LMFDB - Embedded newform 819.2.do.g.667.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(361,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 5]))

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

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

chi := DirichletCharacter("819.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.do (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 $ x^20 + 33x^18 + 455x^16 + 3403x^14 + 15006x^12 + 39799x^10 + 62505x^8 + 55993x^6 + 27166x^4 + 6435*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			667.8
Root			$2.04830i$ of defining polynomial
Character	$\chi$	$=$	819.667
Dual form			819.2.do.g.361.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.77388 - 1.02415i) q^{2} +(1.09777 - 1.90140i) q^{4} +(0.341406 + 0.197111i) q^{5} +(1.69809 + 2.02891i) q^{7} -0.400534i q^{8} +O(q^{10})$	\(q+(1.77388 - 1.02415i) q^{2} +(1.09777 - 1.90140i) q^{4} +(0.341406 + 0.197111i) q^{5} +(1.69809 + 2.02891i) q^{7} -0.400534i q^{8} +0.807484 q^{10} -1.56708i q^{11} +(1.46617 - 3.29398i) q^{13} +(5.09013 + 1.85994i) q^{14} +(1.78534 + 3.09229i) q^{16} +(3.41367 - 5.91265i) q^{17} +7.79477i q^{19} +(0.749571 - 0.432765i) q^{20} +(-1.60493 - 2.77982i) q^{22} +(2.39173 + 4.14260i) q^{23} +(-2.42229 - 4.19554i) q^{25} +(-0.772719 - 7.34472i) q^{26} +(5.72188 - 1.00147i) q^{28} +(3.94172 - 6.82725i) q^{29} +(-5.14505 + 2.97049i) q^{31} +(7.02770 + 4.05744i) q^{32} -13.9845i q^{34} +(0.179819 + 1.02739i) q^{35} +(1.01661 - 0.586939i) q^{37} +(7.98303 + 13.8270i) q^{38} +(0.0789495 - 0.136745i) q^{40} +(-6.17054 - 3.56256i) q^{41} +(3.65167 + 6.32487i) q^{43} +(-2.97964 - 1.72030i) q^{44} +(8.48530 + 4.89899i) q^{46} +(-4.92450 - 2.84316i) q^{47} +(-1.23296 + 6.89056i) q^{49} +(-8.59373 - 4.96159i) q^{50} +(-4.65365 - 6.40382i) q^{52} +(0.964998 + 1.67143i) q^{53} +(0.308888 - 0.535010i) q^{55} +(0.812648 - 0.680144i) q^{56} -16.1477i q^{58} +(-9.91907 - 5.72678i) q^{59} -12.2675 q^{61} +(-6.08447 + 10.5386i) q^{62} +9.48040 q^{64} +(1.14984 - 0.835586i) q^{65} -2.79011i q^{67} +(-7.49487 - 12.9815i) q^{68} +(1.37118 + 1.63831i) q^{70} +(-7.66430 + 4.42499i) q^{71} +(2.23575 - 1.29081i) q^{73} +(1.20223 - 2.08232i) q^{74} +(14.8210 + 8.55689i) q^{76} +(3.17947 - 2.66105i) q^{77} +(1.55611 - 2.69526i) q^{79} +1.40764i q^{80} -14.5944 q^{82} -3.01153i q^{83} +(2.33089 - 1.34574i) q^{85} +(12.9552 + 7.47972i) q^{86} -0.627669 q^{88} +(-10.8205 + 6.24724i) q^{89} +(9.17290 - 2.61876i) q^{91} +10.5023 q^{92} -11.6473 q^{94} +(-1.53643 + 2.66118i) q^{95} +(-9.58078 + 5.53147i) q^{97} +(4.86985 + 13.4858i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} + 13 q^{4} + 6 q^{5} - 5 q^{7}+O(q^{10}) $ 20 * q + 3 * q^2 + 13 * q^4 + 6 * q^5 - 5 * q^7	$ 20 q + 3 q^{2} + 13 q^{4} + 6 q^{5} - 5 q^{7} - 4 q^{10} + 8 q^{13} - 2 q^{14} - 21 q^{16} + 8 q^{17} - 9 q^{22} - 18 q^{23} + 12 q^{25} - 32 q^{26} - 43 q^{28} + 3 q^{29} + 18 q^{31} + 24 q^{32} + 24 q^{35} - 12 q^{37} - 9 q^{38} + 5 q^{40} - 21 q^{41} + 16 q^{43} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 3 q^{49} + 54 q^{50} + 13 q^{52} + 26 q^{53} + 17 q^{55} - 6 q^{56} - 15 q^{59} - 4 q^{62} - 46 q^{64} - 37 q^{65} + 3 q^{68} - 15 q^{71} + 9 q^{73} + 6 q^{74} + 75 q^{76} - 20 q^{77} + 3 q^{79} - 30 q^{82} - 78 q^{85} + 3 q^{86} + 44 q^{88} + 24 q^{89} - 4 q^{91} - 142 q^{92} - 72 q^{94} - 42 q^{95} - 15 q^{97} + 33 q^{98}+O(q^{100}) $ 20 * q + 3 * q^2 + 13 * q^4 + 6 * q^5 - 5 * q^7 - 4 * q^10 + 8 * q^13 - 2 * q^14 - 21 * q^16 + 8 * q^17 - 9 * q^22 - 18 * q^23 + 12 * q^25 - 32 * q^26 - 43 * q^28 + 3 * q^29 + 18 * q^31 + 24 * q^32 + 24 * q^35 - 12 * q^37 - 9 * q^38 + 5 * q^40 - 21 * q^41 + 16 * q^43 - 6 * q^44 + 6 * q^46 + 21 * q^47 + 3 * q^49 + 54 * q^50 + 13 * q^52 + 26 * q^53 + 17 * q^55 - 6 * q^56 - 15 * q^59 - 4 * q^62 - 46 * q^64 - 37 * q^65 + 3 * q^68 - 15 * q^71 + 9 * q^73 + 6 * q^74 + 75 * q^76 - 20 * q^77 + 3 * q^79 - 30 * q^82 - 78 * q^85 + 3 * q^86 + 44 * q^88 + 24 * q^89 - 4 * q^91 - 142 * q^92 - 72 * q^94 - 42 * q^95 - 15 * q^97 + 33 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.77388	−	1.02415i	1.25432	−	0.724184i	0.282359	−	0.959309i	$-0.408883\pi$
$2$	1.77388	−	1.02415i	1.25432	−	0.724184i	0.971965	+	0.235124i	$0.0755498\pi$
$3$		0			0
$3$		0			0
$4$	1.09777	−	1.90140i	0.548886	−	0.950699i
$5$	0.341406	+	0.197111i	0.152681	+	0.0881505i	0.574394	−	0.818579i	$-0.305238\pi$
$5$	0.341406	+	0.197111i	0.152681	+	0.0881505i	−0.421713	+	0.906729i	$0.638571\pi$
$6$		0			0
$7$	1.69809	+	2.02891i	0.641819	+	0.766856i
$7$	1.69809	+	2.02891i	0.641819	+	0.766856i
$8$		−	0.400534i		−	0.141610i
$9$		0			0
$10$	0.807484			0.255349
$11$		−	1.56708i		−	0.472492i	−0.971693	−	0.236246i	$-0.924083\pi$
$11$		−	1.56708i		−	0.472492i	0.971693	−	0.236246i	$-0.0759172\pi$
$12$		0			0
$13$	1.46617	−	3.29398i	0.406643	−	0.913587i
$13$	1.46617	−	3.29398i	0.406643	−	0.913587i
$14$	5.09013	+	1.85994i	1.36039	+	0.497091i
$15$		0			0
$16$	1.78534	+	3.09229i	0.446334	+	0.773074i
$17$	3.41367	−	5.91265i	0.827937	−	1.43403i	−0.0717164	−	0.997425i	$-0.522848\pi$
$17$	3.41367	−	5.91265i	0.827937	−	1.43403i	0.899654	−	0.436604i	$-0.143819\pi$
$18$		0			0
$19$			7.79477i			1.78824i	0.447824	+	0.894122i	$0.352199\pi$
$19$			7.79477i			1.78824i	−0.447824	+	0.894122i	$0.647801\pi$
$20$	0.749571	−	0.432765i	0.167609	−	0.0967692i
$21$		0			0
$22$	−1.60493	−	2.77982i	−0.342172	−	0.592659i
$23$	2.39173	+	4.14260i	0.498710	+	0.863792i	0.999999	−	0.00148841i	$-0.000473777\pi$
$23$	2.39173	+	4.14260i	0.498710	+	0.863792i	−0.501288	+	0.865280i	$0.667140\pi$
$24$		0			0
$25$	−2.42229	−	4.19554i	−0.484459	−	0.839108i
$26$	−0.772719	−	7.34472i	−0.151543	−	1.44042i
$27$		0			0
$28$	5.72188	−	1.00147i	1.08133	−	0.189260i
$29$	3.94172	−	6.82725i	0.731958	−	1.26779i	−0.224087	−	0.974569i	$-0.571940\pi$
$29$	3.94172	−	6.82725i	0.731958	−	1.26779i	0.956045	−	0.293220i	$-0.0947268\pi$
$30$		0			0
$31$	−5.14505	+	2.97049i	−0.924078	+	0.533517i	−0.884934	−	0.465717i	$-0.845796\pi$
$31$	−5.14505	+	2.97049i	−0.924078	+	0.533517i	−0.0391442	+	0.999234i	$0.512463\pi$
$32$	7.02770	+	4.05744i	1.24233	+	0.717262i
$33$		0			0
$34$		−	13.9845i		−	2.39832i
$35$	0.179819	+	1.02739i	0.0303949	+	0.173661i
$36$		0			0
$37$	1.01661	−	0.586939i	0.167129	−	0.0964922i	−0.414102	−	0.910230i	$-0.635904\pi$
$37$	1.01661	−	0.586939i	0.167129	−	0.0964922i	0.581232	+	0.813738i	$0.302571\pi$
$38$	7.98303	+	13.8270i	1.29502	+	2.24304i
$39$		0			0
$40$	0.0789495	−	0.136745i	0.0124830	−	0.0216212i
$41$	−6.17054	−	3.56256i	−0.963676	−	0.556378i	−0.0663733	−	0.997795i	$-0.521143\pi$
$41$	−6.17054	−	3.56256i	−0.963676	−	0.556378i	−0.897302	+	0.441416i	$0.854476\pi$
$42$		0			0
$43$	3.65167	+	6.32487i	0.556874	+	0.964534i	0.997755	+	0.0669682i	$0.0213326\pi$
$43$	3.65167	+	6.32487i	0.556874	+	0.964534i	−0.440881	+	0.897565i	$0.645334\pi$
$44$	−2.97964	−	1.72030i	−0.449198	−	0.259345i
$45$		0			0
$46$	8.48530	+	4.89899i	1.25109	+	0.722317i
$47$	−4.92450	−	2.84316i	−0.718312	−	0.414717i	0.0958193	−	0.995399i	$-0.469453\pi$
$47$	−4.92450	−	2.84316i	−0.718312	−	0.414717i	−0.814131	+	0.580681i	$0.802786\pi$
$48$		0			0
$49$	−1.23296	+	6.89056i	−0.176137	+	0.984366i
$50$	−8.59373	−	4.96159i	−1.21534	−	0.701675i
$51$		0			0
$52$	−4.65365	−	6.40382i	−0.645345	−	0.888051i
$53$	0.964998	+	1.67143i	0.132553	+	0.229588i	0.924660	−	0.380794i	$-0.124349\pi$
$53$	0.964998	+	1.67143i	0.132553	+	0.229588i	−0.792107	+	0.610382i	$0.791016\pi$
