LMFDB - Embedded newform 189.2.p.d.80.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(26,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("189.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.p (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 $ x^12 - 9x^10 + 59x^8 - 180x^6 + 403x^4 - 198*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.5
Root			$1.90412 - 1.09935i$ of defining polynomial
Character	$\chi$	$=$	189.80
Dual form			189.2.p.d.26.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58850 - 0.917122i) q^{2} +(0.682224 - 1.18165i) q^{4} +(-1.90412 - 3.29804i) q^{5} +(2.11581 - 1.58850i) q^{7} +1.16576i q^{8} +O(q^{10})$	\(q+(1.58850 - 0.917122i) q^{2} +(0.682224 - 1.18165i) q^{4} +(-1.90412 - 3.29804i) q^{5} +(2.11581 - 1.58850i) q^{7} +1.16576i q^{8} +(-6.04940 - 3.49262i) q^{10} +(1.00958 + 0.582878i) q^{11} +5.54030i q^{13} +(1.90412 - 4.46379i) q^{14} +(2.43359 + 4.21510i) q^{16} +(1.58850 - 2.75136i) q^{17} +(-0.546672 + 0.315621i) q^{19} -5.19615 q^{20} +2.13828 q^{22} +(-1.52579 + 0.880915i) q^{23} +(-4.75136 + 8.22961i) q^{25} +(5.08112 + 8.80077i) q^{26} +(-0.433589 - 3.58386i) q^{28} +4.83424i q^{29} +(-3.70469 - 2.13891i) q^{31} +(5.71237 + 3.29804i) q^{32} -5.82739i q^{34} +(-9.26770 - 3.95333i) q^{35} +(-2.11581 - 3.66470i) q^{37} +(-0.578926 + 1.00273i) q^{38} +(3.84471 - 2.21974i) q^{40} -4.56491 q^{41} +7.23163 q^{43} +(1.37751 - 0.795307i) q^{44} +(-1.61581 + 2.79867i) q^{46} +(-1.27288 - 2.20469i) q^{47} +(1.95333 - 6.72194i) q^{49} +17.4303i q^{50} +(6.54667 + 3.77972i) q^{52} +(0.0627112 + 0.0362063i) q^{53} -4.43949i q^{55} +(1.85181 + 2.46652i) q^{56} +(4.43359 + 7.67920i) q^{58} +(-3.49262 + 6.04940i) q^{59} +(7.00273 - 4.04303i) q^{61} -7.84655 q^{62} +2.36445 q^{64} +(18.2721 - 10.5494i) q^{65} +(-2.54940 + 4.41569i) q^{67} +(-2.16743 - 3.75409i) q^{68} +(-18.3474 + 2.21974i) q^{70} -4.76183i q^{71} +(4.84744 + 2.79867i) q^{73} +(-6.72194 - 3.88092i) q^{74} +0.861298i q^{76} +(3.06197 - 0.370450i) q^{77} +(-8.54940 - 14.8080i) q^{79} +(9.26770 - 16.0521i) q^{80} +(-7.25136 + 4.18658i) q^{82} -10.1622 q^{83} -12.0988 q^{85} +(11.4874 - 6.63228i) q^{86} +(-0.679494 + 1.17692i) q^{88} +(5.77508 + 10.0027i) q^{89} +(8.80077 + 11.7222i) q^{91} +2.40393i q^{92} +(-4.04394 - 2.33477i) q^{94} +(2.08186 + 1.20196i) q^{95} +0.688287i q^{97} +(-3.06197 - 12.4693i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 8 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 - 8 * q^7	$ 12 q + 8 q^{4} - 8 q^{7} - 6 q^{10} - 4 q^{16} - 6 q^{19} - 40 q^{22} - 24 q^{25} + 28 q^{28} - 12 q^{31} + 8 q^{37} + 12 q^{40} + 20 q^{43} + 14 q^{46} + 24 q^{49} + 78 q^{52} + 20 q^{58} + 18 q^{61} + 28 q^{64} + 36 q^{67} - 120 q^{70} - 42 q^{73} - 36 q^{79} - 54 q^{82} - 12 q^{85} - 74 q^{88} + 6 q^{91} - 114 q^{94}+O(q^{100}) $ 12 * q + 8 * q^4 - 8 * q^7 - 6 * q^10 - 4 * q^16 - 6 * q^19 - 40 * q^22 - 24 * q^25 + 28 * q^28 - 12 * q^31 + 8 * q^37 + 12 * q^40 + 20 * q^43 + 14 * q^46 + 24 * q^49 + 78 * q^52 + 20 * q^58 + 18 * q^61 + 28 * q^64 + 36 * q^67 - 120 * q^70 - 42 * q^73 - 36 * q^79 - 54 * q^82 - 12 * q^85 - 74 * q^88 + 6 * q^91 - 114 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.58850	−	0.917122i	1.12324	−	0.648503i	0.181014	−	0.983481i	$-0.442062\pi$
$2$	1.58850	−	0.917122i	1.12324	−	0.648503i	0.942226	+	0.334978i	$0.108729\pi$
$3$		0			0
$3$		0			0
$4$	0.682224	−	1.18165i	0.341112	−	0.590823i
$5$	−1.90412	−	3.29804i	−0.851549	−	1.47493i	−0.879810	−	0.475326i	$-0.842330\pi$
$5$	−1.90412	−	3.29804i	−0.851549	−	1.47493i	0.0282601	−	0.999601i	$-0.491003\pi$
$6$		0			0
$7$	2.11581	−	1.58850i	0.799702	−	0.600397i
$7$	2.11581	−	1.58850i	0.799702	−	0.600397i
$8$			1.16576i			0.412157i
$9$		0			0
$10$	−6.04940	−	3.49262i	−1.91299	−	1.10446i
$11$	1.00958	+	0.582878i	0.304398	+	0.175744i	0.644417	−	0.764674i	$-0.277100\pi$
$11$	1.00958	+	0.582878i	0.304398	+	0.175744i	−0.340019	+	0.940419i	$0.610433\pi$
$12$		0			0
$13$			5.54030i			1.53660i	0.640089	+	0.768301i	$0.278897\pi$
$13$			5.54030i			1.53660i	−0.640089	+	0.768301i	$0.721103\pi$
$14$	1.90412	−	4.46379i	0.508898	−	1.19300i
$15$		0			0
$16$	2.43359	+	4.21510i	0.608397	+	1.05377i
$17$	1.58850	−	2.75136i	0.385268	−	0.667304i	−0.606538	−	0.795054i	$-0.707442\pi$
$17$	1.58850	−	2.75136i	0.385268	−	0.667304i	0.991806	+	0.127750i	$0.0407756\pi$
$18$		0			0
$19$	−0.546672	+	0.315621i	−0.125415	+	0.0724085i	−0.561395	−	0.827548i	$-0.689735\pi$
$19$	−0.546672	+	0.315621i	−0.125415	+	0.0724085i	0.435980	+	0.899956i	$0.356402\pi$
$20$	−5.19615			−1.16190
$21$		0			0
$22$	2.13828			0.455883
$23$	−1.52579	+	0.880915i	−0.318149	+	0.183684i	−0.650567	−	0.759449i	$-0.725469\pi$
$23$	−1.52579	+	0.880915i	−0.318149	+	0.183684i	0.332418	+	0.943132i	$0.392135\pi$
$24$		0			0
$25$	−4.75136	+	8.22961i	−0.950273	+	1.64592i
$26$	5.08112	+	8.80077i	0.996491	+	1.72597i
$27$		0			0
$28$	−0.433589	−	3.58386i	−0.0819406	−	0.677285i
$29$			4.83424i			0.897696i	0.893608	+	0.448848i	$0.148166\pi$
$29$			4.83424i			0.897696i	−0.893608	+	0.448848i	$0.851834\pi$
$30$		0			0
$31$	−3.70469	−	2.13891i	−0.665382	−	0.384159i	0.128942	−	0.991652i	$-0.458842\pi$
$31$	−3.70469	−	2.13891i	−0.665382	−	0.384159i	−0.794325	+	0.607493i	$0.792175\pi$
$32$	5.71237	+	3.29804i	1.00981	+	0.583016i
$33$		0			0
$34$		−	5.82739i		−	0.999390i
$35$	−9.26770	−	3.95333i	−1.56653	−	0.668234i
$36$		0			0
$37$	−2.11581	−	3.66470i	−0.347837	−	0.602472i	0.638028	−	0.770014i	$-0.279751\pi$
$37$	−2.11581	−	3.66470i	−0.347837	−	0.602472i	−0.985865	+	0.167541i	$0.946417\pi$
$38$	−0.578926	+	1.00273i	−0.0939142	+	0.162664i
$39$		0			0
$40$	3.84471	−	2.21974i	0.607902	−	0.350972i
$41$	−4.56491			−0.712919			−0.356460	−	0.934311i	$-0.616016\pi$
$41$	−4.56491			−0.712919			−0.356460	+	0.934311i	$0.616016\pi$
$42$		0			0
$43$	7.23163			1.10281			0.551406	−	0.834237i	$-0.314091\pi$
$43$	7.23163			1.10281			0.551406	+	0.834237i	$0.314091\pi$
$44$	1.37751	−	0.795307i	0.207668	−	0.119897i
$45$		0			0
$46$	−1.61581	+	2.79867i	−0.238239	+	0.412641i
$47$	−1.27288	−	2.20469i	−0.185669	−	0.321587i	0.758133	−	0.652100i	$-0.226112\pi$
$47$	−1.27288	−	2.20469i	−0.185669	−	0.321587i	−0.943802	+	0.330512i	$0.892778\pi$
$48$		0			0
$49$	1.95333	−	6.72194i	0.279047	−	0.960277i
$50$			17.4303i			2.46502i
$51$		0			0
$52$	6.54667	+	3.77972i	0.907860	+	0.524153i
$53$	0.0627112	+	0.0362063i	0.00861404	+	0.00497332i	0.504301	−	0.863528i	$-0.331750\pi$
$53$	0.0627112	+	0.0362063i	0.00861404	+	0.00497332i	−0.495687	+	0.868501i	$0.665084\pi$
$54$		0			0
$55$		−	4.43949i		−	0.598620i
$56$	1.85181	+	2.46652i	0.247458	+	0.329603i
$57$		0			0
$58$	4.43359	+	7.67920i	0.582159	+	1.00833i
$59$	−3.49262	+	6.04940i	−0.454701	+	0.787565i	−0.998671	−	0.0515396i	$-0.983587\pi$
$59$	−3.49262	+	6.04940i	−0.454701	+	0.787565i	0.543970	+	0.839105i	$0.316920\pi$
$60$		0			0
$61$	7.00273	−	4.04303i	0.896608	−	0.517657i	0.0205096	−	0.999790i	$-0.493471\pi$
$61$	7.00273	−	4.04303i	0.896608	−	0.517657i	0.876098	+	0.482133i	$0.160138\pi$
$62$	−7.84655			−0.996512
$63$		0			0
$64$	2.36445			0.295556
$65$	18.2721	−	10.5494i	2.26638	−	1.30849i
$66$		0			0
$67$	−2.54940	+	4.41569i	−0.311459	+	0.539463i	−0.978678	−	0.205398i	$-0.934151\pi$
$67$	−2.54940	+	4.41569i	−0.311459	+	0.539463i	0.667219	+	0.744861i	$0.267484\pi$
