LMFDB - Embedded newform 495.3.j.c.397.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [495,3,Mod(298,495)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(495, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("495.298"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	495.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$13.4877730858$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			397.14
Character	$\chi$	$=$	495.397
Dual form			495.3.j.c.298.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.768581 + 0.768581i) q^{2} -2.81857i q^{4} +(2.92182 + 4.05746i) q^{5} +(8.07326 + 8.07326i) q^{7} +(5.24062 - 5.24062i) q^{8} +(-0.872829 + 5.36414i) q^{10} -3.31662 q^{11} +(-16.0817 + 16.0817i) q^{13} +12.4099i q^{14} -3.21859 q^{16} +(10.6403 + 10.6403i) q^{17} -5.48150i q^{19} +(11.4362 - 8.23535i) q^{20} +(-2.54909 - 2.54909i) q^{22} +(27.0228 - 27.0228i) q^{23} +(-7.92592 + 23.7103i) q^{25} -24.7201 q^{26} +(22.7550 - 22.7550i) q^{28} -3.30973i q^{29} +10.0291 q^{31} +(-23.4362 - 23.4362i) q^{32} +16.3559i q^{34} +(-9.16829 + 56.3455i) q^{35} +(41.8222 + 41.8222i) q^{37} +(4.21298 - 4.21298i) q^{38} +(36.5757 + 5.95144i) q^{40} -53.7373 q^{41} +(-24.0393 + 24.0393i) q^{43} +9.34813i q^{44} +41.5384 q^{46} +(40.6616 + 40.6616i) q^{47} +81.3550i q^{49} +(-24.3150 + 12.1316i) q^{50} +(45.3273 + 45.3273i) q^{52} +(19.1222 - 19.1222i) q^{53} +(-9.69058 - 13.4571i) q^{55} +84.6178 q^{56} +(2.54380 - 2.54380i) q^{58} -75.3124i q^{59} -1.20242 q^{61} +(7.70818 + 7.70818i) q^{62} -23.1509i q^{64} +(-112.238 - 18.2629i) q^{65} +(-0.221223 - 0.221223i) q^{67} +(29.9904 - 29.9904i) q^{68} +(-50.3527 + 36.2595i) q^{70} +78.2535 q^{71} +(40.4681 - 40.4681i) q^{73} +64.2875i q^{74} -15.4500 q^{76} +(-26.7760 - 26.7760i) q^{77} -42.1339i q^{79} +(-9.40413 - 13.0593i) q^{80} +(-41.3015 - 41.3015i) q^{82} +(-9.45520 + 9.45520i) q^{83} +(-12.0835 + 74.2617i) q^{85} -36.9523 q^{86} +(-17.3812 + 17.3812i) q^{88} -1.24117i q^{89} -259.663 q^{91} +(-76.1655 - 76.1655i) q^{92} +62.5034i q^{94} +(22.2410 - 16.0160i) q^{95} +(16.2790 + 16.2790i) q^{97} +(-62.5279 + 62.5279i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{10} - 88 q^{13} - 296 q^{16} + 168 q^{25} + 248 q^{28} - 32 q^{31} - 24 q^{37} + 296 q^{40} - 48 q^{43} + 48 q^{46} + 64 q^{52} + 104 q^{58} + 576 q^{61} - 544 q^{67} - 1048 q^{70} - 408 q^{73}+ \cdots + 712 q^{97}+O(q^{100}) $ 40 * q + 24 * q^10 - 88 * q^13 - 296 * q^16 + 168 * q^25 + 248 * q^28 - 32 * q^31 - 24 * q^37 + 296 * q^40 - 48 * q^43 + 48 * q^46 + 64 * q^52 + 104 * q^58 + 576 * q^61 - 544 * q^67 - 1048 * q^70 - 408 * q^73 - 96 * q^76 - 280 * q^82 + 160 * q^85 + 264 * q^88 + 528 * q^91 + 712 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.768581	+	0.768581i	0.384290	+	0.384290i	0.872645	−	0.488355i	$-0.162403\pi$
$2$	0.768581	+	0.768581i	0.384290	+	0.384290i	−0.488355	+	0.872645i	$0.662403\pi$
$3$		0			0
$3$		0			0
$4$		−	2.81857i		−	0.704642i
$5$	2.92182	+	4.05746i	0.584364	+	0.811492i
$5$	2.92182	+	4.05746i	0.584364	+	0.811492i
$6$		0			0
$7$	8.07326	+	8.07326i	1.15332	+	1.15332i	0.985882	+	0.167440i	$0.0535501\pi$
$7$	8.07326	+	8.07326i	1.15332	+	1.15332i	0.167440	+	0.985882i	$0.446450\pi$
$8$	5.24062	−	5.24062i	0.655078	−	0.655078i
$9$		0			0
$10$	−0.872829	+	5.36414i	−0.0872829	+	0.536414i
$11$	−3.31662			−0.301511
$11$	−3.31662			−0.301511
$12$		0			0
$13$	−16.0817	+	16.0817i	−1.23705	+	1.23705i	−0.275852	+	0.961200i	$0.588960\pi$
$13$	−16.0817	+	16.0817i	−1.23705	+	1.23705i	−0.961200	+	0.275852i	$0.911040\pi$
$14$			12.4099i			0.886422i
$15$		0			0
$16$	−3.21859			−0.201162
$17$	10.6403	+	10.6403i	0.625901	+	0.625901i	0.947034	−	0.321133i	$-0.104064\pi$
$17$	10.6403	+	10.6403i	0.625901	+	0.625901i	−0.321133	+	0.947034i	$0.604064\pi$
$18$		0			0
$19$		−	5.48150i		−	0.288500i	−0.989541	−	0.144250i	$-0.953923\pi$
$19$		−	5.48150i		−	0.288500i	0.989541	−	0.144250i	$-0.0460769\pi$
$20$	11.4362	−	8.23535i	0.571811	−	0.411767i
$21$		0			0
$22$	−2.54909	−	2.54909i	−0.115868	−	0.115868i
$23$	27.0228	−	27.0228i	1.17490	−	1.17490i	0.193878	−	0.981026i	$-0.437893\pi$
$23$	27.0228	−	27.0228i	1.17490	−	1.17490i	0.981026	−	0.193878i	$-0.0621067\pi$
$24$		0			0
$25$	−7.92592	+	23.7103i	−0.317037	+	0.948413i
$26$	−24.7201			−0.950774
$27$		0			0
$28$	22.7550	−	22.7550i	0.812679	−	0.812679i
$29$		−	3.30973i		−	0.114129i	−0.998371	−	0.0570643i	$-0.981826\pi$
$29$		−	3.30973i		−	0.114129i	0.998371	−	0.0570643i	$-0.0181740\pi$
$30$		0			0
$31$	10.0291			0.323520			0.161760	−	0.986830i	$-0.448283\pi$
$31$	10.0291			0.323520			0.161760	+	0.986830i	$0.448283\pi$
$32$	−23.4362	−	23.4362i	−0.732382	−	0.732382i
$33$		0			0
$34$			16.3559i			0.481056i
$35$	−9.16829	+	56.3455i	−0.261951	+	1.60987i
$36$		0			0
$37$	41.8222	+	41.8222i	1.13033	+	1.13033i	0.990122	+	0.140208i	$0.0447771\pi$
$37$	41.8222	+	41.8222i	1.13033	+	1.13033i	0.140208	+	0.990122i	$0.455223\pi$
$38$	4.21298	−	4.21298i	0.110868	−	0.110868i
$39$		0			0
$40$	36.5757	+	5.95144i	0.914394	+	0.148786i
$41$	−53.7373			−1.31067			−0.655333	−	0.755340i	$-0.727472\pi$
$41$	−53.7373			−1.31067			−0.655333	+	0.755340i	$0.727472\pi$
$42$		0			0
