LMFDB - Embedded newform 1071.2.i.g.613.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1071,2,Mod(613,1071)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1071, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("1071.613");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1071 = 3^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1071.i (of order $3$, 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:	$8.55197805648$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.5743021975227.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 2x^{8} + 10x^{7} - 8x^{6} - 12x^{5} - 24x^{4} + 90x^{3} + 54x^{2} - 324x + 243 $ x^10 - 4x^9 + 2x^8 + 10x^7 - 8x^6 - 12x^5 - 24x^4 + 90x^3 + 54x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 357)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			613.1
Root			$1.66532 + 0.476133i$ of defining polynomial
Character	$\chi$	$=$	1071.613
Dual form			1071.2.i.g.919.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24500 - 2.15641i) q^{2} +(-2.10007 + 3.63743i) q^{4} +(-1.16532 - 2.01840i) q^{5} +(-1.62628 + 2.08692i) q^{7} +5.47838 q^{8} +O(q^{10})$	\(q+(-1.24500 - 2.15641i) q^{2} +(-2.10007 + 3.63743i) q^{4} +(-1.16532 - 2.01840i) q^{5} +(-1.62628 + 2.08692i) q^{7} +5.47838 q^{8} +(-2.90166 + 5.02583i) q^{10} +(-2.57387 + 4.45807i) q^{11} -0.596965 q^{13} +(6.52497 + 0.908700i) q^{14} +(-2.62046 - 4.53877i) q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.946522 - 1.63942i) q^{19} +9.78904 q^{20} +12.8179 q^{22} +(-2.07968 - 3.60212i) q^{23} +(-0.215950 + 0.374037i) q^{25} +(0.743224 + 1.28730i) q^{26} +(-4.17572 - 10.2981i) q^{28} +2.90140 q^{29} +(3.22053 - 5.57813i) q^{31} +(-1.04659 + 1.81275i) q^{32} -2.49001 q^{34} +(6.10736 + 0.850541i) q^{35} +(4.70193 + 8.14397i) q^{37} +(-2.35685 + 4.08218i) q^{38} +(-6.38408 - 11.0575i) q^{40} +2.09319 q^{41} +11.3362 q^{43} +(-10.8106 - 18.7245i) q^{44} +(-5.17843 + 8.96930i) q^{46} +(2.19153 + 3.79584i) q^{47} +(-1.71045 - 6.78781i) q^{49} +1.07544 q^{50} +(1.25367 - 2.17142i) q^{52} +(-5.46554 + 9.46659i) q^{53} +11.9975 q^{55} +(-8.90936 + 11.4329i) q^{56} +(-3.61225 - 6.25660i) q^{58} +(1.60603 - 2.78172i) q^{59} +(-5.29160 - 9.16532i) q^{61} -16.0383 q^{62} -5.26979 q^{64} +(0.695656 + 1.20491i) q^{65} +(7.38448 - 12.7903i) q^{67} +(2.10007 + 3.63743i) q^{68} +(-5.76958 - 14.2289i) q^{70} +6.91028 q^{71} +(-0.217019 + 0.375888i) q^{73} +(11.7078 - 20.2786i) q^{74} +7.95106 q^{76} +(-5.11780 - 12.6215i) q^{77} +(3.07982 + 5.33441i) q^{79} +(-6.10736 + 10.5783i) q^{80} +(-2.60603 - 4.51377i) q^{82} +5.17802 q^{83} -2.33064 q^{85} +(-14.1137 - 24.4456i) q^{86} +(-14.1006 + 24.4230i) q^{88} +(0.197342 + 0.341806i) q^{89} +(0.970830 - 1.24582i) q^{91} +17.4699 q^{92} +(5.45692 - 9.45166i) q^{94} +(-2.20601 + 3.82091i) q^{95} -17.4653 q^{97} +(-12.5078 + 12.1393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7}+O(q^{10}) $ 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7	$ 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7} - 13 q^{10} - 11 q^{11} + 14 q^{13} - 3 q^{14} + 2 q^{16} + 5 q^{17} - 9 q^{19} - 24 q^{20} + 10 q^{22} - 23 q^{23} - 14 q^{25} + 18 q^{26} + 7 q^{28} + 36 q^{29} - 9 q^{31} + 3 q^{32} - 4 q^{34} + 5 q^{35} - 31 q^{40} - 6 q^{41} + 24 q^{43} - 33 q^{44} - 13 q^{46} + 11 q^{47} + 3 q^{49} - 48 q^{50} - 5 q^{52} - 3 q^{53} - 20 q^{55} + 27 q^{56} + 34 q^{58} - 14 q^{59} - 29 q^{61} + 10 q^{62} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 18 q^{70} + 38 q^{71} - 11 q^{73} + 45 q^{74} + 18 q^{76} - 21 q^{77} - q^{79} - 5 q^{80} + 4 q^{82} - 10 q^{83} + 2 q^{85} - 3 q^{86} - 37 q^{88} + 8 q^{89} - 33 q^{91} + 96 q^{92} + 18 q^{94} - 21 q^{95} + 38 q^{97} + 17 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7 - 13 * q^10 - 11 * q^11 + 14 * q^13 - 3 * q^14 + 2 * q^16 + 5 * q^17 - 9 * q^19 - 24 * q^20 + 10 * q^22 - 23 * q^23 - 14 * q^25 + 18 * q^26 + 7 * q^28 + 36 * q^29 - 9 * q^31 + 3 * q^32 - 4 * q^34 + 5 * q^35 - 31 * q^40 - 6 * q^41 + 24 * q^43 - 33 * q^44 - 13 * q^46 + 11 * q^47 + 3 * q^49 - 48 * q^50 - 5 * q^52 - 3 * q^53 - 20 * q^55 + 27 * q^56 + 34 * q^58 - 14 * q^59 - 29 * q^61 + 10 * q^62 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 18 * q^70 + 38 * q^71 - 11 * q^73 + 45 * q^74 + 18 * q^76 - 21 * q^77 - q^79 - 5 * q^80 + 4 * q^82 - 10 * q^83 + 2 * q^85 - 3 * q^86 - 37 * q^88 + 8 * q^89 - 33 * q^91 + 96 * q^92 + 18 * q^94 - 21 * q^95 + 38 * q^97 + 17 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1071\mathbb{Z}\right)^\times$.

$n$	$190$	$596$	$766$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.24500	−	2.15641i	−0.880351	−	1.52481i	−0.850951	−	0.525245i	$-0.823974\pi$
$2$	−1.24500	−	2.15641i	−0.880351	−	1.52481i	−0.0294001	−	0.999568i	$-0.509360\pi$
$3$		0			0
$3$		0			0
$4$	−2.10007	+	3.63743i	−1.05004	+	1.81872i
$5$	−1.16532	−	2.01840i	−0.521148	−	0.902654i	−0.999698	−	0.0245940i	$-0.992171\pi$
$5$	−1.16532	−	2.01840i	−0.521148	−	0.902654i	0.478550	−	0.878060i	$-0.341163\pi$
$6$		0			0
$7$	−1.62628	+	2.08692i	−0.614675	+	0.788781i
$7$	−1.62628	+	2.08692i	−0.614675	+	0.788781i
$8$	5.47838			1.93690
$9$		0			0
$10$	−2.90166	+	5.02583i	−0.917586	+	1.58931i
$11$	−2.57387	+	4.45807i	−0.776050	+	1.34416i	0.158152	+	0.987415i	$0.449446\pi$
$11$	−2.57387	+	4.45807i	−0.776050	+	1.34416i	−0.934202	+	0.356744i	$0.883887\pi$
$12$		0			0
$13$	−0.596965			−0.165568			−0.0827841	−	0.996568i	$-0.526381\pi$
$13$	−0.596965			−0.165568			−0.0827841	+	0.996568i	$0.526381\pi$
$14$	6.52497	+	0.908700i	1.74387	+	0.242860i
$15$		0			0
$16$	−2.62046	−	4.53877i	−0.655115	−	1.13469i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$		0			0
$19$	−0.946522	−	1.63942i	−0.217147	−	0.376110i	0.736788	−	0.676124i	$-0.236342\pi$
$19$	−0.946522	−	1.63942i	−0.217147	−	0.376110i	−0.953935	+	0.300015i	$0.903008\pi$
$20$	9.78904			2.18890
$21$		0			0
$22$	12.8179			2.73279
$23$	−2.07968	−	3.60212i	−0.433644	−	0.751093i	0.563540	−	0.826089i	$-0.309439\pi$
$23$	−2.07968	−	3.60212i	−0.433644	−	0.751093i	−0.997184	+	0.0749957i	$0.976106\pi$
$24$		0			0
$25$	−0.215950	+	0.374037i	−0.0431901	+	0.0748074i
$26$	0.743224	+	1.28730i	0.145758	+	0.252461i
$27$		0			0
$28$	−4.17572	−	10.2981i	−0.789137	−	1.94617i
$29$	2.90140			0.538776			0.269388	−	0.963032i	$-0.413179\pi$
$29$	2.90140			0.538776			0.269388	+	0.963032i	$0.413179\pi$
$30$		0			0
$31$	3.22053	−	5.57813i	0.578425	−	1.00186i	−0.417235	−	0.908799i	$-0.637001\pi$
$31$	3.22053	−	5.57813i	0.578425	−	1.00186i	0.995660	−	0.0930629i	$-0.0296658\pi$
$32$	−1.04659	+	1.81275i	−0.185013	+	0.320453i
$33$		0			0
$34$	−2.49001			−0.427033
$35$	6.10736	+	0.850541i	1.03233	+	0.143768i
$36$		0			0
$37$	4.70193	+	8.14397i	0.772992	+	1.33886i	0.935916	+	0.352222i	$0.114574\pi$
$37$	4.70193	+	8.14397i	0.772992	+	1.33886i	−0.162925	+	0.986639i	$0.552093\pi$
$38$	−2.35685	+	4.08218i	−0.382331	+	0.662217i
$39$		0			0
$40$	−6.38408	−	11.0575i	−1.00941	−	1.74835i
$41$	2.09319			0.326901			0.163451	−	0.986552i	$-0.447738\pi$
$41$	2.09319			0.326901			0.163451	+	0.986552i	$0.447738\pi$
$42$		0			0
$43$	11.3362			1.72876			0.864381	−	0.502838i	$-0.167711\pi$
$43$	11.3362			1.72876			0.864381	+	0.502838i	$0.167711\pi$
$44$	−10.8106	−	18.7245i	−1.62976	−	2.82283i
$45$		0			0
$46$	−5.17843	+	8.96930i	−0.763518	+	1.32245i
$47$	2.19153	+	3.79584i	0.319667	+	0.553679i	0.980419	−	0.196925i	$-0.0630956\pi$
$47$	2.19153	+	3.79584i	0.319667	+	0.553679i	−0.660752	+	0.750605i	$0.729762\pi$
