LMFDB - Embedded newform 570.2.k.b.77.13

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			77.13
Character	$\chi$	$=$	570.77
Dual form			570.2.k.b.533.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.162692 - 1.72439i) q^{3} -1.00000i q^{4} +(-0.520052 - 2.17475i) q^{5} +(-1.33437 - 1.10429i) q^{6} +(0.496606 + 0.496606i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.94706 + 0.561090i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.162692 - 1.72439i) q^{3} -1.00000i q^{4} +(-0.520052 - 2.17475i) q^{5} +(-1.33437 - 1.10429i) q^{6} +(0.496606 + 0.496606i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.94706 + 0.561090i) q^{9} +(-1.90551 - 1.17005i) q^{10} -1.60026i q^{11} +(-1.72439 + 0.162692i) q^{12} +(0.465079 - 0.465079i) q^{13} +0.702307 q^{14} +(-3.66552 + 1.25059i) q^{15} -1.00000 q^{16} +(0.134587 - 0.134587i) q^{17} +(-1.68714 + 2.48064i) q^{18} -1.00000i q^{19} +(-2.17475 + 0.520052i) q^{20} +(0.775550 - 0.937138i) q^{21} +(-1.13156 - 1.13156i) q^{22} +(-0.307276 - 0.307276i) q^{23} +(-1.10429 + 1.33437i) q^{24} +(-4.45909 + 2.26197i) q^{25} -0.657722i q^{26} +(1.44700 + 4.99061i) q^{27} +(0.496606 - 0.496606i) q^{28} +2.93712 q^{29} +(-1.70761 + 3.47621i) q^{30} -1.63168 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.75948 + 0.260350i) q^{33} -0.190335i q^{34} +(0.821734 - 1.33826i) q^{35} +(0.561090 + 2.94706i) q^{36} +(4.03947 + 4.03947i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(-0.877644 - 0.726315i) q^{39} +(-1.17005 + 1.90551i) q^{40} -3.54984i q^{41} +(-0.114260 - 1.21105i) q^{42} +(3.15359 - 3.15359i) q^{43} -1.60026 q^{44} +(2.75286 + 6.11733i) q^{45} -0.434554 q^{46} +(-4.45089 + 4.45089i) q^{47} +(0.162692 + 1.72439i) q^{48} -6.50676i q^{49} +(-1.55360 + 4.75251i) q^{50} +(-0.253977 - 0.210185i) q^{51} +(-0.465079 - 0.465079i) q^{52} +(-2.36753 - 2.36753i) q^{53} +(4.55208 + 2.50571i) q^{54} +(-3.48017 + 0.832220i) q^{55} -0.702307i q^{56} +(-1.72439 + 0.162692i) q^{57} +(2.07686 - 2.07686i) q^{58} +8.58688 q^{59} +(1.25059 + 3.66552i) q^{60} +6.10554 q^{61} +(-1.15377 + 1.15377i) q^{62} +(-1.74217 - 1.18489i) q^{63} +1.00000i q^{64} +(-1.25330 - 0.769567i) q^{65} +(-1.76715 + 2.13534i) q^{66} +(-6.28833 - 6.28833i) q^{67} +(-0.134587 - 0.134587i) q^{68} +(-0.479873 + 0.579855i) q^{69} +(-0.365236 - 1.52734i) q^{70} -13.9322i q^{71} +(2.48064 + 1.68714i) q^{72} +(2.24565 - 2.24565i) q^{73} +5.71267 q^{74} +(4.62598 + 7.32122i) q^{75} -1.00000 q^{76} +(0.794700 - 0.794700i) q^{77} +(-1.13417 + 0.107006i) q^{78} -3.48349i q^{79} +(0.520052 + 2.17475i) q^{80} +(8.37036 - 3.30713i) q^{81} +(-2.51012 - 2.51012i) q^{82} +(1.76187 + 1.76187i) q^{83} +(-0.937138 - 0.775550i) q^{84} +(-0.362685 - 0.222701i) q^{85} -4.45985i q^{86} +(-0.477846 - 5.06474i) q^{87} +(-1.13156 + 1.13156i) q^{88} +14.7492 q^{89} +(6.27217 + 2.37904i) q^{90} +0.461923 q^{91} +(-0.307276 + 0.307276i) q^{92} +(0.265461 + 2.81365i) q^{93} +6.29451i q^{94} +(-2.17475 + 0.520052i) q^{95} +(1.33437 + 1.10429i) q^{96} +(-0.0173490 - 0.0173490i) q^{97} +(-4.60098 - 4.60098i) q^{98} +(0.897892 + 4.71607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	$ 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) $ 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.162692	−	1.72439i	−0.0939303	−	0.995579i
$3$	−0.162692	−	1.72439i	−0.0939303	−	0.995579i
$4$		−	1.00000i		−	0.500000i
$5$	−0.520052	−	2.17475i	−0.232574	−	0.972579i
$5$	−0.520052	−	2.17475i	−0.232574	−	0.972579i
$6$	−1.33437	−	1.10429i	−0.544755	−	0.450824i
$7$	0.496606	+	0.496606i	0.187699	+	0.187699i	0.794701	−	0.607001i	$-0.207628\pi$
$7$	0.496606	+	0.496606i	0.187699	+	0.187699i	−0.607001	+	0.794701i	$0.707628\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.94706	+	0.561090i	−0.982354	+	0.187030i
$10$	−1.90551	−	1.17005i	−0.602577	−	0.370002i
$11$		−	1.60026i		−	0.482497i	−0.970463	−	0.241249i	$-0.922443\pi$
$11$		−	1.60026i		−	0.482497i	0.970463	−	0.241249i	$-0.0775570\pi$
$12$	−1.72439	+	0.162692i	−0.497789	+	0.0469651i
$13$	0.465079	−	0.465079i	0.128990	−	0.128990i	−0.639664	−	0.768654i	$-0.720927\pi$
$13$	0.465079	−	0.465079i	0.128990	−	0.128990i	0.768654	+	0.639664i	$0.220927\pi$
$14$	0.702307			0.187699
$15$	−3.66552	+	1.25059i	−0.946433	+	0.322901i
$16$	−1.00000			−0.250000
$17$	0.134587	−	0.134587i	0.0326421	−	0.0326421i	−0.690597	−	0.723239i	$-0.742652\pi$
$17$	0.134587	−	0.134587i	0.0326421	−	0.0326421i	0.723239	+	0.690597i	$0.242652\pi$
$18$	−1.68714	+	2.48064i	−0.397662	+	0.584692i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	−2.17475	+	0.520052i	−0.486289	+	0.116287i
$21$	0.775550	−	0.937138i	0.169239	−	0.204500i
$22$	−1.13156	−	1.13156i	−0.241249	−	0.241249i
$23$	−0.307276	−	0.307276i	−0.0640714	−	0.0640714i	0.674345	−	0.738416i	$-0.264426\pi$
$23$	−0.307276	−	0.307276i	−0.0640714	−	0.0640714i	−0.738416	+	0.674345i	$0.764426\pi$
$24$	−1.10429	+	1.33437i	−0.225412	+	0.272377i
$25$	−4.45909	+	2.26197i	−0.891818	+	0.452394i
$26$		−	0.657722i		−	0.128990i
$27$	1.44700	+	4.99061i	0.278476	+	0.960443i
$28$	0.496606	−	0.496606i	0.0938497	−	0.0938497i
$29$	2.93712			0.545409			0.272704	−	0.962098i	$-0.412082\pi$
$29$	2.93712			0.545409			0.272704	+	0.962098i	$0.412082\pi$
$30$	−1.70761	+	3.47621i	−0.311766	+	0.634667i
$31$	−1.63168			−0.293058			−0.146529	−	0.989206i	$-0.546810\pi$
$31$	−1.63168			−0.293058			−0.146529	+	0.989206i	$0.546810\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−2.75948	+	0.260350i	−0.480364	+	0.0453211i
$34$		−	0.190335i		−	0.0326421i
$35$	0.821734	−	1.33826i	0.138898	−	0.226207i
$36$	0.561090	+	2.94706i	0.0935150	+	0.491177i
$37$	4.03947	+	4.03947i	0.664085	+	0.664085i	0.956340	−	0.292256i	$-0.0944058\pi$
$37$	4.03947	+	4.03947i	0.664085	+	0.664085i	−0.292256	+	0.956340i	$0.594406\pi$
$38$	−0.707107	−	0.707107i	−0.114708	−	0.114708i
$39$	−0.877644	−	0.726315i	−0.140536	−	0.116303i
$40$	−1.17005	+	1.90551i	−0.185001	+	0.301288i
$41$		−	3.54984i		−	0.554392i	−0.960813	−	0.277196i	$-0.910595\pi$
$41$		−	3.54984i		−	0.554392i	0.960813	−	0.277196i	$-0.0894052\pi$
$42$	−0.114260	−	1.21105i	−0.0176307	−	0.186870i
$43$	3.15359	−	3.15359i	0.480918	−	0.480918i	−0.424507	−	0.905425i	$-0.639553\pi$
$43$	3.15359	−	3.15359i	0.480918	−	0.480918i	0.905425	+	0.424507i	$0.139553\pi$
$44$	−1.60026			−0.241249
$45$	2.75286	+	6.11733i	0.410372	+	0.911918i
$46$	−0.434554			−0.0640714
$47$	−4.45089	+	4.45089i	−0.649229	+	0.649229i	−0.952807	−	0.303578i	$-0.901819\pi$
$47$	−4.45089	+	4.45089i	−0.649229	+	0.649229i	0.303578	+	0.952807i	$0.401819\pi$
$48$	0.162692	+	1.72439i	0.0234826	+	0.248895i
$49$		−	6.50676i		−	0.929538i
$50$	−1.55360	+	4.75251i	−0.219712	+	0.672106i
$51$	−0.253977	−	0.210185i	−0.0355639	−	0.0294317i
$52$	−0.465079	−	0.465079i	−0.0644949	−	0.0644949i
$53$	−2.36753	−	2.36753i	−0.325206	−	0.325206i	0.525554	−	0.850760i	$-0.323858\pi$
$53$	−2.36753	−	2.36753i	−0.325206	−	0.325206i	−0.850760	+	0.525554i	$0.823858\pi$
$54$	4.55208	+	2.50571i	0.619460	+	0.340984i
$55$	−3.48017	+	0.832220i	−0.469267	+	0.112217i
$56$		−	0.702307i		−	0.0938497i
$57$	−1.72439	+	0.162692i	−0.228401	+	0.0215491i
$58$	2.07686	−	2.07686i	0.272704	−	0.272704i
$59$	8.58688			1.11792			0.558958	−	0.829196i	$-0.311201\pi$
$59$	8.58688			1.11792			0.558958	+	0.829196i	$0.311201\pi$
$60$	1.25059	+	3.66552i	0.161450	+	0.473216i
$61$	6.10554			0.781734			0.390867	−	0.920447i	$-0.372175\pi$
$61$	6.10554			0.781734			0.390867	+	0.920447i	$0.372175\pi$
$62$	−1.15377	+	1.15377i	−0.146529	+	0.146529i
$63$	−1.74217	−	1.18489i	−0.219493	−	0.149282i
$64$			1.00000i			0.125000i
$65$	−1.25330	−	0.769567i	−0.155452	−	0.0954530i
$66$	−1.76715	+	2.13534i	−0.217522	+	0.262843i
$67$	−6.28833	−	6.28833i	−0.768241	−	0.768241i	0.209555	−	0.977797i	$-0.432798\pi$
$67$	−6.28833	−	6.28833i	−0.768241	−	0.768241i	−0.977797	+	0.209555i	$0.932798\pi$
$68$	−0.134587	−	0.134587i	−0.0163211	−	0.0163211i
$69$	−0.479873	+	0.579855i	−0.0577699	+	0.0698064i
$70$	−0.365236	−	1.52734i	−0.0436541	−	0.182552i
$71$		−	13.9322i		−	1.65345i	−0.562610	−	0.826723i	$-0.690203\pi$
$71$		−	13.9322i		−	1.65345i	0.562610	−	0.826723i	$-0.309797\pi$
$72$	2.48064	+	1.68714i	0.292346	+	0.198831i
$73$	2.24565	−	2.24565i	0.262833	−	0.262833i	−0.563371	−	0.826204i	$-0.690496\pi$
$73$	2.24565	−	2.24565i	0.262833	−	0.262833i	0.826204	+	0.563371i	$0.190496\pi$
$74$	5.71267			0.664085
$75$	4.62598	+	7.32122i	0.534162	+	0.845382i
$76$	−1.00000			−0.114708
$77$	0.794700	−	0.794700i	0.0905645	−	0.0905645i
$78$	−1.13417	+	0.107006i	−0.128420	+	0.0121161i
$79$		−	3.48349i		−	0.391923i	−0.980612	−	0.195962i	$-0.937217\pi$
$79$		−	3.48349i		−	0.391923i	0.980612	−	0.195962i	$-0.0627828\pi$
$80$	0.520052	+	2.17475i	0.0581436	+	0.243145i
