LMFDB - Embedded newform 484.2.c.d.483.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [484,2,Mod(483,484)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(484, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("484.483");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.c (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:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256 $ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			483.16
Root			$0.656642 - 1.25253i$ of defining polynomial
Character	$\chi$	$=$	484.483
Dual form			484.2.c.d.483.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39414 + 0.237451i) q^{2} -0.918459i q^{3} +(1.88723 + 0.662079i) q^{4} +1.71472 q^{5} +(0.218089 - 1.28046i) q^{6} -2.39055 q^{7} +(2.47385 + 1.37116i) q^{8} +2.15643 q^{9} +O(q^{10})$	\(q+(1.39414 + 0.237451i) q^{2} -0.918459i q^{3} +(1.88723 + 0.662079i) q^{4} +1.71472 q^{5} +(0.218089 - 1.28046i) q^{6} -2.39055 q^{7} +(2.47385 + 1.37116i) q^{8} +2.15643 q^{9} +(2.39055 + 0.407162i) q^{10} +(0.608093 - 1.73335i) q^{12} +1.60861i q^{13} +(-3.33275 - 0.567639i) q^{14} -1.57490i q^{15} +(3.12330 + 2.49900i) q^{16} -6.04576i q^{17} +(3.00636 + 0.512048i) q^{18} -1.32552 q^{19} +(3.23607 + 1.13528i) q^{20} +2.19562i q^{21} +7.25726i q^{23} +(1.25935 - 2.27213i) q^{24} -2.05975 q^{25} +(-0.381966 + 2.24262i) q^{26} -4.73597i q^{27} +(-4.51152 - 1.58273i) q^{28} +0.542644i q^{29} +(0.373961 - 2.19562i) q^{30} -8.23060i q^{31} +(3.76092 + 4.22558i) q^{32} +(1.43557 - 8.42861i) q^{34} -4.09911 q^{35} +(4.06969 + 1.42773i) q^{36} +0.369678 q^{37} +(-1.84796 - 0.314747i) q^{38} +1.47744 q^{39} +(4.24195 + 2.35114i) q^{40} +5.09191i q^{41} +(-0.521353 + 3.06099i) q^{42} -9.45922 q^{43} +3.69767 q^{45} +(-1.72325 + 10.1176i) q^{46} +4.00739i q^{47} +(2.29523 - 2.86862i) q^{48} -1.28528 q^{49} +(-2.87158 - 0.489091i) q^{50} -5.55278 q^{51} +(-1.06503 + 3.03582i) q^{52} -2.47865 q^{53} +(1.12456 - 6.60259i) q^{54} +(-5.91385 - 3.27781i) q^{56} +1.21744i q^{57} +(-0.128852 + 0.756520i) q^{58} -7.05173i q^{59} +(1.04271 - 2.97220i) q^{60} +9.89590i q^{61} +(1.95437 - 11.4746i) q^{62} -5.15506 q^{63} +(4.23987 + 6.78407i) q^{64} +2.75830i q^{65} +4.79085i q^{67} +(4.00277 - 11.4098i) q^{68} +6.66550 q^{69} +(-5.71472 - 0.973339i) q^{70} -3.51190i q^{71} +(5.33469 + 2.95681i) q^{72} +2.10200i q^{73} +(0.515382 + 0.0877806i) q^{74} +1.89180i q^{75} +(-2.50157 - 0.877601i) q^{76} +(2.05975 + 0.350820i) q^{78} -2.58092 q^{79} +(5.35557 + 4.28507i) q^{80} +2.11950 q^{81} +(-1.20908 + 7.09881i) q^{82} +3.97095 q^{83} +(-1.45367 + 4.14365i) q^{84} -10.3668i q^{85} +(-13.1874 - 2.24611i) q^{86} +0.498396 q^{87} -8.45225 q^{89} +(5.15506 + 0.878017i) q^{90} -3.84545i q^{91} +(-4.80489 + 13.6962i) q^{92} -7.55947 q^{93} +(-0.951560 + 5.58685i) q^{94} -2.27289 q^{95} +(3.88102 - 3.45425i) q^{96} -8.32624 q^{97} +(-1.79186 - 0.305193i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^5	$ 16 q + 4 q^{4} + 4 q^{5} - 22 q^{12} - 12 q^{14} - 12 q^{16} + 16 q^{20} - 4 q^{25} - 24 q^{26} - 6 q^{34} + 50 q^{36} - 12 q^{37} + 42 q^{38} + 4 q^{42} + 40 q^{45} + 74 q^{48} - 44 q^{49} - 52 q^{53} - 12 q^{56} - 60 q^{58} - 8 q^{60} + 28 q^{64} + 24 q^{69} - 68 q^{70} + 4 q^{78} - 8 q^{80} - 24 q^{81} + 26 q^{82} - 14 q^{86} - 36 q^{89} + 36 q^{92} + 72 q^{93} - 8 q^{97}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^5 - 22 * q^12 - 12 * q^14 - 12 * q^16 + 16 * q^20 - 4 * q^25 - 24 * q^26 - 6 * q^34 + 50 * q^36 - 12 * q^37 + 42 * q^38 + 4 * q^42 + 40 * q^45 + 74 * q^48 - 44 * q^49 - 52 * q^53 - 12 * q^56 - 60 * q^58 - 8 * q^60 + 28 * q^64 + 24 * q^69 - 68 * q^70 + 4 * q^78 - 8 * q^80 - 24 * q^81 + 26 * q^82 - 14 * q^86 - 36 * q^89 + 36 * q^92 + 72 * q^93 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.39414	+	0.237451i	0.985803	+	0.167904i
$2$	1.39414	+	0.237451i	0.985803	+	0.167904i
$3$		−	0.918459i		−	0.530272i	−0.964211	−	0.265136i	$-0.914583\pi$
$3$		−	0.918459i		−	0.530272i	0.964211	−	0.265136i	$-0.0854169\pi$
$4$	1.88723	+	0.662079i	0.943617	+	0.331040i
$5$	1.71472			0.766844			0.383422	−	0.923573i	$-0.374746\pi$
$5$	1.71472			0.766844			0.383422	+	0.923573i	$0.374746\pi$
$6$	0.218089	−	1.28046i	0.0890346	−	0.522744i
$7$	−2.39055			−0.903542			−0.451771	−	0.892134i	$-0.649208\pi$
$7$	−2.39055			−0.903542			−0.451771	+	0.892134i	$0.649208\pi$
$8$	2.47385	+	1.37116i	0.874638	+	0.484777i
$9$	2.15643			0.718811
$10$	2.39055	+	0.407162i	0.755957	+	0.128756i
$11$		0			0
$11$		0			0
$12$	0.608093	−	1.73335i	0.175541	−	0.500374i
$13$			1.60861i			0.446147i	0.974802	+	0.223074i	$0.0716090\pi$
$13$			1.60861i			0.446147i	−0.974802	+	0.223074i	$0.928391\pi$
$14$	−3.33275	−	0.567639i	−0.890715	−	0.151708i
$15$		−	1.57490i		−	0.406636i
$16$	3.12330	+	2.49900i	0.780825	+	0.624749i
$17$		−	6.04576i		−	1.46631i	−0.680060	−	0.733156i	$-0.738046\pi$
$17$		−	6.04576i		−	1.46631i	0.680060	−	0.733156i	$-0.261954\pi$
$18$	3.00636	+	0.512048i	0.708606	+	0.120691i
$19$	−1.32552			−0.304095			−0.152048	−	0.988373i	$-0.548587\pi$
$19$	−1.32552			−0.304095			−0.152048	+	0.988373i	$0.548587\pi$
$20$	3.23607	+	1.13528i	0.723607	+	0.253856i
$21$			2.19562i			0.479123i
$22$		0			0
$23$			7.25726i			1.51324i	0.653853	+	0.756622i	$0.273152\pi$
$23$			7.25726i			1.51324i	−0.653853	+	0.756622i	$0.726848\pi$
$24$	1.25935	−	2.27213i	0.257064	−	0.463796i
$25$	−2.05975			−0.411950
$26$	−0.381966	+	2.24262i	−0.0749097	+	0.439814i
$27$		−	4.73597i		−	0.911438i
$28$	−4.51152	−	1.58273i	−0.852597	−	0.299108i
$29$			0.542644i			0.100766i	0.998730	+	0.0503832i	$0.0160443\pi$
$29$			0.542644i			0.100766i	−0.998730	+	0.0503832i	$0.983956\pi$
$30$	0.373961	−	2.19562i	0.0682756	−	0.400863i
$31$		−	8.23060i		−	1.47826i	−0.673563	−	0.739130i	$-0.735237\pi$
$31$		−	8.23060i		−	1.47826i	0.673563	−	0.739130i	$-0.264763\pi$
$32$	3.76092	+	4.22558i	0.664843	+	0.746983i
$33$		0			0
$34$	1.43557	−	8.42861i	0.246199	−	1.44550i
$35$	−4.09911			−0.692876
$36$	4.06969	+	1.42773i	0.678282	+	0.237955i
$37$	0.369678			0.0607747			0.0303873	−	0.999538i	$-0.490326\pi$
$37$	0.369678			0.0607747			0.0303873	+	0.999538i	$0.490326\pi$
$38$	−1.84796	−	0.314747i	−0.299778	−	0.0510587i
$39$	1.47744			0.236580
$40$	4.24195	+	2.35114i	0.670711	+	0.371748i
$41$			5.09191i			0.795222i	0.917554	+	0.397611i	$0.130161\pi$
$41$			5.09191i			0.795222i	−0.917554	+	0.397611i	$0.869839\pi$
$42$	−0.521353	+	3.06099i	−0.0804465	+	0.472321i
$43$	−9.45922			−1.44252			−0.721259	−	0.692666i	$-0.756436\pi$
$43$	−9.45922			−1.44252			−0.721259	+	0.692666i	$0.756436\pi$
$44$		0			0
$45$	3.69767			0.551216
$46$	−1.72325	+	10.1176i	−0.254079	+	1.49176i
$47$			4.00739i			0.584538i	0.956336	+	0.292269i	$0.0944102\pi$
$47$			4.00739i			0.584538i	−0.956336	+	0.292269i	$0.905590\pi$
$48$	2.29523	−	2.86862i	0.331287	−	0.414050i
$49$	−1.28528			−0.183612
$50$	−2.87158	−	0.489091i	−0.406102	−	0.0691679i
$51$	−5.55278			−0.777545
$52$	−1.06503	+	3.03582i	−0.147692	+	0.420992i
$53$	−2.47865			−0.340468			−0.170234	−	0.985404i	$-0.554452\pi$
$53$	−2.47865			−0.340468			−0.170234	+	0.985404i	$0.554452\pi$
$54$	1.12456	−	6.60259i	0.153034	−	0.898499i
$55$		0			0
$56$	−5.91385	−	3.27781i	−0.790272	−	0.438016i
$57$			1.21744i			0.161253i
$58$	−0.128852	+	0.756520i	−0.0169190	+	0.0993360i
$59$		−	7.05173i		−	0.918057i	−0.888421	−	0.459029i	$-0.848198\pi$
$59$		−	7.05173i		−	0.918057i	0.888421	−	0.459029i	$-0.151802\pi$
$60$	1.04271	−	2.97220i	0.134613	−	0.383709i
$61$			9.89590i			1.26704i	0.773726	+	0.633520i	$0.218391\pi$
$61$			9.89590i			1.26704i	−0.773726	+	0.633520i	$0.781609\pi$
$62$	1.95437	−	11.4746i	0.248205	−	1.45727i
$63$	−5.15506			−0.649476
$64$	4.23987	+	6.78407i	0.529983	+	0.848008i
$65$			2.75830i			0.342125i
$66$		0			0
