LMFDB - Embedded newform 285.2.k.d.248.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(77,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("285.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.k (of order $4$, 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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			248.3
Character	$\chi$	$=$	285.248
Dual form			285.2.k.d.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53257 - 1.53257i) q^{2} +(1.34142 + 1.09572i) q^{3} +2.69753i q^{4} +(2.05989 - 0.869965i) q^{5} +(-0.376555 - 3.73508i) q^{6} +(1.55058 - 1.55058i) q^{7} +(1.06901 - 1.06901i) q^{8} +(0.598810 + 2.93963i) q^{9} +O(q^{10})$	\(q+(-1.53257 - 1.53257i) q^{2} +(1.34142 + 1.09572i) q^{3} +2.69753i q^{4} +(2.05989 - 0.869965i) q^{5} +(-0.376555 - 3.73508i) q^{6} +(1.55058 - 1.55058i) q^{7} +(1.06901 - 1.06901i) q^{8} +(0.598810 + 2.93963i) q^{9} +(-4.49021 - 1.82365i) q^{10} +2.52140i q^{11} +(-2.95573 + 3.61852i) q^{12} +(-0.427081 - 0.427081i) q^{13} -4.75273 q^{14} +(3.71642 + 1.09007i) q^{15} +2.11839 q^{16} +(1.45764 + 1.45764i) q^{17} +(3.58747 - 5.42290i) q^{18} -1.00000i q^{19} +(2.34676 + 5.55663i) q^{20} +(3.77897 - 0.380980i) q^{21} +(3.86422 - 3.86422i) q^{22} +(3.56822 - 3.56822i) q^{23} +(2.60533 - 0.262659i) q^{24} +(3.48632 - 3.58407i) q^{25} +1.30906i q^{26} +(-2.41775 + 4.59940i) q^{27} +(4.18273 + 4.18273i) q^{28} -6.37067 q^{29} +(-4.02505 - 7.36627i) q^{30} -3.46288 q^{31} +(-5.38460 - 5.38460i) q^{32} +(-2.76274 + 3.38225i) q^{33} -4.46787i q^{34} +(1.84508 - 4.54297i) q^{35} +(-7.92975 + 1.61531i) q^{36} +(6.17292 - 6.17292i) q^{37} +(-1.53257 + 1.53257i) q^{38} +(-0.104935 - 1.04085i) q^{39} +(1.27205 - 3.13206i) q^{40} +4.29278i q^{41} +(-6.37541 - 5.20765i) q^{42} +(-2.42991 - 2.42991i) q^{43} -6.80155 q^{44} +(3.79086 + 5.53438i) q^{45} -10.9371 q^{46} +(-2.49615 - 2.49615i) q^{47} +(2.84164 + 2.32115i) q^{48} +2.19142i q^{49} +(-10.8359 + 0.149808i) q^{50} +(0.358146 + 3.55247i) q^{51} +(1.15206 - 1.15206i) q^{52} +(8.40313 - 8.40313i) q^{53} +(10.7543 - 3.34353i) q^{54} +(2.19353 + 5.19381i) q^{55} -3.31518i q^{56} +(1.09572 - 1.34142i) q^{57} +(9.76349 + 9.76349i) q^{58} -0.181303 q^{59} +(-2.94050 + 10.0251i) q^{60} -14.9722 q^{61} +(5.30710 + 5.30710i) q^{62} +(5.48663 + 3.62963i) q^{63} +12.2678i q^{64} +(-1.25129 - 0.508196i) q^{65} +(9.41762 - 0.949446i) q^{66} +(-6.58649 + 6.58649i) q^{67} +(-3.93204 + 3.93204i) q^{68} +(8.69623 - 0.876719i) q^{69} +(-9.79012 + 4.13471i) q^{70} +14.8059i q^{71} +(3.78265 + 2.50237i) q^{72} +(4.76047 + 4.76047i) q^{73} -18.9208 q^{74} +(8.60374 - 0.987720i) q^{75} +2.69753 q^{76} +(3.90963 + 3.90963i) q^{77} +(-1.43436 + 1.75600i) q^{78} -7.82253i q^{79} +(4.36365 - 1.84292i) q^{80} +(-8.28285 + 3.52056i) q^{81} +(6.57898 - 6.57898i) q^{82} +(-10.7308 + 10.7308i) q^{83} +(1.02771 + 10.1939i) q^{84} +(4.27069 + 1.73449i) q^{85} +7.44800i q^{86} +(-8.54574 - 6.98045i) q^{87} +(2.69541 + 2.69541i) q^{88} +4.99091 q^{89} +(2.67207 - 14.2916i) q^{90} -1.32444 q^{91} +(9.62538 + 9.62538i) q^{92} +(-4.64518 - 3.79434i) q^{93} +7.65103i q^{94} +(-0.869965 - 2.05989i) q^{95} +(-1.32301 - 13.1230i) q^{96} +(-4.73002 + 4.73002i) q^{97} +(3.35849 - 3.35849i) q^{98} +(-7.41198 + 1.50984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) $ 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7	$ 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) $ 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^10 - 18 * q^12 - 8 * q^13 - 8 * q^15 - 84 * q^16 + 8 * q^21 + 40 * q^22 - 20 * q^25 - 14 * q^27 + 36 * q^28 + 28 * q^30 - 28 * q^33 + 92 * q^36 - 4 * q^37 - 20 * q^40 - 100 * q^42 + 16 * q^43 + 28 * q^45 - 24 * q^46 - 58 * q^48 + 32 * q^51 + 148 * q^52 - 72 * q^55 - 2 * q^57 - 12 * q^58 + 58 * q^60 - 112 * q^61 - 64 * q^63 + 92 * q^66 - 8 * q^67 + 8 * q^70 - 88 * q^72 + 76 * q^73 + 80 * q^75 + 36 * q^76 - 36 * q^78 + 4 * q^81 + 20 * q^82 - 28 * q^85 - 4 * q^87 + 140 * q^88 + 76 * q^90 - 24 * q^91 - 48 * q^93 + 32 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.53257	−	1.53257i	−1.08369	−	1.08369i	−0.996162	−	0.0875274i	$-0.972103\pi$
$2$	−1.53257	−	1.53257i	−1.08369	−	1.08369i	−0.0875274	−	0.996162i	$-0.527897\pi$
$3$	1.34142	+	1.09572i	0.774469	+	0.632612i
$3$	1.34142	+	1.09572i	0.774469	+	0.632612i
$4$			2.69753i			1.34877i
$5$	2.05989	−	0.869965i	0.921212	−	0.389060i
$5$	2.05989	−	0.869965i	0.921212	−	0.389060i
$6$	−0.376555	−	3.73508i	−0.153728	−	1.52484i
$7$	1.55058	−	1.55058i	0.586063	−	0.586063i	−0.350499	−	0.936563i	$-0.613988\pi$
$7$	1.55058	−	1.55058i	0.586063	−	0.586063i	0.936563	+	0.350499i	$0.113988\pi$
$8$	1.06901	−	1.06901i	0.377954	−	0.377954i
$9$	0.598810	+	2.93963i	0.199603	+	0.979877i
$10$	−4.49021	−	1.82365i	−1.41993	−	0.576688i
$11$			2.52140i			0.760230i	0.924939	+	0.380115i	$0.124116\pi$
$11$			2.52140i			0.760230i	−0.924939	+	0.380115i	$0.875884\pi$
$12$	−2.95573	+	3.61852i	−0.853246	+	1.04458i
$13$	−0.427081	−	0.427081i	−0.118451	−	0.118451i	0.645397	−	0.763848i	$-0.276692\pi$
$13$	−0.427081	−	0.427081i	−0.118451	−	0.118451i	−0.763848	+	0.645397i	$0.776692\pi$
$14$	−4.75273			−1.27022
$15$	3.71642	+	1.09007i	0.959574	+	0.281455i
$16$	2.11839			0.529597
$17$	1.45764	+	1.45764i	0.353530	+	0.353530i	0.861421	−	0.507891i	$-0.169575\pi$
$17$	1.45764	+	1.45764i	0.353530	+	0.353530i	−0.507891	+	0.861421i	$0.669575\pi$
$18$	3.58747	−	5.42290i	0.845574	−	1.27819i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	2.34676	+	5.55663i	0.524751	+	1.24250i
$21$	3.77897	−	0.380980i	0.824639	−	0.0831367i
$22$	3.86422	−	3.86422i	0.823854	−	0.823854i
$23$	3.56822	−	3.56822i	0.744025	−	0.744025i	−0.229325	−	0.973350i	$-0.573652\pi$
$23$	3.56822	−	3.56822i	0.744025	−	0.744025i	0.973350	+	0.229325i	$0.0736518\pi$
$24$	2.60533	−	0.262659i	0.531812	−	0.0536151i
$25$	3.48632	−	3.58407i	0.697264	−	0.716814i
$26$			1.30906i			0.256728i
$27$	−2.41775	+	4.59940i	−0.465296	+	0.885155i
$28$	4.18273	+	4.18273i	0.790462	+	0.790462i
$29$	−6.37067			−1.18300			−0.591502	−	0.806303i	$-0.701465\pi$
$29$	−6.37067			−1.18300			−0.591502	+	0.806303i	$0.701465\pi$
$30$	−4.02505	−	7.36627i	−0.734870	−	1.34489i
$31$	−3.46288			−0.621952			−0.310976	−	0.950418i	$-0.600656\pi$
$31$	−3.46288			−0.621952			−0.310976	+	0.950418i	$0.600656\pi$
$32$	−5.38460	−	5.38460i	−0.951872	−	0.951872i
$33$	−2.76274	+	3.38225i	−0.480931	+	0.588775i
$34$		−	4.46787i		−	0.766234i
$35$	1.84508	−	4.54297i	0.311875	−	0.767903i
$36$	−7.92975	+	1.61531i	−1.32162	+	0.269218i
$37$	6.17292	−	6.17292i	1.01482	−	1.01482i	0.0149328	−	0.999888i	$-0.495247\pi$
$37$	6.17292	−	6.17292i	1.01482	−	1.01482i	0.999888	−	0.0149328i	$-0.00475344\pi$
$38$	−1.53257	+	1.53257i	−0.248615	+	0.248615i
$39$	−0.104935	−	1.04085i	−0.0168030	−	0.166670i
$40$	1.27205	−	3.13206i	0.201129	−	0.495223i
$41$			4.29278i			0.670420i	0.942144	+	0.335210i	$0.108807\pi$
$41$			4.29278i			0.670420i	−0.942144	+	0.335210i	$0.891193\pi$
$42$	−6.37541	−	5.20765i	−0.983747	−	0.803558i
$43$	−2.42991	−	2.42991i	−0.370557	−	0.370557i	0.497123	−	0.867680i	$-0.334390\pi$
$43$	−2.42991	−	2.42991i	−0.370557	−	0.370557i	−0.867680	+	0.497123i	$0.834390\pi$
$44$	−6.80155			−1.02537
$45$	3.79086	+	5.53438i	0.565108	+	0.825017i
$46$	−10.9371			−1.61258
$47$	−2.49615	−	2.49615i	−0.364101	−	0.364101i	0.501220	−	0.865320i	$-0.332885\pi$
$47$	−2.49615	−	2.49615i	−0.364101	−	0.364101i	−0.865320	+	0.501220i	$0.832885\pi$
$48$	2.84164	+	2.32115i	0.410156	+	0.335029i
$49$			2.19142i			0.313059i
$50$	−10.8359	+	0.149808i	−1.53242	+	0.0211861i
$51$	0.358146	+	3.55247i	0.0501504	+	0.497446i
$52$	1.15206	−	1.15206i	0.159763	−	0.159763i
$53$	8.40313	−	8.40313i	1.15426	−	1.15426i	0.168568	−	0.985690i	$-0.446086\pi$
$53$	8.40313	−	8.40313i	1.15426	−	1.15426i	0.985690	−	0.168568i	$-0.0539144\pi$
$54$	10.7543	−	3.34353i	1.46347	−	0.454997i
$55$	2.19353	+	5.19381i	0.295775	+	0.700334i
$56$		−	3.31518i		−	0.443010i
$57$	1.09572	−	1.34142i	0.145131	−	0.177675i
$58$	9.76349	+	9.76349i	1.28201	+	1.28201i
$59$	−0.181303			−0.0236036			−0.0118018	−	0.999930i	$-0.503757\pi$
$59$	−0.181303			−0.0236036			−0.0118018	+	0.999930i	$0.503757\pi$
$60$	−2.94050	+	10.0251i	−0.379617	+	1.29424i
$61$	−14.9722			−1.91699			−0.958497	−	0.285102i	$-0.907973\pi$
$61$	−14.9722			−1.91699			−0.958497	+	0.285102i	$0.907973\pi$
$62$	5.30710	+	5.30710i	0.674003	+	0.674003i
$63$	5.48663	+	3.62963i	0.691250	+	0.457290i
$64$			12.2678i			1.53347i
$65$	−1.25129	−	0.508196i	−0.155203	−	0.0630339i
$66$	9.41762	−	0.949446i	1.15923	−	0.116869i
$67$	−6.58649	+	6.58649i	−0.804668	+	0.804668i	−0.983821	−	0.179153i	$-0.942664\pi$
