LMFDB - Embedded newform 693.2.m.k.64.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.8
Character	$\chi$	$=$	693.64
Dual form			693.2.m.k.379.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.804651 - 2.47646i) q^{2} +(-3.86736 - 2.80980i) q^{4} +(-1.33452 - 4.10723i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-5.85703 + 4.25538i) q^{8} +O(q^{10})$	\(q+(0.804651 - 2.47646i) q^{2} +(-3.86736 - 2.80980i) q^{4} +(-1.33452 - 4.10723i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-5.85703 + 4.25538i) q^{8} -11.2452 q^{10} +(3.29379 - 0.388483i) q^{11} +(-0.761506 + 2.34367i) q^{13} +(-2.10660 + 1.53054i) q^{14} +(2.87102 + 8.83609i) q^{16} +(-0.366661 - 1.12847i) q^{17} +(2.77243 - 2.01429i) q^{19} +(-6.37943 + 19.6339i) q^{20} +(1.68829 - 8.46954i) q^{22} +8.32084 q^{23} +(-11.0433 + 8.02343i) q^{25} +(5.19127 + 3.77168i) q^{26} +(1.47720 + 4.54635i) q^{28} +(-1.17608 - 0.854470i) q^{29} +(0.923391 - 2.84191i) q^{31} +9.71302 q^{32} -3.08964 q^{34} +(-1.33452 + 4.10723i) q^{35} +(-5.13219 - 3.72875i) q^{37} +(-2.75747 - 8.48661i) q^{38} +(25.2941 + 18.3773i) q^{40} +(4.98751 - 3.62364i) q^{41} +3.15289 q^{43} +(-13.8298 - 7.75250i) q^{44} +(6.69537 - 20.6062i) q^{46} +(-7.06675 + 5.13430i) q^{47} +(0.309017 + 0.951057i) q^{49} +(10.9837 + 33.8044i) q^{50} +(9.53028 - 6.92415i) q^{52} +(-2.06473 + 6.35457i) q^{53} +(-5.99122 - 13.0099i) q^{55} +7.23969 q^{56} +(-3.06239 + 2.22496i) q^{58} +(-9.50987 - 6.90932i) q^{59} +(2.40078 + 7.38884i) q^{61} +(-6.29486 - 4.57348i) q^{62} +(2.07355 - 6.38173i) q^{64} +10.6423 q^{65} +3.11080 q^{67} +(-1.75276 + 5.39443i) q^{68} +(9.09757 + 6.60977i) q^{70} +(1.69576 + 5.21901i) q^{71} +(-7.00611 - 5.09024i) q^{73} +(-13.3637 + 9.70932i) q^{74} -16.3817 q^{76} +(-2.89308 - 1.62175i) q^{77} +(-2.73036 + 8.40318i) q^{79} +(32.4604 - 23.5839i) q^{80} +(-4.96059 - 15.2671i) q^{82} +(-2.98622 - 9.19065i) q^{83} +(-4.14556 + 3.01192i) q^{85} +(2.53698 - 7.80801i) q^{86} +(-17.6387 + 16.2917i) q^{88} +0.985558 q^{89} +(1.99365 - 1.44847i) q^{91} +(-32.1797 - 23.3799i) q^{92} +(7.02861 + 21.6318i) q^{94} +(-11.9730 - 8.69890i) q^{95} +(2.15458 - 6.63113i) q^{97} +2.60390 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) $ 32 * q - 10 * q^4 - 8 * q^7	$ 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) $ 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.804651	−	2.47646i	0.568974	−	1.75112i	−0.0868638	−	0.996220i	$-0.527685\pi$
$2$	0.804651	−	2.47646i	0.568974	−	1.75112i	0.655838	−	0.754902i	$-0.272315\pi$
$3$		0			0
$3$		0			0
$4$	−3.86736	−	2.80980i	−1.93368	−	1.40490i
$5$	−1.33452	−	4.10723i	−0.596815	−	1.83681i	−0.545474	−	0.838128i	$-0.683650\pi$
$5$	−1.33452	−	4.10723i	−0.596815	−	1.83681i	−0.0513414	−	0.998681i	$-0.516350\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−5.85703	+	4.25538i	−2.07077	+	1.50450i
$9$		0			0
$10$	−11.2452			−3.55605
$11$	3.29379	−	0.388483i	0.993116	−	0.117132i
$11$	3.29379	−	0.388483i	0.993116	−	0.117132i
$12$		0			0
$13$	−0.761506	+	2.34367i	−0.211204	+	0.650018i	0.788198	+	0.615422i	$0.211014\pi$
$13$	−0.761506	+	2.34367i	−0.211204	+	0.650018i	−0.999401	+	0.0345961i	$0.988986\pi$
$14$	−2.10660	+	1.53054i	−0.563013	+	0.409053i
$15$		0			0
$16$	2.87102	+	8.83609i	0.717755	+	2.20902i
$17$	−0.366661	−	1.12847i	−0.0889284	−	0.273694i	0.896695	−	0.442648i	$-0.145961\pi$
$17$	−0.366661	−	1.12847i	−0.0889284	−	0.273694i	−0.985624	+	0.168955i	$0.945961\pi$
$18$		0			0
$19$	2.77243	−	2.01429i	0.636039	−	0.462110i	−0.222448	−	0.974945i	$-0.571405\pi$
$19$	2.77243	−	2.01429i	0.636039	−	0.462110i	0.858487	+	0.512835i	$0.171405\pi$
$20$	−6.37943	+	19.6339i	−1.42648	+	4.39027i
$21$		0			0
$22$	1.68829	−	8.46954i	0.359945	−	1.80571i
$23$	8.32084			1.73501			0.867507	−	0.497425i	$-0.165721\pi$
$23$	8.32084			1.73501			0.867507	+	0.497425i	$0.165721\pi$
$24$		0			0
$25$	−11.0433	+	8.02343i	−2.20866	+	1.60469i
$26$	5.19127	+	3.77168i	1.01809	+	0.739687i
$27$		0			0
$28$	1.47720	+	4.54635i	0.279165	+	0.859180i
$29$	−1.17608	−	0.854470i	−0.218392	−	0.158671i	0.473211	−	0.880949i	$-0.343095\pi$
$29$	−1.17608	−	0.854470i	−0.218392	−	0.158671i	−0.691603	+	0.722278i	$0.743095\pi$
$30$		0			0
$31$	0.923391	−	2.84191i	0.165846	−	0.510421i	−0.833252	−	0.552894i	$-0.813523\pi$
$31$	0.923391	−	2.84191i	0.165846	−	0.510421i	0.999098	+	0.0424725i	$0.0135235\pi$
$32$	9.71302			1.71704
$33$		0			0
$34$	−3.08964			−0.529869
$35$	−1.33452	+	4.10723i	−0.225575	+	0.694249i
$36$		0			0
$37$	−5.13219	−	3.72875i	−0.843727	−	0.613003i	0.0796825	−	0.996820i	$-0.474609\pi$
$37$	−5.13219	−	3.72875i	−0.843727	−	0.613003i	−0.923409	+	0.383817i	$0.874609\pi$
$38$	−2.75747	−	8.48661i	−0.447320	−	1.37671i
$39$		0			0
$40$	25.2941	+	18.3773i	3.99936	+	2.90570i
$41$	4.98751	−	3.62364i	0.778918	−	0.565917i	−0.125736	−	0.992064i	$-0.540129\pi$
$41$	4.98751	−	3.62364i	0.778918	−	0.565917i	0.904654	+	0.426147i	$0.140129\pi$
$42$		0			0
$43$	3.15289			0.480811			0.240406	−	0.970673i	$-0.422720\pi$
$43$	3.15289			0.480811			0.240406	+	0.970673i	$0.422720\pi$
$44$	−13.8298	−	7.75250i	−2.08493	−	1.16873i
$45$		0			0
$46$	6.69537	−	20.6062i	0.987178	−	3.03822i
$47$	−7.06675	+	5.13430i	−1.03079	+	0.748914i	−0.968467	−	0.249142i	$-0.919851\pi$
$47$	−7.06675	+	5.13430i	−1.03079	+	0.748914i	−0.0623247	+	0.998056i	$0.519851\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	10.9837	+	33.8044i	1.55333	+	4.78066i
$51$		0			0
$52$	9.53028	−	6.92415i	1.32161	−	0.960207i
$53$	−2.06473	+	6.35457i	−0.283612	+	0.872868i	0.703199	+	0.710993i	$0.251754\pi$
$53$	−2.06473	+	6.35457i	−0.283612	+	0.872868i	−0.986811	+	0.161875i	$0.948246\pi$
$54$		0			0
$55$	−5.99122	−	13.0099i	−0.807856	−	1.75426i
$56$	7.23969			0.967444
$57$		0			0
$58$	−3.06239	+	2.22496i	−0.402112	+	0.292151i
$59$	−9.50987	−	6.90932i	−1.23808	−	0.899517i	−0.240610	−	0.970622i	$-0.577348\pi$
$59$	−9.50987	−	6.90932i	−1.23808	−	0.899517i	−0.997469	+	0.0711045i	$0.977348\pi$
$60$		0			0
$61$	2.40078	+	7.38884i	0.307388	+	0.946044i	0.978775	+	0.204937i	$0.0656989\pi$
$61$	2.40078	+	7.38884i	0.307388	+	0.946044i	−0.671387	+	0.741107i	$0.734301\pi$
$62$	−6.29486	−	4.57348i	−0.799448	−	0.580833i
$63$		0			0
$64$	2.07355	−	6.38173i	0.259194	−	0.797717i
$65$	10.6423			1.32001
$66$		0			0
$67$	3.11080			0.380045			0.190022	−	0.981780i	$-0.439144\pi$
$67$	3.11080			0.380045			0.190022	+	0.981780i	$0.439144\pi$
$68$	−1.75276	+	5.39443i	−0.212553	+	0.654171i
$69$		0			0
$70$	9.09757	+	6.60977i	1.08737	+	0.790019i
$71$	1.69576	+	5.21901i	0.201250	+	0.619383i	0.999847	+	0.0175166i	$0.00557599\pi$
$71$	1.69576	+	5.21901i	0.201250	+	0.619383i	−0.798597	+	0.601866i	$0.794424\pi$
$72$		0			0
$73$	−7.00611	−	5.09024i	−0.820003	−	0.595767i	0.0967102	−	0.995313i	$-0.469168\pi$
$73$	−7.00611	−	5.09024i	−0.820003	−	0.595767i	−0.916713	+	0.399545i	$0.869168\pi$
$74$	−13.3637	+	9.70932i	−1.55350	+	1.12869i
$75$		0			0
$76$	−16.3817			−1.87911
$77$	−2.89308	−	1.62175i	−0.329697	−	0.184816i
$78$		0			0
$79$	−2.73036	+	8.40318i	−0.307189	+	0.945432i	0.671662	+	0.740858i	$0.265581\pi$
$79$	−2.73036	+	8.40318i	−0.307189	+	0.945432i	−0.978851	+	0.204574i	$0.934419\pi$
$80$	32.4604	−	23.5839i	3.62918	−	2.63676i
$81$		0			0
