LMFDB - Embedded newform 1150.3.c.c.1149.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,3,Mod(1149,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.1149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1150.c (of order $2$, degree $1$, not 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:	$31.3352304014$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 230)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1149.14
Character	$\chi$	$=$	1150.1149
Dual form			1150.3.c.c.1149.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -4.30716i q^{3} -2.00000 q^{4} +6.09125 q^{6} -1.47532 q^{7} -2.82843i q^{8} -9.55167 q^{9} +O(q^{10})$	\(q+1.41421i q^{2} -4.30716i q^{3} -2.00000 q^{4} +6.09125 q^{6} -1.47532 q^{7} -2.82843i q^{8} -9.55167 q^{9} +6.04959i q^{11} +8.61433i q^{12} +5.21324i q^{13} -2.08642i q^{14} +4.00000 q^{16} +15.7063 q^{17} -13.5081i q^{18} +4.82663i q^{19} +6.35447i q^{21} -8.55541 q^{22} +(22.8548 + 2.58013i) q^{23} -12.1825 q^{24} -7.37263 q^{26} +2.37613i q^{27} +2.95065 q^{28} +23.4711 q^{29} -20.4887 q^{31} +5.65685i q^{32} +26.0566 q^{33} +22.2121i q^{34} +19.1033 q^{36} +15.5248 q^{37} -6.82589 q^{38} +22.4543 q^{39} +20.3093 q^{41} -8.98657 q^{42} +38.1696 q^{43} -12.0992i q^{44} +(-3.64885 + 32.3216i) q^{46} -13.8273i q^{47} -17.2287i q^{48} -46.8234 q^{49} -67.6497i q^{51} -10.4265i q^{52} +38.2742 q^{53} -3.36035 q^{54} +4.17285i q^{56} +20.7891 q^{57} +33.1932i q^{58} +33.5696 q^{59} -100.567i q^{61} -28.9753i q^{62} +14.0918 q^{63} -8.00000 q^{64} +36.8496i q^{66} -32.4469 q^{67} -31.4126 q^{68} +(11.1130 - 98.4395i) q^{69} -24.1306 q^{71} +27.0162i q^{72} -15.1818i q^{73} +21.9554i q^{74} -9.65326i q^{76} -8.92511i q^{77} +31.7552i q^{78} -11.2095i q^{79} -75.7306 q^{81} +28.7216i q^{82} -44.1310 q^{83} -12.7089i q^{84} +53.9800i q^{86} -101.094i q^{87} +17.1108 q^{88} -111.039i q^{89} -7.69122i q^{91} +(-45.7096 - 5.16026i) q^{92} +88.2480i q^{93} +19.5547 q^{94} +24.3650 q^{96} +154.126 q^{97} -66.2183i q^{98} -57.7837i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10}) $ 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9	$ 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9} + 128 q^{16} + 32 q^{24} + 192 q^{26} + 216 q^{29} - 232 q^{31} + 256 q^{36} - 496 q^{39} - 312 q^{41} - 248 q^{46} + 56 q^{49} - 448 q^{54} - 408 q^{59} - 256 q^{64} + 536 q^{69} + 472 q^{71} - 272 q^{81} + 432 q^{94} - 64 q^{96}+O(q^{100}) $ 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9 + 128 * q^16 + 32 * q^24 + 192 * q^26 + 216 * q^29 - 232 * q^31 + 256 * q^36 - 496 * q^39 - 312 * q^41 - 248 * q^46 + 56 * q^49 - 448 * q^54 - 408 * q^59 - 256 * q^64 + 536 * q^69 + 472 * q^71 - 272 * q^81 + 432 * q^94 - 64 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$-1$

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 $

$2$			1.41421i			0.707107i
$2$			1.41421i			0.707107i
$3$		−	4.30716i		−	1.43572i	−0.696187	−	0.717861i	$-0.745121\pi$
$3$		−	4.30716i		−	1.43572i	0.696187	−	0.717861i	$-0.254879\pi$
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	6.09125			1.01521
$7$	−1.47532			−0.210761			−0.105380	−	0.994432i	$-0.533606\pi$
$7$	−1.47532			−0.210761			−0.105380	+	0.994432i	$0.533606\pi$
$8$		−	2.82843i		−	0.353553i
$9$	−9.55167			−1.06130
$10$		0			0
$11$			6.04959i			0.549963i	0.961450	+	0.274981i	$0.0886717\pi$
$11$			6.04959i			0.549963i	−0.961450	+	0.274981i	$0.911328\pi$
$12$			8.61433i			0.717861i
$13$			5.21324i			0.401018i	0.979692	+	0.200509i	$0.0642597\pi$
$13$			5.21324i			0.401018i	−0.979692	+	0.200509i	$0.935740\pi$
$14$		−	2.08642i		−	0.149030i
$15$		0			0
$16$	4.00000			0.250000
$17$	15.7063			0.923901			0.461951	−	0.886906i	$-0.347150\pi$
$17$	15.7063			0.923901			0.461951	+	0.886906i	$0.347150\pi$
$18$		−	13.5081i		−	0.750450i
$19$			4.82663i			0.254033i	0.991901	+	0.127017i	$0.0405402\pi$
$19$			4.82663i			0.254033i	−0.991901	+	0.127017i	$0.959460\pi$
$20$		0			0
$21$			6.35447i			0.302594i
$22$	−8.55541			−0.388882
$23$	22.8548	+	2.58013i	0.993688	+	0.112180i
$23$	22.8548	+	2.58013i	0.993688	+	0.112180i
$24$	−12.1825			−0.507604
$25$		0			0
$26$	−7.37263			−0.283563
$27$			2.37613i			0.0880047i
$28$	2.95065			0.105380
$29$	23.4711			0.809349			0.404674	−	0.914461i	$-0.367385\pi$
$29$	23.4711			0.809349			0.404674	+	0.914461i	$0.367385\pi$
$30$		0			0
$31$	−20.4887			−0.660924			−0.330462	−	0.943819i	$-0.607205\pi$
$31$	−20.4887			−0.660924			−0.330462	+	0.943819i	$0.607205\pi$
$32$			5.65685i			0.176777i
$33$	26.0566			0.789593
$34$			22.2121i			0.653297i
$35$		0			0
$36$	19.1033			0.530648
$37$	15.5248			0.419589			0.209794	−	0.977746i	$-0.432721\pi$
$37$	15.5248			0.419589			0.209794	+	0.977746i	$0.432721\pi$
$38$	−6.82589			−0.179629
$39$	22.4543			0.575751
$40$		0			0
$41$	20.3093			0.495348			0.247674	−	0.968843i	$-0.420334\pi$
$41$	20.3093			0.495348			0.247674	+	0.968843i	$0.420334\pi$
$42$	−8.98657			−0.213966
$43$	38.1696			0.887666			0.443833	−	0.896109i	$-0.353618\pi$
$43$	38.1696			0.887666			0.443833	+	0.896109i	$0.353618\pi$
$44$		−	12.0992i		−	0.274981i
$45$		0			0
$46$	−3.64885	+	32.3216i	−0.0793229	+	0.702643i
$47$		−	13.8273i		−	0.294198i	−0.989122	−	0.147099i	$-0.953006\pi$
$47$		−	13.8273i		−	0.294198i	0.989122	−	0.147099i	$-0.0469935\pi$
$48$		−	17.2287i		−	0.358930i
$49$	−46.8234			−0.955580
$50$		0			0
$51$		−	67.6497i		−	1.32647i
$52$		−	10.4265i		−	0.200509i
$53$	38.2742			0.722154			0.361077	−	0.932536i	$-0.382409\pi$
$53$	38.2742			0.722154			0.361077	+	0.932536i	$0.382409\pi$
$54$	−3.36035			−0.0622287
$55$		0			0
$56$			4.17285i			0.0745152i
$57$	20.7891			0.364721
$58$			33.1932i			0.572296i
$59$	33.5696			0.568977			0.284488	−	0.958679i	$-0.408176\pi$
$59$	33.5696			0.568977			0.284488	+	0.958679i	$0.408176\pi$
$60$		0			0
$61$		−	100.567i		−	1.64864i	−0.566124	−	0.824320i	$-0.691558\pi$
$61$		−	100.567i		−	1.64864i	0.566124	−	0.824320i	$-0.308442\pi$
$62$		−	28.9753i		−	0.467344i
$63$	14.0918			0.223680
$64$	−8.00000			−0.125000
$65$		0			0
$66$			36.8496i			0.558327i