$67$	−6.58649	+	6.58649i	−0.804668	+	0.804668i	0.179153	+	0.983821i	$0.442664\pi$
$68$	−3.93204	+	3.93204i	−0.476829	+	0.476829i
$69$	8.69623	−	0.876719i	1.04690	−	0.105545i
$70$	−9.79012	+	4.13471i	−1.17014	+	0.494193i
$71$			14.8059i			1.75713i	0.477618	+	0.878567i	$0.341500\pi$
$71$			14.8059i			1.75713i	−0.477618	+	0.878567i	$0.658500\pi$
$72$	3.78265	+	2.50237i	0.445789	+	0.294907i
$73$	4.76047	+	4.76047i	0.557171	+	0.557171i	0.928501	−	0.371330i	$-0.121098\pi$
$73$	4.76047	+	4.76047i	0.557171	+	0.557171i	−0.371330	+	0.928501i	$0.621098\pi$
$74$	−18.9208			−2.19950
$75$	8.60374	−	0.987720i	0.993475	−	0.114052i
$76$	2.69753			0.309428
$77$	3.90963	+	3.90963i	0.445543	+	0.445543i
$78$	−1.43436	+	1.75600i	−0.162409	+	0.198828i
$79$		−	7.82253i		−	0.880104i	−0.897972	−	0.440052i	$-0.854960\pi$
$79$		−	7.82253i		−	0.880104i	0.897972	−	0.440052i	$-0.145040\pi$
$80$	4.36365	−	1.84292i	0.487871	−	0.206045i
$81$	−8.28285	+	3.52056i	−0.920317	+	0.391173i
$82$	6.57898	−	6.57898i	0.726527	−	0.726527i
$83$	−10.7308	+	10.7308i	−1.17786	+	1.17786i	−0.197574	+	0.980288i	$0.563306\pi$
$83$	−10.7308	+	10.7308i	−1.17786	+	1.17786i	−0.980288	+	0.197574i	$0.936694\pi$
$84$	1.02771	+	10.1939i	0.112132	+	1.11224i
$85$	4.27069	+	1.73449i	0.463221	+	0.188132i
$86$			7.44800i			0.803138i
$87$	−8.54574	−	6.98045i	−0.916200	−	0.748383i
$88$	2.69541	+	2.69541i	0.287332	+	0.287332i
$89$	4.99091			0.529036			0.264518	−	0.964381i	$-0.414787\pi$
$89$	4.99091			0.529036			0.264518	+	0.964381i	$0.414787\pi$
$90$	2.67207	−	14.2916i	0.281661	−	1.50646i
$91$	−1.32444			−0.138840
$92$	9.62538	+	9.62538i	1.00352	+	1.00352i
$93$	−4.64518	−	3.79434i	−0.481682	−	0.393455i
$94$			7.65103i			0.789144i
$95$	−0.869965	−	2.05989i	−0.0892565	−	0.211341i
$96$	−1.32301	−	13.1230i	−0.135029	−	1.33936i
$97$	−4.73002	+	4.73002i	−0.480261	+	0.480261i	−0.905215	−	0.424954i	$-0.860290\pi$
$97$	−4.73002	+	4.73002i	−0.480261	+	0.480261i	0.424954	+	0.905215i	$0.360290\pi$
$98$	3.35849	−	3.35849i	0.339259	−	0.339259i
$99$	−7.41198	+	1.50984i	−0.744932	+	0.151744i
$100$	9.66815	+	9.40446i	0.966815	+	0.940446i
$101$		−	4.04795i		−	0.402786i	−0.979511	−	0.201393i	$-0.935453\pi$
$101$		−	4.04795i		−	0.402786i	0.979511	−	0.201393i	$-0.0645468\pi$
$102$	4.89552	−	5.99329i	0.484729	−	0.593424i
$103$	−13.3360	−	13.3360i	−1.31403	−	1.31403i	−0.918416	−	0.395615i	$-0.870531\pi$
$103$	−13.3360	−	13.3360i	−1.31403	−	1.31403i	−0.395615	−	0.918416i	$-0.629469\pi$
$104$	−0.913112			−0.0895380
$105$	7.45283	−	4.07235i	0.727322	−	0.397421i
$106$	−25.7567			−2.50172
$107$	−9.30736	−	9.30736i	−0.899777	−	0.899777i	0.0956395	−	0.995416i	$-0.469510\pi$
$107$	−9.30736	−	9.30736i	−0.899777	−	0.899777i	−0.995416	+	0.0956395i	$0.969510\pi$
$108$	−12.4070	−	6.52195i	−1.19387	−	0.627575i
$109$			6.00071i			0.574764i	0.957816	+	0.287382i	$0.0927849\pi$
$109$			6.00071i			0.574764i	−0.957816	+	0.287382i	$0.907215\pi$
$110$	4.59814	−	11.3216i	0.438415	−	1.07947i
$111$	15.0442	−	1.51670i	1.42794	−	0.143959i
$112$	3.28472	−	3.28472i	0.310377	−	0.310377i
$113$	−7.86148	+	7.86148i	−0.739546	+	0.739546i	−0.972490	−	0.232944i	$-0.925164\pi$
$113$	−7.86148	+	7.86148i	−0.739546	+	0.739546i	0.232944	+	0.972490i	$0.425164\pi$
$114$	−3.73508	+	0.376555i	−0.349822	+	0.0352676i
$115$	4.24592	−	10.4544i	0.395934	−	0.974876i
$116$		−	17.1851i		−	1.59560i
$117$	0.999720	−	1.51120i	0.0924242	−	0.139711i
$118$	0.277859	+	0.277859i	0.0255790	+	0.0255790i
$119$	4.52038			0.414382
$120$	5.13821	−	2.80760i	0.469052	−	0.256298i
$121$	4.64255			0.422050
$122$	22.9459	+	22.9459i	2.07743	+	2.07743i
$123$	−4.70367	+	5.75842i	−0.424116	+	0.519219i
$124$		−	9.34124i		−	0.838868i
$125$	4.06343	−	10.4158i	0.363444	−	0.931616i
$126$	−2.84598	−	13.9713i	−0.253540	−	1.24466i
$127$	−13.6790	+	13.6790i	−1.21382	+	1.21382i	−0.244059	+	0.969760i	$0.578479\pi$
$127$	−13.6790	+	13.6790i	−1.21382	+	1.21382i	−0.969760	+	0.244059i	$0.921521\pi$
$128$	8.03199	−	8.03199i	0.709934	−	0.709934i
$129$	−0.597033	−	5.92201i	−0.0525659	−	0.521404i
$130$	1.13884	+	2.69653i	0.0998827	+	0.236501i
$131$		−	5.03850i		−	0.440216i	−0.975476	−	0.220108i	$-0.929359\pi$
$131$		−	5.03850i		−	0.440216i	0.975476	−	0.220108i	$-0.0706409\pi$
$132$	−9.12373	−	7.45258i	−0.794119	−	0.648664i
$133$	−1.55058	−	1.55058i	−0.134452	−	0.134452i
$134$	20.1885			1.74402
$135$	−0.978984	+	11.5776i	−0.0842575	+	0.996444i
$136$	3.11648			0.267236
$137$	0.0659931	+	0.0659931i	0.00563817	+	0.00563817i	0.709920	−	0.704282i	$-0.248731\pi$
$137$	0.0659931	+	0.0659931i	0.00563817	+	0.00563817i	−0.704282	+	0.709920i	$0.748731\pi$
$138$	−14.6712	−	11.9839i	−1.24890	−	1.02014i
$139$		−	1.34859i		−	0.114386i	−0.998363	−	0.0571929i	$-0.981785\pi$
$139$		−	1.34859i		−	0.114386i	0.998363	−	0.0571929i	$-0.0182150\pi$
$140$	12.2548	+	4.97715i	1.03572	+	0.420646i
$141$	−0.613309	−	6.08345i	−0.0516499	−	0.512319i
$142$	22.6910	−	22.6910i	1.90419	−	1.90419i
$143$	1.07684	−	1.07684i	0.0900500	−	0.0900500i
$144$	1.26851	+	6.22727i	0.105709	+	0.518939i
$145$	−13.1229	+	5.54226i	−1.08980	+	0.460260i
$146$		−	14.5915i		−	1.20760i
$147$	−2.40117	+	2.93961i	−0.198045	+	0.242455i
$148$	16.6516	+	16.6516i	1.36876	+	1.36876i
$149$	14.6008			1.19614			0.598071	−	0.801443i	$-0.295934\pi$
$149$	14.6008			1.19614			0.598071	+	0.801443i	$0.295934\pi$
$150$	−14.6996	−	11.6721i	−1.20022	−	0.953021i
$151$	−12.2407			−0.996134			−0.498067	−	0.867139i	$-0.665957\pi$
$151$	−12.2407			−0.996134			−0.498067	+	0.867139i	$0.665957\pi$
$152$	−1.06901	−	1.06901i	−0.0867086	−	0.0867086i
$153$	−3.41208	+	5.15778i	−0.275850	+	0.416982i
$154$		−	11.9835i		−	0.965661i
$155$	−7.13317	+	3.01259i	−0.572950	+	0.241977i
$156$	2.80774	−	0.283065i	0.224799	−	0.0226633i
$157$	1.50721	−	1.50721i	0.120288	−	0.120288i	−0.644400	−	0.764689i	$-0.722893\pi$
$157$	1.50721	−	1.50721i	0.120288	−	0.120288i	0.764689	+	0.644400i	$0.222893\pi$
$158$	−11.9886	+	11.9886i	−0.953759	+	0.953759i
$159$	20.4796	−	2.06467i	1.62414	−	0.163739i
$160$	−15.7761	−	6.40729i	−1.24721	−	0.506541i
$161$		−	11.0656i		−	0.872092i
$162$	18.0895	+	7.29855i	1.42125	+	0.573428i
$163$	15.9076	+	15.9076i	1.24598	+	1.24598i	0.957479	+	0.288502i	$0.0931573\pi$
$163$	15.9076	+	15.9076i	1.24598	+	1.24598i	0.288502	+	0.957479i	$0.406843\pi$
$164$	−11.5799			−0.904239
$165$	−2.74851	+	9.37057i	−0.213971	+	0.729498i
$166$	32.8915			2.55287
$167$	1.39951	+	1.39951i	0.108297	+	0.108297i	0.759179	−	0.650882i	$-0.225601\pi$
$167$	1.39951	+	1.39951i	0.108297	+	0.108297i	−0.650882	+	0.759179i	$0.725601\pi$
$168$	3.63250	−	4.44705i	0.280254	−	0.343097i
$169$		−	12.6352i		−	0.971939i
$170$	−3.88689	−	9.20334i	−0.298111	−	0.705864i
$171$	2.93963	−	0.598810i	0.224799	−	0.0457921i
$172$	6.55475	−	6.55475i	0.499795	−	0.499795i
$173$	11.8738	−	11.8738i	0.902750	−	0.902750i	−0.0929232	−	0.995673i	$-0.529621\pi$
$173$	11.8738	−	11.8738i	0.902750	−	0.902750i	0.995673	+	0.0929232i	$0.0296211\pi$
$174$	2.39891	+	23.7950i	0.181861	+	1.80389i
$175$	−0.151569	−	10.9632i	−0.0114575	−	0.828740i
$176$			5.34130i			0.402615i
$177$	−0.243203	−	0.198656i	−0.0182802	−	0.0149319i
$178$	−7.64891	−	7.64891i	−0.573310	−	0.573310i
$179$	−4.83322			−0.361252			−0.180626	−	0.983552i	$-0.557812\pi$
$179$	−4.83322			−0.361252			−0.180626	+	0.983552i	$0.557812\pi$
$180$	−14.9292	+	10.2260i	−1.11275	+	0.762198i
$181$	−1.91151			−0.142081			−0.0710407	−	0.997473i	$-0.522632\pi$
$181$	−1.91151			−0.142081			−0.0710407	+	0.997473i	$0.522632\pi$
$182$	2.02980	+	2.02980i	0.150459	+	0.150459i
$183$	−20.0840	−	16.4053i	−1.48465	−	1.21271i
$184$		−	7.62896i		−	0.562414i
$185$	7.34533	−	18.0858i	0.540039	−	1.32969i
$186$	1.30397	+	12.9341i	0.0956115	+	0.948377i
$187$	−3.67530	+	3.67530i	−0.268764	+	0.268764i
$188$	6.73344	−	6.73344i	0.491086	−	0.491086i
$189$	3.38282	+	10.8806i	0.246064	+	0.791450i
$190$	−1.82365	+	4.49021i	−0.132301	+	0.325754i
$191$		−	6.93020i		−	0.501451i	−0.968058	−	0.250726i	$-0.919331\pi$
$191$		−	6.93020i		−	0.501451i	0.968058	−	0.250726i	$-0.0806692\pi$
$192$	−13.4420	+	16.4562i	−0.970093	+	1.18763i
$193$	−0.681839	−	0.681839i	−0.0490799	−	0.0490799i	0.682141	−	0.731221i	$-0.261049\pi$
$193$	−0.681839	−	0.681839i	−0.0490799	−	0.0490799i	−0.731221	+	0.682141i	$0.761049\pi$
$194$	14.4982			1.04091
$195$	−1.12166	−	2.05276i	−0.0803238	−	0.147001i
$196$	−5.91141			−0.422244
$197$	−12.7752	−	12.7752i	−0.910194	−	0.910194i	0.0860930	−	0.996287i	$-0.472562\pi$
$197$	−12.7752	−	12.7752i	−0.910194	−	0.910194i	−0.996287	+	0.0860930i	$0.972562\pi$
$198$	13.6733	+	9.04544i	0.971719	+	0.642831i
$199$		−	11.5337i		−	0.817605i	−0.912623	−	0.408803i	$-0.865946\pi$
$199$		−	11.5337i		−	0.817605i	0.912623	−	0.408803i	$-0.134054\pi$
