LMFDB - Embedded newform 735.2.g.c.734.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(734,735)]

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, 1, 1]))

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

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

chi := DirichletCharacter("735.734");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.g (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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			734.18
Character	$\chi$	$=$	735.734
Dual form			735.2.g.c.734.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.346467 q^{2} +(-1.43364 + 0.971945i) q^{3} -1.87996 q^{4} +(-1.85945 - 1.24195i) q^{5} +(-0.496709 + 0.336746i) q^{6} -1.34428 q^{8} +(1.11065 - 2.78684i) q^{9} +O(q^{10})$	\(q+0.346467 q^{2} +(-1.43364 + 0.971945i) q^{3} -1.87996 q^{4} +(-1.85945 - 1.24195i) q^{5} +(-0.496709 + 0.336746i) q^{6} -1.34428 q^{8} +(1.11065 - 2.78684i) q^{9} +(-0.644238 - 0.430294i) q^{10} +0.537633i q^{11} +(2.69519 - 1.82722i) q^{12} -3.81157 q^{13} +(3.87289 - 0.0267743i) q^{15} +3.29417 q^{16} +3.87812i q^{17} +(0.384802 - 0.965546i) q^{18} -3.11725i q^{19} +(3.49570 + 2.33482i) q^{20} +0.186272i q^{22} +7.75033 q^{23} +(1.92721 - 1.30656i) q^{24} +(1.91512 + 4.61869i) q^{25} -1.32058 q^{26} +(1.11638 + 5.07481i) q^{27} -8.42000i q^{29} +(1.34183 - 0.00927642i) q^{30} +3.02203i q^{31} +3.82988 q^{32} +(-0.522550 - 0.770773i) q^{33} +1.34364i q^{34} +(-2.08797 + 5.23915i) q^{36} +10.4098i q^{37} -1.08002i q^{38} +(5.46442 - 3.70464i) q^{39} +(2.49962 + 1.66953i) q^{40} +8.56674 q^{41} +4.12561i q^{43} -1.01073i q^{44} +(-5.52631 + 3.80262i) q^{45} +2.68523 q^{46} -0.416507i q^{47} +(-4.72266 + 3.20176i) q^{48} +(0.663525 + 1.60022i) q^{50} +(-3.76931 - 5.55982i) q^{51} +7.16560 q^{52} +4.28477 q^{53} +(0.386790 + 1.75825i) q^{54} +(0.667714 - 0.999703i) q^{55} +(3.02979 + 4.46901i) q^{57} -2.91725i q^{58} +10.2988 q^{59} +(-7.28088 + 0.0503347i) q^{60} +0.282318i q^{61} +1.04703i q^{62} -5.26142 q^{64} +(7.08743 + 4.73378i) q^{65} +(-0.181046 - 0.267047i) q^{66} -9.68708i q^{67} -7.29071i q^{68} +(-11.1112 + 7.53289i) q^{69} -1.01073i q^{71} +(-1.49302 + 3.74628i) q^{72} -6.67885 q^{73} +3.60665i q^{74} +(-7.23470 - 4.76015i) q^{75} +5.86030i q^{76} +(1.89324 - 1.28353i) q^{78} -3.87815 q^{79} +(-6.12536 - 4.09120i) q^{80} +(-6.53292 - 6.19039i) q^{81} +2.96809 q^{82} -10.8216i q^{83} +(4.81643 - 7.21117i) q^{85} +1.42939i q^{86} +(8.18377 + 12.0712i) q^{87} -0.722728i q^{88} +6.16842 q^{89} +(-1.91468 + 1.31748i) q^{90} -14.5703 q^{92} +(-2.93724 - 4.33250i) q^{93} -0.144306i q^{94} +(-3.87147 + 5.79637i) q^{95} +(-5.49066 + 3.72243i) q^{96} +8.00908 q^{97} +(1.49830 + 0.597121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 40 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 40 * q^9	$ 32 q + 16 q^{4} + 40 q^{9} + 16 q^{15} - 16 q^{16} + 64 q^{25} + 56 q^{30} - 16 q^{36} - 56 q^{39} - 32 q^{46} - 40 q^{51} + 8 q^{60} - 176 q^{64} + 48 q^{79} - 40 q^{81} - 64 q^{85} + 40 q^{99}+O(q^{100}) $ 32 * q + 16 * q^4 + 40 * q^9 + 16 * q^15 - 16 * q^16 + 64 * q^25 + 56 * q^30 - 16 * q^36 - 56 * q^39 - 32 * q^46 - 40 * q^51 + 8 * q^60 - 176 * q^64 + 48 * q^79 - 40 * q^81 - 64 * q^85 + 40 * 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 $

$2$	0.346467			0.244989			0.122494	−	0.992469i	$-0.460911\pi$
$2$	0.346467			0.244989			0.122494	+	0.992469i	$0.460911\pi$
$3$	−1.43364	+	0.971945i	−0.827712	+	0.561152i
$3$	−1.43364	+	0.971945i	−0.827712	+	0.561152i
$4$	−1.87996			−0.939980
$5$	−1.85945	−	1.24195i	−0.831572	−	0.555417i
$5$	−1.85945	−	1.24195i	−0.831572	−	0.555417i
$6$	−0.496709	+	0.336746i	−0.202780	+	0.137476i
$7$		0			0
$7$		0			0
$8$	−1.34428			−0.475274
$9$	1.11065	−	2.78684i	0.370216	−	0.928946i
$10$	−0.644238	−	0.430294i	−0.203726	−	0.136071i
$11$			0.537633i			0.162103i	0.996710	+	0.0810513i	$0.0258278\pi$
$11$			0.537633i			0.162103i	−0.996710	+	0.0810513i	$0.974172\pi$
$12$	2.69519	−	1.82722i	0.778033	−	0.527472i
$13$	−3.81157			−1.05714			−0.528570	−	0.848890i	$-0.677271\pi$
$13$	−3.81157			−1.05714			−0.528570	+	0.848890i	$0.677271\pi$
$14$		0			0
$15$	3.87289	−	0.0267743i	0.999976	−	0.00691311i
$16$	3.29417			0.823544
$17$			3.87812i			0.940581i	0.882512	+	0.470291i	$0.155851\pi$
$17$			3.87812i			0.940581i	−0.882512	+	0.470291i	$0.844149\pi$
$18$	0.384802	−	0.965546i	0.0906988	−	0.227581i
$19$		−	3.11725i		−	0.715146i	−0.933885	−	0.357573i	$-0.883604\pi$
$19$		−	3.11725i		−	0.715146i	0.933885	−	0.357573i	$-0.116396\pi$
$20$	3.49570	+	2.33482i	0.781661	+	0.522081i
$21$		0			0
$22$			0.186272i			0.0397133i
$23$	7.75033			1.61605			0.808027	−	0.589145i	$-0.200535\pi$
$23$	7.75033			1.61605			0.808027	+	0.589145i	$0.200535\pi$
$24$	1.92721	−	1.30656i	0.393390	−	0.266701i
$25$	1.91512	+	4.61869i	0.383024	+	0.923738i
$26$	−1.32058			−0.258987
$27$	1.11638	+	5.07481i	0.214848	+	0.976647i
$28$		0			0
$29$		−	8.42000i		−	1.56355i	−0.623558	−	0.781777i	$-0.714313\pi$
$29$		−	8.42000i		−	1.56355i	0.623558	−	0.781777i	$-0.285687\pi$
$30$	1.34183	−	0.00927642i	0.244983	−	0.00169363i
$31$			3.02203i			0.542772i	0.962471	+	0.271386i	$0.0874820\pi$
$31$			3.02203i			0.542772i	−0.962471	+	0.271386i	$0.912518\pi$
$32$	3.82988			0.677033
$33$	−0.522550	−	0.770773i	−0.0909643	−	0.134174i
$34$			1.34364i			0.230432i
$35$		0			0
$36$	−2.08797	+	5.23915i	−0.347996	+	0.873191i
$37$			10.4098i			1.71136i	0.517503	+	0.855681i	$0.326862\pi$
$37$			10.4098i			1.71136i	−0.517503	+	0.855681i	$0.673138\pi$
$38$		−	1.08002i		−	0.175203i
$39$	5.46442	−	3.70464i	0.875007	−	0.593216i
$40$	2.49962	+	1.66953i	0.395224	+	0.263975i
$41$	8.56674			1.33790			0.668950	−	0.743307i	$-0.266744\pi$
$41$	8.56674			1.33790			0.668950	+	0.743307i	$0.266744\pi$
$42$		0			0
$43$			4.12561i			0.629150i	0.949233	+	0.314575i	$0.101862\pi$
$43$			4.12561i			0.629150i	−0.949233	+	0.314575i	$0.898138\pi$
$44$		−	1.01073i		−	0.152373i
$45$	−5.52631	+	3.80262i	−0.823813	+	0.566861i
$46$	2.68523			0.395916
$47$		−	0.416507i		−	0.0607538i	−0.999539	−	0.0303769i	$-0.990329\pi$
$47$		−	0.416507i		−	0.0607538i	0.999539	−	0.0303769i	$-0.00967075\pi$
$48$	−4.72266	+	3.20176i	−0.681657	+	0.462134i
$49$		0			0
$50$	0.663525	+	1.60022i	0.0938366	+	0.226306i
$51$	−3.76931	−	5.55982i	−0.527809	−	0.778531i
$52$	7.16560			0.993690
$53$	4.28477			0.588559			0.294279	−	0.955719i	$-0.404920\pi$
$53$	4.28477			0.588559			0.294279	+	0.955719i	$0.404920\pi$
$54$	0.386790	+	1.75825i	0.0526354	+	0.239268i
$55$	0.667714	−	0.999703i	0.0900345	−	0.134800i
$56$		0			0
$57$	3.02979	+	4.46901i	0.401306	+	0.591935i
$58$		−	2.91725i		−	0.383054i
$59$	10.2988			1.34079			0.670395	−	0.742004i	$-0.266125\pi$
$59$	10.2988			1.34079			0.670395	+	0.742004i	$0.266125\pi$
$60$	−7.28088	+	0.0503347i	−0.939958	+	0.00649819i
$61$			0.282318i			0.0361471i	0.999837	+	0.0180735i	$0.00575330\pi$
$61$			0.282318i			0.0361471i	−0.999837	+	0.0180735i	$0.994247\pi$
$62$			1.04703i			0.132973i
$63$		0			0
$64$	−5.26142			−0.657678
$65$	7.08743	+	4.73378i	0.879087	+	0.587153i
$66$	−0.181046	−	0.267047i	−0.0222852	−	0.0328712i
$67$		−	9.68708i		−	1.18347i	−0.806134	−	0.591733i	$-0.798444\pi$
$67$		−	9.68708i		−	1.18347i	0.806134	−	0.591733i	$-0.201556\pi$
$68$		−	7.29071i		−	0.884128i
$69$	−11.1112	+	7.53289i	−1.33763	+	0.906853i
$70$		0			0
$71$		−	1.01073i		−	0.119952i	−0.998200	−	0.0599758i	$-0.980898\pi$