$81$	8.37036	−	3.30713i	0.930040	−	0.367459i
$82$	−2.51012	−	2.51012i	−0.277196	−	0.277196i
$83$	1.76187	+	1.76187i	0.193390	+	0.193390i	0.797159	−	0.603769i	$-0.206335\pi$
$83$	1.76187	+	1.76187i	0.193390	+	0.193390i	−0.603769	+	0.797159i	$0.706335\pi$
$84$	−0.937138	−	0.775550i	−0.102250	−	0.0846195i
$85$	−0.362685	−	0.222701i	−0.0393388	−	0.0241553i
$86$		−	4.45985i		−	0.480918i
$87$	−0.477846	−	5.06474i	−0.0512304	−	0.542998i
$88$	−1.13156	+	1.13156i	−0.120624	+	0.120624i
$89$	14.7492			1.56341			0.781707	−	0.623646i	$-0.214349\pi$
$89$	14.7492			1.56341			0.781707	+	0.623646i	$0.214349\pi$
$90$	6.27217	+	2.37904i	0.661145	+	0.250773i
$91$	0.461923			0.0484226
$92$	−0.307276	+	0.307276i	−0.0320357	+	0.0320357i
$93$	0.265461	+	2.81365i	0.0275270	+	0.291762i
$94$			6.29451i			0.649229i
$95$	−2.17475	+	0.520052i	−0.223125	+	0.0533562i
$96$	1.33437	+	1.10429i	0.136189	+	0.112706i
$97$	−0.0173490	−	0.0173490i	−0.00176152	−	0.00176152i	0.706225	−	0.707987i	$-0.250396\pi$
$97$	−0.0173490	−	0.0173490i	−0.00176152	−	0.00176152i	−0.707987	+	0.706225i	$0.750396\pi$
$98$	−4.60098	−	4.60098i	−0.464769	−	0.464769i
$99$	0.897892	+	4.71607i	0.0902415	+	0.473983i
$100$	2.26197	+	4.45909i	0.226197	+	0.445909i
$101$			1.92211i			0.191258i	0.995417	+	0.0956288i	$0.0304862\pi$
$101$			1.92211i			0.191258i	−0.995417	+	0.0956288i	$0.969514\pi$
$102$	−0.328212	+	0.0309659i	−0.0324978	+	0.00306608i
$103$	8.69498	−	8.69498i	0.856742	−	0.856742i	−0.134211	−	0.990953i	$-0.542850\pi$
$103$	8.69498	−	8.69498i	0.856742	−	0.856742i	0.990953	+	0.134211i	$0.0428499\pi$
$104$	−0.657722			−0.0644949
$105$	−2.44137	−	1.19927i	−0.238253	−	0.117037i
$106$	−3.34820			−0.325206
$107$	−12.4950	+	12.4950i	−1.20794	+	1.20794i	−0.236248	+	0.971693i	$0.575918\pi$
$107$	−12.4950	+	12.4950i	−1.20794	+	1.20794i	−0.971693	+	0.236248i	$0.924082\pi$
$108$	4.99061	−	1.44700i	0.480222	−	0.139238i
$109$		−	0.183803i		−	0.0176051i	−0.999961	−	0.00880257i	$-0.997198\pi$
$109$		−	0.183803i		−	0.0176051i	0.999961	−	0.00880257i	$-0.00280198\pi$
$110$	−1.87239	+	3.04932i	−0.178525	+	0.290742i
$111$	6.30844	−	7.62282i	0.598771	−	0.723526i
$112$	−0.496606	−	0.496606i	−0.0469249	−	0.0469249i
$113$	8.57949	+	8.57949i	0.807091	+	0.807091i	0.984193	−	0.177102i	$-0.0566722\pi$
$113$	8.57949	+	8.57949i	0.807091	+	0.807091i	−0.177102	+	0.984193i	$0.556672\pi$
$114$	−1.10429	+	1.33437i	−0.103426	+	0.124975i
$115$	−0.508449	+	0.828048i	−0.0474131	+	0.0772159i
$116$		−	2.93712i		−	0.272704i
$117$	−1.10967	+	1.63157i	−0.102589	+	0.150839i
$118$	6.07184	−	6.07184i	0.558958	−	0.558958i
$119$	0.133673			0.0122538
$120$	3.47621	+	1.70761i	0.317333	+	0.155883i
$121$	8.43916			0.767196
$122$	4.31727	−	4.31727i	0.390867	−	0.390867i
$123$	−6.12132	+	0.577531i	−0.551941	+	0.0520742i
$124$			1.63168i			0.146529i
$125$	7.23818	+	8.52108i	0.647403	+	0.762148i
$126$	−2.06974	+	0.394057i	−0.184387	+	0.0351054i
$127$	−9.39884	−	9.39884i	−0.834012	−	0.834012i	0.154051	−	0.988063i	$-0.450768\pi$
$127$	−9.39884	−	9.39884i	−0.834012	−	0.834012i	−0.988063	+	0.154051i	$0.950768\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−5.95109	−	4.92496i	−0.523964	−	0.433619i
$130$	−1.43038	+	0.342050i	−0.125453	+	0.0299997i
$131$			7.18140i			0.627441i	0.949515	+	0.313721i	$0.101576\pi$
$131$			7.18140i			0.627441i	−0.949515	+	0.313721i	$0.898424\pi$
$132$	0.260350	+	2.75948i	0.0226606	+	0.240182i
$133$	0.496606	−	0.496606i	0.0430612	−	0.0430612i
$134$	−8.89304			−0.768241
$135$	10.1008	−	5.74225i	0.869340	−	0.494214i
$136$	−0.190335			−0.0163211
$137$	−8.35532	+	8.35532i	−0.713844	+	0.713844i	−0.967337	−	0.253494i	$-0.918420\pi$
$137$	−8.35532	+	8.35532i	−0.713844	+	0.713844i	0.253494	+	0.967337i	$0.418420\pi$
$138$	0.0706984	+	0.749341i	0.00601825	+	0.0637881i
$139$		−	17.4721i		−	1.48197i	−0.671523	−	0.740984i	$-0.734360\pi$
$139$		−	17.4721i		−	1.48197i	0.671523	−	0.740984i	$-0.265640\pi$
$140$	−1.33826	−	0.821734i	−0.113103	−	0.0694492i
$141$	8.39921	+	6.95096i	0.707341	+	0.585376i
$142$	−9.85154	−	9.85154i	−0.826723	−	0.826723i
$143$	−0.744249	−	0.744249i	−0.0622373	−	0.0622373i
$144$	2.94706	−	0.561090i	0.245589	−	0.0467575i
$145$	−1.52745	−	6.38750i	−0.126848	−	0.530453i
$146$		−	3.17582i		−	0.262833i
$147$	−11.2202	+	1.05860i	−0.925428	+	0.0873118i
$148$	4.03947	−	4.03947i	0.332042	−	0.332042i
$149$	12.7621			1.04552			0.522758	−	0.852481i	$-0.324903\pi$
$149$	12.7621			1.04552			0.522758	+	0.852481i	$0.324903\pi$
$150$	8.44795	+	1.90582i	0.689772	+	0.155610i
$151$	1.67214			0.136076			0.0680382	−	0.997683i	$-0.478326\pi$
$151$	1.67214			0.136076			0.0680382	+	0.997683i	$0.478326\pi$
$152$	−0.707107	+	0.707107i	−0.0573539	+	0.0573539i
$153$	−0.321121	+	0.472151i	−0.0259611	+	0.0381712i
$154$		−	1.12388i		−	0.0905645i
$155$	0.848557	+	3.54849i	0.0681577	+	0.285022i
$156$	−0.726315	+	0.877644i	−0.0581517	+	0.0702678i
$157$	5.54265	+	5.54265i	0.442352	+	0.442352i	0.892802	−	0.450450i	$-0.148736\pi$
$157$	5.54265	+	5.54265i	0.442352	+	0.442352i	−0.450450	+	0.892802i	$0.648736\pi$
$158$	−2.46320	−	2.46320i	−0.195962	−	0.195962i
$159$	−3.69738	+	4.46774i	−0.293221	+	0.354315i
$160$	1.90551	+	1.17005i	0.150644	+	0.0925005i
$161$		−	0.305190i		−	0.0240523i
$162$	3.58024	−	8.25723i	0.281290	−	0.648749i
$163$	10.2639	−	10.2639i	0.803934	−	0.803934i	−0.179774	−	0.983708i	$-0.557537\pi$
$163$	10.2639	−	10.2639i	0.803934	−	0.803934i	0.983708	+	0.179774i	$0.0575367\pi$
$164$	−3.54984			−0.277196
$165$	2.00127	+	5.86579i	0.155799	+	0.456651i
$166$	2.49166			0.193390
$167$	−16.4383	+	16.4383i	−1.27204	+	1.27204i	−0.327020	+	0.945018i	$0.606044\pi$
$167$	−16.4383	+	16.4383i	−1.27204	+	1.27204i	−0.945018	+	0.327020i	$0.893956\pi$
$168$	−1.21105	+	0.114260i	−0.0934348	+	0.00881533i
$169$			12.5674i			0.966723i
$170$	−0.413931	+	0.0989840i	−0.0317470	+	0.00759172i
$171$	0.561090	+	2.94706i	0.0429076	+	0.225368i
$172$	−3.15359	−	3.15359i	−0.240459	−	0.240459i
$173$	15.4881	+	15.4881i	1.17754	+	1.17754i	0.980370	+	0.197168i	$0.0631746\pi$
$173$	15.4881	+	15.4881i	1.17754	+	1.17754i	0.197168	+	0.980370i	$0.436825\pi$
$174$	−3.91920	−	3.24343i	−0.297114	−	0.245884i
$175$	−3.33772	−	1.09110i	−0.252308	−	0.0824797i
$176$			1.60026i			0.120624i
$177$	−1.39702	−	14.8072i	−0.105006	−	1.11297i
$178$	10.4293	−	10.4293i	0.781707	−	0.781707i
$179$	−9.93061			−0.742248			−0.371124	−	0.928583i	$-0.621028\pi$
$179$	−9.93061			−0.742248			−0.371124	+	0.928583i	$0.621028\pi$
$180$	6.11733	−	2.75286i	0.455959	−	0.205186i
$181$	14.5675			1.08279			0.541396	−	0.840768i	$-0.317896\pi$
$181$	14.5675			1.08279			0.541396	+	0.840768i	$0.317896\pi$
$182$	0.326629	−	0.326629i	0.0242113	−	0.0242113i
$183$	−0.993322	−	10.5283i	−0.0734285	−	0.778278i
$184$			0.434554i			0.0320357i
$185$	6.68411	−	10.8856i	0.491425	−	0.800323i
$186$	2.17726	+	1.80184i	0.159644	+	0.132117i
$187$	−0.215374	−	0.215374i	−0.0157497	−	0.0157497i
$188$	4.45089	+	4.45089i	0.324614	+	0.324614i
$189$	−1.75978	+	3.19696i	−0.128005	+	0.232544i
$190$	−1.17005	+	1.90551i	−0.0848843	+	0.138241i
$191$		−	5.79370i		−	0.419218i	−0.977785	−	0.209609i	$-0.932781\pi$
$191$		−	5.79370i		−	0.419218i	0.977785	−	0.209609i	$-0.0672190\pi$
$192$	1.72439	−	0.162692i	0.124447	−	0.0117413i
$193$	−2.47519	+	2.47519i	−0.178168	+	0.178168i	−0.790557	−	0.612389i	$-0.790209\pi$
$193$	−2.47519	+	2.47519i	−0.178168	+	0.178168i	0.612389	+	0.790557i	$0.290209\pi$
$194$	−0.0245352			−0.00176152
$195$	−1.12313	+	2.28638i	−0.0804293	+	0.163731i
$196$	−6.50676			−0.464769
$197$	5.78154	−	5.78154i	0.411918	−	0.411918i	−0.470488	−	0.882406i	$-0.655922\pi$
$197$	5.78154	−	5.78154i	0.411918	−	0.411918i	0.882406	+	0.470488i	$0.155922\pi$
$198$	3.96967	+	2.69986i	0.282112	+	0.191871i
$199$			11.7597i			0.833621i	0.908993	+	0.416810i	$0.136852\pi$
$199$			11.7597i			0.833621i	−0.908993	+	0.416810i	$0.863148\pi$
$200$	4.75251	+	1.55360i	0.336053	+	0.109856i
$201$	−9.82049	+	11.8666i	−0.692684	+	0.837006i
$202$	1.35914	+	1.35914i	0.0956288	+	0.0956288i
$203$	1.45859	+	1.45859i	0.102373	+	0.102373i
$204$	−0.210185	+	0.253977i	−0.0147159	+	0.0177819i
$205$	−7.72002	+	1.84610i	−0.539190	+	0.128937i
$206$		−	12.2966i		−	0.856742i
$207$	1.07797	+	0.733152i	0.0749241	+	0.0509576i
$208$	−0.465079	+	0.465079i	−0.0322475	+	0.0322475i
$209$	−1.60026			−0.110692
$210$	−2.57432	+	0.878298i	−0.177645	+	0.0606083i
$211$	−21.4490			−1.47661			−0.738306	−	0.674466i	$-0.764374\pi$
$211$	−21.4490			−1.47661			−0.738306	+	0.674466i	$0.764374\pi$
$212$	−2.36753	+	2.36753i	−0.162603	+	0.162603i
$213$	−24.0245	+	2.26665i	−1.64614	+	0.155309i
$214$			17.6707i			1.20794i
$215$	−8.49830	−	5.21824i	−0.579579	−	0.355881i
$216$	2.50571	−	4.55208i	0.170492	−	0.309730i