$67$	−32.4469			−0.484282			−0.242141	−	0.970241i	$-0.577850\pi$
$67$	−32.4469			−0.484282			−0.242141	+	0.970241i	$0.577850\pi$
$68$	−31.4126			−0.461951
$69$	11.1130	−	98.4395i	0.161059	−	1.42666i
$70$		0			0
$71$	−24.1306			−0.339868			−0.169934	−	0.985455i	$-0.554355\pi$
$71$	−24.1306			−0.339868			−0.169934	+	0.985455i	$0.554355\pi$
$72$			27.0162i			0.375225i
$73$		−	15.1818i		−	0.207969i	−0.994579	−	0.103985i	$-0.966841\pi$
$73$		−	15.1818i		−	0.207969i	0.994579	−	0.103985i	$-0.0331593\pi$
$74$			21.9554i			0.296694i
$75$		0			0
$76$		−	9.65326i		−	0.127017i
$77$		−	8.92511i		−	0.115910i
$78$			31.7552i			0.407117i
$79$		−	11.2095i		−	0.141893i	−0.997480	−	0.0709463i	$-0.977398\pi$
$79$		−	11.2095i		−	0.141893i	0.997480	−	0.0709463i	$-0.0226019\pi$
$80$		0			0
$81$	−75.7306			−0.934946
$82$			28.7216i			0.350264i
$83$	−44.1310			−0.531698			−0.265849	−	0.964015i	$-0.585652\pi$
$83$	−44.1310			−0.531698			−0.265849	+	0.964015i	$0.585652\pi$
$84$		−	12.7089i		−	0.151297i
$85$		0			0
$86$			53.9800i			0.627675i
$87$		−	101.094i		−	1.16200i
$88$	17.1108			0.194441
$89$		−	111.039i		−	1.24763i	−0.781572	−	0.623815i	$-0.785582\pi$
$89$		−	111.039i		−	1.24763i	0.781572	−	0.623815i	$-0.214418\pi$
$90$		0			0
$91$		−	7.69122i		−	0.0845189i
$92$	−45.7096	−	5.16026i	−0.496844	−	0.0560898i
$93$			88.2480i			0.948903i
$94$	19.5547			0.208029
$95$		0			0
$96$	24.3650			0.253802
$97$	154.126			1.58893			0.794463	−	0.607312i	$-0.207752\pi$
$97$	154.126			1.58893			0.794463	+	0.607312i	$0.207752\pi$
$98$		−	66.2183i		−	0.675697i
$99$		−	57.7837i		−	0.583673i
$100$		0			0
$101$	−58.8607			−0.582779			−0.291390	−	0.956604i	$-0.594118\pi$
$101$	−58.8607			−0.582779			−0.291390	+	0.956604i	$0.594118\pi$
$102$	95.6712			0.937952
$103$	54.2662			0.526856			0.263428	−	0.964679i	$-0.415147\pi$
$103$	54.2662			0.526856			0.263428	+	0.964679i	$0.415147\pi$
$104$	14.7453			0.141781
$105$		0			0
$106$			54.1279i			0.510640i
$107$	119.124			1.11331			0.556653	−	0.830745i	$-0.312085\pi$
$107$	119.124			1.11331			0.556653	+	0.830745i	$0.312085\pi$
$108$		−	4.75225i		−	0.0440023i
$109$		−	149.223i		−	1.36902i	−0.729003	−	0.684510i	$-0.760016\pi$
$109$		−	149.223i		−	1.36902i	0.729003	−	0.684510i	$-0.239984\pi$
$110$		0			0
$111$		−	66.8678i		−	0.602413i
$112$	−5.90130			−0.0526902
$113$	−35.3339			−0.312690			−0.156345	−	0.987703i	$-0.549971\pi$
$113$	−35.3339			−0.312690			−0.156345	+	0.987703i	$0.549971\pi$
$114$			29.4002i			0.257897i
$115$		0			0
$116$	−46.9422			−0.404674
$117$		−	49.7951i		−	0.425599i
$118$			47.4746i			0.402327i
$119$	−23.1719			−0.194722
$120$		0			0
$121$	84.4025			0.697541
$122$	142.223			1.16576
$123$		−	87.4753i		−	0.711181i
$124$	40.9773			0.330462
$125$		0			0
$126$			19.9288i			0.158165i
$127$			92.8398i			0.731022i	0.930807	+	0.365511i	$0.119106\pi$
$127$			92.8398i			0.731022i	−0.930807	+	0.365511i	$0.880894\pi$
$128$		−	11.3137i		−	0.0883883i
$129$		−	164.403i		−	1.27444i
$130$		0			0
$131$	151.709			1.15808			0.579042	−	0.815297i	$-0.303427\pi$
$131$	151.709			1.15808			0.579042	+	0.815297i	$0.303427\pi$
$132$	−52.1131			−0.394797
$133$		−	7.12085i		−	0.0535402i
$134$		−	45.8869i		−	0.342439i
$135$		0			0
$136$		−	44.4242i		−	0.326648i
$137$	267.464			1.95229			0.976145	−	0.217121i	$-0.0696666\pi$
$137$	267.464			1.95229			0.976145	+	0.217121i	$0.0696666\pi$
$138$	139.214	+	15.7162i	1.00880	+	0.113886i
$139$	−239.779			−1.72503			−0.862516	−	0.506030i	$-0.831112\pi$
$139$	−239.779			−1.72503			−0.862516	+	0.506030i	$0.831112\pi$
$140$		0			0
$141$	−59.5564			−0.422386
$142$		−	34.1258i		−	0.240323i
$143$	−31.5380			−0.220545
$144$	−38.2067			−0.265324
$145$		0			0
$146$	21.4703			0.147057
$147$			201.676i			1.37195i
$148$	−31.0496			−0.209794
$149$		−	201.647i		−	1.35333i	−0.736290	−	0.676667i	$-0.763424\pi$
$149$		−	201.647i		−	1.35333i	0.736290	−	0.676667i	$-0.236576\pi$
$150$		0			0
$151$	120.787			0.799912			0.399956	−	0.916534i	$-0.369025\pi$
$151$	120.787			0.799912			0.399956	+	0.916534i	$0.369025\pi$
$152$	13.6518			0.0898143
$153$	−150.022			−0.980533
$154$	12.6220			0.0819611
$155$		0			0
$156$	−44.9086			−0.287875
$157$	194.897			1.24138			0.620692	−	0.784055i	$-0.286852\pi$
$157$	194.897			1.24138			0.620692	+	0.784055i	$0.286852\pi$
$158$	15.8526			0.100333
$159$		−	164.853i		−	1.03681i
$160$		0			0
$161$	−33.7183	−	3.80653i	−0.209430	−	0.0236430i
$162$		−	107.099i		−	0.661107i
$163$		−	153.813i		−	0.943635i	−0.881696	−	0.471817i	$-0.843598\pi$
$163$		−	153.813i		−	0.943635i	0.881696	−	0.471817i	$-0.156402\pi$
$164$	−40.6185			−0.247674
$165$		0			0
$166$		−	62.4106i		−	0.375967i
$167$			48.4949i			0.290389i	0.989403	+	0.145194i	$0.0463808\pi$
$167$			48.4949i			0.290389i	−0.989403	+	0.145194i	$0.953619\pi$
$168$	17.9731			0.106983
$169$	141.822			0.839184
$170$		0			0
$171$		−	46.1024i		−	0.269605i
$172$	−76.3393			−0.443833
$173$			111.269i			0.643174i	0.946880	+	0.321587i	$0.104216\pi$
$173$			111.269i			0.643174i	−0.946880	+	0.321587i	$0.895784\pi$
$174$	142.968			0.821658
$175$		0			0
$176$			24.1984i			0.137491i
$177$		−	144.590i		−	0.816892i
$178$	157.033			0.882207
$179$	−262.590			−1.46698			−0.733492	−	0.679698i	$-0.762111\pi$
$179$	−262.590			−1.46698			−0.733492	+	0.679698i	$0.762111\pi$
$180$		0			0
$181$			211.167i			1.16667i	0.812231	+	0.583335i	$0.198253\pi$
$181$			211.167i			1.16667i	−0.812231	+	0.583335i	$0.801747\pi$
$182$	10.8770			0.0597639
$183$	−433.159			−2.36699
$184$	7.29771	−	64.6432i	0.0396615	−	0.351322i
$185$		0			0
$186$	−124.802			−0.670976
$187$			95.0168i			0.508111i
$188$			27.6546i			0.147099i
$189$		−	3.50556i		−	0.0185479i
$190$		0			0
$191$			72.8209i			0.381261i	0.981662	+	0.190631i	$0.0610533\pi$
$191$			72.8209i			0.381261i	−0.981662	+	0.190631i	$0.938947\pi$
$192$			34.4573i			0.179465i
$193$		−	198.550i		−	1.02875i	−0.857564	−	0.514377i	$-0.828023\pi$
$193$		−	198.550i		−	1.02875i	0.857564	−	0.514377i	$-0.171977\pi$
$194$			217.967i			1.12354i
$195$		0			0
$196$	93.6468			0.477790
$197$			28.2055i			0.143175i	0.997434	+	0.0715876i	$0.0228066\pi$