$71$		−	1.01073i		−	0.119952i	0.998200	−	0.0599758i	$-0.0191023\pi$
$72$	−1.49302	+	3.74628i	−0.175954	+	0.441504i
$73$	−6.67885			−0.781700			−0.390850	−	0.920454i	$-0.627819\pi$
$73$	−6.67885			−0.781700			−0.390850	+	0.920454i	$0.627819\pi$
$74$			3.60665i			0.419265i
$75$	−7.23470	−	4.76015i	−0.835392	−	0.549655i
$76$			5.86030i			0.672223i
$77$		0			0
$78$	1.89324	−	1.28353i	0.214367	−	0.145331i
$79$	−3.87815			−0.436326			−0.218163	−	0.975912i	$-0.570006\pi$
$79$	−3.87815			−0.436326			−0.218163	+	0.975912i	$0.570006\pi$
$80$	−6.12536	−	4.09120i	−0.684836	−	0.457410i
$81$	−6.53292	−	6.19039i	−0.725881	−	0.687821i
$82$	2.96809			0.327771
$83$		−	10.8216i		−	1.18783i	−0.804528	−	0.593914i	$-0.797582\pi$
$83$		−	10.8216i		−	1.18783i	0.804528	−	0.593914i	$-0.202418\pi$
$84$		0			0
$85$	4.81643	−	7.21117i	0.522415	−	0.782161i
$86$			1.42939i			0.154135i
$87$	8.18377	+	12.0712i	0.877393	+	1.29417i
$88$		−	0.722728i		−	0.0770431i
$89$	6.16842			0.653851			0.326926	−	0.945050i	$-0.393987\pi$
$89$	6.16842			0.653851			0.326926	+	0.945050i	$0.393987\pi$
$90$	−1.91468	+	1.31748i	−0.201825	+	0.138875i
$91$		0			0
$92$	−14.5703			−1.51906
$93$	−2.93724	−	4.33250i	−0.304578	−	0.449259i
$94$		−	0.144306i		−	0.0148840i
$95$	−3.87147	+	5.79637i	−0.397204	+	0.594695i
$96$	−5.49066	+	3.72243i	−0.560389	+	0.379919i
$97$	8.00908			0.813199			0.406600	−	0.913606i	$-0.366714\pi$
$97$	8.00908			0.813199			0.406600	+	0.913606i	$0.366714\pi$
$98$		0			0
$99$	1.49830	+	0.597121i	0.150585	+	0.0600129i
$100$	−3.60035	−	8.68296i	−0.360035	−	0.868296i
$101$	−0.135516			−0.0134844			−0.00674218	−	0.999977i	$-0.502146\pi$
$101$	−0.135516			−0.0134844			−0.00674218	+	0.999977i	$0.502146\pi$
$102$	−1.30594	−	1.92629i	−0.129307	−	0.190731i
$103$	1.18767			0.117024			0.0585121	−	0.998287i	$-0.481364\pi$
$103$	1.18767			0.117024			0.0585121	+	0.998287i	$0.481364\pi$
$104$	5.12381			0.502431
$105$		0			0
$106$	1.48453			0.144190
$107$	−13.1487			−1.27114			−0.635568	−	0.772045i	$-0.719234\pi$
$107$	−13.1487			−1.27114			−0.635568	+	0.772045i	$0.719234\pi$
$108$	−2.09876	−	9.54044i	−0.201953	−	0.918030i
$109$	−8.71276			−0.834531			−0.417266	−	0.908785i	$-0.637012\pi$
$109$	−8.71276			−0.834531			−0.417266	+	0.908785i	$0.637012\pi$
$110$	0.231341	−	0.346364i	0.0220575	−	0.0330245i
$111$	−10.1178	−	14.9239i	−0.960335	−	1.41652i
$112$		0			0
$113$	5.82398			0.547874			0.273937	−	0.961748i	$-0.411674\pi$
$113$	5.82398			0.547874			0.273937	+	0.961748i	$0.411674\pi$
$114$	1.04972	+	1.54836i	0.0983155	+	0.145017i
$115$	−14.4114	−	9.62552i	−1.34387	−	0.897584i
$116$			15.8293i			1.46971i
$117$	−4.23331	+	10.6222i	−0.391370	+	0.982025i
$118$	3.56819			0.328479
$119$		0			0
$120$	−5.20624	+	0.0359921i	−0.475262	+	0.00328562i
$121$	10.7110			0.973723
$122$			0.0978137i			0.00885564i
$123$	−12.2816	+	8.32640i	−1.10740	+	0.750766i
$124$		−	5.68129i		−	0.510195i
$125$	2.17511	−	10.9667i	0.194548	−	0.980893i
$126$		0			0
$127$			14.2361i			1.26325i	0.775276	+	0.631623i	$0.217611\pi$
$127$			14.2361i			1.26325i	−0.775276	+	0.631623i	$0.782389\pi$
$128$	−9.48266			−0.838157
$129$	−4.00987	−	5.91464i	−0.353049	−	0.520755i
$130$	2.45556	+	1.64010i	0.215367	+	0.143846i
$131$	16.9630			1.48207			0.741034	−	0.671468i	$-0.234336\pi$
$131$	16.9630			1.48207			0.741034	+	0.671468i	$0.234336\pi$
$132$	0.982373	+	1.44902i	0.0855046	+	0.126121i
$133$		0			0
$134$		−	3.35625i		−	0.289936i
$135$	4.22680	−	10.8229i	0.363785	−	0.931483i
$136$		−	5.21326i		−	0.447034i
$137$	12.4558			1.06417			0.532085	−	0.846691i	$-0.321408\pi$
$137$	12.4558			1.06417			0.532085	+	0.846691i	$0.321408\pi$
$138$	−3.84965	+	2.60989i	−0.327704	+	0.222169i
$139$		−	19.0259i		−	1.61375i	−0.590719	−	0.806877i	$-0.701156\pi$
$139$		−	19.0259i		−	1.61375i	0.590719	−	0.806877i	$-0.298844\pi$
$140$		0			0
$141$	0.404822	+	0.597121i	0.0340921	+	0.0502867i
$142$		−	0.350184i		−	0.0293868i
$143$		−	2.04923i		−	0.171365i
$144$	3.65867	−	9.18033i	0.304889	−	0.765027i
$145$	−10.4572	+	15.6566i	−0.868425	+	1.30021i
$146$	−2.31400			−0.191508
$147$		0			0
$148$		−	19.5700i		−	1.60865i
$149$			10.8324i			0.887426i	0.896169	+	0.443713i	$0.146339\pi$
$149$			10.8324i			0.887426i	−0.896169	+	0.443713i	$0.853661\pi$
$150$	−2.50658	−	1.64923i	−0.204662	−	0.134659i
$151$	3.19548			0.260045			0.130022	−	0.991511i	$-0.458495\pi$
$151$	3.19548			0.260045			0.130022	+	0.991511i	$0.458495\pi$
$152$			4.19044i			0.339890i
$153$	10.8077	+	4.30722i	0.873749	+	0.348218i
$154$		0			0
$155$	3.75320	−	5.61931i	0.301465	−	0.451354i
$156$	−10.2729	+	6.96457i	−0.822490	+	0.557612i
$157$	24.0915			1.92271			0.961355	−	0.275310i	$-0.0887806\pi$
$157$	24.0915			1.92271			0.961355	+	0.275310i	$0.0887806\pi$
$158$	−1.34365			−0.106895
$159$	−6.14282	+	4.16456i	−0.487157	+	0.330271i
$160$	−7.12147	−	4.75652i	−0.563002	−	0.376036i
$161$		0			0
$162$	−2.26344	−	2.14476i	−0.177833	−	0.168508i
$163$		−	11.0817i		−	0.867987i	−0.900916	−	0.433994i	$-0.857104\pi$
$163$		−	11.0817i		−	0.867987i	0.900916	−	0.433994i	$-0.142896\pi$
$164$	−16.1051			−1.25760
$165$	0.0143948	+	2.08220i	0.00112063	+	0.162099i
$166$		−	3.74934i		−	0.291005i
$167$		−	12.2802i		−	0.950270i	−0.879913	−	0.475135i	$-0.842399\pi$
$167$		−	12.2802i		−	0.950270i	0.879913	−	0.475135i	$-0.157601\pi$
$168$		0			0
$169$	1.52807			0.117544
$170$	1.66873	−	2.49843i	0.127986	−	0.191621i
$171$	−8.68726	−	3.46216i	−0.664331	−	0.264758i
$172$		−	7.75599i		−	0.591389i
$173$			20.2486i			1.53947i	0.638363	+	0.769735i	$0.279612\pi$
$173$			20.2486i			1.53947i	−0.638363	+	0.769735i	$0.720388\pi$
$174$	2.83540	+	4.18229i	0.214951	+	0.317058i
$175$		0			0
$176$			1.77106i			0.133499i
$177$	−14.7648	+	10.0099i	−1.10979	+	0.752388i
$178$	2.13715			0.160186
$179$			6.46543i			0.483249i	0.970370	+	0.241624i	$0.0776802\pi$
$179$			6.46543i			0.483249i	−0.970370	+	0.241624i	$0.922320\pi$
$180$	10.3892	−	7.14878i	0.774368	−	0.532838i
$181$			16.5297i			1.22864i	0.789056	+	0.614322i	$0.210570\pi$
$181$			16.5297i			1.22864i	−0.789056	+	0.614322i	$0.789430\pi$
$182$		0			0
$183$	−0.274397	−	0.404742i	−0.0202840	−	0.0299194i
$184$	−10.4186			−0.768068
$185$	12.9285	−	19.3565i	0.950520	−	1.42312i
$186$	−1.01766	−	1.50107i	−0.0746182	−	0.110063i
$187$	−2.08500			−0.152471
$188$			0.783017i			0.0571074i
$189$		0			0
$190$	−1.34133	+	2.00825i	−0.0973106	+	0.145694i
$191$			10.2556i			0.742069i	0.928619	+	0.371034i	$0.120997\pi$
$191$			10.2556i			0.742069i	−0.928619	+	0.371034i	$0.879003\pi$
$192$	7.54299	−	5.11381i	0.544368	−	0.369058i
$193$			16.4306i			1.18270i	0.806415	+	0.591350i	$0.201405\pi$
$193$			16.4306i			1.18270i	−0.806415	+	0.591350i	$0.798595\pi$
$194$	2.77488			0.199225
$195$	−14.7618	+	0.102052i	−1.05711	+	0.00730812i
$196$		0			0
$197$	−0.0212992			−0.00151751			−0.000758753	−	1.00000i	$-0.500242\pi$
$197$	−0.0212992			−0.00151751			−0.000758753		1.00000i	$0.500242\pi$
$198$	0.519110	+	0.206883i	0.0368915	+	0.0147025i
$199$			11.1307i			0.789037i	0.918888	+	0.394518i	$0.129089\pi$
$199$			11.1307i			0.789037i	−0.918888	+	0.394518i	$0.870911\pi$
$200$	−2.57445	−	6.20880i	−0.182041	−	0.439029i
$201$	9.41531	+	13.8878i	0.664105	+	0.979569i
$202$	−0.0469519			−0.00330352
$203$		0			0
$204$	7.08616	+	10.4522i	0.496131	+	0.731804i
$205$	−15.9294	−	10.6395i	−1.11256	−	0.743092i
$206$	0.411487			0.0286696
$207$	8.60788	−	21.5989i	0.598289	−	1.50123i