$82$	−4.96059	−	15.2671i	−0.547806	−	1.68597i
$83$	−2.98622	−	9.19065i	−0.327781	−	1.00881i	−0.970170	−	0.242427i	$-0.922057\pi$
$83$	−2.98622	−	9.19065i	−0.327781	−	1.00881i	0.642389	−	0.766379i	$-0.277943\pi$
$84$		0			0
$85$	−4.14556	+	3.01192i	−0.449649	+	0.326689i
$86$	2.53698	−	7.80801i	0.273569	−	0.841959i
$87$		0			0
$88$	−17.6387	+	16.2917i	−1.88029	+	1.73670i
$89$	0.985558			0.104469			0.0522345	−	0.998635i	$-0.483366\pi$
$89$	0.985558			0.104469			0.0522345	+	0.998635i	$0.483366\pi$
$90$		0			0
$91$	1.99365	−	1.44847i	0.208991	−	0.151841i
$92$	−32.1797	−	23.3799i	−3.35496	−	2.43752i
$93$		0			0
$94$	7.02861	+	21.6318i	0.724946	+	2.23115i
$95$	−11.9730	−	8.69890i	−1.22840	−	0.892488i
$96$		0			0
$97$	2.15458	−	6.63113i	0.218765	−	0.673289i	−0.780100	−	0.625655i	$-0.784832\pi$
$97$	2.15458	−	6.63113i	0.218765	−	0.673289i	0.998865	−	0.0476341i	$-0.0151681\pi$
$98$	2.60390			0.263034
$99$		0			0
$100$	65.2527			6.52527
$101$	5.15771	−	15.8738i	0.513212	−	1.57950i	−0.273300	−	0.961929i	$-0.588115\pi$
$101$	5.15771	−	15.8738i	0.513212	−	1.57950i	0.786512	−	0.617575i	$-0.211885\pi$
$102$		0			0
$103$	−9.36699	−	6.80552i	−0.922957	−	0.670568i	0.0213010	−	0.999773i	$-0.493219\pi$
$103$	−9.36699	−	6.80552i	−0.922957	−	0.670568i	−0.944258	+	0.329205i	$0.893219\pi$
$104$	−5.51306	−	16.9675i	−0.540600	−	1.66380i
$105$		0			0
$106$	14.0755	+	10.2264i	1.36713	+	0.993278i
$107$	4.86693	−	3.53603i	0.470504	−	0.341841i	−0.327134	−	0.944978i	$-0.606083\pi$
$107$	4.86693	−	3.53603i	0.470504	−	0.341841i	0.797638	+	0.603137i	$0.206083\pi$
$108$		0			0
$109$	6.68101			0.639924			0.319962	−	0.947430i	$-0.396330\pi$
$109$	6.68101			0.639924			0.319962	+	0.947430i	$0.396330\pi$
$110$	−37.0394	+	4.36857i	−3.53157	+	0.416527i
$111$		0			0
$112$	2.87102	−	8.83609i	0.271286	−	0.834932i
$113$	15.1738	−	11.0244i	1.42743	−	1.03709i	0.436939	−	0.899491i	$-0.356063\pi$
$113$	15.1738	−	11.0244i	1.42743	−	1.03709i	0.990488	−	0.137596i	$-0.0439375\pi$
$114$		0			0
$115$	−11.1043	−	34.1756i	−1.03548	−	3.18689i
$116$	2.14742	+	6.60909i	0.199383	+	0.613638i
$117$		0			0
$118$	−24.7628	+	17.9912i	−2.27960	+	1.65623i
$119$	−0.366661	+	1.12847i	−0.0336118	+	0.103446i
$120$		0			0
$121$	10.6982	−	2.55917i	0.972560	−	0.232651i
$122$	20.2300			1.83153
$123$		0			0
$124$	−11.5563	+	8.39613i	−1.03778	+	0.753994i
$125$	30.2225	+	21.9579i	2.70318	+	1.96398i
$126$		0			0
$127$	0.979590	+	3.01487i	0.0869246	+	0.267526i	0.985065	−	0.172182i	$-0.0550818\pi$
$127$	0.979590	+	3.01487i	0.0869246	+	0.267526i	−0.898141	+	0.439709i	$0.855082\pi$
$128$	1.58037	+	1.14821i	0.139686	+	0.101488i
$129$		0			0
$130$	8.56330	−	26.3551i	0.751051	−	2.31150i
$131$	7.83376			0.684439			0.342220	−	0.939620i	$-0.388821\pi$
$131$	7.83376			0.684439			0.342220	+	0.939620i	$0.388821\pi$
$132$		0			0
$133$	−3.42691			−0.297151
$134$	2.50311	−	7.70377i	0.216236	−	0.665505i
$135$		0			0
$136$	6.94960	+	5.04918i	0.595924	+	0.432964i
$137$	2.22097	+	6.83545i	0.189750	+	0.583992i	0.999998	−	0.00209625i	$-0.000667256\pi$
$137$	2.22097	+	6.83545i	0.189750	+	0.583992i	−0.810247	+	0.586088i	$0.800667\pi$
$138$		0			0
$139$	−2.72478	−	1.97967i	−0.231113	−	0.167913i	0.466202	−	0.884678i	$-0.345622\pi$
$139$	−2.72478	−	1.97967i	−0.231113	−	0.167913i	−0.697315	+	0.716765i	$0.745622\pi$
$140$	16.7016	−	12.1344i	1.41154	−	1.02554i
$141$		0			0
$142$	14.2892			1.19912
$143$	−1.59777	+	8.01541i	−0.133612	+	0.670283i
$144$		0			0
$145$	−1.94001	+	5.97073i	−0.161109	+	0.495842i
$146$	−18.2432	+	13.2545i	−1.50982	+	1.09695i
$147$		0			0
$148$	9.37096	+	28.8409i	0.770288	+	2.37070i
$149$	−5.75496	−	17.7120i	−0.471465	−	1.45102i	−0.850666	−	0.525706i	$-0.823801\pi$
$149$	−5.75496	−	17.7120i	−0.471465	−	1.45102i	0.379201	−	0.925314i	$-0.376199\pi$
$150$		0			0
$151$	−11.6697	+	8.47850i	−0.949663	+	0.689971i	−0.950727	−	0.310029i	$-0.899661\pi$
$151$	−11.6697	+	8.47850i	−0.949663	+	0.689971i	0.00106385	+	0.999999i	$0.499661\pi$
$152$	−7.66664	+	23.5955i	−0.621847	+	1.91385i
$153$		0			0
$154$	−6.34413	+	5.85965i	−0.511225	+	0.472184i
$155$	−12.9046			−1.03653
$156$		0			0
$157$	−4.29957	+	3.12382i	−0.343143	+	0.249308i	−0.745987	−	0.665961i	$-0.768022\pi$
$157$	−4.29957	+	3.12382i	−0.343143	+	0.249308i	0.402844	+	0.915269i	$0.368022\pi$
$158$	18.6132	+	13.5233i	1.48078	+	1.07585i
$159$		0			0
$160$	−12.9622	−	39.8936i	−1.02475	−	3.15387i
$161$	−6.73170	−	4.89087i	−0.530532	−	0.385454i
$162$		0			0
$163$	0.280072	−	0.861973i	0.0219369	−	0.0675149i	−0.939489	−	0.342580i	$-0.888699\pi$
$163$	0.280072	−	0.861973i	0.0219369	−	0.0675149i	0.961426	+	0.275065i	$0.0886993\pi$
$164$	−29.4702			−2.30123
$165$		0			0
$166$	−25.1632			−1.95304
$167$	3.59801	−	11.0735i	0.278422	−	0.856896i	−0.709871	−	0.704332i	$-0.751247\pi$
$167$	3.59801	−	11.0735i	0.278422	−	0.856896i	0.988294	−	0.152564i	$-0.0487531\pi$
$168$		0			0
$169$	5.60430	+	4.07176i	0.431100	+	0.313213i
$170$	4.12318	+	12.6899i	0.316234	+	0.973268i
$171$		0			0
$172$	−12.1934	−	8.85899i	−0.929735	−	0.675492i
$173$	5.54210	−	4.02657i	0.421358	−	0.306135i	−0.356826	−	0.934171i	$-0.616141\pi$
$173$	5.54210	−	4.02657i	0.421358	−	0.306135i	0.778184	+	0.628036i	$0.216141\pi$
$174$		0			0
$175$	13.6503			1.03186
$176$	12.8892	+	27.9889i	0.971561	+	2.10974i
$177$		0			0
$178$	0.793030	−	2.44070i	0.0594401	−	0.182938i
$179$	6.80593	−	4.94480i	0.508699	−	0.369592i	−0.303631	−	0.952790i	$-0.598199\pi$
$179$	6.80593	−	4.94480i	0.508699	−	0.369592i	0.812330	+	0.583198i	$0.198199\pi$
$180$		0			0
$181$	4.02613	+	12.3912i	0.299260	+	0.921028i	0.981757	+	0.190140i	$0.0608940\pi$
$181$	4.02613	+	12.3912i	0.299260	+	0.921028i	−0.682497	+	0.730888i	$0.739106\pi$
$182$	−1.98289	−	6.10270i	−0.146982	−	0.452363i
$183$		0			0
$184$	−48.7354	+	35.4083i	−3.59282	+	2.61034i
$185$	−8.46584	+	26.0552i	−0.622421	+	1.91561i
$186$		0			0
$187$	−1.64610	−	3.57450i	−0.120375	−	0.261393i
$188$	41.7560			3.04537
$189$		0			0
$190$	−31.1766	+	22.6511i	−2.26179	+	1.64328i
$191$	−2.79720	−	2.03229i	−0.202399	−	0.147051i	0.481969	−	0.876188i	$-0.339922\pi$
$191$	−2.79720	−	2.03229i	−0.202399	−	0.147051i	−0.684368	+	0.729137i	$0.739922\pi$
$192$		0			0
$193$	5.26789	+	16.2129i	0.379191	+	1.16703i	0.940607	+	0.339496i	$0.110257\pi$
$193$	5.26789	+	16.2129i	0.379191	+	1.16703i	−0.561417	+	0.827533i	$0.689743\pi$
$194$	−14.6880	−	10.6715i	−1.05454	−	0.766168i
$195$		0			0
$196$	1.47720	−	4.54635i	0.105514	−	0.324740i
$197$	−3.47970			−0.247918			−0.123959	−	0.992287i	$-0.539559\pi$
$197$	−3.47970			−0.247918			−0.123959	+	0.992287i	$0.539559\pi$
$198$		0			0
$199$	8.20279			0.581481			0.290740	−	0.956802i	$-0.406098\pi$
$199$	8.20279			0.581481			0.290740	+	0.956802i	$0.406098\pi$
$200$	30.5382	−	93.9869i	2.15938	−	6.64588i
$201$		0			0
$202$	−35.1607	−	25.5458i	−2.47390	−	1.79739i
$203$	0.449222	+	1.38256i	0.0315292	+	0.0970368i
$204$		0			0
$205$	−21.5390	−	15.6490i	−1.50435	−	1.09298i
$206$	−24.3908	+	17.7209i	−1.69938	+	1.23468i
$207$		0			0
$208$	−22.8952			−1.58750
$209$	8.34930	−	7.71169i	0.577533	−	0.533429i
$210$		0			0
$211$	6.86611	−	21.1317i	0.472683	−	1.45477i	−0.376375	−	0.926467i	$-0.622830\pi$
$211$	6.86611	−	21.1317i	0.472683	−	1.45477i	0.849058	−	0.528300i	$-0.177170\pi$
