LMFDB - Embedded newform 804.2.q.b.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(25,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.q (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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			193.1
Character	$\chi$	$=$	804.193
Dual form			804.2.q.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(-3.19644 - 2.05423i) q^{5} +(-0.0504230 + 0.350699i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(-3.19644 - 2.05423i) q^{5} +(-0.0504230 + 0.350699i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(0.990890 + 0.636806i) q^{11} +(2.04519 + 4.47833i) q^{13} +(-0.540741 - 3.76094i) q^{15} +(2.93464 - 0.861688i) q^{17} +(0.418195 + 2.90861i) q^{19} +(-0.298061 + 0.191552i) q^{21} +(0.101789 + 0.117470i) q^{23} +(3.92029 + 8.58425i) q^{25} +(-0.841254 + 0.540641i) q^{27} +10.1618 q^{29} +(-1.39787 + 3.06091i) q^{31} +(0.167629 + 1.16588i) q^{33} +(0.881590 - 1.01741i) q^{35} +3.68070 q^{37} +(-2.04519 + 4.47833i) q^{39} +(3.40130 - 0.998712i) q^{41} +(3.71322 - 1.09030i) q^{43} +(2.48822 - 2.87156i) q^{45} +(2.23068 + 2.57434i) q^{47} +(6.59600 + 1.93676i) q^{49} +(2.57300 + 1.65357i) q^{51} +(-8.63420 - 2.53523i) q^{53} +(-1.85917 - 4.07102i) q^{55} +(-1.92432 + 2.22079i) q^{57} +(-3.22648 + 7.06500i) q^{59} +(-8.93334 + 5.74111i) q^{61} +(-0.339954 - 0.0998195i) q^{63} +(2.66220 - 18.5160i) q^{65} +(-4.51019 + 6.83068i) q^{67} +(-0.0221208 + 0.153854i) q^{69} +(-9.64253 - 2.83130i) q^{71} +(-1.96622 + 1.26361i) q^{73} +(-3.92029 + 8.58425i) q^{75} +(-0.273291 + 0.315395i) q^{77} +(-3.74200 - 8.19384i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(10.9313 + 7.02512i) q^{83} +(-11.1505 - 3.27408i) q^{85} +(6.65454 + 7.67975i) q^{87} +(-3.15184 + 3.63741i) q^{89} +(-1.67367 + 0.491435i) q^{91} +(-3.22869 + 0.948029i) q^{93} +(4.63821 - 10.1563i) q^{95} +1.62324 q^{97} +(-0.771343 + 0.890177i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$	$1$

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
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$		0			0
$5$	−3.19644	−	2.05423i	−1.42949	−	0.918678i	−0.999877	−	0.0156645i	$-0.995014\pi$
$5$	−3.19644	−	2.05423i	−1.42949	−	0.918678i	−0.429613	−	0.903013i	$-0.641350\pi$
$6$		0			0
$7$	−0.0504230	+	0.350699i	−0.0190581	+	0.132552i	−0.997129	−	0.0757195i	$-0.975875\pi$
$7$	−0.0504230	+	0.350699i	−0.0190581	+	0.132552i	0.978071	+	0.208271i	$0.0667837\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	0.990890	+	0.636806i	0.298765	+	0.192004i	0.681431	−	0.731882i	$-0.261358\pi$
$11$	0.990890	+	0.636806i	0.298765	+	0.192004i	−0.382667	+	0.923886i	$0.624994\pi$
$12$		0			0
$13$	2.04519	+	4.47833i	0.567233	+	1.24207i	0.948258	+	0.317502i	$0.102844\pi$
$13$	2.04519	+	4.47833i	0.567233	+	1.24207i	−0.381025	+	0.924565i	$0.624429\pi$
$14$		0			0
$15$	−0.540741	−	3.76094i	−0.139619	−	0.971070i
$16$		0			0
$17$	2.93464	−	0.861688i	0.711755	−	0.208990i	0.0942403	−	0.995549i	$-0.469958\pi$
$17$	2.93464	−	0.861688i	0.711755	−	0.208990i	0.617515	+	0.786559i	$0.288140\pi$
$18$		0			0
$19$	0.418195	+	2.90861i	0.0959405	+	0.667281i	0.979866	+	0.199654i	$0.0639819\pi$
$19$	0.418195	+	2.90861i	0.0959405	+	0.667281i	−0.883926	+	0.467627i	$0.845109\pi$
$20$		0			0
$21$	−0.298061	+	0.191552i	−0.0650422	+	0.0418001i
$22$		0			0
$23$	0.101789	+	0.117470i	0.0212244	+	0.0244943i	0.766263	−	0.642528i	$-0.222114\pi$
$23$	0.101789	+	0.117470i	0.0212244	+	0.0244943i	−0.745038	+	0.667022i	$0.767569\pi$
$24$		0			0
$25$	3.92029	+	8.58425i	0.784059	+	1.71685i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	10.1618			1.88699			0.943496	−	0.331384i	$-0.107515\pi$
$29$	10.1618			1.88699			0.943496	+	0.331384i	$0.107515\pi$
$30$		0			0
$31$	−1.39787	+	3.06091i	−0.251065	+	0.549755i	−0.992638	−	0.121116i	$-0.961353\pi$
$31$	−1.39787	+	3.06091i	−0.251065	+	0.549755i	0.741573	+	0.670872i	$0.234080\pi$
$32$		0			0
$33$	0.167629	+	1.16588i	0.0291804	+	0.202954i
$34$		0			0
$35$	0.881590	−	1.01741i	0.149016	−	0.171973i
$36$		0			0
$37$	3.68070			0.605103			0.302552	−	0.953133i	$-0.402162\pi$
$37$	3.68070			0.605103			0.302552	+	0.953133i	$0.402162\pi$
$38$		0			0
$39$	−2.04519	+	4.47833i	−0.327492	+	0.717107i
$40$		0			0
$41$	3.40130	−	0.998712i	0.531194	−	0.155973i	−0.00512677	−	0.999987i	$-0.501632\pi$
$41$	3.40130	−	0.998712i	0.531194	−	0.155973i	0.536321	+	0.844014i	$0.319814\pi$
$42$		0			0
$43$	3.71322	−	1.09030i	0.566261	−	0.166269i	0.0139431	−	0.999903i	$-0.495562\pi$
$43$	3.71322	−	1.09030i	0.566261	−	0.166269i	0.552318	+	0.833634i	$0.313743\pi$
$44$		0			0
$45$	2.48822	−	2.87156i	0.370921	−	0.428066i
$46$		0			0
$47$	2.23068	+	2.57434i	0.325378	+	0.375506i	0.894745	−	0.446577i	$-0.147357\pi$
$47$	2.23068	+	2.57434i	0.325378	+	0.375506i	−0.569367	+	0.822083i	$0.692812\pi$
$48$		0			0
$49$	6.59600	+	1.93676i	0.942286	+	0.276680i
$50$		0			0
$51$	2.57300	+	1.65357i	0.360292	+	0.231546i
$52$		0			0
$53$	−8.63420	−	2.53523i	−1.18600	−	0.348241i	−0.371515	−	0.928427i	$-0.621162\pi$
$53$	−8.63420	−	2.53523i	−1.18600	−	0.348241i	−0.814484	+	0.580186i	$0.802980\pi$
$54$		0			0
$55$	−1.85917	−	4.07102i	−0.250691	−	0.548937i
$56$		0			0
$57$	−1.92432	+	2.22079i	−0.254883	+	0.294150i
$58$		0			0
$59$	−3.22648	+	7.06500i	−0.420051	+	0.919784i	0.574786	+	0.818304i	$0.305085\pi$
$59$	−3.22648	+	7.06500i	−0.420051	+	0.919784i	−0.994838	+	0.101481i	$0.967642\pi$
$60$		0			0
$61$	−8.93334	+	5.74111i	−1.14380	+	0.735073i	−0.968394	−	0.249424i	$-0.919759\pi$
$61$	−8.93334	+	5.74111i	−1.14380	+	0.735073i	−0.175402	+	0.984497i	$0.556122\pi$
$62$		0			0
$63$	−0.339954	−	0.0998195i	−0.0428302	−	0.0125761i
$64$		0			0
$65$	2.66220	−	18.5160i	0.330205	−	2.29663i
$66$		0			0
$67$	−4.51019	+	6.83068i	−0.551007	+	0.834500i
$67$	−4.51019	+	6.83068i	−0.551007	+	0.834500i
$68$		0			0
$69$	−0.0221208	+	0.153854i	−0.00266303	+	0.0185218i
$70$		0			0
$71$	−9.64253	−	2.83130i	−1.14436	−	0.336014i	−0.346022	−	0.938226i	$-0.612468\pi$
$71$	−9.64253	−	2.83130i	−1.14436	−	0.336014i	−0.798336	+	0.602212i	$0.794286\pi$
$72$		0			0
$73$	−1.96622	+	1.26361i	−0.230128	+	0.147894i	−0.650624	−	0.759400i	$-0.725493\pi$
$73$	−1.96622	+	1.26361i	−0.230128	+	0.147894i	0.420496	+	0.907295i	$0.361856\pi$
$74$		0			0
$75$	−3.92029	+	8.58425i	−0.452677	+	0.991223i
$76$		0			0
$77$	−0.273291	+	0.315395i	−0.0311444	+	0.0359426i
$78$		0			0
$79$	−3.74200	−	8.19384i	−0.421008	−	0.921879i	−0.994701	−	0.102808i	$-0.967217\pi$
$79$	−3.74200	−	8.19384i	−0.421008	−	0.921879i	0.573693	−	0.819070i	$-0.305510\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	10.9313	+	7.02512i	1.19987	+	0.771107i	0.978933	−	0.204182i	$-0.0654534\pi$
