LMFDB - Embedded newform 735.2.b.c.146.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(146,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("735.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.4
Root			$0.385731i$ of defining polynomial
Character	$\chi$	$=$	735.146
Dual form			735.2.b.c.146.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.385731i q^{2} +(1.56470 + 0.742765i) q^{3} +1.85121 q^{4} +1.00000 q^{5} +(0.286507 - 0.603555i) q^{6} -1.48553i q^{8} +(1.89660 + 2.32442i) q^{9} +O(q^{10})$	\(q-0.385731i q^{2} +(1.56470 + 0.742765i) q^{3} +1.85121 q^{4} +1.00000 q^{5} +(0.286507 - 0.603555i) q^{6} -1.48553i q^{8} +(1.89660 + 2.32442i) q^{9} -0.385731i q^{10} +2.54224i q^{11} +(2.89660 + 1.37502i) q^{12} +3.06718i q^{13} +(1.56470 + 0.742765i) q^{15} +3.12941 q^{16} -6.46130 q^{17} +(0.896599 - 0.731577i) q^{18} +1.19592i q^{19} +1.85121 q^{20} +0.980620 q^{22} -3.05599i q^{23} +(1.10340 - 2.32442i) q^{24} +1.00000 q^{25} +1.18311 q^{26} +(1.24112 + 5.04575i) q^{27} -7.77029i q^{29} +(0.286507 - 0.603555i) q^{30} -6.87392i q^{31} -4.17817i q^{32} +(-1.88829 + 3.97785i) q^{33} +2.49232i q^{34} +(3.51101 + 4.30299i) q^{36} -3.55208 q^{37} +0.461303 q^{38} +(-2.27820 + 4.79923i) q^{39} -1.48553i q^{40} -2.31252 q^{41} +5.46130 q^{43} +4.70623i q^{44} +(1.89660 + 2.32442i) q^{45} -1.17879 q^{46} -3.22018 q^{47} +(4.89660 + 2.32442i) q^{48} -0.385731i q^{50} +(-10.1100 - 4.79923i) q^{51} +5.67800i q^{52} -13.2548i q^{53} +(1.94630 - 0.478738i) q^{54} +2.54224i q^{55} +(-0.888288 + 1.87126i) q^{57} -2.99724 q^{58} -3.96292 q^{59} +(2.89660 + 1.37502i) q^{60} +9.34076i q^{61} -2.65148 q^{62} +4.64717 q^{64} +3.06718i q^{65} +(1.53438 + 0.728371i) q^{66} -3.51932 q^{67} -11.9612 q^{68} +(2.26989 - 4.78173i) q^{69} -0.921861i q^{71} +(3.45299 - 2.81746i) q^{72} +0.296437i q^{73} +1.37015i q^{74} +(1.56470 + 0.742765i) q^{75} +2.21390i q^{76} +(1.85121 + 0.878771i) q^{78} +8.29482 q^{79} +3.12941 q^{80} +(-1.80582 + 8.81697i) q^{81} +0.892008i q^{82} -2.11171 q^{83} -6.46130 q^{85} -2.10659i q^{86} +(5.77151 - 12.1582i) q^{87} +3.77658 q^{88} +18.8301 q^{89} +(0.896599 - 0.731577i) q^{90} -5.65729i q^{92} +(5.10571 - 10.7557i) q^{93} +1.24212i q^{94} +1.19592i q^{95} +(3.10340 - 6.53760i) q^{96} -12.3692i q^{97} +(-5.90923 + 4.82161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{3} - 6 q^{4} + 8 q^{5} - 5 q^{6} + q^{9}+O(q^{10}) $ 8 * q - q^3 - 6 * q^4 + 8 * q^5 - 5 * q^6 + q^9	$ 8 q - q^{3} - 6 q^{4} + 8 q^{5} - 5 q^{6} + q^{9} + 9 q^{12} - q^{15} - 2 q^{16} - 24 q^{17} - 7 q^{18} - 6 q^{20} - 40 q^{22} + 23 q^{24} + 8 q^{25} - 12 q^{26} - 4 q^{27} - 5 q^{30} - 2 q^{33} + 9 q^{36} - 14 q^{37} - 24 q^{38} - 12 q^{39} + 30 q^{41} + 16 q^{43} + q^{45} + 14 q^{46} - 12 q^{47} + 25 q^{48} - 6 q^{51} + 10 q^{54} + 6 q^{57} + 26 q^{58} - 24 q^{59} + 9 q^{60} - 24 q^{62} + 38 q^{64} + 38 q^{66} - 8 q^{67} + 13 q^{69} + q^{72} - q^{75} - 6 q^{78} + 58 q^{79} - 2 q^{80} + 13 q^{81} - 30 q^{83} - 24 q^{85} + 61 q^{87} + 4 q^{88} - 6 q^{89} - 7 q^{90} - 36 q^{93} + 39 q^{96} - 34 q^{99}+O(q^{100}) $ 8 * q - q^3 - 6 * q^4 + 8 * q^5 - 5 * q^6 + q^9 + 9 * q^12 - q^15 - 2 * q^16 - 24 * q^17 - 7 * q^18 - 6 * q^20 - 40 * q^22 + 23 * q^24 + 8 * q^25 - 12 * q^26 - 4 * q^27 - 5 * q^30 - 2 * q^33 + 9 * q^36 - 14 * q^37 - 24 * q^38 - 12 * q^39 + 30 * q^41 + 16 * q^43 + q^45 + 14 * q^46 - 12 * q^47 + 25 * q^48 - 6 * q^51 + 10 * q^54 + 6 * q^57 + 26 * q^58 - 24 * q^59 + 9 * q^60 - 24 * q^62 + 38 * q^64 + 38 * q^66 - 8 * q^67 + 13 * q^69 + q^72 - q^75 - 6 * q^78 + 58 * q^79 - 2 * q^80 + 13 * q^81 - 30 * q^83 - 24 * q^85 + 61 * q^87 + 4 * q^88 - 6 * q^89 - 7 * q^90 - 36 * q^93 + 39 * q^96 - 34 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$		−	0.385731i		−	0.272753i	−0.990657	−	0.136376i	$-0.956454\pi$
$2$		−	0.385731i		−	0.272753i	0.990657	−	0.136376i	$-0.0435457\pi$
$3$	1.56470	+	0.742765i	0.903382	+	0.428836i
$3$	1.56470	+	0.742765i	0.903382	+	0.428836i
$4$	1.85121			0.925606
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.286507	−	0.603555i	0.116966	−	0.246400i
$7$		0			0
$7$		0			0
$8$		−	1.48553i		−	0.525214i
$9$	1.89660	+	2.32442i	0.632200	+	0.774806i
$10$		−	0.385731i		−	0.121979i
$11$			2.54224i			0.766514i	0.923642	+	0.383257i	$0.125198\pi$
$11$			2.54224i			0.766514i	−0.923642	+	0.383257i	$0.874802\pi$
$12$	2.89660	+	1.37502i	0.836176	+	0.396933i
$13$			3.06718i			0.850683i	0.905033	+	0.425342i	$0.139846\pi$
$13$			3.06718i			0.850683i	−0.905033	+	0.425342i	$0.860154\pi$
$14$		0			0
$15$	1.56470	+	0.742765i	0.404005	+	0.191781i
$16$	3.12941			0.782352
$17$	−6.46130			−1.56710			−0.783548	−	0.621331i	$-0.786592\pi$
$17$	−6.46130			−1.56710			−0.783548	+	0.621331i	$0.786592\pi$
$18$	0.896599	−	0.731577i	0.211330	−	0.172434i
$19$			1.19592i			0.274363i	0.990546	+	0.137181i	$0.0438043\pi$
$19$			1.19592i			0.274363i	−0.990546	+	0.137181i	$0.956196\pi$
$20$	1.85121			0.413944
$21$		0			0
$22$	0.980620			0.209069
$23$		−	3.05599i		−	0.637219i	−0.947886	−	0.318609i	$-0.896784\pi$
$23$		−	3.05599i		−	0.637219i	0.947886	−	0.318609i	$-0.103216\pi$
$24$	1.10340	−	2.32442i	0.225231	−	0.474470i
$25$	1.00000			0.200000
$26$	1.18311			0.232026
$27$	1.24112	+	5.04575i	0.238854	+	0.971056i
$28$		0			0
$29$		−	7.77029i		−	1.44291i	−0.692463	−	0.721454i	$-0.743474\pi$
$29$		−	7.77029i		−	1.44291i	0.692463	−	0.721454i	$-0.256526\pi$
$30$	0.286507	−	0.603555i	0.0523089	−	0.110193i
$31$		−	6.87392i		−	1.23459i	−0.786731	−	0.617297i	$-0.788228\pi$
$31$		−	6.87392i		−	1.23459i	0.786731	−	0.617297i	$-0.211772\pi$
$32$		−	4.17817i		−	0.738603i
$33$	−1.88829	+	3.97785i	−0.328709	+	0.692456i
$34$			2.49232i			0.427430i
$35$		0			0
$36$	3.51101	+	4.30299i	0.585168	+	0.717165i
$37$	−3.55208			−0.583958			−0.291979	−	0.956425i	$-0.594314\pi$
$37$	−3.55208			−0.583958			−0.291979	+	0.956425i	$0.594314\pi$
$38$	0.461303			0.0748333
$39$	−2.27820	+	4.79923i	−0.364803	+	0.768492i
$40$		−	1.48553i		−	0.234883i
$41$	−2.31252			−0.361154			−0.180577	−	0.983561i	$-0.557797\pi$
$41$	−2.31252			−0.361154			−0.180577	+	0.983561i	$0.557797\pi$
$42$		0			0
$43$	5.46130			0.832841			0.416420	−	0.909172i	$-0.363284\pi$
$43$	5.46130			0.832841			0.416420	+	0.909172i	$0.363284\pi$
$44$			4.70623i			0.709490i
$45$	1.89660	+	2.32442i	0.282728	+	0.346504i
$46$	−1.17879			−0.173803
$47$	−3.22018			−0.469712			−0.234856	−	0.972030i	$-0.575462\pi$
$47$	−3.22018			−0.469712			−0.234856	+	0.972030i	$0.575462\pi$
$48$	4.89660	+	2.32442i	0.706763	+	0.335501i
$49$		0			0
$50$		−	0.385731i		−	0.0545506i
$51$	−10.1100	−	4.79923i	−1.41569	−	0.672027i
$52$			5.67800i			0.787397i
$53$		−	13.2548i		−	1.82069i	−0.413853	−	0.910344i	$-0.635817\pi$
$53$		−	13.2548i		−	1.82069i	0.413853	−	0.910344i	$-0.364183\pi$
$54$	1.94630	−	0.478738i	0.264858	−	0.0651480i
$55$			2.54224i			0.342796i
$56$		0			0
$57$	−0.888288	+	1.87126i	−0.117657	+	0.247855i
$58$	−2.99724			−0.393557
$59$	−3.96292			−0.515929			−0.257964	−	0.966154i	$-0.583052\pi$
$59$	−3.96292			−0.515929			−0.257964	+	0.966154i	$0.583052\pi$
$60$	2.89660	+	1.37502i	0.373949	+	0.177514i
$61$			9.34076i			1.19596i	0.801511	+	0.597981i	$0.204030\pi$
$61$			9.34076i			1.19596i	−0.801511	+	0.597981i	$0.795970\pi$
