LMFDB - Embedded newform 804.2.y.b.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	804.49
Dual form			804.2.y.b.361.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{3} +(0.370568 + 2.57736i) q^{5} +(5.06200 + 0.483363i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{3} +(0.370568 + 2.57736i) q^{5} +(5.06200 + 0.483363i) q^{7} +(0.415415 + 0.909632i) q^{9} +(1.12351 + 0.449787i) q^{11} +(-1.87649 - 1.78923i) q^{13} +(1.08168 - 2.36856i) q^{15} +(-0.432922 + 1.25085i) q^{17} +(-2.72887 + 0.260576i) q^{19} +(-3.99710 - 3.14336i) q^{21} +(-0.334601 + 7.02413i) q^{23} +(-1.70800 + 0.501514i) q^{25} +(0.142315 - 0.989821i) q^{27} +(-0.475676 + 0.823894i) q^{29} +(2.66411 - 2.54023i) q^{31} +(-0.701987 - 0.985803i) q^{33} +(0.630019 + 13.2257i) q^{35} +(-0.0722595 - 0.125157i) q^{37} +(0.611273 + 2.51970i) q^{39} +(2.86735 - 0.552636i) q^{41} +(2.29395 + 2.64736i) q^{43} +(-2.19051 + 1.40776i) q^{45} +(-2.68982 + 1.38670i) q^{47} +(18.5167 + 3.56881i) q^{49} +(1.04046 - 0.818224i) q^{51} +(3.84849 - 4.44139i) q^{53} +(-0.742925 + 3.06238i) q^{55} +(2.43655 + 1.25613i) q^{57} +(9.06210 + 2.66087i) q^{59} +(-10.6901 + 4.27966i) q^{61} +(1.66315 + 4.80536i) q^{63} +(3.91612 - 5.49942i) q^{65} +(-1.01038 - 8.12275i) q^{67} +(4.07902 - 5.72818i) q^{69} +(1.79677 + 5.19142i) q^{71} +(8.52691 - 3.41366i) q^{73} +(1.70800 + 0.501514i) q^{75} +(5.46983 + 2.81989i) q^{77} +(-3.37120 + 13.8963i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(-9.03833 + 7.10782i) q^{83} +(-3.38431 - 0.652272i) q^{85} +(0.845595 - 0.435934i) q^{87} +(5.42733 - 3.48794i) q^{89} +(-8.63395 - 9.96411i) q^{91} +(-3.61455 + 0.696647i) q^{93} +(-1.68283 - 6.93673i) q^{95} +(-4.30471 - 7.45598i) q^{97} +(0.0575838 + 1.20883i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{23}{33}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$3$	−0.841254	−	0.540641i	−0.485698	−	0.312139i
$4$		0			0
$5$	0.370568	+	2.57736i	0.165723	+	1.15263i	0.887602	+	0.460611i	$0.152370\pi$
$5$	0.370568	+	2.57736i	0.165723	+	1.15263i	−0.721879	+	0.692020i	$0.756721\pi$
$6$		0			0
$7$	5.06200	+	0.483363i	1.91326	+	0.182694i	0.982923	−	0.184017i	$-0.0589102\pi$
$7$	5.06200	+	0.483363i	1.91326	+	0.182694i	0.930335	+	0.366711i	$0.119516\pi$
$8$		0			0
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$		0			0
$11$	1.12351	+	0.449787i	0.338752	+	0.135616i	0.534801	−	0.844978i	$-0.320387\pi$
$11$	1.12351	+	0.449787i	0.338752	+	0.135616i	−0.196048	+	0.980594i	$0.562811\pi$
$12$		0			0
$13$	−1.87649	−	1.78923i	−0.520445	−	0.496243i	0.383707	−	0.923455i	$-0.374647\pi$
$13$	−1.87649	−	1.78923i	−0.520445	−	0.496243i	−0.904152	+	0.427212i	$0.859496\pi$
$14$		0			0
$15$	1.08168	−	2.36856i	0.279290	−	0.611559i
$16$		0			0
$17$	−0.432922	+	1.25085i	−0.104999	+	0.303375i	−0.985247	−	0.171140i	$-0.945255\pi$
$17$	−0.432922	+	1.25085i	−0.104999	+	0.303375i	0.880248	+	0.474514i	$0.157376\pi$
$18$		0			0
$19$	−2.72887	+	0.260576i	−0.626046	+	0.0597802i	−0.403258	−	0.915087i	$-0.632122\pi$
$19$	−2.72887	+	0.260576i	−0.626046	+	0.0597802i	−0.222789	+	0.974867i	$0.571516\pi$
$20$		0			0
$21$	−3.99710	−	3.14336i	−0.872239	−	0.685937i
$22$		0			0
$23$	−0.334601	+	7.02413i	−0.0697690	+	1.46463i	0.644416	+	0.764675i	$0.277101\pi$
$23$	−0.334601	+	7.02413i	−0.0697690	+	1.46463i	−0.714185	+	0.699957i	$0.753202\pi$
$24$		0			0
$25$	−1.70800	+	0.501514i	−0.341600	+	0.100303i
$26$		0			0
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$		0			0
$29$	−0.475676	+	0.823894i	−0.0883307	+	0.152993i	−0.906806	−	0.421549i	$-0.861487\pi$
$29$	−0.475676	+	0.823894i	−0.0883307	+	0.152993i	0.818475	+	0.574542i	$0.194820\pi$
$30$		0			0
$31$	2.66411	−	2.54023i	0.478489	−	0.456238i	−0.412039	−	0.911166i	$-0.635183\pi$
$31$	2.66411	−	2.54023i	0.478489	−	0.456238i	0.890528	+	0.454928i	$0.150335\pi$
$32$		0			0
$33$	−0.701987	−	0.985803i	−0.122200	−	0.171606i
$34$		0			0
$35$	0.630019	+	13.2257i	0.106493	+	2.23556i
$36$		0			0
$37$	−0.0722595	−	0.125157i	−0.0118794	−	0.0205757i	0.860025	−	0.510253i	$-0.170448\pi$
$37$	−0.0722595	−	0.125157i	−0.0118794	−	0.0205757i	−0.871904	+	0.489677i	$0.837115\pi$
$38$		0			0
$39$	0.611273	+	2.51970i	0.0978821	+	0.403475i
$40$		0			0
$41$	2.86735	−	0.552636i	0.447805	−	0.0863073i	0.0396369	−	0.999214i	$-0.487380\pi$
$41$	2.86735	−	0.552636i	0.447805	−	0.0863073i	0.408168	+	0.912907i	$0.366168\pi$
$42$		0			0
$43$	2.29395	+	2.64736i	0.349824	+	0.403719i	0.903205	−	0.429210i	$-0.141208\pi$
$43$	2.29395	+	2.64736i	0.349824	+	0.403719i	−0.553381	+	0.832929i	$0.686662\pi$
$44$		0			0
$45$	−2.19051	+	1.40776i	−0.326542	+	0.209856i
$46$		0			0
$47$	−2.68982	+	1.38670i	−0.392350	+	0.202271i	−0.643101	−	0.765781i	$-0.722353\pi$
$47$	−2.68982	+	1.38670i	−0.392350	+	0.202271i	0.250751	+	0.968052i	$0.419322\pi$
$48$		0			0
$49$	18.5167	+	3.56881i	2.64525	+	0.509830i
$50$		0			0
$51$	1.04046	−	0.818224i	0.145693	−	0.114574i
$52$		0			0
$53$	3.84849	−	4.44139i	0.528630	−	0.610072i	−0.427140	−	0.904185i	$-0.640479\pi$
$53$	3.84849	−	4.44139i	0.528630	−	0.610072i	0.955771	+	0.294113i	$0.0950243\pi$
$54$		0			0
$55$	−0.742925	+	3.06238i	−0.100176	+	0.412931i
$56$		0			0
$57$	2.43655	+	1.25613i	0.322729	+	0.166378i
$58$		0			0
$59$	9.06210	+	2.66087i	1.17978	+	0.346416i	0.812091	−	0.583531i	$-0.198329\pi$
$59$	9.06210	+	2.66087i	1.17978	+	0.346416i	0.367694	+	0.929947i	$0.380148\pi$
$60$		0			0
$61$	−10.6901	+	4.27966i	−1.36872	+	0.547954i	−0.935498	−	0.353332i	$-0.885049\pi$
$61$	−10.6901	+	4.27966i	−1.36872	+	0.547954i	−0.433225	+	0.901286i	$0.642624\pi$
$62$		0			0
$63$	1.66315	+	4.80536i	0.209537	+	0.605418i
$64$		0			0
$65$	3.91612	−	5.49942i	0.485735	−	0.682120i
$66$		0			0
$67$	−1.01038	−	8.12275i	−0.123438	−	0.992352i
$67$	−1.01038	−	8.12275i	−0.123438	−	0.992352i
$68$		0			0
$69$	4.07902	−	5.72818i	0.491056	−	0.689591i
$70$		0			0
$71$	1.79677	+	5.19142i	0.213237	+	0.616109i	0.999999	−	0.00114777i	$-0.000365348\pi$
$71$	1.79677	+	5.19142i	0.213237	+	0.616109i	−0.786762	+	0.617256i	$0.788244\pi$
$72$		0			0
$73$	8.52691	−	3.41366i	0.997999	−	0.399538i	0.185590	−	0.982627i	$-0.440580\pi$
$73$	8.52691	−	3.41366i	0.997999	−	0.399538i	0.812408	+	0.583089i	$0.198156\pi$
$74$		0			0
$75$	1.70800	+	0.501514i	0.197223	+	0.0579099i
$76$		0			0
$77$	5.46983	+	2.81989i	0.623345	+	0.321356i
$78$		0			0
$79$	−3.37120	+	13.8963i	−0.379289	+	1.56345i	0.387696	+	0.921787i	$0.373271\pi$
$79$	−3.37120	+	13.8963i	−0.379289	+	1.56345i	−0.766985	+	0.641665i	$0.778244\pi$
$80$		0			0
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$		0			0
$83$	−9.03833	+	7.10782i	−0.992086	+	0.780185i	−0.975572	−	0.219679i	$-0.929499\pi$
$83$	−9.03833	+	7.10782i	−0.992086	+	0.780185i	−0.0165138	+	0.999864i	$0.505257\pi$
$84$		0			0