$208$	−12.5560			−0.870600
$209$	1.67594			0.115927
$210$		0			0
$211$	−4.75289			−0.327203			−0.163601	−	0.986527i	$-0.552311\pi$
$211$	−4.75289			−0.327203			−0.163601	+	0.986527i	$0.552311\pi$
$212$	−8.05520			−0.553234
$213$	0.982373	+	1.44902i	0.0673111	+	0.0992854i
$214$	−4.55560			−0.311414
$215$	5.12381	−	7.67138i	0.349441	−	0.523184i
$216$	−1.50073	−	6.82195i	−0.102112	−	0.464175i
$217$		0			0
$218$	−3.01868			−0.204451
$219$	9.57507	−	6.49147i	0.647023	−	0.438653i
$220$	−1.25528	+	1.87940i	−0.0846307	+	0.126709i
$221$		−	14.7817i		−	0.994325i
$222$	−3.50547	−	5.17064i	−0.235272	−	0.347031i
$223$	9.93727			0.665449			0.332724	−	0.943024i	$-0.392032\pi$
$223$	9.93727			0.665449			0.332724	+	0.943024i	$0.392032\pi$
$224$		0			0
$225$	14.9986	−	0.207388i	0.999904	−	0.0138259i
$226$	2.01782			0.134223
$227$			14.2069i			0.942945i	0.881881	+	0.471472i	$0.156277\pi$
$227$			14.2069i			0.942945i	−0.881881	+	0.471472i	$0.843723\pi$
$228$	−5.69589	−	8.40156i	−0.377219	−	0.556407i
$229$			15.6032i			1.03109i	0.856863	+	0.515545i	$0.172410\pi$
$229$			15.6032i			1.03109i	−0.856863	+	0.515545i	$0.827590\pi$
$230$	−4.99306	−	3.33492i	−0.329232	−	0.219898i
$231$		0			0
$232$			11.3188i			0.743117i
$233$	10.6492			0.697654			0.348827	−	0.937187i	$-0.386580\pi$
$233$	10.6492			0.697654			0.348827	+	0.937187i	$0.386580\pi$
$234$	−1.46670	+	3.68025i	−0.0958812	+	0.240585i
$235$	−0.517281	+	0.774475i	−0.0337437	+	0.0505212i
$236$	−19.3614			−1.26032
$237$	5.55987	−	3.76935i	0.361152	−	0.244845i
$238$		0			0
$239$			24.4443i			1.58117i	0.612354	+	0.790584i	$0.290223\pi$
$239$			24.4443i			1.58117i	−0.612354	+	0.790584i	$0.709777\pi$
$240$	12.7580	−	0.0881994i	0.823524	−	0.00569325i
$241$			18.8802i			1.21618i	0.793868	+	0.608090i	$0.208064\pi$
$241$			18.8802i			1.21618i	−0.793868	+	0.608090i	$0.791936\pi$
$242$	3.71099			0.238551
$243$	15.3826	+	2.52515i	0.986793	+	0.161988i
$244$		−	0.530746i		−	0.0339776i
$245$		0			0
$246$	−4.25517	+	2.88482i	−0.271300	+	0.183929i
$247$			11.8816i			0.756008i
$248$		−	4.06244i		−	0.257965i
$249$	10.5180	+	15.5143i	0.666553	+	0.983181i
$250$	0.753604	−	3.79960i	0.0476621	−	0.240308i
$251$	−3.44293			−0.217316			−0.108658	−	0.994079i	$-0.534655\pi$
$251$	−3.44293			−0.217316			−0.108658	+	0.994079i	$0.534655\pi$
$252$		0			0
$253$			4.16683i			0.261967i
$254$			4.93232i			0.309481i
$255$	0.103834	+	15.0195i	0.00650234	+	0.940559i
$256$	7.23742			0.452339
$257$		−	3.78360i		−	0.236014i	−0.993013	−	0.118007i	$-0.962349\pi$
$257$		−	3.78360i		−	0.236014i	0.993013	−	0.118007i	$-0.0376506\pi$
$258$	−1.38929	−	2.04923i	−0.0864932	−	0.127579i
$259$		0			0
$260$	−13.3241	−	8.89932i	−0.826325	−	0.551912i
$261$	−23.4652	−	9.35165i	−1.45246	−	0.578853i
$262$	5.87713			0.363090
$263$	−25.7348			−1.58687			−0.793437	−	0.608652i	$-0.791710\pi$
$263$	−25.7348			−1.58687			−0.793437	+	0.608652i	$0.791710\pi$
$264$	0.702452	+	1.03613i	0.0432329	+	0.0637695i
$265$	−7.96733	−	5.32147i	−0.489429	−	0.326896i
$266$		0			0
$267$	−8.84329	+	5.99536i	−0.541201	+	0.366910i
$268$			18.2113i			1.11243i
$269$	−7.35348			−0.448350			−0.224175	−	0.974549i	$-0.571969\pi$
$269$	−7.35348			−0.448350			−0.224175	+	0.974549i	$0.571969\pi$
$270$	1.46445	−	3.74976i	0.0891233	−	0.228203i
$271$		−	24.2868i		−	1.47532i	−0.675172	−	0.737660i	$-0.735931\pi$
$271$		−	24.2868i		−	1.47532i	0.675172	−	0.737660i	$-0.264069\pi$
$272$			12.7752i			0.774610i
$273$		0			0
$274$	4.31552			0.260710
$275$	−2.48316	+	1.02963i	−0.149740	+	0.0620892i
$276$	20.8886	−	14.1615i	1.25734	−	0.852424i
$277$		−	6.05671i		−	0.363912i	−0.983307	−	0.181956i	$-0.941757\pi$
$277$		−	6.05671i		−	0.363912i	0.983307	−	0.181956i	$-0.0582429\pi$
$278$		−	6.59184i		−	0.395352i
$279$	8.42189	+	3.35640i	0.504206	+	0.200943i
$280$		0			0
$281$		−	18.8983i		−	1.12738i	−0.825987	−	0.563689i	$-0.809382\pi$
$281$		−	18.8983i		−	1.12738i	0.825987	−	0.563689i	$-0.190618\pi$
$282$	0.140257	+	0.206883i	0.00835220	+	0.0123197i
$283$	−8.25765			−0.490867			−0.245433	−	0.969413i	$-0.578930\pi$
$283$	−8.25765			−0.490867			−0.245433	+	0.969413i	$0.578930\pi$
$284$			1.90013i			0.112752i
$285$	−0.0834623	−	12.0728i	−0.00494388	−	0.715128i
$286$		−	0.709989i		−	0.0419825i
$287$		0			0
$288$	4.25364	−	10.6732i	0.250648	−	0.628927i
$289$	1.96022			0.115307
$290$	−3.62308	+	5.42448i	−0.212754	+	0.318537i
$291$	−11.4821	+	7.78438i	−0.673095	+	0.456329i
$292$	12.5560			0.734783
$293$			5.23650i			0.305919i	0.988232	+	0.152960i	$0.0488805\pi$
$293$			5.23650i			0.305919i	−0.988232	+	0.152960i	$0.951120\pi$
$294$		0			0
$295$	−19.1501	−	12.7906i	−1.11496	−	0.744698i
$296$		−	13.9937i		−	0.813366i
$297$	−2.72839	+	0.600205i	−0.158317	+	0.0348274i
$298$			3.75307i			0.217409i
$299$	−29.5409			−1.70840
$300$	13.6010	+	8.94890i	0.785252	+	0.516665i
$301$		0			0
$302$	1.10713			0.0637080
$303$	0.194281	−	0.131714i	0.0111612	−	0.00756679i
$304$		−	10.2688i		−	0.588954i
$305$	0.350625	−	0.524956i	0.0200767	−	0.0300589i
$306$	3.74450	+	1.49231i	0.214059	+	0.0853096i
$307$	−1.12127			−0.0639940			−0.0319970	−	0.999488i	$-0.510187\pi$
$307$	−1.12127			−0.0639940			−0.0319970	+	0.999488i	$0.510187\pi$
$308$		0			0
$309$	−1.70269	+	1.15435i	−0.0968624	+	0.0656684i
$310$	1.30036	−	1.94690i	0.0738555	−	0.110577i
$311$	12.9682			0.735357			0.367678	−	0.929953i	$-0.380153\pi$
$311$	12.9682			0.735357			0.367678	+	0.929953i	$0.380153\pi$
$312$	−7.34569	+	4.98006i	−0.415868	+	0.281940i
$313$	13.7436			0.776837			0.388418	−	0.921483i	$-0.373022\pi$
$313$	13.7436			0.776837			0.388418	+	0.921483i	$0.373022\pi$
$314$	8.34690			0.471043
$315$		0			0
$316$	7.29077			0.410138
$317$	18.1591			1.01992			0.509958	−	0.860199i	$-0.329661\pi$
$317$	18.1591			1.01992			0.509958	+	0.860199i	$0.329661\pi$
$318$	−2.12828	+	1.44288i	−0.119348	+	0.0809128i
$319$	4.52687			0.253456
$320$	9.78336	+	6.53443i	0.546907	+	0.365286i
$321$	18.8506	−	12.7798i	1.05214	−	0.713301i
$322$		0			0
$323$	12.0890			0.672652
$324$	12.2816	+	11.6377i	0.682313	+	0.646538i
$325$	−7.29961	−	17.6045i	−0.404910	−	0.976520i
$326$		−	3.83945i		−	0.212647i
$327$	12.4910	−	8.46832i	0.690752	−	0.468299i
$328$	−11.5161			−0.635869
$329$		0			0
$330$	0.00498731	+	0.721411i	0.000274543	+	0.0397124i
$331$	30.9903			1.70338			0.851691	−	0.524045i	$-0.175577\pi$
$331$	30.9903			1.70338			0.851691	+	0.524045i	$0.175577\pi$
$332$			20.3443i			1.11654i
$333$	29.0105	+	11.5616i	1.58976	+	0.633574i
$334$		−	4.25468i		−	0.232806i
$335$	−12.0309	+	18.0127i	−0.657317	+	0.984137i
$336$		0			0
$337$		−	10.6732i		−	0.581409i	−0.956813	−	0.290704i	$-0.906110\pi$
$337$		−	10.6732i		−	0.581409i	0.956813	−	0.290704i	$-0.0938896\pi$
$338$	0.529424			0.0287969
$339$	−8.34949	+	5.66059i	−0.453482	+	0.307441i
$340$	−9.05469	+	13.5567i	−0.491060	+	0.735216i
$341$	−1.62474			−0.0879847
$342$	−3.00985	−	1.19952i	−0.162754	−	0.0648628i
$343$		0			0
$344$		−	5.54597i		−	0.299019i
$345$	30.0162	−	0.207510i	1.61602	−	0.0111720i
$346$			7.01546i			0.377153i
$347$	−2.33751			−0.125484			−0.0627420	−	0.998030i	$-0.519985\pi$
$347$	−2.33751			−0.125484			−0.0627420	+	0.998030i	$0.519985\pi$
$348$	−15.3852	−	22.6935i	−0.824732	−	1.21650i
$349$			4.60715i			0.246615i	0.992368	+	0.123308i	$0.0393502\pi$
$349$			4.60715i			0.246615i	−0.992368	+	0.123308i	$0.960650\pi$
$350$		0			0
$351$	−4.25517	−	19.3430i	−0.227124	−	1.03245i