$200$	−0.104496	−	7.55836i	−0.00738899	−	0.534456i
$201$	−16.0522	+	1.61832i	−1.13223	+	0.114147i
$202$	−6.20375	+	6.20375i	−0.436495	+	0.436495i
$203$	−9.87823	+	9.87823i	−0.693316	+	0.693316i
$204$	−9.58290	+	0.966110i	−0.670938	+	0.0676412i
$205$	3.73457	+	8.84267i	0.260834	+	0.617599i
$206$			40.8765i			2.84800i
$207$	12.6259	+	8.35256i	0.877563	+	0.580543i
$208$	−0.904722	−	0.904722i	−0.0627312	−	0.0627312i
$209$	2.52140			0.174409
$210$	−17.6631	−	5.18082i	−1.21887	−	0.357511i
$211$	19.5145			1.34344			0.671718	−	0.740807i	$-0.265557\pi$
$211$	19.5145			1.34344			0.671718	+	0.740807i	$0.265557\pi$
$212$	22.6677	+	22.6677i	1.55682	+	1.55682i
$213$	−16.2231	+	19.8609i	−1.11159	+	1.36085i
$214$			28.5283i			1.95016i
$215$	−7.11928	−	2.89141i	−0.485531	−	0.197193i
$216$	2.33222	+	7.50144i	0.158688	+	0.510408i
$217$	−5.36947	+	5.36947i	−0.364503	+	0.364503i
$218$	9.19650	−	9.19650i	0.622866	−	0.622866i
$219$	1.16966	+	11.6019i	0.0790382	+	0.783985i
$220$	−14.0105	+	5.91712i	−0.944586	+	0.398932i
$221$		−	1.24506i		−	0.0837520i
$222$	−25.3808	−	20.7319i	−1.70345	−	1.39143i
$223$	14.3578	+	14.3578i	0.961469	+	0.961469i	0.999285	−	0.0378157i	$-0.0120400\pi$
$223$	14.3578	+	14.3578i	0.961469	+	0.961469i	−0.0378157	+	0.999285i	$0.512040\pi$
$224$	−16.6985			−1.11571
$225$	12.6235	+	8.10232i	0.841566	+	0.540155i
$226$	24.0965			1.60288
$227$	−12.1657	−	12.1657i	−0.807467	−	0.807467i	0.176783	−	0.984250i	$-0.443431\pi$
$227$	−12.1657	−	12.1657i	−0.807467	−	0.807467i	−0.984250	+	0.176783i	$0.943431\pi$
$228$	3.61852	+	2.95573i	0.239642	+	0.195748i
$229$			19.4200i			1.28331i	0.766994	+	0.641654i	$0.221751\pi$
$229$			19.4200i			1.28331i	−0.766994	+	0.641654i	$0.778249\pi$
$230$	−22.5292	+	9.51488i	−1.48553	+	0.627392i
$231$	0.960604	+	9.52829i	0.0632031	+	0.626915i
$232$	−6.81035	+	6.81035i	−0.447121	+	0.447121i
$233$	10.2202	−	10.2202i	0.669550	−	0.669550i	−0.288061	−	0.957612i	$-0.593011\pi$
$233$	10.2202	−	10.2202i	0.669550	−	0.669550i	0.957612	+	0.288061i	$0.0930108\pi$
$234$	−3.84816	+	0.783879i	−0.251562	+	0.0512437i
$235$	−7.31336	−	2.97024i	−0.477071	−	0.193757i
$236$		−	0.489070i		−	0.0318357i
$237$	8.57128	−	10.4933i	0.556764	−	0.681613i
$238$	−6.92779	−	6.92779i	−0.449062	−	0.449062i
$239$	−8.47069			−0.547923			−0.273962	−	0.961741i	$-0.588334\pi$
$239$	−8.47069			−0.547923			−0.273962	+	0.961741i	$0.588334\pi$
$240$	7.87280	+	2.30919i	0.508187	+	0.149058i
$241$	12.4151			0.799730			0.399865	−	0.916574i	$-0.369057\pi$
$241$	12.4151			0.799730			0.399865	+	0.916574i	$0.369057\pi$
$242$	−7.11502	−	7.11502i	−0.457371	−	0.457371i
$243$	−14.9683	−	4.35312i	−0.960218	−	0.279253i
$244$		−	40.3880i		−	2.58558i
$245$	1.90645	+	4.51408i	0.121799	+	0.288394i
$246$	16.0339	−	1.61647i	1.02228	−	0.103062i
$247$	−0.427081	+	0.427081i	−0.0271745	+	0.0271745i
$248$	−3.70187	+	3.70187i	−0.235069	+	0.235069i
$249$	−26.1525	+	2.63659i	−1.65735	+	0.167087i
$250$	−22.1904	+	9.73541i	−1.40344	+	0.615721i
$251$			10.4623i			0.660375i	0.943915	+	0.330188i	$0.107112\pi$
$251$			10.4623i			0.660375i	−0.943915	+	0.330188i	$0.892888\pi$
$252$	−9.79103	+	14.8004i	−0.616777	+	0.932335i
$253$	8.99690	+	8.99690i	0.565631	+	0.565631i
$254$	41.9282			2.63081
$255$	3.82827	+	7.00614i	0.239735	+	0.438741i
$256$	−0.0836122			−0.00522576
$257$	−11.1616	−	11.1616i	−0.696240	−	0.696240i	0.267357	−	0.963597i	$-0.413850\pi$
$257$	−11.1616	−	11.1616i	−0.696240	−	0.696240i	−0.963597	+	0.267357i	$0.913850\pi$
$258$	−8.16089	+	9.99088i	−0.508075	+	0.622005i
$259$		−	19.1432i		−	1.18950i
$260$	1.37087	−	3.37539i	0.0850180	−	0.209333i
$261$	−3.81482	−	18.7274i	−0.236131	−	1.15920i
$262$	−7.72185	+	7.72185i	−0.477057	+	0.477057i
$263$	−11.6219	+	11.6219i	−0.716634	+	0.716634i	−0.967914	−	0.251280i	$-0.919148\pi$
$263$	−11.6219	+	11.6219i	−0.716634	+	0.716634i	0.251280	+	0.967914i	$0.419148\pi$
$264$	0.662269	+	6.56909i	0.0407598	+	0.404299i
$265$	9.99912	−	24.6200i	0.614241	−	1.51239i
$266$			4.75273i			0.291409i
$267$	6.69490	+	5.46863i	0.409722	+	0.334675i
$268$	−17.7673	−	17.7673i	−1.08531	−	1.08531i
$269$	24.2656			1.47950			0.739750	−	0.672882i	$-0.234944\pi$
$269$	24.2656			1.47950			0.739750	+	0.672882i	$0.234944\pi$
$270$	19.2439	−	16.2432i	1.17114	−	0.988527i
$271$	11.9046			0.723153			0.361576	−	0.932343i	$-0.382239\pi$
$271$	11.9046			0.723153			0.361576	+	0.932343i	$0.382239\pi$
$272$	3.08785	+	3.08785i	0.187228	+	0.187228i
$273$	−1.77664	−	1.45122i	−0.107527	−	0.0878316i
$274$		−	0.202278i		−	0.0122201i
$275$	9.03687	+	8.79041i	0.544944	+	0.530082i
$276$	2.36498	+	23.4584i	0.142355	+	1.41203i
$277$	16.2773	−	16.2773i	0.978006	−	0.978006i	−0.0217571	−	0.999763i	$-0.506926\pi$
$277$	16.2773	−	16.2773i	0.978006	−	0.978006i	0.999763	+	0.0217571i	$0.00692603\pi$
$278$	−2.06680	+	2.06680i	−0.123959	+	0.123959i
$279$	−2.07361	−	10.1796i	−0.124144	−	0.609436i
$280$	−2.88409	−	6.82892i	−0.172358	−	0.408106i
$281$			19.1583i			1.14289i	0.820640	+	0.571445i	$0.193617\pi$
$281$			19.1583i			1.14289i	−0.820640	+	0.571445i	$0.806383\pi$
$282$	−8.38336	+	10.2632i	−0.499222	+	0.611167i
$283$	4.29088	+	4.29088i	0.255066	+	0.255066i	0.823044	−	0.567978i	$-0.192274\pi$
$283$	4.29088	+	4.29088i	0.255066	+	0.255066i	−0.567978	+	0.823044i	$0.692274\pi$
$284$	−39.9393			−2.36996
$285$	1.09007	−	3.71642i	0.0645703	−	0.220141i
$286$	−3.30067			−0.195173
$287$	6.65629	+	6.65629i	0.392908	+	0.392908i
$288$	12.6044	−	19.0531i	0.742721	−	1.12271i
$289$		−	12.7506i		−	0.750033i
$290$	28.6057	+	11.6179i	1.67978	+	0.682224i
$291$	−11.5277	+	1.16218i	−0.675766	+	0.0681279i
$292$	−12.8415	+	12.8415i	−0.751494	+	0.751494i
$293$	21.5298	−	21.5298i	1.25778	−	1.25778i	0.305635	−	0.952149i	$-0.401131\pi$
$293$	21.5298	−	21.5298i	1.25778	−	1.25778i	0.952149	−	0.305635i	$-0.0988688\pi$
$294$	8.18510	−	0.825189i	0.477365	−	0.0481260i
$295$	−0.373464	+	0.157727i	−0.0217439	+	0.00918322i
$296$		−	13.1979i		−	0.767111i
$297$	−11.5969	−	6.09611i	−0.672922	−	0.353732i
$298$	−22.3767	−	22.3767i	−1.29625	−	1.29625i
$299$	−3.04784			−0.176261
$300$	2.66441	+	23.2089i	0.153830	+	1.33996i
$301$	−7.53552			−0.434340
$302$	18.7597	+	18.7597i	1.07950	+	1.07950i
$303$	4.43540	−	5.42999i	0.254807	−	0.311945i
$304$		−	2.11839i		−	0.121498i
$305$	−30.8411	+	13.0253i	−1.76596	+	0.745826i
$306$	13.1339	−	2.67540i	0.750815	−	0.152943i
$307$	5.71458	−	5.71458i	0.326148	−	0.326148i	−0.524972	−	0.851120i	$-0.675924\pi$
$307$	5.71458	−	5.71458i	0.326148	−	0.326148i	0.851120	+	0.524972i	$0.175924\pi$
$308$	−10.5463	+	10.5463i	−0.600934	+	0.600934i
$309$	−3.27667	−	32.5016i	−0.186404	−	1.84895i
$310$	15.5491	+	6.31507i	0.883128	+	0.358672i
$311$			24.1874i			1.37154i	0.727816	+	0.685772i	$0.240535\pi$
$311$			24.1874i			1.37154i	−0.727816	+	0.685772i	$0.759465\pi$
$312$	−1.22487	−	1.00051i	−0.0693444	−	0.0566428i
$313$	−8.17006	−	8.17006i	−0.461799	−	0.461799i	0.437446	−	0.899245i	$-0.355883\pi$
$313$	−8.17006	−	8.17006i	−0.461799	−	0.461799i	−0.899245	+	0.437446i	$0.855883\pi$
$314$	−4.61981			−0.260711
$315$	14.4595	+	2.70347i	0.814701	+	0.152323i
$316$	21.1015			1.18705
$317$	−11.7569	−	11.7569i	−0.660333	−	0.660333i	0.295125	−	0.955459i	$-0.404639\pi$
$317$	−11.7569	−	11.7569i	−0.660333	−	0.660333i	−0.955459	+	0.295125i	$0.904639\pi$
$318$	−34.5506	−	28.2221i	−1.93750	−	1.58262i
$319$		−	16.0630i		−	0.899356i
$320$	10.6725	+	25.2703i	0.596613	+	1.41265i
$321$	−2.28684	−	22.6833i	−0.127639	−	1.26606i
$322$	−16.9588	+	16.9588i	−0.945077	+	0.945077i
$323$	1.45764	−	1.45764i	0.0811054	−	0.0811054i
$324$	−9.49682	−	22.3433i	−0.527601	−	1.24129i
$325$	−3.01963	+	0.0417471i	−0.167499	+	0.00231571i
$326$		−	48.7591i		−	2.70051i
$327$	−6.57508	+	8.04947i	−0.363603	+	0.445137i
$328$	4.58905	+	4.58905i	0.253388	+	0.253388i
$329$	−7.74094			−0.426772
$330$	18.5733	−	10.1488i	1.02243	−	0.558671i
$331$	5.37127			0.295232			0.147616	−	0.989045i	$-0.452840\pi$
$331$	5.37127			0.295232			0.147616	+	0.989045i	$0.452840\pi$
$332$	−28.9468	−	28.9468i	−1.58866	−	1.58866i
$333$	21.8425	+	14.4497i	1.19696	+	0.791838i
$334$		−	4.28968i		−	0.234721i
$335$	−7.83745	+	19.2975i	−0.428206	+	1.05433i
$336$	8.00532	−	0.807064i	0.436726	−	0.0440289i
$337$	1.76820	−	1.76820i	0.0963201	−	0.0963201i	−0.657305	−	0.753625i	$-0.728304\pi$
$337$	1.76820	−	1.76820i	0.0963201	−	0.0963201i	0.753625	+	0.657305i	$0.228304\pi$
$338$	−19.3643	+	19.3643i	−1.05328	+	1.05328i
$339$	−19.1595	+	1.93158i	−1.04060	+	0.104909i
$340$	−4.67884	+	11.5203i	−0.253746	+	0.624776i
$341$		−	8.73131i		−	0.472827i
$342$	−5.42290	−	3.58747i	−0.293237	−	0.193988i
$343$	14.2520	+	14.2520i	0.769536	+	0.769536i
$344$	−5.19521			−0.280107
