LMFDB - Embedded newform 405.3.l.o.217.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(28,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("405.28");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.l (of order $12$, degree $4$, not 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			217.8
Character	$\chi$	$=$	405.217
Dual form			405.3.l.o.28.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.44665 - 0.923527i) q^{2} +(7.56239 - 4.36615i) q^{4} +(-4.98625 - 0.370516i) q^{5} +(5.99870 - 1.60735i) q^{7} +(11.9402 - 11.9402i) q^{8} +O(q^{10})$	\(q+(3.44665 - 0.923527i) q^{2} +(7.56239 - 4.36615i) q^{4} +(-4.98625 - 0.370516i) q^{5} +(5.99870 - 1.60735i) q^{7} +(11.9402 - 11.9402i) q^{8} +(-17.5280 + 3.32790i) q^{10} +(10.3303 - 17.8926i) q^{11} +(-5.56860 - 1.49210i) q^{13} +(19.1910 - 11.0799i) q^{14} +(12.6619 - 21.9311i) q^{16} +(-3.85449 - 3.85449i) q^{17} +18.4907i q^{19} +(-39.3257 + 18.9687i) q^{20} +(19.0807 - 71.2100i) q^{22} +(19.3656 + 5.18899i) q^{23} +(24.7254 + 3.69498i) q^{25} -20.5710 q^{26} +(38.3466 - 38.3466i) q^{28} +(-9.21485 - 5.32019i) q^{29} +(16.5732 + 28.7057i) q^{31} +(5.90560 - 22.0400i) q^{32} +(-16.8448 - 9.72536i) q^{34} +(-30.5066 + 5.79202i) q^{35} +(-35.8023 - 35.8023i) q^{37} +(17.0766 + 63.7309i) q^{38} +(-63.9607 + 55.1126i) q^{40} +(-6.02916 - 10.4428i) q^{41} +(13.0295 + 48.6267i) q^{43} -180.415i q^{44} +71.5385 q^{46} +(-0.840958 + 0.225334i) q^{47} +(-9.03436 + 5.21599i) q^{49} +(88.6323 - 10.0993i) q^{50} +(-48.6267 + 13.0295i) q^{52} +(-11.6767 + 11.6767i) q^{53} +(-58.1391 + 85.3897i) q^{55} +(52.4335 - 90.8175i) q^{56} +(-36.6737 - 9.82669i) q^{58} +(-72.8545 + 42.0625i) q^{59} +(-34.8873 + 60.4265i) q^{61} +(83.6326 + 83.6326i) q^{62} +19.8770i q^{64} +(27.2136 + 9.50325i) q^{65} +(-14.0760 + 52.5324i) q^{67} +(-45.9785 - 12.3199i) q^{68} +(-99.7965 + 48.1368i) q^{70} +107.003 q^{71} +(8.17407 - 8.17407i) q^{73} +(-156.462 - 90.3335i) q^{74} +(80.7330 + 139.834i) q^{76} +(33.2088 - 123.937i) q^{77} +(63.3057 + 36.5496i) q^{79} +(-71.2613 + 104.662i) q^{80} +(-30.4246 - 30.4246i) q^{82} +(1.53327 + 5.72223i) q^{83} +(17.7913 + 20.6476i) q^{85} +(89.8161 + 155.566i) q^{86} +(-90.2953 - 336.987i) q^{88} -6.20731i q^{89} -35.8027 q^{91} +(169.106 - 45.3118i) q^{92} +(-2.69039 + 1.55330i) q^{94} +(6.85110 - 92.1992i) q^{95} +(75.0582 - 20.1118i) q^{97} +(-26.3212 + 26.3212i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{7}+O(q^{10}) $ 32 * q + 8 * q^7	$ 32 q + 8 q^{7} - 64 q^{10} - 28 q^{13} + 20 q^{16} - 176 q^{22} - 64 q^{25} + 160 q^{28} + 208 q^{31} - 352 q^{37} + 252 q^{40} + 188 q^{43} + 376 q^{46} + 188 q^{52} - 272 q^{55} - 504 q^{58} - 296 q^{61} - 304 q^{67} - 684 q^{70} - 112 q^{73} + 732 q^{76} - 152 q^{82} + 788 q^{85} + 1128 q^{88} + 400 q^{91} + 284 q^{97}+O(q^{100}) $ 32 * q + 8 * q^7 - 64 * q^10 - 28 * q^13 + 20 * q^16 - 176 * q^22 - 64 * q^25 + 160 * q^28 + 208 * q^31 - 352 * q^37 + 252 * q^40 + 188 * q^43 + 376 * q^46 + 188 * q^52 - 272 * q^55 - 504 * q^58 - 296 * q^61 - 304 * q^67 - 684 * q^70 - 112 * q^73 + 732 * q^76 - 152 * q^82 + 788 * q^85 + 1128 * q^88 + 400 * q^91 + 284 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	3.44665	−	0.923527i	1.72332	−	0.461763i	0.744697	−	0.667403i	$-0.232594\pi$
$2$	3.44665	−	0.923527i	1.72332	−	0.461763i	0.978628	+	0.205639i	$0.0659274\pi$
$3$		0			0
$3$		0			0
$4$	7.56239	−	4.36615i	1.89060	−	1.09154i
$5$	−4.98625	−	0.370516i	−0.997251	−	0.0741033i
$5$	−4.98625	−	0.370516i	−0.997251	−	0.0741033i
$6$		0			0
$7$	5.99870	−	1.60735i	0.856958	−	0.229621i	0.196518	−	0.980500i	$-0.437037\pi$
$7$	5.99870	−	1.60735i	0.856958	−	0.229621i	0.660440	+	0.750879i	$0.270370\pi$
$8$	11.9402	−	11.9402i	1.49252	−	1.49252i
$9$		0			0
$10$	−17.5280	+	3.32790i	−1.75280	+	0.332790i
$11$	10.3303	−	17.8926i	0.939120	−	1.62660i	0.172003	−	0.985096i	$-0.444976\pi$
$11$	10.3303	−	17.8926i	0.939120	−	1.62660i	0.767117	−	0.641507i	$-0.221691\pi$
$12$		0			0
$13$	−5.56860	−	1.49210i	−0.428354	−	0.114777i	0.0381995	−	0.999270i	$-0.487838\pi$
$13$	−5.56860	−	1.49210i	−0.428354	−	0.114777i	−0.466553	+	0.884493i	$0.654504\pi$
$14$	19.1910	−	11.0799i	1.37079	−	0.791424i
$15$		0			0
$16$	12.6619	−	21.9311i	0.791369	−	1.37069i
$17$	−3.85449	−	3.85449i	−0.226735	−	0.226735i	0.584592	−	0.811327i	$-0.301254\pi$
$17$	−3.85449	−	3.85449i	−0.226735	−	0.226735i	−0.811327	+	0.584592i	$0.801254\pi$
$18$		0			0
$19$			18.4907i			0.973193i	0.873627	+	0.486597i	$0.161762\pi$
$19$			18.4907i			0.973193i	−0.873627	+	0.486597i	$0.838238\pi$
$20$	−39.3257	+	18.9687i	−1.96629	+	0.948436i
$21$		0			0
$22$	19.0807	−	71.2100i	0.867303	−	3.23682i
$23$	19.3656	+	5.18899i	0.841981	+	0.225608i	0.653934	−	0.756552i	$-0.273117\pi$
$23$	19.3656	+	5.18899i	0.841981	+	0.225608i	0.188047	+	0.982160i	$0.439784\pi$
$24$		0			0
$25$	24.7254	+	3.69498i	0.989017	+	0.147799i
$26$	−20.5710			−0.791193
$27$		0			0
$28$	38.3466	−	38.3466i	1.36952	−	1.36952i
$29$	−9.21485	−	5.32019i	−0.317753	−	0.183455i	0.332637	−	0.943055i	$-0.392061\pi$
$29$	−9.21485	−	5.32019i	−0.317753	−	0.183455i	−0.650391	+	0.759600i	$0.725395\pi$
$30$		0			0
$31$	16.5732	+	28.7057i	0.534620	+	0.925990i	0.999182	+	0.0404488i	$0.0128788\pi$
$31$	16.5732	+	28.7057i	0.534620	+	0.925990i	−0.464561	+	0.885541i	$0.653788\pi$
$32$	5.90560	−	22.0400i	0.184550	−	0.688750i
$33$		0			0
$34$	−16.8448	−	9.72536i	−0.495436	−	0.286040i
$35$	−30.5066	+	5.79202i	−0.871617	+	0.165486i
$36$		0			0
$37$	−35.8023	−	35.8023i	−0.967629	−	0.967629i	0.0318634	−	0.999492i	$-0.489856\pi$
$37$	−35.8023	−	35.8023i	−0.967629	−	0.967629i	−0.999492	+	0.0318634i	$0.989856\pi$
$38$	17.0766	+	63.7309i	0.449385	+	1.67713i
$39$		0			0
$40$	−63.9607	+	55.1126i	−1.59902	+	1.37782i
$41$	−6.02916	−	10.4428i	−0.147053	−	0.254703i	0.783084	−	0.621916i	$-0.213645\pi$
$41$	−6.02916	−	10.4428i	−0.147053	−	0.254703i	−0.930137	+	0.367213i	$0.880312\pi$
$42$		0			0
$43$	13.0295	+	48.6267i	0.303011	+	1.13085i	0.934644	+	0.355585i	$0.115718\pi$
$43$	13.0295	+	48.6267i	0.303011	+	1.13085i	−0.631633	+	0.775268i	$0.717615\pi$
$44$		−	180.415i		−	4.10034i
$45$		0			0
$46$	71.5385			1.55518
$47$	−0.840958	+	0.225334i	−0.0178927	+	0.00479434i	−0.267754	−	0.963487i	$-0.586282\pi$
$47$	−0.840958	+	0.225334i	−0.0178927	+	0.00479434i	0.249862	+	0.968282i	$0.419615\pi$
$48$		0			0
$49$	−9.03436	+	5.21599i	−0.184375	+	0.106449i
$50$	88.6323	−	10.0993i	1.77265	−	0.201986i
$51$		0			0
$52$	−48.6267	+	13.0295i	−0.935128	+	0.250567i
$53$	−11.6767	+	11.6767i	−0.220315	+	0.220315i	−0.808631	−	0.588316i	$-0.799791\pi$
$53$	−11.6767	+	11.6767i	−0.220315	+	0.220315i	0.588316	+	0.808631i	$0.299791\pi$
$54$		0			0
$55$	−58.1391	+	85.3897i	−1.05707	+	1.55254i
$56$	52.4335	−	90.8175i	0.936313	−	1.62174i
$57$		0			0
$58$	−36.6737	−	9.82669i	−0.632305	−	0.169426i
$59$	−72.8545	+	42.0625i	−1.23482	+	0.712924i	−0.968031	−	0.250830i	$-0.919296\pi$
$59$	−72.8545	+	42.0625i	−1.23482	+	0.712924i	−0.266790	+	0.963755i	$0.585963\pi$
$60$		0			0
$61$	−34.8873	+	60.4265i	−0.571922	+	0.990598i	0.424446	+	0.905453i	$0.360469\pi$
$61$	−34.8873	+	60.4265i	−0.571922	+	0.990598i	−0.996369	+	0.0851453i	$0.972865\pi$
$62$	83.6326	+	83.6326i	1.34891	+	1.34891i
$63$		0			0
$64$			19.8770i			0.310578i
$65$	27.2136	+	9.50325i	0.418671	+	0.146204i
$66$		0			0
$67$	−14.0760	+	52.5324i	−0.210090	+	0.784066i	0.777748	+	0.628577i	$0.216362\pi$
$67$	−14.0760	+	52.5324i	−0.210090	+	0.784066i	−0.987838	+	0.155489i	$0.950305\pi$
$68$	−45.9785	−	12.3199i	−0.676154	−	0.181175i
$69$		0			0
$70$	−99.7965	+	48.1368i	−1.42566	+	0.687668i
