LMFDB - Embedded newform 585.2.bf.b.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(199,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("585.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bf (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.6
Character	$\chi$	$=$	585.199
Dual form			585.2.bf.b.244.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.348519 + 0.603653i) q^{2} +(0.757068 + 1.31128i) q^{4} +(-1.15739 + 1.91323i) q^{5} +(0.459373 + 0.795657i) q^{7} -2.44949 q^{8} +O(q^{10})$	\(q+(-0.348519 + 0.603653i) q^{2} +(0.757068 + 1.31128i) q^{4} +(-1.15739 + 1.91323i) q^{5} +(0.459373 + 0.795657i) q^{7} -2.44949 q^{8} +(-0.751553 - 1.36546i) q^{10} +(2.18858 + 1.26358i) q^{11} +(3.59920 - 0.213965i) q^{13} -0.640402 q^{14} +(-0.660442 + 1.14392i) q^{16} +(-3.25836 + 1.88122i) q^{17} +(-2.27121 + 1.31128i) q^{19} +(-3.38501 - 0.0692223i) q^{20} +(-1.52552 + 0.880762i) q^{22} +(-2.84249 - 1.64111i) q^{23} +(-2.32088 - 4.42871i) q^{25} +(-1.12523 + 2.24724i) q^{26} +(-0.695554 + 1.20473i) q^{28} +(-0.320201 + 0.554604i) q^{29} +1.39733i q^{31} +(-2.90984 - 5.04000i) q^{32} -2.62256i q^{34} +(-2.05395 - 0.0420026i) q^{35} +(-2.44427 + 4.23360i) q^{37} -1.82803i q^{38} +(2.83502 - 4.68643i) q^{40} +(1.38355 + 0.798793i) q^{41} +(2.68045 - 1.54756i) q^{43} +3.82646i q^{44} +(1.98133 - 1.14392i) q^{46} +0.562334 q^{47} +(3.07795 - 5.33117i) q^{49} +(3.48228 + 0.142483i) q^{50} +(3.00541 + 4.55757i) q^{52} +7.52487i q^{53} +(-4.95056 + 2.72480i) q^{55} +(-1.12523 - 1.94895i) q^{56} +(-0.223192 - 0.386581i) q^{58} +(-4.05696 + 2.34229i) q^{59} +(-1.72426 - 2.98650i) q^{61} +(-0.843502 - 0.486996i) q^{62} +1.41478 q^{64} +(-3.75632 + 7.13373i) q^{65} +(-7.43457 + 12.8771i) q^{67} +(-4.93361 - 2.84842i) q^{68} +(0.741196 - 1.22523i) q^{70} +(10.8401 - 6.25856i) q^{71} +2.13230 q^{73} +(-1.70375 - 2.95098i) q^{74} +(-3.43892 - 1.98546i) q^{76} +2.32181i q^{77} -3.92892 q^{79} +(-1.42419 - 2.58754i) q^{80} +(-0.964388 + 0.556790i) q^{82} +9.66325 q^{83} +(0.172008 - 8.41130i) q^{85} +2.15742i q^{86} +(-5.36090 - 3.09512i) q^{88} +(10.4172 + 6.01437i) q^{89} +(1.82362 + 2.76544i) q^{91} -4.96974i q^{92} +(-0.195984 + 0.339455i) q^{94} +(0.119897 - 5.86300i) q^{95} +(6.82780 + 11.8261i) q^{97} +(2.14545 + 3.71603i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{4}+O(q^{10}) $ 24 * q - 8 * q^4	$ 24 q - 8 q^{4} + 4 q^{10} + 16 q^{16} + 24 q^{19} + 8 q^{25} - 48 q^{40} - 48 q^{46} - 16 q^{49} + 28 q^{61} - 48 q^{64} - 144 q^{76} + 40 q^{79} + 12 q^{85} + 4 q^{91} - 40 q^{94}+O(q^{100}) $ 24 * q - 8 * q^4 + 4 * q^10 + 16 * q^16 + 24 * q^19 + 8 * q^25 - 48 * q^40 - 48 * q^46 - 16 * q^49 + 28 * q^61 - 48 * q^64 - 144 * q^76 + 40 * q^79 + 12 * q^85 + 4 * q^91 - 40 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.348519	+	0.603653i	−0.246440	+	0.426847i	−0.962536	−	0.271155i	$-0.912594\pi$
$2$	−0.348519	+	0.603653i	−0.246440	+	0.426847i	0.716095	+	0.698003i	$0.245928\pi$
$3$		0			0
$3$		0			0
$4$	0.757068	+	1.31128i	0.378534	+	0.655641i
$5$	−1.15739	+	1.91323i	−0.517602	+	0.855622i
$5$	−1.15739	+	1.91323i	−0.517602	+	0.855622i
$6$		0			0
$7$	0.459373	+	0.795657i	0.173627	+	0.300730i	0.939685	−	0.342041i	$-0.111118\pi$
$7$	0.459373	+	0.795657i	0.173627	+	0.300730i	−0.766058	+	0.642771i	$0.777785\pi$
$8$	−2.44949			−0.866025
$9$		0			0
$10$	−0.751553	−	1.36546i	−0.237662	−	0.431797i
$11$	2.18858	+	1.26358i	0.659881	+	0.380983i	0.792232	−	0.610220i	$-0.208919\pi$
$11$	2.18858	+	1.26358i	0.659881	+	0.380983i	−0.132350	+	0.991203i	$0.542252\pi$
$12$		0			0
$13$	3.59920	−	0.213965i	0.998238	−	0.0593432i
$13$	3.59920	−	0.213965i	0.998238	−	0.0593432i
$14$	−0.640402			−0.171155
$15$		0			0
$16$	−0.660442	+	1.14392i	−0.165111	+	0.285980i
$17$	−3.25836	+	1.88122i	−0.790269	+	0.456262i	−0.840057	−	0.542498i	$-0.817479\pi$
$17$	−3.25836	+	1.88122i	−0.790269	+	0.456262i	0.0497882	+	0.998760i	$0.484145\pi$
$18$		0			0
$19$	−2.27121	+	1.31128i	−0.521050	+	0.300829i	−0.737364	−	0.675495i	$-0.763930\pi$
$19$	−2.27121	+	1.31128i	−0.521050	+	0.300829i	0.216314	+	0.976324i	$0.430597\pi$
$20$	−3.38501	−	0.0692223i	−0.756910	−	0.0154786i
$21$		0			0
$22$	−1.52552	+	0.880762i	−0.325243	+	0.187779i
$23$	−2.84249	−	1.64111i	−0.592700	−	0.342196i	0.173464	−	0.984840i	$-0.444504\pi$
$23$	−2.84249	−	1.64111i	−0.592700	−	0.342196i	−0.766165	+	0.642644i	$0.777837\pi$
$24$		0			0
$25$	−2.32088	−	4.42871i	−0.464177	−	0.885743i
$26$	−1.12523	+	2.24724i	−0.220676	+	0.440720i
$27$		0			0
$28$	−0.695554	+	1.20473i	−0.131447	+	0.227673i
$29$	−0.320201	+	0.554604i	−0.0594598	+	0.102987i	−0.894223	−	0.447622i	$-0.852271\pi$
$29$	−0.320201	+	0.554604i	−0.0594598	+	0.102987i	0.834763	+	0.550609i	$0.185604\pi$
$30$		0			0
$31$			1.39733i			0.250967i	0.992096	+	0.125484i	$0.0400483\pi$
$31$			1.39733i			0.250967i	−0.992096	+	0.125484i	$0.959952\pi$
$32$	−2.90984	−	5.04000i	−0.514393	−	0.890954i
$33$		0			0
$34$		−	2.62256i		−	0.449766i
$35$	−2.05395	−	0.0420026i	−0.347181	−	0.00709974i
$36$		0			0
$37$	−2.44427	+	4.23360i	−0.401836	+	0.696000i	−0.993948	−	0.109856i	$-0.964961\pi$
$37$	−2.44427	+	4.23360i	−0.401836	+	0.696000i	0.592112	+	0.805856i	$0.298294\pi$
$38$		−	1.82803i		−	0.296545i
$39$		0			0
$40$	2.83502	−	4.68643i	0.448256	−	0.740990i
$41$	1.38355	+	0.798793i	0.216074	+	0.124751i	0.604131	−	0.796885i	$-0.293520\pi$
$41$	1.38355	+	0.798793i	0.216074	+	0.124751i	−0.388057	+	0.921635i	$0.626854\pi$
$42$		0			0
$43$	2.68045	−	1.54756i	0.408765	−	0.236001i	−0.281494	−	0.959563i	$-0.590830\pi$
$43$	2.68045	−	1.54756i	0.408765	−	0.236001i	0.690259	+	0.723562i	$0.257497\pi$
$44$			3.82646i			0.576860i
$45$		0			0
$46$	1.98133	−	1.14392i	0.292131	−	0.168662i
$47$	0.562334			0.0820249			0.0410124	−	0.999159i	$-0.486942\pi$
$47$	0.562334			0.0820249			0.0410124	+	0.999159i	$0.486942\pi$
$48$		0			0
$49$	3.07795	−	5.33117i	0.439708	−	0.761596i
$50$	3.48228	+	0.142483i	0.492469	+	0.0201501i
$51$		0			0
$52$	3.00541	+	4.55757i	0.416775	+	0.632022i
$53$			7.52487i			1.03362i	0.856100	+	0.516810i	$0.172881\pi$
$53$			7.52487i			1.03362i	−0.856100	+	0.516810i	$0.827119\pi$
$54$		0			0
$55$	−4.95056	+	2.72480i	−0.667533	+	0.367412i
$56$	−1.12523	−	1.94895i	−0.150365	−	0.260440i
$57$		0			0
$58$	−0.223192	−	0.386581i	−0.0293066	−	0.0507605i
$59$	−4.05696	+	2.34229i	−0.528171	+	0.304940i	−0.740271	−	0.672308i	$-0.765303\pi$
$59$	−4.05696	+	2.34229i	−0.528171	+	0.304940i	0.212100	+	0.977248i	$0.431970\pi$
$60$		0			0
$61$	−1.72426	−	2.98650i	−0.220769	−	0.382383i	0.734273	−	0.678854i	$-0.237523\pi$
$61$	−1.72426	−	2.98650i	−0.220769	−	0.382383i	−0.955042	+	0.296472i	$0.904190\pi$
$62$	−0.843502	−	0.486996i	−0.107125	−	0.0618485i
$63$		0			0
$64$	1.41478			0.176847
$65$	−3.75632	+	7.13373i	−0.465914	+	0.884830i
$66$		0			0
$67$	−7.43457	+	12.8771i	−0.908278	+	1.57318i	−0.0918221	+	0.995775i	$0.529269\pi$
$67$	−7.43457	+	12.8771i	−0.908278	+	1.57318i	−0.816456	+	0.577408i	$0.804064\pi$
$68$	−4.93361	−	2.84842i	−0.598288	−	0.345422i
$69$		0			0
$70$	0.741196	−	1.22523i	0.0885899	−	0.146444i
$71$	10.8401	−	6.25856i	1.28649	−	0.742755i	0.308463	−	0.951236i	$-0.400186\pi$
$71$	10.8401	−	6.25856i	1.28649	−	0.742755i	0.978026	+	0.208482i	$0.0668522\pi$
$72$		0			0
$73$	2.13230			0.249567			0.124784	−	0.992184i	$-0.460176\pi$