$345$	17.1506	−	9.37137i	0.923357	−	0.504537i
$346$	−36.3949			−1.95660
$347$	−7.57252	−	7.57252i	−0.406514	−	0.406514i	0.474007	−	0.880521i	$-0.342807\pi$
$347$	−7.57252	−	7.57252i	−0.406514	−	0.406514i	−0.880521	+	0.474007i	$0.842807\pi$
$348$	18.8300	−	23.0524i	1.00939	−	1.23574i
$349$		−	11.9882i		−	0.641712i	−0.947128	−	0.320856i	$-0.896029\pi$
$349$		−	11.9882i		−	0.641712i	0.947128	−	0.320856i	$-0.103971\pi$
$350$	−16.5696	+	17.0341i	−0.885680	+	0.910513i
$351$	2.99689	−	0.931743i	0.159962	−	0.0497328i
$352$	13.5767	−	13.5767i	0.723642	−	0.723642i
$353$	8.65388	−	8.65388i	0.460599	−	0.460599i	−0.438253	−	0.898852i	$-0.644402\pi$
$353$	8.65388	−	8.65388i	0.460599	−	0.460599i	0.898852	+	0.438253i	$0.144402\pi$
$354$	0.0682705	+	0.677179i	0.00362853	+	0.0359917i
$355$	12.8806	+	30.4985i	0.683631	+	1.61869i
$356$			13.4631i			0.713545i
$357$	6.06372	+	4.95305i	0.320926	+	0.262143i
$358$	7.40724	+	7.40724i	0.391485	+	0.391485i
$359$	−7.44151			−0.392748			−0.196374	−	0.980529i	$-0.562917\pi$
$359$	−7.44151			−0.392748			−0.196374	+	0.980529i	$0.562917\pi$
$360$	9.96882	+	1.86385i	0.525403	+	0.0982336i
$361$	−1.00000			−0.0526316
$362$	2.92952	+	2.92952i	0.153972	+	0.153972i
$363$	6.22760	+	5.08692i	0.326864	+	0.266994i
$364$		−	3.57273i		−	0.187262i
$365$	13.9475	+	5.66462i	0.730046	+	0.296500i
$366$	5.63786	+	55.9223i	0.294696	+	2.92311i
$367$	−18.9349	+	18.9349i	−0.988395	+	0.988395i	−0.999933	−	0.0115387i	$-0.996327\pi$
$367$	−18.9349	+	18.9349i	−0.988395	+	0.988395i	0.0115387	+	0.999933i	$0.496327\pi$
$368$	7.55887	−	7.55887i	0.394033	−	0.394033i
$369$	−12.6192	+	2.57056i	−0.656929	+	0.133818i
$370$	−38.9749	+	16.4605i	−2.02621	+	0.855739i
$371$		−	26.0594i		−	1.35294i
$372$	10.2353	−	12.5305i	0.530678	−	0.649677i
$373$	23.4958	+	23.4958i	1.21657	+	1.21657i	0.968826	+	0.247743i	$0.0796888\pi$
$373$	23.4958	+	23.4958i	1.21657	+	1.21657i	0.247743	+	0.968826i	$0.420311\pi$
$374$	11.2653			0.582514
$375$	16.8635	−	9.51956i	0.870828	−	0.491588i
$376$	−5.33684			−0.275226
$377$	2.72079	+	2.72079i	0.140128	+	0.140128i
$378$	11.4909	−	21.8597i	0.591029	−	1.12434i
$379$		−	11.9710i		−	0.614908i	−0.951563	−	0.307454i	$-0.900523\pi$
$379$		−	11.9710i		−	0.614908i	0.951563	−	0.307454i	$-0.0994770\pi$
$380$	5.55663	−	2.34676i	0.285049	−	0.120386i
$381$	−33.3377	+	3.36097i	−1.70794	+	0.172188i
$382$	−10.6210	+	10.6210i	−0.543418	+	0.543418i
$383$	−5.19022	+	5.19022i	−0.265208	+	0.265208i	−0.827166	−	0.561958i	$-0.810048\pi$
$383$	−5.19022	+	5.19022i	−0.265208	+	0.265208i	0.561958	+	0.827166i	$0.310048\pi$
$384$	19.5751	−	1.97348i	0.998935	−	0.100709i
$385$	11.4547	+	4.65217i	0.583783	+	0.237097i
$386$			2.08993i			0.106375i
$387$	5.68798	−	8.59808i	0.289136	−	0.437065i
$388$	−12.7594	−	12.7594i	−0.647759	−	0.647759i
$389$	−16.4104			−0.832043			−0.416021	−	0.909355i	$-0.636576\pi$
$389$	−16.4104			−0.832043			−0.416021	+	0.909355i	$0.636576\pi$
$390$	−1.42697	+	4.86502i	−0.0722575	+	0.246350i
$391$	10.4024			0.526071
$392$	2.34266	+	2.34266i	0.118322	+	0.118322i
$393$	5.52077	−	6.75874i	0.278486	−	0.340933i
$394$			39.1577i			1.97274i
$395$	−6.80533	−	16.1136i	−0.342413	−	0.810762i
$396$	−4.07284	−	19.9941i	−0.204668	−	1.00474i
$397$	−11.4842	+	11.4842i	−0.576377	+	0.576377i	−0.933903	−	0.357526i	$-0.883620\pi$
$397$	−11.4842	+	11.4842i	−0.576377	+	0.576377i	0.357526	+	0.933903i	$0.383620\pi$
$398$	−17.6763	+	17.6763i	−0.886030	+	0.886030i
$399$	−0.380980	−	3.77897i	−0.0190729	−	0.189185i
$400$	7.38537	−	7.59245i	0.369269	−	0.379622i
$401$		−	0.552147i		−	0.0275729i	−0.999905	−	0.0137864i	$-0.995611\pi$
$401$		−	0.552147i		−	0.0275729i	0.999905	−	0.0137864i	$-0.00438850\pi$
$402$	27.0812	+	22.1209i	1.35069	+	1.10329i
$403$	1.47893	+	1.47893i	0.0736708	+	0.0736708i
$404$	10.9195			0.543263
$405$	−13.9990	+	14.4578i	−0.695618	+	0.718412i
$406$	30.2781			1.50268
$407$	15.5644	+	15.5644i	0.771498	+	0.771498i
$408$	4.18051	+	3.41478i	0.206966	+	0.169057i
$409$			16.8640i			0.833869i	0.908936	+	0.416935i	$0.136896\pi$
$409$			16.8640i			0.833869i	−0.908936	+	0.416935i	$0.863104\pi$
$410$	7.82851	−	19.2755i	0.386623	−	0.951948i
$411$	0.0162147	+	0.160834i	0.000799810	+	0.00793337i
$412$	35.9742	−	35.9742i	1.77232	−	1.77232i
$413$	−0.281124	+	0.281124i	−0.0138332	+	0.0138332i
$414$	−6.54923	−	32.1510i	−0.321877	−	1.58013i
$415$	−12.7689	+	31.4398i	−0.626802	+	1.54332i
$416$			4.59932i			0.225500i
$417$	1.47767	−	1.80902i	0.0723619	−	0.0885882i
$418$	−3.86422	−	3.86422i	−0.189005	−	0.189005i
$419$	2.43587			0.119000			0.0595000	−	0.998228i	$-0.481049\pi$
$419$	2.43587			0.119000			0.0595000	+	0.998228i	$0.481049\pi$
$420$	10.9853	+	20.1043i	0.536028	+	0.980987i
$421$	−11.4536			−0.558214			−0.279107	−	0.960260i	$-0.590038\pi$
$421$	−11.4536			−0.558214			−0.279107	+	0.960260i	$0.590038\pi$
$422$	−29.9074	−	29.9074i	−1.45587	−	1.45587i
$423$	5.84303	−	8.83247i	0.284098	−	0.429449i
$424$		−	17.9661i		−	0.872513i
$425$	10.3061	−	0.142484i	0.499919	−	0.00691150i
$426$	55.3011	−	5.57523i	2.67935	−	0.270121i
$427$	−23.2156	+	23.2156i	−1.12348	+	1.12348i
$428$	25.1069	−	25.1069i	1.21359	−	1.21359i
$429$	2.62441	−	0.264582i	0.126708	−	0.0127742i
$430$	6.47950	+	15.3421i	0.312469	+	0.739861i
$431$			32.9618i			1.58772i	0.608103	+	0.793858i	$0.291931\pi$
$431$			32.9618i			1.58772i	−0.608103	+	0.793858i	$0.708069\pi$
$432$	−5.12172	+	9.74331i	−0.246419	+	0.468775i
$433$	−3.05820	−	3.05820i	−0.146968	−	0.146968i	0.629794	−	0.776762i	$-0.283139\pi$
$433$	−3.05820	−	3.05820i	−0.146968	−	0.146968i	−0.776762	+	0.629794i	$0.783139\pi$
$434$	16.4582			0.790017
$435$	−23.6761	−	6.94449i	−1.13518	−	0.332963i
$436$	−16.1871			−0.775222
$437$	−3.56822	−	3.56822i	−0.170691	−	0.170691i
$438$	15.9882	−	19.5733i	0.763943	−	0.935249i
$439$		−	0.993275i		−	0.0474064i	−0.999719	−	0.0237032i	$-0.992454\pi$
$439$		−	0.993275i		−	0.0474064i	0.999719	−	0.0237032i	$-0.00754568\pi$
$440$	7.89718	+	3.20735i	0.376483	+	0.152904i
$441$	−6.44195	+	1.31224i	−0.306760	+	0.0624876i
$442$	−1.90814	+	1.90814i	−0.0907611	+	0.0907611i
$443$	10.7338	−	10.7338i	0.509980	−	0.509980i	−0.404540	−	0.914520i	$-0.632568\pi$
$443$	10.7338	−	10.7338i	0.509980	−	0.509980i	0.914520	+	0.404540i	$0.132568\pi$
$444$	4.09134	+	40.5823i	0.194167	+	1.92595i
$445$	10.2807	−	4.34192i	0.487354	−	0.205827i
$446$		−	44.0086i		−	2.08387i
$447$	19.5857	+	15.9983i	0.926374	+	0.756694i
$448$	19.0221	+	19.0221i	0.898711	+	0.898711i
$449$	2.24464			0.105931			0.0529656	−	0.998596i	$-0.483133\pi$
$449$	2.24464			0.105931			0.0529656	+	0.998596i	$0.483133\pi$
$450$	−6.92900	−	31.7637i	−0.326636	−	1.49736i
$451$	−10.8238			−0.509673
$452$	−21.2066	−	21.2066i	−0.997475	−	0.997475i
$453$	−16.4199	−	13.4123i	−0.771474	−	0.630167i
$454$			37.2896i			1.75009i
$455$	−2.72822	+	1.15222i	−0.127901	+	0.0540169i
$456$	−0.262659	−	2.60533i	−0.0123001	−	0.122006i
$457$	17.3375	−	17.3375i	0.811016	−	0.811016i	−0.173770	−	0.984786i	$-0.555595\pi$
$457$	17.3375	−	17.3375i	0.811016	−	0.811016i	0.984786	+	0.173770i	$0.0555949\pi$
$458$	29.7624	−	29.7624i	1.39071	−	1.39071i
$459$	−10.2285	+	3.18007i	−0.477425	+	0.148433i
$460$	28.2010	+	11.4535i	1.31488	+	0.534023i
$461$		−	10.9020i		−	0.507758i	−0.967236	−	0.253879i	$-0.918294\pi$
$461$		−	10.9020i		−	0.507758i	0.967236	−	0.253879i	$-0.0817064\pi$
$462$	13.1306	−	16.0749i	0.610889	−	0.747874i
$463$	−25.7646	−	25.7646i	−1.19738	−	1.19738i	−0.974948	−	0.222434i	$-0.928600\pi$
$463$	−25.7646	−	25.7646i	−1.19738	−	1.19738i	−0.222434	−	0.974948i	$-0.571400\pi$
$464$	−13.4955			−0.626515
$465$	−12.8695	−	3.77479i	−0.596809	−	0.175052i
$466$	−31.3264			−1.45117
$467$	−16.8093	−	16.8093i	−0.777840	−	0.777840i	0.201623	−	0.979463i	$-0.435378\pi$
$467$	−16.8093	−	16.8093i	−0.777840	−	0.777840i	−0.979463	+	0.201623i	$0.935378\pi$
$468$	4.07651	+	2.69678i	0.188437	+	0.124659i
$469$			20.4257i			0.943173i
$470$	6.65613	+	15.7603i	0.307024	+	0.726969i
$471$	3.67328	−	0.370325i	0.169256	−	0.0170637i
$472$	−0.193815	+	0.193815i	−0.00892107	+	0.00892107i
$473$	6.12676	−	6.12676i	0.281709	−	0.281709i
$474$	−29.2178	+	2.94562i	−1.34202	+	0.135297i
$475$	−3.58407	−	3.48632i	−0.164448	−	0.159963i
$476$			12.1939i			0.558905i
$477$	29.7340	+	19.6702i	1.36142	+	0.900637i
$478$	12.9819	+	12.9819i	0.593779	+	0.593779i
$479$	1.64892			0.0753411			0.0376705	−	0.999290i	$-0.488006\pi$
$479$	1.64892			0.0753411			0.0376705	+	0.999290i	$0.488006\pi$
$480$	−14.1418	−	25.8810i	−0.645483	−	1.18130i
$481$	−5.27267			−0.240413
$482$	−19.0271	−	19.0271i	−0.866659	−	0.866659i
$483$	12.1248	−	14.8436i	0.551696	−	0.675408i
$484$			12.5234i			0.569246i