$71$	107.003			1.50709			0.753543	−	0.657399i	$-0.228343\pi$
$71$	107.003			1.50709			0.753543	+	0.657399i	$0.228343\pi$
$72$		0			0
$73$	8.17407	−	8.17407i	0.111974	−	0.111974i	−0.648900	−	0.760874i	$-0.724771\pi$
$73$	8.17407	−	8.17407i	0.111974	−	0.111974i	0.760874	+	0.648900i	$0.224771\pi$
$74$	−156.462	−	90.3335i	−2.11435	−	1.22072i
$75$		0			0
$76$	80.7330	+	139.834i	1.06228	+	1.83992i
$77$	33.2088	−	123.937i	0.431284	−	1.60957i
$78$		0			0
$79$	63.3057	+	36.5496i	0.801338	+	0.462653i	0.843939	−	0.536439i	$-0.180231\pi$
$79$	63.3057	+	36.5496i	0.801338	+	0.462653i	−0.0426005	+	0.999092i	$0.513564\pi$
$80$	−71.2613	+	104.662i	−0.890766	+	1.30828i
$81$		0			0
$82$	−30.4246	−	30.4246i	−0.371032	−	0.371032i
$83$	1.53327	+	5.72223i	0.0184731	+	0.0689425i	0.974547	−	0.224183i	$-0.0719713\pi$
$83$	1.53327	+	5.72223i	0.0184731	+	0.0689425i	−0.956074	+	0.293125i	$0.905305\pi$
$84$		0			0
$85$	17.7913	+	20.6476i	0.209310	+	0.242913i
$86$	89.8161	+	155.566i	1.04437	+	1.80891i
$87$		0			0
$88$	−90.2953	−	336.987i	−1.02608	−	3.82939i
$89$		−	6.20731i		−	0.0697451i	−0.999392	−	0.0348725i	$-0.988897\pi$
$89$		−	6.20731i		−	0.0697451i	0.999392	−	0.0348725i	$-0.0111025\pi$
$90$		0			0
$91$	−35.8027			−0.393436
$92$	169.106	−	45.3118i	1.83811	−	0.492519i
$93$		0			0
$94$	−2.69039	+	1.55330i	−0.0286211	+	0.0165244i
$95$	6.85110	−	92.1992i	0.0721168	−	0.970518i
$96$		0			0
$97$	75.0582	−	20.1118i	0.773796	−	0.207338i	0.149748	−	0.988724i	$-0.452154\pi$
$97$	75.0582	−	20.1118i	0.773796	−	0.207338i	0.624048	+	0.781386i	$0.285487\pi$
$98$	−26.3212	+	26.3212i	−0.268583	+	0.268583i
$99$		0			0
$100$	203.116	−	80.0120i	2.03116	−	0.800120i
$101$	14.4165	−	24.9702i	0.142738	−	0.247230i	−0.785789	−	0.618495i	$-0.787743\pi$
$101$	14.4165	−	24.9702i	0.142738	−	0.247230i	0.928527	+	0.371265i	$0.121076\pi$
$102$		0			0
$103$	73.5518	+	19.7081i	0.714095	+	0.191341i	0.597535	−	0.801843i	$-0.296147\pi$
$103$	73.5518	+	19.7081i	0.714095	+	0.191341i	0.116560	+	0.993184i	$0.462813\pi$
$104$	−84.3059	+	48.6740i	−0.810634	+	0.468020i
$105$		0			0
$106$	−29.4618	+	51.0292i	−0.277941	+	0.481408i
$107$	−14.0751	−	14.0751i	−0.131543	−	0.131543i	0.638270	−	0.769813i	$-0.279650\pi$
$107$	−14.0751	−	14.0751i	−0.131543	−	0.131543i	−0.769813	+	0.638270i	$0.779650\pi$
$108$		0			0
$109$			18.6923i			0.171489i	0.996317	+	0.0857447i	$0.0273269\pi$
$109$			18.6923i			0.171489i	−0.996317	+	0.0857447i	$0.972673\pi$
$110$	−121.525	+	348.001i	−1.10478	+	3.16365i
$111$		0			0
$112$	40.7042	−	151.910i	0.363430	−	1.35634i
$113$	−142.222	−	38.1083i	−1.25860	−	0.337242i	−0.432949	−	0.901418i	$-0.642527\pi$
$113$	−142.222	−	38.1083i	−1.25860	−	0.337242i	−0.825654	+	0.564176i	$0.809194\pi$
$114$		0			0
$115$	−94.6390	−	33.0489i	−0.822948	−	0.287381i
$116$	−92.9150			−0.800991
$117$		0			0
$118$	−212.258	+	212.258i	−1.79880	+	1.79880i
$119$	−29.3175	−	16.9265i	−0.246365	−	0.142239i
$120$		0			0
$121$	−152.931	−	264.884i	−1.26389	−	2.18913i
$122$	−64.4386	+	240.488i	−0.528186	+	1.97122i
$123$		0			0
$124$	250.667	+	144.722i	2.02150	+	1.16712i
$125$	−121.918	−	27.5853i	−0.975346	−	0.220682i
$126$		0			0
$127$	−37.9268	−	37.9268i	−0.298637	−	0.298637i	0.541843	−	0.840480i	$-0.317727\pi$
$127$	−37.9268	−	37.9268i	−0.298637	−	0.298637i	−0.840480	+	0.541843i	$0.817727\pi$
$128$	41.9794	+	156.669i	0.327964	+	1.22398i
$129$		0			0
$130$	102.572	+	7.62190i	0.789017	+	0.0586300i
$131$	−32.7093	−	56.6541i	−0.249689	−	0.432474i	0.713750	−	0.700400i	$-0.246995\pi$
$131$	−32.7093	−	56.6541i	−0.249689	−	0.432474i	−0.963440	+	0.267926i	$0.913662\pi$
$132$		0			0
$133$	29.7209	+	110.920i	0.223466	+	0.833985i
$134$			194.060i			1.44821i
$135$		0			0
$136$	−92.0465			−0.676813
$137$	123.460	−	33.0810i	0.901169	−	0.241467i	0.221651	−	0.975126i	$-0.428856\pi$
$137$	123.460	−	33.0810i	0.901169	−	0.241467i	0.679518	+	0.733659i	$0.262189\pi$
$138$		0			0
$139$	214.282	−	123.716i	1.54160	−	0.890042i	0.542860	−	0.839823i	$-0.317342\pi$
$139$	214.282	−	123.716i	1.54160	−	0.890042i	0.998738	−	0.0502184i	$-0.0159918\pi$
$140$	−205.414	+	176.998i	−1.46724	+	1.26427i
$141$		0			0
$142$	368.802	−	98.8202i	2.59720	−	0.695917i
$143$	−84.2231	+	84.2231i	−0.588972	+	0.588972i
$144$		0			0
$145$	43.9763	+	29.9421i	0.303285	+	0.206497i
$146$	20.6242	−	35.7221i	0.141261	−	0.244672i
$147$		0			0
$148$	−427.069	−	114.433i	−2.88560	−	0.773194i
$149$	19.8665	−	11.4699i	0.133332	−	0.0769795i	−0.431850	−	0.901945i	$-0.642139\pi$
$149$	19.8665	−	11.4699i	0.133332	−	0.0769795i	0.565183	+	0.824966i	$0.308806\pi$
$150$		0			0
$151$	2.24079	−	3.88116i	0.0148397	−	0.0257031i	−0.858510	−	0.512796i	$-0.828610\pi$
$151$	2.24079	−	3.88116i	0.0148397	−	0.0257031i	0.873350	+	0.487093i	$0.161943\pi$
$152$	220.782	+	220.782i	1.45251	+	1.45251i
$153$		0			0
$154$		−	457.837i		−	2.97297i
$155$	−72.0024	−	149.274i	−0.464532	−	0.963061i
$156$		0			0
$157$	−47.8070	+	178.418i	−0.304503	+	1.13642i	0.628869	+	0.777511i	$0.283518\pi$
$157$	−47.8070	+	178.418i	−0.304503	+	1.13642i	−0.933372	+	0.358910i	$0.883149\pi$
$158$	251.947	+	67.5091i	1.59460	+	0.427272i
$159$		0			0
$160$	−37.6130	+	107.709i	−0.235081	+	0.673181i
$161$	124.509			0.773347
$162$		0			0
$163$	33.3255	−	33.3255i	0.204451	−	0.204451i	−0.597453	−	0.801904i	$-0.703820\pi$
$163$	33.3255	−	33.3255i	0.204451	−	0.204451i	0.801904	+	0.597453i	$0.203820\pi$
$164$	−91.1898	−	52.6484i	−0.556035	−	0.321027i
$165$		0			0
$166$	10.5693	+	18.3065i	0.0636703	+	0.110280i
$167$	12.0582	−	45.0018i	0.0722048	−	0.269472i	−0.920380	−	0.391025i	$-0.872121\pi$
$167$	12.0582	−	45.0018i	0.0722048	−	0.269472i	0.992585	+	0.121553i	$0.0387874\pi$
$168$		0			0
$169$	−117.575	−	67.8822i	−0.695712	−	0.401670i
$170$	80.3891	+	54.7344i	0.472877	+	0.321967i
$171$		0			0
$172$	310.845	+	310.845i	1.80724	+	1.80724i
$173$	−52.7039	−	196.694i	−0.304647	−	1.13696i	−0.933249	−	0.359230i	$-0.883039\pi$
$173$	−52.7039	−	196.694i	−0.304647	−	1.13696i	0.628602	−	0.777727i	$-0.283627\pi$
$174$		0			0
$175$	154.260	−	17.5773i	0.881484	−	0.100442i
$176$	−261.603	−	453.110i	−1.48638	−	2.57449i
$177$		0			0
$178$	−5.73262	−	21.3944i	−0.0322057	−	0.120193i
$179$		−	151.248i		−	0.844962i	−0.906372	−	0.422481i	$-0.861159\pi$
$179$		−	151.248i		−	0.844962i	0.906372	−	0.422481i	$-0.138841\pi$
$180$		0			0
$181$	76.1404			0.420665			0.210333	−	0.977630i	$-0.432545\pi$
$181$	76.1404			0.420665			0.210333	+	0.977630i	$0.432545\pi$
$182$	−123.399	+	33.0648i	−0.678019	+	0.181675i
$183$		0			0
$184$	293.185	−	169.271i	1.59340	−	0.919949i
$185$	165.254	+	191.784i	0.893264	+	1.03667i
$186$		0			0
$187$	−108.785	+	29.1489i	−0.581739	+	0.155877i
$188$	−5.37581	+	5.37581i	−0.0285947	+	0.0285947i
$189$		0			0
$190$	−61.5351	−	324.105i	−0.323869	−	1.70582i
$191$	102.184	−	176.988i	0.534994	−	0.926637i	−0.464169	−	0.885747i	$-0.653647\pi$
$191$	102.184	−	176.988i	0.534994	−	0.926637i	0.999164	−	0.0408909i	$-0.0130196\pi$
$192$		0			0
$193$	−282.670	−	75.7411i	−1.46461	−	0.392441i	−0.563530	−	0.826095i	$-0.690557\pi$
$193$	−282.670	−	75.7411i	−1.46461	−	0.392441i	−0.901079	+	0.433654i	$0.857224\pi$
$194$	240.125	−	138.636i	1.23776	−	0.714621i
$195$		0			0
$196$	−45.5476	+	78.8907i	−0.232386	+	0.402504i
$197$	52.7467	+	52.7467i	0.267750	+	0.267750i	0.828193	−	0.560443i	$-0.189369\pi$
$197$	52.7467	+	52.7467i	0.267750	+	0.267750i	−0.560443	+	0.828193i	$0.689369\pi$
$198$		0			0
$199$			102.233i			0.513734i	0.966447	+	0.256867i	$0.0826902\pi$
$199$			102.233i			0.513734i	−0.966447	+	0.256867i	$0.917310\pi$
$200$	339.344	−	251.107i	1.69672	−	1.25554i
$201$		0			0
$202$	26.6281	−	99.3776i	0.131822	−	0.491968i