$73$	2.13230			0.249567			0.124784	+	0.992184i	$0.460176\pi$
$74$	−1.70375	−	2.95098i	−0.198057	−	0.343045i
$75$		0			0
$76$	−3.43892	−	1.98546i	−0.394471	−	0.227748i
$77$			2.32181i			0.264595i
$78$		0			0
$79$	−3.92892			−0.442038			−0.221019	−	0.975270i	$-0.570938\pi$
$79$	−3.92892			−0.442038			−0.221019	+	0.975270i	$0.570938\pi$
$80$	−1.42419	−	2.58754i	−0.159229	−	0.289296i
$81$		0			0
$82$	−0.964388	+	0.556790i	−0.106499	+	0.0614872i
$83$	9.66325			1.06068			0.530340	−	0.847785i	$-0.322064\pi$
$83$	9.66325			1.06068			0.530340	+	0.847785i	$0.322064\pi$
$84$		0			0
$85$	0.172008	−	8.41130i	0.0186569	−	0.912333i
$86$			2.15742i			0.232640i
$87$		0			0
$88$	−5.36090	−	3.09512i	−0.571474	−	0.329941i
$89$	10.4172	+	6.01437i	1.10422	+	0.637522i	0.937326	−	0.348452i	$-0.113293\pi$
$89$	10.4172	+	6.01437i	1.10422	+	0.637522i	0.166895	+	0.985975i	$0.446626\pi$
$90$		0			0
$91$	1.82362	+	2.76544i	0.191167	+	0.289897i
$92$		−	4.96974i		−	0.518131i
$93$		0			0
$94$	−0.195984	+	0.339455i	−0.0202143	+	0.0350121i
$95$	0.119897	−	5.86300i	0.0123011	−	0.601531i
$96$		0			0
$97$	6.82780	+	11.8261i	0.693258	+	1.20076i	0.970765	+	0.240034i	$0.0771585\pi$
$97$	6.82780	+	11.8261i	0.693258	+	1.20076i	−0.277507	+	0.960724i	$0.589508\pi$
$98$	2.14545	+	3.71603i	0.216723	+	0.375376i
$99$		0			0
$100$	4.05022	−	6.39617i	0.405022	−	0.639617i
$101$	8.81620	−	15.2701i	0.877244	−	1.51943i	0.0228917	−	0.999738i	$-0.492713\pi$
$101$	8.81620	−	15.2701i	0.877244	−	1.51943i	0.854353	−	0.519694i	$-0.173954\pi$
$102$		0			0
$103$		−	14.2793i		−	1.40698i	−0.710704	−	0.703491i	$-0.751623\pi$
$103$		−	14.2793i		−	1.40698i	0.710704	−	0.703491i	$-0.248377\pi$
$104$	−8.81620	+	0.524105i	−0.864499	+	0.0513927i
$105$		0			0
$106$	−4.54241	−	2.62256i	−0.441198	−	0.254726i
$107$	14.2811	+	8.24518i	1.38060	+	0.797091i	0.992231	−	0.124411i	$-0.0397042\pi$
$107$	14.2811	+	8.24518i	1.38060	+	0.797091i	0.388372	+	0.921503i	$0.373038\pi$
$108$		0			0
$109$			12.0597i			1.15511i	0.816353	+	0.577553i	$0.195992\pi$
$109$			12.0597i			1.15511i	−0.816353	+	0.577553i	$0.804008\pi$
$110$	0.0805322	−	3.93806i	0.00767844	−	0.375480i
$111$		0			0
$112$	−1.21356			−0.114670
$113$	4.73155	−	2.73176i	0.445107	−	0.256983i	−0.260655	−	0.965432i	$-0.583938\pi$
$113$	4.73155	−	2.73176i	0.445107	−	0.256983i	0.705761	+	0.708450i	$0.250605\pi$
$114$		0			0
$115$	6.42970	−	3.53892i	0.599573	−	0.330006i
$116$	−0.969656			−0.0900303
$117$		0			0
$118$		−	3.26533i		−	0.300598i
$119$	−2.99361	−	1.72836i	−0.274424	−	0.158439i
$120$		0			0
$121$	−2.30675	−	3.99540i	−0.209704	−	0.363219i
$122$	2.40375			0.217625
$123$		0			0
$124$	−1.83229	+	1.05787i	−0.164544	+	0.0949998i
$125$	11.1593	+	0.685378i	0.998119	+	0.0613020i
$126$		0			0
$127$	4.47230	+	2.58208i	0.396852	+	0.229123i	0.685125	−	0.728426i	$-0.259748\pi$
$127$	4.47230	+	2.58208i	0.396852	+	0.229123i	−0.288273	+	0.957548i	$0.593081\pi$
$128$	5.32661	−	9.22596i	0.470810	−	0.815467i
$129$		0			0
$130$	−2.99715	−	4.75376i	−0.262867	−	0.416932i
$131$	−14.7415			−1.28797			−0.643987	−	0.765037i	$-0.722721\pi$
$131$	−14.7415			−1.28797			−0.643987	+	0.765037i	$0.722721\pi$
$132$		0			0
$133$	−2.08666	−	1.20473i	−0.180936	−	0.104464i
$134$	−5.18219	−	8.97581i	−0.447673	−	0.775392i
$135$		0			0
$136$	7.98133	−	4.60802i	0.684393	−	0.395135i
$137$	5.18015	+	8.97228i	0.442570	+	0.766553i	0.997879	−	0.0650903i	$-0.0207336\pi$
$137$	5.18015	+	8.97228i	0.442570	+	0.766553i	−0.555310	+	0.831644i	$0.687400\pi$
$138$		0			0
$139$	0.0610840	+	0.105801i	0.00518108	+	0.00897389i	0.868604	−	0.495506i	$-0.165017\pi$
$139$	0.0610840	+	0.105801i	0.00518108	+	0.00897389i	−0.863423	+	0.504480i	$0.831684\pi$
$140$	−1.49990	−	2.72510i	−0.126765	−	0.230313i
$141$		0			0
$142$			8.72492i			0.732179i
$143$	8.14749	+	4.07958i	0.681327	+	0.341152i
$144$		0			0
$145$	−0.690486	−	1.25451i	−0.0573417	−	0.104182i
$146$	−0.743149	+	1.28717i	−0.0615034	+	0.106527i
$147$		0			0
$148$	−7.40192			−0.608434
$149$	11.4896	−	6.63353i	0.941265	−	0.543440i	0.0509083	−	0.998703i	$-0.483788\pi$
$149$	11.4896	−	6.63353i	0.941265	−	0.543440i	0.890357	+	0.455264i	$0.150455\pi$
$150$		0			0
$151$			16.4143i			1.33578i	0.744262	+	0.667888i	$0.232801\pi$
$151$			16.4143i			1.33578i	−0.744262	+	0.667888i	$0.767199\pi$
$152$	5.56329	−	3.21197i	0.451243	−	0.260525i
$153$		0			0
$154$	−1.40157	−	0.809197i	−0.112942	−	0.0652069i
$155$	−2.67341	−	1.61726i	−0.214733	−	0.129901i
$156$		0			0
$157$			19.5639i			1.56137i	0.624926	+	0.780684i	$0.285129\pi$
$157$			19.5639i			1.56137i	−0.624926	+	0.780684i	$0.714871\pi$
$158$	1.36930	−	2.37170i	0.108936	−	0.188683i
$159$		0			0
$160$	13.0105	+	0.266061i	1.02857	+	0.0210339i
$161$		−	3.01553i		−	0.237657i
$162$		0			0
$163$	−1.85048	−	3.20513i	−0.144941	−	0.251045i	0.784410	−	0.620243i	$-0.212966\pi$
$163$	−1.85048	−	3.20513i	−0.144941	−	0.251045i	−0.929351	+	0.369198i	$0.879633\pi$
$164$			2.41896i			0.188889i
$165$		0			0
$166$	−3.36783	+	5.83326i	−0.261394	+	0.452748i
$167$	8.83151	−	15.2966i	0.683403	−	1.18369i	−0.290533	−	0.956865i	$-0.593833\pi$
$167$	8.83151	−	15.2966i	0.683403	−	1.18369i	0.973936	−	0.226824i	$-0.0728341\pi$
$168$		0			0
$169$	12.9084	−	1.54020i	0.992957	−	0.118477i
$170$	5.01756	+	3.03533i	0.384829	+	0.232799i
$171$		0			0
$172$	4.05857	+	2.34322i	0.309463	+	0.178669i
$173$	−6.02049	+	3.47593i	−0.457729	+	0.264270i	−0.711089	−	0.703102i	$-0.751798\pi$
$173$	−6.02049	+	3.47593i	−0.457729	+	0.264270i	0.253360	+	0.967372i	$0.418464\pi$
$174$		0			0
$175$	2.45759	−	3.88106i	0.185776	−	0.293381i
$176$	−2.89086	+	1.66904i	−0.217907	+	0.125809i
$177$		0			0
$178$	−7.26119	+	4.19225i	−0.544249	+	0.314223i
$179$	11.3869	−	19.7226i	0.851094	−	1.47414i	−0.0291287	−	0.999576i	$-0.509273\pi$
$179$	11.3869	−	19.7226i	0.851094	−	1.47414i	0.880222	−	0.474562i	$-0.157393\pi$
$180$		0			0
$181$	0.966262			0.0718217			0.0359108	−	0.999355i	$-0.488567\pi$
$181$	0.966262			0.0718217			0.0359108	+	0.999355i	$0.488567\pi$
$182$	−2.30493	+	0.137023i	−0.170853	+	0.0101569i
$183$		0			0
$184$	6.96265	+	4.01989i	0.513294	+	0.296350i
$185$	−5.27086	−	9.57639i	−0.387522	−	0.704070i
$186$		0			0
$187$	−9.50825			−0.695312
$188$	0.425726	+	0.737378i	0.0310492	+	0.0537788i
$189$		0			0
$190$	3.49743	+	2.11575i	0.253731	+	0.153492i
$191$	8.49600	+	14.7155i	0.614749	+	1.06478i	0.990429	+	0.138026i	$0.0440759\pi$
$191$	8.49600	+	14.7155i	0.614749	+	1.06478i	−0.375680	+	0.926749i	$0.622591\pi$
$192$		0			0
$193$	10.8864	−	18.8557i	0.783618	−	1.35727i	−0.146204	−	0.989255i	$-0.546705\pi$
$193$	10.8864	−	18.8557i	0.783618	−	1.35727i	0.929821	−	0.368011i	$-0.119961\pi$
$194$	−9.51848			−0.683387
$195$		0			0
$196$	9.32088			0.665777
$197$	−8.79688	+	15.2366i	−0.626752	+	1.08557i	0.361447	+	0.932393i	$0.382283\pi$
$197$	−8.79688	+	15.2366i	−0.626752	+	1.08557i	−0.988199	+	0.153174i	$0.951051\pi$
$198$		0			0
$199$	−7.68418	−	13.3094i	−0.544717	−	0.943478i	−0.998625	−	0.0524289i	$-0.983304\pi$
$199$	−7.68418	−	13.3094i	−0.544717	−	0.943478i	0.453908	−	0.891049i	$-0.350030\pi$
$200$	5.68498	+	10.8481i	0.401989	+	0.767076i
$201$		0			0
$202$	6.14523	+	10.6439i	0.432377	+	0.748899i
$203$	−0.588366			−0.0412952
$204$		0			0
$205$	−3.12959	+	1.72253i	−0.218580	+	0.120307i
$206$	8.61975	+	4.97662i	0.600567	+	0.346737i