$48$		0			0
$49$	−1.71045	−	6.78781i	−0.244350	−	0.969687i
$50$	1.07544			0.152090
$51$		0			0
$52$	1.25367	−	2.17142i	0.173853	−	0.301122i
$53$	−5.46554	+	9.46659i	−0.750749	+	1.30034i	0.196710	+	0.980462i	$0.436974\pi$
$53$	−5.46554	+	9.46659i	−0.750749	+	1.30034i	−0.947460	+	0.319875i	$0.896359\pi$
$54$		0			0
$55$	11.9975			1.61775
$56$	−8.90936	+	11.4329i	−1.19056	+	1.52779i
$57$		0			0
$58$	−3.61225	−	6.25660i	−0.474312	−	0.821532i
$59$	1.60603	−	2.78172i	0.209087	−	0.362150i	−0.742340	−	0.670023i	$-0.766284\pi$
$59$	1.60603	−	2.78172i	0.209087	−	0.362150i	0.951427	+	0.307874i	$0.0996174\pi$
$60$		0			0
$61$	−5.29160	−	9.16532i	−0.677520	−	1.17350i	−0.975726	−	0.218997i	$-0.929721\pi$
$61$	−5.29160	−	9.16532i	−0.677520	−	1.17350i	0.298206	−	0.954502i	$-0.403612\pi$
$62$	−16.0383			−2.03687
$63$		0			0
$64$	−5.26979			−0.658724
$65$	0.695656	+	1.20491i	0.0862855	+	0.149451i
$66$		0			0
$67$	7.38448	−	12.7903i	0.902158	−	1.56258i	0.0774709	−	0.996995i	$-0.475316\pi$
$67$	7.38448	−	12.7903i	0.902158	−	1.56258i	0.824687	−	0.565589i	$-0.191351\pi$
$68$	2.10007	+	3.63743i	0.254671	+	0.441103i
$69$		0			0
$70$	−5.76958	−	14.2289i	−0.689596	−	1.70068i
$71$	6.91028			0.820099			0.410050	−	0.912063i	$-0.365511\pi$
$71$	6.91028			0.820099			0.410050	+	0.912063i	$0.365511\pi$
$72$		0			0
$73$	−0.217019	+	0.375888i	−0.0254002	+	0.0439944i	−0.878446	−	0.477842i	$-0.841419\pi$
$73$	−0.217019	+	0.375888i	−0.0254002	+	0.0439944i	0.853046	+	0.521836i	$0.174753\pi$
$74$	11.7078	−	20.2786i	1.36101	−	2.35734i
$75$		0			0
$76$	7.95106			0.912049
$77$	−5.11780	−	12.6215i	−0.583228	−	1.43835i
$78$		0			0
$79$	3.07982	+	5.33441i	0.346507	+	0.600168i	0.985626	−	0.168939i	$-0.0540342\pi$
$79$	3.07982	+	5.33441i	0.346507	+	0.600168i	−0.639119	+	0.769108i	$0.720701\pi$
$80$	−6.10736	+	10.5783i	−0.682824	+	1.18269i
$81$		0			0
$82$	−2.60603	−	4.51377i	−0.287788	−	0.498463i
$83$	5.17802			0.568362			0.284181	−	0.958771i	$-0.408278\pi$
$83$	5.17802			0.568362			0.284181	+	0.958771i	$0.408278\pi$
$84$		0			0
$85$	−2.33064			−0.252794
$86$	−14.1137	−	24.4456i	−1.52192	−	2.63604i
$87$		0			0
$88$	−14.1006	+	24.4230i	−1.50313	+	2.60350i
$89$	0.197342	+	0.341806i	0.0209182	+	0.0362313i	0.876295	−	0.481775i	$-0.160008\pi$
$89$	0.197342	+	0.341806i	0.0209182	+	0.0362313i	−0.855377	+	0.518006i	$0.826674\pi$
$90$		0			0
$91$	0.970830	−	1.24582i	0.101771	−	0.130597i
$92$	17.4699			1.82137
$93$		0			0
$94$	5.45692	−	9.45166i	0.562838	−	0.974865i
$95$	−2.20601	+	3.82091i	−0.226331	+	0.392018i
$96$		0			0
$97$	−17.4653			−1.77334			−0.886668	−	0.462407i	$-0.846986\pi$
$97$	−17.4653			−1.77334			−0.886668	+	0.462407i	$0.846986\pi$
$98$	−12.5078	+	12.1393i	−1.26348	+	1.22625i
$99$		0			0
$100$	−0.907023	−	1.57101i	−0.0907023	−	0.157101i
$101$	7.58116	−	13.1310i	0.754353	−	1.30658i	−0.191342	−	0.981523i	$-0.561284\pi$
$101$	7.58116	−	13.1310i	0.754353	−	1.30658i	0.945695	−	0.325055i	$-0.105383\pi$
$102$		0			0
$103$	6.89030	+	11.9343i	0.678921	+	1.17593i	0.975306	+	0.220857i	$0.0708855\pi$
$103$	6.89030	+	11.9343i	0.678921	+	1.17593i	−0.296385	+	0.955069i	$0.595781\pi$
$104$	−3.27040			−0.320689
$105$		0			0
$106$	27.2185			2.64369
$107$	−0.440707	−	0.763327i	−0.0426048	−	0.0737936i	0.843937	−	0.536443i	$-0.180232\pi$
$107$	−0.440707	−	0.763327i	−0.0426048	−	0.0737936i	−0.886541	+	0.462649i	$0.846899\pi$
$108$		0			0
$109$	−6.94356	+	12.0266i	−0.665072	+	1.15194i	0.314194	+	0.949359i	$0.398266\pi$
$109$	−6.94356	+	12.0266i	−0.665072	+	1.15194i	−0.979266	+	0.202580i	$0.935067\pi$
$110$	−14.9370	−	25.8716i	−1.42419	−	2.46676i
$111$		0			0
$112$	13.7336	+	1.91261i	1.29771	+	0.180725i
$113$	16.4092			1.54365			0.771823	−	0.635838i	$-0.219345\pi$
$113$	16.4092			1.54365			0.771823	+	0.635838i	$0.219345\pi$
$114$		0			0
$115$	−4.84700	+	8.39525i	−0.451985	+	0.782861i
$116$	−6.09314	+	10.5536i	−0.565734	+	0.979880i
$117$		0			0
$118$	−7.99805			−0.736280
$119$	0.994185	+	2.45186i	0.0911368	+	0.224761i
$120$		0			0
$121$	−7.74959	−	13.4227i	−0.704508	−	1.22024i
$122$	−13.1761	+	22.8217i	−1.19291	+	2.06618i
$123$		0			0
$124$	13.5267	+	23.4289i	1.21473	+	2.10398i
$125$	−10.6466			−0.952262
$126$		0			0
$127$	5.62184			0.498858			0.249429	−	0.968393i	$-0.419757\pi$
$127$	5.62184			0.498858			0.249429	+	0.968393i	$0.419757\pi$
$128$	8.65410	+	14.9893i	0.764922	+	1.32488i
$129$		0			0
$130$	1.73219	−	3.00024i	0.151923	−	0.263138i
$131$	4.22187	+	7.31249i	0.368866	+	0.638895i	0.989389	−	0.145294i	$-0.0464127\pi$
$131$	4.22187	+	7.31249i	0.368866	+	0.638895i	−0.620522	+	0.784189i	$0.713079\pi$
$132$		0			0
$133$	4.96065	+	0.690844i	0.430143	+	0.0599038i
$134$	−36.7749			−3.17686
$135$		0			0
$136$	2.73919	−	4.74442i	0.234884	−	0.406830i
$137$	−0.435865	+	0.754941i	−0.0372385	+	0.0644990i	−0.884044	−	0.467404i	$-0.845189\pi$
$137$	−0.435865	+	0.754941i	−0.0372385	+	0.0644990i	0.846805	+	0.531903i	$0.178523\pi$
$138$		0			0
$139$	−12.3738			−1.04954			−0.524768	−	0.851245i	$-0.675848\pi$
$139$	−12.3738			−1.04954			−0.524768	+	0.851245i	$0.675848\pi$
$140$	−15.9197	+	20.4289i	−1.34546	+	1.72656i
$141$		0			0
$142$	−8.60333	−	14.9014i	−0.721975	−	1.25050i
$143$	1.53651	−	2.66131i	0.128489	−	0.222550i
$144$		0			0
$145$	−3.38106	−	5.85617i	−0.280782	−	0.486328i
$146$	1.08076			0.0894442
$147$		0			0
$148$	−39.4975			−3.24668
$149$	−2.56134	−	4.43637i	−0.209833	−	0.363442i	0.741829	−	0.670589i	$-0.233959\pi$
$149$	−2.56134	−	4.43637i	−0.209833	−	0.363442i	−0.951662	+	0.307148i	$0.900625\pi$
$150$		0			0
$151$	1.86857	−	3.23646i	0.152062	−	0.263380i	−0.779923	−	0.625875i	$-0.784742\pi$
$151$	1.86857	−	3.23646i	0.152062	−	0.263380i	0.931985	+	0.362496i	$0.118075\pi$
$152$	−5.18541	−	8.98139i	−0.420592	−	0.728487i
$153$		0			0
$154$	−20.8455	+	26.7499i	−1.67978	+	2.15557i
$155$	−15.0118			−1.20578
$156$		0			0
$157$	1.80862	−	3.13261i	0.144343	−	0.250010i	−0.784785	−	0.619769i	$-0.787226\pi$
$157$	1.80862	−	3.13261i	0.144343	−	0.250010i	0.929128	+	0.369759i	$0.120560\pi$
$158$	7.66879	−	13.2827i	0.610096	−	1.05672i
$159$		0			0
$160$	4.87848			0.385677
$161$	10.8995	+	1.51791i	0.858998	+	0.119628i
$162$		0			0
$163$	2.86964	+	4.97037i	0.224768	+	0.389309i	0.956250	−	0.292552i	$-0.0945043\pi$
$163$	2.86964	+	4.97037i	0.224768	+	0.389309i	−0.731482	+	0.681861i	$0.761171\pi$
$164$	−4.39585	+	7.61383i	−0.343258	+	0.594540i
$165$		0			0
$166$	−6.44666	−	11.1659i	−0.500358	−	0.866646i
$167$	25.0743			1.94031			0.970154	−	0.242490i	$-0.0779641\pi$
$167$	25.0743			1.94031			0.970154	+	0.242490i	$0.0779641\pi$
$168$		0			0
$169$	−12.6436			−0.972587
$170$	2.90166	+	5.02583i	0.222547	+	0.385463i
$171$		0			0
$172$	−23.8069	+	41.2348i	−1.81526	+	3.14413i
$173$	8.26656	+	14.3181i	0.628495	+	1.08858i	0.987854	+	0.155386i	$0.0496620\pi$
$173$	8.26656	+	14.3181i	0.628495	+	1.08858i	−0.359359	+	0.933199i	$0.617005\pi$
$174$		0			0
$175$	−0.429389	−	1.05896i	−0.0324588	−	0.0800497i
$176$	26.9789			2.03361
$177$		0			0
$178$	0.491382	−	0.851099i	0.0368307	−	0.0637926i
$179$	2.28512	−	3.95794i	0.170798	−	0.295830i	−0.767901	−	0.640568i	$-0.778699\pi$
$179$	2.28512	−	3.95794i	0.170798	−	0.295830i	0.938699	+	0.344738i	$0.112032\pi$
$180$		0			0
$181$	23.3136			1.73289			0.866444	−	0.499275i	$-0.166400\pi$
$181$	23.3136			1.73289			0.866444	+	0.499275i	$0.166400\pi$
$182$	−3.89518	−	0.542462i	−0.288730	−	0.0402099i
$183$		0			0
$184$	−11.3933	−	19.7338i	−0.839924	−	1.45479i
