LMFDB - Embedded newform 525.2.bf.g.32.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(32,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("525.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bf (of order $12$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.19
Character	$\chi$	$=$	525.32
Dual form			525.2.bf.g.443.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.61504 + 0.700699i) q^{2} +(-0.977224 - 1.43005i) q^{3} +(4.61542 + 2.66471i) q^{4} +(-1.55345 - 4.42437i) q^{6} +(1.33002 + 2.28715i) q^{7} +(6.37367 + 6.37367i) q^{8} +(-1.09007 + 2.79495i) q^{9} +O(q^{10})$	\(q+(2.61504 + 0.700699i) q^{2} +(-0.977224 - 1.43005i) q^{3} +(4.61542 + 2.66471i) q^{4} +(-1.55345 - 4.42437i) q^{6} +(1.33002 + 2.28715i) q^{7} +(6.37367 + 6.37367i) q^{8} +(-1.09007 + 2.79495i) q^{9} +(-1.45198 - 0.838304i) q^{11} +(-0.699631 - 9.20429i) q^{12} +(1.08642 - 1.08642i) q^{13} +(1.87546 + 6.91293i) q^{14} +(6.87197 + 11.9026i) q^{16} +(-1.33520 - 4.98305i) q^{17} +(-4.80899 + 6.54511i) q^{18} +(-0.559817 + 0.323211i) q^{19} +(1.97100 - 4.13705i) q^{21} +(-3.20960 - 3.20960i) q^{22} +(1.58296 - 5.90767i) q^{23} +(2.88615 - 15.3431i) q^{24} +(3.60230 - 2.07979i) q^{26} +(5.06215 - 1.17244i) q^{27} +(0.0440191 + 14.1003i) q^{28} -5.73864 q^{29} +(-2.54137 + 4.40179i) q^{31} +(4.96450 + 18.5278i) q^{32} +(0.220100 + 2.89562i) q^{33} -13.9665i q^{34} +(-12.4789 + 9.99515i) q^{36} +(-0.397659 + 1.48408i) q^{37} +(-1.69042 + 0.452947i) q^{38} +(-2.61532 - 0.491958i) q^{39} -3.42121i q^{41} +(8.05307 - 9.43748i) q^{42} +(2.91002 - 2.91002i) q^{43} +(-4.46768 - 7.73825i) q^{44} +(8.27899 - 14.3396i) q^{46} +(-7.60419 - 2.03754i) q^{47} +(10.3058 - 21.4587i) q^{48} +(-3.46208 + 6.08391i) q^{49} +(-5.82120 + 6.77896i) q^{51} +(7.90931 - 2.11929i) q^{52} +(-2.37411 + 0.636140i) q^{53} +(14.0593 + 0.481054i) q^{54} +(-6.10039 + 23.0546i) q^{56} +(1.00927 + 0.484716i) q^{57} +(-15.0068 - 4.02105i) q^{58} +(-7.28138 + 12.6117i) q^{59} +(-1.56520 - 2.71100i) q^{61} +(-9.73012 + 9.73012i) q^{62} +(-7.84228 + 1.22420i) q^{63} +24.4417i q^{64} +(-1.45338 + 7.72639i) q^{66} +(5.53719 - 1.48369i) q^{67} +(7.11587 - 26.5568i) q^{68} +(-9.99515 + 3.50941i) q^{69} -2.51730i q^{71} +(-24.7618 + 10.8664i) q^{72} +(-0.618633 - 2.30877i) q^{73} +(-2.07979 + 3.60230i) q^{74} -3.44506 q^{76} +(-0.0138482 - 4.43587i) q^{77} +(-6.49445 - 3.11904i) q^{78} +(0.693657 - 0.400483i) q^{79} +(-6.62350 - 6.09338i) q^{81} +(2.39724 - 8.94661i) q^{82} +(9.09949 + 9.09949i) q^{83} +(20.1210 - 13.8421i) q^{84} +(9.64887 - 5.57078i) q^{86} +(5.60793 + 8.20652i) q^{87} +(-3.91140 - 14.5975i) q^{88} +(-4.64586 - 8.04687i) q^{89} +(3.92978 + 1.03984i) q^{91} +(23.0483 - 23.0483i) q^{92} +(8.77825 - 0.667247i) q^{93} +(-18.4576 - 10.6565i) q^{94} +(21.6442 - 25.2053i) q^{96} +(-8.56296 - 8.56296i) q^{97} +(-13.3165 + 13.4838i) q^{98} +(3.92578 - 3.14442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{6}+O(q^{10}) $ 80 * q + 16 * q^6	$ 80 q + 16 q^{6} + 72 q^{16} + 44 q^{21} + 72 q^{31} - 240 q^{36} - 92 q^{51} - 24 q^{61} - 216 q^{66} - 208 q^{76} - 20 q^{81} - 40 q^{91} - 156 q^{96}+O(q^{100}) $ 80 * q + 16 * q^6 + 72 * q^16 + 44 * q^21 + 72 * q^31 - 240 * q^36 - 92 * q^51 - 24 * q^61 - 216 * q^66 - 208 * q^76 - 20 * q^81 - 40 * q^91 - 156 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.61504	+	0.700699i	1.84911	+	0.495469i	0.999490	−	0.0319203i	$-0.0101623\pi$
$2$	2.61504	+	0.700699i	1.84911	+	0.495469i	0.849624	+	0.527389i	$0.176829\pi$
$3$	−0.977224	−	1.43005i	−0.564200	−	0.825638i
$3$	−0.977224	−	1.43005i	−0.564200	−	0.825638i
$4$	4.61542	+	2.66471i	2.30771	+	1.33236i
$5$		0			0
$5$		0			0
$6$	−1.55345	−	4.42437i	−0.634193	−	1.80624i
$7$	1.33002	+	2.28715i	0.502701	+	0.864460i
$7$	1.33002	+	2.28715i	0.502701	+	0.864460i
$8$	6.37367	+	6.37367i	2.25343	+	2.25343i
$9$	−1.09007	+	2.79495i	−0.363356	+	0.931650i
$10$		0			0
$11$	−1.45198	−	0.838304i	−0.437790	−	0.252758i	0.264870	−	0.964284i	$-0.414671\pi$
$11$	−1.45198	−	0.838304i	−0.437790	−	0.252758i	−0.702660	+	0.711526i	$0.748004\pi$
$12$	−0.699631	−	9.20429i	−0.201966	−	2.65705i
$13$	1.08642	−	1.08642i	0.301320	−	0.301320i	−0.540210	−	0.841530i	$-0.681655\pi$
$13$	1.08642	−	1.08642i	0.301320	−	0.301320i	0.841530	+	0.540210i	$0.181655\pi$
$14$	1.87546	+	6.91293i	0.501239	+	1.84756i
$15$		0			0
$16$	6.87197	+	11.9026i	1.71799	+	2.97565i
$17$	−1.33520	−	4.98305i	−0.323834	−	1.20857i	−0.915478	−	0.402367i	$-0.868187\pi$
$17$	−1.33520	−	4.98305i	−0.323834	−	1.20857i	0.591644	−	0.806199i	$-0.298479\pi$
$18$	−4.80899	+	6.54511i	−1.13349	+	1.54270i
$19$	−0.559817	+	0.323211i	−0.128431	+	0.0741496i	−0.562839	−	0.826567i	$-0.690291\pi$
$19$	−0.559817	+	0.323211i	−0.128431	+	0.0741496i	0.434408	+	0.900716i	$0.356958\pi$
$20$		0			0
$21$	1.97100	−	4.13705i	0.430107	−	0.902778i
$22$	−3.20960	−	3.20960i	−0.684290	−	0.684290i
$23$	1.58296	−	5.90767i	0.330069	−	1.23183i	−0.579048	−	0.815294i	$-0.696576\pi$
$23$	1.58296	−	5.90767i	0.330069	−	1.23183i	0.909117	−	0.416541i	$-0.136758\pi$
$24$	2.88615	−	15.3431i	0.589132	−	3.13191i
$25$		0			0
$26$	3.60230	−	2.07979i	0.706469	−	0.407880i
$27$	5.06215	−	1.17244i	0.974212	−	0.225637i
$28$	0.0440191	+	14.1003i	0.00831882	+	2.66470i
$29$	−5.73864			−1.06564			−0.532819	−	0.846229i	$-0.678867\pi$
$29$	−5.73864			−1.06564			−0.532819	+	0.846229i	$0.678867\pi$
$30$		0			0
$31$	−2.54137	+	4.40179i	−0.456444	+	0.790584i	−0.998770	−	0.0495839i	$-0.984210\pi$
$31$	−2.54137	+	4.40179i	−0.456444	+	0.790584i	0.542326	+	0.840168i	$0.317544\pi$
$32$	4.96450	+	18.5278i	0.877609	+	3.27528i
$33$	0.220100	+	2.89562i	0.0383145	+	0.504062i
$34$		−	13.9665i		−	2.39523i
$35$		0			0
$36$	−12.4789	+	9.99515i	−2.07981	+	1.66586i
$37$	−0.397659	+	1.48408i	−0.0653747	+	0.243982i	−0.990879	−	0.134756i	$-0.956975\pi$
$37$	−0.397659	+	1.48408i	−0.0653747	+	0.243982i	0.925504	+	0.378738i	$0.123642\pi$
$38$	−1.69042	+	0.452947i	−0.274222	+	0.0734776i
$39$	−2.61532	−	0.491958i	−0.418786	−	0.0787764i
$40$		0			0
$41$		−	3.42121i		−	0.534303i	−0.963655	−	0.267152i	$-0.913918\pi$
$41$		−	3.42121i		−	0.534303i	0.963655	−	0.267152i	$-0.0860824\pi$
$42$	8.05307	−	9.43748i	1.24262	−	1.45623i
$43$	2.91002	−	2.91002i	0.443774	−	0.443774i	−0.449504	−	0.893278i	$-0.648399\pi$
$43$	2.91002	−	2.91002i	0.443774	−	0.443774i	0.893278	+	0.449504i	$0.148399\pi$
$44$	−4.46768	−	7.73825i	−0.673528	−	1.16658i
$45$		0			0
$46$	8.27899	−	14.3396i	1.22067	−	2.11426i
$47$	−7.60419	−	2.03754i	−1.10919	−	0.297205i	−0.342686	−	0.939450i	$-0.611337\pi$
$47$	−7.60419	−	2.03754i	−1.10919	−	0.297205i	−0.766500	+	0.642245i	$0.778003\pi$
$48$	10.3058	−	21.4587i	1.48752	−	3.09730i
$49$	−3.46208	+	6.08391i	−0.494583	+	0.869130i
$50$		0			0
$51$	−5.82120	+	6.77896i	−0.815131	+	0.949244i
$52$	7.90931	−	2.11929i	1.09682	−	0.293893i
$53$	−2.37411	+	0.636140i	−0.326108	+	0.0873805i	−0.418159	−	0.908374i	$-0.637325\pi$
$53$	−2.37411	+	0.636140i	−0.326108	+	0.0873805i	0.0920506	+	0.995754i	$0.470658\pi$
$54$	14.0593	+	0.481054i	1.91322	+	0.0654632i
$55$		0			0
$56$	−6.10039	+	23.0546i	−0.815199	+	3.08080i
$57$	1.00927	+	0.484716i	0.133681	+	0.0642022i
$58$	−15.0068	−	4.02105i	−1.97049	−	0.527990i
$59$	−7.28138	+	12.6117i	−0.947955	+	1.64191i	−0.198231	+	0.980155i	$0.563520\pi$
$59$	−7.28138	+	12.6117i	−0.947955	+	1.64191i	−0.749724	+	0.661751i	$0.769814\pi$
$60$		0			0
$61$	−1.56520	−	2.71100i	−0.200403	−	0.347108i	0.748255	−	0.663411i	$-0.230892\pi$
$61$	−1.56520	−	2.71100i	−0.200403	−	0.347108i	−0.948658	+	0.316303i	$0.897558\pi$
$62$	−9.73012	+	9.73012i	−1.23573	+	1.23573i
$63$	−7.84228	+	1.22420i	−0.988034	+	0.154235i
$64$			24.4417i			3.05521i
$65$		0			0
$66$	−1.45338	+	7.72639i	−0.178899	+	0.951052i
$67$	5.53719	−	1.48369i	0.676476	−	0.181261i	0.0958058	−	0.995400i	$-0.469457\pi$
$67$	5.53719	−	1.48369i	0.676476	−	0.181261i	0.580670	+	0.814139i	$0.302791\pi$
$68$	7.11587	−	26.5568i	0.862926	−	3.22048i
$69$	−9.99515	+	3.50941i	−1.20327	+	0.422484i
$70$		0			0
$71$		−	2.51730i		−	0.298748i	−0.988781	−	0.149374i	$-0.952274\pi$
$71$		−	2.51730i		−	0.298748i	0.988781	−	0.149374i	$-0.0477258\pi$
$72$	−24.7618	+	10.8664i	−2.91821	+	1.28061i
$73$	−0.618633	−	2.30877i	−0.0724055	−	0.270221i	0.920227	−	0.391385i	$-0.128004\pi$
