LMFDB - Embedded newform 927.2.f.f.46.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [927,2,Mod(46,927)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(927, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("927.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 927 = 3^{2} \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	927.f (of order $3$, degree $2$, 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:	$7.40213226737$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.12
Character	$\chi$	$=$	927.46
Dual form			927.2.f.f.262.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.711803 + 1.23288i) q^{2} +(-0.0133274 + 0.0230838i) q^{4} +(-0.396502 + 0.686762i) q^{5} +(-0.249615 + 0.432345i) q^{7} +2.80927 q^{8} +O(q^{10})$	\(q+(0.711803 + 1.23288i) q^{2} +(-0.0133274 + 0.0230838i) q^{4} +(-0.396502 + 0.686762i) q^{5} +(-0.249615 + 0.432345i) q^{7} +2.80927 q^{8} -1.12893 q^{10} +(2.68065 - 4.64303i) q^{11} -1.03115 q^{13} -0.710706 q^{14} +(2.02630 + 3.50965i) q^{16} +(0.783256 - 1.35664i) q^{17} +(2.21991 + 3.84499i) q^{19} +(-0.0105687 - 0.0183055i) q^{20} +7.63239 q^{22} +5.69293 q^{23} +(2.18557 + 3.78552i) q^{25} +(-0.733979 - 1.27129i) q^{26} +(-0.00665345 - 0.0115241i) q^{28} +(-1.25596 - 2.17539i) q^{29} +1.48344 q^{31} +(-0.0753864 + 0.130573i) q^{32} +2.23010 q^{34} +(-0.197946 - 0.342852i) q^{35} -6.62674 q^{37} +(-3.16028 + 5.47376i) q^{38} +(-1.11388 + 1.92930i) q^{40} +(1.70676 + 2.95620i) q^{41} +(-3.43519 - 5.94992i) q^{43} +(0.0714525 + 0.123759i) q^{44} +(4.05225 + 7.01870i) q^{46} +(1.61350 - 2.79466i) q^{47} +(3.37538 + 5.84634i) q^{49} +(-3.11139 + 5.38909i) q^{50} +(0.0137426 - 0.0238030i) q^{52} +(-1.01395 + 1.75621i) q^{53} +(2.12577 + 3.68194i) q^{55} +(-0.701234 + 1.21457i) q^{56} +(1.78800 - 3.09690i) q^{58} +(3.36106 + 5.82152i) q^{59} -0.780378 q^{61} +(1.05591 + 1.82890i) q^{62} +7.89056 q^{64} +(0.408855 - 0.708157i) q^{65} +(-3.62137 + 6.27239i) q^{67} +(0.0208776 + 0.0361610i) q^{68} +(0.281796 - 0.488086i) q^{70} +(3.32892 - 5.76587i) q^{71} +12.2880 q^{73} +(-4.71694 - 8.16997i) q^{74} -0.118343 q^{76} +(1.33826 + 2.31794i) q^{77} -11.5258 q^{79} -3.21373 q^{80} +(-2.42976 + 4.20846i) q^{82} +(-1.88139 - 3.25866i) q^{83} +(0.621125 + 1.07582i) q^{85} +(4.89035 - 8.47034i) q^{86} +(7.53067 - 13.0435i) q^{88} -18.4645 q^{89} +(0.257391 - 0.445815i) q^{91} +(-0.0758722 + 0.131415i) q^{92} +4.59397 q^{94} -3.52079 q^{95} +(0.821501 + 1.42288i) q^{97} +(-4.80522 + 8.32288i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 18 q^{4} + 8 q^{7}+O(q^{10}) $ 32 * q - 18 * q^4 + 8 * q^7	$ 32 q - 18 q^{4} + 8 q^{7} - 32 q^{10} - 4 q^{13} - 18 q^{16} + 4 q^{19} - 40 q^{22} - 26 q^{25} + 8 q^{28} + 32 q^{31} + 8 q^{34} - 48 q^{37} + 22 q^{40} + 2 q^{43} + 18 q^{46} - 8 q^{49} - 68 q^{52} - 32 q^{55} - 24 q^{58} - 20 q^{61} + 68 q^{64} + 8 q^{67} + 38 q^{70} - 64 q^{73} - 188 q^{76} - 20 q^{79} + 60 q^{82} + 8 q^{85} + 6 q^{88} - 30 q^{91} - 92 q^{94} + 32 q^{97}+O(q^{100}) $ 32 * q - 18 * q^4 + 8 * q^7 - 32 * q^10 - 4 * q^13 - 18 * q^16 + 4 * q^19 - 40 * q^22 - 26 * q^25 + 8 * q^28 + 32 * q^31 + 8 * q^34 - 48 * q^37 + 22 * q^40 + 2 * q^43 + 18 * q^46 - 8 * q^49 - 68 * q^52 - 32 * q^55 - 24 * q^58 - 20 * q^61 + 68 * q^64 + 8 * q^67 + 38 * q^70 - 64 * q^73 - 188 * q^76 - 20 * q^79 + 60 * q^82 + 8 * q^85 + 6 * q^88 - 30 * q^91 - 92 * q^94 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/927\mathbb{Z}\right)^\times$.

$n$	$722$	$829$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.711803	+	1.23288i	0.503321	+	0.871777i	0.999993	+	0.00383882i	$0.00122194\pi$
$2$	0.711803	+	1.23288i	0.503321	+	0.871777i	−0.496672	+	0.867938i	$0.665445\pi$
$3$		0			0
$3$		0			0
$4$	−0.0133274	+	0.0230838i	−0.00666372	+	0.0115419i
$5$	−0.396502	+	0.686762i	−0.177321	+	0.307129i	−0.940962	−	0.338512i	$-0.890076\pi$
$5$	−0.396502	+	0.686762i	−0.177321	+	0.307129i	0.763641	+	0.645641i	$0.223410\pi$
$6$		0			0
$7$	−0.249615	+	0.432345i	−0.0943455	+	0.163411i	−0.909335	−	0.416064i	$-0.863409\pi$
$7$	−0.249615	+	0.432345i	−0.0943455	+	0.163411i	0.814990	+	0.579475i	$0.196743\pi$
$8$	2.80927			0.993226
$9$		0			0
$10$	−1.12893			−0.356998
$11$	2.68065	−	4.64303i	0.808248	−	1.39993i	−0.105829	−	0.994384i	$-0.533749\pi$
$11$	2.68065	−	4.64303i	0.808248	−	1.39993i	0.914076	−	0.405542i	$-0.132917\pi$
$12$		0			0
$13$	−1.03115			−0.285991			−0.142995	−	0.989723i	$-0.545673\pi$
$13$	−1.03115			−0.285991			−0.142995	+	0.989723i	$0.545673\pi$
$14$	−0.710706			−0.189944
$15$		0			0
$16$	2.02630	+	3.50965i	0.506575	+	0.877413i
$17$	0.783256	−	1.35664i	0.189967	−	0.329033i	−0.755272	−	0.655412i	$-0.772495\pi$
$17$	0.783256	−	1.35664i	0.189967	−	0.329033i	0.945239	+	0.326379i	$0.105828\pi$
$18$		0			0
$19$	2.21991	+	3.84499i	0.509282	+	0.882102i	0.999942	+	0.0107511i	$0.00342225\pi$
$19$	2.21991	+	3.84499i	0.509282	+	0.882102i	−0.490660	+	0.871351i	$0.663244\pi$
$20$	−0.0105687	−	0.0183055i	−0.00236324	−	0.00409325i
$21$		0			0
$22$	7.63239			1.62723
$23$	5.69293			1.18706			0.593529	−	0.804812i	$-0.297734\pi$
$23$	5.69293			1.18706			0.593529	+	0.804812i	$0.297734\pi$
$24$		0			0
$25$	2.18557	+	3.78552i	0.437114	+	0.757104i
$26$	−0.733979	−	1.27129i	−0.143945	−	0.249320i
$27$		0			0
$28$	−0.00665345	−	0.0115241i	−0.00125738	−	0.00217785i
$29$	−1.25596	−	2.17539i	−0.233227	−	0.403961i	0.725529	−	0.688191i	$-0.241595\pi$
$29$	−1.25596	−	2.17539i	−0.233227	−	0.403961i	−0.958756	+	0.284231i	$0.908262\pi$
$30$		0			0
$31$	1.48344			0.266433			0.133217	−	0.991087i	$-0.457469\pi$
$31$	1.48344			0.266433			0.133217	+	0.991087i	$0.457469\pi$
$32$	−0.0753864	+	0.130573i	−0.0133266	+	0.0230823i
$33$		0			0
$34$	2.23010			0.382458
$35$	−0.197946	−	0.342852i	−0.0334589	−	0.0579525i
$36$		0			0
$37$	−6.62674			−1.08943			−0.544715	−	0.838621i	$-0.683362\pi$
$37$	−6.62674			−1.08943			−0.544715	+	0.838621i	$0.683362\pi$
$38$	−3.16028	+	5.47376i	−0.512664	+	0.887961i
$39$		0			0
$40$	−1.11388	+	1.92930i	−0.176120	+	0.305049i
$41$	1.70676	+	2.95620i	0.266551	+	0.461680i	0.967969	−	0.251070i	$-0.0807825\pi$
$41$	1.70676	+	2.95620i	0.266551	+	0.461680i	−0.701418	+	0.712751i	$0.747449\pi$
$42$		0			0
$43$	−3.43519	−	5.94992i	−0.523861	−	0.907354i	−0.999614	−	0.0277752i	$-0.991158\pi$
$43$	−3.43519	−	5.94992i	−0.523861	−	0.907354i	0.475753	−	0.879579i	$-0.342176\pi$
$44$	0.0714525	+	0.123759i	0.0107719	+	0.0186574i
$45$		0			0
$46$	4.05225	+	7.01870i	0.597471	+	1.03485i
$47$	1.61350	−	2.79466i	0.235353	−	0.407643i	−0.724022	−	0.689777i	$-0.757709\pi$
$47$	1.61350	−	2.79466i	0.235353	−	0.407643i	0.959375	+	0.282133i	$0.0910421\pi$
$48$		0			0
$49$	3.37538	+	5.84634i	0.482198	+	0.835191i
$50$	−3.11139	+	5.38909i	−0.440018	+	0.762133i
$51$		0			0
$52$	0.0137426	−	0.0238030i	0.00190576	−	0.00330088i
$53$	−1.01395	+	1.75621i	−0.139276	+	0.241233i	−0.927223	−	0.374510i	$-0.877811\pi$
$53$	−1.01395	+	1.75621i	−0.139276	+	0.241233i	0.787947	+	0.615743i	$0.211144\pi$
$54$		0			0
$55$	2.12577	+	3.68194i	0.286639	+	0.496473i
$56$	−0.701234	+	1.21457i	−0.0937064	+	0.162304i
$57$		0			0
$58$	1.78800	−	3.09690i	0.234776	−	0.406644i
$59$	3.36106	+	5.82152i	0.437572	+	0.757898i	0.997502	−	0.0706427i	$-0.0225050\pi$
$59$	3.36106	+	5.82152i	0.437572	+	0.757898i	−0.559929	+	0.828540i	$0.689172\pi$