$68$	−2.16743	−	3.75409i	−0.262839	−	0.455251i
$69$		0			0
$70$	−18.3474	+	2.21974i	−2.19294	+	0.265310i
$71$		−	4.76183i		−	0.565125i	−0.959249	−	0.282563i	$-0.908815\pi$
$71$		−	4.76183i		−	0.565125i	0.959249	−	0.282563i	$-0.0911845\pi$
$72$		0			0
$73$	4.84744	+	2.79867i	0.567350	+	0.327560i	0.756090	−	0.654467i	$-0.227107\pi$
$73$	4.84744	+	2.79867i	0.567350	+	0.327560i	−0.188740	+	0.982027i	$0.560440\pi$
$74$	−6.72194	−	3.88092i	−0.781410	−	0.451147i
$75$		0			0
$76$			0.861298i			0.0987976i
$77$	3.06197	−	0.370450i	0.348944	−	0.0422166i
$78$		0			0
$79$	−8.54940	−	14.8080i	−0.961883	−	1.66603i	−0.717766	−	0.696284i	$-0.754835\pi$
$79$	−8.54940	−	14.8080i	−0.961883	−	1.66603i	−0.244116	−	0.969746i	$-0.578498\pi$
$80$	9.26770	−	16.0521i	1.03616	−	1.79468i
$81$		0			0
$82$	−7.25136	+	4.18658i	−0.800779	+	0.462330i
$83$	−10.1622			−1.11545			−0.557726	−	0.830025i	$-0.688326\pi$
$83$	−10.1622			−1.11545			−0.557726	+	0.830025i	$0.688326\pi$
$84$		0			0
$85$	−12.0988			−1.31230
$86$	11.4874	−	6.63228i	1.23872	−	0.715177i
$87$		0			0
$88$	−0.679494	+	1.17692i	−0.0724344	+	0.125460i
$89$	5.77508	+	10.0027i	0.612157	+	1.06029i	0.990876	+	0.134776i	$0.0430313\pi$
$89$	5.77508	+	10.0027i	0.612157	+	1.06029i	−0.378719	+	0.925512i	$0.623635\pi$
$90$		0			0
$91$	8.80077	+	11.7222i	0.922571	+	1.22882i
$92$			2.40393i			0.250627i
$93$		0			0
$94$	−4.04394	−	2.33477i	−0.417101	−	0.240813i
$95$	2.08186	+	1.20196i	0.213594	+	0.123319i
$96$		0			0
$97$			0.688287i			0.0698849i	0.999389	+	0.0349425i	$0.0111248\pi$
$97$			0.688287i			0.0698849i	−0.999389	+	0.0349425i	$0.988875\pi$
$98$	−3.06197	−	12.4693i	−0.309306	−	1.25958i
$99$		0			0
$100$	6.48299	+	11.2289i	0.648299	+	1.12289i
$101$	−3.29203	+	5.70196i	−0.327569	+	0.567367i	−0.982029	−	0.188730i	$-0.939563\pi$
$101$	−3.29203	+	5.70196i	−0.327569	+	0.567367i	0.654460	+	0.756097i	$0.272896\pi$
$102$		0			0
$103$	−8.09607	+	4.67427i	−0.797730	+	0.460570i	−0.842677	−	0.538420i	$-0.819021\pi$
$103$	−8.09607	+	4.67427i	−0.797730	+	0.460570i	0.0449469	+	0.998989i	$0.485688\pi$
$104$	−6.45864			−0.633322
$105$		0			0
$106$	0.132822			0.0129009
$107$	−13.6549	+	7.88364i	−1.32007	+	0.762141i	−0.983739	−	0.179604i	$-0.942518\pi$
$107$	−13.6549	+	7.88364i	−1.32007	+	0.762141i	−0.336328	+	0.941745i	$0.609185\pi$
$108$		0			0
$109$	7.23163	−	12.5255i	0.692664	−	1.19973i	−0.278298	−	0.960495i	$-0.589770\pi$
$109$	7.23163	−	12.5255i	0.692664	−	1.19973i	0.970962	−	0.239235i	$-0.0768965\pi$
$110$	−4.07155	−	7.05213i	−0.388207	−	0.672394i
$111$		0			0
$112$	11.8447	+	5.05260i	1.11922	+	0.477426i
$113$		−	19.8606i		−	1.86833i	−0.356840	−	0.934166i	$-0.616146\pi$
$113$		−	19.8606i		−	1.86833i	0.356840	−	0.934166i	$-0.383854\pi$
$114$		0			0
$115$	5.81058	+	3.35474i	0.541840	+	0.312831i
$116$	5.71237	+	3.29804i	0.530380	+	0.306215i
$117$		0			0
$118$			12.8126i			1.17950i
$119$	−1.00958	−	8.34471i	−0.0925476	−	0.764958i
$120$		0			0
$121$	−4.82051	−	8.34936i	−0.438228	−	0.759033i
$122$	7.41590	−	12.8447i	0.671404	−	1.16291i
$123$		0			0
$124$	−5.05486	+	2.91843i	−0.453940	+	0.262082i
$125$	17.1475			1.53372
$126$		0			0
$127$	−8.90666			−0.790338			−0.395169	−	0.918608i	$-0.629314\pi$
$127$	−8.90666			−0.790338			−0.395169	+	0.918608i	$0.629314\pi$
$128$	−7.66881	+	4.42759i	−0.677833	+	0.391347i
$129$		0			0
$130$	19.3502	−	33.5155i	1.69712	−	2.93950i
$131$	3.37760	+	5.85017i	0.295102	+	0.511132i	0.975009	−	0.222167i	$-0.0713131\pi$
$131$	3.37760	+	5.85017i	0.295102	+	0.511132i	−0.679907	+	0.733299i	$0.737980\pi$
$132$		0			0
$133$	−0.655291	+	1.53618i	−0.0568209	+	0.133204i
$134$			9.35245i			0.807928i
$135$		0			0
$136$	3.20742	+	1.85181i	0.275034	+	0.158791i
$137$	14.6017	+	8.43032i	1.24751	+	0.720251i	0.970612	−	0.240649i	$-0.0773602\pi$
$137$	14.6017	+	8.43032i	1.24751	+	0.720251i	0.276898	+	0.960899i	$0.410693\pi$
$138$		0			0
$139$			0.813709i			0.0690179i	0.999404	+	0.0345089i	$0.0109867\pi$
$139$			0.813709i			0.0690179i	−0.999404	+	0.0345089i	$0.989013\pi$
$140$	−10.9941	+	8.25409i	−0.929170	+	0.697598i
$141$		0			0
$142$	−4.36718	−	7.56417i	−0.366485	−	0.634771i
$143$	−3.22932	+	5.59334i	−0.270049	+	0.467739i
$144$		0			0
$145$	15.9435	−	9.20499i	1.32404	−	0.764433i
$146$	10.2669			0.849693
$147$		0			0
$148$	−5.77383			−0.474606
$149$	7.30087	−	4.21516i	0.598110	−	0.345319i	−0.170187	−	0.985412i	$-0.554437\pi$
$149$	7.30087	−	4.21516i	0.598110	−	0.345319i	0.768298	+	0.640092i	$0.221104\pi$
$150$		0			0
$151$	−1.51974	+	2.63227i	−0.123675	+	0.214211i	−0.921214	−	0.389056i	$-0.872801\pi$
$151$	−1.51974	+	2.63227i	−0.123675	+	0.214211i	0.797539	+	0.603267i	$0.206135\pi$
$152$	−0.367938	−	0.637287i	−0.0298437	−	0.0516908i
$153$		0			0
$154$	4.52420	−	3.39666i	0.364571	−	0.273711i
$155$			16.2910i			1.30852i
$156$		0			0
$157$	−3.29804	−	1.90412i	−0.263212	−	0.151966i	0.362587	−	0.931950i	$-0.381894\pi$
$157$	−3.29804	−	1.90412i	−0.263212	−	0.151966i	−0.625799	+	0.779984i	$0.715227\pi$
$158$	−27.1615	−	15.6817i	−2.16085	−	1.24757i
$159$		0			0
$160$		−	25.1195i		−	1.98587i
$161$	−1.82895	+	4.28757i	−0.144142	+	0.337908i
$162$		0			0
$163$	5.54667	+	9.60712i	0.434449	+	0.752488i	0.997250	−	0.0741045i	$-0.0236098\pi$
$163$	5.54667	+	9.60712i	0.434449	+	0.752488i	−0.562802	+	0.826592i	$0.690276\pi$
$164$	−3.11429	+	5.39411i	−0.243185	+	0.421209i
$165$		0			0
$166$	−16.1427	+	9.32002i	−1.25292	+	0.723374i
$167$	−3.70361			−0.286594			−0.143297	−	0.989680i	$-0.545770\pi$
$167$	−3.70361			−0.286594			−0.143297	+	0.989680i	$0.545770\pi$
$168$		0			0
$169$	−17.6949			−1.36114
$170$	−19.2190	+	11.0961i	−1.47403	+	0.851030i
$171$		0			0
$172$	4.93359	−	8.54523i	0.376183	−	0.651567i
$173$	−4.81782	−	8.34471i	−0.366292	−	0.634436i	0.622691	−	0.782468i	$-0.286040\pi$
$173$	−4.81782	−	8.34471i	−0.366292	−	0.634436i	−0.988983	+	0.148032i	$0.952706\pi$
$174$		0			0
$175$	3.01974	+	24.9599i	0.228271	+	1.88679i
$176$			5.67395i			0.427690i
$177$		0			0
$178$	18.3474	+	10.5929i	1.37520	+	0.793971i
$179$	15.9792	+	9.22562i	1.19435	+	0.689556i	0.959289	−	0.282426i	$-0.0911392\pi$
$179$	15.9792	+	9.22562i	1.19435	+	0.689556i	0.235056	+	0.971982i	$0.424473\pi$
$180$		0			0
$181$			16.6209i			1.23542i	0.786406	+	0.617710i	$0.211940\pi$
$181$			16.6209i			1.23542i	−0.786406	+	0.617710i	$0.788060\pi$
$182$	24.7307	+	10.5494i	1.83316	+	0.781974i
$183$		0			0
$184$	−1.02693	−	1.77870i	−0.0757065	−	0.131128i
$185$	−8.05753	+	13.9561i	−0.592402	+	1.02607i
$186$		0			0
$187$	3.20742	−	1.85181i	0.234550	−	0.135417i
$188$	−3.47356			−0.253335
$189$		0			0
$190$	4.40939			0.319890
$191$	−6.20573	+	3.58288i	−0.449031	+	0.259248i	−0.707421	−	0.706793i	$-0.750141\pi$
$191$	−6.20573	+	3.58288i	−0.449031	+	0.259248i	0.258390	+	0.966041i	$0.416808\pi$
$192$		0			0
$193$	1.58888	−	2.75202i	0.114370	−	0.198095i	−0.803158	−	0.595766i	$-0.796848\pi$
$193$	1.58888	−	2.75202i	0.114370	−	0.198095i	0.917528	+	0.397672i	$0.130182\pi$
$194$	0.631243	+	1.09334i	0.0453206	+	0.0784975i
$195$		0			0
$196$	−6.61035	−	6.89401i	−0.472168	−	0.492430i
$197$			1.93305i			0.137724i	0.997626	+	0.0688619i	$0.0219368\pi$
$197$			1.93305i			0.137724i	−0.997626	+	0.0688619i	$0.978063\pi$
$198$		0			0
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	0.210032	−	0.977695i	$-0.432643\pi$
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	−0.741693	+	0.670740i	$0.765977\pi$
