LMFDB - Embedded newform 756.2.bt.a.103.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(103,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14, 15]))

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

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

chi := DirichletCharacter("756.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bt (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			103.14
Character	$\chi$	$=$	756.103
Dual form			756.2.bt.a.367.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34481 - 0.437584i) q^{2} +(1.72493 - 0.156906i) q^{3} +(1.61704 + 1.17694i) q^{4} +(-4.40150 - 0.776103i) q^{5} +(-2.38837 - 0.543792i) q^{6} +(-2.15811 + 1.53054i) q^{7} +(-1.65961 - 2.29035i) q^{8} +(2.95076 - 0.541305i) q^{9} +O(q^{10})$	\(q+(-1.34481 - 0.437584i) q^{2} +(1.72493 - 0.156906i) q^{3} +(1.61704 + 1.17694i) q^{4} +(-4.40150 - 0.776103i) q^{5} +(-2.38837 - 0.543792i) q^{6} +(-2.15811 + 1.53054i) q^{7} +(-1.65961 - 2.29035i) q^{8} +(2.95076 - 0.541305i) q^{9} +(5.57958 + 2.96974i) q^{10} +(2.41224 - 0.425343i) q^{11} +(2.97395 + 1.77641i) q^{12} +(0.340909 - 0.406280i) q^{13} +(3.57199 - 1.11394i) q^{14} +(-7.71405 - 0.648100i) q^{15} +(1.22964 + 3.80631i) q^{16} +4.48133i q^{17} +(-4.20509 - 0.563254i) q^{18} +1.74663 q^{19} +(-6.20398 - 6.43528i) q^{20} +(-3.48243 + 2.97870i) q^{21} +(-3.43013 - 0.483552i) q^{22} +(4.02878 - 4.80132i) q^{23} +(-3.22207 - 3.69029i) q^{24} +(14.0724 + 5.12194i) q^{25} +(-0.636241 + 0.397194i) q^{26} +(5.00492 - 1.39671i) q^{27} +(-5.29110 - 0.0650108i) q^{28} +(-1.37257 + 1.15173i) q^{29} +(10.0904 + 4.24712i) q^{30} +(7.82994 - 2.84987i) q^{31} +(0.0119535 - 5.65684i) q^{32} +(4.09420 - 1.11218i) q^{33} +(1.96096 - 6.02654i) q^{34} +(10.6868 - 5.06177i) q^{35} +(5.40858 + 2.59755i) q^{36} +(1.85751 + 3.21730i) q^{37} +(-2.34889 - 0.764299i) q^{38} +(0.524297 - 0.754295i) q^{39} +(5.52720 + 11.3690i) q^{40} +(3.55736 - 4.23950i) q^{41} +(5.98665 - 2.48193i) q^{42} +(-1.62214 + 4.45679i) q^{43} +(4.40129 + 2.15126i) q^{44} +(-13.4079 + 0.0924577i) q^{45} +(-7.51894 + 4.69394i) q^{46} +(-0.118177 - 0.0430127i) q^{47} +(2.71827 + 6.37268i) q^{48} +(2.31487 - 6.60616i) q^{49} +(-16.6835 - 13.0459i) q^{50} +(0.703149 + 7.72997i) q^{51} +(1.02943 - 0.255742i) q^{52} +(1.24810 + 2.16178i) q^{53} +(-7.34185 - 0.311768i) q^{54} -10.9476 q^{55} +(7.08709 + 2.40273i) q^{56} +(3.01282 - 0.274058i) q^{57} +(2.34983 - 0.948239i) q^{58} +(0.0178638 + 0.0149895i) q^{59} +(-11.7112 - 10.1270i) q^{60} +(-2.25738 + 6.20210i) q^{61} +(-11.7769 + 0.406274i) q^{62} +(-5.53957 + 5.68446i) q^{63} +(-2.49142 + 7.60216i) q^{64} +(-1.81583 + 1.52366i) q^{65} +(-5.99261 - 0.295883i) q^{66} +(6.98051 + 1.23085i) q^{67} +(-5.27424 + 7.24648i) q^{68} +(6.19601 - 8.91407i) q^{69} +(-16.5867 + 2.13076i) q^{70} +(9.07352 + 5.23860i) q^{71} +(-6.13688 - 5.85993i) q^{72} +(-12.3893 - 7.15295i) q^{73} +(-1.09016 - 5.13948i) q^{74} +(25.0776 + 6.62693i) q^{75} +(2.82437 + 2.05568i) q^{76} +(-4.55487 + 4.60997i) q^{77} +(-1.03515 + 0.784961i) q^{78} +(4.15015 - 0.731783i) q^{79} +(-2.45815 - 17.7078i) q^{80} +(8.41398 - 3.19452i) q^{81} +(-6.63912 + 4.14468i) q^{82} +(-9.40748 + 7.89382i) q^{83} +(-9.13698 + 0.718069i) q^{84} +(3.47797 - 19.7246i) q^{85} +(4.13170 - 5.28373i) q^{86} +(-2.18688 + 2.20201i) q^{87} +(-4.97755 - 4.81897i) q^{88} +2.97747i q^{89} +(18.0715 + 5.74274i) q^{90} +(-0.113891 + 1.39857i) q^{91} +(12.1656 - 3.02229i) q^{92} +(13.0589 - 6.14439i) q^{93} +(0.140104 + 0.109556i) q^{94} +(-7.68780 - 1.35557i) q^{95} +(-0.866976 - 9.75953i) q^{96} +(2.30392 - 6.32998i) q^{97} +(-6.00382 + 7.87109i) q^{98} +(6.88770 - 2.56084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.34481	−	0.437584i	−0.950926	−	0.309419i
$2$	−1.34481	−	0.437584i	−0.950926	−	0.309419i
$3$	1.72493	−	0.156906i	0.995888	−	0.0905899i
$3$	1.72493	−	0.156906i	0.995888	−	0.0905899i
$4$	1.61704	+	1.17694i	0.808520	+	0.588469i
$5$	−4.40150	−	0.776103i	−1.96841	−	0.347084i	−0.990277	−	0.139108i	$-0.955576\pi$
$5$	−4.40150	−	0.776103i	−1.96841	−	0.347084i	−0.978134	−	0.207976i	$-0.933312\pi$
$6$	−2.38837	−	0.543792i	−0.975046	−	0.222002i
$7$	−2.15811	+	1.53054i	−0.815689	+	0.578491i
$7$	−2.15811	+	1.53054i	−0.815689	+	0.578491i
$8$	−1.65961	−	2.29035i	−0.586759	−	0.809762i
$9$	2.95076	−	0.541305i	0.983587	−	0.180435i
$10$	5.57958	+	2.96974i	1.76442	+	0.939115i
$11$	2.41224	−	0.425343i	0.727318	−	0.128246i	0.202284	−	0.979327i	$-0.435164\pi$
$11$	2.41224	−	0.425343i	0.727318	−	0.128246i	0.525034	+	0.851081i	$0.324053\pi$
$12$	2.97395	+	1.77641i	0.858505	+	0.512805i
$13$	0.340909	−	0.406280i	0.0945513	−	0.112682i	−0.716694	−	0.697388i	$-0.754346\pi$
$13$	0.340909	−	0.406280i	0.0945513	−	0.112682i	0.811245	+	0.584706i	$0.198790\pi$
$14$	3.57199	−	1.11394i	0.954656	−	0.297713i
$15$	−7.71405	−	0.648100i	−1.99176	−	0.167339i
$16$	1.22964	+	3.80631i	0.307409	+	0.951578i
$17$			4.48133i			1.08688i	0.839448	+	0.543441i	$0.182879\pi$
$17$			4.48133i			1.08688i	−0.839448	+	0.543441i	$0.817121\pi$
$18$	−4.20509	−	0.563254i	−0.991148	−	0.132760i
$19$	1.74663			0.400705			0.200352	−	0.979724i	$-0.435791\pi$
$19$	1.74663			0.400705			0.200352	+	0.979724i	$0.435791\pi$
$20$	−6.20398	−	6.43528i	−1.38725	−	1.43897i
$21$	−3.48243	+	2.97870i	−0.759929	+	0.650006i
$22$	−3.43013	−	0.483552i	−0.731307	−	0.103094i
$23$	4.02878	−	4.80132i	0.840059	−	1.00114i	−0.159843	−	0.987142i	$-0.551099\pi$
$23$	4.02878	−	4.80132i	0.840059	−	1.00114i	0.999902	−	0.0140010i	$-0.00445681\pi$
$24$	−3.22207	−	3.69029i	−0.657703	−	0.753278i
$25$	14.0724	+	5.12194i	2.81448	+	1.02439i
$26$	−0.636241	+	0.397194i	−0.124777	+	0.0778961i
$27$	5.00492	−	1.39671i	0.963197	−	0.268796i
$28$	−5.29110	−	0.0650108i	−0.999925	−	0.0122859i
$29$	−1.37257	+	1.15173i	−0.254881	+	0.213870i	−0.761271	−	0.648434i	$-0.775424\pi$
$29$	−1.37257	+	1.15173i	−0.254881	+	0.213870i	0.506390	+	0.862305i	$0.330980\pi$
$30$	10.0904	+	4.24712i	1.84224	+	0.775415i
$31$	7.82994	−	2.84987i	1.40630	−	0.511851i	0.476258	−	0.879306i	$-0.341993\pi$
$31$	7.82994	−	2.84987i	1.40630	−	0.511851i	0.930041	+	0.367455i	$0.119771\pi$
$32$	0.0119535	−	5.65684i	0.00211309	−	0.999998i
$33$	4.09420	−	1.11218i	0.712709	−	0.193606i
$34$	1.96096	−	6.02654i	0.336302	−	1.03354i
$35$	10.6868	−	5.06177i	1.80640	−	0.855596i
$36$	5.40858	+	2.59755i	0.901430	+	0.432925i
$37$	1.85751	+	3.21730i	0.305372	+	0.528920i	0.977344	−	0.211656i	$-0.0678857\pi$
$37$	1.85751	+	3.21730i	0.305372	+	0.528920i	−0.671972	+	0.740577i	$0.734552\pi$
$38$	−2.34889	−	0.764299i	−0.381041	−	0.123986i
$39$	0.524297	−	0.754295i	0.0839547	−	0.120784i
$40$	5.52720	+	11.3690i	0.873928	+	1.79760i
$41$	3.55736	−	4.23950i	0.555567	−	0.662099i	−0.413035	−	0.910715i	$-0.635531\pi$
$41$	3.55736	−	4.23950i	0.555567	−	0.662099i	0.968602	+	0.248616i	$0.0799759\pi$
$42$	5.98665	−	2.48193i	0.923761	−	0.382971i
$43$	−1.62214	+	4.45679i	−0.247374	+	0.679655i	0.752406	+	0.658699i	$0.228893\pi$
$43$	−1.62214	+	4.45679i	−0.247374	+	0.679655i	−0.999780	+	0.0209554i	$0.993329\pi$
$44$	4.40129	+	2.15126i	0.663519	+	0.324315i
$45$	−13.4079	+	0.0924577i	−1.99873	+	0.0137828i
$46$	−7.51894	+	4.69394i	−1.10861	+	0.692083i
$47$	−0.118177	−	0.0430127i	−0.0172378	−	0.00627405i	0.333387	−	0.942790i	$-0.391808\pi$
$47$	−0.118177	−	0.0430127i	−0.0172378	−	0.00627405i	−0.350625	+	0.936516i	$0.614031\pi$
$48$	2.71827	+	6.37268i	0.392348	+	0.919817i
$49$	2.31487	−	6.60616i	0.330696	−	0.943737i
$50$	−16.6835	−	13.0459i	−2.35940	−	1.84497i
$51$	0.703149	+	7.72997i	0.0984605	+	1.08241i
$52$	1.02943	−	0.255742i	0.142756	−	0.0354650i
$53$	1.24810	+	2.16178i	0.171440	+	0.296943i	0.938924	−	0.344126i	$-0.111825\pi$
$53$	1.24810	+	2.16178i	0.171440	+	0.296943i	−0.767484	+	0.641069i	$0.778491\pi$
$54$	−7.34185	−	0.311768i	−0.999100	−	0.0424263i
$55$	−10.9476			−1.47617
$56$	7.08709	+	2.40273i	0.947053	+	0.321079i
$57$	3.01282	−	0.274058i	0.399057	−	0.0362998i
$58$	2.34983	−	0.948239i	0.308548	−	0.124510i
$59$	0.0178638	+	0.0149895i	0.00232567	+	0.00195147i	0.643950	−	0.765068i	$-0.277295\pi$
$59$	0.0178638	+	0.0149895i	0.00232567	+	0.00195147i	−0.641624	+	0.767019i	$0.721739\pi$
$60$	−11.7112	−	10.1270i	−1.51190	−	1.30739i
$61$	−2.25738	+	6.20210i	−0.289028	+	0.794098i	0.707175	+	0.707038i	$0.249969\pi$
$61$	−2.25738	+	6.20210i	−0.289028	+	0.794098i	−0.996203	+	0.0870593i	$0.972253\pi$
$62$	−11.7769	+	0.406274i	−1.49566	+	0.0515968i
$63$	−5.53957	+	5.68446i	−0.697921	+	0.716175i
$64$	−2.49142	+	7.60216i	−0.311428	+	0.950270i
$65$	−1.81583	+	1.52366i	−0.225226	+	0.188987i
$66$	−5.99261	−	0.295883i	−0.737639	−	0.0364207i
$67$	6.98051	+	1.23085i	0.852805	+	0.150373i	0.582930	−	0.812523i	$-0.301906\pi$
$67$	6.98051	+	1.23085i	0.852805	+	0.150373i	0.269876	+	0.962895i	$0.413017\pi$
$68$	−5.27424	+	7.24648i	−0.639596	+	0.878765i
$69$	6.19601	−	8.91407i	0.745912	−	1.07313i
$70$	−16.5867	+	2.13076i	−1.98249	+	0.254675i
$71$	9.07352	+	5.23860i	1.07683	+	0.621707i	0.930039	−	0.367460i	$-0.119773\pi$
$71$	9.07352	+	5.23860i	1.07683	+	0.621707i	0.146790	+	0.989168i	$0.453106\pi$
$72$	−6.13688	−	5.85993i	−0.723238	−	0.690599i
$73$	−12.3893	−	7.15295i	−1.45005	−	0.837189i	−0.451570	−	0.892236i	$-0.649136\pi$
$73$	−12.3893	−	7.15295i	−1.45005	−	0.837189i	−0.998484	+	0.0550466i	$0.982469\pi$
$74$	−1.09016	−	5.13948i	−0.126728	−	0.597452i