$60$		0			0
$61$	−0.780378			−0.0999172			−0.0499586	−	0.998751i	$-0.515909\pi$
$61$	−0.780378			−0.0999172			−0.0499586	+	0.998751i	$0.515909\pi$
$62$	1.05591	+	1.82890i	0.134101	+	0.232270i
$63$		0			0
$64$	7.89056			0.986320
$65$	0.408855	−	0.708157i	0.0507122	−	0.0878361i
$66$		0			0
$67$	−3.62137	+	6.27239i	−0.442420	+	0.766294i	−0.997869	−	0.0652567i	$-0.979213\pi$
$67$	−3.62137	+	6.27239i	−0.442420	+	0.766294i	0.555448	+	0.831551i	$0.312547\pi$
$68$	0.0208776	+	0.0361610i	0.00253178	+	0.00438517i
$69$		0			0
$70$	0.281796	−	0.488086i	0.0336811	−	0.0583374i
$71$	3.32892	−	5.76587i	0.395071	−	0.684282i	−0.598040	−	0.801467i	$-0.704053\pi$
$71$	3.32892	−	5.76587i	0.395071	−	0.684282i	0.993110	+	0.117184i	$0.0373868\pi$
$72$		0			0
$73$	12.2880			1.43821			0.719103	−	0.694904i	$-0.244553\pi$
$73$	12.2880			1.43821			0.719103	+	0.694904i	$0.244553\pi$
$74$	−4.71694	−	8.16997i	−0.548333	−	0.949740i
$75$		0			0
$76$	−0.118343			−0.0135748
$77$	1.33826	+	2.31794i	0.152509	+	0.264154i
$78$		0			0
$79$	−11.5258			−1.29676			−0.648378	−	0.761318i	$-0.724553\pi$
$79$	−11.5258			−1.29676			−0.648378	+	0.761318i	$0.724553\pi$
$80$	−3.21373			−0.359306
$81$		0			0
$82$	−2.42976	+	4.20846i	−0.268322	+	0.464747i
$83$	−1.88139	−	3.25866i	−0.206509	−	0.357685i	0.744103	−	0.668065i	$-0.232877\pi$
$83$	−1.88139	−	3.25866i	−0.206509	−	0.357685i	−0.950613	+	0.310380i	$0.899544\pi$
$84$		0			0
$85$	0.621125	+	1.07582i	0.0673705	+	0.116689i
$86$	4.89035	−	8.47034i	0.527340	−	0.913380i
$87$		0			0
$88$	7.53067	−	13.0435i	0.802773	−	1.39044i
$89$	−18.4645			−1.95723			−0.978616	−	0.205695i	$-0.934054\pi$
$89$	−18.4645			−1.95723			−0.978616	+	0.205695i	$0.934054\pi$
$90$		0			0
$91$	0.257391	−	0.445815i	0.0269819	−	0.0467341i
$92$	−0.0758722	+	0.131415i	−0.00791023	+	0.0137009i
$93$		0			0
$94$	4.59397			0.473832
$95$	−3.52079			−0.361226
$96$		0			0
$97$	0.821501	+	1.42288i	0.0834108	+	0.144472i	0.904713	−	0.426022i	$-0.140085\pi$
$97$	0.821501	+	1.42288i	0.0834108	+	0.144472i	−0.821302	+	0.570494i	$0.806752\pi$
$98$	−4.80522	+	8.32288i	−0.485400	+	0.840738i
$99$		0			0
$100$	−0.116512			−0.0116512
$101$	−5.63790	−	9.76513i	−0.560992	−	0.971667i	−0.997410	−	0.0719231i	$-0.977086\pi$
$101$	−5.63790	−	9.76513i	−0.560992	−	0.971667i	0.436418	−	0.899744i	$-0.356247\pi$
$102$		0			0
$103$	−4.20218	+	9.23806i	−0.414053	+	0.910253i
$103$	−4.20218	+	9.23806i	−0.414053	+	0.910253i
$104$	−2.89679			−0.284053
$105$		0			0
$106$	−2.88692			−0.280402
$107$	−1.16270	+	2.01386i	−0.112403	+	0.194687i	−0.916738	−	0.399488i	$-0.869188\pi$
$107$	−1.16270	+	2.01386i	−0.112403	+	0.194687i	0.804336	+	0.594175i	$0.202521\pi$
$108$		0			0
$109$	−7.20327	−	12.4764i	−0.689949	−	1.19503i	−0.971854	−	0.235584i	$-0.924300\pi$
$109$	−7.20327	−	12.4764i	−0.689949	−	1.19503i	0.281905	−	0.959442i	$-0.409034\pi$
$110$	−3.02626	+	5.24164i	−0.288543	+	0.499770i
$111$		0			0
$112$	−2.02318			−0.191172
$113$	7.09242			0.667198			0.333599	−	0.942715i	$-0.391737\pi$
$113$	7.09242			0.667198			0.333599	+	0.942715i	$0.391737\pi$
$114$		0			0
$115$	−2.25726	+	3.90969i	−0.210491	+	0.364580i
$116$	0.0669552			0.00621663
$117$		0			0
$118$	−4.78482	+	8.28756i	−0.440479	+	0.762931i
$119$	0.391024	+	0.677274i	0.0358451	+	0.0620856i
$120$		0			0
$121$	−8.87182	−	15.3664i	−0.806529	−	1.39695i
$122$	−0.555476	−	0.962112i	−0.0502904	−	0.0871055i
$123$		0			0
$124$	−0.0197704	+	0.0342434i	−0.00177544	+	0.00307514i
$125$	−7.43136			−0.664681
$126$		0			0
$127$	5.91034			0.524458			0.262229	−	0.965006i	$-0.415543\pi$
$127$	5.91034			0.524458			0.262229	+	0.965006i	$0.415543\pi$
$128$	5.76730	+	9.98925i	0.509762	+	0.882933i
$129$		0			0
$130$	1.16410			0.102098
$131$	−2.09351	−	3.62607i	−0.182911	−	0.316812i	0.759959	−	0.649971i	$-0.225219\pi$
$131$	−2.09351	−	3.62607i	−0.182911	−	0.316812i	−0.942871	+	0.333159i	$0.891885\pi$
$132$		0			0
$133$	−2.21649			−0.192194
$134$	−10.3108			−0.890717
$135$		0			0
$136$	2.20037	−	3.81116i	0.188681	−	0.326804i
$137$	−1.11300			−0.0950903			−0.0475451	−	0.998869i	$-0.515140\pi$
$137$	−1.11300			−0.0950903			−0.0475451	+	0.998869i	$0.515140\pi$
$138$		0			0
$139$	−5.16059	+	8.93840i	−0.437716	+	0.758146i	−0.997513	−	0.0704840i	$-0.977546\pi$
$139$	−5.16059	+	8.93840i	−0.437716	+	0.758146i	0.559797	+	0.828630i	$0.310879\pi$
$140$	0.0105524			0.000891843
$141$		0			0
$142$	9.47815			0.795389
$143$	−2.76417	+	4.78768i	−0.231151	+	0.400366i
$144$		0			0
$145$	1.99197			0.165424
$146$	8.74666	+	15.1497i	0.723879	+	1.25380i
$147$		0			0
$148$	0.0883175	−	0.152970i	0.00725966	−	0.0125741i
$149$	−4.62315	−	8.00753i	−0.378743	−	0.656003i	0.612136	−	0.790752i	$-0.290310\pi$
$149$	−4.62315	−	8.00753i	−0.378743	−	0.656003i	−0.990880	+	0.134750i	$0.956977\pi$
$150$		0			0
$151$	−8.67058	−	15.0179i	−0.705602	−	1.22214i	−0.966474	−	0.256765i	$-0.917343\pi$
$151$	−8.67058	−	15.0179i	−0.705602	−	1.22214i	0.260872	−	0.965373i	$-0.415990\pi$
$152$	6.23631	+	10.8016i	0.505832	+	0.876126i
$153$		0			0
$154$	−1.90516	+	3.29983i	−0.153522	+	0.265908i
$155$	−0.588186	+	1.01877i	−0.0472442	+	0.0818294i
$156$		0			0
$157$	−8.14992	−	14.1161i	−0.650435	−	1.12659i	−0.983018	−	0.183512i	$-0.941254\pi$
$157$	−8.14992	−	14.1161i	−0.650435	−	1.12659i	0.332583	−	0.943074i	$-0.392080\pi$
$158$	−8.20412	−	14.2100i	−0.652685	−	1.13048i
$159$		0			0
$160$	−0.0597817	−	0.103545i	−0.00472616	−	0.00818595i
$161$	−1.42104	+	2.46131i	−0.111994	+	0.193979i
$162$		0			0
$163$	−1.69347	−	2.93317i	−0.132643	−	0.229744i	0.792052	−	0.610454i	$-0.209013\pi$
$163$	−1.69347	−	2.93317i	−0.132643	−	0.229744i	−0.924694	+	0.380710i	$0.875680\pi$
$164$	−0.0909870			−0.00710489
$165$		0			0
$166$	2.67836	−	4.63905i	0.207881	−	0.360060i
$167$	16.4594			1.27366			0.636832	−	0.771002i	$-0.280244\pi$
$167$	16.4594			1.27366			0.636832	+	0.771002i	$0.280244\pi$
$168$		0			0
$169$	−11.9367			−0.918209
$170$	−0.884237	+	1.53154i	−0.0678179	+	0.117464i
$171$		0			0
$172$	0.183129			0.0139635
$173$	4.20121	−	7.27671i	0.319412	−	0.553238i	−0.660953	−	0.750427i	$-0.729848\pi$
$173$	4.20121	−	7.27671i	0.319412	−	0.553238i	0.980366	+	0.197189i	$0.0631812\pi$
$174$		0			0
$175$	−2.18220			−0.164959
$176$	21.7272			1.63775
$177$		0			0
$178$	−13.1431	−	22.7645i	−0.985116	−	1.70627i
$179$	−14.1656			−1.05879			−0.529394	−	0.848376i	$-0.677581\pi$
$179$	−14.1656			−1.05879			−0.529394	+	0.848376i	$0.677581\pi$
$180$		0			0
$181$	7.32494	+	12.6872i	0.544459	+	0.943030i	0.998641	+	0.0521214i	$0.0165983\pi$
$181$	7.32494	+	12.6872i	0.544459	+	0.943030i	−0.454182	+	0.890909i	$0.650068\pi$
$182$	0.732848			0.0543223
$183$		0			0
$184$	15.9930			1.17902
$185$	2.62752	−	4.55099i	0.193179	−	0.334596i
$186$		0			0
$187$	−4.19928	−	7.27336i	−0.307082	−	0.531881i
$188$	0.0430076	+	0.0744914i	0.00313665	+	0.00543284i
$189$		0			0
$190$	−2.50611	−	4.34071i	−0.181812	−	0.314908i
$191$	6.39444	−	11.0755i	0.462686	−	0.801395i	−0.536408	−	0.843959i	$-0.680219\pi$
$191$	6.39444	−	11.0755i	0.462686	−	0.801395i	0.999094	+	0.0425637i	$0.0135525\pi$
$192$		0			0
$193$	−5.66939			−0.408091			−0.204046	−	0.978961i	$-0.565409\pi$
$193$	−5.66939			−0.408091			−0.204046	+	0.978961i	$0.565409\pi$
$194$	−1.16949	+	2.02562i	−0.0839648	+	0.145431i
$195$		0			0
$196$	−0.179941			−0.0128529