$217$	−0.810300	−	0.810300i	−0.0550068	−	0.0550068i
$218$	−0.129968	−	0.129968i	−0.00880257	−	0.00880257i
$219$	−4.23773	−	3.50703i	−0.286359	−	0.236983i
$220$	0.832220	+	3.48017i	0.0561083	+	0.234633i
$221$		−	0.125187i		−	0.00842100i
$222$	−0.929406	−	9.85089i	−0.0623777	−	0.661148i
$223$	−7.58068	+	7.58068i	−0.507640	+	0.507640i	−0.913801	−	0.406162i	$-0.866867\pi$
$223$	−7.58068	+	7.58068i	−0.507640	+	0.507640i	0.406162	+	0.913801i	$0.366867\pi$
$224$	−0.702307			−0.0469249
$225$	11.8721	−	9.16812i	0.791470	−	0.611208i
$226$	12.1332			0.807091
$227$	−15.3160	+	15.3160i	−1.01656	+	1.01656i	−0.0167011	+	0.999861i	$0.505316\pi$
$227$	−15.3160	+	15.3160i	−1.01656	+	1.01656i	−0.999861	+	0.0167011i	$0.994684\pi$
$228$	0.162692	+	1.72439i	0.0107745	+	0.114201i
$229$			15.7592i			1.04140i	0.853741	+	0.520698i	$0.174328\pi$
$229$			15.7592i			1.04140i	−0.853741	+	0.520698i	$0.825672\pi$
$230$	0.225991	+	0.945046i	0.0149014	+	0.0623145i
$231$	−1.49967	−	1.24108i	−0.0986709	−	0.0816574i
$232$	−2.07686	−	2.07686i	−0.136352	−	0.136352i
$233$	1.34227	+	1.34227i	0.0879351	+	0.0879351i	0.749706	−	0.661771i	$-0.230195\pi$
$233$	1.34227	+	1.34227i	0.0879351	+	0.0879351i	−0.661771	+	0.749706i	$0.730195\pi$
$234$	0.369041	+	1.93835i	0.0241250	+	0.126714i
$235$	11.9943	+	7.36488i	0.782420	+	0.480432i
$236$		−	8.58688i		−	0.558958i
$237$	−6.00691	+	0.566736i	−0.390191	+	0.0368135i
$238$	0.0945214	−	0.0945214i	0.00612691	−	0.00612691i
$239$	27.4444			1.77523			0.887616	−	0.460585i	$-0.152360\pi$
$239$	27.4444			1.77523			0.887616	+	0.460585i	$0.152360\pi$
$240$	3.66552	−	1.25059i	0.236608	−	0.0807252i
$241$	−29.4204			−1.89513			−0.947567	−	0.319557i	$-0.896466\pi$
$241$	−29.4204			−1.89513			−0.947567	+	0.319557i	$0.896466\pi$
$242$	5.96739	−	5.96739i	0.383598	−	0.383598i
$243$	−7.06459	−	13.8957i	−0.453194	−	0.891412i
$244$		−	6.10554i		−	0.390867i
$245$	−14.1506	+	3.38386i	−0.904049	+	0.216187i
$246$	−3.92005	+	4.73680i	−0.249933	+	0.302008i
$247$	−0.465079	−	0.465079i	−0.0295923	−	0.0295923i
$248$	1.15377	+	1.15377i	0.0732644	+	0.0732644i
$249$	2.75151	−	3.32480i	0.174370	−	0.210700i
$250$	11.1435	+	0.907143i	0.704775	+	0.0573728i
$251$			13.3163i			0.840516i	0.907405	+	0.420258i	$0.138060\pi$
$251$			13.3163i			0.840516i	−0.907405	+	0.420258i	$0.861940\pi$
$252$	−1.18489	+	1.74217i	−0.0746410	+	0.109746i
$253$	−0.491722	+	0.491722i	−0.0309143	+	0.0309143i
$254$	−13.2920			−0.834012
$255$	−0.325018	+	0.661644i	−0.0203534	+	0.0414337i
$256$	1.00000			0.0625000
$257$	15.5278	−	15.5278i	0.968596	−	0.968596i	−0.0309257	−	0.999522i	$-0.509846\pi$
$257$	15.5278	−	15.5278i	0.968596	−	0.968596i	0.999522	+	0.0309257i	$0.00984554\pi$
$258$	−7.69053	+	0.725581i	−0.478791	+	0.0451727i
$259$			4.01205i			0.249297i
$260$	−0.769567	+	1.25330i	−0.0477265	+	0.0777262i
$261$	−8.65587	+	1.64799i	−0.535785	+	0.102008i
$262$	5.07801	+	5.07801i	0.313721	+	0.313721i
$263$	−10.7691	−	10.7691i	−0.664054	−	0.664054i	0.292279	−	0.956333i	$-0.405586\pi$
$263$	−10.7691	−	10.7691i	−0.664054	−	0.664054i	−0.956333	+	0.292279i	$0.905586\pi$
$264$	2.13534	+	1.76715i	0.131421	+	0.108761i
$265$	−3.91756	+	6.38004i	−0.240654	+	0.391923i
$266$		−	0.702307i		−	0.0430612i
$267$	−2.39958	−	25.4335i	−0.146852	−	1.55650i
$268$	−6.28833	+	6.28833i	−0.384121	+	0.384121i
$269$	−2.46904			−0.150540			−0.0752701	−	0.997163i	$-0.523982\pi$
$269$	−2.46904			−0.150540			−0.0752701	+	0.997163i	$0.523982\pi$
$270$	3.08197	−	11.2027i	0.187563	−	0.681777i
$271$	20.6505			1.25443			0.627215	−	0.778846i	$-0.284195\pi$
$271$	20.6505			1.25443			0.627215	+	0.778846i	$0.284195\pi$
$272$	−0.134587	+	0.134587i	−0.00816053	+	0.00816053i
$273$	−0.0751511	−	0.796536i	−0.00454835	−	0.0482086i
$274$			11.8162i			0.713844i
$275$	3.61975	+	7.13572i	0.218279	+	0.430300i
$276$	0.579855	+	0.479873i	0.0349032	+	0.0288850i
$277$	7.11389	+	7.11389i	0.427432	+	0.427432i	0.887753	−	0.460321i	$-0.152266\pi$
$277$	7.11389	+	7.11389i	0.427432	+	0.427432i	−0.460321	+	0.887753i	$0.652266\pi$
$278$	−12.3547	−	12.3547i	−0.740984	−	0.740984i
$279$	4.80865	−	0.915517i	0.287886	−	0.0548106i
$280$	−1.52734	+	0.365236i	−0.0912762	+	0.0218270i
$281$			4.48551i			0.267583i	0.991009	+	0.133792i	$0.0427153\pi$
$281$			4.48551i			0.267583i	−0.991009	+	0.133792i	$0.957285\pi$
$282$	10.8542	−	1.02407i	0.646358	−	0.0609823i
$283$	−11.2511	+	11.2511i	−0.668808	+	0.668808i	−0.957440	−	0.288632i	$-0.906799\pi$
$283$	−11.2511	+	11.2511i	−0.668808	+	0.668808i	0.288632	+	0.957440i	$0.406799\pi$
$284$	−13.9322			−0.826723
$285$	1.25059	+	3.66552i	0.0740785	+	0.217127i
$286$	−1.05253			−0.0622373
$287$	1.76287	−	1.76287i	0.104059	−	0.104059i
$288$	1.68714	−	2.48064i	0.0994155	−	0.146173i
$289$			16.9638i			0.997869i
$290$	−5.59672	−	3.43657i	−0.328651	−	0.201802i
$291$	−0.0270940	+	0.0327390i	−0.00158828	+	0.00191920i
$292$	−2.24565	−	2.24565i	−0.131417	−	0.131417i
$293$	−10.0085	−	10.0085i	−0.584702	−	0.584702i	0.351490	−	0.936192i	$-0.385675\pi$
$293$	−10.0085	−	10.0085i	−0.584702	−	0.584702i	−0.936192	+	0.351490i	$0.885675\pi$
$294$	−7.18535	+	8.68244i	−0.419058	+	0.506370i
$295$	−4.46563	−	18.6743i	−0.259999	−	1.08726i
$296$		−	5.71267i		−	0.332042i
$297$	7.98629	−	2.31559i	0.463411	−	0.134364i
$298$	9.02420	−	9.02420i	0.522758	−	0.522758i
$299$	−0.285815			−0.0165291
$300$	7.32122	−	4.62598i	0.422691	−	0.267081i
$301$	3.13218			0.180536
$302$	1.18238	−	1.18238i	0.0680382	−	0.0680382i
$303$	3.31448	−	0.312713i	0.190412	−	0.0179649i
$304$			1.00000i			0.0573539i
$305$	−3.17520	−	13.2780i	−0.181811	−	0.760298i
$306$	0.106795	+	0.560928i	0.00610506	+	0.0320661i
$307$	20.2254	+	20.2254i	1.15432	+	1.15432i	0.985677	+	0.168645i	$0.0539391\pi$
$307$	20.2254	+	20.2254i	1.15432	+	1.15432i	0.168645	+	0.985677i	$0.446061\pi$
$308$	−0.794700	−	0.794700i	−0.0452823	−	0.0452823i
$309$	−16.4082	−	13.5790i	−0.933428	−	0.772480i
$310$	3.10918	+	1.90914i	0.176590	+	0.108432i
$311$		−	9.46101i		−	0.536485i	−0.963351	−	0.268242i	$-0.913557\pi$
$311$		−	9.46101i		−	0.536485i	0.963351	−	0.268242i	$-0.0864428\pi$
$312$	0.107006	+	1.13417i	0.00605803	+	0.0642098i
$313$	−19.0390	+	19.0390i	−1.07615	+	1.07615i	−0.0792948	+	0.996851i	$0.525267\pi$
$313$	−19.0390	+	19.0390i	−1.07615	+	1.07615i	−0.996851	+	0.0792948i	$0.974733\pi$
$314$	7.83849			0.442352
$315$	−1.67082	+	4.40499i	−0.0941400	+	0.248193i
$316$	−3.48349			−0.195962
$317$	18.1388	−	18.1388i	1.01878	−	1.01878i	0.0189572	−	0.999820i	$-0.493965\pi$
$317$	18.1388	−	18.1388i	1.01878	−	1.01878i	0.999820	−	0.0189572i	$-0.00603464\pi$
$318$	0.544725	+	5.77361i	0.0305467	+	0.323768i
$319$		−	4.70016i		−	0.263158i
$320$	2.17475	−	0.520052i	0.121572	−	0.0290718i
$321$	23.5792	+	19.5135i	1.31606	+	1.08914i
$322$	−0.215802	−	0.215802i	−0.0120262	−	0.0120262i
$323$	−0.134587	−	0.134587i	−0.00748862	−	0.00748862i
$324$	−3.30713	−	8.37036i	−0.183730	−	0.465020i
$325$	−1.02184	+	3.12583i	−0.0566813	+	0.173390i
$326$		−	14.5154i		−	0.803934i
$327$	−0.316949	+	0.0299033i	−0.0175273	+	0.00165366i
$328$	−2.51012	+	2.51012i	−0.138598	+	0.138598i
$329$	−4.42068			−0.243720
$330$	5.56285	+	2.73263i	0.306225	+	0.150426i
$331$	−10.0709			−0.553546			−0.276773	−	0.960935i	$-0.589265\pi$
$331$	−10.0709			−0.553546			−0.276773	+	0.960935i	$0.589265\pi$
$332$	1.76187	−	1.76187i	0.0966951	−	0.0966951i
$333$	−14.1711	−	9.63806i	−0.776570	−	0.528163i
$334$			23.2473i			1.27204i
$335$	−10.4053	+	16.9458i	−0.568502	+	0.925848i
$336$	−0.775550	+	0.937138i	−0.0423097	+	0.0511251i
$337$	−20.9018	−	20.9018i	−1.13860	−	1.13860i	−0.988702	−	0.149893i	$-0.952107\pi$
$337$	−20.9018	−	20.9018i	−1.13860	−	1.13860i	−0.149893	−	0.988702i	$-0.547893\pi$
$338$	8.88650	+	8.88650i	0.483362	+	0.483362i
$339$	13.3986	−	16.1902i	0.727712	−	0.879332i
$340$	−0.222701	+	0.362685i	−0.0120777	+	0.0196694i
$341$			2.61111i			0.141400i
$342$	2.48064	+	1.68714i	0.134138	+	0.0912299i
$343$	6.70754	−	6.70754i	0.362173	−	0.362173i
$344$	−4.45985			−0.240459
$345$	1.51060	+	0.742049i	0.0813280	+	0.0399506i
$346$	21.9035			1.17754
$347$	−15.5656	+	15.5656i	−0.835605	+	0.835605i	−0.988277	−	0.152672i	$-0.951212\pi$
$347$	−15.5656	+	15.5656i	−0.835605	+	0.835605i	0.152672	+	0.988277i	$0.451212\pi$
$348$	−5.06474	+	0.477846i	−0.271499	+	0.0256152i
$349$			24.7339i			1.32397i	0.749515	+	0.661987i	$0.230287\pi$
$349$			24.7339i			1.32397i	−0.749515	+	0.661987i	$0.769713\pi$
$350$	−3.13165	+	1.58860i	−0.167394	+	0.0849141i
$351$	2.99400	+	1.64806i	0.159808	+	0.0879668i
$352$	1.13156	+	1.13156i	0.0603122	+	0.0603122i
$353$	−12.1857	−	12.1857i	−0.648577	−	0.648577i	0.304072	−	0.952649i	$-0.401654\pi$
$353$	−12.1857	−	12.1857i	−0.648577	−	0.648577i	−0.952649	+	0.304072i	$0.901654\pi$
$354$	−11.4581	−	9.48240i	−0.608990	−	0.503984i