$83$	10.9313	+	7.02512i	1.19987	+	0.771107i	0.220933	+	0.975289i	$0.429090\pi$
$84$		0			0
$85$	−11.1505	−	3.27408i	−1.20944	−	0.355124i
$86$		0			0
$87$	6.65454	+	7.67975i	0.713442	+	0.823355i
$88$		0			0
$89$	−3.15184	+	3.63741i	−0.334094	+	0.385565i	−0.897795	−	0.440414i	$-0.854832\pi$
$89$	−3.15184	+	3.63741i	−0.334094	+	0.385565i	0.563701	+	0.825979i	$0.309377\pi$
$90$		0			0
$91$	−1.67367	+	0.491435i	−0.175449	+	0.0515164i
$92$		0			0
$93$	−3.22869	+	0.948029i	−0.334800	+	0.0983061i
$94$		0			0
$95$	4.63821	−	10.1563i	0.475870	−	1.04201i
$96$		0			0
$97$	1.62324			0.164815			0.0824075	−	0.996599i	$-0.473739\pi$
$97$	1.62324			0.164815			0.0824075	+	0.996599i	$0.473739\pi$
$98$		0			0
$99$	−0.771343	+	0.890177i	−0.0775229	+	0.0894662i
$100$		0			0
$101$	−2.15735	−	15.0047i	−0.214665	−	1.49302i	−0.757306	−	0.653060i	$-0.773485\pi$
$101$	−2.15735	−	15.0047i	−0.214665	−	1.49302i	0.542641	−	0.839965i	$-0.317424\pi$
$102$		0			0
$103$	7.65969	−	16.7724i	0.754731	−	1.65263i	−0.00294037	−	0.999996i	$-0.500936\pi$
$103$	7.65969	−	16.7724i	0.754731	−	1.65263i	0.757672	−	0.652636i	$-0.226337\pi$
$104$		0			0
$105$	1.34622			0.131378
$106$		0			0
$107$	−7.38961	+	4.74901i	−0.714381	+	0.459105i	−0.846678	−	0.532106i	$-0.821401\pi$
$107$	−7.38961	+	4.74901i	−0.714381	+	0.459105i	0.132297	+	0.991210i	$0.457765\pi$
$108$		0			0
$109$	0.637789	+	1.39656i	0.0610891	+	0.133766i	0.937714	−	0.347407i	$-0.112938\pi$
$109$	0.637789	+	1.39656i	0.0610891	+	0.133766i	−0.876625	+	0.481174i	$0.840211\pi$
$110$		0			0
$111$	2.41035	+	2.78169i	0.228780	+	0.264026i
$112$		0			0
$113$	−1.84619	+	1.18647i	−0.173675	+	0.111614i	−0.624590	−	0.780953i	$-0.714734\pi$
$113$	−1.84619	+	1.18647i	−0.173675	+	0.111614i	0.450915	+	0.892567i	$0.351098\pi$
$114$		0			0
$115$	−0.0840505	−	0.584584i	−0.00783775	−	0.0545127i
$116$		0			0
$117$	−4.72381	+	1.38704i	−0.436717	+	0.128232i
$118$		0			0
$119$	0.154220	+	1.07263i	0.0141374	+	0.0983274i
$120$		0			0
$121$	−3.99322	−	8.74394i	−0.363020	−	0.794904i
$122$		0			0
$123$	2.98216	+	1.91651i	0.268892	+	0.172806i
$124$		0			0
$125$	2.39930	−	16.6875i	0.214600	−	1.49257i
$126$		0			0
$127$	−0.783573	+	5.44987i	−0.0695309	+	0.483598i	0.925068	+	0.379802i	$0.124008\pi$
$127$	−0.783573	+	5.44987i	−0.0695309	+	0.483598i	−0.994599	+	0.103796i	$0.966901\pi$
$128$		0			0
$129$	3.25564	+	2.09227i	0.286643	+	0.184214i
$130$		0			0
$131$	8.56859	+	9.88868i	0.748641	+	0.863978i	0.994436	−	0.105344i	$-0.0335945\pi$
$131$	8.56859	+	9.88868i	0.748641	+	0.863978i	−0.245795	+	0.969322i	$0.579049\pi$
$132$		0			0
$133$	−1.04113			−0.0902778
$134$		0			0
$135$	3.79961			0.327019
$136$		0			0
$137$	4.77631	+	5.51215i	0.408068	+	0.470935i	0.922165	−	0.386797i	$-0.126418\pi$
$137$	4.77631	+	5.51215i	0.408068	+	0.470935i	−0.514097	+	0.857732i	$0.671873\pi$
$138$		0			0
$139$	17.3993	+	11.1818i	1.47579	+	0.948431i	0.997532	+	0.0702105i	$0.0223671\pi$
$139$	17.3993	+	11.1818i	1.47579	+	0.948431i	0.478256	+	0.878221i	$0.341269\pi$
$140$		0			0
$141$	−0.484772	+	3.37167i	−0.0408252	+	0.283946i
$142$		0			0
$143$	−0.825277	+	5.73993i	−0.0690131	+	0.479997i
$144$		0			0
$145$	−32.4814	−	20.8746i	−2.69744	−	1.73354i
$146$		0			0
$147$	2.85576	+	6.25324i	0.235539	+	0.515758i
$148$		0			0
$149$	−3.19812	−	22.2434i	−0.262000	−	1.82225i	−0.517775	−	0.855517i	$-0.673240\pi$
$149$	−3.19812	−	22.2434i	−0.262000	−	1.82225i	0.255775	−	0.966736i	$-0.417669\pi$
$150$		0			0
$151$	−0.482637	+	0.141715i	−0.0392765	+	0.0115326i	−0.301312	−	0.953526i	$-0.597424\pi$
$151$	−0.482637	+	0.141715i	−0.0392765	+	0.0115326i	0.262035	+	0.965058i	$0.415606\pi$
$152$		0			0
$153$	0.435275	+	3.02740i	0.0351899	+	0.244751i
$154$		0			0
$155$	10.7560	−	6.91246i	0.863943	−	0.555222i
$156$		0			0
$157$	10.1380	+	11.6999i	0.809104	+	0.933756i	0.998844	−	0.0480786i	$-0.0153098\pi$
$157$	10.1380	+	11.6999i	0.809104	+	0.933756i	−0.189740	+	0.981834i	$0.560764\pi$
$158$		0			0
$159$	−3.73820	−	8.18552i	−0.296459	−	0.649154i
$160$		0			0
$161$	−0.0463293	+	0.0297740i	−0.00365126	+	0.00234652i
$162$		0			0
$163$	12.8084			1.00323			0.501616	−	0.865090i	$-0.332739\pi$
$163$	12.8084			1.00323			0.501616	+	0.865090i	$0.332739\pi$
$164$		0			0
$165$	1.85917	−	4.07102i	0.144737	−	0.316929i
$166$		0			0
$167$	−1.20015	−	8.34719i	−0.0928700	−	0.645925i	−0.982085	−	0.188436i	$-0.939658\pi$
$167$	−1.20015	−	8.34719i	−0.0928700	−	0.645925i	0.889215	−	0.457489i	$-0.151251\pi$
$168$		0			0
$169$	−7.35950	+	8.49332i	−0.566116	+	0.653332i
$170$		0			0
$171$	−2.93852			−0.224714
$172$		0			0
$173$	2.72820	−	5.97394i	0.207422	−	0.454190i	−0.777117	−	0.629356i	$-0.783319\pi$
$173$	2.72820	−	5.97394i	0.207422	−	0.454190i	0.984539	+	0.175166i	$0.0560461\pi$
$174$		0			0
$175$	−3.20816	+	0.942002i	−0.242514	+	0.0712086i
$176$		0			0
$177$	−7.45226	+	2.18818i	−0.560146	+	0.164474i
$178$		0			0
$179$	−1.71515	+	1.97939i	−0.128196	+	0.147946i	−0.816219	−	0.577743i	$-0.803934\pi$
$179$	−1.71515	+	1.97939i	−0.128196	+	0.147946i	0.688022	+	0.725689i	$0.258479\pi$
$180$		0			0
$181$	4.25971	+	4.91597i	0.316622	+	0.365401i	0.891644	−	0.452736i	$-0.149552\pi$
$181$	4.25971	+	4.91597i	0.316622	+	0.365401i	−0.575022	+	0.818138i	$0.695007\pi$
$182$		0			0
$183$	−10.1889	−	2.99174i	−0.753187	−	0.221156i
$184$		0			0
$185$	−11.7651	−	7.56099i	−0.864989	−	0.555895i
$186$		0			0
$187$	3.45664	+	1.01496i	0.252774	+	0.0742212i
$188$		0			0
$189$	−0.147184	−	0.322288i	−0.0107061	−	0.0234430i
$190$		0			0
$191$	3.84249	−	4.43447i	0.278033	−	0.320867i	−0.599508	−	0.800369i	$-0.704637\pi$
$191$	3.84249	−	4.43447i	0.278033	−	0.320867i	0.877541	+	0.479502i	$0.159183\pi$
$192$		0			0
$193$	9.68025	−	21.1968i	0.696800	−	1.52578i	−0.147009	−	0.989135i	$-0.546965\pi$
$193$	9.68025	−	21.1968i	0.696800	−	1.52578i	0.843809	−	0.536644i	$-0.180308\pi$
$194$		0			0
$195$	15.7368	−	10.1134i	1.12694	−	0.724239i
$196$		0			0
$197$	−5.60867	−	1.64685i	−0.399601	−	0.117334i	0.0757560	−	0.997126i	$-0.475863\pi$
$197$	−5.60867	−	1.64685i	−0.399601	−	0.117334i	−0.475357	+	0.879793i	$0.657681\pi$
$198$		0			0
$199$	−0.136409	+	0.948747i	−0.00966979	+	0.0672549i	−0.994085	−	0.108605i	$-0.965362\pi$
$199$	−0.136409	+	0.948747i	−0.00966979	+	0.0672549i	0.984415	+	0.175860i	$0.0562706\pi$
$200$		0			0
$201$	−8.11583	+	1.06457i	−0.572446	+	0.0750890i
$202$		0			0
$203$	−0.512386	+	3.56372i	−0.0359625	+	0.250124i
$204$		0			0
$205$	−12.9236	−	3.79472i	−0.902625	−	0.265035i
$206$		0			0
$207$	−0.130761	+	0.0840349i	−0.00908850	+	0.00584083i
$208$		0			0
$209$	−1.43784	+	3.14842i	−0.0994573	+	0.217781i
$210$		0			0
$211$	−7.94880	+	9.17340i	−0.547218	+	0.631523i	−0.960233	−	0.279201i	$-0.909930\pi$