$197$	10.4230			0.742609			0.371305	−	0.928511i	$-0.378911\pi$
$197$	10.4230			0.742609			0.371305	+	0.928511i	$0.378911\pi$
$198$		0			0
$199$	−7.80540	+	13.5193i	−0.553310	+	0.958361i	0.444723	+	0.895668i	$0.353302\pi$
$199$	−7.80540	+	13.5193i	−0.553310	+	0.958361i	−0.998033	+	0.0626928i	$0.980031\pi$
$200$	6.13986	+	10.6345i	0.434153	+	0.751976i
$201$		0			0
$202$	8.02615	−	13.9017i	0.564718	−	0.978121i
$203$	1.25403			0.0880156
$204$		0			0
$205$	−2.70694			−0.189061
$206$	−14.3805	+	1.39489i	−1.00194	+	0.0971868i
$207$		0			0
$208$	−2.08943	−	3.61900i	−0.144876	−	0.250932i
$209$	23.8032			1.64650
$210$		0			0
$211$	2.81455	−	4.87494i	0.193762	−	0.335605i	−0.752732	−	0.658327i	$-0.771265\pi$
$211$	2.81455	−	4.87494i	0.193762	−	0.335605i	0.946494	+	0.322722i	$0.104598\pi$
$212$	−0.0270266	−	0.0468115i	−0.00185619	−	0.00321502i
$213$		0			0
$214$	−3.31046			−0.226298
$215$	5.44823			0.371566
$216$		0			0
$217$	−0.370288	+	0.641357i	−0.0251368	+	0.0435382i
$218$	10.2546	−	17.7615i	0.694531	−	1.20296i
$219$		0			0
$220$	−0.113324			−0.00764032
$221$	−0.807658	+	1.39890i	−0.0543289	+	0.0941005i
$222$		0			0
$223$	−8.01610	+	13.8843i	−0.536798	+	0.929761i	0.462276	+	0.886736i	$0.347033\pi$
$223$	−8.01610	+	13.8843i	−0.536798	+	0.929761i	−0.999074	+	0.0430249i	$0.986301\pi$
$224$	−0.0376351	−	0.0651859i	−0.00251460	−	0.00435542i
$225$		0			0
$226$	5.04840	+	8.74409i	0.335815	+	0.581648i
$227$	−14.3381	+	24.8344i	−0.951656	+	1.64832i	−0.209813	+	0.977741i	$0.567286\pi$
$227$	−14.3381	+	24.8344i	−0.951656	+	1.64832i	−0.741842	+	0.670574i	$0.766048\pi$
$228$		0			0
$229$	−22.2413			−1.46975			−0.734874	−	0.678203i	$-0.762759\pi$
$229$	−22.2413			−1.46975			−0.734874	+	0.678203i	$0.762759\pi$
$230$	−6.42690			−0.423777
$231$		0			0
$232$	−3.52834	−	6.11126i	−0.231647	−	0.401224i
$233$	−8.13939			−0.533229			−0.266615	−	0.963803i	$-0.585905\pi$
$233$	−8.13939			−0.533229			−0.266615	+	0.963803i	$0.585905\pi$
$234$		0			0
$235$	1.27951	+	2.21618i	0.0834661	+	0.144568i
$236$	−0.179177			−0.0116634
$237$		0			0
$238$	−0.556665	+	0.964172i	−0.0360832	+	0.0624980i
$239$	9.37445	−	16.2370i	0.606382	−	1.05029i	−0.385449	−	0.922729i	$-0.625953\pi$
$239$	9.37445	−	16.2370i	0.606382	−	1.05029i	0.991831	−	0.127556i	$-0.0407133\pi$
$240$		0			0
$241$	−10.9584	−	18.9806i	−0.705896	−	1.22265i	−0.966367	−	0.257166i	$-0.917211\pi$
$241$	−10.9584	−	18.9806i	−0.705896	−	1.22265i	0.260472	−	0.965481i	$-0.416122\pi$
$242$	12.6300	−	21.8758i	0.811886	−	1.40623i
$243$		0			0
$244$	0.0104004	−	0.0180141i	0.000665820	−	0.00115323i
$245$	−5.35339			−0.342015
$246$		0			0
$247$	−2.28907	−	3.96478i	−0.145650	−	0.252273i
$248$	4.16737			0.264628
$249$		0			0
$250$	−5.28966	−	9.16196i	−0.334548	−	0.579453i
$251$	−7.63374	+	13.2220i	−0.481837	+	0.834566i	−0.999783	−	0.0208472i	$-0.993364\pi$
$251$	−7.63374	+	13.2220i	−0.481837	+	0.834566i	0.517946	+	0.855414i	$0.326697\pi$
$252$		0			0
$253$	15.2608	−	26.4325i	0.959438	−	1.66179i
$254$	4.20700	+	7.28673i	0.263970	+	0.457210i
$255$		0			0
$256$	−0.319802	+	0.553913i	−0.0199876	+	0.0346196i
$257$	−4.19495	+	7.26587i	−0.261674	+	0.453232i	−0.966687	−	0.255962i	$-0.917608\pi$
$257$	−4.19495	+	7.26587i	−0.261674	+	0.453232i	0.705013	+	0.709194i	$0.250941\pi$
$258$		0			0
$259$	1.65413	−	2.86504i	0.102783	−	0.178025i
$260$	0.0108980	+	0.0188758i	0.000675864	+	0.00117063i
$261$		0			0
$262$	2.98034	−	5.16210i	0.184126	−	0.318916i
$263$	−9.02208	−	15.6267i	−0.556325	−	0.963584i	−0.997799	−	0.0663097i	$-0.978877\pi$
$263$	−9.02208	−	15.6267i	−0.556325	−	0.963584i	0.441474	−	0.897274i	$-0.354456\pi$
$264$		0			0
$265$	−0.804063	−	1.39268i	−0.0493932	−	0.0855515i
$266$	−1.57770	−	2.73266i	−0.0967352	−	0.167550i
$267$		0			0
$268$	−0.0965271	−	0.167190i	−0.00589633	−	0.0102127i
$269$	5.06153	−	8.76682i	0.308607	−	0.534522i	−0.669451	−	0.742856i	$-0.733471\pi$
$269$	5.06153	−	8.76682i	0.308607	−	0.534522i	0.978058	+	0.208334i	$0.0668040\pi$
$270$		0			0
$271$	−5.36465	+	9.29185i	−0.325879	+	0.564440i	−0.981690	−	0.190486i	$-0.938994\pi$
$271$	−5.36465	+	9.29185i	−0.325879	+	0.564440i	0.655811	+	0.754926i	$0.272327\pi$
$272$	6.34844			0.384931
$273$		0			0
$274$	−0.792239	−	1.37220i	−0.0478609	−	0.0828975i
$275$	23.4351			1.41319
$276$		0			0
$277$	1.12390	−	1.94665i	0.0675284	−	0.116963i	−0.830284	−	0.557340i	$-0.811822\pi$
$277$	1.12390	−	1.94665i	0.0675284	−	0.116963i	0.897813	+	0.440377i	$0.145155\pi$
$278$	−14.6933			−0.881245
$279$		0			0
$280$	−0.556082	−	0.963162i	−0.0332322	−	0.0575599i
$281$	6.41957	+	11.1190i	0.382959	+	0.663305i	0.991484	−	0.130230i	$-0.0415716\pi$
$281$	6.41957	+	11.1190i	0.382959	+	0.663305i	−0.608524	+	0.793535i	$0.708238\pi$
$282$		0			0
$283$	13.3349	+	23.0967i	0.792676	+	1.37295i	0.924305	+	0.381656i	$0.124646\pi$
$283$	13.3349	+	23.0967i	0.792676	+	1.37295i	−0.131629	+	0.991299i	$0.542021\pi$
$284$	0.0887321	+	0.153688i	0.00526528	+	0.00911973i
$285$		0			0
$286$	−7.87018			−0.465373
$287$	−1.70413			−0.100592
$288$		0			0
$289$	7.27302	+	12.5972i	0.427825	+	0.741014i
$290$	1.41789	+	2.45586i	0.0832614	+	0.144213i
$291$		0			0
$292$	−0.163768	+	0.283655i	−0.00958380	+	0.0165996i
$293$	16.0284	+	27.7620i	0.936389	+	1.62187i	0.772138	+	0.635455i	$0.219188\pi$
$293$	16.0284	+	27.7620i	0.936389	+	1.62187i	0.164251	+	0.986419i	$0.447479\pi$
$294$		0			0
$295$	−5.33066			−0.310363
$296$	−18.6163			−1.08205
$297$		0			0
$298$	6.58155	−	11.3996i	0.381259	−	0.660360i
$299$	−5.87029			−0.339488
$300$		0			0
$301$	3.42989			0.197696
$302$	12.3435	−	21.3796i	0.710288	−	1.23026i
$303$		0			0
$304$	−8.99640	+	15.5822i	−0.515979	+	0.893701i
$305$	0.309422	−	0.535934i	0.0177174	−	0.0306875i
$306$		0			0
$307$	3.03945	+	5.26448i	0.173471	+	0.300460i	0.939631	−	0.342190i	$-0.111169\pi$
$307$	3.03945	+	5.26448i	0.173471	+	0.300460i	−0.766160	+	0.642649i	$0.777835\pi$
$308$	−0.0713424			−0.00406511
$309$		0			0
$310$	−1.67469			−0.0951160
$311$	−2.74801	−	4.75969i	−0.155825	−	0.269897i	0.777534	−	0.628841i	$-0.216470\pi$
$311$	−2.74801	−	4.75969i	−0.155825	−	0.269897i	−0.933359	+	0.358944i	$0.883137\pi$
$312$		0			0
$313$	10.4794	−	18.1508i	0.592331	−	1.02595i	−0.401587	−	0.915821i	$-0.631541\pi$
$313$	10.4794	−	18.1508i	0.592331	−	1.02595i	0.993918	−	0.110126i	$-0.0351254\pi$
$314$	11.6023	−	20.0957i	0.654754	−	1.13407i
$315$		0			0
$316$	0.153610	−	0.266060i	0.00864122	−	0.0149670i
$317$	22.0410			1.23795			0.618974	−	0.785412i	$-0.287549\pi$
$317$	22.0410			1.23795			0.618974	+	0.785412i	$0.287549\pi$
$318$		0			0
$319$	−13.4672			−0.754020
$320$	−3.12862	+	5.41893i	−0.174895	+	0.302928i
$321$		0			0
$322$	−4.04600			−0.225475
$323$	6.95502			0.386988
$324$		0			0
$325$	−2.25366	−	3.90346i	−0.125011	−	0.216525i
$326$	2.41083	−	4.17568i	0.133524	−	0.231270i
$327$		0			0
$328$	4.79475	+	8.30475i	0.264746	+	0.458553i
$329$	0.805506	+	1.39518i	0.0444090	+	0.0769186i
$330$		0			0
$331$	−13.6761			−0.751706			−0.375853	−	0.926679i	$-0.622650\pi$
$331$	−13.6761			−0.751706			−0.375853	+	0.926679i	$0.622650\pi$
$332$	0.100296			0.00550448
$333$		0			0
$334$	11.7158	+	20.2924i	0.641062	+	1.11035i
$335$	−2.87176	−	4.97403i	−0.156901	−	0.271760i
$336$		0			0
$337$	7.48346	+	12.9617i	0.407650	+	0.706071i	0.994626	−	0.103534i	$-0.0330149\pi$
