LMFDB - Embedded newform 675.2.l.f.151.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 0]))

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

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

chi := DirichletCharacter("675.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.9
Character	$\chi$	$=$	675.151
Dual form			675.2.l.f.76.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02568 + 0.860644i) q^{2} +(0.817526 - 1.52697i) q^{3} +(-0.0359939 - 0.204131i) q^{4} +(2.15270 - 0.862581i) q^{6} +(0.0601126 - 0.340915i) q^{7} +(1.47769 - 2.55944i) q^{8} +(-1.66330 - 2.49668i) q^{9} +O(q^{10})$	\(q+(1.02568 + 0.860644i) q^{2} +(0.817526 - 1.52697i) q^{3} +(-0.0359939 - 0.204131i) q^{4} +(2.15270 - 0.862581i) q^{6} +(0.0601126 - 0.340915i) q^{7} +(1.47769 - 2.55944i) q^{8} +(-1.66330 - 2.49668i) q^{9} +(-0.377953 + 0.137564i) q^{11} +(-0.341129 - 0.111921i) q^{12} +(-0.575738 + 0.483102i) q^{13} +(0.355063 - 0.297933i) q^{14} +(3.32884 - 1.21160i) q^{16} +(0.670872 + 1.16198i) q^{17} +(0.442749 - 3.99230i) q^{18} +(1.87243 - 3.24314i) q^{19} +(-0.471425 - 0.370498i) q^{21} +(-0.506050 - 0.184187i) q^{22} +(-0.536470 - 3.04247i) q^{23} +(-2.70014 - 4.34880i) q^{24} -1.00630 q^{26} +(-5.17216 + 0.498713i) q^{27} -0.0717552 q^{28} +(3.79094 + 3.18098i) q^{29} +(-0.774172 - 4.39054i) q^{31} +(-1.09724 - 0.399363i) q^{32} +(-0.0989303 + 0.689586i) q^{33} +(-0.311958 + 1.76920i) q^{34} +(-0.449783 + 0.429397i) q^{36} +(1.25087 + 2.16657i) q^{37} +(4.71170 - 1.71492i) q^{38} +(0.267003 + 1.27409i) q^{39} +(1.73862 - 1.45887i) q^{41} +(-0.164663 - 0.785740i) q^{42} +(-8.03293 + 2.92375i) q^{43} +(0.0416850 + 0.0722005i) q^{44} +(2.06824 - 3.58230i) q^{46} +(-2.13658 + 12.1171i) q^{47} +(0.871334 - 6.07356i) q^{48} +(6.46524 + 2.35315i) q^{49} +(2.32278 - 0.0744513i) q^{51} +(0.119339 + 0.100137i) q^{52} +10.1571 q^{53} +(-5.73418 - 3.93988i) q^{54} +(-0.783723 - 0.657622i) q^{56} +(-3.42144 - 5.51051i) q^{57} +(1.15059 + 6.52530i) q^{58} +(12.7550 + 4.64243i) q^{59} +(2.31667 - 13.1385i) q^{61} +(2.98465 - 5.16956i) q^{62} +(-0.951143 + 0.416963i) q^{63} +(-4.32418 - 7.48970i) q^{64} +(-0.694958 + 0.622148i) q^{66} +(-9.40381 + 7.89073i) q^{67} +(0.213050 - 0.178770i) q^{68} +(-5.08436 - 1.66813i) q^{69} +(-1.14446 - 1.98226i) q^{71} +(-8.84795 + 0.567785i) q^{72} +(-6.23540 + 10.8000i) q^{73} +(-0.581658 + 3.29875i) q^{74} +(-0.729423 - 0.265488i) q^{76} +(0.0241778 + 0.137119i) q^{77} +(-0.822676 + 1.53659i) q^{78} +(9.11223 + 7.64607i) q^{79} +(-3.46686 + 8.30547i) q^{81} +3.03883 q^{82} +(3.71780 + 3.11961i) q^{83} +(-0.0586617 + 0.109568i) q^{84} +(-10.7555 - 3.91468i) q^{86} +(7.95646 - 3.18814i) q^{87} +(-0.206412 + 1.17062i) q^{88} +(-0.197409 + 0.341923i) q^{89} +(0.130088 + 0.225318i) q^{91} +(-0.601754 + 0.219021i) q^{92} +(-7.33715 - 2.40725i) q^{93} +(-12.6200 + 10.5894i) q^{94} +(-1.50684 + 1.34897i) q^{96} +(13.9340 - 5.07158i) q^{97} +(4.60601 + 7.97784i) q^{98} +(0.972102 + 0.714819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	$ 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	1.02568	+	0.860644i	0.725262	+	0.608567i	0.928836	−	0.370492i	$-0.120811\pi$
$2$	1.02568	+	0.860644i	0.725262	+	0.608567i	−0.203573	+	0.979060i	$0.565255\pi$
$3$	0.817526	−	1.52697i	0.471999	−	0.881599i
$3$	0.817526	−	1.52697i	0.471999	−	0.881599i
$4$	−0.0359939	−	0.204131i	−0.0179969	−	0.102066i
$5$		0			0
$5$		0			0
$6$	2.15270	−	0.862581i	0.878836	−	0.352147i
$7$	0.0601126	−	0.340915i	0.0227204	−	0.128854i	−0.971338	−	0.237703i	$-0.923605\pi$
$7$	0.0601126	−	0.340915i	0.0227204	−	0.128854i	0.994058	+	0.108849i	$0.0347166\pi$
$8$	1.47769	−	2.55944i	0.522443	−	0.904897i
$9$	−1.66330	−	2.49668i	−0.554434	−	0.832228i
$10$		0			0
$11$	−0.377953	+	0.137564i	−0.113957	+	0.0414770i	−0.398369	−	0.917225i	$-0.630424\pi$
$11$	−0.377953	+	0.137564i	−0.113957	+	0.0414770i	0.284412	+	0.958702i	$0.408202\pi$
$12$	−0.341129	−	0.111921i	−0.0984755	−	0.0323088i
$13$	−0.575738	+	0.483102i	−0.159681	+	0.133988i	−0.719127	−	0.694878i	$-0.755458\pi$
$13$	−0.575738	+	0.483102i	−0.159681	+	0.133988i	0.559446	+	0.828867i	$0.311014\pi$
$14$	0.355063	−	0.297933i	0.0948945	−	0.0796260i
$15$		0			0
$16$	3.32884	−	1.21160i	0.832209	−	0.302899i
$17$	0.670872	+	1.16198i	0.162710	+	0.281823i	0.935840	−	0.352426i	$-0.114643\pi$
$17$	0.670872	+	1.16198i	0.162710	+	0.281823i	−0.773129	+	0.634248i	$0.781310\pi$
$18$	0.442749	−	3.99230i	0.104357	−	0.940994i
$19$	1.87243	−	3.24314i	0.429565	−	0.744028i	−0.567270	−	0.823532i	$-0.692000\pi$
$19$	1.87243	−	3.24314i	0.429565	−	0.744028i	0.996835	+	0.0795040i	$0.0253336\pi$
$20$		0			0
$21$	−0.471425	−	0.370498i	−0.102873	−	0.0808492i
$22$	−0.506050	−	0.184187i	−0.107890	−	0.0392688i
$23$	−0.536470	−	3.04247i	−0.111862	−	0.634399i	−0.988256	−	0.152806i	$-0.951169\pi$
$23$	−0.536470	−	3.04247i	−0.111862	−	0.634399i	0.876395	−	0.481594i	$-0.159942\pi$
$24$	−2.70014	−	4.34880i	−0.551164	−	0.887696i
$25$		0			0
$26$	−1.00630			−0.197352
$27$	−5.17216	+	0.498713i	−0.995384	+	0.0959773i
$28$	−0.0717552			−0.0135605
$29$	3.79094	+	3.18098i	0.703960	+	0.590693i	0.922897	−	0.385046i	$-0.125815\pi$
$29$	3.79094	+	3.18098i	0.703960	+	0.590693i	−0.218937	+	0.975739i	$0.570259\pi$
$30$		0			0
$31$	−0.774172	−	4.39054i	−0.139045	−	0.788565i	−0.971957	−	0.235159i	$-0.924439\pi$
$31$	−0.774172	−	4.39054i	−0.139045	−	0.788565i	0.832912	−	0.553406i	$-0.186672\pi$
$32$	−1.09724	−	0.399363i	−0.193966	−	0.0705980i
$33$	−0.0989303	+	0.689586i	−0.0172216	+	0.120041i
$34$	−0.311958	+	1.76920i	−0.0535003	+	0.303415i
$35$		0			0
$36$	−0.449783	+	0.429397i	−0.0749638	+	0.0715662i
$37$	1.25087	+	2.16657i	0.205641	+	0.356181i	0.950337	−	0.311223i	$-0.100739\pi$
$37$	1.25087	+	2.16657i	0.205641	+	0.356181i	−0.744696	+	0.667404i	$0.767405\pi$
$38$	4.71170	−	1.71492i	0.764338	−	0.278196i
$39$	0.267003	+	1.27409i	0.0427546	+	0.204017i
$40$		0			0
$41$	1.73862	−	1.45887i	0.271526	−	0.227838i	−0.496849	−	0.867837i	$-0.665510\pi$
$41$	1.73862	−	1.45887i	0.271526	−	0.227838i	0.768376	+	0.639999i	$0.221065\pi$
$42$	−0.164663	−	0.785740i	−0.0254080	−	0.121242i
$43$	−8.03293	+	2.92375i	−1.22501	+	0.445867i	−0.871886	−	0.489709i	$-0.837103\pi$
$43$	−8.03293	+	2.92375i	−1.22501	+	0.445867i	−0.353124	+	0.935576i	$0.614881\pi$
$44$	0.0416850	+	0.0722005i	0.00628425	+	0.0108846i
$45$		0			0
$46$	2.06824	−	3.58230i	0.304946	−	0.528181i
$47$	−2.13658	+	12.1171i	−0.311652	+	1.76746i	0.278760	+	0.960361i	$0.410077\pi$
$47$	−2.13658	+	12.1171i	−0.311652	+	1.76746i	−0.590411	+	0.807103i	$0.701034\pi$
$48$	0.871334	−	6.07356i	0.125766	−	0.876643i
$49$	6.46524	+	2.35315i	0.923606	+	0.336165i
$50$		0			0
$51$	2.32278	−	0.0744513i	0.325254	−	0.0104253i