$43$	−24.0393	+	24.0393i	−0.559053	+	0.559053i	−0.929038	−	0.369985i	$-0.879363\pi$
$43$	−24.0393	+	24.0393i	−0.559053	+	0.559053i	0.369985	+	0.929038i	$0.379363\pi$
$44$			9.34813i			0.212457i
$45$		0			0
$46$	41.5384			0.903009
$47$	40.6616	+	40.6616i	0.865140	+	0.865140i	0.991930	−	0.126790i	$-0.0404673\pi$
$47$	40.6616	+	40.6616i	0.865140	+	0.865140i	−0.126790	+	0.991930i	$0.540467\pi$
$48$		0			0
$49$			81.3550i			1.66031i
$50$	−24.3150	+	12.1316i	−0.486300	+	0.242632i
$51$		0			0
$52$	45.3273	+	45.3273i	0.871678	+	0.871678i
$53$	19.1222	−	19.1222i	0.360795	−	0.360795i	−0.503310	−	0.864106i	$-0.667885\pi$
$53$	19.1222	−	19.1222i	0.360795	−	0.360795i	0.864106	+	0.503310i	$0.167885\pi$
$54$		0			0
$55$	−9.69058	−	13.4571i	−0.176192	−	0.244674i
$56$	84.6178			1.51103
$57$		0			0
$58$	2.54380	−	2.54380i	0.0438585	−	0.0438585i
$59$		−	75.3124i		−	1.27648i	−0.769837	−	0.638241i	$-0.779662\pi$
$59$		−	75.3124i		−	1.27648i	0.769837	−	0.638241i	$-0.220338\pi$
$60$		0			0
$61$	−1.20242			−0.0197118			−0.00985592	−	0.999951i	$-0.503137\pi$
$61$	−1.20242			−0.0197118			−0.00985592	+	0.999951i	$0.503137\pi$
$62$	7.70818	+	7.70818i	0.124325	+	0.124325i
$63$		0			0
$64$		−	23.1509i		−	0.361733i
$65$	−112.238	−	18.2629i	−1.72675	−	0.280968i
$66$		0			0
$67$	−0.221223	−	0.221223i	−0.00330183	−	0.00330183i	0.705454	−	0.708756i	$-0.250743\pi$
$67$	−0.221223	−	0.221223i	−0.00330183	−	0.00330183i	−0.708756	+	0.705454i	$0.750743\pi$
$68$	29.9904	−	29.9904i	0.441036	−	0.441036i
$69$		0			0
$70$	−50.3527	+	36.2595i	−0.719324	+	0.517993i
$71$	78.2535			1.10216			0.551081	−	0.834452i	$-0.314216\pi$
$71$	78.2535			1.10216			0.551081	+	0.834452i	$0.314216\pi$
$72$		0			0
$73$	40.4681	−	40.4681i	0.554357	−	0.554357i	−0.373338	−	0.927695i	$-0.621787\pi$
$73$	40.4681	−	40.4681i	0.554357	−	0.554357i	0.927695	+	0.373338i	$0.121787\pi$
$74$			64.2875i			0.868750i
$75$		0			0
$76$	−15.4500			−0.203289
$77$	−26.7760	−	26.7760i	−0.347740	−	0.347740i
$78$		0			0
$79$		−	42.1339i		−	0.533341i	−0.963788	−	0.266670i	$-0.914076\pi$
$79$		−	42.1339i		−	0.533341i	0.963788	−	0.266670i	$-0.0859235\pi$
$80$	−9.40413	−	13.0593i	−0.117552	−	0.163241i
$81$		0			0
$82$	−41.3015	−	41.3015i	−0.503676	−	0.503676i
$83$	−9.45520	+	9.45520i	−0.113918	+	0.113918i	−0.761768	−	0.647850i	$-0.775668\pi$
$83$	−9.45520	+	9.45520i	−0.113918	+	0.113918i	0.647850	+	0.761768i	$0.275668\pi$
$84$		0			0
$85$	−12.0835	+	74.2617i	−0.142159	+	0.873667i
$86$	−36.9523			−0.429678
$87$		0			0
$88$	−17.3812	+	17.3812i	−0.197513	+	0.197513i
$89$		−	1.24117i		−	0.0139457i	−0.999976	−	0.00697287i	$-0.997780\pi$
$89$		−	1.24117i		−	0.0139457i	0.999976	−	0.00697287i	$-0.00221955\pi$
$90$		0			0
$91$	−259.663			−2.85344
$92$	−76.1655	−	76.1655i	−0.827886	−	0.827886i
$93$		0			0
$94$			62.5034i			0.664930i
$95$	22.2410	−	16.0160i	0.234115	−	0.168589i
$96$		0			0
$97$	16.2790	+	16.2790i	0.167824	+	0.167824i	0.786022	−	0.618198i	$-0.212137\pi$
$97$	16.2790	+	16.2790i	0.167824	+	0.167824i	−0.618198	+	0.786022i	$0.712137\pi$
$98$	−62.5279	+	62.5279i	−0.638040	+	0.638040i
$99$		0			0
$100$	66.8291	+	22.3397i	0.668291	+	0.223397i
$101$	58.0443			0.574696			0.287348	−	0.957826i	$-0.407226\pi$
$101$	58.0443			0.574696			0.287348	+	0.957826i	$0.407226\pi$
$102$		0			0
$103$	10.4306	−	10.4306i	0.101268	−	0.101268i	−0.654658	−	0.755926i	$-0.727187\pi$
$103$	10.4306	−	10.4306i	0.101268	−	0.101268i	0.755926	+	0.654658i	$0.227187\pi$
$104$			168.556i			1.62073i
$105$		0			0
$106$	29.3938			0.277300
$107$	−132.740	−	132.740i	−1.24056	−	1.24056i	−0.959767	−	0.280797i	$-0.909401\pi$
$107$	−132.740	−	132.740i	−1.24056	−	1.24056i	−0.280797	−	0.959767i	$-0.590599\pi$
$108$		0			0
$109$		−	136.453i		−	1.25187i	−0.779877	−	0.625933i	$-0.784719\pi$
$109$		−	136.453i		−	1.25187i	0.779877	−	0.625933i	$-0.215281\pi$
$110$	2.89485	−	17.7908i	0.0263168	−	0.161735i
$111$		0			0
$112$	−25.9845	−	25.9845i	−0.232004	−	0.232004i
$113$	106.950	−	106.950i	0.946461	−	0.946461i	−0.0521766	−	0.998638i	$-0.516616\pi$
$113$	106.950	−	106.950i	0.946461	−	0.946461i	0.998638	+	0.0521766i	$0.0166159\pi$
$114$		0			0
$115$	188.600	+	30.6881i	1.64000	+	0.266853i
$116$	−9.32870			−0.0804198
$117$		0			0
$118$	57.8837	−	57.8837i	0.490540	−	0.490540i
$119$			171.804i			1.44373i
$120$		0			0
$121$	11.0000			0.0909091
$122$	−0.924159	−	0.924159i	−0.00757507	−	0.00757507i
$123$		0			0
$124$		−	28.2677i		−	0.227965i
$125$	−119.362	+	37.1182i	−0.954894	+	0.296946i
$126$		0			0
$127$	−134.333	−	134.333i	−1.05774	−	1.05774i	−0.998228	−	0.0595125i	$-0.981045\pi$
$127$	−134.333	−	134.333i	−1.05774	−	1.05774i	−0.0595125	−	0.998228i	$-0.518955\pi$
$128$	−75.9515	+	75.9515i	−0.593371	+	0.593371i
$129$		0			0
$130$	−72.2278	−	100.301i	−0.555599	−	0.771545i
$131$	41.0958			0.313708			0.156854	−	0.987622i	$-0.449865\pi$
$131$	41.0958			0.313708			0.156854	+	0.987622i	$0.449865\pi$
$132$		0			0
$133$	44.2536	−	44.2536i	0.332734	−	0.332734i
$134$		−	0.340055i		−	0.00253773i
$135$		0			0
$136$	111.524			0.820027
$137$	−137.075	−	137.075i	−1.00055	−	1.00055i	−1.00000		0.000549516i	$-0.999825\pi$
$137$	−137.075	−	137.075i	−1.00055	−	1.00055i	−0.000549516	−	1.00000i	$-0.500175\pi$