$197$			28.2055i			0.143175i	−0.997434	+	0.0715876i	$0.977193\pi$
$198$	81.7184			0.412719
$199$			214.499i			1.07788i	0.842343	+	0.538941i	$0.181175\pi$
$199$			214.499i			1.07788i	−0.842343	+	0.538941i	$0.818825\pi$
$200$		0			0
$201$			139.754i			0.695295i
$202$		−	83.2416i		−	0.412087i
$203$	−34.6275			−0.170579
$204$			135.299i			0.663233i
$205$		0			0
$206$			76.7439i			0.372543i
$207$	−218.302	−	24.6445i	−1.05460	−	0.119056i
$208$			20.8530i			0.100255i
$209$	−29.1991			−0.139709
$210$		0			0
$211$	240.262			1.13868			0.569340	−	0.822102i	$-0.307199\pi$
$211$	240.262			1.13868			0.569340	+	0.822102i	$0.307199\pi$
$212$	−76.5483			−0.361077
$213$			103.935i			0.487956i
$214$			168.466i			0.787226i
$215$		0			0
$216$	6.72070			0.0311144
$217$	30.2274			0.139297
$218$	211.034			0.968044
$219$	−65.3904			−0.298586
$220$		0			0
$221$			81.8808i			0.370501i
$222$	94.5654			0.425970
$223$		−	257.402i		−	1.15427i	−0.816648	−	0.577136i	$-0.804170\pi$
$223$		−	257.402i		−	1.15427i	0.816648	−	0.577136i	$-0.195830\pi$
$224$		−	8.34570i		−	0.0372576i
$225$		0			0
$226$		−	49.9697i		−	0.221105i
$227$	−106.401			−0.468727			−0.234363	−	0.972149i	$-0.575301\pi$
$227$	−106.401			−0.468727			−0.234363	+	0.972149i	$0.575301\pi$
$228$	−41.5782			−0.182360
$229$			328.507i			1.43453i	0.696801	+	0.717265i	$0.254606\pi$
$229$			328.507i			1.43453i	−0.696801	+	0.717265i	$0.745394\pi$
$230$		0			0
$231$	−38.4419			−0.166415
$232$		−	66.3863i		−	0.286148i
$233$			149.213i			0.640400i	0.947350	+	0.320200i	$0.103750\pi$
$233$			149.213i			0.640400i	−0.947350	+	0.320200i	$0.896250\pi$
$234$	70.4210			0.300944
$235$		0			0
$236$	−67.1393			−0.284488
$237$	−48.2812			−0.203718
$238$		−	32.7701i		−	0.137689i
$239$	343.168			1.43585			0.717925	−	0.696121i	$-0.245092\pi$
$239$	343.168			1.43585			0.717925	+	0.696121i	$0.245092\pi$
$240$		0			0
$241$			348.748i			1.44709i	0.690278	+	0.723544i	$0.257488\pi$
$241$			348.748i			1.44709i	−0.690278	+	0.723544i	$0.742512\pi$
$242$			119.363i			0.493236i
$243$			347.570i			1.43033i
$244$			201.134i			0.824320i
$245$		0			0
$246$	123.709			0.502881
$247$	−25.1624			−0.101872
$248$			57.9507i			0.233672i
$249$			190.079i			0.763371i
$250$		0			0
$251$			225.099i			0.896809i	0.893831	+	0.448405i	$0.148008\pi$
$251$			225.099i			0.896809i	−0.893831	+	0.448405i	$0.851992\pi$
$252$	−28.1836			−0.111840
$253$	−15.6087	+	138.262i	−0.0616946	+	0.546491i
$254$	−131.295			−0.516911
$255$		0			0
$256$	16.0000			0.0625000
$257$		−	393.632i		−	1.53164i	−0.643054	−	0.765821i	$-0.722333\pi$
$257$		−	393.632i		−	1.53164i	0.643054	−	0.765821i	$-0.277667\pi$
$258$	232.501			0.901166
$259$	−22.9041			−0.0884328
$260$		0			0
$261$	−224.188			−0.858959
$262$			214.549i			0.818890i
$263$	−132.720			−0.504640			−0.252320	−	0.967644i	$-0.581194\pi$
$263$	−132.720			−0.504640			−0.252320	+	0.967644i	$0.581194\pi$
$264$		−	73.6991i		−	0.279163i
$265$		0			0
$266$	10.0704			0.0378586
$267$	−478.263			−1.79125
$268$	64.8938			0.242141
$269$	438.116			1.62868			0.814341	−	0.580386i	$-0.197098\pi$
$269$	438.116			1.62868			0.814341	+	0.580386i	$0.197098\pi$
$270$		0			0
$271$	−204.698			−0.755342			−0.377671	−	0.925940i	$-0.623275\pi$
$271$	−204.698			−0.755342			−0.377671	+	0.925940i	$0.623275\pi$
$272$	62.8253			0.230975
$273$	−33.1274			−0.121346
$274$			378.251i			1.38048i
$275$		0			0
$276$	−22.2261	+	196.879i	−0.0805293	+	0.713330i
$277$			173.804i			0.627452i	0.949514	+	0.313726i	$0.101577\pi$
$277$			173.804i			0.627452i	−0.949514	+	0.313726i	$0.898423\pi$
$278$		−	339.099i		−	1.21978i
$279$	195.701			0.701437
$280$		0			0
$281$			143.605i			0.511051i	0.966802	+	0.255526i	$0.0822485\pi$
$281$			143.605i			0.511051i	−0.966802	+	0.255526i	$0.917752\pi$
$282$		−	84.2255i		−	0.298672i
$283$	−72.1714			−0.255023			−0.127511	−	0.991837i	$-0.540699\pi$
$283$	−72.1714			−0.255023			−0.127511	+	0.991837i	$0.540699\pi$
$284$	48.2612			0.169934
$285$		0			0
$286$		−	44.6014i		−	0.155949i
$287$	−29.9627			−0.104400
$288$		−	54.0324i		−	0.187612i
$289$	−42.3114			−0.146406
$290$		0			0
$291$		−	663.845i		−	2.28126i
$292$			30.3635i			0.103985i
$293$	−124.199			−0.423889			−0.211944	−	0.977282i	$-0.567980\pi$
$293$	−124.199			−0.423889			−0.211944	+	0.977282i	$0.567980\pi$
$294$	−285.213			−0.970113
$295$		0			0
$296$		−	43.9107i		−	0.148347i
$297$	−14.3746			−0.0483993
$298$	285.171			0.956951
$299$	−13.4508	+	119.148i	−0.0449861	+	0.398487i
$300$		0			0
$301$	−56.3126			−0.187085
$302$			170.818i			0.565623i
$303$			253.523i			0.836709i
$304$			19.3065i			0.0635083i
$305$		0			0
$306$		−	212.163i		−	0.693342i
$307$			219.717i			0.715690i	0.933781	+	0.357845i	$0.116488\pi$
$307$			219.717i			0.715690i	−0.933781	+	0.357845i	$0.883512\pi$
$308$			17.8502i			0.0579552i
$309$		−	233.733i		−	0.756418i
$310$		0			0
$311$	−317.069			−1.01951			−0.509757	−	0.860319i	$-0.670265\pi$
$311$	−317.069			−1.01951			−0.509757	+	0.860319i	$0.670265\pi$
$312$		−	63.5103i		−	0.203559i
$313$	484.654			1.54841			0.774207	−	0.632932i	$-0.218149\pi$
$313$	484.654			1.54841			0.774207	+	0.632932i	$0.218149\pi$
$314$			275.626i			0.877791i
$315$		0			0
$316$			22.4190i			0.0709463i
$317$		−	521.910i		−	1.64640i	−0.567748	−	0.823202i	$-0.692185\pi$
$317$		−	521.910i		−	1.64640i	0.567748	−	0.823202i	$-0.307815\pi$
$318$	233.138			0.733137
$319$			141.991i			0.445111i
$320$		0			0
$321$		−	513.086i		−	1.59840i
$322$	5.38325	−	47.6849i	0.0167182	−	0.148090i
$323$			75.8086i			0.234702i
$324$	151.461			0.467473
$325$		0			0
$326$	217.524			0.667251
$327$	−642.729			−1.96553
$328$		−	57.4432i		−	0.175132i
$329$			20.3997i			0.0620053i
$330$		0			0
$331$	−318.270			−0.961540			−0.480770	−	0.876847i	$-0.659643\pi$
$331$	−318.270			−0.961540			−0.480770	+	0.876847i	$0.659643\pi$
$332$	88.2619			0.265849
$333$	−148.288			−0.445308
$334$	−68.5822			−0.205336
$335$		0			0
$336$			25.4179i			0.0756484i
$337$	116.539			0.345812			0.172906	−	0.984938i	$-0.444684\pi$
$337$	116.539			0.345812			0.172906	+	0.984938i	$0.444684\pi$
