LMFDB - Embedded newform 483.2.h.b.160.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(160,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("483.160");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.h (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 14x^{10} + 67x^{8} + 141x^{6} + 129x^{4} + 39x^{2} + 1 $ x^12 + 14x^10 + 67x^8 + 141x^6 + 129x^4 + 39*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			160.5
Root			$-1.51343i$ of defining polynomial
Character	$\chi$	$=$	483.160
Dual form			483.2.h.b.160.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.254102 q^{2} -1.00000i q^{3} -1.93543 q^{4} -0.458377 q^{5} -0.254102i q^{6} +(1.07291 + 2.41844i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+0.254102 q^{2} -1.00000i q^{3} -1.93543 q^{4} -0.458377 q^{5} -0.254102i q^{6} +(1.07291 + 2.41844i) q^{7} -1.00000 q^{8} -1.00000 q^{9} -0.116474 q^{10} +1.34554i q^{11} +1.93543i q^{12} +4.42723i q^{13} +(0.272628 + 0.614531i) q^{14} +0.458377i q^{15} +3.61676 q^{16} +7.09918 q^{17} -0.254102 q^{18} +4.40811 q^{19} +0.887158 q^{20} +(2.41844 - 1.07291i) q^{21} +0.341903i q^{22} +(-4.44364 + 1.80391i) q^{23} +1.00000i q^{24} -4.78989 q^{25} +1.12497i q^{26} +1.00000i q^{27} +(-2.07654 - 4.68073i) q^{28} +4.18953 q^{29} +0.116474i q^{30} -4.31867i q^{31} +2.91903 q^{32} +1.34554 q^{33} +1.80391 q^{34} +(-0.491797 - 1.10856i) q^{35} +1.93543 q^{36} +8.56119i q^{37} +1.12011 q^{38} +4.42723 q^{39} +0.458377 q^{40} +3.81047i q^{41} +(0.614531 - 0.272628i) q^{42} +7.18606i q^{43} -2.60419i q^{44} +0.458377 q^{45} +(-1.12914 + 0.458377i) q^{46} +7.23353i q^{47} -3.61676i q^{48} +(-4.69774 + 5.18953i) q^{49} -1.21712 q^{50} -7.09918i q^{51} -8.56860i q^{52} -8.35783i q^{53} +0.254102i q^{54} -0.616763i q^{55} +(-1.07291 - 2.41844i) q^{56} -4.40811i q^{57} +1.06457 q^{58} -8.10856i q^{59} -0.887158i q^{60} -10.2486 q^{61} -1.09738i q^{62} +(-1.07291 - 2.41844i) q^{63} -6.49180 q^{64} -2.02934i q^{65} +0.341903 q^{66} +5.84052i q^{67} -13.7400 q^{68} +(1.80391 + 4.44364i) q^{69} +(-0.124966 - 0.281687i) q^{70} +8.42723 q^{71} +1.00000 q^{72} -7.04399i q^{73} +2.17541i q^{74} +4.78989i q^{75} -8.53159 q^{76} +(-3.25410 + 1.44364i) q^{77} +1.12497 q^{78} +6.86623i q^{79} -1.65784 q^{80} +1.00000 q^{81} +0.968246i q^{82} -4.95336 q^{83} +(-4.68073 + 2.07654i) q^{84} -3.25410 q^{85} +1.82599i q^{86} -4.18953i q^{87} -1.34554i q^{88} +16.0023 q^{89} +0.116474 q^{90} +(-10.7070 + 4.75001i) q^{91} +(8.60036 - 3.49135i) q^{92} -4.31867 q^{93} +1.83805i q^{94} -2.02058 q^{95} -2.91903i q^{96} -3.86285 q^{97} +(-1.19370 + 1.31867i) q^{98} -1.34554i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 12 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q + 8 * q^4 - 12 * q^8 - 12 * q^9	$ 12 q + 8 q^{4} - 12 q^{8} - 12 q^{9} - 16 q^{16} - 16 q^{23} + 24 q^{25} + 16 q^{29} + 16 q^{32} - 12 q^{35} - 8 q^{36} + 28 q^{39} - 76 q^{46} - 16 q^{49} + 92 q^{50} + 44 q^{58} - 84 q^{64} + 64 q^{70} + 76 q^{71} + 12 q^{72} - 36 q^{77} - 52 q^{78} + 12 q^{81} - 36 q^{85} + 56 q^{92} - 80 q^{93} - 140 q^{95} - 108 q^{98}+O(q^{100}) $ 12 * q + 8 * q^4 - 12 * q^8 - 12 * q^9 - 16 * q^16 - 16 * q^23 + 24 * q^25 + 16 * q^29 + 16 * q^32 - 12 * q^35 - 8 * q^36 + 28 * q^39 - 76 * q^46 - 16 * q^49 + 92 * q^50 + 44 * q^58 - 84 * q^64 + 64 * q^70 + 76 * q^71 + 12 * q^72 - 36 * q^77 - 52 * q^78 + 12 * q^81 - 36 * q^85 + 56 * q^92 - 80 * q^93 - 140 * q^95 - 108 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.254102			0.179677			0.0898385	−	0.995956i	$-0.471365\pi$
$2$	0.254102			0.179677			0.0898385	+	0.995956i	$0.471365\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.93543			−0.967716
$5$	−0.458377			−0.204993			−0.102496	−	0.994733i	$-0.532683\pi$
$5$	−0.458377			−0.204993			−0.102496	+	0.994733i	$0.532683\pi$
$6$		−	0.254102i		−	0.103737i
$7$	1.07291	+	2.41844i	0.405521	+	0.914086i
$7$	1.07291	+	2.41844i	0.405521	+	0.914086i
$8$	−1.00000			−0.353553
$9$	−1.00000			−0.333333
$10$	−0.116474			−0.0368325
$11$			1.34554i			0.405694i	0.979210	+	0.202847i	$0.0650194\pi$
$11$			1.34554i			0.405694i	−0.979210	+	0.202847i	$0.934981\pi$
$12$			1.93543i			0.558711i
$13$			4.42723i			1.22789i	0.789348	+	0.613946i	$0.210419\pi$
$13$			4.42723i			1.22789i	−0.789348	+	0.613946i	$0.789581\pi$
$14$	0.272628	+	0.614531i	0.0728628	+	0.164240i
$15$			0.458377i			0.118353i
$16$	3.61676			0.904191
$17$	7.09918			1.72180			0.860902	−	0.508771i	$-0.169900\pi$
$17$	7.09918			1.72180			0.860902	+	0.508771i	$0.169900\pi$
$18$	−0.254102			−0.0598923
$19$	4.40811			1.01129			0.505644	−	0.862742i	$-0.331255\pi$
$19$	4.40811			1.01129			0.505644	+	0.862742i	$0.331255\pi$
$20$	0.887158			0.198375
$21$	2.41844	−	1.07291i	0.527748	−	0.234128i
$22$			0.341903i			0.0728939i
$23$	−4.44364	+	1.80391i	−0.926562	+	0.376142i
$23$	−4.44364	+	1.80391i	−0.926562	+	0.376142i
$24$			1.00000i			0.204124i
$25$	−4.78989			−0.957978
$26$			1.12497i			0.220624i
$27$			1.00000i			0.192450i
$28$	−2.07654	−	4.68073i	−0.392429	−	0.884576i
$29$	4.18953			0.777977			0.388988	−	0.921243i	$-0.372825\pi$
$29$	4.18953			0.777977			0.388988	+	0.921243i	$0.372825\pi$
$30$			0.116474i			0.0212652i
$31$		−	4.31867i		−	0.775656i	−0.921732	−	0.387828i	$-0.873225\pi$
$31$		−	4.31867i		−	0.775656i	0.921732	−	0.387828i	$-0.126775\pi$
$32$	2.91903			0.516016
$33$	1.34554			0.234228
$34$	1.80391			0.309369
$35$	−0.491797	−	1.10856i	−0.0831288	−	0.187381i
$36$	1.93543			0.322572
$37$			8.56119i			1.40745i	0.710472	+	0.703725i	$0.248481\pi$
$37$			8.56119i			1.40745i	−0.710472	+	0.703725i	$0.751519\pi$
$38$	1.12011			0.181705
$39$	4.42723			0.708924
$40$	0.458377			0.0724758
$41$			3.81047i			0.595095i	0.954707	+	0.297547i	$0.0961686\pi$
$41$			3.81047i			0.595095i	−0.954707	+	0.297547i	$0.903831\pi$
$42$	0.614531	−	0.272628i	0.0948241	−	0.0420674i
$43$			7.18606i			1.09586i	0.836523	+	0.547932i	$0.184585\pi$
$43$			7.18606i			1.09586i	−0.836523	+	0.547932i	$0.815415\pi$
$44$		−	2.60419i		−	0.392597i
$45$	0.458377			0.0683309
$46$	−1.12914	+	0.458377i	−0.166482	+	0.0675840i
$47$			7.23353i			1.05512i	0.849518	+	0.527559i	$0.176893\pi$
$47$			7.23353i			1.05512i	−0.849518	+	0.527559i	$0.823107\pi$
$48$		−	3.61676i		−	0.522035i
$49$	−4.69774	+	5.18953i	−0.671105	+	0.741362i
$50$	−1.21712			−0.172127
$51$		−	7.09918i		−	0.994084i
$52$		−	8.56860i		−	1.18825i
$53$		−	8.35783i		−	1.14804i	−0.818842	−	0.574018i	$-0.805384\pi$
$53$		−	8.35783i		−	1.14804i	0.818842	−	0.574018i	$-0.194616\pi$
$54$			0.254102i			0.0345789i
$55$		−	0.616763i		−	0.0831643i
$56$	−1.07291	−	2.41844i	−0.143373	−	0.323178i
$57$		−	4.40811i		−	0.583868i
$58$	1.06457			0.139785
$59$		−	8.10856i		−	1.05564i	−0.849355	−	0.527822i	$-0.823009\pi$
$59$		−	8.10856i		−	1.05564i	0.849355	−	0.527822i	$-0.176991\pi$
$60$		−	0.887158i		−	0.114532i
$61$	−10.2486			−1.31220			−0.656101	−	0.754673i	$-0.727795\pi$
$61$	−10.2486			−1.31220			−0.656101	+	0.754673i	$0.727795\pi$
$62$		−	1.09738i		−	0.139368i
