LMFDB - Embedded newform 690.3.f.a.229.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(229,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("690.229");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.f (of order $2$, degree $1$, 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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.15
Character	$\chi$	$=$	690.229
Dual form			690.3.f.a.229.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(-4.27075 + 2.60014i) q^{5} +2.44949 q^{6} -3.19570 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(-4.27075 + 2.60014i) q^{5} +2.44949 q^{6} -3.19570 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(-3.67715 - 6.03975i) q^{10} -11.2032i q^{11} +3.46410i q^{12} +14.7022i q^{13} -4.51940i q^{14} +(4.50357 + 7.39715i) q^{15} +4.00000 q^{16} -10.6897 q^{17} -4.24264i q^{18} -9.81553i q^{19} +(8.54150 - 5.20027i) q^{20} +5.53511i q^{21} +15.8437 q^{22} +(22.2781 + 5.71720i) q^{23} -4.89898 q^{24} +(11.4786 - 22.2091i) q^{25} -20.7920 q^{26} +5.19615i q^{27} +6.39140 q^{28} +24.7684 q^{29} +(-10.4612 + 6.36901i) q^{30} +37.7890 q^{31} +5.65685i q^{32} -19.4044 q^{33} -15.1176i q^{34} +(13.6480 - 8.30925i) q^{35} +6.00000 q^{36} -45.5299 q^{37} +13.8813 q^{38} +25.4649 q^{39} +(7.35430 + 12.0795i) q^{40} +57.0782 q^{41} -7.82783 q^{42} +15.9581 q^{43} +22.4063i q^{44} +(12.8122 - 7.80041i) q^{45} +(-8.08534 + 31.5060i) q^{46} -12.7398i q^{47} -6.92820i q^{48} -38.7875 q^{49} +(31.4083 + 16.2332i) q^{50} +18.5152i q^{51} -29.4043i q^{52} +62.0971 q^{53} -7.34847 q^{54} +(29.1297 + 47.8459i) q^{55} +9.03880i q^{56} -17.0010 q^{57} +35.0278i q^{58} +76.6723 q^{59} +(-9.00714 - 14.7943i) q^{60} +39.0469i q^{61} +53.4418i q^{62} +9.58710 q^{63} -8.00000 q^{64} +(-38.2276 - 62.7892i) q^{65} -27.4420i q^{66} -18.2212 q^{67} +21.3795 q^{68} +(9.90248 - 38.5868i) q^{69} +(11.7511 + 19.3012i) q^{70} +94.9316 q^{71} +8.48528i q^{72} -8.59349i q^{73} -64.3891i q^{74} +(-38.4672 - 19.8815i) q^{75} +19.6311i q^{76} +35.8019i q^{77} +36.0128i q^{78} -96.9457i q^{79} +(-17.0830 + 10.4005i) q^{80} +9.00000 q^{81} +80.7208i q^{82} +69.0270 q^{83} -11.0702i q^{84} +(45.6532 - 27.7948i) q^{85} +22.5682i q^{86} -42.9001i q^{87} -31.6873 q^{88} -91.6181i q^{89} +(11.0314 + 18.1193i) q^{90} -46.9837i q^{91} +(-44.5562 - 11.4344i) q^{92} -65.4525i q^{93} +18.0168 q^{94} +(25.5217 + 41.9196i) q^{95} +9.79796 q^{96} +99.7353 q^{97} -54.8538i q^{98} +33.6095i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) $ 48 * q - 96 * q^4 - 144 * q^9	$ 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) $ 48 * q - 96 * q^4 - 144 * q^9 + 192 * q^16 + 96 * q^25 + 64 * q^26 - 152 * q^29 - 8 * q^31 + 56 * q^35 + 288 * q^36 - 48 * q^39 + 40 * q^41 - 160 * q^46 + 424 * q^49 + 96 * q^50 + 32 * q^55 + 360 * q^59 - 384 * q^64 + 192 * q^69 - 496 * q^70 - 152 * q^71 + 144 * q^75 + 432 * q^81 - 136 * q^85 + 256 * q^94 + 496 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−2.00000			−0.500000
$5$	−4.27075	+	2.60014i	−0.854150	+	0.520027i
$5$	−4.27075	+	2.60014i	−0.854150	+	0.520027i
$6$	2.44949			0.408248
$7$	−3.19570			−0.456529			−0.228264	−	0.973599i	$-0.573305\pi$
$7$	−3.19570			−0.456529			−0.228264	+	0.973599i	$0.573305\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−3.00000			−0.333333
$10$	−3.67715	−	6.03975i	−0.367715	−	0.603975i
$11$		−	11.2032i		−	1.01847i	−0.860628	−	0.509234i	$-0.829929\pi$
$11$		−	11.2032i		−	1.01847i	0.860628	−	0.509234i	$-0.170071\pi$
$12$			3.46410i			0.288675i
$13$			14.7022i			1.13094i	0.824771	+	0.565468i	$0.191304\pi$
$13$			14.7022i			1.13094i	−0.824771	+	0.565468i	$0.808696\pi$
$14$		−	4.51940i		−	0.322814i
$15$	4.50357	+	7.39715i	0.300238	+	0.493144i
$16$	4.00000			0.250000
$17$	−10.6897			−0.628808			−0.314404	−	0.949289i	$-0.601805\pi$
$17$	−10.6897			−0.628808			−0.314404	+	0.949289i	$0.601805\pi$
$18$		−	4.24264i		−	0.235702i
$19$		−	9.81553i		−	0.516607i	−0.966064	−	0.258303i	$-0.916837\pi$
$19$		−	9.81553i		−	0.516607i	0.966064	−	0.258303i	$-0.0831634\pi$
$20$	8.54150	−	5.20027i	0.427075	−	0.260014i
$21$			5.53511i			0.263577i
$22$	15.8437			0.720166
$23$	22.2781	+	5.71720i	0.968613	+	0.248574i
$23$	22.2781	+	5.71720i	0.968613	+	0.248574i
$24$	−4.89898			−0.204124
$25$	11.4786	−	22.2091i	0.459143	−	0.888362i
$26$	−20.7920			−0.799692
$27$			5.19615i			0.192450i
$28$	6.39140			0.228264
$29$	24.7684			0.854083			0.427042	−	0.904232i	$-0.359556\pi$
$29$	24.7684			0.854083			0.427042	+	0.904232i	$0.359556\pi$
$30$	−10.4612	+	6.36901i	−0.348705	+	0.212300i
$31$	37.7890			1.21900			0.609501	−	0.792786i	$-0.291370\pi$
$31$	37.7890			1.21900			0.609501	+	0.792786i	$0.291370\pi$
$32$			5.65685i			0.176777i
$33$	−19.4044			−0.588013
$34$		−	15.1176i		−	0.444635i
$35$	13.6480	−	8.30925i	0.389944	−	0.237407i
$36$	6.00000			0.166667
$37$	−45.5299			−1.23054			−0.615269	−	0.788317i	$-0.710953\pi$
$37$	−45.5299			−1.23054			−0.615269	+	0.788317i	$0.710953\pi$
$38$	13.8813			0.365296
$39$	25.4649			0.652946
$40$	7.35430	+	12.0795i	0.183857	+	0.301988i
$41$	57.0782			1.39215			0.696076	−	0.717968i	$-0.254928\pi$
$41$	57.0782			1.39215			0.696076	+	0.717968i	$0.254928\pi$
$42$	−7.82783			−0.186377
$43$	15.9581			0.371119			0.185560	−	0.982633i	$-0.440590\pi$
$43$	15.9581			0.371119			0.185560	+	0.982633i	$0.440590\pi$
$44$			22.4063i			0.509234i
$45$	12.8122	−	7.80041i	0.284717	−	0.173342i
$46$	−8.08534	+	31.5060i	−0.175768	+	0.684913i
$47$		−	12.7398i		−	0.271060i	−0.990773	−	0.135530i	$-0.956726\pi$
$47$		−	12.7398i		−	0.271060i	0.990773	−	0.135530i	$-0.0432737\pi$
$48$		−	6.92820i		−	0.144338i
$49$	−38.7875			−0.791582
$50$	31.4083	+	16.2332i	0.628167	+	0.324663i
$51$			18.5152i			0.363043i
$52$		−	29.4043i		−	0.565468i
$53$	62.0971			1.17164			0.585822	−	0.810440i	$-0.300772\pi$
$53$	62.0971			1.17164			0.585822	+	0.810440i	$0.300772\pi$
$54$	−7.34847			−0.136083
$55$	29.1297	+	47.8459i	0.529632	+	0.869925i
$56$			9.03880i			0.161407i
$57$	−17.0010			−0.298263
$58$			35.0278i			0.603928i
$59$	76.6723			1.29953			0.649765	−	0.760135i	$-0.274867\pi$
$59$	76.6723			1.29953			0.649765	+	0.760135i	$0.274867\pi$
$60$	−9.00714	−	14.7943i	−0.150119	−	0.246572i
$61$			39.0469i			0.640113i	0.947398	+	0.320057i	$0.103702\pi$
$61$			39.0469i			0.640113i	−0.947398	+	0.320057i	$0.896298\pi$
$62$			53.4418i			0.861964i
$63$	9.58710			0.152176
$64$	−8.00000			−0.125000
$65$	−38.2276	−	62.7892i	−0.588117	−	0.965988i
$66$		−	27.4420i		−	0.415788i
$67$	−18.2212			−0.271958			−0.135979	−	0.990712i	$-0.543418\pi$
$67$	−18.2212			−0.271958			−0.135979	+	0.990712i	$0.543418\pi$
$68$	21.3795			0.314404
$69$	9.90248	−	38.5868i	0.143514	−	0.559229i
$70$	11.7511	+	19.3012i	0.167872	+	0.275732i
$71$	94.9316			1.33707			0.668533	−	0.743683i	$-0.266923\pi$
$71$	94.9316			1.33707			0.668533	+	0.743683i	$0.266923\pi$
$72$			8.48528i			0.117851i
$73$		−	8.59349i		−	0.117719i	−0.998266	−	0.0588595i	$-0.981254\pi$
$73$		−	8.59349i		−	0.117719i	0.998266	−	0.0588595i	$-0.0187464\pi$