$67$			4.79085i			0.585296i	0.956220	+	0.292648i	$0.0945364\pi$
$67$			4.79085i			0.585296i	−0.956220	+	0.292648i	$0.905464\pi$
$68$	4.00277	−	11.4098i	0.485408	−	1.38364i
$69$	6.66550			0.802432
$70$	−5.71472	−	0.973339i	−0.683039	−	0.116336i
$71$		−	3.51190i		−	0.416785i	−0.978045	−	0.208393i	$-0.933177\pi$
$71$		−	3.51190i		−	0.416785i	0.978045	−	0.208393i	$-0.0668232\pi$
$72$	5.33469	+	2.95681i	0.628699	+	0.348463i
$73$			2.10200i			0.246021i	0.992405	+	0.123010i	$0.0392549\pi$
$73$			2.10200i			0.246021i	−0.992405	+	0.123010i	$0.960745\pi$
$74$	0.515382	+	0.0877806i	0.0599119	+	0.0102043i
$75$			1.89180i			0.218446i
$76$	−2.50157	−	0.877601i	−0.286950	−	0.100668i
$77$		0			0
$78$	2.05975	+	0.350820i	0.233221	+	0.0397226i
$79$	−2.58092			−0.290376			−0.145188	−	0.989404i	$-0.546379\pi$
$79$	−2.58092			−0.290376			−0.145188	+	0.989404i	$0.546379\pi$
$80$	5.35557	+	4.28507i	0.598771	+	0.479085i
$81$	2.11950			0.235500
$82$	−1.20908	+	7.09881i	−0.133521	+	0.783933i
$83$	3.97095			0.435869			0.217934	−	0.975963i	$-0.430068\pi$
$83$	3.97095			0.435869			0.217934	+	0.975963i	$0.430068\pi$
$84$	−1.45367	+	4.14365i	−0.158609	+	0.452109i
$85$		−	10.3668i		−	1.12443i
$86$	−13.1874	−	2.24611i	−1.42204	−	0.242204i
$87$	0.498396			0.0534337
$88$		0			0
$89$	−8.45225			−0.895937			−0.447969	−	0.894049i	$-0.647852\pi$
$89$	−8.45225			−0.895937			−0.447969	+	0.894049i	$0.647852\pi$
$90$	5.15506	+	0.878017i	0.543391	+	0.0925511i
$91$		−	3.84545i		−	0.403113i
$92$	−4.80489	+	13.6962i	−0.500944	+	1.42792i
$93$	−7.55947			−0.783881
$94$	−0.951560	+	5.58685i	−0.0981460	+	0.576239i
$95$	−2.27289			−0.233194
$96$	3.88102	−	3.45425i	0.396105	−	0.352548i
$97$	−8.32624			−0.845401			−0.422701	−	0.906269i	$-0.638918\pi$
$97$	−8.32624			−0.845401			−0.422701	+	0.906269i	$0.638918\pi$
$98$	−1.79186	−	0.305193i	−0.181005	−	0.0308291i
$99$		0			0
$100$	−3.88723	−	1.36372i	−0.388723	−	0.136372i
$101$		−	9.02983i		−	0.898501i	−0.893406	−	0.449251i	$-0.851691\pi$
$101$		−	9.02983i		−	0.898501i	0.893406	−	0.449251i	$-0.148309\pi$
$102$	−7.74134	−	1.31852i	−0.766506	−	0.130553i
$103$			8.99410i			0.886215i	0.896469	+	0.443107i	$0.146124\pi$
$103$			8.99410i			0.886215i	−0.896469	+	0.443107i	$0.853876\pi$
$104$	−2.20565	+	3.97945i	−0.216282	+	0.390217i
$105$			3.76486i			0.367413i
$106$	−3.45557	−	0.588558i	−0.335635	−	0.0571658i
$107$	−3.08303			−0.298048			−0.149024	−	0.988834i	$-0.547613\pi$
$107$	−3.08303			−0.298048			−0.149024	+	0.988834i	$0.547613\pi$
$108$	3.13559	−	8.93789i	0.301722	−	0.860048i
$109$		−	9.68863i		−	0.928002i	−0.885835	−	0.464001i	$-0.846413\pi$
$109$		−	9.68863i		−	0.928002i	0.885835	−	0.464001i	$-0.153587\pi$
$110$		0			0
$111$		−	0.339534i		−	0.0322271i
$112$	−7.46640	−	5.97397i	−0.705508	−	0.564487i
$113$	−10.7557			−1.01181			−0.505904	−	0.862590i	$-0.668841\pi$
$113$	−10.7557			−1.01181			−0.505904	+	0.862590i	$0.668841\pi$
$114$	−0.289082	+	1.69727i	−0.0270750	+	0.158964i
$115$			12.4441i			1.16042i
$116$	−0.359274	+	1.02410i	−0.0333577	+	0.0950850i
$117$			3.46885i			0.320696i
$118$	1.67444	−	9.83108i	0.154145	−	0.905024i
$119$			14.4527i			1.32487i
$120$	2.15943	−	3.89605i	0.197128	−	0.355659i
$121$		0			0
$122$	−2.34980	+	13.7962i	−0.212740	+	1.24905i
$123$	4.67671			0.421684
$124$	5.44931	−	15.5331i	0.489363	−	1.39491i
$125$	−12.1055			−1.08275
$126$	−7.18685	−	1.22408i	−0.640256	−	0.109049i
$127$	0.326431			0.0289661			0.0144830	−	0.999895i	$-0.495390\pi$
$127$	0.326431			0.0289661			0.0144830	+	0.999895i	$0.495390\pi$
$128$	4.30007	+	10.4647i	0.380076	+	0.924955i
$129$			8.68790i			0.764927i
$130$	−0.654963	+	3.84545i	−0.0574440	+	0.337268i
$131$	10.8360			0.946745			0.473372	−	0.880862i	$-0.343037\pi$
$131$	10.8360			0.946745			0.473372	+	0.880862i	$0.343037\pi$
$132$		0			0
$133$	3.16872			0.274763
$134$	−1.13759	+	6.67910i	−0.0982732	+	0.576987i
$135$		−	8.12084i		−	0.698931i
$136$	8.28968	−	14.9563i	0.710834	−	1.28249i
$137$	−1.26246			−0.107859			−0.0539297	−	0.998545i	$-0.517175\pi$
$137$	−1.26246			−0.107859			−0.0539297	+	0.998545i	$0.517175\pi$
$138$	9.29261	+	1.58273i	0.791040	+	0.134731i
$139$	10.0496			0.852397			0.426199	−	0.904630i	$-0.359852\pi$
$139$	10.0496			0.852397			0.426199	+	0.904630i	$0.359852\pi$
$140$	−7.73597	−	2.71393i	−0.653809	−	0.229369i
$141$	3.68062			0.309964
$142$	0.833905	−	4.89606i	0.0699797	−	0.410869i
$143$		0			0
$144$	6.73519	+	5.38892i	0.561266	+	0.449077i
$145$			0.930480i			0.0772722i
$146$	−0.499124	+	2.93048i	−0.0413078	+	0.242528i
$147$			1.18048i			0.0973645i
$148$	0.697669	+	0.244756i	0.0573480	+	0.0201188i
$149$			2.36308i			0.193591i	0.995304	+	0.0967957i	$0.0308594\pi$
$149$			2.36308i			0.193591i	−0.995304	+	0.0967957i	$0.969141\pi$
$150$	−0.449210	+	2.63742i	−0.0366778	+	0.215345i
$151$	19.1020			1.55450			0.777251	−	0.629191i	$-0.216614\pi$
$151$	19.1020			1.55450			0.777251	+	0.629191i	$0.216614\pi$
$152$	−3.27914	−	1.81750i	−0.265973	−	0.147418i
$153$		−	13.0373i		−	1.05400i
$154$		0			0
$155$		−	14.1131i		−	1.13359i
$156$	2.78827	+	0.978182i	0.223241	+	0.0783173i
$157$	9.81066			0.782976			0.391488	−	0.920183i	$-0.371960\pi$
$157$	9.81066			0.782976			0.391488	+	0.920183i	$0.371960\pi$
$158$	−3.59815	−	0.612843i	−0.286254	−	0.0487551i
$159$			2.27654i			0.180541i
$160$	6.44890	+	7.24566i	0.509831	+	0.572820i
$161$		−	17.3488i		−	1.36728i
$162$	2.95488	+	0.503279i	0.232157	+	0.0395414i
$163$		−	14.2471i		−	1.11592i	−0.829867	−	0.557961i	$-0.811584\pi$
$163$		−	14.2471i		−	1.11592i	0.829867	−	0.557961i	$-0.188416\pi$
$164$	−3.37125	+	9.60962i	−0.263250	+	0.750385i
$165$		0			0
$166$	5.53605	+	0.942909i	0.429681	+	0.0731839i
$167$	−0.0701254			−0.00542647			−0.00271323	−	0.999996i	$-0.500864\pi$
$167$	−0.0701254			−0.00542647			−0.00271323	+	0.999996i	$0.500864\pi$
$168$	−3.01054	+	5.43163i	−0.232268	+	0.419059i
$169$	10.4124			0.800953
$170$	2.46160	−	14.4527i	0.188796	−	1.10847i
$171$	−2.85840			−0.218587
$172$	−17.8518	−	6.26276i	−1.36118	−	0.477531i
$173$		−	19.8281i		−	1.50750i	−0.657161	−	0.753750i	$-0.728243\pi$
$173$		−	19.8281i		−	1.50750i	0.657161	−	0.753750i	$-0.271757\pi$
$174$	0.694833	+	0.118345i	0.0526751	+	0.00897171i
$175$	4.92393			0.372214
$176$		0			0
$177$	−6.47672			−0.486820
$178$	−11.7836	−	2.00700i	−0.883218	−	0.150431i
$179$			3.44573i			0.257546i	0.991674	+	0.128773i	$0.0411039\pi$
$179$			3.44573i			0.257546i	−0.991674	+	0.128773i	$0.958896\pi$
$180$	6.97836	+	2.44815i	0.520137	+	0.182474i
$181$	15.7604			1.17146			0.585729	−	0.810507i	$-0.300808\pi$
$181$	15.7604			1.17146			0.585729	+	0.810507i	$0.300808\pi$
$182$	0.913108	−	5.36108i	0.0676840	−	0.397390i
$183$	9.08898			0.671876
$184$	−9.95084	+	17.9534i	−0.733585	+	1.32354i
$185$	0.633892			0.0466047
$186$	−10.5389	−	1.79501i	−0.772752	−	0.131616i
$187$		0			0
$188$	−2.65321	+	7.56288i	−0.193505	+	0.551580i
$189$			11.3216i			0.823523i
$190$	−3.16872	−	0.539701i	−0.229883	−	0.0391541i
$191$			7.12388i			0.515466i	0.966216	+	0.257733i	$0.0829754\pi$
$191$			7.12388i			0.515466i	−0.966216	+	0.257733i	$0.917025\pi$
$192$	6.23089	−	3.89414i	0.449675	−	0.281035i
$193$		−	16.8625i		−	1.21379i	−0.794782	−	0.606895i	$-0.792415\pi$
$193$		−	16.8625i		−	1.21379i	0.794782	−	0.606895i	$-0.207585\pi$
$194$	−11.6079	−	1.97708i	−0.833400	−	0.141946i
$195$	2.53339			0.181420
$196$	−2.42563	−	0.850961i	−0.173259	−	0.0607829i
$197$			24.6863i			1.75883i	0.476058	+	0.879414i	$0.342065\pi$
$197$			24.6863i			1.75883i	−0.476058	+	0.879414i	$0.657935\pi$
$198$		0			0
$199$		−	15.7596i		−	1.11717i	−0.829449	−	0.558583i	$-0.811345\pi$
$199$		−	15.7596i		−	1.11717i	0.829449	−	0.558583i	$-0.188655\pi$
$200$	−5.09552	−	2.82424i	−0.360307	−	0.199704i
$201$	4.40020			0.310366
$202$	2.14415	−	12.5888i	0.150862	−	0.885746i