$337$	7.48346	+	12.9617i	0.407650	+	0.706071i	−0.586976	+	0.809605i	$0.699682\pi$
$338$	−8.49660	−	14.7165i	−0.462154	−	0.800474i
$339$		0			0
$340$	−0.0331120			−0.00179575
$341$	3.97658	−	6.88764i	0.215344	−	0.372987i
$342$		0			0
$343$	−6.86479			−0.370664
$344$	−9.65036	−	16.7149i	−0.520312	−	0.901207i
$345$		0			0
$346$	11.9617			0.643067
$347$	−10.8865	+	18.8559i	−0.584415	+	1.01224i	0.410533	+	0.911846i	$0.365343\pi$
$347$	−10.8865	+	18.8559i	−0.584415	+	1.01224i	−0.994948	+	0.100391i	$0.967991\pi$
$348$		0			0
$349$	5.72955	−	9.92387i	0.306696	−	0.531212i	−0.670942	−	0.741510i	$-0.734110\pi$
$349$	5.72955	−	9.92387i	0.306696	−	0.531212i	0.977637	+	0.210298i	$0.0674433\pi$
$350$	−1.55330	−	2.69039i	−0.0830274	−	0.143808i
$351$		0			0
$352$	0.404170	+	0.700043i	0.0215423	+	0.0373124i
$353$	−4.51021	−	7.81192i	−0.240054	−	0.415786i	0.720675	−	0.693273i	$-0.243832\pi$
$353$	−4.51021	−	7.81192i	−0.240054	−	0.415786i	−0.960730	+	0.277487i	$0.910499\pi$
$354$		0			0
$355$	2.63985	+	4.57235i	0.140109	+	0.242675i
$356$	0.246084	−	0.426231i	0.0130424	−	0.0225902i
$357$		0			0
$358$	−10.0831	−	17.4645i	−0.532910	−	0.923027i
$359$	−13.5949	+	23.5471i	−0.717513	+	1.24277i	0.244469	+	0.969657i	$0.421386\pi$
$359$	−13.5949	+	23.5471i	−0.717513	+	1.24277i	−0.961982	+	0.273112i	$0.911947\pi$
$360$		0			0
$361$	−0.355983	+	0.616581i	−0.0187360	+	0.0324516i
$362$	−10.4278	+	18.0615i	−0.548075	+	0.949294i
$363$		0			0
$364$	0.00686074	+	0.0118831i	0.000359600	+	0.000622846i
$365$	−4.87223	+	8.43895i	−0.255024	+	0.441715i
$366$		0			0
$367$	5.41246	−	9.37466i	0.282528	−	0.489353i	−0.689479	−	0.724306i	$-0.742160\pi$
$367$	5.41246	−	9.37466i	0.282528	−	0.489353i	0.972007	+	0.234953i	$0.0754936\pi$
$368$	11.5356	+	19.9802i	0.601334	+	1.04154i
$369$		0			0
$370$	7.48110			0.388924
$371$	−0.506192	−	0.876750i	−0.0262802	−	0.0455186i
$372$		0			0
$373$	0.836250			0.0432994			0.0216497	−	0.999766i	$-0.493108\pi$
$373$	0.836250			0.0432994			0.0216497	+	0.999766i	$0.493108\pi$
$374$	5.97812	−	10.3544i	0.309121	−	0.535413i
$375$		0			0
$376$	4.53275	−	7.85095i	0.233759	−	0.404882i
$377$	1.29509	+	2.24317i	0.0667007	+	0.115529i
$378$		0			0
$379$	−14.1962	+	24.5885i	−0.729209	+	1.26303i	0.228009	+	0.973659i	$0.426778\pi$
$379$	−14.1962	+	24.5885i	−0.729209	+	1.26303i	−0.957218	+	0.289368i	$0.906555\pi$
$380$	0.0469231	−	0.0812733i	0.00240711	−	0.00416923i
$381$		0			0
$382$	18.2063			0.931517
$383$	−4.99235	−	8.64700i	−0.255097	−	0.441841i	0.709825	−	0.704378i	$-0.248774\pi$
$383$	−4.99235	−	8.64700i	−0.255097	−	0.441841i	−0.964922	+	0.262537i	$0.915441\pi$
$384$		0			0
$385$	−2.12249			−0.108172
$386$	−4.03549	−	6.98967i	−0.205401	−	0.355765i
$387$		0			0
$388$	−0.0437940			−0.00222331
$389$	−8.36428			−0.424086			−0.212043	−	0.977260i	$-0.568012\pi$
$389$	−8.36428			−0.424086			−0.212043	+	0.977260i	$0.568012\pi$
$390$		0			0
$391$	4.45902	−	7.72325i	0.225502	−	0.390582i
$392$	9.48236	+	16.4239i	0.478931	+	0.829533i
$393$		0			0
$394$	7.41914	+	12.8503i	0.373771	+	0.647390i
$395$	4.57001	−	7.91550i	0.229942	−	0.398272i
$396$		0			0
$397$	−2.03227	+	3.52000i	−0.101997	+	0.176664i	−0.912507	−	0.409061i	$-0.865856\pi$
$397$	−2.03227	+	3.52000i	−0.101997	+	0.176664i	0.810510	+	0.585724i	$0.199190\pi$
$398$	−22.2236			−1.11397
$399$		0			0
$400$	−8.85725	+	15.3412i	−0.442862	+	0.767060i
$401$	−15.4101	+	26.6910i	−0.769542	+	1.33289i	0.168270	+	0.985741i	$0.446182\pi$
$401$	−15.4101	+	26.6910i	−0.769542	+	1.33289i	−0.937812	+	0.347144i	$0.887151\pi$
$402$		0			0
$403$	−1.52965			−0.0761974
$404$	0.300555			0.0149532
$405$		0			0
$406$	0.892622	+	1.54607i	0.0443001	+	0.0767300i
$407$	−17.7640	+	30.7682i	−0.880529	+	1.52512i
$408$		0			0
$409$	15.4937			0.766114			0.383057	−	0.923725i	$-0.374871\pi$
$409$	15.4937			0.766114			0.383057	+	0.923725i	$0.374871\pi$
$410$	−1.92681	−	3.33733i	−0.0951582	−	0.164819i
$411$		0			0
$412$	−0.157245	−	0.220122i	−0.00774691	−	0.0108446i
$413$	−3.35588			−0.165132
$414$		0			0
$415$	2.98390			0.146474
$416$	0.0777350	−	0.134641i	0.00381127	−	0.00660132i
$417$		0			0
$418$	16.9432	+	29.3465i	0.828720	+	1.43538i
$419$	−5.50841	+	9.54084i	−0.269103	+	0.466101i	−0.968631	−	0.248505i	$-0.920061\pi$
$419$	−5.50841	+	9.54084i	−0.269103	+	0.466101i	0.699527	+	0.714606i	$0.253394\pi$
$420$		0			0
$421$	24.0374			1.17151			0.585756	−	0.810487i	$-0.300798\pi$
$421$	24.0374			1.17151			0.585756	+	0.810487i	$0.300798\pi$
$422$	8.01362			0.390097
$423$		0			0
$424$	−2.84844	+	4.93365i	−0.138333	+	0.239599i
$425$	6.84745			0.332150
$426$		0			0
$427$	0.194794	−	0.337393i	0.00942674	−	0.0163276i
$428$	−0.0309917	−	0.0536792i	−0.00149804	−	0.00259468i
$429$		0			0
$430$	3.87807	+	6.71701i	0.187017	+	0.323923i
$431$	−13.2337	−	22.9214i	−0.637444	−	1.10408i	−0.985992	−	0.166794i	$-0.946659\pi$
$431$	−13.2337	−	22.9214i	−0.637444	−	1.10408i	0.348548	−	0.937291i	$-0.386675\pi$
$432$		0			0
$433$	−2.63294	+	4.56038i	−0.126531	+	0.219158i	−0.922330	−	0.386402i	$-0.873718\pi$
$433$	−2.63294	+	4.56038i	−0.126531	+	0.219158i	0.795799	+	0.605560i	$0.207051\pi$
$434$	−1.05429			−0.0506074
$435$		0			0
$436$	0.384005			0.0183905
$437$	12.6378	+	21.8893i	0.604547	+	1.04711i
$438$		0			0
$439$	19.2622			0.919337			0.459668	−	0.888091i	$-0.347968\pi$
$439$	19.2622			0.919337			0.459668	+	0.888091i	$0.347968\pi$
$440$	5.97185	+	10.3436i	0.284697	+	0.493110i
$441$		0			0
$442$	−2.29957			−0.109380
$443$	−20.1058			−0.955254			−0.477627	−	0.878563i	$-0.658503\pi$
$443$	−20.1058			−0.955254			−0.477627	+	0.878563i	$0.658503\pi$
$444$		0			0
$445$	7.32121	−	12.6807i	0.347059	−	0.601123i
$446$	−22.8235			−1.08073
$447$		0			0
$448$	−1.96960	+	3.41145i	−0.0930548	+	0.161176i
$449$	−7.15720			−0.337769			−0.168885	−	0.985636i	$-0.554017\pi$
$449$	−7.15720			−0.337769			−0.168885	+	0.985636i	$0.554017\pi$
$450$		0			0
$451$	18.3010			0.861758
$452$	−0.0945238	+	0.163720i	−0.00444602	+	0.00770074i
$453$		0			0
$454$	−40.8237			−1.91595
$455$	0.204112	+	0.353533i	0.00956894	+	0.0165739i
$456$		0			0
$457$	−5.35158	+	9.26921i	−0.250336	+	0.433596i	−0.963618	−	0.267282i	$-0.913875\pi$
$457$	−5.35158	+	9.26921i	−0.250336	+	0.433596i	0.713282	+	0.700877i	$0.247208\pi$
$458$	−15.8315	−	27.4209i	−0.739755	−	1.28129i
$459$		0			0
$460$	−0.0601670	−	0.104212i	−0.00280530	−	0.00485892i
$461$	−4.07377	−	7.05598i	−0.189734	−	0.328630i	0.755427	−	0.655233i	$-0.227429\pi$
$461$	−4.07377	−	7.05598i	−0.189734	−	0.328630i	−0.945162	+	0.326603i	$0.894096\pi$
$462$		0			0
$463$	−0.934831	+	1.61917i	−0.0434453	+	0.0752494i	−0.886930	−	0.461903i	$-0.847167\pi$
$463$	−0.934831	+	1.61917i	−0.0434453	+	0.0752494i	0.843485	+	0.537153i	$0.180500\pi$
$464$	5.08992	−	8.81600i	0.236294	−	0.409273i
$465$		0			0
$466$	−5.79365	−	10.0349i	−0.268385	−	0.464857i
$467$	−0.799104	−	1.38409i	−0.0369781	−	0.0640480i	0.846944	−	0.531682i	$-0.178440\pi$
$467$	−0.799104	−	1.38409i	−0.0369781	−	0.0640480i	−0.883922	+	0.467634i	$0.845107\pi$
$468$		0			0
$469$	−1.80789	−	3.13136i	−0.0834807	−	0.144593i
$470$	−1.82152	+	3.15496i	−0.0840204	+	0.145528i
$471$		0			0
$472$	9.44211	+	16.3542i	0.434608	+	0.752763i
$473$	−36.8342			−1.69364
$474$		0			0
$475$	−9.70354	+	16.8070i	−0.445229	+	0.771159i
$476$	−0.0208454			−0.000955448
$477$		0			0
$478$	26.6910			1.22082