$74$		−	64.3891i		−	0.870122i
$75$	−38.4672	−	19.8815i	−0.512896	−	0.265087i
$76$			19.6311i			0.258303i
$77$			35.8019i			0.464960i
$78$			36.0128i			0.461702i
$79$		−	96.9457i		−	1.22716i	−0.789632	−	0.613580i	$-0.789729\pi$
$79$		−	96.9457i		−	1.22716i	0.789632	−	0.613580i	$-0.210271\pi$
$80$	−17.0830	+	10.4005i	−0.213537	+	0.130007i
$81$	9.00000			0.111111
$82$			80.7208i			0.984400i
$83$	69.0270			0.831651			0.415825	−	0.909444i	$-0.363493\pi$
$83$	69.0270			0.831651			0.415825	+	0.909444i	$0.363493\pi$
$84$		−	11.0702i		−	0.131788i
$85$	45.6532	−	27.7948i	0.537096	−	0.326997i
$86$			22.5682i			0.262421i
$87$		−	42.9001i		−	0.493105i
$88$	−31.6873			−0.360083
$89$		−	91.6181i		−	1.02942i	−0.857365	−	0.514708i	$-0.827900\pi$
$89$		−	91.6181i		−	1.02942i	0.857365	−	0.514708i	$-0.172100\pi$
$90$	11.0314	+	18.1193i	0.122572	+	0.201325i
$91$		−	46.9837i		−	0.516304i
$92$	−44.5562	−	11.4344i	−0.484306	−	0.124287i
$93$		−	65.4525i		−	0.703791i
$94$	18.0168			0.191668
$95$	25.5217	+	41.9196i	0.268650	+	0.441259i
$96$	9.79796			0.102062
$97$	99.7353			1.02820			0.514099	−	0.857731i	$-0.328126\pi$
$97$	99.7353			1.02820			0.514099	+	0.857731i	$0.328126\pi$
$98$		−	54.8538i		−	0.559733i
$99$			33.6095i			0.339490i
$100$	−22.9572	+	44.4181i	−0.229572	+	0.444181i
$101$	24.8729			0.246267			0.123133	−	0.992390i	$-0.460706\pi$
$101$	24.8729			0.246267			0.123133	+	0.992390i	$0.460706\pi$
$102$	−26.1844			−0.256710
$103$	40.9185			0.397267			0.198633	−	0.980074i	$-0.436350\pi$
$103$	40.9185			0.397267			0.198633	+	0.980074i	$0.436350\pi$
$104$	41.5840			0.399846
$105$	−14.3921	−	23.6391i	−0.137067	−	0.225134i
$106$			87.8185i			0.828477i
$107$	−17.8171			−0.166515			−0.0832575	−	0.996528i	$-0.526532\pi$
$107$	−17.8171			−0.166515			−0.0832575	+	0.996528i	$0.526532\pi$
$108$		−	10.3923i		−	0.0962250i
$109$			73.8190i			0.677239i	0.940923	+	0.338619i	$0.109960\pi$
$109$			73.8190i			0.677239i	−0.940923	+	0.338619i	$0.890040\pi$
$110$	−67.6643	+	41.1957i	−0.615130	+	0.374506i
$111$			78.8602i			0.710452i
$112$	−12.7828			−0.114132
$113$	−118.752			−1.05090			−0.525450	−	0.850824i	$-0.676103\pi$
$113$	−118.752			−1.05090			−0.525450	+	0.850824i	$0.676103\pi$
$114$		−	24.0430i		−	0.210904i
$115$	−110.010	+	33.5094i	−0.956606	+	0.291386i
$116$	−49.5368			−0.427042
$117$		−	44.1065i		−	0.376978i
$118$			108.431i			0.918906i
$119$	34.1612			0.287069
$120$	20.9223	−	12.7380i	0.174353	−	0.106150i
$121$	−4.51074			−0.0372788
$122$	−55.2207			−0.452628
$123$		−	98.8624i		−	0.803759i
$124$	−75.5781			−0.609501
$125$	8.72443	+	124.695i	0.0697955	+	0.997561i
$126$			13.5582i			0.107605i
$127$			137.061i			1.07922i	0.841916	+	0.539609i	$0.181428\pi$
$127$			137.061i			1.07922i	−0.841916	+	0.539609i	$0.818572\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	27.6403i		−	0.214266i
$130$	88.7973	−	54.0620i	0.683057	−	0.415862i
$131$	56.4354			0.430805			0.215402	−	0.976525i	$-0.430894\pi$
$131$	56.4354			0.430805			0.215402	+	0.976525i	$0.430894\pi$
$132$	38.8089			0.294007
$133$			31.3675i			0.235846i
$134$		−	25.7686i		−	0.192303i
$135$	−13.5107	−	22.1915i	−0.100079	−	0.164381i
$136$			30.2352i			0.222317i
$137$	−185.263			−1.35228			−0.676141	−	0.736772i	$-0.736349\pi$
$137$	−185.263			−1.35228			−0.676141	+	0.736772i	$0.736349\pi$
$138$	54.5700	+	14.0042i	0.395435	+	0.101480i
$139$	−216.501			−1.55756			−0.778780	−	0.627297i	$-0.784161\pi$
$139$	−216.501			−1.55756			−0.778780	+	0.627297i	$0.784161\pi$
$140$	−27.2961	+	16.6185i	−0.194972	+	0.118704i
$141$	−22.0660			−0.156496
$142$			134.254i			0.945448i
$143$	164.711			1.15182
$144$	−12.0000			−0.0833333
$145$	−105.780	+	64.4012i	−0.729515	+	0.444147i
$146$	12.1530			0.0832399
$147$			67.1819i			0.457020i
$148$	91.0599			0.615269
$149$			42.7648i			0.287012i	0.989649	+	0.143506i	$0.0458377\pi$
$149$			42.7648i			0.287012i	−0.989649	+	0.143506i	$0.954162\pi$
$150$	28.1167	−	54.4009i	0.187444	−	0.362672i
$151$	−232.802			−1.54173			−0.770867	−	0.636996i	$-0.780177\pi$
$151$	−232.802			−1.54173			−0.770867	+	0.636996i	$0.780177\pi$
$152$	−27.7625			−0.182648
$153$	32.0692			0.209603
$154$	−50.6316			−0.328776
$155$	−161.387	+	98.2566i	−1.04121	+	0.633914i
$156$	−50.9298			−0.326473
$157$	225.331			1.43523			0.717613	−	0.696442i	$-0.245235\pi$
$157$	225.331			1.43523			0.717613	+	0.696442i	$0.245235\pi$
$158$	137.102			0.867733
$159$		−	107.555i		−	0.676448i
$160$	−14.7086	−	24.1590i	−0.0919287	−	0.150994i
$161$	−71.1941	−	18.2705i	−0.442199	−	0.113481i
$162$			12.7279i			0.0785674i
$163$		−	160.569i		−	0.985086i	−0.870288	−	0.492543i	$-0.836067\pi$
$163$		−	160.569i		−	0.985086i	0.870288	−	0.492543i	$-0.163933\pi$
$164$	−114.156			−0.696076
$165$	82.8715	−	50.4542i	0.502251	−	0.305783i
$166$			97.6189i			0.588066i
$167$		−	168.699i		−	1.01017i	−0.863069	−	0.505086i	$-0.831461\pi$
$167$		−	168.699i		−	1.01017i	0.863069	−	0.505086i	$-0.168539\pi$
$168$	15.6557			0.0931885
$169$	−47.1534			−0.279014
$170$	39.3078	+	64.5634i	0.231222	+	0.379784i
$171$			29.4466i			0.172202i
$172$	−31.9162			−0.185560
$173$			48.8655i			0.282460i	0.989977	+	0.141230i	$0.0451057\pi$
$173$			48.8655i			0.282460i	−0.989977	+	0.141230i	$0.954894\pi$
$174$	60.6700			0.348678
$175$	−36.6821	+	70.9735i	−0.209612	+	0.405563i
$176$		−	44.8126i		−	0.254617i
$177$		−	132.800i		−	0.750284i
$178$	129.568			0.727908
$179$	141.731			0.791794			0.395897	−	0.918295i	$-0.370434\pi$
$179$	141.731			0.791794			0.395897	+	0.918295i	$0.370434\pi$
$180$	−25.6245	+	15.6008i	−0.142358	+	0.0866712i
$181$		−	97.7581i		−	0.540100i	−0.962846	−	0.270050i	$-0.912960\pi$
$181$		−	97.7581i		−	0.540100i	0.962846	−	0.270050i	$-0.0870402\pi$
$182$	66.4449			0.365082
$183$	67.6312			0.369570
$184$	16.1707	−	63.0120i	0.0878841	−	0.342456i
$185$	194.447	−	118.384i	1.05106	−	0.639914i
$186$	92.5639			0.497655
$187$			119.759i			0.640422i
$188$			25.4796i			0.135530i
$189$		−	16.6053i		−	0.0878590i
$190$	−59.2833	+	36.0931i	−0.312018	+	0.189964i
$191$			93.5071i			0.489566i	0.969578	+	0.244783i	$0.0787167\pi$
$191$			93.5071i			0.489566i	−0.969578	+	0.244783i	$0.921283\pi$
$192$			13.8564i			0.0721688i
$193$			39.3466i			0.203869i	0.994791	+	0.101934i	$0.0325031\pi$
$193$			39.3466i			0.203869i	−0.994791	+	0.101934i	$0.967497\pi$
$194$			141.047i			0.727046i
$195$	−108.754	+	66.2122i	−0.557713	+	0.339550i
$196$	77.5750			0.395791
$197$		−	327.431i		−	1.66209i	−0.556208	−	0.831043i	$-0.687744\pi$
$197$		−	327.431i		−	1.66209i	0.556208	−	0.831043i	$-0.312256\pi$
$198$	−47.5310			−0.240055
$199$		−	174.324i		−	0.876001i	−0.898975	−	0.438000i	$-0.855687\pi$
$199$		−	174.324i		−	0.876001i	0.898975	−	0.438000i	$-0.144313\pi$
$200$	−62.8167	−	32.4663i	−0.314083	−	0.162332i
$201$			31.5600i			0.157015i
$202$			35.1756i			0.174137i
$203$	−79.1524			−0.389913
$204$		−	37.0303i		−	0.181521i
$205$	−243.767	+	148.411i	−1.18911	+	0.723957i
$206$			57.8674i			0.280910i
$207$	−66.8343	−	17.1516i	−0.322871	−	0.0828580i
