0352262\pi$
$409$	8.11573	+	14.0569i	0.401297	+	0.695067i	−0.592586	+	0.805507i	$0.701893\pi$
$410$	−14.2789	−	9.93850i	−0.705185	−	0.490828i
$411$	−7.88540	−	6.60691i	−0.388958	−	0.325895i
$412$	−1.60850	+	9.43204i	−0.0792451	+	0.464683i
$413$	−15.8102	+	21.5740i	−0.777967	+	1.06159i
$414$	0.323501	+	3.52467i	0.0158992	+	0.173228i
$415$	35.5897	−	20.5477i	1.74703	−	1.00865i
$416$	4.27126	+	5.92109i	0.209416	+	0.290305i
$417$	9.69790	+	26.5848i	0.474908	+	1.30187i
$418$	−10.1058	+	4.74704i	−0.494291	+	0.232185i
$419$	−8.45467	−	4.88131i	−0.413038	−	0.238468i	0.279056	−	0.960275i	$-0.409978\pi$
$419$	−8.45467	−	4.88131i	−0.413038	−	0.238468i	−0.692094	+	0.721807i	$0.743312\pi$
$420$	−17.5362	+	36.1599i	−0.855681	+	1.76442i
$421$	0.968784	−	0.559328i	0.0472157	−	0.0272600i	−0.476206	−	0.879334i	$-0.657988\pi$
$421$	0.968784	−	0.559328i	0.0472157	−	0.0272600i	0.523422	+	0.852074i	$0.324655\pi$
$422$	−0.463275	+	0.665600i	−0.0225519	+	0.0324009i
$423$	−21.5021	−	7.79087i	−1.04547	−	0.378805i
$424$	−12.1000	+	12.3058i	−0.587626	+	0.597622i
$425$	−31.9457	−	18.4439i	−1.54959	−	0.894658i
$426$	18.7057	−	18.8384i	0.906292	−	0.912722i
$427$	12.8240	+	1.40112i	0.620595	+	0.0678048i
$428$	11.6366	−	4.30960i	0.562475	−	0.208313i
$429$	2.95975	+	8.11356i	0.142898	+	0.391726i
$430$	21.6516	+	46.0933i	1.04413	+	2.22281i
$431$	−17.7695	+	30.7778i	−0.855929	+	1.48251i	0.0198515	+	0.999803i	$0.493681\pi$
$431$	−17.7695	+	30.7778i	−0.855929	+	1.48251i	−0.875781	+	0.482710i	$0.839653\pi$
$432$	13.5725	+	15.7413i	0.653007	+	0.757352i
$433$	−8.72241			−0.419172			−0.209586	−	0.977790i	$-0.567212\pi$
$433$	−8.72241			−0.419172			−0.209586	+	0.977790i	$0.567212\pi$
$434$	4.29515	−	4.92809i	0.206174	−	0.236556i
$435$	23.4700	+	4.12087i	1.12530	+	0.197581i
$436$	−23.2732	−	19.3066i	−1.11458	−	0.924619i
$437$	−0.852406	−	1.47641i	−0.0407761	−	0.0706263i
$438$	6.07681	+	22.3624i	0.290361	+	1.06852i
$439$	−13.7780	−	7.95471i	−0.657586	−	0.379658i	0.133770	−	0.991012i	$-0.457292\pi$
$439$	−13.7780	−	7.95471i	−0.657586	−	0.379658i	−0.791357	+	0.611355i	$0.790625\pi$
$440$	−12.0108	+	46.3860i	−0.572591	+	2.21137i
$441$	−17.7333	−	11.2485i	−0.844444	−	0.535644i
$442$	−2.01207	−	4.28342i	−0.0957045	−	0.203742i
$443$	−24.3825	−	14.0772i	−1.15845	−	0.668830i	−0.207516	−	0.978232i	$-0.566538\pi$
$443$	−24.3825	−	14.0772i	−1.15845	−	0.668830i	−0.950931	+	0.309402i	$0.899871\pi$
$444$	7.78497	−	21.8189i	0.369458	−	1.03548i
$445$	6.99887	−	4.04080i	0.331778	−	0.191552i
$446$	−18.6677	+	8.76886i	−0.883941	+	0.415218i
$447$	−21.5938	+	25.7723i	−1.02135	+	1.21899i
$448$	−21.0766	−	1.94368i	−0.995775	−	0.0918303i
$449$		−	12.1006i		−	0.571064i	−0.958369	−	0.285532i	$-0.907830\pi$
$449$		−	12.1006i		−	0.571064i	0.958369	−	0.285532i	$-0.0921702\pi$
$450$	5.51675	+	60.1070i	0.260062	+	2.83347i
$451$	5.41947	−	9.38680i	0.255193	−	0.442007i
$452$	−19.2388	−	15.9598i	−0.904918	−	0.750688i
$453$	−3.56969	−	2.99092i	−0.167719	−	0.140526i
$454$	1.38368	−	16.3446i	0.0649392	−	0.767088i
$455$	−14.8843	−	1.62622i	−0.697786	−	0.0762386i
$456$	−9.11142	−	4.14758i	−0.426682	−	0.194228i
$457$	13.1995	−	22.8622i	0.617448	−	1.06945i	−0.372502	−	0.928031i	$-0.621500\pi$
$457$	13.1995	−	22.8622i	0.617448	−	1.06945i	0.989950	−	0.141419i	$-0.0451665\pi$
$458$	−1.12743	+	13.3176i	−0.0526812	+	0.622292i
$459$	−6.76165	−	11.6530i	−0.315607	−	0.543915i
$460$	−7.21213	−	1.22993i	−0.336267	−	0.0573456i
$461$	−15.0297	−	26.0322i	−0.700002	−	1.21244i	−0.968465	−	0.249150i	$-0.919849\pi$
$461$	−15.0297	−	26.0322i	−0.700002	−	1.21244i	0.268463	−	0.963290i	$-0.413484\pi$
$462$	−23.3701	−	8.98625i	−1.08727	−	0.418078i
$463$	15.9088	+	9.18492i	0.739343	+	0.426860i	0.821830	−	0.569732i	$-0.192953\pi$
$463$	15.9088	+	9.18492i	0.739343	+	0.426860i	−0.0824876	+	0.996592i	$0.526287\pi$
$464$	2.31815	+	12.3342i	0.107617	+	0.572603i
$465$	2.29469	−	13.0691i	0.106413	−	0.606067i
$466$	−12.0772	+	5.67309i	−0.559467	+	0.262801i
$467$	1.90588	−	1.10036i	0.0881934	−	0.0509185i	−0.455255	−	0.890361i	$-0.650452\pi$
$467$	1.90588	−	1.10036i	0.0881934	−	0.0509185i	0.543448	+	0.839443i	$0.317118\pi$
$468$	−3.82437	+	6.73350i	−0.176782	+	0.311256i
$469$	31.4264	+	23.0303i	1.45113	+	1.06344i
$470$	27.0058	−	38.7999i	1.24568	−	1.78971i
$471$	−6.60395	+	37.6121i	−0.304294	+	1.73307i
$472$	−27.5559	+	7.63323i	−1.26837	+	0.351348i
$473$	−27.4772	+	15.8640i	−1.26340	+	0.729426i
$474$	−6.92655	+	1.88223i	−0.318147	+	0.0864538i
$475$	−14.5363	−	25.1776i	−0.666970	−	1.15523i
$476$	13.1941	+	3.76172i	0.604751	+	0.172418i
$477$	−17.2101	−	6.23575i	−0.787996	−	0.285515i
$478$	4.51526	−	6.48719i	0.206523	−	0.296717i
$479$	10.0229			0.457958			0.228979	−	0.973431i	$-0.426461\pi$
$479$	10.0229			0.457958			0.228979	+	0.973431i	$0.426461\pi$
$480$	−38.6647	+	18.7302i	−1.76480	+	0.854914i
$481$	8.63104			0.393542
$482$	−5.62204	−	0.475944i	−0.256077	−	0.0216786i
$483$	1.06621	−	3.67140i	0.0485142	−	0.167054i
$484$	−7.74119	−	1.32015i	−0.351872	−	0.0600068i
$485$	0.175070	+	0.303231i	0.00794953	+	0.0137690i
$486$	−9.18810	+	20.0394i	−0.416781	+	0.909007i
$487$	13.9155	+	8.03413i	0.630573	+	0.364061i	0.780974	−	0.624564i	$-0.214723\pi$