$138$		0			0
$139$			94.0771i			0.676814i	0.941000	+	0.338407i	$0.109888\pi$
$139$			94.0771i			0.676814i	−0.941000	+	0.338407i	$0.890112\pi$
$140$	158.814	+	25.8414i	1.13438	+	0.184582i
$141$		0			0
$142$	60.1441	+	60.1441i	0.423550	+	0.423550i
$143$	53.3369	−	53.3369i	0.372985	−	0.372985i
$144$		0			0
$145$	13.4291	−	9.67044i	0.0926144	−	0.0666927i
$146$	62.2060			0.426069
$147$		0			0
$148$	117.879	−	117.879i	0.796478	−	0.796478i
$149$		−	147.010i		−	0.986647i	−0.869846	−	0.493323i	$-0.835782\pi$
$149$		−	147.010i		−	0.986647i	0.869846	−	0.493323i	$-0.164218\pi$
$150$		0			0
$151$	−100.312			−0.664316			−0.332158	−	0.943224i	$-0.607777\pi$
$151$	−100.312			−0.664316			−0.332158	+	0.943224i	$0.607777\pi$
$152$	−28.7265	−	28.7265i	−0.188990	−	0.188990i
$153$		0			0
$154$		−	41.1590i		−	0.267266i
$155$	29.3033	+	40.6927i	0.189053	+	0.262533i
$156$		0			0
$157$	−123.818	−	123.818i	−0.788649	−	0.788649i	0.192624	−	0.981273i	$-0.438300\pi$
$157$	−123.818	−	123.818i	−0.788649	−	0.788649i	−0.981273	+	0.192624i	$0.938300\pi$
$158$	32.3833	−	32.3833i	0.204958	−	0.204958i
$159$		0			0
$160$	26.6150	−	163.568i	0.166344	−	1.02230i
$161$	436.324			2.71009
$162$		0			0
$163$	−86.6303	+	86.6303i	−0.531474	+	0.531474i	−0.921011	−	0.389537i	$-0.872635\pi$
$163$	−86.6303	+	86.6303i	−0.531474	+	0.531474i	0.389537	+	0.921011i	$0.372635\pi$
$164$			151.462i			0.923550i
$165$		0			0
$166$	−14.5342			−0.0875553
$167$	32.7308	+	32.7308i	0.195993	+	0.195993i	0.798280	−	0.602287i	$-0.205744\pi$
$167$	32.7308	+	32.7308i	0.195993	+	0.195993i	−0.602287	+	0.798280i	$0.705744\pi$
$168$		0			0
$169$		−	348.240i		−	2.06059i
$170$	−66.3633	+	47.7890i	−0.390372	+	0.281112i
$171$		0			0
$172$	67.7563	+	67.7563i	0.393932	+	0.393932i
$173$	−33.9507	+	33.9507i	−0.196247	+	0.196247i	−0.798389	−	0.602142i	$-0.794314\pi$
$173$	−33.9507	+	33.9507i	−0.196247	+	0.196247i	0.602142	+	0.798389i	$0.294314\pi$
$174$		0			0
$175$	−255.408	+	127.432i	−1.45947	+	0.728180i
$176$	10.6748			0.0606525
$177$		0			0
$178$	0.953941	−	0.953941i	0.00535922	−	0.00535922i
$179$		−	27.5198i		−	0.153742i	−0.997041	−	0.0768709i	$-0.975507\pi$
$179$		−	27.5198i		−	0.153742i	0.997041	−	0.0768709i	$-0.0244929\pi$
$180$		0			0
$181$	−254.288			−1.40491			−0.702453	−	0.711730i	$-0.747912\pi$
$181$	−254.288			−1.40491			−0.702453	+	0.711730i	$0.747912\pi$
$182$	−199.572	−	199.572i	−1.09655	−	1.09655i
$183$		0			0
$184$		−	283.232i		−	1.53931i
$185$	−47.4948	+	291.889i	−0.256729	+	1.57778i
$186$		0			0
$187$	−35.2899	−	35.2899i	−0.188716	−	0.188716i
$188$	114.607	−	114.607i	0.609614	−	0.609614i
$189$		0			0
$190$	29.4035	+	4.78441i	0.154755	+	0.0251811i
$191$	237.552			1.24373			0.621863	−	0.783126i	$-0.286376\pi$
$191$	237.552			1.24373			0.621863	+	0.783126i	$0.286376\pi$
$192$		0			0
$193$	−165.292	+	165.292i	−0.856436	+	0.856436i	−0.990916	−	0.134480i	$-0.957063\pi$
$193$	−165.292	+	165.292i	−0.856436	+	0.856436i	0.134480	+	0.990916i	$0.457063\pi$
$194$			25.0234i			0.128987i
$195$		0			0
$196$	229.304			1.16992
$197$	171.438	+	171.438i	0.870244	+	0.870244i	0.992499	−	0.122255i	$-0.0390125\pi$
$197$	171.438	+	171.438i	0.870244	+	0.870244i	−0.122255	+	0.992499i	$0.539012\pi$
$198$		0			0
$199$			77.2554i			0.388218i	0.980980	+	0.194109i	$0.0621816\pi$
$199$			77.2554i			0.388218i	−0.980980	+	0.194109i	$0.937818\pi$
$200$	82.7201	+	165.794i	0.413600	+	0.828968i
$201$		0			0
$202$	44.6117	+	44.6117i	0.220850	+	0.220850i
$203$	26.7203	−	26.7203i	0.131627	−	0.131627i
$204$		0			0
$205$	−157.011	−	218.037i	−0.765906	−	1.06359i
$206$	16.0335			0.0778326
$207$		0			0
$208$	51.7602	−	51.7602i	0.248847	−	0.248847i
$209$			18.1801i			0.0869860i
$210$		0			0
$211$	−347.895			−1.64879			−0.824397	−	0.566013i	$-0.808485\pi$
$211$	−347.895			−1.64879			−0.824397	+	0.566013i	$0.808485\pi$
$212$	−53.8971	−	53.8971i	−0.254231	−	0.254231i
$213$		0			0
$214$		−	204.043i		−	0.953474i
$215$	−167.777	−	27.2999i	−0.780358	−	0.126976i
$216$		0			0
$217$	80.9676	+	80.9676i	0.373122	+	0.373122i
$218$	104.875	−	104.875i	0.481080	−	0.481080i
$219$		0			0
$220$	−37.9296	+	27.3136i	−0.172407	+	0.124153i
$221$	−342.228			−1.54854
$222$		0			0
$223$	280.490	−	280.490i	1.25780	−	1.25780i	0.305661	−	0.952140i	$-0.401123\pi$
$223$	280.490	−	280.490i	1.25780	−	1.25780i	0.952140	−	0.305661i	$-0.0988774\pi$
$224$		−	378.413i		−	1.68935i
$225$		0			0
$226$	164.400			0.727432
$227$	−63.5588	−	63.5588i	−0.279995	−	0.279995i	0.553112	−	0.833107i	$-0.313440\pi$
$227$	−63.5588	−	63.5588i	−0.279995	−	0.279995i	−0.833107	+	0.553112i	$0.813440\pi$
$228$		0			0
$229$			260.698i			1.13842i	0.822193	+	0.569210i	$0.192751\pi$
$229$			260.698i			1.13842i	−0.822193	+	0.569210i	$0.807249\pi$
$230$	121.368	+	168.540i	0.527686	+	0.732784i
$231$		0			0
$232$	−17.3450	−	17.3450i	−0.0747631	−	0.0747631i
$233$	−143.864	+	143.864i	−0.617442	+	0.617442i	−0.944875	−	0.327433i	$-0.893817\pi$
$233$	−143.864	+	143.864i	−0.617442	+	0.617442i	0.327433	+	0.944875i	$0.393817\pi$
$234$		0			0
$235$	−46.1768	+	283.788i	−0.196497	+	1.20761i
$236$	−212.273			−0.899462
$237$		0			0
$238$	−132.045	+	132.045i	−0.554812	+	0.554812i
