LMFDB - Embedded newform 804.2.q.b.625.1

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			625.1
Character	$\chi$	$=$	804.625
Dual form			804.2.q.b.265.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{3} +(-1.42271 + 3.11530i) q^{5} +(2.11496 - 0.621007i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{3} +(-1.42271 + 3.11530i) q^{5} +(2.11496 - 0.621007i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(-0.794441 + 1.73958i) q^{11} +(0.629292 + 0.726242i) q^{13} +(-3.28606 - 0.964876i) q^{15} +(5.57190 + 3.58084i) q^{17} +(-7.43980 - 2.18452i) q^{19} +(0.915676 + 2.00505i) q^{21} +(0.573090 + 3.98593i) q^{23} +(-4.40669 - 5.08559i) q^{25} +(-0.415415 - 0.909632i) q^{27} -0.158121 q^{29} +(-0.313948 + 0.362315i) q^{31} +(-1.83494 - 0.538786i) q^{33} +(-1.07435 + 7.47224i) q^{35} -4.87640 q^{37} +(-0.629292 + 0.726242i) q^{39} +(-6.45260 - 4.14683i) q^{41} +(-0.750192 - 0.482119i) q^{43} +(0.487399 - 3.38993i) q^{45} +(-0.408040 - 2.83798i) q^{47} +(-1.80138 + 1.15768i) q^{49} +(-2.75143 + 6.02479i) q^{51} +(-0.988260 + 0.635116i) q^{53} +(-4.28906 - 4.94984i) q^{55} +(1.10349 - 7.67497i) q^{57} +(-4.69850 + 5.42236i) q^{59} +(3.47016 + 7.59859i) q^{61} +(-1.85433 + 1.19170i) q^{63} +(-3.15776 + 0.927203i) q^{65} +(8.18240 + 0.219983i) q^{67} +(-3.86380 + 1.13451i) q^{69} +(7.18046 - 4.61460i) q^{71} +(4.82513 + 10.5656i) q^{73} +(4.40669 - 5.08559i) q^{75} +(-0.599914 + 4.17250i) q^{77} +(-5.28952 - 6.10443i) q^{79} +(0.841254 - 0.540641i) q^{81} +(3.65286 - 7.99865i) q^{83} +(-19.0826 + 12.2636i) q^{85} +(-0.0225030 - 0.156512i) q^{87} +(-1.53875 + 10.7022i) q^{89} +(1.78193 + 1.14518i) q^{91} +(-0.403307 - 0.259190i) q^{93} +(17.3901 - 20.0693i) q^{95} +15.3671 q^{97} +(0.272163 - 1.89294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$	$1$

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
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$4$		0			0
$5$	−1.42271	+	3.11530i	−0.636255	+	1.39320i	0.266830	+	0.963744i	$0.414024\pi$
$5$	−1.42271	+	3.11530i	−0.636255	+	1.39320i	−0.903085	+	0.429461i	$0.858703\pi$
$6$		0			0
$7$	2.11496	−	0.621007i	0.799379	−	0.234719i	0.143564	−	0.989641i	$-0.454144\pi$
$7$	2.11496	−	0.621007i	0.799379	−	0.234719i	0.655814	+	0.754922i	$0.272325\pi$
$8$		0			0
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$		0			0
$11$	−0.794441	+	1.73958i	−0.239533	+	0.524504i	−0.990774	−	0.135524i	$-0.956728\pi$
$11$	−0.794441	+	1.73958i	−0.239533	+	0.524504i	0.751241	+	0.660028i	$0.229456\pi$
$12$		0			0
$13$	0.629292	+	0.726242i	0.174534	+	0.201423i	0.836276	−	0.548308i	$-0.184728\pi$
$13$	0.629292	+	0.726242i	0.174534	+	0.201423i	−0.661742	+	0.749732i	$0.730183\pi$
$14$		0			0
$15$	−3.28606	−	0.964876i	−0.848458	−	0.249130i
$16$		0			0
$17$	5.57190	+	3.58084i	1.35138	+	0.868482i	0.997759	−	0.0669060i	$-0.0213128\pi$
$17$	5.57190	+	3.58084i	1.35138	+	0.868482i	0.353624	+	0.935388i	$0.384949\pi$
$18$		0			0
$19$	−7.43980	−	2.18452i	−1.70681	−	0.501164i	−0.724633	−	0.689135i	$-0.757991\pi$
$19$	−7.43980	−	2.18452i	−1.70681	−	0.501164i	−0.982175	+	0.187971i	$0.939809\pi$
$20$		0			0
$21$	0.915676	+	2.00505i	0.199817	+	0.437538i
$22$		0			0
$23$	0.573090	+	3.98593i	0.119497	+	0.831123i	0.958111	+	0.286396i	$0.0924575\pi$
$23$	0.573090	+	3.98593i	0.119497	+	0.831123i	−0.838614	+	0.544727i	$0.816633\pi$
$24$		0			0
$25$	−4.40669	−	5.08559i	−0.881338	−	1.01712i
$26$		0			0
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$		0			0
$29$	−0.158121			−0.0293624			−0.0146812	−	0.999892i	$-0.504673\pi$
$29$	−0.158121			−0.0293624			−0.0146812	+	0.999892i	$0.504673\pi$
$30$		0			0
$31$	−0.313948	+	0.362315i	−0.0563867	+	0.0650738i	−0.783242	−	0.621717i	$-0.786436\pi$
$31$	−0.313948	+	0.362315i	−0.0563867	+	0.0650738i	0.726855	+	0.686790i	$0.240981\pi$
$32$		0			0
$33$	−1.83494	−	0.538786i	−0.319422	−	0.0937906i
$34$		0			0
$35$	−1.07435	+	7.47224i	−0.181598	+	1.26304i
$36$		0			0
$37$	−4.87640			−0.801675			−0.400837	−	0.916149i	$-0.631281\pi$
$37$	−4.87640			−0.801675			−0.400837	+	0.916149i	$0.631281\pi$
$38$		0			0
$39$	−0.629292	+	0.726242i	−0.100767	+	0.116292i
$40$		0			0
$41$	−6.45260	−	4.14683i	−1.00773	−	0.647627i	−0.0709230	−	0.997482i	$-0.522594\pi$
$41$	−6.45260	−	4.14683i	−1.00773	−	0.647627i	−0.936804	+	0.349855i	$0.886231\pi$
$42$		0			0
$43$	−0.750192	−	0.482119i	−0.114403	−	0.0735225i	0.482188	−	0.876068i	$-0.339842\pi$
$43$	−0.750192	−	0.482119i	−0.114403	−	0.0735225i	−0.596591	+	0.802545i	$0.703479\pi$
$44$		0			0
$45$	0.487399	−	3.38993i	0.0726571	−	0.505341i
$46$		0			0
$47$	−0.408040	−	2.83798i	−0.0595187	−	0.413962i	−0.997698	−	0.0678123i	$-0.978398\pi$
$47$	−0.408040	−	2.83798i	−0.0595187	−	0.413962i	0.938179	−	0.346149i	$-0.112511\pi$
$48$		0			0
$49$	−1.80138	+	1.15768i	−0.257340	+	0.165383i
$50$		0			0
$51$	−2.75143	+	6.02479i	−0.385277	+	0.843639i
$52$		0			0
$53$	−0.988260	+	0.635116i	−0.135748	+	0.0872399i	−0.606752	−	0.794891i	$-0.707528\pi$
$53$	−0.988260	+	0.635116i	−0.135748	+	0.0872399i	0.471004	+	0.882131i	$0.343892\pi$
$54$		0			0
$55$	−4.28906	−	4.94984i	−0.578337	−	0.667437i
$56$		0			0
$57$	1.10349	−	7.67497i	0.146161	−	1.01657i
$58$		0			0
$59$	−4.69850	+	5.42236i	−0.611693	+	0.705932i	−0.974107	−	0.226086i	$-0.927407\pi$
$59$	−4.69850	+	5.42236i	−0.611693	+	0.705932i	0.362414	+	0.932017i	$0.381953\pi$
$60$		0			0
$61$	3.47016	+	7.59859i	0.444308	+	0.972899i	0.990787	+	0.135427i	$0.0432405\pi$
$61$	3.47016	+	7.59859i	0.444308	+	0.972899i	−0.546479	+	0.837473i	$0.684032\pi$
$62$		0			0
$63$	−1.85433	+	1.19170i	−0.233623	+	0.150141i
$64$		0			0
$65$	−3.15776	+	0.927203i	−0.391672	+	0.115005i
$66$		0			0
$67$	8.18240	+	0.219983i	0.999639	+	0.0268752i
$67$	8.18240	+	0.219983i	0.999639	+	0.0268752i
$68$		0			0
$69$	−3.86380	+	1.13451i	−0.465146	+	0.136579i
$70$		0			0
$71$	7.18046	−	4.61460i	0.852163	−	0.547652i	−0.0400854	−	0.999196i	$-0.512763\pi$
$71$	7.18046	−	4.61460i	0.852163	−	0.547652i	0.892249	+	0.451544i	$0.149127\pi$
$72$		0			0
$73$	4.82513	+	10.5656i	0.564739	+	1.23661i	0.949552	+	0.313611i	$0.101539\pi$
$73$	4.82513	+	10.5656i	0.564739	+	1.23661i	−0.384813	+	0.922995i	$0.625734\pi$
$74$		0			0
$75$	4.40669	−	5.08559i	0.508841	−	0.587234i
$76$		0			0
$77$	−0.599914	+	4.17250i	−0.0683666	+	0.475500i
$78$		0			0
$79$	−5.28952	−	6.10443i	−0.595118	−	0.686802i	0.375667	−	0.926755i	$-0.377414\pi$
$79$	−5.28952	−	6.10443i	−0.595118	−	0.686802i	−0.970785	+	0.239952i	$0.922868\pi$
$80$		0			0
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$		0			0
$83$	3.65286	−	7.99865i	0.400954	−	0.877966i	−0.596219	−	0.802822i	$-0.703331\pi$