$211$	−7.94880	+	9.17340i	−0.547218	+	0.631523i	0.413015	+	0.910724i	$0.364476\pi$
$212$		0			0
$213$	−4.17476	−	9.14145i	−0.286050	−	0.626362i
$214$		0			0
$215$	−14.1088	−	4.14272i	−0.962212	−	0.282531i
$216$		0			0
$217$	−1.00297	−	0.644572i	−0.0680863	−	0.0437564i
$218$		0			0
$219$	−2.24257	−	0.658478i	−0.151539	−	0.0444958i
$220$		0			0
$221$	9.86082	+	11.3800i	0.663310	+	0.765501i
$222$		0			0
$223$	−13.9501	+	16.0992i	−0.934166	+	1.07809i	0.0626249	+	0.998037i	$0.480053\pi$
$223$	−13.9501	+	16.0992i	−0.934166	+	1.07809i	−0.996791	+	0.0800480i	$0.974493\pi$
$224$		0			0
$225$	−9.05479	+	2.65873i	−0.603653	+	0.177248i
$226$		0			0
$227$	4.47940	−	1.31527i	0.297308	−	0.0872975i	−0.129677	−	0.991556i	$-0.541394\pi$
$227$	4.47940	−	1.31527i	0.297308	−	0.0872975i	0.426985	+	0.904259i	$0.359576\pi$
$228$		0			0
$229$	−0.665416	+	1.45706i	−0.0439719	+	0.0962851i	−0.930343	−	0.366690i	$-0.880491\pi$
$229$	−0.665416	+	1.45706i	−0.0439719	+	0.0962851i	0.886371	+	0.462975i	$0.153218\pi$
$230$		0			0
$231$	−0.417327			−0.0274581
$232$		0			0
$233$	12.5886	−	14.5281i	0.824709	−	0.951764i	−0.174752	−	0.984613i	$-0.555912\pi$
$233$	12.5886	−	14.5281i	0.824709	−	0.951764i	0.999460	+	0.0328480i	$0.0104577\pi$
$234$		0			0
$235$	−1.84195	−	12.8110i	−0.120155	−	0.835699i
$236$		0			0
$237$	3.74200	−	8.19384i	0.243069	−	0.532247i
$238$		0			0
$239$	−12.1902			−0.788519			−0.394259	−	0.918999i	$-0.628999\pi$
$239$	−12.1902			−0.788519			−0.394259	+	0.918999i	$0.628999\pi$
$240$		0			0
$241$	2.56763	−	1.65012i	0.165396	−	0.106293i	−0.455324	−	0.890326i	$-0.650477\pi$
$241$	2.56763	−	1.65012i	0.165396	−	0.106293i	0.620720	+	0.784032i	$0.286840\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	−17.1052	−	19.7404i	−1.09281	−	1.26117i
$246$		0			0
$247$	−12.1704	+	7.82147i	−0.774387	+	0.497668i
$248$		0			0
$249$	1.84925	+	12.8618i	0.117191	+	0.815083i
$250$		0			0
$251$	−26.2792	+	7.71628i	−1.65873	+	0.487047i	−0.971032	−	0.238950i	$-0.923197\pi$
$251$	−26.2792	+	7.71628i	−1.65873	+	0.487047i	−0.687698	+	0.725997i	$0.741379\pi$
$252$		0			0
$253$	0.0260555	+	0.181220i	0.00163810	+	0.0113932i
$254$		0			0
$255$	−4.82764	−	10.5711i	−0.302318	−	0.661985i
$256$		0			0
$257$	−20.7090	−	13.3088i	−1.29179	−	0.830182i	−0.299496	−	0.954098i	$-0.596819\pi$
$257$	−20.7090	−	13.3088i	−1.29179	−	0.830182i	−0.992293	+	0.123915i	$0.960455\pi$
$258$		0			0
$259$	−0.185592	+	1.29082i	−0.0115321	+	0.0802076i
$260$		0			0
$261$	−1.44617	+	10.0583i	−0.0895157	+	0.622595i
$262$		0			0
$263$	−4.65896	−	2.99413i	−0.287284	−	0.184626i	0.389059	−	0.921213i	$-0.372800\pi$
$263$	−4.65896	−	2.99413i	−0.287284	−	0.184626i	−0.676343	+	0.736587i	$0.736436\pi$
$264$		0			0
$265$	22.3908	+	25.8403i	1.37545	+	1.58736i
$266$		0			0
$267$	−4.81299			−0.294550
$268$		0			0
$269$	−16.3292			−0.995609			−0.497804	−	0.867289i	$-0.665860\pi$
$269$	−16.3292			−0.995609			−0.497804	+	0.867289i	$0.665860\pi$
$270$		0			0
$271$	−6.16037	−	7.10945i	−0.374216	−	0.431868i	0.537136	−	0.843495i	$-0.319506\pi$
$271$	−6.16037	−	7.10945i	−0.374216	−	0.431868i	−0.911352	+	0.411627i	$0.864961\pi$
$272$		0			0
$273$	−1.46743	−	0.943057i	−0.0888126	−	0.0570764i
$274$		0			0
$275$	−1.58192	+	11.0025i	−0.0953935	+	0.663477i
$276$		0			0
$277$	0.0346367	−	0.240903i	0.00208112	−	0.0144745i	−0.988754	−	0.149548i	$-0.952218\pi$
$277$	0.0346367	−	0.240903i	0.00208112	−	0.0144745i	0.990836	+	0.135074i	$0.0431272\pi$
$278$		0			0
$279$	−2.83082	−	1.81925i	−0.169477	−	0.108916i
$280$		0			0
$281$	2.95729	+	6.47555i	0.176417	+	0.386299i	0.977097	−	0.212792i	$-0.0682558\pi$
$281$	2.95729	+	6.47555i	0.176417	+	0.386299i	−0.800681	+	0.599092i	$0.795529\pi$
$282$		0			0
$283$	−0.805306	−	5.60103i	−0.0478705	−	0.332947i	−0.999657	−	0.0261857i	$-0.991664\pi$
$283$	−0.805306	−	5.60103i	−0.0478705	−	0.332947i	0.951787	−	0.306761i	$-0.0992452\pi$
$284$		0			0
$285$	10.7130	−	3.14561i	0.634582	−	0.186330i
$286$		0			0
$287$	0.178744	+	1.24319i	0.0105509	+	0.0733833i
$288$		0			0
$289$	−6.43170	+	4.13340i	−0.378335	+	0.243141i
$290$		0			0
$291$	1.06300	+	1.22676i	0.0623139	+	0.0719141i
$292$		0			0
$293$	−0.531981	−	1.16488i	−0.0310787	−	0.0680528i	0.893456	−	0.449151i	$-0.148273\pi$
$293$	−0.531981	−	1.16488i	−0.0310787	−	0.0680528i	−0.924535	+	0.381098i	$0.875546\pi$
$294$		0			0
$295$	24.8263	−	15.9549i	1.44544	−	0.928931i
$296$		0			0
$297$	−1.17787			−0.0683472
$298$		0			0
$299$	−0.317895	+	0.696093i	−0.0183843	+	0.0402561i
$300$		0			0
$301$	0.195136	+	1.35720i	0.0112475	+	0.0782278i
$302$		0			0
$303$	9.92704	−	11.4564i	0.570294	−	0.658154i
$304$		0			0
$305$	40.3484			2.31034
$306$		0			0
$307$	−10.3712	+	22.7098i	−0.591916	+	1.29611i	0.342362	+	0.939568i	$0.388773\pi$
$307$	−10.3712	+	22.7098i	−0.591916	+	1.29611i	−0.934278	+	0.356547i	$0.883954\pi$
$308$		0			0
$309$	17.6917	−	5.19477i	1.00645	−	0.295520i
$310$		0			0
$311$	11.9827	−	3.51845i	0.679478	−	0.199513i	0.0762587	−	0.997088i	$-0.475703\pi$
$311$	11.9827	−	3.51845i	0.679478	−	0.199513i	0.603219	+	0.797575i	$0.293884\pi$
$312$		0			0
$313$	9.97368	−	11.5102i	0.563746	−	0.650597i	−0.400284	−	0.916391i	$-0.631089\pi$
$313$	9.97368	−	11.5102i	0.563746	−	0.650597i	0.964030	+	0.265794i	$0.0856340\pi$
$314$		0			0
$315$	0.881590	+	1.01741i	0.0496719	+	0.0573245i
$316$		0			0
$317$	5.74303	+	1.68630i	0.322560	+	0.0947123i	0.439004	−	0.898485i	$-0.355331\pi$
$317$	5.74303	+	1.68630i	0.322560	+	0.0947123i	−0.116444	+	0.993197i	$0.537149\pi$
$318$		0			0
$319$	10.0692	+	6.47108i	0.563767	+	0.362311i
$320$		0			0
$321$	−8.42823	−	2.47475i	−0.470418	−	0.138127i
$322$		0			0
$323$	3.73357	+	8.17538i	0.207741	+	0.454890i
$324$		0			0
$325$	−30.4254	+	35.1128i	−1.68770	+	1.94771i
$326$		0			0
$327$	−0.637789	+	1.39656i	−0.0352698	+	0.0772301i
$328$		0			0
$329$	−1.01530	+	0.652491i	−0.0559751	+	0.0359730i
$330$		0			0
$331$	26.1610	+	7.68156i	1.43794	+	0.422217i	0.905534	−	0.424273i	$-0.139470\pi$
$331$	26.1610	+	7.68156i	1.43794	+	0.422217i	0.532404	+	0.846490i	$0.321289\pi$
$332$		0			0
$333$	−0.523818	+	3.64324i	−0.0287051	+	0.199648i
$334$		0			0
$335$	28.4483	−	12.5689i	1.55430	−	0.686712i
$336$		0			0
$337$	4.21333	−	29.3044i	0.229515	−	1.59631i	−0.470644	−	0.882323i	$-0.655978\pi$
$337$	4.21333	−	29.3044i	0.229515	−	1.59631i	0.700159	−	0.713987i	$-0.253113\pi$
$338$		0			0
$339$	−2.10567	−	0.618281i	−0.114364	−	0.0335804i
$340$		0			0
$341$	−3.33434	+	2.14285i	−0.180565	+	0.116042i
$342$		0			0
$343$	−2.04210	+	4.47157i	−0.110263	+	0.241442i
$344$		0			0
$345$	0.386758	−	0.446342i	0.0208223	−	0.0240303i
$346$		0			0
$347$	10.3942	+	22.7601i	0.557990	+	1.22183i	0.952950	+	0.303129i	$0.0980313\pi$
