LMFDB - Embedded newform 405.3.l.o.352.8

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			352.8
Character	$\chi$	$=$	405.352
Dual form			405.3.l.o.298.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923527 - 3.44665i) q^{2} +(-7.56239 - 4.36615i) q^{4} +(-2.17225 - 4.50348i) q^{5} +(-1.60735 + 5.99870i) q^{7} +(-11.9402 + 11.9402i) q^{8} +O(q^{10})$	\(q+(0.923527 - 3.44665i) q^{2} +(-7.56239 - 4.36615i) q^{4} +(-2.17225 - 4.50348i) q^{5} +(-1.60735 + 5.99870i) q^{7} +(-11.9402 + 11.9402i) q^{8} +(-17.5280 + 3.32790i) q^{10} +(-10.3303 - 17.8926i) q^{11} +(1.49210 + 5.56860i) q^{13} +(19.1910 + 11.0799i) q^{14} +(12.6619 + 21.9311i) q^{16} +(3.85449 + 3.85449i) q^{17} +18.4907i q^{19} +(-3.23546 + 43.5414i) q^{20} +(-71.2100 + 19.0807i) q^{22} +(5.18899 + 19.3656i) q^{23} +(-15.5627 + 19.5654i) q^{25} +20.5710 q^{26} +(38.3466 - 38.3466i) q^{28} +(-9.21485 + 5.32019i) q^{29} +(16.5732 - 28.7057i) q^{31} +(22.0400 - 5.90560i) q^{32} +(16.8448 - 9.72536i) q^{34} +(30.5066 - 5.79202i) q^{35} +(-35.8023 - 35.8023i) q^{37} +(63.7309 + 17.0766i) q^{38} +(79.7093 + 27.8353i) q^{40} +(6.02916 - 10.4428i) q^{41} +(-48.6267 - 13.0295i) q^{43} +180.415i q^{44} +71.5385 q^{46} +(-0.225334 + 0.840958i) q^{47} +(9.03436 + 5.21599i) q^{49} +(53.0624 + 71.7082i) q^{50} +(13.0295 - 48.6267i) q^{52} +(11.6767 - 11.6767i) q^{53} +(-58.1391 + 85.3897i) q^{55} +(-52.4335 - 90.8175i) q^{56} +(9.82669 + 36.6737i) q^{58} +(-72.8545 - 42.0625i) q^{59} +(-34.8873 - 60.4265i) q^{61} +(-83.6326 - 83.6326i) q^{62} +19.8770i q^{64} +(21.8369 - 18.8160i) q^{65} +(52.5324 - 14.0760i) q^{67} +(-12.3199 - 45.9785i) q^{68} +(8.21059 - 110.495i) q^{70} -107.003 q^{71} +(8.17407 - 8.17407i) q^{73} +(-156.462 + 90.3335i) q^{74} +(80.7330 - 139.834i) q^{76} +(123.937 - 33.2088i) q^{77} +(-63.3057 + 36.5496i) q^{79} +(71.2613 - 104.662i) q^{80} +(-30.4246 - 30.4246i) q^{82} +(5.72223 + 1.53327i) q^{83} +(8.98571 - 25.7316i) q^{85} +(-89.8161 + 155.566i) q^{86} +(336.987 + 90.2953i) q^{88} +6.20731i q^{89} -35.8027 q^{91} +(45.3118 - 169.106i) q^{92} +(2.69039 + 1.55330i) q^{94} +(83.2724 - 40.1664i) q^{95} +(-20.1118 + 75.0582i) q^{97} +(26.3212 - 26.3212i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.923527	−	3.44665i	0.461763	−	1.72332i	−0.205639	−	0.978628i	$-0.565927\pi$
$2$	0.923527	−	3.44665i	0.461763	−	1.72332i	0.667403	−	0.744697i	$-0.267406\pi$
$3$		0			0
$3$		0			0
$4$	−7.56239	−	4.36615i	−1.89060	−	1.09154i
$5$	−2.17225	−	4.50348i	−0.434450	−	0.900696i
$5$	−2.17225	−	4.50348i	−0.434450	−	0.900696i
$6$		0			0
$7$	−1.60735	+	5.99870i	−0.229621	+	0.856958i	0.750879	+	0.660440i	$0.229630\pi$
$7$	−1.60735	+	5.99870i	−0.229621	+	0.856958i	−0.980500	+	0.196518i	$0.937037\pi$
$8$	−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	−0.767117	−	0.641507i	$-0.778309\pi$
$11$	−10.3303	−	17.8926i	−0.939120	−	1.62660i	−0.172003	−	0.985096i	$-0.555024\pi$
$12$		0			0
$13$	1.49210	+	5.56860i	0.114777	+	0.428354i	0.999270	−	0.0381995i	$-0.0121622\pi$
$13$	1.49210	+	5.56860i	0.114777	+	0.428354i	−0.884493	+	0.466553i	$0.845496\pi$
$14$	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	0.811327	−	0.584592i	$-0.198746\pi$
$17$	3.85449	+	3.85449i	0.226735	+	0.226735i	−0.584592	+	0.811327i	$0.698746\pi$
$18$		0			0
$19$			18.4907i			0.973193i	0.873627	+	0.486597i	$0.161762\pi$
$19$			18.4907i			0.973193i	−0.873627	+	0.486597i	$0.838238\pi$
$20$	−3.23546	+	43.5414i	−0.161773	+	2.17707i
$21$		0			0
$22$	−71.2100	+	19.0807i	−3.23682	+	0.867303i
$23$	5.18899	+	19.3656i	0.225608	+	0.841981i	0.982160	+	0.188047i	$0.0602159\pi$
$23$	5.18899	+	19.3656i	0.225608	+	0.841981i	−0.756552	+	0.653934i	$0.773117\pi$
$24$		0			0
$25$	−15.5627	+	19.5654i	−0.622506	+	0.782615i
$26$	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	−0.650391	−	0.759600i	$-0.725395\pi$
$29$	−9.21485	+	5.32019i	−0.317753	+	0.183455i	0.332637	+	0.943055i	$0.392061\pi$
$30$		0			0
$31$	16.5732	−	28.7057i	0.534620	−	0.925990i	−0.464561	−	0.885541i	$-0.653788\pi$
$31$	16.5732	−	28.7057i	0.534620	−	0.925990i	0.999182	−	0.0404488i	$-0.0128788\pi$
$32$	22.0400	−	5.90560i	0.688750	−	0.184550i
$33$		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	$0.989856\pi$
$38$	63.7309	+	17.0766i	1.67713	+	0.449385i
$39$		0			0
$40$	79.7093	+	27.8353i	1.99273	+	0.695882i
$41$	6.02916	−	10.4428i	0.147053	−	0.254703i	−0.783084	−	0.621916i	$-0.786355\pi$
$41$	6.02916	−	10.4428i	0.147053	−	0.254703i	0.930137	+	0.367213i	$0.119688\pi$
$42$		0			0
$43$	−48.6267	−	13.0295i	−1.13085	−	0.303011i	−0.355585	−	0.934644i	$-0.615718\pi$
$43$	−48.6267	−	13.0295i	−1.13085	−	0.303011i	−0.775268	+	0.631633i	$0.782385\pi$
$44$			180.415i			4.10034i
$45$		0			0
$46$	71.5385			1.55518
$47$	−0.225334	+	0.840958i	−0.00479434	+	0.0178927i	−0.968282	−	0.249862i	$-0.919615\pi$
$47$	−0.225334	+	0.840958i	−0.00479434	+	0.0178927i	0.963487	+	0.267754i	$0.0862815\pi$
$48$		0			0
$49$	9.03436	+	5.21599i	0.184375	+	0.106449i
$50$	53.0624	+	71.7082i	1.06125	+	1.43416i
$51$		0			0
$52$	13.0295	−	48.6267i	0.250567	−	0.935128i
$53$	11.6767	−	11.6767i	0.220315	−	0.220315i	−0.588316	−	0.808631i	$-0.700209\pi$
$53$	11.6767	−	11.6767i	0.220315	−	0.220315i	0.808631	+	0.588316i	$0.200209\pi$
$54$		0			0
$55$	−58.1391	+	85.3897i	−1.05707	+	1.55254i
$56$	−52.4335	−	90.8175i	−0.936313	−	1.62174i
$57$		0			0
$58$	9.82669	+	36.6737i	0.169426	+	0.632305i
$59$	−72.8545	−	42.0625i	−1.23482	−	0.712924i	−0.266790	−	0.963755i	$-0.585963\pi$
$59$	−72.8545	−	42.0625i	−1.23482	−	0.712924i	−0.968031	+	0.250830i	$0.919296\pi$
$60$		0			0
$61$	−34.8873	−	60.4265i	−0.571922	−	0.990598i	−0.996369	−	0.0851453i	$-0.972865\pi$
$61$	−34.8873	−	60.4265i	−0.571922	−	0.990598i	0.424446	−	0.905453i	$-0.360469\pi$
$62$	−83.6326	−	83.6326i	−1.34891	−	1.34891i
$63$		0			0
$64$			19.8770i			0.310578i
$65$	21.8369	−	18.8160i	0.335952	−	0.289478i
$66$		0			0
$67$	52.5324	−	14.0760i	0.784066	−	0.210090i	0.155489	−	0.987838i	$-0.450305\pi$
$67$	52.5324	−	14.0760i	0.784066	−	0.210090i	0.628577	+	0.777748i	$0.283638\pi$
$68$	−12.3199	−	45.9785i	−0.181175	−	0.676154i
$69$		0			0
$70$	8.21059	−	110.495i	0.117294	−	1.57850i
$71$	−107.003			−1.50709			−0.753543	−	0.657399i	$-0.771657\pi$