$200$	−9.59372	−	5.53894i	−0.678378	−	0.391662i
$201$		0			0
$202$			12.0768i			0.849718i
$203$	7.67920	+	10.2284i	0.538974	+	0.717890i
$204$		0			0
$205$	8.69215	+	15.0552i	0.607086	+	1.05150i
$206$	−8.57375	+	14.8502i	−0.597361	+	1.03466i
$207$		0			0
$208$	−23.3529	+	13.4828i	−1.61923	+	0.934864i
$209$	−0.735875			−0.0509016
$210$		0			0
$211$	12.4183			0.854912			0.427456	−	0.904036i	$-0.359410\pi$
$211$	12.4183			0.854912			0.427456	+	0.904036i	$0.359410\pi$
$212$	0.0855662	−	0.0494016i	0.00587671	−	0.00339292i
$213$		0			0
$214$	−14.4605	+	25.0464i	−0.988501	+	1.71213i
$215$	−13.7699	−	23.8502i	−0.939099	−	1.62657i
$216$		0			0
$217$	−11.2361	+	1.35939i	−0.762755	+	0.0922811i
$218$		−	26.5291i		−	1.79678i
$219$		0			0
$220$	−5.24591	−	3.02873i	−0.353679	−	0.204197i
$221$	15.2434	+	8.80077i	1.02538	+	0.592004i
$222$		0			0
$223$		−	18.9366i		−	1.26809i	−0.773297	−	0.634044i	$-0.781394\pi$
$223$		−	18.9366i		−	1.26809i	0.773297	−	0.634044i	$-0.218606\pi$
$224$	17.3252	−	2.09607i	1.15759	−	0.140050i
$225$		0			0
$226$	−18.2146	−	31.5486i	−1.21162	−	2.09858i
$227$	−2.86138	+	4.95606i	−0.189917	+	0.328945i	−0.945222	−	0.326428i	$-0.894155\pi$
$227$	−2.86138	+	4.95606i	−0.189917	+	0.328945i	0.755306	+	0.655373i	$0.227488\pi$
$228$		0			0
$229$	9.64548	−	5.56882i	0.637391	−	0.367998i	−0.146218	−	0.989252i	$-0.546710\pi$
$229$	9.64548	−	5.56882i	0.637391	−	0.367998i	0.783609	+	0.621255i	$0.213377\pi$
$230$	12.3068			0.811488
$231$		0			0
$232$	−5.63555			−0.369992
$233$	8.95208	−	5.16849i	0.586470	−	0.338599i	−0.177230	−	0.984169i	$-0.556714\pi$
$233$	8.95208	−	5.16849i	0.586470	−	0.338599i	0.763701	+	0.645571i	$0.223380\pi$
$234$		0			0
$235$	−4.84744	+	8.39601i	−0.316212	+	0.547695i
$236$	4.76550	+	8.25409i	0.310208	+	0.537296i
$237$		0			0
$238$	−9.25682	−	12.3297i	−0.600031	−	0.799214i
$239$		−	16.5806i		−	1.07251i	−0.844056	−	0.536255i	$-0.819839\pi$
$239$		−	16.5806i		−	1.07251i	0.844056	−	0.536255i	$-0.180161\pi$
$240$		0			0
$241$	20.6921	+	11.9466i	1.33290	+	0.769549i	0.985743	−	0.168258i	$-0.0538143\pi$
$241$	20.6921	+	11.9466i	1.33290	+	0.769549i	0.347155	+	0.937808i	$0.387148\pi$
$242$	−15.3148	−	8.84198i	−0.984470	−	0.568384i
$243$		0			0
$244$		−	11.0330i		−	0.706316i
$245$	−25.8886	+	6.35725i	−1.65396	+	0.406150i
$246$		0			0
$247$	−1.74864	−	3.02873i	−0.111263	−	0.192713i
$248$	2.49344	−	4.31877i	0.158334	−	0.274242i
$249$		0			0
$250$	27.2388	−	15.7263i	1.72273	−	0.994621i
$251$	19.9233			1.25755			0.628774	−	0.777588i	$-0.283557\pi$
$251$	19.9233			1.25755			0.628774	+	0.777588i	$0.283557\pi$
$252$		0			0
$253$	−2.05387			−0.129125
$254$	−14.1482	+	8.16849i	−0.887739	+	0.512536i
$255$		0			0
$256$	−10.4857	+	18.1618i	−0.655358	+	1.13511i
$257$	11.6025	+	20.0961i	0.723742	+	1.25356i	0.959490	+	0.281744i	$0.0909130\pi$
$257$	11.6025	+	20.0961i	0.723742	+	1.25356i	−0.235747	+	0.971814i	$0.575754\pi$
$258$		0			0
$259$	−10.2980	−	4.39284i	−0.639889	−	0.272958i
$260$		−	28.7882i		−	1.78537i
$261$		0			0
$262$	10.7306	+	6.19533i	0.662941	+	0.382749i
$263$	−8.33330	−	4.81123i	−0.513853	−	0.296673i	0.220563	−	0.975373i	$-0.429211\pi$
$263$	−8.33330	−	4.81123i	−0.513853	−	0.296673i	−0.734416	+	0.678699i	$0.762544\pi$
$264$		0			0
$265$		−	0.275765i		−	0.0169401i
$266$	0.367938	+	3.04121i	0.0225597	+	0.186469i
$267$		0			0
$268$	3.47853	+	6.02498i	0.212485	+	0.368034i
$269$	10.4152	−	18.0396i	0.635024	−	1.09989i	−0.351487	−	0.936193i	$-0.614324\pi$
$269$	10.4152	−	18.0396i	0.635024	−	1.09989i	0.986510	−	0.163700i	$-0.0523429\pi$
$270$		0			0
$271$	17.0467	−	9.84190i	1.03551	−	0.597853i	0.116953	−	0.993137i	$-0.462687\pi$
$271$	17.0467	−	9.84190i	1.03551	−	0.597853i	0.918559	+	0.395285i	$0.129354\pi$
$272$	15.4630			0.937584
$273$		0			0
$274$	30.9265			1.86834
$275$	−9.59372	+	5.53894i	−0.578523	+	0.334010i
$276$		0			0
$277$	−4.15802	+	7.20190i	−0.249831	+	0.432720i	−0.963479	−	0.267784i	$-0.913708\pi$
$277$	−4.15802	+	7.20190i	−0.249831	+	0.432720i	0.713648	+	0.700505i	$0.247042\pi$
$278$	0.746270	+	1.29258i	0.0447583	+	0.0775237i
$279$		0			0
$280$	4.60862	−	10.8039i	0.275418	−	0.645656i
$281$		−	22.7618i		−	1.35786i	−0.734204	−	0.678928i	$-0.762445\pi$
$281$		−	22.7618i		−	1.35786i	0.734204	−	0.678928i	$-0.237555\pi$
$282$		0			0
$283$	−14.7514	−	8.51670i	−0.876878	−	0.506266i	−0.00724998	−	0.999974i	$-0.502308\pi$
$283$	−14.7514	−	8.51670i	−0.876878	−	0.506266i	−0.869628	+	0.493708i	$0.835641\pi$
$284$	−5.62680	−	3.24864i	−0.333889	−	0.192771i
$285$		0			0
$286$			11.8467i			0.700511i
$287$	−9.65849	+	7.25136i	−0.570123	+	0.428035i
$288$		0			0
$289$	3.45333	+	5.98134i	0.203137	+	0.351843i
$290$	16.8842	−	29.2443i	0.991474	−	1.71728i
$291$		0			0
$292$	6.61408	−	3.81864i	0.387060	−	0.223469i
$293$	21.4159			1.25113			0.625564	−	0.780173i	$-0.284869\pi$
$293$	21.4159			1.25113			0.625564	+	0.780173i	$0.284869\pi$
$294$		0			0
$295$	26.6015			1.54880
$296$	4.27214	−	2.46652i	0.248313	−	0.143364i
$297$		0			0
$298$	7.73163	−	13.3916i	0.447881	−	0.775753i
$299$	−4.88053	−	8.45333i	−0.282248	−	0.488869i
$300$		0			0
$301$	15.3008	−	11.4874i	0.881922	−	0.662125i
$302$			5.57514i			0.320813i
$303$		0			0
$304$	−2.66075	−	1.53618i	−0.152604	−	0.0881062i
$305$	−26.6681	−	15.3968i	−1.52701	−	0.881621i
$306$		0			0
$307$		−	19.4537i		−	1.11028i	−0.831756	−	0.555142i	$-0.812664\pi$
$307$		−	19.4537i		−	1.11028i	0.831756	−	0.555142i	$-0.187336\pi$
$308$	1.65121	−	3.87090i	0.0940866	−	0.220565i
$309$		0			0
$310$	14.9408	+	25.8782i	0.848579	+	1.46978i
$311$	−3.40706	+	5.90120i	−0.193197	+	0.334626i	−0.946308	−	0.323267i	$-0.895219\pi$
$311$	−3.40706	+	5.90120i	−0.193197	+	0.334626i	0.753111	+	0.657893i	$0.228552\pi$
$312$		0			0
$313$	−14.4121	+	8.32084i	−0.814621	+	0.470322i	−0.848558	−	0.529102i	$-0.822529\pi$
$313$	−14.4121	+	8.32084i	−0.814621	+	0.470322i	0.0339371	+	0.999424i	$0.489195\pi$
$314$	−6.98525			−0.394200
$315$		0			0
$316$	−23.3304			−1.31244
$317$	−4.39757	+	2.53894i	−0.246992	+	0.142601i	−0.618386	−	0.785874i	$-0.712213\pi$
$317$	−4.39757	+	2.53894i	−0.246992	+	0.142601i	0.371394	+	0.928475i	$0.378880\pi$
$318$		0			0
$319$	−2.81778	+	4.88053i	−0.157765	+	0.273257i
$320$	−4.50220	−	7.79804i	−0.251681	−	0.435924i
$321$		0			0
$322$	1.02693	+	8.48818i	0.0572287	+	0.473028i
$323$			2.00546i			0.111587i
$324$		0			0
$325$	−45.5944	−	26.3240i	−2.52912	−	1.46019i
$326$	17.6218	+	10.1739i	0.975981	+	0.563483i
$327$		0			0
$328$		−	5.32157i		−	0.293835i
$329$	−6.19533	−	2.64275i	−0.341560	−	0.145699i
$330$		0			0
$331$	−8.16521	−	14.1426i	−0.448801	−	0.777346i	0.549507	−	0.835489i	$-0.314815\pi$
$331$	−8.16521	−	14.1426i	−0.448801	−	0.777346i	−0.998308	+	0.0581430i	$0.981482\pi$
$332$	−6.93293	+	12.0082i	−0.380494	+	0.659035i
$333$		0			0
$334$	−5.88319	+	3.39666i	−0.321914	+	0.185857i
$335$	19.4175			1.06089
$336$		0			0
$337$	−3.95506			−0.215446			−0.107723	−	0.994181i	$-0.534356\pi$
$337$	−3.95506			−0.215446			−0.107723	+	0.994181i	$0.534356\pi$
$338$	−28.1083	+	16.2284i	−1.52889	+	0.882706i
$339$		0			0
$340$	−8.25409	+	14.2965i	−0.447641	+	0.775337i
$341$	−2.49344	−	4.31877i	−0.135028	−	0.233875i
$342$		0			0
$343$	−6.54494	−	17.3252i	−0.353393	−	0.935475i
$344$			8.43032i			0.454532i
$345$		0			0
$346$	−15.3062	−	8.83705i	−0.822868	−	0.475083i
