LMFDB - Embedded newform 804.2.y.a.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$5$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			157.2
Character	$\chi$	$=$	804.157
Dual form			804.2.y.a.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 + 0.989821i) q^{3} +(-0.793528 - 1.73758i) q^{5} +(-0.366312 + 0.349278i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.142315 + 0.989821i) q^{3} +(-0.793528 - 1.73758i) q^{5} +(-0.366312 + 0.349278i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(1.09309 + 0.104378i) q^{11} +(2.91134 + 0.561115i) q^{13} +(1.83283 - 0.538167i) q^{15} +(-1.62830 - 0.839446i) q^{17} +(1.59035 + 1.51640i) q^{19} +(-0.293591 - 0.412291i) q^{21} +(5.67802 - 2.27314i) q^{23} +(0.884794 - 1.02111i) q^{25} +(0.415415 - 0.909632i) q^{27} +(2.60110 - 4.50523i) q^{29} +(4.61022 - 0.888546i) q^{31} +(-0.258878 + 1.06711i) q^{33} +(0.897578 + 0.359336i) q^{35} +(1.49125 + 2.58293i) q^{37} +(-0.969731 + 2.80185i) q^{39} +(-0.258770 - 5.43225i) q^{41} +(6.09038 - 3.91405i) q^{43} +(0.271850 + 1.89076i) q^{45} +(5.63764 + 4.43349i) q^{47} +(-0.320884 + 6.73618i) q^{49} +(1.06263 - 1.49226i) q^{51} +(-2.42205 - 1.55655i) q^{53} +(-0.686033 - 1.98216i) q^{55} +(-1.72730 + 1.35836i) q^{57} +(0.237271 + 0.273826i) q^{59} +(-0.840692 + 0.0802764i) q^{61} +(0.449877 - 0.231928i) q^{63} +(-1.33525 - 5.50396i) q^{65} +(-2.47018 + 7.80373i) q^{67} +(1.44193 + 5.94373i) q^{69} +(0.509495 - 0.262663i) q^{71} +(-5.22539 + 0.498964i) q^{73} +(0.884794 + 1.02111i) q^{75} +(-0.436869 + 0.343558i) q^{77} +(1.05520 + 3.04879i) q^{79} +(0.841254 + 0.540641i) q^{81} +(5.73051 - 8.04738i) q^{83} +(-0.166508 + 3.49543i) q^{85} +(4.08920 + 3.21578i) q^{87} +(-0.455159 - 3.16570i) q^{89} +(-1.26245 + 0.811324i) q^{91} +(0.223400 + 4.68974i) q^{93} +(1.37288 - 3.96668i) q^{95} +(5.11351 + 8.85686i) q^{97} +(-1.01941 - 0.408109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	$ 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) $ 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{14}{33}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$		0			0
$5$	−0.793528	−	1.73758i	−0.354876	−	0.777071i	−0.999917	−	0.0129222i	$-0.995887\pi$
$5$	−0.793528	−	1.73758i	−0.354876	−	0.777071i	0.645040	−	0.764149i	$-0.276841\pi$
$6$		0			0
$7$	−0.366312	+	0.349278i	−0.138453	+	0.132015i	−0.756141	−	0.654408i	$-0.772918\pi$
$7$	−0.366312	+	0.349278i	−0.138453	+	0.132015i	0.617688	+	0.786423i	$0.288069\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	1.09309	+	0.104378i	0.329579	+	0.0314710i	0.258534	−	0.966002i	$-0.416761\pi$
$11$	1.09309	+	0.104378i	0.329579	+	0.0314710i	0.0710451	+	0.997473i	$0.477367\pi$
$12$		0			0
$13$	2.91134	+	0.561115i	0.807461	+	0.155625i	0.576245	−	0.817277i	$-0.304517\pi$
$13$	2.91134	+	0.561115i	0.807461	+	0.155625i	0.231216	+	0.972902i	$0.425730\pi$
$14$		0			0
$15$	1.83283	−	0.538167i	0.473234	−	0.138954i
$16$		0			0
$17$	−1.62830	−	0.839446i	−0.394920	−	0.203595i	0.249316	−	0.968422i	$-0.419794\pi$
$17$	−1.62830	−	0.839446i	−0.394920	−	0.203595i	−0.644236	+	0.764827i	$0.722825\pi$
$18$		0			0
$19$	1.59035	+	1.51640i	0.364852	+	0.347886i	0.850223	−	0.526422i	$-0.176467\pi$
$19$	1.59035	+	1.51640i	0.364852	+	0.347886i	−0.485371	+	0.874308i	$0.661315\pi$
$20$		0			0
$21$	−0.293591	−	0.412291i	−0.0640668	−	0.0899693i
$22$		0			0
$23$	5.67802	−	2.27314i	1.18395	−	0.473982i	0.305673	−	0.952136i	$-0.401119\pi$
$23$	5.67802	−	2.27314i	1.18395	−	0.473982i	0.878276	+	0.478155i	$0.158694\pi$
$24$		0			0
$25$	0.884794	−	1.02111i	0.176959	−	0.204221i
$26$		0			0
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$		0			0
$29$	2.60110	−	4.50523i	0.483012	−	0.836601i	−0.516798	−	0.856107i	$-0.672876\pi$
$29$	2.60110	−	4.50523i	0.483012	−	0.836601i	0.999810	+	0.0195067i	$0.00620958\pi$
$30$		0			0
$31$	4.61022	−	0.888546i	0.828019	−	0.159588i	0.242403	−	0.970176i	$-0.422065\pi$
$31$	4.61022	−	0.888546i	0.828019	−	0.159588i	0.585617	+	0.810588i	$0.300852\pi$
$32$		0			0
$33$	−0.258878	+	1.06711i	−0.0450649	+	0.185760i
$34$		0			0
$35$	0.897578	+	0.359336i	0.151718	+	0.0607389i
$36$		0			0
$37$	1.49125	+	2.58293i	0.245161	+	0.424631i	0.962177	−	0.272426i	$-0.0878259\pi$
$37$	1.49125	+	2.58293i	0.245161	+	0.424631i	−0.717016	+	0.697057i	$0.754493\pi$
$38$		0			0
$39$	−0.969731	+	2.80185i	−0.155281	+	0.448656i
$40$		0			0
$41$	−0.258770	−	5.43225i	−0.0404131	−	0.848376i	−0.924530	−	0.381110i	$-0.875542\pi$
$41$	−0.258770	−	5.43225i	−0.0404131	−	0.848376i	0.884117	−	0.467266i	$-0.154761\pi$
$42$		0			0
$43$	6.09038	−	3.91405i	0.928775	−	0.596887i	0.0135840	−	0.999908i	$-0.495676\pi$
$43$	6.09038	−	3.91405i	0.928775	−	0.596887i	0.915191	+	0.403020i	$0.132040\pi$
$44$		0			0
$45$	0.271850	+	1.89076i	0.0405251	+	0.281858i
$46$		0			0
$47$	5.63764	+	4.43349i	0.822334	+	0.646691i	0.938015	−	0.346596i	$-0.112662\pi$
$47$	5.63764	+	4.43349i	0.822334	+	0.646691i	−0.115680	+	0.993287i	$0.536905\pi$
$48$		0			0
$49$	−0.320884	+	6.73618i	−0.0458406	+	0.962312i
$50$		0			0
$51$	1.06263	−	1.49226i	0.148798	−	0.208958i
$52$		0			0
$53$	−2.42205	−	1.55655i	−0.332694	−	0.213809i	0.363619	−	0.931548i	$-0.381541\pi$
$53$	−2.42205	−	1.55655i	−0.332694	−	0.213809i	−0.696313	+	0.717739i	$0.745177\pi$
$54$		0			0
$55$	−0.686033	−	1.98216i	−0.0925047	−	0.267275i
$56$		0			0
$57$	−1.72730	+	1.35836i	−0.228786	+	0.179919i
$58$		0			0
$59$	0.237271	+	0.273826i	0.0308901	+	0.0356491i	0.770984	−	0.636854i	$-0.219765\pi$
$59$	0.237271	+	0.273826i	0.0308901	+	0.0356491i	−0.740094	+	0.672503i	$0.765219\pi$
$60$		0			0
$61$	−0.840692	+	0.0802764i	−0.107640	+	0.0102783i	−0.148737	−	0.988877i	$-0.547521\pi$
$61$	−0.840692	+	0.0802764i	−0.107640	+	0.0102783i	0.0410972	+	0.999155i	$0.486915\pi$
$62$		0			0
$63$	0.449877	−	0.231928i	0.0566791	−	0.0292201i
$64$		0			0
$65$	−1.33525	−	5.50396i	−0.165617	−	0.682682i
$66$		0			0
$67$	−2.47018	+	7.80373i	−0.301780	+	0.953378i
$67$	−2.47018	+	7.80373i	−0.301780	+	0.953378i
$68$		0			0
$69$	1.44193	+	5.94373i	0.173588	+	0.715540i
$70$		0			0
$71$	0.509495	−	0.262663i	0.0604659	−	0.0311723i	−0.427728	−	0.903907i	$-0.640686\pi$
$71$	0.509495	−	0.262663i	0.0604659	−	0.0311723i	0.488194	+	0.872735i	$0.337656\pi$
$72$		0			0
$73$	−5.22539	+	0.498964i	−0.611585	+	0.0583993i	−0.396253	−	0.918141i	$-0.629690\pi$
$73$	−5.22539	+	0.498964i	−0.611585	+	0.0583993i	−0.215333	+	0.976541i	$0.569084\pi$
$74$		0			0
$75$	0.884794	+	1.02111i	0.102167	+	0.117907i
$76$		0			0
$77$	−0.436869	+	0.343558i	−0.0497859	+	0.0391520i
$78$		0			0
$79$	1.05520	+	3.04879i	0.118719	+	0.343016i	0.988667	−	0.150128i	$-0.0479687\pi$
$79$	1.05520	+	3.04879i	0.118719	+	0.343016i	−0.869948	+	0.493144i	$0.835847\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	5.73051	−	8.04738i	0.629005	−	0.883314i	−0.369948	−	0.929052i	$-0.620625\pi$
$83$	5.73051	−	8.04738i	0.629005	−	0.883314i	0.998953	+	0.0457380i	$0.0145639\pi$
$84$		0			0
$85$	−0.166508	+	3.49543i	−0.0180603	+	0.379132i
