LMFDB - Embedded newform 369.3.l.b.55.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,3,Mod(55,369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("369.55");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	369.l (of order $8$, degree $4$, 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:	$10.0545217549$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 66 x^{18} + 1853 x^{16} + 28868 x^{14} + 272678 x^{12} + 1600296 x^{10} + 5739482 x^{8} + \cdots + 776161 $ x^20 + 66x^18 + 1853x^16 + 28868x^14 + 272678x^12 + 1600296x^10 + 5739482x^8 + 11863964x^6 + 12547553x^4 + 5476470*x^2 + 776161
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 41)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			55.4
Root			$-2.46048i$ of defining polynomial
Character	$\chi$	$=$	369.55
Dual form			369.3.l.b.208.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73982 + 1.73982i) q^{2} +2.05398i q^{4} +(3.70619 - 3.70619i) q^{5} +(-3.57359 - 8.62742i) q^{7} +(3.38573 - 3.38573i) q^{8} +O(q^{10})$	\(q+(1.73982 + 1.73982i) q^{2} +2.05398i q^{4} +(3.70619 - 3.70619i) q^{5} +(-3.57359 - 8.62742i) q^{7} +(3.38573 - 3.38573i) q^{8} +12.8962 q^{10} +(-12.7853 + 5.29582i) q^{11} +(-3.72817 - 9.00060i) q^{13} +(8.79277 - 21.2276i) q^{14} +19.9971 q^{16} +(2.63591 - 6.36366i) q^{17} +(8.83468 - 21.3288i) q^{19} +(7.61243 + 7.61243i) q^{20} +(-31.4579 - 13.0303i) q^{22} -6.23370i q^{23} -2.47163i q^{25} +(9.17310 - 22.1458i) q^{26} +(17.7205 - 7.34009i) q^{28} +(0.964227 + 2.32785i) q^{29} +44.1622i q^{31} +(21.2485 + 21.2485i) q^{32} +(15.6577 - 6.48562i) q^{34} +(-45.2192 - 18.7304i) q^{35} +44.8421 q^{37} +(52.4792 - 21.7376i) q^{38} -25.0963i q^{40} +(8.25236 + 40.1609i) q^{41} +(47.3348 + 47.3348i) q^{43} +(-10.8775 - 26.2606i) q^{44} +(10.8455 - 10.8455i) q^{46} +(-27.4079 + 66.1685i) q^{47} +(-27.0135 + 27.0135i) q^{49} +(4.30020 - 4.30020i) q^{50} +(18.4871 - 7.65759i) q^{52} +(58.1018 - 24.0665i) q^{53} +(-27.7572 + 67.0118i) q^{55} +(-41.3094 - 17.1109i) q^{56} +(-2.37247 + 5.72764i) q^{58} +17.9880 q^{59} +(-61.7940 - 61.7940i) q^{61} +(-76.8345 + 76.8345i) q^{62} -6.05107i q^{64} +(-47.1752 - 19.5406i) q^{65} +(43.6507 - 105.382i) q^{67} +(13.0708 + 5.41411i) q^{68} +(-46.0859 - 111.261i) q^{70} +(-23.3796 - 56.4435i) q^{71} +(35.5014 + 35.5014i) q^{73} +(78.0173 + 78.0173i) q^{74} +(43.8089 + 18.1462i) q^{76} +(91.3786 + 91.3786i) q^{77} +(-46.8487 + 19.4053i) q^{79} +(74.1129 - 74.1129i) q^{80} +(-55.5153 + 84.2306i) q^{82} -98.6881 q^{83} +(-13.8157 - 33.3541i) q^{85} +164.708i q^{86} +(-25.3572 + 61.2177i) q^{88} +(-18.3084 - 44.2004i) q^{89} +(-64.3290 + 64.3290i) q^{91} +12.8039 q^{92} +(-162.807 + 67.4367i) q^{94} +(-46.3055 - 111.791i) q^{95} +(81.1506 + 33.6137i) q^{97} -93.9975 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{2} + 12 q^{5} - 4 q^{7} - 36 q^{8}+O(q^{10}) $ 20 * q + 8 * q^2 + 12 * q^5 - 4 * q^7 - 36 * q^8	$ 20 q + 8 q^{2} + 12 q^{5} - 4 q^{7} - 36 q^{8} + 16 q^{10} + 12 q^{11} - 48 q^{13} - 88 q^{14} - 36 q^{16} + 28 q^{17} + 76 q^{19} + 16 q^{20} - 116 q^{22} - 40 q^{26} + 72 q^{28} + 24 q^{29} - 176 q^{32} + 80 q^{34} - 60 q^{35} + 208 q^{37} + 380 q^{38} + 116 q^{41} - 40 q^{43} - 116 q^{44} - 176 q^{46} + 64 q^{47} + 168 q^{49} + 148 q^{50} - 184 q^{52} + 120 q^{53} + 20 q^{55} - 188 q^{56} + 36 q^{58} + 512 q^{59} - 460 q^{61} - 68 q^{62} - 432 q^{65} + 300 q^{67} - 120 q^{68} + 308 q^{70} + 108 q^{71} + 60 q^{73} - 140 q^{74} + 872 q^{76} - 112 q^{77} - 208 q^{79} + 68 q^{80} - 376 q^{82} + 120 q^{83} + 172 q^{85} + 316 q^{88} - 268 q^{89} - 800 q^{91} + 448 q^{92} - 212 q^{94} + 184 q^{95} - 120 q^{97} + 20 q^{98}+O(q^{100}) $ 20 * q + 8 * q^2 + 12 * q^5 - 4 * q^7 - 36 * q^8 + 16 * q^10 + 12 * q^11 - 48 * q^13 - 88 * q^14 - 36 * q^16 + 28 * q^17 + 76 * q^19 + 16 * q^20 - 116 * q^22 - 40 * q^26 + 72 * q^28 + 24 * q^29 - 176 * q^32 + 80 * q^34 - 60 * q^35 + 208 * q^37 + 380 * q^38 + 116 * q^41 - 40 * q^43 - 116 * q^44 - 176 * q^46 + 64 * q^47 + 168 * q^49 + 148 * q^50 - 184 * q^52 + 120 * q^53 + 20 * q^55 - 188 * q^56 + 36 * q^58 + 512 * q^59 - 460 * q^61 - 68 * q^62 - 432 * q^65 + 300 * q^67 - 120 * q^68 + 308 * q^70 + 108 * q^71 + 60 * q^73 - 140 * q^74 + 872 * q^76 - 112 * q^77 - 208 * q^79 + 68 * q^80 - 376 * q^82 + 120 * q^83 + 172 * q^85 + 316 * q^88 - 268 * q^89 - 800 * q^91 + 448 * q^92 - 212 * q^94 + 184 * q^95 - 120 * q^97 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	1.73982	+	1.73982i	0.869912	+	0.869912i	0.992462	−	0.122550i	$-0.0391072\pi$
$2$	1.73982	+	1.73982i	0.869912	+	0.869912i	−0.122550	+	0.992462i	$0.539107\pi$
$3$		0			0
$3$		0			0
$4$			2.05398i			0.513495i
$5$	3.70619	−	3.70619i	0.741237	−	0.741237i	−0.231579	−	0.972816i	$-0.574389\pi$
$5$	3.70619	−	3.70619i	0.741237	−	0.741237i	0.972816	+	0.231579i	$0.0743892\pi$
$6$		0			0
$7$	−3.57359	−	8.62742i	−0.510513	−	1.23249i	−0.943586	−	0.331129i	$-0.892571\pi$
$7$	−3.57359	−	8.62742i	−0.510513	−	1.23249i	0.433072	−	0.901359i	$-0.357429\pi$
$8$	3.38573	−	3.38573i	0.423217	−	0.423217i
$9$		0			0
$10$	12.8962			1.28962
$11$	−12.7853	+	5.29582i	−1.16230	+	0.481439i	−0.878639	−	0.477487i	$-0.841548\pi$
$11$	−12.7853	+	5.29582i	−1.16230	+	0.481439i	−0.283657	+	0.958926i	$0.591548\pi$
$12$		0			0
$13$	−3.72817	−	9.00060i	−0.286782	−	0.692354i	0.713180	−	0.700981i	$-0.247254\pi$
$13$	−3.72817	−	9.00060i	−0.286782	−	0.692354i	−0.999963	+	0.00862657i	$0.997254\pi$
$14$	8.79277	−	21.2276i	0.628055	−	1.51626i
$15$		0			0
$16$	19.9971			1.24982
$17$	2.63591	−	6.36366i	0.155054	−	0.374333i	−0.827195	−	0.561915i	$-0.810065\pi$
$17$	2.63591	−	6.36366i	0.155054	−	0.374333i	0.982249	+	0.187582i	$0.0600650\pi$
$18$		0			0
$19$	8.83468	−	21.3288i	0.464983	−	1.12257i	−0.501343	−	0.865249i	$-0.667161\pi$
$19$	8.83468	−	21.3288i	0.464983	−	1.12257i	0.966326	−	0.257320i	$-0.0828394\pi$
$20$	7.61243	+	7.61243i	0.380621	+	0.380621i
$21$		0			0
$22$	−31.4579	−	13.0303i	−1.42990	−	0.592286i
$23$		−	6.23370i		−	0.271030i	−0.990775	−	0.135515i	$-0.956731\pi$
$23$		−	6.23370i		−	0.271030i	0.990775	−	0.135515i	$-0.0432690\pi$
$24$		0			0
$25$		−	2.47163i		−	0.0988650i
$26$	9.17310	−	22.1458i	0.352812	−	0.851763i
$27$		0			0
$28$	17.7205	−	7.34009i	0.632876	−	0.262146i
$29$	0.964227	+	2.32785i	0.0332492	+	0.0802707i	0.939632	−	0.342187i	$-0.111168\pi$
$29$	0.964227	+	2.32785i	0.0332492	+	0.0802707i	−0.906383	+	0.422458i	$0.861168\pi$
$30$		0			0
$31$			44.1622i			1.42459i	0.701882	+	0.712293i	$0.252343\pi$
$31$			44.1622i			1.42459i	−0.701882	+	0.712293i	$0.747657\pi$
$32$	21.2485	+	21.2485i	0.664015	+	0.664015i
$33$		0			0
$34$	15.6577	−	6.48562i	0.460520	−	0.190753i
$35$	−45.2192	−	18.7304i	−1.29198	−	0.535154i
$36$		0			0
$37$	44.8421			1.21195			0.605974	−	0.795484i	$-0.292784\pi$
$37$	44.8421			1.21195			0.605974	+	0.795484i	$0.292784\pi$
$38$	52.4792	−	21.7376i	1.38103	−	0.572042i
$39$		0			0
$40$		−	25.0963i		−	0.627408i
$41$	8.25236	+	40.1609i	0.201277	+	0.979534i
$41$	8.25236	+	40.1609i	0.201277	+	0.979534i
$42$		0			0
$43$	47.3348	+	47.3348i	1.10081	+	1.10081i	0.994313	+	0.106495i	$0.0339629\pi$
$43$	47.3348	+	47.3348i	1.10081	+	1.10081i	0.106495	+	0.994313i	$0.466037\pi$
$44$	−10.8775	−	26.2606i	−0.247216	−	0.596833i
$45$		0			0
$46$	10.8455	−	10.8455i	0.235773	−	0.235773i
$47$	−27.4079	+	66.1685i	−0.583147	+	1.40784i	0.306799	+	0.951774i	$0.400742\pi$
$47$	−27.4079	+	66.1685i	−0.583147	+	1.40784i	−0.889946	+	0.456066i	$0.849258\pi$
$48$		0			0
$49$	−27.0135	+	27.0135i	−0.551296	+	0.551296i
$50$	4.30020	−	4.30020i	0.0860039	−	0.0860039i
$51$		0			0
