LMFDB - Embedded newform 585.2.bs.c.334.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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, 2]))

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

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

chi := DirichletCharacter("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			334.2
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.c.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.32723 - 1.34363i) q^{2} +(2.61067 + 4.52182i) q^{4} +(2.23433 - 0.0881535i) q^{5} +(3.14272 - 1.81445i) q^{7} -8.65659i q^{8} +O(q^{10})$	\(q+(-2.32723 - 1.34363i) q^{2} +(2.61067 + 4.52182i) q^{4} +(2.23433 - 0.0881535i) q^{5} +(3.14272 - 1.81445i) q^{7} -8.65659i q^{8} +(-5.31825 - 2.79696i) q^{10} +(1.80641 - 3.12879i) q^{11} +(1.66311 + 3.19907i) q^{13} -9.75179 q^{14} +(-6.40989 + 11.1023i) q^{16} +(-1.37732 + 0.795195i) q^{17} +(-2.37378 - 4.11151i) q^{19} +(6.23172 + 9.87310i) q^{20} +(-8.40786 + 4.85428i) q^{22} +(3.63959 + 2.10132i) q^{23} +(4.98446 - 0.393928i) q^{25} +(0.427922 - 9.67959i) q^{26} +(16.4092 + 9.47388i) q^{28} +(-2.32166 + 4.02124i) q^{29} +7.07222 q^{31} +(14.8410 - 8.56844i) q^{32} +4.27378 q^{34} +(6.86192 - 4.33112i) q^{35} +(-7.72556 - 4.46035i) q^{37} +12.7579i q^{38} +(-0.763109 - 19.3417i) q^{40} +(-3.49741 + 6.05769i) q^{41} +(-1.42679 + 0.823755i) q^{43} +18.8638 q^{44} +(-5.64678 - 9.78052i) q^{46} +6.71359i q^{47} +(3.08446 - 5.34244i) q^{49} +(-12.1293 - 5.78050i) q^{50} +(-10.1238 + 15.8720i) q^{52} -6.29507i q^{53} +(3.76030 - 7.14999i) q^{55} +(-15.7070 - 27.2052i) q^{56} +(10.8061 - 6.23890i) q^{58} +(-0.407233 - 0.705349i) q^{59} +(-5.29922 - 9.17852i) q^{61} +(-16.4587 - 9.50244i) q^{62} -20.4116 q^{64} +(3.99794 + 7.00117i) q^{65} +(7.53270 + 4.34901i) q^{67} +(-7.19146 - 4.15199i) q^{68} +(-21.7887 + 0.859654i) q^{70} +(-2.74958 - 4.76242i) q^{71} -1.32903i q^{73} +(11.9861 + 20.7606i) q^{74} +(12.3944 - 21.4676i) q^{76} -13.1105i q^{77} -6.22135 q^{79} +(-13.3431 + 25.3712i) q^{80} +(16.2786 - 9.39843i) q^{82} -6.63916i q^{83} +(-3.00728 + 1.89814i) q^{85} +4.42728 q^{86} +(-27.0847 - 15.6373i) q^{88} +(-6.68230 + 11.5741i) q^{89} +(11.0312 + 7.03616i) q^{91} +21.9434i q^{92} +(9.02057 - 15.6241i) q^{94} +(-5.66626 - 8.97722i) q^{95} +(5.41028 - 3.12363i) q^{97} +(-14.3565 + 8.28873i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4}+O(q^{10}) $ 32 * q + 20 * q^4	$ 32 q + 20 q^{4} - 6 q^{10} - 28 q^{16} - 8 q^{19} + 28 q^{25} + 8 q^{31} - 8 q^{34} - 20 q^{40} - 8 q^{46} + 44 q^{49} + 20 q^{55} - 56 q^{61} - 136 q^{64} - 80 q^{70} + 88 q^{76} - 72 q^{79} - 50 q^{85} - 28 q^{91} + 48 q^{94}+O(q^{100}) $ 32 * q + 20 * q^4 - 6 * q^10 - 28 * q^16 - 8 * q^19 + 28 * q^25 + 8 * q^31 - 8 * q^34 - 20 * q^40 - 8 * q^46 + 44 * q^49 + 20 * q^55 - 56 * q^61 - 136 * q^64 - 80 * q^70 + 88 * q^76 - 72 * q^79 - 50 * q^85 - 28 * q^91 + 48 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−2.32723	−	1.34363i	−1.64560	−	0.950089i	−0.978791	−	0.204862i	$-0.934325\pi$
$2$	−2.32723	−	1.34363i	−1.64560	−	0.950089i	−0.666811	−	0.745227i	$-0.732341\pi$
$3$		0			0
$3$		0			0
$4$	2.61067	+	4.52182i	1.30534	+	2.26091i
$5$	2.23433	−	0.0881535i	0.999223	−	0.0394234i
$5$	2.23433	−	0.0881535i	0.999223	−	0.0394234i
$6$		0			0
$7$	3.14272	−	1.81445i	1.18784	−	0.685798i	0.230022	−	0.973185i	$-0.426120\pi$
$7$	3.14272	−	1.81445i	1.18784	−	0.685798i	0.957814	+	0.287388i	$0.0927869\pi$
$8$		−	8.65659i		−	3.06057i
$9$		0			0
$10$	−5.31825	−	2.79696i	−1.68178	−	0.884475i
$11$	1.80641	−	3.12879i	0.544652	−	0.943366i	−0.453976	−	0.891014i	$-0.649995\pi$
$11$	1.80641	−	3.12879i	0.544652	−	0.943366i	0.998629	−	0.0523519i	$-0.0166717\pi$
$12$		0			0
$13$	1.66311	+	3.19907i	0.461264	+	0.887263i
$13$	1.66311	+	3.19907i	0.461264	+	0.887263i
$14$	−9.75179			−2.60627
$15$		0			0
$16$	−6.40989	+	11.1023i	−1.60247	+	2.77557i
$17$	−1.37732	+	0.795195i	−0.334049	+	0.192863i	−0.657637	−	0.753335i	$-0.728444\pi$
$17$	−1.37732	+	0.795195i	−0.334049	+	0.192863i	0.323589	+	0.946198i	$0.395111\pi$
$18$		0			0
$19$	−2.37378	−	4.11151i	−0.544583	−	0.943246i	−0.998633	−	0.0522695i	$-0.983355\pi$
$19$	−2.37378	−	4.11151i	−0.544583	−	0.943246i	0.454050	−	0.890976i	$-0.349979\pi$
$20$	6.23172	+	9.87310i	1.39346	+	2.20769i
$21$		0			0
$22$	−8.40786	+	4.85428i	−1.79256	+	1.03494i
$23$	3.63959	+	2.10132i	0.758907	+	0.438155i	0.828903	−	0.559392i	$-0.188965\pi$
$23$	3.63959	+	2.10132i	0.758907	+	0.438155i	−0.0699959	+	0.997547i	$0.522299\pi$
$24$		0			0
$25$	4.98446	−	0.393928i	0.996892	−	0.0787856i
$26$	0.427922	−	9.67959i	0.0839224	−	1.89832i
$27$		0			0
$28$	16.4092	+	9.47388i	3.10105	+	1.79039i
$29$	−2.32166	+	4.02124i	−0.431122	+	0.746725i	−0.996970	−	0.0777842i	$-0.975215\pi$
$29$	−2.32166	+	4.02124i	−0.431122	+	0.746725i	0.565848	+	0.824509i	$0.308549\pi$
$30$		0			0
$31$	7.07222			1.27021			0.635104	−	0.772426i	$-0.280957\pi$
$31$	7.07222			1.27021			0.635104	+	0.772426i	$0.280957\pi$
$32$	14.8410	−	8.56844i	2.62354	−	1.51470i
$33$		0			0
$34$	4.27378			0.732948
$35$	6.86192	−	4.33112i	1.15988	−	0.732093i
$36$		0			0
$37$	−7.72556	−	4.46035i	−1.27007	−	0.733278i	−0.295072	−	0.955475i	$-0.595344\pi$
$37$	−7.72556	−	4.46035i	−1.27007	−	0.733278i	−0.975002	+	0.222197i	$0.928677\pi$
$38$			12.7579i			2.06961i
$39$		0			0
$40$	−0.763109	−	19.3417i	−0.120658	−	3.05819i
$41$	−3.49741	+	6.05769i	−0.546203	+	0.946052i	0.452327	+	0.891852i	$0.350594\pi$
$41$	−3.49741	+	6.05769i	−0.546203	+	0.946052i	−0.998530	+	0.0541995i	$0.982739\pi$
$42$		0			0
$43$	−1.42679	+	0.823755i	−0.217583	+	0.125621i	−0.604830	−	0.796354i	$-0.706759\pi$
$43$	−1.42679	+	0.823755i	−0.217583	+	0.125621i	0.387248	+	0.921976i	$0.373426\pi$
$44$	18.8638			2.84382
$45$		0			0
$46$	−5.64678	−	9.78052i	−0.832573	−	1.44206i
$47$			6.71359i			0.979278i	0.871925	+	0.489639i	$0.162871\pi$
$47$			6.71359i			0.979278i	−0.871925	+	0.489639i	$0.837129\pi$
$48$		0			0
$49$	3.08446	−	5.34244i	0.440637	−	0.763205i
$50$	−12.1293	−	5.78050i	−1.71534	−	0.817486i
$51$		0			0
$52$	−10.1238	+	15.8720i	−1.40392	+	2.20105i
$53$		−	6.29507i		−	0.864695i	−0.901707	−	0.432347i	$-0.857685\pi$
$53$		−	6.29507i		−	0.864695i	0.901707	−	0.432347i	$-0.142315\pi$
$54$		0			0
$55$	3.76030	−	7.14999i	0.507038	−	0.964104i
$56$	−15.7070	−	27.2052i	−2.09893	−	3.63545i
$57$		0			0
$58$	10.8061	−	6.23890i	1.41891	−	0.819208i
$59$	−0.407233	−	0.705349i	−0.0530173	−	0.0918286i	0.838299	−	0.545211i	$-0.183551\pi$
$59$	−0.407233	−	0.705349i	−0.0530173	−	0.0918286i	−0.891316	+	0.453382i	$0.850217\pi$
$60$		0			0
$61$	−5.29922	−	9.17852i	−0.678495	−	1.17519i	−0.975434	−	0.220292i	$-0.929299\pi$
$61$	−5.29922	−	9.17852i	−0.678495	−	1.17519i	0.296938	−	0.954897i	$-0.404034\pi$
$62$	−16.4587	−	9.50244i	−2.09026	−	1.20681i
$63$		0			0
$64$	−20.4116			−2.55145
$65$	3.99794	+	7.00117i	0.495884	+	0.868389i
$66$		0			0
$67$	7.53270	+	4.34901i	0.920266	+	0.531316i	0.883720	−	0.468016i	$-0.155031\pi$
$67$	7.53270	+	4.34901i	0.920266	+	0.531316i	0.0365463	+	0.999332i	$0.488364\pi$
$68$	−7.19146	−	4.15199i	−0.872092	−	0.503503i
$69$		0			0
$70$	−21.7887	+	0.859654i	−2.60425	+	0.102748i
$71$	−2.74958	−	4.76242i	−0.326316	−	0.565195i	0.655462	−	0.755228i	$-0.272474\pi$