$347$	10.3942	+	22.7601i	0.557990	+	1.22183i	−0.394960	+	0.918698i	$0.629241\pi$
$348$		0			0
$349$	17.8085	+	5.22905i	0.953268	+	0.279905i	0.721147	−	0.692782i	$-0.243615\pi$
$349$	17.8085	+	5.22905i	0.953268	+	0.279905i	0.232121	+	0.972687i	$0.425433\pi$
$350$		0			0
$351$	−4.14169	−	2.66170i	−0.221067	−	0.142071i
$352$		0			0
$353$	19.4090	+	5.69900i	1.03304	+	0.303327i	0.753945	−	0.656937i	$-0.228148\pi$
$353$	19.4090	+	5.69900i	1.03304	+	0.303327i	0.279092	+	0.960264i	$0.409967\pi$
$354$		0			0
$355$	25.0056	+	28.8580i	1.32716	+	1.53162i
$356$		0			0
$357$	−0.709644	+	0.818972i	−0.0375583	+	0.0433446i
$358$		0			0
$359$	−32.4753	+	9.53560i	−1.71398	+	0.503269i	−0.983690	−	0.179870i	$-0.942432\pi$
$359$	−32.4753	+	9.53560i	−1.71398	+	0.503269i	−0.730288	+	0.683139i	$0.760614\pi$
$360$		0			0
$361$	9.94524	−	2.92018i	0.523433	−	0.153694i
$362$		0			0
$363$	3.99322	−	8.74394i	0.209590	−	0.458938i
$364$		0			0
$365$	8.88063			0.464833
$366$		0			0
$367$	17.3088	−	19.9754i	0.903510	−	1.04271i	−0.0953729	−	0.995442i	$-0.530404\pi$
$367$	17.3088	−	19.9754i	0.903510	−	1.04271i	0.998882	−	0.0472640i	$-0.0150502\pi$
$368$		0			0
$369$	0.504491	+	3.50881i	0.0262628	+	0.182661i
$370$		0			0
$371$	1.32447	−	2.90018i	0.0687629	−	0.150570i
$372$		0			0
$373$	−14.2728			−0.739017			−0.369508	−	0.929227i	$-0.620474\pi$
$373$	−14.2728			−0.739017			−0.369508	+	0.929227i	$0.620474\pi$
$374$		0			0
$375$	14.1828	−	9.11471i	0.732395	−	0.470682i
$376$		0			0
$377$	20.7827	+	45.5078i	1.07036	+	2.34377i
$378$		0			0
$379$	−23.2036	−	26.7784i	−1.19189	−	1.37551i	−0.909231	−	0.416293i	$-0.863329\pi$
$379$	−23.2036	−	26.7784i	−1.19189	−	1.37551i	−0.282659	−	0.959221i	$-0.591216\pi$
$380$		0			0
$381$	−4.63187	+	2.97672i	−0.237298	+	0.152502i
$382$		0			0
$383$	2.62435	+	18.2527i	0.134098	+	0.932672i	0.940134	+	0.340805i	$0.110700\pi$
$383$	2.62435	+	18.2527i	0.134098	+	0.932672i	−0.806036	+	0.591867i	$0.798391\pi$
$384$		0			0
$385$	1.52145	−	0.446738i	0.0775403	−	0.0227679i
$386$		0			0
$387$	0.550756	+	3.83059i	0.0279965	+	0.194720i
$388$		0			0
$389$	14.2617	+	31.2288i	0.723098	+	1.58336i	0.809512	+	0.587104i	$0.199732\pi$
$389$	14.2617	+	31.2288i	0.723098	+	1.58336i	−0.0864137	+	0.996259i	$0.527541\pi$
$390$		0			0
$391$	0.399936	+	0.257023i	0.0202256	+	0.0129982i
$392$		0			0
$393$	−1.86213	+	12.9514i	−0.0939321	+	0.653312i
$394$		0			0
$395$	−4.87092	+	33.8780i	−0.245083	+	1.70459i
$396$		0			0
$397$	2.48859	+	1.59932i	0.124899	+	0.0802675i	0.601598	−	0.798799i	$-0.294531\pi$
$397$	2.48859	+	1.59932i	0.124899	+	0.0802675i	−0.476700	+	0.879066i	$0.658167\pi$
$398$		0			0
$399$	−0.681798	−	0.786837i	−0.0341326	−	0.0393911i
$400$		0			0
$401$	−31.3647			−1.56628			−0.783140	−	0.621845i	$-0.786383\pi$
$401$	−31.3647			−1.56628			−0.783140	+	0.621845i	$0.786383\pi$
$402$		0			0
$403$	−16.5667			−0.825245
$404$		0			0
$405$	2.48822	+	2.87156i	0.123640	+	0.142689i
$406$		0			0
$407$	3.64717	+	2.34389i	0.180783	+	0.116182i
$408$		0			0
$409$	1.55104	−	10.7877i	0.0766939	−	0.533418i	−0.914865	−	0.403760i	$-0.867703\pi$
$409$	1.55104	−	10.7877i	0.0766939	−	0.533418i	0.991559	−	0.129658i	$-0.0413879\pi$
$410$		0			0
$411$	−1.03799	+	7.21939i	−0.0512003	+	0.356106i
$412$		0			0
$413$	−2.31500	−	1.48776i	−0.113914	−	0.0732080i
$414$		0			0
$415$	−20.5100	−	44.9107i	−1.00680	−	2.20458i
$416$		0			0
$417$	2.94344	+	20.4720i	0.144141	+	1.00252i
$418$		0			0
$419$	8.88773	−	2.60967i	0.434194	−	0.127491i	−0.0573292	−	0.998355i	$-0.518258\pi$
$419$	8.88773	−	2.60967i	0.434194	−	0.127491i	0.491523	+	0.870864i	$0.336440\pi$
$420$		0			0
$421$	−0.172086	−	1.19688i	−0.00838696	−	0.0583326i	0.985198	−	0.171419i	$-0.0548353\pi$
$421$	−0.172086	−	1.19688i	−0.00838696	−	0.0583326i	−0.993585	+	0.113087i	$0.963926\pi$
$422$		0			0
$423$	−2.86559	+	1.84161i	−0.139330	+	0.0895419i
$424$		0			0
$425$	18.9016	+	21.8136i	0.916862	+	1.05812i
$426$		0			0
$427$	−1.56296	−	3.42240i	−0.0756368	−	0.165622i
$428$		0			0
$429$	−4.87839	+	3.13515i	−0.235531	+	0.151366i
$430$		0			0
$431$	17.6289			0.849156			0.424578	−	0.905391i	$-0.360423\pi$
$431$	17.6289			0.849156			0.424578	+	0.905391i	$0.360423\pi$
$432$		0			0
$433$	11.6413	−	25.4909i	0.559444	−	1.22501i	−0.392785	−	0.919630i	$-0.628488\pi$
$433$	11.6413	−	25.4909i	0.559444	−	1.22501i	0.952230	−	0.305382i	$-0.0987842\pi$
$434$		0			0
$435$	−5.49488	−	38.2178i	−0.263460	−	1.83240i
$436$		0			0
$437$	−0.299108	+	0.345189i	−0.0143083	+	0.0165126i
$438$		0			0
$439$	26.4401			1.26192			0.630959	−	0.775816i	$-0.282661\pi$
$439$	26.4401			1.26192			0.630959	+	0.775816i	$0.282661\pi$
$440$		0			0
$441$	−2.85576	+	6.25324i	−0.135988	+	0.297773i
$442$		0			0
$443$	−0.325591	+	0.0956022i	−0.0154693	+	0.00454220i	−0.289458	−	0.957191i	$-0.593475\pi$
$443$	−0.325591	+	0.0956022i	−0.0154693	+	0.00454220i	0.273989	+	0.961733i	$0.411657\pi$
$444$		0			0
$445$	17.5467	−	5.15218i	0.831794	−	0.244237i
$446$		0			0
$447$	14.7161	−	16.9833i	0.696049	−	0.803284i
$448$		0			0
$449$	5.46323	+	6.30490i	0.257826	+	0.297547i	0.869874	−	0.493273i	$-0.164200\pi$
$449$	5.46323	+	6.30490i	0.257826	+	0.297547i	−0.612049	+	0.790820i	$0.709654\pi$
$450$		0			0
$451$	4.00630	+	1.17636i	0.188649	+	0.0553925i
$452$		0			0
$453$	−0.423161	−	0.271949i	−0.0198819	−	0.0127773i
$454$		0			0
$455$	6.35931	+	1.86726i	0.298129	+	0.0875386i
$456$		0			0
$457$	−6.74236	−	14.7637i	−0.315394	−	0.690617i	0.683845	−	0.729628i	$-0.260307\pi$
$457$	−6.74236	−	14.7637i	−0.315394	−	0.690617i	−0.999239	+	0.0390106i	$0.987579\pi$
$458$		0			0
$459$	−2.00291	+	2.31149i	−0.0934880	+	0.107891i
$460$		0			0
$461$	1.21962	−	2.67060i	0.0568034	−	0.124382i	−0.879102	−	0.476634i	$-0.841857\pi$
$461$	1.21962	−	2.67060i	0.0568034	−	0.124382i	0.935905	+	0.352252i	$0.114584\pi$
$462$		0			0
$463$	−12.0853	+	7.76675i	−0.561652	+	0.360952i	−0.790454	−	0.612521i	$-0.790155\pi$
$463$	−12.0853	+	7.76675i	−0.561652	+	0.360952i	0.228802	+	0.973473i	$0.426519\pi$
$464$		0			0
$465$	12.2678	+	3.60214i	0.568904	+	0.167045i
$466$		0			0
$467$	3.48857	−	24.2635i	0.161432	−	1.12278i	−0.734506	−	0.678602i	$-0.762586\pi$
$467$	3.48857	−	24.2635i	0.161432	−	1.12278i	0.895938	−	0.444180i	$-0.146505\pi$
$468$		0			0
$469$	−2.16810	−	1.92614i	−0.100113	−	0.0889411i
$470$		0			0
$471$	−2.20321	+	15.3236i	−0.101518	+	0.706076i
$472$		0			0
$473$	4.37371	+	1.28424i	0.201103	+	0.0590492i
$474$		0			0
$475$	−23.3288	+	14.9925i	−1.07040	+	0.687903i
$476$		0			0
$477$	3.73820	−	8.18552i	0.171160	−	0.374789i
$478$		0			0
$479$	−26.7115	+	30.8267i	−1.22048	+	1.40851i	−0.336045	+	0.941846i	$0.609089\pi$