$347$	−6.35400	−	3.66849i	−0.341101	−	0.196935i	0.319658	−	0.947533i	$-0.396432\pi$
$347$	−6.35400	−	3.66849i	−0.341101	−	0.196935i	−0.660759	+	0.750598i	$0.729765\pi$
$348$		0			0
$349$			25.5093i			1.36548i	0.730660	+	0.682741i	$0.239212\pi$
$349$			25.5093i			1.36548i	−0.730660	+	0.682741i	$0.760788\pi$
$350$	27.6881	+	36.8793i	1.47999	+	1.97128i
$351$		0			0
$352$	3.84471	+	6.65923i	0.204924	+	0.354938i
$353$	0.0103948	−	0.0180043i	0.000553260	−	0.000958274i	−0.865749	−	0.500479i	$-0.833157\pi$
$353$	0.0103948	−	0.0180043i	0.000553260	−	0.000958274i	0.866302	+	0.499521i	$0.166491\pi$
$354$		0			0
$355$	−15.7047	+	9.06711i	−0.833519	+	0.481232i
$356$	15.7596			0.835257
$357$		0			0
$358$	33.8441			1.78872
$359$	31.3709	−	18.1120i	1.65569	−	0.955915i	0.681024	−	0.732261i	$-0.261535\pi$
$359$	31.3709	−	18.1120i	1.65569	−	0.955915i	0.974669	−	0.223654i	$-0.0717985\pi$
$360$		0			0
$361$	−9.30077	+	16.1094i	−0.489514	+	0.847863i
$362$	15.2434	+	26.4023i	0.801174	+	1.38767i
$363$		0			0
$364$	19.8556	−	2.40221i	1.04072	−	0.125910i
$365$		−	21.3160i		−	1.11573i
$366$		0			0
$367$	−7.68942	−	4.43949i	−0.401384	−	0.231739i	0.285697	−	0.958320i	$-0.407775\pi$
$367$	−7.68942	−	4.43949i	−0.401384	−	0.231739i	−0.687081	+	0.726581i	$0.741108\pi$
$368$	−7.42629	−	4.28757i	−0.387122	−	0.223505i
$369$		0			0
$370$			29.5590i			1.53670i
$371$	0.190199	−	0.0230110i	0.00987464	−	0.00119467i
$372$		0			0
$373$	6.40939	+	11.1014i	0.331865	+	0.574808i	0.982878	−	0.184260i	$-0.0589887\pi$
$373$	6.40939	+	11.1014i	0.331865	+	0.574808i	−0.651012	+	0.759067i	$0.725655\pi$
$374$	3.39666	−	5.88319i	0.175637	−	0.304213i
$375$		0			0
$376$	2.57014	−	1.48387i	0.132545	−	0.0765247i
$377$	−26.7831			−1.37940
$378$		0			0
$379$	3.13828			0.161203			0.0806013	−	0.996746i	$-0.474316\pi$
$379$	3.13828			0.161203			0.0806013	+	0.996746i	$0.474316\pi$
$380$	2.84059	−	1.64002i	0.145719	−	0.0841311i
$381$		0			0
$382$	−6.57187	+	11.3828i	−0.336246	+	0.582395i
$383$	−13.7595	−	23.8322i	−0.703078	−	1.21777i	−0.967381	−	0.253327i	$-0.918475\pi$
$383$	−13.7595	−	23.8322i	−0.703078	−	1.21777i	0.264303	−	0.964440i	$-0.414858\pi$
$384$		0			0
$385$	−7.05213	−	9.39312i	−0.359410	−	0.478718i
$386$		−	5.82878i		−	0.296677i
$387$		0			0
$388$	0.813312	+	0.469566i	0.0412896	+	0.0238386i
$389$	−15.7994	−	9.12181i	−0.801064	−	0.462494i	0.0427793	−	0.999085i	$-0.486379\pi$
$389$	−15.7994	−	9.12181i	−0.801064	−	0.462494i	−0.843843	+	0.536590i	$0.819712\pi$
$390$		0			0
$391$			5.59734i			0.283070i
$392$	7.83615	+	2.27711i	0.395785	+	0.115011i
$393$		0			0
$394$	1.77284	+	3.07065i	0.0893143	+	0.154697i
$395$	−32.5582	+	56.3925i	−1.63818	+	2.83741i
$396$		0			0
$397$	1.01255	−	0.584593i	0.0508182	−	0.0293399i	−0.474376	−	0.880323i	$-0.657326\pi$
$397$	1.01255	−	0.584593i	0.0508182	−	0.0293399i	0.525194	+	0.850983i	$0.323993\pi$
$398$	−15.8850			−0.796244
$399$		0			0
$400$	−46.2515			−2.31257
$401$	−12.0892	+	6.97972i	−0.603707	+	0.348551i	−0.770499	−	0.637442i	$-0.779993\pi$
$401$	−12.0892	+	6.97972i	−0.603707	+	0.348551i	0.166791	+	0.985992i	$0.446659\pi$
$402$		0			0
$403$	11.8502	−	20.5251i	0.590299	−	1.02243i
$404$	4.49180	+	7.78003i	0.223476	+	0.387071i
$405$		0			0
$406$	21.5791	+	9.20499i	1.07095	+	0.456836i
$407$		−	4.93305i		−	0.244522i
$408$		0			0
$409$	17.6427	+	10.1860i	0.872378	+	0.503667i	0.868138	−	0.496324i	$-0.165317\pi$
$409$	17.6427	+	10.1860i	0.872378	+	0.503667i	0.00424001	+	0.999991i	$0.498650\pi$
$410$	27.6150	+	15.9435i	1.36381	+	0.787394i
$411$		0			0
$412$			12.7556i			0.628423i
$413$	2.21974	+	18.3474i	0.109226	+	0.902818i
$414$		0			0
$415$	19.3502	+	33.5155i	0.949862	+	1.64521i
$416$	−18.2721	+	31.6482i	−0.895863	+	1.55168i
$417$		0			0
$418$	−1.16894	+	0.674887i	−0.0571747	+	0.0330098i
$419$	−25.5207			−1.24677			−0.623383	−	0.781917i	$-0.714242\pi$
$419$	−25.5207			−1.24677			−0.623383	+	0.781917i	$0.714242\pi$
$420$		0			0
$421$	0.0933442			0.00454932			0.00227466	−	0.999997i	$-0.499276\pi$
$421$	0.0933442			0.00454932			0.00227466	+	0.999997i	$0.499276\pi$
$422$	19.7265	−	11.3891i	0.960271	−	0.554413i
$423$		0			0
$424$	−0.0422078	+	0.0731060i	−0.00204979	+	0.00355034i
$425$	15.0951	+	26.1455i	0.732220	+	1.26824i
$426$		0			0
$427$	8.39411	−	19.6781i	0.406219	−	0.952292i
$428$			21.5136i			1.03990i
$429$		0			0
$430$	−43.7470	−	25.2573i	−2.10967	−	1.21802i
$431$	28.7271	+	16.5856i	1.38374	+	0.798901i	0.992600	−	0.121432i	$-0.0387486\pi$
$431$	28.7271	+	16.5856i	1.38374	+	0.798901i	0.391137	+	0.920333i	$0.372082\pi$
$432$		0			0
$433$		−	17.9518i		−	0.862706i	−0.902183	−	0.431353i	$-0.858036\pi$
$433$		−	17.9518i		−	0.862706i	0.902183	−	0.431353i	$-0.141964\pi$
$434$	−16.6018	+	12.4642i	−0.796913	+	0.598303i
$435$		0			0
$436$	−9.86718	−	17.0905i	−0.472552	−	0.818484i
$437$	0.556071	−	0.963144i	0.0266005	−	0.0460734i
$438$		0			0
$439$	−8.69215	+	5.01841i	−0.414854	+	0.239516i	−0.692873	−	0.721060i	$-0.743655\pi$
$439$	−8.69215	+	5.01841i	−0.414854	+	0.239516i	0.278019	+	0.960575i	$0.410322\pi$
$440$	5.17536			0.246726
$441$		0			0
$442$	32.2855			1.53566
$443$	−22.8266	+	13.1790i	−1.08453	+	0.626151i	−0.932114	−	0.362166i	$-0.882037\pi$
$443$	−22.8266	+	13.1790i	−1.08453	+	0.626151i	−0.152412	+	0.988317i	$0.548704\pi$
$444$		0			0
$445$	21.9929	−	38.0928i	1.04256	−	1.80577i
$446$	−17.3672	−	30.0808i	−0.822359	−	1.42437i
$447$		0			0
$448$	5.00273	−	3.75593i	0.236357	−	0.177451i
$449$			24.0264i			1.13388i	0.823761	+	0.566938i	$0.191872\pi$
$449$			24.0264i			1.13388i	−0.823761	+	0.566938i	$0.808128\pi$
$450$		0			0
$451$	−4.60862	−	2.66079i	−0.217011	−	0.125292i
$452$	−23.4683	−	13.5494i	−1.10385	−	0.637310i
$453$		0			0
$454$			10.4969i			0.492646i
$455$	21.9026	−	51.3458i	1.02681	−	2.40713i
$456$		0			0
$457$	−10.4111	−	18.0326i	−0.487012	−	0.843529i	0.512877	−	0.858462i	$-0.328580\pi$
$457$	−10.4111	−	18.0326i	−0.487012	−	0.843529i	−0.999888	+	0.0149333i	$0.995246\pi$
$458$	10.2146	−	17.6921i	0.477295	−	0.826700i
$459$		0			0
$460$	7.92824	−	4.57737i	0.369656	−	0.213421i
$461$	8.35237			0.389008			0.194504	−	0.980902i	$-0.437690\pi$
$461$	8.35237			0.389008			0.194504	+	0.980902i	$0.437690\pi$
$462$		0			0
$463$	11.8133			0.549011			0.274506	−	0.961586i	$-0.411486\pi$
$463$	11.8133			0.549011			0.274506	+	0.961586i	$0.411486\pi$
$464$	−20.3768	+	11.7646i	−0.945970	+	0.546156i
$465$		0			0
$466$	9.48026	−	16.4203i	0.439165	−	0.760655i
$467$	−14.5789	−	25.2514i	−0.674630	−	1.16849i	−0.976577	−	0.215169i	$-0.930970\pi$
$467$	−14.5789	−	25.2514i	−0.674630	−	1.16849i	0.301947	−	0.953325i	$-0.402364\pi$
$468$		0			0
$469$	1.62028	+	13.3925i	0.0748174	+	0.618409i
$470$			17.7828i			0.820258i
$471$		0			0
$472$	−7.05213	−	4.07155i	−0.324601	−	0.187408i
$473$	7.30087	+	4.21516i	0.335694	+	0.193813i
$474$		0			0
$475$		−	5.99853i		−	0.275231i
$476$	−10.5493	−	4.50000i	−0.483524	−	0.206257i
$477$		0			0
$478$	−15.2064	−	26.3383i	−0.695526	−	1.20469i
$479$	20.2618	−	35.0944i	0.925785	−	1.60351i	0.135491	−	0.990779i	$-0.456739\pi$
$479$	20.2618	−	35.0944i	0.925785	−	1.60351i	0.790294	−	0.612728i	$-0.209928\pi$
$480$		0			0
$481$	20.3035	−	11.7222i	0.925760	−	0.534488i
$482$	43.8260			1.99622
$483$		0			0
$484$	−13.1547			−0.597939
$485$	2.26999	−	1.31058i	0.103075	−	0.0595105i
$486$		0			0