$54$		0			0
$55$	0.308888	−	0.535010i	0.0416505	−	0.0721407i
$56$	0.812648	−	0.680144i	0.108595	−	0.0908881i
$57$		0			0
$58$		−	16.1477i		−	2.12029i
$59$	−9.91907	−	5.72678i	−1.29135	−	0.745563i	−0.312459	−	0.949931i	$-0.601153\pi$
$59$	−9.91907	−	5.72678i	−1.29135	−	0.745563i	−0.978894	+	0.204368i	$0.934486\pi$
$60$		0			0
$61$	−12.2675			−1.57070			−0.785348	−	0.619055i	$-0.787516\pi$
$61$	−12.2675			−1.57070			−0.785348	+	0.619055i	$0.787516\pi$
$62$	−6.08447	+	10.5386i	−0.772729	+	1.33841i
$63$		0			0
$64$	9.48040			1.18505
$65$	1.14984	−	0.835586i	0.142620	−	0.103642i
$66$		0			0
$67$		−	2.79011i		−	0.340866i	−0.985369	−	0.170433i	$-0.945483\pi$
$67$		−	2.79011i		−	0.340866i	0.985369	−	0.170433i	$-0.0545167\pi$
$68$	−7.49487	−	12.9815i	−0.908886	−	1.57424i
$69$		0			0
$70$	1.37118	+	1.63831i	0.163888	+	0.195816i
$71$	−7.66430	+	4.42499i	−0.909586	+	0.525150i	−0.880298	−	0.474422i	$-0.842657\pi$
$71$	−7.66430	+	4.42499i	−0.909586	+	0.525150i	−0.0292878	+	0.999571i	$0.509324\pi$
$72$		0			0
$73$	2.23575	−	1.29081i	0.261675	−	0.151078i	−0.363423	−	0.931624i	$-0.618392\pi$
$73$	2.23575	−	1.29081i	0.261675	−	0.151078i	0.625098	+	0.780546i	$0.285059\pi$
$74$	1.20223	−	2.08232i	0.139756	−	0.242065i
$75$		0			0
$76$	14.8210	+	8.55689i	1.70008	+	0.981542i
$77$	3.17947	−	2.66105i	0.362334	−	0.303255i
$78$		0			0
$79$	1.55611	−	2.69526i	0.175076	−	0.303240i	−0.765112	−	0.643898i	$-0.777316\pi$
$79$	1.55611	−	2.69526i	0.175076	−	0.303240i	0.940187	+	0.340657i	$0.110650\pi$
$80$			1.40764i			0.157378i
$81$		0			0
$82$	−14.5944			−1.61168
$83$		−	3.01153i		−	0.330559i	−0.986247	−	0.165279i	$-0.947147\pi$
$83$		−	3.01153i		−	0.330559i	0.986247	−	0.165279i	$-0.0528526\pi$
$84$		0			0
$85$	2.33089	−	1.34574i	0.252821	−	0.145966i
$86$	12.9552	+	7.47972i	1.39700	+	0.806559i
$87$		0			0
$88$	−0.627669			−0.0669097
$89$	−10.8205	+	6.24724i	−1.14697	+	0.662206i	−0.948148	−	0.317829i	$-0.897046\pi$
$89$	−10.8205	+	6.24724i	−1.14697	+	0.662206i	−0.198826	+	0.980035i	$0.563713\pi$
$90$		0			0
$91$	9.17290	−	2.61876i	0.961581	−	0.274520i
$92$	10.5023			1.09494
$93$		0			0
$94$	−11.6473			−1.20133
$95$	−1.53643	+	2.66118i	−0.157635	+	0.273031i
$96$		0			0
$97$	−9.58078	+	5.53147i	−0.972781	+	0.561635i	−0.900083	−	0.435719i	$-0.856494\pi$
$97$	−9.58078	+	5.53147i	−0.972781	+	0.561635i	−0.0726979	+	0.997354i	$0.523161\pi$
$98$	4.86985	+	13.4858i	0.491930	+	1.36227i
$99$		0			0
$100$	−10.6365			−1.06365
$101$	5.26469			0.523856			0.261928	−	0.965087i	$-0.415642\pi$
$101$	5.26469			0.523856			0.261928	+	0.965087i	$0.415642\pi$
$102$		0			0
$103$	1.12396	−	1.94676i	0.110747	−	0.191820i	−0.805325	−	0.592834i	$-0.798009\pi$
$103$	1.12396	−	1.94676i	0.110747	−	0.191820i	0.916072	+	0.401015i	$0.131342\pi$
$104$	−1.31935	−	0.587253i	−0.129373	−	0.0575848i
$105$		0			0
$106$	3.42359	+	1.97661i	0.332528	+	0.191985i
$107$	1.93139	+	3.34526i	0.186714	+	0.323398i	0.944153	−	0.329508i	$-0.106883\pi$
$107$	1.93139	+	3.34526i	0.186714	+	0.323398i	−0.757439	+	0.652906i	$0.773550\pi$
$108$		0			0
$109$	−8.85859	+	5.11451i	−0.848499	+	0.489881i	−0.860144	−	0.510051i	$-0.829627\pi$
$109$	−8.85859	+	5.11451i	−0.848499	+	0.489881i	0.0116449	+	0.999932i	$0.496293\pi$
$110$		−	1.26539i		−	0.120650i
$111$		0			0
$112$	−3.24232	+	8.87329i	−0.306370	+	0.838447i
$113$	6.18490	+	10.7126i	0.581826	+	1.00775i	0.995263	+	0.0972197i	$0.0309949\pi$
$113$	6.18490	+	10.7126i	0.581826	+	1.00775i	−0.413437	+	0.910533i	$0.635672\pi$
$114$		0			0
$115$			1.88574i			0.175846i
$116$	−8.65421	−	14.9895i	−0.803524	−	1.39174i
$117$		0			0
$118$	−23.4604			−2.15970
$119$	17.7930	−	3.11420i	1.63108	−	0.285478i
$120$		0			0
$121$	8.54426			0.776751
$122$	−21.7611	+	12.5638i	−1.97016	+	1.13747i
$123$		0			0
$124$			13.0437i			1.17136i
$125$		−	3.88095i		−	0.347122i
$126$		0			0
$127$	2.15693	−	3.73590i	0.191396	−	0.331508i	−0.754317	−	0.656510i	$-0.772032\pi$
$127$	2.15693	−	3.73590i	0.191396	−	0.331508i	0.945713	+	0.325002i	$0.105365\pi$
$128$	2.76172	−	1.59448i	0.244104	−	0.140933i
$129$		0			0
$130$	1.18391	−	2.65984i	0.103836	−	0.233283i
$131$	5.88647	−	10.1957i	0.514303	−	0.890800i	−0.485559	−	0.874204i	$-0.661384\pi$
$131$	5.88647	−	10.1957i	0.514303	−	0.890800i	0.999862	−	0.0165956i	$-0.00528279\pi$
$132$		0			0
$133$	−15.8149	+	13.2363i	−1.37133	+	1.14773i
$134$	−2.85750	−	4.94933i	−0.246850	−	0.427557i
$135$		0			0
$136$	−2.36822	−	1.36729i	−0.203073	−	0.117244i
$137$	6.60760	+	3.81490i	0.564526	+	0.325929i	0.754960	−	0.655771i	$-0.227656\pi$
$137$	6.60760	+	3.81490i	0.564526	+	0.325929i	−0.190434	+	0.981700i	$0.560990\pi$
$138$		0			0
$139$	−1.70630	−	2.95540i	−0.144726	−	0.250673i	0.784544	−	0.620073i	$-0.212897\pi$
$139$	−1.70630	−	2.95540i	−0.144726	−	0.250673i	−0.929271	+	0.369399i	$0.879564\pi$
$140$	2.15088	+	0.785937i	0.181783	+	0.0664238i
$141$		0			0
$142$	−9.06372	+	15.6988i	−0.760610	+	1.31742i
$143$	−5.16194	−	2.29761i	−0.431663	−	0.192136i
$144$		0			0
$145$	2.69145	−	1.55391i	0.223513	−	0.129045i
$146$	2.64397	−	4.57950i	0.218817	−	0.379002i
$147$		0			0
$148$		−	2.57730i		−	0.211853i
$149$			8.55584i			0.700922i	0.936577	+	0.350461i	$0.113975\pi$
$149$			8.55584i			0.700922i	−0.936577	+	0.350461i	$0.886025\pi$
$150$		0			0
$151$	18.5011	−	10.6816i	1.50560	−	0.869258i	0.505620	−	0.862756i	$-0.331264\pi$
$151$	18.5011	−	10.6816i	1.50560	−	0.869258i	0.999979	−	0.00650133i	$-0.00206945\pi$
$152$	3.12207			0.253233
$153$		0			0
$154$	2.91468	−	7.97664i	0.234872	−	0.642776i
$155$	−2.34206			−0.188119
$156$		0			0
$157$	1.41769	+	2.45552i	0.113144	+	0.195972i	0.917036	−	0.398804i	$-0.130574\pi$
$157$	1.41769	+	2.45552i	0.113144	+	0.195972i	−0.803892	+	0.594775i	$0.797241\pi$
$158$		−	6.37476i		−	0.507149i
$159$		0			0
$160$	1.59953	+	2.77047i	0.126454	+	0.219025i
$161$	−4.34358	+	11.8871i	−0.342322	+	0.936837i
$162$		0			0
$163$			10.3832i			0.813278i	0.913589	+	0.406639i	$0.133299\pi$
$163$			10.3832i			0.813278i	−0.913589	+	0.406639i	$0.866701\pi$
$164$	−13.5477	+	7.82176i	−1.05790	+	0.610777i
$165$		0			0
$166$	−3.08427	−	5.34211i	−0.239386	−	0.414628i
$167$	−5.99510	−	3.46127i	−0.463915	−	0.267841i	0.249774	−	0.968304i	$-0.419644\pi$
$167$	−5.99510	−	3.46127i	−0.463915	−	0.267841i	−0.713689	+	0.700463i	$0.752977\pi$
$168$		0			0
$169$	−8.70067	−	9.65911i	−0.669282	−	0.743008i
$170$	2.75649	−	4.77438i	0.211413	−	0.366178i
$171$		0			0
$172$	16.0348			1.22264
$173$	9.99585			0.759970			0.379985	−	0.924993i	$-0.375929\pi$
$173$	9.99585			0.759970			0.379985	+	0.924993i	$0.375929\pi$
$174$		0			0
$175$	4.39909	−	12.0390i	0.332540	−	0.910065i
$176$	4.84587	−	2.79777i	0.365271	−	0.210890i
$177$		0			0
$178$	−12.7962	+	22.1637i	−0.959119	+	1.66124i
$179$	−21.5497			−1.61070			−0.805351	−	0.592798i	$-0.798023\pi$
$179$	−21.5497			−1.61070			−0.805351	+	0.592798i	$0.798023\pi$
$180$		0			0
$181$	9.40672			0.699196			0.349598	−	0.936900i	$-0.386318\pi$
$181$	9.40672			0.699196			0.349598	+	0.936900i	$0.386318\pi$
$182$	13.5896	−	14.0398i	1.00733	−	1.04070i
$183$		0			0
$184$	1.65925	−	0.957970i	0.122322	−	0.0706225i
$185$	0.462768			0.0340234
$186$		0			0
$187$	−9.26560	−	5.34950i	−0.677568	−	0.391194i
$188$	−10.8120	+	6.24228i	−0.788543	+	0.455265i
$189$		0			0
$190$			6.29416i			0.456626i
$191$	−10.4168			−0.753736			−0.376868	−	0.926267i	$-0.622999\pi$
$191$	−10.4168			−0.753736			−0.376868	+	0.926267i	$0.622999\pi$
$192$		0			0
$193$		−	22.4346i		−	1.61487i	−0.589953	−	0.807437i	$-0.700854\pi$