$52$	0.119339	+	0.100137i	0.0165494	+	0.0138866i
$53$	10.1571			1.39519			0.697593	−	0.716494i	$-0.254254\pi$
$53$	10.1571			1.39519			0.697593	+	0.716494i	$0.254254\pi$
$54$	−5.73418	−	3.93988i	−0.780323	−	0.536149i
$55$		0			0
$56$	−0.783723	−	0.657622i	−0.104729	−	0.0878784i
$57$	−3.42144	−	5.51051i	−0.453180	−	0.729884i
$58$	1.15059	+	6.52530i	0.151079	+	0.856814i
$59$	12.7550	+	4.64243i	1.66055	+	0.604392i	0.990450	−	0.137874i	$-0.0440269\pi$
$59$	12.7550	+	4.64243i	1.66055	+	0.604392i	0.670105	+	0.742266i	$0.266249\pi$
$60$		0			0
$61$	2.31667	−	13.1385i	0.296619	−	1.68221i	−0.363927	−	0.931427i	$-0.618564\pi$
$61$	2.31667	−	13.1385i	0.296619	−	1.68221i	0.660546	−	0.750785i	$-0.270325\pi$
$62$	2.98465	−	5.16956i	0.379051	−	0.656535i
$63$	−0.951143	+	0.416963i	−0.119833	+	0.0525324i
$64$	−4.32418	−	7.48970i	−0.540522	−	0.936212i
$65$		0			0
$66$	−0.694958	+	0.622148i	−0.0855435	+	0.0765811i
$67$	−9.40381	+	7.89073i	−1.14886	+	0.964006i	−0.999692	−	0.0248058i	$-0.992103\pi$
$67$	−9.40381	+	7.89073i	−1.14886	+	0.964006i	−0.149166	+	0.988812i	$0.547659\pi$
$68$	0.213050	−	0.178770i	0.0258361	−	0.0216791i
$69$	−5.08436	−	1.66813i	−0.612085	−	0.200819i
$70$		0			0
$71$	−1.14446	−	1.98226i	−0.135822	−	0.235251i	0.790089	−	0.612992i	$-0.210034\pi$
$71$	−1.14446	−	1.98226i	−0.135822	−	0.235251i	−0.925911	+	0.377741i	$0.876701\pi$
$72$	−8.84795	+	0.567785i	−1.04274	+	0.0669141i
$73$	−6.23540	+	10.8000i	−0.729799	+	1.26405i	0.227169	+	0.973855i	$0.427053\pi$
$73$	−6.23540	+	10.8000i	−0.729799	+	1.26405i	−0.956968	+	0.290194i	$0.906280\pi$
$74$	−0.581658	+	3.29875i	−0.0676164	+	0.383471i
$75$		0			0
$76$	−0.729423	−	0.265488i	−0.0836705	−	0.0304536i
$77$	0.0241778	+	0.137119i	0.00275532	+	0.0156262i
$78$	−0.822676	+	1.53659i	−0.0931498	+	0.173985i
$79$	9.11223	+	7.64607i	1.02521	+	0.860250i	0.990273	−	0.139140i	$-0.0444338\pi$
$79$	9.11223	+	7.64607i	1.02521	+	0.860250i	0.0349328	+	0.999390i	$0.488878\pi$
$80$		0			0
$81$	−3.46686	+	8.30547i	−0.385207	+	0.922830i
$82$	3.03883			0.335583
$83$	3.71780	+	3.11961i	0.408082	+	0.342421i	0.823608	−	0.567160i	$-0.191958\pi$
$83$	3.71780	+	3.11961i	0.408082	+	0.342421i	−0.415526	+	0.909581i	$0.636402\pi$
$84$	−0.0586617	+	0.109568i	−0.00640052	+	0.0119549i
$85$		0			0
$86$	−10.7555	−	3.91468i	−1.15979	−	0.422130i
$87$	7.95646	−	3.18814i	0.853022	−	0.341804i
$88$	−0.206412	+	1.17062i	−0.0220036	+	0.124789i
$89$	−0.197409	+	0.341923i	−0.0209253	+	0.0362438i	−0.876298	−	0.481769i	$-0.839995\pi$
$89$	−0.197409	+	0.341923i	−0.0209253	+	0.0362438i	0.855373	+	0.518012i	$0.173328\pi$
$90$		0			0
$91$	0.130088	+	0.225318i	0.0136369	+	0.0236198i
$92$	−0.601754	+	0.219021i	−0.0627372	+	0.0228345i
$93$	−7.33715	−	2.40725i	−0.760827	−	0.249620i
$94$	−12.6200	+	10.5894i	−1.30165	+	1.09221i
$95$		0			0
$96$	−1.50684	+	1.34897i	−0.153791	+	0.137678i
$97$	13.9340	−	5.07158i	1.41479	−	0.514941i	0.482257	−	0.876030i	$-0.339817\pi$
$97$	13.9340	−	5.07158i	1.41479	−	0.514941i	0.932531	+	0.361089i	$0.117595\pi$
$98$	4.60601	+	7.97784i	0.465277	+	0.805884i
$99$	0.972102	+	0.714819i	0.0976999	+	0.0718420i
$100$		0			0
$101$	−2.32075	+	13.1616i	−0.230924	+	1.30963i	0.620107	+	0.784517i	$0.287089\pi$
$101$	−2.32075	+	13.1616i	−0.230924	+	1.30963i	−0.851031	+	0.525116i	$0.824022\pi$
$102$	2.44649	+	1.92272i	0.242239	+	0.190378i
$103$	−6.76551	−	2.46244i	−0.666625	−	0.242632i	−0.0135311	−	0.999908i	$-0.504307\pi$
$103$	−6.76551	−	2.46244i	−0.666625	−	0.242632i	−0.653094	+	0.757277i	$0.726529\pi$
$104$	0.385705	+	2.18744i	0.0378215	+	0.214496i
$105$		0			0
$106$	10.4179	+	8.74166i	1.01188	+	0.849065i
$107$	8.94985			0.865215			0.432607	−	0.901582i	$-0.357594\pi$
$107$	8.94985			0.865215			0.432607	+	0.901582i	$0.357594\pi$
$108$	0.287969	+	1.03785i	0.0277098	+	0.0998672i
$109$	−7.74154			−0.741505			−0.370752	−	0.928732i	$-0.620900\pi$
$109$	−7.74154			−0.741505			−0.370752	+	0.928732i	$0.620900\pi$
$110$		0			0
$111$	4.33091	−	0.138817i	0.411072	−	0.0131760i
$112$	−0.212947	−	1.20768i	−0.0201216	−	0.114115i
$113$	−3.88427	−	1.41376i	−0.365401	−	0.132995i	0.152793	−	0.988258i	$-0.451173\pi$
$113$	−3.88427	−	1.41376i	−0.365401	−	0.132995i	−0.518194	+	0.855263i	$0.673396\pi$
$114$	1.23330	−	8.59663i	0.115509	−	0.805148i
$115$		0			0
$116$	0.512886	−	0.888345i	0.0476203	−	0.0824808i
$117$	2.16378	+	0.633893i	0.200041	+	0.0586034i
$118$	9.08698	+	15.7391i	0.836524	+	1.44890i
$119$	0.436466	−	0.158861i	0.0400108	−	0.0145627i
$120$		0			0
$121$	−8.30256	+	6.96668i	−0.754779	+	0.633334i
$122$	13.6837	−	11.4820i	1.23887	−	1.03953i
$123$	−0.806296	−	3.84749i	−0.0727013	−	0.346917i
$124$	−0.868382	+	0.316065i	−0.0779830	+	0.0283835i
$125$		0			0
$126$	−1.33442	−	0.390927i	−0.118880	−	0.0348266i
$127$	−1.13280	+	1.96206i	−0.100519	+	0.174105i	−0.911899	−	0.410415i	$-0.865384\pi$
$127$	−1.13280	+	1.96206i	−0.100519	+	0.174105i	0.811379	+	0.584520i	$0.198717\pi$
$128$	1.60524	−	9.10374i	0.141884	−	0.804665i
$129$	−2.10265	+	14.6563i	−0.185128	+	1.29042i
$130$		0			0
$131$	−0.0505139	−	0.286479i	−0.00441342	−	0.0250298i	0.982522	−	0.186149i	$-0.0596007\pi$
$131$	−0.0505139	−	0.286479i	−0.00441342	−	0.0250298i	−0.986935	+	0.161119i	$0.948490\pi$
$132$	0.144327	−	0.00462607i	0.0125620	−	0.000402648i
$133$	−0.993081	−	0.833294i	−0.0861110	−	0.0722557i
$134$	−16.4364			−1.41989
$135$		0			0
$136$	3.96537			0.340027
$137$	7.40550	+	6.21395i	0.632694	+	0.530893i	0.901765	−	0.432227i	$-0.142272\pi$
$137$	7.40550	+	6.21395i	0.632694	+	0.530893i	−0.269071	+	0.963120i	$0.586717\pi$
$138$	−3.77924	−	6.08678i	−0.321710	−	0.518141i
$139$	0.516258	+	2.92785i	0.0437885	+	0.248337i	0.998843	−	0.0480940i	$-0.0153147\pi$
$139$	0.516258	+	2.92785i	0.0437885	+	0.248337i	−0.955054	+	0.296431i	$0.904204\pi$
$140$		0			0
$141$	16.7558	+	13.1686i	1.41109	+	1.10899i
$142$	0.532177	−	3.01813i	0.0446593	−	0.253275i
$143$	0.151145	−	0.261790i	0.0126393	−	0.0218920i
$144$	−8.56183	−	6.29580i	−0.713486	−	0.524650i
$145$		0			0
$146$	−15.6905	+	5.71087i	−1.29855	+	0.472635i
$147$	8.87871	−	7.94849i	0.732304	−	0.655580i
$148$	0.397240	−	0.333324i	0.0326530	−	0.0273991i
$149$	12.7219	−	10.6749i	1.04221	−	0.874522i	0.0499614	−	0.998751i	$-0.484090\pi$
$149$	12.7219	−	10.6749i	1.04221	−	0.874522i	0.992254	+	0.124229i	$0.0396457\pi$
$150$		0			0
$151$	−8.75299	+	3.18583i	−0.712308	+	0.259259i	−0.672657	−	0.739955i	$-0.734847\pi$
$151$	−8.75299	+	3.18583i	−0.712308	+	0.259259i	−0.0396512	+	0.999214i	$0.512625\pi$
$152$	−5.53375	−	9.58473i	−0.448846	−	0.777424i
$153$	1.78525	−	3.60768i	0.144329	−	0.291664i
$154$	−0.0932122	+	0.161448i	−0.00751125	+	0.0130099i
$155$		0			0
$156$	0.250470	−	0.100363i	0.0200537	−	0.00803546i
$157$	−14.4391	−	5.25541i	−1.15237	−	0.419427i	−0.306002	−	0.952031i	$-0.598992\pi$