$487$	−6.20916	+	10.7546i	−0.281364	+	0.487336i	−0.971721	−	0.236132i	$-0.924120\pi$
$487$	−6.20916	+	10.7546i	−0.281364	+	0.487336i	0.690357	+	0.723469i	$0.257453\pi$
$488$	4.71319	+	8.16348i	0.213356	+	0.369543i
$489$		0			0
$490$	−35.2937	+	33.8415i	−1.59441	+	1.52880i
$491$		−	6.17122i		−	0.278503i	−0.990257	−	0.139252i	$-0.955530\pi$
$491$		−	6.17122i		−	0.278503i	0.990257	−	0.139252i	$-0.0444697\pi$
$492$		0			0
$493$	13.3008	+	7.67920i	0.599036	+	0.345854i
$494$	−5.55542	−	3.20742i	−0.249950	−	0.144309i
$495$		0			0
$496$		−	20.8209i		−	0.934884i
$497$	−7.56417	−	10.0751i	−0.339300	−	0.451932i
$498$		0			0
$499$	1.48026	+	2.56389i	0.0662656	+	0.114775i	0.897255	−	0.441513i	$-0.145558\pi$
$499$	1.48026	+	2.56389i	0.0662656	+	0.114775i	−0.830989	+	0.556289i	$0.812225\pi$
$500$	11.6984	−	20.2623i	0.523170	−	0.906157i
$501$		0			0
$502$	31.6482	−	18.2721i	1.41253	−	0.815524i
$503$	4.33485			0.193282			0.0966408	−	0.995319i	$-0.469190\pi$
$503$	4.33485			0.193282			0.0966408	+	0.995319i	$0.469190\pi$
$504$		0			0
$505$	25.0737			1.11577
$506$	−3.26257	+	1.88364i	−0.145039	+	0.0837382i
$507$		0			0
$508$	−6.07633	+	10.5245i	−0.269594	+	0.466950i
$509$	14.4742	+	25.0701i	0.641560	+	1.11121i	0.985085	+	0.172071i	$0.0550457\pi$
$509$	14.4742	+	25.0701i	0.641560	+	1.11121i	−0.343525	+	0.939144i	$0.611621\pi$
$510$		0			0
$511$	14.7020	−	1.77870i	0.650377	−	0.0786851i
$512$			20.7564i			0.917311i
$513$		0			0
$514$	36.8611	+	21.2818i	1.62587	+	0.938698i
$515$	30.8318	+	17.8008i	1.35861	+	0.784395i
$516$		0			0
$517$		−	2.96774i		−	0.130521i
$518$	−20.3872	+	2.46652i	−0.895763	+	0.108373i
$519$		0			0
$520$	12.2980	+	21.3008i	0.539305	+	0.934103i
$521$	6.08031	−	10.5314i	0.266383	−	0.461389i	−0.701542	−	0.712628i	$-0.747505\pi$
$521$	6.08031	−	10.5314i	0.266383	−	0.461389i	0.967925	+	0.251239i	$0.0808381\pi$
$522$		0			0
$523$	−33.1564	+	19.1429i	−1.44983	+	0.837059i	−0.998471	−	0.0552848i	$-0.982393\pi$
$523$	−33.1564	+	19.1429i	−1.44983	+	0.837059i	−0.451357	+	0.892343i	$0.649060\pi$
$524$	9.21711			0.402651
$525$		0			0
$526$	−17.6499			−0.769574
$527$	−11.7698	+	6.79531i	−0.512701	+	0.296008i
$528$		0			0
$529$	−9.94798	+	17.2304i	−0.432521	+	0.749148i
$530$	−0.252910	−	0.438053i	−0.0109857	−	0.0190278i
$531$		0			0
$532$	1.36817	+	1.82234i	0.0593178	+	0.0790087i
$533$		−	25.2910i		−	1.09547i
$534$		0			0
$535$	52.0011	+	30.0229i	2.24820	+	1.29800i
$536$	−5.14762	−	2.97198i	−0.222344	−	0.128370i
$537$		0			0
$538$		−	38.2079i		−	1.64726i
$539$	5.89011	−	5.64775i	0.253705	−	0.243266i
$540$		0			0
$541$	−0.254094	−	0.440104i	−0.0109244	−	0.0189216i	0.860512	−	0.509431i	$-0.170144\pi$
$541$	−0.254094	−	0.440104i	−0.0109244	−	0.0189216i	−0.871436	+	0.490509i	$0.836811\pi$
$542$	18.0524	−	31.2677i	0.775419	−	1.34306i
$543$		0			0
$544$	18.1482	−	10.4779i	0.778098	−	0.449235i
$545$	−55.0796			−2.35935
$546$		0			0
$547$	−40.2964			−1.72295			−0.861475	−	0.507800i	$-0.830459\pi$
$547$	−40.2964			−1.72295			−0.861475	+	0.507800i	$0.830459\pi$
$548$	19.9233	−	11.5027i	0.851082	−	0.491372i
$549$		0			0
$550$	−10.1598	+	17.5972i	−0.433213	+	0.750348i
$551$	−1.52579	−	2.64275i	−0.0650008	−	0.112585i
$552$		0			0
$553$	−41.6115	−	17.7502i	−1.76950	−	0.754816i
$554$			15.2536i			0.648065i
$555$		0			0
$556$	0.961517	+	0.555132i	0.0407774	+	0.0235428i
$557$	−37.6165	−	21.7179i	−1.59386	−	0.920216i	−0.992636	−	0.121137i	$-0.961346\pi$
$557$	−37.6165	−	21.7179i	−1.59386	−	0.920216i	−0.601226	−	0.799079i	$-0.705321\pi$
$558$		0			0
$559$			40.0653i			1.69458i
$560$	−5.89011	−	48.6851i	−0.248902	−	2.05732i
$561$		0			0
$562$	−20.8754	−	36.1572i	−0.880574	−	1.52520i
$563$	3.16661	−	5.48473i	0.133457	−	0.231154i	−0.791550	−	0.611104i	$-0.790726\pi$
$563$	3.16661	−	5.48473i	0.133457	−	0.231154i	0.925007	+	0.379951i	$0.124059\pi$
$564$		0			0
$565$	−65.5011	+	37.8171i	−2.75565	+	1.59098i
$566$	−31.2434			−1.31326
$567$		0			0
$568$	5.55114			0.232921
$569$	7.12974	−	4.11636i	0.298894	−	0.172567i	−0.343052	−	0.939316i	$-0.611461\pi$
$569$	7.12974	−	4.11636i	0.298894	−	0.172567i	0.641946	+	0.766750i	$0.278127\pi$
$570$		0			0
$571$	−4.24864	+	7.35885i	−0.177800	+	0.307958i	−0.941127	−	0.338054i	$-0.890231\pi$
$571$	−4.24864	+	7.35885i	−0.177800	+	0.307958i	0.763327	+	0.646013i	$0.223565\pi$
$572$	4.40624	+	7.63183i	0.184234	+	0.319103i
$573$		0			0
$574$	−8.69215	+	20.3768i	−0.362803	+	0.850512i
$575$		−	16.7422i		−	0.698198i
$576$		0			0
$577$	34.1905	+	19.7399i	1.42337	+	0.821783i	0.996585	−	0.0825702i	$-0.0263129\pi$
$577$	34.1905	+	19.7399i	1.42337	+	0.821783i	0.426785	+	0.904353i	$0.359646\pi$
$578$	10.9712	+	6.33424i	0.456343	+	0.263470i
$579$		0			0
$580$		−	25.1195i		−	1.04303i
$581$	−21.5014	+	16.1427i	−0.892029	+	0.669714i
$582$		0			0
$583$	0.0422078	+	0.0731060i	0.00174807	+	0.00302774i
$584$	−3.26257	+	5.65093i	−0.135006	+	0.233837i
$585$		0			0
$586$	34.0191	−	19.6409i	1.40532	−	0.811360i
$587$	24.1120			0.995207			0.497603	−	0.867405i	$-0.334213\pi$
$587$	24.1120			0.995207			0.497603	+	0.867405i	$0.334213\pi$
$588$		0			0
$589$	2.70034			0.111265
$590$	42.2566	−	24.3968i	1.73968	−	1.00440i
$591$		0			0
$592$	10.2980	−	17.8367i	0.423247	−	0.733085i
$593$	−9.46830	−	16.3996i	−0.388816	−	0.673450i	0.603474	−	0.797382i	$-0.293783\pi$
$593$	−9.46830	−	16.3996i	−0.388816	−	0.673450i	−0.992291	+	0.123933i	$0.960449\pi$
$594$		0			0
$595$	−25.5988	+	19.2190i	−1.04945	+	0.787901i
$596$		−	11.5027i		−	0.471170i
$597$		0			0
$598$	−15.5055	−	8.95208i	−0.634065	−	0.366078i
$599$	30.0332	+	17.3397i	1.22713	+	0.708481i	0.966427	−	0.256939i	$-0.0827141\pi$
$599$	30.0332	+	17.3397i	1.22713	+	0.708481i	0.260698	+	0.965420i	$0.416047\pi$
$600$		0			0
$601$		−	13.2709i		−	0.541330i	−0.962674	−	0.270665i	$-0.912756\pi$
$601$		−	13.2709i		−	0.541330i	0.962674	−	0.270665i	$-0.0872436\pi$
$602$	13.7699	−	32.2805i	0.561219	−	1.31565i
$603$		0			0
$604$	2.07361	+	3.59159i	0.0843738	+	0.146140i
$605$	−18.3577	+	31.7964i	−0.746345	+	1.29271i
$606$		0			0
$607$	−21.6635	+	12.5074i	−0.879294	+	0.507660i	−0.870425	−	0.492300i	$-0.836156\pi$
$607$	−21.6635	+	12.5074i	−0.879294	+	0.507660i	−0.00886811	+	0.999961i	$0.502823\pi$
$608$	−4.16372			−0.168861
$609$		0			0
$610$	−56.4831			−2.28693
$611$	12.2146	−	7.05213i	0.494152	−	0.285299i
$612$		0			0
$613$	22.0549	−	38.2001i	0.890787	−	1.54289i	0.0518543	−	0.998655i	$-0.483487\pi$
$613$	22.0549	−	38.2001i	0.890787	−	1.54289i	0.838933	−	0.544234i	$-0.183180\pi$
$614$	−17.8415	−	30.9023i	−0.720022	−	1.24712i
$615$		0			0
$616$	0.431854	+	3.56952i	0.0173999	+	0.143820i
$617$			19.3370i			0.778477i	0.921137	+	0.389239i	$0.127262\pi$
$617$			19.3370i			0.778477i	−0.921137	+	0.389239i	$0.872738\pi$
$618$		0			0
$619$	9.57807	+	5.52990i	0.384975	+	0.222265i	0.679981	−	0.733230i	$-0.261988\pi$
$619$	9.57807	+	5.52990i	0.384975	+	0.222265i	−0.295006	+	0.955496i	$0.595321\pi$
$620$	19.2501	+	11.1141i	0.773105	+	0.446352i
$621$		0			0
$622$			12.4987i			0.501154i
$623$	28.1083	+	11.9902i	1.12614	+	0.480377i
$624$		0			0
$625$	−8.89411	−	15.4051i	−0.355764	−	0.616202i
$626$	−15.2624	+	26.4353i	−0.610010	+	1.05657i
$627$		0			0
$628$	−4.50000	+	2.59808i	−0.179570	+	0.103675i
$629$	−13.4439			−0.536043
$630$		0			0
$631$	−27.6015			−1.09880			−0.549400	−	0.835560i	$-0.685144\pi$
$631$	−27.6015			−1.09880			−0.549400	+	0.835560i	$0.685144\pi$
