LMFDB - Embedded newform 230.3.d.a.91.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(91,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.d (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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 $ x^16 + 78x^14 + 2165x^12 + 28310x^10 + 184804x^8 + 569634x^6 + 696037x^4 + 285578*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.15
Root			$-1.00527i$ of defining polynomial
Character	$\chi$	$=$	230.91
Dual form			230.3.d.a.91.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +4.30716 q^{3} +2.00000 q^{4} -2.23607i q^{5} +6.09125 q^{6} +1.47532i q^{7} +2.82843 q^{8} +9.55167 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +4.30716 q^{3} +2.00000 q^{4} -2.23607i q^{5} +6.09125 q^{6} +1.47532i q^{7} +2.82843 q^{8} +9.55167 q^{9} -3.16228i q^{10} +6.04959i q^{11} +8.61433 q^{12} -5.21324 q^{13} +2.08642i q^{14} -9.63111i q^{15} +4.00000 q^{16} -15.7063i q^{17} +13.5081 q^{18} -4.82663i q^{19} -4.47214i q^{20} +6.35447i q^{21} +8.55541i q^{22} +(-2.58013 + 22.8548i) q^{23} +12.1825 q^{24} -5.00000 q^{25} -7.37263 q^{26} +2.37613 q^{27} +2.95065i q^{28} -23.4711 q^{29} -13.6205i q^{30} -20.4887 q^{31} +5.65685 q^{32} +26.0566i q^{33} -22.2121i q^{34} +3.29893 q^{35} +19.1033 q^{36} -15.5248i q^{37} -6.82589i q^{38} -22.4543 q^{39} -6.32456i q^{40} +20.3093 q^{41} +8.98657i q^{42} +38.1696i q^{43} +12.0992i q^{44} -21.3582i q^{45} +(-3.64885 + 32.3216i) q^{46} -13.8273 q^{47} +17.2287 q^{48} +46.8234 q^{49} -7.07107 q^{50} -67.6497i q^{51} -10.4265 q^{52} +38.2742i q^{53} +3.36035 q^{54} +13.5273 q^{55} +4.17285i q^{56} -20.7891i q^{57} -33.1932 q^{58} -33.5696 q^{59} -19.2622i q^{60} -100.567i q^{61} -28.9753 q^{62} +14.0918i q^{63} +8.00000 q^{64} +11.6572i q^{65} +36.8496i q^{66} +32.4469i q^{67} -31.4126i q^{68} +(-11.1130 + 98.4395i) q^{69} +4.66539 q^{70} -24.1306 q^{71} +27.0162 q^{72} +15.1818 q^{73} -21.9554i q^{74} -21.5358 q^{75} -9.65326i q^{76} -8.92511 q^{77} -31.7552 q^{78} +11.2095i q^{79} -8.94427i q^{80} -75.7306 q^{81} +28.7216 q^{82} -44.1310i q^{83} +12.7089i q^{84} -35.1204 q^{85} +53.9800i q^{86} -101.094 q^{87} +17.1108i q^{88} +111.039i q^{89} -30.2050i q^{90} -7.69122i q^{91} +(-5.16026 + 45.7096i) q^{92} -88.2480 q^{93} -19.5547 q^{94} -10.7927 q^{95} +24.3650 q^{96} -154.126i q^{97} +66.2183 q^{98} +57.7837i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 + 24 * q^13 + 64 * q^16 - 32 * q^18 + 4 * q^23 - 16 * q^24 - 80 * q^25 + 96 * q^26 - 96 * q^27 - 108 * q^29 - 116 * q^31 + 60 * q^35 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 - 128 * q^47 - 28 * q^49 + 48 * q^52 + 224 * q^54 + 160 * q^58 + 204 * q^59 + 64 * q^62 + 128 * q^64 - 268 * q^69 - 120 * q^70 + 236 * q^71 - 64 * q^72 - 112 * q^73 - 936 * q^77 - 432 * q^78 - 136 * q^81 - 64 * q^82 + 60 * q^85 - 152 * q^87 + 8 * q^92 + 856 * q^93 - 216 * q^94 - 160 * q^95 - 32 * q^96 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	4.30716			1.43572			0.717861	−	0.696187i	$-0.245121\pi$
$3$	4.30716			1.43572			0.717861	+	0.696187i	$0.245121\pi$
$4$	2.00000			0.500000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	6.09125			1.01521
$7$			1.47532i			0.210761i	0.994432	+	0.105380i	$0.0336060\pi$
$7$			1.47532i			0.210761i	−0.994432	+	0.105380i	$0.966394\pi$
$8$	2.82843			0.353553
$9$	9.55167			1.06130
$10$		−	3.16228i		−	0.316228i
$11$			6.04959i			0.549963i	0.961450	+	0.274981i	$0.0886717\pi$
$11$			6.04959i			0.549963i	−0.961450	+	0.274981i	$0.911328\pi$
$12$	8.61433			0.717861
$13$	−5.21324			−0.401018			−0.200509	−	0.979692i	$-0.564260\pi$
$13$	−5.21324			−0.401018			−0.200509	+	0.979692i	$0.564260\pi$
$14$			2.08642i			0.149030i
$15$		−	9.63111i		−	0.642074i
$16$	4.00000			0.250000
$17$		−	15.7063i		−	0.923901i	−0.886906	−	0.461951i	$-0.847150\pi$
$17$		−	15.7063i		−	0.923901i	0.886906	−	0.461951i	$-0.152850\pi$
$18$	13.5081			0.750450
$19$		−	4.82663i		−	0.254033i	−0.991901	−	0.127017i	$-0.959460\pi$
$19$		−	4.82663i		−	0.254033i	0.991901	−	0.127017i	$-0.0405402\pi$
$20$		−	4.47214i		−	0.223607i
$21$			6.35447i			0.302594i
$22$			8.55541i			0.388882i
$23$	−2.58013	+	22.8548i	−0.112180	+	0.993688i
$23$	−2.58013	+	22.8548i	−0.112180	+	0.993688i
$24$	12.1825			0.507604
$25$	−5.00000			−0.200000
$26$	−7.37263			−0.283563
$27$	2.37613			0.0880047
$28$			2.95065i			0.105380i
$29$	−23.4711			−0.809349			−0.404674	−	0.914461i	$-0.632615\pi$
$29$	−23.4711			−0.809349			−0.404674	+	0.914461i	$0.632615\pi$
$30$		−	13.6205i		−	0.454015i
$31$	−20.4887			−0.660924			−0.330462	−	0.943819i	$-0.607205\pi$
$31$	−20.4887			−0.660924			−0.330462	+	0.943819i	$0.607205\pi$
$32$	5.65685			0.176777
$33$			26.0566i			0.789593i
$34$		−	22.2121i		−	0.653297i
$35$	3.29893			0.0942550
$36$	19.1033			0.530648
$37$		−	15.5248i		−	0.419589i	−0.977746	−	0.209794i	$-0.932721\pi$
$37$		−	15.5248i		−	0.419589i	0.977746	−	0.209794i	$-0.0672795\pi$
$38$		−	6.82589i		−	0.179629i
$39$	−22.4543			−0.575751
$40$		−	6.32456i		−	0.158114i
$41$	20.3093			0.495348			0.247674	−	0.968843i	$-0.420334\pi$
$41$	20.3093			0.495348			0.247674	+	0.968843i	$0.420334\pi$
$42$			8.98657i			0.213966i
$43$			38.1696i			0.887666i	0.896109	+	0.443833i	$0.146382\pi$
$43$			38.1696i			0.887666i	−0.896109	+	0.443833i	$0.853618\pi$
$44$			12.0992i			0.274981i
$45$		−	21.3582i		−	0.474626i
$46$	−3.64885	+	32.3216i	−0.0793229	+	0.702643i
$47$	−13.8273			−0.294198			−0.147099	−	0.989122i	$-0.546994\pi$
$47$	−13.8273			−0.294198			−0.147099	+	0.989122i	$0.546994\pi$
$48$	17.2287			0.358930
$49$	46.8234			0.955580
$50$	−7.07107			−0.141421
$51$		−	67.6497i		−	1.32647i
$52$	−10.4265			−0.200509
$53$			38.2742i			0.722154i	0.932536	+	0.361077i	$0.117591\pi$
$53$			38.2742i			0.722154i	−0.932536	+	0.361077i	$0.882409\pi$
$54$	3.36035			0.0622287
$55$	13.5273			0.245951
$56$			4.17285i			0.0745152i
$57$		−	20.7891i		−	0.364721i
$58$	−33.1932			−0.572296
$59$	−33.5696			−0.568977			−0.284488	−	0.958679i	$-0.591824\pi$
$59$	−33.5696			−0.568977			−0.284488	+	0.958679i	$0.591824\pi$
$60$		−	19.2622i		−	0.321037i
$61$		−	100.567i		−	1.64864i	−0.566124	−	0.824320i	$-0.691558\pi$
$61$		−	100.567i		−	1.64864i	0.566124	−	0.824320i	$-0.308442\pi$
$62$	−28.9753			−0.467344
$63$			14.0918i			0.223680i
$64$	8.00000			0.125000
$65$			11.6572i			0.179341i
$66$			36.8496i			0.558327i
$67$			32.4469i			0.484282i	0.970241	+	0.242141i	$0.0778497\pi$
$67$			32.4469i			0.484282i	−0.970241	+	0.242141i	$0.922150\pi$
$68$		−	31.4126i		−	0.461951i
$69$	−11.1130	+	98.4395i	−0.161059	+	1.42666i