$185$	10.9585	−	18.9807i	0.805686	−	1.39549i
$186$		0			0
$187$	2.57387	+	4.45807i	0.188220	+	0.326006i
$188$	−18.4095			−1.34265
$189$		0			0
$190$	10.9859			0.797005
$191$	9.13188	+	15.8169i	0.660760	+	1.14447i	0.980416	+	0.196936i	$0.0630991\pi$
$191$	9.13188	+	15.8169i	0.660760	+	1.14447i	−0.319657	+	0.947533i	$0.603568\pi$
$192$		0			0
$193$	0.0449554	−	0.0778650i	0.00323596	−	0.00560484i	−0.864403	−	0.502800i	$-0.832303\pi$
$193$	0.0449554	−	0.0778650i	0.00323596	−	0.00560484i	0.867639	+	0.497195i	$0.165637\pi$
$194$	21.7444	+	37.6624i	1.56116	+	2.70401i
$195$		0			0
$196$	28.2823	+	8.03326i	2.02016	+	0.573804i
$197$	−4.49561			−0.320299			−0.160150	−	0.987093i	$-0.551198\pi$
$197$	−4.49561			−0.320299			−0.160150	+	0.987093i	$0.551198\pi$
$198$		0			0
$199$	7.16288	−	12.4065i	0.507763	−	0.879471i	−0.492197	−	0.870484i	$-0.663806\pi$
$199$	7.16288	−	12.4065i	0.507763	−	0.879471i	0.999960	−	0.00898737i	$-0.00286081\pi$
$200$	−1.18306	+	2.04912i	−0.0836548	+	0.144894i
$201$		0			0
$202$	−37.7543			−2.65638
$203$	−4.71847	+	6.05497i	−0.331172	+	0.424976i
$204$		0			0
$205$	−2.43924	−	4.22489i	−0.170364	−	0.295079i
$206$	17.1569	−	29.7166i	1.19538	−	2.07046i
$207$		0			0
$208$	1.56432	+	2.70949i	0.108466	+	0.187869i
$209$	9.74489			0.674068
$210$		0			0
$211$	17.5551			1.20854			0.604270	−	0.796780i	$-0.293465\pi$
$211$	17.5551			1.20854			0.604270	+	0.796780i	$0.293465\pi$
$212$	−22.9560	−	39.7610i	−1.57663	−	2.73080i
$213$		0			0
$214$	−1.09736	+	1.90069i	−0.0750143	+	0.129929i
$215$	−13.2104	−	22.8810i	−0.900940	−	1.56047i
$216$		0			0
$217$	6.40361	+	15.7926i	0.434706	+	1.07207i
$218$	34.5790			2.34199
$219$		0			0
$220$	−25.1957	+	43.6402i	−1.69869	+	2.94222i
$221$	−0.298482	+	0.516987i	−0.0200781	+	0.0347763i
$222$		0			0
$223$	24.8716			1.66553			0.832764	−	0.553628i	$-0.186757\pi$
$223$	24.8716			1.66553			0.832764	+	0.553628i	$0.186757\pi$
$224$	−2.08102	−	5.13220i	−0.139044	−	0.342909i
$225$		0			0
$226$	−20.4295	−	35.3849i	−1.35895	−	2.35377i
$227$	−4.16368	+	7.21171i	−0.276353	+	0.478658i	−0.970476	−	0.241199i	$-0.922459\pi$
$227$	−4.16368	+	7.21171i	−0.276353	+	0.478658i	0.694122	+	0.719857i	$0.255793\pi$
$228$		0			0
$229$	−8.51284	−	14.7447i	−0.562544	−	0.974355i	−0.997273	−	0.0737941i	$-0.976489\pi$
$229$	−8.51284	−	14.7447i	−0.562544	−	0.974355i	0.434729	−	0.900561i	$-0.356844\pi$
$230$	24.1381			1.59162
$231$		0			0
$232$	15.8949			1.04355
$233$	−7.69984	−	13.3365i	−0.504433	−	0.873704i	−0.999987	−	0.00512668i	$-0.998368\pi$
$233$	−7.69984	−	13.3365i	−0.504433	−	0.873704i	0.495554	−	0.868577i	$-0.334965\pi$
$234$		0			0
$235$	5.10767	−	8.84674i	0.333188	−	0.577098i
$236$	6.74555	+	11.6836i	0.439098	+	0.760540i
$237$		0			0
$238$	4.04944	−	5.19644i	0.262486	−	0.336835i
$239$	−12.0954			−0.782388			−0.391194	−	0.920308i	$-0.627938\pi$
$239$	−12.0954			−0.782388			−0.391194	+	0.920308i	$0.627938\pi$
$240$		0			0
$241$	−7.39732	+	12.8125i	−0.476503	+	0.825328i	−0.999638	−	0.0269222i	$-0.991429\pi$
$241$	−7.39732	+	12.8125i	−0.476503	+	0.825328i	0.523134	+	0.852250i	$0.324763\pi$
$242$	−19.2965	+	33.4226i	−1.24043	+	2.14849i
$243$		0			0
$244$	44.4510			2.84568
$245$	−11.7073	+	11.3623i	−0.747950	+	0.725914i
$246$		0			0
$247$	0.565040	+	0.978678i	0.0359527	+	0.0622718i
$248$	17.6433	−	30.5591i	1.12035	−	1.94050i
$249$		0			0
$250$	13.2551	+	22.9585i	0.838325	+	1.45202i
$251$	11.4881			0.725121			0.362560	−	0.931960i	$-0.381903\pi$
$251$	11.4881			0.725121			0.362560	+	0.931960i	$0.381903\pi$
$252$		0			0
$253$	21.4113			1.34612
$254$	−6.99922	−	12.1230i	−0.439170	−	0.760664i
$255$		0			0
$256$	16.2790	−	28.1960i	1.01744	−	1.76225i
$257$	3.92761	+	6.80282i	0.244997	+	0.424348i	0.962131	−	0.272588i	$-0.0878795\pi$
$257$	3.92761	+	6.80282i	0.244997	+	0.424348i	−0.717133	+	0.696936i	$0.754546\pi$
$258$		0			0
$259$	−24.6424	−	3.43183i	−1.53121	−	0.213243i
$260$	−5.84371			−0.362412
$261$		0			0
$262$	10.5125	−	18.2082i	0.649464	−	1.12490i
$263$	7.82870	−	13.5597i	0.482738	−	0.836127i	−0.517065	−	0.855946i	$-0.672976\pi$
$263$	7.82870	−	13.5597i	0.482738	−	0.836127i	0.999804	+	0.0198187i	$0.00630889\pi$
$264$		0			0
$265$	25.4764			1.56501
$266$	−4.68629	−	11.5573i	−0.287335	−	0.708624i
$267$		0			0
$268$	31.0159	+	53.7211i	1.89460	+	3.28154i
$269$	14.3835	−	24.9129i	0.876975	−	1.51897i	0.0223313	−	0.999751i	$-0.492891\pi$
$269$	14.3835	−	24.9129i	0.876975	−	1.51897i	0.854644	−	0.519215i	$-0.173776\pi$
$270$		0			0
$271$	2.43463	+	4.21690i	0.147893	+	0.256158i	0.930449	−	0.366423i	$-0.119418\pi$
$271$	2.43463	+	4.21690i	0.147893	+	0.256158i	−0.782556	+	0.622581i	$0.786084\pi$
$272$	−5.24092			−0.317778
$273$		0			0
$274$	2.17062			0.131132
$275$	−1.11166	−	1.92544i	−0.0670353	−	0.116109i
$276$		0			0
$277$	−9.62936	+	16.6785i	−0.578572	+	1.00212i	0.417071	+	0.908874i	$0.363057\pi$
$277$	−9.62936	+	16.6785i	−0.578572	+	1.00212i	−0.995643	+	0.0932428i	$0.970277\pi$
$278$	15.4055	+	26.6831i	0.923960	+	1.60035i
$279$		0			0
$280$	33.4584	+	4.65959i	1.99952	+	0.278464i
$281$	−14.6294			−0.872716			−0.436358	−	0.899773i	$-0.643732\pi$
$281$	−14.6294			−0.872716			−0.436358	+	0.899773i	$0.643732\pi$
$282$		0			0
$283$	−5.99015	+	10.3752i	−0.356078	+	0.616744i	−0.987302	−	0.158856i	$-0.949219\pi$
$283$	−5.99015	+	10.3752i	−0.356078	+	0.616744i	0.631224	+	0.775600i	$0.282553\pi$
$284$	−14.5121	+	25.1357i	−0.861134	+	1.49153i
$285$		0			0
$286$	−7.65184			−0.452463
$287$	−3.40410	+	4.36831i	−0.200938	+	0.257853i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−8.41887	+	14.5819i	−0.494373	+	0.856279i
$291$		0			0
$292$	−0.911511	−	1.57878i	−0.0533422	−	0.0923913i
$293$	7.08802			0.414087			0.207043	−	0.978332i	$-0.433616\pi$
$293$	7.08802			0.414087			0.207043	+	0.978332i	$0.433616\pi$
$294$		0			0
$295$	−7.48616			−0.435861
$296$	25.7589	+	44.6158i	1.49721	+	2.59324i
$297$		0			0
$298$	−6.37776	+	11.0466i	−0.369454	+	0.639912i
$299$	1.24150	+	2.15034i	0.0717976	+	0.124357i
$300$		0			0
$301$	−18.4359	+	23.6578i	−1.06263	+	1.36361i
$302$	−9.30553			−0.535473
$303$		0			0
$304$	−4.96065	+	8.59210i	−0.284513	+	0.492791i
$305$	−12.3328	+	21.3611i	−0.706176	+	1.22313i
$306$		0			0
$307$	30.7472			1.75484			0.877418	−	0.479726i	$-0.159264\pi$
$307$	30.7472			1.75484			0.877418	+	0.479726i	$0.159264\pi$
$308$	56.6576	+	7.89042i	3.22837	+	0.449598i
$309$		0			0
$310$	18.6898	+	32.3717i	1.06151	+	1.83859i
$311$	16.4415	−	28.4776i	0.932313	−	1.61481i	0.152957	−	0.988233i	$-0.451120\pi$
$311$	16.4415	−	28.4776i	0.932313	−	1.61481i	0.779356	−	0.626581i	$-0.215546\pi$
$312$		0			0
$313$	1.17705	+	2.03871i	0.0665306	+	0.115234i	0.897372	−	0.441275i	$-0.145474\pi$
$313$	1.17705	+	2.03871i	0.0665306	+	0.115234i	−0.830841	+	0.556509i	$0.812140\pi$
$314$	−9.00694			−0.508291
$315$		0			0
$316$	−25.8714			−1.45538
$317$	15.2899	+	26.4828i	0.858765	+	1.48742i	0.873108	+	0.487527i	$0.162101\pi$
$317$	15.2899	+	26.4828i	0.858765	+	1.48742i	−0.0143426	+	0.999897i	$0.504566\pi$
$318$		0			0
$319$	−7.46781	+	12.9346i	−0.418117	+	0.724200i
$320$	6.14100	+	10.6365i	0.343292	+	0.594600i
$321$		0			0
$322$	−10.2966	−	25.3935i	−0.573809	−	1.41513i
$323$	−1.89304			−0.105332
$324$		0			0
$325$	0.128915	−	0.223287i	0.00715090	−	0.0123857i
$326$	7.14543	−	12.3763i	0.395749	−	0.685457i
$327$		0			0
$328$	11.4673			0.633175
$329$	−11.4856	−	1.59954i	−0.633223	−	0.0881857i
$330$		0			0
$331$	2.00378	+	3.47065i	0.110138	+	0.190764i	0.915826	−	0.401576i	$-0.131537\pi$