$208$			58.8086i			0.282734i
$209$	−109.965			−0.526148
$210$	33.4307	−	20.3534i	0.159194	−	0.0969211i
$211$	−276.060			−1.30834			−0.654170	−	0.756348i	$-0.726982\pi$
$211$	−276.060			−1.30834			−0.654170	+	0.756348i	$0.726982\pi$
$212$	−124.194			−0.585822
$213$		−	164.426i		−	0.771955i
$214$		−	25.1972i		−	0.117744i
$215$	−68.1531	+	41.4933i	−0.316991	+	0.192992i
$216$	14.6969			0.0680414
$217$	−120.762			−0.556509
$218$	−104.396			−0.478880
$219$	−14.8844			−0.0679651
$220$	−58.2595	−	95.6917i	−0.264816	−	0.434962i
$221$		−	157.162i		−	0.711141i
$222$	−111.525			−0.502365
$223$			239.528i			1.07412i	0.843545	+	0.537059i	$0.180465\pi$
$223$			239.528i			1.07412i	−0.843545	+	0.537059i	$0.819535\pi$
$224$		−	18.0776i		−	0.0807036i
$225$	−34.4357	+	66.6272i	−0.153048	+	0.296121i
$226$		−	167.940i		−	0.743099i
$227$	164.561			0.724936			0.362468	−	0.931996i	$-0.381934\pi$
$227$	164.561			0.724936			0.362468	+	0.931996i	$0.381934\pi$
$228$	34.0020			0.149132
$229$			88.8399i			0.387947i	0.981007	+	0.193974i	$0.0621376\pi$
$229$			88.8399i			0.387947i	−0.981007	+	0.193974i	$0.937862\pi$
$230$	−47.3894	−	155.577i	−0.206041	−	0.676422i
$231$	62.0108			0.268445
$232$		−	70.0557i		−	0.301964i
$233$		−	206.041i		−	0.884296i	−0.896942	−	0.442148i	$-0.854217\pi$
$233$		−	206.041i		−	0.884296i	0.896942	−	0.442148i	$-0.145783\pi$
$234$	62.3760			0.266564
$235$	33.1252	+	54.4085i	0.140958	+	0.231526i
$236$	−153.345			−0.649765
$237$	−167.915			−0.708501
$238$			48.3112i			0.202988i
$239$	153.776			0.643413			0.321706	−	0.946839i	$-0.395744\pi$
$239$	153.776			0.643413			0.321706	+	0.946839i	$0.395744\pi$
$240$	18.0143	+	29.5886i	0.0750595	+	0.123286i
$241$			390.573i			1.62063i	0.585991	+	0.810317i	$0.300705\pi$
$241$			390.573i			1.62063i	−0.585991	+	0.810317i	$0.699295\pi$
$242$		−	6.37914i		−	0.0263601i
$243$		−	15.5885i		−	0.0641500i
$244$		−	78.0938i		−	0.320057i
$245$	165.652	−	100.853i	0.676129	−	0.411644i
$246$	139.813			0.568344
$247$	144.309			0.584249
$248$		−	106.884i		−	0.430982i
$249$		−	119.558i		−	0.480154i
$250$	−176.346	+	12.3382i	−0.705382	+	0.0493529i
$251$		−	403.416i		−	1.60723i	−0.595147	−	0.803617i	$-0.702906\pi$
$251$		−	403.416i		−	1.60723i	0.595147	−	0.803617i	$-0.297094\pi$
$252$	−19.1742			−0.0760881
$253$	64.0507	−	249.585i	0.253165	−	0.986502i
$254$	−193.833			−0.763122
$255$	−48.1420	−	79.0736i	−0.188792	−	0.310093i
$256$	16.0000			0.0625000
$257$		−	310.575i		−	1.20846i	−0.796809	−	0.604231i	$-0.793480\pi$
$257$		−	310.575i		−	1.20846i	0.796809	−	0.604231i	$-0.206520\pi$
$258$	39.0893			0.151509
$259$	145.500			0.561776
$260$	76.4552	+	125.578i	0.294059	+	0.482994i
$261$	−74.3052			−0.284694
$262$			79.8117i			0.304625i
$263$	222.756			0.846980			0.423490	−	0.905901i	$-0.360805\pi$
$263$	222.756			0.846980			0.423490	+	0.905901i	$0.360805\pi$
$264$			54.8840i			0.207894i
$265$	−265.201	+	161.461i	−1.00076	+	0.609286i
$266$	−44.3603			−0.166768
$267$	−158.687			−0.594334
$268$	36.4423			0.135979
$269$	42.0265			0.156232			0.0781161	−	0.996944i	$-0.475110\pi$
$269$	42.0265			0.156232			0.0781161	+	0.996944i	$0.475110\pi$
$270$	31.3835	−	19.1070i	0.116235	−	0.0707667i
$271$	170.649			0.629700			0.314850	−	0.949141i	$-0.398046\pi$
$271$	170.649			0.629700			0.314850	+	0.949141i	$0.398046\pi$
$272$	−42.7590			−0.157202
$273$	−81.3781			−0.298088
$274$		−	262.001i		−	0.956208i
$275$	−248.812	−	128.596i	−0.904769	−	0.467623i
$276$	−19.8050	+	77.1736i	−0.0717571	+	0.279614i
$277$		−	412.691i		−	1.48986i	−0.667143	−	0.744930i	$-0.732483\pi$
$277$		−	412.691i		−	1.48986i	0.667143	−	0.744930i	$-0.267517\pi$
$278$		−	306.178i		−	1.10136i
$279$	−113.367			−0.406334
$280$	−23.5021	−	38.6025i	−0.0839361	−	0.137866i
$281$		−	20.8145i		−	0.0740729i	−0.999314	−	0.0370364i	$-0.988208\pi$
$281$		−	20.8145i		−	0.0740729i	0.999314	−	0.0370364i	$-0.0117918\pi$
$282$		−	31.2060i		−	0.110660i
$283$	402.588			1.42257			0.711286	−	0.702903i	$-0.248113\pi$
$283$	402.588			1.42257			0.711286	+	0.702903i	$0.248113\pi$
$284$	−189.863			−0.668533
$285$	72.6070	−	44.2049i	0.254761	−	0.155105i
$286$			232.936i			0.814461i
$287$	−182.405			−0.635557
$288$		−	16.9706i		−	0.0589256i
$289$	−174.729			−0.604600
$290$	−91.0771	−	149.595i	−0.314059	−	0.515845i
$291$		−	172.747i		−	0.593631i
$292$			17.1870i			0.0588595i
$293$	107.231			0.365977			0.182988	−	0.983115i	$-0.441423\pi$
$293$	107.231			0.365977			0.182988	+	0.983115i	$0.441423\pi$
$294$	−95.0096			−0.323162
$295$	−327.448	+	199.358i	−1.10999	+	0.675791i
$296$			128.778i			0.435061i
$297$	58.2133			0.196004
$298$	−60.4786			−0.202948
$299$	−84.0552	+	327.536i	−0.281121	+	1.09544i
$300$	76.9344	+	39.7630i	0.256448	+	0.132543i
$301$	−50.9974			−0.169426
$302$		−	329.231i		−	1.09017i
$303$		−	43.0812i		−	0.142182i
$304$		−	39.2621i		−	0.129152i
$305$	−101.527	−	166.760i	−0.332876	−	0.546753i
$306$			45.3527i			0.148212i
$307$			225.517i			0.734582i	0.930106	+	0.367291i	$0.119715\pi$
$307$			225.517i			0.734582i	−0.930106	+	0.367291i	$0.880285\pi$
$308$		−	71.6039i		−	0.232480i
$309$		−	70.8729i		−	0.229362i
$310$	−138.956	−	228.236i	−0.448245	−	0.736246i
$311$	−284.663			−0.915314			−0.457657	−	0.889129i	$-0.651311\pi$
$311$	−284.663			−0.915314			−0.457657	+	0.889129i	$0.651311\pi$
$312$		−	72.0256i		−	0.230851i
$313$	−152.480			−0.487158			−0.243579	−	0.969881i	$-0.578321\pi$
$313$	−152.480			−0.487158			−0.243579	+	0.969881i	$0.578321\pi$
$314$			318.665i			1.01486i
$315$	−40.9441	+	24.9278i	−0.129981	+	0.0791358i
$316$			193.891i			0.613580i
$317$			570.042i			1.79824i	0.437704	+	0.899119i	$0.355792\pi$
$317$			570.042i			1.79824i	−0.437704	+	0.899119i	$0.644208\pi$
$318$	152.106			0.478321
$319$		−	277.484i		−	0.869857i
$320$	34.1660	−	20.8011i	0.106769	−	0.0650034i
$321$			30.8601i			0.0961375i
$322$	25.8383	−	100.684i	0.0802432	−	0.312682i
$323$			104.925i			0.324847i
$324$	−18.0000			−0.0555556
$325$	326.521	+	168.760i	1.00468	+	0.519261i
$326$	227.079			0.696561
$327$	127.858			0.391004
$328$		−	161.442i		−	0.492200i
$329$			40.7126i			0.123747i
$330$	71.3530	+	117.198i	0.216221	+	0.355145i
$331$	124.401			0.375835			0.187917	−	0.982185i	$-0.439826\pi$
$331$	124.401			0.375835			0.187917	+	0.982185i	$0.439826\pi$
$332$	−138.054			−0.415825
$333$	136.590			0.410180
$334$	238.576			0.714300
$335$	77.8180	−	47.3775i	0.232292	−	0.141425i
$336$			22.1405i			0.0658942i
$337$	214.663			0.636983			0.318491	−	0.947926i	$-0.396824\pi$
$337$	214.663			0.636983			0.318491	+	0.947926i	$0.396824\pi$
$338$		−	66.6849i		−	0.197293i
$339$			205.684i			0.606738i
$340$	−91.3064	+	55.5896i	−0.268548	+	0.163499i
$341$		−	423.356i		−	1.24151i
$342$	−41.6438			−0.121765
$343$	280.542			0.817908
$344$		−	45.1364i		−	0.131210i
$345$	58.0399	+	190.542i	0.168232	+	0.552297i
$346$	−69.1063			−0.199729
$347$			550.835i			1.58742i	0.608296	+	0.793710i	$0.291853\pi$
$347$			550.835i			1.58742i	−0.608296	+	0.793710i	$0.708147\pi$
$348$			85.8003i			0.246553i