$355$	−30.2990	+	7.24546i	−1.60811	+	0.384549i
$356$		−	14.7492i		−	0.781707i
$357$	−0.0217476	−	0.230505i	−0.00115100	−	0.0121996i
$358$	−7.02200	+	7.02200i	−0.371124	+	0.371124i
$359$	−26.0241			−1.37350			−0.686750	−	0.726894i	$-0.740963\pi$
$359$	−26.0241			−1.37350			−0.686750	+	0.726894i	$0.740963\pi$
$360$	2.37904	−	6.27217i	0.125387	−	0.330573i
$361$	−1.00000			−0.0526316
$362$	10.3008	−	10.3008i	0.541396	−	0.541396i
$363$	−1.37298	−	14.5524i	−0.0720630	−	0.763804i
$364$		−	0.461923i		−	0.0242113i
$365$	−6.05158	−	3.71587i	−0.316754	−	0.194498i
$366$	−8.14705	−	6.74228i	−0.425853	−	0.352425i
$367$	2.46917	+	2.46917i	0.128890	+	0.128890i	0.768609	−	0.639719i	$-0.220949\pi$
$367$	2.46917	+	2.46917i	0.128890	+	0.128890i	−0.639719	+	0.768609i	$0.720949\pi$
$368$	0.307276	+	0.307276i	0.0160179	+	0.0160179i
$369$	1.99178	+	10.4616i	0.103688	+	0.544609i
$370$	−2.97089	−	12.4236i	−0.154449	−	0.645874i
$371$		−	2.35146i		−	0.122082i
$372$	2.81365	−	0.265461i	0.145881	−	0.0137635i
$373$	−8.01922	+	8.01922i	−0.415220	+	0.415220i	−0.883552	−	0.468333i	$-0.844855\pi$
$373$	−8.01922	+	8.01922i	−0.415220	+	0.415220i	0.468333	+	0.883552i	$0.344855\pi$
$374$	−0.304585			−0.0157497
$375$	13.5161	−	13.8678i	0.697968	−	0.716129i
$376$	6.29451			0.324614
$377$	1.36599	−	1.36599i	0.0703522	−	0.0703522i
$378$	1.01624	+	3.50494i	0.0522698	+	0.180275i
$379$		−	31.2502i		−	1.60521i	−0.596509	−	0.802606i	$-0.703446\pi$
$379$		−	31.2502i		−	1.60521i	0.596509	−	0.802606i	$-0.296554\pi$
$380$	0.520052	+	2.17475i	0.0266781	+	0.111562i
$381$	−14.6782	+	17.7364i	−0.751986	+	0.908664i
$382$	−4.09677	−	4.09677i	−0.209609	−	0.209609i
$383$	0.978037	+	0.978037i	0.0499753	+	0.0499753i	0.731653	−	0.681677i	$-0.238749\pi$
$383$	0.978037	+	0.978037i	0.0499753	+	0.0499753i	−0.681677	+	0.731653i	$0.738749\pi$
$384$	1.10429	−	1.33437i	0.0563530	−	0.0680943i
$385$	−2.14156	−	1.31499i	−0.109144	−	0.0670181i
$386$			3.50044i			0.178168i
$387$	−7.52437	+	11.0633i	−0.382485	+	0.562377i
$388$	−0.0173490	+	0.0173490i	−0.000880762	+	0.000880762i
$389$	4.44034			0.225134			0.112567	−	0.993644i	$-0.464093\pi$
$389$	4.44034			0.225134			0.112567	+	0.993644i	$0.464093\pi$
$390$	0.822540	+	2.41089i	0.0416509	+	0.122080i
$391$	−0.0827106			−0.00418285
$392$	−4.60098	+	4.60098i	−0.232384	+	0.232384i
$393$	12.3835	−	1.16836i	0.624667	−	0.0589358i
$394$		−	8.17634i		−	0.411918i
$395$	−7.57573	+	1.81160i	−0.381176	+	0.0911513i
$396$	4.71607	−	0.897892i	0.236992	−	0.0451207i
$397$	19.6310	+	19.6310i	0.985250	+	0.985250i	0.999893	−	0.0146427i	$-0.00466108\pi$
$397$	19.6310	+	19.6310i	0.985250	+	0.985250i	−0.0146427	+	0.999893i	$0.504661\pi$
$398$	8.31534	+	8.31534i	0.416810	+	0.416810i
$399$	−0.937138	−	0.775550i	−0.0469156	−	0.0388261i
$400$	4.45909	−	2.26197i	0.222955	−	0.113098i
$401$			19.4963i			0.973598i	0.873514	+	0.486799i	$0.161836\pi$
$401$			19.4963i			0.973598i	−0.873514	+	0.486799i	$0.838164\pi$
$402$	1.44683	+	15.3351i	0.0721611	+	0.764845i
$403$	−0.758859	+	0.758859i	−0.0378015	+	0.0378015i
$404$	1.92211			0.0956288
$405$	−11.5452	−	16.4836i	−0.573687	−	0.819075i
$406$	2.06276			0.102373
$407$	6.46421	−	6.46421i	0.320419	−	0.320419i
$408$	0.0309659	+	0.328212i	0.00153304	+	0.0162489i
$409$		−	3.38039i		−	0.167150i	−0.996502	−	0.0835748i	$-0.973366\pi$
$409$		−	3.38039i		−	0.167150i	0.996502	−	0.0835748i	$-0.0266337\pi$
$410$	−4.15349	+	6.76427i	−0.205126	+	0.334064i
$411$	15.7672	+	13.0485i	0.777739	+	0.643636i
$412$	−8.69498	−	8.69498i	−0.428371	−	0.428371i
$413$	4.26430	+	4.26430i	0.209832	+	0.209832i
$414$	1.28066	−	0.243824i	0.0629408	−	0.0119833i
$415$	2.91536	−	4.74789i	0.143110	−	0.233065i
$416$			0.657722i			0.0322475i
$417$	−30.1288	+	2.84258i	−1.47542	+	0.139202i
$418$	−1.13156	+	1.13156i	−0.0553462	+	0.0553462i
$419$	22.8080			1.11425			0.557123	−	0.830430i	$-0.311905\pi$
$419$	22.8080			1.11425			0.557123	+	0.830430i	$0.311905\pi$
$420$	−1.19927	+	2.44137i	−0.0585183	+	0.119127i
$421$	−20.2915			−0.988946			−0.494473	−	0.869193i	$-0.664639\pi$
$421$	−20.2915			−0.988946			−0.494473	+	0.869193i	$0.664639\pi$
$422$	−15.1667	+	15.1667i	−0.738306	+	0.738306i
$423$	10.6197	−	15.6144i	0.516347	−	0.759198i
$424$			3.34820i			0.162603i
$425$	−0.295704	+	0.904567i	−0.0143437	+	0.0438779i
$426$	−15.3852	+	18.5907i	−0.745413	+	0.900722i
$427$	3.03205	+	3.03205i	0.146731	+	0.146731i
$428$	12.4950	+	12.4950i	0.603971	+	0.603971i
$429$	−1.16229	+	1.40446i	−0.0561161	+	0.0678081i
$430$	−9.69906	+	2.31935i	−0.467730	+	0.111849i
$431$		−	30.3366i		−	1.46126i	−0.682772	−	0.730631i	$-0.739226\pi$
$431$		−	30.3366i		−	1.46126i	0.682772	−	0.730631i	$-0.260774\pi$
$432$	−1.44700	−	4.99061i	−0.0696190	−	0.240111i
$433$	−8.49095	+	8.49095i	−0.408049	+	0.408049i	−0.881058	−	0.473009i	$-0.843168\pi$
$433$	−8.49095	+	8.49095i	−0.408049	+	0.408049i	0.473009	+	0.881058i	$0.343168\pi$
$434$	−1.14594			−0.0550068
$435$	−10.7661	+	3.67313i	−0.516193	+	0.176113i
$436$	−0.183803			−0.00880257
$437$	−0.307276	+	0.307276i	−0.0146990	+	0.0146990i
$438$	−5.47637	+	0.516681i	−0.261671	+	0.0246880i
$439$		−	20.3565i		−	0.971563i	−0.874080	−	0.485781i	$-0.838535\pi$
$439$		−	20.3565i		−	0.971563i	0.874080	−	0.485781i	$-0.161465\pi$
$440$	3.04932	+	1.87239i	0.145371	+	0.0892625i
$441$	3.65088	+	19.1758i	0.173851	+	0.913135i
$442$	−0.0885207	−	0.0885207i	−0.00421050	−	0.00421050i
$443$	13.7782	+	13.7782i	0.654621	+	0.654621i	0.954102	−	0.299481i	$-0.0968135\pi$
$443$	13.7782	+	13.7782i	0.654621	+	0.654621i	−0.299481	+	0.954102i	$0.596814\pi$
$444$	−7.62282	−	6.30844i	−0.361763	−	0.299385i
$445$	−7.67036	−	32.0759i	−0.363610	−	1.52054i
$446$			10.7207i			0.507640i
$447$	−2.07630	−	22.0070i	−0.0982056	−	1.04089i
$448$	−0.496606	+	0.496606i	−0.0234624	+	0.0234624i
$449$	22.3302			1.05383			0.526913	−	0.849919i	$-0.323349\pi$
$449$	22.3302			1.05383			0.526913	+	0.849919i	$0.323349\pi$
$450$	1.91197	−	14.8776i	0.0901312	−	0.701339i
$451$	−5.68068			−0.267493
$452$	8.57949	−	8.57949i	0.403545	−	0.403545i
$453$	−0.272043	−	2.88342i	−0.0127817	−	0.135475i
$454$			21.6602i			1.01656i
$455$	−0.240224	−	1.00457i	−0.0112619	−	0.0470948i
$456$	1.33437	+	1.10429i	0.0624876	+	0.0517131i
$457$	20.8943	+	20.8943i	0.977393	+	0.977393i	0.999750	−	0.0223568i	$-0.00711697\pi$
$457$	20.8943	+	20.8943i	0.977393	+	0.977393i	−0.0223568	+	0.999750i	$0.507117\pi$
$458$	11.1434	+	11.1434i	0.520698	+	0.520698i
$459$	0.866418	+	0.476923i	0.0404410	+	0.0222609i
$460$	0.828048	+	0.508449i	0.0386079	+	0.0237066i
$461$			15.6734i			0.729982i	0.931011	+	0.364991i	$0.118928\pi$
$461$			15.6734i			0.729982i	−0.931011	+	0.364991i	$0.881072\pi$
$462$	−1.93800	+	0.182846i	−0.0901641	+	0.00850675i
$463$	−5.68075	+	5.68075i	−0.264007	+	0.264007i	−0.826680	−	0.562673i	$-0.809773\pi$
$463$	−5.68075	+	5.68075i	−0.264007	+	0.264007i	0.562673	+	0.826680i	$0.309773\pi$
$464$	−2.93712			−0.136352
$465$	5.98094	−	2.04056i	0.277359	−	0.0946285i
$466$	1.89826			0.0879351
$467$	10.4678	−	10.4678i	0.484394	−	0.484394i	−0.422138	−	0.906532i	$-0.638720\pi$
$467$	10.4678	−	10.4678i	0.484394	−	0.484394i	0.906532	+	0.422138i	$0.138720\pi$
$468$	1.63157	+	1.10967i	0.0754193	+	0.0512944i
$469$		−	6.24564i		−	0.288397i
$470$	13.6890	−	3.27347i	0.631426	−	0.150994i
$471$	8.65596	−	10.4595i	0.398846	−	0.481946i
$472$	−6.07184	−	6.07184i	−0.279479	−	0.279479i
$473$	−5.04657	−	5.04657i	−0.232041	−	0.232041i
$474$	−3.84678	+	4.64827i	−0.176689	+	0.213502i
$475$	2.26197	+	4.45909i	0.103786	+	0.204597i
$476$		−	0.133673i		−	0.00612691i
$477$	8.30567	+	5.64887i	0.380290	+	0.258644i
$478$	19.4061	−	19.4061i	0.887616	−	0.887616i
$479$	6.32202			0.288860			0.144430	−	0.989515i	$-0.453865\pi$
$479$	6.32202			0.288860			0.144430	+	0.989515i	$0.453865\pi$
$480$	1.70761	−	3.47621i	0.0779415	−	0.158667i
$481$	3.75735			0.171320
$482$	−20.8034	+	20.8034i	−0.947567	+	0.947567i
$483$	−0.526268	+	0.0496520i	−0.0239460	+	0.00225924i
$484$		−	8.43916i		−	0.383598i
$485$	−0.0287074	+	0.0467522i	−0.00130354	+	0.00212291i
$486$	−14.8212	−	4.83035i	−0.672303	−	0.219109i
$487$	25.1640	+	25.1640i	1.14029	+	1.14029i	0.988397	+	0.151891i	$0.0485363\pi$
$487$	25.1640	+	25.1640i	1.14029	+	1.14029i	0.151891	+	0.988397i	$0.451464\pi$
$488$	−4.31727	−	4.31727i	−0.195433	−	0.195433i
$489$	−19.3689	−	16.0292i	−0.875893	−	0.724866i
$490$	−7.61324	+	12.3987i	−0.343931	+	0.560118i
$491$		−	12.0526i		−	0.543925i	−0.962308	−	0.271962i	$-0.912327\pi$
$491$		−	12.0526i		−	0.543925i	0.962308	−	0.271962i	$-0.0876727\pi$
$492$	0.577531	+	6.12132i	0.0260371	+	0.275971i
$493$	0.395298	−	0.395298i	0.0178033	−	0.0178033i
$494$	−0.657722			−0.0295923
$495$	9.78934	−	4.40530i	0.439998	−	0.198003i
$496$	1.63168			0.0732644