$338$			200.567i			0.593393i
$339$			152.189i			0.448935i
$340$		0			0
$341$		−	123.948i		−	0.363484i
$342$	65.1986			0.190639
$343$	141.371			0.412159
$344$		−	107.960i		−	0.313837i
$345$		0			0
$346$	−157.358			−0.454793
$347$		−	100.715i		−	0.290245i	−0.989414	−	0.145122i	$-0.953642\pi$
$347$		−	100.715i		−	0.290245i	0.989414	−	0.145122i	$-0.0463576\pi$
$348$			202.188i			0.581000i
$349$	−143.476			−0.411106			−0.205553	−	0.978646i	$-0.565899\pi$
$349$	−143.476			−0.411106			−0.205553	+	0.978646i	$0.565899\pi$
$350$		0			0
$351$	−12.3873			−0.0352915
$352$	−34.2216			−0.0972206
$353$			274.394i			0.777320i	0.921381	+	0.388660i	$0.127062\pi$
$353$			274.394i			0.777320i	−0.921381	+	0.388660i	$0.872938\pi$
$354$	204.481			0.577630
$355$		0			0
$356$			222.078i			0.623815i
$357$			99.8053i			0.279567i
$358$		−	371.358i		−	1.03731i
$359$		−	476.871i		−	1.32833i	−0.747586	−	0.664166i	$-0.768787\pi$
$359$		−	476.871i		−	1.32833i	0.747586	−	0.664166i	$-0.231213\pi$
$360$		0			0
$361$	337.704			0.935467
$362$	−298.636			−0.824961
$363$		−	363.535i		−	1.00147i
$364$			15.3824i			0.0422595i
$365$		0			0
$366$		−	612.579i		−	1.67371i
$367$	−14.0319			−0.0382340			−0.0191170	−	0.999817i	$-0.506086\pi$
$367$	−14.0319			−0.0382340			−0.0191170	+	0.999817i	$0.506086\pi$
$368$	91.4193	+	10.3205i	0.248422	+	0.0280449i
$369$	−193.987			−0.525711
$370$		0			0
$371$	−56.4668			−0.152202
$372$		−	176.496i		−	0.474452i
$373$	105.662			0.283277			0.141639	−	0.989918i	$-0.454763\pi$
$373$	105.662			0.283277			0.141639	+	0.989918i	$0.454763\pi$
$374$	−134.374			−0.359289
$375$		0			0
$376$	−39.1095			−0.104015
$377$			122.361i			0.324564i
$378$	4.95761			0.0131154
$379$			339.983i			0.897053i	0.893770	+	0.448527i	$0.148051\pi$
$379$			339.983i			0.897053i	−0.893770	+	0.448527i	$0.851949\pi$
$380$		0			0
$381$	399.876			1.04954
$382$	−102.984			−0.269592
$383$	−699.796			−1.82714			−0.913572	−	0.406676i	$-0.866688\pi$
$383$	−699.796			−1.82714			−0.913572	+	0.406676i	$0.866688\pi$
$384$	−48.7300			−0.126901
$385$		0			0
$386$	280.792			0.727439
$387$	−364.584			−0.942077
$388$	−308.252			−0.794463
$389$		−	124.817i		−	0.320867i	−0.987047	−	0.160433i	$-0.948711\pi$
$389$		−	124.817i		−	0.320867i	0.987047	−	0.160433i	$-0.0512892\pi$
$390$		0			0
$391$	358.965	+	40.5244i	0.918070	+	0.103643i
$392$			132.437i			0.337849i
$393$		−	653.436i		−	1.66269i
$394$	−39.8886			−0.101240
$395$		0			0
$396$			115.567i			0.291837i
$397$		−	149.557i		−	0.376719i	−0.982100	−	0.188360i	$-0.939683\pi$
$397$		−	149.557i		−	0.376719i	0.982100	−	0.188360i	$-0.0603170\pi$
$398$	−303.347			−0.762178
$399$	−30.6707			−0.0768688
$400$		0			0
$401$			426.696i			1.06408i	0.846719	+	0.532040i	$0.178574\pi$
$401$			426.696i			1.06408i	−0.846719	+	0.532040i	$0.821426\pi$
$402$	−197.642			−0.491647
$403$		−	106.812i		−	0.265043i
$404$	117.721			0.291390
$405$		0			0
$406$		−	48.9707i		−	0.120617i
$407$			93.9186i			0.230758i
$408$	−191.342			−0.468976
$409$	−346.263			−0.846610			−0.423305	−	0.905987i	$-0.639130\pi$
$409$	−346.263			−0.846610			−0.423305	+	0.905987i	$0.639130\pi$
$410$		0			0
$411$		−	1152.01i		−	2.80294i
$412$	−108.532			−0.263428
$413$	−49.5261			−0.119918
$414$	34.8527	−	308.725i	0.0841852	−	0.745713i
$415$		0			0
$416$	−29.4905			−0.0708907
$417$			1032.77i			2.47667i
$418$		−	41.2938i		−	0.0987890i
$419$		−	158.433i		−	0.378121i	−0.981965	−	0.189060i	$-0.939456\pi$
$419$		−	158.433i		−	0.378121i	0.981965	−	0.189060i	$-0.0605442\pi$
$420$		0			0
$421$			18.0568i			0.0428902i	0.999770	+	0.0214451i	$0.00682671\pi$
$421$			18.0568i			0.0428902i	−0.999770	+	0.0214451i	$0.993173\pi$
$422$			339.781i			0.805169i
$423$			132.074i			0.312231i
$424$		−	108.256i		−	0.255320i
$425$		0			0
$426$	−146.986			−0.345037
$427$			148.369i			0.347469i
$428$	−238.247			−0.556653
$429$			135.839i			0.316641i
$430$		0			0
$431$			151.730i			0.352041i	0.984387	+	0.176020i	$0.0563225\pi$
$431$			151.730i			0.352041i	−0.984387	+	0.176020i	$0.943678\pi$
$432$			9.50451i			0.0220012i
$433$	−625.471			−1.44451			−0.722253	−	0.691629i	$-0.756894\pi$
$433$	−625.471			−1.44451			−0.722253	+	0.691629i	$0.756894\pi$
$434$			42.7480i			0.0984978i
$435$		0			0
$436$			298.447i			0.684510i
$437$	−12.4533	+	110.312i	−0.0284973	+	0.252430i
$438$		−	92.4759i		−	0.211132i
$439$	−272.842			−0.621509			−0.310755	−	0.950490i	$-0.600582\pi$
$439$	−272.842			−0.621509			−0.310755	+	0.950490i	$0.600582\pi$
$440$		0			0
$441$	447.242			1.01415
$442$	−115.797			−0.261984
$443$		−	5.57528i		−	0.0125853i	−0.999980	−	0.00629264i	$-0.997997\pi$
$443$		−	5.57528i		−	0.0125853i	0.999980	−	0.00629264i	$-0.00200302\pi$
$444$			133.736i			0.301206i
$445$		0			0
$446$	364.022			0.816193
$447$	−868.525			−1.94301
$448$	11.8026			0.0263451
$449$	−455.331			−1.01410			−0.507050	−	0.861916i	$-0.669264\pi$
$449$	−455.331			−1.01410			−0.507050	+	0.861916i	$0.669264\pi$
$450$		0			0
$451$			122.863i			0.272423i
$452$	70.6679			0.156345
$453$		−	520.248i		−	1.14845i
$454$		−	150.474i		−	0.331440i
$455$		0			0
$456$		−	58.8004i		−	0.128948i
$457$	597.785			1.30806			0.654032	−	0.756467i	$-0.273076\pi$
$457$	597.785			1.30806			0.654032	+	0.756467i	$0.273076\pi$
$458$	−464.579			−1.01437
$459$			37.3202i			0.0813077i
$460$		0			0
$461$	−340.556			−0.738734			−0.369367	−	0.929284i	$-0.620425\pi$
$461$	−340.556			−0.738734			−0.369367	+	0.929284i	$0.620425\pi$
$462$		−	54.3651i		−	0.117673i
$463$			471.395i			1.01813i	0.860727	+	0.509066i	$0.170009\pi$
$463$			471.395i			1.01813i	−0.860727	+	0.509066i	$0.829991\pi$
$464$	93.8844			0.202337
$465$		0			0
$466$	−211.019			−0.452831
$467$	−245.681			−0.526084			−0.263042	−	0.964784i	$-0.584726\pi$
$467$	−245.681			−0.526084			−0.263042	+	0.964784i	$0.584726\pi$
$468$			99.5903i			0.212800i
$469$	47.8697			0.102068
$470$		0			0
$471$		−	839.455i		−	1.78228i
$472$		−	94.9493i		−	0.201164i
$473$			230.911i			0.488183i
$474$		−	68.2800i		−	0.144051i
$475$		0			0
$476$	46.3439			0.0973610
$477$	−365.582			−0.766420
$478$			485.313i			1.01530i