$485$	−5.62838	+	13.8583i	−0.255572	+	0.629272i
$486$	16.2685	+	29.6114i	0.737954	+	1.34320i
$487$	12.7342	−	12.7342i	0.577042	−	0.577042i	−0.357045	−	0.934087i	$-0.616216\pi$
$487$	12.7342	−	12.7342i	0.577042	−	0.577042i	0.934087	+	0.357045i	$0.116216\pi$
$488$	−16.0055	+	16.0055i	−0.724536	+	0.724536i
$489$	3.90854	+	38.7690i	0.176750	+	1.75320i
$490$	3.99637	−	9.83991i	0.180537	−	0.444522i
$491$		−	5.82676i		−	0.262958i	−0.991319	−	0.131479i	$-0.958027\pi$
$491$		−	5.82676i		−	0.262958i	0.991319	−	0.131479i	$-0.0419726\pi$
$492$	−15.5335	−	12.6883i	−0.700305	−	0.572033i
$493$	−9.28616	−	9.28616i	−0.418228	−	0.418228i
$494$	1.30906			0.0588975
$495$	−13.9544	+	9.55827i	−0.627203	+	0.429612i
$496$	−7.33572			−0.329384
$497$	22.9577	+	22.9577i	1.02979	+	1.02979i
$498$	44.1212	+	36.0397i	1.97712	+	1.61498i
$499$		−	10.1282i		−	0.453402i	−0.973964	−	0.226701i	$-0.927206\pi$
$499$		−	10.1282i		−	0.453402i	0.973964	−	0.226701i	$-0.0727940\pi$
$500$	28.0969	+	10.9612i	1.25653	+	0.490201i
$501$	0.343862	+	3.41079i	0.0153626	+	0.152383i
$502$	16.0342	−	16.0342i	0.715642	−	0.715642i
$503$	−28.2167	+	28.2167i	−1.25812	+	1.25812i	−0.306134	+	0.951988i	$0.599036\pi$
$503$	−28.2167	+	28.2167i	−1.25812	+	1.25812i	−0.951988	+	0.306134i	$0.900964\pi$
$504$	9.74541	−	1.98516i	0.434095	−	0.0884262i
$505$	−3.52157	−	8.33834i	−0.156708	−	0.371051i
$506$		−	27.5767i		−	1.22594i
$507$	13.8446	−	16.9491i	0.614860	−	0.752736i
$508$	−36.8997	−	36.8997i	−1.63716	−	1.63716i
$509$	24.8752			1.10257			0.551287	−	0.834316i	$-0.314137\pi$
$509$	24.8752			1.10257			0.551287	+	0.834316i	$0.314137\pi$
$510$	4.87030	−	16.6045i	0.215661	−	0.735258i
$511$	14.7630			0.653075
$512$	−15.9358	−	15.9358i	−0.704271	−	0.704271i
$513$	4.59940	+	2.41775i	0.203069	+	0.106746i
$514$			34.2118i			1.50902i
$515$	−39.0725	−	15.8688i	−1.72174	−	0.699265i
$516$	15.9748	−	1.61052i	0.703252	−	0.0708990i
$517$	6.29378	−	6.29378i	0.276800	−	0.276800i
$518$	−29.3382	+	29.3382i	−1.28905	+	1.28905i
$519$	28.9381	−	2.91742i	1.27024	−	0.128061i
$520$	−1.88091	+	0.794376i	−0.0824835	+	0.0348357i
$521$		−	7.87895i		−	0.345183i	−0.984993	−	0.172592i	$-0.944786\pi$
$521$		−	7.87895i		−	0.345183i	0.984993	−	0.172592i	$-0.0552141\pi$
$522$	−22.8546	+	34.5475i	−1.00032	+	1.51210i
$523$	−0.420649	−	0.420649i	−0.0183937	−	0.0183937i	0.697850	−	0.716244i	$-0.254140\pi$
$523$	−0.420649	−	0.420649i	−0.0183937	−	0.0183937i	−0.716244	+	0.697850i	$0.754140\pi$
$524$	13.5915			0.593748
$525$	11.8092	−	14.8723i	0.515397	−	0.649081i
$526$	35.6226			1.55322
$527$	−5.04764	−	5.04764i	−0.219879	−	0.219879i
$528$	−5.85255	+	7.16492i	−0.254700	+	0.311813i
$529$		−	2.46437i		−	0.107147i
$530$	−53.0561	+	22.4075i	−2.30461	+	0.973318i
$531$	−0.108566	−	0.532963i	−0.00471135	−	0.0231286i
$532$	4.18273	−	4.18273i	0.181344	−	0.181344i
$533$	1.83336	−	1.83336i	0.0794118	−	0.0794118i
$534$	−1.87935	−	18.6414i	−0.0813276	−	0.806694i
$535$	−27.2692	−	11.0751i	−1.17895	−	0.478818i
$536$			14.0821i			0.608255i
$537$	−6.48337	−	5.29584i	−0.279778	−	0.228532i
$538$	−37.1887	−	37.1887i	−1.60332	−	1.60332i
$539$	−5.52543			−0.237997
$540$	−31.2310	−	2.64084i	−1.34397	−	0.113644i
$541$	−34.9116			−1.50097			−0.750483	−	0.660890i	$-0.770179\pi$
$541$	−34.9116			−1.50097			−0.750483	+	0.660890i	$0.770179\pi$
$542$	−18.2446	−	18.2446i	−0.783673	−	0.783673i
$543$	−2.56413	−	2.09447i	−0.110038	−	0.0898824i
$544$		−	15.6976i		−	0.673031i
$545$	5.22041	+	12.3608i	0.223618	+	0.529480i
$546$	0.498727	+	4.94690i	0.0213435	+	0.211708i
$547$	−2.26481	+	2.26481i	−0.0968361	+	0.0968361i	−0.753865	−	0.657029i	$-0.771813\pi$
$547$	−2.26481	+	2.26481i	−0.0968361	+	0.0968361i	0.657029	+	0.753865i	$0.271813\pi$
$548$	−0.178019	+	0.178019i	−0.00760458	+	0.00760458i
$549$	−8.96550	−	44.0128i	−0.382638	−	1.87842i
$550$	−0.377727	−	27.3215i	−0.0161063	−	1.16499i
$551$			6.37067i			0.271400i
$552$	8.35918	−	10.2336i	0.355790	−	0.435572i
$553$	−12.1294	−	12.1294i	−0.515797	−	0.515797i
$554$	−49.8921			−2.11971
$555$	29.6700	−	16.2122i	1.25942	−	0.688170i
$556$	3.63786			0.154280
$557$	20.6806	+	20.6806i	0.876264	+	0.876264i	0.993146	−	0.116882i	$-0.0372898\pi$
$557$	20.6806	+	20.6806i	0.876264	+	0.876264i	−0.116882	+	0.993146i	$0.537290\pi$
$558$	−12.4230	+	18.7789i	−0.525907	+	0.794973i
$559$			2.07553i			0.0877857i
$560$	3.90858	−	9.62377i	0.165168	−	0.406679i
$561$	−8.95720	+	0.903029i	−0.378173	+	0.0381259i
$562$	29.3614	−	29.3614i	1.23854	−	1.23854i
$563$	8.15718	−	8.15718i	0.343784	−	0.343784i	−0.514004	−	0.857788i	$-0.671838\pi$
$563$	8.15718	−	8.15718i	0.343784	−	0.343784i	0.857788	+	0.514004i	$0.171838\pi$
$564$	16.4103	−	1.65442i	0.690998	−	0.0696636i
$565$	−9.35460	+	23.0330i	−0.393551	+	0.969007i
$566$		−	13.1521i		−	0.552825i
$567$	−7.38431	+	18.3021i	−0.310112	+	0.768616i
$568$	15.8277	+	15.8277i	0.664116	+	0.664116i
$569$	29.2097			1.22453			0.612266	−	0.790652i	$-0.290258\pi$
$569$	29.2097			1.22453			0.612266	+	0.790652i	$0.290258\pi$
$570$	−7.36627	+	4.02505i	−0.308539	+	0.168591i
$571$	−5.05326			−0.211472			−0.105736	−	0.994394i	$-0.533720\pi$
$571$	−5.05326			−0.211472			−0.105736	+	0.994394i	$0.533720\pi$
$572$	2.90481	+	2.90481i	0.121456	+	0.121456i
$573$	7.59353	−	9.29630i	0.317224	−	0.388358i
$574$		−	20.4024i		−	0.851581i
$575$	−0.348793	−	25.2287i	−0.0145457	−	1.05211i
$576$	−36.0627	+	7.34606i	−1.50261	+	0.306086i
$577$	−15.7866	+	15.7866i	−0.657204	+	0.657204i	−0.954718	−	0.297513i	$-0.903843\pi$
$577$	−15.7866	+	15.7866i	−0.657204	+	0.657204i	0.297513	+	0.954718i	$0.403843\pi$
$578$	−19.5411	+	19.5411i	−0.812803	+	0.812803i
$579$	−0.167529	−	1.66173i	−0.00696228	−	0.0690593i
$580$	−14.9504	−	35.3995i	−0.620783	−	1.46988i
$581$			33.2780i			1.38060i
$582$	19.4481	+	15.8859i	0.806150	+	0.658490i
$583$	21.1876	+	21.1876i	0.877502	+	0.877502i
$584$	10.1780			0.421170
$585$	0.744625	−	3.98263i	0.0307865	−	0.164662i
$586$	−65.9918			−2.72609
$587$	17.8025	+	17.8025i	0.734787	+	0.734787i	0.971564	−	0.236777i	$-0.0760912\pi$
$587$	17.8025	+	17.8025i	0.734787	+	0.734787i	−0.236777	+	0.971564i	$0.576091\pi$
$588$	−7.92968	−	6.47723i	−0.327014	−	0.267117i
$589$			3.46288i			0.142686i
$590$	0.814087	+	0.330632i	0.0335154	+	0.0136119i
$591$	−3.13889	−	31.1349i	−0.129117	−	1.28072i
$592$	13.0766	−	13.0766i	0.537446	−	0.537446i
$593$	−2.19999	+	2.19999i	−0.0903426	+	0.0903426i	−0.750834	−	0.660491i	$-0.770348\pi$
$593$	−2.19999	+	2.19999i	−0.0903426	+	0.0903426i	0.660491	+	0.750834i	$0.270348\pi$
$594$	8.43038	+	27.1158i	0.345903	+	1.11257i
$595$	9.31149	−	3.93257i	0.381734	−	0.161220i
$596$			39.3860i			1.61331i
$597$	12.6377	−	15.4716i	0.517227	−	0.633210i
$598$	4.67102	+	4.67102i	0.191012	+	0.191012i
$599$	33.5964			1.37271			0.686355	−	0.727266i	$-0.259209\pi$
$599$	33.5964			1.37271			0.686355	+	0.727266i	$0.259209\pi$
$600$	8.14164	−	10.2534i	0.332381	−	0.418594i
$601$	34.5782			1.41047			0.705237	−	0.708972i	$-0.250841\pi$
$601$	34.5782			1.41047			0.705237	+	0.708972i	$0.250841\pi$
$602$	11.5487	+	11.5487i	0.470690	+	0.470690i
$603$	−23.3059	−	15.4178i	−0.949090	−	0.627861i
$604$		−	33.0197i		−	1.34355i
$605$	9.56315	−	4.03885i	0.388797	−	0.164203i
$606$	−15.1194	+	1.52428i	−0.614183	+	0.0619195i
$607$	7.57208	−	7.57208i	0.307341	−	0.307341i	−0.536536	−	0.843877i	$-0.680267\pi$
$607$	7.57208	−	7.57208i	0.307341	−	0.307341i	0.843877	+	0.536536i	$0.180267\pi$
$608$	−5.38460	+	5.38460i	−0.218374	+	0.218374i
$609$	−24.0746	+	2.42710i	−0.975551	+	0.0983511i
$610$	67.2283	+	27.3040i	2.72200	+	1.10551i
$611$			2.13211i			0.0862561i
$612$	−13.9133	−	9.20419i	−0.562411	−	0.372057i
$613$	7.50258	+	7.50258i	0.303026	+	0.303026i	0.842197	−	0.539170i	$-0.181262\pi$
$613$	7.50258	+	7.50258i	0.303026	+	0.303026i	−0.539170	+	0.842197i	$0.681262\pi$
$614$	−17.5160			−0.706887
$615$	−4.67944	+	15.9538i	−0.188693	+	0.643317i
$616$	8.35890			0.336790
$617$	20.5696	+	20.5696i	0.828103	+	0.828103i	0.987254	−	0.159152i	$-0.0508758\pi$
$617$	20.5696	+	20.5696i	0.828103	+	0.828103i	−0.159152	+	0.987254i	$0.550876\pi$
$618$	−44.7891	+	54.8326i	−1.80168	+	2.20569i
$619$		−	4.28381i		−	0.172181i	−0.996287	−	0.0860905i	$-0.972563\pi$
$619$		−	4.28381i		−	0.172181i	0.996287	−	0.0860905i	$-0.0274374\pi$
$620$	−8.12655	−	19.2420i	−0.326370	−	0.772775i
$621$	7.78462	+	25.0387i	0.312386	+	1.00477i
$622$	37.0689	−	37.0689i	1.48633	−	1.48633i
$623$	7.73880	−	7.73880i	0.310048	−	0.310048i
$624$	−0.222292	−	2.20493i	−0.00889881	−	0.0882679i
$625$	−0.691130	−	24.9904i	−0.0276452	−	0.999618i
$626$			25.0423i			1.00089i
$627$	3.38225	+	2.76274i	0.135074	+	0.110333i
$628$	4.06575	+	4.06575i	0.162241	+	0.162241i
$629$	17.9958			0.717540