$75$	25.0776	+	6.62693i	2.89571	+	0.765212i
$76$	2.82437	+	2.05568i	0.323978	+	0.235802i
$77$	−4.55487	+	4.60997i	−0.519076	+	0.525355i
$78$	−1.03515	+	0.784961i	−0.117207	+	0.0888794i
$79$	4.15015	−	0.731783i	0.466928	−	0.0823320i	0.0647660	−	0.997900i	$-0.479370\pi$
$79$	4.15015	−	0.731783i	0.466928	−	0.0823320i	0.402162	+	0.915568i	$0.368259\pi$
$80$	−2.45815	−	17.7078i	−0.274830	−	1.97979i
$81$	8.41398	−	3.19452i	0.934886	−	0.354947i
$82$	−6.63912	+	4.14468i	−0.733169	+	0.457704i
$83$	−9.40748	+	7.89382i	−1.03261	+	0.866459i	−0.991159	−	0.132682i	$-0.957641\pi$
$83$	−9.40748	+	7.89382i	−1.03261	+	0.866459i	−0.0414468	+	0.999141i	$0.513197\pi$
$84$	−9.13698	+	0.718069i	−0.996926	+	0.0783477i
$85$	3.47797	−	19.7246i	0.377239	−	2.13943i
$86$	4.13170	−	5.28373i	0.445532	−	0.569759i
$87$	−2.18688	+	2.20201i	−0.234458	+	0.236080i
$88$	−4.97755	−	4.81897i	−0.530609	−	0.513704i
$89$			2.97747i			0.315611i	0.987470	+	0.157806i	$0.0504420\pi$
$89$			2.97747i			0.315611i	−0.987470	+	0.157806i	$0.949558\pi$
$90$	18.0715	+	5.74274i	1.90491	+	0.605338i
$91$	−0.113891	+	1.39857i	−0.0119390	+	0.146610i
$92$	12.1656	−	3.02229i	1.26835	−	0.315096i
$93$	13.0589	−	6.14439i	1.35415	−	0.637143i
$94$	0.140104	+	0.109556i	0.0144506	+	0.0112999i
$95$	−7.68780	−	1.35557i	−0.788752	−	0.139078i
$96$	−0.866976	−	9.75953i	−0.0884853	−	0.996077i
$97$	2.30392	−	6.32998i	0.233928	−	0.642712i	−0.766072	−	0.642755i	$-0.777791\pi$
$97$	2.30392	−	6.32998i	0.233928	−	0.642712i	1.00000		4.28389e-5i	$1.36360e-5\pi$
$98$	−6.00382	+	7.87109i	−0.606478	+	0.795100i
$99$	6.88770	−	2.56084i	0.692240	−	0.257374i
$100$	16.7274	+	24.8447i	1.67274	+	2.48447i
$101$	8.93400	+	10.6471i	0.888966	+	1.05943i	0.997861	+	0.0653755i	$0.0208245\pi$
$101$	8.93400	+	10.6471i	0.888966	+	1.05943i	−0.108894	+	0.994053i	$0.534731\pi$
$102$	2.43691	−	10.7030i	0.241290	−	1.05976i
$103$	0.325529	−	1.84617i	0.0320754	−	0.181908i	−0.964561	−	0.263860i	$-0.915004\pi$
$103$	0.325529	−	1.84617i	0.0320754	−	0.181908i	0.996636	+	0.0819518i	$0.0261153\pi$
$104$	−1.49630	−	0.106538i	−0.146724	−	0.0104469i
$105$	17.6397	−	10.4080i	1.72146	−	1.01572i
$106$	−0.732503	−	3.45333i	−0.0711470	−	0.335417i
$107$	14.2101	+	8.20423i	1.37375	+	0.793133i	0.991398	−	0.130885i	$-0.0417819\pi$
$107$	14.2101	+	8.20423i	1.37375	+	0.793133i	0.382349	+	0.924018i	$0.375115\pi$
$108$	9.73699	+	3.63195i	0.936942	+	0.349485i
$109$	−5.68240	−	9.84221i	−0.544275	−	0.942713i	−0.998652	−	0.0519031i	$-0.983471\pi$
$109$	−5.68240	−	9.84221i	−0.544275	−	0.942713i	0.454377	−	0.890810i	$-0.349862\pi$
$110$	14.7224	+	4.79049i	1.40373	+	0.456756i
$111$	3.70888	+	5.25815i	0.352032	+	0.499082i
$112$	−8.47941	−	6.33242i	−0.801229	−	0.598358i
$113$	2.32409	−	0.845900i	0.218632	−	0.0795756i	−0.230382	−	0.973100i	$-0.573998\pi$
$113$	2.32409	−	0.845900i	0.218632	−	0.0795756i	0.449014	+	0.893525i	$0.351775\pi$
$114$	−4.17160	−	0.949805i	−0.390706	−	0.0889574i
$115$	−21.4590	+	18.0062i	−2.00106	+	1.67909i
$116$	−3.57502	+	0.246953i	−0.331932	+	0.0229290i
$117$	0.786021	−	1.38337i	0.0726677	−	0.127893i
$118$	−0.0174643	−	0.0279750i	−0.00160772	−	0.00257531i
$119$	−6.85886	−	9.67119i	−0.628751	−	0.886557i
$120$	11.3179	+	18.7435i	1.03318	+	1.71104i
$121$	−4.69864	+	1.71016i	−0.427149	+	0.155469i
$122$	5.74969	−	7.35287i	0.520553	−	0.665697i
$123$	5.47099	−	7.87101i	0.493303	−	0.709705i
$124$	16.0154	+	4.60701i	1.43823	+	0.413722i
$125$	−38.6115	−	22.2924i	−3.45352	−	1.99389i
$126$	9.93712	−	5.22050i	0.885269	−	0.465079i
$127$	9.29300	−	5.36532i	0.824620	−	0.476095i	−0.0273868	−	0.999625i	$-0.508719\pi$
$127$	9.29300	−	5.36532i	0.824620	−	0.476095i	0.852007	+	0.523530i	$0.175385\pi$
$128$	6.67708	−	9.13327i	0.590176	−	0.807275i
$129$	−2.09878	+	7.94218i	−0.184787	+	0.699270i
$130$	3.10868	−	1.25446i	0.272649	−	0.110023i
$131$	0.351199	+	0.294691i	0.0306844	+	0.0257473i	0.658001	−	0.753017i	$-0.271402\pi$
$131$	0.351199	+	0.294691i	0.0306844	+	0.0257473i	−0.627316	+	0.778764i	$0.715847\pi$
$132$	7.92946	+	3.02018i	0.690171	+	0.262873i
$133$	−3.76942	+	2.67330i	−0.326850	+	0.231804i
$134$	−8.84887	−	4.70983i	−0.764426	−	0.406867i
$135$	−23.1131	+	2.26327i	−1.98926	+	0.194791i
$136$	10.2638	−	7.43723i	0.880115	−	0.637737i
$137$	−1.41520	−	0.515091i	−0.120909	−	0.0440072i	0.280857	−	0.959750i	$-0.409381\pi$
$137$	−1.41520	−	0.515091i	−0.120909	−	0.0440072i	−0.401766	+	0.915742i	$0.631603\pi$
$138$	−12.2331	+	9.27647i	−1.04135	+	0.789666i
$139$	1.75376	−	9.94604i	0.148752	−	0.843612i	−0.815526	−	0.578720i	$-0.803552\pi$
$139$	1.75376	−	9.94604i	0.148752	−	0.843612i	0.964278	−	0.264892i	$-0.0853364\pi$
$140$	23.2383	+	4.39259i	1.96400	+	0.371241i
$141$	−0.210595	−	0.0556513i	−0.0177353	−	0.00468668i
$142$	−9.90985	−	11.0154i	−0.831616	−	0.924389i
$143$	0.649547	−	1.12505i	0.0543178	−	0.0940813i
$144$	5.68873	+	10.5659i	0.474061	+	0.880492i
$145$	6.93524	−	4.00407i	0.575941	−	0.332520i
$146$	13.5312	+	15.0407i	1.11985	+	1.24478i
$147$	2.95644	−	11.7584i	0.243843	−	0.969815i
$148$	−0.782895	+	7.38867i	−0.0643536	+	0.607345i
$149$	−4.02397	+	1.46460i	−0.329656	+	0.119985i	−0.501546	−	0.865131i	$-0.667235\pi$
$149$	−4.02397	+	1.46460i	−0.329656	+	0.119985i	0.171889	+	0.985116i	$0.445013\pi$
$150$	−30.8248	−	19.8855i	−2.51683	−	1.62365i
$151$	14.9066	−	2.62843i	1.21308	−	0.213899i	0.469736	−	0.882807i	$-0.344349\pi$
$151$	14.9066	−	2.62843i	1.21308	−	0.213899i	0.743345	+	0.668908i	$0.233238\pi$
$152$	−2.89872	−	4.00040i	−0.235117	−	0.324475i
$153$	2.42576	+	13.2233i	0.196111	+	1.06904i
$154$	8.14270	−	4.20641i	0.656157	−	0.338962i
$155$	−36.6753	+	6.46684i	−2.94583	+	0.519429i
$156$	1.73557	−	0.602661i	0.138957	−	0.0482515i
$157$	−15.0041	+	17.8812i	−1.19746	+	1.42707i	−0.320002	+	0.947417i	$0.603683\pi$
$157$	−15.0041	+	17.8812i	−1.19746	+	1.42707i	−0.877456	+	0.479657i	$0.840761\pi$
$158$	−5.90139	−	0.831929i	−0.469489	−	0.0661848i
$159$	2.49208	+	3.53307i	0.197635	+	0.280191i
$160$	−4.44291	+	24.8893i	−0.351243	+	1.96767i
$161$	−1.34593	+	16.5280i	−0.106074	+	1.30259i
$162$	−12.7131	+	0.614206i	−0.998835	+	0.0482565i
$163$	−13.2829	−	7.66886i	−1.04039	−	0.600672i	−0.120449	−	0.992719i	$-0.538433\pi$
$163$	−13.2829	−	7.66886i	−1.04039	−	0.600672i	−0.919945	+	0.392048i	$0.871767\pi$
$164$	10.7420	−	2.66865i	0.838811	−	0.208386i
$165$	−18.8838	+	1.71775i	−1.47010	+	0.133726i
$166$	16.1055	−	6.49913i	1.25003	−	0.504430i
$167$	−1.04906	+	0.381826i	−0.0811786	+	0.0295466i	−0.382290	−	0.924042i	$-0.624865\pi$
$167$	−1.04906	+	0.381826i	−0.0811786	+	0.0295466i	0.301112	+	0.953589i	$0.402642\pi$
$168$	12.6017	+	3.03253i	0.972245	+	0.233965i
$169$	2.20858	+	12.5255i	0.169891	+	0.963499i
$170$	−13.3084	+	25.0039i	−1.02071	+	1.91771i
$171$	5.15389	−	0.945460i	0.394128	−	0.0723011i
$172$	−7.86843	+	5.29765i	−0.599962	+	0.403942i
$173$	−11.2868	−	13.4511i	−0.858120	−	1.02267i	−0.999465	−	0.0327074i	$-0.989587\pi$
$173$	−11.2868	−	13.4511i	−0.858120	−	1.02267i	0.141345	−	0.989960i	$-0.454857\pi$
$174$	3.90451	−	2.00435i	0.296000	−	0.151949i
$175$	−38.2092	+	10.4847i	−2.88834	+	0.792571i
$176$	4.58516	+	8.65871i	0.345620	+	0.652675i
$177$	0.0331657	+	0.0230529i	0.00249289	+	0.00173276i
$178$	1.30290	−	4.00414i	0.0976561	−	0.300123i
$179$			10.1801i			0.760898i	0.924802	+	0.380449i	$0.124231\pi$
$179$			10.1801i			0.760898i	−0.924802	+	0.380449i	$0.875769\pi$
$180$	−21.7899	−	15.6307i	−1.62412	−	1.16505i
$181$	21.5618	−	12.4487i	1.60267	−	0.925304i	0.611723	−	0.791072i	$-0.290477\pi$
$181$	21.5618	−	12.4487i	1.60267	−	0.925304i	0.990950	−	0.134232i	$-0.0428567\pi$
$182$	0.765156	−	1.83098i	0.0567171	−	0.135721i
$183$	−2.92067	+	11.0524i	−0.215902	+	0.817016i
$184$	−17.6829	−	1.25904i	−1.30360	−	0.0928176i
$185$	−5.67887	−	15.6026i	−0.417518	−	1.14712i
$186$	−20.2505	+	2.54866i	−1.48484	+	0.186877i
$187$	1.90610	+	10.8100i	0.139388	+	0.790508i
$188$	−0.140473	−	0.208640i	−0.0102450	−	0.0152166i
$189$	−8.66345	+	10.6745i	−0.630173	+	0.776455i
$190$	9.74548	+	5.18705i	0.707011	+	0.376308i
$191$	1.17475	−	0.207141i	0.0850022	−	0.0149882i	−0.130985	−	0.991384i	$-0.541814\pi$
$191$	1.17475	−	0.207141i	0.0850022	−	0.0149882i	0.215988	+	0.976396i	$0.430703\pi$
$192$	−3.10470	+	13.5041i	−0.224062	+	0.974575i
$193$	−0.331372	+	0.120609i	−0.0238527	+	0.00868166i	−0.353919	−	0.935276i	$-0.615151\pi$
$193$	−0.331372	+	0.120609i	−0.0238527	+	0.00868166i	0.330066	+	0.943958i	$0.392929\pi$
$194$	−5.86824	+	7.50447i	−0.421315	+	0.538790i
$195$	−2.89310	+	2.91312i	−0.207179	+	0.208613i
$196$	11.5183	−	7.95796i	0.822734	−	0.568426i
$197$	4.19159	+	7.26004i	0.298638	+	0.517257i	0.975825	−	0.218555i	$-0.0701343\pi$
$197$	4.19159	+	7.26004i	0.298638	+	0.517257i	−0.677186	+	0.735812i	$0.736801\pi$
$198$	−10.3832	+	0.429900i	−0.737905	+	0.0305517i
$199$	5.92518			0.420025			0.210013	−	0.977699i	$-0.432650\pi$
$199$	5.92518			0.420025			0.210013	+	0.977699i	$0.432650\pi$
$200$	−11.6236	−	40.7312i	−0.821913	−	2.88013i
$201$	12.2340	+	1.02785i	0.862921	+	0.0724987i
$202$	−7.35554	−	18.2278i	−0.517534	−	1.28250i
$203$	1.19940	−	4.58634i	0.0841812	−	0.321898i
$204$	−7.96067	+	13.3272i	−0.557359	+	0.933093i
$205$	−18.9480	+	15.8993i	−1.32339	+	1.11045i
$206$	−1.24563	+	2.34030i	−0.0867872	+	0.163057i
$207$	9.28900	−	16.3483i	0.645630	−	1.13629i
$208$	1.96562	+	0.798031i	0.136291	+	0.0553335i