$70$	4.66539			0.0666484
$71$	−24.1306			−0.339868			−0.169934	−	0.985455i	$-0.554355\pi$
$71$	−24.1306			−0.339868			−0.169934	+	0.985455i	$0.554355\pi$
$72$	27.0162			0.375225
$73$	15.1818			0.207969			0.103985	−	0.994579i	$-0.466841\pi$
$73$	15.1818			0.207969			0.103985	+	0.994579i	$0.466841\pi$
$74$		−	21.9554i		−	0.296694i
$75$	−21.5358			−0.287144
$76$		−	9.65326i		−	0.127017i
$77$	−8.92511			−0.115910
$78$	−31.7552			−0.407117
$79$			11.2095i			0.141893i	0.997480	+	0.0709463i	$0.0226019\pi$
$79$			11.2095i			0.141893i	−0.997480	+	0.0709463i	$0.977398\pi$
$80$		−	8.94427i		−	0.111803i
$81$	−75.7306			−0.934946
$82$	28.7216			0.350264
$83$		−	44.1310i		−	0.531698i	−0.964015	−	0.265849i	$-0.914348\pi$
$83$		−	44.1310i		−	0.531698i	0.964015	−	0.265849i	$-0.0856523\pi$
$84$			12.7089i			0.151297i
$85$	−35.1204			−0.413181
$86$			53.9800i			0.627675i
$87$	−101.094			−1.16200
$88$			17.1108i			0.194441i
$89$			111.039i			1.24763i	0.781572	+	0.623815i	$0.214418\pi$
$89$			111.039i			1.24763i	−0.781572	+	0.623815i	$0.785582\pi$
$90$		−	30.2050i		−	0.335611i
$91$		−	7.69122i		−	0.0845189i
$92$	−5.16026	+	45.7096i	−0.0560898	+	0.496844i
$93$	−88.2480			−0.948903
$94$	−19.5547			−0.208029
$95$	−10.7927			−0.113607
$96$	24.3650			0.253802
$97$		−	154.126i		−	1.58893i	−0.607312	−	0.794463i	$-0.707752\pi$
$97$		−	154.126i		−	1.58893i	0.607312	−	0.794463i	$-0.292248\pi$
$98$	66.2183			0.675697
$99$			57.7837i			0.583673i
$100$	−10.0000			−0.100000
$101$	−58.8607			−0.582779			−0.291390	−	0.956604i	$-0.594118\pi$
$101$	−58.8607			−0.582779			−0.291390	+	0.956604i	$0.594118\pi$
$102$		−	95.6712i		−	0.937952i
$103$			54.2662i			0.526856i	0.964679	+	0.263428i	$0.0848531\pi$
$103$			54.2662i			0.526856i	−0.964679	+	0.263428i	$0.915147\pi$
$104$	−14.7453			−0.141781
$105$	14.2090			0.135324
$106$			54.1279i			0.510640i
$107$		−	119.124i		−	1.11331i	−0.830745	−	0.556653i	$-0.812085\pi$
$107$		−	119.124i		−	1.11331i	0.830745	−	0.556653i	$-0.187915\pi$
$108$	4.75225			0.0440023
$109$			149.223i			1.36902i	0.729003	+	0.684510i	$0.239984\pi$
$109$			149.223i			1.36902i	−0.729003	+	0.684510i	$0.760016\pi$
$110$	19.1305			0.173913
$111$		−	66.8678i		−	0.602413i
$112$			5.90130i			0.0526902i
$113$		−	35.3339i		−	0.312690i	−0.987703	−	0.156345i	$-0.950029\pi$
$113$		−	35.3339i		−	0.312690i	0.987703	−	0.156345i	$-0.0499711\pi$
$114$		−	29.4002i		−	0.257897i
$115$	51.1049	+	5.76935i	0.444391	+	0.0501682i
$116$	−46.9422			−0.404674
$117$	−49.7951			−0.425599
$118$	−47.4746			−0.402327
$119$	23.1719			0.194722
$120$		−	27.2409i		−	0.227008i
$121$	84.4025			0.697541
$122$		−	142.223i		−	1.16576i
$123$	87.4753			0.711181
$124$	−40.9773			−0.330462
$125$			11.1803i			0.0894427i
$126$			19.9288i			0.158165i
$127$	92.8398			0.731022			0.365511	−	0.930807i	$-0.380894\pi$
$127$	92.8398			0.731022			0.365511	+	0.930807i	$0.380894\pi$
$128$	11.3137			0.0883883
$129$			164.403i			1.27444i
$130$			16.4857i			0.126813i
$131$	151.709			1.15808			0.579042	−	0.815297i	$-0.303427\pi$
$131$	151.709			1.15808			0.579042	+	0.815297i	$0.303427\pi$
$132$			52.1131i			0.394797i
$133$	7.12085			0.0535402
$134$			45.8869i			0.342439i
$135$		−	5.31318i		−	0.0393569i
$136$		−	44.4242i		−	0.326648i
$137$		−	267.464i		−	1.95229i	−0.217121	−	0.976145i	$-0.569667\pi$
$137$		−	267.464i		−	1.95229i	0.217121	−	0.976145i	$-0.430333\pi$
$138$	−15.7162	+	139.214i	−0.113886	+	1.00880i
$139$	239.779			1.72503			0.862516	−	0.506030i	$-0.168888\pi$
$139$	239.779			1.72503			0.862516	+	0.506030i	$0.168888\pi$
$140$	6.59785			0.0471275
$141$	−59.5564			−0.422386
$142$	−34.1258			−0.240323
$143$		−	31.5380i		−	0.220545i
$144$	38.2067			0.265324
$145$			52.4830i			0.361952i
$146$	21.4703			0.147057
$147$	201.676			1.37195
$148$		−	31.0496i		−	0.209794i
$149$			201.647i			1.35333i	0.736290	+	0.676667i	$0.236576\pi$
$149$			201.647i			1.35333i	−0.736290	+	0.676667i	$0.763424\pi$
$150$	−30.4563			−0.203042
$151$	120.787			0.799912			0.399956	−	0.916534i	$-0.369025\pi$
$151$	120.787			0.799912			0.399956	+	0.916534i	$0.369025\pi$
$152$		−	13.6518i		−	0.0898143i
$153$		−	150.022i		−	0.980533i
$154$	−12.6220			−0.0819611
$155$			45.8140i			0.295574i
$156$	−44.9086			−0.287875
$157$		−	194.897i		−	1.24138i	−0.784055	−	0.620692i	$-0.786852\pi$
$157$		−	194.897i		−	1.24138i	0.784055	−	0.620692i	$-0.213148\pi$
$158$			15.8526i			0.100333i
$159$			164.853i			1.03681i
$160$		−	12.6491i		−	0.0790569i
$161$	−33.7183	−	3.80653i	−0.209430	−	0.0236430i
$162$	−107.099			−0.661107
$163$	153.813			0.943635			0.471817	−	0.881696i	$-0.343598\pi$
$163$	153.813			0.943635			0.471817	+	0.881696i	$0.343598\pi$
$164$	40.6185			0.247674
$165$	58.2643			0.353117
$166$		−	62.4106i		−	0.375967i
$167$	48.4949			0.290389			0.145194	−	0.989403i	$-0.453619\pi$
$167$	48.4949			0.290389			0.145194	+	0.989403i	$0.453619\pi$
$168$			17.9731i			0.106983i
$169$	−141.822			−0.839184
$170$	−49.6678			−0.292163
$171$		−	46.1024i		−	0.269605i
$172$			76.3393i			0.443833i
$173$	−111.269			−0.643174			−0.321587	−	0.946880i	$-0.604216\pi$
$173$	−111.269			−0.643174			−0.321587	+	0.946880i	$0.604216\pi$
$174$	−142.968			−0.821658
$175$		−	7.37662i		−	0.0421521i
$176$			24.1984i			0.137491i
$177$	−144.590			−0.816892
$178$			157.033i			0.882207i
$179$	262.590			1.46698			0.733492	−	0.679698i	$-0.237889\pi$
$179$	262.590			1.46698			0.733492	+	0.679698i	$0.237889\pi$
$180$		−	42.7164i		−	0.237313i
$181$			211.167i			1.16667i	0.812231	+	0.583335i	$0.198253\pi$
$181$			211.167i			1.16667i	−0.812231	+	0.583335i	$0.801747\pi$
$182$		−	10.8770i		−	0.0597639i
$183$		−	433.159i		−	2.36699i
$184$	−7.29771	+	64.6432i	−0.0396615	+	0.351322i
$185$	−34.7145			−0.187646
$186$	−124.802			−0.670976
$187$	95.0168			0.508111
$188$	−27.6546			−0.147099
$189$			3.50556i			0.0185479i
$190$	−15.2631			−0.0803324
$191$			72.8209i			0.381261i	0.981662	+	0.190631i	$0.0610533\pi$
$191$			72.8209i			0.381261i	−0.981662	+	0.190631i	$0.938947\pi$
$192$	34.4573			0.179465
$193$	198.550			1.02875			0.514377	−	0.857564i	$-0.328023\pi$
$193$	198.550			1.02875			0.514377	+	0.857564i	$0.328023\pi$
$194$		−	217.967i		−	1.12354i
$195$			50.2093i			0.257484i
$196$	93.6468			0.477790
$197$	28.2055			0.143175			0.0715876	−	0.997434i	$-0.477193\pi$
$197$	28.2055			0.143175			0.0715876	+	0.997434i	$0.477193\pi$
$198$			81.7184i			0.412719i
$199$		−	214.499i		−	1.07788i	−0.842343	−	0.538941i	$-0.818825\pi$
$199$		−	214.499i		−	1.07788i	0.842343	−	0.538941i	$-0.181175\pi$
$200$	−14.1421			−0.0707107
$201$			139.754i			0.695295i