$497$	6.91880	−	6.91880i	0.310351	−	0.310351i
$498$	−0.405373	−	4.29660i	−0.0181652	−	0.192535i
$499$		−	5.62152i		−	0.251654i	−0.992052	−	0.125827i	$-0.959842\pi$
$499$		−	5.62152i		−	0.251654i	0.992052	−	0.125827i	$-0.0401584\pi$
$500$	8.52108	−	7.23818i	0.381074	−	0.323701i
$501$	31.0205	+	25.6718i	1.38590	+	1.14693i
$502$	9.41603	+	9.41603i	0.420258	+	0.420258i
$503$	23.1237	+	23.1237i	1.03104	+	1.03104i	0.999503	+	0.0315338i	$0.0100392\pi$
$503$	23.1237	+	23.1237i	1.03104	+	1.03104i	0.0315338	+	0.999503i	$0.489961\pi$
$504$	0.394057	+	2.06974i	0.0175527	+	0.0921937i
$505$	4.18012	−	0.999600i	0.186013	−	0.0444816i
$506$			0.695400i			0.0309143i
$507$	21.6711	−	2.04462i	0.962449	−	0.0908046i
$508$	−9.39884	+	9.39884i	−0.417006	+	0.417006i
$509$	20.8753			0.925282			0.462641	−	0.886546i	$-0.346902\pi$
$509$	20.8753			0.925282			0.462641	+	0.886546i	$0.346902\pi$
$510$	0.238030	+	0.697675i	0.0105402	+	0.0308936i
$511$	2.23040			0.0986672
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	4.99061	−	1.44700i	0.220341	−	0.0638868i
$514$		−	21.9596i		−	0.968596i
$515$	−23.4313	−	14.3876i	−1.03251	−	0.633993i
$516$	−4.92496	+	5.95109i	−0.216809	+	0.261982i
$517$	7.12259	+	7.12259i	0.313251	+	0.313251i
$518$	2.83695	+	2.83695i	0.124648	+	0.124648i
$519$	24.1878	−	29.2274i	1.06173	−	1.28294i
$520$	0.342050	+	1.43038i	0.0149999	+	0.0627264i
$521$		−	24.8032i		−	1.08665i	−0.839523	−	0.543325i	$-0.817165\pi$
$521$		−	24.8032i		−	1.08665i	0.839523	−	0.543325i	$-0.182835\pi$
$522$	−4.95532	+	7.28593i	−0.216888	+	0.318896i
$523$	1.48367	−	1.48367i	0.0648764	−	0.0648764i	−0.673924	−	0.738801i	$-0.735393\pi$
$523$	1.48367	−	1.48367i	0.0648764	−	0.0648764i	0.738801	+	0.673924i	$0.235393\pi$
$524$	7.18140			0.313721
$525$	−1.33847	+	5.93305i	−0.0584157	+	0.258940i
$526$	−15.2299			−0.664054
$527$	−0.219602	+	0.219602i	−0.00956602	+	0.00956602i
$528$	2.75948	−	0.260350i	0.120091	−	0.0113303i
$529$		−	22.8112i		−	0.991790i
$530$	1.74124	+	7.28150i	0.0756345	+	0.316288i
$531$	−25.3061	+	4.81801i	−1.09819	+	0.209084i
$532$	−0.496606	−	0.496606i	−0.0215306	−	0.0215306i
$533$	−1.65096	−	1.65096i	−0.0715109	−	0.0715109i
$534$	−19.6809	−	16.2874i	−0.851677	−	0.704825i
$535$	33.6717	+	20.6755i	1.45575	+	0.893881i
$536$			8.89304i			0.384121i
$537$	1.61563	+	17.1243i	0.0697196	+	0.738967i
$538$	−1.74588	+	1.74588i	−0.0752701	+	0.0752701i
$539$	−10.4125			−0.448500
$540$	−5.74225	−	10.1008i	−0.247107	−	0.434670i
$541$	45.1030			1.93913			0.969564	−	0.244838i	$-0.0787348\pi$
$541$	45.1030			1.93913			0.969564	+	0.244838i	$0.0787348\pi$
$542$	14.6021	−	14.6021i	0.627215	−	0.627215i
$543$	−2.37001	−	25.1201i	−0.101707	−	1.07800i
$544$			0.190335i			0.00816053i
$545$	−0.399726	+	0.0955872i	−0.0171224	+	0.00409450i
$546$	−0.616376	−	0.510096i	−0.0263785	−	0.0218301i
$547$	4.01648	+	4.01648i	0.171732	+	0.171732i	0.787740	−	0.616008i	$-0.211251\pi$
$547$	4.01648	+	4.01648i	0.171732	+	0.171732i	−0.616008	+	0.787740i	$0.711251\pi$
$548$	8.35532	+	8.35532i	0.356922	+	0.356922i
$549$	−17.9934	+	3.42576i	−0.767939	+	0.146208i
$550$	7.60526	+	2.48617i	0.324289	+	0.106011i
$551$		−	2.93712i		−	0.125125i
$552$	0.749341	−	0.0706984i	0.0318941	−	0.00300912i
$553$	1.72992	−	1.72992i	0.0735638	−	0.0735638i
$554$	10.0606			0.427432
$555$	−19.8585	−	9.75503i	−0.842945	−	0.414078i
$556$	−17.4721			−0.740984
$557$	18.3814	−	18.3814i	0.778844	−	0.778844i	−0.200790	−	0.979634i	$-0.564351\pi$
$557$	18.3814	−	18.3814i	0.778844	−	0.778844i	0.979634	+	0.200790i	$0.0643509\pi$
$558$	2.75286	−	4.04760i	0.116538	−	0.171348i
$559$		−	2.93334i		−	0.124067i
$560$	−0.821734	+	1.33826i	−0.0347246	+	0.0565516i
$561$	−0.336351	+	0.406430i	−0.0142007	+	0.0171595i
$562$	3.17174	+	3.17174i	0.133792	+	0.133792i
$563$	4.15736	+	4.15736i	0.175212	+	0.175212i	0.789265	−	0.614053i	$-0.210462\pi$
$563$	4.15736	+	4.15736i	0.175212	+	0.175212i	−0.614053	+	0.789265i	$0.710462\pi$
$564$	6.95096	−	8.39921i	0.292688	−	0.353670i
$565$	14.1965	−	23.1200i	0.597250	−	0.972668i
$566$			15.9114i			0.668808i
$567$	5.79911	+	2.51443i	0.243540	+	0.105596i
$568$	−9.85154	+	9.85154i	−0.413361	+	0.413361i
$569$	−25.7668			−1.08020			−0.540100	−	0.841601i	$-0.681614\pi$
$569$	−25.7668			−1.08020			−0.540100	+	0.841601i	$0.681614\pi$
$570$	3.47621	+	1.70761i	0.145603	+	0.0715240i
$571$	10.3705			0.433994			0.216997	−	0.976172i	$-0.430374\pi$
$571$	10.3705			0.433994			0.216997	+	0.976172i	$0.430374\pi$
$572$	−0.744249	+	0.744249i	−0.0311186	+	0.0311186i
$573$	−9.99062	+	0.942589i	−0.417364	+	0.0393772i
$574$		−	2.49308i		−	0.104059i
$575$	2.06522	+	0.675122i	0.0861256	+	0.0281546i
$576$	−0.561090	−	2.94706i	−0.0233788	−	0.122794i
$577$	8.95610	+	8.95610i	0.372847	+	0.372847i	0.868513	−	0.495666i	$-0.165076\pi$
$577$	8.95610	+	8.95610i	0.372847	+	0.372847i	−0.495666	+	0.868513i	$0.665076\pi$
$578$	11.9952	+	11.9952i	0.498934	+	0.498934i
$579$	4.67089	+	3.86550i	0.194115	+	0.160645i
$580$	−6.38750	+	1.52745i	−0.265227	+	0.0634241i
$581$			1.74991i			0.0725985i
$582$	0.00399168	+	0.0423083i	0.000165461	+	0.00175374i
$583$	−3.78868	+	3.78868i	−0.156911	+	0.156911i
$584$	−3.17582			−0.131417
$585$	4.12534	+	1.56475i	0.170562	+	0.0646944i
$586$	−14.1541			−0.584702
$587$	−20.5743	+	20.5743i	−0.849191	+	0.849191i	−0.990032	−	0.140841i	$-0.955019\pi$
$587$	−20.5743	+	20.5743i	−0.849191	+	0.849191i	0.140841	+	0.990032i	$0.455019\pi$
$588$	1.05860	+	11.2202i	0.0436559	+	0.462714i
$589$			1.63168i			0.0672320i
$590$	−16.3624	−	10.0471i	−0.673631	−	0.413632i
$591$	−10.9103	−	9.02904i	−0.448788	−	0.371405i
$592$	−4.03947	−	4.03947i	−0.166021	−	0.166021i
$593$	−10.9829	−	10.9829i	−0.451015	−	0.451015i	0.444676	−	0.895691i	$-0.353319\pi$
$593$	−10.9829	−	10.9829i	−0.451015	−	0.451015i	−0.895691	+	0.444676i	$0.853319\pi$
$594$	4.00979	−	7.28452i	0.164524	−	0.298888i
$595$	−0.0695171	−	0.290706i	−0.00284992	−	0.0119178i
$596$		−	12.7621i		−	0.522758i
$597$	20.2783	−	1.91320i	0.829935	−	0.0783022i
$598$	−0.202102	+	0.202102i	−0.00826456	+	0.00826456i
$599$	15.1478			0.618921			0.309461	−	0.950912i	$-0.399852\pi$
$599$	15.1478			0.618921			0.309461	+	0.950912i	$0.399852\pi$
$600$	1.90582	−	8.44795i	0.0778049	−	0.344886i
$601$	−29.3684			−1.19796			−0.598982	−	0.800763i	$-0.704428\pi$
$601$	−29.3684			−1.19796			−0.598982	+	0.800763i	$0.704428\pi$
$602$	2.21479	−	2.21479i	0.0902680	−	0.0902680i
$603$	22.0604	+	15.0038i	0.898369	+	0.611001i
$604$		−	1.67214i		−	0.0680382i
$605$	−4.38880	−	18.3531i	−0.178430	−	0.746159i
$606$	2.12257	−	2.56481i	0.0862236	−	0.104188i
$607$	24.8764	+	24.8764i	1.00970	+	1.00970i	0.999952	+	0.00975060i	$0.00310376\pi$
$607$	24.8764	+	24.8764i	1.00970	+	1.00970i	0.00975060	+	0.999952i	$0.496896\pi$
$608$	0.707107	+	0.707107i	0.0286770	+	0.0286770i
$609$	2.27788	−	2.75248i	0.0923044	−	0.111536i
$610$	−11.6342	−	7.14378i	−0.471054	−	0.289243i
$611$			4.14003i			0.167488i
$612$	0.472151	+	0.321121i	0.0190856	+	0.0129805i
$613$	3.82720	−	3.82720i	0.154579	−	0.154579i	−0.625580	−	0.780160i	$-0.715138\pi$
$613$	3.82720	−	3.82720i	0.154579	−	0.154579i	0.780160	+	0.625580i	$0.215138\pi$
$614$	28.6030			1.15432
$615$	4.43939	+	13.0120i	0.179014	+	0.524695i
$616$	−1.12388			−0.0452823
$617$	12.3701	−	12.3701i	0.498001	−	0.498001i	−0.412815	−	0.910815i	$-0.635454\pi$
$617$	12.3701	−	12.3701i	0.498001	−	0.498001i	0.910815	+	0.412815i	$0.135454\pi$
$618$	−21.2041	+	2.00055i	−0.852954	+	0.0804740i
$619$		−	1.71966i		−	0.0691190i	−0.999403	−	0.0345595i	$-0.988997\pi$
$619$		−	1.71966i		−	0.0691190i	0.999403	−	0.0345595i	$-0.0110028\pi$
$620$	3.54849	−	0.848557i	0.142511	−	0.0340789i
$621$	1.08886	−	1.97812i	0.0436946	−	0.0793793i
$622$	−6.68994	−	6.68994i	−0.268242	−	0.268242i
$623$	7.32455	+	7.32455i	0.293452	+	0.293452i
$624$	0.877644	+	0.726315i	0.0351339	+	0.0290759i
$625$	14.7670	−	20.1727i	0.590680	−	0.806906i
$626$			26.9252i			1.07615i
$627$	0.260350	+	2.75948i	0.0103974	+	0.110203i
$628$	5.54265	−	5.54265i	0.221176	−	0.221176i
$629$	1.08732			0.0433543
$630$	1.93335	+	4.29625i	0.0770266	+	0.171167i
$631$	36.5998			1.45701			0.728507	−	0.685039i	$-0.240215\pi$
$631$	36.5998			1.45701			0.728507	+	0.685039i	$0.240215\pi$
$632$	−2.46320	+	2.46320i	−0.0979808	+	0.0979808i
$633$	3.48958	+	36.9865i	0.138699	+	1.47008i
$634$		−	25.6522i		−	1.01878i
$635$	−15.5523	+	25.3280i	−0.617172	+	1.00511i
$636$	4.46774	+	3.69738i	0.177157	+	0.146611i
$637$	−3.02616	−	3.02616i	−0.119901	−	0.119901i
$638$	−3.32351	−	3.32351i	−0.131579	−	0.131579i
$639$	7.81721	+	41.0590i	0.309244	+	1.62427i
$640$	1.17005	−	1.90551i	0.0462503	−	0.0753221i
$641$		−	34.9202i		−	1.37926i	−0.724160	−	0.689632i	$-0.757772\pi$
$641$		−	34.9202i		−	1.37926i	0.724160	−	0.689632i	$-0.242228\pi$