$62$	−2.65148			−0.336739
$63$		0			0
$64$	4.64717			0.580896
$65$			3.06718i			0.380437i
$66$	1.53438	+	0.728371i	0.188869	+	0.0896563i
$67$	−3.51932			−0.429953			−0.214977	−	0.976619i	$-0.568967\pi$
$67$	−3.51932			−0.429953			−0.214977	+	0.976619i	$0.568967\pi$
$68$	−11.9612			−1.45051
$69$	2.26989	−	4.78173i	0.273262	−	0.575652i
$70$		0			0
$71$		−	0.921861i		−	0.109405i	−0.998503	−	0.0547024i	$-0.982579\pi$
$71$		−	0.921861i		−	0.109405i	0.998503	−	0.0547024i	$-0.0174210\pi$
$72$	3.45299	−	2.81746i	0.406939	−	0.332040i
$73$			0.296437i			0.0346953i	0.999850	+	0.0173477i	$0.00552221\pi$
$73$			0.296437i			0.0346953i	−0.999850	+	0.0173477i	$0.994478\pi$
$74$			1.37015i			0.159276i
$75$	1.56470	+	0.742765i	0.180676	+	0.0857672i
$76$			2.21390i			0.253952i
$77$		0			0
$78$	1.85121	+	0.878771i	0.209608	+	0.0995012i
$79$	8.29482			0.933240			0.466620	−	0.884458i	$-0.345472\pi$
$79$	8.29482			0.933240			0.466620	+	0.884458i	$0.345472\pi$
$80$	3.12941			0.349879
$81$	−1.80582	+	8.81697i	−0.200647	+	0.979664i
$82$			0.892008i			0.0985058i
$83$	−2.11171			−0.231790			−0.115895	−	0.993261i	$-0.536974\pi$
$83$	−2.11171			−0.231790			−0.115895	+	0.993261i	$0.536974\pi$
$84$		0			0
$85$	−6.46130			−0.700827
$86$		−	2.10659i		−	0.227160i
$87$	5.77151	−	12.1582i	0.618770	−	1.30350i
$88$	3.77658			0.402584
$89$	18.8301			1.99599			0.997996	−	0.0632783i	$-0.0201556\pi$
$89$	18.8301			1.99599			0.997996	+	0.0632783i	$0.0201556\pi$
$90$	0.896599	−	0.731577i	0.0945098	−	0.0771149i
$91$		0			0
$92$		−	5.65729i		−	0.589813i
$93$	5.10571	−	10.7557i	0.529438	−	1.11531i
$94$			1.24212i			0.128115i
$95$			1.19592i			0.122699i
$96$	3.10340	−	6.53760i	0.316740	−	0.667241i
$97$		−	12.3692i		−	1.25590i	−0.778252	−	0.627952i	$-0.783894\pi$
$97$		−	12.3692i		−	1.25590i	0.778252	−	0.627952i	$-0.216106\pi$
$98$		0			0
$99$	−5.90923	+	4.82161i	−0.593900	+	0.484590i
$100$	1.85121			0.185121
$101$	−6.97630			−0.694168			−0.347084	−	0.937834i	$-0.612828\pi$
$101$	−6.97630			−0.694168			−0.347084	+	0.937834i	$0.612828\pi$
$102$	−1.85121	+	3.89975i	−0.183297	+	0.386133i
$103$		−	3.77318i		−	0.371782i	−0.982570	−	0.185891i	$-0.940483\pi$
$103$		−	3.77318i		−	0.371782i	0.982570	−	0.185891i	$-0.0595171\pi$
$104$	4.55639			0.446791
$105$		0			0
$106$	−5.11279			−0.496598
$107$			13.2337i			1.27935i	0.768646	+	0.639674i	$0.220931\pi$
$107$			13.2337i			1.27935i	−0.768646	+	0.639674i	$0.779069\pi$
$108$	2.29758	+	9.34076i	0.221084	+	0.898815i
$109$	2.50162			0.239612			0.119806	−	0.992797i	$-0.461773\pi$
$109$	2.50162			0.239612			0.119806	+	0.992797i	$0.461773\pi$
$110$	0.980620			0.0934985
$111$	−5.55795	−	2.63836i	−0.527537	−	0.250422i
$112$		0			0
$113$			7.18425i			0.675837i	0.941175	+	0.337919i	$0.109723\pi$
$113$			7.18425i			0.675837i	−0.941175	+	0.337919i	$0.890277\pi$
$114$	0.721803	+	0.342640i	0.0676031	+	0.0320912i
$115$		−	3.05599i		−	0.284973i
$116$		−	14.3845i		−	1.33556i
$117$	−7.12941	+	5.81721i	−0.659114	+	0.537802i
$118$			1.52862i			0.140721i
$119$		0			0
$120$	1.10340	−	2.32442i	0.100726	−	0.212189i
$121$	4.53701			0.412456
$122$	3.60302			0.326202
$123$	−3.61840	−	1.71766i	−0.326260	−	0.154876i
$124$		−	12.7251i		−	1.14275i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−11.1965			−0.993528			−0.496764	−	0.867886i	$-0.665478\pi$
$127$	−11.1965			−0.993528			−0.496764	+	0.867886i	$0.665478\pi$
$128$		−	10.1489i		−	0.897044i
$129$	8.54532	+	4.05647i	0.752374	+	0.357152i
$130$	1.18311			0.103765
$131$	−15.6637			−1.36854			−0.684270	−	0.729228i	$-0.739879\pi$
$131$	−15.6637			−1.36854			−0.684270	+	0.729228i	$0.739879\pi$
$132$	−3.49562	+	7.36385i	−0.304255	+	0.640941i
$133$		0			0
$134$			1.35751i			0.117271i
$135$	1.24112	+	5.04575i	0.106819	+	0.434269i
$136$			9.59847i			0.823062i
$137$			5.82840i			0.497954i	0.968509	+	0.248977i	$0.0800944\pi$
$137$			5.82840i			0.497954i	−0.968509	+	0.248977i	$0.919906\pi$
$138$	−1.84446	−	0.875565i	−0.157011	−	0.0745330i
$139$		−	12.0365i		−	1.02092i	−0.859900	−	0.510462i	$-0.829475\pi$
$139$		−	12.0365i		−	1.02092i	0.859900	−	0.510462i	$-0.170525\pi$
$140$		0			0
$141$	−5.03863	−	2.39184i	−0.424330	−	0.201429i
$142$	−0.355590			−0.0298405
$143$	−7.79751			−0.652061
$144$	5.93523	+	7.27405i	0.494603	+	0.606171i
$145$		−	7.77029i		−	0.645288i
$146$	0.114345			0.00946324
$147$		0			0
$148$	−6.57565			−0.540515
$149$			18.6975i			1.53176i	0.642985	+	0.765879i	$0.277696\pi$
$149$			18.6975i			1.53176i	−0.642985	+	0.765879i	$0.722304\pi$
$150$	0.286507	−	0.603555i	0.0233932	−	0.0492800i
$151$	−5.95062			−0.484254			−0.242127	−	0.970245i	$-0.577845\pi$
$151$	−5.95062			−0.484254			−0.242127	+	0.970245i	$0.577845\pi$
$152$	1.77658			0.144099
$153$	−12.2545	−	15.0188i	−0.990718	−	1.21419i
$154$		0			0
$155$		−	6.87392i		−	0.552127i
$156$	−4.21742	+	8.88440i	−0.337664	+	0.711321i
$157$			6.41279i			0.511796i	0.966704	+	0.255898i	$0.0823711\pi$
$157$			6.41279i			0.511796i	−0.966704	+	0.255898i	$0.917629\pi$
$158$		−	3.19957i		−	0.254544i
$159$	9.84521	−	20.7399i	0.780776	−	1.64478i
$160$		−	4.17817i		−	0.330313i
$161$		0			0
$162$	3.40098	+	0.696562i	0.267206	+	0.0547271i
$163$	−16.4435			−1.28795			−0.643976	−	0.765045i	$-0.722717\pi$
$163$	−16.4435			−1.28795			−0.643976	+	0.765045i	$0.722717\pi$
$164$	−4.28096			−0.334286
$165$	−1.88829	+	3.97785i	−0.147003	+	0.309676i
$166$			0.814552i			0.0632215i
$167$	4.81089			0.372278			0.186139	−	0.982523i	$-0.440402\pi$
$167$	4.81089			0.372278			0.186139	+	0.982523i	$0.440402\pi$
$168$		0			0
$169$	3.59239			0.276338
$170$			2.49232i			0.191152i
$171$	−2.77982	+	2.26818i	−0.212578	+	0.173452i
$172$	10.1100			0.770882
$173$	−6.81521			−0.518151			−0.259075	−	0.965857i	$-0.583418\pi$
$173$	−6.81521			−0.518151			−0.259075	+	0.965857i	$0.583418\pi$
$174$	−4.68980	−	2.22625i	−0.355533	−	0.168771i
$175$		0			0
$176$			7.95571i			0.599684i
$177$	−6.20080	−	2.94352i	−0.466081	−	0.221249i
$178$		−	7.26337i		−	0.544412i
$179$			19.9684i			1.49251i	0.665661	+	0.746254i	$0.268150\pi$
$179$			19.9684i			1.49251i	−0.665661	+	0.746254i	$0.731850\pi$
$180$	3.51101	+	4.30299i	0.261695	+	0.320726i
$181$		−	5.18808i		−	0.385627i	−0.981235	−	0.192813i	$-0.938239\pi$
$181$		−	5.18808i		−	0.385627i	0.981235	−	0.192813i	$-0.0617612\pi$
$182$		0			0
$183$	−6.93799	+	14.6155i	−0.512871	+	1.08041i
$184$	−4.53977			−0.334676
$185$	−3.55208			−0.261154
$186$	−4.14879	−	1.96943i	−0.304204	−	0.144406i
$187$		−	16.4262i		−	1.20120i
$188$	−5.96124			−0.434768
$189$		0			0
$190$	0.461303			0.0334665
$191$		−	8.64099i		−	0.625240i	−0.949878	−	0.312620i	$-0.898793\pi$
$191$		−	8.64099i		−	0.625240i	0.949878	−	0.312620i	$-0.101207\pi$
$192$	7.27144	+	3.45176i	0.524771	+	0.249109i
$193$	−23.7721			−1.71116			−0.855578	−	0.517674i	$-0.826798\pi$
$193$	−23.7721			−1.71116			−0.855578	+	0.517674i	$0.826798\pi$
$194$	−4.77119			−0.342551
$195$	−2.27820	+	4.79923i	−0.163145	+	0.343680i
$196$		0			0
$197$			11.6843i			0.832475i	0.909256	+	0.416238i	$0.136652\pi$
$197$			11.6843i			0.832475i	−0.909256	+	0.416238i	$0.863348\pi$
$198$	1.85984	+	2.27937i	0.132173	+	0.161988i
$199$		−	14.1268i		−	1.00142i	−0.865615	−	0.500709i	$-0.833073\pi$
