LMFDB - Embedded newform 693.2.m.k.64.1

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			64.1
Character	$\chi$	$=$	693.64
Dual form			693.2.m.k.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.804651 + 2.47646i) q^{2} +(-3.86736 - 2.80980i) q^{4} +(1.33452 + 4.10723i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(5.85703 - 4.25538i) q^{8} +O(q^{10})$	\(q+(-0.804651 + 2.47646i) q^{2} +(-3.86736 - 2.80980i) q^{4} +(1.33452 + 4.10723i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(5.85703 - 4.25538i) q^{8} -11.2452 q^{10} +(-3.29379 + 0.388483i) q^{11} +(-0.761506 + 2.34367i) q^{13} +(2.10660 - 1.53054i) q^{14} +(2.87102 + 8.83609i) q^{16} +(0.366661 + 1.12847i) q^{17} +(2.77243 - 2.01429i) q^{19} +(6.37943 - 19.6339i) q^{20} +(1.68829 - 8.46954i) q^{22} -8.32084 q^{23} +(-11.0433 + 8.02343i) q^{25} +(-5.19127 - 3.77168i) q^{26} +(1.47720 + 4.54635i) q^{28} +(1.17608 + 0.854470i) q^{29} +(0.923391 - 2.84191i) q^{31} -9.71302 q^{32} -3.08964 q^{34} +(1.33452 - 4.10723i) q^{35} +(-5.13219 - 3.72875i) q^{37} +(2.75747 + 8.48661i) q^{38} +(25.2941 + 18.3773i) q^{40} +(-4.98751 + 3.62364i) q^{41} +3.15289 q^{43} +(13.8298 + 7.75250i) q^{44} +(6.69537 - 20.6062i) q^{46} +(7.06675 - 5.13430i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-10.9837 - 33.8044i) q^{50} +(9.53028 - 6.92415i) q^{52} +(2.06473 - 6.35457i) q^{53} +(-5.99122 - 13.0099i) q^{55} -7.23969 q^{56} +(-3.06239 + 2.22496i) q^{58} +(9.50987 + 6.90932i) q^{59} +(2.40078 + 7.38884i) q^{61} +(6.29486 + 4.57348i) q^{62} +(2.07355 - 6.38173i) q^{64} -10.6423 q^{65} +3.11080 q^{67} +(1.75276 - 5.39443i) q^{68} +(9.09757 + 6.60977i) q^{70} +(-1.69576 - 5.21901i) q^{71} +(-7.00611 - 5.09024i) q^{73} +(13.3637 - 9.70932i) q^{74} -16.3817 q^{76} +(2.89308 + 1.62175i) q^{77} +(-2.73036 + 8.40318i) q^{79} +(-32.4604 + 23.5839i) q^{80} +(-4.96059 - 15.2671i) q^{82} +(2.98622 + 9.19065i) q^{83} +(-4.14556 + 3.01192i) q^{85} +(-2.53698 + 7.80801i) q^{86} +(-17.6387 + 16.2917i) q^{88} -0.985558 q^{89} +(1.99365 - 1.44847i) q^{91} +(32.1797 + 23.3799i) q^{92} +(7.02861 + 21.6318i) q^{94} +(11.9730 + 8.69890i) q^{95} +(2.15458 - 6.63113i) q^{97} -2.60390 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.472315\pi$
$2$	−0.804651	+	2.47646i	−0.568974	+	1.75112i	−0.655838	+	0.754902i	$0.727685\pi$
$3$		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	$0.316350\pi$
$5$	1.33452	+	4.10723i	0.596815	+	1.83681i	0.0513414	+	0.998681i	$0.483650\pi$
$6$		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	0.985624	−	0.168955i	$-0.0540391\pi$
$17$	0.366661	+	1.12847i	0.0889284	+	0.273694i	−0.896695	+	0.442648i	$0.854039\pi$
$18$		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	$-0.834279\pi$
$23$	−8.32084			−1.73501			−0.867507	+	0.497425i	$0.834279\pi$
$24$		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	0.691603	−	0.722278i	$-0.256905\pi$
$29$	1.17608	+	0.854470i	0.218392	+	0.158671i	−0.473211	+	0.880949i	$0.656905\pi$
$30$		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	−0.904654	−	0.426147i	$-0.859871\pi$
$41$	−4.98751	+	3.62364i	−0.778918	+	0.565917i	0.125736	+	0.992064i	$0.459871\pi$
$42$		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	0.0623247	−	0.998056i	$-0.480149\pi$
$47$	7.06675	−	5.13430i	1.03079	−	0.748914i	0.968467	+	0.249142i	$0.0801486\pi$
$48$		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	$-0.748246\pi$