$331$	2.00378	+	3.47065i	0.110138	+	0.190764i	−0.805688	+	0.592340i	$0.798204\pi$
$332$	−10.8742	+	18.8347i	−0.596801	+	1.03369i
$333$		0			0
$334$	−31.2176	−	54.0705i	−1.70815	−	2.95861i
$335$	−34.4212			−1.88063
$336$		0			0
$337$	−23.1664			−1.26195			−0.630977	−	0.775801i	$-0.717346\pi$
$337$	−23.1664			−1.26195			−0.630977	+	0.775801i	$0.717346\pi$
$338$	15.7414	+	27.2649i	0.856218	+	1.48301i
$339$		0			0
$340$	4.89452	−	8.47756i	0.265443	−	0.459760i
$341$	16.5785	+	28.7147i	0.897774	+	1.55499i
$342$		0			0
$343$	16.9473	+	7.46930i	0.915066	+	0.403304i
$344$	62.1043			3.34844
$345$		0			0
$346$	20.5838	−	35.6522i	1.10659	−	1.91667i
$347$	−2.95625	+	5.12037i	−0.158700	+	0.274876i	−0.934400	−	0.356225i	$-0.884063\pi$
$347$	−2.95625	+	5.12037i	−0.158700	+	0.274876i	0.775700	+	0.631101i	$0.217397\pi$
$348$		0			0
$349$	26.4483			1.41575			0.707874	−	0.706339i	$-0.249655\pi$
$349$	26.4483			1.41575			0.707874	+	0.706339i	$0.249655\pi$
$350$	−1.74896	+	2.24435i	−0.0934857	+	0.119965i
$351$		0			0
$352$	−5.38759	−	9.33158i	−0.287160	−	0.497375i
$353$	−2.16542	+	3.75061i	−0.115254	+	0.199625i	−0.917881	−	0.396856i	$-0.870101\pi$
$353$	−2.16542	+	3.75061i	−0.115254	+	0.199625i	0.802628	+	0.596481i	$0.203435\pi$
$354$		0			0
$355$	−8.05270	−	13.9477i	−0.427393	−	0.740266i
$356$	−1.65773			−0.0878593
$357$		0			0
$358$	−11.3799			−0.601448
$359$	0.698715	+	1.21021i	0.0368768	+	0.0638724i	0.883875	−	0.467724i	$-0.154926\pi$
$359$	0.698715	+	1.21021i	0.0368768	+	0.0638724i	−0.846998	+	0.531596i	$0.821592\pi$
$360$		0			0
$361$	7.70819	−	13.3510i	0.405694	−	0.702683i
$362$	−29.0256	−	50.2737i	−1.52555	−	2.64233i
$363$		0			0
$364$	2.49276	+	6.14763i	0.130656	+	0.322223i
$365$	1.01159			0.0529489
$366$		0			0
$367$	0.829833	−	1.43731i	0.0433169	−	0.0750272i	−0.843554	−	0.537044i	$-0.819541\pi$
$367$	0.829833	−	1.43731i	0.0433169	−	0.0750272i	0.886871	+	0.462017i	$0.152874\pi$
$368$	−10.8995	+	18.8784i	−0.568173	+	0.984105i
$369$		0			0
$370$	−54.5736			−2.83715
$371$	−10.8675	−	26.8014i	−0.564213	−	1.39146i
$372$		0			0
$373$	−0.920052	−	1.59358i	−0.0476385	−	0.0825123i	0.841223	−	0.540688i	$-0.181836\pi$
$373$	−0.920052	−	1.59358i	−0.0476385	−	0.0825123i	−0.888861	+	0.458176i	$0.848503\pi$
$374$	6.40895	−	11.1006i	0.331399	−	0.574000i
$375$		0			0
$376$	12.0060	+	20.7950i	0.619163	+	1.07242i
$377$	−1.73203			−0.0892041
$378$		0			0
$379$	−4.60612			−0.236600			−0.118300	−	0.992978i	$-0.537745\pi$
$379$	−4.60612			−0.236600			−0.118300	+	0.992978i	$0.537745\pi$
$380$	−9.26554	−	16.0484i	−0.475312	−	0.823265i
$381$		0			0
$382$	22.7385	−	39.3842i	1.16340	−	2.01507i
$383$	−5.68567	−	9.84787i	−0.290524	−	0.503203i	0.683410	−	0.730035i	$-0.260496\pi$
$383$	−5.68567	−	9.84787i	−0.290524	−	0.503203i	−0.973934	+	0.226832i	$0.927163\pi$
$384$		0			0
$385$	−19.5113	+	25.0379i	−0.994389	+	1.27605i
$386$	−0.223879			−0.0113951
$387$		0			0
$388$	36.6785	−	63.5290i	1.86207	−	3.22519i
$389$	1.62680	−	2.81770i	0.0824821	−	0.142863i	−0.821833	−	0.569728i	$-0.807049\pi$
$389$	1.62680	−	2.81770i	0.0824821	−	0.142863i	0.904315	+	0.426865i	$0.140382\pi$
$390$		0			0
$391$	−4.15937			−0.210348
$392$	−9.37048	−	37.1862i	−0.473281	−	1.87819i
$393$		0			0
$394$	5.59706	+	9.69439i	0.281976	+	0.488396i
$395$	7.17797	−	12.4326i	0.361163	−	0.625553i
$396$		0			0
$397$	−0.0664812	−	0.115149i	−0.00333660	−	0.00577916i	0.864352	−	0.502887i	$-0.167729\pi$
$397$	−0.0664812	−	0.115149i	−0.00333660	−	0.00577916i	−0.867689	+	0.497108i	$0.834395\pi$
$398$	−35.6713			−1.78804
$399$		0			0
$400$	2.26356			0.113178
$401$	−5.09167	−	8.81904i	−0.254266	−	0.440402i	0.710430	−	0.703768i	$-0.248501\pi$
$401$	−5.09167	−	8.81904i	−0.254266	−	0.440402i	−0.964696	+	0.263366i	$0.915167\pi$
$402$		0			0
$403$	−1.92254	+	3.32995i	−0.0957688	+	0.165876i
$404$	31.8420	+	55.1519i	1.58420	+	2.74391i
$405$		0			0
$406$	18.9315	+	2.63650i	0.939556	+	0.130847i
$407$	−48.4085			−2.39952
$408$		0			0
$409$	7.03167	−	12.1792i	0.347694	−	0.602223i	−0.638146	−	0.769916i	$-0.720298\pi$
$409$	7.03167	−	12.1792i	0.347694	−	0.602223i	0.985839	+	0.167693i	$0.0536316\pi$
$410$	−6.07373	+	10.5200i	−0.299960	+	0.519546i
$411$		0			0
$412$	−57.8805			−2.85157
$413$	3.19338	+	7.87550i	0.157136	+	0.387528i
$414$		0			0
$415$	−6.03407	−	10.4513i	−0.296201	−	0.513035i
$416$	0.624780	−	1.08215i	0.0306323	−	0.0530568i
$417$		0			0
$418$	−12.1324	−	21.0140i	−0.593417	−	1.02783i
$419$	−26.5734			−1.29820			−0.649098	−	0.760704i	$-0.724854\pi$
$419$	−26.5734			−1.29820			−0.649098	+	0.760704i	$0.724854\pi$
$420$		0			0
$421$	−11.0420			−0.538155			−0.269077	−	0.963119i	$-0.586719\pi$
$421$	−11.0420			−0.538155			−0.269077	+	0.963119i	$0.586719\pi$
$422$	−21.8561	−	37.8559i	−1.06394	−	1.84280i
$423$		0			0
$424$	−29.9423	+	51.8616i	−1.45413	+	2.51862i
$425$	0.215950	+	0.374037i	0.0104751	+	0.0181435i
$426$		0			0
$427$	27.7329	+	3.86221i	1.34209	+	0.186906i
$428$	3.70207			0.178946
$429$		0			0
$430$	−32.8940	+	56.9740i	−1.58629	+	2.74753i
$431$	−3.20784	+	5.55614i	−0.154516	+	0.267630i	−0.932883	−	0.360180i	$-0.882715\pi$
$431$	−3.20784	+	5.55614i	−0.154516	+	0.267630i	0.778367	+	0.627810i	$0.216049\pi$
$432$		0			0
$433$	−20.9787			−1.00817			−0.504086	−	0.863654i	$-0.668170\pi$
$433$	−20.9787			−1.00817			−0.504086	+	0.863654i	$0.668170\pi$
$434$	26.0827	−	33.4706i	1.25201	−	1.60664i
$435$		0			0
$436$	−29.1639	−	50.5134i	−1.39670	−	2.41915i
$437$	−3.93693	+	6.81896i	−0.188329	+	0.326195i
$438$		0			0
$439$	3.56767	+	6.17939i	0.170276	+	0.294926i	0.938516	−	0.345235i	$-0.112201\pi$
$439$	3.56767	+	6.17939i	0.170276	+	0.294926i	−0.768241	+	0.640161i	$0.778868\pi$
$440$	65.7271			3.13341
$441$		0			0
$442$	1.48645			0.0707031
$443$	11.9249	+	20.6545i	0.566569	+	0.981327i	0.996902	+	0.0786566i	$0.0250631\pi$
$443$	11.9249	+	20.6545i	0.566569	+	0.981327i	−0.430332	+	0.902671i	$0.641604\pi$
$444$		0			0
$445$	0.459933	−	0.796627i	0.0218029	−	0.0377638i
$446$	−30.9653	−	53.6335i	−1.46625	−	2.53962i
$447$		0			0
$448$	8.57014	−	10.9976i	0.404901	−	0.519588i
$449$	−31.7250			−1.49720			−0.748598	−	0.663025i	$-0.769273\pi$
$449$	−31.7250			−1.49720			−0.748598	+	0.663025i	$0.769273\pi$
$450$		0			0
$451$	−5.38759	+	9.33158i	−0.253692	+	0.439407i
$452$	−34.4604	+	59.6872i	−1.62088	+	2.80745i
$453$		0			0
$454$	20.7352			0.973152
$455$	−3.64588	−	0.507743i	−0.170921	−	0.0238034i
$456$		0			0
$457$	−13.8608	−	24.0076i	−0.648379	−	1.12303i	−0.983510	−	0.180854i	$-0.942114\pi$
$457$	−13.8608	−	24.0076i	−0.648379	−	1.12303i	0.335130	−	0.942172i	$-0.391220\pi$
$458$	−21.1970	+	36.7144i	−0.990473	+	1.71555i
$459$		0			0
$460$	−20.3581	−	35.2613i	−0.949201	−	1.64406i
$461$	22.6069			1.05291			0.526453	−	0.850204i	$-0.323522\pi$
$461$	22.6069			1.05291			0.526453	+	0.850204i	$0.323522\pi$
$462$		0			0
$463$	7.23081			0.336044			0.168022	−	0.985783i	$-0.446262\pi$
$463$	7.23081			0.336044			0.168022	+	0.985783i	$0.446262\pi$
$464$	−7.60300	−	13.1688i	−0.352960	−	0.611345i
$465$		0			0
$466$	−19.1727	+	33.2080i	−0.888157	+	1.53833i
$467$	−15.4473	−	26.7556i	−0.714818	−	1.23810i	−0.963030	−	0.269395i	$-0.913176\pi$
$467$	−15.4473	−	26.7556i	−0.714818	−	1.23810i	0.248212	−	0.968706i	$-0.420157\pi$
$468$		0			0
$469$	14.6831	+	36.2114i	0.678002	+	1.67209i
$470$	−25.4363			−1.17329
$471$		0			0
$472$	8.79844	−	15.2393i	0.404981	−	0.701447i
$473$	−29.1780	+	50.5378i	−1.34161	+	2.32373i
$474$		0			0
$475$	0.817607			0.0375144