$479$	−2.19289	+	3.79819i	−0.100195	+	0.173544i	−0.911765	−	0.410712i	$-0.865280\pi$
$479$	−2.19289	+	3.79819i	−0.100195	+	0.173544i	0.811570	+	0.584256i	$0.198613\pi$
$480$		0			0
$481$	6.83319			0.311567
$482$	15.6005	−	27.0209i	0.710584	−	1.23077i
$483$		0			0
$484$	0.472955			0.0214979
$485$	−1.30291			−0.0591620
$486$		0			0
$487$	21.5120	+	37.2599i	0.974802	+	1.68841i	0.680586	+	0.732668i	$0.261725\pi$
$487$	21.5120	+	37.2599i	0.974802	+	1.68841i	0.294216	+	0.955739i	$0.404942\pi$
$488$	−2.19229			−0.0992403
$489$		0			0
$490$	−3.81056	−	6.60008i	−0.172143	−	0.298161i
$491$	−16.6390			−0.750906			−0.375453	−	0.926841i	$-0.622513\pi$
$491$	−16.6390			−0.750906			−0.375453	+	0.926841i	$0.622513\pi$
$492$		0			0
$493$	−3.93497			−0.177222
$494$	3.25873	−	5.64429i	0.146617	−	0.253949i
$495$		0			0
$496$	3.00589	+	5.20635i	0.134968	+	0.233772i
$497$	1.66190	+	2.87849i	0.0745463	+	0.129118i
$498$		0			0
$499$	0.192309	+	0.333090i	0.00860895	+	0.0149111i	0.870298	−	0.492526i	$-0.163926\pi$
$499$	0.192309	+	0.333090i	0.00860895	+	0.0149111i	−0.861689	+	0.507437i	$0.830593\pi$
$500$	0.0990409	−	0.171544i	0.00442925	−	0.00767168i
$501$		0			0
$502$	−21.7349			−0.970075
$503$	−0.332294	+	0.575549i	−0.0148162	+	0.0256625i	−0.873338	−	0.487114i	$-0.838050\pi$
$503$	−0.332294	+	0.575549i	−0.0148162	+	0.0256625i	0.858522	+	0.512776i	$0.171383\pi$
$504$		0			0
$505$	8.94176			0.397903
$506$	43.4507			1.93162
$507$		0			0
$508$	−0.0787697	+	0.136433i	−0.00349484	+	0.00605324i
$509$	−18.6579	−	32.3165i	−0.826999	−	1.43240i	−0.900382	−	0.435100i	$-0.856713\pi$
$509$	−18.6579	−	32.3165i	−0.826999	−	1.43240i	0.0733836	−	0.997304i	$-0.476620\pi$
$510$		0			0
$511$	−3.06728	+	5.31268i	−0.135688	+	0.235019i
$512$	22.1586			0.979283
$513$		0			0
$514$	−11.9439			−0.526824
$515$	−4.67817	−	6.54881i	−0.206145	−	0.288575i
$516$		0			0
$517$	−8.65047	−	14.9830i	−0.380447	−	0.658954i
$518$	4.70967			0.206931
$519$		0			0
$520$	1.14858	−	1.98940i	0.0503687	−	0.0872411i
$521$	−3.24693	−	5.62385i	−0.142251	−	0.246385i	0.786093	−	0.618108i	$-0.212101\pi$
$521$	−3.24693	−	5.62385i	−0.142251	−	0.246385i	−0.928344	+	0.371723i	$0.878767\pi$
$522$		0			0
$523$	19.1218			0.836140			0.418070	−	0.908415i	$-0.362707\pi$
$523$	19.1218			0.836140			0.418070	+	0.908415i	$0.362707\pi$
$524$	0.111605			0.00487548
$525$		0			0
$526$	12.8439	−	22.2463i	0.560020	−	0.969984i
$527$	1.16191	−	2.01249i	0.0506136	−	0.0876653i
$528$		0			0
$529$	9.40950			0.409108
$530$	1.14467	−	1.98263i	0.0497213	−	0.0861197i
$531$		0			0
$532$	0.0295401	−	0.0511650i	0.00128073	−	0.00221828i
$533$	−1.75993	−	3.04830i	−0.0762312	−	0.132036i
$534$		0			0
$535$	−0.922027	−	1.59700i	−0.0398627	−	0.0690442i
$536$	−10.1734	+	17.6208i	−0.439423	+	0.761103i
$537$		0			0
$538$	14.4112			0.621313
$539$	36.1930			1.55894
$540$		0			0
$541$	−1.66443	−	2.88287i	−0.0715593	−	0.123944i	0.828026	−	0.560690i	$-0.189464\pi$
$541$	−1.66443	−	2.88287i	−0.0715593	−	0.123944i	−0.899585	+	0.436746i	$0.856131\pi$
$542$	−15.2743			−0.656088
$543$		0			0
$544$	0.118094	+	0.204544i	0.00506322	+	0.00876976i
$545$	11.4245			0.489370
$546$		0			0
$547$	−6.87250	+	11.9035i	−0.293847	+	0.508958i	−0.974716	−	0.223447i	$-0.928269\pi$
$547$	−6.87250	+	11.9035i	−0.293847	+	0.508958i	0.680869	+	0.732405i	$0.261602\pi$
$548$	0.0148335	−	0.0256923i	0.000633655	−	0.00109752i
$549$		0			0
$550$	16.6812	+	28.8926i	0.711287	+	1.23198i
$551$	5.57625	−	9.65835i	0.237556	−	0.411460i
$552$		0			0
$553$	2.87702	−	4.98314i	0.122343	−	0.211905i
$554$	3.19997			0.135954
$555$		0			0
$556$	−0.137555	−	0.238252i	−0.00583363	−	0.0101041i
$557$	5.22582			0.221425			0.110713	−	0.993852i	$-0.464687\pi$
$557$	5.22582			0.221425			0.110713	+	0.993852i	$0.464687\pi$
$558$		0			0
$559$	3.54221	+	6.13528i	0.149819	+	0.259495i
$560$	0.802194	−	1.38944i	0.0338989	−	0.0587146i
$561$		0			0
$562$	−9.13894	+	15.8291i	−0.385503	+	0.667711i
$563$	18.5523	+	32.1336i	0.781888	+	1.35427i	0.930841	+	0.365425i	$0.119076\pi$
$563$	18.5523	+	32.1336i	0.781888	+	1.35427i	−0.148953	+	0.988844i	$0.547590\pi$
$564$		0			0
$565$	−2.81216	+	4.87080i	−0.118308	+	0.204916i
$566$	−18.9836	+	32.8806i	−0.797940	+	1.38207i
$567$		0			0
$568$	9.35183	−	16.1979i	0.392394	−	0.679647i
$569$	−20.1643	−	34.9256i	−0.845332	−	1.46416i	−0.885332	−	0.464959i	$-0.846069\pi$
$569$	−20.1643	−	34.9256i	−0.845332	−	1.46416i	0.0399999	−	0.999200i	$-0.487264\pi$
$570$		0			0
$571$	−8.36554	+	14.4895i	−0.350087	+	0.606368i	−0.986264	−	0.165175i	$-0.947181\pi$
$571$	−8.36554	+	14.4895i	−0.350087	+	0.606368i	0.636178	+	0.771543i	$0.280515\pi$
$572$	−0.0736786	−	0.127615i	−0.00308066	−	0.00533585i
$573$		0			0
$574$	−1.21301	−	2.10099i	−0.0506299	−	0.0876935i
$575$	12.4423	+	21.5507i	0.518881	+	0.898727i
$576$		0			0
$577$	8.95716	+	15.5143i	0.372891	+	0.645867i	0.990009	−	0.141004i	$-0.0450331\pi$
$577$	8.95716	+	15.5143i	0.372891	+	0.645867i	−0.617118	+	0.786871i	$0.711700\pi$
$578$	−10.3539	+	17.9335i	−0.430666	+	0.745936i
$579$		0			0
$580$	−0.0265479	+	0.0459822i	−0.00110234	+	0.00190931i
$581$	1.87849			0.0779329
$582$		0			0
$583$	5.43608	+	9.41556i	0.225139	+	0.389953i
$584$	34.5204			1.42846
$585$		0			0
$586$	−22.8181	+	39.5222i	−0.942608	+	1.63265i
$587$	13.2017			0.544892			0.272446	−	0.962171i	$-0.412167\pi$
$587$	13.2017			0.544892			0.272446	+	0.962171i	$0.412167\pi$
$588$		0			0
$589$	3.29309	+	5.70380i	0.135690	+	0.235021i
$590$	−3.79438	−	6.57207i	−0.156212	−	0.270568i
$591$		0			0
$592$	−13.4278	−	23.2576i	−0.551878	−	0.955880i
$593$	12.0171	+	20.8142i	0.493482	+	0.854737i	0.999972	−	0.00750950i	$-0.00239037\pi$
$593$	12.0171	+	20.8142i	0.493482	+	0.854737i	−0.506489	+	0.862246i	$0.669057\pi$
$594$		0			0
$595$	−0.620168			−0.0254244
$596$	0.246459			0.0100954
$597$		0			0
$598$	−4.17849	−	7.23736i	−0.170871	−	0.295958i
$599$	−7.92659	−	13.7292i	−0.323872	−	0.560962i	0.657412	−	0.753531i	$-0.271651\pi$
$599$	−7.92659	−	13.7292i	−0.323872	−	0.560962i	−0.981283	+	0.192570i	$0.938318\pi$
$600$		0			0
$601$	9.28220	−	16.0773i	0.378629	−	0.655805i	−0.612234	−	0.790677i	$-0.709729\pi$
$601$	9.28220	−	16.0773i	0.378629	−	0.655805i	0.990863	+	0.134872i	$0.0430623\pi$
$602$	2.44141	+	4.22864i	0.0995044	+	0.172347i
$603$		0			0
$604$	0.462227			0.0188077
$605$	14.0708			0.572059
$606$		0			0
$607$	−4.01575	+	6.95548i	−0.162994	+	0.282314i	−0.935941	−	0.352156i	$-0.885449\pi$
$607$	−4.01575	+	6.95548i	−0.162994	+	0.282314i	0.772947	+	0.634471i	$0.218782\pi$
$608$	−0.669403			−0.0271479
$609$		0			0
$610$	0.880989			0.0356702
$611$	−1.66377	+	2.88173i	−0.0673088	+	0.116582i
$612$		0			0
$613$	16.5991	−	28.7506i	0.670433	−	1.16122i	−0.307348	−	0.951597i	$-0.599442\pi$
$613$	16.5991	−	28.7506i	0.670433	−	1.16122i	0.977781	−	0.209627i	$-0.0672250\pi$
$614$	−4.32698	+	7.49455i	−0.174623	+	0.302455i
$615$		0			0
$616$	3.75954	+	6.51171i	0.151476	+	0.262364i
$617$	−4.18795			−0.168600			−0.0843002	−	0.996440i	$-0.526865\pi$
$617$	−4.18795			−0.168600			−0.0843002	+	0.996440i	$0.526865\pi$
$618$		0			0
$619$	9.92196			0.398797			0.199399	−	0.979918i	$-0.436101\pi$
$619$	9.92196			0.398797			0.199399	+	0.979918i	$0.436101\pi$
$620$	−0.0156780	−	0.0271551i	−0.000629644	−	0.00109058i
$621$		0			0
$622$	3.91208	−	6.77593i	0.156860	−	0.271690i