$212$	25.8401	−	18.7739i	1.77471	−	1.28940i
$213$		0			0
$214$	−4.84067	−	14.8980i	−0.330901	−	1.01841i
$215$	−4.20759	−	12.9496i	−0.286955	−	0.883158i
$216$		0			0
$217$	−2.41747	+	1.75639i	−0.164109	+	0.119232i
$218$	5.37588	−	16.5453i	0.364100	−	1.12059i
$219$		0			0
$220$	−13.3851	+	67.1482i	−0.902424	+	4.52713i
$221$	2.92397			0.196688
$222$		0			0
$223$	−17.6651	+	12.8345i	−1.18294	+	0.859459i	−0.992501	−	0.122239i	$-0.960993\pi$
$223$	−17.6651	+	12.8345i	−1.18294	+	0.859459i	−0.190444	+	0.981698i	$0.560993\pi$
$224$	−7.85800	−	5.70917i	−0.525035	−	0.381460i
$225$		0			0
$226$	−15.0919	−	46.4480i	−1.00390	−	3.08968i
$227$	19.7164	+	14.3248i	1.30862	+	0.950771i	1.00000		0.000413245i	$-0.000131540\pi$
$227$	19.7164	+	14.3248i	1.30862	+	0.950771i	0.308624	+	0.951184i	$0.400132\pi$
$228$		0			0
$229$	−0.797689	+	2.45503i	−0.0527127	+	0.162233i	−0.973947	−	0.226774i	$-0.927182\pi$
$229$	−0.797689	+	2.45503i	−0.0527127	+	0.162233i	0.921235	+	0.389008i	$0.127182\pi$
$230$	−93.5696			−6.16980
$231$		0			0
$232$	10.5244			0.690962
$233$	−4.40489	+	13.5569i	−0.288574	+	0.888140i	0.696730	+	0.717333i	$0.254637\pi$
$233$	−4.40489	+	13.5569i	−0.288574	+	0.888140i	−0.985305	+	0.170807i	$0.945363\pi$
$234$		0			0
$235$	30.5185	+	22.1730i	1.99080	+	1.44640i
$236$	17.3643	+	53.4417i	1.13032	+	3.47876i
$237$		0			0
$238$	2.49957	+	1.81604i	0.162023	+	0.117717i
$239$	8.93861	−	6.49428i	0.578191	−	0.420080i	−0.259881	−	0.965641i	$-0.583683\pi$
$239$	8.93861	−	6.49428i	0.578191	−	0.420080i	0.838071	+	0.545561i	$0.183683\pi$
$240$		0			0
$241$	−11.0131			−0.709419			−0.354709	−	0.934977i	$-0.615420\pi$
$241$	−11.0131			−0.709419			−0.354709	+	0.934977i	$0.615420\pi$
$242$	2.27061	−	28.5528i	0.145960	−	1.83544i
$243$		0			0
$244$	11.4765	−	35.3210i	0.734707	−	2.26120i
$245$	3.49382	−	2.53841i	0.223212	−	0.162173i
$246$		0			0
$247$	2.60961	+	8.03157i	0.166046	+	0.511036i
$248$	6.68506	+	20.5745i	0.424502	+	1.30648i
$249$		0			0
$250$	78.6965	−	57.1764i	4.97720	−	3.61615i
$251$	−3.49099	+	10.7441i	−0.220349	+	0.678165i	0.778381	+	0.627792i	$0.216041\pi$
$251$	−3.49099	+	10.7441i	−0.220349	+	0.678165i	−0.998730	+	0.0503730i	$0.983959\pi$
$252$		0			0
$253$	27.4071	−	3.23250i	1.72307	−	0.203226i
$254$	8.25443			0.517929
$255$		0			0
$256$	14.9724	−	10.8781i	0.935774	−	0.679880i
$257$	−4.13397	−	3.00350i	−0.257870	−	0.187353i	0.451338	−	0.892353i	$-0.350947\pi$
$257$	−4.13397	−	3.00350i	−0.257870	−	0.187353i	−0.709207	+	0.705000i	$0.750947\pi$
$258$		0			0
$259$	1.96032	+	6.03325i	0.121808	+	0.374888i
$260$	−41.1574	−	29.9026i	−2.55247	−	1.85448i
$261$		0			0
$262$	6.30344	−	19.4000i	0.389428	−	1.19854i
$263$	−6.56589			−0.404870			−0.202435	−	0.979296i	$-0.564885\pi$
$263$	−6.56589			−0.404870			−0.202435	+	0.979296i	$0.564885\pi$
$264$		0			0
$265$	28.8551			1.77256
$266$	−2.75747	+	8.48661i	−0.169071	+	0.520348i
$267$		0			0
$268$	−12.0306	−	8.74073i	−0.734885	−	0.533925i
$269$	−3.58748	−	11.0411i	−0.218732	−	0.673189i	−0.998868	−	0.0475779i	$-0.984850\pi$
$269$	−3.58748	−	11.0411i	−0.218732	−	0.673189i	0.780135	−	0.625611i	$-0.215150\pi$
$270$		0			0
$271$	11.8705	+	8.62444i	0.721083	+	0.523897i	0.886730	−	0.462288i	$-0.152971\pi$
$271$	11.8705	+	8.62444i	0.721083	+	0.523897i	−0.165647	+	0.986185i	$0.552971\pi$
$272$	8.91855	−	6.47970i	0.540766	−	0.392890i
$273$		0			0
$274$	18.7148			1.13060
$275$	−33.2574	+	30.7177i	−2.00550	+	1.85235i
$276$		0			0
$277$	−7.19248	+	22.1362i	−0.432154	+	1.33003i	0.463820	+	0.885929i	$0.346478\pi$
$277$	−7.19248	+	22.1362i	−0.432154	+	1.33003i	−0.895975	+	0.444105i	$0.853522\pi$
$278$	−7.09507	+	5.15487i	−0.425534	+	0.309169i
$279$		0			0
$280$	−9.66150	−	29.7351i	−0.577385	−	1.77701i
$281$	−3.15549	−	9.71160i	−0.188241	−	0.579345i	0.811748	−	0.584007i	$-0.198516\pi$
$281$	−3.15549	−	9.71160i	−0.188241	−	0.579345i	−0.999989	+	0.00466199i	$0.998516\pi$
$282$		0			0
$283$	5.19055	−	3.77115i	0.308546	−	0.224172i	−0.422726	−	0.906257i	$-0.638927\pi$
$283$	5.19055	−	3.77115i	0.308546	−	0.224172i	0.731272	+	0.682086i	$0.238927\pi$
$284$	8.10627	−	24.9485i	0.481019	−	1.48042i
$285$		0			0
$286$	18.5642	+	10.4064i	1.09772	+	0.615344i
$287$	−6.16490			−0.363902
$288$		0			0
$289$	12.6143	−	9.16482i	0.742017	−	0.539107i
$290$	13.2252	+	9.60870i	0.776613	+	0.564242i
$291$		0			0
$292$	12.7926	+	39.3716i	0.748630	+	2.30405i
$293$	−12.7704	−	9.27824i	−0.746055	−	0.542040i	0.148547	−	0.988905i	$-0.452540\pi$
$293$	−12.7704	−	9.27824i	−0.746055	−	0.542040i	−0.894601	+	0.446865i	$0.852540\pi$
$294$		0			0
$295$	−15.6871	+	48.2798i	−0.913337	+	2.81096i
$296$	45.9266			2.66943
$297$		0			0
$298$	−48.4937			−2.80916
$299$	−6.33637	+	19.5013i	−0.366442	+	1.12779i
$300$		0			0
$301$	−2.55074	−	1.85322i	−0.147022	−	0.106818i
$302$	11.6067	+	35.7217i	0.667889	+	2.05555i
$303$		0			0
$304$	25.7581	+	18.7144i	1.47733	+	1.07334i
$305$	27.1438	−	19.7211i	1.55425	−	1.12923i
$306$		0			0
$307$	17.4204			0.994235			0.497117	−	0.867683i	$-0.334392\pi$
$307$	17.4204			0.994235			0.497117	+	0.867683i	$0.334392\pi$
$308$	6.63177	+	14.4009i	0.377880	+	0.820567i
$309$		0			0
$310$	−10.3837	+	31.9578i	−0.589756	+	1.81508i
$311$	−10.6750	+	7.75584i	−0.605323	+	0.439793i	−0.847764	−	0.530373i	$-0.822052\pi$
$311$	−10.6750	+	7.75584i	−0.605323	+	0.439793i	0.242441	+	0.970166i	$0.422052\pi$
$312$		0			0
$313$	5.56661	+	17.1323i	0.314644	+	0.968373i	0.975901	+	0.218214i	$0.0700232\pi$
$313$	5.56661	+	17.1323i	0.314644	+	0.968373i	−0.661257	+	0.750159i	$0.729977\pi$
$314$	4.27637	+	13.1613i	0.241329	+	0.742736i
$315$		0			0
$316$	34.1705	−	24.8264i	1.92224	−	1.39659i
$317$	−2.07176	+	6.37621i	−0.116361	+	0.358124i	−0.992229	−	0.124429i	$-0.960290\pi$
$317$	−2.07176	+	6.37621i	−0.116361	+	0.358124i	0.875867	+	0.482552i	$0.160290\pi$
$318$		0			0
$319$	−4.20570	−	2.35756i	−0.235474	−	0.131998i
$320$	−28.9784			−1.61994
$321$		0			0
$322$	−17.5287	+	12.7353i	−0.976836	+	0.709713i
$323$	−3.28960	−	2.39004i	−0.183038	−	0.132985i
$324$		0			0
$325$	−10.3948	−	31.9918i	−0.576598	−	1.77459i
$326$	−1.90928	−	1.38717i	−0.105745	−	0.0768285i
$327$		0			0
$328$	−13.7920	+	42.4475i	−0.761537	+	2.34377i
$329$	8.73499			0.481575
$330$		0			0
$331$	3.96252			0.217800			0.108900	−	0.994053i	$-0.465267\pi$
$331$	3.96252			0.217800			0.108900	+	0.994053i	$0.465267\pi$
$332$	−14.2751	+	43.9343i	−0.783448	+	2.41121i
$333$		0			0
$334$	−24.5280	−	17.8207i	−1.34211	−	0.975103i
$335$	−4.15142	−	12.7768i	−0.226817	−	0.698069i
$336$		0			0
$337$	9.91886	+	7.20647i	0.540315	+	0.392562i	0.824202	−	0.566296i	$-0.191624\pi$
$337$	9.91886	+	7.20647i	0.540315	+	0.392562i	−0.283887	+	0.958858i	$0.591624\pi$
$338$	14.5931	−	10.6025i	0.793758	−	0.576699i
$339$		0			0
$340$	24.4953			1.32844
$341$	1.93743	−	9.71937i	0.104918	−	0.526334i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−18.4666	+	13.4167i	−0.995651	+	0.723382i
$345$		0			0
$346$	−5.51219	−	16.9648i	−0.296337	−	0.912033i
$347$	−3.53014	−	10.8647i	−0.189508	−	0.583245i	0.810489	−	0.585754i	$-0.199202\pi$
$347$	−3.53014	−	10.8647i	−0.189508	−	0.583245i	−0.999997	+	0.00250851i	$0.999202\pi$
$348$		0			0
$349$	23.6506	−	17.1832i	1.26599	−	0.919796i	0.266955	−	0.963709i	$-0.413983\pi$
