LMFDB - Embedded newform 735.2.d.c.589.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(589,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.589"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.309760000.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 8x^{6} - 2x^{5} - x^{4} - 2x^{3} + 18x^{2} + 6x + 1 $ x^8 - 4x^7 + 8x^6 - 2x^5 - x^4 - 2x^3 + 18x^2 + 6x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.7
Root			$-0.748606 - 0.748606i$ of defining polynomial
Character	$\chi$	$=$	735.589
Dual form			735.2.d.c.589.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.49721i q^{2} -1.00000i q^{3} -4.23607 q^{4} +(1.54336 - 1.61803i) q^{5} +2.49721 q^{6} -5.58394i q^{8} -1.00000 q^{9} +(4.04057 + 3.85410i) q^{10} -4.47214 q^{11} +4.23607i q^{12} -5.23607i q^{13} +(-1.61803 - 1.54336i) q^{15} +5.47214 q^{16} +0.763932i q^{17} -2.49721i q^{18} -8.08115 q^{19} +(-6.53779 + 6.85410i) q^{20} -11.1679i q^{22} -3.08672i q^{23} -5.58394 q^{24} +(-0.236068 - 4.99442i) q^{25} +13.0756 q^{26} +1.00000i q^{27} -2.00000 q^{29} +(3.85410 - 4.04057i) q^{30} -1.90770 q^{31} +2.49721i q^{32} +4.47214i q^{33} -1.90770 q^{34} +4.23607 q^{36} -6.17345i q^{37} -20.1803i q^{38} -5.23607 q^{39} +(-9.03500 - 8.61803i) q^{40} +6.90212 q^{41} +9.98885i q^{43} +18.9443 q^{44} +(-1.54336 + 1.61803i) q^{45} +7.70820 q^{46} -4.94427i q^{47} -5.47214i q^{48} +(12.4721 - 0.589512i) q^{50} +0.763932 q^{51} +22.1803i q^{52} -1.90770i q^{53} -2.49721 q^{54} +(-6.90212 + 7.23607i) q^{55} +8.08115i q^{57} -4.99442i q^{58} +9.98885 q^{59} +(6.85410 + 6.53779i) q^{60} +3.81540 q^{61} -4.76393i q^{62} +4.70820 q^{64} +(-8.47214 - 8.08115i) q^{65} -11.1679 q^{66} +6.17345i q^{67} -3.23607i q^{68} -3.08672 q^{69} +0.472136 q^{71} +5.58394i q^{72} -2.76393i q^{73} +15.4164 q^{74} +(-4.99442 + 0.236068i) q^{75} +34.2323 q^{76} -13.0756i q^{78} -12.9443 q^{79} +(8.44549 - 8.85410i) q^{80} +1.00000 q^{81} +17.2361i q^{82} -6.47214i q^{83} +(1.23607 + 1.17902i) q^{85} -24.9443 q^{86} +2.00000i q^{87} +24.9721i q^{88} +9.26017 q^{89} +(-4.04057 - 3.85410i) q^{90} +13.0756i q^{92} +1.90770i q^{93} +12.3469 q^{94} +(-12.4721 + 13.0756i) q^{95} +2.49721 q^{96} +10.1803i q^{97} +4.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{4} - 8 q^{9} - 4 q^{15} + 8 q^{16} + 16 q^{25} - 16 q^{29} + 4 q^{30} + 16 q^{36} - 24 q^{39} + 80 q^{44} + 8 q^{46} + 64 q^{50} + 24 q^{51} + 28 q^{60} - 16 q^{64} - 32 q^{65} - 32 q^{71} + 16 q^{74}+ \cdots - 64 q^{95}+O(q^{100}) $ 8 * q - 16 * q^4 - 8 * q^9 - 4 * q^15 + 8 * q^16 + 16 * q^25 - 16 * q^29 + 4 * q^30 + 16 * q^36 - 24 * q^39 + 80 * q^44 + 8 * q^46 + 64 * q^50 + 24 * q^51 + 28 * q^60 - 16 * q^64 - 32 * q^65 - 32 * q^71 + 16 * q^74 - 32 * q^79 + 8 * q^81 - 8 * q^85 - 128 * q^86 - 64 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$			2.49721i			1.76580i	0.469565	+	0.882898i	$0.344411\pi$
$2$			2.49721i			1.76580i	−0.469565	+	0.882898i	$0.655589\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−4.23607			−2.11803
$5$	1.54336	−	1.61803i	0.690212	−	0.723607i
$5$	1.54336	−	1.61803i	0.690212	−	0.723607i
$6$	2.49721			1.01948
$7$		0			0
$7$		0			0
$8$		−	5.58394i		−	1.97422i
$9$	−1.00000			−0.333333
$10$	4.04057	+	3.85410i	1.27774	+	1.21877i
$11$	−4.47214			−1.34840			−0.674200	−	0.738549i	$-0.735511\pi$
$11$	−4.47214			−1.34840			−0.674200	+	0.738549i	$0.735511\pi$
$12$			4.23607i			1.22285i
$13$		−	5.23607i		−	1.45222i	−0.687576	−	0.726112i	$-0.741325\pi$
$13$		−	5.23607i		−	1.45222i	0.687576	−	0.726112i	$-0.258675\pi$
$14$		0			0
$15$	−1.61803	−	1.54336i	−0.417775	−	0.398494i
$16$	5.47214			1.36803
$17$			0.763932i			0.185281i	0.995700	+	0.0926404i	$0.0295307\pi$
$17$			0.763932i			0.185281i	−0.995700	+	0.0926404i	$0.970469\pi$
$18$		−	2.49721i		−	0.588599i
$19$	−8.08115			−1.85394			−0.926971	−	0.375132i	$-0.877597\pi$
$19$	−8.08115			−1.85394			−0.926971	+	0.375132i	$0.877597\pi$
$20$	−6.53779	+	6.85410i	−1.46189	+	1.53262i
$21$		0			0
$22$		−	11.1679i		−	2.38100i
$23$		−	3.08672i		−	0.643626i	−0.946803	−	0.321813i	$-0.895708\pi$
$23$		−	3.08672i		−	0.643626i	0.946803	−	0.321813i	$-0.104292\pi$
$24$	−5.58394			−1.13982
$25$	−0.236068	−	4.99442i	−0.0472136	−	0.998885i
$26$	13.0756			2.56433
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	3.85410	−	4.04057i	0.703660	−	0.737705i
$31$	−1.90770			−0.342633			−0.171317	−	0.985216i	$-0.554802\pi$
$31$	−1.90770			−0.342633			−0.171317	+	0.985216i	$0.554802\pi$
$32$			2.49721i			0.441449i
$33$			4.47214i			0.778499i
$34$	−1.90770			−0.327168
$35$		0			0
$36$	4.23607			0.706011
$37$		−	6.17345i		−	1.01491i	−0.861679	−	0.507454i	$-0.830587\pi$
$37$		−	6.17345i		−	1.01491i	0.861679	−	0.507454i	$-0.169413\pi$
$38$		−	20.1803i		−	3.27368i
$39$	−5.23607			−0.838442
$40$	−9.03500	−	8.61803i	−1.42856	−	1.36263i
$41$	6.90212			1.07793			0.538965	−	0.842328i	$-0.318815\pi$
$41$	6.90212			1.07793			0.538965	+	0.842328i	$0.318815\pi$
$42$		0			0
$43$			9.98885i			1.52329i	0.647997	+	0.761643i	$0.275607\pi$
$43$			9.98885i			1.52329i	−0.647997	+	0.761643i	$0.724393\pi$
$44$	18.9443			2.85596
$45$	−1.54336	+	1.61803i	−0.230071	+	0.241202i
$46$	7.70820			1.13651
$47$		−	4.94427i		−	0.721196i	−0.932721	−	0.360598i	$-0.882573\pi$
$47$		−	4.94427i		−	0.721196i	0.932721	−	0.360598i	$-0.117427\pi$
$48$		−	5.47214i		−	0.789835i
$49$		0			0
$50$	12.4721	−	0.589512i	1.76383	−	0.0833696i
$51$	0.763932			0.106972
$52$			22.1803i			3.07586i
$53$		−	1.90770i		−	0.262043i	−0.991380	−	0.131021i	$-0.958174\pi$
$53$		−	1.90770i		−	0.262043i	0.991380	−	0.131021i	$-0.0418257\pi$
$54$	−2.49721			−0.339828
$55$	−6.90212	+	7.23607i	−0.930682	+	0.975711i
$56$		0			0
$57$			8.08115i			1.07037i
$58$		−	4.99442i		−	0.655800i
$59$	9.98885			1.30044			0.650219	−	0.759747i	$-0.274677\pi$
$59$	9.98885			1.30044			0.650219	+	0.759747i	$0.274677\pi$
$60$	6.85410	+	6.53779i	0.884861	+	0.844025i
$61$	3.81540			0.488512			0.244256	−	0.969711i	$-0.421456\pi$
$61$	3.81540			0.488512			0.244256	+	0.969711i	$0.421456\pi$
$62$		−	4.76393i		−	0.605020i
$63$		0			0
$64$	4.70820			0.588525
$65$	−8.47214	−	8.08115i	−1.05084	−	1.00234i
$66$	−11.1679			−1.37467
$67$			6.17345i			0.754207i	0.926171	+	0.377103i	$0.123080\pi$
$67$			6.17345i			0.754207i	−0.926171	+	0.377103i	$0.876920\pi$
$68$		−	3.23607i		−	0.392431i
$69$	−3.08672			−0.371598
$70$		0			0
$71$	0.472136			0.0560322			0.0280161	−	0.999607i	$-0.491081\pi$
$71$	0.472136			0.0560322			0.0280161	+	0.999607i	$0.491081\pi$
$72$			5.58394i			0.658073i
$73$		−	2.76393i		−	0.323494i	−0.986832	−	0.161747i	$-0.948287\pi$