$476$	−11.0063	−	1.53279i	−0.504474	−	0.0702555i
$477$		0			0
$478$	15.0589	+	26.0827i	0.688776	+	1.19300i
$479$	−10.9056	+	18.8890i	−0.498289	+	0.863061i	−0.999998	−	0.00197495i	$-0.999371\pi$
$479$	−10.9056	+	18.8890i	−0.498289	+	0.863061i	0.501709	+	0.865036i	$0.332705\pi$
$480$		0			0
$481$	−2.80688	−	4.86166i	−0.127983	−	0.221673i
$482$	36.8388			1.67796
$483$		0			0
$484$	65.0988			2.95904
$485$	20.3527	+	35.2520i	0.924170	+	1.60071i
$486$		0			0
$487$	−2.27912	+	3.94755i	−0.103277	+	0.178880i	−0.913033	−	0.407886i	$-0.866266\pi$
$487$	−2.27912	+	3.94755i	−0.103277	+	0.178880i	0.809756	+	0.586767i	$0.199599\pi$
$488$	−28.9894	−	50.2111i	−1.31229	−	2.27295i
$489$		0			0
$490$	39.0775	+	11.0995i	1.76534	+	0.501425i
$491$	1.59981			0.0721983			0.0360992	−	0.999348i	$-0.488507\pi$
$491$	1.59981			0.0721983			0.0360992	+	0.999348i	$0.488507\pi$
$492$		0			0
$493$	1.45070	−	2.51268i	0.0653362	−	0.113166i
$494$	1.40696	−	2.43692i	0.0633019	−	0.109642i
$495$		0			0
$496$	−33.7571			−1.51574
$497$	−11.2380	+	14.4212i	−0.504094	+	0.646878i
$498$		0			0
$499$	12.5765	+	21.7832i	0.563003	+	0.975150i	0.997232	+	0.0743474i	$0.0236874\pi$
$499$	12.5765	+	21.7832i	0.563003	+	0.975150i	−0.434229	+	0.900802i	$0.642979\pi$
$500$	22.3587	−	38.7263i	0.999909	−	1.73189i
$501$		0			0
$502$	−14.3027	−	24.7730i	−0.638361	−	1.10567i
$503$	−17.2499			−0.769135			−0.384568	−	0.923097i	$-0.625649\pi$
$503$	−17.2499			−0.769135			−0.384568	+	0.923097i	$0.625649\pi$
$504$		0			0
$505$	−35.3380			−1.57252
$506$	−26.6572	−	46.1716i	−1.18506	−	2.05258i
$507$		0			0
$508$	−11.8063	+	20.4491i	−0.523818	+	0.907280i
$509$	−7.76030	−	13.4412i	−0.343969	−	0.595772i	0.641197	−	0.767377i	$-0.278438\pi$
$509$	−7.76030	−	13.4412i	−0.343969	−	0.595772i	−0.985166	+	0.171604i	$0.945105\pi$
$510$		0			0
$511$	−0.431514	−	1.06420i	−0.0190891	−	0.0470774i
$512$	−46.4533			−2.05296
$513$		0			0
$514$	9.77978	−	16.9391i	0.431368	−	0.747151i
$515$	16.0588	−	27.8147i	0.707637	−	1.22566i
$516$		0			0
$517$	−22.5628			−0.992311
$518$	23.2795	+	57.4118i	1.02284	+	2.52253i
$519$		0			0
$520$	3.81107	+	6.60096i	0.167126	+	0.289471i
$521$	12.7448	−	22.0747i	0.558361	−	0.967110i	−0.439272	−	0.898354i	$-0.644764\pi$
$521$	12.7448	−	22.0747i	0.558361	−	0.967110i	0.997633	−	0.0687562i	$-0.0219030\pi$
$522$		0			0
$523$	−4.51439	−	7.81915i	−0.197400	−	0.341907i	0.750284	−	0.661115i	$-0.229917\pi$
$523$	−4.51439	−	7.81915i	−0.197400	−	0.341907i	−0.947685	+	0.319208i	$0.896583\pi$
$524$	−35.4649			−1.54929
$525$		0			0
$526$	−38.9871			−1.69992
$527$	−3.22053	−	5.57813i	−0.140289	−	0.242987i
$528$		0			0
$529$	2.84984	−	4.93607i	0.123906	−	0.214612i
$530$	−31.7183	−	54.9377i	−1.37775	−	2.38634i
$531$		0			0
$532$	−12.9306	+	16.5932i	−0.560614	+	0.719407i
$533$	−1.24956			−0.0541244
$534$		0			0
$535$	−1.02713	+	1.77904i	−0.0444068	+	0.0769148i
$536$	40.4550	−	70.0701i	1.74739	−	3.02657i
$537$		0			0
$538$	−71.6299			−3.08818
$539$	34.6630	+	9.84563i	1.49304	+	0.424081i
$540$		0			0
$541$	17.1995	+	29.7904i	0.739464	+	1.28079i	0.952737	+	0.303796i	$0.0982543\pi$
$541$	17.1995	+	29.7904i	0.739464	+	1.28079i	−0.213273	+	0.976993i	$0.568412\pi$
$542$	6.06224	−	10.5001i	0.260396	−	0.451018i
$543$		0			0
$544$	1.04659	+	1.81275i	0.0448724	+	0.0777212i
$545$	32.3659			1.38640
$546$		0			0
$547$	−24.1154			−1.03110			−0.515551	−	0.856859i	$-0.672413\pi$
$547$	−24.1154			−1.03110			−0.515551	+	0.856859i	$0.672413\pi$
$548$	−1.83070	−	3.17086i	−0.0782035	−	0.135453i
$549$		0			0
$550$	−2.76803	+	4.79437i	−0.118029	+	0.204433i
$551$	−2.74624	−	4.75662i	−0.116994	−	0.202639i
$552$		0			0
$553$	−16.1411	−	2.24789i	−0.686390	−	0.0955901i
$554$	47.9544			2.03739
$555$		0			0
$556$	25.9860	−	45.0090i	1.10205	−	1.90881i
$557$	9.19967	−	15.9343i	0.389803	−	0.675158i	−0.602620	−	0.798028i	$-0.705877\pi$
$557$	9.19967	−	15.9343i	0.389803	−	0.675158i	0.992423	+	0.122870i	$0.0392099\pi$
$558$		0			0
$559$	−6.76734			−0.286228
$560$	−12.1437	−	29.9487i	−0.513165	−	1.26557i
$561$		0			0
$562$	18.2137	+	31.5470i	0.768297	+	1.33073i
$563$	−6.83677	+	11.8416i	−0.288136	+	0.499065i	−0.973365	−	0.229262i	$-0.926369\pi$
$563$	−6.83677	+	11.8416i	−0.288136	+	0.499065i	0.685229	+	0.728328i	$0.259702\pi$
$564$		0			0
$565$	−19.1220	−	33.1202i	−0.804467	−	1.39338i
$566$	29.8311			1.25389
$567$		0			0
$568$	37.8571			1.58845
$569$	−11.7978	−	20.4343i	−0.494588	−	0.856652i	0.505392	−	0.862890i	$-0.331348\pi$
$569$	−11.7978	−	20.4343i	−0.494588	−	0.856652i	−0.999981	+	0.00623751i	$0.998015\pi$
$570$		0			0
$571$	2.85804	−	4.95027i	0.119605	−	0.207162i	−0.800006	−	0.599992i	$-0.795170\pi$
$571$	2.85804	−	4.95027i	0.119605	−	0.207162i	0.919611	+	0.392830i	$0.128504\pi$
$572$	6.45356	+	11.1779i	0.269837	+	0.467371i
$573$		0			0
$574$	13.6580	+	1.90208i	0.570074	+	0.0793913i
$575$	1.79643			0.0749164
$576$		0			0
$577$	12.6215	−	21.8611i	0.525440	−	0.910089i	−0.474121	−	0.880460i	$-0.657234\pi$
$577$	12.6215	−	21.8611i	0.525440	−	0.910089i	0.999561	−	0.0296294i	$-0.00943272\pi$
$578$	−1.24500	+	2.15641i	−0.0517854	+	0.0896949i
$579$		0			0
$580$	28.4019			1.17932
$581$	−8.42090	+	10.8061i	−0.349358	+	0.448313i
$582$		0			0
$583$	−28.1351	−	48.7315i	−1.16524	−	2.01825i
$584$	−1.18891	+	2.05926i	−0.0491975	+	0.0852126i
$585$		0			0
$586$	−8.82462	−	15.2847i	−0.364542	−	0.631405i
$587$	−10.1988			−0.420950			−0.210475	−	0.977599i	$-0.567501\pi$
$587$	−10.1988			−0.420950			−0.210475	+	0.977599i	$0.567501\pi$
$588$		0			0
$589$	−12.1932			−0.502413
$590$	9.32031	+	16.1432i	0.383711	+	0.664607i
$591$		0			0
$592$	24.6424	−	42.6819i	1.01280	−	1.75422i
$593$	−1.62267	−	2.81054i	−0.0666349	−	0.115415i	0.830783	−	0.556596i	$-0.187893\pi$
$593$	−1.62267	−	2.81054i	−0.0666349	−	0.115415i	−0.897418	+	0.441181i	$0.854560\pi$
$594$		0			0
$595$	3.79027	−	4.86386i	0.155386	−	0.199399i
$596$	21.5160			0.881329
$597$		0			0
$598$	3.09134	−	5.35436i	0.126414	−	0.218956i
$599$	−10.5704	+	18.3085i	−0.431895	+	0.748064i	−0.997037	−	0.0769299i	$-0.975488\pi$
$599$	−10.5704	+	18.3085i	−0.431895	+	0.748064i	0.565142	+	0.824994i	$0.308822\pi$
$600$		0			0
$601$	8.77314			0.357864			0.178932	−	0.983861i	$-0.442736\pi$
$601$	8.77314			0.357864			0.178932	+	0.983861i	$0.442736\pi$
$602$	73.9687	+	10.3012i	3.01474	+	0.419847i
$603$		0			0
$604$	7.84828	+	13.5936i	0.319342	+	0.553116i
$605$	−18.0615	+	31.2835i	−0.734306	+	1.27185i
$606$		0			0
$607$	10.2399	+	17.7359i	0.415623	+	0.719880i	0.995494	−	0.0948287i	$-0.0302303\pi$
$607$	10.2399	+	17.7359i	0.415623	+	0.719880i	−0.579871	+	0.814708i	$0.696897\pi$
$608$	3.96250			0.160701
$609$		0			0
$610$	61.4177			2.48673
$611$	−1.30826	−	2.26598i	−0.0529267	−	0.0916717i
$612$		0			0
$613$	−15.0441	+	26.0572i	−0.607626	+	1.05244i	0.384005	+	0.923331i	$0.374545\pi$
$613$	−15.0441	+	26.0572i	−0.607626	+	1.05244i	−0.991631	+	0.129108i	$0.958789\pi$
$614$	−38.2804	−	66.3036i	−1.54487	−	2.67580i
$615$		0			0
$616$	−28.0373	−	69.1454i	−1.12965	−	2.78595i
$617$	−37.8597			−1.52417			−0.762086	−	0.647476i	$-0.775825\pi$
$617$	−37.8597			−1.52417			−0.762086	+	0.647476i	$0.775825\pi$
$618$		0			0
$619$	5.54171	−	9.59852i	0.222740	−	0.385797i	−0.732899	−	0.680338i	$-0.761833\pi$
$619$	5.54171	−	9.59852i	0.222740	−	0.385797i	0.955639	+	0.294540i	$0.0951665\pi$
$620$	31.5259	−	54.6045i	1.26611	−	2.19297i
$621$		0			0
$622$	−81.8791			−3.28305
$623$	−1.03425	−	0.144035i	−0.0414364	−	0.00577064i
$624$		0			0