$71$	−107.003			−1.50709			−0.753543	+	0.657399i	$0.771657\pi$
$72$		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
$77$	123.937	−	33.2088i	1.60957	−	0.431284i
$78$		0			0
$79$	−63.3057	+	36.5496i	−0.801338	+	0.462653i	−0.843939	−	0.536439i	$-0.819769\pi$
$79$	−63.3057	+	36.5496i	−0.801338	+	0.462653i	0.0426005	+	0.999092i	$0.486436\pi$
$80$	71.2613	−	104.662i	0.890766	−	1.30828i
$81$		0			0
$82$	−30.4246	−	30.4246i	−0.371032	−	0.371032i
$83$	5.72223	+	1.53327i	0.0689425	+	0.0184731i	0.293125	−	0.956074i	$-0.405305\pi$
$83$	5.72223	+	1.53327i	0.0689425	+	0.0184731i	−0.224183	+	0.974547i	$0.571971\pi$
$84$		0			0
$85$	8.98571	−	25.7316i	0.105714	−	0.302724i
$86$	−89.8161	+	155.566i	−1.04437	+	1.80891i
$87$		0			0
$88$	336.987	+	90.2953i	3.82939	+	1.02608i
$89$			6.20731i			0.0697451i	0.999392	+	0.0348725i	$0.0111025\pi$
$89$			6.20731i			0.0697451i	−0.999392	+	0.0348725i	$0.988897\pi$
$90$		0			0
$91$	−35.8027			−0.393436
$92$	45.3118	−	169.106i	0.492519	−	1.83811i
$93$		0			0
$94$	2.69039	+	1.55330i	0.0286211	+	0.0165244i
$95$	83.2724	−	40.1664i	0.876551	−	0.422804i
$96$		0			0
$97$	−20.1118	+	75.0582i	−0.207338	+	0.773796i	0.781386	+	0.624048i	$0.214513\pi$
$97$	−20.1118	+	75.0582i	−0.207338	+	0.773796i	−0.988724	+	0.149748i	$0.952154\pi$
$98$	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	$-0.212257\pi$
$101$	−14.4165	−	24.9702i	−0.142738	−	0.247230i	−0.928527	+	0.371265i	$0.878924\pi$
$102$		0			0
$103$	−19.7081	−	73.5518i	−0.191341	−	0.714095i	−0.993184	−	0.116560i	$-0.962813\pi$
$103$	−19.7081	−	73.5518i	−0.191341	−	0.714095i	0.801843	−	0.597535i	$-0.203853\pi$
$104$	−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	0.769813	−	0.638270i	$-0.220350\pi$
$107$	14.0751	+	14.0751i	0.131543	+	0.131543i	−0.638270	+	0.769813i	$0.720350\pi$
$108$		0			0
$109$			18.6923i			0.171489i	0.996317	+	0.0857447i	$0.0273269\pi$
$109$			18.6923i			0.171489i	−0.996317	+	0.0857447i	$0.972673\pi$
$110$	240.615	+	279.245i	2.18741	+	2.53859i
$111$		0			0
$112$	−151.910	+	40.7042i	−1.35634	+	0.363430i
$113$	−38.1083	−	142.222i	−0.337242	−	1.25860i	−0.901418	−	0.432949i	$-0.857473\pi$
$113$	−38.1083	−	142.222i	−0.337242	−	1.25860i	0.564176	−	0.825654i	$-0.309194\pi$
$114$		0			0
$115$	75.9407	−	65.4354i	0.660354	−	0.569003i
$116$	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
$122$	−240.488	+	64.4386i	−1.97122	+	0.528186i
$123$		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	$0.817727\pi$
$128$	156.669	+	41.9794i	1.22398	+	0.327964i
$129$		0			0
$130$	−44.6854	−	92.6411i	−0.343734	−	0.712624i
$131$	32.7093	−	56.6541i	0.249689	−	0.432474i	−0.713750	−	0.700400i	$-0.753005\pi$
$131$	32.7093	−	56.6541i	0.249689	−	0.432474i	0.963440	+	0.267926i	$0.0863382\pi$
$132$		0			0
$133$	−110.920	−	29.7209i	−0.833985	−	0.223466i
$134$		−	194.060i		−	1.44821i
$135$		0			0
$136$	−92.0465			−0.676813
$137$	33.0810	−	123.460i	0.241467	−	0.901169i	−0.733659	−	0.679518i	$-0.762189\pi$
$137$	33.0810	−	123.460i	0.241467	−	0.901169i	0.975126	−	0.221651i	$-0.0711445\pi$
$138$		0			0
$139$	−214.282	−	123.716i	−1.54160	−	0.890042i	−0.998738	−	0.0502184i	$-0.984008\pi$
$139$	−214.282	−	123.716i	−1.54160	−	0.890042i	−0.542860	−	0.839823i	$-0.682658\pi$
$140$	−255.992	−	89.3948i	−1.82851	−	0.638534i
$141$		0			0
$142$	−98.8202	+	368.802i	−0.695917	+	2.59720i
$143$	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
$148$	114.433	+	427.069i	0.773194	+	2.88560i
$149$	19.8665	+	11.4699i	0.133332	+	0.0769795i	0.565183	−	0.824966i	$-0.308806\pi$
$149$	19.8665	+	11.4699i	0.133332	+	0.0769795i	−0.431850	+	0.901945i	$0.642139\pi$
$150$		0			0
$151$	2.24079	+	3.88116i	0.0148397	+	0.0257031i	0.873350	−	0.487093i	$-0.161943\pi$
$151$	2.24079	+	3.88116i	0.0148397	+	0.0257031i	−0.858510	+	0.512796i	$0.828610\pi$
$152$	−220.782	−	220.782i	−1.45251	−	1.45251i
$153$		0			0
$154$		−	457.837i		−	2.97297i
$155$	−165.277	−	12.2813i	−1.06630	−	0.0792343i
$156$		0			0
$157$	178.418	−	47.8070i	1.13642	−	0.304503i	0.358910	−	0.933372i	$-0.383149\pi$
$157$	178.418	−	47.8070i	1.13642	−	0.304503i	0.777511	+	0.628869i	$0.216482\pi$
$158$	67.5091	+	251.947i	0.427272	+	1.59460i
$159$		0			0
$160$	−74.4722	−	86.4283i	−0.465451	−	0.540177i
$161$	−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
$167$	45.0018	−	12.0582i	0.269472	−	0.0722048i	−0.121553	−	0.992585i	$-0.538787\pi$
$167$	45.0018	−	12.0582i	0.269472	−	0.0722048i	0.391025	+	0.920380i	$0.372121\pi$
$168$		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
$173$	−196.694	−	52.7039i	−1.13696	−	0.304647i	−0.359230	−	0.933249i	$-0.616961\pi$
$173$	−196.694	−	52.7039i	−1.13696	−	0.304647i	−0.777727	+	0.628602i	$0.783627\pi$
$174$		0			0
$175$	−92.3522	−	124.804i	−0.527727	−	0.713167i
$176$	261.603	−	453.110i	1.48638	−	2.57449i
$177$		0			0
$178$	21.3944	+	5.73262i	0.120193	+	0.0322057i
$179$			151.248i			0.844962i	0.906372	+	0.422481i	$0.138841\pi$
$179$			151.248i			0.844962i	−0.906372	+	0.422481i	$0.861159\pi$
$180$		0			0
$181$	76.1404			0.420665			0.210333	−	0.977630i	$-0.432545\pi$
$181$	76.1404			0.420665			0.210333	+	0.977630i	$0.432545\pi$
$182$	−33.0648	+	123.399i	−0.181675	+	0.678019i
$183$		0			0
$184$	−293.185	−	169.271i	−1.59340	−	0.919949i
$185$	−83.4633	+	239.006i	−0.451153	+	1.29193i
$186$		0			0
$187$	29.1489	−	108.785i	0.155877	−	0.581739i
$188$	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	−0.999164	−	0.0408909i	$-0.986980\pi$
$191$	−102.184	−	176.988i	−0.534994	−	0.926637i	0.464169	−	0.885747i	$-0.346353\pi$
$192$		0			0
$193$	75.7411	+	282.670i	0.392441	+	1.46461i	0.826095	+	0.563530i	$0.190557\pi$
$193$	75.7411	+	282.670i	0.392441	+	1.46461i	−0.433654	+	0.901079i	$0.642776\pi$
$194$	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	0.560443	−	0.828193i	$-0.310631\pi$
$197$	−52.7467	−	52.7467i	−0.267750	−	0.267750i	−0.828193	+	0.560443i	$0.810631\pi$
$198$		0			0
$199$			102.233i			0.513734i	0.966447	+	0.256867i	$0.0826902\pi$
$199$			102.233i			0.513734i	−0.966447	+	0.256867i	$0.917310\pi$
$200$	−47.7929	−	419.434i	−0.238965	−	2.09717i
$201$		0			0
$202$	−99.3776	+	26.6281i	−0.491968	+	0.131822i
$203$	−17.1028	−	63.8285i	−0.0842503	−	0.314426i
$204$		0			0
$205$	−60.1259	−	4.46781i	−0.293297	−	0.0217942i