$207$		0			0
$208$	−2.13230	+	4.25850i	−0.147849	+	0.295274i
$209$	−6.62762			−0.458442
$210$		0			0
$211$	8.52827	−	14.7714i	0.587111	−	1.01691i	−0.407498	−	0.913206i	$-0.633599\pi$
$211$	8.52827	−	14.7714i	0.587111	−	1.01691i	0.994609	−	0.103699i	$-0.0330680\pi$
$212$	−9.86722	+	5.69684i	−0.677683	+	0.391261i
$213$		0			0
$214$	−9.95446	+	5.74721i	−0.680473	+	0.392871i
$215$	−0.141501	+	6.91945i	−0.00965026	+	0.471902i
$216$		0			0
$217$	−1.11179	+	0.641895i	−0.0754735	+	0.0435746i
$218$	−7.27986	−	4.20303i	−0.493054	−	0.284665i
$219$		0			0
$220$	−7.32088	−	4.42871i	−0.493574	−	0.298584i
$221$	−11.3250	+	7.46804i	−0.761800	+	0.502355i
$222$		0			0
$223$	3.36302	−	5.82492i	0.225204	−	0.390065i	−0.731176	−	0.682188i	$-0.761028\pi$
$223$	3.36302	−	5.82492i	0.225204	−	0.390065i	0.956381	+	0.292123i	$0.0943617\pi$
$224$	2.67341	−	4.63048i	0.178625	−	0.309387i
$225$		0			0
$226$			3.80829i			0.253324i
$227$	−5.04544	−	8.73896i	−0.334878	−	0.580025i	0.648584	−	0.761143i	$-0.275362\pi$
$227$	−5.04544	−	8.73896i	−0.334878	−	0.580025i	−0.983461	+	0.181118i	$0.942028\pi$
$228$		0			0
$229$		−	10.8250i		−	0.715334i	−0.933849	−	0.357667i	$-0.883572\pi$
$229$		−	10.8250i		−	0.715334i	0.933849	−	0.357667i	$-0.116428\pi$
$230$	−0.104594	+	5.11469i	−0.00689672	+	0.337253i
$231$		0			0
$232$	0.784329	−	1.35850i	0.0514937	−	0.0891897i
$233$			25.4353i			1.66632i	0.553031	+	0.833161i	$0.313471\pi$
$233$			25.4353i			1.66632i	−0.553031	+	0.833161i	$0.686529\pi$
$234$		0			0
$235$	−0.650842	+	1.07587i	−0.0424562	+	0.0701823i
$236$	−6.14279	−	3.54654i	−0.399862	−	0.230860i
$237$		0			0
$238$	2.08666	−	1.20473i	0.135258	−	0.0780913i
$239$			12.6358i			0.817340i	0.912682	+	0.408670i	$0.134007\pi$
$239$			12.6358i			0.817340i	−0.912682	+	0.408670i	$0.865993\pi$
$240$		0			0
$241$	−8.71012	+	5.02879i	−0.561068	+	0.323933i	−0.753574	−	0.657363i	$-0.771672\pi$
$241$	−8.71012	+	5.02879i	−0.561068	+	0.323933i	0.192506	+	0.981296i	$0.438339\pi$
$242$	3.21579			0.206718
$243$		0			0
$244$	2.61076	−	4.52197i	0.167137	−	0.289490i
$245$	6.63735	+	12.0591i	0.424045	+	0.770427i
$246$		0			0
$247$	−7.89395	+	5.20552i	−0.502280	+	0.331219i
$248$		−	3.42274i		−	0.217344i
$249$		0			0
$250$	−4.30297	+	6.49749i	−0.272144	+	0.410937i
$251$	−7.20614	−	12.4814i	−0.454847	−	0.787819i	0.543832	−	0.839194i	$-0.316973\pi$
$251$	−7.20614	−	12.4814i	−0.454847	−	0.787819i	−0.998679	+	0.0513752i	$0.983640\pi$
$252$		0			0
$253$	−4.14734	−	7.18341i	−0.260741	−	0.451617i
$254$	−3.11737	+	1.79981i	−0.195601	+	0.112930i
$255$		0			0
$256$	5.12763	+	8.88132i	0.320477	+	0.555082i
$257$	−19.5619	−	11.2941i	−1.22024	−	0.704506i	−0.255271	−	0.966870i	$-0.582165\pi$
$257$	−19.5619	−	11.2941i	−1.22024	−	0.704506i	−0.964969	+	0.262364i	$0.915498\pi$
$258$		0			0
$259$	−4.49133			−0.279077
$260$	−12.1981	+	0.475128i	−0.756495	+	0.0294662i
$261$		0			0
$262$	5.13771	−	8.89877i	0.317409	−	0.549768i
$263$	−15.6208	−	9.01868i	−0.963220	−	0.556115i	−0.0660576	−	0.997816i	$-0.521042\pi$
$263$	−15.6208	−	9.01868i	−0.963220	−	0.556115i	−0.897163	+	0.441700i	$0.854375\pi$
$264$		0			0
$265$	−14.3968	−	8.70923i	−0.884388	−	0.535003i
$266$	1.45448	−	0.839746i	0.0891801	−	0.0514882i
$267$		0			0
$268$	−22.5139			−1.37526
$269$	15.2173	+	26.3571i	0.927816	+	1.60702i	0.786969	+	0.616992i	$0.211649\pi$
$269$	15.2173	+	26.3571i	0.927816	+	1.60702i	0.140846	+	0.990031i	$0.455018\pi$
$270$		0			0
$271$	−22.5848	−	13.0394i	−1.37193	−	0.792084i	−0.380759	−	0.924674i	$-0.624337\pi$
$271$	−22.5848	−	13.0394i	−1.37193	−	0.792084i	−0.991171	+	0.132590i	$0.957671\pi$
$272$		−	4.96974i		−	0.301335i
$273$		0			0
$274$	−7.22153			−0.436268
$275$	0.516579	−	12.6252i	0.0311509	−	0.761328i
$276$		0			0
$277$	−3.38899	+	1.95664i	−0.203625	+	0.117563i	−0.598345	−	0.801238i	$-0.704175\pi$
$277$	−3.38899	+	1.95664i	−0.203625	+	0.117563i	0.394720	+	0.918801i	$0.370841\pi$
$278$	−0.0851559			−0.00510731
$279$		0			0
$280$	5.03113	+	0.102885i	0.300667	+	0.00614855i
$281$			24.8074i			1.47989i	0.672669	+	0.739943i	$0.265148\pi$
$281$			24.8074i			1.47989i	−0.672669	+	0.739943i	$0.734852\pi$
$282$		0			0
$283$	21.2962	+	12.2954i	1.26593	+	0.730884i	0.974215	−	0.225622i	$-0.0724415\pi$
$283$	21.2962	+	12.2954i	1.26593	+	0.730884i	0.291713	+	0.956506i	$0.405775\pi$
$284$	16.4135	+	9.47632i	0.973960	+	0.562316i
$285$		0			0
$286$	−5.30221	+	3.49644i	−0.313526	+	0.206749i
$287$			1.46778i			0.0866401i
$288$		0			0
$289$	−1.42205	+	2.46306i	−0.0836498	+	0.144886i
$290$	0.997938	+	0.0204075i	0.0586009	+	0.00119837i
$291$		0			0
$292$	1.61430	+	2.79605i	0.0944697	+	0.163626i
$293$	−9.48407	−	16.4269i	−0.554065	−	0.959669i	−0.997976	−	0.0635979i	$-0.979743\pi$
$293$	−9.48407	−	16.4269i	−0.554065	−	0.959669i	0.443910	−	0.896071i	$-0.353591\pi$
$294$		0			0
$295$	0.214166	−	10.4728i	0.0124692	−	0.609752i
$296$	5.98722	−	10.3702i	0.348000	−	0.602753i
$297$		0			0
$298$			9.24765i			0.535702i
$299$	−10.5818	−	5.29850i	−0.611963	−	0.306420i
$300$		0			0
$301$	2.46265	+	1.42181i	0.141945	+	0.0819520i
$302$	−9.90854	−	5.72070i	−0.570172	−	0.329189i
$303$		0			0
$304$		−	3.46410i		−	0.198680i
$305$	7.70951	+	0.157657i	0.441445	+	0.00902741i
$306$		0			0
$307$	−1.36513			−0.0779121			−0.0389561	−	0.999241i	$-0.512403\pi$
$307$	−1.36513			−0.0779121			−0.0389561	+	0.999241i	$0.512403\pi$
$308$	−3.04455	+	1.75777i	−0.173479	+	0.100158i
$309$		0			0
$310$	1.90800	−	1.05017i	0.108367	−	0.0596454i
$311$	−29.5887			−1.67782			−0.838911	−	0.544268i	$-0.816807\pi$
$311$	−29.5887			−1.67782			−0.838911	+	0.544268i	$0.816807\pi$
$312$		0			0
$313$			12.8582i			0.726789i	0.931635	+	0.363394i	$0.118382\pi$
$313$			12.8582i			0.726789i	−0.931635	+	0.363394i	$0.881618\pi$
$314$	−11.8098	−	6.81839i	−0.666466	−	0.384784i
$315$		0			0
$316$	−2.97446	−	5.15191i	−0.167326	−	0.289818i
$317$	−17.7977			−0.999620			−0.499810	−	0.866135i	$-0.666597\pi$
$317$	−17.7977			−0.999620			−0.499810	+	0.866135i	$0.666597\pi$
$318$		0			0
$319$	−1.40157	+	0.809197i	−0.0784728	+	0.0453063i
$320$	−1.63745	+	2.70679i	−0.0915365	+	0.151314i
$321$		0			0
$322$	1.82034	+	1.05097i	0.101443	+	0.0585683i
$323$	4.93361	−	8.54526i	0.274513	−	0.475471i
$324$		0			0
$325$	−9.30091	−	15.4432i	−0.515922	−	0.856636i
$326$	2.57971			0.142877
$327$		0			0
$328$	−3.38899	−	1.95664i	−0.187126	−	0.108037i
$329$	0.258321	+	0.447425i	0.0142417	+	0.0246674i
$330$		0			0
$331$	23.9864	−	13.8485i	1.31841	−	0.761185i	0.334938	−	0.942240i	$-0.391285\pi$
$331$	23.9864	−	13.8485i	1.31841	−	0.761185i	0.983473	+	0.181055i	$0.0579512\pi$
$332$	7.31575	+	12.6712i	0.401504	+	0.695425i
$333$		0			0
$334$	6.15591	+	10.6623i	0.336836	+	0.583417i
$335$	−16.0320	−	29.1279i	−0.875924	−	1.59142i
$336$		0			0
$337$		−	8.42950i		−	0.459184i	−0.973287	−	0.229592i	$-0.926261\pi$
$337$		−	8.42950i		−	0.459184i	0.973287	−	0.229592i	$-0.0737392\pi$
$338$	−3.56909	+	8.32901i	−0.194133	+	0.453039i
$339$		0			0
$340$	11.1598	−	6.14238i	0.605225	−	0.333117i
$341$	−1.76563	+	3.05816i	−0.0956143	+	0.165609i
$342$		0			0
$343$	12.0869			0.652633
$344$	−6.56574	+	3.79073i	−0.354001	+	0.204382i
$345$		0			0
$346$		−	4.84572i		−	0.260507i
$347$	18.0084	−	10.3971i	0.966740	−	0.558148i	0.0684995	−	0.997651i	$-0.478179\pi$