$73$	−0.618633	−	2.30877i	−0.0724055	−	0.270221i	−0.992632	+	0.121164i	$0.961337\pi$
$74$	−2.07979	+	3.60230i	−0.241771	+	0.418759i
$75$		0			0
$76$	−3.44506			−0.395175
$77$	−0.0138482	−	4.43587i	−0.00157814	−	0.505514i
$78$	−6.49445	−	3.11904i	−0.735352	−	0.353162i
$79$	0.693657	−	0.400483i	0.0780425	−	0.0450579i	−0.460471	−	0.887675i	$-0.652319\pi$
$79$	0.693657	−	0.400483i	0.0780425	−	0.0450579i	0.538513	+	0.842617i	$0.318986\pi$
$80$		0			0
$81$	−6.62350	−	6.09338i	−0.735945	−	0.677042i
$82$	2.39724	−	8.94661i	0.264730	−	0.987987i
$83$	9.09949	+	9.09949i	0.998799	+	0.998799i	0.999999	−	0.00120051i	$-0.000382134\pi$
$83$	9.09949	+	9.09949i	0.998799	+	0.998799i	−0.00120051	+	0.999999i	$0.500382\pi$
$84$	20.1210	−	13.8421i	2.19538	−	1.51029i
$85$		0			0
$86$	9.64887	−	5.57078i	1.04046	−	0.600712i
$87$	5.60793	+	8.20652i	0.601233	+	0.879831i
$88$	−3.91140	−	14.5975i	−0.416957	−	1.55610i
$89$	−4.64586	−	8.04687i	−0.492460	−	0.852966i	0.507502	−	0.861651i	$-0.330569\pi$
$89$	−4.64586	−	8.04687i	−0.492460	−	0.852966i	−0.999962	+	0.00868447i	$0.997236\pi$
$90$		0			0
$91$	3.92978	+	1.03984i	0.411953	+	0.109005i
$92$	23.0483	−	23.0483i	2.40295	−	2.40295i
$93$	8.77825	−	0.667247i	0.910262	−	0.0691903i
$94$	−18.4576	−	10.6565i	−1.90375	−	1.09913i
$95$		0			0
$96$	21.6442	−	25.2053i	2.20905	−	2.57250i
$97$	−8.56296	−	8.56296i	−0.869437	−	0.869437i	0.122973	−	0.992410i	$-0.460757\pi$
$97$	−8.56296	−	8.56296i	−0.869437	−	0.869437i	−0.992410	+	0.122973i	$0.960757\pi$
$98$	−13.3165	+	13.4838i	−1.34517	+	1.36207i
$99$	3.92578	−	3.14442i	0.394556	−	0.316026i
$100$		0			0
$101$	9.76827	+	5.63971i	0.971979	+	0.561173i	0.899839	−	0.436222i	$-0.143684\pi$
$101$	9.76827	+	5.63971i	0.971979	+	0.561173i	0.0721403	+	0.997394i	$0.477017\pi$
$102$	−19.9727	+	13.6484i	−1.97759	+	1.35139i
$103$	8.91630	+	2.38912i	0.878550	+	0.235407i	0.669781	−	0.742558i	$-0.266388\pi$
$103$	8.91630	+	2.38912i	0.878550	+	0.235407i	0.208768	+	0.977965i	$0.433055\pi$
$104$	13.8490			1.35801
$105$		0			0
$106$	−6.65413			−0.646306
$107$	−3.57254	−	0.957259i	−0.345370	−	0.0925417i	0.0819642	−	0.996635i	$-0.473881\pi$
$107$	−3.57254	−	0.957259i	−0.345370	−	0.0925417i	−0.427335	+	0.904094i	$0.640547\pi$
$108$	26.4882	+	8.07787i	2.54883	+	0.777293i
$109$	7.53860	+	4.35241i	0.722067	+	0.416885i	0.815513	−	0.578739i	$-0.196455\pi$
$109$	7.53860	+	4.35241i	0.722067	+	0.416885i	−0.0934461	+	0.995624i	$0.529788\pi$
$110$		0			0
$111$	2.51091	−	0.881610i	0.238325	−	0.0836787i
$112$	−18.0831	+	31.5479i	−1.70869	+	2.98100i
$113$	−0.200176	−	0.200176i	−0.0188309	−	0.0188309i	0.697629	−	0.716460i	$-0.254239\pi$
$113$	−0.200176	−	0.200176i	−0.0188309	−	0.0188309i	−0.716460	+	0.697629i	$0.754239\pi$
$114$	2.29965	+	1.97475i	0.215382	+	0.184952i
$115$		0			0
$116$	−26.4862	−	15.2918i	−2.45918	−	1.41981i
$117$	1.85223	+	4.22078i	0.171238	+	0.390211i
$118$	−27.8781	+	27.8781i	−2.56639	+	2.56639i
$119$	9.62111	−	9.68137i	0.881966	−	0.887490i
$120$		0			0
$121$	−4.09449	−	7.09187i	−0.372227	−	0.644715i
$122$	−2.19346	−	8.18611i	−0.198587	−	0.741136i
$123$	−4.89249	+	3.34329i	−0.441141	+	0.301454i
$124$	−23.4590	+	13.5441i	−2.10668	+	1.21629i
$125$		0			0
$126$	−21.3657	−	2.29374i	−1.90341	−	0.204342i
$127$	9.46140	+	9.46140i	0.839563	+	0.839563i	0.988801	−	0.149238i	$-0.0476821\pi$
$127$	9.46140	+	9.46140i	0.839563	+	0.839563i	−0.149238	+	0.988801i	$0.547682\pi$
$128$	−7.19725	+	26.8605i	−0.636153	+	2.37416i
$129$	−7.00520	−	1.31772i	−0.616774	−	0.116019i
$130$		0			0
$131$	6.23258	−	3.59838i	0.544543	−	0.314392i	−0.202375	−	0.979308i	$-0.564866\pi$
$131$	6.23258	−	3.59838i	0.544543	−	0.314392i	0.746918	+	0.664916i	$0.231533\pi$
$132$	−6.70014	+	13.9510i	−0.583172	+	1.21428i
$133$	−1.48380	−	0.850507i	−0.128662	−	0.0737483i
$134$	15.5196			1.34069
$135$		0			0
$136$	23.2501	−	40.2704i	1.99368	−	3.45316i
$137$	−1.71534	−	6.40175i	−0.146552	−	0.546938i	−0.999681	−	0.0252394i	$-0.991965\pi$
$137$	−1.71534	−	6.40175i	−0.146552	−	0.546938i	0.853130	−	0.521699i	$-0.174701\pi$
$138$	−28.5968	+	2.17368i	−2.43432	+	0.185036i
$139$			2.02434i			0.171703i	0.996308	+	0.0858513i	$0.0273610\pi$
$139$			2.02434i			0.171703i	−0.996308	+	0.0858513i	$0.972639\pi$
$140$		0			0
$141$	4.51722	+	12.8655i	0.380419	+	1.08347i
$142$	1.76387	−	6.58283i	0.148020	−	0.552419i
$143$	−2.48823	+	0.666718i	−0.208076	+	0.0557538i
$144$	−40.7581	+	6.23217i	−3.39651	+	0.519347i
$145$		0			0
$146$		−	6.47101i		−	0.535544i
$147$	12.0835	−	0.994403i	0.996631	−	0.0820170i
$148$	−5.79002	+	5.79002i	−0.475937	+	0.475937i
$149$	6.45539	+	11.1811i	0.528846	+	0.915988i	0.999434	+	0.0336351i	$0.0107084\pi$
$149$	6.45539	+	11.1811i	0.528846	+	0.915988i	−0.470588	+	0.882353i	$0.655958\pi$
$150$		0			0
$151$	−6.33797	+	10.9777i	−0.515777	+	0.893352i	0.484055	+	0.875037i	$0.339163\pi$
$151$	−6.33797	+	10.9777i	−0.515777	+	0.893352i	−0.999832	+	0.0183146i	$0.994170\pi$
$152$	−5.62813	−	1.50805i	−0.456501	−	0.122319i
$153$	15.3828	+	1.70003i	1.24363	+	0.137440i
$154$	3.07199	−	11.6097i	0.247548	−	0.935535i
$155$		0			0
$156$	−10.7599	−	9.23966i	−0.861478	−	0.739765i
$157$	−13.2715	+	3.55609i	−1.05918	+	0.283807i	−0.746041	−	0.665900i	$-0.768048\pi$
$157$	−13.2715	+	3.55609i	−1.05918	+	0.283807i	−0.313140	+	0.949707i	$0.601381\pi$
$158$	2.09456	−	0.561236i	0.166634	−	0.0446495i
$159$	3.22974	+	2.77343i	0.256135	+	0.219947i
$160$		0			0
$161$	15.6171	−	4.23688i	1.23080	−	0.333913i
$162$	−13.0511	−	20.5755i	−1.02539	−	1.61657i
$163$	22.7676	+	6.10055i	1.78329	+	0.477832i	0.991178	−	0.132541i	$-0.0423135\pi$
$163$	22.7676	+	6.10055i	1.78329	+	0.477832i	0.792115	+	0.610372i	$0.208980\pi$
$164$	9.11654	−	15.7903i	0.711882	−	1.23302i
$165$		0			0
$166$	17.4196	+	30.1716i	1.35202	+	2.34177i
$167$	−11.0645	+	11.0645i	−0.856199	+	0.856199i	−0.990888	−	0.134689i	$-0.956997\pi$
$167$	−11.0645	+	11.0645i	−0.856199	+	0.856199i	0.134689	+	0.990888i	$0.456997\pi$
$168$	38.9307	−	13.8057i	3.00357	−	1.06513i
$169$			10.6394i			0.818413i
$170$		0			0
$171$	−0.293119	−	1.91698i	−0.0224154	−	0.146595i
$172$	21.1853	−	5.67659i	1.61537	−	0.432836i
$173$	1.22632	−	4.57669i	0.0932353	−	0.347959i	−0.903511	−	0.428566i	$-0.859019\pi$
$173$	1.22632	−	4.57669i	0.0932353	−	0.347959i	0.996746	+	0.0806066i	$0.0256857\pi$
$174$	8.91468	+	25.3899i	0.675820	+	1.92480i
$175$		0			0
$176$		−	23.0432i		−	1.73695i
$177$	25.1509	−	1.91175i	1.89046	−	0.143696i
$178$	−6.51069	−	24.2982i	−0.487997	−	1.82123i
$179$	10.8365	−	18.7693i	0.809955	−	1.40288i	−0.102940	−	0.994688i	$-0.532825\pi$
$179$	10.8365	−	18.7693i	0.809955	−	1.40288i	0.912895	−	0.408195i	$-0.133842\pi$
$180$		0			0
$181$	11.0030			0.817850			0.408925	−	0.912568i	$-0.365904\pi$
$181$	11.0030			0.817850			0.408925	+	0.912568i	$0.365904\pi$
$182$	9.54793	+	5.47283i	0.707739	+	0.405673i
$183$	−2.34731	+	4.88756i	−0.173518	+	0.361299i
$184$	47.7428	−	27.5643i	3.51964	−	2.03207i
$185$		0			0
$186$	23.4230	+	4.40603i	1.71746	+	0.323066i
$187$	−2.23861	+	8.35462i	−0.163704	+	0.610950i
$188$	−29.6671	−	29.6671i	−2.16369	−	2.16369i
$189$	9.41432	+	10.0185i	0.684791	+	0.728739i
$190$		0			0
$191$	5.65629	−	3.26566i	0.409275	−	0.236295i	−0.281203	−	0.959648i	$-0.590734\pi$
$191$	5.65629	−	3.26566i	0.409275	−	0.236295i	0.690478	+	0.723353i	$0.257400\pi$
$192$	34.9528	−	23.8850i	2.52250	−	1.72375i
$193$	−6.20030	−	23.1398i	−0.446308	−	1.66564i	−0.712461	−	0.701712i	$-0.752419\pi$
$193$	−6.20030	−	23.1398i	−0.446308	−	1.66564i	0.266153	−	0.963931i	$-0.414247\pi$
$194$	−16.3925	−	28.3926i	−1.17691	−	2.03847i
$195$		0			0
$196$	−32.1908	+	18.8543i	−2.29935	+	1.34674i
$197$	−6.21500	+	6.21500i	−0.442800	+	0.442800i	−0.892952	−	0.450152i	$-0.851370\pi$
$197$	−6.21500	+	6.21500i	−0.442800	+	0.442800i	0.450152	+	0.892952i	$0.351370\pi$
$198$	12.4694	−	5.47200i	0.886160	−	0.388878i
$199$	17.1284	+	9.88909i	1.21420	+	0.701019i	0.963672	−	0.267090i	$-0.0860621\pi$
$199$	17.1284	+	9.88909i	1.21420	+	0.701019i	0.250529	+	0.968109i	$0.419395\pi$
$200$		0			0
$201$	−7.53282	−	6.46855i	−0.531324	−	0.456257i
$202$	21.5927	+	21.5927i	1.51926	+	1.51926i
$203$	−7.63252	−	13.1251i	−0.535698	−	0.921202i
$204$	−44.9312	+	15.7759i	−3.14582	+	1.10453i
$205$		0			0
$206$	21.6425	+	12.4953i	1.50790	+	0.870588i
$207$	14.7861	+	10.8640i	1.02771	+	0.755104i
$208$	20.3971	+	5.46540i	1.41429	+	0.378957i