$71$	−2.74958	−	4.76242i	−0.326316	−	0.565195i	−0.981778	+	0.190033i	$0.939141\pi$
$72$		0			0
$73$		−	1.32903i		−	0.155551i	−0.996971	−	0.0777755i	$-0.975218\pi$
$73$		−	1.32903i		−	0.155551i	0.996971	−	0.0777755i	$-0.0247817\pi$
$74$	11.9861	+	20.7606i	1.39336	+	2.41337i
$75$		0			0
$76$	12.3944	−	21.4676i	1.42173	−	2.46251i
$77$		−	13.1105i		−	1.49409i
$78$		0			0
$79$	−6.22135			−0.699956			−0.349978	−	0.936758i	$-0.613811\pi$
$79$	−6.22135			−0.699956			−0.349978	+	0.936758i	$0.613811\pi$
$80$	−13.3431	+	25.3712i	−1.49181	+	2.83658i
$81$		0			0
$82$	16.2786	−	9.39843i	1.79767	−	1.03788i
$83$		−	6.63916i		−	0.728743i	−0.931254	−	0.364371i	$-0.881284\pi$
$83$		−	6.63916i		−	0.728743i	0.931254	−	0.364371i	$-0.118716\pi$
$84$		0			0
$85$	−3.00728	+	1.89814i	−0.326186	+	0.205882i
$86$	4.42728			0.477406
$87$		0			0
$88$	−27.0847	−	15.6373i	−2.88723	−	1.66695i
$89$	−6.68230	+	11.5741i	−0.708322	+	1.22685i	0.257157	+	0.966370i	$0.417214\pi$
$89$	−6.68230	+	11.5741i	−0.708322	+	1.22685i	−0.965479	+	0.260481i	$0.916119\pi$
$90$		0			0
$91$	11.0312	+	7.03616i	1.15639	+	0.737590i
$92$			21.9434i			2.28776i
$93$		0			0
$94$	9.02057	−	15.6241i	0.930401	−	1.61150i
$95$	−5.66626	−	8.97722i	−0.581346	−	0.921043i
$96$		0			0
$97$	5.41028	−	3.12363i	0.549331	−	0.317156i	−0.199521	−	0.979893i	$-0.563939\pi$
$97$	5.41028	−	3.12363i	0.549331	−	0.317156i	0.748852	+	0.662737i	$0.230605\pi$
$98$	−14.3565	+	8.28873i	−1.45023	+	0.837288i
$99$		0			0
$100$	14.7941	+	21.5104i	1.47941	+	2.15104i
$101$	9.00396	−	15.5953i	0.895928	−	1.55179i	0.0632758	−	0.997996i	$-0.479845\pi$
$101$	9.00396	−	15.5953i	0.895928	−	1.55179i	0.832652	−	0.553796i	$-0.186821\pi$
$102$		0			0
$103$			5.61029i			0.552798i	0.961043	+	0.276399i	$0.0891412\pi$
$103$			5.61029i			0.552798i	−0.961043	+	0.276399i	$0.910859\pi$
$104$	27.6931	−	14.3969i	2.71553	−	1.41173i
$105$		0			0
$106$	−8.45824	+	14.6501i	−0.821537	+	1.42294i
$107$	9.48489	+	5.47610i	0.916939	+	0.529395i	0.882657	−	0.470017i	$-0.155752\pi$
$107$	9.48489	+	5.47610i	0.916939	+	0.529395i	0.0342818	+	0.999412i	$0.489086\pi$
$108$		0			0
$109$	9.06561			0.868328			0.434164	−	0.900834i	$-0.357044\pi$
$109$	9.06561			0.868328			0.434164	+	0.900834i	$0.357044\pi$
$110$	−18.3580	+	11.5872i	−1.75037	+	1.10480i
$111$		0			0
$112$			46.5217i			4.39589i
$113$	4.80715	−	2.77541i	0.452219	−	0.261089i	−0.256548	−	0.966531i	$-0.582585\pi$
$113$	4.80715	−	2.77541i	0.452219	−	0.261089i	0.708767	+	0.705443i	$0.249252\pi$
$114$		0			0
$115$	8.31729	+	4.37420i	0.775591	+	0.407896i
$116$	−24.2444			−2.25104
$117$		0			0
$118$			2.18868i			0.201484i
$119$	−2.88568	+	4.99815i	−0.264530	+	0.458179i
$120$		0			0
$121$	−1.02622	−	1.77746i	−0.0932925	−	0.161587i
$122$			28.4807i			2.57852i
$123$		0			0
$124$	18.4633	+	31.9793i	1.65805	+	2.87183i
$125$	11.1022	−	1.31956i	0.993011	−	0.118025i
$126$		0			0
$127$	−8.69701	−	5.02122i	−0.771735	−	0.445561i	0.0617583	−	0.998091i	$-0.480329\pi$
$127$	−8.69701	−	5.02122i	−0.771735	−	0.445561i	−0.833493	+	0.552530i	$0.813663\pi$
$128$	17.8206	+	10.2887i	1.57514	+	0.909405i
$129$		0			0
$130$	0.102829	−	21.6651i	0.00901870	−	1.90016i
$131$	−1.88635			−0.164812			−0.0824058	−	0.996599i	$-0.526260\pi$
$131$	−1.88635			−0.164812			−0.0824058	+	0.996599i	$0.526260\pi$
$132$		0			0
$133$	−14.9203	−	8.61422i	−1.29375	−	0.746948i
$134$	−11.6869	−	20.2423i	−1.00959	−	1.74867i
$135$		0			0
$136$	6.88368	+	11.9229i	0.590270	+	1.02238i
$137$	14.0205	−	8.09472i	1.19785	−	0.691579i	0.237774	−	0.971320i	$-0.423582\pi$
$137$	14.0205	−	8.09472i	1.19785	−	0.691579i	0.960075	+	0.279742i	$0.0902489\pi$
$138$		0			0
$139$	−2.05902	−	3.56633i	−0.174644	−	0.302492i	0.765394	−	0.643562i	$-0.222544\pi$
$139$	−2.05902	−	3.56633i	−0.174644	−	0.302492i	−0.940038	+	0.341070i	$0.889211\pi$
$140$	37.4988	+	19.7212i	3.16923	+	1.66675i
$141$		0			0
$142$			14.7777i			1.24012i
$143$	13.0135	+	0.575309i	1.08824	+	0.0481098i
$144$		0			0
$145$	−4.83287	+	9.18943i	−0.401348	+	0.763141i
$146$	−1.78572	+	3.09296i	−0.147787	+	0.255975i
$147$		0			0
$148$		−	46.5781i		−	3.82870i
$149$	0.427922	+	0.741182i	0.0350567	+	0.0607200i	0.883021	−	0.469333i	$-0.155505\pi$
$149$	0.427922	+	0.741182i	0.0350567	+	0.0607200i	−0.847965	+	0.530053i	$0.822172\pi$
$150$		0			0
$151$	−12.9887			−1.05701			−0.528503	−	0.848932i	$-0.677246\pi$
$151$	−12.9887			−1.05701			−0.528503	+	0.848932i	$0.677246\pi$
$152$	−35.5917	+	20.5489i	−2.88687	+	1.66673i
$153$		0			0
$154$	−17.6157	+	30.5113i	−1.41951	+	2.45867i
$155$	15.8017	−	0.623441i	1.26922	−	0.0500760i
$156$		0			0
$157$			8.84891i			0.706220i	0.935582	+	0.353110i	$0.114876\pi$
$157$			8.84891i			0.706220i	−0.935582	+	0.353110i	$0.885124\pi$
$158$	14.4785	+	8.35918i	1.15185	+	0.665021i
$159$		0			0
$160$	32.4043	−	20.4530i	2.56178	−	1.61695i
$161$	15.2510			1.20194
$162$		0			0
$163$	−17.6565	+	10.1940i	−1.38296	+	0.798455i	−0.992509	−	0.122168i	$-0.961015\pi$
$163$	−17.6565	+	10.1940i	−1.38296	+	0.798455i	−0.390454	+	0.920622i	$0.627682\pi$
$164$	−36.5224			−2.85192
$165$		0			0
$166$	−8.92057	+	15.4509i	−0.692370	+	1.19922i
$167$	5.99010	+	3.45839i	0.463528	+	0.267618i	0.713526	−	0.700628i	$-0.247097\pi$
$167$	5.99010	+	3.45839i	0.463528	+	0.267618i	−0.249999	+	0.968246i	$0.580430\pi$
$168$		0			0
$169$	−7.46813	+	10.6408i	−0.574472	+	0.818524i
$170$	9.54904	−	0.376749i	0.732378	−	0.0288953i
$171$		0			0
$172$	−7.44975	−	4.30111i	−0.568038	−	0.327957i
$173$	−11.1781	+	6.45368i	−0.849856	+	0.490664i	−0.860602	−	0.509278i	$-0.829913\pi$
$173$	−11.1781	+	6.45368i	−0.849856	+	0.490664i	0.0107466	+	0.999942i	$0.496579\pi$
$174$		0			0
$175$	14.9500	−	10.2821i	1.13011	−	0.777250i
$176$	23.1578	+	40.1104i	1.74558	+	3.02344i
$177$		0			0
$178$	31.1025	−	17.9571i	2.33123	−	1.34594i
$179$	−11.1510	+	19.3140i	−0.833462	+	1.44360i	0.0618148	+	0.998088i	$0.480311\pi$
$179$	−11.1510	+	19.3140i	−0.833462	+	1.44360i	−0.895277	+	0.445511i	$0.853022\pi$
$180$		0			0
$181$	4.37048			0.324855			0.162428	−	0.986720i	$-0.448068\pi$
$181$	4.37048			0.324855			0.162428	+	0.986720i	$0.448068\pi$
$182$	−16.2183	−	31.1967i	−1.20218	−	2.31245i
$183$		0			0
$184$	18.1903	−	31.5065i	1.34100	−	2.32269i
$185$	−17.6546	−	9.28486i	−1.29800	−	0.682637i
$186$		0			0
$187$			5.74578i			0.420173i
$188$	−30.3576	+	17.5270i	−2.21406	+	1.27829i
$189$		0			0
$190$	1.12466	+	28.5054i	0.0815911	+	2.06800i
$191$	0.543330	+	0.941076i	0.0393140	+	0.0680939i	0.885013	−	0.465567i	$-0.154149\pi$
$191$	0.543330	+	0.941076i	0.0393140	+	0.0680939i	−0.845699	+	0.533660i	$0.820816\pi$
$192$		0			0
$193$	−7.25689	−	4.18977i	−0.522362	−	0.301586i	0.215538	−	0.976495i	$-0.430849\pi$
$193$	−7.25689	−	4.18977i	−0.522362	−	0.301586i	−0.737901	+	0.674909i	$0.764183\pi$
$194$	−16.7880			−1.20531
$195$		0			0
$196$	32.2100			2.30072
$197$	−4.25034	−	2.45393i	−0.302824	−	0.174836i	0.340887	−	0.940104i	$-0.389273\pi$
$197$	−4.25034	−	2.45393i	−0.302824	−	0.174836i	−0.643711	+	0.765269i	$0.722606\pi$
$198$		0			0
$199$	6.95824	+	12.0520i	0.493257	+	0.854345i	0.999970	−	0.00776922i	$-0.00247305\pi$
$199$	6.95824	+	12.0520i	0.493257	+	0.854345i	−0.506713	+	0.862115i	$0.669140\pi$
$200$	−3.41007	−	43.1484i	−0.241129	−	3.05105i
$201$		0			0