$63$	−1.07291	−	2.41844i	−0.135174	−	0.304695i
$64$	−6.49180			−0.811475
$65$		−	2.02934i		−	0.251709i
$66$	0.341903			0.0420853
$67$			5.84052i			0.713533i	0.934194	+	0.356767i	$0.116121\pi$
$67$			5.84052i			0.713533i	−0.934194	+	0.356767i	$0.883879\pi$
$68$	−13.7400			−1.66622
$69$	1.80391	+	4.44364i	0.217166	+	0.534951i
$70$	−0.124966	−	0.281687i	−0.0149363	−	0.0336680i
$71$	8.42723			1.00013			0.500064	−	0.865988i	$-0.333310\pi$
$71$	8.42723			1.00013			0.500064	+	0.865988i	$0.333310\pi$
$72$	1.00000			0.117851
$73$		−	7.04399i		−	0.824437i	−0.911085	−	0.412218i	$-0.864754\pi$
$73$		−	7.04399i		−	0.824437i	0.911085	−	0.412218i	$-0.135246\pi$
$74$			2.17541i			0.252887i
$75$			4.78989i			0.553089i
$76$	−8.53159			−0.978641
$77$	−3.25410	+	1.44364i	−0.370839	+	0.164518i
$78$	1.12497			0.127377
$79$			6.86623i			0.772511i	0.922392	+	0.386256i	$0.126232\pi$
$79$			6.86623i			0.772511i	−0.922392	+	0.386256i	$0.873768\pi$
$80$	−1.65784			−0.185352
$81$	1.00000			0.111111
$82$			0.968246i			0.106925i
$83$	−4.95336			−0.543702			−0.271851	−	0.962339i	$-0.587636\pi$
$83$	−4.95336			−0.543702			−0.271851	+	0.962339i	$0.587636\pi$
$84$	−4.68073	+	2.07654i	−0.510710	+	0.226569i
$85$	−3.25410			−0.352957
$86$			1.82599i			0.196901i
$87$		−	4.18953i		−	0.449165i
$88$		−	1.34554i		−	0.143435i
$89$	16.0023			1.69624			0.848118	−	0.529807i	$-0.177736\pi$
$89$	16.0023			1.69624			0.848118	+	0.529807i	$0.177736\pi$
$90$	0.116474			0.0122775
$91$	−10.7070	+	4.75001i	−1.12240	+	0.497936i
$92$	8.60036	−	3.49135i	0.896649	−	0.363999i
$93$	−4.31867			−0.447825
$94$			1.83805i			0.189581i
$95$	−2.02058			−0.207307
$96$		−	2.91903i		−	0.297922i
$97$	−3.86285			−0.392213			−0.196107	−	0.980583i	$-0.562830\pi$
$97$	−3.86285			−0.392213			−0.196107	+	0.980583i	$0.562830\pi$
$98$	−1.19370	+	1.31867i	−0.120582	+	0.133206i
$99$		−	1.34554i		−	0.135231i
$100$	9.27051			0.927051
$101$		−	12.6496i		−	1.25868i	−0.777130	−	0.629340i	$-0.783325\pi$
$101$		−	12.6496i		−	1.25868i	0.777130	−	0.629340i	$-0.216675\pi$
$102$		−	1.80391i		−	0.178614i
$103$	−7.52796			−0.741752			−0.370876	−	0.928682i	$-0.620942\pi$
$103$	−7.52796			−0.741752			−0.370876	+	0.928682i	$0.620942\pi$
$104$		−	4.42723i		−	0.434126i
$105$	−1.10856	+	0.491797i	−0.108184	+	0.0479944i
$106$		−	2.12374i		−	0.206276i
$107$		−	20.1553i		−	1.94849i	−0.225490	−	0.974246i	$-0.572398\pi$
$107$		−	20.1553i		−	1.94849i	0.225490	−	0.974246i	$-0.427602\pi$
$108$		−	1.93543i		−	0.186237i
$109$			5.06232i			0.484882i	0.970166	+	0.242441i	$0.0779481\pi$
$109$			5.06232i			0.484882i	−0.970166	+	0.242441i	$0.922052\pi$
$110$		−	0.156721i		−	0.0149427i
$111$	8.56119			0.812592
$112$	3.88045	+	8.74694i	0.366668	+	0.826508i
$113$			3.38240i			0.318189i	0.987263	+	0.159095i	$0.0508575\pi$
$113$			3.38240i			0.318189i	−0.987263	+	0.159095i	$0.949143\pi$
$114$		−	1.12011i		−	0.104908i
$115$	2.03686	−	0.826873i	0.189938	−	0.0771063i
$116$	−8.10856			−0.752861
$117$		−	4.42723i		−	0.409297i
$118$		−	2.06040i		−	0.189675i
$119$	7.61676	+	17.1690i	0.698228	+	1.57388i
$120$		−	0.458377i		−	0.0418439i
$121$	9.18953			0.835412
$122$	−2.60419			−0.235773
$123$	3.81047			0.343578
$124$			8.35849i			0.750615i
$125$	4.48746			0.401371
$126$	−0.272628	−	0.614531i	−0.0242876	−	0.0547467i
$127$	−12.2981			−1.09128			−0.545640	−	0.838020i	$-0.683713\pi$
$127$	−12.2981			−1.09128			−0.545640	+	0.838020i	$0.683713\pi$
$128$	−7.48763			−0.661819
$129$	7.18606			0.632697
$130$		−	0.515659i		−	0.0452263i
$131$		−	5.17313i		−	0.451978i	−0.974130	−	0.225989i	$-0.927439\pi$
$131$		−	5.17313i		−	0.451978i	0.974130	−	0.225989i	$-0.0725614\pi$
$132$	−2.60419			−0.226666
$133$	4.72949	+	10.6608i	0.410099	+	0.924405i
$134$			1.48409i			0.128205i
$135$		−	0.458377i		−	0.0394508i
$136$	−7.09918			−0.608749
$137$		−	9.10644i		−	0.778016i	−0.921234	−	0.389008i	$-0.872818\pi$
$137$		−	9.10644i		−	0.778016i	0.921234	−	0.389008i	$-0.127182\pi$
$138$	0.458377	+	1.12914i	0.0390197	+	0.0961184i
$139$		−	17.8503i		−	1.51404i	−0.653391	−	0.757021i	$-0.726654\pi$
$139$		−	17.8503i		−	1.51404i	0.653391	−	0.757021i	$-0.273346\pi$
$140$	0.951839	+	2.14554i	0.0804451	+	0.181331i
$141$	7.23353			0.609173
$142$	2.14137			0.179700
$143$	−5.95699			−0.498149
$144$	−3.61676			−0.301397
$145$	−1.92039			−0.159479
$146$		−	1.78989i		−	0.148132i
$147$	5.18953	+	4.69774i	0.428026	+	0.387463i
$148$		−	16.5696i		−	1.36201i
$149$			20.1849i			1.65362i	0.562485	+	0.826808i	$0.309845\pi$
$149$			20.1849i			1.65362i	−0.562485	+	0.826808i	$0.690155\pi$
$150$			1.21712i			0.0993774i
$151$	−11.5798			−0.942349			−0.471175	−	0.882040i	$-0.656170\pi$
$151$	−11.5798			−0.942349			−0.471175	+	0.882040i	$0.656170\pi$
$152$	−4.40811			−0.357545
$153$	−7.09918			−0.573934
$154$	−0.826873	+	0.366830i	−0.0666313	+	0.0295600i
$155$			1.97958i			0.159004i
$156$	−8.56860			−0.686037
$157$	20.2643			1.61727			0.808634	−	0.588312i	$-0.200207\pi$
$157$	20.2643			1.61727			0.808634	+	0.588312i	$0.200207\pi$
$158$			1.74472i			0.138802i
$159$	−8.35783			−0.662819
$160$	−1.33802			−0.105779
$161$	−9.13027	−	8.81125i	−0.719566	−	0.694424i
$162$	0.254102			0.0199641
$163$	7.97942			0.624997			0.312498	−	0.949918i	$-0.398834\pi$
$163$	7.97942			0.624997			0.312498	+	0.949918i	$0.398834\pi$
$164$		−	7.37490i		−	0.575883i
$165$	−0.616763			−0.0480149
$166$	−1.25866			−0.0976908
$167$		−	3.04399i		−	0.235551i	−0.993040	−	0.117776i	$-0.962424\pi$
$167$		−	3.04399i		−	0.235551i	0.993040	−	0.117776i	$-0.0375763\pi$
$168$	−2.41844	+	1.07291i	−0.186587	+	0.0827766i
$169$	−6.60036			−0.507720
$170$	−0.826873			−0.0634182
$171$	−4.40811			−0.337096
$172$		−	13.9081i		−	1.06048i
$173$			13.4231i			1.02054i	0.860015	+	0.510268i	$0.170454\pi$
$173$			13.4231i			1.02054i	−0.860015	+	0.510268i	$0.829546\pi$
$174$		−	1.06457i		−	0.0807047i
$175$	−5.13911	−	11.5841i	−0.388480	−	0.875674i
$176$			4.86648i			0.366825i
$177$	−8.10856			−0.609477
$178$	4.06620			0.304775
$179$	14.2294			1.06355			0.531776	−	0.846885i	$-0.321525\pi$
$179$	14.2294			1.06355			0.531776	+	0.846885i	$0.321525\pi$
$180$	−0.887158			−0.0661249
$181$	19.6026			1.45705			0.728524	−	0.685020i	$-0.240207\pi$
$181$	19.6026			1.45705			0.728524	+	0.685020i	$0.240207\pi$
$182$	−2.72067	+	1.20699i	−0.201669	+	0.0894677i
$183$			10.2486i			0.757600i
$184$	4.44364	−	1.80391i	0.327589	−	0.132986i
$185$		−	3.92425i		−	0.288517i
$186$	−1.09738			−0.0804639
$187$			9.55220i			0.698526i
$188$		−	14.0000i		−	1.02105i
$189$	−2.41844	+	1.07291i	−0.175916	+	0.0780426i
$190$	−0.513432			−0.0372483
$191$		−	21.1811i		−	1.53261i	−0.642478	−	0.766304i	$-0.722094\pi$
$191$		−	21.1811i		−	1.53261i	0.642478	−	0.766304i	$-0.277906\pi$
$192$			6.49180i			0.468505i
$193$	10.0328			0.722178			0.361089	−	0.932531i	$-0.382405\pi$
$193$	10.0328			0.722178			0.361089	+	0.932531i	$0.382405\pi$
$194$	−0.981557			−0.0704717
$195$	−2.02934			−0.145324
$196$	9.09215	−	10.0440i	0.649439	−	0.717428i
$197$	5.53996			0.394706			0.197353	−	0.980333i	$-0.436766\pi$