$52$	18.4871	−	7.65759i	0.355520	−	0.147261i
$53$	58.1018	−	24.0665i	1.09626	−	0.454086i	0.240074	−	0.970754i	$-0.422828\pi$
$53$	58.1018	−	24.0665i	1.09626	−	0.454086i	0.856185	+	0.516669i	$0.172828\pi$
$54$		0			0
$55$	−27.7572	+	67.0118i	−0.504676	+	1.21840i
$56$	−41.3094	−	17.1109i	−0.737667	−	0.305552i
$57$		0			0
$58$	−2.37247	+	5.72764i	−0.0409046	+	0.0987524i
$59$	17.9880			0.304882			0.152441	−	0.988313i	$-0.451287\pi$
$59$	17.9880			0.304882			0.152441	+	0.988313i	$0.451287\pi$
$60$		0			0
$61$	−61.7940	−	61.7940i	−1.01302	−	1.01302i	−0.999914	−	0.0131027i	$-0.995829\pi$
$61$	−61.7940	−	61.7940i	−1.01302	−	1.01302i	−0.0131027	−	0.999914i	$-0.504171\pi$
$62$	−76.8345	+	76.8345i	−1.23927	+	1.23927i
$63$		0			0
$64$		−	6.05107i		−	0.0945479i
$65$	−47.1752	−	19.5406i	−0.725772	−	0.300625i
$66$		0			0
$67$	43.6507	−	105.382i	0.651503	−	1.57287i	−0.159094	−	0.987263i	$-0.550857\pi$
$67$	43.6507	−	105.382i	0.651503	−	1.57287i	0.810597	−	0.585604i	$-0.199143\pi$
$68$	13.0708	+	5.41411i	0.192218	+	0.0796193i
$69$		0			0
$70$	−46.0859	−	111.261i	−0.658369	−	1.58944i
$71$	−23.3796	−	56.4435i	−0.329291	−	0.794978i	−0.998645	−	0.0520351i	$-0.983429\pi$
$71$	−23.3796	−	56.4435i	−0.329291	−	0.794978i	0.669354	−	0.742943i	$-0.266571\pi$
$72$		0			0
$73$	35.5014	+	35.5014i	0.486320	+	0.486320i	0.907143	−	0.420823i	$-0.138258\pi$
$73$	35.5014	+	35.5014i	0.486320	+	0.486320i	−0.420823	+	0.907143i	$0.638258\pi$
$74$	78.0173	+	78.0173i	1.05429	+	1.05429i
$75$		0			0
$76$	43.8089	+	18.1462i	0.576433	+	0.238766i
$77$	91.3786	+	91.3786i	1.18673	+	1.18673i
$78$		0			0
$79$	−46.8487	+	19.4053i	−0.593021	+	0.245637i	−0.658950	−	0.752187i	$-0.728999\pi$
$79$	−46.8487	+	19.4053i	−0.593021	+	0.245637i	0.0659287	+	0.997824i	$0.478999\pi$
$80$	74.1129	−	74.1129i	0.926411	−	0.926411i
$81$		0			0
$82$	−55.5153	+	84.2306i	−0.677016	+	1.02720i
$83$	−98.6881			−1.18901			−0.594507	−	0.804090i	$-0.702653\pi$
$83$	−98.6881			−1.18901			−0.594507	+	0.804090i	$0.702653\pi$
$84$		0			0
$85$	−13.8157	−	33.3541i	−0.162538	−	0.392401i
$86$			164.708i			1.91521i
$87$		0			0
$88$	−25.3572	+	61.2177i	−0.288150	+	0.695656i
$89$	−18.3084	−	44.2004i	−0.205712	−	0.496633i	0.787027	−	0.616918i	$-0.211619\pi$
$89$	−18.3084	−	44.2004i	−0.205712	−	0.496633i	−0.992739	+	0.120285i	$0.961619\pi$
$90$		0			0
$91$	−64.3290	+	64.3290i	−0.706912	+	0.706912i
$92$	12.8039			0.139173
$93$		0			0
$94$	−162.807	+	67.4367i	−1.73198	+	0.717411i
$95$	−46.3055	−	111.791i	−0.487427	−	1.17675i
$96$		0			0
$97$	81.1506	+	33.6137i	0.836604	+	0.346533i	0.759514	−	0.650491i	$-0.225437\pi$
$97$	81.1506	+	33.6137i	0.836604	+	0.346533i	0.0770903	+	0.997024i	$0.475437\pi$
$98$	−93.9975			−0.959158
$99$		0			0
$100$	5.07667			0.0507667
$101$	17.7716	−	42.9045i	0.175957	−	0.424797i	−0.811155	−	0.584832i	$-0.801161\pi$
$101$	17.7716	−	42.9045i	0.175957	−	0.424797i	0.987111	+	0.160034i	$0.0511605\pi$
$102$		0			0
$103$	0.00784952	−	0.00784952i	7.62090e−5	−	7.62090e-5i	−0.707069	−	0.707145i	$-0.749983\pi$
$103$	0.00784952	−	0.00784952i	7.62090e−5	−	7.62090e-5i	0.707145	+	0.707069i	$0.249983\pi$
$104$	−43.0962	−	17.8510i	−0.414387	−	0.171645i
$105$		0			0
$106$	142.958	+	59.2153i	1.34866	+	0.558635i
$107$			158.071i			1.47730i	0.674091	+	0.738649i	$0.264536\pi$
$107$			158.071i			1.47730i	−0.674091	+	0.738649i	$0.735464\pi$
$108$		0			0
$109$	94.6355	+	39.1993i	0.868215	+	0.359627i	0.771915	−	0.635726i	$-0.219299\pi$
$109$	94.6355	+	39.1993i	0.868215	+	0.359627i	0.0963004	+	0.995352i	$0.469299\pi$
$110$	−164.881	+	68.2961i	−1.49892	+	0.620874i
$111$		0			0
$112$	−71.4614	−	172.523i	−0.638049	−	1.54039i
$113$		−	159.427i		−	1.41086i	−0.708780	−	0.705429i	$-0.750754\pi$
$113$		−	159.427i		−	1.41086i	0.708780	−	0.705429i	$-0.249246\pi$
$114$		0			0
$115$	−23.1032	−	23.1032i	−0.200898	−	0.200898i
$116$	−4.78136	+	1.98050i	−0.0412186	+	0.0170733i
$117$		0			0
$118$	31.2960	+	31.2960i	0.265220	+	0.265220i
$119$	−64.3216			−0.540517
$120$		0			0
$121$	49.8570	−	49.8570i	0.412041	−	0.412041i
$122$		−	215.022i		−	1.76247i
$123$		0			0
$124$	−90.7082			−0.731518
$125$	83.4943	+	83.4943i	0.667955	+	0.667955i
$126$		0			0
$127$			105.511i			0.830795i	0.909640	+	0.415398i	$0.136358\pi$
$127$			105.511i			0.830795i	−0.909640	+	0.415398i	$0.863642\pi$
$128$	95.5217	−	95.5217i	0.746264	−	0.746264i
$129$		0			0
$130$	−48.0793	−	116.074i	−0.369841	−	0.892875i
$131$	−40.3312	+	40.3312i	−0.307872	+	0.307872i	−0.844083	−	0.536212i	$-0.819855\pi$
$131$	−40.3312	+	40.3312i	−0.307872	+	0.307872i	0.536212	+	0.844083i	$0.319855\pi$
$132$		0			0
$133$	−215.584			−1.62093
$134$	259.291	−	107.402i	1.93501	−	0.801506i
$135$		0			0
$136$	−12.6211	−	30.4701i	−0.0928026	−	0.224045i
$137$	48.6390	−	117.425i	0.355029	−	0.857117i	−0.640954	−	0.767579i	$-0.721461\pi$
$137$	48.6390	−	117.425i	0.355029	−	0.857117i	0.995983	−	0.0895375i	$-0.0285389\pi$
$138$		0			0
$139$	−63.7487			−0.458624			−0.229312	−	0.973353i	$-0.573648\pi$
$139$	−63.7487			−0.458624			−0.229312	+	0.973353i	$0.573648\pi$
$140$	38.4719	−	92.8793i	0.274799	−	0.663424i
$141$		0			0
$142$	57.5252	−	138.878i	0.405107	−	0.978016i
$143$	95.3312	+	95.3312i	0.666652	+	0.666652i
$144$		0			0
$145$	12.2011	+	5.05384i	0.0841452	+	0.0348541i
$146$			123.532i			0.846112i
$147$		0			0
$148$			92.1047i			0.622329i
$149$	−40.4199	+	97.5823i	−0.271274	+	0.654915i	−0.999538	−	0.0303823i	$-0.990328\pi$
$149$	−40.4199	+	97.5823i	−0.271274	+	0.654915i	0.728264	+	0.685297i	$0.240328\pi$
$150$		0			0
$151$	−10.7345	+	4.44638i	−0.0710895	+	0.0294462i	−0.417945	−	0.908472i	$-0.637249\pi$
$151$	−10.7345	+	4.44638i	−0.0710895	+	0.0294462i	0.346855	+	0.937919i	$0.387249\pi$
$152$	−42.3018	−	102.126i	−0.278301	−	0.671878i
$153$		0			0
$154$			317.965i			2.06471i
$155$	163.673	+	163.673i	1.05596	+	1.05596i
$156$		0			0
$157$	6.17966	−	2.55970i	0.0393609	−	0.0163038i	−0.362916	−	0.931822i	$-0.618219\pi$
$157$	6.17966	−	2.55970i	0.0393609	−	0.0163038i	0.402277	+	0.915518i	$0.368219\pi$
$158$	−115.270	−	47.7465i	−0.729559	−	0.302193i
$159$		0			0
$160$	157.502			0.984385
$161$	−53.7807	+	22.2767i	−0.334042	+	0.138365i
$162$		0			0
$163$		−	76.6668i		−	0.470348i	−0.971953	−	0.235174i	$-0.924434\pi$
$163$		−	76.6668i		−	0.470348i	0.971953	−	0.235174i	$-0.0755660\pi$
$164$	−82.4897	+	16.9502i	−0.502986	+	0.103355i
$165$		0			0
$166$	−171.700	−	171.700i	−1.03434	−	1.03434i
$167$	−31.9487	−	77.1309i	−0.191309	−	0.461862i	0.798898	−	0.601467i	$-0.205417\pi$
$167$	−31.9487	−	77.1309i	−0.191309	−	0.461862i	−0.990207	+	0.139605i	$0.955417\pi$
$168$		0			0
$169$	52.3895	−	52.3895i	0.309997	−	0.309997i
$170$	33.9933	−	82.0671i	0.199961	−	0.482748i
$171$		0			0
$172$	−97.2246	+	97.2246i	−0.565259	+	0.565259i
$173$	−107.550	+	107.550i	−0.621678	+	0.621678i	−0.945960	−	0.324283i	$-0.894877\pi$
$173$	−107.550	+	107.550i	−0.621678	+	0.621678i	0.324283	+	0.945960i	$0.394877\pi$
$174$		0			0
$175$	−21.3237	+	8.83258i	−0.121850	+	0.0504719i
$176$	−255.668	+	105.901i	−1.45266	+	0.601711i
$177$		0			0
$178$	45.0475	−	108.754i	0.253076	−	0.610979i
$179$	−23.3967	−	9.69123i	−0.130708	−	0.0541409i	0.316371	−	0.948636i	$-0.397536\pi$
$179$	−23.3967	−	9.69123i	−0.130708	−	0.0541409i	−0.447079	+	0.894495i	$0.647536\pi$
$180$		0			0
$181$	−111.742	+	269.768i	−0.617356	+	1.49043i	0.237406	+	0.971411i	$0.423703\pi$
$181$	−111.742	+	269.768i	−0.617356	+	1.49043i	−0.854762	+	0.519020i	$0.826297\pi$
$182$	−223.842			−1.22990
$183$		0			0
$184$	−21.1056	−	21.1056i	−0.114705	−	0.114705i
$185$	166.193	−	166.193i	0.898341	−	0.898341i
$186$		0			0
$187$			95.3203i			0.509734i
