LMFDB - Embedded newform 570.2.k.a.533.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(77,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, 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("570.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.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:	$4.55147291521$
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			533.3
Character	$\chi$	$=$	570.533
Dual form			570.2.k.a.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-1.10477 - 1.33397i) q^{3} +1.00000i q^{4} +(-2.20748 + 0.356413i) q^{5} +(-0.162066 + 1.72445i) q^{6} +(1.29452 - 1.29452i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.558949 + 2.94747i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.10477 - 1.33397i) q^{3} +1.00000i q^{4} +(-2.20748 + 0.356413i) q^{5} +(-0.162066 + 1.72445i) q^{6} +(1.29452 - 1.29452i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.558949 + 2.94747i) q^{9} +(1.81295 + 1.30890i) q^{10} +4.05199i q^{11} +(1.33397 - 1.10477i) q^{12} +(0.882575 + 0.882575i) q^{13} -1.83072 q^{14} +(2.91421 + 2.55096i) q^{15} -1.00000 q^{16} +(1.10167 + 1.10167i) q^{17} +(2.47941 - 1.68894i) q^{18} -1.00000i q^{19} +(-0.356413 - 2.20748i) q^{20} +(-3.15700 - 0.296698i) q^{21} +(2.86519 - 2.86519i) q^{22} +(0.877184 - 0.877184i) q^{23} +(-1.72445 - 0.162066i) q^{24} +(4.74594 - 1.57355i) q^{25} -1.24815i q^{26} +(4.54935 - 2.51067i) q^{27} +(1.29452 + 1.29452i) q^{28} -5.03943 q^{29} +(-0.256861 - 3.86446i) q^{30} +9.76541 q^{31} +(0.707107 + 0.707107i) q^{32} +(5.40524 - 4.47654i) q^{33} -1.55800i q^{34} +(-2.39624 + 3.31901i) q^{35} +(-2.94747 - 0.558949i) q^{36} +(3.02131 - 3.02131i) q^{37} +(-0.707107 + 0.707107i) q^{38} +(0.202282 - 2.15237i) q^{39} +(-1.30890 + 1.81295i) q^{40} -1.87632i q^{41} +(2.02254 + 2.44213i) q^{42} +(-0.199462 - 0.199462i) q^{43} -4.05199 q^{44} +(0.183351 - 6.70570i) q^{45} -1.24053 q^{46} +(8.33748 + 8.33748i) q^{47} +(1.10477 + 1.33397i) q^{48} +3.64845i q^{49} +(-4.46855 - 2.24322i) q^{50} +(0.252498 - 2.68669i) q^{51} +(-0.882575 + 0.882575i) q^{52} +(6.34099 - 6.34099i) q^{53} +(-4.99218 - 1.44156i) q^{54} +(-1.44418 - 8.94470i) q^{55} -1.83072i q^{56} +(-1.33397 + 1.10477i) q^{57} +(3.56341 + 3.56341i) q^{58} +1.21543 q^{59} +(-2.55096 + 2.91421i) q^{60} +1.45771 q^{61} +(-6.90519 - 6.90519i) q^{62} +(3.09198 + 4.53912i) q^{63} -1.00000i q^{64} +(-2.26283 - 1.63371i) q^{65} +(-6.98747 - 0.656689i) q^{66} +(-2.25803 + 2.25803i) q^{67} +(-1.10167 + 1.10167i) q^{68} +(-2.13923 - 0.201047i) q^{69} +(4.04129 - 0.652495i) q^{70} -7.22853i q^{71} +(1.68894 + 2.47941i) q^{72} +(-3.04969 - 3.04969i) q^{73} -4.27277 q^{74} +(-7.34226 - 4.59252i) q^{75} +1.00000 q^{76} +(5.24538 + 5.24538i) q^{77} +(-1.66499 + 1.37892i) q^{78} +13.1389i q^{79} +(2.20748 - 0.356413i) q^{80} +(-8.37515 - 3.29497i) q^{81} +(-1.32676 + 1.32676i) q^{82} +(-4.01176 + 4.01176i) q^{83} +(0.296698 - 3.15700i) q^{84} +(-2.82457 - 2.03927i) q^{85} +0.282082i q^{86} +(5.56743 + 6.72244i) q^{87} +(2.86519 + 2.86519i) q^{88} +15.5041 q^{89} +(-4.87129 + 4.61200i) q^{90} +2.28502 q^{91} +(0.877184 + 0.877184i) q^{92} +(-10.7886 - 13.0268i) q^{93} -11.7910i q^{94} +(0.356413 + 2.20748i) q^{95} +(0.162066 - 1.72445i) q^{96} +(-7.86520 + 7.86520i) q^{97} +(2.57984 - 2.57984i) q^{98} +(-11.9431 - 2.26486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.10477	−	1.33397i	−0.637842	−	0.770168i
$3$	−1.10477	−	1.33397i	−0.637842	−	0.770168i
$4$			1.00000i			0.500000i
$5$	−2.20748	+	0.356413i	−0.987215	+	0.159393i
$5$	−2.20748	+	0.356413i	−0.987215	+	0.159393i
$6$	−0.162066	+	1.72445i	−0.0661630	+	0.704005i
$7$	1.29452	−	1.29452i	0.489282	−	0.489282i	−0.418798	−	0.908080i	$-0.637548\pi$
$7$	1.29452	−	1.29452i	0.489282	−	0.489282i	0.908080	+	0.418798i	$0.137548\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.558949	+	2.94747i	−0.186316	+	0.982490i
$10$	1.81295	+	1.30890i	0.573304	+	0.413911i
$11$			4.05199i			1.22172i	0.791738	+	0.610861i	$0.209177\pi$
$11$			4.05199i			1.22172i	−0.791738	+	0.610861i	$0.790823\pi$
$12$	1.33397	−	1.10477i	0.385084	−	0.318921i
$13$	0.882575	+	0.882575i	0.244782	+	0.244782i	0.818825	−	0.574043i	$-0.194626\pi$
$13$	0.882575	+	0.882575i	0.244782	+	0.244782i	−0.574043	+	0.818825i	$0.694626\pi$
$14$	−1.83072			−0.489282
$15$	2.91421	+	2.55096i	0.752446	+	0.658654i
$16$	−1.00000			−0.250000
$17$	1.10167	+	1.10167i	0.267194	+	0.267194i	0.827969	−	0.560774i	$-0.189496\pi$
$17$	1.10167	+	1.10167i	0.267194	+	0.267194i	−0.560774	+	0.827969i	$0.689496\pi$
$18$	2.47941	−	1.68894i	0.584403	−	0.398087i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−0.356413	−	2.20748i	−0.0796965	−	0.493608i
$21$	−3.15700	−	0.296698i	−0.688913	−	0.0647447i
$22$	2.86519	−	2.86519i	0.610861	−	0.610861i
$23$	0.877184	−	0.877184i	0.182905	−	0.182905i	−0.609715	−	0.792621i	$-0.708716\pi$
$23$	0.877184	−	0.877184i	0.182905	−	0.182905i	0.792621	+	0.609715i	$0.208716\pi$
$24$	−1.72445	−	0.162066i	−0.352002	−	0.0330815i
$25$	4.74594	−	1.57355i	0.949188	−	0.314710i
$26$		−	1.24815i		−	0.244782i
$27$	4.54935	−	2.51067i	0.875522	−	0.483178i
$28$	1.29452	+	1.29452i	0.244641	+	0.244641i
$29$	−5.03943			−0.935798			−0.467899	−	0.883782i	$-0.654989\pi$
$29$	−5.03943			−0.935798			−0.467899	+	0.883782i	$0.654989\pi$
$30$	−0.256861	−	3.86446i	−0.0468962	−	0.705550i
$31$	9.76541			1.75392			0.876960	−	0.480564i	$-0.159568\pi$
$31$	9.76541			1.75392			0.876960	+	0.480564i	$0.159568\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	5.40524	−	4.47654i	0.940931	−	0.779265i
$34$		−	1.55800i		−	0.267194i
$35$	−2.39624	+	3.31901i	−0.405038	+	0.561014i
$36$	−2.94747	−	0.558949i	−0.491245	−	0.0931581i
$37$	3.02131	−	3.02131i	0.496700	−	0.496700i	−0.413709	−	0.910409i	$-0.635767\pi$
$37$	3.02131	−	3.02131i	0.496700	−	0.496700i	0.910409	+	0.413709i	$0.135767\pi$
$38$	−0.707107	+	0.707107i	−0.114708	+	0.114708i
$39$	0.202282	−	2.15237i	0.0323911	−	0.344656i
$40$	−1.30890	+	1.81295i	−0.206956	+	0.286652i
$41$		−	1.87632i		−	0.293032i	−0.989208	−	0.146516i	$-0.953194\pi$
$41$		−	1.87632i		−	0.293032i	0.989208	−	0.146516i	$-0.0468060\pi$
$42$	2.02254	+	2.44213i	0.312084	+	0.376829i
$43$	−0.199462	−	0.199462i	−0.0304177	−	0.0304177i	0.691734	−	0.722152i	$-0.256847\pi$
$43$	−0.199462	−	0.199462i	−0.0304177	−	0.0304177i	−0.722152	+	0.691734i	$0.756847\pi$
$44$	−4.05199			−0.610861
$45$	0.183351	−	6.70570i	0.0273324	−	0.999626i
$46$	−1.24053			−0.182905
$47$	8.33748	+	8.33748i	1.21615	+	1.21615i	0.968971	+	0.247176i	$0.0795025\pi$
$47$	8.33748	+	8.33748i	1.21615	+	1.21615i	0.247176	+	0.968971i	$0.420497\pi$
$48$	1.10477	+	1.33397i	0.159460	+	0.192542i
$49$			3.64845i			0.521207i
$50$	−4.46855	−	2.24322i	−0.631949	−	0.317239i
$51$	0.252498	−	2.68669i	0.0353568	−	0.376212i
$52$	−0.882575	+	0.882575i	−0.122391	+	0.122391i
$53$	6.34099	−	6.34099i	0.871002	−	0.871002i	−0.121580	−	0.992582i	$-0.538796\pi$
$53$	6.34099	−	6.34099i	0.871002	−	0.871002i	0.992582	+	0.121580i	$0.0387960\pi$
$54$	−4.99218	−	1.44156i	−0.679350	−	0.196172i
$55$	−1.44418	−	8.94470i	−0.194734	−	1.20610i
$56$		−	1.83072i		−	0.244641i
$57$	−1.33397	+	1.10477i	−0.176689	+	0.146331i
$58$	3.56341	+	3.56341i	0.467899	+	0.467899i
$59$	1.21543			0.158236			0.0791178	−	0.996865i	$-0.474790\pi$
$59$	1.21543			0.158236			0.0791178	+	0.996865i	$0.474790\pi$
$60$	−2.55096	+	2.91421i	−0.329327	+	0.376223i
$61$	1.45771			0.186641			0.0933205	−	0.995636i	$-0.470252\pi$
$61$	1.45771			0.186641			0.0933205	+	0.995636i	$0.470252\pi$
$62$	−6.90519	−	6.90519i	−0.876960	−	0.876960i
$63$	3.09198	+	4.53912i	0.389553	+	0.571875i
$64$		−	1.00000i		−	0.125000i
$65$	−2.26283	−	1.63371i	−0.280669	−	0.202636i
$66$	−6.98747	−	0.656689i	−0.860098	−	0.0808328i
$67$	−2.25803	+	2.25803i	−0.275862	+	0.275862i	−0.831455	−	0.555593i	$-0.812491\pi$
$67$	−2.25803	+	2.25803i	−0.275862	+	0.275862i	0.555593	+	0.831455i	$0.312491\pi$
$68$	−1.10167	+	1.10167i	−0.133597	+	0.133597i
$69$	−2.13923	−	0.201047i	−0.257533	−	0.0242032i
$70$	4.04129	−	0.652495i	0.483026	−	0.0779880i
$71$		−	7.22853i		−	0.857869i	−0.903336	−	0.428935i	$-0.858889\pi$
$71$		−	7.22853i		−	0.857869i	0.903336	−	0.428935i	$-0.141111\pi$
$72$	1.68894	+	2.47941i	0.199043	+	0.292202i
$73$	−3.04969	−	3.04969i	−0.356940	−	0.356940i	0.505744	−	0.862684i	$-0.331218\pi$
$73$	−3.04969	−	3.04969i	−0.356940	−	0.356940i	−0.862684	+	0.505744i	$0.831218\pi$
$74$	−4.27277			−0.496700
$75$	−7.34226	−	4.59252i	−0.847811	−	0.530298i
$76$	1.00000			0.114708
$77$	5.24538	+	5.24538i	0.597766	+	0.597766i
$78$	−1.66499	+	1.37892i	−0.188523	+	0.156132i