$193$		−	22.4346i		−	1.61487i	0.589953	−	0.807437i	$-0.299146\pi$
$194$	−11.3301	+	19.6243i	−0.813455	+	1.40895i
$195$		0			0
$196$	11.7482	+	9.90861i	0.839156	+	0.707758i
$197$	−19.9893	−	11.5408i	−1.42418	−	0.822248i	−0.427524	−	0.904004i	$-0.640614\pi$
$197$	−19.9893	−	11.5408i	−1.42418	−	0.822248i	−0.996652	+	0.0817559i	$0.973947\pi$
$198$		0			0
$199$	0.261898	−	0.453621i	0.0185655	−	0.0321563i	−0.856593	−	0.515992i	$-0.827423\pi$
$199$	0.261898	−	0.453621i	0.0185655	−	0.0321563i	0.875159	+	0.483836i	$0.160757\pi$
$200$	−1.68046	+	0.970211i	−0.118826	+	0.0686043i
$201$		0			0
$202$	9.33894	−	5.39184i	0.657085	−	0.379368i
$203$	20.5453	−	3.59592i	1.44200	−	0.252384i
$204$		0			0
$205$	−1.40444	−	2.43256i	−0.0980901	−	0.169897i
$206$		−	4.60442i		−	0.320805i
$207$		0			0
$208$	12.8036	−	1.34703i	0.887769	−	0.0933998i
$209$	12.2150			0.844932
$210$		0			0
$211$	−4.44244	+	7.69452i	−0.305830	+	0.529713i	−0.977446	−	0.211187i	$-0.932267\pi$
$211$	−4.44244	+	7.69452i	−0.305830	+	0.529713i	0.671616	+	0.740900i	$0.265601\pi$
$212$	4.23739			0.291025
$213$		0			0
$214$	6.85210	+	3.95606i	0.468400	+	0.270431i
$215$			2.87913i			0.196355i
$216$		0			0
$217$	−14.7636	−	5.39467i	−1.00222	−	0.366214i
$218$	−10.4761	+	18.1451i	−0.709529	+	1.22894i
$219$		0			0
$220$	−0.678178	−	1.17464i	−0.0457227	−	0.0791941i
$221$	−14.4712	−	19.9136i	−0.973435	−	1.33953i
$222$		0			0
$223$	−0.701588	−	0.405062i	−0.0469818	−	0.0271249i	0.476325	−	0.879269i	$-0.341969\pi$
$223$	−0.701588	−	0.405062i	−0.0469818	−	0.0271249i	−0.523307	+	0.852144i	$0.675302\pi$
$224$	3.70150	+	21.1485i	0.247317	+	1.41304i
$225$		0			0
$226$	21.9426	+	12.6685i	1.45960	+	0.842699i
$227$	−0.482073	−	0.278325i	−0.0319963	−	0.0184731i	0.483917	−	0.875114i	$-0.339214\pi$
$227$	−0.482073	−	0.278325i	−0.0319963	−	0.0184731i	−0.515913	+	0.856641i	$0.672547\pi$
$228$		0			0
$229$	−14.2673	−	8.23721i	−0.942807	−	0.544330i	−0.0519681	−	0.998649i	$-0.516549\pi$
$229$	−14.2673	−	8.23721i	−0.942807	−	0.544330i	−0.890839	+	0.454319i	$0.849883\pi$
$230$	1.93129	+	3.34508i	0.127345	+	0.220568i
$231$		0			0
$232$	−2.73455	−	1.57879i	−0.179532	−	0.103653i
$233$	−3.31050	+	5.73395i	−0.216878	+	0.375644i	−0.953852	−	0.300278i	$-0.902921\pi$
$233$	−3.31050	+	5.73395i	−0.216878	+	0.375644i	0.736974	+	0.675921i	$0.236254\pi$
$234$		0			0
$235$	−1.12083	−	1.94134i	−0.0731151	−	0.126639i
$236$	−21.7778	+	12.5734i	−1.41761	+	0.818458i
$237$		0			0
$238$	28.3732	−	23.7469i	1.83916	−	1.53929i
$239$		−	6.07400i		−	0.392894i	−0.980514	−	0.196447i	$-0.937060\pi$
$239$		−	6.07400i		−	0.392894i	0.980514	−	0.196447i	$-0.0629404\pi$
$240$		0			0
$241$	17.8983	+	10.3336i	1.15293	+	0.665644i	0.949599	−	0.313466i	$-0.101490\pi$
$241$	17.8983	+	10.3336i	1.15293	+	0.665644i	0.203330	+	0.979110i	$0.434823\pi$
$242$	15.1565	−	8.75062i	0.974297	−	0.562511i
$243$		0			0
$244$	−13.4670	+	23.3254i	−0.862133	+	1.49326i
$245$	−1.77914	+	2.10945i	−0.113665	+	0.134768i
$246$		0			0
$247$	25.6759	+	11.4285i	1.63372	+	0.727178i
$248$	1.18978	+	2.06077i	0.0755514	+	0.130859i
$249$		0			0
$250$	−3.97468	−	6.88434i	−0.251381	−	0.435404i
$251$	7.61211	+	13.1846i	0.480472	+	0.832202i	0.999749	−	0.0224037i	$-0.00713193\pi$
$251$	7.61211	+	13.1846i	0.480472	+	0.832202i	−0.519277	+	0.854606i	$0.673799\pi$
$252$		0			0
$253$	6.49179	−	3.74803i	0.408135	−	0.235637i
$254$		−	8.83607i		−	0.554425i
$255$		0			0
$256$	−6.21443	+	10.7637i	−0.388402	+	0.672732i
$257$	−0.850367	−	1.47288i	−0.0530444	−	0.0918756i	0.838284	−	0.545234i	$-0.183559\pi$
$257$	−0.850367	−	1.47288i	−0.0530444	−	0.0918756i	−0.891328	+	0.453358i	$0.850226\pi$
$258$		0			0
$259$	2.91714	+	1.06593i	0.181262	+	0.0662337i
$260$	−0.326520	−	3.10358i	−0.0202499	−	0.192476i
$261$		0			0
$262$		−	24.1146i		−	1.48980i
$263$	−8.18309			−0.504591			−0.252295	−	0.967650i	$-0.581185\pi$
$263$	−8.18309			−0.504591			−0.252295	+	0.967650i	$0.581185\pi$
$264$		0			0
$265$			0.760846i			0.0467384i
$266$	−14.4978	+	39.6764i	−0.888920	+	2.43272i
$267$		0			0
$268$	−5.30511	−	3.06291i	−0.324061	−	0.187097i
$269$	−5.83024	+	10.0983i	−0.355476	+	0.615702i	−0.987199	−	0.159492i	$-0.949014\pi$
$269$	−5.83024	+	10.0983i	−0.355476	+	0.615702i	0.631723	+	0.775194i	$0.282348\pi$
$270$		0			0
$271$	4.89222	−	2.82452i	0.297181	−	0.171578i	−0.343995	−	0.938972i	$-0.611780\pi$
$271$	4.89222	−	2.82452i	0.297181	−	0.171578i	0.641176	+	0.767394i	$0.278447\pi$
$272$	24.3782			1.47815
$273$		0			0
$274$	15.6281			0.944131
$275$	−6.57474	+	3.79593i	−0.396472	+	0.228903i
$276$		0			0
$277$	11.9857	−	20.7599i	0.720152	−	1.24734i	−0.240787	−	0.970578i	$-0.577405\pi$
$277$	11.9857	−	20.7599i	0.720152	−	1.24734i	0.960939	−	0.276762i	$-0.0892612\pi$
$278$	−6.05355	−	3.49502i	−0.363068	−	0.209617i
$279$		0			0
$280$	0.411506	−	0.0720235i	0.0245922	−	0.00430423i
$281$		−	20.2883i		−	1.21030i	−0.796113	−	0.605148i	$-0.793114\pi$
$281$		−	20.2883i		−	1.21030i	0.796113	−	0.605148i	$-0.206886\pi$
$282$		0			0
$283$	−2.10814			−0.125316			−0.0626578	−	0.998035i	$-0.519958\pi$
$283$	−2.10814			−0.125316			−0.0626578	+	0.998035i	$0.519958\pi$
$284$			19.4305i			1.15299i
$285$		0			0
$286$	−11.5098	+	1.21091i	−0.680587	+	0.0716028i
$287$	−3.25003	−	18.5690i	−0.191843	−	1.09609i
$288$		0			0
$289$	−14.8063	−	25.6453i	−0.870960	−	1.50855i
$290$	3.18287	−	5.51290i	0.186905	−	0.323729i
$291$		0			0
$292$		−	5.66807i		−	0.331699i
$293$	2.59210	−	1.49655i	0.151432	−	0.0874294i	−0.422369	−	0.906424i	$-0.638801\pi$
$293$	2.59210	−	1.49655i	0.151432	−	0.0874294i	0.573801	+	0.818994i	$0.305468\pi$
$294$		0			0
$295$	−2.25762	−	3.91031i	−0.131444	−	0.227667i
$296$	−0.235089	−	0.407186i	−0.0136643	−	0.0236672i
$297$		0			0
$298$	8.76248	+	15.1771i	0.507597	+	0.879183i
$299$	17.1524	−	1.80455i	0.991946	−	0.104360i
$300$		0			0
$301$	−6.63173	+	18.1491i	−0.382246	+	1.04610i
$302$	21.8792	−	37.8959i	1.25901	−	2.18066i
$303$		0			0
$304$	−24.1037	+	13.9163i	−1.38244	+	0.798154i
$305$	−4.18820	−	2.41806i	−0.239816	−	0.138458i
$306$		0			0
$307$		−	1.91377i		−	0.109225i	−0.998508	−	0.0546124i	$-0.982608\pi$
$307$		−	1.91377i		−	0.109225i	0.998508	−	0.0546124i	$-0.0173923\pi$
$308$	−1.56938	−	8.96665i	−0.0894238	−	0.510922i
$309$		0			0
$310$	−4.15455	+	2.39863i	−0.235962	+	0.136233i
$311$	3.37549	+	5.84652i	0.191406	+	0.331526i	0.945717	−	0.324993i	$-0.105362\pi$
$311$	3.37549	+	5.84652i	0.191406	+	0.331526i	−0.754310	+	0.656518i	$0.772029\pi$
$312$		0			0
$313$	5.51032	−	9.54416i	0.311462	−	0.539468i	−0.667217	−	0.744863i	$-0.732515\pi$
$313$	5.51032	−	9.54416i	0.311462	−	0.539468i	0.978679	+	0.205396i	$0.0658481\pi$
$314$	5.02964	+	2.90386i	0.283839	+	0.163875i
$315$		0			0
$316$	−3.41650	−	5.91756i	−0.192193	−	0.332889i
$317$	10.7991	+	6.23485i	0.606536	+	0.350184i	0.771609	−	0.636098i	$-0.219452\pi$
$317$	10.7991	+	6.23485i	0.606536	+	0.350184i	−0.165072	+	0.986281i	$0.552786\pi$
$318$		0			0
$319$	−10.6989	−	6.17699i	−0.599021	−	0.345845i
$320$	3.23666	+	1.86869i	0.180935	+	0.104463i
$321$		0			0
$322$	4.46922	+	25.5349i	0.249060	+	1.42300i
$323$	46.0878	+	26.6088i	2.56439	+	1.48055i
$324$		0			0
$325$	−17.3715	+	1.82761i	−0.963600	+	0.101378i
$326$	10.6340	+	18.4186i	0.588963	+	1.02011i
$327$		0			0
$328$	−1.42693	+	2.47151i	−0.0787888	+	0.136466i
$329$	−2.59374	−	14.8193i	−0.142997	−	0.817015i
$330$		0			0
$331$			19.1044i			1.05008i	0.851079	+	0.525038i	$0.175949\pi$
$331$			19.1044i			1.05008i	−0.851079	+	0.525038i	$0.824051\pi$
$332$	−5.72612	−	3.30598i	−0.314262	−	0.181439i