$209$	1.08380			0.0749677
$210$		0			0
$211$	−6.75099			−0.464757			−0.232379	−	0.972625i	$-0.574651\pi$
$211$	−6.75099			−0.464757			−0.232379	+	0.972625i	$0.574651\pi$
$212$	−12.6526	−	3.39026i	−0.868985	−	0.232844i
$213$	−3.59985	+	2.45996i	−0.246658	+	0.168554i
$214$	−8.67159	−	5.00654i	−0.592778	−	0.342240i
$215$		0			0
$216$	39.7372	+	24.7917i	2.70378	+	1.68686i
$217$	−13.4476	+	0.0419816i	−0.912884	+	0.00284990i
$218$	16.6640	+	16.6640i	1.12863	+	1.12863i
$219$	−2.69711	+	3.14086i	−0.182254	+	0.212239i
$220$		0			0
$221$	−6.86430	−	3.96311i	−0.461743	−	0.266587i
$222$	7.18388	−	0.546057i	0.482150	−	0.0366489i
$223$	−8.86255	+	8.86255i	−0.593480	+	0.593480i	−0.938570	−	0.345090i	$-0.887848\pi$
$223$	−8.86255	+	8.86255i	−0.593480	+	0.593480i	0.345090	+	0.938570i	$0.387848\pi$
$224$	−35.7729	+	35.9969i	−2.39017	+	2.40514i
$225$		0			0
$226$	−0.383205	−	0.663730i	−0.0254904	−	0.0441507i
$227$	4.47781	+	16.7114i	0.297203	+	1.10918i	0.939452	+	0.342680i	$0.111335\pi$
$227$	4.47781	+	16.7114i	0.297203	+	1.10918i	−0.642250	+	0.766495i	$0.721999\pi$
$228$	3.36659	+	4.92659i	0.222958	+	0.326271i
$229$	9.48704	−	5.47734i	0.626921	−	0.361953i	−0.152638	−	0.988282i	$-0.548777\pi$
$229$	9.48704	−	5.47734i	0.626921	−	0.361953i	0.779559	+	0.626329i	$0.215443\pi$
$230$		0			0
$231$	−6.32996	+	4.35464i	−0.416481	+	0.286514i
$232$	−36.5762	−	36.5762i	−2.40134	−	2.40134i
$233$	5.58209	−	20.8326i	0.365695	−	1.36479i	−0.500782	−	0.865573i	$-0.666954\pi$
$233$	5.58209	−	20.8326i	0.365695	−	1.36479i	0.866477	−	0.499217i	$-0.166379\pi$
$234$	1.88616	+	12.3354i	0.123302	+	0.806388i
$235$		0			0
$236$	−67.2132	+	38.8056i	−4.37521	+	2.52603i
$237$	−1.25057	−	0.600601i	−0.0812331	−	0.0390132i
$238$	31.9433	−	18.5757i	2.07058	−	1.20408i
$239$	−5.56541			−0.359997			−0.179998	−	0.983667i	$-0.557609\pi$
$239$	−5.56541			−0.359997			−0.179998	+	0.983667i	$0.557609\pi$
$240$		0			0
$241$	−3.56203	+	6.16961i	−0.229450	+	0.397420i	−0.957645	−	0.287950i	$-0.907026\pi$
$241$	−3.56203	+	6.16961i	−0.229450	+	0.397420i	0.728195	+	0.685370i	$0.240360\pi$
$242$	−5.73801	−	21.4145i	−0.368853	−	1.37658i
$243$	−2.24117	+	15.4265i	−0.143771	+	0.989611i
$244$		−	16.6832i		−	1.06803i
$245$		0			0
$246$	−15.1367	+	5.31467i	−0.965081	+	0.338851i
$247$	−0.257055	+	0.959343i	−0.0163560	+	0.0610415i
$248$	−44.2534	+	11.8577i	−2.81009	+	0.752962i
$249$	4.12046	−	21.9049i	0.261124	−	1.38817i
$250$		0			0
$251$			19.9450i			1.25892i	0.777033	+	0.629460i	$0.216724\pi$
$251$			19.9450i			1.25892i	−0.777033	+	0.629460i	$0.783276\pi$
$252$	−39.4575	−	15.2472i	−2.48559	−	0.960485i
$253$	−7.25085	+	7.25085i	−0.455857	+	0.455857i
$254$	18.1124	+	31.3715i	1.13647	+	1.96843i
$255$		0			0
$256$	−13.2006	+	22.8640i	−0.825035	+	1.42900i
$257$	−6.75694	−	1.81052i	−0.421486	−	0.112937i	0.0418408	−	0.999124i	$-0.486678\pi$
$257$	−6.75694	−	1.81052i	−0.421486	−	0.112937i	−0.463327	+	0.886187i	$0.653344\pi$
$258$	−17.3956	−	8.35444i	−1.08300	−	0.520125i
$259$	−3.92321	+	1.06436i	−0.243776	+	0.0661361i
$260$		0			0
$261$	6.25551	−	16.0392i	0.387206	−	0.992802i
$262$	18.8198	−	5.04276i	1.16269	−	0.311543i
$263$	−9.22535	+	2.47193i	−0.568859	+	0.152425i	−0.531773	−	0.846887i	$-0.678474\pi$
$263$	−9.22535	+	2.47193i	−0.568859	+	0.152425i	−0.0370860	+	0.999312i	$0.511808\pi$
$264$	−17.0529	+	19.8585i	−1.04953	+	1.22221i
$265$		0			0
$266$	−3.28425	−	3.26381i	−0.201370	−	0.200117i
$267$	−6.96735	+	14.5074i	−0.426395	+	0.887837i
$268$	29.5101	+	7.90720i	1.80261	+	0.483009i
$269$	6.91904	−	11.9841i	0.421861	−	0.730685i	−0.574260	−	0.818673i	$-0.694710\pi$
$269$	6.91904	−	11.9841i	0.421861	−	0.730685i	0.996122	+	0.0879877i	$0.0280436\pi$
$270$		0			0
$271$	−8.90276	−	15.4200i	−0.540804	−	0.936700i	−0.998858	−	0.0477757i	$-0.984787\pi$
$271$	−8.90276	−	15.4200i	−0.540804	−	0.936700i	0.458054	−	0.888924i	$-0.348547\pi$
$272$	50.1357	−	50.1357i	3.03992	−	3.03992i
$273$	−2.35325	−	6.63593i	−0.142425	−	0.401625i
$274$		−	17.9428i		−	1.08396i
$275$		0			0
$276$	−55.4834	−	10.4368i	−3.33971	−	0.628221i
$277$	−19.7304	+	5.28675i	−1.18549	+	0.317650i	−0.797101	−	0.603846i	$-0.793634\pi$
$277$	−19.7304	+	5.28675i	−1.18549	+	0.317650i	−0.388386	+	0.921497i	$0.626967\pi$
$278$	−1.41845	+	5.29374i	−0.0850732	+	0.317498i
$279$	−9.53251	−	11.9013i	−0.570696	−	0.712510i
$280$		0			0
$281$			7.79434i			0.464971i	0.972600	+	0.232486i	$0.0746859\pi$
$281$			7.79434i			0.464971i	−0.972600	+	0.232486i	$0.925314\pi$
$282$	2.79790	+	36.8090i	0.166613	+	2.19194i
$283$	7.02788	+	26.2284i	0.417764	+	1.55912i	0.779234	+	0.626733i	$0.215608\pi$
$283$	7.02788	+	26.2284i	0.417764	+	1.55912i	−0.361471	+	0.932384i	$0.617725\pi$
$284$	6.70787	−	11.6184i	0.398039	−	0.689424i
$285$		0			0
$286$	−6.97398			−0.412380
$287$	7.82481	−	4.55028i	0.461884	−	0.268595i
$288$	−57.1959	−	6.32100i	−3.37030	−	0.372469i
$289$	−8.32557	+	4.80677i	−0.489739	+	0.282751i
$290$		0			0
$291$	−3.87751	+	20.6134i	−0.227304	+	1.20838i
$292$	3.29696	−	12.3044i	0.192940	−	0.720061i
$293$	20.0716	+	20.0716i	1.17259	+	1.17259i	0.981589	+	0.191003i	$0.0611741\pi$
$293$	20.0716	+	20.0716i	1.17259	+	1.17259i	0.191003	+	0.981589i	$0.438826\pi$
$294$	32.2957	+	5.86649i	1.88352	+	0.342141i
$295$		0			0
$296$	−11.9936	+	6.92451i	−0.697114	+	0.402479i
$297$	−8.33303	−	2.54125i	−0.483532	−	0.147458i
$298$	9.04656	+	33.7622i	0.524053	+	1.95579i
$299$	−4.69848	−	8.13800i	−0.271720	−	0.470633i
$300$		0			0
$301$	10.5260	+	2.78525i	0.606710	+	0.160539i
$302$	−24.2661	+	24.2661i	−1.39636	+	1.39636i
$303$	−1.48073	−	19.4803i	−0.0850656	−	1.11912i
$304$	−7.69409	−	4.44219i	−0.441286	−	0.254777i
$305$		0			0
$306$	39.0356	+	15.2244i	2.23151	+	0.870321i
$307$	−13.1833	−	13.1833i	−0.752410	−	0.752410i	0.222518	−	0.974929i	$-0.428572\pi$
$307$	−13.1833	−	13.1833i	−0.752410	−	0.752410i	−0.974929	+	0.222518i	$0.928572\pi$
$308$	11.7564	−	20.5103i	0.669883	−	1.16868i
$309$	−5.29667	−	15.0854i	−0.301317	−	0.858180i
$310$		0			0
$311$	3.59283	+	2.07432i	0.203731	+	0.117624i	0.598394	−	0.801202i	$-0.295806\pi$
$311$	3.59283	+	2.07432i	0.203731	+	0.117624i	−0.394664	+	0.918826i	$0.629139\pi$
$312$	−13.5336	−	19.8047i	−0.766188	−	1.12122i
$313$	−23.4084	−	6.27228i	−1.32312	−	0.354530i	−0.472977	−	0.881075i	$-0.656820\pi$
$313$	−23.4084	−	6.27228i	−1.32312	−	0.354530i	−0.850147	+	0.526545i	$0.823487\pi$
$314$	−37.1973			−2.09916
$315$		0			0
$316$	4.26869			0.240133
$317$	12.8997	+	3.45645i	0.724517	+	0.194134i	0.602186	−	0.798356i	$-0.294296\pi$
$317$	12.8997	+	3.45645i	0.724517	+	0.194134i	0.122331	+	0.992489i	$0.460963\pi$
$318$	6.50257	+	9.51572i	0.364646	+	0.533615i
$319$	8.33242	+	4.81072i	0.466526	+	0.269349i
$320$		0			0
$321$	2.12224	+	6.04435i	0.118452	+	0.337363i
$322$	43.8081	−	0.136763i	2.44133	−	0.00762149i
$323$	2.35804	+	2.35804i	0.131205	+	0.131205i
$324$	−14.3331	−	45.7732i	−0.796285	−	2.54296i
$325$		0			0
$326$	55.2635	+	31.9064i	3.06076	+	1.76713i
$327$	−1.14274	−	15.0338i	−0.0631938	−	0.831373i
$328$	21.8056	−	21.8056i	1.20402	−	1.20402i
$329$	−5.45360	−	20.1019i	−0.300667	−	1.10825i
$330$		0			0
$331$	7.01913	+	12.1575i	0.385806	+	0.668236i	0.991881	−	0.127172i	$-0.0405900\pi$
$331$	7.01913	+	12.1575i	0.385806	+	0.668236i	−0.606074	+	0.795408i	$0.707257\pi$
$332$	17.7504	+	66.2455i	0.974181	+	3.63569i
$333$	−3.71446	−	2.72919i	−0.203551	−	0.149559i
$334$	−36.6871	+	21.1813i	−2.00743	+	1.15899i
$335$		0			0
$336$	62.7862	−	4.96966i	3.42527	−	0.271117i
$337$	−9.43624	−	9.43624i	−0.514025	−	0.514025i	0.401732	−	0.915757i	$-0.368408\pi$
$337$	−9.43624	−	9.43624i	−0.514025	−	0.514025i	−0.915757	+	0.401732i	$0.868408\pi$
$338$	−7.45499	+	27.8224i	−0.405498	+	1.51334i
$339$	−0.0906442	+	0.481877i	−0.00492312	+	0.0261719i
$340$		0			0
$341$	7.38007	−	4.26089i	0.399653	−	0.230740i
$342$	0.576709	−	5.21838i	0.0311849	−	0.282178i
$343$	−18.5194	+	0.173450i	−0.999956	+	0.00936542i
$344$	37.0950			2.00003
$345$		0			0
$346$	6.41376	−	11.1089i	0.344806	−	0.597221i
$347$	−5.69038	−	21.2368i	−0.305475	−	1.14005i	−0.932535	−	0.361079i	$-0.882409\pi$
$347$	−5.69038	−	21.2368i	−0.305475	−	1.14005i	0.627060	−	0.778971i	$-0.284258\pi$
$348$	4.01493	+	52.8201i	0.215223	+	2.83145i
$349$		−	15.3591i		−	0.822156i	−0.911600	−	0.411078i	$-0.865152\pi$
$349$		−	15.3591i		−	0.822156i	0.911600	−	0.411078i	$-0.134848\pi$