$202$	−83.2416			−0.412087
$203$		−	34.6275i		−	0.170579i
$204$		−	135.299i		−	0.663233i
$205$		−	45.4129i		−	0.221526i
$206$			76.7439i			0.372543i
$207$	−24.6445	+	218.302i	−0.119056	+	1.05460i
$208$	−20.8530			−0.100255
$209$	29.1991			0.139709
$210$	20.0946			0.0956885
$211$	240.262			1.13868			0.569340	−	0.822102i	$-0.307199\pi$
$211$	240.262			1.13868			0.569340	+	0.822102i	$0.307199\pi$
$212$			76.5483i			0.361077i
$213$	−103.935			−0.487956
$214$		−	168.466i		−	0.787226i
$215$	85.3499			0.396976
$216$	6.72070			0.0311144
$217$		−	30.2274i		−	0.139297i
$218$			211.034i			0.968044i
$219$	65.3904			0.298586
$220$	27.0546			0.122975
$221$			81.8808i			0.370501i
$222$		−	94.5654i		−	0.425970i
$223$	257.402			1.15427			0.577136	−	0.816648i	$-0.304170\pi$
$223$	257.402			1.15427			0.577136	+	0.816648i	$0.304170\pi$
$224$			8.34570i			0.0372576i
$225$	−47.7583			−0.212259
$226$		−	49.9697i		−	0.221105i
$227$			106.401i			0.468727i	0.972149	+	0.234363i	$0.0753005\pi$
$227$			106.401i			0.468727i	−0.972149	+	0.234363i	$0.924699\pi$
$228$		−	41.5782i		−	0.182360i
$229$		−	328.507i		−	1.43453i	−0.696801	−	0.717265i	$-0.745394\pi$
$229$		−	328.507i		−	1.43453i	0.696801	−	0.717265i	$-0.254606\pi$
$230$	72.2733	+	8.15909i	0.314232	+	0.0354743i
$231$	−38.4419			−0.166415
$232$	−66.3863			−0.286148
$233$	−149.213			−0.640400			−0.320200	−	0.947350i	$-0.603750\pi$
$233$	−149.213			−0.640400			−0.320200	+	0.947350i	$0.603750\pi$
$234$	−70.4210			−0.300944
$235$			30.9187i			0.131569i
$236$	−67.1393			−0.284488
$237$			48.2812i			0.203718i
$238$	32.7701			0.137689
$239$	−343.168			−1.43585			−0.717925	−	0.696121i	$-0.754908\pi$
$239$	−343.168			−1.43585			−0.717925	+	0.696121i	$0.754908\pi$
$240$		−	38.5245i		−	0.160519i
$241$			348.748i			1.44709i	0.690278	+	0.723544i	$0.257488\pi$
$241$			348.748i			1.44709i	−0.690278	+	0.723544i	$0.742512\pi$
$242$	119.363			0.493236
$243$	−347.570			−1.43033
$244$		−	201.134i		−	0.824320i
$245$		−	104.700i		−	0.427348i
$246$	123.709			0.502881
$247$			25.1624i			0.101872i
$248$	−57.9507			−0.233672
$249$		−	190.079i		−	0.763371i
$250$			15.8114i			0.0632456i
$251$			225.099i			0.896809i	0.893831	+	0.448405i	$0.148008\pi$
$251$			225.099i			0.896809i	−0.893831	+	0.448405i	$0.851992\pi$
$252$			28.1836i			0.111840i
$253$	−138.262	−	15.6087i	−0.546491	−	0.0616946i
$254$	131.295			0.516911
$255$	−151.269			−0.593213
$256$	16.0000			0.0625000
$257$	−393.632			−1.53164			−0.765821	−	0.643054i	$-0.777667\pi$
$257$	−393.632			−1.53164			−0.765821	+	0.643054i	$0.777667\pi$
$258$			232.501i			0.901166i
$259$	22.9041			0.0884328
$260$			23.3143i			0.0896704i
$261$	−224.188			−0.858959
$262$	214.549			0.818890
$263$		−	132.720i		−	0.504640i	−0.967644	−	0.252320i	$-0.918806\pi$
$263$		−	132.720i		−	0.504640i	0.967644	−	0.252320i	$-0.0811935\pi$
$264$			73.6991i			0.279163i
$265$	85.5836			0.322957
$266$	10.0704			0.0378586
$267$			478.263i			1.79125i
$268$			64.8938i			0.242141i
$269$	−438.116			−1.62868			−0.814341	−	0.580386i	$-0.802902\pi$
$269$	−438.116			−1.62868			−0.814341	+	0.580386i	$0.802902\pi$
$270$		−	7.51397i		−	0.0278295i
$271$	−204.698			−0.755342			−0.377671	−	0.925940i	$-0.623275\pi$
$271$	−204.698			−0.755342			−0.377671	+	0.925940i	$0.623275\pi$
$272$		−	62.8253i		−	0.230975i
$273$		−	33.1274i		−	0.121346i
$274$		−	378.251i		−	1.38048i
$275$		−	30.2479i		−	0.109993i
$276$	−22.2261	+	196.879i	−0.0805293	+	0.713330i
$277$	173.804			0.627452			0.313726	−	0.949514i	$-0.398423\pi$
$277$	173.804			0.627452			0.313726	+	0.949514i	$0.398423\pi$
$278$	339.099			1.21978
$279$	−195.701			−0.701437
$280$	9.33077			0.0333242
$281$			143.605i			0.511051i	0.966802	+	0.255526i	$0.0822485\pi$
$281$			143.605i			0.511051i	−0.966802	+	0.255526i	$0.917752\pi$
$282$	−84.2255			−0.298672
$283$		−	72.1714i		−	0.255023i	−0.991837	−	0.127511i	$-0.959301\pi$
$283$		−	72.1714i		−	0.255023i	0.991837	−	0.127511i	$-0.0406989\pi$
$284$	−48.2612			−0.169934
$285$	−46.4858			−0.163108
$286$		−	44.6014i		−	0.155949i
$287$			29.9627i			0.104400i
$288$	54.0324			0.187612
$289$	42.3114			0.146406
$290$			74.2222i			0.255939i
$291$		−	663.845i		−	2.28126i
$292$	30.3635			0.103985
$293$		−	124.199i		−	0.423889i	−0.977282	−	0.211944i	$-0.932020\pi$
$293$		−	124.199i		−	0.423889i	0.977282	−	0.211944i	$-0.0679796\pi$
$294$	285.213			0.970113
$295$			75.0640i			0.254454i
$296$		−	43.9107i		−	0.148347i
$297$			14.3746i			0.0483993i
$298$			285.171i			0.956951i
$299$	13.4508	−	119.148i	0.0449861	−	0.398487i
$300$	−43.0716			−0.143572
$301$	−56.3126			−0.187085
$302$	170.818			0.565623
$303$	−253.523			−0.836709
$304$		−	19.3065i		−	0.0635083i
$305$	−224.875			−0.737294
$306$		−	212.163i		−	0.693342i
$307$	219.717			0.715690			0.357845	−	0.933781i	$-0.383512\pi$
$307$	219.717			0.715690			0.357845	+	0.933781i	$0.383512\pi$
$308$	−17.8502			−0.0579552
$309$			233.733i			0.756418i
$310$			64.7908i			0.209003i
$311$	−317.069			−1.01951			−0.509757	−	0.860319i	$-0.670265\pi$
$311$	−317.069			−1.01951			−0.509757	+	0.860319i	$0.670265\pi$
$312$	−63.5103			−0.203559
$313$			484.654i			1.54841i	0.632932	+	0.774207i	$0.281851\pi$
$313$			484.654i			1.54841i	−0.632932	+	0.774207i	$0.718149\pi$
$314$		−	275.626i		−	0.877791i
$315$	31.5103			0.100033
$316$			22.4190i			0.0709463i
$317$	−521.910			−1.64640			−0.823202	−	0.567748i	$-0.807815\pi$
$317$	−521.910			−1.64640			−0.823202	+	0.567748i	$0.807815\pi$
$318$			233.138i			0.733137i
$319$		−	141.991i		−	0.445111i
$320$		−	17.8885i		−	0.0559017i
$321$		−	513.086i		−	1.59840i
$322$	−47.6849	−	5.38325i	−0.148090	−	0.0167182i
$323$	−75.8086			−0.234702
$324$	−151.461			−0.467473
$325$	26.0662			0.0802037
$326$	217.524			0.667251
$327$			642.729i			1.96553i
$328$	57.4432			0.175132
$329$		−	20.3997i		−	0.0620053i
$330$	82.3981			0.249691
$331$	−318.270			−0.961540			−0.480770	−	0.876847i	$-0.659643\pi$
$331$	−318.270			−0.961540			−0.480770	+	0.876847i	$0.659643\pi$
$332$		−	88.2619i		−	0.265849i
$333$		−	148.288i		−	0.445308i
$334$	68.5822			0.205336
$335$	72.5535			0.216578
$336$			25.4179i			0.0756484i
$337$		−	116.539i		−	0.345812i	−0.984938	−	0.172906i	$-0.944684\pi$
$337$		−	116.539i		−	0.345812i	0.984938	−	0.172906i	$-0.0553156\pi$
$338$	−200.567			−0.593393
$339$		−	152.189i		−	0.448935i
$340$	−70.2408			−0.206591
$341$		−	123.948i		−	0.363484i
$342$		−	65.1986i		−	0.190639i
$343$			141.371i			0.412159i
$344$			107.960i			0.313837i
$345$	220.117	+	24.8495i	0.638021	+	0.0720276i
$346$	−157.358			−0.454793