$487$	13.9155	+	8.03413i	0.630573	+	0.364061i	−0.150401	+	0.988625i	$0.548057\pi$
$488$	9.83358	+	9.66910i	0.445145	+	0.437700i
$489$	31.4451	+	5.52115i	1.42200	+	0.249675i
$490$	31.9059	−	29.4321i	1.44136	−	1.32961i
$491$	−4.05631	−	2.34191i	−0.183059	−	0.105689i	0.405670	−	0.914019i	$-0.367038\pi$
$491$	−4.05631	−	2.34191i	−0.183059	−	0.105689i	−0.588729	+	0.808331i	$0.700371\pi$
$492$	9.55995	−	1.74830i	0.430996	−	0.0788196i
$493$		−	8.13507i		−	0.366385i
$494$	0.314629	−	3.71653i	0.0141558	−	0.167215i
$495$	−50.0374	+	8.89767i	−2.24901	+	0.399921i
$496$	6.86826	−	1.29085i	0.308394	−	0.0579609i
$497$	−26.2435	+	11.5555i	−1.17718	+	0.518333i
$498$	−5.86328	+	22.1956i	−0.262740	+	0.994610i
$499$	−7.29188			−0.326430			−0.163215	−	0.986591i	$-0.552186\pi$
$499$	−7.29188			−0.326430			−0.163215	+	0.986591i	$0.552186\pi$
$500$	−79.7657	−	13.6029i	−3.56723	−	0.608340i
$501$	2.52985	+	6.93507i	0.113025	+	0.309836i
$502$	−1.97605	+	23.3419i	−0.0881955	+	1.04180i
$503$	−5.58927			−0.249213			−0.124607	−	0.992206i	$-0.539767\pi$
$503$	−5.58927			−0.249213			−0.124607	+	0.992206i	$0.539767\pi$
$504$	−7.43145	−	21.1843i	−0.331023	−	0.943623i
$505$	15.8925			0.707205
$506$	0.384511	−	4.54200i	0.0170936	−	0.201916i
$507$	19.3358	+	3.39498i	0.858732	+	0.150777i
$508$	−4.32792	+	25.3784i	−0.192021	+	1.12598i
$509$	−17.6198			−0.780984			−0.390492	−	0.920606i	$-0.627695\pi$
$509$	−17.6198			−0.780984			−0.390492	+	0.920606i	$0.627695\pi$
$510$	26.8739	−	7.30276i	1.19000	−	0.323372i
$511$	2.71856	−	24.8821i	0.120262	−	1.10072i
$512$	−16.3996	−	15.5901i	−0.724768	−	0.688993i
$513$	−0.0230644	−	10.6183i	−0.00101832	−	0.468808i
$514$	−0.206614	+	2.44061i	−0.00911336	+	0.107651i
$515$		−	20.9776i		−	0.924383i
$516$	−26.7937	−	9.55999i	−1.17953	−	0.420855i
$517$	25.5067	+	14.7263i	1.12178	+	0.647661i
$518$	−16.4405	+	18.8633i	−0.722356	+	0.828804i
$519$	3.89614	+	10.6805i	0.171022	+	0.468822i
$520$	−11.4135	−	11.2226i	−0.500513	−	0.492142i
$521$	−30.2825	−	17.4836i	−1.32670	−	0.765970i	−0.341911	−	0.939732i	$-0.611074\pi$
$521$	−30.2825	−	17.4836i	−1.32670	−	0.765970i	−0.984788	+	0.173762i	$0.944408\pi$
$522$	−10.8715	+	7.68153i	−0.475833	+	0.336211i
$523$	18.2681	+	31.6412i	0.798807	+	1.38357i	0.920394	+	0.390993i	$0.127868\pi$
$523$	18.2681	+	31.6412i	0.798807	+	1.38357i	−0.121587	+	0.992581i	$0.538798\pi$
$524$	−4.07290	+	23.8830i	−0.177925	+	1.04333i
$525$	18.1823	−	62.6092i	0.793540	−	2.73249i
$526$	−16.3534	−	1.38443i	−0.713042	−	0.0603638i
$527$	−4.52997			−0.197329
$528$	−13.6600	−	23.0190i	−0.594473	−	1.00178i
$529$	−22.3040			−0.969739
$530$	21.6152	−	31.0552i	0.938905	−	1.34895i
$531$	−19.5282	−	23.2044i	−0.847451	−	1.00699i
$532$	7.52321	+	7.76692i	0.326173	+	0.336739i
$533$	1.81042	+	3.13574i	0.0784180	+	0.135824i
$534$	−1.15304	+	4.36486i	−0.0498968	+	0.188886i
$535$	−23.5608	+	13.6029i	−1.01862	+	0.588103i
$536$	11.1192	+	40.1402i	0.480275	+	1.73379i
$537$	22.9411	−	8.36868i	0.989980	−	0.361135i
$538$	−4.11472	+	5.91173i	−0.177398	+	0.254873i
$539$	19.9486	+	18.2607i	0.859246	+	0.786542i
$540$	−35.1349	−	29.0180i	−1.51196	−	1.24874i
$541$	−21.7801	+	12.5747i	−0.936400	+	0.540631i	−0.888830	−	0.458237i	$-0.848481\pi$
$541$	−21.7801	+	12.5747i	−0.936400	+	0.540631i	−0.0475698	+	0.998868i	$0.515148\pi$
$542$	13.1482	−	6.17619i	0.564766	−	0.265290i
$543$	−22.1267	−	18.5392i	−0.949549	−	0.795595i
$544$	8.58077	+	11.8952i	0.367898	+	0.510003i
$545$	57.4143	+	33.1482i	2.45936	+	1.41991i
$546$	6.50322	−	5.26006i	0.278312	−	0.225110i
$547$	4.40044	+	7.62179i	0.188149	+	0.325884i	0.944633	−	0.328128i	$-0.106418\pi$
$547$	4.40044	+	7.62179i	0.188149	+	0.325884i	−0.756484	+	0.654012i	$0.773084\pi$
$548$	−1.99694	+	11.7098i	−0.0853052	+	0.500219i
$549$	−4.98300	+	13.7526i	−0.212669	+	0.586947i
$550$	6.55715	−	77.4557i	0.279598	−	3.30272i
$551$	3.20577	−	5.55256i	0.136571	−	0.236547i
$552$	3.32631	−	2.37479i	0.141577	−	0.101078i
$553$	7.70698	+	0.842048i	0.327734	+	0.0358075i
$554$	−3.86539	+	45.6596i	−0.164225	+	1.93989i
$555$	−8.78337	+	50.0247i	−0.372833	+	2.12343i
$556$	20.8628	−	25.1492i	0.884781	−	1.06656i
$557$	10.1021	−	17.4973i	0.428038	−	0.741384i	−0.568661	−	0.822572i	$-0.692538\pi$
$557$	10.1021	−	17.4973i	0.428038	−	0.741384i	0.996699	+	0.0811886i	$0.0258716\pi$
$558$	4.27742	+	6.05375i	0.181078	+	0.256276i
$559$		−	10.5990i		−	0.448289i
$560$	46.2676	−	3.56738i	1.95516	−	0.150749i
$561$	5.94600	+	16.2998i	0.251040	+	0.688177i
$562$	−35.9113	+	16.8688i	−1.51483	+	0.711566i
$563$	−8.68687	+	5.01537i	−0.366108	+	0.211373i	−0.671757	−	0.740772i	$-0.734460\pi$
$563$	−8.68687	+	5.01537i	−0.366108	+	0.211373i	0.305649	+	0.952144i	$0.401127\pi$
$564$	4.75065	+	25.9772i	0.200038	+	1.09384i
$565$	47.4617	+	27.4020i	1.99673	+	1.15281i
$566$	−13.1112	−	27.9119i	−0.551104	−	1.17322i
$567$	17.1488	−	16.5203i	0.720180	−	0.693787i
$568$	−29.6761	−	7.68405i	−1.24518	−	0.322415i
$569$	−10.6111	−	6.12632i	−0.444840	−	0.256829i	0.260808	−	0.965391i	$-0.416011\pi$
$569$	−10.6111	−	6.12632i	−0.444840	−	0.256829i	−0.705649	+	0.708562i	$0.749344\pi$
$570$	21.2205	+	5.60568i	0.888828	+	0.234796i