$350$		0			0
$351$	4.22587	−	6.77341i	0.225560	−	0.361538i
$352$	8.32353	−	31.0638i	0.443645	−	1.65571i
$353$	27.9751	−	7.49591i	1.48897	−	0.398967i	0.579578	−	0.814917i	$-0.303217\pi$
$353$	27.9751	−	7.49591i	1.48897	−	0.398967i	0.909388	+	0.415950i	$0.136551\pi$
$354$	67.1102	+	12.6239i	3.56687	+	0.670951i
$355$		0			0
$356$		−	49.5195i		−	2.62453i
$357$	−23.2468	−	4.29778i	−1.23035	−	0.227463i
$358$	41.4894	−	41.4894i	2.19278	−	2.19278i
$359$	12.0055	+	20.7941i	0.633625	+	1.09747i	0.986805	+	0.161916i	$0.0517673\pi$
$359$	12.0055	+	20.7941i	0.633625	+	1.09747i	−0.353179	+	0.935556i	$0.614899\pi$
$360$		0			0
$361$	−9.29107	+	16.0926i	−0.489004	+	0.846979i
$362$	28.7734	+	7.70982i	1.51230	+	0.405219i
$363$	−6.14047	+	12.7857i	−0.322291	+	0.671073i
$364$	15.3667	+	15.2710i	0.805434	+	0.800420i
$365$		0			0
$366$	−9.56302	+	11.1364i	−0.499867	+	0.582110i
$367$	20.3887	−	5.46313i	1.06428	−	0.285173i	0.316139	−	0.948713i	$-0.397613\pi$
$367$	20.3887	−	5.46313i	1.06428	−	0.285173i	0.748141	+	0.663540i	$0.230947\pi$
$368$	81.1946	−	21.7560i	4.23256	−	1.13411i
$369$	9.56211	+	3.72935i	0.497784	+	0.194142i
$370$		0			0
$371$	−4.61256	−	4.58385i	−0.239472	−	0.237982i
$372$	42.2933	+	20.3119i	2.19281	+	1.05312i
$373$	−19.5679	−	5.24320i	−1.01319	−	0.271483i	−0.286226	−	0.958162i	$-0.592401\pi$
$373$	−19.5679	−	5.24320i	−1.01319	−	0.271483i	−0.726960	+	0.686679i	$0.759068\pi$
$374$	−11.7081	+	20.2791i	−0.605413	+	1.04861i
$375$		0			0
$376$	−35.4800	−	61.4532i	−1.82974	−	3.16920i
$377$	−6.23459	+	6.23459i	−0.321098	+	0.321098i
$378$	17.5989	+	32.7954i	0.905190	+	1.68681i
$379$			7.90786i			0.406200i	0.979158	+	0.203100i	$0.0651016\pi$
$379$			7.90786i			0.406200i	−0.979158	+	0.203100i	$0.934898\pi$
$380$		0			0
$381$	4.28434	−	22.7761i	0.219493	−	1.16686i
$382$	17.0797	−	4.57648i	0.873872	−	0.234153i
$383$	−1.52384	+	5.68704i	−0.0778645	+	0.290594i	−0.993868	−	0.110577i	$-0.964730\pi$
$383$	−1.52384	+	5.68704i	−0.0778645	+	0.290594i	0.916003	+	0.401171i	$0.131397\pi$
$384$	45.4451	−	15.9563i	2.31911	−	0.814268i
$385$		0			0
$386$		−	64.8562i		−	3.30109i
$387$	4.96124	+	11.3055i	0.252194	+	0.574690i
$388$	−16.7038	−	62.3395i	−0.848008	−	3.16481i
$389$	−13.1633	+	22.7994i	−0.667404	+	1.15598i	0.311224	+	0.950337i	$0.399261\pi$
$389$	−13.1633	+	22.7994i	−0.667404	+	1.15598i	−0.978628	+	0.205640i	$0.934072\pi$
$390$		0			0
$391$	−31.5518			−1.59564
$392$	−60.8430	+	16.7107i	−3.07304	+	0.844017i
$393$	−11.2365	−	5.39646i	−0.566805	−	0.272215i
$394$	−20.6073	+	11.8976i	−1.03818	+	0.599394i
$395$		0			0
$396$	26.4981	−	4.05173i	1.33158	−	0.203607i
$397$	−0.116274	+	0.433942i	−0.00583564	+	0.0217789i	−0.968782	−	0.247913i	$-0.920255\pi$
$397$	−0.116274	+	0.433942i	−0.00583564	+	0.0217789i	0.962947	+	0.269692i	$0.0869219\pi$
$398$	37.8622	+	37.8622i	1.89786	+	1.89786i
$399$	0.233739	+	2.95304i	0.0117016	+	0.147837i
$400$		0			0
$401$	−0.129764	+	0.0749191i	−0.00648009	+	0.00374128i	−0.503237	−	0.864149i	$-0.667858\pi$
$401$	−0.129764	+	0.0749191i	−0.00648009	+	0.00374128i	0.496756	+	0.867890i	$0.334524\pi$
$402$	−15.1661	−	22.1938i	−0.756418	−	1.10693i
$403$	2.02120	+	7.54322i	0.100683	+	0.375754i
$404$	30.0564	+	52.0593i	1.49536	+	2.59005i
$405$		0			0
$406$	−10.7626	−	39.6708i	−0.534139	−	1.96883i
$407$	1.82151	−	1.82151i	0.0902888	−	0.0902888i
$408$	−80.3092	+	6.10442i	−3.97590	+	0.302214i
$409$	−24.9767	−	14.4203i	−1.23502	−	0.713038i	−0.266946	−	0.963711i	$-0.586015\pi$
$409$	−24.9767	−	14.4203i	−1.23502	−	0.713038i	−0.968072	+	0.250674i	$0.919348\pi$
$410$		0			0
$411$	−7.47852	+	8.70896i	−0.368888	+	0.429581i
$412$	34.7862	+	34.7862i	1.71379	+	1.71379i
$413$	−38.5293	+	0.120283i	−1.89590	+	0.00591874i
$414$	31.0539	+	38.7706i	1.52622	+	1.90547i
$415$		0			0
$416$	25.5226	+	14.7355i	1.25135	+	0.722466i
$417$	2.89491	−	1.97824i	0.141764	−	0.0968746i
$418$	2.83417	+	0.759414i	0.138624	+	0.0371441i
$419$	−2.47327			−0.120827			−0.0604136	−	0.998173i	$-0.519242\pi$
$419$	−2.47327			−0.120827			−0.0604136	+	0.998173i	$0.519242\pi$
$420$		0			0
$421$	33.4246			1.62902			0.814508	−	0.580153i	$-0.197007\pi$
$421$	33.4246			1.62902			0.814508	+	0.580153i	$0.197007\pi$
$422$	−17.6541	−	4.73041i	−0.859389	−	0.230273i
$423$	13.9839	−	19.0323i	0.679921	−	0.925381i
$424$	−19.1863	−	11.0772i	−0.931769	−	0.537957i
$425$		0			0
$426$	−11.1375	+	3.91049i	−0.539611	+	0.189464i
$427$	4.11871	−	7.18552i	0.199318	−	0.347732i
$428$	−13.9379	−	13.9379i	−0.673716	−	0.673716i
$429$	3.38499	+	2.90675i	0.163429	+	0.140339i
$430$		0			0
$431$	−30.2348	−	17.4561i	−1.45636	−	0.840830i	−0.457530	−	0.889194i	$-0.651266\pi$
$431$	−30.2348	−	17.4561i	−1.45636	−	0.840830i	−0.998830	+	0.0483640i	$0.984599\pi$
$432$	48.7420	+	52.1957i	2.34510	+	2.51127i
$433$	19.0825	−	19.0825i	0.917046	−	0.917046i	−0.0797676	−	0.996813i	$-0.525418\pi$
$433$	19.0825	−	19.0825i	0.917046	−	0.917046i	0.996813	+	0.0797676i	$0.0254178\pi$
$434$	−35.1955	−	9.31294i	−1.68944	−	0.447036i
$435$		0			0
$436$	23.1959	+	40.1764i	1.11088	+	1.92410i
$437$	1.02326	+	3.81885i	0.0489490	+	0.182680i
$438$	−9.25384	+	6.32362i	−0.442166	+	0.302154i
$439$	28.5754	−	16.4980i	1.36383	−	0.787406i	0.373697	−	0.927551i	$-0.378090\pi$
$439$	28.5754	−	16.4980i	1.36383	−	0.787406i	0.990131	+	0.140145i	$0.0447568\pi$
$440$		0			0
$441$	−13.2303	−	16.3082i	−0.630016	−	0.776582i
$442$	−15.1735	−	15.1735i	−0.721730	−	0.721730i
$443$	−2.47910	+	9.25212i	−0.117786	+	0.439582i	−0.999480	−	0.0322388i	$-0.989736\pi$
$443$	−2.47910	+	9.25212i	−0.117786	+	0.439582i	0.881695	+	0.471820i	$0.156403\pi$
$444$	13.9381	+	2.62186i	0.661475	+	0.124428i
$445$		0			0
$446$	−29.3859	+	16.9660i	−1.39146	+	0.803362i
$447$	9.68108	−	20.1579i	0.457899	−	0.953436i
$448$	−55.9018	+	32.5080i	−2.64111	+	1.53586i
$449$	13.0426			0.615521			0.307760	−	0.951464i	$-0.400421\pi$
$449$	13.0426			0.615521			0.307760	+	0.951464i	$0.400421\pi$
$450$		0			0
$451$	−2.86801	+	4.96754i	−0.135049	+	0.233913i
$452$	−0.390483	−	1.45730i	−0.0183668	−	0.0685458i
$453$	21.8922	−	1.66406i	1.02859	−	0.0781843i
$454$			46.8386i			2.19825i
$455$		0			0
$456$	3.34335	+	9.52219i	0.156567	+	0.445917i
$457$	−0.575078	+	2.14622i	−0.0269010	+	0.100396i	−0.978071	−	0.208271i	$-0.933216\pi$
$457$	−0.575078	+	2.14622i	−0.0269010	+	0.100396i	0.951170	+	0.308667i	$0.0998830\pi$
$458$	28.6470	−	7.67593i	1.33859	−	0.358673i
$459$	−12.6013	−	23.6595i	−0.588180	−	1.10433i
$460$		0			0
$461$			17.6561i			0.822328i	0.911561	+	0.411164i	$0.134878\pi$
$461$			17.6561i			0.822328i	−0.911561	+	0.411164i	$0.865122\pi$
$462$	−19.6044	+	6.95216i	−0.912080	+	0.323444i
$463$	−17.6479	+	17.6479i	−0.820167	+	0.820167i	−0.986132	−	0.165965i	$-0.946926\pi$
$463$	−17.6479	+	17.6479i	−0.820167	+	0.820167i	0.165965	+	0.986132i	$0.446926\pi$
$464$	−39.4357	−	68.3047i	−1.83076	−	3.17096i
$465$		0			0
$466$	29.1948	−	50.5669i	1.35242	−	2.34246i
$467$	20.3320	+	5.44793i	0.940851	+	0.252100i	0.696476	−	0.717581i	$-0.254750\pi$
$467$	20.3320	+	5.44793i	0.940851	+	0.252100i	0.244375	+	0.969681i	$0.421417\pi$
$468$	−2.69837	+	24.4163i	−0.124732	+	1.12864i
$469$	10.7580	+	10.6910i	0.496758	+	0.493666i
$470$		0			0
$471$	18.0546	+	15.5038i	0.831912	+	0.714376i
$472$	−126.792	+	33.9738i	−5.83608	+	1.56377i
$473$	−6.66478	+	1.78582i	−0.306447	+	0.0821122i
$474$	−2.84945	−	2.44687i	−0.130879	−	0.112388i
$475$		0			0
$476$	70.2035	−	19.0461i	3.21777	−	0.872976i
$477$	0.809958	−	7.32894i	0.0370854	−	0.335569i
$478$	−14.5538	−	3.89968i	−0.665675	−	0.178367i
$479$	−17.4134	+	30.1609i	−0.795638	+	1.37809i	0.126795	+	0.991929i	$0.459531\pi$
$479$	−17.4134	+	30.1609i	−0.795638	+	1.37809i	−0.922433	+	0.386157i	$0.873802\pi$
$480$		0			0
$481$	1.18032	+	2.04437i	0.0538178	+	0.0932152i
$482$	−13.6379	+	13.6379i	−0.621189	+	0.621189i
$483$	−21.3203	−	18.1928i	−0.970108	−	0.827800i
$484$		−	43.6426i		−	1.98375i
$485$		0			0
$486$	−16.6701	+	38.7706i	−0.756171	+	1.75867i
$487$	18.4329	−	4.93909i	0.835276	−	0.223812i	0.184262	−	0.982877i	$-0.441010\pi$
$487$	18.4329	−	4.93909i	0.835276	−	0.223812i	0.651014	+	0.759066i	$0.274344\pi$
$488$	7.30297	−	27.2550i	0.330590	−	1.23378i
$489$	−13.5249	−	38.5203i	−0.611618	−	1.74195i
$490$		0			0
$491$		−	21.6237i		−	0.975862i	−0.872882	−	0.487931i	$-0.837752\pi$
$491$		−	21.6237i		−	0.975862i	0.872882	−	0.487931i	$-0.162248\pi$