$85$	−3.38431	−	0.652272i	−0.367080	−	0.0707489i
$86$		0			0
$87$	0.845595	−	0.435934i	0.0906573	−	0.0467371i
$88$		0			0
$89$	5.42733	−	3.48794i	0.575296	−	0.369720i	−0.220406	−	0.975408i	$-0.570738\pi$
$89$	5.42733	−	3.48794i	0.575296	−	0.369720i	0.795702	+	0.605688i	$0.207102\pi$
$90$		0			0
$91$	−8.63395	−	9.96411i	−0.905084	−	1.04452i
$92$		0			0
$93$	−3.61455	+	0.696647i	−0.374811	+	0.0722389i
$94$		0			0
$95$	−1.68283	−	6.93673i	−0.172655	−	0.711693i
$96$		0			0
$97$	−4.30471	−	7.45598i	−0.437077	−	0.757040i	0.560385	−	0.828232i	$-0.310653\pi$
$97$	−4.30471	−	7.45598i	−0.437077	−	0.757040i	−0.997463	+	0.0711919i	$0.977320\pi$
$98$		0			0
$99$	0.0575838	+	1.20883i	0.00578739	+	0.121492i
$100$		0			0
$101$	−8.85696	−	12.4379i	−0.881301	−	1.23761i	−0.970379	−	0.241589i	$-0.922331\pi$
$101$	−8.85696	−	12.4379i	−0.881301	−	1.23761i	0.0890778	−	0.996025i	$-0.471608\pi$
$102$		0			0
$103$	2.14835	−	2.04844i	0.211683	−	0.201839i	−0.576818	−	0.816872i	$-0.695706\pi$
$103$	2.14835	−	2.04844i	0.211683	−	0.201839i	0.788501	+	0.615033i	$0.210857\pi$
$104$		0			0
$105$	6.62036	−	11.4668i	0.646081	−	1.11905i
$106$		0			0
$107$	−0.782903	+	5.44521i	−0.0756861	+	0.526408i	0.916343	+	0.400395i	$0.131127\pi$
$107$	−0.782903	+	5.44521i	−0.0756861	+	0.526408i	−0.992029	+	0.126013i	$0.959782\pi$
$108$		0			0
$109$	13.8640	−	4.07083i	1.32793	−	0.389915i	0.460581	−	0.887618i	$-0.347641\pi$
$109$	13.8640	−	4.07083i	1.32793	−	0.389915i	0.867348	+	0.497703i	$0.165823\pi$
$110$		0			0
$111$	−0.00687649	+	0.144355i	−0.000652687	+	0.0137016i
$112$		0			0
$113$	−8.89916	−	6.99837i	−0.837162	−	0.658352i	0.104643	−	0.994510i	$-0.466630\pi$
$113$	−8.89916	−	6.99837i	−0.837162	−	0.658352i	−0.941806	+	0.336158i	$0.890872\pi$
$114$		0			0
$115$	−18.2277	+	1.74054i	−1.69974	+	0.162306i
$116$		0			0
$117$	0.848018	−	2.45019i	0.0783993	−	0.226520i
$118$		0			0
$119$	−2.79607	+	6.12253i	−0.256315	+	0.561252i
$120$		0			0
$121$	−6.90110	−	6.58018i	−0.627373	−	0.598198i
$122$		0			0
$123$	−2.71095	−	1.08530i	−0.244438	−	0.0978581i
$124$		0			0
$125$	3.48291	+	7.62650i	0.311521	+	0.682135i
$126$		0			0
$127$	−8.06798	−	0.770399i	−0.715917	−	0.0683618i	−0.269261	−	0.963067i	$-0.586779\pi$
$127$	−8.06798	−	0.770399i	−0.715917	−	0.0683618i	−0.446657	+	0.894705i	$0.647385\pi$
$128$		0			0
$129$	−0.498523	−	3.46730i	−0.0438925	−	0.305279i
$130$		0			0
$131$	−8.27935	−	5.32081i	−0.723370	−	0.464882i	0.126438	−	0.991975i	$-0.459646\pi$
$131$	−8.27935	−	5.32081i	−0.723370	−	0.464882i	−0.849808	+	0.527093i	$0.823282\pi$
$132$		0			0
$133$	−13.9395			−1.20871
$134$		0			0
$135$	2.60386			0.224105
$136$		0			0
$137$	13.1755	+	8.46737i	1.12566	+	0.723416i	0.964649	−	0.263537i	$-0.0848892\pi$
$137$	13.1755	+	8.46737i	1.12566	+	0.723416i	0.161008	+	0.986953i	$0.448526\pi$
$138$		0			0
$139$	−1.21327	−	8.43848i	−0.102908	−	0.715742i	−0.974316	−	0.225184i	$-0.927702\pi$
$139$	−1.21327	−	8.43848i	−0.102908	−	0.715742i	0.871408	−	0.490559i	$-0.163207\pi$
$140$		0			0
$141$	3.01252	+	0.287661i	0.253700	+	0.0242254i
$142$		0			0
$143$	−1.30349	−	2.85425i	−0.109003	−	0.238684i
$144$		0			0
$145$	−2.29974	−	0.920678i	−0.190983	−	0.0764582i
$146$		0			0
$147$	−13.6478	−	13.0132i	−1.12565	−	1.07331i
$148$		0			0
$149$	−6.29448	+	13.7830i	−0.515664	+	1.12915i	0.455392	+	0.890291i	$0.349499\pi$
$149$	−6.29448	+	13.7830i	−0.515664	+	1.12915i	−0.971055	+	0.238855i	$0.923228\pi$
$150$		0			0
$151$	−2.64275	+	7.63574i	−0.215064	+	0.621388i	0.784934	+	0.619579i	$0.212697\pi$
$151$	−2.64275	+	7.63574i	−0.215064	+	0.621388i	−0.999998	+	0.00180825i	$0.999424\pi$
$152$		0			0
$153$	−1.31765	+	0.125821i	−0.106526	+	0.0101720i
$154$		0			0
$155$	7.53432	+	5.92506i	0.605171	+	0.475912i
$156$		0			0
$157$	0.606027	−	12.7221i	0.0483663	−	1.01533i	−0.836056	−	0.548645i	$-0.815144\pi$
$157$	0.606027	−	12.7221i	0.0483663	−	1.01533i	0.884422	−	0.466688i	$-0.154553\pi$
$158$		0			0
$159$	−5.63875	+	1.65569i	−0.447182	+	0.131305i
$160$		0			0
$161$	−5.08895	+	35.3944i	−0.401066	+	2.78947i
$162$		0			0
$163$	7.73805	−	13.4027i	0.606091	−	1.04978i	−0.385787	−	0.922588i	$-0.626070\pi$
$163$	7.73805	−	13.4027i	0.606091	−	1.04978i	0.991878	−	0.127192i	$-0.0405966\pi$
$164$		0			0
$165$	2.28064	−	2.17458i	0.177547	−	0.169291i
$166$		0			0
$167$	10.3247	+	14.4991i	0.798953	+	1.12197i	0.990094	+	0.140409i	$0.0448418\pi$
$167$	10.3247	+	14.4991i	0.798953	+	1.12197i	−0.191141	+	0.981563i	$0.561219\pi$
$168$		0			0
$169$	−0.298693	−	6.27033i	−0.0229764	−	0.482333i
$170$		0			0
$171$	−1.37064	−	2.37402i	−0.104816	−	0.181546i
$172$		0			0
$173$	−5.65157	−	23.2961i	−0.429681	−	1.77117i	−0.615038	−	0.788498i	$-0.710859\pi$
$173$	−5.65157	−	23.2961i	−0.429681	−	1.77117i	0.185357	−	0.982671i	$-0.440656\pi$
$174$		0			0
$175$	−8.88832	+	1.71308i	−0.671894	+	0.129497i
$176$		0			0
$177$	−6.18494	−	7.13781i	−0.464889	−	0.536510i
$178$		0			0
$179$	4.97089	−	3.19460i	0.371542	−	0.238775i	−0.341523	−	0.939873i	$-0.610943\pi$
$179$	4.97089	−	3.19460i	0.371542	−	0.238775i	0.713065	+	0.701098i	$0.247306\pi$
$180$		0			0
$181$	−6.30900	+	3.25251i	−0.468944	+	0.241757i	−0.676467	−	0.736473i	$-0.736490\pi$
$181$	−6.30900	+	3.25251i	−0.468944	+	0.241757i	0.207523	+	0.978230i	$0.433460\pi$
$182$		0			0
$183$	11.3068	+	2.17921i	0.835824	+	0.161092i
$184$		0			0
$185$	0.295798	−	0.232618i	0.0217475	−	0.0171024i
$186$		0			0
$187$	−1.04901	+	1.21062i	−0.0767112	+	0.0885294i
$188$		0			0
$189$	1.19884	−	4.94169i	0.0872029	−	0.359455i
$190$		0			0
$191$	−24.0238	−	12.3851i	−1.73830	−	0.896155i	−0.965056	−	0.262044i	$-0.915603\pi$
$191$	−24.0238	−	12.3851i	−1.73830	−	0.896155i	−0.773242	−	0.634111i	$-0.781366\pi$
$192$		0			0
$193$	14.3949	+	4.22671i	1.03616	+	0.304245i	0.755215	−	0.655477i	$-0.227532\pi$
$193$	14.3949	+	4.22671i	1.03616	+	0.304245i	0.280950	+	0.959723i	$0.409351\pi$
$194$		0			0
$195$	−6.26766	+	2.50919i	−0.448837	+	0.179687i
$196$		0			0
$197$	0.246166	+	0.711249i	0.0175386	+	0.0506744i	0.953430	−	0.301613i	$-0.0975251\pi$
$197$	0.246166	+	0.711249i	0.0175386	+	0.0506744i	−0.935892	+	0.352288i	$0.885404\pi$
$198$		0			0
$199$	0.166767	−	0.234192i	0.0118218	−	0.0166014i	−0.808623	−	0.588328i	$-0.799787\pi$
$199$	0.166767	−	0.234192i	0.0118218	−	0.0166014i	0.820445	+	0.571726i	$0.193726\pi$
$200$		0			0
$201$	−3.54150	+	7.37955i	−0.249798	+	0.520513i
$202$		0			0
$203$	−2.80611	+	3.94063i	−0.196950	+	0.276578i
$204$		0			0
$205$	2.48689	+	7.18541i	0.173692	+	0.501850i
$206$		0			0
$207$	−6.52837	+	2.61357i	−0.453753	+	0.181655i
$208$		0			0
$209$	−3.18313	−	0.934652i	−0.220182	−	0.0646513i
$210$		0			0
$211$	−10.1264	−	5.22055i	−0.697133	−	0.359397i	0.0729543	−	0.997335i	$-0.476757\pi$
$211$	−10.1264	−	5.22055i	−0.697133	−	0.359397i	−0.770088	+	0.637938i	$0.779788\pi$