$199$		−	14.1268i		−	1.00142i	0.865615	−	0.500709i	$-0.166927\pi$
$200$		−	1.48553i		−	0.105043i
$201$	−5.50669	−	2.61403i	−0.388412	−	0.184379i
$202$			2.69098i			0.189336i
$203$		0			0
$204$	−18.7158	−	8.88440i	−1.31037	−	0.622032i
$205$	−2.31252			−0.161513
$206$	−1.45543			−0.101405
$207$	7.10340	−	5.79599i	0.493720	−	0.402849i
$208$			9.59847i			0.665534i
$209$	−3.04032			−0.210303
$210$		0			0
$211$	4.49838			0.309681			0.154841	−	0.987939i	$-0.450514\pi$
$211$	4.49838			0.309681			0.154841	+	0.987939i	$0.450514\pi$
$212$		−	24.5375i		−	1.68524i
$213$	0.684727	−	1.44244i	0.0469167	−	0.0988344i
$214$	5.10464			0.348946
$215$	5.46130			0.372458
$216$	7.49562	−	1.84372i	0.510012	−	0.125449i
$217$		0			0
$218$		−	0.964952i		−	0.0653548i
$219$	−0.220183	+	0.463836i	−0.0148786	+	0.0313431i
$220$			4.70623i			0.317294i
$221$		−	19.8180i		−	1.33310i
$222$	−1.01770	+	2.14387i	−0.0683033	+	0.143887i
$223$			7.20662i			0.482591i	0.970452	+	0.241296i	$0.0775724\pi$
$223$			7.20662i			0.482591i	−0.970452	+	0.241296i	$0.922428\pi$
$224$		0			0
$225$	1.89660	+	2.32442i	0.126440	+	0.154961i
$226$	2.77119			0.184336
$227$	1.86304			0.123654			0.0618270	−	0.998087i	$-0.480307\pi$
$227$	1.86304			0.123654			0.0618270	+	0.998087i	$0.480307\pi$
$228$	−1.64441	+	3.46410i	−0.108904	+	0.229416i
$229$			20.1064i			1.32867i	0.747437	+	0.664333i	$0.231284\pi$
$229$			20.1064i			1.32867i	−0.747437	+	0.664333i	$0.768716\pi$
$230$	−1.17879			−0.0777271
$231$		0			0
$232$	−11.5430			−0.757836
$233$			1.56530i			0.102546i	0.998685	+	0.0512731i	$0.0163279\pi$
$233$			1.56530i			0.102546i	−0.998685	+	0.0512731i	$0.983672\pi$
$234$	2.24388	+	2.75003i	0.146687	+	0.179775i
$235$	−3.22018			−0.210062
$236$	−7.33621			−0.477547
$237$	12.9789	+	6.16110i	0.843073	+	0.400207i
$238$		0			0
$239$		−	5.69230i		−	0.368205i	−0.982907	−	0.184102i	$-0.941062\pi$
$239$		−	5.69230i		−	0.368205i	0.982907	−	0.184102i	$-0.0589378\pi$
$240$	4.89660	+	2.32442i	0.316074	+	0.150040i
$241$			13.3329i			0.858848i	0.903103	+	0.429424i	$0.141283\pi$
$241$			13.3329i			0.858848i	−0.903103	+	0.429424i	$0.858717\pi$
$242$		−	1.75007i		−	0.112498i
$243$	−9.37452	+	12.4546i	−0.601376	+	0.798966i
$244$			17.2917i			1.10699i
$245$		0			0
$246$	−0.662553	+	1.39573i	−0.0422428	+	0.0889884i
$247$	−3.66811			−0.233396
$248$	−10.2114			−0.648426
$249$	−3.30420	−	1.56851i	−0.209395	−	0.0994001i
$250$		−	0.385731i		−	0.0243958i
$251$	−5.32590			−0.336168			−0.168084	−	0.985773i	$-0.553758\pi$
$251$	−5.32590			−0.336168			−0.168084	+	0.985773i	$0.553758\pi$
$252$		0			0
$253$	7.76907			0.488437
$254$			4.31883i			0.270987i
$255$	−10.1100	−	4.79923i	−0.633115	−	0.300540i
$256$	5.37959			0.336225
$257$	6.50006			0.405463			0.202731	−	0.979234i	$-0.435018\pi$
$257$	6.50006			0.405463			0.202731	+	0.979234i	$0.435018\pi$
$258$	1.56470	−	3.29619i	0.0974142	−	0.205212i
$259$		0			0
$260$			5.67800i			0.352135i
$261$	18.0614	−	14.7371i	1.11797	−	0.912206i
$262$			6.04196i			0.373273i
$263$			14.8265i			0.914242i	0.889404	+	0.457121i	$0.151119\pi$
$263$			14.8265i			0.914242i	−0.889404	+	0.457121i	$0.848881\pi$
$264$	5.90923	+	2.80511i	0.363688	+	0.172643i
$265$		−	13.2548i		−	0.814236i
$266$		0			0
$267$	29.4636	+	13.9864i	1.80314	+	0.855953i
$268$	−6.51500			−0.397967
$269$	24.6084			1.50040			0.750201	−	0.661210i	$-0.229957\pi$
$269$	24.6084			1.50040			0.750201	+	0.661210i	$0.229957\pi$
$270$	1.94630	−	0.478738i	0.118448	−	0.0291351i
$271$		−	3.81190i		−	0.231557i	−0.993275	−	0.115778i	$-0.963064\pi$
$271$		−	3.81190i		−	0.231557i	0.993275	−	0.115778i	$-0.0369362\pi$
$272$	−20.2201			−1.22602
$273$		0			0
$274$	2.24819			0.135818
$275$			2.54224i			0.153303i
$276$	4.20204	−	8.85199i	0.252933	−	0.532827i
$277$	−18.7754			−1.12810			−0.564052	−	0.825740i	$-0.690758\pi$
$277$	−18.7754			−1.12810			−0.564052	+	0.825740i	$0.690758\pi$
$278$	−4.64285			−0.278460
$279$	15.9779	−	13.0371i	0.956570	−	0.780509i
$280$		0			0
$281$		−	23.6885i		−	1.41314i	−0.707643	−	0.706570i	$-0.750242\pi$
$281$		−	23.6885i		−	1.41314i	0.707643	−	0.706570i	$-0.249758\pi$
$282$	−0.922607	+	1.94356i	−0.0549404	+	0.115737i
$283$		−	5.04409i		−	0.299840i	−0.988698	−	0.149920i	$-0.952098\pi$
$283$		−	5.04409i		−	0.299840i	0.988698	−	0.149920i	$-0.0479016\pi$
$284$		−	1.70656i		−	0.101266i
$285$	−0.888288	+	1.87126i	−0.0526177	+	0.110844i
$286$			3.00774i			0.177851i
$287$		0			0
$288$	9.71181	−	7.92431i	0.572274	−	0.466945i
$289$	24.7484			1.45579
$290$	−2.99724			−0.176004
$291$	9.18742	−	19.3542i	0.538576	−	1.13456i
$292$			0.548767i			0.0321142i
$293$	−6.29421			−0.367712			−0.183856	−	0.982953i	$-0.558858\pi$
$293$	−6.29421			−0.367712			−0.183856	+	0.982953i	$0.558858\pi$
$294$		0			0
$295$	−3.96292			−0.230730
$296$			5.27672i			0.306703i
$297$	−12.8275	+	3.15523i	−0.744328	+	0.183085i
$298$	7.21219			0.417791
$299$	9.37329			0.542071
$300$	2.89660	+	1.37502i	0.167235	+	0.0793866i
$301$		0			0
$302$			2.29534i			0.132082i
$303$	−10.9159	−	5.18176i	−0.627099	−	0.297684i
$304$			3.74252i			0.214648i
$305$			9.34076i			0.534850i
$306$	−5.79320	+	4.72694i	−0.331175	+	0.270221i
$307$		−	16.0397i		−	0.915432i	−0.889099	−	0.457716i	$-0.848668\pi$
$307$		−	16.0397i		−	0.915432i	0.889099	−	0.457716i	$-0.151332\pi$
$308$		0			0
$309$	2.80258	−	5.90390i	0.159433	−	0.335861i
$310$	−2.65148			−0.150594
$311$	18.0725			1.02480			0.512398	−	0.858748i	$-0.328757\pi$
$311$	18.0725			1.02480			0.512398	+	0.858748i	$0.328757\pi$
$312$	7.12941	+	3.38433i	0.403623	+	0.191600i
$313$			18.6221i			1.05258i	0.850305	+	0.526291i	$0.176418\pi$
$313$			18.6221i			1.05258i	−0.850305	+	0.526291i	$0.823582\pi$
$314$	2.47361			0.139594
$315$		0			0
$316$	15.3555			0.863812
$317$		−	2.63650i		−	0.148080i	−0.997255	−	0.0740402i	$-0.976411\pi$
$317$		−	2.63650i		−	0.148080i	0.997255	−	0.0740402i	$-0.0235893\pi$
$318$	−8.00000	−	3.79760i	−0.448618	−	0.212959i
$319$	19.7540			1.10601
$320$	4.64717			0.259785
$321$	−9.82952	+	20.7068i	−0.548630	+	1.15574i
$322$		0			0
$323$		−	7.72720i		−	0.429953i
$324$	−3.34296	+	16.3221i	−0.185720	+	0.906782i
$325$			3.06718i			0.170137i
$326$			6.34276i			0.351293i
$327$	3.91430	+	1.85812i	0.216461	+	0.102754i
$328$			3.43531i			0.189683i
$329$		0			0
$330$	1.53438	+	0.728371i	0.0844649	+	0.0400955i
$331$	−30.3408			−1.66768			−0.833842	−	0.552004i	$-0.813863\pi$
$331$	−30.3408			−1.66768			−0.833842	+	0.552004i	$0.813863\pi$
$332$	−3.90923			−0.214547
$333$	−6.73687	−	8.25651i	−0.369178	−	0.452454i
$334$		−	1.85571i		−	0.101540i
$335$	−3.51932			−0.192281
$336$		0			0
$337$	−1.84215			−0.100348			−0.0501741	−	0.998740i	$-0.515978\pi$
$337$	−1.84215			−0.100348			−0.0501741	+	0.998740i	$0.515978\pi$
$338$		−	1.38570i		−	0.0753720i
$339$	−5.33621	+	11.2412i	−0.289823	+	0.610539i
$340$	−11.9612			−0.648689
$341$	17.4752			0.946333
$342$	0.874907	+	1.07226i	0.0473096	+	0.0579812i
$343$		0			0
$344$		−	8.11293i		−	0.437420i
$345$	2.26989	−	4.78173i	0.122207	−	0.257439i
$346$			2.62884i			0.141327i
$347$		−	8.19039i		−	0.439683i	−0.975536	−	0.219842i	$-0.929446\pi$
$347$		−	8.19039i		−	0.439683i	0.975536	−	0.219842i	$-0.0705541\pi$
$348$	10.6843	−	22.5074i	0.572738	−	1.20652i