$347$	18.0084	−	10.3971i	0.966740	−	0.558148i	0.898241	+	0.439503i	$0.144846\pi$
$348$		0			0
$349$	18.2763	+	10.5518i	0.978306	+	0.564825i	0.901758	−	0.432241i	$-0.142277\pi$
$349$	18.2763	+	10.5518i	0.978306	+	0.564825i	0.0765479	+	0.997066i	$0.475610\pi$
$350$	1.48630	+	2.83615i	0.0794460	+	0.151599i
$351$		0			0
$352$		−	14.7072i		−	0.783899i
$353$	−8.91188	+	15.4358i	−0.474331	+	0.821566i	−0.999568	−	0.0293900i	$-0.990644\pi$
$353$	−8.91188	+	15.4358i	−0.474331	+	0.821566i	0.525237	+	0.850956i	$0.323977\pi$
$354$		0			0
$355$	−0.572249	+	27.9833i	−0.0303718	+	1.48520i
$356$			18.2132i			0.965296i
$357$		0			0
$358$	7.93708	+	13.7474i	0.419488	+	0.726574i
$359$			20.0986i			1.06076i	0.847759	+	0.530381i	$0.177951\pi$
$359$			20.0986i			1.06076i	−0.847759	+	0.530381i	$0.822049\pi$
$360$		0			0
$361$	−6.06108	+	10.4981i	−0.319004	+	0.552532i
$362$	−0.336761	+	0.583287i	−0.0176998	+	0.0306569i
$363$		0			0
$364$	−2.24566	+	4.48490i	−0.117705	+	0.235073i
$365$	−2.46791	+	4.07958i	−0.129176	+	0.213535i
$366$		0			0
$367$	−10.7976	−	6.23399i	−0.563630	−	0.325412i	0.190971	−	0.981596i	$-0.438836\pi$
$367$	−10.7976	−	6.23399i	−0.563630	−	0.325412i	−0.754601	+	0.656184i	$0.772170\pi$
$368$	3.75460	−	2.16772i	0.195722	−	0.113000i
$369$		0			0
$370$	7.61781	+	0.155782i	0.396031	+	0.00809872i
$371$	−5.98722	+	3.45672i	−0.310841	+	0.179464i
$372$		0			0
$373$	21.2962	−	12.2954i	1.10268	−	0.636630i	0.165753	−	0.986167i	$-0.446995\pi$
$373$	21.2962	−	12.2954i	1.10268	−	0.636630i	0.936922	+	0.349537i	$0.113661\pi$
$374$	3.31381	−	5.73968i	0.171353	−	0.296792i
$375$		0			0
$376$	−1.37743			−0.0710356
$377$	−1.03380	+	2.06464i	−0.0532434	+	0.106334i
$378$		0			0
$379$	18.2763	+	10.5518i	0.938789	+	0.542010i	0.889580	−	0.456778i	$-0.150997\pi$
$379$	18.2763	+	10.5518i	0.938789	+	0.542010i	0.0492084	+	0.998789i	$0.484330\pi$
$380$	7.77881	−	4.28148i	0.399045	−	0.219635i
$381$		0			0
$382$	−11.8441			−0.605996
$383$	−14.6760	−	25.4195i	−0.749907	−	1.29888i	−0.947867	−	0.318667i	$-0.896765\pi$
$383$	−14.6760	−	25.4195i	−0.749907	−	1.29888i	0.197960	−	0.980210i	$-0.436569\pi$
$384$		0			0
$385$	−4.44216	−	2.68725i	−0.226393	−	0.136955i
$386$	7.58822	+	13.1432i	0.386230	+	0.668970i
$387$		0			0
$388$	−10.3382	+	17.9063i	−0.524844	+	0.909056i
$389$	−11.0048			−0.557964			−0.278982	−	0.960296i	$-0.589997\pi$
$389$	−11.0048			−0.557964			−0.278982	+	0.960296i	$0.589997\pi$
$390$		0			0
$391$	12.3492			0.624524
$392$	−7.53941	+	13.0586i	−0.380798	+	0.659561i
$393$		0			0
$394$	−6.13177	−	10.6205i	−0.308914	−	0.535055i
$395$	4.54730	−	7.51691i	0.228799	−	0.378217i
$396$		0			0
$397$	−4.38353	−	7.59249i	−0.220003	−	0.381056i	0.734806	−	0.678278i	$-0.237273\pi$
$397$	−4.38353	−	7.59249i	−0.220003	−	0.381056i	−0.954809	+	0.297222i	$0.903940\pi$
$398$	10.7123			0.536961
$399$		0			0
$400$	6.59890	+	0.270004i	0.329945	+	0.0135002i
$401$	10.9111	+	6.29952i	0.544873	+	0.314583i	0.747052	−	0.664766i	$-0.231469\pi$
$401$	10.9111	+	6.29952i	0.544873	+	0.314583i	−0.202178	+	0.979349i	$0.564802\pi$
$402$		0			0
$403$	0.298979	+	5.02926i	0.0148932	+	0.250525i
$404$	26.6979			1.32827
$405$		0			0
$406$	0.205057	−	0.355169i	0.0101768	−	0.0176268i
$407$	−10.6990	+	6.17705i	−0.530328	+	0.306185i
$408$		0			0
$409$	−26.3424	+	15.2088i	−1.30255	+	0.752027i	−0.980841	−	0.194812i	$-0.937590\pi$
$409$	−26.3424	+	15.2088i	−1.30255	+	0.752027i	−0.321708	+	0.946839i	$0.604257\pi$
$410$	0.0509099	−	2.48952i	0.00251426	−	0.122949i
$411$		0			0
$412$	18.7242	−	10.8104i	0.922475	−	0.532591i
$413$	−3.72731	−	2.15197i	−0.183409	−	0.105891i
$414$		0			0
$415$	−11.1842	+	18.4880i	−0.549010	+	0.907541i
$416$	−11.5515	−	17.5173i	−0.566358	−	0.858858i
$417$		0			0
$418$	2.30985	−	4.00078i	0.112979	−	0.195685i
$419$	7.10339	−	12.3034i	0.347023	−	0.601062i	−0.638696	−	0.769459i	$-0.720526\pi$
$419$	7.10339	−	12.3034i	0.347023	−	0.601062i	0.985719	+	0.168397i	$0.0538591\pi$
$420$		0			0
$421$		−	1.23470i		−	0.0601755i	−0.999547	−	0.0300878i	$-0.990421\pi$
$421$		−	1.23470i		−	0.0601755i	0.999547	−	0.0300878i	$-0.00957868\pi$
$422$	5.94454	+	10.2962i	0.289376	+	0.501213i
$423$		0			0
$424$		−	18.4321i		−	0.895141i
$425$	15.8937	+	10.0643i	0.770955	+	0.488189i
$426$		0			0
$427$	1.58416	−	2.74384i	0.0766626	−	0.132784i
$428$			24.9687i			1.20691i
$429$		0			0
$430$	−4.12763	−	2.49698i	−0.199052	−	0.120415i
$431$	−16.6009	−	9.58451i	−0.799635	−	0.461670i	0.0437084	−	0.999044i	$-0.486083\pi$
$431$	−16.6009	−	9.58451i	−0.799635	−	0.461670i	−0.843344	+	0.537375i	$0.819416\pi$
$432$		0			0
$433$	−6.29264	+	3.63306i	−0.302405	+	0.174593i	−0.643523	−	0.765427i	$-0.722528\pi$
$433$	−6.29264	+	3.63306i	−0.302405	+	0.174593i	0.341118	+	0.940021i	$0.389194\pi$
$434$		−	0.894851i		−	0.0429542i
$435$		0			0
$436$	−15.8136	+	9.13000i	−0.757335	+	0.437247i
$437$	8.60784			0.411769
$438$		0			0
$439$	0.789879	−	1.36811i	0.0376989	−	0.0652963i	−0.846560	−	0.532293i	$-0.821331\pi$
$439$	0.789879	−	1.36811i	0.0376989	−	0.0652963i	0.884259	+	0.466996i	$0.154664\pi$
$440$	12.1263	−	6.67436i	0.578100	−	0.318188i
$441$		0			0
$442$	−0.561136	−	9.43912i	−0.0266905	−	0.448973i
$443$			2.19488i			0.104282i	0.998640	+	0.0521408i	$0.0166045\pi$
$443$			2.19488i			0.104282i	−0.998640	+	0.0521408i	$0.983396\pi$
$444$		0			0
$445$	−23.5637	+	12.9695i	−1.11702	+	0.614813i
$446$	2.34415	+	4.06019i	0.110999	+	0.192256i
$447$		0			0
$448$	0.649911	+	1.12568i	0.0307054	+	0.0531833i
$449$	−4.47085	+	2.58125i	−0.210993	+	0.121817i	−0.601773	−	0.798667i	$-0.705539\pi$
$449$	−4.47085	+	2.58125i	−0.210993	+	0.121817i	0.390780	+	0.920484i	$0.372205\pi$
$450$		0			0
$451$	2.01867	+	3.49644i	0.0950556	+	0.164641i
$452$	7.16422	+	4.13626i	0.336976	+	0.194553i
$453$		0			0
$454$	7.03374			0.330110
$455$	−7.40155	+	0.288297i	−0.346990	+	0.0135156i
$456$		0			0
$457$	6.82780	−	11.8261i	0.319391	−	0.553201i	−0.660970	−	0.750412i	$-0.729855\pi$
$457$	6.82780	−	11.8261i	0.319391	−	0.553201i	0.980361	+	0.197211i	$0.0631884\pi$
$458$	6.53453	+	3.77271i	0.305339	+	0.176287i
$459$		0			0
$460$	9.50825	+	5.75194i	0.443324	+	0.268186i
$461$	−0.681269	+	0.393331i	−0.0317299	+	0.0183193i	−0.515781	−	0.856720i	$-0.672498\pi$
$461$	−0.681269	+	0.393331i	−0.0317299	+	0.0183193i	0.484051	+	0.875040i	$0.339165\pi$
$462$		0			0
$463$	26.4837			1.23080			0.615401	−	0.788214i	$-0.288994\pi$
$463$	26.4837			1.23080			0.615401	+	0.788214i	$0.288994\pi$
$464$	−0.422948	−	0.732568i	−0.0196349	−	0.0340086i
$465$		0			0
$466$	−15.3541	−	8.86469i	−0.711265	−	0.410649i
$467$		−	7.58353i		−	0.350924i	−0.984486	−	0.175462i	$-0.943858\pi$
$467$		−	7.58353i		−	0.350924i	0.984486	−	0.175462i	$-0.0561419\pi$
$468$		0			0
$469$	−13.6610			−0.630805
$470$	−0.422624	−	0.767846i	−0.0194942	−	0.0354181i
$471$		0			0
$472$	9.93748	−	5.73740i	0.457409	−	0.264085i
$473$	7.82184			0.359649
$474$		0			0
$475$	11.0785	+	7.01518i	0.508316	+	0.321879i
$476$		−	5.23395i		−	0.239898i
$477$		0			0
$478$	−7.62762	−	4.40381i	−0.348879	−	0.201426i
$479$	−3.36663	−	1.94373i	−0.153825	−	0.0888112i	0.421112	−	0.907009i	$-0.361640\pi$
$479$	−3.36663	−	1.94373i	−0.153825	−	0.0888112i	−0.574937	+	0.818198i	$0.694973\pi$
$480$		0			0
$481$	−7.89157	+	15.7606i	−0.359825	+	0.718619i
$482$		−	7.01052i		−	0.319321i
$483$		0			0
$484$	3.49273	−	6.04959i	0.158761	−	0.274981i