$203$		−	1.29722i		−	0.0910467i
$204$	−10.4794	−	3.67638i	−0.733704	−	0.257398i
$205$			8.73117i			0.609811i
$206$	−2.13566	+	12.5390i	−0.148799	+	0.873634i
$207$			15.6498i			1.08774i
$208$	−4.01990	+	5.02416i	−0.278730	+	0.348363i
$209$		0			0
$210$	−0.893972	+	5.24873i	−0.0616899	+	0.362197i
$211$	23.8936			1.64490			0.822452	−	0.568834i	$-0.192605\pi$
$211$	23.8936			1.64490			0.822452	+	0.568834i	$0.192605\pi$
$212$	−4.67779	−	1.64106i	−0.321272	−	0.112709i
$213$	−3.22553			−0.221010
$214$	−4.29817	−	0.732070i	−0.293817	−	0.0500433i
$215$	−16.2199			−1.10619
$216$	6.49375	−	11.7161i	0.441844	−	0.797178i
$217$			19.6756i			1.33567i
$218$	2.30058	−	13.5073i	0.155815	−	0.914828i
$219$	1.93060			0.130458
$220$		0			0
$221$	9.72525			0.654191
$222$	0.0806228	−	0.473357i	0.00541105	−	0.0317696i
$223$			18.8664i			1.26339i	0.775219	+	0.631693i	$0.217640\pi$
$223$			18.8664i			1.26339i	−0.775219	+	0.631693i	$0.782360\pi$
$224$	−8.99065	−	10.1014i	−0.600713	−	0.674931i
$225$	−4.44172			−0.296115
$226$	−14.9949	−	2.55395i	−0.997444	−	0.169886i
$227$	11.2685			0.747913			0.373957	−	0.927446i	$-0.378001\pi$
$227$	11.2685			0.747913			0.373957	+	0.927446i	$0.378001\pi$
$228$	−0.806040	+	2.29759i	−0.0533813	+	0.152161i
$229$	21.8518			1.44401			0.722003	−	0.691890i	$-0.243222\pi$
$229$	21.8518			1.44401			0.722003	+	0.691890i	$0.243222\pi$
$230$	−2.95488	+	17.3488i	−0.194839	+	1.14395i
$231$		0			0
$232$	−0.744050	+	1.34242i	−0.0488492	+	0.0881342i
$233$		−	6.35320i		−	0.416212i	−0.978106	−	0.208106i	$-0.933270\pi$
$233$		−	6.35320i		−	0.416212i	0.978106	−	0.208106i	$-0.0667299\pi$
$234$	−0.823684	+	4.83606i	−0.0538459	+	0.316143i
$235$			6.87153i			0.448249i
$236$	4.66881	−	13.3083i	0.303913	−	0.866294i
$237$			2.37047i			0.153978i
$238$	−3.43181	+	20.1490i	−0.222451	+	1.30607i
$239$	−14.9551			−0.967368			−0.483684	−	0.875243i	$-0.660702\pi$
$239$	−14.9551			−0.967368			−0.483684	+	0.875243i	$0.660702\pi$
$240$	3.93566	−	4.91887i	0.254046	−	0.317512i
$241$		−	0.457365i		−	0.0294615i	−0.999891	−	0.0147307i	$-0.995311\pi$
$241$		−	0.457365i		−	0.0294615i	0.999891	−	0.0147307i	$-0.00468911\pi$
$242$		0			0
$243$		−	16.1546i		−	1.03632i
$244$	−6.55187	+	18.6759i	−0.419441	+	1.19560i
$245$	−2.20390			−0.140802
$246$	6.51997	+	1.11049i	0.415698	+	0.0708023i
$247$		−	2.13224i		−	0.135671i
$248$	11.2854	−	20.3613i	0.716626	−	1.29294i
$249$		−	3.64716i		−	0.231129i
$250$	−16.8767	−	2.87446i	−1.06737	−	0.181797i
$251$			12.7158i			0.802617i	0.915943	+	0.401308i	$0.131444\pi$
$251$			12.7158i			0.802617i	−0.915943	+	0.401308i	$0.868556\pi$
$252$	−9.72879	−	3.41306i	−0.612856	−	0.215002i
$253$		0			0
$254$	0.455090	+	0.0775115i	0.0285549	+	0.00486351i
$255$	−9.52144			−0.596256
$256$	3.51003	+	15.6102i	0.219377	+	0.975640i
$257$	−1.49094			−0.0930020			−0.0465010	−	0.998918i	$-0.514807\pi$
$257$	−1.49094			−0.0930020			−0.0465010	+	0.998918i	$0.514807\pi$
$258$	−2.06296	+	12.1121i	−0.128434	+	0.754068i
$259$	−0.883733			−0.0549125
$260$	−1.82622	+	5.20556i	−0.113257	+	0.322835i
$261$			1.17018i			0.0724321i
$262$	15.1068	+	2.57302i	0.933304	+	0.158962i
$263$	14.7580			0.910017			0.455008	−	0.890487i	$-0.349636\pi$
$263$	14.7580			0.910017			0.455008	+	0.890487i	$0.349636\pi$
$264$		0			0
$265$	−4.25017			−0.261086
$266$	4.41763	+	0.752417i	0.270862	+	0.0461337i
$267$			7.76305i			0.475091i
$268$	−3.17192	+	9.04146i	−0.193756	+	0.552295i
$269$	13.1441			0.801413			0.400706	−	0.916207i	$-0.368765\pi$
$269$	13.1441			0.801413			0.400706	+	0.916207i	$0.368765\pi$
$270$	1.92831	−	11.3216i	0.117353	−	0.689008i
$271$	11.3027			0.686591			0.343295	−	0.939227i	$-0.388457\pi$
$271$	11.3027			0.686591			0.343295	+	0.939227i	$0.388457\pi$
$272$	15.1083	−	18.8827i	0.916077	−	1.14493i
$273$	−3.53189			−0.213760
$274$	−1.76004	−	0.299773i	−0.106328	−	0.0181100i
$275$		0			0
$276$	12.5794	+	4.41309i	0.757188	+	0.265637i
$277$			1.58163i			0.0950308i	0.998871	+	0.0475154i	$0.0151303\pi$
$277$			1.58163i			0.0950308i	−0.998871	+	0.0475154i	$0.984870\pi$
$278$	14.0105	+	2.38630i	0.840296	+	0.143120i
$279$		−	17.7487i		−	1.06259i
$280$	−10.1406	−	5.62051i	−0.606015	−	0.335890i
$281$		−	8.81505i		−	0.525862i	−0.964815	−	0.262931i	$-0.915311\pi$
$281$		−	8.81505i		−	0.525862i	0.964815	−	0.262931i	$-0.0846891\pi$
$282$	5.13129	+	0.873969i	0.305564	+	0.0520441i
$283$	20.2782			1.20542			0.602708	−	0.797962i	$-0.294089\pi$
$283$	20.2782			1.20542			0.602708	+	0.797962i	$0.294089\pi$
$284$	2.32515	−	6.62777i	0.137973	−	0.393286i
$285$			2.08756i			0.123656i
$286$		0			0
$287$		−	12.1724i		−	0.718516i
$288$	8.11017	+	9.11217i	0.477896	+	0.536940i
$289$	−19.5512			−1.15007
$290$	−0.220944	+	1.29722i	−0.0129743	+	0.0761752i
$291$			7.64731i			0.448293i
$292$	−1.39169	+	3.96697i	−0.0814427	+	0.232149i
$293$			13.9518i			0.815071i	0.913189	+	0.407535i	$0.133612\pi$
$293$			13.9518i			0.815071i	−0.913189	+	0.407535i	$0.866388\pi$
$294$	−0.280307	+	1.64575i	−0.0163478	+	0.0959822i
$295$		−	12.0917i		−	0.704007i
$296$	0.914528	+	0.506886i	0.0531558	+	0.0294621i
$297$		0			0
$298$	−0.561118	+	3.29446i	−0.0325047	+	0.190843i
$299$	−11.6741			−0.675130
$300$	−1.25252	+	3.57026i	−0.0723143	+	0.206129i
$301$	22.6127			1.30337
$302$	26.6308	+	4.53580i	1.53243	+	0.261006i
$303$	−8.29352			−0.476451
$304$	−4.14000	−	3.31247i	−0.237445	−	0.189983i
$305$			16.9686i			0.971622i
$306$	3.09572	−	18.1757i	0.176971	−	1.03904i
$307$	−5.88829			−0.336062			−0.168031	−	0.985782i	$-0.553741\pi$
$307$	−5.88829			−0.336062			−0.168031	+	0.985782i	$0.553741\pi$
$308$		0			0
$309$	8.26071			0.469935
$310$	3.35118	−	19.6756i	0.190335	−	1.11750i
$311$		−	26.2334i		−	1.48756i	−0.668425	−	0.743780i	$-0.733031\pi$
$311$		−	26.2334i		−	1.48756i	0.668425	−	0.743780i	$-0.266969\pi$
$312$	3.65496	+	2.02580i	0.206922	+	0.114688i
$313$	−17.1319			−0.968350			−0.484175	−	0.874971i	$-0.660880\pi$
$313$	−17.1319			−0.968350			−0.484175	+	0.874971i	$0.660880\pi$
$314$	13.6774	+	2.32956i	0.771860	+	0.131464i
$315$	−8.83945			−0.498047
$316$	−4.87079	−	1.70877i	−0.274004	−	0.0961260i
$317$	0.797186			0.0447744			0.0223872	−	0.999749i	$-0.492873\pi$
$317$	0.797186			0.0447744			0.0223872	+	0.999749i	$0.492873\pi$
$318$	−0.540567	+	3.17380i	−0.0303135	+	0.177978i
$319$		0			0
$320$	7.27016	+	11.6327i	0.406414	+	0.650290i
$321$			2.83164i			0.158047i
$322$	4.11950	−	24.1866i	0.229571	−	1.34787i
$323$			8.01378i			0.445899i
$324$	4.00000	+	1.40328i	0.222222	+	0.0779600i
$325$		−	3.31333i		−	0.183791i
$326$	3.38300	−	19.8625i	0.187367	−	1.10008i
$327$	−8.89861			−0.492094
$328$	−6.98179	+	12.5966i	−0.385505	+	0.695531i
$329$		−	9.57985i		−	0.528154i
$330$		0			0
$331$			21.2979i			1.17064i	0.810803	+	0.585319i	$0.199031\pi$
$331$			21.2979i			1.17064i	−0.810803	+	0.585319i	$0.800969\pi$
$332$	7.49412	+	2.62909i	0.411293	+	0.144290i
$333$	0.797186			0.0436855
$334$	−0.0977644	−	0.0166514i	−0.00534943	−	0.000911123i
$335$			8.21495i			0.448830i
$336$	−5.48685	+	6.85758i	−0.299332	+	0.374112i
$337$		−	10.8759i		−	0.592446i	−0.955119	−	0.296223i	$-0.904273\pi$
$337$		−	10.8759i		−	0.592446i	0.955119	−	0.296223i	$-0.0957272\pi$
$338$	14.5163	+	2.47244i	0.789582	+	0.134483i
$339$			9.87864i			0.536534i
$340$	6.86362	−	19.5645i	0.372232	−	1.06103i
$341$		0			0
$342$	−3.98500	−	0.678731i	−0.215484	−	0.0367016i
$343$	19.8064			1.06944
$344$	−23.4007	−	12.9701i	−1.26168	−	0.699299i
$345$	11.4294			0.615340
$346$	4.70820	−	27.6430i	0.253115	−	1.48610i
$347$	−0.643534			−0.0345467			−0.0172734	−	0.999851i	$-0.505499\pi$
$347$	−0.643534			−0.0345467			−0.0172734	+	0.999851i	$0.505499\pi$
$348$	0.940590	+	0.329978i	0.0504209	+	0.0176887i
$349$		−	17.2797i		−	0.924961i	−0.886630	−	0.462480i	$-0.846960\pi$
$349$		−	17.2797i		−	0.924961i	0.886630	−	0.462480i	$-0.153040\pi$