$73$		−	2.76393i		−	0.323494i	0.986832	−	0.161747i	$-0.0517128\pi$
$74$	15.4164			1.79212
$75$	−4.99442	+	0.236068i	−0.576706	+	0.0272588i
$76$	34.2323			3.92671
$77$		0			0
$78$		−	13.0756i		−	1.48052i
$79$	−12.9443			−1.45634			−0.728172	−	0.685394i	$-0.759630\pi$
$79$	−12.9443			−1.45634			−0.728172	+	0.685394i	$0.759630\pi$
$80$	8.44549	−	8.85410i	0.944234	−	0.989919i
$81$	1.00000			0.111111
$82$			17.2361i			1.90341i
$83$		−	6.47214i		−	0.710409i	−0.934789	−	0.355205i	$-0.884411\pi$
$83$		−	6.47214i		−	0.710409i	0.934789	−	0.355205i	$-0.115589\pi$
$84$		0			0
$85$	1.23607	+	1.17902i	0.134070	+	0.127883i
$86$	−24.9443			−2.68981
$87$			2.00000i			0.214423i
$88$			24.9721i			2.66204i
$89$	9.26017			0.981576			0.490788	−	0.871279i	$-0.336709\pi$
$89$	9.26017			0.981576			0.490788	+	0.871279i	$0.336709\pi$
$90$	−4.04057	−	3.85410i	−0.425914	−	0.406258i
$91$		0			0
$92$			13.0756i			1.36322i
$93$			1.90770i			0.197819i
$94$	12.3469			1.27349
$95$	−12.4721	+	13.0756i	−1.27961	+	1.34153i
$96$	2.49721			0.254871
$97$			10.1803i			1.03366i	0.856089	+	0.516828i	$0.172887\pi$
$97$			10.1803i			1.03366i	−0.856089	+	0.516828i	$0.827113\pi$
$98$		0			0
$99$	4.47214			0.449467
$100$	1.00000	+	21.1567i	0.100000	+	2.11567i
$101$	−13.0756			−1.30107			−0.650534	−	0.759477i	$-0.725455\pi$
$101$	−13.0756			−1.30107			−0.650534	+	0.759477i	$0.725455\pi$
$102$			1.90770i			0.188890i
$103$		−	1.52786i		−	0.150545i	−0.997163	−	0.0752725i	$-0.976017\pi$
$103$		−	1.52786i		−	0.150545i	0.997163	−	0.0752725i	$-0.0239827\pi$
$104$	−29.2379			−2.86701
$105$		0			0
$106$	4.76393			0.462714
$107$		−	6.90212i		−	0.667254i	−0.942705	−	0.333627i	$-0.891727\pi$
$107$		−	6.90212i		−	0.667254i	0.942705	−	0.333627i	$-0.108273\pi$
$108$		−	4.23607i		−	0.407616i
$109$	−12.4721			−1.19461			−0.597307	−	0.802013i	$-0.703763\pi$
$109$	−12.4721			−1.19461			−0.597307	+	0.802013i	$0.703763\pi$
$110$	−18.0700	−	17.2361i	−1.72291	−	1.64339i
$111$	−6.17345			−0.585958
$112$		0			0
$113$			4.26575i			0.401288i	0.979664	+	0.200644i	$0.0643034\pi$
$113$			4.26575i			0.401288i	−0.979664	+	0.200644i	$0.935697\pi$
$114$	−20.1803			−1.89006
$115$	−4.99442	−	4.76393i	−0.465732	−	0.444239i
$116$	8.47214			0.786618
$117$			5.23607i			0.484075i
$118$			24.9443i			2.29631i
$119$		0			0
$120$	−8.61803	+	9.03500i	−0.786715	+	0.824779i
$121$	9.00000			0.818182
$122$			9.52786i			0.862612i
$123$		−	6.90212i		−	0.622344i
$124$	8.08115			0.725709
$125$	−8.44549	−	7.32624i	−0.755387	−	0.655279i
$126$		0			0
$127$		−	3.81540i		−	0.338562i	−0.985568	−	0.169281i	$-0.945855\pi$
$127$		−	3.81540i		−	0.338562i	0.985568	−	0.169281i	$-0.0541445\pi$
$128$			16.7518i			1.48066i
$129$	9.98885			0.879469
$130$	20.1803	−	21.1567i	1.76993	−	1.85557i
$131$	9.98885			0.872730			0.436365	−	0.899770i	$-0.356266\pi$
$131$	9.98885			0.872730			0.436365	+	0.899770i	$0.356266\pi$
$132$		−	18.9443i		−	1.64889i
$133$		0			0
$134$	−15.4164			−1.33177
$135$	1.61803	+	1.54336i	0.139258	+	0.132831i
$136$	4.26575			0.365785
$137$		−	8.08115i		−	0.690419i	−0.938526	−	0.345210i	$-0.887808\pi$
$137$		−	8.08115i		−	0.690419i	0.938526	−	0.345210i	$-0.112192\pi$
$138$		−	7.70820i		−	0.656166i
$139$	14.2546			1.20906			0.604530	−	0.796583i	$-0.293361\pi$
$139$	14.2546			1.20906			0.604530	+	0.796583i	$0.293361\pi$
$140$		0			0
$141$	−4.94427			−0.416383
$142$			1.17902i			0.0989415i
$143$			23.4164i			1.95818i
$144$	−5.47214			−0.456011
$145$	−3.08672	+	3.23607i	−0.256338	+	0.268741i
$146$	6.90212			0.571224
$147$		0			0
$148$			26.1511i			2.14961i
$149$	18.9443			1.55198			0.775988	−	0.630748i	$-0.217252\pi$
$149$	18.9443			1.55198			0.775988	+	0.630748i	$0.217252\pi$
$150$	−0.589512	−	12.4721i	−0.0481334	−	1.01835i
$151$	−8.94427			−0.727875			−0.363937	−	0.931423i	$-0.618568\pi$
$151$	−8.94427			−0.727875			−0.363937	+	0.931423i	$0.618568\pi$
$152$			45.1246i			3.66009i
$153$		−	0.763932i		−	0.0617602i
$154$		0			0
$155$	−2.94427	+	3.08672i	−0.236490	+	0.247932i
$156$	22.1803			1.77585
$157$		−	8.65248i		−	0.690543i	−0.938503	−	0.345271i	$-0.887787\pi$
$157$		−	8.65248i		−	0.690543i	0.938503	−	0.345271i	$-0.112213\pi$
$158$		−	32.3246i		−	2.57161i
$159$	−1.90770			−0.151290
$160$	4.04057	+	3.85410i	0.319435	+	0.304694i
$161$		0			0
$162$			2.49721i			0.196200i
$163$		−	3.81540i		−	0.298845i	−0.988773	−	0.149423i	$-0.952259\pi$
$163$		−	3.81540i		−	0.298845i	0.988773	−	0.149423i	$-0.0477415\pi$
$164$	−29.2379			−2.28309
$165$	7.23607	+	6.90212i	0.563327	+	0.537330i
$166$	16.1623			1.25444
$167$		−	15.4164i		−	1.19296i	−0.802629	−	0.596479i	$-0.796566\pi$
$167$		−	15.4164i		−	1.19296i	0.802629	−	0.596479i	$-0.203434\pi$
$168$		0			0
$169$	−14.4164			−1.10895
$170$	−2.94427	+	3.08672i	−0.225815	+	0.236741i
$171$	8.08115			0.617981
$172$		−	42.3134i		−	3.22637i
$173$		−	19.2361i		−	1.46249i	−0.682114	−	0.731246i	$-0.738939\pi$
$173$		−	19.2361i		−	1.46249i	0.682114	−	0.731246i	$-0.261061\pi$
$174$	−4.99442			−0.378626
$175$		0			0
$176$	−24.4721			−1.84466
$177$		−	9.98885i		−	0.750808i
$178$			23.1246i			1.73326i
$179$	7.52786			0.562659			0.281329	−	0.959611i	$-0.409225\pi$
$179$	7.52786			0.562659			0.281329	+	0.959611i	$0.409225\pi$
$180$	6.53779	−	6.85410i	0.487298	−	0.510875i
$181$	−9.98885			−0.742465			−0.371233	−	0.928540i	$-0.621065\pi$
$181$	−9.98885			−0.742465			−0.371233	+	0.928540i	$0.621065\pi$
$182$		0			0
$183$		−	3.81540i		−	0.282043i
$184$	−17.2361			−1.27066
$185$	−9.98885	−	9.52786i	−0.734395	−	0.700502i
$186$	−4.76393			−0.349308
$187$		−	3.41641i		−	0.249832i
$188$			20.9443i			1.52752i
$189$		0			0
$190$	−32.6525	−	31.1456i	−2.36886	−	2.25954i
$191$	−3.52786			−0.255267			−0.127634	−	0.991821i	$-0.540738\pi$
$191$	−3.52786			−0.255267			−0.127634	+	0.991821i	$0.540738\pi$
$192$		−	4.70820i		−	0.339785i
$193$			13.8042i			0.993652i	0.867850	+	0.496826i	$0.165501\pi$
$193$			13.8042i			0.993652i	−0.867850	+	0.496826i	$0.834499\pi$
$194$	−25.4225			−1.82523
$195$	−8.08115	+	8.47214i	−0.578703	+	0.606702i
$196$		0			0
$197$		−	1.90770i		−	0.135918i	−0.997688	−	0.0679590i	$-0.978351\pi$
$197$		−	1.90770i		−	0.135918i	0.997688	−	0.0679590i	$-0.0216487\pi$
$198$			11.1679i			0.793666i
$199$	11.8965			0.843324			0.421662	−	0.906753i	$-0.361447\pi$
$199$	11.8965			0.843324			0.421662	+	0.906753i	$0.361447\pi$
$200$	−27.8885	+	1.31819i	−1.97202	+	0.0932100i
$201$	6.17345			0.435441
$202$		−	32.6525i		−	2.29742i
$203$		0			0
$204$	−3.23607			−0.226570
$205$	10.6525	−	11.1679i	0.744001	−	0.779998i
$206$	3.81540			0.265832