$86$		0			0
$87$	4.08920	+	3.21578i	0.438408	+	0.344768i
$88$		0			0
$89$	−0.455159	−	3.16570i	−0.0482468	−	0.335564i	−0.999621	−	0.0275265i	$-0.991237\pi$
$89$	−0.455159	−	3.16570i	−0.0482468	−	0.335564i	0.951374	−	0.308037i	$-0.0996722\pi$
$90$		0			0
$91$	−1.26245	+	0.811324i	−0.132340	+	0.0850499i
$92$		0			0
$93$	0.223400	+	4.68974i	0.0231655	+	0.486304i
$94$		0			0
$95$	1.37288	−	3.96668i	0.140855	−	0.406973i
$96$		0			0
$97$	5.11351	+	8.85686i	0.519198	+	0.899277i	0.999751	+	0.0223117i	$0.00710263\pi$
$97$	5.11351	+	8.85686i	0.519198	+	0.899277i	−0.480553	+	0.876966i	$0.659564\pi$
$98$		0			0
$99$	−1.01941	−	0.408109i	−0.102454	−	0.0410165i
$100$		0			0
$101$	−2.06189	+	8.49923i	−0.205166	+	0.845705i	0.772411	+	0.635124i	$0.219051\pi$
$101$	−2.06189	+	8.49923i	−0.205166	+	0.845705i	−0.977576	+	0.210581i	$0.932464\pi$
$102$		0			0
$103$	−8.93365	+	1.72182i	−0.880259	+	0.169656i	−0.609305	−	0.792936i	$-0.708551\pi$
$103$	−8.93365	+	1.72182i	−0.880259	+	0.169656i	−0.270954	+	0.962592i	$0.587339\pi$
$104$		0			0
$105$	−0.483417	+	0.837303i	−0.0471767	+	0.0817124i
$106$		0			0
$107$	5.16579	−	11.3115i	0.499396	−	1.09352i	−0.477269	−	0.878757i	$-0.658373\pi$
$107$	5.16579	−	11.3115i	0.499396	−	1.09352i	0.976665	−	0.214767i	$-0.0688993\pi$
$108$		0			0
$109$	2.65961	−	3.06935i	0.254744	−	0.293990i	−0.613944	−	0.789349i	$-0.710418\pi$
$109$	2.65961	−	3.06935i	0.254744	−	0.293990i	0.868688	+	0.495359i	$0.164963\pi$
$110$		0			0
$111$	−2.76887	+	1.10849i	−0.262809	+	0.105213i
$112$		0			0
$113$	−5.71922	−	8.03152i	−0.538019	−	0.755542i	0.452671	−	0.891678i	$-0.350471\pi$
$113$	−5.71922	−	8.03152i	−0.538019	−	0.755542i	−0.990690	+	0.136135i	$0.956532\pi$
$114$		0			0
$115$	−8.45543	−	8.06223i	−0.788473	−	0.751807i
$116$		0			0
$117$	−2.63533	−	1.35861i	−0.243636	−	0.125603i
$118$		0			0
$119$	0.889665	−	0.261229i	0.0815554	−	0.0239468i
$120$		0			0
$121$	−9.61726	−	1.85358i	−0.874297	−	0.168507i
$122$		0			0
$123$	5.41379	+	0.516954i	0.488145	+	0.0466122i
$124$		0			0
$125$	−11.6405	−	3.41796i	−1.04116	−	0.305712i
$126$		0			0
$127$	0.815127	−	0.777222i	0.0723308	−	0.0689673i	−0.653051	−	0.757314i	$-0.726511\pi$
$127$	0.815127	−	0.777222i	0.0723308	−	0.0689673i	0.725382	+	0.688346i	$0.241663\pi$
$128$		0			0
$129$	3.00746	+	6.58542i	0.264792	+	0.579814i
$130$		0			0
$131$	0.605776	−	4.21327i	0.0529269	−	0.368115i	−0.946095	−	0.323890i	$-0.895009\pi$
$131$	0.605776	−	4.21327i	0.0529269	−	0.368115i	0.999022	−	0.0442246i	$-0.0140817\pi$
$132$		0			0
$133$	−1.11221			−0.0964409
$134$		0			0
$135$	−1.91020			−0.164404
$136$		0			0
$137$	−0.480759	+	3.34375i	−0.0410740	+	0.285676i	0.958924	+	0.283663i	$0.0915498\pi$
$137$	−0.480759	+	3.34375i	−0.0410740	+	0.285676i	−0.999998	+	0.00201285i	$0.999359\pi$
$138$		0			0
$139$	−2.27676	−	4.98541i	−0.193112	−	0.422857i	0.788163	−	0.615466i	$-0.211032\pi$
$139$	−2.27676	−	4.98541i	−0.193112	−	0.422857i	−0.981275	+	0.192609i	$0.938305\pi$
$140$		0			0
$141$	−5.19068	+	4.94931i	−0.437134	+	0.416807i
$142$		0			0
$143$	3.12380	+	0.917229i	0.261225	+	0.0767025i
$144$		0			0
$145$	−9.89226	−	0.944596i	−0.821507	−	0.0784444i
$146$		0			0
$147$	−6.62195	−	1.27628i	−0.546169	−	0.105266i
$148$		0			0
$149$	−10.5643	+	3.10195i	−0.865458	+	0.254121i	−0.684183	−	0.729311i	$-0.739841\pi$
$149$	−10.5643	+	3.10195i	−0.865458	+	0.254121i	−0.181276	+	0.983432i	$0.558023\pi$
$150$		0			0
$151$	−2.36014	−	1.21674i	−0.192065	−	0.0990166i	0.359511	−	0.933141i	$-0.382943\pi$
$151$	−2.36014	−	1.21674i	−0.192065	−	0.0990166i	−0.551577	+	0.834124i	$0.685974\pi$
$152$		0			0
$153$	1.32584	+	1.26419i	0.107188	+	0.102203i
$154$		0			0
$155$	−5.20226	−	7.30555i	−0.417855	−	0.586796i
$156$		0			0
$157$	−8.34829	+	3.34215i	−0.666266	+	0.266733i	−0.680043	−	0.733172i	$-0.738039\pi$
$157$	−8.34829	+	3.34215i	−0.666266	+	0.266733i	0.0137766	+	0.999905i	$0.495615\pi$
$158$		0			0
$159$	1.88540	−	2.17587i	0.149522	−	0.172558i
$160$		0			0
$161$	−1.28597	+	2.81588i	−0.101349	+	0.221923i
$162$		0			0
$163$	8.40033	−	14.5498i	0.657965	−	1.13963i	−0.323177	−	0.946339i	$-0.604751\pi$
$163$	8.40033	−	14.5498i	0.657965	−	1.13963i	0.981142	−	0.193290i	$-0.0619157\pi$
$164$		0			0
$165$	2.05962	−	0.396959i	0.160341	−	0.0309032i
$166$		0			0
$167$	−0.354141	+	1.45979i	−0.0274043	+	0.112962i	−0.983871	−	0.178879i	$-0.942753\pi$
$167$	−0.354141	+	1.45979i	−0.0274043	+	0.112962i	0.956467	+	0.291841i	$0.0942679\pi$
$168$		0			0
$169$	−3.90772	−	1.56441i	−0.300594	−	0.120340i
$170$		0			0
$171$	−1.09871	−	1.90303i	−0.0840208	−	0.145528i
$172$		0			0
$173$	1.00999	−	2.91818i	0.0767883	−	0.221865i	−0.900073	−	0.435739i	$-0.856487\pi$
$173$	1.00999	−	2.91818i	0.0767883	−	0.221865i	0.976861	+	0.213874i	$0.0686082\pi$
$174$		0			0
$175$	0.0325392	+	0.683082i	0.00245973	+	0.0516362i
$176$		0			0
$177$	−0.304806	+	0.195887i	−0.0229106	+	0.0147238i
$178$		0			0
$179$	−2.17078	−	15.0981i	−0.162252	−	1.12848i	−0.894377	−	0.447314i	$-0.852380\pi$
$179$	−2.17078	−	15.0981i	−0.162252	−	1.12848i	0.732125	−	0.681170i	$-0.238529\pi$
$180$		0			0
$181$	6.12121	+	4.81377i	0.454986	+	0.357805i	0.819198	−	0.573511i	$-0.194419\pi$
$181$	6.12121	+	4.81377i	0.454986	+	0.357805i	−0.364212	+	0.931316i	$0.618662\pi$
$182$		0			0
$183$	0.0401837	−	0.843560i	0.00297046	−	0.0623577i
$184$		0			0
$185$	3.30470	−	4.64080i	0.242966	−	0.341199i
$186$		0			0
$187$	−1.69226	−	1.08755i	−0.123750	−	0.0795294i
$188$		0			0
$189$	0.165543	+	0.478304i	0.0120415	+	0.0347915i
$190$		0			0
$191$	−13.1963	+	10.3777i	−0.954851	+	0.750903i	−0.968503	−	0.249004i	$-0.919897\pi$
$191$	−13.1963	+	10.3777i	−0.954851	+	0.750903i	0.0136517	+	0.999907i	$0.495654\pi$
$192$		0			0
$193$	9.21053	+	10.6295i	0.662989	+	0.765130i	0.983262	−	0.182195i	$-0.0583204\pi$
$193$	9.21053	+	10.6295i	0.662989	+	0.765130i	−0.320274	+	0.947325i	$0.603775\pi$
$194$		0			0
$195$	5.63796	−	0.538360i	0.403743	−	0.0385528i
$196$		0			0
$197$	0.988816	−	0.509770i	0.0704502	−	0.0363196i	−0.422641	−	0.906297i	$-0.638897\pi$
$197$	0.988816	−	0.509770i	0.0704502	−	0.0363196i	0.493092	+	0.869977i	$0.335867\pi$
$198$		0			0
$199$	3.28597	+	13.5449i	0.232936	+	0.960175i	0.961414	+	0.275106i	$0.0887130\pi$
$199$	3.28597	+	13.5449i	0.232936	+	0.960175i	−0.728478	+	0.685069i	$0.759772\pi$
$200$		0			0
$201$	−7.37276	−	3.55562i	−0.520034	−	0.250794i
$202$		0			0
$203$	0.620764	+	2.55883i	0.0435691	+	0.179594i
$204$		0			0
$205$	−9.23365	+	4.76028i	−0.644906	+	0.332472i
$206$		0			0
$207$	−6.08844	+	0.581375i	−0.423175	+	0.0404084i
$208$		0			0
$209$	1.58012	+	1.82356i	0.109299	+	0.126138i
$210$		0			0
$211$	−6.54336	+	5.14576i	−0.450464	+	0.354249i	−0.817471	−	0.575969i	$-0.804625\pi$
$211$	−6.54336	+	5.14576i	−0.450464	+	0.354249i	0.367008	+	0.930218i	$0.380382\pi$
$212$		0			0
$213$	0.187481	+	0.541689i	0.0128460	+	0.0371160i
$214$		0			0
$215$	−11.6339	−	7.47664i	−0.793424	−	0.509903i
$216$		0			0
$217$	−1.37843	+	1.93573i	−0.0935738	+	0.131406i