$83$	3.65286	−	7.99865i	0.400954	−	0.877966i	0.997173	−	0.0751442i	$-0.0239417\pi$
$84$		0			0
$85$	−19.0826	+	12.2636i	−2.06980	+	1.33018i
$86$		0			0
$87$	−0.0225030	−	0.156512i	−0.00241258	−	0.0167798i
$88$		0			0
$89$	−1.53875	+	10.7022i	−0.163107	+	1.13443i	0.729625	+	0.683847i	$0.239695\pi$
$89$	−1.53875	+	10.7022i	−0.163107	+	1.13443i	−0.892732	+	0.450587i	$0.851215\pi$
$90$		0			0
$91$	1.78193	+	1.14518i	0.186797	+	0.120047i
$92$		0			0
$93$	−0.403307	−	0.259190i	−0.0418210	−	0.0268767i
$94$		0			0
$95$	17.3901	−	20.0693i	1.78419	−	2.05906i
$96$		0			0
$97$	15.3671			1.56029			0.780145	−	0.625599i	$-0.215145\pi$
$97$	15.3671			1.56029			0.780145	+	0.625599i	$0.215145\pi$
$98$		0			0
$99$	0.272163	−	1.89294i	0.0273534	−	0.190247i
$100$		0			0
$101$	10.7238	+	3.14879i	1.06706	+	0.313316i	0.767690	−	0.640822i	$-0.221406\pi$
$101$	10.7238	+	3.14879i	1.06706	+	0.313316i	0.299367	+	0.954138i	$0.403224\pi$
$102$		0			0
$103$	6.89880	−	7.96163i	0.679759	−	0.784483i	−0.306111	−	0.951996i	$-0.599028\pi$
$103$	6.89880	−	7.96163i	0.679759	−	0.784483i	0.985870	+	0.167513i	$0.0535735\pi$
$104$		0			0
$105$	−7.54908			−0.736715
$106$		0			0
$107$	4.88768	+	10.7025i	0.472510	+	1.03465i	0.984455	+	0.175634i	$0.0561976\pi$
$107$	4.88768	+	10.7025i	0.472510	+	1.03465i	−0.511946	+	0.859018i	$0.671075\pi$
$108$		0			0
$109$	−2.43495	−	2.81008i	−0.233226	−	0.269157i	0.627058	−	0.778973i	$-0.284259\pi$
$109$	−2.43495	−	2.81008i	−0.233226	−	0.269157i	−0.860284	+	0.509816i	$0.829714\pi$
$110$		0			0
$111$	−0.693984	−	4.82676i	−0.0658700	−	0.458136i
$112$		0			0
$113$	6.21204	+	13.6025i	0.584379	+	1.27961i	0.938780	+	0.344519i	$0.111958\pi$
$113$	6.21204	+	13.6025i	0.584379	+	1.27961i	−0.354400	+	0.935094i	$0.615315\pi$
$114$		0			0
$115$	−13.2327	−	3.88547i	−1.23396	−	0.362322i
$116$		0			0
$117$	−0.808407	−	0.519532i	−0.0747373	−	0.0480307i
$118$		0			0
$119$	14.0081	+	4.11314i	1.28412	+	0.377050i
$120$		0			0
$121$	4.80846	+	5.54925i	0.437132	+	0.504478i
$122$		0			0
$123$	3.18632	−	6.97708i	0.287301	−	0.629102i
$124$		0			0
$125$	5.68227	−	1.66847i	0.508238	−	0.149232i
$126$		0			0
$127$	3.81987	−	1.12162i	0.338959	−	0.0995273i	−0.107823	−	0.994170i	$-0.534388\pi$
$127$	3.81987	−	1.12162i	0.338959	−	0.0995273i	0.446782	+	0.894643i	$0.352570\pi$
$128$		0			0
$129$	0.370448	−	0.811169i	0.0326162	−	0.0714194i
$130$		0			0
$131$	0.441724	+	3.07226i	0.0385936	+	0.268425i	0.999977	−	0.00678825i	$-0.00216078\pi$
$131$	0.441724	+	3.07226i	0.0385936	+	0.268425i	−0.961383	+	0.275213i	$0.911252\pi$
$132$		0			0
$133$	−17.0915			−1.48202
$134$		0			0
$135$	3.42479			0.294759
$136$		0			0
$137$	−2.15316	−	14.9756i	−0.183957	−	1.27945i	−0.847293	−	0.531126i	$-0.821769\pi$
$137$	−2.15316	−	14.9756i	−0.183957	−	1.27945i	0.663336	−	0.748322i	$-0.269140\pi$
$138$		0			0
$139$	4.54419	−	9.95039i	0.385433	−	0.843981i	−0.613109	−	0.789999i	$-0.710081\pi$
$139$	4.54419	−	9.95039i	0.385433	−	0.843981i	0.998542	−	0.0539825i	$-0.0171915\pi$
$140$		0			0
$141$	2.75102	−	0.807773i	0.231678	−	0.0680268i
$142$		0			0
$143$	−1.76329	+	0.517750i	−0.147454	+	0.0432964i
$144$		0			0
$145$	0.224961	−	0.492595i	0.0186820	−	0.0409078i
$146$		0			0
$147$	−1.40226	−	1.61829i	−0.115656	−	0.133474i
$148$		0			0
$149$	−18.5426	−	5.44459i	−1.51907	−	0.446039i	−0.587384	−	0.809309i	$-0.699842\pi$
$149$	−18.5426	−	5.44459i	−1.51907	−	0.446039i	−0.931684	+	0.363270i	$0.881660\pi$
$150$		0			0
$151$	−9.22887	−	5.93104i	−0.751035	−	0.482661i	0.108272	−	0.994121i	$-0.465468\pi$
$151$	−9.22887	−	5.93104i	−0.751035	−	0.482661i	−0.859307	+	0.511460i	$0.829105\pi$
$152$		0			0
$153$	−6.35504	−	1.86601i	−0.513774	−	0.150858i
$154$		0			0
$155$	−0.682064	−	1.49351i	−0.0547847	−	0.119962i
$156$		0			0
$157$	0.578114	+	4.02087i	0.0461385	+	0.320900i	0.999800	+	0.0200175i	$0.00637219\pi$
$157$	0.578114	+	4.02087i	0.0461385	+	0.320900i	−0.953661	+	0.300883i	$0.902719\pi$
$158$		0			0
$159$	−0.769296	−	0.887815i	−0.0610091	−	0.0704083i
$160$		0			0
$161$	3.68735	+	8.07417i	0.290604	+	0.636334i
$162$		0			0
$163$	13.1972			1.03368			0.516841	−	0.856081i	$-0.327108\pi$
$163$	13.1972			1.03368			0.516841	+	0.856081i	$0.327108\pi$
$164$		0			0
$165$	4.28906	−	4.94984i	0.333903	−	0.385345i
$166$		0			0
$167$	20.1799	+	5.92535i	1.56157	+	0.458518i	0.944532	−	0.328418i	$-0.106515\pi$
$167$	20.1799	+	5.92535i	1.56157	+	0.458518i	0.617035	+	0.786936i	$0.288334\pi$
$168$		0			0
$169$	1.71867	−	11.9536i	0.132206	−	0.919511i
$170$		0			0
$171$	7.75389			0.592955
$172$		0			0
$173$	−4.42395	+	5.10550i	−0.336346	+	0.388164i	−0.898577	−	0.438816i	$-0.855398\pi$
$173$	−4.42395	+	5.10550i	−0.336346	+	0.388164i	0.562231	+	0.826981i	$0.309943\pi$
$174$		0			0
$175$	−12.4782	−	8.01922i	−0.943260	−	0.606196i
$176$		0			0
$177$	−6.03584	−	3.87900i	−0.453681	−	0.291563i
$178$		0			0
$179$	−2.02075	+	14.0546i	−0.151038	+	1.05049i	0.763446	+	0.645872i	$0.223506\pi$
$179$	−2.02075	+	14.0546i	−0.151038	+	1.05049i	−0.914484	+	0.404622i	$0.867403\pi$
$180$		0			0
$181$	0.856199	+	5.95499i	0.0636408	+	0.442631i	0.996582	+	0.0826038i	$0.0263236\pi$
$181$	0.856199	+	5.95499i	0.0636408	+	0.442631i	−0.932942	+	0.360027i	$0.882767\pi$
$182$		0			0
$183$	−7.02739	+	4.51623i	−0.519480	+	0.333849i
$184$		0			0
$185$	6.93770	−	15.1914i	0.510070	−	1.11690i
$186$		0			0
$187$	−10.6557	+	6.84801i	−0.779223	+	0.500776i
$188$		0			0
$189$	−1.44347	−	1.66586i	−0.104997	−	0.121173i
$190$		0			0
$191$	1.05446	−	7.33396i	0.0762983	−	0.530666i	−0.915447	−	0.402440i	$-0.868162\pi$
$191$	1.05446	−	7.33396i	0.0762983	−	0.530666i	0.991745	−	0.128227i	$-0.0409286\pi$
$192$		0			0
$193$	1.94581	−	2.24558i	0.140062	−	0.161640i	−0.681385	−	0.731926i	$-0.738622\pi$
$193$	1.94581	−	2.24558i	0.140062	−	0.161640i	0.821447	+	0.570285i	$0.193167\pi$
$194$		0			0
$195$	−1.36716	−	2.99367i	−0.0979045	−	0.214381i
$196$		0			0
$197$	−11.6008	+	7.45539i	−0.826524	+	0.531175i	−0.884172	−	0.467162i	$-0.845276\pi$
$197$	−11.6008	+	7.45539i	−0.826524	+	0.531175i	0.0576477	+	0.998337i	$0.481640\pi$
$198$		0			0
$199$	25.8803	−	7.59915i	1.83461	−	0.538690i	0.834681	−	0.550734i	$-0.185652\pi$
$199$	25.8803	−	7.59915i	1.83461	−	0.538690i	0.999927	+	0.0120447i	$0.00383403\pi$
$200$		0			0
$201$	0.946733	+	8.13042i	0.0667774	+	0.573475i
$202$		0			0
$203$	−0.334420	+	0.0981945i	−0.0234717	+	0.00689190i
$204$		0			0
$205$	22.0988	−	14.2020i	1.54345	−	0.991914i
$206$		0			0
$207$	−1.67284	−	3.66301i	−0.116270	−	0.254597i
$208$		0			0
$209$	9.71064	−	11.2067i	0.671699	−	0.775182i
$210$		0			0
$211$	0.754514	−	5.24776i	0.0519429	−	0.361271i	−0.947228	−	0.320560i	$-0.896129\pi$