$485$	−30.5284	−	0.624297i	−1.38623	−	0.0283479i
$486$		0			0
$487$	−18.7933	−	32.5510i	−0.851606	−	1.47502i	−0.879758	−	0.475421i	$-0.842296\pi$
$487$	−18.7933	−	32.5510i	−0.851606	−	1.47502i	0.0281527	−	0.999604i	$-0.491038\pi$
$488$	4.22355	+	7.31541i	0.191191	+	0.331153i
$489$		0			0
$490$	−9.59275	−	0.196169i	−0.433356	−	0.00886200i
$491$	11.5424	−	19.9921i	0.520903	−	0.902230i	−0.478802	−	0.877923i	$-0.658929\pi$
$491$	11.5424	−	19.9921i	0.520903	−	0.902230i	0.999705	−	0.0243068i	$-0.00773784\pi$
$492$		0			0
$493$		−	2.40947i		−	0.108517i
$494$	−0.391134	−	6.57943i	−0.0175979	−	0.296023i
$495$		0			0
$496$	−1.59843	−	0.922854i	−0.0717716	−	0.0414374i
$497$	9.95934	+	5.75003i	0.446738	+	0.257924i
$498$		0			0
$499$		−	1.79049i		−	0.0801532i	−0.999197	−	0.0400766i	$-0.987240\pi$
$499$		−	1.79049i		−	0.0801532i	0.999197	−	0.0400766i	$-0.0127602\pi$
$500$	7.54964	+	15.1519i	0.337630	+	0.677612i
$501$		0			0
$502$	10.0459			0.448371
$503$	28.1580	−	16.2570i	1.25550	−	0.724866i	0.283307	−	0.959029i	$-0.408569\pi$
$503$	28.1580	−	16.2570i	1.25550	−	0.724866i	0.972197	+	0.234164i	$0.0752352\pi$
$504$		0			0
$505$	19.0114	+	34.5409i	0.845996	+	1.53705i
$506$	5.78172			0.257029
$507$		0			0
$508$			7.81926i			0.346923i
$509$	−2.40603	−	1.38912i	−0.106646	−	0.0615718i	0.445729	−	0.895168i	$-0.352945\pi$
$509$	−2.40603	−	1.38912i	−0.106646	−	0.0615718i	−0.552374	+	0.833596i	$0.686278\pi$
$510$		0			0
$511$	0.979522	+	1.69658i	0.0433315	+	0.0750524i
$512$	14.1581			0.625706
$513$		0			0
$514$	13.6354	−	7.87242i	0.601433	−	0.347237i
$515$	27.3196	+	16.5268i	1.20384	+	0.728257i
$516$		0			0
$517$	1.23071	+	0.710553i	0.0541267	+	0.0312501i
$518$	1.56531	−	2.71120i	0.0687760	−	0.119123i
$519$		0			0
$520$	9.20107	−	17.4740i	0.403494	−	0.766285i
$521$	2.64334			0.115807			0.0579035	−	0.998322i	$-0.481558\pi$
$521$	2.64334			0.115807			0.0579035	+	0.998322i	$0.481558\pi$
$522$		0			0
$523$	17.6514	+	10.1910i	0.771840	+	0.445622i	0.833531	−	0.552473i	$-0.186316\pi$
$523$	17.6514	+	10.1910i	0.771840	+	0.445622i	−0.0616905	+	0.998095i	$0.519649\pi$
$524$	−11.1603	−	19.3303i	−0.487542	−	0.844448i
$525$		0			0
$526$	10.8883	−	6.28637i	0.474753	−	0.274099i
$527$	−2.62868	−	4.55300i	−0.114507	−	0.198332i
$528$		0			0
$529$	−6.11350	−	10.5889i	−0.265804	−	0.460386i
$530$	10.2749	−	5.65533i	0.446314	−	0.245652i
$531$		0			0
$532$		−	3.64826i		−	0.158172i
$533$	5.15058	+	2.57898i	0.223097	+	0.111708i
$534$		0			0
$535$	−32.3037	+	17.7800i	−1.39661	+	0.768698i
$536$	18.2109	−	31.5422i	0.786592	−	1.36242i
$537$		0			0
$538$	−21.2141			−0.914605
$539$	13.4727	−	7.77846i	0.580310	−	0.335042i
$540$		0			0
$541$			21.5030i			0.924487i	0.886753	+	0.462244i	$0.152955\pi$
$541$			21.5030i			0.924487i	−0.886753	+	0.462244i	$0.847045\pi$
$542$	15.7425	−	9.08893i	0.676198	−	0.390403i
$543$		0			0
$544$	18.9627	+	10.9481i	0.813017	+	0.469396i
$545$	−23.0729	−	13.9578i	−0.988334	−	0.597885i
$546$		0			0
$547$		−	29.4024i		−	1.25716i	−0.777747	−	0.628578i	$-0.783637\pi$
$547$		−	29.4024i		−	1.25716i	0.777747	−	0.628578i	$-0.216363\pi$
$548$	−7.84345	+	13.5853i	−0.335056	+	0.580333i
$549$		0			0
$550$	7.44121	+	4.71196i	0.317294	+	0.200919i
$551$		−	1.67949i		−	0.0715488i
$552$		0			0
$553$	−1.80484	−	3.12607i	−0.0767495	−	0.132934i
$554$		−	2.72770i		−	0.115889i
$555$		0			0
$556$	−0.0924896	+	0.160197i	−0.00392243	+	0.00679385i
$557$	6.34739	−	10.9940i	0.268948	−	0.465831i	−0.699643	−	0.714493i	$-0.746657\pi$
$557$	6.34739	−	10.9940i	0.268948	−	0.465831i	0.968590	+	0.248662i	$0.0799908\pi$
$558$		0			0
$559$	9.31635	−	6.14349i	0.394040	−	0.259842i
$560$	1.40456	−	2.32181i	0.0593536	−	0.0981145i
$561$		0			0
$562$	−14.9751	−	8.64587i	−0.631686	−	0.364704i
$563$	35.8124	−	20.6763i	1.50931	−	0.871403i	0.509373	−	0.860546i	$-0.329877\pi$
$563$	35.8124	−	20.6763i	1.50931	−	0.871403i	0.999941	−	0.0108570i	$-0.00345595\pi$
$564$		0			0
$565$	−0.249778	+	12.2143i	−0.0105082	+	0.513858i
$566$	−14.8443	+	8.57035i	−0.623952	+	0.360239i
$567$		0			0
$568$	−26.5528	+	15.3303i	−1.11413	+	0.643244i
$569$	17.2503	−	29.8784i	0.723171	−	1.25257i	−0.236552	−	0.971619i	$-0.576017\pi$
$569$	17.2503	−	29.8784i	0.723171	−	1.25257i	0.959723	−	0.280950i	$-0.0906494\pi$
$570$		0			0
$571$	22.7411			0.951687			0.475843	−	0.879530i	$-0.342143\pi$
$571$	22.7411			0.951687			0.475843	+	0.879530i	$0.342143\pi$
$572$	0.818727	+	13.7722i	0.0342327	+	0.575843i
$573$		0			0
$574$	−0.886028	−	0.511548i	−0.0369821	−	0.0213516i
$575$	−0.670924	+	16.3974i	−0.0279795	+	0.683819i
$576$		0			0
$577$	27.0080			1.12436			0.562180	−	0.827015i	$-0.309963\pi$
$577$	27.0080			1.12436			0.562180	+	0.827015i	$0.309963\pi$
$578$	−0.991222	−	1.71685i	−0.0412294	−	0.0714114i
$579$		0			0
$580$	1.12227	−	1.85517i	0.0465998	−	0.0770318i
$581$	4.43904	+	7.68864i	0.184162	+	0.318978i
$582$		0			0
$583$	−9.50825	+	16.4688i	−0.393791	+	0.682067i
$584$	−5.22305			−0.216132
$585$		0			0
$586$	13.2215			0.546176
$587$	20.3047	−	35.1688i	0.838065	−	1.45157i	−0.0534448	−	0.998571i	$-0.517020\pi$
$587$	20.3047	−	35.1688i	0.838065	−	1.45157i	0.891510	−	0.453001i	$-0.149647\pi$
$588$		0			0
$589$	−1.83229	−	3.17362i	−0.0754982	−	0.130767i
$590$	6.24732	+	3.77927i	0.257198	+	0.155590i
$591$		0			0
$592$	−3.22860	−	5.59210i	−0.132695	−	0.229834i
$593$	−12.6121			−0.517919			−0.258959	−	0.965888i	$-0.583380\pi$
$593$	−12.6121			−0.517919			−0.258959	+	0.965888i	$0.583380\pi$
$594$		0			0
$595$	6.77153	−	3.72706i	0.277606	−	0.152795i
$596$	17.3968	+	10.0441i	0.712602	+	0.411421i
$597$		0			0
$598$	6.88643	−	4.54113i	0.281607	−	0.185700i
$599$	−42.4090			−1.73279			−0.866393	−	0.499362i	$-0.833568\pi$
$599$	−42.4090			−1.73279			−0.866393	+	0.499362i	$0.833568\pi$
$600$		0			0
$601$	19.5921	−	33.9345i	0.799178	−	1.38422i	−0.120974	−	0.992656i	$-0.538602\pi$
$601$	19.5921	−	33.9345i	0.799178	−	1.38422i	0.920152	−	0.391561i	$-0.128065\pi$
$602$	−1.71657	+	0.991059i	−0.0699620	+	0.0403926i
$603$		0			0
$604$	−21.5237	+	12.4267i	−0.875788	+	0.505637i
$605$	10.3139	+	0.210917i	0.419321	+	0.00857498i
$606$		0			0
$607$	−10.3554	+	5.97868i	−0.420312	+	0.242667i	−0.695211	−	0.718806i	$-0.744689\pi$
$607$	−10.3554	+	5.97868i	−0.420312	+	0.242667i	0.274899	+	0.961473i	$0.411356\pi$
$608$	13.2177	+	7.63125i	0.536049	+	0.309488i
$609$		0			0
$610$	−2.78208	+	4.59892i	−0.112643	+	0.186205i
$611$	2.02395	−	0.120320i	0.0818803	−	0.00486762i
$612$		0			0
$613$	−1.28934	+	2.23321i	−0.0520761	+	0.0901985i	−0.890888	−	0.454222i	$-0.849917\pi$
$613$	−1.28934	+	2.23321i	−0.0520761	+	0.0901985i	0.838812	+	0.544421i	$0.183251\pi$
$614$	0.475775	−	0.824066i	0.0192007	−	0.0332566i
$615$		0			0
$616$		−	5.68725i		−	0.229146i
$617$	3.57225	+	6.18733i	0.143814	+	0.249092i	0.928930	−	0.370256i	$-0.120730\pi$
$617$	3.57225	+	6.18733i	0.143814	+	0.249092i	−0.785116	+	0.619349i	$0.787397\pi$
$618$		0			0
$619$			5.03352i			0.202314i	0.994870	+	0.101157i	$0.0322545\pi$
$619$			5.03352i			0.202314i	−0.994870	+	0.101157i	$0.967745\pi$
$620$	0.0967262	−	4.72996i	0.00388462	−	0.189960i
$621$		0			0
$622$	10.3122	−	17.8613i	0.413483	−	0.716174i
$623$			11.0514i			0.442763i
$624$		0			0
$625$	−14.2270	+	20.5571i	−0.569080	+	0.822282i
$626$	−7.76190	−	4.48133i	−0.310228	−	0.179110i
$627$		0			0