$209$	4.21329	−	0.742918i	0.291440	−	0.0513887i
$210$	−28.2765	+	6.27797i	−1.95126	+	0.433221i
$211$	−7.79627	−	21.4201i	−0.536717	−	1.47462i	−0.850937	−	0.525268i	$-0.823965\pi$
$211$	−7.79627	−	21.4201i	−0.536717	−	1.47462i	0.314219	−	0.949350i	$-0.398257\pi$
$212$	−0.526045	+	4.96462i	−0.0361289	+	0.340971i
$213$	16.4731	+	7.61252i	1.12872	+	0.521601i
$214$	−15.5199	−	17.2513i	−1.06092	−	1.17927i
$215$	10.5988	−	18.3576i	0.722831	−	1.25198i
$216$	−11.5051	−	9.14504i	−0.782825	−	0.622241i
$217$	−12.5360	+	18.1344i	−0.851001	+	1.23104i
$218$	3.33497	+	15.7225i	0.225872	+	1.06486i
$219$	−22.4929	−	10.3944i	−1.51993	−	0.702386i
$220$	−17.7027	−	12.8846i	−1.19351	−	0.868681i
$221$	1.82067	+	1.52773i	0.122472	+	0.102766i
$222$	−2.68686	−	8.69418i	−0.180331	−	0.583515i
$223$	2.03238	+	11.5262i	0.136098	+	0.771853i	0.974089	+	0.226167i	$0.0726195\pi$
$223$	2.03238	+	11.5262i	0.136098	+	0.771853i	−0.837990	+	0.545685i	$0.816269\pi$
$224$	8.63225	+	12.2264i	0.576766	+	0.816909i
$225$	44.2969	+	7.49615i	2.95312	+	0.499744i
$226$	−3.49562	+	0.120591i	−0.232525	+	0.00802157i
$227$	4.59176	+	26.0412i	0.304766	+	1.72841i	0.624606	+	0.780940i	$0.285260\pi$
$227$	4.59176	+	26.0412i	0.304766	+	1.72841i	−0.319840	+	0.947472i	$0.603629\pi$
$228$	5.19439	+	3.10274i	0.344007	+	0.205484i
$229$	−2.17370	−	5.97219i	−0.143642	−	0.394654i	0.846920	−	0.531721i	$-0.178455\pi$
$229$	−2.17370	−	5.97219i	−0.143642	−	0.394654i	−0.990562	+	0.137067i	$0.956232\pi$
$230$	36.7376	−	14.8249i	2.42240	−	0.977524i
$231$	−7.13350	+	8.66657i	−0.469350	+	0.570218i
$232$	4.91579	+	1.23227i	0.322737	+	0.0809022i
$233$	−4.55736	−	7.89358i	−0.298563	−	0.517126i	0.677245	−	0.735758i	$-0.263174\pi$
$233$	−4.55736	−	7.89358i	−0.298563	−	0.517126i	−0.975807	+	0.218632i	$0.929841\pi$
$234$	−1.66239	+	1.51642i	−0.108674	+	0.0991317i
$235$	0.486772	+	0.281038i	0.0317535	+	0.0183329i
$236$	0.0112447	+	0.0452632i	0.000731971	+	0.00294638i
$237$	7.04389	−	1.91346i	0.457550	−	0.124293i
$238$	4.99192	+	16.0073i	0.323578	+	1.03760i
$239$	−0.994195	−	0.175303i	−0.0643091	−	0.0113394i	0.141401	−	0.989952i	$-0.454839\pi$
$239$	−0.994195	−	0.175303i	−0.0643091	−	0.0113394i	−0.205710	+	0.978613i	$0.565950\pi$
$240$	−7.01860	−	30.1590i	−0.453049	−	1.94676i
$241$	3.17578	−	8.72539i	0.204570	−	0.562052i	−0.794401	−	0.607393i	$-0.792215\pi$
$241$	3.17578	−	8.72539i	0.204570	−	0.562052i	0.998972	+	0.0453413i	$0.0144375\pi$
$242$	7.06713	−	0.243799i	0.454292	−	0.0156720i
$243$	14.0123	−	6.83053i	0.898888	−	0.438179i
$244$	−10.9498	+	7.37225i	−0.700987	+	0.471960i
$245$	−15.3160	+	27.2804i	−0.978502	+	1.74288i
$246$	−10.8017	+	8.19101i	−0.688691	+	0.522240i
$247$	0.595443	−	0.709622i	0.0378872	−	0.0451522i
$248$	−19.5218	−	13.2037i	−1.23964	−	0.838434i
$249$	−14.9887	+	15.0924i	−0.949867	+	0.956440i
$250$	42.1704	+	46.8748i	2.66709	+	2.96463i
$251$	−6.12760	−	10.6133i	−0.386771	−	0.669907i	0.605242	−	0.796041i	$-0.293076\pi$
$251$	−6.12760	−	10.6133i	−0.386771	−	0.669907i	−0.992013	+	0.126134i	$0.959743\pi$
$252$	−15.6480	+	2.67227i	−0.985729	+	0.168337i
$253$	7.67618	−	13.2955i	0.482597	−	0.835883i
$254$	−14.8451	+	3.14887i	−0.931465	+	0.197578i
$255$	2.90435	−	34.5692i	0.181877	−	2.16481i
$256$	−12.9760	+	9.36075i	−0.811000	+	0.585047i
$257$	−6.21156	−	17.0661i	−0.387467	−	1.06456i	−0.968138	−	0.250418i	$-0.919432\pi$
$257$	−6.21156	−	17.0661i	−0.387467	−	1.06456i	0.580671	−	0.814138i	$-0.302790\pi$
$258$	6.29783	−	9.76234i	0.392086	−	0.607777i
$259$	−8.93292	−	4.10028i	−0.555064	−	0.254779i
$260$	−4.72952	+	0.326704i	−0.293313	+	0.0202613i
$261$	−3.42670	+	4.14145i	−0.212108	+	0.256349i
$262$	−0.343345	−	0.549983i	−0.0212119	−	0.0339781i
$263$	13.1285	+	15.6459i	0.809538	+	0.964770i	0.999856	−	0.0169526i	$-0.00539643\pi$
$263$	13.1285	+	15.6459i	0.809538	+	0.964770i	−0.190318	+	0.981722i	$0.560952\pi$
$264$	−9.34205	−	7.53138i	−0.574963	−	0.463524i
$265$	−3.81576	−	10.4837i	−0.234400	−	0.644009i
$266$	6.23896	−	1.94564i	0.382535	−	0.119295i
$267$	0.467184	+	5.13593i	0.0285912	+	0.314314i
$268$	9.83913	+	10.2060i	0.601020	+	0.623428i
$269$	−19.9171	+	11.4991i	−1.21437	+	0.701114i	−0.963707	−	0.266961i	$-0.913980\pi$
$269$	−19.9171	+	11.4991i	−1.21437	+	0.701114i	−0.250659	+	0.968076i	$0.580647\pi$
$270$	32.0732	+	7.07028i	1.95191	+	0.430284i
$271$	−7.96089	+	13.7887i	−0.483590	+	0.837602i	−0.999822	−	0.0188467i	$-0.994001\pi$
$271$	−7.96089	+	13.7887i	−0.483590	+	0.837602i	0.516233	+	0.856448i	$0.327334\pi$
$272$	−17.0573	+	5.51040i	−1.03425	+	0.334117i
$273$	0.0229918	+	2.43031i	0.00139153	+	0.147089i
$274$	1.67778	+	1.31197i	0.101359	+	0.0792591i
$275$	36.1246	+	6.36974i	2.17840	+	0.384110i
$276$	20.5105	−	7.12209i	1.23459	−	0.428700i
$277$	8.04262	−	6.74856i	0.483234	−	0.405482i	−0.368360	−	0.929683i	$-0.620081\pi$
$277$	8.04262	−	6.74856i	0.483234	−	0.405482i	0.851594	+	0.524202i	$0.175636\pi$
$278$	−6.71070	+	12.6081i	−0.402481	+	0.756186i
$279$	21.5616	−	12.6477i	1.29086	−	0.757196i
$280$	−29.3291	−	16.0759i	−1.75275	−	0.960721i
$281$	−8.09418	−	2.94604i	−0.482858	−	0.175746i	0.0891101	−	0.996022i	$-0.471598\pi$
$281$	−8.09418	−	2.94604i	−0.482858	−	0.175746i	−0.571968	+	0.820276i	$0.693820\pi$
$282$	0.258859	+	0.166994i	0.0154148	+	0.00994433i
$283$	−0.451237	+	2.55909i	−0.0268232	+	0.152122i	−0.995278	−	0.0970684i	$-0.969053\pi$
$283$	−0.451237	+	2.55909i	−0.0268232	+	0.152122i	0.968454	+	0.249191i	$0.0801645\pi$
$284$	8.50674	+	19.1500i	0.504782	+	1.13634i
$285$	−13.4736	−	1.13199i	−0.798108	−	0.0670534i
$286$	−1.36582	+	1.22875i	−0.0807628	+	0.0726573i
$287$	−1.18844	+	14.5940i	−0.0701514	+	0.861457i
$288$	−3.02680	−	16.6985i	−0.178356	−	0.983966i
$289$	−3.08228			−0.181311
$290$	−11.0787	+	2.34996i	−0.650565	+	0.137994i
$291$	2.98089	−	11.2803i	0.174743	−	0.661261i
$292$	−11.6154	−	26.1480i	−0.679738	−	1.53020i
$293$	−7.89665	−	1.39239i	−0.461327	−	0.0813444i	−0.0618456	−	0.998086i	$-0.519699\pi$
$293$	−7.89665	−	1.39239i	−0.461327	−	0.0813444i	−0.399481	+	0.916741i	$0.630810\pi$
$294$	−9.12114	+	14.5191i	−0.531956	+	0.846772i
$295$	−0.0669941	−	0.0798404i	−0.00390055	−	0.00464849i
$296$	4.28601	−	9.59379i	0.249119	−	0.557628i
$297$	11.4790	−	5.49799i	0.666078	−	0.319026i
$298$	6.05237	−	0.208792i	0.350604	−	0.0120950i
$299$	−0.577229	−	3.27363i	−0.0333820	−	0.189319i
$300$	32.7520	+	40.2308i	1.89094	+	2.32272i
$301$	−3.32056	−	12.1010i	−0.191394	−	0.697490i
$302$	−21.1967	−	2.98814i	−1.21973	−	0.171948i
$303$	17.0811	+	16.9637i	0.981285	+	0.974541i
$304$	2.14772	+	6.64822i	0.123180	+	0.381302i
$305$	14.7493	−	25.5466i	0.844544	−	1.46279i
$306$	2.52412	−	18.8444i	0.144295	−	1.07726i
$307$	−3.78911	+	6.56293i	−0.216256	+	0.374566i	−0.953660	−	0.300885i	$-0.902718\pi$
$307$	−3.78911	+	6.56293i	−0.216256	+	0.374566i	0.737404	+	0.675452i	$0.236051\pi$
$308$	−12.7911	+	2.09371i	−0.728838	+	0.119300i
$309$	0.271840	−	3.23559i	0.0154644	−	0.184066i
$310$	52.1512	+	7.35185i	2.96199	+	0.417557i
$311$	1.53815	−	8.72327i	0.0872204	−	0.494651i	−0.909635	−	0.415409i	$-0.863639\pi$
$311$	1.53815	−	8.72327i	0.0872204	−	0.494651i	0.996855	−	0.0792429i	$-0.0252503\pi$
$312$	−2.59773	+	0.0510084i	−0.147067	+	0.00288778i
$313$	13.8169	+	16.4664i	0.780979	+	0.930735i	0.998977	−	0.0452145i	$-0.0143971\pi$
$313$	13.8169	+	16.4664i	0.780979	+	0.930735i	−0.217998	+	0.975949i	$0.569953\pi$
$314$	28.0022	−	17.4813i	1.58026	−	0.986526i
$315$	28.7942	−	20.7209i	1.62237	−	1.16749i
$316$	7.57222	+	3.70114i	0.425971	+	0.208206i
$317$	5.63558	+	2.05118i	0.316526	+	0.115206i	0.495397	−	0.868667i	$-0.335022\pi$
$317$	5.63558	+	2.05118i	0.316526	+	0.115206i	−0.178872	+	0.983872i	$0.557245\pi$
$318$	−1.80537	−	5.84182i	−0.101240	−	0.327593i
$319$	−2.82110	+	3.36205i	−0.157951	+	0.188239i
$320$	16.8661	−	31.5273i	0.942841	−	1.76243i
$321$	25.7988	+	11.9221i	1.43995	+	0.665424i
$322$	9.04242	−	21.6381i	0.503914	−	1.20584i
$323$			7.82723i			0.435519i
$324$	17.3655	+	4.73706i	0.964749	+	0.263170i
$325$	6.87836	−	3.97122i	0.381543	−	0.220284i
$326$	14.5072	+	16.1256i	0.803478	+	0.893112i
$327$	−11.3460	−	16.0855i	−0.627438	−	0.889531i
$328$	−15.6138	−	1.11172i	−0.862126	−	0.0613842i
$329$	0.320871	−	0.0880481i	0.0176902	−	0.00485425i
$330$	26.1468	+	5.95321i	1.43934	+	0.327714i
$331$	9.44044	−	25.9374i	0.518893	−	1.42565i	−0.352848	−	0.935681i	$-0.614787\pi$
$331$	9.44044	−	25.9374i	0.518893	−	1.42565i	0.871741	−	0.489967i	$-0.162991\pi$
$332$	−24.5028	+	1.69259i	−1.34477	+	0.0928931i
$333$	7.22260	+	8.48800i	0.395796	+	0.465139i
$334$	1.57787	−	0.0544328i	0.0863371	−	0.00297843i
$335$	−29.7695	−	10.8352i	−1.62648	−	0.591990i
$336$	−15.6200	−	9.59251i	−0.852140	−	0.523314i
$337$	−3.21387	−	2.69676i	−0.175071	−	0.146902i	0.551042	−	0.834478i	$-0.314230\pi$
$337$	−3.21387	−	2.69676i	−0.175071	−	0.146902i	−0.726113	+	0.687576i	$0.758675\pi$
$338$	2.51083	−	17.8109i	0.136571	−	0.968784i
$339$	3.87616	−	1.82378i	0.210524	−	0.0990542i
$340$	28.8386	−	27.8020i	1.56399	−	1.50778i
$341$	17.6755	−	10.2050i	0.957183	−	0.552630i
$342$	−7.34474	−	0.983797i	−0.397158	−	0.0531977i
$343$	5.11527	+	17.7998i	0.276198	+	0.961101i
$344$	12.8997	−	3.68125i	0.695507	−	0.198479i
$345$	−34.1900	+	34.4265i	−1.84073	+	1.85346i
$346$	9.29265	+	23.0281i	0.499576	+	1.23800i
$347$	−1.28194	−	3.52210i	−0.0688180	−	0.189076i	0.900516	−	0.434823i	$-0.143189\pi$