$211$	0.754514	−	5.24776i	0.0519429	−	0.361271i	0.999171	−	0.0407104i	$-0.0129621\pi$
$212$		0			0
$213$	5.58951	+	6.45064i	0.382987	+	0.441991i
$214$		0			0
$215$	2.56925	−	1.65116i	0.175222	−	0.112608i
$216$		0			0
$217$	−0.438986	+	0.961246i	−0.0298003	+	0.0652536i
$218$		0			0
$219$	−9.77133	+	6.27965i	−0.660285	+	0.424340i
$220$		0			0
$221$	0.905795	+	6.29994i	0.0609304	+	0.423780i
$222$		0			0
$223$	−0.565255	+	3.93144i	−0.0378523	+	0.263269i	−0.999956	−	0.00941646i	$-0.997003\pi$
$223$	−0.565255	+	3.93144i	−0.0378523	+	0.263269i	0.962103	+	0.272685i	$0.0879117\pi$
$224$		0			0
$225$	5.66097	+	3.63808i	0.377398	+	0.242539i
$226$		0			0
$227$	−2.54308	−	1.63434i	−0.168790	−	0.108475i	0.453518	−	0.891247i	$-0.350169\pi$
$227$	−2.54308	−	1.63434i	−0.168790	−	0.108475i	−0.622308	+	0.782772i	$0.713805\pi$
$228$		0			0
$229$	14.4345	−	16.6583i	0.953856	−	1.10081i	−0.0409639	−	0.999161i	$-0.513043\pi$
$229$	14.4345	−	16.6583i	0.953856	−	1.10081i	0.994820	−	0.101648i	$-0.0324117\pi$
$230$		0			0
$231$	−4.21540			−0.277353
$232$		0			0
$233$	−0.902244	+	6.27524i	−0.0591080	+	0.411105i	0.938689	+	0.344765i	$0.112041\pi$
$233$	−0.902244	+	6.27524i	−0.0591080	+	0.411105i	−0.997797	+	0.0663401i	$0.978868\pi$
$234$		0			0
$235$	9.42168	+	2.76645i	0.614603	+	0.180464i
$236$		0			0
$237$	5.28952	−	6.10443i	0.343591	−	0.396526i
$238$		0			0
$239$	13.0625			0.844945			0.422473	−	0.906376i	$-0.361162\pi$
$239$	13.0625			0.844945			0.422473	+	0.906376i	$0.361162\pi$
$240$		0			0
$241$	7.93320	+	17.3713i	0.511022	+	1.11898i	0.972728	+	0.231949i	$0.0745104\pi$
$241$	7.93320	+	17.3713i	0.511022	+	1.11898i	−0.461706	+	0.887033i	$0.652762\pi$
$242$		0			0
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$		0			0
$245$	−1.04367	−	7.25889i	−0.0666777	−	0.463753i
$246$		0			0
$247$	−3.09532	−	6.77780i	−0.196950	−	0.431261i
$248$		0			0
$249$	8.43709	+	2.47735i	0.534679	+	0.156996i
$250$		0			0
$251$	17.6620	+	11.3507i	1.11482	+	0.716450i	0.962338	−	0.271856i	$-0.0876375\pi$
$251$	17.6620	+	11.3507i	1.11482	+	0.716450i	0.152481	+	0.988306i	$0.451274\pi$
$252$		0			0
$253$	−7.38913	−	2.16965i	−0.464551	−	0.136404i
$254$		0			0
$255$	−14.8545	−	17.1431i	−0.930228	−	1.07354i
$256$		0			0
$257$	−9.27322	+	20.3055i	−0.578448	+	1.26662i	0.363728	+	0.931505i	$0.381504\pi$
$257$	−9.27322	+	20.3055i	−0.578448	+	1.26662i	−0.942176	+	0.335119i	$0.891224\pi$
$258$		0			0
$259$	−10.3134	+	3.02828i	−0.640842	+	0.188168i
$260$		0			0
$261$	0.151716	−	0.0445479i	0.00939100	−	0.00275745i
$262$		0			0
$263$	4.98816	−	10.9225i	0.307583	−	0.673513i	−0.691209	−	0.722655i	$-0.742922\pi$
$263$	4.98816	−	10.9225i	0.307583	−	0.673513i	0.998792	+	0.0491424i	$0.0156488\pi$
$264$		0			0
$265$	−0.572570	−	3.98231i	−0.0351727	−	0.244632i
$266$		0			0
$267$	−10.8123			−0.661701
$268$		0			0
$269$	22.3231			1.36107			0.680533	−	0.732717i	$-0.261748\pi$
$269$	22.3231			1.36107			0.680533	+	0.732717i	$0.261748\pi$
$270$		0			0
$271$	−2.21991	−	15.4398i	−0.134850	−	0.937903i	−0.939108	−	0.343622i	$-0.888346\pi$
$271$	−2.21991	−	15.4398i	−0.134850	−	0.937903i	0.804258	−	0.594280i	$-0.202563\pi$
$272$		0			0
$273$	−0.879924	+	1.92677i	−0.0532554	+	0.116613i
$274$		0			0
$275$	12.3477	−	3.62560i	0.744592	−	0.218632i
$276$		0			0
$277$	4.77077	−	1.40082i	0.286648	−	0.0841674i	−0.135248	−	0.990812i	$-0.543183\pi$
$277$	4.77077	−	1.40082i	0.286648	−	0.0841674i	0.421896	+	0.906644i	$0.361365\pi$
$278$		0			0
$279$	0.199155	−	0.436089i	0.0119231	−	0.0261079i
$280$		0			0
$281$	−13.0457	−	15.0555i	−0.778241	−	0.898137i	0.218741	−	0.975783i	$-0.429805\pi$
$281$	−13.0457	−	15.0555i	−0.778241	−	0.898137i	−0.996981	+	0.0776456i	$0.975260\pi$
$282$		0			0
$283$	−21.2358	−	6.23540i	−1.26234	−	0.370656i	−0.418974	−	0.907998i	$-0.637610\pi$
$283$	−21.2358	−	6.23540i	−1.26234	−	0.370656i	−0.843364	+	0.537343i	$0.819428\pi$
$284$		0			0
$285$	22.3399	+	14.3570i	1.32330	+	0.850433i
$286$		0			0
$287$	−16.2222	−	4.76326i	−0.957565	−	0.281167i
$288$		0			0
$289$	11.1616	+	24.4404i	0.656563	+	1.43767i
$290$		0			0
$291$	2.18696	+	15.2107i	0.128202	+	0.891665i
$292$		0			0
$293$	6.08199	+	7.01899i	0.355314	+	0.410054i	0.905064	−	0.425275i	$-0.139823\pi$
$293$	6.08199	+	7.01899i	0.355314	+	0.410054i	−0.549751	+	0.835329i	$0.685277\pi$
$294$		0			0
$295$	−10.2077	−	22.3517i	−0.594314	−	1.30137i
$296$		0			0
$297$	1.91240			0.110969
$298$		0			0
$299$	−2.53411	+	2.92451i	−0.146551	+	0.169129i
$300$		0			0
$301$	−1.88602	−	0.553787i	−0.108709	−	0.0319197i
$302$		0			0
$303$	−1.59058	+	11.0628i	−0.0913766	+	0.635539i
$304$		0			0
$305$	−28.6089			−1.63814
$306$		0			0
$307$	12.6743	−	14.6269i	0.723362	−	0.834804i	−0.268345	−	0.963323i	$-0.586477\pi$
$307$	12.6743	−	14.6269i	0.723362	−	0.834804i	0.991707	+	0.128519i	$0.0410222\pi$
$308$		0			0
$309$	8.86240	+	5.69552i	0.504164	+	0.324007i
$310$		0			0
$311$	−1.44196	−	0.926695i	−0.0817663	−	0.0525480i	0.499119	−	0.866534i	$-0.333657\pi$
$311$	−1.44196	−	0.926695i	−0.0817663	−	0.0525480i	−0.580885	+	0.813986i	$0.697293\pi$
$312$		0			0
$313$	2.06229	−	14.3435i	0.116568	−	0.810745i	−0.844722	−	0.535205i	$-0.820234\pi$
$313$	2.06229	−	14.3435i	0.116568	−	0.810745i	0.961290	−	0.275540i	$-0.0888566\pi$
$314$		0			0
$315$	−1.07435	−	7.47224i	−0.0605325	−	0.421013i
$316$		0			0
$317$	−19.7280	+	12.6784i	−1.10803	+	0.712089i	−0.960863	−	0.277022i	$-0.910652\pi$
$317$	−19.7280	+	12.6784i	−1.10803	+	0.712089i	−0.147169	+	0.989111i	$0.547016\pi$
$318$		0			0
$319$	0.125618	−	0.275065i	0.00703326	−	0.0154007i
$320$		0			0
$321$	−9.89800	+	6.36106i	−0.552452	+	0.355040i
$322$		0			0
$323$	−33.6314	−	38.8127i	−1.87130	−	2.15960i
$324$		0			0
$325$	0.920274	−	6.40065i	0.0510476	−	0.355044i
$326$		0			0
$327$	2.43495	−	2.81008i	0.134653	−	0.155398i
$328$		0			0
$329$	−2.62539	−	5.74881i	−0.144743	−	0.316942i
$330$		0			0
$331$	−22.3351	+	14.3539i	−1.22765	+	0.788963i	−0.983523	−	0.180781i	$-0.942138\pi$
$331$	−22.3351	+	14.3539i	−1.22765	+	0.788963i	−0.244126	+	0.969743i	$0.578501\pi$
$332$		0			0
$333$	4.67887	−	1.37384i	0.256400	−	0.0752860i
$334$		0			0
$335$	−12.3265	+	25.1777i	−0.673468	+	1.37560i
$336$		0			0
$337$	−12.5146	+	3.67462i	−0.681715	+	0.200170i	−0.604213	−	0.796823i	$-0.706512\pi$
$337$	−12.5146	+	3.67462i	−0.681715	+	0.200170i	−0.0775017	+	0.996992i	$0.524694\pi$
$338$		0			0
$339$	−12.5799	+	8.08464i	−0.683249	+	0.439097i
$340$		0			0
$341$	−0.380865	−	0.833977i	−0.0206250	−	0.0451624i
$342$		0			0
$343$	−13.1952	+	15.2281i	−0.712475	+	0.822241i
$344$		0			0
$345$	1.96271	−	13.6510i	0.105669	−	0.734943i
$346$		0			0
$347$	19.5624	+	22.5762i	1.05016	+	1.21195i	0.976690	+	0.214654i	$0.0688625\pi$
