LMFDB - Embedded newform 460.2.m.b.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	460.81
Dual form			460.2.m.b.301.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0891733 - 0.620214i) q^{3} +(0.959493 - 0.281733i) q^{5} +(0.926390 + 1.06911i) q^{7} +(2.50177 + 0.734585i) q^{9} +O(q^{10})$	\(q+(0.0891733 - 0.620214i) q^{3} +(0.959493 - 0.281733i) q^{5} +(0.926390 + 1.06911i) q^{7} +(2.50177 + 0.734585i) q^{9} +(1.68527 + 1.08306i) q^{11} +(-3.03360 + 3.50096i) q^{13} +(-0.0891733 - 0.620214i) q^{15} +(-0.997471 - 2.18416i) q^{17} +(2.56814 - 5.62344i) q^{19} +(0.745687 - 0.479224i) q^{21} +(4.53610 + 1.55684i) q^{23} +(0.841254 - 0.540641i) q^{25} +(1.45958 - 3.19603i) q^{27} +(2.89994 + 6.34999i) q^{29} +(-1.24376 - 8.65054i) q^{31} +(0.822010 - 0.948650i) q^{33} +(1.19007 + 0.764811i) q^{35} +(10.0197 + 2.94204i) q^{37} +(1.90083 + 2.19367i) q^{39} +(-9.67193 + 2.83993i) q^{41} +(-0.592850 + 4.12336i) q^{43} +2.60738 q^{45} -10.6148 q^{47} +(0.711404 - 4.94792i) q^{49} +(-1.44359 + 0.423877i) q^{51} +(-5.79641 - 6.68941i) q^{53} +(1.92214 + 0.564391i) q^{55} +(-3.25873 - 2.09426i) q^{57} +(9.52662 - 10.9943i) q^{59} +(1.45700 + 10.1336i) q^{61} +(1.53226 + 3.35518i) q^{63} +(-1.92438 + 4.21381i) q^{65} +(-4.23908 + 2.72429i) q^{67} +(1.37008 - 2.67453i) q^{69} +(-2.83358 + 1.82103i) q^{71} +(-4.40632 + 9.64850i) q^{73} +(-0.260296 - 0.569968i) q^{75} +(0.403309 + 2.80508i) q^{77} +(-0.180681 + 0.208517i) q^{79} +(4.72834 + 3.03872i) q^{81} +(-15.5928 - 4.57847i) q^{83} +(-1.57241 - 1.81466i) q^{85} +(4.19695 - 1.23234i) q^{87} +(0.0315466 - 0.219411i) q^{89} -6.55321 q^{91} -5.47610 q^{93} +(0.879805 - 6.11918i) q^{95} +(-3.16223 + 0.928514i) q^{97} +(3.42056 + 3.94753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9	$ 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) $ 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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			0
$2$		0			0
$3$	0.0891733	−	0.620214i	0.0514842	−	0.358081i	−0.947752	−	0.319008i	$-0.896650\pi$
$3$	0.0891733	−	0.620214i	0.0514842	−	0.358081i	0.999236	−	0.0390731i	$-0.0124405\pi$
$4$		0			0
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$6$		0			0
$7$	0.926390	+	1.06911i	0.350143	+	0.404086i	0.903313	−	0.428982i	$-0.141128\pi$
$7$	0.926390	+	1.06911i	0.350143	+	0.404086i	−0.553170	+	0.833068i	$0.686582\pi$
$8$		0			0
$9$	2.50177	+	0.734585i	0.833922	+	0.244862i
$10$		0			0
$11$	1.68527	+	1.08306i	0.508129	+	0.326554i	0.769460	−	0.638695i	$-0.220525\pi$
$11$	1.68527	+	1.08306i	0.508129	+	0.326554i	−0.261332	+	0.965249i	$0.584162\pi$
$12$		0			0
$13$	−3.03360	+	3.50096i	−0.841369	+	0.970992i	−0.999866	−	0.0163679i	$-0.994790\pi$
$13$	−3.03360	+	3.50096i	−0.841369	+	0.970992i	0.158497	+	0.987359i	$0.449335\pi$
$14$		0			0
$15$	−0.0891733	−	0.620214i	−0.0230245	−	0.160139i
$16$		0			0
$17$	−0.997471	−	2.18416i	−0.241922	−	0.529736i	0.749255	−	0.662282i	$-0.230412\pi$
$17$	−0.997471	−	2.18416i	−0.241922	−	0.529736i	−0.991177	+	0.132546i	$0.957685\pi$
$18$		0			0
$19$	2.56814	−	5.62344i	0.589172	−	1.29011i	−0.346770	−	0.937950i	$-0.612722\pi$
$19$	2.56814	−	5.62344i	0.589172	−	1.29011i	0.935941	−	0.352156i	$-0.114551\pi$
$20$		0			0
$21$	0.745687	−	0.479224i	0.162722	−	0.104575i
$22$		0			0
$23$	4.53610	+	1.55684i	0.945843	+	0.324625i
$23$	4.53610	+	1.55684i	0.945843	+	0.324625i
$24$		0			0
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$		0			0
$27$	1.45958	−	3.19603i	0.280896	−	0.615076i
$28$		0			0
$29$	2.89994	+	6.34999i	0.538506	+	1.17916i	0.961946	+	0.273239i	$0.0880951\pi$
$29$	2.89994	+	6.34999i	0.538506	+	1.17916i	−0.423440	+	0.905924i	$0.639178\pi$
$30$		0			0
$31$	−1.24376	−	8.65054i	−0.223386	−	1.55368i	−0.725097	−	0.688647i	$-0.758205\pi$
$31$	−1.24376	−	8.65054i	−0.223386	−	1.55368i	0.501711	−	0.865035i	$-0.332704\pi$
$32$		0			0
$33$	0.822010	−	0.948650i	0.143093	−	0.165139i
$34$		0			0
$35$	1.19007	+	0.764811i	0.201158	+	0.129277i
$36$		0			0
$37$	10.0197	+	2.94204i	1.64722	+	0.483668i	0.968143	−	0.250398i	$-0.0805616\pi$
$37$	10.0197	+	2.94204i	1.64722	+	0.483668i	0.679078	+	0.734066i	$0.262380\pi$
$38$		0			0
$39$	1.90083	+	2.19367i	0.304376	+	0.351269i
$40$		0			0
$41$	−9.67193	+	2.83993i	−1.51050	+	0.443523i	−0.929018	−	0.370035i	$-0.879346\pi$
$41$	−9.67193	+	2.83993i	−1.51050	+	0.443523i	−0.581483	+	0.813558i	$0.697527\pi$
$42$		0			0
$43$	−0.592850	+	4.12336i	−0.0904087	+	0.628807i	0.893357	+	0.449348i	$0.148344\pi$
$43$	−0.592850	+	4.12336i	−0.0904087	+	0.628807i	−0.983766	+	0.179459i	$0.942565\pi$
$44$		0			0
$45$	2.60738			0.388686
$46$		0			0
$47$	−10.6148			−1.54833			−0.774167	−	0.632982i	$-0.781831\pi$
$47$	−10.6148			−1.54833			−0.774167	+	0.632982i	$0.781831\pi$
$48$		0			0
$49$	0.711404	−	4.94792i	0.101629	−	0.706846i
$50$		0			0
$51$	−1.44359	+	0.423877i	−0.202143	+	0.0593547i
$52$		0			0
$53$	−5.79641	−	6.68941i	−0.796198	−	0.918861i	0.201969	−	0.979392i	$-0.435266\pi$
$53$	−5.79641	−	6.68941i	−0.796198	−	0.918861i	−0.998166	+	0.0605308i	$0.980721\pi$
$54$		0			0
$55$	1.92214	+	0.564391i	0.259181	+	0.0761025i
$56$		0			0
$57$	−3.25873	−	2.09426i	−0.431629	−	0.277391i
$58$		0			0
$59$	9.52662	−	10.9943i	1.24026	−	1.43134i	0.377280	−	0.926099i	$-0.376860\pi$
$59$	9.52662	−	10.9943i	1.24026	−	1.43134i	0.862981	−	0.505237i	$-0.168595\pi$
$60$		0			0
$61$	1.45700	+	10.1336i	0.186549	+	1.29748i	0.840860	+	0.541252i	$0.182050\pi$
$61$	1.45700	+	10.1336i	0.186549	+	1.29748i	−0.654311	+	0.756225i	$0.727041\pi$
$62$		0			0
$63$	1.53226	+	3.35518i	0.193046	+	0.422713i
$64$		0			0
$65$	−1.92438	+	4.21381i	−0.238690	+	0.522659i
$66$		0			0
$67$	−4.23908	+	2.72429i	−0.517886	+	0.332825i	−0.773335	−	0.633997i	$-0.781413\pi$
$67$	−4.23908	+	2.72429i	−0.517886	+	0.332825i	0.255449	+	0.966822i	$0.417777\pi$
$68$		0			0
$69$	1.37008	−	2.67453i	0.164938	−	0.321975i
$70$		0			0
$71$	−2.83358	+	1.82103i	−0.336284	+	0.216116i	−0.697874	−	0.716221i	$-0.745870\pi$
$71$	−2.83358	+	1.82103i	−0.336284	+	0.216116i	0.361590	+	0.932337i	$0.382234\pi$
$72$		0			0
$73$	−4.40632	+	9.64850i	−0.515721	+	1.12927i	0.455314	+	0.890331i	$0.349527\pi$
$73$	−4.40632	+	9.64850i	−0.515721	+	1.12927i	−0.971034	+	0.238940i	$0.923200\pi$
$74$		0			0
$75$	−0.260296	−	0.569968i	−0.0300564	−	0.0658142i
$76$		0			0
$77$	0.403309	+	2.80508i	0.0459614	+	0.319668i
$78$		0			0
$79$	−0.180681	+	0.208517i	−0.0203282	+	0.0234600i	−0.765823	−	0.643052i	$-0.777668\pi$
$79$	−0.180681	+	0.208517i	−0.0203282	+	0.0234600i	0.745494	+	0.666512i	$0.232213\pi$
$80$		0			0
$81$	4.72834	+	3.03872i	0.525371	+	0.337636i
$82$		0			0
$83$	−15.5928	−	4.57847i	−1.71154	−	0.502553i	−0.728358	−	0.685196i	$-0.759716\pi$
$83$	−15.5928	−	4.57847i	−1.71154	−	0.502553i	−0.983179	+	0.182644i	$0.941535\pi$
$84$		0			0
$85$	−1.57241	−	1.81466i	−0.170552	−	0.196828i