$206$	−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	−0.650064	−	0.759879i	$-0.725258\pi$
$211$	70.2719	−	121.715i	0.333042	−	0.576846i	0.983107	+	0.183033i	$0.0585915\pi$
$212$	−139.286	+	37.3216i	−0.657009	+	0.176045i
$213$		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
$218$	64.4259	+	17.2629i	0.295532	+	0.0791875i
$219$		0			0
$220$	812.495	−	391.906i	3.69316	−	1.78139i
$221$	−15.7128	+	27.2154i	−0.0710988	+	0.123147i
$222$		0			0
$223$	340.666	+	91.2813i	1.52765	+	0.409333i	0.922252	−	0.386589i	$-0.126347\pi$
$223$	340.666	+	91.2813i	1.52765	+	0.409333i	0.605400	+	0.795922i	$0.293013\pi$
$224$			141.704i			0.632607i
$225$		0			0
$226$	−525.384			−2.32471
$227$	−65.9265	+	246.041i	−0.290425	+	1.08388i	0.654358	+	0.756185i	$0.272939\pi$
$227$	−65.9265	+	246.041i	−0.290425	+	1.08388i	−0.944783	+	0.327696i	$0.893728\pi$
$228$		0			0
$229$	266.828	+	154.053i	1.16519	+	0.672720i	0.952541	−	0.304409i	$-0.0984591\pi$
$229$	266.828	+	154.053i	1.16519	+	0.672720i	0.212644	+	0.977130i	$0.431792\pi$
$230$	−155.399	−	322.172i	−0.675650	−	1.40075i
$231$		0			0
$232$	46.5028	−	173.551i	0.200443	−	0.748063i
$233$	278.738	−	278.738i	1.19630	−	1.19630i	0.221033	−	0.975266i	$-0.429057\pi$
$233$	278.738	−	278.738i	1.19630	−	1.19630i	0.975266	−	0.221033i	$-0.0709429\pi$
$234$		0			0
$235$	4.27672	−	0.811984i	0.0181988	−	0.00345525i
$236$	367.303	+	636.187i	1.55637	+	2.69571i
$237$		0			0
$238$	31.2641	+	116.679i	0.131362	+	0.490248i
$239$	−340.164	−	196.394i	−1.42328	−	0.821732i	−0.426703	−	0.904392i	$-0.640325\pi$
$239$	−340.164	−	196.394i	−1.42328	−	0.821732i	−0.996578	+	0.0826603i	$0.973658\pi$
$240$		0			0
$241$	62.2167	+	107.762i	0.258160	+	0.447147i	0.965749	−	0.259478i	$-0.0835504\pi$
$241$	62.2167	+	107.762i	0.258160	+	0.447147i	−0.707589	+	0.706625i	$0.750217\pi$
$242$	771.728	+	771.728i	3.18896	+	3.18896i
$243$		0			0
$244$			609.292i			2.49710i
$245$	3.86522	−	52.0165i	0.0157764	−	0.212312i
$246$		0			0
$247$	−102.967	+	27.5900i	−0.416871	+	0.111700i
$248$	144.863	+	540.638i	0.584127	+	2.17999i
$249$		0			0
$250$	207.672	−	394.734i	0.830686	−	1.57893i
$251$	11.9714			0.0476946			0.0238473	−	0.999716i	$-0.492408\pi$
$251$	11.9714			0.0476946			0.0238473	+	0.999716i	$0.492408\pi$
$252$		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
$257$	290.149	−	77.7451i	1.12898	−	0.302510i	0.354470	−	0.935067i	$-0.384661\pi$
$257$	290.149	−	77.7451i	1.12898	−	0.302510i	0.774514	+	0.632557i	$0.217995\pi$
$258$		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
$263$	3.02025	+	0.809272i	0.0114838	+	0.00307708i	0.264556	−	0.964370i	$-0.414774\pi$
$263$	3.02025	+	0.809272i	0.0114838	+	0.00307708i	−0.253073	+	0.967447i	$0.581441\pi$
$264$		0			0
$265$	−77.9505	−	27.2211i	−0.294153	−	0.102721i
$266$	−204.875	+	354.855i	−0.770208	+	1.33404i
$267$		0			0
$268$	−458.729	−	122.916i	−1.71167	−	0.458642i
$269$		−	441.324i		−	1.64061i	−0.571927	−	0.820304i	$-0.693804\pi$
$269$		−	441.324i		−	1.64061i	0.571927	−	0.820304i	$-0.306196\pi$
$270$		0			0
$271$	395.437			1.45918			0.729589	−	0.683886i	$-0.239711\pi$
$271$	395.437			1.45918			0.729589	+	0.683886i	$0.239711\pi$
$272$	−35.7279	+	133.338i	−0.131353	+	0.490214i
$273$		0			0
$274$	−394.973	−	228.038i	−1.44151	−	0.832254i
$275$	510.843	+	76.3406i	1.85761	+	0.277602i
$276$		0			0
$277$	34.8254	−	129.970i	0.125724	−	0.469207i	−0.874141	−	0.485673i	$-0.838575\pi$
$277$	34.8254	−	129.970i	0.125724	−	0.469207i	0.999864	+	0.0164656i	$0.00524141\pi$
$278$	−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	0.972193	+	0.234181i	$0.0752410\pi$
$281$	193.582	+	335.294i	0.688904	+	1.19322i	−0.283289	+	0.959034i	$0.591426\pi$
$282$		0			0
$283$	−14.3388	−	53.5130i	−0.0506671	−	0.189092i	0.935954	−	0.352122i	$-0.114540\pi$
$283$	−14.3388	−	53.5130i	−0.0506671	−	0.189092i	−0.986621	+	0.163030i	$0.947873\pi$
$284$	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
$290$	143.813	−	123.919i	0.495908	−	0.427306i
$291$		0			0
$292$	−97.5047	+	26.1263i	−0.333920	+	0.0894736i
$293$	−113.817	−	424.772i	−0.388455	−	1.44973i	−0.832649	−	0.553802i	$-0.813177\pi$
$293$	−113.817	−	424.772i	−0.388455	−	1.44973i	0.444194	−	0.895931i	$-0.353490\pi$
$294$		0			0
$295$	−31.1697	+	419.469i	−0.105660	+	1.42193i
$296$	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
$302$	15.4464	−	4.13886i	0.0511471	−	0.0137048i
$303$		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	$-0.551588\pi$
$308$	−1082.26	−	289.989i	−3.51382	−	0.941524i
$309$		0			0
$310$	−194.967	+	558.309i	−0.628925	+	1.80100i
$311$	−95.5992	+	165.583i	−0.307393	+	0.532420i	−0.977791	−	0.209581i	$-0.932790\pi$
$311$	−95.5992	+	165.583i	−0.307393	+	0.532420i	0.670398	+	0.742001i	$0.266123\pi$
$312$		0			0
$313$	208.844	+	55.9597i	0.667234	+	0.178785i	0.576509	−	0.817091i	$-0.304415\pi$
$313$	208.844	+	55.9597i	0.667234	+	0.178785i	0.0907257	+	0.995876i	$0.471081\pi$
$314$		−	659.096i		−	2.09903i
$315$		0			0
$316$	638.324			2.02001
$317$	35.1549	−	131.200i	0.110899	−	0.413879i	−0.888049	−	0.459749i	$-0.847939\pi$
$317$	35.1549	−	131.200i	0.110899	−	0.413879i	0.998947	+	0.0458699i	$0.0146060\pi$
$318$		0			0
$319$	190.385	+	109.919i	0.596817	+	0.344572i
$320$	89.5158	−	43.1779i	0.279737	−	0.134931i
$321$		0			0
$322$	−114.987	+	429.138i	−0.357103	+	1.33273i
$323$	−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
$328$	52.6997	+	196.678i	0.160670	+	0.599628i
$329$	−4.68247	−	2.70343i	−0.0142324	−	0.00821710i
$330$		0			0
$331$	185.875	+	321.945i	0.561556	+	0.972643i	0.997361	+	0.0726021i	$0.0231303\pi$
$331$	185.875	+	321.945i	0.561556	+	0.972643i	−0.435805	+	0.900041i	$0.643536\pi$
$332$	−36.5792	−	36.5792i	−0.110178	−	0.110178i
$333$		0			0
$334$		−	166.242i		−	0.497729i
$335$	−177.505	−	206.002i	−0.529864	−	0.614931i
$336$		0			0
$337$	−494.658	+	132.543i	−1.46783	+	0.393303i	−0.902186	−	0.431348i	$-0.858038\pi$
$337$	−494.658	+	132.543i	−1.46783	+	0.393303i	−0.565642	+	0.824651i	$0.691371\pi$
$338$	−125.382	−	467.932i	−0.370953	−	1.38441i
$339$		0			0
$340$	−180.301	+	155.359i	−0.530298	+	0.456938i
$341$	−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
$347$	−28.4380	+	7.61995i	−0.0819540	+	0.0219595i	−0.299563	−	0.954077i	$-0.596841\pi$