$630$	−18.0169	−	26.3034i	−0.717812	−	1.04795i
$631$	25.8652			1.02968			0.514839	−	0.857287i	$-0.327852\pi$
$631$	25.8652			1.02968			0.514839	+	0.857287i	$0.327852\pi$
$632$	−8.36240	−	8.36240i	−0.332639	−	0.332639i
$633$	26.1772	+	21.3824i	1.04045	+	0.849874i
$634$			36.0365i			1.43119i
$635$	−16.2771	+	40.0777i	−0.645936	+	1.59043i
$636$	5.56950	+	55.2443i	0.220845	+	2.19058i
$637$	0.935912	−	0.935912i	0.0370822	−	0.0370822i
$638$	−24.6177	+	24.6177i	−0.974623	+	0.974623i
$639$	−43.5238	+	8.86590i	−1.72178	+	0.350730i
$640$	9.55749	−	23.5326i	0.377793	−	0.930207i
$641$		−	12.3040i		−	0.485981i	−0.970029	−	0.242990i	$-0.921872\pi$
$641$		−	12.3040i		−	0.485981i	0.970029	−	0.242990i	$-0.0781283\pi$
$642$	−31.2590	+	38.2684i	−1.23369	+	1.51034i
$643$	−7.72519	−	7.72519i	−0.304652	−	0.304652i	0.538179	−	0.842831i	$-0.319112\pi$
$643$	−7.72519	−	7.72519i	−0.304652	−	0.304652i	−0.842831	+	0.538179i	$0.819112\pi$
$644$	29.8498			1.17625
$645$	−6.38177	−	11.6793i	−0.251282	−	0.459873i
$646$	−4.46787			−0.175786
$647$	23.7301	+	23.7301i	0.932927	+	0.932927i	0.997888	−	0.0649608i	$-0.0206922\pi$
$647$	23.7301	+	23.7301i	0.932927	+	0.932927i	−0.0649608	+	0.997888i	$0.520692\pi$
$648$	−5.09097	+	12.6180i	−0.199992	+	0.495683i
$649$		−	0.457136i		−	0.0179442i
$650$	4.69177	+	4.56381i	0.184026	+	0.179007i
$651$	−13.0861	+	1.31929i	−0.512886	+	0.0517071i
$652$	−42.9113	+	42.9113i	−1.68054	+	1.68054i
$653$	−22.7926	+	22.7926i	−0.891944	+	0.891944i	−0.994706	−	0.102762i	$-0.967232\pi$
$653$	−22.7926	+	22.7926i	−0.891944	+	0.891944i	0.102762	+	0.994706i	$0.467232\pi$
$654$	22.4131	−	2.25960i	0.876422	−	0.0883574i
$655$	−4.38332	−	10.3788i	−0.171270	−	0.405532i
$656$			9.09377i			0.355052i
$657$	−11.1434	+	16.8446i	−0.434746	+	0.657172i
$658$	11.8635	+	11.8635i	0.462488	+	0.462488i
$659$	−31.4968			−1.22694			−0.613470	−	0.789718i	$-0.710227\pi$
$659$	−31.4968			−1.22694			−0.613470	+	0.789718i	$0.710227\pi$
$660$	−25.2774	−	7.41418i	−0.983921	−	0.288597i
$661$	−5.04347			−0.196168			−0.0980842	−	0.995178i	$-0.531271\pi$
$661$	−5.04347			−0.196168			−0.0980842	+	0.995178i	$0.531271\pi$
$662$	−8.23183	−	8.23183i	−0.319939	−	0.319939i
$663$	1.36424	−	1.67015i	0.0529825	−	0.0648633i
$664$			22.9428i			0.890355i
$665$	−4.54297	−	1.84508i	−0.176169	−	0.0715490i
$666$	−11.3300	−	55.6203i	−0.439028	−	2.15524i
$667$	−22.7320	+	22.7320i	−0.880185	+	0.880185i
$668$	−3.77522	+	3.77522i	−0.146067	+	0.146067i
$669$	3.52774	+	34.9919i	0.136390	+	1.35286i
$670$	41.5861	−	17.5633i	1.60661	−	0.678529i
$671$		−	37.7509i		−	1.45736i
$672$	−22.3997	−	18.2968i	−0.864086	−	0.705815i
$673$	7.79536	+	7.79536i	0.300489	+	0.300489i	0.841205	−	0.540716i	$-0.181847\pi$
$673$	7.79536	+	7.79536i	0.300489	+	0.300489i	−0.540716	+	0.841205i	$0.681847\pi$
$674$	−5.41978			−0.208762
$675$	8.05554	+	24.7004i	0.310058	+	0.950718i
$676$	34.0839			1.31092
$677$	20.8940	+	20.8940i	0.803020	+	0.803020i	0.983566	−	0.180546i	$-0.0577866\pi$
$677$	20.8940	+	20.8940i	0.803020	+	0.803020i	−0.180546	+	0.983566i	$0.557787\pi$
$678$	32.3235	+	26.4030i	1.24138	+	1.01400i
$679$			14.6685i			0.562926i
$680$	6.41962	−	2.71123i	0.246181	−	0.103971i
$681$	−2.98914	−	29.6495i	−0.114544	−	1.13617i
$682$	−13.3813	+	13.3813i	−0.512398	+	0.512398i
$683$	20.9518	−	20.9518i	0.801698	−	0.801698i	−0.181663	−	0.983361i	$-0.558148\pi$
$683$	20.9518	−	20.9518i	0.801698	−	0.801698i	0.983361	+	0.181663i	$0.0581480\pi$
$684$	1.61531	+	7.92975i	0.0617628	+	0.303201i
$685$	0.193351	+	0.0785271i	0.00738754	+	0.00300037i
$686$		−	43.6844i		−	1.66788i
$687$	−21.2788	+	26.0503i	−0.811836	+	0.993881i
$688$	−5.14748	−	5.14748i	−0.196246	−	0.196246i
$689$	−7.17763			−0.273446
$690$	−40.6467	−	11.9222i	−1.54739	−	0.453870i
$691$	27.3570			1.04071			0.520354	−	0.853950i	$-0.325800\pi$
$691$	27.3570			1.04071			0.520354	+	0.853950i	$0.325800\pi$
$692$	32.0300	+	32.0300i	1.21760	+	1.21760i
$693$	−9.15174	+	13.8340i	−0.347646	+	0.525509i
$694$			23.2108i			0.881071i
$695$	−1.17323	−	2.77795i	−0.0445030	−	0.105374i
$696$	−16.5977	+	1.67332i	−0.629136	+	0.0634269i
$697$	−6.25734	+	6.25734i	−0.237014	+	0.237014i
$698$	−18.3727	+	18.3727i	−0.695417	+	0.695417i
$699$	24.9081	−	2.51114i	0.942112	−	0.0949799i
$700$	29.5736	−	0.408862i	1.11778	−	0.0154535i
$701$		−	37.3153i		−	1.40938i	−0.709515	−	0.704690i	$-0.751086\pi$
$701$		−	37.3153i		−	1.40938i	0.709515	−	0.704690i	$-0.248914\pi$
$702$	−6.02090	−	3.16498i	−0.227244	−	0.119455i
$703$	−6.17292	−	6.17292i	−0.232816	−	0.232816i
$704$	−30.9319			−1.16579
$705$	−6.55574	−	11.9977i	−0.246903	−	0.451860i
$706$	−26.5253			−0.998293
$707$	−6.27666	−	6.27666i	−0.236058	−	0.236058i
$708$	0.535882	−	0.656047i	0.0201397	−	0.0246558i
$709$			5.79368i			0.217586i	0.994064	+	0.108793i	$0.0346986\pi$
$709$			5.79368i			0.217586i	−0.994064	+	0.108793i	$0.965301\pi$
$710$	27.0007	−	66.4815i	1.01332	−	2.49501i
$711$	22.9954	−	4.68421i	0.862393	−	0.175671i
$712$	5.33536	−	5.33536i	0.199951	−	0.199951i
$713$	−12.3563	+	12.3563i	−0.462748	+	0.462748i
$714$	−1.70217	−	16.8840i	−0.0637022	−	0.631866i
$715$	1.28136	−	3.15499i	0.0479203	−	0.117990i
$716$		−	13.0378i		−	0.487244i
$717$	−11.3627	−	9.28148i	−0.424349	−	0.346623i
$718$	11.4046	+	11.4046i	0.425617	+	0.425617i
$719$	16.7937			0.626298			0.313149	−	0.949704i	$-0.398616\pi$
$719$	16.7937			0.626298			0.313149	+	0.949704i	$0.398616\pi$
$720$	8.03051	+	11.7240i	0.299279	+	0.436926i
$721$	−41.3569			−1.54021
$722$	1.53257	+	1.53257i	0.0570363	+	0.0570363i
$723$	16.6539	+	13.6035i	0.619366	+	0.505919i
$724$		−	5.15636i		−	0.191634i
$725$	−22.2102	+	22.8329i	−0.824867	+	0.847994i
$726$	−1.74818	−	17.3403i	−0.0648809	−	0.643558i
$727$	0.162766	−	0.162766i	0.00603665	−	0.00603665i	−0.704082	−	0.710119i	$-0.748641\pi$
$727$	0.162766	−	0.162766i	0.00603665	−	0.00603665i	0.710119	+	0.704082i	$0.248641\pi$
$728$	−1.41585	+	1.41585i	−0.0524749	+	0.0524749i
$729$	−15.3090	−	22.2404i	−0.567000	−	0.823718i
$730$	−12.6941	−	30.0569i	−0.469830	−	1.11246i
$731$		−	7.08387i		−	0.262006i
$732$	44.2538	−	54.1772i	1.63567	−	2.00245i
$733$	1.14668	+	1.14668i	0.0423534	+	0.0423534i	0.727966	−	0.685613i	$-0.240466\pi$
$733$	1.14668	+	1.14668i	0.0423534	+	0.0423534i	−0.685613	+	0.727966i	$0.740466\pi$
$734$	58.0381			2.14223
$735$	−2.38880	+	8.14421i	−0.0881122	+	0.300404i
$736$	−38.4269			−1.41643
$737$	−16.6072	−	16.6072i	−0.611733	−	0.611733i
$738$	23.2793	+	15.4002i	0.856924	+	0.566890i
$739$		−	25.1897i		−	0.926618i	−0.886197	−	0.463309i	$-0.846662\pi$
$739$		−	25.1897i		−	0.926618i	0.886197	−	0.463309i	$-0.153338\pi$
$740$	48.7869	+	19.8143i	1.79344	+	0.728386i
$741$	−1.04085	+	0.104935i	−0.0382367	+	0.00385487i
$742$	−39.9378	+	39.9378i	−1.46616	+	1.46616i
$743$	16.5219	−	16.5219i	0.606130	−	0.606130i	−0.335802	−	0.941933i	$-0.609007\pi$
$743$	16.5219	−	16.5219i	0.606130	−	0.606130i	0.941933	+	0.335802i	$0.109007\pi$
$744$	−9.02197	+	0.909558i	−0.330761	+	0.0333460i
$745$	30.0760	−	12.7022i	1.10190	−	0.465371i
$746$		−	72.0180i		−	2.63677i
$747$	−37.9704	−	25.1190i	−1.38926	−	0.919055i
$748$	−9.91423	−	9.91423i	−0.362500	−	0.362500i
$749$	−28.8636			−1.05465
$750$	−40.4339	−	11.2551i	−1.47644	−	0.410979i
$751$	42.5119			1.55128			0.775641	−	0.631175i	$-0.217427\pi$
$751$	42.5119			1.55128			0.775641	+	0.631175i	$0.217427\pi$
$752$	−5.28780	−	5.28780i	−0.192826	−	0.192826i
$753$	−11.4637	+	14.0343i	−0.417762	+	0.511440i
$754$		−	8.33960i		−	0.303710i
$755$	−25.2145	+	10.6490i	−0.917651	+	0.387556i
$756$	−29.3509	+	9.12528i	−1.06748	+	0.331883i
$757$	−9.29020	+	9.29020i	−0.337658	+	0.337658i	−0.855485	−	0.517827i	$-0.826741\pi$
$757$	−9.29020	+	9.29020i	−0.337658	+	0.337658i	0.517827	+	0.855485i	$0.326741\pi$
$758$	−18.3464	+	18.3464i	−0.666370	+	0.666370i
$759$	2.21056	+	21.9267i	0.0802382	+	0.795888i
$760$	−3.13206	−	1.27205i	−0.113612	−	0.0461421i
$761$			38.0927i			1.38086i	0.723399	+	0.690430i	$0.242579\pi$
$761$			38.0927i			1.38086i	−0.723399	+	0.690430i	$0.757421\pi$
$762$	56.2432	+	45.9414i	2.03748	+	1.66428i
$763$	9.30457	+	9.30457i	0.336848	+	0.336848i
$764$	18.6944			0.676341
$765$	−2.54143	+	13.5929i	−0.0918856	+	0.491451i
$766$	15.9087			0.574806
$767$	0.0774309	+	0.0774309i	0.00279587	+	0.00279587i
$768$	−0.112159	−	0.0916153i	−0.00404719	−	0.00330588i
$769$			2.65507i			0.0957443i	0.998853	+	0.0478722i	$0.0152440\pi$
$769$			2.65507i			0.0957443i	−0.998853	+	0.0478722i	$0.984756\pi$
$770$	−10.4253	−	24.6848i	−0.375700	−	0.889579i
$771$	−2.74242	−	27.2023i	−0.0987660	−	0.979666i
$772$	1.83928	−	1.83928i	0.0661972	−	0.0661972i
$773$	−16.2128	+	16.2128i	−0.583134	+	0.583134i	−0.935763	−	0.352630i	$-0.885288\pi$