$79$			13.1389i			1.47824i	0.673572	+	0.739122i	$0.264759\pi$
$79$			13.1389i			1.47824i	−0.673572	+	0.739122i	$0.735241\pi$
$80$	2.20748	−	0.356413i	0.246804	−	0.0398482i
$81$	−8.37515	−	3.29497i	−0.930572	−	0.366108i
$82$	−1.32676	+	1.32676i	−0.146516	+	0.146516i
$83$	−4.01176	+	4.01176i	−0.440348	+	0.440348i	−0.892129	−	0.451781i	$-0.850789\pi$
$83$	−4.01176	+	4.01176i	−0.440348	+	0.440348i	0.451781	+	0.892129i	$0.350789\pi$
$84$	0.296698	−	3.15700i	0.0323724	−	0.344457i
$85$	−2.82457	−	2.03927i	−0.306367	−	0.221189i
$86$			0.282082i			0.0304177i
$87$	5.56743	+	6.72244i	0.596891	+	0.720721i
$88$	2.86519	+	2.86519i	0.305431	+	0.305431i
$89$	15.5041			1.64343			0.821715	−	0.569898i	$-0.193017\pi$
$89$	15.5041			1.64343			0.821715	+	0.569898i	$0.193017\pi$
$90$	−4.87129	+	4.61200i	−0.513479	+	0.486147i
$91$	2.28502			0.239535
$92$	0.877184	+	0.877184i	0.0914527	+	0.0914527i
$93$	−10.7886	−	13.0268i	−1.11872	−	1.35081i
$94$		−	11.7910i		−	1.21615i
$95$	0.356413	+	2.20748i	0.0365672	+	0.226483i
$96$	0.162066	−	1.72445i	0.0165408	−	0.176001i
$97$	−7.86520	+	7.86520i	−0.798590	+	0.798590i	−0.982873	−	0.184283i	$-0.941004\pi$
$97$	−7.86520	+	7.86520i	−0.798590	+	0.798590i	0.184283	+	0.982873i	$0.441004\pi$
$98$	2.57984	−	2.57984i	0.260603	−	0.260603i
$99$	−11.9431	−	2.26486i	−1.20033	−	0.227627i
$100$	1.57355	+	4.74594i	0.157355	+	0.474594i
$101$			1.64156i			0.163341i	0.996659	+	0.0816705i	$0.0260255\pi$
$101$			1.64156i			0.163341i	−0.996659	+	0.0816705i	$0.973974\pi$
$102$	−2.07832	+	1.72123i	−0.205784	+	0.170428i
$103$	6.66370	+	6.66370i	0.656594	+	0.656594i	0.954573	−	0.297979i	$-0.0963124\pi$
$103$	6.66370	+	6.66370i	0.656594	+	0.656594i	−0.297979	+	0.954573i	$0.596312\pi$
$104$	1.24815			0.122391
$105$	7.07475	−	0.470242i	0.690425	−	0.0458909i
$106$	−8.96751			−0.871002
$107$	13.0841	+	13.0841i	1.26488	+	1.26488i	0.948697	+	0.316188i	$0.102403\pi$
$107$	13.0841	+	13.0841i	1.26488	+	1.26488i	0.316188	+	0.948697i	$0.397597\pi$
$108$	2.51067	+	4.54935i	0.241589	+	0.437761i
$109$			13.1807i			1.26248i	0.775587	+	0.631241i	$0.217454\pi$
$109$			13.1807i			1.26248i	−0.775587	+	0.631241i	$0.782546\pi$
$110$	−5.30366	+	7.34605i	−0.505684	+	0.700418i
$111$	−7.36819	−	0.692470i	−0.699358	−	0.0657263i
$112$	−1.29452	+	1.29452i	−0.122320	+	0.122320i
$113$	7.56560	−	7.56560i	0.711712	−	0.711712i	−0.255181	−	0.966893i	$-0.582135\pi$
$113$	7.56560	−	7.56560i	0.711712	−	0.711712i	0.966893	+	0.255181i	$0.0821352\pi$
$114$	1.72445	+	0.162066i	0.161510	+	0.0151788i
$115$	−1.62373	+	2.24901i	−0.151413	+	0.209721i
$116$		−	5.03943i		−	0.467899i
$117$	−3.09468	+	2.10805i	−0.286103	+	0.194889i
$118$	−0.859440	−	0.859440i	−0.0791178	−	0.0791178i
$119$	2.85226			0.261466
$120$	3.86446	−	0.256861i	0.352775	−	0.0234481i
$121$	−5.41865			−0.492605
$122$	−1.03076	−	1.03076i	−0.0933205	−	0.0933205i
$123$	−2.50296	+	2.07291i	−0.225684	+	0.186908i
$124$			9.76541i			0.876960i
$125$	−9.91573	+	5.16510i	−0.886890	+	0.461981i
$126$	1.02328	−	5.39600i	0.0911611	−	0.480714i
$127$	1.08300	−	1.08300i	0.0961010	−	0.0961010i	−0.657422	−	0.753523i	$-0.728353\pi$
$127$	1.08300	−	1.08300i	0.0961010	−	0.0961010i	0.753523	+	0.657422i	$0.228353\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−0.0457158	+	0.486437i	−0.00402505	+	0.0428284i
$130$	0.444857	+	2.75527i	0.0390166	+	0.241653i
$131$			6.00990i			0.525087i	0.964920	+	0.262544i	$0.0845613\pi$
$131$			6.00990i			0.525087i	−0.964920	+	0.262544i	$0.915439\pi$
$132$	4.47654	+	5.40524i	0.389633	+	0.470465i
$133$	−1.29452	−	1.29452i	−0.112249	−	0.112249i
$134$	3.19333			0.275862
$135$	−9.14776	+	7.16370i	−0.787314	+	0.616553i
$136$	1.55800			0.133597
$137$	−1.40049	−	1.40049i	−0.119652	−	0.119652i	0.644746	−	0.764397i	$-0.276963\pi$
$137$	−1.40049	−	1.40049i	−0.119652	−	0.119652i	−0.764397	+	0.644746i	$0.776963\pi$
$138$	1.37050	+	1.65482i	0.116665	+	0.140868i
$139$			23.4290i			1.98722i	0.112872	+	0.993610i	$0.463995\pi$
$139$			23.4290i			1.98722i	−0.112872	+	0.993610i	$0.536005\pi$
$140$	−3.31901	−	2.39624i	−0.280507	−	0.202519i
$141$	1.91091	−	20.3330i	0.160928	−	1.71235i
$142$	−5.11134	+	5.11134i	−0.428935	+	0.428935i
$143$	−3.57619	+	3.57619i	−0.299056	+	0.299056i
$144$	0.558949	−	2.94747i	0.0465791	−	0.245622i
$145$	11.1244	−	1.79612i	0.923834	−	0.149160i
$146$			4.31292i			0.356940i
$147$	4.86692	−	4.03071i	0.401417	−	0.332447i
$148$	3.02131	+	3.02131i	0.248350	+	0.248350i
$149$	−4.36654			−0.357721			−0.178861	−	0.983874i	$-0.557241\pi$
$149$	−4.36654			−0.357721			−0.178861	+	0.983874i	$0.557241\pi$
$150$	1.94436	+	8.43916i	0.158756	+	0.689055i
$151$	−20.3330			−1.65468			−0.827340	−	0.561701i	$-0.810147\pi$
$151$	−20.3330			−1.65468			−0.827340	+	0.561701i	$0.810147\pi$
$152$	−0.707107	−	0.707107i	−0.0573539	−	0.0573539i
$153$	−3.86292	+	2.63136i	−0.312298	+	0.212733i
$154$		−	7.41808i		−	0.597766i
$155$	−21.5569	+	3.48052i	−1.73150	+	0.279562i
$156$	2.15237	+	0.202282i	0.172328	+	0.0161955i
$157$	8.36917	−	8.36917i	0.667932	−	0.667932i	−0.289305	−	0.957237i	$-0.593424\pi$
$157$	8.36917	−	8.36917i	0.667932	−	0.667932i	0.957237	+	0.289305i	$0.0934241\pi$
$158$	9.29061	−	9.29061i	0.739122	−	0.739122i
$159$	−15.4640	−	1.45333i	−1.22638	−	0.115256i
$160$	−1.81295	−	1.30890i	−0.143326	−	0.103478i
$161$		−	2.27106i		−	0.178985i
$162$	3.59223	+	8.25202i	0.282232	+	0.648340i
$163$	−9.51819	−	9.51819i	−0.745522	−	0.745522i	0.228112	−	0.973635i	$-0.426745\pi$
$163$	−9.51819	−	9.51819i	−0.745522	−	0.745522i	−0.973635	+	0.228112i	$0.926745\pi$
$164$	1.87632			0.146516
$165$	−10.3365	+	11.8084i	−0.804692	+	0.919280i
$166$	5.67349			0.440348
$167$	−9.41306	−	9.41306i	−0.728404	−	0.728404i	0.241897	−	0.970302i	$-0.422230\pi$
$167$	−9.41306	−	9.41306i	−0.728404	−	0.728404i	−0.970302	+	0.241897i	$0.922230\pi$
$168$	−2.44213	+	2.02254i	−0.188414	+	0.156042i
$169$		−	11.4421i		−	0.880163i
$170$	0.555291	+	3.43925i	0.0425889	+	0.263778i
$171$	2.94747	+	0.558949i	0.225399	+	0.0427439i
$172$	0.199462	−	0.199462i	0.0152088	−	0.0152088i
$173$	9.79289	−	9.79289i	0.744539	−	0.744539i	−0.228909	−	0.973448i	$-0.573516\pi$
$173$	9.79289	−	9.79289i	0.744539	−	0.744539i	0.973448	+	0.228909i	$0.0735157\pi$
$174$	0.816718	−	8.69025i	0.0619152	−	0.658806i
$175$	4.10671	−	8.18069i	0.310438	−	0.618402i
$176$		−	4.05199i		−	0.305431i
$177$	−1.34278	−	1.62135i	−0.100929	−	0.121868i
$178$	−10.9631	−	10.9631i	−0.821715	−	0.821715i
$179$	−2.70878			−0.202464			−0.101232	−	0.994863i	$-0.532278\pi$
$179$	−2.70878			−0.202464			−0.101232	+	0.994863i	$0.532278\pi$
$180$	6.70570	+	0.183351i	0.499813	+	0.0136662i
$181$	13.3331			0.991043			0.495522	−	0.868596i	$-0.334977\pi$
$181$	13.3331			0.991043			0.495522	+	0.868596i	$0.334977\pi$
$182$	−1.61575	−	1.61575i	−0.119767	−	0.119767i
$183$	−1.61044	−	1.94454i	−0.119047	−	0.143745i
$184$		−	1.24053i		−	0.0914527i
$185$	−5.59264	+	7.74631i	−0.411179	+	0.569520i
$186$	−1.58264	+	16.8400i	−0.116045	+	1.23477i
$187$	−4.46396	+	4.46396i	−0.326437	+	0.326437i
$188$	−8.33748	+	8.33748i	−0.608073	+	0.608073i
$189$	2.63911	−	9.13931i	0.191967	−	0.664787i
$190$	1.30890	−	1.81295i	0.0949577	−	0.131525i
$191$			15.6275i			1.13077i	0.824828	+	0.565383i	$0.191272\pi$
$191$			15.6275i			1.13077i	−0.824828	+	0.565383i	$0.808728\pi$
$192$	−1.33397	+	1.10477i	−0.0962710	+	0.0797302i
$193$	−11.7380	−	11.7380i	−0.844922	−	0.844922i	0.144572	−	0.989494i	$-0.453819\pi$
$193$	−11.7380	−	11.7380i	−0.844922	−	0.844922i	−0.989494	+	0.144572i	$0.953819\pi$
$194$	11.1231			0.798590
$195$	0.320601	+	4.82342i	0.0229587	+	0.345412i
$196$	−3.64845			−0.260603
$197$	−10.4406	−	10.4406i	−0.743863	−	0.743863i	0.229456	−	0.973319i	$-0.426305\pi$
$197$	−10.4406	−	10.4406i	−0.743863	−	0.743863i	−0.973319	+	0.229456i	$0.926305\pi$
$198$	6.84357	+	10.0466i	0.486351	+	0.713978i
$199$		−	7.28579i		−	0.516476i	−0.966081	−	0.258238i	$-0.916858\pi$
$199$		−	7.28579i		−	0.516476i	0.966081	−	0.258238i	$-0.0831419\pi$
$200$	2.24322	−	4.46855i	0.158619	−	0.315975i
$201$	5.50674	+	0.517529i	0.388416	+	0.0365037i
$202$	1.16076	−	1.16076i	0.0816705	−	0.0816705i
$203$	−6.52363	+	6.52363i	−0.457869	+	0.457869i
$204$	2.68669	+	0.252498i	0.188106	+	0.0176784i
$205$	0.668746	+	4.14194i	0.0467073	+	0.289286i
$206$		−	9.42390i		−	0.656594i
$207$	2.09517	+	3.07577i	0.145624	+	0.213781i
$208$	−0.882575	−	0.882575i	−0.0611956	−	0.0611956i
$209$	4.05199			0.280282
$210$	−5.33512	−	4.67010i	−0.368158	−	0.322267i
$211$	1.27863			0.0880248			0.0440124	−	0.999031i	$-0.485986\pi$
$211$	1.27863			0.0880248			0.0440124	+	0.999031i	$0.485986\pi$
$212$	6.34099	+	6.34099i	0.435501	+	0.435501i
$213$	−9.64264	+	7.98589i	−0.660703	+	0.547185i