$347$	−28.4380	+	7.61995i	−0.0819540	+	0.0219595i	0.217609	+	0.976036i	$0.430174\pi$
$348$		0			0
$349$	−384.508	+	221.996i	−1.10174	+	0.636092i	−0.936678	−	0.350191i	$-0.886117\pi$
$349$	−384.508	+	221.996i	−1.10174	+	0.636092i	−0.165065	+	0.986283i	$0.552783\pi$
$350$	−515.446	+	203.046i	−1.47270	+	0.580131i
$351$		0			0
$352$	−333.347	−	333.347i	−0.947009	−	0.947009i
$353$	183.840	+	49.2599i	0.520794	+	0.139546i	0.509634	−	0.860391i	$-0.329781\pi$
$353$	183.840	+	49.2599i	0.520794	+	0.139546i	0.0111603	+	0.999938i	$0.496447\pi$
$354$		0			0
$355$	232.437	+	481.886i	0.654753	+	1.35743i
$356$	27.1020	−	46.9421i	0.0761293	−	0.131860i
$357$		0			0
$358$	521.300	+	139.682i	1.45614	+	0.390173i
$359$			216.292i			0.602484i	0.953548	+	0.301242i	$0.0974011\pi$
$359$			216.292i			0.602484i	−0.953548	+	0.301242i	$0.902599\pi$
$360$		0			0
$361$	19.0951			0.0528949
$362$	70.3177	−	262.429i	0.194248	−	0.724943i
$363$		0			0
$364$	270.754	+	156.320i	0.743830	+	0.429450i
$365$	−54.5679	−	19.0556i	−0.149501	−	0.0522072i
$366$		0			0
$367$	88.8833	−	331.717i	0.242189	−	0.903862i	−0.732587	−	0.680674i	$-0.761687\pi$
$367$	88.8833	−	331.717i	0.242189	−	0.903862i	0.974776	−	0.223188i	$-0.0716463\pi$
$368$	−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
$373$	−152.046	−	567.442i	−0.407629	−	1.52129i	−0.799155	−	0.601126i	$-0.794719\pi$
$373$	−152.046	−	567.442i	−0.407629	−	1.52129i	0.391525	−	0.920167i	$-0.371948\pi$
$374$	−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	$0.963039\pi$
$380$	−805.110	−	59.8258i	−2.11871	−	0.157436i
$381$		0			0
$382$	−704.384	+	188.739i	−1.84394	+	0.494082i
$383$	57.6225	+	215.050i	0.150450	+	0.561488i	0.999452	+	0.0330982i	$0.0105374\pi$
$383$	57.6225	+	215.050i	0.150450	+	0.561488i	−0.849002	+	0.528390i	$0.822796\pi$
$384$		0			0
$385$	−418.778	−	486.010i	−1.08773	−	1.26236i
$386$	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	0.183802	−	0.982963i	$-0.441160\pi$
$389$	438.393	−	253.106i	1.12697	−	0.650659i	0.943172	+	0.332305i	$0.107826\pi$
$390$		0			0
$391$	−54.6435	+	94.6454i	−0.139753	+	0.242060i
$392$	−170.152	+	45.5920i	−0.434060	+	0.116306i
$393$		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	$-0.531669\pi$
$398$	352.361	+	94.4150i	0.885330	+	0.237224i
$399$		0			0
$400$	−626.142	−	93.5709i	−1.56536	−	0.233927i
$401$	−189.456	+	328.147i	−0.472459	+	0.818323i	−0.999503	−	0.0315151i	$-0.989967\pi$
$401$	−189.456	+	328.147i	−0.472459	+	0.818323i	0.527045	+	0.849838i	$0.323300\pi$
$402$		0			0
$403$	184.579	+	49.4579i	0.458013	+	0.122724i
$404$			251.779i			0.623216i
$405$		0			0
$406$	−235.790			−0.580762
$407$	−270.748	+	1010.45i	−0.665229	+	2.48267i
$408$		0			0
$409$	−118.058	−	68.1609i	−0.288651	−	0.166652i	0.348683	−	0.937241i	$-0.386629\pi$
$409$	−118.058	−	68.1609i	−0.288651	−	0.166652i	−0.637333	+	0.770588i	$0.719962\pi$
$410$	−70.9268	+	203.107i	−0.172992	+	0.495382i
$411$		0			0
$412$	−172.097	+	642.276i	−0.417712	+	1.55892i
$413$	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
$418$	−352.814	−	1316.72i	−0.844053	−	3.15005i
$419$	−343.171	−	198.130i	−0.819024	−	0.472864i	0.0310557	−	0.999518i	$-0.490113\pi$
$419$	−343.171	−	198.130i	−0.819024	−	0.472864i	−0.850080	+	0.526654i	$0.823446\pi$
$420$		0			0
$421$	303.293	+	525.318i	0.720410	+	1.24779i	0.960835	+	0.277120i	$0.0893798\pi$
$421$	303.293	+	525.318i	0.720410	+	1.24779i	−0.240425	+	0.970668i	$0.577287\pi$
$422$	−354.609	−	354.609i	−0.840307	−	0.840307i
$423$		0			0
$424$			278.843i			0.657650i
$425$	−135.401	+	15.4284i	−0.318590	+	0.0363021i
$426$		0			0
$427$	418.557	−	112.152i	0.980226	−	0.262651i
$428$	−44.9875	−	167.896i	−0.105111	−	0.392279i
$429$		0			0
$430$	895.691	+	66.5567i	2.08300	+	0.154783i
$431$	−137.454			−0.318920			−0.159460	−	0.987204i	$-0.550975\pi$
$431$	−137.454			−0.318920			−0.159460	+	0.987204i	$0.550975\pi$
$432$		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
$437$	−358.082	+	95.9479i	−0.819410	+	0.219560i
$438$		0			0
$439$	−708.594	+	409.107i	−1.61411	+	0.931906i	−0.625704	+	0.780060i	$0.715188\pi$
$439$	−708.594	+	409.107i	−1.61411	+	0.931906i	−0.988404	+	0.151846i	$0.951478\pi$
$440$	−325.376	−	1713.76i	−0.739491	−	3.89490i
$441$		0			0
$442$	79.2908	+	79.2908i	0.179391	+	0.179391i
$443$	178.997	+	47.9620i	0.404056	+	0.108266i	0.455123	−	0.890429i	$-0.349595\pi$
$443$	178.997	+	47.9620i	0.404056	+	0.108266i	−0.0510668	+	0.998695i	$0.516262\pi$
$444$		0			0
$445$	27.9545	−	13.4838i	0.0628191	−	0.0303007i
$446$	629.229	−	1089.86i	1.41083	−	2.44363i
$447$		0			0
$448$	−119.236	−	31.9493i	−0.266153	−	0.0713154i
$449$		−	548.270i		−	1.22109i	−0.791981	−	0.610546i	$-0.790950\pi$
$449$		−	548.270i		−	1.22109i	0.791981	−	0.610546i	$-0.209050\pi$
$450$		0			0
$451$	−249.133			−0.552401
$452$	−332.773	+	1241.93i	−0.736224	+	2.74762i
$453$		0			0
$454$	787.132	+	454.451i	1.73377	+	1.00099i
$455$	77.7724	+	161.237i	0.170928	+	0.354367i
$456$		0			0
$457$	90.9333	−	339.368i	0.198979	−	0.742599i	−0.792222	−	0.610233i	$-0.791076\pi$
$457$	90.9333	−	339.368i	0.198979	−	0.742599i	0.991201	−	0.132366i	$-0.0422574\pi$
$458$	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	$-0.218471\pi$
$461$	−74.6957	−	129.377i	−0.162030	−	0.280644i	−0.935597	+	0.353071i	$0.885137\pi$
$462$		0			0
$463$	128.846	+	480.860i	0.278285	+	1.03857i	0.953608	+	0.301052i	$0.0973377\pi$
$463$	128.846	+	480.860i	0.278285	+	1.03857i	−0.675323	+	0.737522i	$0.735996\pi$
$464$	−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	0.998304	−	0.0582090i	$-0.0185390\pi$
$467$	439.025	+	439.025i	0.940095	+	0.940095i	−0.0582090	+	0.998304i	$0.518539\pi$
$468$		0			0
$469$			337.751i			0.720152i
$470$	1.15104	−	15.4902i	0.00244903	−	0.0329580i
$471$		0			0
$472$	1372.13	−	367.660i	2.90705	−	0.778942i
$473$	269.197	+	1004.66i	0.569127	+	2.12401i
$474$		0			0
$475$	−361.777	−	287.764i	−0.761635	−	0.605819i
$476$	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	−0.740886	−	0.671631i	$-0.765594\pi$
$479$	−253.717	+	146.483i	−0.529680	+	0.305811i	0.211206	+	0.977442i	$0.432261\pi$
$480$		0			0
$481$	145.948	−	252.789i	0.303426	−	0.525549i
$482$	428.878	−	114.918i	0.889789	−	0.238418i
$483$		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	$0.461446\pi$