$352$			2.05907i			0.109749i
$353$			6.00819i			0.319784i	0.987135	+	0.159892i	$0.0511146\pi$
$353$			6.00819i			0.319784i	−0.987135	+	0.159892i	$0.948885\pi$
$354$	−5.11551	+	3.46809i	−0.271886	+	0.184327i
$355$	−1.25528	+	1.87940i	−0.0666231	+	0.0997484i
$356$	−11.5964			−0.614607
$357$		0			0
$358$			2.24006i			0.118391i
$359$		−	19.5396i		−	1.03126i	−0.856810	−	0.515631i	$-0.827557\pi$
$359$		−	19.5396i		−	1.03126i	0.856810	−	0.515631i	$-0.172443\pi$
$360$	7.42889	−	5.11178i	0.391537	−	0.269414i
$361$	9.28277			0.488567
$362$			5.72699i			0.301004i
$363$	−15.3556	+	10.4105i	−0.805962	+	0.546407i
$364$		0			0
$365$	12.4190	+	8.29480i	0.650040	+	0.434170i
$366$	−0.0950695	−	0.140230i	−0.00496936	−	0.00732992i
$367$	−19.0384			−0.993797			−0.496898	−	0.867809i	$-0.665528\pi$
$367$	−19.0384			−0.993797			−0.496898	+	0.867809i	$0.665528\pi$
$368$	25.5309			1.33089
$369$	9.51463	−	23.8741i	0.495312	−	1.24284i
$370$	4.47928	−	6.70640i	0.232867	−	0.348649i
$371$		0			0
$372$	5.52190	+	8.14492i	0.286297	+	0.422295i
$373$		−	20.1837i		−	1.04507i	−0.852618	−	0.522535i	$-0.824986\pi$
$373$		−	20.1837i		−	1.04507i	0.852618	−	0.522535i	$-0.175014\pi$
$374$	−0.722385			−0.0373536
$375$	7.54071	+	17.8364i	0.389401	+	0.921068i
$376$			0.559901i			0.0288747i
$377$			32.0934i			1.65290i
$378$		0			0
$379$	6.25621			0.321360			0.160680	−	0.987007i	$-0.448631\pi$
$379$	6.25621			0.321360			0.160680	+	0.987007i	$0.448631\pi$
$380$	7.27820	−	10.8969i	0.373364	−	0.559002i
$381$	−13.8367	−	20.4094i	−0.708874	−	1.04560i
$382$			3.55322i			0.181799i
$383$		−	16.1645i		−	0.825965i	−0.910739	−	0.412982i	$-0.864487\pi$
$383$		−	16.1645i		−	0.825965i	0.910739	−	0.412982i	$-0.135513\pi$
$384$	13.5947	−	9.21662i	0.693753	−	0.470334i
$385$		0			0
$386$			5.69265i			0.289748i
$387$	11.4974	+	4.58210i	0.584446	+	0.232921i
$388$	−15.0568			−0.764391
$389$		−	31.7346i		−	1.60901i	−0.593949	−	0.804503i	$-0.702432\pi$
$389$		−	31.7346i		−	1.60901i	0.593949	−	0.804503i	$-0.297568\pi$
$390$	−5.11447	+	0.0353577i	−0.258981	+	0.00179041i
$391$			30.0567i			1.52003i
$392$		0			0
$393$	−24.3189	+	16.4871i	−1.22673	+	0.831666i
$394$	−0.00737947			−0.000371772
$395$	7.21123	+	4.81647i	0.362836	+	0.242343i
$396$	−2.81674	−	1.12256i	−0.141546	−	0.0564110i
$397$	−9.13554			−0.458500			−0.229250	−	0.973368i	$-0.573627\pi$
$397$	−9.13554			−0.458500			−0.229250	+	0.973368i	$0.573627\pi$
$398$			3.85643i			0.193305i
$399$		0			0
$400$	6.30874	+	15.2148i	0.315437	+	0.760739i
$401$		−	8.01379i		−	0.400190i	−0.979777	−	0.200095i	$-0.935875\pi$
$401$		−	8.01379i		−	0.400190i	0.979777	−	0.200095i	$-0.0641250\pi$
$402$	3.26209	+	4.81166i	0.162698	+	0.239984i
$403$		−	11.5187i		−	0.573785i
$404$	0.254765			0.0126750
$405$	4.45950	+	19.6243i	0.221595	+	0.975139i
$406$		0			0
$407$	−5.59666			−0.277416
$408$	5.06700	+	7.47394i	0.250854	+	0.370015i
$409$		−	7.69842i		−	0.380662i	−0.981720	−	0.190331i	$-0.939044\pi$
$409$		−	7.69842i		−	0.380662i	0.981720	−	0.190331i	$-0.0609562\pi$
$410$	−5.51902	−	3.68622i	−0.272565	−	0.182049i
$411$	−17.8571	+	12.1063i	−0.880828	+	0.597162i
$412$	−2.23277			−0.110000
$413$		0			0
$414$	2.98234	−	7.48330i	0.146574	−	0.367784i
$415$	−13.4399	+	20.1223i	−0.659740	+	0.987765i
$416$	−14.5978			−0.715718
$417$	18.4921	+	27.2763i	0.905563	+	1.33572i
$418$	0.580656			0.0284008
$419$	−0.801768			−0.0391689			−0.0195845	−	0.999808i	$-0.506234\pi$
$419$	−0.801768			−0.0391689			−0.0195845	+	0.999808i	$0.506234\pi$
$420$		0			0
$421$	19.7801			0.964022			0.482011	−	0.876165i	$-0.339907\pi$
$421$	19.7801			0.964022			0.482011	+	0.876165i	$0.339907\pi$
$422$	−1.64672			−0.0801610
$423$	−1.16074	−	0.462592i	−0.0564370	−	0.0224920i
$424$	−5.75992			−0.279727
$425$	−17.9118	+	7.42705i	−0.868851	+	0.360265i
$426$	0.340360	+	0.502038i	0.0164905	+	0.0243238i
$427$		0			0
$428$	24.7191			1.19484
$429$	1.99174	+	2.93785i	0.0961619	+	0.141841i
$430$	1.77523	−	2.65788i	0.0856091	−	0.128174i
$431$		−	17.7838i		−	0.856617i	−0.903632	−	0.428309i	$-0.859110\pi$
$431$		−	17.7838i		−	0.856617i	0.903632	−	0.428309i	$-0.140890\pi$
$432$	3.67756	+	16.7173i	0.176937	+	0.804312i
$433$	−20.1791			−0.969746			−0.484873	−	0.874584i	$-0.661134\pi$
$433$	−20.1791			−0.969746			−0.484873	+	0.874584i	$0.661134\pi$
$434$		0			0
$435$	−0.225440	−	32.6097i	−0.0108090	−	1.56352i
$436$	16.3797			0.784443
$437$		−	24.1597i		−	1.15571i
$438$	3.31744	−	2.24908i	0.158513	−	0.107465i
$439$			17.0114i			0.811908i	0.913893	+	0.405954i	$0.133061\pi$
$439$			17.0114i			0.811908i	−0.913893	+	0.405954i	$0.866939\pi$
$440$	−0.897593	+	1.34388i	−0.0427910	+	0.0640669i
$441$		0			0
$442$		−	5.12137i		−	0.243599i
$443$	15.7437			0.748003			0.374002	−	0.927428i	$-0.377985\pi$
$443$	15.7437			0.748003			0.374002	+	0.927428i	$0.377985\pi$
$444$	19.0210	+	28.0564i	0.902697	+	1.33150i
$445$	−11.4699	−	7.66087i	−0.543724	−	0.363160i
$446$	3.44293			0.163028
$447$	−10.5285	−	15.5298i	−0.497981	−	0.734533i
$448$		0			0
$449$			17.8876i			0.844166i	0.906557	+	0.422083i	$0.138701\pi$
$449$			17.8876i			0.844166i	−0.906557	+	0.422083i	$0.861299\pi$
$450$	5.19650	−	0.0718531i	0.244966	−	0.00338719i
$451$			4.60577i			0.216877i
$452$	−10.9489			−0.514991
$453$	−4.58117	+	3.10583i	−0.215242	+	0.145925i
$454$			4.92222i			0.231011i
$455$		0			0
$456$	−4.07288	−	6.00759i	−0.190730	−	0.281331i
$457$			12.2637i			0.573674i	0.957979	+	0.286837i	$0.0926038\pi$
$457$			12.2637i			0.573674i	−0.957979	+	0.286837i	$0.907396\pi$
$458$			5.40600i			0.252606i
$459$	−19.6807	+	4.32946i	−0.918616	+	0.202082i
$460$	27.0928	+	18.0956i	1.26321	+	0.843712i
$461$	−4.02980			−0.187687			−0.0938433	−	0.995587i	$-0.529915\pi$
$461$	−4.02980			−0.187687			−0.0938433	+	0.995587i	$0.529915\pi$
$462$		0			0
$463$			19.2199i			0.893223i	0.894728	+	0.446611i	$0.147369\pi$
$463$			19.2199i			0.893223i	−0.894728	+	0.446611i	$0.852631\pi$
$464$		−	27.7369i		−	1.28766i
$465$	0.0809128	+	11.7040i	0.00375224	+	0.542759i
$466$	3.68960			0.170918
$467$		−	25.7729i		−	1.19263i	−0.802751	−	0.596314i	$-0.796631\pi$
$467$		−	25.7729i		−	1.19263i	0.802751	−	0.596314i	$-0.203369\pi$
$468$	7.95846	−	19.9694i	0.367880	−	0.923084i
$469$		0			0
$470$	−0.179221	+	0.268330i	−0.00826683	+	0.0123771i
$471$	−34.5385	+	23.4156i	−1.59145	+	1.07893i
$472$	−13.8445			−0.637243
$473$	−2.21807			−0.101987
$474$	1.92631	−	1.30595i	0.0884783	−	0.0599844i
$475$	14.3976	−	5.96990i	0.660607	−	0.273918i
$476$		0			0
$477$	4.75887	−	11.9410i	0.217894	−	0.546739i
$478$			8.46912i			0.387369i
$479$	22.4140			1.02412			0.512061	−	0.858949i	$-0.328882\pi$
$479$	22.4140			1.02412			0.512061	+	0.858949i	$0.328882\pi$
$480$	14.8327	−	0.102542i	0.677017	−	0.00468040i
$481$		−	39.6777i		−	1.80915i
$482$			6.54136i			0.297951i
$483$		0			0
$484$	−20.1362			−0.915280
$485$	−14.8925	−	9.94688i	−0.676234	−	0.451665i
$486$	5.32955	+	0.874879i	0.241753	+	0.0396853i
$487$		−	4.64849i		−	0.210643i	−0.994438	−	0.105322i	$-0.966413\pi$
$487$		−	4.64849i		−	0.210643i	0.994438	−	0.105322i	$-0.0335872\pi$
$488$		−	0.379513i		−	0.0171798i
$489$	10.7708	+	15.8872i	0.487073	+	0.718444i
$490$		0			0
$491$			38.5971i			1.74186i	0.491406	+	0.870931i	$0.336483\pi$
$491$			38.5971i			1.74186i	−0.491406	+	0.870931i	$0.663517\pi$
$492$	23.0890	−	15.6533i	1.04093	−	0.705705i
$493$	32.6537			1.47065
$494$			4.11658i			0.185214i
$495$	−2.04442	−	2.97113i	−0.0918896	−	0.133542i