$350$	6.86464	+	1.16920i	0.366930	+	0.0624961i
$351$	7.61832			0.406636
$352$		0			0
$353$	−28.3825			−1.51065			−0.755324	−	0.655352i	$-0.772520\pi$
$353$	−28.3825			−1.51065			−0.755324	+	0.655352i	$0.772520\pi$
$354$	−9.02944	−	1.53791i	−0.479909	−	0.0817389i
$355$		−	6.02190i		−	0.319609i
$356$	−15.9514	−	5.59606i	−0.845421	−	0.296591i
$357$	13.2742			0.702544
$358$	−0.818194	+	4.80382i	−0.0432429	+	0.253890i
$359$	−28.5533			−1.50699			−0.753494	−	0.657455i	$-0.771633\pi$
$359$	−28.5533			−1.50699			−0.753494	+	0.657455i	$0.771633\pi$
$360$	9.14748	+	5.07008i	0.482114	+	0.267217i
$361$	−17.2430			−0.907526
$362$	21.9721	+	3.74232i	1.15483	+	0.196692i
$363$		0			0
$364$	2.54599	−	7.25726i	0.133446	−	0.380384i
$365$			3.60434i			0.188660i
$366$	12.6713	+	2.15819i	0.662338	+	0.112810i
$367$			0.389429i			0.0203280i	0.999948	+	0.0101640i	$0.00323536\pi$
$367$			0.389429i			0.0203280i	−0.999948	+	0.0101640i	$0.996765\pi$
$368$	−18.1359	+	22.6666i	−0.945398	+	1.18158i
$369$			10.9804i			0.571614i
$370$	0.883733	+	0.150519i	0.0459431	+	0.00782509i
$371$	5.92532			0.307627
$372$	−14.2665	−	5.00497i	−0.739683	−	0.259496i
$373$			9.95150i			0.515269i	0.966242	+	0.257635i	$0.0829430\pi$
$373$			9.95150i			0.515269i	−0.966242	+	0.257635i	$0.917057\pi$
$374$		0			0
$375$			11.1184i			0.574150i
$376$	−5.49475	+	9.91368i	−0.283370	+	0.511259i
$377$	−0.872901			−0.0449567
$378$	−2.68832	+	15.7838i	−0.138272	+	0.811831i
$379$		−	20.1124i		−	1.03311i	−0.856256	−	0.516553i	$-0.827215\pi$
$379$		−	20.1124i		−	1.03311i	0.856256	−	0.516553i	$-0.172785\pi$
$380$	−4.28948	−	1.50483i	−0.220046	−	0.0771964i
$381$		−	0.299814i		−	0.0153599i
$382$	−1.69157	+	9.93166i	−0.0865485	+	0.508148i
$383$		−	10.2816i		−	0.525367i	−0.964882	−	0.262684i	$-0.915392\pi$
$383$		−	10.2816i		−	0.525367i	0.964882	−	0.262684i	$-0.0846075\pi$
$384$	9.61137	−	3.94943i	0.490478	−	0.201544i
$385$		0			0
$386$	4.00402	−	23.5086i	0.203799	−	1.19656i
$387$	−20.3982			−1.03690
$388$	−15.7136	−	5.51263i	−0.797735	−	0.279861i
$389$	−19.2799			−0.977528			−0.488764	−	0.872416i	$-0.662552\pi$
$389$	−19.2799			−0.977528			−0.488764	+	0.872416i	$0.662552\pi$
$390$	3.53189	+	0.601556i	0.178844	+	0.0304610i
$391$	43.8757			2.21889
$392$	−3.17960	−	1.76233i	−0.160594	−	0.0890109i
$393$		−	9.95241i		−	0.502033i
$394$	−5.86180	+	34.4161i	−0.295313	+	1.73386i
$395$	−4.42554			−0.222673
$396$		0			0
$397$	38.1030			1.91233			0.956167	−	0.292823i	$-0.0945945\pi$
$397$	38.1030			1.91233			0.956167	+	0.292823i	$0.0945945\pi$
$398$	3.74213	−	21.9710i	0.187576	−	1.10131i
$399$		−	2.91034i		−	0.145699i
$400$	−6.43323	−	5.14731i	−0.321661	−	0.257366i
$401$	−4.15178			−0.207330			−0.103665	−	0.994612i	$-0.533057\pi$
$401$	−4.15178			−0.207330			−0.103665	+	0.994612i	$0.533057\pi$
$402$	6.13448	+	1.04483i	0.305960	+	0.0521116i
$403$	13.2398			0.659522
$404$	5.97846	−	17.0414i	0.297440	−	0.847841i
$405$	3.63435			0.180592
$406$	0.308026	−	1.80850i	0.0152871	−	0.0897542i
$407$		0			0
$408$	−13.7367	−	7.61373i	−0.680070	−	0.376936i
$409$		−	11.3220i		−	0.559837i	−0.960024	−	0.279919i	$-0.909693\pi$
$409$		−	11.3220i		−	0.559837i	0.960024	−	0.279919i	$-0.0903075\pi$
$410$	−2.07323	+	12.1724i	−0.102389	+	0.601154i
$411$			1.15952i			0.0571949i
$412$	−5.95481	+	16.9740i	−0.293372	+	0.836247i
$413$			16.8575i			0.829503i
$414$	−3.71607	+	21.8180i	−0.182635	+	1.07229i
$415$	6.80905			0.334243
$416$	−6.79729	+	6.04984i	−0.333265	+	0.296618i
$417$		−	9.23016i		−	0.452003i
$418$		0			0
$419$			21.2095i			1.03615i	0.855335	+	0.518075i	$0.173351\pi$
$419$			21.2095i			1.03615i	−0.855335	+	0.518075i	$0.826649\pi$
$420$	−2.49264	+	7.10517i	−0.121628	+	0.346697i
$421$	24.7834			1.20787			0.603933	−	0.797035i	$-0.293599\pi$
$421$	24.7834			1.20787			0.603933	+	0.797035i	$0.293599\pi$
$422$	33.3110	+	5.67357i	1.62155	+	0.276185i
$423$			8.64167i			0.420172i
$424$	−6.13180	−	3.39861i	−0.297787	−	0.165051i
$425$			12.4528i			0.604048i
$426$	−4.49683	−	0.765907i	−0.217872	−	0.0371083i
$427$		−	23.6566i		−	1.14482i
$428$	−5.81840	−	2.04121i	−0.281243	−	0.0986657i
$429$		0			0
$430$	−22.6127	−	3.85143i	−1.09048	−	0.185732i
$431$	1.76731			0.0851283			0.0425642	−	0.999094i	$-0.486447\pi$
$431$	1.76731			0.0851283			0.0425642	+	0.999094i	$0.486447\pi$
$432$	11.8352	−	14.7919i	0.569420	−	0.711674i
$433$	−32.9514			−1.58354			−0.791772	−	0.610817i	$-0.790841\pi$
$433$	−32.9514			−1.58354			−0.791772	+	0.610817i	$0.790841\pi$
$434$	−4.67201	+	27.4305i	−0.224264	+	1.31671i
$435$	0.854608			0.0409753
$436$	6.41464	−	18.2847i	0.307206	−	0.875679i
$437$		−	9.61966i		−	0.460171i
$438$	2.69152	+	0.458425i	0.128606	+	0.0219044i
$439$	−27.3520			−1.30544			−0.652719	−	0.757600i	$-0.726372\pi$
$439$	−27.3520			−1.30544			−0.652719	+	0.757600i	$0.726372\pi$
$440$		0			0
$441$	−2.77163			−0.131982
$442$	13.5583	+	2.30927i	0.644904	+	0.109841i
$443$			1.69533i			0.0805474i	0.999189	+	0.0402737i	$0.0128230\pi$
$443$			1.69533i			0.0805474i	−0.999189	+	0.0402737i	$0.987177\pi$
$444$	0.224798	−	0.640780i	0.0106685	−	0.0304101i
$445$	−14.4932			−0.687044
$446$	−4.47985	+	26.3023i	−0.212127	+	1.24545i
$447$	2.17040			0.102656
$448$	−10.1356	−	16.2176i	−0.478862	−	0.766211i
$449$	−18.5331			−0.874630			−0.437315	−	0.899308i	$-0.644071\pi$
$449$	−18.5331			−0.874630			−0.437315	+	0.899308i	$0.644071\pi$
$450$	−6.19236	−	1.05469i	−0.291911	−	0.0497187i
$451$		0			0
$452$	−20.2985	−	7.12111i	−0.954759	−	0.334949i
$453$		−	17.5444i		−	0.824309i
$454$	15.7098	+	2.67571i	0.737296	+	0.125577i
$455$		−	6.59385i		−	0.309125i
$456$	−1.66930	+	3.01176i	−0.0781719	+	0.141038i
$457$			10.8830i			0.509086i	0.967061	+	0.254543i	$0.0819250\pi$
$457$			10.8830i			0.509086i	−0.967061	+	0.254543i	$0.918075\pi$
$458$	30.4644	+	5.18874i	1.42351	+	0.242454i
$459$	−28.6325			−1.33645
$460$	−8.23901	+	23.4850i	−0.384146	+	1.09499i
$461$		−	13.8278i		−	0.644024i	−0.946736	−	0.322012i	$-0.895641\pi$
$461$		−	13.8278i		−	0.644024i	0.946736	−	0.322012i	$-0.104359\pi$
$462$		0			0
$463$			37.3657i			1.73653i	0.496099	+	0.868266i	$0.334765\pi$
$463$			37.3657i			1.73653i	−0.496099	+	0.868266i	$0.665235\pi$
$464$	−1.35607	+	1.69484i	−0.0629538	+	0.0786810i
$465$	−12.9623			−0.601114
$466$	1.50858	−	8.85722i	0.0698834	−	0.410303i
$467$		−	13.7952i		−	0.638368i	−0.947693	−	0.319184i	$-0.896591\pi$
$467$		−	13.7952i		−	0.638368i	0.947693	−	0.319184i	$-0.103409\pi$
$468$	−2.29666	+	6.54654i	−0.106163	+	0.302614i
$469$		−	11.4528i		−	0.528839i
$470$	−1.63165	+	9.57985i	−0.0752626	+	0.441886i
$471$		−	9.01069i		−	0.415191i
$472$	9.66902	−	17.4449i	0.445053	−	0.802968i
$473$		0			0
$474$	−0.562871	+	3.30475i	−0.0258535	+	0.151792i
$475$	2.73025			0.125272
$476$	−9.56882	+	27.2756i	−0.438586	+	1.25017i
$477$	−5.34504			−0.244732
$478$	−20.8495	−	3.55112i	−0.953635	−	0.162424i
$479$	−13.5071			−0.617154			−0.308577	−	0.951199i	$-0.599853\pi$
$479$	−13.5071			−0.617154			−0.308577	+	0.951199i	$0.599853\pi$
$480$	6.65484	−	5.92305i	0.303750	−	0.270349i
$481$			0.594667i			0.0271145i
$482$	0.108602	−	0.637630i	0.00494669	−	0.0290432i
$483$	−15.9342			−0.725031
$484$		0			0
$485$	−14.2771			−0.648291
$486$	3.83593	−	22.5217i	0.174001	−	1.02161i
$487$			35.7386i			1.61947i	0.586794	+	0.809736i	$0.300390\pi$
$487$			35.7386i			1.61947i	−0.586794	+	0.809736i	$0.699610\pi$
$488$	−13.5688	+	24.4810i	−0.614231	+	1.10820i
$489$	−13.0854			−0.591743
$490$	−3.07253	−	0.523319i	−0.138803	−	0.0236411i
$491$	−40.3486			−1.82090			−0.910452	−	0.413614i	$-0.864266\pi$
$491$	−40.3486			−1.82090			−0.910452	+	0.413614i	$0.864266\pi$
$492$	8.82604	+	3.09635i	0.397908	+	0.139594i
$493$	3.28070			0.147755
$494$	0.506304	−	2.97264i	0.0227797	−	0.133745i
$495$		0			0