$207$			3.08672i			0.214542i
$208$		−	28.6525i		−	1.98669i
$209$	36.1400			2.49986
$210$		0			0
$211$	−12.9443			−0.891120			−0.445560	−	0.895252i	$-0.646995\pi$
$211$	−12.9443			−0.891120			−0.445560	+	0.895252i	$0.646995\pi$
$212$			8.08115i			0.555016i
$213$		−	0.472136i		−	0.0323502i
$214$	17.2361			1.17823
$215$	16.1623	+	15.4164i	1.10226	+	1.05139i
$216$	5.58394			0.379939
$217$		0			0
$218$		−	31.1456i		−	2.10944i
$219$	−2.76393			−0.186769
$220$	29.2379	−	30.6525i	1.97122	−	2.06659i
$221$	4.00000			0.269069
$222$		−	15.4164i		−	1.03468i
$223$			17.8885i			1.19791i	0.800784	+	0.598953i	$0.204416\pi$
$223$			17.8885i			1.19791i	−0.800784	+	0.598953i	$0.795584\pi$
$224$		0			0
$225$	0.236068	+	4.99442i	0.0157379	+	0.332962i
$226$	−10.6525			−0.708592
$227$		−	1.52786i		−	0.101408i	−0.998714	−	0.0507039i	$-0.983854\pi$
$227$		−	1.52786i		−	0.101408i	0.998714	−	0.0507039i	$-0.0161465\pi$
$228$		−	34.2323i		−	2.26709i
$229$	−22.3357			−1.47599			−0.737994	−	0.674808i	$-0.764227\pi$
$229$	−22.3357			−1.47599			−0.737994	+	0.674808i	$0.764227\pi$
$230$	11.8965	−	12.4721i	0.784435	−	0.822388i
$231$		0			0
$232$			11.1679i			0.733207i
$233$			11.8965i			0.779369i	0.920948	+	0.389684i	$0.127416\pi$
$233$			11.8965i			0.779369i	−0.920948	+	0.389684i	$0.872584\pi$
$234$	−13.0756			−0.854777
$235$	−8.00000	−	7.63080i	−0.521862	−	0.497779i
$236$	−42.3134			−2.75437
$237$			12.9443i			0.840821i
$238$		0			0
$239$	7.52786			0.486937			0.243469	−	0.969909i	$-0.421715\pi$
$239$	7.52786			0.486937			0.243469	+	0.969909i	$0.421715\pi$
$240$	−8.85410	−	8.44549i	−0.571530	−	0.545154i
$241$	−6.17345			−0.397667			−0.198833	−	0.980033i	$-0.563715\pi$
$241$	−6.17345			−0.397667			−0.198833	+	0.980033i	$0.563715\pi$
$242$			22.4749i			1.44474i
$243$		−	1.00000i		−	0.0641500i
$244$	−16.1623			−1.03468
$245$		0			0
$246$	17.2361			1.09893
$247$			42.3134i			2.69234i
$248$			10.6525i			0.676433i
$249$	−6.47214			−0.410155
$250$	18.2952	−	21.0902i	1.15709	−	1.33386i
$251$	2.35805			0.148839			0.0744193	−	0.997227i	$-0.476290\pi$
$251$	2.35805			0.148839			0.0744193	+	0.997227i	$0.476290\pi$
$252$		0			0
$253$			13.8042i			0.867866i
$254$	9.52786			0.597831
$255$	1.17902	−	1.23607i	0.0738333	−	0.0774056i
$256$	−32.4164			−2.02603
$257$			21.7082i			1.35412i	0.735928	+	0.677060i	$0.236746\pi$
$257$			21.7082i			1.35412i	−0.735928	+	0.677060i	$0.763254\pi$
$258$			24.9443i			1.55296i
$259$		0			0
$260$	35.8885	+	34.2323i	2.22571	+	2.12300i
$261$	2.00000			0.123797
$262$			24.9443i			1.54106i
$263$			15.4336i			0.951678i	0.879532	+	0.475839i	$0.157855\pi$
$263$			15.4336i			0.951678i	−0.879532	+	0.475839i	$0.842145\pi$
$264$	24.9721			1.53693
$265$	−3.08672	−	2.94427i	−0.189616	−	0.180865i
$266$		0			0
$267$		−	9.26017i		−	0.566713i
$268$		−	26.1511i		−	1.59744i
$269$	6.90212			0.420830			0.210415	−	0.977612i	$-0.432518\pi$
$269$	6.90212			0.420830			0.210415	+	0.977612i	$0.432518\pi$
$270$	−3.85410	+	4.04057i	−0.234553	+	0.245902i
$271$	−18.0700			−1.09767			−0.548837	−	0.835929i	$-0.684929\pi$
$271$	−18.0700			−1.09767			−0.548837	+	0.835929i	$0.684929\pi$
$272$			4.18034i			0.253470i
$273$		0			0
$274$	20.1803			1.21914
$275$	1.05573	+	22.3357i	0.0636628	+	1.34690i
$276$	13.0756			0.787057
$277$			9.98885i			0.600172i	0.953912	+	0.300086i	$0.0970153\pi$
$277$			9.98885i			0.600172i	−0.953912	+	0.300086i	$0.902985\pi$
$278$			35.5967i			2.13495i
$279$	1.90770			0.114211
$280$		0			0
$281$	−22.0000			−1.31241			−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000			−1.31241			−0.656205	+	0.754583i	$0.727839\pi$
$282$		−	12.3469i		−	0.735247i
$283$		−	12.3607i		−	0.734766i	−0.930070	−	0.367383i	$-0.880254\pi$
$283$		−	12.3607i		−	0.734766i	0.930070	−	0.367383i	$-0.119746\pi$
$284$	−2.00000			−0.118678
$285$	13.0756	+	12.4721i	0.774530	+	0.738786i
$286$	−58.4757			−3.45774
$287$		0			0
$288$		−	2.49721i		−	0.147150i
$289$	16.4164			0.965671
$290$	−8.08115	−	7.70820i	−0.474541	−	0.452641i
$291$	10.1803			0.596782
$292$			11.7082i			0.685171i
$293$		−	20.1803i		−	1.17895i	−0.807787	−	0.589474i	$-0.799335\pi$
$293$		−	20.1803i		−	1.17895i	0.807787	−	0.589474i	$-0.200665\pi$
$294$		0			0
$295$	15.4164	−	16.1623i	0.897578	−	0.941005i
$296$	−34.4721			−2.00365
$297$		−	4.47214i		−	0.259500i
$298$			47.3079i			2.74047i
$299$	−16.1623			−0.934690
$300$	21.1567	−	1.00000i	1.22148	−	0.0577350i
$301$		0			0
$302$		−	22.3357i		−	1.28528i
$303$			13.0756i			0.751172i
$304$	−44.2211			−2.53626
$305$	5.88854	−	6.17345i	0.337177	−	0.353491i
$306$	1.90770			0.109056
$307$			2.47214i			0.141092i	0.997509	+	0.0705461i	$0.0224742\pi$
$307$			2.47214i			0.141092i	−0.997509	+	0.0705461i	$0.977526\pi$
$308$		0			0
$309$	−1.52786			−0.0869171
$310$	−7.70820	−	7.35247i	−0.437797	−	0.417592i
$311$	−3.81540			−0.216352			−0.108176	−	0.994132i	$-0.534501\pi$
$311$	−3.81540			−0.216352			−0.108176	+	0.994132i	$0.534501\pi$
$312$			29.2379i			1.65527i
$313$		−	24.6525i		−	1.39344i	−0.717343	−	0.696720i	$-0.754642\pi$
$313$		−	24.6525i		−	1.39344i	0.717343	−	0.696720i	$-0.245358\pi$
$314$	21.6071			1.21936
$315$		0			0
$316$	54.8328			3.08459
$317$		−	10.4392i		−	0.586324i	−0.956063	−	0.293162i	$-0.905293\pi$
$317$		−	10.4392i		−	0.586324i	0.956063	−	0.293162i	$-0.0947075\pi$
$318$		−	4.76393i		−	0.267148i
$319$	8.94427			0.500783
$320$	7.26646	−	7.61803i	0.406208	−	0.425861i
$321$	−6.90212			−0.385239
$322$		0			0
$323$		−	6.17345i		−	0.343500i
$324$	−4.23607			−0.235337
$325$	−26.1511	+	1.23607i	−1.45060	+	0.0685647i
$326$	9.52786			0.527700
$327$			12.4721i			0.689711i
$328$		−	38.5410i		−	2.12807i
$329$		0			0
$330$	−17.2361	+	18.0700i	−0.948814	+	0.994721i
$331$	8.00000			0.439720			0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000			0.439720			0.219860	+	0.975531i	$0.429440\pi$
$332$			27.4164i			1.50467i
$333$			6.17345i			0.338303i
$334$	38.4980			2.10652
$335$	9.98885	+	9.52786i	0.545749	+	0.520563i
$336$		0			0
$337$		−	3.81540i		−	0.207838i	−0.994586	−	0.103919i	$-0.966862\pi$
$337$		−	3.81540i		−	0.207838i	0.994586	−	0.103919i	$-0.0331383\pi$
$338$		−	36.0008i		−	1.95819i
$339$	4.26575			0.231684
$340$	−5.23607	−	4.99442i	−0.283966	−	0.270861i
$341$	8.53149			0.462006
$342$			20.1803i			1.09123i
$343$		0			0
$344$	55.7771			3.00730
$345$	−4.76393	+	4.99442i	−0.256481	+	0.268891i
$346$	48.0365			2.58246
$347$			25.4225i			1.36475i	0.731003	+	0.682375i	$0.239053\pi$
$347$			25.4225i			1.36475i	−0.731003	+	0.682375i	$0.760947\pi$
$348$		−	8.47214i		−	0.454154i