$347$	−100.715			−0.290245			−0.145122	−	0.989414i	$-0.546358\pi$
$347$	−100.715			−0.290245			−0.145122	+	0.989414i	$0.546358\pi$
$348$	−202.188			−0.581000
$349$	143.476			0.411106			0.205553	−	0.978646i	$-0.434101\pi$
$349$	143.476			0.411106			0.205553	+	0.978646i	$0.434101\pi$
$350$		−	10.4321i		−	0.0298061i
$351$	−12.3873			−0.0352915
$352$			34.2216i			0.0972206i
$353$	−274.394			−0.777320			−0.388660	−	0.921381i	$-0.627062\pi$
$353$	−274.394			−0.777320			−0.388660	+	0.921381i	$0.627062\pi$
$354$	−204.481			−0.577630
$355$			53.9577i			0.151994i
$356$			222.078i			0.623815i
$357$	99.8053			0.279567
$358$	371.358			1.03731
$359$			476.871i			1.32833i	0.747586	+	0.664166i	$0.231213\pi$
$359$			476.871i			1.32833i	−0.747586	+	0.664166i	$0.768787\pi$
$360$		−	60.4101i		−	0.167806i
$361$	337.704			0.935467
$362$			298.636i			0.824961i
$363$	363.535			1.00147
$364$		−	15.3824i		−	0.0422595i
$365$		−	33.9475i		−	0.0930067i
$366$		−	612.579i		−	1.67371i
$367$			14.0319i			0.0382340i	0.999817	+	0.0191170i	$0.00608551\pi$
$367$			14.0319i			0.0382340i	−0.999817	+	0.0191170i	$0.993914\pi$
$368$	−10.3205	+	91.4193i	−0.0280449	+	0.248422i
$369$	193.987			0.525711
$370$	−49.0937			−0.132686
$371$	−56.4668			−0.152202
$372$	−176.496			−0.474452
$373$			105.662i			0.283277i	0.989918	+	0.141639i	$0.0452371\pi$
$373$			105.662i			0.283277i	−0.989918	+	0.141639i	$0.954763\pi$
$374$	134.374			0.359289
$375$			48.1556i			0.128415i
$376$	−39.1095			−0.104015
$377$	122.361			0.324564
$378$			4.95761i			0.0131154i
$379$		−	339.983i		−	0.897053i	−0.893770	−	0.448527i	$-0.851949\pi$
$379$		−	339.983i		−	0.897053i	0.893770	−	0.448527i	$-0.148051\pi$
$380$	−21.5854			−0.0568036
$381$	399.876			1.04954
$382$			102.984i			0.269592i
$383$		−	699.796i		−	1.82714i	−0.406676	−	0.913572i	$-0.633312\pi$
$383$		−	699.796i		−	1.82714i	0.406676	−	0.913572i	$-0.366688\pi$
$384$	48.7300			0.126901
$385$			19.9571i			0.0518367i
$386$	280.792			0.727439
$387$			364.584i			0.942077i
$388$		−	308.252i		−	0.794463i
$389$			124.817i			0.320867i	0.987047	+	0.160433i	$0.0512892\pi$
$389$			124.817i			0.320867i	−0.987047	+	0.160433i	$0.948711\pi$
$390$			71.0067i			0.182068i
$391$	358.965	+	40.5244i	0.918070	+	0.103643i
$392$	132.437			0.337849
$393$	653.436			1.66269
$394$	39.8886			0.101240
$395$	25.0652			0.0634563
$396$			115.567i			0.291837i
$397$	−149.557			−0.376719			−0.188360	−	0.982100i	$-0.560317\pi$
$397$	−149.557			−0.376719			−0.188360	+	0.982100i	$0.560317\pi$
$398$		−	303.347i		−	0.762178i
$399$	30.6707			0.0768688
$400$	−20.0000			−0.0500000
$401$			426.696i			1.06408i	0.846719	+	0.532040i	$0.178574\pi$
$401$			426.696i			1.06408i	−0.846719	+	0.532040i	$0.821426\pi$
$402$			197.642i			0.491647i
$403$	106.812			0.265043
$404$	−117.721			−0.291390
$405$			169.339i			0.418121i
$406$		−	48.9707i		−	0.120617i
$407$	93.9186			0.230758
$408$		−	191.342i		−	0.468976i
$409$	346.263			0.846610			0.423305	−	0.905987i	$-0.360870\pi$
$409$	346.263			0.846610			0.423305	+	0.905987i	$0.360870\pi$
$410$		−	64.2235i		−	0.156643i
$411$		−	1152.01i		−	2.80294i
$412$			108.532i			0.263428i
$413$		−	49.5261i		−	0.119918i
$414$	−34.8527	+	308.725i	−0.0841852	+	0.745713i
$415$	−98.6798			−0.237783
$416$	−29.4905			−0.0708907
$417$	1032.77			2.47667
$418$	41.2938			0.0987890
$419$			158.433i			0.378121i	0.981965	+	0.189060i	$0.0605442\pi$
$419$			158.433i			0.378121i	−0.981965	+	0.189060i	$0.939456\pi$
$420$	28.4180			0.0676620
$421$			18.0568i			0.0428902i	0.999770	+	0.0214451i	$0.00682671\pi$
$421$			18.0568i			0.0428902i	−0.999770	+	0.0214451i	$0.993173\pi$
$422$	339.781			0.805169
$423$	−132.074			−0.312231
$424$			108.256i			0.255320i
$425$			78.5316i			0.184780i
$426$	−146.986			−0.345037
$427$	148.369			0.347469
$428$		−	238.247i		−	0.556653i
$429$		−	135.839i		−	0.316641i
$430$	120.703			0.280705
$431$			151.730i			0.352041i	0.984387	+	0.176020i	$0.0563225\pi$
$431$			151.730i			0.352041i	−0.984387	+	0.176020i	$0.943678\pi$
$432$	9.50451			0.0220012
$433$		−	625.471i		−	1.44451i	−0.691629	−	0.722253i	$-0.743106\pi$
$433$		−	625.471i		−	1.44451i	0.691629	−	0.722253i	$-0.256894\pi$
$434$		−	42.7480i		−	0.0984978i
$435$			226.053i			0.519662i
$436$			298.447i			0.684510i
$437$	110.312	+	12.4533i	0.252430	+	0.0284973i
$438$	92.4759			0.211132
$439$	272.842			0.621509			0.310755	−	0.950490i	$-0.399418\pi$
$439$	272.842			0.621509			0.310755	+	0.950490i	$0.399418\pi$
$440$	38.2610			0.0869567
$441$	447.242			1.01415
$442$			115.797i			0.261984i
$443$	5.57528			0.0125853			0.00629264	−	0.999980i	$-0.497997\pi$
$443$	5.57528			0.0125853			0.00629264	+	0.999980i	$0.497997\pi$
$444$		−	133.736i		−	0.301206i
$445$	248.291			0.557957
$446$	364.022			0.816193
$447$			868.525i			1.94301i
$448$			11.8026i			0.0263451i
$449$	455.331			1.01410			0.507050	−	0.861916i	$-0.330736\pi$
$449$	455.331			1.01410			0.507050	+	0.861916i	$0.330736\pi$
$450$	−67.5405			−0.150090
$451$			122.863i			0.272423i
$452$		−	70.6679i		−	0.156345i
$453$	520.248			1.14845
$454$			150.474i			0.331440i
$455$	−17.1981			−0.0377980
$456$		−	58.8004i		−	0.128948i
$457$		−	597.785i		−	1.30806i	−0.756467	−	0.654032i	$-0.773076\pi$
$457$		−	597.785i		−	1.30806i	0.756467	−	0.654032i	$-0.226924\pi$
$458$		−	464.579i		−	1.01437i
$459$		−	37.3202i		−	0.0813077i
$460$	102.210	+	11.5387i	0.222195	+	0.0250841i
$461$	−340.556			−0.738734			−0.369367	−	0.929284i	$-0.620425\pi$
$461$	−340.556			−0.738734			−0.369367	+	0.929284i	$0.620425\pi$
$462$	−54.3651			−0.117673
$463$	−471.395			−1.01813			−0.509066	−	0.860727i	$-0.670009\pi$
$463$	−471.395			−1.01813			−0.509066	+	0.860727i	$0.670009\pi$
$464$	−93.8844			−0.202337
$465$			197.329i			0.424362i
$466$	−211.019			−0.452831
$467$			245.681i			0.526084i	0.964784	+	0.263042i	$0.0847257\pi$
$467$			245.681i			0.526084i	−0.964784	+	0.263042i	$0.915274\pi$
$468$	−99.5903			−0.212800
$469$	−47.8697			−0.102068
$470$			43.7257i			0.0930334i
$471$		−	839.455i		−	1.78228i
$472$	−94.9493			−0.201164
$473$	−230.911			−0.488183
$474$			68.2800i			0.144051i
$475$			24.1332i			0.0508066i
$476$	46.3439			0.0973610
$477$			365.582i			0.766420i
$478$	−485.313			−1.01530
$479$		−	203.940i		−	0.425763i	−0.977078	−	0.212881i	$-0.931715\pi$
$479$		−	203.940i		−	0.425763i	0.977078	−	0.212881i	$-0.0682848\pi$
$480$		−	54.4818i		−	0.113504i
$481$			80.9345i			0.168263i
$482$			493.205i			1.02325i
$483$	−145.230	−	16.3954i	−0.300684	−	0.0339448i
$484$	168.805			0.348771
$485$	−344.636			−0.710589
$486$	−491.538			−1.01139