$496$	20.5683	−	25.7067i	0.923542	−	1.15426i
$497$			8.39535i			0.376583i
$498$	0.866023	−	5.08464i	0.0388074	−	0.227848i
$499$			4.07024i			0.182209i	0.995841	+	0.0911045i	$0.0290397\pi$
$499$			4.07024i			0.182209i	−0.995841	+	0.0911045i	$0.970960\pi$
$500$	−22.8458	−	8.01478i	−1.02170	−	0.358432i
$501$			0.0644073i			0.00287751i
$502$	−3.01939	+	17.7276i	−0.134762	+	0.791222i
$503$	−19.5167			−0.870209			−0.435104	−	0.900380i	$-0.643288\pi$
$503$	−19.5167			−0.870209			−0.435104	+	0.900380i	$0.643288\pi$
$504$	−12.7528	−	7.06838i	−0.568056	−	0.314851i
$505$		−	15.4836i		−	0.689010i
$506$		0			0
$507$		−	9.56335i		−	0.424723i
$508$	0.616052	+	0.216123i	0.0273329	+	0.00958892i
$509$	23.4697			1.04028			0.520138	−	0.854082i	$-0.325880\pi$
$509$	23.4697			1.04028			0.520138	+	0.854082i	$0.325880\pi$
$510$	−13.2742	−	2.26088i	−0.587791	−	0.100113i
$511$		−	5.02494i		−	0.222290i
$512$	1.18678	+	22.5963i	0.0524488	+	0.998624i
$513$			6.27763i			0.277164i
$514$	−2.07857	−	0.354025i	−0.0916817	−	0.0156154i
$515$			15.4223i			0.679588i
$516$	−5.75208	+	16.3961i	−0.253221	+	0.721798i
$517$		0			0
$518$	−1.23204	−	0.209844i	−0.0541329	−	0.00922000i
$519$	−18.2113			−0.799386
$520$	−3.78206	+	6.82363i	−0.165854	+	0.299236i
$521$	20.4639			0.896539			0.448269	−	0.893899i	$-0.352041\pi$
$521$	20.4639			0.896539			0.448269	+	0.893899i	$0.352041\pi$
$522$	−0.277860	+	1.63139i	−0.0121616	+	0.0714038i
$523$	8.23408			0.360051			0.180026	−	0.983662i	$-0.442382\pi$
$523$	8.23408			0.360051			0.180026	+	0.983662i	$0.442382\pi$
$524$	20.4500	+	7.17429i	0.893364	+	0.313410i
$525$		−	4.52243i		−	0.197375i
$526$	20.5747	+	3.50431i	0.897098	+	0.152795i
$527$	−49.7602			−2.16759
$528$		0			0
$529$	−29.6679			−1.28991
$530$	−5.92532	−	1.00921i	−0.257380	−	0.0438373i
$531$		−	15.2066i		−	0.659910i
$532$	5.98012	+	2.09795i	0.259271	+	0.0909575i
$533$	−8.19088			−0.354786
$534$	−1.84335	+	10.8227i	−0.0797694	+	0.468346i
$535$	−5.28652			−0.228556
$536$	−6.56900	+	11.8518i	−0.283738	+	0.511922i
$537$	3.16476			0.136570
$538$	18.3247	+	3.12110i	0.790035	+	0.134560i
$539$		0			0
$540$	5.37664	−	15.3259i	0.231374	−	0.659523i
$541$			21.9905i			0.945446i	0.881211	+	0.472723i	$0.156729\pi$
$541$			21.9905i			0.945446i	−0.881211	+	0.472723i	$0.843271\pi$
$542$	15.7575	+	2.68385i	0.676844	+	0.115281i
$543$		−	14.4752i		−	0.621192i
$544$	25.5468	−	22.7376i	1.09531	−	0.974867i
$545$		−	16.6132i		−	0.711633i
$546$	−4.92393	−	0.838652i	−0.210725	−	0.0358910i
$547$	−25.3583			−1.08424			−0.542121	−	0.840301i	$-0.682378\pi$
$547$	−25.3583			−1.08424			−0.542121	+	0.840301i	$0.682378\pi$
$548$	−2.38256	−	0.835850i	−0.101778	−	0.0357057i
$549$			21.3398i			0.910762i
$550$		0			0
$551$		−	0.719286i		−	0.0306426i
$552$	16.4894	+	9.13943i	0.701837	+	0.389000i
$553$	6.16980			0.262367
$554$	−0.375560	+	2.20500i	−0.0159560	+	0.0936816i
$555$		−	0.582204i		−	0.0247132i
$556$	18.9660	+	6.65364i	0.804336	+	0.282177i
$557$		−	4.52743i		−	0.191834i	−0.995389	−	0.0959168i	$-0.969422\pi$
$557$		−	4.52743i		−	0.191834i	0.995389	−	0.0959168i	$-0.0305783\pi$
$558$	4.21446	−	24.7442i	0.178413	−	1.04750i
$559$		−	15.2162i		−	0.643575i
$560$	−12.8027	−	10.2437i	−0.541015	−	0.432874i
$561$		0			0
$562$	2.09315	−	12.2894i	0.0882940	−	0.518396i
$563$	−38.9984			−1.64359			−0.821793	−	0.569786i	$-0.807026\pi$
$563$	−38.9984			−1.64359			−0.821793	+	0.569786i	$0.807026\pi$
$564$	6.94619	+	2.43686i	0.292488	+	0.102610i
$565$	−18.4429			−0.775899
$566$	28.2706	+	4.81509i	1.18830	+	0.202393i
$567$	−5.06677			−0.212785
$568$	4.81536	−	8.68790i	0.202048	−	0.364536i
$569$			35.1994i			1.47564i	0.675000	+	0.737818i	$0.264144\pi$
$569$			35.1994i			1.47564i	−0.675000	+	0.737818i	$0.735856\pi$
$570$	−0.495694	+	2.91034i	−0.0207623	+	0.121901i
$571$	28.8320			1.20658			0.603291	−	0.797521i	$-0.293856\pi$
$571$	28.8320			1.20658			0.603291	+	0.797521i	$0.293856\pi$
$572$		0			0
$573$	6.54299			0.273337
$574$	2.89036	−	16.9700i	0.120641	−	0.708316i
$575$		−	14.9482i		−	0.623382i
$576$	9.14299	+	14.6294i	0.380958	+	0.609558i
$577$	−5.70243			−0.237395			−0.118698	−	0.992930i	$-0.537872\pi$
$577$	−5.70243			−0.237395			−0.118698	+	0.992930i	$0.537872\pi$
$578$	−27.2571	−	4.64246i	−1.13374	−	0.193101i
$579$	−15.4875			−0.643639
$580$	−0.616052	+	1.75603i	−0.0255802	+	0.0729153i
$581$	−9.49275			−0.393826
$582$	−1.81586	+	10.6614i	−0.0752700	+	0.441929i
$583$		0			0
$584$	−2.88217	+	5.20004i	−0.119265	+	0.215179i
$585$			5.94810i			0.245923i
$586$	−3.31287	+	19.4507i	−0.136853	+	0.803500i
$587$		−	42.2567i		−	1.74412i	−0.489400	−	0.872059i	$-0.662784\pi$
$587$		−	42.2567i		−	1.74412i	0.489400	−	0.872059i	$-0.337216\pi$
$588$	−0.781572	+	2.22784i	−0.0322315	+	0.0918747i
$589$			10.9098i			0.449532i
$590$	2.87119	−	16.8575i	0.118205	−	0.694012i
$591$	22.6734			0.932658
$592$	1.15462	+	0.923824i	0.0474544	+	0.0379689i
$593$			21.6694i			0.889855i	0.895567	+	0.444927i	$0.146771\pi$
$593$			21.6694i			0.889855i	−0.895567	+	0.444927i	$0.853229\pi$
$594$		0			0
$595$			24.7822i			1.01597i
$596$	−1.56455	+	4.45969i	−0.0640865	+	0.182676i
$597$	−14.4745			−0.592402
$598$	−16.2753	−	2.77203i	−0.665545	−	0.113357i
$599$		−	18.8378i		−	0.769693i	−0.922981	−	0.384846i	$-0.874254\pi$
$599$		−	18.8378i		−	0.769693i	0.922981	−	0.384846i	$-0.125746\pi$
$600$	−2.59395	+	4.68002i	−0.105898	+	0.191061i
$601$		−	15.1483i		−	0.617913i	−0.951076	−	0.308957i	$-0.900020\pi$
$601$		−	15.1483i		−	0.617913i	0.951076	−	0.308957i	$-0.0999798\pi$
$602$	31.5252	+	5.36942i	1.28487	+	0.218841i
$603$			10.3312i			0.420717i
$604$	36.0500	+	12.6471i	1.46685	+	0.514602i
$605$		0			0
$606$	−11.5623	−	1.96931i	−0.469687	−	0.0799977i
$607$	6.78889			0.275553			0.137776	−	0.990463i	$-0.456004\pi$
$607$	6.78889			0.275553			0.137776	+	0.990463i	$0.456004\pi$
$608$	−4.98518	−	5.60109i	−0.202176	−	0.227154i
$609$	−1.19144			−0.0482796
$610$	−4.02923	+	23.6566i	−0.163139	+	0.957828i
$611$	−6.44631			−0.260790
$612$	8.63171	−	24.6044i	0.348916	−	0.994573i
$613$		−	8.96542i		−	0.362110i	−0.983473	−	0.181055i	$-0.942049\pi$
$613$		−	8.96542i		−	0.362110i	0.983473	−	0.181055i	$-0.0579512\pi$
$614$	−8.20908	−	1.39818i	−0.331292	−	0.0564261i
$615$	8.01922			0.323366
$616$		0			0
$617$	41.7476			1.68069			0.840347	−	0.542049i	$-0.182351\pi$
$617$	41.7476			1.68069			0.840347	+	0.542049i	$0.182351\pi$
$618$	11.5166	+	1.96152i	0.463264	+	0.0789038i
$619$			6.05952i			0.243553i	0.992558	+	0.121776i	$0.0388590\pi$
$619$			6.05952i			0.243553i	−0.992558	+	0.121776i	$0.961141\pi$
$620$	9.34402	−	26.6348i	0.375265	−	1.06968i
$621$	34.3702			1.37923
$622$	6.22916	−	36.5729i	0.249766	−	1.46644i
$623$	20.2055			0.809517
$624$	4.61449	+	3.69212i	0.184727	+	0.147803i
$625$	−10.4587			−0.418346
$626$	−23.8841	−	4.06798i	−0.954603	−	0.162589i
$627$		0			0
$628$	18.5150	+	6.49544i	0.738829	+	0.259196i
$629$		−	2.23498i		−	0.0891146i
$630$	−12.3234	−	2.09894i	−0.490976	−	0.0836238i
$631$			16.0578i			0.639252i	0.947544	+	0.319626i	$0.103557\pi$
$631$			16.0578i			0.639252i	−0.947544	+	0.319626i	$0.896443\pi$
$632$	−6.38480	−	3.53884i	−0.253974	−	0.140767i
$633$		−	21.9453i		−	0.872248i
$634$	1.11139	+	0.189293i	0.0441388	+	0.00751778i
$635$	0.559736			0.0222125
$636$	−1.50725	+	4.29635i	−0.0597662	+	0.170362i
$637$		−	2.06752i		−	0.0819181i
$638$		0			0
$639$		−	7.57317i		−	0.299590i
$640$	7.37339	+	17.9439i	0.291459	+	0.709296i
$641$	−20.0847			−0.793300			−0.396650	−	0.917970i	$-0.629827\pi$
$641$	−20.0847			−0.793300			−0.396650	+	0.917970i	$0.629827\pi$
$642$	−0.672376	+	3.94769i	−0.0265366	+	0.155803i
$643$		−	4.36357i		−	0.172083i	−0.996292	−	0.0860413i	$-0.972578\pi$
$643$		−	4.36357i		−	0.172083i	0.996292	−	0.0860413i	$-0.0274217\pi$
$644$	11.4863	−	32.7413i	0.452624	−	1.29019i