$188$	−135.909	−	56.2952i	−0.722919	−	0.299443i
$189$		0			0
$190$	113.934	−	275.061i	0.599653	−	1.44769i
$191$	55.2027	+	22.8657i	0.289019	+	0.119716i	0.522483	−	0.852650i	$-0.325006\pi$
$191$	55.2027	+	22.8657i	0.289019	+	0.119716i	−0.233464	+	0.972366i	$0.575006\pi$
$192$		0			0
$193$	106.669	+	257.522i	0.552689	+	1.33431i	0.915452	+	0.402428i	$0.131834\pi$
$193$	106.669	+	257.522i	0.552689	+	1.33431i	−0.362763	+	0.931882i	$0.618166\pi$
$194$	82.7059	+	199.670i	0.426319	+	1.02923i
$195$		0			0
$196$	−55.4852	−	55.4852i	−0.283088	−	0.283088i
$197$	−153.560	−	153.560i	−0.779492	−	0.779492i	0.200252	−	0.979744i	$-0.435824\pi$
$197$	−153.560	−	153.560i	−0.779492	−	0.779492i	−0.979744	+	0.200252i	$0.935824\pi$
$198$		0			0
$199$	47.8910	+	19.8371i	0.240658	+	0.0996839i	0.499753	−	0.866168i	$-0.333424\pi$
$199$	47.8910	+	19.8371i	0.240658	+	0.0996839i	−0.259095	+	0.965852i	$0.583424\pi$
$200$	−8.36827	−	8.36827i	−0.0418413	−	0.0418413i
$201$		0			0
$202$	105.566	−	43.7268i	0.522603	−	0.216469i
$203$	16.6376	−	16.6376i	0.0819585	−	0.0819585i
$204$		0			0
$205$	179.429	+	118.259i	0.875261	+	0.576873i
$206$	0.0273136			0.000132590
$207$		0			0
$208$	−74.5526	−	179.986i	−0.358426	−	0.865316i
$209$			319.481i			1.52862i
$210$		0			0
$211$	75.2704	−	181.719i	0.356732	−	0.861226i	−0.639024	−	0.769187i	$-0.720661\pi$
$211$	75.2704	−	181.719i	0.356732	−	0.861226i	0.995755	−	0.0920392i	$-0.0293385\pi$
$212$	49.4322	+	119.340i	0.233171	+	0.562924i
$213$		0			0
$214$	−275.015	+	275.015i	−1.28512	+	1.28512i
$215$	350.863			1.63192
$216$		0			0
$217$	381.006	−	157.818i	1.75579	−	0.727270i
$218$	96.4492	+	232.849i	0.442428	+	1.06811i
$219$		0			0
$220$	−137.641	−	57.0127i	−0.625641	−	0.259149i
$221$	−67.1039			−0.303637
$222$		0			0
$223$	−256.287			−1.14927			−0.574634	−	0.818411i	$-0.694855\pi$
$223$	−256.287			−1.14927			−0.574634	+	0.818411i	$0.694855\pi$
$224$	107.386	−	259.253i	0.479402	−	1.15738i
$225$		0			0
$226$	277.375	−	277.375i	1.22732	−	1.22732i
$227$	260.667	+	107.972i	1.14831	+	0.475647i	0.873967	−	0.485985i	$-0.161539\pi$
$227$	260.667	+	107.972i	1.14831	+	0.475647i	0.274345	+	0.961631i	$0.411539\pi$
$228$		0			0
$229$	173.494	+	71.8635i	0.757615	+	0.313815i	0.727845	−	0.685742i	$-0.240522\pi$
$229$	173.494	+	71.8635i	0.757615	+	0.313815i	0.0297708	+	0.999557i	$0.490522\pi$
$230$		−	80.3912i		−	0.349527i
$231$		0			0
$232$	11.1461	+	4.61687i	0.0480435	+	0.0199003i
$233$	−142.344	+	58.9608i	−0.610919	+	0.253051i	−0.666621	−	0.745397i	$-0.732260\pi$
$233$	−142.344	+	58.9608i	−0.610919	+	0.253051i	0.0557026	+	0.998447i	$0.482260\pi$
$234$		0			0
$235$	143.654	+	346.812i	0.611294	+	1.47579i
$236$			36.9470i			0.156555i
$237$		0			0
$238$	−111.908	−	111.908i	−0.470203	−	0.470203i
$239$	−178.380	+	73.8874i	−0.746360	+	0.309152i	−0.723255	−	0.690581i	$-0.757355\pi$
$239$	−178.380	+	73.8874i	−0.746360	+	0.309152i	−0.0231044	+	0.999733i	$0.507355\pi$
$240$		0			0
$241$	−99.3519	−	99.3519i	−0.412249	−	0.412249i	0.470273	−	0.882521i	$-0.344156\pi$
$241$	−99.3519	−	99.3519i	−0.412249	−	0.412249i	−0.882521	+	0.470273i	$0.844156\pi$
$242$	173.485			0.716879
$243$		0			0
$244$	126.924	−	126.924i	0.520179	−	0.520179i
$245$			200.234i			0.817282i
$246$		0			0
$247$	−224.909			−0.910564
$248$	149.521	+	149.521i	0.602909	+	0.602909i
$249$		0			0
$250$			290.531i			1.16212i
$251$	110.524	−	110.524i	0.440334	−	0.440334i	−0.451790	−	0.892124i	$-0.649214\pi$
$251$	110.524	−	110.524i	0.440334	−	0.440334i	0.892124	+	0.451790i	$0.149214\pi$
$252$		0			0
$253$	33.0126	+	79.6994i	0.130484	+	0.315017i
$254$	−183.571	+	183.571i	−0.722719	+	0.722719i
$255$		0			0
$256$	308.178			1.20382
$257$	298.505	−	123.645i	1.16150	−	0.481108i	0.283124	−	0.959083i	$-0.408629\pi$
$257$	298.505	−	123.645i	1.16150	−	0.481108i	0.878373	+	0.477976i	$0.158629\pi$
$258$		0			0
$259$	−160.247	−	386.871i	−0.618715	−	1.49371i
$260$	40.1360	−	96.8969i	0.154369	−	0.372680i
$261$		0			0
$262$	−140.338			−0.535643
$263$	−129.948	+	313.721i	−0.494098	+	1.19286i	0.458519	+	0.888684i	$0.348380\pi$
$263$	−129.948	+	313.721i	−0.494098	+	1.19286i	−0.952617	+	0.304173i	$0.901620\pi$
$264$		0			0
$265$	126.141	−	304.531i	0.476003	−	1.14917i
$266$	−375.078	−	375.078i	−1.41007	−	1.41007i
$267$		0			0
$268$	216.453	+	89.6576i	0.807659	+	0.334543i
$269$		−	335.698i		−	1.24795i	−0.781445	−	0.623974i	$-0.785517\pi$
$269$		−	335.698i		−	1.24795i	0.781445	−	0.623974i	$-0.214483\pi$
$270$		0			0
$271$			183.624i			0.677578i	0.940862	+	0.338789i	$0.110017\pi$
$271$			183.624i			0.677578i	−0.940862	+	0.338789i	$0.889983\pi$
$272$	52.7106	−	127.255i	0.193789	−	0.467848i
$273$		0			0
$274$	288.922	−	119.676i	1.05446	−	0.436772i
$275$	13.0893	+	31.6004i	0.0475974	+	0.114910i
$276$		0			0
$277$		−	46.8127i		−	0.168999i	−0.996424	−	0.0844995i	$-0.973071\pi$
$277$		−	46.8127i		−	0.168999i	0.996424	−	0.0844995i	$-0.0269291\pi$
$278$	−110.912	−	110.912i	−0.398963	−	0.398963i
$279$		0			0
$280$	−216.516	+	89.6840i	−0.773273	+	0.320300i
$281$	244.389	+	101.229i	0.869712	+	0.360246i	0.772498	−	0.635017i	$-0.219007\pi$
$281$	244.389	+	101.229i	0.869712	+	0.360246i	0.0972138	+	0.995264i	$0.469007\pi$
$282$		0			0
$283$	342.391			1.20986			0.604931	−	0.796278i	$-0.293201\pi$
$283$	342.391			1.20986			0.604931	+	0.796278i	$0.293201\pi$
$284$	115.934	−	48.0213i	0.408217	−	0.169089i
$285$		0			0
$286$			331.719i			1.15986i
$287$	316.994	−	214.715i	1.10451	−	0.748137i
$288$		0			0
$289$	170.806	+	170.806i	0.591023	+	0.591023i
$290$	12.4349	+	30.0205i	0.0428789	+	0.103519i
$291$		0			0
$292$	−72.9191	+	72.9191i	−0.249723	+	0.249723i
$293$	−51.8649	+	125.213i	−0.177013	+	0.427348i	−0.987337	−	0.158634i	$-0.949291\pi$
$293$	−51.8649	+	125.213i	−0.177013	+	0.427348i	0.810324	+	0.585982i	$0.199291\pi$
$294$		0			0
$295$	66.6670	−	66.6670i	0.225990	−	0.225990i
$296$	151.823	−	151.823i	0.512917	−	0.512917i
$297$		0			0
$298$	−240.100	+	99.4525i	−0.805703	+	0.333733i
$299$	−56.1070	+	23.2403i	−0.187649	+	0.0777267i
$300$		0			0
$301$	239.222	−	577.532i	0.794756	−	1.91871i
$302$	−26.4121	−	10.9403i	−0.0874573	−	0.0362260i
$303$		0			0
$304$	176.668	−	426.514i	0.581144	−	1.40301i
$305$	−458.040			−1.50177
$306$		0			0
$307$	−128.881	−	128.881i	−0.419808	−	0.419808i	0.465329	−	0.885138i	$-0.345936\pi$
$307$	−128.881	−	128.881i	−0.419808	−	0.419808i	−0.885138	+	0.465329i	$0.845936\pi$
$308$	−187.690	+	187.690i	−0.609382	+	0.609382i
$309$		0			0
$310$			569.526i			1.83718i
$311$	−205.061	−	84.9389i	−0.659359	−	0.273115i	0.0278099	−	0.999613i	$-0.491147\pi$
$311$	−205.061	−	84.9389i	−0.659359	−	0.273115i	−0.687169	+	0.726498i	$0.741147\pi$
$312$		0			0
$313$	−92.2381	+	222.682i	−0.294690	+	0.711446i	0.705306	+	0.708903i	$0.250809\pi$
$313$	−92.2381	+	222.682i	−0.294690	+	0.711446i	−0.999997	+	0.00254298i	$0.999191\pi$
$314$	15.2050	+	6.29810i	0.0484234	+	0.0200576i
$315$		0			0
$316$	−39.8582	−	96.2262i	−0.126134	−	0.304513i
$317$	14.1625	+	34.1913i	0.0446766	+	0.107859i	0.944642	−	0.328101i	$-0.106409\pi$
$317$	14.1625	+	34.1913i	0.0446766	+	0.107859i	−0.899966	+	0.435960i	$0.856409\pi$
$318$		0			0
$319$	−24.6558	−	24.6558i	−0.0772908	−	0.0772908i
$320$	−22.4264	−	22.4264i	−0.0700824	−	0.0700824i
$321$		0			0
$322$	−132.327	−	54.8114i	−0.410952	−	0.170222i
$323$	−112.442	−	112.442i	−0.348117	−	0.348117i
$324$		0			0
$325$	−22.2461	+	9.21465i	−0.0684496	+	0.0283528i
$326$	133.387	−	133.387i	0.409162	−	0.409162i
$327$		0			0
$328$	163.914	+	108.034i	0.499739	+	0.329372i
$329$	668.808			2.03285
$330$		0			0
$331$	−182.614	−	440.868i	−0.551703	−	1.33193i	−0.916199	−	0.400723i	$-0.868759\pi$