$349$	−8.53149			−0.456680			−0.228340	−	0.973581i	$-0.573330\pi$
$349$	−8.53149			−0.456680			−0.228340	+	0.973581i	$0.573330\pi$
$350$		0			0
$351$	5.23607			0.279481
$352$		−	11.1679i		−	0.595250i
$353$			3.23607i			0.172239i	0.996285	+	0.0861193i	$0.0274466\pi$
$353$			3.23607i			0.172239i	−0.996285	+	0.0861193i	$0.972553\pi$
$354$	24.9443			1.32577
$355$	0.728677	−	0.763932i	0.0386741	−	0.0405453i
$356$	−39.2267			−2.07901
$357$		0			0
$358$			18.7987i			0.993541i
$359$	−20.4721			−1.08048			−0.540239	−	0.841512i	$-0.681666\pi$
$359$	−20.4721			−1.08048			−0.540239	+	0.841512i	$0.681666\pi$
$360$	9.03500	+	8.61803i	0.476186	+	0.454210i
$361$	46.3050			2.43710
$362$		−	24.9443i		−	1.31104i
$363$		−	9.00000i		−	0.472377i
$364$		0			0
$365$	−4.47214	−	4.26575i	−0.234082	−	0.223279i
$366$	9.52786			0.498029
$367$		−	16.0000i		−	0.835193i	−0.908633	−	0.417597i	$-0.862873\pi$
$367$		−	16.0000i		−	0.835193i	0.908633	−	0.417597i	$-0.137127\pi$
$368$		−	16.8910i		−	0.880503i
$369$	−6.90212			−0.359310
$370$	23.7931	−	24.9443i	1.23694	−	1.29679i
$371$		0			0
$372$		−	8.08115i		−	0.418988i
$373$		−	32.3246i		−	1.67370i	−0.547429	−	0.836852i	$-0.684393\pi$
$373$		−	32.3246i		−	1.67370i	0.547429	−	0.836852i	$-0.315607\pi$
$374$	8.53149			0.441153
$375$	−7.32624	+	8.44549i	−0.378325	+	0.436123i
$376$	−27.6085			−1.42380
$377$			10.4721i			0.539342i
$378$		0			0
$379$	−3.05573			−0.156962			−0.0784811	−	0.996916i	$-0.525007\pi$
$379$	−3.05573			−0.156962			−0.0784811	+	0.996916i	$0.525007\pi$
$380$	52.8328	−	55.3890i	2.71027	−	2.84140i
$381$	−3.81540			−0.195469
$382$		−	8.80982i		−	0.450750i
$383$		−	10.4721i		−	0.535101i	−0.963544	−	0.267551i	$-0.913786\pi$
$383$		−	10.4721i		−	0.535101i	0.963544	−	0.267551i	$-0.0862142\pi$
$384$	16.7518			0.854862
$385$		0			0
$386$	−34.4721			−1.75459
$387$		−	9.98885i		−	0.507762i
$388$		−	43.1246i		−	2.18932i
$389$	11.8885			0.602773			0.301387	−	0.953502i	$-0.402551\pi$
$389$	11.8885			0.602773			0.301387	+	0.953502i	$0.402551\pi$
$390$	−21.1567	−	20.1803i	−1.07131	−	1.02187i
$391$	2.35805			0.119252
$392$		0			0
$393$		−	9.98885i		−	0.503871i
$394$	4.76393			0.240003
$395$	−19.9777	+	20.9443i	−1.00519	+	1.05382i
$396$	−18.9443			−0.951985
$397$		−	9.23607i		−	0.463545i	−0.972770	−	0.231772i	$-0.925548\pi$
$397$		−	9.23607i		−	0.463545i	0.972770	−	0.231772i	$-0.0744525\pi$
$398$			29.7082i			1.48914i
$399$		0			0
$400$	−1.29180	−	27.3302i	−0.0645898	−	1.36651i
$401$	36.8328			1.83934			0.919672	−	0.392689i	$-0.128455\pi$
$401$	36.8328			1.83934			0.919672	+	0.392689i	$0.128455\pi$
$402$			15.4164i			0.768901i
$403$			9.98885i			0.497580i
$404$	55.3890			2.75571
$405$	1.54336	−	1.61803i	0.0766903	−	0.0804008i
$406$		0			0
$407$			27.6085i			1.36850i
$408$		−	4.26575i		−	0.211186i
$409$	33.7819			1.67041			0.835205	−	0.549939i	$-0.185349\pi$
$409$	33.7819			1.67041			0.835205	+	0.549939i	$0.185349\pi$
$410$	27.8885	+	26.6015i	1.37732	+	1.31375i
$411$	−8.08115			−0.398614
$412$			6.47214i			0.318859i
$413$		0			0
$414$	−7.70820			−0.378838
$415$	−10.4721	−	9.98885i	−0.514057	−	0.490333i
$416$	13.0756			0.641083
$417$		−	14.2546i		−	0.698051i
$418$			90.2492i			4.41423i
$419$	1.45735			0.0711964			0.0355982	−	0.999366i	$-0.488666\pi$
$419$	1.45735			0.0711964			0.0355982	+	0.999366i	$0.488666\pi$
$420$		0			0
$421$	16.4721			0.802803			0.401401	−	0.915902i	$-0.368523\pi$
$421$	16.4721			0.802803			0.401401	+	0.915902i	$0.368523\pi$
$422$		−	32.3246i		−	1.57354i
$423$			4.94427i			0.240399i
$424$	−10.6525			−0.517330
$425$	3.81540	−	0.180340i	0.185074	−	0.00874777i
$426$	1.17902			0.0571239
$427$		0			0
$428$			29.2379i			1.41327i
$429$	23.4164			1.13055
$430$	−38.4980	+	40.3607i	−1.85654	+	1.94636i
$431$	−4.47214			−0.215415			−0.107708	−	0.994183i	$-0.534351\pi$
$431$	−4.47214			−0.215415			−0.107708	+	0.994183i	$0.534351\pi$
$432$			5.47214i			0.263278i
$433$		−	35.7082i		−	1.71603i	−0.513627	−	0.858013i	$-0.671699\pi$
$433$		−	35.7082i		−	1.71603i	0.513627	−	0.858013i	$-0.328301\pi$
$434$		0			0
$435$	3.23607	+	3.08672i	0.155158	+	0.147997i
$436$	52.8328			2.53023
$437$			24.9443i			1.19325i
$438$		−	6.90212i		−	0.329796i
$439$	24.2434			1.15708			0.578538	−	0.815655i	$-0.303623\pi$
$439$	24.2434			1.15708			0.578538	+	0.815655i	$0.303623\pi$
$440$	40.4057	+	38.5410i	1.92627	+	1.83737i
$441$		0			0
$442$			9.98885i			0.475121i
$443$			31.5959i			1.50117i	0.660775	+	0.750584i	$0.270228\pi$
$443$			31.5959i			1.50117i	−0.660775	+	0.750584i	$0.729772\pi$
$444$	26.1511			1.24108
$445$	14.2918	−	14.9833i	0.677496	−	0.710275i
$446$	−44.6715			−2.11526
$447$		−	18.9443i		−	0.896033i
$448$		0			0
$449$	17.0557			0.804910			0.402455	−	0.915440i	$-0.368157\pi$
$449$	17.0557			0.804910			0.402455	+	0.915440i	$0.368157\pi$
$450$	−12.4721	+	0.589512i	−0.587942	+	0.0277899i
$451$	−30.8672			−1.45348
$452$		−	18.0700i		−	0.849941i
$453$			8.94427i			0.420239i
$454$	3.81540			0.179066
$455$		0			0
$456$	45.1246			2.11315
$457$			23.7931i			1.11299i	0.830850	+	0.556497i	$0.187855\pi$
$457$			23.7931i			1.11299i	−0.830850	+	0.556497i	$0.812145\pi$
$458$		−	55.7771i		−	2.60629i
$459$	−0.763932			−0.0356573
$460$	21.1567	+	20.1803i	0.986437	+	0.940913i
$461$	−36.8687			−1.71715			−0.858573	−	0.512692i	$-0.828648\pi$
$461$	−36.8687			−1.71715			−0.858573	+	0.512692i	$0.828648\pi$
$462$		0			0
$463$		−	28.5092i		−	1.32493i	−0.749091	−	0.662467i	$-0.769509\pi$
$463$		−	28.5092i		−	1.32493i	0.749091	−	0.662467i	$-0.230491\pi$
$464$	−10.9443			−0.508075
$465$	3.08672	+	2.94427i	0.143143	+	0.136537i
$466$	−29.7082			−1.37621
$467$		−	27.4164i		−	1.26868i	−0.773054	−	0.634340i	$-0.781272\pi$
$467$		−	27.4164i		−	1.26868i	0.773054	−	0.634340i	$-0.218728\pi$
$468$		−	22.1803i		−	1.02529i
$469$		0			0
$470$	19.0557	−	19.9777i	0.878975	−	0.921502i
$471$	−8.65248			−0.398685
$472$		−	55.7771i		−	2.56735i
$473$		−	44.6715i		−	2.05400i
$474$	−32.3246			−1.48472
$475$	1.90770	+	40.3607i	0.0875313	+	1.85187i
$476$		0			0
$477$			1.90770i			0.0873476i
$478$			18.7987i			0.859831i
$479$	28.5092			1.30262			0.651309	−	0.758813i	$-0.274220\pi$
$479$	28.5092			1.30262			0.651309	+	0.758813i	$0.274220\pi$
$480$	3.85410	−	4.04057i	0.175915	−	0.184426i
$481$	−32.3246			−1.47387
$482$		−	15.4164i		−	0.702198i
$483$		0			0
$484$	−38.1246			−1.73294
$485$	16.4721	+	15.7119i	0.747961	+	0.713443i
$486$	2.49721			0.113276
$487$			9.98885i			0.452638i	0.974053	+	0.226319i	$0.0726692\pi$
$487$			9.98885i			0.452638i	−0.974053	+	0.226319i	$0.927331\pi$
$488$		−	21.3050i		−	0.964430i
$489$	−3.81540			−0.172538