$239$			250.451i			1.04791i	0.851745	+	0.523956i	$0.175544\pi$
$239$			250.451i			1.04791i	−0.851745	+	0.523956i	$0.824456\pi$
$240$		0			0
$241$	405.781			1.68374			0.841869	−	0.539682i	$-0.181455\pi$
$241$	405.781			1.68374			0.841869	+	0.539682i	$0.181455\pi$
$242$	8.45439	+	8.45439i	0.0349355	+	0.0349355i
$243$		0			0
$244$			3.38911i			0.0138898i
$245$	−330.094	+	237.705i	−1.34732	+	0.970223i
$246$		0			0
$247$	88.1517	+	88.1517i	0.356889	+	0.356889i
$248$	52.5587	−	52.5587i	0.211930	−	0.211930i
$249$		0			0
$250$	−120.268	−	63.2108i	−0.481070	−	0.252843i
$251$	131.739			0.524857			0.262428	−	0.964951i	$-0.415477\pi$
$251$	131.739			0.524857			0.262428	+	0.964951i	$0.415477\pi$
$252$		0			0
$253$	−89.6245	+	89.6245i	−0.354247	+	0.354247i
$254$		−	206.492i		−	0.812959i
$255$		0			0
$256$	−209.354			−0.817787
$257$	−181.261	−	181.261i	−0.705297	−	0.705297i	0.260246	−	0.965542i	$-0.416196\pi$
$257$	−181.261	−	181.261i	−0.705297	−	0.705297i	−0.965542	+	0.260246i	$0.916196\pi$
$258$		0			0
$259$			675.283i			2.60727i
$260$	−51.4753	+	316.352i	−0.197982	+	1.21674i
$261$		0			0
$262$	31.5855	+	31.5855i	0.120555	+	0.120555i
$263$	287.089	−	287.089i	1.09159	−	1.09159i	0.0962330	−	0.995359i	$-0.469321\pi$
$263$	287.089	−	287.089i	1.09159	−	1.09159i	0.995359	−	0.0962330i	$-0.0306794\pi$
$264$		0			0
$265$	133.459	+	21.7158i	0.503618	+	0.0819465i
$266$	68.0249			0.255733
$267$		0			0
$268$	−0.623531	+	0.623531i	−0.00232661	+	0.00232661i
$269$		−	521.974i		−	1.94042i	−0.242258	−	0.970212i	$-0.577888\pi$
$269$		−	521.974i		−	1.94042i	0.242258	−	0.970212i	$-0.422112\pi$
$270$		0			0
$271$	318.233			1.17429			0.587146	−	0.809481i	$-0.300251\pi$
$271$	318.233			1.17429			0.587146	+	0.809481i	$0.300251\pi$
$272$	−34.2468	−	34.2468i	−0.125907	−	0.125907i
$273$		0			0
$274$		−	210.707i		−	0.769003i
$275$	26.2873	−	78.6383i	0.0955903	−	0.285957i
$276$		0			0
$277$	−317.276	−	317.276i	−1.14540	−	1.14540i	−0.987447	−	0.157953i	$-0.949511\pi$
$277$	−317.276	−	317.276i	−1.14540	−	1.14540i	−0.157953	−	0.987447i	$-0.550489\pi$
$278$	−72.3059	+	72.3059i	−0.260093	+	0.260093i
$279$		0			0
$280$	247.238	+	343.333i	0.882993	+	1.22619i
$281$	−234.943			−0.836096			−0.418048	−	0.908425i	$-0.637286\pi$
$281$	−234.943			−0.836096			−0.418048	+	0.908425i	$0.637286\pi$
$282$		0			0
$283$	28.4690	−	28.4690i	0.100597	−	0.100597i	−0.655017	−	0.755614i	$-0.727339\pi$
$283$	28.4690	−	28.4690i	0.100597	−	0.100597i	0.755614	+	0.655017i	$0.227339\pi$
$284$		−	220.563i		−	0.776629i
$285$		0			0
$286$	81.9874			0.286669
$287$	−433.835	−	433.835i	−1.51162	−	1.51162i
$288$		0			0
$289$		−	62.5674i		−	0.216496i
$290$	17.7539	+	2.88883i	0.0612202	+	0.00996147i
$291$		0			0
$292$	−114.062	−	114.062i	−0.390623	−	0.390623i
$293$	−10.6817	+	10.6817i	−0.0364564	+	0.0364564i	−0.725100	−	0.688644i	$-0.758206\pi$
$293$	−10.6817	+	10.6817i	−0.0364564	+	0.0364564i	0.688644	+	0.725100i	$0.258206\pi$
$294$		0			0
$295$	305.577	−	220.049i	1.03585	−	0.745930i
$296$	438.349			1.48091
$297$		0			0
$298$	112.989	−	112.989i	0.379159	−	0.379159i
$299$			869.143i			2.90683i
$300$		0			0
$301$	−388.151			−1.28954
$302$	−77.0976	−	77.0976i	−0.255290	−	0.255290i
$303$		0			0
$304$			17.6427i			0.0580351i
$305$	−3.51326	−	4.87878i	−0.0115189	−	0.0159960i
$306$		0			0
$307$	341.219	+	341.219i	1.11146	+	1.11146i	0.992953	+	0.118511i	$0.0378120\pi$
$307$	341.219	+	341.219i	1.11146	+	1.11146i	0.118511	+	0.992953i	$0.462188\pi$
$308$	−75.4698	+	75.4698i	−0.245032	+	0.245032i
$309$		0			0
$310$	−8.75369	+	53.7975i	−0.0282377	+	0.173540i
$311$	−12.2226			−0.0393010			−0.0196505	−	0.999807i	$-0.506255\pi$
$311$	−12.2226			−0.0393010			−0.0196505	+	0.999807i	$0.506255\pi$
$312$		0			0
$313$	−105.793	+	105.793i	−0.337996	+	0.337996i	−0.855612	−	0.517617i	$-0.826819\pi$
$313$	−105.793	+	105.793i	−0.337996	+	0.337996i	0.517617	+	0.855612i	$0.326819\pi$
$314$		−	190.328i		−	0.606140i
$315$		0			0
$316$	−118.757			−0.375814
$317$	405.231	+	405.231i	1.27833	+	1.27833i	0.941601	+	0.336731i	$0.109321\pi$
$317$	405.231	+	405.231i	1.27833	+	1.27833i	0.336731	+	0.941601i	$0.390679\pi$
$318$		0			0
$319$			10.9771i			0.0344111i
$320$	93.9339	−	67.6429i	0.293543	−	0.211384i
$321$		0			0
$322$	335.350	+	335.350i	1.04146	+	1.04146i
$323$	58.3249	−	58.3249i	0.180572	−	0.180572i
$324$		0			0
$325$	−253.840	−	508.764i	−0.781045	−	1.56543i
$326$	−133.165			−0.408481
$327$		0			0
$328$	−281.617	+	281.617i	−0.858588	+	0.858588i
$329$			656.543i			1.99557i
$330$		0			0
$331$	358.177			1.08211			0.541054	−	0.840988i	$-0.318026\pi$
$331$	358.177			1.08211			0.541054	+	0.840988i	$0.318026\pi$
$332$	26.6501	+	26.6501i	0.0802715	+	0.0802715i
$333$		0			0
$334$			50.3126i			0.150637i
$335$	0.251229	−	1.54398i	0.000749937	−	0.00460888i
$336$		0			0
$337$	−189.096	−	189.096i	−0.561117	−	0.561117i	0.368508	−	0.929625i	$-0.379869\pi$
$337$	−189.096	−	189.096i	−0.561117	−	0.561117i	−0.929625	+	0.368508i	$0.879869\pi$
$338$	267.651	−	267.651i	0.791867	−	0.791867i
$339$		0			0
$340$	209.312	+	34.0582i	0.615622	+	0.100171i
$341$	−33.2628			−0.0975448
$342$		0			0
$343$	−261.210	+	261.210i	−0.761545	+	0.761545i
$344$			251.962i			0.732446i
$345$		0			0