$333$		0			0
$334$	−14.1795			−0.775866
$335$	0.549961	−	0.952560i	0.0300476	−	0.0520439i
$336$		0			0
$337$	35.4527			1.93123			0.965616	−	0.259972i	$-0.0837134\pi$
$337$	35.4527			1.93123			0.965616	+	0.259972i	$0.0837134\pi$
$338$	−25.3263	−	8.22332i	−1.37757	−	0.447290i
$339$		0			0
$340$		−	5.90927i		−	0.320475i
$341$	4.65500	+	8.06270i	0.252083	+	0.436620i
$342$		0			0
$343$	−16.0740	+	9.19925i	−0.867915	+	0.496713i
$344$	2.53333	−	1.46262i	0.136588	−	0.0788590i
$345$		0			0
$346$	17.7315	−	10.2373i	0.953249	−	0.550359i
$347$	9.02426	−	15.6305i	0.484448	−	0.839088i	−0.515393	−	0.856954i	$-0.672354\pi$
$347$	9.02426	−	15.6305i	0.484448	−	0.839088i	0.999840	+	0.0178660i	$0.00568722\pi$
$348$		0			0
$349$	−12.1606	−	7.02095i	−0.650945	−	0.375823i	0.137873	−	0.990450i	$-0.455973\pi$
$349$	−12.1606	−	7.02095i	−0.650945	−	0.375823i	−0.788818	+	0.614627i	$0.789307\pi$
$350$	−4.52633	−	25.8612i	−0.241942	−	1.38234i
$351$		0			0
$352$	6.35834	−	11.0130i	0.338901	−	0.586993i
$353$			1.12314i			0.0597789i	0.999553	+	0.0298894i	$0.00951552\pi$
$353$			1.12314i			0.0597789i	−0.999553	+	0.0298894i	$0.990484\pi$
$354$		0			0
$355$	−3.48885			−0.185169
$356$			27.4322i			1.45390i
$357$		0			0
$358$	−38.2267	+	22.0702i	−2.02034	+	1.16645i
$359$	6.38193	+	3.68461i	0.336826	+	0.194466i	0.658867	−	0.752259i	$-0.271036\pi$
$359$	6.38193	+	3.68461i	0.336826	+	0.194466i	−0.322042	+	0.946725i	$0.604369\pi$
$360$		0			0
$361$	−41.7585			−2.19782
$362$	16.6864	−	9.63391i	0.877019	−	0.506347i
$363$		0			0
$364$	5.09046	−	20.3161i	0.266813	−	1.06485i
$365$	1.01773			0.0532705
$366$		0			0
$367$	19.7738			1.03218			0.516091	−	0.856534i	$-0.327386\pi$
$367$	19.7738			1.03218			0.516091	+	0.856534i	$0.327386\pi$
$368$	−8.54009	+	14.7919i	−0.445183	+	0.771080i
$369$		0			0
$370$	0.820895	−	0.473944i	0.0426763	−	0.0246392i
$371$	−1.75252	+	4.79613i	−0.0909862	+	0.249003i
$372$		0			0
$373$	9.31644			0.482387			0.241194	−	0.970477i	$-0.422461\pi$
$373$	9.31644			0.482387			0.241194	+	0.970477i	$0.422461\pi$
$374$	−21.9148			−1.13319
$375$		0			0
$376$	−1.13878	+	1.97243i	−0.0587282	+	0.101720i
$377$	−16.7096	−	22.9939i	−0.860590	−	1.18425i
$378$		0			0
$379$	−10.8308	−	6.25315i	−0.556340	−	0.321203i	0.195335	−	0.980736i	$-0.437420\pi$
$379$	−10.8308	−	6.25315i	−0.556340	−	0.321203i	−0.751675	+	0.659534i	$0.770754\pi$
$380$	3.37331	+	5.84274i	0.173047	+	0.299726i
$381$		0			0
$382$	−18.4782	+	10.6684i	−0.945429	+	0.545844i
$383$		−	34.8251i		−	1.77948i	−0.456467	−	0.889740i	$-0.650885\pi$
$383$		−	34.8251i		−	1.77948i	0.456467	−	0.889740i	$-0.349115\pi$
$384$		0			0
$385$	1.61001	−	0.281790i	0.0820536	−	0.0143614i
$386$	−22.9764	−	39.7963i	−1.16947	−	2.02558i
$387$		0			0
$388$			24.2892i			1.23309i
$389$	7.22866	+	12.5204i	0.366508	+	0.634810i	0.989017	−	0.147802i	$-0.0472200\pi$
$389$	7.22866	+	12.5204i	0.366508	+	0.634810i	−0.622509	+	0.782613i	$0.713887\pi$
$390$		0			0
$391$	32.6583			1.65160
$392$	2.75990	+	0.493842i	0.139396	+	0.0249428i
$393$		0			0
$394$	−47.2781			−2.38184
$395$	1.06253	−	0.613451i	0.0534616	−	0.0308660i
$396$		0			0
$397$			3.81898i			0.191669i	0.995397	+	0.0958346i	$0.0305520\pi$
$397$			3.81898i			0.191669i	−0.995397	+	0.0958346i	$0.969448\pi$
$398$		−	1.07289i		−	0.0537793i
$399$		0			0
$400$	8.64922	−	14.9809i	0.432461	−	0.749045i
$401$	10.9311	−	6.31110i	0.545875	−	0.315161i	−0.201581	−	0.979472i	$-0.564608\pi$
$401$	10.9311	−	6.31110i	0.545875	−	0.315161i	0.747457	+	0.664310i	$0.231275\pi$
$402$		0			0
$403$	2.24123	+	21.3030i	0.111644	+	1.06118i
$404$	5.77943	−	10.0103i	0.287537	−	0.498029i
$405$		0			0
$406$	32.7622	−	27.4202i	1.62596	−	1.36084i
$407$	−0.919781	−	1.59311i	−0.0455918	−	0.0789674i
$408$		0			0
$409$	27.3181	+	15.7721i	1.35079	+	0.779882i	0.988361	−	0.152128i	$-0.0486126\pi$
$409$	27.3181	+	15.7721i	1.35079	+	0.779882i	0.362434	+	0.932010i	$0.381946\pi$
$410$	−4.98261	−	2.87671i	−0.246074	−	0.142071i
$411$		0			0
$412$	−2.46770	−	4.27419i	−0.121575	−	0.210574i
$413$	−5.22439	−	29.8495i	−0.257075	−	1.46880i
$414$		0			0
$415$	0.593605	−	1.02815i	0.0291389	−	0.0504701i
$416$	23.6690	−	17.2002i	1.16047	−	0.843310i
$417$		0			0
$418$	21.6680	−	12.5100i	1.05982	−	0.611886i
$419$	−5.19320	+	8.99489i	−0.253705	+	0.439429i	−0.964543	−	0.263926i	$-0.914982\pi$
$419$	−5.19320	+	8.99489i	−0.253705	+	0.439429i	0.710838	+	0.703356i	$0.248316\pi$
$420$		0			0
$421$			0.368085i			0.0179394i	0.999960	+	0.00896969i	$0.00285518\pi$
$421$			0.368085i			0.0179394i	−0.999960	+	0.00896969i	$0.997145\pi$
$422$			18.1989i			0.885909i
$423$		0			0
$424$	0.669463	−	0.386515i	0.0325120	−	0.0187708i
$425$	−33.0757			−1.60441
$426$		0			0
$427$	−20.8314	−	24.8897i	−1.00810	−	1.20450i
$428$	8.48089			0.409939
$429$		0			0
$430$	2.94866	+	5.10723i	0.142197	+	0.246293i
$431$			15.3928i			0.741446i	0.928744	+	0.370723i	$0.120890\pi$
$431$			15.3928i			0.741446i	−0.928744	+	0.370723i	$0.879110\pi$
$432$		0			0
$433$	9.13817	+	15.8278i	0.439152	+	0.760634i	0.997624	−	0.0688892i	$-0.0219455\pi$
$433$	9.13817	+	15.8278i	0.439152	+	0.760634i	−0.558472	+	0.829523i	$0.688612\pi$
$434$	−31.7139	+	5.55070i	−1.52232	+	0.266442i
$435$		0			0
$436$			22.4583i			1.07556i
$437$	−32.2906	+	18.6430i	−1.54467	+	0.891816i
$438$		0			0
$439$	−14.7172	−	25.4909i	−0.702414	−	1.21662i	−0.967617	−	0.252424i	$-0.918772\pi$
$439$	−14.7172	−	25.4909i	−0.702414	−	1.21662i	0.265203	−	0.964193i	$-0.414561\pi$
$440$	−0.214290	−	0.123720i	−0.0102159	−	0.00589813i
$441$		0			0
$442$	−46.0646	−	20.5037i	−2.19107	−	0.975260i
$443$	−0.974301	+	1.68754i	−0.0462904	+	0.0801773i	−0.888242	−	0.459375i	$-0.848073\pi$
$443$	−0.974301	+	1.68754i	−0.0462904	+	0.0801773i	0.841952	+	0.539553i	$0.181407\pi$
$444$		0			0
$445$	−4.92559			−0.233495
$446$	−1.65938			−0.0785738
$447$		0			0
$448$	16.0986	+	19.2349i	0.760588	+	0.908763i
$449$	18.7184	−	10.8071i	0.883376	−	0.510017i	0.0116058	−	0.999933i	$-0.496306\pi$
$449$	18.7184	−	10.8071i	0.883376	−	0.510017i	0.871770	+	0.489915i	$0.162972\pi$
$450$		0			0
$451$	−5.58282	+	9.66972i	−0.262885	+	0.455329i
$452$	27.1584			1.27743
$453$		0			0
$454$	−1.14019			−0.0535117
$455$	3.64786	+	0.914018i	0.171015	+	0.0428498i
$456$		0			0
$457$	−16.5997	+	9.58384i	−0.776501	+	0.448313i	−0.835189	−	0.549963i	$-0.814642\pi$
$457$	−16.5997	+	9.58384i	−0.776501	+	0.448313i	0.0586878	+	0.998276i	$0.481308\pi$
$458$	−33.7446			−1.57678
$459$		0			0
$460$	3.58555	+	2.07012i	0.167177	+	0.0965196i
$461$	−6.88906	+	3.97740i	−0.320856	+	0.185246i	−0.651774	−	0.758413i	$-0.725975\pi$
$461$	−6.88906	+	3.97740i	−0.320856	+	0.185246i	0.330918	+	0.943659i	$0.392642\pi$
$462$		0			0
$463$			9.39286i			0.436523i	0.975890	+	0.218262i	$0.0700386\pi$
$463$			9.39286i			0.436523i	−0.975890	+	0.218262i	$0.929961\pi$
$464$	28.1492			1.30679
$465$		0			0
$466$			13.5618i			0.628238i
$467$	−16.4836	+	28.5505i	−0.762771	+	1.32116i	0.178645	+	0.983914i	$0.442829\pi$
$467$	−16.4836	+	28.5505i	−0.762771	+	1.32116i	−0.941417	+	0.337245i	$0.890505\pi$
$468$		0			0
$469$	5.66089	−	4.73787i	0.261395	−	0.218774i
$470$	−3.97645	−	2.29581i	−0.183420	−	0.105898i
$471$		0			0
$472$	−2.29377	+	3.97293i	−0.105579	+	0.182869i
$473$	9.91158	−	5.72245i	0.455735	−	0.263119i
$474$		0			0
$475$	32.7033	−	18.8812i	1.50053	−	0.866331i
$476$	13.6113	−	37.2502i	0.623873	−	1.70736i
$477$		0			0
$478$	−6.22070	−	10.7746i	−0.284528	−	0.492817i
$479$			1.13404i			0.0518156i	0.999664	+	0.0259078i	$0.00824763\pi$