$479$			203.940i			0.425763i	0.977078	+	0.212881i	$0.0682848\pi$
$479$			203.940i			0.425763i	−0.977078	+	0.212881i	$0.931715\pi$
$480$		0			0
$481$			80.9345i			0.168263i
$482$	−493.205			−1.02325
$483$	−16.3954	+	145.230i	−0.0339448	+	0.300684i
$484$	−168.805			−0.348771
$485$		0			0
$486$	−491.538			−1.01139
$487$		−	681.456i		−	1.39929i	−0.714489	−	0.699647i	$-0.753341\pi$
$487$		−	681.456i		−	1.39929i	0.714489	−	0.699647i	$-0.246659\pi$
$488$	−284.447			−0.582882
$489$	−662.496			−1.35480
$490$		0			0
$491$	−329.666			−0.671417			−0.335709	−	0.941966i	$-0.608976\pi$
$491$	−329.666			−0.671417			−0.335709	+	0.941966i	$0.608976\pi$
$492$			174.951i			0.355591i
$493$	368.645			0.747758
$494$		−	35.5850i		−	0.0720344i
$495$		0			0
$496$	−81.9546			−0.165231
$497$	35.6005			0.0716308
$498$	−268.813			−0.539785
$499$	993.708			1.99140			0.995700	−	0.0926377i	$-0.0295298\pi$
$499$	993.708			1.99140			0.995700	+	0.0926377i	$0.0295298\pi$
$500$		0			0
$501$	208.876			0.416918
$502$	−318.338			−0.634140
$503$	−880.515			−1.75053			−0.875264	−	0.483646i	$-0.839312\pi$
$503$	−880.515			−1.75053			−0.875264	+	0.483646i	$0.839312\pi$
$504$		−	39.8577i		−	0.0790827i
$505$		0			0
$506$	−195.532	−	22.0741i	−0.386428	−	0.0436246i
$507$		−	610.851i		−	1.20483i
$508$		−	185.680i		−	0.365511i
$509$	689.907			1.35542			0.677708	−	0.735331i	$-0.262973\pi$
$509$	689.907			1.35542			0.677708	+	0.735331i	$0.262973\pi$
$510$		0			0
$511$			22.3980i			0.0438318i
$512$			22.6274i			0.0441942i
$513$	−11.4687			−0.0223561
$514$	556.680			1.08303
$515$		0			0
$516$			328.806i			0.637221i
$517$	83.6494			0.161798
$518$		−	32.3913i		−	0.0625315i
$519$	479.255			0.923419
$520$		0			0
$521$			408.559i			0.784183i	0.919926	+	0.392092i	$0.128248\pi$
$521$			408.559i			0.784183i	−0.919926	+	0.392092i	$0.871752\pi$
$522$		−	317.050i		−	0.607376i
$523$	516.837			0.988216			0.494108	−	0.869400i	$-0.335495\pi$
$523$	516.837			0.988216			0.494108	+	0.869400i	$0.335495\pi$
$524$	−303.418			−0.579042
$525$		0			0
$526$		−	187.695i		−	0.356834i
$527$	−321.801			−0.610629
$528$	104.226			0.197398
$529$	515.686	+	117.937i	0.974831	+	0.222943i
$530$		0			0
$531$	−320.646			−0.603853
$532$			14.2417i			0.0267701i
$533$			105.877i			0.198644i
$534$		−	676.367i		−	1.26660i
$535$		0			0
$536$			91.7737i			0.171220i
$537$			1131.02i			2.10618i
$538$			619.589i			1.15165i
$539$		−	283.262i		−	0.525533i
$540$		0			0
$541$	−825.026			−1.52500			−0.762501	−	0.646987i	$-0.776029\pi$
$541$	−825.026			−1.52500			−0.762501	+	0.646987i	$0.776029\pi$
$542$		−	289.486i		−	0.534107i
$543$	909.533			1.67501
$544$			88.8484i			0.163324i
$545$		0			0
$546$		−	46.8492i		−	0.0858043i
$547$		−	749.566i		−	1.37032i	−0.728392	−	0.685161i	$-0.759732\pi$
$547$		−	749.566i		−	1.37032i	0.728392	−	0.685161i	$-0.240268\pi$
$548$	−534.927			−0.976145
$549$			960.583i			1.74970i
$550$		0			0
$551$			113.286i			0.205601i
$552$	−278.429	−	31.4324i	−0.504400	−	0.0569428i
$553$			16.5377i			0.0299054i
$554$	−245.796			−0.443675
$555$		0			0
$556$	479.559			0.862516
$557$	406.149			0.729173			0.364586	−	0.931170i	$-0.381210\pi$
$557$	406.149			0.729173			0.364586	+	0.931170i	$0.381210\pi$
$558$			276.763i			0.495991i
$559$			198.988i			0.355971i
$560$		0			0
$561$	409.253			0.729506
$562$	−203.089			−0.361368
$563$	285.771			0.507587			0.253793	−	0.967258i	$-0.418322\pi$
$563$	285.771			0.507587			0.253793	+	0.967258i	$0.418322\pi$
$564$	119.113			0.211193
$565$		0			0
$566$		−	102.066i		−	0.180328i
$567$	111.727			0.197050
$568$			68.2517i			0.120161i
$569$		−	315.624i		−	0.554699i	−0.960769	−	0.277349i	$-0.910544\pi$
$569$		−	315.624i		−	0.554699i	0.960769	−	0.277349i	$-0.0894560\pi$
$570$		0			0
$571$		−	383.907i		−	0.672342i	−0.941801	−	0.336171i	$-0.890868\pi$
$571$		−	383.907i		−	0.672342i	0.941801	−	0.336171i	$-0.109132\pi$
$572$	63.0759			0.110273
$573$	313.652			0.547385
$574$		−	42.3737i		−	0.0738218i
$575$		0			0
$576$	76.4133			0.132662
$577$		−	717.832i		−	1.24408i	−0.782987	−	0.622038i	$-0.786305\pi$
$577$		−	717.832i		−	1.24408i	0.782987	−	0.622038i	$-0.213695\pi$
$578$		−	59.8374i		−	0.103525i
$579$	−855.186			−1.47701
$580$		0			0
$581$	65.1075			0.112061
$582$	938.819			1.61309
$583$			231.543i			0.397158i
$584$	−42.9405			−0.0735283
$585$		0			0
$586$		−	175.644i		−	0.299735i
$587$		−	296.393i		−	0.504928i	−0.967606	−	0.252464i	$-0.918759\pi$
$587$		−	296.393i		−	0.504928i	0.967606	−	0.252464i	$-0.0812410\pi$
$588$		−	403.352i		−	0.685973i
$589$		−	98.8912i		−	0.167897i
$590$		0			0
$591$	121.486			0.205560
$592$	62.0992			0.104897
$593$		−	654.259i		−	1.10330i	−0.834075	−	0.551652i	$-0.813998\pi$
$593$		−	654.259i		−	1.10330i	0.834075	−	0.551652i	$-0.186002\pi$
$594$		−	20.3287i		−	0.0342235i
$595$		0			0
$596$			403.293i			0.676667i
$597$	923.881			1.54754
$598$	−168.500	−	19.0224i	−0.281773	−	0.0318100i
$599$	−368.673			−0.615480			−0.307740	−	0.951470i	$-0.599573\pi$
$599$	−368.673			−0.615480			−0.307740	+	0.951470i	$0.599573\pi$
$600$		0			0
$601$	148.316			0.246782			0.123391	−	0.992358i	$-0.460623\pi$
$601$	148.316			0.246782			0.123391	+	0.992358i	$0.460623\pi$
$602$		−	79.6381i		−	0.132289i
$603$	309.922			0.513967
$604$	−241.573			−0.399956
$605$		0			0
$606$	−358.535			−0.591643
$607$			939.932i			1.54849i	0.632887	+	0.774244i	$0.281870\pi$
$607$			939.932i			1.54849i	−0.632887	+	0.774244i	$0.718130\pi$
$608$	−27.3036			−0.0449072
$609$			149.146i			0.244904i
$610$		0			0
$611$	72.0850			0.117979
$612$	300.043			0.490267
$613$	602.963			0.983626			0.491813	−	0.870701i	$-0.336334\pi$
$613$	602.963			0.983626			0.491813	+	0.870701i	$0.336334\pi$
$614$	−310.727			−0.506069
$615$		0			0
$616$	−25.2440			−0.0409805
$617$	885.697			1.43549			0.717745	−	0.696306i	$-0.245174\pi$
$617$	885.697			1.43549			0.717745	+	0.696306i	$0.245174\pi$
$618$	330.549			0.534869
$619$			85.9838i			0.138908i	0.997585	+	0.0694538i	$0.0221257\pi$
$619$			85.9838i			0.138908i	−0.997585	+	0.0694538i	$0.977874\pi$
$620$		0			0
$621$	−6.13072	+	54.3060i	−0.00987233	+	0.0874492i