$645$			14.8973i			0.586580i
$646$	−1.90288	+	11.1723i	−0.0748680	+	0.439569i
$647$		−	9.63189i		−	0.378669i	−0.981913	−	0.189334i	$-0.939367\pi$
$647$		−	9.63189i		−	0.378669i	0.981913	−	0.189334i	$-0.0606330\pi$
$648$	5.24334	+	2.90617i	0.205978	+	0.114165i
$649$		0			0
$650$	0.786755	−	4.61924i	0.0308591	−	0.181181i
$651$	18.0713			0.708269
$652$	9.43274	−	26.8877i	0.369415	−	1.05300i
$653$	18.2712			0.715009			0.357505	−	0.933911i	$-0.383628\pi$
$653$	18.2712			0.715009			0.357505	+	0.933911i	$0.383628\pi$
$654$	−12.4059	−	2.11299i	−0.485108	−	0.0826243i
$655$	18.5806			0.726005
$656$	−12.7247	+	15.9036i	−0.496814	+	0.620930i
$657$			4.53283i			0.176843i
$658$	2.27475	−	13.3556i	0.0886790	−	0.520656i
$659$	17.9779			0.700318			0.350159	−	0.936690i	$-0.386128\pi$
$659$	17.9779			0.700318			0.350159	+	0.936690i	$0.386128\pi$
$660$		0			0
$661$	2.57645			0.100212			0.0501062	−	0.998744i	$-0.484044\pi$
$661$	2.57645			0.100212			0.0501062	+	0.998744i	$0.484044\pi$
$662$	−5.05721	+	29.6921i	−0.196554	+	1.15402i
$663$		−	8.93224i		−	0.346900i
$664$	9.82354	+	5.44480i	0.381227	+	0.211299i
$665$	5.43345			0.210700
$666$	1.11139	+	0.189293i	0.0430653	+	0.00733495i
$667$	−3.93811			−0.152484
$668$	−0.132343	−	0.0464286i	−0.00512050	−	0.00179638i
$669$	17.3280			0.669939
$670$	−1.95065	+	11.4528i	−0.0753602	+	0.442459i
$671$		0			0
$672$	−9.27776	+	8.25754i	−0.357897	+	0.318542i
$673$		−	34.3360i		−	1.32355i	−0.749701	−	0.661777i	$-0.769802\pi$
$673$		−	34.3360i		−	1.32355i	0.749701	−	0.661777i	$-0.230198\pi$
$674$	2.58249	−	15.1624i	0.0994738	−	0.584036i
$675$			9.75493i			0.375467i
$676$	19.6506	+	6.89383i	0.755792	+	0.265147i
$677$			17.2604i			0.663370i	0.943390	+	0.331685i	$0.107617\pi$
$677$			17.2604i			0.663370i	−0.943390	+	0.331685i	$0.892383\pi$
$678$	−2.34570	+	13.7722i	−0.0900859	+	0.528917i
$679$	19.9043			0.763856
$680$	14.2144	−	25.6458i	0.545099	−	0.983471i
$681$		−	10.3496i		−	0.396598i
$682$		0			0
$683$		−	0.254052i		−	0.00972104i	−0.999988	−	0.00486052i	$-0.998453\pi$
$683$		−	0.254052i		−	0.00972104i	0.999988	−	0.00486052i	$-0.00154716\pi$
$684$	−5.39447	−	1.89249i	−0.206263	−	0.0723610i
$685$	−2.16476			−0.0827113
$686$	27.6128	+	4.70305i	1.05426	+	0.179563i
$687$		−	20.0700i		−	0.765717i
$688$	−29.5440	−	23.6386i	−1.12635	−	0.901212i
$689$		−	3.98717i		−	0.151899i
$690$	15.9342	+	2.71393i	0.606604	+	0.103318i
$691$		−	9.48528i		−	0.360837i	−0.983590	−	0.180419i	$-0.942255\pi$
$691$		−	9.48528i		−	0.360837i	0.983590	−	0.180419i	$-0.0577452\pi$
$692$	13.1278	−	37.4202i	0.499043	−	1.42250i
$693$		0			0
$694$	−0.897175	−	0.152808i	−0.0340563	−	0.00580052i
$695$	17.2322			0.653656
$696$	1.23296	+	0.683379i	0.0467351	+	0.0259034i
$697$	30.7844			1.16604
$698$	4.10309	−	24.0903i	0.155304	−	0.911829i
$699$	−5.83515			−0.220706
$700$	9.29261	+	3.26004i	0.351228	+	0.123218i
$701$		−	8.57977i		−	0.324053i	−0.986786	−	0.162027i	$-0.948197\pi$
$701$		−	8.57977i		−	0.324053i	0.986786	−	0.162027i	$-0.0518031\pi$
$702$	10.6210	+	1.80898i	0.400863	+	0.0682756i
$703$	−0.490016			−0.0184813
$704$		0			0
$705$	6.31122			0.237694
$706$	−39.5691	−	6.73946i	−1.48920	−	0.253643i
$707$			21.5862i			0.811834i
$708$	−12.2231	−	4.28811i	−0.459372	−	0.161157i
$709$	6.91669			0.259762			0.129881	−	0.991530i	$-0.458541\pi$
$709$	6.91669			0.259762			0.129881	+	0.991530i	$0.458541\pi$
$710$	1.42991	−	8.39535i	0.0536635	−	0.315072i
$711$	−5.56558			−0.208725
$712$	−20.9096	−	11.5894i	−0.783621	−	0.434329i
$713$	59.7317			2.23697
$714$	18.5060	+	3.15197i	0.692571	+	0.117960i
$715$		0			0
$716$	−2.28135	+	6.50290i	−0.0852580	+	0.243025i
$717$			13.7357i			0.512969i
$718$	−39.8073	−	6.78003i	−1.48559	−	0.253029i
$719$			19.0320i			0.709774i	0.934909	+	0.354887i	$0.115481\pi$
$719$			19.0320i			0.709774i	−0.934909	+	0.354887i	$0.884519\pi$
$720$	11.5489	+	9.24046i	0.430403	+	0.344372i
$721$		−	21.5008i		−	0.800732i
$722$	−24.0391	−	4.09437i	−0.894642	−	0.152377i
$723$	−0.420071			−0.0156226
$724$	29.7435	+	10.4346i	1.10541	+	0.387799i
$725$		−	1.11771i		−	0.0415108i
$726$		0			0
$727$		−	19.7014i		−	0.730685i	−0.930873	−	0.365342i	$-0.880952\pi$
$727$		−	19.7014i		−	0.730685i	0.930873	−	0.365342i	$-0.119048\pi$
$728$	5.27271	−	9.51307i	0.195420	−	0.352578i
$729$	−8.47882			−0.314030
$730$	−0.855855	+	5.02494i	−0.0316766	+	0.185981i
$731$			57.1882i			2.11518i
$732$	17.1530	+	6.01762i	0.633994	+	0.222418i
$733$			49.8315i			1.84057i	0.391249	+	0.920285i	$0.372043\pi$
$733$			49.8315i			1.84057i	−0.391249	+	0.920285i	$0.627957\pi$
$734$	−0.0924704	+	0.542917i	−0.00341314	+	0.0200394i
$735$			2.02419i			0.0746633i
$736$	−30.6661	+	27.2940i	−1.13037	+	1.00607i
$737$		0			0
$738$	−2.60730	+	15.3081i	−0.0959761	+	0.563500i
$739$	16.4239			0.604163			0.302082	−	0.953282i	$-0.402318\pi$
$739$	16.4239			0.604163			0.302082	+	0.953282i	$0.402318\pi$
$740$	1.19630	+	0.419687i	0.0439770	+	0.0154280i
$741$	−1.95838			−0.0719428
$742$	8.26071	+	1.40698i	0.303260	+	0.0516517i
$743$	2.99103			0.109730			0.0548652	−	0.998494i	$-0.482527\pi$
$743$	2.99103			0.109730			0.0548652	+	0.998494i	$0.482527\pi$
$744$	−18.7010	−	10.3652i	−0.685612	−	0.380007i
$745$			4.05202i			0.148454i
$746$	−2.36300	+	13.8737i	−0.0865155	+	0.507954i
$747$	8.56310			0.313307
$748$		0			0
$749$	7.37013			0.269299
$750$	−2.64007	+	15.5005i	−0.0964018	+	0.565999i
$751$		−	41.6152i		−	1.51856i	−0.650764	−	0.759280i	$-0.725551\pi$
$751$		−	41.6152i		−	1.51856i	0.650764	−	0.759280i	$-0.274449\pi$
$752$	−10.0145	+	12.5163i	−0.365190	+	0.456422i
$753$	11.6790			0.425605
$754$	−1.21694	−	0.207272i	−0.0443185	−	0.00754839i
$755$	32.7545			1.19206
$756$	−7.49577	+	21.3664i	−0.272619	+	0.777090i
$757$	−22.8923			−0.832036			−0.416018	−	0.909356i	$-0.636575\pi$
$757$	−22.8923			−0.832036			−0.416018	+	0.909356i	$0.636575\pi$
$758$	4.77572	−	28.0394i	0.173462	−	1.01844i
$759$		0			0
$760$	−5.62279	−	3.11649i	−0.203960	−	0.113047i
$761$			47.9435i			1.73795i	0.494855	+	0.868975i	$0.335221\pi$
$761$			47.9435i			1.73795i	−0.494855	+	0.868975i	$0.664779\pi$
$762$	0.0711912	−	0.417981i	0.00257898	−	0.0151419i
$763$			23.1611i			0.838489i
$764$	−4.71657	+	13.4444i	−0.170640	+	0.486402i
$765$		−	22.3552i		−	0.808255i
$766$	2.44139	−	14.3340i	0.0882110	−	0.517909i
$767$	11.3435			0.409589
$768$	14.3374	−	3.22381i	0.517355	−	0.116329i
$769$			43.0718i			1.55321i	0.629989	+	0.776604i	$0.283059\pi$
$769$			43.0718i			1.55321i	−0.629989	+	0.776604i	$0.716941\pi$
$770$		0			0
$771$			1.36936i			0.0493164i
$772$	11.1643	−	31.8235i	0.401812	−	1.14535i
$773$	−12.8534			−0.462304			−0.231152	−	0.972918i	$-0.574249\pi$
$773$	−12.8534			−0.462304			−0.231152	+	0.972918i	$0.574249\pi$
$774$	−28.4378	−	4.84358i	−1.02218	−	0.174099i
$775$			16.9530i			0.608970i
$776$	−20.5979	−	11.4166i	−0.739420	−	0.409831i
$777$			0.811672i			0.0291186i
$778$	−26.8788	−	4.57803i	−0.963650	−	0.164130i
$779$		−	6.74943i		−	0.241823i
$780$	4.78109	+	1.67730i	0.171191	+	0.0600571i
$781$		0			0
$782$	61.1687	+	10.4183i	2.18739	+	0.372559i
$783$	2.56995			0.0918424
$784$	−4.01433	−	3.21192i	−0.143369	−	0.114712i
$785$	16.8225			0.600420
$786$	2.36321	−	13.8750i	0.0842931	−	0.494906i
$787$	−39.8671			−1.42111			−0.710555	−	0.703642i	$-0.751556\pi$
$787$	−39.8671			−1.42111			−0.710555	+	0.703642i	$0.751556\pi$
$788$	−16.3443	+	46.5888i	−0.582242	+	1.65966i
$789$		−	13.5546i		−	0.482557i
$790$	−6.16980	−	1.05085i	−0.219512	−	0.0373876i
$791$	25.7119			0.914211
$792$		0			0
$793$	−15.9186			−0.565287
$794$	53.1208	+	9.04761i	1.88519	+	0.321088i
$795$			3.90361i			0.138447i
$796$	10.4341	−	29.7420i	0.369826	−	1.05418i
$797$	−26.8921			−0.952568			−0.476284	−	0.879292i	$-0.658016\pi$
$797$	−26.8921			−0.952568			−0.476284	+	0.879292i	$0.658016\pi$