$86$		0			0
$87$	4.19695	−	1.23234i	0.449960	−	0.132120i
$88$		0			0
$89$	0.0315466	−	0.219411i	0.00334393	−	0.0232576i	−0.988081	−	0.153934i	$-0.950806\pi$
$89$	0.0315466	−	0.219411i	0.00334393	−	0.0232576i	0.991425	+	0.130676i	$0.0417148\pi$
$90$		0			0
$91$	−6.55321			−0.686963
$92$		0			0
$93$	−5.47610			−0.567845
$94$		0			0
$95$	0.879805	−	6.11918i	0.0902661	−	0.627815i
$96$		0			0
$97$	−3.16223	+	0.928514i	−0.321076	+	0.0942763i	−0.438299	−	0.898829i	$-0.644419\pi$
$97$	−3.16223	+	0.928514i	−0.321076	+	0.0942763i	0.117223	+	0.993106i	$0.462601\pi$
$98$		0			0
$99$	3.42056	+	3.94753i	0.343779	+	0.396742i
$100$		0			0
$101$	−8.85133	−	2.59898i	−0.880740	−	0.258609i	−0.190063	−	0.981772i	$-0.560869\pi$
$101$	−8.85133	−	2.59898i	−0.880740	−	0.258609i	−0.690677	+	0.723163i	$0.742687\pi$
$102$		0			0
$103$	−9.85716	−	6.33481i	−0.971255	−	0.624188i	−0.0441642	−	0.999024i	$-0.514062\pi$
$103$	−9.85716	−	6.33481i	−0.971255	−	0.624188i	−0.927091	+	0.374837i	$0.877699\pi$
$104$		0			0
$105$	0.580469	−	0.669897i	0.0566480	−	0.0653752i
$106$		0			0
$107$	0.192153	+	1.33646i	0.0185762	+	0.129200i	0.996999	−	0.0774114i	$-0.0246655\pi$
$107$	0.192153	+	1.33646i	0.0185762	+	0.129200i	−0.978423	+	0.206611i	$0.933756\pi$
$108$		0			0
$109$	−0.0673934	−	0.147571i	−0.00645511	−	0.0141347i	0.906377	−	0.422470i	$-0.138837\pi$
$109$	−0.0673934	−	0.147571i	−0.00645511	−	0.0141347i	−0.912832	+	0.408335i	$0.866109\pi$
$110$		0			0
$111$	2.71818	−	5.95198i	0.257998	−	0.564937i
$112$		0			0
$113$	−13.4024	+	8.61321i	−1.26079	+	0.810263i	−0.988393	−	0.151921i	$-0.951454\pi$
$113$	−13.4024	+	8.61321i	−1.26079	+	0.810263i	−0.272400	+	0.962184i	$0.587818\pi$
$114$		0			0
$115$	4.79097	+	0.215814i	0.446761	+	0.0201247i
$116$		0			0
$117$	−10.1611	+	6.53014i	−0.939394	+	0.603712i
$118$		0			0
$119$	1.41106	−	3.08979i	0.129352	−	0.283241i
$120$		0			0
$121$	−2.90244	−	6.35546i	−0.263858	−	0.577769i
$122$		0			0
$123$	0.898889	+	6.25191i	0.0810501	+	0.563716i
$124$		0			0
$125$	0.654861	−	0.755750i	0.0585725	−	0.0675963i
$126$		0			0
$127$	6.40081	+	4.11355i	0.567980	+	0.365018i	0.792894	−	0.609360i	$-0.208574\pi$
$127$	6.40081	+	4.11355i	0.567980	+	0.365018i	−0.224914	+	0.974379i	$0.572210\pi$
$128$		0			0
$129$	2.50450	+	0.735388i	0.220509	+	0.0647473i
$130$		0			0
$131$	−0.850199	−	0.981182i	−0.0742822	−	0.0857263i	0.717392	−	0.696670i	$-0.245336\pi$
$131$	−0.850199	−	0.981182i	−0.0742822	−	0.0857263i	−0.791674	+	0.610944i	$0.790790\pi$
$132$		0			0
$133$	8.39119	−	2.46387i	0.727608	−	0.213645i
$134$		0			0
$135$	0.500029	−	3.47778i	0.0430356	−	0.299319i
$136$		0			0
$137$	−8.11332			−0.693168			−0.346584	−	0.938019i	$-0.612658\pi$
$137$	−8.11332			−0.693168			−0.346584	+	0.938019i	$0.612658\pi$
$138$		0			0
$139$	21.3782			1.81328			0.906640	−	0.421906i	$-0.138639\pi$
$139$	21.3782			1.81328			0.906640	+	0.421906i	$0.138639\pi$
$140$		0			0
$141$	−0.946560	+	6.58347i	−0.0797148	+	0.554428i
$142$		0			0
$143$	−8.90418	+	2.61450i	−0.744605	+	0.218636i
$144$		0			0
$145$	4.57147	+	5.27576i	0.379640	+	0.438128i
$146$		0			0
$147$	−3.00533	−	0.882445i	−0.247876	−	0.0727829i
$148$		0			0
$149$	−5.33922	−	3.43131i	−0.437406	−	0.281104i	0.303348	−	0.952880i	$-0.401895\pi$
$149$	−5.33922	−	3.43131i	−0.437406	−	0.281104i	−0.740755	+	0.671776i	$0.765532\pi$
$150$		0			0
$151$	−5.26094	+	6.07145i	−0.428130	+	0.494088i	−0.928296	−	0.371841i	$-0.878727\pi$
$151$	−5.26094	+	6.07145i	−0.428130	+	0.494088i	0.500167	+	0.865929i	$0.333272\pi$
$152$		0			0
$153$	−0.890991	−	6.19698i	−0.0720323	−	0.500996i
$154$		0			0
$155$	−3.63052	−	7.94972i	−0.291610	−	0.638537i
$156$		0			0
$157$	3.39472	−	7.43339i	0.270928	−	0.593249i	−0.724445	−	0.689332i	$-0.757904\pi$
$157$	3.39472	−	7.43339i	0.270928	−	0.593249i	0.995373	+	0.0960828i	$0.0306314\pi$
$158$		0			0
$159$	−4.66575	+	2.99850i	−0.370018	+	0.237796i
$160$		0			0
$161$	2.53776	+	6.29185i	0.200004	+	0.495867i
$162$		0			0
$163$	8.38638	−	5.38960i	0.656872	−	0.422146i	−0.169299	−	0.985565i	$-0.554150\pi$
$163$	8.38638	−	5.38960i	0.656872	−	0.422146i	0.826172	+	0.563419i	$0.190514\pi$
$164$		0			0
$165$	0.521447	−	1.14181i	0.0405946	−	0.0888897i
$166$		0			0
$167$	−0.560228	−	1.22673i	−0.0433518	−	0.0949271i	0.886717	−	0.462313i	$-0.152980\pi$
$167$	−0.560228	−	1.22673i	−0.0433518	−	0.0949271i	−0.930069	+	0.367386i	$0.880253\pi$
$168$		0			0
$169$	−1.20390	−	8.37334i	−0.0926080	−	0.644103i
$170$		0			0
$171$	10.5558	−	12.1820i	0.807220	−	0.931582i
$172$		0			0
$173$	11.4999	+	7.39052i	0.874319	+	0.561890i	0.899071	−	0.437803i	$-0.144243\pi$
$173$	11.4999	+	7.39052i	0.874319	+	0.561890i	−0.0247522	+	0.999694i	$0.507880\pi$
$174$		0			0
$175$	1.35733	+	0.398549i	0.102605	+	0.0301275i
$176$		0			0
$177$	−5.96930	−	6.88894i	−0.448680	−	0.517805i
$178$		0			0
$179$	−13.4619	+	3.95277i	−1.00619	+	0.295444i	−0.742993	−	0.669299i	$-0.766595\pi$
$179$	−13.4619	+	3.95277i	−1.00619	+	0.295444i	−0.263195	+	0.964743i	$0.584776\pi$
$180$		0			0
$181$	−3.60694	+	25.0868i	−0.268102	+	1.86469i	0.198333	+	0.980135i	$0.436447\pi$
$181$	−3.60694	+	25.0868i	−0.268102	+	1.86469i	−0.466435	+	0.884555i	$0.654462\pi$
$182$		0			0
$183$	6.41494			0.474206
$184$		0			0
$185$	10.4427			0.767759
$186$		0			0
$187$	0.684560	−	4.76122i	0.0500600	−	0.348175i
$188$		0			0
$189$	4.76905	−	1.40032i	0.346897	−	0.101858i
$190$		0			0
$191$	−4.77881	−	5.51505i	−0.345783	−	0.399055i	0.556044	−	0.831153i	$-0.312319\pi$
$191$	−4.77881	−	5.51505i	−0.345783	−	0.399055i	−0.901826	+	0.432098i	$0.857773\pi$
$192$		0			0
$193$	−16.8911	−	4.95967i	−1.21585	−	0.357005i	−0.389955	−	0.920834i	$-0.627509\pi$
$193$	−16.8911	−	4.95967i	−1.21585	−	0.357005i	−0.825891	+	0.563830i	$0.809328\pi$
$194$		0			0
$195$	2.44186	+	1.56929i	0.174865	+	0.112379i
$196$		0			0
$197$	9.22456	−	10.6457i	0.657223	−	0.758476i	−0.325098	−	0.945680i	$-0.605397\pi$
$197$	9.22456	−	10.6457i	0.657223	−	0.758476i	0.982321	+	0.187205i	$0.0599428\pi$
$198$		0			0
$199$	1.54053	+	10.7146i	0.109205	+	0.759540i	0.968671	+	0.248347i	$0.0798873\pi$
$199$	1.54053	+	10.7146i	0.109205	+	0.759540i	−0.859466	+	0.511193i	$0.829204\pi$
$200$		0			0
$201$	1.31163	+	2.87207i	0.0925153	+	0.202580i
$202$		0			0
$203$	−4.10237	+	8.98293i	−0.287930	+	0.630478i
$204$		0			0
$205$	−8.48004	+	5.44979i	−0.592272	+	0.380630i
$206$		0			0
$207$	10.2046	+	7.22701i	0.709271	+	0.502312i
$208$		0			0
$209$	10.4185	−	6.69558i	0.720665	−	0.463143i
$210$		0			0
$211$	9.17870	−	20.0986i	0.631888	−	1.38364i	−0.274661	−	0.961541i	$-0.588566\pi$
$211$	9.17870	−	20.0986i	0.631888	−	1.38364i	0.906549	−	0.422100i	$-0.138707\pi$
$212$		0			0
$213$	0.876748	+	1.91981i	0.0600738	+	0.131543i
$214$		0			0
$215$	0.592850	+	4.12336i	0.0404320	+	0.281211i
$216$		0			0
$217$	8.09618	−	9.34349i	0.549605	−	0.634278i
$218$		0			0