$487$	−681.456			−1.39929			−0.699647	−	0.714489i	$-0.746659\pi$
$487$	−681.456			−1.39929			−0.699647	+	0.714489i	$0.746659\pi$
$488$		−	284.447i		−	0.582882i
$489$	662.496			1.35480
$490$		−	148.069i		−	0.302181i
$491$	−329.666			−0.671417			−0.335709	−	0.941966i	$-0.608976\pi$
$491$	−329.666			−0.671417			−0.335709	+	0.941966i	$0.608976\pi$
$492$	174.951			0.355591
$493$			368.645i			0.747758i
$494$			35.5850i			0.0720344i
$495$	129.208			0.261027
$496$	−81.9546			−0.165231
$497$		−	35.6005i		−	0.0716308i
$498$		−	268.813i		−	0.539785i
$499$	−993.708			−1.99140			−0.995700	−	0.0926377i	$-0.970470\pi$
$499$	−993.708			−1.99140			−0.995700	+	0.0926377i	$0.970470\pi$
$500$			22.3607i			0.0447214i
$501$	208.876			0.416918
$502$			318.338i			0.634140i
$503$		−	880.515i		−	1.75053i	−0.483646	−	0.875264i	$-0.660688\pi$
$503$		−	880.515i		−	1.75053i	0.483646	−	0.875264i	$-0.339312\pi$
$504$			39.8577i			0.0790827i
$505$			131.617i			0.260627i
$506$	−195.532	−	22.0741i	−0.386428	−	0.0436246i
$507$	−610.851			−1.20483
$508$	185.680			0.365511
$509$	−689.907			−1.35542			−0.677708	−	0.735331i	$-0.737027\pi$
$509$	−689.907			−1.35542			−0.677708	+	0.735331i	$0.737027\pi$
$510$	−213.927			−0.419465
$511$			22.3980i			0.0438318i
$512$	22.6274			0.0441942
$513$		−	11.4687i		−	0.0223561i
$514$	−556.680			−1.08303
$515$	121.343			0.235617
$516$			328.806i			0.637221i
$517$		−	83.6494i		−	0.161798i
$518$	32.3913			0.0625315
$519$	−479.255			−0.923419
$520$			32.9714i			0.0634066i
$521$			408.559i			0.784183i	0.919926	+	0.392092i	$0.128248\pi$
$521$			408.559i			0.784183i	−0.919926	+	0.392092i	$0.871752\pi$
$522$	−317.050			−0.607376
$523$			516.837i			0.988216i	0.869400	+	0.494108i	$0.164505\pi$
$523$			516.837i			0.988216i	−0.869400	+	0.494108i	$0.835495\pi$
$524$	303.418			0.579042
$525$		−	31.7723i		−	0.0605187i
$526$		−	187.695i		−	0.356834i
$527$			321.801i			0.610629i
$528$			104.226i			0.197398i
$529$	−515.686	−	117.937i	−0.974831	−	0.222943i
$530$	121.034			0.228365
$531$	−320.646			−0.603853
$532$	14.2417			0.0267701
$533$	−105.877			−0.198644
$534$			676.367i			1.26660i
$535$	−266.369			−0.497886
$536$			91.7737i			0.171220i
$537$	1131.02			2.10618
$538$	−619.589			−1.15165
$539$			283.262i			0.525533i
$540$		−	10.6264i		−	0.0196784i
$541$	−825.026			−1.52500			−0.762501	−	0.646987i	$-0.776029\pi$
$541$	−825.026			−1.52500			−0.762501	+	0.646987i	$0.776029\pi$
$542$	−289.486			−0.534107
$543$			909.533i			1.67501i
$544$		−	88.8484i		−	0.163324i
$545$	333.673			0.612245
$546$		−	46.8492i		−	0.0858043i
$547$	−749.566			−1.37032			−0.685161	−	0.728392i	$-0.740268\pi$
$547$	−749.566			−1.37032			−0.685161	+	0.728392i	$0.740268\pi$
$548$		−	534.927i		−	0.976145i
$549$		−	960.583i		−	1.74970i
$550$		−	42.7770i		−	0.0777765i
$551$			113.286i			0.205601i
$552$	−31.4324	+	278.429i	−0.0569428	+	0.504400i
$553$	−16.5377			−0.0299054
$554$	245.796			0.443675
$555$	−149.521			−0.269407
$556$	479.559			0.862516
$557$		−	406.149i		−	0.729173i	−0.931170	−	0.364586i	$-0.881210\pi$
$557$		−	406.149i		−	0.729173i	0.931170	−	0.364586i	$-0.118790\pi$
$558$	−276.763			−0.495991
$559$		−	198.988i		−	0.355971i
$560$	13.1957			0.0235638
$561$	409.253			0.729506
$562$			203.089i			0.361368i
$563$			285.771i			0.507587i	0.967258	+	0.253793i	$0.0816784\pi$
$563$			285.771i			0.507587i	−0.967258	+	0.253793i	$0.918322\pi$
$564$	−119.113			−0.211193
$565$	−79.0091			−0.139839
$566$		−	102.066i		−	0.180328i
$567$		−	111.727i		−	0.197050i
$568$	−68.2517			−0.120161
$569$			315.624i			0.554699i	0.960769	+	0.277349i	$0.0894560\pi$
$569$			315.624i			0.554699i	−0.960769	+	0.277349i	$0.910544\pi$
$570$	−65.7409			−0.115335
$571$		−	383.907i		−	0.672342i	−0.941801	−	0.336171i	$-0.890868\pi$
$571$		−	383.907i		−	0.672342i	0.941801	−	0.336171i	$-0.109132\pi$
$572$		−	63.0759i		−	0.110273i
$573$			313.652i			0.547385i
$574$			42.3737i			0.0738218i
$575$	12.9007	−	114.274i	0.0224359	−	0.198738i
$576$	76.4133			0.132662
$577$	−717.832			−1.24408			−0.622038	−	0.782987i	$-0.713695\pi$
$577$	−717.832			−1.24408			−0.622038	+	0.782987i	$0.713695\pi$
$578$	59.8374			0.103525
$579$	855.186			1.47701
$580$			104.966i			0.180976i
$581$	65.1075			0.112061
$582$		−	938.819i		−	1.61309i
$583$	−231.543			−0.397158
$584$	42.9405			0.0735283
$585$			111.345i			0.190334i
$586$		−	175.644i		−	0.299735i
$587$	−296.393			−0.504928			−0.252464	−	0.967606i	$-0.581241\pi$
$587$	−296.393			−0.504928			−0.252464	+	0.967606i	$0.581241\pi$
$588$	403.352			0.685973
$589$			98.8912i			0.167897i
$590$			106.157i			0.179926i
$591$	121.486			0.205560
$592$		−	62.0992i		−	0.104897i
$593$	654.259			1.10330			0.551652	−	0.834075i	$-0.313998\pi$
$593$	654.259			1.10330			0.551652	+	0.834075i	$0.313998\pi$
$594$			20.3287i			0.0342235i
$595$		−	51.8140i		−	0.0870824i
$596$			403.293i			0.676667i
$597$		−	923.881i		−	1.54754i
$598$	19.0224	−	168.500i	0.0318100	−	0.281773i
$599$	368.673			0.615480			0.307740	−	0.951470i	$-0.400427\pi$
$599$	368.673			0.615480			0.307740	+	0.951470i	$0.400427\pi$
$600$	−60.9125			−0.101521
$601$	148.316			0.246782			0.123391	−	0.992358i	$-0.460623\pi$
$601$	148.316			0.246782			0.123391	+	0.992358i	$0.460623\pi$
$602$	−79.6381			−0.132289
$603$			309.922i			0.513967i
$604$	241.573			0.399956
$605$		−	188.730i		−	0.311950i
$606$	−358.535			−0.591643
$607$	939.932			1.54849			0.774244	−	0.632887i	$-0.218130\pi$
$607$	939.932			1.54849			0.774244	+	0.632887i	$0.218130\pi$
$608$		−	27.3036i		−	0.0449072i
$609$		−	149.146i		−	0.244904i
$610$	−318.021			−0.521346
$611$	72.0850			0.117979
$612$		−	300.043i		−	0.490267i
$613$			602.963i			0.983626i	0.870701	+	0.491813i	$0.163666\pi$
$613$			602.963i			0.983626i	−0.870701	+	0.491813i	$0.836334\pi$
$614$	310.727			0.506069
$615$		−	195.601i		−	0.318050i
$616$	−25.2440			−0.0409805
$617$		−	885.697i		−	1.43549i	−0.696306	−	0.717745i	$-0.745174\pi$
$617$		−	885.697i		−	1.43549i	0.696306	−	0.717745i	$-0.254826\pi$
$618$			330.549i			0.534869i
$619$		−	85.9838i		−	0.138908i	−0.997585	−	0.0694538i	$-0.977874\pi$
$619$		−	85.9838i		−	0.138908i	0.997585	−	0.0694538i	$-0.0221257\pi$
$620$			91.6280i			0.147787i
$621$	−6.13072	+	54.3060i	−0.00987233	+	0.0874492i
$622$	−448.403			−0.720905
$623$	−163.819			−0.262951
$624$	−89.8171			−0.143938
$625$	25.0000			0.0400000
$626$			685.404i			1.09489i
$627$	125.765			0.200583
$628$		−	389.794i		−	0.620692i
$629$	−243.837			−0.387659
$630$	44.5622			0.0707337
$631$			645.385i			1.02280i	0.859344	+	0.511398i	$0.170872\pi$