$623$	4.60901	−	7.98304i	0.184656	−	0.319834i
$624$		0			0
$625$	−7.98131	+	13.8240i	−0.319253	+	0.552962i
$626$	29.8371			1.19253
$627$		0			0
$628$	0.434470			0.0173373
$629$	−5.19043	+	8.99009i	−0.206956	+	0.358459i
$630$		0			0
$631$	12.6437			0.503338			0.251669	−	0.967813i	$-0.419021\pi$
$631$	12.6437			0.503338			0.251669	+	0.967813i	$0.419021\pi$
$632$	−32.3791			−1.28797
$633$		0			0
$634$	15.6889	+	27.1739i	0.623085	+	1.07921i
$635$	−2.34346	+	4.05899i	−0.0929974	+	0.161076i
$636$		0			0
$637$	−3.48054	−	6.02848i	−0.137904	−	0.238857i
$638$	−9.58602	−	16.6035i	−0.379514	−	0.657338i
$639$		0			0
$640$	−9.14698			−0.361566
$641$	38.6423			1.52628			0.763139	−	0.646234i	$-0.223657\pi$
$641$	38.6423			1.52628			0.763139	+	0.646234i	$0.223657\pi$
$642$		0			0
$643$	−21.6536	−	37.5051i	−0.853934	−	1.47906i	−0.877630	−	0.479338i	$-0.840877\pi$
$643$	−21.6536	−	37.5051i	−0.853934	−	1.47906i	0.0236960	−	0.999719i	$-0.492457\pi$
$644$	−0.0378777	−	0.0656060i	−0.00149259	−	0.00258524i
$645$		0			0
$646$	4.95061	+	8.57470i	0.194779	+	0.337367i
$647$	12.4689	+	21.5968i	0.490204	+	0.849058i	0.999936	−	0.0112748i	$-0.00358896\pi$
$647$	12.4689	+	21.5968i	0.490204	+	0.849058i	−0.509732	+	0.860333i	$0.670256\pi$
$648$		0			0
$649$	36.0393			1.41467
$650$	3.20833	−	5.55699i	0.125841	−	0.217963i
$651$		0			0
$652$	0.0902784			0.00353558
$653$	−22.0432	−	38.1799i	−0.862615	−	1.49409i	−0.869396	−	0.494117i	$-0.835492\pi$
$653$	−22.0432	−	38.1799i	−0.862615	−	1.49409i	0.00678013	−	0.999977i	$-0.497842\pi$
$654$		0			0
$655$	3.32033			0.129736
$656$	−6.91682	+	11.9803i	−0.270056	+	0.467751i
$657$		0			0
$658$	−1.14672	+	1.98618i	−0.0447039	+	0.0774295i
$659$	6.96520	+	12.0641i	0.271326	+	0.469950i	0.969202	−	0.246269i	$-0.0792047\pi$
$659$	6.96520	+	12.0641i	0.271326	+	0.469950i	−0.697876	+	0.716219i	$0.745871\pi$
$660$		0			0
$661$	−2.57315	−	4.45683i	−0.100084	−	0.173351i	0.811635	−	0.584165i	$-0.198578\pi$
$661$	−2.57315	−	4.45683i	−0.100084	−	0.173351i	−0.911719	+	0.410814i	$0.865245\pi$
$662$	−9.73469	−	16.8610i	−0.378349	−	0.655321i
$663$		0			0
$664$	−5.28532	−	9.15445i	−0.205110	−	0.355262i
$665$	0.878842	−	1.52220i	0.0340800	−	0.0590283i
$666$		0			0
$667$	−7.15012	−	12.3844i	−0.276854	−	0.479525i
$668$	−0.219361	+	0.379945i	−0.00848735	+	0.0147005i
$669$		0			0
$670$	4.08825	−	7.08106i	0.157943	−	0.273565i
$671$	−2.09192	+	3.62332i	−0.0807579	+	0.139877i
$672$		0			0
$673$	−13.0369	−	22.5806i	−0.502537	−	0.870419i	−0.999996	−	0.00293163i	$-0.999067\pi$
$673$	−13.0369	−	22.5806i	−0.502537	−	0.870419i	0.497459	−	0.867487i	$-0.334267\pi$
$674$	−10.6535	+	18.4524i	−0.410358	+	0.710760i
$675$		0			0
$676$	0.159086	−	0.275545i	0.00611869	−	0.0105979i
$677$	12.0214	+	20.8216i	0.462018	+	0.800239i	0.999061	−	0.0433158i	$-0.0137921\pi$
$677$	12.0214	+	20.8216i	0.462018	+	0.800239i	−0.537043	+	0.843555i	$0.680459\pi$
$678$		0			0
$679$	−0.820236			−0.0314778
$680$	1.74491	+	3.02226i	0.0669141	+	0.115899i
$681$		0			0
$682$	11.3222			0.433548
$683$	24.0939	−	41.7318i	0.921927	−	1.59682i	0.125497	−	0.992094i	$-0.459948\pi$
$683$	24.0939	−	41.7318i	0.921927	−	1.59682i	0.796430	−	0.604730i	$-0.206719\pi$
$684$		0			0
$685$	0.441308	−	0.764368i	0.0168615	−	0.0292050i
$686$	−4.88638	−	8.46346i	−0.186563	−	0.323136i
$687$		0			0
$688$	13.9214	−	24.1126i	0.530750	−	0.919286i
$689$	1.04553	−	1.81092i	0.0398317	−	0.0689905i
$690$		0			0
$691$	−33.8142			−1.28635			−0.643177	−	0.765717i	$-0.722384\pi$
$691$	−33.8142			−1.28635			−0.643177	+	0.765717i	$0.722384\pi$
$692$	0.111983	+	0.193960i	0.00425695	+	0.00737325i
$693$		0			0
$694$	−30.9960			−1.17659
$695$	−4.09237	−	7.08819i	−0.155232	−	0.268870i
$696$		0			0
$697$	5.34732			0.202544
$698$	16.3132			0.617465
$699$		0			0
$700$	0.0290832	−	0.0503736i	0.00109924	−	0.00190394i
$701$	2.15364	+	3.73022i	0.0813420	+	0.140889i	0.903827	−	0.427899i	$-0.140746\pi$
$701$	2.15364	+	3.73022i	0.0813420	+	0.140889i	−0.822485	+	0.568787i	$0.807413\pi$
$702$		0			0
$703$	−14.7108	−	25.4798i	−0.554827	−	0.960988i
$704$	21.1519	−	36.6361i	0.797191	−	1.38077i
$705$		0			0
$706$	6.42077	−	11.1211i	0.241649	−	0.418548i
$707$	5.62922			0.211708
$708$		0			0
$709$	−14.4055	+	24.9510i	−0.541009	+	0.937054i	0.457838	+	0.889036i	$0.348624\pi$
$709$	−14.4055	+	24.9510i	−0.541009	+	0.937054i	−0.998846	+	0.0480187i	$0.984709\pi$
$710$	−3.75811	+	6.50923i	−0.141039	+	0.244287i
$711$		0			0
$712$	−51.8717			−1.94397
$713$	8.44511			0.316272
$714$		0			0
$715$	−2.19200	−	3.79665i	−0.0819761	−	0.141987i
$716$	0.188791	−	0.326996i	0.00705547	−	0.0122204i
$717$		0			0
$718$	−38.7077			−1.44456
$719$	−12.0942	−	20.9478i	−0.451038	−	0.781221i	0.547413	−	0.836863i	$-0.315613\pi$
$719$	−12.0942	−	20.9478i	−0.451038	−	0.781221i	−0.998451	+	0.0556421i	$0.982279\pi$
$720$		0			0
$721$	−2.94510	−	4.12275i	−0.109681	−	0.153539i
$722$	−1.01356			−0.0377208
$723$		0			0
$724$	−0.390491			−0.0145125
$725$	5.49000	−	9.50896i	0.203894	−	0.353154i
$726$		0			0
$727$	11.6180	+	20.1230i	0.430888	+	0.746321i	0.996950	−	0.0780424i	$-0.0248669\pi$
$727$	11.6180	+	20.1230i	0.430888	+	0.746321i	−0.566062	+	0.824363i	$0.691534\pi$
$728$	0.723081	−	1.25241i	0.0267992	−	0.0464175i
$729$		0			0
$730$	−13.8723			−0.513436
$731$	−10.7625			−0.398066
$732$		0			0
$733$	2.65005	−	4.59003i	0.0978820	−	0.169537i	−0.812926	−	0.582367i	$-0.802127\pi$
$733$	2.65005	−	4.59003i	0.0978820	−	0.169537i	0.910808	+	0.412831i	$0.135460\pi$
$734$	15.4104			0.568809
$735$		0			0
$736$	−0.429170	+	0.743344i	−0.0158194	+	0.0274000i
$737$	19.4153	+	33.6282i	0.715171	+	1.23871i
$738$		0			0
$739$	18.8249	+	32.6058i	0.692487	+	1.19942i	0.971021	+	0.238996i	$0.0768183\pi$
$739$	18.8249	+	32.6058i	0.692487	+	1.19942i	−0.278534	+	0.960426i	$0.589848\pi$
$740$	0.0700361	+	0.121306i	0.00257458	+	0.00445930i
$741$		0			0
$742$	0.720618	−	1.24815i	0.0264547	−	0.0458209i
$743$	3.98500			0.146196			0.0730978	−	0.997325i	$-0.476711\pi$
$743$	3.98500			0.146196			0.0730978	+	0.997325i	$0.476711\pi$
$744$		0			0
$745$	7.33236			0.268637
$746$	0.595246	+	1.03100i	0.0217935	+	0.0377474i
$747$		0			0
$748$	0.223862			0.00818522
$749$	−0.580455	−	1.00538i	−0.0212094	−	0.0367357i
$750$		0			0
$751$	47.3532			1.72794			0.863972	−	0.503540i	$-0.167969\pi$
$751$	47.3532			1.72794			0.863972	+	0.503540i	$0.167969\pi$
$752$	13.0777			0.476896
$753$		0			0
$754$	−1.84370	+	3.19339i	−0.0671437	+	0.116296i
$755$	13.7516			0.500472
$756$		0			0
$757$	22.2718	−	38.5759i	0.809483	−	1.40207i	−0.103739	−	0.994605i	$-0.533081\pi$
$757$	22.2718	−	38.5759i	0.809483	−	1.40207i	0.913222	−	0.407461i	$-0.133586\pi$
$758$	−40.4195			−1.46810
$759$		0			0
$760$	−9.89084			−0.358779
$761$	5.06122	−	8.76628i	0.183469	−	0.317778i	−0.759591	−	0.650402i	$-0.774601\pi$
$761$	5.06122	−	8.76628i	0.183469	−	0.317778i	0.943060	+	0.332624i	$0.107934\pi$
$762$		0			0
$763$	7.19217			0.260374
$764$	0.170443	+	0.295216i	0.00616642	+	0.0106805i
$765$		0			0
$766$	7.10714	−	12.3099i	0.256791	−	0.444776i
$767$	−3.46577	−	6.00289i	−0.125142	−	0.216752i
$768$		0			0
$769$	10.3398	+	17.9090i	0.372862	+	0.645816i	0.990005	−	0.141035i	$-0.0450432\pi$
$769$	10.3398	+	17.9090i	0.372862	+	0.645816i	−0.617143	+	0.786851i	$0.711710\pi$
$770$	−1.51080	−	2.61678i	−0.0544454	−	0.0943022i
$771$		0			0