$219$	5.59121	+	3.59325i	0.377819	+	0.242809i
$220$		0			0
$221$	10.6726	+	3.13375i	0.717915	+	0.210799i
$222$		0			0
$223$	−0.350628	−	0.404647i	−0.0234798	−	0.0270971i	0.743888	−	0.668304i	$-0.232979\pi$
$223$	−0.350628	−	0.404647i	−0.0234798	−	0.0270971i	−0.767368	+	0.641207i	$0.778434\pi$
$224$		0			0
$225$	2.50177	−	0.734585i	0.166784	−	0.0489723i
$226$		0			0
$227$	−2.12111	+	14.7527i	−0.140783	+	0.979169i	0.789872	+	0.613272i	$0.210147\pi$
$227$	−2.12111	+	14.7527i	−0.140783	+	0.979169i	−0.930655	+	0.365897i	$0.880762\pi$
$228$		0			0
$229$	27.1661			1.79518			0.897592	−	0.440827i	$-0.145315\pi$
$229$	27.1661			1.79518			0.897592	+	0.440827i	$0.145315\pi$
$230$		0			0
$231$	1.77571			0.116833
$232$		0			0
$233$	2.17686	−	15.1404i	0.142611	−	0.991882i	−0.785309	−	0.619103i	$-0.787496\pi$
$233$	2.17686	−	15.1404i	0.142611	−	0.991882i	0.927920	−	0.372778i	$-0.121595\pi$
$234$		0			0
$235$	−10.1849	+	2.99055i	−0.664387	+	0.195082i
$236$		0			0
$237$	0.113213	+	0.130655i	0.00735400	+	0.00848696i
$238$		0			0
$239$	−2.65004	−	0.778120i	−0.171417	−	0.0503324i	0.194898	−	0.980824i	$-0.437562\pi$
$239$	−2.65004	−	0.778120i	−0.171417	−	0.0503324i	−0.366315	+	0.930491i	$0.619381\pi$
$240$		0			0
$241$	−8.31867	−	5.34608i	−0.535852	−	0.344371i	0.244562	−	0.969634i	$-0.421356\pi$
$241$	−8.31867	−	5.34608i	−0.535852	−	0.344371i	−0.780415	+	0.625262i	$0.784992\pi$
$242$		0			0
$243$	9.20894	−	10.6277i	0.590754	−	0.681766i
$244$		0			0
$245$	−0.711404	−	4.94792i	−0.0454499	−	0.316111i
$246$		0			0
$247$	11.8967	+	26.0502i	0.756971	+	1.65754i
$248$		0			0
$249$	−4.23010	+	9.26263i	−0.268072	+	0.586995i
$250$		0			0
$251$	−6.07181	+	3.90211i	−0.383249	+	0.246299i	−0.718053	−	0.695989i	$-0.754966\pi$
$251$	−6.07181	+	3.90211i	−0.383249	+	0.246299i	0.334804	+	0.942288i	$0.391330\pi$
$252$		0			0
$253$	5.95841	+	7.53657i	0.374602	+	0.473820i
$254$		0			0
$255$	−1.26570	+	0.813414i	−0.0792610	+	0.0509380i
$256$		0			0
$257$	0.756884	−	1.65734i	0.0472131	−	0.103382i	−0.884556	−	0.466435i	$-0.845538\pi$
$257$	0.756884	−	1.65734i	0.0472131	−	0.103382i	0.931769	+	0.363053i	$0.118265\pi$
$258$		0			0
$259$	6.13675	+	13.4376i	0.381319	+	0.834972i
$260$		0			0
$261$	2.59037	+	18.0164i	0.160340	+	1.11519i
$262$		0			0
$263$	7.16521	−	8.26909i	0.441826	−	0.509894i	−0.490536	−	0.871421i	$-0.663199\pi$
$263$	7.16521	−	8.26909i	0.441826	−	0.509894i	0.932362	+	0.361527i	$0.117744\pi$
$264$		0			0
$265$	−7.44624	−	4.78541i	−0.457419	−	0.293965i
$266$		0			0
$267$	−0.133269	−	0.0391313i	−0.00815593	−	0.00239480i
$268$		0			0
$269$	−15.3864	−	17.7569i	−0.938126	−	1.08265i	−0.996436	−	0.0843564i	$-0.973117\pi$
$269$	−15.3864	−	17.7569i	−0.938126	−	1.08265i	0.0583098	−	0.998299i	$-0.481429\pi$
$270$		0			0
$271$	11.9702	−	3.51477i	0.727139	−	0.213507i	0.102846	−	0.994697i	$-0.467205\pi$
$271$	11.9702	−	3.51477i	0.727139	−	0.213507i	0.624293	+	0.781190i	$0.285387\pi$
$272$		0			0
$273$	−0.584372	+	4.06440i	−0.0353678	+	0.245988i
$274$		0			0
$275$	2.00329			0.120803
$276$		0			0
$277$	27.0129			1.62305			0.811524	−	0.584318i	$-0.198638\pi$
$277$	27.0129			1.62305			0.811524	+	0.584318i	$0.198638\pi$
$278$		0			0
$279$	3.24296	−	22.5553i	0.194151	−	1.35035i
$280$		0			0
$281$	8.80507	−	2.58540i	0.525266	−	0.154232i	−0.00833971	−	0.999965i	$-0.502655\pi$
$281$	8.80507	−	2.58540i	0.525266	−	0.154232i	0.533606	+	0.845733i	$0.320836\pi$
$282$		0			0
$283$	−1.44542	−	1.66811i	−0.0859215	−	0.0991587i	0.711161	−	0.703029i	$-0.248170\pi$
$283$	−1.44542	−	1.66811i	−0.0859215	−	0.0991587i	−0.797082	+	0.603871i	$0.793624\pi$
$284$		0			0
$285$	−3.71675	−	1.09134i	−0.220161	−	0.0646451i
$286$		0			0
$287$	−11.9962	−	7.70948i	−0.708112	−	0.455076i
$288$		0			0
$289$	7.35704	−	8.49048i	0.432767	−	0.499440i
$290$		0			0
$291$	0.293891	+	2.04406i	0.0172282	+	0.119825i
$292$		0			0
$293$	3.03851	+	6.65341i	0.177512	+	0.388696i	0.977384	−	0.211475i	$-0.0678266\pi$
$293$	3.03851	+	6.65341i	0.177512	+	0.388696i	−0.799872	+	0.600171i	$0.795099\pi$
$294$		0			0
$295$	6.04327	−	13.2329i	0.351853	−	0.770450i
$296$		0			0
$297$	5.92127	−	3.80537i	0.343587	−	0.220810i
$298$		0			0
$299$	−19.2112	+	11.1579i	−1.11101	+	0.645276i
$300$		0			0
$301$	−4.95754	+	3.18602i	−0.285748	+	0.183639i
$302$		0			0
$303$	−2.40123	+	5.25796i	−0.137947	+	0.302062i
$304$		0			0
$305$	4.25295	+	9.31266i	0.243523	+	0.533241i
$306$		0			0
$307$	−1.21575	−	8.45572i	−0.0693865	−	0.482593i	−0.994653	−	0.103275i	$-0.967068\pi$
$307$	−1.21575	−	8.45572i	−0.0693865	−	0.482593i	0.925266	−	0.379318i	$-0.123841\pi$
$308$		0			0
$309$	−4.80794	+	5.54866i	−0.273514	+	0.315652i
$310$		0			0
$311$	−1.54523	−	0.993061i	−0.0876221	−	0.0563113i	0.496096	−	0.868268i	$-0.334766\pi$
$311$	−1.54523	−	0.993061i	−0.0876221	−	0.0563113i	−0.583718	+	0.811956i	$0.698403\pi$
$312$		0			0
$313$	9.10106	+	2.67231i	0.514422	+	0.151048i	0.528632	−	0.848851i	$-0.322705\pi$
$313$	9.10106	+	2.67231i	0.514422	+	0.151048i	−0.0142099	+	0.999899i	$0.504523\pi$
$314$		0			0
$315$	2.41545	+	2.78758i	0.136095	+	0.157062i
$316$		0			0
$317$	−4.09993	+	1.20385i	−0.230275	+	0.0676149i	−0.394834	−	0.918752i	$-0.629198\pi$
$317$	−4.09993	+	1.20385i	−0.230275	+	0.0676149i	0.164559	+	0.986367i	$0.447380\pi$
$318$		0			0
$319$	−1.99022	+	13.8423i	−0.111431	+	0.775018i
$320$		0			0
$321$	0.846024			0.0472205
$322$		0			0
$323$	−14.8441			−0.825949
$324$		0			0
$325$	−0.659264	+	4.58528i	−0.0365694	+	0.254346i
$326$		0			0
$327$	−0.0975352	+	0.0286389i	−0.00539371	+	0.00158374i
$328$		0			0
$329$	−9.83348	−	11.3484i	−0.542137	−	0.625660i
$330$		0			0
$331$	−8.53142	−	2.50505i	−0.468929	−	0.137690i	0.0387268	−	0.999250i	$-0.487670\pi$
$331$	−8.53142	−	2.50505i	−0.468929	−	0.137690i	−0.507656	+	0.861560i	$0.669488\pi$
$332$		0			0
$333$	22.9056	+	14.7206i	1.25522	+	0.806682i
$334$		0			0
$335$	−3.29985	+	3.80822i	−0.180290	+	0.208066i
$336$		0			0
$337$	−3.22727	−	22.4462i	−0.175801	−	1.22272i	−0.866351	−	0.499436i	$-0.833541\pi$
$337$	−3.22727	−	22.4462i	−0.175801	−	1.22272i	0.690550	−	0.723284i	$-0.257368\pi$
$338$		0			0
$339$	4.14690	+	9.08044i	0.225228	+	0.493182i
$340$		0			0
$341$	7.27297	−	15.9256i	0.393853	−	0.862418i
$342$		0			0
$343$	14.2794	−	9.17681i	0.771015	−	0.495501i
$344$		0			0
$345$	0.561078	−	2.95218i	0.0302074	−	0.158940i
$346$		0			0
$347$	−23.3433	+	15.0019i	−1.25314	+	0.805342i	−0.987329	−	0.158684i	$-0.949275\pi$
$347$	−23.3433	+	15.0019i	−1.25314	+	0.805342i	−0.265807	+	0.964026i	$0.585638\pi$
$348$		0			0
$349$	4.20158	−	9.20017i	0.224905	−	0.492474i	−0.763217	−	0.646142i	$-0.776381\pi$
$349$	4.20158	−	9.20017i	0.224905	−	0.492474i	0.988123	+	0.153668i	$0.0491087\pi$
$350$		0			0
$351$	6.76140	+	14.8054i	0.360897	+	0.790253i
$352$		0			0
$353$	−4.53811	−	31.5633i	−0.241539	−	1.67994i	−0.644405	−	0.764684i	$-0.722895\pi$