$347$	19.5624	+	22.5762i	1.05016	+	1.21195i	0.0734721	+	0.997297i	$0.476592\pi$
$348$		0			0
$349$	−2.63684	+	1.69459i	−0.141147	+	0.0907095i	−0.609308	−	0.792933i	$-0.708553\pi$
$349$	−2.63684	+	1.69459i	−0.141147	+	0.0907095i	0.468162	+	0.883643i	$0.344916\pi$
$350$		0			0
$351$	0.399195	−	0.874116i	0.0213075	−	0.0466569i
$352$		0			0
$353$	15.2350	−	9.79094i	0.810877	−	0.521119i	−0.0682717	−	0.997667i	$-0.521748\pi$
$353$	15.2350	−	9.79094i	0.810877	−	0.521119i	0.879149	+	0.476548i	$0.158112\pi$
$354$		0			0
$355$	4.16016	+	28.9345i	0.220798	+	1.53568i
$356$		0			0
$357$	−2.07772	+	14.4508i	−0.109964	+	0.764819i
$358$		0			0
$359$	−25.4151	−	16.3333i	−1.34136	−	0.862037i	−0.344311	−	0.938856i	$-0.611888\pi$
$359$	−25.4151	−	16.3333i	−1.34136	−	0.862037i	−0.997045	+	0.0768181i	$0.975524\pi$
$360$		0			0
$361$	34.5947	+	22.2327i	1.82077	+	1.17014i
$362$		0			0
$363$	−4.80846	+	5.54925i	−0.252378	+	0.291260i
$364$		0			0
$365$	−39.7797			−2.08216
$366$		0			0
$367$	−0.404403	+	2.81269i	−0.0211097	+	0.146821i	−0.997650	−	0.0685124i	$-0.978175\pi$
$367$	−0.404403	+	2.81269i	−0.0211097	+	0.146821i	0.976541	+	0.215333i	$0.0690838\pi$
$368$		0			0
$369$	7.35952	+	2.16095i	0.383121	+	0.112495i
$370$		0			0
$371$	−1.69572	+	1.95696i	−0.0880372	+	0.101600i
$372$		0			0
$373$	−33.0527			−1.71140			−0.855701	−	0.517471i	$-0.826874\pi$
$373$	−33.0527			−1.71140			−0.855701	+	0.517471i	$0.826874\pi$
$374$		0			0
$375$	2.46015	+	5.38699i	0.127042	+	0.278183i
$376$		0			0
$377$	−0.0995045	−	0.114834i	−0.00512474	−	0.00591427i
$378$		0			0
$379$	5.17838	+	36.0164i	0.265995	+	1.85004i	0.485256	+	0.874372i	$0.338726\pi$
$379$	5.17838	+	36.0164i	0.265995	+	1.85004i	−0.219261	+	0.975666i	$0.570365\pi$
$380$		0			0
$381$	1.65382	+	3.62137i	0.0847280	+	0.185528i
$382$		0			0
$383$	−23.8331	−	6.99803i	−1.21782	−	0.357583i	−0.391177	−	0.920316i	$-0.627932\pi$
$383$	−23.8331	−	6.99803i	−1.21782	−	0.357583i	−0.826639	+	0.562733i	$0.809750\pi$
$384$		0			0
$385$	−12.1451	−	7.80517i	−0.618970	−	0.397788i
$386$		0			0
$387$	0.855633	+	0.251236i	0.0434943	+	0.0127711i
$388$		0			0
$389$	−2.58105	−	2.97869i	−0.130864	−	0.151025i	0.686535	−	0.727096i	$-0.259131\pi$
$389$	−2.58105	−	2.97869i	−0.130864	−	0.151025i	−0.817400	+	0.576071i	$0.804585\pi$
$390$		0			0
$391$	−11.0798	+	24.2613i	−0.560328	+	1.22695i
$392$		0			0
$393$	−2.97812	+	0.874456i	−0.150226	+	0.0441105i
$394$		0			0
$395$	26.5426	−	7.79361i	1.33550	−	0.392139i
$396$		0			0
$397$	15.2373	−	33.3651i	0.764740	−	1.67455i	0.0268359	−	0.999640i	$-0.491457\pi$
$397$	15.2373	−	33.3651i	0.764740	−	1.67455i	0.737904	−	0.674906i	$-0.235816\pi$
$398$		0			0
$399$	−2.43237	−	16.9175i	−0.121771	−	0.846934i
$400$		0			0
$401$	−19.9008			−0.993798			−0.496899	−	0.867808i	$-0.665528\pi$
$401$	−19.9008			−0.993798			−0.496899	+	0.867808i	$0.665528\pi$
$402$		0			0
$403$	−0.460694			−0.0229488
$404$		0			0
$405$	0.487399	+	3.38993i	0.0242190	+	0.168447i
$406$		0			0
$407$	3.87401	−	8.48290i	0.192028	−	0.420482i
$408$		0			0
$409$	−11.8899	+	3.49118i	−0.587916	+	0.172628i	−0.562143	−	0.827040i	$-0.690023\pi$
$409$	−11.8899	+	3.49118i	−0.587916	+	0.172628i	−0.0257731	+	0.999668i	$0.508205\pi$
$410$		0			0
$411$	14.5167	−	4.26249i	0.716056	−	0.210253i
$412$		0			0
$413$	−6.56981	+	14.3859i	−0.323279	+	0.707882i
$414$		0			0
$415$	19.7212	+	22.7595i	0.968078	+	1.11722i
$416$		0			0
$417$	10.4958	+	3.08185i	0.513982	+	0.150919i
$418$		0			0
$419$	15.3890	+	9.88989i	0.751800	+	0.483153i	0.859567	−	0.511023i	$-0.170733\pi$
$419$	15.3890	+	9.88989i	0.751800	+	0.483153i	−0.107766	+	0.994176i	$0.534370\pi$
$420$		0			0
$421$	36.6203	+	10.7527i	1.78476	+	0.524054i	0.995896	−	0.0905091i	$-0.0288494\pi$
$421$	36.6203	+	10.7527i	1.78476	+	0.524054i	0.788868	+	0.614563i	$0.210668\pi$
$422$		0			0
$423$	1.19106	+	2.60806i	0.0579114	+	0.126808i
$424$		0			0
$425$	−6.34293	−	44.1161i	−0.307677	−	2.13994i
$426$		0			0
$427$	12.0580	+	13.9157i	0.583528	+	0.673428i
$428$		0			0
$429$	−0.763423	−	1.67166i	−0.0368584	−	0.0807086i
$430$		0			0
$431$	11.9112			0.573744			0.286872	−	0.957969i	$-0.407385\pi$
$431$	11.9112			0.573744			0.286872	+	0.957969i	$0.407385\pi$
$432$		0			0
$433$	−17.0461	+	19.6722i	−0.819182	+	0.945386i	−0.999268	−	0.0382645i	$-0.987817\pi$
$433$	−17.0461	+	19.6722i	−0.819182	+	0.945386i	0.180086	+	0.983651i	$0.442363\pi$
$434$		0			0
$435$	0.519597	+	0.152567i	0.0249128	+	0.00731505i
$436$		0			0
$437$	4.44367	−	30.9064i	0.212570	−	1.47846i
$438$		0			0
$439$	−20.7749			−0.991530			−0.495765	−	0.868457i	$-0.665112\pi$
$439$	−20.7749			−0.991530			−0.495765	+	0.868457i	$0.665112\pi$
$440$		0			0
$441$	1.40226	−	1.61829i	0.0667742	−	0.0770615i
$442$		0			0
$443$	−0.105792	−	0.0679881i	−0.00502631	−	0.00323021i	0.538125	−	0.842865i	$-0.319133\pi$
$443$	−0.105792	−	0.0679881i	−0.00502631	−	0.00323021i	−0.543152	+	0.839635i	$0.682769\pi$
$444$		0			0
$445$	−31.1515	−	20.0198i	−1.47672	−	0.949032i
$446$		0			0
$447$	2.75029	−	19.1287i	0.130084	−	0.904756i
$448$		0			0
$449$	3.61922	+	25.1722i	0.170801	+	1.18795i	0.877196	+	0.480132i	$0.159411\pi$
$449$	3.61922	+	25.1722i	0.170801	+	1.18795i	−0.706395	+	0.707818i	$0.749680\pi$
$450$		0			0
$451$	12.3400	−	7.93042i	0.581067	−	0.373429i
$452$		0			0
$453$	4.55726	−	9.97901i	0.214119	−	0.468855i
$454$		0			0
$455$	−6.10273	+	3.92199i	−0.286100	+	0.183866i
$456$		0			0
$457$	19.5482	+	22.5599i	0.914429	+	1.05531i	0.998268	+	0.0588275i	$0.0187362\pi$
$457$	19.5482	+	22.5599i	0.914429	+	1.05531i	−0.0838396	+	0.996479i	$0.526718\pi$
$458$		0			0
$459$	0.942598	−	6.55591i	0.0439967	−	0.306004i
$460$		0			0
$461$	−7.14512	+	8.24591i	−0.332781	+	0.384050i	−0.897338	−	0.441344i	$-0.854502\pi$
$461$	−7.14512	+	8.24591i	−0.332781	+	0.384050i	0.564556	+	0.825394i	$0.309047\pi$
$462$		0			0
$463$	−1.06410	−	2.33004i	−0.0494527	−	0.108286i	0.883293	−	0.468822i	$-0.155321\pi$
$463$	−1.06410	−	2.33004i	−0.0494527	−	0.108286i	−0.932746	+	0.360535i	$0.882594\pi$
$464$		0			0
$465$	1.38124	−	0.887671i	0.0640536	−	0.0411648i
$466$		0			0
$467$	−5.06121	+	1.48610i	−0.234205	+	0.0687687i	−0.396729	−	0.917936i	$-0.629855\pi$
$467$	−5.06121	+	1.48610i	−0.234205	+	0.0687687i	0.162524	+	0.986705i	$0.448036\pi$
$468$		0			0
$469$	17.4420	−	4.61607i	0.805398	−	0.213151i
$470$		0			0
$471$	−3.89767	+	1.14446i	−0.179595	+	0.0527339i
$472$		0			0
$473$	1.43467	−	0.922006i	0.0659662	−	0.0423939i
$474$		0			0
$475$	21.6753	+	47.4623i	0.994532	+	2.17772i
$476$		0			0
$477$	0.769296	−	0.887815i	0.0352236	−	0.0406502i
$478$		0			0
$479$	3.86971	−	26.9144i	0.176812	−	1.22975i	−0.687271	−	0.726402i	$-0.741191\pi$