$773$	−16.2128	+	16.2128i	−0.583134	+	0.583134i	0.352630	+	0.935763i	$0.385288\pi$
$774$	−21.8944	+	4.45993i	−0.786976	+	0.160309i
$775$	−12.0727	+	12.4112i	−0.433665	+	0.445824i
$776$			10.1129i			0.363033i
$777$	20.9755	−	25.6790i	0.752492	−	0.921230i
$778$	25.1501	+	25.1501i	0.901676	+	0.901676i
$779$	4.29278			0.153805
$780$	5.53738	−	3.02572i	0.198270	−	0.108338i
$781$	−37.3315			−1.33583
$782$	−15.9423	−	15.9423i	−0.570097	−	0.570097i
$783$	15.4027	−	29.3013i	0.550447	−	1.04714i
$784$			4.64226i			0.165795i
$785$	1.79347	−	4.41591i	0.0640117	−	0.157611i
$786$	−18.8192	+	1.89727i	−0.671258	+	0.0676735i
$787$	16.8057	−	16.8057i	0.599059	−	0.599059i	−0.341003	−	0.940062i	$-0.610767\pi$
$787$	16.8057	−	16.8057i	0.599059	−	0.599059i	0.940062	+	0.341003i	$0.110767\pi$
$788$	34.4615	−	34.4615i	1.22764	−	1.22764i
$789$	−28.3240	+	2.85552i	−1.00836	+	0.101659i
$790$	−14.2655	+	35.1248i	−0.507545	+	1.24968i
$791$			24.3797i			0.866842i
$792$	−6.30948	+	9.53756i	−0.224198	+	0.338902i
$793$	6.39434	+	6.39434i	0.227070	+	0.227070i
$794$	35.2007			1.24923
$795$	40.3895	−	22.0695i	1.43247	−	0.782725i
$796$	31.1126			1.10276
$797$	22.0216	+	22.0216i	0.780044	+	0.780044i	0.979838	−	0.199794i	$-0.0640272\pi$
$797$	22.0216	+	22.0216i	0.780044	+	0.780044i	−0.199794	+	0.979838i	$0.564027\pi$
$798$	−5.20765	+	6.37541i	−0.184349	+	0.225687i
$799$		−	7.27698i		−	0.257441i
$800$	−38.0712	+	0.526344i	−1.34602	+	0.0186091i
$801$	2.98861	+	14.6714i	0.105597	+	0.518390i
$802$	−0.846203	+	0.846203i	−0.0298805	+	0.0298805i
$803$	−12.0031	+	12.0031i	−0.423579	+	0.423579i
$804$	−4.36546	−	43.3012i	−0.153958	−	1.52712i
$805$	−9.62669	−	22.7940i	−0.339296	−	0.803382i
$806$		−	4.53313i		−	0.159673i
$807$	32.5503	+	26.5882i	1.14583	+	0.935950i
$808$	−4.32731	−	4.32731i	−0.152234	−	0.152234i
$809$	23.9724			0.842826			0.421413	−	0.906869i	$-0.361534\pi$
$809$	23.9724			0.842826			0.421413	+	0.906869i	$0.361534\pi$
$810$	43.6120	−	0.703041i	1.53237	−	0.0247023i
$811$	−32.3088			−1.13452			−0.567258	−	0.823540i	$-0.691996\pi$
$811$	−32.3088			−1.13452			−0.567258	+	0.823540i	$0.691996\pi$
$812$	−26.6468	−	26.6468i	−0.935120	−	0.935120i
$813$	15.9691	+	13.0441i	0.560059	+	0.457475i
$814$		−	47.7070i		−	1.67213i
$815$	46.6071	+	18.9289i	1.63258	+	0.663052i
$816$	0.758691	+	7.52551i	0.0265595	+	0.263445i
$817$	−2.42991	+	2.42991i	−0.0850117	+	0.0850117i
$818$	25.8452	−	25.8452i	0.903655	−	0.903655i
$819$	−0.793090	−	3.89338i	−0.0277128	−	0.136046i
$820$	−23.8534	+	10.0741i	−0.832996	+	0.351803i
$821$			23.0284i			0.803698i	0.915706	+	0.401849i	$0.131632\pi$
$821$			23.0284i			0.803698i	−0.915706	+	0.401849i	$0.868368\pi$
$822$	0.221639	−	0.271339i	0.00773056	−	0.00946405i
$823$	3.68340	+	3.68340i	0.128395	+	0.128395i	0.768384	−	0.639989i	$-0.221061\pi$
$823$	3.68340	+	3.68340i	0.128395	+	0.128395i	−0.639989	+	0.768384i	$0.721061\pi$
$824$	−28.5127			−0.993287
$825$	2.49044	+	21.6935i	0.0867059	+	0.755270i
$826$	0.861683			0.0299818
$827$	9.27192	+	9.27192i	0.322416	+	0.322416i	0.849693	−	0.527277i	$-0.176787\pi$
$827$	9.27192	+	9.27192i	0.322416	+	0.322416i	−0.527277	+	0.849693i	$0.676787\pi$
$828$	−22.5313	+	34.0588i	−0.783017	+	1.18363i
$829$			8.34756i			0.289923i	0.989437	+	0.144961i	$0.0463058\pi$
$829$			8.34756i			0.289923i	−0.989437	+	0.144961i	$0.953694\pi$
$830$	67.7529	−	28.6144i	2.35174	−	0.993222i
$831$	39.6699	−	3.99936i	1.37613	−	0.138736i
$832$	5.23933	−	5.23933i	0.181641	−	0.181641i
$833$	−3.19430	+	3.19430i	−0.110676	+	0.110676i
$834$	−5.03708	+	0.507818i	−0.174420	+	0.0175843i
$835$	4.10036	+	1.66531i	0.141899	+	0.0576305i
$836$			6.80155i			0.235237i
$837$	8.37238	−	15.9272i	0.289392	−	0.550524i
$838$	−3.73314	−	3.73314i	−0.128959	−	0.128959i
$839$	−22.1211			−0.763706			−0.381853	−	0.924223i	$-0.624714\pi$
$839$	−22.1211			−0.763706			−0.381853	+	0.924223i	$0.624714\pi$
$840$	3.61379	−	12.3206i	0.124688	−	0.425101i
$841$	11.5855			0.399499
$842$	17.5534	+	17.5534i	0.604930	+	0.604930i
$843$	−20.9921	+	25.6993i	−0.723006	+	0.885132i
$844$			52.6411i			1.81198i
$845$	−10.9922	−	26.0272i	−0.378143	−	0.895362i
$846$	−22.4912	+	4.58151i	−0.773264	+	0.157516i
$847$	7.19863	−	7.19863i	0.247348	−	0.247348i
$848$	17.8011	−	17.8011i	0.611291	−	0.611291i
$849$	1.05428	+	10.4575i	0.0361827	+	0.358899i
$850$	−16.0132	−	15.5764i	−0.549247	−	0.534267i
$851$		−	44.0526i		−	1.51010i
$852$	−53.5754	−	43.7622i	−1.83546	−	1.49927i
$853$	−8.83378	−	8.83378i	−0.302463	−	0.302463i	0.539514	−	0.841977i	$-0.318608\pi$
$853$	−8.83378	−	8.83378i	−0.302463	−	0.302463i	−0.841977	+	0.539514i	$0.818608\pi$
$854$	71.1589			2.43501
$855$	5.53438	−	3.79086i	0.189272	−	0.129645i
$856$	−19.8994			−0.680148
$857$	−0.229356	−	0.229356i	−0.00783465	−	0.00783465i	0.703179	−	0.711013i	$-0.251763\pi$
$857$	−0.229356	−	0.229356i	−0.00783465	−	0.00783465i	−0.711013	+	0.703179i	$0.751763\pi$
$858$	−4.42758	−	3.61660i	−0.151155	−	0.123469i
$859$		−	53.2729i		−	1.81765i	−0.417181	−	0.908824i	$-0.636982\pi$
$859$		−	53.2729i		−	1.81765i	0.417181	−	0.908824i	$-0.363018\pi$
$860$	7.79968	−	19.2045i	0.265967	−	0.654868i
$861$	1.63546	+	16.2223i	0.0557365	+	0.552854i
$862$	50.5163	−	50.5163i	1.72059	−	1.72059i
$863$	31.1295	−	31.1295i	1.05966	−	1.05966i	0.0615560	−	0.998104i	$-0.480394\pi$
$863$	31.1295	−	31.1295i	1.05966	−	1.05966i	0.998104	−	0.0615560i	$-0.0196063\pi$
$864$	37.7846	−	11.7473i	1.28546	−	0.399652i
$865$	14.1290	−	34.7886i	0.480400	−	1.18285i
$866$			9.37379i			0.318534i
$867$	13.9710	−	17.1038i	0.474480	−	0.580877i
$868$	−14.4843	−	14.4843i	−0.491630	−	0.491630i
$869$	19.7237			0.669082
$870$	25.6423	+	46.9281i	0.869355	+	1.59101i
$871$	5.62593			0.190627
$872$	6.41485	+	6.41485i	0.217234	+	0.217234i
$873$	−16.7369	−	11.0721i	−0.566458	−	0.374735i
$874$			10.9371i			0.369952i
$875$	−9.84981	−	22.4512i	−0.332984	−	0.758988i
$876$	−31.2965	+	3.15519i	−1.05741	+	0.106604i
$877$	−19.6751	+	19.6751i	−0.664381	+	0.664381i	−0.956409	−	0.292029i	$-0.905670\pi$
$877$	−19.6751	+	19.6751i	−0.664381	+	0.664381i	0.292029	+	0.956409i	$0.405670\pi$
$878$	−1.52226	+	1.52226i	−0.0513739	+	0.0513739i
$879$	52.4710	−	5.28992i	1.76980	−	0.178424i
$880$	4.64674	+	11.0025i	0.156642	+	0.370894i
$881$			46.8612i			1.57880i	0.613882	+	0.789398i	$0.289607\pi$
$881$			46.8612i			1.57880i	−0.613882	+	0.789398i	$0.710393\pi$
$882$	11.8838	+	7.86163i	0.400149	+	0.264715i
$883$	−9.50785	−	9.50785i	−0.319965	−	0.319965i	0.528789	−	0.848754i	$-0.322646\pi$
$883$	−9.50785	−	9.50785i	−0.319965	−	0.319965i	−0.848754	+	0.528789i	$0.822646\pi$
$884$	3.35860			0.112962
$885$	−0.673796	−	0.197633i	−0.0226494	−	0.00664336i
$886$	−32.9007			−1.10532
$887$	−24.4989	−	24.4989i	−0.822593	−	0.822593i	0.163886	−	0.986479i	$-0.447597\pi$
$887$	−24.4989	−	24.4989i	−0.822593	−	0.822593i	−0.986479	+	0.163886i	$0.947597\pi$
$888$	14.4611	−	17.7039i	0.485284	−	0.594104i
$889$			42.4209i			1.42275i
$890$	−22.4102	−	9.10166i	−0.751193	−	0.305088i
$891$	−8.87673	−	20.8844i	−0.297382	−	0.699653i
$892$	−38.7306	+	38.7306i	−1.29680	+	1.29680i
$893$	−2.49615	+	2.49615i	−0.0835304	+	0.0835304i
$894$	−5.49800	−	54.5350i	−0.183880	−	1.82392i
$895$	−9.95591	+	4.20473i	−0.332789	+	0.140549i
$896$		−	24.9085i		−	0.832133i
$897$	−4.08843	−	3.33957i	−0.136509	−	0.111505i
$898$	−3.44007	−	3.44007i	−0.114797	−	0.114797i
$899$	22.0609			0.735772
$900$	−21.8563	+	34.0523i	−0.728542	+	1.13508i
$901$	24.4975			0.816130
$902$	16.5882	+	16.5882i	0.552328	+	0.552328i
$903$	−10.1083	−	8.25680i	−0.336383	−	0.274769i
$904$			16.8081i			0.559029i
$905$	−3.93751	+	1.66295i	−0.130887	+	0.0552782i
$906$	4.60930	+	45.7200i	0.153134	+	1.51894i
$907$	−0.115676	+	0.115676i	−0.00384096	+	0.00384096i	−0.709025	−	0.705184i	$-0.750865\pi$
$907$	−0.115676	+	0.115676i	−0.00384096	+	0.00384096i	0.705184	+	0.709025i	$0.250865\pi$
$908$	32.8174	−	32.8174i	1.08908	−	1.08908i
$909$	11.8995	−	2.42395i	0.394680	−	0.0803973i
$910$	5.94703	+	2.41532i	0.197142	+	0.0800670i
$911$			14.6475i			0.485293i	0.970115	+	0.242646i	$0.0780154\pi$
$911$			14.6475i			0.485293i	−0.970115	+	0.242646i	$0.921985\pi$
$912$	2.32115	−	2.84164i	0.0768610	−	0.0940962i
$913$	−27.0567	−	27.0567i	−0.895447	−	0.895447i
$914$	−53.1420			−1.75778
$915$	−55.6429	−	16.3208i	−1.83950	−	0.539548i
$916$	−52.3860			−1.73088
$917$	−7.81259	−	7.81259i	−0.257994	−	0.257994i
$918$	20.5495	+	10.8022i	0.678236	+	0.356525i
$919$			17.1024i			0.564156i	0.959391	+	0.282078i	$0.0910237\pi$
$919$			17.1024i			0.564156i	−0.959391	+	0.282078i	$0.908976\pi$
$920$	−6.63693	−	15.7148i	−0.218813	−	0.518103i
$921$	13.9272	−	1.40408i	0.458917	−	0.0462661i
$922$	−16.7081	+	16.7081i	−0.550252	+	0.550252i