$203$	−63.8285	−	17.1028i	−0.314426	−	0.0842503i
$204$		0			0
$205$	26.1937	+	54.3044i	0.127774	+	0.264900i
$206$	271.708			1.31897
$207$		0			0
$208$	−103.232	+	103.232i	−0.496310	+	0.496310i
$209$	330.847	+	191.015i	1.58300	+	0.913945i
$210$		0			0
$211$	70.2719	+	121.715i	0.333042	+	0.576846i	0.983107	−	0.183033i	$-0.0585915\pi$
$211$	70.2719	+	121.715i	0.333042	+	0.576846i	−0.650064	+	0.759879i	$0.725258\pi$
$212$	−37.3216	+	139.286i	−0.176045	+	0.657009i
$213$		0			0
$214$	−61.5108	−	35.5132i	−0.287433	−	0.165950i
$215$	−46.9513	−	247.292i	−0.218378	−	1.15020i
$216$		0			0
$217$	145.558	+	145.558i	0.670774	+	0.670774i
$218$	17.2629	+	64.4259i	0.0791875	+	0.295532i
$219$		0			0
$220$	−66.8467	+	899.594i	−0.303848	+	4.08906i
$221$	15.7128	+	27.2154i	0.0710988	+	0.123147i
$222$		0			0
$223$	−91.2813	−	340.666i	−0.409333	−	1.52765i	−0.795922	−	0.605400i	$-0.793013\pi$
$223$	−91.2813	−	340.666i	−0.409333	−	1.52765i	0.386589	−	0.922252i	$-0.373653\pi$
$224$		−	141.704i		−	0.632607i
$225$		0			0
$226$	−525.384			−2.32471
$227$	−246.041	+	65.9265i	−1.08388	+	0.290425i	−0.756185	−	0.654358i	$-0.772939\pi$
$227$	−246.041	+	65.9265i	−1.08388	+	0.290425i	−0.327696	+	0.944783i	$0.606272\pi$
$228$		0			0
$229$	−266.828	+	154.053i	−1.16519	+	0.672720i	−0.952541	−	0.304409i	$-0.901541\pi$
$229$	−266.828	+	154.053i	−1.16519	+	0.672720i	−0.212644	+	0.977130i	$0.568208\pi$
$230$	−356.709	−	26.5062i	−1.55091	−	0.115244i
$231$		0			0
$232$	−173.551	+	46.5028i	−0.748063	+	0.200443i
$233$	−278.738	+	278.738i	−1.19630	+	1.19630i	−0.221033	+	0.975266i	$0.570943\pi$
$233$	−278.738	+	278.738i	−1.19630	+	1.19630i	−0.975266	+	0.221033i	$0.929057\pi$
$234$		0			0
$235$	4.27672	−	0.811984i	0.0181988	−	0.00345525i
$236$	−367.303	+	636.187i	−1.55637	+	2.69571i
$237$		0			0
$238$	−116.679	−	31.2641i	−0.490248	−	0.131362i
$239$	−340.164	+	196.394i	−1.42328	+	0.821732i	−0.996578	−	0.0826603i	$-0.973658\pi$
$239$	−340.164	+	196.394i	−1.42328	+	0.821732i	−0.426703	+	0.904392i	$0.640325\pi$
$240$		0			0
$241$	62.2167	−	107.762i	0.258160	−	0.447147i	−0.707589	−	0.706625i	$-0.750217\pi$
$241$	62.2167	−	107.762i	0.258160	−	0.447147i	0.965749	+	0.259478i	$0.0835504\pi$
$242$	−771.728	−	771.728i	−3.18896	−	3.18896i
$243$		0			0
$244$			609.292i			2.49710i
$245$	46.9802	−	22.6609i	0.191756	−	0.0924934i
$246$		0			0
$247$	27.5900	−	102.967i	0.111700	−	0.416871i
$248$	540.638	+	144.863i	2.17999	+	0.584127i
$249$		0			0
$250$	−445.685	+	17.5180i	−1.78274	+	0.0700720i
$251$	−11.9714			−0.0476946			−0.0238473	−	0.999716i	$-0.507592\pi$
$251$	−11.9714			−0.0476946			−0.0238473	+	0.999716i	$0.507592\pi$
$252$		0			0
$253$	292.897	−	292.897i	1.15770	−	1.15770i
$254$	−165.747	−	95.6941i	−0.652547	−	0.376748i
$255$		0			0
$256$	249.622	+	432.359i	0.975087	+	1.68890i
$257$	77.7451	−	290.149i	0.302510	−	1.12898i	−0.632557	−	0.774514i	$-0.717995\pi$
$257$	77.7451	−	290.149i	0.302510	−	1.12898i	0.935067	−	0.354470i	$-0.115339\pi$
$258$		0			0
$259$	−272.314	−	157.221i	−1.05141	−	0.607029i
$260$	247.292	−	46.9513i	0.951125	−	0.180582i
$261$		0			0
$262$	−165.059	−	165.059i	−0.629997	−	0.629997i
$263$	0.809272	+	3.02025i	0.00307708	+	0.0114838i	0.967447	−	0.253073i	$-0.0814411\pi$
$263$	0.809272	+	3.02025i	0.00307708	+	0.0114838i	−0.964370	+	0.264556i	$0.914774\pi$
$264$		0			0
$265$	62.5494	−	53.8966i	0.236035	−	0.203383i
$266$	204.875	+	354.855i	0.770208	+	1.33404i
$267$		0			0
$268$	122.916	+	458.729i	0.458642	+	1.71167i
$269$			441.324i			1.64061i	0.571927	+	0.820304i	$0.306196\pi$
$269$			441.324i			1.64061i	−0.571927	+	0.820304i	$0.693804\pi$
$270$		0			0
$271$	395.437			1.45918			0.729589	−	0.683886i	$-0.239711\pi$
$271$	395.437			1.45918			0.729589	+	0.683886i	$0.239711\pi$
$272$	−133.338	+	35.7279i	−0.490214	+	0.131353i
$273$		0			0
$274$	394.973	−	228.038i	1.44151	−	0.832254i
$275$	321.535	−	404.233i	1.16922	−	1.46994i
$276$		0			0
$277$	−129.970	+	34.8254i	−0.469207	+	0.125724i	−0.485673	−	0.874141i	$-0.661425\pi$
$277$	−129.970	+	34.8254i	−0.469207	+	0.125724i	0.0164656	+	0.999864i	$0.494759\pi$
$278$	624.300	−	624.300i	2.24568	−	2.24568i
$279$		0			0
$280$	−295.096	+	433.411i	−1.05391	+	1.54790i
$281$	−193.582	+	335.294i	−0.688904	+	1.19322i	0.283289	+	0.959034i	$0.408574\pi$
$281$	−193.582	+	335.294i	−0.688904	+	1.19322i	−0.972193	+	0.234181i	$0.924759\pi$
$282$		0			0
$283$	53.5130	+	14.3388i	0.189092	+	0.0506671i	0.352122	−	0.935954i	$-0.385460\pi$
$283$	53.5130	+	14.3388i	0.189092	+	0.0506671i	−0.163030	+	0.986621i	$0.552127\pi$
$284$	809.199	−	467.191i	2.84929	−	1.64504i
$285$		0			0
$286$	−212.505	+	368.070i	−0.743025	+	1.28696i
$287$	−52.9524	−	52.9524i	−0.184503	−	0.184503i
$288$		0			0
$289$		−	259.286i		−	0.897183i
$290$	179.223	+	62.5865i	0.618012	+	0.215816i
$291$		0			0
$292$	26.1263	−	97.5047i	0.0894736	−	0.333920i
$293$	−424.772	−	113.817i	−1.44973	−	0.388455i	−0.553802	−	0.832649i	$-0.686823\pi$
$293$	−424.772	−	113.817i	−1.44973	−	0.388455i	−0.895931	+	0.444194i	$0.853490\pi$
$294$		0			0
$295$	378.856	−	182.741i	1.28426	−	0.619460i
$296$	−854.970			−2.88841
$297$		0			0
$298$	57.8802	−	57.8802i	0.194229	−	0.194229i
$299$	−100.097	−	57.7908i	−0.334771	−	0.193280i
$300$		0			0
$301$	156.320	+	270.754i	0.519335	+	0.899515i
$302$	4.13886	−	15.4464i	0.0137048	−	0.0511471i
$303$		0			0
$304$	405.520	+	234.127i	1.33395	+	0.770155i
$305$	196.346	−	288.376i	0.643756	−	0.945494i
$306$		0			0
$307$	−352.515	−	352.515i	−1.14826	−	1.14826i	−0.986895	−	0.161361i	$-0.948412\pi$
$307$	−352.515	−	352.515i	−1.14826	−	1.14826i	−0.161361	−	0.986895i	$-0.551588\pi$
$308$	−289.989	−	1082.26i	−0.941524	−	3.51382i
$309$		0			0
$310$	−386.026	−	448.001i	−1.24525	−	1.44516i
$311$	95.5992	+	165.583i	0.307393	+	0.532420i	0.977791	−	0.209581i	$-0.0672101\pi$
$311$	95.5992	+	165.583i	0.307393	+	0.532420i	−0.670398	+	0.742001i	$0.733877\pi$
$312$		0			0
$313$	−55.9597	−	208.844i	−0.178785	−	0.667234i	−0.995876	−	0.0907257i	$-0.971081\pi$
$313$	−55.9597	−	208.844i	−0.178785	−	0.667234i	0.817091	−	0.576509i	$-0.195585\pi$
$314$			659.096i			2.09903i
$315$		0			0
$316$	638.324			2.02001
$317$	131.200	−	35.1549i	0.413879	−	0.110899i	−0.0458699	−	0.998947i	$-0.514606\pi$
$317$	131.200	−	35.1549i	0.413879	−	0.110899i	0.459749	+	0.888049i	$0.347939\pi$
$318$		0			0
$319$	−190.385	+	109.919i	−0.596817	+	0.344572i
$320$	7.36476	−	99.1118i	0.0230149	−	0.309725i
$321$		0			0
$322$	429.138	−	114.987i	1.33273	−	0.357103i
$323$	71.2722	−	71.2722i	0.220657	−	0.220657i
$324$		0			0
$325$	−132.173	−	57.4687i	−0.406685	−	0.176827i
$326$	84.0844	−	145.639i	0.257928	−	0.446744i
$327$		0			0
$328$	−196.678	−	52.6997i	−0.599628	−	0.160670i
$329$	−4.68247	+	2.70343i	−0.0142324	+	0.00821710i
$330$		0			0
$331$	185.875	−	321.945i	0.561556	−	0.972643i	−0.435805	−	0.900041i	$-0.643536\pi$
$331$	185.875	−	321.945i	0.561556	−	0.972643i	0.997361	−	0.0726021i	$-0.0231303\pi$
$332$	36.5792	+	36.5792i	0.110178	+	0.110178i
$333$		0			0
$334$		−	166.242i		−	0.497729i
$335$	89.6507	−	256.725i	0.267614	−	0.766342i
$336$		0			0
$337$	132.543	−	494.658i	0.393303	−	1.46783i	−0.431348	−	0.902186i	$-0.641962\pi$
$337$	132.543	−	494.658i	0.393303	−	1.46783i	0.824651	−	0.565642i	$-0.191371\pi$
$338$	−467.932	−	125.382i	−1.38441	−	0.370953i
$339$		0			0
$340$	224.696	+	78.4659i	0.660869	+	0.230782i
$341$	684.827			2.00829
$342$		0			0
$343$	−260.987	+	260.987i	−0.760895	+	0.760895i
$344$	736.184	+	425.036i	2.14007	+	1.23557i
$345$		0			0
$346$	−363.304	−	629.261i	−1.05001	−	1.81867i
$347$	−7.61995	+	28.4380i	−0.0219595	+	0.0819540i	−0.976036	−	0.217609i	$-0.930174\pi$