$490$		0			0
$491$	18.3607			0.828606			0.414303	−	0.910139i	$-0.364025\pi$
$491$	18.3607			0.828606			0.414303	+	0.910139i	$0.364025\pi$
$492$			29.2379i			1.31814i
$493$		−	1.52786i		−	0.0688115i
$494$	−105.666			−4.75412
$495$	6.90212	−	7.23607i	0.310227	−	0.325237i
$496$	−10.4392			−0.468734
$497$		0			0
$498$		−	16.1623i		−	0.724250i
$499$	−8.00000			−0.358129			−0.179065	−	0.983837i	$-0.557307\pi$
$499$	−8.00000			−0.358129			−0.179065	+	0.983837i	$0.557307\pi$
$500$	35.7757	+	31.0344i	1.59994	+	1.38790i
$501$	−15.4164			−0.688754
$502$			5.88854i			0.262819i
$503$		−	29.5279i		−	1.31658i	−0.752763	−	0.658291i	$-0.771280\pi$
$503$		−	29.5279i		−	1.31658i	0.752763	−	0.658291i	$-0.228720\pi$
$504$		0			0
$505$	−20.1803	+	21.1567i	−0.898013	+	0.941462i
$506$	−34.4721			−1.53247
$507$			14.4164i			0.640255i
$508$			16.1623i			0.717086i
$509$	13.0756			0.579565			0.289782	−	0.957093i	$-0.406417\pi$
$509$	13.0756			0.579565			0.289782	+	0.957093i	$0.406417\pi$
$510$	3.08672	+	2.94427i	0.136682	+	0.130375i
$511$		0			0
$512$		−	47.4470i		−	2.09688i
$513$		−	8.08115i		−	0.356791i
$514$	−54.2100			−2.39110
$515$	−2.47214	−	2.35805i	−0.108935	−	0.103908i
$516$	−42.3134			−1.86275
$517$			22.1115i			0.972461i
$518$		0			0
$519$	−19.2361			−0.844370
$520$	−45.1246	+	47.3079i	−1.97885	+	2.07459i
$521$	39.2267			1.71855			0.859277	−	0.511511i	$-0.170914\pi$
$521$	39.2267			1.71855			0.859277	+	0.511511i	$0.170914\pi$
$522$			4.99442i			0.218600i
$523$		−	15.0557i		−	0.658341i	−0.944270	−	0.329171i	$-0.893231\pi$
$523$		−	15.0557i		−	0.658341i	0.944270	−	0.329171i	$-0.106769\pi$
$524$	−42.3134			−1.84847
$525$		0			0
$526$	−38.5410			−1.68047
$527$		−	1.45735i		−	0.0634833i
$528$			24.4721i			1.06501i
$529$	13.4721			0.585745
$530$	7.35247	−	7.70820i	0.319371	−	0.334823i
$531$	−9.98885			−0.433479
$532$		0			0
$533$		−	36.1400i		−	1.56540i
$534$	23.1246			1.00070
$535$	−11.1679	−	10.6525i	−0.482829	−	0.460547i
$536$	34.4721			1.48897
$537$		−	7.52786i		−	0.324851i
$538$			17.2361i			0.743100i
$539$		0			0
$540$	−6.85410	−	6.53779i	−0.294954	−	0.281342i
$541$	−24.4721			−1.05214			−0.526070	−	0.850441i	$-0.676335\pi$
$541$	−24.4721			−1.05214			−0.526070	+	0.850441i	$0.676335\pi$
$542$		−	45.1246i		−	1.93827i
$543$			9.98885i			0.428663i
$544$	−1.90770			−0.0817920
$545$	−19.2490	+	20.1803i	−0.824537	+	0.864431i
$546$		0			0
$547$		−	38.4980i		−	1.64606i	−0.568000	−	0.823029i	$-0.692283\pi$
$547$		−	38.4980i		−	1.64606i	0.568000	−	0.823029i	$-0.307717\pi$
$548$			34.2323i			1.46233i
$549$	−3.81540			−0.162837
$550$	−55.7771	+	2.63638i	−2.37834	+	0.112415i
$551$	16.1623			0.688537
$552$			17.2361i			0.733616i
$553$		0			0
$554$	−24.9443			−1.05978
$555$	−9.52786	+	9.98885i	−0.404435	+	0.424003i
$556$	−60.3834			−2.56083
$557$		−	30.4169i		−	1.28881i	−0.764686	−	0.644403i	$-0.777106\pi$
$557$		−	30.4169i		−	1.28881i	0.764686	−	0.644403i	$-0.222894\pi$
$558$			4.76393i			0.201673i
$559$	52.3023			2.21215
$560$		0			0
$561$	−3.41641			−0.144241
$562$		−	54.9387i		−	2.31745i
$563$		−	13.8885i		−	0.585332i	−0.956215	−	0.292666i	$-0.905458\pi$
$563$		−	13.8885i		−	0.585332i	0.956215	−	0.292666i	$-0.0945425\pi$
$564$	20.9443			0.881913
$565$	6.90212	+	6.58359i	0.290375	+	0.276974i
$566$	30.8672			1.29745
$567$		0			0
$568$		−	2.63638i		−	0.110620i
$569$	−36.8328			−1.54411			−0.772056	−	0.635555i	$-0.780772\pi$
$569$	−36.8328			−1.54411			−0.772056	+	0.635555i	$0.780772\pi$
$570$	−31.1456	+	32.6525i	−1.30454	+	1.36766i
$571$	−42.8328			−1.79250			−0.896249	−	0.443552i	$-0.853718\pi$
$571$	−42.8328			−1.79250			−0.896249	+	0.443552i	$0.853718\pi$
$572$		−	99.1935i		−	4.14749i
$573$			3.52786i			0.147379i
$574$		0			0
$575$	−15.4164	+	0.728677i	−0.642909	+	0.0303879i
$576$	−4.70820			−0.196175
$577$			16.6525i			0.693252i	0.938003	+	0.346626i	$0.112673\pi$
$577$			16.6525i			0.693252i	−0.938003	+	0.346626i	$0.887327\pi$
$578$			40.9953i			1.70518i
$579$	13.8042			0.573685
$580$	13.0756	−	13.7082i	0.542934	−	0.569202i
$581$		0			0
$582$			25.4225i			1.05380i
$583$			8.53149i			0.353338i
$584$	−15.4336			−0.638648
$585$	8.47214	+	8.08115i	0.350280	+	0.334114i
$586$	50.3946			2.08178
$587$			8.94427i			0.369170i	0.982817	+	0.184585i	$0.0590940\pi$
$587$			8.94427i			0.369170i	−0.982817	+	0.184585i	$0.940906\pi$
$588$		0			0
$589$	15.4164			0.635222
$590$	40.3607	+	38.4980i	1.66162	+	1.58494i
$591$	−1.90770			−0.0784723
$592$		−	33.7819i		−	1.38843i
$593$			17.7082i			0.727189i	0.931557	+	0.363594i	$0.118451\pi$
$593$			17.7082i			0.727189i	−0.931557	+	0.363594i	$0.881549\pi$
$594$	11.1679			0.458223
$595$		0			0
$596$	−80.2492			−3.28714
$597$		−	11.8965i		−	0.486893i
$598$		−	40.3607i		−	1.65047i
$599$	−9.41641			−0.384744			−0.192372	−	0.981322i	$-0.561618\pi$
$599$	−9.41641			−0.384744			−0.192372	+	0.981322i	$0.561618\pi$
$600$	1.31819	+	27.8885i	0.0538148	+	1.13855i
$601$	−12.3469			−0.503640			−0.251820	−	0.967774i	$-0.581029\pi$
$601$	−12.3469			−0.503640			−0.251820	+	0.967774i	$0.581029\pi$
$602$		0			0
$603$		−	6.17345i		−	0.251402i
$604$	37.8885			1.54166
$605$	13.8903	−	14.5623i	0.564719	−	0.592042i
$606$	−32.6525			−1.32642
$607$			38.8328i			1.57618i	0.615563	+	0.788088i	$0.288929\pi$
$607$			38.8328i			1.57618i	−0.615563	+	0.788088i	$0.711071\pi$
$608$		−	20.1803i		−	0.818421i
$609$		0			0
$610$	15.4164	+	14.7049i	0.624192	+	0.595386i
$611$	−25.8885			−1.04734
$612$			3.23607i			0.130810i
$613$		−	44.6715i		−	1.80426i	−0.431460	−	0.902132i	$-0.642001\pi$
$613$		−	44.6715i		−	1.80426i	0.431460	−	0.902132i	$-0.357999\pi$
$614$	−6.17345			−0.249140
$615$	−11.1679	−	10.6525i	−0.450332	−	0.429549i
$616$		0			0
$617$			20.4280i			0.822402i	0.911545	+	0.411201i	$0.134891\pi$
$617$			20.4280i			0.822402i	−0.911545	+	0.411201i	$0.865109\pi$
$618$		−	3.81540i		−	0.153478i
$619$	−22.7861			−0.915850			−0.457925	−	0.888991i	$-0.651407\pi$
$619$	−22.7861			−0.915850			−0.457925	+	0.888991i	$0.651407\pi$
$620$	12.4721	−	13.0756i	0.500893	−	0.525128i
$621$	3.08672			0.123866
$622$		−	9.52786i		−	0.382033i
$623$		0			0
$624$	−28.6525			−1.14702
$625$	−24.8885	+	2.35805i	−0.995542	+	0.0943219i
$626$	61.5625			2.46053
$627$		−	36.1400i		−	1.44329i
$628$			36.6525i			1.46259i
$629$	4.71609			0.188043
$630$		0			0
$631$	27.0557			1.07707			0.538536	−	0.842603i	$-0.318978\pi$
$631$	27.0557			1.07707			0.538536	+	0.842603i	$0.318978\pi$
$632$			72.2800i			2.87514i
$633$			12.9443i			0.514489i
$634$	26.0689			1.03533
$635$	−6.17345	−	5.88854i	−0.244986	−	0.233680i
$636$	8.08115			0.320438