$488$	1138.06	+	304.943i	2.33209	+	0.624883i
$489$		0			0
$490$	−175.713	−	61.3607i	−0.358598	−	0.125226i
$491$	−341.362	+	591.256i	−0.695238	+	1.20419i	0.274863	+	0.961483i	$0.411368\pi$
$491$	−341.362	+	591.256i	−0.695238	+	1.20419i	−0.970100	+	0.242704i	$0.921966\pi$
$492$		0			0
$493$	−56.0252	−	15.0119i	−0.113641	−	0.0304501i
$494$			380.372i			0.769983i
$495$		0			0
$496$	839.395			1.69233
$497$	171.991	−	641.880i	0.346059	−	1.29151i
$498$		0			0
$499$	−355.232	−	205.093i	−0.711887	−	0.411008i	0.0998723	−	0.995000i	$-0.468157\pi$
$499$	−355.232	−	205.093i	−0.711887	−	0.411008i	−0.811759	+	0.583992i	$0.801490\pi$
$500$	−801.552	−	740.924i	−1.60310	−	1.48185i
$501$		0			0
$502$	11.0559	−	41.2610i	0.0220236	−	0.0821933i
$503$	−543.846	+	543.846i	−1.08120	+	1.08120i	−0.0848064	+	0.996397i	$0.527027\pi$
$503$	−543.846	+	543.846i	−1.08120	+	1.08120i	−0.996397	+	0.0848064i	$0.972973\pi$
$504$		0			0
$505$	−81.1364	+	119.166i	−0.160666	+	0.235973i
$506$	−739.016	−	1280.01i	−1.46051	−	2.52967i
$507$		0			0
$508$	121.223	+	452.412i	0.238629	+	0.890574i
$509$	101.406	+	58.5471i	0.199227	+	0.115024i	0.596295	−	0.802766i	$-0.296639\pi$
$509$	101.406	+	58.5471i	0.199227	+	0.115024i	−0.397068	+	0.917789i	$0.629972\pi$
$510$		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
$515$	−288.428	+	248.528i	−0.560054	+	0.482579i
$516$		0			0
$517$	17.3747	−	4.65555i	0.0336068	−	0.00900493i
$518$	−290.395	−	1083.77i	−0.560608	−	2.09222i
$519$		0			0
$520$	−36.0691	+	485.402i	−0.0693636	+	0.933466i
$521$	−400.865			−0.769414			−0.384707	−	0.923039i	$-0.625698\pi$
$521$	−400.865			−0.769414			−0.384707	+	0.923039i	$0.625698\pi$
$522$		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
$527$	174.527	−	46.7644i	0.331171	−	0.0887371i
$528$		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
$533$	67.1480	+	17.9923i	0.125981	+	0.0337566i
$534$		0			0
$535$	32.8123	−	93.9617i	0.0613315	−	0.175629i
$536$	−459.176	+	795.315i	−0.856671	+	1.48380i
$537$		0			0
$538$	−1521.09	−	407.574i	−2.82730	−	0.757573i
$539$		−	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	$0.575128\pi$
$542$	365.197	−	1362.93i	0.673795	−	2.51464i
$543$		0			0
$544$	107.716	+	62.1900i	0.198008	+	0.114320i
$545$	84.1806	−	40.6044i	0.154460	−	0.0745035i
$546$		0			0
$547$	201.103	−	750.527i	0.367647	−	1.37208i	−0.496149	−	0.868237i	$-0.665253\pi$
$547$	201.103	−	750.527i	0.367647	−	1.37208i	0.863797	−	0.503841i	$-0.168080\pi$
$548$	−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
$553$	−117.496	−	438.500i	−0.212470	−	0.792948i
$554$	−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	0.993239	−	0.116091i	$-0.0370365\pi$
$557$	488.571	+	488.571i	0.877147	+	0.877147i	−0.116091	+	0.993239i	$0.537037\pi$
$558$		0			0
$559$		−	290.224i		−	0.519184i
$560$	513.297	+	595.704i	0.916601	+	1.06376i
$561$		0			0
$562$	1334.42	−	357.556i	2.37441	−	0.636221i
$563$	−264.448	−	986.935i	−0.469713	−	1.75299i	−0.640771	−	0.767732i	$-0.721385\pi$
$563$	−264.448	−	986.935i	−0.469713	−	1.75299i	0.171058	−	0.985261i	$-0.445281\pi$
$564$		0			0
$565$	−557.714	+	480.562i	−0.987104	+	0.850553i
$566$	−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	−0.465491	−	0.885052i	$-0.654122\pi$
$569$	38.8289	−	22.4179i	0.0682406	−	0.0393987i	0.533732	+	0.845654i	$0.320789\pi$
$570$		0			0
$571$	58.7139	−	101.695i	0.102826	−	0.178101i	−0.810022	−	0.586400i	$-0.800545\pi$
$571$	58.7139	−	101.695i	0.102826	−	0.178101i	0.912848	+	0.408299i	$0.133878\pi$
$572$	−1004.66	+	269.197i	−1.75640	+	0.470625i
$573$		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	$0.567303\pi$
$578$	−893.667	−	239.457i	−1.54614	−	0.414286i
$579$		0			0
$580$	−201.835	−	418.441i	−0.347991	−	0.721450i
$581$	−18.3952	+	31.8615i	−0.0316613	+	0.0548390i
$582$		0			0
$583$	−329.551	−	88.3030i	−0.565268	−	0.151463i
$584$			195.199i			0.334246i
$585$		0			0
$586$	−1569.15			−2.67773
$587$	66.9210	−	249.752i	0.114005	−	0.425473i	−0.885206	−	0.465200i	$-0.845982\pi$
$587$	66.9210	−	249.752i	0.114005	−	0.425473i	0.999211	+	0.0397276i	$0.0126490\pi$
$588$		0			0
$589$	530.787	+	306.450i	0.901167	+	0.520289i
$590$	1416.98	+	494.822i	2.40165	+	0.838681i
$591$		0			0
$592$	331.857	−	1238.51i	0.560569	−	2.09207i
$593$	545.602	−	545.602i	0.920071	−	0.920071i	−0.0769628	−	0.997034i	$-0.524522\pi$
$593$	545.602	−	545.602i	0.920071	−	0.920071i	0.997034	+	0.0769628i	$0.0245223\pi$
$594$		0			0
$595$	139.913	+	95.2622i	0.235148	+	0.160104i
$596$	−100.159	−	173.480i	−0.168052	−	0.291075i
$597$		0			0
$598$	106.743	+	398.369i	0.178500	+	0.666169i
$599$	−101.602	−	58.6598i	−0.169619	−	0.0979296i	0.412787	−	0.910828i	$-0.364555\pi$
$599$	−101.602	−	58.6598i	−0.169619	−	0.0979296i	−0.582406	+	0.812898i	$0.697889\pi$
$600$		0			0
$601$	−500.357	−	866.643i	−0.832540	−	1.44200i	−0.896017	−	0.444019i	$-0.853552\pi$
$601$	−500.357	−	866.643i	−0.832540	−	1.44200i	0.0634770	−	0.997983i	$-0.479781\pi$
$602$	−788.829	−	788.829i	−1.31035	−	1.31035i
$603$		0			0
$604$		−	39.1345i		−	0.0647922i
$605$	1525.11	+	113.327i	2.52084	+	0.187317i
$606$		0			0
$607$	−438.106	+	117.390i	−0.721757	+	0.193394i	−0.600955	−	0.799283i	$-0.705213\pi$
$607$	−438.106	+	117.390i	−0.721757	+	0.193394i	−0.120801	+	0.992677i	$0.538546\pi$
$608$	109.199	+	407.535i	0.179603	+	0.670287i
$609$		0			0
$610$	812.599	+	943.057i	1.33213	+	1.54600i
$611$	−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
$617$	346.874	−	92.9446i	0.562194	−	0.150640i	0.0334801	−	0.999439i	$-0.489341\pi$
$617$	346.874	−	92.9446i	0.562194	−	0.150640i	0.528714	+	0.848800i	$0.322674\pi$
$618$		0			0
$619$	−372.454	+	215.037i	−0.601703	+	0.347393i	−0.769711	−	0.638392i	$-0.779600\pi$
$619$	−372.454	+	215.037i	−0.601703	+	0.347393i	0.168008	+	0.985786i	$0.446266\pi$
$620$	1196.26	+	814.498i	1.92946	+	1.31371i
$621$		0			0
$622$	482.417	+	482.417i	0.775590	+	0.775590i
$623$	−37.2358	−	9.97731i	−0.0597686	−	0.0160149i
$624$		0			0
$625$	−140.607	−	608.978i	−0.224971	−	0.974365i
$626$	385.747	−	668.133i	0.616209	−	1.06731i
$627$		0			0
$628$	−1558.00	−	417.465i	−2.48089	−	0.664753i
$629$		−	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	$0.510749\pi$
$632$	319.473	−	1192.29i	0.505495	−	1.88653i
$633$		0			0
$634$	−419.733	−	242.333i	−0.662039	−	0.382229i