$157$	−14.4391	−	5.25541i	−1.15237	−	0.419427i	−0.846365	+	0.532603i	$0.821214\pi$
$158$	2.76565	+	15.6848i	0.220023	+	1.24781i
$159$	8.30371	−	15.5096i	0.658527	−	1.23000i
$160$		0			0
$161$	−1.06947			−0.0842864
$162$	−10.7039	+	5.53499i	−0.840980	+	0.434870i
$163$	−4.28453			−0.335590			−0.167795	−	0.985822i	$-0.553665\pi$
$163$	−4.28453			−0.335590			−0.167795	+	0.985822i	$0.553665\pi$
$164$	−0.360381	−	0.302396i	−0.0281411	−	0.0236131i
$165$		0			0
$166$	1.12839	+	6.39941i	0.0875799	+	0.496690i
$167$	−12.2900	−	4.47320i	−0.951030	−	0.346147i	−0.180518	−	0.983572i	$-0.557777\pi$
$167$	−12.2900	−	4.47320i	−0.951030	−	0.346147i	−0.770512	+	0.637425i	$0.780000\pi$
$168$	−1.64489	+	0.659102i	−0.126906	+	0.0508508i
$169$	−2.15934	+	12.2462i	−0.166103	+	0.942017i
$170$		0			0
$171$	−11.2115	+	0.719459i	−0.857366	+	0.0550184i
$172$	0.885964	+	1.53453i	0.0675541	+	0.117007i
$173$	1.03146	−	0.375420i	0.0784202	−	0.0285426i	−0.302512	−	0.953146i	$-0.597825\pi$
$173$	1.03146	−	0.375420i	0.0784202	−	0.0285426i	0.380932	+	0.924603i	$0.375603\pi$
$174$	10.9046	+	3.57769i	0.826676	+	0.271224i
$175$		0			0
$176$	−1.09147	+	0.915853i	−0.0822727	+	0.0690350i
$177$	17.5164	−	15.6812i	1.31661	−	1.17867i
$178$	−0.496752	+	0.180803i	−0.0372331	+	0.0135518i
$179$	−8.45761	−	14.6490i	−0.632151	−	1.09492i	−0.987111	−	0.160037i	$-0.948839\pi$
$179$	−8.45761	−	14.6490i	−0.632151	−	1.09492i	0.354960	−	0.934882i	$-0.384495\pi$
$180$		0			0
$181$	−1.06581	+	1.84604i	−0.0792210	+	0.137215i	−0.902914	−	0.429821i	$-0.858577\pi$
$181$	−1.06581	+	1.84604i	−0.0792210	+	0.137215i	0.823693	+	0.567036i	$0.191910\pi$
$182$	−0.0604912	+	0.343063i	−0.00448391	+	0.0254295i
$183$	−18.1682	−	14.2786i	−1.34303	−	1.05550i
$184$	−8.57975	−	3.12277i	−0.632508	−	0.230214i
$185$		0			0
$186$	−5.45376	−	8.78373i	−0.399889	−	0.644055i
$187$	−0.413404	−	0.346887i	−0.0302311	−	0.0253669i
$188$	2.55039			0.186006
$189$	−0.140893	+	1.79325i	−0.0102485	+	0.130440i
$190$		0			0
$191$	10.3330	+	8.67044i	0.747671	+	0.627371i	0.934886	−	0.354948i	$-0.115501\pi$
$191$	10.3330	+	8.67044i	0.747671	+	0.627371i	−0.187214	+	0.982319i	$0.559946\pi$
$192$	−14.9717	+	0.479884i	−1.08049	+	0.0346326i
$193$	−1.63254	−	9.25860i	−0.117513	−	0.666448i	−0.985475	−	0.169819i	$-0.945682\pi$
$193$	−1.63254	−	9.25860i	−0.117513	−	0.666448i	0.867963	−	0.496630i	$-0.165429\pi$
$194$	18.6566	+	6.79046i	1.33947	+	0.487527i
$195$		0			0
$196$	0.247644	−	1.40446i	0.0176888	−	0.100318i
$197$	4.22400	−	7.31619i	0.300948	−	0.521257i	−0.675403	−	0.737449i	$-0.736030\pi$
$197$	4.22400	−	7.31619i	0.300948	−	0.521257i	0.976351	+	0.216192i	$0.0693637\pi$
$198$	0.381857	+	1.56981i	0.0271374	+	0.111561i
$199$	−6.77278	−	11.7308i	−0.480109	−	0.831574i	0.519630	−	0.854391i	$-0.326070\pi$
$199$	−6.77278	−	11.7308i	−0.480109	−	0.831574i	−0.999740	+	0.0228175i	$0.992736\pi$
$200$		0			0
$201$	4.36108	+	20.8103i	0.307607	+	1.46784i
$202$	−13.7078	+	11.5022i	−0.964480	+	0.809295i
$203$	1.31233	−	1.10117i	0.0921073	−	0.0772872i
$204$	−0.0988035	−	0.471471i	−0.00691763	−	0.0330096i
$205$		0			0
$206$	−4.81993	−	8.34836i	−0.335820	−	0.581658i
$207$	−6.70378	+	6.39994i	−0.465945	+	0.444827i
$208$	−1.33121	+	2.30573i	−0.0923031	+	0.159874i
$209$	−0.261552	+	1.48333i	−0.0180919	+	0.102604i
$210$		0			0
$211$	−10.4837	−	3.81575i	−0.721726	−	0.262687i	−0.0450677	−	0.998984i	$-0.514350\pi$
$211$	−10.4837	−	3.81575i	−0.721726	−	0.262687i	−0.676658	+	0.736297i	$0.736573\pi$
$212$	−0.365594	−	2.07338i	−0.0251091	−	0.142401i
$213$	−3.96248	+	0.127008i	−0.271505	+	0.00870247i
$214$	9.17964	+	7.70264i	0.627508	+	0.526541i
$215$		0			0
$216$	−6.36644	+	13.9748i	−0.433181	+	0.950863i
$217$	−1.54334			−0.104769
$218$	−7.94031	−	6.66271i	−0.537785	−	0.451256i
$219$	11.3938	+	18.3506i	0.769920	+	1.24002i
$220$		0			0
$221$	−0.947603	−	0.344899i	−0.0637427	−	0.0232004i
$222$	4.56158	+	3.58499i	0.306153	+	0.240609i
$223$	3.33930	−	18.9381i	0.223616	−	1.26819i	−0.641698	−	0.766957i	$-0.721770\pi$
$223$	3.33930	−	18.9381i	0.223616	−	1.26819i	0.865314	−	0.501231i	$-0.167119\pi$
$224$	−0.202107	+	0.350059i	−0.0135038	+	0.0233893i
$225$		0			0
$226$	−2.76726	−	4.79303i	−0.184075	−	0.318828i
$227$	−14.5183	+	5.28423i	−0.963614	+	0.350727i	−0.775449	−	0.631411i	$-0.782476\pi$
$227$	−14.5183	+	5.28423i	−0.963614	+	0.350727i	−0.188165	+	0.982137i	$0.560254\pi$
$228$	−1.00172	+	0.896766i	−0.0663403	+	0.0593898i
$229$	−9.01052	+	7.56072i	−0.595432	+	0.499627i	−0.889974	−	0.456012i	$-0.849277\pi$
$229$	−9.01052	+	7.56072i	−0.595432	+	0.499627i	0.294542	+	0.955639i	$0.404833\pi$
$230$		0			0
$231$	0.229143	+	0.0751796i	0.0150765	+	0.00494646i
$232$	13.7433	−	5.00217i	0.902295	−	0.328408i
$233$	8.08145	+	13.9975i	0.529434	+	0.917006i	0.999411	+	0.0343274i	$0.0109289\pi$
$233$	8.08145	+	13.9975i	0.529434	+	0.917006i	−0.469977	+	0.882679i	$0.655738\pi$
$234$	1.67378	+	2.51241i	0.109418	+	0.164241i
$235$		0			0
$236$	0.488564	−	2.77079i	0.0318028	−	0.180363i
$237$	19.1248	−	7.66327i	1.24229	−	0.497783i
$238$	0.584395	+	0.212702i	0.0378807	+	0.0137875i
$239$	−3.74110	−	21.2168i	−0.241992	−	1.37240i	−0.827377	−	0.561647i	$-0.810168\pi$
$239$	−3.74110	−	21.2168i	−0.241992	−	1.37240i	0.585386	−	0.810755i	$-0.300943\pi$
$240$		0			0
$241$	3.36630	+	2.82466i	0.216842	+	0.181952i	0.744738	−	0.667357i	$-0.232574\pi$
$241$	3.36630	+	2.82466i	0.216842	+	0.181952i	−0.527896	+	0.849309i	$0.677019\pi$
$242$	−14.5116			−0.932839
$243$	9.84799	+	12.0837i	0.631749	+	0.775173i
$244$	−2.76537			−0.177034
$245$		0			0
$246$	2.48432	−	4.64021i	0.158395	−	0.295849i
$247$	0.488739	+	2.77178i	0.0310977	+	0.176364i
$248$	−12.3813	−	4.50643i	−0.786214	−	0.286158i
$249$	7.80296	−	3.12663i	0.494492	−	0.198142i
$250$		0			0
$251$	2.98966	−	5.17825i	0.188706	−	0.326848i	−0.756113	−	0.654441i	$-0.772904\pi$
$251$	2.98966	−	5.17825i	0.188706	−	0.326848i	0.944819	+	0.327593i	$0.106237\pi$
$252$	0.119350	+	0.179150i	0.00751837	+	0.0112854i
$253$	0.621293	+	1.07611i	0.0390604	+	0.0676546i
$254$	−2.85052	+	1.03750i	−0.178857	+	0.0650988i
$255$		0			0
$256$	−3.76852	+	3.16216i	−0.235532	+	0.197635i
$257$	13.4968	−	11.3252i	0.841909	−	0.706446i	−0.116083	−	0.993239i	$-0.537034\pi$
$257$	13.4968	−	11.3252i	0.841909	−	0.706446i	0.957992	+	0.286794i	$0.0925895\pi$
$258$	−14.7705	+	13.2230i	−0.919571	+	0.823228i
$259$	0.813808	−	0.296202i	0.0505676	−	0.0184051i
$260$		0			0
$261$	1.63642	−	14.7557i	0.101292	−	0.913355i
$262$	0.194745	−	0.337309i	0.0120314	−	0.0208390i
$263$	−0.703963	+	3.99237i	−0.0434082	+	0.246180i	−0.998789	−	0.0491964i	$-0.984334\pi$
$263$	−0.703963	+	3.99237i	−0.0434082	+	0.246180i	0.955381	+	0.295377i	$0.0954451\pi$
$264$	1.61876	+	1.27220i	0.0996279	+	0.0782985i
$265$		0			0