$632$	17.2625	−	9.96652i	0.686666	−	0.396447i
$633$		0			0
$634$	−4.65703	+	8.06621i	−0.184954	+	0.320350i
$635$	16.9594	+	29.3745i	0.673012	+	1.16569i
$636$		0			0
$637$	37.2415	+	10.8220i	1.47556	+	0.428784i
$638$			10.3370i			0.409245i
$639$		0			0
$640$	29.2047	+	16.8613i	1.15442	+	0.666503i
$641$	5.25886	+	3.03621i	0.207713	+	0.119923i	0.600248	−	0.799814i	$-0.295069\pi$
$641$	5.25886	+	3.03621i	0.207713	+	0.119923i	−0.392535	+	0.919737i	$0.628402\pi$
$642$		0			0
$643$			13.2709i			0.523352i	0.965156	+	0.261676i	$0.0842752\pi$
$643$			13.2709i			0.523352i	−0.965156	+	0.261676i	$0.915725\pi$
$644$	3.81864	+	5.08626i	0.150475	+	0.200427i
$645$		0			0
$646$	1.83925	+	3.18567i	0.0723643	+	0.125339i
$647$	15.3688	−	26.6195i	0.604210	−	1.04652i	−0.387966	−	0.921674i	$-0.626822\pi$
$647$	15.3688	−	26.6195i	0.604210	−	1.04652i	0.992176	−	0.124848i	$-0.0398444\pi$
$648$		0			0
$649$	−7.05213	+	4.07155i	−0.276820	+	0.159822i
$650$	−96.5691			−3.78775
$651$		0			0
$652$	15.1363			0.592783
$653$	32.2322	−	18.6093i	1.26134	−	0.728237i	0.288009	−	0.957628i	$-0.407007\pi$
$653$	32.2322	−	18.6093i	1.26134	−	0.728237i	0.973334	+	0.229391i	$0.0736734\pi$
$654$		0			0
$655$	12.8627	−	22.2789i	0.502588	−	0.870508i
$656$	−11.1091	−	19.2415i	−0.433738	−	0.751256i
$657$		0			0
$658$	−12.2650	+	1.48387i	−0.478140	+	0.0578472i
$659$			46.2545i			1.80182i	0.434005	+	0.900911i	$0.357100\pi$
$659$			46.2545i			1.80182i	−0.434005	+	0.900911i	$0.642900\pi$
$660$		0			0
$661$	11.4219	+	6.59445i	0.444262	+	0.256495i	0.705404	−	0.708806i	$-0.250766\pi$
$661$	11.4219	+	6.59445i	0.444262	+	0.256495i	−0.261142	+	0.965300i	$0.584099\pi$
$662$	−25.9409	−	14.9770i	−1.00822	−	0.582097i
$663$		0			0
$664$		−	11.8467i		−	0.459742i
$665$	6.31415	−	0.763910i	0.244852	−	0.0296232i
$666$		0			0
$667$	−4.25856	−	7.37604i	−0.164892	−	0.285601i
$668$	−2.52669	+	4.37636i	−0.0977607	+	0.169326i
$669$		0			0
$670$	30.8447	−	17.8082i	1.19164	−	0.687991i
$671$	9.42637			0.363901
$672$		0			0
$673$	40.9265			1.57760			0.788800	−	0.614649i	$-0.210703\pi$
$673$	40.9265			1.57760			0.788800	+	0.614649i	$0.210703\pi$
$674$	−6.28262	+	3.62727i	−0.241998	+	0.139717i
$675$		0			0
$676$	−12.0719	+	20.9091i	−0.464303	+	0.804196i
$677$	0.808981	+	1.40120i	0.0310917	+	0.0538524i	0.881153	−	0.472832i	$-0.156768\pi$
$677$	0.808981	+	1.40120i	0.0310917	+	0.0538524i	−0.850061	+	0.526684i	$0.823435\pi$
$678$		0			0
$679$	1.09334	+	1.45629i	0.0419587	+	0.0558871i
$680$		−	14.1043i		−	0.540874i
$681$		0			0
$682$	−7.92168	−	4.57358i	−0.303337	−	0.175131i
$683$	22.9977	+	13.2778i	0.879984	+	0.508059i	0.870653	−	0.491897i	$-0.163696\pi$
$683$	22.9977	+	13.2778i	0.879984	+	0.508059i	0.00933109	+	0.999956i	$0.497030\pi$
$684$		0			0
$685$		−	64.2094i		−	2.45332i
$686$	−26.2860	−	21.5187i	−1.00360	−	0.821586i
$687$		0			0
$688$	17.5988	+	30.4820i	0.670948	+	1.16212i
$689$	−0.200594	+	0.347439i	−0.00764201	+	0.0132364i
$690$		0			0
$691$	32.5917	−	18.8168i	1.23985	−	0.715826i	0.270784	−	0.962640i	$-0.412717\pi$
$691$	32.5917	−	18.8168i	1.23985	−	0.715826i	0.969063	+	0.246814i	$0.0793836\pi$
$692$	−13.1473			−0.499787
$693$		0			0
$694$	−13.4578			−0.510851
$695$	2.68364	−	1.54940i	0.101796	−	0.0587722i
$696$		0			0
$697$	−7.25136	+	12.5597i	−0.274665	+	0.475734i
$698$	23.3951	+	40.5216i	0.885519	+	1.53376i
$699$		0			0
$700$	31.5539	+	13.4599i	1.19262	+	0.508738i
$701$			24.3228i			0.918659i	0.888266	+	0.459330i	$0.151910\pi$
$701$			24.3228i			0.918659i	−0.888266	+	0.459330i	$0.848090\pi$
$702$		0			0
$703$	2.31331	+	1.33559i	0.0872482	+	0.0503728i
$704$	2.38709	+	1.37819i	0.0899668	+	0.0519423i
$705$		0			0
$706$		−	0.0381332i		−	0.00143516i
$707$	2.09226	+	17.2937i	0.0786874	+	0.650396i
$708$		0			0
$709$	−0.517010	−	0.895487i	−0.0194167	−	0.0336307i	0.856154	−	0.516721i	$-0.172848\pi$
$709$	−0.517010	−	0.895487i	−0.0194167	−	0.0336307i	−0.875570	+	0.483090i	$0.839514\pi$
$710$	−16.6313	+	28.8062i	−0.624161	+	1.08108i
$711$		0			0
$712$	−11.6608	+	6.73234i	−0.437005	+	0.252305i
$713$	7.53678			0.282255
$714$		0			0
$715$	24.5961			0.919841
$716$	21.8029	−	12.5879i	0.814811	−	0.470431i
$717$		0			0
$718$	33.2218	−	57.5419i	1.23983	−	2.14744i
$719$	8.37315	+	14.5027i	0.312266	+	0.540861i	0.978853	−	0.204567i	$-0.0655787\pi$
$719$	8.37315	+	14.5027i	0.312266	+	0.540861i	−0.666587	+	0.745428i	$0.732245\pi$
$720$		0			0
$721$	−9.70469	+	22.7505i	−0.361422	+	0.847273i
$722$			34.1197i			1.26981i
$723$		0			0
$724$	19.6400	+	11.3392i	0.729915	+	0.421417i
$725$	−39.7839	−	22.9693i	−1.47754	−	0.853057i
$726$		0			0
$727$			32.8976i			1.22011i	0.792361	+	0.610053i	$0.208852\pi$
$727$			32.8976i			1.22011i	−0.792361	+	0.610053i	$0.791148\pi$
$728$	−13.6653	+	10.2596i	−0.506469	+	0.380244i
$729$		0			0
$730$	−19.5494	−	33.8606i	−0.723556	−	1.25324i
$731$	11.4874	−	19.8968i	0.424879	−	0.735911i
$732$		0			0
$733$	−17.2443	+	9.95599i	−0.636932	+	0.367733i	−0.783432	−	0.621478i	$-0.786533\pi$
$733$	−17.2443	+	9.95599i	−0.636932	+	0.367733i	0.146500	+	0.989211i	$0.453199\pi$
$734$	−16.2862			−0.601135
$735$		0			0
$736$	−11.6212			−0.428362
$737$	−5.14762	+	2.97198i	−0.189615	+	0.109474i
$738$		0			0
$739$	25.3349	−	43.8813i	0.931959	−	1.61420i	0.151990	−	0.988382i	$-0.451432\pi$
$739$	25.3349	−	43.8813i	0.931959	−	1.61420i	0.779969	−	0.625819i	$-0.215235\pi$
$740$	10.9941	+	19.0423i	0.404151	+	0.700009i
$741$		0			0
$742$	0.281027	−	0.210989i	0.0103168	−	0.00774563i
$743$			44.2491i			1.62334i	0.584115	+	0.811671i	$0.301442\pi$
$743$			44.2491i			1.62334i	−0.584115	+	0.811671i	$0.698558\pi$
$744$		0			0
$745$	−27.8035	−	16.0524i	−1.01864	−	0.588113i
$746$	20.3626	+	11.7564i	0.745529	+	0.430431i
$747$		0			0
$748$		−	5.05339i		−	0.184770i
$749$	−16.3680	+	38.3711i	−0.598073	+	1.40205i
$750$		0			0
$751$	−1.17230	−	2.03048i	−0.0427779	−	0.0740934i	0.843844	−	0.536589i	$-0.180287\pi$
$751$	−1.17230	−	2.03048i	−0.0427779	−	0.0740934i	−0.886622	+	0.462496i	$0.846954\pi$
$752$	6.19533	−	10.7306i	0.225921	−	0.391306i
$753$		0			0
$754$	−42.5450	+	24.5634i	−1.54940	+	0.894546i
$755$	11.5751			0.421260
$756$		0			0
$757$	−24.8530			−0.903298			−0.451649	−	0.892196i	$-0.649164\pi$
$757$	−24.8530			−0.903298			−0.451649	+	0.892196i	$0.649164\pi$
$758$	4.98516	−	2.87819i	0.181069	−	0.104540i
$759$		0			0
$760$	−1.40120	+	2.42694i	−0.0508267	+	0.0880345i
$761$	−0.441044	−	0.763910i	−0.0159878	−	0.0276917i	0.857921	−	0.513782i	$-0.171756\pi$
$761$	−0.441044	−	0.763910i	−0.0159878	−	0.0276917i	−0.873909	+	0.486090i	$0.838423\pi$
$762$		0			0
$763$	−4.59607	−	37.9892i	−0.166389	−	1.37530i
$764$			9.77730i			0.353730i
$765$		0			0
$766$	−43.7140	−	25.2383i	−1.57945	−	0.911896i
$767$	−33.5155	−	19.3502i	−1.21017	−	0.698694i
$768$		0			0
$769$		−	20.7049i		−	0.746638i	−0.927703	−	0.373319i	$-0.878220\pi$
$769$		−	20.7049i		−	0.746638i	0.927703	−	0.373319i	$-0.121780\pi$
$770$	−19.8170	−	8.45333i	−0.714154	−	0.304637i
$771$		0			0
$772$	−2.16794	−	3.75499i	−0.0780260	−	0.135145i
$773$	4.70279	−	8.14548i	0.169148	−	0.292972i	−0.768973	−	0.639282i	$-0.779232\pi$
$773$	4.70279	−	8.14548i	0.169148	−	0.292972i	0.938120	+	0.346309i	$0.112565\pi$
$774$		0			0
$775$	35.2047	−	20.3254i	1.26459	−	0.730111i
$776$	−0.802375			−0.0288036
$777$		0			0
$778$	−33.4633			−1.19972