$331$	−182.614	−	440.868i	−0.551703	−	1.33193i	0.364497	−	0.931205i	$-0.381241\pi$
$332$		−	202.703i		−	0.610553i
$333$		0			0
$334$	78.6092	−	189.779i	0.235357	−	0.568202i
$335$	−228.788	−	552.343i	−0.682950	−	1.64879i
$336$		0			0
$337$	99.2031	−	99.2031i	0.294371	−	0.294371i	−0.544433	−	0.838804i	$-0.683255\pi$
$337$	99.2031	−	99.2031i	0.294371	−	0.294371i	0.838804	+	0.544433i	$0.183255\pi$
$338$	182.297			0.539340
$339$		0			0
$340$	68.5086	−	28.3772i	0.201496	−	0.0834623i
$341$	−233.875	−	564.625i	−0.685851	−	1.65579i
$342$		0			0
$343$	−93.1514	−	38.5846i	−0.271578	−	0.112491i
$344$	320.526			0.931761
$345$		0			0
$346$	−374.237			−1.08161
$347$	60.2669	−	145.497i	0.173680	−	0.419300i	−0.812938	−	0.582350i	$-0.802133\pi$
$347$	60.2669	−	145.497i	0.173680	−	0.419300i	0.986618	+	0.163050i	$0.0521332\pi$
$348$		0			0
$349$	−186.842	+	186.842i	−0.535363	+	0.535363i	−0.922164	−	0.386800i	$-0.873580\pi$
$349$	−186.842	+	186.842i	−0.535363	+	0.535363i	0.386800	+	0.922164i	$0.373580\pi$
$350$	−52.4667	−	21.7324i	−0.149905	−	0.0620927i
$351$		0			0
$352$	−384.195	−	159.139i	−1.09146	−	0.452099i
$353$		−	60.6437i		−	0.171795i	−0.996304	−	0.0858976i	$-0.972624\pi$
$353$		−	60.6437i		−	0.171795i	0.996304	−	0.0858976i	$-0.0273758\pi$
$354$		0			0
$355$	−295.839	−	122.541i	−0.833350	−	0.345185i
$356$	90.7867	−	37.6051i	0.255019	−	0.105632i
$357$		0			0
$358$	−23.8451	−	57.5672i	−0.0666065	−	0.160802i
$359$			353.797i			0.985508i	0.870169	+	0.492754i	$0.164010\pi$
$359$			353.797i			0.985508i	−0.870169	+	0.492754i	$0.835990\pi$
$360$		0			0
$361$	−121.601	−	121.601i	−0.336844	−	0.336844i
$362$	−663.759	+	274.938i	−1.83359	+	0.759498i
$363$		0			0
$364$	−132.130	−	132.130i	−0.362996	−	0.362996i
$365$	263.150			0.720958
$366$		0			0
$367$	−269.550	+	269.550i	−0.734469	+	0.734469i	−0.971502	−	0.237033i	$-0.923825\pi$
$367$	−269.550	+	269.550i	−0.734469	+	0.734469i	0.237033	+	0.971502i	$0.423825\pi$
$368$		−	124.656i		−	0.338739i
$369$		0			0
$370$	578.294			1.56296
$371$	−415.264	−	415.264i	−1.11931	−	1.11931i
$372$		0			0
$373$			460.540i			1.23469i	0.786692	+	0.617346i	$0.211792\pi$
$373$			460.540i			1.23469i	−0.786692	+	0.617346i	$0.788208\pi$
$374$	−165.841	+	165.841i	−0.443424	+	0.443424i
$375$		0			0
$376$	131.233	+	316.825i	0.349024	+	0.842619i
$377$	17.3573	−	17.3573i	0.0460405	−	0.0460405i
$378$		0			0
$379$	359.502			0.948555			0.474277	−	0.880375i	$-0.342709\pi$
$379$	359.502			0.948555			0.474277	+	0.880375i	$0.342709\pi$
$380$	229.617	−	95.1106i	0.604256	−	0.250291i
$381$		0			0
$382$	56.2606	+	135.825i	0.147279	+	0.355563i
$383$	−27.3084	+	65.9283i	−0.0713013	+	0.172136i	−0.955512	−	0.294951i	$-0.904697\pi$
$383$	−27.3084	+	65.9283i	−0.0713013	+	0.172136i	0.884211	+	0.467087i	$0.154697\pi$
$384$		0			0
$385$	677.332			1.75930
$386$	−262.457	+	633.628i	−0.679941	+	1.64152i
$387$		0			0
$388$	−69.0418	+	166.682i	−0.177943	+	0.429592i
$389$	467.297	+	467.297i	1.20128	+	1.20128i	0.973778	+	0.227499i	$0.0730550\pi$
$389$	467.297	+	467.297i	1.20128	+	1.20128i	0.227499	+	0.973778i	$0.426945\pi$
$390$		0			0
$391$	−39.6691	−	16.4315i	−0.101456	−	0.0420242i
$392$			182.921i			0.466635i
$393$		0			0
$394$		−	534.335i		−	1.35618i
$395$	−101.710	+	245.550i	−0.257494	+	0.621645i
$396$		0			0
$397$	−365.881	+	151.553i	−0.921614	+	0.381745i	−0.792491	−	0.609883i	$-0.791216\pi$
$397$	−365.881	+	151.553i	−0.921614	+	0.381745i	−0.129123	+	0.991629i	$0.541216\pi$
$398$	48.8089	+	117.835i	0.122635	+	0.296068i
$399$		0			0
$400$		−	49.4253i		−	0.123563i
$401$	−62.2986	−	62.2986i	−0.155358	−	0.155358i	0.625148	−	0.780506i	$-0.285039\pi$
$401$	−62.2986	−	62.2986i	−0.155358	−	0.155358i	−0.780506	+	0.625148i	$0.785039\pi$
$402$		0			0
$403$	397.486	−	164.644i	0.986318	−	0.408546i
$404$	88.1250	+	36.5026i	0.218131	+	0.0903529i
$405$		0			0
$406$	57.8929			0.142593
$407$	−573.317	+	237.476i	−1.40864	+	0.583478i
$408$		0			0
$409$		−	215.826i		−	0.527692i	−0.964565	−	0.263846i	$-0.915009\pi$
$409$		−	215.826i		−	0.527692i	0.964565	−	0.263846i	$-0.0849911\pi$
$410$	106.424	+	517.924i	0.259571	+	1.26323i
$411$		0			0
$412$	0.0161228	+	0.0161228i	3.91329e−5	+	3.91329e-5i
$413$	−64.2819	−	155.190i	−0.155646	−	0.375763i
$414$		0			0
$415$	−365.757	+	365.757i	−0.881341	+	0.881341i
$416$	112.031	−	270.467i	0.269306	−	0.650161i
$417$		0			0
$418$	−555.841	+	555.841i	−1.32976	+	1.32976i
$419$	65.5153	−	65.5153i	0.156361	−	0.156361i	−0.624591	−	0.780952i	$-0.714734\pi$
$419$	65.5153	−	65.5153i	0.156361	−	0.156361i	0.780952	+	0.624591i	$0.214734\pi$
$420$		0			0
$421$	−381.511	+	158.027i	−0.906203	+	0.375362i	−0.786602	−	0.617460i	$-0.788162\pi$
$421$	−381.511	+	158.027i	−0.906203	+	0.375362i	−0.119601	+	0.992822i	$0.538162\pi$
$422$	447.116	−	185.201i	1.05952	−	0.438866i
$423$		0			0
$424$	115.234	−	278.200i	0.271779	−	0.656132i
$425$	−15.7286	−	6.51499i	−0.0370084	−	0.0153294i
$426$		0			0
$427$	−312.296	+	753.949i	−0.731373	+	1.76569i
$428$	−324.674			−0.758585
$429$		0			0
$430$	610.440	+	610.440i	1.41963	+	1.41963i
$431$	−44.5498	+	44.5498i	−0.103364	+	0.103364i	−0.756897	−	0.653534i	$-0.773286\pi$
$431$	−44.5498	+	44.5498i	−0.103364	+	0.103364i	0.653534	+	0.756897i	$0.273286\pi$
$432$		0			0
$433$		−	585.958i		−	1.35325i	−0.736327	−	0.676626i	$-0.763442\pi$
$433$		−	585.958i		−	1.35325i	0.736327	−	0.676626i	$-0.236558\pi$
$434$	937.458	+	388.308i	2.16004	+	0.894718i
$435$		0			0
$436$	−80.5146	+	194.379i	−0.184666	+	0.445824i
$437$	−132.957	−	55.0727i	−0.304250	−	0.126025i
$438$		0			0
$439$	7.88683	+	19.0405i	0.0179654	+	0.0433724i	0.932608	−	0.360892i	$-0.117528\pi$
$439$	7.88683	+	19.0405i	0.0179654	+	0.0433724i	−0.914642	+	0.404264i	$0.867528\pi$
$440$	132.906	+	320.863i	0.302058	+	0.729234i
$441$		0			0
$442$	−116.749	−	116.749i	−0.264138	−	0.264138i
$443$	114.623	+	114.623i	0.258744	+	0.258744i	0.824543	−	0.565799i	$-0.191432\pi$
$443$	114.623	+	114.623i	0.258744	+	0.258744i	−0.565799	+	0.824543i	$0.691432\pi$
$444$		0			0
$445$	−231.669	−	95.9605i	−0.520605	−	0.215642i
$446$	−445.894	−	445.894i	−0.999762	−	0.999762i
$447$		0			0
$448$	−52.2051	+	21.6241i	−0.116529	+	0.0482680i
$449$	53.5135	−	53.5135i	0.119184	−	0.119184i	−0.644999	−	0.764183i	$-0.723142\pi$
$449$	53.5135	−	53.5135i	0.119184	−	0.119184i	0.764183	+	0.644999i	$0.223142\pi$
$450$		0			0
$451$	−318.194	−	469.764i	−0.705529	−	1.04161i
$452$	327.460			0.724469
$453$		0			0
$454$	265.663	+	641.367i	0.585160	+	1.41270i
$455$			476.830i			1.04798i
$456$		0			0
$457$	2.45894	−	5.93640i	0.00538060	−	0.0129899i	−0.921166	−	0.389169i	$-0.872762\pi$
$457$	2.45894	−	5.93640i	0.00538060	−	0.0129899i	0.926547	+	0.376179i	$0.122762\pi$
$458$	176.819	+	426.879i	0.386068	+	0.932050i
$459$		0			0
$460$	47.4536	−	47.4536i	0.103160	−	0.103160i
$461$	−419.226			−0.909384			−0.454692	−	0.890649i	$-0.650251\pi$
$461$	−419.226			−0.909384			−0.454692	+	0.890649i	$0.650251\pi$
$462$		0			0
$463$	−18.0132	+	7.46130i	−0.0389054	+	0.0161151i	−0.402051	−	0.915617i	$-0.631703\pi$
$463$	−18.0132	+	7.46130i	−0.0389054	+	0.0161151i	0.363146	+	0.931732i	$0.381703\pi$
$464$	19.2817	+	46.5502i	0.0415555	+	0.100324i
$465$		0			0
$466$	−350.235	−	145.072i	−0.751578	−	0.311314i
$467$	−557.273			−1.19330			−0.596652	−	0.802500i	$-0.703503\pi$
$467$	−557.273			−1.19330			−0.596652	+	0.802500i	$0.703503\pi$
$468$		0			0
$469$	−1065.17			−2.27114
$470$	−353.458	+	853.324i	−0.752039	+	1.81558i
$471$		0			0
$472$	60.9027	−	60.9027i	0.129031	−	0.129031i
$473$	−855.863	−	354.510i	−1.80944	−	0.749493i
$474$		0			0
$475$	−52.7168	−	21.8360i	−0.110983	−	0.0459706i