$635$	−88.4162	+	253.189i	−0.139238	+	0.398723i
$636$		0			0
$637$	−15.5656	+	58.0915i	−0.0244358	+	0.0911955i
$638$	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	0.977968	+	0.208756i	$0.0669414\pi$
$641$	429.324	+	743.610i	0.669772	+	1.16008i	−0.308196	+	0.951323i	$0.599725\pi$
$642$		0			0
$643$	260.843	+	973.479i	0.405666	+	1.51396i	0.802825	+	0.596215i	$0.203329\pi$
$643$	260.843	+	973.479i	0.405666	+	1.51396i	−0.397159	+	0.917750i	$0.630004\pi$
$644$	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	0.193113	−	0.981176i	$-0.438141\pi$
$647$	−509.877	−	509.877i	−0.788063	−	0.788063i	−0.981176	+	0.193113i	$0.938141\pi$
$648$		0			0
$649$			1738.08i			2.67809i
$650$	−320.140	+	402.479i	−0.492523	+	0.619199i
$651$		0			0
$652$	−397.525	+	106.517i	−0.609701	+	0.163369i
$653$	−13.7056	−	51.1501i	−0.0209887	−	0.0783309i	0.954637	−	0.297772i	$-0.0962434\pi$
$653$	−13.7056	−	51.1501i	−0.0209887	−	0.0783309i	−0.975626	+	0.219441i	$0.929577\pi$
$654$		0			0
$655$	−326.194	−	24.2387i	−0.498005	−	0.0370056i
$656$	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	−0.933835	−	0.357704i	$-0.883560\pi$
$659$	−718.950	+	415.086i	−1.09097	+	0.629873i	−0.157137	+	0.987577i	$0.550226\pi$
$660$		0			0
$661$	−350.839	+	607.670i	−0.530770	+	0.919320i	0.468586	+	0.883418i	$0.344764\pi$
$661$	−350.839	+	607.670i	−0.530770	+	0.919320i	−0.999355	+	0.0359018i	$0.988570\pi$
$662$	1281.29	−	343.321i	1.93549	−	0.518612i
$663$		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
$668$	−392.969	−	105.296i	−0.588277	−	0.157628i
$669$		0			0
$670$	−873.947	+	421.548i	−1.30440	+	0.629176i
$671$	−720.793	+	1248.45i	−1.07421	+	1.86058i
$672$		0			0
$673$	497.594	+	133.330i	0.739367	+	0.198113i	0.608797	−	0.793326i	$-0.291652\pi$
$673$	497.594	+	133.330i	0.739367	+	0.198113i	0.130570	+	0.991439i	$0.458319\pi$
$674$			1827.32i			2.71116i
$675$		0			0
$676$	−1185.53			−1.75375
$677$	−138.719	+	517.705i	−0.204902	+	0.764704i	0.784577	+	0.620031i	$0.212880\pi$
$677$	−138.719	+	517.705i	−0.204902	+	0.764704i	−0.989479	+	0.144674i	$0.953787\pi$
$678$		0			0
$679$	−417.925	−	241.289i	−0.615501	−	0.355360i
$680$	199.948	+	414.530i	0.294041	+	0.609603i
$681$		0			0
$682$	−632.456	+	2360.36i	−0.927356	+	3.46094i
$683$	−111.371	+	111.371i	−0.163061	+	0.163061i	−0.783921	−	0.620860i	$-0.786784\pi$
$683$	−111.371	+	111.371i	−0.163061	+	0.163061i	0.620860	+	0.783921i	$0.286784\pi$
$684$		0			0
$685$	−627.861	+	119.206i	−0.916585	+	0.174024i
$686$	658.502	+	1140.56i	0.959916	+	1.66262i
$687$		0			0
$688$	−329.956	−	1231.41i	−0.479587	−	1.78984i
$689$	82.4457	+	47.6001i	0.119660	+	0.0690857i
$690$		0			0
$691$	−340.544	−	589.840i	−0.492828	−	0.853603i	0.507138	−	0.861865i	$-0.330703\pi$
$691$	−340.544	−	589.840i	−0.492828	−	0.853603i	−0.999966	+	0.00826205i	$0.997370\pi$
$692$	1257.36	+	1257.36i	1.81700	+	1.81700i
$693$		0			0
$694$			105.053i			0.151373i
$695$	−91.6775	+	1233.76i	−0.131910	+	1.77519i
$696$		0			0
$697$	63.4911	−	17.0124i	0.0910920	−	0.0244080i
$698$	410.039	+	1530.28i	0.587448	+	2.19239i
$699$		0			0
$700$	153.490	+	1347.04i	0.219272	+	1.92434i
$701$	−722.405			−1.03053			−0.515267	−	0.857030i	$-0.672307\pi$
$701$	−722.405			−1.03053			−0.515267	+	0.857030i	$0.672307\pi$
$702$		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
$707$	172.961	−	46.3448i	0.244641	−	0.0655514i
$708$		0			0
$709$	505.198	−	291.676i	0.712550	−	0.411391i	−0.0994544	−	0.995042i	$-0.531710\pi$
$709$	505.198	−	291.676i	0.712550	−	0.411391i	0.812005	+	0.583651i	$0.198376\pi$
$710$	1875.55	−	356.095i	2.64163	−	0.501543i
$711$		0			0
$712$	−74.1163	−	74.1163i	−0.104096	−	0.104096i
$713$	641.900	+	171.997i	0.900281	+	0.241230i
$714$		0			0
$715$	−562.250	−	196.343i	−0.786364	−	0.274606i
$716$	660.372	−	1143.80i	0.922308	−	1.59748i
$717$		0			0
$718$	745.481	+	199.751i	1.03827	+	0.278205i
$719$			1116.43i			1.55276i	0.630266	+	0.776379i	$0.282946\pi$
$719$			1116.43i			1.55276i	−0.630266	+	0.776379i	$0.717054\pi$
$720$		0			0
$721$	472.893			0.655885
$722$	17.6348	−	65.8139i	0.0244249	−	0.0911551i
$723$		0			0
$724$	−575.803	−	332.440i	−0.795308	−	0.459172i
$725$	39.3160	−	263.088i	0.0542290	−	0.362880i
$726$		0			0
$727$	−108.957	+	406.633i	−0.149872	+	0.559329i	0.849618	+	0.527398i	$0.176832\pi$
$727$	−108.957	+	406.633i	−0.149872	+	0.559329i	−0.999490	+	0.0319312i	$0.989834\pi$
$728$	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
$733$	−98.8503	−	368.915i	−0.134857	−	0.503294i	−0.999998	−	0.00176568i	$-0.999438\pi$
$733$	−98.8503	−	368.915i	−0.134857	−	0.503294i	0.865141	−	0.501528i	$-0.167229\pi$
$734$	−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	$-0.400281\pi$
$740$	1674.72	−	1443.05i	2.26313	−	1.95006i
$741$		0			0
$742$	353.465	−	94.7106i	0.476367	−	0.127642i
$743$	−49.5046	−	184.754i	−0.0666280	−	0.248659i	0.924577	−	0.380996i	$-0.124419\pi$
$743$	−49.5046	−	184.754i	−0.0666280	−	0.248659i	−0.991205	+	0.132337i	$0.957752\pi$
$744$		0			0
$745$	8.49961	−	114.384i	0.0114089	−	0.153536i
$746$	−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	−0.825154	−	0.564908i	$-0.808912\pi$
$751$	57.5621	−	99.7004i	0.0766472	−	0.132757i	0.901801	+	0.432151i	$0.142245\pi$
$752$	−21.2963	+	5.70632i	−0.0283195	+	0.00758819i
$753$		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	$0.992085\pi$
$758$	302.683	+	81.1036i	0.399317	+	0.106997i
$759$		0			0
$760$	−514.693	+	1473.88i	−0.677227	+	1.93931i
$761$	505.692	−	875.884i	0.664509	−	1.15096i	−0.314909	−	0.949122i	$-0.601974\pi$
$761$	505.692	−	875.884i	0.664509	−	1.15096i	0.979418	−	0.201842i	$-0.0646928\pi$
$762$		0			0
$763$	−112.130	−	30.0451i	−0.146959	−	0.0393776i
$764$			1784.60i			2.33586i
$765$		0			0
$766$	794.418			1.03710
$767$	125.523	−	468.459i	0.163655	−	0.610768i
$768$		0			0
$769$	−566.011	−	326.787i	−0.736035	−	0.424950i	0.0845906	−	0.996416i	$-0.473042\pi$
$769$	−566.011	−	326.787i	−0.736035	−	0.424950i	−0.820626	+	0.571466i	$0.806375\pi$
$770$	−2061.86	+	994.536i	−2.67774	+	1.29161i
$771$		0			0
$772$	661.394	−	2468.36i	0.856728	−	3.19735i
$773$	2.30444	−	2.30444i	0.00298116	−	0.00298116i	−0.705615	−	0.708596i	$-0.749329\pi$
$773$	2.30444	−	2.30444i	0.00298116	−	0.00298116i	0.708596	+	0.705615i	$0.249329\pi$