$571$	−7.16018	−	12.4018i	−0.299644	−	0.518999i	0.676410	−	0.736525i	$-0.263535\pi$
$571$	−7.16018	−	12.4018i	−0.299644	−	0.518999i	−0.976055	+	0.217526i	$0.930201\pi$
$572$	6.36723	−	7.67539i	0.266227	−	0.320924i
$573$	−0.376727	−	1.03272i	−0.0157380	−	0.0431426i
$574$	−10.3017	−	2.01630i	−0.429985	−	0.0841588i
$575$	11.8690			0.494972
$576$	7.79409	−	22.6992i	0.324754	−	0.945799i
$577$	6.91236	−	11.9726i	0.287765	−	0.498424i	−0.685511	−	0.728063i	$-0.740421\pi$
$577$	6.91236	−	11.9726i	0.287765	−	0.498424i	0.973276	+	0.229638i	$0.0737543\pi$
$578$	6.17948	+	13.1553i	0.257032	+	0.547187i
$579$	27.8323	+	4.88680i	1.15667	+	0.203089i
$580$	−9.55602	−	25.8027i	−0.396792	−	1.07140i
$581$	14.6572	−	20.0007i	0.608083	−	0.829768i
$582$	−0.189110	−	0.0499561i	−0.00783888	−	0.00207075i
$583$	20.4153	+	11.7868i	0.845517	+	0.488160i
$584$	18.7608	−	19.0799i	0.776326	−	0.789531i
$585$	5.78358	−	15.9621i	0.239122	−	0.659953i
$586$	−0.261970	+	0.376379i	−0.0108219	+	0.0155481i
$587$	−23.3668	+	13.4908i	−0.964450	+	0.556825i	−0.897540	−	0.440934i	$-0.854647\pi$
$587$	−23.3668	+	13.4908i	−0.964450	+	0.556825i	−0.0669100	+	0.997759i	$0.521314\pi$
$588$	−0.891504	+	24.2323i	−0.0367650	+	0.999324i
$589$	−3.09192	−	1.78512i	−0.127400	−	0.0735546i
$590$	56.7412	−	26.6533i	2.33600	−	1.09730i
$591$	−14.1353	+	16.8706i	−0.581450	+	0.693965i
$592$	−26.2896	+	4.94099i	−1.08050	+	0.203073i
$593$	−13.8382	+	7.98950i	−0.568268	+	0.328090i	−0.756457	−	0.654043i	$-0.773071\pi$
$593$	−13.8382	+	7.98950i	−0.568268	+	0.328090i	0.188189	+	0.982133i	$0.439738\pi$
$594$	16.1681	−	23.3371i	0.663386	−	0.957534i
$595$	−29.9019	−	3.26701i	−1.22586	−	0.133934i
$596$	38.2719	+	6.52673i	1.56768	+	0.267345i
$597$	−17.2781	+	6.30287i	−0.707144	+	0.257959i
$598$	1.24979	+	0.869886i	0.0511076	+	0.0355723i
$599$	−11.5441	−	19.9949i	−0.471678	−	0.816970i	0.527797	−	0.849371i	$-0.323018\pi$
$599$	−11.5441	−	19.9949i	−0.471678	−	0.816970i	−0.999475	+	0.0324004i	$0.989685\pi$
$600$	56.7243	−	40.4979i	2.31576	−	1.65332i
$601$	−11.4094	−	19.7616i	−0.465398	−	0.806094i	0.533821	−	0.845598i	$-0.320756\pi$
$601$	−11.4094	−	19.7616i	−0.465398	−	0.806094i	−0.999219	+	0.0395037i	$0.987422\pi$
$602$	23.1642	+	20.1891i	0.944103	+	0.822845i
$603$	−33.8015	+	28.4463i	−1.37650	+	1.15842i
$604$	−0.904008	+	5.30099i	−0.0367836	+	0.215694i
$605$	17.2170			0.699971
$606$	−6.25542	+	6.29980i	−0.254109	+	0.255912i
$607$		−	1.09571i		−	0.0444733i	−0.999753	−	0.0222367i	$-0.992921\pi$
$607$		−	1.09571i		−	0.0444733i	0.999753	−	0.0222367i	$-0.00707873\pi$
$608$	1.16925	+	11.5004i	0.0474193	+	0.466404i
$609$	13.9626	−	3.43116i	0.565795	−	0.139038i
$610$	−24.8163	−	17.2728i	−1.00478	−	0.699354i
$611$	−8.52071	+	4.91944i	−0.344711	+	0.199019i
$612$	−7.68299	+	13.5273i	−0.310566	+	0.546809i
$613$	−25.9526	−	14.9837i	−1.04821	−	0.605187i	−0.126065	−	0.992022i	$-0.540235\pi$
$613$	−25.9526	−	14.9837i	−1.04821	−	0.605187i	−0.922149	+	0.386835i	$0.873568\pi$
$614$	−18.8758	−	1.59797i	−0.761766	−	0.0644887i
$615$	−20.0168	+	7.30195i	−0.807156	+	0.294443i
$616$	4.64629	+	28.5358i	0.187204	+	1.14974i
$617$	11.0806	+	6.39736i	0.446086	+	0.257548i	0.706176	−	0.708036i	$-0.250419\pi$
$617$	11.0806	+	6.39736i	0.446086	+	0.257548i	−0.260090	+	0.965585i	$0.583752\pi$
$618$	8.31555	+	8.25697i	0.334501	+	0.332144i
$619$	−10.1911			−0.409615			−0.204808	−	0.978802i	$-0.565657\pi$
$619$	−10.1911			−0.409615			−0.204808	+	0.978802i	$0.565657\pi$
$620$	−14.3681	+	5.32122i	−0.577036	+	0.213705i
$621$	3.75889	+	2.15932i	0.150839	+	0.0866507i
$622$	−2.49862	−	5.31923i	−0.100186	−	0.213282i
$623$	2.88240	−	3.93322i	0.115481	−	0.157581i
$624$	8.94108	−	0.107015i	0.357930	−	0.00428402i
$625$	106.270			4.25082
$626$	16.5485	−	23.7757i	0.661412	−	0.950269i
$627$	−2.36480	+	13.4685i	−0.0944411	+	0.537879i
$628$	41.3503	−	15.3141i	1.65006	−	0.611100i
$629$	17.3394			0.691367
$630$	23.8688	+	43.0450i	0.950956	+	1.71495i
$631$			5.59028i			0.222546i	0.993790	+	0.111273i	$0.0354927\pi$
$631$			5.59028i			0.222546i	−0.993790	+	0.111273i	$0.964507\pi$
$632$	5.90981	+	5.81097i	0.235080	+	0.231148i
$633$	0.340374	+	0.933068i	0.0135287	+	0.0370861i
$634$	−4.52249	+	6.49759i	−0.179611	+	0.258052i
$635$		−	56.4435i		−	2.23989i
$636$	3.80238	+	20.7919i	0.150774	+	0.824453i
$637$	−8.61485	+	2.72112i	−0.341333	+	0.107815i
$638$	15.5163	−	7.28854i	0.614297	−	0.288556i
$639$	−5.69241	−	32.0121i	−0.225188	−	1.26638i
$640$	41.1893	+	27.6494i	1.62815	+	1.09294i
$641$		−	42.3480i		−	1.67265i	−0.548237	−	0.836323i	$-0.684701\pi$
$641$		−	42.3480i		−	1.67265i	0.548237	−	0.836323i	$-0.315299\pi$
$642$	3.88156	−	14.6938i	0.153193	−	0.579917i
$643$	12.0191	−	20.8177i	0.473986	−	0.820968i	−0.525570	−	0.850750i	$-0.676148\pi$
$643$	12.0191	−	20.8177i	0.473986	−	0.820968i	0.999556	+	0.0297820i	$0.00948130\pi$
$644$	−4.28176	+	1.07446i	−0.168725	+	0.0423396i
$645$	61.4307	+	10.7860i	2.41883	+	0.424700i
$646$	0.632077	−	7.46634i	0.0248687	−	0.293759i
$647$	−8.84729	+	15.3240i	−0.347823	+	0.602447i	−0.985862	−	0.167557i	$-0.946412\pi$
$647$	−8.84729	+	15.3240i	−0.347823	+	0.602447i	0.638039	+	0.770004i	$0.279746\pi$
$648$	25.3322	−	2.50578i	0.995143	−	0.0984362i