$798$	0.691064	−	4.05741i	0.0244634	−	0.143631i
$799$	24.2277			0.857115
$800$	−7.74656	−	8.70364i	−0.273882	−	0.307720i
$801$	−18.2267			−0.644010
$802$	−5.78815	−	0.985846i	−0.204387	−	0.0348114i
$803$		0			0
$804$	8.30421	+	2.91328i	0.292867	+	0.102744i
$805$		−	29.7483i		−	1.04849i
$806$	18.4581	+	3.14381i	0.650159	+	0.110736i
$807$		−	12.0724i		−	0.424967i
$808$	12.3813	−	22.3384i	0.435572	−	0.785863i
$809$		−	11.5994i		−	0.407811i	−0.978991	−	0.203906i	$-0.934636\pi$
$809$		−	11.5994i		−	0.407811i	0.978991	−	0.203906i	$-0.0653636\pi$
$810$	5.06677	+	0.862981i	0.178028	+	0.0303221i
$811$	36.6094			1.28553			0.642766	−	0.766063i	$-0.277787\pi$
$811$	36.6094			1.28553			0.642766	+	0.766063i	$0.277787\pi$
$812$	0.858860	−	2.44815i	0.0301401	−	0.0859132i
$813$		−	10.3811i		−	0.364080i
$814$		0			0
$815$		−	24.4298i		−	0.855738i
$816$	−17.3430	−	13.8764i	−0.607127	−	0.485771i
$817$	12.5384			0.438663
$818$	2.68843	−	15.7844i	0.0939986	−	0.551889i
$819$		−	8.29246i		−	0.289762i
$820$	−5.78073	+	16.4778i	−0.201872	+	0.575428i
$821$		−	31.7120i		−	1.10676i	−0.832930	−	0.553379i	$-0.813338\pi$
$821$		−	31.7120i		−	1.10676i	0.832930	−	0.553379i	$-0.186662\pi$
$822$	−0.275329	+	1.61653i	−0.00960322	+	0.0563829i
$823$			18.4601i			0.643477i	0.946829	+	0.321739i	$0.104267\pi$
$823$			18.4601i			0.643477i	−0.946829	+	0.321739i	$0.895733\pi$
$824$	−12.3323	+	22.2500i	−0.429616	+	0.775117i
$825$		0			0
$826$	−4.00284	+	23.5016i	−0.139276	+	0.817727i
$827$	18.9347			0.658424			0.329212	−	0.944256i	$-0.393217\pi$
$827$	18.9347			0.658424			0.329212	+	0.944256i	$0.393217\pi$
$828$	−10.3614	+	29.5348i	−0.360084	+	1.02641i
$829$	8.19150			0.284503			0.142251	−	0.989831i	$-0.454566\pi$
$829$	8.19150			0.284503			0.142251	+	0.989831i	$0.454566\pi$
$830$	9.49275	+	1.61682i	0.329498	+	0.0561206i
$831$	1.45266			0.0503922
$832$	−10.9129	+	6.82028i	−0.378337	+	0.236451i
$833$			7.77052i			0.269233i
$834$	2.19171	−	12.8681i	0.0758929	−	0.445586i
$835$	−0.120245			−0.00416125
$836$		0			0
$837$	−38.9799			−1.34734
$838$	−5.03622	+	29.5689i	−0.173973	+	1.02144i
$839$			36.3391i			1.25457i	0.778791	+	0.627283i	$0.215833\pi$
$839$			36.3391i			1.25457i	−0.778791	+	0.627283i	$0.784167\pi$
$840$	−5.16221	+	9.31370i	−0.178113	+	0.321353i
$841$	28.7055			0.989846
$842$	34.5514	+	5.88484i	1.19072	+	0.202805i
$843$	−8.09626			−0.278850
$844$	45.0928	+	15.8195i	1.55216	+	0.544529i
$845$	17.8543			0.614206
$846$	−2.05198	+	12.0477i	−0.0705484	+	0.414207i
$847$		0			0
$848$	−7.74156	−	6.19413i	−0.265846	−	0.212707i
$849$		−	18.6247i		−	0.639199i
$850$	−2.95693	+	17.3609i	−0.101422	+	0.595472i
$851$			2.68285i			0.0919669i
$852$	−6.08733	−	2.13556i	−0.208549	−	0.0731630i
$853$		−	11.8909i		−	0.407137i	−0.979061	−	0.203569i	$-0.934746\pi$
$853$		−	11.8909i		−	0.407137i	0.979061	−	0.203569i	$-0.0652540\pi$
$854$	5.61730	−	32.9805i	0.192220	−	1.12857i
$855$	−4.90134			−0.167622
$856$	−7.62696	−	4.22732i	−0.260684	−	0.144487i
$857$		−	35.7039i		−	1.21962i	−0.792547	−	0.609811i	$-0.791245\pi$
$857$		−	35.7039i		−	1.21962i	0.792547	−	0.609811i	$-0.208755\pi$
$858$		0			0
$859$		−	40.2518i		−	1.37337i	−0.726953	−	0.686687i	$-0.759064\pi$
$859$		−	40.2518i		−	1.37337i	0.726953	−	0.686687i	$-0.240936\pi$
$860$	−30.6107	−	10.7388i	−1.04382	−	0.366191i
$861$	−11.1799			−0.381009
$862$	2.46387	+	0.419650i	0.0839198	+	0.0142933i
$863$			18.1901i			0.619197i	0.950867	+	0.309599i	$0.100195\pi$
$863$			18.1901i			0.619197i	−0.950867	+	0.309599i	$0.899805\pi$
$864$	20.0122	−	17.8116i	0.680829	−	0.605963i
$865$		−	33.9995i		−	1.15602i
$866$	−45.9388	−	7.82436i	−1.56106	−	0.265883i
$867$			17.9570i			0.609851i
$868$	−13.0268	+	37.1325i	−0.442160	+	1.26036i
$869$		0			0
$870$	1.19144	+	0.202928i	0.0403936	+	0.00687990i
$871$	−7.70660			−0.261128
$872$	13.2846	−	23.9682i	0.449874	−	0.811666i
$873$	−17.9550			−0.607684
$874$	2.28420	−	13.4111i	0.0772643	−	0.453638i
$875$	28.9387			0.978306
$876$	3.64350	+	1.27821i	0.123102	+	0.0431868i
$877$			39.9426i			1.34877i	0.738382	+	0.674383i	$0.235590\pi$
$877$			39.9426i			1.34877i	−0.738382	+	0.674383i	$0.764410\pi$
$878$	−38.1324	−	6.49476i	−1.28691	−	0.219188i
$879$	12.8141			0.432210
$880$		0			0
$881$	21.8173			0.735045			0.367522	−	0.930015i	$-0.380206\pi$
$881$	21.8173			0.735045			0.367522	+	0.930015i	$0.380206\pi$
$882$	−3.86403	−	0.658128i	−0.130109	−	0.0221603i
$883$			15.4310i			0.519294i	0.965704	+	0.259647i	$0.0836063\pi$
$883$			15.4310i			0.519294i	−0.965704	+	0.259647i	$0.916394\pi$
$884$	18.3538	+	6.43889i	0.617306	+	0.216563i
$885$	−11.1057			−0.373315
$886$	−0.402558	+	2.36352i	−0.0135242	+	0.0794039i
$887$	16.9342			0.568596			0.284298	−	0.958736i	$-0.408240\pi$
$887$	16.9342			0.568596			0.284298	+	0.958736i	$0.408240\pi$
$888$	0.465554	−	0.839956i	0.0156230	−	0.0281871i
$889$	−0.780349			−0.0261721
$890$	−20.2055	−	3.44143i	−0.677290	−	0.115357i
$891$		0			0
$892$	−12.4910	+	35.6053i	−0.418231	+	1.19215i
$893$		−	5.31188i		−	0.177755i
$894$	3.02583	+	0.515364i	0.101199	+	0.0172363i
$895$			5.90845i			0.197498i
$896$	−10.2795	−	25.0163i	−0.343414	−	0.835736i
$897$			10.7222i			0.358003i
$898$	−25.8376	−	4.40071i	−0.862213	−	0.146853i
$899$	4.46629			0.148959
$900$	−8.38256	−	2.94077i	−0.279419	−	0.0980257i
$901$			14.9853i			0.499233i
$902$		0			0
$903$		−	20.7688i		−	0.691144i
$904$	−26.6079	−	14.7477i	−0.884966	−	0.490501i
$905$	27.0245			0.898326
$906$	4.16595	−	24.4593i	0.138404	−	0.812607i
$907$		−	24.9435i		−	0.828237i	−0.910223	−	0.414118i	$-0.864090\pi$
$907$		−	24.9435i		−	0.828237i	0.910223	−	0.414118i	$-0.135910\pi$
$908$	21.2662	+	7.46061i	0.705744	+	0.247589i
$909$		−	19.4722i		−	0.645853i
$910$	1.56572	−	9.19273i	0.0519031	−	0.304736i
$911$			44.4084i			1.47132i	0.677353	+	0.735658i	$0.263127\pi$
$911$			44.4084i			1.47132i	−0.677353	+	0.735658i	$0.736873\pi$
$912$	−3.04237	+	3.80242i	−0.100743	+	0.125911i
$913$		0			0
$914$	−2.58419	+	15.1724i	−0.0854773	+	0.501858i
$915$	15.5850			0.515224
$916$	41.2394	+	14.4676i	1.36259	+	0.478024i
$917$	−25.9039			−0.855424
$918$	−39.9177	−	6.79884i	−1.31748	−	0.224395i
$919$	−48.4576			−1.59847			−0.799234	−	0.601019i	$-0.794761\pi$
$919$	−48.4576			−1.59847			−0.799234	+	0.601019i	$0.794761\pi$
$920$	−17.0628	+	30.7849i	−0.562546	+	1.01495i
$921$			5.40815i			0.178205i
$922$	3.28343	−	19.2778i	0.108134	−	0.634881i
$923$	5.64926			0.185948
$924$		0			0
$925$	−0.761445			−0.0250362
$926$	−8.87254	+	52.0929i	−0.291570	+	1.71188i
$927$			19.3952i			0.637021i
$928$	−2.29298	+	2.04084i	−0.0752709	+	0.0669939i
$929$	22.3889			0.734555			0.367277	−	0.930111i	$-0.380290\pi$
$929$	22.3889			0.734555			0.367277	+	0.930111i	$0.380290\pi$
$930$	−18.0713	−	3.07793i	−0.592580	−	0.100929i
$931$	1.70367			0.0558356
$932$	4.20632	−	11.9900i	0.137783	−	0.392744i
$933$	−24.0943			−0.788812
$934$	3.27570	−	19.2324i	0.107184	−	0.629305i
$935$		0			0
$936$	−4.75634	+	8.58142i	−0.155466	+	0.280493i
$937$			35.9715i			1.17514i	0.809174	+	0.587569i	$0.199915\pi$
$937$			35.9715i			1.17514i	−0.809174	+	0.587569i	$0.800085\pi$
$938$	2.71947	−	15.9667i	0.0887940	−	0.521331i
$939$			15.7349i			0.513489i
$940$	−4.54950	+	12.9682i	−0.148388	+	0.422976i
$941$			49.5835i			1.61638i	0.588925	+	0.808188i	$0.299551\pi$
$941$			49.5835i			1.61638i	−0.588925	+	0.808188i	$0.700449\pi$
$942$	2.13960	−	12.5621i	0.0697120	−	0.409296i
$943$	−36.9533			−1.20337
$944$	17.6223	−	22.0247i	0.573556	−	0.716842i
$945$			19.4133i			0.631513i
$946$		0			0
$947$		−	45.1846i		−	1.46830i	−0.678985	−	0.734152i	$-0.737580\pi$
$947$		−	45.1846i		−	1.46830i	0.678985	−	0.734152i	$-0.262420\pi$
$948$	−1.56944	+	4.47362i	−0.0509730	+	0.145297i
$949$	−3.38130			−0.109762
$950$	3.80634	+	0.648301i	0.123494	+	0.0210337i