$353$	−4.53811	−	31.5633i	−0.241539	−	1.67994i	0.402866	−	0.915259i	$-0.368014\pi$
$354$		0			0
$355$	−2.20575	+	2.54557i	−0.117069	+	0.135105i
$356$		0			0
$357$	−1.79050	−	1.15069i	−0.0947634	−	0.0609008i
$358$		0			0
$359$	12.3146	+	3.61591i	0.649942	+	0.190840i	0.590053	−	0.807365i	$-0.299107\pi$
$359$	12.3146	+	3.61591i	0.649942	+	0.190840i	0.0598894	+	0.998205i	$0.480925\pi$
$360$		0			0
$361$	−12.5854	−	14.5243i	−0.662389	−	0.764438i
$362$		0			0
$363$	−4.20056	+	1.23340i	−0.220472	+	0.0647365i
$364$		0			0
$365$	−1.50954	+	10.4991i	−0.0790128	+	0.549546i
$366$		0			0
$367$	−22.5460			−1.17689			−0.588446	−	0.808536i	$-0.700260\pi$
$367$	−22.5460			−1.17689			−0.588446	+	0.808536i	$0.700260\pi$
$368$		0			0
$369$	−26.2831			−1.36824
$370$		0			0
$371$	1.78199	−	12.3940i	0.0925163	−	0.643465i
$372$		0			0
$373$	−10.1683	+	2.98568i	−0.526495	+	0.154593i	−0.534169	−	0.845378i	$-0.679375\pi$
$373$	−10.1683	+	2.98568i	−0.526495	+	0.154593i	0.00767422	+	0.999971i	$0.497557\pi$
$374$		0			0
$375$	−0.410330	−	0.473547i	−0.0211894	−	0.0244538i
$376$		0			0
$377$	−31.0283	−	9.11074i	−1.59804	−	0.469227i
$378$		0			0
$379$	−11.3883	−	7.31884i	−0.584979	−	0.375943i	0.214422	−	0.976741i	$-0.431213\pi$
$379$	−11.3883	−	7.31884i	−0.584979	−	0.375943i	−0.799401	+	0.600798i	$0.794850\pi$
$380$		0			0
$381$	3.12206	−	3.60305i	0.159948	−	0.184590i
$382$		0			0
$383$	1.43841	+	10.0043i	0.0734991	+	0.511197i	0.993000	+	0.118110i	$0.0376837\pi$
$383$	1.43841	+	10.0043i	0.0734991	+	0.511197i	−0.919501	+	0.393087i	$0.871407\pi$
$384$		0			0
$385$	1.17725	+	2.57783i	0.0599984	+	0.131378i
$386$		0			0
$387$	−4.51213	+	9.88018i	−0.229364	+	0.502238i
$388$		0			0
$389$	−19.2729	+	12.3859i	−0.977175	+	0.627992i	−0.928700	−	0.370832i	$-0.879072\pi$
$389$	−19.2729	+	12.3859i	−0.977175	+	0.627992i	−0.0484749	+	0.998824i	$0.515436\pi$
$390$		0			0
$391$	−1.12424	−	11.4605i	−0.0568552	−	0.579581i
$392$		0			0
$393$	−0.684358	+	0.439810i	−0.0345213	+	0.0221855i
$394$		0			0
$395$	−0.114616	+	0.250974i	−0.00576697	+	0.0126279i
$396$		0			0
$397$	11.3262	+	24.8009i	0.568444	+	1.24472i	0.947622	+	0.319395i	$0.103480\pi$
$397$	11.3262	+	24.8009i	0.568444	+	1.24472i	−0.379177	+	0.925324i	$0.623793\pi$
$398$		0			0
$399$	−0.779860	−	5.42404i	−0.0390418	−	0.271542i
$400$		0			0
$401$	8.65805	−	9.99192i	0.432362	−	0.498973i	−0.497201	−	0.867635i	$-0.665639\pi$
$401$	8.65805	−	9.99192i	0.432362	−	0.498973i	0.929563	+	0.368663i	$0.120184\pi$
$402$		0			0
$403$	34.0583	+	21.8879i	1.69656	+	1.09031i
$404$		0			0
$405$	5.39292	+	1.58350i	0.267976	+	0.0786849i
$406$		0			0
$407$	13.6994	+	15.8100i	0.679056	+	0.783673i
$408$		0			0
$409$	−22.6878	+	6.66175i	−1.12184	+	0.329402i	−0.789496	−	0.613756i	$-0.789658\pi$
$409$	−22.6878	+	6.66175i	−1.12184	+	0.329402i	−0.332345	+	0.943158i	$0.607840\pi$
$410$		0			0
$411$	−0.723492	+	5.03200i	−0.0356872	+	0.248210i
$412$		0			0
$413$	20.5795			1.01265
$414$		0			0
$415$	−16.2511			−0.797737
$416$		0			0
$417$	1.90637	−	13.2591i	0.0933553	−	0.649300i
$418$		0			0
$419$	−26.4667	+	7.77132i	−1.29298	+	0.379654i	−0.854671	−	0.519170i	$-0.826241\pi$
$419$	−26.4667	+	7.77132i	−1.29298	+	0.379654i	−0.438311	+	0.898824i	$0.644423\pi$
$420$		0			0
$421$	2.60385	+	3.00500i	0.126904	+	0.146455i	0.815646	−	0.578552i	$-0.196382\pi$
$421$	2.60385	+	3.00500i	0.126904	+	0.146455i	−0.688742	+	0.725007i	$0.741837\pi$
$422$		0			0
$423$	−26.5558	−	7.79749i	−1.29119	−	0.379127i
$424$		0			0
$425$	−2.01997	−	1.29816i	−0.0979830	−	0.0629698i
$426$		0			0
$427$	−9.48423	+	10.9454i	−0.458974	+	0.529684i
$428$		0			0
$429$	0.827537	+	5.75564i	0.0399539	+	0.277885i
$430$		0			0
$431$	1.45512	+	3.18627i	0.0700908	+	0.153477i	0.941435	−	0.337195i	$-0.109478\pi$
$431$	1.45512	+	3.18627i	0.0700908	+	0.153477i	−0.871344	+	0.490673i	$0.836751\pi$
$432$		0			0
$433$	9.83352	−	21.5324i	0.472569	−	1.03478i	−0.511872	−	0.859062i	$-0.671048\pi$
$433$	9.83352	−	21.5324i	0.472569	−	1.03478i	0.984440	−	0.175719i	$-0.0562251\pi$
$434$		0			0
$435$	3.67976	−	2.36484i	0.176431	−	0.113385i
$436$		0			0
$437$	20.4042	−	21.5103i	0.976064	−	1.02898i
$438$		0			0
$439$	−30.7361	+	19.7529i	−1.46695	+	0.942755i	−0.468721	+	0.883346i	$0.655285\pi$
$439$	−30.7361	+	19.7529i	−1.46695	+	0.942755i	−0.998234	+	0.0594084i	$0.981079\pi$
$440$		0			0
$441$	5.41443	−	11.8560i	0.257830	−	0.564569i
$442$		0			0
$443$	7.28939	+	15.9615i	0.346330	+	0.758356i	0.999999	+	0.00157561i	$0.000501533\pi$
$443$	7.28939	+	15.9615i	0.346330	+	0.758356i	−0.653669	+	0.756780i	$0.726771\pi$
$444$		0			0
$445$	−0.0315466	−	0.219411i	−0.00149545	−	0.0104011i
$446$		0			0
$447$	−2.60426	+	3.00548i	−0.123177	+	0.142154i
$448$		0			0
$449$	4.38387	+	2.81734i	0.206888	+	0.132959i	0.639982	−	0.768390i	$-0.278942\pi$
$449$	4.38387	+	2.81734i	0.206888	+	0.132959i	−0.433094	+	0.901349i	$0.642578\pi$
$450$		0			0
$451$	−19.3756	−	5.68920i	−0.912363	−	0.267894i
$452$		0			0
$453$	3.29646	+	3.80432i	0.154881	+	0.178743i
$454$		0			0
$455$	−6.28776	+	1.84625i	−0.294775	+	0.0865537i
$456$		0			0
$457$	0.502360	−	3.49399i	0.0234994	−	0.163442i	−0.974692	−	0.223550i	$-0.928235\pi$
$457$	0.502360	−	3.49399i	0.0234994	−	0.163442i	0.998192	+	0.0601079i	$0.0191445\pi$
$458$		0			0
$459$	−8.43652			−0.393783
$460$		0			0
$461$	18.8670			0.878726			0.439363	−	0.898310i	$-0.355204\pi$
$461$	18.8670			0.878726			0.439363	+	0.898310i	$0.355204\pi$
$462$		0			0
$463$	−0.619829	+	4.31101i	−0.0288059	+	0.200349i	−0.999142	−	0.0414094i	$-0.986815\pi$
$463$	−0.619829	+	4.31101i	−0.0288059	+	0.200349i	0.970336	+	0.241759i	$0.0777243\pi$
$464$		0			0
$465$	−5.25428	+	1.54279i	−0.243661	+	0.0715454i
$466$		0			0
$467$	23.1079	+	26.6679i	1.06930	+	1.23404i	0.971048	+	0.238883i	$0.0767811\pi$
$467$	23.1079	+	26.6679i	1.06930	+	1.23404i	0.0982564	+	0.995161i	$0.468673\pi$
$468$		0			0
$469$	−6.83961	−	2.00829i	−0.315824	−	0.0927343i
$470$		0			0
$471$	−4.30758	−	2.76831i	−0.198483	−	0.127557i
$472$		0			0
$473$	−5.46495	+	6.30689i	−0.251279	+	0.289991i
$474$		0			0
$475$	−0.879805	−	6.11918i	−0.0403682	−	0.280767i
$476$		0			0
$477$	−9.58731	−	20.9933i	−0.438973	−	0.961217i
$478$		0			0
$479$	−11.2024	+	24.5297i	−0.511848	+	1.12079i	0.460586	+	0.887615i	$0.347639\pi$
$479$	−11.2024	+	24.5297i	−0.511848	+	1.12079i	−0.972434	+	0.233177i	$0.925088\pi$
$480$		0			0
$481$	−40.6956	+	26.1534i	−1.85556	+	1.19249i
$482$		0			0
$483$	4.12859	−	1.01289i	0.187857	−	0.0460881i
$484$		0			0
$485$	−2.77254	+	1.78180i	−0.125895	+	0.0809076i
$486$		0			0
$487$	17.6913	−	38.7386i	0.801670	−	1.75541i	0.161960	−	0.986797i	$-0.448218\pi$
$487$	17.6913	−	38.7386i	0.801670	−	1.75541i	0.639710	−	0.768616i	$-0.279054\pi$
$488$		0			0
$489$	−2.59487	−	5.68196i	−0.117344	−	0.256947i
$490$		0			0