$479$	3.86971	−	26.9144i	0.176812	−	1.22975i	0.864082	−	0.503351i	$-0.167900\pi$
$480$		0			0
$481$	−3.06868	−	3.54144i	−0.139920	−	0.161476i
$482$		0			0
$483$	−7.46722	+	4.79889i	−0.339770	+	0.218357i
$484$		0			0
$485$	−21.8629	+	47.8731i	−0.992743	+	2.17380i
$486$		0			0
$487$	−19.0757	+	12.2592i	−0.864402	+	0.555518i	−0.896036	−	0.443982i	$-0.853565\pi$
$487$	−19.0757	+	12.2592i	−0.864402	+	0.555518i	0.0316335	+	0.999500i	$0.489929\pi$
$488$		0			0
$489$	1.87815	+	13.0628i	0.0849331	+	0.590722i
$490$		0			0
$491$	−2.58484	+	17.9779i	−0.116652	+	0.811333i	0.844548	+	0.535480i	$0.179869\pi$
$491$	−2.58484	+	17.9779i	−0.116652	+	0.811333i	−0.961200	+	0.275853i	$0.911040\pi$
$492$		0			0
$493$	−0.881036	−	0.566207i	−0.0396798	−	0.0255007i
$494$		0			0
$495$	5.50986	+	3.54097i	0.247650	+	0.159155i
$496$		0			0
$497$	12.3207	−	14.2188i	0.552657	−	0.637800i
$498$		0			0
$499$	2.76799			0.123912			0.0619562	−	0.998079i	$-0.480266\pi$
$499$	2.76799			0.123912			0.0619562	+	0.998079i	$0.480266\pi$
$500$		0			0
$501$	−2.99314	+	20.8178i	−0.133724	+	0.930069i
$502$		0			0
$503$	−19.8030	−	5.81467i	−0.882971	−	0.259264i	−0.191348	−	0.981522i	$-0.561286\pi$
$503$	−19.8030	−	5.81467i	−0.882971	−	0.259264i	−0.691623	+	0.722259i	$0.743104\pi$
$504$		0			0
$505$	−25.0663	+	28.9280i	−1.11543	+	1.28728i
$506$		0			0
$507$	12.0766			0.536339
$508$		0			0
$509$	−4.88784	−	10.7029i	−0.216650	−	0.474396i	0.769837	−	0.638241i	$-0.220338\pi$
$509$	−4.88784	−	10.7029i	−0.216650	−	0.474396i	−0.986486	+	0.163845i	$0.947610\pi$
$510$		0			0
$511$	16.7662	+	19.3493i	0.741694	+	0.855961i
$512$		0			0
$513$	1.10349	+	7.67497i	0.0487204	+	0.338858i
$514$		0			0
$515$	14.9879	+	32.8189i	0.660446	+	1.44617i
$516$		0			0
$517$	5.26106	+	1.54479i	0.231381	+	0.0679397i
$518$		0			0
$519$	−5.68313	−	3.65233i	−0.249462	−	0.160319i
$520$		0			0
$521$	14.5384	+	4.26886i	0.636940	+	0.187022i	0.584231	−	0.811588i	$-0.301396\pi$
$521$	14.5384	+	4.26886i	0.636940	+	0.187022i	0.0527088	+	0.998610i	$0.483214\pi$
$522$		0			0
$523$	−0.714748	−	0.824863i	−0.0312537	−	0.0360687i	0.739908	−	0.672709i	$-0.234869\pi$
$523$	−0.714748	−	0.824863i	−0.0312537	−	0.0360687i	−0.771161	+	0.636640i	$0.780324\pi$
$524$		0			0
$525$	6.16177	−	13.4924i	0.268922	−	0.588856i
$526$		0			0
$527$	−3.04668	+	0.894586i	−0.132715	+	0.0389688i
$528$		0			0
$529$	6.50916	−	1.91126i	0.283007	−	0.0830984i
$530$		0			0
$531$	2.98053	−	6.52644i	0.129344	−	0.283223i
$532$		0			0
$533$	−1.04897	−	7.29572i	−0.0454358	−	0.316013i
$534$		0			0
$535$	−40.2953			−1.74212
$536$		0			0
$537$	−14.1992			−0.612739
$538$		0			0
$539$	−0.582785	−	4.05336i	−0.0251023	−	0.174591i
$540$		0			0
$541$	14.4457	−	31.6316i	0.621068	−	1.35995i	−0.293672	−	0.955906i	$-0.594877\pi$
$541$	14.4457	−	31.6316i	0.621068	−	1.35995i	0.914740	−	0.404043i	$-0.132395\pi$
$542$		0			0
$543$	−5.77253	+	1.69497i	−0.247723	+	0.0727380i
$544$		0			0
$545$	12.2185	−	3.58767i	0.523382	−	0.153679i
$546$		0			0
$547$	13.6256	−	29.8358i	0.582587	−	1.27569i	−0.357233	−	0.934015i	$-0.616280\pi$
$547$	13.6256	−	29.8358i	0.582587	−	1.27569i	0.939820	−	0.341671i	$-0.110993\pi$
$548$		0			0
$549$	−5.47036	−	6.31313i	−0.233469	−	0.269438i
$550$		0			0
$551$	1.17639	+	0.345420i	0.0501160	+	0.0147154i
$552$		0			0
$553$	−14.9780	−	9.62578i	−0.636930	−	0.409330i
$554$		0			0
$555$	16.0242	+	4.70512i	0.680188	+	0.199721i
$556$		0			0
$557$	−2.89730	−	6.34420i	−0.122763	−	0.268812i	0.838266	−	0.545261i	$-0.183570\pi$
$557$	−2.89730	−	6.34420i	−0.122763	−	0.268812i	−0.961029	+	0.276449i	$0.910842\pi$
$558$		0			0
$559$	−0.121955	−	0.848215i	−0.00515814	−	0.0358757i
$560$		0			0
$561$	−8.29477	−	9.57268i	−0.350206	−	0.404159i
$562$		0			0
$563$	−12.6424	−	27.6829i	−0.532812	−	1.16670i	−0.964357	−	0.264605i	$-0.914758\pi$
$563$	−12.6424	−	27.6829i	−0.532812	−	1.16670i	0.431544	−	0.902092i	$-0.357969\pi$
$564$		0			0
$565$	−51.2137			−2.15458
$566$		0			0
$567$	1.44347	−	1.66586i	0.0606202	−	0.0699594i
$568$		0			0
$569$	−22.1342	−	6.49920i	−0.927915	−	0.272460i	−0.217351	−	0.976093i	$-0.569742\pi$
$569$	−22.1342	−	6.49920i	−0.927915	−	0.272460i	−0.710564	+	0.703633i	$0.751560\pi$
$570$		0			0
$571$	6.41722	−	44.6328i	0.268552	−	1.86782i	−0.193680	−	0.981065i	$-0.562042\pi$
$571$	6.41722	−	44.6328i	0.268552	−	1.86782i	0.462233	−	0.886759i	$-0.347048\pi$
$572$		0			0
$573$	7.40937			0.309531
$574$		0			0
$575$	17.7454	−	20.4792i	0.740033	−	0.854043i
$576$		0			0
$577$	16.0558	+	10.3184i	0.668411	+	0.429562i	0.830352	−	0.557239i	$-0.188139\pi$
$577$	16.0558	+	10.3184i	0.668411	+	0.429562i	−0.161941	+	0.986800i	$0.551775\pi$
$578$		0			0
$579$	2.49964	+	1.60642i	0.103881	+	0.0667606i
$580$		0			0
$581$	2.75842	−	19.1853i	0.114439	−	0.795938i
$582$		0			0
$583$	−0.319723	−	2.22372i	−0.0132416	−	0.0920972i
$584$		0			0
$585$	2.76863	−	1.77929i	0.114469	−	0.0735645i
$586$		0			0
$587$	14.0970	−	30.8681i	0.581845	−	1.27406i	−0.358401	−	0.933568i	$-0.616678\pi$
$587$	14.0970	−	30.8681i	0.581845	−	1.27406i	0.940246	−	0.340495i	$-0.110595\pi$
$588$		0			0
$589$	3.12720	−	2.00973i	0.128854	−	0.0828094i
$590$		0			0
$591$	−9.03047	−	10.4217i	−0.371464	−	0.428692i
$592$		0			0
$593$	2.66185	−	18.5135i	0.109309	−	0.760260i	−0.859264	−	0.511532i	$-0.829078\pi$
$593$	2.66185	−	18.5135i	0.109309	−	0.760260i	0.968573	−	0.248728i	$-0.0800126\pi$
$594$		0			0
$595$	−32.7431	+	37.7875i	−1.34233	+	1.54914i
$596$		0			0
$597$	11.2050	+	24.5354i	0.458588	+	1.00417i
$598$		0			0
$599$	−24.3301	+	15.6360i	−0.994100	+	0.638869i	−0.933231	−	0.359277i	$-0.883023\pi$
$599$	−24.3301	+	15.6360i	−0.994100	+	0.638869i	−0.0608688	+	0.998146i	$0.519387\pi$
$600$		0			0
$601$	14.4010	−	4.22851i	0.587429	−	0.172485i	0.0255066	−	0.999675i	$-0.491880\pi$
$601$	14.4010	−	4.22851i	0.587429	−	0.172485i	0.561922	+	0.827190i	$0.310062\pi$
$602$		0			0
$603$	−7.91293	+	2.09418i	−0.322239	+	0.0852814i
$604$		0			0
$605$	−24.1286	+	7.08481i	−0.980968	+	0.288038i
$606$		0			0
$607$	21.2316	−	13.6447i	0.861764	−	0.553822i	−0.0334593	−	0.999440i	$-0.510652\pi$
$607$	21.2316	−	13.6447i	0.861764	−	0.553822i	0.895223	+	0.445618i	$0.147016\pi$
$608$		0			0
$609$	−0.144788	−	0.317041i	−0.00586710	−	0.0128472i
$610$		0			0
$611$	1.80428	−	2.08225i	0.0729935	−	0.0842390i
$612$		0			0
$613$	5.45981	−	37.9738i	0.220520	−	1.53375i	−0.515560	−	0.856854i	$-0.672416\pi$
$613$	5.45981	−	37.9738i	0.220520	−	1.53375i	0.736080	−	0.676895i	$-0.236675\pi$
$614$		0			0
$615$	17.2025	+	19.8527i	0.693671	+	0.800539i
$616$		0			0
$617$	4.79741	−	3.08311i	0.193136	−	0.124121i	−0.440499	−	0.897753i	$-0.645198\pi$
$617$	4.79741	−	3.08311i	0.193136	−	0.124121i	0.633635	+	0.773632i	$0.281562\pi$