$197$	5.53996			0.394706			0.197353	+	0.980333i	$0.436766\pi$
$198$		−	0.341903i		−	0.0242980i
$199$	−6.69808			−0.474814			−0.237407	−	0.971410i	$-0.576298\pi$
$199$	−6.69808			−0.474814			−0.237407	+	0.971410i	$0.576298\pi$
$200$	4.78989			0.338696
$201$	5.84052			0.411958
$202$		−	3.21428i		−	0.226156i
$203$	4.49498	+	10.1322i	0.315486	+	0.711138i
$204$			13.7400i			0.961991i
$205$		−	1.74663i		−	0.121990i
$206$	−1.91287			−0.133276
$207$	4.44364	−	1.80391i	0.308854	−	0.125381i
$208$			16.0122i			1.11025i
$209$			5.93126i			0.410274i
$210$	−0.281687	+	0.124966i	−0.0194382	+	0.00862350i
$211$	−9.33508			−0.642653			−0.321327	−	0.946968i	$-0.604129\pi$
$211$	−9.33508			−0.642653			−0.321327	+	0.946968i	$0.604129\pi$
$212$			16.1760i			1.11097i
$213$		−	8.42723i		−	0.577424i
$214$		−	5.12151i		−	0.350099i
$215$		−	3.29392i		−	0.224644i
$216$		−	1.00000i		−	0.0680414i
$217$	10.4445	−	4.63353i	0.709016	−	0.314545i
$218$			1.28634i			0.0871221i
$219$	−7.04399			−0.475989
$220$			1.19370i			0.0804794i
$221$			31.4297i			2.11419i
$222$	2.17541			0.146004
$223$		−	10.3257i		−	0.691459i	−0.938334	−	0.345729i	$-0.887632\pi$
$223$		−	10.3257i		−	0.691459i	0.938334	−	0.345729i	$-0.112368\pi$
$224$	3.13185	+	7.05950i	0.209255	+	0.471683i
$225$	4.78989			0.319326
$226$			0.859473i			0.0571713i
$227$	24.6428			1.63560			0.817800	−	0.575502i	$-0.195193\pi$
$227$	24.6428			1.63560			0.817800	+	0.575502i	$0.195193\pi$
$228$			8.53159i			0.565018i
$229$	8.21928			0.543146			0.271573	−	0.962418i	$-0.412456\pi$
$229$	8.21928			0.543146			0.271573	+	0.962418i	$0.412456\pi$
$230$	0.517570	−	0.210110i	0.0341276	−	0.0138542i
$231$	1.44364	+	3.25410i	0.0949843	+	0.214104i
$232$	−4.18953			−0.275056
$233$	−11.3749			−0.745194			−0.372597	−	0.927993i	$-0.621533\pi$
$233$	−11.3749			−0.745194			−0.372597	+	0.927993i	$0.621533\pi$
$234$		−	1.12497i		−	0.0735414i
$235$		−	3.31568i		−	0.216291i
$236$			15.6936i			1.02156i
$237$	6.86623			0.446009
$238$	1.93543	+	4.36266i	0.125455	+	0.282789i
$239$	−26.9547			−1.74355			−0.871777	−	0.489904i	$-0.837032\pi$
$239$	−26.9547			−1.74355			−0.871777	+	0.489904i	$0.837032\pi$
$240$			1.65784i			0.107013i
$241$	−5.40422			−0.348116			−0.174058	−	0.984735i	$-0.555688\pi$
$241$	−5.40422			−0.348116			−0.174058	+	0.984735i	$0.555688\pi$
$242$	2.33508			0.150104
$243$		−	1.00000i		−	0.0641500i
$244$	19.8355			1.26984
$245$	2.15334	−	2.37876i	0.137572	−	0.151974i
$246$	0.968246			0.0617331
$247$			19.5157i			1.24175i
$248$			4.31867i			0.274236i
$249$			4.95336i			0.313907i
$250$	1.14027			0.0721171
$251$	−19.4067			−1.22494			−0.612471	−	0.790493i	$-0.709824\pi$
$251$	−19.4067			−1.22494			−0.612471	+	0.790493i	$0.709824\pi$
$252$	2.07654	+	4.68073i	0.130810	+	0.294859i
$253$	−2.42723	−	5.97907i	−0.152599	−	0.375901i
$254$	−3.12497			−0.196078
$255$			3.25410i			0.203780i
$256$	11.0810			0.692561
$257$			4.34625i			0.271112i	0.990770	+	0.135556i	$0.0432821\pi$
$257$			4.34625i			0.271112i	−0.990770	+	0.135556i	$0.956718\pi$
$258$	1.82599			0.113681
$259$	−20.7047	+	9.18537i	−1.28653	+	0.570751i
$260$			3.92765i			0.243583i
$261$	−4.18953			−0.259326
$262$		−	1.31450i		−	0.0812101i
$263$			1.57848i			0.0973335i	0.998815	+	0.0486668i	$0.0154972\pi$
$263$			1.57848i			0.0973335i	−0.998815	+	0.0486668i	$0.984503\pi$
$264$	−1.34554			−0.0828120
$265$			3.83104i			0.235339i
$266$	1.20177	+	2.70892i	0.0736854	+	0.166094i
$267$		−	16.0023i		−	0.979323i
$268$		−	11.3039i		−	0.690497i
$269$			21.4025i			1.30493i	0.757818	+	0.652466i	$0.226266\pi$
$269$			21.4025i			1.30493i	−0.757818	+	0.652466i	$0.773734\pi$
$270$		−	0.116474i		−	0.00708841i
$271$		−	15.3267i		−	0.931033i	−0.885039	−	0.465517i	$-0.845869\pi$
$271$		−	15.3267i		−	0.931033i	0.885039	−	0.465517i	$-0.154131\pi$
$272$	25.6760			1.55684
$273$	4.75001	+	10.7070i	0.287484	+	0.648017i
$274$		−	2.31396i		−	0.139792i
$275$		−	6.44497i		−	0.388646i
$276$	−3.49135	−	8.60036i	−0.210155	−	0.517681i
$277$	10.5152			0.631798			0.315899	−	0.948793i	$-0.397694\pi$
$277$	10.5152			0.631798			0.315899	+	0.948793i	$0.397694\pi$
$278$		−	4.53579i		−	0.272039i
$279$			4.31867i			0.258552i
$280$	0.491797	+	1.10856i	0.0293905	+	0.0662491i
$281$		−	5.30278i		−	0.316338i	−0.987412	−	0.158169i	$-0.949441\pi$
$281$		−	5.30278i		−	0.316338i	0.987412	−	0.158169i	$-0.0505590\pi$
$282$	1.83805			0.109454
$283$	2.05894			0.122391			0.0611956	−	0.998126i	$-0.480509\pi$
$283$	2.05894			0.122391			0.0611956	+	0.998126i	$0.480509\pi$
$284$	−16.3103			−0.967840
$285$			2.02058i			0.119689i
$286$	−1.51368			−0.0895059
$287$	−9.21540	+	4.08828i	−0.543968	+	0.241323i
$288$	−2.91903			−0.172005
$289$	33.3983			1.96461
$290$	−0.487974			−0.0286548
$291$			3.86285i			0.226444i
$292$			13.6332i			0.797821i
$293$	17.4939			1.02200			0.511001	−	0.859580i	$-0.329275\pi$
$293$	17.4939			1.02200			0.511001	+	0.859580i	$0.329275\pi$
$294$	1.31867	+	1.19370i	0.0769064	+	0.0696182i
$295$			3.71678i			0.216399i
$296$		−	8.56119i		−	0.497609i
$297$	−1.34554			−0.0780759
$298$			5.12903i			0.297117i
$299$	−7.98634	−	19.6730i	−0.461862	−	1.13772i
$300$		−	9.27051i		−	0.535233i
$301$	−17.3791	+	7.70998i	−1.00171	+	0.444396i
$302$	−2.94244			−0.169318
$303$	−12.6496			−0.726699
$304$	15.9431			0.914398
$305$	4.69774			0.268992
$306$	−1.80391			−0.103123
$307$			31.8573i			1.81819i	0.416587	+	0.909096i	$0.363226\pi$
$307$			31.8573i			1.81819i	−0.416587	+	0.909096i	$0.636774\pi$
$308$	6.29809	−	2.79406i	0.358867	−	0.159206i
$309$			7.52796i			0.428251i
$310$			0.503015i			0.0285693i
$311$		−	2.71831i		−	0.154141i	−0.997026	−	0.0770707i	$-0.975443\pi$
$311$		−	2.71831i		−	0.154141i	0.997026	−	0.0770707i	$-0.0245567\pi$
$312$	−4.42723			−0.250642
$313$	21.1811			1.19722			0.598612	−	0.801039i	$-0.295719\pi$
$313$	21.1811			1.19722			0.598612	+	0.801039i	$0.295719\pi$
$314$	5.14919			0.290586
$315$	0.491797	+	1.10856i	0.0277096	+	0.0624603i
$316$		−	13.2891i		−	0.747571i
$317$	−11.2541			−0.632093			−0.316047	−	0.948744i	$-0.602356\pi$
$317$	−11.2541			−0.632093			−0.316047	+	0.948744i	$0.602356\pi$
$318$	−2.12374			−0.119093
$319$			5.63717i			0.315621i
$320$	2.97569			0.166346
$321$	−20.1553			−1.12496
$322$	−2.32002	−	2.23895i	−0.129290	−	0.124772i
$323$	31.2939			1.74124
$324$	−1.93543			−0.107524
$325$		−	21.2059i		−	1.17629i
$326$	2.02759			0.112298
$327$	5.06232			0.279947
$328$		−	3.81047i		−	0.210398i
$329$	−17.4939	+	7.76091i	−0.964468	+	0.427873i
$330$	−0.156721			−0.00862718
$331$	8.54102			0.469457			0.234728	−	0.972061i	$-0.424580\pi$
$331$	8.54102			0.469457			0.234728	+	0.972061i	$0.424580\pi$
$332$	9.58690			0.526149
$333$		−	8.56119i		−	0.469150i
$334$		−	0.773483i		−	0.0423231i
$335$		−	2.67716i		−	0.146269i
$336$	8.74694	−	3.88045i	0.477185	−	0.211696i
$337$			8.24136i			0.448935i	0.974482	+	0.224468i	$0.0720643\pi$
$337$			8.24136i			0.448935i	−0.974482	+	0.224468i	$0.927936\pi$
$338$	−1.67716			−0.0912256
$339$	3.38240			0.183707
$340$	6.29809			0.341562
$341$	5.81092			0.314679
$342$	−1.12011			−0.0605685