$625$	13.4865	+	23.3593i	0.539459	+	0.934371i
$626$	2.93086	−	5.07639i	0.117141	−	0.202894i
$627$		0			0
$628$	7.59645	+	13.1574i	0.303131	+	0.525039i
$629$	9.40385			0.374956
$630$		0			0
$631$	−23.5684			−0.938243			−0.469122	−	0.883134i	$-0.655429\pi$
$631$	−23.5684			−0.938243			−0.469122	+	0.883134i	$0.655429\pi$
$632$	16.8724	+	29.2239i	0.671150	+	1.16247i
$633$		0			0
$634$	38.0719	−	65.9425i	1.51203	−	2.61891i
$635$	−6.55125	−	11.3471i	−0.259979	−	0.450296i
$636$		0			0
$637$	1.02108	+	4.05208i	0.0404565	+	0.160549i
$638$	37.1898			1.47236
$639$		0			0
$640$	20.1696	−	34.9348i	0.797274	−	1.38092i
$641$	12.4440	−	21.5537i	0.491510	−	0.851320i	−0.508442	−	0.861096i	$-0.669778\pi$
$641$	12.4440	−	21.5537i	0.491510	−	0.851320i	0.999952	+	0.00977574i	$0.00311177\pi$
$642$		0			0
$643$	21.5679			0.850557			0.425278	−	0.905063i	$-0.360176\pi$
$643$	21.5679			0.850557			0.425278	+	0.905063i	$0.360176\pi$
$644$	−28.4109	+	36.4583i	−1.11955	+	1.43666i
$645$		0			0
$646$	2.35685	+	4.08218i	0.0927290	+	0.160611i
$647$	−11.1073	+	19.2384i	−0.436674	+	0.756341i	−0.997431	−	0.0716393i	$-0.977177\pi$
$647$	−11.1073	+	19.2384i	−0.436674	+	0.756341i	0.560757	+	0.827981i	$0.310510\pi$
$648$		0			0
$649$	8.26741	+	14.3196i	0.324524	+	0.562093i
$650$	−0.641998			−0.0251812
$651$		0			0
$652$	−24.1058			−0.944057
$653$	−11.2721	−	19.5239i	−0.441112	−	0.764028i	0.556660	−	0.830740i	$-0.312082\pi$
$653$	−11.2721	−	19.5239i	−0.441112	−	0.764028i	−0.997772	+	0.0667120i	$0.978749\pi$
$654$		0			0
$655$	9.83967	−	17.0428i	0.384468	−	0.665918i
$656$	−5.48512	−	9.50051i	−0.214158	−	0.370933i
$657$		0			0
$658$	10.8504	+	26.7592i	0.422992	+	1.04318i
$659$	38.3546			1.49408			0.747041	−	0.664778i	$-0.231474\pi$
$659$	38.3546			1.49408			0.747041	+	0.664778i	$0.231474\pi$
$660$		0			0
$661$	−14.1377	+	24.4873i	−0.549895	+	0.952445i	0.448387	+	0.893840i	$0.351999\pi$
$661$	−14.1377	+	24.4873i	−0.549895	+	0.952445i	−0.998281	+	0.0586056i	$0.981335\pi$
$662$	4.98943	−	8.64195i	0.193920	−	0.335879i
$663$		0			0
$664$	28.3672			1.10086
$665$	−4.38636	−	10.8176i	−0.170096	−	0.419489i
$666$		0			0
$667$	−6.03398	−	10.4512i	−0.233637	−	0.404671i
$668$	−52.6578	+	91.2061i	−2.03739	+	3.52887i
$669$		0			0
$670$	42.8545	+	74.2262i	1.65562	+	2.86761i
$671$	54.4795			2.10316
$672$		0			0
$673$	21.8417			0.841937			0.420969	−	0.907075i	$-0.361690\pi$
$673$	21.8417			0.841937			0.420969	+	0.907075i	$0.361690\pi$
$674$	28.8423	+	49.9563i	1.11096	+	1.92424i
$675$		0			0
$676$	26.5525	−	45.9904i	1.02125	−	1.76886i
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		0			0
$679$	28.4035	−	36.4487i	1.09002	−	1.39877i
$680$	−12.7682			−0.489636
$681$		0			0
$682$	41.2805	−	71.4999i	1.58071	−	2.73787i
$683$	6.80646	−	11.7891i	0.260442	−	0.451099i	−0.705917	−	0.708294i	$-0.749465\pi$
$683$	6.80646	−	11.7891i	0.260442	−	0.451099i	0.966359	+	0.257195i	$0.0827984\pi$
$684$		0			0
$685$	2.03169			0.0776271
$686$	−4.99254	−	45.8446i	−0.190616	−	1.75035i
$687$		0			0
$688$	−29.7062	−	51.4527i	−1.13254	−	1.96161i
$689$	3.26273	−	5.65122i	0.124300	−	0.215294i
$690$		0			0
$691$	10.9400	+	18.9487i	0.416178	+	0.720842i	0.995551	−	0.0942206i	$-0.0300359\pi$
$691$	10.9400	+	18.9487i	0.416178	+	0.720842i	−0.579373	+	0.815062i	$0.696703\pi$
$692$	−69.4415			−2.63977
$693$		0			0
$694$	14.7222			0.558846
$695$	14.4195	+	24.9753i	0.546963	+	0.947368i
$696$		0			0
$697$	1.04659	−	1.81275i	0.0396426	−	0.0686630i
$698$	−32.9283	−	57.0335i	−1.24635	−	2.15875i
$699$		0			0
$700$	4.75364	+	0.662015i	0.179671	+	0.0250218i
$701$	23.2153			0.876829			0.438414	−	0.898773i	$-0.355540\pi$
$701$	23.2153			0.876829			0.438414	+	0.898773i	$0.355540\pi$
$702$		0			0
$703$	8.90095	−	15.4169i	0.335706	−	0.581459i
$704$	13.5637	−	23.4931i	0.511203	−	0.885429i
$705$		0			0
$706$	10.7838			0.405854
$707$	15.0741	+	37.1758i	0.566922	+	1.39814i
$708$		0			0
$709$	−1.28712	−	2.22935i	−0.0483387	−	0.0837251i	0.840844	−	0.541278i	$-0.182059\pi$
$709$	−1.28712	−	2.22935i	−0.0483387	−	0.0837251i	−0.889182	+	0.457553i	$0.848726\pi$
$710$	−20.0513	+	34.7299i	−0.752512	+	1.30339i
$711$		0			0
$712$	1.08111	+	1.87254i	0.0405164	+	0.0701764i
$713$	−26.7908			−1.00332
$714$		0			0
$715$	−7.16211			−0.267848
$716$	9.59783	+	16.6239i	0.358688	+	0.621265i
$717$		0			0
$718$	1.73981	−	3.01343i	0.0649290	−	0.112460i
$719$	9.41387	+	16.3053i	0.351078	+	0.608085i	0.986439	−	0.164130i	$-0.0524818\pi$
$719$	9.41387	+	16.3053i	0.351078	+	0.608085i	−0.635360	+	0.772216i	$0.719148\pi$
$720$		0			0
$721$	−36.1115	−	5.02907i	−1.34486	−	0.187292i
$722$	−38.3869			−1.42861
$723$		0			0
$724$	−48.9603	+	84.8017i	−1.81959	+	3.15163i
$725$	−0.626558	+	1.08523i	−0.0232698	+	0.0403044i
$726$		0			0
$727$	−16.5235			−0.612823			−0.306411	−	0.951899i	$-0.599128\pi$
$727$	−16.5235			−0.612823			−0.306411	+	0.951899i	$0.599128\pi$
$728$	5.31857	−	6.82505i	0.197119	−	0.252953i
$729$		0			0
$730$	−1.25943	−	2.18140i	−0.0466137	−	0.0807372i
$731$	5.66812	−	9.81748i	0.209643	−	0.363113i
$732$		0			0
$733$	8.03661	+	13.9198i	0.296839	+	0.514140i	0.975411	−	0.220394i	$-0.0707342\pi$
$733$	8.03661	+	13.9198i	0.296839	+	0.514140i	−0.678572	+	0.734534i	$0.737401\pi$
$734$	−4.13258			−0.152536
$735$		0			0
$736$	8.70634			0.320920
$737$	38.0134	+	65.8411i	1.40024	+	2.42529i
$738$		0			0
$739$	3.17347	−	5.49661i	0.116738	−	0.202196i	−0.801735	−	0.597679i	$-0.796090\pi$
$739$	3.17347	−	5.49661i	0.116738	−	0.202196i	0.918473	+	0.395483i	$0.129423\pi$
$740$	46.0273	+	79.7217i	1.69200	+	2.93063i
$741$		0			0
$742$	−44.2648	+	56.8027i	−1.62501	+	2.08529i
$743$	−8.14793			−0.298918			−0.149459	−	0.988768i	$-0.547753\pi$
$743$	−8.14793			−0.298918			−0.149459	+	0.988768i	$0.547753\pi$
$744$		0			0
$745$	−5.96957	+	10.3396i	−0.218708	+	0.378814i
$746$	−2.29094	+	3.96802i	−0.0838772	+	0.145280i
$747$		0			0
$748$	−21.6212			−0.790550
$749$	2.30971	+	0.321662i	0.0843951	+	0.0117533i
$750$		0			0
$751$	−18.5765	−	32.1754i	−0.677864	−	1.17410i	−0.975623	−	0.219454i	$-0.929572\pi$
$751$	−18.5765	−	32.1754i	−0.677864	−	1.17410i	0.297758	−	0.954641i	$-0.403761\pi$
$752$	11.4856	−	19.8937i	0.418838	−	0.725448i
$753$		0			0
$754$	2.15639	+	3.73497i	0.0785310	+	0.136020i
$755$	−8.70996			−0.316988
$756$		0			0
$757$	9.61543			0.349479			0.174739	−	0.984615i	$-0.444092\pi$
$757$	9.61543			0.349479			0.174739	+	0.984615i	$0.444092\pi$
$758$	5.73464	+	9.93268i	0.208291	+	0.360771i
$759$		0			0
$760$	−12.0853	+	20.9324i	−0.438381	+	0.759299i
$761$	−0.0792099	−	0.137196i	−0.00287136	−	0.00497334i	0.864586	−	0.502485i	$-0.167581\pi$
$761$	−0.0792099	−	0.137196i	−0.00287136	−	0.00497334i	−0.867458	+	0.497511i	$0.834247\pi$
$762$		0			0
$763$	−13.8064	−	34.0492i	−0.499824	−	1.23266i
$764$	−76.7104			−2.77529
$765$		0			0
$766$	−14.1574	+	24.5213i	−0.511527	+	0.885990i
$767$	−0.958743	+	1.66059i	−0.0346182	+	0.0599605i
$768$		0			0
$769$	25.6975			0.926674			0.463337	−	0.886182i	$-0.346652\pi$
$769$	25.6975			0.926674			0.463337	+	0.886182i	$0.346652\pi$
$770$	78.2836	+	10.9022i	2.82115	+	0.392887i
$771$		0			0
$772$	0.188819	+	0.327044i	0.00679575	+	0.0117706i
$773$	−15.7495	+	27.2790i	−0.566472	+	0.981158i	0.430439	+	0.902620i	$0.358359\pi$
$773$	−15.7495	+	27.2790i	−0.566472	+	0.981158i	−0.996911	+	0.0785385i	$0.974975\pi$
$774$		0			0
$775$	1.39095	+	2.40920i	0.0499644	+	0.0865410i
$776$	−95.6817			−3.43477
$777$		0			0
$778$	−8.10150			−0.290453
$779$	−1.98125	−	3.43162i	−0.0709856	−	0.122951i