$479$	−26.7115	+	30.8267i	−1.22048	+	1.40851i	−0.884435	+	0.466663i	$0.845456\pi$
$480$		0			0
$481$	7.52772	+	16.4834i	0.343234	+	0.751578i
$482$		0			0
$483$	−0.0528410	−	0.0155155i	−0.00240435	−	0.000705980i
$484$		0			0
$485$	−5.18858	−	3.33450i	−0.235601	−	0.151412i
$486$		0			0
$487$	−0.262833	−	0.0771748i	−0.0119101	−	0.00349712i	0.275772	−	0.961223i	$-0.411066\pi$
$487$	−0.262833	−	0.0771748i	−0.0119101	−	0.00349712i	−0.287682	+	0.957726i	$0.592885\pi$
$488$		0			0
$489$	8.38772	+	9.67995i	0.379306	+	0.437742i
$490$		0			0
$491$	−8.01760	+	9.25281i	−0.361829	+	0.417573i	−0.907252	−	0.420588i	$-0.861824\pi$
$491$	−8.01760	+	9.25281i	−0.361829	+	0.417573i	0.545422	+	0.838161i	$0.316369\pi$
$492$		0			0
$493$	29.8211	−	8.75627i	1.34308	−	0.394363i
$494$		0			0
$495$	4.29418	−	1.26088i	0.193009	−	0.0566725i
$496$		0			0
$497$	1.47914	−	3.23887i	0.0663486	−	0.145283i
$498$		0			0
$499$	−19.5844			−0.876718			−0.438359	−	0.898800i	$-0.644440\pi$
$499$	−19.5844			−0.876718			−0.438359	+	0.898800i	$0.644440\pi$
$500$		0			0
$501$	5.52246	−	6.37326i	0.246725	−	0.284736i
$502$		0			0
$503$	−4.56388	−	31.7425i	−0.203494	−	1.41533i	−0.793814	−	0.608160i	$-0.791908\pi$
$503$	−4.56388	−	31.7425i	−0.203494	−	1.41533i	0.590321	−	0.807169i	$-0.299001\pi$
$504$		0			0
$505$	−23.9272	+	52.3933i	−1.06475	+	2.33147i
$506$		0			0
$507$	−11.2383			−0.499109
$508$		0			0
$509$	−6.22712	+	4.00193i	−0.276012	+	0.177382i	−0.671322	−	0.741165i	$-0.734273\pi$
$509$	−6.22712	+	4.00193i	−0.276012	+	0.177382i	0.395310	+	0.918548i	$0.370637\pi$
$510$		0			0
$511$	−0.344005	−	0.753266i	−0.0152179	−	0.0333225i
$512$		0			0
$513$	−1.92432	−	2.22079i	−0.0849609	−	0.0980501i
$514$		0			0
$515$	−58.9380	+	37.8771i	−2.59712	+	1.66907i
$516$		0			0
$517$	0.571001	+	3.97140i	0.0251126	+	0.174662i
$518$		0			0
$519$	6.30139	−	1.85026i	0.276600	−	0.0812172i
$520$		0			0
$521$	−0.426051	−	2.96325i	−0.0186656	−	0.129822i	0.978358	−	0.206920i	$-0.0663439\pi$
$521$	−0.426051	−	2.96325i	−0.0186656	−	0.129822i	−0.997024	+	0.0770974i	$0.975435\pi$
$522$		0			0
$523$	−9.87342	−	21.6198i	−0.431735	−	0.945367i	−0.993042	−	0.117760i	$-0.962429\pi$
$523$	−9.87342	−	21.6198i	−0.431735	−	0.945367i	0.561307	−	0.827607i	$-0.310299\pi$
$524$		0			0
$525$	−2.81282	−	1.80769i	−0.122761	−	0.0788940i
$526$		0			0
$527$	−1.46470	+	10.1872i	−0.0638032	+	0.443761i
$528$		0			0
$529$	3.26980	−	22.7420i	0.142165	−	0.988782i
$530$		0			0
$531$	−6.53391	−	4.19909i	−0.283548	−	0.182225i
$532$		0			0
$533$	11.4289	+	13.1896i	0.495039	+	0.571306i
$534$		0			0
$535$	33.3760			1.44297
$536$		0			0
$537$	−2.61910			−0.113023
$538$		0			0
$539$	5.30257	+	6.11950i	0.228398	+	0.263585i
$540$		0			0
$541$	−14.9170	−	9.58656i	−0.641331	−	0.412158i	0.179158	−	0.983820i	$-0.442663\pi$
$541$	−14.9170	−	9.58656i	−0.641331	−	0.412158i	−0.820489	+	0.571662i	$0.806299\pi$
$542$		0			0
$543$	−0.925724	+	6.43855i	−0.0397266	+	0.276305i
$544$		0			0
$545$	0.830203	−	5.77419i	0.0355620	−	0.247339i
$546$		0			0
$547$	−34.1543	−	21.9496i	−1.46033	−	0.938498i	−0.998676	−	0.0514381i	$-0.983620\pi$
$547$	−34.1543	−	21.9496i	−1.46033	−	0.938498i	−0.461655	−	0.887060i	$-0.652744\pi$
$548$		0			0
$549$	−4.41132	−	9.65945i	−0.188271	−	0.412255i
$550$		0			0
$551$	4.24960	+	29.5566i	0.181039	+	1.25915i
$552$		0			0
$553$	3.06226	−	0.899160i	0.130220	−	0.0382362i
$554$		0			0
$555$	−1.99031	−	13.8429i	−0.0844838	−	0.587598i
$556$		0			0
$557$	−19.6051	+	12.5994i	−0.830693	+	0.533854i	−0.885498	−	0.464643i	$-0.846183\pi$
$557$	−19.6051	+	12.5994i	−0.830693	+	0.533854i	0.0548052	+	0.998497i	$0.482546\pi$
$558$		0			0
$559$	12.4770	+	14.3992i	0.527719	+	0.609021i
$560$		0			0
$561$	1.49656	+	3.27701i	0.0631848	+	0.138355i
$562$		0			0
$563$	10.6220	−	6.82634i	0.447664	−	0.287696i	−0.297321	−	0.954778i	$-0.596093\pi$
$563$	10.6220	−	6.82634i	0.447664	−	0.287696i	0.744985	+	0.667082i	$0.232457\pi$
$564$		0			0
$565$	8.33850			0.350803
$566$		0			0
$567$	0.147184	−	0.322288i	0.00618114	−	0.0135348i
$568$		0			0
$569$	−6.32134	−	43.9659i	−0.265004	−	1.84314i	−0.493682	−	0.869643i	$-0.664349\pi$
$569$	−6.32134	−	43.9659i	−0.265004	−	1.84314i	0.228678	−	0.973502i	$-0.426560\pi$
$570$		0			0
$571$	5.84462	−	6.74505i	0.244590	−	0.282271i	−0.620159	−	0.784476i	$-0.712932\pi$
$571$	5.84462	−	6.74505i	0.244590	−	0.282271i	0.864749	+	0.502204i	$0.167478\pi$
$572$		0			0
$573$	5.86764			0.245124
$574$		0			0
$575$	−0.609353	+	1.33430i	−0.0254118	+	0.0556441i
$576$		0			0
$577$	−42.8229	+	12.5739i	−1.78274	+	0.523459i	−0.995633	−	0.0933579i	$-0.970240\pi$
$577$	−42.8229	+	12.5739i	−1.78274	+	0.523459i	−0.787106	+	0.616817i	$0.788422\pi$
$578$		0			0
$579$	22.3587	−	6.56510i	0.929195	−	0.272836i
$580$		0			0
$581$	−3.01489	+	3.47937i	−0.125079	+	0.144349i
$582$		0			0
$583$	−6.94110	−	8.01045i	−0.287471	−	0.331759i
$584$		0			0
$585$	17.9487	+	5.27020i	0.742086	+	0.217896i
$586$		0			0
$587$	−12.2014	−	7.84136i	−0.503606	−	0.323648i	0.264051	−	0.964509i	$-0.414941\pi$
$587$	−12.2014	−	7.84136i	−0.503606	−	0.323648i	−0.767657	+	0.640861i	$0.778578\pi$
$588$		0			0
$589$	−9.48758	−	2.78580i	−0.390929	−	0.114787i
$590$		0			0
$591$	−2.42829	−	5.31721i	−0.0998865	−	0.218721i
$592$		0			0
$593$	9.23657	−	10.6596i	0.379301	−	0.437736i	−0.533713	−	0.845666i	$-0.679204\pi$
$593$	9.23657	−	10.6596i	0.379301	−	0.437736i	0.913013	+	0.407930i	$0.133749\pi$
$594$		0			0
$595$	1.71046	−	3.74538i	0.0701220	−	0.153546i
$596$		0			0
$597$	−0.806344	+	0.518206i	−0.0330015	+	0.0212088i
$598$		0			0
$599$	31.6690	+	9.29886i	1.29396	+	0.379941i	0.855030	−	0.518579i	$-0.173539\pi$
$599$	31.6690	+	9.29886i	1.29396	+	0.379941i	0.438931	+	0.898521i	$0.355357\pi$
$600$		0			0
$601$	1.84726	−	12.8480i	0.0753515	−	0.524081i	−0.916830	−	0.399278i	$-0.869261\pi$
$601$	1.84726	−	12.8480i	0.0753515	−	0.524081i	0.992181	−	0.124803i	$-0.0398300\pi$
$602$		0			0
$603$	−6.11929	−	5.43639i	−0.249197	−	0.221387i
$604$		0			0
$605$	−5.19794	+	36.1524i	−0.211326	+	1.46981i
$606$		0			0
$607$	36.0732	+	10.5920i	1.46417	+	0.429918i	0.914198	−	0.405268i	$-0.132822\pi$
$607$	36.0732	+	10.5920i	1.46417	+	0.429918i	0.549968	+	0.835186i	$0.314640\pi$
$608$		0			0
$609$	−3.02883	+	1.94651i	−0.122734	+	0.0788765i
$610$		0			0
$611$	−6.96660	+	15.2547i	−0.281838	+	0.617140i
$612$		0			0
$613$	22.4269	−	25.8820i	0.905813	−	1.04536i	−0.0929514	−	0.995671i	$-0.529630\pi$
$613$	22.4269	−	25.8820i	0.905813	−	1.04536i	0.998765	−	0.0496934i	$-0.0158244\pi$
$614$		0			0
$615$	−5.59532	−	12.2520i	−0.225625	−	0.494050i
$616$		0			0
$617$	12.2630	+	3.60074i	0.493689	+	0.144960i	0.519094	−	0.854717i	$-0.326269\pi$