$774$		0			0
$775$	303.714	+	770.998i	0.391888	+	0.994836i
$776$	−656.069	−	1136.34i	−0.845450	−	1.46436i
$777$		0			0
$778$	−467.501	−	1744.74i	−0.600901	−	2.24259i
$779$	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
$785$	−602.866	−	699.654i	−0.767983	−	0.891278i
$786$		0			0
$787$	50.1368	−	13.4341i	0.0637062	−	0.0170700i	−0.226825	−	0.973935i	$-0.572835\pi$
$787$	50.1368	−	13.4341i	0.0637062	−	0.0170700i	0.290531	+	0.956865i	$0.406168\pi$
$788$	168.591	+	629.191i	0.213948	+	0.798466i
$789$		0			0
$790$	987.993	−	851.318i	1.25062	−	1.07762i
$791$	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
$797$	−882.386	+	236.435i	−1.10713	+	0.296656i	−0.765667	−	0.643238i	$-0.777591\pi$
$797$	−882.386	+	236.435i	−1.10713	+	0.296656i	−0.341468	+	0.939893i	$0.610924\pi$
$798$		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
$803$	−230.696	−	61.8149i	−0.287293	−	0.0769800i
$804$		0			0
$805$	270.464	+	560.723i	0.335980	+	0.696550i
$806$	340.928	−	590.505i	0.422988	−	0.732636i
$807$		0			0
$808$	470.284	+	126.012i	0.582035	+	0.155956i
$809$		−	467.239i		−	0.577552i	−0.957397	−	0.288776i	$-0.906752\pi$
$809$		−	467.239i		−	0.577552i	0.957397	−	0.288776i	$-0.0932483\pi$
$810$		0			0
$811$	984.857			1.21437			0.607187	−	0.794559i	$-0.292298\pi$
$811$	984.857			1.21437			0.607187	+	0.794559i	$0.292298\pi$
$812$	−149.347	+	557.370i	−0.183925	+	0.686416i
$813$		0			0
$814$	3232.61	+	1866.35i	3.97127	+	2.29281i
$815$	−222.472	−	77.6895i	−0.272972	−	0.0953246i
$816$		0			0
$817$	240.924	−	899.140i	0.294888	−	1.10054i
$818$	−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	−0.994442	−	0.105287i	$-0.966424\pi$
$821$	−483.078	−	836.716i	−0.588402	−	1.01914i	0.406040	−	0.913855i	$-0.366909\pi$
$822$		0			0
$823$	−7.96649	−	29.7313i	−0.00967981	−	0.0361256i	0.960917	−	0.276837i	$-0.0892861\pi$
$823$	−7.96649	−	29.7313i	−0.00967981	−	0.0361256i	−0.970597	+	0.240711i	$0.922619\pi$
$824$	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	0.919368	−	0.393398i	$-0.128700\pi$
$827$	434.978	+	434.978i	0.525971	+	0.525971i	−0.393398	+	0.919368i	$0.628700\pi$
$828$		0			0
$829$		−	308.711i		−	0.372390i	−0.982513	−	0.186195i	$-0.940384\pi$
$829$		−	308.711i		−	0.372390i	0.982513	−	0.186195i	$-0.0596156\pi$
$830$	−105.402	−	7.83217i	−0.126990	−	0.00943635i
$831$		0			0
$832$	−110.687	+	29.6585i	−0.133037	+	0.0356473i
$833$	14.7179	+	54.9279i	0.0176685	+	0.0659398i
$834$		0			0
$835$	−152.059	−	176.471i	−0.182107	−	0.211343i
$836$	−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	−0.308730	−	0.951150i	$-0.599904\pi$
$839$	302.565	−	174.686i	0.360625	−	0.208207i	0.669355	+	0.742943i	$0.266571\pi$
$840$		0			0
$841$	−363.891	+	630.278i	−0.432689	+	0.749439i
$842$	2090.69	−	560.198i	2.48300	−	0.665318i
$843$		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
$848$	403.932	+	108.233i	0.476334	+	0.127633i
$849$		0			0
$850$	−71.8700	+	480.927i	−0.0845529	+	0.565797i
$851$	507.554	−	879.109i	0.596420	−	1.03303i
$852$		0			0
$853$	650.129	+	174.201i	0.762167	+	0.204222i	0.618908	−	0.785463i	$-0.287575\pi$
$853$	650.129	+	174.201i	0.762167	+	0.204222i	0.143259	+	0.989685i	$0.454242\pi$
$854$		−	1546.19i		−	1.81053i
$855$		0			0
$856$	−336.118			−0.392662
$857$	402.983	−	1503.95i	0.470225	−	1.75490i	−0.168732	−	0.985662i	$-0.553967\pi$
$857$	402.983	−	1503.95i	0.470225	−	1.75490i	0.638957	−	0.769242i	$-0.279366\pi$
$858$		0			0
$859$	323.898	+	187.002i	0.377064	+	0.217698i	0.676540	−	0.736406i	$-0.263479\pi$
$859$	323.898	+	187.002i	0.377064	+	0.217698i	−0.299476	+	0.954104i	$0.596812\pi$
$860$	724.652	−	2075.12i	0.842618	−	2.41293i
$861$		0			0
$862$	−126.943	+	473.757i	−0.147265	+	0.549602i
$863$	−169.154	+	169.154i	−0.196007	+	0.196007i	−0.798286	−	0.602279i	$-0.794260\pi$
$863$	−169.154	+	169.154i	−0.196007	+	0.196007i	0.602279	+	0.798286i	$0.294260\pi$
$864$		0			0
$865$	189.917	+	1000.29i	0.219557	+	1.15641i
$866$	−256.647	−	444.526i	−0.296359	−	0.513309i
$867$		0			0
$868$	−465.238	−	1736.29i	−0.535989	−	2.00034i
$869$	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
$875$	−361.441	+	687.012i	−0.413075	+	0.785157i
$876$		0			0
$877$	1182.71	−	316.907i	1.34859	−	0.361353i	0.488974	−	0.872298i	$-0.337371\pi$
$877$	1182.71	−	316.907i	1.34859	−	0.361353i	0.859613	+	0.510945i	$0.170705\pi$
$878$	755.642	+	2820.10i	0.860640	+	3.21195i
$879$		0			0
$880$	−2608.84	−	193.856i	−2.96459	−	0.220291i
$881$	1252.48			1.42165			0.710827	−	0.703366i	$-0.248321\pi$
$881$	1252.48			1.42165			0.710827	+	0.703366i	$0.248321\pi$
$882$		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
$887$	−658.011	+	176.313i	−0.741839	+	0.198775i	−0.609895	−	0.792482i	$-0.708788\pi$
$887$	−658.011	+	176.313i	−0.741839	+	0.198775i	−0.131943	+	0.991257i	$0.542122\pi$
$888$		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
$893$	−15.5499	−	4.16658i	−0.0174131	−	0.00466582i
$894$		0			0
$895$	681.143	−	328.549i	0.761054	−	0.367094i
$896$	−503.644	+	872.337i	−0.562102	+	0.973590i
$897$		0			0
$898$	−1889.69	−	506.342i	−2.10434	−	0.563856i
$899$			352.691i			0.392315i
$900$		0			0
$901$	90.0155			0.0999062
$902$	−230.081	+	858.673i	−0.255079	+	0.951966i
$903$		0			0
$904$	2153.18	+	1243.14i	2.38183	+	1.37515i
$905$	−165.396	−	342.897i	−0.182758	−	0.378891i
$906$		0			0
$907$	−22.8467	+	85.2651i	−0.0251893	+	0.0940078i	−0.977376	−	0.211509i	$-0.932162\pi$
$907$	−22.8467	+	85.2651i	−0.0251893	+	0.0940078i	0.952187	+	0.305516i	$0.0988291\pi$
$908$	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	−0.959360	−	0.282183i	$-0.908941\pi$
$911$	−659.617	−	1142.49i	−0.724058	−	1.25411i	0.235302	−	0.971922i	$-0.424392\pi$
$912$		0			0
$913$	−31.6783	−	118.225i	−0.0346969	−	0.129491i
$914$	−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	$0.881328\pi$
$920$	−125.435	+	1688.05i	−0.136343	+	1.83484i
$921$		0			0
$922$	−514.900	+	137.967i	−0.558460	+	0.149639i
$923$	−159.659	−	595.857i	−0.172979	−	0.645566i
$924$		0			0
$925$	1257.66	−	143.306i	1.35964	−	0.154925i
$926$	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	−0.982971	−	0.183760i	$-0.941173\pi$
$929$	−1221.93	+	705.481i	−1.31532	+	0.759398i	−0.332345	+	0.943158i	$0.607840\pi$
$930$		0			0