$649$	19.5287	+	33.8247i	0.766568	+	1.32774i
$650$	21.3129	+	14.8344i	0.835962	+	0.581852i
$651$	−1.91062	−	7.77503i	−0.0748832	−	0.304727i
$652$	−12.8032	−	34.5705i	−0.501411	−	1.35388i
$653$	−40.2200			−1.57393			−0.786965	−	0.616998i	$-0.788349\pi$
$653$	−40.2200			−1.57393			−0.786965	+	0.616998i	$0.788349\pi$
$654$	−35.7388	+	9.71173i	−1.39750	+	0.379759i
$655$		−	53.1176i		−	2.07547i
$656$	−7.30954	−	8.51487i	−0.285389	−	0.332450i
$657$	26.6839	+	9.66841i	1.04104	+	0.377201i
$658$	5.47888	−	27.9927i	0.213589	−	1.09127i
$659$	3.41858	−	1.97372i	0.133169	−	0.0768851i	−0.431936	−	0.901904i	$-0.642169\pi$
$659$	3.41858	−	1.97372i	0.133169	−	0.0768851i	0.565104	+	0.825019i	$0.308836\pi$
$660$	38.0063	+	44.7147i	1.47939	+	1.74052i
$661$	0.756637	−	0.436845i	0.0294298	−	0.0169913i	−0.485213	−	0.874396i	$-0.661258\pi$
$661$	0.756637	−	0.436845i	0.0294298	−	0.0169913i	0.514643	+	0.857405i	$0.327925\pi$
$662$	6.54030	−	9.39662i	0.254196	−	0.365210i
$663$	−5.70873	−	1.00234i	−0.221709	−	0.0389277i
$664$	25.5464	−	7.07658i	0.991394	−	0.274625i
$665$	−19.1220	−	14.0133i	−0.741518	−	0.543411i
$666$	−16.3727	−	23.1719i	−0.634429	−	0.897894i
$667$	1.30877	+	2.26686i	0.0506759	+	0.0877732i
$668$	5.44239	−	6.56055i	0.210573	−	0.253835i
$669$	−4.36833	+	24.8793i	−0.168889	+	0.961891i
$670$	−38.8253	−	82.6538i	−1.49995	−	3.19319i
$671$	9.41886	−	16.3139i	0.363611	−	0.629793i
$672$	−16.7972	+	19.7447i	−0.647967	+	0.761669i
$673$	24.6669	+	42.7243i	0.950840	+	1.64690i	0.743614	+	0.668609i	$0.233110\pi$
$673$	24.6669	+	42.7243i	0.950840	+	1.64690i	0.207226	+	0.978293i	$0.433557\pi$
$674$	3.38233	−	4.85949i	0.130283	−	0.187180i
$675$	64.1012	+	36.8234i	2.46726	+	1.41734i
$676$	−7.87274	−	21.2576i	−0.302798	−	0.817598i
$677$	17.4555	−	30.2338i	0.670870	−	1.16198i	−0.306788	−	0.951778i	$-0.599254\pi$
$677$	17.4555	−	30.2338i	0.670870	−	1.16198i	0.977658	−	0.210202i	$-0.0674123\pi$
$678$	−29.5435	+	8.02821i	−1.13461	+	0.308322i
$679$	0.170409	+	0.124882i	0.00653970	+	0.00479253i
$680$	−22.9291	−	22.5456i	−0.879292	−	0.864585i
$681$	−15.3988	−	12.9021i	−0.590083	−	0.494411i
$682$	−4.05859	−	8.64018i	−0.155411	−	0.330849i
$683$	−4.93956	−	2.85186i	−0.189007	−	0.109123i	0.402511	−	0.915415i	$-0.368138\pi$
$683$	−4.93956	−	2.85186i	−0.189007	−	0.109123i	−0.591518	+	0.806292i	$0.701471\pi$
$684$	−10.5747	+	6.20539i	−0.404333	+	0.237269i
$685$		−	26.0436i		−	0.995073i
$686$	10.4626	−	24.0111i	0.399466	−	0.916748i
$687$	12.5470	+	10.5127i	0.478699	+	0.401086i
$688$	6.06757	+	32.2838i	0.231324	+	1.23081i
$689$	−6.81991	+	3.93748i	−0.259818	+	0.150006i
$690$	−6.31362	+	6.35842i	−0.240355	+	0.242061i
$691$	−3.00930	+	5.21227i	−0.114479	+	0.198284i	−0.917572	−	0.397571i	$-0.869853\pi$
$691$	−3.00930	+	5.21227i	−0.114479	+	0.198284i	0.803092	+	0.595855i	$0.203187\pi$
$692$	8.38167	−	10.1037i	0.318623	−	0.384085i
$693$	−25.4683	+	17.0802i	−0.967460	+	0.648825i
$694$	−34.0442	+	15.9917i	−1.29230	+	0.607038i
$695$	−35.8201	+	62.0423i	−1.35873	+	2.35340i
$696$	13.9896	+	6.36814i	0.530273	+	0.241384i
$697$	3.63705	+	6.29956i	0.137763	+	0.238613i
$698$	−18.8227	+	8.84168i	−0.712450	+	0.334662i
$699$	−2.82613	+	16.0959i	−0.106894	+	0.608803i
$700$	−73.0179	+	18.3230i	−2.75982	+	0.692544i
$701$	−12.0833			−0.456382			−0.228191	−	0.973616i	$-0.573281\pi$
$701$	−12.0833			−0.456382			−0.228191	+	0.973616i	$0.573281\pi$
$702$	4.05095	+	8.57546i	0.152893	+	0.323660i
$703$	11.8349	+	6.83290i	0.446363	+	0.257708i
$704$	−15.0003	+	27.0238i	−0.565344	+	1.01850i
$705$	−19.8415	−	54.3915i	−0.747274	−	2.04850i
$706$	0.148243	−	1.75111i	0.00557921	−	0.0659039i
$707$	8.77617	−	3.86430i	0.330062	−	0.145332i
$708$	−11.7684	+	32.9833i	−0.442285	+	1.23959i
$709$	31.0160	+	17.9071i	1.16483	+	0.672515i	0.952457	−	0.304674i	$-0.0985475\pi$
$709$	31.0160	+	17.9071i	1.16483	+	0.672515i	0.212373	+	0.977189i	$0.431881\pi$
$710$	66.9687	+	5.66936i	2.51329	+	0.212767i
$711$	−2.99470	+	8.26508i	−0.112310	+	0.309965i
$712$	5.02381	−	1.39164i	0.188275	−	0.0521539i
$713$	1.26229	−	0.728783i	0.0472731	−	0.0272932i
$714$	13.0647	−	10.5672i	0.488934	−	0.395468i
$715$	−10.9321	+	18.9350i	−0.408838	+	0.708128i
$716$	−21.7021	−	18.0033i	−0.811047	−	0.672816i
$717$	−3.31742	−	9.09404i	−0.123891	−	0.339623i
$718$	−5.74536	−	12.2311i	−0.214415	−	0.456460i
$719$	−14.9649	−	25.9199i	−0.558096	−	0.966650i	−0.997655	−	0.0684366i	$-0.978199\pi$
$719$	−14.9649	−	25.9199i	−0.558096	−	0.966650i	0.439560	−	0.898213i	$-0.355134\pi$
$720$	−8.47863	+	51.9306i	−0.315980	+	1.93534i
$721$	−5.10076	−	11.5843i	−0.189962	−	0.431422i
$722$	−11.9764	+	17.2069i	−0.445716	+	0.640373i
$723$	−4.43795	+	5.29673i	−0.165049	+	0.196988i
$724$	−5.60350	+	32.8582i	−0.208252	+	1.22117i
$725$	22.3188	+	38.6573i	0.828900	+	1.43570i
$726$	−6.77677	+	6.82485i	−0.251510	+	0.253294i
$727$	−16.4880	+	9.51935i	−0.611506	+	0.353053i	−0.773555	−	0.633730i	$-0.781523\pi$
$727$	−16.4880	+	9.51935i	−0.611506	+	0.353053i	0.162049	+	0.986783i	$0.448190\pi$
$728$	−9.03157	−	3.42213i	−0.334732	−	0.126833i
$729$	13.6015	+	23.3238i	0.503758	+	0.863845i
$730$	−33.5140	+	48.1505i	−1.24041	+	1.78213i
$731$		−	21.2929i		−	0.787546i