$780$		0			0
$781$	−17.7861	+	30.8065i	−0.636438	+	1.10234i
$782$	5.17843	+	8.96930i	0.185180	+	0.320742i
$783$		0			0
$784$	−26.3262	+	25.5505i	−0.940220	+	0.912519i
$785$	−8.43048			−0.300897
$786$		0			0
$787$	−17.6356	+	30.5458i	−0.628642	+	1.08884i	0.359182	+	0.933267i	$0.383056\pi$
$787$	−17.6356	+	30.5458i	−0.628642	+	1.08884i	−0.987824	+	0.155573i	$0.950278\pi$
$788$	9.44111	−	16.3525i	0.336326	−	0.582533i
$789$		0			0
$790$	−35.7464			−1.27180
$791$	−26.6859	+	34.2446i	−0.948840	+	1.21760i
$792$		0			0
$793$	3.15890	+	5.47137i	0.112176	+	0.194294i
$794$	−0.165539	+	0.286722i	−0.00587476	+	0.0101754i
$795$		0			0
$796$	30.0851	+	52.1090i	1.06634	+	1.84695i
$797$	−2.97165			−0.105261			−0.0526306	−	0.998614i	$-0.516761\pi$
$797$	−2.97165			−0.105261			−0.0526306	+	0.998614i	$0.516761\pi$
$798$		0			0
$799$	4.38305			0.155061
$800$	−0.452025	−	0.782930i	−0.0159815	−	0.0276808i
$801$		0			0
$802$	−12.6783	+	21.9595i	−0.447687	+	0.775416i
$803$	−1.11716	−	1.93497i	−0.0394236	−	0.0682837i
$804$		0			0
$805$	−9.63763	−	23.7683i	−0.339682	−	0.837722i
$806$	9.57431			0.337241
$807$		0			0
$808$	41.5325	−	71.9363i	1.46111	−	2.53071i
$809$	23.0577	−	39.9371i	0.810665	−	1.40411i	−0.101734	−	0.994812i	$-0.532439\pi$
$809$	23.0577	−	39.9371i	0.810665	−	1.40411i	0.912399	−	0.409302i	$-0.134228\pi$
$810$		0			0
$811$	−28.0004			−0.983227			−0.491614	−	0.870813i	$-0.663593\pi$
$811$	−28.0004			−0.983227			−0.491614	+	0.870813i	$0.663593\pi$
$812$	−12.1154	−	29.8790i	−0.425168	−	1.04855i
$813$		0			0
$814$	60.2688	+	104.389i	2.11242	+	3.65882i
$815$	6.68811	−	11.5842i	0.234274	−	0.405775i
$816$		0			0
$817$	−10.7300	−	18.5849i	−0.375396	−	0.650204i
$818$	−35.0178			−1.22437
$819$		0			0
$820$	20.4903			0.715553
$821$	7.06991	+	12.2454i	0.246741	+	0.427369i	0.962620	−	0.270856i	$-0.0873068\pi$
$821$	7.06991	+	12.2454i	0.246741	+	0.427369i	−0.715878	+	0.698225i	$0.753973\pi$
$822$		0			0
$823$	16.8643	−	29.2098i	0.587852	−	1.01819i	−0.406661	−	0.913579i	$-0.633307\pi$
$823$	16.8643	−	29.2098i	0.587852	−	1.01819i	0.994513	−	0.104611i	$-0.0333597\pi$
$824$	37.7477	+	65.3809i	1.31500	+	2.27765i
$825$		0			0
$826$	13.0070	−	16.6913i	0.452573	−	0.580764i
$827$	43.8428			1.52456			0.762282	−	0.647245i	$-0.224079\pi$
$827$	43.8428			1.52456			0.762282	+	0.647245i	$0.224079\pi$
$828$		0			0
$829$	−15.4144	+	26.6986i	−0.535365	+	0.927279i	0.463781	+	0.885950i	$0.346493\pi$
$829$	−15.4144	+	26.6986i	−0.535365	+	0.927279i	−0.999146	+	0.0413291i	$0.986841\pi$
$830$	−15.0249	+	26.0239i	−0.521521	+	0.903301i
$831$		0			0
$832$	3.14588			0.109064
$833$	−6.73364	−	1.91261i	−0.233307	−	0.0662682i
$834$		0			0
$835$	−29.2196	−	50.6099i	−1.01119	−	1.75143i
$836$	−20.4650	+	35.4464i	−0.707796	+	1.22594i
$837$		0			0
$838$	33.0840	+	57.3032i	1.14287	+	1.97951i
$839$	0.689347			0.0237989			0.0118995	−	0.999929i	$-0.496212\pi$
$839$	0.689347			0.0237989			0.0118995	+	0.999929i	$0.496212\pi$
$840$		0			0
$841$	−20.5819			−0.709721
$842$	13.7474	+	23.8111i	0.473765	+	0.820586i
$843$		0			0
$844$	−36.8669	+	63.8553i	−1.26901	+	2.19799i
$845$	14.7339	+	25.5199i	0.506862	+	0.877910i
$846$		0			0
$847$	40.6150	+	5.65624i	1.39555	+	0.194351i
$848$	57.2889			1.96731
$849$		0			0
$850$	0.537718	−	0.931356i	0.0184436	−	0.0319452i
$851$	19.5570	−	33.8738i	0.670406	−	1.16118i
$852$		0			0
$853$	−8.18346			−0.280196			−0.140098	−	0.990138i	$-0.544742\pi$
$853$	−8.18346			−0.280196			−0.140098	+	0.990138i	$0.544742\pi$
$854$	−26.1990	−	64.6119i	−0.896512	−	2.21097i
$855$		0			0
$856$	−2.41436	−	4.18180i	−0.0825211	−	0.142931i
$857$	25.5105	−	44.1855i	0.871423	−	1.50935i	0.0108975	−	0.999941i	$-0.496531\pi$
$857$	25.5105	−	44.1855i	0.871423	−	1.50935i	0.860525	−	0.509408i	$-0.170136\pi$
$858$		0			0
$859$	−9.77387	−	16.9288i	−0.333480	−	0.577605i	0.649712	−	0.760181i	$-0.274890\pi$
$859$	−9.77387	−	16.9288i	−0.333480	−	0.577605i	−0.983192	+	0.182576i	$0.941556\pi$
$860$	110.971			3.78408
$861$		0			0
$862$	15.9751			0.544114
$863$	−0.427888	−	0.741123i	−0.0145655	−	0.0252281i	0.858651	−	0.512561i	$-0.171303\pi$
$863$	−0.427888	−	0.741123i	−0.0145655	−	0.0252281i	−0.873216	+	0.487333i	$0.837970\pi$
$864$		0			0
$865$	19.2664	−	33.3704i	0.655077	−	1.13463i
$866$	26.1186	+	45.2387i	0.887545	+	1.53727i
$867$		0			0
$868$	−70.8924	−	9.87283i	−2.40625	−	0.335106i
$869$	−31.7082			−1.07563
$870$		0			0
$871$	−4.40828	+	7.63536i	−0.149369	+	0.258714i
$872$	−38.0394	+	65.8862i	−1.28818	+	2.23119i
$873$		0			0
$874$	19.6060			0.663182
$875$	17.3143	−	22.2186i	0.585331	−	0.751126i
$876$		0			0
$877$	5.01076	+	8.67889i	0.169201	+	0.293065i	0.938139	−	0.346258i	$-0.112548\pi$
$877$	5.01076	+	8.67889i	0.169201	+	0.293065i	−0.768938	+	0.639323i	$0.779214\pi$
$878$	8.88353	−	15.3867i	0.299805	−	0.519277i
$879$		0			0
$880$	−31.4391	−	54.4541i	−1.05981	−	1.83565i
$881$	−32.1954			−1.08469			−0.542345	−	0.840156i	$-0.682463\pi$
$881$	−32.1954			−1.08469			−0.542345	+	0.840156i	$0.682463\pi$
$882$		0			0
$883$	19.5142			0.656706			0.328353	−	0.944555i	$-0.393506\pi$
$883$	19.5142			0.656706			0.328353	+	0.944555i	$0.393506\pi$
$884$	−1.25367	−	2.17142i	−0.0421654	−	0.0730327i
$885$		0			0
$886$	29.6931	−	51.4300i	0.997560	−	1.72782i
$887$	0.141967	+	0.245894i	0.00476678	+	0.00825630i	0.868399	−	0.495866i	$-0.165149\pi$
$887$	0.141967	+	0.245894i	0.00476678	+	0.00825630i	−0.863632	+	0.504122i	$0.831816\pi$
$888$		0			0
$889$	−9.14267	+	11.7323i	−0.306635	+	0.393489i
$890$	−2.29047			−0.0767769
$891$		0			0
$892$	−52.2323	+	90.4689i	−1.74887	+	3.02912i
$893$	4.14866	−	7.18568i	0.138830	−	0.240460i
$894$		0			0
$895$	−10.6516			−0.356044
$896$	−45.3555	−	6.31643i	−1.51522	−	0.211017i
$897$		0			0
$898$	39.4978	+	68.4121i	1.31806	+	2.28294i
$899$	9.34405	−	16.1844i	0.311641	−	0.539779i
$900$		0			0
$901$	5.46554	+	9.46659i	0.182083	+	0.315378i
$902$	26.8303			0.893351
$903$		0			0
$904$	89.8957			2.98989
$905$	−27.1679	−	47.0561i	−0.903090	−	1.56420i
$906$		0			0
$907$	−6.85534	+	11.8738i	−0.227628	+	0.394263i	−0.957105	−	0.289743i	$-0.906430\pi$
$907$	−6.85534	+	11.8738i	−0.227628	+	0.394263i	0.729477	+	0.684006i	$0.239764\pi$
$908$	−17.4881	−	30.2902i	−0.580362	−	1.00522i
$909$		0			0
$910$	3.44423	+	8.49416i	0.114175	+	0.281579i
$911$	24.6522			0.816762			0.408381	−	0.912811i	$-0.366093\pi$
$911$	24.6522			0.816762			0.408381	+	0.912811i	$0.366093\pi$
$912$		0			0
$913$	−13.3276	+	23.0840i	−0.441078	+	0.763969i
$914$	−34.5134	+	59.7790i	−1.14160	+	1.97731i
$915$		0			0
$916$	71.5103			2.36277
$917$	−22.1265	−	3.08144i	−0.730681	−	0.101758i
$918$		0			0
$919$	2.82238	+	4.88850i	0.0931017	+	0.161257i	0.908815	−	0.417200i	$-0.136988\pi$
$919$	2.82238	+	4.88850i	0.0931017	+	0.161257i	−0.815713	+	0.578457i	$0.803655\pi$
$920$	−26.5537	+	45.9924i	−0.875450	+	1.51632i
$921$		0			0
$922$	−28.1456	−	48.7497i	−0.926927	−	1.60548i
$923$	−4.12519			−0.135782
$924$		0			0
$925$	−4.06153			−0.133542
$926$	−9.00239	−	15.5926i	−0.295837	−	0.512404i
$927$		0			0
$928$	−3.03658	+	5.25952i	−0.0996808	+	0.172652i
$929$	14.7322	+	25.5169i	0.483348	+	0.837184i	0.999817	−	0.0191223i	$-0.00608720\pi$
$929$	14.7322	+	25.5169i	0.483348	+	0.837184i	−0.516469	+	0.856306i	$0.672754\pi$
$930$		0			0
$931$	−9.50913	+	9.22896i	−0.311649	+	0.302467i
$932$	64.6809			2.11869
$933$		0			0
$934$	−38.4640	+	66.6216i	−1.25858	+	2.17993i
$935$	5.99877	−	10.3902i	0.196181	−	0.339795i
$936$		0			0
$937$	0.947116			0.0309409			0.0154705	−	0.999880i	$-0.495075\pi$