$492$	−31.4898	+	2.39358i	−1.41967	+	0.107911i
$493$	7.66225	+	28.5959i	0.345090	+	1.28789i
$494$	−1.34442	+	2.32860i	−0.0604883	+	0.104769i
$495$		0			0
$496$	−69.8569			−3.13667
$497$	5.75742	−	3.34806i	0.258256	−	0.150181i
$498$	26.1239	−	54.3951i	1.17064	−	2.43750i
$499$	−7.34272	+	4.23932i	−0.328705	+	0.189778i	−0.655266	−	0.755398i	$-0.727444\pi$
$499$	−7.34272	+	4.23932i	−0.328705	+	0.189778i	0.326561	+	0.945176i	$0.394110\pi$
$500$		0			0
$501$	26.6353	+	5.01028i	1.18998	+	0.223843i
$502$	−13.9755	+	52.1571i	−0.623755	+	2.32789i
$503$	−15.2596	−	15.2596i	−0.680391	−	0.680391i	0.279697	−	0.960088i	$-0.409766\pi$
$503$	−15.2596	−	15.2596i	−0.680391	−	0.680391i	−0.960088	+	0.279697i	$0.909766\pi$
$504$	−57.7867	−	42.1814i	−2.57403	−	1.87891i
$505$		0			0
$506$	−24.0419	+	13.8806i	−1.06879	+	0.617069i
$507$	15.2148	−	10.3970i	0.675713	−	0.461749i
$508$	18.4564	+	68.8802i	0.818870	+	3.05606i
$509$	−2.04970	−	3.55018i	−0.0908513	−	0.157359i	0.817018	−	0.576612i	$-0.195625\pi$
$509$	−2.04970	−	3.55018i	−0.0908513	−	0.157359i	−0.907870	+	0.419253i	$0.862292\pi$
$510$		0			0
$511$	4.45770	−	4.48562i	0.197197	−	0.198432i
$512$	−11.2143	+	11.2143i	−0.495606	+	0.495606i
$513$	−2.45493	+	2.29250i	−0.108388	+	0.101216i
$514$	−16.4010	−	9.46915i	−0.723419	−	0.417666i
$515$		0			0
$516$	−28.8206	−	24.7487i	−1.26876	−	1.08950i
$517$	9.33310	+	9.33310i	0.410469	+	0.410469i
$518$	−11.0052	+	0.0343566i	−0.483539	+	0.00150954i
$519$	−7.74326	+	2.71875i	−0.339892	+	0.119340i
$520$		0			0
$521$	−28.4378	−	16.4186i	−1.24588	−	0.719312i	−0.275599	−	0.961273i	$-0.588876\pi$
$521$	−28.4378	−	16.4186i	−1.24588	−	0.719312i	−0.970286	+	0.241961i	$0.922209\pi$
$522$	27.5971	−	37.5600i	1.20789	−	1.64396i
$523$	11.4061	+	3.05626i	0.498755	+	0.133641i	0.499422	−	0.866359i	$-0.333546\pi$
$523$	11.4061	+	3.05626i	0.498755	+	0.133641i	−0.000667252		1.00000i	$0.500212\pi$
$524$	38.3546			1.67553
$525$		0			0
$526$	−25.8568			−1.12741
$527$	25.3276	+	6.78650i	1.10329	+	0.295625i
$528$	−32.9528	+	22.5183i	−1.43409	+	0.979985i
$529$	−12.4762	−	7.20316i	−0.542446	−	0.313181i
$530$		0			0
$531$	−27.3119	−	34.0987i	−1.18524	−	1.47976i
$532$	−4.58200	−	7.87935i	−0.198655	−	0.341613i
$533$	−3.71688	−	3.71688i	−0.160996	−	0.160996i
$534$	−28.3852	+	33.0554i	−1.22835	+	1.43045i
$535$		0			0
$536$	44.7488	+	25.8357i	1.93285	+	1.11593i
$537$	−37.4306	+	2.84515i	−1.61525	+	0.122777i
$538$	26.4908	−	26.4908i	1.14210	−	1.14210i
$539$	10.1271	−	5.93147i	0.436203	−	0.255487i
$540$		0			0
$541$	−0.935311	−	1.62001i	−0.0402122	−	0.0696495i	0.845219	−	0.534420i	$-0.179470\pi$
$541$	−0.935311	−	1.62001i	−0.0402122	−	0.0696495i	−0.885431	+	0.464771i	$0.846137\pi$
$542$	−12.4763	−	46.5622i	−0.535903	−	2.00002i
$543$	−10.7524	−	15.7349i	−0.461431	−	0.675248i
$544$	85.6962	−	49.4767i	3.67419	−	2.12130i
$545$		0			0
$546$	−1.50406	−	19.0022i	−0.0643678	−	0.813217i
$547$	−1.77517	−	1.77517i	−0.0759008	−	0.0759008i	0.668137	−	0.744038i	$-0.267092\pi$
$547$	−1.77517	−	1.77517i	−0.0759008	−	0.0759008i	−0.744038	+	0.668137i	$0.767092\pi$
$548$	9.14179	−	34.1176i	0.390518	−	1.45743i
$549$	9.28328	−	1.41947i	0.396201	−	0.0605816i
$550$		0			0
$551$	3.21259	−	1.85479i	0.136861	−	0.0790167i
$552$	−86.0736	−	41.3379i	−3.66354	−	1.75946i
$553$	1.83854	+	1.05384i	0.0781828	+	0.0448140i
$554$	−55.3003			−2.34949
$555$		0			0
$556$	−5.39429	+	9.34319i	−0.228769	+	0.396240i
$557$	−10.5854	−	39.5052i	−0.448517	−	1.67389i	−0.706480	−	0.707733i	$-0.749718\pi$
$557$	−10.5854	−	39.5052i	−0.448517	−	1.67389i	0.257963	−	0.966155i	$-0.416949\pi$
$558$	−16.5887	−	37.8017i	−0.702257	−	1.60027i
$559$		−	6.32303i		−	0.267436i
$560$		0			0
$561$	14.1351	−	4.96301i	0.596785	−	0.209538i
$562$	−5.46148	+	20.3825i	−0.230379	+	0.859785i
$563$	−4.77535	+	1.27955i	−0.201257	+	0.0539266i	−0.358039	−	0.933707i	$-0.616555\pi$
$563$	−4.77535	+	1.27955i	−0.201257	+	0.0539266i	0.156782	+	0.987633i	$0.449888\pi$
$564$	−13.4339	+	71.4167i	−0.565671	+	3.00718i
$565$		0			0
$566$			73.5128i			3.08997i
$567$	5.12704	−	23.2532i	0.215315	−	0.976545i
$568$	16.0444	−	16.0444i	0.673208	−	0.673208i
$569$	18.6327	+	32.2728i	0.781125	+	1.35295i	0.931287	+	0.364286i	$0.118687\pi$
$569$	18.6327	+	32.2728i	0.781125	+	1.35295i	−0.150163	+	0.988661i	$0.547980\pi$
$570$		0			0
$571$	−8.64289	+	14.9699i	−0.361694	+	0.626472i	−0.988240	−	0.152912i	$-0.951135\pi$
$571$	−8.64289	+	14.9699i	−0.361694	+	0.626472i	0.626546	+	0.779385i	$0.284468\pi$
$572$	−13.2608	−	3.55322i	−0.554462	−	0.148568i
$573$	−10.1975	−	4.89748i	−0.426007	−	0.204595i
$574$	23.6506	−	6.41636i	0.987156	−	0.267813i
$575$		0			0
$576$	−68.3134	−	26.6431i	−2.84639	−	1.11013i
$577$	−20.1724	+	5.40518i	−0.839788	+	0.225021i	−0.652979	−	0.757376i	$-0.726481\pi$
$577$	−20.1724	+	5.40518i	−0.839788	+	0.225021i	−0.186809	+	0.982396i	$0.559814\pi$
$578$	−25.1398	+	6.73619i	−1.04568	+	0.280189i
$579$	−27.0320	+	31.4795i	−1.12341	+	1.30824i
$580$		0			0
$581$	−8.70935	+	32.9144i	−0.361325	+	1.36552i
$582$	−24.5836	+	51.1879i	−1.01902	+	2.12180i
$583$	3.98044	+	1.06656i	0.164853	+	0.0441723i
$584$	10.7724	−	18.6583i	0.445764	−	0.772085i
$585$		0			0
$586$	38.4239	+	66.5521i	1.58727	+	2.74924i
$587$	−8.21162	+	8.21162i	−0.338930	+	0.338930i	−0.855964	−	0.517035i	$-0.827036\pi$
$587$	−8.21162	+	8.21162i	−0.338930	+	0.338930i	0.517035	+	0.855964i	$0.327036\pi$
$588$	58.4202	+	27.6095i	2.40921	+	1.13860i
$589$		−	3.28560i		−	0.135381i
$590$		0			0
$591$	14.9612	+	2.81430i	0.615420	+	0.115765i
$592$	−20.3971	+	5.46540i	−0.838317	+	0.224626i
$593$	−9.15550	+	34.1688i	−0.375971	+	1.40314i	0.475949	+	0.879473i	$0.342105\pi$
$593$	−9.15550	+	34.1688i	−0.375971	+	1.40314i	−0.851920	+	0.523671i	$0.824562\pi$
$594$	−20.0106	−	12.4844i	−0.821044	−	0.512242i
$595$		0			0
$596$			68.8070i			2.81845i
$597$	−2.59642	−	34.1583i	−0.106264	−	1.39801i
$598$	−6.58443	−	24.5734i	−0.269257	−	1.00488i
$599$	−7.96413	+	13.7943i	−0.325406	+	0.563619i	−0.981594	−	0.190978i	$-0.938834\pi$
$599$	−7.96413	+	13.7943i	−0.325406	+	0.563619i	0.656189	+	0.754597i	$0.272168\pi$
$600$		0			0
$601$	7.38616			0.301288			0.150644	−	0.988588i	$-0.451865\pi$
$601$	7.38616			0.301288			0.150644	+	0.988588i	$0.451865\pi$
$602$	25.5744	+	14.6591i	1.04233	+	0.597461i
$603$	−1.88909	+	17.0935i	−0.0769296	+	0.696101i
$604$	−58.5048	+	33.7778i	−2.38053	+	1.37440i
$605$		0			0
$606$	9.77768	−	51.9795i	0.397191	−	2.11152i
$607$	12.2935	−	45.8801i	0.498979	−	1.86222i	−0.00751272	−	0.999972i	$-0.502391\pi$
$607$	12.2935	−	45.8801i	0.498979	−	1.86222i	0.506492	−	0.862245i	$-0.330942\pi$
$608$	−8.76759	−	8.76759i	−0.355573	−	0.355573i
$609$	−11.3108	+	23.7410i	−0.458339	+	0.962035i
$610$		0			0
$611$	−10.4750	+	6.04775i	−0.423773	+	0.244666i
$612$	66.4681	+	48.8372i	2.68682	+	1.97413i
$613$	−6.94799	−	25.9303i	−0.280627	−	1.04731i	−0.951976	−	0.306173i	$-0.900952\pi$
$613$	−6.94799	−	25.9303i	−0.280627	−	1.04731i	0.671349	−	0.741141i	$-0.265715\pi$
$614$	−25.2374	−	43.7124i	−1.01850	−	1.76409i
$615$		0			0
$616$	28.1845	−	28.3610i	1.13558	−	1.14270i
$617$	16.4113	−	16.4113i	0.660692	−	0.660692i	−0.294851	−	0.955543i	$-0.595270\pi$
$617$	16.4113	−	16.4113i	0.660692	−	0.660692i	0.955543	+	0.294851i	$0.0952700\pi$
$618$	−3.28068	−	43.1604i	−0.131968	−	1.73617i
$619$	21.2739	+	12.2825i	0.855072	+	0.493676i	0.862359	−	0.506297i	$-0.168986\pi$
$619$	21.2739	+	12.2825i	0.855072	+	0.493676i	−0.00728692	+	0.999973i	$0.502320\pi$
$620$		0			0
$621$	1.08675	−	31.7615i	0.0436100	−	1.27454i
$622$	7.94193	+	7.94193i	0.318442	+	0.318442i
$623$	12.2253	−	21.3283i	0.489795	−	0.854499i
$624$	−12.1168	−	34.5098i	−0.485060	−	1.38150i
$625$		0			0
$626$	−56.8191	−	32.8045i	−2.27095	−	1.31113i
$627$	−1.05911	−	1.54988i	−0.0422968	−	0.0618962i
$628$	−70.7295	−	18.9519i	−2.82241	−	0.756264i
$629$	7.92621			0.316039
$630$		0			0
$631$	−22.8195			−0.908430			−0.454215	−	0.890892i	$-0.650080\pi$
$631$	−22.8195			−0.908430			−0.454215	+	0.890892i	$0.650080\pi$
$632$	6.97369	+	1.86859i	0.277398	+	0.0743287i
$633$	6.59722	+	9.65423i	0.262216	+	0.383721i
$634$	31.3112	+	18.0775i	1.24353	+	0.717951i
$635$		0			0
$636$	7.51621	+	21.4069i	0.298037	+	0.848838i
$637$	2.84842	+	10.3710i	0.112859	+	0.410914i
$638$	18.4188	+	18.4188i	0.729205	+	0.729205i