$218$		0			0
$219$	0.249765	−	5.24321i	0.0168776	−	0.354303i
$220$		0			0
$221$	−4.26951	−	3.35758i	−0.287198	−	0.225855i
$222$		0			0
$223$	0.879823	+	6.11931i	0.0589173	+	0.409779i	0.997842	+	0.0656570i	$0.0209143\pi$
$223$	0.879823	+	6.11931i	0.0589173	+	0.409779i	−0.938925	+	0.344122i	$0.888177\pi$
$224$		0			0
$225$	−1.13663	+	0.730469i	−0.0757755	+	0.0486980i
$226$		0			0
$227$	0.716533	+	15.0419i	0.0475580	+	0.998365i	0.888969	+	0.457968i	$0.151423\pi$
$227$	0.716533	+	15.0419i	0.0475580	+	0.998365i	−0.841411	+	0.540396i	$0.818274\pi$
$228$		0			0
$229$	−1.08679	+	3.14007i	−0.0718171	+	0.207502i	−0.975197	−	0.221340i	$-0.928957\pi$
$229$	−1.08679	+	3.14007i	−0.0718171	+	0.207502i	0.903380	+	0.428842i	$0.141078\pi$
$230$		0			0
$231$	−0.277888	−	0.481316i	−0.0182837	−	0.0316683i
$232$		0			0
$233$	−12.8606	−	5.14860i	−0.842525	−	0.337296i	−0.0900666	−	0.995936i	$-0.528708\pi$
$233$	−12.8606	−	5.14860i	−0.842525	−	0.337296i	−0.752459	+	0.658640i	$0.771132\pi$
$234$		0			0
$235$	3.22993	−	13.3140i	0.210698	−	0.868508i
$236$		0			0
$237$	−3.16793	+	0.610569i	−0.205779	+	0.0396607i
$238$		0			0
$239$	−2.12631	+	3.68289i	−0.137540	+	0.238226i	−0.926565	−	0.376135i	$-0.877253\pi$
$239$	−2.12631	+	3.68289i	−0.137540	+	0.238226i	0.789025	+	0.614361i	$0.210586\pi$
$240$		0			0
$241$	−10.0495	+	22.0053i	−0.647345	+	1.41749i	0.246514	+	0.969139i	$0.420715\pi$
$241$	−10.0495	+	22.0053i	−0.647345	+	1.41749i	−0.893859	+	0.448348i	$0.852013\pi$
$242$		0			0
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$		0			0
$245$	11.9593	−	4.78778i	0.764052	−	0.305880i
$246$		0			0
$247$	3.77919	+	5.30713i	0.240464	+	0.337685i
$248$		0			0
$249$	7.14993	+	6.81744i	0.453108	+	0.432038i
$250$		0			0
$251$	1.34998	+	0.695964i	0.0852102	+	0.0439289i	0.500305	−	0.865849i	$-0.333221\pi$
$251$	1.34998	+	0.695964i	0.0852102	+	0.0439289i	−0.415095	+	0.909778i	$0.636252\pi$
$252$		0			0
$253$	6.44386	−	1.89209i	0.405122	−	0.118954i
$254$		0			0
$255$	−3.43615	−	0.662264i	−0.215180	−	0.0414726i
$256$		0			0
$257$	−15.6528	−	1.49467i	−0.976398	−	0.0932347i	−0.405359	−	0.914158i	$-0.632853\pi$
$257$	−15.6528	−	1.49467i	−0.976398	−	0.0932347i	−0.571039	+	0.820923i	$0.693459\pi$
$258$		0			0
$259$	−1.44842	−	0.425296i	−0.0900007	−	0.0264266i
$260$		0			0
$261$	−3.76500	+	3.58992i	−0.233048	+	0.222211i
$262$		0			0
$263$	11.9893	+	26.2530i	0.739294	+	1.61883i	0.784712	+	0.619860i	$0.212811\pi$
$263$	11.9893	+	26.2530i	0.739294	+	1.61883i	−0.0454182	+	0.998968i	$0.514462\pi$
$264$		0			0
$265$	−0.782682	+	5.44367i	−0.0480798	+	0.334402i
$266$		0			0
$267$	3.19826			0.195730
$268$		0			0
$269$	6.80405			0.414850			0.207425	−	0.978251i	$-0.433492\pi$
$269$	6.80405			0.414850			0.207425	+	0.978251i	$0.433492\pi$
$270$		0			0
$271$	−0.784565	+	5.45677i	−0.0476589	+	0.331475i	0.952018	+	0.306043i	$0.0990052\pi$
$271$	−0.784565	+	5.45677i	−0.0476589	+	0.331475i	−0.999677	+	0.0254319i	$0.991904\pi$
$272$		0			0
$273$	−0.623401	−	1.36506i	−0.0377300	−	0.0826171i
$274$		0			0
$275$	1.07374	−	1.02381i	0.0647490	−	0.0617381i
$276$		0			0
$277$	26.8354	+	7.87959i	1.61238	+	0.473439i	0.958957	−	0.283551i	$-0.0915126\pi$
$277$	26.8354	+	7.87959i	1.61238	+	0.473439i	0.653427	+	0.756990i	$0.273331\pi$
$278$		0			0
$279$	−4.67380	−	0.446294i	−0.279813	−	0.0267189i
$280$		0			0
$281$	−12.7022	−	2.44815i	−0.757749	−	0.146044i	−0.204278	−	0.978913i	$-0.565485\pi$
$281$	−12.7022	−	2.44815i	−0.757749	−	0.146044i	−0.553471	+	0.832869i	$0.686697\pi$
$282$		0			0
$283$	3.93945	−	1.15673i	0.234176	−	0.0687602i	−0.162539	−	0.986702i	$-0.551968\pi$
$283$	3.93945	−	1.15673i	0.234176	−	0.0687602i	0.396715	+	0.917942i	$0.370150\pi$
$284$		0			0
$285$	3.73092	+	1.92342i	0.221001	+	0.113934i
$286$		0			0
$287$	1.99216	+	1.89952i	0.117593	+	0.112125i
$288$		0			0
$289$	−7.91428	−	11.1141i	−0.465546	−	0.653768i
$290$		0			0
$291$	−9.49443	+	3.80100i	−0.556574	+	0.222818i
$292$		0			0
$293$	6.36979	−	7.35113i	0.372127	−	0.429458i	−0.538539	−	0.842601i	$-0.681024\pi$
$293$	6.36979	−	7.35113i	0.372127	−	0.429458i	0.910666	+	0.413143i	$0.135569\pi$
$294$		0			0
$295$	0.287514	−	0.629567i	0.0167397	−	0.0366548i
$296$		0			0
$297$	0.549032	−	0.950951i	0.0318580	−	0.0551798i
$298$		0			0
$299$	17.8061	−	3.43185i	1.02976	−	0.198469i
$300$		0			0
$301$	−0.863890	+	3.56100i	−0.0497938	+	0.205253i
$302$		0			0
$303$	−8.11928	−	3.25047i	−0.466441	−	0.186735i
$304$		0			0
$305$	0.806600	+	1.39707i	0.0461858	+	0.0799961i
$306$		0			0
$307$	10.6804	−	30.8590i	0.609564	−	1.76122i	−0.0380801	−	0.999275i	$-0.512124\pi$
$307$	10.6804	−	30.8590i	0.609564	−	1.76122i	0.647644	−	0.761943i	$-0.275755\pi$
$308$		0			0
$309$	−0.432903	−	9.08776i	−0.0246270	−	0.516985i
$310$		0			0
$311$	−2.54611	+	1.63629i	−0.144377	+	0.0927854i	−0.610835	−	0.791758i	$-0.709166\pi$
$311$	−2.54611	+	1.63629i	−0.144377	+	0.0927854i	0.466458	+	0.884543i	$0.345530\pi$
$312$		0			0
$313$	−2.67396	−	18.5978i	−0.151141	−	1.05121i	−0.914312	−	0.405011i	$-0.867268\pi$
$313$	−2.67396	−	18.5978i	−0.151141	−	1.05121i	0.763171	−	0.646197i	$-0.223641\pi$
$314$		0			0
$315$	−0.759983	−	0.597657i	−0.0428202	−	0.0336742i
$316$		0			0
$317$	−0.219586	+	4.60967i	−0.0123332	+	0.258905i	0.984277	+	0.176633i	$0.0565206\pi$
$317$	−0.219586	+	4.60967i	−0.0123332	+	0.258905i	−0.996610	+	0.0822718i	$0.973782\pi$
$318$		0			0
$319$	3.31348	−	4.65313i	0.185519	−	0.260525i
$320$		0			0
$321$	10.4612	+	6.72301i	0.583887	+	0.375242i
$322$		0			0
$323$	−1.31663	−	3.80417i	−0.0732595	−	0.211669i
$324$		0			0
$325$	3.14890	−	2.47632i	0.174669	−	0.137361i
$326$		0			0
$327$	2.65961	+	3.06935i	0.147077	+	0.169735i
$328$		0			0
$329$	−3.61366	+	0.345062i	−0.199227	+	0.0190239i
$330$		0			0
$331$	−2.37894	+	1.22643i	−0.130758	+	0.0674105i	−0.522364	−	0.852722i	$-0.674950\pi$
$331$	−2.37894	+	1.22643i	−0.130758	+	0.0674105i	0.391606	+	0.920133i	$0.371920\pi$
$332$		0			0
$333$	−0.703153	−	2.89844i	−0.0385325	−	0.158833i
$334$		0			0
$335$	15.5198	−	1.90034i	0.847937	−	0.103826i
$336$		0			0
$337$	3.56986	+	14.7152i	0.194463	+	0.801586i	0.982546	+	0.186018i	$0.0595583\pi$
$337$	3.56986	+	14.7152i	0.194463	+	0.801586i	−0.788084	+	0.615568i	$0.788927\pi$
$338$		0			0
$339$	8.76370	−	4.51800i	0.475979	−	0.245384i
$340$		0			0
$341$	5.13213	−	0.490059i	0.277920	−	0.0265382i
$342$		0			0
$343$	−4.55542	−	5.25724i	−0.245970	−	0.283864i
$344$		0			0
$345$	9.18351	−	7.22199i	0.494423	−	0.388819i
$346$		0			0
$347$	5.04233	+	14.5689i	0.270687	+	0.782098i	0.995638	+	0.0932980i	$0.0297409\pi$
$347$	5.04233	+	14.5689i	0.270687	+	0.782098i	−0.724952	+	0.688800i	$0.758138\pi$
$348$		0			0
$349$	−3.72457	−	2.39364i	−0.199372	−	0.128129i	0.437146	−	0.899391i	$-0.355989\pi$
$349$	−3.72457	−	2.39364i	−0.199372	−	0.128129i	−0.636518	+	0.771262i	$0.719626\pi$
$350$		0			0
$351$	1.71982	−	2.41515i	0.0917974	−	0.128911i
$352$		0			0
$353$	0.359215	−	7.54086i	0.0191191	−	0.401360i	−0.968941	−	0.247291i	$-0.920459\pi$