$349$	−369.105			−1.05761			−0.528804	−	0.848744i	$-0.677359\pi$
$349$	−369.105			−1.05761			−0.528804	+	0.848744i	$0.677359\pi$
$350$	−100.372	−	51.8763i	−0.286776	−	0.148218i
$351$	−76.3946			−0.217649
$352$	63.3746			0.180042
$353$		−	414.260i		−	1.17354i	−0.809753	−	0.586770i	$-0.800399\pi$
$353$		−	414.260i		−	1.17354i	0.809753	−	0.586770i	$-0.199601\pi$
$354$	187.808			0.530531
$355$	−405.429	+	246.835i	−1.14205	+	0.695311i
$356$			183.236i			0.514708i
$357$		−	59.1689i		−	0.165739i
$358$			200.438i			0.559883i
$359$			285.478i			0.795202i	0.917558	+	0.397601i	$0.130157\pi$
$359$			285.478i			0.795202i	−0.917558	+	0.397601i	$0.869843\pi$
$360$	−22.0629	−	36.2385i	−0.0612858	−	0.100663i
$361$	264.655			0.733118
$362$	138.251			0.381908
$363$			7.81282i			0.0215229i
$364$			93.9673i			0.258152i
$365$	22.3442	+	36.7006i	0.0612171	+	0.100550i
$366$			95.6450i			0.261325i
$367$	−273.124			−0.744208			−0.372104	−	0.928191i	$-0.621363\pi$
$367$	−273.124			−0.744208			−0.372104	+	0.928191i	$0.621363\pi$
$368$	89.1124	+	22.8688i	0.242153	+	0.0621435i
$369$	−171.235			−0.464051
$370$	167.420	+	274.989i	0.452487	+	0.743215i
$371$	−198.444			−0.534888
$372$			130.905i			0.351895i
$373$	481.201			1.29008			0.645042	−	0.764147i	$-0.276840\pi$
$373$	481.201			1.29008			0.645042	+	0.764147i	$0.276840\pi$
$374$	−169.365			−0.452846
$375$	215.978	−	15.1112i	0.575942	−	0.0402964i
$376$	−36.0336			−0.0958341
$377$			364.149i			0.965913i
$378$	23.4835			0.0621257
$379$			502.144i			1.32492i	0.749098	+	0.662459i	$0.230487\pi$
$379$			502.144i			1.32492i	−0.749098	+	0.662459i	$0.769513\pi$
$380$	−51.0434	−	83.8393i	−0.134325	−	0.220630i
$381$	237.396			0.623087
$382$	−132.239			−0.346175
$383$	579.743			1.51369			0.756844	−	0.653595i	$-0.226740\pi$
$383$	579.743			1.51369			0.756844	+	0.653595i	$0.226740\pi$
$384$	−19.5959			−0.0510310
$385$	−93.0899	−	152.901i	−0.241792	−	0.397145i
$386$	−55.6445			−0.144157
$387$	−47.8744			−0.123706
$388$	−199.471			−0.514099
$389$		−	282.311i		−	0.725736i	−0.931841	−	0.362868i	$-0.881798\pi$
$389$		−	282.311i		−	0.725736i	0.931841	−	0.362868i	$-0.118202\pi$
$390$	−93.6381	−	153.802i	−0.240098	−	0.394363i
$391$	−238.147	−	61.1154i	−0.609072	−	0.156305i
$392$			109.708i			0.279866i
$393$		−	97.7490i		−	0.248725i
$394$	463.057			1.17527
$395$	252.072	+	414.031i	0.638157	+	1.04818i
$396$		−	67.2189i		−	0.169745i
$397$		−	44.7863i		−	0.112812i	−0.998408	−	0.0564059i	$-0.982036\pi$
$397$		−	44.7863i		−	0.112812i	0.998408	−	0.0564059i	$-0.0179641\pi$
$398$	246.532			0.619426
$399$	54.3301			0.136166
$400$	45.9143	−	88.8362i	0.114786	−	0.222091i
$401$			176.453i			0.440032i	0.975496	+	0.220016i	$0.0706110\pi$
$401$			176.453i			0.440032i	−0.975496	+	0.220016i	$0.929389\pi$
$402$	−44.6325			−0.111026
$403$			555.580i			1.37861i
$404$	−49.7459			−0.123133
$405$	−38.4367	+	23.4012i	−0.0949055	+	0.0577808i
$406$		−	111.938i		−	0.275710i
$407$			510.079i			1.25327i
$408$	52.3688			0.128355
$409$	546.610			1.33645			0.668227	−	0.743957i	$-0.267053\pi$
$409$	546.610			1.33645			0.668227	+	0.743957i	$0.267053\pi$
$410$	−209.885	−	344.738i	−0.511915	−	0.840825i
$411$			320.884i			0.780741i
$412$	−81.8369			−0.198633
$413$	−245.021			−0.593272
$414$	24.2560	−	94.5180i	0.0585894	−	0.228304i
$415$	−294.797	+	179.480i	−0.710354	+	0.432481i
$416$	−83.1679			−0.199923
$417$			374.990i			0.899258i
$418$		−	155.514i		−	0.372043i
$419$			695.370i			1.65959i	0.558066	+	0.829797i	$0.311544\pi$
$419$			695.370i			1.65959i	−0.558066	+	0.829797i	$0.688456\pi$
$420$	28.7841	+	47.2782i	0.0685336	+	0.112567i
$421$		−	376.599i		−	0.894534i	−0.894400	−	0.447267i	$-0.852397\pi$
$421$		−	376.599i		−	0.894534i	0.894400	−	0.447267i	$-0.147603\pi$
$422$		−	390.407i		−	0.925136i
$423$			38.2194i			0.0903533i
$424$		−	175.637i		−	0.414238i
$425$	−122.703	+	237.409i	−0.288713	+	0.558609i
$426$	232.534			0.545855
$427$		−	124.782i		−	0.292230i
$428$	35.6342			0.0832575
$429$		−	285.287i		−	0.665005i
$430$	−58.6804	−	96.3831i	−0.136466	−	0.224147i
$431$		−	717.791i		−	1.66541i	−0.553718	−	0.832704i	$-0.686792\pi$
$431$		−	717.791i		−	1.66541i	0.553718	−	0.832704i	$-0.313208\pi$
$432$			20.7846i			0.0481125i
$433$	426.428			0.984823			0.492411	−	0.870363i	$-0.336116\pi$
$433$	426.428			0.984823			0.492411	+	0.870363i	$0.336116\pi$
$434$		−	170.784i		−	0.393511i
$435$	111.546	+	183.216i	0.256428	+	0.421186i
$436$		−	147.638i		−	0.338619i
$437$	56.1173	−	218.671i	0.128415	−	0.500392i
$438$		−	21.0497i		−	0.0480586i
$439$	−454.954			−1.03634			−0.518171	−	0.855277i	$-0.673387\pi$
$439$	−454.954			−1.03634			−0.518171	+	0.855277i	$0.673387\pi$
$440$	135.329	−	82.3913i	0.307565	−	0.187253i
$441$	116.363			0.263861
$442$	222.261			0.502853
$443$			745.667i			1.68322i	0.540085	+	0.841611i	$0.318392\pi$
$443$			745.667i			1.68322i	−0.540085	+	0.841611i	$0.681608\pi$
$444$		−	157.720i		−	0.355226i
$445$	238.220	+	391.278i	0.535325	+	0.879276i
$446$	−338.744			−0.759516
$447$	74.0708			0.165707
$448$	25.5656			0.0570661
$449$	504.255			1.12306			0.561532	−	0.827455i	$-0.310212\pi$
$449$	504.255			1.12306			0.561532	+	0.827455i	$0.310212\pi$
$450$	−94.2250	−	48.6995i	−0.209389	−	0.108221i
$451$		−	639.457i		−	1.41786i
$452$	237.503			0.525450
$453$			403.225i			0.890120i
$454$			232.724i			0.512607i
$455$	122.164	+	200.655i	0.268492	+	0.441001i
$456$			48.0861i			0.105452i
$457$	290.397			0.635443			0.317721	−	0.948184i	$-0.397082\pi$
$457$	290.397			0.635443			0.317721	+	0.948184i	$0.397082\pi$
$458$	−125.639			−0.274320
$459$		−	55.5455i		−	0.121014i
$460$	220.019	−	67.0187i	0.478303	−	0.145693i
$461$	537.525			1.16600			0.582999	−	0.812473i	$-0.301879\pi$
$461$	537.525			1.16600			0.582999	+	0.812473i	$0.301879\pi$
$462$			87.6964i			0.189819i
$463$		−	604.525i		−	1.30567i	−0.757500	−	0.652835i	$-0.773580\pi$
$463$		−	604.525i		−	1.30567i	0.757500	−	0.652835i	$-0.226420\pi$
$464$	99.0737			0.213521
$465$	170.185	+	279.531i	0.365990	+	0.601143i
$466$	291.386			0.625292
$467$	42.4654			0.0909323			0.0454661	−	0.998966i	$-0.485523\pi$
$467$	42.4654			0.0909323			0.0454661	+	0.998966i	$0.485523\pi$
$468$			88.2129i			0.188489i
$469$	58.2293			0.124156
$470$	−76.9453	+	46.8462i	−0.163713	+	0.0996727i
$471$		−	390.284i		−	0.828628i
$472$		−	216.862i		−	0.459453i
$473$		−	178.781i		−	0.377973i
$474$		−	237.467i		−	0.500986i
$475$	−217.994	−	112.668i	−0.458934	−	0.237196i
$476$	−68.3224			−0.143534
$477$	−186.291			−0.390548
$478$			217.472i			0.454961i
$479$			411.978i			0.860079i	0.902810	+	0.430039i	$0.141500\pi$
$479$			411.978i			0.860079i	−0.902810	+	0.430039i	$0.858500\pi$
$480$	−41.8446	+	25.4760i	−0.0871763	+	0.0530751i
$481$		−	669.388i		−	1.39166i
$482$	−552.353			−1.14596
$483$	−31.6454	+	123.312i	−0.0655183	+	0.255304i
$484$	9.02147			0.0186394
$485$	−425.944	+	259.325i	−0.878235	+	0.534691i
$486$	22.0454			0.0453609
$487$			593.535i			1.21876i	0.792879	+	0.609379i	$0.208581\pi$
$487$			593.535i			1.21876i	−0.792879	+	0.609379i	$0.791419\pi$