$349$	23.6506	−	17.1832i	1.26599	−	0.919796i	0.999035	+	0.0439135i	$0.0139826\pi$
$350$	10.9837	−	33.8044i	0.587104	−	1.80692i
$351$		0			0
$352$	31.9927	−	3.77334i	1.70522	−	0.201120i
$353$	7.76081			0.413066			0.206533	−	0.978440i	$-0.433782\pi$
$353$	7.76081			0.413066			0.206533	+	0.978440i	$0.433782\pi$
$354$		0			0
$355$	19.1727	−	13.9298i	1.01758	−	0.739314i
$356$	−3.81151	−	2.76922i	−0.202009	−	0.146768i
$357$		0			0
$358$	−6.76920	−	20.8335i	−0.357763	−	1.10108i
$359$	−24.2457	−	17.6155i	−1.27964	−	0.929712i	−0.280096	−	0.959972i	$-0.590366\pi$
$359$	−24.2457	−	17.6155i	−1.27964	−	0.929712i	−0.999542	+	0.0302604i	$0.990366\pi$
$360$		0			0
$361$	−2.24231	+	6.90112i	−0.118016	+	0.363217i
$362$	33.9259			1.78310
$363$		0			0
$364$	−11.7801			−0.617443
$365$	−11.5570	+	35.5687i	−0.604920	+	1.86175i
$366$		0			0
$367$	2.49751	+	1.81455i	0.130369	+	0.0947187i	0.651059	−	0.759027i	$-0.274325\pi$
$367$	2.49751	+	1.81455i	0.130369	+	0.0947187i	−0.520690	+	0.853746i	$0.674325\pi$
$368$	23.8893	+	73.5237i	1.24531	+	3.83269i
$369$		0			0
$370$	57.7126	+	41.9306i	3.00033	+	2.17987i
$371$	5.40552	−	3.92734i	0.280641	−	0.203897i
$372$		0			0
$373$	29.2948			1.51683			0.758413	−	0.651774i	$-0.225975\pi$
$373$	29.2948			1.51683			0.758413	+	0.651774i	$0.225975\pi$
$374$	−10.1766	+	1.20027i	−0.526221	+	0.0620646i
$375$		0			0
$376$	19.5418	−	60.1434i	1.00779	−	3.10166i
$377$	2.89819	−	2.10566i	0.149264	−	0.108447i
$378$		0			0
$379$	4.84753	+	14.9192i	0.249001	+	0.766346i	0.994953	+	0.100346i	$0.0319950\pi$
$379$	4.84753	+	14.9192i	0.249001	+	0.766346i	−0.745952	+	0.666000i	$0.768005\pi$
$380$	21.8618	+	67.2835i	1.12148	+	3.45157i
$381$		0			0
$382$	−7.28365	+	5.29188i	−0.372664	+	0.270756i
$383$	2.48323	−	7.64260i	0.126887	−	0.390518i	−0.867353	−	0.497693i	$-0.834180\pi$
$383$	2.48323	−	7.64260i	0.126887	−	0.390518i	0.994240	+	0.107175i	$0.0341805\pi$
$384$		0			0
$385$	−2.80004	+	14.0468i	−0.142703	+	0.715892i
$386$	44.3894			2.25936
$387$		0			0
$388$	−26.9647	+	19.5910i	−1.36892	+	0.994582i
$389$	23.2895	+	16.9208i	1.18082	+	0.857918i	0.992264	−	0.124143i	$-0.0396183\pi$
$389$	23.2895	+	16.9208i	1.18082	+	0.857918i	0.188559	+	0.982062i	$0.439618\pi$
$390$		0			0
$391$	−3.05093	−	9.38979i	−0.154292	−	0.474862i
$392$	−5.85703	−	4.25538i	−0.295825	−	0.214929i
$393$		0			0
$394$	−2.79994	+	8.61734i	−0.141059	+	0.434135i
$395$	38.1575			1.91991
$396$		0			0
$397$	−33.7315			−1.69293			−0.846467	−	0.532441i	$-0.821275\pi$
$397$	−33.7315			−1.69293			−0.846467	+	0.532441i	$0.821275\pi$
$398$	6.60038	−	20.3139i	0.330847	−	1.01824i
$399$		0			0
$400$	−102.601	−	74.5442i	−5.13007	−	3.72721i
$401$	0.285702	+	0.879301i	0.0142673	+	0.0439102i	0.957937	−	0.286980i	$-0.0926512\pi$
$401$	0.285702	+	0.879301i	0.0142673	+	0.0439102i	−0.943669	+	0.330890i	$0.892651\pi$
$402$		0			0
$403$	5.95733	+	4.32826i	0.296756	+	0.215606i
$404$	−64.5490	+	46.8976i	−3.21143	+	2.33324i
$405$		0			0
$406$	3.78533			0.187863
$407$	−18.3529	−	10.2880i	−0.909721	−	0.509956i
$408$		0			0
$409$	7.97025	−	24.5299i	0.394104	−	1.21293i	−0.535554	−	0.844501i	$-0.679897\pi$
$409$	7.97025	−	24.5299i	0.394104	−	1.21293i	0.929657	−	0.368425i	$-0.120103\pi$
$410$	−56.0856	+	40.7486i	−2.76987	+	2.01243i
$411$		0			0
$412$	17.1034	+	52.6388i	0.842623	+	2.59333i
$413$	3.63245	+	11.1795i	0.178741	+	0.550108i
$414$		0			0
$415$	−33.7630	+	24.5302i	−1.65736	+	1.20414i
$416$	−7.39652	+	22.7642i	−0.362644	+	1.11610i
$417$		0			0
$418$	−12.3794	−	26.8819i	−0.605498	−	1.31484i
$419$	9.41300			0.459855			0.229928	−	0.973208i	$-0.426151\pi$
$419$	9.41300			0.459855			0.229928	+	0.973208i	$0.426151\pi$
$420$		0			0
$421$	23.7078	−	17.2247i	1.15545	−	0.839483i	0.166253	−	0.986083i	$-0.446833\pi$
$421$	23.7078	−	17.2247i	1.15545	−	0.839483i	0.989196	+	0.146600i	$0.0468332\pi$
$422$	−46.8070	−	34.0073i	−2.27853	−	1.65545i
$423$		0			0
$424$	−14.9480	−	46.0051i	−0.725937	−	2.23421i
$425$	13.1033	+	9.52013i	0.635605	+	0.461794i
$426$		0			0
$427$	2.40078	−	7.38884i	0.116182	−	0.357571i
$428$	−28.7577			−1.39006
$429$		0			0
$430$	−35.4549			−1.70979
$431$	2.15592	−	6.63524i	0.103847	−	0.319608i	−0.885611	−	0.464428i	$-0.846260\pi$
$431$	2.15592	−	6.63524i	0.103847	−	0.319608i	0.989458	+	0.144819i	$0.0462601\pi$
$432$		0			0
$433$	−1.07530	−	0.781251i	−0.0516756	−	0.0375445i	0.561648	−	0.827377i	$-0.310168\pi$
$433$	−1.07530	−	0.781251i	−0.0516756	−	0.0375445i	−0.613323	+	0.789832i	$0.710168\pi$
$434$	2.40442	+	7.40005i	0.115416	+	0.355214i
$435$		0			0
$436$	−25.8379	−	18.7723i	−1.23741	−	0.899030i
$437$	23.0689	−	16.7606i	1.10354	−	0.801767i
$438$		0			0
$439$	−3.63801			−0.173633			−0.0868163	−	0.996224i	$-0.527669\pi$
$439$	−3.63801			−0.173633			−0.0868163	+	0.996224i	$0.527669\pi$
$440$	90.4530	+	50.7046i	4.31218	+	2.41725i
$441$		0			0
$442$	2.35278	−	7.24111i	0.111910	−	0.344424i
$443$	−10.8489	+	7.88216i	−0.515445	+	0.374493i	−0.814885	−	0.579622i	$-0.803200\pi$
$443$	−10.8489	+	7.88216i	−0.515445	+	0.374493i	0.299440	+	0.954115i	$0.403200\pi$
$444$		0			0
$445$	−1.31525	−	4.04791i	−0.0623487	−	0.191889i
$446$	17.5698	+	54.0743i	0.831954	+	2.56049i
$447$		0			0
$448$	−5.42863	+	3.94413i	−0.256479	+	0.186343i
$449$	4.63503	−	14.2651i	0.218740	−	0.673214i	−0.780126	−	0.625622i	$-0.784845\pi$
$449$	4.63503	−	14.2651i	0.218740	−	0.673214i	0.998867	−	0.0475920i	$-0.0151547\pi$
$450$		0			0
$451$	15.0201	−	13.8731i	0.707269	−	0.653258i
$452$	−89.6587			−4.21719
$453$		0			0
$454$	51.3396	−	37.3004i	2.40949	−	1.75060i
$455$	−8.60976	−	6.25536i	−0.403632	−	0.293256i
$456$		0			0
$457$	−6.09138	−	18.7473i	−0.284943	−	0.876963i	−0.986416	−	0.164267i	$-0.947474\pi$
$457$	−6.09138	−	18.7473i	−0.284943	−	0.876963i	0.701473	−	0.712696i	$-0.252526\pi$
$458$	5.43793	+	3.95089i	0.254098	+	0.184613i
$459$		0			0
$460$	−53.0822	+	163.370i	−2.47497	+	7.61718i
$461$	16.3627			0.762086			0.381043	−	0.924557i	$-0.375565\pi$
$461$	16.3627			0.762086			0.381043	+	0.924557i	$0.375565\pi$
$462$		0			0
$463$	−7.48587			−0.347898			−0.173949	−	0.984755i	$-0.555653\pi$
$463$	−7.48587			−0.347898			−0.173949	+	0.984755i	$0.555653\pi$
$464$	4.17363	−	12.8451i	0.193756	−	0.596320i
$465$		0			0
$466$	30.0286	+	21.8171i	1.39105	+	1.01066i
$467$	−0.899306	−	2.76778i	−0.0416149	−	0.128078i	0.928091	−	0.372354i	$-0.121449\pi$
$467$	−0.899306	−	2.76778i	−0.0416149	−	0.128078i	−0.969706	+	0.244277i	$0.921449\pi$
$468$		0			0
$469$	−2.51669	−	1.82848i	−0.116210	−	0.0844315i
$470$	79.4671	−	57.7363i	3.66555	−	2.66317i
$471$		0			0
$472$	85.1014			3.91711
$473$	10.3850	−	1.22484i	0.477501	−	0.0563184i
$474$		0			0
$475$	−14.4553	+	44.4888i	−0.663254	+	2.04129i
$476$	4.58878	−	3.33394i	0.210326	−	0.152811i
$477$		0			0
$478$	−8.89037	−	27.3617i	−0.406636	−	1.25150i
$479$	−8.19737	−	25.2289i	−0.374547	−	1.15274i	−0.943784	−	0.330564i	$-0.892761\pi$
$479$	−8.19737	−	25.2289i	−0.374547	−	1.15274i	0.569236	−	0.822174i	$-0.307239\pi$
$480$		0			0
$481$	12.6472	−	9.18871i	0.576662	−	0.418969i
$482$	−8.86173	+	27.2736i	−0.403641	+	1.24228i
$483$		0			0
$484$	−48.5644	−	20.1625i	−2.20747	−	0.916477i
$485$	−30.1109			−1.36727
$486$		0			0
$487$	2.27918	−	1.65592i	0.103280	−	0.0750370i	−0.534947	−	0.844886i	$-0.679668\pi$