$779$	2.49551	−	1.44078i	0.0894109	−	0.0516214i
$780$		0			0
$781$	2.77557	−	4.80743i	0.0993176	−	0.172023i
$782$	5.13344	+	8.89138i	0.183571	+	0.317955i
$783$		0			0
$784$	33.0873	−	8.12497i	1.18169	−	0.290178i
$785$			14.5027i			0.517625i
$786$		0			0
$787$	−21.7855	−	12.5779i	−0.776569	−	0.448352i	0.0586440	−	0.998279i	$-0.481322\pi$
$787$	−21.7855	−	12.5779i	−0.776569	−	0.448352i	−0.835213	+	0.549927i	$0.814656\pi$
$788$	2.28418	+	1.31877i	0.0813705	+	0.0469793i
$789$		0			0
$790$			119.439i			4.24946i
$791$	−31.5486	−	42.0214i	−1.12174	−	1.49411i
$792$		0			0
$793$	22.3996	+	38.7972i	0.795432	+	1.37773i
$794$	1.07229	−	1.85725i	0.0380540	−	0.0659115i
$795$		0			0
$796$	−10.2334	+	5.90823i	−0.362712	+	0.209412i
$797$	−30.7168			−1.08805			−0.544023	−	0.839071i	$-0.683099\pi$
$797$	−30.7168			−1.08805			−0.544023	+	0.839071i	$0.683099\pi$
$798$		0			0
$799$	−8.08789			−0.286129
$800$	−54.2831	+	31.3404i	−1.91920	+	1.10805i
$801$		0			0
$802$	−12.8025	+	22.1746i	−0.452072	+	0.783012i
$803$	3.26257	+	5.65093i	0.115134	+	0.199417i
$804$		0			0
$805$	17.6231	−	2.13211i	0.621133	−	0.0751471i
$806$		−	43.4722i		−	1.53124i
$807$		0			0
$808$	−6.64710	−	3.83771i	−0.233844	−	0.135010i
$809$	12.3629	+	7.13774i	0.434657	+	0.250950i	0.701329	−	0.712838i	$-0.252591\pi$
$809$	12.3629	+	7.13774i	0.434657	+	0.250950i	−0.266671	+	0.963788i	$0.585924\pi$
$810$		0			0
$811$			10.0160i			0.351711i	0.984416	+	0.175855i	$0.0562691\pi$
$811$			10.0160i			0.351711i	−0.984416	+	0.175855i	$0.943731\pi$
$812$	17.3252	−	2.09607i	0.607997	−	0.0735578i
$813$		0			0
$814$	−4.52420	−	7.83615i	−0.158573	−	0.274657i
$815$	21.1231	−	36.5863i	0.739909	−	1.28156i
$816$		0			0
$817$	−3.95333	+	2.28245i	−0.138309	+	0.0798530i
$818$	37.3674			1.30652
$819$		0			0
$820$	23.7200			0.828337
$821$	10.7914	−	6.23043i	0.376623	−	0.217444i	−0.299725	−	0.954026i	$-0.596895\pi$
$821$	10.7914	−	6.23043i	0.376623	−	0.217444i	0.676348	+	0.736582i	$0.263562\pi$
$822$		0			0
$823$	2.29804	−	3.98032i	0.0801045	−	0.138745i	−0.823190	−	0.567766i	$-0.807808\pi$
$823$	2.29804	−	3.98032i	0.0801045	−	0.138745i	0.903295	+	0.429021i	$0.141141\pi$
$824$	−5.44906	−	9.43805i	−0.189827	−	0.328790i
$825$		0			0
$826$	20.3529	+	27.1092i	0.708168	+	0.943248i
$827$			37.9330i			1.31906i	0.751678	+	0.659531i	$0.229245\pi$
$827$			37.9330i			1.31906i	−0.751678	+	0.659531i	$0.770755\pi$
$828$		0			0
$829$	−31.8690	−	18.3996i	−1.10686	−	0.639044i	−0.168843	−	0.985643i	$-0.554003\pi$
$829$	−31.8690	−	18.3996i	−1.10686	−	0.639044i	−0.938013	+	0.346599i	$0.887337\pi$
$830$	61.4755	+	35.4929i	2.13385	+	1.23198i
$831$		0			0
$832$			13.0997i			0.454152i
$833$	−15.3917	−	16.0521i	−0.533289	−	0.556173i
$834$		0			0
$835$	7.05213	+	12.2146i	0.244049	+	0.422705i
$836$	−0.502032	+	0.869545i	−0.0173631	+	0.0300738i
$837$		0			0
$838$	−40.5396	+	23.4055i	−1.40042	+	0.808531i
$839$	21.3569			0.737323			0.368662	−	0.929564i	$-0.379816\pi$
$839$	21.3569			0.737323			0.368662	+	0.929564i	$0.379816\pi$
$840$		0			0
$841$	5.63009			0.194141
$842$	0.148277	−	0.0856080i	0.00510997	−	0.00295025i
$843$		0			0
$844$	8.47207	−	14.6741i	0.291621	−	0.505102i
$845$	33.6932	+	58.3584i	1.15908	+	2.00759i
$846$		0			0
$847$	−23.4623	−	10.0083i	−0.806173	−	0.343889i
$848$			0.352445i			0.0121030i
$849$		0			0
$850$	47.9572	+	27.6881i	1.64492	+	0.949693i
$851$	6.45657	+	3.72770i	0.221328	+	0.127784i
$852$		0			0
$853$			49.5031i			1.69495i	0.530833	+	0.847476i	$0.321879\pi$
$853$			49.5031i			1.69495i	−0.530833	+	0.847476i	$0.678121\pi$
$854$	−4.71319	−	38.9572i	−0.161282	−	1.33309i
$855$		0			0
$856$	−9.19041	−	15.9183i	−0.314122	−	0.544075i
$857$	−7.00810	+	12.1384i	−0.239392	+	0.414639i	−0.960540	−	0.278142i	$-0.910282\pi$
$857$	−7.00810	+	12.1384i	−0.239392	+	0.414639i	0.721148	+	0.692781i	$0.243615\pi$
$858$		0			0
$859$	1.05213	−	0.607448i	0.0358983	−	0.0207259i	−0.481943	−	0.876202i	$-0.660069\pi$
$859$	1.05213	−	0.607448i	0.0358983	−	0.0207259i	0.517842	+	0.855476i	$0.326736\pi$
$860$	−37.5766			−1.28135
$861$		0			0
$862$	60.8441			2.07236
$863$	−31.2396	+	18.0362i	−1.06341	+	0.613960i	−0.926373	−	0.376606i	$-0.877091\pi$
$863$	−31.2396	+	18.0362i	−1.06341	+	0.613960i	−0.137036	+	0.990566i	$0.543758\pi$
$864$		0			0
$865$	−18.3474	+	31.7787i	−0.623832	+	1.08051i
$866$	−16.4639	−	28.5164i	−0.559467	−	0.969026i
$867$		0			0
$868$	−6.05922	+	14.2045i	−0.205663	+	0.482132i
$869$		−	19.9330i		−	0.676182i
$870$		0			0
$871$	−24.4642	−	14.1244i	−0.828939	−	0.478588i
$872$	14.6017	+	8.43032i	0.494477	+	0.285487i
$873$		0			0
$874$		−	2.03994i		−	0.0690020i
$875$	36.2809	−	27.2388i	1.22652	−	0.920840i
$876$		0			0
$877$	5.59607	+	9.69268i	0.188966	+	0.327299i	0.944906	−	0.327342i	$-0.106153\pi$
$877$	5.59607	+	9.69268i	0.188966	+	0.327299i	−0.755940	+	0.654641i	$0.772820\pi$
$878$	−9.20499	+	15.9435i	−0.310653	+	0.538067i
$879$		0			0
$880$	18.7129	−	10.8039i	0.630811	−	0.364199i
$881$	4.16372			0.140279			0.0701397	−	0.997537i	$-0.477655\pi$
$881$	4.16372			0.140279			0.0701397	+	0.997537i	$0.477655\pi$
$882$		0			0
$883$	−38.7433			−1.30382			−0.651908	−	0.758298i	$-0.726031\pi$
$883$	−38.7433			−1.30382			−0.651908	+	0.758298i	$0.726031\pi$
$884$	20.7988	−	12.0082i	0.699539	−	0.403879i
$885$		0			0
$886$	−24.1734	+	41.8696i	−0.812121	+	1.40664i
$887$	−19.0412	−	32.9804i	−0.639342	−	1.10737i	−0.985577	−	0.169225i	$-0.945874\pi$
$887$	−19.0412	−	32.9804i	−0.639342	−	1.10737i	0.346236	−	0.938148i	$-0.387460\pi$
$888$		0			0
$889$	−18.8448	+	14.1482i	−0.632035	+	0.474517i
$890$		−	80.6807i		−	2.70442i
$891$		0			0
$892$	−22.3764	−	12.9190i	−0.749216	−	0.432560i
$893$	1.39170	+	0.803496i	0.0465713	+	0.0268880i
$894$		0			0
$895$		−	70.2669i		−	2.34876i
$896$	−9.19253	+	21.5499i	−0.307101	+	0.719930i
$897$		0			0
$898$	22.0351	+	38.1660i	0.735322	+	1.27361i
$899$	10.3400	−	17.9094i	0.344858	−	0.597311i
$900$		0			0
$901$	0.199234	−	0.115028i	0.00663743	−	0.00383212i
$902$	−9.76106			−0.325008
$903$		0			0
$904$	23.1527			0.770046
$905$	54.8163	−	31.6482i	1.82216	−	1.05202i
$906$		0			0
$907$	−0.773833	+	1.34032i	−0.0256947	+	0.0445046i	−0.878587	−	0.477583i	$-0.841513\pi$
$907$	−0.773833	+	1.34032i	−0.0256947	+	0.0445046i	0.852892	+	0.522087i	$0.174846\pi$
$908$	3.90421	+	6.76228i	0.129566	+	0.224414i
$909$		0			0
$910$	−12.2980	−	101.650i	−0.407676	−	3.36967i
$911$		−	38.9704i		−	1.29115i	−0.763699	−	0.645573i	$-0.776619\pi$
$911$		−	38.9704i		−	1.29115i	0.763699	−	0.645573i	$-0.223381\pi$
$912$		0			0
$913$	−10.2596	−	5.92336i	−0.339542	−	0.196034i
$914$	−33.0762	−	19.0965i	−1.09406	−	0.631657i
$915$		0			0
$916$		−	15.1967i		−	0.502114i
$917$	16.4394	+	7.01255i	0.542875	+	0.231575i
$918$		0			0
$919$	−5.86991	−	10.1670i	−0.193630	−	0.335378i	0.752820	−	0.658226i	$-0.228693\pi$
$919$	−5.86991	−	10.1670i	−0.193630	−	0.335378i	−0.946451	+	0.322848i	$0.895360\pi$
$920$	−3.91081	+	6.77373i	−0.128936	+	0.223323i
$921$		0			0
$922$	13.2677	−	7.66013i	0.436950	−	0.252273i
$923$	26.3819			0.868372
$924$		0			0
$925$	40.2120			1.32216
$926$	18.7655	−	10.8342i	0.616671	−	0.356035i
$927$		0			0
$928$	−15.9435	+	27.6150i	−0.523371	+	0.906506i
$929$	−22.3142	−	38.6493i	−0.732105	−	1.26804i	−0.955982	−	0.293425i	$-0.905205\pi$
$929$	−22.3142	−	38.6493i	−0.732105	−	1.26804i	0.223877	−	0.974617i	$-0.428129\pi$
$930$		0			0