$923$	6.32331	−	6.32331i	0.208134	−	0.208134i
$924$	−25.7029	+	2.59126i	−0.845562	+	0.0852462i
$925$	−0.603402	−	43.6449i	−0.0198397	−	1.43504i
$926$			78.9720i			2.59518i
$927$	31.2171	−	47.1885i	1.02530	−	1.54987i
$928$	34.3035	+	34.3035i	1.12607	+	1.12607i
$929$	−22.0374			−0.723024			−0.361512	−	0.932367i	$-0.617739\pi$
$929$	−22.0374			−0.723024			−0.361512	+	0.932367i	$0.617739\pi$
$930$	13.9383	+	25.5085i	0.457054	+	0.836458i
$931$	2.19142			0.0718207
$932$	27.5694	+	27.5694i	0.903067	+	0.903067i
$933$	−26.5026	+	32.4455i	−0.867656	+	1.06222i
$934$			51.5227i			1.68587i
$935$	−4.37334	+	10.7681i	−0.143024	+	0.352155i
$936$	−0.546780	−	2.68421i	−0.0178721	−	0.0877362i
$937$	−30.2576	+	30.2576i	−0.988474	+	0.988474i	−0.999934	−	0.0114607i	$-0.996352\pi$
$937$	−30.2576	+	30.2576i	−0.988474	+	0.988474i	0.0114607	+	0.999934i	$0.496352\pi$
$938$	31.3038	−	31.3038i	1.02211	−	1.02211i
$939$	−2.00740	−	19.9115i	−0.0655091	−	0.649789i
$940$	8.01231	−	19.7280i	0.261333	−	0.643457i
$941$		−	57.1786i		−	1.86397i	−0.362499	−	0.931984i	$-0.618076\pi$
$941$		−	57.1786i		−	1.86397i	0.362499	−	0.931984i	$-0.381924\pi$
$942$	−6.19709	−	5.06200i	−0.201912	−	0.164929i
$943$	15.3176	+	15.3176i	0.498809	+	0.498809i
$944$	−0.384069			−0.0125004
$945$	16.4340	+	19.4700i	0.534599	+	0.633360i
$946$	−18.7794			−0.610570
$947$	−29.5048	−	29.5048i	−0.958778	−	0.958778i	0.0404054	−	0.999183i	$-0.487135\pi$
$947$	−29.5048	−	29.5048i	−0.958778	−	0.958778i	−0.999183	+	0.0404054i	$0.987135\pi$
$948$	28.3060	+	23.1213i	0.919336	+	0.750945i
$949$		−	4.06622i		−	0.131995i
$950$	0.149808	+	10.8359i	0.00486042	+	0.351562i
$951$	−2.88869	−	28.6531i	−0.0936723	−	0.929142i
$952$	4.83235	−	4.83235i	0.156617	−	0.156617i
$953$	40.6566	−	40.6566i	1.31700	−	1.31700i	0.400857	−	0.916140i	$-0.368712\pi$
$953$	40.6566	−	40.6566i	1.31700	−	1.31700i	0.916140	−	0.400857i	$-0.131288\pi$
$954$	−15.4234	−	75.7153i	−0.499350	−	2.45137i
$955$	−6.02903	−	14.2755i	−0.195095	−	0.461943i
$956$		−	22.8500i		−	0.739020i
$957$	17.6005	−	21.5472i	0.568944	−	0.696523i
$958$	−2.52708	−	2.52708i	−0.0816463	−	0.0816463i
$959$	0.204655			0.00660865
$960$	−13.3727	+	45.5921i	−0.431604	+	1.47148i
$961$	−19.0084			−0.613176
$962$	8.08073	+	8.08073i	0.260533	+	0.260533i
$963$	21.7869	−	32.9335i	0.702072	−	1.06127i
$964$			33.4903i			1.07865i
$965$	−1.99769	−	0.811340i	−0.0643080	−	0.0261179i
$966$	−41.3309	+	4.16681i	−1.32980	+	0.134065i
$967$	18.1405	−	18.1405i	0.583360	−	0.583360i	−0.352465	−	0.935825i	$-0.614657\pi$
$967$	18.1405	−	18.1405i	0.583360	−	0.583360i	0.935825	+	0.352465i	$0.114657\pi$
$968$	4.96295	−	4.96295i	0.159515	−	0.159515i
$969$	3.55247	−	0.358146i	0.114122	−	0.0115053i
$970$	29.8646	−	12.6129i	0.958896	−	0.404975i
$971$			39.2528i			1.25968i	0.776724	+	0.629841i	$0.216880\pi$
$971$			39.2528i			1.25968i	−0.776724	+	0.629841i	$0.783120\pi$
$972$	11.7427	−	40.3775i	0.376647	−	1.29511i
$973$	−2.09109	−	2.09109i	−0.0670373	−	0.0670373i
$974$	−39.0321			−1.25067
$975$	−4.09633	−	3.25266i	−0.131188	−	0.104168i
$976$	−31.7169			−1.01523
$977$	−1.19989	−	1.19989i	−0.0383880	−	0.0383880i	0.687652	−	0.726040i	$-0.258641\pi$
$977$	−1.19989	−	1.19989i	−0.0383880	−	0.0383880i	−0.726040	+	0.687652i	$0.758641\pi$
$978$	53.4261	−	65.4063i	1.70838	−	2.09146i
$979$			12.5841i			0.402189i
$980$	−12.1769	+	5.14272i	−0.388976	+	0.164278i
$981$	−17.6399	+	3.59328i	−0.563198	+	0.114725i
$982$	−8.92991	+	8.92991i	−0.284965	+	0.284965i
$983$	−6.51264	+	6.51264i	−0.207721	+	0.207721i	−0.803298	−	0.595577i	$-0.796923\pi$
$983$	−6.51264	+	6.51264i	−0.207721	+	0.207721i	0.595577	+	0.803298i	$0.296923\pi$
$984$	1.12754	+	11.1841i	0.0359446	+	0.356537i
$985$	−37.4295	−	15.2015i	−1.19260	−	0.484362i
$986$			28.4634i			0.906458i
$987$	−10.3838	−	8.48188i	−0.330521	−	0.269981i
$988$	−1.15206	−	1.15206i	−0.0366521	−	0.0366521i
$989$	−17.3409			−0.551408
$990$	36.0348	+	6.73735i	1.14526	+	0.214127i
$991$	36.7886			1.16863			0.584314	−	0.811528i	$-0.301364\pi$
$991$	36.7886			1.16863			0.584314	+	0.811528i	$0.301364\pi$
$992$	18.6462	+	18.6462i	0.592019	+	0.592019i
$993$	7.20512	+	5.88539i	0.228648	+	0.186767i
$994$		−	70.3684i		−	2.23195i
$995$	−10.0340	−	23.7583i	−0.318098	−	0.753188i
$996$	−7.11228	−	70.5472i	−0.225361	−	2.23537i
$997$	37.6011	−	37.6011i	1.19084	−	1.19084i	0.214005	−	0.976832i	$-0.431349\pi$
$997$	37.6011	−	37.6011i	1.19084	−	1.19084i	0.976832	−	0.214005i	$-0.0686510\pi$
$998$	−15.5222	+	15.5222i	−0.491347	+	0.491347i
$999$	13.4672	+	43.3163i	0.426082	+	1.37047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.k.d.248.3	yes	36
3.2	odd	2	inner	285.2.k.d.248.16	yes	36
5.2	odd	4	inner	285.2.k.d.77.16	yes	36
15.2	even	4	inner	285.2.k.d.77.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.k.d.77.3	✓	36	15.2	even	4	inner
285.2.k.d.77.16	yes	36	5.2	odd	4	inner
285.2.k.d.248.3	yes	36	1.1	even	1	trivial
285.2.k.d.248.16	yes	36	3.2	odd	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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53257 - 1.53257i) q^{2} +(1.34142 + 1.09572i) q^{3} +2.69753i q^{4} +(2.05989 - 0.869965i) q^{5} +(-0.376555 - 3.73508i) q^{6} +(1.55058 - 1.55058i) q^{7} +(1.06901 - 1.06901i) q^{8} +(0.598810 + 2.93963i) q^{9} +O(q^{10})\)	\(q+(-1.53257 - 1.53257i) q^{2} +(1.34142 + 1.09572i) q^{3} +2.69753i q^{4} +(2.05989 - 0.869965i) q^{5} +(-0.376555 - 3.73508i) q^{6} +(1.55058 - 1.55058i) q^{7} +(1.06901 - 1.06901i) q^{8} +(0.598810 + 2.93963i) q^{9} +(-4.49021 - 1.82365i) q^{10} +2.52140i q^{11} +(-2.95573 + 3.61852i) q^{12} +(-0.427081 - 0.427081i) q^{13} -4.75273 q^{14} +(3.71642 + 1.09007i) q^{15} +2.11839 q^{16} +(1.45764 + 1.45764i) q^{17} +(3.58747 - 5.42290i) q^{18} -1.00000i q^{19} +(2.34676 + 5.55663i) q^{20} +(3.77897 - 0.380980i) q^{21} +(3.86422 - 3.86422i) q^{22} +(3.56822 - 3.56822i) q^{23} +(2.60533 - 0.262659i) q^{24} +(3.48632 - 3.58407i) q^{25} +1.30906i q^{26} +(-2.41775 + 4.59940i) q^{27} +(4.18273 + 4.18273i) q^{28} -6.37067 q^{29} +(-4.02505 - 7.36627i) q^{30} -3.46288 q^{31} +(-5.38460 - 5.38460i) q^{32} +(-2.76274 + 3.38225i) q^{33} -4.46787i q^{34} +(1.84508 - 4.54297i) q^{35} +(-7.92975 + 1.61531i) q^{36} +(6.17292 - 6.17292i) q^{37} +(-1.53257 + 1.53257i) q^{38} +(-0.104935 - 1.04085i) q^{39} +(1.27205 - 3.13206i) q^{40} +4.29278i q^{41} +(-6.37541 - 5.20765i) q^{42} +(-2.42991 - 2.42991i) q^{43} -6.80155 q^{44} +(3.79086 + 5.53438i) q^{45} -10.9371 q^{46} +(-2.49615 - 2.49615i) q^{47} +(2.84164 + 2.32115i) q^{48} +2.19142i q^{49} +(-10.8359 + 0.149808i) q^{50} +(0.358146 + 3.55247i) q^{51} +(1.15206 - 1.15206i) q^{52} +(8.40313 - 8.40313i) q^{53} +(10.7543 - 3.34353i) q^{54} +(2.19353 + 5.19381i) q^{55} -3.31518i q^{56} +(1.09572 - 1.34142i) q^{57} +(9.76349 + 9.76349i) q^{58} -0.181303 q^{59} +(-2.94050 + 10.0251i) q^{60} -14.9722 q^{61} +(5.30710 + 5.30710i) q^{62} +(5.48663 + 3.62963i) q^{63} +12.2678i q^{64} +(-1.25129 - 0.508196i) q^{65} +(9.41762 - 0.949446i) q^{66} +(-6.58649 + 6.58649i) q^{67} +(-3.93204 + 3.93204i) q^{68} +(8.69623 - 0.876719i) q^{69} +(-9.79012 + 4.13471i) q^{70} +14.8059i q^{71} +(3.78265 + 2.50237i) q^{72} +(4.76047 + 4.76047i) q^{73} -18.9208 q^{74} +(8.60374 - 0.987720i) q^{75} +2.69753 q^{76} +(3.90963 + 3.90963i) q^{77} +(-1.43436 + 1.75600i) q^{78} -7.82253i q^{79} +(4.36365 - 1.84292i) q^{80} +(-8.28285 + 3.52056i) q^{81} +(6.57898 - 6.57898i) q^{82} +(-10.7308 + 10.7308i) q^{83} +(1.02771 + 10.1939i) q^{84} +(4.27069 + 1.73449i) q^{85} +7.44800i q^{86} +(-8.54574 - 6.98045i) q^{87} +(2.69541 + 2.69541i) q^{88} +4.99091 q^{89} +(2.67207 - 14.2916i) q^{90} -1.32444 q^{91} +(9.62538 + 9.62538i) q^{92} +(-4.64518 - 3.79434i) q^{93} +7.65103i q^{94} +(-0.869965 - 2.05989i) q^{95} +(-1.32301 - 13.1230i) q^{96} +(-4.73002 + 4.73002i) q^{97} +(3.35849 - 3.35849i) q^{98} +(-7.41198 + 1.50984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7	\( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) \) 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^10 - 18 * q^12 - 8 * q^13 - 8 * q^15 - 84 * q^16 + 8 * q^21 + 40 * q^22 - 20 * q^25 - 14 * q^27 + 36 * q^28 + 28 * q^30 - 28 * q^33 + 92 * q^36 - 4 * q^37 - 20 * q^40 - 100 * q^42 + 16 * q^43 + 28 * q^45 - 24 * q^46 - 58 * q^48 + 32 * q^51 + 148 * q^52 - 72 * q^55 - 2 * q^57 - 12 * q^58 + 58 * q^60 - 112 * q^61 - 64 * q^63 + 92 * q^66 - 8 * q^67 + 8 * q^70 - 88 * q^72 + 76 * q^73 + 80 * q^75 + 36 * q^76 - 36 * q^78 + 4 * q^81 + 20 * q^82 - 28 * q^85 - 4 * q^87 + 140 * q^88 + 76 * q^90 - 24 * q^91 - 48 * q^93 + 32 * q^96 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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