$732$	16.6149	−	3.03849i	0.614103	−	0.112306i
$733$		−	46.7923i		−	1.72831i	−0.503224	−	0.864156i	$-0.667853\pi$
$733$		−	46.7923i		−	1.72831i	0.503224	−	0.864156i	$-0.332147\pi$
$734$	0.508839	−	6.01061i	0.0187816	−	0.221856i
$735$	−7.00447	−	52.7000i	−0.258364	−	1.94387i
$736$	−4.30476	−	1.93416i	−0.158676	−	0.0712940i
$737$	49.2717	−	28.4471i	1.81495	−	1.04786i
$738$	4.98430	−	10.8088i	0.183475	−	0.397878i
$739$	−8.62325	+	14.9359i	−0.317211	+	0.549426i	−0.979905	−	0.199464i	$-0.936080\pi$
$739$	−8.62325	+	14.9359i	−0.317211	+	0.549426i	0.662694	+	0.748891i	$0.269413\pi$
$740$	54.9967	−	20.3680i	2.02172	−	0.748744i
$741$	−3.50148	−	2.93377i	−0.128630	−	0.107775i
$742$	4.38525	−	22.4052i	0.160988	−	0.822520i
$743$	7.72330	−	13.3771i	0.283340	−	0.490760i	−0.688865	−	0.724890i	$-0.741891\pi$
$743$	7.72330	−	13.3771i	0.283340	−	0.490760i	0.972205	+	0.234130i	$0.0752241\pi$
$744$	3.54606	−	7.79002i	0.130005	−	0.285596i
$745$	−85.1197			−3.11855
$746$	0.0160253	−	0.189297i	0.000586727	−	0.00693066i
$747$	18.1041	+	21.5123i	0.662394	+	0.787093i
$748$	12.7915	−	15.4195i	0.467703	−	0.563793i
$749$	−9.70325	+	13.2407i	−0.354549	+	0.483804i
$750$	−69.8282	+	70.3237i	−2.54977	+	2.56786i
$751$		−	22.6675i		−	0.827149i	−0.910470	−	0.413574i	$-0.864280\pi$
$751$		−	22.6675i		−	0.827149i	0.910470	−	0.413574i	$-0.135720\pi$
$752$	23.1374	−	19.8621i	0.843733	−	0.724298i
$753$	21.9913	+	18.4258i	0.801407	+	0.671472i
$754$	−0.483078	+	5.70631i	−0.0175927	+	0.207812i
$755$		−	11.7898i		−	0.429075i
$756$	−26.4581	−	7.48125i	−0.962272	−	0.272091i
$757$		−	21.0997i		−	0.766880i	−0.923566	−	0.383440i	$-0.874739\pi$
$757$		−	21.0997i		−	0.766880i	0.923566	−	0.383440i	$-0.125261\pi$
$758$	−0.547847	−	0.0463790i	−0.0198987	−	0.00168456i
$759$	−4.27918	−	3.58538i	−0.155324	−	0.130141i
$760$	−6.76568	−	24.4241i	−0.245417	−	0.885954i
$761$			24.9627i			0.904896i	0.891791	+	0.452448i	$0.149449\pi$
$761$			24.9627i			0.904896i	−0.891791	+	0.452448i	$0.850551\pi$
$762$	22.3743	+	22.2167i	0.810536	+	0.804825i
$763$	39.7656	+	4.34470i	1.43961	+	0.157289i
$764$	−0.810443	+	0.976951i	−0.0293208	+	0.0353448i
$765$	11.6190	−	32.0672i	0.420084	−	1.15939i
$766$	−12.5141	−	1.05940i	−0.452153	−	0.0382778i
$767$	−13.0474			−0.471116
$768$	−27.1727	+	5.44444i	−0.980512	+	0.196459i
$769$	−17.8104	+	30.8486i	−0.642261	+	1.11243i	0.342666	+	0.939457i	$0.388670\pi$
$769$	−17.8104	+	30.8486i	−0.642261	+	1.11243i	−0.984927	+	0.172971i	$0.944663\pi$
$770$	−20.5590	−	59.9599i	−0.740895	−	2.16080i
$771$	2.29939	+	1.92658i	0.0828105	+	0.0693841i
$772$	−11.3322	−	30.5985i	−0.407854	−	1.10127i
$773$	−0.908270	+	1.57317i	−0.0326682	+	0.0565830i	−0.881897	−	0.471442i	$-0.843734\pi$
$773$	−0.908270	+	1.57317i	−0.0326682	+	0.0565830i	0.849229	+	0.528025i	$0.177067\pi$
$774$	−28.4553	+	20.1058i	−1.02280	+	0.722687i
$775$	21.5261	−	12.4281i	0.773241	−	0.446431i
$776$	0.0602936	+	0.217660i	0.00216442	+	0.00781353i
$777$	7.31329	+	29.7605i	0.262363	+	1.06765i
$778$	24.1523	+	2.04465i	0.865902	+	0.0733044i
$779$			5.73299i			0.205406i
$780$	−19.2842	+	3.52666i	−0.690487	+	0.126275i
$781$			41.8728i			1.49832i
$782$	2.51077	+	1.74756i	0.0897849	+	0.0624927i
$783$	0.0354128	+	16.3031i	0.00126555	+	0.582627i
$784$	24.6826	−	13.2201i	0.881520	−	0.472146i
$785$	−83.7231	+	48.3375i	−2.98820	+	1.72524i
$786$	21.0559	+	20.9076i	0.751039	+	0.745748i
$787$	−14.2231	−	24.6351i	−0.506998	−	0.878146i	−0.999967	−	0.00809955i	$-0.997422\pi$
$787$	−14.2231	−	24.6351i	−0.506998	−	0.878146i	0.492969	−	0.870047i	$-0.335912\pi$
$788$	25.0529	+	4.27242i	0.892473	+	0.152199i
$789$	−12.9091	+	15.4071i	−0.459577	+	0.548509i
$790$	−14.9141	−	10.3806i	−0.530621	−	0.369327i
$791$	32.8723	+	3.59155i	1.16880	+	0.127701i
$792$	−32.6846	−	2.53436i	−1.16140	−	0.0900547i
$793$	3.14645	+	5.44981i	0.111734	+	0.193528i
$794$	−34.0439	+	15.9916i	−1.20817	+	0.567520i
$795$	−15.8810	−	43.5346i	−0.563241	−	1.54401i
$796$	16.3450	+	13.5592i	0.579332	+	0.480593i
$797$	−15.4667	+	26.7891i	−0.547859	+	0.948920i	0.450562	+	0.892745i	$0.351224\pi$
$797$	−15.4667	+	26.7891i	−0.547859	+	0.948920i	−0.998421	+	0.0561744i	$0.982110\pi$
$798$	13.0815	−	2.06424i	0.463079	−	0.0730733i
$799$	−17.1177	+	9.88293i	−0.605582	+	0.349633i
$800$	−73.4101	−	32.9836i	−2.59544	−	1.16615i
$801$	3.56024	+	4.23048i	0.125795	+	0.149477i
$802$	0.899122	−	10.6208i	0.0317491	−	0.375033i
$803$	−31.6536	−	18.2752i	−1.11703	−	0.644918i
$804$	48.0461	+	17.1428i	1.69446	+	0.604582i
$805$	8.85783	−	3.90026i	0.312198	−	0.137466i
$806$	3.17753	+	0.268999i	0.111924	+	0.00947510i
$807$	3.02314	+	8.28733i	0.106420	+	0.291728i
$808$	9.92407	+	2.56965i	0.349128	+	0.0903999i
$809$	5.37967	+	3.10596i	0.189139	+	0.109200i	0.591580	−	0.806247i	$-0.298505\pi$
$809$	5.37967	+	3.10596i	0.189139	+	0.109200i	−0.402440	+	0.915446i	$0.631838\pi$
$810$	−53.8250	+	14.7521i	−1.89122	+	0.518337i
$811$	37.0250			1.30012			0.650062	−	0.759881i	$-0.274743\pi$
$811$	37.0250			1.30012			0.650062	+	0.759881i	$0.274743\pi$
$812$	−11.5510	−	11.9252i	−0.405362	−	0.418494i
$813$	3.07675	−	17.5233i	0.107906	−	0.614569i
$814$	15.5351	+	33.0720i	0.544504	+	1.15917i
$815$	40.4120	+	69.9957i	1.41557	+	2.45184i