$353$	0.359215	−	7.54086i	0.0191191	−	0.401360i	0.988060	−	0.154068i	$-0.0492375\pi$
$354$		0			0
$355$	−0.860696	−	0.676859i	−0.0456810	−	0.0359240i
$356$		0			0
$357$	0.131958	+	0.917786i	0.00698394	+	0.0485744i
$358$		0			0
$359$	−10.5408	+	6.77416i	−0.556322	+	0.357526i	−0.788392	−	0.615173i	$-0.789086\pi$
$359$	−10.5408	+	6.77416i	−0.556322	+	0.357526i	0.232071	+	0.972699i	$0.425450\pi$
$360$		0			0
$361$	−0.674298	−	14.1553i	−0.0354894	−	0.745013i
$362$		0			0
$363$	3.20339	−	9.25558i	0.168134	−	0.485792i
$364$		0			0
$365$	5.01348	+	8.68361i	0.262418	+	0.454521i
$366$		0			0
$367$	8.77094	+	3.51135i	0.457839	+	0.183291i	0.589106	−	0.808056i	$-0.299480\pi$
$367$	8.77094	+	3.51135i	0.457839	+	0.183291i	−0.131266	+	0.991347i	$0.541904\pi$
$368$		0			0
$369$	−1.28215	+	5.28511i	−0.0667463	+	0.275132i
$370$		0			0
$371$	1.43089	−	0.275782i	0.0742883	−	0.0143179i
$372$		0			0
$373$	15.1976	−	26.3230i	0.786903	−	1.36296i	−0.140953	−	0.990016i	$-0.545017\pi$
$373$	15.1976	−	26.3230i	0.786903	−	1.36296i	0.927856	−	0.372939i	$-0.121650\pi$
$374$		0			0
$375$	5.03979	−	11.0356i	0.260254	−	0.569876i
$376$		0			0
$377$	10.1006	−	11.6568i	0.520209	−	0.600354i
$378$		0			0
$379$	15.7980	−	6.32455i	0.811487	−	0.324870i	0.0714566	−	0.997444i	$-0.477235\pi$
$379$	15.7980	−	6.32455i	0.811487	−	0.324870i	0.740031	+	0.672573i	$0.234811\pi$
$380$		0			0
$381$	0.653306	+	0.917440i	0.0334699	+	0.0470019i
$382$		0			0
$383$	15.1543	+	14.4496i	0.774347	+	0.738338i	0.970203	−	0.242294i	$-0.0779000\pi$
$383$	15.1543	+	14.4496i	0.774347	+	0.738338i	−0.195856	+	0.980633i	$0.562748\pi$
$384$		0			0
$385$	0.943628	+	0.486474i	0.0480917	+	0.0247930i
$386$		0			0
$387$	−6.94640	+	2.03965i	−0.353105	+	0.103681i
$388$		0			0
$389$	−14.2632	−	2.74901i	−0.723174	−	0.139380i	−0.185634	−	0.982619i	$-0.559434\pi$
$389$	−14.2632	−	2.74901i	−0.723174	−	0.139380i	−0.537540	+	0.843239i	$0.680646\pi$
$390$		0			0
$391$	−11.1537	−	1.06505i	−0.564066	−	0.0538617i
$392$		0			0
$393$	4.08417	+	1.19922i	0.206019	+	0.0604927i
$394$		0			0
$395$	4.46020	−	4.25280i	0.224417	−	0.213981i
$396$		0			0
$397$	−3.01166	−	6.59462i	−0.151151	−	0.330975i	0.818876	−	0.573970i	$-0.194597\pi$
$397$	−3.01166	−	6.59462i	−0.151151	−	0.330975i	−0.970027	+	0.242995i	$0.921870\pi$
$398$		0			0
$399$	0.158284	−	1.10089i	0.00792412	−	0.0551134i
$400$		0			0
$401$	12.9392			0.646153			0.323076	−	0.946373i	$-0.395283\pi$
$401$	12.9392			0.646153			0.323076	+	0.946373i	$0.395283\pi$
$402$		0			0
$403$	13.9205			0.693429
$404$		0			0
$405$	0.271850	−	1.89076i	0.0135084	−	0.0939527i
$406$		0			0
$407$	1.36048	+	2.97903i	0.0674363	+	0.147665i
$408$		0			0
$409$	−13.6220	+	12.9886i	−0.673566	+	0.642244i	−0.947594	−	0.319478i	$-0.896492\pi$
$409$	−13.6220	+	12.9886i	−0.673566	+	0.642244i	0.274028	+	0.961722i	$0.411644\pi$
$410$		0			0
$411$	−3.24130	−	0.951732i	−0.159882	−	0.0469455i
$412$		0			0
$413$	−0.182557	−	0.0174321i	−0.00898303	−	0.000857775i
$414$		0			0
$415$	−18.5303	−	3.57142i	−0.909617	−	0.175314i
$416$		0			0
$417$	5.25868	−	1.54409i	0.257519	−	0.0756143i
$418$		0			0
$419$	15.4093	+	7.94403i	0.752792	+	0.388091i	0.791508	−	0.611159i	$-0.209296\pi$
$419$	15.4093	+	7.94403i	0.752792	+	0.388091i	−0.0387159	+	0.999250i	$0.512327\pi$
$420$		0			0
$421$	6.06790	+	5.78574i	0.295732	+	0.281979i	0.823388	−	0.567478i	$-0.192081\pi$
$421$	6.06790	+	5.78574i	0.295732	+	0.281979i	−0.527657	+	0.849458i	$0.676929\pi$
$422$		0			0
$423$	−4.16022	−	5.84221i	−0.202277	−	0.284058i
$424$		0			0
$425$	−2.29787	+	0.919929i	−0.111463	+	0.0446231i
$426$		0			0
$427$	0.279917	−	0.323041i	0.0135461	−	0.0156331i
$428$		0			0
$429$	−1.35246	+	2.96146i	−0.0652972	+	0.142981i
$430$		0			0
$431$	−11.4697	+	19.8661i	−0.552476	+	0.956916i	0.445620	+	0.895222i	$0.352983\pi$
$431$	−11.4697	+	19.8661i	−0.552476	+	0.956916i	−0.998095	+	0.0616934i	$0.980350\pi$
$432$		0			0
$433$	22.4613	−	4.32906i	1.07942	−	0.208042i	0.381611	−	0.924323i	$-0.375370\pi$
$433$	22.4613	−	4.32906i	1.07942	−	0.208042i	0.697811	+	0.716282i	$0.254157\pi$
$434$		0			0
$435$	2.34280	−	9.65714i	0.112329	−	0.463024i
$436$		0			0
$437$	12.4770	+	4.99506i	0.596858	+	0.238946i
$438$		0			0
$439$	3.80826	+	6.59610i	0.181758	+	0.314815i	0.942479	−	0.334264i	$-0.108488\pi$
$439$	3.80826	+	6.59610i	0.181758	+	0.314815i	−0.760721	+	0.649079i	$0.775154\pi$
$440$		0			0
$441$	2.20569	−	6.37292i	0.105033	−	0.303472i
$442$		0			0
$443$	−0.837843	−	17.5885i	−0.0398071	−	0.835655i	−0.927183	−	0.374608i	$-0.877777\pi$
$443$	−0.837843	−	17.5885i	−0.0398071	−	0.835655i	0.887376	−	0.461046i	$-0.152526\pi$
$444$		0			0
$445$	−5.13949	+	3.30295i	−0.243635	+	0.156575i
$446$		0			0
$447$	−1.56692	−	10.8982i	−0.0741129	−	0.515467i
$448$		0			0
$449$	10.5269	+	8.27848i	0.496797	+	0.390686i	0.834881	−	0.550430i	$-0.185536\pi$
$449$	10.5269	+	8.27848i	0.496797	+	0.390686i	−0.338084	+	0.941116i	$0.609779\pi$
$450$		0			0
$451$	0.284146	−	5.96496i	0.0133799	−	0.280879i
$452$		0			0
$453$	1.54023	−	2.16296i	0.0723665	−	0.101625i
$454$		0			0
$455$	2.41153	+	1.54980i	0.113054	+	0.0726555i
$456$		0			0
$457$	−7.79734	−	22.5289i	−0.364744	−	1.05386i	−0.966828	−	0.255427i	$-0.917784\pi$
$457$	−7.79734	−	22.5289i	−0.364744	−	1.05386i	0.602084	−	0.798433i	$-0.294337\pi$
$458$		0			0
$459$	−1.44001	+	1.13243i	−0.0672137	+	0.0528575i
$460$		0			0
$461$	5.37195	+	6.19956i	0.250197	+	0.288742i	0.866930	−	0.498430i	$-0.166090\pi$
$461$	5.37195	+	6.19956i	0.250197	+	0.288742i	−0.616733	+	0.787172i	$0.711544\pi$
$462$		0			0
$463$	−2.75074	+	0.262664i	−0.127838	+	0.0122070i	−0.158779	−	0.987314i	$-0.550756\pi$
$463$	−2.75074	+	0.262664i	−0.127838	+	0.0122070i	0.0309410	+	0.999521i	$0.490150\pi$
$464$		0			0
$465$	7.97155	−	4.10962i	0.369672	−	0.190579i
$466$		0			0
$467$	7.09287	+	29.2372i	0.328219	+	1.35294i	0.861826	+	0.507204i	$0.169321\pi$
$467$	7.09287	+	29.2372i	0.328219	+	1.35294i	−0.533607	+	0.845732i	$0.679164\pi$
$468$		0			0
$469$	−1.82081	−	3.72138i	−0.0840774	−	0.171837i
$470$		0			0
$471$	−2.12005	−	8.73896i	−0.0976867	−	0.402670i
$472$		0			0
$473$	7.06589	−	3.64272i	0.324890	−	0.167492i
$474$		0			0
$475$	2.95554	−	0.282220i	0.135610	−	0.0129491i
$476$		0			0
$477$	1.88540	+	2.17587i	0.0863267	+	0.0996263i
$478$		0			0
$479$	−16.4582	+	12.9428i	−0.751993	+	0.591374i	−0.918850	−	0.394607i	$-0.870881\pi$
$479$	−16.4582	+	12.9428i	−0.751993	+	0.591374i	0.166857	+	0.985981i	$0.446638\pi$
$480$		0			0
$481$	2.89223	+	8.35655i	0.131874	+	0.381026i
$482$		0			0
$483$	−2.60421	−	1.67362i	−0.118496	−	0.0761525i
$484$		0			0
$485$	11.3318	−	15.9133i	0.514551	−	0.722586i
$486$		0			0
$487$	0.892791	−	18.7420i	0.0404562	−	0.849280i	−0.883883	−	0.467708i	$-0.845080\pi$
$487$	0.892791	−	18.7420i	0.0404562	−	0.849280i	0.924339	−	0.381572i	$-0.124617\pi$
$488$		0			0
$489$	13.2062	+	10.3855i	0.597206	+	0.469648i
$490$		0			0
$491$	4.00940	+	27.8860i	0.180942	+	1.25848i	0.854542	+	0.519382i	$0.173838\pi$