$491$	−2.04990	−	14.2573i	−0.0925105	−	0.643425i	−0.982336	−	0.187124i	$-0.940083\pi$
$491$	−2.04990	−	14.2573i	−0.0925105	−	0.643425i	0.889826	−	0.456300i	$-0.150826\pi$
$492$		0			0
$493$	10.9768	−	12.6679i	0.494369	−	0.570532i
$494$		0			0
$495$	4.39415	+	2.82395i	0.197502	+	0.126927i
$496$		0			0
$497$	−4.57188	−	1.34243i	−0.205077	−	0.0602160i
$498$		0			0
$499$	−0.914186	−	1.05503i	−0.0409246	−	0.0472295i	0.734918	−	0.678156i	$-0.237221\pi$
$499$	−0.914186	−	1.05503i	−0.0409246	−	0.0472295i	−0.775843	+	0.630926i	$0.782675\pi$
$500$		0			0
$501$	−0.810792	+	0.238070i	−0.0362235	+	0.0106362i
$502$		0			0
$503$	−1.59610	+	11.1011i	−0.0711666	+	0.494975i	0.922799	+	0.385282i	$0.125896\pi$
$503$	−1.59610	+	11.1011i	−0.0711666	+	0.494975i	−0.993966	+	0.109693i	$0.965013\pi$
$504$		0			0
$505$	−9.22500			−0.410507
$506$		0			0
$507$	−5.30062			−0.235409
$508$		0			0
$509$	−0.0122097	+	0.0849204i	−0.000541186	+	0.00376403i	−0.990090	−	0.140433i	$-0.955151\pi$
$509$	−0.0122097	+	0.0849204i	−0.000541186	+	0.00376403i	0.989549	+	0.144197i	$0.0460598\pi$
$510$		0			0
$511$	−14.3973	+	4.22743i	−0.636899	+	0.187010i
$512$		0			0
$513$	−14.2243	−	16.4157i	−0.628017	−	0.724771i
$514$		0			0
$515$	−11.2426	−	3.30113i	−0.495408	−	0.145465i
$516$		0			0
$517$	−17.8889	−	11.4965i	−0.786752	−	0.505615i
$518$		0			0
$519$	5.60918	−	6.47334i	0.246216	−	0.284148i
$520$		0			0
$521$	5.95053	+	41.3868i	0.260697	+	1.81319i	0.527629	+	0.849475i	$0.323081\pi$
$521$	5.95053	+	41.3868i	0.260697	+	1.81319i	−0.266932	+	0.963715i	$0.586010\pi$
$522$		0			0
$523$	−3.03581	−	6.64749i	−0.132747	−	0.290675i	0.831573	−	0.555416i	$-0.187441\pi$
$523$	−3.03581	−	6.64749i	−0.132747	−	0.290675i	−0.964320	+	0.264741i	$0.914714\pi$
$524$		0			0
$525$	0.368224	−	0.806298i	0.0160706	−	0.0351897i
$526$		0			0
$527$	−17.6535	+	11.3452i	−0.769000	+	0.494206i
$528$		0			0
$529$	18.1525	+	14.1240i	0.789238	+	0.614088i
$530$		0			0
$531$	31.9096	−	20.5071i	1.38476	−	0.889931i
$532$		0			0
$533$	19.3982	−	42.4762i	0.840231	−	1.83985i
$534$		0			0
$535$	0.560893	+	1.22818i	0.0242495	+	0.0530991i
$536$		0			0
$537$	1.25112	+	8.70173i	0.0539898	+	0.375507i
$538$		0			0
$539$	6.55780	−	7.56810i	0.282464	−	0.325981i
$540$		0			0
$541$	8.59442	+	5.52330i	0.369503	+	0.237465i	0.712193	−	0.701983i	$-0.247702\pi$
$541$	8.59442	+	5.52330i	0.369503	+	0.237465i	−0.342691	+	0.939448i	$0.611338\pi$
$542$		0			0
$543$	15.2376	+	4.47415i	0.653907	+	0.192004i
$544$		0			0
$545$	−0.106239	−	0.122606i	−0.00455078	−	0.00525188i
$546$		0			0
$547$	33.6865	−	9.89125i	1.44033	−	0.422919i	0.533998	−	0.845485i	$-0.320689\pi$
$547$	33.6865	−	9.89125i	1.44033	−	0.422919i	0.906332	+	0.422566i	$0.138871\pi$
$548$		0			0
$549$	−3.79894	+	26.4222i	−0.162135	+	1.12767i
$550$		0			0
$551$	43.1563			1.83852
$552$		0			0
$553$	−0.390309			−0.0165976
$554$		0			0
$555$	0.931206	−	6.47668i	0.0395275	−	0.274920i
$556$		0			0
$557$	−15.5787	+	4.57433i	−0.660092	+	0.193820i	−0.594586	−	0.804032i	$-0.702684\pi$
$557$	−15.5787	+	4.57433i	−0.660092	+	0.193820i	−0.0655054	+	0.997852i	$0.520866\pi$
$558$		0			0
$559$	−12.6372	−	14.5842i	−0.534499	−	0.616844i
$560$		0			0
$561$	−2.89193	−	0.849147i	−0.122097	−	0.0358510i
$562$		0			0
$563$	5.54467	+	3.56334i	0.233680	+	0.150177i	0.652241	−	0.758012i	$-0.273829\pi$
$563$	5.54467	+	3.56334i	0.233680	+	0.150177i	−0.418561	+	0.908189i	$0.637465\pi$
$564$		0			0
$565$	−10.4329	+	12.0402i	−0.438915	+	0.506535i
$566$		0			0
$567$	1.13156	+	7.87017i	0.0475210	+	0.330516i
$568$		0			0
$569$	7.90780	+	17.3157i	0.331512	+	0.725910i	0.999839	−	0.0179577i	$-0.00571641\pi$
$569$	7.90780	+	17.3157i	0.331512	+	0.725910i	−0.668327	+	0.743868i	$0.732989\pi$
$570$		0			0
$571$	−15.0294	+	32.9098i	−0.628961	+	1.37723i	0.279858	+	0.960041i	$0.409713\pi$
$571$	−15.0294	+	32.9098i	−0.628961	+	1.37723i	−0.908819	+	0.417191i	$0.863015\pi$
$572$		0			0
$573$	−3.84665	+	2.47209i	−0.160696	+	0.103273i
$574$		0			0
$575$	4.65771	−	1.14270i	0.194240	−	0.0476539i
$576$		0			0
$577$	18.0471	−	11.5981i	0.751309	−	0.482837i	−0.108091	−	0.994141i	$-0.534474\pi$
$577$	18.0471	−	11.5981i	0.751309	−	0.482837i	0.859400	+	0.511304i	$0.170837\pi$
$578$		0			0
$579$	−4.58229	+	10.0338i	−0.190433	+	0.416991i
$580$		0			0
$581$	−9.55017	−	20.9119i	−0.396208	−	0.867574i
$582$		0			0
$583$	−2.52350	−	17.5513i	−0.104513	−	0.726902i
$584$		0			0
$585$	−7.90975	+	9.12834i	−0.327028	+	0.377410i
$586$		0			0
$587$	15.5659	+	10.0036i	0.642474	+	0.412893i	0.820909	−	0.571059i	$-0.193467\pi$
$587$	15.5659	+	10.0036i	0.642474	+	0.412893i	−0.178435	+	0.983952i	$0.557104\pi$
$588$		0			0
$589$	−51.8399	−	15.2216i	−2.13603	−	0.627194i
$590$		0			0
$591$	−5.78004	−	6.67052i	−0.237759	−	0.274388i
$592$		0			0
$593$	−0.978353	+	0.287270i	−0.0401761	+	0.0117968i	−0.301759	−	0.953384i	$-0.597574\pi$
$593$	−0.978353	+	0.287270i	−0.0401761	+	0.0117968i	0.261583	+	0.965181i	$0.415756\pi$
$594$		0			0
$595$	0.483408	−	3.36217i	0.0198178	−	0.137836i
$596$		0			0
$597$	6.78274			0.277599
$598$		0			0
$599$	−8.50266			−0.347409			−0.173705	−	0.984798i	$-0.555574\pi$
$599$	−8.50266			−0.347409			−0.173705	+	0.984798i	$0.555574\pi$
$600$		0			0
$601$	0.495256	−	3.44458i	0.0202019	−	0.140507i	−0.977224	−	0.212210i	$-0.931934\pi$
$601$	0.495256	−	3.44458i	0.0202019	−	0.140507i	0.997426	+	0.0717022i	$0.0228431\pi$
$602$		0			0
$603$	−12.6064	+	3.70157i	−0.513372	+	0.150740i
$604$		0			0
$605$	−4.57541	−	5.28030i	−0.186017	−	0.214675i
$606$		0			0
$607$	−12.1446	−	3.56597i	−0.492933	−	0.144738i	0.0258128	−	0.999667i	$-0.491783\pi$
$607$	−12.1446	−	3.56597i	−0.492933	−	0.144738i	−0.518746	+	0.854929i	$0.673601\pi$
$608$		0			0
$609$	5.20552	+	3.34538i	0.210938	+	0.135562i
$610$		0			0
$611$	32.2012	−	37.1621i	1.30272	−	1.50342i
$612$		0			0
$613$	4.37036	+	30.3965i	0.176517	+	1.22770i	0.864746	+	0.502210i	$0.167480\pi$
$613$	4.37036	+	30.3965i	0.176517	+	1.22770i	−0.688228	+	0.725494i	$0.741611\pi$
$614$		0			0
$615$	2.62384	+	5.74542i	0.105804	+	0.231678i
$616$		0			0
$617$	11.5374	−	25.2633i	0.464476	−	1.01706i	−0.521968	−	0.852965i	$-0.674802\pi$
$617$	11.5374	−	25.2633i	0.464476	−	1.01706i	0.986444	−	0.164096i	$-0.0524708\pi$
$618$		0			0
$619$	12.5586	−	8.07089i	0.504771	−	0.324397i	−0.263351	−	0.964700i	$-0.584828\pi$
$619$	12.5586	−	8.07089i	0.504771	−	0.324397i	0.768122	+	0.640303i	$0.221191\pi$
$620$		0			0
$621$	11.5965	−	12.2252i	0.465352	−	0.490580i
$622$		0			0
$623$	0.263800	−	0.169534i	0.0105689	−	0.00679223i
$624$		0			0
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$		0			0
$627$	−3.22364	−	7.05879i	−0.128740	−	0.281901i
$628$		0			0
$629$	−3.56845	−	24.8191i	−0.142283	−	0.989602i
$630$		0			0
$631$	−7.19450	+	8.30290i	−0.286409	+	0.330533i	−0.880662	−	0.473744i	$-0.842902\pi$
$631$	−7.19450	+	8.30290i	−0.286409	+	0.330533i	0.594254	+	0.804278i	$0.297448\pi$