$476$		−	132.115i		−	0.277553i
$477$		0			0
$478$	−438.901	−	181.799i	−0.918203	−	0.380332i
$479$	394.533	−	163.421i	0.823660	−	0.341171i	0.0692706	−	0.997598i	$-0.477933\pi$
$479$	394.533	−	163.421i	0.823660	−	0.341171i	0.754390	+	0.656427i	$0.227933\pi$
$480$		0			0
$481$	−167.179	−	403.606i	−0.347565	−	0.839097i
$482$		−	345.710i		−	0.717240i
$483$		0			0
$484$	102.405	+	102.405i	0.211581	+	0.211581i
$485$	425.338	−	176.181i	0.876985	−	0.363259i
$486$		0			0
$487$	12.8470	+	12.8470i	0.0263799	+	0.0263799i	0.720174	−	0.693794i	$-0.244062\pi$
$487$	12.8470	+	12.8470i	0.0263799	+	0.0263799i	−0.693794	+	0.720174i	$0.744062\pi$
$488$	−418.436			−0.857451
$489$		0			0
$490$	−348.372	+	348.372i	−0.710964	+	0.710964i
$491$			460.441i			0.937761i	0.883262	+	0.468881i	$0.155343\pi$
$491$			460.441i			0.937761i	−0.883262	+	0.468881i	$0.844657\pi$
$492$		0			0
$493$	17.3553			0.0352034
$494$	−391.303	−	391.303i	−0.792111	−	0.792111i
$495$		0			0
$496$			883.115i			1.78047i
$497$	−403.412	+	403.412i	−0.811694	+	0.811694i
$498$		0			0
$499$	230.628	+	556.785i	0.462180	+	1.11580i	0.967500	+	0.252870i	$0.0813745\pi$
$499$	230.628	+	556.785i	0.462180	+	1.11580i	−0.505320	+	0.862932i	$0.668626\pi$
$500$	−171.496	+	171.496i	−0.342991	+	0.342991i
$501$		0			0
$502$	384.584			0.766104
$503$	−746.849	+	309.355i	−1.48479	+	0.615020i	−0.970176	−	0.242403i	$-0.922064\pi$
$503$	−746.849	+	309.355i	−1.48479	+	0.615020i	−0.514613	+	0.857423i	$0.672064\pi$
$504$		0			0
$505$	−93.1471	−	224.877i	−0.184450	−	0.445301i
$506$	−81.2269	+	196.099i	−0.160527	+	0.387548i
$507$		0			0
$508$	−216.717			−0.426609
$509$	−118.879	+	287.000i	−0.233555	+	0.563852i	−0.996591	−	0.0825047i	$-0.973708\pi$
$509$	−118.879	+	287.000i	−0.233555	+	0.563852i	0.763036	+	0.646356i	$0.223708\pi$
$510$		0			0
$511$	179.418	−	433.153i	0.351111	−	0.847657i
$512$	154.089	+	154.089i	0.300954	+	0.300954i
$513$		0			0
$514$	734.466	+	304.226i	1.42892	+	0.591879i
$515$		−	0.0581836i		−	0.000112978i
$516$		0			0
$517$		−	991.128i		−	1.91708i
$518$	394.286	−	951.890i	0.761170	−	1.83763i
$519$		0			0
$520$	−225.882	+	93.5634i	−0.434388	+	0.179930i
$521$	−251.711	−	607.685i	−0.483131	−	1.16638i	−0.958114	−	0.286387i	$-0.907546\pi$
$521$	−251.711	−	607.685i	−0.483131	−	1.16638i	0.474983	−	0.879995i	$-0.342454\pi$
$522$		0			0
$523$		−	186.412i		−	0.356429i	−0.983992	−	0.178215i	$-0.942968\pi$
$523$		−	186.412i		−	0.356429i	0.983992	−	0.178215i	$-0.0570321\pi$
$524$	−82.8394	−	82.8394i	−0.158091	−	0.158091i
$525$		0			0
$526$	−771.906	+	319.734i	−1.46750	+	0.607860i
$527$	281.033	+	116.408i	0.533269	+	0.220887i
$528$		0			0
$529$	490.141			0.926543
$530$	749.294	−	310.368i	1.41376	−	0.585599i
$531$		0			0
$532$		−	442.805i		−	0.832340i
$533$	330.706	−	224.003i	0.620462	−	0.420268i
$534$		0			0
$535$	585.840	+	585.840i	1.09503	+	1.09503i
$536$	−209.006	−	504.586i	−0.389937	−	0.941391i
$537$		0			0
$538$	584.056	−	584.056i	1.08561	−	1.08561i
$539$	202.316	−	488.433i	0.375354	−	0.906184i
$540$		0			0
$541$	598.116	−	598.116i	1.10558	−	1.10558i	0.111850	−	0.993725i	$-0.464322\pi$
$541$	598.116	−	598.116i	1.10558	−	1.10558i	0.993725	−	0.111850i	$-0.0356778\pi$
$542$	−319.473	+	319.473i	−0.589434	+	0.589434i
$543$		0			0
$544$	191.227	−	79.2089i	0.351521	−	0.145605i
$545$	496.017	−	205.457i	0.910122	−	0.376985i
$546$		0			0
$547$	−397.495	+	959.638i	−0.726682	+	1.75437i	−0.0733346	+	0.997307i	$0.523364\pi$
$547$	−397.495	+	959.638i	−0.726682	+	1.75437i	−0.653347	+	0.757058i	$0.726636\pi$
$548$	241.189	+	99.9036i	0.440125	+	0.182306i
$549$		0			0
$550$	−32.2060	+	77.7522i	−0.0585564	+	0.141368i
$551$	58.1689			0.105570
$552$		0			0
$553$	334.836	+	334.836i	0.605490	+	0.605490i
$554$	81.4460	−	81.4460i	0.147014	−	0.147014i
$555$		0			0
$556$		−	130.939i		−	0.235501i
$557$	−95.0710	−	39.3797i	−0.170684	−	0.0706996i	0.295705	−	0.955279i	$-0.404445\pi$
$557$	−95.0710	−	39.3797i	−0.170684	−	0.0706996i	−0.466389	+	0.884580i	$0.654445\pi$
$558$		0			0
$559$	249.569	−	602.513i	0.446457	−	1.07784i
$560$	−904.252	−	374.554i	−1.61474	−	0.668846i
$561$		0			0
$562$	249.073	+	601.315i	0.443190	+	1.06996i
$563$	−111.117	−	268.260i	−0.197366	−	0.476483i	0.793950	−	0.607983i	$-0.208021\pi$
$563$	−111.117	−	268.260i	−0.197366	−	0.476483i	−0.991316	+	0.131499i	$0.958021\pi$
$564$		0			0
$565$	−590.866	−	590.866i	−1.04578	−	1.04578i
$566$	595.700	+	595.700i	1.05247	+	1.05247i
$567$		0			0
$568$	−270.260	−	111.945i	−0.475810	−	0.197087i
$569$	210.279	+	210.279i	0.369559	+	0.369559i	0.867316	−	0.497757i	$-0.165843\pi$
$569$	210.279	+	210.279i	0.369559	+	0.369559i	−0.497757	+	0.867316i	$0.665843\pi$
$570$		0			0
$571$	−451.072	+	186.840i	−0.789969	+	0.327216i	−0.740931	−	0.671581i	$-0.765615\pi$
$571$	−451.072	+	186.840i	−0.789969	+	0.327216i	−0.0490378	+	0.998797i	$0.515615\pi$
$572$	−195.808	+	195.808i	−0.342322	+	0.342322i
$573$		0			0
$574$	925.081	+	177.948i	1.61164	+	0.310013i
$575$	−15.4074			−0.0267954
$576$		0			0
$577$	−168.027	−	405.653i	−0.291208	−	0.703039i	0.708789	−	0.705421i	$-0.249242\pi$
$577$	−168.027	−	405.653i	−0.291208	−	0.703039i	−0.999997	+	0.00238178i	$0.999242\pi$
$578$			594.344i			1.02828i
$579$		0			0
$580$	−10.3805	+	25.0607i	−0.0178974	+	0.0432081i
$581$	352.671	+	851.424i	0.607007	+	1.46545i
$582$		0			0
$583$	−615.394	+	615.394i	−1.05556	+	1.05556i
$584$	240.397			0.411638
$585$		0			0
$586$	−308.085	+	127.613i	−0.525742	+	0.217769i
$587$	−219.970	−	531.053i	−0.374735	−	0.904691i	−0.992934	−	0.118669i	$-0.962137\pi$
$587$	−219.970	−	531.053i	−0.374735	−	0.904691i	0.618199	−	0.786022i	$-0.287863\pi$
$588$		0			0
$589$	941.927	+	390.159i	1.59920	+	0.662409i
$590$	231.978			0.393182
$591$		0			0
$592$	896.711			1.51471
$593$	−32.0547	+	77.3870i	−0.0540552	+	0.130501i	−0.948600	−	0.316477i	$-0.897500\pi$
$593$	−32.0547	+	77.3870i	−0.0540552	+	0.130501i	0.894545	+	0.446978i	$0.147500\pi$
$594$		0			0
$595$	−238.388	+	238.388i	−0.400652	+	0.400652i
$596$	−200.432	−	83.0216i	−0.336295	−	0.139298i
$597$		0			0
$598$	−138.050	−	57.1824i	−0.230854	−	0.0956227i
$599$		−	468.367i		−	0.781915i	−0.920409	−	0.390958i	$-0.872144\pi$
$599$		−	468.367i		−	0.781915i	0.920409	−	0.390958i	$-0.127856\pi$
$600$		0			0
$601$	−874.346	−	362.166i	−1.45482	−	0.602605i	−0.491478	−	0.870890i	$-0.663543\pi$
$601$	−874.346	−	362.166i	−1.45482	−	0.602605i	−0.963340	+	0.268284i	$0.913543\pi$
$602$	1421.01	−	588.601i	2.36048	−	0.977742i
$603$		0			0
$604$	−9.13278	−	22.0485i	−0.0151205	−	0.0365041i
$605$		−	369.558i		−	0.610840i
$606$		0			0
$607$	−118.483	−	118.483i	−0.195195	−	0.195195i	0.602742	−	0.797936i	$-0.294075\pi$
$607$	−118.483	−	118.483i	−0.195195	−	0.195195i	−0.797936	+	0.602742i	$0.794075\pi$
$608$	640.928	−	265.481i	1.05416	−	0.436647i
$609$		0			0
$610$	−796.910	−	796.910i	−1.30641	−	1.30641i
$611$	697.738			1.14196
$612$		0			0
$613$	786.108	−	786.108i	1.28240	−	1.28240i	0.343095	−	0.939301i	$-0.388525\pi$
$613$	786.108	−	786.108i	1.28240	−	1.28240i	0.939301	−	0.343095i	$-0.111475\pi$
$614$		−	448.461i		−	0.730393i
$615$		0			0
$616$	618.767			1.00449
$617$	361.489	+	361.489i	0.585882	+	0.585882i	0.936514	−	0.350631i	$-0.114033\pi$
$617$	361.489	+	361.489i	0.585882	+	0.585882i	−0.350631	+	0.936514i	$0.614033\pi$
$618$		0			0
$619$			621.128i			1.00344i	0.865031	+	0.501719i	$0.167299\pi$
$619$			621.128i			1.00344i	−0.865031	+	0.501719i	$0.832701\pi$
$620$	−336.182	+	336.182i	−0.542228	+	0.542228i
$621$		0			0
$622$	−208.991	−	504.548i	−0.335998	−	0.811171i
$623$	−315.908	+	315.908i	−0.507076	+	0.507076i
$624$		0			0
$625$	680.682			1.08909