$931$	−96.4472	+	167.051i	−0.103595	+	0.179432i
$932$	−3324.93	+	890.913i	−3.56753	+	0.955916i
$933$		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	$0.868677\pi$
$938$	1164.11	+	311.923i	1.24106	+	0.332540i
$939$		0			0
$940$	−35.8875	−	12.5323i	−0.0381782	−	0.0133322i
$941$	367.359	−	636.284i	0.390392	−	0.676179i	−0.602109	−	0.798414i	$-0.705673\pi$
$941$	367.359	−	636.284i	0.390392	−	0.676179i	0.992501	+	0.122235i	$0.0390062\pi$
$942$		0			0
$943$	233.516	+	62.5705i	0.247631	+	0.0663526i
$944$		−	2130.37i		−	2.25674i
$945$		0			0
$946$	3711.31			3.92317
$947$	−178.196	+	665.038i	−0.188169	+	0.702258i	0.805760	+	0.592242i	$0.201757\pi$
$947$	−178.196	+	665.038i	−0.188169	+	0.702258i	−0.993930	+	0.110016i	$0.964910\pi$
$948$		0			0
$949$	57.7147	+	33.3216i	0.0608163	+	0.0351123i
$950$	−1325.93	+	981.160i	−1.39572	+	1.03280i
$951$		0			0
$952$	147.951	−	552.160i	0.155411	−	0.580000i
$953$	−47.5647	+	47.5647i	−0.0499105	+	0.0499105i	−0.731622	−	0.681711i	$-0.761236\pi$
$953$	−47.5647	+	47.5647i	−0.0499105	+	0.0499105i	0.681711	+	0.731622i	$0.261236\pi$
$954$		0			0
$955$	−575.092	+	844.645i	−0.602190	+	0.884445i
$956$	1714.97	+	2970.41i	1.79390	+	3.10713i
$957$		0			0
$958$	270.563	+	1009.75i	0.282424	+	1.05402i
$959$	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
$965$	1108.47	−	955.128i	1.14867	−	0.989770i
$966$		0			0
$967$	1056.23	−	283.016i	1.09227	−	0.292674i	0.332659	−	0.943047i	$-0.392054\pi$
$967$	1056.23	−	283.016i	1.09227	−	0.292674i	0.759615	+	0.650373i	$0.225387\pi$
$968$	−1336.74	−	4988.78i	−1.38093	−	5.15370i
$969$		0			0
$970$	102.734	−	1382.55i	0.105912	−	1.42531i
$971$	1595.62			1.64327			0.821637	−	0.570011i	$-0.193061\pi$
$971$	1595.62			1.64327			0.821637	+	0.570011i	$0.193061\pi$
$972$		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
$977$	−1389.80	+	372.395i	−1.42251	+	0.381161i	−0.886375	−	0.462968i	$-0.846784\pi$
$977$	−1389.80	+	372.395i	−1.42251	+	0.381161i	−0.536139	+	0.844130i	$0.680118\pi$
$978$		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
$983$	−367.259	−	98.4066i	−0.373610	−	0.100108i	0.0671278	−	0.997744i	$-0.478616\pi$
$983$	−367.259	−	98.4066i	−0.373610	−	0.100108i	−0.440738	+	0.897636i	$0.645283\pi$
$984$		0			0
$985$	−122.965	+	352.123i	−0.124837	+	0.357485i
$986$	−103.482	+	179.235i	−0.104951	+	0.181780i
$987$		0			0
$988$	899.140	+	240.924i	0.910060	+	0.243850i
$989$		−	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	$0.408222\pi$
$992$	195.750	−	730.549i	0.197329	−	0.736440i
$993$		0			0
$994$	−2053.50	−	1185.59i	−2.06589	−	1.19274i
$995$	460.404	−	222.076i	0.462718	−	0.223192i
$996$		0			0
$997$	−316.507	+	1181.22i	−0.317459	+	1.18477i	0.604219	+	0.796818i	$0.293485\pi$
$997$	−316.507	+	1181.22i	−0.317459	+	1.18477i	−0.921678	+	0.387956i	$0.873181\pi$
$998$	−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.352.8		32
3.2	odd	2	inner	405.3.l.o.352.1		32
5.3	odd	4	inner	405.3.l.o.28.1		32
9.2	odd	6	inner	405.3.l.o.217.8		32
9.4	even	3		135.3.g.a.82.8	yes	16
9.5	odd	6		135.3.g.a.82.1	yes	16
9.7	even	3	inner	405.3.l.o.217.1		32
15.8	even	4	inner	405.3.l.o.28.8		32
45.4	even	6		675.3.g.k.82.1		16
45.13	odd	12		135.3.g.a.28.8	yes	16
45.14	odd	6		675.3.g.k.82.8		16
45.22	odd	12		675.3.g.k.568.1		16
45.23	even	12		135.3.g.a.28.1	✓	16
45.32	even	12		675.3.g.k.568.8		16
45.38	even	12	inner	405.3.l.o.298.1		32
45.43	odd	12	inner	405.3.l.o.298.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.3.g.a.28.1	✓	16	45.23	even	12
135.3.g.a.28.8	yes	16	45.13	odd	12
135.3.g.a.82.1	yes	16	9.5	odd	6
135.3.g.a.82.8	yes	16	9.4	even	3
405.3.l.o.28.1		32	5.3	odd	4	inner
405.3.l.o.28.8		32	15.8	even	4	inner
405.3.l.o.217.1		32	9.7	even	3	inner
405.3.l.o.217.8		32	9.2	odd	6	inner
405.3.l.o.298.1		32	45.38	even	12	inner
405.3.l.o.298.8		32	45.43	odd	12	inner
405.3.l.o.352.1		32	3.2	odd	2	inner
405.3.l.o.352.8		32	1.1	even	1	trivial
675.3.g.k.82.1		16	45.4	even	6
675.3.g.k.82.8		16	45.14	odd	6
675.3.g.k.568.1		16	45.22	odd	12
675.3.g.k.568.8		16	45.32	even	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)

\(f(q)\)	\(=\)	\(q+(0.923527 - 3.44665i) q^{2} +(-7.56239 - 4.36615i) q^{4} +(-2.17225 - 4.50348i) q^{5} +(-1.60735 + 5.99870i) q^{7} +(-11.9402 + 11.9402i) q^{8} +O(q^{10})\)	\(q+(0.923527 - 3.44665i) q^{2} +(-7.56239 - 4.36615i) q^{4} +(-2.17225 - 4.50348i) q^{5} +(-1.60735 + 5.99870i) q^{7} +(-11.9402 + 11.9402i) q^{8} +(-17.5280 + 3.32790i) q^{10} +(-10.3303 - 17.8926i) q^{11} +(1.49210 + 5.56860i) q^{13} +(19.1910 + 11.0799i) q^{14} +(12.6619 + 21.9311i) q^{16} +(3.85449 + 3.85449i) q^{17} +18.4907i q^{19} +(-3.23546 + 43.5414i) q^{20} +(-71.2100 + 19.0807i) q^{22} +(5.18899 + 19.3656i) q^{23} +(-15.5627 + 19.5654i) q^{25} +20.5710 q^{26} +(38.3466 - 38.3466i) q^{28} +(-9.21485 + 5.32019i) q^{29} +(16.5732 - 28.7057i) q^{31} +(22.0400 - 5.90560i) q^{32} +(16.8448 - 9.72536i) q^{34} +(30.5066 - 5.79202i) q^{35} +(-35.8023 - 35.8023i) q^{37} +(63.7309 + 17.0766i) q^{38} +(79.7093 + 27.8353i) q^{40} +(6.02916 - 10.4428i) q^{41} +(-48.6267 - 13.0295i) q^{43} +180.415i q^{44} +71.5385 q^{46} +(-0.225334 + 0.840958i) q^{47} +(9.03436 + 5.21599i) q^{49} +(53.0624 + 71.7082i) q^{50} +(13.0295 - 48.6267i) q^{52} +(11.6767 - 11.6767i) q^{53} +(-58.1391 + 85.3897i) q^{55} +(-52.4335 - 90.8175i) q^{56} +(9.82669 + 36.6737i) q^{58} +(-72.8545 - 42.0625i) q^{59} +(-34.8873 - 60.4265i) q^{61} +(-83.6326 - 83.6326i) q^{62} +19.8770i q^{64} +(21.8369 - 18.8160i) q^{65} +(52.5324 - 14.0760i) q^{67} +(-12.3199 - 45.9785i) q^{68} +(8.21059 - 110.495i) q^{70} -107.003 q^{71} +(8.17407 - 8.17407i) q^{73} +(-156.462 + 90.3335i) q^{74} +(80.7330 - 139.834i) q^{76} +(123.937 - 33.2088i) q^{77} +(-63.3057 + 36.5496i) q^{79} +(71.2613 - 104.662i) q^{80} +(-30.4246 - 30.4246i) q^{82} +(5.72223 + 1.53327i) q^{83} +(8.98571 - 25.7316i) q^{85} +(-89.8161 + 155.566i) q^{86} +(336.987 + 90.2953i) q^{88} +6.20731i q^{89} -35.8027 q^{91} +(45.3118 - 169.106i) q^{92} +(2.69039 + 1.55330i) q^{94} +(83.2724 - 40.1664i) q^{95} +(-20.1118 + 75.0582i) q^{97} +(26.3212 - 26.3212i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{7}+O(q^{10}) \) 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

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