$349$			36.3291i			1.94465i	0.233627	+	0.972326i	$0.424941\pi$
$349$			36.3291i			1.94465i	−0.233627	+	0.972326i	$0.575059\pi$
$350$		0			0
$351$	−15.4762	+	3.80674i	−0.826061	+	0.203189i
$352$	10.6219			0.566150
$353$	5.71473			0.304164			0.152082	−	0.988368i	$-0.451402\pi$
$353$	5.71473			0.304164			0.152082	+	0.988368i	$0.451402\pi$
$354$	−1.13541	+	2.39184i	−0.0603462	+	0.127125i
$355$		−	0.921861i		−	0.0489273i
$356$	34.8586			1.84750
$357$		0			0
$358$	7.70242			0.407086
$359$			4.80564i			0.253632i	0.991926	+	0.126816i	$0.0404758\pi$
$359$			4.80564i			0.253632i	−0.991926	+	0.126816i	$0.959524\pi$
$360$	3.45299	−	2.81746i	0.181989	−	0.148493i
$361$	17.5698			0.924725
$362$	−2.00120			−0.105181
$363$	7.09909	+	3.36994i	0.372605	+	0.176876i
$364$		0			0
$365$			0.296437i			0.0155162i
$366$	5.63766	+	2.67620i	0.294685	+	0.139887i
$367$		−	24.5762i		−	1.28287i	−0.767179	−	0.641433i	$-0.778340\pi$
$367$		−	24.5762i		−	1.28287i	0.767179	−	0.641433i	$-0.221660\pi$
$368$		−	9.56345i		−	0.498529i
$369$	−4.38591	−	5.37525i	−0.228322	−	0.279824i
$370$			1.37015i			0.0712305i
$371$		0			0
$372$	9.45176	−	19.9110i	0.490051	−	1.03234i
$373$	26.5026			1.37225			0.686126	−	0.727483i	$-0.259310\pi$
$373$	26.5026			1.37225			0.686126	+	0.727483i	$0.259310\pi$
$374$	−6.33609			−0.327631
$375$	1.56470	+	0.742765i	0.0808010	+	0.0383562i
$376$			4.78368i			0.246700i
$377$	23.8329			1.22746
$378$		0			0
$379$	13.0939			0.672588			0.336294	−	0.941757i	$-0.390826\pi$
$379$	13.0939			0.672588			0.336294	+	0.941757i	$0.390826\pi$
$380$			2.21390i			0.113571i
$381$	−17.5192	−	8.31636i	−0.897535	−	0.426060i
$382$	−3.33310			−0.170536
$383$	16.9660			0.866922			0.433461	−	0.901172i	$-0.357292\pi$
$383$	16.9660			0.866922			0.433461	+	0.901172i	$0.357292\pi$
$384$	7.53825	−	15.8800i	0.384685	−	0.810374i
$385$		0			0
$386$			9.16964i			0.466723i
$387$	10.3579	+	12.6943i	0.526522	+	0.645290i
$388$		−	22.8980i		−	1.16247i
$389$			2.46478i			0.124970i	0.998046	+	0.0624848i	$0.0199025\pi$
$389$			2.46478i			0.124970i	−0.998046	+	0.0624848i	$0.980098\pi$
$390$	1.85121	+	0.878771i	0.0937398	+	0.0444983i
$391$			19.7457i			0.998583i
$392$		0			0
$393$	−24.5090	−	11.6344i	−1.23632	−	0.586879i
$394$	4.50701			0.227060
$395$	8.29482			0.417358
$396$	−10.9392	+	8.92582i	−0.549717	+	0.448539i
$397$		−	3.35368i		−	0.168316i	−0.996452	−	0.0841582i	$-0.973180\pi$
$397$		−	3.35368i		−	0.168316i	0.996452	−	0.0841582i	$-0.0268201\pi$
$398$	−5.44912			−0.273140
$399$		0			0
$400$	3.12941			0.156470
$401$		−	6.24683i		−	0.311952i	−0.987761	−	0.155976i	$-0.950148\pi$
$401$		−	6.24683i		−	0.311952i	0.987761	−	0.155976i	$-0.0498523\pi$
$402$	−1.00831	+	2.12410i	−0.0502900	+	0.105940i
$403$	21.0836			1.05025
$404$	−12.9146			−0.642526
$405$	−1.80582	+	8.81697i	−0.0897321	+	0.438119i
$406$		0			0
$407$		−	9.03024i		−	0.447612i
$408$	−7.12941	+	15.0188i	−0.352958	+	0.743539i
$409$		−	11.7950i		−	0.583223i	−0.956537	−	0.291611i	$-0.905809\pi$
$409$		−	11.7950i		−	0.583223i	0.956537	−	0.291611i	$-0.0941914\pi$
$410$			0.892008i			0.0440531i
$411$	−4.32914	+	9.11973i	−0.213541	+	0.449843i
$412$		−	6.98495i		−	0.344124i
$413$		0			0
$414$	−2.23569	−	2.74000i	−0.109878	−	0.134664i
$415$	−2.11171			−0.103660
$416$	12.8152			0.628317
$417$	8.94030	−	18.8336i	0.437809	−	0.922284i
$418$			1.17274i			0.0573608i
$419$	12.0419			0.588284			0.294142	−	0.955762i	$-0.404966\pi$
$419$	12.0419			0.588284			0.294142	+	0.955762i	$0.404966\pi$
$420$		0			0
$421$	11.4264			0.556888			0.278444	−	0.960453i	$-0.410181\pi$
$421$	11.4264			0.556888			0.278444	+	0.960453i	$0.410181\pi$
$422$		−	1.73516i		−	0.0844664i
$423$	−6.10740	−	7.48505i	−0.296952	−	0.363935i
$424$	−19.6904			−0.956252
$425$	−6.46130			−0.313419
$426$	−0.556394	−	0.264120i	−0.0269574	−	0.0127967i
$427$		0			0
$428$			24.4983i			1.18417i
$429$	−12.2008	−	5.79172i	−0.589060	−	0.279627i
$430$		−	2.10659i		−	0.101589i
$431$			32.6026i			1.57041i	0.619236	+	0.785205i	$0.287442\pi$
$431$			32.6026i			1.57041i	−0.619236	+	0.785205i	$0.712558\pi$
$432$	3.88397	+	15.7902i	0.186868	+	0.759707i
$433$			4.37644i			0.210318i	0.994455	+	0.105159i	$0.0335352\pi$
$433$			4.37644i			0.210318i	−0.994455	+	0.105159i	$0.966465\pi$
$434$		0			0
$435$	5.77151	−	12.1582i	0.276723	−	0.582942i
$436$	4.63103			0.221786
$437$	3.65472			0.174829
$438$	0.178916	+	0.0849314i	0.00854893	+	0.00405818i
$439$			14.8282i			0.707711i	0.935300	+	0.353855i	$0.115129\pi$
$439$			14.8282i			0.707711i	−0.935300	+	0.353855i	$0.884871\pi$
$440$	3.77658			0.180041
$441$		0			0
$442$	−7.64441			−0.363607
$443$		−	15.9124i		−	0.756023i	−0.925801	−	0.378011i	$-0.876608\pi$
$443$		−	15.9124i		−	0.756023i	0.925801	−	0.378011i	$-0.123392\pi$
$444$	−10.2889	−	4.88416i	−0.488292	−	0.231792i
$445$	18.8301			0.892635
$446$	2.77982			0.131628
$447$	−13.8878	+	29.2560i	−0.656872	+	1.38376i
$448$		0			0
$449$			35.1881i			1.66063i	0.557294	+	0.830315i	$0.311839\pi$
$449$			35.1881i			1.66063i	−0.557294	+	0.830315i	$0.688161\pi$
$450$	0.896599	−	0.731577i	0.0422661	−	0.0344869i
$451$		−	5.87897i		−	0.276830i
$452$			13.2996i			0.625559i
$453$	−9.31096	−	4.41991i	−0.437467	−	0.207666i
$454$		−	0.718630i		−	0.0337270i
$455$		0			0
$456$	2.77982	+	1.31958i	0.130177	+	0.0617950i
$457$	14.0591			0.657656			0.328828	−	0.944390i	$-0.393346\pi$
$457$	14.0591			0.657656			0.328828	+	0.944390i	$0.393346\pi$
$458$	7.75564			0.362397
$459$	−8.01925	−	32.6021i	−0.374307	−	1.52174i
$460$		−	5.65729i		−	0.263773i
$461$	−13.5161			−0.629506			−0.314753	−	0.949174i	$-0.601922\pi$
$461$	−13.5161			−0.629506			−0.314753	+	0.949174i	$0.601922\pi$
$462$		0			0
$463$	17.8381			0.829009			0.414504	−	0.910047i	$-0.363955\pi$
$463$	17.8381			0.829009			0.414504	+	0.910047i	$0.363955\pi$
$464$		−	24.3164i		−	1.12886i
$465$	5.10571	−	10.7557i	0.236772	−	0.498782i
$466$	0.603785			0.0279698
$467$	−9.18941			−0.425235			−0.212618	−	0.977135i	$-0.568199\pi$
$467$	−9.18941			−0.425235			−0.212618	+	0.977135i	$0.568199\pi$
$468$	−13.1980	+	10.7689i	−0.610080	+	0.497792i
$469$		0			0
$470$			1.24212i			0.0572949i
$471$	−4.76320	+	10.0341i	−0.219476	+	0.462348i
$472$			5.88705i			0.270973i
$473$			13.8839i			0.638384i
$474$	2.37653	−	5.00638i	0.109158	−	0.229950i
$475$			1.19592i			0.0548726i
$476$		0			0
$477$	30.8097	−	25.1391i	1.41068	−	1.15104i
$478$	−2.19570			−0.100429
$479$	−18.8807			−0.862683			−0.431341	−	0.902189i	$-0.641960\pi$
$479$	−18.8807			−0.862683			−0.431341	+	0.902189i	$0.641960\pi$
$480$	3.10340	−	6.53760i	0.141650	−	0.298399i
$481$		−	10.8949i		−	0.496763i
$482$	5.14291			0.234253
$483$		0			0
$484$	8.39897			0.381772
$485$		−	12.3692i		−	0.561657i
$486$	4.80414	+	3.61604i	0.217920	+	0.164027i
$487$	−5.23525			−0.237232			−0.118616	−	0.992940i	$-0.537846\pi$
$487$	−5.23525			−0.237232			−0.118616	+	0.992940i	$0.537846\pi$
$488$	13.8760			0.628136
$489$	−25.7292	−	12.2136i	−1.16351	−	0.552320i
$490$		0			0
$491$			19.5201i			0.880930i	0.897770	+	0.440465i	$0.145186\pi$
$491$			19.5201i			0.880930i	−0.897770	+	0.440465i	$0.854814\pi$
$492$	−6.69843	−	3.17975i	−0.301988	−	0.143354i
$493$			50.2062i			2.26117i
$494$			1.41490i			0.0636594i
$495$	−5.90923	+	4.82161i	−0.265600	+	0.216715i