$346$	−52.1877			−0.150831
$347$	−420.192	−	420.192i	−1.21093	−	1.21093i	−0.970722	−	0.240204i	$-0.922786\pi$
$347$	−420.192	−	420.192i	−1.21093	−	1.21093i	−0.240204	−	0.970722i	$-0.577214\pi$
$348$		0			0
$349$			350.571i			1.00450i	0.864722	+	0.502251i	$0.167495\pi$
$349$			350.571i			1.00450i	−0.864722	+	0.502251i	$0.832505\pi$
$350$	−294.243	−	98.3600i	−0.840694	−	0.281028i
$351$		0			0
$352$	77.7292	+	77.7292i	0.220821	+	0.220821i
$353$	308.547	−	308.547i	0.874071	−	0.874071i	−0.118842	−	0.992913i	$-0.537918\pi$
$353$	308.547	−	308.547i	0.874071	−	0.874071i	0.992913	+	0.118842i	$0.0379183\pi$
$354$		0			0
$355$	228.643	+	317.510i	0.644064	+	0.894395i
$356$	−3.49832			−0.00982675
$357$		0			0
$358$	21.1512	−	21.1512i	0.0590815	−	0.0590815i
$359$			376.193i			1.04789i	0.851752	+	0.523945i	$0.175540\pi$
$359$			376.193i			1.04789i	−0.851752	+	0.523945i	$0.824460\pi$
$360$		0			0
$361$	330.953			0.916768
$362$	−195.441	−	195.441i	−0.539892	−	0.539892i
$363$		0			0
$364$			731.877i			2.01065i
$365$	282.438	+	45.9571i	0.773803	+	0.125910i
$366$		0			0
$367$	−24.7162	−	24.7162i	−0.0673465	−	0.0673465i	0.672631	−	0.739978i	$-0.265164\pi$
$367$	−24.7162	−	24.7162i	−0.0673465	−	0.0673465i	−0.739978	+	0.672631i	$0.765164\pi$
$368$	−86.9752	+	86.9752i	−0.236346	+	0.236346i
$369$		0			0
$370$	−260.844	+	187.837i	−0.704983	+	0.507666i
$371$	308.756			0.832227
$372$		0			0
$373$	−32.1589	+	32.1589i	−0.0862170	+	0.0862170i	−0.748900	−	0.662683i	$-0.769418\pi$
$373$	−32.1589	+	32.1589i	−0.0862170	+	0.0862170i	0.662683	+	0.748900i	$0.269418\pi$
$374$		−	54.2463i		−	0.145044i
$375$		0			0
$376$	426.184			1.13347
$377$	53.2260	+	53.2260i	0.141183	+	0.141183i
$378$		0			0
$379$		−	98.6282i		−	0.260233i	−0.991499	−	0.130116i	$-0.958465\pi$
$379$		−	98.6282i		−	0.260233i	0.991499	−	0.130116i	$-0.0415351\pi$
$380$	−45.1421	−	62.6876i	−0.118795	−	0.164967i
$381$		0			0
$382$	182.578	+	182.578i	0.477952	+	0.477952i
$383$	−361.224	+	361.224i	−0.943144	+	0.943144i	−0.998468	−	0.0553240i	$-0.982381\pi$
$383$	−361.224	+	361.224i	−0.943144	+	0.943144i	0.0553240	+	0.998468i	$0.482381\pi$
$384$		0			0
$385$	30.4078	−	186.877i	0.0789812	−	0.485395i
$386$	−254.081			−0.658240
$387$		0			0
$388$	45.8833	−	45.8833i	0.118256	−	0.118256i
$389$		−	467.287i		−	1.20125i	−0.799530	−	0.600626i	$-0.794918\pi$
$389$		−	467.287i		−	1.20125i	0.799530	−	0.600626i	$-0.205082\pi$
$390$		0			0
$391$	575.062			1.47075
$392$	426.351	+	426.351i	1.08763	+	1.08763i
$393$		0			0
$394$			263.528i			0.668853i
$395$	170.957	−	123.108i	0.432802	−	0.311665i
$396$		0			0
$397$	44.0432	+	44.0432i	0.110940	+	0.110940i	0.760398	−	0.649458i	$-0.225004\pi$
$397$	44.0432	+	44.0432i	0.110940	+	0.110940i	−0.649458	+	0.760398i	$0.725004\pi$
$398$	−59.3770	+	59.3770i	−0.149189	+	0.149189i
$399$		0			0
$400$	25.5103	−	76.3137i	0.0637757	−	0.190784i
$401$	−34.5620			−0.0861895			−0.0430947	−	0.999071i	$-0.513722\pi$
$401$	−34.5620			−0.0861895			−0.0430947	+	0.999071i	$0.513722\pi$
$402$		0			0
$403$	−161.285	+	161.285i	−0.400210	+	0.400210i
$404$		−	163.602i		−	0.404955i
$405$		0			0
$406$	41.0734			0.101166
$407$	−138.709	−	138.709i	−0.340807	−	0.340807i
$408$		0			0
$409$			15.8648i			0.0387892i	0.999812	+	0.0193946i	$0.00617388\pi$
$409$			15.8648i			0.0387892i	−0.999812	+	0.0193946i	$0.993826\pi$
$410$	46.9035	−	288.254i	0.114399	−	0.703060i
$411$		0			0
$412$	−29.3993	−	29.3993i	−0.0713576	−	0.0713576i
$413$	608.016	−	608.016i	1.47219	−	1.47219i
$414$		0			0
$415$	−65.9905	−	10.7377i	−0.159013	−	0.0258739i
$416$	753.787			1.81199
$417$		0			0
$418$	−13.9729	+	13.9729i	−0.0334279	+	0.0334279i
$419$			764.470i			1.82451i	0.409621	+	0.912256i	$0.365661\pi$
$419$			764.470i			1.82451i	−0.409621	+	0.912256i	$0.634339\pi$
$420$		0			0
$421$	−384.575			−0.913479			−0.456740	−	0.889600i	$-0.650983\pi$
$421$	−384.575			−0.913479			−0.456740	+	0.889600i	$0.650983\pi$
$422$	−267.386	−	267.386i	−0.633616	−	0.633616i
$423$		0			0
$424$		−	200.424i		−	0.472698i
$425$	−336.620	+	167.951i	−0.792046	+	0.395179i
$426$		0			0
$427$	−9.70747	−	9.70747i	−0.0227341	−	0.0227341i
$428$	−374.138	+	374.138i	−0.874153	+	0.874153i
$429$		0			0
$430$	−107.968	−	149.932i	−0.251088	−	0.348680i
$431$	235.568			0.546562			0.273281	−	0.961934i	$-0.411891\pi$
$431$	235.568			0.546562			0.273281	+	0.961934i	$0.411891\pi$
$432$		0			0
$433$	122.331	−	122.331i	0.282519	−	0.282519i	−0.551594	−	0.834113i	$-0.685980\pi$
$433$	122.331	−	122.331i	0.282519	−	0.282519i	0.834113	+	0.551594i	$0.185980\pi$
$434$			124.460i			0.286775i
$435$		0			0
$436$	−384.603			−0.882116
$437$	−148.125	−	148.125i	−0.338960	−	0.338960i
$438$		0			0
$439$			581.820i			1.32533i	0.748915	+	0.662666i	$0.230575\pi$
$439$			581.820i			1.32533i	−0.748915	+	0.662666i	$0.769425\pi$
$440$	−121.308	−	19.7387i	−0.275700	−	0.0448607i
$441$		0			0
$442$	−263.030	−	263.030i	−0.595091	−	0.595091i
$443$	−68.1013	+	68.1013i	−0.153727	+	0.153727i	−0.779780	−	0.626053i	$-0.784669\pi$
$443$	−68.1013	+	68.1013i	−0.153727	+	0.153727i	0.626053	+	0.779780i	$0.284669\pi$
$444$		0			0
$445$	5.03600	−	3.62648i	0.0113169	−	0.00814939i
$446$	431.158			0.966722
$447$		0			0