$931$	1.05376	+	4.29121i	0.0345355	+	0.140639i
$932$		−	14.1043i		−	0.462000i
$933$		0			0
$934$	−46.3171	−	26.7412i	−1.51554	−	0.874999i
$935$	−12.2146	−	7.05213i	−0.399462	−	0.230629i
$936$		0			0
$937$		−	33.3351i		−	1.08901i	−0.838758	−	0.544505i	$-0.816718\pi$
$937$		−	33.3351i		−	1.08901i	0.838758	−	0.544505i	$-0.183282\pi$
$938$	14.8564	+	19.7880i	0.485078	+	0.646102i
$939$		0			0
$940$	6.61408	+	11.4559i	0.215727	+	0.373651i
$941$	−16.9992	+	29.4435i	−0.554159	+	0.959831i	0.443810	+	0.896121i	$0.353627\pi$
$941$	−16.9992	+	29.4435i	−0.554159	+	0.959831i	−0.997968	+	0.0637100i	$0.979707\pi$
$942$		0			0
$943$	6.96509	−	4.02130i	0.226815	−	0.130952i
$944$	−33.9984			−1.10655
$945$		0			0
$946$	15.4633			0.502754
$947$	−39.9637	+	23.0731i	−1.29865	+	0.749774i	−0.980170	−	0.198157i	$-0.936504\pi$
$947$	−39.9637	+	23.0731i	−1.29865	+	0.749774i	−0.318476	+	0.947931i	$0.603171\pi$
$948$		0			0
$949$	−15.5055	+	26.8562i	−0.503329	+	0.871791i
$950$	−5.50138	−	9.52867i	−0.178488	−	0.309151i
$951$		0			0
$952$	9.72790	−	1.17692i	0.315283	−	0.0381442i
$953$			35.1143i			1.13746i	0.822523	+	0.568731i	$0.192566\pi$
$953$			35.1143i			1.13746i	−0.822523	+	0.568731i	$0.807434\pi$
$954$		0			0
$955$	23.6329	+	13.6445i	0.764744	+	0.441525i
$956$	−19.5924	−	11.3117i	−0.633664	−	0.365846i
$957$		0			0
$958$		−	74.3301i		−	2.40150i
$959$	44.2861	−	5.35790i	1.43007	−	0.173016i
$960$		0			0
$961$	−6.35017	−	10.9988i	−0.204844	−	0.354800i
$962$	21.5014	−	37.2415i	0.693234	−	1.20072i
$963$		0			0
$964$	28.2334	−	16.3005i	0.909335	−	0.525005i
$965$	−12.1017			−0.389567
$966$		0			0
$967$	−13.4148			−0.431392			−0.215696	−	0.976461i	$-0.569202\pi$
$967$	−13.4148			−0.431392			−0.215696	+	0.976461i	$0.569202\pi$
$968$	9.73332	−	5.61954i	0.312841	−	0.180619i
$969$		0			0
$970$	2.40393	−	4.16372i	0.0771854	−	0.133689i
$971$	−9.19460	−	15.9255i	−0.295069	−	0.511074i	0.679932	−	0.733275i	$-0.262009\pi$
$971$	−9.19460	−	15.9255i	−0.295069	−	0.511074i	−0.975001	+	0.222201i	$0.928676\pi$
$972$		0			0
$973$	1.29258	+	1.72166i	0.0414381	+	0.0551938i
$974$			22.7782i			0.729861i
$975$		0			0
$976$	34.0835	+	19.6781i	1.09099	+	0.629882i
$977$	−19.6181	−	11.3265i	−0.627638	−	0.362367i	0.152199	−	0.988350i	$-0.451365\pi$
$977$	−19.6181	−	11.3265i	−0.627638	−	0.362367i	−0.779837	+	0.625983i	$0.784698\pi$
$978$		0			0
$979$			13.4647i			0.430333i
$980$	−10.1498	+	34.9282i	−0.324223	+	1.11574i
$981$		0			0
$982$	−5.65976	−	9.80298i	−0.180610	−	0.312826i
$983$	−19.6704	+	34.0701i	−0.627388	+	1.08667i	0.360685	+	0.932688i	$0.382543\pi$
$983$	−19.6704	+	34.0701i	−0.627388	+	1.08667i	−0.988074	+	0.153981i	$0.950791\pi$
$984$		0			0
$985$	6.37526	−	3.68076i	0.203133	−	0.117279i
$986$	28.1710			0.897149
$987$		0			0
$988$	−4.77184			−0.151813
$989$	−11.0339	+	6.37045i	−0.350859	+	0.202569i
$990$		0			0
$991$	−0.475797	+	0.824104i	−0.0151142	+	0.0261785i	−0.873484	−	0.486854i	$-0.838145\pi$
$991$	−0.475797	+	0.824104i	−0.0151142	+	0.0261785i	0.858369	+	0.513032i	$0.171478\pi$
$992$	−14.1084	−	24.4364i	−0.447941	−	0.775857i
$993$		0			0
$994$	−21.2558	−	9.06711i	−0.674194	−	0.287591i
$995$			32.9804i			1.04555i
$996$		0			0
$997$	−27.2486	−	15.7320i	−0.862973	−	0.498238i	0.00203378	−	0.999998i	$-0.499353\pi$
$997$	−27.2486	−	15.7320i	−0.862973	−	0.498238i	−0.865007	+	0.501760i	$0.832686\pi$
$998$	4.70279	+	2.71516i	0.148864	+	0.0859468i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.p.d.80.5	yes	12
3.2	odd	2	inner	189.2.p.d.80.2	yes	12
7.3	odd	6		1323.2.c.d.1322.9		12
7.4	even	3		1323.2.c.d.1322.10		12
7.5	odd	6	inner	189.2.p.d.26.2	✓	12
9.2	odd	6		567.2.s.f.458.5		12
9.4	even	3		567.2.i.f.269.5		12
9.5	odd	6		567.2.i.f.269.2		12
9.7	even	3		567.2.s.f.458.2		12
21.5	even	6	inner	189.2.p.d.26.5	yes	12
21.11	odd	6		1323.2.c.d.1322.3		12
21.17	even	6		1323.2.c.d.1322.4		12
63.5	even	6		567.2.s.f.26.2		12
63.40	odd	6		567.2.s.f.26.5		12
63.47	even	6		567.2.i.f.215.2		12
63.61	odd	6		567.2.i.f.215.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.d.26.2	✓	12	7.5	odd	6	inner
189.2.p.d.26.5	yes	12	21.5	even	6	inner
189.2.p.d.80.2	yes	12	3.2	odd	2	inner
189.2.p.d.80.5	yes	12	1.1	even	1	trivial
567.2.i.f.215.2		12	63.47	even	6
567.2.i.f.215.5		12	63.61	odd	6
567.2.i.f.269.2		12	9.5	odd	6
567.2.i.f.269.5		12	9.4	even	3
567.2.s.f.26.2		12	63.5	even	6
567.2.s.f.26.5		12	63.40	odd	6
567.2.s.f.458.2		12	9.7	even	3
567.2.s.f.458.5		12	9.2	odd	6
1323.2.c.d.1322.3		12	21.11	odd	6
1323.2.c.d.1322.4		12	21.17	even	6
1323.2.c.d.1322.9		12	7.3	odd	6
1323.2.c.d.1322.10		12	7.4	even	3

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58850 - 0.917122i) q^{2} +(0.682224 - 1.18165i) q^{4} +(-1.90412 - 3.29804i) q^{5} +(2.11581 - 1.58850i) q^{7} +1.16576i q^{8} +O(q^{10})\)	\(q+(1.58850 - 0.917122i) q^{2} +(0.682224 - 1.18165i) q^{4} +(-1.90412 - 3.29804i) q^{5} +(2.11581 - 1.58850i) q^{7} +1.16576i q^{8} +(-6.04940 - 3.49262i) q^{10} +(1.00958 + 0.582878i) q^{11} +5.54030i q^{13} +(1.90412 - 4.46379i) q^{14} +(2.43359 + 4.21510i) q^{16} +(1.58850 - 2.75136i) q^{17} +(-0.546672 + 0.315621i) q^{19} -5.19615 q^{20} +2.13828 q^{22} +(-1.52579 + 0.880915i) q^{23} +(-4.75136 + 8.22961i) q^{25} +(5.08112 + 8.80077i) q^{26} +(-0.433589 - 3.58386i) q^{28} +4.83424i q^{29} +(-3.70469 - 2.13891i) q^{31} +(5.71237 + 3.29804i) q^{32} -5.82739i q^{34} +(-9.26770 - 3.95333i) q^{35} +(-2.11581 - 3.66470i) q^{37} +(-0.578926 + 1.00273i) q^{38} +(3.84471 - 2.21974i) q^{40} -4.56491 q^{41} +7.23163 q^{43} +(1.37751 - 0.795307i) q^{44} +(-1.61581 + 2.79867i) q^{46} +(-1.27288 - 2.20469i) q^{47} +(1.95333 - 6.72194i) q^{49} +17.4303i q^{50} +(6.54667 + 3.77972i) q^{52} +(0.0627112 + 0.0362063i) q^{53} -4.43949i q^{55} +(1.85181 + 2.46652i) q^{56} +(4.43359 + 7.67920i) q^{58} +(-3.49262 + 6.04940i) q^{59} +(7.00273 - 4.04303i) q^{61} -7.84655 q^{62} +2.36445 q^{64} +(18.2721 - 10.5494i) q^{65} +(-2.54940 + 4.41569i) q^{67} +(-2.16743 - 3.75409i) q^{68} +(-18.3474 + 2.21974i) q^{70} -4.76183i q^{71} +(4.84744 + 2.79867i) q^{73} +(-6.72194 - 3.88092i) q^{74} +0.861298i q^{76} +(3.06197 - 0.370450i) q^{77} +(-8.54940 - 14.8080i) q^{79} +(9.26770 - 16.0521i) q^{80} +(-7.25136 + 4.18658i) q^{82} -10.1622 q^{83} -12.0988 q^{85} +(11.4874 - 6.63228i) q^{86} +(-0.679494 + 1.17692i) q^{88} +(5.77508 + 10.0027i) q^{89} +(8.80077 + 11.7222i) q^{91} +2.40393i q^{92} +(-4.04394 - 2.33477i) q^{94} +(2.08186 + 1.20196i) q^{95} +0.688287i q^{97} +(-3.06197 - 12.4693i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 8 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 - 8 * q^7	\( 12 q + 8 q^{4} - 8 q^{7} - 6 q^{10} - 4 q^{16} - 6 q^{19} - 40 q^{22} - 24 q^{25} + 28 q^{28} - 12 q^{31} + 8 q^{37} + 12 q^{40} + 20 q^{43} + 14 q^{46} + 24 q^{49} + 78 q^{52} + 20 q^{58} + 18 q^{61} + 28 q^{64} + 36 q^{67} - 120 q^{70} - 42 q^{73} - 36 q^{79} - 54 q^{82} - 12 q^{85} - 74 q^{88} + 6 q^{91} - 114 q^{94}+O(q^{100}) \) 12 * q + 8 * q^4 - 8 * q^7 - 6 * q^10 - 4 * q^16 - 6 * q^19 - 40 * q^22 - 24 * q^25 + 28 * q^28 - 12 * q^31 + 8 * q^37 + 12 * q^40 + 20 * q^43 + 14 * q^46 + 24 * q^49 + 78 * q^52 + 20 * q^58 + 18 * q^61 + 28 * q^64 + 36 * q^67 - 120 * q^70 - 42 * q^73 - 36 * q^79 - 54 * q^82 - 12 * q^85 - 74 * q^88 + 6 * q^91 - 114 * q^94

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