$491$	4.00940	+	27.8860i	0.180942	+	1.25848i	−0.673601	+	0.739095i	$0.735253\pi$
$492$		0			0
$493$	−8.01726	+	5.15238i	−0.361079	+	0.232051i
$494$		0			0
$495$	0.0998043	+	2.09515i	0.00448587	+	0.0941700i
$496$		0			0
$497$	−0.0948917	+	0.274172i	−0.00425648	+	0.0122983i
$498$		0			0
$499$	11.8718	+	20.5625i	0.531454	+	0.920506i	0.999326	+	0.0367093i	$0.0116876\pi$
$499$	11.8718	+	20.5625i	0.531454	+	0.920506i	−0.467872	+	0.883796i	$0.654979\pi$
$500$		0			0
$501$	−1.39453	−	0.558286i	−0.0623031	−	0.0249424i
$502$		0			0
$503$	−6.62107	+	27.2924i	−0.295219	+	1.21691i	0.610151	+	0.792285i	$0.291109\pi$
$503$	−6.62107	+	27.2924i	−0.295219	+	1.21691i	−0.905370	+	0.424624i	$0.860406\pi$
$504$		0			0
$505$	16.4043	−	3.16167i	0.729981	−	0.140692i
$506$		0			0
$507$	2.10462	−	3.64530i	0.0934693	−	0.161894i
$508$		0			0
$509$	−4.52844	+	9.91591i	−0.200720	+	0.439515i	−0.983047	−	0.183352i	$-0.941305\pi$
$509$	−4.52844	+	9.91591i	−0.200720	+	0.439515i	0.782328	+	0.622867i	$0.214032\pi$
$510$		0			0
$511$	1.73985	−	2.00789i	0.0769662	−	0.0888238i
$512$		0			0
$513$	2.04002	−	0.816702i	0.0900692	−	0.0360583i
$514$		0			0
$515$	10.0809	+	14.1567i	0.444218	+	0.623817i
$516$		0			0
$517$	5.69970	+	5.43465i	0.250672	+	0.239016i
$518$		0			0
$519$	2.74474	+	1.41501i	0.120481	+	0.0621121i
$520$		0			0
$521$	−26.6536	+	7.82620i	−1.16771	+	0.342872i	−0.807426	−	0.589969i	$-0.799140\pi$
$521$	−26.6536	+	7.82620i	−1.16771	+	0.342872i	−0.360289	+	0.932841i	$0.617322\pi$
$522$		0			0
$523$	−7.05939	−	1.36059i	−0.308686	−	0.0594943i	0.0325559	−	0.999470i	$-0.489635\pi$
$523$	−7.05939	−	1.36059i	−0.308686	−	0.0594943i	−0.341242	+	0.939976i	$0.610847\pi$
$524$		0			0
$525$	−0.680760	−	0.0650047i	−0.0297108	−	0.00283704i
$526$		0			0
$527$	−8.25269	−	2.42321i	−0.359493	−	0.105557i
$528$		0			0
$529$	10.4269	−	9.94200i	0.453342	−	0.432261i
$530$		0			0
$531$	−0.150515	−	0.329581i	−0.00653178	−	0.0143026i
$532$		0			0
$533$	2.29475	−	15.9604i	0.0993968	−	0.691320i
$534$		0			0
$535$	−23.7539			−1.02697
$536$		0			0
$537$	15.2534			0.658231
$538$		0			0
$539$	−1.05386	+	7.32977i	−0.0453930	+	0.315715i
$540$		0			0
$541$	−17.8548	−	39.0966i	−0.767638	−	1.68089i	−0.731784	−	0.681536i	$-0.761312\pi$
$541$	−17.8548	−	39.0966i	−0.767638	−	1.68089i	−0.0358538	−	0.999357i	$-0.511415\pi$
$542$		0			0
$543$	−5.63592	+	5.37383i	−0.241860	+	0.230613i
$544$		0			0
$545$	−7.44372	−	2.18567i	−0.318854	−	0.0936240i
$546$		0			0
$547$	−32.7588	−	3.12808i	−1.40066	−	0.133747i	−0.632777	−	0.774334i	$-0.718085\pi$
$547$	−32.7588	−	3.12808i	−1.40066	−	0.133747i	−0.767886	+	0.640587i	$0.778691\pi$
$548$		0			0
$549$	0.829255	+	0.159826i	0.0353917	+	0.00682120i
$550$		0			0
$551$	10.9684	−	3.22061i	0.467269	−	0.137203i
$552$		0			0
$553$	−1.45141	−	0.748253i	−0.0617201	−	0.0318189i
$554$		0			0
$555$	4.12326	+	3.93152i	0.175023	+	0.166884i
$556$		0			0
$557$	20.7270	+	29.1070i	0.878233	+	1.23331i	0.971351	+	0.237650i	$0.0763771\pi$
$557$	20.7270	+	29.1070i	0.878233	+	1.23331i	−0.0931183	+	0.995655i	$0.529683\pi$
$558$		0			0
$559$	19.9274	−	7.97774i	0.842841	−	0.337422i
$560$		0			0
$561$	1.31731	−	1.52026i	0.0556170	−	0.0641854i
$562$		0			0
$563$	0.809403	−	1.77235i	0.0341123	−	0.0746955i	−0.891809	−	0.452412i	$-0.850563\pi$
$563$	0.809403	−	1.77235i	0.0341123	−	0.0746955i	0.925921	+	0.377717i	$0.123291\pi$
$564$		0			0
$565$	−9.41708	+	16.3109i	−0.396179	+	0.686203i
$566$		0			0
$567$	−0.496995	+	0.0957880i	−0.0208718	+	0.00402272i
$568$		0			0
$569$	6.71630	−	27.6850i	0.281562	−	1.16061i	−0.638745	−	0.769418i	$-0.720546\pi$
$569$	6.71630	−	27.6850i	0.281562	−	1.16061i	0.920307	−	0.391196i	$-0.127939\pi$
$570$		0			0
$571$	14.9586	+	5.98853i	0.625999	+	0.250612i	0.662902	−	0.748707i	$-0.269325\pi$
$571$	14.9586	+	5.98853i	0.625999	+	0.250612i	−0.0369023	+	0.999319i	$0.511749\pi$
$572$		0			0
$573$	−8.39403	−	14.5389i	−0.350665	−	0.607370i
$574$		0			0
$575$	2.70276	−	7.80912i	0.112713	−	0.325663i
$576$		0			0
$577$	−0.0735402	−	1.54380i	−0.00306152	−	0.0642692i	0.996820	−	0.0796919i	$-0.0253936\pi$
$577$	−0.0735402	−	1.54380i	−0.00306152	−	0.0642692i	−0.999881	+	0.0154227i	$0.995091\pi$
$578$		0			0
$579$	−11.8321	+	7.60404i	−0.491726	+	0.316013i
$580$		0			0
$581$	0.711615	+	4.94939i	0.0295228	+	0.205335i
$582$		0			0
$583$	−2.48505	−	1.95426i	−0.102920	−	0.0809373i
$584$		0			0
$585$	−0.269485	+	5.65719i	−0.0111418	+	0.233896i
$586$		0			0
$587$	6.49365	−	9.11906i	0.268022	−	0.376384i	−0.658528	−	0.752556i	$-0.728821\pi$
$587$	6.49365	−	9.11906i	0.268022	−	0.376384i	0.926550	+	0.376172i	$0.122760\pi$
$588$		0			0
$589$	8.67927	+	5.57783i	0.357623	+	0.229830i
$590$		0			0
$591$	0.363858	+	1.05130i	0.0149671	+	0.0432447i
$592$		0			0
$593$	15.0024	−	11.7980i	0.616076	−	0.484487i	−0.260679	−	0.965426i	$-0.583946\pi$
$593$	15.0024	−	11.7980i	0.616076	−	0.484487i	0.876755	+	0.480938i	$0.159704\pi$
$594$		0			0
$595$	−1.15988	−	1.33857i	−0.0475505	−	0.0548762i
$596$		0			0
$597$	−13.8747	+	1.32487i	−0.567854	+	0.0542235i
$598$		0			0
$599$	−28.7811	+	14.8377i	−1.17596	+	0.606252i	−0.931619	−	0.363437i	$-0.881603\pi$
$599$	−28.7811	+	14.8377i	−1.17596	+	0.606252i	−0.244345	+	0.969688i	$0.578573\pi$
$600$		0			0
$601$	4.74174	+	19.5457i	0.193420	+	0.797287i	0.982995	+	0.183633i	$0.0587858\pi$
$601$	4.74174	+	19.5457i	0.193420	+	0.797287i	−0.789575	+	0.613654i	$0.789699\pi$
$602$		0			0
$603$	4.56868	−	6.79170i	0.186051	−	0.276579i
$604$		0			0
$605$	4.41082	+	18.1817i	0.179325	+	0.739190i
$606$		0			0
$607$	0.300372	−	0.154853i	0.0121917	−	0.00628527i	−0.452120	−	0.891957i	$-0.649332\pi$
$607$	0.300372	−	0.154853i	0.0121917	−	0.00628527i	0.464312	+	0.885672i	$0.346302\pi$
$608$		0			0
$609$	−2.62112	+	0.250287i	−0.106213	+	0.0101421i
$610$		0			0
$611$	13.9254	+	16.0708i	0.563362	+	0.650154i
$612$		0			0
$613$	34.4462	−	27.0888i	1.39127	−	1.09411i	0.407790	−	0.913076i	$-0.366299\pi$
$613$	34.4462	−	27.0888i	1.39127	−	1.09411i	0.983478	−	0.181030i	$-0.0579430\pi$
$614$		0			0
$615$	−3.39774	−	9.81713i	−0.137010	−	0.395865i
$616$		0			0
$617$	−34.3112	−	22.0505i	−1.38132	−	0.887718i	−0.381981	−	0.924170i	$-0.624758\pi$
$617$	−34.3112	−	22.0505i	−1.38132	−	0.887718i	−0.999335	+	0.0364523i	$0.988394\pi$
$618$		0			0
$619$	14.9779	−	21.0335i	0.602012	−	0.845408i	−0.395310	−	0.918548i	$-0.629363\pi$
$619$	14.9779	−	21.0335i	0.602012	−	0.845408i	0.997322	+	0.0731404i	$0.0233021\pi$
$620$		0			0
$621$	0.291017	−	6.10920i	0.0116781	−	0.245154i
$622$		0			0
$623$	1.27244	+	1.00066i	0.0509792	+	0.0400905i
$624$		0			0
$625$	2.33665	+	16.2518i	0.0934661	+	0.650071i
$626$		0			0
$627$	−2.02987	+	1.30452i	−0.0810654	+	0.0520976i
$628$		0			0
$629$	−0.259978	−	5.45760i	−0.0103660	−	0.217609i
$630$		0			0
$631$	−3.02102	+	8.72867i	−0.120265	+	0.347483i	−0.989025	−	0.147751i	$-0.952796\pi$
$631$	−3.02102	+	8.72867i	−0.120265	+	0.347483i	0.868760	+	0.495234i	$0.164918\pi$
$632$		0			0