$816$	17.9622	−	0.214988i	0.628804	−	0.00752608i
$817$	8.39085	−	14.5334i	0.293559	−	0.508458i
$818$	−9.75954	−	20.7767i	−0.341234	−	0.726441i
$819$	−0.687419	−	10.2209i	−0.0240204	−	0.357149i
$820$	18.9358	+	15.7085i	0.661268	+	0.548564i
$821$	−23.5397	+	40.7719i	−0.821541	+	1.42295i	0.0829940	+	0.996550i	$0.473552\pi$
$821$	−23.5397	+	40.7719i	−0.821541	+	1.42295i	−0.904535	+	0.426400i	$0.859782\pi$
$822$	10.3237	+	10.2510i	0.360081	+	0.357544i
$823$	6.86571	−	3.96392i	0.239324	−	0.138174i	−0.375542	−	0.926805i	$-0.622543\pi$
$823$	6.86571	−	3.96392i	0.239324	−	0.138174i	0.614866	+	0.788632i	$0.289210\pi$
$824$	3.39186	−	13.0995i	0.118161	−	0.456342i
$825$	−72.9739	−	61.1424i	−2.54062	−	2.12870i
$826$	24.8529	−	28.5154i	0.864744	−	0.992176i
$827$		−	33.2279i		−	1.15545i	−0.816232	−	0.577724i	$-0.803941\pi$
$827$		−	33.2279i		−	1.15545i	0.816232	−	0.577724i	$-0.196059\pi$
$828$	−0.0353903	−	5.00546i	−0.00122990	−	0.173952i
$829$	−21.9735	−	12.6864i	−0.763171	−	0.440617i	0.0672624	−	0.997735i	$-0.478574\pi$
$829$	−21.9735	−	12.6864i	−0.763171	−	0.440617i	−0.830433	+	0.557119i	$0.811907\pi$
$830$	−52.6034	+	24.7096i	−1.82589	+	0.857683i
$831$	43.0176	+	36.0430i	1.49226	+	1.25032i
$832$	−5.31258	−	8.85338i	−0.184181	−	0.306936i
$833$	−17.3069	+	5.46661i	−0.599647	+	0.189407i
$834$	−10.4945	−	38.6196i	−0.363397	−	1.33729i
$835$	−9.34424	+	16.1847i	−0.323371	+	0.560094i
$836$	14.8071	−	5.48382i	0.512115	−	0.189662i
$837$	9.07832	−	0.0197194i	0.313793	−	0.000681603i
$838$	11.3318	+	7.88722i	0.391450	+	0.272459i
$839$	−8.91318	−	15.4381i	−0.307717	−	0.532982i	0.670146	−	0.742230i	$-0.266232\pi$
$839$	−8.91318	−	15.4381i	−0.307717	−	0.532982i	−0.977863	+	0.209248i	$0.932898\pi$
$840$	29.0253	−	48.8636i	1.00147	−	1.68595i
$841$	9.57790	−	16.5894i	0.330272	−	0.572048i
$842$	−1.43191	+	0.672618i	−0.0493469	+	0.0231799i
$843$	−8.40340	+	47.8607i	−0.289428	+	1.64841i
$844$	0.732238	−	0.882678i	0.0252047	−	0.0303830i
$845$	24.8496	+	43.0407i	0.854851	+	1.48065i
$846$	29.3707	+	13.5438i	1.00979	+	0.465645i
$847$	9.50762	−	4.18637i	0.326686	−	0.143845i
$848$	18.5190	−	15.8975i	0.635944	−	0.545922i
$849$	−37.1995	−	6.53151i	−1.27668	−	0.224161i
$850$	42.8167	+	29.8016i	1.46860	+	1.02219i
$851$	−4.83167	+	2.78956i	−0.165627	+	0.0956251i
$852$	−28.6068	+	24.3150i	−0.980054	+	0.833019i
$853$	−27.2669	+	15.7425i	−0.933600	+	0.539014i	−0.887948	−	0.459943i	$-0.847870\pi$
$853$	−27.2669	+	15.7425i	−0.933600	+	0.539014i	−0.0456517	+	0.998957i	$0.514536\pi$
$854$	−17.9040	−	3.50426i	−0.612663	−	0.119913i
$855$	20.5671	−	17.3087i	0.703382	−	0.591945i
$856$	−16.9121	+	4.68478i	−0.578042	+	0.160123i
$857$			11.0778i			0.378411i	0.981938	+	0.189206i	$0.0605912\pi$
$857$			11.0778i			0.378411i	−0.981938	+	0.189206i	$0.939409\pi$
$858$	−3.20288	−	11.7865i	−0.109345	−	0.402384i
$859$	41.8053			1.42638			0.713189	−	0.700972i	$-0.247250\pi$
$859$	41.8053			1.42638			0.713189	+	0.700972i	$0.247250\pi$
$860$	−25.0121	−	67.5363i	−0.852905	−	2.30297i
$861$	−9.27825	+	8.89945i	−0.316202	+	0.303292i
$862$	28.7120	−	41.2513i	0.977936	−	1.40503i
$863$	−20.2109	−	35.0063i	−0.687986	−	1.19163i	−0.972488	−	0.232951i	$-0.925162\pi$
$863$	−20.2109	−	35.0063i	−0.687986	−	1.19163i	0.284502	−	0.958675i	$-0.408172\pi$
$864$	−17.2481	−	23.8013i	−0.586793	−	0.809737i
$865$	−14.3908	+	24.9256i	−0.489301	+	0.847495i
$866$	12.2914	+	1.04055i	0.417678	+	0.0353593i
$867$	17.5326	+	3.07839i	0.595440	+	0.104548i
$868$	−6.64050	+	6.43214i	−0.225393	+	0.218321i
$869$	5.66057	−	9.80440i	0.192022	−	0.332592i
$870$	−32.5816	−	8.60689i	−1.10462	−	0.291801i
$871$			19.0059i			0.643992i
$872$	30.4928	+	29.9828i	1.03262	+	1.01534i
$873$	−0.183288	+	0.154250i	−0.00620336	+	0.00522057i
$874$	1.02506	+	2.18221i	0.0346731	+	0.0738142i
$875$	97.9670	−	43.1366i	3.31189	−	1.45828i
$876$	−5.89552	−	32.2375i	−0.199191	−	1.08920i
$877$		−	12.6284i		−	0.426431i	−0.977005	−	0.213215i	$-0.931606\pi$
$877$		−	12.6284i		−	0.426431i	0.977005	−	0.213215i	$-0.0683936\pi$
$878$	18.4666	+	12.8532i	0.623217	+	0.433775i
$879$	0.192473	+	0.527625i	0.00649194	+	0.0177964i
$880$	22.4589	−	63.9331i	0.757090	−	2.15518i
$881$			10.5477i			0.355363i	0.984088	+	0.177681i	$0.0568596\pi$
$881$			10.5477i			0.355363i	−0.984088	+	0.177681i	$0.943140\pi$
$882$	23.6474	+	17.9666i	0.796250	+	0.604968i
$883$	44.9084			1.51129			0.755643	−	0.654983i	$-0.227324\pi$
$883$	44.9084			1.51129			0.755643	+	0.654983i	$0.227324\pi$
$884$	2.32436	+	6.27612i	0.0781768	+	0.211089i
$885$	13.2777	−	75.6217i	0.446325	−	2.54200i
$886$	32.6798	+	22.7460i	1.09790	+	0.764167i
$887$	46.4327			1.55906			0.779528	−	0.626367i	$-0.215459\pi$
$887$	46.4327			1.55906			0.779528	+	0.626367i	$0.215459\pi$
$888$	−13.5733	+	29.8178i	−0.455489	+	1.00062i
$889$	−13.7244	−	31.1694i	−0.460302	−	1.04539i
$890$	−10.3447	+	4.85925i	−0.346754	+	0.162882i
$891$	−11.9871	−	32.6398i	−0.401582	−	1.09347i
$892$	27.3521	−	10.1299i	0.915817	−	0.339173i
$893$	−15.5782			−0.521304
$894$	33.5039	−	33.7416i	1.12054	−	1.12849i
$895$	53.5386	+	30.9105i	1.78960	+	1.03322i
$896$	29.4687	+	5.25333i	0.984479	+	0.175502i
$897$	1.75201	−	0.639116i	0.0584979	−	0.0213395i