$266$	−0.301409	−	1.70938i	−0.0184806	−	0.104809i
$267$	0.360720	+	0.580970i	0.0220757	+	0.0355548i
$268$	1.94922	+	1.63559i	0.119068	+	0.0999098i
$269$	−13.0325			−0.794604			−0.397302	−	0.917688i	$-0.630054\pi$
$269$	−13.0325			−0.794604			−0.397302	+	0.917688i	$0.630054\pi$
$270$		0			0
$271$	−5.58778			−0.339434			−0.169717	−	0.985493i	$-0.554285\pi$
$271$	−5.58778			−0.339434			−0.169717	+	0.985493i	$0.554285\pi$
$272$	3.64108	+	3.05523i	0.220773	+	0.185250i
$273$	0.450406	−	0.0144367i	0.0272598	−	0.000873751i
$274$	2.24764	+	12.7470i	0.135785	+	0.770074i
$275$		0			0
$276$	−0.157511	+	1.09792i	−0.00948106	+	0.0660869i
$277$	−3.33752	+	18.9280i	−0.200532	+	1.13728i	0.703785	+	0.710413i	$0.251492\pi$
$277$	−3.33752	+	18.9280i	−0.200532	+	1.13728i	−0.904317	+	0.426862i	$0.859619\pi$
$278$	−1.99032	+	3.44734i	−0.119372	+	0.206758i
$279$	−9.67412	+	9.23566i	−0.579175	+	0.552924i
$280$		0			0
$281$	10.9339	−	3.97961i	0.652261	−	0.237404i	0.00536937	−	0.999986i	$-0.498291\pi$
$281$	10.9339	−	3.97961i	0.652261	−	0.237404i	0.646892	+	0.762582i	$0.276069\pi$
$282$	5.85260	+	27.9275i	0.348517	+	1.66306i
$283$	21.5765	−	18.1048i	1.28259	−	1.07622i	0.289707	−	0.957115i	$-0.406442\pi$
$283$	21.5765	−	18.1048i	1.28259	−	1.07622i	0.992882	−	0.119105i	$-0.0380025\pi$
$284$	−0.363447	+	0.304969i	−0.0215666	+	0.0180966i
$285$		0			0
$286$	0.380334	−	0.138430i	0.0224896	−	0.00818554i
$287$	−0.392840	−	0.680418i	−0.0231886	−	0.0401638i
$288$	0.827958	+	3.40372i	0.0487879	+	0.200566i
$289$	7.59986	−	13.1633i	0.447051	−	0.774315i
$290$		0			0
$291$	3.64728	−	25.4231i	0.213807	−	1.49033i
$292$	2.42906	+	0.884106i	0.142150	+	0.0517384i
$293$	0.0144323	+	0.0818497i	0.000843144	+	0.00478171i	0.985226	−	0.171257i	$-0.0547828\pi$
$293$	0.0144323	+	0.0818497i	0.000843144	+	0.00478171i	−0.984383	+	0.176039i	$0.943672\pi$
$294$	15.9475	−	0.511161i	0.930077	−	0.0298115i
$295$		0			0
$296$	7.39358			0.429743
$297$	1.88623	−	0.899991i	0.109450	−	0.0522228i
$298$	22.2358			1.28809
$299$	1.77869	+	1.49250i	0.102864	+	0.0863134i
$300$		0			0
$301$	0.513870	+	2.91430i	0.0296190	+	0.167978i
$302$	−11.7196	−	4.26558i	−0.674387	−	0.245457i
$303$	18.2002	+	14.3037i	1.04558	+	0.821728i
$304$	2.30363	−	13.0645i	0.132122	−	0.749302i
$305$		0			0
$306$	4.93602	−	2.16385i	0.282173	−	0.123699i
$307$	−8.06146	−	13.9629i	−0.460092	−	0.796902i	0.538873	−	0.842387i	$-0.318850\pi$
$307$	−8.06146	−	13.9629i	−0.460092	−	0.796902i	−0.998965	+	0.0454847i	$0.985517\pi$
$308$	0.0271201	−	0.00987089i	0.00154531	−	0.000562446i
$309$	−9.29107	+	8.31764i	−0.528550	+	0.473174i
$310$		0			0
$311$	25.8269	−	21.6714i	1.46451	−	1.22887i	0.543454	−	0.839439i	$-0.317116\pi$
$311$	25.8269	−	21.6714i	1.46451	−	1.22887i	0.921056	−	0.389431i	$-0.127328\pi$
$312$	3.65549	+	1.19933i	0.206951	+	0.0678986i
$313$	−23.4509	+	8.53543i	−1.32552	+	0.482451i	−0.905224	−	0.424935i	$-0.860297\pi$
$313$	−23.4509	+	8.53543i	−1.32552	+	0.482451i	−0.420299	+	0.907386i	$0.638075\pi$
$314$	−10.2868	−	17.8173i	−0.580519	−	1.00549i
$315$		0			0
$316$	1.23282	−	2.13530i	0.0693514	−	0.120120i
$317$	−2.72538	+	15.4564i	−0.153073	+	0.868119i	0.807454	+	0.589931i	$0.200845\pi$
$317$	−2.72538	+	15.4564i	−0.153073	+	0.868119i	−0.960527	+	0.278188i	$0.910266\pi$
$318$	21.8652	−	8.76134i	1.22614	−	0.491311i
$319$	−1.87038	−	0.680763i	−0.104721	−	0.0381154i
$320$		0			0
$321$	7.31674	−	13.6662i	0.408381	−	0.762772i
$322$	−1.09693	−	0.920437i	−0.0611297	−	0.0512939i
$323$	5.02464			0.279578
$324$	1.82019	+	0.408749i	0.101122	+	0.0227083i
$325$		0			0
$326$	−4.39454	−	3.68746i	−0.243391	−	0.204229i
$327$	−6.32891	+	11.8211i	−0.349990	+	0.653710i
$328$	−1.16475	−	6.60565i	−0.0643128	−	0.364736i
$329$	4.00248	+	1.45678i	0.220664	+	0.0803150i
$330$		0			0
$331$	5.25148	−	29.7826i	0.288647	−	1.63700i	−0.403312	−	0.915063i	$-0.632141\pi$
$331$	5.25148	−	29.7826i	0.288647	−	1.63700i	0.691959	−	0.721937i	$-0.256748\pi$
$332$	0.502991	−	0.871206i	0.0276052	−	0.0478136i
$333$	3.32866	−	6.72667i	0.182410	−	0.368619i
$334$	−8.75574	−	15.1654i	−0.479093	−	0.829813i
$335$		0			0
$336$	−2.01819	−	0.662148i	−0.110101	−	0.0361232i
$337$	−5.28309	+	4.43304i	−0.287788	+	0.241483i	−0.775240	−	0.631667i	$-0.782371\pi$
$337$	−5.28309	+	4.43304i	−0.287788	+	0.241483i	0.487452	+	0.873150i	$0.337927\pi$
$338$	−12.7544	+	10.7022i	−0.693749	+	0.582125i
$339$	−5.33427	+	4.77540i	−0.289718	+	0.259364i
$340$		0			0
$341$	0.896579	+	1.55292i	0.0485525	+	0.0840953i
$342$	−12.1186	−	8.91120i	−0.655298	−	0.481862i
$343$	2.40248	−	4.16122i	0.129722	−	0.224685i
$344$	−4.38704	+	24.8802i	−0.236534	+	1.34145i
$345$		0			0
$346$	1.38104	+	0.502659i	0.0742453	+	0.0270231i
$347$	6.15856	+	34.9269i	0.330609	+	1.87497i	0.466906	+	0.884307i	$0.345369\pi$
$347$	6.15856	+	34.9269i	0.330609	+	1.87497i	−0.136298	+	0.990668i	$0.543520\pi$
$348$	−0.937182	−	1.50941i	−0.0502382	−	0.0809129i
$349$	18.7347	+	15.7203i	1.00285	+	0.841488i	0.987376	−	0.158392i	$-0.0506310\pi$
$349$	18.7347	+	15.7203i	1.00285	+	0.841488i	0.0154704	+	0.999880i	$0.495075\pi$
$350$		0			0
$351$	2.73688	−	2.78581i	0.146084	−	0.148696i
$352$	0.469642			0.0250320
$353$	7.10672	+	5.96325i	0.378253	+	0.317392i	0.812016	−	0.583635i	$-0.198370\pi$
$353$	7.10672	+	5.96325i	0.378253	+	0.317392i	−0.433763	+	0.901027i	$0.642815\pi$
$354$	31.4621	−	1.00845i	1.67219	−	0.0535983i
$355$		0			0
$356$	0.0769027	+	0.0279903i	0.00407584	+	0.00148348i
$357$	0.114246	−	0.796345i	0.00604656	−	0.0421471i
$358$	3.93282	−	22.3041i	0.207856	−	1.17881i
$359$	3.57306	−	6.18872i	0.188579	−	0.326628i	−0.756198	−	0.654343i	$-0.772945\pi$
$359$	3.57306	−	6.18872i	0.188579	−	0.326628i	0.944777	+	0.327715i	$0.106279\pi$
$360$		0			0
$361$	2.48802	+	4.30937i	0.130948	+	0.226809i
$362$	−2.68196	+	0.976152i	−0.140961	+	0.0513054i
$363$	3.85037	+	18.3732i	0.202092	+	0.964345i
$364$	0.0413122	−	0.0346650i	0.00216535	−	0.00181694i
$365$		0			0
$366$	−6.34593	−	30.2816i	−0.331707	−	1.58284i
$367$	10.8281	−	3.94110i	0.565222	−	0.205724i	−0.0435748	−	0.999050i	$-0.513875\pi$
$367$	10.8281	−	3.94110i	0.565222	−	0.205724i	0.608797	+	0.793326i	$0.291652\pi$
$368$	−5.47207	−	9.47791i	−0.285252	−	0.494070i
$369$	−6.53419	−	1.91423i	−0.340156	−	0.0996510i
$370$		0			0
$371$	0.610570	−	3.46272i	0.0316992	−	0.179775i
$372$	−0.227302	+	1.58439i	−0.0117851	+	0.0821467i
$373$	29.0373	+	10.5687i	1.50349	+	0.547227i	0.956962	−	0.290213i	$-0.0937260\pi$
$373$	29.0373	+	10.5687i	1.50349	+	0.547227i	0.546531	+	0.837439i	$0.315948\pi$
$374$	−0.125472	−	0.711588i	−0.00648801	−	0.0367954i
$375$		0			0
$376$	27.8558	+	23.3738i	1.43655	+	1.20541i
$377$	−3.71932			−0.191555
$378$	−1.68786	+	1.71803i	−0.0868142	+	0.0883661i
$379$	−2.84713			−0.146247			−0.0731236	−	0.997323i	$-0.523297\pi$