$212$		0			0
$213$	1.29516	−	5.33871i	0.0887427	−	0.365802i
$214$		0			0
$215$	−5.97314	+	6.89337i	−0.407364	+	0.470124i
$216$		0			0
$217$	14.7136	−	11.5709i	0.998825	−	0.785485i
$218$		0			0
$219$	−9.01885	−	1.73824i	−0.609438	−	0.117459i
$220$		0			0
$221$	3.05043	−	1.57260i	0.205194	−	0.105785i
$222$		0			0
$223$	14.2642	−	9.16706i	0.955203	−	0.613872i	0.0325368	−	0.999471i	$-0.489641\pi$
$223$	14.2642	−	9.16706i	0.955203	−	0.613872i	0.922667	+	0.385599i	$0.126005\pi$
$224$		0			0
$225$	−1.16572	−	1.34532i	−0.0777149	−	0.0896877i
$226$		0			0
$227$	26.7183	−	5.14952i	1.77335	−	0.341786i	0.805364	−	0.592780i	$-0.201970\pi$
$227$	26.7183	−	5.14952i	1.77335	−	0.341786i	0.967989	+	0.250994i	$0.0807575\pi$
$228$		0			0
$229$	−2.80822	−	11.5756i	−0.185572	−	0.764940i	−0.986170	−	0.165738i	$-0.947000\pi$
$229$	−2.80822	−	11.5756i	−0.185572	−	0.764940i	0.800597	−	0.599203i	$-0.204516\pi$
$230$		0			0
$231$	−3.07696	−	5.32946i	−0.202449	−	0.350652i
$232$		0			0
$233$	0.0987032	+	2.07203i	0.00646626	+	0.135744i	0.999792	+	0.0203998i	$0.00649391\pi$
$233$	0.0987032	+	2.07203i	0.00646626	+	0.135744i	−0.993326	+	0.115344i	$0.963203\pi$
$234$		0			0
$235$	−4.57078	−	6.41876i	−0.298165	−	0.418714i
$236$		0			0
$237$	10.3489	−	9.86768i	0.672235	−	0.640975i
$238$		0			0
$239$	11.6048	−	20.1001i	0.750652	−	1.30017i	−0.196854	−	0.980433i	$-0.563073\pi$
$239$	11.6048	−	20.1001i	0.750652	−	1.30017i	0.947507	−	0.319736i	$-0.103594\pi$
$240$		0			0
$241$	3.73281	−	25.9622i	0.240451	−	1.67237i	−0.409432	−	0.912341i	$-0.634273\pi$
$241$	3.73281	−	25.9622i	0.240451	−	1.67237i	0.649883	−	0.760034i	$-0.274818\pi$
$242$		0			0
$243$	0.959493	−	0.281733i	0.0615515	−	0.0180732i
$244$		0			0
$245$	−2.33639	+	49.0468i	−0.149266	+	3.13349i
$246$		0			0
$247$	5.58693	+	4.39361i	0.355488	+	0.279559i
$248$		0			0
$249$	11.4463	−	1.09299i	0.725380	−	0.0692654i
$250$		0			0
$251$	8.97241	−	25.9241i	0.566333	−	1.63631i	−0.189746	−	0.981833i	$-0.560767\pi$
$251$	8.97241	−	25.9241i	0.566333	−	1.63631i	0.756080	−	0.654480i	$-0.227112\pi$
$252$		0			0
$253$	−3.53530	+	7.74122i	−0.222262	+	0.486686i
$254$		0			0
$255$	2.49442	+	2.37842i	0.156206	+	0.148943i
$256$		0			0
$257$	−20.3242	−	8.13657i	−1.26779	−	0.507545i	−0.362356	−	0.932040i	$-0.618027\pi$
$257$	−20.3242	−	8.13657i	−1.26779	−	0.507545i	−0.905430	+	0.424495i	$0.860452\pi$
$258$		0			0
$259$	−0.305281	−	0.668473i	−0.0189693	−	0.0415369i
$260$		0			0
$261$	−0.947043	−	0.0904317i	−0.0586205	−	0.00559758i
$262$		0			0
$263$	−1.09377	−	7.60733i	−0.0674447	−	0.469088i	−0.995354	−	0.0962824i	$-0.969305\pi$
$263$	−1.09377	−	7.60733i	−0.0674447	−	0.469088i	0.927909	−	0.372806i	$-0.121604\pi$
$264$		0			0
$265$	12.8732	+	8.27310i	0.790794	+	0.508213i
$266$		0			0
$267$	−6.45148			−0.394824
$268$		0			0
$269$	−18.0212			−1.09877			−0.549386	−	0.835568i	$-0.685138\pi$
$269$	−18.0212			−1.09877			−0.549386	+	0.835568i	$0.685138\pi$
$270$		0			0
$271$	2.05234	+	1.31896i	0.124671	+	0.0801209i	0.601490	−	0.798880i	$-0.294574\pi$
$271$	2.05234	+	1.31896i	0.124671	+	0.0801209i	−0.476819	+	0.879001i	$0.658210\pi$
$272$		0			0
$273$	1.87634	+	13.0502i	0.113561	+	0.789835i
$274$		0			0
$275$	−2.14454	−	0.204779i	−0.129321	−	0.0123486i
$276$		0			0
$277$	−1.59627	−	3.49535i	−0.0959107	−	0.210015i	0.855595	−	0.517645i	$-0.173191\pi$
$277$	−1.59627	−	3.49535i	−0.0959107	−	0.210015i	−0.951506	+	0.307630i	$0.900464\pi$
$278$		0			0
$279$	3.41739	+	1.36811i	0.204594	+	0.0819069i
$280$		0			0
$281$	−23.0547	−	21.9826i	−1.37533	−	1.31137i	−0.902801	−	0.430058i	$-0.858493\pi$
$281$	−23.0547	−	21.9826i	−1.37533	−	1.31137i	−0.472528	−	0.881316i	$-0.656658\pi$
$282$		0			0
$283$	−9.67117	+	21.1769i	−0.574891	+	1.25884i	0.369261	+	0.929326i	$0.379611\pi$
$283$	−9.67117	+	21.1769i	−0.574891	+	1.25884i	−0.944152	+	0.329511i	$0.893116\pi$
$284$		0			0
$285$	−2.33459	+	6.74536i	−0.138289	+	0.399560i
$286$		0			0
$287$	14.7817	−	1.41148i	0.872534	−	0.0833169i
$288$		0			0
$289$	11.9857	+	9.42566i	0.705042	+	0.554451i
$290$		0			0
$291$	−0.409653	+	8.59967i	−0.0240143	+	0.504122i
$292$		0			0
$293$	7.53424	−	2.21225i	0.440155	−	0.129241i	−0.0541438	−	0.998533i	$-0.517243\pi$
$293$	7.53424	−	2.21225i	0.440155	−	0.129241i	0.494299	+	0.869292i	$0.335425\pi$
$294$		0			0
$295$	−3.49990	+	24.3423i	−0.203772	+	1.41726i
$296$		0			0
$297$	0.605102	−	1.04807i	0.0351116	−	0.0608151i
$298$		0			0
$299$	13.1957	−	12.5820i	0.763125	−	0.727638i
$300$		0			0
$301$	10.3324	+	14.5098i	0.595547	+	0.836329i
$302$		0			0
$303$	0.726534	+	15.2518i	0.0417383	+	0.876195i
$304$		0			0
$305$	−14.9916	−	25.9663i	−0.858418	−	1.48682i
$306$		0			0
$307$	−0.457844	−	1.88726i	−0.0261305	−	0.107711i	0.957253	−	0.289252i	$-0.0934067\pi$
$307$	−0.457844	−	1.88726i	−0.0261305	−	0.107711i	−0.983383	+	0.181541i	$0.941892\pi$
$308$		0			0
$309$	−2.91477	+	0.561777i	−0.165816	+	0.0319584i
$310$		0			0
$311$	−0.886652	−	1.02325i	−0.0502774	−	0.0580232i	0.730054	−	0.683390i	$-0.239495\pi$
$311$	−0.886652	−	1.02325i	−0.0502774	−	0.0580232i	−0.780331	+	0.625366i	$0.784950\pi$
$312$		0			0
$313$	5.10202	−	3.27887i	0.288383	−	0.185333i	−0.388449	−	0.921470i	$-0.626989\pi$
$313$	5.10202	−	3.27887i	0.288383	−	0.185333i	0.676832	+	0.736138i	$0.263353\pi$
$314$		0			0
$315$	−11.7688	+	6.06725i	−0.663098	+	0.341851i
$316$		0			0
$317$	−3.72444	−	0.717828i	−0.209186	−	0.0403172i	0.0835818	−	0.996501i	$-0.473364\pi$
$317$	−3.72444	−	0.717828i	−0.209186	−	0.0403172i	−0.292767	+	0.956184i	$0.594576\pi$
$318$		0			0
$319$	−0.905006	+	0.711705i	−0.0506706	+	0.0398478i
$320$		0			0
$321$	3.60252	−	4.15753i	0.201073	−	0.232051i
$322$		0			0
$323$	0.855449	−	3.52621i	0.0475985	−	0.196204i
$324$		0			0
$325$	4.10237	+	2.11492i	0.227559	+	0.117315i
$326$		0			0
$327$	−13.8640	−	4.07083i	−0.766680	−	0.225118i
$328$		0			0
$329$	−14.2861	+	5.71931i	−0.787621	+	0.315316i
$330$		0			0
$331$	4.71666	+	13.6279i	0.259251	+	0.749056i	0.997240	+	0.0742437i	$0.0236543\pi$
$331$	4.71666	+	13.6279i	0.259251	+	0.749056i	−0.737989	+	0.674812i	$0.764225\pi$
$332$		0			0
$333$	0.0838292	−	0.117722i	0.00459381	−	0.00645111i
$334$		0			0
$335$	20.5608	−	5.61416i	1.12336	−	0.306734i
$336$		0			0
$337$	−5.08101	+	7.13528i	−0.276780	+	0.388683i	−0.929443	−	0.368965i	$-0.879712\pi$
$337$	−5.08101	+	7.13528i	−0.276780	+	0.388683i	0.652663	+	0.757648i	$0.273652\pi$
$338$		0			0
$339$	3.70284	+	10.6987i	0.201111	+	0.581071i
$340$		0			0
$341$	4.13574	−	1.65570i	0.223963	−	0.0896611i
$342$		0			0
$343$	57.8535	+	16.9873i	3.12379	+	0.917229i
$344$		0			0
$345$	16.2751	+	8.39041i	0.876224	+	0.451725i
$346$		0			0
$347$	−8.07631	+	33.2910i	−0.433559	+	1.78716i	0.165237	+	0.986254i	$0.447161\pi$
$347$	−8.07631	+	33.2910i	−0.433559	+	1.78716i	−0.598797	+	0.800901i	$0.704354\pi$