$626$	−547.907	+	226.950i	−0.875250	+	0.362540i
$627$		0			0
$628$	5.25757	+	12.6929i	0.00837193	+	0.0202116i
$629$	118.200	−	285.359i	0.187917	−	0.453672i
$630$		0			0
$631$	−628.988			−0.996811			−0.498405	−	0.866944i	$-0.666081\pi$
$631$	−628.988			−0.996811			−0.498405	+	0.866944i	$0.666081\pi$
$632$	−92.9158	+	224.318i	−0.147019	+	0.354934i
$633$		0			0
$634$	−34.8465	+	84.1270i	−0.0549630	+	0.132692i
$635$	391.043	+	391.043i	0.615816	+	0.615816i
$636$		0			0
$637$	343.849	+	142.427i	0.539794	+	0.223590i
$638$		−	85.7934i		−	0.134472i
$639$		0			0
$640$		−	708.043i		−	1.10632i
$641$	381.990	−	922.205i	0.595928	−	1.43870i	−0.281769	−	0.959482i	$-0.590921\pi$
$641$	381.990	−	922.205i	0.595928	−	1.43870i	0.877697	−	0.479215i	$-0.159079\pi$
$642$		0			0
$643$	−212.622	+	88.0708i	−0.330672	+	0.136969i	−0.541841	−	0.840481i	$-0.682273\pi$
$643$	−212.622	+	88.0708i	−0.330672	+	0.136969i	0.211170	+	0.977449i	$0.432273\pi$
$644$	−45.7559	−	110.464i	−0.0710495	−	0.171529i
$645$		0			0
$646$		−	391.258i		−	0.605662i
$647$	−569.026	−	569.026i	−0.879484	−	0.879484i	0.113997	−	0.993481i	$-0.463634\pi$
$647$	−569.026	−	569.026i	−0.879484	−	0.879484i	−0.993481	+	0.113997i	$0.963634\pi$
$648$		0			0
$649$	−229.981	+	95.2614i	−0.354363	+	0.146782i
$650$	−54.7362	−	22.6725i	−0.0842096	−	0.0348807i
$651$		0			0
$652$	157.472			0.241521
$653$	−368.492	+	152.634i	−0.564306	+	0.233743i	−0.646553	−	0.762869i	$-0.723790\pi$
$653$	−368.492	+	152.634i	−0.564306	+	0.233743i	0.0822473	+	0.996612i	$0.473790\pi$
$654$		0			0
$655$			298.950i			0.456412i
$656$	165.023	+	803.101i	0.251560	+	1.22424i
$657$		0			0
$658$	1163.61	+	1163.61i	1.76840	+	1.76840i
$659$	−133.189	−	321.547i	−0.202108	−	0.487932i	0.790032	−	0.613066i	$-0.210064\pi$
$659$	−133.189	−	321.547i	−0.202108	−	0.487932i	−0.992140	+	0.125134i	$0.960064\pi$
$660$		0			0
$661$	554.984	−	554.984i	0.839613	−	0.839613i	−0.149195	−	0.988808i	$-0.547668\pi$
$661$	554.984	−	554.984i	0.839613	−	0.839613i	0.988808	+	0.149195i	$0.0476683\pi$
$662$	449.318	−	1084.75i	0.678728	−	1.63859i
$663$		0			0
$664$	−334.132	+	334.132i	−0.503211	+	0.503211i
$665$	−798.994	+	798.994i	−1.20150	+	1.20150i
$666$		0			0
$667$	14.5111	−	6.01070i	0.0217558	−	0.00901155i
$668$	158.425	−	65.6219i	0.237164	−	0.0982364i
$669$		0			0
$670$	562.929	−	1359.03i	0.840193	−	2.02841i
$671$	1117.30	+	462.802i	1.66513	+	0.689720i
$672$		0			0
$673$	−265.167	+	640.171i	−0.394008	+	0.951220i	0.595049	+	0.803689i	$0.297133\pi$
$673$	−265.167	+	640.171i	−0.394008	+	0.951220i	−0.989057	+	0.147531i	$0.952867\pi$
$674$	345.192			0.512154
$675$		0			0
$676$	107.607	+	107.607i	0.159182	+	0.159182i
$677$	161.691	−	161.691i	0.238834	−	0.238834i	−0.577533	−	0.816367i	$-0.695985\pi$
$677$	161.691	−	161.691i	0.238834	−	0.238834i	0.816367	+	0.577533i	$0.195985\pi$
$678$		0			0
$679$		−	820.241i		−	1.20801i
$680$	−159.704	−	66.1517i	−0.234859	−	0.0972819i
$681$		0			0
$682$	575.446	−	1389.25i	0.843763	−	2.03702i
$683$	−331.899	−	137.477i	−0.485942	−	0.201284i	0.126241	−	0.992000i	$-0.459709\pi$
$683$	−331.899	−	137.477i	−0.485942	−	0.201284i	−0.612184	+	0.790716i	$0.709709\pi$
$684$		0			0
$685$	−254.934	−	615.464i	−0.372166	−	0.898488i
$686$	−94.9367	−	229.198i	−0.138392	−	0.334107i
$687$		0			0
$688$	946.557	+	946.557i	1.37581	+	1.37581i
$689$	−433.227	−	433.227i	−0.628776	−	0.628776i
$690$		0			0
$691$	358.316	+	148.419i	0.518547	+	0.214789i	0.626578	−	0.779358i	$-0.284455\pi$
$691$	358.316	+	148.419i	0.518547	+	0.214789i	−0.108032	+	0.994147i	$0.534455\pi$
$692$	−220.906	−	220.906i	−0.319228	−	0.319228i
$693$		0			0
$694$	357.993	−	148.286i	0.515841	−	0.213668i
$695$	−236.265	+	236.265i	−0.339949	+	0.339949i
$696$		0			0
$697$	277.323	+	53.3455i	0.397880	+	0.0765358i
$698$	−650.144			−0.931438
$699$		0			0
$700$	−18.1419	−	43.7985i	−0.0259171	−	0.0625693i
$701$		−	1129.91i		−	1.61185i	−0.592015	−	0.805927i	$-0.701667\pi$
$701$		−	1129.91i		−	1.61185i	0.592015	−	0.805927i	$-0.298333\pi$
$702$		0			0
$703$	396.165	−	956.428i	0.563535	−	1.36049i
$704$	32.0454	+	77.3644i	0.0455190	+	0.109893i
$705$		0			0
$706$	105.509	−	105.509i	0.149447	−	0.149447i
$707$	−433.664			−0.613386
$708$		0			0
$709$	−827.622	+	342.812i	−1.16731	+	0.483515i	−0.880302	−	0.474413i	$-0.842660\pi$
$709$	−827.622	+	342.812i	−1.16731	+	0.483515i	−0.287007	+	0.957929i	$0.592660\pi$
$710$	−301.509	−	727.908i	−0.424661	−	1.02522i
$711$		0			0
$712$	−211.638	−	87.6634i	−0.297245	−	0.123123i
$713$	275.294			0.386106
$714$		0			0
$715$	706.630			0.988294
$716$	19.9056	−	48.0563i	0.0278011	−	0.0671178i
$717$		0			0
$718$	−615.545	+	615.545i	−0.857306	+	0.857306i
$719$	−62.6904	−	25.9672i	−0.0871910	−	0.0361157i	0.338662	−	0.940908i	$-0.390026\pi$
$719$	−62.6904	−	25.9672i	−0.0871910	−	0.0361157i	−0.425853	+	0.904793i	$0.640026\pi$
$720$		0			0
$721$	−0.0957721	−	0.0396701i	−0.000132832	−	5.50210e-5i
$722$		−	423.128i		−	0.586049i
$723$		0			0
$724$	−554.098	−	229.515i	−0.765328	−	0.317009i
$725$	5.75358	−	2.38321i	0.00793597	−	0.00328719i
$726$		0			0
$727$	−4.01648	−	9.69665i	−0.00552474	−	0.0133379i	0.921093	−	0.389342i	$-0.127298\pi$
$727$	−4.01648	−	9.69665i	−0.00552474	−	0.0133379i	−0.926618	+	0.376005i	$0.877298\pi$
$728$			435.602i			0.598354i
$729$		0			0
$730$	457.834	+	457.834i	0.627170	+	0.627170i
$731$	425.992	−	176.452i	0.582753	−	0.241384i
$732$		0			0
$733$	412.311	+	412.311i	0.562497	+	0.562497i	0.930016	−	0.367519i	$-0.119793\pi$
$733$	412.311	+	412.311i	0.562497	+	0.562497i	−0.367519	+	0.930016i	$0.619793\pi$
$734$	−937.939			−1.27785
$735$		0			0
$736$	132.457	−	132.457i	0.179968	−	0.179968i
$737$			1578.50i			2.14180i
$738$		0			0
$739$	−1291.04			−1.74702			−0.873508	−	0.486811i	$-0.838160\pi$
$739$	−1291.04			−1.74702			−0.873508	+	0.486811i	$0.838160\pi$
$740$	341.357	+	341.357i	0.461293	+	0.461293i
$741$		0			0
$742$		−	1444.97i		−	1.94740i
$743$	737.411	−	737.411i	0.992478	−	0.992478i	−0.00749353	−	0.999972i	$-0.502385\pi$
$743$	737.411	−	737.411i	0.992478	−	0.992478i	0.999972	+	0.00749353i	$0.00238529\pi$
$744$		0			0
$745$	211.854	+	511.462i	0.284368	+	0.686526i
$746$	−801.259	+	801.259i	−1.07407	+	1.07407i
$747$		0			0
$748$	−195.786			−0.261746
$749$	1363.74	−	564.881i	1.82075	−	0.754180i
$750$		0			0
$751$	−304.927	−	736.158i	−0.406027	−	0.980237i	−0.986172	−	0.165723i	$-0.947004\pi$
$751$	−304.927	−	736.158i	−0.406027	−	0.980237i	0.580145	−	0.814513i	$-0.302996\pi$
$752$	−548.078	+	1323.18i	−0.728827	+	1.75954i
$753$		0			0
$754$	60.3971			0.0801023
$755$	−23.3050	+	56.2632i	−0.0308675	+	0.0745208i
$756$		0			0
$757$	−207.844	+	501.779i	−0.274562	+	0.662852i	−0.999667	−	0.0257862i	$-0.991791\pi$
$757$	−207.844	+	501.779i	−0.274562	+	0.662852i	0.725105	+	0.688638i	$0.241791\pi$
$758$	625.471	+	625.471i	0.825159	+	0.825159i
$759$		0			0
$760$	−535.274	−	221.718i	−0.704308	−	0.291734i
$761$		−	166.601i		−	0.218923i	−0.993991	−	0.109462i	$-0.965087\pi$
$761$		−	166.601i		−	0.218923i	0.993991	−	0.109462i	$-0.0349127\pi$
$762$		0			0
$763$		−	956.542i		−	1.25366i
$764$	−46.9657	+	113.385i	−0.0614734	+	0.148410i
$765$		0			0
$766$	−162.215	+	67.1918i	−0.211769	+	0.0877178i
$767$	−67.0624	−	161.903i	−0.0874347	−	0.211086i
$768$		0			0
$769$			455.826i			0.592752i	0.955071	+	0.296376i	$0.0957781\pi$
$769$			455.826i			0.592752i	−0.955071	+	0.296376i	$0.904222\pi$
$770$	1178.44	+	1178.44i	1.53044	+	1.53044i
$771$		0			0
$772$	−528.944	+	219.096i	−0.685161	+	0.283803i
$773$	−101.963	−	42.2344i	−0.131905	−	0.0546370i	0.315754	−	0.948841i	$-0.397742\pi$
$773$	−101.963	−	42.2344i	−0.131905	−	0.0546370i	−0.447660	+	0.894204i	$0.647742\pi$