$347$	−1.28194	−	3.52210i	−0.0688180	−	0.189076i	−0.969334	+	0.245747i	$0.920967\pi$
$348$	−6.12790	+	0.986920i	−0.328490	+	0.0529044i
$349$	−5.41124	−	6.44886i	−0.289657	−	0.345200i	0.601518	−	0.798859i	$-0.294563\pi$
$349$	−5.41124	−	6.44886i	−0.289657	−	0.345200i	−0.891175	+	0.453659i	$0.850118\pi$
$350$	55.9721	+	2.61973i	2.99183	+	0.140031i
$351$	1.13877	−	2.50955i	0.0607831	−	0.133950i
$352$	−2.37726	−	13.6507i	−0.126709	−	0.727587i
$353$	4.40378	−	12.0993i	0.234390	−	0.643980i	−0.765610	−	0.643305i	$-0.777563\pi$
$353$	4.40378	−	12.0993i	0.234390	−	0.643980i	1.00000		0.000675426i	$-0.000214995\pi$
$354$	−0.0345141	−	0.0455146i	−0.00183440	−	0.00241907i
$355$	−35.8714	−	30.0997i	−1.90386	−	1.59753i
$356$	−3.50430	+	4.81469i	−0.185727	+	0.255178i
$357$	−13.3485	−	15.6059i	−0.706479	−	0.825953i
$358$	4.45467	−	13.6904i	0.235436	−	0.723558i
$359$		−	9.88765i		−	0.521850i	−0.965359	−	0.260925i	$-0.915972\pi$
$359$		−	9.88765i		−	0.521850i	0.965359	−	0.260925i	$-0.0840276\pi$
$360$	22.4636	+	30.5553i	1.18393	+	1.61041i
$361$	−15.9493			−0.839436
$362$	−34.4439	+	7.30606i	−1.81033	+	0.383998i
$363$	−7.83648	+	3.68716i	−0.411309	+	0.193526i
$364$	−1.83020	+	2.12751i	−0.0959285	+	0.111512i
$365$	48.9799	+	41.0991i	2.56373	+	2.15122i
$366$	8.76410	−	13.5853i	0.458107	−	0.710117i
$367$	0.395227	+	2.24145i	0.0206307	+	0.117003i	0.993384	−	0.114840i	$-0.0366356\pi$
$367$	0.395227	+	2.24145i	0.0206307	+	0.117003i	−0.972753	+	0.231843i	$0.925525\pi$
$368$	23.2292	+	9.43093i	1.21091	+	0.491621i
$369$	8.20206	−	14.4354i	0.426982	−	0.751475i
$370$	0.809573	+	23.4675i	0.0420877	+	1.22002i
$371$	−6.00223	−	2.75507i	−0.311620	−	0.143036i
$372$	28.3484	+	5.43384i	1.46979	+	0.281731i
$373$	1.40496	−	7.96792i	0.0727460	−	0.412563i	−0.926588	−	0.376078i	$-0.877273\pi$
$373$	1.40496	−	7.96792i	0.0727460	−	0.412563i	0.999334	−	0.0364855i	$-0.0116163\pi$
$374$	2.16695	−	15.3715i	0.112051	−	0.794844i
$375$	−70.0999	−	32.3944i	−3.61994	−	1.67284i
$376$	0.0976121	+	0.342050i	0.00503396	+	0.0176399i
$377$			0.950284i			0.0489421i
$378$	16.3217	−	10.5642i	0.839497	−	0.543364i
$379$			1.39322i			0.0715649i	0.999360	+	0.0357824i	$0.0113923\pi$
$379$			1.39322i			0.0715649i	−0.999360	+	0.0357824i	$0.988608\pi$
$380$	−10.8361	−	11.2401i	−0.555878	−	0.576603i
$381$	15.1879	−	10.7129i	0.778100	−	0.548839i
$382$	−1.67047	−	0.235489i	−0.0854685	−	0.0120486i
$383$	−2.66661	+	15.1231i	−0.136258	+	0.772755i	0.837718	+	0.546103i	$0.183889\pi$
$383$	−2.66661	+	15.1231i	−0.136258	+	0.772755i	−0.973976	+	0.226652i	$0.927222\pi$
$384$	10.0844	−	16.8019i	0.514618	−	0.857419i
$385$	23.6261	−	16.7558i	1.20410	−	0.853952i
$386$	0.498410	−	0.0171940i	0.0253684	−	0.000875149i
$387$	−2.37406	+	14.0290i	−0.120680	+	0.713134i
$388$	11.1755	−	7.52425i	0.567351	−	0.381986i
$389$	−1.78002	−	10.0950i	−0.0902504	−	0.511836i	−0.996100	−	0.0882353i	$-0.971877\pi$
$389$	−1.78002	−	10.0950i	−0.0902504	−	0.511836i	0.905849	−	0.423600i	$-0.139234\pi$
$390$	5.16542	−	2.65163i	0.261561	−	0.134270i
$391$	21.5163	+	18.0543i	1.08812	+	0.913045i
$392$	−18.9722	+	5.66175i	−0.958241	+	0.285961i
$393$	0.652032	+	0.453216i	0.0328907	+	0.0228617i
$394$	−2.46002	−	11.5976i	−0.123934	−	0.584277i
$395$	−18.8348			−0.947683
$396$	14.1516	+	3.96541i	0.711147	+	0.199269i
$397$			38.3343i			1.92394i	0.273152	+	0.961971i	$0.411934\pi$
$397$			38.3343i			1.92394i	−0.273152	+	0.961971i	$0.588066\pi$
$398$	−7.96826	−	2.59277i	−0.399413	−	0.129964i
$399$	−6.08253	+	5.20269i	−0.304507	+	0.260460i
$400$	−2.19175	+	59.8621i	−0.109588	+	2.99310i
$401$	18.5573	+	15.5714i	0.926709	+	0.777601i	0.975224	−	0.221222i	$-0.0710044\pi$
$401$	18.5573	+	15.5714i	0.926709	+	0.777601i	−0.0485149	+	0.998822i	$0.515449\pi$
$402$	−16.0027	−	6.73567i	−0.798141	−	0.335945i
$403$	1.51146	−	4.15270i	0.0752911	−	0.206861i
$404$	1.91563	+	27.7316i	0.0953061	+	1.37970i
$405$	−39.5134	+	7.53057i	−1.96344	+	0.374197i
$406$	−3.61987	+	5.64292i	−0.179651	+	0.280054i
$407$	5.84921	+	6.97081i	0.289934	+	0.345530i
$408$	16.5374	−	14.4392i	0.818723	−	0.714845i
$409$	7.71969	+	21.2097i	0.381714	+	1.04875i	0.970634	+	0.240559i	$0.0773309\pi$
$409$	7.71969	+	21.2097i	0.381714	+	1.04875i	−0.588920	+	0.808191i	$0.700447\pi$
$410$	32.4388	−	13.0902i	1.60204	−	0.646478i
$411$	−2.52194	−	0.666442i	−0.124398	−	0.0328731i
$412$	2.69922	−	2.60220i	0.132981	−	0.128201i
$413$	−0.0614941	−	0.00500767i	−0.00302593	−	0.000246412i
$414$	−19.6457	+	17.9207i	−0.965535	+	0.880755i
$415$	47.5335	−	27.4435i	2.33333	−	1.34715i
$416$	−2.29419	−	1.93333i	−0.112482	−	0.0947892i
$417$	1.46451	−	17.4314i	0.0717172	−	0.853619i
$418$	−5.99118	−	0.844587i	−0.293038	−	0.0413101i
$419$	10.2265	+	8.58103i	0.499596	+	0.419211i	0.857450	−	0.514566i	$-0.172047\pi$
$419$	10.2265	+	8.58103i	0.499596	+	0.419211i	−0.357854	+	0.933777i	$0.616492\pi$
$420$	40.7737	+	3.93066i	1.98955	+	0.191797i
$421$	15.9652	+	5.81087i	0.778098	+	0.283205i	0.700379	−	0.713771i	$-0.253014\pi$
$421$	15.9652	+	5.81087i	0.778098	+	0.283205i	0.0777188	+	0.996975i	$0.475236\pi$
$422$	1.11143	+	32.2175i	0.0541035	+	1.56832i
$423$	−0.371994	−	0.0629508i	−0.0180869	−	0.00306077i
$424$	2.87987	−	6.44629i	0.139859	−	0.313059i
$425$	−22.9531	+	63.0631i	−1.11339	+	3.05901i
$426$	−18.8222	−	17.4458i	−0.911937	−	0.845252i
$427$	−4.62091	−	16.8398i	−0.223622	−	0.814937i
$428$	13.3225	+	29.9910i	0.643967	+	1.44967i
$429$	0.943895	−	2.04255i	0.0455717	−	0.0986151i
$430$	−22.2864	+	20.0497i	−1.07475	+	0.966883i
$431$	1.94205	−	1.12124i	0.0935452	−	0.0540083i	−0.452498	−	0.891766i	$-0.649467\pi$
$431$	1.94205	−	1.12124i	0.0935452	−	0.0540083i	0.546043	+	0.837757i	$0.316134\pi$
$432$	11.4705	+	17.3328i	0.551876	+	0.833926i
$433$		−	27.3244i		−	1.31313i	−0.754271	−	0.656564i	$-0.772009\pi$
$433$		−	27.3244i		−	1.31313i	0.754271	−	0.656564i	$-0.227991\pi$
$434$	24.7939	−	18.9018i	1.19015	−	0.907314i
$435$	11.3345	−	7.99491i	0.543450	−	0.383327i
$436$	2.39500	−	22.6031i	0.114700	−	1.08249i
$437$	7.03680	−	8.38613i	0.336616	−	0.401163i
$438$	25.7004	+	23.8210i	1.22801	+	1.13821i
$439$	−11.5677	−	4.21030i	−0.552097	−	0.200947i	0.0508812	−	0.998705i	$-0.483797\pi$
$439$	−11.5677	−	4.21030i	−0.552097	−	0.200947i	−0.602978	+	0.797758i	$0.706019\pi$
$440$	18.1687	+	25.0738i	0.866157	+	1.19535i
$441$	3.25469	−	20.7463i	0.154985	−	0.987917i
$442$	−1.77995	−	2.85120i	−0.0846638	−	0.135618i
$443$	−4.58049	−	5.45881i	−0.217625	−	0.259356i	0.646176	−	0.763189i	$-0.276367\pi$
$443$	−4.58049	−	5.45881i	−0.217625	−	0.259356i	−0.863801	+	0.503833i	$0.831923\pi$
$444$	−0.191109	+	12.8678i	−0.00906965	+	0.610677i
$445$	2.31083	−	13.1053i	0.109544	−	0.621253i
$446$	2.31052	−	16.3899i	0.109406	−	0.776086i
$447$	−6.71125	+	3.15772i	−0.317431	+	0.149355i
$448$	−6.25868	−	20.2195i	−0.295695	−	0.955283i
$449$	−13.3907	+	23.1934i	−0.631947	+	1.09456i	0.355207	+	0.934788i	$0.384411\pi$
$449$	−13.3907	+	23.1934i	−0.631947	+	1.09456i	−0.987153	+	0.159776i	$0.948923\pi$
$450$	−56.2907	−	29.4645i	−2.65357	−	1.38897i
$451$	6.77797	−	11.7398i	0.319162	−	0.552805i
$452$	4.75372	+	1.36746i	0.223596	+	0.0643197i
$453$	25.3004	−	6.87280i	1.18872	−	0.322912i
$454$	5.22015	−	37.0297i	0.244994	−	1.73789i
$455$	1.58673	−	6.06743i	0.0743869	−	0.284446i
$456$	−5.62777	−	6.44558i	−0.263545	−	0.301842i
$457$	−4.27651	−	24.2533i	−0.200047	−	1.13452i	−0.905046	−	0.425314i	$-0.860164\pi$
$457$	−4.27651	−	24.2533i	−0.200047	−	1.13452i	0.704999	−	0.709208i	$-0.250947\pi$
$458$	0.309881	+	8.98266i	0.0144798	+	0.419732i
$459$	6.25909	+	22.4287i	0.292149	+	1.04688i
$460$	−55.8923	+	3.86090i	−2.60599	+	0.180015i
$461$	2.62013	+	3.12255i	0.122032	+	0.145432i	0.823601	−	0.567169i	$-0.191961\pi$
$461$	2.62013	+	3.12255i	0.122032	+	0.145432i	−0.701570	+	0.712601i	$0.747517\pi$
$462$	13.3856	−	8.53340i	0.622753	−	0.397010i
$463$	−25.8486	−	4.55781i	−1.20129	−	0.211819i	−0.463033	−	0.886341i	$-0.653239\pi$
$463$	−25.8486	−	4.55781i	−1.20129	−	0.211819i	−0.738255	+	0.674522i	$0.764350\pi$
$464$	−6.07159	−	3.80824i	−0.281867	−	0.176793i
$465$	−62.2476	+	16.9094i	−2.88666	+	0.784156i
$466$	2.67469	+	12.6096i	0.123903	+	0.584129i
$467$	−15.8396			−0.732970			−0.366485	−	0.930424i	$-0.619439\pi$
$467$	−15.8396			−0.732970			−0.366485	+	0.930424i	$0.619439\pi$
$468$	2.89917	−	1.31187i	0.134014	−	0.0606412i
$469$	−16.9486	+	8.02766i	−0.782613	+	0.370683i
$470$	−0.531639	−	0.590947i	−0.0245227	−	0.0272583i
$471$	−23.0753	+	33.1980i	−1.06326	+	1.52968i
$472$	0.00468438	−	0.0657910i	0.000215616	−	0.00302828i
$473$	−2.01732	+	11.4408i	−0.0927567	+	0.526049i
$474$	−10.3100	−	0.509054i	−0.473554	−	0.0233816i
$475$	24.5793	+	8.94614i	1.12778	+	0.410477i
$476$	0.291335	−	23.7112i	0.0133533	−	1.08680i
$477$	4.85303	+	5.70328i	0.222205	+	0.261135i
$478$	1.26030	+	0.670794i	0.0576446	+	0.0306814i
$479$	13.4857	−	11.3159i	0.616179	−	0.517036i	−0.280421	−	0.959877i	$-0.590474\pi$
$479$	13.4857	−	11.3159i	0.616179	−	0.517036i	0.896600	+	0.442841i	$0.146029\pi$
$480$	−3.75841	+	43.6294i	−0.171547	+	1.99140i
$481$	1.94037	+	0.342139i	0.0884731	+	0.0156002i
$482$	−8.08893	+	10.3443i	−0.368440	+	0.471172i
$483$	0.271712	+	28.7208i	0.0123633	+	1.30684i
$484$	−9.61064	−	2.76460i	−0.436847	−	0.125664i
$485$	−15.0534	+	26.0733i	−0.683542	+	1.18393i
$486$	−21.8328	+	3.05423i	−0.990356	+	0.138543i