$496$			9.95508i			0.446996i
$497$		0			0
$498$	3.64415	+	5.37520i	0.163298	+	0.240868i
$499$	−11.0269			−0.493632			−0.246816	−	0.969062i	$-0.579384\pi$
$499$	−11.0269			−0.493632			−0.246816	+	0.969062i	$0.579384\pi$
$500$	−4.08913	+	20.6170i	−0.182871	+	0.922020i
$501$	11.9357	+	17.6054i	0.533246	+	0.786550i
$502$	−1.19286			−0.0532400
$503$			3.76757i			0.167988i	0.996466	+	0.0839939i	$0.0267676\pi$
$503$			3.76757i			0.167988i	−0.996466	+	0.0839939i	$0.973232\pi$
$504$		0			0
$505$	0.251986	+	0.168304i	0.0112132	+	0.00748945i
$506$			1.44367i			0.0641789i
$507$	−2.19070	+	1.48520i	−0.0972923	+	0.0659599i
$508$		−	26.7632i		−	1.18743i
$509$	29.5970			1.31187			0.655933	−	0.754819i	$-0.272275\pi$
$509$	29.5970			1.31187			0.655933	+	0.754819i	$0.272275\pi$
$510$	0.0359750	+	5.20376i	0.00159300	+	0.230426i
$511$		0			0
$512$	21.4728			0.948975
$513$	15.8194	−	3.48004i	0.698445	−	0.153648i
$514$		−	1.31089i		−	0.0578209i
$515$	−2.20841	−	1.47502i	−0.0973141	−	0.0649973i
$516$	7.53839	+	11.1193i	0.331859	+	0.489500i
$517$	0.223928			0.00984835
$518$		0			0
$519$	−19.6805	−	29.0292i	−0.863878	−	1.27424i
$520$	−9.52747	−	6.36351i	−0.417807	−	0.279058i
$521$	−8.00601			−0.350750			−0.175375	−	0.984502i	$-0.556114\pi$
$521$	−8.00601			−0.350750			−0.175375	+	0.984502i	$0.556114\pi$
$522$	−8.12990	−	3.24004i	−0.355836	−	0.141812i
$523$	20.3338			0.889134			0.444567	−	0.895746i	$-0.353358\pi$
$523$	20.3338			0.889134			0.444567	+	0.895746i	$0.353358\pi$
$524$	−31.8898			−1.39311
$525$		0			0
$526$	−8.91624			−0.388767
$527$	−11.7198			−0.510521
$528$	−1.72137	−	2.53906i	−0.0749130	−	0.110498i
$529$	37.0676			1.61163
$530$	−2.76041	−	1.84371i	−0.119905	−	0.0800858i
$531$	11.4383	−	28.7011i	0.496382	−	1.24552i
$532$		0			0
$533$	−32.6527			−1.41435
$534$	−3.06391	+	2.07719i	−0.132588	+	0.0898889i
$535$	24.4494	+	16.3301i	1.05704	+	0.706011i
$536$			13.0221i			0.562470i
$537$	−6.28404	−	9.26910i	−0.271176	−	0.399991i
$538$	−2.54774			−0.109841
$539$		0			0
$540$	−7.94622	+	20.3465i	−0.341951	+	0.875576i
$541$	11.0195			0.473767			0.236883	−	0.971538i	$-0.423874\pi$
$541$	11.0195			0.473767			0.236883	+	0.971538i	$0.423874\pi$
$542$		−	8.41458i		−	0.361437i
$543$	−16.0660	−	23.6976i	−0.689456	−	1.01696i
$544$			14.8527i			0.636804i
$545$	16.2010	+	10.8208i	0.693973	+	0.463513i
$546$		0			0
$547$		−	32.5977i		−	1.39378i	−0.717179	−	0.696889i	$-0.754567\pi$
$547$		−	32.5977i		−	1.39378i	0.717179	−	0.696889i	$-0.245433\pi$
$548$	−23.4164			−1.00030
$549$	0.786774	+	0.313555i	0.0335787	+	0.0133822i
$550$	−0.860333	+	0.356733i	−0.0366847	+	0.0152112i
$551$	−26.2472			−1.11817
$552$	14.9365	−	10.1263i	0.635740	−	0.431004i
$553$		0			0
$554$		−	2.09845i		−	0.0891545i
$555$	0.278716	+	40.3161i	0.0118308	+	1.71132i
$556$			35.7679i			1.51690i
$557$	−30.6114			−1.29705			−0.648524	−	0.761194i	$-0.724613\pi$
$557$	−30.6114			−1.29705			−0.648524	+	0.761194i	$0.724613\pi$
$558$	2.91791	+	1.16288i	0.123525	+	0.0492287i
$559$		−	15.7251i		−	0.665099i
$560$		0			0
$561$	2.98915	−	2.02651i	0.126202	−	0.0855593i
$562$		−	6.54763i		−	0.276195i
$563$			4.90111i			0.206557i	0.994652	+	0.103279i	$0.0329333\pi$
$563$			4.90111i			0.206557i	−0.994652	+	0.103279i	$0.967067\pi$
$564$	−0.761049	−	1.12256i	−0.0320459	−	0.0472685i
$565$	−10.8294	−	7.23309i	−0.455597	−	0.304299i
$566$	−2.86100			−0.120257
$567$		0			0
$568$			1.35870i			0.0570098i
$569$			30.1646i			1.26457i	0.774737	+	0.632283i	$0.217882\pi$
$569$			30.1646i			1.26457i	−0.774737	+	0.632283i	$0.782118\pi$
$570$	−0.0289169	−	4.18281i	−0.00121120	−	0.175199i
$571$	−12.1384			−0.507975			−0.253988	−	0.967207i	$-0.581742\pi$
$571$	−12.1384			−0.507975			−0.253988	+	0.967207i	$0.581742\pi$
$572$			3.85247i			0.161080i
$573$	−9.96787	−	14.7028i	−0.416414	−	0.614220i
$574$		0			0
$575$	14.8428	+	35.7964i	0.618988	+	1.49281i
$576$	−5.84359	+	14.6627i	−0.243483	+	0.610947i
$577$	−0.560058			−0.0233155			−0.0116578	−	0.999932i	$-0.503711\pi$
$577$	−0.560058			−0.0233155			−0.0116578	+	0.999932i	$0.503711\pi$
$578$	0.679151			0.0282490
$579$	−15.9696	−	23.5555i	−0.663675	−	0.978935i
$580$	19.6592	−	29.4338i	0.816302	−	1.22217i
$581$		0			0
$582$	−3.97818	+	2.69703i	−0.164901	+	0.111795i
$583$			2.30364i			0.0954069i
$584$	8.97823			0.371522
$585$	21.0639	−	14.4940i	0.870886	−	0.599251i
$586$			1.81427i			0.0749469i
$587$		−	20.4166i		−	0.842683i	−0.906902	−	0.421342i	$-0.861559\pi$
$587$		−	20.4166i		−	0.842683i	0.906902	−	0.421342i	$-0.138441\pi$
$588$		0			0
$589$	9.42040			0.388161
$590$	−6.63488	−	4.43152i	−0.273154	−	0.182443i
$591$	0.0305354	−	0.0207017i	0.00125606	−	0.000851553i
$592$			34.2917i			1.40938i
$593$			32.5076i			1.33493i	0.744643	+	0.667463i	$0.232620\pi$
$593$			32.5076i			1.33493i	−0.744643	+	0.667463i	$0.767380\pi$
$594$	−0.945295	+	0.207951i	−0.0387859	+	0.00853233i
$595$		0			0
$596$		−	20.3645i		−	0.834163i
$597$	−10.8185	−	15.9575i	−0.442770	−	0.653095i
$598$	−10.2349			−0.418538
$599$			8.94238i			0.365376i	0.983171	+	0.182688i	$0.0584798\pi$
$599$			8.94238i			0.365376i	−0.983171	+	0.182688i	$0.941520\pi$
$600$	9.72545	+	6.39896i	0.397040	+	0.261237i
$601$		−	9.31473i		−	0.379956i	−0.981788	−	0.189978i	$-0.939158\pi$
$601$		−	9.31473i		−	0.379956i	0.981788	−	0.189978i	$-0.0608417\pi$
$602$		0			0
$603$	−26.9963	−	10.7589i	−1.09938	−	0.438138i
$604$	−6.00738			−0.244437
$605$	−19.9165	−	13.3025i	−0.809721	−	0.540822i
$606$	0.0673121	−	0.0456346i	0.00273437	−	0.00185378i
$607$	−13.7906			−0.559743			−0.279871	−	0.960037i	$-0.590292\pi$
$607$	−13.7906			−0.559743			−0.279871	+	0.960037i	$0.590292\pi$
$608$		−	11.9387i		−	0.484177i
$609$		0			0
$610$	0.121480	−	0.181880i	0.00491857	−	0.00736410i
$611$			1.58755i			0.0642252i
$612$	−20.3180	−	8.09740i	−0.821307	−	0.327318i
$613$			6.40291i			0.258611i	0.991605	+	0.129306i	$0.0412748\pi$
$613$			6.40291i			0.258611i	−0.991605	+	0.129306i	$0.958725\pi$
$614$	−0.388481			−0.0156778
$615$	33.1780	−	0.229369i	1.33787	−	0.00924904i
$616$		0			0
$617$	26.2321			1.05607			0.528033	−	0.849224i	$-0.322930\pi$
$617$	26.2321			1.05607			0.528033	+	0.849224i	$0.322930\pi$
$618$	−0.589924	+	0.399942i	−0.0237302	+	0.0160880i
$619$		−	38.5973i		−	1.55136i	−0.631129	−	0.775678i	$-0.717408\pi$
$619$		−	38.5973i		−	1.55136i	0.631129	−	0.775678i	$-0.282592\pi$
$620$	−7.05588	+	10.5641i	−0.283371	+	0.424264i
$621$	8.65233	+	39.3314i	0.347206	+	1.57832i
$622$	4.49304			0.180154
$623$		0			0
$624$	18.0008	−	12.2037i	0.720607	−	0.488540i
$625$	−17.6646	+	17.6907i	−0.706585	+	0.707628i
$626$	4.76171			0.190316
$627$	−2.40269	+	1.62892i	−0.0959542	+	0.0650527i
$628$	−45.2911			−1.80731
$629$	−40.3705			−1.60968
$630$		0			0
$631$	−11.8214			−0.470602			−0.235301	−	0.971923i	$-0.575608\pi$
$631$	−11.8214			−0.470602			−0.235301	+	0.971923i	$0.575608\pi$
$632$	5.21331			0.207374
$633$	6.81394	−	4.61955i	0.270830	−	0.183611i
$634$	6.29152			0.249868
$635$	17.6805	−	26.4713i	0.701628	−	1.05048i
$636$	11.5483	−	7.82921i	0.457918	−	0.310448i
$637$		0			0
$638$	1.56841			0.0620940
$639$	−2.81674	−	1.12256i	−0.111428	−	0.0444080i
$640$	17.6325	+	11.7770i	0.696988	+	0.465526i
$641$		−	25.7547i		−	1.01725i	−0.860989	−	0.508624i	$-0.830154\pi$
$641$		−	25.7547i		−	1.01725i	0.860989	−	0.508624i	$-0.169846\pi$
$642$	6.53109	−	4.42779i	0.257762	−	0.174751i
$643$	33.0845			1.30472			0.652362	−	0.757907i	$-0.273778\pi$