$347$	−7.61995	+	28.4380i	−0.0219595	+	0.0819540i	0.954077	+	0.299563i	$0.0968409\pi$
$348$		0			0
$349$	384.508	+	221.996i	1.10174	+	0.636092i	0.936678	−	0.350191i	$-0.113883\pi$
$349$	384.508	+	221.996i	1.10174	+	0.636092i	0.165065	+	0.986283i	$0.447217\pi$
$350$	515.446	−	203.046i	1.47270	−	0.580131i
$351$		0			0
$352$	−333.347	−	333.347i	−0.947009	−	0.947009i
$353$	49.2599	+	183.840i	0.139546	+	0.520794i	0.999938	+	0.0111603i	$0.00355250\pi$
$353$	49.2599	+	183.840i	0.139546	+	0.520794i	−0.860391	+	0.509634i	$0.829781\pi$
$354$		0			0
$355$	−533.544	−	39.6464i	−1.50294	−	0.111680i
$356$	−27.1020	−	46.9421i	−0.0761293	−	0.131860i
$357$		0			0
$358$	−139.682	−	521.300i	−0.390173	−	1.45614i
$359$		−	216.292i		−	0.602484i	−0.953548	−	0.301242i	$-0.902599\pi$
$359$		−	216.292i		−	0.602484i	0.953548	−	0.301242i	$-0.0974011\pi$
$360$		0			0
$361$	19.0951			0.0528949
$362$	262.429	−	70.3177i	0.724943	−	0.194248i
$363$		0			0
$364$	−270.754	+	156.320i	−0.743830	+	0.429450i
$365$	−43.7866	+	37.7293i	−0.119963	+	0.103368i
$366$		0			0
$367$	−331.717	+	88.8833i	−0.903862	+	0.242189i	−0.680674	−	0.732587i	$-0.738313\pi$
$367$	−331.717	+	88.8833i	−0.903862	+	0.242189i	−0.223188	+	0.974776i	$0.571646\pi$
$368$	359.005	−	359.005i	0.975557	−	0.975557i
$369$		0			0
$370$	746.690	+	508.398i	2.01808	+	1.37405i
$371$	−51.2766	+	88.8136i	−0.138212	+	0.239390i
$372$		0			0
$373$	567.442	+	152.046i	1.52129	+	0.407629i	0.920167	−	0.391525i	$-0.128052\pi$
$373$	567.442	+	152.046i	1.52129	+	0.407629i	0.601126	+	0.799155i	$0.294719\pi$
$374$	−348.025	+	200.932i	−0.930547	+	0.537252i
$375$		0			0
$376$	−7.35065	+	12.7317i	−0.0195496	+	0.0338609i
$377$	43.3755	+	43.3755i	0.115054	+	0.115054i
$378$		0			0
$379$			87.8194i			0.231713i	0.993266	+	0.115857i	$0.0369613\pi$
$379$			87.8194i			0.231713i	−0.993266	+	0.115857i	$0.963039\pi$
$380$	−350.745	−	727.159i	−0.923012	−	1.91358i
$381$		0			0
$382$	188.739	−	704.384i	0.494082	−	1.84394i
$383$	215.050	+	57.6225i	0.561488	+	0.150450i	0.528390	−	0.849002i	$-0.322796\pi$
$383$	215.050	+	57.6225i	0.561488	+	0.150450i	0.0330982	+	0.999452i	$0.489463\pi$
$384$		0			0
$385$	−211.508	+	605.677i	−0.549372	+	1.57319i
$386$	−1044.21			−2.70521
$387$		0			0
$388$	479.808	−	479.808i	1.23662	−	1.23662i
$389$	438.393	+	253.106i	1.12697	+	0.650659i	0.943172	−	0.332305i	$-0.107826\pi$
$389$	438.393	+	253.106i	1.12697	+	0.650659i	0.183802	+	0.982963i	$0.441160\pi$
$390$		0			0
$391$	−54.6435	−	94.6454i	−0.139753	−	0.242060i
$392$	−45.5920	+	170.152i	−0.116306	+	0.434060i
$393$		0			0
$394$	230.512	+	133.086i	0.585057	+	0.337783i
$395$	−302.116	−	205.701i	−0.764851	−	0.520763i
$396$		0			0
$397$	−434.470	−	434.470i	−1.09438	−	1.09438i	−0.995055	−	0.0993269i	$-0.968331\pi$
$397$	−434.470	−	434.470i	−1.09438	−	1.09438i	−0.0993269	−	0.995055i	$-0.531669\pi$
$398$	94.4150	+	352.361i	0.237224	+	0.885330i
$399$		0			0
$400$	394.106	−	495.469i	0.985264	−	1.23867i
$401$	189.456	+	328.147i	0.472459	+	0.818323i	0.999503	−	0.0315151i	$-0.0100332\pi$
$401$	189.456	+	328.147i	0.472459	+	0.818323i	−0.527045	+	0.849838i	$0.676700\pi$
$402$		0			0
$403$	−49.4579	−	184.579i	−0.122724	−	0.458013i
$404$		−	251.779i		−	0.623216i
$405$		0			0
$406$	−235.790			−0.580762
$407$	−1010.45	+	270.748i	−2.48267	+	0.665229i
$408$		0			0
$409$	118.058	−	68.1609i	0.288651	−	0.166652i	−0.348683	−	0.937241i	$-0.613371\pi$
$409$	118.058	−	68.1609i	0.288651	−	0.166652i	0.637333	+	0.770588i	$0.280038\pi$
$410$	140.432	+	162.978i	0.342517	+	0.397507i
$411$		0			0
$412$	642.276	−	172.097i	1.55892	−	0.417712i
$413$	−369.423	+	369.423i	−0.894487	+	0.894487i
$414$		0			0
$415$	−5.52507	−	29.1006i	−0.0133134	−	0.0701219i
$416$	−65.7719	+	113.920i	−0.158106	+	0.273847i
$417$		0			0
$418$	1316.72	+	352.814i	3.15005	+	0.844053i
$419$	−343.171	+	198.130i	−0.819024	+	0.472864i	−0.850080	−	0.526654i	$-0.823446\pi$
$419$	−343.171	+	198.130i	−0.819024	+	0.472864i	0.0310557	+	0.999518i	$0.490113\pi$
$420$		0			0
$421$	303.293	−	525.318i	0.720410	−	1.24779i	−0.240425	−	0.970668i	$-0.577287\pi$
$421$	303.293	−	525.318i	0.720410	−	1.24779i	0.960835	−	0.277120i	$-0.0893798\pi$
$422$	354.609	+	354.609i	0.840307	+	0.840307i
$423$		0			0
$424$			278.843i			0.657650i
$425$	−81.0617	−	109.546i	−0.190734	−	0.257756i
$426$		0			0
$427$	−112.152	+	418.557i	−0.262651	+	0.980226i
$428$	−167.896	−	44.9875i	−0.392279	−	0.105111i
$429$		0			0
$430$	−390.206	−	808.970i	−0.907455	−	1.88132i
$431$	137.454			0.318920			0.159460	−	0.987204i	$-0.449025\pi$
$431$	137.454			0.318920			0.159460	+	0.987204i	$0.449025\pi$
$432$		0			0
$433$	101.718	−	101.718i	0.234915	−	0.234915i	−0.579826	−	0.814740i	$-0.696879\pi$
$433$	101.718	−	101.718i	0.234915	−	0.234915i	0.814740	+	0.579826i	$0.196879\pi$
$434$	636.114	+	367.261i	1.46570	+	0.846222i
$435$		0			0
$436$	81.6135	+	141.359i	0.187187	+	0.324217i
$437$	−95.9479	+	358.082i	−0.219560	+	0.819410i
$438$		0			0
$439$	708.594	+	409.107i	1.61411	+	0.931906i	0.988404	+	0.151846i	$0.0485217\pi$
$439$	708.594	+	409.107i	1.61411	+	0.931906i	0.625704	+	0.780060i	$0.284812\pi$
$440$	325.376	+	1713.76i	0.739491	+	3.89490i
$441$		0			0
$442$	79.2908	+	79.2908i	0.179391	+	0.179391i
$443$	47.9620	+	178.997i	0.108266	+	0.404056i	0.998695	−	0.0510668i	$-0.0162621\pi$
$443$	47.9620	+	178.997i	0.108266	+	0.404056i	−0.890429	+	0.455123i	$0.849595\pi$
$444$		0			0
$445$	−2.29991	+	30.9512i	−0.00516834	+	0.0695533i
$446$	−629.229	−	1089.86i	−1.41083	−	2.44363i
$447$		0			0
$448$	31.9493	+	119.236i	0.0713154	+	0.266153i
$449$			548.270i			1.22109i	0.791981	+	0.610546i	$0.209050\pi$
$449$			548.270i			1.22109i	−0.791981	+	0.610546i	$0.790950\pi$
$450$		0			0
$451$	−249.133			−0.552401
$452$	−1241.93	+	332.773i	−2.74762	+	0.736224i
$453$		0			0
$454$	−787.132	+	454.451i	−1.73377	+	1.00099i
$455$	178.521	+	13.2655i	0.392355	+	0.0291549i
$456$		0			0
$457$	−339.368	+	90.9333i	−0.742599	+	0.198979i	−0.610233	−	0.792222i	$-0.708924\pi$
$457$	−339.368	+	90.9333i	−0.742599	+	0.198979i	−0.132366	+	0.991201i	$0.542257\pi$
$458$	−777.389	+	777.389i	−1.69736	+	1.69736i
$459$		0			0
$460$	−859.993	+	163.279i	−1.86955	+	0.354955i
$461$	74.6957	−	129.377i	0.162030	−	0.280644i	−0.773567	−	0.633715i	$-0.781529\pi$
$461$	74.6957	−	129.377i	0.162030	−	0.280644i	0.935597	+	0.353071i	$0.114863\pi$
$462$		0			0
$463$	−480.860	−	128.846i	−1.03857	−	0.278285i	−0.301052	−	0.953608i	$-0.597338\pi$
$463$	−480.860	−	128.846i	−1.03857	−	0.278285i	−0.737522	+	0.675323i	$0.764004\pi$
$464$	−233.355	+	134.728i	−0.502920	+	0.290361i
$465$		0			0
$466$	−703.290	+	1218.13i	−1.50920	+	2.61402i
$467$	−439.025	−	439.025i	−0.940095	−	0.940095i	0.0582090	−	0.998304i	$-0.481461\pi$
$467$	−439.025	−	439.025i	−0.940095	−	0.940095i	−0.998304	+	0.0582090i	$0.981461\pi$
$468$		0			0
$469$			337.751i			0.720152i
$470$	13.9905	−	6.74829i	0.0297670	−	0.0143581i
$471$		0			0
$472$	−367.660	+	1372.13i	−0.778942	+	2.90705i
$473$	1004.66	+	269.197i	2.12401	+	0.569127i
$474$		0			0
$475$	−68.3226	+	457.190i	−0.143837	+	0.962505i
$476$	−295.614			−0.621037
$477$		0			0
$478$	−991.051	+	991.051i	−2.07333	+	2.07333i
$479$	−253.717	−	146.483i	−0.529680	−	0.305811i	0.211206	−	0.977442i	$-0.432261\pi$
$479$	−253.717	−	146.483i	−0.529680	−	0.305811i	−0.740886	+	0.671631i	$0.765594\pi$
$480$		0			0
$481$	145.948	+	252.789i	0.303426	+	0.525549i
$482$	114.918	−	428.878i	0.238418	−	0.889789i
$483$		0			0
$484$	−2313.05	−	1335.44i	−4.77903	−	2.75917i
$485$	−381.711	+	72.4721i	−0.787033	+	0.149427i
$486$		0			0
$487$	542.274	+	542.274i	1.11350	+	1.11350i	0.992674	+	0.120824i	$0.0385538\pi$