$628$	−25.6538	+	14.8112i	−1.02370	+	0.591031i
$629$		−	18.3928i		−	0.733369i
$630$		0			0
$631$	−13.0693	+	7.54555i	−0.520280	+	0.300384i	−0.737049	−	0.675839i	$-0.763781\pi$
$631$	−13.0693	+	7.54555i	−0.520280	+	0.300384i	0.216769	+	0.976223i	$0.430448\pi$
$632$	9.62384			0.382816
$633$		0			0
$634$	6.20285	−	10.7437i	0.246347	−	0.426685i
$635$	−10.1163	+	5.56805i	−0.401454	+	0.220961i
$636$		0			0
$637$	9.93748	−	19.8465i	0.393737	−	0.786347i
$638$		−	1.12808i		−	0.0446612i
$639$		0			0
$640$	11.4864	+	20.8691i	0.454039	+	0.824923i
$641$	−6.68950	−	11.5865i	−0.264219	−	0.457641i	0.703140	−	0.711052i	$-0.251781\pi$
$641$	−6.68950	−	11.5865i	−0.264219	−	0.457641i	−0.967359	+	0.253411i	$0.918448\pi$
$642$		0			0
$643$	0.416240	+	0.720950i	0.0164149	+	0.0284315i	0.874116	−	0.485717i	$-0.161441\pi$
$643$	0.416240	+	0.720950i	0.0164149	+	0.0284315i	−0.857701	+	0.514148i	$0.828108\pi$
$644$	3.95421	−	2.28296i	0.155818	−	0.0899614i
$645$		0			0
$646$	3.43892	+	5.95638i	0.135302	+	0.234351i
$647$	−24.7897	−	14.3124i	−0.974585	−	0.562677i	−0.0739539	−	0.997262i	$-0.523562\pi$
$647$	−24.7897	−	14.3124i	−0.974585	−	0.562677i	−0.900631	+	0.434585i	$0.856895\pi$
$648$		0			0
$649$	−11.8386			−0.464707
$650$	12.5639	−	0.232263i	0.492797	−	0.00911009i
$651$		0			0
$652$	2.80188	−	4.85300i	0.109730	−	0.190058i
$653$	−12.4546	−	7.19065i	−0.487385	−	0.281392i	0.236104	−	0.971728i	$-0.424129\pi$
$653$	−12.4546	−	7.19065i	−0.487385	−	0.281392i	−0.723489	+	0.690336i	$0.757463\pi$
$654$		0			0
$655$	17.0617	−	28.2039i	0.666657	−	1.10202i
$656$	−1.82751	+	1.05511i	−0.0713523	+	0.0411953i
$657$		0			0
$658$	−0.360120			−0.0140389
$659$	4.50092	+	7.79582i	0.175331	+	0.303682i	0.940276	−	0.340414i	$-0.110567\pi$
$659$	4.50092	+	7.79582i	0.175331	+	0.303682i	−0.764945	+	0.644096i	$0.777234\pi$
$660$		0			0
$661$	−31.7257	−	18.3168i	−1.23399	−	0.712442i	−0.266127	−	0.963938i	$-0.585744\pi$
$661$	−31.7257	−	18.3168i	−1.23399	−	0.712442i	−0.967858	+	0.251496i	$0.919077\pi$
$662$			19.3060i			0.750347i
$663$		0			0
$664$	−23.6700			−0.918576
$665$	4.72002	−	2.59791i	0.183034	−	0.100743i
$666$		0			0
$667$	1.82034	−	1.05097i	0.0704837	−	0.0406938i
$668$	26.7442			1.03477
$669$		0			0
$670$	23.1706	+	0.473831i	0.895158	+	0.0183057i
$671$		−	8.71493i		−	0.336436i
$672$		0			0
$673$	−19.0295	−	10.9867i	−0.733533	−	0.423505i	0.0861805	−	0.996280i	$-0.472534\pi$
$673$	−19.0295	−	10.9867i	−0.733533	−	0.423505i	−0.819713	+	0.572774i	$0.805867\pi$
$674$	5.08849	+	2.93784i	0.196001	+	0.113161i
$675$		0			0
$676$	11.7922	+	15.7606i	0.453547	+	0.606175i
$677$			26.6767i			1.02527i	0.858607	+	0.512635i	$0.171331\pi$
$677$			26.6767i			1.02527i	−0.858607	+	0.512635i	$0.828669\pi$
$678$		0			0
$679$	−6.27301	+	10.8652i	−0.240736	+	0.416967i
$680$	−0.421333	+	20.6034i	−0.0161574	+	0.790104i
$681$		0			0
$682$	−1.23071	−	2.13166i	−0.0471264	−	0.0816254i
$683$	−1.85759	−	3.21745i	−0.0710788	−	0.123112i	0.828296	−	0.560291i	$-0.189311\pi$
$683$	−1.85759	−	3.21745i	−0.0710788	−	0.123112i	−0.899374	+	0.437179i	$0.855978\pi$
$684$		0			0
$685$	−23.1615	−	0.473645i	−0.884955	−	0.0180970i
$686$	−4.21253	+	7.29632i	−0.160835	+	0.278575i
$687$		0			0
$688$			4.08829i			0.155865i
$689$	1.61006	+	27.0835i	0.0613383	+	1.03180i
$690$		0			0
$691$	−35.2016	−	20.3236i	−1.33913	−	0.773148i	−0.352453	−	0.935830i	$-0.614652\pi$
$691$	−35.2016	−	20.3236i	−1.33913	−	0.773148i	−0.986679	+	0.162682i	$0.947986\pi$
$692$	−9.11584	−	5.26303i	−0.346532	−	0.200070i
$693$		0			0
$694$			14.4944i			0.550201i
$695$	−0.273119	−	0.00558520i	−0.0103600	−	0.000211859i
$696$		0			0
$697$	−6.01081			−0.227676
$698$	−12.7393	+	7.35502i	−0.482188	+	0.278392i
$699$		0			0
$700$	6.94972	+	0.284358i	0.262675	+	0.0107477i
$701$	4.25340			0.160649			0.0803243	−	0.996769i	$-0.474404\pi$
$701$	4.25340			0.160649			0.0803243	+	0.996769i	$0.474404\pi$
$702$		0			0
$703$		−	12.8205i		−	0.483534i
$704$	3.09636	+	1.78768i	0.116698	+	0.0673758i
$705$		0			0
$706$	−6.21193	−	10.7594i	−0.233789	−	0.404934i
$707$	16.1997			0.609252
$708$		0			0
$709$	10.6408	−	6.14349i	0.399625	−	0.230724i	−0.286697	−	0.958021i	$-0.592557\pi$
$709$	10.6408	−	6.14349i	0.399625	−	0.230724i	0.686322	+	0.727298i	$0.259224\pi$
$710$	−16.6928	−	10.0982i	−0.626468	−	0.378977i
$711$		0			0
$712$	−25.5168	−	14.7321i	−0.956283	−	0.552110i
$713$	2.29317	−	3.97189i	0.0858800	−	0.148749i
$714$		0			0
$715$	−17.2350	+	10.8663i	−0.644553	+	0.406378i
$716$	34.4825			1.28867
$717$		0			0
$718$	−12.1326	−	7.00475i	−0.452784	−	0.261415i
$719$	6.73036	+	11.6573i	0.251000	+	0.434745i	0.963801	−	0.266621i	$-0.0859072\pi$
$719$	6.73036	+	11.6573i	0.251000	+	0.434745i	−0.712801	+	0.701366i	$0.752574\pi$
$720$		0			0
$721$	11.3614	−	6.55953i	0.423122	−	0.244290i
$722$	−4.22481	−	7.31759i	−0.157231	−	0.272332i
$723$		0			0
$724$	0.731527	+	1.26704i	0.0271870	+	0.0470892i
$725$	3.19933	+	0.130905i	0.118820	+	0.00486170i
$726$		0			0
$727$		−	24.9737i		−	0.926222i	−0.886300	−	0.463111i	$-0.846733\pi$
$727$		−	24.9737i		−	0.926222i	0.886300	−	0.463111i	$-0.153267\pi$
$728$	−4.46693	−	6.77391i	−0.165555	−	0.251058i
$729$		0			0
$730$	−1.60254	−	2.91158i	−0.0593126	−	0.107762i
$731$	−5.82259	+	10.0850i	−0.215356	+	0.373008i
$732$		0			0
$733$	37.2918			1.37740			0.688702	−	0.725045i	$-0.258181\pi$
$733$	37.2918			1.37740			0.688702	+	0.725045i	$0.258181\pi$
$734$	7.52634	−	4.34533i	0.277802	−	0.160389i
$735$		0			0
$736$			19.1015i			0.704092i
$737$	−32.5423	+	18.7883i	−1.19871	+	0.692076i
$738$		0			0
$739$	5.85916	+	3.38279i	0.215533	+	0.124438i	0.603880	−	0.797075i	$-0.293621\pi$
$739$	5.85916	+	3.38279i	0.215533	+	0.124438i	−0.388347	+	0.921513i	$0.626954\pi$
$740$	8.56693	−	14.1616i	0.314927	−	0.520589i
$741$		0			0
$742$		−	4.81894i		−	0.176909i
$743$	−14.1613	+	24.5281i	−0.519527	+	0.899847i	0.480215	+	0.877151i	$0.340559\pi$
$743$	−14.1613	+	24.5281i	−0.519527	+	0.899847i	−0.999742	+	0.0226967i	$0.992775\pi$
$744$		0			0
$745$	−0.606534	+	29.6598i	−0.0222217	+	1.08665i
$746$			17.1407i			0.627566i
$747$		0			0
$748$	−7.19839	−	12.4680i	−0.263199	−	0.455875i
$749$			15.1504i			0.553585i
$750$		0			0
$751$	−17.9882	+	31.1565i	−0.656399	+	1.13692i	0.325143	+	0.945665i	$0.394588\pi$
$751$	−17.9882	+	31.1565i	−0.656399	+	1.13692i	−0.981541	+	0.191251i	$0.938746\pi$
$752$	−0.371389	+	0.643265i	−0.0135432	+	0.0234575i
$753$		0			0
$754$	−0.886028	−	1.34362i	−0.0322672	−	0.0489319i
$755$	−31.4043	−	18.9978i	−1.14292	−	0.691400i
$756$		0			0
$757$	28.4531	+	16.4274i	1.03415	+	0.597065i	0.918170	−	0.396187i	$-0.129667\pi$
$757$	28.4531	+	16.4274i	1.03415	+	0.597065i	0.115977	+	0.993252i	$0.463000\pi$
$758$	−12.7393	+	7.35502i	−0.462711	+	0.267146i
$759$		0			0
$760$	−0.293685	+	14.3614i	−0.0106531	+	0.520941i
$761$	25.1678	−	14.5306i	0.912332	−	0.526735i	0.0311509	−	0.999515i	$-0.490083\pi$
$761$	25.1678	−	14.5306i	0.912332	−	0.526735i	0.881181	+	0.472780i	$0.156749\pi$
$762$		0			0
$763$	−9.59536	+	5.53989i	−0.347376	+	0.200557i
$764$	−12.8641	+	22.2813i	−0.465407	+	0.806108i
$765$		0			0
$766$	20.4594			0.739230
$767$	−14.1006	+	9.29839i	−0.509144	+	0.335746i
$768$		0			0
$769$	−3.23386	−	1.86707i	−0.116616	−	0.0673282i	0.440557	−	0.897724i	$-0.354781\pi$
$769$	−3.23386	−	1.86707i	−0.116616	−	0.0673282i	−0.557173	+	0.830396i	$0.688114\pi$