$633$	−4.16216	−	7.20908i	−0.165431	−	0.286535i
$634$		0			0
$635$	−1.99731	−	0.799603i	−0.0792609	−	0.0317313i
$636$		0			0
$637$	−4.71398	+	19.4313i	−0.186775	+	0.769895i
$638$		0			0
$639$	−0.562857	+	0.108482i	−0.0222663	+	0.00429147i
$640$		0			0
$641$	−9.67386	+	16.7556i	−0.382095	+	0.661807i	−0.991361	−	0.131158i	$-0.958130\pi$
$641$	−9.67386	+	16.7556i	−0.382095	+	0.661807i	0.609267	+	0.792965i	$0.291464\pi$
$642$		0			0
$643$	−9.34410	+	20.4607i	−0.368495	+	0.806892i	0.631020	+	0.775766i	$0.282637\pi$
$643$	−9.34410	+	20.4607i	−0.368495	+	0.806892i	−0.999515	+	0.0311258i	$0.990091\pi$
$644$		0			0
$645$	9.05622	−	10.4514i	0.356588	−	0.411525i
$646$		0			0
$647$	−19.7019	+	7.88746i	−0.774562	+	0.310088i	−0.725060	−	0.688686i	$-0.758188\pi$
$647$	−19.7019	+	7.88746i	−0.774562	+	0.310088i	−0.0495027	+	0.998774i	$0.515764\pi$
$648$		0			0
$649$	0.230778	+	0.324082i	0.00905883	+	0.0127213i
$650$		0			0
$651$	−1.71986	−	1.63988i	−0.0674065	−	0.0642720i
$652$		0			0
$653$	2.30601	+	1.18883i	0.0902412	+	0.0465226i	0.502756	−	0.864428i	$-0.332319\pi$
$653$	2.30601	+	1.18883i	0.0902412	+	0.0465226i	−0.412515	+	0.910951i	$0.635350\pi$
$654$		0			0
$655$	−7.80160	+	2.29076i	−0.304834	+	0.0895073i
$656$		0			0
$657$	5.15430	+	0.993410i	0.201088	+	0.0387566i
$658$		0			0
$659$	−24.0464	−	2.29616i	−0.936716	−	0.0894456i	−0.384480	−	0.923133i	$-0.625619\pi$
$659$	−24.0464	−	2.29616i	−0.936716	−	0.0894456i	−0.552236	+	0.833688i	$0.686225\pi$
$660$		0			0
$661$	−27.5334	−	8.08453i	−1.07092	−	0.314452i	−0.301682	−	0.953409i	$-0.597548\pi$
$661$	−27.5334	−	8.08453i	−1.07092	−	0.314452i	−0.769242	+	0.638957i	$0.779366\pi$
$662$		0			0
$663$	3.93102	−	3.74822i	0.152668	−	0.145569i
$664$		0			0
$665$	0.882570	+	1.93256i	0.0342246	+	0.0749414i
$666$		0			0
$667$	4.52807	−	31.4934i	0.175328	−	1.21943i
$668$		0			0
$669$	−6.18223			−0.239019
$670$		0			0
$671$	−0.927332			−0.0357993
$672$		0			0
$673$	−1.89843	+	13.2038i	−0.0731789	+	0.508971i	0.919958	+	0.392016i	$0.128222\pi$
$673$	−1.89843	+	13.2038i	−0.0731789	+	0.508971i	−0.993137	+	0.116954i	$0.962687\pi$
$674$		0			0
$675$	−0.561274	−	1.22902i	−0.0216035	−	0.0473050i
$676$		0			0
$677$	−23.5628	+	22.4671i	−0.905593	+	0.863481i	−0.991136	−	0.132853i	$-0.957586\pi$
$677$	−23.5628	+	22.4671i	−0.905593	+	0.863481i	0.0855425	+	0.996335i	$0.472738\pi$
$678$		0			0
$679$	−4.96664	−	1.45834i	−0.190602	−	0.0559659i
$680$		0			0
$681$	−14.9907	−	1.43144i	−0.574447	−	0.0548530i
$682$		0			0
$683$	−28.5087	−	5.49460i	−1.09086	−	0.210245i	−0.388058	−	0.921635i	$-0.626854\pi$
$683$	−28.5087	−	5.49460i	−1.09086	−	0.210245i	−0.702798	+	0.711390i	$0.748066\pi$
$684$		0			0
$685$	6.19155	−	1.81800i	0.236567	−	0.0694623i
$686$		0			0
$687$	−2.95345	−	1.52261i	−0.112681	−	0.0580911i
$688$		0			0
$689$	−6.17800	−	5.89071i	−0.235363	−	0.224418i
$690$		0			0
$691$	−17.1293	−	24.0547i	−0.651627	−	0.915083i	0.348122	−	0.937449i	$-0.386819\pi$
$691$	−17.1293	−	24.0547i	−0.651627	−	0.915083i	−0.999750	+	0.0223664i	$0.992880\pi$
$692$		0			0
$693$	0.515964	−	0.206561i	0.0195999	−	0.00784660i
$694$		0			0
$695$	−6.85589	+	7.91212i	−0.260059	+	0.300124i
$696$		0			0
$697$	−4.13873	+	9.06255i	−0.156765	+	0.343269i
$698$		0			0
$699$	6.92645	−	11.9970i	0.261982	−	0.453767i
$700$		0			0
$701$	15.9477	−	3.07366i	0.602335	−	0.116091i	0.121038	−	0.992648i	$-0.461378\pi$
$701$	15.9477	−	3.07366i	0.602335	−	0.116091i	0.481297	+	0.876557i	$0.340166\pi$
$702$		0			0
$703$	−1.54513	+	6.36911i	−0.0582756	+	0.240215i
$704$		0			0
$705$	12.7188	+	5.09183i	0.479017	+	0.191770i
$706$		0			0
$707$	−2.21330	−	3.83354i	−0.0832396	−	0.144175i
$708$		0			0
$709$	4.10477	−	11.8599i	0.154158	−	0.445410i	−0.841305	−	0.540561i	$-0.818212\pi$
$709$	4.10477	−	11.8599i	0.154158	−	0.445410i	0.995463	+	0.0951509i	$0.0303334\pi$
$710$		0			0
$711$	−0.153510	−	3.22258i	−0.00575709	−	0.120856i
$712$		0			0
$713$	24.1571	−	15.5248i	0.904691	−	0.581409i
$714$		0			0
$715$	−0.885056	−	6.15570i	−0.0330992	−	0.230210i
$716$		0			0
$717$	−3.34279	−	2.62880i	−0.124839	−	0.0981744i
$718$		0			0
$719$	−1.63246	+	34.2695i	−0.0608803	+	1.27803i	0.737279	+	0.675588i	$0.236110\pi$
$719$	−1.63246	+	34.2695i	−0.0608803	+	1.27803i	−0.798159	+	0.602446i	$0.794193\pi$
$720$		0			0
$721$	2.67111	−	3.75105i	0.0994773	−	0.139696i
$722$		0			0
$723$	−20.3511	−	13.0789i	−0.756867	−	0.486409i
$724$		0			0
$725$	−2.29889	−	6.64220i	−0.0853785	−	0.246685i
$726$		0			0
$727$	−30.4806	+	23.9702i	−1.13046	+	0.889005i	−0.994810	−	0.101752i	$-0.967555\pi$
$727$	−30.4806	+	23.9702i	−1.13046	+	0.889005i	−0.135652	+	0.990757i	$0.543313\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	−13.2026	+	1.26069i	−0.488316	+	0.0466285i
$732$		0			0
$733$	3.57276	−	1.84188i	0.131963	−	0.0680316i	−0.390981	−	0.920399i	$-0.627864\pi$
$733$	3.57276	−	1.84188i	0.131963	−	0.0680316i	0.522944	+	0.852367i	$0.324834\pi$
$734$		0			0
$735$	3.03707	+	12.5190i	0.112024	+	0.461769i
$736$		0			0
$737$	−3.51466	+	8.27236i	−0.129464	+	0.304716i
$738$		0			0
$739$	2.82467	+	11.6434i	0.103907	+	0.428311i	0.999875	−	0.0158079i	$-0.00503201\pi$
$739$	2.82467	+	11.6434i	0.103907	+	0.428311i	−0.895968	+	0.444119i	$0.853517\pi$
$740$		0			0
$741$	−5.79095	+	2.98544i	−0.212736	+	0.109673i
$742$		0			0
$743$	17.3006	−	1.65201i	0.634698	−	0.0606063i	0.227253	−	0.973836i	$-0.427026\pi$
$743$	17.3006	−	1.65201i	0.634698	−	0.0606063i	0.407446	+	0.913229i	$0.366420\pi$
$744$		0			0
$745$	13.7729	+	15.8948i	0.504601	+	0.582341i
$746$		0			0
$747$	−7.76559	+	6.10693i	−0.284128	+	0.223441i
$748$		0			0
$749$	2.05857	+	5.94784i	0.0752184	+	0.217329i
$750$		0			0
$751$	−9.92671	−	6.37951i	−0.362231	−	0.232792i	0.346847	−	0.937922i	$-0.387252\pi$
$751$	−9.92671	−	6.37951i	−0.362231	−	0.232792i	−0.709078	+	0.705130i	$0.750889\pi$
$752$		0			0
$753$	−0.881003	+	1.23720i	−0.0321055	+	0.0450859i
$754$		0			0
$755$	−0.241345	+	5.06645i	−0.00878344	+	0.184387i
$756$		0			0
$757$	−31.6304	−	24.8744i	−1.14963	−	0.904076i	−0.153171	−	0.988200i	$-0.548948\pi$
$757$	−31.6304	−	24.8744i	−1.14963	−	0.904076i	−0.996455	+	0.0841238i	$0.973191\pi$
$758$		0			0
$759$	0.955772	+	6.64754i	0.0346923	+	0.241290i
$760$		0			0
$761$	−15.9202	+	10.2313i	−0.577106	+	0.370884i	−0.796395	−	0.604776i	$-0.793263\pi$
$761$	−15.9202	+	10.2313i	−0.577106	+	0.370884i	0.219289	+	0.975660i	$0.429626\pi$
$762$		0			0
$763$	0.0978098	+	2.05328i	0.00354095	+	0.0743338i
$764$		0			0
$765$	1.14454	−	3.30693i	0.0413809	−	0.119562i
$766$		0			0
$767$	0.537131	+	0.930338i	0.0193947	+	0.0335925i
$768$		0			0
$769$	5.34870	+	2.14130i	0.192879	+	0.0772171i	0.466091	−	0.884737i	$-0.345662\pi$
$769$	5.34870	+	2.14130i	0.192879	+	0.0772171i	−0.273212	+	0.961954i	$0.588086\pi$
$770$		0			0
$771$	3.70708	−	15.2808i	0.133507	−	0.550325i
$772$		0			0
$773$	15.6111	−	3.00879i	0.561492	−	0.108219i	0.0993950	−	0.995048i	$-0.468309\pi$
$773$	15.6111	−	3.00879i	0.561492	−	0.108219i	0.462097	+	0.886829i	$0.347097\pi$