$487$	542.274	+	542.274i	1.11350	+	1.11350i	0.120824	+	0.992674i	$0.461446\pi$
$488$	304.943	+	1138.06i	0.624883	+	2.33209i
$489$		0			0
$490$	140.996	−	121.492i	0.287748	−	0.247942i
$491$	341.362	+	591.256i	0.695238	+	1.20419i	0.970100	+	0.242704i	$0.0780343\pi$
$491$	341.362	+	591.256i	0.695238	+	1.20419i	−0.274863	+	0.961483i	$0.588632\pi$
$492$		0			0
$493$	15.0119	+	56.0252i	0.0304501	+	0.113641i
$494$		−	380.372i		−	0.769983i
$495$		0			0
$496$	839.395			1.69233
$497$	641.880	−	171.991i	1.29151	−	0.346059i
$498$		0			0
$499$	355.232	−	205.093i	0.711887	−	0.411008i	−0.0998723	−	0.995000i	$-0.531843\pi$
$499$	355.232	−	205.093i	0.711887	−	0.411008i	0.811759	+	0.583992i	$0.198510\pi$
$500$	−1042.43	+	323.702i	−2.08487	+	0.647405i
$501$		0			0
$502$	−41.2610	+	11.0559i	−0.0821933	+	0.0220236i
$503$	543.846	−	543.846i	1.08120	−	1.08120i	0.0848064	−	0.996397i	$-0.472973\pi$
$503$	543.846	−	543.846i	1.08120	−	1.08120i	0.996397	−	0.0848064i	$-0.0270272\pi$
$504$		0			0
$505$	−81.1364	+	119.166i	−0.160666	+	0.235973i
$506$	739.016	−	1280.01i	1.46051	−	2.52967i
$507$		0			0
$508$	−452.412	−	121.223i	−0.890574	−	0.238629i
$509$	101.406	−	58.5471i	0.199227	−	0.115024i	−0.397068	−	0.917789i	$-0.629972\pi$
$509$	101.406	−	58.5471i	0.199227	−	0.115024i	0.596295	+	0.802766i	$0.296639\pi$
$510$		0			0
$511$	35.8952	−	62.1724i	0.0702451	−	0.121668i
$512$	800.897	+	800.897i	1.56425	+	1.56425i
$513$		0			0
$514$		−	1071.84i		−	2.08529i
$515$	−359.446	−	125.522i	−0.697953	−	0.243732i
$516$		0			0
$517$	−4.65555	+	17.3747i	−0.00900493	+	0.0336068i
$518$	−1083.77	−	290.395i	−2.09222	−	0.560608i
$519$		0			0
$520$	438.405	−	211.464i	0.843087	−	0.406662i
$521$	400.865			0.769414			0.384707	−	0.923039i	$-0.374302\pi$
$521$	400.865			0.769414			0.384707	+	0.923039i	$0.374302\pi$
$522$		0			0
$523$	−212.510	+	212.510i	−0.406330	+	0.406330i	−0.880457	−	0.474127i	$-0.842764\pi$
$523$	−212.510	+	212.510i	−0.406330	+	0.406330i	0.474127	+	0.880457i	$0.342764\pi$
$524$	−494.721	−	285.627i	−0.944124	−	0.545090i
$525$		0			0
$526$	5.57856	+	9.66234i	0.0106056	+	0.0183695i
$527$	46.7644	−	174.527i	0.0887371	−	0.331171i
$528$		0			0
$529$	−110.028	−	63.5246i	−0.207992	−	0.120084i
$530$	165.811	−	243.529i	0.312851	−	0.459488i
$531$		0			0
$532$	709.055	+	709.055i	1.33281	+	1.33281i
$533$	17.9923	+	67.1480i	0.0337566	+	0.125981i
$534$		0			0
$535$	64.9670	+	75.3972i	0.121434	+	0.140929i
$536$	459.176	+	795.315i	0.856671	+	1.48380i
$537$		0			0
$538$	407.574	+	1521.09i	0.757573	+	2.82730i
$539$			215.531i			0.399873i
$540$		0			0
$541$	−253.010			−0.467671			−0.233836	−	0.972276i	$-0.575128\pi$
$541$	−253.010			−0.467671			−0.233836	+	0.972276i	$0.575128\pi$
$542$	1362.93	−	365.197i	2.51464	−	0.673795i
$543$		0			0
$544$	−107.716	+	62.1900i	−0.198008	+	0.114320i
$545$	6.92582	−	93.2047i	0.0127079	−	0.171018i
$546$		0			0
$547$	−750.527	+	201.103i	−1.37208	+	0.367647i	−0.868237	−	0.496149i	$-0.834747\pi$
$547$	−750.527	+	201.103i	−1.37208	+	0.367647i	−0.503841	+	0.863797i	$0.668080\pi$
$548$	789.217	−	789.217i	1.44018	−	1.44018i
$549$		0			0
$550$	734.897	−	1690.20i	1.33618	−	3.07308i
$551$	98.3740	−	170.389i	0.178537	−	0.309235i
$552$		0			0
$553$	438.500	+	117.496i	0.792948	+	0.212470i
$554$	−415.800	+	240.062i	−0.750541	+	0.433325i
$555$		0			0
$556$	1080.32	−	1871.17i	1.94303	−	3.36542i
$557$	−488.571	−	488.571i	−0.877147	−	0.877147i	0.116091	−	0.993239i	$-0.462963\pi$
$557$	−488.571	−	488.571i	−0.877147	−	0.877147i	−0.993239	+	0.116091i	$0.962963\pi$
$558$		0			0
$559$		−	290.224i		−	0.519184i
$560$	−259.246	+	742.380i	−0.462940	+	1.32568i
$561$		0			0
$562$	−357.556	+	1334.42i	−0.636221	+	2.37441i
$563$	−986.935	−	264.448i	−1.75299	−	0.469713i	−0.767732	−	0.640771i	$-0.778615\pi$
$563$	−986.935	−	264.448i	−1.75299	−	0.469713i	−0.985261	+	0.171058i	$0.945281\pi$
$564$		0			0
$565$	695.036	+	242.713i	1.23015	+	0.429581i
$566$	197.683			0.349263
$567$		0			0
$568$	1277.63	−	1277.63i	2.24936	−	2.24936i
$569$	38.8289	+	22.4179i	0.0682406	+	0.0393987i	0.533732	−	0.845654i	$-0.320789\pi$
$569$	38.8289	+	22.4179i	0.0682406	+	0.0393987i	−0.465491	+	0.885052i	$0.654122\pi$
$570$		0			0
$571$	58.7139	+	101.695i	0.102826	+	0.178101i	0.912848	−	0.408299i	$-0.133878\pi$
$571$	58.7139	+	101.695i	0.102826	+	0.178101i	−0.810022	+	0.586400i	$0.800545\pi$
$572$	−269.197	+	1004.66i	−0.470625	+	1.75640i
$573$		0			0
$574$	−231.411	−	133.605i	−0.403156	−	0.232762i
$575$	459.649	+	199.855i	0.799389	+	0.347574i
$576$		0			0
$577$	443.056	+	443.056i	0.767862	+	0.767862i	0.977730	−	0.209868i	$-0.0673034\pi$
$577$	443.056	+	443.056i	0.767862	+	0.767862i	−0.209868	+	0.977730i	$0.567303\pi$
$578$	−239.457	−	893.667i	−0.414286	−	1.54614i
$579$		0			0
$580$	463.298	+	34.4265i	0.798789	+	0.0593561i
$581$	18.3952	+	31.8615i	0.0316613	+	0.0548390i
$582$		0			0
$583$	88.3030	+	329.551i	0.151463	+	0.565268i
$584$		−	195.199i		−	0.334246i
$585$		0			0
$586$	−1569.15			−2.67773
$587$	249.752	−	66.9210i	0.425473	−	0.114005i	−0.0397276	−	0.999211i	$-0.512649\pi$
$587$	249.752	−	66.9210i	0.425473	−	0.114005i	0.465200	+	0.885206i	$0.345982\pi$
$588$		0			0
$589$	−530.787	+	306.450i	−0.901167	+	0.520289i
$590$	1137.02	−	979.726i	1.92715	−	1.66055i
$591$		0			0
$592$	−1238.51	+	331.857i	−2.09207	+	0.560569i
$593$	−545.602	+	545.602i	−0.920071	+	0.920071i	−0.997034	−	0.0769628i	$-0.975478\pi$
$593$	−545.602	+	545.602i	−0.920071	+	0.920071i	0.0769628	+	0.997034i	$0.475478\pi$
$594$		0			0
$595$	139.913	+	95.2622i	0.235148	+	0.160104i
$596$	100.159	−	173.480i	0.168052	−	0.291075i
$597$		0			0
$598$	−398.369	−	106.743i	−0.666169	−	0.178500i
$599$	−101.602	+	58.6598i	−0.169619	+	0.0979296i	−0.582406	−	0.812898i	$-0.697889\pi$
$599$	−101.602	+	58.6598i	−0.169619	+	0.0979296i	0.412787	+	0.910828i	$0.364555\pi$
$600$		0			0
$601$	−500.357	+	866.643i	−0.832540	+	1.44200i	0.0634770	+	0.997983i	$0.479781\pi$
$601$	−500.357	+	866.643i	−0.832540	+	1.44200i	−0.896017	+	0.444019i	$0.853552\pi$
$602$	788.829	+	788.829i	1.31035	+	1.31035i
$603$		0			0
$604$		−	39.1345i		−	0.0647922i
$605$	664.409	+	1377.44i	1.09820	+	2.27677i
$606$		0			0
$607$	117.390	−	438.106i	0.193394	−	0.721757i	−0.799283	−	0.600955i	$-0.794787\pi$
$607$	117.390	−	438.106i	0.193394	−	0.721757i	0.992677	−	0.120801i	$-0.0385464\pi$
$608$	407.535	+	109.199i	0.670287	+	0.179603i
$609$		0			0
$610$	410.412	−	1175.26i	0.672807	−	1.92666i
$611$	5.01918			0.00821470
$612$		0			0
$613$	−508.458	+	508.458i	−0.829459	+	0.829459i	−0.987442	−	0.157983i	$-0.949501\pi$
$613$	−508.458	+	508.458i	−0.829459	+	0.829459i	0.157983	+	0.987442i	$0.449501\pi$
$614$	−1540.55	−	889.438i	−2.50904	−	1.44860i
$615$		0			0
$616$	−1083.31	−	1876.35i	−1.75862	−	3.04602i
$617$	92.9446	−	346.874i	0.150640	−	0.562194i	−0.848800	−	0.528714i	$-0.822674\pi$
$617$	92.9446	−	346.874i	0.150640	−	0.562194i	0.999439	−	0.0334801i	$-0.0106590\pi$
$618$		0			0
$619$	372.454	+	215.037i	0.601703	+	0.347393i	0.769711	−	0.638392i	$-0.220400\pi$
$619$	372.454	+	215.037i	0.601703	+	0.347393i	−0.168008	+	0.985786i	$0.553734\pi$
$620$	−1196.26	−	814.498i	−1.92946	−	1.31371i
$621$		0			0
$622$	482.417	+	482.417i	0.775590	+	0.775590i
$623$	−9.97731	−	37.2358i	−0.0160149	−	0.0597686i
$624$		0			0
$625$	597.694	+	182.720i	0.956311	+	0.292352i
$626$	−385.747	−	668.133i	−0.616209	−	1.06731i
$627$		0			0
$628$	417.465	+	1558.00i	0.664753	+	2.48089i
$629$			275.999i			0.438790i
$630$		0			0
$631$	−42.6090			−0.0675261			−0.0337631	−	0.999430i	$-0.510749\pi$
$631$	−42.6090			−0.0675261			−0.0337631	+	0.999430i	$0.510749\pi$
$632$	1192.29	−	319.473i	1.88653	−	0.505495i
$633$		0			0