$53$	2.06473	−	6.35457i	0.283612	−	0.872868i	0.986811	−	0.161875i	$-0.0517541\pi$
$54$		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	0.997469	−	0.0711045i	$-0.0226524\pi$
$59$	9.50987	+	6.90932i	1.23808	+	0.899517i	0.240610	+	0.970622i	$0.422652\pi$
$60$		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	$-0.994424\pi$
$71$	−1.69576	−	5.21901i	−0.201250	−	0.619383i	0.798597	−	0.601866i	$-0.205576\pi$
$72$		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	$0.0779434\pi$
$83$	2.98622	+	9.19065i	0.327781	+	1.00881i	−0.642389	+	0.766379i	$0.722057\pi$
$84$		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	$-0.516634\pi$
$89$	−0.985558			−0.104469			−0.0522345	+	0.998635i	$0.516634\pi$
$90$		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	$0.411885\pi$
$101$	−5.15771	+	15.8738i	−0.513212	+	1.57950i	−0.786512	+	0.617575i	$0.788115\pi$
$102$		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	−0.797638	−	0.603137i	$-0.793917\pi$
$107$	−4.86693	+	3.53603i	−0.470504	+	0.341841i	0.327134	+	0.944978i	$0.393917\pi$
$108$		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	$0.643937\pi$
$113$	−15.1738	+	11.0244i	−1.42743	+	1.03709i	−0.990488	+	0.137596i	$0.956063\pi$
$114$		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	$-0.611179\pi$
$131$	−7.83376			−0.684439			−0.342220	+	0.939620i	$0.611179\pi$
$132$		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	0.810247	−	0.586088i	$-0.199333\pi$
$137$	−2.22097	−	6.83545i	−0.189750	−	0.583992i	−0.999998	+	0.00209625i	$0.999333\pi$
$138$		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	$0.176199\pi$
$149$	5.75496	+	17.7120i	0.471465	+	1.45102i	−0.379201	+	0.925314i	$0.623801\pi$
$150$		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	$0.248753\pi$
$167$	−3.59801	+	11.0735i	−0.278422	+	0.856896i	−0.988294	+	0.152564i	$0.951247\pi$
$168$		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	−0.778184	−	0.628036i	$-0.783859\pi$
$173$	−5.54210	+	4.02657i	−0.421358	+	0.306135i	0.356826	+	0.934171i	$0.383859\pi$
$174$		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	−0.812330	−	0.583198i	$-0.801801\pi$
$179$	−6.80593	+	4.94480i	−0.508699	+	0.369592i	0.303631	+	0.952790i	$0.401801\pi$
$180$		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	0.684368	−	0.729137i	$-0.260078\pi$
$191$	2.79720	+	2.03229i	0.202399	+	0.147051i	−0.481969	+	0.876188i	$0.660078\pi$
$192$		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	$-0.460441\pi$
$197$	3.47970			0.247918			0.123959	+	0.992287i	$0.460441\pi$
$198$		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	−0.308624	−	0.951184i	$-0.599868\pi$
$227$	−19.7164	−	14.3248i	−1.30862	−	0.950771i	−1.00000		0.000413245i	$0.999868\pi$
$228$		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	$-0.745363\pi$
$233$	4.40489	−	13.5569i	0.288574	−	0.888140i	0.985305	−	0.170807i	$-0.0546374\pi$
$234$		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	−0.838071	−	0.545561i	$-0.816317\pi$
$239$	−8.93861	+	6.49428i	−0.578191	+	0.420080i	0.259881	+	0.965641i	$0.416317\pi$
$240$		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	$-0.783959\pi$
$251$	3.49099	−	10.7441i	0.220349	−	0.678165i	0.998730	−	0.0503730i	$-0.0160410\pi$
$252$		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	0.709207	−	0.705000i	$-0.249053\pi$
$257$	4.13397	+	3.00350i	0.257870	+	0.187353i	−0.451338	+	0.892353i	$0.649053\pi$