$479$			1.13404i			0.0518156i	−0.999664	+	0.0259078i	$0.991752\pi$
$480$		0			0
$481$	−0.442844	−	4.20925i	−0.0201919	−	0.191925i
$482$	42.3326			1.92820
$483$		0			0
$484$	9.37965	−	16.2460i	0.426348	−	0.738456i
$485$	−4.36124			−0.198034
$486$		0			0
$487$	−35.2195	−	20.3340i	−1.59595	−	0.921420i	−0.992257	−	0.124199i	$-0.960364\pi$
$487$	−35.2195	−	20.3340i	−1.59595	−	0.921420i	−0.603689	−	0.797220i	$-0.706303\pi$
$488$			4.91356i			0.222427i
$489$		0			0
$490$	−0.995594	+	5.56402i	−0.0449764	+	0.251357i
$491$	14.7283	−	25.5102i	0.664679	−	1.15126i	−0.314693	−	0.949194i	$-0.601902\pi$
$491$	14.7283	−	25.5102i	0.664679	−	1.15126i	0.979372	−	0.202065i	$-0.0647651\pi$
$492$		0			0
$493$	−26.9115	−	46.6120i	−1.21203	−	2.09930i
$494$	57.2505	−	6.02317i	2.57582	−	0.270995i
$495$		0			0
$496$	−18.3713	−	10.6067i	−0.824895	−	0.476253i
$497$	−21.9926	−	8.03615i	−0.986503	−	0.360470i
$498$		0			0
$499$	16.4691	+	9.50845i	0.737259	+	0.425657i	0.821072	−	0.570825i	$-0.193376\pi$
$499$	16.4691	+	9.50845i	0.737259	+	0.425657i	−0.0838128	+	0.996482i	$0.526710\pi$
$500$	−7.37922	−	4.26039i	−0.330009	−	0.190531i
$501$		0			0
$502$	27.0060	+	15.5919i	1.20534	+	0.695901i
$503$	4.49406	+	7.78393i	0.200380	+	0.347068i	0.948651	−	0.316325i	$-0.102449\pi$
$503$	4.49406	+	7.78393i	0.200380	+	0.347068i	−0.748271	+	0.663393i	$0.769116\pi$
$504$		0			0
$505$	1.79739	+	1.03773i	0.0799830	+	0.0461782i
$506$	7.67711	−	13.2971i	0.341289	−	0.591130i
$507$		0			0
$508$	−4.73563	−	8.20234i	−0.210109	−	0.363920i
$509$	−1.81871	+	1.05003i	−0.0806127	+	0.0465418i	−0.539765	−	0.841816i	$-0.681487\pi$
$509$	−1.81871	+	1.05003i	−0.0806127	+	0.0465418i	0.459152	+	0.888358i	$0.348153\pi$
$510$		0			0
$511$	6.41546	+	2.34422i	0.283803	+	0.103702i
$512$			31.8360i			1.40696i
$513$		0			0
$514$	−3.01690	−	1.74181i	−0.133070	−	0.0768279i
$515$	0.767452	−	0.443089i	0.0338180	−	0.0195248i
$516$		0			0
$517$	−4.45546	+	7.71708i	−0.195951	+	0.339397i
$518$	6.26634	−	1.09676i	0.275327	−	0.0481889i
$519$		0			0
$520$	−0.334681	−	0.460550i	−0.0146767	−	0.0201964i
$521$	15.5547	+	26.9416i	0.681464	+	1.18033i	0.974534	+	0.224240i	$0.0719899\pi$
$521$	15.5547	+	26.9416i	0.681464	+	1.18033i	−0.293070	+	0.956091i	$0.594677\pi$
$522$		0			0
$523$	21.6208	+	37.4484i	0.945413	+	1.63750i	0.754922	+	0.655814i	$0.227675\pi$
$523$	21.6208	+	37.4484i	0.945413	+	1.63750i	0.190491	+	0.981689i	$0.438992\pi$
$524$	−12.9240	−	22.3850i	−0.564588	−	0.977895i
$525$		0			0
$526$	−14.5158	+	8.38072i	−0.632920	+	0.365417i
$527$			40.5612i			1.76687i
$528$		0			0
$529$	0.0592432	−	0.102612i	0.00257579	−	0.00446140i
$530$	0.779221	+	1.34965i	0.0338472	+	0.0586251i
$531$		0			0
$532$	7.80622	+	44.6008i	0.338442	+	1.93369i
$533$	−20.7821	+	15.1023i	−0.900172	+	0.654154i
$534$		0			0
$535$			1.52279i			0.0658358i
$536$	−1.11753			−0.0482701
$537$		0			0
$538$			23.8842i			1.02972i
$539$	10.7981	+	1.93214i	0.465105	+	0.0832233i
$540$		0			0
$541$	14.8267	+	8.56020i	0.637450	+	0.368032i	0.783631	−	0.621226i	$-0.213365\pi$
$541$	14.8267	+	8.56020i	0.637450	+	0.368032i	−0.146182	+	0.989258i	$0.546698\pi$
$542$	5.78548	−	10.0207i	0.248508	−	0.430428i
$543$		0			0
$544$	47.9805	−	27.7016i	2.05715	−	1.18770i
$545$	−4.03250			−0.172733
$546$		0			0
$547$	−5.89728			−0.252149			−0.126075	−	0.992021i	$-0.540238\pi$
$547$	−5.89728			−0.252149			−0.126075	+	0.992021i	$0.540238\pi$
$548$	14.5073	−	8.37579i	0.619721	−	0.357796i
$549$		0			0
$550$	−7.77521	+	13.4671i	−0.331536	+	0.574238i
$551$	53.2169	+	30.7248i	2.26712	+	1.30892i
$552$		0			0
$553$	8.11085	−	1.41959i	0.344909	−	0.0603673i
$554$		−	49.1008i		−	2.08609i
$555$		0			0
$556$	−7.49251			−0.317753
$557$			37.4899i			1.58850i	0.607592	+	0.794249i	$0.292136\pi$
$557$			37.4899i			1.58850i	−0.607592	+	0.794249i	$0.707864\pi$
$558$		0			0
$559$	26.1880	−	2.75517i	1.10763	−	0.116531i
$560$	−2.85597	+	2.39030i	−0.120687	+	0.101008i
$561$		0			0
$562$	−20.7783	−	35.9890i	−0.876478	−	1.51810i
$563$	18.7354	−	32.4506i	0.789602	−	1.36763i	−0.136608	−	0.990625i	$-0.543620\pi$
$563$	18.7354	−	32.4506i	0.789602	−	1.36763i	0.926211	−	0.377006i	$-0.123047\pi$
$564$		0			0
$565$			4.87643i			0.205153i
$566$	−3.73958	+	2.15905i	−0.157186	+	0.0907516i
$567$		0			0
$568$	1.77236	+	3.06981i	0.0743665	+	0.128807i
$569$	−21.8309	−	37.8123i	−0.915200	−	1.58517i	−0.806608	−	0.591086i	$-0.798699\pi$
$569$	−21.8309	−	37.8123i	−0.915200	−	1.58517i	−0.108592	−	0.994086i	$-0.534634\pi$
$570$		0			0
$571$	5.02695	+	8.70694i	0.210371	+	0.364374i	0.951831	−	0.306624i	$-0.0991993\pi$
$571$	5.02695	+	8.70694i	0.210371	+	0.364374i	−0.741459	+	0.670998i	$0.765866\pi$
$572$	−10.0353	+	7.29264i	−0.419597	+	0.304921i
$573$		0			0
$574$	−24.7827	−	29.6107i	−1.03441	−	1.23593i
$575$	11.5870	−	20.0692i	0.483209	−	0.836943i
$576$		0			0
$577$	18.7295	−	10.8135i	0.779719	−	0.450171i	−0.0566114	−	0.998396i	$-0.518030\pi$
$577$	18.7295	−	10.8135i	0.779719	−	0.450171i	0.836331	+	0.548225i	$0.184696\pi$
$578$	−52.5293	−	30.3278i	−2.18493	−	1.26147i
$579$		0			0
$580$		−	6.82335i		−	0.283324i
$581$	6.11013	−	5.11387i	0.253491	−	0.212159i
$582$		0			0
$583$	2.61926	−	1.51223i	0.108479	−	0.0626302i
$584$	−0.517014	−	0.895495i	−0.0213942	−	0.0370558i
$585$		0			0
$586$	3.06539	−	5.30941i	0.126630	−	0.219330i
$587$	−10.4783	−	6.04967i	−0.432487	−	0.249697i	0.267918	−	0.963442i	$-0.413664\pi$
$587$	−10.4783	−	6.04967i	−0.432487	−	0.249697i	−0.700406	+	0.713745i	$0.746998\pi$
$588$		0			0
$589$	−23.1543	−	40.1045i	−0.954058	−	1.65248i
$590$	−8.00950	−	4.62428i	−0.329746	−	0.190379i
$591$		0			0
$592$	3.62998	+	2.09577i	0.149191	+	0.0861355i
$593$	11.4586	+	6.61565i	0.470550	+	0.271672i	0.716470	−	0.697618i	$-0.245757\pi$
$593$	11.4586	+	6.61565i	0.470550	+	0.271672i	−0.245920	+	0.969290i	$0.579090\pi$
$594$		0			0
$595$	6.68847	+	2.44398i	0.274200	+	0.100193i
$596$	16.2681	+	9.39237i	0.666366	+	0.384726i
$597$		0			0
$598$	28.5781	−	20.7677i	1.16865	−	0.849253i
$599$	−3.64418	−	6.31190i	−0.148897	−	0.257897i	0.781923	−	0.623375i	$-0.214239\pi$
$599$	−3.64418	−	6.31190i	−0.148897	−	0.257897i	−0.930820	+	0.365478i	$0.880906\pi$
$600$		0			0
$601$	8.80780	−	15.2556i	0.359278	−	0.622287i	−0.628563	−	0.777759i	$-0.716356\pi$
$601$	8.80780	−	15.2556i	0.359278	−	0.622287i	0.987840	+	0.155472i	$0.0496897\pi$
$602$	6.82354	+	38.9863i	0.278107	+	1.58896i
$603$		0			0
$604$		−	46.9039i		−	1.90849i
$605$	2.91706	+	1.68416i	0.118595	+	0.0684710i
$606$		0			0
$607$	30.9965			1.25811			0.629055	−	0.777361i	$-0.283442\pi$
$607$	30.9965			1.25811			0.629055	+	0.777361i	$0.283442\pi$
$608$	−31.6269	+	54.7793i	−1.28264	+	2.22160i
$609$		0			0
$610$	−9.90584			−0.401076
$611$	−16.5855	+	12.0527i	−0.670977	+	0.487598i
$612$		0			0
$613$			38.7895i			1.56669i	0.621586	+	0.783346i	$0.286489\pi$
$613$			38.7895i			1.56669i	−0.621586	+	0.783346i	$0.713511\pi$
$614$	−1.95999	−	3.39481i	−0.0790989	−	0.137003i
$615$		0			0
$616$	−1.06584	−	1.27348i	−0.0429439	−	0.0513101i
$617$	20.2564	−	11.6951i	0.815493	−	0.470825i	−0.0333668	−	0.999443i	$-0.510623\pi$
$617$	20.2564	−	11.6951i	0.815493	−	0.470825i	0.848860	+	0.528618i	$0.177290\pi$
$618$		0			0
$619$	12.2074	−	7.04795i	0.490657	−	0.283281i	−0.234190	−	0.972191i	$-0.575244\pi$
$619$	12.2074	−	7.04795i	0.490657	−	0.283281i	0.724847	+	0.688910i	$0.241910\pi$
$620$	−2.57105	+	4.45319i	−0.103256	+	0.178845i
$621$		0			0
$622$	11.9754	+	6.91402i	0.480171	+	0.277227i
$623$	−31.0494	−	11.3455i	−1.24397	−	0.454548i
$624$		0			0