$898$	−1.44356	+	17.0519i	−0.0481721	+	0.569028i
$899$	4.74729	+	2.74085i	0.158331	+	0.0914124i
$900$	−0.603519	−	85.3593i	−0.0201173	−	2.84531i
$901$	−13.7009	+	7.91022i	−0.456443	+	0.263528i
$902$	−8.75679	+	12.5811i	−0.291569	+	0.418905i
$903$	36.5461	−	8.98077i	1.21618	−	0.298861i
$904$	25.2069	+	24.7853i	0.838369	+	0.824346i
$905$		−	73.0792i		−	2.42923i
$906$	4.67350	+	4.64058i	0.155267	+	0.154173i
$907$	−19.5346			−0.648636			−0.324318	−	0.945948i	$-0.605135\pi$
$907$	−19.5346			−0.648636			−0.324318	+	0.945948i	$0.605135\pi$
$908$	−3.89968	+	22.8672i	−0.129415	+	0.758876i
$909$	1.90362	+	10.7053i	0.0631390	+	0.355072i
$910$	20.7805	+	4.06727i	0.688867	+	0.134829i
$911$	−9.82256	−	17.0132i	−0.325436	−	0.563672i	0.656165	−	0.754618i	$-0.272178\pi$
$911$	−9.82256	−	17.0132i	−0.325436	−	0.563672i	−0.981600	+	0.190946i	$0.938844\pi$
$912$	12.3448	+	6.93161i	0.408777	+	0.229529i
$913$	−18.1046	−	31.3580i	−0.599174	−	1.03780i
$914$	−21.3278	+	30.6422i	−0.705460	+	1.01355i
$915$	−34.7886	+	12.6905i	−1.15007	+	0.419536i
$916$	3.17748	−	18.6323i	0.104987	−	0.615630i
$917$	−12.9157	−	29.3327i	−0.426514	−	0.968651i
$918$	8.13818	+	17.2277i	0.268600	+	0.568600i
$919$	17.6347	−	10.1814i	0.581716	−	0.335854i	−0.180099	−	0.983648i	$-0.557642\pi$
$919$	17.6347	−	10.1814i	0.581716	−	0.335854i	0.761815	+	0.647795i	$0.224309\pi$
$920$	10.0164	+	2.59356i	0.330231	+	0.0855070i
$921$	−14.9003	+	17.7836i	−0.490981	+	0.585990i
$922$	18.0739	+	38.4768i	0.595232	+	1.26717i
$923$	−12.1139	−	6.99397i	−0.398734	−	0.230209i
$924$	31.8604	+	15.4511i	1.04813	+	0.508305i
$925$	−82.3956	+	47.5711i	−2.70915	+	1.56413i
$926$	−21.3225	−	14.8410i	−0.700700	−	0.487705i
$927$	14.1306	−	2.51272i	0.464111	−	0.0825285i
$928$	−1.79525	−	17.6576i	−0.0589320	−	0.579640i
$929$	35.3562	+	20.4129i	1.16000	+	0.669726i	0.951304	−	0.308254i	$-0.0997447\pi$
$929$	35.3562	+	20.4129i	1.16000	+	0.669726i	0.208696	+	0.977981i	$0.433078\pi$
$930$	−4.79270	+	18.1429i	−0.157159	+	0.594930i
$931$	−13.9669	−	3.08887i	−0.457748	−	0.101234i
$932$	17.6957	−	6.55360i	0.579641	−	0.214670i
$933$	−7.08919	−	1.24472i	−0.232090	−	0.0407504i
$934$	−2.81698	+	1.32323i	−0.0921743	+	0.0432975i
$935$	−21.9621	+	38.0395i	−0.718239	+	1.24403i
$936$	6.19248	−	9.03244i	0.202407	−	0.295234i
$937$	2.11782			0.0691862			0.0345931	−	0.999401i	$-0.488986\pi$
$937$	2.11782			0.0691862			0.0345931	+	0.999401i	$0.488986\pi$
$938$	−41.5377	−	36.2028i	−1.35626	−	1.18206i
$939$	−12.1584	−	33.3299i	−0.396775	−	1.08768i
$940$	−42.6845	+	51.4542i	−1.39222	+	1.67825i
$941$	21.4702	+	37.1874i	0.699907	+	1.21227i	0.968498	+	0.249020i	$0.0801086\pi$
$941$	21.4702	+	37.1874i	0.699907	+	1.21227i	−0.268591	+	0.963254i	$0.586558\pi$
$942$	13.7931	−	52.2141i	0.449403	−	1.70123i
$943$	−2.02695	−	1.17026i	−0.0660066	−	0.0381089i
$944$	39.7417	−	7.46923i	1.29348	−	0.243103i
$945$	59.9392	+	6.41711i	1.94982	+	0.208749i
$946$	40.6126	−	19.0772i	1.32043	−	0.620252i
$947$	29.0791	+	16.7888i	0.944945	+	0.545564i	0.891507	−	0.453007i	$-0.149649\pi$
$947$	29.0791	+	16.7888i	0.944945	+	0.545564i	0.0534377	+	0.998571i	$0.482982\pi$
$948$	9.98525	−	1.82608i	0.324306	−	0.0593084i
$949$	10.5741	−	6.10499i	0.343251	−	0.198176i
$950$	17.4805	+	37.2137i	0.567144	+	1.20737i
$951$	3.32273	+	9.10861i	0.107747	+	0.295367i
$952$	−18.1440	−	6.87491i	−0.588051	−	0.222817i
$953$		−	18.7881i		−	0.608607i	−0.952575	−	0.304303i	$-0.901576\pi$
$953$		−	18.7881i		−	0.608607i	0.952575	−	0.304303i	$-0.0984236\pi$
$954$	23.5081	+	10.8403i	0.761102	+	0.350969i
$955$	1.39148	−	2.41011i	0.0450272	−	0.0779893i
$956$	−7.13667	+	8.60292i	−0.230816	+	0.278238i
$957$	3.63089	−	20.6793i	0.117370	−	0.668468i
$958$	−14.1240	−	1.19569i	−0.456326	−	0.0386311i
$959$	−6.33257	−	14.3818i	−0.204489	−	0.464414i
$960$	56.7197	−	21.7816i	1.83062	−	0.702998i
$961$	−13.9738	+	24.2033i	−0.450767	+	0.780751i
$962$	−12.1626	−	1.02965i	−0.392139	−	0.0331972i
$963$	−11.9851	−	14.2414i	−0.386215	−	0.458922i
$964$	7.86565	+	1.34137i	0.253335	+	0.0432027i
$965$	35.7689	+	61.9536i	1.15144	+	1.99436i
$966$	−1.94045	+	5.04644i	−0.0624331	+	0.162366i
$967$	−20.4877	−	11.8286i	−0.658841	−	0.380382i	0.132994	−	0.991117i	$-0.457541\pi$
$967$	−20.4877	−	11.8286i	−0.658841	−	0.380382i	−0.791835	+	0.610735i	$0.790874\pi$
$968$	10.7512	+	2.78381i	0.345556	+	0.0894751i
$969$	−7.03432	−	5.89382i	−0.225975	−	0.189337i
$970$	−0.210530	−	0.448189i	−0.00675971	−	0.0143905i
$971$	−38.2464	+	22.0816i	−1.22739	+	0.708632i	−0.966482	−	0.256733i	$-0.917354\pi$
$971$	−38.2464	+	22.0816i	−1.22739	+	0.708632i	−0.260904	+	0.965365i	$0.584021\pi$
$972$	15.3383	−	27.1429i	0.491975	−	0.870610i
$973$	−4.69491	+	42.9709i	−0.150512	+	1.37758i
$974$	−18.6509	−	12.9815i	−0.597615	−	0.415956i
$975$	29.8774	−	10.8990i	0.956843	−	0.349047i
$976$	−12.7037	−	14.7985i	−0.406636	−	0.473690i
$977$	12.2818	−	7.09090i	0.392930	−	0.226858i	−0.290499	−	0.956875i	$-0.593821\pi$
$977$	12.2818	−	7.09090i	0.392930	−	0.226858i	0.683429	+	0.730017i	$0.260488\pi$
$978$	−43.6530	−	11.5315i	−1.39587	−	0.368738i
$979$	−3.56034	−	6.16668i	−0.113789	−	0.197088i
$980$	−48.4721	+	37.6687i	−1.54838	+	1.20328i