$487$	2.27918	−	1.65592i	0.103280	−	0.0750370i	0.638226	+	0.769849i	$0.279668\pi$
$488$	−45.5038	−	33.0604i	−2.05986	−	1.49657i
$489$		0			0
$490$	−3.47496	−	10.6948i	−0.156983	−	0.483143i
$491$	−4.59431	−	3.33796i	−0.207338	−	0.150640i	0.479270	−	0.877667i	$-0.340901\pi$
$491$	−4.59431	−	3.33796i	−0.207338	−	0.150640i	−0.686609	+	0.727027i	$0.740901\pi$
$492$		0			0
$493$	−0.533020	+	1.64047i	−0.0240060	+	0.0738829i
$494$	21.9897			0.989363
$495$		0			0
$496$	27.7624			1.24657
$497$	1.69576	−	5.21901i	0.0760652	−	0.234105i
$498$		0			0
$499$	−28.5542	−	20.7458i	−1.27826	−	0.928711i	−0.278761	−	0.960360i	$-0.589924\pi$
$499$	−28.5542	−	20.7458i	−1.27826	−	0.928711i	−0.999499	+	0.0316498i	$0.989924\pi$
$500$	−55.1838	−	169.838i	−2.46790	−	7.59540i
$501$		0			0
$502$	23.7984	+	17.2906i	1.06218	+	0.771716i
$503$	−23.9962	+	17.4343i	−1.06994	+	0.777357i	−0.975901	−	0.218212i	$-0.929978\pi$
$503$	−23.9962	+	17.4343i	−1.06994	+	0.777357i	−0.0940383	+	0.995569i	$0.529978\pi$
$504$		0			0
$505$	−72.0805			−3.20754
$506$	14.0480	−	70.4737i	0.624510	−	3.13294i
$507$		0			0
$508$	4.68276	−	14.4120i	0.207764	−	0.639431i
$509$	−3.81365	+	2.77078i	−0.169037	+	0.122813i	−0.669087	−	0.743184i	$-0.733315\pi$
$509$	−3.81365	+	2.77078i	−0.169037	+	0.122813i	0.500050	+	0.865996i	$0.333315\pi$
$510$		0			0
$511$	2.67610	+	8.23618i	0.118384	+	0.364347i
$512$	−13.6843	−	42.1159i	−0.604766	−	1.86128i
$513$		0			0
$514$	−10.7645	+	7.82084i	−0.474800	+	0.344962i
$515$	−15.4514	+	47.5545i	−0.680870	+	2.09550i
$516$		0			0
$517$	−21.2818	+	19.6566i	−0.935974	+	0.864497i
$518$	16.5185			0.725780
$519$		0			0
$520$	−62.3320	+	45.2868i	−2.73344	+	1.98596i
$521$	18.3276	+	13.3158i	0.802945	+	0.583374i	0.911777	−	0.410686i	$-0.134711\pi$
$521$	18.3276	+	13.3158i	0.802945	+	0.583374i	−0.108832	+	0.994060i	$0.534711\pi$
$522$		0			0
$523$	−4.65181	−	14.3168i	−0.203410	−	0.626030i	−0.999775	−	0.0212145i	$-0.993247\pi$
$523$	−4.65181	−	14.3168i	−0.203410	−	0.626030i	0.796365	−	0.604816i	$-0.206753\pi$
$524$	−30.2960	−	22.0113i	−1.32349	−	0.961569i
$525$		0			0
$526$	−5.28324	+	16.2602i	−0.230360	+	0.708976i
$527$	−3.54557			−0.154447
$528$		0			0
$529$	46.2363			2.01027
$530$	23.2183	−	71.4585i	1.00854	−	3.10396i
$531$		0			0
$532$	13.2531	+	9.62894i	0.574595	+	0.417468i
$533$	4.69461	+	14.4485i	0.203346	+	0.625835i
$534$		0			0
$535$	−21.0183	−	15.2707i	−0.908701	−	0.660210i
$536$	−18.2200	+	13.2376i	−0.786986	+	0.571779i
$537$		0			0
$538$	−30.2296			−1.30329
$539$	1.38731	+	3.01254i	0.0597556	+	0.129759i
$540$		0			0
$541$	4.81257	−	14.8116i	0.206908	−	0.636799i	−0.792721	−	0.609584i	$-0.791336\pi$
$541$	4.81257	−	14.8116i	0.206908	−	0.636799i	0.999630	−	0.0272144i	$-0.00866368\pi$
$542$	30.9097	−	22.4572i	1.32769	−	0.964620i
$543$		0			0
$544$	−3.56139	−	10.9608i	−0.152693	−	0.469942i
$545$	−8.91594	−	27.4404i	−0.381917	−	1.17542i
$546$		0			0
$547$	−13.7287	+	9.97448i	−0.586997	+	0.426478i	−0.841240	−	0.540662i	$-0.818174\pi$
$547$	−13.7287	+	9.97448i	−0.586997	+	0.426478i	0.254243	+	0.967140i	$0.418174\pi$
$548$	10.6170	−	32.6756i	0.453534	−	1.39583i
$549$		0			0
$550$	49.3105	+	107.078i	2.10261	+	4.56581i
$551$	−4.98174			−0.212229
$552$		0			0
$553$	7.14817	−	5.19345i	0.303971	−	0.220848i
$554$	49.0320	+	35.6238i	2.08317	+	1.51351i
$555$		0			0
$556$	4.97523	+	15.3122i	0.210997	+	0.649381i
$557$	2.15143	+	1.56311i	0.0911591	+	0.0662310i	0.632431	−	0.774617i	$-0.282057\pi$
$557$	2.15143	+	1.56311i	0.0911591	+	0.0662310i	−0.541272	+	0.840848i	$0.682057\pi$
$558$		0			0
$559$	−2.40094	+	7.38935i	−0.101549	+	0.312536i
$560$	−40.1233			−1.69552
$561$		0			0
$562$	−26.5895			−1.12161
$563$	−4.65120	+	14.3149i	−0.196025	+	0.603302i	0.803938	+	0.594712i	$0.202734\pi$
$563$	−4.65120	+	14.3149i	−0.196025	+	0.603302i	−0.999963	+	0.00858929i	$0.997266\pi$
$564$		0			0
$565$	−65.5294	−	47.6099i	−2.75684	−	2.00296i
$566$	−5.16253	−	15.8886i	−0.216997	−	0.667850i
$567$		0			0
$568$	−32.1410	−	23.3518i	−1.34861	−	0.979820i
$569$	−29.7320	+	21.6016i	−1.24643	+	0.905585i	−0.998009	−	0.0630667i	$-0.979912\pi$
$569$	−29.7320	+	21.6016i	−1.24643	+	0.905585i	−0.248422	+	0.968652i	$0.579912\pi$
$570$		0			0
$571$	−3.56292			−0.149104			−0.0745519	−	0.997217i	$-0.523753\pi$
$571$	−3.56292			−0.149104			−0.0745519	+	0.997217i	$0.523753\pi$
$572$	28.7009	−	26.5091i	1.20004	−	1.10840i
$573$		0			0
$574$	−4.96059	+	15.2671i	−0.207051	+	0.637238i
$575$	−91.8895	+	66.7617i	−3.83206	+	2.78415i
$576$		0			0
$577$	6.09657	+	18.7633i	0.253804	+	0.781127i	0.994063	+	0.108806i	$0.0347026\pi$
$577$	6.09657	+	18.7633i	0.253804	+	0.781127i	−0.740260	+	0.672321i	$0.765297\pi$
$578$	−12.5462	−	38.6133i	−0.521854	−	1.60610i
$579$		0			0
$580$	24.2793	−	17.6399i	1.00814	−	0.732458i
$581$	−2.98622	+	9.19065i	−0.123889	+	0.381293i
$582$		0			0
$583$	−4.33214	+	21.7328i	−0.179419	+	0.900079i
$584$	62.6959			2.59437
$585$		0			0
$586$	−33.2529	+	24.1596i	−1.37366	+	0.998026i
$587$	6.75186	+	4.90551i	0.278679	+	0.202472i	0.718341	−	0.695691i	$-0.244902\pi$
$587$	6.75186	+	4.90551i	0.278679	+	0.202472i	−0.439662	+	0.898163i	$0.644902\pi$
$588$		0			0
$589$	−3.16438	−	9.73896i	−0.130386	−	0.401287i
$590$	106.940	+	77.6968i	4.40267	+	3.19873i
$591$		0			0
$592$	18.2130	−	56.0538i	0.748549	−	2.30380i
$593$	−15.7459			−0.646605			−0.323302	−	0.946296i	$-0.604793\pi$
$593$	−15.7459			−0.646605			−0.323302	+	0.946296i	$0.604793\pi$
$594$		0			0
$595$	5.12419			0.210071
$596$	−27.5106	+	84.6688i	−1.12688	+	3.46817i
$597$		0			0
$598$	43.1957	+	31.3835i	1.76640	+	1.28337i
$599$	0.0131088	+	0.0403449i	0.000535613	+	0.00164845i	0.951324	−	0.308193i	$-0.0997241\pi$
$599$	0.0131088	+	0.0403449i	0.000535613	+	0.00164845i	−0.950788	+	0.309841i	$0.899724\pi$
$600$		0			0
$601$	−3.53155	−	2.56582i	−0.144055	−	0.104662i	0.513424	−	0.858135i	$-0.328377\pi$
$601$	−3.53155	−	2.56582i	−0.144055	−	0.104662i	−0.657479	+	0.753473i	$0.728377\pi$
$602$	−6.64189	+	4.82561i	−0.270703	+	0.196677i
$603$		0			0
$604$	68.9537			2.80569
$605$	−24.7880	−	40.5245i	−1.00778	−	1.64756i
$606$		0			0
$607$	−1.07067	+	3.29517i	−0.0434570	+	0.133747i	−0.970431	−	0.241379i	$-0.922400\pi$
$607$	−1.07067	+	3.29517i	−0.0434570	+	0.133747i	0.926974	+	0.375126i	$0.122400\pi$
$608$	26.9287	−	19.5648i	1.09210	−	0.793459i
$609$		0			0
$610$	−26.9973	−	83.0891i	−1.09309	−	3.36418i
$611$	−6.65174	−	20.4720i	−0.269101	−	0.828207i
$612$		0			0
$613$	−5.57773	+	4.05246i	−0.225282	+	0.163677i	−0.694701	−	0.719298i	$-0.744463\pi$
$613$	−5.57773	+	4.05246i	−0.225282	+	0.163677i	0.469419	+	0.882976i	$0.344463\pi$
$614$	14.0173	−	43.1409i	0.565694	−	1.74103i
$615$		0			0
$616$	23.8460	−	2.81249i	0.960784	−	0.113319i
$617$	13.8954			0.559409			0.279705	−	0.960086i	$-0.409763\pi$
$617$	13.8954			0.559409			0.279705	+	0.960086i	$0.409763\pi$
$618$		0			0
$619$	24.8153	−	18.0294i	0.997412	−	0.724662i	0.0358799	−	0.999356i	$-0.488577\pi$
$619$	24.8153	−	18.0294i	0.997412	−	0.724662i	0.961532	+	0.274694i	$0.0885766\pi$
$620$	49.9069	+	36.2595i	2.00431	+	1.45622i
$621$		0			0
$622$	10.6174	+	32.6769i	0.425718	+	1.31023i
$623$	−0.797333	−	0.579296i	−0.0319445	−	0.0232090i
$624$		0			0
$625$	28.7629	−	88.5231i	1.15052	−	3.54092i