$488$	110.441			0.226314
$489$	−278.114			−0.568740
$490$	142.627	+	234.267i	0.291076	+	0.478096i
$491$	−155.028			−0.315739			−0.157869	−	0.987460i	$-0.550462\pi$
$491$	−155.028			−0.315739			−0.157869	+	0.987460i	$0.550462\pi$
$492$			197.725i			0.401880i
$493$	−264.768			−0.537055
$494$			204.084i			0.413126i
$495$	−87.3892	−	143.538i	−0.176544	−	0.289975i
$496$	151.156			0.304750
$497$	−303.373			−0.610409
$498$	169.081			0.339520
$499$	−4.87786			−0.00977527			−0.00488764	−	0.999988i	$-0.501556\pi$
$499$	−4.87786			−0.00977527			−0.00488764	+	0.999988i	$0.501556\pi$
$500$	−17.4489	−	249.390i	−0.0348977	−	0.498781i
$501$	−292.195			−0.583224
$502$	570.516			1.13649
$503$	385.678			0.766756			0.383378	−	0.923592i	$-0.374761\pi$
$503$	385.678			0.766756			0.383378	+	0.923592i	$0.374761\pi$
$504$		−	27.1164i		−	0.0538024i
$505$	−106.226	+	64.6730i	−0.210349	+	0.128065i
$506$	352.967	+	90.5814i	0.697562	+	0.179015i
$507$			81.6720i			0.161089i
$508$		−	274.121i		−	0.539609i
$509$	406.891			0.799392			0.399696	−	0.916648i	$-0.369116\pi$
$509$	406.891			0.799392			0.399696	+	0.916648i	$0.369116\pi$
$510$	111.827	−	68.0830i	0.219269	−	0.133496i
$511$			27.4622i			0.0537421i
$512$			22.6274i			0.0441942i
$513$	51.0030			0.0994210
$514$	439.219			0.854511
$515$	−174.752	+	106.394i	−0.339325	+	0.206589i
$516$			55.2805i			0.107133i
$517$	−142.726			−0.276066
$518$			205.768i			0.397236i
$519$	84.6376			0.163078
$520$	−177.595	+	108.124i	−0.341528	+	0.207931i
$521$		−	501.963i		−	0.963461i	−0.876320	−	0.481730i	$-0.840009\pi$
$521$		−	501.963i		−	0.963461i	0.876320	−	0.481730i	$-0.159991\pi$
$522$		−	105.083i		−	0.201309i
$523$	−217.341			−0.415565			−0.207783	−	0.978175i	$-0.566625\pi$
$523$	−217.341			−0.415565			−0.207783	+	0.978175i	$0.566625\pi$
$524$	−112.871			−0.215402
$525$	122.930	+	63.5353i	0.234152	+	0.121020i
$526$			315.024i			0.598905i
$527$	−403.955			−0.766518
$528$	−77.6178			−0.147003
$529$	463.627	+	254.737i	0.876422	+	0.481544i
$530$	−228.340	−	375.051i	−0.430830	−	0.707643i
$531$	−230.017			−0.433177
$532$		−	62.7350i		−	0.117923i
$533$			839.173i			1.57443i
$534$		−	224.418i		−	0.420258i
$535$	76.0924	−	46.3269i	0.142229	−	0.0865923i
$536$			51.5372i			0.0961515i
$537$		−	245.486i		−	0.457143i
$538$			59.4344i			0.110473i
$539$			434.543i			0.806201i
$540$	27.0214	+	44.3829i	0.0500396	+	0.0821906i
$541$	140.244			0.259231			0.129616	−	0.991564i	$-0.458626\pi$
$541$	140.244			0.259231			0.129616	+	0.991564i	$0.458626\pi$
$542$			241.334i			0.445265i
$543$	−169.322			−0.311827
$544$		−	60.4703i		−	0.111159i
$545$	−191.939	−	315.262i	−0.352183	−	0.578463i
$546$		−	115.086i		−	0.210780i
$547$			83.5353i			0.152715i	0.997080	+	0.0763577i	$0.0243291\pi$
$547$			83.5353i			0.152715i	−0.997080	+	0.0763577i	$0.975671\pi$
$548$	370.525			0.676141
$549$		−	117.141i		−	0.213371i
$550$	181.863	−	351.873i	0.330660	−	0.639768i
$551$		−	243.115i		−	0.441225i
$552$	−109.140	−	28.0084i	−0.197717	−	0.0507399i
$553$			309.809i			0.560234i
$554$	583.633			1.05349
$555$	−205.047	−	336.792i	−0.369454	−	0.606832i
$556$	433.002			0.778780
$557$	−900.002			−1.61580			−0.807901	−	0.589318i	$-0.799396\pi$
$557$	−900.002			−1.61580			−0.807901	+	0.589318i	$0.799396\pi$
$558$		−	160.325i		−	0.287321i
$559$			234.619i			0.419712i
$560$	54.5921	−	33.2370i	0.0974859	−	0.0593518i
$561$	207.428			0.369748
$562$	29.4361			0.0523774
$563$	1.27327			0.00226159			0.00113079	−	0.999999i	$-0.499640\pi$
$563$	1.27327			0.00226159			0.00113079	+	0.999999i	$0.499640\pi$
$564$	44.1320			0.0782482
$565$	507.159	−	308.771i	0.897626	−	0.546497i
$566$			569.345i			1.00591i
$567$	−28.7613			−0.0507254
$568$		−	268.507i		−	0.472724i
$569$			1129.75i			1.98550i	0.120191	+	0.992751i	$0.461649\pi$
$569$			1129.75i			1.98550i	−0.120191	+	0.992751i	$0.538351\pi$
$570$	62.5152	+	102.682i	0.109676	+	0.180143i
$571$			153.556i			0.268925i	0.990919	+	0.134462i	$0.0429307\pi$
$571$			153.556i			0.268925i	−0.990919	+	0.134462i	$0.957069\pi$
$572$	−329.421			−0.575911
$573$	161.959			0.282651
$574$		−	257.959i		−	0.449407i
$575$	382.695	−	429.150i	0.665556	−	0.746348i
$576$	24.0000			0.0416667
$577$		−	602.704i		−	1.04455i	−0.852778	−	0.522274i	$-0.825084\pi$
$577$		−	602.704i		−	1.04455i	0.852778	−	0.522274i	$-0.174916\pi$
$578$		−	247.105i		−	0.427517i
$579$	68.1504			0.117704
$580$	211.559	−	128.802i	0.364757	−	0.222073i
$581$	−220.590			−0.379672
$582$	244.300			0.419760
$583$		−	695.683i		−	1.19328i
$584$	−24.3060			−0.0416199
$585$	114.683	+	188.368i	0.196039	+	0.321996i
$586$			151.648i			0.258785i
$587$			163.210i			0.278042i	0.990289	+	0.139021i	$0.0443955\pi$
$587$			163.210i			0.278042i	−0.990289	+	0.139021i	$0.955605\pi$
$588$		−	134.364i		−	0.228510i
$589$		−	370.919i		−	0.629744i
$590$	−281.935	−	463.081i	−0.477856	−	0.784883i
$591$	−567.127			−0.959606
$592$	−182.120			−0.307635
$593$		−	890.275i		−	1.50131i	−0.660696	−	0.750653i	$-0.729739\pi$
$593$		−	890.275i		−	1.50131i	0.660696	−	0.750653i	$-0.270261\pi$
$594$			82.3261i			0.138596i
$595$	−145.894	+	88.8238i	−0.245200	+	0.149284i
$596$		−	85.5296i		−	0.143506i
$597$	−301.938			−0.505759
$598$	−463.206	−	118.872i	−0.774592	−	0.198783i
$599$	643.232			1.07384			0.536921	−	0.843632i	$-0.319587\pi$
$599$	643.232			1.07384			0.536921	+	0.843632i	$0.319587\pi$
$600$	−56.2333	+	108.802i	−0.0937222	+	0.181336i
$601$	−185.138			−0.308050			−0.154025	−	0.988067i	$-0.549224\pi$
$601$	−185.138			−0.308050			−0.154025	+	0.988067i	$0.549224\pi$
$602$		−	72.1212i		−	0.119803i
$603$	54.6635			0.0906525
$604$	465.604			0.770867
$605$	19.2642	−	11.7285i	0.0318417	−	0.0193860i
$606$	60.9260			0.100538
$607$		−	722.082i		−	1.18959i	−0.803877	−	0.594796i	$-0.797233\pi$
$607$		−	722.082i		−	1.18959i	0.803877	−	0.594796i	$-0.202767\pi$
$608$	55.5250			0.0913240
$609$			137.096i			0.225117i
$610$	235.834	−	143.581i	0.386612	−	0.235379i
$611$	187.303			0.306551
$612$	−64.1384			−0.104801
$613$	779.332			1.27134			0.635671	−	0.771960i	$-0.280724\pi$
$613$	779.332			1.27134			0.635671	+	0.771960i	$0.280724\pi$
$614$	−318.929			−0.519428
$615$	257.056	+	422.216i	0.417977	+	0.686531i
$616$	101.263			0.164388
$617$	906.051			1.46848			0.734239	−	0.678891i	$-0.237539\pi$
$617$	906.051			1.46848			0.734239	+	0.678891i	$0.237539\pi$
$618$	100.229			0.162183
$619$		−	829.532i		−	1.34012i	−0.742308	−	0.670058i	$-0.766269\pi$
$619$		−	829.532i		−	1.34012i	0.742308	−	0.670058i	$-0.233731\pi$
$620$	322.775	−	196.513i	0.520605	−	0.316957i
$621$	−29.7074	+	115.760i	−0.0478381	+	0.186410i
$622$		−	402.574i		−	0.647225i
$623$			292.784i			0.469958i
$624$	101.860			0.163236
$625$	−361.484	−	509.857i	−0.578375	−	0.815771i
$626$		−	215.640i		−	0.344473i
$627$			190.465i			0.303772i
$628$	−450.661			−0.717613
$629$	486.703			0.773773
$630$	−35.2532	−	57.9037i	−0.0559574	−	0.0919106i
$631$			1078.38i			1.70900i	0.519451	+	0.854500i	$0.326136\pi$
$631$			1078.38i			1.70900i	−0.519451	+	0.854500i	$0.673864\pi$