$496$		−	21.5113i		−	0.965887i
$497$		0			0
$498$	−0.605021	+	1.27453i	−0.0271116	+	0.0571132i
$499$	−36.6350			−1.64001			−0.820005	−	0.572356i	$-0.806029\pi$
$499$	−36.6350			−1.64001			−0.820005	+	0.572356i	$0.806029\pi$
$500$	1.85121			0.0827887
$501$	7.52763	+	3.57337i	0.336310	+	0.159646i
$502$			2.05436i			0.0916907i
$503$	40.7156			1.81542			0.907708	−	0.419602i	$-0.137830\pi$
$503$	40.7156			1.81542			0.907708	+	0.419602i	$0.137830\pi$
$504$		0			0
$505$	−6.97630			−0.310441
$506$		−	2.99677i		−	0.133223i
$507$	5.62104	+	2.66831i	0.249639	+	0.118504i
$508$	−20.7271			−0.919615
$509$	17.7277			0.785765			0.392883	−	0.919589i	$-0.371478\pi$
$509$	17.7277			0.785765			0.392883	+	0.919589i	$0.371478\pi$
$510$	−1.85121	+	3.89975i	−0.0819730	+	0.172684i
$511$		0			0
$512$		−	22.3729i		−	0.988751i
$513$	−6.03432	+	1.48428i	−0.266422	+	0.0655326i
$514$		−	2.50727i		−	0.110591i
$515$		−	3.77318i		−	0.166266i
$516$	15.8192	+	7.50938i	0.696402	+	0.330582i
$517$		−	8.18648i		−	0.360041i
$518$		0			0
$519$	−10.6638	−	5.06210i	−0.468088	−	0.222202i
$520$	4.55639			0.199811
$521$	3.51561			0.154022			0.0770108	−	0.997030i	$-0.475462\pi$
$521$	3.51561			0.154022			0.0770108	+	0.997030i	$0.475462\pi$
$522$	−5.68457	−	6.96684i	−0.248807	−	0.304930i
$523$		−	4.85583i		−	0.212330i	−0.994349	−	0.106165i	$-0.966143\pi$
$523$		−	4.85583i		−	0.212330i	0.994349	−	0.106165i	$-0.0338572\pi$
$524$	−28.9968			−1.26673
$525$		0			0
$526$	5.71904			0.249362
$527$			44.4145i			1.93473i
$528$	−5.90923	+	12.4483i	−0.257166	+	0.541744i
$529$	13.6609			0.593952
$530$	−5.11279			−0.222085
$531$	−7.51608	−	9.21148i	−0.326170	−	0.399744i
$532$		0			0
$533$		−	7.09290i		−	0.307228i
$534$	5.39498	−	11.3650i	0.233464	−	0.491813i
$535$			13.2337i			0.572142i
$536$			5.22805i			0.225818i
$537$	−14.8318	+	31.2446i	−0.640041	+	1.34831i
$538$		−	9.49222i		−	0.409239i
$539$		0			0
$540$	2.29758	+	9.34076i	0.0988719	+	0.401962i
$541$	−0.0386341			−0.00166101			−0.000830506	−	1.00000i	$-0.500264\pi$
$541$	−0.0386341			−0.00166101			−0.000830506		1.00000i	$0.500264\pi$
$542$	−1.47037			−0.0631577
$543$	3.85352	−	8.11781i	0.165371	−	0.348368i
$544$			26.9964i			1.15746i
$545$	2.50162			0.107158
$546$		0			0
$547$	−36.3881			−1.55584			−0.777921	−	0.628362i	$-0.783726\pi$
$547$	−36.3881			−1.55584			−0.777921	+	0.628362i	$0.783726\pi$
$548$			10.7896i			0.460909i
$549$	−21.7118	+	17.7157i	−0.926637	+	0.756086i
$550$	0.980620			0.0418138
$551$	9.29265			0.395880
$552$	−7.10340	−	3.37199i	−0.302341	−	0.143521i
$553$		0			0
$554$			7.24224i			0.307693i
$555$	−5.55795	−	2.63836i	−0.235922	−	0.111992i
$556$		−	22.2821i		−	0.944973i
$557$			17.3756i			0.736227i	0.929781	+	0.368114i	$0.119996\pi$
$557$			17.3756i			0.736227i	−0.929781	+	0.368114i	$0.880004\pi$
$558$	−5.02880	−	6.16315i	−0.212886	−	0.260907i
$559$			16.7508i			0.708484i
$560$		0			0
$561$	12.2008	−	25.7021i	0.515118	−	1.08514i
$562$	−9.13740			−0.385438
$563$	20.9091			0.881214			0.440607	−	0.897700i	$-0.354763\pi$
$563$	20.9091			0.881214			0.440607	+	0.897700i	$0.354763\pi$
$564$	−9.32758	−	4.42780i	−0.392762	−	0.186444i
$565$			7.18425i			0.302244i
$566$	−1.94566			−0.0817822
$567$		0			0
$568$	−1.36945			−0.0574610
$569$		−	28.7374i		−	1.20473i	−0.798219	−	0.602367i	$-0.794224\pi$
$569$		−	28.7374i		−	1.20473i	0.798219	−	0.602367i	$-0.205776\pi$
$570$	0.721803	+	0.342640i	0.0302330	+	0.0143516i
$571$	−30.4998			−1.27638			−0.638188	−	0.769881i	$-0.720316\pi$
$571$	−30.4998			−1.27638			−0.638188	+	0.769881i	$0.720316\pi$
$572$	−14.4348			−0.603551
$573$	6.41823	−	13.5206i	0.268125	−	0.564831i
$574$		0			0
$575$		−	3.05599i		−	0.127444i
$576$	8.81381	+	10.8020i	0.367242	+	0.450081i
$577$			23.5062i			0.978577i	0.872122	+	0.489289i	$0.162744\pi$
$577$			23.5062i			0.978577i	−0.872122	+	0.489289i	$0.837256\pi$
$578$		−	9.54623i		−	0.397071i
$579$	−37.1964	−	17.6571i	−1.54583	−	0.733805i
$580$		−	14.3845i		−	0.597282i
$581$		0			0
$582$	−7.46549	−	3.54387i	−0.309455	−	0.146898i
$583$	33.6969			1.39558
$584$	0.440366			0.0182225
$585$	−7.12941	+	5.81721i	−0.294765	+	0.240512i
$586$			2.42787i			0.100294i
$587$	−24.4613			−1.00963			−0.504813	−	0.863229i	$-0.668439\pi$
$587$	−24.4613			−1.00963			−0.504813	+	0.863229i	$0.668439\pi$
$588$		0			0
$589$	8.22067			0.338727
$590$			1.52862i			0.0629324i
$591$	−8.67873	+	18.2825i	−0.356995	+	0.752043i
$592$	−11.1159			−0.456861
$593$	−3.75012			−0.153999			−0.0769995	−	0.997031i	$-0.524534\pi$
$593$	−3.75012			−0.153999			−0.0769995	+	0.997031i	$0.524534\pi$
$594$	1.21707	+	4.94797i	0.0499369	+	0.203018i
$595$		0			0
$596$			34.6130i			1.41780i
$597$	10.4929	−	22.1042i	0.429444	−	0.904664i
$598$		−	3.61557i		−	0.147851i
$599$		−	33.1010i		−	1.35247i	−0.736686	−	0.676235i	$-0.763610\pi$
$599$		−	33.1010i		−	1.35247i	0.736686	−	0.676235i	$-0.236390\pi$
$600$	1.10340	−	2.32442i	0.0450462	−	0.0948939i
$601$		−	3.36032i		−	0.137070i	−0.997649	−	0.0685352i	$-0.978167\pi$
$601$		−	3.36032i		−	0.137070i	0.997649	−	0.0685352i	$-0.0218325\pi$
$602$		0			0
$603$	−6.67473	−	8.18036i	−0.271816	−	0.333130i
$604$	−11.0159			−0.448229
$605$	4.53701			0.184456
$606$	−1.99876	+	4.21058i	−0.0811942	+	0.171043i
$607$		−	44.5044i		−	1.80638i	−0.429241	−	0.903190i	$-0.641219\pi$
$607$		−	44.5044i		−	1.80638i	0.429241	−	0.903190i	$-0.358781\pi$
$608$	4.99676			0.202645
$609$		0			0
$610$	3.60302			0.145882
$611$		−	9.87689i		−	0.399576i
$612$	−22.6857	−	27.8029i	−0.917014	−	1.12387i
$613$	40.3135			1.62825			0.814123	−	0.580693i	$-0.197218\pi$
$613$	40.3135			1.62825			0.814123	+	0.580693i	$0.197218\pi$
$614$	−6.18699			−0.249687
$615$	−3.61840	−	1.71766i	−0.145908	−	0.0692626i
$616$		0			0
$617$			37.7372i			1.51924i	0.650366	+	0.759621i	$0.274616\pi$
$617$			37.7372i			1.51924i	−0.650366	+	0.759621i	$0.725384\pi$
$618$	−2.27732	−	1.08104i	−0.0916071	−	0.0434859i
$619$			14.6788i			0.589992i	0.955499	+	0.294996i	$0.0953182\pi$
$619$			14.6788i			0.589992i	−0.955499	+	0.294996i	$0.904682\pi$
$620$		−	12.7251i		−	0.511052i
$621$	15.4198	−	3.79286i	0.618775	−	0.152202i
$622$		−	6.97111i		−	0.279516i
$623$		0			0
$624$	−7.12941	+	15.0188i	−0.285405	+	0.601232i
$625$	1.00000			0.0400000
$626$	7.18311			0.287095
$627$	−4.75720	−	2.25824i	−0.189984	−	0.0901855i
$628$			11.8714i			0.473721i
$629$	22.9511			0.915118
$630$		0			0
$631$	−35.8363			−1.42662			−0.713311	−	0.700848i	$-0.752805\pi$
$631$	−35.8363			−1.42662			−0.713311	+	0.700848i	$0.752805\pi$
$632$		−	12.3222i		−	0.490151i
$633$	7.03863	+	3.34124i	0.279761	+	0.132802i
$634$	−1.01698			−0.0403894
$635$	−11.1965			−0.444319
$636$	18.2256	−	38.3939i	0.722691	−	1.52242i
$637$		0			0
$638$		−	7.61971i		−	0.301667i
$639$	2.14279	−	1.74840i	0.0847674	−	0.0691657i
$640$		−	10.1489i		−	0.401170i
$641$			15.6174i			0.616852i	0.951248	+	0.308426i	$0.0998022\pi$
$641$			15.6174i			0.616852i	−0.951248	+	0.308426i	$0.900198\pi$
$642$	7.98725	+	3.79155i	0.315232	+	0.149640i
$643$			29.3208i			1.15630i	0.815931	+	0.578149i	$0.196225\pi$
$643$			29.3208i			1.15630i	−0.815931	+	0.578149i	$0.803775\pi$
$644$		0			0
$645$	8.54532	+	4.05647i	0.336472	+	0.159723i
$646$	−2.98062			−0.117271