$348$		0			0
$349$	−3.88577	+	4.48442i	−0.208001	+	0.240045i	−0.850158	−	0.526527i	$-0.823494\pi$
$349$	−3.88577	+	4.48442i	−0.208001	+	0.240045i	0.642158	+	0.766572i	$0.278039\pi$
$350$		0			0
$351$	−2.03807	+	1.60276i	−0.108784	+	0.0855488i
$352$		0			0
$353$	−22.7398	−	4.38274i	−1.21032	−	0.233270i	−0.456121	−	0.889918i	$-0.650761\pi$
$353$	−22.7398	−	4.38274i	−1.21032	−	0.233270i	−0.754197	+	0.656648i	$0.771974\pi$
$354$		0			0
$355$	−12.7143	+	6.55470i	−0.674807	+	0.347887i
$356$		0			0
$357$	5.66229	−	3.63893i	0.299680	−	0.192593i
$358$		0			0
$359$	8.17560	+	9.43514i	0.431491	+	0.497968i	0.929303	−	0.369317i	$-0.120408\pi$
$359$	8.17560	+	9.43514i	0.431491	+	0.497968i	−0.497812	+	0.867285i	$0.665863\pi$
$360$		0			0
$361$	−11.2778	+	2.17362i	−0.593568	+	0.114401i
$362$		0			0
$363$	2.24806	+	9.26662i	0.117992	+	0.486371i
$364$		0			0
$365$	11.9580	+	20.7119i	0.625912	+	1.08411i
$366$		0			0
$367$	−0.592003	−	12.4277i	−0.0309023	−	0.648719i	−0.960187	−	0.279356i	$-0.909879\pi$
$367$	−0.592003	−	12.4277i	−0.0309023	−	0.648719i	0.929285	−	0.369363i	$-0.120424\pi$
$368$		0			0
$369$	1.69384	+	2.37866i	0.0881776	+	0.123828i
$370$		0			0
$371$	21.6279	−	20.6221i	1.12286	−	1.07065i
$372$		0			0
$373$	−0.271346	+	0.469985i	−0.0140497	+	0.0243349i	−0.872965	−	0.487783i	$-0.837806\pi$
$373$	−0.271346	+	0.469985i	−0.0140497	+	0.0243349i	0.858915	+	0.512118i	$0.171139\pi$
$374$		0			0
$375$	1.19319	−	8.29882i	0.0616161	−	0.428549i
$376$		0			0
$377$	2.36674	−	0.694937i	0.121893	−	0.0357911i
$378$		0			0
$379$	−1.31960	+	27.7018i	−0.0677833	+	1.42295i	0.667209	+	0.744870i	$0.267489\pi$
$379$	−1.31960	+	27.7018i	−0.0677833	+	1.42295i	−0.734992	+	0.678075i	$0.762814\pi$
$380$		0			0
$381$	6.37071	+	5.00998i	0.326381	+	0.256669i
$382$		0			0
$383$	17.7168	−	1.69175i	0.905287	−	0.0864445i	0.367983	−	0.929833i	$-0.380049\pi$
$383$	17.7168	−	1.69175i	0.905287	−	0.0864445i	0.537305	+	0.843388i	$0.319443\pi$
$384$		0			0
$385$	−5.24093	+	15.1427i	−0.267103	+	0.771742i
$386$		0			0
$387$	−1.45518	+	3.18640i	−0.0739711	+	0.161974i
$388$		0			0
$389$	−6.32465	−	6.03054i	−0.320673	−	0.305761i	0.512595	−	0.858630i	$-0.328684\pi$
$389$	−6.32465	−	6.03054i	−0.320673	−	0.305761i	−0.833268	+	0.552870i	$0.813533\pi$
$390$		0			0
$391$	−8.64125	−	3.45944i	−0.437007	−	0.174951i
$392$		0			0
$393$	4.08838	+	8.95231i	0.206232	+	0.451584i
$394$		0			0
$395$	−37.0650	−	3.53927i	−1.86494	−	0.178080i
$396$		0			0
$397$	−1.36545	−	9.49691i	−0.0685299	−	0.476636i	−0.994968	−	0.100190i	$-0.968055\pi$
$397$	−1.36545	−	9.49691i	−0.0685299	−	0.476636i	0.926438	−	0.376446i	$-0.122854\pi$
$398$		0			0
$399$	11.7267	+	7.53627i	0.587068	+	0.377286i
$400$		0			0
$401$	−8.91046			−0.444967			−0.222484	−	0.974936i	$-0.571416\pi$
$401$	−8.91046			−0.444967			−0.222484	+	0.974936i	$0.571416\pi$
$402$		0			0
$403$	−9.54424			−0.475432
$404$		0			0
$405$	−2.19051	−	1.40776i	−0.108847	−	0.0699519i
$406$		0			0
$407$	−0.0248905	−	0.173117i	−0.00123378	−	0.00858110i
$408$		0			0
$409$	3.79478	+	0.362357i	0.187640	+	0.0179174i	0.188453	−	0.982082i	$-0.439653\pi$
$409$	3.79478	+	0.362357i	0.187640	+	0.0179174i	−0.000813102		1.00000i	$0.500259\pi$
$410$		0			0
$411$	−6.50611	−	14.2464i	−0.320923	−	0.702723i
$412$		0			0
$413$	44.5862	+	17.8496i	2.19394	+	0.878322i
$414$		0			0
$415$	−21.6687	−	20.6611i	−1.06368	−	1.01421i
$416$		0			0
$417$	−3.54152	+	7.75484i	−0.173429	+	0.379756i
$418$		0			0
$419$	5.70812	−	16.4925i	0.278860	−	0.805712i	−0.715400	−	0.698716i	$-0.753755\pi$
$419$	5.70812	−	16.4925i	0.278860	−	0.805712i	0.994259	−	0.106997i	$-0.0341235\pi$
$420$		0			0
$421$	−14.9859	+	1.43098i	−0.730368	+	0.0697417i	−0.453613	−	0.891199i	$-0.649865\pi$
$421$	−14.9859	+	1.43098i	−0.730368	+	0.0697417i	−0.276755	+	0.960941i	$0.589259\pi$
$422$		0			0
$423$	−2.37877	−	1.87069i	−0.115660	−	0.0909560i
$424$		0			0
$425$	0.112114	−	2.35356i	0.00543833	−	0.114165i
$426$		0			0
$427$	−56.1818	+	16.4965i	−2.71883	+	0.798320i
$428$		0			0
$429$	−0.446556	+	3.10587i	−0.0215599	+	0.149953i
$430$		0			0
$431$	13.0662	−	22.6314i	0.629379	−	1.09012i	−0.358298	−	0.933607i	$-0.616643\pi$
$431$	13.0662	−	22.6314i	0.629379	−	1.09012i	0.987677	−	0.156509i	$-0.0500240\pi$
$432$		0			0
$433$	10.5696	−	10.0781i	0.507942	−	0.484322i	−0.392223	−	0.919870i	$-0.628294\pi$
$433$	10.5696	−	10.0781i	0.507942	−	0.484322i	0.900165	+	0.435548i	$0.143445\pi$
$434$		0			0
$435$	1.43691	+	2.01786i	0.0688946	+	0.0967489i
$436$		0			0
$437$	−0.917236	−	19.2552i	−0.0438773	−	0.921099i
$438$		0			0
$439$	17.4413	+	30.2092i	0.832427	+	1.44181i	0.896108	+	0.443836i	$0.146383\pi$
$439$	17.4413	+	30.2092i	0.832427	+	1.44181i	−0.0636808	+	0.997970i	$0.520284\pi$
$440$		0			0
$441$	4.44583	+	18.3260i	0.211706	+	0.872665i
$442$		0			0
$443$	−6.93574	+	1.33675i	−0.329527	+	0.0635111i	−0.351331	−	0.936251i	$-0.614271\pi$
$443$	−6.93574	+	1.33675i	−0.329527	+	0.0635111i	0.0218046	+	0.999762i	$0.493059\pi$
$444$		0			0
$445$	11.0009	+	12.6957i	0.521491	+	0.601833i
$446$		0			0
$447$	12.7469	−	8.19193i	0.602907	−	0.387465i
$448$		0			0
$449$	−4.57360	+	2.35786i	−0.215842	+	0.111274i	−0.562757	−	0.826622i	$-0.690259\pi$
$449$	−4.57360	+	2.35786i	−0.215842	+	0.111274i	0.346915	+	0.937896i	$0.387229\pi$
$450$		0			0
$451$	3.47008	+	0.668803i	0.163400	+	0.0314927i
$452$		0			0
$453$	6.35142	−	4.99481i	0.298416	−	0.234677i
$454$		0			0
$455$	22.4816	−	25.9452i	1.05396	−	1.21633i
$456$		0			0
$457$	4.22750	−	17.4260i	0.197754	−	0.815153i	−0.783336	−	0.621599i	$-0.786483\pi$
$457$	4.22750	−	17.4260i	0.197754	−	0.815153i	0.981090	−	0.193554i	$-0.0620015\pi$
$458$		0			0
$459$	1.17650	+	0.606530i	0.0549145	+	0.0283104i
$460$		0			0
$461$	12.8005	+	3.75855i	0.596177	+	0.175053i	0.565880	−	0.824488i	$-0.308537\pi$
$461$	12.8005	+	3.75855i	0.596177	+	0.175053i	0.0302969	+	0.999541i	$0.490355\pi$
$462$		0			0
$463$	−30.5708	+	12.2387i	−1.42074	+	0.568780i	−0.949653	−	0.313305i	$-0.898564\pi$
$463$	−30.5708	+	12.2387i	−1.42074	+	0.568780i	−0.471091	+	0.882085i	$0.656140\pi$
$464$		0			0
$465$	−3.13495	−	9.05783i	−0.145380	−	0.420047i
$466$		0			0
$467$	−21.4167	+	30.0755i	−0.991045	+	1.39173i	−0.0720750	+	0.997399i	$0.522962\pi$
$467$	−21.4167	+	30.0755i	−0.991045	+	1.39173i	−0.918970	+	0.394328i	$0.870977\pi$
$468$		0			0
$469$	−1.18833	−	41.6058i	−0.0548721	−	1.92118i
$470$		0			0
$471$	−7.38790	+	10.3749i	−0.340416	+	0.478048i
$472$		0			0
$473$	1.38654	+	4.00614i	0.0637531	+	0.184202i
$474$		0			0
$475$	4.53024	−	1.81363i	0.207862	−	0.0832152i
$476$		0			0
$477$	5.63875	+	1.65569i	0.258181	+	0.0758087i
$478$		0			0
$479$	−24.6666	−	12.7165i	−1.12705	−	0.581032i	−0.209161	−	0.977881i	$-0.567073\pi$