$631$			645.385i			1.02280i	−0.859344	+	0.511398i	$0.829128\pi$
$632$			31.7053i			0.0501666i
$633$	1034.85			1.63483
$634$	−738.092			−1.16418
$635$		−	207.596i		−	0.326923i
$636$			329.706i			0.518406i
$637$	−244.102			−0.383205
$638$		−	200.805i		−	0.314741i
$639$	−230.488			−0.360701
$640$		−	25.2982i		−	0.0395285i
$641$			140.119i			0.218594i	0.994009	+	0.109297i	$0.0348599\pi$
$641$			140.119i			0.218594i	−0.994009	+	0.109297i	$0.965140\pi$
$642$		−	725.613i		−	1.13024i
$643$			1028.11i			1.59892i	0.600718	+	0.799461i	$0.294882\pi$
$643$			1028.11i			1.59892i	−0.600718	+	0.799461i	$0.705118\pi$
$644$	−67.4366	−	7.61306i	−0.104715	−	0.0118215i
$645$	367.616			0.569948
$646$	−107.210			−0.165959
$647$	1248.29			1.92934			0.964672	−	0.263455i	$-0.0848621\pi$
$647$	1248.29			1.92934			0.964672	+	0.263455i	$0.0848621\pi$
$648$	−214.199			−0.330553
$649$		−	203.082i		−	0.312916i
$650$	36.8632			0.0567126
$651$		−	130.194i		−	0.199992i
$652$	307.625			0.471817
$653$	−457.504			−0.700618			−0.350309	−	0.936634i	$-0.613923\pi$
$653$	−457.504			−0.700618			−0.350309	+	0.936634i	$0.613923\pi$
$654$			908.956i			1.38984i
$655$		−	339.232i		−	0.517911i
$656$	81.2370			0.123837
$657$	145.011			0.220717
$658$		−	28.8496i		−	0.0438444i
$659$		−	173.014i		−	0.262540i	−0.991347	−	0.131270i	$-0.958095\pi$
$659$		−	173.014i		−	0.262540i	0.991347	−	0.131270i	$-0.0419055\pi$
$660$	116.529			0.176558
$661$			582.673i			0.881502i	0.897629	+	0.440751i	$0.145288\pi$
$661$			582.673i			0.881502i	−0.897629	+	0.440751i	$0.854712\pi$
$662$	−450.101			−0.679911
$663$			352.674i			0.531937i
$664$		−	124.821i		−	0.187984i
$665$		−	15.9227i		−	0.0239439i
$666$		−	209.710i		−	0.314880i
$667$	60.5585	−	536.428i	0.0907924	−	0.804240i
$668$	96.9899			0.145194
$669$	1108.67			1.65721
$670$	102.606			0.153144
$671$	608.389			0.906690
$672$			35.9463i			0.0534915i
$673$	−390.678			−0.580502			−0.290251	−	0.956951i	$-0.593739\pi$
$673$	−390.678			−0.580502			−0.290251	+	0.956951i	$0.593739\pi$
$674$		−	164.810i		−	0.244526i
$675$	−11.8806			−0.0176009
$676$	−283.644			−0.419592
$677$			952.947i			1.40760i	0.710397	+	0.703801i	$0.248515\pi$
$677$			952.947i			1.40760i	−0.710397	+	0.703801i	$0.751485\pi$
$678$		−	215.228i		−	0.317445i
$679$	227.386			0.334883
$680$	−99.3355			−0.146082
$681$			458.286i			0.672961i
$682$		−	175.289i		−	0.257022i
$683$	299.732			0.438847			0.219423	−	0.975630i	$-0.429582\pi$
$683$	299.732			0.438847			0.219423	+	0.975630i	$0.429582\pi$
$684$		−	92.2048i		−	0.134802i
$685$	−598.067			−0.873090
$686$			199.928i			0.291441i
$687$		−	1414.93i		−	2.05958i
$688$			152.679i			0.221917i
$689$		−	199.532i		−	0.289597i
$690$	311.293	+	35.1425i	0.451149	+	0.0509312i
$691$	165.585			0.239631			0.119815	−	0.992796i	$-0.461770\pi$
$691$	165.585			0.239631			0.119815	+	0.992796i	$0.461770\pi$
$692$	−222.538			−0.321587
$693$	−85.2497			−0.123015
$694$	−142.432			−0.205234
$695$		−	536.163i		−	0.771458i
$696$	−285.937			−0.410829
$697$		−	318.984i		−	0.457652i
$698$	202.906			0.290696
$699$	−642.685			−0.919436
$700$		−	14.7532i		−	0.0210761i
$701$			831.750i			1.18652i	0.805011	+	0.593260i	$0.202159\pi$
$701$			831.750i			1.18652i	−0.805011	+	0.593260i	$0.797841\pi$
$702$	−17.5183			−0.0249549
$703$	−74.9324			−0.106590
$704$			48.3967i			0.0687453i
$705$			133.172i			0.188897i
$706$	−388.052			−0.549649
$707$		−	86.8387i		−	0.122827i
$708$	−289.180			−0.408446
$709$		−	835.784i		−	1.17882i	−0.807834	−	0.589410i	$-0.799360\pi$
$709$		−	835.784i		−	1.17882i	0.807834	−	0.589410i	$-0.200640\pi$
$710$			76.3077i			0.107476i
$711$			107.070i			0.150590i
$712$			314.066i			0.441104i
$713$	52.8634	−	468.265i	0.0741422	−	0.656753i
$714$	141.146			0.197683
$715$	−70.5210			−0.0986308
$716$	525.180			0.733492
$717$	−1478.08			−2.06148
$718$			674.397i			0.939272i
$719$	881.656			1.22623			0.613113	−	0.789996i	$-0.289917\pi$
$719$	881.656			1.22623			0.613113	+	0.789996i	$0.289917\pi$
$720$		−	85.4327i		−	0.118657i
$721$	−80.0602			−0.111041
$722$	477.585			0.661475
$723$			1502.12i			2.07762i
$724$			422.335i			0.583335i
$725$	117.356			0.161870
$726$	514.117			0.708150
$727$			531.577i			0.731193i	0.930774	+	0.365596i	$0.119135\pi$
$727$			531.577i			0.731193i	−0.930774	+	0.365596i	$0.880865\pi$
$728$		−	21.7541i		−	0.0298820i
$729$	−815.463			−1.11861
$730$		−	48.0090i		−	0.0657657i
$731$	599.505			0.820116
$732$		−	866.318i		−	1.18349i
$733$			18.4847i			0.0252178i	0.999921	+	0.0126089i	$0.00401364\pi$
$733$			18.4847i			0.0252178i	−0.999921	+	0.0126089i	$0.995986\pi$
$734$			19.8441i			0.0270356i
$735$		−	450.962i		−	0.613553i
$736$	−14.5954	+	129.286i	−0.0198307	+	0.175661i
$737$	−196.290			−0.266337
$738$	274.339			0.371734
$739$	−960.371			−1.29955			−0.649777	−	0.760125i	$-0.725138\pi$
$739$	−960.371			−1.29955			−0.649777	+	0.760125i	$0.725138\pi$
$740$	−69.4290			−0.0938229
$741$			108.379i			0.146260i
$742$	−79.8562			−0.107623
$743$		−	248.966i		−	0.335082i	−0.985865	−	0.167541i	$-0.946417\pi$
$743$		−	248.966i		−	0.335082i	0.985865	−	0.167541i	$-0.0535826\pi$
$744$	−249.603			−0.335488
$745$	450.896			0.605229
$746$			149.429i			0.200307i
$747$		−	421.524i		−	0.564289i
$748$	190.034			0.254056
$749$	175.746			0.234641
$750$			68.1023i			0.0908030i
$751$		−	24.0757i		−	0.0320582i	−0.999872	−	0.0160291i	$-0.994898\pi$
$751$		−	24.0757i		−	0.0320582i	0.999872	−	0.0160291i	$-0.00510244\pi$
$752$	−55.3091			−0.0735494
$753$			969.539i			1.28757i
$754$	173.044			0.229501
$755$		−	270.087i		−	0.357731i
$756$			7.01112i			0.00927396i
$757$		−	914.334i		−	1.20784i	−0.797045	−	0.603920i	$-0.793605\pi$
$757$		−	914.334i		−	1.20784i	0.797045	−	0.603920i	$-0.206395\pi$
$758$		−	480.809i		−	0.634312i
$759$	−595.518	−	67.2294i	−0.784609	−	0.0885762i
$760$	−30.5263			−0.0401662
$761$	313.770			0.412312			0.206156	−	0.978519i	$-0.433905\pi$
$761$	313.770			0.412312			0.206156	+	0.978519i	$0.433905\pi$
$762$	565.511			0.742140
$763$	−220.153			−0.288536
$764$			145.642i			0.190631i
$765$	−335.458			−0.438508
$766$		−	989.662i		−	1.29199i
$767$	175.007			0.228170
$768$	68.9146			0.0897326
$769$			309.335i			0.402257i	0.979565	+	0.201128i	$0.0644608\pi$
$769$			309.335i			0.402257i	−0.979565	+	0.201128i	$0.935539\pi$
$770$			28.2237i			0.0366541i
$771$	−1695.44			−2.19901
$772$	397.099			0.514377
$773$		−	233.356i		−	0.301884i	−0.988543	−	0.150942i	$-0.951769\pi$
$773$		−	233.356i		−	0.301884i	0.988543	−	0.150942i	$-0.0482306\pi$
$774$			515.599i			0.666149i
$775$	102.443			0.132185
$776$		−	435.934i		−	0.561770i