$647$	6.66811			0.262150			0.131075	−	0.991372i	$-0.458157\pi$
$647$	6.66811			0.262150			0.131075	+	0.991372i	$0.458157\pi$
$648$	13.0979	+	2.68261i	0.514533	+	0.105383i
$649$		−	10.0747i		−	0.395467i
$650$	1.18311			0.0464053
$651$		0			0
$652$	−30.4404			−1.19214
$653$			44.1287i			1.72689i	0.504445	+	0.863444i	$0.331697\pi$
$653$			44.1287i			1.72689i	−0.504445	+	0.863444i	$0.668303\pi$
$654$	0.716733	−	1.50986i	0.0280265	−	0.0590404i
$655$	−15.6637			−0.612030
$656$	−7.23680			−0.282550
$657$	−0.689043	+	0.562222i	−0.0268821	+	0.0219344i
$658$		0			0
$659$		−	7.10057i		−	0.276599i	−0.990390	−	0.138299i	$-0.955836\pi$
$659$		−	7.10057i		−	0.276599i	0.990390	−	0.138299i	$-0.0441636\pi$
$660$	−3.49562	+	7.36385i	−0.136067	+	0.286638i
$661$		−	23.7358i		−	0.923214i	−0.887085	−	0.461607i	$-0.847273\pi$
$661$		−	23.7358i		−	0.923214i	0.887085	−	0.461607i	$-0.152727\pi$
$662$			11.7034i			0.454865i
$663$	14.7201	−	31.0093i	0.571682	−	1.20430i
$664$			3.13701i			0.121740i
$665$		0			0
$666$	−3.18479	+	2.59862i	−0.123408	+	0.100694i
$667$	−23.7460			−0.919448
$668$	8.90599			0.344583
$669$	−5.35283	+	11.2762i	−0.206952	+	0.435965i
$670$			1.35751i			0.0524451i
$671$	−23.7464			−0.916721
$672$		0			0
$673$	−14.7915			−0.570171			−0.285086	−	0.958502i	$-0.592022\pi$
$673$	−14.7915			−0.570171			−0.285086	+	0.958502i	$0.592022\pi$
$674$			0.710573i			0.0273702i
$675$	1.24112	+	5.04575i	0.0477707	+	0.194211i
$676$	6.65028			0.255780
$677$	36.5179			1.40350			0.701749	−	0.712424i	$-0.252403\pi$
$677$	36.5179			1.40350			0.701749	+	0.712424i	$0.252403\pi$
$678$	4.33609	+	2.05834i	0.166526	+	0.0790501i
$679$		0			0
$680$			9.59847i			0.368084i
$681$	2.91510	+	1.38380i	0.111707	+	0.0530273i
$682$		−	6.74071i		−	0.258115i
$683$			21.9194i			0.838723i	0.907819	+	0.419362i	$0.137746\pi$
$683$			21.9194i			0.838723i	−0.907819	+	0.419362i	$0.862254\pi$
$684$	−5.14603	+	4.19888i	−0.196763	+	0.160548i
$685$			5.82840i			0.222692i
$686$		0			0
$687$	−14.9343	+	31.4605i	−0.569779	+	1.20029i
$688$	17.0906			0.651575
$689$	40.6549			1.54883
$690$	−1.84446	−	0.875565i	−0.0702173	−	0.0333322i
$691$		−	31.4114i		−	1.19495i	−0.801889	−	0.597473i	$-0.796172\pi$
$691$		−	31.4114i		−	1.19495i	0.801889	−	0.597473i	$-0.203828\pi$
$692$	−12.6164			−0.479604
$693$		0			0
$694$	−3.15929			−0.119925
$695$		−	12.0365i		−	0.456571i
$696$	−18.0614	−	8.57375i	−0.684616	−	0.324987i
$697$	14.9419			0.565963
$698$	14.0133			0.530410
$699$	−1.16265	+	2.44923i	−0.0439755	+	0.0926385i
$700$		0			0
$701$		−	29.6988i		−	1.12171i	−0.827915	−	0.560854i	$-0.810473\pi$
$701$		−	29.6988i		−	1.12171i	0.827915	−	0.560854i	$-0.189527\pi$
$702$	1.46838	+	5.96966i	0.0554203	+	0.225310i
$703$		−	4.24800i		−	0.160216i
$704$			11.8142i			0.445265i
$705$	−5.03863	−	2.39184i	−0.189766	−	0.0900819i
$706$		−	2.20435i		−	0.0829617i
$707$		0			0
$708$	−11.4790	−	5.44908i	−0.431407	−	0.204789i
$709$	13.3268			0.500500			0.250250	−	0.968181i	$-0.419487\pi$
$709$	13.3268			0.500500			0.250250	+	0.968181i	$0.419487\pi$
$710$	−0.355590			−0.0133451
$711$	15.7319	+	19.2806i	0.589994	+	0.723079i
$712$		−	27.9728i		−	1.04832i
$713$	−21.0067			−0.786706
$714$		0			0
$715$	−7.79751			−0.291610
$716$			36.9657i			1.38147i
$717$	4.22805	−	8.90677i	0.157899	−	0.332630i
$718$	1.85368			0.0691789
$719$	−51.1725			−1.90841			−0.954207	−	0.299147i	$-0.903298\pi$
$719$	−51.1725			−1.90841			−0.954207	+	0.299147i	$0.903298\pi$
$720$	5.93523	+	7.27405i	0.221193	+	0.271088i
$721$		0			0
$722$		−	6.77720i		−	0.252221i
$723$	−9.90323	+	20.8621i	−0.368305	+	0.775869i
$724$		−	9.60423i		−	0.356938i
$725$		−	7.77029i		−	0.288581i
$726$	1.29989	−	2.73834i	0.0482434	−	0.101629i
$727$		−	51.6371i		−	1.91511i	−0.288246	−	0.957556i	$-0.593072\pi$
$727$		−	51.6371i		−	1.91511i	0.288246	−	0.957556i	$-0.406928\pi$
$728$		0			0
$729$	−23.9192	+	12.5248i	−0.885898	+	0.463880i
$730$	0.114345			0.00423209
$731$	−35.2871			−1.30514
$732$	−12.8437	+	27.0564i	−0.474716	+	1.00003i
$733$		−	21.9443i		−	0.810530i	−0.914199	−	0.405265i	$-0.867179\pi$
$733$		−	21.9443i		−	0.810530i	0.914199	−	0.405265i	$-0.132821\pi$
$734$	−9.47979			−0.349905
$735$		0			0
$736$	−12.7685			−0.470652
$737$		−	8.94695i		−	0.329565i
$738$	−2.07340	+	1.69178i	−0.0763229	+	0.0622754i
$739$	−38.5749			−1.41900			−0.709500	−	0.704705i	$-0.751079\pi$
$739$	−38.5749			−1.41900			−0.709500	+	0.704705i	$0.751079\pi$
$740$	−6.57565			−0.241726
$741$	−5.73950	−	2.72454i	−0.210846	−	0.100089i
$742$		0			0
$743$		−	3.81873i		−	0.140096i	−0.997544	−	0.0700478i	$-0.977685\pi$
$743$		−	3.81873i		−	0.140096i	0.997544	−	0.0700478i	$-0.0223152\pi$
$744$	−15.9779	−	7.58469i	−0.585777	−	0.278068i
$745$			18.6975i			0.685023i
$746$		−	10.2229i		−	0.374285i
$747$	−4.00507	−	4.90850i	−0.146538	−	0.179593i
$748$		−	30.4083i		−	1.11184i
$749$		0			0
$750$	0.286507	−	0.603555i	0.0104618	−	0.0220387i
$751$	21.0542			0.768277			0.384139	−	0.923275i	$-0.374498\pi$
$751$	21.0542			0.768277			0.384139	+	0.923275i	$0.374498\pi$
$752$	−10.0773			−0.367480
$753$	−8.33345	−	3.95589i	−0.303688	−	0.144161i
$754$		−	9.19309i		−	0.334792i
$755$	−5.95062			−0.216565
$756$		0			0
$757$	28.6903			1.04277			0.521383	−	0.853323i	$-0.325416\pi$
$757$	28.6903			1.04277			0.521383	+	0.853323i	$0.325416\pi$
$758$		−	5.05072i		−	0.183450i
$759$	12.1563	+	5.77060i	0.441246	+	0.209459i
$760$	1.77658			0.0644432
$761$	10.6975			0.387784			0.193892	−	0.981023i	$-0.437889\pi$
$761$	10.6975			0.387784			0.193892	+	0.981023i	$0.437889\pi$
$762$	−3.20788	+	6.75769i	−0.116209	+	0.244805i
$763$		0			0
$764$		−	15.9963i		−	0.578726i
$765$	−12.2545	−	15.0188i	−0.443062	−	0.543004i
$766$		−	6.54430i		−	0.236455i
$767$		−	12.1550i		−	0.438892i
$768$	8.41747	+	3.99578i	0.303739	+	0.144185i
$769$		−	38.6874i		−	1.39510i	−0.716535	−	0.697551i	$-0.754273\pi$
$769$		−	38.6874i		−	1.39510i	0.716535	−	0.697551i	$-0.245727\pi$
$770$		0			0
$771$	10.1707	+	4.82802i	0.366288	+	0.173877i
$772$	−44.0073			−1.58386
$773$	22.8875			0.823207			0.411603	−	0.911363i	$-0.364969\pi$
$773$	22.8875			0.823207			0.411603	+	0.911363i	$0.364969\pi$
$774$	4.89660	−	3.99536i	0.176005	−	0.143610i
$775$		−	6.87392i		−	0.246919i
$776$	−18.3748			−0.659618
$777$		0			0
$778$	0.950743			0.0340858
$779$		−	2.76558i		−	0.0990873i
$780$	−4.21742	+	8.88440i	−0.151008	+	0.318112i
$781$	2.34359			0.0838603
$782$	7.61652			0.272366
$783$	39.2070	−	9.64387i	1.40114	−	0.344644i
$784$		0			0
$785$			6.41279i			0.228882i
$786$	−4.48776	+	9.45388i	−0.160073	+	0.337209i
$787$			32.5195i			1.15919i	0.814903	+	0.579597i	$0.196790\pi$
$787$			32.5195i			1.15919i	−0.814903	+	0.579597i	$0.803210\pi$
$788$			21.6302i			0.770544i
$789$	−11.0126	+	23.1991i	−0.392060	+	0.825911i
$790$		−	3.19957i		−	0.113835i
$791$		0			0
$792$	7.16265	+	8.77834i	0.254514	+	0.311925i
$793$	−28.6498			−1.01738
$794$	−1.29362			−0.0459088
$795$	9.84521	−	20.7399i	0.349174	−	0.735567i
$796$		−	26.1516i		−	0.926919i
$797$	31.9080			1.13024			0.565120	−	0.825009i	$-0.308830\pi$
$797$	31.9080			1.13024			0.565120	+	0.825009i	$0.308830\pi$
$798$		0			0
$799$	20.8066			0.736084
$800$		−	4.17817i		−	0.147721i
$801$	35.7132	+	43.7691i	1.26187	+	1.54651i
$802$	−2.40960			−0.0850858