$479$	−24.6666	−	12.7165i	−1.12705	−	0.581032i	−0.917884	+	0.396849i	$0.870104\pi$
$480$		0			0
$481$	−0.0883406	+	0.364145i	−0.00402798	+	0.0166036i
$482$		0			0
$483$	23.4168	−	27.0244i	1.06550	−	1.22965i
$484$		0			0
$485$	17.6216	−	13.8577i	0.800154	−	0.629248i
$486$		0			0
$487$	35.5223	+	6.84636i	1.60967	+	0.310238i	0.913250	−	0.407399i	$-0.133564\pi$
$487$	35.5223	+	6.84636i	1.60967	+	0.310238i	0.696417	+	0.717637i	$0.254776\pi$
$488$		0			0
$489$	−13.7557	+	7.09156i	−0.622055	+	0.320691i
$490$		0			0
$491$	0.788951	−	0.507028i	0.0356049	−	0.0228819i	−0.522717	−	0.852506i	$-0.675082\pi$
$491$	0.788951	−	0.507028i	0.0356049	−	0.0228819i	0.558322	+	0.829624i	$0.311445\pi$
$492$		0			0
$493$	−0.824635	−	0.951679i	−0.0371397	−	0.0428615i
$494$		0			0
$495$	−3.09426	+	0.596370i	−0.139077	+	0.0268048i
$496$		0			0
$497$	6.58591	+	27.1475i	0.295419	+	1.21773i
$498$		0			0
$499$	−3.98180	−	6.89668i	−0.178250	−	0.308738i	0.763031	−	0.646361i	$-0.223710\pi$
$499$	−3.98180	−	6.89668i	−0.178250	−	0.308738i	−0.941281	+	0.337624i	$0.890377\pi$
$500$		0			0
$501$	−0.846936	−	17.7794i	−0.0378383	−	0.794324i
$502$		0			0
$503$	15.4275	+	21.6648i	0.687876	+	0.965987i	0.999874	+	0.0159039i	$0.00506257\pi$
$503$	15.4275	+	21.6648i	0.687876	+	0.965987i	−0.311997	+	0.950083i	$0.600998\pi$
$504$		0			0
$505$	28.7748	−	27.4367i	1.28046	−	1.22092i
$506$		0			0
$507$	−3.13872	+	5.43642i	−0.139395	+	0.241440i
$508$		0			0
$509$	2.43555	−	16.9396i	0.107954	−	0.750834i	−0.861888	−	0.507099i	$-0.830718\pi$
$509$	2.43555	−	16.9396i	0.107954	−	0.750834i	0.969842	−	0.243736i	$-0.0783729\pi$
$510$		0			0
$511$	44.8133	−	13.1584i	1.98242	−	0.582092i
$512$		0			0
$513$	−0.130436	+	2.73818i	−0.00575887	+	0.120894i
$514$		0			0
$515$	6.07568	+	4.77797i	0.267727	+	0.210543i
$516$		0			0
$517$	−3.64577	+	0.348129i	−0.160341	+	0.0153107i
$518$		0			0
$519$	−7.84041	+	22.6534i	−0.344156	+	0.994374i
$520$		0			0
$521$	−1.01120	+	2.21421i	−0.0443013	+	0.0970064i	−0.930489	−	0.366321i	$-0.880617\pi$
$521$	−1.01120	+	2.21421i	−0.0443013	+	0.0970064i	0.886187	+	0.463327i	$0.153345\pi$
$522$		0			0
$523$	−1.20110	−	1.14524i	−0.0525203	−	0.0500780i	0.663364	−	0.748296i	$-0.269128\pi$
$523$	−1.20110	−	1.14524i	−0.0525203	−	0.0500780i	−0.715885	+	0.698218i	$0.753976\pi$
$524$		0			0
$525$	8.40350	+	3.36425i	0.366759	+	0.146828i
$526$		0			0
$527$	2.02408	+	4.43212i	0.0881704	+	0.193066i
$528$		0			0
$529$	−26.3306	−	2.51427i	−1.14481	−	0.109316i
$530$		0			0
$531$	1.34412	+	9.34854i	0.0583297	+	0.405692i
$532$		0			0
$533$	−6.36935	−	4.09333i	−0.275887	−	0.177302i
$534$		0			0
$535$	−14.3244			−0.619297
$536$		0			0
$537$	−5.90891			−0.254988
$538$		0			0
$539$	19.1986	+	12.3382i	0.826944	+	0.531444i
$540$		0			0
$541$	5.78919	+	40.2647i	0.248897	+	1.73111i	0.604612	+	0.796520i	$0.293328\pi$
$541$	5.78919	+	40.2647i	0.248897	+	1.73111i	−0.355715	+	0.934595i	$0.615763\pi$
$542$		0			0
$543$	7.06591	+	0.674712i	0.303227	+	0.0289547i
$544$		0			0
$545$	15.6296	+	34.2240i	0.669497	+	1.46599i
$546$		0			0
$547$	39.4045	+	15.7752i	1.68481	+	0.674498i	0.998600	−	0.0529010i	$-0.0168468\pi$
$547$	39.4045	+	15.7752i	1.68481	+	0.674498i	0.686215	+	0.727399i	$0.259271\pi$
$548$		0			0
$549$	−8.33373	−	7.94620i	−0.355675	−	0.339135i
$550$		0			0
$551$	1.08337	−	2.37225i	0.0461532	−	0.101061i
$552$		0			0
$553$	−23.7820	+	68.7135i	−1.01131	+	2.92199i
$554$		0			0
$555$	−0.374604	+	0.0357703i	−0.0159010	+	0.00151837i
$556$		0			0
$557$	0.201999	+	0.158854i	0.00855898	+	0.00673086i	0.622429	−	0.782676i	$-0.286146\pi$
$557$	0.201999	+	0.158854i	0.00855898	+	0.00673086i	−0.613870	+	0.789407i	$0.710388\pi$
$558$		0			0
$559$	0.432160	−	9.07215i	0.0182784	−	0.383711i
$560$		0			0
$561$	1.53699	−	0.451302i	0.0648920	−	0.0190540i
$562$		0			0
$563$	0.0655681	−	0.456036i	0.00276337	−	0.0192196i	−0.988393	−	0.151918i	$-0.951455\pi$
$563$	0.0655681	−	0.456036i	0.00276337	−	0.0192196i	0.991156	+	0.132698i	$0.0423641\pi$
$564$		0			0
$565$	14.7396	−	25.5297i	0.620099	−	1.07404i
$566$		0			0
$567$	−3.68021	+	3.50907i	−0.154554	+	0.147367i
$568$		0			0
$569$	−18.2488	−	25.6269i	−0.765030	−	1.07433i	−0.994876	−	0.101107i	$-0.967761\pi$
$569$	−18.2488	−	25.6269i	−0.765030	−	1.07433i	0.229846	−	0.973227i	$-0.426178\pi$
$570$		0			0
$571$	0.210531	+	4.41959i	0.00881045	+	0.184954i	0.998983	+	0.0450994i	$0.0143605\pi$
$571$	0.210531	+	4.41959i	0.00881045	+	0.184954i	−0.990172	+	0.139855i	$0.955336\pi$
$572$		0			0
$573$	13.5142	+	23.4072i	0.564563	+	0.977851i
$574$		0			0
$575$	−2.95120	−	12.1650i	−0.123074	−	0.507317i
$576$		0			0
$577$	−17.2535	+	3.32534i	−0.718272	+	0.138436i	−0.535275	−	0.844678i	$-0.679792\pi$
$577$	−17.2535	+	3.32534i	−0.718272	+	0.138436i	−0.182997	+	0.983113i	$0.558580\pi$
$578$		0			0
$579$	−9.82459	−	11.3382i	−0.408296	−	0.471199i
$580$		0			0
$581$	−49.1877	+	31.6110i	−2.04065	+	1.31145i
$582$		0			0
$583$	6.32152	−	3.25897i	0.261810	−	0.134973i
$584$		0			0
$585$	6.62927	+	1.27769i	0.274086	+	0.0528258i
$586$		0			0
$587$	18.2836	−	14.3784i	0.754646	−	0.593460i	−0.164961	−	0.986300i	$-0.552750\pi$
$587$	18.2836	−	14.3784i	0.754646	−	0.593460i	0.919607	+	0.392840i	$0.128507\pi$
$588$		0			0
$589$	−6.60811	+	7.62616i	−0.272282	+	0.314231i
$590$		0			0
$591$	0.177442	−	0.731428i	0.00729901	−	0.0300869i
$592$		0			0
$593$	−14.2831	−	7.36343i	−0.586535	−	0.302380i	0.139298	−	0.990250i	$-0.455515\pi$
$593$	−14.2831	−	7.36343i	−0.586535	−	0.302380i	−0.725833	+	0.687871i	$0.758546\pi$
$594$		0			0
$595$	−16.8161	−	4.93765i	−0.689393	−	0.202424i
$596$		0			0
$597$	−0.266907	+	0.106854i	−0.0109238	+	0.00437323i
$598$		0			0
$599$	−6.12830	−	17.7066i	−0.250396	−	0.723471i	−0.998224	−	0.0595782i	$-0.981024\pi$
$599$	−6.12830	−	17.7066i	−0.250396	−	0.723471i	0.747828	−	0.663893i	$-0.231097\pi$
$600$		0			0
$601$	10.5969	−	14.8812i	0.432256	−	0.607019i	−0.539793	−	0.841798i	$-0.681497\pi$
$601$	10.5969	−	14.8812i	0.432256	−	0.607019i	0.972049	+	0.234779i	$0.0754368\pi$
$602$		0			0
$603$	6.96899	−	4.29339i	0.283799	−	0.174840i
$604$		0			0
$605$	14.4022	−	20.2250i	0.585532	−	0.822264i
$606$		0			0
$607$	10.3878	+	30.0135i	0.421627	+	1.21821i	0.933321	+	0.359043i	$0.116897\pi$
$607$	10.3878	+	30.0135i	0.421627	+	1.21821i	−0.511694	+	0.859168i	$0.670982\pi$
$608$		0			0
$609$	4.49112	−	1.79797i	0.181989	−	0.0728575i
$610$		0			0
$611$	7.52854	+	2.21058i	0.304572	+	0.0894304i
$612$		0			0
$613$	40.5561	+	20.9081i	1.63805	+	0.844472i	0.997036	+	0.0769403i	$0.0245151\pi$
$613$	40.5561	+	20.9081i	1.63805	+	0.844472i	0.641011	+	0.767532i	$0.278515\pi$
$614$		0			0
$615$	1.79262	−	7.38926i	0.0722853	−	0.297964i
$616$		0			0
$617$	7.95089	−	9.17582i	0.320091	−	0.369404i	−0.572786	−	0.819705i	$-0.694138\pi$
$617$	7.95089	−	9.17582i	0.320091	−	0.369404i	0.892877	+	0.450300i	$0.148683\pi$