$639$	7.03572	+	2.74402i	0.278329	+	0.108552i
$640$		0			0
$641$	−8.98653	−	5.18838i	−0.354947	−	0.204928i	0.311915	−	0.950110i	$-0.399030\pi$
$641$	−8.98653	−	5.18838i	−0.354947	−	0.204928i	−0.666862	+	0.745181i	$0.732363\pi$
$642$	1.31449	+	17.2933i	0.0518787	+	0.682512i
$643$	10.2840	−	10.2840i	0.405560	−	0.405560i	−0.474627	−	0.880187i	$-0.657417\pi$
$643$	10.2840	−	10.2840i	0.405560	−	0.405560i	0.880187	+	0.474627i	$0.157417\pi$
$644$	83.3694	+	22.0600i	3.28522	+	0.869288i
$645$		0			0
$646$	4.51411	+	7.81867i	0.177605	+	0.307621i
$647$	−6.63661	−	24.7682i	−0.260912	−	0.973738i	−0.964705	−	0.263332i	$-0.915178\pi$
$647$	−6.63661	−	24.7682i	−0.260912	−	0.973738i	0.703793	−	0.710405i	$-0.251488\pi$
$648$	−3.37885	−	81.0531i	−0.132734	−	3.18407i
$649$	21.1449	−	12.2080i	0.830010	−	0.479207i
$650$		0			0
$651$	13.2014	+	19.1897i	0.517402	+	0.752104i
$652$	88.8256	+	88.8256i	3.47868	+	3.47868i
$653$	3.63601	−	13.5698i	0.142288	−	0.531027i	−0.857573	−	0.514362i	$-0.828029\pi$
$653$	3.63601	−	13.5698i	0.142288	−	0.531027i	0.999861	−	0.0166644i	$-0.00530468\pi$
$654$	7.54586	−	40.1148i	0.295067	−	1.56861i
$655$		0			0
$656$	40.7213	−	23.5104i	1.58990	−	0.917928i
$657$	7.12725	+	0.787668i	0.278060	+	0.0307299i
$658$	−0.176037	−	56.3886i	−0.00686265	−	2.19826i
$659$	−36.5821			−1.42504			−0.712518	−	0.701653i	$-0.752446\pi$
$659$	−36.5821			−1.42504			−0.712518	+	0.701653i	$0.752446\pi$
$660$		0			0
$661$	19.9200	−	34.5024i	0.774797	−	1.34199i	−0.160112	−	0.987099i	$-0.551185\pi$
$661$	19.9200	−	34.5024i	0.774797	−	1.34199i	0.934909	−	0.354889i	$-0.115481\pi$
$662$	9.83659	+	36.7106i	0.382310	+	1.42680i
$663$	1.04053	+	13.6891i	0.0404108	+	0.531641i
$664$			115.994i			4.50145i
$665$		0			0
$666$	−7.80114	−	9.73966i	−0.302288	−	0.377404i
$667$	−9.08401	+	33.9020i	−0.351734	+	1.31269i
$668$	−80.5513	+	21.5836i	−3.11662	+	0.835096i
$669$	21.3345	+	4.01317i	0.824841	+	0.155158i
$670$		0			0
$671$			5.24844i			0.202614i
$672$	86.4354	+	15.9798i	3.33432	+	0.616436i
$673$	−11.2800	+	11.2800i	−0.434812	+	0.434812i	−0.890262	−	0.455449i	$-0.849479\pi$
$673$	−11.2800	+	11.2800i	−0.434812	+	0.434812i	0.455449	+	0.890262i	$0.349479\pi$
$674$	−18.0642	−	31.2881i	−0.695807	−	1.20517i
$675$		0			0
$676$	−28.3509	+	49.1051i	−1.09042	+	1.88866i
$677$	40.4874	+	10.8486i	1.55606	+	0.416944i	0.931412	−	0.363966i	$-0.118578\pi$
$677$	40.4874	+	10.8486i	1.55606	+	0.416944i	0.624644	+	0.780910i	$0.285244\pi$
$678$	−0.574689	+	1.19661i	−0.0220708	+	0.0459557i
$679$	8.19582	−	30.9737i	0.314527	−	1.18866i
$680$		0			0
$681$	19.5223	−	22.7343i	0.748095	−	0.871179i
$682$	22.2848	−	5.97119i	0.853329	−	0.228649i
$683$	−20.4077	+	5.46822i	−0.780878	+	0.209236i	−0.627172	−	0.778881i	$-0.715788\pi$
$683$	−20.4077	+	5.46822i	−0.780878	+	0.209236i	−0.153706	+	0.988117i	$0.549121\pi$
$684$	3.75535	−	9.62876i	0.143589	−	0.368165i
$685$		0			0
$686$	−48.5507	−	12.5230i	−1.85367	−	0.478129i
$687$	−17.1038	−	8.21432i	−0.652551	−	0.313396i
$688$	54.6343	+	14.6392i	2.08291	+	0.558115i
$689$	−1.88817	+	3.27040i	−0.0719335	+	0.124592i
$690$		0			0
$691$	−19.9058	−	34.4778i	−0.757252	−	1.31160i	−0.944247	−	0.329238i	$-0.893208\pi$
$691$	−19.9058	−	34.4778i	−0.757252	−	1.31160i	0.186995	−	0.982361i	$-0.440125\pi$
$692$	17.8555	−	17.8555i	0.678766	−	0.678766i
$693$	12.4131	+	4.79669i	0.471536	+	0.182211i
$694$		−	59.5223i		−	2.25944i
$695$		0			0
$696$	−16.5625	+	88.0487i	−0.627802	+	3.33748i
$697$	−17.0480	+	4.56801i	−0.645741	+	0.173026i
$698$	10.7621	−	40.1648i	0.407353	−	1.52026i
$699$	−35.2466	+	12.3755i	−1.33315	+	0.468084i
$700$		0			0
$701$		−	4.95994i		−	0.187334i	−0.995604	−	0.0936672i	$-0.970141\pi$
$701$		−	4.95994i		−	0.187334i	0.995604	−	0.0936672i	$-0.0298590\pi$
$702$	15.7970	−	14.7517i	0.596218	−	0.556767i
$703$	−0.257055	−	0.959343i	−0.00969502	−	0.0361823i
$704$	20.4896	−	35.4890i	0.772230	−	1.33754i
$705$		0			0
$706$	78.4085			2.95094
$707$	0.0931639	+	29.8424i	0.00350379	+	1.12234i
$708$	121.176	+	58.1964i	4.55408	+	2.18715i
$709$	−10.4511	+	6.03396i	−0.392500	+	0.226610i	−0.683243	−	0.730191i	$-0.739431\pi$
$709$	−10.4511	+	6.03396i	−0.392500	+	0.226610i	0.290743	+	0.956801i	$0.406098\pi$
$710$		0			0
$711$	0.363197	+	2.37529i	0.0136210	+	0.0890804i
$712$	21.6769	−	80.8992i	0.812375	−	3.03183i
$713$	21.9814	+	21.9814i	0.823211	+	0.823211i
$714$	−57.7799	−	27.5279i	−2.16236	−	1.03020i
$715$		0			0
$716$	100.030	−	57.7521i	3.73828	−	2.15830i
$717$	5.43865	+	7.95880i	0.203110	+	0.297227i
$718$	16.8245	+	62.7897i	0.627883	+	2.34329i
$719$	−12.6663	−	21.9387i	−0.472373	−	0.818174i	0.527127	−	0.849786i	$-0.323269\pi$
$719$	−12.6663	−	21.9387i	−0.472373	−	0.818174i	−0.999500	+	0.0316123i	$0.989936\pi$
$720$		0			0
$721$	6.39462	+	23.5705i	0.238148	+	0.877810i
$722$	−35.5726	+	35.5726i	−1.32388	+	1.32388i
$723$	12.3037	−	0.935224i	0.457581	−	0.0347814i
$724$	50.7836	+	29.3200i	1.88736	+	1.08967i
$725$		0			0
$726$	−25.0165	+	29.1324i	−0.928449	+	1.08121i
$727$	−18.8370	−	18.8370i	−0.698627	−	0.698627i	0.265487	−	0.964114i	$-0.414467\pi$
$727$	−18.8370	−	18.8370i	−0.698627	−	0.698627i	−0.964114	+	0.265487i	$0.914467\pi$
$728$	18.4195	+	31.6747i	0.682672	+	1.17394i
$729$	24.2508	−	11.8702i	0.898176	−	0.439636i
$730$		0			0
$731$	−18.3862	−	10.6153i	−0.680039	−	0.392621i
$732$	−23.8578	+	16.3032i	−0.881808	+	0.602584i
$733$	8.94100	+	2.39573i	0.330244	+	0.0884885i	0.420131	−	0.907463i	$-0.361984\pi$
$733$	8.94100	+	2.39573i	0.330244	+	0.0884885i	−0.0898876	+	0.995952i	$0.528651\pi$
$734$	57.1452			2.10927
$735$		0			0
$736$	117.315			4.32428
$737$	−9.28370	−	2.48756i	−0.341970	−	0.0916305i
$738$	22.3922	+	16.4526i	0.824267	+	0.605627i
$739$	−30.1349	−	17.3984i	−1.10853	−	0.640011i	−0.170083	−	0.985430i	$-0.554404\pi$
$739$	−30.1349	−	17.3984i	−1.10853	−	0.640011i	−0.938449	+	0.345419i	$0.887737\pi$
$740$		0			0
$741$	1.62311	−	0.569892i	0.0596263	−	0.0209355i
$742$	−8.85014	−	15.2190i	−0.324899	−	0.558706i
$743$	11.8523	+	11.8523i	0.434819	+	0.434819i	0.890264	−	0.455445i	$-0.150520\pi$
$743$	11.8523	+	11.8523i	0.434819	+	0.434819i	−0.455445	+	0.890264i	$0.650520\pi$
$744$	60.2025	+	51.6968i	2.20713	+	1.89530i
$745$		0			0
$746$	−47.4970	−	27.4224i	−1.73899	−	1.00400i
$747$	−35.3517	+	15.5136i	−1.29345	+	0.567612i
$748$	−32.5948	+	32.5948i	−1.19178	+	1.19178i
$749$	−2.56216	−	9.44410i	−0.0936194	−	0.345080i
$750$		0			0
$751$	−9.13762	−	15.8268i	−0.333437	−	0.577529i	0.649747	−	0.760151i	$-0.274875\pi$
$751$	−9.13762	−	15.8268i	−0.333437	−	0.577529i	−0.983183	+	0.182622i	$0.941542\pi$
$752$	−28.0038	−	104.511i	−1.02119	−	3.81114i
$753$	28.5223	−	19.4908i	1.03941	−	0.710283i
$754$	−20.6723	+	11.9352i	−0.752841	+	0.434653i
$755$		0			0
$756$	16.7546	+	71.3261i	0.609359	+	2.59410i
$757$	6.15278	+	6.15278i	0.223626	+	0.223626i	0.810024	−	0.586397i	$-0.199454\pi$
$757$	6.15278	+	6.15278i	0.223626	+	0.223626i	−0.586397	+	0.810024i	$0.699454\pi$
$758$	−5.54103	+	20.6794i	−0.201259	+	0.751110i
$759$	17.4548	+	3.28336i	0.633568	+	0.119178i
$760$		0			0
$761$	−4.99113	+	2.88163i	−0.180928	+	0.104459i	−0.587729	−	0.809058i	$-0.699978\pi$
$761$	−4.99113	+	2.88163i	−0.180928	+	0.104459i	0.406800	+	0.913517i	$0.366644\pi$
$762$	27.1629	−	56.5585i	0.984010	−	2.04890i
$763$	0.0718986	+	23.0307i	0.00260290	+	0.833767i
$764$	34.8082			1.25932
$765$		0			0
$766$	−7.96980	+	13.8041i	−0.287961	+	0.498763i
$767$	5.79101	+	21.6123i	0.209101	+	0.780377i
$768$	45.5965	−	3.46586i	1.64532	−	0.125063i
$769$		−	0.995467i		−	0.0358974i	−0.999839	−	0.0179487i	$-0.994286\pi$
$769$		−	0.995467i		−	0.0358974i	0.999839	−	0.0179487i	$-0.00571356\pi$
$770$		0			0
$771$	4.01391	+	11.4320i	0.144558	+	0.411714i
$772$	33.0441	−	123.322i	1.18928	−	4.43846i
$773$	−41.3589	+	11.0821i	−1.48758	+	0.398595i	−0.908918	−	0.416976i	$-0.863090\pi$
$773$	−41.3589	+	11.0821i	−1.48758	+	0.398595i	−0.578658	+	0.815571i	$0.696423\pi$
$774$	5.05212	+	33.0406i	0.181595	+	1.18762i
$775$		0			0
$776$		−	109.155i		−	3.91843i
$777$	5.35594	+	4.57026i	0.192143	+	0.163957i
$778$	−50.3980	+	50.3980i	−1.80686	+	1.80686i
$779$	1.10577	+	1.91525i	0.0396184	+	0.0686210i
$780$		0			0
$781$	−2.11026	+	3.65508i	−0.0755110	+	0.130789i
$782$	−82.5092	−	22.1083i	−2.95052	−	0.790591i
$783$	−29.0499	+	6.72822i	−1.03816	+	0.240447i
$784$	−96.2056	+	0.600687i	−3.43592	+	0.0214531i