$637$		0			0
$638$			22.3357i			0.884281i
$639$	−0.472136			−0.0186774
$640$	27.1050	+	25.8541i	1.07142	+	1.02197i
$641$	18.0000			0.710957			0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000			0.710957			0.355479	+	0.934684i	$0.384318\pi$
$642$		−	17.2361i		−	0.680253i
$643$		−	28.3607i		−	1.11844i	−0.829021	−	0.559218i	$-0.811101\pi$
$643$		−	28.3607i		−	1.11844i	0.829021	−	0.559218i	$-0.188899\pi$
$644$		0			0
$645$	15.4164	−	16.1623i	0.607020	−	0.636390i
$646$	15.4164			0.606550
$647$		−	47.4164i		−	1.86413i	−0.362289	−	0.932066i	$-0.618005\pi$
$647$		−	47.4164i		−	1.86413i	0.362289	−	0.932066i	$-0.381995\pi$
$648$		−	5.58394i		−	0.219358i
$649$	−44.6715			−1.75351
$650$	−3.08672	−	65.3050i	−0.121071	−	2.56147i
$651$		0			0
$652$			16.1623i			0.632964i
$653$		−	42.7638i		−	1.67348i	−0.547603	−	0.836738i	$-0.684460\pi$
$653$		−	42.7638i		−	1.67348i	0.547603	−	0.836738i	$-0.315540\pi$
$654$	−31.1456			−1.21789
$655$	15.4164	−	16.1623i	0.602369	−	0.631513i
$656$	37.7694			1.47465
$657$			2.76393i			0.107831i
$658$		0			0
$659$	8.47214			0.330028			0.165014	−	0.986291i	$-0.447233\pi$
$659$	8.47214			0.330028			0.165014	+	0.986291i	$0.447233\pi$
$660$	−30.6525	−	29.2379i	−1.19315	−	1.13808i
$661$	−3.81540			−0.148402			−0.0742009	−	0.997243i	$-0.523641\pi$
$661$	−3.81540			−0.148402			−0.0742009	+	0.997243i	$0.523641\pi$
$662$			19.9777i			0.776455i
$663$		−	4.00000i		−	0.155347i
$664$	−36.1400			−1.40250
$665$		0			0
$666$	−15.4164			−0.597374
$667$			6.17345i			0.239037i
$668$			65.3050i			2.52672i
$669$	17.8885			0.691611
$670$	−23.7931	+	24.9443i	−0.919208	+	0.963681i
$671$	−17.0630			−0.658709
$672$		0			0
$673$			30.8672i			1.18984i	0.803783	+	0.594922i	$0.202817\pi$
$673$			30.8672i			1.18984i	−0.803783	+	0.594922i	$0.797183\pi$
$674$	9.52786			0.367000
$675$	4.99442	−	0.236068i	0.192235	−	0.00908626i
$676$	61.0689			2.34880
$677$			31.5967i			1.21436i	0.794564	+	0.607181i	$0.207700\pi$
$677$			31.5967i			1.21436i	−0.794564	+	0.607181i	$0.792300\pi$
$678$			10.6525i			0.409106i
$679$		0			0
$680$	6.58359	−	6.90212i	0.252469	−	0.264684i
$681$	−1.52786			−0.0585479
$682$			21.3050i			0.815809i
$683$			26.8798i			1.02853i	0.857632	+	0.514264i	$0.171935\pi$
$683$			26.8798i			1.02853i	−0.857632	+	0.514264i	$0.828065\pi$
$684$	−34.2323			−1.30890
$685$	−13.0756	−	12.4721i	−0.499592	−	0.476536i
$686$		0			0
$687$			22.3357i			0.852162i
$688$			54.6603i			2.08391i
$689$	−9.98885			−0.380545
$690$	−12.4721	−	11.8965i	−0.474806	−	0.452894i
$691$	34.2323			1.30226			0.651129	−	0.758967i	$-0.274296\pi$
$691$	34.2323			1.30226			0.651129	+	0.758967i	$0.274296\pi$
$692$			81.4853i			3.09761i
$693$		0			0
$694$	−63.4853			−2.40987
$695$	22.0000	−	23.0644i	0.834508	−	0.874883i
$696$	11.1679			0.423317
$697$			5.27275i			0.199720i
$698$		−	21.3050i		−	0.806404i
$699$	11.8965			0.449969
$700$		0			0
$701$	8.83282			0.333611			0.166805	−	0.985990i	$-0.446655\pi$
$701$	8.83282			0.333611			0.166805	+	0.985990i	$0.446655\pi$
$702$			13.0756i			0.493506i
$703$			49.8885i			1.88158i
$704$	−21.0557			−0.793568
$705$	−7.63080	+	8.00000i	−0.287393	+	0.301297i
$706$	−8.08115			−0.304138
$707$		0			0
$708$			42.3134i			1.59024i
$709$	34.0000			1.27690			0.638448	−	0.769665i	$-0.279577\pi$
$709$	34.0000			1.27690			0.638448	+	0.769665i	$0.279577\pi$
$710$	1.90770	+	1.81966i	0.0715947	+	0.0682906i
$711$	12.9443			0.485448
$712$		−	51.7082i		−	1.93785i
$713$			5.88854i			0.220528i
$714$		0			0
$715$	37.8885	+	36.1400i	1.41695	+	1.35156i
$716$	−31.8885			−1.19173
$717$		−	7.52786i		−	0.281133i
$718$		−	51.1233i		−	1.90790i
$719$	−23.7931			−0.887333			−0.443666	−	0.896192i	$-0.646322\pi$
$719$	−23.7931			−0.887333			−0.443666	+	0.896192i	$0.646322\pi$
$720$	−8.44549	+	8.85410i	−0.314745	+	0.329973i
$721$		0			0
$722$			115.633i			4.30343i
$723$			6.17345i			0.229593i
$724$	42.3134			1.57257
$725$	0.472136	+	9.98885i	0.0175347	+	0.370977i
$726$	22.4749			0.834122
$727$		−	1.52786i		−	0.0566653i	−0.999599	−	0.0283327i	$-0.990980\pi$
$727$		−	1.52786i		−	0.0566653i	0.999599	−	0.0283327i	$-0.00901978\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	10.6525	−	11.1679i	0.394266	−	0.413341i
$731$	−7.63080			−0.282235
$732$			16.1623i			0.597376i
$733$		−	34.1803i		−	1.26248i	−0.775588	−	0.631240i	$-0.782546\pi$
$733$		−	34.1803i		−	1.26248i	0.775588	−	0.631240i	$-0.217454\pi$
$734$	39.9554			1.47478
$735$		0			0
$736$	7.70820			0.284128
$737$		−	27.6085i		−	1.01697i
$738$		−	17.2361i		−	0.634468i
$739$	−24.9443			−0.917590			−0.458795	−	0.888542i	$-0.651719\pi$
$739$	−24.9443			−0.917590			−0.458795	+	0.888542i	$0.651719\pi$
$740$	42.3134	+	40.3607i	1.55547	+	1.48369i
$741$	42.3134			1.55442
$742$		0			0
$743$		−	3.08672i		−	0.113241i	−0.998396	−	0.0566205i	$-0.981968\pi$
$743$		−	3.08672i		−	0.113241i	0.998396	−	0.0566205i	$-0.0180325\pi$
$744$	10.6525			0.390539
$745$	29.2379	−	30.6525i	1.07119	−	1.12302i
$746$	80.7214			2.95542
$747$			6.47214i			0.236803i
$748$			14.4721i			0.529154i
$749$		0			0
$750$	−21.0902	−	18.2952i	−0.770104	−	0.668045i
$751$	−10.8328			−0.395295			−0.197648	−	0.980273i	$-0.563330\pi$
$751$	−10.8328			−0.395295			−0.197648	+	0.980273i	$0.563330\pi$
$752$		−	27.0557i		−	0.986621i
$753$		−	2.35805i		−	0.0859320i
$754$	−26.1511			−0.952368
$755$	−13.8042	+	14.4721i	−0.502388	+	0.526695i
$756$		0			0
$757$		−	28.5092i		−	1.03618i	−0.855325	−	0.518092i	$-0.826642\pi$
$757$		−	28.5092i		−	1.03618i	0.855325	−	0.518092i	$-0.173358\pi$
$758$		−	7.63080i		−	0.277163i
$759$	13.8042			0.501062
$760$	73.0132	+	69.6436i	2.64847	+	2.52624i
$761$	4.54408			0.164723			0.0823613	−	0.996603i	$-0.473754\pi$
$761$	4.54408			0.164723			0.0823613	+	0.996603i	$0.473754\pi$
$762$		−	9.52786i		−	0.345158i
$763$		0			0
$764$	14.9443			0.540665
$765$	−1.23607	−	1.17902i	−0.0446901	−	0.0426277i
$766$	26.1511			0.944879
$767$		−	52.3023i		−	1.88853i
$768$			32.4164i			1.16973i
$769$		0			0			−	1.00000i	$-0.5\pi$
$769$		0			0				1.00000i	$0.5\pi$
$770$		0			0
$771$	21.7082			0.781802
$772$		−	58.4757i		−	2.10459i
$773$		−	14.6525i		−	0.527013i	−0.964658	−	0.263506i	$-0.915121\pi$
$773$		−	14.6525i		−	0.527013i	0.964658	−	0.263506i	$-0.0848790\pi$
$774$	24.9443			0.896603
$775$	0.450347	+	9.52786i	0.0161769	+	0.342251i
$776$	56.8464			2.04067
$777$		0			0
$778$			29.6882i			1.06437i
$779$	−55.7771			−1.99842
$780$	34.2323	−	35.8885i	1.22571	−	1.28502i
$781$	−2.11146			−0.0755538
$782$			5.88854i			0.210574i
$783$		−	2.00000i		−	0.0714742i
$784$		0			0