$343$	−17.5908	−	5.79332i	−0.949816	−	0.312810i
$344$		−	7.18606i		−	0.387446i
$345$	−0.826873	−	2.03686i	−0.0445173	−	0.109661i
$346$			3.41082i			0.183367i
$347$	−10.6649			−0.572523			−0.286262	−	0.958152i	$-0.592413\pi$
$347$	−10.6649			−0.572523			−0.286262	+	0.958152i	$0.592413\pi$
$348$			8.10856i			0.434664i
$349$		−	1.00417i		−	0.0537519i	−0.999639	−	0.0268760i	$-0.991444\pi$
$349$		−	1.00417i		−	0.0537519i	0.999639	−	0.0268760i	$-0.00855592\pi$
$350$	−1.30586	−	2.94353i	−0.0698010	−	0.157339i
$351$	−4.42723			−0.236308
$352$			3.92765i			0.209345i
$353$		−	35.7693i		−	1.90381i	−0.306396	−	0.951904i	$-0.599123\pi$
$353$		−	35.7693i		−	1.90381i	0.306396	−	0.951904i	$-0.400877\pi$
$354$	−2.06040			−0.109509
$355$	−3.86285			−0.205019
$356$	−30.9713			−1.64148
$357$	17.1690	−	7.61676i	0.908678	−	0.403122i
$358$	3.61570			0.191096
$359$			20.6433i			1.08951i	0.838594	+	0.544756i	$0.183378\pi$
$359$			20.6433i			1.08951i	−0.838594	+	0.544756i	$0.816622\pi$
$360$	−0.458377			−0.0241586
$361$	0.431398			0.0227052
$362$	4.98105			0.261798
$363$		−	9.18953i		−	0.482325i
$364$	20.7227	−	9.19332i	1.08616	−	0.481861i
$365$			3.22881i			0.169003i
$366$			2.60419i			0.136123i
$367$	−25.7352			−1.34337			−0.671684	−	0.740838i	$-0.734429\pi$
$367$	−25.7352			−1.34337			−0.671684	+	0.740838i	$0.734429\pi$
$368$	−16.0716	+	6.52433i	−0.837789	+	0.340104i
$369$		−	3.81047i		−	0.198365i
$370$		−	0.997160i		−	0.0518399i
$371$	20.2130	−	8.96719i	1.04940	−	0.465553i
$372$	8.35849			0.433368
$373$		−	16.6786i		−	0.863583i	−0.901974	−	0.431791i	$-0.857882\pi$
$373$		−	16.6786i		−	0.863583i	0.901974	−	0.431791i	$-0.142118\pi$
$374$			2.42723i			0.125509i
$375$		−	4.48746i		−	0.231732i
$376$		−	7.23353i		−	0.373041i
$377$			18.5480i			0.955272i
$378$	−0.614531	+	0.272628i	−0.0316080	+	0.0140225i
$379$		−	30.9492i		−	1.58976i	−0.606770	−	0.794878i	$-0.707535\pi$
$379$		−	30.9492i		−	1.58976i	0.606770	−	0.794878i	$-0.292465\pi$
$380$	3.91069			0.200614
$381$			12.2981i			0.630050i
$382$		−	5.38214i		−	0.275374i
$383$	−18.6858			−0.954801			−0.477400	−	0.878686i	$-0.658421\pi$
$383$	−18.6858			−0.954801			−0.477400	+	0.878686i	$0.658421\pi$
$384$			7.48763i			0.382101i
$385$	1.49161	−	0.661730i	0.0760193	−	0.0337249i
$386$	2.54935			0.129759
$387$		−	7.18606i		−	0.365288i
$388$	7.47629			0.379551
$389$		−	26.5059i		−	1.34390i	−0.740595	−	0.671952i	$-0.765456\pi$
$389$		−	26.5059i		−	1.34390i	0.740595	−	0.671952i	$-0.234544\pi$
$390$	−0.515659			−0.0261114
$391$	−31.5462	+	12.8063i	−1.59536	+	0.647642i
$392$	4.69774	−	5.18953i	0.237272	−	0.262111i
$393$	−5.17313			−0.260950
$394$	1.40771			0.0709195
$395$		−	3.14732i		−	0.158359i
$396$			2.60419i			0.130866i
$397$			8.63734i			0.433496i	0.976228	+	0.216748i	$0.0695449\pi$
$397$			8.63734i			0.433496i	−0.976228	+	0.216748i	$0.930455\pi$
$398$	−1.70199			−0.0853132
$399$	10.6608	−	4.72949i	0.533705	−	0.236771i
$400$	−17.3239			−0.866195
$401$			12.9322i			0.645802i	0.946433	+	0.322901i	$0.104658\pi$
$401$			12.9322i			0.645802i	−0.946433	+	0.322901i	$0.895342\pi$
$402$	1.48409			0.0740195
$403$	19.1197			0.952422
$404$			24.4824i			1.21804i
$405$	−0.458377			−0.0227770
$406$	1.14218	+	2.57460i	0.0566856	+	0.127775i
$407$	−11.5194			−0.570995
$408$			7.09918i			0.351462i
$409$		−	4.40665i		−	0.217895i	−0.994048	−	0.108947i	$-0.965252\pi$
$409$		−	4.40665i		−	0.217895i	0.994048	−	0.108947i	$-0.0347480\pi$
$410$		−	0.443822i		−	0.0219188i
$411$	−9.10644			−0.449188
$412$	14.5699			0.717805
$413$	19.6101	−	8.69974i	0.964950	−	0.428086i
$414$	1.12914	−	0.458377i	0.0554940	−	0.0225280i
$415$	2.27051			0.111455
$416$			12.9232i			0.633612i
$417$	−17.8503			−0.874132
$418$			1.50714i			0.0737168i
$419$	−5.91988			−0.289205			−0.144602	−	0.989490i	$-0.546190\pi$
$419$	−5.91988			−0.289205			−0.144602	+	0.989490i	$0.546190\pi$
$420$	2.14554	−	0.951839i	0.104692	−	0.0464450i
$421$		−	10.4816i		−	0.510841i	−0.966830	−	0.255420i	$-0.917786\pi$
$421$		−	10.4816i		−	0.510841i	0.966830	−	0.255420i	$-0.0822139\pi$
$422$	−2.37206			−0.115470
$423$		−	7.23353i		−	0.351706i
$424$			8.35783i			0.405892i
$425$	−34.0043			−1.64945
$426$		−	2.14137i		−	0.103750i
$427$	−10.9958	−	24.7857i	−0.532126	−	1.19947i
$428$			39.0093i			1.88559i
$429$			5.95699i			0.287606i
$430$		−	0.836992i		−	0.0403633i
$431$		−	21.0129i		−	1.01216i	−0.862488	−	0.506078i	$-0.831095\pi$
$431$		−	21.0129i		−	1.01216i	0.862488	−	0.506078i	$-0.168905\pi$
$432$			3.61676i			0.174012i
$433$	−7.21565			−0.346762			−0.173381	−	0.984855i	$-0.555469\pi$
$433$	−7.21565			−0.346762			−0.173381	+	0.984855i	$0.555469\pi$
$434$	2.65395	−	1.17739i	0.127394	−	0.0565165i
$435$			1.92039i			0.0920755i
$436$		−	9.79777i		−	0.469228i
$437$	−19.5880	+	7.95184i	−0.937022	+	0.380388i
$438$	−1.78989			−0.0855243
$439$		−	37.1565i		−	1.77338i	−0.462364	−	0.886690i	$-0.652999\pi$
$439$		−	37.1565i		−	1.77338i	0.462364	−	0.886690i	$-0.347001\pi$
$440$			0.616763i			0.0294030i
$441$	4.69774	−	5.18953i	0.223702	−	0.247121i
$442$			7.98634i			0.379871i
$443$	−16.8461			−0.800383			−0.400192	−	0.916431i	$-0.631056\pi$
$443$	−16.8461			−0.800383			−0.400192	+	0.916431i	$0.631056\pi$
$444$	−16.5696			−0.786358
$445$	−7.33508			−0.347716
$446$		−	2.62377i		−	0.124239i
$447$	20.1849			0.954715
$448$	−6.96510	−	15.7000i	−0.329070	−	0.741757i
$449$	0.583949			0.0275583			0.0137791	−	0.999905i	$-0.495614\pi$
$449$	0.583949			0.0275583			0.0137791	+	0.999905i	$0.495614\pi$
$450$	1.21712			0.0573755
$451$	−5.12712			−0.241427
$452$		−	6.54640i		−	0.307917i
$453$			11.5798i			0.544066i
$454$	6.26178			0.293880
$455$	4.90785	−	2.17730i	0.230083	−	0.102073i
$456$			4.40811i			0.206428i
$457$			16.8617i			0.788759i	0.918948	+	0.394379i	$0.129040\pi$
$457$			16.8617i			0.788759i	−0.918948	+	0.394379i	$0.870960\pi$
$458$	2.08853			0.0975908
$459$			7.09918i			0.331361i
$460$	−3.94221	+	1.60036i	−0.183806	+	0.0746170i
$461$		−	5.50403i		−	0.256348i	−0.991752	−	0.128174i	$-0.959088\pi$
$461$		−	5.50403i		−	0.256348i	0.991752	−	0.128174i	$-0.0409117\pi$
$462$	0.366830	+	0.826873i	0.0170665	+	0.0384696i
$463$	14.3103			0.665058			0.332529	−	0.943093i	$-0.392098\pi$
$463$	14.3103			0.665058			0.332529	+	0.943093i	$0.392098\pi$
$464$	15.1526			0.703440
$465$	1.97958			0.0918008
$466$	−2.89038			−0.133894
$467$	9.88465			0.457407			0.228703	−	0.973496i	$-0.426551\pi$
$467$	9.88465			0.457407			0.228703	+	0.973496i	$0.426551\pi$
$468$			8.56860i			0.396084i
$469$	−14.1250	+	6.26634i	−0.652230	+	0.289353i
$470$		−	0.842521i		−	0.0388626i
$471$		−	20.2643i		−	0.933730i
$472$			8.10856i			0.373227i
$473$	−9.66909			−0.444585
$474$	1.74472			0.0801377
$475$	−21.1143			−0.968793
$476$	−14.7417	−	33.2294i	−0.675686	−	1.52307i
$477$			8.35783i			0.382679i
$478$	−6.84923			−0.313276
$479$	0.894679			0.0408789			0.0204395	−	0.999791i	$-0.493493\pi$
$479$	0.894679			0.0408789			0.0204395	+	0.999791i	$0.493493\pi$
$480$			1.33802i			0.0610718i
$481$	−37.9023			−1.72820