$214$		−	18.5037i		−	1.26488i
$215$	0.511400	+	0.369218i	0.0348772	+	0.0251804i
$216$	1.44156	−	4.99218i	0.0980860	−	0.339675i
$217$	12.6415	−	12.6415i	0.858161	−	0.858161i
$218$	9.32016	−	9.32016i	0.631241	−	0.631241i
$219$	−0.698976	+	7.43742i	−0.0472324	+	0.502574i
$220$	8.94470	−	1.44418i	0.603051	−	0.0973669i
$221$			1.94461i			0.130809i
$222$	4.72045	+	5.69975i	0.316816	+	0.382542i
$223$	19.5872	+	19.5872i	1.31166	+	1.31166i	0.920194	+	0.391462i	$0.128030\pi$
$223$	19.5872	+	19.5872i	1.31166	+	1.31166i	0.391462	+	0.920194i	$0.371970\pi$
$224$	1.83072			0.122320
$225$	1.98526	+	14.8680i	0.132350	+	0.991203i
$226$	−10.6994			−0.711712
$227$	2.14570	+	2.14570i	0.142415	+	0.142415i	0.774720	−	0.632305i	$-0.217891\pi$
$227$	2.14570	+	2.14570i	0.142415	+	0.142415i	−0.632305	+	0.774720i	$0.717891\pi$
$228$	−1.10477	−	1.33397i	−0.0731654	−	0.0883443i
$229$			18.1839i			1.20163i	0.799389	+	0.600813i	$0.205156\pi$
$229$			18.1839i			1.20163i	−0.799389	+	0.600813i	$0.794844\pi$
$230$	2.73844	−	0.442140i	0.180567	−	0.0291538i
$231$	1.20222	−	12.7921i	0.0791000	−	0.841660i
$232$	−3.56341	+	3.56341i	−0.233950	+	0.233950i
$233$	5.13824	−	5.13824i	0.336617	−	0.336617i	−0.518475	−	0.855092i	$-0.673500\pi$
$233$	5.13824	−	5.13824i	0.336617	−	0.336617i	0.855092	+	0.518475i	$0.173500\pi$
$234$	3.67888	+	0.697652i	0.240496	+	0.0456069i
$235$	−21.3764	−	15.4332i	−1.39444	−	1.00675i
$236$			1.21543i			0.0791178i
$237$	17.5269	−	14.5155i	1.13849	−	0.942885i
$238$	−2.01685	−	2.01685i	−0.130733	−	0.130733i
$239$	25.9094			1.67594			0.837970	−	0.545716i	$-0.183742\pi$
$239$	25.9094			1.67594			0.837970	+	0.545716i	$0.183742\pi$
$240$	−2.91421	−	2.55096i	−0.188112	−	0.164663i
$241$	23.3453			1.50380			0.751902	−	0.659275i	$-0.229137\pi$
$241$	23.3453			1.50380			0.751902	+	0.659275i	$0.229137\pi$
$242$	3.83157	+	3.83157i	0.246302	+	0.246302i
$243$	4.85726	+	14.8124i	0.311594	+	0.950215i
$244$			1.45771i			0.0933205i
$245$	−1.30036	−	8.05388i	−0.0830767	−	0.514543i
$246$	3.23563	+	0.304087i	0.206296	+	0.0193879i
$247$	0.882575	−	0.882575i	0.0561569	−	0.0561569i
$248$	6.90519	−	6.90519i	0.438480	−	0.438480i
$249$	9.78366	+	0.919478i	0.620014	+	0.0582695i
$250$	10.6638	+	3.35921i	0.674435	+	0.212455i
$251$		−	26.5769i		−	1.67752i	−0.544504	−	0.838758i	$-0.683282\pi$
$251$		−	26.5769i		−	1.67752i	0.544504	−	0.838758i	$-0.316718\pi$
$252$	−4.53912	+	3.09198i	−0.285938	+	0.194777i
$253$	3.55434	+	3.55434i	0.223460	+	0.223460i
$254$	−1.53160			−0.0961010
$255$	0.400189	+	6.02081i	0.0250608	+	0.377038i
$256$	1.00000			0.0625000
$257$	−3.31338	−	3.31338i	−0.206683	−	0.206683i	0.596173	−	0.802856i	$-0.296687\pi$
$257$	−3.31338	−	3.31338i	−0.206683	−	0.206683i	−0.802856	+	0.596173i	$0.796687\pi$
$258$	0.376289	−	0.311637i	0.0234267	−	0.0194017i
$259$		−	7.82227i		−	0.486052i
$260$	1.63371	−	2.26283i	0.101318	−	0.140335i
$261$	2.81678	−	14.8536i	0.174354	−	0.919412i
$262$	4.24964	−	4.24964i	0.262544	−	0.262544i
$263$	8.50623	−	8.50623i	0.524517	−	0.524517i	−0.394416	−	0.918932i	$-0.629053\pi$
$263$	8.50623	−	8.50623i	0.524517	−	0.524517i	0.918932	+	0.394416i	$0.129053\pi$
$264$	0.656689	−	6.98747i	0.0404164	−	0.430049i
$265$	−11.7376	+	16.2576i	−0.721035	+	0.998698i
$266$			1.83072i			0.112249i
$267$	−17.1285	−	20.6820i	−1.04825	−	1.26572i
$268$	−2.25803	−	2.25803i	−0.137931	−	0.137931i
$269$	−19.1132			−1.16535			−0.582676	−	0.812704i	$-0.697994\pi$
$269$	−19.1132			−1.16535			−0.582676	+	0.812704i	$0.697994\pi$
$270$	11.5339	+	1.40294i	0.701933	+	0.0853804i
$271$	16.0634			0.975780			0.487890	−	0.872905i	$-0.337767\pi$
$271$	16.0634			0.975780			0.487890	+	0.872905i	$0.337767\pi$
$272$	−1.10167	−	1.10167i	−0.0667986	−	0.0667986i
$273$	−2.52443	−	3.04814i	−0.152785	−	0.184482i
$274$			1.98059i			0.119652i
$275$	6.37602	+	19.2305i	0.384488	+	1.15964i
$276$	0.201047	−	2.13923i	0.0121016	−	0.128766i
$277$	−10.2934	+	10.2934i	−0.618473	+	0.618473i	−0.945140	−	0.326667i	$-0.894075\pi$
$277$	−10.2934	+	10.2934i	−0.618473	+	0.618473i	0.326667	+	0.945140i	$0.394075\pi$
$278$	16.5668	−	16.5668i	0.993610	−	0.993610i
$279$	−5.45836	+	28.7832i	−0.326784	+	1.72321i
$280$	0.652495	+	4.04129i	0.0389940	+	0.241513i
$281$		−	22.3640i		−	1.33413i	−0.745001	−	0.667063i	$-0.767551\pi$
$281$		−	22.3640i		−	1.33413i	0.745001	−	0.667063i	$-0.232449\pi$
$282$	−15.7288	+	13.0264i	−0.936637	+	0.775709i
$283$	−22.8633	−	22.8633i	−1.35908	−	1.35908i	−0.875052	−	0.484030i	$-0.839173\pi$
$283$	−22.8633	−	22.8633i	−1.35908	−	1.35908i	−0.484030	−	0.875052i	$-0.660827\pi$
$284$	7.22853			0.428935
$285$	2.55096	−	2.91421i	0.151106	−	0.172623i
$286$	5.05750			0.299056
$287$	−2.42893	−	2.42893i	−0.143375	−	0.143375i
$288$	−2.47941	+	1.68894i	−0.146101	+	0.0995217i
$289$		−	14.5726i		−	0.857214i
$290$	−9.13621	−	6.59612i	−0.536497	−	0.387337i
$291$	19.1812	+	1.80267i	1.12442	+	0.105674i
$292$	3.04969	−	3.04969i	0.178470	−	0.178470i
$293$	−16.7421	+	16.7421i	−0.978084	+	0.978084i	−0.999765	−	0.0216809i	$-0.993098\pi$
$293$	−16.7421	+	16.7421i	−0.978084	+	0.978084i	0.0216809	+	0.999765i	$0.493098\pi$
$294$	−6.29157	−	0.591288i	−0.366932	−	0.0344846i
$295$	−2.68304	+	0.433196i	−0.156213	+	0.0252216i
$296$		−	4.27277i		−	0.248350i
$297$	10.1732	+	18.4339i	0.590309	+	1.06964i
$298$	3.08761	+	3.08761i	0.178861	+	0.178861i
$299$	1.54836			0.0895440
$300$	4.59252	−	7.34226i	0.265149	−	0.423906i
$301$	−0.516414			−0.0297656
$302$	14.3776	+	14.3776i	0.827340	+	0.827340i
$303$	2.18979	−	1.81355i	0.125800	−	0.104186i
$304$			1.00000i			0.0573539i
$305$	−3.21787	+	0.519548i	−0.184255	+	0.0297493i
$306$	4.59215	+	0.870840i	0.262516	+	0.0497826i
$307$	0.385994	−	0.385994i	0.0220298	−	0.0220298i	−0.696006	−	0.718036i	$-0.745041\pi$
$307$	0.385994	−	0.385994i	0.0220298	−	0.0220298i	0.718036	+	0.696006i	$0.245041\pi$
$308$	−5.24538	+	5.24538i	−0.298883	+	0.298883i
$309$	1.52729	−	16.2511i	0.0868845	−	0.924490i
$310$	17.7042	+	12.7820i	1.00553	+	0.725967i
$311$			29.7986i			1.68972i	0.534984	+	0.844862i	$0.320318\pi$
$311$			29.7986i			1.68972i	−0.534984	+	0.844862i	$0.679682\pi$
$312$	−1.37892	−	1.66499i	−0.0780662	−	0.0942617i
$313$	−14.6220	−	14.6220i	−0.826486	−	0.826486i	0.160543	−	0.987029i	$-0.448675\pi$
$313$	−14.6220	−	14.6220i	−0.826486	−	0.826486i	−0.987029	+	0.160543i	$0.948675\pi$
$314$	−11.8358			−0.667932
$315$	−8.44329	−	8.91800i	−0.475726	−	0.502472i
$316$	−13.1389			−0.739122
$317$	−2.69314	−	2.69314i	−0.151262	−	0.151262i	0.627420	−	0.778681i	$-0.284111\pi$
$317$	−2.69314	−	2.69314i	−0.151262	−	0.151262i	−0.778681	+	0.627420i	$0.784111\pi$
$318$	9.90707	+	11.9624i	0.555561	+	0.670817i
$319$		−	20.4197i		−	1.14329i
$320$	0.356413	+	2.20748i	0.0199241	+	0.123402i
$321$	2.99881	−	31.9087i	0.167377	−	1.78097i
$322$	−1.60588	+	1.60588i	−0.0894923	+	0.0894923i
$323$	1.10167	−	1.10167i	0.0612986	−	0.0612986i
$324$	3.29497	−	8.37515i	0.183054	−	0.465286i
$325$	5.57742	+	2.79987i	0.309380	+	0.155309i
$326$			13.4608i			0.745522i
$327$	17.5826	−	14.5617i	0.972323	−	0.805263i
$328$	−1.32676	−	1.32676i	−0.0732581	−	0.0732581i
$329$	21.5860			1.19008
$330$	15.6588	−	1.04080i	0.861986	−	0.0572941i
$331$	−3.14392			−0.172805			−0.0864027	−	0.996260i	$-0.527537\pi$
$331$	−3.14392			−0.172805			−0.0864027	+	0.996260i	$0.527537\pi$
$332$	−4.01176	−	4.01176i	−0.220174	−	0.220174i
$333$	7.21645	+	10.5940i	0.395459	+	0.580546i
$334$			13.3121i			0.728404i
$335$	4.17976	−	5.78934i	0.228364	−	0.316305i
$336$	3.15700	+	0.296698i	0.172228	+	0.0161862i
$337$	−0.402927	+	0.402927i	−0.0219488	+	0.0219488i	−0.717996	−	0.696047i	$-0.754940\pi$
$337$	−0.402927	+	0.402927i	−0.0219488	+	0.0219488i	0.696047	+	0.717996i	$0.254940\pi$
$338$	−8.09080	+	8.09080i	−0.440082	+	0.440082i
$339$	−18.4506	−	1.73400i	−1.00210	−	0.0941780i
$340$	2.03927	−	2.82457i	0.110595	−	0.153184i
$341$			39.5694i			2.14280i
$342$	−1.68894	−	2.47941i	−0.0913274	−	0.134071i
$343$	13.7846	+	13.7846i	0.744299	+	0.744299i
$344$	−0.282082			−0.0152088
$345$	4.79396	−	0.318643i	0.258098	−	0.0171551i
$346$	−13.8492			−0.744539
$347$	−14.5943	−	14.5943i	−0.783464	−	0.783464i	0.196950	−	0.980414i	$-0.436896\pi$
$347$	−14.5943	−	14.5943i	−0.783464	−	0.783464i	−0.980414	+	0.196950i	$0.936896\pi$
$348$	−6.72244	+	5.56743i	−0.360361	+	0.298445i
$349$		−	6.25742i		−	0.334952i	−0.985876	−	0.167476i	$-0.946438\pi$
$349$		−	6.25742i		−	0.334952i	0.985876	−	0.167476i	$-0.0535617\pi$
$350$	−8.68851	+	2.88074i	−0.464420	+	0.153982i
$351$	6.23099	+	1.79929i	0.332586	+	0.0960389i
$352$	−2.86519	+	2.86519i	−0.152715	+	0.152715i
$353$	−0.898203	+	0.898203i	−0.0478065	+	0.0478065i	−0.730606	−	0.682799i	$-0.760762\pi$