$774$		0			0
$775$	109.152			0.140842
$776$	388.561	−	160.947i	0.500723	−	0.207406i
$777$		0			0
$778$			1626.03i			2.09001i
$779$	929.491	+	178.796i	1.19318	+	0.229520i
$780$		0			0
$781$	597.829	+	597.829i	0.765466	+	0.765466i
$782$	−40.4294	−	97.6052i	−0.0517000	−	0.124815i
$783$		0			0
$784$	−540.191	+	540.191i	−0.689020	+	0.689020i
$785$	13.4163	−	32.3897i	0.0170908	−	0.0412608i
$786$		0			0
$787$	−872.534	+	872.534i	−1.10868	+	1.10868i	−0.115360	+	0.993324i	$0.536802\pi$
$787$	−872.534	+	872.534i	−1.10868	+	1.10868i	−0.993324	+	0.115360i	$0.963198\pi$
$788$	315.409	−	315.409i	0.400265	−	0.400265i
$789$		0			0
$790$	−604.171	+	250.256i	−0.764773	+	0.316779i
$791$	−1375.44	+	569.727i	−1.73887	+	0.720262i
$792$		0			0
$793$	−325.805	+	786.562i	−0.410851	+	0.991882i
$794$	−900.244	−	372.893i	−1.13381	−	0.469639i
$795$		0			0
$796$	−40.7450	+	98.3672i	−0.0511872	+	0.123577i
$797$	−1319.67			−1.65580			−0.827900	−	0.560875i	$-0.810465\pi$
$797$	−1319.67			−1.65580			−0.827900	+	0.560875i	$0.810465\pi$
$798$		0			0
$799$	348.829	+	348.829i	0.436582	+	0.436582i
$800$	52.5183	−	52.5183i	0.0656479	−	0.0656479i
$801$		0			0
$802$		−	216.777i		−	0.270296i
$803$	−641.903	−	265.885i	−0.799382	−	0.331115i
$804$		0			0
$805$	−116.760	+	281.883i	−0.145043	+	0.350165i
$806$	978.008	+	405.104i	1.21341	+	0.502611i
$807$		0			0
$808$	−85.0933	−	205.433i	−0.105313	−	0.254249i
$809$	462.258	+	1115.99i	0.571394	+	1.37947i	0.900368	+	0.435129i	$0.143297\pi$
$809$	462.258	+	1115.99i	0.571394	+	1.37947i	−0.328974	+	0.944339i	$0.606703\pi$
$810$		0			0
$811$	998.554	+	998.554i	1.23126	+	1.23126i	0.963479	+	0.267784i	$0.0862913\pi$
$811$	998.554	+	998.554i	1.23126	+	1.23126i	0.267784	+	0.963479i	$0.413709\pi$
$812$	34.1732	+	34.1732i	0.0420853	+	0.0420853i
$813$		0			0
$814$	−1410.64	−	584.305i	−1.73297	−	0.717820i
$815$	−284.141	−	284.141i	−0.348640	−	0.348640i
$816$		0			0
$817$	1427.78	−	591.406i	1.74759	−	0.723876i
$818$	375.500	−	375.500i	0.459046	−	0.459046i
$819$		0			0
$820$	−242.902	+	368.543i	−0.296221	+	0.449442i
$821$	−256.360			−0.312254			−0.156127	−	0.987737i	$-0.549901\pi$
$821$	−256.360			−0.312254			−0.156127	+	0.987737i	$0.549901\pi$
$822$		0			0
$823$	−192.952	−	465.828i	−0.234450	−	0.566012i	0.762242	−	0.647293i	$-0.224099\pi$
$823$	−192.952	−	465.828i	−0.234450	−	0.566012i	−0.996691	+	0.0812811i	$0.974099\pi$
$824$		−	0.0531528i		−	6.45058e-5i
$825$		0			0
$826$	158.164	−	381.843i	0.191482	−	0.462279i
$827$	197.444	+	476.672i	0.238747	+	0.576387i	0.997154	−	0.0753950i	$-0.0240218\pi$
$827$	197.444	+	476.672i	0.238747	+	0.576387i	−0.758407	+	0.651782i	$0.774022\pi$
$828$		0			0
$829$	509.916	−	509.916i	0.615098	−	0.615098i	−0.329172	−	0.944270i	$-0.606770\pi$
$829$	509.916	−	509.916i	0.615098	−	0.615098i	0.944270	+	0.329172i	$0.106770\pi$
$830$	−1272.70			−1.53338
$831$		0			0
$832$	−54.4633	+	22.5594i	−0.0654606	+	0.0271147i
$833$	100.699	+	243.110i	0.120888	+	0.291849i
$834$		0			0
$835$	−404.269	−	167.454i	−0.484155	−	0.200543i
$836$	−656.207			−0.784937
$837$		0			0
$838$	227.970			0.272041
$839$	−429.694	+	1037.37i	−0.512151	+	1.23644i	0.430479	+	0.902601i	$0.358345\pi$
$839$	−429.694	+	1037.37i	−0.512151	+	1.23644i	−0.942630	+	0.333840i	$0.891655\pi$
$840$		0			0
$841$	590.188	−	590.188i	0.701769	−	0.701769i
$842$	−938.703	−	388.823i	−1.11485	−	0.461785i
$843$		0			0
$844$	373.247	+	154.604i	0.442235	+	0.183180i
$845$		−	388.330i		−	0.459562i
$846$		0			0
$847$	−608.305	−	251.968i	−0.718188	−	0.297483i
$848$	1161.87	−	481.261i	1.37013	−	0.567524i
$849$		0			0
$850$	−16.0300	−	38.6999i	−0.0188589	−	0.0455293i
$851$		−	279.532i		−	0.328475i
$852$		0			0
$853$	26.2852	+	26.2852i	0.0308150	+	0.0308150i	0.722346	−	0.691531i	$-0.243064\pi$
$853$	26.2852	+	26.2852i	0.0308150	+	0.0308150i	−0.691531	+	0.722346i	$0.743064\pi$
$854$	−1855.08	+	768.399i	−2.17222	+	0.899765i
$855$		0			0
$856$	535.186	+	535.186i	0.625217	+	0.625217i
$857$	1341.52			1.56537			0.782684	−	0.622419i	$-0.213850\pi$
$857$	1341.52			1.56537			0.782684	+	0.622419i	$0.213850\pi$
$858$		0			0
$859$	263.322	−	263.322i	0.306545	−	0.306545i	−0.537023	−	0.843568i	$-0.680451\pi$
$859$	263.322	−	263.322i	0.306545	−	0.306545i	0.843568	+	0.537023i	$0.180451\pi$
$860$			720.665i			0.837983i
$861$		0			0
$862$	−155.018			−0.179835
$863$	944.021	+	944.021i	1.09388	+	1.09388i	0.995110	+	0.0987735i	$0.0314919\pi$
$863$	944.021	+	944.021i	1.09388	+	1.09388i	0.0987735	+	0.995110i	$0.468508\pi$
$864$		0			0
$865$			797.202i			0.921621i
$866$	1019.46	−	1019.46i	1.17721	−	1.17721i
$867$		0			0
$868$	324.154	+	782.578i	0.373450	+	0.901587i
$869$	496.205	−	496.205i	0.571006	−	0.571006i
$870$		0			0
$871$	−1111.24			−1.27582
$872$	453.129	−	187.692i	0.519643	−	0.215243i
$873$		0			0
$874$	−135.506	−	327.139i	−0.155041	−	0.374301i
$875$	421.966	−	1018.72i	0.482246	−	1.16425i
$876$		0			0
$877$	561.994			0.640815			0.320407	−	0.947280i	$-0.396180\pi$
$877$	561.994			0.640815			0.320407	+	0.947280i	$0.396180\pi$
$878$	−19.4054	+	46.8488i	−0.0221018	+	0.0533586i
$879$		0			0
$880$	−555.063	+	1340.04i	−0.630754	+	1.52277i
$881$	−608.321	−	608.321i	−0.690490	−	0.690490i	0.271850	−	0.962340i	$-0.412365\pi$
$881$	−608.321	−	608.321i	−0.690490	−	0.690490i	−0.962340	+	0.271850i	$0.912365\pi$
$882$		0			0
$883$	591.223	+	244.893i	0.669562	+	0.277342i	0.691456	−	0.722419i	$-0.256970\pi$
$883$	591.223	+	244.893i	0.669562	+	0.277342i	−0.0218938	+	0.999760i	$0.506970\pi$
$884$		−	137.830i		−	0.155916i
$885$		0			0
$886$			398.850i			0.450169i
$887$	−93.9883	+	226.908i	−0.105962	+	0.255815i	−0.967964	−	0.251091i	$-0.919211\pi$
$887$	−93.9883	+	226.908i	−0.105962	+	0.255815i	0.862002	+	0.506906i	$0.169211\pi$
$888$		0			0
$889$	910.287	−	377.053i	1.02394	−	0.424132i
$890$	−236.109	−	570.018i	−0.265291	−	0.640470i
$891$		0			0
$892$		−	526.407i		−	0.590143i
$893$	1169.15	+	1169.15i	1.30924	+	1.30924i
$894$		0			0
$895$	−122.630	+	50.7950i	−0.137017	+	0.0567542i
$896$	−1165.46	−	482.750i	−1.30074	−	0.538783i
$897$		0			0
$898$	186.208			0.207359
$899$	−102.803	+	42.5824i	−0.114353	+	0.0473664i
$900$		0			0
$901$		−	433.177i		−	0.480773i
$902$	263.706	−	1370.91i	0.292357	−	1.51985i
$903$		0			0
$904$	−539.777	−	539.777i	−0.597099	−	0.597099i
$905$	585.675	+	1413.94i	0.647155	+	1.56237i
$906$		0			0
$907$	−984.967	+	984.967i	−1.08596	+	1.08596i	−0.0900216	+	0.995940i	$0.528694\pi$
$907$	−984.967	+	984.967i	−1.08596	+	1.08596i	−0.995940	+	0.0900216i	$0.971306\pi$
$908$	−221.772	+	535.404i	−0.244242	+	0.589652i
$909$		0			0
$910$	−829.601	+	829.601i	−0.911649	+	0.911649i
$911$	−272.626	+	272.626i	−0.299260	+	0.299260i	−0.840724	−	0.541464i	$-0.817870\pi$
$911$	−272.626	+	272.626i	−0.299260	+	0.299260i	0.541464	+	0.840724i	$0.317870\pi$
$912$		0			0
$913$	1261.75	−	522.635i	1.38199	−	0.572437i
$914$	14.6064	−	6.05017i	0.0159807	−	0.00661944i
$915$		0			0
$916$	−147.606	+	356.353i	−0.161142	+	0.389032i
$917$	492.081	+	203.827i	0.536621	+	0.222276i
$918$		0			0
$919$	−361.369	+	872.421i	−0.393219	+	0.949316i	0.596015	+	0.802974i	$0.296750\pi$
$919$	−361.369	+	872.421i	−0.393219	+	0.949316i	−0.989234	+	0.146342i	$0.953250\pi$
$920$	−156.443			−0.170047
$921$		0			0
$922$	−729.380	−	729.380i	−0.791084	−	0.791084i
$923$	−420.862	+	420.862i	−0.455972	+	0.455972i
$924$		0			0
$925$		−	110.833i		−	0.119819i
$926$	−44.3211	−	18.3584i	−0.0478630	−	0.0198255i
$927$		0			0
$928$	−28.9749	+	69.9517i	−0.0312230	+	0.0753789i
$929$	−1202.26	−	497.992i	−1.29414	−	0.536051i	−0.373925	−	0.927459i	$-0.621988\pi$