$626$	46.9066			1.87476
$627$		0			0
$628$	25.4053			1.01378
$629$	−2.32600	+	7.15870i	−0.0927438	+	0.285436i
$630$		0			0
$631$	36.5976	+	26.5897i	1.45693	+	1.05852i	0.984150	+	0.177337i	$0.0567484\pi$
$631$	36.5976	+	26.5897i	1.45693	+	1.05852i	0.472777	+	0.881182i	$0.343252\pi$
$632$	−19.7669	−	60.8364i	−0.786287	−	2.41994i
$633$		0			0
$634$	14.1234	+	10.2612i	0.560912	+	0.407526i
$635$	11.0755	−	8.04681i	0.439517	−	0.319328i
$636$		0			0
$637$	−2.46429			−0.0976385
$638$	−9.22253	+	8.51824i	−0.365124	+	0.337241i
$639$		0			0
$640$	2.60691	−	8.02325i	0.103047	−	0.317147i
$641$	−13.0279	+	9.46530i	−0.514570	+	0.373857i	−0.814554	−	0.580087i	$-0.803018\pi$
$641$	−13.0279	+	9.46530i	−0.514570	+	0.373857i	0.299985	+	0.953944i	$0.403018\pi$
$642$		0			0
$643$	15.2454	+	46.9206i	0.601220	+	1.85037i	0.520939	+	0.853594i	$0.325582\pi$
$643$	15.2454	+	46.9206i	0.601220	+	1.85037i	0.0802813	+	0.996772i	$0.474418\pi$
$644$	12.2915	+	37.8295i	0.484354	+	1.49069i
$645$		0			0
$646$	−8.56581	+	6.22342i	−0.337017	+	0.244857i
$647$	−10.8350	+	33.3467i	−0.425968	+	1.31100i	0.476096	+	0.879393i	$0.342052\pi$
$647$	−10.8350	+	33.3467i	−0.425968	+	1.31100i	−0.902064	+	0.431602i	$0.857948\pi$
$648$		0			0
$649$	−34.0077	−	19.0635i	−1.33492	−	0.748307i
$650$	−87.5906			−3.43559
$651$		0			0
$652$	−3.50511	+	2.54661i	−0.137271	+	0.0997330i
$653$	20.1089	+	14.6100i	0.786921	+	0.571732i	0.907048	−	0.421027i	$-0.138330\pi$
$653$	20.1089	+	14.6100i	0.786921	+	0.571732i	−0.120127	+	0.992759i	$0.538330\pi$
$654$		0			0
$655$	−10.4543	−	32.1751i	−0.408484	−	1.25718i
$656$	46.3380	+	33.6665i	1.80920	+	1.31446i
$657$		0			0
$658$	7.02861	−	21.6318i	0.274004	−	0.843297i
$659$	12.3854			0.482468			0.241234	−	0.970467i	$-0.422448\pi$
$659$	12.3854			0.482468			0.241234	+	0.970467i	$0.422448\pi$
$660$		0			0
$661$	−39.9739			−1.55480			−0.777402	−	0.629004i	$-0.783463\pi$
$661$	−39.9739			−1.55480			−0.777402	+	0.629004i	$0.783463\pi$
$662$	3.18844	−	9.81301i	0.123922	−	0.381394i
$663$		0			0
$664$	56.6001	+	41.1224i	2.19651	+	1.59586i
$665$	4.57328	+	14.0751i	0.177344	+	0.545810i
$666$		0			0
$667$	−9.78595	−	7.10991i	−0.378913	−	0.275297i
$668$	−45.0292	+	32.7157i	−1.74223	+	1.26581i
$669$		0			0
$670$	−34.9816			−1.35146
$671$	10.7781	+	23.4047i	0.416084	+	0.903527i
$672$		0			0
$673$	−2.57016	+	7.91013i	−0.0990722	+	0.304913i	−0.988294	−	0.152564i	$-0.951247\pi$
$673$	−2.57016	+	7.91013i	−0.0990722	+	0.304913i	0.889221	+	0.457477i	$0.151247\pi$
$674$	25.8278	−	18.7650i	0.994848	−	0.722800i
$675$		0			0
$676$	−10.2330	−	31.4940i	−0.393577	−	1.21131i
$677$	9.49217	+	29.2139i	0.364814	+	1.12278i	0.950098	+	0.311953i	$0.100983\pi$
$677$	9.49217	+	29.2139i	0.364814	+	1.12278i	−0.585284	+	0.810828i	$0.699017\pi$
$678$		0			0
$679$	−5.64077	+	4.09826i	−0.216473	+	0.157277i
$680$	11.4638	−	35.2819i	0.439615	−	1.35300i
$681$		0			0
$682$	−22.5107	−	12.6187i	−0.861979	−	0.483194i
$683$	13.9802			0.534936			0.267468	−	0.963567i	$-0.413813\pi$
$683$	13.9802			0.534936			0.267468	+	0.963567i	$0.413813\pi$
$684$		0			0
$685$	25.1108	−	18.2441i	0.959435	−	0.697071i
$686$	−2.10660	−	1.53054i	−0.0804305	−	0.0584362i
$687$		0			0
$688$	9.05201	+	27.8592i	0.345105	+	1.06212i
$689$	−13.3207	−	9.67809i	−0.507480	−	0.368706i
$690$		0			0
$691$	8.75941	−	26.9587i	0.333224	−	1.02556i	−0.634367	−	0.773032i	$-0.718739\pi$
$691$	8.75941	−	26.9587i	0.333224	−	1.02556i	0.967590	−	0.252525i	$-0.0812609\pi$
$692$	−32.7472			−1.24486
$693$		0			0
$694$	−29.7464			−1.12916
$695$	−4.49468	+	13.8332i	−0.170493	+	0.524724i
$696$		0			0
$697$	−5.91788	−	4.29959i	−0.224156	−	0.162859i
$698$	−23.5230	−	72.3964i	−0.890359	−	2.74024i
$699$		0			0
$700$	−52.7905	−	38.3546i	−1.99529	−	1.44967i
$701$	10.5288	−	7.64965i	0.397669	−	0.288923i	−0.370922	−	0.928664i	$-0.620958\pi$
$701$	10.5288	−	7.64965i	0.397669	−	0.288923i	0.768591	+	0.639741i	$0.220958\pi$
$702$		0			0
$703$	−21.7394			−0.819918
$704$	4.35066	−	21.8257i	0.163972	−	0.822586i
$705$		0			0
$706$	6.24474	−	19.2193i	0.235024	−	0.723329i
$707$	−13.5031	+	9.81056i	−0.507835	+	0.368964i
$708$		0			0
$709$	6.95736	+	21.4126i	0.261289	+	0.804165i	0.992525	+	0.122041i	$0.0389439\pi$
$709$	6.95736	+	21.4126i	0.261289	+	0.804165i	−0.731236	+	0.682125i	$0.761056\pi$
$710$	−19.0692	−	58.6889i	−0.715654	−	2.20256i
$711$		0			0
$712$	−5.77244	+	4.19392i	−0.216331	+	0.157174i
$713$	7.68339	−	23.6470i	0.287745	−	0.885588i
$714$		0			0
$715$	35.0534	−	4.13433i	1.31092	−	0.154615i
$716$	−40.2149			−1.50290
$717$		0			0
$718$	−63.1334	+	45.8691i	−2.35612	+	1.71182i
$719$	−10.8878	−	7.91043i	−0.406045	−	0.295009i	0.365954	−	0.930633i	$-0.380743\pi$
$719$	−10.8878	−	7.91043i	−0.406045	−	0.295009i	−0.771999	+	0.635624i	$0.780743\pi$
$720$		0			0
$721$	3.57787	+	11.0116i	0.133247	+	0.410092i
$722$	15.2861	+	11.1060i	0.568889	+	0.413322i
$723$		0			0
$724$	19.2462	−	59.2337i	0.715279	−	2.20140i
$725$	19.8436			0.736971
$726$		0			0
$727$	−25.2856			−0.937793			−0.468896	−	0.883253i	$-0.655348\pi$
$727$	−25.2856			−0.937793			−0.468896	+	0.883253i	$0.655348\pi$
$728$	−5.51306	+	16.9675i	−0.204328	+	0.628856i
$729$		0			0
$730$	78.7852	+	57.2408i	2.91597	+	2.11858i
$731$	−1.15604	−	3.55793i	−0.0427578	−	0.131595i
$732$		0			0
$733$	33.0519	+	24.0136i	1.22080	+	0.886963i	0.996166	−	0.0874801i	$-0.0278814\pi$
$733$	33.0519	+	24.0136i	1.22080	+	0.886963i	0.224634	+	0.974443i	$0.427881\pi$
$734$	6.50329	−	4.72492i	0.240041	−	0.174400i
$735$		0			0
$736$	80.8205			2.97908
$737$	10.2463	−	1.20849i	0.377429	−	0.0445154i
$738$		0			0
$739$	11.5303	−	35.4866i	0.424149	−	1.30540i	−0.479658	−	0.877455i	$-0.659239\pi$
$739$	11.5303	−	35.4866i	0.424149	−	1.30540i	0.903807	−	0.427940i	$-0.140761\pi$
$740$	105.950	−	76.9774i	3.89481	−	2.82975i
$741$		0			0
$742$	−5.37635	−	16.5467i	−0.197372	−	0.607448i
$743$	−12.3554	−	38.0261i	−0.453277	−	1.39504i	−0.873146	−	0.487459i	$-0.837924\pi$
$743$	−12.3554	−	38.0261i	−0.453277	−	1.39504i	0.419869	−	0.907585i	$-0.362076\pi$
$744$		0			0
$745$	−65.0670	+	47.2739i	−2.38387	+	1.73198i
$746$	23.5721	−	72.5474i	0.863035	−	2.65615i
$747$		0			0
$748$	−3.67758	+	18.4491i	−0.134466	+	0.674565i
$749$	−6.01586			−0.219815
$750$		0			0
$751$	−23.6986	+	17.2180i	−0.864774	+	0.628295i	−0.929180	−	0.369629i	$-0.879485\pi$
$751$	−23.6986	+	17.2180i	−0.864774	+	0.628295i	0.0644056	+	0.997924i	$0.479485\pi$
$752$	−65.6559	−	47.7018i	−2.39422	−	1.73951i
$753$		0			0
$754$	−2.88255	−	8.87157i	−0.104976	−	0.323084i
$755$	50.3966	+	36.6152i	1.83412	+	1.33256i
$756$		0			0
$757$	−10.1486	+	31.2342i	−0.368857	+	1.13523i	0.578673	+	0.815560i	$0.303571\pi$
$757$	−10.1486	+	31.2342i	−0.368857	+	1.13523i	−0.947530	+	0.319666i	$0.896429\pi$
$758$	40.8473			1.48364
$759$		0			0
$760$	107.143			3.88650
$761$	−13.3845	+	41.1934i	−0.485189	+	1.49326i	0.346517	+	0.938044i	$0.387364\pi$
$761$	−13.3845	+	41.1934i	−0.485189	+	1.49326i	−0.831707	+	0.555215i	$0.812636\pi$
$762$		0			0
$763$	−5.40505	−	3.92700i	−0.195676	−	0.142167i
$764$	5.10747	+	15.7192i	0.184782	+	0.568700i
$765$		0			0
$766$	−16.9285	−	12.2992i	−0.611650	−	0.444390i
$767$	23.4350	−	17.0265i	0.846190	−	0.614793i
$768$		0			0