$487$	−11.3425	+	6.54861i	−0.513979	+	0.296746i	−0.734468	−	0.678644i	$-0.762568\pi$
$487$	−11.3425	+	6.54861i	−0.513979	+	0.296746i	0.220489	+	0.975389i	$0.429235\pi$
$488$	17.9514	−	5.12284i	0.812619	−	0.231900i
$489$	−24.1153	−	11.1441i	−1.09053	−	0.503953i
$490$	32.5346	−	29.9850i	1.46976	−	1.35459i
$491$	1.34315	+	3.69026i	0.0606153	+	0.166539i	0.966304	−	0.257405i	$-0.0828675\pi$
$491$	1.34315	+	3.69026i	0.0606153	+	0.166539i	−0.905688	+	0.423944i	$0.860645\pi$
$492$	18.1105	−	6.28872i	0.816484	−	0.283517i
$493$	−5.16126	−	6.15095i	−0.232452	−	0.277025i
$494$	−1.11128	+	0.693751i	−0.0499988	+	0.0312134i
$495$	−32.3037	+	5.92598i	−1.45194	+	0.266353i
$496$	20.4754	+	26.2989i	0.919375	+	1.18086i
$497$	−27.5996	+	2.58195i	−1.23801	+	0.115816i
$498$	26.7611	−	13.7376i	1.19919	−	0.615597i
$499$	−8.07986	−	22.1992i	−0.361704	−	0.993774i	−0.978427	−	0.206594i	$-0.933762\pi$
$499$	−8.07986	−	22.1992i	−0.361704	−	0.993774i	0.616722	−	0.787181i	$-0.288460\pi$
$500$	−36.1996	−	81.4910i	−1.61890	−	3.64439i
$501$	−1.74964	+	0.823227i	−0.0781682	+	0.0367791i
$502$	3.59625	+	16.9543i	0.160509	+	0.756706i
$503$	−5.24777	+	9.08941i	−0.233987	+	0.405277i	−0.958978	−	0.283482i	$-0.908511\pi$
$503$	−5.24777	+	9.08941i	−0.233987	+	0.405277i	0.724991	+	0.688758i	$0.241844\pi$
$504$	22.2129	+	3.25361i	0.989442	+	0.144927i
$505$	−31.0597	−	53.7971i	−1.38214	−	2.39394i
$506$	−16.1409	+	14.5210i	−0.717552	+	0.645538i
$507$	5.77498	+	21.2590i	0.256476	+	0.944147i
$508$	21.3418	+	2.26135i	0.946889	+	0.100331i
$509$	20.2678	−	24.1543i	0.898356	−	1.07062i	−0.0987895	−	0.995108i	$-0.531497\pi$
$509$	20.2678	−	24.1543i	0.898356	−	1.07062i	0.997145	−	0.0755101i	$-0.0240585\pi$
$510$	−19.0327	+	45.2182i	−0.842784	+	2.00229i
$511$	37.6853	−	3.52547i	1.66710	−	0.155958i
$512$	21.5464	−	6.91035i	0.952225	−	0.305397i
$513$	8.74175	−	2.43953i	0.385958	−	0.107708i
$514$	0.885514	+	25.6688i	0.0390583	+	1.13220i
$515$	−2.86564	+	7.87327i	−0.126275	+	0.346938i
$516$	−12.7413	+	10.3727i	−0.560902	+	0.456632i
$517$	−0.303365	−	0.0534915i	−0.0133420	−	0.00235255i
$518$	10.2189	+	9.42302i	0.448992	+	0.414024i
$519$	−21.5795	−	21.4312i	−0.947235	−	0.940726i
$520$	6.50328	+	1.63021i	0.285188	+	0.0714894i
$521$	24.7102	+	14.2664i	1.08257	+	0.625023i	0.931589	−	0.363514i	$-0.118423\pi$
$521$	24.7102	+	14.2664i	1.08257	+	0.625023i	0.150982	+	0.988536i	$0.451756\pi$
$522$	6.42051	−	4.07000i	0.281018	−	0.178139i
$523$	−4.90911	−	8.50283i	−0.214661	−	0.371803i	0.738507	−	0.674246i	$-0.235531\pi$
$523$	−4.90911	−	8.50283i	−0.214661	−	0.371803i	−0.953168	+	0.302443i	$0.902198\pi$
$524$	0.221070	+	0.889866i	0.00965748	+	0.0388740i
$525$	−64.2630	+	24.0807i	−2.80467	+	1.05097i
$526$	−10.8089	−	26.7857i	−0.471293	−	1.16791i
$527$	12.7712	+	35.0885i	0.556321	+	1.52848i
$528$	9.26769	+	14.2162i	0.403324	+	0.618682i
$529$	−2.82764	−	16.0363i	−0.122941	−	0.697232i
$530$	0.543971	+	15.7683i	0.0236286	+	0.684933i
$531$	0.0608256	+	0.0345607i	0.00263961	+	0.00149981i
$532$	−9.24161	−	0.113550i	−0.400675	−	0.00492302i
$533$	−0.509686	−	2.89057i	−0.0220769	−	0.125205i
$534$	1.61913	−	7.11129i	0.0700665	−	0.307736i
$535$	−56.1786	−	47.1395i	−2.42881	−	2.03802i
$536$	−8.76581	−	18.0306i	−0.378625	−	0.778801i
$537$	1.59733	+	17.5600i	0.0689297	+	0.757770i
$538$	31.8166	−	6.74877i	1.37171	−	0.290960i
$539$	2.77415	−	16.9203i	0.119491	−	0.728807i
$540$	−40.0386	−	23.5429i	−1.72299	−	1.01313i
$541$	16.0644	−	27.8244i	0.690665	−	1.19627i	−0.280956	−	0.959721i	$-0.590651\pi$
$541$	16.0644	−	27.8244i	0.690665	−	1.19627i	0.971620	−	0.236545i	$-0.0760152\pi$
$542$	16.7396	−	15.0596i	0.719028	−	0.646865i
$543$	35.2392	−	24.8563i	1.51226	−	1.06669i
$544$	25.3502	+	0.0535674i	1.08688	+	0.00229668i
$545$	17.3725	+	47.7306i	0.744157	+	2.04456i
$546$	1.03255	−	3.27837i	0.0441889	−	0.140301i
$547$	−4.84915	+	0.855036i	−0.207335	+	0.0365587i	−0.276351	−	0.961057i	$-0.589125\pi$
$547$	−4.84915	+	0.855036i	−0.207335	+	0.0365587i	0.0690161	+	0.997616i	$0.478014\pi$
$548$	−1.68221	−	2.49853i	−0.0718603	−	0.106732i
$549$	−3.30376	+	19.5228i	−0.141001	+	0.833215i
$550$	−45.7935	−	24.3737i	−1.95264	−	1.03930i
$551$	−2.39738	+	2.01164i	−0.102132	+	0.0856988i
$552$	−30.6993	+	0.602805i	−1.30665	+	0.0256571i
$553$	−7.83645	+	7.93125i	−0.333240	+	0.337271i
$554$	−13.7689	+	5.55622i	−0.584984	+	0.236061i
$555$	−12.2438	−	26.0222i	−0.519720	−	1.10458i
$556$	14.5418	−	14.0191i	0.616708	−	0.594542i
$557$	4.71034			0.199584			0.0997918	−	0.995008i	$-0.468182\pi$
$557$	4.71034			0.199584			0.0997918	+	0.995008i	$0.468182\pi$
$558$	−34.5308	+	7.57369i	−1.46180	+	0.320620i
$559$	1.25770	+	2.17841i	0.0531952	+	0.0921368i
$560$	32.4075	+	34.4531i	1.36947	+	1.45591i
$561$	4.98405	+	18.3475i	0.210427	+	0.774630i
$562$	9.59601	+	7.50376i	0.404783	+	0.316527i
$563$	−5.56862	+	2.02681i	−0.234690	+	0.0854200i	−0.456688	−	0.889627i	$-0.650964\pi$
$563$	−5.56862	+	2.02681i	−0.234690	+	0.0854200i	0.221998	+	0.975047i	$0.428742\pi$
$564$	−0.275043	−	0.337848i	−0.0115814	−	0.0142260i
$565$	−10.8860	+	1.91949i	−0.457977	+	0.0807537i
$566$	1.72665	−	3.24404i	0.0725764	−	0.136357i
$567$	−13.2689	+	19.7721i	−0.557243	+	0.830350i
$568$	−3.06023	−	29.4756i	−0.128404	−	1.23677i
$569$	−2.38211	−	13.5096i	−0.0998634	−	0.566354i	−0.993148	−	0.116862i	$-0.962716\pi$
$569$	−2.38211	−	13.5096i	−0.0998634	−	0.566354i	0.893285	−	0.449491i	$-0.148395\pi$
$570$	17.6241	+	7.41816i	0.738194	+	0.310712i
$571$	15.2168	+	41.8078i	0.636802	+	1.74960i	0.661544	+	0.749906i	$0.269902\pi$
$571$	15.2168	+	41.8078i	0.636802	+	1.74960i	−0.0247415	+	0.999694i	$0.507876\pi$
$572$	2.37446	−	1.05477i	0.0992810	−	0.0441022i
$573$	1.99387	−	0.541630i	0.0832950	−	0.0226269i
$574$	7.98434	−	19.1062i	0.333260	−	0.797475i
$575$	81.2867	−	46.9309i	3.38989	−	1.95715i
$576$	−3.23650	+	23.7808i	−0.134854	+	0.990865i
$577$		−	24.1803i		−	1.00664i	−0.864101	−	0.503319i	$-0.832112\pi$
$577$		−	24.1803i		−	1.00664i	0.864101	−	0.503319i	$-0.167888\pi$
$578$	4.14509	+	1.34876i	0.172413	+	0.0561010i
$579$	−0.552668	+	0.260037i	−0.0229681	+	0.0108068i
$580$	15.9271	+	1.68762i	0.661337	+	0.0700745i
$581$	8.22055	−	31.4343i	0.341046	−	1.30411i
$582$	−8.94481	+	13.8654i	−0.370774	+	0.574741i
$583$	3.93022	+	4.68385i	0.162773	+	0.193985i
$584$	4.17853	+	40.2468i	0.172909	+	1.66543i
$585$	−4.53331	+	5.47888i	−0.187429	+	0.226524i
$586$	10.0102	+	5.32795i	0.413518	+	0.220096i
$587$	−6.47386	−	36.7151i	−0.267205	−	1.51539i	−0.762682	−	0.646773i	$-0.776118\pi$
$587$	−6.47386	−	36.7151i	−0.267205	−	1.51539i	0.495477	−	0.868621i	$-0.334993\pi$
$588$	18.6196	−	15.5342i	0.767858	−	0.640620i
$589$	13.6760	−	4.97767i	0.563511	−	0.205101i
$590$	0.0551575	+	0.136686i	0.00227080	+	0.00562727i
$591$	8.36934	+	11.8654i	0.344269	+	0.488076i
$592$	−9.96197	+	11.0264i	−0.409435	+	0.453180i
$593$	−5.57249	−	3.21728i	−0.228835	−	0.132118i	0.381200	−	0.924493i	$-0.375511\pi$
$593$	−5.57249	−	3.21728i	−0.228835	−	0.132118i	−0.610034	+	0.792375i	$0.708844\pi$
$594$	−17.8429	+	2.37075i	−0.732104	+	0.0972729i
$595$	22.6835	+	47.8910i	0.929931	+	1.96334i
$596$	−8.23066	−	2.36764i	−0.337141	−	0.0969821i
$597$	10.2205	−	0.929699i	0.418298	−	0.0380500i
$598$	−0.656224	+	4.65500i	−0.0268350	+	0.190357i
$599$	3.51745	−	4.19193i	0.143719	−	0.171278i	−0.689383	−	0.724397i	$-0.742118\pi$
$599$	3.51745	−	4.19193i	0.143719	−	0.171278i	0.833102	+	0.553119i	$0.186563\pi$
$600$	−26.4409	−	68.4346i	−1.07944	−	2.79383i
$601$	−44.7404	+	7.88894i	−1.82500	+	0.321797i	−0.977810	−	0.209493i	$-0.932819\pi$
$601$	−44.7404	+	7.88894i	−1.82500	+	0.321797i	−0.847190	+	0.531290i	$0.821708\pi$
$602$	−0.829681	+	17.7266i	−0.0338153	+	0.722482i
$603$	21.2641	−	0.146632i	0.865940	−	0.00597133i
$604$	27.1981	+	13.2938i	1.10667	+	0.540919i
$605$	22.0083	−	3.88066i	0.894765	−	0.157771i
$606$	−15.5478	−	30.2875i	−0.631587	−	1.23034i
$607$	29.7893	−	10.8424i	1.20911	−	0.440081i	0.342716	−	0.939439i	$-0.388653\pi$
$607$	29.7893	−	10.8424i	1.20911	−	0.440081i	0.866395	+	0.499358i	$0.166431\pi$
$608$	0.0208783	−	9.88042i	0.000846727	−	0.400704i
$609$	1.34925	−	8.09930i	0.0546744	−	0.328200i
$610$	−31.0139	+	27.9013i	−1.25571	+	1.12969i
$611$	−0.0577627	+	0.0333493i	−0.00233683	+	0.00134917i
$612$	−11.6405	+	24.2376i	−0.470538	+	0.979747i
$613$	−5.90843	+	10.2337i	−0.238639	+	0.413336i	−0.960324	−	0.278886i	$-0.910035\pi$
$613$	−5.90843	+	10.2337i	−0.238639	+	0.413336i	0.721685	+	0.692222i	$0.243368\pi$
$614$	7.96748	−	7.16786i	0.321541	−	0.289271i
$615$	−30.1893	+	30.3982i	−1.21735	+	1.22577i
$616$	18.1177	+	2.78152i	0.729985	+	0.112071i
$617$	5.44470	−	30.8785i	0.219196	−	1.24312i	−0.654280	−	0.756252i	$-0.727028\pi$
$617$	5.44470	−	30.8785i	0.219196	−	1.24312i	0.873476	−	0.486868i	$-0.161861\pi$
$618$	−1.78142	+	4.23231i	−0.0716591	+	0.170248i
$619$	−12.1496	−	4.42210i	−0.488335	−	0.177739i	0.0861052	−	0.996286i	$-0.472558\pi$
$619$	−12.1496	−	4.42210i	−0.488335	−	0.177739i	−0.574440	+	0.818547i	$0.694780\pi$
$620$	−66.9165	−	32.7074i	−2.68743	−	1.31356i
$621$	13.4577	−	29.6572i	0.540039	−	1.19010i
$622$	−5.88569	+	11.0581i	−0.235995	+	0.443389i
$623$	−4.55715	−	6.42571i	−0.182578	−	0.257441i
$624$	3.51578	+	1.06813i	0.140744	+	0.0427593i
$625$	95.2877	+	79.9559i	3.81151	+	3.19824i
$626$	−11.3757	−	28.1903i	−0.454666	−	1.12671i
$627$	7.15107	−	1.94257i	0.285586	−	0.0775789i
$628$	−45.3073	+	11.2557i	−1.80796	+	0.449151i