$785$		0			0
$786$	−25.6026	−	21.9853i	−0.913213	−	0.784191i
$787$	1.23694	−	0.331437i	0.0440921	−	0.0118144i	−0.236706	−	0.971581i	$-0.576068\pi$
$787$	1.23694	−	0.331437i	0.0440921	−	0.0118144i	0.280798	+	0.959767i	$0.409401\pi$
$788$	−45.2460	+	12.1236i	−1.61182	+	0.431886i
$789$	12.5502	+	10.7771i	0.446799	+	0.383674i
$790$		0			0
$791$	0.191593	−	0.724069i	0.00681226	−	0.0257449i
$792$	45.0631	+	4.98015i	1.60125	+	0.176962i
$793$	−4.64576	−	1.24483i	−0.164976	−	0.0442051i
$794$	−0.608125	+	1.05330i	−0.0215815	+	0.0373803i
$795$		0			0
$796$	52.7032	+	91.2846i	1.86801	+	3.23550i
$797$	−33.5278	+	33.5278i	−1.18761	+	1.18761i	−0.209889	+	0.977725i	$0.567310\pi$
$797$	−33.5278	+	33.5278i	−1.18761	+	1.18761i	−0.977725	+	0.209889i	$0.932690\pi$
$798$	−1.45795	+	7.88610i	−0.0516110	+	0.279165i
$799$			40.6126i			1.43677i
$800$		0			0
$801$	27.5549	−	4.21332i	0.973605	−	0.148870i
$802$	−0.391833	+	0.104991i	−0.0138361	+	0.00370737i
$803$	−1.03720	+	3.87090i	−0.0366022	+	0.136601i
$804$	−17.5303	−	49.9279i	−0.618245	−	1.76082i
$805$		0			0
$806$			21.1421i			0.744698i
$807$	−23.8993	+	1.81662i	−0.841295	+	0.0639481i
$808$	26.3141	+	98.2054i	0.925725	+	3.45485i
$809$	10.1094	−	17.5101i	0.355429	−	0.615622i	−0.631762	−	0.775162i	$-0.717668\pi$
$809$	10.1094	−	17.5101i	0.355429	−	0.615622i	0.987191	+	0.159541i	$0.0510013\pi$
$810$		0			0
$811$	−4.78181			−0.167912			−0.0839560	−	0.996469i	$-0.526756\pi$
$811$	−4.78181			−0.167912			−0.0839560	+	0.996469i	$0.526756\pi$
$812$	−0.252610	−	80.9163i	−0.00886486	−	2.83961i
$813$	−13.3514	+	27.8002i	−0.468253	+	0.974995i
$814$	6.03965	−	3.48699i	0.211690	−	0.122219i
$815$		0			0
$816$	−120.690	−	22.7026i	−4.22500	−	0.794751i
$817$	−0.688530	+	2.56963i	−0.0240886	+	0.0898999i
$818$	−55.2108	−	55.2108i	−1.93040	−	1.93040i
$819$	−7.19004	+	9.85004i	−0.251240	+	0.344188i
$820$		0			0
$821$	2.69688	−	1.55704i	0.0941218	−	0.0543412i	−0.452200	−	0.891916i	$-0.649361\pi$
$821$	2.69688	−	1.55704i	0.0941218	−	0.0543412i	0.546322	+	0.837575i	$0.316027\pi$
$822$	−25.6590	+	17.5341i	−0.894961	+	0.611572i
$823$	−4.85498	−	18.1190i	−0.169234	−	0.631590i	−0.997462	−	0.0711990i	$-0.977317\pi$
$823$	−4.85498	−	18.1190i	−0.169234	−	0.631590i	0.828228	−	0.560391i	$-0.189349\pi$
$824$	41.6021	+	72.0570i	1.44928	+	2.51022i
$825$		0			0
$826$	−100.840	−	26.6828i	−3.50867	−	0.928415i
$827$	17.8671	−	17.8671i	0.621301	−	0.621301i	−0.324563	−	0.945864i	$-0.605217\pi$
$827$	17.8671	−	17.8671i	0.621301	−	0.621301i	0.945864	+	0.324563i	$0.105217\pi$
$828$	39.2946	+	89.5429i	1.36558	+	3.11183i
$829$	−36.1849	−	20.8914i	−1.25675	−	0.725587i	−0.284312	−	0.958732i	$-0.591765\pi$
$829$	−36.1849	−	20.8914i	−1.25675	−	0.725587i	−0.972442	+	0.233145i	$0.925098\pi$
$830$		0			0
$831$	26.8414	+	23.0491i	0.931116	+	0.799565i
$832$	26.5541	+	26.5541i	0.920596	+	0.920596i
$833$	34.9390	+	9.12846i	1.21057	+	0.316282i
$834$	8.95645	−	3.14471i	0.310136	−	0.108893i
$835$		0			0
$836$	5.00217	+	2.88800i	0.173004	+	0.0998837i
$837$	−7.70397	+	25.2621i	−0.266288	+	0.873187i
$838$	−6.46770	−	1.73302i	−0.223423	−	0.0598660i
$839$	21.3972			0.738712			0.369356	−	0.929288i	$-0.379578\pi$
$839$	21.3972			0.738712			0.369356	+	0.929288i	$0.379578\pi$
$840$		0			0
$841$	3.93196			0.135585
$842$	87.4068	+	23.4206i	3.01224	+	0.807126i
$843$	11.1463	−	7.61681i	0.383898	−	0.262337i
$844$	−31.1586	−	17.9894i	−1.07252	−	0.619222i
$845$		0			0
$846$	49.9044	−	39.9717i	1.71575	−	1.37426i
$847$	10.7744	−	18.7971i	0.370212	−	0.645874i
$848$	−23.8865	−	23.8865i	−0.820265	−	0.820265i
$849$	30.6400	−	35.6812i	1.05156	−	1.22458i
$850$		0			0
$851$	8.13800	+	4.69848i	0.278967	+	0.161062i
$852$	−23.1699	+	1.76118i	−0.793788	+	0.0603369i
$853$	−0.0489072	+	0.0489072i	−0.00167455	+	0.00167455i	−0.707944	−	0.706269i	$-0.750377\pi$
$853$	−0.0489072	+	0.0489072i	−0.00167455	+	0.00167455i	0.706269	+	0.707944i	$0.250377\pi$
$854$	15.8055	−	15.9045i	0.540852	−	0.544240i
$855$		0			0
$856$	−16.6689	−	28.8714i	−0.569732	−	0.986805i
$857$	2.18996	+	8.17305i	0.0748077	+	0.279186i	0.993190	−	0.116509i	$-0.0371704\pi$
$857$	2.18996	+	8.17305i	0.0748077	+	0.279186i	−0.918382	+	0.395695i	$0.870504\pi$
$858$	6.81514	+	9.97312i	0.232665	+	0.340477i
$859$	−9.78661	+	5.65030i	−0.333915	+	0.192786i	−0.657578	−	0.753387i	$-0.728419\pi$
$859$	−9.78661	+	5.65030i	−0.333915	+	0.192786i	0.323663	+	0.946172i	$0.395086\pi$
$860$		0			0
$861$	−14.1537	−	6.74320i	−0.482357	−	0.229808i
$862$	−66.8339	−	66.8339i	−2.27637	−	2.27637i
$863$	−10.8570	+	40.5190i	−0.369578	+	1.37928i	0.491530	+	0.870861i	$0.336438\pi$
$863$	−10.8570	+	40.5190i	−0.369578	+	1.37928i	−0.861108	+	0.508422i	$0.830229\pi$
$864$	46.8538	+	87.9698i	1.59400	+	2.99279i
$865$		0			0
$866$	63.2726	−	36.5304i	2.15009	−	1.24136i
$867$	15.0098	+	7.20867i	0.509761	+	0.244819i
$868$	−62.1782	−	35.6403i	−2.11047	−	1.20971i
$869$	−1.34291			−0.0455550
$870$		0			0
$871$	4.40383	−	7.62766i	0.149218	−	0.258453i
$872$	20.3077	+	75.7894i	0.687705	+	2.56655i
$873$	33.2673	−	14.5988i	1.12593	−	0.494096i
$874$			10.7034i			0.362049i
$875$		0			0
$876$	−20.8178	+	7.30936i	−0.703367	+	0.246960i
$877$	−0.164917	+	0.615478i	−0.00556885	+	0.0207832i	−0.968654	−	0.248412i	$-0.920091\pi$
$877$	−0.164917	+	0.615478i	−0.00556885	+	0.0207832i	0.963086	+	0.269196i	$0.0867578\pi$
$878$	86.2859	−	23.1202i	2.91201	−	0.780270i
$879$	9.08887	−	48.3177i	0.306560	−	1.62971i
$880$		0			0
$881$			10.6847i			0.359978i	0.983669	+	0.179989i	$0.0576061\pi$
$881$			10.6847i			0.359978i	−0.983669	+	0.179989i	$0.942394\pi$
$882$	−23.1707	−	51.9172i	−0.780199	−	1.74814i
$883$	25.1554	−	25.1554i	0.846546	−	0.846546i	−0.143154	−	0.989700i	$-0.545724\pi$
$883$	25.1554	−	25.1554i	0.846546	−	0.846546i	0.989700	+	0.143154i	$0.0457245\pi$
$884$	−21.1211	−	36.5828i	−0.710379	−	1.23041i
$885$		0			0
$886$	−12.9659	+	22.4576i	−0.435598	+	0.754478i
$887$	35.1247	+	9.41164i	1.17937	+	0.316012i	0.794678	−	0.607032i	$-0.207640\pi$
$887$	35.1247	+	9.41164i	1.17937	+	0.316012i	0.384695	+	0.923044i	$0.374307\pi$
$888$	21.6228	+	10.3846i	0.725613	+	0.348485i
$889$	−9.05573	+	34.2235i	−0.303720	+	1.14782i
$890$		0			0
$891$	4.50912	+	14.4000i	0.151061	+	0.482418i
$892$	−64.5205	+	17.2882i	−2.16031	+	0.578852i
$893$	4.91551	−	1.31711i	0.164491	−	0.0440753i
$894$	39.4411	−	45.9302i	1.31911	−	1.53614i
$895$		0			0
$896$	−71.0065	+	19.2639i	−2.37216	+	0.643562i
$897$	−7.04626	+	14.6717i	−0.235268	+	0.489873i
$898$	34.1071	+	9.13896i	1.13817	+	0.304971i
$899$	14.5840	−	25.2603i	0.486404	−	0.842477i
$900$		0			0
$901$	6.33983	+	10.9809i	0.211210	+	0.365827i
$902$	−10.9807	+	10.9807i	−0.365618	+	0.365618i
$903$	−6.30324	−	17.7745i	−0.209759	−	0.591499i
$904$		−	2.55170i		−	0.0848684i
$905$		0			0
$906$	58.4151	+	10.9883i	1.94071	+	0.365061i
$907$	−6.29874	+	1.68774i	−0.209146	+	0.0560406i	−0.361871	−	0.932228i	$-0.617862\pi$
$907$	−6.29874	+	1.68774i	−0.209146	+	0.0560406i	0.152725	+	0.988269i	$0.451195\pi$
$908$	−23.8642	+	89.0622i	−0.791960	+	2.95563i
$909$	−26.4108	+	21.1542i	−0.875991	+	0.701639i
$910$		0			0
$911$			42.5492i			1.40972i	0.709348	+	0.704858i	$0.248989\pi$
$911$			42.5492i			1.40972i	−0.709348	+	0.704858i	$0.751011\pi$
$912$	1.16631	+	15.3439i	0.0386205	+	0.508088i
$913$	−5.58418	−	20.8405i	−0.184810	−	0.689719i
$914$	−3.00771	+	5.20950i	−0.0994861	+	0.172315i
$915$		0			0
$916$	58.3822			1.92900
$917$	16.5195	+	9.46889i	0.545522	+	0.312690i
$918$	−16.3749	−	70.7003i	−0.540451	−	2.33346i
$919$	37.5625	−	21.6867i	1.23907	−	0.715379i	0.270168	−	0.962813i	$-0.412921\pi$
$919$	37.5625	−	21.6867i	1.23907	−	0.715379i	0.968905	+	0.247434i	$0.0795875\pi$
$920$		0			0
$921$	−5.96970	+	31.7357i	−0.196708	+	1.04573i
$922$	−12.3716	+	46.1716i	−0.407438	+	1.52058i
$923$	−2.73485	−	2.73485i	−0.0900187	−	0.0900187i
$924$	−40.8193	+	3.23093i	−1.34286	+	0.106290i
$925$		0			0
$926$	−58.5158	+	33.7841i	−1.92295	+	1.11022i
$927$	−16.3968	+	22.3163i	−0.538543	+	0.732964i
$928$	−28.4895	−	106.324i	−0.935213	−	3.49026i
$929$	8.75521	+	15.1645i	0.287249	+	0.497530i	0.973152	−	0.230163i	$-0.0739259\pi$
$929$	8.75521	+	15.1645i	0.287249	+	0.497530i	−0.685903	+	0.727693i	$0.740593\pi$
$930$		0			0
$931$	−0.0282523	−	4.52486i	−0.000925930	−	0.148296i
$932$	81.2766	−	81.2766i	2.66230	−	2.66230i