$625$	−11.3465	+	19.6527i	−0.453860	+	0.786108i
$626$		−	22.5736i		−	0.902223i
$627$		0			0
$628$	6.22522			0.248413
$629$		−	8.01447i		−	0.319558i
$630$		0			0
$631$	12.5153	−	7.22569i	0.498224	−	0.287650i	−0.229756	−	0.973248i	$-0.573793\pi$
$631$	12.5153	−	7.22569i	0.498224	−	0.287650i	0.727980	+	0.685598i	$0.240459\pi$
$632$	−1.07954	−	0.623274i	−0.0429419	−	0.0247925i
$633$		0			0
$634$	25.5417			1.01439
$635$	1.47277	−	0.850306i	0.0584452	−	0.0337434i
$636$		0			0
$637$	20.8897	+	14.1641i	0.827679	+	0.561202i
$638$	−25.3047			−1.00182
$639$		0			0
$640$	1.25715			0.0496934
$641$	−7.62425	+	13.2056i	−0.301140	+	0.521589i	−0.976394	−	0.215995i	$-0.930700\pi$
$641$	−7.62425	+	13.2056i	−0.301140	+	0.521589i	0.675255	+	0.737585i	$0.264034\pi$
$642$		0			0
$643$	−23.1303	+	13.3543i	−0.912171	+	0.526642i	−0.881129	−	0.472876i	$-0.843216\pi$
$643$	−23.1303	+	13.3543i	−0.912171	+	0.526642i	−0.0310418	+	0.999518i	$0.509882\pi$
$644$	17.8339	+	21.3082i	0.702754	+	0.839662i
$645$		0			0
$646$	109.006			4.28878
$647$	46.2690			1.81902			0.909511	−	0.415680i	$-0.136456\pi$
$647$	46.2690			1.81902			0.909511	+	0.415680i	$0.136456\pi$
$648$		0			0
$649$	−8.97432	+	15.5440i	−0.352273	+	0.610155i
$650$	−28.9433	+	21.0331i	−1.13525	+	0.824984i
$651$		0			0
$652$	19.7427	+	11.3984i	0.773182	+	0.446397i
$653$	14.7408	+	25.5319i	0.576854	+	0.999140i	0.995838	+	0.0911461i	$0.0290530\pi$
$653$	14.7408	+	25.5319i	0.576854	+	0.999140i	−0.418984	+	0.907994i	$0.637614\pi$
$654$		0			0
$655$	4.01935	−	2.32057i	0.157049	−	0.0906722i
$656$		−	25.4415i		−	0.993323i
$657$		0			0
$658$	−19.7782	−	23.6313i	−0.771035	−	0.921246i
$659$	15.5729	+	26.9730i	0.606633	+	1.05072i	0.991791	+	0.127868i	$0.0408135\pi$
$659$	15.5729	+	26.9730i	0.606633	+	1.05072i	−0.385158	+	0.922850i	$0.625853\pi$
$660$		0			0
$661$			21.1304i			0.821877i	0.911663	+	0.410939i	$0.134799\pi$
$661$			21.1304i			0.821877i	−0.911663	+	0.410939i	$0.865201\pi$
$662$	19.5658	+	33.8890i	0.760448	+	1.31713i
$663$		0			0
$664$	−1.20622			−0.0468105
$665$	−8.00830	+	1.40165i	−0.310549	+	0.0543535i
$666$		0			0
$667$	37.7101			1.46014
$668$	−13.1625	+	7.59937i	−0.509272	+	0.294029i
$669$		0			0
$670$		−	2.25297i		−	0.0870399i
$671$			19.2242i			0.742142i
$672$		0			0
$673$	10.9573	−	18.9786i	0.422372	−	0.731570i	−0.573799	−	0.818996i	$-0.694531\pi$
$673$	10.9573	−	18.9786i	0.422372	−	0.731570i	0.996171	+	0.0874263i	$0.0278642\pi$
$674$	62.8889	−	36.3089i	2.42239	−	1.39857i
$675$		0			0
$676$	−27.9172	+	5.93992i	−1.07374	+	0.228459i
$677$	−7.94438	+	13.7601i	−0.305327	+	0.528843i	−0.977334	−	0.211702i	$-0.932099\pi$
$677$	−7.94438	+	13.7601i	−0.305327	+	0.528843i	0.672007	+	0.740545i	$0.265433\pi$
$678$		0			0
$679$	−27.4919	−	10.0456i	−1.05504	−	0.385515i
$680$	−0.539015	−	0.933602i	−0.0206703	−	0.0358020i
$681$		0			0
$682$	16.5149	+	9.53486i	0.632387	+	0.365109i
$683$	−22.7450	−	13.1319i	−0.870315	−	0.502476i	−0.00286197	−	0.999996i	$-0.500911\pi$
$683$	−22.7450	−	13.1319i	−0.870315	−	0.502476i	−0.867453	+	0.497519i	$0.834244\pi$
$684$		0			0
$685$	1.50392	+	2.60486i	0.0574616	+	0.0995265i
$686$	−19.0920	+	32.7806i	−0.728935	+	1.25157i
$687$		0			0
$688$	−13.0389	+	22.5840i	−0.497104	+	0.861009i
$689$	6.92051	−	0.728088i	0.263650	−	0.0277379i
$690$		0			0
$691$	−21.4997	+	12.4129i	−0.817888	+	0.472208i	−0.849688	−	0.527286i	$-0.823210\pi$
$691$	−21.4997	+	12.4129i	−0.817888	+	0.472208i	0.0317996	+	0.999494i	$0.489876\pi$
$692$	10.9732	−	19.0061i	0.417137	−	0.722503i
$693$		0			0
$694$		−	36.9688i		−	1.40332i
$695$		−	1.34532i		−	0.0510308i
$696$		0			0
$697$	−42.1284	+	24.3228i	−1.59573	+	0.921293i
$698$	−28.7621			−1.08866
$699$		0			0
$700$	−18.0618	−	21.5805i	−0.682671	−	0.815667i
$701$	−7.27739			−0.274863			−0.137432	−	0.990511i	$-0.543885\pi$
$701$	−7.27739			−0.274863			−0.137432	+	0.990511i	$0.543885\pi$
$702$		0			0
$703$	4.57506	+	7.92423i	0.172552	+	0.298868i
$704$		−	14.8566i		−	0.559927i
$705$		0			0
$706$	1.15027	+	1.99232i	0.0432909	+	0.0749821i
$707$	8.93993	+	10.6816i	0.336221	+	0.401722i
$708$		0			0
$709$			20.0090i			0.751452i	0.926731	+	0.375726i	$0.122607\pi$
$709$			20.0090i			0.751452i	−0.926731	+	0.375726i	$0.877393\pi$
$710$	−6.18881	+	3.57311i	−0.232262	+	0.134096i
$711$		0			0
$712$	2.50223	+	4.33399i	0.0937751	+	0.162423i
$713$	−24.6111	−	14.2093i	−0.921695	−	0.532141i
$714$		0			0
$715$	−1.30943	−	1.80189i	−0.0489699	−	0.0673869i
$716$	−23.6567	+	40.9746i	−0.884092	+	1.53129i
$717$		0			0
$718$	15.0944			0.563318
$719$	−23.4767			−0.875535			−0.437767	−	0.899088i	$-0.644231\pi$
$719$	−23.4767			−0.875535			−0.437767	+	0.899088i	$0.644231\pi$
$720$		0			0
$721$	5.85838	−	1.02536i	0.218178	−	0.0381863i
$722$	−74.0747	+	42.7670i	−2.75677	+	1.59162i
$723$		0			0
$724$	10.3264	−	17.8859i	0.383779	−	0.664725i
$725$	−38.1920			−1.41842
$726$		0			0
$727$	−19.2442			−0.713727			−0.356863	−	0.934157i	$-0.616154\pi$
$727$	−19.2442			−0.713727			−0.356863	+	0.934157i	$0.616154\pi$
$728$	−1.04890	−	3.67406i	−0.0388749	−	0.136170i
$729$		0			0
$730$	1.80534	−	1.04231i	0.0668185	−	0.0385777i
$731$	49.8624			1.84423
$732$		0			0
$733$	22.6286	+	13.0646i	0.835808	+	0.482554i	0.855837	−	0.517246i	$-0.173043\pi$
$733$	22.6286	+	13.0646i	0.835808	+	0.482554i	−0.0200293	+	0.999799i	$0.506376\pi$
$734$	35.0763	−	20.2513i	1.29469	−	0.747491i
$735$		0			0
$736$			38.8173i			1.43082i
$737$	−4.37233			−0.161057
$738$		0			0
$739$			18.5985i			0.684158i	0.939671	+	0.342079i	$0.111131\pi$
$739$			18.5985i			0.684158i	−0.939671	+	0.342079i	$0.888869\pi$
$740$	0.508013	−	0.879905i	0.0186749	−	0.0323460i
$741$		0			0
$742$	1.80321	+	10.3026i	0.0661978	+	0.378221i
$743$	−31.1212	−	17.9678i	−1.14173	−	0.659176i	−0.194869	−	0.980829i	$-0.562428\pi$
$743$	−31.1212	−	17.9678i	−1.14173	−	0.659176i	−0.946858	+	0.321653i	$0.895762\pi$
$744$		0			0
$745$	−1.68645	+	2.92101i	−0.0617866	+	0.107018i
$746$	16.5263	−	9.54145i	0.605070	−	0.349337i
$747$		0			0
$748$	−20.3430	+	11.7451i	−0.743815	+	0.429442i
$749$	−3.50756	+	9.59917i	−0.128163	+	0.350746i
$750$		0			0
$751$	0.104323	+	0.180692i	0.00380679	+	0.00659356i	0.867923	−	0.496700i	$-0.165455\pi$
$751$	0.104323	+	0.180692i	0.00380679	+	0.00659356i	−0.864116	+	0.503293i	$0.832122\pi$
$752$		−	20.3040i		−	0.740410i
$753$		0			0
$754$	−53.1901	−	23.6753i	−1.93707	−	0.862203i
$755$	8.42184			0.306502
$756$		0			0
$757$	−16.7911	+	29.0830i	−0.610282	+	1.05704i	0.380910	+	0.924612i	$0.375611\pi$
$757$	−16.7911	+	29.0830i	−0.610282	+	1.05704i	−0.991193	+	0.132428i	$0.957723\pi$
$758$	−25.6167			−0.930440
$759$		0			0
$760$	1.06589	+	0.615393i	0.0386640	+	0.0223227i
$761$			13.2279i			0.479512i	0.970833	+	0.239756i	$0.0770674\pi$
$761$			13.2279i			0.479512i	−0.970833	+	0.239756i	$0.922933\pi$
$762$		0			0
$763$	−25.4196	−	9.28838i	−0.920252	−	0.336262i
$764$	−11.4353	+	19.8065i	−0.413715	+	0.716576i
$765$		0			0
$766$	−35.6662	−	61.7757i	−1.28867	−	2.23205i
$767$	−33.4070	+	24.2768i	−1.20626	+	0.876585i
$768$		0			0
$769$	3.35265	+	1.93565i	0.120900	+	0.0698014i	0.559230	−	0.829012i	$-0.311097\pi$
$769$	3.35265	+	1.93565i	0.120900	+	0.0698014i	−0.438331	+	0.898814i	$0.644430\pi$
$770$	2.56737	−	2.14875i	0.0925216	−	0.0774358i
$771$		0			0
$772$	−42.6570	−	24.6280i	−1.53526	−	0.886382i
$773$	−10.2462	−	5.91567i	−0.368532	−	0.212772i	0.304285	−	0.952581i	$-0.401582\pi$
$773$	−10.2462	−	5.91567i	−0.368532	−	0.212772i	−0.672817	+	0.739809i	$0.734916\pi$
$774$		0			0