$617$	12.2630	+	3.60074i	0.493689	+	0.144960i	−0.0254051	+	0.999677i	$0.508088\pi$
$618$		0			0
$619$	23.7216	+	15.2450i	0.953453	+	0.612747i	0.922179	−	0.386764i	$-0.126407\pi$
$619$	23.7216	+	15.2450i	0.953453	+	0.612747i	0.0312738	+	0.999511i	$0.490044\pi$
$620$		0			0
$621$	−0.149139	−	0.0437913i	−0.00598476	−	0.00175728i
$622$		0			0
$623$	−1.11671	−	1.28876i	−0.0447402	−	0.0516329i
$624$		0			0
$625$	−11.0493	+	12.7516i	−0.441971	+	0.510062i
$626$		0			0
$627$	−3.32100	+	0.975134i	−0.132628	+	0.0389431i
$628$		0			0
$629$	10.8015	−	3.17162i	0.430685	−	0.126461i
$630$		0			0
$631$	−0.481429	+	1.05418i	−0.0191654	+	0.0419663i	−0.918973	−	0.394321i	$-0.870980\pi$
$631$	−0.481429	+	1.05418i	−0.0191654	+	0.0419663i	0.899807	+	0.436288i	$0.143707\pi$
$632$		0			0
$633$	−12.1381			−0.482448
$634$		0			0
$635$	13.6999	−	15.8105i	0.543664	−	0.627422i
$636$		0			0
$637$	4.81659	+	33.5001i	0.190840	+	1.32732i
$638$		0			0
$639$	4.17476	−	9.14145i	0.165151	−	0.361630i
$640$		0			0
$641$	−24.6079			−0.971952			−0.485976	−	0.873972i	$-0.661536\pi$
$641$	−24.6079			−0.971952			−0.485976	+	0.873972i	$0.661536\pi$
$642$		0			0
$643$	40.1111	−	25.7779i	1.58183	−	1.01658i	0.606703	−	0.794928i	$-0.292492\pi$
$643$	40.1111	−	25.7779i	1.58183	−	1.01658i	0.975126	−	0.221651i	$-0.0711447\pi$
$644$		0			0
$645$	−6.10844	−	13.3756i	−0.240520	−	0.526665i
$646$		0			0
$647$	24.7607	+	28.5754i	0.973444	+	1.12341i	0.992333	+	0.123592i	$0.0394416\pi$
$647$	24.7607	+	28.5754i	0.973444	+	1.12341i	−0.0188892	+	0.999822i	$0.506013\pi$
$648$		0			0
$649$	−7.69612	+	4.94600i	−0.302099	+	0.194147i
$650$		0			0
$651$	−0.169673	−	1.18010i	−0.00665001	−	0.0462519i
$652$		0			0
$653$	−15.3387	+	4.50386i	−0.600251	+	0.176250i	−0.567721	−	0.823221i	$-0.692175\pi$
$653$	−15.3387	+	4.50386i	−0.600251	+	0.176250i	−0.0325305	+	0.999471i	$0.510357\pi$
$654$		0			0
$655$	−7.07538	−	49.2103i	−0.276458	−	1.92281i
$656$		0			0
$657$	−0.970927	−	2.12603i	−0.0378795	−	0.0829445i
$658$		0			0
$659$	−6.47946	−	4.16409i	−0.252404	−	0.162210i	0.408321	−	0.912839i	$-0.366115\pi$
$659$	−6.47946	−	4.16409i	−0.252404	−	0.162210i	−0.660725	+	0.750628i	$0.729751\pi$
$660$		0			0
$661$	−1.89605	+	13.1873i	−0.0737477	+	0.512926i	0.919146	+	0.393918i	$0.128881\pi$
$661$	−1.89605	+	13.1873i	−0.0737477	+	0.512926i	−0.992893	+	0.119008i	$0.962028\pi$
$662$		0			0
$663$	−2.14296	+	14.9046i	−0.0832257	+	0.578847i
$664$		0			0
$665$	3.32792	+	2.13873i	0.129051	+	0.0829362i
$666$		0			0
$667$	1.03435	+	1.19371i	0.0400503	+	0.0462205i
$668$		0			0
$669$	−21.3024			−0.823597
$670$		0			0
$671$	−12.5079			−0.482863
$672$		0			0
$673$	8.51241	+	9.82384i	0.328129	+	0.378681i	0.895712	−	0.444635i	$-0.146667\pi$
$673$	8.51241	+	9.82384i	0.328129	+	0.378681i	−0.567583	+	0.823316i	$0.692121\pi$
$674$		0			0
$675$	−7.93896	−	5.10206i	−0.305571	−	0.196378i
$676$		0			0
$677$	−0.361503	+	2.51431i	−0.0138937	+	0.0966327i	−0.995588	−	0.0938288i	$-0.970089\pi$
$677$	−0.361503	+	2.51431i	−0.0138937	+	0.0966327i	0.981695	+	0.190462i	$0.0609985\pi$
$678$		0			0
$679$	−0.0818485	+	0.569269i	−0.00314106	+	0.0218465i
$680$		0			0
$681$	3.92740	+	2.52398i	0.150498	+	0.0967193i
$682$		0			0
$683$	−8.28073	−	18.1323i	−0.316853	−	0.693812i	0.682458	−	0.730925i	$-0.260911\pi$
$683$	−8.28073	−	18.1323i	−0.316853	−	0.693812i	−0.999311	+	0.0371131i	$0.988184\pi$
$684$		0			0
$685$	−3.94396	−	27.4309i	−0.150691	−	1.04808i
$686$		0			0
$687$	−1.53693	+	0.451282i	−0.0586374	+	0.0172175i
$688$		0			0
$689$	−6.30495	−	43.8519i	−0.240199	−	1.67062i
$690$		0			0
$691$	−33.6260	+	21.6101i	−1.27919	+	0.822089i	−0.990788	−	0.135419i	$-0.956762\pi$
$691$	−33.6260	+	21.6101i	−1.27919	+	0.822089i	−0.288407	+	0.957508i	$0.593125\pi$
$692$		0			0
$693$	−0.273291	−	0.315395i	−0.0103815	−	0.0119809i
$694$		0			0
$695$	−32.6457	−	71.4841i	−1.23832	−	2.71155i
$696$		0			0
$697$	9.12102	−	5.86172i	0.345483	−	0.222029i
$698$		0			0
$699$	19.2234			0.727095
$700$		0			0
$701$	0.768533	−	1.68285i	0.0290271	−	0.0635604i	−0.894563	−	0.446942i	$-0.852513\pi$
$701$	0.768533	−	1.68285i	0.0290271	−	0.0635604i	0.923590	+	0.383381i	$0.125240\pi$
$702$		0			0
$703$	1.53925	+	10.7057i	0.0580539	+	0.403774i
$704$		0			0
$705$	8.47571	−	9.78149i	0.319214	−	0.368392i
$706$		0			0
$707$	5.37092			0.201994
$708$		0			0
$709$	11.7210	−	25.6655i	0.440193	−	0.963888i	−0.551370	−	0.834261i	$-0.685895\pi$
$709$	11.7210	−	25.6655i	0.440193	−	0.963888i	0.991563	−	0.129627i	$-0.0413779\pi$
$710$		0			0
$711$	8.64298	−	2.53781i	0.324137	−	0.0951752i
$712$		0			0
$713$	−0.501854	+	0.147358i	−0.0187946	+	0.00551858i
$714$		0			0
$715$	14.4290	−	16.6520i	0.539616	−	0.622750i
$716$		0			0
$717$	−7.98289	−	9.21274i	−0.298126	−	0.344056i
$718$		0			0
$719$	−27.3864	−	8.04136i	−1.02134	−	0.299892i	−0.272154	−	0.962254i	$-0.587736\pi$
$719$	−27.3864	−	8.04136i	−1.02134	−	0.299892i	−0.749184	+	0.662361i	$0.769554\pi$
$720$		0			0
$721$	5.49584	+	3.53196i	0.204676	+	0.131537i
$722$		0			0
$723$	2.92852	+	0.859891i	0.108913	+	0.0319797i
$724$		0			0
$725$	39.8371	+	87.2311i	1.47951	+	3.23968i
$726$		0			0
$727$	−21.6009	+	24.9287i	−0.801131	+	0.924555i	−0.998443	−	0.0557859i	$-0.982234\pi$
$727$	−21.6009	+	24.9287i	−0.801131	+	0.924555i	0.197311	+	0.980341i	$0.436779\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	9.95747	−	6.39928i	0.368290	−	0.236686i
$732$		0			0
$733$	−13.6055	−	3.99494i	−0.502531	−	0.147557i	0.0206350	−	0.999787i	$-0.493431\pi$
$733$	−13.6055	−	3.99494i	−0.502531	−	0.147557i	−0.523166	+	0.852231i	$0.675249\pi$
$734$		0			0
$735$	3.71731	−	25.8544i	0.137115	−	0.953656i
$736$		0			0
$737$	−8.81892	+	3.89634i	−0.324849	+	0.143523i
$738$		0			0
$739$	0.500901	−	3.48385i	0.0184260	−	0.128155i	−0.978532	−	0.206094i	$-0.933925\pi$
$739$	0.500901	−	3.48385i	0.0184260	−	0.128155i	0.996958	+	0.0779387i	$0.0248338\pi$
$740$		0			0
$741$	−13.8810	−	4.07584i	−0.509932	−	0.149730i
$742$		0			0
$743$	18.6088	−	11.9592i	0.682691	−	0.438739i	−0.152790	−	0.988259i	$-0.548826\pi$
$743$	18.6088	−	11.9592i	0.682691	−	0.438739i	0.835481	+	0.549520i	$0.185189\pi$
$744$		0			0
$745$	−35.4704	+	77.6694i	−1.29954	+	2.84559i
$746$		0			0
$747$	−8.50930	+	9.82026i	−0.311339	+	0.359304i
$748$		0			0
$749$	−1.29287	−	2.83099i	−0.0472405	−	0.103442i
$750$		0			0
$751$	−41.9740	−	12.3247i	−1.53165	−	0.449734i	−0.596096	−	0.802913i	$-0.703282\pi$
$751$	−41.9740	−	12.3247i	−1.53165	−	0.449734i	−0.935556	+	0.353179i	$0.885101\pi$
$752$		0			0
$753$	−23.0408	−	14.8074i	−0.839653	−	0.539613i
$754$		0			0
$755$	1.83383	+	0.538462i	0.0667401	+	0.0195967i
$756$		0			0
$757$	15.3995	+	17.7720i	0.559705	+	0.645934i	0.963117	−	0.269084i	$-0.0867211\pi$