$981$	−15.4517	+	42.6452i	−0.493335	+	1.36156i
$982$	5.43666	+	3.78406i	0.173491	+	0.120754i
$983$	−42.7059			−1.36211			−0.681053	−	0.732234i	$-0.738478\pi$
$983$	−42.7059			−1.36211			−0.681053	+	0.732234i	$0.738478\pi$
$984$	−13.6802	+	1.32320i	−0.436108	+	0.0421820i
$985$	−55.7196			−1.77537
$986$	−0.970482	+	11.4637i	−0.0309064	+	0.365079i
$987$	−24.1824	−	25.2117i	−0.769734	−	0.802497i
$988$	−0.886734	+	5.19970i	−0.0282108	+	0.165424i
$989$	3.42560	+	5.93332i	0.108928	+	0.188669i
$990$	71.5728	−	6.56910i	2.27473	−	0.208780i
$991$	−9.08091	−	5.24286i	−0.288464	−	0.166545i	0.348785	−	0.937203i	$-0.386594\pi$
$991$	−9.08091	−	5.24286i	−0.288464	−	0.166545i	−0.637249	+	0.770658i	$0.719928\pi$
$992$	−9.83256	+	0.999676i	−0.312184	+	0.0317397i
$993$	−4.80524	−	13.1726i	−0.152490	−	0.418020i
$994$	38.3601	−	13.1529i	1.21671	−	0.417185i
$995$	−40.3226	−	23.2802i	−1.27831	−	0.738034i
$996$	10.9102	−	30.5780i	0.345704	−	0.968901i
$997$		−	22.1662i		−	0.702010i	−0.936374	−	0.351005i	$-0.885840\pi$
$997$		−	22.1662i		−	0.702010i	0.936374	−	0.351005i	$-0.114160\pi$
$998$	10.2755	+	0.869893i	0.325266	+	0.0275360i
$999$	−34.7491	+	0.0754801i	−1.09941	+	0.00238808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cy.a.347.4	yes	184
7.2	even	3		504.2.bt.a.275.59	yes	184
8.3	odd	2	inner	504.2.cy.a.347.29	yes	184
9.2	odd	6		504.2.bt.a.11.34	✓	184
56.51	odd	6		504.2.bt.a.275.34	yes	184
63.2	odd	6	inner	504.2.cy.a.443.29	yes	184
72.11	even	6		504.2.bt.a.11.59	yes	184
504.443	even	6	inner	504.2.cy.a.443.4	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bt.a.11.34	✓	184	9.2	odd	6
504.2.bt.a.11.59	yes	184	72.11	even	6
504.2.bt.a.275.34	yes	184	56.51	odd	6
504.2.bt.a.275.59	yes	184	7.2	even	3
504.2.cy.a.347.4	yes	184	1.1	even	1	trivial
504.2.cy.a.347.29	yes	184	8.3	odd	2	inner
504.2.cy.a.443.4	yes	184	504.443	even	6	inner
504.2.cy.a.443.29	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)

\(f(q)\)	\(=\)	\(q+(-1.40917 - 0.119296i) q^{2} +(-1.11238 + 1.32763i) q^{3} +(1.97154 + 0.336217i) q^{4} -4.38485 q^{5} +(1.72592 - 1.73816i) q^{6} +(-2.42141 + 1.06619i) q^{7} +(-2.73813 - 0.708985i) q^{8} +(-0.525222 - 2.95367i) q^{9} +O(q^{10})\)	\(q+(-1.40917 - 0.119296i) q^{2} +(-1.11238 + 1.32763i) q^{3} +(1.97154 + 0.336217i) q^{4} -4.38485 q^{5} +(1.72592 - 1.73816i) q^{6} +(-2.42141 + 1.06619i) q^{7} +(-2.73813 - 0.708985i) q^{8} +(-0.525222 - 2.95367i) q^{9} +(6.17901 + 0.523095i) q^{10} +3.86348i q^{11} +(-2.63947 + 2.24348i) q^{12} +(-1.11772 - 0.645313i) q^{13} +(3.53938 - 1.21358i) q^{14} +(4.87762 - 5.82147i) q^{15} +(3.77392 + 1.32573i) q^{16} +(-2.24544 - 1.29641i) q^{17} +(0.387768 + 4.22488i) q^{18} +(-1.02175 - 1.76971i) q^{19} +(-8.64489 - 1.47426i) q^{20} +(1.27802 - 4.40076i) q^{21} +(0.460898 - 5.44431i) q^{22} +0.834265 q^{23} +(3.98711 - 2.84657i) q^{24} +14.2269 q^{25} +(1.49807 + 1.04270i) q^{26} +(4.50563 + 2.58830i) q^{27} +(-5.13238 + 1.28791i) q^{28} +(1.56877 + 2.71720i) q^{29} +(-7.56789 + 7.62158i) q^{30} +(1.51306 - 0.873564i) q^{31} +(-5.15995 - 2.31840i) q^{32} +(-5.12929 - 4.29766i) q^{33} +(3.00956 + 2.09473i) q^{34} +(10.6175 - 4.67508i) q^{35} +(-0.0424210 - 5.99985i) q^{36} +(-5.79153 + 3.34374i) q^{37} +(1.22870 + 2.61572i) q^{38} +(2.10006 - 0.766083i) q^{39} +(12.0063 + 3.10879i) q^{40} +(-2.42962 - 1.40274i) q^{41} +(-2.32595 + 6.04896i) q^{42} +(4.10614 + 7.11204i) q^{43} +(-1.29897 + 7.61699i) q^{44} +(2.30302 + 12.9514i) q^{45} +(-1.17562 - 0.0995245i) q^{46} +(3.81166 - 6.60200i) q^{47} +(-5.95811 + 3.53566i) q^{48} +(4.72648 - 5.16337i) q^{49} +(-20.0482 - 1.69721i) q^{50} +(4.21894 - 1.53903i) q^{51} +(-1.98665 - 1.64805i) q^{52} +(3.05083 - 5.28419i) q^{53} +(-6.04044 - 4.18486i) q^{54} -16.9408i q^{55} +(7.38605 - 1.20262i) q^{56} +(3.48610 + 0.612091i) q^{57} +(-1.88652 - 4.01615i) q^{58} +(8.75498 - 5.05469i) q^{59} +(11.5737 - 9.83731i) q^{60} +(-4.22260 - 2.43792i) q^{61} +(-2.23637 + 1.05050i) q^{62} +(4.42095 + 6.59206i) q^{63} +(6.99468 + 3.88258i) q^{64} +(4.90102 + 2.82960i) q^{65} +(6.71536 + 6.66805i) q^{66} +(-7.36306 - 12.7532i) q^{67} +(-3.99110 - 3.31087i) q^{68} +(-0.928019 + 1.10760i) q^{69} +(-15.5197 + 5.32137i) q^{70} +10.8381 q^{71} +(-0.655980 + 8.45989i) q^{72} +(-4.73025 + 8.19303i) q^{73} +(8.56016 - 4.02100i) q^{74} +(-15.8257 + 18.8881i) q^{75} +(-1.41940 - 3.83259i) q^{76} +(-4.11920 - 9.35508i) q^{77} +(-3.05074 + 0.829015i) q^{78} +(-2.53771 - 1.46515i) q^{79} +(-16.5481 - 5.81313i) q^{80} +(-8.44828 + 3.10266i) q^{81} +(3.25642 + 2.26655i) q^{82} +(-8.11652 + 4.68608i) q^{83} +(3.99928 - 8.24656i) q^{84} +(9.84592 + 5.68455i) q^{85} +(-4.93782 - 10.5119i) q^{86} +(-5.35251 - 0.939797i) q^{87} +(2.73915 - 10.5787i) q^{88} +(-1.59615 + 0.921536i) q^{89} +(-1.70031 - 18.5255i) q^{90} +(3.39448 + 0.370873i) q^{91} +(1.64478 + 0.280494i) q^{92} +(-0.523321 + 2.98052i) q^{93} +(-6.15889 + 8.84864i) q^{94} +(4.48020 + 7.75993i) q^{95} +(8.81780 - 4.27158i) q^{96} +(-0.0399262 - 0.0691541i) q^{97} +(-7.27640 + 6.71223i) q^{98} +(11.4114 - 2.02919i) 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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