$618$		0			0
$619$	−0.450694	+	0.986882i	−0.0181149	+	0.0396661i	−0.918473	−	0.395483i	$-0.870577\pi$
$619$	−0.450694	+	0.986882i	−0.0181149	+	0.0396661i	0.900358	+	0.435149i	$0.143304\pi$
$620$		0			0
$621$	3.38766	−	2.17711i	0.135942	−	0.0873646i
$622$		0			0
$623$	3.39178	+	23.5903i	0.135889	+	0.945127i
$624$		0			0
$625$	1.90187	−	13.2278i	0.0760749	−	0.529113i
$626$		0			0
$627$	12.4746	+	8.01693i	0.498187	+	0.320165i
$628$		0			0
$629$	−27.1708	−	17.4616i	−1.08337	−	0.696240i
$630$		0			0
$631$	−12.4877	+	14.4116i	−0.497127	+	0.573716i	−0.947756	−	0.318996i	$-0.896654\pi$
$631$	−12.4877	+	14.4116i	−0.497127	+	0.573716i	0.450629	+	0.892711i	$0.351200\pi$
$632$		0			0
$633$	5.30172			0.210725
$634$		0			0
$635$	−1.94040	+	13.4958i	−0.0770025	+	0.535564i
$636$		0			0
$637$	−1.97435	−	0.579721i	−0.0782266	−	0.0229694i
$638$		0			0
$639$	−5.58951	+	6.45064i	−0.221118	+	0.255184i
$640$		0			0
$641$	−0.0564206			−0.00222848			−0.00111424	−	0.999999i	$-0.500355\pi$
$641$	−0.0564206			−0.00222848			−0.00111424	+	0.999999i	$0.500355\pi$
$642$		0			0
$643$	12.5242	+	27.4243i	0.493908	+	1.08151i	0.978402	+	0.206713i	$0.0662765\pi$
$643$	12.5242	+	27.4243i	0.493908	+	1.08151i	−0.484494	+	0.874795i	$0.660996\pi$
$644$		0			0
$645$	1.99999	+	2.30812i	0.0787497	+	0.0908820i
$646$		0			0
$647$	1.70621	+	11.8670i	0.0670781	+	0.466538i	0.995481	+	0.0949627i	$0.0302732\pi$
$647$	1.70621	+	11.8670i	0.0670781	+	0.466538i	−0.928403	+	0.371575i	$0.878818\pi$
$648$		0			0
$649$	−5.69997	−	12.4812i	−0.223743	−	0.489929i
$650$		0			0
$651$	−1.01394	−	0.297718i	−0.0397393	−	0.0116685i
$652$		0			0
$653$	−39.2864	−	25.2478i	−1.53739	−	0.988024i	−0.988344	−	0.152234i	$-0.951353\pi$
$653$	−39.2864	−	25.2478i	−1.53739	−	0.988024i	−0.549050	−	0.835789i	$-0.685011\pi$
$654$		0			0
$655$	−10.1995	−	2.99483i	−0.398526	−	0.117018i
$656$		0			0
$657$	−7.60634	−	8.77819i	−0.296752	−	0.342470i
$658$		0			0
$659$	−14.7641	+	32.3288i	−0.575127	+	1.25935i	0.368896	+	0.929471i	$0.379736\pi$
$659$	−14.7641	+	32.3288i	−0.575127	+	1.25935i	−0.944023	+	0.329881i	$0.892991\pi$
$660$		0			0
$661$	10.8736	−	3.19279i	0.422936	−	0.124185i	−0.0633371	−	0.997992i	$-0.520174\pi$
$661$	10.8736	−	3.19279i	0.422936	−	0.124185i	0.486273	+	0.873807i	$0.338356\pi$
$662$		0			0
$663$	−6.10691	+	1.79315i	−0.237173	+	0.0696402i
$664$		0			0
$665$	24.3162	−	53.2451i	0.942942	−	2.06476i
$666$		0			0
$667$	−0.0906177	−	0.630260i	−0.00350873	−	0.0244038i
$668$		0			0
$669$	−3.97187			−0.153561
$670$		0			0
$671$	−15.9752			−0.616716
$672$		0			0
$673$	3.48972	+	24.2716i	0.134519	+	0.935600i	0.939561	+	0.342382i	$0.111234\pi$
$673$	3.48972	+	24.2716i	0.134519	+	0.935600i	−0.805042	+	0.593218i	$0.797857\pi$
$674$		0			0
$675$	−2.79541	+	6.12110i	−0.107595	+	0.235601i
$676$		0			0
$677$	−34.0653	+	10.0025i	−1.30923	+	0.384426i	−0.860596	−	0.509288i	$-0.829909\pi$
$677$	−34.0653	+	10.0025i	−1.30923	+	0.384426i	−0.448638	+	0.893714i	$0.648091\pi$
$678$		0			0
$679$	32.5007	−	9.54307i	1.24726	−	0.366229i
$680$		0			0
$681$	1.25578	−	2.74978i	0.0481218	−	0.105372i
$682$		0			0
$683$	−20.3315	−	23.4638i	−0.777964	−	0.897819i	0.218996	−	0.975726i	$-0.429722\pi$
$683$	−20.3315	−	23.4638i	−0.777964	−	0.897819i	−0.996961	+	0.0779071i	$0.975176\pi$
$684$		0			0
$685$	49.7167	+	14.5981i	1.89958	+	0.557766i
$686$		0			0
$687$	18.5429	+	11.9168i	0.707457	+	0.454655i
$688$		0			0
$689$	−1.08315	−	0.318042i	−0.0412648	−	0.0121164i
$690$		0			0
$691$	0.266779	+	0.584165i	0.0101488	+	0.0222227i	0.914639	−	0.404273i	$-0.132475\pi$
$691$	0.266779	+	0.584165i	0.0101488	+	0.0222227i	−0.904490	+	0.426495i	$0.859748\pi$
$692$		0			0
$693$	−0.599914	−	4.17250i	−0.0227889	−	0.158500i
$694$		0			0
$695$	24.5334	+	28.3130i	0.930605	+	1.07398i
$696$		0			0
$697$	−21.1041	−	46.2115i	−0.799374	−	1.75038i
$698$		0			0
$699$	−6.33977			−0.239792
$700$		0			0
$701$	11.0617	−	12.7659i	0.417794	−	0.482160i	−0.507370	−	0.861729i	$-0.669382\pi$
$701$	11.0617	−	12.7659i	0.417794	−	0.482160i	0.925164	+	0.379569i	$0.123928\pi$
$702$		0			0
$703$	36.2794	+	10.6526i	1.36831	+	0.401771i
$704$		0			0
$705$	−1.39745	+	9.71949i	−0.0526311	+	0.366057i
$706$		0			0
$707$	24.6358			0.926523
$708$		0			0
$709$	18.7837	−	21.6775i	0.705436	−	0.814117i	−0.284040	−	0.958812i	$-0.591675\pi$
$709$	18.7837	−	21.6775i	0.705436	−	0.814117i	0.989476	+	0.144696i	$0.0462203\pi$
$710$		0			0
$711$	6.79508	+	4.36693i	0.254835	+	0.163773i
$712$		0			0
$713$	−1.62408	−	1.04373i	−0.0608224	−	0.0390882i
$714$		0			0
$715$	0.895710	−	6.22980i	0.0334976	−	0.232981i
$716$		0			0
$717$	1.85899	+	12.9296i	0.0694253	+	0.482864i
$718$		0			0
$719$	16.6441	−	10.6965i	0.620721	−	0.398913i	−0.192143	−	0.981367i	$-0.561544\pi$
$719$	16.6441	−	10.6965i	0.620721	−	0.398913i	0.812864	+	0.582454i	$0.197907\pi$
$720$		0			0
$721$	9.64642	−	21.1227i	0.359252	−	0.786651i
$722$		0			0
$723$	−16.0655	+	10.3246i	−0.597481	+	0.383978i
$724$		0			0
$725$	0.696792	+	0.804140i	0.0258782	+	0.0298650i
$726$		0			0
$727$	4.73697	−	32.9464i	0.175685	−	1.22191i	−0.690925	−	0.722926i	$-0.742797\pi$
$727$	4.73697	−	32.9464i	0.175685	−	1.22191i	0.866610	−	0.498987i	$-0.166294\pi$
$728$		0			0
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$		0			0
$731$	−2.45360	−	5.37264i	−0.0907497	−	0.198714i
$732$		0			0
$733$	42.5947	−	27.3739i	1.57327	−	1.01108i	0.595006	−	0.803721i	$-0.297150\pi$
$733$	42.5947	−	27.3739i	1.57327	−	1.01108i	0.978265	−	0.207358i	$-0.0664866\pi$
$734$		0			0
$735$	7.03647	−	2.06609i	0.259544	−	0.0762091i
$736$		0			0
$737$	−6.88311	+	14.0592i	−0.253543	+	0.517877i
$738$		0			0
$739$	38.9458	−	11.4355i	1.43264	−	0.420663i	0.528882	−	0.848695i	$-0.322611\pi$
$739$	38.9458	−	11.4355i	1.43264	−	0.420663i	0.903763	+	0.428033i	$0.140793\pi$
$740$		0			0
$741$	6.26830	−	4.02839i	0.230272	−	0.147987i
$742$		0			0
$743$	−21.5214	−	47.1254i	−0.789545	−	1.72886i	−0.677948	−	0.735109i	$-0.737131\pi$
$743$	−21.5214	−	47.1254i	−0.789545	−	1.72886i	−0.111597	−	0.993754i	$-0.535597\pi$
$744$		0			0
$745$	43.3423	−	50.0196i	1.58794	−	1.83258i
$746$		0			0
$747$	−1.25141	+	8.70378i	−0.0457869	+	0.318455i
$748$		0			0
$749$	16.9836	+	19.6001i	0.620566	+	0.716172i
$750$		0			0
$751$	−2.50030	+	1.60685i	−0.0912372	+	0.0586346i	−0.585464	−	0.810698i	$-0.699088\pi$
$751$	−2.50030	+	1.60685i	−0.0912372	+	0.0586346i	0.494227	+	0.869333i	$0.335451\pi$
$752$		0			0
$753$	−8.72160	+	19.0976i	−0.317833	+	0.695957i
$754$		0			0
$755$	31.6070	−	20.3126i	1.15030	−	0.739250i
$756$		0			0
$757$	3.50790	+	24.3980i	0.127497	+	0.886759i	0.948712	+	0.316141i	$0.102387\pi$