$803$	−0.753614			−0.0265944
$804$	−10.1941	−	4.83912i	−0.359516	−	0.170663i
$805$		0			0
$806$		−	8.13258i		−	0.286458i
$807$	38.5049	+	18.2783i	1.35544	+	0.643426i
$808$			10.3635i			0.364587i
$809$		−	20.7686i		−	0.730187i	−0.930971	−	0.365093i	$-0.881037\pi$
$809$		−	20.7686i		−	0.730187i	0.930971	−	0.365093i	$-0.118963\pi$
$810$	3.40098	+	0.696562i	0.119498	+	0.0244747i
$811$			5.77041i			0.202627i	0.994855	+	0.101313i	$0.0323044\pi$
$811$			5.77041i			0.202627i	−0.994855	+	0.101313i	$0.967696\pi$
$812$		0			0
$813$	2.83135	−	5.96450i	0.0992998	−	0.209184i
$814$	−3.48324			−0.122087
$815$	−16.4435			−0.575990
$816$	−31.6384	−	15.0188i	−1.10757	−	0.525762i
$817$			6.53128i			0.228501i
$818$	−4.54968			−0.159076
$819$		0			0
$820$	−4.28096			−0.149497
$821$			14.7695i			0.515461i	0.966217	+	0.257730i	$0.0829746\pi$
$821$			14.7695i			0.515461i	−0.966217	+	0.257730i	$0.917025\pi$
$822$	3.51776	+	1.66988i	0.122696	+	0.0582438i
$823$	27.4108			0.955482			0.477741	−	0.878501i	$-0.341456\pi$
$823$	27.4108			0.955482			0.477741	+	0.878501i	$0.341456\pi$
$824$	−5.60517			−0.195265
$825$	−1.88829	+	3.97785i	−0.0657418	+	0.138491i
$826$		0			0
$827$			27.6521i			0.961557i	0.876842	+	0.480779i	$0.159646\pi$
$827$			27.6521i			0.961557i	−0.876842	+	0.480779i	$0.840354\pi$
$828$	13.1499	−	10.7296i	0.456991	−	0.372880i
$829$		−	21.5065i		−	0.746953i	−0.927640	−	0.373476i	$-0.878166\pi$
$829$		−	21.5065i		−	0.746953i	0.927640	−	0.373476i	$-0.121834\pi$
$830$			0.814552i			0.0282735i
$831$	−29.3779	−	13.9457i	−1.01911	−	0.483771i
$832$			14.2537i			0.494158i
$833$		0			0
$834$	−7.26469	−	3.44855i	−0.251556	−	0.119414i
$835$	4.81089			0.166488
$836$	−5.62827			−0.194658
$837$	34.6841	−	8.53137i	1.19886	−	0.294887i
$838$		−	4.64492i		−	0.160456i
$839$	−26.4538			−0.913286			−0.456643	−	0.889650i	$-0.650948\pi$
$839$	−26.4538			−0.913286			−0.456643	+	0.889650i	$0.650948\pi$
$840$		0			0
$841$	−31.3775			−1.08198
$842$		−	4.40751i		−	0.151893i
$843$	17.5950	−	37.0656i	0.606005	−	1.27661i
$844$	8.32745			0.286643
$845$	3.59239			0.123582
$846$	−2.88721	+	2.35581i	−0.0992644	+	0.0809944i
$847$		0			0
$848$		−	41.4797i		−	1.42442i
$849$	3.74657	−	7.89251i	0.128582	−	0.270870i
$850$			2.49232i			0.0854860i
$851$			10.8551i			0.372109i
$852$	1.26757	−	2.67026i	0.0434264	−	0.0914817i
$853$		−	6.05997i		−	0.207490i	−0.994604	−	0.103745i	$-0.966917\pi$
$853$		−	6.05997i		−	0.207490i	0.994604	−	0.103745i	$-0.0330825\pi$
$854$		0			0
$855$	−2.77982	+	2.26818i	−0.0950677	+	0.0775702i
$856$	19.6590			0.671932
$857$	10.3398			0.353199			0.176600	−	0.984283i	$-0.443490\pi$
$857$	10.3398			0.353199			0.176600	+	0.984283i	$0.443490\pi$
$858$	−2.23405	+	4.70623i	−0.0762691	+	0.160668i
$859$			35.4947i			1.21106i	0.795821	+	0.605531i	$0.207039\pi$
$859$			35.4947i			1.21106i	−0.795821	+	0.605531i	$0.792961\pi$
$860$	10.1100			0.344749
$861$		0			0
$862$	12.5758			0.428334
$863$			15.1410i			0.515405i	0.966224	+	0.257702i	$0.0829654\pi$
$863$			15.1410i			0.515405i	−0.966224	+	0.257702i	$0.917035\pi$
$864$	21.0820	−	5.18561i	0.717225	−	0.176418i
$865$	−6.81521			−0.231724
$866$	1.68813			0.0573649
$867$	38.7240	+	18.3823i	1.31514	+	0.624295i
$868$		0			0
$869$			21.0874i			0.715342i
$870$	−4.68980	−	2.22625i	−0.158999	−	0.0754769i
$871$		−	10.7944i		−	0.365754i
$872$		−	3.71623i		−	0.125848i
$873$	28.7512	−	23.4594i	0.973081	−	0.793982i
$874$		−	1.40974i		−	0.0476852i
$875$		0			0
$876$	−0.407605	+	0.858658i	−0.0137717	+	0.0290114i
$877$	19.5895			0.661491			0.330745	−	0.943720i	$-0.392700\pi$
$877$	19.5895			0.661491			0.330745	+	0.943720i	$0.392700\pi$
$878$	5.71969			0.193030
$879$	−9.84858	−	4.67512i	−0.332184	−	0.157688i
$880$			7.95571i			0.268187i
$881$	28.7481			0.968548			0.484274	−	0.874917i	$-0.339084\pi$
$881$	28.7481			0.968548			0.484274	+	0.874917i	$0.339084\pi$
$882$		0			0
$883$	5.77550			0.194361			0.0971805	−	0.995267i	$-0.469018\pi$
$883$	5.77550			0.194361			0.0971805	+	0.995267i	$0.469018\pi$
$884$		−	36.6873i		−	1.23393i
$885$	−6.20080	−	2.94352i	−0.208438	−	0.0989454i
$886$	−6.13792			−0.206207
$887$	13.1383			0.441143			0.220571	−	0.975371i	$-0.429208\pi$
$887$	13.1383			0.441143			0.220571	+	0.975371i	$0.429208\pi$
$888$	−3.91937	+	8.25651i	−0.131525	+	0.277070i
$889$		0			0
$890$		−	7.26337i		−	0.243469i
$891$	−22.4149	−	4.59084i	−0.750926	−	0.153799i
$892$			13.3410i			0.446689i
$893$		−	3.85108i		−	0.128872i
$894$	11.2849	+	5.35697i	0.377425	+	0.179164i
$895$			19.9684i			0.667470i
$896$		0			0
$897$	14.6664	+	6.96215i	0.489698	+	0.232460i
$898$	13.5731			0.452942
$899$	−53.4124			−1.78140
$900$	3.51101	+	4.30299i	0.117034	+	0.143433i
$901$			85.6433i			2.85319i
$902$	−2.26770			−0.0755061
$903$		0			0
$904$	10.6724			0.354959
$905$		−	5.18808i		−	0.172457i
$906$	−1.70490	+	3.59152i	−0.0566414	+	0.119320i
$907$	−6.17008			−0.204874			−0.102437	−	0.994739i	$-0.532664\pi$
$907$	−6.17008			−0.204874			−0.102437	+	0.994739i	$0.532664\pi$
$908$	3.44887			0.114455
$909$	−13.2313	−	16.2158i	−0.438853	−	0.537845i
$910$		0			0
$911$		−	53.7961i		−	1.78234i	−0.453665	−	0.891172i	$-0.649884\pi$
$911$		−	53.7961i		−	1.78234i	0.453665	−	0.891172i	$-0.350116\pi$
$912$	−2.77982	+	5.85594i	−0.0920489	+	0.193910i
$913$		−	5.36848i		−	0.177671i
$914$		−	5.42302i		−	0.179378i
$915$	−6.93799	+	14.6155i	−0.229363	+	0.483174i
$916$			37.2211i			1.22982i
$917$		0			0
$918$	−12.5756	+	3.09327i	−0.415058	+	0.102093i
$919$	−0.620281			−0.0204612			−0.0102306	−	0.999948i	$-0.503257\pi$
$919$	−0.620281			−0.0204612			−0.0102306	+	0.999948i	$0.503257\pi$
$920$	−4.53977			−0.149672
$921$	11.9137	−	25.0973i	0.392570	−	0.826985i
$922$			5.21357i			0.171700i
$923$	2.82752			0.0930688
$924$		0			0
$925$	−3.55208			−0.116792
$926$		−	6.88072i		−	0.226114i
$927$	8.77043	−	7.15620i	0.288059	−	0.235040i
$928$	−32.4656			−1.06574
$929$	−52.9609			−1.73759			−0.868796	−	0.495170i	$-0.835106\pi$
$929$	−52.9609			−1.73759			−0.868796	+	0.495170i	$0.835106\pi$
$930$	−4.14879	−	1.96943i	−0.136044	−	0.0645802i
$931$		0			0
$932$			2.89770i			0.0949174i
$933$	28.2781	+	13.4236i	0.925783	+	0.439469i
$934$			3.54464i			0.115984i
$935$		−	16.4262i		−	0.537194i
$936$	8.64165	+	10.5910i	0.282461	+	0.346176i
$937$			0.667265i			0.0217986i	0.999941	+	0.0108993i	$0.00346942\pi$
$937$			0.667265i			0.0217986i	−0.999941	+	0.0108993i	$0.996531\pi$
$938$		0			0
$939$	−13.8318	+	29.1380i	−0.451385	+	0.950884i
$940$	−5.96124			−0.194434
$941$	−24.9683			−0.813944			−0.406972	−	0.913441i	$-0.633415\pi$
$941$	−24.9683			−0.813944			−0.406972	+	0.913441i	$0.633415\pi$
$942$	3.87047	+	1.83731i	0.126107	+	0.0598628i
$943$			7.06703i			0.230134i
$944$	−12.4016			−0.403638
$945$		0			0
$946$	5.35547			0.174121
$947$		−	54.9967i		−	1.78715i	−0.448910	−	0.893577i	$-0.648188\pi$
$947$		−	54.9967i		−	1.78715i	0.448910	−	0.893577i	$-0.351812\pi$
$948$	24.0268	+	11.4055i	0.780353	+	0.370434i
$949$	−0.909226			−0.0295147
$950$	0.461303			0.0149667
$951$	1.95830	−	4.12534i	0.0635022	−	0.133773i
$952$		0			0
$953$			35.8657i			1.16180i	0.813974	+	0.580902i	$0.197300\pi$
$953$			35.8657i			1.16180i	−0.813974	+	0.580902i	$0.802700\pi$
$954$	−9.69691	−	11.8842i	−0.313949	−	0.384767i