$772$	0.0755584	−	0.130871i	0.00271941	−	0.00471015i
$773$	7.00827	−	12.1387i	0.252070	−	0.436598i	−0.712026	−	0.702154i	$-0.752222\pi$
$773$	7.00827	−	12.1387i	0.252070	−	0.436598i	0.964096	+	0.265555i	$0.0855553\pi$
$774$		0			0
$775$	3.24216	+	5.61558i	0.116462	+	0.201718i
$776$	2.30782	+	3.99726i	0.0828458	+	0.143493i
$777$		0			0
$778$	−5.95372	−	10.3121i	−0.213451	−	0.369708i
$779$	−7.57771	+	13.1250i	−0.271499	+	0.470251i
$780$		0			0
$781$	−17.8474	−	30.9126i	−0.638630	−	1.10614i
$782$	12.6958			0.454000
$783$		0			0
$784$	−13.6791	+	23.6929i	−0.488539	+	0.846174i
$785$	12.9258			0.461343
$786$		0			0
$787$	−39.5044			−1.40818			−0.704089	−	0.710111i	$-0.748645\pi$
$787$	−39.5044			−1.40818			−0.704089	+	0.710111i	$0.748645\pi$
$788$	−0.138912	+	0.240603i	−0.00494854	+	0.00857112i
$789$		0			0
$790$	13.0118			0.462939
$791$	−1.77037	+	3.06637i	−0.0629472	+	0.109028i
$792$		0			0
$793$	0.804691			0.0285754
$794$	−5.78631			−0.205349
$795$		0			0
$796$	−0.208052	−	0.360357i	−0.00737421	−	0.0127725i
$797$	−46.0987			−1.63290			−0.816449	−	0.577417i	$-0.804061\pi$
$797$	−46.0987			−1.63290			−0.816449	+	0.577417i	$0.804061\pi$
$798$		0			0
$799$	−2.52756	−	4.37787i	−0.0894188	−	0.154878i
$800$	−0.659050			−0.0233009
$801$		0			0
$802$	−43.8757			−1.54931
$803$	32.9400	−	57.0537i	1.16243	−	2.01338i
$804$		0			0
$805$	−1.12689	−	1.95183i	−0.0397177	−	0.0687930i
$806$	−1.08881	−	1.88588i	−0.0383517	−	0.0664272i
$807$		0			0
$808$	−15.8384	−	27.4329i	−0.557192	−	0.965085i
$809$	4.72427	−	8.18268i	0.166097	−	0.287688i	−0.770948	−	0.636899i	$-0.780217\pi$
$809$	4.72427	−	8.18268i	0.166097	−	0.287688i	0.937044	+	0.349211i	$0.113550\pi$
$810$		0			0
$811$	18.2647			0.641362			0.320681	−	0.947187i	$-0.396088\pi$
$811$	18.2647			0.641362			0.320681	+	0.947187i	$0.396088\pi$
$812$	−0.0167130	+	0.0289478i	−0.000586511	+	0.00101587i
$813$		0			0
$814$	−50.5779			−1.77275
$815$	2.68585			0.0940814
$816$		0			0
$817$	15.2516	−	26.4165i	0.533586	−	0.924198i
$818$	11.0285	+	19.1019i	0.385601	+	0.667881i
$819$		0			0
$820$	0.0360765	−	0.0624864i	0.00125985	−	0.00218212i
$821$	−1.74175			−0.0607874			−0.0303937	−	0.999538i	$-0.509676\pi$
$821$	−1.74175			−0.0607874			−0.0303937	+	0.999538i	$0.509676\pi$
$822$		0			0
$823$	33.2419			1.15874			0.579370	−	0.815065i	$-0.303299\pi$
$823$	33.2419			1.15874			0.579370	+	0.815065i	$0.303299\pi$
$824$	−11.8051	+	25.9522i	−0.411248	+	0.904086i
$825$		0			0
$826$	−2.38872	−	4.13739i	−0.0831144	−	0.143958i
$827$	22.4076			0.779190			0.389595	−	0.920986i	$-0.372615\pi$
$827$	22.4076			0.779190			0.389595	+	0.920986i	$0.372615\pi$
$828$		0			0
$829$	13.1951	−	22.8546i	0.458284	−	0.793771i	−0.540586	−	0.841289i	$-0.681798\pi$
$829$	13.1951	−	22.8546i	0.458284	−	0.793771i	0.998870	+	0.0475172i	$0.0151309\pi$
$830$	2.12395	+	3.67879i	0.0737233	+	0.127693i
$831$		0			0
$832$	−8.13638			−0.282078
$833$	10.5752			0.366407
$834$		0			0
$835$	−6.52618	+	11.3037i	−0.225848	+	0.391180i
$836$	−0.317236	+	0.549469i	−0.0109718	+	0.0190038i
$837$		0			0
$838$	−15.6836			−0.541781
$839$	−0.296109	+	0.512877i	−0.0102228	+	0.0177065i	−0.871092	−	0.491121i	$-0.836587\pi$
$839$	−0.296109	+	0.512877i	−0.0102228	+	0.0177065i	0.860869	+	0.508827i	$0.169921\pi$
$840$		0			0
$841$	11.3451	−	19.6503i	0.391211	−	0.677597i
$842$	17.1099	+	29.6353i	0.589647	+	1.02130i
$843$		0			0
$844$	0.0750215	+	0.129941i	0.00258235	+	0.00447276i
$845$	4.73293	−	8.19768i	0.162818	−	0.282009i
$846$		0			0
$847$	8.85815			0.304370
$848$	−8.21823			−0.282215
$849$		0			0
$850$	4.87403	+	8.44208i	0.167178	+	0.289561i
$851$	−37.7256			−1.29322
$852$		0			0
$853$	−24.2318	−	41.9707i	−0.829681	−	1.43705i	−0.898289	−	0.439405i	$-0.855189\pi$
$853$	−24.2318	−	41.9707i	−0.829681	−	1.43705i	0.0686083	−	0.997644i	$-0.478144\pi$
$854$	0.554620			0.0189787
$855$		0			0
$856$	−3.26634	+	5.65747i	−0.111641	+	0.193368i
$857$	−27.7301	+	48.0300i	−0.947244	+	1.64067i	−0.196049	+	0.980594i	$0.562811\pi$
$857$	−27.7301	+	48.0300i	−0.947244	+	1.64067i	−0.751195	+	0.660080i	$0.770522\pi$
$858$		0			0
$859$	17.0215	+	29.4821i	0.580765	+	1.00592i	0.995389	+	0.0959220i	$0.0305800\pi$
$859$	17.0215	+	29.4821i	0.580765	+	1.00592i	−0.414623	+	0.909993i	$0.636087\pi$
$860$	−0.0726110	+	0.125766i	−0.00247602	+	0.00428858i
$861$		0			0
$862$	18.8395	−	32.6310i	0.641677	−	1.11142i
$863$	17.7375			0.603790			0.301895	−	0.953341i	$-0.402381\pi$
$863$	17.7375			0.603790			0.301895	+	0.953341i	$0.402381\pi$
$864$		0			0
$865$	3.33158	+	5.77046i	0.113277	+	0.196202i
$866$	−7.49654			−0.254743
$867$		0			0
$868$	−0.00986998	−	0.0170953i	−0.000335009	−	0.000580252i
$869$	−30.8968	+	53.5148i	−1.04810	+	1.81536i
$870$		0			0
$871$	3.73419	−	6.46780i	0.126528	−	0.219153i
$872$	−20.2359	−	35.0496i	−0.685275	−	1.18693i
$873$		0			0
$874$	−17.9912	+	31.1617i	−0.608563	+	1.05406i
$875$	1.85498	−	3.21291i	0.0627096	−	0.108616i
$876$		0			0
$877$	−8.06145	+	13.9628i	−0.272216	+	0.471492i	−0.969429	−	0.245372i	$-0.921090\pi$
$877$	−8.06145	+	13.9628i	−0.272216	+	0.471492i	0.697213	+	0.716864i	$0.254423\pi$
$878$	13.7109	+	23.7480i	0.462721	+	0.801457i
$879$		0			0
$880$	−8.61489	+	14.9214i	−0.290408	+	0.503001i
$881$	−7.31564	−	12.6711i	−0.246470	−	0.426899i	0.716074	−	0.698025i	$-0.245937\pi$
$881$	−7.31564	−	12.6711i	−0.246470	−	0.426899i	−0.962544	+	0.271126i	$0.912604\pi$
$882$		0			0
$883$	−10.9984	−	19.0497i	−0.370124	−	0.641074i	0.619460	−	0.785028i	$-0.287352\pi$
$883$	−10.9984	−	19.0497i	−0.370124	−	0.641074i	−0.989584	+	0.143954i	$0.954018\pi$
$884$	−0.0215280	−	0.0372876i	−0.000724066	−	0.00125412i
$885$		0			0
$886$	−14.3113	−	24.7880i	−0.480799	−	0.832768i
$887$	0.330351	−	0.572184i	0.0110921	−	0.0192121i	−0.860426	−	0.509575i	$-0.829803\pi$
$887$	0.330351	−	0.572184i	0.0110921	−	0.0192121i	0.871518	+	0.490363i	$0.163136\pi$
$888$		0			0
$889$	−1.47531	+	2.55531i	−0.0494802	+	0.0857022i
$890$	20.8450			0.698727
$891$		0			0
$892$	−0.213668	−	0.370084i	−0.00715414	−	0.0123913i
$893$	14.3273			0.479444
$894$		0			0
$895$	5.61670	−	9.72840i	0.187745	−	0.325185i
$896$	−5.75841			−0.192375
$897$		0			0
$898$	−5.09452	−	8.82397i	−0.170006	−	0.294460i
$899$	−1.86314	−	3.22706i	−0.0621393	−	0.107628i
$900$		0			0
$901$	1.58836	+	2.75112i	0.0529159	+	0.0916530i
$902$	13.0267	+	22.5629i	0.433741	+	0.751261i
$903$		0			0
$904$	19.9245			0.662679
$905$	−11.6174			−0.386176
$906$		0			0
$907$	−3.57706	−	6.19565i	−0.118774	−	0.205723i	0.800508	−	0.599322i	$-0.204563\pi$
$907$	−3.57706	−	6.19565i	−0.118774	−	0.205723i	−0.919282	+	0.393599i	$0.871230\pi$
$908$	−0.382181	−	0.661958i	−0.0126831	−	0.0219678i
$909$		0			0
$910$	−0.290576	+	0.503292i	−0.00963249	+	0.0166840i
$911$	22.7309	+	39.3710i	0.753107	+	1.30442i	0.946310	+	0.323261i	$0.104779\pi$
$911$	22.7309	+	39.3710i	0.753107	+	1.30442i	−0.193203	+	0.981159i	$0.561887\pi$
$912$		0			0
$913$	−20.1734			−0.667643
$914$	−15.2371			−0.503998
$915$		0			0
$916$	0.296420	−	0.513415i	0.00979399	−	0.0169637i
$917$	2.09029			0.0690274
$918$		0			0
$919$	−29.8271			−0.983906			−0.491953	−	0.870622i	$-0.663717\pi$
$919$	−29.8271			−0.983906			−0.491953	+	0.870622i	$0.663717\pi$
$920$	−6.34124	+	10.9834i	−0.209065	+	0.362111i
$921$		0			0
$922$	5.79945	−	10.0449i	0.190995	−	0.330812i