$379$	−2.84713			−0.146247			−0.0731236	+	0.997323i	$0.523297\pi$
$380$		0			0
$381$	2.06992	+	3.33379i	0.106045	+	0.170795i
$382$	3.13617	+	17.7861i	0.160461	+	0.910017i
$383$	−32.9304	−	11.9857i	−1.68266	−	0.612439i	−0.688992	−	0.724769i	$-0.741947\pi$
$383$	−32.9304	−	11.9857i	−1.68266	−	0.612439i	−0.993671	+	0.112329i	$0.964169\pi$
$384$	−12.5889	−	9.89370i	−0.642422	−	0.504886i
$385$		0			0
$386$	6.29390	−	10.9014i	0.320351	−	0.554864i
$387$	20.6608	+	15.1926i	1.05025	+	0.772284i
$388$	−1.53681	−	2.66183i	−0.0780196	−	0.135134i
$389$	−17.3917	+	6.33006i	−0.881795	+	0.320947i	−0.742934	−	0.669365i	$-0.766566\pi$
$389$	−17.3917	+	6.33006i	−0.881795	+	0.320947i	−0.138861	+	0.990312i	$0.544344\pi$
$390$		0			0
$391$	3.17540	−	2.66448i	0.160587	−	0.134748i
$392$	15.5764	−	13.0701i	0.786726	−	0.660141i
$393$	−0.478742	−	0.157071i	−0.0241494	−	0.00792316i
$394$	10.6291	−	3.86867i	0.535486	−	0.194901i
$395$		0			0
$396$	0.110927	−	0.224165i	0.00557430	−	0.0112647i
$397$	14.7500	−	25.5478i	0.740284	−	1.28221i	−0.212083	−	0.977252i	$-0.568025\pi$
$397$	14.7500	−	25.5478i	0.740284	−	1.28221i	0.952366	−	0.304957i	$-0.0986421\pi$
$398$	3.14937	−	17.8609i	0.157863	−	0.895288i
$399$	−2.08429	+	0.835169i	−0.104345	+	0.0418107i
$400$		0			0
$401$	4.06740	+	23.0673i	0.203116	+	1.15193i	0.900377	+	0.435111i	$0.143291\pi$
$401$	4.06740	+	23.0673i	0.203116	+	1.15193i	−0.697261	+	0.716817i	$0.745598\pi$
$402$	−13.4372	+	25.0979i	−0.670185	+	1.25177i
$403$	2.56680	+	2.15380i	0.127861	+	0.107288i
$404$	2.77024			0.137824
$405$		0			0
$406$	2.29374			0.113836
$407$	−0.770809	−	0.646786i	−0.0382076	−	0.0320600i
$408$	3.24179	−	6.05501i	0.160493	−	0.299768i
$409$	1.34566	+	7.63161i	0.0665386	+	0.377359i	0.999833	+	0.0182481i	$0.00580888\pi$
$409$	1.34566	+	7.63161i	0.0665386	+	0.377359i	−0.933295	+	0.359111i	$0.883080\pi$
$410$		0			0
$411$	15.5427	−	6.22793i	0.766666	−	0.307201i
$412$	−0.259145	+	1.46968i	−0.0127672	+	0.0724062i
$413$	2.34941	−	4.06929i	0.115607	−	0.200237i
$414$	−12.3840	+	0.794697i	−0.608639	+	0.0390572i
$415$		0			0
$416$	0.824656	−	0.300150i	0.0404321	−	0.0147161i
$417$	4.89280	+	1.60528i	0.239602	+	0.0786109i
$418$	−1.54489	+	1.29632i	−0.0755630	+	0.0634049i
$419$	−13.6412	+	11.4463i	−0.666415	+	0.559189i	−0.912002	−	0.410186i	$-0.865464\pi$
$419$	−13.6412	+	11.4463i	−0.666415	+	0.559189i	0.245587	+	0.969375i	$0.421019\pi$
$420$		0			0
$421$	−28.5312	+	10.3845i	−1.39053	+	0.506110i	−0.925352	−	0.379108i	$-0.876231\pi$
$421$	−28.5312	+	10.3845i	−1.39053	+	0.506110i	−0.465175	+	0.885219i	$0.654009\pi$
$422$	−7.46885	−	12.9364i	−0.363578	−	0.629736i
$423$	33.8064	−	14.8201i	1.64372	−	0.720576i
$424$	15.0091	−	25.9965i	0.728905	−	1.26250i
$425$		0			0
$426$	−4.17353	−	3.28002i	−0.202208	−	0.158917i
$427$	−4.33985	−	1.57958i	−0.210020	−	0.0764411i
$428$	−0.322140	−	1.82694i	−0.0155712	−	0.0883087i
$429$	−0.276182	−	0.444814i	−0.0133342	−	0.0214758i
$430$		0			0
$431$	−22.4604			−1.08188			−0.540939	−	0.841062i	$-0.681931\pi$
$431$	−22.4604			−1.08188			−0.540939	+	0.841062i	$0.681931\pi$
$432$	−16.6131	+	7.92672i	−0.799296	+	0.381374i
$433$	−9.65028			−0.463763			−0.231882	−	0.972744i	$-0.574488\pi$
$433$	−9.65028			−0.463763			−0.231882	+	0.972744i	$0.574488\pi$
$434$	−1.58297	−	1.32827i	−0.0759849	−	0.0637589i
$435$		0			0
$436$	0.278648	+	1.58029i	0.0133448	+	0.0756821i
$437$	−10.8717	−	3.95697i	−0.520063	−	0.189287i
$438$	−4.10704	+	28.6278i	−0.196242	+	1.36789i
$439$	5.34208	−	30.2964i	0.254963	−	1.44597i	−0.541203	−	0.840892i	$-0.682031\pi$
$439$	5.34208	−	30.2964i	0.254963	−	1.44597i	0.796167	−	0.605077i	$-0.206858\pi$
$440$		0			0
$441$	−4.87856	−	20.0557i	−0.232312	−	0.955031i
$442$	−0.675098	−	1.16930i	−0.0321111	−	0.0556181i
$443$	−16.0557	+	5.84380i	−0.762830	+	0.277647i	−0.693994	−	0.719981i	$-0.744151\pi$
$443$	−16.0557	+	5.84380i	−0.762830	+	0.277647i	−0.0688358	+	0.997628i	$0.521928\pi$
$444$	−0.184223	−	0.879077i	−0.00874284	−	0.0417192i
$445$		0			0
$446$	19.7240	−	16.5504i	0.933958	−	0.783684i
$447$	−5.89985	−	28.1530i	−0.279053	−	1.33159i
$448$	−2.81329	+	1.02395i	−0.132915	+	0.0483773i
$449$	−3.63246	−	6.29160i	−0.171426	−	0.296919i	0.767492	−	0.641058i	$-0.221504\pi$
$449$	−3.63246	−	6.29160i	−0.171426	−	0.296919i	−0.938919	+	0.344139i	$0.888171\pi$
$450$		0			0
$451$	−0.456427	+	0.790555i	−0.0214923	+	0.0372258i
$452$	−0.148783	+	0.843788i	−0.00699814	+	0.0396884i
$453$	−2.29112	+	15.9701i	−0.107646	+	0.750340i
$454$	−19.4389	−	7.07519i	−0.912314	−	0.332055i
$455$		0			0
$456$	−19.1596	+	0.614118i	−0.897231	+	0.0287587i
$457$	−7.64333	−	6.41352i	−0.357540	−	0.300012i	0.446269	−	0.894899i	$-0.352752\pi$
$457$	−7.64333	−	6.41352i	−0.357540	−	0.300012i	−0.803809	+	0.594887i	$0.797197\pi$
$458$	−15.7490			−0.735901
$459$	−4.04936	−	5.67540i	−0.189008	−	0.264905i
$460$		0			0
$461$	4.66867	+	3.91748i	0.217441	+	0.182455i	0.745002	−	0.667063i	$-0.232449\pi$
$461$	4.66867	+	3.91748i	0.217441	+	0.182455i	−0.527560	+	0.849518i	$0.676893\pi$
$462$	0.170324	+	0.274321i	0.00792419	+	0.0127626i
$463$	−4.40269	−	24.9689i	−0.204611	−	1.16040i	−0.898051	−	0.439891i	$-0.855017\pi$
$463$	−4.40269	−	24.9689i	−0.204611	−	1.16040i	0.693441	−	0.720514i	$-0.256094\pi$
$464$	16.4735	+	5.99586i	0.764762	+	0.278351i
$465$		0			0
$466$	−3.75791	+	21.3121i	−0.174082	+	0.987266i
$467$	−13.8113	+	23.9220i	−0.639113	+	1.10698i	0.346515	+	0.938044i	$0.387365\pi$
$467$	−13.8113	+	23.9220i	−0.639113	+	1.10698i	−0.985628	+	0.168932i	$0.945968\pi$
$468$	0.0515146	−	0.464511i	0.00238126	−	0.0214720i
$469$	2.12478	+	3.68023i	0.0981134	+	0.169937i
$470$		0			0
$471$	−19.8292	+	17.7517i	−0.913683	+	0.817957i
$472$	30.7299	−	25.7854i	1.41446	−	1.18687i
$473$	2.63387	−	2.21008i	0.121105	−	0.101619i
$474$	26.2112	+	8.59964i	1.20392	+	0.394995i
$475$		0			0
$476$	−0.0481385	−	0.0833784i	−0.00220643	−	0.00382164i
$477$	−16.8943	−	25.3591i	−0.773538	−	1.16111i
$478$	14.4230	−	24.9813i	0.659692	−	1.14262i
$479$	−4.94905	+	28.0675i	−0.226128	+	1.28244i	0.634389	+	0.773014i	$0.281252\pi$
$479$	−4.94905	+	28.0675i	−0.226128	+	1.28244i	−0.860517	+	0.509422i	$0.829859\pi$
$480$		0			0
$481$	−1.76684	−	0.643079i	−0.0805611	−	0.0293219i
$482$	1.02170	+	5.79437i	0.0465374	+	0.263926i
$483$	−0.874323	+	1.63306i	−0.0397831	+	0.0743068i
$484$	1.72096	+	1.44406i	0.0782254	+	0.0656389i
$485$		0			0
$486$	−0.298959	+	20.8696i	−0.0135611	+	0.946666i
$487$	−24.3015			−1.10121			−0.550603	−	0.834767i	$-0.685602\pi$
$487$	−24.3015			−1.10121			−0.550603	+	0.834767i	$0.685602\pi$
$488$	−30.2038	−	25.3440i	−1.36726	−	1.14727i
$489$	−3.50272	+	6.54237i	−0.158398	+	0.295856i
$490$		0			0
$491$	14.9080	+	5.42607i	0.672789	+	0.244875i	0.655748	−	0.754980i	$-0.272353\pi$