$622$		−	448.403i		−	0.720905i
$623$			163.819i			0.262951i
$624$	89.8171			0.143938
$625$		0			0
$626$			685.404i			1.09489i
$627$			125.765i			0.200583i
$628$	−389.794			−0.620692
$629$	243.837			0.387659
$630$		0			0
$631$			645.385i			1.02280i	0.859344	+	0.511398i	$0.170872\pi$
$631$			645.385i			1.02280i	−0.859344	+	0.511398i	$0.829128\pi$
$632$	−31.7053			−0.0501666
$633$		−	1034.85i		−	1.63483i
$634$	738.092			1.16418
$635$		0			0
$636$			329.706i			0.518406i
$637$		−	244.102i		−	0.383205i
$638$	−200.805			−0.314741
$639$	230.488			0.360701
$640$		0			0
$641$			140.119i			0.218594i	0.994009	+	0.109297i	$0.0348599\pi$
$641$			140.119i			0.218594i	−0.994009	+	0.109297i	$0.965140\pi$
$642$	725.613			1.13024
$643$	1028.11			1.59892			0.799461	−	0.600718i	$-0.205118\pi$
$643$	1028.11			1.59892			0.799461	+	0.600718i	$0.205118\pi$
$644$	67.4366	+	7.61306i	0.104715	+	0.0118215i
$645$		0			0
$646$	−107.210			−0.165959
$647$			1248.29i			1.92934i	0.263455	+	0.964672i	$0.415138\pi$
$647$			1248.29i			1.92934i	−0.263455	+	0.964672i	$0.584862\pi$
$648$			214.199i			0.330553i
$649$			203.082i			0.312916i
$650$		0			0
$651$		−	130.194i		−	0.199992i
$652$			307.625i			0.471817i
$653$			457.504i			0.700618i	0.936634	+	0.350309i	$0.113923\pi$
$653$			457.504i			0.700618i	−0.936634	+	0.350309i	$0.886077\pi$
$654$		−	908.956i		−	1.38984i
$655$		0			0
$656$	81.2370			0.123837
$657$			145.011i			0.220717i
$658$	−28.8496			−0.0438444
$659$			173.014i			0.262540i	0.991347	+	0.131270i	$0.0419055\pi$
$659$			173.014i			0.262540i	−0.991347	+	0.131270i	$0.958095\pi$
$660$		0			0
$661$			582.673i			0.881502i	0.897629	+	0.440751i	$0.145288\pi$
$661$			582.673i			0.881502i	−0.897629	+	0.440751i	$0.854712\pi$
$662$		−	450.101i		−	0.679911i
$663$	352.674			0.531937
$664$			124.821i			0.187984i
$665$		0			0
$666$		−	209.710i		−	0.314880i
$667$	536.428	+	60.5585i	0.804240	+	0.0907924i
$668$		−	96.9899i		−	0.145194i
$669$	−1108.67			−1.65721
$670$		0			0
$671$	608.389			0.906690
$672$	−35.9463			−0.0534915
$673$			390.678i			0.580502i	0.956951	+	0.290251i	$0.0937388\pi$
$673$			390.678i			0.580502i	−0.956951	+	0.290251i	$0.906261\pi$
$674$			164.810i			0.244526i
$675$		0			0
$676$	−283.644			−0.419592
$677$	−952.947			−1.40760			−0.703801	−	0.710397i	$-0.748515\pi$
$677$	−952.947			−1.40760			−0.703801	+	0.710397i	$0.748515\pi$
$678$	−215.228			−0.317445
$679$	−227.386			−0.334883
$680$		0			0
$681$			458.286i			0.672961i
$682$	175.289			0.257022
$683$		−	299.732i		−	0.438847i	−0.975630	−	0.219423i	$-0.929582\pi$
$683$		−	299.732i		−	0.438847i	0.975630	−	0.219423i	$-0.0704176\pi$
$684$			92.2048i			0.134802i
$685$		0			0
$686$			199.928i			0.291441i
$687$	1414.93			2.05958
$688$	152.679			0.221917
$689$			199.532i			0.289597i
$690$		0			0
$691$	165.585			0.239631			0.119815	−	0.992796i	$-0.461770\pi$
$691$	165.585			0.239631			0.119815	+	0.992796i	$0.461770\pi$
$692$		−	222.538i		−	0.321587i
$693$			85.2497i			0.123015i
$694$	142.432			0.205234
$695$		0			0
$696$	−285.937			−0.410829
$697$	318.984			0.457652
$698$		−	202.906i		−	0.290696i
$699$	642.685			0.919436
$700$		0			0
$701$			831.750i			1.18652i	0.805011	+	0.593260i	$0.202159\pi$
$701$			831.750i			1.18652i	−0.805011	+	0.593260i	$0.797841\pi$
$702$		−	17.5183i		−	0.0249549i
$703$			74.9324i			0.106590i
$704$		−	48.3967i		−	0.0687453i
$705$		0			0
$706$	−388.052			−0.549649
$707$	86.8387			0.122827
$708$			289.180i			0.408446i
$709$			835.784i			1.17882i	0.807834	+	0.589410i	$0.200640\pi$
$709$			835.784i			1.17882i	−0.807834	+	0.589410i	$0.799360\pi$
$710$		0			0
$711$			107.070i			0.150590i
$712$	−314.066			−0.441104
$713$	−468.265	−	52.8634i	−0.656753	−	0.0741422i
$714$	−141.146			−0.197683
$715$		0			0
$716$	525.180			0.733492
$717$		−	1478.08i		−	2.06148i
$718$	674.397			0.939272
$719$	−881.656			−1.22623			−0.613113	−	0.789996i	$-0.710083\pi$
$719$	−881.656			−1.22623			−0.613113	+	0.789996i	$0.710083\pi$
$720$		0			0
$721$	−80.0602			−0.111041
$722$			477.585i			0.661475i
$723$	1502.12			2.07762
$724$		−	422.335i		−	0.583335i
$725$		0			0
$726$	514.117			0.708150
$727$	−531.577			−0.731193			−0.365596	−	0.930774i	$-0.619135\pi$
$727$	−531.577			−0.731193			−0.365596	+	0.930774i	$0.619135\pi$
$728$	−21.7541			−0.0298820
$729$	815.463			1.11861
$730$		0			0
$731$	599.505			0.820116
$732$	866.318			1.18349
$733$	18.4847			0.0252178			0.0126089	−	0.999921i	$-0.495986\pi$
$733$	18.4847			0.0252178			0.0126089	+	0.999921i	$0.495986\pi$
$734$		−	19.8441i		−	0.0270356i
$735$		0			0
$736$	−14.5954	+	129.286i	−0.0198307	+	0.175661i
$737$		−	196.290i		−	0.266337i
$738$		−	274.339i		−	0.371734i
$739$	960.371			1.29955			0.649777	−	0.760125i	$-0.274862\pi$
$739$	960.371			1.29955			0.649777	+	0.760125i	$0.274862\pi$
$740$		0			0
$741$			108.379i			0.146260i
$742$		−	79.8562i		−	0.107623i
$743$	−248.966			−0.335082			−0.167541	−	0.985865i	$-0.553583\pi$
$743$	−248.966			−0.335082			−0.167541	+	0.985865i	$0.553583\pi$
$744$	249.603			0.335488
$745$		0			0
$746$			149.429i			0.200307i
$747$	421.524			0.564289
$748$		−	190.034i		−	0.254056i
$749$	−175.746			−0.234641
$750$		0			0
$751$		−	24.0757i		−	0.0320582i	−0.999872	−	0.0160291i	$-0.994898\pi$
$751$		−	24.0757i		−	0.0320582i	0.999872	−	0.0160291i	$-0.00510244\pi$
$752$		−	55.3091i		−	0.0735494i
$753$	969.539			1.28757
$754$	−173.044			−0.229501
$755$		0			0
$756$			7.01112i			0.00927396i
$757$	914.334			1.20784			0.603920	−	0.797045i	$-0.293605\pi$
$757$	914.334			1.20784			0.603920	+	0.797045i	$0.293605\pi$
$758$	−480.809			−0.634312
$759$	595.518	+	67.2294i	0.784609	+	0.0885762i
$760$		0			0
$761$	313.770			0.412312			0.206156	−	0.978519i	$-0.433905\pi$
$761$	313.770			0.412312			0.206156	+	0.978519i	$0.433905\pi$
$762$			565.511i			0.742140i
$763$			220.153i			0.288536i
$764$		−	145.642i		−	0.190631i
$765$		0			0
$766$		−	989.662i		−	1.29199i
$767$			175.007i			0.228170i
$768$		−	68.9146i		−	0.0897326i
$769$		−	309.335i		−	0.402257i	−0.979565	−	0.201128i	$-0.935539\pi$
$769$		−	309.335i		−	0.402257i	0.979565	−	0.201128i	$-0.0644608\pi$