$258$		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	$-0.435115\pi$
$263$	6.56589			0.404870			0.202435	+	0.979296i	$0.435115\pi$
$264$		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	$0.0151502\pi$
$269$	3.58748	+	11.0411i	0.218732	+	0.673189i	−0.780135	+	0.625611i	$0.784850\pi$
$270$		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	0.999989	−	0.00466199i	$-0.00148396\pi$
$281$	3.15549	+	9.71160i	0.188241	+	0.579345i	−0.811748	+	0.584007i	$0.801484\pi$
$282$		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	0.894601	−	0.446865i	$-0.147460\pi$
$293$	12.7704	+	9.27824i	0.746055	+	0.542040i	−0.148547	+	0.988905i	$0.547460\pi$
$294$		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	−0.242441	−	0.970166i	$-0.577948\pi$
$311$	10.6750	−	7.75584i	0.605323	−	0.439793i	0.847764	+	0.530373i	$0.177948\pi$
$312$		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	−0.875867	−	0.482552i	$-0.839710\pi$
$317$	2.07176	−	6.37621i	0.116361	−	0.358124i	0.992229	+	0.124429i	$0.0397098\pi$
$318$		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	0.999997	−	0.00250851i	$-0.000798486\pi$
$347$	3.53014	+	10.8647i	0.189508	+	0.583245i	−0.810489	+	0.585754i	$0.800798\pi$
$348$		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	$-0.566218\pi$
$353$	−7.76081			−0.413066			−0.206533	+	0.978440i	$0.566218\pi$
$354$		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	0.999542	−	0.0302604i	$-0.00963367\pi$
$359$	24.2457	+	17.6155i	1.27964	+	0.929712i	0.280096	+	0.959972i	$0.409634\pi$
$360$		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	−0.994240	−	0.107175i	$-0.965820\pi$
$383$	−2.48323	+	7.64260i	−0.126887	+	0.390518i	0.867353	+	0.497693i	$0.165820\pi$
$384$		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	−0.188559	−	0.982062i	$-0.560382\pi$
$389$	−23.2895	−	16.9208i	−1.18082	−	0.857918i	−0.992264	+	0.124143i	$0.960382\pi$
$390$		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	0.943669	−	0.330890i	$-0.107349\pi$
$401$	−0.285702	−	0.879301i	−0.0142673	−	0.0439102i	−0.957937	+	0.286980i	$0.907349\pi$
$402$		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	$-0.573849\pi$
$419$	−9.41300			−0.459855			−0.229928	+	0.973208i	$0.573849\pi$
$420$		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	−0.989458	−	0.144819i	$-0.953740\pi$
$431$	−2.15592	+	6.63524i	−0.103847	+	0.319608i	0.885611	+	0.464428i	$0.153740\pi$
$432$		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	−0.299440	−	0.954115i	$-0.596800\pi$
$443$	10.8489	−	7.88216i	0.515445	−	0.374493i	0.814885	+	0.579622i	$0.196800\pi$
$444$		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	$0.215155\pi$
$449$	−4.63503	+	14.2651i	−0.218740	+	0.673214i	−0.998867	+	0.0475920i	$0.984845\pi$
$450$		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	$-0.624435\pi$
$461$	−16.3627			−0.762086			−0.381043	+	0.924557i	$0.624435\pi$
$462$		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	0.969706	−	0.244277i	$-0.0785506\pi$
$467$	0.899306	+	2.76778i	0.0416149	+	0.128078i	−0.928091	+	0.372354i	$0.878551\pi$
$468$		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	$0.107239\pi$
$479$	8.19737	+	25.2289i	0.374547	+	1.15274i	−0.569236	+	0.822174i	$0.692761\pi$
$480$		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	0.686609	−	0.727027i	$-0.259099\pi$
$491$	4.59431	+	3.33796i	0.207338	+	0.150640i	−0.479270	+	0.877667i	$0.659099\pi$