$202$	−41.9086	+	24.1960i	−2.94868	+	1.70242i
$203$			16.8502i			1.18265i
$204$		0			0
$205$	−7.28035	+	13.8432i	−0.508482	+	0.966849i
$206$	7.53814	−	13.0564i	0.525207	−	0.909686i
$207$		0			0
$208$	−46.1773	−	2.04144i	−3.20182	−	0.141548i
$209$	−17.1521			−1.18643
$210$		0			0
$211$	−7.01068	+	12.1428i	−0.482635	+	0.835948i	−0.999801	−	0.0199368i	$-0.993653\pi$
$211$	−7.01068	+	12.1428i	−0.482635	+	0.835948i	0.517166	+	0.855885i	$0.326987\pi$
$212$	28.4652	−	16.4344i	1.95500	−	1.12872i
$213$		0			0
$214$	−14.7157	−	25.4883i	−1.00594	−	1.74235i
$215$	−3.11529	+	1.96632i	−0.212461	+	0.134102i
$216$		0			0
$217$	22.2260	−	12.8322i	1.50880	−	0.871106i
$218$	−21.0978	−	12.1808i	−1.42892	−	0.824988i
$219$		0			0
$220$	42.1479	−	1.66291i	2.84161	−	0.112113i
$221$	−4.83452	−	3.08364i	−0.325205	−	0.207428i
$222$		0			0
$223$	−1.57080	−	0.906899i	−0.105188	−	0.0607305i	0.446483	−	0.894792i	$-0.352676\pi$
$223$	−1.57080	−	0.906899i	−0.105188	−	0.0607305i	−0.551671	+	0.834062i	$0.686010\pi$
$224$	31.0940	−	53.8564i	2.07756	−	3.59843i
$225$		0			0
$226$	−14.9165			−0.992230
$227$	21.1132	−	12.1897i	1.40133	−	0.809058i	0.406801	−	0.913517i	$-0.366644\pi$
$227$	21.1132	−	12.1897i	1.40133	−	0.809058i	0.994529	+	0.104458i	$0.0333109\pi$
$228$		0			0
$229$	1.59844			0.105628			0.0528139	−	0.998604i	$-0.483181\pi$
$229$	1.59844			0.105628			0.0528139	+	0.998604i	$0.483181\pi$
$230$	−13.4790	−	21.3551i	−0.888777	−	1.40811i
$231$		0			0
$232$	34.8102	+	20.0977i	2.28540	+	1.31948i
$233$		−	10.0225i		−	0.656599i	−0.944574	−	0.328299i	$-0.893525\pi$
$233$		−	10.0225i		−	0.656599i	0.944574	−	0.328299i	$-0.106475\pi$
$234$		0			0
$235$	0.591826	+	15.0004i	0.0386065	+	0.978516i
$236$	2.12631	−	3.68287i	0.138411	−	0.239735i
$237$		0			0
$238$	13.4313	−	7.75457i	0.870622	−	0.502654i
$239$	−14.6112			−0.945117			−0.472559	−	0.881299i	$-0.656669\pi$
$239$	−14.6112			−0.945117			−0.472559	+	0.881299i	$0.656669\pi$
$240$		0			0
$241$	−6.62794	−	11.4799i	−0.426943	−	0.739487i	0.569657	−	0.821883i	$-0.307076\pi$
$241$	−6.62794	−	11.4799i	−0.426943	−	0.739487i	−0.996600	+	0.0823959i	$0.973743\pi$
$242$			5.51542i			0.354545i
$243$		0			0
$244$	27.6691	−	47.9242i	1.77133	−	3.06804i
$245$	6.42074	−	12.2087i	0.410206	−	0.779983i
$246$		0			0
$247$	9.20517	−	14.4318i	0.585711	−	0.918274i
$248$		−	61.2213i		−	3.88756i
$249$		0			0
$250$	−27.6104	−	11.8463i	−1.74623	−	0.749226i
$251$	12.5887	+	21.8043i	0.794592	+	1.37627i	0.923098	+	0.384565i	$0.125648\pi$
$251$	12.5887	+	21.8043i	0.794592	+	1.37627i	−0.128506	+	0.991709i	$0.541018\pi$
$252$		0			0
$253$	13.1492	−	7.59168i	0.826682	−	0.477285i
$254$	13.4933	+	23.3711i	0.846646	+	1.46643i
$255$		0			0
$256$	−7.23689	−	12.5347i	−0.452306	−	0.783416i
$257$	−23.6813	−	13.6724i	−1.47720	−	0.852862i	−0.477532	−	0.878614i	$-0.658468\pi$
$257$	−23.6813	−	13.6724i	−1.47720	−	0.852862i	−0.999668	+	0.0257526i	$0.991802\pi$
$258$		0			0
$259$	−32.3724			−2.01152
$260$	−21.2207	+	36.3558i	−1.31605	+	2.25469i
$261$		0			0
$262$	4.38998	+	2.53456i	0.271214	+	0.156586i
$263$	13.4299	+	7.75373i	0.828120	+	0.478116i	0.853209	−	0.521570i	$-0.174653\pi$
$263$	13.4299	+	7.75373i	0.828120	+	0.478116i	−0.0250883	+	0.999685i	$0.507987\pi$
$264$		0			0
$265$	−0.554933	−	14.0653i	−0.0340893	−	0.864023i
$266$	23.1486	+	40.0946i	1.41933	+	2.45836i
$267$		0			0
$268$			45.4154i			2.77419i
$269$	−5.33189	−	9.23510i	−0.325091	−	0.563074i	0.656440	−	0.754378i	$-0.272062\pi$
$269$	−5.33189	−	9.23510i	−0.325091	−	0.563074i	−0.981531	+	0.191304i	$0.938728\pi$
$270$		0			0
$271$	−1.01068	+	1.75054i	−0.0613942	+	0.106338i	−0.895089	−	0.445888i	$-0.852888\pi$
$271$	−1.01068	+	1.75054i	−0.0613942	+	0.106338i	0.833695	+	0.552226i	$0.186221\pi$
$272$		−	20.3885i		−	1.23623i
$273$		0			0
$274$	−43.5052			−2.62824
$275$	7.77145	−	16.3069i	0.468636	−	0.983344i
$276$		0			0
$277$	3.35635	−	1.93779i	0.201664	−	0.116431i	−0.395768	−	0.918351i	$-0.629521\pi$
$277$	3.35635	−	1.93779i	0.201664	−	0.116431i	0.597431	+	0.801920i	$0.296188\pi$
$278$			11.0662i			0.663709i
$279$		0			0
$280$	−37.4927	−	59.4008i	−2.24062	−	3.54988i
$281$	−23.7976			−1.41964			−0.709822	−	0.704381i	$-0.751225\pi$
$281$	−23.7976			−1.41964			−0.709822	+	0.704381i	$0.751225\pi$
$282$		0			0
$283$	−5.81677	−	3.35831i	−0.345771	−	0.199631i	0.317050	−	0.948409i	$-0.397308\pi$
$283$	−5.81677	−	3.35831i	−0.345771	−	0.199631i	−0.662821	+	0.748778i	$0.730641\pi$
$284$	14.3565	−	24.8663i	0.851904	−	1.47554i
$285$		0			0
$286$	−29.5124	−	18.8242i	−1.74510	−	1.11310i
$287$			25.3835i			1.49834i
$288$		0			0
$289$	−7.23533	+	12.5320i	−0.425608	+	0.737174i
$290$	23.5944	−	14.8924i	1.38551	−	0.874510i
$291$		0			0
$292$	6.00962	−	3.46966i	0.351687	−	0.203046i
$293$	−10.6371	+	6.14131i	−0.621424	+	0.358779i	−0.777423	−	0.628978i	$-0.783474\pi$
$293$	−10.6371	+	6.14131i	−0.621424	+	0.358779i	0.155999	+	0.987757i	$0.450140\pi$
$294$		0			0
$295$	−0.972073	−	1.54008i	−0.0565963	−	0.0896671i
$296$	−38.6115	+	66.8770i	−2.24425	+	3.88715i
$297$		0			0
$298$		−	2.29987i		−	0.133228i
$299$	−0.669233	+	15.1380i	−0.0387028	+	0.875456i
$300$		0			0
$301$	−2.98932	+	5.17766i	−0.172302	+	0.298435i
$302$	30.2277	+	17.4520i	1.73941	+	1.00425i
$303$		0			0
$304$	60.8628			3.49072
$305$	−12.6493	−	20.0407i	−0.724298	−	1.14753i
$306$		0			0
$307$		−	9.63676i		−	0.549999i	−0.961444	−	0.275000i	$-0.911322\pi$
$307$		−	9.63676i		−	0.549999i	0.961444	−	0.275000i	$-0.0886777\pi$
$308$	59.2835	−	34.2274i	3.37799	−	1.95029i
$309$		0			0
$310$	−37.6118	−	19.7807i	−2.13621	−	1.12347i
$311$	15.0763			0.854898			0.427449	−	0.904039i	$-0.359412\pi$
$311$	15.0763			0.854898			0.427449	+	0.904039i	$0.359412\pi$
$312$		0			0
$313$			23.8506i			1.34811i	0.738679	+	0.674057i	$0.235450\pi$
$313$			23.8506i			1.34811i	−0.738679	+	0.674057i	$0.764550\pi$
$314$	11.8896	−	20.5935i	0.670971	−	1.16216i
$315$		0			0
$316$	−16.2419	−	28.1318i	−0.913679	−	1.58254i
$317$			8.74937i			0.491413i	0.969344	+	0.245707i	$0.0790200\pi$
$317$			8.74937i			0.491413i	−0.969344	+	0.245707i	$0.920980\pi$
$318$		0			0
$319$	8.38774	+	14.5280i	0.469623	+	0.813411i
$320$	−45.6063	+	1.79936i	−2.54947	+	0.100587i
$321$		0			0
$322$	−35.4925	−	20.4916i	−1.97792	−	1.14195i
$323$	6.53891	+	3.77524i	0.363835	+	0.210060i
$324$		0			0
$325$	9.54990	+	15.2905i	0.529733	+	0.848164i
$326$	54.7877			3.03441
$327$		0			0
$328$	52.4389	+	30.2756i	2.89545	+	1.67169i
$329$	12.1815	+	21.0989i	0.671586	+	1.16322i
$330$		0			0
$331$	7.75415	+	13.4306i	0.426207	+	0.738212i	0.996532	−	0.0832070i	$-0.0265163\pi$
$331$	7.75415	+	13.4306i	0.426207	+	0.738212i	−0.570325	+	0.821419i	$0.693183\pi$
$332$	30.0211	−	17.3327i	1.64762	−	0.951255i
$333$		0			0
$334$	−9.29357	−	16.0969i	−0.508522	−	0.880785i
$335$	17.2139	+	9.05308i	0.940497	+	0.494623i
$336$		0			0
$337$			33.0731i			1.80160i	0.434229	+	0.900802i	$0.357021\pi$
$337$			33.0731i			1.80160i	−0.434229	+	0.900802i	$0.642979\pi$
$338$	31.6774	−	14.7293i	1.72302	−	0.801166i
$339$		0			0
$340$	−16.4341	−	8.64296i	−0.891264	−	0.468730i
$341$	12.7753	−	22.1275i	0.691822	−	1.19827i
$342$		0			0
$343$			3.01593i			0.162845i
$344$	7.13091	+	12.3511i	0.384473	+	0.665927i
$345$		0			0
$346$	34.6854			1.86470