$629$	−14.4178	+	8.32410i	−0.574874	+	0.331903i
$630$	−47.7899	+	15.2658i	−1.90399	+	0.608205i
$631$	27.9276	+	16.1240i	1.11178	+	0.641886i	0.939290	−	0.343125i	$-0.111485\pi$
$631$	27.9276	+	16.1240i	1.11178	+	0.641886i	0.172490	+	0.985011i	$0.444819\pi$
$632$	−8.56365	−	8.29083i	−0.340644	−	0.329791i
$633$	−16.8090	−	35.7248i	−0.668096	−	1.41993i
$634$	−6.68123	−	5.22450i	−0.265345	−	0.207491i
$635$	−45.0672	+	16.4031i	−1.78844	+	0.650938i
$636$	−0.128411	+	8.64615i	−0.00509182	+	0.342842i
$637$	−1.89479	−	3.19259i	−0.0750743	−	0.126495i
$638$	5.26503	−	3.28686i	0.208445	−	0.130128i
$639$	29.6095	+	10.5463i	1.17133	+	0.417206i
$640$	−36.4775	+	35.0180i	−1.44190	+	1.38421i
$641$	26.8894	−	22.5628i	1.06207	−	0.891179i	0.0677555	−	0.997702i	$-0.478416\pi$
$641$	26.8894	−	22.5628i	1.06207	−	0.891179i	0.994310	+	0.106523i	$0.0339718\pi$
$642$	−29.4776	−	27.3221i	−1.16339	−	1.07832i
$643$	11.4213	−	4.15700i	0.450410	−	0.163936i	−0.106848	−	0.994275i	$-0.534076\pi$
$643$	11.4213	−	4.15700i	0.450410	−	0.163936i	0.557258	+	0.830339i	$0.311853\pi$
$644$	−21.6288	+	25.1423i	−0.852296	+	0.990747i
$645$	15.4017	−	33.3286i	0.606442	−	1.31231i
$646$	3.42507	−	10.5262i	0.134758	−	0.414146i
$647$	−16.1783	−	28.0216i	−0.636034	−	1.10164i	−0.986295	−	0.164991i	$-0.947241\pi$
$647$	−16.1783	−	28.0216i	−0.636034	−	1.10164i	0.350261	−	0.936652i	$-0.386093\pi$
$648$	−21.2805	−	13.9693i	−0.835975	−	0.548767i
$649$	0.0494674	+	0.0285600i	0.00194177	+	0.00112108i
$650$	−10.9878	+	2.33069i	−0.430979	+	0.0914170i
$651$	−18.7784	+	33.2475i	−0.735982	+	1.30307i
$652$	−12.4531	−	28.0340i	−0.487703	−	1.09789i
$653$	3.51399	−	19.9288i	0.137513	−	0.779876i	−0.835563	−	0.549394i	$-0.814859\pi$
$653$	3.51399	−	19.9288i	0.137513	−	0.779876i	0.973077	−	0.230482i	$-0.0740303\pi$
$654$	8.21953	+	26.5968i	0.321409	+	1.04002i
$655$	−1.31709	−	1.56965i	−0.0514631	−	0.0613313i
$656$	20.5111	+	8.32739i	0.800824	+	0.325130i
$657$	−40.4297	−	14.4003i	−1.57731	−	0.561808i
$658$	−0.470039	−	0.0219999i	−0.0183240	−	0.000857644i
$659$	12.1205	−	33.3007i	0.472146	−	1.29721i	−0.443877	−	0.896088i	$-0.646397\pi$
$659$	12.1205	−	33.3007i	0.472146	−	1.29721i	0.916024	−	0.401124i	$-0.131380\pi$
$660$	−32.5575	−	19.4474i	−1.26730	−	0.756989i
$661$	−34.5867	−	6.09857i	−1.34527	−	0.237207i	−0.545800	−	0.837916i	$-0.683774\pi$
$661$	−34.5867	−	6.09857i	−1.34527	−	0.237207i	−0.799468	+	0.600709i	$0.794885\pi$
$662$	−24.0454	+	30.7499i	−0.934551	+	1.19513i
$663$	3.38024	+	2.34954i	0.131278	+	0.0912488i
$664$	33.6923	+	8.44583i	1.30752	+	0.327762i
$665$	18.6659	−	8.84105i	0.723832	−	0.342841i
$666$	−5.99882	−	14.5753i	−0.232450	−	0.564780i
$667$			11.2302i			0.434836i
$668$	−2.14576	−	0.617249i	−0.0830218	−	0.0238821i
$669$	5.31425	+	19.5630i	0.205461	+	0.756350i
$670$	35.2930	+	27.5980i	1.36349	+	1.06620i
$671$	−2.80732	+	15.9211i	−0.108375	+	0.614628i
$672$	16.8084	+	19.7352i	0.648398	+	0.761301i
$673$	10.8131	−	9.07327i	0.416814	−	0.349749i	−0.410135	−	0.912025i	$-0.634519\pi$
$673$	10.8131	−	9.07327i	0.416814	−	0.349749i	0.826950	+	0.562276i	$0.190074\pi$
$674$	3.14199	+	5.03297i	0.121025	+	0.193863i
$675$	77.5851	+	5.97988i	2.98625	+	0.230166i
$676$	−11.1704	+	22.8536i	−0.429629	+	0.878984i
$677$	15.2408	−	2.68736i	0.585750	−	0.103284i	0.127084	−	0.991892i	$-0.459438\pi$
$677$	15.2408	−	2.68736i	0.585750	−	0.103284i	0.458667	+	0.888608i	$0.348327\pi$
$678$	−6.01077	+	0.756495i	−0.230842	+	0.0290530i
$679$	4.71619	+	17.1870i	0.180991	+	0.659578i
$680$	−50.9482	+	24.7692i	−1.95378	+	0.949856i
$681$	12.0065	+	44.1987i	0.460089	+	1.69370i
$682$	−28.2358	+	5.98923i	−1.08120	+	0.229340i
$683$	28.6054	+	16.5153i	1.09456	+	0.631942i	0.934786	−	0.355212i	$-0.115591\pi$
$683$	28.6054	+	16.5153i	1.09456	+	0.631942i	0.159770	+	0.987154i	$0.448925\pi$
$684$	9.44680	+	4.53696i	0.361207	+	0.173475i
$685$	5.82925	+	3.36552i	0.222724	+	0.128590i
$686$	0.909857	−	26.1758i	0.0347385	−	0.999396i
$687$	−4.68656	−	9.96054i	−0.178803	−	0.380018i
$688$	−18.9586	−	0.694138i	−0.722789	−	0.0264638i
$689$	1.30378	+	0.229891i	0.0496699	+	0.00875815i
$690$	61.0436	−	31.3362i	2.32389	−	1.19295i
$691$	−20.6571	+	17.3334i	−0.785834	+	0.659393i	−0.944711	−	0.327905i	$-0.893657\pi$
$691$	−20.6571	+	17.3334i	−0.785834	+	0.659393i	0.158876	+	0.987298i	$0.449213\pi$
$692$	−2.42012	−	35.0348i	−0.0919991	−	1.33182i
$693$	−10.9449	+	16.0685i	−0.415764	+	0.610392i
$694$	0.182752	+	5.29751i	0.00693716	+	0.201091i
$695$	−15.4383	+	42.4164i	−0.585609	+	1.60895i
$696$	8.67274	+	1.35425i	0.328739	+	0.0513328i
$697$	18.9986	+	15.9417i	0.719623	+	0.603835i
$698$	4.45518	+	11.0404i	0.168631	+	0.417885i
$699$	−9.09968	−	12.9008i	−0.344182	−	0.487953i
$700$	−74.1256	−	28.0156i	−2.80168	−	1.05889i
$701$	−37.6524			−1.42211			−0.711057	−	0.703135i	$-0.751783\pi$
$701$	−37.6524			−1.42211			−0.711057	+	0.703135i	$0.751783\pi$
$702$	−2.62957	+	2.87656i	−0.0992468	+	0.108569i
$703$	3.24438	+	5.61943i	0.122364	+	0.211941i
$704$	−2.77638	+	19.3979i	−0.104639	+	0.731087i
$705$	0.883743	+	0.408393i	0.0332837	+	0.0153810i
$706$	−11.2167	+	14.3442i	−0.422147	+	0.539853i
$707$	−35.5764	−	9.30379i	−1.33799	−	0.349905i
$708$	0.0264985	+	0.0763114i	0.000995874	+	0.00286796i
$709$	−4.32671	−	1.57479i	−0.162493	−	0.0591427i	0.259493	−	0.965745i	$-0.416445\pi$
$709$	−4.32671	−	1.57479i	−0.162493	−	0.0591427i	−0.421986	+	0.906602i	$0.638667\pi$
$710$	35.0692	+	56.1752i	1.31612	+	2.10822i
$711$	11.8500	−	4.40581i	0.444409	−	0.165231i
$712$	6.81946	−	4.94143i	0.255570	−	0.185188i
$713$	17.8620	−	49.0755i	0.668938	−	1.83789i
$714$	11.1224	+	26.8281i	0.416244	+	1.00402i
$715$	−3.73214	+	4.44779i	−0.139574	+	0.166338i
$716$	−11.9814	+	16.4617i	−0.447765	+	0.615202i
$717$	−1.74242	−	0.146390i	−0.0650719	−	0.00546705i
$718$	−4.32668	+	13.2970i	−0.161470	+	0.496241i
$719$	13.5405	+	23.4528i	0.504975	+	0.874642i	0.999983	+	0.00575424i	$0.00183164\pi$
$719$	13.5405	+	23.4528i	0.504975	+	0.874642i	−0.495008	+	0.868888i	$0.664835\pi$
$720$	−16.8387	−	50.9209i	−0.627542	−	1.89771i
$721$	2.12311	+	4.48247i	0.0790689	+	0.166936i
$722$	21.4488	+	6.97915i	0.798241	+	0.259737i
$723$	4.10893	−	15.5490i	0.152813	−	0.578273i
$724$	49.5176	+	5.24683i	1.84031	+	0.194997i
$725$	−25.2145	+	9.17733i	−0.936443	+	0.340837i
$726$	12.1520	−	1.52941i	0.451004	−	0.0567618i
$727$	−6.62110	+	5.55577i	−0.245563	+	0.206052i	−0.757259	−	0.653115i	$-0.773462\pi$
$727$	−6.62110	+	5.55577i	−0.245563	+	0.206052i	0.511696	+	0.859167i	$0.329017\pi$
$728$	3.39224	−	2.06023i	0.125725	−	0.0763572i
$729$	23.0984	−	13.9808i	0.855497	−	0.517807i
$730$	−47.8845	−	76.7034i	−1.77229	−	2.83892i
$731$	−19.9723	−	7.26934i	−0.738704	−	0.268866i
$732$	−17.7308	+	14.4347i	−0.655349	+	0.533522i
$733$	−30.8571	+	36.7741i	−1.13973	+	1.35828i	−0.215476	+	0.976509i	$0.569130\pi$
$733$	−30.8571	+	36.7741i	−1.13973	+	1.35828i	−0.924257	+	0.381772i	$0.875314\pi$
$734$	0.449315	−	3.18727i	0.0165845	−	0.117644i
$735$	−22.1385	+	49.4600i	−0.816591	+	1.82436i
$736$	−27.1121	−	22.8476i	−0.999366	−	0.842173i
$737$	17.3622			0.639545
$738$	−17.3469	+	15.8238i	−0.638549	+	0.582481i
$739$			27.7884i			1.02221i	0.859518	+	0.511106i	$0.170764\pi$
$739$			27.7884i			1.02221i	−0.859518	+	0.511106i	$0.829236\pi$
$740$	9.18028	−	31.9136i	0.337474	−	1.17317i
$741$	0.915754	−	1.31748i	0.0336410	−	0.0483987i
$742$	6.86630	+	6.33154i	0.252070	+	0.232438i
$743$	−18.4279	+	21.9615i	−0.676053	+	0.805688i	−0.989594	−	0.143886i	$-0.954040\pi$
$743$	−18.4279	+	21.9615i	−0.676053	+	0.805688i	0.313541	+	0.949575i	$0.398485\pi$
$744$	−35.7455	−	19.7123i	−1.31049	−	0.722688i
$745$	18.8482	−	3.32344i	0.690544	−	0.121762i
$746$	−5.37604	+	10.1006i	−0.196831	+	0.369808i
$747$	−23.4863	+	28.3851i	−0.859318	+	1.03856i
$748$	−9.64049	+	19.7236i	−0.352491	+	0.721167i
$749$	−43.2240	+	4.04362i	−1.57937	+	0.147750i
$750$	80.0960	+	74.2390i	2.92469	+	2.71082i
$751$	23.3064	+	4.10954i	0.850462	+	0.149959i	0.581857	−	0.813291i	$-0.302326\pi$
$751$	23.3064	+	4.10954i	0.850462	+	0.149959i	0.268605	+	0.963251i	$0.413437\pi$
$752$	0.0184058	−	0.502706i	0.000671190	−	0.0183318i
$753$	−12.2350	−	17.3458i	−0.445868	−	0.632115i
$754$	0.415829	−	1.27795i	0.0151436	−	0.0465403i
$755$	−67.6513			−2.46208
$756$	−26.5723	+	7.06474i	−0.966427	+	0.256942i
$757$	−49.9802			−1.81656			−0.908282	−	0.418359i	$-0.862605\pi$
$757$	−49.9802			−1.81656			−0.908282	+	0.418359i	$0.862605\pi$
$758$	0.609651	−	1.87362i	0.0221435	−	0.0680529i
$759$	11.1547	−	24.1383i	0.404890	−	0.876165i
$760$	9.65399	+	19.8575i	0.350187	+	0.720306i
$761$	5.10664	+	0.900438i	0.185115	+	0.0326408i	0.265437	−	0.964128i	$-0.414484\pi$
$761$	5.10664	+	0.900438i	0.185115	+	0.0326408i	−0.0803218	+	0.996769i	$0.525595\pi$
$762$	−25.1127	+	7.76087i	−0.909737	+	0.281147i
$763$	27.3272	+	12.5434i	0.989310	+	0.454102i
$764$	2.14342	+	1.04766i	0.0775461	+	0.0379029i
$765$	−0.414333	−	60.0851i	−0.0149803	−	2.17238i
$766$	10.2037	−	19.1709i	0.368676	−	0.692672i
$767$	0.0121799	−	0.00214764i	0.000439790	−	7.75468e-5i
$768$	−20.9139	+	18.1826i	−0.754666	+	0.656110i
$769$	−5.95043	+	7.09145i	−0.214578	+	0.255724i	−0.862587	−	0.505908i	$-0.831157\pi$
$769$	−5.95043	+	7.09145i	−0.214578	+	0.255724i	0.648009	+	0.761633i	$0.275602\pi$
$770$	−39.1047	+	12.1949i	−1.40924	+	0.439475i
$771$	−13.3923	−	28.4632i	−0.482312	−	1.02508i