$769$	31.4543			1.13427			0.567135	−	0.823625i	$-0.308052\pi$
$769$	31.4543			1.13427			0.567135	+	0.823625i	$0.308052\pi$
$770$	32.5333	+	18.2370i	1.17242	+	0.657215i
$771$		0			0
$772$	25.1822	−	77.5028i	0.906327	−	2.78939i
$773$	33.8275	−	24.5771i	1.21669	−	0.883979i	0.220871	−	0.975303i	$-0.429110\pi$
$773$	33.8275	−	24.5771i	1.21669	−	0.883979i	0.995821	+	0.0913245i	$0.0291100\pi$
$774$		0			0
$775$	12.6045	+	38.7928i	0.452769	+	1.39348i
$776$	15.5985	+	48.0073i	0.559954	+	1.72336i
$777$		0			0
$778$	60.6436	−	44.0601i	2.17418	−	1.57963i
$779$	6.52847	−	20.0926i	0.233907	−	0.719891i
$780$		0			0
$781$	7.61298	+	16.5316i	0.272414	+	0.591546i
$782$	−25.7084			−0.919330
$783$		0			0
$784$	−7.51643	+	5.46100i	−0.268444	+	0.195036i
$785$	18.5681	+	13.4905i	0.662725	+	0.481498i
$786$		0			0
$787$	−14.3401	−	44.1342i	−0.511168	−	1.57321i	−0.790147	−	0.612917i	$-0.789996\pi$
$787$	−14.3401	−	44.1342i	−0.511168	−	1.57321i	0.278979	−	0.960297i	$-0.410004\pi$
$788$	13.4572	+	9.77726i	0.479394	+	0.348300i
$789$		0			0
$790$	30.7035	−	94.4956i	1.09238	−	3.36200i
$791$	−18.7558			−0.666880
$792$		0			0
$793$	−19.1452			−0.679867
$794$	−27.1421	+	83.5347i	−0.963236	+	2.96454i
$795$		0			0
$796$	−31.7232	−	23.0482i	−1.12440	−	0.816923i
$797$	10.9379	+	33.6634i	0.387440	+	1.19242i	0.934695	+	0.355452i	$0.115673\pi$
$797$	10.9379	+	33.6634i	0.387440	+	1.19242i	−0.547255	+	0.836966i	$0.684327\pi$
$798$		0			0
$799$	8.38499	+	6.09205i	0.296640	+	0.215521i
$800$	−107.264	+	77.9318i	−3.79235	+	2.75530i
$801$		0			0
$802$	2.40744			0.0850098
$803$	−25.0542	−	14.0444i	−0.884142	−	0.495618i
$804$		0			0
$805$	−11.1043	+	34.1756i	−0.391376	+	1.20453i
$806$	15.5123	−	11.2704i	0.546398	−	0.396982i
$807$		0			0
$808$	37.3402	+	114.921i	1.31362	+	4.04292i
$809$	−7.34959	−	22.6197i	−0.258398	−	0.795267i	−0.993141	−	0.116922i	$-0.962697\pi$
$809$	−7.34959	−	22.6197i	−0.258398	−	0.795267i	0.734743	−	0.678345i	$-0.237303\pi$
$810$		0			0
$811$	5.83900	−	4.24228i	0.205035	−	0.148967i	−0.480529	−	0.876979i	$-0.659555\pi$
$811$	5.83900	−	4.24228i	0.205035	−	0.148967i	0.685564	+	0.728012i	$0.259555\pi$
$812$	2.14742	−	6.60909i	0.0753597	−	0.231933i
$813$		0			0
$814$	−40.2455	+	37.1721i	−1.41060	+	1.30288i
$815$	−3.91408			−0.137104
$816$		0			0
$817$	8.74117	−	6.35083i	0.305815	−	0.222187i
$818$	−54.3341	−	39.4760i	−1.89975	−	1.38025i
$819$		0			0
$820$	39.3285	+	121.041i	1.37341	+	4.22693i
$821$	−37.5681	−	27.2948i	−1.31114	−	0.952596i	−0.999998	−	0.00223147i	$-0.999290\pi$
$821$	−37.5681	−	27.2948i	−1.31114	−	0.952596i	−0.311138	−	0.950365i	$-0.600710\pi$
$822$		0			0
$823$	6.92802	−	21.3222i	0.241496	−	0.743247i	−0.754698	−	0.656073i	$-0.772216\pi$
$823$	6.92802	−	21.3222i	0.241496	−	0.743247i	0.996193	−	0.0871740i	$-0.0277836\pi$
$824$	83.8228			2.92011
$825$		0			0
$826$	30.6085			1.06501
$827$	9.41128	−	28.9650i	0.327262	−	1.00721i	−0.643147	−	0.765743i	$-0.722371\pi$
$827$	9.41128	−	28.9650i	0.327262	−	1.00721i	0.970409	−	0.241467i	$-0.0776286\pi$
$828$		0			0
$829$	35.5485	+	25.8275i	1.23465	+	0.897025i	0.997230	−	0.0743821i	$-0.0236984\pi$
$829$	35.5485	+	25.8275i	1.23465	+	0.897025i	0.237419	+	0.971407i	$0.423698\pi$
$830$	33.5807	+	103.351i	1.16560	+	3.58736i
$831$		0			0
$832$	13.3777	+	9.71946i	0.463788	+	0.336962i
$833$	0.959932	−	0.697431i	0.0332597	−	0.0241646i
$834$		0			0
$835$	−50.2832			−1.74012
$836$	−53.9581	+	6.36403i	−1.86618	+	0.220104i
$837$		0			0
$838$	7.57418	−	23.3109i	0.261646	−	0.805262i
$839$	−2.26645	+	1.64667i	−0.0782466	+	0.0568495i	−0.626221	−	0.779646i	$-0.715399\pi$
$839$	−2.26645	+	1.64667i	−0.0782466	+	0.0568495i	0.547974	+	0.836495i	$0.315399\pi$
$840$		0			0
$841$	−8.30845	−	25.5708i	−0.286498	−	0.881751i
$842$	−23.5799	−	72.5714i	−0.812616	−	2.50098i
$843$		0			0
$844$	−85.9296	+	62.4315i	−2.95782	+	2.14898i
$845$	9.24462	−	28.4520i	0.318025	−	0.978779i
$846$		0			0
$847$	−10.1592	−	4.21781i	−0.349075	−	0.144926i
$848$	−62.0774			−2.13175
$849$		0			0
$850$	34.1198	−	24.7895i	1.17030	−	0.850273i
$851$	−42.7041	−	31.0263i	−1.46388	−	1.06357i
$852$		0			0
$853$	−2.59036	−	7.97231i	−0.0886922	−	0.272967i	0.896866	−	0.442302i	$-0.145838\pi$
$853$	−2.59036	−	7.97231i	−0.0886922	−	0.272967i	−0.985559	+	0.169335i	$0.945838\pi$
$854$	−16.3664	−	11.8909i	−0.560046	−	0.406897i
$855$		0			0
$856$	−13.4586	+	41.4213i	−0.460005	+	1.41575i
$857$	−53.1740			−1.81639			−0.908194	−	0.418550i	$-0.862539\pi$
$857$	−53.1740			−1.81639			−0.908194	+	0.418550i	$0.862539\pi$
$858$		0			0
$859$	39.7762			1.35715			0.678573	−	0.734533i	$-0.262599\pi$
$859$	39.7762			1.35715			0.678573	+	0.734533i	$0.262599\pi$
$860$	−20.1136	+	61.9034i	−0.685869	+	2.11089i
$861$		0			0
$862$	−14.6971	−	10.6781i	−0.500587	−	0.363697i
$863$	−2.81762	−	8.67174i	−0.0959129	−	0.295189i	0.891578	−	0.452868i	$-0.149599\pi$
$863$	−2.81762	−	8.67174i	−0.0959129	−	0.295189i	−0.987491	+	0.157678i	$0.949599\pi$
$864$		0			0
$865$	−23.9341	−	17.3891i	−0.813784	−	0.591249i
$866$	−2.79998	+	2.03430i	−0.0951471	+	0.0691285i
$867$		0			0
$868$	14.2843			0.484842
$869$	−5.72875	+	28.7390i	−0.194334	+	0.974905i
$870$		0			0
$871$	−2.36889	+	7.29070i	−0.0802669	+	0.247036i
$872$	−39.1309	+	28.4302i	−1.32514	+	0.962769i
$873$		0			0
$874$	−22.9444	−	70.6157i	−0.776107	−	2.38861i
$875$	−11.5440	−	35.5287i	−0.390257	−	1.20109i
$876$		0			0
$877$	18.8858	−	13.7213i	0.637727	−	0.463336i	−0.221342	−	0.975196i	$-0.571044\pi$
$877$	18.8858	−	13.7213i	0.637727	−	0.463336i	0.859069	+	0.511861i	$0.171044\pi$
$878$	−2.92733	+	9.00938i	−0.0987925	+	0.304052i
$879$		0			0
$880$	97.7560	−	90.2907i	3.29535	−	3.04370i
$881$	55.3515			1.86484			0.932419	−	0.361379i	$-0.117694\pi$
$881$	55.3515			1.86484			0.932419	+	0.361379i	$0.117694\pi$
$882$		0			0
$883$	−25.7607	+	18.7162i	−0.866916	+	0.629852i	−0.929758	−	0.368172i	$-0.879984\pi$
$883$	−25.7607	+	18.7162i	−0.866916	+	0.629852i	0.0628414	+	0.998024i	$0.479984\pi$
$884$	−11.3081	−	8.21579i	−0.380331	−	0.276327i
$885$		0			0
$886$	10.7903	+	33.2092i	0.362508	+	1.11568i
$887$	28.5322	+	20.7298i	0.958016	+	0.696040i	0.952689	−	0.303946i	$-0.0983043\pi$
$887$	28.5322	+	20.7298i	0.958016	+	0.696040i	0.00532707	+	0.999986i	$0.498304\pi$
$888$		0			0
$889$	0.979590	−	3.01487i	0.0328544	−	0.101115i
$890$	−11.0828			−0.371497
$891$		0			0
$892$	104.380			3.49489
$893$	−9.25012	+	28.4690i	−0.309544	+	0.952677i
$894$		0			0
$895$	−29.3921	−	21.3546i	−0.982469	−	0.713805i
$896$	−0.603648	−	1.85784i	−0.0201665	−	0.0620660i
$897$		0			0
$898$	−31.5975	−	22.9569i	−1.05442	−	0.766082i
$899$	−3.51430	+	2.55329i	−0.117209	+	0.0851570i
$900$		0			0
$901$	7.92798			0.264119
$902$	−22.2702	−	48.3597i	−0.741516	−	1.61020i
$903$		0			0
$904$	−41.9602	+	129.140i	−1.39558	+	4.29514i
$905$	45.5204	−	33.0725i	1.51315	−	1.09937i
$906$		0			0
$907$	−1.42358	−	4.38134i	−0.0472693	−	0.145480i	0.924636	−	0.380852i	$-0.124369\pi$
$907$	−1.42358	−	4.38134i	−0.0472693	−	0.145480i	−0.971905	+	0.235372i	$0.924369\pi$
$908$	−36.0006	−	110.798i	−1.19472	−	3.67697i
$909$		0			0
$910$	−22.4190	+	16.2884i	−0.743183	+	0.539954i
$911$	1.90181	−	5.85318i	0.0630099	−	0.193925i	−0.914596	−	0.404369i	$-0.867491\pi$
$911$	1.90181	−	5.85318i	0.0630099	−	0.193925i	0.977606	+	0.210445i	$0.0674911\pi$