$482$	−1.37322			−0.0625485
$483$	−8.81125	+	9.13027i	−0.400926	+	0.415442i
$484$	−17.7857			−0.808442
$485$	1.77064			0.0804008
$486$		−	0.254102i		−	0.0115263i
$487$	4.41499			0.200062			0.100031	−	0.994984i	$-0.468106\pi$
$487$	4.41499			0.200062			0.100031	+	0.994984i	$0.468106\pi$
$488$	10.2486			0.463933
$489$		−	7.97942i		−	0.360842i
$490$	0.547166	−	0.604448i	0.0247185	−	0.0273062i
$491$	26.5480			1.19810			0.599048	−	0.800713i	$-0.295546\pi$
$491$	26.5480			1.19810			0.599048	+	0.800713i	$0.295546\pi$
$492$	−7.37490			−0.332486
$493$	29.7422			1.33952
$494$			4.95897i			0.223115i
$495$			0.616763i			0.0277214i
$496$		−	15.6196i		−	0.701341i
$497$	9.04164	+	20.3808i	0.405573	+	0.914203i
$498$			1.25866i			0.0564018i
$499$	20.0206			0.896244			0.448122	−	0.893972i	$-0.352093\pi$
$499$	20.0206			0.896244			0.448122	+	0.893972i	$0.352093\pi$
$500$	−8.68518			−0.388413
$501$	−3.04399			−0.135996
$502$	−4.93129			−0.220094
$503$	1.17739			0.0524972			0.0262486	−	0.999655i	$-0.491644\pi$
$503$	1.17739			0.0524972			0.0262486	+	0.999655i	$0.491644\pi$
$504$	1.07291	+	2.41844i	0.0477911	+	0.107726i
$505$			5.79828i			0.258020i
$506$	−0.616763	−	1.51929i	−0.0274185	−	0.0675408i
$507$			6.60036i			0.293132i
$508$	23.8021			1.05605
$509$		−	8.24993i		−	0.365672i	−0.983143	−	0.182836i	$-0.941472\pi$
$509$		−	8.24993i		−	0.365672i	0.983143	−	0.182836i	$-0.0585277\pi$
$510$			0.826873i			0.0366145i
$511$	17.0355	−	7.55755i	0.753606	−	0.334327i
$512$	17.7909			0.786256
$513$			4.40811i			0.194623i
$514$			1.10439i			0.0487126i
$515$	3.45065			0.152054
$516$	−13.9081			−0.612271
$517$	−9.73297			−0.428055
$518$	−5.26111	+	2.33402i	−0.231160	+	0.102551i
$519$	13.4231			0.589207
$520$			2.02934i			0.0889925i
$521$	−25.7850			−1.12966			−0.564831	−	0.825207i	$-0.691058\pi$
$521$	−25.7850			−1.12966			−0.564831	+	0.825207i	$0.691058\pi$
$522$	−1.06457			−0.0465949
$523$	26.9939			1.18036			0.590180	−	0.807272i	$-0.299057\pi$
$523$	26.9939			1.18036			0.590180	+	0.807272i	$0.299057\pi$
$524$			10.0122i			0.437387i
$525$	−11.5841	+	5.13911i	−0.505571	+	0.224289i
$526$			0.401096i			0.0174886i
$527$		−	30.6590i		−	1.33553i
$528$	4.86648			0.211786
$529$	16.4918	−	16.0319i	0.717035	−	0.697038i
$530$			0.973474i			0.0422850i
$531$			8.10856i			0.351882i
$532$	−9.15361	−	20.6332i	−0.396859	−	0.894561i
$533$	−16.8698			−0.730712
$534$		−	4.06620i		−	0.175962i
$535$			9.23875i			0.399426i
$536$		−	5.84052i		−	0.252272i
$537$		−	14.2294i		−	0.614042i
$538$			5.43841i			0.234466i
$539$	−6.98270	−	6.32097i	−0.300766	−	0.272264i
$540$			0.887158i			0.0381772i
$541$	−12.6373			−0.543322			−0.271661	−	0.962393i	$-0.587573\pi$
$541$	−12.6373			−0.543322			−0.271661	+	0.962393i	$0.587573\pi$
$542$		−	3.89455i		−	0.167285i
$543$		−	19.6026i		−	0.841227i
$544$	20.7227			0.888478
$545$		−	2.32045i		−	0.0993972i
$546$	1.20699	+	2.72067i	0.0516542	+	0.116434i
$547$	2.52878			0.108123			0.0540614	−	0.998538i	$-0.482783\pi$
$547$	2.52878			0.108123			0.0540614	+	0.998538i	$0.482783\pi$
$548$			17.6249i			0.752899i
$549$	10.2486			0.437401
$550$		−	1.63768i		−	0.0698308i
$551$	18.4679			0.786759
$552$	−1.80391	−	4.44364i	−0.0767796	−	0.189134i
$553$	−16.6056	+	7.36683i	−0.706141	+	0.313269i
$554$	2.67193			0.113520
$555$	−3.92425			−0.166575
$556$			34.5480i			1.46516i
$557$			30.2654i			1.28239i	0.767379	+	0.641194i	$0.221560\pi$
$557$			30.2654i			1.28239i	−0.767379	+	0.641194i	$0.778440\pi$
$558$			1.09738i			0.0464558i
$559$	−31.8143			−1.34560
$560$	−1.77871	−	4.00940i	−0.0751643	−	0.169428i
$561$	9.55220			0.403294
$562$		−	1.34745i		−	0.0568386i
$563$	−36.6381			−1.54411			−0.772055	−	0.635555i	$-0.780771\pi$
$563$	−36.6381			−1.54411			−0.772055	+	0.635555i	$0.780771\pi$
$564$	−14.0000			−0.589506
$565$		−	1.55041i		−	0.0652264i
$566$	0.523180			0.0219909
$567$	1.07291	+	2.41844i	0.0450579	+	0.101565i
$568$	−8.42723			−0.353599
$569$		−	27.1085i		−	1.13645i	−0.822875	−	0.568223i	$-0.807631\pi$
$569$		−	27.1085i		−	1.13645i	0.822875	−	0.568223i	$-0.192369\pi$
$570$			0.513432i			0.0215053i
$571$			7.95674i			0.332979i	0.986043	+	0.166490i	$0.0532432\pi$
$571$			7.95674i			0.332979i	−0.986043	+	0.166490i	$0.946757\pi$
$572$	11.5294			0.482067
$573$	−21.1811			−0.884851
$574$	−2.34165	+	1.03884i	−0.0977385	+	0.0433603i
$575$	21.2845	−	8.64054i	0.887626	−	0.360336i
$576$	6.49180			0.270492
$577$			19.9672i			0.831245i	0.909537	+	0.415622i	$0.136436\pi$
$577$			19.9672i			0.831245i	−0.909537	+	0.415622i	$0.863564\pi$
$578$	8.48657			0.352995
$579$		−	10.0328i		−	0.416950i
$580$	3.71678			0.154331
$581$	−5.31450	−	11.9794i	−0.220483	−	0.496990i
$582$			0.981557i			0.0406868i
$583$	11.2458			0.465752
$584$			7.04399i			0.291482i
$585$			2.02934i			0.0839029i
$586$	4.44522			0.183630
$587$		−	21.8555i		−	0.902074i	−0.892505	−	0.451037i	$-0.851054\pi$
$587$		−	21.8555i		−	0.902074i	0.892505	−	0.451037i	$-0.148946\pi$
$588$	−10.0440	−	9.09215i	−0.414207	−	0.374954i
$589$		−	19.0372i		−	0.784412i
$590$			0.944440i			0.0388820i
$591$		−	5.53996i		−	0.227883i
$592$			30.9638i			1.27260i
$593$		−	36.9117i		−	1.51578i	−0.652380	−	0.757892i	$-0.726229\pi$
$593$		−	36.9117i		−	1.51578i	0.652380	−	0.757892i	$-0.273771\pi$
$594$	−0.341903			−0.0140284
$595$	−3.49135	−	7.86986i	−0.143131	−	0.322633i
$596$		−	39.0666i		−	1.60023i
$597$			6.69808i			0.274134i
$598$	−2.02934	−	4.99894i	−0.0829859	−	0.204422i
$599$	−32.2898			−1.31932			−0.659662	−	0.751563i	$-0.729300\pi$
$599$	−32.2898			−1.31932			−0.659662	+	0.751563i	$0.729300\pi$
$600$		−	4.78989i		−	0.195546i
$601$			24.6496i			1.00548i	0.864438	+	0.502739i	$0.167674\pi$
$601$			24.6496i			1.00548i	−0.864438	+	0.502739i	$0.832326\pi$
$602$	−4.41605	+	1.95912i	−0.179985	+	0.0798477i
$603$		−	5.84052i		−	0.237844i
$604$	22.4119			0.911927
$605$	−4.21227			−0.171253
$606$	−3.21428			−0.130571
$607$		−	23.4988i		−	0.953787i	−0.878961	−	0.476894i	$-0.841763\pi$
$607$		−	23.4988i		−	0.953787i	0.878961	−	0.476894i	$-0.158237\pi$
$608$	12.8674			0.521841
$609$	10.1322	−	4.49498i	0.410575	−	0.182146i
$610$	1.19370			0.0483316
$611$	−32.0245			−1.29557
$612$	13.7400			0.555406
$613$		−	1.34554i		−	0.0543457i	−0.999631	−	0.0271728i	$-0.991350\pi$
$613$		−	1.34554i		−	0.0543457i	0.999631	−	0.0271728i	$-0.00865045\pi$
$614$			8.09499i			0.326687i
$615$	−1.74663			−0.0704310
$616$	3.25410	−	1.44364i	0.131111	−	0.0581657i
$617$			20.2347i			0.814619i	0.913290	+	0.407309i	$0.133533\pi$
$617$			20.2347i			0.814619i	−0.913290	+	0.407309i	$0.866467\pi$
$618$			1.91287i			0.0769468i
$619$	−37.2425			−1.49690			−0.748452	−	0.663189i	$-0.769202\pi$
$619$	−37.2425			−1.49690			−0.748452	+	0.663189i	$0.769202\pi$
$620$		−	3.83134i		−	0.153870i
$621$	−1.80391	−	4.44364i	−0.0723885	−	0.178317i
$622$		−	0.690728i		−	0.0276957i
$623$	17.1690	+	38.7006i	0.687860	+	1.55051i
$624$	16.0122			0.641003
$625$	21.8925			0.875700
$626$	5.38214			0.215114
$627$	5.93126			0.236872
$628$	−39.2202			−1.56506
$629$			60.7774i			2.42335i