$491$	14.9080	+	5.42607i	0.672789	+	0.244875i	0.0170405	+	0.999855i	$0.494576\pi$
$492$	−0.756372	+	0.303076i	−0.0340999	+	0.0136637i
$493$	−1.15301	+	6.53904i	−0.0519289	+	0.294504i
$494$	−1.88422	+	3.26357i	−0.0847753	+	0.146835i
$495$		0			0
$496$	−7.89666	−	13.6774i	−0.354571	−	0.614134i
$497$	−0.744578	+	0.271004i	−0.0333989	+	0.0121562i
$498$	10.6942	+	3.50867i	0.479219	+	0.157227i
$499$	26.8594	−	22.5377i	1.20239	−	1.00893i	0.202835	−	0.979213i	$-0.434985\pi$
$499$	26.8594	−	22.5377i	1.20239	−	1.00893i	0.999558	−	0.0297149i	$-0.00945993\pi$
$500$		0			0
$501$	−16.8779	+	15.1096i	−0.754048	+	0.675046i
$502$	7.52305	−	2.73817i	0.335770	−	0.122210i
$503$	−3.62507	−	6.27881i	−0.161634	−	0.279958i	0.773821	−	0.633405i	$-0.218343\pi$
$503$	−3.62507	−	6.27881i	−0.161634	−	0.279958i	−0.935455	+	0.353446i	$0.885010\pi$
$504$	−0.338306	+	3.05053i	−0.0150694	+	0.135881i
$505$		0			0
$506$	−0.288904	+	1.63845i	−0.0128433	+	0.0728382i
$507$	16.9343	+	13.3089i	0.752081	+	0.591067i
$508$	0.441292	+	0.160617i	0.0195791	+	0.00712623i
$509$	−6.17449	−	35.0173i	−0.273679	−	1.55211i	−0.743126	−	0.669152i	$-0.766657\pi$
$509$	−6.17449	−	35.0173i	−0.273679	−	1.55211i	0.469446	−	0.882961i	$-0.344454\pi$
$510$		0			0
$511$	3.30707	+	2.77496i	0.146296	+	0.122757i
$512$	−25.0751			−1.10817
$513$	−8.06712	+	17.7079i	−0.356172	+	0.781822i
$514$	23.5903			1.04052
$515$		0			0
$516$	3.06749	−	0.0983216i	0.135039	−	0.00432837i
$517$	−0.859349	−	4.87361i	−0.0377941	−	0.214341i
$518$	1.08963	+	0.396592i	0.0478755	+	0.0174253i
$519$	0.269987	−	1.88192i	0.0118511	−	0.0826073i
$520$		0			0
$521$	−19.0101	+	32.9265i	−0.832849	+	1.44254i	0.0629204	+	0.998019i	$0.479959\pi$
$521$	−19.0101	+	32.9265i	−0.832849	+	1.44254i	−0.895770	+	0.444519i	$0.853375\pi$
$522$	14.3778	−	13.7262i	0.629301	−	0.600779i
$523$	−8.03916	−	13.9242i	−0.351528	−	0.608864i	0.634990	−	0.772521i	$-0.281004\pi$
$523$	−8.03916	−	13.9242i	−0.351528	−	0.608864i	−0.986517	+	0.163657i	$0.947671\pi$
$524$	−0.0566611	+	0.0206230i	−0.00247525	+	0.000900918i
$525$		0			0
$526$	−4.15805	+	3.48902i	−0.181300	+	0.152128i
$527$	4.58237	−	3.84507i	0.199611	−	0.167494i
$528$	0.506177	+	2.41538i	0.0220285	+	0.105116i
$529$	12.6441	−	4.60207i	0.549743	−	0.200090i
$530$		0			0
$531$	−9.62467	−	39.5669i	−0.417675	−	1.71706i
$532$	−0.134356	+	0.232712i	−0.00582509	+	0.0100894i
$533$	−0.296204	+	1.67986i	−0.0128300	+	0.0727627i
$534$	−0.130026	+	0.906339i	−0.00562680	+	0.0392211i
$535$		0			0
$536$	6.29990	+	35.7285i	0.272114	+	1.54324i
$537$	−29.2830	+	0.938599i	−1.26365	+	0.0405036i
$538$	−13.3671	−	11.2163i	−0.576297	−	0.483570i
$539$	−2.76726			−0.119194
$540$		0			0
$541$	−17.0592			−0.733433			−0.366717	−	0.930333i	$-0.619518\pi$
$541$	−17.0592			−0.733433			−0.366717	+	0.930333i	$0.619518\pi$
$542$	−5.73125	−	4.80909i	−0.246178	−	0.206568i
$543$	1.94752	+	3.13665i	0.0835762	+	0.134606i
$544$	−0.272054	−	1.54290i	−0.0116642	−	0.0661511i
$545$		0			0
$546$	0.474395	+	0.372832i	0.0203022	+	0.0159557i
$547$	−3.24265	+	18.3900i	−0.138646	+	0.786298i	0.833606	+	0.552360i	$0.186273\pi$
$547$	−3.24265	+	18.3900i	−0.138646	+	0.786298i	−0.972251	+	0.233938i	$0.924839\pi$
$548$	1.00191	−	1.73536i	0.0427994	−	0.0741308i
$549$	−36.6560	+	16.0693i	−1.56444	+	0.685820i
$550$		0			0
$551$	17.4146	−	6.33841i	0.741888	−	0.270025i
$552$	−11.7826	+	10.5481i	−0.501499	+	0.448957i
$553$	3.15442	−	2.64687i	0.134140	−	0.112556i
$554$	−19.7135	+	16.5416i	−0.837547	+	0.702786i
$555$		0			0
$556$	0.579083	−	0.210769i	0.0245586	−	0.00893860i
$557$	2.69508	+	4.66802i	0.114194	+	0.197790i	0.917457	−	0.397834i	$-0.130238\pi$
$557$	2.69508	+	4.66802i	0.114194	+	0.197790i	−0.803263	+	0.595624i	$0.796905\pi$
$558$	−17.8711	+	1.14682i	−0.756545	+	0.0485486i
$559$	3.21240	−	5.56403i	0.135870	−	0.235334i
$560$		0			0
$561$	−0.867657	+	0.347668i	−0.0366325	+	0.0146786i
$562$	14.6396	+	5.32840i	0.617536	+	0.224765i
$563$	0.149078	+	0.845464i	0.00628289	+	0.0356321i	0.987788	−	0.155804i	$-0.0497967\pi$
$563$	0.149078	+	0.845464i	0.00628289	+	0.0356321i	−0.981505	+	0.191436i	$0.938686\pi$
$564$	2.08501	−	3.89438i	0.0877947	−	0.163983i
$565$		0			0
$566$	37.7123			1.58517
$567$	2.62306	+	1.68117i	0.110158	+	0.0706025i
$568$	−6.76462			−0.283837
$569$	22.5944	+	18.9589i	0.947206	+	0.794800i	0.978825	−	0.204700i	$-0.0656218\pi$
$569$	22.5944	+	18.9589i	0.947206	+	0.794800i	−0.0316187	+	0.999500i	$0.510066\pi$
$570$		0			0
$571$	2.15888	+	12.2436i	0.0903464	+	0.512380i	0.996074	+	0.0885205i	$0.0282139\pi$
$571$	2.15888	+	12.2436i	0.0903464	+	0.512380i	−0.905728	+	0.423860i	$0.860675\pi$
$572$	−0.0588798	−	0.0214305i	−0.00246189	−	0.000896054i
$573$	21.6871	−	8.68995i	0.905990	−	0.363028i
$574$	0.182672	−	1.03598i	0.00762458	−	0.0432411i
$575$		0			0
$576$	−11.5070	+	23.2537i	−0.479458	+	0.968905i
$577$	−16.7199	−	28.9597i	−0.696057	−	1.20561i	−0.969823	−	0.243810i	$-0.921603\pi$
$577$	−16.7199	−	28.9597i	−0.696057	−	1.20561i	0.273766	−	0.961796i	$-0.411731\pi$
$578$	19.1240	−	6.96055i	0.795452	−	0.289521i
$579$	−15.4723	−	5.07630i	−0.643006	−	0.210964i
$580$		0			0
$581$	1.28701	−	1.07993i	0.0533941	−	0.0448030i
$582$	25.6212	−	22.9368i	1.06203	−	0.950762i
$583$	−3.83891	+	1.39725i	−0.158991	+	0.0578681i
$584$	18.4280	+	31.9182i	0.762556	+	1.32079i
$585$		0			0
$586$	−0.0556406	+	0.0963723i	−0.00229849	+	0.00398110i
$587$	3.81058	−	21.6109i	0.157280	−	0.891977i	−0.799392	−	0.600809i	$-0.794845\pi$
$587$	3.81058	−	21.6109i	0.157280	−	0.891977i	0.956672	−	0.291168i	$-0.0940437\pi$
$588$	−1.94211	−	1.52633i	−0.0800914	−	0.0629446i
$589$	−15.6887	−	5.71024i	−0.646444	−	0.235286i
$590$		0			0
$591$	−7.71840	−	12.4311i	−0.317493	−	0.511348i
$592$	6.78894	+	5.69660i	0.279024	+	0.234129i
$593$	−11.2798			−0.463205			−0.231602	−	0.972811i	$-0.574397\pi$
$593$	−11.2798			−0.463205			−0.231602	+	0.972811i	$0.574397\pi$
$594$	2.70923	+	0.700273i	0.111161	+	0.0287325i
$595$		0			0
$596$	−2.63699	−	2.21270i	−0.108015	−	0.0906356i
$597$	−23.4495	+	0.751622i	−0.959726	+	0.0307618i
$598$	0.539850	+	3.06164i	0.0220761	+	0.125200i
$599$	−5.06912	−	1.84501i	−0.207119	−	0.0753850i	0.236378	−	0.971661i	$-0.424040\pi$
$599$	−5.06912	−	1.84501i	−0.207119	−	0.0753850i	−0.443496	+	0.896276i	$0.646262\pi$
$600$		0			0
$601$	1.30738	−	7.41452i	0.0533291	−	0.302445i	−0.946463	−	0.322811i	$-0.895372\pi$
$601$	1.30738	−	7.41452i	0.0533291	−	0.302445i	0.999793	+	0.0203664i	$0.00648328\pi$
$602$	−1.98111	+	3.43139i	−0.0807441	+	0.139853i
$603$	35.3420	+	10.3537i	1.43924	+	0.421634i
$604$	0.965381	+	1.67209i	0.0392808	+	0.0680363i
$605$		0			0
$606$	6.35711	+	30.3349i	0.258240	+	1.23227i
$607$	16.5993	−	13.9285i	0.673745	−	0.565339i	−0.240427	−	0.970667i	$-0.577287\pi$