$642$	30.4712	−	2.87487i	1.20260	−	0.113462i
$643$	−24.8779	+	24.8779i	−0.981088	+	0.981088i	−0.999824	−	0.0187362i	$-0.994036\pi$
$643$	−24.8779	+	24.8779i	−0.981088	+	0.981088i	0.0187362	+	0.999824i	$0.494036\pi$
$644$	−0.305190			−0.0120262
$645$	−7.61569	+	15.5034i	−0.299868	+	0.610445i
$646$	−0.190335			−0.00748862
$647$	−2.44228	+	2.44228i	−0.0960160	+	0.0960160i	−0.753483	−	0.657467i	$-0.771628\pi$
$647$	−2.44228	+	2.44228i	−0.0960160	+	0.0960160i	0.657467	+	0.753483i	$0.271628\pi$
$648$	−8.25723	−	3.58024i	−0.324375	−	0.140645i
$649$		−	13.7413i		−	0.539392i
$650$	1.48775	+	2.93284i	0.0583542	+	0.115035i
$651$	−1.26545	+	1.52911i	−0.0495968	+	0.0599304i
$652$	−10.2639	−	10.2639i	−0.401967	−	0.401967i
$653$	20.0032	+	20.0032i	0.782785	+	0.782785i	0.980300	−	0.197515i	$-0.0632870\pi$
$653$	20.0032	+	20.0032i	0.782785	+	0.782785i	−0.197515	+	0.980300i	$0.563287\pi$
$654$	−0.202972	+	0.245261i	−0.00793682	+	0.00959048i
$655$	15.6178	−	3.73470i	0.610236	−	0.145927i
$656$			3.54984i			0.138598i
$657$	−5.35805	+	7.87807i	−0.209037	+	0.307353i
$658$	−3.12589	+	3.12589i	−0.121860	+	0.121860i
$659$	12.1175			0.472029			0.236015	−	0.971750i	$-0.424159\pi$
$659$	12.1175			0.472029			0.236015	+	0.971750i	$0.424159\pi$
$660$	5.86579	−	2.00127i	0.228326	−	0.0778994i
$661$	−15.0877			−0.586842			−0.293421	−	0.955983i	$-0.594794\pi$
$661$	−15.0877			−0.586842			−0.293421	+	0.955983i	$0.594794\pi$
$662$	−7.12120	+	7.12120i	−0.276773	+	0.276773i
$663$	−0.215872	+	0.0203670i	−0.00838377	+	0.000790987i
$664$		−	2.49166i		−	0.0966951i
$665$	−1.33826	−	0.821734i	−0.0518953	−	0.0318655i
$666$	−16.8356	+	3.20532i	−0.652366	+	0.124204i
$667$	−0.902505	−	0.902505i	−0.0349451	−	0.0349451i
$668$	16.4383	+	16.4383i	0.636019	+	0.636019i
$669$	14.3054	+	11.8388i	0.553078	+	0.457713i
$670$	4.62484	+	19.3402i	0.178673	+	0.747175i
$671$		−	9.77046i		−	0.377185i
$672$	0.114260	+	1.21105i	0.00440767	+	0.0467174i
$673$	−0.936746	+	0.936746i	−0.0361089	+	0.0361089i	−0.724931	−	0.688822i	$-0.758128\pi$
$673$	−0.936746	+	0.936746i	−0.0361089	+	0.0361089i	0.688822	+	0.724931i	$0.258128\pi$
$674$	−29.5596			−1.13860
$675$	−17.7409	−	18.9805i	−0.682848	−	0.730560i
$676$	12.5674			0.483362
$677$	17.3503	−	17.3503i	0.666826	−	0.666826i	−0.290154	−	0.956980i	$-0.593706\pi$
$677$	17.3503	−	17.3503i	0.666826	−	0.666826i	0.956980	+	0.290154i	$0.0937064\pi$
$678$	−1.97398	−	20.9225i	−0.0758103	−	0.803522i
$679$		−	0.0172312i		−	0.000661274i
$680$	0.0989840	+	0.413931i	0.00379586	+	0.0158735i
$681$	28.9027	+	23.9191i	1.10755	+	0.916581i
$682$	1.84633	+	1.84633i	0.0706998	+	0.0706998i
$683$	−10.9787	−	10.9787i	−0.420088	−	0.420088i	0.465146	−	0.885234i	$-0.346002\pi$
$683$	−10.9787	−	10.9787i	−0.420088	−	0.420088i	−0.885234	+	0.465146i	$0.846002\pi$
$684$	2.94706	−	0.561090i	0.112684	−	0.0214538i
$685$	22.5160	+	13.8256i	0.860291	+	0.528247i
$686$		−	9.48590i		−	0.362173i
$687$	27.1750	−	2.56389i	1.03679	−	0.0978187i
$688$	−3.15359	+	3.15359i	−0.120229	+	0.120229i
$689$	−2.20218			−0.0838964
$690$	1.59286	−	0.543448i	0.0606393	−	0.0206887i
$691$	−29.8179			−1.13433			−0.567163	−	0.823606i	$-0.691959\pi$
$691$	−29.8179			−1.13433			−0.567163	+	0.823606i	$0.691959\pi$
$692$	15.4881	−	15.4881i	0.588769	−	0.588769i
$693$	−1.89613	+	2.78793i	−0.0720281	+	0.105905i
$694$			22.0131i			0.835605i
$695$	−37.9976	+	9.08643i	−1.44133	+	0.344668i
$696$	−3.24343	+	3.91920i	−0.122942	+	0.148557i
$697$	−0.477762	−	0.477762i	−0.0180965	−	0.0180965i
$698$	17.4895	+	17.4895i	0.661987	+	0.661987i
$699$	2.09622	−	2.53298i	0.0792865	−	0.0958060i
$700$	−1.09110	+	3.33772i	−0.0412399	+	0.126154i
$701$			30.1321i			1.13807i	0.822312	+	0.569036i	$0.192684\pi$
$701$			30.1321i			1.13807i	−0.822312	+	0.569036i	$0.807316\pi$
$702$	3.28243	−	0.951725i	0.123887	−	0.0359206i
$703$	4.03947	−	4.03947i	0.152351	−	0.152351i
$704$	1.60026			0.0603122
$705$	10.7486	−	21.8810i	0.404815	−	0.824088i
$706$	−17.2331			−0.648577
$707$	−0.954534	+	0.954534i	−0.0358989	+	0.0358989i
$708$	−14.8072	+	1.39702i	−0.556487	+	0.0525031i
$709$		−	40.2650i		−	1.51218i	−0.654465	−	0.756092i	$-0.727106\pi$
$709$		−	40.2650i		−	1.51218i	0.654465	−	0.756092i	$-0.272894\pi$
$710$	−16.3013	+	26.5480i	−0.611778	+	0.996327i
$711$	1.95455	+	10.2661i	0.0733014	+	0.385008i
$712$	−10.4293	−	10.4293i	−0.390854	−	0.390854i
$713$	0.501374	+	0.501374i	0.0187766	+	0.0187766i
$714$	−0.178370	−	0.147614i	−0.00667532	−	0.00552432i
$715$	−1.23151	+	2.00561i	−0.0460558	+	0.0750054i
$716$			9.93061i			0.371124i
$717$	−4.46499	−	47.3250i	−0.166748	−	1.76738i
$718$	−18.4018	+	18.4018i	−0.686750	+	0.686750i
$719$	−14.0389			−0.523562			−0.261781	−	0.965127i	$-0.584310\pi$
$719$	−14.0389			−0.523562			−0.261781	+	0.965127i	$0.584310\pi$
$720$	−2.75286	−	6.11733i	−0.102593	−	0.227980i
$721$	8.63596			0.321620
$722$	−0.707107	+	0.707107i	−0.0263158	+	0.0263158i
$723$	4.78646	+	50.7323i	0.178010	+	1.88675i
$724$		−	14.5675i		−	0.541396i
$725$	−13.0969	+	6.64367i	−0.486406	+	0.246740i
$726$	−11.2610	−	9.31927i	−0.417934	−	0.345871i
$727$	4.11587	+	4.11587i	0.152649	+	0.152649i	0.779300	−	0.626651i	$-0.215575\pi$
$727$	4.11587	+	4.11587i	0.152649	+	0.152649i	−0.626651	+	0.779300i	$0.715575\pi$
$728$	−0.326629	−	0.326629i	−0.0121057	−	0.0121057i
$729$	−22.8124	+	14.4429i	−0.844902	+	0.534921i
$730$	−6.90663	+	1.65159i	−0.255626	+	0.0611282i
$731$		−	0.848863i		−	0.0313963i
$732$	−10.5283	+	0.993322i	−0.389139	+	0.0367142i
$733$	26.3118	−	26.3118i	0.971848	−	0.971848i	−0.0277661	−	0.999614i	$-0.508839\pi$
$733$	26.3118	−	26.3118i	0.971848	−	0.971848i	0.999614	+	0.0277661i	$0.00883936\pi$
$734$	3.49194			0.128890
$735$	8.13729	+	23.8507i	0.300148	+	0.879745i
$736$	0.434554			0.0160179
$737$	−10.0630	+	10.0630i	−0.370675	+	0.370675i
$738$	8.80587	+	5.98907i	0.324149	+	0.220461i
$739$		−	3.65844i		−	0.134578i	−0.997734	−	0.0672889i	$-0.978565\pi$
$739$		−	3.65844i		−	0.134578i	0.997734	−	0.0672889i	$-0.0214349\pi$
$740$	−10.8856	−	6.68411i	−0.400162	−	0.245713i
$741$	−0.726315	+	0.877644i	−0.0266818	+	0.0322411i
$742$	−1.66274	−	1.66274i	−0.0610409	−	0.0610409i
$743$	10.1780	+	10.1780i	0.373394	+	0.373394i	0.868712	−	0.495318i	$-0.164948\pi$
$743$	10.1780	+	10.1780i	0.373394	+	0.373394i	−0.495318	+	0.868712i	$0.664948\pi$
$744$	1.80184	−	2.17726i	0.0660587	−	0.0798222i
$745$	−6.63698	−	27.7545i	−0.243160	−	1.01685i
$746$			11.3409i			0.415220i
$747$	−6.18090	−	4.20377i	−0.226147	−	0.153808i
$748$	−0.215374	+	0.215374i	−0.00787487	+	0.00787487i
$749$	−12.4102			−0.453460
$750$	−0.248684	−	19.3633i	−0.00908066	−	0.707048i
$751$	−31.8982			−1.16398			−0.581991	−	0.813195i	$-0.697726\pi$
$751$	−31.8982			−1.16398			−0.581991	+	0.813195i	$0.697726\pi$
$752$	4.45089	−	4.45089i	0.162307	−	0.162307i
$753$	22.9625	−	2.16645i	0.836800	−	0.0789499i
$754$		−	1.93181i		−	0.0703522i
$755$	−0.869598	−	3.63648i	−0.0316479	−	0.132345i
$756$	3.19696	+	1.75978i	0.116272	+	0.0640024i
$757$	−24.1785	−	24.1785i	−0.878783	−	0.878783i	0.114626	−	0.993409i	$-0.463433\pi$
$757$	−24.1785	−	24.1785i	−0.878783	−	0.878783i	−0.993409	+	0.114626i	$0.963433\pi$
$758$	−22.0972	−	22.0972i	−0.802606	−	0.802606i
$759$	0.927921	+	0.767923i	0.0336814	+	0.0278738i
$760$	1.90551	+	1.17005i	0.0691203	+	0.0424422i
$761$		−	2.79700i		−	0.101391i	−0.998714	−	0.0506956i	$-0.983856\pi$
$761$		−	2.79700i		−	0.101391i	0.998714	−	0.0506956i	$-0.0161438\pi$
$762$	2.16250	+	22.9206i	0.0783390	+	0.830325i
$763$	0.0912777	−	0.0912777i	0.00330447	−	0.00330447i
$764$	−5.79370			−0.209609
$765$	1.19381	+	0.452814i	0.0431624	+	0.0163715i
$766$	1.38315			0.0499753
$767$	3.99358	−	3.99358i	0.144200	−	0.144200i
$768$	−0.162692	−	1.72439i	−0.00587064	−	0.0622237i
$769$		−	0.345966i		−	0.0124759i	−0.999981	−	0.00623793i	$-0.998014\pi$
$769$		−	0.345966i		−	0.0124759i	0.999981	−	0.00623793i	$-0.00198561\pi$
$770$	−2.44415	+	0.584474i	−0.0880811	+	0.0210630i
$771$	−29.3022	−	24.2497i	−1.05529	−	0.873333i
$772$	2.47519	+	2.47519i	0.0890839	+	0.0890839i
$773$	−24.4179	−	24.4179i	−0.878251	−	0.878251i	0.115102	−	0.993354i	$-0.463280\pi$
$773$	−24.4179	−	24.4179i	−0.878251	−	0.878251i	−0.993354	+	0.115102i	$0.963280\pi$
$774$	2.50237	+	13.1434i	0.0899460	+	0.472431i
$775$	7.27579	−	3.69080i	0.261354	−	0.132577i
$776$			0.0245352i			0.000880762i
$777$	6.91835	−	0.652728i	0.248194	−	0.0234165i
$778$	3.13979	−	3.13979i	0.112567	−	0.112567i
$779$	−3.54984			−0.127186
$780$	2.28638	+	1.12313i	0.0818656	+	0.0402146i
$781$	−22.2951			−0.797783
$782$	−0.0584852	+	0.0584852i	−0.00209143	+	0.00209143i
$783$	4.25002	+	14.6580i	0.151883	+	0.523834i
$784$			6.50676i			0.232384i
$785$	9.17142	−	14.9364i	0.327342	−	0.533101i
$786$	7.93034	−	9.58264i	0.282866	−	0.341802i