$757$	3.50790	+	24.3980i	0.127497	+	0.886759i	−0.821216	+	0.570618i	$0.806704\pi$
$758$		0			0
$759$	1.09598	−	7.62270i	0.0397815	−	0.276686i
$760$		0			0
$761$	30.7105	+	19.7364i	1.11325	+	0.715445i	0.962000	−	0.273050i	$-0.0880324\pi$
$761$	30.7105	+	19.7364i	1.11325	+	0.715445i	0.151254	+	0.988495i	$0.451669\pi$
$762$		0			0
$763$	−6.89489	−	4.43108i	−0.249612	−	0.160416i
$764$		0			0
$765$	14.8545	−	17.1431i	0.537067	−	0.619809i
$766$		0			0
$767$	−6.89468			−0.248952
$768$		0			0
$769$	−7.04914	+	49.0278i	−0.254198	+	1.76799i	0.318210	+	0.948020i	$0.396918\pi$
$769$	−7.04914	+	49.0278i	−0.254198	+	1.76799i	−0.572409	+	0.819968i	$0.693991\pi$
$770$		0			0
$771$	−21.4186	−	6.28906i	−0.771371	−	0.226495i
$772$		0			0
$773$	32.4095	−	37.4026i	1.16569	−	1.34528i	0.238296	−	0.971193i	$-0.423411\pi$
$773$	32.4095	−	37.4026i	1.16569	−	1.34528i	0.927394	−	0.374085i	$-0.122043\pi$
$774$		0			0
$775$	3.22606			0.115884
$776$		0			0
$777$	−4.46520	−	9.77743i	−0.160188	−	0.350763i
$778$		0			0
$779$	38.9472	+	44.9475i	1.39543	+	1.61041i
$780$		0			0
$781$	2.32303	+	16.1570i	0.0831245	+	0.578144i
$782$		0			0
$783$	0.0656860	+	0.143832i	0.00234742	+	0.00514014i
$784$		0			0
$785$	−13.3487	−	3.91953i	−0.476436	−	0.139894i
$786$		0			0
$787$	8.19097	+	5.26402i	0.291977	+	0.187642i	0.678426	−	0.734669i	$-0.262662\pi$
$787$	8.19097	+	5.26402i	0.291977	+	0.187642i	−0.386450	+	0.922311i	$0.626299\pi$
$788$		0			0
$789$	11.5213	+	3.38295i	0.410167	+	0.120436i
$790$		0			0
$791$	21.5854	+	24.9109i	0.767489	+	0.885730i
$792$		0			0
$793$	−3.33467	+	7.30191i	−0.118418	+	0.259298i
$794$		0			0
$795$	3.86029	−	1.13348i	0.136911	−	0.0402006i
$796$		0			0
$797$	1.16070	−	0.340813i	0.0411142	−	0.0120722i	−0.261111	−	0.965309i	$-0.584089\pi$
$797$	1.16070	−	0.340813i	0.0411142	−	0.0120722i	0.302225	+	0.953237i	$0.402271\pi$
$798$		0			0
$799$	7.88879	−	17.2741i	0.279086	−	0.611112i
$800$		0			0
$801$	−1.53875	−	10.7022i	−0.0543690	−	0.378145i
$802$		0			0
$803$	−22.2129			−0.783878
$804$		0			0
$805$	−30.3995			−1.07144
$806$		0			0
$807$	3.17691	+	22.0959i	0.111833	+	0.777813i
$808$		0			0
$809$	3.38282	−	7.40734i	0.118934	−	0.260428i	−0.840797	−	0.541351i	$-0.817913\pi$
$809$	3.38282	−	7.40734i	0.118934	−	0.260428i	0.959730	+	0.280923i	$0.0906404\pi$
$810$		0			0
$811$	22.8440	−	6.70761i	0.802163	−	0.235536i	0.145144	−	0.989411i	$-0.453635\pi$
$811$	22.8440	−	6.70761i	0.802163	−	0.235536i	0.657019	+	0.753874i	$0.271817\pi$
$812$		0			0
$813$	14.9667	−	4.39463i	0.524907	−	0.154127i
$814$		0			0
$815$	−18.7758	+	41.1132i	−0.657686	+	1.44013i
$816$		0			0
$817$	4.52808	+	5.22568i	0.158418	+	0.182824i
$818$		0			0
$819$	−2.03238	−	0.596761i	−0.0710171	−	0.0208525i
$820$		0			0
$821$	32.0829	+	20.6185i	1.11970	+	0.719589i	0.963386	−	0.268118i	$-0.0864018\pi$
$821$	32.0829	+	20.6185i	1.11970	+	0.719589i	0.156316	+	0.987707i	$0.450038\pi$
$822$		0			0
$823$	−50.6549	−	14.8736i	−1.76572	−	0.518462i	−0.772531	−	0.634978i	$-0.781009\pi$
$823$	−50.6549	−	14.8736i	−1.76572	−	0.518462i	−0.993189	+	0.116516i	$0.962828\pi$
$824$		0			0
$825$	5.34595	+	11.7060i	0.186122	+	0.407551i
$826$		0			0
$827$	−1.24611	−	8.66687i	−0.0433314	−	0.301377i	−0.999950	−	0.0100323i	$-0.996807\pi$
$827$	−1.24611	−	8.66687i	−0.0433314	−	0.301377i	0.956618	−	0.291344i	$-0.0941025\pi$
$828$		0			0
$829$	30.2048	+	34.8582i	1.04906	+	1.21067i	0.976992	+	0.213275i	$0.0684130\pi$
$829$	30.2048	+	34.8582i	1.04906	+	1.21067i	0.0720636	+	0.997400i	$0.477042\pi$
$830$		0			0
$831$	2.06552	+	4.52285i	0.0716520	+	0.156896i
$832$		0			0
$833$	−14.1826			−0.491397
$834$		0			0
$835$	−47.1694	+	54.4364i	−1.63236	+	1.88385i
$836$		0			0
$837$	0.459992	+	0.135066i	0.0158997	+	0.00466856i
$838$		0			0
$839$	−3.95377	+	27.4991i	−0.136499	+	0.949375i	0.800323	+	0.599569i	$0.204661\pi$
$839$	−3.95377	+	27.4991i	−0.136499	+	0.949375i	−0.936822	+	0.349805i	$0.886248\pi$
$840$		0			0
$841$	−28.9750			−0.999138
$842$		0			0
$843$	13.0457	−	15.0555i	0.449317	−	0.518540i
$844$		0			0
$845$	34.7940	+	22.3608i	1.19695	+	0.769233i
$846$		0			0
$847$	13.6158	+	8.75035i	0.467845	+	0.300665i
$848$		0			0
$849$	3.14976	−	21.9070i	0.108099	−	0.751848i
$850$		0			0
$851$	−2.79461	−	19.4370i	−0.0957981	−	0.666291i
$852$		0			0
$853$	−19.5918	+	12.5909i	−0.670809	+	0.431103i	−0.831217	−	0.555948i	$-0.812355\pi$
$853$	−19.5918	+	12.5909i	−0.670809	+	0.431103i	0.160408	+	0.987051i	$0.448719\pi$
$854$		0			0
$855$	−11.0315	+	24.1557i	−0.377271	+	0.826108i
$856$		0			0
$857$	1.50832	−	0.969338i	0.0515232	−	0.0331120i	−0.514626	−	0.857415i	$-0.672069\pi$
$857$	1.50832	−	0.969338i	0.0515232	−	0.0331120i	0.566149	+	0.824303i	$0.308433\pi$
$858$		0			0
$859$	−29.1443	−	33.6343i	−0.994390	−	1.14759i	−0.989047	−	0.147602i	$-0.952845\pi$
$859$	−29.1443	−	33.6343i	−0.994390	−	1.14759i	−0.00534358	−	0.999986i	$-0.501701\pi$
$860$		0			0
$861$	2.40612	−	16.7350i	0.0820004	−	0.570326i
$862$		0			0
$863$	−0.736713	+	0.850212i	−0.0250780	+	0.0289416i	−0.768150	−	0.640270i	$-0.778823\pi$
$863$	−0.736713	+	0.850212i	−0.0250780	+	0.0289416i	0.743072	+	0.669211i	$0.233368\pi$
$864$		0			0
$865$	−9.61119	−	21.0456i	−0.326790	−	0.715571i
$866$		0			0
$867$	−22.6032	+	14.5262i	−0.767645	+	0.493335i
$868$		0			0
$869$	14.8214	−	4.35195i	0.502781	−	0.147630i
$870$		0			0
$871$	4.98936	+	6.08083i	0.169058	+	0.206041i
$872$		0			0
$873$	−14.7446	+	4.32941i	−0.499029	+	0.146528i
$874$		0			0
$875$	10.9816	−	7.05746i	0.371247	−	0.238586i
$876$		0			0
$877$	2.29211	+	5.01903i	0.0773992	+	0.169481i	0.944376	−	0.328868i	$-0.106667\pi$
$877$	2.29211	+	5.01903i	0.0773992	+	0.169481i	−0.866977	+	0.498349i	$0.833940\pi$
$878$		0			0
$879$	−6.08199	+	7.01899i	−0.205140	+	0.236745i
$880$		0			0
$881$	1.95326	−	13.5852i	0.0658071	−	0.457699i	−0.930099	−	0.367308i	$-0.880279\pi$
$881$	1.95326	−	13.5852i	0.0658071	−	0.457699i	0.995906	−	0.0903904i	$-0.0288115\pi$
$882$		0			0
$883$	14.9869	+	17.2959i	0.504351	+	0.582052i	0.949643	−	0.313333i	$-0.101446\pi$
$883$	14.9869	+	17.2959i	0.504351	+	0.582052i	−0.445292	+	0.895385i	$0.646900\pi$
$884$		0			0
$885$	20.6715	−	13.2848i	0.694865	−	0.446562i
$886$		0			0
$887$	21.7306	−	47.5833i	0.729642	−	1.59769i	−0.0702372	−	0.997530i	$-0.522376\pi$
$887$	21.7306	−	47.5833i	0.729642	−	1.59769i	0.799879	−	0.600162i	$-0.204897\pi$
$888$		0			0
$889$	7.38233	−	4.74434i	0.247596	−	0.159120i
$890$		0			0
$891$	0.272163	+	1.89294i	0.00911781	+	0.0634158i
$892$		0			0
$893$	−3.16390	+	22.0054i	−0.105876	+	0.736382i
$894$		0			0
$895$	−40.9095	−	26.2909i	−1.36745	−	0.878809i
$896$		0			0
$897$	−3.25539	−	2.09211i	−0.108694	−	0.0698535i
$898$		0			0