$607$	16.5993	−	13.9285i	0.673745	−	0.565339i	0.914171	+	0.405329i	$0.132843\pi$
$608$	−3.34969	+	2.81073i	−0.135848	+	0.113990i
$609$	−0.608601	−	2.90413i	−0.0246618	−	0.117681i
$610$		0			0
$611$	−4.62369	−	8.00847i	−0.187055	−	0.323988i
$612$	−0.800699	−	0.234570i	−0.0323663	−	0.00948193i
$613$	−18.7168	+	32.4185i	−0.755965	+	1.30937i	0.188928	+	0.981991i	$0.439499\pi$
$613$	−18.7168	+	32.4185i	−0.755965	+	1.30937i	−0.944893	+	0.327379i	$0.893835\pi$
$614$	3.74861	−	21.2594i	0.151281	−	0.857960i
$615$		0			0
$616$	0.386675	+	0.140738i	0.0155796	+	0.00567050i
$617$	6.46292	+	36.6531i	0.260187	+	1.47560i	0.782397	+	0.622780i	$0.213997\pi$
$617$	6.46292	+	36.6531i	0.260187	+	1.47560i	−0.522210	+	0.852817i	$0.674892\pi$
$618$	−16.6882	+	0.534901i	−0.671296	+	0.0215169i
$619$	−7.26024	−	6.09206i	−0.291814	−	0.244861i	0.485114	−	0.874451i	$-0.338778\pi$
$619$	−7.26024	−	6.09206i	−0.291814	−	0.244861i	−0.776927	+	0.629591i	$0.783223\pi$
$620$		0			0
$621$	4.29203	+	15.4686i	0.172233	+	0.620735i
$622$	45.1414			1.81000
$623$	0.104700	+	0.0878537i	0.00419472	+	0.00351979i
$624$	2.43249	+	3.91772i	0.0973774	+	0.156834i
$625$		0			0
$626$	−31.3990	−	11.4283i	−1.25496	−	0.456766i
$627$	2.05119	+	1.61205i	0.0819164	+	0.0643789i
$628$	−0.553074	+	3.13664i	−0.0220701	+	0.125166i
$629$	−1.67834	+	2.90698i	−0.0669199	+	0.115909i
$630$		0			0
$631$	9.32426	+	16.1501i	0.371193	+	0.642925i	0.989749	−	0.142815i	$-0.0456155\pi$
$631$	9.32426	+	16.1501i	0.371193	+	0.642925i	−0.618556	+	0.785740i	$0.712282\pi$
$632$	33.0347	−	12.0236i	1.31405	−	0.478275i
$633$	−14.3972	+	12.8888i	−0.572238	+	0.512285i
$634$	−16.0978	+	13.5077i	−0.639327	+	0.536459i
$635$		0			0
$636$	−3.46489	−	1.13679i	−0.137392	−	0.0450768i
$637$	−4.85910	+	1.76857i	−0.192524	+	0.0700732i
$638$	−1.33251	−	2.30798i	−0.0527546	−	0.0913737i
$639$	−3.04549	+	6.15444i	−0.120478	+	0.243466i
$640$		0			0
$641$	−4.29405	+	24.3528i	−0.169605	+	0.961876i	0.774584	+	0.632471i	$0.217959\pi$
$641$	−4.29405	+	24.3528i	−0.169605	+	0.961876i	−0.944189	+	0.329405i	$0.893152\pi$
$642$	19.2663	−	7.71997i	0.760381	−	0.304683i
$643$	7.44549	+	2.70994i	0.293622	+	0.106870i	0.484631	−	0.874719i	$-0.338954\pi$
$643$	7.44549	+	2.70994i	0.293622	+	0.106870i	−0.191009	+	0.981588i	$0.561176\pi$
$644$	0.0384945	+	0.218313i	0.00151690	+	0.00860274i
$645$		0			0
$646$	5.15365	+	4.32443i	0.202768	+	0.170142i
$647$	−3.79376			−0.149148			−0.0745741	−	0.997215i	$-0.523760\pi$
$647$	−3.79376			−0.149148			−0.0745741	+	0.997215i	$0.523760\pi$
$648$	16.1344	+	21.1461i	0.633818	+	0.830698i
$649$	−5.45940			−0.214300
$650$		0			0
$651$	−1.26172	+	2.35664i	−0.0494508	+	0.0923641i
$652$	0.154217	+	0.874607i	0.00603959	+	0.0342522i
$653$	13.8907	+	5.05580i	0.543585	+	0.197849i	0.599194	−	0.800604i	$-0.295488\pi$
$653$	13.8907	+	5.05580i	0.543585	+	0.197849i	−0.0556090	+	0.998453i	$0.517710\pi$
$654$	−16.6652	+	6.67770i	−0.651661	+	0.261119i
$655$		0			0
$656$	4.02001	−	6.96286i	0.156955	−	0.271854i
$657$	37.3356	−	2.39588i	1.45660	−	0.0934722i
$658$	2.85147	+	4.93889i	0.111162	+	0.192538i
$659$	−38.5064	+	14.0152i	−1.49999	+	0.545953i	−0.956059	−	0.293174i	$-0.905289\pi$
$659$	−38.5064	+	14.0152i	−1.49999	+	0.545953i	−0.543935	+	0.839127i	$0.683066\pi$
$660$		0			0
$661$	12.0162	−	10.0828i	0.467375	−	0.392174i	−0.378461	−	0.925617i	$-0.623547\pi$
$661$	12.0162	−	10.0828i	0.467375	−	0.392174i	0.845836	+	0.533443i	$0.179102\pi$
$662$	31.0185	−	26.0276i	1.20557	−	1.01159i
$663$	−1.30134	+	1.16500i	−0.0505400	+	0.0452449i
$664$	13.4782	−	4.90566i	0.523055	−	0.190377i
$665$		0			0
$666$	9.20340	−	4.03459i	0.356624	−	0.156337i
$667$	7.64431	−	13.2403i	0.295989	−	0.512668i
$668$	−0.470755	+	2.66978i	−0.0182141	+	0.103297i
$669$	−26.1880	−	20.5814i	−1.01249	−	0.795723i
$670$		0			0
$671$	0.931786	+	5.28442i	0.0359712	+	0.204003i
$672$	0.369304	+	0.594794i	0.0142462	+	0.0229447i
$673$	18.3294	+	15.3802i	0.706545	+	0.592861i	0.923627	−	0.383292i	$-0.125210\pi$
$673$	18.3294	+	15.3802i	0.706545	+	0.592861i	−0.217083	+	0.976153i	$0.569654\pi$
$674$	−9.23400			−0.355681
$675$		0			0
$676$	2.57756			0.0991369
$677$	−19.5799	−	16.4295i	−0.752518	−	0.631437i	0.183650	−	0.982992i	$-0.441209\pi$
$677$	−19.5799	−	16.4295i	−0.752518	−	0.631437i	−0.936167	+	0.351554i	$0.885653\pi$
$678$	−9.58115	+	0.307102i	−0.367962	+	0.0117942i
$679$	−0.891367	−	5.05520i	−0.0342075	−	0.194001i
$680$		0			0
$681$	−3.80021	+	26.4891i	−0.145625	+	1.01506i
$682$	−0.416913	+	2.36443i	−0.0159644	+	0.0905386i
$683$	−21.6297	+	37.4638i	−0.827639	+	1.43351i	0.0722470	+	0.997387i	$0.476983\pi$
$683$	−21.6297	+	37.4638i	−0.827639	+	1.43351i	−0.899886	+	0.436126i	$0.856350\pi$
$684$	0.550410	+	2.26273i	0.0210454	+	0.0865175i
$685$		0			0
$686$	6.04549	−	2.20038i	0.230818	−	0.0840109i
$687$	4.17869	+	19.9399i	0.159427	+	0.760756i
$688$	−23.1979	+	19.4654i	−0.884412	+	0.742110i
$689$	−5.84784	+	4.90692i	−0.222785	+	0.186939i
$690$		0			0
$691$	−42.4251	+	15.4415i	−1.61393	+	0.587422i	−0.982211	−	0.187778i	$-0.939871\pi$
$691$	−42.4251	+	15.4415i	−1.61393	+	0.587422i	−0.631716	+	0.775200i	$0.717649\pi$
$692$	−0.113761	−	0.197040i	−0.00432454	−	0.00749033i
$693$	0.302128	−	0.288435i	0.0114769	−	0.0109567i
$694$	−23.7430	+	41.1240i	−0.901270	+	1.56105i
$695$		0			0
$696$	3.59737	−	25.0751i	0.136358	−	0.950471i
$697$	2.86158	+	1.04153i	0.108390	+	0.0394507i
$698$	5.68617	+	32.2479i	0.215225	+	1.22060i
$699$	27.9806	−	0.896855i	1.05832	−	0.0339222i
$700$		0			0
$701$	−52.1690			−1.97039			−0.985197	−	0.171425i	$-0.945163\pi$
$701$	−52.1690			−1.97039			−0.985197	+	0.171425i	$0.945163\pi$
$702$	5.20475	−	0.501854i	0.196441	−	0.0189413i
$703$	9.36864			0.353345
$704$	2.66464	+	2.23590i	0.100428	+	0.0842687i
$705$		0			0
$706$	2.15696	+	12.2327i	0.0811782	+	0.460384i
$707$	4.34750	+	1.58236i	0.163505	+	0.0595108i
$708$	−3.83150	−	3.01122i	−0.143997	−	0.113168i
$709$	0.837721	−	4.75095i	0.0314613	−	0.178426i	−0.965028	−	0.262147i	$-0.915569\pi$
$709$	0.837721	−	4.75095i	0.0314613	−	0.178426i	0.996489	+	0.0837213i	$0.0266805\pi$
$710$		0			0
$711$	3.93343	−	35.4681i	0.147515	−	1.33016i
$712$	0.583420	+	1.01051i	0.0218646	+	0.0378706i
$713$	−12.9428	+	4.71079i	−0.484711	+	0.176421i
$714$	0.802550	−	0.718467i	0.0300347	−	0.0268879i
$715$		0			0
$716$	−2.68590	+	2.25374i	−0.100377	+	0.0842261i
$717$	−35.4560	−	11.6328i	−1.32413	−	0.434433i
$718$	8.99108	−	3.27249i	0.335544	−	0.122128i
$719$	−4.65459	−	8.06199i	−0.173587	−	0.300662i	0.766084	−	0.642740i	$-0.222202\pi$
$719$	−4.65459	−	8.06199i	−0.173587	−	0.300662i	−0.939671	+	0.342078i	$0.888869\pi$
$720$		0			0
$721$	−1.24618	+	2.15844i	−0.0464100	+	0.0803846i
$722$	−1.15694	+	6.56131i	−0.0430567	+	0.244187i
$723$	7.06522	−	2.83102i	0.262758	−	0.105287i
$724$	0.415197	+	0.151119i	0.0154307	+	0.00561630i