$618$		0			0
$619$	−14.0746	+	11.0684i	−0.565707	+	0.444877i	−0.859604	−	0.510960i	$-0.829290\pi$
$619$	−14.0746	+	11.0684i	−0.565707	+	0.444877i	0.293897	+	0.955837i	$0.405048\pi$
$620$		0			0
$621$	6.90502	+	1.33083i	0.277089	+	0.0534045i
$622$		0			0
$623$	29.1591	−	15.0326i	1.16824	−	0.602267i
$624$		0			0
$625$	−25.8532	+	16.6148i	−1.03413	+	0.664594i
$626$		0			0
$627$	2.17251	+	2.50721i	0.0867617	+	0.100128i
$628$		0			0
$629$	0.187835	−	0.0362022i	0.00748947	−	0.00144348i
$630$		0			0
$631$	−9.06774	−	37.3777i	−0.360981	−	1.48798i	−0.805706	−	0.592316i	$-0.798214\pi$
$631$	−9.06774	−	37.3777i	−0.360981	−	1.48798i	0.444725	−	0.895667i	$-0.353302\pi$
$632$		0			0
$633$	5.69647	+	9.86657i	0.226414	+	0.392161i
$634$		0			0
$635$	−1.00414	−	21.0796i	−0.0398482	−	0.836517i
$636$		0			0
$637$	−28.3611	−	39.8276i	−1.12371	−	1.57803i
$638$		0			0
$639$	−3.97588	+	3.79099i	−0.157283	+	0.149969i
$640$		0			0
$641$	−22.2329	+	38.5085i	−0.878148	+	1.52100i	−0.0247760	+	0.999693i	$0.507887\pi$
$641$	−22.2329	+	38.5085i	−0.878148	+	1.52100i	−0.853372	+	0.521303i	$0.825446\pi$
$642$		0			0
$643$	−4.71859	+	32.8185i	−0.186083	+	1.29424i	0.655948	+	0.754806i	$0.272269\pi$
$643$	−4.71859	+	32.8185i	−0.186083	+	1.29424i	−0.842031	+	0.539430i	$0.818640\pi$
$644$		0			0
$645$	8.75176	−	2.56975i	0.344600	−	0.101184i
$646$		0			0
$647$	−0.109205	+	2.29250i	−0.00429329	+	0.0901273i	−0.999997	−	0.00246981i	$-0.999214\pi$
$647$	−0.109205	+	2.29250i	−0.00429329	+	0.0901273i	0.995704	+	0.0925971i	$0.0295169\pi$
$648$		0			0
$649$	8.98457	+	7.06555i	0.352675	+	0.277347i
$650$		0			0
$651$	−18.6336	+	1.77929i	−0.730308	+	0.0697359i
$652$		0			0
$653$	8.01127	−	23.1470i	0.313505	−	0.905814i	−0.672646	−	0.739964i	$-0.734842\pi$
$653$	8.01127	−	23.1470i	0.313505	−	0.905814i	0.986151	−	0.165849i	$-0.0530365\pi$
$654$		0			0
$655$	10.6456	−	23.3106i	0.415958	−	0.910820i
$656$		0			0
$657$	6.64738	+	6.33826i	0.259339	+	0.247279i
$658$		0			0
$659$	−36.4518	−	14.5931i	−1.41996	−	0.568466i	−0.470513	−	0.882393i	$-0.655931\pi$
$659$	−36.4518	−	14.5931i	−1.41996	−	0.568466i	−0.949447	+	0.313927i	$0.898355\pi$
$660$		0			0
$661$	−5.44884	−	11.9313i	−0.211935	−	0.464074i	0.773572	−	0.633709i	$-0.218468\pi$
$661$	−5.44884	−	11.9313i	−0.211935	−	0.464074i	−0.985507	+	0.169635i	$0.945741\pi$
$662$		0			0
$663$	−3.41640	−	0.326226i	−0.132682	−	0.0126696i
$664$		0			0
$665$	−5.16555	−	35.9272i	−0.200311	−	1.39320i
$666$		0			0
$667$	−5.62798	−	3.61688i	−0.217916	−	0.140046i
$668$		0			0
$669$	−16.9559			−0.655554
$670$		0			0
$671$	−13.9354			−0.537970
$672$		0			0
$673$	14.6855	+	9.43778i	0.566083	+	0.363800i	0.792163	−	0.610309i	$-0.208955\pi$
$673$	14.6855	+	9.43778i	0.566083	+	0.363800i	−0.226080	+	0.974109i	$0.572591\pi$
$674$		0			0
$675$	0.253336	+	1.76199i	0.00975090	+	0.0678190i
$676$		0			0
$677$	−24.4573	−	2.33539i	−0.939971	−	0.0897564i	−0.386191	−	0.922419i	$-0.626209\pi$
$677$	−24.4573	−	2.33539i	−0.939971	−	0.0897564i	−0.553781	+	0.832663i	$0.686815\pi$
$678$		0			0
$679$	−18.1865	−	39.8229i	−0.697935	−	1.52826i
$680$		0			0
$681$	−25.2609	−	10.1129i	−0.967999	−	0.387528i
$682$		0			0
$683$	−35.0684	−	33.4376i	−1.34185	−	1.27945i	−0.929689	−	0.368345i	$-0.879925\pi$
$683$	−35.0684	−	33.4376i	−1.34185	−	1.27945i	−0.412164	−	0.911110i	$-0.635227\pi$
$684$		0			0
$685$	−16.9410	+	37.0957i	−0.647284	+	1.41735i
$686$		0			0
$687$	−3.89584	+	11.2563i	−0.148636	+	0.429454i
$688$		0			0
$689$	−15.1683	+	1.44840i	−0.577867	+	0.0551796i
$690$		0			0
$691$	−32.5304	−	25.5822i	−1.23751	−	0.973192i	−0.999998	−	0.00180900i	$-0.999424\pi$
$691$	−32.5304	−	25.5822i	−1.23751	−	0.973192i	−0.237517	−	0.971383i	$-0.576333\pi$
$692$		0			0
$693$	−0.292816	+	6.14695i	−0.0111231	+	0.233503i
$694$		0			0
$695$	21.2994	−	6.25407i	0.807932	−	0.237230i
$696$		0			0
$697$	−0.550076	+	3.82586i	−0.0208356	+	0.144915i
$698$		0			0
$699$	1.03719	−	1.79647i	0.0392302	−	0.0679487i
$700$		0			0
$701$	−2.84899	+	2.71650i	−0.107605	+	0.102601i	−0.741972	−	0.670431i	$-0.766109\pi$
$701$	−2.84899	+	2.71650i	−0.107605	+	0.102601i	0.634367	+	0.773032i	$0.281261\pi$
$702$		0			0
$703$	0.229800	+	0.322709i	0.00866707	+	0.0121712i
$704$		0			0
$705$	0.374940	+	7.87096i	0.0141211	+	0.296437i
$706$		0			0
$707$	−38.8220	−	67.2417i	−1.46005	−	2.52888i
$708$		0			0
$709$	11.4182	+	47.0664i	0.428819	+	1.76762i	0.618516	+	0.785772i	$0.287734\pi$
$709$	11.4182	+	47.0664i	0.428819	+	1.76762i	−0.189697	+	0.981843i	$0.560751\pi$
$710$		0			0
$711$	−14.0409	+	2.70617i	−0.526576	+	0.101489i
$712$		0			0
$713$	16.9515	+	19.5631i	0.634838	+	0.732642i
$714$		0			0
$715$	6.87339	−	4.41726i	0.257050	−	0.165196i
$716$		0			0
$717$	−20.6295	+	10.6353i	−0.770424	+	0.397181i
$718$		0			0
$719$	−7.88549	−	1.51980i	−0.294079	−	0.0566791i	0.0400778	−	0.999197i	$-0.487239\pi$
$719$	−7.88549	−	1.51980i	−0.294079	−	0.0566791i	−0.334157	+	0.942517i	$0.608452\pi$
$720$		0			0
$721$	11.8651	−	9.33080i	0.441878	−	0.347497i
$722$		0			0
$723$	−17.1765	+	19.8227i	−0.638800	+	0.737215i
$724$		0			0
$725$	0.399260	−	1.64577i	0.0148281	−	0.0611224i
$726$		0			0
$727$	14.2289	+	7.33552i	0.527721	+	0.272059i	0.701431	−	0.712738i	$-0.252545\pi$
$727$	14.2289	+	7.33552i	0.527721	+	0.272059i	−0.173709	+	0.984797i	$0.555575\pi$
$728$		0			0
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$		0			0
$731$	−4.30454	+	1.72328i	−0.159209	+	0.0637378i
$732$		0			0
$733$	6.07907	+	17.5643i	0.224535	+	0.648753i	0.999852	+	0.0171803i	$0.00546892\pi$
$733$	6.07907	+	17.5643i	0.224535	+	0.648753i	−0.775317	+	0.631572i	$0.782410\pi$
$734$		0			0
$735$	28.4822	−	39.9977i	1.05058	−	1.47534i
$736$		0			0
$737$	2.51833	−	9.58049i	0.0927639	−	0.352902i
$738$		0			0
$739$	25.8843	−	36.3495i	0.952171	−	1.33714i	0.0107361	−	0.999942i	$-0.496583\pi$
$739$	25.8843	−	36.3495i	0.952171	−	1.33714i	0.941435	−	0.337195i	$-0.109478\pi$
$740$		0			0
$741$	−2.32466	−	6.71667i	−0.0853986	−	0.246743i
$742$		0			0
$743$	18.9324	−	7.57941i	0.694564	−	0.278061i	0.00260315	−	0.999997i	$-0.499171\pi$
$743$	18.9324	−	7.57941i	0.694564	−	0.278061i	0.691961	+	0.721935i	$0.256747\pi$
$744$		0			0
$745$	−37.8563	−	11.1156i	−1.38695	−	0.407244i
$746$		0			0
$747$	−10.2202	−	5.26886i	−0.373936	−	0.192778i
$748$		0			0
$749$	−6.59507	+	27.1852i	−0.240979	+	0.993327i
$750$		0			0
$751$	20.5666	−	23.7351i	0.750486	−	0.866107i	−0.244129	−	0.969743i	$-0.578502\pi$
$751$	20.5666	−	23.7351i	0.750486	−	0.866107i	0.994615	+	0.103636i	$0.0330476\pi$
$752$		0			0
$753$	−21.5637	+	16.9579i	−0.785824	+	0.617979i
$754$		0			0
$755$	−20.6594	−	3.98177i	−0.751872	−	0.144911i
$756$		0			0
$757$	30.7784	−	15.8674i	1.11866	−	0.576709i	0.203208	−	0.979136i	$-0.434863\pi$