$770$	3.17034	−	1.74496i	0.114251	−	0.0628841i
$771$		0			0
$772$	32.9669			1.18650
$773$	−14.6296	−	25.3392i	−0.526190	−	0.911387i	−0.999534	−	0.0305100i	$-0.990287\pi$
$773$	−14.6296	−	25.3392i	−0.526190	−	0.911387i	0.473345	−	0.880877i	$-0.343046\pi$
$774$		0			0
$775$	6.18836	−	3.24304i	0.222293	−	0.116493i
$776$	−16.7246	−	28.9679i	−0.600379	−	1.03989i
$777$		0			0
$778$	3.83538	−	6.64307i	0.137505	−	0.238166i
$779$	−4.18977			−0.150114
$780$		0			0
$781$	31.6327			1.13191
$782$	−4.30392	+	7.45461i	−0.153908	+	0.266576i
$783$		0			0
$784$	4.06562	+	7.04186i	0.145201	+	0.251495i
$785$	−37.4302	−	22.6431i	−1.33594	−	0.808167i
$786$		0			0
$787$	−27.2810	−	47.2521i	−0.972464	−	1.68436i	−0.688062	−	0.725652i	$-0.741538\pi$
$787$	−27.2810	−	47.2521i	−0.972464	−	1.68436i	−0.284402	−	0.958705i	$-0.591795\pi$
$788$	−26.6394			−0.948988
$789$		0			0
$790$	2.95279	+	5.36478i	0.105055	+	0.190870i
$791$	4.34709	+	2.50980i	0.154565	+	0.0892381i
$792$		0			0
$793$	−6.84495	−	10.3801i	−0.243071	−	0.368608i
$794$	6.11097			0.216870
$795$		0			0
$796$	11.6349	−	20.1522i	0.412388	−	0.714277i
$797$	2.87205	−	1.65818i	0.101733	−	0.0587358i	−0.448270	−	0.893898i	$-0.647960\pi$
$797$	2.87205	−	1.65818i	0.101733	−	0.0587358i	0.550003	+	0.835162i	$0.314626\pi$
$798$		0			0
$799$	−1.83229	+	1.05787i	−0.0648217	+	0.0374248i
$800$	−15.5673	+	24.5841i	−0.550387	+	0.869180i
$801$		0			0
$802$	−7.60545	+	4.39101i	−0.268558	+	0.155052i
$803$	4.66671	+	2.69433i	0.164685	+	0.0950808i
$804$		0			0
$805$	5.76940	+	3.49015i	0.203345	+	0.123012i
$806$	−3.14013	−	1.57231i	−0.110606	−	0.0553824i
$807$		0			0
$808$	−21.5952	+	37.4040i	−0.759716	+	1.31587i
$809$	−16.0223	+	27.7515i	−0.563315	+	0.975691i	0.433889	+	0.900966i	$0.357141\pi$
$809$	−16.0223	+	27.7515i	−0.563315	+	0.975691i	−0.997204	+	0.0747244i	$0.976192\pi$
$810$		0			0
$811$		−	0.393159i		−	0.0138057i	−0.999976	−	0.00690283i	$-0.997803\pi$
$811$		−	0.393159i		−	0.0138057i	0.999976	−	0.00690283i	$-0.00219726\pi$
$812$	−0.445434	−	0.771514i	−0.0156317	−	0.0270748i
$813$		0			0
$814$		−	8.61128i		−	0.301825i
$815$	8.27387	+	0.169198i	0.289821	+	0.00592675i
$816$		0			0
$817$	−4.05857	+	7.02965i	−0.141991	+	0.245936i
$818$		−	21.2022i		−	0.741319i
$819$		0			0
$820$	−4.62803	−	2.79969i	−0.161618	−	0.0977695i
$821$	33.7484	+	19.4847i	1.17783	+	0.680019i	0.955511	−	0.294955i	$-0.0953047\pi$
$821$	33.7484	+	19.4847i	1.17783	+	0.680019i	0.222317	+	0.974974i	$0.428638\pi$
$822$		0			0
$823$	39.6498	−	22.8918i	1.38211	−	0.797959i	0.389696	−	0.920943i	$-0.372580\pi$
$823$	39.6498	−	22.8918i	1.38211	−	0.797959i	0.992409	+	0.122985i	$0.0392466\pi$
$824$			34.9770i			1.21848i
$825$		0			0
$826$	2.59808	−	1.50000i	0.0903988	−	0.0521918i
$827$	8.69681			0.302418			0.151209	−	0.988502i	$-0.451683\pi$
$827$	8.69681			0.302418			0.151209	+	0.988502i	$0.451683\pi$
$828$		0			0
$829$	16.2197	−	28.0934i	0.563334	−	0.975724i	−0.433868	−	0.900976i	$-0.642852\pi$
$829$	16.2197	−	28.0934i	0.563334	−	0.975724i	0.997203	−	0.0747472i	$-0.0238150\pi$
$830$	−7.26245	−	13.1948i	−0.252083	−	0.457998i
$831$		0			0
$832$	5.09207	−	0.302713i	0.176536	−	0.0104947i
$833$			23.1612i			0.802488i
$834$		0			0
$835$	19.0444	+	34.6009i	0.659059	+	1.19741i
$836$	−5.01756	−	8.69067i	−0.173536	−	0.300573i
$837$		0			0
$838$	4.95134	+	8.57597i	0.171041	+	0.296252i
$839$	−11.9245	+	6.88462i	−0.411680	+	0.237683i	−0.691511	−	0.722366i	$-0.743055\pi$
$839$	−11.9245	+	6.88462i	−0.411680	+	0.237683i	0.279831	+	0.960049i	$0.409721\pi$
$840$		0			0
$841$	14.2949	+	24.7596i	0.492929	+	0.853778i
$842$	0.745330	+	0.430316i	0.0256858	+	0.0148297i
$843$		0			0
$844$	25.8259			0.888966
$845$	−11.9934	+	26.4794i	−0.412584	+	0.910919i
$846$		0			0
$847$	2.11931	−	3.67076i	0.0728205	−	0.126129i
$848$	−8.60784	−	4.96974i	−0.295595	−	0.170662i
$849$		0			0
$850$	−11.6146	+	6.08666i	−0.398377	+	0.208771i
$851$	13.8956	−	8.02265i	0.476336	−	0.275013i
$852$		0			0
$853$	−23.9310			−0.819382			−0.409691	−	0.912224i	$-0.634364\pi$
$853$	−23.9310			−0.819382			−0.409691	+	0.912224i	$0.634364\pi$
$854$	1.10422	+	1.91256i	0.0377856	+	0.0654465i
$855$		0			0
$856$	−34.9813	−	20.1965i	−1.19564	−	0.690301i
$857$		−	9.17825i		−	0.313523i	−0.987636	−	0.156761i	$-0.949895\pi$
$857$		−	9.17825i		−	0.313523i	0.987636	−	0.156761i	$-0.0501054\pi$
$858$		0			0
$859$	5.15591			0.175917			0.0879586	−	0.996124i	$-0.471966\pi$
$859$	5.15591			0.175917			0.0879586	+	0.996124i	$0.471966\pi$
$860$	−9.18047	+	5.05295i	−0.313051	+	0.172304i
$861$		0			0
$862$	11.5714	−	6.68077i	0.394125	−	0.227548i
$863$	−37.2329			−1.26742			−0.633711	−	0.773569i	$-0.718469\pi$
$863$	−37.2329			−1.26742			−0.633711	+	0.773569i	$0.718469\pi$
$864$		0			0
$865$	0.317820	−	15.5416i	0.0108062	−	0.528430i
$866$		−	5.06476i		−	0.172108i
$867$		0			0
$868$	−1.68341	−	0.971916i	−0.0571386	−	0.0329890i
$869$	−8.59874	−	4.96449i	−0.291692	−	0.168409i
$870$		0			0
$871$	−24.0033	+	47.9378i	−0.813319	+	1.62431i
$872$		−	29.5400i		−	1.00035i
$873$		0			0
$874$	−3.00000	+	5.19615i	−0.101477	+	0.175762i
$875$	4.58096	+	9.19383i	0.154865	+	0.310808i
$876$		0			0
$877$	10.2494	+	17.7526i	0.346099	+	0.599461i	0.985553	−	0.169368i	$-0.0541728\pi$
$877$	10.2494	+	17.7526i	0.346099	+	0.599461i	−0.639454	+	0.768830i	$0.720839\pi$
$878$	0.550576	+	0.953626i	0.0185810	+	0.0321833i
$879$		0			0
$880$	0.152608	−	7.46261i	0.00514441	−	0.251564i
$881$	−7.69097	+	13.3211i	−0.259115	+	0.448801i	−0.966005	−	0.258523i	$-0.916764\pi$
$881$	−7.69097	+	13.3211i	−0.259115	+	0.448801i	0.706890	+	0.707324i	$0.250098\pi$
$882$		0			0
$883$			40.9768i			1.37898i	0.724296	+	0.689490i	$0.242165\pi$
$883$			40.9768i			1.37898i	−0.724296	+	0.689490i	$0.757835\pi$
$884$	−18.3665	−	9.19641i	−0.617732	−	0.309309i
$885$		0			0
$886$	−1.32494	−	0.764957i	−0.0445124	−	0.0256992i
$887$	−10.4226	−	6.01748i	−0.349956	−	0.202047i	0.314710	−	0.949188i	$-0.398093\pi$
$887$	−10.4226	−	6.01748i	−0.349956	−	0.202047i	−0.664666	+	0.747141i	$0.731426\pi$
$888$		0			0
$889$			4.74456i			0.159127i
$890$	0.383317	−	18.7444i	0.0128488	−	0.628314i
$891$		0			0
$892$	10.1841			0.340990
$893$	−1.27718	+	0.737378i	−0.0427391	+	0.0246754i
$894$		0			0
$895$	24.5548	+	44.6125i	0.820776	+	1.49123i
$896$	9.78760			0.326981
$897$		0			0
$898$		−	3.59846i		−	0.120082i
$899$	−0.774964	−	0.447425i	−0.0258465	−	0.0149225i
$900$		0			0
$901$	−14.1559	−	24.5187i	−0.471602	−	0.816838i
$902$	−2.81419			−0.0937022
$903$		0			0
$904$	−11.5899	+	6.69142i	−0.385474	+	0.222553i
$905$	−1.11834	+	1.84868i	−0.0371750	+	0.0614522i
$906$		0			0
$907$	−17.4282	−	10.0622i	−0.578693	−	0.334109i	0.181921	−	0.983313i	$-0.441769\pi$
$907$	−17.4282	−	10.0622i	−0.578693	−	0.334109i	−0.760614	+	0.649205i	$0.775102\pi$
$908$	7.63949	−	13.2320i	0.253525	−	0.439119i
$909$		0			0
$910$	2.40555	−	4.56845i	0.0797433	−	0.151443i
$911$	−7.06252			−0.233992			−0.116996	−	0.993132i	$-0.537326\pi$
$911$	−7.06252			−0.233992			−0.116996	+	0.993132i	$0.537326\pi$
$912$		0			0
$913$	21.1488	+	12.2103i	0.699923	+	0.404101i
$914$	4.75924	+	8.24324i	0.157422	+	0.272662i
$915$		0			0
$916$	14.1946	−	8.19524i	0.469002	−	0.270778i
$917$	−6.77186	−	11.7292i	−0.223627	−	0.387333i
$918$		0			0
$919$	−2.26160	−	3.91721i	−0.0746035	−	0.129217i	0.826310	−	0.563215i	$-0.190436\pi$