$725$		0			0
$726$	−11.8636	+	22.1588i	−0.440299	+	0.822390i
$727$	−5.03265	−	4.22289i	−0.186651	−	0.156618i	0.544674	−	0.838648i	$-0.316653\pi$
$727$	−5.03265	−	4.22289i	−0.186651	−	0.156618i	−0.731325	+	0.682029i	$0.761098\pi$
$728$	0.768918			0.0284980
$729$	26.5026	−	5.15885i	0.981577	−	0.191068i
$730$		0			0
$731$	−8.78641	−	7.37268i	−0.324977	−	0.272688i
$732$	−2.26076	+	4.22264i	−0.0835601	+	0.156073i
$733$	2.62552	+	14.8900i	0.0969756	+	0.549976i	0.994124	+	0.108247i	$0.0345237\pi$
$733$	2.62552	+	14.8900i	0.0969756	+	0.549976i	−0.897148	+	0.441729i	$0.854365\pi$
$734$	14.4980	+	5.27684i	0.535131	+	0.194772i
$735$		0			0
$736$	−0.626414	+	3.55257i	−0.0230899	+	0.130949i
$737$	2.46872	−	4.27594i	0.0909364	−	0.157506i
$738$	−5.05449	−	7.58700i	−0.186058	−	0.279281i
$739$	19.1802	+	33.2210i	0.705554	+	1.22206i	0.966491	+	0.256700i	$0.0826351\pi$
$739$	19.1802	+	33.2210i	0.705554	+	1.22206i	−0.260937	+	0.965356i	$0.584032\pi$
$740$		0			0
$741$	4.63199	+	1.51971i	0.170160	+	0.0558279i
$742$	3.60641	−	3.02614i	0.132396	−	0.111093i
$743$	19.6038	−	16.4495i	0.719192	−	0.603474i	−0.207970	−	0.978135i	$-0.566686\pi$
$743$	19.6038	−	16.4495i	0.719192	−	0.603474i	0.927162	+	0.374661i	$0.122241\pi$
$744$	−17.0032	+	15.2218i	−0.623369	+	0.558059i
$745$		0			0
$746$	20.6869	+	35.8308i	0.757403	+	1.31186i
$747$	1.60485	−	14.4710i	0.0587183	−	0.529467i
$748$	−0.0559306	+	0.0968746i	−0.00204502	+	0.00354209i
$749$	0.537998	−	3.05114i	0.0196580	−	0.111486i
$750$		0			0
$751$	40.5586	+	14.7621i	1.48000	+	0.538677i	0.950797	−	0.309816i	$-0.100267\pi$
$751$	40.5586	+	14.7621i	1.48000	+	0.538677i	0.529207	+	0.848493i	$0.322490\pi$
$752$	7.56876	+	42.9246i	0.276004	+	1.56530i
$753$	−5.46292	−	8.79849i	−0.199080	−	0.320635i
$754$	−3.81482	−	3.20102i	−0.138928	−	0.116574i
$755$		0			0
$756$	0.371130	−	0.0357852i	0.0134978	−	0.00130150i
$757$	−40.4910			−1.47167			−0.735835	−	0.677161i	$-0.763210\pi$
$757$	−40.4910			−1.47167			−0.735835	+	0.677161i	$0.763210\pi$
$758$	−2.92023	−	2.45037i	−0.106068	−	0.0890013i
$759$	2.15112	−	0.0689492i	0.0780807	−	0.00250270i
$760$		0			0
$761$	−10.7121	−	3.89889i	−0.388314	−	0.141335i	0.140483	−	0.990083i	$-0.455134\pi$
$761$	−10.7121	−	3.89889i	−0.388314	−	0.141335i	−0.528797	+	0.848748i	$0.677357\pi$
$762$	−0.746132	+	5.20085i	−0.0270295	+	0.188407i
$763$	−0.465364	+	2.63921i	−0.0168473	+	0.0955457i
$764$	1.39798	−	2.42138i	0.0505772	−	0.0876023i
$765$		0			0
$766$	−23.4605	−	40.6348i	−0.847662	−	1.46819i
$767$	−9.58628	+	3.48912i	−0.346141	+	0.125985i
$768$	1.74768	+	8.33958i	0.0630638	+	0.300929i
$769$	−5.73459	+	4.81189i	−0.206795	+	0.173521i	−0.740303	−	0.672274i	$-0.765318\pi$
$769$	−5.73459	+	4.81189i	−0.206795	+	0.173521i	0.533508	+	0.845795i	$0.320873\pi$
$770$		0			0
$771$	−6.25925	−	29.8680i	−0.225421	−	1.07567i
$772$	−1.83121	+	0.666505i	−0.0659066	+	0.0239880i
$773$	2.29721	+	3.97889i	0.0826250	+	0.143111i	0.904377	−	0.426735i	$-0.140336\pi$
$773$	2.29721	+	3.97889i	0.0826250	+	0.143111i	−0.821752	+	0.569846i	$0.807003\pi$
$774$	8.11590	+	33.3643i	0.291720	+	1.19926i
$775$		0			0

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02568 + 0.860644i) q^{2} +(0.817526 - 1.52697i) q^{3} +(-0.0359939 - 0.204131i) q^{4} +(2.15270 - 0.862581i) q^{6} +(0.0601126 - 0.340915i) q^{7} +(1.47769 - 2.55944i) q^{8} +(-1.66330 - 2.49668i) q^{9} +O(q^{10})\)	\(q+(1.02568 + 0.860644i) q^{2} +(0.817526 - 1.52697i) q^{3} +(-0.0359939 - 0.204131i) q^{4} +(2.15270 - 0.862581i) q^{6} +(0.0601126 - 0.340915i) q^{7} +(1.47769 - 2.55944i) q^{8} +(-1.66330 - 2.49668i) q^{9} +(-0.377953 + 0.137564i) q^{11} +(-0.341129 - 0.111921i) q^{12} +(-0.575738 + 0.483102i) q^{13} +(0.355063 - 0.297933i) q^{14} +(3.32884 - 1.21160i) q^{16} +(0.670872 + 1.16198i) q^{17} +(0.442749 - 3.99230i) q^{18} +(1.87243 - 3.24314i) q^{19} +(-0.471425 - 0.370498i) q^{21} +(-0.506050 - 0.184187i) q^{22} +(-0.536470 - 3.04247i) q^{23} +(-2.70014 - 4.34880i) q^{24} -1.00630 q^{26} +(-5.17216 + 0.498713i) q^{27} -0.0717552 q^{28} +(3.79094 + 3.18098i) q^{29} +(-0.774172 - 4.39054i) q^{31} +(-1.09724 - 0.399363i) q^{32} +(-0.0989303 + 0.689586i) q^{33} +(-0.311958 + 1.76920i) q^{34} +(-0.449783 + 0.429397i) q^{36} +(1.25087 + 2.16657i) q^{37} +(4.71170 - 1.71492i) q^{38} +(0.267003 + 1.27409i) q^{39} +(1.73862 - 1.45887i) q^{41} +(-0.164663 - 0.785740i) q^{42} +(-8.03293 + 2.92375i) q^{43} +(0.0416850 + 0.0722005i) q^{44} +(2.06824 - 3.58230i) q^{46} +(-2.13658 + 12.1171i) q^{47} +(0.871334 - 6.07356i) q^{48} +(6.46524 + 2.35315i) q^{49} +(2.32278 - 0.0744513i) q^{51} +(0.119339 + 0.100137i) q^{52} +10.1571 q^{53} +(-5.73418 - 3.93988i) q^{54} +(-0.783723 - 0.657622i) q^{56} +(-3.42144 - 5.51051i) q^{57} +(1.15059 + 6.52530i) q^{58} +(12.7550 + 4.64243i) q^{59} +(2.31667 - 13.1385i) q^{61} +(2.98465 - 5.16956i) q^{62} +(-0.951143 + 0.416963i) q^{63} +(-4.32418 - 7.48970i) q^{64} +(-0.694958 + 0.622148i) q^{66} +(-9.40381 + 7.89073i) q^{67} +(0.213050 - 0.178770i) q^{68} +(-5.08436 - 1.66813i) q^{69} +(-1.14446 - 1.98226i) q^{71} +(-8.84795 + 0.567785i) q^{72} +(-6.23540 + 10.8000i) q^{73} +(-0.581658 + 3.29875i) q^{74} +(-0.729423 - 0.265488i) q^{76} +(0.0241778 + 0.137119i) q^{77} +(-0.822676 + 1.53659i) q^{78} +(9.11223 + 7.64607i) q^{79} +(-3.46686 + 8.30547i) q^{81} +3.03883 q^{82} +(3.71780 + 3.11961i) q^{83} +(-0.0586617 + 0.109568i) q^{84} +(-10.7555 - 3.91468i) q^{86} +(7.95646 - 3.18814i) q^{87} +(-0.206412 + 1.17062i) q^{88} +(-0.197409 + 0.341923i) q^{89} +(0.130088 + 0.225318i) q^{91} +(-0.601754 + 0.219021i) q^{92} +(-7.33715 - 2.40725i) q^{93} +(-12.6200 + 10.5894i) q^{94} +(-1.50684 + 1.34897i) q^{96} +(13.9340 - 5.07158i) q^{97} +(4.60601 + 7.97784i) q^{98} +(0.972102 + 0.714819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9 + 15 * q^11 - 18 * q^12 + 15 * q^14 + 18 * q^16 - 30 * q^17 + 12 * q^18 + 12 * q^19 + 12 * q^21 + 45 * q^22 - 36 * q^23 - 39 * q^24 + 6 * q^26 - 51 * q^27 + 36 * q^28 - 15 * q^29 + 3 * q^31 - 27 * q^32 + 3 * q^33 + 30 * q^36 - 6 * q^37 + 12 * q^38 - 15 * q^39 + 39 * q^41 - 48 * q^42 - 12 * q^43 + 51 * q^44 + 9 * q^46 - 30 * q^47 + 132 * q^48 - 6 * q^49 - 9 * q^52 + 24 * q^53 + 75 * q^54 + 144 * q^56 - 33 * q^57 - 27 * q^58 + 45 * q^59 - 54 * q^61 - 66 * q^62 + 120 * q^63 - 24 * q^64 + 48 * q^66 - 9 * q^67 + 69 * q^68 + 51 * q^69 - 15 * q^71 - 9 * q^72 + 15 * q^73 + 96 * q^74 - 48 * q^76 + 36 * q^77 + 18 * q^78 + 48 * q^79 - 54 * q^81 + 36 * q^82 - 30 * q^83 + 57 * q^84 - 111 * q^86 + 33 * q^87 - 36 * q^88 - 12 * q^89 + 9 * q^91 + 219 * q^92 - 63 * q^93 + 36 * q^94 - 249 * q^96 - 57 * q^97 - 75 * q^98 - 48 * q^99

Introduction

L-functions

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