$899$	0.0496419	−	0.0572898i	0.00165565	−	0.00191072i
$900$		0			0
$901$	−7.78073			−0.259214
$902$		0			0
$903$	0.279741	−	1.94564i	0.00930918	−	0.0647468i
$904$		0			0
$905$	−19.7697	−	5.80491i	−0.657168	−	0.192962i
$906$		0			0
$907$	11.9547	−	13.7964i	0.396948	−	0.458102i	−0.521730	−	0.853111i	$-0.674713\pi$
$907$	11.9547	−	13.7964i	0.396948	−	0.458102i	0.918677	+	0.395009i	$0.129258\pi$
$908$		0			0
$909$	−11.1765			−0.370702
$910$		0			0
$911$	7.23268	+	15.8374i	0.239629	+	0.524715i	0.990790	−	0.135404i	$-0.0432332\pi$
$911$	7.23268	+	15.8374i	0.239629	+	0.524715i	−0.751161	+	0.660119i	$0.770506\pi$
$912$		0			0
$913$	11.0123	+	12.7089i	0.364455	+	0.420604i
$914$		0			0
$915$	−4.07147	−	28.3177i	−0.134599	−	0.936155i
$916$		0			0
$917$	2.84212	+	6.22338i	0.0938552	+	0.205514i
$918$		0			0
$919$	−29.2981	−	8.60270i	−0.966455	−	0.283777i	−0.239833	−	0.970814i	$-0.577093\pi$
$919$	−29.2981	−	8.60270i	−0.966455	−	0.283777i	−0.726622	+	0.687037i	$0.758911\pi$
$920$		0			0
$921$	16.2818	+	10.4637i	0.536504	+	0.344790i
$922$		0			0
$923$	7.86992	+	2.31082i	0.259042	+	0.0760615i
$924$		0			0
$925$	21.4888	+	24.7994i	0.706547	+	0.815398i
$926$		0			0
$927$	−4.37629	+	9.58275i	−0.143736	+	0.314739i
$928$		0			0
$929$	15.6329	−	4.59024i	0.512900	−	0.150601i	−0.0150332	−	0.999887i	$-0.504785\pi$
$929$	15.6329	−	4.59024i	0.512900	−	0.150601i	0.527933	+	0.849286i	$0.322967\pi$
$930$		0			0
$931$	15.9309	−	4.67774i	0.522114	−	0.153307i
$932$		0			0
$933$	0.712049	−	1.55917i	0.0233114	−	0.0510449i
$934$		0			0
$935$	−6.17362	−	42.9385i	−0.201899	−	1.40424i
$936$		0			0
$937$	−28.6470			−0.935855			−0.467928	−	0.883767i	$-0.654999\pi$
$937$	−28.6470			−0.935855			−0.467928	+	0.883767i	$0.654999\pi$
$938$		0			0
$939$	14.4910			0.472897
$940$		0			0
$941$	−6.59148	−	45.8448i	−0.214876	−	1.49450i	−0.756565	−	0.653918i	$-0.773124\pi$
$941$	−6.59148	−	45.8448i	−0.214876	−	1.49450i	0.541689	−	0.840579i	$-0.317785\pi$
$942$		0			0
$943$	12.8311	−	28.0961i	0.417837	−	0.914935i
$944$		0			0
$945$	7.24329	−	2.12682i	0.235624	−	0.0691855i
$946$		0			0
$947$	−18.7820	+	5.51488i	−0.610332	+	0.179210i	−0.572269	−	0.820066i	$-0.693937\pi$
$947$	−18.7820	+	5.51488i	−0.610332	+	0.179210i	−0.0380624	+	0.999275i	$0.512119\pi$
$948$		0			0
$949$	−4.63674	+	10.1530i	−0.150515	+	0.329582i
$950$		0			0
$951$	−15.3569	−	17.7228i	−0.497982	−	0.574702i
$952$		0			0
$953$	−34.8704	−	10.2389i	−1.12956	−	0.331669i	−0.337027	−	0.941495i	$-0.609421\pi$
$953$	−34.8704	−	10.2389i	−1.12956	−	0.331669i	−0.792535	+	0.609826i	$0.791239\pi$
$954$		0			0
$955$	21.3473	+	13.7191i	0.690782	+	0.443938i
$956$		0			0
$957$	0.290143	+	0.0851936i	0.00937898	+	0.00275392i
$958$		0			0
$959$	−13.8538	−	30.3355i	−0.447361	−	0.979585i
$960$		0			0
$961$	4.37905	+	30.4570i	0.141260	+	0.982483i
$962$		0			0
$963$	−7.70494	−	8.89198i	−0.248288	−	0.286540i
$964$		0			0
$965$	4.22734	+	9.25658i	0.136083	+	0.297980i
$966$		0			0
$967$	0.769735			0.0247530			0.0123765	−	0.999923i	$-0.496060\pi$
$967$	0.769735			0.0247530			0.0123765	+	0.999923i	$0.496060\pi$
$968$		0			0
$969$	33.6314	−	38.8127i	1.08040	−	1.24684i
$970$		0			0
$971$	−18.3109	−	5.37658i	−0.587626	−	0.172543i	−0.0256145	−	0.999672i	$-0.508154\pi$
$971$	−18.3109	−	5.37658i	−0.587626	−	0.172543i	−0.562012	+	0.827129i	$0.689972\pi$
$972$		0			0
$973$	3.43150	−	23.8666i	0.110009	−	0.765129i
$974$		0			0
$975$	6.46647			0.207093
$976$		0			0
$977$	23.7678	−	27.4295i	0.760400	−	0.877548i	−0.235133	−	0.971963i	$-0.575553\pi$
$977$	23.7678	−	27.4295i	0.760400	−	0.877548i	0.995533	+	0.0944151i	$0.0300981\pi$
$978$		0			0
$979$	−17.3950	−	11.1791i	−0.555946	−	0.357285i
$980$		0			0
$981$	3.12801	+	2.01025i	0.0998696	+	0.0641823i
$982$		0			0
$983$	−3.39842	+	23.6365i	−0.108393	+	0.753888i	0.861041	+	0.508535i	$0.169813\pi$
$983$	−3.39842	+	23.6365i	−0.108393	+	0.753888i	−0.969434	+	0.245353i	$0.921096\pi$
$984$		0			0
$985$	−6.72119	−	46.7469i	−0.214155	−	1.48948i
$986$		0			0
$987$	5.31666	−	3.41681i	0.169231	−	0.108758i
$988$		0			0
$989$	1.49176	−	3.26651i	0.0474353	−	0.103869i
$990$		0			0
$991$	37.4640	−	24.0767i	1.19008	−	0.764821i	0.212871	−	0.977080i	$-0.431719\pi$
$991$	37.4640	−	24.0767i	1.19008	−	0.764821i	0.977213	+	0.212260i	$0.0680823\pi$
$992$		0			0
$993$	−17.3864	−	20.0650i	−0.551742	−	0.636744i
$994$		0			0
$995$	−13.1466	+	91.4364i	−0.416774	+	2.89873i
$996$		0			0
$997$	−23.6133	+	27.2513i	−0.747842	+	0.863056i	−0.994357	−	0.106083i	$-0.966169\pi$
$997$	−23.6133	+	27.2513i	−0.747842	+	0.863056i	0.246515	+	0.969139i	$0.420714\pi$
$998$		0			0
$999$	2.02573	+	4.43573i	0.0640912	+	0.140340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.625.1	yes	60
67.64	even	11	inner	804.2.q.b.265.1	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.265.1	✓	60	67.64	even	11	inner
804.2.q.b.625.1	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)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{3} +(-1.42271 + 3.11530i) q^{5} +(2.11496 - 0.621007i) q^{7} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{3} +(-1.42271 + 3.11530i) q^{5} +(2.11496 - 0.621007i) q^{7} +(-0.959493 + 0.281733i) q^{9} +(-0.794441 + 1.73958i) q^{11} +(0.629292 + 0.726242i) q^{13} +(-3.28606 - 0.964876i) q^{15} +(5.57190 + 3.58084i) q^{17} +(-7.43980 - 2.18452i) q^{19} +(0.915676 + 2.00505i) q^{21} +(0.573090 + 3.98593i) q^{23} +(-4.40669 - 5.08559i) q^{25} +(-0.415415 - 0.909632i) q^{27} -0.158121 q^{29} +(-0.313948 + 0.362315i) q^{31} +(-1.83494 - 0.538786i) q^{33} +(-1.07435 + 7.47224i) q^{35} -4.87640 q^{37} +(-0.629292 + 0.726242i) q^{39} +(-6.45260 - 4.14683i) q^{41} +(-0.750192 - 0.482119i) q^{43} +(0.487399 - 3.38993i) q^{45} +(-0.408040 - 2.83798i) q^{47} +(-1.80138 + 1.15768i) q^{49} +(-2.75143 + 6.02479i) q^{51} +(-0.988260 + 0.635116i) q^{53} +(-4.28906 - 4.94984i) q^{55} +(1.10349 - 7.67497i) q^{57} +(-4.69850 + 5.42236i) q^{59} +(3.47016 + 7.59859i) q^{61} +(-1.85433 + 1.19170i) q^{63} +(-3.15776 + 0.927203i) q^{65} +(8.18240 + 0.219983i) q^{67} +(-3.86380 + 1.13451i) q^{69} +(7.18046 - 4.61460i) q^{71} +(4.82513 + 10.5656i) q^{73} +(4.40669 - 5.08559i) q^{75} +(-0.599914 + 4.17250i) q^{77} +(-5.28952 - 6.10443i) q^{79} +(0.841254 - 0.540641i) q^{81} +(3.65286 - 7.99865i) q^{83} +(-19.0826 + 12.2636i) q^{85} +(-0.0225030 - 0.156512i) q^{87} +(-1.53875 + 10.7022i) q^{89} +(1.78193 + 1.14518i) q^{91} +(-0.403307 - 0.259190i) q^{93} +(17.3901 - 20.0693i) q^{95} +15.3671 q^{97} +(0.272163 - 1.89294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 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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