$770$		0			0
$771$	−1695.44			−2.19901
$772$			397.099i			0.514377i
$773$	−233.356			−0.301884			−0.150942	−	0.988543i	$-0.548231\pi$
$773$	−233.356			−0.301884			−0.150942	+	0.988543i	$0.548231\pi$
$774$		−	515.599i		−	0.666149i
$775$		0			0
$776$		−	435.934i		−	0.561770i
$777$			98.6518i			0.126965i
$778$	176.518			0.226887
$779$			98.0253i			0.125835i
$780$		0			0
$781$		−	145.980i		−	0.186915i
$782$	−57.3101	+	507.653i	−0.0732866	+	0.649173i
$783$			55.7703i			0.0712265i
$784$	−187.294			−0.238895
$785$		0			0
$786$	924.098			1.17570
$787$	690.751			0.877702			0.438851	−	0.898560i	$-0.355386\pi$
$787$	690.751			0.877702			0.438851	+	0.898560i	$0.355386\pi$
$788$		−	56.4111i		−	0.0715876i
$789$			571.648i			0.724522i
$790$		0			0
$791$	52.1290			0.0659027
$792$	−163.437			−0.206360
$793$	524.280			0.661135
$794$	211.506			0.266381
$795$		0			0
$796$		−	428.997i		−	0.538941i
$797$	−91.6732			−0.115023			−0.0575114	−	0.998345i	$-0.518317\pi$
$797$	−91.6732			−0.115023			−0.0575114	+	0.998345i	$0.518317\pi$
$798$		−	43.3749i		−	0.0543545i
$799$		−	217.176i		−	0.271810i
$800$		0			0
$801$			1060.61i			1.32410i
$802$	−603.439			−0.752418
$803$	91.8434			0.114375
$804$		−	279.508i		−	0.347647i
$805$		0			0
$806$	151.055			0.187414
$807$		−	1887.04i		−	2.33833i
$808$			166.483i			0.206044i
$809$	−1071.73			−1.32476			−0.662382	−	0.749166i	$-0.730454\pi$
$809$	−1071.73			−1.32476			−0.662382	+	0.749166i	$0.730454\pi$
$810$		0			0
$811$	−257.388			−0.317371			−0.158685	−	0.987329i	$-0.550726\pi$
$811$	−257.388			−0.317371			−0.158685	+	0.987329i	$0.550726\pi$
$812$	69.2550			0.0852894
$813$			881.666i			1.08446i
$814$	−132.821			−0.163171
$815$		0			0
$816$		−	270.599i		−	0.331616i
$817$			184.231i			0.225497i
$818$		−	489.690i		−	0.598643i
$819$			73.4640i			0.0896996i
$820$		0			0
$821$	−349.772			−0.426032			−0.213016	−	0.977049i	$-0.568329\pi$
$821$	−349.772			−0.426032			−0.213016	+	0.977049i	$0.568329\pi$
$822$	1629.19			1.98198
$823$		−	1438.73i		−	1.74815i	−0.485789	−	0.874076i	$-0.661468\pi$
$823$		−	1438.73i		−	1.74815i	0.485789	−	0.874076i	$-0.338532\pi$
$824$		−	153.488i		−	0.186272i
$825$		0			0
$826$		−	70.0405i		−	0.0847948i
$827$	−996.093			−1.20447			−0.602233	−	0.798320i	$-0.705722\pi$
$827$	−996.093			−1.20447			−0.602233	+	0.798320i	$0.705722\pi$
$828$	436.603	+	49.2891i	0.527299	+	0.0595279i
$829$	234.343			0.282681			0.141341	−	0.989961i	$-0.454859\pi$
$829$	234.343			0.282681			0.141341	+	0.989961i	$0.454859\pi$
$830$		0			0
$831$	748.603			0.900846
$832$		−	41.7059i		−	0.0501273i
$833$	−735.424			−0.882862
$834$	−1460.56			−1.75127
$835$		0			0
$836$	58.3983			0.0698544
$837$		−	48.6836i		−	0.0581644i
$838$	224.058			0.267372
$839$		−	742.848i		−	0.885397i	−0.896670	−	0.442699i	$-0.854021\pi$
$839$		−	742.848i		−	0.885397i	0.896670	−	0.442699i	$-0.145979\pi$
$840$		0			0
$841$	−290.107			−0.344955
$842$	−25.5361			−0.0303280
$843$	618.532			0.733727
$844$	−480.523			−0.569340
$845$		0			0
$846$	−186.780			−0.220781
$847$	−124.521			−0.147014
$848$	153.097			0.180539
$849$			310.854i			0.366142i
$850$		0			0
$851$	354.816	+	40.0560i	0.416940	+	0.0470693i
$852$		−	207.869i		−	0.243978i
$853$		−	482.186i		−	0.565283i	−0.959226	−	0.282642i	$-0.908789\pi$
$853$		−	482.186i		−	0.565283i	0.959226	−	0.282642i	$-0.0912107\pi$
$854$	−209.826			−0.245697
$855$		0			0
$856$		−	336.933i		−	0.393613i
$857$			685.909i			0.800361i	0.916436	+	0.400180i	$0.131053\pi$
$857$			685.909i			0.800361i	−0.916436	+	0.400180i	$0.868947\pi$
$858$	−192.106			−0.223899
$859$	−670.668			−0.780754			−0.390377	−	0.920655i	$-0.627655\pi$
$859$	−670.668			−0.780754			−0.390377	+	0.920655i	$0.627655\pi$
$860$		0			0
$861$			129.054i			0.149889i
$862$	−214.578			−0.248931
$863$		−	891.818i		−	1.03339i	−0.856169	−	0.516696i	$-0.827162\pi$
$863$		−	891.818i		−	1.03339i	0.856169	−	0.516696i	$-0.172838\pi$
$864$	−13.4414			−0.0155572
$865$		0			0
$866$		−	884.550i		−	1.02142i
$867$			182.242i			0.210199i
$868$	−60.4548			−0.0696484
$869$	67.8129			0.0780356
$870$		0			0
$871$		−	169.154i		−	0.194206i
$872$	−422.067			−0.484022
$873$	−1472.16			−1.68632
$874$	−156.004	−	17.6117i	−0.178495	−	0.0201507i
$875$		0			0
$876$	130.781			0.149293
$877$			181.676i			0.207156i	0.994621	+	0.103578i	$0.0330291\pi$
$877$			181.676i			0.207156i	−0.994621	+	0.103578i	$0.966971\pi$
$878$		−	385.858i		−	0.439473i
$879$			534.947i			0.608586i
$880$		0			0
$881$		−	316.887i		−	0.359691i	−0.983695	−	0.179845i	$-0.942440\pi$
$881$		−	316.887i		−	0.359691i	0.983695	−	0.179845i	$-0.0575597\pi$
$882$			632.495i			0.717115i
$883$			1361.85i			1.54230i	0.636656	+	0.771148i	$0.280317\pi$
$883$			1361.85i			1.54230i	−0.636656	+	0.771148i	$0.719683\pi$
$884$		−	163.762i		−	0.185251i
$885$		0			0
$886$	7.88463			0.00889914
$887$			1628.63i			1.83611i	0.396449	+	0.918057i	$0.370242\pi$
$887$			1628.63i			1.83611i	−0.396449	+	0.918057i	$0.629758\pi$
$888$	−189.131			−0.212985
$889$		−	136.969i		−	0.154071i
$890$		0			0
$891$		−	458.139i		−	0.514185i
$892$			514.805i			0.577136i
$893$	66.7392			0.0747360
$894$		−	1228.28i		−	1.37392i
$895$		0			0
$896$			16.6914i			0.0186288i
$897$	513.189	+	57.9350i	0.572117	+	0.0645875i
$898$		−	643.936i		−	0.717078i
$899$	−480.891			−0.534918
$900$		0			0
$901$	601.146			0.667199
$902$	−173.754			−0.192632
$903$			242.548i			0.268602i
$904$			99.9395i			0.110552i
$905$		0			0
$906$	735.742			0.812077
$907$	1551.21			1.71026			0.855130	−	0.518413i	$-0.173477\pi$
$907$	1551.21			1.71026			0.855130	+	0.518413i	$0.173477\pi$
$908$	212.802			0.234363
$909$	562.218			0.618502
$910$		0			0
$911$			1672.31i			1.83569i	0.396937	+	0.917846i	$0.370073\pi$
$911$			1672.31i			1.83569i	−0.396937	+	0.917846i	$0.629927\pi$
$912$	83.1564			0.0911802
$913$		−	266.974i		−	0.292414i
$914$			845.396i			0.924941i
$915$		0			0
$916$		−	657.014i		−	0.717265i
$917$	−223.820			−0.244079
$918$	−52.7788			−0.0574932
$919$		−	1670.00i		−	1.81719i	−0.417673	−	0.908597i	$-0.637154\pi$
$919$		−	1670.00i		−	1.81719i	0.417673	−	0.908597i	$-0.362846\pi$