$777$	98.6518			0.126965
$778$			176.518i			0.226887i
$779$		−	98.0253i		−	0.125835i
$780$			100.419i			0.128742i
$781$		−	145.980i		−	0.186915i
$782$	507.653	+	57.3101i	0.649173	+	0.0732866i
$783$	−55.7703			−0.0712265
$784$	187.294			0.238895
$785$	−435.803			−0.555164
$786$	924.098			1.17570
$787$		−	690.751i		−	0.877702i	−0.898560	−	0.438851i	$-0.855386\pi$
$787$		−	690.751i		−	0.877702i	0.898560	−	0.438851i	$-0.144614\pi$
$788$	56.4111			0.0715876
$789$		−	571.648i		−	0.724522i
$790$	35.4476			0.0448704
$791$	52.1290			0.0659027
$792$			163.437i			0.206360i
$793$			524.280i			0.661135i
$794$	−211.506			−0.266381
$795$	368.623			0.463677
$796$		−	428.997i		−	0.538941i
$797$			91.6732i			0.115023i	0.998345	+	0.0575114i	$0.0183166\pi$
$797$			91.6732i			0.115023i	−0.998345	+	0.0575114i	$0.981683\pi$
$798$	43.3749			0.0543545
$799$			217.176i			0.271810i
$800$	−28.2843			−0.0353553
$801$			1060.61i			1.32410i
$802$			603.439i			0.752418i
$803$			91.8434i			0.114375i
$804$			279.508i			0.347647i
$805$	−8.51166	+	75.3964i	−0.0105735	+	0.0936601i
$806$	151.055			0.187414
$807$	−1887.04			−2.33833
$808$	−166.483			−0.206044
$809$	1071.73			1.32476			0.662382	−	0.749166i	$-0.269546\pi$
$809$	1071.73			1.32476			0.662382	+	0.749166i	$0.269546\pi$
$810$			239.481i			0.295656i
$811$	−257.388			−0.317371			−0.158685	−	0.987329i	$-0.550726\pi$
$811$	−257.388			−0.317371			−0.158685	+	0.987329i	$0.550726\pi$
$812$		−	69.2550i		−	0.0852894i
$813$	−881.666			−1.08446
$814$	132.821			0.163171
$815$		−	343.935i		−	0.422006i
$816$		−	270.599i		−	0.331616i
$817$	184.231			0.225497
$818$	489.690			0.598643
$819$		−	73.4640i		−	0.0896996i
$820$		−	90.8257i		−	0.110763i
$821$	−349.772			−0.426032			−0.213016	−	0.977049i	$-0.568329\pi$
$821$	−349.772			−0.426032			−0.213016	+	0.977049i	$0.568329\pi$
$822$		−	1629.19i		−	1.98198i
$823$	1438.73			1.74815			0.874076	−	0.485789i	$-0.161468\pi$
$823$	1438.73			1.74815			0.874076	+	0.485789i	$0.161468\pi$
$824$			153.488i			0.186272i
$825$		−	130.283i		−	0.157919i
$826$		−	70.0405i		−	0.0847948i
$827$			996.093i			1.20447i	0.798320	+	0.602233i	$0.205722\pi$
$827$			996.093i			1.20447i	−0.798320	+	0.602233i	$0.794278\pi$
$828$	−49.2891	+	436.603i	−0.0595279	+	0.527299i
$829$	−234.343			−0.282681			−0.141341	−	0.989961i	$-0.545141\pi$
$829$	−234.343			−0.282681			−0.141341	+	0.989961i	$0.545141\pi$
$830$	−139.554			−0.168138
$831$	748.603			0.900846
$832$	−41.7059			−0.0501273
$833$		−	735.424i		−	0.882862i
$834$	1460.56			1.75127
$835$		−	108.438i		−	0.129866i
$836$	58.3983			0.0698544
$837$	−48.6836			−0.0581644
$838$			224.058i			0.267372i
$839$			742.848i			0.885397i	0.896670	+	0.442699i	$0.145979\pi$
$839$			742.848i			0.885397i	−0.896670	+	0.442699i	$0.854021\pi$
$840$	40.1892			0.0478443
$841$	−290.107			−0.344955
$842$			25.5361i			0.0303280i
$843$			618.532i			0.733727i
$844$	480.523			0.569340
$845$			317.124i			0.375295i
$846$	−186.780			−0.220781
$847$			124.521i			0.147014i
$848$			153.097i			0.180539i
$849$		−	310.854i		−	0.366142i
$850$			111.060i			0.130659i
$851$	354.816	+	40.0560i	0.416940	+	0.0470693i
$852$	−207.869			−0.243978
$853$	482.186			0.565283			0.282642	−	0.959226i	$-0.408789\pi$
$853$	482.186			0.565283			0.282642	+	0.959226i	$0.408789\pi$
$854$	209.826			0.245697
$855$	−103.088			−0.120571
$856$		−	336.933i		−	0.393613i
$857$	685.909			0.800361			0.400180	−	0.916436i	$-0.368947\pi$
$857$	685.909			0.800361			0.400180	+	0.916436i	$0.368947\pi$
$858$		−	192.106i		−	0.223899i
$859$	670.668			0.780754			0.390377	−	0.920655i	$-0.372345\pi$
$859$	670.668			0.780754			0.390377	+	0.920655i	$0.372345\pi$
$860$	170.700			0.198488
$861$			129.054i			0.149889i
$862$			214.578i			0.248931i
$863$	891.818			1.03339			0.516696	−	0.856169i	$-0.327162\pi$
$863$	891.818			1.03339			0.516696	+	0.856169i	$0.327162\pi$
$864$	13.4414			0.0155572
$865$			248.805i			0.287636i
$866$		−	884.550i		−	1.02142i
$867$	182.242			0.210199
$868$		−	60.4548i		−	0.0696484i
$869$	−67.8129			−0.0780356
$870$			319.687i			0.367456i
$871$		−	169.154i		−	0.194206i
$872$			422.067i			0.484022i
$873$		−	1472.16i		−	1.68632i
$874$	156.004	+	17.6117i	0.178495	+	0.0201507i
$875$	−16.4946			−0.0188510
$876$	130.781			0.149293
$877$	181.676			0.207156			0.103578	−	0.994621i	$-0.466971\pi$
$877$	181.676			0.207156			0.103578	+	0.994621i	$0.466971\pi$
$878$	385.858			0.439473
$879$		−	534.947i		−	0.608586i
$880$	54.1092			0.0614877
$881$		−	316.887i		−	0.359691i	−0.983695	−	0.179845i	$-0.942440\pi$
$881$		−	316.887i		−	0.359691i	0.983695	−	0.179845i	$-0.0575597\pi$
$882$	632.495			0.717115
$883$	−1361.85			−1.54230			−0.771148	−	0.636656i	$-0.780317\pi$
$883$	−1361.85			−1.54230			−0.771148	+	0.636656i	$0.780317\pi$
$884$			163.762i			0.185251i
$885$			323.313i			0.365325i
$886$	7.88463			0.00889914
$887$	1628.63			1.83611			0.918057	−	0.396449i	$-0.129758\pi$
$887$	1628.63			1.83611			0.918057	+	0.396449i	$0.129758\pi$
$888$		−	189.131i		−	0.212985i
$889$			136.969i			0.154071i
$890$	351.136			0.394535
$891$		−	458.139i		−	0.514185i
$892$	514.805			0.577136
$893$			66.7392i			0.0747360i
$894$			1228.28i			1.37392i
$895$		−	587.169i		−	0.656055i
$896$			16.6914i			0.0186288i
$897$	57.9350	−	513.189i	0.0645875	−	0.572117i
$898$	643.936			0.717078
$899$	480.891			0.534918
$900$	−95.5167			−0.106130
$901$	601.146			0.667199
$902$			173.754i			0.192632i
$903$	−242.548			−0.268602
$904$		−	99.9395i		−	0.110552i
$905$	472.185			0.521751
$906$	735.742			0.812077
$907$		−	1551.21i		−	1.71026i	−0.518413	−	0.855130i	$-0.673477\pi$
$907$		−	1551.21i		−	1.71026i	0.518413	−	0.855130i	$-0.326523\pi$
$908$			212.802i			0.234363i
$909$	−562.218			−0.618502
$910$	−24.3218			−0.0267272
$911$			1672.31i			1.83569i	0.396937	+	0.917846i	$0.370073\pi$
$911$			1672.31i			1.83569i	−0.396937	+	0.917846i	$0.629927\pi$
$912$		−	83.1564i		−	0.0911802i
$913$	266.974			0.292414
$914$		−	845.396i		−	0.924941i
$915$	−968.573			−1.05855
$916$		−	657.014i		−	0.717265i
$917$			223.820i			0.244079i
$918$		−	52.7788i		−	0.0574932i
$919$			1670.00i			1.81719i	0.417673	+	0.908597i	$0.362846\pi$
$919$			1670.00i			1.81719i	−0.417673	+	0.908597i	$0.637154\pi$
$920$	144.547	+	16.3182i	0.157116	+	0.0177371i
$921$	946.357			1.02753
$922$	−481.619			−0.522364
$923$	125.799			0.136293
$924$	−76.8838			−0.0832076
$925$			77.6240i			0.0839178i
$926$	−666.653			−0.719928
$927$			518.332i			0.559150i
$928$	−132.773			−0.143074
$929$	−877.260			−0.944306			−0.472153	−	0.881517i	$-0.656523\pi$