$643$	33.0845			1.30472			0.652362	+	0.757907i	$0.273778\pi$
$644$		0			0
$645$	0.110461	+	15.9781i	0.00434938	+	0.629135i
$646$	4.18845			0.164792
$647$		−	38.3934i		−	1.50940i	−0.656070	−	0.754700i	$-0.727782\pi$
$647$		−	38.3934i		−	1.50940i	0.656070	−	0.754700i	$-0.272218\pi$
$648$	8.78206	+	8.32160i	0.344992	+	0.326903i
$649$			5.53698i			0.217346i
$650$	−2.52907	−	6.09936i	−0.0991984	−	0.239237i
$651$		0			0
$652$			20.8332i			0.815891i
$653$	−29.0750			−1.13779			−0.568896	−	0.822410i	$-0.692629\pi$
$653$	−29.0750			−1.13779			−0.568896	+	0.822410i	$0.692629\pi$
$654$	4.32770	−	2.93399i	0.169227	−	0.114728i
$655$	−31.5419	−	21.0672i	−1.23245	−	0.823165i
$656$	28.2203			1.10182
$657$	−7.41785	+	18.6129i	−0.289398	+	0.726157i
$658$		0			0
$659$		−	29.3766i		−	1.14435i	−0.820132	−	0.572175i	$-0.806100\pi$
$659$		−	29.3766i		−	1.14435i	0.820132	−	0.572175i	$-0.193900\pi$
$660$	−0.0270616	−	3.91445i	−0.00105337	−	0.152370i
$661$		−	19.6326i		−	0.763619i	−0.924241	−	0.381809i	$-0.875301\pi$
$661$		−	19.6326i		−	0.763619i	0.924241	−	0.381809i	$-0.124699\pi$
$662$	10.7371			0.417310
$663$	14.3670	+	21.1916i	0.557968	+	0.823015i
$664$			14.5473i			0.564544i
$665$		0			0
$666$	10.0512	+	4.00572i	0.389474	+	0.155219i
$667$		−	65.2578i		−	2.52679i
$668$			23.0863i			0.893235i
$669$	−14.2465	+	9.65847i	−0.550800	+	0.373418i
$670$	−4.16830	+	6.24079i	−0.161035	+	0.241103i
$671$	−0.151783			−0.00585954
$672$		0			0
$673$			7.40581i			0.285473i	0.989761	+	0.142736i	$0.0455901\pi$
$673$			7.40581i			0.285473i	−0.989761	+	0.142736i	$0.954410\pi$
$674$		−	3.69792i		−	0.142439i
$675$	−21.3010	+	14.8751i	−0.819875	+	0.572543i
$676$	−2.87271			−0.110489
$677$			45.5279i			1.74978i	0.484322	+	0.874890i	$0.339066\pi$
$677$			45.5279i			1.74978i	−0.484322	+	0.874890i	$0.660934\pi$
$678$	−2.89282	+	1.96121i	−0.111098	+	0.0753196i
$679$		0			0
$680$	−6.47461	+	9.69381i	−0.248290	+	0.371741i
$681$	−13.8083	−	20.3676i	−0.529136	−	0.780487i
$682$	−0.562919			−0.0215553
$683$	−7.43410			−0.284458			−0.142229	−	0.989834i	$-0.545427\pi$
$683$	−7.43410			−0.284458			−0.142229	+	0.989834i	$0.545427\pi$
$684$	16.3317	+	6.50873i	0.624459	+	0.248867i
$685$	−23.1610	−	15.4695i	−0.884935	−	0.591059i
$686$		0			0
$687$	−15.1655	−	22.3694i	−0.578599	−	0.853446i
$688$			13.5905i			0.518133i
$689$	−16.3317			−0.622189
$690$	10.3996	−	0.0718953i	0.395906	−	0.00273701i
$691$		−	2.91642i		−	0.110946i	−0.998460	−	0.0554729i	$-0.982333\pi$
$691$		−	2.91642i		−	0.110946i	0.998460	−	0.0554729i	$-0.0176667\pi$
$692$		−	38.0665i		−	1.44707i
$693$		0			0
$694$	−0.809869			−0.0307422
$695$	−23.6292	+	35.3777i	−0.896307	+	1.34195i
$696$	−11.0013	−	16.2271i	−0.417002	−	0.615087i
$697$			33.2228i			1.25840i
$698$			1.59622i			0.0604180i
$699$	−15.2672	+	10.3505i	−0.577457	+	0.391491i
$700$		0			0
$701$			25.2600i			0.954057i	0.878888	+	0.477029i	$0.158286\pi$
$701$			25.2600i			0.954057i	−0.878888	+	0.477029i	$0.841714\pi$
$702$	−1.47428	−	6.70170i	−0.0556429	−	0.252939i
$703$	32.4500			1.22387
$704$		−	2.82872i		−	0.106611i
$705$	−0.0111517	−	1.61309i	−0.000419997	−	0.0607523i
$706$			2.08164i			0.0783435i
$707$		0			0
$708$	27.7572	−	18.8182i	1.04318	−	0.707230i
$709$	1.76514			0.0662912			0.0331456	−	0.999451i	$-0.489447\pi$
$709$	1.76514			0.0662912			0.0331456	+	0.999451i	$0.489447\pi$
$710$	−0.434911	+	0.651151i	−0.0163219	+	0.0244372i
$711$	−4.30726	+	10.8078i	−0.161535	+	0.405323i
$712$	−8.29206			−0.310758
$713$			23.4217i			0.877149i
$714$		0			0
$715$	−2.54504	+	3.81044i	−0.0951790	+	0.142502i
$716$		−	12.1548i		−	0.454244i
$717$	−23.7585	−	35.0443i	−0.887276	−	1.30875i
$718$		−	6.76984i		−	0.252648i
$719$	14.0014			0.522166			0.261083	−	0.965316i	$-0.415920\pi$
$719$	14.0014			0.522166			0.261083	+	0.965316i	$0.415920\pi$
$720$	−18.2046	+	12.5265i	−0.678446	+	0.466835i
$721$		0			0
$722$	3.21617			0.119693
$723$	−18.3505	−	27.0674i	−0.682463	−	1.00665i
$724$		−	31.0752i		−	1.15490i
$725$	38.8894	−	16.1253i	1.44432	−	0.598879i
$726$	−5.32022	+	3.60687i	−0.197452	+	0.133864i
$727$	−32.1893			−1.19383			−0.596917	−	0.802303i	$-0.703608\pi$
$727$	−32.1893			−1.19383			−0.596917	+	0.802303i	$0.703608\pi$
$728$		0			0
$729$	−24.5074	+	11.3309i	−0.907681	+	0.419662i
$730$	4.30277	+	2.87387i	0.159253	+	0.106367i
$731$	−15.9996			−0.591767
$732$	0.515856	+	0.760899i	0.0190666	+	0.0281236i
$733$	2.46880			0.0911870			0.0455935	−	0.998960i	$-0.485482\pi$
$733$	2.46880			0.0911870			0.0455935	+	0.998960i	$0.485482\pi$
$734$	−6.59617			−0.243469
$735$		0			0
$736$	29.6828			1.09412
$737$	5.20810			0.191843
$738$	3.29650	−	8.27158i	0.121346	−	0.304481i
$739$	−39.1013			−1.43836			−0.719182	−	0.694822i	$-0.755483\pi$
$739$	−39.1013			−1.43836			−0.719182	+	0.694822i	$0.755483\pi$
$740$	−24.3050	+	36.3895i	−0.893470	+	1.33771i
$741$	−11.5483	−	17.0339i	−0.424236	−	0.625758i
$742$		0			0
$743$	−23.3132			−0.855280			−0.427640	−	0.903949i	$-0.640655\pi$
$743$	−23.3132			−0.855280			−0.427640	+	0.903949i	$0.640655\pi$
$744$	3.94847	+	5.82408i	0.144758	+	0.213521i
$745$	13.4533	−	20.1423i	0.492891	−	0.737958i
$746$		−	6.99296i		−	0.256031i
$747$	−30.1581	−	12.0190i	−1.10343	−	0.439753i
$748$	3.91973			0.143319
$749$		0			0
$750$	2.61261	+	6.17972i	0.0953989	+	0.225652i
$751$	1.30898			0.0477655			0.0238828	−	0.999715i	$-0.492397\pi$
$751$	1.30898			0.0477655			0.0238828	+	0.999715i	$0.492397\pi$
$752$		−	1.37205i		−	0.0500334i
$753$	4.93593	−	3.34634i	0.179875	−	0.121947i
$754$			11.1193i			0.404941i
$755$	−5.94184	−	3.96863i	−0.216246	−	0.144433i
$756$		0			0
$757$		−	16.4529i		−	0.597992i	−0.954254	−	0.298996i	$-0.903348\pi$
$757$		−	16.4529i		−	0.597992i	0.954254	−	0.298996i	$-0.0966518\pi$
$758$	2.16757			0.0787296
$759$	−4.04993	−	5.97374i	−0.147003	−	0.216833i
$760$	5.20432	−	7.79193i	0.188781	−	0.282643i
$761$	−5.87873			−0.213104			−0.106552	−	0.994307i	$-0.533981\pi$
$761$	−5.87873			−0.213104			−0.106552	+	0.994307i	$0.533981\pi$
$762$	−4.79394	−	7.07117i	−0.173666	−	0.256162i
$763$		0			0
$764$		−	19.2801i		−	0.697530i
$765$	−14.7470	−	21.4317i	−0.533179	−	0.774863i
$766$		−	5.60044i		−	0.202352i
$767$	−39.2546			−1.41740
$768$	−10.3759	+	7.03437i	−0.374407	+	0.253831i
$769$		−	3.63344i		−	0.131025i	−0.997852	−	0.0655127i	$-0.979132\pi$
$769$		−	3.63344i		−	0.131025i	0.997852	−	0.0655127i	$-0.0208683\pi$
$770$		0			0
$771$	3.67745	+	5.42432i	0.132440	+	0.195352i
$772$		−	30.8889i		−	1.11171i
$773$		−	30.2162i		−	1.08680i	−0.839473	−	0.543401i	$-0.817136\pi$
$773$		−	30.2162i		−	1.08680i	0.839473	−	0.543401i	$-0.182864\pi$
$774$	3.98347	+	1.58755i	0.143183	+	0.0570632i
$775$	−13.9578	+	5.78754i	−0.501379	+	0.207895i
$776$	−10.7664			−0.386492
$777$		0			0
$778$		−	10.9950i		−	0.394189i
$779$		−	26.7046i		−	0.956793i
$780$	27.7516	−	0.191854i	0.993667	−	0.00686949i
$781$	0.543402			0.0194445
$782$			10.4136i			0.372391i
$783$	42.7299	−	9.39994i	1.52704	−	0.335927i
$784$		0			0
$785$	−44.7970	−	29.9204i	−1.59887	−	1.06791i
$786$	−8.42568	+	5.71224i	−0.300534	+	0.203749i
$787$	−50.8487			−1.81256			−0.906279	−	0.422679i	$-0.861090\pi$
$787$	−50.8487			−1.81256			−0.906279	+	0.422679i	$0.861090\pi$
$788$	0.0400417			0.00142643
$789$	36.8944	−	25.0128i	1.31348	−	0.890478i
$790$	2.49845	+	1.66875i	0.0888909	+	0.0593713i
$791$		0			0
$792$	−2.01413	−	0.802696i	−0.0715689	−	0.0285226i
$793$		−	1.07607i		−	0.0382125i