$347$	−12.1439	+	7.01129i	−0.651919	+	0.376386i	−0.789191	−	0.614148i	$-0.789500\pi$
$347$	−12.1439	+	7.01129i	−0.651919	+	0.376386i	0.137272	+	0.990533i	$0.456167\pi$
$348$		0			0
$349$	3.48776	−	6.04098i	0.186696	−	0.323366i	−0.757451	−	0.652892i	$-0.773555\pi$
$349$	3.48776	−	6.04098i	0.186696	−	0.323366i	0.944147	+	0.329526i	$0.106889\pi$
$350$	−48.6074	+	3.84150i	−2.59817	+	0.205337i
$351$		0			0
$352$		−	61.9124i		−	3.29994i
$353$	−12.1978	−	7.04243i	−0.649226	−	0.374831i	0.138934	−	0.990302i	$-0.455632\pi$
$353$	−12.1978	−	7.04243i	−0.649226	−	0.374831i	−0.788159	+	0.615471i	$0.788966\pi$
$354$		0			0
$355$	−6.56330	−	10.3984i	−0.348344	−	0.551891i
$356$	−69.7812			−3.69840
$357$		0			0
$358$	51.9018	−	29.9655i	2.74309	−	1.58373i
$359$	9.02923			0.476545			0.238272	−	0.971198i	$-0.423419\pi$
$359$	9.02923			0.476545			0.238272	+	0.971198i	$0.423419\pi$
$360$		0			0
$361$	−1.76970	+	3.06520i	−0.0931419	+	0.161326i
$362$	−10.1711	−	5.87230i	−0.534582	−	0.308641i
$363$		0			0
$364$	−3.01726	+	68.2504i	−0.158148	+	3.57729i
$365$	−0.117158	−	2.96949i	−0.00613235	−	0.155430i
$366$		0			0
$367$	−29.0631	−	16.7796i	−1.51708	−	0.875887i	−0.999799	−	0.0200712i	$-0.993611\pi$
$367$	−29.0631	−	16.7796i	−1.51708	−	0.875887i	−0.517281	−	0.855815i	$-0.673056\pi$
$368$	−46.6588	+	26.9385i	−2.43226	+	1.40426i
$369$		0			0
$370$	28.6110	+	45.3293i	1.48742	+	2.35656i
$371$	−11.4221	−	19.7837i	−0.593006	−	1.02712i
$372$		0			0
$373$	−21.3986	+	12.3545i	−1.10798	+	0.639690i	−0.938304	−	0.345811i	$-0.887604\pi$
$373$	−21.3986	+	12.3545i	−1.10798	+	0.639690i	−0.169671	+	0.985501i	$0.554271\pi$
$374$	7.72020	−	13.3718i	0.399202	−	0.691438i
$375$		0			0
$376$	58.1168			2.99714
$377$	−16.7254	−	0.739409i	−0.861403	−	0.0380815i
$378$		0			0
$379$	14.0796	−	24.3866i	0.723220	−	1.25265i	−0.236483	−	0.971636i	$-0.575995\pi$
$379$	14.0796	−	24.3866i	0.723220	−	1.25265i	0.959702	−	0.281018i	$-0.0906721\pi$
$380$	25.8006	−	49.0584i	1.32354	−	2.51664i
$381$		0			0
$382$		−	2.92014i		−	0.149407i
$383$	−4.00942	+	2.31484i	−0.204872	+	0.118283i	−0.598926	−	0.800805i	$-0.704406\pi$
$383$	−4.00942	+	2.31484i	−0.204872	+	0.118283i	0.394054	+	0.919087i	$0.371072\pi$
$384$		0			0
$385$	−1.15574	−	29.2933i	−0.0589020	−	1.49292i
$386$	11.2590	+	19.5011i	0.573067	+	0.992581i
$387$		0			0
$388$	28.2490	+	16.3095i	1.43412	+	0.827992i
$389$	−3.02917			−0.153585			−0.0767924	−	0.997047i	$-0.524468\pi$
$389$	−3.02917			−0.153585			−0.0767924	+	0.997047i	$0.524468\pi$
$390$		0			0
$391$	−6.68383			−0.338016
$392$	−46.2473	−	26.7009i	−2.33584	−	1.34860i
$393$		0			0
$394$	6.59435	+	11.4217i	0.332219	+	0.575419i
$395$	−13.9005	+	0.548434i	−0.699412	+	0.0275947i
$396$		0			0
$397$	0.117341	−	0.0677469i	0.00588918	−	0.00340012i	−0.497053	−	0.867720i	$-0.665584\pi$
$397$	0.117341	−	0.0677469i	0.00588918	−	0.00340012i	0.502942	+	0.864320i	$0.332251\pi$
$398$		−	37.3972i		−	1.87455i
$399$		0			0
$400$	−27.5764	+	57.8638i	−1.37882	+	2.89319i
$401$	−7.51746	+	13.0206i	−0.375404	+	0.650219i	−0.990387	−	0.138321i	$-0.955829\pi$
$401$	−7.51746	+	13.0206i	−0.375404	+	0.650219i	0.614984	+	0.788540i	$0.289163\pi$
$402$		0			0
$403$	11.7619	+	22.6245i	0.585901	+	1.12701i
$404$	94.0257			4.67795
$405$		0			0
$406$	22.6404	−	39.2143i	1.12362	−	1.94617i
$407$	−27.9110	+	16.1144i	−1.38350	+	0.798763i
$408$		0			0
$409$	8.62387	+	14.9370i	0.426423	+	0.738586i	0.996552	−	0.0829687i	$-0.0264401\pi$
$409$	8.62387	+	14.9370i	0.426423	+	0.738586i	−0.570129	+	0.821555i	$0.693107\pi$
$410$	35.5432	−	22.4342i	1.75535	−	1.10795i
$411$		0			0
$412$	−25.3687	+	14.6466i	−1.24983	+	0.721588i
$413$	−2.55964	−	1.47781i	−0.125952	−	0.0727182i
$414$		0			0
$415$	−0.585266	−	14.8341i	−0.0287296	−	0.728176i
$416$	52.0932	+	33.2271i	2.55408	+	1.62909i
$417$		0			0
$418$	39.9169	+	23.0460i	1.95240	+	1.12722i
$419$	−2.70821	+	4.69075i	−0.132305	+	0.229158i	−0.924565	−	0.381025i	$-0.875571\pi$
$419$	−2.70821	+	4.69075i	−0.132305	+	0.229158i	0.792260	+	0.610184i	$0.208904\pi$
$420$		0			0
$421$	−32.9444			−1.60561			−0.802807	−	0.596239i	$-0.796661\pi$
$421$	−32.9444			−1.60561			−0.802807	+	0.596239i	$0.796661\pi$
$422$	32.6309	−	18.8395i	1.58845	−	0.917092i
$423$		0			0
$424$	−54.4939			−2.64646
$425$	−6.55193	+	4.50618i	−0.317815	+	0.218582i
$426$		0			0
$427$	−33.3079	−	19.2303i	−1.61188	−	0.930621i
$428$			57.1853i			2.76416i
$429$		0			0
$430$	9.89201	−	0.390280i	0.477035	−	0.0188210i
$431$	−5.24456	+	9.08384i	−0.252621	+	0.437553i	−0.964247	−	0.265006i	$-0.914626\pi$
$431$	−5.24456	+	9.08384i	−0.252621	+	0.437553i	0.711625	+	0.702559i	$0.247959\pi$
$432$		0			0
$433$	−18.3388	+	10.5879i	−0.881307	+	0.508823i	−0.871089	−	0.491125i	$-0.836586\pi$
$433$	−18.3388	+	10.5879i	−0.881307	+	0.508823i	−0.0102176	+	0.999948i	$0.503252\pi$
$434$	−68.9668			−3.31051
$435$		0			0
$436$	23.6674	+	40.9931i	1.13346	+	1.96321i
$437$		−	19.9523i		−	0.954448i
$438$		0			0
$439$	6.00328	−	10.3980i	0.286521	−	0.496269i	−0.686456	−	0.727171i	$-0.740835\pi$
$439$	6.00328	−	10.3980i	0.286521	−	0.496269i	0.972977	+	0.230903i	$0.0741679\pi$
$440$	−61.8945	−	32.5514i	−2.95071	−	1.55182i
$441$		0			0
$442$	7.10777	+	13.6721i	0.338082	+	0.650318i
$443$		−	28.9381i		−	1.37489i	−0.726236	−	0.687446i	$-0.758732\pi$
$443$		−	28.9381i		−	1.37489i	0.726236	−	0.687446i	$-0.241268\pi$
$444$		0			0
$445$	−13.9102	+	26.4494i	−0.659405	+	1.25382i
$446$	2.43707	+	4.22113i	0.115399	+	0.199876i
$447$		0			0
$448$	−64.1480	+	37.0359i	−3.03071	+	1.74978i
$449$	−7.93624	−	13.7460i	−0.374534	−	0.648713i	0.615723	−	0.787963i	$-0.288864\pi$
$449$	−7.93624	−	13.7460i	−0.374534	−	0.648713i	−0.990257	+	0.139250i	$0.955531\pi$
$450$		0			0
$451$	12.6355	+	21.8853i	0.594982	+	1.03054i
$452$	25.0998	+	14.4914i	1.18060	+	0.681617i
$453$		0			0
$454$	−65.5137			−3.07471
$455$	25.2677	+	14.7487i	1.18457	+	0.691428i
$456$		0			0
$457$	27.5389	+	15.8996i	1.28821	+	0.743751i	0.978336	−	0.207026i	$-0.0663784\pi$
$457$	27.5389	+	15.8996i	1.28821	+	0.743751i	0.309878	+	0.950776i	$0.399712\pi$
$458$	−3.71994	−	2.14771i	−0.173821	−	0.100356i
$459$		0			0
$460$	1.93439	+	49.0289i	0.0901915	+	2.28598i
$461$	10.5869	+	18.3371i	0.493083	+	0.854045i	0.999968	−	0.00796874i	$-0.00253656\pi$
$461$	10.5869	+	18.3371i	0.493083	+	0.854045i	−0.506885	+	0.862014i	$0.669203\pi$
$462$		0			0
$463$		−	27.1764i		−	1.26299i	−0.775378	−	0.631497i	$-0.782441\pi$
$463$		−	27.1764i		−	1.26299i	0.775378	−	0.631497i	$-0.217559\pi$
$464$	−29.7632	−	51.5514i	−1.38172	−	2.39321i
$465$		0			0
$466$	−13.4666	+	23.3248i	−0.623827	+	1.08050i
$467$			6.32195i			0.292545i	0.989244	+	0.146272i	$0.0467276\pi$
$467$			6.32195i			0.292545i	−0.989244	+	0.146272i	$0.953272\pi$
$468$		0			0
$469$	31.5642			1.45750
$470$	18.7776	−	35.7045i	0.866146	−	1.64693i
$471$		0			0
$472$	−6.10592	+	3.52525i	−0.281048	+	0.162263i
$473$			5.95215i			0.273680i
$474$		0			0
$475$	−13.4517	−	19.5586i	−0.617205	−	0.897409i
$476$	−30.1343			−1.38120
$477$		0			0
$478$	34.0036	+	19.6320i	1.55529	+	0.897945i
$479$	−8.30491	+	14.3845i	−0.379461	+	0.657245i	−0.990984	−	0.133981i	$-0.957224\pi$
$479$	−8.30491	+	14.3845i	−0.379461	+	0.657245i	0.611523	+	0.791227i	$0.290557\pi$
$480$		0			0
$481$	1.42054	−	32.1327i	0.0647712	−	1.46512i