$929$	−1202.26	−	497.992i	−1.29414	−	0.536051i	−0.920217	+	0.391408i	$0.871988\pi$
$930$		0			0
$931$	337.510	+	814.821i	0.362524	+	0.875211i
$932$	−121.104	−	292.372i	−0.129940	−	0.313704i
$933$		0			0
$934$	−969.557	−	969.557i	−1.03807	−	1.03807i
$935$	353.275	+	353.275i	0.377834	+	0.377834i
$936$		0			0
$937$	−163.620	−	67.7737i	−0.174621	−	0.0723305i	0.293660	−	0.955910i	$-0.405127\pi$
$937$	−163.620	−	67.7737i	−0.174621	−	0.0723305i	−0.468281	+	0.883579i	$0.655127\pi$
$938$	−1853.20	−	1853.20i	−1.97569	−	1.97569i
$939$		0			0
$940$	−712.344	+	295.062i	−0.757812	+	0.313896i
$941$	−403.528	+	403.528i	−0.428829	+	0.428829i	−0.888229	−	0.459400i	$-0.848064\pi$
$941$	−403.528	+	403.528i	−0.428829	+	0.428829i	0.459400	+	0.888229i	$0.348064\pi$
$942$		0			0
$943$	250.351	−	51.4427i	0.265484	−	0.0545522i
$944$	359.708			0.381047
$945$		0			0
$946$	−872.267	−	2105.84i	−0.922058	−	2.22604i
$947$			1749.71i			1.84763i	0.382838	+	0.923816i	$0.374947\pi$
$947$			1749.71i			1.84763i	−0.382838	+	0.923816i	$0.625053\pi$
$948$		0			0
$949$	187.179	−	451.889i	0.197238	−	0.476174i
$950$	−53.7272	−	129.709i	−0.0565549	−	0.136536i
$951$		0			0
$952$	−217.776	+	217.776i	−0.228756	+	0.228756i
$953$	−721.124			−0.756689			−0.378344	−	0.925665i	$-0.623506\pi$
$953$	−721.124			−0.756689			−0.378344	+	0.925665i	$0.623506\pi$
$954$		0			0
$955$	289.336	−	119.847i	0.302969	−	0.125494i
$956$	−151.763	−	366.389i	−0.158748	−	0.383252i
$957$		0			0
$958$	970.743	+	402.095i	1.01330	+	0.419723i
$959$	−1186.89			−1.23763
$960$		0			0
$961$	−989.299			−1.02945
$962$	411.341	−	993.065i	0.427589	−	1.03229i
$963$		0			0
$964$	204.067	−	204.067i	0.211687	−	0.211687i
$965$	1349.76	+	559.088i	1.39871	+	0.579366i
$966$		0			0
$967$	−616.328	−	255.291i	−0.637361	−	0.264003i	0.0405161	−	0.999179i	$-0.487100\pi$
$967$	−616.328	−	255.291i	−0.637361	−	0.264003i	−0.677877	+	0.735175i	$0.737100\pi$
$968$		−	337.605i		−	0.348765i
$969$		0			0
$970$	1046.54	+	433.489i	1.07890	+	0.446896i
$971$	−375.354	+	155.477i	−0.386565	+	0.160120i	−0.567497	−	0.823375i	$-0.692088\pi$
$971$	−375.354	+	155.477i	−0.386565	+	0.160120i	0.180933	+	0.983495i	$0.442088\pi$
$972$		0			0
$973$	227.812	+	549.987i	0.234134	+	0.565249i
$974$			44.7031i			0.0458964i
$975$		0			0
$976$	−1235.70	−	1235.70i	−1.26609	−	1.26609i
$977$	−1044.64	+	432.704i	−1.06923	+	0.442890i	−0.846719	−	0.532040i	$-0.821426\pi$
$977$	−1044.64	+	432.704i	−1.06923	+	0.442890i	−0.222512	+	0.974930i	$0.571426\pi$
$978$		0			0
$979$	468.155	+	468.155i	0.478197	+	0.478197i
$980$	−411.277			−0.419670
$981$		0			0
$982$	−801.086	+	801.086i	−0.815770	+	0.815770i
$983$		−	1049.71i		−	1.06786i	−0.845529	−	0.533930i	$-0.820715\pi$
$983$		−	1049.71i		−	1.06786i	0.845529	−	0.533930i	$-0.179285\pi$
$984$		0			0
$985$	−1138.24			−1.15558
$986$	30.1951	+	30.1951i	0.0306238	+	0.0306238i
$987$		0			0
$988$		−	461.959i		−	0.467570i
$989$	295.071	−	295.071i	0.298353	−	0.298353i
$990$		0			0
$991$	−27.7236	−	66.9308i	−0.0279754	−	0.0675386i	0.909274	−	0.416197i	$-0.136637\pi$
$991$	−27.7236	−	66.9308i	−0.0279754	−	0.0675386i	−0.937250	+	0.348658i	$0.886637\pi$
$992$	−938.380	+	938.380i	−0.945947	+	0.945947i
$993$		0			0
$994$	−1403.73			−1.41221
$995$	251.013	−	103.973i	0.252274	−	0.104495i
$996$		0			0
$997$	125.792	+	303.688i	0.126170	+	0.304602i	0.974325	−	0.225147i	$-0.0722862\pi$
$997$	125.792	+	303.688i	0.126170	+	0.304602i	−0.848155	+	0.529749i	$0.822286\pi$
$998$	−567.456	+	1369.96i	−0.568594	+	1.37271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.3.l.b.55.4		20
3.2	odd	2		41.3.e.b.14.2	yes	20
41.3	odd	8	inner	369.3.l.b.208.4		20
123.44	even	8		41.3.e.b.3.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.3.e.b.3.2	✓	20	123.44	even	8
41.3.e.b.14.2	yes	20	3.2	odd	2
369.3.l.b.55.4		20	1.1	even	1	trivial
369.3.l.b.208.4		20	41.3	odd	8	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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	369.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73982 + 1.73982i) q^{2} +2.05398i q^{4} +(3.70619 - 3.70619i) q^{5} +(-3.57359 - 8.62742i) q^{7} +(3.38573 - 3.38573i) q^{8} +O(q^{10})\)	\(q+(1.73982 + 1.73982i) q^{2} +2.05398i q^{4} +(3.70619 - 3.70619i) q^{5} +(-3.57359 - 8.62742i) q^{7} +(3.38573 - 3.38573i) q^{8} +12.8962 q^{10} +(-12.7853 + 5.29582i) q^{11} +(-3.72817 - 9.00060i) q^{13} +(8.79277 - 21.2276i) q^{14} +19.9971 q^{16} +(2.63591 - 6.36366i) q^{17} +(8.83468 - 21.3288i) q^{19} +(7.61243 + 7.61243i) q^{20} +(-31.4579 - 13.0303i) q^{22} -6.23370i q^{23} -2.47163i q^{25} +(9.17310 - 22.1458i) q^{26} +(17.7205 - 7.34009i) q^{28} +(0.964227 + 2.32785i) q^{29} +44.1622i q^{31} +(21.2485 + 21.2485i) q^{32} +(15.6577 - 6.48562i) q^{34} +(-45.2192 - 18.7304i) q^{35} +44.8421 q^{37} +(52.4792 - 21.7376i) q^{38} -25.0963i q^{40} +(8.25236 + 40.1609i) q^{41} +(47.3348 + 47.3348i) q^{43} +(-10.8775 - 26.2606i) q^{44} +(10.8455 - 10.8455i) q^{46} +(-27.4079 + 66.1685i) q^{47} +(-27.0135 + 27.0135i) q^{49} +(4.30020 - 4.30020i) q^{50} +(18.4871 - 7.65759i) q^{52} +(58.1018 - 24.0665i) q^{53} +(-27.7572 + 67.0118i) q^{55} +(-41.3094 - 17.1109i) q^{56} +(-2.37247 + 5.72764i) q^{58} +17.9880 q^{59} +(-61.7940 - 61.7940i) q^{61} +(-76.8345 + 76.8345i) q^{62} -6.05107i q^{64} +(-47.1752 - 19.5406i) q^{65} +(43.6507 - 105.382i) q^{67} +(13.0708 + 5.41411i) q^{68} +(-46.0859 - 111.261i) q^{70} +(-23.3796 - 56.4435i) q^{71} +(35.5014 + 35.5014i) q^{73} +(78.0173 + 78.0173i) q^{74} +(43.8089 + 18.1462i) q^{76} +(91.3786 + 91.3786i) q^{77} +(-46.8487 + 19.4053i) q^{79} +(74.1129 - 74.1129i) q^{80} +(-55.5153 + 84.2306i) q^{82} -98.6881 q^{83} +(-13.8157 - 33.3541i) q^{85} +164.708i q^{86} +(-25.3572 + 61.2177i) q^{88} +(-18.3084 - 44.2004i) q^{89} +(-64.3290 + 64.3290i) q^{91} +12.8039 q^{92} +(-162.807 + 67.4367i) q^{94} +(-46.3055 - 111.791i) q^{95} +(81.1506 + 33.6137i) q^{97} -93.9975 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{2} + 12 q^{5} - 4 q^{7} - 36 q^{8}+O(q^{10}) \) 20 * q + 8 * q^2 + 12 * q^5 - 4 * q^7 - 36 * q^8	\( 20 q + 8 q^{2} + 12 q^{5} - 4 q^{7} - 36 q^{8} + 16 q^{10} + 12 q^{11} - 48 q^{13} - 88 q^{14} - 36 q^{16} + 28 q^{17} + 76 q^{19} + 16 q^{20} - 116 q^{22} - 40 q^{26} + 72 q^{28} + 24 q^{29} - 176 q^{32} + 80 q^{34} - 60 q^{35} + 208 q^{37} + 380 q^{38} + 116 q^{41} - 40 q^{43} - 116 q^{44} - 176 q^{46} + 64 q^{47} + 168 q^{49} + 148 q^{50} - 184 q^{52} + 120 q^{53} + 20 q^{55} - 188 q^{56} + 36 q^{58} + 512 q^{59} - 460 q^{61} - 68 q^{62} - 432 q^{65} + 300 q^{67} - 120 q^{68} + 308 q^{70} + 108 q^{71} + 60 q^{73} - 140 q^{74} + 872 q^{76} - 112 q^{77} - 208 q^{79} + 68 q^{80} - 376 q^{82} + 120 q^{83} + 172 q^{85} + 316 q^{88} - 268 q^{89} - 800 q^{91} + 448 q^{92} - 212 q^{94} + 184 q^{95} - 120 q^{97} + 20 q^{98}+O(q^{100}) \) 20 * q + 8 * q^2 + 12 * q^5 - 4 * q^7 - 36 * q^8 + 16 * q^10 + 12 * q^11 - 48 * q^13 - 88 * q^14 - 36 * q^16 + 28 * q^17 + 76 * q^19 + 16 * q^20 - 116 * q^22 - 40 * q^26 + 72 * q^28 + 24 * q^29 - 176 * q^32 + 80 * q^34 - 60 * q^35 + 208 * q^37 + 380 * q^38 + 116 * q^41 - 40 * q^43 - 116 * q^44 - 176 * q^46 + 64 * q^47 + 168 * q^49 + 148 * q^50 - 184 * q^52 + 120 * q^53 + 20 * q^55 - 188 * q^56 + 36 * q^58 + 512 * q^59 - 460 * q^61 - 68 * q^62 - 432 * q^65 + 300 * q^67 - 120 * q^68 + 308 * q^70 + 108 * q^71 + 60 * q^73 - 140 * q^74 + 872 * q^76 - 112 * q^77 - 208 * q^79 + 68 * q^80 - 376 * q^82 + 120 * q^83 + 172 * q^85 + 316 * q^88 - 268 * q^89 - 800 * q^91 + 448 * q^92 - 212 * q^94 + 184 * q^95 - 120 * q^97 + 20 * q^98

Introduction

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