$634$	419.733	−	242.333i	0.662039	−	0.382229i
$635$	175.060	+	203.165i	0.275686	+	0.319945i
$636$		0			0
$637$	58.0915	−	15.5656i	0.0911955	−	0.0244358i
$638$	−554.676	+	554.676i	−0.869399	+	0.869399i
$639$		0			0
$640$	−151.271	−	796.746i	−0.236361	−	1.24492i
$641$	−429.324	+	743.610i	−0.669772	+	1.16008i	0.308196	+	0.951323i	$0.400275\pi$
$641$	−429.324	+	743.610i	−0.669772	+	1.16008i	−0.977968	+	0.208756i	$0.933059\pi$
$642$		0			0
$643$	−973.479	−	260.843i	−1.51396	−	0.405666i	−0.596215	−	0.802825i	$-0.703329\pi$
$643$	−973.479	−	260.843i	−1.51396	−	0.405666i	−0.917750	+	0.397159i	$0.869996\pi$
$644$	941.584	−	543.624i	1.46209	−	0.844136i
$645$		0			0
$646$	179.828	−	311.472i	0.278372	−	0.482155i
$647$	509.877	+	509.877i	0.788063	+	0.788063i	0.981176	−	0.193113i	$-0.0618585\pi$
$647$	509.877	+	509.877i	0.788063	+	0.788063i	−0.193113	+	0.981176i	$0.561859\pi$
$648$		0			0
$649$			1738.08i			2.67809i
$650$	−508.627	−	76.0094i	−0.782503	−	0.116938i
$651$		0			0
$652$	106.517	−	397.525i	0.163369	−	0.609701i
$653$	−51.1501	−	13.7056i	−0.0783309	−	0.0209887i	0.219441	−	0.975626i	$-0.429577\pi$
$653$	−51.1501	−	13.7056i	−0.0783309	−	0.0209887i	−0.297772	+	0.954637i	$0.596243\pi$
$654$		0			0
$655$	142.105	+	294.611i	0.216955	+	0.449788i
$656$	−305.363			−0.465492
$657$		0			0
$658$	−13.6421	+	13.6421i	−0.0207327	+	0.0207327i
$659$	−718.950	−	415.086i	−1.09097	−	0.629873i	−0.157137	−	0.987577i	$-0.550226\pi$
$659$	−718.950	−	415.086i	−1.09097	−	0.629873i	−0.933835	+	0.357704i	$0.883560\pi$
$660$		0			0
$661$	−350.839	−	607.670i	−0.530770	−	0.919320i	−0.999355	−	0.0359018i	$-0.988570\pi$
$661$	−350.839	−	607.670i	−0.530770	−	0.919320i	0.468586	−	0.883418i	$-0.344764\pi$
$662$	343.321	−	1281.29i	0.518612	−	1.93549i
$663$		0			0
$664$	86.6318	+	50.0169i	0.130470	+	0.0753266i
$665$	−107.098	−	564.088i	−0.161050	−	0.848252i
$666$		0			0
$667$	−150.844	−	150.844i	−0.226153	−	0.226153i
$668$	−105.296	−	392.969i	−0.157628	−	0.588277i
$669$		0			0
$670$	71.9026	−	967.634i	0.107317	−	1.44423i
$671$	720.793	+	1248.45i	1.07421	+	1.86058i
$672$		0			0
$673$	−133.330	−	497.594i	−0.198113	−	0.739367i	−0.991439	−	0.130570i	$-0.958319\pi$
$673$	−133.330	−	497.594i	−0.198113	−	0.739367i	0.793326	−	0.608797i	$-0.208348\pi$
$674$		−	1827.32i		−	2.71116i
$675$		0			0
$676$	−1185.53			−1.75375
$677$	−517.705	+	138.719i	−0.764704	+	0.204902i	−0.620031	−	0.784577i	$-0.712880\pi$
$677$	−517.705	+	138.719i	−0.764704	+	0.204902i	−0.144674	+	0.989479i	$0.546213\pi$
$678$		0			0
$679$	417.925	−	241.289i	0.615501	−	0.355360i
$680$	458.967	+	34.1048i	0.674952	+	0.0501541i
$681$		0			0
$682$	2360.36	−	632.456i	3.46094	−	0.927356i
$683$	111.371	−	111.371i	0.163061	−	0.163061i	−0.620860	−	0.783921i	$-0.713216\pi$
$683$	111.371	−	111.371i	0.163061	−	0.163061i	0.783921	+	0.620860i	$0.213216\pi$
$684$		0			0
$685$	−627.861	+	119.206i	−0.916585	+	0.174024i
$686$	−658.502	+	1140.56i	−0.959916	+	1.66262i
$687$		0			0
$688$	1231.41	+	329.956i	1.78984	+	0.479587i
$689$	82.4457	−	47.6001i	0.119660	−	0.0690857i
$690$		0			0
$691$	−340.544	+	589.840i	−0.492828	+	0.853603i	−0.999966	−	0.00826205i	$-0.997370\pi$
$691$	−340.544	+	589.840i	−0.492828	+	0.853603i	0.507138	+	0.861865i	$0.330703\pi$
$692$	−1257.36	−	1257.36i	−1.81700	−	1.81700i
$693$		0			0
$694$			105.053i			0.151373i
$695$	−1114.30	+	537.483i	−1.60331	+	0.773357i
$696$		0			0
$697$	−17.0124	+	63.4911i	−0.0244080	+	0.0910920i
$698$	1530.28	+	410.039i	2.19239	+	0.587448i
$699$		0			0
$700$	1089.83	−	806.447i	1.55690	−	1.15207i
$701$	722.405			1.03053			0.515267	−	0.857030i	$-0.327693\pi$
$701$	722.405			1.03053			0.515267	+	0.857030i	$0.327693\pi$
$702$		0			0
$703$	662.008	−	662.008i	0.941690	−	0.941690i
$704$	355.652	+	205.336i	0.505188	+	0.291670i
$705$		0			0
$706$	339.563	+	588.141i	0.480968	+	0.833060i
$707$	46.3448	−	172.961i	0.0655514	−	0.244641i
$708$		0			0
$709$	−505.198	−	291.676i	−0.712550	−	0.411391i	0.0994544	−	0.995042i	$-0.468290\pi$
$709$	−505.198	−	291.676i	−0.712550	−	0.411391i	−0.812005	+	0.583651i	$0.801624\pi$
$710$	−1875.55	+	356.095i	−2.64163	+	0.501543i
$711$		0			0
$712$	−74.1163	−	74.1163i	−0.104096	−	0.104096i
$713$	171.997	+	641.900i	0.241230	+	0.900281i
$714$		0			0
$715$	451.164	−	388.751i	0.630998	−	0.543708i
$716$	−660.372	−	1143.80i	−0.922308	−	1.59748i
$717$		0			0
$718$	−199.751	−	745.481i	−0.278205	−	1.03827i
$719$		−	1116.43i		−	1.55276i	−0.630266	−	0.776379i	$-0.717054\pi$
$719$		−	1116.43i		−	1.55276i	0.630266	−	0.776379i	$-0.282946\pi$
$720$		0			0
$721$	472.893			0.655885
$722$	65.8139	−	17.6348i	0.0911551	−	0.0244249i
$723$		0			0
$724$	575.803	−	332.440i	0.795308	−	0.459172i
$725$	−208.183	−	165.593i	−0.287149	−	0.228404i
$726$		0			0
$727$	406.633	−	108.957i	0.559329	−	0.149872i	0.0319312	−	0.999490i	$-0.489834\pi$
$727$	406.633	−	108.957i	0.559329	−	0.149872i	0.527398	+	0.849618i	$0.323168\pi$
$728$	−427.490	+	427.490i	−0.587212	+	0.587212i
$729$		0			0
$730$	−116.073	+	170.478i	−0.159004	+	0.233531i
$731$	137.209	−	237.653i	0.187701	−	0.325107i
$732$		0			0
$733$	368.915	+	98.8503i	0.503294	+	0.134857i	0.501528	−	0.865141i	$-0.332771\pi$
$733$	368.915	+	98.8503i	0.503294	+	0.134857i	0.00176568	+	0.999998i	$0.499438\pi$
$734$	−1061.23	+	612.700i	−1.44581	+	0.834740i
$735$		0			0
$736$	228.731	−	396.173i	0.310775	−	0.538279i
$737$	794.534	+	794.534i	1.07806	+	1.07806i
$738$		0			0
$739$		−	1406.06i		−	1.90266i	−0.308177	−	0.951329i	$-0.599719\pi$
$739$		−	1406.06i		−	1.90266i	0.308177	−	0.951329i	$-0.400281\pi$
$740$	2087.07	+	728.826i	2.82037	+	0.984901i
$741$		0			0
$742$	−94.7106	+	353.465i	−0.127642	+	0.476367i
$743$	−184.754	−	49.5046i	−0.248659	−	0.0666280i	0.132337	−	0.991205i	$-0.457752\pi$
$743$	−184.754	−	49.5046i	−0.248659	−	0.0666280i	−0.380996	+	0.924577i	$0.624419\pi$
$744$		0			0
$745$	−103.309	+	49.8312i	−0.138670	+	0.0668875i
$746$	2096.19			2.80991
$747$		0			0
$748$	−695.408	+	695.408i	−0.929689	+	0.929689i
$749$	−107.056	−	61.8089i	−0.142932	−	0.0825218i
$750$		0			0
$751$	57.5621	+	99.7004i	0.0766472	+	0.132757i	0.901801	−	0.432151i	$-0.142245\pi$
$751$	57.5621	+	99.7004i	0.0766472	+	0.132757i	−0.825154	+	0.564908i	$0.808912\pi$
$752$	−5.70632	+	21.2963i	−0.00758819	+	0.0283195i
$753$		0			0
$754$	189.559	+	109.442i	0.251404	+	0.145148i
$755$	−12.6112	+	18.5222i	−0.0167035	+	0.0245327i
$756$		0			0
$757$	−737.945	−	737.945i	−0.974828	−	0.974828i	0.0248625	−	0.999691i	$-0.492085\pi$
$757$	−737.945	−	737.945i	−0.974828	−	0.974828i	−0.999691	+	0.0248625i	$0.992085\pi$
$758$	81.1036	+	302.683i	0.106997	+	0.399317i
$759$		0			0
$760$	−1019.07	−	1182.68i	−1.34088	−	1.55615i
$761$	−505.692	−	875.884i	−0.664509	−	1.15096i	−0.979418	−	0.201842i	$-0.935307\pi$
$761$	−505.692	−	875.884i	−0.664509	−	1.15096i	0.314909	−	0.949122i	$-0.398026\pi$
$762$		0			0
$763$	30.0451	+	112.130i	0.0393776	+	0.146959i
$764$		−	1784.60i		−	2.33586i
$765$		0			0
$766$	794.418			1.03710
$767$	468.459	−	125.523i	0.610768	−	0.163655i
$768$		0			0
$769$	566.011	−	326.787i	0.736035	−	0.424950i	−0.0845906	−	0.996416i	$-0.526958\pi$
$769$	566.011	−	326.787i	0.736035	−	0.424950i	0.820626	+	0.571466i	$0.193625\pi$
$770$	−169.636	+	2282.89i	−0.220307	+	2.96479i
$771$		0			0
$772$	−2468.36	+	661.394i	−3.19735	+	0.856728i
$773$	−2.30444	+	2.30444i	−0.00298116	+	0.00298116i	−0.708596	−	0.705615i	$-0.750671\pi$
$773$	−2.30444	+	2.30444i	−0.00298116	+	0.00298116i	0.705615	+	0.708596i	$0.250671\pi$
$774$		0			0
$775$	303.714	+	770.998i	0.391888	+	0.994836i
$776$	656.069	−	1136.34i	0.845450	−	1.46436i
$777$		0			0
$778$	1744.74	+	467.501i	2.24259	+	0.600901i