$482$			35.6219i			1.62253i
$483$		0			0
$484$	5.35824	−	9.28075i	0.243556	−	0.421852i
$485$	11.8130	−	7.45615i	0.536400	−	0.338566i
$486$		0			0
$487$	24.0859	−	13.9060i	1.09144	−	0.630142i	0.157479	−	0.987522i	$-0.449663\pi$
$487$	24.0859	−	13.9060i	1.09144	−	0.630142i	0.933959	+	0.357380i	$0.116330\pi$
$488$	−79.4547	+	45.8732i	−3.59674	+	2.07658i
$489$		0			0
$490$	−31.3465	+	19.7853i	−1.41609	+	0.893810i
$491$	15.9781	−	27.6749i	0.721081	−	1.24895i	−0.239486	−	0.970900i	$-0.576979\pi$
$491$	15.9781	−	27.6749i	0.721081	−	1.24895i	0.960567	−	0.278049i	$-0.0896878\pi$
$492$		0			0
$493$		−	7.38470i		−	0.332590i
$494$	−40.8135	+	21.2178i	−1.83629	+	0.954636i
$495$		0			0
$496$	−45.3322	+	78.5176i	−2.03548	+	3.52555i
$497$	−17.2823	−	9.97797i	−0.775219	−	0.447573i
$498$		0			0
$499$	40.2772			1.80306			0.901528	−	0.432721i	$-0.142446\pi$
$499$	40.2772			1.80306			0.901528	+	0.432721i	$0.142446\pi$
$500$	34.9510	+	46.7572i	1.56306	+	2.09105i
$501$		0			0
$502$		−	67.6582i		−	3.01973i
$503$	−23.3031	+	13.4541i	−1.03903	+	0.599887i	−0.919560	−	0.392951i	$-0.871454\pi$
$503$	−23.3031	+	13.4541i	−1.03903	+	0.599887i	−0.119474	+	0.992837i	$0.538121\pi$
$504$		0			0
$505$	18.7430	−	35.6388i	0.834054	−	1.58591i
$506$	−40.8016			−1.81385
$507$		0			0
$508$		−	52.4351i		−	2.32643i
$509$	−9.14920	+	15.8469i	−0.405531	+	0.702400i	−0.994383	−	0.105840i	$-0.966247\pi$
$509$	−9.14920	+	15.8469i	−0.405531	+	0.702400i	0.588852	+	0.808241i	$0.299580\pi$
$510$		0			0
$511$	−2.41145	−	4.17676i	−0.106676	−	0.184769i
$512$		−	2.26022i		−	0.0998885i
$513$		0			0
$514$	36.7413	+	63.6378i	1.62059	+	2.80694i
$515$	0.494567	+	12.5352i	0.0217932	+	0.552369i
$516$		0			0
$517$	21.0054	+	12.1275i	0.923817	+	0.533366i
$518$	75.3380	+	43.4964i	3.31016	+	1.91112i
$519$		0			0
$520$	60.6063	−	34.6086i	2.65776	−	1.51769i
$521$	14.3803			0.630014			0.315007	−	0.949089i	$-0.397993\pi$
$521$	14.3803			0.630014			0.315007	+	0.949089i	$0.397993\pi$
$522$		0			0
$523$	−13.4105	−	7.74257i	−0.586401	−	0.338559i	0.177272	−	0.984162i	$-0.443273\pi$
$523$	−13.4105	−	7.74257i	−0.586401	−	0.338559i	−0.763673	+	0.645603i	$0.776606\pi$
$524$	−4.92466	−	8.52976i	−0.215135	−	0.372624i
$525$		0			0
$526$	−20.8363	−	36.0895i	−0.908504	−	1.57358i
$527$	−9.74069	+	5.62379i	−0.424311	+	0.244976i
$528$		0			0
$529$	−2.66891	−	4.62269i	−0.116040	−	0.200987i
$530$	−17.6070	+	33.4788i	−0.764801	+	1.45423i
$531$		0			0
$532$		−	89.9557i		−	3.90008i
$533$	−25.1956	−	1.11386i	−1.09134	−	0.0482467i
$534$		0			0
$535$	21.6751	+	11.3993i	0.937097	+	0.492835i
$536$	37.6476	−	65.2075i	1.62613	−	2.81654i
$537$		0			0
$538$			28.6563i			1.23546i
$539$	−11.1436	−	19.3012i	−0.479988	−	0.831363i
$540$		0			0
$541$	32.2986			1.38863			0.694313	−	0.719673i	$-0.255708\pi$
$541$	32.2986			1.38863			0.694313	+	0.719673i	$0.255708\pi$
$542$	4.70416	−	2.71595i	0.202061	−	0.116660i
$543$		0			0
$544$	−13.6272	+	23.6029i	−0.584259	+	1.01197i
$545$	20.2556	−	0.799165i	0.867653	−	0.0342325i
$546$		0			0
$547$			28.0514i			1.19939i	0.800227	+	0.599697i	$0.204712\pi$
$547$			28.0514i			1.19939i	−0.800227	+	0.599697i	$0.795288\pi$
$548$	73.2058	+	42.2654i	3.12719	+	1.80549i
$549$		0			0
$550$	−39.9964	+	27.5081i	−1.70545	+	1.17295i
$551$	22.0445			0.939127
$552$		0			0
$553$	−19.5520	+	11.2883i	−0.831434	+	0.480028i
$554$	−10.4147			−0.442478
$555$		0			0
$556$	10.7509	−	18.6211i	0.455939	−	0.789709i
$557$	−5.04757	−	2.91421i	−0.213872	−	0.123479i	0.389237	−	0.921137i	$-0.372739\pi$
$557$	−5.04757	−	2.91421i	−0.213872	−	0.123479i	−0.603110	+	0.797658i	$0.706072\pi$
$558$		0			0
$559$	−5.00815	−	3.19440i	−0.211822	−	0.135109i
$560$	4.10105	+	103.945i	0.173301	+	4.39247i
$561$		0			0
$562$	55.3825	+	31.9751i	2.33617	+	1.34879i
$563$	25.1078	−	14.4960i	1.05817	−	0.610934i	0.133243	−	0.991083i	$-0.457461\pi$
$563$	25.1078	−	14.4960i	1.05817	−	0.610934i	0.924925	+	0.380149i	$0.124127\pi$
$564$		0			0
$565$	10.4961	−	6.62495i	0.441574	−	0.278714i
$566$	9.02465	+	15.6312i	0.379334	+	0.657026i
$567$		0			0
$568$	−41.2263	+	23.8020i	−1.72982	+	0.998711i
$569$	−13.2681	+	22.9811i	−0.556229	+	0.963417i	0.441578	+	0.897223i	$0.354419\pi$
$569$	−13.2681	+	22.9811i	−0.556229	+	0.963417i	−0.997807	+	0.0661939i	$0.978914\pi$
$570$		0			0
$571$	4.95418			0.207326			0.103663	−	0.994612i	$-0.466944\pi$
$571$	4.95418			0.207326			0.103663	+	0.994612i	$0.466944\pi$
$572$	31.3725	+	60.3466i	1.31175	+	2.52322i
$573$		0			0
$574$	34.1060	−	59.0733i	1.42356	−	2.46567i
$575$	18.9692	+	9.04020i	0.791069	+	0.377002i
$576$		0			0
$577$			15.3342i			0.638373i	0.947692	+	0.319187i	$0.103410\pi$
$577$			15.3342i			0.638373i	−0.947692	+	0.319187i	$0.896590\pi$
$578$	33.6766	−	19.4432i	1.40076	−	0.808730i
$579$		0			0
$580$	−54.1700	+	2.13723i	−2.24929	+	0.0887437i
$581$	−12.0464	−	20.8650i	−0.499770	−	0.865627i
$582$		0			0
$583$	−19.6960	−	11.3715i	−0.815723	−	0.470958i
$584$	−11.5049			−0.476074
$585$		0			0
$586$	33.0066			1.36349
$587$	36.9151	+	21.3129i	1.52365	+	0.879679i	0.999608	+	0.0279853i	$0.00890915\pi$
$587$	36.9151	+	21.3129i	1.52365	+	0.879679i	0.524040	+	0.851694i	$0.324424\pi$
$588$		0			0
$589$	−16.7879	−	29.0775i	−0.691734	−	1.19812i
$590$	0.192940	+	4.89024i	0.00794321	+	0.201328i
$591$		0			0
$592$	99.0400	−	57.1808i	4.07052	−	2.35012i
$593$		−	29.2256i		−	1.20015i	−0.799944	−	0.600075i	$-0.795137\pi$
$593$		−	29.2256i		−	1.20015i	0.799944	−	0.600075i	$-0.204863\pi$
$594$		0			0
$595$	−6.00696	+	11.4219i	−0.246261	+	0.468252i
$596$	−2.23433	+	3.86997i	−0.0915217	+	0.158520i
$597$		0			0
$598$	21.8974	−	34.3305i	0.895450	−	1.40388i
$599$	−1.80922			−0.0739225			−0.0369613	−	0.999317i	$-0.511768\pi$
$599$	−1.80922			−0.0739225			−0.0369613	+	0.999317i	$0.511768\pi$
$600$		0			0
$601$	9.15668	−	15.8598i	0.373509	−	0.646936i	−0.616594	−	0.787281i	$-0.711488\pi$
$601$	9.15668	−	15.8598i	0.373509	−	0.646936i	0.990103	+	0.140345i	$0.0448213\pi$
$602$	13.9137	−	8.03308i	0.567080	−	0.327404i
$603$		0			0
$604$	−33.9093	−	58.7326i	−1.37975	−	2.38979i
$605$	−2.44960	−	3.88097i	−0.0995903	−	0.157784i
$606$		0			0
$607$	−2.18573	+	1.26193i	−0.0887161	+	0.0512202i	−0.543702	−	0.839279i	$-0.682978\pi$
$607$	−2.18573	+	1.26193i	−0.0887161	+	0.0512202i	0.454986	+	0.890499i	$0.349644\pi$
$608$	−70.4585	−	40.6792i	−2.85747	−	1.64976i
$609$		0			0
$610$	2.51068	+	63.6353i	0.101654	+	2.57652i
$611$	−21.4773	+	11.1654i	−0.868877	+	0.451705i
$612$		0			0
$613$	−6.35394	−	3.66845i	−0.256633	−	0.148167i	0.366165	−	0.930550i	$-0.380671\pi$
$613$	−6.35394	−	3.66845i	−0.256633	−	0.148167i	−0.622798	+	0.782383i	$0.714004\pi$
$614$	−12.9482	+	22.4270i	−0.522548	+	0.905080i
$615$		0			0
$616$	−113.493			−4.57275
$617$	−32.4440	+	18.7315i	−1.30614	+	0.754103i	−0.981450	−	0.191716i	$-0.938595\pi$
$617$	−32.4440	+	18.7315i	−1.30614	+	0.754103i	−0.324694	+	0.945819i	$0.605261\pi$
$618$		0			0
$619$	−16.5344			−0.664573			−0.332287	−	0.943178i	$-0.607820\pi$
$619$	−16.5344			−0.664573			−0.332287	+	0.943178i	$0.607820\pi$
$620$	44.0721	+	69.8247i	1.76998	+	2.80423i
$621$		0			0
$622$	−35.0860	−	20.2569i	−1.40682	−	0.812229i
$623$			48.4988i			1.94306i
$624$		0			0
$625$	24.6896	−	3.92703i	0.987586	−	0.157081i
$626$	32.0463	−	55.5059i	1.28083	−	2.21846i