$757$	30.7784	−	15.8674i	1.11866	−	0.576709i	0.915452	+	0.402426i	$0.131833\pi$
$758$		0			0
$759$	7.15930	−	4.60100i	0.259866	−	0.167006i
$760$		0			0
$761$	−21.9926	−	25.3808i	−0.797232	−	0.920055i	0.200994	−	0.979592i	$-0.435583\pi$
$761$	−21.9926	−	25.3808i	−0.797232	−	0.920055i	−0.998226	+	0.0595378i	$0.981037\pi$
$762$		0			0
$763$	72.1472	−	13.9052i	2.61190	−	0.503403i
$764$		0			0
$765$	−0.812565	−	3.34944i	−0.0293784	−	0.121099i
$766$		0			0
$767$	−12.2440	−	21.2073i	−0.442106	−	0.765750i
$768$		0			0
$769$	−0.998755	−	20.9664i	−0.0360160	−	0.756069i	−0.942576	−	0.333992i	$-0.891604\pi$
$769$	−0.998755	−	20.9664i	−0.0360160	−	0.756069i	0.906560	−	0.422077i	$-0.138699\pi$
$770$		0			0
$771$	12.6988	+	17.8330i	0.457336	+	0.642239i
$772$		0			0
$773$	7.21325	−	6.87782i	0.259442	−	0.247378i	−0.549182	−	0.835703i	$-0.685061\pi$
$773$	7.21325	−	6.87782i	0.259442	−	0.247378i	0.808625	+	0.588325i	$0.200212\pi$
$774$		0			0
$775$	−3.27635	+	5.67480i	−0.117690	+	0.203845i
$776$		0			0
$777$	−0.104585	+	0.727403i	−0.00375196	+	0.0260954i
$778$		0			0
$779$	−7.68063	+	2.25524i	−0.275187	+	0.0808023i
$780$		0			0
$781$	−0.316341	+	6.64081i	−0.0113196	+	0.237627i
$782$		0			0
$783$	0.747813	+	0.588086i	0.0267246	+	0.0210165i
$784$		0			0
$785$	33.0140	−	3.15245i	1.17832	−	0.112516i
$786$		0			0
$787$	−2.21892	+	6.41116i	−0.0790961	+	0.228533i	−0.977615	−	0.210402i	$-0.932523\pi$
$787$	−2.21892	+	6.41116i	−0.0790961	+	0.228533i	0.898519	+	0.438935i	$0.144644\pi$
$788$		0			0
$789$	−3.19270	+	6.99103i	−0.113663	+	0.248887i
$790$		0			0
$791$	−41.6648	−	39.7273i	−1.48143	−	1.41254i
$792$		0			0
$793$	27.7171	+	11.0963i	0.984263	+	0.394040i
$794$		0			0
$795$	−6.35685	−	13.9195i	−0.225454	−	0.493676i
$796$		0			0
$797$	3.85303	+	0.367919i	0.136481	+	0.0130324i	0.163073	−	0.986614i	$-0.447859\pi$
$797$	3.85303	+	0.367919i	0.136481	+	0.0130324i	−0.0265919	+	0.999646i	$0.508465\pi$
$798$		0			0
$799$	−0.570064	−	3.96488i	−0.0201674	−	0.140267i
$800$		0			0
$801$	5.42733	+	3.48794i	0.191765	+	0.123240i
$802$		0			0
$803$	11.1155			0.392258
$804$		0			0
$805$	−93.1101			−3.28170
$806$		0			0
$807$	15.1604	+	9.74300i	0.533672	+	0.342970i
$808$		0			0
$809$	−7.52841	−	52.3613i	−0.264685	−	1.84092i	−0.496343	−	0.868127i	$-0.665324\pi$
$809$	−7.52841	−	52.3613i	−0.264685	−	1.84092i	0.231658	−	0.972797i	$-0.425585\pi$
$810$		0			0
$811$	−12.9148	−	1.23321i	−0.453498	−	0.0433038i	−0.134192	−	0.990955i	$-0.542844\pi$
$811$	−12.9148	−	1.23321i	−0.453498	−	0.0433038i	−0.319306	+	0.947652i	$0.603450\pi$
$812$		0			0
$813$	−1.01345	−	2.21915i	−0.0355434	−	0.0778291i
$814$		0			0
$815$	37.4111	+	14.9771i	1.31045	+	0.524626i
$816$		0			0
$817$	−6.94974	−	6.62656i	−0.243141	−	0.231834i
$818$		0			0
$819$	5.47700	−	11.9930i	0.191382	−	0.419068i
$820$		0			0
$821$	−14.0956	+	40.7266i	−0.491941	+	1.42137i	0.376889	+	0.926258i	$0.376994\pi$
$821$	−14.0956	+	40.7266i	−0.491941	+	1.42137i	−0.868830	+	0.495111i	$0.835127\pi$
$822$		0			0
$823$	−1.47837	+	0.141167i	−0.0515326	+	0.00492077i	−0.120791	−	0.992678i	$-0.538543\pi$
$823$	−1.47837	+	0.141167i	−0.0515326	+	0.00492077i	0.0692579	+	0.997599i	$0.477937\pi$
$824$		0			0
$825$	1.69339	+	1.33170i	0.0589563	+	0.0463637i
$826$		0			0
$827$	−0.762319	+	16.0031i	−0.0265084	+	0.556481i	0.946078	+	0.323939i	$0.105007\pi$
$827$	−0.762319	+	16.0031i	−0.0265084	+	0.556481i	−0.972586	+	0.232542i	$0.925296\pi$
$828$		0			0
$829$	−7.53555	+	2.21264i	−0.261721	+	0.0768481i	−0.409960	−	0.912103i	$-0.634457\pi$
$829$	−7.53555	+	2.21264i	−0.261721	+	0.0768481i	0.148240	+	0.988951i	$0.452639\pi$
$830$		0			0
$831$	−0.546858	+	3.80348i	−0.0189703	+	0.131941i
$832$		0			0
$833$	−12.4803	+	21.6166i	−0.432418	+	0.748970i
$834$		0			0
$835$	−33.5433	+	31.9835i	−1.16081	+	1.10683i
$836$		0			0
$837$	−2.13523	−	2.99851i	−0.0738043	−	0.103644i
$838$		0			0
$839$	0.556571	+	11.6839i	0.0192150	+	0.403372i	0.987901	+	0.155084i	$0.0495648\pi$
$839$	0.556571	+	11.6839i	0.0192150	+	0.403372i	−0.968686	+	0.248288i	$0.920132\pi$
$840$		0			0
$841$	14.0475	+	24.3309i	0.484395	+	0.838997i
$842$		0			0
$843$	7.51016	+	30.9573i	0.258664	+	1.06623i
$844$		0			0
$845$	16.0502	−	3.09343i	0.552144	−	0.106417i
$846$		0			0
$847$	−31.7528	−	36.6447i	−1.09104	−	1.25913i
$848$		0			0
$849$	19.5850	−	12.5865i	0.672156	−	0.431968i
$850$		0			0
$851$	0.903298	−	0.465682i	0.0309646	−	0.0159634i
$852$		0			0
$853$	20.5162	+	3.95418i	0.702463	+	0.135389i	0.527961	−	0.849268i	$-0.322957\pi$
$853$	20.5162	+	3.95418i	0.702463	+	0.135389i	0.174501	+	0.984657i	$0.444169\pi$
$854$		0			0
$855$	5.61080	−	4.41238i	0.191885	−	0.150900i
$856$		0			0
$857$	17.8400	−	20.5884i	0.609402	−	0.703288i	−0.364256	−	0.931299i	$-0.618677\pi$
$857$	17.8400	−	20.5884i	0.609402	−	0.703288i	0.973659	+	0.228011i	$0.0732222\pi$
$858$		0			0
$859$	−1.00555	+	4.14492i	−0.0343088	+	0.141423i	−0.986390	−	0.164423i	$-0.947424\pi$
$859$	−1.00555	+	4.14492i	−0.0343088	+	0.141423i	0.952081	+	0.305845i	$0.0989391\pi$
$860$		0			0
$861$	−13.1982	−	6.80416i	−0.449794	−	0.231885i
$862$		0			0
$863$	41.9400	+	12.3147i	1.42765	+	0.419197i	0.902086	−	0.431556i	$-0.142035\pi$
$863$	41.9400	+	12.3147i	1.42765	+	0.419197i	0.525566	+	0.850753i	$0.323853\pi$
$864$		0			0
$865$	57.9481	−	23.1989i	1.97030	−	0.788787i
$866$		0			0
$867$	−4.98712	−	14.4093i	−0.169371	−	0.489367i
$868$		0			0
$869$	−10.0380	+	14.0963i	−0.340514	+	0.478186i
$870$		0			0
$871$	−12.6375	+	17.0501i	−0.428205	+	0.577720i
$872$		0			0
$873$	4.99396	−	7.01303i	0.169020	−	0.237355i
$874$		0			0
$875$	13.9441	+	40.2889i	0.471397	+	1.36201i
$876$		0			0
$877$	−12.4727	+	4.99331i	−0.421173	+	0.168612i	−0.572561	−	0.819862i	$-0.694050\pi$
$877$	−12.4727	+	4.99331i	−0.421173	+	0.168612i	0.151388	+	0.988474i	$0.451626\pi$
$878$		0			0
$879$	−7.53424	−	2.21225i	−0.254124	−	0.0746175i
$880$		0			0
$881$	−42.0457	−	21.6761i	−1.41656	−	0.730285i	−0.431434	−	0.902144i	$-0.641992\pi$
$881$	−42.0457	−	21.6761i	−1.41656	−	0.730285i	−0.985122	+	0.171859i	$0.945023\pi$
$882$		0			0
$883$	10.3965	−	42.8548i	0.349869	−	1.44218i	−0.476561	−	0.879141i	$-0.658117\pi$
$883$	10.3965	−	42.8548i	0.349869	−	1.44218i	0.826430	−	0.563039i	$-0.190368\pi$
$884$		0			0
$885$	16.1048	−	18.5859i	0.541355	−	0.624757i
$886$		0			0
$887$	−13.8397	+	10.8837i	−0.464692	+	0.365438i	−0.822883	−	0.568210i	$-0.807636\pi$
$887$	−13.8397	+	10.8837i	−0.464692	+	0.365438i	0.358191	+	0.933648i	$0.383394\pi$
$888$		0			0
$889$	−40.4678	−	7.79952i	−1.35725	−	0.261588i
$890$		0			0
$891$	−1.07567	+	0.554548i	−0.0360364	+	0.0185780i
$892$		0			0
$893$	6.97883	−	4.48502i	0.233538	−	0.150086i
$894$		0			0
$895$	10.0757	+	11.6280i	0.336793	+	0.388680i
$896$		0			0
$897$	−17.9033	+	3.45057i	−0.597772	+	0.115211i
$898$		0			0