$912$		0			0
$913$	−13.4064	−	29.1120i	−0.443688	−	0.963467i
$914$	−51.3285			−1.69779
$915$		0			0
$916$	9.98310	−	7.25315i	0.329851	−	0.239651i
$917$	−6.33765	−	4.60457i	−0.209288	−	0.152056i
$918$		0			0
$919$	6.17532	+	19.0057i	0.203705	+	0.626940i	0.999764	+	0.0217208i	$0.00691448\pi$
$919$	6.17532	+	19.0057i	0.203705	+	0.626940i	−0.796059	+	0.605219i	$0.793086\pi$
$920$	210.468	+	152.914i	6.93894	+	5.04143i
$921$		0			0
$922$	13.1662	−	40.5215i	0.433607	−	1.33451i
$923$	−13.5230			−0.445115
$924$		0			0
$925$	86.5937			2.84718
$926$	−6.02351	+	18.5385i	−0.197945	+	0.609211i
$927$		0			0
$928$	−11.4233	−	8.29949i	−0.374987	−	0.272444i
$929$	−2.27185	−	6.99203i	−0.0745370	−	0.229401i	0.906846	−	0.421462i	$-0.138483\pi$
$929$	−2.27185	−	6.99203i	−0.0745370	−	0.229401i	−0.981383	+	0.192061i	$0.938483\pi$
$930$		0			0
$931$	2.77243	+	2.01429i	0.0908627	+	0.0660156i
$932$	55.1274	−	40.0524i	1.80576	−	1.31196i
$933$		0			0
$934$	−7.57793			−0.247957
$935$	−12.4845	+	11.5311i	−0.408288	+	0.377108i
$936$		0			0
$937$	−6.92309	+	21.3071i	−0.226167	+	0.696072i	0.772004	+	0.635618i	$0.219255\pi$
$937$	−6.92309	+	21.3071i	−0.226167	+	0.696072i	−0.998171	+	0.0604535i	$0.980745\pi$
$938$	−6.55322	+	4.76119i	−0.213970	+	0.155458i
$939$		0			0
$940$	−55.7242	−	171.502i	−1.81752	−	5.59376i
$941$	−1.50334	−	4.62680i	−0.0490074	−	0.150829i	0.923558	−	0.383459i	$-0.125267\pi$
$941$	−1.50334	−	4.62680i	−0.0490074	−	0.150829i	−0.972565	+	0.232629i	$0.925267\pi$
$942$		0			0
$943$	41.5002	−	30.1517i	1.35143	−	0.981874i
$944$	33.7484	−	103.867i	1.09842	−	3.38058i
$945$		0			0
$946$	5.32300	−	26.7035i	0.173066	−	0.868207i
$947$	29.6187			0.962477			0.481238	−	0.876590i	$-0.340187\pi$
$947$	29.6187			0.962477			0.481238	+	0.876590i	$0.340187\pi$
$948$		0			0
$949$	17.2651	−	12.5438i	0.560447	−	0.407189i
$950$	98.5433	+	71.5959i	3.19717	+	2.32288i
$951$		0			0
$952$	−2.65451	−	8.16975i	−0.0860332	−	0.264783i
$953$	−4.53974	−	3.29832i	−0.147057	−	0.106843i	0.511824	−	0.859090i	$-0.328970\pi$
$953$	−4.53974	−	3.29832i	−0.147057	−	0.106843i	−0.658881	+	0.752247i	$0.728970\pi$
$954$		0			0
$955$	−4.61415	+	14.2009i	−0.149310	+	0.459530i
$956$	−52.8165			−1.70821
$957$		0			0
$958$	−69.0744			−2.23169
$959$	2.22097	−	6.83545i	0.0717189	−	0.220728i
$960$		0			0
$961$	17.8558	+	12.9730i	0.575992	+	0.418483i
$962$	−12.5789	−	38.7139i	−0.405561	−	1.24819i
$963$		0			0
$964$	42.5918	+	30.9447i	1.37179	+	0.996663i
$965$	59.5600	−	43.2729i	1.91730	−	1.39300i
$966$		0			0
$967$	−49.9946			−1.60772			−0.803858	−	0.594821i	$-0.797223\pi$
$967$	−49.9946			−1.60772			−0.803858	+	0.594821i	$0.797223\pi$
$968$	−51.7692	+	60.5139i	−1.66393	+	1.94499i
$969$		0			0
$970$	−24.2288	+	74.5684i	−0.777938	+	2.39425i
$971$	−48.0964	+	34.9441i	−1.54349	+	1.12141i	−0.595386	+	0.803439i	$0.703001\pi$
$971$	−48.0964	+	34.9441i	−1.54349	+	1.12141i	−0.948101	+	0.317970i	$0.896999\pi$
$972$		0			0
$973$	1.04077	+	3.20317i	0.0333657	+	0.102689i
$974$	−2.26688	−	6.97674i	−0.0726356	−	0.223549i
$975$		0			0
$976$	−58.3958	+	42.4270i	−1.86920	+	1.35806i
$977$	6.28312	−	19.3374i	0.201015	−	0.618660i	−0.798839	−	0.601545i	$-0.794552\pi$
$977$	6.28312	−	19.3374i	0.201015	−	0.618660i	0.999854	−	0.0171146i	$-0.00544802\pi$
$978$		0			0
$979$	3.24623	−	0.382872i	0.103750	−	0.0122367i
$980$	−20.6443			−0.659457
$981$		0			0
$982$	−11.9632	+	8.69174i	−0.381760	+	0.277365i
$983$	20.2626	+	14.7217i	0.646278	+	0.469548i	0.862001	−	0.506906i	$-0.169211\pi$
$983$	20.2626	+	14.7217i	0.646278	+	0.469548i	−0.215723	+	0.976454i	$0.569211\pi$
$984$		0			0
$985$	4.64373	+	14.2919i	0.147961	+	0.455378i
$986$	3.63365	+	2.64000i	0.115719	+	0.0840749i
$987$		0			0
$988$	12.4748	−	38.3935i	0.396876	−	1.22146i
$989$	26.2347			0.834214
$990$		0			0
$991$	10.5368			0.334713			0.167356	−	0.985896i	$-0.446477\pi$
$991$	10.5368			0.334713			0.167356	+	0.985896i	$0.446477\pi$
$992$	8.96892	−	27.6035i	0.284763	−	0.876412i
$993$		0			0
$994$	−11.5602	−	8.39897i	−0.366667	−	0.266399i
$995$	−10.9468	−	33.6908i	−0.347037	−	1.06807i
$996$		0			0
$997$	27.5808	+	20.0386i	0.873492	+	0.634629i	0.931522	−	0.363686i	$-0.118482\pi$
$997$	27.5808	+	20.0386i	0.873492	+	0.634629i	−0.0580294	+	0.998315i	$0.518482\pi$
$998$	−74.3524	+	54.0201i	−2.35358	+	1.70998i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.k.64.8	yes	32
3.2	odd	2	inner	693.2.m.k.64.1	✓	32
11.4	even	5		7623.2.a.dc.1.15		16
11.5	even	5	inner	693.2.m.k.379.8	yes	32
11.7	odd	10		7623.2.a.db.1.2		16
33.5	odd	10	inner	693.2.m.k.379.1	yes	32
33.26	odd	10		7623.2.a.dc.1.2		16
33.29	even	10		7623.2.a.db.1.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.k.64.1	✓	32	3.2	odd	2	inner
693.2.m.k.64.8	yes	32	1.1	even	1	trivial
693.2.m.k.379.1	yes	32	33.5	odd	10	inner
693.2.m.k.379.8	yes	32	11.5	even	5	inner
7623.2.a.db.1.2		16	11.7	odd	10
7623.2.a.db.1.15		16	33.29	even	10
7623.2.a.dc.1.2		16	33.26	odd	10
7623.2.a.dc.1.15		16	11.4	even	5

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.804651 - 2.47646i) q^{2} +(-3.86736 - 2.80980i) q^{4} +(-1.33452 - 4.10723i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-5.85703 + 4.25538i) q^{8} +O(q^{10})\)	\(q+(0.804651 - 2.47646i) q^{2} +(-3.86736 - 2.80980i) q^{4} +(-1.33452 - 4.10723i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-5.85703 + 4.25538i) q^{8} -11.2452 q^{10} +(3.29379 - 0.388483i) q^{11} +(-0.761506 + 2.34367i) q^{13} +(-2.10660 + 1.53054i) q^{14} +(2.87102 + 8.83609i) q^{16} +(-0.366661 - 1.12847i) q^{17} +(2.77243 - 2.01429i) q^{19} +(-6.37943 + 19.6339i) q^{20} +(1.68829 - 8.46954i) q^{22} +8.32084 q^{23} +(-11.0433 + 8.02343i) q^{25} +(5.19127 + 3.77168i) q^{26} +(1.47720 + 4.54635i) q^{28} +(-1.17608 - 0.854470i) q^{29} +(0.923391 - 2.84191i) q^{31} +9.71302 q^{32} -3.08964 q^{34} +(-1.33452 + 4.10723i) q^{35} +(-5.13219 - 3.72875i) q^{37} +(-2.75747 - 8.48661i) q^{38} +(25.2941 + 18.3773i) q^{40} +(4.98751 - 3.62364i) q^{41} +3.15289 q^{43} +(-13.8298 - 7.75250i) q^{44} +(6.69537 - 20.6062i) q^{46} +(-7.06675 + 5.13430i) q^{47} +(0.309017 + 0.951057i) q^{49} +(10.9837 + 33.8044i) q^{50} +(9.53028 - 6.92415i) q^{52} +(-2.06473 + 6.35457i) q^{53} +(-5.99122 - 13.0099i) q^{55} +7.23969 q^{56} +(-3.06239 + 2.22496i) q^{58} +(-9.50987 - 6.90932i) q^{59} +(2.40078 + 7.38884i) q^{61} +(-6.29486 - 4.57348i) q^{62} +(2.07355 - 6.38173i) q^{64} +10.6423 q^{65} +3.11080 q^{67} +(-1.75276 + 5.39443i) q^{68} +(9.09757 + 6.60977i) q^{70} +(1.69576 + 5.21901i) q^{71} +(-7.00611 - 5.09024i) q^{73} +(-13.3637 + 9.70932i) q^{74} -16.3817 q^{76} +(-2.89308 - 1.62175i) q^{77} +(-2.73036 + 8.40318i) q^{79} +(32.4604 - 23.5839i) q^{80} +(-4.96059 - 15.2671i) q^{82} +(-2.98622 - 9.19065i) q^{83} +(-4.14556 + 3.01192i) q^{85} +(2.53698 - 7.80801i) q^{86} +(-17.6387 + 16.2917i) q^{88} +0.985558 q^{89} +(1.99365 - 1.44847i) q^{91} +(-32.1797 - 23.3799i) q^{92} +(7.02861 + 21.6318i) q^{94} +(-11.9730 - 8.69890i) q^{95} +(2.15458 - 6.63113i) q^{97} +2.60390 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) \) 32 * q - 10 * q^4 - 8 * q^7	\( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) \) 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more