$627$		0			0
$628$	−40.0132	+	23.1016i	−1.59670	+	0.921855i
$629$	14.1874			0.565689
$630$		0			0
$631$	−1.97472	−	3.42031i	−0.0786123	−	0.136161i	0.824039	−	0.566533i	$-0.191716\pi$
$631$	−1.97472	−	3.42031i	−0.0786123	−	0.136161i	−0.902651	+	0.430372i	$0.858382\pi$
$632$			53.8557i			2.14226i
$633$		0			0
$634$	11.7559	−	20.3618i	0.466886	−	0.808671i
$635$	−19.8746	−	10.4524i	−0.788700	−	0.414791i
$636$		0			0
$637$	22.2206	+	0.982345i	0.880413	+	0.0389219i
$638$		−	45.0800i		−	1.78474i
$639$		0			0
$640$	40.7242	+	21.4175i	1.60976	+	0.846601i
$641$	9.64376	+	16.7035i	0.380906	+	0.659748i	0.991192	−	0.132433i	$-0.0422789\pi$
$641$	9.64376	+	16.7035i	0.380906	+	0.659748i	−0.610286	+	0.792181i	$0.708946\pi$
$642$		0			0
$643$	13.4668	−	7.77507i	0.531079	−	0.306619i	−0.210377	−	0.977620i	$-0.567469\pi$
$643$	13.4668	−	7.77507i	0.531079	−	0.306619i	0.741456	+	0.671002i	$0.234136\pi$
$644$	39.8153	+	68.9621i	1.56894	+	2.71749i
$645$		0			0
$646$	−10.1450	−	17.5717i	−0.399151	−	0.691350i
$647$	24.6729	+	14.2449i	0.969993	+	0.560025i	0.899234	−	0.437468i	$-0.144125\pi$
$647$	24.6729	+	14.2449i	0.969993	+	0.560025i	0.0707586	+	0.997493i	$0.477458\pi$
$648$		0			0
$649$	−2.94252			−0.115504
$650$	−1.68010	−	48.4161i	−0.0658990	−	1.89903i
$651$		0			0
$652$	−92.1907	−	53.2264i	−3.61047	−	2.08450i
$653$	−40.5547	−	23.4143i	−1.58703	−	0.916270i	−0.993794	−	0.111240i	$-0.964518\pi$
$653$	−40.5547	−	23.4143i	−1.58703	−	0.916270i	−0.593233	−	0.805031i	$-0.702149\pi$
$654$		0			0
$655$	−4.21474	+	0.166289i	−0.164683	+	0.00649744i
$656$	−44.8360	−	77.6583i	−1.75055	−	3.03205i
$657$		0			0
$658$		−	65.4695i		−	2.55227i
$659$	−17.1521	−	29.7083i	−0.668150	−	1.15727i	−0.978421	−	0.206622i	$-0.933753\pi$
$659$	−17.1521	−	29.7083i	−0.668150	−	1.15727i	0.310271	−	0.950648i	$-0.399580\pi$
$660$		0			0
$661$	4.69747	−	8.13626i	0.182711	−	0.316464i	−0.760092	−	0.649815i	$-0.774846\pi$
$661$	4.69747	−	8.13626i	0.182711	−	0.316464i	0.942803	+	0.333351i	$0.108180\pi$
$662$		−	41.6748i		−	1.61974i
$663$		0			0
$664$	−57.4725			−2.23037
$665$	−34.0962	−	17.9317i	−1.32219	−	0.695363i
$666$		0			0
$667$	−16.8998	+	9.75711i	−0.654363	+	0.377797i
$668$			36.1149i			1.39733i
$669$		0			0
$670$	−27.8968	−	44.1978i	−1.07775	−	1.70751i
$671$	−38.2902			−1.47818
$672$		0			0
$673$	−39.7851	−	22.9699i	−1.53360	−	0.885426i	−0.999192	−	0.0402007i	$-0.987200\pi$
$673$	−39.7851	−	22.9699i	−1.53360	−	0.885426i	−0.534411	−	0.845225i	$-0.679466\pi$
$674$	44.4379	−	76.9687i	1.71168	−	2.96472i
$675$		0			0
$676$	−67.6127	−	5.98985i	−2.60049	−	0.230379i
$677$			9.98701i			0.383832i	0.981411	+	0.191916i	$0.0614701\pi$
$677$			9.98701i			0.383832i	−0.981411	+	0.191916i	$0.938530\pi$
$678$		0			0
$679$	11.3353	−	19.6334i	0.435010	−	0.753459i
$680$	16.4314	+	26.0328i	0.630117	+	0.998313i
$681$		0			0
$682$	−59.4623	+	34.3305i	−2.27693	+	1.31458i
$683$	−11.5330	+	6.65861i	−0.441300	+	0.254785i	−0.704149	−	0.710052i	$-0.748671\pi$
$683$	−11.5330	+	6.65861i	−0.441300	+	0.254785i	0.262849	+	0.964837i	$0.415338\pi$
$684$		0			0
$685$	30.6128	−	19.3222i	1.16965	−	0.738264i
$686$	4.05229	−	7.01877i	0.154717	−	0.267978i
$687$		0			0
$688$		−	21.1207i		−	0.805220i
$689$	20.1384	−	10.4694i	0.767212	−	0.398852i
$690$		0			0
$691$	22.2896	−	38.6068i	0.847938	−	1.46867i	−0.0351073	−	0.999384i	$-0.511177\pi$
$691$	22.2896	−	38.6068i	0.847938	−	1.46867i	0.883045	−	0.469288i	$-0.155489\pi$
$692$	−58.3648	−	33.6969i	−2.21870	−	1.28096i
$693$		0			0
$694$	37.6823			1.43040
$695$	−4.91492	−	7.78685i	−0.186433	−	0.295372i
$696$		0			0
$697$		−	11.1245i		−	0.421370i
$698$	−16.2337	+	9.37252i	−0.614454	+	0.354755i
$699$		0			0
$700$	85.5232	+	40.7581i	3.23247	+	1.54051i
$701$	9.39895			0.354994			0.177497	−	0.984121i	$-0.443200\pi$
$701$	9.39895			0.354994			0.177497	+	0.984121i	$0.443200\pi$
$702$		0			0
$703$			42.3517i			1.59732i
$704$	−36.8717	+	63.8637i	−1.38965	+	2.40695i
$705$		0			0
$706$	18.9248	+	32.7787i	0.712245	+	1.23364i
$707$		−	65.3490i		−	2.45770i
$708$		0			0
$709$	−3.80896	−	6.59731i	−0.143048	−	0.247767i	0.785595	−	0.618741i	$-0.212357\pi$
$709$	−3.80896	−	6.59731i	−0.143048	−	0.247767i	−0.928643	+	0.370974i	$0.879024\pi$
$710$	1.30270	+	33.0182i	0.0488896	+	1.23915i
$711$		0			0
$712$	100.192	+	57.8459i	3.75486	+	2.16787i
$713$	25.7400	+	14.8610i	0.963970	+	0.556549i
$714$		0			0
$715$	29.1271	+	0.138246i	1.08929	+	0.00517011i
$716$	−116.446			−4.35180
$717$		0			0
$718$	−21.0131	−	12.1319i	−0.784203	−	0.452760i
$719$	−9.60830	−	16.6421i	−0.358329	−	0.620644i	0.629353	−	0.777120i	$-0.283320\pi$
$719$	−9.60830	−	16.6421i	−0.358329	−	0.620644i	−0.987682	+	0.156475i	$0.949987\pi$
$720$		0			0
$721$	10.1796	+	17.6316i	0.379108	+	0.656634i
$722$	8.23699	−	4.75563i	0.306549	−	0.176986i
$723$		0			0
$724$	11.4099	+	19.7625i	0.424045	+	0.734468i
$725$	−9.98815	+	20.9583i	−0.370951	+	0.778370i
$726$		0			0
$727$			12.8044i			0.474889i	0.971401	+	0.237444i	$0.0763097\pi$
$727$			12.8044i			0.474889i	−0.971401	+	0.237444i	$0.923690\pi$
$728$	60.9092	−	95.4930i	2.25744	−	3.53921i
$729$		0			0
$730$	−3.71723	+	7.06810i	−0.137581	+	0.261602i
$731$	1.31009	−	2.26914i	0.0484555	−	0.0839273i
$732$		0			0
$733$			16.0430i			0.592562i	0.955101	+	0.296281i	$0.0957465\pi$
$733$			16.0430i			0.592562i	−0.955101	+	0.296281i	$0.904253\pi$
$734$	45.0910	+	78.0999i	1.66434	+	2.88272i
$735$		0			0
$736$	72.0201			2.65470
$737$	27.2143	−	15.7122i	1.00245	−	0.578765i
$738$		0			0
$739$	−0.730305	+	1.26492i	−0.0268647	+	0.0465310i	−0.879145	−	0.476554i	$-0.841886\pi$
$739$	−0.730305	+	1.26492i	−0.0268647	+	0.0465310i	0.852280	+	0.523085i	$0.175219\pi$
$740$	−4.10602	−	104.071i	−0.150940	−	3.82572i
$741$		0			0
$742$			61.3882i			2.25363i
$743$	6.65356	+	3.84143i	0.244095	+	0.140928i	0.617058	−	0.786918i	$-0.288325\pi$
$743$	6.65356	+	3.84143i	0.244095	+	0.140928i	−0.372962	+	0.927847i	$0.621658\pi$
$744$		0			0
$745$	1.02146	+	1.61832i	0.0374233	+	0.0592908i
$746$	66.3992			2.43105
$747$		0			0
$748$	−25.9814	+	15.0004i	−0.949974	+	0.548468i
$749$	39.7445			1.45223
$750$		0			0
$751$	5.85165	−	10.1354i	0.213530	−	0.369845i	−0.739287	−	0.673391i	$-0.764837\pi$
$751$	5.85165	−	10.1354i	0.213530	−	0.369845i	0.952817	+	0.303546i	$0.0981706\pi$
$752$	−74.5360	−	43.0334i	−2.71805	−	1.56927i
$753$		0			0
$754$	37.9304	+	24.1935i	1.38135	+	0.881076i
$755$	−29.0210	+	1.14500i	−1.05618	+	0.0416708i
$756$		0			0
$757$	−25.2869	−	14.5994i	−0.919068	−	0.530624i	−0.0357302	−	0.999361i	$-0.511376\pi$
$757$	−25.2869	−	14.5994i	−0.919068	−	0.530624i	−0.883338	+	0.468737i	$0.844709\pi$
$758$	−65.5330	+	37.8355i	−2.38026	+	1.37425i
$759$		0			0
$760$	−77.7121	+	49.0505i	−2.81891	+	1.77925i
$761$	−3.92358	−	6.79584i	−0.142230	−	0.246349i	0.786106	−	0.618091i	$-0.212094\pi$
$761$	−3.92358	−	6.79584i	−0.142230	−	0.246349i	−0.928336	+	0.371742i	$0.878760\pi$
$762$		0			0
$763$	28.4907	−	16.4491i	1.03143	−	0.595497i
$764$	−2.83692	+	4.91369i	−0.102636	+	0.177771i
$765$		0			0
$766$	12.4411			0.449516
$767$	1.57919	−	2.47584i	0.0570212	−	0.0893975i
$768$		0			0
$769$	−24.5396	+	42.5038i	−0.884920	+	1.53273i	−0.0391142	+	0.999235i	$0.512454\pi$
$769$	−24.5396	+	42.5038i	−0.884920	+	1.53273i	−0.845806	+	0.533491i	$0.820880\pi$