$919$	−2.26160	−	3.91721i	−0.0746035	−	0.129217i	−0.900914	+	0.433998i	$0.857102\pi$
$920$	−15.7495	+	8.66855i	−0.519245	+	0.285794i
$921$		0			0
$922$		−	0.548334i		−	0.0180584i
$923$	37.6767	−	24.8452i	1.24014	−	0.817790i
$924$		0			0
$925$	24.4223	+	0.999273i	0.802999	+	0.0328559i
$926$	−9.23009	+	15.9870i	−0.303320	+	0.525365i
$927$		0			0
$928$	3.72694			0.122343
$929$	5.95715	−	3.43936i	0.195448	−	0.112842i	−0.399083	−	0.916915i	$-0.630671\pi$
$929$	5.95715	−	3.43936i	0.195448	−	0.112842i	0.594530	+	0.804073i	$0.297338\pi$
$930$		0			0
$931$			16.1442i			0.529106i
$932$	−33.3528	+	19.2563i	−1.09251	+	0.630760i
$933$		0			0
$934$	4.57782	+	2.64301i	0.149791	+	0.0864819i
$935$	11.0048	−	18.1914i	0.359895	−	0.594924i
$936$		0			0
$937$		−	11.5744i		−	0.378120i	−0.981966	−	0.189060i	$-0.939456\pi$
$937$		−	11.5744i		−	0.378120i	0.981966	−	0.189060i	$-0.0605440\pi$
$938$	4.76111	−	8.24649i	0.155456	−	0.269257i
$939$		0			0
$940$	−1.90350	−	0.0389261i	−0.0620855	−	0.00126963i
$941$		−	3.49144i		−	0.113818i	−0.998379	−	0.0569088i	$-0.981876\pi$
$941$		−	3.49144i		−	0.113818i	0.998379	−	0.0569088i	$-0.0181244\pi$
$942$		0			0
$943$	−2.62182	−	4.54113i	−0.0853782	−	0.147879i
$944$		−	6.18778i		−	0.201395i
$945$		0			0
$946$	−2.72606	+	4.72168i	−0.0886319	+	0.153515i
$947$	−25.3143	+	43.8456i	−0.822603	+	1.42479i	0.0811340	+	0.996703i	$0.474146\pi$
$947$	−25.3143	+	43.8456i	−0.822603	+	1.42479i	−0.903737	+	0.428087i	$0.859188\pi$
$948$		0			0
$949$	7.67458	−	0.456238i	0.249127	−	0.0148101i
$950$	−8.09581	+	4.24264i	−0.262663	+	0.137649i
$951$		0			0
$952$	7.33281	+	4.23360i	0.237658	+	0.137212i
$953$	−21.2550	+	12.2716i	−0.688516	+	0.397515i	−0.803056	−	0.595904i	$-0.796794\pi$
$953$	−21.2550	+	12.2716i	−0.688516	+	0.397515i	0.114540	+	0.993419i	$0.463461\pi$
$954$		0			0
$955$	−37.9873	−	0.776828i	−1.22924	−	0.0251376i
$956$	−16.5690	+	9.56614i	−0.535881	+	0.309391i
$957$		0			0
$958$	2.34668	−	1.35485i	0.0758176	−	0.0437733i
$959$	−4.75924	+	8.24324i	−0.153684	+	0.266188i
$960$		0			0
$961$	29.0475			0.937015
$962$	−6.76354	−	10.2566i	−0.218065	−	0.330687i
$963$		0			0
$964$	−13.1883	−	7.61428i	−0.424767	−	0.245239i
$965$	23.4755	+	42.6516i	0.755704	+	1.37300i
$966$		0			0
$967$	−21.9813			−0.706870			−0.353435	−	0.935459i	$-0.614986\pi$
$967$	−21.9813			−0.706870			−0.353435	+	0.935459i	$0.614986\pi$
$968$	5.65035	+	9.78670i	0.181609	+	0.314556i
$969$		0			0
$970$	11.0166	−	18.2110i	0.353722	−	0.584721i
$971$	−8.81620	−	15.2701i	−0.282925	−	0.490041i	0.689179	−	0.724591i	$-0.257971\pi$
$971$	−8.81620	−	15.2701i	−0.282925	−	0.490041i	−0.972104	+	0.234551i	$0.924638\pi$
$972$		0			0
$973$	−0.0561207	+	0.0972039i	−0.00179915	+	0.00311621i
$974$	26.1993			0.839480
$975$		0			0
$976$	4.55509			0.145805
$977$	17.8238	−	30.8717i	0.570233	−	0.987672i	−0.426309	−	0.904578i	$-0.640186\pi$
$977$	17.8238	−	30.8717i	0.570233	−	0.987672i	0.996542	−	0.0830942i	$-0.0264803\pi$
$978$		0			0
$979$	15.1992	+	26.3259i	0.485770	+	0.841378i
$980$	−10.7879	+	17.8330i	−0.344608	+	0.569654i
$981$		0			0
$982$	8.04552	+	13.9353i	0.256743	+	0.444692i
$983$	−44.4295			−1.41708			−0.708540	−	0.705670i	$-0.750646\pi$
$983$	−44.4295			−1.41708			−0.708540	+	0.705670i	$0.750646\pi$
$984$		0			0
$985$	−18.9697	−	34.4652i	−0.604426	−	1.09815i
$986$	1.45448	+	0.839746i	0.0463202	+	0.0267430i
$987$		0			0
$988$	−12.8022	−	6.41025i	−0.407291	−	0.203937i
$989$	−10.1589			−0.323034
$990$		0			0
$991$	28.2152	−	48.8701i	0.896285	−	1.55241i	0.0640786	−	0.997945i	$-0.479589\pi$
$991$	28.2152	−	48.8701i	0.896285	−	1.55241i	0.832206	−	0.554466i	$-0.187078\pi$
$992$	7.04253	−	4.06601i	0.223600	−	0.129096i
$993$		0			0
$994$	−6.94205	+	4.00799i	−0.220188	+	0.127126i
$995$	34.3575	+	0.702600i	1.08921	+	0.0222739i
$996$		0			0
$997$	13.5170	−	7.80405i	0.428088	−	0.247157i	−0.270444	−	0.962736i	$-0.587170\pi$
$997$	13.5170	−	7.80405i	0.428088	−	0.247157i	0.698532	+	0.715579i	$0.253837\pi$
$998$	1.08083	+	0.624019i	0.0342132	+	0.0197530i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bf.b.199.6	yes	24
3.2	odd	2	inner	585.2.bf.b.199.7	yes	24
5.4	even	2	inner	585.2.bf.b.199.8	yes	24
13.10	even	6	inner	585.2.bf.b.244.7	yes	24
15.14	odd	2	inner	585.2.bf.b.199.5	✓	24
39.23	odd	6	inner	585.2.bf.b.244.6	yes	24
65.49	even	6	inner	585.2.bf.b.244.5	yes	24
195.179	odd	6	inner	585.2.bf.b.244.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bf.b.199.5	✓	24	15.14	odd	2	inner
585.2.bf.b.199.6	yes	24	1.1	even	1	trivial
585.2.bf.b.199.7	yes	24	3.2	odd	2	inner
585.2.bf.b.199.8	yes	24	5.4	even	2	inner
585.2.bf.b.244.5	yes	24	65.49	even	6	inner
585.2.bf.b.244.6	yes	24	39.23	odd	6	inner
585.2.bf.b.244.7	yes	24	13.10	even	6	inner
585.2.bf.b.244.8	yes	24	195.179	odd	6	inner

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.348519 + 0.603653i) q^{2} +(0.757068 + 1.31128i) q^{4} +(-1.15739 + 1.91323i) q^{5} +(0.459373 + 0.795657i) q^{7} -2.44949 q^{8} +O(q^{10})\)	\(q+(-0.348519 + 0.603653i) q^{2} +(0.757068 + 1.31128i) q^{4} +(-1.15739 + 1.91323i) q^{5} +(0.459373 + 0.795657i) q^{7} -2.44949 q^{8} +(-0.751553 - 1.36546i) q^{10} +(2.18858 + 1.26358i) q^{11} +(3.59920 - 0.213965i) q^{13} -0.640402 q^{14} +(-0.660442 + 1.14392i) q^{16} +(-3.25836 + 1.88122i) q^{17} +(-2.27121 + 1.31128i) q^{19} +(-3.38501 - 0.0692223i) q^{20} +(-1.52552 + 0.880762i) q^{22} +(-2.84249 - 1.64111i) q^{23} +(-2.32088 - 4.42871i) q^{25} +(-1.12523 + 2.24724i) q^{26} +(-0.695554 + 1.20473i) q^{28} +(-0.320201 + 0.554604i) q^{29} +1.39733i q^{31} +(-2.90984 - 5.04000i) q^{32} -2.62256i q^{34} +(-2.05395 - 0.0420026i) q^{35} +(-2.44427 + 4.23360i) q^{37} -1.82803i q^{38} +(2.83502 - 4.68643i) q^{40} +(1.38355 + 0.798793i) q^{41} +(2.68045 - 1.54756i) q^{43} +3.82646i q^{44} +(1.98133 - 1.14392i) q^{46} +0.562334 q^{47} +(3.07795 - 5.33117i) q^{49} +(3.48228 + 0.142483i) q^{50} +(3.00541 + 4.55757i) q^{52} +7.52487i q^{53} +(-4.95056 + 2.72480i) q^{55} +(-1.12523 - 1.94895i) q^{56} +(-0.223192 - 0.386581i) q^{58} +(-4.05696 + 2.34229i) q^{59} +(-1.72426 - 2.98650i) q^{61} +(-0.843502 - 0.486996i) q^{62} +1.41478 q^{64} +(-3.75632 + 7.13373i) q^{65} +(-7.43457 + 12.8771i) q^{67} +(-4.93361 - 2.84842i) q^{68} +(0.741196 - 1.22523i) q^{70} +(10.8401 - 6.25856i) q^{71} +2.13230 q^{73} +(-1.70375 - 2.95098i) q^{74} +(-3.43892 - 1.98546i) q^{76} +2.32181i q^{77} -3.92892 q^{79} +(-1.42419 - 2.58754i) q^{80} +(-0.964388 + 0.556790i) q^{82} +9.66325 q^{83} +(0.172008 - 8.41130i) q^{85} +2.15742i q^{86} +(-5.36090 - 3.09512i) q^{88} +(10.4172 + 6.01437i) q^{89} +(1.82362 + 2.76544i) q^{91} -4.96974i q^{92} +(-0.195984 + 0.339455i) q^{94} +(0.119897 - 5.86300i) q^{95} +(6.82780 + 11.8261i) q^{97} +(2.14545 + 3.71603i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{4}+O(q^{10}) \) 24 * q - 8 * q^4	\( 24 q - 8 q^{4} + 4 q^{10} + 16 q^{16} + 24 q^{19} + 8 q^{25} - 48 q^{40} - 48 q^{46} - 16 q^{49} + 28 q^{61} - 48 q^{64} - 144 q^{76} + 40 q^{79} + 12 q^{85} + 4 q^{91} - 40 q^{94}+O(q^{100}) \) 24 * q - 8 * q^4 + 4 * q^10 + 16 * q^16 + 24 * q^19 + 8 * q^25 - 48 * q^40 - 48 * q^46 - 16 * q^49 + 28 * q^61 - 48 * q^64 - 144 * q^76 + 40 * q^79 + 12 * q^85 + 4 * q^91 - 40 * q^94

Introduction

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