$448$	186.903	−	186.903i	0.417195	−	0.417195i
$449$			286.869i			0.638906i	0.947602	+	0.319453i	$0.103499\pi$
$449$			286.869i			0.638906i	−0.947602	+	0.319453i	$0.896501\pi$
$450$		0			0
$451$	178.226			0.395181
$452$	−301.446	−	301.446i	−0.666916	−	0.666916i
$453$		0			0
$454$		−	97.7002i		−	0.215199i
$455$	−758.689	−	1053.57i	−1.66745	−	2.31554i
$456$		0			0
$457$	−82.9531	−	82.9531i	−0.181517	−	0.181517i	0.610500	−	0.792016i	$-0.290969\pi$
$457$	−82.9531	−	82.9531i	−0.181517	−	0.181517i	−0.792016	+	0.610500i	$0.790969\pi$
$458$	−200.367	+	200.367i	−0.437484	+	0.437484i
$459$		0			0
$460$	86.4964	−	531.580i	0.188036	−	1.15561i
$461$	−181.392			−0.393476			−0.196738	−	0.980456i	$-0.563035\pi$
$461$	−181.392			−0.393476			−0.196738	+	0.980456i	$0.563035\pi$
$462$		0			0
$463$	145.688	−	145.688i	0.314660	−	0.314660i	−0.532052	−	0.846712i	$-0.678579\pi$
$463$	145.688	−	145.688i	0.314660	−	0.314660i	0.846712	+	0.532052i	$0.178579\pi$
$464$			10.6526i			0.0229583i
$465$		0			0
$466$	−221.142			−0.474554
$467$	639.354	+	639.354i	1.36907	+	1.36907i	0.861773	+	0.507294i	$0.169354\pi$
$467$	639.354	+	639.354i	1.36907	+	1.36907i	0.507294	+	0.861773i	$0.330646\pi$
$468$		0			0
$469$		−	3.57198i		−	0.00761616i
$470$	−253.605	+	182.624i	−0.539585	+	0.388561i
$471$		0			0
$472$	−394.684	−	394.684i	−0.836194	−	0.836194i
$473$	79.7293	−	79.7293i	0.168561	−	0.168561i
$474$		0			0
$475$	129.968	+	43.4460i	0.273617	+	0.0914652i
$476$	484.241			1.01731
$477$		0			0
$478$	−192.492	+	192.492i	−0.402703	+	0.402703i
$479$		−	422.415i		−	0.881868i	−0.897540	−	0.440934i	$-0.854647\pi$
$479$		−	422.415i		−	0.881868i	0.897540	−	0.440934i	$-0.145353\pi$
$480$		0			0
$481$	−1345.14			−2.79655
$482$	311.875	+	311.875i	0.647044	+	0.647044i
$483$		0			0
$484$		−	31.0042i		−	0.0640583i
$485$	−18.4870	+	113.615i	−0.0381175	+	0.234259i
$486$		0			0
$487$	161.254	+	161.254i	0.331117	+	0.331117i	0.853011	−	0.521894i	$-0.174774\pi$
$487$	161.254	+	161.254i	0.331117	+	0.331117i	−0.521894	+	0.853011i	$0.674774\pi$
$488$	−6.30144	+	6.30144i	−0.0129128	+	0.0129128i
$489$		0			0
$490$	−436.400	−	71.0090i	−0.890611	−	0.144916i
$491$	−428.048			−0.871789			−0.435894	−	0.899998i	$-0.643568\pi$
$491$	−428.048			−0.871789			−0.435894	+	0.899998i	$0.643568\pi$
$492$		0			0
$493$	35.2166	−	35.2166i	0.0714332	−	0.0714332i
$494$			135.503i			0.274298i
$495$		0			0
$496$	−32.2795			−0.0650797
$497$	631.761	+	631.761i	1.27115	+	1.27115i
$498$		0			0
$499$			7.42214i			0.0148740i	0.999972	+	0.00743702i	$0.00236730\pi$
$499$			7.42214i			0.0148740i	−0.999972	+	0.00743702i	$0.997633\pi$
$500$	104.620	+	336.429i	0.209240	+	0.672858i
$501$		0			0
$502$	101.252	+	101.252i	0.201697	+	0.201697i
$503$	−133.185	+	133.185i	−0.264782	+	0.264782i	−0.826993	−	0.562212i	$-0.809951\pi$
$503$	−133.185	+	133.185i	−0.264782	+	0.264782i	0.562212	+	0.826993i	$0.309951\pi$
$504$		0			0
$505$	169.595	+	235.512i	0.335832	+	0.466361i
$506$	−137.767			−0.272267
$507$		0			0
$508$	−378.626	+	378.626i	−0.745328	+	0.745328i
$509$		−	686.673i		−	1.34906i	−0.738246	−	0.674532i	$-0.764346\pi$
$509$		−	686.673i		−	1.34906i	0.738246	−	0.674532i	$-0.235654\pi$
$510$		0			0
$511$	653.419			1.27871
$512$	142.901	+	142.901i	0.279104	+	0.279104i
$513$		0			0
$514$		−	278.628i		−	0.542078i
$515$	72.7980	+	11.8454i	0.141355	+	0.0230007i
$516$		0			0
$517$	−134.859	−	134.859i	−0.260850	−	0.260850i
$518$	−519.010	+	519.010i	−1.00195	+	1.00195i
$519$		0			0
$520$	−683.908	+	492.490i	−1.31521	+	0.947096i
$521$	−552.214			−1.05991			−0.529956	−	0.848025i	$-0.677792\pi$
$521$	−552.214			−1.05991			−0.529956	+	0.848025i	$0.677792\pi$
$522$		0			0
$523$	−16.9634	+	16.9634i	−0.0324348	+	0.0324348i	−0.723138	−	0.690703i	$-0.757301\pi$
$523$	−16.9634	+	16.9634i	−0.0324348	+	0.0324348i	0.690703	+	0.723138i	$0.257301\pi$
$524$		−	115.831i		−	0.221052i
$525$		0			0
$526$	441.302			0.838977
$527$	106.713	+	106.713i	0.202491	+	0.202491i
$528$		0			0
$529$		−	931.462i		−	1.76080i
$530$	85.8835	+	119.264i	0.162044	+	0.225027i
$531$		0			0
$532$	−124.732	−	124.732i	−0.234458	−	0.234458i
$533$	864.186	−	864.186i	1.62136	−	1.62136i
$534$		0			0
$535$	150.745	−	926.432i	0.281766	−	1.73165i
$536$	−2.31869			−0.00432591
$537$		0			0
$538$	401.179	−	401.179i	0.745686	−	0.745686i
$539$		−	269.824i		−	0.500601i
$540$		0			0
$541$	541.947			1.00175			0.500875	−	0.865520i	$-0.333012\pi$
$541$	541.947			1.00175			0.500875	+	0.865520i	$0.333012\pi$
$542$	244.588	+	244.588i	0.451269	+	0.451269i
$543$		0			0
$544$		−	498.738i		−	0.916797i
$545$	553.653	−	398.692i	1.01588	−	0.731545i
$546$		0			0
$547$	463.546	+	463.546i	0.847434	+	0.847434i	0.989812	−	0.142378i	$-0.0454749\pi$
$547$	463.546	+	463.546i	0.847434	+	0.847434i	−0.142378	+	0.989812i	$0.545475\pi$
$548$	−386.356	+	386.356i	−0.705029	+	0.705029i
$549$		0			0
$550$	80.6438	−	40.2359i	0.146625	−	0.0731563i
$551$	−18.1423			−0.0329261
$552$		0			0
$553$	340.158	−	340.158i	0.615114	−	0.615114i
$554$		−	487.704i		−	0.880332i
$555$		0			0
$556$	265.163			0.476911
$557$	317.853	+	317.853i	0.570652	+	0.570652i	0.932311	−	0.361659i	$-0.117789\pi$
$557$	317.853	+	317.853i	0.570652	+	0.570652i	−0.361659	+	0.932311i	$0.617789\pi$