$770$	−36.6696	+	69.7252i	−1.32148	+	2.51272i
$771$		0			0
$772$		−	43.7525i		−	1.57469i
$773$	−15.6080	+	9.01131i	−0.561382	+	0.324114i	−0.753700	−	0.657218i	$-0.771733\pi$
$773$	−15.6080	+	9.01131i	−0.561382	+	0.324114i	0.192318	+	0.981333i	$0.438400\pi$
$774$		0			0
$775$	35.2512	−	2.78595i	1.26626	−	0.100074i
$776$	−27.0400	−	46.8346i	−0.970678	−	1.68126i
$777$		0			0
$778$	7.04957	+	4.07007i	0.252739	+	0.145919i
$779$	33.2083			1.18981
$780$		0			0
$781$	−19.8675			−0.710915
$782$	15.5548	+	8.98059i	0.556240	+	0.321145i
$783$		0			0
$784$	39.5421	+	68.4889i	1.41222	+	2.44603i
$785$	0.780062	+	19.7714i	0.0278416	+	0.705671i
$786$		0			0
$787$	11.6749	−	6.74053i	0.416167	−	0.240274i	−0.277269	−	0.960792i	$-0.589429\pi$
$787$	11.6749	−	6.74053i	0.416167	−	0.240274i	0.693436	+	0.720518i	$0.256096\pi$
$788$		−	25.6257i		−	0.912877i
$789$		0			0
$790$	33.0867	+	17.4008i	1.17717	+	0.619094i
$791$	10.0717	−	17.4447i	0.358108	−	0.620261i
$792$		0			0
$793$	20.5496	−	32.2175i	0.729736	−	1.14408i
$794$	−0.364107			−0.0129217
$795$		0			0
$796$	−36.3314	+	62.9278i	−1.28773	+	2.23042i
$797$	4.54308	−	2.62295i	0.160924	−	0.0929095i	−0.417375	−	0.908734i	$-0.637050\pi$
$797$	4.54308	−	2.62295i	0.160924	−	0.0929095i	0.578299	+	0.815825i	$0.303717\pi$
$798$		0			0
$799$	−5.33861	−	9.24674i	−0.188866	−	0.327126i
$800$	70.5988	−	48.5553i	2.49605	−	1.71669i
$801$		0			0
$802$	34.9897	−	20.2013i	1.23553	−	0.713334i
$803$	−4.15825	−	2.40077i	−0.146741	−	0.0847212i
$804$		0			0
$805$	34.0757	−	1.34443i	1.20101	−	0.0473848i
$806$	3.02636	−	68.4562i	0.106599	−	2.41127i
$807$		0			0
$808$	−135.002	−	77.9436i	−4.74937	−	2.74205i
$809$	17.2215	−	29.8286i	0.605477	−	1.04872i	−0.386499	−	0.922290i	$-0.626316\pi$
$809$	17.2215	−	29.8286i	0.605477	−	1.04872i	0.991976	−	0.126427i	$-0.0403509\pi$
$810$		0			0
$811$	7.51649			0.263939			0.131970	−	0.991254i	$-0.457870\pi$
$811$	7.51649			0.263939			0.131970	+	0.991254i	$0.457870\pi$
$812$	−76.1934	+	43.9903i	−2.67386	+	1.54376i
$813$		0			0
$814$	86.6072			3.03558
$815$	−38.5518	+	24.3332i	−1.35041	+	0.852355i
$816$		0			0
$817$	6.77376	+	3.91083i	0.236984	+	0.136823i
$818$		−	46.3491i		−	1.62056i
$819$		0			0
$820$	−81.6030	+	3.21957i	−2.84970	+	0.112432i
$821$	−26.4507	+	45.8139i	−0.923135	+	1.59892i	−0.128602	+	0.991696i	$0.541049\pi$
$821$	−26.4507	+	45.8139i	−0.923135	+	1.59892i	−0.794533	+	0.607220i	$0.792284\pi$
$822$		0			0
$823$	−24.3129	+	14.0371i	−0.847495	+	0.489302i	−0.859805	−	0.510623i	$-0.829415\pi$
$823$	−24.3129	+	14.0371i	−0.847495	+	0.489302i	0.0123098	+	0.999924i	$0.496082\pi$
$824$	48.5660			1.69188
$825$		0			0
$826$	3.97125	+	6.87841i	0.138178	+	0.239331i
$827$		−	37.9748i		−	1.32051i	−0.751040	−	0.660256i	$-0.770448\pi$
$827$		−	37.9748i		−	1.32051i	0.751040	−	0.660256i	$-0.229552\pi$
$828$		0			0
$829$	3.60157	−	6.23809i	0.125088	−	0.216658i	−0.796680	−	0.604402i	$-0.793412\pi$
$829$	3.60157	−	6.23809i	0.125088	−	0.216658i	0.921767	+	0.387744i	$0.126745\pi$
$830$	−18.5694	+	35.3087i	−0.644555	+	1.22558i
$831$		0			0
$832$	−33.9468	−	65.2982i	−1.17689	−	2.26381i
$833$			9.81097i			0.339930i
$834$		0			0
$835$	13.6887	+	7.19912i	0.473718	+	0.249136i
$836$	−44.7785	−	77.5586i	−1.54870	−	2.68242i
$837$		0			0
$838$	12.6053	−	7.27765i	0.435441	−	0.251402i
$839$	17.5519	+	30.4008i	0.605960	+	1.04955i	0.991899	+	0.127029i	$0.0405442\pi$
$839$	17.5519	+	30.4008i	0.605960	+	1.04955i	−0.385939	+	0.922524i	$0.626123\pi$
$840$		0			0
$841$	3.71976	+	6.44282i	0.128268	+	0.222166i
$842$	76.6694	+	44.2651i	2.64220	+	1.52548i
$843$		0			0
$844$	−73.2104			−2.52000
$845$	−15.7482	+	24.4334i	−0.541756	+	0.840536i
$846$		0			0
$847$	−6.45023	−	3.72404i	−0.221632	−	0.127960i
$848$	69.8896	+	40.3508i	2.40002	+	1.38565i
$849$		0			0
$850$	21.3025	−	1.68356i	0.730670	−	0.0577457i
$851$	−18.7453	−	32.4677i	−0.642579	−	1.11298i
$852$		0			0
$853$		−	18.1189i		−	0.620379i	−0.950675	−	0.310190i	$-0.899607\pi$
$853$		−	18.1189i		−	0.620379i	0.950675	−	0.310190i	$-0.100393\pi$
$854$	51.6768	+	89.5069i	1.76835	+	3.06286i
$855$		0			0
$856$	47.4044	−	82.1068i	1.62025	−	2.80635i
$857$			41.6090i			1.42134i	0.703527	+	0.710669i	$0.251608\pi$
$857$			41.6090i			1.42134i	−0.703527	+	0.710669i	$0.748392\pi$
$858$		0			0
$859$	−39.8609			−1.36004			−0.680019	−	0.733195i	$-0.738028\pi$
$859$	−39.8609			−1.36004			−0.680019	+	0.733195i	$0.738028\pi$
$860$	−17.0243	−	8.95338i	−0.580525	−	0.305308i
$861$		0			0
$862$	24.4106	−	14.0935i	0.831429	−	0.480026i
$863$			40.0570i			1.36355i	0.731560	+	0.681777i	$0.238793\pi$
$863$			40.0570i			1.36355i	−0.731560	+	0.681777i	$0.761207\pi$
$864$		0			0
$865$	−24.4067	+	15.4050i	−0.829851	+	0.523787i
$866$	56.9049			1.93371
$867$		0			0
$868$	116.050	+	67.0013i	3.93898	+	2.27417i
$869$	−11.2383	+	19.4653i	−0.381233	+	0.660315i
$870$		0			0
$871$	−1.38508	+	31.3305i	−0.0469317	+	1.06160i
$872$		−	78.4773i		−	2.65758i
$873$		0			0
$874$	−26.8085	+	46.4337i	−0.906811	+	1.57064i
$875$	32.4968	−	24.2914i	1.09859	−	0.821199i
$876$		0			0
$877$	43.1914	−	24.9366i	1.45847	−	0.842048i	0.459534	−	0.888160i	$-0.348016\pi$
$877$	43.1914	−	24.9366i	1.45847	−	0.842048i	0.998936	+	0.0461120i	$0.0146831\pi$
$878$	−27.9421	+	16.1324i	−0.942999	+	0.544441i
$879$		0			0
$880$	55.2780	+	87.5785i	1.86342	+	2.95227i
$881$	3.10495	−	5.37793i	0.104608	−	0.181187i	−0.808970	−	0.587850i	$-0.799974\pi$
$881$	3.10495	−	5.37793i	0.104608	−	0.181187i	0.913578	+	0.406663i	$0.133308\pi$
$882$		0			0
$883$			30.9168i			1.04043i	0.854034	+	0.520216i	$0.174149\pi$
$883$			30.9168i			1.04043i	−0.854034	+	0.520216i	$0.825851\pi$
$884$	1.32234	−	29.9112i	0.0444749	−	1.00602i
$885$		0			0
$886$	−38.8821	+	67.3458i	−1.30627	+	2.26252i
$887$	39.7009	+	22.9213i	1.33303	+	0.769622i	0.985762	−	0.168145i	$-0.0537778\pi$
$887$	39.7009	+	22.9213i	1.33303	+	0.769622i	0.347263	+	0.937768i	$0.387111\pi$
$888$		0			0
$889$	−36.4430			−1.22226
$890$	67.9103	−	42.8638i	2.27636	−	1.43680i
$891$		0			0
$892$		−	9.47048i		−	0.317095i
$893$	27.6030	−	15.9366i	0.923700	−	0.533298i
$894$		0			0
$895$	−23.2123	+	44.1369i	−0.775902	+	1.47533i
$896$	74.6737			2.49467
$897$		0			0
$898$			42.6534i			1.42336i
$899$	−16.4193	+	28.4391i	−0.547615	+	0.948497i
$900$		0			0
$901$	5.00581	+	8.67032i	0.166768	+	0.288850i
$902$		−	67.9096i		−	2.26114i
$903$		0			0
$904$	−24.0256	−	41.6136i	−0.799079	−	1.38405i
$905$	9.76509	−	0.385273i	0.324602	−	0.0128069i
$906$		0			0
$907$	12.4257	+	7.17400i	0.412590	+	0.238209i	0.691902	−	0.721992i	$-0.256773\pi$
$907$	12.4257	+	7.17400i	0.412590	+	0.238209i	−0.279312	+	0.960200i	$0.590106\pi$
$908$	110.239	+	63.6466i	3.65842	+	2.11219i
$909$		0			0
$910$	−38.9871	−	68.2739i	−1.29241	−	2.26326i
$911$	−21.6473			−0.717209			−0.358604	−	0.933490i	$-0.616747\pi$
$911$	−21.6473			−0.717209			−0.358604	+	0.933490i	$0.616747\pi$
$912$		0			0
$913$	−20.7726	−	11.9930i	−0.687471	−	0.396912i
$914$	−42.7262	−	74.0040i	−1.41326	−	2.44783i
$915$		0			0
$916$	4.17300	+	7.22785i	0.137880	+	0.238815i
$917$	−5.92828	+	3.42269i	−0.195769	+	0.113027i
$918$		0			0
$919$	−5.51570	−	9.55348i	−0.181946	−	0.315140i	0.760597	−	0.649224i	$-0.224906\pi$
$919$	−5.51570	−	9.55348i	−0.181946	−	0.315140i	−0.942543	+	0.334084i	$0.891573\pi$