$757$	15.3995	+	17.7720i	0.559705	+	0.645934i	−0.403411	+	0.915019i	$0.632176\pi$
$758$		0			0
$759$	−0.119894	+	0.138365i	−0.00435188	+	0.00502234i
$760$		0			0
$761$	−34.9472	+	10.2614i	−1.26683	+	0.371976i	−0.845034	−	0.534712i	$-0.820420\pi$
$761$	−34.9472	+	10.2614i	−1.26683	+	0.371976i	−0.421801	+	0.906689i	$0.638602\pi$
$762$		0			0
$763$	−0.521933	+	0.153253i	−0.0188952	+	0.00554814i
$764$		0			0
$765$	4.82764	−	10.5711i	0.174544	−	0.382197i
$766$		0			0
$767$	−38.2382			−1.38070
$768$		0			0
$769$	−0.204041	+	0.235476i	−0.00735792	+	0.00849150i	−0.759417	−	0.650605i	$-0.774516\pi$
$769$	−0.204041	+	0.235476i	−0.00735792	+	0.00849150i	0.752059	+	0.659096i	$0.229061\pi$
$770$		0			0
$771$	−3.50333	−	24.3662i	−0.126169	−	0.877528i
$772$		0			0
$773$	21.4537	−	46.9770i	0.771635	−	1.68964i	0.0486139	−	0.998818i	$-0.484520\pi$
$773$	21.4537	−	46.9770i	0.771635	−	1.68964i	0.723021	−	0.690826i	$-0.242753\pi$
$774$		0			0
$775$	−31.7557			−1.14070
$776$		0			0
$777$	−1.09707	+	0.705046i	−0.0393573	+	0.0252934i
$778$		0			0
$779$	4.32727	+	9.47541i	0.155041	+	0.339492i
$780$		0			0
$781$	−7.75170	−	8.94594i	−0.277378	−	0.320111i
$782$		0			0
$783$	−8.54862	+	5.49386i	−0.305503	+	0.196335i
$784$		0			0
$785$	−8.37134	−	58.2239i	−0.298786	−	2.07810i
$786$		0			0
$787$	42.5651	−	12.4983i	1.51728	−	0.445515i	0.586153	−	0.810200i	$-0.300642\pi$
$787$	42.5651	−	12.4983i	1.51728	−	0.445515i	0.931131	+	0.364686i	$0.118824\pi$
$788$		0			0
$789$	−0.788156	−	5.48175i	−0.0280591	−	0.195155i
$790$		0			0
$791$	−0.323005	−	0.707282i	−0.0114847	−	0.0251481i
$792$		0			0
$793$	−43.9809	−	28.2648i	−1.56181	−	1.00371i
$794$		0			0
$795$	−4.86598	+	33.8436i	−0.172578	+	1.20031i
$796$		0			0
$797$	−2.84183	+	19.7653i	−0.100663	+	0.700124i	0.875521	+	0.483180i	$0.160518\pi$
$797$	−2.84183	+	19.7653i	−0.100663	+	0.700124i	−0.976184	+	0.216944i	$0.930391\pi$
$798$		0			0
$799$	8.76451	+	5.63261i	0.310066	+	0.199267i
$800$		0			0
$801$	−3.15184	−	3.63741i	−0.111365	−	0.128522i
$802$		0			0
$803$	−2.75298			−0.0971506
$804$		0			0
$805$	0.209251			0.00737514
$806$		0			0
$807$	−10.6934	−	12.3408i	−0.376424	−	0.434416i
$808$		0			0
$809$	35.0651	+	22.5350i	1.23282	+	0.792287i	0.984328	−	0.176346i	$-0.0564277\pi$
$809$	35.0651	+	22.5350i	1.23282	+	0.792287i	0.248495	+	0.968633i	$0.420064\pi$
$810$		0			0
$811$	2.78744	−	19.3871i	0.0978803	−	0.680773i	−0.880513	−	0.474021i	$-0.842802\pi$
$811$	2.78744	−	19.3871i	0.0978803	−	0.680773i	0.978394	−	0.206751i	$-0.0662890\pi$
$812$		0			0
$813$	1.33878	−	9.31139i	0.0469529	−	0.326565i
$814$		0			0
$815$	−40.9413	−	26.3114i	−1.43411	−	0.921647i
$816$		0			0
$817$	4.72411	+	10.3444i	0.165276	+	0.361903i
$818$		0			0
$819$	−0.248244	−	1.72658i	−0.00867436	−	0.0603315i
$820$		0			0
$821$	−23.3529	+	6.85703i	−0.815022	+	0.239312i	−0.662571	−	0.748999i	$-0.730535\pi$
$821$	−23.3529	+	6.85703i	−0.815022	+	0.239312i	−0.152451	+	0.988311i	$0.548717\pi$
$822$		0			0
$823$	−5.67022	−	39.4373i	−0.197652	−	1.37470i	−0.811075	−	0.584943i	$-0.801117\pi$
$823$	−5.67022	−	39.4373i	−0.197652	−	1.37470i	0.613423	−	0.789754i	$-0.289792\pi$
$824$		0			0
$825$	−9.35109	+	6.00958i	−0.325563	+	0.209227i
$826$		0			0
$827$	−21.6142	−	24.9441i	−0.751598	−	0.867391i	0.243124	−	0.969995i	$-0.421828\pi$
$827$	−21.6142	−	24.9441i	−0.751598	−	0.867391i	−0.994722	+	0.102604i	$0.967282\pi$
$828$		0			0
$829$	−8.17296	−	17.8963i	−0.283859	−	0.621564i	0.712965	−	0.701199i	$-0.247352\pi$
$829$	−8.17296	−	17.8963i	−0.283859	−	0.621564i	−0.996824	+	0.0796355i	$0.974624\pi$
$830$		0			0
$831$	0.204745	−	0.131582i	0.00710252	−	0.00456451i
$832$		0			0
$833$	21.0258			0.728500
$834$		0			0
$835$	−13.3108	+	29.1467i	−0.460640	+	1.00866i
$836$		0			0
$837$	−0.478889	−	3.33075i	−0.0165528	−	0.115127i
$838$		0			0
$839$	−35.9655	+	41.5064i	−1.24167	+	1.43296i	−0.380385	+	0.924828i	$0.624209\pi$
$839$	−35.9655	+	41.5064i	−1.24167	+	1.43296i	−0.861280	+	0.508130i	$0.830337\pi$
$840$		0			0
$841$	74.2614			2.56074
$842$		0			0
$843$	−2.95729	+	6.47555i	−0.101854	+	0.223030i
$844$		0			0
$845$	40.9714	−	12.0303i	1.40946	−	0.413854i
$846$		0			0
$847$	3.26785	−	0.959526i	0.112284	−	0.0329697i
$848$		0			0
$849$	3.70561	−	4.27650i	0.127176	−	0.146769i
$850$		0			0
$851$	0.374654	+	0.432373i	0.0128430	+	0.0148216i
$852$		0			0
$853$	40.2777	+	11.8266i	1.37908	+	0.404935i	0.885449	−	0.464736i	$-0.153851\pi$
$853$	40.2777	+	11.8266i	1.37908	+	0.404935i	0.493632	+	0.869671i	$0.335669\pi$
$854$		0			0
$855$	9.39280	+	6.03638i	0.321227	+	0.206440i
$856$		0			0
$857$	6.50049	+	1.90872i	0.222052	+	0.0652005i	0.390866	−	0.920447i	$-0.372175\pi$
$857$	6.50049	+	1.90872i	0.222052	+	0.0652005i	−0.168814	+	0.985648i	$0.553994\pi$
$858$		0			0
$859$	−5.29073	−	11.5851i	−0.180517	−	0.395278i	0.797643	−	0.603130i	$-0.206080\pi$
$859$	−5.29073	−	11.5851i	−0.180517	−	0.395278i	−0.978160	+	0.207852i	$0.933353\pi$
$860$		0			0
$861$	−0.822490	+	0.949204i	−0.0280304	+	0.0323488i
$862$		0			0
$863$	10.7612	−	23.5637i	0.366314	−	0.802116i	−0.633288	−	0.773916i	$-0.718295\pi$
$863$	10.7612	−	23.5637i	0.366314	−	0.802116i	0.999602	−	0.0282000i	$-0.00897752\pi$
$864$		0			0
$865$	−20.9923	+	13.4910i	−0.713761	+	0.458706i
$866$		0			0
$867$	−7.33568	−	2.15395i	−0.249133	−	0.0731520i
$868$		0			0
$869$	1.50998	−	10.5021i	0.0512225	−	0.356260i
$870$		0			0
$871$	−39.8143	−	6.22812i	−1.34905	−	0.211032i
$872$		0			0
$873$	−0.231011	+	1.60672i	−0.00781854	+	0.0543791i
$874$		0			0
$875$	5.73131	+	1.68287i	0.193754	+	0.0568912i
$876$		0			0
$877$	9.56231	−	6.14532i	0.322896	−	0.207513i	−0.369143	−	0.929373i	$-0.620349\pi$
$877$	9.56231	−	6.14532i	0.322896	−	0.207513i	0.692039	+	0.721860i	$0.256712\pi$
$878$		0			0
$879$	0.531981	−	1.16488i	0.0179433	−	0.0392903i
$880$		0			0
$881$	20.5936	−	23.7662i	0.693814	−	0.800705i	−0.294088	−	0.955778i	$-0.595016\pi$
$881$	20.5936	−	23.7662i	0.693814	−	0.800705i	0.987903	+	0.155074i	$0.0495615\pi$
$882$		0			0
$883$	6.31827	+	13.8351i	0.212627	+	0.465587i	0.985653	−	0.168787i	$-0.0539851\pi$
$883$	6.31827	+	13.8351i	0.212627	+	0.465587i	−0.773026	+	0.634374i	$0.781258\pi$
$884$		0			0
$885$	28.3157	+	8.31424i	0.951822	+	0.279480i
$886$		0			0
$887$	5.41273	+	3.47855i	0.181742	+	0.116798i	0.628348	−	0.777932i	$-0.283731\pi$
$887$	5.41273	+	3.47855i	0.181742	+	0.116798i	−0.446607	+	0.894730i	$0.647368\pi$
$888$		0			0
$889$	−1.87176	−	0.549597i	−0.0627767	−	0.0184329i
$890$		0			0
$891$	−0.771343	−	0.890177i	−0.0258410	−	0.0298221i
$892$		0			0
$893$	−6.55489	+	7.56475i	−0.219351	+	0.253145i
$894$		0			0
$895$	9.54847	−	2.80368i	0.319170	−	0.0937168i
$896$		0			0
$897$	−0.734249	+	0.215595i	−0.0245159	+	0.00719850i