$632$	−274.204			−0.433867
$633$			478.150i			0.755370i
$634$	−806.161			−1.27155
$635$	−356.377	−	585.352i	−0.561223	−	0.921814i
$636$			215.111i			0.338224i
$637$		−	570.260i		−	0.895227i
$638$	392.422			0.615082
$639$	−284.795			−0.445688
$640$	29.4172	+	48.3180i	0.0459644	+	0.0754969i
$641$		−	744.723i		−	1.16182i	−0.813970	−	0.580908i	$-0.802698\pi$
$641$		−	744.723i		−	1.16182i	0.813970	−	0.580908i	$-0.197302\pi$
$642$	−43.6428			−0.0679795
$643$	−373.410			−0.580731			−0.290365	−	0.956916i	$-0.593777\pi$
$643$	−373.410			−0.580731			−0.290365	+	0.956916i	$0.593777\pi$
$644$	142.388	+	36.5409i	0.221100	+	0.0567405i
$645$	71.8685	+	118.045i	0.111424	+	0.183015i
$646$	−148.387			−0.229701
$647$		−	174.894i		−	0.270315i	−0.990824	−	0.135157i	$-0.956846\pi$
$647$		−	174.894i		−	0.270315i	0.990824	−	0.135157i	$-0.0431540\pi$
$648$		−	25.4558i		−	0.0392837i
$649$		−	858.971i		−	1.32353i
$650$	−238.663	+	461.770i	−0.367173	+	0.710416i
$651$			209.167i			0.321300i
$652$			321.138i			0.492543i
$653$		−	343.261i		−	0.525668i	−0.964841	−	0.262834i	$-0.915343\pi$
$653$		−	343.261i		−	0.525668i	0.964841	−	0.262834i	$-0.0846572\pi$
$654$			180.819i			0.276481i
$655$	−241.021	+	146.740i	−0.367972	+	0.224030i
$656$	228.313			0.348038
$657$			25.7805i			0.0392397i
$658$	−57.5763			−0.0875020
$659$			206.113i			0.312766i	0.987696	+	0.156383i	$0.0499834\pi$
$659$			206.113i			0.312766i	−0.987696	+	0.156383i	$0.950017\pi$
$660$	−165.743	+	100.908i	−0.251126	+	0.152891i
$661$			876.964i			1.32672i	0.748299	+	0.663362i	$0.230871\pi$
$661$			876.964i			1.32672i	−0.748299	+	0.663362i	$0.769129\pi$
$662$			175.930i			0.265755i
$663$	−272.213			−0.410578
$664$		−	195.238i		−	0.294033i
$665$	−81.5597	−	133.963i	−0.122646	−	0.201448i
$666$			193.167i			0.290041i
$667$	551.793	+	141.606i	0.827276	+	0.212303i
$668$			337.398i			0.505086i
$669$	414.875			0.620142
$670$	67.0019	+	110.051i	0.100003	+	0.164256i
$671$	437.449			0.651935
$672$	−31.3113			−0.0465942
$673$		−	434.411i		−	0.645485i	−0.946487	−	0.322743i	$-0.895395\pi$
$673$		−	434.411i		−	0.645485i	0.946487	−	0.322743i	$-0.104605\pi$
$674$			303.580i			0.450415i
$675$	115.402	+	59.6445i	0.170965	+	0.0883622i
$676$	94.3067			0.139507
$677$	665.420			0.982895			0.491447	−	0.870907i	$-0.336468\pi$
$677$	665.420			0.982895			0.491447	+	0.870907i	$0.336468\pi$
$678$	−290.881			−0.429028
$679$	−318.724			−0.469402
$680$	−78.6155	−	129.127i	−0.115611	−	0.189892i
$681$		−	285.027i		−	0.418542i
$682$	598.716			0.877883
$683$			513.018i			0.751124i	0.926797	+	0.375562i	$0.122550\pi$
$683$			513.018i			0.751124i	−0.926797	+	0.375562i	$0.877450\pi$
$684$		−	58.8932i		−	0.0861011i
$685$	791.210	−	481.708i	1.15505	−	0.703224i
$686$			396.747i			0.578348i
$687$	153.875			0.223981
$688$	63.8325			0.0927798
$689$			912.961i			1.32505i
$690$	−269.467	+	82.0809i	−0.390533	+	0.118958i
$691$	−521.187			−0.754251			−0.377125	−	0.926162i	$-0.623087\pi$
$691$	−521.187			−0.754251			−0.377125	+	0.926162i	$0.623087\pi$
$692$		−	97.7311i		−	0.141230i
$693$		−	107.406i		−	0.154987i
$694$	−778.998			−1.12248
$695$	924.620	−	562.932i	1.33039	−	0.809973i
$696$	−121.340			−0.174339
$697$	−610.152			−0.875397
$698$		−	521.993i		−	0.747841i
$699$	−356.874			−0.510549
$700$	73.3642	−	141.947i	0.104806	−	0.202781i
$701$			148.024i			0.211161i	0.994411	+	0.105580i	$0.0336700\pi$
$701$			148.024i			0.211161i	−0.994411	+	0.105580i	$0.966330\pi$
$702$		−	108.038i		−	0.153901i
$703$			446.900i			0.635705i
$704$			89.6253i			0.127309i
$705$	94.2383	−	57.3746i	0.133671	−	0.0813824i
$706$	585.852			0.829819
$707$	−79.4864			−0.112428
$708$			265.600i			0.375142i
$709$			1053.52i			1.48592i	0.669336	+	0.742960i	$0.266579\pi$
$709$			1053.52i			1.48592i	−0.669336	+	0.742960i	$0.733421\pi$
$710$	−349.078	−	573.363i	−0.491659	−	0.807554i
$711$			290.837i			0.409053i
$712$	−259.135			−0.363954
$713$	841.868	+	216.047i	1.18074	+	0.303012i
$714$	83.6775			0.117195
$715$	−703.437	+	428.270i	−0.983828	+	0.598979i
$716$	−283.462			−0.395897
$717$		−	266.347i		−	0.371474i
$718$	−403.726			−0.562293
$719$	−516.738			−0.718689			−0.359345	−	0.933205i	$-0.617000\pi$
$719$	−516.738			−0.718689			−0.359345	+	0.933205i	$0.617000\pi$
$720$	51.2490	−	31.2016i	0.0711791	−	0.0433356i
$721$	−130.763			−0.181364
$722$			374.279i			0.518392i
$723$	676.492			0.935674
$724$			195.516i			0.270050i
$725$	284.306	−	550.083i	0.392147	−	0.758735i
$726$	−11.0490			−0.0152190
$727$	−348.090			−0.478803			−0.239401	−	0.970921i	$-0.576951\pi$
$727$	−348.090			−0.478803			−0.239401	+	0.970921i	$0.576951\pi$
$728$	−132.890			−0.182541
$729$	−27.0000			−0.0370370
$730$	−51.9025	+	31.5995i	−0.0710993	+	0.0432870i
$731$	−170.588			−0.233363
$732$	−135.262			−0.184785
$733$	−1172.59			−1.59972			−0.799858	−	0.600189i	$-0.795092\pi$
$733$	−1172.59			−1.59972			−0.799858	+	0.600189i	$0.795092\pi$
$734$		−	386.256i		−	0.526234i
$735$	−174.682	−	286.917i	−0.237663	−	0.390363i
$736$	−32.3414	+	126.024i	−0.0439421	+	0.171228i
$737$			204.134i			0.276980i
$738$		−	242.162i		−	0.328133i
$739$	−586.911			−0.794196			−0.397098	−	0.917776i	$-0.629983\pi$
$739$	−586.911			−0.794196			−0.397098	+	0.917776i	$0.629983\pi$
$740$	−388.894	+	236.768i	−0.525532	+	0.319957i
$741$		−	249.951i		−	0.337316i
$742$		−	280.642i		−	0.378223i
$743$	−256.074			−0.344648			−0.172324	−	0.985040i	$-0.555128\pi$
$743$	−256.074			−0.344648			−0.172324	+	0.985040i	$0.555128\pi$
$744$	−185.128			−0.248828
$745$	−111.194	−	182.638i	−0.149254	−	0.245151i
$746$			680.521i			0.912227i
$747$	−207.081			−0.277217
$748$		−	239.518i		−	0.320211i
$749$	56.9381			0.0760188
$750$	21.3704	+	305.440i	0.0284939	+	0.407253i
$751$		−	839.297i		−	1.11757i	−0.829312	−	0.558786i	$-0.811267\pi$
$751$		−	839.297i		−	1.11757i	0.829312	−	0.558786i	$-0.188733\pi$
$752$		−	50.9592i		−	0.0677650i
$753$	−698.736			−0.927937
$754$	−514.985			−0.683003
$755$	994.238	−	605.316i	1.31687	−	0.801744i
$756$			33.2107i			0.0439295i
$757$	−979.027			−1.29330			−0.646649	−	0.762788i	$-0.723830\pi$
$757$	−979.027			−1.29330			−0.646649	+	0.762788i	$0.723830\pi$
$758$	−710.139			−0.936858
$759$	−432.294	−	110.939i	−0.569557	−	0.146165i
$760$	118.567	−	72.1863i	0.156009	−	0.0949820i
$761$	419.697			0.551507			0.275753	−	0.961228i	$-0.411073\pi$
$761$	419.697			0.551507			0.275753	+	0.961228i	$0.411073\pi$
$762$			335.729i			0.440589i
$763$		−	235.903i		−	0.309179i
$764$		−	187.014i		−	0.244783i
$765$	−136.960	+	83.3843i	−0.179032	+	0.108999i
$766$			819.880i			1.07034i
$767$			1127.25i			1.46968i
$768$		−	27.7128i		−	0.0360844i
$769$		−	215.482i		−	0.280211i	−0.990137	−	0.140105i	$-0.955256\pi$
$769$		−	215.482i		−	0.280211i	0.990137	−	0.140105i	$-0.0447442\pi$
$770$	216.235	−	131.649i	0.280824	−	0.170973i
$771$	−537.931			−0.697706
$772$		−	78.6932i		−	0.101934i
$773$	−1480.63			−1.91543			−0.957716	−	0.287715i	$-0.907104\pi$
$773$	−1480.63			−1.91543			−0.957716	+	0.287715i	$0.907104\pi$