$787$	−11.8113	−	11.8113i	−0.421029	−	0.421029i	0.464529	−	0.885558i	$-0.346224\pi$
$787$	−11.8113	−	11.8113i	−0.421029	−	0.421029i	−0.885558	+	0.464529i	$0.846224\pi$
$788$	−5.78154	−	5.78154i	−0.205959	−	0.205959i
$789$	−16.8182	+	20.3223i	−0.598743	+	0.723493i
$790$	−4.07586	+	6.63784i	−0.145012	+	0.236164i
$791$			8.52125i			0.302981i
$792$	2.69986	−	3.96967i	0.0959355	−	0.141056i
$793$	2.83956	−	2.83956i	0.100836	−	0.100836i
$794$	27.7624			0.985250
$795$	11.6390	+	5.71742i	0.412794	+	0.202776i
$796$	11.7597			0.416810
$797$	−27.3911	+	27.3911i	−0.970244	+	0.970244i	−0.999570	−	0.0293260i	$-0.990664\pi$
$797$	−27.3911	+	27.3911i	−0.970244	+	0.970244i	0.0293260	+	0.999570i	$0.490664\pi$
$798$	−1.21105	+	0.114260i	−0.0428708	+	0.00404475i
$799$			1.19806i			0.0423844i
$800$	1.55360	−	4.75251i	0.0549281	−	0.168027i
$801$	−43.4669	+	8.27564i	−1.53583	+	0.292405i
$802$	13.7860	+	13.7860i	0.486799	+	0.486799i
$803$	−3.59362	−	3.59362i	−0.126816	−	0.126816i
$804$	11.8666	+	9.82049i	0.418503	+	0.346342i
$805$	−0.663713	+	0.158715i	−0.0233928	+	0.00559396i
$806$			1.07319i			0.0378015i
$807$	0.401693	+	4.25760i	0.0141403	+	0.149875i
$808$	1.35914	−	1.35914i	0.0478144	−	0.0478144i
$809$	−36.4074			−1.28002			−0.640008	−	0.768368i	$-0.721069\pi$
$809$	−36.4074			−1.28002			−0.640008	+	0.768368i	$0.721069\pi$
$810$	−19.8193	−	3.49194i	−0.696381	−	0.122694i
$811$	−49.1751			−1.72677			−0.863386	−	0.504543i	$-0.831661\pi$
$811$	−49.1751			−1.72677			−0.863386	+	0.504543i	$0.831661\pi$
$812$	1.45859	−	1.45859i	0.0511865	−	0.0511865i
$813$	−3.35967	−	35.6096i	−0.117829	−	1.24888i
$814$		−	9.14178i		−	0.320419i
$815$	−27.6593	−	16.9837i	−0.968863	−	0.594914i
$816$	0.253977	+	0.210185i	0.00889097	+	0.00735793i
$817$	−3.15359	−	3.15359i	−0.110330	−	0.110330i
$818$	−2.39030	−	2.39030i	−0.0835748	−	0.0835748i
$819$	−1.36131	+	0.259180i	−0.0475682	+	0.00905649i
$820$	1.84610	+	7.72002i	0.0644687	+	0.269595i
$821$		−	15.2753i		−	0.533113i	−0.963819	−	0.266557i	$-0.914114\pi$
$821$		−	15.2753i		−	0.533113i	0.963819	−	0.266557i	$-0.0858859\pi$
$822$	20.3758	−	1.92240i	0.710688	−	0.0670515i
$823$	−12.2981	+	12.2981i	−0.428686	+	0.428686i	−0.888180	−	0.459495i	$-0.848030\pi$
$823$	−12.2981	+	12.2981i	−0.428686	+	0.428686i	0.459495	+	0.888180i	$0.348030\pi$
$824$	−12.2966			−0.428371
$825$	11.7159	−	7.40279i	0.407895	−	0.257732i
$826$	6.03063			0.209832
$827$	11.9411	−	11.9411i	0.415234	−	0.415234i	−0.468323	−	0.883557i	$-0.655142\pi$
$827$	11.9411	−	11.9411i	0.415234	−	0.415234i	0.883557	+	0.468323i	$0.155142\pi$
$828$	0.733152	−	1.07797i	0.0254788	−	0.0374621i
$829$		−	4.76231i		−	0.165402i	−0.996574	−	0.0827010i	$-0.973645\pi$
$829$		−	4.76231i		−	0.165402i	0.996574	−	0.0827010i	$-0.0263546\pi$
$830$	−1.29579	−	5.41874i	−0.0449776	−	0.188087i
$831$	11.1098	−	13.4245i	0.385394	−	0.465691i
$832$	0.465079	+	0.465079i	0.0161237	+	0.0161237i
$833$	−0.875725	−	0.875725i	−0.0303421	−	0.0303421i
$834$	−19.2943	+	23.3143i	−0.668107	+	0.807309i
$835$	44.2981	+	27.2005i	1.53300	+	0.941313i
$836$			1.60026i			0.0553462i
$837$	−2.36104	−	8.14306i	−0.0816095	−	0.281465i
$838$	16.1277	−	16.1277i	0.557123	−	0.557123i
$839$	−40.5673			−1.40054			−0.700269	−	0.713879i	$-0.746937\pi$
$839$	−40.5673			−1.40054			−0.700269	+	0.713879i	$0.746937\pi$
$840$	0.878298	+	2.57432i	0.0303041	+	0.0888225i
$841$	−20.3733			−0.702529
$842$	−14.3482	+	14.3482i	−0.494473	+	0.494473i
$843$	7.73479	−	0.729757i	0.266400	−	0.0251342i
$844$			21.4490i			0.738306i
$845$	27.3310	−	6.53571i	0.940214	−	0.224835i
$846$	−3.53179	−	18.5503i	−0.121425	−	0.637773i
$847$	4.19094	+	4.19094i	0.144002	+	0.144002i
$848$	2.36753	+	2.36753i	0.0813014	+	0.0813014i
$849$	21.2318	+	17.5708i	0.728672	+	0.603029i
$850$	0.430531	+	0.848720i	0.0147671	+	0.0291108i
$851$		−	2.48246i		−	0.0850977i
$852$	2.26665	+	24.0245i	0.0776543	+	0.823068i
$853$	11.0822	−	11.0822i	0.379448	−	0.379448i	−0.491455	−	0.870903i	$-0.663535\pi$
$853$	11.0822	−	11.0822i	0.379448	−	0.379448i	0.870903	+	0.491455i	$0.163535\pi$
$854$	4.28796			0.146731
$855$	6.11733	−	2.75286i	0.209208	−	0.0941458i
$856$	17.6707			0.603971
$857$	−17.9548	+	17.9548i	−0.613324	+	0.613324i	−0.943811	−	0.330487i	$-0.892787\pi$
$857$	−17.9548	+	17.9548i	−0.613324	+	0.613324i	0.330487	+	0.943811i	$0.392787\pi$
$858$	0.171238	+	1.81497i	0.00584596	+	0.0619621i
$859$			6.64928i			0.226870i	0.993545	+	0.113435i	$0.0361854\pi$
$859$			6.64928i			0.226870i	−0.993545	+	0.113435i	$0.963815\pi$
$860$	−5.21824	+	8.49830i	−0.177940	+	0.289790i
$861$	−3.32669	−	2.75308i	−0.113373	−	0.0938247i
$862$	−21.4512	−	21.4512i	−0.730631	−	0.730631i
$863$	−11.1405	−	11.1405i	−0.379225	−	0.379225i	0.491597	−	0.870823i	$-0.336413\pi$
$863$	−11.1405	−	11.1405i	−0.379225	−	0.379225i	−0.870823	+	0.491597i	$0.836413\pi$
$864$	−4.55208	−	2.50571i	−0.154865	−	0.0852459i
$865$	25.6281	−	41.7374i	0.871383	−	1.41911i
$866$			12.0080i			0.408049i
$867$	29.2522	−	2.75987i	0.993457	−	0.0937301i
$868$	−0.810300	+	0.810300i	−0.0275034	+	0.0275034i
$869$	−5.57450			−0.189102
$870$	−5.01546	+	10.2100i	−0.170040	+	0.346153i
$871$	−5.84914			−0.198191
$872$	−0.129968	+	0.129968i	−0.00440128	+	0.00440128i
$873$	0.0608630	+	0.0413943i	0.00205990	+	0.00140098i
$874$			0.434554i			0.0146990i
$875$	−0.637093	+	7.82614i	−0.0215377	+	0.264572i
$876$	−3.50703	+	4.23773i	−0.118492	+	0.143179i
$877$	−22.8362	−	22.8362i	−0.771124	−	0.771124i	0.207179	−	0.978303i	$-0.433572\pi$
$877$	−22.8362	−	22.8362i	−0.771124	−	0.771124i	−0.978303	+	0.207179i	$0.933572\pi$
$878$	−14.3942	−	14.3942i	−0.485781	−	0.485781i
$879$	−15.6303	+	18.8869i	−0.527196	+	0.637038i
$880$	3.48017	−	0.832220i	0.117317	−	0.0280541i
$881$		−	8.48351i		−	0.285817i	−0.989736	−	0.142908i	$-0.954355\pi$
$881$		−	8.48351i		−	0.285817i	0.989736	−	0.142908i	$-0.0456454\pi$
$882$	16.1409	+	10.9778i	0.543493	+	0.369642i
$883$	−38.2754	+	38.2754i	−1.28807	+	1.28807i	−0.352110	+	0.935959i	$0.614536\pi$
$883$	−38.2754	+	38.2754i	−1.28807	+	1.28807i	−0.935959	+	0.352110i	$0.885464\pi$
$884$	−0.125187			−0.00421050
$885$	−31.4754	+	10.7387i	−1.05803	+	0.360976i
$886$	19.4853			0.654621
$887$	15.5899	−	15.5899i	0.523459	−	0.523459i	−0.395155	−	0.918614i	$-0.629309\pi$
$887$	15.5899	−	15.5899i	0.523459	−	0.523459i	0.918614	+	0.395155i	$0.129309\pi$
$888$	−9.85089	+	0.929406i	−0.330574	+	0.0311888i
$889$		−	9.33504i		−	0.313087i
$890$	−28.1049	−	17.2573i	−0.942077	−	0.578467i
$891$	−5.29229	−	13.3948i	−0.177298	−	0.448742i
$892$	7.58068	+	7.58068i	0.253820	+	0.253820i
$893$	4.45089	+	4.45089i	0.148943	+	0.148943i
$894$	−17.0294	−	14.0931i	−0.569549	−	0.471344i
$895$	5.16443	+	21.5966i	0.172628	+	0.721895i
$896$			0.702307i			0.0234624i
$897$	0.0464999	+	0.492858i	0.00155259	+	0.0164560i
$898$	15.7898	−	15.7898i	0.526913	−	0.526913i
$899$	−4.79242			−0.159836
$900$	−9.16812	−	11.8721i	−0.305604	−	0.395735i
$901$	−0.637278			−0.0212308
$902$	−4.01685	+	4.01685i	−0.133746	+	0.133746i
$903$	−0.509581	−	5.40111i	−0.0169578	−	0.179738i
$904$		−	12.1332i		−	0.403545i
$905$	−7.57585	−	31.6807i	−0.251830	−	1.05310i
$906$	−2.23125	−	1.84652i	−0.0741283	−	0.0613466i
$907$	−20.2010	−	20.2010i	−0.670763	−	0.670763i	0.287129	−	0.957892i	$-0.407299\pi$
$907$	−20.2010	−	20.2010i	−0.670763	−	0.670763i	−0.957892	+	0.287129i	$0.907299\pi$
$908$	15.3160	+	15.3160i	0.508281	+	0.508281i
$909$	−1.07848	−	5.66459i	−0.0357709	−	0.187883i
$910$	−0.880200	−	0.540472i	−0.0291783	−	0.0179165i
$911$		−	58.3022i		−	1.93164i	−0.259217	−	0.965819i	$-0.583464\pi$
$911$		−	58.3022i		−	1.93164i	0.259217	−	0.965819i	$-0.416536\pi$
$912$	1.72439	−	0.162692i	0.0571004	−	0.00538727i
$913$	2.81945	−	2.81945i	0.0933103	−	0.0933103i
$914$	29.5490			0.977393
$915$	−22.3800	+	7.63552i	−0.739858	+	0.252422i
$916$	15.7592			0.520698
$917$	−3.56632	+	3.56632i	−0.117770	+	0.117770i
$918$	0.949886	−	0.275415i	0.0313509	−	0.00909005i
$919$			26.5126i			0.874568i	0.899323	+	0.437284i	$0.144060\pi$
$919$			26.5126i			0.874568i	−0.899323	+	0.437284i	$0.855940\pi$
$920$	0.945046	−	0.225991i	0.0311572	−	0.00745069i
$921$	31.5859	−	38.1670i	1.04079	−	1.25764i
$922$	11.0828	+	11.0828i	0.364991	+	0.364991i
$923$	−6.47957	−	6.47957i	−0.213278	−	0.213278i
$924$	−1.24108	+	1.49967i	−0.0408287	+	0.0493354i
$925$	−27.1495	−	8.87521i	−0.892670	−	0.291815i
$926$			8.03379i			0.264007i
$927$	−20.7460	+	30.5033i	−0.681388	+	1.00186i
$928$	−2.07686	+	2.07686i	−0.0681761	+	0.0681761i
$929$	−59.6654			−1.95756			−0.978780	−	0.204916i	$-0.934308\pi$
$929$	−59.6654			−1.95756			−0.978780	+	0.204916i	$0.934308\pi$
$930$	2.78627	−	5.67205i	0.0913654	−	0.185994i
$931$	−6.50676			−0.213251
$932$	1.34227	−	1.34227i	0.0439675	−	0.0439675i
$933$	−16.3145	+	1.53923i	−0.534113	+	0.0503922i