$785$	−14.0000	−	13.3539i	−0.499681	−	0.476621i
$786$	24.9443			0.889733
$787$		−	40.9443i		−	1.45951i	−0.683711	−	0.729753i	$-0.739635\pi$
$787$		−	40.9443i		−	1.45951i	0.683711	−	0.729753i	$-0.260365\pi$
$788$			8.08115i			0.287879i
$789$	15.4336			0.549451
$790$	−52.3023	−	49.8885i	−1.86083	−	1.77495i
$791$		0			0
$792$		−	24.9721i		−	0.887346i
$793$		−	19.9777i		−	0.709429i
$794$	23.0644			0.818526
$795$	−2.94427	+	3.08672i	−0.104423	+	0.109475i
$796$	−50.3946			−1.78619
$797$			27.2361i			0.964751i	0.875965	+	0.482376i	$0.160226\pi$
$797$			27.2361i			0.964751i	−0.875965	+	0.482376i	$0.839774\pi$
$798$		0			0
$799$	3.77709			0.133624
$800$	12.4721	−	0.589512i	0.440957	−	0.0208424i
$801$	−9.26017			−0.327192
$802$			91.9794i			3.24790i
$803$			12.3607i			0.436199i
$804$	−26.1511			−0.922280
$805$		0			0
$806$	−24.9443			−0.878625
$807$		−	6.90212i		−	0.242966i
$808$			73.0132i			2.56859i
$809$	30.9443			1.08794			0.543971	−	0.839104i	$-0.316920\pi$
$809$	30.9443			1.08794			0.543971	+	0.839104i	$0.316920\pi$
$810$	4.04057	+	3.85410i	0.141971	+	0.135419i
$811$	30.4169			1.06808			0.534041	−	0.845459i	$-0.320673\pi$
$811$	30.4169			1.06808			0.534041	+	0.845459i	$0.320673\pi$
$812$		0			0
$813$			18.0700i			0.633742i
$814$	−68.9443			−2.41650
$815$	−6.17345	−	5.88854i	−0.216246	−	0.206267i
$816$	4.18034			0.146341
$817$		−	80.7214i		−	2.82408i
$818$			84.3607i			2.94960i
$819$		0			0
$820$	−45.1246	+	47.3079i	−1.57582	+	1.65206i
$821$	7.88854			0.275312			0.137656	−	0.990480i	$-0.456043\pi$
$821$	7.88854			0.275312			0.137656	+	0.990480i	$0.456043\pi$
$822$		−	20.1803i		−	0.703870i
$823$		−	11.4462i		−	0.398990i	−0.979899	−	0.199495i	$-0.936070\pi$
$823$		−	11.4462i		−	0.398990i	0.979899	−	0.199495i	$-0.0639301\pi$
$824$	−8.53149			−0.297209
$825$	22.3357	−	1.05573i	0.777631	−	0.0367557i
$826$		0			0
$827$		−	46.8575i		−	1.62940i	−0.579886	−	0.814698i	$-0.696903\pi$
$827$		−	46.8575i		−	1.62940i	0.579886	−	0.814698i	$-0.303097\pi$
$828$		−	13.0756i		−	0.454408i
$829$	−17.6196			−0.611956			−0.305978	−	0.952039i	$-0.598983\pi$
$829$	−17.6196			−0.611956			−0.305978	+	0.952039i	$0.598983\pi$
$830$	24.9443	−	26.1511i	0.865828	−	0.907719i
$831$	9.98885			0.346509
$832$		−	24.6525i		−	0.854671i
$833$		0			0
$834$	35.5967			1.23261
$835$	−24.9443	−	23.7931i	−0.863232	−	0.823394i
$836$	−153.091			−5.29478
$837$		−	1.90770i		−	0.0659398i
$838$			3.63932i			0.125718i
$839$	−52.3023			−1.80568			−0.902838	−	0.429981i	$-0.858520\pi$
$839$	−52.3023			−1.80568			−0.902838	+	0.429981i	$0.858520\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$			41.1344i			1.41759i
$843$			22.0000i			0.757720i
$844$	54.8328			1.88742
$845$	−22.2497	+	23.3262i	−0.765414	+	0.802447i
$846$	−12.3469			−0.424495
$847$		0			0
$848$		−	10.4392i		−	0.358483i
$849$	−12.3607			−0.424217
$850$	0.450347	+	9.52786i	0.0154468	+	0.326803i
$851$	−19.0557			−0.653222
$852$			2.00000i			0.0685189i
$853$		−	4.87539i		−	0.166930i	−0.996511	−	0.0834651i	$-0.973401\pi$
$853$		−	4.87539i		−	0.166930i	0.996511	−	0.0834651i	$-0.0265987\pi$
$854$		0			0
$855$	12.4721	−	13.0756i	0.426538	−	0.447175i
$856$	−38.5410			−1.31730
$857$			45.1246i			1.54143i	0.637182	+	0.770714i	$0.280100\pi$
$857$			45.1246i			1.54143i	−0.637182	+	0.770714i	$0.719900\pi$
$858$			58.4757i			1.99633i
$859$	0.450347			0.0153656			0.00768282	−	0.999970i	$-0.497554\pi$
$859$	0.450347			0.0153656			0.00768282	+	0.999970i	$0.497554\pi$
$860$	−68.4646	−	65.3050i	−2.33462	−	2.22688i
$861$		0			0
$862$		−	11.1679i		−	0.380379i
$863$		−	10.7175i		−	0.364829i	−0.983222	−	0.182414i	$-0.941609\pi$
$863$		−	10.7175i		−	0.364829i	0.983222	−	0.182414i	$-0.0583912\pi$
$864$	−2.49721			−0.0849569
$865$	−31.1246	−	29.6882i	−1.05827	−	1.00943i
$866$	89.1710			3.03015
$867$		−	16.4164i		−	0.557530i
$868$		0			0
$869$	57.8885			1.96373
$870$	−7.70820	+	8.08115i	−0.261333	+	0.273977i
$871$	32.3246			1.09528
$872$			69.6436i			2.35843i
$873$		−	10.1803i		−	0.344552i
$874$	−62.2911			−2.10703
$875$		0			0
$876$	11.7082			0.395584
$877$			15.2616i			0.515348i	0.966232	+	0.257674i	$0.0829560\pi$
$877$			15.2616i			0.515348i	−0.966232	+	0.257674i	$0.917044\pi$
$878$			60.5410i			2.04316i
$879$	−20.1803			−0.680666
$880$	−37.7694	+	39.5967i	−1.27320	+	1.33481i
$881$	41.5848			1.40103			0.700513	−	0.713640i	$-0.252955\pi$
$881$	41.5848			1.40103			0.700513	+	0.713640i	$0.252955\pi$
$882$		0			0
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−16.9443			−0.569898
$885$	−16.1623	−	15.4164i	−0.543290	−	0.518217i
$886$	−78.9017			−2.65075
$887$			35.7771i			1.20128i	0.799521	+	0.600639i	$0.205087\pi$
$887$			35.7771i			1.20128i	−0.799521	+	0.600639i	$0.794913\pi$
$888$			34.4721i			1.15681i
$889$		0			0
$890$	37.4164	+	35.6896i	1.25420	+	1.19632i
$891$	−4.47214			−0.149822
$892$		−	75.7771i		−	2.53720i
$893$			39.9554i			1.33706i
$894$	47.3079			1.58221
$895$	11.6182	−	12.1803i	0.388354	−	0.407144i
$896$		0			0
$897$			16.1623i			0.539643i
$898$			42.5918i			1.42131i
$899$	3.81540			0.127251
$900$	−1.00000	−	21.1567i	−0.0333333	−	0.705224i
$901$	1.45735			0.0485515
$902$		−	77.0820i		−	2.56655i
$903$		0			0
$904$	23.8197			0.792230
$905$	−15.4164	+	16.1623i	−0.512459	+	0.537253i
$906$	−22.3357			−0.742055
$907$			39.9554i			1.32670i	0.748311	+	0.663349i	$0.230865\pi$
$907$			39.9554i			1.32670i	−0.748311	+	0.663349i	$0.769135\pi$
$908$			6.47214i			0.214785i
$909$	13.0756			0.433689
$910$		0			0
$911$	25.4164			0.842083			0.421042	−	0.907041i	$-0.361665\pi$
$911$	25.4164			0.842083			0.421042	+	0.907041i	$0.361665\pi$
$912$			44.2211i			1.46431i
$913$			28.9443i			0.957916i
$914$	−59.4164			−1.96532
$915$	−6.17345	−	5.88854i	−0.204088	−	0.194669i
$916$	94.6157			3.12619
$917$		0			0
$918$		−	1.90770i		−	0.0629635i
$919$	−4.00000			−0.131948			−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000			−0.131948			−0.0659739	+	0.997821i	$0.521015\pi$
$920$	−26.6015	+	27.8885i	−0.877025	+	0.919458i
$921$	2.47214			0.0814596
$922$		−	92.0689i		−	3.03213i
$923$		−	2.47214i		−	0.0813713i
$924$		0			0
$925$	−30.8328	+	1.45735i	−1.01378	+	0.0479175i
$926$	71.1935			2.33956
$927$			1.52786i			0.0501816i
$928$		−	4.99442i		−	0.163950i
$929$	3.08672			0.101272			0.0506361	−	0.998717i	$-0.483875\pi$
$929$	3.08672			0.101272			0.0506361	+	0.998717i	$0.483875\pi$
$930$	−7.35247	+	7.70820i	−0.241097	+	0.252762i
$931$		0			0
$932$		−	50.3946i		−	1.65073i
$933$			3.81540i			0.124911i
$934$	68.4646			2.24023
$935$	−5.52786	−	5.27275i	−0.180780	−	0.172437i
$936$	29.2379			0.955670