$774$		−	67.7046i		−	0.0874736i
$775$	433.765	−	839.259i	0.559696	−	1.08291i
$776$		−	282.094i		−	0.363523i
$777$		−	252.013i		−	0.324342i
$778$	399.249			0.513173
$779$		−	560.253i		−	0.719195i
$780$	217.508	−	132.424i	0.278857	−	0.169775i
$781$		−	1063.53i		−	1.36176i
$782$	86.4302	−	336.791i	0.110525	−	0.430679i
$783$			128.700i			0.164368i
$784$	−155.150			−0.197895
$785$	−962.330	+	585.890i	−1.22590	+	0.746357i
$786$	138.238			0.175875
$787$	464.168			0.589795			0.294897	−	0.955529i	$-0.404715\pi$
$787$	464.168			0.589795			0.294897	+	0.955529i	$0.404715\pi$
$788$			654.862i			0.831043i
$789$		−	385.824i		−	0.489004i
$790$	−585.528	+	356.484i	−0.741174	+	0.451245i
$791$	379.495			0.479766
$792$	95.0619			0.120028
$793$	−574.074			−0.723926
$794$	63.3374			0.0797700
$795$	279.658	+	459.342i	0.351772	+	0.577788i
$796$			348.648i			0.438000i
$797$	584.750			0.733689			0.366844	−	0.930282i	$-0.380438\pi$
$797$	584.750			0.733689			0.366844	+	0.930282i	$0.380438\pi$
$798$			76.8343i			0.0962836i
$799$			136.185i			0.170445i
$800$	125.633	+	64.9327i	0.157042	+	0.0811658i
$801$			274.854i			0.343139i
$802$	−249.542			−0.311150
$803$	−96.2742			−0.119893
$804$		−	63.1199i		−	0.0785074i
$805$	351.558	−	107.086i	0.436718	−	0.133026i
$806$	−785.709			−0.974825
$807$		−	72.7920i		−	0.0902007i
$808$		−	70.3513i		−	0.0870684i
$809$	−665.496			−0.822615			−0.411308	−	0.911497i	$-0.634928\pi$
$809$	−665.496			−0.822615			−0.411308	+	0.911497i	$0.634928\pi$
$810$	−33.0943	−	54.3578i	−0.0408572	−	0.0671083i
$811$	858.250			1.05826			0.529131	−	0.848540i	$-0.322518\pi$
$811$	858.250			1.05826			0.529131	+	0.848540i	$0.322518\pi$
$812$	158.305			0.194957
$813$		−	295.572i		−	0.363557i
$814$	−721.361			−0.886193
$815$	417.501	+	685.750i	0.512272	+	0.841411i
$816$			74.0607i			0.0907607i
$817$		−	156.637i		−	0.191723i
$818$			773.023i			0.945016i
$819$			140.951i			0.172101i
$820$	487.534	−	296.822i	0.594553	−	0.361979i
$821$	−1050.76			−1.27985			−0.639927	−	0.768436i	$-0.721035\pi$
$821$	−1050.76			−1.27985			−0.639927	+	0.768436i	$0.721035\pi$
$822$	−453.799			−0.552067
$823$		−	1241.28i		−	1.50824i	−0.656739	−	0.754118i	$-0.728065\pi$
$823$		−	1241.28i		−	1.50824i	0.656739	−	0.754118i	$-0.271935\pi$
$824$		−	115.735i		−	0.140455i
$825$	−222.735	+	430.954i	−0.269982	+	0.522369i
$826$		−	346.513i		−	0.419507i
$827$	−615.457			−0.744205			−0.372102	−	0.928192i	$-0.621363\pi$
$827$	−615.457			−0.744205			−0.372102	+	0.928192i	$0.621363\pi$
$828$	133.669	+	34.3032i	0.161435	+	0.0414290i
$829$	1487.12			1.79387			0.896936	−	0.442159i	$-0.145787\pi$
$829$	1487.12			1.79387			0.896936	+	0.442159i	$0.145787\pi$
$830$	−253.823	−	416.906i	−0.305810	−	0.502296i
$831$	−714.802			−0.860171
$832$		−	117.617i		−	0.141367i
$833$	414.628			0.497753
$834$	−530.316			−0.635871
$835$	438.640	+	720.470i	0.525317	+	0.862839i
$836$	219.930			0.263074
$837$			196.358i			0.234597i
$838$	−983.401			−1.17351
$839$			727.270i			0.866830i	0.901195	+	0.433415i	$0.142692\pi$
$839$			727.270i			0.866830i	−0.901195	+	0.433415i	$0.857308\pi$
$840$	−66.8614	+	40.7069i	−0.0795969	+	0.0484606i
$841$	−227.526			−0.270542
$842$	532.591			0.632531
$843$	−36.0517			−0.0427660
$844$	552.119			0.654170
$845$	201.380	−	122.605i	0.238320	−	0.145095i
$846$	−54.0504			−0.0638894
$847$	14.4150			0.0170188
$848$	248.388			0.292911
$849$		−	697.303i		−	0.821323i
$850$	−335.747	−	173.528i	−0.394997	−	0.204151i
$851$	−1014.32	−	260.304i	−1.19192	−	0.305880i
$852$			328.853i			0.385978i
$853$			169.747i			0.198999i	0.995038	+	0.0994997i	$0.0317242\pi$
$853$			169.747i			0.198999i	−0.995038	+	0.0994997i	$0.968276\pi$
$854$	176.469			0.206638
$855$	−76.5651	−	125.759i	−0.0895499	−	0.147086i
$856$			50.3944i			0.0588719i
$857$		−	370.253i		−	0.432034i	−0.976390	−	0.216017i	$-0.930693\pi$
$857$		−	370.253i		−	0.432034i	0.976390	−	0.216017i	$-0.0693066\pi$
$858$	403.457			0.470229
$859$	−457.241			−0.532294			−0.266147	−	0.963932i	$-0.585751\pi$
$859$	−457.241			−0.532294			−0.266147	+	0.963932i	$0.585751\pi$
$860$	136.306	−	82.9866i	0.158496	−	0.0964960i
$861$			315.935i			0.366939i
$862$	1015.11			1.17762
$863$		−	1404.82i		−	1.62783i	−0.580983	−	0.813916i	$-0.697332\pi$
$863$		−	1404.82i		−	1.62783i	0.580983	−	0.813916i	$-0.302668\pi$
$864$	−29.3939			−0.0340207
$865$	−127.057	−	208.692i	−0.146887	−	0.241263i
$866$			603.061i			0.696375i
$867$			302.640i			0.349066i
$868$	241.525			0.278254
$869$	−1086.10			−1.24982
$870$	−259.106	+	157.750i	−0.297823	+	0.181322i
$871$		−	267.890i		−	0.307566i
$872$	208.792			0.239440
$873$	−299.206			−0.342733
$874$	309.248	+	79.3619i	0.353831	+	0.0908031i
$875$	−27.8807	−	398.488i	−0.0318636	−	0.455415i
$876$	29.7687			0.0339825
$877$			63.8174i			0.0727679i	0.999338	+	0.0363839i	$0.0115839\pi$
$877$			63.8174i			0.0727679i	−0.999338	+	0.0363839i	$0.988416\pi$
$878$		−	643.402i		−	0.732804i
$879$		−	185.730i		−	0.211297i
$880$	116.519	+	191.383i	0.132408	+	0.217481i
$881$			1395.77i			1.58431i	0.610323	+	0.792153i	$0.291040\pi$
$881$			1395.77i			1.58431i	−0.610323	+	0.792153i	$0.708960\pi$
$882$			164.561i			0.186578i
$883$			322.412i			0.365132i	0.983194	+	0.182566i	$0.0584404\pi$
$883$			322.412i			0.365132i	−0.983194	+	0.182566i	$0.941560\pi$
$884$			314.324i			0.355571i
$885$	345.299	+	567.156i	0.390168	+	0.640855i
$886$	−1054.53			−1.19022
$887$		−	563.100i		−	0.634837i	−0.948286	−	0.317419i	$-0.897184\pi$
$887$		−	563.100i		−	0.634837i	0.948286	−	0.317419i	$-0.102816\pi$
$888$	223.050			0.251183
$889$		−	438.005i		−	0.492694i
$890$	−553.350	+	336.893i	−0.621742	+	0.378532i
$891$		−	100.828i		−	0.113163i
$892$		−	479.057i		−	0.537059i
$893$	−125.048			−0.140031
$894$			104.752i			0.117172i
$895$	−605.298	+	368.520i	−0.676311	+	0.411755i
$896$			36.1552i			0.0403518i
$897$	567.309	+	145.588i	0.632452	+	0.162305i
$898$			713.125i			0.794126i
$899$	935.974			1.04113
$900$	68.8715	−	133.254i	0.0765239	−	0.148060i
$901$	−663.802			−0.736739
$902$	904.328			1.00258
$903$			88.3300i			0.0978184i
$904$			335.881i			0.371549i
$905$	254.184	+	417.500i	0.280867	+	0.461326i
$906$	−570.246			−0.629410
$907$	1551.45			1.71053			0.855264	−	0.518193i	$-0.173395\pi$
$907$	1551.45			1.71053			0.855264	+	0.518193i	$0.173395\pi$
$908$	−329.121			−0.362468
$909$	−74.6188			−0.0820889
$910$	−283.770	+	172.766i	−0.311835	+	0.189853i
$911$		−	1054.70i		−	1.15774i	−0.815420	−	0.578870i	$-0.803494\pi$
$911$		−	1054.70i		−	1.15774i	0.815420	−	0.578870i	$-0.196506\pi$
$912$	−68.0040			−0.0745658
$913$		−	773.320i		−	0.847010i
$914$			410.684i			0.449326i
$915$	−288.836	+	175.850i	−0.315668	+	0.192186i
$916$		−	177.680i		−	0.193974i
$917$	−180.351			−0.196675
$918$	78.5532			0.0855700
$919$			855.524i			0.930930i	0.885066	+	0.465465i	$0.154113\pi$
$919$			855.524i			0.930930i	−0.885066	+	0.465465i	$0.845887\pi$
$920$	94.7788	+	311.154i	0.103020	+	0.338211i
$921$	390.606			0.424111
$922$			760.175i			0.824485i
$923$			1395.70i			1.51213i