$492$		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	0.0940383	−	0.995569i	$-0.470022\pi$
$503$	23.9962	−	17.4343i	1.06994	−	0.777357i	0.975901	+	0.218212i	$0.0700224\pi$
$504$		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	−0.500050	−	0.865996i	$-0.666685\pi$
$509$	3.81365	−	2.77078i	0.169037	−	0.122813i	0.669087	+	0.743184i	$0.266685\pi$
$510$		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	0.108832	−	0.994060i	$-0.465289\pi$
$521$	−18.3276	−	13.3158i	−0.802945	−	0.583374i	−0.911777	+	0.410686i	$0.865289\pi$
$522$		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	0.541272	−	0.840848i	$-0.317943\pi$
$557$	−2.15143	−	1.56311i	−0.0911591	−	0.0662310i	−0.632431	+	0.774617i	$0.717943\pi$
$558$		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	$-0.797266\pi$
$563$	4.65120	−	14.3149i	0.196025	−	0.603302i	0.999963	−	0.00858929i	$-0.00273409\pi$
$564$		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	0.248422	−	0.968652i	$-0.420088\pi$
$569$	29.7320	−	21.6016i	1.24643	−	0.905585i	0.998009	+	0.0630667i	$0.0200881\pi$
$570$		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	0.439662	−	0.898163i	$-0.355098\pi$
$587$	−6.75186	−	4.90551i	−0.278679	−	0.202472i	−0.718341	+	0.695691i	$0.755098\pi$
$588$		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	$-0.395207\pi$
$593$	15.7459			0.646605			0.323302	+	0.946296i	$0.395207\pi$
$594$		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	0.950788	−	0.309841i	$-0.100276\pi$
$599$	−0.0131088	−	0.0403449i	−0.000535613	−	0.00164845i	−0.951324	+	0.308193i	$0.900276\pi$
$600$		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	$-0.590237\pi$
$617$	−13.8954			−0.559409			−0.279705	+	0.960086i	$0.590237\pi$
$618$		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	−0.299985	−	0.953944i	$-0.596982\pi$
$641$	13.0279	−	9.46530i	0.514570	−	0.373857i	0.814554	+	0.580087i	$0.196982\pi$
$642$		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	$-0.657948\pi$
$647$	10.8350	−	33.3467i	0.425968	−	1.31100i	0.902064	−	0.431602i	$-0.142052\pi$
$648$		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	0.120127	−	0.992759i	$-0.461670\pi$
$653$	−20.1089	−	14.6100i	−0.786921	−	0.571732i	−0.907048	+	0.421027i	$0.861670\pi$
$654$		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	$-0.577552\pi$
$659$	−12.3854			−0.482468			−0.241234	+	0.970467i	$0.577552\pi$
$660$		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	$-0.899017\pi$
$677$	−9.49217	−	29.2139i	−0.364814	−	1.12278i	0.585284	−	0.810828i	$-0.300983\pi$
$678$		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	$-0.586187\pi$
$683$	−13.9802			−0.534936			−0.267468	+	0.963567i	$0.586187\pi$
$684$		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	−0.768591	−	0.639741i	$-0.779042\pi$
$701$	−10.5288	+	7.64965i	−0.397669	+	0.288923i	0.370922	+	0.928664i	$0.379042\pi$
$702$		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	0.771999	−	0.635624i	$-0.219257\pi$
$719$	10.8878	+	7.91043i	0.406045	+	0.295009i	−0.365954	+	0.930633i	$0.619257\pi$
$720$		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	$0.162076\pi$
$743$	12.3554	+	38.0261i	0.453277	+	1.39504i	−0.419869	+	0.907585i	$0.637924\pi$
$744$		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	$-0.612636\pi$
$761$	13.3845	−	41.1934i	0.485189	−	1.49326i	0.831707	−	0.555215i	$-0.187364\pi$
$762$		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	−0.995821	−	0.0913245i	$-0.970890\pi$