$353$	−0.898203	+	0.898203i	−0.0478065	+	0.0478065i	0.682799	+	0.730606i	$0.260762\pi$
$354$	−0.196980	+	2.09595i	−0.0104694	+	0.111399i
$355$	2.57635	+	15.9568i	0.136738	+	0.846901i
$356$			15.5041i			0.821715i
$357$	−3.15111	−	3.80483i	−0.166774	−	0.201373i
$358$	1.91540	+	1.91540i	0.101232	+	0.101232i
$359$	0.967026			0.0510377			0.0255188	−	0.999674i	$-0.491876\pi$
$359$	0.967026			0.0510377			0.0255188	+	0.999674i	$0.491876\pi$
$360$	−4.61200	−	4.87129i	−0.243074	−	0.256740i
$361$	−1.00000			−0.0526316
$362$	−9.42794	−	9.42794i	−0.495522	−	0.495522i
$363$	5.98639	+	7.22832i	0.314204	+	0.379388i
$364$			2.28502i			0.119767i
$365$	7.81909	+	5.64519i	0.409270	+	0.295483i
$366$	−0.236245	+	2.51376i	−0.0123487	+	0.131396i
$367$	−19.7540	+	19.7540i	−1.03115	+	1.03115i	−0.0316528	+	0.999499i	$0.510077\pi$
$367$	−19.7540	+	19.7540i	−1.03115	+	1.03115i	−0.999499	+	0.0316528i	$0.989923\pi$
$368$	−0.877184	+	0.877184i	−0.0457264	+	0.0457264i
$369$	5.53040	+	1.04877i	0.287901	+	0.0545967i
$370$	9.43206	−	1.52287i	0.490350	−	0.0791704i
$371$		−	16.4170i		−	0.852330i
$372$	13.0268	−	10.7886i	0.675406	−	0.559361i
$373$	−9.91796	−	9.91796i	−0.513532	−	0.513532i	0.402075	−	0.915607i	$-0.368289\pi$
$373$	−9.91796	−	9.91796i	−0.513532	−	0.513532i	−0.915607	+	0.402075i	$0.868289\pi$
$374$	6.31299			0.326437
$375$	17.8447	+	7.52102i	0.921498	+	0.388384i
$376$	11.7910			0.608073
$377$	−4.44767	−	4.44767i	−0.229067	−	0.229067i
$378$	−8.32860	+	4.59634i	−0.428377	+	0.236410i
$379$		−	21.6057i		−	1.10981i	−0.831913	−	0.554906i	$-0.812754\pi$
$379$		−	21.6057i		−	1.10981i	0.831913	−	0.554906i	$-0.187246\pi$
$380$	−2.20748	+	0.356413i	−0.113241	+	0.0182836i
$381$	−2.64117	−	0.248220i	−0.135311	−	0.0127167i
$382$	11.0503	−	11.0503i	0.565383	−	0.565383i
$383$	21.2148	−	21.2148i	1.08403	−	1.08403i	0.0878986	−	0.996129i	$-0.471985\pi$
$383$	21.2148	−	21.2148i	1.08403	−	1.08403i	0.996129	−	0.0878986i	$-0.0280151\pi$
$384$	1.72445	+	0.162066i	0.0880006	+	0.00827038i
$385$	−13.4486	−	9.70955i	−0.685404	−	0.494844i
$386$			16.6001i			0.844922i
$387$	0.699397	−	0.476419i	0.0355524	−	0.0242178i
$388$	−7.86520	−	7.86520i	−0.399295	−	0.399295i
$389$	−27.1443			−1.37627			−0.688136	−	0.725581i	$-0.741571\pi$
$389$	−27.1443			−1.37627			−0.688136	+	0.725581i	$0.741571\pi$
$390$	3.18397	−	3.63737i	0.161227	−	0.184186i
$391$	1.93273			0.0977426
$392$	2.57984	+	2.57984i	0.130302	+	0.130302i
$393$	8.01702	−	6.63958i	0.404405	−	0.334922i
$394$			14.7653i			0.743863i
$395$	−4.68288	−	29.0039i	−0.235621	−	1.45934i
$396$	2.26486	−	11.9431i	0.113813	−	0.600165i
$397$	6.88529	−	6.88529i	0.345563	−	0.345563i	−0.512891	−	0.858454i	$-0.671426\pi$
$397$	6.88529	−	6.88529i	0.345563	−	0.345563i	0.858454	+	0.512891i	$0.171426\pi$
$398$	−5.15183	+	5.15183i	−0.258238	+	0.258238i
$399$	−0.296698	+	3.15700i	−0.0148535	+	0.158048i
$400$	−4.74594	+	1.57355i	−0.237297	+	0.0786776i
$401$			23.1091i			1.15401i	0.816740	+	0.577006i	$0.195779\pi$
$401$			23.1091i			1.15401i	−0.816740	+	0.577006i	$0.804221\pi$
$402$	−3.52791	−	4.25980i	−0.175956	−	0.212460i
$403$	8.61871	+	8.61871i	0.429328	+	0.429328i
$404$	−1.64156			−0.0816705
$405$	19.6624	+	4.28856i	0.977030	+	0.213100i
$406$	9.22580			0.457869
$407$	12.2423	+	12.2423i	0.606829	+	0.606829i
$408$	−1.72123	−	2.07832i	−0.0852138	−	0.102892i
$409$			23.2391i			1.14910i	0.818469	+	0.574550i	$0.194823\pi$
$409$			23.2391i			1.14910i	−0.818469	+	0.574550i	$0.805177\pi$
$410$	2.45592	−	3.40167i	0.121289	−	0.167997i
$411$	−0.320985	+	3.41543i	−0.0158330	+	0.168471i
$412$	−6.66370	+	6.66370i	−0.328297	+	0.328297i
$413$	1.57340	−	1.57340i	0.0774218	−	0.0774218i
$414$	0.693390	−	3.65641i	0.0340783	−	0.179703i
$415$	7.42604	−	10.2857i	0.364530	−	0.504907i
$416$			1.24815i			0.0611956i
$417$	31.2535	−	25.8837i	1.53049	−	1.26753i
$418$	−2.86519	−	2.86519i	−0.140141	−	0.140141i
$419$	−18.0505			−0.881827			−0.440913	−	0.897550i	$-0.645345\pi$
$419$	−18.0505			−0.881827			−0.440913	+	0.897550i	$0.645345\pi$
$420$	0.470242	+	7.07475i	0.0229455	+	0.345213i
$421$	16.0363			0.781559			0.390780	−	0.920484i	$-0.372205\pi$
$421$	16.0363			0.781559			0.390780	+	0.920484i	$0.372205\pi$
$422$	−0.904131	−	0.904131i	−0.0440124	−	0.0440124i
$423$	−29.2347	+	19.9142i	−1.42144	+	0.968264i
$424$		−	8.96751i		−	0.435501i
$425$	6.96199	+	3.49492i	0.337706	+	0.169529i
$426$	12.4653	+	1.17150i	0.603944	+	0.0567592i
$427$	1.88703	−	1.88703i	0.0913200	−	0.0913200i
$428$	−13.0841	+	13.0841i	−0.632442	+	0.632442i
$429$	8.72141	+	0.819646i	0.421074	+	0.0395729i
$430$	−0.100538	−	0.622690i	−0.00484836	−	0.0300288i
$431$			26.9716i			1.29918i	0.760285	+	0.649589i	$0.225059\pi$
$431$			26.9716i			1.29918i	−0.760285	+	0.649589i	$0.774941\pi$
$432$	−4.54935	+	2.51067i	−0.218881	+	0.120795i
$433$	−24.4001	−	24.4001i	−1.17259	−	1.17259i	−0.981589	−	0.191004i	$-0.938825\pi$
$433$	−24.4001	−	24.4001i	−1.17259	−	1.17259i	−0.191004	−	0.981589i	$-0.561175\pi$
$434$	−17.8778			−0.858161
$435$	−14.6860	−	12.8554i	−0.704138	−	0.616367i
$436$	−13.1807			−0.631241
$437$	−0.877184	−	0.877184i	−0.0419614	−	0.0419614i
$438$	5.75330	−	4.76480i	0.274903	−	0.227671i
$439$		−	30.0037i		−	1.43200i	−0.698102	−	0.715999i	$-0.745972\pi$
$439$		−	30.0037i		−	1.43200i	0.698102	−	0.715999i	$-0.254028\pi$
$440$	−7.34605	−	5.30366i	−0.350209	−	0.252842i
$441$	−10.7537	−	2.03930i	−0.512080	−	0.0971093i
$442$	1.37505	−	1.37505i	0.0654044	−	0.0654044i
$443$	15.2430	−	15.2430i	0.724218	−	0.724218i	−0.245244	−	0.969461i	$-0.578868\pi$
$443$	15.2430	−	15.2430i	0.724218	−	0.724218i	0.969461	+	0.245244i	$0.0788680\pi$
$444$	0.692470	−	7.36819i	0.0328632	−	0.349679i
$445$	−34.2250	+	5.52587i	−1.62242	+	0.261951i
$446$		−	27.7005i		−	1.31166i
$447$	4.82404	+	5.82483i	0.228169	+	0.275505i
$448$	−1.29452	−	1.29452i	−0.0611602	−	0.0611602i
$449$	−31.8336			−1.50232			−0.751159	−	0.660121i	$-0.770505\pi$
$449$	−31.8336			−1.50232			−0.751159	+	0.660121i	$0.770505\pi$
$450$	9.10951	−	11.9171i	0.429426	−	0.561777i
$451$	7.60285			0.358004
$452$	7.56560	+	7.56560i	0.355856	+	0.355856i
$453$	22.4634	+	27.1237i	1.05542	+	1.27438i
$454$		−	3.03448i		−	0.142415i
$455$	−5.04413	+	0.814411i	−0.236473	+	0.0381802i
$456$	−0.162066	+	1.72445i	−0.00758942	+	0.0807549i
$457$	−14.6130	+	14.6130i	−0.683567	+	0.683567i	−0.960802	−	0.277235i	$-0.910582\pi$
$457$	−14.6130	+	14.6130i	−0.683567	+	0.683567i	0.277235	+	0.960802i	$0.410582\pi$
$458$	12.8580	−	12.8580i	0.600813	−	0.600813i
$459$	7.77781	+	2.24595i	0.363037	+	0.104832i
$460$	−2.24901	−	1.62373i	−0.104860	−	0.0757066i
$461$			23.6296i			1.10054i	0.834987	+	0.550270i	$0.185475\pi$
$461$			23.6296i			1.10054i	−0.834987	+	0.550270i	$0.814525\pi$
$462$	−9.89550	+	8.19531i	−0.460380	+	0.381280i
$463$	−4.82963	−	4.82963i	−0.224452	−	0.224452i	0.585918	−	0.810370i	$-0.300734\pi$
$463$	−4.82963	−	4.82963i	−0.224452	−	0.224452i	−0.810370	+	0.585918i	$0.800734\pi$
$464$	5.03943			0.233950
$465$	28.4585	+	24.9111i	1.31973	+	1.15523i
$466$	−7.26656			−0.336617
$467$	−14.3607	−	14.3607i	−0.664534	−	0.664534i	0.291911	−	0.956445i	$-0.405709\pi$
$467$	−14.3607	−	14.3607i	−0.664534	−	0.664534i	−0.956445	+	0.291911i	$0.905709\pi$
$468$	−2.10805	−	3.09468i	−0.0974446	−	0.143052i
$469$			5.84611i			0.269948i
$470$	4.20246	+	26.0284i	0.193845	+	1.20060i
$471$	−20.4103	−	1.91817i	−0.940455	−	0.0883848i
$472$	0.859440	−	0.859440i	0.0395589	−	0.0395589i
$473$	0.808219	−	0.808219i	0.0371620	−	0.0371620i
$474$	−22.6574	−	2.12937i	−1.04069	−	0.0978050i
$475$	−1.57355	−	4.74594i	−0.0721995	−	0.217759i
$476$			2.85226i			0.130733i
$477$	15.1456	+	22.2342i	0.693469	+	1.01803i
$478$	−18.3207	−	18.3207i	−0.837970	−	0.837970i
$479$	33.8055			1.54461			0.772307	−	0.635249i	$-0.219103\pi$
$479$	33.8055			1.54461			0.772307	+	0.635249i	$0.219103\pi$
$480$	0.256861	+	3.86446i	0.0117240	+	0.176387i
$481$	5.33306			0.243167
$482$	−16.5076	−	16.5076i	−0.751902	−	0.751902i
$483$	−3.02952	+	2.50901i	−0.137848	+	0.114164i
$484$		−	5.41865i		−	0.246302i
$485$	14.5590	−	20.1655i	0.661091	−	0.915670i
$486$	7.03934	−	13.9085i	0.319311	−	0.630905i
$487$	7.43111	−	7.43111i	0.336736	−	0.336736i	−0.518402	−	0.855137i	$-0.673473\pi$
$487$	7.43111	−	7.43111i	0.336736	−	0.336736i	0.855137	+	0.518402i	$0.173473\pi$
$488$	1.03076	−	1.03076i	0.0466602	−	0.0466602i
$489$	−2.18153	+	23.2124i	−0.0986520	+	1.04970i
$490$	−4.77546	+	6.61444i	−0.215733	+	0.298810i
$491$			13.2044i			0.595905i	0.954581	+	0.297952i	$0.0963036\pi$
$491$			13.2044i			0.595905i	−0.954581	+	0.297952i	$0.903696\pi$
$492$	−2.07291	−	2.50296i	−0.0934541	−	0.112842i
$493$	−5.55179	−	5.55179i	−0.250040	−	0.250040i