$794$	−3.16516			−0.112327
$795$	16.5945	−	0.114722i	0.588545	−	0.00406877i
$796$		−	20.9253i		−	0.741679i
$797$		−	10.1940i		−	0.361089i	−0.983567	−	0.180545i	$-0.942214\pi$
$797$		−	10.1940i		−	0.361089i	0.983567	−	0.180545i	$-0.0577860\pi$
$798$		0			0
$799$	1.61526			0.0571439
$800$	7.33467	+	17.6890i	0.259320	+	0.625401i
$801$	6.85094	−	17.1904i	0.242066	−	0.607392i
$802$		−	2.77651i		−	0.0980420i
$803$		−	3.59077i		−	0.126716i
$804$	−17.7004	−	26.1085i	−0.624245	−	0.920776i
$805$		0			0
$806$		−	3.99083i		−	0.140571i
$807$	10.5422	−	7.14718i	0.371105	−	0.251593i
$808$	0.182171			0.00640877
$809$		−	12.6044i		−	0.443149i	−0.975143	−	0.221574i	$-0.928880\pi$
$809$		−	12.6044i		−	0.443149i	0.975143	−	0.221574i	$-0.0711195\pi$
$810$	1.54507	+	6.79916i	0.0542882	+	0.238898i
$811$			40.1743i			1.41071i	0.708853	+	0.705356i	$0.249213\pi$
$811$			40.1743i			1.41071i	−0.708853	+	0.705356i	$0.750787\pi$
$812$		0			0
$813$	23.6055	+	34.8186i	0.827880	+	1.22114i
$814$	−1.93906			−0.0679639
$815$	−13.7629	+	20.6059i	−0.482095	+	0.721794i
$816$	−12.4168	−	18.3150i	−0.434674	−	0.641154i
$817$	12.8606			0.449934
$818$		−	2.66725i		−	0.0932581i
$819$		0			0
$820$	29.9467	+	20.0018i	1.04578	+	0.698492i
$821$			43.1485i			1.50589i	0.658081	+	0.752947i	$0.271368\pi$
$821$			43.1485i			1.50589i	−0.658081	+	0.752947i	$0.728632\pi$
$822$	−6.18690	+	4.19445i	−0.215793	+	0.146298i
$823$			29.4530i			1.02667i	0.858189	+	0.513333i	$0.171590\pi$
$823$			29.4530i			1.02667i	−0.858189	+	0.513333i	$0.828410\pi$
$824$	−1.59655			−0.0556185
$825$	2.55922	−	3.88962i	0.0891005	−	0.135419i
$826$		0			0
$827$	−4.77349			−0.165991			−0.0829953	−	0.996550i	$-0.526449\pi$
$827$	−4.77349			−0.165991			−0.0829953	+	0.996550i	$0.526449\pi$
$828$	−16.1825	+	40.6051i	−0.562380	+	1.41112i
$829$			34.9619i			1.21428i	0.794596	+	0.607138i	$0.207683\pi$
$829$			34.9619i			1.21428i	−0.794596	+	0.607138i	$0.792317\pi$
$830$	−4.65649	+	6.97171i	−0.161629	+	0.241992i
$831$	5.88678	+	8.68314i	0.204210	+	0.301215i
$832$	20.0543			0.695257
$833$		0			0
$834$	6.40690	+	9.45032i	0.221853	+	0.327238i
$835$	−15.2514	+	22.8344i	−0.527796	+	0.790218i
$836$	−3.15069			−0.108969
$837$	−15.3362	+	3.37374i	−0.530097	+	0.116613i
$838$	−0.277786			−0.00959596
$839$	35.3328			1.21982			0.609911	−	0.792470i	$-0.291205\pi$
$839$	35.3328			1.21982			0.609911	+	0.792470i	$0.291205\pi$
$840$		0			0
$841$	−41.8964			−1.44470
$842$	6.85314			0.236175
$843$	18.3681	+	27.0933i	0.632631	+	0.933144i
$844$	8.93525			0.307564
$845$	−2.84137	−	1.89778i	−0.0977460	−	0.0652857i
$846$	−0.402157	−	0.160273i	−0.0138264	−	0.00551029i
$847$		0			0
$848$	14.1148			0.484704
$849$	11.8385	−	8.02598i	0.406296	−	0.275451i
$850$	−6.20585	+	2.57323i	−0.212859	+	0.0882610i
$851$			80.6795i			2.76566i
$852$	−1.84682	−	2.72411i	−0.0632711	−	0.0933263i
$853$	14.5110			0.496846			0.248423	−	0.968652i	$-0.420088\pi$
$853$	14.5110			0.496846			0.248423	+	0.968652i	$0.420088\pi$
$854$		0			0
$855$	11.8537	+	17.2269i	0.405388	+	0.589146i
$856$	17.6755			0.604138
$857$		−	9.42204i		−	0.321851i	−0.986967	−	0.160925i	$-0.948552\pi$
$857$		−	9.42204i		−	0.321851i	0.986967	−	0.160925i	$-0.0514478\pi$
$858$	0.690070	+	1.01787i	0.0235586	+	0.0347495i
$859$			9.34505i			0.318849i	0.987210	+	0.159424i	$0.0509638\pi$
$859$			9.34505i			0.318849i	−0.987210	+	0.159424i	$0.949036\pi$
$860$	−9.63256	+	14.4219i	−0.328467	+	0.491782i
$861$		0			0
$862$		−	6.16151i		−	0.209862i
$863$	−12.3835			−0.421538			−0.210769	−	0.977536i	$-0.567597\pi$
$863$	−12.3835			−0.421538			−0.210769	+	0.977536i	$0.567597\pi$
$864$	4.27561	+	19.4359i	0.145459	+	0.661222i
$865$	25.1477	−	37.6512i	0.855048	−	1.28018i
$866$	−6.99139			−0.237577
$867$	−2.81025	+	1.90523i	−0.0954411	+	0.0647048i
$868$		0			0
$869$		−	2.08502i		−	0.0707295i
$870$	−0.0781075	−	11.2982i	−0.00264809	−	0.383044i
$871$			36.9230i			1.25109i
$872$	11.7124			0.396631
$873$	8.89527	−	22.3200i	0.301059	−	0.755418i
$874$		−	8.37053i		−	0.283137i
$875$		0			0
$876$	−18.0008	+	12.2037i	−0.608189	+	0.412325i
$877$		−	10.7863i		−	0.364229i	−0.983277	−	0.182114i	$-0.941706\pi$
$877$		−	10.7863i		−	0.364229i	0.983277	−	0.182114i	$-0.0582941\pi$
$878$			5.89387i			0.198909i
$879$	−5.08958	−	7.50725i	−0.171667	−	0.253213i
$880$	2.19957	−	3.29320i	0.0741474	−	0.111014i
$881$	16.5184			0.556520			0.278260	−	0.960506i	$-0.410242\pi$
$881$	16.5184			0.556520			0.278260	+	0.960506i	$0.410242\pi$
$882$		0			0
$883$		−	16.5025i		−	0.555352i	−0.960675	−	0.277676i	$-0.910436\pi$
$883$		−	16.5025i		−	0.555352i	0.960675	−	0.277676i	$-0.0895641\pi$
$884$			27.7890i			0.934646i
$885$	39.8862	−	0.275744i	1.34076	−	0.00926903i
$886$	5.45465			0.183253
$887$		−	45.0029i		−	1.51105i	−0.655119	−	0.755525i	$-0.727382\pi$
$887$		−	45.0029i		−	1.51105i	0.655119	−	0.755525i	$-0.272618\pi$
$888$	13.6011	+	20.0619i	0.456422	+	0.673233i
$889$		0			0
$890$	−3.97393	−	2.65424i	−0.133206	−	0.0889702i
$891$	3.32816	−	3.51232i	0.111498	−	0.117667i
$892$	−18.6817			−0.625509
$893$	−1.29836			−0.0434478
$894$	−3.64778	−	5.38055i	−0.122000	−	0.179953i
$895$	8.02974	−	12.0222i	0.268405	−	0.401856i
$896$		0			0
$897$	42.3510	−	28.7121i	1.41406	−	0.958670i
$898$			6.19744i			0.206811i
$899$	25.4455			0.848653
$900$	−28.1967	+	0.389882i	−0.939891	+	0.0129961i
$901$			16.6168i			0.553587i
$902$			1.59574i			0.0531325i
$903$		0			0
$904$	−7.82905			−0.260390
$905$	20.5291	−	30.7362i	0.682409	−	1.02171i
$906$	−1.58722	+	1.07607i	−0.0527319	+	0.0357499i
$907$		−	7.76559i		−	0.257852i	−0.991654	−	0.128926i	$-0.958847\pi$
$907$		−	7.76559i		−	0.257852i	0.991654	−	0.128926i	$-0.0411530\pi$
$908$		−	26.7084i		−	0.886350i
$909$	−0.150511	+	0.377662i	−0.00499213	+	0.0125262i
$910$		0			0
$911$		−	12.5284i		−	0.415085i	−0.978226	−	0.207543i	$-0.933453\pi$
$911$		−	12.5284i		−	0.415085i	0.978226	−	0.207543i	$-0.0665466\pi$
$912$	9.98066	+	14.7217i	0.330493	+	0.487484i
$913$	5.81807			0.192550
$914$			4.24898i			0.140544i
$915$	0.00755887	+	1.09339i	0.000249889	+	0.0361462i
$916$		−	29.3334i		−	0.969204i
$917$		0			0
$918$	−6.81871	+	1.50001i	−0.225051	+	0.0495079i
$919$	−34.2726			−1.13055			−0.565274	−	0.824903i	$-0.691230\pi$
$919$	−34.2726			−1.13055			−0.565274	+	0.824903i	$0.691230\pi$
$920$	19.3729	+	12.9394i	0.638704	+	0.426598i
$921$	1.60749	−	1.08981i	0.0529687	−	0.0359104i
$922$	−1.39619			−0.0459811
$923$			3.85247i			0.126806i
$924$		0			0
$925$	−48.0797	+	19.9360i	−1.58085	+	0.655493i
$926$			6.65904i			0.218830i
$927$	1.31908	−	3.30983i	0.0433242	−	0.108709i
$928$		−	32.2476i		−	1.05858i
$929$	−45.5641			−1.49491			−0.747455	−	0.664312i	$-0.768725\pi$
$929$	−45.5641			−1.49491			−0.747455	+	0.664312i	$0.768725\pi$
$930$	0.0280336	+	4.05504i	0.000919257	+	0.132970i
$931$		0			0
$932$	−20.0201			−0.655781
$933$	−18.5917	+	12.6043i	−0.608664	+	0.412647i
$934$		−	8.92945i		−	0.292181i
$935$	3.87696	+	2.58947i	0.126790	+	0.0846848i
$936$	5.69074	−	14.2792i	0.186008	−	0.466731i
$937$	−15.5172			−0.506924			−0.253462	−	0.967345i	$-0.581569\pi$
$937$	−15.5172			−0.506924			−0.253462	+	0.967345i	$0.581569\pi$
$938$		0			0
$939$	−19.7034	+	13.3581i	−0.642997	+	0.435924i
$940$	0.972468	−	1.45598i	0.0317184	−	0.0474889i
$941$	19.2258			0.626744			0.313372	−	0.949630i	$-0.398541\pi$
$941$	19.2258			0.626744			0.313372	+	0.949630i	$0.398541\pi$
$942$	−11.9665	+	8.11273i	−0.389888	+	0.264327i