$632$		0			0
$633$	−11.6469	−	7.48502i	−0.462923	−	0.297503i
$634$		0			0
$635$	7.30045	+	2.14361i	0.289710	+	0.0850664i
$636$		0			0
$637$	15.1644	+	17.5006i	0.600834	+	0.693399i
$638$		0			0
$639$	−8.42664	+	2.47428i	−0.333353	+	0.0978812i
$640$		0			0
$641$	−0.952493	+	6.62473i	−0.0376212	+	0.261661i	−0.999948	−	0.0102356i	$-0.996742\pi$
$641$	−0.952493	+	6.62473i	−0.0376212	+	0.261661i	0.962326	+	0.271897i	$0.0876509\pi$
$642$		0			0
$643$	15.4337			0.608644			0.304322	−	0.952569i	$-0.401570\pi$
$643$	15.4337			0.608644			0.304322	+	0.952569i	$0.401570\pi$
$644$		0			0
$645$	2.61023			0.102778
$646$		0			0
$647$	2.63618	−	18.3350i	0.103639	−	0.720824i	−0.870053	−	0.492957i	$-0.835916\pi$
$647$	2.63618	−	18.3350i	0.103639	−	0.720824i	0.973692	−	0.227867i	$-0.0731750\pi$
$648$		0			0
$649$	27.9624	−	8.21051i	1.09762	−	0.322291i
$650$		0			0
$651$	−5.07300	−	5.85456i	−0.198827	−	0.229458i
$652$		0			0
$653$	42.0534	+	12.3480i	1.64567	+	0.483214i	0.967749	−	0.251916i	$-0.0810608\pi$
$653$	42.0534	+	12.3480i	1.64567	+	0.483214i	0.677926	+	0.735130i	$0.262879\pi$
$654$		0			0
$655$	−1.09219	−	0.701908i	−0.0426754	−	0.0274258i
$656$		0			0
$657$	−18.1112	+	20.9015i	−0.706586	+	0.815443i
$658$		0			0
$659$	−3.59966	−	25.0362i	−0.140223	−	0.975271i	−0.931481	−	0.363789i	$-0.881483\pi$
$659$	−3.59966	−	25.0362i	−0.140223	−	0.975271i	0.791258	−	0.611482i	$-0.209426\pi$
$660$		0			0
$661$	15.6820	+	34.3388i	0.609960	+	1.33563i	0.922601	+	0.385755i	$0.126059\pi$
$661$	15.6820	+	34.3388i	0.609960	+	1.33563i	−0.312641	+	0.949871i	$0.601214\pi$
$662$		0			0
$663$	2.89531	−	6.33983i	0.112444	−	0.246219i
$664$		0			0
$665$	7.35713	−	4.72814i	0.285297	−	0.183349i
$666$		0			0
$667$	3.26849	+	33.3190i	0.126557	+	1.29012i
$668$		0			0
$669$	−0.282234	+	0.181381i	−0.0109118	+	0.00701259i
$670$		0			0
$671$	−8.51987	+	18.6559i	−0.328906	+	0.720204i
$672$		0			0
$673$	10.2202	+	22.3792i	0.393961	+	0.862655i	0.997847	+	0.0655843i	$0.0208911\pi$
$673$	10.2202	+	22.3792i	0.393961	+	0.862655i	−0.603886	+	0.797071i	$0.706382\pi$
$674$		0			0
$675$	−0.500029	−	3.47778i	−0.0192461	−	0.133860i
$676$		0			0
$677$	−1.85660	+	2.14264i	−0.0713551	+	0.0823482i	−0.790305	−	0.612714i	$-0.790078\pi$
$677$	−1.85660	+	2.14264i	−0.0713551	+	0.0823482i	0.718950	+	0.695062i	$0.244623\pi$
$678$		0			0
$679$	−3.92214	−	2.52061i	−0.150518	−	0.0967320i
$680$		0			0
$681$	8.96066	+	2.63109i	0.343373	+	0.100824i
$682$		0			0
$683$	−1.72170	−	1.98695i	−0.0658792	−	0.0760286i	0.721853	−	0.692046i	$-0.243291\pi$
$683$	−1.72170	−	1.98695i	−0.0658792	−	0.0760286i	−0.787733	+	0.616017i	$0.788745\pi$
$684$		0			0
$685$	−7.78468	+	2.28579i	−0.297437	+	0.0873354i
$686$		0			0
$687$	2.42249	−	16.8488i	0.0924237	−	0.642821i
$688$		0			0
$689$	41.0033			1.56210
$690$		0			0
$691$	−0.606979			−0.0230906			−0.0115453	−	0.999933i	$-0.503675\pi$
$691$	−0.606979			−0.0230906			−0.0115453	+	0.999933i	$0.503675\pi$
$692$		0			0
$693$	−1.05158	+	7.31391i	−0.0399463	+	0.277833i
$694$		0			0
$695$	20.5123	−	6.02295i	0.778075	−	0.228463i
$696$		0			0
$697$	15.8503	+	18.2923i	0.600374	+	0.692869i
$698$		0			0
$699$	−9.19618	−	2.70024i	−0.347832	−	0.102133i
$700$		0			0
$701$	12.9776	+	8.34019i	0.490157	+	0.315005i	0.762268	−	0.647261i	$-0.224086\pi$
$701$	12.9776	+	8.34019i	0.490157	+	0.315005i	−0.272112	+	0.962266i	$0.587722\pi$
$702$		0			0
$703$	42.2762	−	48.7894i	1.59448	−	1.84013i
$704$		0			0
$705$	0.946560	+	6.58347i	0.0356495	+	0.247948i
$706$		0			0
$707$	−5.42118	−	11.8707i	−0.203884	−	0.446445i
$708$		0			0
$709$	10.2902	−	22.5324i	0.386456	−	0.846220i	−0.612010	−	0.790850i	$-0.709639\pi$
$709$	10.2902	−	22.5324i	0.386456	−	0.846220i	0.998466	−	0.0553704i	$-0.0176340\pi$
$710$		0			0
$711$	−0.605195	+	0.388935i	−0.0226966	+	0.0145862i
$712$		0			0
$713$	7.82572	−	41.1761i	0.293076	−	1.54206i
$714$		0			0
$715$	−7.80691	+	5.01720i	−0.291962	+	0.187633i
$716$		0			0
$717$	−0.718914	+	1.57420i	−0.0268483	+	0.0587896i
$718$		0			0
$719$	8.27561	+	18.1211i	0.308628	+	0.675802i	0.998857	−	0.0477892i	$-0.0152176\pi$
$719$	8.27561	+	18.1211i	0.308628	+	0.675802i	−0.690229	+	0.723591i	$0.742490\pi$
$720$		0			0
$721$	−2.35896	−	16.4069i	−0.0878522	−	0.611026i
$722$		0			0
$723$	−4.05752	+	4.68263i	−0.150901	+	0.174149i
$724$		0			0
$725$	5.87265	+	3.77412i	0.218105	+	0.140167i
$726$		0			0
$727$	44.0047	+	12.9209i	1.63204	+	0.479211i	0.964219	−	0.265108i	$-0.0854076\pi$
$727$	44.0047	+	12.9209i	1.63204	+	0.479211i	0.667824	+	0.744319i	$0.267226\pi$
$728$		0			0
$729$	5.27187	+	6.08406i	0.195254	+	0.225335i
$730$		0			0
$731$	9.59742	−	2.81806i	0.354973	−	0.104230i
$732$		0			0
$733$	−0.0134933	+	0.0938480i	−0.000498387	+	0.00346635i	−0.990069	−	0.140581i	$-0.955103\pi$
$733$	−0.0134933	+	0.0938480i	−0.000498387	+	0.00346635i	0.989571	+	0.144048i	$0.0460119\pi$
$734$		0			0
$735$	−3.13221			−0.115533
$736$		0			0
$737$	−10.0946			−0.371838
$738$		0			0
$739$	−3.39442	+	23.6087i	−0.124866	+	0.868461i	0.827056	+	0.562120i	$0.190014\pi$
$739$	−3.39442	+	23.6087i	−0.124866	+	0.868461i	−0.951922	+	0.306341i	$0.900895\pi$
$740$		0			0
$741$	17.2176	−	5.05554i	0.632504	−	0.185720i
$742$		0			0
$743$	20.0694	+	23.1613i	0.736276	+	0.849707i	0.993163	−	0.116734i	$-0.0372425\pi$
$743$	20.0694	+	23.1613i	0.736276	+	0.849707i	−0.256888	+	0.966441i	$0.582697\pi$
$744$		0			0
$745$	−6.08966	−	1.78809i	−0.223108	−	0.0655104i
$746$		0			0
$747$	−35.6464	−	22.9085i	−1.30423	−	0.838179i
$748$		0			0
$749$	−1.25081	+	1.44351i	−0.0457037	+	0.0527449i
$750$		0			0
$751$	−6.71719	−	46.7191i	−0.245114	−	1.70480i	−0.625704	−	0.780060i	$-0.715188\pi$
$751$	−6.71719	−	46.7191i	−0.245114	−	1.70480i	0.380591	−	0.924744i	$-0.375721\pi$
$752$		0			0
$753$	1.87870	+	4.11378i	0.0684637	+	0.149915i
$754$		0			0
$755$	−3.33731	+	7.30770i	−0.121457	+	0.265954i
$756$		0			0
$757$	−42.1576	+	27.0930i	−1.53224	+	0.984713i	−0.542788	+	0.839870i	$0.682631\pi$
$757$	−42.1576	+	27.0930i	−1.53224	+	0.984713i	−0.989455	+	0.144843i	$0.953732\pi$
$758$		0			0
$759$	5.20562	−	3.02343i	0.188952	−	0.109744i
$760$		0			0
$761$	−3.34400	+	2.14906i	−0.121220	+	0.0779032i	−0.599846	−	0.800116i	$-0.704771\pi$
$761$	−3.34400	+	2.14906i	−0.121220	+	0.0779032i	0.478626	+	0.878019i	$0.341135\pi$
$762$		0			0
$763$	0.0953371	−	0.208759i	0.00345144	−	0.00755759i
$764$		0			0
$765$	−2.60079	−	5.69493i	−0.0940317	−	0.205901i
$766$		0			0
$767$	9.59068	+	66.7046i	0.346299	+	2.40856i
$768$		0			0
$769$	9.53488	−	11.0038i	0.343836	−	0.396808i	−0.557323	−	0.830296i	$-0.688172\pi$
$769$	9.53488	−	11.0038i	0.343836	−	0.396808i	0.901160	+	0.433487i	$0.142717\pi$
$770$		0			0
$771$	−0.960414	−	0.617221i	−0.0345885	−	0.0222287i
$772$		0			0
$773$	−6.98360	−	2.05057i	−0.251183	−	0.0737539i	0.153717	−	0.988115i	$-0.450875\pi$