$924$	−124.022			−0.134222
$925$	−522.619	+	1011.18i	−0.564994	+	1.09316i
$926$	854.927			0.923248
$927$	−122.755			−0.132422
$928$			140.111i			0.150982i
$929$	−1270.78			−1.36790			−0.683951	−	0.729528i	$-0.739740\pi$
$929$	−1270.78			−1.36790			−0.683951	+	0.729528i	$0.739740\pi$
$930$	−395.317	+	240.679i	−0.425072	+	0.258794i
$931$			380.720i			0.408936i
$932$			412.082i			0.442148i
$933$			493.050i			0.528457i
$934$			60.0551i			0.0642988i
$935$	−311.389	−	511.460i	−0.333037	−	0.547016i
$936$	−124.752			−0.133282
$937$	−1051.53			−1.12223			−0.561116	−	0.827737i	$-0.689628\pi$
$937$	−1051.53			−1.12223			−0.561116	+	0.827737i	$0.689628\pi$
$938$			82.3487i			0.0877918i
$939$			264.104i			0.281261i
$940$	−66.2505	−	108.817i	−0.0704792	−	0.115763i
$941$			392.729i			0.417353i	0.977985	+	0.208677i	$0.0669156\pi$
$941$			392.729i			0.417353i	−0.977985	+	0.208677i	$0.933084\pi$
$942$	551.945			0.585929
$943$	1271.59	+	326.328i	1.34846	+	0.346053i
$944$	306.689			0.324882
$945$	43.1762	+	70.9172i	0.0456891	+	0.0750447i
$946$	252.835			0.267267
$947$		−	405.516i		−	0.428212i	−0.976810	−	0.214106i	$-0.931316\pi$
$947$		−	405.516i		−	0.428212i	0.976810	−	0.214106i	$-0.0686837\pi$
$948$	335.830			0.354251
$949$	126.343			0.133133
$950$	159.337	−	308.289i	0.167723	−	0.324515i
$951$	987.341			1.03821
$952$		−	96.6225i		−	0.101494i
$953$	−762.883			−0.800507			−0.400254	−	0.916404i	$-0.631078\pi$
$953$	−762.883			−0.800507			−0.400254	+	0.916404i	$0.631078\pi$
$954$		−	263.456i		−	0.276159i
$955$	−243.131	−	399.345i	−0.254588	−	0.418162i
$956$	−307.551			−0.321706
$957$	−480.617			−0.502212
$958$	−582.625			−0.608168
$959$	592.044			0.617356
$960$	−36.0285	−	59.1772i	−0.0375297	−	0.0616429i
$961$	467.011			0.485964
$962$	946.658			0.984052
$963$	53.4513			0.0555050
$964$		−	781.146i		−	0.810317i
$965$	−102.307	−	168.040i	−0.106017	−	0.174134i
$966$	−174.389	−	44.7533i	−0.180527	−	0.0463285i
$967$		−	1235.35i		−	1.27750i	−0.769413	−	0.638751i	$-0.779451\pi$
$967$		−	1235.35i		−	1.27750i	0.769413	−	0.638751i	$-0.220549\pi$
$968$			12.7583i			0.0131800i
$969$	181.736			0.187550
$970$	−366.741	−	602.376i	−0.378084	−	0.621006i
$971$			781.163i			0.804493i	0.915531	+	0.402247i	$0.131771\pi$
$971$			781.163i			0.804493i	−0.915531	+	0.402247i	$0.868229\pi$
$972$			31.1769i			0.0320750i
$973$	691.871			0.711070
$974$	−839.386			−0.861792
$975$	292.301	−	565.551i	0.299796	−	0.580052i
$976$			156.188i			0.160028i
$977$	−664.267			−0.679905			−0.339952	−	0.940443i	$-0.610411\pi$
$977$	−664.267			−0.679905			−0.339952	+	0.940443i	$0.610411\pi$
$978$		−	393.312i		−	0.402160i
$979$	−1026.41			−1.04843
$980$	−331.303	+	201.706i	−0.338065	+	0.205822i
$981$		−	221.457i		−	0.225746i
$982$		−	219.242i		−	0.223261i
$983$	−1687.78			−1.71696			−0.858482	−	0.512844i	$-0.828592\pi$
$983$	−1687.78			−1.71696			−0.858482	+	0.512844i	$0.828592\pi$
$984$	−279.625			−0.284172
$985$	851.365	+	1398.38i	0.864330	+	1.41967i
$986$		−	374.438i		−	0.379755i
$987$	70.5163			0.0714451
$988$	−288.619			−0.292124
$989$	355.517	+	91.2358i	0.359471	+	0.0922505i
$990$	202.993	−	123.587i	0.205043	−	0.124835i
$991$	1195.42			1.20627			0.603136	−	0.797638i	$-0.293918\pi$
$991$	1195.42			1.20627			0.603136	+	0.797638i	$0.293918\pi$
$992$			213.767i			0.215491i
$993$		−	215.469i		−	0.216988i
$994$		−	429.034i		−	0.431624i
$995$	453.267	+	744.495i	0.455544	+	0.748236i
$996$			239.117i			0.240077i
$997$		−	277.792i		−	0.278628i	−0.990248	−	0.139314i	$-0.955510\pi$
$997$		−	277.792i		−	0.278628i	0.990248	−	0.139314i	$-0.0444898\pi$
$998$		−	6.89834i		−	0.00691216i
$999$		−	236.580i		−	0.236817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.f.a.229.15	yes	48
5.4	even	2	inner	690.3.f.a.229.14	yes	48
23.22	odd	2	inner	690.3.f.a.229.16	yes	48
115.114	odd	2	inner	690.3.f.a.229.13	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.f.a.229.13	✓	48	115.114	odd	2	inner
690.3.f.a.229.14	yes	48	5.4	even	2	inner
690.3.f.a.229.15	yes	48	1.1	even	1	trivial
690.3.f.a.229.16	yes	48	23.22	odd	2	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(-4.27075 + 2.60014i) q^{5} +2.44949 q^{6} -3.19570 q^{7} -2.82843i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -1.73205i q^{3} -2.00000 q^{4} +(-4.27075 + 2.60014i) q^{5} +2.44949 q^{6} -3.19570 q^{7} -2.82843i q^{8} -3.00000 q^{9} +(-3.67715 - 6.03975i) q^{10} -11.2032i q^{11} +3.46410i q^{12} +14.7022i q^{13} -4.51940i q^{14} +(4.50357 + 7.39715i) q^{15} +4.00000 q^{16} -10.6897 q^{17} -4.24264i q^{18} -9.81553i q^{19} +(8.54150 - 5.20027i) q^{20} +5.53511i q^{21} +15.8437 q^{22} +(22.2781 + 5.71720i) q^{23} -4.89898 q^{24} +(11.4786 - 22.2091i) q^{25} -20.7920 q^{26} +5.19615i q^{27} +6.39140 q^{28} +24.7684 q^{29} +(-10.4612 + 6.36901i) q^{30} +37.7890 q^{31} +5.65685i q^{32} -19.4044 q^{33} -15.1176i q^{34} +(13.6480 - 8.30925i) q^{35} +6.00000 q^{36} -45.5299 q^{37} +13.8813 q^{38} +25.4649 q^{39} +(7.35430 + 12.0795i) q^{40} +57.0782 q^{41} -7.82783 q^{42} +15.9581 q^{43} +22.4063i q^{44} +(12.8122 - 7.80041i) q^{45} +(-8.08534 + 31.5060i) q^{46} -12.7398i q^{47} -6.92820i q^{48} -38.7875 q^{49} +(31.4083 + 16.2332i) q^{50} +18.5152i q^{51} -29.4043i q^{52} +62.0971 q^{53} -7.34847 q^{54} +(29.1297 + 47.8459i) q^{55} +9.03880i q^{56} -17.0010 q^{57} +35.0278i q^{58} +76.6723 q^{59} +(-9.00714 - 14.7943i) q^{60} +39.0469i q^{61} +53.4418i q^{62} +9.58710 q^{63} -8.00000 q^{64} +(-38.2276 - 62.7892i) q^{65} -27.4420i q^{66} -18.2212 q^{67} +21.3795 q^{68} +(9.90248 - 38.5868i) q^{69} +(11.7511 + 19.3012i) q^{70} +94.9316 q^{71} +8.48528i q^{72} -8.59349i q^{73} -64.3891i q^{74} +(-38.4672 - 19.8815i) q^{75} +19.6311i q^{76} +35.8019i q^{77} +36.0128i q^{78} -96.9457i q^{79} +(-17.0830 + 10.4005i) q^{80} +9.00000 q^{81} +80.7208i q^{82} +69.0270 q^{83} -11.0702i q^{84} +(45.6532 - 27.7948i) q^{85} +22.5682i q^{86} -42.9001i q^{87} -31.6873 q^{88} -91.6181i q^{89} +(11.0314 + 18.1193i) q^{90} -46.9837i q^{91} +(-44.5562 - 11.4344i) q^{92} -65.4525i q^{93} +18.0168 q^{94} +(25.5217 + 41.9196i) q^{95} +9.79796 q^{96} +99.7353 q^{97} -54.8538i q^{98} +33.6095i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{4} - 144 q^{9}+O(q^{10}) \) 48 * q - 96 * q^4 - 144 * q^9	\( 48 q - 96 q^{4} - 144 q^{9} + 192 q^{16} + 96 q^{25} + 64 q^{26} - 152 q^{29} - 8 q^{31} + 56 q^{35} + 288 q^{36} - 48 q^{39} + 40 q^{41} - 160 q^{46} + 424 q^{49} + 96 q^{50} + 32 q^{55} + 360 q^{59} - 384 q^{64} + 192 q^{69} - 496 q^{70} - 152 q^{71} + 144 q^{75} + 432 q^{81} - 136 q^{85} + 256 q^{94} + 496 q^{95}+O(q^{100}) \) 48 * q - 96 * q^4 - 144 * q^9 + 192 * q^16 + 96 * q^25 + 64 * q^26 - 152 * q^29 - 8 * q^31 + 56 * q^35 + 288 * q^36 - 48 * q^39 + 40 * q^41 - 160 * q^46 + 424 * q^49 + 96 * q^50 + 32 * q^55 + 360 * q^59 - 384 * q^64 + 192 * q^69 - 496 * q^70 - 152 * q^71 + 144 * q^75 + 432 * q^81 - 136 * q^85 + 256 * q^94 + 496 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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