$774$		0			0
$775$	3.17179	−	5.49370i	0.113934	−	0.197340i
$776$		0			0
$777$	0.627099	−	1.37316i	0.0224971	−	0.0492617i
$778$		0			0
$779$	7.82593	−	9.03161i	0.280393	−	0.323591i
$780$		0			0
$781$	0.584340	−	0.233934i	0.0209093	−	0.00837083i
$782$		0			0
$783$	−3.01757	−	4.23758i	−0.107839	−	0.151439i
$784$		0			0
$785$	12.4319	+	11.8538i	0.443713	+	0.423079i
$786$		0			0
$787$	0.215154	+	0.110920i	0.00766941	+	0.00395386i	0.462057	−	0.886850i	$-0.347112\pi$
$787$	0.215154	+	0.110920i	0.00766941	+	0.00395386i	−0.454388	+	0.890804i	$0.650142\pi$
$788$		0			0
$789$	−27.6920	+	8.13111i	−0.985862	+	0.289475i
$790$		0			0
$791$	4.90025	+	0.944446i	0.174233	+	0.0335806i
$792$		0			0
$793$	−2.49259	−	0.238013i	−0.0885144	−	0.00845210i
$794$		0			0
$795$	−5.27688	−	1.54943i	−0.187152	−	0.0549527i
$796$		0			0
$797$	−7.87568	+	7.50945i	−0.278971	+	0.265998i	−0.816627	−	0.577166i	$-0.804158\pi$
$797$	−7.87568	+	7.50945i	−0.278971	+	0.265998i	0.537656	+	0.843164i	$0.319310\pi$
$798$		0			0
$799$	−5.45808	−	11.9515i	−0.193093	−	0.422815i
$800$		0			0
$801$	−0.455159	+	3.16570i	−0.0160823	+	0.111855i
$802$		0			0
$803$	−5.76391			−0.203404
$804$		0			0
$805$	5.91328			0.208416
$806$		0			0
$807$	−0.968317	+	6.73479i	−0.0340864	+	0.237076i
$808$		0			0
$809$	−19.7154	−	43.1707i	−0.693156	−	1.51780i	−0.848077	−	0.529873i	$-0.822240\pi$
$809$	−19.7154	−	43.1707i	−0.693156	−	1.51780i	0.154921	−	0.987927i	$-0.450488\pi$
$810$		0			0
$811$	−18.2274	+	17.3797i	−0.640049	+	0.610285i	−0.938973	−	0.343992i	$-0.888221\pi$
$811$	−18.2274	+	17.3797i	−0.640049	+	0.610285i	0.298924	+	0.954277i	$0.403372\pi$
$812$		0			0
$813$	−5.28957	−	1.55316i	−0.185513	−	0.0544716i
$814$		0			0
$815$	−31.9474	−	3.05061i	−1.11907	−	0.106858i
$816$		0			0
$817$	15.6211	+	3.01073i	0.546514	+	0.105332i
$818$		0			0
$819$	1.43988	−	0.422788i	0.0503136	−	0.0147734i
$820$		0			0
$821$	−36.1920	−	18.6583i	−1.26311	−	0.651178i	−0.309122	−	0.951022i	$-0.600035\pi$
$821$	−36.1920	−	18.6583i	−1.26311	−	0.651178i	−0.953988	+	0.299844i	$0.903065\pi$
$822$		0			0
$823$	16.2311	+	15.4764i	0.565782	+	0.539472i	0.918069	−	0.396420i	$-0.129747\pi$
$823$	16.2311	+	15.4764i	0.565782	+	0.539472i	−0.352287	+	0.935892i	$0.614596\pi$
$824$		0			0
$825$	0.860580	+	1.20852i	0.0299615	+	0.0420751i
$826$		0			0
$827$	−4.53569	+	1.81582i	−0.157721	+	0.0631421i	−0.449180	−	0.893441i	$-0.648284\pi$
$827$	−4.53569	+	1.81582i	−0.157721	+	0.0631421i	0.291458	+	0.956583i	$0.405859\pi$
$828$		0			0
$829$	−9.90464	+	11.4306i	−0.344003	+	0.397000i	−0.901217	−	0.433369i	$-0.857325\pi$
$829$	−9.90464	+	11.4306i	−0.344003	+	0.397000i	0.557214	+	0.830369i	$0.311870\pi$
$830$		0			0
$831$	−11.6185	+	25.4409i	−0.403040	+	0.882535i
$832$		0			0
$833$	6.17715	−	10.6991i	0.214026	−	0.370703i
$834$		0			0
$835$	2.81753	−	0.543034i	0.0975045	−	0.0187925i
$836$		0			0
$837$	1.10690	−	4.56271i	0.0382602	−	0.157710i
$838$		0			0
$839$	−28.9345	−	11.5836i	−0.998931	−	0.399912i	−0.186175	−	0.982517i	$-0.559609\pi$
$839$	−28.9345	−	11.5836i	−0.998931	−	0.399912i	−0.812756	+	0.582605i	$0.802034\pi$
$840$		0			0
$841$	0.968591	+	1.67765i	0.0333997	+	0.0578500i
$842$		0			0
$843$	4.23094	−	12.2245i	0.145721	−	0.421034i
$844$		0			0
$845$	0.382582	+	8.03139i	0.0131612	+	0.276288i
$846$		0			0
$847$	4.17033	−	2.68011i	0.143294	−	0.0920897i
$848$		0			0
$849$	0.584310	+	4.06397i	0.0200535	+	0.139475i
$850$		0			0
$851$	14.3387	+	11.2761i	0.491525	+	0.386539i
$852$		0			0
$853$	2.06553	−	43.3609i	0.0707226	−	1.48465i	−0.632988	−	0.774162i	$-0.718172\pi$
$853$	2.06553	−	43.3609i	0.0707226	−	1.48465i	0.703710	−	0.710487i	$-0.251525\pi$
$854$		0			0
$855$	−2.43481	+	3.41922i	−0.0832688	+	0.116935i
$856$		0			0
$857$	−4.54022	−	2.91783i	−0.155091	−	0.0996710i	0.460793	−	0.887507i	$-0.347565\pi$
$857$	−4.54022	−	2.91783i	−0.155091	−	0.0996710i	−0.615885	+	0.787836i	$0.711201\pi$
$858$		0			0
$859$	18.9309	+	54.6972i	0.645913	+	1.86624i	0.472321	+	0.881426i	$0.343416\pi$
$859$	18.9309	+	54.6972i	0.645913	+	1.86624i	0.173592	+	0.984818i	$0.444463\pi$
$860$		0			0
$861$	−2.16370	+	1.70155i	−0.0737386	+	0.0579887i
$862$		0			0
$863$	−3.73475	−	4.31013i	−0.127132	−	0.146719i	0.688615	−	0.725128i	$-0.258219\pi$
$863$	−3.73475	−	4.31013i	−0.127132	−	0.146719i	−0.815747	+	0.578409i	$0.803674\pi$
$864$		0			0
$865$	−5.87204	+	0.560712i	−0.199655	+	0.0190648i
$866$		0			0
$867$	12.1273	−	6.25203i	0.411863	−	0.212330i
$868$		0			0
$869$	0.835202	+	3.44275i	0.0283323	+	0.116787i
$870$		0			0
$871$	−11.5703	+	21.3333i	−0.392046	+	0.722851i
$872$		0			0
$873$	−2.41111	−	9.93873i	−0.0816037	−	0.336375i
$874$		0			0
$875$	5.45788	−	2.81373i	0.184510	−	0.0951215i
$876$		0			0
$877$	−16.5577	+	1.58107i	−0.559114	+	0.0533889i	−0.370788	−	0.928718i	$-0.620912\pi$
$877$	−16.5577	+	1.58107i	−0.559114	+	0.0533889i	−0.188326	+	0.982107i	$0.560306\pi$
$878$		0			0
$879$	6.36979	+	7.35113i	0.214848	+	0.247948i
$880$		0			0
$881$	−12.2134	+	9.60470i	−0.411479	+	0.323590i	−0.802349	−	0.596855i	$-0.796417\pi$
$881$	−12.2134	+	9.60470i	−0.411479	+	0.323590i	0.390870	+	0.920446i	$0.372174\pi$
$882$		0			0
$883$	−18.8534	−	54.4733i	−0.634467	−	1.83317i	−0.547228	−	0.836983i	$-0.684317\pi$
$883$	−18.8534	−	54.4733i	−0.634467	−	1.83317i	−0.0872384	−	0.996187i	$-0.527804\pi$
$884$		0			0
$885$	0.582242	+	0.374184i	0.0195718	+	0.0125781i
$886$		0			0
$887$	9.93711	−	13.9547i	0.333656	−	0.468554i	−0.613331	−	0.789826i	$-0.710171\pi$
$887$	9.93711	−	13.9547i	0.333656	−	0.468554i	0.946987	+	0.321272i	$0.104110\pi$
$888$		0			0
$889$	−0.0271244	+	0.569411i	−0.000909723	+	0.0190974i
$890$		0			0
$891$	0.863136	+	0.678778i	0.0289161	+	0.0227399i
$892$		0			0
$893$	2.24290	+	15.5997i	0.0750559	+	0.522025i
$894$		0			0
$895$	−24.5116	+	15.7527i	−0.819333	+	0.526554i
$896$		0			0
$897$	0.862843	+	18.1133i	0.0288095	+	0.604786i
$898$		0			0
$899$	7.98851	−	23.0813i	0.266432	−	0.769804i
$900$		0			0
$901$	2.63717	+	4.56771i	0.0878568	+	0.152172i
$902$		0			0
$903$	−3.40181	−	1.36188i	−0.113205	−	0.0453205i
$904$		0			0
$905$	3.50698	−	14.4560i	0.116576	−	0.480533i
$906$		0			0
$907$	−13.2348	+	2.55079i	−0.439453	+	0.0846976i	−0.404179	−	0.914680i	$-0.632443\pi$
$907$	−13.2348	+	2.55079i	−0.439453	+	0.0846976i	−0.0352743	+	0.999378i	$0.511230\pi$
$908$		0			0
$909$	4.37288	−	7.57405i	0.145039	−	0.251215i
$910$		0			0
$911$	−6.32091	+	13.8409i	−0.209421	+	0.458568i	−0.984971	−	0.172718i	$-0.944745\pi$
$911$	−6.32091	+	13.8409i	−0.209421	+	0.458568i	0.775550	+	0.631286i	$0.217472\pi$
$912$		0			0
$913$	7.10394	−	8.19838i	0.235106	−	0.271327i
$914$		0			0
$915$	−1.49764	+	0.599566i	−0.0495105	+	0.0198210i
$916$		0			0
$917$	1.24970	+	1.75495i	0.0412686	+	0.0579537i
$918$		0			0
$919$	−5.98746	−	5.70903i	−0.197508	−	0.188323i	0.584871	−	0.811127i	$-0.301145\pi$
$919$	−5.98746	−	5.70903i	−0.197508	−	0.188323i	−0.782379	+	0.622803i	$0.785994\pi$
$920$		0			0
$921$	29.0250	+	14.9634i	0.956405	+	0.493061i