$775$	24.9256	+	14.3908i	0.895356	+	0.516934i
$776$	2.21554	+	3.83743i	0.0795332	+	0.137756i
$777$		0			0
$778$	25.6456	+	14.8065i	0.919439	+	0.530838i
$779$	27.7693	−	48.0979i	0.994940	−	1.72329i
$780$		0			0
$781$	6.93431	+	12.0106i	0.248129	+	0.429772i
$782$	57.9321	−	33.4471i	2.07165	−	1.19607i
$783$		0			0
$784$	−23.5089	+	8.48930i	−0.839603	+	0.303189i
$785$			1.11777i			0.0398949i
$786$		0			0
$787$	−40.7027	−	23.4997i	−1.45089	−	0.837674i	−0.452361	−	0.891835i	$-0.649418\pi$
$787$	−40.7027	−	23.4997i	−1.45089	−	0.837674i	−0.998532	+	0.0541612i	$0.982752\pi$
$788$	−43.8873	+	25.3383i	−1.56342	+	0.902641i
$789$		0			0
$790$	1.25653	−	2.17638i	0.0447054	−	0.0774321i
$791$	−11.2323	+	30.7395i	−0.399374	+	1.09297i
$792$		0			0
$793$	−17.9863	+	40.4090i	−0.638713	+	1.43497i
$794$	3.91121	+	6.77442i	0.138804	+	0.240415i
$795$		0			0
$796$	−0.575009	−	0.995945i	−0.0203807	−	0.0353003i
$797$	−25.8005	−	44.6879i	−0.913902	−	1.58293i	−0.808500	−	0.588496i	$-0.799720\pi$
$797$	−25.8005	−	44.6879i	−0.913902	−	1.58293i	−0.105402	−	0.994430i	$-0.533613\pi$
$798$		0			0
$799$	−33.6212	+	19.4112i	−1.18943	+	0.686720i
$800$		−	39.3133i		−	1.38994i
$801$		0			0
$802$	12.9270	−	22.3903i	0.456470	−	0.790629i
$803$	−2.02281	−	3.50360i	−0.0713833	−	0.123639i
$804$		0			0
$805$	−3.82600	+	3.20217i	−0.134849	+	0.112862i
$806$	25.7931	+	35.4936i	0.908525	+	1.25021i
$807$		0			0
$808$		−	2.10869i		−	0.0741833i
$809$	−9.68476			−0.340498			−0.170249	−	0.985401i	$-0.554457\pi$
$809$	−9.68476			−0.340498			−0.170249	+	0.985401i	$0.554457\pi$
$810$		0			0
$811$		−	3.81953i		−	0.134122i	−0.997749	−	0.0670609i	$-0.978638\pi$
$811$		−	3.81953i		−	0.134122i	0.997749	−	0.0670609i	$-0.0213622\pi$
$812$	15.7168	−	43.0123i	0.551551	−	1.50943i
$813$		0			0
$814$	−3.26316	−	1.88399i	−0.114374	−	0.0660338i
$815$	−2.04665	+	3.54489i	−0.0716909	+	0.124172i
$816$		0			0
$817$	−49.3009	+	28.4639i	−1.72482	+	0.995826i
$818$	64.6122			2.25911
$819$		0			0
$820$	−6.16701			−0.215361
$821$	13.7192	−	7.92077i	0.478802	−	0.276437i	−0.241115	−	0.970497i	$-0.577513\pi$
$821$	13.7192	−	7.92077i	0.478802	−	0.276437i	0.719917	+	0.694060i	$0.244180\pi$
$822$		0			0
$823$	−14.2018	+	24.5983i	−0.495044	+	0.857442i	−0.999984	−	0.00571309i	$-0.998181\pi$
$823$	−14.2018	+	24.5983i	−0.495044	+	0.857442i	0.504940	+	0.863155i	$0.331515\pi$
$824$	−0.779742	−	0.450184i	−0.0271636	−	0.0156829i
$825$		0			0
$826$	−39.8379	−	47.5990i	−1.38614	−	1.65618i
$827$			8.88006i			0.308790i	0.988009	+	0.154395i	$0.0493428\pi$
$827$			8.88006i			0.308790i	−0.988009	+	0.154395i	$0.950657\pi$
$828$		0			0
$829$	53.2728			1.85024			0.925120	−	0.379676i	$-0.123964\pi$
$829$	53.2728			1.85024			0.925120	+	0.379676i	$0.123964\pi$
$830$		−	2.43177i		−	0.0844079i
$831$		0			0
$832$	13.8999	−	31.2283i	0.481893	−	1.08265i
$833$	36.5326	+	30.8122i	1.26578	+	1.06758i
$834$		0			0
$835$	−1.36451	−	2.36339i	−0.0472207	−	0.0817886i
$836$	13.4093	−	23.2256i	0.463771	−	0.803275i
$837$		0			0
$838$			21.2745i			0.734916i
$839$	−13.0429	+	7.53032i	−0.450291	+	0.259976i	−0.707953	−	0.706260i	$-0.750381\pi$
$839$	−13.0429	+	7.53032i	−0.450291	+	0.259976i	0.257662	+	0.966235i	$0.417048\pi$
$840$		0			0
$841$	−16.5743	−	28.7075i	−0.571526	−	0.989913i
$842$	0.376975	+	0.652940i	0.0129914	+	0.0225018i
$843$		0			0
$844$	9.75356	+	16.8937i	0.335732	+	0.581504i
$845$	−1.06654	−	5.01267i	−0.0366902	−	0.172441i
$846$		0			0
$847$	14.5090	+	17.3355i	0.498533	+	0.595656i
$848$	−3.44569	+	5.96812i	−0.118326	+	0.204946i
$849$		0			0
$850$	−58.6724	+	33.8745i	−2.01245	+	1.16189i
$851$	4.86291	+	2.80760i	0.166698	+	0.0962433i
$852$		0			0
$853$		−	14.1733i		−	0.485283i	−0.970116	−	0.242642i	$-0.921986\pi$
$853$		−	14.1733i		−	0.485283i	0.970116	−	0.242642i	$-0.0780139\pi$
$854$	−62.4433	−	22.8169i	−2.13677	−	0.780779i
$855$		0			0
$856$	1.33989	−	0.773586i	0.0457965	−	0.0264406i
$857$	−16.5154	−	28.6055i	−0.564156	−	0.977147i	−0.997128	−	0.0757394i	$-0.975868\pi$
$857$	−16.5154	−	28.6055i	−0.564156	−	0.977147i	0.432972	−	0.901408i	$-0.357465\pi$
$858$		0			0
$859$	−0.596346	+	1.03290i	−0.0203471	+	0.0352421i	−0.876020	−	0.482275i	$-0.839810\pi$
$859$	−0.596346	+	1.03290i	−0.0203471	+	0.0352421i	0.855673	+	0.517518i	$0.173144\pi$
$860$	5.47437	+	3.16063i	0.186674	+	0.107776i
$861$		0			0
$862$	15.7646	+	27.3050i	0.536943	+	0.930013i
$863$	−4.99176	−	2.88199i	−0.169921	−	0.0981042i	0.412627	−	0.910900i	$-0.364611\pi$
$863$	−4.99176	−	2.88199i	−0.169921	−	0.0981042i	−0.582549	+	0.812796i	$0.697945\pi$
$864$		0			0
$865$	3.41264	+	1.97029i	0.116033	+	0.0669918i
$866$	32.4201	+	18.7177i	1.10168	+	0.636055i
$867$		0			0
$868$	−26.4645	+	22.1494i	−0.898264	+	0.751801i
$869$	−4.22368	−	2.43855i	−0.143279	−	0.0827220i
$870$		0			0
$871$	−9.19058	−	4.09079i	−0.311411	−	0.138611i
$872$	2.04854	+	3.54817i	0.0693722	+	0.120156i
$873$		0			0
$874$	−38.1865	+	66.1410i	−1.29168	+	2.23725i
$875$	7.87409	−	6.59021i	0.266193	−	0.222790i
$876$		0			0
$877$		−	5.02221i		−	0.169588i	−0.996399	−	0.0847940i	$-0.972977\pi$
$877$		−	5.02221i		−	0.169588i	0.996399	−	0.0847940i	$-0.0270232\pi$
$878$	−52.2132	−	30.1453i	−1.76211	−	1.01735i
$879$		0			0
$880$	2.20588			0.0743601
$881$	6.29570	−	10.9045i	0.212108	−	0.367381i	−0.740266	−	0.672314i	$-0.765301\pi$
$881$	6.29570	−	10.9045i	0.212108	−	0.367381i	0.952374	+	0.304933i	$0.0986339\pi$
$882$		0			0
$883$	10.5722			0.355783			0.177891	−	0.984050i	$-0.443072\pi$
$883$	10.5722			0.355783			0.177891	+	0.984050i	$0.443072\pi$
$884$	−53.7496	+	5.65485i	−1.80780	+	0.190193i
$885$		0			0
$886$			3.99132i			0.134091i
$887$	4.47643	+	7.75341i	0.150304	+	0.260334i	0.931339	−	0.364153i	$-0.118641\pi$
$887$	4.47643	+	7.75341i	0.150304	+	0.260334i	−0.781035	+	0.624487i	$0.785308\pi$
$888$		0			0
$889$	11.2425	−	1.96771i	0.377061	−	0.0659947i
$890$	−8.73741	+	5.04455i	−0.292879	+	0.169094i
$891$		0			0
$892$	−1.54037	+	0.889331i	−0.0515753	+	0.0297770i
$893$	22.1618	−	38.3853i	0.741616	−	1.28452i
$894$		0			0
$895$	−7.35720	−	4.24768i	−0.245924	−	0.141984i
$896$	7.92471	+	2.89571i	0.264746	+	0.0967387i
$897$		0			0
$898$	22.1362	−	38.3409i	0.738693	−	1.27945i
$899$			46.8354i			1.56205i
$900$		0			0
$901$	13.1768			0.438981
$902$			22.8706i			0.761508i
$903$		0			0
$904$	4.29074	−	2.47726i	0.142708	−	0.0823925i
$905$	3.21151	+	1.85416i	0.106754	+	0.0616345i
$906$		0			0
$907$	−36.3423			−1.20673			−0.603363	−	0.797467i	$-0.706173\pi$
$907$	−36.3423			−1.20673			−0.603363	+	0.797467i	$0.706173\pi$
$908$	−1.05841	+	0.611075i	−0.0351247	+	0.0202792i
$909$		0			0
$910$	7.40697	−	2.11461i	0.245539	−	0.0700985i
$911$	−3.79484			−0.125729			−0.0628643	−	0.998022i	$-0.520024\pi$
$911$	−3.79484			−0.125729			−0.0628643	+	0.998022i	$0.520024\pi$
$912$		0			0
$913$	−4.71932			−0.156187
$914$	−19.6306	+	34.0012i	−0.649323	+	1.12466i
$915$		0			0
$916$	−31.3244	+	18.0852i	−1.03499	+	0.597550i
$917$	30.6819	−	5.37007i	1.01320	−	0.177335i
$918$		0			0
$919$	−3.37277			−0.111257			−0.0556286	−	0.998452i	$-0.517716\pi$
$919$	−3.37277			−0.111257			−0.0556286	+	0.998452i	$0.517716\pi$
$920$	0.755304			0.0249016
$921$		0			0
$922$	−8.14693	+	14.1109i	−0.268305	+	0.464717i
$923$	3.33864	+	31.7339i	0.109893	+	1.04453i
$924$		0			0
$925$	−4.92505	−	2.84348i	−0.161935	−	0.0934930i
$926$	9.61971	+	16.6618i	0.316123	+	0.547542i
$927$		0			0
$928$	55.4024	−	31.9866i	1.81867	−	1.05001i
$929$			34.1704i			1.12110i	0.828122	+	0.560548i	$0.189409\pi$
$929$			34.1704i			1.12110i	−0.828122	+	0.560548i	$0.810591\pi$