$773$	−33.8275	+	24.5771i	−1.21669	+	0.883979i	−0.220871	+	0.975303i	$0.570890\pi$
$774$		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	$-0.884327\pi$
$797$	−10.9379	−	33.6634i	−0.387440	−	1.19242i	0.547255	−	0.836966i	$-0.315673\pi$
$798$		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	$0.0373026\pi$
$809$	7.34959	+	22.6197i	0.258398	+	0.795267i	−0.734743	+	0.678345i	$0.762697\pi$
$810$		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	$0.000710300\pi$
$821$	37.5681	+	27.2948i	1.31114	+	0.952596i	0.311138	+	0.950365i	$0.399290\pi$
$822$		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	$0.277629\pi$
$827$	−9.41128	+	28.9650i	−0.327262	+	1.00721i	−0.970409	+	0.241467i	$0.922371\pi$
$828$		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	−0.547974	−	0.836495i	$-0.684601\pi$
$839$	2.26645	−	1.64667i	0.0782466	−	0.0568495i	0.626221	+	0.779646i	$0.284601\pi$
$840$		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	$-0.137461\pi$
$857$	53.1740			1.81639			0.908194	+	0.418550i	$0.137461\pi$
$858$		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	0.987491	−	0.157678i	$-0.0504009\pi$
$863$	2.81762	+	8.67174i	0.0959129	+	0.295189i	−0.891578	+	0.452868i	$0.850401\pi$
$864$		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	$-0.882306\pi$
$881$	−55.3515			−1.86484			−0.932419	+	0.361379i	$0.882306\pi$
$882$		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	−0.00532707	−	0.999986i	$-0.501696\pi$
$887$	−28.5322	−	20.7298i	−0.958016	−	0.696040i	−0.952689	+	0.303946i	$0.901696\pi$
$888$		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	−0.977606	−	0.210445i	$-0.932509\pi$
$911$	−1.90181	+	5.85318i	−0.0630099	+	0.193925i	0.914596	+	0.404369i	$0.132509\pi$
$912$		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	0.981383	−	0.192061i	$-0.0615171\pi$
$929$	2.27185	+	6.99203i	0.0745370	+	0.229401i	−0.906846	+	0.421462i	$0.861517\pi$
$930$		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	0.972565	−	0.232629i	$-0.0747329\pi$
$941$	1.50334	+	4.62680i	0.0490074	+	0.150829i	−0.923558	+	0.383459i	$0.874733\pi$
$942$		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	$-0.659813\pi$
$947$	−29.6187			−0.962477			−0.481238	+	0.876590i	$0.659813\pi$
$948$		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	0.658881	−	0.752247i	$-0.271030\pi$
$953$	4.53974	+	3.29832i	0.147057	+	0.106843i	−0.511824	+	0.859090i	$0.671030\pi$
$954$		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	$-0.296999\pi$
$971$	48.0964	−	34.9441i	1.54349	−	1.12141i	0.948101	−	0.317970i	$-0.103001\pi$
$972$		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	$0.205448\pi$
$977$	−6.28312	+	19.3374i	−0.201015	+	0.618660i	−0.999854	+	0.0171146i	$0.994552\pi$
$978$		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	0.215723	−	0.976454i	$-0.430789\pi$
$983$	−20.2626	−	14.7217i	−0.646278	−	0.469548i	−0.862001	+	0.506906i	$0.830789\pi$
$984$		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.64.1	✓	32
3.2	odd	2	inner	693.2.m.k.64.8	yes	32
11.4	even	5		7623.2.a.dc.1.2		16
11.5	even	5	inner	693.2.m.k.379.1	yes	32
11.7	odd	10		7623.2.a.db.1.15		16
33.5	odd	10	inner	693.2.m.k.379.8	yes	32
33.26	odd	10		7623.2.a.dc.1.15		16
33.29	even	10		7623.2.a.db.1.2		16

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

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

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