$773$	−6.98360	−	2.05057i	−0.251183	−	0.0737539i	−0.404900	+	0.914361i	$0.632694\pi$
$774$		0			0
$775$	−5.72315	−	6.60487i	−0.205582	−	0.237254i
$776$		0			0
$777$	8.88142	−	2.60782i	0.318619	−	0.0935551i
$778$		0			0
$779$	−8.86865	+	61.6828i	−0.317753	+	2.21002i
$780$		0			0
$781$	−6.74763			−0.241449
$782$		0			0
$783$	24.5274			0.876539
$784$		0			0
$785$	1.16298	−	8.08869i	0.0415085	−	0.288698i
$786$		0			0
$787$	44.8830	−	13.1788i	1.59991	−	0.469775i	0.644385	−	0.764701i	$-0.277113\pi$
$787$	44.8830	−	13.1788i	1.59991	−	0.469775i	0.955520	+	0.294927i	$0.0952952\pi$
$788$		0			0
$789$	−4.48966	−	5.18135i	−0.159836	−	0.184461i
$790$		0			0
$791$	−21.6243	−	6.34948i	−0.768873	−	0.225762i
$792$		0			0
$793$	−39.8974	−	25.6405i	−1.41680	−	0.910520i
$794$		0			0
$795$	−3.63198	+	4.19153i	−0.128813	+	0.148658i
$796$		0			0
$797$	−5.84484	−	40.6518i	−0.207035	−	1.43996i	−0.782764	−	0.622319i	$-0.786191\pi$
$797$	−5.84484	−	40.6518i	−0.207035	−	1.43996i	0.575729	−	0.817641i	$-0.304718\pi$
$798$		0			0
$799$	10.5880	+	23.1845i	0.374576	+	0.820208i
$800$		0			0
$801$	0.240098	−	0.525742i	0.00848346	−	0.0185762i
$802$		0			0
$803$	−17.8757	+	11.4880i	−0.630821	+	0.405404i
$804$		0			0
$805$	4.20758	+	5.32201i	0.148298	+	0.187576i
$806$		0			0
$807$	−12.3851	+	7.95943i	−0.435977	+	0.280185i
$808$		0			0
$809$	−3.38548	+	7.41317i	−0.119027	+	0.260633i	−0.959762	−	0.280813i	$-0.909396\pi$
$809$	−3.38548	+	7.41317i	−0.119027	+	0.260633i	0.840735	+	0.541446i	$0.182123\pi$
$810$		0			0
$811$	−3.51953	−	7.70670i	−0.123587	−	0.270619i	0.837718	−	0.546103i	$-0.183889\pi$
$811$	−3.51953	−	7.70670i	−0.123587	−	0.270619i	−0.961306	+	0.275484i	$0.911162\pi$
$812$		0			0
$813$	−1.11249	−	7.73753i	−0.0390167	−	0.271367i
$814$		0			0
$815$	6.52825	−	7.53400i	0.228675	−	0.263905i
$816$		0			0
$817$	21.6650	+	13.9232i	0.757961	+	0.487112i
$818$		0			0
$819$	−16.3946	−	4.81389i	−0.572874	−	0.168211i
$820$		0			0
$821$	16.4911	+	19.0318i	0.575544	+	0.664213i	0.966641	−	0.256136i	$-0.0824496\pi$
$821$	16.4911	+	19.0318i	0.575544	+	0.664213i	−0.391097	+	0.920350i	$0.627904\pi$
$822$		0			0
$823$	−21.9812	+	6.45427i	−0.766218	+	0.224982i	−0.641409	−	0.767199i	$-0.721650\pi$
$823$	−21.9812	+	6.45427i	−0.766218	+	0.224982i	−0.124809	+	0.992181i	$0.539832\pi$
$824$		0			0
$825$	0.178640	−	1.24247i	0.00621944	−	0.0432571i
$826$		0			0
$827$	−21.4435			−0.745664			−0.372832	−	0.927899i	$-0.621613\pi$
$827$	−21.4435			−0.745664			−0.372832	+	0.927899i	$0.621613\pi$
$828$		0			0
$829$	−9.46763			−0.328824			−0.164412	−	0.986392i	$-0.552573\pi$
$829$	−9.46763			−0.328824			−0.164412	+	0.986392i	$0.552573\pi$
$830$		0			0
$831$	2.40883	−	16.7538i	0.0835615	−	0.581183i
$832$		0			0
$833$	−11.5166	+	3.38159i	−0.399028	+	0.117165i
$834$		0			0
$835$	−0.883145	−	1.01920i	−0.0305625	−	0.0352710i
$836$		0			0
$837$	−29.4627	−	8.65104i	−1.01838	−	0.299024i
$838$		0			0
$839$	−23.3729	−	15.0209i	−0.806923	−	0.518578i	0.0709451	−	0.997480i	$-0.477398\pi$
$839$	−23.3729	−	15.0209i	−0.806923	−	0.518578i	−0.877868	+	0.478902i	$0.841035\pi$
$840$		0			0
$841$	−12.9217	+	14.9125i	−0.445577	+	0.514224i
$842$		0			0
$843$	−0.818325	−	5.69158i	−0.0281846	−	0.196028i
$844$		0			0
$845$	−3.51418	−	7.69498i	−0.120891	−	0.264715i
$846$		0			0
$847$	4.10590	−	8.99066i	0.141080	−	0.308923i
$848$		0			0
$849$	−1.16348	+	0.747721i	−0.0399304	+	0.0256617i
$850$		0			0
$851$	40.8699	+	28.9444i	1.40100	+	0.992202i
$852$		0			0
$853$	−14.8782	+	9.56166i	−0.509421	+	0.327385i	−0.769975	−	0.638074i	$-0.779731\pi$
$853$	−14.8782	+	9.56166i	−0.509421	+	0.327385i	0.260554	+	0.965459i	$0.416095\pi$
$854$		0			0
$855$	6.69612	−	14.6625i	0.229003	−	0.501446i
$856$		0			0
$857$	3.11313	+	6.81681i	0.106343	+	0.232858i	0.955321	−	0.295569i	$-0.0955093\pi$
$857$	3.11313	+	6.81681i	0.106343	+	0.232858i	−0.848979	+	0.528427i	$0.822782\pi$
$858$		0			0
$859$	−3.34778	−	23.2843i	−0.114225	−	0.794450i	−0.963732	−	0.266873i	$-0.914010\pi$
$859$	−3.34778	−	23.2843i	−0.114225	−	0.794450i	0.849507	−	0.527577i	$-0.176899\pi$
$860$		0			0
$861$	−5.85127	+	6.75272i	−0.199411	+	0.230132i
$862$		0			0
$863$	−18.6422	−	11.9806i	−0.634588	−	0.407825i	0.183418	−	0.983035i	$-0.441284\pi$
$863$	−18.6422	−	11.9806i	−0.634588	−	0.407825i	−0.818006	+	0.575210i	$0.804920\pi$
$864$		0			0
$865$	13.1162	+	3.85126i	0.445964	+	0.130947i
$866$		0			0
$867$	−4.60986	−	5.32006i	−0.156559	−	0.180679i
$868$		0			0
$869$	−0.530333	+	0.155720i	−0.0179903	+	0.00528243i
$870$		0			0
$871$	3.32203	−	23.1053i	0.112563	−	0.782892i
$872$		0			0
$873$	−8.59322			−0.290837
$874$		0			0
$875$	1.41464			0.0478235
$876$		0			0
$877$	0.628810	−	4.37347i	0.0212334	−	0.147682i	−0.976447	−	0.215759i	$-0.930777\pi$
$877$	0.628810	−	4.37347i	0.0212334	−	0.147682i	0.997680	+	0.0680775i	$0.0216865\pi$
$878$		0			0
$879$	4.39749	−	1.29122i	0.148324	−	0.0435518i
$880$		0			0
$881$	28.4626	+	32.8476i	0.958930	+	1.10666i	0.994228	+	0.107288i	$0.0342166\pi$
$881$	28.4626	+	32.8476i	0.958930	+	1.10666i	−0.0352976	+	0.999377i	$0.511238\pi$
$882$		0			0
$883$	−3.24248	−	0.952078i	−0.109118	−	0.0320400i	0.226718	−	0.973961i	$-0.427201\pi$
$883$	−3.24248	−	0.952078i	−0.109118	−	0.0320400i	−0.335836	+	0.941921i	$0.609019\pi$
$884$		0			0
$885$	−7.66834	−	4.92815i	−0.257769	−	0.165658i
$886$		0			0
$887$	7.11572	−	8.21198i	0.238923	−	0.275731i	−0.623607	−	0.781738i	$-0.714333\pi$
$887$	7.11572	−	8.21198i	0.238923	−	0.275731i	0.862530	+	0.506007i	$0.168879\pi$
$888$		0			0
$889$	1.53180	+	10.6539i	0.0513751	+	0.357321i
$890$		0			0
$891$	4.67743	+	10.2421i	0.156700	+	0.343125i
$892$		0			0
$893$	−27.2604	+	59.6919i	−0.912234	+	1.99751i
$894$		0			0
$895$	−11.8030	+	7.58530i	−0.394529	+	0.253549i
$896$		0			0
$897$	5.20715	+	12.9100i	0.173862	+	0.431053i
$898$		0			0
$899$	51.3240	−	32.9839i	1.71175	−	1.10008i
$900$		0			0
$901$	−8.82898	+	19.3328i	−0.294136	+	0.644068i
$902$		0			0
$903$	1.53393	+	3.35885i	0.0510461	+	0.111775i
$904$		0			0
$905$	3.60694	+	25.0868i	0.119899	+	0.833915i
$906$		0			0
$907$	5.05042	−	5.82850i	0.167696	−	0.193532i	−0.665681	−	0.746237i	$-0.731859\pi$
$907$	5.05042	−	5.82850i	0.167696	−	0.193532i	0.833377	+	0.552705i	$0.186404\pi$
$908$		0			0
$909$	−20.2348	−	13.0041i	−0.671145	−	0.431319i
$910$		0			0
$911$	−2.30144	−	0.675763i	−0.0762500	−	0.0223890i	0.243385	−	0.969930i	$-0.421742\pi$
$911$	−2.30144	−	0.675763i	−0.0762500	−	0.0223890i	−0.319635	+	0.947541i	$0.603560\pi$
$912$		0			0
$913$	−21.3194	−	24.6039i	−0.705570	−	0.814272i
$914$		0			0
$915$	6.15509	−	1.80730i	0.203481	−	0.0597474i
$916$		0			0
$917$	0.261377	−	1.81792i	0.00863142	−	0.0600328i
$918$		0			0
$919$	44.0764			1.45395			0.726973	−	0.686666i	$-0.240927\pi$
$919$	44.0764			1.45395			0.726973	+	0.686666i	$0.240927\pi$
$920$		0			0
$921$	−5.35277			−0.176380
$922$		0			0