$933$	−0.544621	−	7.16499i	−0.0178301	−	0.234571i
$934$	49.3516	+	28.4931i	1.61483	+	0.932324i
$935$		0			0
$936$	−15.0964	+	38.7073i	−0.493440	+	1.26519i
$937$	39.5312	+	39.5312i	1.29143	+	1.29143i	0.933903	+	0.357525i	$0.116379\pi$
$937$	39.5312	+	39.5312i	1.29143	+	1.29143i	0.357525	+	0.933903i	$0.383621\pi$
$938$	20.6414	+	35.4956i	0.673967	+	1.15897i
$939$	13.9056	+	39.6046i	0.453793	+	1.29245i
$940$		0			0
$941$	29.9659	+	17.3008i	0.976861	+	0.563991i	0.901321	−	0.433152i	$-0.142599\pi$
$941$	29.9659	+	17.3008i	0.976861	+	0.563991i	0.0755397	+	0.997143i	$0.475932\pi$
$942$	36.3501	+	53.1939i	1.18435	+	1.73315i
$943$	−20.2114	−	5.41562i	−0.658173	−	0.176357i
$944$	−200.150			−6.51431
$945$		0			0
$946$	−18.6800			−0.607340
$947$	−37.9052	−	10.1567i	−1.23175	−	0.330047i	−0.416491	−	0.909140i	$-0.636740\pi$
$947$	−37.9052	−	10.1567i	−1.23175	−	0.330047i	−0.815262	+	0.579092i	$0.803407\pi$
$948$	−4.17146	−	6.10443i	−0.135483	−	0.198263i
$949$	−3.18040	−	1.83621i	−0.103240	−	0.0596057i
$950$		0			0
$951$	−7.66296	−	21.8248i	−0.248488	−	0.707719i
$952$	123.028	−	0.384075i	3.98735	−	0.0124479i
$953$	−24.2813	−	24.2813i	−0.786547	−	0.786547i	0.194379	−	0.980926i	$-0.437731\pi$
$953$	−24.2813	−	24.2813i	−0.786547	−	0.786547i	−0.980926	+	0.194379i	$0.937731\pi$
$954$	7.25346	−	18.5980i	0.234839	−	0.602131i
$955$		0			0
$956$	−25.6867	−	14.8302i	−0.830768	−	0.479644i
$957$	−1.26307	−	16.6169i	−0.0408294	−	0.537148i
$958$	−66.6705	+	66.6705i	−2.15402	+	2.15402i
$959$	12.3603	−	12.4377i	0.399135	−	0.401634i
$960$		0			0
$961$	2.58285	+	4.47362i	0.0833176	+	0.144310i
$962$	1.65409	+	6.17316i	0.0533301	+	0.199031i
$963$	6.56980	−	8.94159i	0.211709	−	0.288139i
$964$	−32.8805	+	18.9836i	−1.05901	+	0.611419i
$965$		0			0
$966$	−43.0059	−	62.5140i	−1.38369	−	2.01135i
$967$	17.6518	+	17.6518i	0.567642	+	0.567642i	0.931467	−	0.363825i	$-0.118529\pi$
$967$	17.6518	+	17.6518i	0.567642	+	0.567642i	−0.363825	+	0.931467i	$0.618529\pi$
$968$	19.1043	−	71.2982i	0.614035	−	2.29161i
$969$	1.06778	−	5.67645i	0.0343020	−	0.182354i
$970$		0			0
$971$	12.3815	−	7.14846i	0.397341	−	0.229405i	−0.287995	−	0.957632i	$-0.592989\pi$
$971$	12.3815	−	7.14846i	0.397341	−	0.229405i	0.685336	+	0.728227i	$0.259655\pi$
$972$	−51.4512	+	65.2277i	−1.65030	+	2.09218i
$973$	−4.62997	+	2.69242i	−0.148430	+	0.0863151i
$974$	51.6637			1.65541
$975$		0			0
$976$	21.5119	−	37.2598i	0.688581	−	1.19266i
$977$	8.31740	+	31.0410i	0.266097	+	0.993088i	0.961575	+	0.274541i	$0.0885259\pi$
$977$	8.31740	+	31.0410i	0.266097	+	0.993088i	−0.695478	+	0.718547i	$0.744807\pi$
$978$	−8.37714	−	110.209i	−0.267871	−	3.52410i
$979$			15.5786i			0.497893i
$980$		0			0
$981$	−20.3824	+	16.3256i	−0.650759	+	0.521236i
$982$	15.1517	−	56.5468i	0.483509	−	1.80448i
$983$	37.4624	−	10.0380i	1.19487	−	0.320164i	0.394059	−	0.919085i	$-0.371071\pi$
$983$	37.4624	−	10.0380i	1.19487	−	0.320164i	0.800808	+	0.598922i	$0.204404\pi$
$984$	−52.4921	−	9.87411i	−1.67339	−	0.314775i
$985$		0			0
$986$			80.1484i			2.55245i
$987$	−23.4172	+	27.4429i	−0.745379	+	0.873518i
$988$	−3.74279	+	3.74279i	−0.119074	+	0.119074i
$989$	−12.5850	−	21.7979i	−0.400180	−	0.693132i
$990$		0			0
$991$	11.4918	−	19.9044i	0.365049	−	0.632283i	−0.623735	−	0.781636i	$-0.714386\pi$
$991$	11.4918	−	19.9044i	0.365049	−	0.632283i	0.988784	+	0.149353i	$0.0477190\pi$
$992$	−94.1720	−	25.2333i	−2.98996	−	0.801159i
$993$	10.5265	−	21.9183i	0.334049	−	0.695555i
$994$	17.4019	−	4.72110i	0.551954	−	0.149744i
$995$		0			0
$996$	77.3880	−	90.1206i	2.45213	−	2.85558i
$997$	34.3903	−	9.21485i	1.08915	−	0.291837i	0.330812	−	0.943697i	$-0.392678\pi$
$997$	34.3903	−	9.21485i	1.08915	−	0.291837i	0.758340	+	0.651860i	$0.226011\pi$
$998$	−22.1720	+	5.94098i	−0.701843	+	0.188058i
$999$	−0.273007	+	7.97889i	−0.00863755	+	0.252441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bf.g.32.19	yes	80
3.2	odd	2	inner	525.2.bf.g.32.1	✓	80
5.2	odd	4	inner	525.2.bf.g.368.1	yes	80
5.3	odd	4	inner	525.2.bf.g.368.20	yes	80
5.4	even	2	inner	525.2.bf.g.32.2	yes	80
7.2	even	3	inner	525.2.bf.g.107.2	yes	80
15.2	even	4	inner	525.2.bf.g.368.19	yes	80
15.8	even	4	inner	525.2.bf.g.368.2	yes	80
15.14	odd	2	inner	525.2.bf.g.32.20	yes	80
21.2	odd	6	inner	525.2.bf.g.107.20	yes	80
35.2	odd	12	inner	525.2.bf.g.443.20	yes	80
35.9	even	6	inner	525.2.bf.g.107.19	yes	80
35.23	odd	12	inner	525.2.bf.g.443.1	yes	80
105.2	even	12	inner	525.2.bf.g.443.2	yes	80
105.23	even	12	inner	525.2.bf.g.443.19	yes	80
105.44	odd	6	inner	525.2.bf.g.107.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bf.g.32.1	✓	80	3.2	odd	2	inner
525.2.bf.g.32.2	yes	80	5.4	even	2	inner
525.2.bf.g.32.19	yes	80	1.1	even	1	trivial
525.2.bf.g.32.20	yes	80	15.14	odd	2	inner
525.2.bf.g.107.1	yes	80	105.44	odd	6	inner
525.2.bf.g.107.2	yes	80	7.2	even	3	inner
525.2.bf.g.107.19	yes	80	35.9	even	6	inner
525.2.bf.g.107.20	yes	80	21.2	odd	6	inner
525.2.bf.g.368.1	yes	80	5.2	odd	4	inner
525.2.bf.g.368.2	yes	80	15.8	even	4	inner
525.2.bf.g.368.19	yes	80	15.2	even	4	inner
525.2.bf.g.368.20	yes	80	5.3	odd	4	inner
525.2.bf.g.443.1	yes	80	35.23	odd	12	inner
525.2.bf.g.443.2	yes	80	105.2	even	12	inner
525.2.bf.g.443.19	yes	80	105.23	even	12	inner
525.2.bf.g.443.20	yes	80	35.2	odd	12	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.61504 + 0.700699i) q^{2} +(-0.977224 - 1.43005i) q^{3} +(4.61542 + 2.66471i) q^{4} +(-1.55345 - 4.42437i) q^{6} +(1.33002 + 2.28715i) q^{7} +(6.37367 + 6.37367i) q^{8} +(-1.09007 + 2.79495i) q^{9} +O(q^{10})\)	\(q+(2.61504 + 0.700699i) q^{2} +(-0.977224 - 1.43005i) q^{3} +(4.61542 + 2.66471i) q^{4} +(-1.55345 - 4.42437i) q^{6} +(1.33002 + 2.28715i) q^{7} +(6.37367 + 6.37367i) q^{8} +(-1.09007 + 2.79495i) q^{9} +(-1.45198 - 0.838304i) q^{11} +(-0.699631 - 9.20429i) q^{12} +(1.08642 - 1.08642i) q^{13} +(1.87546 + 6.91293i) q^{14} +(6.87197 + 11.9026i) q^{16} +(-1.33520 - 4.98305i) q^{17} +(-4.80899 + 6.54511i) q^{18} +(-0.559817 + 0.323211i) q^{19} +(1.97100 - 4.13705i) q^{21} +(-3.20960 - 3.20960i) q^{22} +(1.58296 - 5.90767i) q^{23} +(2.88615 - 15.3431i) q^{24} +(3.60230 - 2.07979i) q^{26} +(5.06215 - 1.17244i) q^{27} +(0.0440191 + 14.1003i) q^{28} -5.73864 q^{29} +(-2.54137 + 4.40179i) q^{31} +(4.96450 + 18.5278i) q^{32} +(0.220100 + 2.89562i) q^{33} -13.9665i q^{34} +(-12.4789 + 9.99515i) q^{36} +(-0.397659 + 1.48408i) q^{37} +(-1.69042 + 0.452947i) q^{38} +(-2.61532 - 0.491958i) q^{39} -3.42121i q^{41} +(8.05307 - 9.43748i) q^{42} +(2.91002 - 2.91002i) q^{43} +(-4.46768 - 7.73825i) q^{44} +(8.27899 - 14.3396i) q^{46} +(-7.60419 - 2.03754i) q^{47} +(10.3058 - 21.4587i) q^{48} +(-3.46208 + 6.08391i) q^{49} +(-5.82120 + 6.77896i) q^{51} +(7.90931 - 2.11929i) q^{52} +(-2.37411 + 0.636140i) q^{53} +(14.0593 + 0.481054i) q^{54} +(-6.10039 + 23.0546i) q^{56} +(1.00927 + 0.484716i) q^{57} +(-15.0068 - 4.02105i) q^{58} +(-7.28138 + 12.6117i) q^{59} +(-1.56520 - 2.71100i) q^{61} +(-9.73012 + 9.73012i) q^{62} +(-7.84228 + 1.22420i) q^{63} +24.4417i q^{64} +(-1.45338 + 7.72639i) q^{66} +(5.53719 - 1.48369i) q^{67} +(7.11587 - 26.5568i) q^{68} +(-9.99515 + 3.50941i) q^{69} -2.51730i q^{71} +(-24.7618 + 10.8664i) q^{72} +(-0.618633 - 2.30877i) q^{73} +(-2.07979 + 3.60230i) q^{74} -3.44506 q^{76} +(-0.0138482 - 4.43587i) q^{77} +(-6.49445 - 3.11904i) q^{78} +(0.693657 - 0.400483i) q^{79} +(-6.62350 - 6.09338i) q^{81} +(2.39724 - 8.94661i) q^{82} +(9.09949 + 9.09949i) q^{83} +(20.1210 - 13.8421i) q^{84} +(9.64887 - 5.57078i) q^{86} +(5.60793 + 8.20652i) q^{87} +(-3.91140 - 14.5975i) q^{88} +(-4.64586 - 8.04687i) q^{89} +(3.92978 + 1.03984i) q^{91} +(23.0483 - 23.0483i) q^{92} +(8.77825 - 0.667247i) q^{93} +(-18.4576 - 10.6565i) q^{94} +(21.6442 - 25.2053i) q^{96} +(-8.56296 - 8.56296i) q^{97} +(-13.3165 + 13.4838i) q^{98} +(3.92578 - 3.14442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{6}+O(q^{10}) \) 80 * q + 16 * q^6	\( 80 q + 16 q^{6} + 72 q^{16} + 44 q^{21} + 72 q^{31} - 240 q^{36} - 92 q^{51} - 24 q^{61} - 216 q^{66} - 208 q^{76} - 20 q^{81} - 40 q^{91} - 156 q^{96}+O(q^{100}) \) 80 * q + 16 * q^6 + 72 * q^16 + 44 * q^21 + 72 * q^31 - 240 * q^36 - 92 * q^51 - 24 * q^61 - 216 * q^66 - 208 * q^76 - 20 * q^81 - 40 * q^91 - 156 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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