$922$		0			0
$923$	1.63070	−	0.478816i	0.0536751	−	0.0157604i
$924$		0			0
$925$	3.95690	+	0.762629i	0.130102	+	0.0250751i
$926$		0			0
$927$	9.05687	+	0.864826i	0.297467	+	0.0284046i
$928$		0			0
$929$	−35.4359	−	10.4049i	−1.16261	−	0.341374i	−0.357165	−	0.934041i	$-0.616257\pi$
$929$	−35.4359	−	10.4049i	−1.16261	−	0.341374i	−0.805447	+	0.592667i	$0.798075\pi$
$930$		0			0
$931$	−10.7251	+	10.2263i	−0.351500	+	0.335154i
$932$		0			0
$933$	−1.25728	−	2.75307i	−0.0411616	−	0.0901314i
$934$		0			0
$935$	−0.546852	+	3.80344i	−0.0178840	+	0.124386i
$936$		0			0
$937$	35.0944			1.14648			0.573241	−	0.819387i	$-0.305686\pi$
$937$	35.0944			1.14648			0.573241	+	0.819387i	$0.305686\pi$
$938$		0			0
$939$	18.7890			0.613156
$940$		0			0
$941$	−0.0578003	+	0.402010i	−0.00188424	+	0.0131051i	−0.990742	−	0.135759i	$-0.956653\pi$
$941$	−0.0578003	+	0.402010i	−0.00188424	+	0.0131051i	0.988858	+	0.148864i	$0.0475618\pi$
$942$		0			0
$943$	−13.8176	−	30.2562i	−0.449961	−	0.985278i
$944$		0			0
$945$	0.699731	−	0.667192i	0.0227623	−	0.0217038i
$946$		0			0
$947$	10.4074	+	3.05588i	0.338194	+	0.0993027i	0.446420	−	0.894824i	$-0.352699\pi$
$947$	10.4074	+	3.05588i	0.338194	+	0.0993027i	−0.108226	+	0.994126i	$0.534517\pi$
$948$		0			0
$949$	−15.4929	−	1.47939i	−0.502920	−	0.0480230i
$950$		0			0
$951$	−4.53150	−	0.873375i	−0.146944	−	0.0283211i
$952$		0			0
$953$	50.9001	−	14.9456i	1.64882	−	0.484136i	0.680268	−	0.732964i	$-0.261864\pi$
$953$	50.9001	−	14.9456i	1.64882	−	0.484136i	0.968548	+	0.248828i	$0.0800454\pi$
$954$		0			0
$955$	28.5037	+	14.6947i	0.922359	+	0.475509i
$956$		0			0
$957$	4.13421	+	3.94196i	0.133640	+	0.127426i
$958$		0			0
$959$	−0.991791	−	1.39278i	−0.0320266	−	0.0449751i
$960$		0			0
$961$	−8.31483	+	3.32876i	−0.268220	+	0.107379i
$962$		0			0
$963$	−8.14336	+	9.39794i	−0.262416	+	0.302844i
$964$		0			0
$965$	11.1609	−	24.4389i	0.359281	−	0.786716i
$966$		0			0
$967$	−24.6678	+	42.7259i	−0.793264	+	1.37397i	0.130672	+	0.991426i	$0.458286\pi$
$967$	−24.6678	+	42.7259i	−0.793264	+	1.37397i	−0.923936	+	0.382547i	$0.875047\pi$
$968$		0			0
$969$	3.95282	−	0.761844i	0.126983	−	0.0244740i
$970$		0			0
$971$	−2.71498	+	11.1913i	−0.0871280	+	0.359147i	−0.998641	−	0.0521258i	$-0.983400\pi$
$971$	−2.71498	+	11.1913i	−0.0871280	+	0.359147i	0.911513	+	0.411272i	$0.134915\pi$
$972$		0			0
$973$	2.57530	+	1.03099i	0.0825602	+	0.0330521i
$974$		0			0
$975$	2.00298	+	3.46926i	0.0641467	+	0.111105i
$976$		0			0
$977$	10.4088	−	30.0743i	0.333007	−	0.962162i	−0.646877	−	0.762595i	$-0.723925\pi$
$977$	10.4088	−	30.0743i	0.333007	−	0.962162i	0.979884	−	0.199567i	$-0.0639536\pi$
$978$		0			0
$979$	−0.167102	−	3.50791i	−0.00534061	−	0.112113i
$980$		0			0
$981$	−3.41661	+	2.19572i	−0.109084	+	0.0701040i
$982$		0			0
$983$	−3.29100	−	22.8894i	−0.104967	−	0.730060i	−0.972538	−	0.232746i	$-0.925229\pi$
$983$	−3.29100	−	22.8894i	−0.104967	−	0.730060i	0.867571	−	0.497314i	$-0.165680\pi$
$984$		0			0
$985$	−1.67042	−	1.31363i	−0.0532240	−	0.0418558i
$986$		0			0
$987$	0.172727	−	3.62598i	0.00549795	−	0.115416i
$988$		0			0
$989$	25.6841	−	36.0683i	0.816708	−	1.14691i
$990$		0			0
$991$	−13.6230	−	8.75497i	−0.432749	−	0.278111i	0.306078	−	0.952007i	$-0.400983\pi$
$991$	−13.6230	−	8.75497i	−0.432749	−	0.278111i	−0.738826	+	0.673896i	$0.764620\pi$
$992$		0			0
$993$	−0.875386	−	2.52926i	−0.0277795	−	0.0802637i
$994$		0			0
$995$	20.9280	−	16.4579i	0.663461	−	0.521751i
$996$		0			0
$997$	32.6909	+	37.7273i	1.03533	+	1.19484i	0.980536	+	0.196339i	$0.0629053\pi$
$997$	32.6909	+	37.7273i	1.03533	+	1.19484i	0.0547958	+	0.998498i	$0.482549\pi$
$998$		0			0
$999$	2.96900	−	0.283505i	0.0939351	−	0.00896972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.a.157.2	✓	100
67.35	even	33	inner	804.2.y.a.169.2	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.a.157.2	✓	100	1.1	even	1	trivial
804.2.y.a.169.2	yes	100	67.35	even	33	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.142315 + 0.989821i) q^{3} +(-0.793528 - 1.73758i) q^{5} +(-0.366312 + 0.349278i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.142315 + 0.989821i) q^{3} +(-0.793528 - 1.73758i) q^{5} +(-0.366312 + 0.349278i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(1.09309 + 0.104378i) q^{11} +(2.91134 + 0.561115i) q^{13} +(1.83283 - 0.538167i) q^{15} +(-1.62830 - 0.839446i) q^{17} +(1.59035 + 1.51640i) q^{19} +(-0.293591 - 0.412291i) q^{21} +(5.67802 - 2.27314i) q^{23} +(0.884794 - 1.02111i) q^{25} +(0.415415 - 0.909632i) q^{27} +(2.60110 - 4.50523i) q^{29} +(4.61022 - 0.888546i) q^{31} +(-0.258878 + 1.06711i) q^{33} +(0.897578 + 0.359336i) q^{35} +(1.49125 + 2.58293i) q^{37} +(-0.969731 + 2.80185i) q^{39} +(-0.258770 - 5.43225i) q^{41} +(6.09038 - 3.91405i) q^{43} +(0.271850 + 1.89076i) q^{45} +(5.63764 + 4.43349i) q^{47} +(-0.320884 + 6.73618i) q^{49} +(1.06263 - 1.49226i) q^{51} +(-2.42205 - 1.55655i) q^{53} +(-0.686033 - 1.98216i) q^{55} +(-1.72730 + 1.35836i) q^{57} +(0.237271 + 0.273826i) q^{59} +(-0.840692 + 0.0802764i) q^{61} +(0.449877 - 0.231928i) q^{63} +(-1.33525 - 5.50396i) q^{65} +(-2.47018 + 7.80373i) q^{67} +(1.44193 + 5.94373i) q^{69} +(0.509495 - 0.262663i) q^{71} +(-5.22539 + 0.498964i) q^{73} +(0.884794 + 1.02111i) q^{75} +(-0.436869 + 0.343558i) q^{77} +(1.05520 + 3.04879i) q^{79} +(0.841254 + 0.540641i) q^{81} +(5.73051 - 8.04738i) q^{83} +(-0.166508 + 3.49543i) q^{85} +(4.08920 + 3.21578i) q^{87} +(-0.455159 - 3.16570i) q^{89} +(-1.26245 + 0.811324i) q^{91} +(0.223400 + 4.68974i) q^{93} +(1.37288 - 3.96668i) q^{95} +(5.11351 + 8.85686i) q^{97} +(-1.01941 - 0.408109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9}+O(q^{10}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9	\( 100 q - 10 q^{3} + 2 q^{5} - 3 q^{7} - 10 q^{9} - 13 q^{11} - 3 q^{13} - 9 q^{15} - 44 q^{17} - 16 q^{19} - 3 q^{21} - 16 q^{23} + 28 q^{25} - 10 q^{27} - 7 q^{29} + 20 q^{31} - 2 q^{33} - 19 q^{35} - 22 q^{37} - 3 q^{39} - 14 q^{41} - 27 q^{43} + 2 q^{45} + 4 q^{47} - 92 q^{49} + 22 q^{51} + 8 q^{53} - 13 q^{55} + 17 q^{57} + 22 q^{59} + 17 q^{61} - 3 q^{63} + 56 q^{65} - 14 q^{67} + 17 q^{69} - q^{71} + 26 q^{73} + 28 q^{75} + 112 q^{77} + 69 q^{79} - 10 q^{81} + 15 q^{83} + 69 q^{85} + 4 q^{87} + 73 q^{89} - 40 q^{91} - 13 q^{93} + 59 q^{95} + 29 q^{97} - 2 q^{99}+O(q^{100}) \) 100 * q - 10 * q^3 + 2 * q^5 - 3 * q^7 - 10 * q^9 - 13 * q^11 - 3 * q^13 - 9 * q^15 - 44 * q^17 - 16 * q^19 - 3 * q^21 - 16 * q^23 + 28 * q^25 - 10 * q^27 - 7 * q^29 + 20 * q^31 - 2 * q^33 - 19 * q^35 - 22 * q^37 - 3 * q^39 - 14 * q^41 - 27 * q^43 + 2 * q^45 + 4 * q^47 - 92 * q^49 + 22 * q^51 + 8 * q^53 - 13 * q^55 + 17 * q^57 + 22 * q^59 + 17 * q^61 - 3 * q^63 + 56 * q^65 - 14 * q^67 + 17 * q^69 - q^71 + 26 * q^73 + 28 * q^75 + 112 * q^77 + 69 * q^79 - 10 * q^81 + 15 * q^83 + 69 * q^85 + 4 * q^87 + 73 * q^89 - 40 * q^91 - 13 * q^93 + 59 * q^95 + 29 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more