$923$	2.22058	−	15.4445i	0.0730914	−	0.508362i
$924$		0			0
$925$	10.0197	−	2.94204i	0.329444	−	0.0967335i
$926$		0			0
$927$	−20.0069	−	23.0891i	−0.657111	−	0.758347i
$928$		0			0
$929$	21.9335	+	6.44025i	0.719614	+	0.211298i	0.620980	−	0.783826i	$-0.286735\pi$
$929$	21.9335	+	6.44025i	0.719614	+	0.211298i	0.0986335	+	0.995124i	$0.468553\pi$
$930$		0			0
$931$	−25.9974	−	16.7075i	−0.852029	−	0.547566i
$932$		0			0
$933$	−0.753704	+	0.869821i	−0.0246752	+	0.0284767i
$934$		0			0
$935$	−0.684560	−	4.76122i	−0.0223875	−	0.155708i
$936$		0			0
$937$	−9.67166	−	21.1780i	−0.315959	−	0.691854i	0.683308	−	0.730130i	$-0.260541\pi$
$937$	−9.67166	−	21.1780i	−0.315959	−	0.691854i	−0.999267	+	0.0382759i	$0.987813\pi$
$938$		0			0
$939$	2.46898	−	5.40631i	0.0805720	−	0.176428i
$940$		0			0
$941$	20.8147	−	13.3768i	0.678541	−	0.436072i	−0.155455	−	0.987843i	$-0.549684\pi$
$941$	20.8147	−	13.3768i	0.678541	−	0.436072i	0.833995	+	0.551771i	$0.186048\pi$
$942$		0			0
$943$	−48.2942	−	2.17545i	−1.57268	−	0.0708425i
$944$		0			0
$945$	4.18135	−	2.68719i	0.136019	−	0.0874144i
$946$		0			0
$947$	19.8454	−	43.4553i	0.644887	−	1.41211i	−0.251071	−	0.967969i	$-0.580783\pi$
$947$	19.8454	−	43.4553i	0.644887	−	1.41211i	0.895959	−	0.444138i	$-0.146490\pi$
$948$		0			0
$949$	−20.4120	−	44.6960i	−0.662601	−	1.45089i
$950$		0			0
$951$	0.381040	+	2.65019i	0.0123561	+	0.0859383i
$952$		0			0
$953$	7.26972	−	8.38971i	0.235489	−	0.271769i	−0.625688	−	0.780073i	$-0.715182\pi$
$953$	7.26972	−	8.38971i	0.235489	−	0.271769i	0.861178	+	0.508304i	$0.169727\pi$
$954$		0			0
$955$	−6.13901	−	3.94530i	−0.198654	−	0.127667i
$956$		0			0
$957$	8.40770	+	2.46872i	0.271782	+	0.0798025i
$958$		0			0
$959$	−7.51610	−	8.67405i	−0.242708	−	0.280100i
$960$		0			0
$961$	−43.5406	+	12.7847i	−1.40454	+	0.412409i
$962$		0			0
$963$	−0.501018	+	3.48465i	−0.0161451	+	0.112291i
$964$		0			0
$965$	−17.6042			−0.566698
$966$		0			0
$967$	−11.8292			−0.380401			−0.190201	−	0.981745i	$-0.560914\pi$
$967$	−11.8292			−0.380401			−0.190201	+	0.981745i	$0.560914\pi$
$968$		0			0
$969$	−1.32370	+	9.20654i	−0.0425234	+	0.295757i
$970$		0			0
$971$	−38.9861	+	11.4474i	−1.25112	+	0.367363i	−0.839184	−	0.543847i	$-0.816967\pi$
$971$	−38.9861	+	11.4474i	−1.25112	+	0.367363i	−0.411941	+	0.911211i	$0.635149\pi$
$972$		0			0
$973$	19.8046	+	22.8557i	0.634906	+	0.732721i
$974$		0			0
$975$	2.78507	+	0.817770i	0.0891936	+	0.0261896i
$976$		0			0
$977$	37.2296	+	23.9260i	1.19108	+	0.765461i	0.977391	−	0.211440i	$-0.0678154\pi$
$977$	37.2296	+	23.9260i	1.19108	+	0.765461i	0.213690	+	0.976902i	$0.431452\pi$
$978$		0			0
$979$	0.290800	−	0.335601i	0.00929401	−	0.0107259i
$980$		0			0
$981$	−0.0601991	−	0.418694i	−0.00192201	−	0.0133679i
$982$		0			0
$983$	7.72389	+	16.9130i	0.246354	+	0.539440i	0.991901	−	0.127013i	$-0.0405390\pi$
$983$	7.72389	+	16.9130i	0.246354	+	0.539440i	−0.745547	+	0.666453i	$0.767812\pi$
$984$		0			0
$985$	5.85166	−	12.8133i	0.186449	−	0.408267i
$986$		0			0
$987$	−7.91535	+	5.08689i	−0.251948	+	0.161917i
$988$		0			0
$989$	−9.10866	+	17.7810i	−0.289639	+	0.565403i
$990$		0			0
$991$	−33.2093	+	21.3423i	−1.05493	+	0.677960i	−0.948634	−	0.316374i	$-0.897534\pi$
$991$	−33.2093	+	21.3423i	−1.05493	+	0.677960i	−0.106293	+	0.994335i	$0.533898\pi$
$992$		0			0
$993$	−2.31444	+	5.06792i	−0.0734466	+	0.160826i
$994$		0			0
$995$	4.49679	+	9.84660i	0.142558	+	0.312158i
$996$		0			0
$997$	0.0162377	+	0.112936i	0.000514253	+	0.00357671i	0.990077	−	0.140526i	$-0.0448794\pi$
$997$	0.0162377	+	0.112936i	0.000514253	+	0.00357671i	−0.989563	+	0.144103i	$0.953970\pi$
$998$		0			0
$999$	24.0273	−	27.7290i	0.760190	−	0.877306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.b.81.3	✓	50
23.2	even	11	inner	460.2.m.b.301.3	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.b.81.3	✓	50	1.1	even	1	trivial
460.2.m.b.301.3	yes	50	23.2	even	11	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0891733 - 0.620214i) q^{3} +(0.959493 - 0.281733i) q^{5} +(0.926390 + 1.06911i) q^{7} +(2.50177 + 0.734585i) q^{9} +O(q^{10})\)	\(q+(0.0891733 - 0.620214i) q^{3} +(0.959493 - 0.281733i) q^{5} +(0.926390 + 1.06911i) q^{7} +(2.50177 + 0.734585i) q^{9} +(1.68527 + 1.08306i) q^{11} +(-3.03360 + 3.50096i) q^{13} +(-0.0891733 - 0.620214i) q^{15} +(-0.997471 - 2.18416i) q^{17} +(2.56814 - 5.62344i) q^{19} +(0.745687 - 0.479224i) q^{21} +(4.53610 + 1.55684i) q^{23} +(0.841254 - 0.540641i) q^{25} +(1.45958 - 3.19603i) q^{27} +(2.89994 + 6.34999i) q^{29} +(-1.24376 - 8.65054i) q^{31} +(0.822010 - 0.948650i) q^{33} +(1.19007 + 0.764811i) q^{35} +(10.0197 + 2.94204i) q^{37} +(1.90083 + 2.19367i) q^{39} +(-9.67193 + 2.83993i) q^{41} +(-0.592850 + 4.12336i) q^{43} +2.60738 q^{45} -10.6148 q^{47} +(0.711404 - 4.94792i) q^{49} +(-1.44359 + 0.423877i) q^{51} +(-5.79641 - 6.68941i) q^{53} +(1.92214 + 0.564391i) q^{55} +(-3.25873 - 2.09426i) q^{57} +(9.52662 - 10.9943i) q^{59} +(1.45700 + 10.1336i) q^{61} +(1.53226 + 3.35518i) q^{63} +(-1.92438 + 4.21381i) q^{65} +(-4.23908 + 2.72429i) q^{67} +(1.37008 - 2.67453i) q^{69} +(-2.83358 + 1.82103i) q^{71} +(-4.40632 + 9.64850i) q^{73} +(-0.260296 - 0.569968i) q^{75} +(0.403309 + 2.80508i) q^{77} +(-0.180681 + 0.208517i) q^{79} +(4.72834 + 3.03872i) q^{81} +(-15.5928 - 4.57847i) q^{83} +(-1.57241 - 1.81466i) q^{85} +(4.19695 - 1.23234i) q^{87} +(0.0315466 - 0.219411i) q^{89} -6.55321 q^{91} -5.47610 q^{93} +(0.879805 - 6.11918i) q^{95} +(-3.16223 + 0.928514i) q^{97} +(3.42056 + 3.94753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9}+O(q^{10}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9	\( 50 q + 5 q^{5} - q^{7} - 25 q^{9} - 6 q^{13} + 12 q^{17} + 19 q^{19} + 39 q^{21} - 16 q^{23} - 5 q^{25} + 21 q^{27} - 6 q^{29} + 34 q^{31} + 50 q^{33} - 10 q^{35} + 7 q^{37} - 70 q^{39} - 51 q^{41} - 18 q^{43} - 74 q^{45} + 30 q^{47} - 16 q^{49} - 80 q^{51} - 23 q^{53} - 33 q^{55} + 27 q^{57} - 18 q^{59} + 76 q^{61} + 138 q^{63} + 6 q^{65} + 25 q^{67} - 30 q^{69} - 37 q^{71} + 20 q^{73} + 92 q^{77} + 18 q^{79} + 25 q^{81} - 22 q^{83} - 12 q^{85} - 109 q^{87} + 8 q^{89} + 110 q^{91} + 64 q^{93} + 3 q^{95} - 38 q^{97} - 126 q^{99}+O(q^{100}) \) 50 * q + 5 * q^5 - q^7 - 25 * q^9 - 6 * q^13 + 12 * q^17 + 19 * q^19 + 39 * q^21 - 16 * q^23 - 5 * q^25 + 21 * q^27 - 6 * q^29 + 34 * q^31 + 50 * q^33 - 10 * q^35 + 7 * q^37 - 70 * q^39 - 51 * q^41 - 18 * q^43 - 74 * q^45 + 30 * q^47 - 16 * q^49 - 80 * q^51 - 23 * q^53 - 33 * q^55 + 27 * q^57 - 18 * q^59 + 76 * q^61 + 138 * q^63 + 6 * q^65 + 25 * q^67 - 30 * q^69 - 37 * q^71 + 20 * q^73 + 92 * q^77 + 18 * q^79 + 25 * q^81 - 22 * q^83 - 12 * q^85 - 109 * q^87 + 8 * q^89 + 110 * q^91 + 64 * q^93 + 3 * q^95 - 38 * q^97 - 126 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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