$937$	0.947116			0.0309409			0.0154705	+	0.999880i	$0.495075\pi$
$938$	59.8061	−	76.7461i	1.95274	−	2.50585i
$939$		0			0
$940$	21.4529	+	37.1576i	0.699718	+	1.21195i
$941$	−2.77876	+	4.81295i	−0.0905850	+	0.156898i	−0.907757	−	0.419495i	$-0.862207\pi$
$941$	−2.77876	+	4.81295i	−0.0905850	+	0.156898i	0.817172	+	0.576393i	$0.195540\pi$
$942$		0			0
$943$	−4.35317	−	7.53991i	−0.141759	−	0.245533i
$944$	−16.8342			−0.547905
$945$		0			0
$946$	145.307			4.72434
$947$	15.1118	+	26.1744i	0.491068	+	0.850554i	0.999947	−	0.0102836i	$-0.00327344\pi$
$947$	15.1118	+	26.1744i	0.491068	+	0.850554i	−0.508879	+	0.860838i	$0.669940\pi$
$948$		0			0
$949$	0.129553	−	0.224392i	0.00420546	−	0.00728407i
$950$	−1.01792	−	1.76310i	−0.0330258	−	0.0572024i
$951$		0			0
$952$	5.44652	+	13.4322i	0.176523	+	0.435340i
$953$	−47.8740			−1.55079			−0.775395	−	0.631476i	$-0.782449\pi$
$953$	−47.8740			−1.55079			−0.775395	+	0.631476i	$0.782449\pi$
$954$		0			0
$955$	21.2832	−	36.8635i	0.688707	−	1.19288i
$956$	25.4013	−	43.9963i	0.821536	−	1.42294i
$957$		0			0
$958$	54.3100			1.75468
$959$	−0.866662	−	2.13736i	−0.0279860	−	0.0690189i
$960$		0			0
$961$	−5.24368	−	9.08232i	−0.169151	−	0.292978i
$962$	−6.98916	+	12.1056i	−0.225340	+	0.390300i
$963$		0			0
$964$	−31.0698	−	53.8145i	−1.00069	−	1.73325i
$965$	−0.209550			−0.00674565
$966$		0			0
$967$	−32.5941			−1.04816			−0.524078	−	0.851671i	$-0.675590\pi$
$967$	−32.5941			−1.04816			−0.524078	+	0.851671i	$0.675590\pi$
$968$	−42.4552	−	73.5345i	−1.36456	−	2.36349i
$969$		0			0
$970$	50.6785	−	87.7777i	1.62719	−	2.81837i
$971$	−30.2776	−	52.4423i	−0.971654	−	1.68295i	−0.690562	−	0.723273i	$-0.742637\pi$
$971$	−30.2776	−	52.4423i	−0.971654	−	1.68295i	−0.281092	−	0.959681i	$-0.590697\pi$
$972$		0			0
$973$	20.1233	−	25.8232i	0.645123	−	0.827853i
$974$	11.3500			0.363679
$975$		0			0
$976$	−27.7329	+	48.0347i	−0.887707	+	1.53755i
$977$	−1.11354	+	1.92871i	−0.0356253	+	0.0617048i	−0.883288	−	0.468830i	$-0.844676\pi$
$977$	−1.11354	+	1.92871i	−0.0356253	+	0.0617048i	0.847663	+	0.530535i	$0.178009\pi$
$978$		0			0
$979$	−2.03172			−0.0649342
$980$	−16.7436	−	66.4462i	−0.534856	−	2.12254i
$981$		0			0
$982$	−1.99177	−	3.44984i	−0.0635599	−	0.110089i
$983$	−16.4458	+	28.4850i	−0.524541	+	0.908531i	0.475051	+	0.879958i	$0.342430\pi$
$983$	−16.4458	+	28.4850i	−0.524541	+	0.908531i	−0.999592	+	0.0285730i	$0.990904\pi$
$984$		0			0
$985$	5.23884	+	9.07393i	0.166923	+	0.289120i
$986$	−7.22450			−0.230075
$987$		0			0
$988$	−4.74650			−0.151006
$989$	−23.5758	−	40.8345i	−0.749667	−	1.29846i
$990$		0			0
$991$	19.6589	−	34.0503i	0.624487	−	1.08164i	−0.364153	−	0.931339i	$-0.618641\pi$
$991$	19.6589	−	34.0503i	0.624487	−	1.08164i	0.988640	−	0.150304i	$-0.0480252\pi$
$992$	6.74118	+	11.6761i	0.214033	+	0.370716i
$993$		0			0
$994$	45.0894	+	6.27937i	1.43015	+	0.199170i
$995$	−33.3882			−1.05848
$996$		0			0
$997$	19.3188	−	33.4611i	0.611832	−	1.05972i	−0.379099	−	0.925356i	$-0.623766\pi$
$997$	19.3188	−	33.4611i	0.611832	−	1.05972i	0.990931	−	0.134368i	$-0.0429006\pi$
$998$	31.3157	−	54.2403i	0.991280	−	1.71695i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1071.2.i.g.613.1		10
3.2	odd	2		357.2.i.f.256.5	yes	10
7.2	even	3	inner	1071.2.i.g.919.1		10
7.3	odd	6		7497.2.a.bw.1.5		5
7.4	even	3		7497.2.a.bv.1.5		5
21.2	odd	6		357.2.i.f.205.5	✓	10
21.11	odd	6		2499.2.a.ba.1.1		5
21.17	even	6		2499.2.a.bb.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.i.f.205.5	✓	10	21.2	odd	6
357.2.i.f.256.5	yes	10	3.2	odd	2
1071.2.i.g.613.1		10	1.1	even	1	trivial
1071.2.i.g.919.1		10	7.2	even	3	inner
2499.2.a.ba.1.1		5	21.11	odd	6
2499.2.a.bb.1.1		5	21.17	even	6
7497.2.a.bv.1.5		5	7.4	even	3
7497.2.a.bw.1.5		5	7.3	odd	6

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:	\( N \)	\(=\)	\( 1071 = 3^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1071.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24500 - 2.15641i) q^{2} +(-2.10007 + 3.63743i) q^{4} +(-1.16532 - 2.01840i) q^{5} +(-1.62628 + 2.08692i) q^{7} +5.47838 q^{8} +O(q^{10})\)	\(q+(-1.24500 - 2.15641i) q^{2} +(-2.10007 + 3.63743i) q^{4} +(-1.16532 - 2.01840i) q^{5} +(-1.62628 + 2.08692i) q^{7} +5.47838 q^{8} +(-2.90166 + 5.02583i) q^{10} +(-2.57387 + 4.45807i) q^{11} -0.596965 q^{13} +(6.52497 + 0.908700i) q^{14} +(-2.62046 - 4.53877i) q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.946522 - 1.63942i) q^{19} +9.78904 q^{20} +12.8179 q^{22} +(-2.07968 - 3.60212i) q^{23} +(-0.215950 + 0.374037i) q^{25} +(0.743224 + 1.28730i) q^{26} +(-4.17572 - 10.2981i) q^{28} +2.90140 q^{29} +(3.22053 - 5.57813i) q^{31} +(-1.04659 + 1.81275i) q^{32} -2.49001 q^{34} +(6.10736 + 0.850541i) q^{35} +(4.70193 + 8.14397i) q^{37} +(-2.35685 + 4.08218i) q^{38} +(-6.38408 - 11.0575i) q^{40} +2.09319 q^{41} +11.3362 q^{43} +(-10.8106 - 18.7245i) q^{44} +(-5.17843 + 8.96930i) q^{46} +(2.19153 + 3.79584i) q^{47} +(-1.71045 - 6.78781i) q^{49} +1.07544 q^{50} +(1.25367 - 2.17142i) q^{52} +(-5.46554 + 9.46659i) q^{53} +11.9975 q^{55} +(-8.90936 + 11.4329i) q^{56} +(-3.61225 - 6.25660i) q^{58} +(1.60603 - 2.78172i) q^{59} +(-5.29160 - 9.16532i) q^{61} -16.0383 q^{62} -5.26979 q^{64} +(0.695656 + 1.20491i) q^{65} +(7.38448 - 12.7903i) q^{67} +(2.10007 + 3.63743i) q^{68} +(-5.76958 - 14.2289i) q^{70} +6.91028 q^{71} +(-0.217019 + 0.375888i) q^{73} +(11.7078 - 20.2786i) q^{74} +7.95106 q^{76} +(-5.11780 - 12.6215i) q^{77} +(3.07982 + 5.33441i) q^{79} +(-6.10736 + 10.5783i) q^{80} +(-2.60603 - 4.51377i) q^{82} +5.17802 q^{83} -2.33064 q^{85} +(-14.1137 - 24.4456i) q^{86} +(-14.1006 + 24.4230i) q^{88} +(0.197342 + 0.341806i) q^{89} +(0.970830 - 1.24582i) q^{91} +17.4699 q^{92} +(5.45692 - 9.45166i) q^{94} +(-2.20601 + 3.82091i) q^{95} -17.4653 q^{97} +(-12.5078 + 12.1393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7}+O(q^{10}) \) 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7	\( 10 q - 2 q^{2} - 8 q^{4} + q^{5} - 5 q^{7} - 13 q^{10} - 11 q^{11} + 14 q^{13} - 3 q^{14} + 2 q^{16} + 5 q^{17} - 9 q^{19} - 24 q^{20} + 10 q^{22} - 23 q^{23} - 14 q^{25} + 18 q^{26} + 7 q^{28} + 36 q^{29} - 9 q^{31} + 3 q^{32} - 4 q^{34} + 5 q^{35} - 31 q^{40} - 6 q^{41} + 24 q^{43} - 33 q^{44} - 13 q^{46} + 11 q^{47} + 3 q^{49} - 48 q^{50} - 5 q^{52} - 3 q^{53} - 20 q^{55} + 27 q^{56} + 34 q^{58} - 14 q^{59} - 29 q^{61} + 10 q^{62} - 8 q^{65} - 16 q^{67} + 8 q^{68} + 18 q^{70} + 38 q^{71} - 11 q^{73} + 45 q^{74} + 18 q^{76} - 21 q^{77} - q^{79} - 5 q^{80} + 4 q^{82} - 10 q^{83} + 2 q^{85} - 3 q^{86} - 37 q^{88} + 8 q^{89} - 33 q^{91} + 96 q^{92} + 18 q^{94} - 21 q^{95} + 38 q^{97} + 17 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 8 * q^4 + q^5 - 5 * q^7 - 13 * q^10 - 11 * q^11 + 14 * q^13 - 3 * q^14 + 2 * q^16 + 5 * q^17 - 9 * q^19 - 24 * q^20 + 10 * q^22 - 23 * q^23 - 14 * q^25 + 18 * q^26 + 7 * q^28 + 36 * q^29 - 9 * q^31 + 3 * q^32 - 4 * q^34 + 5 * q^35 - 31 * q^40 - 6 * q^41 + 24 * q^43 - 33 * q^44 - 13 * q^46 + 11 * q^47 + 3 * q^49 - 48 * q^50 - 5 * q^52 - 3 * q^53 - 20 * q^55 + 27 * q^56 + 34 * q^58 - 14 * q^59 - 29 * q^61 + 10 * q^62 - 8 * q^65 - 16 * q^67 + 8 * q^68 + 18 * q^70 + 38 * q^71 - 11 * q^73 + 45 * q^74 + 18 * q^76 - 21 * q^77 - q^79 - 5 * q^80 + 4 * q^82 - 10 * q^83 + 2 * q^85 - 3 * q^86 - 37 * q^88 + 8 * q^89 - 33 * q^91 + 96 * q^92 + 18 * q^94 - 21 * q^95 + 38 * q^97 + 17 * q^98

Introduction

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