$494$	−1.24815			−0.0561569
$495$	27.1714	+	0.742937i	1.22127	+	0.0333925i
$496$	−9.76541			−0.438480
$497$	−9.35746	−	9.35746i	−0.419740	−	0.419740i
$498$	−6.26792	−	7.56826i	−0.280872	−	0.339142i
$499$			8.93586i			0.400024i	0.979793	+	0.200012i	$0.0640981\pi$
$499$			8.93586i			0.400024i	−0.979793	+	0.200012i	$0.935902\pi$
$500$	−5.16510	−	9.91573i	−0.230990	−	0.443445i
$501$	−2.15743	+	22.9560i	−0.0963869	+	1.02560i
$502$	−18.7927	+	18.7927i	−0.838758	+	0.838758i
$503$	−2.19515	+	2.19515i	−0.0978767	+	0.0978767i	−0.754350	−	0.656473i	$-0.772048\pi$
$503$	−2.19515	+	2.19515i	−0.0978767	+	0.0978767i	0.656473	+	0.754350i	$0.272048\pi$
$504$	5.39600	+	1.02328i	0.240357	+	0.0455806i
$505$	−0.585073	−	3.62370i	−0.0260354	−	0.161253i
$506$		−	5.02660i		−	0.223460i
$507$	−15.2634	+	12.6410i	−0.677873	+	0.561405i
$508$	1.08300	+	1.08300i	0.0480505	+	0.0480505i
$509$	3.39889			0.150653			0.0753265	−	0.997159i	$-0.476000\pi$
$509$	3.39889			0.150653			0.0753265	+	0.997159i	$0.476000\pi$
$510$	3.97438	−	4.54033i	0.175988	−	0.201049i
$511$	−7.89577			−0.349288
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−2.51067	−	4.54935i	−0.110849	−	0.200859i
$514$			4.68583i			0.206683i
$515$	−17.0850	−	12.3350i	−0.752856	−	0.543543i
$516$	−0.486437	−	0.0457158i	−0.0214142	−	0.00201253i
$517$	−33.7834	+	33.7834i	−1.48579	+	1.48579i
$518$	−5.53118	+	5.53118i	−0.243026	+	0.243026i
$519$	−23.8823	−	2.24448i	−1.04832	−	0.0985219i
$520$	−2.75527	+	0.444857i	−0.120826	+	0.0195083i
$521$		−	7.98825i		−	0.349972i	−0.984571	−	0.174986i	$-0.944012\pi$
$521$		−	7.98825i		−	0.349972i	0.984571	−	0.174986i	$-0.0559879\pi$
$522$	−12.4948	+	8.51128i	−0.546883	+	0.372529i
$523$	26.3556	+	26.3556i	1.15245	+	1.15245i	0.986060	+	0.166388i	$0.0532105\pi$
$523$	26.3556	+	26.3556i	1.15245	+	1.15245i	0.166388	+	0.986060i	$0.446790\pi$
$524$	−6.00990			−0.262544
$525$	−15.4498	+	3.55959i	−0.674284	+	0.155353i
$526$	−12.0296			−0.524517
$527$	10.7583	+	10.7583i	0.468637	+	0.468637i
$528$	−5.40524	+	4.47654i	−0.235233	+	0.194816i
$529$			21.4611i			0.933091i
$530$	19.7956	−	3.19614i	0.859866	−	0.138832i
$531$	−0.679364	+	3.58245i	−0.0294819	+	0.155465i
$532$	1.29452	−	1.29452i	0.0561245	−	0.0561245i
$533$	1.65600	−	1.65600i	0.0717291	−	0.0717291i
$534$	−2.51268	+	26.7361i	−0.108734	+	1.15698i
$535$	−33.5462	−	24.2195i	−1.45033	−	1.04710i
$536$			3.19333i			0.137931i
$537$	2.99259	+	3.61343i	0.129140	+	0.155931i
$538$	13.5151	+	13.5151i	0.582676	+	0.582676i
$539$	−14.7835			−0.636770
$540$	−7.16370	−	9.14776i	−0.308276	−	0.393657i
$541$	6.97397			0.299834			0.149917	−	0.988699i	$-0.452099\pi$
$541$	6.97397			0.299834			0.149917	+	0.988699i	$0.452099\pi$
$542$	−11.3585	−	11.3585i	−0.487890	−	0.487890i
$543$	−14.7301	−	17.7860i	−0.632128	−	0.763269i
$544$			1.55800i			0.0667986i
$545$	−4.69778	−	29.0961i	−0.201231	−	1.24634i
$546$	−0.370323	+	3.94040i	−0.0158484	+	0.168634i
$547$	−2.68199	+	2.68199i	−0.114674	+	0.114674i	−0.762115	−	0.647442i	$-0.775839\pi$
$547$	−2.68199	+	2.68199i	−0.114674	+	0.114674i	0.647442	+	0.762115i	$0.275839\pi$
$548$	1.40049	−	1.40049i	0.0598258	−	0.0598258i
$549$	−0.814787	+	4.29656i	−0.0347743	+	0.183373i
$550$	9.08950	−	18.1066i	0.387578	−	0.772066i
$551$			5.03943i			0.214687i
$552$	−1.65482	+	1.37050i	−0.0704339	+	0.0583324i
$553$	17.0086	+	17.0086i	0.723277	+	0.723277i
$554$	14.5571			0.618473
$555$	16.5119	−	1.09751i	0.700893	−	0.0465867i
$556$	−23.4290			−0.993610
$557$	6.84374	+	6.84374i	0.289979	+	0.289979i	0.837072	−	0.547093i	$-0.184266\pi$
$557$	6.84374	+	6.84374i	0.289979	+	0.289979i	−0.547093	+	0.837072i	$0.684266\pi$
$558$	24.2125	−	16.4932i	1.02500	−	0.698212i
$559$		−	0.352081i		−	0.0148914i
$560$	2.39624	−	3.31901i	0.101260	−	0.140254i
$561$	10.8865	+	1.02312i	0.459626	+	0.0431961i
$562$	−15.8138	+	15.8138i	−0.667063	+	0.667063i
$563$	−24.0154	+	24.0154i	−1.01213	+	1.01213i	−0.0122028	+	0.999926i	$0.503884\pi$
$563$	−24.0154	+	24.0154i	−1.01213	+	1.01213i	−0.999926	+	0.0122028i	$0.996116\pi$
$564$	20.3330	+	1.91091i	0.856173	+	0.0804639i
$565$	−14.0044	+	19.3974i	−0.589171	+	0.816054i
$566$			32.3336i			1.35908i
$567$	−15.1072	+	6.57639i	−0.634442	+	0.276182i
$568$	−5.11134	−	5.11134i	−0.214467	−	0.214467i
$569$	12.3367			0.517182			0.258591	−	0.965987i	$-0.416742\pi$
$569$	12.3367			0.517182			0.258591	+	0.965987i	$0.416742\pi$
$570$	−3.86446	+	0.256861i	−0.161864	+	0.0107587i
$571$	−2.43566			−0.101929			−0.0509646	−	0.998700i	$-0.516230\pi$
$571$	−2.43566			−0.101929			−0.0509646	+	0.998700i	$0.516230\pi$
$572$	−3.57619	−	3.57619i	−0.149528	−	0.149528i
$573$	20.8466	−	17.2649i	0.870880	−	0.721250i
$574$			3.43503i			0.143375i
$575$	2.78277	−	5.54335i	0.116049	−	0.231174i
$576$	2.94747	+	0.558949i	0.122811	+	0.0232895i
$577$	20.3964	−	20.3964i	0.849115	−	0.849115i	−0.140908	−	0.990023i	$-0.545002\pi$
$577$	20.3964	−	20.3964i	0.849115	−	0.849115i	0.990023	+	0.140908i	$0.0450021\pi$
$578$	−10.3044	+	10.3044i	−0.428607	+	0.428607i
$579$	−2.69030	+	28.6260i	−0.111805	+	1.18966i
$580$	1.79612	+	11.1244i	0.0745798	+	0.461917i
$581$			10.3866i			0.430909i
$582$	−12.2885	−	14.8378i	−0.509374	−	0.615048i
$583$	25.6936	+	25.6936i	1.06412	+	1.06412i
$584$	−4.31292			−0.178470
$585$	6.08010	−	5.75646i	0.251381	−	0.238000i
$586$	23.6769			0.978084
$587$	−7.30666	−	7.30666i	−0.301578	−	0.301578i	0.540053	−	0.841631i	$-0.318404\pi$
$587$	−7.30666	−	7.30666i	−0.301578	−	0.301578i	−0.841631	+	0.540053i	$0.818404\pi$
$588$	4.03071	+	4.86692i	0.166224	+	0.200708i
$589$		−	9.76541i		−	0.402377i
$590$	2.20351	+	1.59088i	0.0907172	+	0.0654955i
$591$	−2.39294	+	25.4620i	−0.0984325	+	1.04737i
$592$	−3.02131	+	3.02131i	−0.124175	+	0.124175i
$593$	−30.5679	+	30.5679i	−1.25527	+	1.25527i	−0.301950	+	0.953324i	$0.597638\pi$
$593$	−30.5679	+	30.5679i	−1.25527	+	1.25527i	−0.953324	+	0.301950i	$0.902362\pi$
$594$	5.84121	−	20.2283i	0.239668	−	0.829977i
$595$	−6.29631	+	1.01658i	−0.258124	+	0.0416759i
$596$		−	4.36654i		−	0.178861i
$597$	−9.71902	+	8.04915i	−0.397773	+	0.329430i
$598$	−1.09486	−	1.09486i	−0.0447720	−	0.0447720i
$599$	23.0022			0.939843			0.469921	−	0.882708i	$-0.344282\pi$
$599$	23.0022			0.939843			0.469921	+	0.882708i	$0.344282\pi$
$600$	−8.43916	+	1.94436i	−0.344527	+	0.0793781i
$601$	−13.6513			−0.556847			−0.278423	−	0.960458i	$-0.589812\pi$
$601$	−13.6513			−0.556847			−0.278423	+	0.960458i	$0.589812\pi$
$602$	0.365160	+	0.365160i	0.0148828	+	0.0148828i
$603$	−5.39334	−	7.91758i	−0.219634	−	0.322429i
$604$		−	20.3330i		−	0.827340i
$605$	11.9616	−	1.93128i	0.486307	−	0.0785177i
$606$	−2.83079	−	0.266040i	−0.114993	−	0.0108071i
$607$	1.96645	−	1.96645i	0.0798158	−	0.0798158i	−0.666072	−	0.745888i	$-0.732026\pi$
$607$	1.96645	−	1.96645i	0.0798158	−	0.0798158i	0.745888	+	0.666072i	$0.232026\pi$
$608$	0.707107	−	0.707107i	0.0286770	−	0.0286770i
$609$	15.9095	+	1.49519i	0.644684	+	0.0605880i
$610$	2.64276	+	1.90800i	0.107002	+	0.0772528i
$611$			14.7169i			0.595382i
$612$	−2.63136	−	3.86292i	−0.106366	−	0.156149i
$613$	−12.1077	−	12.1077i	−0.489025	−	0.489025i	0.418973	−	0.907999i	$-0.362390\pi$
$613$	−12.1077	−	12.1077i	−0.489025	−	0.489025i	−0.907999	+	0.418973i	$0.862390\pi$
$614$	−0.545878			−0.0220298
$615$	4.78641	−	5.46800i	0.193007	−	0.220491i
$616$	7.41808			0.298883
$617$	−30.8463	−	30.8463i	−1.24183	−	1.24183i	−0.959243	−	0.282582i	$-0.908809\pi$
$617$	−30.8463	−	30.8463i	−1.24183	−	1.24183i	−0.282582	−	0.959243i	$-0.591191\pi$
$618$	−12.5712	+	10.4113i	−0.505687	+	0.418803i
$619$			28.1904i			1.13307i	0.824039	+	0.566534i	$0.191716\pi$
$619$			28.1904i			1.13307i	−0.824039	+	0.566534i	$0.808284\pi$
$620$	−3.48052	−	21.5569i	−0.139781	−	0.865748i
$621$	1.78830	−	6.19293i	0.0717619	−	0.248514i
$622$	21.0708	−	21.0708i	0.844862	−	0.844862i
$623$	20.0703	−	20.0703i	0.804101	−	0.804101i
$624$	−0.202282	+	2.15237i	−0.00809777	+	0.0861639i
$625$	20.0479	−	14.9360i	0.801915	−	0.597438i
$626$			20.6787i			0.826486i
$627$	−4.47654	−	5.40524i	−0.178776	−	0.215864i
$628$	8.36917	+	8.36917i	0.333966	+	0.333966i
$629$	6.65697			0.265431
$630$	−0.335665	+	12.2763i	−0.0133732	+	0.489099i
$631$	−44.8116			−1.78392			−0.891961	−	0.452113i	$-0.850670\pi$
$631$	−44.8116			−1.78392			−0.891961	+	0.452113i	$0.850670\pi$
$632$	9.29061	+	9.29061i	0.369561	+	0.369561i
$633$	−1.41260	−	1.70566i	−0.0561459	−	0.0677939i
$634$			3.80868i			0.151262i
$635$	−2.00471	+	2.77671i	−0.0795546	+	0.110190i
$636$	1.45333	−	15.4640i	0.0576281	−	0.613189i
$637$	−3.22003	+	3.22003i	−0.127582	+	0.127582i
$638$	−14.4389	+	14.4389i	−0.571643	+	0.571643i
$639$	21.3059	+	4.04038i	0.842848	+	0.159835i