$920$		0			0
$921$	946.357			1.02753
$922$		−	481.619i		−	0.522364i
$923$		−	125.799i		−	0.136293i
$924$	76.8838			0.0832076
$925$		0			0
$926$	−666.653			−0.719928
$927$	−518.332			−0.559150
$928$			132.773i			0.143074i
$929$	877.260			0.944306			0.472153	−	0.881517i	$-0.343477\pi$
$929$	877.260			0.944306			0.472153	+	0.881517i	$0.343477\pi$
$930$		0			0
$931$		−	225.999i		−	0.242749i
$932$		−	298.426i		−	0.320200i
$933$			1365.67i			1.46374i
$934$		−	347.445i		−	0.371997i
$935$		0			0
$936$	−140.842			−0.150472
$937$	−726.689			−0.775549			−0.387774	−	0.921754i	$-0.626756\pi$
$937$	−726.689			−0.775549			−0.387774	+	0.921754i	$0.626756\pi$
$938$			67.6980i			0.0721727i
$939$		−	2087.48i		−	2.22309i
$940$		0			0
$941$			289.839i			0.308011i	0.988070	+	0.154006i	$0.0492174\pi$
$941$			289.839i			0.308011i	−0.988070	+	0.154006i	$0.950783\pi$
$942$	1187.17			1.26026
$943$	464.164	+	52.4005i	0.492221	+	0.0555679i
$944$	134.279			0.142244
$945$		0			0
$946$	−326.557			−0.345198
$947$		−	1420.59i		−	1.50010i	−0.661381	−	0.750050i	$-0.730030\pi$
$947$		−	1420.59i		−	1.50010i	0.661381	−	0.750050i	$-0.269970\pi$
$948$	96.5624			0.101859
$949$	79.1462			0.0833996
$950$		0			0
$951$	−2247.95			−2.36378
$952$			65.5401i			0.0688446i
$953$	−1465.45			−1.53772			−0.768860	−	0.639418i	$-0.779176\pi$
$953$	−1465.45			−1.53772			−0.768860	+	0.639418i	$0.779176\pi$
$954$		−	517.011i		−	0.541941i
$955$		0			0
$956$	−686.336			−0.717925
$957$	611.577			0.639056
$958$	−288.415			−0.301060
$959$	−394.596			−0.411466
$960$		0			0
$961$	−541.215			−0.563179
$962$	−114.459			−0.118980
$963$	−1137.83			−1.18155
$964$		−	697.497i		−	0.723544i
$965$		0			0
$966$	−205.387	−	23.1865i	−0.212615	−	0.0240026i
$967$		−	1536.47i		−	1.58890i	−0.607328	−	0.794451i	$-0.707759\pi$
$967$		−	1536.47i		−	1.58890i	0.607328	−	0.794451i	$-0.292241\pi$
$968$		−	238.726i		−	0.246618i
$969$	326.520			0.336966
$970$		0			0
$971$		−	1693.09i		−	1.74366i	−0.489812	−	0.871828i	$-0.662935\pi$
$971$		−	1693.09i		−	1.74366i	0.489812	−	0.871828i	$-0.337065\pi$
$972$		−	695.139i		−	0.715164i
$973$	353.752			0.363569
$974$	963.724			0.989450
$975$		0			0
$976$		−	402.268i		−	0.412160i
$977$	−1295.96			−1.32647			−0.663235	−	0.748411i	$-0.730817\pi$
$977$	−1295.96			−1.32647			−0.663235	+	0.748411i	$0.730817\pi$
$978$		−	936.911i		−	0.957986i
$979$	671.740			0.686150
$980$		0			0
$981$			1425.33i			1.45294i
$982$		−	466.218i		−	0.474764i
$983$	−1692.07			−1.72133			−0.860667	−	0.509168i	$-0.829953\pi$
$983$	−1692.07			−1.72133			−0.860667	+	0.509168i	$0.829953\pi$
$984$	−247.418			−0.251441
$985$		0			0
$986$			521.343i			0.528745i
$987$	87.8650			0.0890223
$988$	50.3248			0.0509360
$989$	872.361	+	98.4827i	0.882063	+	0.0995780i
$990$		0			0
$991$	45.3192			0.0457308			0.0228654	−	0.999739i	$-0.492721\pi$
$991$	45.3192			0.0457308			0.0228654	+	0.999739i	$0.492721\pi$
$992$		−	115.901i		−	0.116836i
$993$			1370.84i			1.38050i
$994$			50.3467i			0.0506506i
$995$		0			0
$996$		−	380.159i		−	0.381685i
$997$			1358.89i			1.36298i	0.731830	+	0.681488i	$0.238667\pi$
$997$			1358.89i			1.36298i	−0.731830	+	0.681488i	$0.761333\pi$
$998$			1405.32i			1.40813i
$999$			36.8889i			0.0369258i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.15	✓	16	5.3	odd	4
230.3.d.a.91.16	yes	16	115.68	even	4
1150.3.c.c.1149.13		32	115.114	odd	2	inner
1150.3.c.c.1149.14		32	1.1	even	1	trivial
1150.3.c.c.1149.19		32	5.4	even	2	inner
1150.3.c.c.1149.20		32	23.22	odd	2	inner
1150.3.d.b.551.1		16	5.2	odd	4
1150.3.d.b.551.2		16	115.22	even	4
1840.3.k.d.321.3		16	20.3	even	4
1840.3.k.d.321.4		16	460.183	odd	4
2070.3.c.a.91.2		16	345.68	odd	4
2070.3.c.a.91.7		16	15.8	even	4

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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -4.30716i q^{3} -2.00000 q^{4} +6.09125 q^{6} -1.47532 q^{7} -2.82843i q^{8} -9.55167 q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} -4.30716i q^{3} -2.00000 q^{4} +6.09125 q^{6} -1.47532 q^{7} -2.82843i q^{8} -9.55167 q^{9} +6.04959i q^{11} +8.61433i q^{12} +5.21324i q^{13} -2.08642i q^{14} +4.00000 q^{16} +15.7063 q^{17} -13.5081i q^{18} +4.82663i q^{19} +6.35447i q^{21} -8.55541 q^{22} +(22.8548 + 2.58013i) q^{23} -12.1825 q^{24} -7.37263 q^{26} +2.37613i q^{27} +2.95065 q^{28} +23.4711 q^{29} -20.4887 q^{31} +5.65685i q^{32} +26.0566 q^{33} +22.2121i q^{34} +19.1033 q^{36} +15.5248 q^{37} -6.82589 q^{38} +22.4543 q^{39} +20.3093 q^{41} -8.98657 q^{42} +38.1696 q^{43} -12.0992i q^{44} +(-3.64885 + 32.3216i) q^{46} -13.8273i q^{47} -17.2287i q^{48} -46.8234 q^{49} -67.6497i q^{51} -10.4265i q^{52} +38.2742 q^{53} -3.36035 q^{54} +4.17285i q^{56} +20.7891 q^{57} +33.1932i q^{58} +33.5696 q^{59} -100.567i q^{61} -28.9753i q^{62} +14.0918 q^{63} -8.00000 q^{64} +36.8496i q^{66} -32.4469 q^{67} -31.4126 q^{68} +(11.1130 - 98.4395i) q^{69} -24.1306 q^{71} +27.0162i q^{72} -15.1818i q^{73} +21.9554i q^{74} -9.65326i q^{76} -8.92511i q^{77} +31.7552i q^{78} -11.2095i q^{79} -75.7306 q^{81} +28.7216i q^{82} -44.1310 q^{83} -12.7089i q^{84} +53.9800i q^{86} -101.094i q^{87} +17.1108 q^{88} -111.039i q^{89} -7.69122i q^{91} +(-45.7096 - 5.16026i) q^{92} +88.2480i q^{93} +19.5547 q^{94} +24.3650 q^{96} +154.126 q^{97} -66.2183i q^{98} -57.7837i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10}) \) 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9	\( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9} + 128 q^{16} + 32 q^{24} + 192 q^{26} + 216 q^{29} - 232 q^{31} + 256 q^{36} - 496 q^{39} - 312 q^{41} - 248 q^{46} + 56 q^{49} - 448 q^{54} - 408 q^{59} - 256 q^{64} + 536 q^{69} + 472 q^{71} - 272 q^{81} + 432 q^{94} - 64 q^{96}+O(q^{100}) \) 32 * q - 64 * q^4 - 16 * q^6 - 128 * q^9 + 128 * q^16 + 32 * q^24 + 192 * q^26 + 216 * q^29 - 232 * q^31 + 256 * q^36 - 496 * q^39 - 312 * q^41 - 248 * q^46 + 56 * q^49 - 448 * q^54 - 408 * q^59 - 256 * q^64 + 536 * q^69 + 472 * q^71 - 272 * q^81 + 432 * q^94 - 64 * q^96

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