$558$		0			0
$559$		−	773.184i		−	1.38316i
$560$	29.5089	−	181.353i	0.0526945	−	0.323844i
$561$		0			0
$562$	−180.573	−	180.573i	−0.321304	−	0.321304i
$563$	543.392	−	543.392i	0.965172	−	0.965172i	−0.0342420	−	0.999414i	$-0.510902\pi$
$563$	543.392	−	543.392i	0.965172	−	0.965172i	0.999414	+	0.0342420i	$0.0109017\pi$
$564$		0			0
$565$	746.435	+	121.456i	1.32112	+	0.214967i
$566$	43.7615			0.0773172
$567$		0			0
$568$	410.097	−	410.097i	0.722002	−	0.722002i
$569$			336.113i			0.590708i	0.955388	+	0.295354i	$0.0954376\pi$
$569$			336.113i			0.590708i	−0.955388	+	0.295354i	$0.904562\pi$
$570$		0			0
$571$	−58.4226			−0.102316			−0.0511581	−	0.998691i	$-0.516291\pi$
$571$	−58.4226			−0.102316			−0.0511581	+	0.998691i	$0.516291\pi$
$572$	−150.334	−	150.334i	−0.262821	−	0.262821i
$573$		0			0
$574$		−	666.875i		−	1.16180i
$575$	426.539	+	854.900i	0.741806	+	1.48678i
$576$		0			0
$577$	32.8358	+	32.8358i	0.0569078	+	0.0569078i	0.734988	−	0.678080i	$-0.237188\pi$
$577$	32.8358	+	32.8358i	0.0569078	+	0.0569078i	−0.678080	+	0.734988i	$0.737188\pi$
$578$	48.0881	−	48.0881i	0.0831974	−	0.0831974i
$579$		0			0
$580$	−27.2568	−	37.8508i	−0.0469944	−	0.0652600i
$581$	−152.669			−0.262769
$582$		0			0
$583$	−63.4210	+	63.4210i	−0.108784	+	0.108784i
$584$		−	424.156i		−	0.726294i
$585$		0			0
$586$	−16.4195			−0.0280197
$587$	−715.832	−	715.832i	−1.21948	−	1.21948i	−0.967816	−	0.251660i	$-0.919023\pi$
$587$	−715.832	−	715.832i	−1.21948	−	1.21948i	−0.251660	−	0.967816i	$-0.580977\pi$
$588$		0			0
$589$		−	54.9746i		−	0.0933354i
$590$	403.986	+	65.7348i	0.684723	+	0.111415i
$591$		0			0
$592$	−134.608	−	134.608i	−0.227379	−	0.227379i
$593$	−564.755	+	564.755i	−0.952369	+	0.952369i	−0.998916	−	0.0465475i	$-0.985178\pi$
$593$	−564.755	+	564.755i	−0.952369	+	0.952369i	0.0465475	+	0.998916i	$0.485178\pi$
$594$		0			0
$595$	−697.088	+	501.981i	−1.17158	+	0.843665i
$596$	−414.358			−0.695232
$597$		0			0
$598$	−668.007	+	668.007i	−1.11707	+	1.11707i
$599$		−	96.7556i		−	0.161529i	−0.996733	−	0.0807643i	$-0.974264\pi$
$599$		−	96.7556i		−	0.161529i	0.996733	−	0.0807643i	$-0.0257361\pi$
$600$		0			0
$601$	426.359			0.709416			0.354708	−	0.934977i	$-0.384580\pi$
$601$	426.359			0.709416			0.354708	+	0.934977i	$0.384580\pi$
$602$	−298.325	−	298.325i	−0.495557	−	0.495557i
$603$		0			0
$604$			282.735i			0.468104i
$605$	32.1400	+	44.6320i	0.0531240	+	0.0737720i
$606$		0			0
$607$	−45.0874	−	45.0874i	−0.0742790	−	0.0742790i	0.668991	−	0.743270i	$-0.266726\pi$
$607$	−45.0874	−	45.0874i	−0.0742790	−	0.0742790i	−0.743270	+	0.668991i	$0.766726\pi$
$608$	−128.466	+	128.466i	−0.211292	+	0.211292i
$609$		0			0
$610$	1.04951	−	6.44996i	0.00172051	−	0.0105737i
$611$	−1307.81			−2.14045
$612$		0			0
$613$	515.429	−	515.429i	0.840830	−	0.840830i	−0.148137	−	0.988967i	$-0.547328\pi$
$613$	515.429	−	515.429i	0.840830	−	0.840830i	0.988967	+	0.148137i	$0.0473276\pi$
$614$			524.509i			0.854250i
$615$		0			0
$616$	−280.645			−0.455593
$617$	386.821	+	386.821i	0.626938	+	0.626938i	0.947296	−	0.320359i	$-0.103803\pi$
$617$	386.821	+	386.821i	0.626938	+	0.626938i	−0.320359	+	0.947296i	$0.603803\pi$
$618$		0			0
$619$		−	390.086i		−	0.630188i	−0.949060	−	0.315094i	$-0.897964\pi$
$619$		−	390.086i		−	0.630188i	0.949060	−	0.315094i	$-0.102036\pi$
$620$	114.695	−	82.5932i	0.184992	−	0.133215i
$621$		0			0
$622$	−9.39406	−	9.39406i	−0.0151030	−	0.0151030i
$623$	10.0203	−	10.0203i	0.0160839	−	0.0160839i
$624$		0			0
$625$	−499.359	−	375.853i	−0.798975	−	0.601364i
$626$	−162.620			−0.259777
$627$		0			0
$628$	−348.989	+	348.989i	−0.555715	+	0.555715i
$629$			890.003i			1.41495i
$630$		0			0
$631$	425.765			0.674747			0.337374	−	0.941371i	$-0.390461\pi$
$631$	425.765			0.674747			0.337374	+	0.941371i	$0.390461\pi$
$632$	−220.808	−	220.808i	−0.349380	−	0.349380i
$633$		0			0
$634$			622.906i			0.982502i
$635$	152.553	−	937.547i	0.240242	−	1.47645i
$636$		0			0
$637$	−1308.32	−	1308.32i	−2.05388	−	2.05388i
$638$	−8.43682	+	8.43682i	−0.0132238	+	0.0132238i
$639$		0			0
$640$	−530.087	−	86.2534i	−0.828261	−	0.134771i
$641$	−1118.86			−1.74549			−0.872743	−	0.488180i	$-0.837661\pi$
$641$	−1118.86			−1.74549			−0.872743	+	0.488180i	$0.837661\pi$
$642$		0			0
$643$	−780.511	+	780.511i	−1.21386	+	1.21386i	−0.244110	+	0.969747i	$0.578496\pi$
$643$	−780.511	+	780.511i	−1.21386	+	1.21386i	−0.969747	+	0.244110i	$0.921504\pi$
$644$		−	1229.81i		−	1.90964i
$645$		0			0
$646$	89.6548			0.138785
$647$	−333.052	−	333.052i	−0.514763	−	0.514763i	0.401219	−	0.915982i	$-0.368587\pi$
$647$	−333.052	−	333.052i	−0.514763	−	0.514763i	−0.915982	+	0.401219i	$0.868587\pi$
$648$		0			0
$649$			249.783i			0.384874i
$650$	195.930	−	586.123i	0.301431	−	0.901727i
$651$		0			0
$652$	244.173	+	244.173i	0.374499	+	0.374499i
$653$	−128.255	+	128.255i	−0.196409	+	0.196409i	−0.798459	−	0.602050i	$-0.794351\pi$
$653$	−128.255	+	128.255i	−0.196409	+	0.196409i	0.602050	+	0.798459i	$0.294351\pi$
$654$		0			0
$655$	120.075	+	166.744i	0.183320	+	0.254572i
$656$	172.958			0.263656
$657$		0			0
$658$	−504.606	+	504.606i	−0.766879	+	0.766879i
$659$		−	466.438i		−	0.707797i	−0.935284	−	0.353899i	$-0.884856\pi$