$640$	1.30890	−	1.81295i	0.0517389	−	0.0716630i
$641$		−	9.11894i		−	0.360176i	−0.983650	−	0.180088i	$-0.942362\pi$
$641$		−	9.11894i		−	0.360176i	0.983650	−	0.180088i	$-0.0576383\pi$
$642$	−24.6833	+	20.4424i	−0.974173	+	0.806796i
$643$	12.0846	+	12.0846i	0.476572	+	0.476572i	0.904034	−	0.427462i	$-0.140592\pi$
$643$	12.0846	+	12.0846i	0.476572	+	0.476572i	−0.427462	+	0.904034i	$0.640592\pi$
$644$	2.27106			0.0894923
$645$	−0.0724559	−	1.09009i	−0.00285295	−	0.0429224i
$646$	−1.55800			−0.0612986
$647$	1.21178	+	1.21178i	0.0476399	+	0.0476399i	0.730525	−	0.682886i	$-0.239275\pi$
$647$	1.21178	+	1.21178i	0.0476399	+	0.0476399i	−0.682886	+	0.730525i	$0.739275\pi$
$648$	−8.25202	+	3.59223i	−0.324170	+	0.141116i
$649$			4.92492i			0.193320i
$650$	−1.96403	−	5.92364i	−0.0770355	−	0.232344i
$651$	−30.8294	−	2.89737i	−1.20830	−	0.113557i
$652$	9.51819	−	9.51819i	0.372761	−	0.372761i
$653$	−7.87945	+	7.87945i	−0.308347	+	0.308347i	−0.844268	−	0.535921i	$-0.819964\pi$
$653$	−7.87945	+	7.87945i	−0.308347	+	0.308347i	0.535921	+	0.844268i	$0.319964\pi$
$654$	−22.7295	−	2.13614i	−0.888793	−	0.0835296i
$655$	−2.14201	−	13.2667i	−0.0836952	−	0.518374i
$656$			1.87632i			0.0732581i
$657$	10.6935	−	7.28426i	0.417193	−	0.284186i
$658$	−15.2636	−	15.2636i	−0.595038	−	0.595038i
$659$	30.2646			1.17894			0.589471	−	0.807789i	$-0.299336\pi$
$659$	30.2646			1.17894			0.589471	+	0.807789i	$0.299336\pi$
$660$	−11.8084	−	10.3365i	−0.459640	−	0.402346i
$661$	−21.0286			−0.817917			−0.408958	−	0.912553i	$-0.634108\pi$
$661$	−21.0286			−0.817917			−0.408958	+	0.912553i	$0.634108\pi$
$662$	2.22309	+	2.22309i	0.0864027	+	0.0864027i
$663$	2.59405	−	2.14836i	0.100745	−	0.0834353i
$664$			5.67349i			0.220174i
$665$	3.31901	+	2.39624i	0.128706	+	0.0929222i
$666$	2.38826	−	12.5939i	0.0925433	−	0.488002i
$667$	−4.42050	+	4.42050i	−0.171163	+	0.171163i
$668$	9.41306	−	9.41306i	0.364202	−	0.364202i
$669$	4.48930	−	47.7682i	0.173566	−	1.84682i
$670$	−7.04921	+	1.13815i	−0.272335	+	0.0439704i
$671$			5.90664i			0.228023i
$672$	−2.02254	−	2.44213i	−0.0780210	−	0.0942072i
$673$	−22.0700	−	22.0700i	−0.850736	−	0.850736i	0.139488	−	0.990224i	$-0.455454\pi$
$673$	−22.0700	−	22.0700i	−0.850736	−	0.850736i	−0.990224	+	0.139488i	$0.955454\pi$
$674$	0.569824			0.0219488
$675$	17.6403	−	19.0741i	0.678974	−	0.734162i
$676$	11.4421			0.440082
$677$	18.2077	+	18.2077i	0.699780	+	0.699780i	0.964363	−	0.264583i	$-0.0852342\pi$
$677$	18.2077	+	18.2077i	0.699780	+	0.699780i	−0.264583	+	0.964363i	$0.585234\pi$
$678$	11.8204	+	14.2726i	0.453959	+	0.548137i
$679$			20.3633i			0.781471i
$680$	−3.43925	+	0.555291i	−0.131889	+	0.0212944i
$681$	0.491785	−	5.23282i	0.0188452	−	0.200522i
$682$	27.9798	−	27.9798i	1.07140	−	1.07140i
$683$	27.5676	−	27.5676i	1.05484	−	1.05484i	0.0564381	−	0.998406i	$-0.482026\pi$
$683$	27.5676	−	27.5676i	1.05484	−	1.05484i	0.998406	−	0.0564381i	$-0.0179744\pi$
$684$	−0.558949	+	2.94747i	−0.0213719	+	0.112699i
$685$	3.59070	+	2.59239i	0.137194	+	0.0990503i
$686$		−	19.4944i		−	0.744299i
$687$	24.2568	−	20.0891i	0.925454	−	0.766447i
$688$	0.199462	+	0.199462i	0.00760442	+	0.00760442i
$689$	11.1928			0.426412
$690$	−3.61515	−	3.16452i	−0.137627	−	0.120471i
$691$	16.3113			0.620510			0.310255	−	0.950653i	$-0.399586\pi$
$691$	16.3113			0.620510			0.310255	+	0.950653i	$0.399586\pi$
$692$	9.79289	+	9.79289i	0.372270	+	0.372270i
$693$	−18.3925	+	12.5287i	−0.698673	+	0.475926i
$694$			20.6395i			0.783464i
$695$	−8.35040	−	51.7190i	−0.316749	−	1.96181i
$696$	8.69025	+	0.816718i	0.329403	+	0.0309576i
$697$	2.06709	−	2.06709i	0.0782965	−	0.0782965i
$698$	−4.42467	+	4.42467i	−0.167476	+	0.167476i
$699$	−12.5308	−	1.17766i	−0.473960	−	0.0445432i
$700$	8.18069	+	4.10671i	0.309201	+	0.155219i
$701$		−	16.2155i		−	0.612453i	−0.951959	−	0.306226i	$-0.900934\pi$
$701$		−	16.2155i		−	0.612453i	0.951959	−	0.306226i	$-0.0990664\pi$
$702$	−3.13369	−	5.67827i	−0.118273	−	0.214312i
$703$	−3.02131	−	3.02131i	−0.113951	−	0.113951i
$704$	4.05199			0.152715
$705$	3.02864	+	45.5657i	0.114065	+	1.71610i
$706$	1.27025			0.0478065
$707$	2.12502	+	2.12502i	0.0799198	+	0.0799198i
$708$	1.62135	−	1.34278i	0.0609340	−	0.0504646i
$709$		−	27.2559i		−	1.02362i	−0.859100	−	0.511808i	$-0.828976\pi$
$709$		−	27.2559i		−	1.02362i	0.859100	−	0.511808i	$-0.171024\pi$
$710$	9.46144	−	13.1049i	0.355082	−	0.491820i
$711$	−38.7265	−	7.34398i	−1.45236	−	0.275421i
$712$	10.9631	−	10.9631i	0.410858	−	0.410858i
$713$	8.56606	−	8.56606i	0.320801	−	0.320801i
$714$	−0.462254	+	4.91859i	−0.0172994	+	0.184074i
$715$	6.61977	−	9.16897i	0.247565	−	0.342900i
$716$		−	2.70878i		−	0.101232i
$717$	−28.6240	−	34.5624i	−1.06898	−	1.29076i
$718$	−0.683791	−	0.683791i	−0.0255188	−	0.0255188i
$719$	27.9463			1.04222			0.521111	−	0.853489i	$-0.325518\pi$
$719$	27.9463			1.04222			0.521111	+	0.853489i	$0.325518\pi$
$720$	−0.183351	+	6.70570i	−0.00683309	+	0.249907i
$721$	17.2526			0.642519
$722$	0.707107	+	0.707107i	0.0263158	+	0.0263158i
$723$	−25.7913	−	31.1419i	−0.959189	−	1.15818i
$724$			13.3331i			0.495522i
$725$	−23.9168	+	7.92979i	−0.888248	+	0.294505i
$726$	0.878178	−	9.34421i	0.0325922	−	0.346796i
$727$	0.785783	−	0.785783i	0.0291431	−	0.0291431i	−0.692385	−	0.721528i	$-0.743440\pi$
$727$	0.785783	−	0.785783i	0.0291431	−	0.0291431i	0.721528	+	0.692385i	$0.243440\pi$
$728$	1.61575	−	1.61575i	0.0598837	−	0.0598837i
$729$	14.3931	−	22.8438i	0.533078	−	0.846066i
$730$	−1.53718	−	9.52068i	−0.0568937	−	0.352376i
$731$		−	0.439483i		−	0.0162549i
$732$	1.94454	−	1.61044i	0.0718724	−	0.0595237i
$733$	32.5824	+	32.5824i	1.20346	+	1.20346i	0.973107	+	0.230353i	$0.0739880\pi$
$733$	32.5824	+	32.5824i	1.20346	+	1.20346i	0.230353	+	0.973107i	$0.426012\pi$
$734$	27.9364			1.03115
$735$	−9.30703	+	10.6323i	−0.343295	+	0.392180i
$736$	1.24053			0.0457264
$737$	−9.14951	−	9.14951i	−0.337026	−	0.337026i
$738$	−3.16899	−	4.65218i	−0.116652	−	0.171249i
$739$		−	29.4181i		−	1.08216i	−0.840970	−	0.541082i	$-0.818015\pi$
$739$		−	29.4181i		−	1.08216i	0.840970	−	0.541082i	$-0.181985\pi$
$740$	−7.74631	−	5.59264i	−0.284760	−	0.205590i
$741$	−2.15237	−	0.202282i	−0.0790694	−	0.00743102i
$742$	−11.6086	+	11.6086i	−0.426165	+	0.426165i
$743$	−15.5044	+	15.5044i	−0.568802	+	0.568802i	−0.931793	−	0.362991i	$-0.881756\pi$
$743$	−15.5044	+	15.5044i	−0.568802	+	0.568802i	0.362991	+	0.931793i	$0.381756\pi$
$744$	−16.8400	−	1.58264i	−0.617384	−	0.0580223i
$745$	9.63905	−	1.55629i	0.353148	−	0.0570182i
$746$			14.0261i			0.513532i
$747$	−9.58218	−	14.0669i	−0.350594	−	0.514682i
$748$	−4.46396	−	4.46396i	−0.163219	−	0.163219i
$749$	33.8751			1.23777
$750$	−7.29997	−	17.9363i	−0.266557	−	0.654941i
$751$	−30.2158			−1.10259			−0.551295	−	0.834311i	$-0.685866\pi$
$751$	−30.2158			−1.10259			−0.551295	+	0.834311i	$0.685866\pi$
$752$	−8.33748	−	8.33748i	−0.304037	−	0.304037i
$753$	−35.4527	+	29.3614i	−1.29197	+	1.06999i
$754$			6.28996i			0.229067i
$755$	44.8848	−	7.24697i	1.63353	−	0.263744i
$756$	9.13931	+	2.63911i	0.332394	+	0.0959834i
$757$	26.1455	−	26.1455i	0.950273	−	0.950273i	−0.0485482	−	0.998821i	$-0.515459\pi$
$757$	26.1455	−	26.1455i	0.950273	−	0.950273i	0.998821	+	0.0485482i	$0.0154594\pi$
$758$	−15.2776	+	15.2776i	−0.554906	+	0.554906i
$759$	0.814639	−	8.66813i	0.0295695	−	0.314633i
$760$	1.81295	+	1.30890i	0.0657625	+	0.0474789i
$761$			21.4239i			0.776614i	0.921530	+	0.388307i	$0.126940\pi$
$761$			21.4239i			0.776614i	−0.921530	+	0.388307i	$0.873060\pi$
$762$	1.69207	+	2.04311i	0.0612972	+	0.0740139i
$763$	17.0626	+	17.0626i	0.617709	+	0.617709i
$764$	−15.6275			−0.565383
$765$	7.58946	−	7.18547i	0.274397	−	0.259791i
$766$	−30.0023			−1.08403
$767$	1.07271	+	1.07271i	0.0387333	+	0.0387333i
$768$	−1.10477	−	1.33397i	−0.0398651	−	0.0481355i
$769$			5.25678i			0.189564i	0.995498	+	0.0947821i	$0.0302154\pi$
$769$			5.25678i			0.189564i	−0.995498	+	0.0947821i	$0.969785\pi$
$770$	2.64390	+	16.3753i	0.0952797	+	0.590124i
$771$	−0.759413	+	8.08049i	−0.0273496	+	0.291012i
$772$	11.7380	−	11.7380i	0.422461	−	0.422461i
$773$	−28.7467	+	28.7467i	−1.03395	+	1.03395i	−0.0345431	+	0.999403i	$0.510998\pi$
$773$	−28.7467	+	28.7467i	−1.03395	+	1.03395i	−0.999403	+	0.0345431i	$0.989002\pi$
$774$	−0.831428	−	0.157669i	−0.0298851	−	0.00566731i
$775$	46.3460	−	15.3664i	1.66480	−	0.551976i
$776$			11.1231i			0.399295i
$777$	−10.4347	+	8.64184i	−0.374342	+	0.310024i
$778$	19.1939	+	19.1939i	0.688136	+	0.688136i
$779$	−1.87632			−0.0672262
$780$	−4.82342	+	0.320601i	−0.172706	+	0.0114794i
$781$	29.2900			1.04808
$782$	−1.36665	−	1.36665i	−0.0488713	−	0.0488713i
$783$	−22.9261	+	12.6523i	−0.819312	+	0.452157i