$630$	0.124966	+	0.281687i	0.00497878	+	0.0112227i
$631$			39.5546i			1.57464i	0.616543	+	0.787321i	$0.288533\pi$
$631$			39.5546i			1.57464i	−0.616543	+	0.787321i	$0.711467\pi$
$632$		−	6.86623i		−	0.273124i
$633$			9.33508i			0.371036i
$634$	−2.85969			−0.113573
$635$	5.63717			0.223704
$636$	16.1760			0.641421
$637$	−22.9753	−	20.7980i	−0.910313	−	0.824045i
$638$			1.43241i			0.0567098i
$639$	−8.42723			−0.333376
$640$	3.43216			0.135668
$641$		−	19.8430i		−	0.783753i	−0.920018	−	0.391877i	$-0.871826\pi$
$641$		−	19.8430i		−	0.783753i	0.920018	−	0.391877i	$-0.128174\pi$
$642$	−5.12151			−0.202130
$643$	47.0309			1.85472			0.927358	−	0.374176i	$-0.122074\pi$
$643$	47.0309			1.85472			0.927358	+	0.374176i	$0.122074\pi$
$644$	17.6710	+	17.0536i	0.696336	+	0.672005i
$645$	−3.29392			−0.129698
$646$	7.95184			0.312861
$647$			29.5592i			1.16209i	0.813871	+	0.581046i	$0.197356\pi$
$647$			29.5592i			1.16209i	−0.813871	+	0.581046i	$0.802644\pi$
$648$	−1.00000			−0.0392837
$649$	10.9104			0.428269
$650$		−	5.38847i		−	0.211353i
$651$	−4.63353	−	10.4445i	−0.181603	−	0.409351i
$652$	−15.4436			−0.604819
$653$	31.9466			1.25017			0.625084	−	0.780558i	$-0.285065\pi$
$653$	31.9466			1.25017			0.625084	+	0.780558i	$0.285065\pi$
$654$	1.28634			0.0503000
$655$			2.37124i			0.0926522i
$656$			13.7816i			0.538079i
$657$			7.04399i			0.274812i
$658$	−4.44522	+	1.97206i	−0.173293	+	0.0768789i
$659$		−	32.7104i		−	1.27422i	−0.770774	−	0.637108i	$-0.780130\pi$
$659$		−	32.7104i		−	1.27422i	0.770774	−	0.637108i	$-0.219870\pi$
$660$	1.19370			0.0464648
$661$	11.9361			0.464259			0.232130	−	0.972685i	$-0.425431\pi$
$661$	11.9361			0.464259			0.232130	+	0.972685i	$0.425431\pi$
$662$	2.17029			0.0843506
$663$	31.4297			1.22063
$664$	4.95336			0.192228
$665$	−2.16789	−	4.88665i	−0.0840672	−	0.189496i
$666$		−	2.17541i		−	0.0842955i
$667$	−18.6168	+	7.55755i	−0.720844	+	0.292630i
$668$			5.89144i			0.227947i
$669$	−10.3257			−0.399214
$670$		−	0.680271i		−	0.0262812i
$671$		−	13.7899i		−	0.532353i
$672$	7.05950	−	3.13185i	0.272326	−	0.120814i
$673$	−18.0521			−0.695856			−0.347928	−	0.937521i	$-0.613115\pi$
$673$	−18.0521			−0.695856			−0.347928	+	0.937521i	$0.613115\pi$
$674$			2.09414i			0.0806634i
$675$		−	4.78989i		−	0.184363i
$676$	12.7745			0.491329
$677$	50.0582			1.92389			0.961947	−	0.273237i	$-0.0880943\pi$
$677$	50.0582			1.92389			0.961947	+	0.273237i	$0.0880943\pi$
$678$	0.859473			0.0330079
$679$	−4.14448	−	9.34209i	−0.159051	−	0.358516i
$680$	3.25410			0.124789
$681$		−	24.6428i		−	0.944315i
$682$	1.47657			0.0565406
$683$	3.61782			0.138432			0.0692161	−	0.997602i	$-0.477950\pi$
$683$	3.61782			0.138432			0.0692161	+	0.997602i	$0.477950\pi$
$684$	8.53159			0.326214
$685$			4.17419i			0.159487i
$686$	−4.46986	−	1.47209i	−0.170660	−	0.0562048i
$687$		−	8.21928i		−	0.313585i
$688$			25.9903i			0.990869i
$689$	37.0020			1.40967
$690$	−0.210110	−	0.517570i	−0.00799874	−	0.0197036i
$691$		−	9.24887i		−	0.351844i	−0.984404	−	0.175922i	$-0.943709\pi$
$691$		−	9.24887i		−	0.351844i	0.984404	−	0.175922i	$-0.0562906\pi$
$692$		−	25.9794i		−	0.987590i
$693$	3.25410	−	1.44364i	0.123613	−	0.0548392i
$694$	−2.70998			−0.102869
$695$			8.18217i			0.310367i
$696$			4.18953i			0.158804i
$697$			27.0512i			1.02464i
$698$		−	0.255161i		−	0.00965799i
$699$			11.3749i			0.430238i
$700$	9.94640	+	22.4202i	0.375939	+	0.847404i
$701$			26.8478i			1.01403i	0.861938	+	0.507014i	$0.169251\pi$
$701$			26.8478i			1.01403i	−0.861938	+	0.507014i	$0.830749\pi$
$702$	−1.12497			−0.0424591
$703$			37.7386i			1.42334i
$704$		−	8.73494i		−	0.329211i
$705$	−3.31568			−0.124876
$706$		−	9.08904i		−	0.342071i
$707$	30.5923	−	13.5718i	1.15054	−	0.510421i
$708$	15.6936			0.589800
$709$			23.7632i			0.892445i	0.894922	+	0.446222i	$0.147231\pi$
$709$			23.7632i			0.892445i	−0.894922	+	0.446222i	$0.852769\pi$
$710$	−0.981557			−0.0368372
$711$		−	6.86623i		−	0.257504i
$712$	−16.0023			−0.599710
$713$	7.79050	+	19.1906i	0.291757	+	0.718693i
$714$	4.36266	−	1.93543i	0.163268	−	0.0724317i
$715$	2.73055			0.102117
$716$	−27.5400			−1.02922
$717$			26.9547i			1.00664i
$718$			5.24550i			0.195760i
$719$		−	43.0768i		−	1.60649i	−0.595646	−	0.803247i	$-0.703104\pi$
$719$		−	43.0768i		−	1.60649i	0.595646	−	0.803247i	$-0.296896\pi$
$720$	1.65784			0.0617841
$721$	−8.07681	−	18.2059i	−0.300796	−	0.678025i
$722$	0.109619			0.00407959
$723$			5.40422i			0.200985i
$724$	−37.9395			−1.41001
$725$	−20.0674			−0.745285
$726$		−	2.33508i		−	0.0866628i
$727$	32.3389			1.19938			0.599692	−	0.800231i	$-0.295290\pi$
$727$	32.3389			1.19938			0.599692	+	0.800231i	$0.295290\pi$
$728$	10.7070	−	4.75001i	0.396828	−	0.176047i
$729$	−1.00000			−0.0370370
$730$			0.820445i			0.0303660i
$731$			51.0151i			1.88686i
$732$		−	19.8355i		−	0.733142i
$733$	35.4940			1.31100			0.655500	−	0.755195i	$-0.272458\pi$
$733$	35.4940			1.31100			0.655500	+	0.755195i	$0.272458\pi$
$734$	−6.53937			−0.241372
$735$	−2.37876	−	2.15334i	−0.0877421	−	0.0794270i
$736$	−12.9711	+	5.26567i	−0.478121	+	0.194095i
$737$	−7.85863			−0.289476
$738$		−	0.968246i		−	0.0356416i
$739$	−19.9641			−0.734390			−0.367195	−	0.930144i	$-0.619682\pi$
$739$	−19.9641			−0.734390			−0.367195	+	0.930144i	$0.619682\pi$
$740$			7.59513i			0.279202i
$741$	19.5157			0.716927
$742$	5.13614	−	2.27858i	0.188554	−	0.0836492i
$743$		−	1.29577i		−	0.0475373i	−0.999717	−	0.0237687i	$-0.992433\pi$
$743$		−	1.29577i		−	0.0475373i	0.999717	−	0.0237687i	$-0.00756652\pi$
$744$	4.31867			0.158330
$745$		−	9.25232i		−	0.338979i
$746$		−	4.23805i		−	0.155166i
$747$	4.95336			0.181234
$748$		−	18.4876i		−	0.675975i
$749$	48.7446	−	21.6248i	1.78109	−	0.790154i
$750$		−	1.14027i		−	0.0416368i
$751$			45.7445i			1.66924i	0.550825	+	0.834620i	$0.314313\pi$
$751$			45.7445i			1.66924i	−0.550825	+	0.834620i	$0.685687\pi$
$752$			26.1619i			0.954028i
$753$			19.4067i			0.707221i
$754$			4.71308i			0.171640i
$755$	5.30791			0.193175
$756$	4.68073	−	2.07654i	0.170237	−	0.0755231i
$757$			20.4601i			0.743636i	0.928306	+	0.371818i	$0.121265\pi$
$757$			20.4601i			0.743636i	−0.928306	+	0.371818i	$0.878735\pi$
$758$		−	7.86425i		−	0.285642i
$759$	−5.97907	+	2.42723i	−0.217026	+	0.0881028i
$760$	2.02058			0.0732940
$761$		−	41.9177i		−	1.51952i	−0.650206	−	0.759758i	$-0.725318\pi$
$761$		−	41.9177i		−	1.51952i	0.650206	−	0.759758i	$-0.274682\pi$
$762$			3.12497i			0.113206i
$763$	−12.2429	+	5.43140i	−0.443224	+	0.196630i
$764$			40.9945i			1.48313i
$765$	3.25410			0.117652
$766$	−4.74810			−0.171556
$767$	35.8984			1.29622
$768$		−	11.0810i		−	0.399850i
$769$	−9.95087			−0.358838			−0.179419	−	0.983773i	$-0.557422\pi$
$769$	−9.95087			−0.358838			−0.179419	+	0.983773i	$0.557422\pi$
$770$	0.379020	−	0.168147i	0.0136589	−	0.00605959i
$771$	4.34625			0.156527
$772$	−19.4178			−0.698863
$773$	25.9367			0.932877			0.466439	−	0.884554i	$-0.345537\pi$
$773$	25.9367			0.932877			0.466439	+	0.884554i	$0.345537\pi$
$774$		−	1.82599i		−	0.0656338i
$775$			20.6860i			0.743061i