$923$	−3.43263	+	5.94550i	−0.112987	+	0.195698i
$924$		0			0
$925$	−14.4832	−	25.0857i	−0.476205	−	0.824812i
$926$	−2.66166			−0.0874677
$927$		0			0
$928$	0.378731			0.0124324
$929$	−27.2547	−	47.2065i	−0.894198	−	1.54880i	−0.834794	−	0.550562i	$-0.814413\pi$
$929$	−27.2547	−	47.2065i	−0.894198	−	1.54880i	−0.0594041	−	0.998234i	$-0.518920\pi$
$930$		0			0
$931$	−14.9861	+	25.9567i	−0.491149	+	0.850695i
$932$	0.108477	−	0.187888i	0.00355329	−	0.00615448i
$933$		0			0
$934$	1.13761	−	1.97040i	0.0372237	−	0.0644734i
$935$	6.66009			0.217808
$936$		0			0
$937$	27.9441			0.912893			0.456446	−	0.889751i	$-0.349122\pi$
$937$	27.9441			0.912893			0.456446	+	0.889751i	$0.349122\pi$
$938$	2.57373	−	4.45783i	0.0840352	−	0.145553i
$939$		0			0
$940$	−0.0682104			−0.00222478
$941$	24.5401			0.799984			0.399992	−	0.916519i	$-0.369013\pi$
$941$	24.5401			0.799984			0.399992	+	0.916519i	$0.369013\pi$
$942$		0			0
$943$	9.71648	+	16.8294i	0.316412	+	0.548042i
$944$	−13.6210	+	23.5923i	−0.443326	+	0.767864i
$945$		0			0
$946$	−26.2187	−	45.4121i	−0.852444	−	1.47648i
$947$	−11.0975	−	19.2214i	−0.360620	−	0.624612i	0.627443	−	0.778662i	$-0.284101\pi$
$947$	−11.0975	−	19.2214i	−0.360620	−	0.624612i	−0.988063	+	0.154050i	$0.950768\pi$
$948$		0			0
$949$	−12.6709			−0.411314
$950$	−27.6280			−0.896372
$951$		0			0
$952$	1.09849	+	1.90264i	0.0356023	+	0.0616650i
$953$	−12.2913	−	21.2892i	−0.398155	−	0.689624i	0.595344	−	0.803471i	$-0.297016\pi$
$953$	−12.2913	−	21.2892i	−0.398155	−	0.689624i	−0.993498	+	0.113847i	$0.963683\pi$
$954$		0			0
$955$	5.07082	+	8.78292i	0.164088	+	0.284208i
$956$	0.249875	+	0.432796i	0.00808153	+	0.0139976i
$957$		0			0
$958$	−6.24361			−0.201722
$959$	0.277822	−	0.481202i	0.00897134	−	0.0155388i
$960$		0			0
$961$	−28.7994			−0.929013
$962$	4.86389	+	8.42450i	0.156818	+	0.271617i
$963$		0			0
$964$	0.584192			0.0188156
$965$	2.24792	−	3.89352i	0.0723632	−	0.125337i
$966$		0			0
$967$	15.4270	−	26.7203i	0.496099	−	0.859268i	−0.503891	−	0.863767i	$-0.668099\pi$
$967$	15.4270	−	26.7203i	0.496099	−	0.859268i	0.999990	+	0.00449900i	$0.00143208\pi$
$968$	−24.9233	−	43.1684i	−0.801066	−	1.38749i
$969$		0			0
$970$	−0.927414	−	1.60633i	−0.0297775	−	0.0515761i
$971$	−25.9432	−	44.9350i	−0.832558	−	1.44203i	−0.896003	−	0.444047i	$-0.853542\pi$
$971$	−25.9432	−	44.9350i	−0.832558	−	1.44203i	0.0634454	−	0.997985i	$-0.479791\pi$
$972$		0			0
$973$	−2.57632	−	4.46232i	−0.0825930	−	0.143055i
$974$	−30.6246	+	53.0434i	−0.981276	+	1.69962i
$975$		0			0
$976$	−1.58128	−	2.73886i	−0.0506155	−	0.0876687i
$977$	8.72125	−	15.1057i	0.279018	−	0.483273i	−0.692123	−	0.721779i	$-0.743325\pi$
$977$	8.72125	−	15.1057i	0.279018	−	0.483273i	0.971141	+	0.238507i	$0.0766579\pi$
$978$		0			0
$979$	−49.4969	+	85.7312i	−1.58193	+	2.73998i
$980$	0.0713470	−	0.123577i	0.00227909	−	0.00394751i
$981$		0			0
$982$	−11.8437	−	20.5138i	−0.377947	−	0.654623i
$983$	14.4881	−	25.0941i	0.462098	−	0.800377i	−0.536967	−	0.843603i	$-0.680430\pi$
$983$	14.4881	−	25.0941i	0.462098	−	0.800377i	0.999065	+	0.0432258i	$0.0137635\pi$
$984$		0			0
$985$	−4.13275	+	7.15813i	−0.131680	+	0.228077i
$986$	−2.80092	−	4.85134i	−0.0891995	−	0.154498i
$987$		0			0
$988$	0.122030			0.00388228
$989$	−19.5563	−	33.8725i	−0.621854	−	1.07708i
$990$		0			0
$991$	−20.7651			−0.659626			−0.329813	−	0.944046i	$-0.606986\pi$
$991$	−20.7651			−0.659626			−0.329813	+	0.944046i	$0.606986\pi$
$992$	−0.111831	+	0.193697i	−0.00355064	+	0.00614988i
$993$		0			0
$994$	−2.36589	+	4.09784i	−0.0750414	+	0.129976i
$995$	−6.18971	−	10.7209i	−0.196227	−	0.339875i
$996$		0			0
$997$	30.2384	−	52.3744i	0.957660	−	1.65872i	0.229499	−	0.973309i	$-0.426291\pi$
$997$	30.2384	−	52.3744i	0.957660	−	1.65872i	0.728161	−	0.685406i	$-0.240375\pi$
$998$	−0.273773	+	0.474188i	−0.00866613	+	0.0150102i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	927.2.f.f.46.12	yes	32
3.2	odd	2	inner	927.2.f.f.46.5	✓	32
103.56	even	3	inner	927.2.f.f.262.12	yes	32
309.56	odd	6	inner	927.2.f.f.262.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
927.2.f.f.46.5	✓	32	3.2	odd	2	inner
927.2.f.f.46.12	yes	32	1.1	even	1	trivial
927.2.f.f.262.5	yes	32	309.56	odd	6	inner
927.2.f.f.262.12	yes	32	103.56	even	3	inner

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:	\( N \)	\(=\)	\( 927 = 3^{2} \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	927.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.711803 + 1.23288i) q^{2} +(-0.0133274 + 0.0230838i) q^{4} +(-0.396502 + 0.686762i) q^{5} +(-0.249615 + 0.432345i) q^{7} +2.80927 q^{8} +O(q^{10})\)	\(q+(0.711803 + 1.23288i) q^{2} +(-0.0133274 + 0.0230838i) q^{4} +(-0.396502 + 0.686762i) q^{5} +(-0.249615 + 0.432345i) q^{7} +2.80927 q^{8} -1.12893 q^{10} +(2.68065 - 4.64303i) q^{11} -1.03115 q^{13} -0.710706 q^{14} +(2.02630 + 3.50965i) q^{16} +(0.783256 - 1.35664i) q^{17} +(2.21991 + 3.84499i) q^{19} +(-0.0105687 - 0.0183055i) q^{20} +7.63239 q^{22} +5.69293 q^{23} +(2.18557 + 3.78552i) q^{25} +(-0.733979 - 1.27129i) q^{26} +(-0.00665345 - 0.0115241i) q^{28} +(-1.25596 - 2.17539i) q^{29} +1.48344 q^{31} +(-0.0753864 + 0.130573i) q^{32} +2.23010 q^{34} +(-0.197946 - 0.342852i) q^{35} -6.62674 q^{37} +(-3.16028 + 5.47376i) q^{38} +(-1.11388 + 1.92930i) q^{40} +(1.70676 + 2.95620i) q^{41} +(-3.43519 - 5.94992i) q^{43} +(0.0714525 + 0.123759i) q^{44} +(4.05225 + 7.01870i) q^{46} +(1.61350 - 2.79466i) q^{47} +(3.37538 + 5.84634i) q^{49} +(-3.11139 + 5.38909i) q^{50} +(0.0137426 - 0.0238030i) q^{52} +(-1.01395 + 1.75621i) q^{53} +(2.12577 + 3.68194i) q^{55} +(-0.701234 + 1.21457i) q^{56} +(1.78800 - 3.09690i) q^{58} +(3.36106 + 5.82152i) q^{59} -0.780378 q^{61} +(1.05591 + 1.82890i) q^{62} +7.89056 q^{64} +(0.408855 - 0.708157i) q^{65} +(-3.62137 + 6.27239i) q^{67} +(0.0208776 + 0.0361610i) q^{68} +(0.281796 - 0.488086i) q^{70} +(3.32892 - 5.76587i) q^{71} +12.2880 q^{73} +(-4.71694 - 8.16997i) q^{74} -0.118343 q^{76} +(1.33826 + 2.31794i) q^{77} -11.5258 q^{79} -3.21373 q^{80} +(-2.42976 + 4.20846i) q^{82} +(-1.88139 - 3.25866i) q^{83} +(0.621125 + 1.07582i) q^{85} +(4.89035 - 8.47034i) q^{86} +(7.53067 - 13.0435i) q^{88} -18.4645 q^{89} +(0.257391 - 0.445815i) q^{91} +(-0.0758722 + 0.131415i) q^{92} +4.59397 q^{94} -3.52079 q^{95} +(0.821501 + 1.42288i) q^{97} +(-4.80522 + 8.32288i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 18 q^{4} + 8 q^{7}+O(q^{10}) \) 32 * q - 18 * q^4 + 8 * q^7	\( 32 q - 18 q^{4} + 8 q^{7} - 32 q^{10} - 4 q^{13} - 18 q^{16} + 4 q^{19} - 40 q^{22} - 26 q^{25} + 8 q^{28} + 32 q^{31} + 8 q^{34} - 48 q^{37} + 22 q^{40} + 2 q^{43} + 18 q^{46} - 8 q^{49} - 68 q^{52} - 32 q^{55} - 24 q^{58} - 20 q^{61} + 68 q^{64} + 8 q^{67} + 38 q^{70} - 64 q^{73} - 188 q^{76} - 20 q^{79} + 60 q^{82} + 8 q^{85} + 6 q^{88} - 30 q^{91} - 92 q^{94} + 32 q^{97}+O(q^{100}) \) 32 * q - 18 * q^4 + 8 * q^7 - 32 * q^10 - 4 * q^13 - 18 * q^16 + 4 * q^19 - 40 * q^22 - 26 * q^25 + 8 * q^28 + 32 * q^31 + 8 * q^34 - 48 * q^37 + 22 * q^40 + 2 * q^43 + 18 * q^46 - 8 * q^49 - 68 * q^52 - 32 * q^55 - 24 * q^58 - 20 * q^61 + 68 * q^64 + 8 * q^67 + 38 * q^70 - 64 * q^73 - 188 * q^76 - 20 * q^79 + 60 * q^82 + 8 * q^85 + 6 * q^88 - 30 * q^91 - 92 * q^94 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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