$784$		−	3.64845i		−	0.130302i
$785$	−15.4919	+	21.4577i	−0.552929	+	0.765857i
$786$	−10.3638	−	0.973998i	−0.369664	−	0.0347413i
$787$	36.5999	−	36.5999i	1.30465	−	1.30465i	0.379424	−	0.925223i	$-0.376122\pi$
$787$	36.5999	−	36.5999i	1.30465	−	1.30465i	0.925223	−	0.379424i	$-0.123878\pi$
$788$	10.4406	−	10.4406i	0.371932	−	0.371932i
$789$	−20.7445	−	1.94959i	−0.738524	−	0.0694072i
$790$	−17.1975	+	23.8201i	−0.611861	+	0.847483i
$791$		−	19.5876i		−	0.696455i
$792$	−10.0466	+	6.84357i	−0.356989	+	0.243176i
$793$	1.28654	+	1.28654i	0.0456864	+	0.0456864i
$794$	−9.73727			−0.345563
$795$	34.6546	−	2.30340i	1.22907	−	0.0816933i
$796$	7.28579			0.258238
$797$	−23.9802	−	23.9802i	−0.849422	−	0.849422i	0.140639	−	0.990061i	$-0.455084\pi$
$797$	−23.9802	−	23.9802i	−0.849422	−	0.849422i	−0.990061	+	0.140639i	$0.955084\pi$
$798$	2.44213	−	2.02254i	0.0864505	−	0.0715970i
$799$			18.3703i			0.649895i
$800$	4.46855	+	2.24322i	0.157987	+	0.0793097i
$801$	−8.66600	+	45.6978i	−0.306198	+	1.61465i
$802$	16.3406	−	16.3406i	0.577006	−	0.577006i
$803$	12.3573	−	12.3573i	0.436081	−	0.436081i
$804$	−0.517529	+	5.50674i	−0.0182518	+	0.194208i
$805$	0.809436	+	5.01332i	0.0285289	+	0.176696i
$806$		−	12.1887i		−	0.429328i
$807$	21.1158	+	25.4964i	0.743310	+	0.897517i
$808$	1.16076	+	1.16076i	0.0408352	+	0.0408352i
$809$	38.2583			1.34509			0.672546	−	0.740056i	$-0.265201\pi$
$809$	38.2583			1.34509			0.672546	+	0.740056i	$0.265201\pi$
$810$	−10.8709	−	16.9359i	−0.381965	−	0.595065i
$811$	21.9071			0.769261			0.384630	−	0.923071i	$-0.374329\pi$
$811$	21.9071			0.769261			0.384630	+	0.923071i	$0.374329\pi$
$812$	−6.52363	−	6.52363i	−0.228934	−	0.228934i
$813$	−17.7464	−	21.4280i	−0.622393	−	0.751514i
$814$		−	17.3133i		−	0.606829i
$815$	24.4036	+	17.6188i	0.854822	+	0.617160i
$816$	−0.252498	+	2.68669i	−0.00883919	+	0.0940530i
$817$	−0.199462	+	0.199462i	−0.00697829	+	0.00697829i
$818$	16.4325	−	16.4325i	0.574550	−	0.574550i
$819$	−1.27721	+	6.73502i	−0.0446293	+	0.235341i
$820$	−4.14194	+	0.668746i	−0.144643	+	0.0233536i
$821$		−	5.40450i		−	0.188618i	−0.995543	−	0.0943092i	$-0.969936\pi$
$821$		−	5.40450i		−	0.188618i	0.995543	−	0.0943092i	$-0.0300642\pi$
$822$	2.64204	−	2.18810i	0.0921518	−	0.0763188i
$823$	37.3101	+	37.3101i	1.30055	+	1.30055i	0.928022	+	0.372524i	$0.121508\pi$
$823$	37.3101	+	37.3101i	1.30055	+	1.30055i	0.372524	+	0.928022i	$0.378492\pi$
$824$	9.42390			0.328297
$825$	18.6089	−	29.7508i	0.647877	−	1.03579i
$826$	−2.22512			−0.0774218
$827$	6.56098	+	6.56098i	0.228148	+	0.228148i	0.811918	−	0.583771i	$-0.198423\pi$
$827$	6.56098	+	6.56098i	0.228148	+	0.228148i	−0.583771	+	0.811918i	$0.698423\pi$
$828$	−3.07577	+	2.09517i	−0.106891	+	0.0728122i
$829$		−	44.6157i		−	1.54957i	−0.632227	−	0.774783i	$-0.717859\pi$
$829$		−	44.6157i		−	1.54957i	0.632227	−	0.774783i	$-0.282141\pi$
$830$	−12.5241	+	2.02211i	−0.434718	+	0.0701884i
$831$	25.1031	+	2.35921i	0.870816	+	0.0818401i
$832$	0.882575	−	0.882575i	0.0305978	−	0.0305978i
$833$	−4.01939	+	4.01939i	−0.139263	+	0.139263i
$834$	−40.4021	−	3.79703i	−1.39901	−	0.131480i
$835$	24.1341	+	17.4242i	0.835194	+	0.602989i
$836$			4.05199i			0.140141i
$837$	44.4262	−	24.5177i	1.53560	−	0.847455i
$838$	12.7637	+	12.7637i	0.440913	+	0.440913i
$839$	26.5712			0.917341			0.458671	−	0.888606i	$-0.348326\pi$
$839$	26.5712			0.917341			0.458671	+	0.888606i	$0.348326\pi$
$840$	4.67010	−	5.33512i	0.161134	−	0.184079i
$841$	−3.60418			−0.124282
$842$	−11.3393	−	11.3393i	−0.390780	−	0.390780i
$843$	−29.8329	+	24.7072i	−1.02750	+	0.850961i
$844$			1.27863i			0.0440124i
$845$	4.07813	+	25.2583i	0.140292	+	0.868911i
$846$	34.7535	+	6.59055i	1.19485	+	0.226588i
$847$	−7.01454	+	7.01454i	−0.241023	+	0.241023i
$848$	−6.34099	+	6.34099i	−0.217750	+	0.217750i
$849$	−5.24016	+	55.7577i	−0.179842	+	1.91360i
$850$	−2.45159	−	7.39416i	−0.0840888	−	0.253618i
$851$		−	5.30048i		−	0.181698i
$852$	−7.98589	−	9.64264i	−0.273592	−	0.330351i
$853$	23.2147	+	23.2147i	0.794856	+	0.794856i	0.982279	−	0.187423i	$-0.0600135\pi$
$853$	23.2147	+	23.2147i	0.794856	+	0.794856i	−0.187423	+	0.982279i	$0.560014\pi$
$854$	−2.66867			−0.0913200
$855$	−6.70570	−	0.183351i	−0.229330	−	0.00627047i
$856$	18.5037			0.632442
$857$	−26.6952	−	26.6952i	−0.911892	−	0.911892i	0.0845288	−	0.996421i	$-0.473062\pi$
$857$	−26.6952	−	26.6952i	−0.911892	−	0.911892i	−0.996421	+	0.0845288i	$0.973062\pi$
$858$	−5.58739	−	6.74654i	−0.190750	−	0.230323i
$859$		−	9.24536i		−	0.315448i	−0.987483	−	0.157724i	$-0.949584\pi$
$859$		−	9.24536i		−	0.315448i	0.987483	−	0.157724i	$-0.0504156\pi$
$860$	−0.369218	+	0.511400i	−0.0125902	+	0.0174386i
$861$	−0.556700	+	5.92354i	−0.0189723	+	0.201874i
$862$	19.0718	−	19.0718i	0.649589	−	0.649589i
$863$	−5.81284	+	5.81284i	−0.197871	+	0.197871i	−0.799087	−	0.601216i	$-0.794683\pi$
$863$	−5.81284	+	5.81284i	−0.197871	+	0.197871i	0.601216	+	0.799087i	$0.294683\pi$
$864$	4.99218	+	1.44156i	0.169838	+	0.0490430i
$865$	−18.1273	+	25.1079i	−0.616346	+	0.853695i
$866$			34.5069i			1.17259i
$867$	−19.4395	+	16.0995i	−0.660199	+	0.546767i
$868$	12.6415	+	12.6415i	0.429080	+	0.429080i
$869$	−53.2388			−1.80600
$870$	1.29443	+	19.4746i	0.0438854	+	0.660252i
$871$	−3.98575			−0.135052
$872$	9.32016	+	9.32016i	0.315620	+	0.315620i
$873$	−18.7862	−	27.5787i	−0.635816	−	0.933397i
$874$			1.24053i			0.0419614i
$875$	−6.14978	+	19.5224i	−0.207900	+	0.659978i
$876$	−7.43742	−	0.698976i	−0.251287	−	0.0236162i
$877$	−4.52006	+	4.52006i	−0.152631	+	0.152631i	−0.779292	−	0.626661i	$-0.784421\pi$
$877$	−4.52006	+	4.52006i	−0.152631	+	0.152631i	0.626661	+	0.779292i	$0.284421\pi$
$878$	−21.2158	+	21.2158i	−0.715999	+	0.715999i
$879$	40.8297	+	3.83721i	1.37715	+	0.129426i
$880$	1.44418	+	8.94470i	0.0486835	+	0.301526i
$881$		−	10.7215i		−	0.361217i	−0.983555	−	0.180609i	$-0.942193\pi$
$881$		−	10.7215i		−	0.361217i	0.983555	−	0.180609i	$-0.0578068\pi$
$882$	6.16201	+	9.04601i	0.207486	+	0.304595i
$883$	4.65216	+	4.65216i	0.156558	+	0.156558i	0.781039	−	0.624482i	$-0.214690\pi$
$883$	4.65216	+	4.65216i	0.156558	+	0.156558i	−0.624482	+	0.781039i	$0.714690\pi$
$884$	−1.94461			−0.0654044
$885$	3.54202	+	3.10051i	0.119064	+	0.104223i
$886$	−21.5569			−0.724218
$887$	−4.58671	−	4.58671i	−0.154007	−	0.154007i	0.625898	−	0.779905i	$-0.284733\pi$
$887$	−4.58671	−	4.58671i	−0.154007	−	0.154007i	−0.779905	+	0.625898i	$0.784733\pi$
$888$	−5.69975	+	4.72045i	−0.191271	+	0.158408i
$889$		−	2.80393i		−	0.0940410i
$890$	28.1081	+	20.2933i	0.942186	+	0.680234i
$891$	13.3512	−	33.9361i	0.447282	−	1.13690i
$892$	−19.5872	+	19.5872i	−0.655828	+	0.655828i
$893$	8.33748	−	8.33748i	0.279003	−	0.279003i
$894$	0.707666	−	7.52989i	0.0236679	−	0.251837i
$895$	5.97958	−	0.965446i	0.199875	−	0.0322713i
$896$			1.83072i			0.0611602i
$897$	−1.71059	−	2.06547i	−0.0571149	−	0.0689639i
$898$	22.5097	+	22.5097i	0.751159	+	0.751159i
$899$	−49.2121			−1.64131
$900$	−14.8680	+	1.98526i	−0.495601	+	0.0661752i
$901$	13.9714			0.465453
$902$	−5.37602	−	5.37602i	−0.179002	−	0.179002i
$903$	0.570521	+	0.688881i	0.0189858	+	0.0229245i
$904$		−	10.6994i		−	0.355856i
$905$	−29.4326	+	4.75210i	−0.978373	+	0.157965i
$906$	3.29529	−	35.0634i	0.109479	−	1.16490i
$907$	−19.4277	+	19.4277i	−0.645087	+	0.645087i	−0.951801	−	0.306715i	$-0.900770\pi$
$907$	−19.4277	+	19.4277i	−0.645087	+	0.645087i	0.306715	+	0.951801i	$0.400770\pi$
$908$	−2.14570	+	2.14570i	−0.0712076	+	0.0712076i
$909$	−4.83844	−	0.917546i	−0.160481	−	0.0304331i
$910$	4.14262	+	2.99086i	0.137326	+	0.0991462i
$911$		−	12.7713i		−	0.423132i	−0.977364	−	0.211566i	$-0.932144\pi$
$911$		−	12.7713i		−	0.423132i	0.977364	−	0.211566i	$-0.0678563\pi$
$912$	1.33397	−	1.10477i	0.0441721	−	0.0365827i
$913$	−16.2556	−	16.2556i	−0.537983	−	0.537983i
$914$	20.6659			0.683567
$915$	4.24808	+	3.71856i	0.140437	+	0.122932i
$916$	−18.1839			−0.600813
$917$	7.77992	+	7.77992i	0.256915	+	0.256915i
$918$	−3.91161	−	7.08787i	−0.129102	−	0.233934i
$919$			9.01507i			0.297380i	0.988884	+	0.148690i	$0.0475056\pi$
$919$			9.01507i			0.297380i	−0.988884	+	0.148690i	$0.952494\pi$
$920$	0.442140	+	2.73844i	0.0145769	+	0.0902835i
$921$	−0.941340	−	0.0884680i	−0.0310182	−	0.00291512i
$922$	16.7086	−	16.7086i	0.550270	−	0.550270i
$923$	6.37972	−	6.37972i	0.209991	−	0.209991i
$924$	12.7921	+	1.20222i	0.420830	+	0.0395500i
$925$	9.58476	−	19.0931i	0.315145	−	0.627778i
$926$			6.83013i			0.224452i
$927$	−23.3657	+	15.9164i	−0.767431	+	0.522763i
$928$	−3.56341	−	3.56341i	−0.116975	−	0.116975i
$929$	−35.1135			−1.15204			−0.576018	−	0.817437i	$-0.695394\pi$
$929$	−35.1135			−1.15204			−0.576018	+	0.817437i	$0.695394\pi$