$930$		0			0
$931$	−53.7104	−	9.61063i	−1.76029	−	0.314976i
$932$	7.26834	+	12.5891i	0.238083	+	0.412371i
$933$		0			0
$934$			67.5269i			2.20955i
$935$	−2.10889	−	3.65270i	−0.0689679	−	0.119456i
$936$		0			0
$937$	−12.8036			−0.418275			−0.209138	−	0.977886i	$-0.567066\pi$
$937$	−12.8036			−0.418275			−0.209138	+	0.977886i	$0.567066\pi$
$938$	5.18945	−	14.2020i	0.169442	−	0.463713i
$939$		0			0
$940$	−4.92168			−0.160528
$941$	−42.7039	+	24.6551i	−1.39211	+	0.803733i	−0.993548	−	0.113410i	$-0.963823\pi$
$941$	−42.7039	+	24.6551i	−1.39211	+	0.803733i	−0.398558	+	0.917143i	$0.630489\pi$
$942$		0			0
$943$		−	34.0827i		−	1.10989i
$944$		−	40.8969i		−	1.33108i
$945$		0			0
$946$	11.7213	−	20.3019i	0.381093	−	0.660072i
$947$	15.2927	−	8.82923i	0.496945	−	0.286911i	−0.230506	−	0.973071i	$-0.574038\pi$
$947$	15.2927	−	8.82923i	0.496945	−	0.286911i	0.727451	+	0.686159i	$0.240705\pi$
$948$		0			0
$949$	−0.973914	−	9.25709i	−0.0316146	−	0.300498i
$950$	38.6745	−	66.9862i	1.25477	−	2.17332i
$951$		0			0
$952$	−1.24734	−	7.12669i	−0.0404266	−	0.230978i
$953$	21.5862	+	37.3884i	0.699245	+	1.21113i	0.968729	+	0.248123i	$0.0798136\pi$
$953$	21.5862	+	37.3884i	0.699245	+	1.21113i	−0.269484	+	0.963005i	$0.586853\pi$
$954$		0			0
$955$	−3.55637	−	2.05327i	−0.115081	−	0.0664422i
$956$	−11.5491	−	6.66787i	−0.373524	−	0.215654i
$957$		0			0
$958$	1.16143	+	2.01165i	0.0375240	+	0.0649935i
$959$	3.48023	+	19.8843i	0.112383	+	0.642097i
$960$		0			0
$961$	2.14768	−	3.71989i	0.0692800	−	0.119996i
$962$	−5.09646	−	7.01317i	−0.164316	−	0.226114i
$963$		0			0
$964$	39.2965	−	22.6878i	1.26565	−	0.730726i
$965$	4.42209	−	7.65928i	0.142352	−	0.246561i
$966$		0			0
$967$			7.19961i			0.231524i	0.993277	+	0.115762i	$0.0369310\pi$
$967$			7.19961i			0.231524i	−0.993277	+	0.115762i	$0.963069\pi$
$968$		−	3.42227i		−	0.109996i
$969$		0			0
$970$	−7.73633	+	4.46657i	−0.248399	+	0.143413i
$971$	18.6301			0.597869			0.298934	−	0.954274i	$-0.403369\pi$
$971$	18.6301			0.597869			0.298934	+	0.954274i	$0.403369\pi$
$972$		0			0
$973$	3.09878	−	8.48047i	0.0993424	−	0.271871i
$974$	−83.3002			−2.66911
$975$		0			0
$976$	−21.9017	−	37.9348i	−0.701055	−	1.21426i
$977$			11.3608i			0.363464i	0.983348	+	0.181732i	$0.0581704\pi$
$977$			11.3608i			0.363464i	−0.983348	+	0.181732i	$0.941830\pi$
$978$		0			0
$979$	9.78992	+	16.9566i	0.312887	+	0.541937i
$980$	2.05780	+	5.69855i	0.0657341	+	0.182033i
$981$		0			0
$982$		−	60.3361i		−	1.92540i
$983$	−9.52228	+	5.49769i	−0.303714	+	0.175349i	−0.644110	−	0.764933i	$-0.722772\pi$
$983$	−9.52228	+	5.49769i	−0.303714	+	0.175349i	0.340396	+	0.940282i	$0.389439\pi$
$984$		0			0
$985$	−4.54963	−	7.88019i	−0.144963	−	0.251084i
$986$	−95.4755	−	55.1228i	−3.04056	−	1.75547i
$987$		0			0
$988$	49.9164	−	36.2741i	1.58805	−	1.15403i
$989$	−17.4676	+	30.2548i	−0.555437	+	0.962046i
$990$		0			0
$991$	38.3560			1.21842			0.609210	−	0.793009i	$-0.291487\pi$
$991$	38.3560			1.21842			0.609210	+	0.793009i	$0.291487\pi$
$992$	−48.2105			−1.53068
$993$		0			0
$994$	−47.2425	+	8.26858i	−1.49844	+	0.262264i
$995$	0.178827	−	0.103246i	0.00566920	−	0.00327311i
$996$		0			0
$997$	12.7596	−	22.1004i	0.404102	−	0.699925i	−0.590114	−	0.807320i	$-0.700917\pi$
$997$	12.7596	−	22.1004i	0.404102	−	0.699925i	0.994217	+	0.107394i	$0.0342507\pi$
$998$	38.9524			1.23302
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.do.g.667.8		20
3.2	odd	2		273.2.bl.d.121.3	yes	20
7.4	even	3		819.2.bm.g.550.8		20
13.10	even	6		819.2.bm.g.478.3		20
21.11	odd	6		273.2.t.d.4.3	✓	20
39.23	odd	6		273.2.t.d.205.8	yes	20
91.88	even	6	inner	819.2.do.g.361.8		20
273.179	odd	6		273.2.bl.d.88.3	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.3	✓	20	21.11	odd	6
273.2.t.d.205.8	yes	20	39.23	odd	6
273.2.bl.d.88.3	yes	20	273.179	odd	6
273.2.bl.d.121.3	yes	20	3.2	odd	2
819.2.bm.g.478.3		20	13.10	even	6
819.2.bm.g.550.8		20	7.4	even	3
819.2.do.g.361.8		20	91.88	even	6	inner
819.2.do.g.667.8		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.do (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.77388 - 1.02415i) q^{2} +(1.09777 - 1.90140i) q^{4} +(0.341406 + 0.197111i) q^{5} +(1.69809 + 2.02891i) q^{7} -0.400534i q^{8} +O(q^{10})\)	\(q+(1.77388 - 1.02415i) q^{2} +(1.09777 - 1.90140i) q^{4} +(0.341406 + 0.197111i) q^{5} +(1.69809 + 2.02891i) q^{7} -0.400534i q^{8} +0.807484 q^{10} -1.56708i q^{11} +(1.46617 - 3.29398i) q^{13} +(5.09013 + 1.85994i) q^{14} +(1.78534 + 3.09229i) q^{16} +(3.41367 - 5.91265i) q^{17} +7.79477i q^{19} +(0.749571 - 0.432765i) q^{20} +(-1.60493 - 2.77982i) q^{22} +(2.39173 + 4.14260i) q^{23} +(-2.42229 - 4.19554i) q^{25} +(-0.772719 - 7.34472i) q^{26} +(5.72188 - 1.00147i) q^{28} +(3.94172 - 6.82725i) q^{29} +(-5.14505 + 2.97049i) q^{31} +(7.02770 + 4.05744i) q^{32} -13.9845i q^{34} +(0.179819 + 1.02739i) q^{35} +(1.01661 - 0.586939i) q^{37} +(7.98303 + 13.8270i) q^{38} +(0.0789495 - 0.136745i) q^{40} +(-6.17054 - 3.56256i) q^{41} +(3.65167 + 6.32487i) q^{43} +(-2.97964 - 1.72030i) q^{44} +(8.48530 + 4.89899i) q^{46} +(-4.92450 - 2.84316i) q^{47} +(-1.23296 + 6.89056i) q^{49} +(-8.59373 - 4.96159i) q^{50} +(-4.65365 - 6.40382i) q^{52} +(0.964998 + 1.67143i) q^{53} +(0.308888 - 0.535010i) q^{55} +(0.812648 - 0.680144i) q^{56} -16.1477i q^{58} +(-9.91907 - 5.72678i) q^{59} -12.2675 q^{61} +(-6.08447 + 10.5386i) q^{62} +9.48040 q^{64} +(1.14984 - 0.835586i) q^{65} -2.79011i q^{67} +(-7.49487 - 12.9815i) q^{68} +(1.37118 + 1.63831i) q^{70} +(-7.66430 + 4.42499i) q^{71} +(2.23575 - 1.29081i) q^{73} +(1.20223 - 2.08232i) q^{74} +(14.8210 + 8.55689i) q^{76} +(3.17947 - 2.66105i) q^{77} +(1.55611 - 2.69526i) q^{79} +1.40764i q^{80} -14.5944 q^{82} -3.01153i q^{83} +(2.33089 - 1.34574i) q^{85} +(12.9552 + 7.47972i) q^{86} -0.627669 q^{88} +(-10.8205 + 6.24724i) q^{89} +(9.17290 - 2.61876i) q^{91} +10.5023 q^{92} -11.6473 q^{94} +(-1.53643 + 2.66118i) q^{95} +(-9.58078 + 5.53147i) q^{97} +(4.86985 + 13.4858i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} + 13 q^{4} + 6 q^{5} - 5 q^{7}+O(q^{10}) \) 20 * q + 3 * q^2 + 13 * q^4 + 6 * q^5 - 5 * q^7	\( 20 q + 3 q^{2} + 13 q^{4} + 6 q^{5} - 5 q^{7} - 4 q^{10} + 8 q^{13} - 2 q^{14} - 21 q^{16} + 8 q^{17} - 9 q^{22} - 18 q^{23} + 12 q^{25} - 32 q^{26} - 43 q^{28} + 3 q^{29} + 18 q^{31} + 24 q^{32} + 24 q^{35} - 12 q^{37} - 9 q^{38} + 5 q^{40} - 21 q^{41} + 16 q^{43} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 3 q^{49} + 54 q^{50} + 13 q^{52} + 26 q^{53} + 17 q^{55} - 6 q^{56} - 15 q^{59} - 4 q^{62} - 46 q^{64} - 37 q^{65} + 3 q^{68} - 15 q^{71} + 9 q^{73} + 6 q^{74} + 75 q^{76} - 20 q^{77} + 3 q^{79} - 30 q^{82} - 78 q^{85} + 3 q^{86} + 44 q^{88} + 24 q^{89} - 4 q^{91} - 142 q^{92} - 72 q^{94} - 42 q^{95} - 15 q^{97} + 33 q^{98}+O(q^{100}) \) 20 * q + 3 * q^2 + 13 * q^4 + 6 * q^5 - 5 * q^7 - 4 * q^10 + 8 * q^13 - 2 * q^14 - 21 * q^16 + 8 * q^17 - 9 * q^22 - 18 * q^23 + 12 * q^25 - 32 * q^26 - 43 * q^28 + 3 * q^29 + 18 * q^31 + 24 * q^32 + 24 * q^35 - 12 * q^37 - 9 * q^38 + 5 * q^40 - 21 * q^41 + 16 * q^43 - 6 * q^44 + 6 * q^46 + 21 * q^47 + 3 * q^49 + 54 * q^50 + 13 * q^52 + 26 * q^53 + 17 * q^55 - 6 * q^56 - 15 * q^59 - 4 * q^62 - 46 * q^64 - 37 * q^65 + 3 * q^68 - 15 * q^71 + 9 * q^73 + 6 * q^74 + 75 * q^76 - 20 * q^77 + 3 * q^79 - 30 * q^82 - 78 * q^85 + 3 * q^86 + 44 * q^88 + 24 * q^89 - 4 * q^91 - 142 * q^92 - 72 * q^94 - 42 * q^95 - 15 * q^97 + 33 * q^98

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