$929$	−877.260			−0.944306			−0.472153	+	0.881517i	$0.656523\pi$
$930$			279.065i			0.300070i
$931$		−	225.999i		−	0.242749i
$932$	−298.426			−0.320200
$933$	−1365.67			−1.46374
$934$			347.445i			0.371997i
$935$		−	212.464i		−	0.227234i
$936$	−140.842			−0.150472
$937$			726.689i			0.775549i	0.921754	+	0.387774i	$0.126756\pi$
$937$			726.689i			0.775549i	−0.921754	+	0.387774i	$0.873244\pi$
$938$	−67.6980			−0.0721727
$939$			2087.48i			2.22309i
$940$			61.8375i			0.0657846i
$941$			289.839i			0.308011i	0.988070	+	0.154006i	$0.0492174\pi$
$941$			289.839i			0.308011i	−0.988070	+	0.154006i	$0.950783\pi$
$942$		−	1187.17i		−	1.26026i
$943$	−52.4005	+	464.164i	−0.0555679	+	0.492221i
$944$	−134.279			−0.142244
$945$	7.83867			0.00829489
$946$	−326.557			−0.345198
$947$	−1420.59			−1.50010			−0.750050	−	0.661381i	$-0.769970\pi$
$947$	−1420.59			−1.50010			−0.750050	+	0.661381i	$0.769970\pi$
$948$			96.5624i			0.101859i
$949$	−79.1462			−0.0833996
$950$			34.1294i			0.0359257i
$951$	−2247.95			−2.36378
$952$	65.5401			0.0688446
$953$		−	1465.45i		−	1.53772i	−0.639418	−	0.768860i	$-0.720824\pi$
$953$		−	1465.45i		−	1.53772i	0.639418	−	0.768860i	$-0.279176\pi$
$954$			517.011i			0.541941i
$955$	162.832			0.170505
$956$	−686.336			−0.717925
$957$		−	611.577i		−	0.639056i
$958$		−	288.415i		−	0.301060i
$959$	394.596			0.411466
$960$		−	77.0489i		−	0.0802593i
$961$	−541.215			−0.563179
$962$			114.459i			0.118980i
$963$		−	1137.83i		−	1.18155i
$964$			697.497i			0.723544i
$965$		−	443.970i		−	0.460073i
$966$	−205.387	−	23.1865i	−0.212615	−	0.0240026i
$967$	−1536.47			−1.58890			−0.794451	−	0.607328i	$-0.792241\pi$
$967$	−1536.47			−1.58890			−0.794451	+	0.607328i	$0.792241\pi$
$968$	238.726			0.246618
$969$	−326.520			−0.336966
$970$	−487.389			−0.502463
$971$		−	1693.09i		−	1.74366i	−0.489812	−	0.871828i	$-0.662935\pi$
$971$		−	1693.09i		−	1.74366i	0.489812	−	0.871828i	$-0.337065\pi$
$972$	−695.139			−0.715164
$973$			353.752i			0.363569i
$974$	−963.724			−0.989450
$975$	112.271			0.115150
$976$		−	402.268i		−	0.412160i
$977$			1295.96i			1.32647i	0.748411	+	0.663235i	$0.230817\pi$
$977$			1295.96i			1.32647i	−0.748411	+	0.663235i	$0.769183\pi$
$978$	936.911			0.957986
$979$	−671.740			−0.686150
$980$		−	209.401i		−	0.213674i
$981$			1425.33i			1.45294i
$982$	−466.218			−0.474764
$983$		−	1692.07i		−	1.72133i	−0.509168	−	0.860667i	$-0.670047\pi$
$983$		−	1692.07i		−	1.72133i	0.509168	−	0.860667i	$-0.329953\pi$
$984$	247.418			0.251441
$985$		−	63.0695i		−	0.0640299i
$986$			521.343i			0.528745i
$987$		−	87.8650i		−	0.0890223i
$988$			50.3248i			0.0509360i
$989$	−872.361	−	98.4827i	−0.882063	−	0.0995780i
$990$	182.728			0.184574
$991$	45.3192			0.0457308			0.0228654	−	0.999739i	$-0.492721\pi$
$991$	45.3192			0.0457308			0.0228654	+	0.999739i	$0.492721\pi$
$992$	−115.901			−0.116836
$993$	−1370.84			−1.38050
$994$		−	50.3467i		−	0.0506506i
$995$	−479.633			−0.482044
$996$		−	380.159i		−	0.381685i
$997$	1358.89			1.36298			0.681488	−	0.731830i	$-0.261333\pi$
$997$	1358.89			1.36298			0.681488	+	0.731830i	$0.261333\pi$
$998$	−1405.32			−1.40813
$999$		−	36.8889i		−	0.0369258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.d.a.91.15	✓	16
3.2	odd	2		2070.3.c.a.91.7		16
4.3	odd	2		1840.3.k.d.321.3		16
5.2	odd	4		1150.3.c.c.1149.14		32
5.3	odd	4		1150.3.c.c.1149.19		32
5.4	even	2		1150.3.d.b.551.1		16
23.22	odd	2	inner	230.3.d.a.91.16	yes	16
69.68	even	2		2070.3.c.a.91.2		16
92.91	even	2		1840.3.k.d.321.4		16
115.22	even	4		1150.3.c.c.1149.20		32
115.68	even	4		1150.3.c.c.1149.13		32
115.114	odd	2		1150.3.d.b.551.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.15	✓	16	1.1	even	1	trivial
230.3.d.a.91.16	yes	16	23.22	odd	2	inner
1150.3.c.c.1149.13		32	115.68	even	4
1150.3.c.c.1149.14		32	5.2	odd	4
1150.3.c.c.1149.19		32	5.3	odd	4
1150.3.c.c.1149.20		32	115.22	even	4
1150.3.d.b.551.1		16	5.4	even	2
1150.3.d.b.551.2		16	115.114	odd	2
1840.3.k.d.321.3		16	4.3	odd	2
1840.3.k.d.321.4		16	92.91	even	2
2070.3.c.a.91.2		16	69.68	even	2
2070.3.c.a.91.7		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +4.30716 q^{3} +2.00000 q^{4} -2.23607i q^{5} +6.09125 q^{6} +1.47532i q^{7} +2.82843 q^{8} +9.55167 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +4.30716 q^{3} +2.00000 q^{4} -2.23607i q^{5} +6.09125 q^{6} +1.47532i q^{7} +2.82843 q^{8} +9.55167 q^{9} -3.16228i q^{10} +6.04959i q^{11} +8.61433 q^{12} -5.21324 q^{13} +2.08642i q^{14} -9.63111i q^{15} +4.00000 q^{16} -15.7063i q^{17} +13.5081 q^{18} -4.82663i q^{19} -4.47214i q^{20} +6.35447i q^{21} +8.55541i q^{22} +(-2.58013 + 22.8548i) q^{23} +12.1825 q^{24} -5.00000 q^{25} -7.37263 q^{26} +2.37613 q^{27} +2.95065i q^{28} -23.4711 q^{29} -13.6205i q^{30} -20.4887 q^{31} +5.65685 q^{32} +26.0566i q^{33} -22.2121i q^{34} +3.29893 q^{35} +19.1033 q^{36} -15.5248i q^{37} -6.82589i q^{38} -22.4543 q^{39} -6.32456i q^{40} +20.3093 q^{41} +8.98657i q^{42} +38.1696i q^{43} +12.0992i q^{44} -21.3582i q^{45} +(-3.64885 + 32.3216i) q^{46} -13.8273 q^{47} +17.2287 q^{48} +46.8234 q^{49} -7.07107 q^{50} -67.6497i q^{51} -10.4265 q^{52} +38.2742i q^{53} +3.36035 q^{54} +13.5273 q^{55} +4.17285i q^{56} -20.7891i q^{57} -33.1932 q^{58} -33.5696 q^{59} -19.2622i q^{60} -100.567i q^{61} -28.9753 q^{62} +14.0918i q^{63} +8.00000 q^{64} +11.6572i q^{65} +36.8496i q^{66} +32.4469i q^{67} -31.4126i q^{68} +(-11.1130 + 98.4395i) q^{69} +4.66539 q^{70} -24.1306 q^{71} +27.0162 q^{72} +15.1818 q^{73} -21.9554i q^{74} -21.5358 q^{75} -9.65326i q^{76} -8.92511 q^{77} -31.7552 q^{78} +11.2095i q^{79} -8.94427i q^{80} -75.7306 q^{81} +28.7216 q^{82} -44.1310i q^{83} +12.7089i q^{84} -35.1204 q^{85} +53.9800i q^{86} -101.094 q^{87} +17.1108i q^{88} +111.039i q^{89} -30.2050i q^{90} -7.69122i q^{91} +(-5.16026 + 45.7096i) q^{92} -88.2480 q^{93} -19.5547 q^{94} -10.7927 q^{95} +24.3650 q^{96} -154.126i q^{97} +66.2183 q^{98} +57.7837i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 + 24 * q^13 + 64 * q^16 - 32 * q^18 + 4 * q^23 - 16 * q^24 - 80 * q^25 + 96 * q^26 - 96 * q^27 - 108 * q^29 - 116 * q^31 + 60 * q^35 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 - 128 * q^47 - 28 * q^49 + 48 * q^52 + 224 * q^54 + 160 * q^58 + 204 * q^59 + 64 * q^62 + 128 * q^64 - 268 * q^69 - 120 * q^70 + 236 * q^71 - 64 * q^72 - 112 * q^73 - 936 * q^77 - 432 * q^78 - 136 * q^81 - 64 * q^82 + 60 * q^85 - 152 * q^87 + 8 * q^92 + 856 * q^93 - 216 * q^94 - 160 * q^95 - 32 * q^96 + 256 * q^98

Introduction

L-functions

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