$943$	66.3950			2.16212
$944$	33.9261			1.10420
$945$		0			0
$946$	−0.768487			−0.0249857
$947$	37.3061			1.21228			0.606142	−	0.795356i	$-0.292716\pi$
$947$	37.3061			1.21228			0.606142	+	0.795356i	$0.292716\pi$
$948$	−10.4523	+	7.08622i	−0.339476	+	0.230150i
$949$	25.4569			0.826366
$950$	4.98829	−	2.06837i	0.161842	−	0.0671068i
$951$	−26.0336	+	17.6496i	−0.844197	+	0.572328i
$952$		0			0
$953$	10.1356			0.328326			0.164163	−	0.986433i	$-0.447508\pi$
$953$	10.1356			0.328326			0.164163	+	0.986433i	$0.447508\pi$
$954$	1.64879	−	4.13715i	0.0533816	−	0.133945i
$955$	12.7369	−	19.0698i	0.412158	−	0.617084i
$956$		−	45.9542i		−	1.48627i
$957$	−6.48991	+	4.39987i	−0.209789	+	0.142228i
$958$	7.76571			0.250899
$959$		0			0
$960$	−20.3769	+	0.140871i	−0.657662	+	0.00454660i
$961$	21.8674			0.705399
$962$		−	13.7470i		−	0.443221i
$963$	−14.6036	+	36.6434i	−0.470595	+	1.18082i
$964$		−	35.4940i		−	1.14319i
$965$	20.4060	−	30.5519i	0.656891	−	0.983500i
$966$		0			0
$967$			7.96860i			0.256253i	0.991758	+	0.128126i	$0.0408963\pi$
$967$			7.96860i			0.256253i	−0.991758	+	0.128126i	$0.959104\pi$
$968$	−14.3985			−0.462785
$969$	−17.3313	+	11.7499i	−0.556763	+	0.377461i
$970$	−5.15976	−	3.44626i	−0.165670	−	0.110653i
$971$	25.6635			0.823581			0.411790	−	0.911279i	$-0.364904\pi$
$971$	25.6635			0.823581			0.411790	+	0.911279i	$0.364904\pi$
$972$	−28.9186	−	4.74717i	−0.927566	−	0.152266i
$973$		0			0
$974$		−	1.61055i		−	0.0516053i
$975$	27.5756	+	18.1437i	0.883125	+	0.581062i
$976$			0.930004i			0.0297687i
$977$	1.62020			0.0518348			0.0259174	−	0.999664i	$-0.491749\pi$
$977$	1.62020			0.0518348			0.0259174	+	0.999664i	$0.491749\pi$
$978$	3.73173	+	5.50439i	0.119328	+	0.176011i
$979$			3.31635i			0.105991i
$980$		0			0
$981$	−9.67681	+	24.2811i	−0.308957	+	0.775234i
$982$			13.3726i			0.426737i
$983$			12.7929i			0.408029i	0.978968	+	0.204014i	$0.0653989\pi$
$983$			12.7929i			0.408029i	−0.978968	+	0.204014i	$0.934601\pi$
$984$	16.5099	−	11.1930i	0.526316	−	0.356819i
$985$	0.0396049	+	0.0264526i	0.00126192	+	0.000842849i
$986$	11.3134			0.360293
$987$		0			0
$988$		−	22.3370i		−	0.710633i
$989$			31.9749i			1.01674i
$990$	−0.708322	−	1.02940i	−0.0225119	−	0.0327164i
$991$	30.3004			0.962524			0.481262	−	0.876577i	$-0.340179\pi$
$991$	30.3004			0.962524			0.481262	+	0.876577i	$0.340179\pi$
$992$			11.5740i			0.367474i
$993$	−44.4290	+	30.1209i	−1.40991	+	0.955857i
$994$		0			0
$995$	13.8238	−	20.6971i	0.438244	−	0.656141i
$996$	−19.7735	−	29.1663i	−0.626547	−	0.924171i
$997$	−28.2838			−0.895757			−0.447879	−	0.894094i	$-0.647820\pi$
$997$	−28.2838			−0.895757			−0.447879	+	0.894094i	$0.647820\pi$
$998$	−3.82046			−0.120934
$999$	−52.8278	+	11.6213i	−1.67140	+	0.367683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.g.c.734.18	yes	32
3.2	odd	2	inner	735.2.g.c.734.13	✓	32
5.4	even	2	inner	735.2.g.c.734.15	yes	32
7.2	even	3		735.2.p.g.374.14		64
7.3	odd	6		735.2.p.g.509.13		64
7.4	even	3		735.2.p.g.509.16		64
7.5	odd	6		735.2.p.g.374.15		64
7.6	odd	2	inner	735.2.g.c.734.19	yes	32
15.14	odd	2	inner	735.2.g.c.734.20	yes	32
21.2	odd	6		735.2.p.g.374.20		64
21.5	even	6		735.2.p.g.374.17		64
21.11	odd	6		735.2.p.g.509.18		64
21.17	even	6		735.2.p.g.509.19		64
21.20	even	2	inner	735.2.g.c.734.16	yes	32
35.4	even	6		735.2.p.g.509.17		64
35.9	even	6		735.2.p.g.374.19		64
35.19	odd	6		735.2.p.g.374.18		64
35.24	odd	6		735.2.p.g.509.20		64
35.34	odd	2	inner	735.2.g.c.734.14	yes	32
105.44	odd	6		735.2.p.g.374.13		64
105.59	even	6		735.2.p.g.509.14		64
105.74	odd	6		735.2.p.g.509.15		64
105.89	even	6		735.2.p.g.374.16		64
105.104	even	2	inner	735.2.g.c.734.17	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.g.c.734.13	✓	32	3.2	odd	2	inner
735.2.g.c.734.14	yes	32	35.34	odd	2	inner
735.2.g.c.734.15	yes	32	5.4	even	2	inner
735.2.g.c.734.16	yes	32	21.20	even	2	inner
735.2.g.c.734.17	yes	32	105.104	even	2	inner
735.2.g.c.734.18	yes	32	1.1	even	1	trivial
735.2.g.c.734.19	yes	32	7.6	odd	2	inner
735.2.g.c.734.20	yes	32	15.14	odd	2	inner
735.2.p.g.374.13		64	105.44	odd	6
735.2.p.g.374.14		64	7.2	even	3
735.2.p.g.374.15		64	7.5	odd	6
735.2.p.g.374.16		64	105.89	even	6
735.2.p.g.374.17		64	21.5	even	6
735.2.p.g.374.18		64	35.19	odd	6
735.2.p.g.374.19		64	35.9	even	6
735.2.p.g.374.20		64	21.2	odd	6
735.2.p.g.509.13		64	7.3	odd	6
735.2.p.g.509.14		64	105.59	even	6
735.2.p.g.509.15		64	105.74	odd	6
735.2.p.g.509.16		64	7.4	even	3
735.2.p.g.509.17		64	35.4	even	6
735.2.p.g.509.18		64	21.11	odd	6
735.2.p.g.509.19		64	21.17	even	6
735.2.p.g.509.20		64	35.24	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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.346467 q^{2} +(-1.43364 + 0.971945i) q^{3} -1.87996 q^{4} +(-1.85945 - 1.24195i) q^{5} +(-0.496709 + 0.336746i) q^{6} -1.34428 q^{8} +(1.11065 - 2.78684i) q^{9} +O(q^{10})\)	\(q+0.346467 q^{2} +(-1.43364 + 0.971945i) q^{3} -1.87996 q^{4} +(-1.85945 - 1.24195i) q^{5} +(-0.496709 + 0.336746i) q^{6} -1.34428 q^{8} +(1.11065 - 2.78684i) q^{9} +(-0.644238 - 0.430294i) q^{10} +0.537633i q^{11} +(2.69519 - 1.82722i) q^{12} -3.81157 q^{13} +(3.87289 - 0.0267743i) q^{15} +3.29417 q^{16} +3.87812i q^{17} +(0.384802 - 0.965546i) q^{18} -3.11725i q^{19} +(3.49570 + 2.33482i) q^{20} +0.186272i q^{22} +7.75033 q^{23} +(1.92721 - 1.30656i) q^{24} +(1.91512 + 4.61869i) q^{25} -1.32058 q^{26} +(1.11638 + 5.07481i) q^{27} -8.42000i q^{29} +(1.34183 - 0.00927642i) q^{30} +3.02203i q^{31} +3.82988 q^{32} +(-0.522550 - 0.770773i) q^{33} +1.34364i q^{34} +(-2.08797 + 5.23915i) q^{36} +10.4098i q^{37} -1.08002i q^{38} +(5.46442 - 3.70464i) q^{39} +(2.49962 + 1.66953i) q^{40} +8.56674 q^{41} +4.12561i q^{43} -1.01073i q^{44} +(-5.52631 + 3.80262i) q^{45} +2.68523 q^{46} -0.416507i q^{47} +(-4.72266 + 3.20176i) q^{48} +(0.663525 + 1.60022i) q^{50} +(-3.76931 - 5.55982i) q^{51} +7.16560 q^{52} +4.28477 q^{53} +(0.386790 + 1.75825i) q^{54} +(0.667714 - 0.999703i) q^{55} +(3.02979 + 4.46901i) q^{57} -2.91725i q^{58} +10.2988 q^{59} +(-7.28088 + 0.0503347i) q^{60} +0.282318i q^{61} +1.04703i q^{62} -5.26142 q^{64} +(7.08743 + 4.73378i) q^{65} +(-0.181046 - 0.267047i) q^{66} -9.68708i q^{67} -7.29071i q^{68} +(-11.1112 + 7.53289i) q^{69} -1.01073i q^{71} +(-1.49302 + 3.74628i) q^{72} -6.67885 q^{73} +3.60665i q^{74} +(-7.23470 - 4.76015i) q^{75} +5.86030i q^{76} +(1.89324 - 1.28353i) q^{78} -3.87815 q^{79} +(-6.12536 - 4.09120i) q^{80} +(-6.53292 - 6.19039i) q^{81} +2.96809 q^{82} -10.8216i q^{83} +(4.81643 - 7.21117i) q^{85} +1.42939i q^{86} +(8.18377 + 12.0712i) q^{87} -0.722728i q^{88} +6.16842 q^{89} +(-1.91468 + 1.31748i) q^{90} -14.5703 q^{92} +(-2.93724 - 4.33250i) q^{93} -0.144306i q^{94} +(-3.87147 + 5.79637i) q^{95} +(-5.49066 + 3.72243i) q^{96} +8.00908 q^{97} +(1.49830 + 0.597121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 40 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 40 * q^9	\( 32 q + 16 q^{4} + 40 q^{9} + 16 q^{15} - 16 q^{16} + 64 q^{25} + 56 q^{30} - 16 q^{36} - 56 q^{39} - 32 q^{46} - 40 q^{51} + 8 q^{60} - 176 q^{64} + 48 q^{79} - 40 q^{81} - 64 q^{85} + 40 q^{99}+O(q^{100}) \) 32 * q + 16 * q^4 + 40 * q^9 + 16 * q^15 - 16 * q^16 + 64 * q^25 + 56 * q^30 - 16 * q^36 - 56 * q^39 - 32 * q^46 - 40 * q^51 + 8 * q^60 - 176 * q^64 + 48 * q^79 - 40 * q^81 - 64 * q^85 + 40 * q^99

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