$955$		−	8.64099i		−	0.279616i
$956$		−	10.5377i		−	0.340812i
$957$	30.9091	+	14.6726i	0.999149	+	0.474296i
$958$			7.28288i			0.235299i
$959$		0			0
$960$	7.27144	+	3.45176i	0.234685	+	0.111405i
$961$	−16.2508			−0.524220
$962$	−4.20249			−0.135494
$963$	−30.7606	+	25.0990i	−0.991246	+	0.808803i
$964$			24.6820i			0.794955i
$965$	−23.7721			−0.765252
$966$		0			0
$967$	11.8780			0.381971			0.190986	−	0.981593i	$-0.438832\pi$
$967$	11.8780			0.381971			0.190986	+	0.981593i	$0.438832\pi$
$968$		−	6.73987i		−	0.216628i
$969$	5.73950	−	12.0908i	0.184379	−	0.388412i
$970$	−4.77119			−0.153194
$971$	5.22666			0.167732			0.0838658	−	0.996477i	$-0.473273\pi$
$971$	5.22666			0.167732			0.0838658	+	0.996477i	$0.473273\pi$
$972$	−17.3542	+	23.0562i	−0.556637	+	0.739528i
$973$		0			0
$974$			2.01940i			0.0647056i
$975$	−2.27820	+	4.79923i	−0.0729607	+	0.153698i
$976$			29.2310i			0.935663i
$977$		−	17.9198i		−	0.573307i	−0.958034	−	0.286653i	$-0.907457\pi$
$977$		−	17.9198i		−	0.573307i	0.958034	−	0.286653i	$-0.0925428\pi$
$978$	−4.71118	+	9.92454i	−0.150647	+	0.317352i
$979$			47.8708i			1.52996i
$980$		0			0
$981$	4.74457	+	5.81481i	0.151482	+	0.185653i
$982$	7.52951			0.240276
$983$	−41.8828			−1.33585			−0.667926	−	0.744227i	$-0.732818\pi$
$983$	−41.8828			−1.33585			−0.667926	+	0.744227i	$0.732818\pi$
$984$	−2.55163	+	5.37525i	−0.0813430	+	0.171357i
$985$			11.6843i			0.372294i
$986$	19.3661			0.616742
$987$		0			0
$988$	−6.79044			−0.216033
$989$		−	16.6897i		−	0.530702i
$990$	1.85984	+	2.27937i	0.0591097	+	0.0724431i
$991$	9.76830			0.310300			0.155150	−	0.987891i	$-0.450414\pi$
$991$	9.76830			0.310300			0.155150	+	0.987891i	$0.450414\pi$
$992$	−28.7204			−0.911875
$993$	−47.4744	−	22.5361i	−1.50656	−	0.715162i
$994$		0			0
$995$		−	14.1268i		−	0.447848i
$996$	−6.11678	−	2.90364i	−0.193818	−	0.0920053i
$997$		−	35.1740i		−	1.11397i	−0.830522	−	0.556986i	$-0.811958\pi$
$997$		−	35.1740i		−	1.11397i	0.830522	−	0.556986i	$-0.188042\pi$
$998$			14.1313i			0.447317i
$999$	−4.40856	−	17.9229i	−0.139481	−	0.567056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.b.c.146.4		8
3.2	odd	2		735.2.b.d.146.5		8
7.2	even	3		735.2.s.k.521.3		8
7.3	odd	6		735.2.s.l.656.2		8
7.4	even	3		105.2.s.d.26.2	yes	8
7.5	odd	6		105.2.s.c.101.3	yes	8
7.6	odd	2		735.2.b.d.146.4		8
21.2	odd	6		735.2.s.l.521.2		8
21.5	even	6		105.2.s.d.101.2	yes	8
21.11	odd	6		105.2.s.c.26.3	✓	8
21.17	even	6		735.2.s.k.656.3		8
21.20	even	2	inner	735.2.b.c.146.5		8
35.4	even	6		525.2.t.f.26.3		8
35.12	even	12		525.2.q.f.374.4		16
35.18	odd	12		525.2.q.e.299.5		16
35.19	odd	6		525.2.t.g.101.2		8
35.32	odd	12		525.2.q.e.299.4		16
35.33	even	12		525.2.q.f.374.5		16
105.32	even	12		525.2.q.f.299.5		16
105.47	odd	12		525.2.q.e.374.5		16
105.53	even	12		525.2.q.f.299.4		16
105.68	odd	12		525.2.q.e.374.4		16
105.74	odd	6		525.2.t.g.26.2		8
105.89	even	6		525.2.t.f.101.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.c.26.3	✓	8	21.11	odd	6
105.2.s.c.101.3	yes	8	7.5	odd	6
105.2.s.d.26.2	yes	8	7.4	even	3
105.2.s.d.101.2	yes	8	21.5	even	6
525.2.q.e.299.4		16	35.32	odd	12
525.2.q.e.299.5		16	35.18	odd	12
525.2.q.e.374.4		16	105.68	odd	12
525.2.q.e.374.5		16	105.47	odd	12
525.2.q.f.299.4		16	105.53	even	12
525.2.q.f.299.5		16	105.32	even	12
525.2.q.f.374.4		16	35.12	even	12
525.2.q.f.374.5		16	35.33	even	12
525.2.t.f.26.3		8	35.4	even	6
525.2.t.f.101.3		8	105.89	even	6
525.2.t.g.26.2		8	105.74	odd	6
525.2.t.g.101.2		8	35.19	odd	6
735.2.b.c.146.4		8	1.1	even	1	trivial
735.2.b.c.146.5		8	21.20	even	2	inner
735.2.b.d.146.4		8	7.6	odd	2
735.2.b.d.146.5		8	3.2	odd	2
735.2.s.k.521.3		8	7.2	even	3
735.2.s.k.656.3		8	21.17	even	6
735.2.s.l.521.2		8	21.2	odd	6
735.2.s.l.656.2		8	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.385731i q^{2} +(1.56470 + 0.742765i) q^{3} +1.85121 q^{4} +1.00000 q^{5} +(0.286507 - 0.603555i) q^{6} -1.48553i q^{8} +(1.89660 + 2.32442i) q^{9} +O(q^{10})\)	\(q-0.385731i q^{2} +(1.56470 + 0.742765i) q^{3} +1.85121 q^{4} +1.00000 q^{5} +(0.286507 - 0.603555i) q^{6} -1.48553i q^{8} +(1.89660 + 2.32442i) q^{9} -0.385731i q^{10} +2.54224i q^{11} +(2.89660 + 1.37502i) q^{12} +3.06718i q^{13} +(1.56470 + 0.742765i) q^{15} +3.12941 q^{16} -6.46130 q^{17} +(0.896599 - 0.731577i) q^{18} +1.19592i q^{19} +1.85121 q^{20} +0.980620 q^{22} -3.05599i q^{23} +(1.10340 - 2.32442i) q^{24} +1.00000 q^{25} +1.18311 q^{26} +(1.24112 + 5.04575i) q^{27} -7.77029i q^{29} +(0.286507 - 0.603555i) q^{30} -6.87392i q^{31} -4.17817i q^{32} +(-1.88829 + 3.97785i) q^{33} +2.49232i q^{34} +(3.51101 + 4.30299i) q^{36} -3.55208 q^{37} +0.461303 q^{38} +(-2.27820 + 4.79923i) q^{39} -1.48553i q^{40} -2.31252 q^{41} +5.46130 q^{43} +4.70623i q^{44} +(1.89660 + 2.32442i) q^{45} -1.17879 q^{46} -3.22018 q^{47} +(4.89660 + 2.32442i) q^{48} -0.385731i q^{50} +(-10.1100 - 4.79923i) q^{51} +5.67800i q^{52} -13.2548i q^{53} +(1.94630 - 0.478738i) q^{54} +2.54224i q^{55} +(-0.888288 + 1.87126i) q^{57} -2.99724 q^{58} -3.96292 q^{59} +(2.89660 + 1.37502i) q^{60} +9.34076i q^{61} -2.65148 q^{62} +4.64717 q^{64} +3.06718i q^{65} +(1.53438 + 0.728371i) q^{66} -3.51932 q^{67} -11.9612 q^{68} +(2.26989 - 4.78173i) q^{69} -0.921861i q^{71} +(3.45299 - 2.81746i) q^{72} +0.296437i q^{73} +1.37015i q^{74} +(1.56470 + 0.742765i) q^{75} +2.21390i q^{76} +(1.85121 + 0.878771i) q^{78} +8.29482 q^{79} +3.12941 q^{80} +(-1.80582 + 8.81697i) q^{81} +0.892008i q^{82} -2.11171 q^{83} -6.46130 q^{85} -2.10659i q^{86} +(5.77151 - 12.1582i) q^{87} +3.77658 q^{88} +18.8301 q^{89} +(0.896599 - 0.731577i) q^{90} -5.65729i q^{92} +(5.10571 - 10.7557i) q^{93} +1.24212i q^{94} +1.19592i q^{95} +(3.10340 - 6.53760i) q^{96} -12.3692i q^{97} +(-5.90923 + 4.82161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{3} - 6 q^{4} + 8 q^{5} - 5 q^{6} + q^{9}+O(q^{10}) \) 8 * q - q^3 - 6 * q^4 + 8 * q^5 - 5 * q^6 + q^9	\( 8 q - q^{3} - 6 q^{4} + 8 q^{5} - 5 q^{6} + q^{9} + 9 q^{12} - q^{15} - 2 q^{16} - 24 q^{17} - 7 q^{18} - 6 q^{20} - 40 q^{22} + 23 q^{24} + 8 q^{25} - 12 q^{26} - 4 q^{27} - 5 q^{30} - 2 q^{33} + 9 q^{36} - 14 q^{37} - 24 q^{38} - 12 q^{39} + 30 q^{41} + 16 q^{43} + q^{45} + 14 q^{46} - 12 q^{47} + 25 q^{48} - 6 q^{51} + 10 q^{54} + 6 q^{57} + 26 q^{58} - 24 q^{59} + 9 q^{60} - 24 q^{62} + 38 q^{64} + 38 q^{66} - 8 q^{67} + 13 q^{69} + q^{72} - q^{75} - 6 q^{78} + 58 q^{79} - 2 q^{80} + 13 q^{81} - 30 q^{83} - 24 q^{85} + 61 q^{87} + 4 q^{88} - 6 q^{89} - 7 q^{90} - 36 q^{93} + 39 q^{96} - 34 q^{99}+O(q^{100}) \) 8 * q - q^3 - 6 * q^4 + 8 * q^5 - 5 * q^6 + q^9 + 9 * q^12 - q^15 - 2 * q^16 - 24 * q^17 - 7 * q^18 - 6 * q^20 - 40 * q^22 + 23 * q^24 + 8 * q^25 - 12 * q^26 - 4 * q^27 - 5 * q^30 - 2 * q^33 + 9 * q^36 - 14 * q^37 - 24 * q^38 - 12 * q^39 + 30 * q^41 + 16 * q^43 + q^45 + 14 * q^46 - 12 * q^47 + 25 * q^48 - 6 * q^51 + 10 * q^54 + 6 * q^57 + 26 * q^58 - 24 * q^59 + 9 * q^60 - 24 * q^62 + 38 * q^64 + 38 * q^66 - 8 * q^67 + 13 * q^69 + q^72 - q^75 - 6 * q^78 + 58 * q^79 - 2 * q^80 + 13 * q^81 - 30 * q^83 - 24 * q^85 + 61 * q^87 + 4 * q^88 - 6 * q^89 - 7 * q^90 - 36 * q^93 + 39 * q^96 - 34 * q^99

Introduction

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