$934$		−	14.8038i		−	0.484394i
$935$	−0.356380	+	0.580392i	−0.0116549	+	0.0189808i
$936$	1.93835	−	0.369041i	0.0633568	−	0.0120625i
$937$	27.6627	+	27.6627i	0.903701	+	0.903701i	0.995754	−	0.0920534i	$-0.0293431\pi$
$937$	27.6627	+	27.6627i	0.903701	+	0.903701i	−0.0920534	+	0.995754i	$0.529343\pi$
$938$	−4.41634	−	4.41634i	−0.144199	−	0.144199i
$939$	35.9281	+	29.7332i	1.17247	+	0.970305i
$940$	7.36488	−	11.9943i	0.240216	−	0.391210i
$941$		−	4.74491i		−	0.154680i	−0.997005	−	0.0773398i	$-0.975357\pi$
$941$		−	4.74491i		−	0.154680i	0.997005	−	0.0773398i	$-0.0246426\pi$
$942$	−1.27526	−	13.5166i	−0.0415502	−	0.440396i
$943$	−1.09078	+	1.09078i	−0.0355207	+	0.0355207i
$944$	−8.58688			−0.279479
$945$	7.86777	+	2.16449i	0.255938	+	0.0704109i
$946$	−7.13693			−0.232041
$947$	−10.8483	+	10.8483i	−0.352523	+	0.352523i	−0.861048	−	0.508524i	$-0.830191\pi$
$947$	−10.8483	+	10.8483i	−0.352523	+	0.352523i	0.508524	+	0.861048i	$0.330191\pi$
$948$	0.566736	+	6.00691i	0.0184067	+	0.195095i
$949$		−	2.08881i		−	0.0678056i
$950$	4.75251	+	1.55360i	0.154192	+	0.0504054i
$951$	−34.2295	−	28.3274i	−1.10997	−	0.918579i
$952$	−0.0945214	−	0.0945214i	−0.00306345	−	0.00306345i
$953$	26.4330	+	26.4330i	0.856248	+	0.856248i	0.990894	−	0.134646i	$-0.0429897\pi$
$953$	26.4330	+	26.4330i	0.856248	+	0.856248i	−0.134646	+	0.990894i	$0.542990\pi$
$954$	9.86735	−	1.87864i	0.319467	−	0.0608232i
$955$	−12.5999	+	3.01303i	−0.407722	+	0.0974993i
$956$		−	27.4444i		−	0.887616i
$957$	−8.10492	+	0.764678i	−0.261995	+	0.0247185i
$958$	4.47034	−	4.47034i	0.144430	−	0.144430i
$959$	−8.29861			−0.267976
$960$	−1.25059	−	3.66552i	−0.0403626	−	0.118304i
$961$	−28.3376			−0.914117
$962$	2.65685	−	2.65685i	0.0856601	−	0.0856601i
$963$	29.8128	−	43.8345i	0.960705	−	1.41255i
$964$			29.4204i			0.947567i
$965$	6.67014	+	4.09569i	0.214719	+	0.131845i
$966$	−0.337018	+	0.407237i	−0.0108434	+	0.0131026i
$967$	−23.7603	−	23.7603i	−0.764078	−	0.764078i	0.212979	−	0.977057i	$-0.431684\pi$
$967$	−23.7603	−	23.7603i	−0.764078	−	0.764078i	−0.977057	+	0.212979i	$0.931684\pi$
$968$	−5.96739	−	5.96739i	−0.191799	−	0.191799i
$969$	−0.210185	+	0.253977i	−0.00675210	+	0.00815892i
$970$	0.0127596	+	0.0533580i	0.000409686	+	0.00171322i
$971$		−	15.8739i		−	0.509419i	−0.967018	−	0.254710i	$-0.918020\pi$
$971$		−	15.8739i		−	0.509419i	0.967018	−	0.254710i	$-0.0819799\pi$
$972$	−13.8957	+	7.06459i	−0.445706	+	0.226597i
$973$	8.67677	−	8.67677i	0.278165	−	0.278165i
$974$	35.5872			1.14029
$975$	5.55640	+	1.25350i	0.177947	+	0.0401441i
$976$	−6.10554			−0.195433
$977$	0.135931	−	0.135931i	0.00434883	−	0.00434883i	−0.704929	−	0.709278i	$-0.749021\pi$
$977$	0.135931	−	0.135931i	0.00434883	−	0.00434883i	0.709278	+	0.704929i	$0.249021\pi$
$978$	−25.0303	+	2.36154i	−0.800379	+	0.0755137i
$979$		−	23.6026i		−	0.754343i
$980$	3.38386	+	14.1506i	0.108093	+	0.452024i
$981$	0.103130	+	0.541679i	0.00329269	+	0.0172945i
$982$	−8.52246	−	8.52246i	−0.271962	−	0.271962i
$983$	20.3698	+	20.3698i	0.649695	+	0.649695i	0.952919	−	0.303225i	$-0.0980632\pi$
$983$	20.3698	+	20.3698i	0.649695	+	0.649695i	−0.303225	+	0.952919i	$0.598063\pi$
$984$	4.73680	+	3.92005i	0.151004	+	0.124967i
$985$	−15.5801	−	9.56672i	−0.496424	−	0.304821i
$986$		−	0.559035i		−	0.0178033i
$987$	0.719209	+	7.62298i	0.0228927	+	0.242642i
$988$	−0.465079	+	0.465079i	−0.0147961	+	0.0147961i
$989$	−1.93804			−0.0616261
$990$	3.80710	−	10.0371i	0.120997	−	0.319001i
$991$	4.93454			0.156751			0.0783754	−	0.996924i	$-0.475027\pi$
$991$	4.93454			0.156751			0.0783754	+	0.996924i	$0.475027\pi$
$992$	1.15377	−	1.15377i	0.0366322	−	0.0366322i
$993$	1.63845	+	17.3662i	0.0519948	+	0.551099i
$994$		−	9.78467i		−	0.310351i
$995$	25.5744	−	6.11564i	0.810762	−	0.193879i
$996$	−3.32480	−	2.75151i	−0.105350	−	0.0871850i
$997$	−14.6900	−	14.6900i	−0.465237	−	0.465237i	0.435130	−	0.900368i	$-0.356702\pi$
$997$	−14.6900	−	14.6900i	−0.465237	−	0.465237i	−0.900368	+	0.435130i	$0.856702\pi$
$998$	−3.97502	−	3.97502i	−0.125827	−	0.125827i
$999$	−14.3143	+	26.0045i	−0.452884	+	0.822747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.k.b.77.13	yes	36
3.2	odd	2	inner	570.2.k.b.77.9	✓	36
5.3	odd	4	inner	570.2.k.b.533.9	yes	36
15.8	even	4	inner	570.2.k.b.533.13	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.k.b.77.9	✓	36	3.2	odd	2	inner
570.2.k.b.77.13	yes	36	1.1	even	1	trivial
570.2.k.b.533.9	yes	36	5.3	odd	4	inner
570.2.k.b.533.13	yes	36	15.8	even	4	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)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.162692 - 1.72439i) q^{3} -1.00000i q^{4} +(-0.520052 - 2.17475i) q^{5} +(-1.33437 - 1.10429i) q^{6} +(0.496606 + 0.496606i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.94706 + 0.561090i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.162692 - 1.72439i) q^{3} -1.00000i q^{4} +(-0.520052 - 2.17475i) q^{5} +(-1.33437 - 1.10429i) q^{6} +(0.496606 + 0.496606i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.94706 + 0.561090i) q^{9} +(-1.90551 - 1.17005i) q^{10} -1.60026i q^{11} +(-1.72439 + 0.162692i) q^{12} +(0.465079 - 0.465079i) q^{13} +0.702307 q^{14} +(-3.66552 + 1.25059i) q^{15} -1.00000 q^{16} +(0.134587 - 0.134587i) q^{17} +(-1.68714 + 2.48064i) q^{18} -1.00000i q^{19} +(-2.17475 + 0.520052i) q^{20} +(0.775550 - 0.937138i) q^{21} +(-1.13156 - 1.13156i) q^{22} +(-0.307276 - 0.307276i) q^{23} +(-1.10429 + 1.33437i) q^{24} +(-4.45909 + 2.26197i) q^{25} -0.657722i q^{26} +(1.44700 + 4.99061i) q^{27} +(0.496606 - 0.496606i) q^{28} +2.93712 q^{29} +(-1.70761 + 3.47621i) q^{30} -1.63168 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.75948 + 0.260350i) q^{33} -0.190335i q^{34} +(0.821734 - 1.33826i) q^{35} +(0.561090 + 2.94706i) q^{36} +(4.03947 + 4.03947i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(-0.877644 - 0.726315i) q^{39} +(-1.17005 + 1.90551i) q^{40} -3.54984i q^{41} +(-0.114260 - 1.21105i) q^{42} +(3.15359 - 3.15359i) q^{43} -1.60026 q^{44} +(2.75286 + 6.11733i) q^{45} -0.434554 q^{46} +(-4.45089 + 4.45089i) q^{47} +(0.162692 + 1.72439i) q^{48} -6.50676i q^{49} +(-1.55360 + 4.75251i) q^{50} +(-0.253977 - 0.210185i) q^{51} +(-0.465079 - 0.465079i) q^{52} +(-2.36753 - 2.36753i) q^{53} +(4.55208 + 2.50571i) q^{54} +(-3.48017 + 0.832220i) q^{55} -0.702307i q^{56} +(-1.72439 + 0.162692i) q^{57} +(2.07686 - 2.07686i) q^{58} +8.58688 q^{59} +(1.25059 + 3.66552i) q^{60} +6.10554 q^{61} +(-1.15377 + 1.15377i) q^{62} +(-1.74217 - 1.18489i) q^{63} +1.00000i q^{64} +(-1.25330 - 0.769567i) q^{65} +(-1.76715 + 2.13534i) q^{66} +(-6.28833 - 6.28833i) q^{67} +(-0.134587 - 0.134587i) q^{68} +(-0.479873 + 0.579855i) q^{69} +(-0.365236 - 1.52734i) q^{70} -13.9322i q^{71} +(2.48064 + 1.68714i) q^{72} +(2.24565 - 2.24565i) q^{73} +5.71267 q^{74} +(4.62598 + 7.32122i) q^{75} -1.00000 q^{76} +(0.794700 - 0.794700i) q^{77} +(-1.13417 + 0.107006i) q^{78} -3.48349i q^{79} +(0.520052 + 2.17475i) q^{80} +(8.37036 - 3.30713i) q^{81} +(-2.51012 - 2.51012i) q^{82} +(1.76187 + 1.76187i) q^{83} +(-0.937138 - 0.775550i) q^{84} +(-0.362685 - 0.222701i) q^{85} -4.45985i q^{86} +(-0.477846 - 5.06474i) q^{87} +(-1.13156 + 1.13156i) q^{88} +14.7492 q^{89} +(6.27217 + 2.37904i) q^{90} +0.461923 q^{91} +(-0.307276 + 0.307276i) q^{92} +(0.265461 + 2.81365i) q^{93} +6.29451i q^{94} +(-2.17475 + 0.520052i) q^{95} +(1.33437 + 1.10429i) q^{96} +(-0.0173490 - 0.0173490i) q^{97} +(-4.60098 - 4.60098i) q^{98} +(0.897892 + 4.71607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7}+O(q^{10}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7	\( 36 q + 4 q^{3} + 4 q^{6} + 20 q^{7} - 4 q^{10} - 4 q^{12} + 8 q^{13} + 4 q^{15} - 36 q^{16} + 16 q^{21} - 4 q^{22} + 16 q^{25} - 44 q^{27} + 20 q^{28} + 32 q^{30} - 24 q^{31} - 4 q^{33} + 4 q^{36} - 8 q^{40} + 12 q^{42} - 8 q^{43} + 28 q^{45} - 16 q^{46} - 4 q^{48} + 40 q^{51} - 8 q^{52} - 36 q^{55} - 4 q^{57} + 44 q^{58} + 16 q^{60} - 120 q^{61} - 12 q^{63} + 80 q^{67} - 36 q^{70} + 44 q^{73} + 4 q^{75} - 36 q^{76} - 64 q^{78} + 36 q^{81} + 8 q^{82} - 24 q^{85} - 28 q^{87} - 4 q^{88} + 44 q^{90} - 72 q^{93} - 4 q^{96} + 92 q^{97}+O(q^{100}) \) 36 * q + 4 * q^3 + 4 * q^6 + 20 * q^7 - 4 * q^10 - 4 * q^12 + 8 * q^13 + 4 * q^15 - 36 * q^16 + 16 * q^21 - 4 * q^22 + 16 * q^25 - 44 * q^27 + 20 * q^28 + 32 * q^30 - 24 * q^31 - 4 * q^33 + 4 * q^36 - 8 * q^40 + 12 * q^42 - 8 * q^43 + 28 * q^45 - 16 * q^46 - 4 * q^48 + 40 * q^51 - 8 * q^52 - 36 * q^55 - 4 * q^57 + 44 * q^58 + 16 * q^60 - 120 * q^61 - 12 * q^63 + 80 * q^67 - 36 * q^70 + 44 * q^73 + 4 * q^75 - 36 * q^76 - 64 * q^78 + 36 * q^81 + 8 * q^82 - 24 * q^85 - 28 * q^87 - 4 * q^88 + 44 * q^90 - 72 * q^93 - 4 * q^96 + 92 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more