$772$	−0.677791	−	0.194974i	−0.0243942	−	0.00701725i
$773$		−	29.3683i		−	1.05630i	−0.849150	−	0.528151i	$-0.822885\pi$
$773$		−	29.3683i		−	1.05630i	0.849150	−	0.528151i	$-0.177115\pi$
$774$	9.33154	−	17.8275i	0.335415	−	0.640797i
$775$	124.783			4.48234
$776$	−18.3215	+	5.22847i	−0.657703	+	0.187691i
$777$	−16.0520	−	5.67107i	−0.575863	−	0.203448i
$778$	−2.02362	+	14.3548i	−0.0725501	+	0.514643i
$779$	6.21340	−	7.40485i	0.222618	−	0.265306i
$780$	−8.10683	+	1.30563i	−0.290271	+	0.0467491i
$781$	24.1157	+	8.77740i	0.862928	+	0.314080i
$782$	−21.0351	−	33.6948i	−0.752212	−	1.20492i
$783$	−5.26100	+	7.68138i	−0.188013	+	0.274510i
$784$	27.9915	+	0.687958i	0.999698	+	0.0245699i
$785$	79.9182	−	67.0593i	2.85240	−	2.39345i
$786$	−0.678541	−	0.894809i	−0.0242028	−	0.0319168i
$787$	−13.9800	+	5.08829i	−0.498332	+	0.181378i	−0.578944	−	0.815368i	$-0.696535\pi$
$787$	−13.9800	+	5.08829i	−0.498332	+	0.181378i	0.0806117	+	0.996746i	$0.474313\pi$
$788$	−1.76665	+	16.6730i	−0.0629345	+	0.593952i
$789$	25.1007	+	24.9282i	0.893608	+	0.887467i
$790$	25.3293	+	8.24183i	0.901176	+	0.293231i
$791$	−3.72096	+	5.38267i	−0.132302	+	0.191386i
$792$	−17.2961	−	11.5253i	−0.614590	−	0.409533i
$793$	1.75023	+	3.03148i	0.0621524	+	0.107651i
$794$	16.7745	−	51.5524i	0.595304	−	1.82953i
$795$	−8.22688	−	17.4849i	−0.291777	−	0.620127i
$796$	9.58126	+	6.97357i	0.339599	+	0.247172i
$797$	17.4777	−	20.8291i	0.619092	−	0.737805i	−0.361822	−	0.932247i	$-0.617845\pi$
$797$	17.4777	−	20.8291i	0.619092	−	0.737805i	0.980914	+	0.194442i	$0.0622896\pi$
$798$	10.4565	−	4.33502i	0.370155	−	0.153458i
$799$	0.192754	−	0.529588i	0.00681915	−	0.0187355i
$800$	29.1422	−	79.5442i	1.03033	−	2.81231i
$801$	1.61172	+	8.78581i	0.0569473	+	0.310431i
$802$	−18.1423	−	29.0611i	−0.640627	−	1.02618i
$803$	−32.9283	−	11.9849i	−1.16202	−	0.422939i
$804$	18.5732	+	16.0607i	0.655025	+	0.566419i
$805$	18.7515	−	71.7034i	0.660905	−	2.52721i
$806$	−3.84978	+	4.92321i	−0.135603	+	0.173413i
$807$	−32.5513	+	22.9603i	−1.14586	+	0.808241i
$808$	9.55875	−	38.1320i	0.336276	−	1.34148i
$809$	15.0949	+	26.1451i	0.530708	+	0.919213i	0.999358	+	0.0358292i	$0.0114072\pi$
$809$	15.0949	+	26.1451i	0.530708	+	0.919213i	−0.468650	+	0.883384i	$0.655259\pi$
$810$	56.4334	+	7.16325i	1.98287	+	0.251691i
$811$	7.93253			0.278549			0.139274	−	0.990254i	$-0.455523\pi$
$811$	7.93253			0.278549			0.139274	+	0.990254i	$0.455523\pi$
$812$	7.33731	−	6.00467i	0.257489	−	0.210723i
$813$	−11.5684	+	25.0336i	−0.405723	+	0.877966i
$814$	−4.81577	−	11.9340i	−0.168792	−	0.418285i
$815$	52.5127	+	44.0634i	1.83944	+	1.54347i
$816$	−28.5580	+	12.1814i	−0.999732	+	0.426436i
$817$	−2.83328	+	7.78438i	−0.0991240	+	0.272341i
$818$	−1.10051	−	31.9010i	−0.0384784	−	1.11539i
$819$	0.420990	+	4.18851i	0.0147106	+	0.146358i
$820$	−49.3522	+	3.40912i	−1.72345	+	0.119052i
$821$	−27.0869	+	22.7286i	−0.945340	+	0.793234i	−0.978507	−	0.206216i	$-0.933885\pi$
$821$	−27.0869	+	22.7286i	−0.945340	+	0.793234i	0.0331668	+	0.999450i	$0.489441\pi$
$822$	3.09992	+	1.99980i	0.108122	+	0.0697511i
$823$	3.89223	+	0.686305i	0.135675	+	0.0239231i	0.241073	−	0.970507i	$-0.422501\pi$
$823$	3.89223	+	0.686305i	0.135675	+	0.0239231i	−0.105398	+	0.994430i	$0.533612\pi$
$824$	−4.76863	+	2.31834i	−0.166123	+	0.0807630i
$825$	63.3118	+	5.31917i	2.20424	+	0.185190i
$826$	0.0805067	+	0.0336432i	0.00280119	+	0.00117060i
$827$	−14.1432	−	8.16560i	−0.491808	−	0.283946i	0.233516	−	0.972353i	$-0.424977\pi$
$827$	−14.1432	−	8.16560i	−0.491808	−	0.283946i	−0.725324	+	0.688407i	$0.758310\pi$
$828$	34.2616	−	15.5033i	1.19067	−	0.538778i
$829$	22.1594	+	12.7937i	0.769627	+	0.444344i	0.832742	−	0.553662i	$-0.186770\pi$
$829$	22.1594	+	12.7937i	0.769627	+	0.444344i	−0.0631145	+	0.998006i	$0.520103\pi$
$830$	−75.9324	+	16.1064i	−2.63565	+	0.559061i
$831$	12.8141	−	12.9027i	0.444515	−	0.447591i
$832$	2.23926	+	3.60386i	0.0776323	+	0.124941i
$833$	29.6044	+	10.3737i	1.02573	+	0.359428i
$834$	−9.59719	+	22.8011i	−0.332324	+	0.789538i
$835$	4.91377	−	0.866431i	0.170048	−	0.0299841i
$836$	7.68743	+	3.75746i	0.265875	+	0.129954i
$837$	35.2078	−	25.1995i	1.21696	−	0.871021i
$838$	−9.99777	−	16.0148i	−0.345367	−	0.553223i
$839$	27.6100	−	23.1675i	0.953203	−	0.799832i	−0.0266309	−	0.999645i	$-0.508478\pi$
$839$	27.6100	−	23.1675i	0.953203	−	0.799832i	0.979834	+	0.199813i	$0.0640334\pi$
$840$	−53.1130	−	23.1279i	−1.83257	−	0.797990i
$841$	−4.47831	+	25.3978i	−0.154425	+	0.875785i
$842$	−18.9275	−	14.8007i	−0.652285	−	0.510065i
$843$	−14.4241	−	3.81168i	−0.496794	−	0.131281i
$844$	12.6032	−	43.8128i	0.433821	−	1.50810i
$845$		−	56.8451i		−	1.95553i
$846$	0.472715	+	0.247436i	0.0162523	+	0.00850701i
$847$	7.52269	−	10.8822i	0.258483	−	0.373916i
$848$	−6.69368	+	7.40886i	−0.229862	+	0.254421i
$849$	−0.376814	+	4.48505i	−0.0129322	+	0.153927i
$850$	58.4630	−	74.7641i	2.00526	−	2.56439i
$851$	22.9308	+	4.04331i	0.786056	+	0.138603i
$852$	17.6783	+	31.6976i	0.605648	+	1.08594i
$853$	8.65932	−	23.7913i	0.296490	−	0.814599i	−0.698590	−	0.715522i	$-0.746189\pi$
$853$	8.65932	−	23.7913i	0.296490	−	0.814599i	0.995080	−	0.0990765i	$-0.0315889\pi$
$854$	−1.15459	+	24.6684i	−0.0395092	+	0.844137i
$855$	−23.4186	+	0.161490i	−0.800901	+	0.00552283i
$856$	−4.79266	−	46.1620i	−0.163810	−	1.57779i
$857$	−0.677250	−	0.807115i	−0.0231344	−	0.0275705i	0.754353	−	0.656469i	$-0.227951\pi$
$857$	−0.677250	−	0.807115i	−0.0231344	−	0.0275705i	−0.777488	+	0.628898i	$0.783506\pi$
$858$	−2.16315	+	2.33381i	−0.0738487	+	0.0796749i
$859$	−4.49917	+	25.5161i	−0.153510	+	0.870597i	0.806626	+	0.591062i	$0.201291\pi$
$859$	−4.49917	+	25.5161i	−0.153510	+	0.870597i	−0.960136	+	0.279534i	$0.909820\pi$
$860$	38.7444	−	17.2109i	1.32117	−	0.586887i
$861$	0.239918	+	25.3601i	0.00817638	+	0.864270i
$862$	−3.10233	+	0.658050i	−0.105666	+	0.0224133i
$863$	24.4904	+	14.1396i	0.833664	+	0.481316i	0.855106	−	0.518454i	$-0.173492\pi$
$863$	24.4904	+	14.1396i	0.833664	+	0.481316i	−0.0214415	+	0.999770i	$0.506826\pi$
$864$	−7.84111	−	28.3287i	−0.266760	−	0.963763i
$865$	39.2395	+	67.9647i	1.33418	+	2.31087i
$866$	−11.9567	+	36.7462i	−0.406306	+	1.24869i
$867$	−5.31672	+	0.483630i	−0.180565	+	0.0164249i
$868$	−41.6143	+	14.5699i	−1.41248	+	0.494535i
$869$	9.69989	−	3.53047i	0.329046	−	0.119763i
$870$	−18.7413	+	5.79184i	−0.635389	+	0.196362i
$871$	2.87979	−	2.41643i	0.0975781	−	0.0818777i
$872$	−13.1116	+	29.3489i	−0.444014	+	0.993879i
$873$	3.37188	−	19.9254i	0.114121	−	0.674372i
$874$	−13.1328	+	8.19858i	−0.444224	+	0.277321i
$875$	117.447	−	10.9872i	3.97044	−	0.371436i
$876$	−24.1385	−	43.2809i	−0.815563	−	1.46233i
$877$	−43.6613	+	15.8914i	−1.47434	+	0.536615i	−0.949275	−	0.314448i	$-0.898181\pi$
$877$	−43.6613	+	15.8914i	−1.47434	+	0.536615i	−0.525063	+	0.851063i	$0.675958\pi$
$878$	13.7140	+	10.7239i	0.462826	+	0.361915i
$879$	−13.8396	−	1.16274i	−0.466799	−	0.0392183i
$880$	−13.4615	−	41.6699i	−0.453788	−	1.40469i
$881$	−10.9775	−	6.33784i	−0.369840	−	0.213527i	0.303548	−	0.952816i	$-0.401829\pi$
$881$	−10.9775	−	6.33784i	−0.369840	−	0.213527i	−0.673389	+	0.739289i	$0.735162\pi$
$882$	−13.4552	+	26.4756i	−0.453060	+	0.891480i
$883$	−38.9424	+	22.4834i	−1.31052	+	0.756627i	−0.982182	−	0.187934i	$-0.939821\pi$
$883$	−38.9424	+	22.4834i	−1.31052	+	0.756627i	−0.328335	+	0.944561i	$0.606487\pi$
$884$	1.14606	+	4.61321i	0.0385463	+	0.155159i
$885$	−0.128088	−	0.127207i	−0.00430561	−	0.00427603i
$886$	3.77120	+	9.34542i	0.126696	+	0.313966i
$887$	−14.4176	−	12.0978i	−0.484095	−	0.406204i	0.367809	−	0.929901i	$-0.380108\pi$
$887$	−14.4176	−	12.0978i	−0.484095	−	0.406204i	−0.851905	+	0.523697i	$0.824552\pi$
$888$	5.88774	−	17.2211i	0.197580	−	0.577902i
$889$	−11.8435	+	25.8023i	−0.397217	+	0.865381i
$890$	−8.84232	+	16.6130i	−0.296395	+	0.556871i
$891$	18.9378	−	11.2848i	0.634439	−	0.378054i
$892$	−10.2792	+	21.0303i	−0.344173	+	0.704148i
$893$	−0.206411	−	0.0751274i	−0.00690728	−	0.00251404i
$894$	10.4071	−	1.30981i	0.348067	−	0.0438065i
$895$	7.90083	−	44.8078i	0.264096	−	1.49776i
$896$	−0.431003	+	29.9302i	−0.0143988	+	0.999896i
$897$	−1.50933	−	5.55621i	−0.0503951	−	0.185516i
$898$	28.1571	−	25.3312i	0.939613	−	0.845313i
$899$	−7.46491	+	12.9296i	−0.248969	+	0.431226i
$900$	62.8073	+	64.2562i	2.09358	+	2.14187i
$901$	−9.68762	+	5.59315i	−0.322742	+	0.186335i
$902$	−14.2522	+	12.8219i	−0.474548	+	0.426922i
$903$	−7.62645	−	20.3524i	−0.253793	−	0.677284i
$904$	−5.79448	−	3.91913i	−0.192722	−	0.130348i
$905$	−104.566	+	38.0588i	−3.47588	+	1.26512i
$906$	−37.0317	−	1.82843i	−1.23030	−	0.0607455i
$907$	−44.5662	+	7.85823i	−1.47980	+	0.260928i	−0.854497	−	0.519457i	$-0.826134\pi$
$907$	−44.5662	+	7.85823i	−1.47980	+	0.260928i	−0.625300	+	0.780385i	$0.715023\pi$
$908$	−23.2238	+	47.5138i	−0.770707	+	1.57680i
$909$	32.1254	+	26.5811i	1.06553	+	0.881640i
$910$	−4.78886	+	7.46523i	−0.158749	+	0.247470i
$911$	−37.2544	+	6.56896i	−1.23429	+	0.217639i	−0.752468	−	0.658628i	$-0.771137\pi$
$911$	−37.2544	+	6.56896i	−1.23429	+	0.217639i	−0.481825	+	0.876268i	$0.660026\pi$
$912$	4.74781	+	11.1307i	0.157216	+	0.368575i
$913$	−19.3355	+	23.0432i	−0.639912	+	0.762618i
$914$	−4.86176	+	34.4875i	−0.160813	+	1.14074i
$915$	21.4331	−	46.3803i	0.708557	−	1.53329i
$916$	3.51394	−	12.2156i	0.116104	−	0.403614i
$917$	−1.20896	−	0.0984500i	−0.0399235	−	0.00325111i