$898$		0			0
$899$	−14.2048	+	31.1042i	−0.473758	+	1.03738i
$900$		0			0
$901$	−27.5229			−0.916920
$902$		0			0
$903$	−0.897917	+	1.03625i	−0.0298808	+	0.0344843i
$904$		0			0
$905$	−3.51739	−	24.4640i	−0.116922	−	0.813211i
$906$		0			0
$907$	9.12832	−	19.9882i	0.303101	−	0.663698i	−0.695389	−	0.718633i	$-0.744768\pi$
$907$	9.12832	−	19.9882i	0.303101	−	0.663698i	0.998490	+	0.0549351i	$0.0174952\pi$
$908$		0			0
$909$	15.1590			0.502793
$910$		0			0
$911$	44.0609	−	28.3162i	1.45980	−	0.938158i	0.461093	−	0.887352i	$-0.347457\pi$
$911$	44.0609	−	28.3162i	1.45980	−	0.938158i	0.998709	−	0.0508059i	$-0.0161790\pi$
$912$		0			0
$913$	6.35808	+	13.9222i	0.210422	+	0.460759i
$914$		0			0
$915$	26.4226	+	30.4933i	0.873503	+	1.00808i
$916$		0			0
$917$	−3.90001	+	2.50638i	−0.128790	+	0.0827680i
$918$		0			0
$919$	−6.62424	−	46.0726i	−0.218514	−	1.51979i	−0.743530	−	0.668703i	$-0.766850\pi$
$919$	−6.62424	−	46.0726i	−0.218514	−	1.51979i	0.525016	−	0.851092i	$-0.324059\pi$
$920$		0			0
$921$	−23.9546	+	7.03370i	−0.789331	+	0.231768i
$922$		0			0
$923$	−7.04126	−	48.9730i	−0.231766	−	1.61197i
$924$		0			0
$925$	14.4294	+	31.5960i	0.474437	+	1.03887i
$926$		0			0
$927$	15.5116	+	9.96868i	0.509467	+	0.327414i
$928$		0			0
$929$	−1.58244	+	11.0061i	−0.0519182	+	0.361099i	0.947256	+	0.320477i	$0.103843\pi$
$929$	−1.58244	+	11.0061i	−0.0519182	+	0.361099i	−0.999175	+	0.0406222i	$0.987066\pi$
$930$		0			0
$931$	−2.87487	+	19.9952i	−0.0942200	+	0.655315i
$932$		0			0
$933$	10.5061	+	6.75185i	0.343954	+	0.221046i
$934$		0			0
$935$	−8.96396	−	10.3450i	−0.293153	−	0.338317i
$936$		0			0
$937$	−36.1534			−1.18108			−0.590540	−	0.807008i	$-0.701085\pi$
$937$	−36.1534			−1.18108			−0.590540	+	0.807008i	$0.701085\pi$
$938$		0			0
$939$	15.2302			0.497020
$940$		0			0
$941$	19.7276	+	22.7669i	0.643102	+	0.742179i	0.979920	−	0.199391i	$-0.0638963\pi$
$941$	19.7276	+	22.7669i	0.643102	+	0.742179i	−0.336818	+	0.941570i	$0.609351\pi$
$942$		0			0
$943$	0.463533	+	0.297895i	0.0150947	+	0.00970079i
$944$		0			0
$945$	−0.191588	+	1.33252i	−0.00623235	+	0.0433469i
$946$		0			0
$947$	−3.22755	+	22.4481i	−0.104881	+	0.729466i	0.867731	+	0.497034i	$0.165577\pi$
$947$	−3.22755	+	22.4481i	−0.104881	+	0.729466i	−0.972613	+	0.232432i	$0.925332\pi$
$948$		0			0
$949$	−9.68015	−	6.22106i	−0.314231	−	0.201944i
$950$		0			0
$951$	2.48646	+	5.44458i	0.0806289	+	0.176553i
$952$		0			0
$953$	−8.03084	−	55.8557i	−0.260145	−	1.80935i	−0.531712	−	0.846926i	$-0.678451\pi$
$953$	−8.03084	−	55.8557i	−0.260145	−	1.80935i	0.271567	−	0.962420i	$-0.412458\pi$
$954$		0			0
$955$	−21.3917	+	6.28116i	−0.692218	+	0.203253i
$956$		0			0
$957$	1.70341	+	11.8474i	0.0550633	+	0.382973i
$958$		0			0
$959$	−2.17394	+	1.39711i	−0.0702003	+	0.0451150i
$960$		0			0
$961$	12.8856	+	14.8707i	0.415663	+	0.479701i
$962$		0			0
$963$	−3.64902	−	7.99025i	−0.117588	−	0.257482i
$964$		0			0
$965$	−74.4853	+	47.8688i	−2.39777	+	1.54095i
$966$		0			0
$967$	50.1802			1.61369			0.806843	−	0.590766i	$-0.201174\pi$
$967$	50.1802			1.61369			0.806843	+	0.590766i	$0.201174\pi$
$968$		0			0
$969$	−3.73357	+	8.17538i	−0.119940	+	0.262631i
$970$		0			0
$971$	5.11547	+	35.5788i	0.164163	+	1.14178i	0.890680	+	0.454631i	$0.150229\pi$
$971$	5.11547	+	35.5788i	0.164163	+	1.14178i	−0.726517	+	0.687149i	$0.758862\pi$
$972$		0			0
$973$	−4.79879	+	5.53810i	−0.153842	+	0.177543i
$974$		0			0
$975$	−46.4609			−1.48794
$976$		0			0
$977$	2.09311	−	4.58328i	0.0669647	−	0.146632i	−0.873190	−	0.487380i	$-0.837953\pi$
$977$	2.09311	−	4.58328i	0.0669647	−	0.146632i	0.940155	+	0.340747i	$0.110680\pi$
$978$		0			0
$979$	−5.43945	+	1.59717i	−0.173846	+	0.0510457i
$980$		0			0
$981$	−1.47311	+	0.432545i	−0.0470329	+	0.0138101i
$982$		0			0
$983$	5.25865	−	6.06881i	0.167725	−	0.193565i	−0.665664	−	0.746251i	$-0.731852\pi$
$983$	5.25865	−	6.06881i	0.167725	−	0.193565i	0.833389	+	0.552686i	$0.186397\pi$
$984$		0			0
$985$	14.5448	+	16.7855i	0.463434	+	0.534832i
$986$		0			0
$987$	−1.15800	−	0.340019i	−0.0368595	−	0.0108229i
$988$		0			0
$989$	0.506042	+	0.325213i	0.0160912	+	0.0103412i
$990$		0			0
$991$	−38.6768	−	11.3565i	−1.22861	−	0.360752i	−0.397883	−	0.917436i	$-0.630255\pi$
$991$	−38.6768	−	11.3565i	−1.22861	−	0.360752i	−0.830724	+	0.556684i	$0.812073\pi$
$992$		0			0
$993$	11.3265	+	24.8015i	0.359435	+	0.787052i
$994$		0			0
$995$	2.38496	−	2.75239i	0.0756084	−	0.0872568i
$996$		0			0
$997$	15.7693	−	34.5299i	0.499418	−	1.09357i	−0.477239	−	0.878773i	$-0.658363\pi$
$997$	15.7693	−	34.5299i	0.499418	−	1.09357i	0.976658	−	0.214801i	$-0.0689102\pi$
$998$		0			0
$999$	−3.09640	+	1.98994i	−0.0979658	+	0.0629588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.193.1	yes	60
67.25	even	11	inner	804.2.q.b.25.1	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.25.1	✓	60	67.25	even	11	inner
804.2.q.b.193.1	yes	60	1.1	even	1	trivial

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.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(-3.19644 - 2.05423i) q^{5} +(-0.0504230 + 0.350699i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(-3.19644 - 2.05423i) q^{5} +(-0.0504230 + 0.350699i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(0.990890 + 0.636806i) q^{11} +(2.04519 + 4.47833i) q^{13} +(-0.540741 - 3.76094i) q^{15} +(2.93464 - 0.861688i) q^{17} +(0.418195 + 2.90861i) q^{19} +(-0.298061 + 0.191552i) q^{21} +(0.101789 + 0.117470i) q^{23} +(3.92029 + 8.58425i) q^{25} +(-0.841254 + 0.540641i) q^{27} +10.1618 q^{29} +(-1.39787 + 3.06091i) q^{31} +(0.167629 + 1.16588i) q^{33} +(0.881590 - 1.01741i) q^{35} +3.68070 q^{37} +(-2.04519 + 4.47833i) q^{39} +(3.40130 - 0.998712i) q^{41} +(3.71322 - 1.09030i) q^{43} +(2.48822 - 2.87156i) q^{45} +(2.23068 + 2.57434i) q^{47} +(6.59600 + 1.93676i) q^{49} +(2.57300 + 1.65357i) q^{51} +(-8.63420 - 2.53523i) q^{53} +(-1.85917 - 4.07102i) q^{55} +(-1.92432 + 2.22079i) q^{57} +(-3.22648 + 7.06500i) q^{59} +(-8.93334 + 5.74111i) q^{61} +(-0.339954 - 0.0998195i) q^{63} +(2.66220 - 18.5160i) q^{65} +(-4.51019 + 6.83068i) q^{67} +(-0.0221208 + 0.153854i) q^{69} +(-9.64253 - 2.83130i) q^{71} +(-1.96622 + 1.26361i) q^{73} +(-3.92029 + 8.58425i) q^{75} +(-0.273291 + 0.315395i) q^{77} +(-3.74200 - 8.19384i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(10.9313 + 7.02512i) q^{83} +(-11.1505 - 3.27408i) q^{85} +(6.65454 + 7.67975i) q^{87} +(-3.15184 + 3.63741i) q^{89} +(-1.67367 + 0.491435i) q^{91} +(-3.22869 + 0.948029i) q^{93} +(4.63821 - 10.1563i) q^{95} +1.62324 q^{97} +(-0.771343 + 0.890177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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