$937$		−	26.5410i		−	0.867057i	−0.901140	−	0.433529i	$-0.857268\pi$
$937$		−	26.5410i		−	0.867057i	0.901140	−	0.433529i	$-0.142732\pi$
$938$		0			0
$939$	−24.6525			−0.804503
$940$	33.8885	+	32.3246i	1.10532	+	1.05431i
$941$	−35.4113			−1.15438			−0.577188	−	0.816611i	$-0.695850\pi$
$941$	−35.4113			−1.15438			−0.577188	+	0.816611i	$0.695850\pi$
$942$		−	21.6071i		−	0.703996i
$943$		−	21.3050i		−	0.693785i
$944$	54.6603			1.77904
$945$		0			0
$946$	111.554			3.62694
$947$			14.5329i			0.472257i	0.971722	+	0.236128i	$0.0758786\pi$
$947$			14.5329i			0.472257i	−0.971722	+	0.236128i	$0.924121\pi$
$948$		−	54.8328i		−	1.78089i
$949$	−14.4721			−0.469785
$950$	−100.789	+	4.76393i	−3.27003	+	0.154562i
$951$	−10.4392			−0.338514
$952$		0			0
$953$			51.8519i			1.67965i	0.542858	+	0.839825i	$0.317342\pi$
$953$			51.8519i			1.67965i	−0.542858	+	0.839825i	$0.682658\pi$
$954$	−4.76393			−0.154238
$955$	−5.44477	+	5.70820i	−0.176189	+	0.184713i
$956$	−31.8885			−1.03135
$957$		−	8.94427i		−	0.289127i
$958$			71.1935i			2.30016i
$959$		0			0
$960$	−7.61803	−	7.26646i	−0.245871	−	0.234524i
$961$	−27.3607			−0.882603
$962$		−	80.7214i		−	2.60256i
$963$			6.90212i			0.222418i
$964$	26.1511			0.842272
$965$	22.3357	+	21.3050i	0.719013	+	0.685831i
$966$		0			0
$967$			26.1511i			0.840964i	0.907301	+	0.420482i	$0.138139\pi$
$967$			26.1511i			0.840964i	−0.907301	+	0.420482i	$0.861861\pi$
$968$		−	50.2554i		−	1.61527i
$969$	−6.17345			−0.198320
$970$	−39.2361	+	41.1344i	−1.25979	+	1.32075i
$971$	−58.4757			−1.87658			−0.938288	−	0.345855i	$-0.887589\pi$
$971$	−58.4757			−1.87658			−0.938288	+	0.345855i	$0.887589\pi$
$972$			4.23607i			0.135872i
$973$		0			0
$974$	−24.9443			−0.799266
$975$	1.23607	+	26.1511i	0.0395859	+	0.837507i
$976$	20.8784			0.668301
$977$		−	24.2434i		−	0.775616i	−0.921740	−	0.387808i	$-0.873232\pi$
$977$		−	24.2434i		−	0.775616i	0.921740	−	0.387808i	$-0.126768\pi$
$978$		−	9.52786i		−	0.304667i
$979$	−41.4127			−1.32356
$980$		0			0
$981$	12.4721			0.398205
$982$			45.8505i			1.46315i
$983$			38.8328i			1.23857i	0.785165	+	0.619287i	$0.212578\pi$
$983$			38.8328i			1.23857i	−0.785165	+	0.619287i	$0.787422\pi$
$984$	−38.5410			−1.22864
$985$	−3.08672	−	2.94427i	−0.0983512	−	0.0938123i
$986$	3.81540			0.121507
$987$		0			0
$988$		−	179.243i		−	5.70247i
$989$	30.8328			0.980427
$990$	18.0700	+	17.2361i	0.574302	+	0.547798i
$991$	36.0000			1.14358			0.571789	−	0.820401i	$-0.306250\pi$
$991$	36.0000			1.14358			0.571789	+	0.820401i	$0.306250\pi$
$992$		−	4.76393i		−	0.151255i
$993$		−	8.00000i		−	0.253872i
$994$		0			0
$995$	18.3607	−	19.2490i	0.582073	−	0.610235i
$996$	27.4164			0.868722
$997$			27.7082i			0.877528i	0.898602	+	0.438764i	$0.144584\pi$
$997$			27.7082i			0.877528i	−0.898602	+	0.438764i	$0.855416\pi$
$998$		−	19.9777i		−	0.632383i
$999$	6.17345			0.195319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.d.c.589.7	yes	8
3.2	odd	2		2205.2.d.m.1324.1		8
5.2	odd	4		3675.2.a.bt.1.1		4
5.3	odd	4		3675.2.a.bv.1.4		4
5.4	even	2	inner	735.2.d.c.589.2	yes	8
7.2	even	3		735.2.q.h.214.8		16
7.3	odd	6		735.2.q.h.79.2		16
7.4	even	3		735.2.q.h.79.1		16
7.5	odd	6		735.2.q.h.214.7		16
7.6	odd	2	inner	735.2.d.c.589.8	yes	8
15.14	odd	2		2205.2.d.m.1324.7		8
21.20	even	2		2205.2.d.m.1324.2		8
35.4	even	6		735.2.q.h.79.8		16
35.9	even	6		735.2.q.h.214.1		16
35.13	even	4		3675.2.a.bt.1.4		4
35.19	odd	6		735.2.q.h.214.2		16
35.24	odd	6		735.2.q.h.79.7		16
35.27	even	4		3675.2.a.bv.1.1		4
35.34	odd	2	inner	735.2.d.c.589.1	✓	8
105.104	even	2		2205.2.d.m.1324.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.d.c.589.1	✓	8	35.34	odd	2	inner
735.2.d.c.589.2	yes	8	5.4	even	2	inner
735.2.d.c.589.7	yes	8	1.1	even	1	trivial
735.2.d.c.589.8	yes	8	7.6	odd	2	inner
735.2.q.h.79.1		16	7.4	even	3
735.2.q.h.79.2		16	7.3	odd	6
735.2.q.h.79.7		16	35.24	odd	6
735.2.q.h.79.8		16	35.4	even	6
735.2.q.h.214.1		16	35.9	even	6
735.2.q.h.214.2		16	35.19	odd	6
735.2.q.h.214.7		16	7.5	odd	6
735.2.q.h.214.8		16	7.2	even	3
2205.2.d.m.1324.1		8	3.2	odd	2
2205.2.d.m.1324.2		8	21.20	even	2
2205.2.d.m.1324.7		8	15.14	odd	2
2205.2.d.m.1324.8		8	105.104	even	2
3675.2.a.bt.1.1		4	5.2	odd	4
3675.2.a.bt.1.4		4	35.13	even	4
3675.2.a.bv.1.1		4	35.27	even	4
3675.2.a.bv.1.4		4	5.3	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.49721i q^{2} -1.00000i q^{3} -4.23607 q^{4} +(1.54336 - 1.61803i) q^{5} +2.49721 q^{6} -5.58394i q^{8} -1.00000 q^{9} +(4.04057 + 3.85410i) q^{10} -4.47214 q^{11} +4.23607i q^{12} -5.23607i q^{13} +(-1.61803 - 1.54336i) q^{15} +5.47214 q^{16} +0.763932i q^{17} -2.49721i q^{18} -8.08115 q^{19} +(-6.53779 + 6.85410i) q^{20} -11.1679i q^{22} -3.08672i q^{23} -5.58394 q^{24} +(-0.236068 - 4.99442i) q^{25} +13.0756 q^{26} +1.00000i q^{27} -2.00000 q^{29} +(3.85410 - 4.04057i) q^{30} -1.90770 q^{31} +2.49721i q^{32} +4.47214i q^{33} -1.90770 q^{34} +4.23607 q^{36} -6.17345i q^{37} -20.1803i q^{38} -5.23607 q^{39} +(-9.03500 - 8.61803i) q^{40} +6.90212 q^{41} +9.98885i q^{43} +18.9443 q^{44} +(-1.54336 + 1.61803i) q^{45} +7.70820 q^{46} -4.94427i q^{47} -5.47214i q^{48} +(12.4721 - 0.589512i) q^{50} +0.763932 q^{51} +22.1803i q^{52} -1.90770i q^{53} -2.49721 q^{54} +(-6.90212 + 7.23607i) q^{55} +8.08115i q^{57} -4.99442i q^{58} +9.98885 q^{59} +(6.85410 + 6.53779i) q^{60} +3.81540 q^{61} -4.76393i q^{62} +4.70820 q^{64} +(-8.47214 - 8.08115i) q^{65} -11.1679 q^{66} +6.17345i q^{67} -3.23607i q^{68} -3.08672 q^{69} +0.472136 q^{71} +5.58394i q^{72} -2.76393i q^{73} +15.4164 q^{74} +(-4.99442 + 0.236068i) q^{75} +34.2323 q^{76} -13.0756i q^{78} -12.9443 q^{79} +(8.44549 - 8.85410i) q^{80} +1.00000 q^{81} +17.2361i q^{82} -6.47214i q^{83} +(1.23607 + 1.17902i) q^{85} -24.9443 q^{86} +2.00000i q^{87} +24.9721i q^{88} +9.26017 q^{89} +(-4.04057 - 3.85410i) q^{90} +13.0756i q^{92} +1.90770i q^{93} +12.3469 q^{94} +(-12.4721 + 13.0756i) q^{95} +2.49721 q^{96} +10.1803i q^{97} +4.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{4} - 8 q^{9} - 4 q^{15} + 8 q^{16} + 16 q^{25} - 16 q^{29} + 4 q^{30} + 16 q^{36} - 24 q^{39} + 80 q^{44} + 8 q^{46} + 64 q^{50} + 24 q^{51} + 28 q^{60} - 16 q^{64} - 32 q^{65} - 32 q^{71} + 16 q^{74}+ \cdots - 64 q^{95}+O(q^{100}) \) 8 * q - 16 * q^4 - 8 * q^9 - 4 * q^15 + 8 * q^16 + 16 * q^25 - 16 * q^29 + 4 * q^30 + 16 * q^36 - 24 * q^39 + 80 * q^44 + 8 * q^46 + 64 * q^50 + 24 * q^51 + 28 * q^60 - 16 * q^64 - 32 * q^65 - 32 * q^71 + 16 * q^74 - 32 * q^79 + 8 * q^81 - 8 * q^85 - 128 * q^86 - 64 * q^95

Introduction

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