$918$	1.39713	−	32.9012i	0.0461123	−	1.08590i
$919$	−42.9300	−	24.7857i	−1.41613	−	0.817604i	−0.420175	−	0.907443i	$-0.638031\pi$
$919$	−42.9300	−	24.7857i	−1.41613	−	0.817604i	−0.995956	+	0.0898394i	$0.971365\pi$
$920$	76.8541	+	19.2654i	2.53380	+	0.635162i
$921$	−5.50618	+	11.9151i	−0.181435	+	0.392617i
$922$	−2.15721	−	5.34577i	−0.0710438	−	0.176054i
$923$	5.22159	−	1.90050i	0.171871	−	0.0625558i
$924$	−21.7352	+	5.61850i	−0.715034	+	0.184835i
$925$	9.66081	+	54.7892i	0.317645	+	1.80146i
$926$	32.7671	+	17.4404i	1.07679	+	0.573126i
$927$	−0.0387806	−	5.62382i	−0.00127372	−	0.184710i
$928$	6.49873	+	7.77820i	0.213331	+	0.255332i
$929$	4.47931	+	5.33824i	0.146962	+	0.175142i	0.834503	−	0.551003i	$-0.185755\pi$
$929$	4.47931	+	5.33824i	0.146962	+	0.175142i	−0.687542	+	0.726145i	$0.741310\pi$
$930$	91.1106	+	4.49856i	2.98764	+	0.147514i
$931$	4.04323	−	11.5385i	0.132512	−	0.378160i
$932$	1.92082	−	18.1280i	0.0629185	−	0.593801i
$933$	1.28446	−	15.2884i	0.0420513	−	0.500519i
$934$	21.3013	+	6.93117i	0.697000	+	0.226795i
$935$		−	49.0597i		−	1.60442i
$936$	−4.47289	+	0.495586i	−0.146201	+	0.0161987i
$937$	−22.5621	+	13.0262i	−0.737072	+	0.425549i	−0.821004	−	0.570923i	$-0.806586\pi$
$937$	−22.5621	+	13.0262i	−0.737072	+	0.425549i	0.0839319	+	0.996471i	$0.473252\pi$
$938$	26.3054	−	3.37926i	0.858903	−	0.110337i
$939$	26.4169	+	26.2354i	0.862083	+	0.856159i
$940$	0.456365	+	1.02735i	0.0148850	+	0.0335084i
$941$	7.86925	+	21.6206i	0.256530	+	0.704811i	0.999375	+	0.0353473i	$0.0112537\pi$
$941$	7.86925	+	21.6206i	0.256530	+	0.704811i	−0.742845	+	0.669464i	$0.766524\pi$
$942$	45.5589	−	34.5477i	1.48439	−	1.12562i
$943$	−6.02334	−	34.1600i	−0.196147	−	1.11240i
$944$	−0.0350887	+	0.0864267i	−0.00114204	+	0.00281295i
$945$	46.4167	−	40.2600i	1.50993	−	1.30966i
$946$	7.71925	−	14.5030i	0.250974	−	0.471533i
$947$	−30.0085	+	5.29131i	−0.975145	+	0.171944i	−0.638445	−	0.769667i	$-0.720422\pi$
$947$	−30.0085	+	5.29131i	−0.975145	+	0.171944i	−0.336700	+	0.941612i	$0.609311\pi$
$948$	13.6423	+	5.19608i	0.443080	+	0.168761i
$949$	−7.12972	+	2.59501i	−0.231440	+	0.0842374i
$950$	−29.1399	−	22.7864i	−0.945423	−	0.739289i
$951$	10.0428	+	2.65389i	0.325661	+	0.0860582i
$952$	−10.7674	+	31.7596i	−0.348974	+	1.02933i
$953$	−9.13079	−	15.8150i	−0.295775	−	0.512298i	0.679390	−	0.733778i	$-0.262245\pi$
$953$	−9.13079	−	15.8150i	−0.295775	−	0.512298i	−0.975165	+	0.221480i	$0.928911\pi$
$954$	−4.03075	−	9.79345i	−0.130500	−	0.317075i
$955$	−5.33145			−0.172522
$956$	−1.40133	−	1.45358i	−0.0453223	−	0.0470121i
$957$	−4.33867	+	6.24195i	−0.140249	+	0.201774i
$958$	−23.0874	+	9.31659i	−0.745922	+	0.301005i
$959$	3.84253	−	1.05440i	0.124082	−	0.0340485i
$960$	24.1459	−	57.0288i	0.779306	−	1.84060i
$961$	29.4389	−	24.7022i	0.949642	−	0.796844i
$962$	−2.45971	−	1.30919i	−0.0793043	−	0.0422099i
$963$	46.3717	+	16.5167i	1.49431	+	0.532243i
$964$	15.4046	−	10.3716i	0.496149	−	0.334047i
$965$	1.55214	−	0.273684i	0.0499651	−	0.00881020i
$966$	12.2024	−	38.7430i	0.392605	−	1.24653i
$967$	−4.30802	−	11.8362i	−0.138537	−	0.380626i	0.850951	−	0.525245i	$-0.176026\pi$
$967$	−4.30802	−	11.8362i	−0.138537	−	0.380626i	−0.989487	+	0.144619i	$0.953804\pi$
$968$	11.7148	+	7.92333i	0.376527	+	0.254666i
$969$	1.22814	+	13.5014i	0.0394536	+	0.433728i
$970$	31.6533	−	28.4766i	1.01633	−	0.914328i
$971$	9.83152	−	17.0287i	0.315509	−	0.546477i	−0.664037	−	0.747700i	$-0.731158\pi$
$971$	9.83152	−	17.0287i	0.315509	−	0.546477i	0.979545	+	0.201223i	$0.0644916\pi$
$972$	30.6975	+	5.44634i	0.984623	+	0.174691i
$973$	11.4381	+	24.1488i	0.366687	+	0.774176i
$974$	18.1191	−	3.84334i	0.580574	−	0.123148i
$975$	11.2416	−	7.92934i	0.360019	−	0.253942i
$976$	−26.3829	−	0.965967i	−0.844495	−	0.0309198i
$977$	−24.4243	−	20.4944i	−0.781402	−	0.655674i	0.162199	−	0.986758i	$-0.448141\pi$
$977$	−24.4243	−	20.4944i	−0.781402	−	0.655674i	−0.943601	+	0.331084i	$0.892586\pi$
$978$	27.5541	+	25.5392i	0.881082	+	0.816653i
$979$	1.26645	+	7.18238i	0.0404758	+	0.229550i
$980$	−56.8739	+	26.0876i	−1.81677	+	0.833338i
$981$	−22.0950	−	25.9661i	−0.705440	−	0.829034i
$982$	−0.191477	−	5.55045i	−0.00611029	−	0.177122i
$983$	5.07159	+	28.7624i	0.161759	+	0.917378i	0.952344	+	0.305026i	$0.0986653\pi$
$983$	5.07159	+	28.7624i	0.161759	+	0.917378i	−0.790585	+	0.612352i	$0.790224\pi$
$984$	−27.1071	+	0.532269i	−0.864142	+	0.0169681i
$985$	−12.8147	−	35.2082i	−0.408311	−	1.12183i
$986$	4.24937	+	10.5304i	0.135327	+	0.335355i
$987$	0.539664	−	0.202223i	0.0171777	−	0.00643684i
$988$	1.79804	−	0.446687i	0.0572032	−	0.0142110i
$989$	14.8632	+	25.7439i	0.472623	+	0.818607i
$990$	46.0355	+	6.16627i	1.46311	+	0.195977i
$991$	−29.9596	−	17.2972i	−0.951697	−	0.549463i	−0.0580895	−	0.998311i	$-0.518501\pi$
$991$	−29.9596	−	17.2972i	−0.951697	−	0.549463i	−0.893608	+	0.448849i	$0.851834\pi$
$992$	−16.0276	−	44.3268i	−0.508878	−	1.40738i
$993$	12.2143	−	46.2214i	0.387610	−	1.46679i
$994$	38.2460	+	8.60490i	1.21309	+	0.272931i
$995$	−26.0797	−	4.59855i	−0.826782	−	0.145784i
$996$	−42.0000	+	6.76425i	−1.33082	+	0.214333i
$997$	−11.8123	+	32.4541i	−0.374101	+	1.02783i	0.599659	+	0.800255i	$0.295303\pi$
$997$	−11.8123	+	32.4541i	−0.374101	+	1.02783i	−0.973760	+	0.227578i	$0.926919\pi$
$998$	1.15186	+	33.3894i	0.0364614	+	1.05692i
$999$	13.7903	+	13.5079i	0.436305	+	0.427372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bt.a.103.14	✓	840
4.3	odd	2	inner	756.2.bt.a.103.112	yes	840
7.3	odd	6		756.2.cd.a.535.109	yes	840
27.16	even	9		756.2.cd.a.691.78	yes	840
28.3	even	6		756.2.cd.a.535.78	yes	840
108.43	odd	18		756.2.cd.a.691.109	yes	840
189.178	odd	18	inner	756.2.bt.a.367.112	yes	840
756.367	even	18	inner	756.2.bt.a.367.14	yes	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.14	✓	840	1.1	even	1	trivial
756.2.bt.a.103.112	yes	840	4.3	odd	2	inner
756.2.bt.a.367.14	yes	840	756.367	even	18	inner
756.2.bt.a.367.112	yes	840	189.178	odd	18	inner
756.2.cd.a.535.78	yes	840	28.3	even	6
756.2.cd.a.535.109	yes	840	7.3	odd	6
756.2.cd.a.691.78	yes	840	27.16	even	9
756.2.cd.a.691.109	yes	840	108.43	odd	18

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34481 - 0.437584i) q^{2} +(1.72493 - 0.156906i) q^{3} +(1.61704 + 1.17694i) q^{4} +(-4.40150 - 0.776103i) q^{5} +(-2.38837 - 0.543792i) q^{6} +(-2.15811 + 1.53054i) q^{7} +(-1.65961 - 2.29035i) q^{8} +(2.95076 - 0.541305i) q^{9} +O(q^{10})\)	\(q+(-1.34481 - 0.437584i) q^{2} +(1.72493 - 0.156906i) q^{3} +(1.61704 + 1.17694i) q^{4} +(-4.40150 - 0.776103i) q^{5} +(-2.38837 - 0.543792i) q^{6} +(-2.15811 + 1.53054i) q^{7} +(-1.65961 - 2.29035i) q^{8} +(2.95076 - 0.541305i) q^{9} +(5.57958 + 2.96974i) q^{10} +(2.41224 - 0.425343i) q^{11} +(2.97395 + 1.77641i) q^{12} +(0.340909 - 0.406280i) q^{13} +(3.57199 - 1.11394i) q^{14} +(-7.71405 - 0.648100i) q^{15} +(1.22964 + 3.80631i) q^{16} +4.48133i q^{17} +(-4.20509 - 0.563254i) q^{18} +1.74663 q^{19} +(-6.20398 - 6.43528i) q^{20} +(-3.48243 + 2.97870i) q^{21} +(-3.43013 - 0.483552i) q^{22} +(4.02878 - 4.80132i) q^{23} +(-3.22207 - 3.69029i) q^{24} +(14.0724 + 5.12194i) q^{25} +(-0.636241 + 0.397194i) q^{26} +(5.00492 - 1.39671i) q^{27} +(-5.29110 - 0.0650108i) q^{28} +(-1.37257 + 1.15173i) q^{29} +(10.0904 + 4.24712i) q^{30} +(7.82994 - 2.84987i) q^{31} +(0.0119535 - 5.65684i) q^{32} +(4.09420 - 1.11218i) q^{33} +(1.96096 - 6.02654i) q^{34} +(10.6868 - 5.06177i) q^{35} +(5.40858 + 2.59755i) q^{36} +(1.85751 + 3.21730i) q^{37} +(-2.34889 - 0.764299i) q^{38} +(0.524297 - 0.754295i) q^{39} +(5.52720 + 11.3690i) q^{40} +(3.55736 - 4.23950i) q^{41} +(5.98665 - 2.48193i) q^{42} +(-1.62214 + 4.45679i) q^{43} +(4.40129 + 2.15126i) q^{44} +(-13.4079 + 0.0924577i) q^{45} +(-7.51894 + 4.69394i) q^{46} +(-0.118177 - 0.0430127i) q^{47} +(2.71827 + 6.37268i) q^{48} +(2.31487 - 6.60616i) q^{49} +(-16.6835 - 13.0459i) q^{50} +(0.703149 + 7.72997i) q^{51} +(1.02943 - 0.255742i) q^{52} +(1.24810 + 2.16178i) q^{53} +(-7.34185 - 0.311768i) q^{54} -10.9476 q^{55} +(7.08709 + 2.40273i) q^{56} +(3.01282 - 0.274058i) q^{57} +(2.34983 - 0.948239i) q^{58} +(0.0178638 + 0.0149895i) q^{59} +(-11.7112 - 10.1270i) q^{60} +(-2.25738 + 6.20210i) q^{61} +(-11.7769 + 0.406274i) q^{62} +(-5.53957 + 5.68446i) q^{63} +(-2.49142 + 7.60216i) q^{64} +(-1.81583 + 1.52366i) q^{65} +(-5.99261 - 0.295883i) q^{66} +(6.98051 + 1.23085i) q^{67} +(-5.27424 + 7.24648i) q^{68} +(6.19601 - 8.91407i) q^{69} +(-16.5867 + 2.13076i) q^{70} +(9.07352 + 5.23860i) q^{71} +(-6.13688 - 5.85993i) q^{72} +(-12.3893 - 7.15295i) q^{73} +(-1.09016 - 5.13948i) q^{74} +(25.0776 + 6.62693i) q^{75} +(2.82437 + 2.05568i) q^{76} +(-4.55487 + 4.60997i) q^{77} +(-1.03515 + 0.784961i) q^{78} +(4.15015 - 0.731783i) q^{79} +(-2.45815 - 17.7078i) q^{80} +(8.41398 - 3.19452i) q^{81} +(-6.63912 + 4.14468i) q^{82} +(-9.40748 + 7.89382i) q^{83} +(-9.13698 + 0.718069i) q^{84} +(3.47797 - 19.7246i) q^{85} +(4.13170 - 5.28373i) q^{86} +(-2.18688 + 2.20201i) q^{87} +(-4.97755 - 4.81897i) q^{88} +2.97747i q^{89} +(18.0715 + 5.74274i) q^{90} +(-0.113891 + 1.39857i) q^{91} +(12.1656 - 3.02229i) q^{92} +(13.0589 - 6.14439i) q^{93} +(0.140104 + 0.109556i) q^{94} +(-7.68780 - 1.35557i) q^{95} +(-0.866976 - 9.75953i) q^{96} +(2.30392 - 6.32998i) q^{97} +(-6.00382 + 7.87109i) q^{98} +(6.88770 - 2.56084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more