$920$	37.8656	−	71.9994i	1.24839	−	2.37375i
$921$		0			0
$922$		−	56.8997i		−	1.87389i
$923$	10.6625	−	16.7165i	0.350959	−	0.550232i
$924$		0			0
$925$	−40.2648	−	19.1891i	−1.32390	−	0.630935i
$926$	−36.5150	+	63.2458i	−1.19996	+	2.07839i
$927$		0			0
$928$			79.5721i			2.61208i
$929$	−17.9504	−	31.0910i	−0.588934	−	1.02006i	−0.994372	−	0.105941i	$-0.966214\pi$
$929$	−17.9504	−	31.0910i	−0.588934	−	1.02006i	0.405438	−	0.914122i	$-0.367119\pi$
$930$		0			0
$931$	−29.2873			−0.959853
$932$	45.3201	−	26.1656i	1.48451	−	0.857083i
$933$		0			0
$934$	8.49435	−	14.7126i	0.277944	−	0.481413i
$935$	0.506511	+	12.8380i	0.0165647	+	0.419847i
$936$		0			0
$937$			16.7027i			0.545652i	0.962063	+	0.272826i	$0.0879584\pi$
$937$			16.7027i			0.545652i	−0.962063	+	0.272826i	$0.912042\pi$
$938$	−73.4573	−	42.4106i	−2.39847	−	1.38476i
$939$		0			0
$940$	−66.2839	+	41.8372i	−2.16194	+	1.36458i
$941$	−36.3982			−1.18655			−0.593274	−	0.805000i	$-0.702165\pi$
$941$	−36.3982			−1.18655			−0.593274	+	0.805000i	$0.702165\pi$
$942$		0			0
$943$	−25.4583	+	14.6983i	−0.829035	+	0.478644i
$944$	10.4413			0.339835
$945$		0			0
$946$	7.99748	−	13.8520i	0.260020	−	0.450369i
$947$	−21.7433	−	12.5535i	−0.706563	−	0.407935i	0.103224	−	0.994658i	$-0.467084\pi$
$947$	−21.7433	−	12.5535i	−0.706563	−	0.407935i	−0.809787	+	0.586724i	$0.800418\pi$
$948$		0			0
$949$	4.25166	−	2.21032i	0.138015	−	0.0717500i
$950$	5.02571	+	63.5914i	0.163055	+	2.06318i
$951$		0			0
$952$	43.2669	+	24.9802i	1.40229	+	0.809612i
$953$	12.4181	−	7.16961i	0.402262	−	0.232246i	−0.285197	−	0.958469i	$-0.592059\pi$
$953$	12.4181	−	7.16961i	0.402262	−	0.232246i	0.687460	+	0.726222i	$0.258726\pi$
$954$		0			0
$955$	1.29694	+	2.05478i	0.0419679	+	0.0664910i
$956$	−38.1450	−	66.0690i	−1.23370	−	2.13682i
$957$		0			0
$958$	38.6549	−	22.3174i	1.24888	−	0.721043i
$959$	29.3749	−	50.8789i	0.948566	−	1.64296i
$960$		0			0
$961$	19.0163			0.613429
$962$	−46.4803	+	72.8715i	−1.49859	+	2.34947i
$963$		0			0
$964$	34.6068	−	59.9407i	1.11461	−	1.93056i
$965$	−16.5836	−	8.72160i	−0.533846	−	0.280758i
$966$		0			0
$967$		−	12.4611i		−	0.400722i	−0.979722	−	0.200361i	$-0.935788\pi$
$967$		−	12.4611i		−	0.400722i	0.979722	−	0.200361i	$-0.0642115\pi$
$968$	−15.3868	+	8.88355i	−0.494549	+	0.285528i
$969$		0			0
$970$	−37.5099	+	1.47992i	−1.20437	+	0.0475173i
$971$	28.1119	+	48.6912i	0.902152	+	1.56257i	0.824695	+	0.565578i	$0.191347\pi$
$971$	28.1119	+	48.6912i	0.902152	+	1.56257i	0.0774574	+	0.996996i	$0.475320\pi$
$972$		0			0
$973$	−12.9419	−	7.47198i	−0.414897	−	0.239541i
$974$	−74.7381			−2.39476
$975$		0			0
$976$	135.870			4.34908
$977$	28.5793	+	16.5003i	0.914334	+	0.527891i	0.881823	−	0.471580i	$-0.156316\pi$
$977$	28.5793	+	16.5003i	0.914334	+	0.527891i	0.0325110	+	0.999471i	$0.489650\pi$
$978$		0			0
$979$	24.1419	+	41.8150i	0.771579	+	1.33641i
$980$	71.9679	−	2.83943i	2.29893	−	0.0907022i
$981$		0			0
$982$	−74.3695	+	42.9372i	−2.37322	+	1.37018i
$983$			8.72308i			0.278223i	0.990277	+	0.139111i	$0.0444246\pi$
$983$			8.72308i			0.278223i	−0.990277	+	0.139111i	$0.955575\pi$
$984$		0			0
$985$	−9.71298	−	5.10821i	−0.309481	−	0.162761i
$986$	−9.92229	+	17.1859i	−0.315990	+	0.547311i
$987$		0			0
$988$	89.2897	+	3.94738i	2.84068	+	0.125583i
$989$	−6.92389			−0.220167
$990$		0			0
$991$	−1.93361	+	3.34911i	−0.0614231	+	0.106388i	−0.895102	−	0.445862i	$-0.852897\pi$
$991$	−1.93361	+	3.34911i	−0.0614231	+	0.106388i	0.833679	+	0.552250i	$0.186231\pi$
$992$	104.959	−	60.5979i	3.33244	−	1.92398i
$993$		0			0
$994$	26.8134	+	46.4421i	0.850468	+	1.47305i
$995$	16.6094	+	26.3148i	0.526554	+	0.834235i
$996$		0			0
$997$	−16.6839	+	9.63247i	−0.528385	+	0.305063i	−0.740359	−	0.672212i	$-0.765344\pi$
$997$	−16.6839	+	9.63247i	−0.528385	+	0.305063i	0.211974	+	0.977275i	$0.432011\pi$
$998$	−93.7345	−	54.1176i	−2.96711	−	1.71306i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.c.334.2	yes	32
3.2	odd	2	inner	585.2.bs.c.334.15	yes	32
5.4	even	2	inner	585.2.bs.c.334.16	yes	32
13.3	even	3	inner	585.2.bs.c.289.16	yes	32
15.14	odd	2	inner	585.2.bs.c.334.1	yes	32
39.29	odd	6	inner	585.2.bs.c.289.1	✓	32
65.29	even	6	inner	585.2.bs.c.289.2	yes	32
195.29	odd	6	inner	585.2.bs.c.289.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bs.c.289.1	✓	32	39.29	odd	6	inner
585.2.bs.c.289.2	yes	32	65.29	even	6	inner
585.2.bs.c.289.15	yes	32	195.29	odd	6	inner
585.2.bs.c.289.16	yes	32	13.3	even	3	inner
585.2.bs.c.334.1	yes	32	15.14	odd	2	inner
585.2.bs.c.334.2	yes	32	1.1	even	1	trivial
585.2.bs.c.334.15	yes	32	3.2	odd	2	inner
585.2.bs.c.334.16	yes	32	5.4	even	2	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.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.32723 - 1.34363i) q^{2} +(2.61067 + 4.52182i) q^{4} +(2.23433 - 0.0881535i) q^{5} +(3.14272 - 1.81445i) q^{7} -8.65659i q^{8} +O(q^{10})\)	\(q+(-2.32723 - 1.34363i) q^{2} +(2.61067 + 4.52182i) q^{4} +(2.23433 - 0.0881535i) q^{5} +(3.14272 - 1.81445i) q^{7} -8.65659i q^{8} +(-5.31825 - 2.79696i) q^{10} +(1.80641 - 3.12879i) q^{11} +(1.66311 + 3.19907i) q^{13} -9.75179 q^{14} +(-6.40989 + 11.1023i) q^{16} +(-1.37732 + 0.795195i) q^{17} +(-2.37378 - 4.11151i) q^{19} +(6.23172 + 9.87310i) q^{20} +(-8.40786 + 4.85428i) q^{22} +(3.63959 + 2.10132i) q^{23} +(4.98446 - 0.393928i) q^{25} +(0.427922 - 9.67959i) q^{26} +(16.4092 + 9.47388i) q^{28} +(-2.32166 + 4.02124i) q^{29} +7.07222 q^{31} +(14.8410 - 8.56844i) q^{32} +4.27378 q^{34} +(6.86192 - 4.33112i) q^{35} +(-7.72556 - 4.46035i) q^{37} +12.7579i q^{38} +(-0.763109 - 19.3417i) q^{40} +(-3.49741 + 6.05769i) q^{41} +(-1.42679 + 0.823755i) q^{43} +18.8638 q^{44} +(-5.64678 - 9.78052i) q^{46} +6.71359i q^{47} +(3.08446 - 5.34244i) q^{49} +(-12.1293 - 5.78050i) q^{50} +(-10.1238 + 15.8720i) q^{52} -6.29507i q^{53} +(3.76030 - 7.14999i) q^{55} +(-15.7070 - 27.2052i) q^{56} +(10.8061 - 6.23890i) q^{58} +(-0.407233 - 0.705349i) q^{59} +(-5.29922 - 9.17852i) q^{61} +(-16.4587 - 9.50244i) q^{62} -20.4116 q^{64} +(3.99794 + 7.00117i) q^{65} +(7.53270 + 4.34901i) q^{67} +(-7.19146 - 4.15199i) q^{68} +(-21.7887 + 0.859654i) q^{70} +(-2.74958 - 4.76242i) q^{71} -1.32903i q^{73} +(11.9861 + 20.7606i) q^{74} +(12.3944 - 21.4676i) q^{76} -13.1105i q^{77} -6.22135 q^{79} +(-13.3431 + 25.3712i) q^{80} +(16.2786 - 9.39843i) q^{82} -6.63916i q^{83} +(-3.00728 + 1.89814i) q^{85} +4.42728 q^{86} +(-27.0847 - 15.6373i) q^{88} +(-6.68230 + 11.5741i) q^{89} +(11.0312 + 7.03616i) q^{91} +21.9434i q^{92} +(9.02057 - 15.6241i) q^{94} +(-5.66626 - 8.97722i) q^{95} +(5.41028 - 3.12363i) q^{97} +(-14.3565 + 8.28873i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4}+O(q^{10}) \) 32 * q + 20 * q^4	\( 32 q + 20 q^{4} - 6 q^{10} - 28 q^{16} - 8 q^{19} + 28 q^{25} + 8 q^{31} - 8 q^{34} - 20 q^{40} - 8 q^{46} + 44 q^{49} + 20 q^{55} - 56 q^{61} - 136 q^{64} - 80 q^{70} + 88 q^{76} - 72 q^{79} - 50 q^{85} - 28 q^{91} + 48 q^{94}+O(q^{100}) \) 32 * q + 20 * q^4 - 6 * q^10 - 28 * q^16 - 8 * q^19 + 28 * q^25 + 8 * q^31 - 8 * q^34 - 20 * q^40 - 8 * q^46 + 44 * q^49 + 20 * q^55 - 56 * q^61 - 136 * q^64 - 80 * q^70 + 88 * q^76 - 72 * q^79 - 50 * q^85 - 28 * q^91 + 48 * q^94

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