$930$	−2.50835	−	37.7380i	−0.0822521	−	1.23748i
$931$	3.64845			0.119573
$932$	5.13824	+	5.13824i	0.168308	+	0.168308i
$933$	39.7504	−	32.9207i	1.30137	−	1.07778i
$934$			20.3091i			0.664534i
$935$	8.26309	−	11.4451i	0.270232	−	0.374295i
$936$	−0.697652	+	3.67888i	−0.0228035	+	0.120248i
$937$	−14.1924	+	14.1924i	−0.463647	+	0.463647i	−0.899849	−	0.436202i	$-0.856323\pi$
$937$	−14.1924	+	14.1924i	−0.463647	+	0.463647i	0.436202	+	0.899849i	$0.356323\pi$
$938$	4.13382	−	4.13382i	0.134974	−	0.134974i
$939$	−3.35130	+	35.6594i	−0.109366	+	1.16370i
$940$	15.4332	−	21.3764i	0.503377	−	0.697222i
$941$		−	55.2343i		−	1.80059i	−0.435285	−	0.900293i	$-0.643352\pi$
$941$		−	55.2343i		−	1.80059i	0.435285	−	0.900293i	$-0.356648\pi$
$942$	13.0759	+	15.7886i	0.426035	+	0.514420i
$943$	−1.64588	−	1.64588i	−0.0535972	−	0.0535972i
$944$	−1.21543			−0.0395589
$945$	−2.56840	+	21.1155i	−0.0835501	+	0.686886i
$946$	−1.14299			−0.0371620
$947$	−3.79361	−	3.79361i	−0.123276	−	0.123276i	0.642777	−	0.766053i	$-0.277782\pi$
$947$	−3.79361	−	3.79361i	−0.123276	−	0.123276i	−0.766053	+	0.642777i	$0.777782\pi$
$948$	14.5155	+	17.5269i	0.471442	+	0.569247i
$949$		−	5.38317i		−	0.174745i
$950$	−2.24322	+	4.46855i	−0.0727796	+	0.144979i
$951$	−0.617256	+	6.56788i	−0.0200159	+	0.212978i
$952$	2.01685	−	2.01685i	0.0653666	−	0.0653666i
$953$	−13.2183	+	13.2183i	−0.428183	+	0.428183i	−0.888009	−	0.459826i	$-0.847912\pi$
$953$	−13.2183	+	13.2183i	−0.428183	+	0.428183i	0.459826	+	0.888009i	$0.347912\pi$
$954$	5.01238	−	26.4315i	0.162282	−	0.855750i
$955$	−5.56985	−	34.4974i	−0.180236	−	1.11631i
$956$			25.9094i			0.837970i
$957$	−27.2393	+	22.5592i	−0.880521	+	0.729235i
$958$	−23.9041	−	23.9041i	−0.772307	−	0.772307i
$959$	−3.62591			−0.117087
$960$	2.55096	−	2.91421i	0.0823317	−	0.0940558i
$961$	64.3632			2.07623
$962$	−3.77104	−	3.77104i	−0.121583	−	0.121583i
$963$	−45.8782	+	31.2516i	−1.47840	+	1.00707i
$964$			23.3453i			0.751902i
$965$	30.0951	+	21.7279i	0.968794	+	0.699445i
$966$	3.91633	+	0.368061i	0.126006	+	0.0118422i
$967$	10.2991	−	10.2991i	0.331198	−	0.331198i	−0.521844	−	0.853041i	$-0.674756\pi$
$967$	10.2991	−	10.2991i	0.331198	−	0.331198i	0.853041	+	0.521844i	$0.174756\pi$
$968$	−3.83157	+	3.83157i	−0.123151	+	0.123151i
$969$	−2.68669	−	0.252498i	−0.0863089	−	0.00811140i
$970$	−24.5540	+	3.96441i	−0.788380	+	0.127290i
$971$		−	31.6341i		−	1.01519i	−0.861597	−	0.507593i	$-0.830535\pi$
$971$		−	31.6341i		−	1.01519i	0.861597	−	0.507593i	$-0.169465\pi$
$972$	−14.8124	+	4.85726i	−0.475108	+	0.155797i
$973$	30.3292	+	30.3292i	0.972310	+	0.972310i
$974$	−10.5092			−0.336736
$975$	−2.42685	−	10.5333i	−0.0777215	−	0.337337i
$976$	−1.45771			−0.0466602
$977$	8.83239	+	8.83239i	0.282573	+	0.282573i	0.834134	−	0.551561i	$-0.185968\pi$
$977$	8.83239	+	8.83239i	0.282573	+	0.282573i	−0.551561	+	0.834134i	$0.685968\pi$
$978$	17.9562	−	14.8711i	0.574177	−	0.475525i
$979$			62.8225i			2.00782i
$980$	8.05388	−	1.30036i	0.257272	−	0.0415383i
$981$	−38.8497	−	7.36734i	−1.24038	−	0.235221i
$982$	9.33689	−	9.33689i	0.297952	−	0.297952i
$983$	36.6972	−	36.6972i	1.17046	−	1.17046i	0.188360	−	0.982100i	$-0.439683\pi$
$983$	36.6972	−	36.6972i	1.17046	−	1.17046i	0.982100	−	0.188360i	$-0.0603171\pi$
$984$	−0.304087	+	3.23563i	−0.00969395	+	0.103148i
$985$	26.7686	+	19.3263i	0.852920	+	0.615787i
$986$			7.85141i			0.250040i
$987$	−23.8477	−	28.7951i	−0.759080	−	0.916558i
$988$	0.882575	+	0.882575i	0.0280785	+	0.0280785i
$989$	−0.349930			−0.0111271
$990$	−18.6878	−	19.7384i	−0.593937	−	0.627329i
$991$	−26.0021			−0.825982			−0.412991	−	0.910735i	$-0.635516\pi$
$991$	−26.0021			−0.825982			−0.412991	+	0.910735i	$0.635516\pi$
$992$	6.90519	+	6.90519i	0.219240	+	0.219240i
$993$	3.47332	+	4.19389i	0.110223	+	0.133089i
$994$			13.2335i			0.419740i
$995$	2.59675	+	16.0832i	0.0823226	+	0.509873i
$996$	−0.919478	+	9.78366i	−0.0291348	+	0.310007i
$997$	−22.4051	+	22.4051i	−0.709577	+	0.709577i	−0.966446	−	0.256869i	$-0.917309\pi$
$997$	−22.4051	+	22.4051i	−0.709577	+	0.709577i	0.256869	+	0.966446i	$0.417309\pi$
$998$	6.31861	−	6.31861i	0.200012	−	0.200012i
$999$	6.15948	−	21.3305i	0.194877	−	0.674866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.a.533.3	yes	36
3.2	odd	2	inner	570.2.k.a.533.11	yes	36
5.2	odd	4	inner	570.2.k.a.77.11	yes	36
15.2	even	4	inner	570.2.k.a.77.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.a.77.3	✓	36	15.2	even	4	inner
570.2.k.a.77.11	yes	36	5.2	odd	4	inner
570.2.k.a.533.3	yes	36	1.1	even	1	trivial
570.2.k.a.533.11	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.10477 - 1.33397i) q^{3} +1.00000i q^{4} +(-2.20748 + 0.356413i) q^{5} +(-0.162066 + 1.72445i) q^{6} +(1.29452 - 1.29452i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.558949 + 2.94747i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.10477 - 1.33397i) q^{3} +1.00000i q^{4} +(-2.20748 + 0.356413i) q^{5} +(-0.162066 + 1.72445i) q^{6} +(1.29452 - 1.29452i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.558949 + 2.94747i) q^{9} +(1.81295 + 1.30890i) q^{10} +4.05199i q^{11} +(1.33397 - 1.10477i) q^{12} +(0.882575 + 0.882575i) q^{13} -1.83072 q^{14} +(2.91421 + 2.55096i) q^{15} -1.00000 q^{16} +(1.10167 + 1.10167i) q^{17} +(2.47941 - 1.68894i) q^{18} -1.00000i q^{19} +(-0.356413 - 2.20748i) q^{20} +(-3.15700 - 0.296698i) q^{21} +(2.86519 - 2.86519i) q^{22} +(0.877184 - 0.877184i) q^{23} +(-1.72445 - 0.162066i) q^{24} +(4.74594 - 1.57355i) q^{25} -1.24815i q^{26} +(4.54935 - 2.51067i) q^{27} +(1.29452 + 1.29452i) q^{28} -5.03943 q^{29} +(-0.256861 - 3.86446i) q^{30} +9.76541 q^{31} +(0.707107 + 0.707107i) q^{32} +(5.40524 - 4.47654i) q^{33} -1.55800i q^{34} +(-2.39624 + 3.31901i) q^{35} +(-2.94747 - 0.558949i) q^{36} +(3.02131 - 3.02131i) q^{37} +(-0.707107 + 0.707107i) q^{38} +(0.202282 - 2.15237i) q^{39} +(-1.30890 + 1.81295i) q^{40} -1.87632i q^{41} +(2.02254 + 2.44213i) q^{42} +(-0.199462 - 0.199462i) q^{43} -4.05199 q^{44} +(0.183351 - 6.70570i) q^{45} -1.24053 q^{46} +(8.33748 + 8.33748i) q^{47} +(1.10477 + 1.33397i) q^{48} +3.64845i q^{49} +(-4.46855 - 2.24322i) q^{50} +(0.252498 - 2.68669i) q^{51} +(-0.882575 + 0.882575i) q^{52} +(6.34099 - 6.34099i) q^{53} +(-4.99218 - 1.44156i) q^{54} +(-1.44418 - 8.94470i) q^{55} -1.83072i q^{56} +(-1.33397 + 1.10477i) q^{57} +(3.56341 + 3.56341i) q^{58} +1.21543 q^{59} +(-2.55096 + 2.91421i) q^{60} +1.45771 q^{61} +(-6.90519 - 6.90519i) q^{62} +(3.09198 + 4.53912i) q^{63} -1.00000i q^{64} +(-2.26283 - 1.63371i) q^{65} +(-6.98747 - 0.656689i) q^{66} +(-2.25803 + 2.25803i) q^{67} +(-1.10167 + 1.10167i) q^{68} +(-2.13923 - 0.201047i) q^{69} +(4.04129 - 0.652495i) q^{70} -7.22853i q^{71} +(1.68894 + 2.47941i) q^{72} +(-3.04969 - 3.04969i) q^{73} -4.27277 q^{74} +(-7.34226 - 4.59252i) q^{75} +1.00000 q^{76} +(5.24538 + 5.24538i) q^{77} +(-1.66499 + 1.37892i) q^{78} +13.1389i q^{79} +(2.20748 - 0.356413i) q^{80} +(-8.37515 - 3.29497i) q^{81} +(-1.32676 + 1.32676i) q^{82} +(-4.01176 + 4.01176i) q^{83} +(0.296698 - 3.15700i) q^{84} +(-2.82457 - 2.03927i) q^{85} +0.282082i q^{86} +(5.56743 + 6.72244i) q^{87} +(2.86519 + 2.86519i) q^{88} +15.5041 q^{89} +(-4.87129 + 4.61200i) q^{90} +2.28502 q^{91} +(0.877184 + 0.877184i) q^{92} +(-10.7886 - 13.0268i) q^{93} -11.7910i q^{94} +(0.356413 + 2.20748i) q^{95} +(0.162066 - 1.72445i) q^{96} +(-7.86520 + 7.86520i) q^{97} +(2.57984 - 2.57984i) q^{98} +(-11.9431 - 2.26486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} - 12 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} - 32 q^{21} - 4 q^{22} + 32 q^{25} + 28 q^{27} - 12 q^{28} - 8 q^{30} + 8 q^{31} + 36 q^{33} + 4 q^{36} - 32 q^{37} - 8 q^{40} + 12 q^{42} - 24 q^{43} - 28 q^{45} - 16 q^{46} - 4 q^{48} - 40 q^{51} - 8 q^{52} - 4 q^{55} + 4 q^{57} - 4 q^{58} - 24 q^{60} + 200 q^{61} + 28 q^{63} + 12 q^{70} - 68 q^{73} - 36 q^{75} + 36 q^{76} + 24 q^{78} - 92 q^{81} + 24 q^{82} + 24 q^{85} + 28 q^{87} - 4 q^{88} - 68 q^{90} + 64 q^{91} + 16 q^{93} - 4 q^{96} - 148 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 - 12 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 - 32 * q^21 - 4 * q^22 + 32 * q^25 + 28 * q^27 - 12 * q^28 - 8 * q^30 + 8 * q^31 + 36 * q^33 + 4 * q^36 - 32 * q^37 - 8 * q^40 + 12 * q^42 - 24 * q^43 - 28 * q^45 - 16 * q^46 - 4 * q^48 - 40 * q^51 - 8 * q^52 - 4 * q^55 + 4 * q^57 - 4 * q^58 - 24 * q^60 + 200 * q^61 + 28 * q^63 + 12 * q^70 - 68 * q^73 - 36 * q^75 + 36 * q^76 + 24 * q^78 - 92 * q^81 + 24 * q^82 + 24 * q^85 + 28 * q^87 - 4 * q^88 - 68 * q^90 + 64 * q^91 + 16 * q^93 - 4 * q^96 - 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more