$899$	0.825625	+	3.40327i	0.0275361	+	0.113506i
$900$		0			0
$901$	3.88940	+	6.73664i	0.129575	+	0.224430i
$902$		0			0
$903$	−0.847560	−	17.7925i	−0.0282050	−	0.592097i
$904$		0			0
$905$	−10.7208	−	15.0553i	−0.356372	−	0.500454i
$906$		0			0
$907$	5.96422	−	5.68688i	0.198039	−	0.188830i	−0.584570	−	0.811343i	$-0.698737\pi$
$907$	5.96422	−	5.68688i	0.198039	−	0.188830i	0.782609	+	0.622513i	$0.213888\pi$
$908$		0			0
$909$	7.63456	−	13.2235i	0.253223	−	0.438594i
$910$		0			0
$911$	−4.38806	+	30.5196i	−0.145383	+	1.01116i	0.778270	+	0.627930i	$0.216098\pi$
$911$	−4.38806	+	30.5196i	−0.145383	+	1.01116i	−0.923653	+	0.383230i	$0.874812\pi$
$912$		0			0
$913$	−13.3517	+	3.92042i	−0.441877	+	0.129747i
$914$		0			0
$915$	−1.42666	+	29.9493i	−0.0471639	+	0.990093i
$916$		0			0
$917$	−39.3382	−	30.9359i	−1.29906	−	1.02159i
$918$		0			0
$919$	19.1984	−	1.83323i	0.633298	−	0.0604726i	0.226530	−	0.974004i	$-0.427262\pi$
$919$	19.1984	−	1.83323i	0.633298	−	0.0604726i	0.406768	+	0.913532i	$0.366656\pi$
$920$		0			0
$921$	−0.635166	+	1.83519i	−0.0209294	+	0.0604716i
$922$		0			0
$923$	5.91703	−	12.9565i	0.194761	−	0.426468i
$924$		0			0
$925$	0.186187	+	0.177529i	0.00612180	+	0.00583713i
$926$		0			0
$927$	2.75578	+	1.10325i	0.0905118	+	0.0362355i
$928$		0			0
$929$	13.8789	+	30.3905i	0.455351	+	0.997079i	0.988523	+	0.151072i	$0.0482726\pi$
$929$	13.8789	+	30.3905i	0.455351	+	0.997079i	−0.533172	+	0.846007i	$0.679000\pi$
$930$		0			0
$931$	−51.4598	−	4.91382i	−1.68653	−	0.161044i
$932$		0			0
$933$	0.192688	+	1.34017i	0.00630832	+	0.0438753i
$934$		0			0
$935$	−3.50894	−	2.25506i	−0.114755	−	0.0737483i
$936$		0			0
$937$	32.0606			1.04737			0.523686	−	0.851911i	$-0.324556\pi$
$937$	32.0606			1.04737			0.523686	+	0.851911i	$0.324556\pi$
$938$		0			0
$939$	−6.06478			−0.197917
$940$		0			0
$941$	16.8386	+	10.8215i	0.548923	+	0.352771i	0.785520	−	0.618837i	$-0.212396\pi$
$941$	16.8386	+	10.8215i	0.548923	+	0.352771i	−0.236597	+	0.971608i	$0.576032\pi$
$942$		0			0
$943$	2.92237	+	20.3256i	0.0951656	+	0.661891i
$944$		0			0
$945$	13.1808	+	1.25861i	0.428771	+	0.0409426i
$946$		0			0
$947$	15.0040	+	32.8542i	0.487565	+	1.06762i	0.980314	+	0.197447i	$0.0632651\pi$
$947$	15.0040	+	32.8542i	0.487565	+	1.06762i	−0.492748	+	0.870172i	$0.664008\pi$
$948$		0			0
$949$	−22.1085	−	8.85090i	−0.717671	−	0.287312i
$950$		0			0
$951$	2.74511	+	2.61746i	0.0890164	+	0.0848770i
$952$		0			0
$953$	8.22334	−	18.0066i	0.266380	−	0.583291i	−0.728421	−	0.685130i	$-0.759745\pi$
$953$	8.22334	−	18.0066i	0.266380	−	0.583291i	0.994801	+	0.101839i	$0.0324727\pi$
$954$		0			0
$955$	23.0184	−	66.5074i	0.744859	−	2.15213i
$956$		0			0
$957$	1.14612	−	0.109441i	0.0370487	−	0.00353772i
$958$		0			0
$959$	62.6015	+	49.2304i	2.02151	+	1.58973i
$960$		0			0
$961$	−0.830292	+	17.4300i	−0.0267836	+	0.562257i
$962$		0			0
$963$	−5.27837	+	1.54987i	−0.170093	+	0.0499438i
$964$		0			0
$965$	−5.55948	+	38.6670i	−0.178966	+	1.24474i
$966$		0			0
$967$	−22.3414	+	38.6965i	−0.718452	+	1.24439i	0.243162	+	0.969986i	$0.421815\pi$
$967$	−22.3414	+	38.6965i	−0.718452	+	1.24439i	−0.961613	+	0.274409i	$0.911518\pi$
$968$		0			0
$969$	−2.62606	+	2.50395i	−0.0843613	+	0.0804383i
$970$		0			0
$971$	−29.8578	−	41.9294i	−0.958183	−	1.34558i	−0.938317	−	0.345777i	$-0.887615\pi$
$971$	−29.8578	−	41.9294i	−0.958183	−	1.34558i	−0.0198664	−	0.999803i	$-0.506324\pi$
$972$		0			0
$973$	−2.06273	−	43.3021i	−0.0661281	−	1.38820i
$974$		0			0
$975$	−2.30772	−	3.99709i	−0.0739063	−	0.128009i
$976$		0			0
$977$	1.90848	+	7.86688i	0.0610578	+	0.251684i	0.994158	−	0.107932i	$-0.0344229\pi$
$977$	1.90848	+	7.86688i	0.0610578	+	0.251684i	−0.933100	+	0.359616i	$0.882908\pi$
$978$		0			0
$979$	7.66652	−	1.47760i	0.245023	−	0.0472243i
$980$		0			0
$981$	9.46227	+	10.9200i	0.302107	+	0.348650i
$982$		0			0
$983$	17.2558	−	11.0896i	0.550373	−	0.353703i	−0.235711	−	0.971823i	$-0.575742\pi$
$983$	17.2558	−	11.0896i	0.550373	−	0.353703i	0.786084	+	0.618120i	$0.212105\pi$
$984$		0			0
$985$	−1.74192	+	0.898024i	−0.0555023	+	0.0286134i
$986$		0			0
$987$	15.1104	+	2.91228i	0.480968	+	0.0926990i
$988$		0			0
$989$	−19.3630	+	15.2272i	−0.615706	+	0.484197i
$990$		0			0
$991$	−29.0713	+	33.5500i	−0.923480	+	1.06575i	0.0741711	+	0.997246i	$0.476369\pi$
$991$	−29.0713	+	33.5500i	−0.923480	+	1.06575i	−0.997651	+	0.0685067i	$0.978177\pi$
$992$		0			0
$993$	3.39989	−	14.0145i	0.107892	−	0.444737i
$994$		0			0
$995$	0.665396	+	0.343036i	0.0210945	+	0.0108750i
$996$		0			0
$997$	−23.1155	−	6.78733i	−0.732076	−	0.214957i	−0.105612	−	0.994407i	$-0.533680\pi$
$997$	−23.1155	−	6.78733i	−0.732076	−	0.214957i	−0.626464	+	0.779451i	$0.715498\pi$
$998$		0			0
$999$	−0.134167	+	0.0537123i	−0.00424485	+	0.00169938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.49.5	✓	120
67.26	even	33	inner	804.2.y.b.361.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.49.5	✓	120	1.1	even	1	trivial
804.2.y.b.361.5	yes	120	67.26	even	33	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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{3} +(0.370568 + 2.57736i) q^{5} +(5.06200 + 0.483363i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{3} +(0.370568 + 2.57736i) q^{5} +(5.06200 + 0.483363i) q^{7} +(0.415415 + 0.909632i) q^{9} +(1.12351 + 0.449787i) q^{11} +(-1.87649 - 1.78923i) q^{13} +(1.08168 - 2.36856i) q^{15} +(-0.432922 + 1.25085i) q^{17} +(-2.72887 + 0.260576i) q^{19} +(-3.99710 - 3.14336i) q^{21} +(-0.334601 + 7.02413i) q^{23} +(-1.70800 + 0.501514i) q^{25} +(0.142315 - 0.989821i) q^{27} +(-0.475676 + 0.823894i) q^{29} +(2.66411 - 2.54023i) q^{31} +(-0.701987 - 0.985803i) q^{33} +(0.630019 + 13.2257i) q^{35} +(-0.0722595 - 0.125157i) q^{37} +(0.611273 + 2.51970i) q^{39} +(2.86735 - 0.552636i) q^{41} +(2.29395 + 2.64736i) q^{43} +(-2.19051 + 1.40776i) q^{45} +(-2.68982 + 1.38670i) q^{47} +(18.5167 + 3.56881i) q^{49} +(1.04046 - 0.818224i) q^{51} +(3.84849 - 4.44139i) q^{53} +(-0.742925 + 3.06238i) q^{55} +(2.43655 + 1.25613i) q^{57} +(9.06210 + 2.66087i) q^{59} +(-10.6901 + 4.27966i) q^{61} +(1.66315 + 4.80536i) q^{63} +(3.91612 - 5.49942i) q^{65} +(-1.01038 - 8.12275i) q^{67} +(4.07902 - 5.72818i) q^{69} +(1.79677 + 5.19142i) q^{71} +(8.52691 - 3.41366i) q^{73} +(1.70800 + 0.501514i) q^{75} +(5.46983 + 2.81989i) q^{77} +(-3.37120 + 13.8963i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(-9.03833 + 7.10782i) q^{83} +(-3.38431 - 0.652272i) q^{85} +(0.845595 - 0.435934i) q^{87} +(5.42733 - 3.48794i) q^{89} +(-8.63395 - 9.96411i) q^{91} +(-3.61455 + 0.696647i) q^{93} +(-1.68283 - 6.93673i) q^{95} +(-4.30471 - 7.45598i) q^{97} +(0.0575838 + 1.20883i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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