$779$	193.095	−	111.483i	0.247875	−	0.143111i
$780$		0			0
$781$	1105.38	−	1914.57i	1.41533	−	2.45143i
$782$	−275.745	−	275.745i	−0.352615	−	0.352615i
$783$		0			0
$784$			264.177i			0.336961i
$785$	304.485	−	871.924i	0.387878	−	1.11073i
$786$		0			0
$787$	−13.4341	+	50.1368i	−0.0170700	+	0.0637062i	−0.973935	−	0.226825i	$-0.927165\pi$
$787$	−13.4341	+	50.1368i	−0.0170700	+	0.0637062i	0.956865	+	0.290531i	$0.0938321\pi$
$788$	629.191	+	168.591i	0.798466	+	0.213948i
$789$		0			0
$790$	−1231.26	−	429.968i	−1.55856	−	0.544263i
$791$	−914.402			−1.15601
$792$		0			0
$793$	284.436	−	284.436i	0.358683	−	0.358683i
$794$	−1898.71	−	1096.22i	−2.39132	−	1.38063i
$795$		0			0
$796$	446.365	+	773.126i	0.560759	+	0.971264i
$797$	−236.435	+	882.386i	−0.296656	+	1.10713i	0.643238	+	0.765667i	$0.277591\pi$
$797$	−236.435	+	882.386i	−0.296656	+	1.10713i	−0.939893	+	0.341468i	$0.889076\pi$
$798$		0			0
$799$	4.11002	+	2.37292i	0.00514395	+	0.00296986i
$800$	227.456	−	523.128i	0.284320	−	0.653910i
$801$		0			0
$802$	956.041	+	956.041i	1.19207	+	1.19207i
$803$	−61.8149	−	230.696i	−0.0769800	−	0.287293i
$804$		0			0
$805$	−620.832	−	46.1326i	−0.771220	−	0.0573075i
$806$	−340.928	−	590.505i	−0.422988	−	0.732636i
$807$		0			0
$808$	−126.012	−	470.284i	−0.155956	−	0.582035i
$809$			467.239i			0.577552i	0.957397	+	0.288776i	$0.0932483\pi$
$809$			467.239i			0.577552i	−0.957397	+	0.288776i	$0.906752\pi$
$810$		0			0
$811$	984.857			1.21437			0.607187	−	0.794559i	$-0.292298\pi$
$811$	984.857			1.21437			0.607187	+	0.794559i	$0.292298\pi$
$812$	−557.370	+	149.347i	−0.686416	+	0.183925i
$813$		0			0
$814$	−3232.61	+	1866.35i	−3.97127	+	2.29281i
$815$	−178.517	+	153.822i	−0.219040	+	0.188739i
$816$		0			0
$817$	−899.140	+	240.924i	−1.10054	+	0.294888i
$818$	343.956	−	343.956i	0.420485	−	0.420485i
$819$		0			0
$820$	435.188	+	296.306i	0.530717	+	0.361348i
$821$	483.078	−	836.716i	0.588402	−	1.01914i	−0.406040	−	0.913855i	$-0.633091\pi$
$821$	483.078	−	836.716i	0.588402	−	1.01914i	0.994442	−	0.105287i	$-0.0335760\pi$
$822$		0			0
$823$	29.7313	+	7.96649i	0.0361256	+	0.00967981i	0.276837	−	0.960917i	$-0.410714\pi$
$823$	29.7313	+	7.96649i	0.0361256	+	0.00967981i	−0.240711	+	0.970597i	$0.577381\pi$
$824$	1113.54	−	642.902i	1.35138	−	0.780221i
$825$		0			0
$826$	−932.100	+	1614.44i	−1.12845	+	1.95453i
$827$	−434.978	−	434.978i	−0.525971	−	0.525971i	0.393398	−	0.919368i	$-0.371300\pi$
$827$	−434.978	−	434.978i	−0.525971	−	0.525971i	−0.919368	+	0.393398i	$0.871300\pi$
$828$		0			0
$829$		−	308.711i		−	0.372390i	−0.982513	−	0.186195i	$-0.940384\pi$
$829$		−	308.711i		−	0.372390i	0.982513	−	0.186195i	$-0.0596156\pi$
$830$	−45.9182	−	95.1969i	−0.0553231	−	0.114695i
$831$		0			0
$832$	29.6585	−	110.687i	0.0356473	−	0.133037i
$833$	54.9279	+	14.7179i	0.0659398	+	0.0176685i
$834$		0			0
$835$	−76.7992	+	219.923i	−0.0919750	+	0.263380i
$836$	3335.99			3.99042
$837$		0			0
$838$	−999.812	+	999.812i	−1.19309	+	1.19309i
$839$	302.565	+	174.686i	0.360625	+	0.208207i	0.669355	−	0.742943i	$-0.266571\pi$
$839$	302.565	+	174.686i	0.360625	+	0.208207i	−0.308730	+	0.951150i	$0.599904\pi$
$840$		0			0
$841$	−363.891	−	630.278i	−0.432689	−	0.749439i
$842$	560.198	−	2090.69i	0.665318	−	2.48300i
$843$		0			0
$844$	1062.85	+	613.635i	1.25930	+	0.727056i
$845$	561.109	+	382.041i	0.664034	+	0.452120i
$846$		0			0
$847$	−1343.15	−	1343.15i	−1.58577	−	1.58577i
$848$	108.233	+	403.932i	0.127633	+	0.476334i
$849$		0			0
$850$	−380.560	−	302.705i	−0.447718	−	0.356123i
$851$	−507.554	−	879.109i	−0.596420	−	1.03303i
$852$		0			0
$853$	−174.201	−	650.129i	−0.204222	−	0.762167i	−0.989685	−	0.143259i	$-0.954242\pi$
$853$	−174.201	−	650.129i	−0.204222	−	0.762167i	0.785463	−	0.618908i	$-0.212425\pi$
$854$			1546.19i			1.81053i
$855$		0			0
$856$	−336.118			−0.392662
$857$	1503.95	−	402.983i	1.75490	−	0.470225i	0.769242	−	0.638957i	$-0.220634\pi$
$857$	1503.95	−	402.983i	1.75490	−	0.470225i	0.985662	+	0.168732i	$0.0539673\pi$
$858$		0			0
$859$	−323.898	+	187.002i	−0.377064	+	0.217698i	−0.676540	−	0.736406i	$-0.736521\pi$
$859$	−323.898	+	187.002i	−0.377064	+	0.217698i	0.299476	+	0.954104i	$0.403188\pi$
$860$	−1434.78	−	1665.13i	−1.66835	−	1.93619i
$861$		0			0
$862$	473.757	−	126.943i	0.549602	−	0.147265i
$863$	169.154	−	169.154i	0.196007	−	0.196007i	−0.602279	−	0.798286i	$-0.705740\pi$
$863$	169.154	−	169.154i	0.196007	−	0.196007i	0.798286	+	0.602279i	$0.205740\pi$
$864$		0			0
$865$	189.917	+	1000.29i	0.219557	+	1.15641i
$866$	256.647	−	444.526i	0.296359	−	0.513309i
$867$		0			0
$868$	1736.29	+	465.238i	2.00034	+	0.535989i
$869$	1307.94	−	755.138i	1.50511	−	0.868973i
$870$		0			0
$871$	156.767	−	271.529i	0.179986	−	0.311744i
$872$	223.190	+	223.190i	0.255951	+	0.255951i
$873$		0			0
$874$			1322.79i			1.51350i
$875$	−775.690	+	30.4891i	−0.886503	+	0.0348447i
$876$		0			0
$877$	−316.907	+	1182.71i	−0.361353	+	1.34859i	0.510945	+	0.859613i	$0.329295\pi$
$877$	−316.907	+	1182.71i	−0.361353	+	1.34859i	−0.872298	+	0.488974i	$0.837371\pi$
$878$	2820.10	+	755.642i	3.21195	+	0.860640i
$879$		0			0
$880$	1136.53	+	2356.25i	1.29152	+	2.67755i
$881$	−1252.48			−1.42165			−0.710827	−	0.703366i	$-0.751679\pi$
$881$	−1252.48			−1.42165			−0.710827	+	0.703366i	$0.751679\pi$
$882$		0			0
$883$	997.163	−	997.163i	1.12929	−	1.12929i	0.138998	−	0.990293i	$-0.455612\pi$
$883$	997.163	−	997.163i	1.12929	−	1.12929i	0.990293	−	0.138998i	$-0.0443880\pi$
$884$	237.653	+	137.209i	0.268838	+	0.155214i
$885$		0			0
$886$	330.617	+	572.645i	0.373156	+	0.646326i
$887$	−176.313	+	658.011i	−0.198775	+	0.741839i	0.792482	+	0.609895i	$0.208788\pi$
$887$	−176.313	+	658.011i	−0.198775	+	0.741839i	−0.991257	+	0.131943i	$0.957878\pi$
$888$		0			0
$889$	−288.474	−	166.550i	−0.324492	−	0.187346i
$890$	20.6573	+	108.802i	0.0232104	+	0.122249i
$891$		0			0
$892$	−2177.70	−	2177.70i	−2.44137	−	2.44137i
$893$	−4.16658	−	15.5499i	−0.00466582	−	0.0174131i
$894$		0			0
$895$	−56.0400	+	754.162i	−0.0626145	+	0.842639i
$896$	503.644	+	872.337i	0.562102	+	0.973590i
$897$		0			0
$898$	506.342	+	1889.69i	0.563856	+	2.10434i
$899$		−	352.691i		−	0.392315i
$900$		0			0
$901$	90.0155			0.0999062
$902$	−858.673	+	230.081i	−0.951966	+	0.255079i
$903$		0			0
$904$	−2153.18	+	1243.14i	−2.38183	+	1.37515i
$905$	−379.655	−	28.2113i	−0.419509	−	0.0311727i
$906$		0			0
$907$	85.2651	−	22.8467i	0.0940078	−	0.0251893i	−0.211509	−	0.977376i	$-0.567838\pi$
$907$	85.2651	−	22.8467i	0.0940078	−	0.0251893i	0.305516	+	0.952187i	$0.401171\pi$
$908$	−1572.81	+	1572.81i	−1.73217	+	1.73217i
$909$		0			0
$910$	627.552	−	119.148i	0.689617	−	0.130932i
$911$	659.617	−	1142.49i	0.724058	−	1.25411i	−0.235302	−	0.971922i	$-0.575608\pi$
$911$	659.617	−	1142.49i	0.724058	−	1.25411i	0.959360	−	0.282183i	$-0.0910587\pi$
$912$		0			0
$913$	118.225	+	31.6783i	0.129491	+	0.0346969i
$914$	−1085.70	+	626.830i	−1.18786	+	0.685810i
$915$		0			0
$916$	−1345.24	+	2330.02i	−1.46860	+	2.54369i
$917$	−287.276	−	287.276i	−0.313278	−	0.313278i
$918$		0			0
$919$			669.478i			0.728486i	0.931304	+	0.364243i	$0.118672\pi$
$919$			669.478i			0.728486i	−0.931304	+	0.364243i	$0.881328\pi$
$920$	−1524.61	+	735.396i	−1.65719	+	0.799344i
$921$		0			0
$922$	137.967	−	514.900i	0.149639	−	0.558460i
$923$	−595.857	−	159.659i	−0.645566	−	0.172979i
$924$		0			0
$925$	−752.938	−	1017.52i	−0.813987	−	1.10002i
$926$	−1776.35			−1.91830
$927$		0			0
$928$	−171.676	+	171.676i	−0.184996	+	0.184996i
$929$	−1221.93	−	705.481i	−1.31532	−	0.759398i	−0.332345	−	0.943158i	$-0.607840\pi$
$929$	−1221.93	−	705.481i	−1.31532	−	0.759398i	−0.982971	+	0.183760i	$0.941173\pi$