$776$	3.86285			0.138668
$777$	9.18537	+	20.7047i	0.329523	+	0.742779i
$778$		−	6.73520i		−	0.241469i
$779$			16.7969i			0.601813i
$780$	3.92765			0.140633
$781$			11.3391i			0.405746i
$782$	−8.01593	+	3.25410i	−0.286649	+	0.116366i
$783$			4.18953i			0.149722i
$784$	−16.9906	+	18.7693i	−0.606807	+	0.670333i
$785$	−9.28870			−0.331528
$786$	−1.31450			−0.0468867
$787$	4.70586			0.167746			0.0838728	−	0.996476i	$-0.473271\pi$
$787$	4.70586			0.167746			0.0838728	+	0.996476i	$0.473271\pi$
$788$	−10.7222			−0.381963
$789$	1.57848			0.0561955
$790$		−	0.799740i		−	0.0284535i
$791$	−8.18014	+	3.62900i	−0.290852	+	0.129032i
$792$			1.34554i			0.0478115i
$793$		−	45.3730i		−	1.61124i
$794$			2.19476i			0.0778892i
$795$	3.83104			0.135873
$796$	12.9637			0.459486
$797$	1.91287			0.0677572			0.0338786	−	0.999426i	$-0.489214\pi$
$797$	1.91287			0.0677572			0.0338786	+	0.999426i	$0.489214\pi$
$798$	2.70892	−	1.20177i	0.0958946	−	0.0425423i
$799$			51.3521i			1.81671i
$800$	−13.9818			−0.494332
$801$	−16.0023			−0.565412
$802$			3.28609i			0.116036i
$803$	9.47794			0.334469
$804$	−11.3039			−0.398659
$805$	4.18511	+	4.03888i	0.147506	+	0.142352i
$806$	4.85836			0.171128
$807$	21.4025			0.753403
$808$			12.6496i			0.445011i
$809$	−9.22652			−0.324387			−0.162194	−	0.986759i	$-0.551857\pi$
$809$	−9.22652			−0.324387			−0.162194	+	0.986759i	$0.551857\pi$
$810$	−0.116474			−0.00409249
$811$		−	24.0192i		−	0.843430i	−0.906728	−	0.421715i	$-0.861428\pi$
$811$		−	24.0192i		−	0.843430i	0.906728	−	0.421715i	$-0.138572\pi$
$812$	−8.69974	−	19.6101i	−0.305301	−	0.688179i
$813$	−15.3267			−0.537532
$814$	−2.92709			−0.102595
$815$	−3.65759			−0.128120
$816$		−	25.6760i		−	0.898841i
$817$			31.6769i			1.10823i
$818$		−	1.11974i		−	0.0391507i
$819$	10.7070	−	4.75001i	0.374133	−	0.165979i
$820$			3.38049i			0.118052i
$821$	35.7334			1.24710			0.623552	−	0.781782i	$-0.285689\pi$
$821$	35.7334			1.24710			0.623552	+	0.781782i	$0.285689\pi$
$822$	−2.31396			−0.0807087
$823$	−45.1166			−1.57267			−0.786333	−	0.617802i	$-0.788023\pi$
$823$	−45.1166			−1.57267			−0.786333	+	0.617802i	$0.788023\pi$
$824$	7.52796			0.262249
$825$	−6.44497			−0.224385
$826$	4.98296	−	2.21062i	0.173379	−	0.0769172i
$827$		−	12.9618i		−	0.450725i	−0.974275	−	0.225362i	$-0.927643\pi$
$827$		−	12.9618i		−	0.450725i	0.974275	−	0.225362i	$-0.0723566\pi$
$828$	−8.60036	+	3.49135i	−0.298883	+	0.121333i
$829$			4.76125i			0.165365i	0.996576	+	0.0826824i	$0.0263487\pi$
$829$			4.76125i			0.165365i	−0.996576	+	0.0826824i	$0.973651\pi$
$830$	0.576940			0.0200259
$831$		−	10.5152i		−	0.364769i
$832$		−	28.7407i		−	0.996403i
$833$	−33.3501	+	36.8414i	−1.15551	+	1.27648i
$834$	−4.53579			−0.157062
$835$			1.39530i			0.0482862i
$836$		−	11.4796i		−	0.397029i
$837$	4.31867			0.149275
$838$	−1.50425			−0.0519635
$839$	6.23409			0.215225			0.107612	−	0.994193i	$-0.465679\pi$
$839$	6.23409			0.215225			0.107612	+	0.994193i	$0.465679\pi$
$840$	1.10856	−	0.491797i	0.0382489	−	0.0169686i
$841$	−11.4478			−0.394752
$842$		−	2.66339i		−	0.0917863i
$843$	−5.30278			−0.182638
$844$	18.0674			0.621906
$845$	3.02545			0.104079
$846$		−	1.83805i		−	0.0631935i
$847$	9.85952	+	22.2244i	0.338777	+	0.763638i
$848$		−	30.2283i		−	1.03804i
$849$		−	2.05894i		−	0.0706626i
$850$	−8.64054			−0.296368
$851$	−15.4436	−	38.0428i	−0.529401	−	1.30409i
$852$			16.3103i			0.558783i
$853$			2.15361i			0.0737382i	0.999320	+	0.0368691i	$0.0117385\pi$
$853$			2.15361i			0.0737382i	−0.999320	+	0.0368691i	$0.988262\pi$
$854$	−2.79406	−	6.29809i	−0.0956107	−	0.215516i
$855$	2.02058			0.0691022
$856$			20.1553i			0.688896i
$857$			48.5222i			1.65749i	0.559628	+	0.828744i	$0.310944\pi$
$857$			48.5222i			1.65749i	−0.559628	+	0.828744i	$0.689056\pi$
$858$			1.51368i			0.0516763i
$859$		−	27.0081i		−	0.921503i	−0.887529	−	0.460752i	$-0.847580\pi$
$859$		−	27.0081i		−	0.921503i	0.887529	−	0.460752i	$-0.152420\pi$
$860$			6.37517i			0.217391i
$861$	4.08828	+	9.21540i	0.139328	+	0.314060i
$862$		−	5.33942i		−	0.181861i
$863$	2.82164			0.0960499			0.0480249	−	0.998846i	$-0.484707\pi$
$863$	2.82164			0.0960499			0.0480249	+	0.998846i	$0.484707\pi$
$864$			2.91903i			0.0993073i
$865$		−	6.15283i		−	0.209202i
$866$	−1.83351			−0.0623052
$867$		−	33.3983i		−	1.13427i
$868$	−20.2145	+	8.96789i	−0.686126	+	0.304390i
$869$	−9.23875			−0.313403
$870$			0.487974i			0.0165439i
$871$	−25.8573			−0.876142
$872$		−	5.06232i		−	0.171432i
$873$	3.86285			0.130738
$874$	−4.97735	+	2.02058i	−0.168361	+	0.0683470i
$875$	4.81463	+	10.8527i	0.162764	+	0.366887i
$876$	13.6332			0.460622
$877$	0.194762			0.00657666			0.00328833	−	0.999995i	$-0.498953\pi$
$877$	0.194762			0.00657666			0.00328833	+	0.999995i	$0.498953\pi$
$878$		−	9.44152i		−	0.318636i
$879$		−	17.4939i		−	0.590054i
$880$		−	2.23069i		−	0.0751964i
$881$	−11.1799			−0.376662			−0.188331	−	0.982106i	$-0.560308\pi$
$881$	−11.1799			−0.376662			−0.188331	+	0.982106i	$0.560308\pi$
$882$	1.19370	−	1.31867i	0.0401941	−	0.0444019i
$883$	17.6279			0.593227			0.296614	−	0.954998i	$-0.404143\pi$
$883$	17.6279			0.593227			0.296614	+	0.954998i	$0.404143\pi$
$884$		−	60.8300i		−	2.04594i
$885$	3.71678			0.124938
$886$	−4.28063			−0.143810
$887$			13.1442i			0.441339i	0.975349	+	0.220670i	$0.0708243\pi$
$887$			13.1442i			0.441339i	−0.975349	+	0.220670i	$0.929176\pi$
$888$	−8.56119			−0.287295
$889$	−13.1947	−	29.7422i	−0.442537	−	0.997523i
$890$	−1.86386			−0.0624766
$891$			1.34554i			0.0450771i
$892$			19.9847i			0.669136i
$893$			31.8861i			1.06703i
$894$	5.12903			0.171540
$895$	−6.52241			−0.218020
$896$	−8.03353	−	18.1084i	−0.268382	−	0.604959i
$897$	−19.6730	+	7.98634i	−0.656862	+	0.266656i
$898$	0.148383			0.00495159
$899$		−	18.0932i		−	0.603442i
$900$	−9.27051			−0.309017
$901$		−	59.3337i		−	1.97669i
$902$	−1.30281			−0.0433788
$903$	7.70998	+	17.3791i	0.256572	+	0.578339i
$904$		−	3.38240i		−	0.112497i
$905$	−8.98537			−0.298684
$906$			2.94244i			0.0977561i
$907$			30.0048i			0.996293i	0.867093	+	0.498146i	$0.165986\pi$
$907$			30.0048i			0.996293i	−0.867093	+	0.498146i	$0.834014\pi$
$908$	−47.6945			−1.58280
$909$			12.6496i			0.419560i
$910$	1.24709	−	0.553255i	0.0413407	−	0.0183402i
$911$			7.15646i			0.237104i	0.992948	+	0.118552i	$0.0378252\pi$
$911$			7.15646i			0.237104i	−0.992948	+	0.118552i	$0.962175\pi$
$912$		−	15.9431i		−	0.527928i
$913$		−	6.66492i		−	0.220577i
$914$			4.28460i			0.141722i
$915$		−	4.69774i		−	0.155302i
$916$	−15.9079			−0.525611
$917$	12.5109	−	5.55029i	0.413147	−	0.183287i
$918$			1.80391i			0.0595380i
$919$			27.3193i			0.901181i	0.892731	+	0.450591i	$0.148787\pi$
$919$			27.3193i			0.901181i	−0.892731	+	0.450591i	$0.851213\pi$
$920$	−2.03686	+	0.826873i	−0.0671533	+	0.0272612i
$921$	31.8573			1.04973
$922$		−	1.39858i		−	0.0460599i
$923$			37.3093i			1.22805i
$924$	−2.79406	−	6.29809i	−0.0919178	−	0.207192i
$925$		−	41.0071i		−	1.34831i
$926$	3.63628			0.119496
$927$	7.52796			0.247251
$928$	12.2294			0.401448
$929$		−	41.9383i		−	1.37595i	−0.725734	−	0.687975i	$-0.758500\pi$