$951$		−	0.732182i		−	0.0237426i
$952$	−19.8169	+	35.7537i	−0.642268	+	1.15879i
$953$			29.7930i			0.965089i	0.875871	+	0.482545i	$0.160287\pi$
$953$			29.7930i			0.965089i	−0.875871	+	0.482545i	$0.839713\pi$
$954$	−7.45171	−	1.26919i	−0.241258	−	0.0410914i
$955$			12.2154i			0.395282i
$956$	−28.2239	−	9.90149i	−0.912825	−	0.320237i
$957$		0			0
$958$	−18.8307	−	3.20728i	−0.608393	−	0.103622i
$959$	3.01797			0.0974555
$960$	10.6842	−	6.67734i	0.344831	−	0.215510i
$961$	−36.7428			−1.18525
$962$	−0.141204	+	0.829046i	−0.00455261	+	0.0267295i
$963$	−6.64835			−0.214240
$964$	0.302812	−	0.863155i	0.00975292	−	0.0278004i
$965$		−	28.9144i		−	0.930787i
$966$	−22.2144	−	3.78360i	−0.714738	−	0.121735i
$967$	−2.10906			−0.0678227			−0.0339113	−	0.999425i	$-0.510796\pi$
$967$	−2.10906			−0.0678227			−0.0339113	+	0.999425i	$0.510796\pi$
$968$		0			0
$969$	7.36033			0.236448
$970$	−19.9043	−	3.39012i	−0.639087	−	0.108850i
$971$		−	57.4340i		−	1.84314i	−0.388207	−	0.921572i	$-0.626906\pi$
$971$		−	57.4340i		−	1.84314i	0.388207	−	0.921572i	$-0.373094\pi$
$972$	10.6956	−	30.4875i	0.343062	−	0.977887i
$973$	−24.0241			−0.770177
$974$	−8.48619	+	49.8246i	−0.271915	+	1.59648i
$975$	−3.04316			−0.0974591
$976$	−24.7298	+	30.9079i	−0.791582	+	0.989337i
$977$	5.22956			0.167308			0.0836542	−	0.996495i	$-0.473341\pi$
$977$	5.22956			0.167308			0.0836542	+	0.996495i	$0.473341\pi$
$978$	−18.2429	−	3.10715i	−0.583342	−	0.0993557i
$979$		0			0
$980$	−4.15927	−	1.45916i	−0.132863	−	0.0466110i
$981$		−	20.8929i		−	0.667058i
$982$	−56.2514	−	9.58082i	−1.79505	−	0.305736i
$983$		−	28.5578i		−	0.910854i	−0.890273	−	0.455427i	$-0.849487\pi$
$983$		−	28.5578i		−	0.910854i	0.890273	−	0.455427i	$-0.150513\pi$
$984$	11.5695	+	6.41249i	0.368821	+	0.204423i
$985$			42.3300i			1.34875i
$986$	4.57374	+	0.779006i	0.145658	+	0.0248086i
$987$	−8.79870			−0.280066
$988$	1.41171	−	4.02404i	0.0449126	−	0.128022i
$989$		−	68.6481i		−	2.18288i
$990$		0			0
$991$		−	0.537995i		−	0.0170900i	−0.999963	−	0.00854499i	$-0.997280\pi$
$991$		−	0.537995i		−	0.0170900i	0.999963	−	0.00854499i	$-0.00271999\pi$
$992$	34.7790	−	30.9546i	1.10424	−	0.982810i
$993$	19.5612			0.620757
$994$	−1.99349	+	11.7043i	−0.0632296	+	0.371237i
$995$		−	27.0232i		−	0.856692i
$996$	2.41471	−	6.88304i	0.0765130	−	0.218097i
$997$		−	24.2970i		−	0.769494i	−0.923022	−	0.384747i	$-0.874289\pi$
$997$		−	24.2970i		−	0.769494i	0.923022	−	0.384747i	$-0.125711\pi$
$998$	−0.966484	+	5.67447i	−0.0305935	+	0.179622i
$999$		−	1.75078i		−	0.0553924i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.c.d.483.16		16
4.3	odd	2	inner	484.2.c.d.483.2		16
11.2	odd	10		484.2.g.f.403.4		16
11.3	even	5		484.2.g.i.475.2		16
11.4	even	5		44.2.g.a.39.4	yes	16
11.5	even	5		484.2.g.f.239.1		16
11.6	odd	10		484.2.g.j.239.4		16
11.7	odd	10		484.2.g.i.215.1		16
11.8	odd	10		44.2.g.a.35.3	✓	16
11.9	even	5		484.2.g.j.403.1		16
11.10	odd	2	inner	484.2.c.d.483.1		16
33.8	even	10		396.2.r.a.343.2		16
33.26	odd	10		396.2.r.a.127.1		16
44.3	odd	10		484.2.g.i.475.1		16
44.7	even	10		484.2.g.i.215.2		16
44.15	odd	10		44.2.g.a.39.3	yes	16
44.19	even	10		44.2.g.a.35.4	yes	16
44.27	odd	10		484.2.g.f.239.4		16
44.31	odd	10		484.2.g.j.403.4		16
44.35	even	10		484.2.g.f.403.1		16
44.39	even	10		484.2.g.j.239.1		16
44.43	even	2	inner	484.2.c.d.483.15		16
88.19	even	10		704.2.u.c.255.3		16
88.37	even	10		704.2.u.c.127.3		16
88.59	odd	10		704.2.u.c.127.2		16
88.85	odd	10		704.2.u.c.255.2		16
132.59	even	10		396.2.r.a.127.2		16
132.107	odd	10		396.2.r.a.343.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.35.3	✓	16	11.8	odd	10
44.2.g.a.35.4	yes	16	44.19	even	10
44.2.g.a.39.3	yes	16	44.15	odd	10
44.2.g.a.39.4	yes	16	11.4	even	5
396.2.r.a.127.1		16	33.26	odd	10
396.2.r.a.127.2		16	132.59	even	10
396.2.r.a.343.1		16	132.107	odd	10
396.2.r.a.343.2		16	33.8	even	10
484.2.c.d.483.1		16	11.10	odd	2	inner
484.2.c.d.483.2		16	4.3	odd	2	inner
484.2.c.d.483.15		16	44.43	even	2	inner
484.2.c.d.483.16		16	1.1	even	1	trivial
484.2.g.f.239.1		16	11.5	even	5
484.2.g.f.239.4		16	44.27	odd	10
484.2.g.f.403.1		16	44.35	even	10
484.2.g.f.403.4		16	11.2	odd	10
484.2.g.i.215.1		16	11.7	odd	10
484.2.g.i.215.2		16	44.7	even	10
484.2.g.i.475.1		16	44.3	odd	10
484.2.g.i.475.2		16	11.3	even	5
484.2.g.j.239.1		16	44.39	even	10
484.2.g.j.239.4		16	11.6	odd	10
484.2.g.j.403.1		16	11.9	even	5
484.2.g.j.403.4		16	44.31	odd	10
704.2.u.c.127.2		16	88.59	odd	10
704.2.u.c.127.3		16	88.37	even	10
704.2.u.c.255.2		16	88.85	odd	10
704.2.u.c.255.3		16	88.19	even	10

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39414 + 0.237451i) q^{2} -0.918459i q^{3} +(1.88723 + 0.662079i) q^{4} +1.71472 q^{5} +(0.218089 - 1.28046i) q^{6} -2.39055 q^{7} +(2.47385 + 1.37116i) q^{8} +2.15643 q^{9} +O(q^{10})\)	\(q+(1.39414 + 0.237451i) q^{2} -0.918459i q^{3} +(1.88723 + 0.662079i) q^{4} +1.71472 q^{5} +(0.218089 - 1.28046i) q^{6} -2.39055 q^{7} +(2.47385 + 1.37116i) q^{8} +2.15643 q^{9} +(2.39055 + 0.407162i) q^{10} +(0.608093 - 1.73335i) q^{12} +1.60861i q^{13} +(-3.33275 - 0.567639i) q^{14} -1.57490i q^{15} +(3.12330 + 2.49900i) q^{16} -6.04576i q^{17} +(3.00636 + 0.512048i) q^{18} -1.32552 q^{19} +(3.23607 + 1.13528i) q^{20} +2.19562i q^{21} +7.25726i q^{23} +(1.25935 - 2.27213i) q^{24} -2.05975 q^{25} +(-0.381966 + 2.24262i) q^{26} -4.73597i q^{27} +(-4.51152 - 1.58273i) q^{28} +0.542644i q^{29} +(0.373961 - 2.19562i) q^{30} -8.23060i q^{31} +(3.76092 + 4.22558i) q^{32} +(1.43557 - 8.42861i) q^{34} -4.09911 q^{35} +(4.06969 + 1.42773i) q^{36} +0.369678 q^{37} +(-1.84796 - 0.314747i) q^{38} +1.47744 q^{39} +(4.24195 + 2.35114i) q^{40} +5.09191i q^{41} +(-0.521353 + 3.06099i) q^{42} -9.45922 q^{43} +3.69767 q^{45} +(-1.72325 + 10.1176i) q^{46} +4.00739i q^{47} +(2.29523 - 2.86862i) q^{48} -1.28528 q^{49} +(-2.87158 - 0.489091i) q^{50} -5.55278 q^{51} +(-1.06503 + 3.03582i) q^{52} -2.47865 q^{53} +(1.12456 - 6.60259i) q^{54} +(-5.91385 - 3.27781i) q^{56} +1.21744i q^{57} +(-0.128852 + 0.756520i) q^{58} -7.05173i q^{59} +(1.04271 - 2.97220i) q^{60} +9.89590i q^{61} +(1.95437 - 11.4746i) q^{62} -5.15506 q^{63} +(4.23987 + 6.78407i) q^{64} +2.75830i q^{65} +4.79085i q^{67} +(4.00277 - 11.4098i) q^{68} +6.66550 q^{69} +(-5.71472 - 0.973339i) q^{70} -3.51190i q^{71} +(5.33469 + 2.95681i) q^{72} +2.10200i q^{73} +(0.515382 + 0.0877806i) q^{74} +1.89180i q^{75} +(-2.50157 - 0.877601i) q^{76} +(2.05975 + 0.350820i) q^{78} -2.58092 q^{79} +(5.35557 + 4.28507i) q^{80} +2.11950 q^{81} +(-1.20908 + 7.09881i) q^{82} +3.97095 q^{83} +(-1.45367 + 4.14365i) q^{84} -10.3668i q^{85} +(-13.1874 - 2.24611i) q^{86} +0.498396 q^{87} -8.45225 q^{89} +(5.15506 + 0.878017i) q^{90} -3.84545i q^{91} +(-4.80489 + 13.6962i) q^{92} -7.55947 q^{93} +(-0.951560 + 5.58685i) q^{94} -2.27289 q^{95} +(3.88102 - 3.45425i) q^{96} -8.32624 q^{97} +(-1.79186 - 0.305193i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^5	\( 16 q + 4 q^{4} + 4 q^{5} - 22 q^{12} - 12 q^{14} - 12 q^{16} + 16 q^{20} - 4 q^{25} - 24 q^{26} - 6 q^{34} + 50 q^{36} - 12 q^{37} + 42 q^{38} + 4 q^{42} + 40 q^{45} + 74 q^{48} - 44 q^{49} - 52 q^{53} - 12 q^{56} - 60 q^{58} - 8 q^{60} + 28 q^{64} + 24 q^{69} - 68 q^{70} + 4 q^{78} - 8 q^{80} - 24 q^{81} + 26 q^{82} - 14 q^{86} - 36 q^{89} + 36 q^{92} + 72 q^{93} - 8 q^{97}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^5 - 22 * q^12 - 12 * q^14 - 12 * q^16 + 16 * q^20 - 4 * q^25 - 24 * q^26 - 6 * q^34 + 50 * q^36 - 12 * q^37 + 42 * q^38 + 4 * q^42 + 40 * q^45 + 74 * q^48 - 44 * q^49 - 52 * q^53 - 12 * q^56 - 60 * q^58 - 8 * q^60 + 28 * q^64 + 24 * q^69 - 68 * q^70 + 4 * q^78 - 8 * q^80 - 24 * q^81 + 26 * q^82 - 14 * q^86 - 36 * q^89 + 36 * q^92 + 72 * q^93 - 8 * q^97

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