$930$		0			0
$931$	−96.4472	−	167.051i	−0.103595	−	0.179432i
$932$	−890.913	+	3324.93i	−0.955916	+	3.56753i
$933$		0			0
$934$	−1918.61	−	1107.71i	−2.05419	−	1.18599i
$935$	553.231	−	105.037i	0.591691	−	0.112339i
$936$		0			0
$937$	−482.685	−	482.685i	−0.515139	−	0.515139i	0.400958	−	0.916097i	$-0.368677\pi$
$937$	−482.685	−	482.685i	−0.515139	−	0.515139i	−0.916097	+	0.400958i	$0.868677\pi$
$938$	311.923	+	1164.11i	0.332540	+	1.24106i
$939$		0			0
$940$	28.7970	−	24.8133i	0.0306351	−	0.0263972i
$941$	−367.359	−	636.284i	−0.390392	−	0.676179i	0.602109	−	0.798414i	$-0.294327\pi$
$941$	−367.359	−	636.284i	−0.390392	−	0.676179i	−0.992501	+	0.122235i	$0.960994\pi$
$942$		0			0
$943$	−62.5705	−	233.516i	−0.0663526	−	0.247631i
$944$			2130.37i			2.25674i
$945$		0			0
$946$	3711.31			3.92317
$947$	−665.038	+	178.196i	−0.702258	+	0.188169i	−0.592242	−	0.805760i	$-0.701757\pi$
$947$	−665.038	+	178.196i	−0.702258	+	0.188169i	−0.110016	+	0.993930i	$0.535090\pi$
$948$		0			0
$949$	−57.7147	+	33.3216i	−0.0608163	+	0.0351123i
$950$	186.743	+	1638.87i	0.196572	+	1.72513i
$951$		0			0
$952$	−552.160	+	147.951i	−0.580000	+	0.155411i
$953$	47.5647	−	47.5647i	0.0499105	−	0.0499105i	−0.681711	−	0.731622i	$-0.738764\pi$
$953$	47.5647	−	47.5647i	0.0499105	−	0.0499105i	0.731622	+	0.681711i	$0.238764\pi$
$954$		0			0
$955$	−575.092	+	844.645i	−0.602190	+	0.884445i
$956$	−1714.97	+	2970.41i	−1.79390	+	3.10713i
$957$		0			0
$958$	−1009.75	−	270.563i	−1.05402	−	0.282424i
$959$	687.428	−	396.887i	0.716818	−	0.413855i
$960$		0			0
$961$	−68.8442	+	119.242i	−0.0716381	+	0.124081i
$962$	736.489	+	736.489i	0.765581	+	0.765581i
$963$		0			0
$964$		−	1086.59i		−	1.12717i
$965$	1381.40	+	482.398i	1.43150	+	0.499894i
$966$		0			0
$967$	−283.016	+	1056.23i	−0.292674	+	1.09227i	0.650373	+	0.759615i	$0.274613\pi$
$967$	−283.016	+	1056.23i	−0.292674	+	1.09227i	−0.943047	+	0.332659i	$0.892054\pi$
$968$	−4988.78	−	1336.74i	−5.15370	−	1.38093i
$969$		0			0
$970$	−1248.69	+	602.306i	−1.28731	+	0.620934i
$971$	−1595.62			−1.64327			−0.821637	−	0.570011i	$-0.806939\pi$
$971$	−1595.62			−1.64327			−0.821637	+	0.570011i	$0.806939\pi$
$972$		0			0
$973$	1086.56	−	1086.56i	1.11671	−	1.11671i
$974$	2369.83	+	1368.22i	2.43309	+	1.40475i
$975$		0			0
$976$	883.478	+	1530.23i	0.905203	+	1.56786i
$977$	−372.395	+	1389.80i	−0.381161	+	1.42251i	0.462968	+	0.886375i	$0.346784\pi$
$977$	−372.395	+	1389.80i	−0.381161	+	1.42251i	−0.844130	+	0.536139i	$0.819882\pi$
$978$		0			0
$979$	−111.065	−	64.1235i	−0.113448	−	0.0654990i
$980$	256.342	−	376.493i	0.261574	−	0.384176i
$981$		0			0
$982$	1722.60	+	1722.60i	1.75417	+	1.75417i
$983$	−98.4066	−	367.259i	−0.100108	−	0.373610i	0.897636	−	0.440738i	$-0.145283\pi$
$983$	−98.4066	−	367.259i	−0.100108	−	0.373610i	−0.997744	+	0.0671278i	$0.978616\pi$
$984$		0			0
$985$	−243.465	−	282.552i	−0.247173	−	0.286855i
$986$	103.482	+	179.235i	0.104951	+	0.181780i
$987$		0			0
$988$	−240.924	−	899.140i	−0.243850	−	0.910060i
$989$			1009.29i			1.02052i
$990$		0			0
$991$	563.583			0.568701			0.284350	−	0.958720i	$-0.408222\pi$
$991$	563.583			0.568701			0.284350	+	0.958720i	$0.408222\pi$
$992$	730.549	−	195.750i	0.736440	−	0.197329i
$993$		0			0
$994$	2053.50	−	1185.59i	2.06589	−	1.19274i
$995$	37.8790	−	509.760i	0.0380694	−	0.512321i
$996$		0			0
$997$	1181.22	−	316.507i	1.18477	−	0.317459i	0.387956	−	0.921678i	$-0.373181\pi$
$997$	1181.22	−	316.507i	1.18477	−	0.317459i	0.796818	+	0.604219i	$0.206515\pi$
$998$	1034.95	−	1034.95i	1.03702	−	1.03702i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.l.o.217.8		32
3.2	odd	2	inner	405.3.l.o.217.1		32
5.3	odd	4	inner	405.3.l.o.298.1		32
9.2	odd	6		135.3.g.a.82.8	yes	16
9.4	even	3	inner	405.3.l.o.352.1		32
9.5	odd	6	inner	405.3.l.o.352.8		32
9.7	even	3		135.3.g.a.82.1	yes	16
15.8	even	4	inner	405.3.l.o.298.8		32
45.2	even	12		675.3.g.k.568.1		16
45.7	odd	12		675.3.g.k.568.8		16
45.13	odd	12	inner	405.3.l.o.28.8		32
45.23	even	12	inner	405.3.l.o.28.1		32
45.29	odd	6		675.3.g.k.82.1		16
45.34	even	6		675.3.g.k.82.8		16
45.38	even	12		135.3.g.a.28.8	yes	16
45.43	odd	12		135.3.g.a.28.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.a.28.1	✓	16	45.43	odd	12
135.3.g.a.28.8	yes	16	45.38	even	12
135.3.g.a.82.1	yes	16	9.7	even	3
135.3.g.a.82.8	yes	16	9.2	odd	6
405.3.l.o.28.1		32	45.23	even	12	inner
405.3.l.o.28.8		32	45.13	odd	12	inner
405.3.l.o.217.1		32	3.2	odd	2	inner
405.3.l.o.217.8		32	1.1	even	1	trivial
405.3.l.o.298.1		32	5.3	odd	4	inner
405.3.l.o.298.8		32	15.8	even	4	inner
405.3.l.o.352.1		32	9.4	even	3	inner
405.3.l.o.352.8		32	9.5	odd	6	inner
675.3.g.k.82.1		16	45.29	odd	6
675.3.g.k.82.8		16	45.34	even	6
675.3.g.k.568.1		16	45.2	even	12
675.3.g.k.568.8		16	45.7	odd	12

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.44665 - 0.923527i) q^{2} +(7.56239 - 4.36615i) q^{4} +(-4.98625 - 0.370516i) q^{5} +(5.99870 - 1.60735i) q^{7} +(11.9402 - 11.9402i) q^{8} +O(q^{10})\)	\(q+(3.44665 - 0.923527i) q^{2} +(7.56239 - 4.36615i) q^{4} +(-4.98625 - 0.370516i) q^{5} +(5.99870 - 1.60735i) q^{7} +(11.9402 - 11.9402i) q^{8} +(-17.5280 + 3.32790i) q^{10} +(10.3303 - 17.8926i) q^{11} +(-5.56860 - 1.49210i) q^{13} +(19.1910 - 11.0799i) q^{14} +(12.6619 - 21.9311i) q^{16} +(-3.85449 - 3.85449i) q^{17} +18.4907i q^{19} +(-39.3257 + 18.9687i) q^{20} +(19.0807 - 71.2100i) q^{22} +(19.3656 + 5.18899i) q^{23} +(24.7254 + 3.69498i) q^{25} -20.5710 q^{26} +(38.3466 - 38.3466i) q^{28} +(-9.21485 - 5.32019i) q^{29} +(16.5732 + 28.7057i) q^{31} +(5.90560 - 22.0400i) q^{32} +(-16.8448 - 9.72536i) q^{34} +(-30.5066 + 5.79202i) q^{35} +(-35.8023 - 35.8023i) q^{37} +(17.0766 + 63.7309i) q^{38} +(-63.9607 + 55.1126i) q^{40} +(-6.02916 - 10.4428i) q^{41} +(13.0295 + 48.6267i) q^{43} -180.415i q^{44} +71.5385 q^{46} +(-0.840958 + 0.225334i) q^{47} +(-9.03436 + 5.21599i) q^{49} +(88.6323 - 10.0993i) q^{50} +(-48.6267 + 13.0295i) q^{52} +(-11.6767 + 11.6767i) q^{53} +(-58.1391 + 85.3897i) q^{55} +(52.4335 - 90.8175i) q^{56} +(-36.6737 - 9.82669i) q^{58} +(-72.8545 + 42.0625i) q^{59} +(-34.8873 + 60.4265i) q^{61} +(83.6326 + 83.6326i) q^{62} +19.8770i q^{64} +(27.2136 + 9.50325i) q^{65} +(-14.0760 + 52.5324i) q^{67} +(-45.9785 - 12.3199i) q^{68} +(-99.7965 + 48.1368i) q^{70} +107.003 q^{71} +(8.17407 - 8.17407i) q^{73} +(-156.462 - 90.3335i) q^{74} +(80.7330 + 139.834i) q^{76} +(33.2088 - 123.937i) q^{77} +(63.3057 + 36.5496i) q^{79} +(-71.2613 + 104.662i) q^{80} +(-30.4246 - 30.4246i) q^{82} +(1.53327 + 5.72223i) q^{83} +(17.7913 + 20.6476i) q^{85} +(89.8161 + 155.566i) q^{86} +(-90.2953 - 336.987i) q^{88} -6.20731i q^{89} -35.8027 q^{91} +(169.106 - 45.3118i) q^{92} +(-2.69039 + 1.55330i) q^{94} +(6.85110 - 92.1992i) q^{95} +(75.0582 - 20.1118i) q^{97} +(-26.3212 + 26.3212i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7}+O(q^{10}) \) 32 * q + 8 * q^7	\( 32 q + 8 q^{7} - 64 q^{10} - 28 q^{13} + 20 q^{16} - 176 q^{22} - 64 q^{25} + 160 q^{28} + 208 q^{31} - 352 q^{37} + 252 q^{40} + 188 q^{43} + 376 q^{46} + 188 q^{52} - 272 q^{55} - 504 q^{58} - 296 q^{61} - 304 q^{67} - 684 q^{70} - 112 q^{73} + 732 q^{76} - 152 q^{82} + 788 q^{85} + 1128 q^{88} + 400 q^{91} + 284 q^{97}+O(q^{100}) \) 32 * q + 8 * q^7 - 64 * q^10 - 28 * q^13 + 20 * q^16 - 176 * q^22 - 64 * q^25 + 160 * q^28 + 208 * q^31 - 352 * q^37 + 252 * q^40 + 188 * q^43 + 376 * q^46 + 188 * q^52 - 272 * q^55 - 504 * q^58 - 296 * q^61 - 304 * q^67 - 684 * q^70 - 112 * q^73 + 732 * q^76 - 152 * q^82 + 788 * q^85 + 1128 * q^88 + 400 * q^91 + 284 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more