$929$		−	41.9383i		−	1.37595i	0.725734	−	0.687975i	$-0.241500\pi$
$930$	0.503015			0.0164945
$931$	−20.7081	+	22.8760i	−0.678681	+	0.749731i
$932$	22.0153			0.721137
$933$	−2.71831			−0.0889936
$934$	2.51171			0.0821855
$935$		−	4.37851i		−	0.143193i
$936$			4.42723i			0.144709i
$937$	−16.1835			−0.528693			−0.264347	−	0.964428i	$-0.585156\pi$
$937$	−16.1835			−0.528693			−0.264347	+	0.964428i	$0.585156\pi$
$938$	−3.58918	+	1.59229i	−0.117191	+	0.0519900i
$939$		−	21.1811i		−	0.691218i
$940$			6.41728i			0.209309i
$941$	−16.7358			−0.545573			−0.272786	−	0.962075i	$-0.587945\pi$
$941$	−16.7358			−0.545573			−0.272786	+	0.962075i	$0.587945\pi$
$942$		−	5.14919i		−	0.167770i
$943$	−6.87375	−	16.9323i	−0.223840	−	0.551392i
$944$		−	29.3267i		−	0.954504i
$945$	1.10856	−	0.491797i	0.0360614	−	0.0159981i
$946$	−2.45693			−0.0798818
$947$	−4.16195			−0.135245			−0.0676226	−	0.997711i	$-0.521541\pi$
$947$	−4.16195			−0.135245			−0.0676226	+	0.997711i	$0.521541\pi$
$948$	−13.2891			−0.431611
$949$	31.1854			1.01232
$950$	−5.36519			−0.174070
$951$			11.2541i			0.364939i
$952$	−7.61676	−	17.1690i	−0.246861	−	0.556449i
$953$		−	8.11785i		−	0.262963i	−0.991319	−	0.131481i	$-0.958027\pi$
$953$		−	8.11785i		−	0.262963i	0.991319	−	0.131481i	$-0.0419734\pi$
$954$			2.12374i			0.0687586i
$955$			9.70892i			0.314173i
$956$	52.1690			1.68726
$957$	5.63717			0.182224
$958$	0.227339			0.00734500
$959$	22.0234	−	9.77037i	0.711173	−	0.315502i
$960$		−	2.97569i		−	0.0960401i
$961$	12.3491			0.398358
$962$	−9.63105			−0.310517
$963$			20.1553i			0.649497i
$964$	10.4595			0.336878
$965$	−4.59881			−0.148041
$966$	−2.23895	+	2.32002i	−0.0720371	+	0.0746453i
$967$	7.40381			0.238091			0.119045	−	0.992889i	$-0.462017\pi$
$967$	7.40381			0.238091			0.119045	+	0.992889i	$0.462017\pi$
$968$	−9.18953			−0.295363
$969$		−	31.2939i		−	1.00531i
$970$	0.449923			0.0144462
$971$	−14.0152			−0.449768			−0.224884	−	0.974386i	$-0.572200\pi$
$971$	−14.0152			−0.449768			−0.224884	+	0.974386i	$0.572200\pi$
$972$			1.93543i			0.0620790i
$973$	43.1699	−	19.1517i	1.38396	−	0.613976i
$974$	1.12186			0.0359466
$975$	−21.2059			−0.679134
$976$	−37.0668			−1.18648
$977$			26.5778i			0.850298i	0.905123	+	0.425149i	$0.139778\pi$
$977$			26.5778i			0.850298i	−0.905123	+	0.425149i	$0.860222\pi$
$978$		−	2.02759i		−	0.0648350i
$979$			21.5316i			0.688154i
$980$	−4.16764	+	4.60394i	−0.133130	+	0.147067i
$981$		−	5.06232i		−	0.161627i
$982$	6.74590			0.215270
$983$	32.3741			1.03257			0.516287	−	0.856416i	$-0.327314\pi$
$983$	32.3741			1.03257			0.516287	+	0.856416i	$0.327314\pi$
$984$	−3.81047			−0.121473
$985$	−2.53939			−0.0809117
$986$	7.55755			0.240682
$987$	7.76091	+	17.4939i	0.247032	+	0.556836i
$988$		−	37.7713i		−	1.20167i
$989$	−12.9630	−	31.9322i	−0.412200	−	1.01539i
$990$			0.156721i			0.00498090i
$991$	−7.50926			−0.238540			−0.119270	−	0.992862i	$-0.538055\pi$
$991$	−7.50926			−0.238540			−0.119270	+	0.992862i	$0.538055\pi$
$992$		−	12.6063i		−	0.400251i
$993$		−	8.54102i		−	0.271041i
$994$	2.29750	+	5.17879i	0.0728722	+	0.164261i
$995$	3.07025			0.0973334
$996$		−	9.58690i		−	0.303772i
$997$		−	22.3983i		−	0.709362i	−0.934987	−	0.354681i	$-0.884590\pi$
$997$		−	22.3983i		−	0.709362i	0.934987	−	0.354681i	$-0.115410\pi$
$998$	5.08726			0.161034
$999$	−8.56119			−0.270864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.h.b.160.5	✓	12
3.2	odd	2		1449.2.h.h.1126.8		12
7.6	odd	2	inner	483.2.h.b.160.8	yes	12
21.20	even	2		1449.2.h.h.1126.6		12
23.22	odd	2	inner	483.2.h.b.160.6	yes	12
69.68	even	2		1449.2.h.h.1126.5		12
161.160	even	2	inner	483.2.h.b.160.7	yes	12
483.482	odd	2		1449.2.h.h.1126.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.h.b.160.5	✓	12	1.1	even	1	trivial
483.2.h.b.160.6	yes	12	23.22	odd	2	inner
483.2.h.b.160.7	yes	12	161.160	even	2	inner
483.2.h.b.160.8	yes	12	7.6	odd	2	inner
1449.2.h.h.1126.5		12	69.68	even	2
1449.2.h.h.1126.6		12	21.20	even	2
1449.2.h.h.1126.7		12	483.482	odd	2
1449.2.h.h.1126.8		12	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.254102 q^{2} -1.00000i q^{3} -1.93543 q^{4} -0.458377 q^{5} -0.254102i q^{6} +(1.07291 + 2.41844i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+0.254102 q^{2} -1.00000i q^{3} -1.93543 q^{4} -0.458377 q^{5} -0.254102i q^{6} +(1.07291 + 2.41844i) q^{7} -1.00000 q^{8} -1.00000 q^{9} -0.116474 q^{10} +1.34554i q^{11} +1.93543i q^{12} +4.42723i q^{13} +(0.272628 + 0.614531i) q^{14} +0.458377i q^{15} +3.61676 q^{16} +7.09918 q^{17} -0.254102 q^{18} +4.40811 q^{19} +0.887158 q^{20} +(2.41844 - 1.07291i) q^{21} +0.341903i q^{22} +(-4.44364 + 1.80391i) q^{23} +1.00000i q^{24} -4.78989 q^{25} +1.12497i q^{26} +1.00000i q^{27} +(-2.07654 - 4.68073i) q^{28} +4.18953 q^{29} +0.116474i q^{30} -4.31867i q^{31} +2.91903 q^{32} +1.34554 q^{33} +1.80391 q^{34} +(-0.491797 - 1.10856i) q^{35} +1.93543 q^{36} +8.56119i q^{37} +1.12011 q^{38} +4.42723 q^{39} +0.458377 q^{40} +3.81047i q^{41} +(0.614531 - 0.272628i) q^{42} +7.18606i q^{43} -2.60419i q^{44} +0.458377 q^{45} +(-1.12914 + 0.458377i) q^{46} +7.23353i q^{47} -3.61676i q^{48} +(-4.69774 + 5.18953i) q^{49} -1.21712 q^{50} -7.09918i q^{51} -8.56860i q^{52} -8.35783i q^{53} +0.254102i q^{54} -0.616763i q^{55} +(-1.07291 - 2.41844i) q^{56} -4.40811i q^{57} +1.06457 q^{58} -8.10856i q^{59} -0.887158i q^{60} -10.2486 q^{61} -1.09738i q^{62} +(-1.07291 - 2.41844i) q^{63} -6.49180 q^{64} -2.02934i q^{65} +0.341903 q^{66} +5.84052i q^{67} -13.7400 q^{68} +(1.80391 + 4.44364i) q^{69} +(-0.124966 - 0.281687i) q^{70} +8.42723 q^{71} +1.00000 q^{72} -7.04399i q^{73} +2.17541i q^{74} +4.78989i q^{75} -8.53159 q^{76} +(-3.25410 + 1.44364i) q^{77} +1.12497 q^{78} +6.86623i q^{79} -1.65784 q^{80} +1.00000 q^{81} +0.968246i q^{82} -4.95336 q^{83} +(-4.68073 + 2.07654i) q^{84} -3.25410 q^{85} +1.82599i q^{86} -4.18953i q^{87} -1.34554i q^{88} +16.0023 q^{89} +0.116474 q^{90} +(-10.7070 + 4.75001i) q^{91} +(8.60036 - 3.49135i) q^{92} -4.31867 q^{93} +1.83805i q^{94} -2.02058 q^{95} -2.91903i q^{96} -3.86285 q^{97} +(-1.19370 + 1.31867i) q^{98} -1.34554i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 12 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q + 8 * q^4 - 12 * q^8 - 12 * q^9	\( 12 q + 8 q^{4} - 12 q^{8} - 12 q^{9} - 16 q^{16} - 16 q^{23} + 24 q^{25} + 16 q^{29} + 16 q^{32} - 12 q^{35} - 8 q^{36} + 28 q^{39} - 76 q^{46} - 16 q^{49} + 92 q^{50} + 44 q^{58} - 84 q^{64} + 64 q^{70} + 76 q^{71} + 12 q^{72} - 36 q^{77} - 52 q^{78} + 12 q^{81} - 36 q^{85} + 56 q^{92} - 80 q^{93} - 140 q^{95} - 108 q^{98}+O(q^{100}) \) 12 * q + 8 * q^4 - 12 * q^8 - 12 * q^9 - 16 * q^16 - 16 * q^23 + 24 * q^25 + 16 * q^29 + 16 * q^32 - 12 * q^35 - 8 * q^36 + 28 * q^39 - 76 * q^46 - 16 * q^49 + 92 * q^50 + 44 * q^58 - 84 * q^64 + 64 * q^70 + 76 * q^71 + 12 * q^72 - 36 * q^77 - 52 * q^78 + 12 * q^81 - 36 * q^85 + 56 * q^92 - 80 * q^93 - 140 * q^95 - 108 * q^98

Introduction

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