$659$		−	466.438i		−	0.707797i	0.935284	−	0.353899i	$-0.115144\pi$
$660$		0			0
$661$	−275.104			−0.416194			−0.208097	−	0.978108i	$-0.566727\pi$
$661$	−275.104			−0.416194			−0.208097	+	0.978108i	$0.566727\pi$
$662$	275.288	+	275.288i	0.415843	+	0.415843i
$663$		0			0
$664$			99.1023i			0.149250i
$665$	308.858	+	50.2560i	0.464448	+	0.0755729i
$666$		0			0
$667$	−89.4381	−	89.4381i	−0.134090	−	0.134090i
$668$	92.2541	−	92.2541i	0.138105	−	0.138105i
$669$		0			0
$670$	1.37976	−	0.993581i	0.00205934	−	0.00148296i
$671$	3.98798			0.00594334
$672$		0			0
$673$	840.275	−	840.275i	1.24855	−	1.24855i	0.292192	−	0.956360i	$-0.405615\pi$
$673$	840.275	−	840.275i	1.24855	−	1.24855i	0.956360	−	0.292192i	$-0.0943846\pi$
$674$		−	290.672i		−	0.431264i
$675$		0			0
$676$	−981.539			−1.45198
$677$	201.452	+	201.452i	0.297566	+	0.297566i	0.840060	−	0.542494i	$-0.182520\pi$
$677$	201.452	+	201.452i	0.297566	+	0.297566i	−0.542494	+	0.840060i	$0.682520\pi$
$678$		0			0
$679$			262.848i			0.387111i
$680$	325.852	+	452.503i	0.479195	+	0.665445i
$681$		0			0
$682$	−25.5651	−	25.5651i	−0.0374855	−	0.0374855i
$683$	287.808	−	287.808i	0.421388	−	0.421388i	−0.464293	−	0.885681i	$-0.653692\pi$
$683$	287.808	−	287.808i	0.421388	−	0.421388i	0.885681	+	0.464293i	$0.153692\pi$
$684$		0			0
$685$	155.668	−	956.686i	0.227252	−	1.39662i
$686$	−401.522			−0.585309
$687$		0			0
$688$	77.3725	−	77.3725i	0.112460	−	0.112460i
$689$			615.032i			0.892645i
$690$		0			0
$691$	−1166.93			−1.68875			−0.844374	−	0.535754i	$-0.820028\pi$
$691$	−1166.93			−1.68875			−0.844374	+	0.535754i	$0.820028\pi$
$692$	95.6922	+	95.6922i	0.138284	+	0.138284i
$693$		0			0
$694$		−	645.902i		−	0.930695i
$695$	−381.714	+	274.876i	−0.549229	+	0.395506i
$696$		0			0
$697$	−571.782	−	571.782i	−0.820347	−	0.820347i
$698$	−269.442	+	269.442i	−0.386020	+	0.386020i
$699$		0			0
$700$	359.174	+	719.883i	0.513106	+	1.02840i
$701$	−900.819			−1.28505			−0.642524	−	0.766265i	$-0.722113\pi$
$701$	−900.819			−1.28505			−0.642524	+	0.766265i	$0.722113\pi$
$702$		0			0
$703$	229.248	−	229.248i	0.326100	−	0.326100i
$704$			76.7829i			0.109067i
$705$		0			0
$706$	474.287			0.671794
$707$	468.606	+	468.606i	0.662810	+	0.662810i
$708$		0			0
$709$		−	1291.13i		−	1.82106i	−0.413440	−	0.910531i	$-0.635673\pi$
$709$		−	1291.13i		−	1.82106i	0.413440	−	0.910531i	$-0.364327\pi$
$710$	−68.3019	+	419.763i	−0.0961999	+	0.591215i
$711$		0			0
$712$	−6.50451	−	6.50451i	−0.00913554	−	0.00913554i
$713$	271.014	−	271.014i	0.380104	−	0.380104i
$714$		0			0
$715$	372.253	+	60.5713i	0.520633	+	0.0847151i
$716$	−77.5664			−0.108333
$717$		0			0
$718$	−289.135	+	289.135i	−0.402694	+	0.402694i
$719$		−	85.6949i		−	0.119186i	−0.998223	−	0.0595931i	$-0.981020\pi$
$719$		−	85.6949i		−	0.119186i	0.998223	−	0.0595931i	$-0.0189803\pi$
$720$		0			0
$721$	168.418			0.233589
$722$	254.364	+	254.364i	0.352305	+	0.352305i
$723$		0			0
$724$			716.728i			0.989955i
$725$	78.4748	+	26.2327i	0.108241	+	0.0361830i
$726$		0			0
$727$	361.019	+	361.019i	0.496588	+	0.496588i	0.910374	−	0.413786i	$-0.135794\pi$
$727$	361.019	+	361.019i	0.496588	+	0.496588i	−0.413786	+	0.910374i	$0.635794\pi$
$728$	−1360.80	+	1360.80i	−1.86922	+	1.86922i
$729$		0			0
$730$	181.755	+	252.398i	0.248979	+	0.345751i
$731$	−511.571			−0.699824
$732$		0			0
$733$	443.921	−	443.921i	0.605622	−	0.605622i	−0.336177	−	0.941799i	$-0.609134\pi$
$733$	443.921	−	443.921i	0.605622	−	0.605622i	0.941799	+	0.336177i	$0.109134\pi$
$734$		−	37.9927i		−	0.0517612i
$735$		0			0
$736$	−1266.62			−1.72096
$737$	0.733713	+	0.733713i	0.000995540	+	0.000995540i
$738$		0			0
$739$			1212.42i			1.64062i	0.571922	+	0.820308i	$0.306198\pi$
$739$			1212.42i			1.64062i	−0.571922	+	0.820308i	$0.693802\pi$
$740$	822.708	+	133.867i	1.11177	+	0.180902i
$741$		0			0
$742$	237.304	+	237.304i	0.319817	+	0.319817i
$743$	−482.125	+	482.125i	−0.648889	+	0.648889i	−0.952725	−	0.303835i	$-0.901733\pi$
$743$	−482.125	+	482.125i	−0.648889	+	0.648889i	0.303835	+	0.952725i	$0.401733\pi$
$744$		0			0
$745$	596.488	−	429.538i	0.800655	−	0.576561i
$746$	−49.4335			−0.0662647
$747$		0			0
$748$	−99.4670	+	99.4670i	−0.132977	+	0.132977i
$749$		−	2143.29i		−	2.86154i
$750$		0			0
$751$	−271.762			−0.361867			−0.180934	−	0.983495i	$-0.557912\pi$
$751$	−271.762			−0.361867			−0.180934	+	0.983495i	$0.557912\pi$
$752$	−130.873	−	130.873i	−0.174033	−	0.174033i
$753$		0			0
$754$			81.8170i			0.108511i
$755$	−293.093	−	407.010i	−0.388202	−	0.539086i
$756$		0			0
$757$	998.012	+	998.012i	1.31838	+	1.31838i	0.915060	+	0.403318i	$0.132143\pi$
$757$	998.012	+	998.012i	1.31838	+	1.31838i	0.403318	+	0.915060i	$0.367857\pi$
$758$	75.8038	−	75.8038i	0.100005	−	0.100005i
$759$		0			0
$760$	32.6228	−	200.490i	0.0429248	−	0.263803i
$761$	652.825			0.857851			0.428925	−	0.903340i	$-0.358892\pi$
$761$	652.825			0.857851			0.428925	+	0.903340i	$0.358892\pi$
$762$		0			0
$763$	1101.62	−	1101.62i	1.44380	−	1.44380i
$764$		−	669.555i		−	0.876381i
$765$		0			0
$766$	−555.260			−0.724883
$767$	1211.15	+	1211.15i	1.57907	+	1.57907i
$768$		0			0
$769$			691.281i			0.898935i	0.893297	+	0.449468i	$0.148386\pi$
$769$			691.281i			0.898935i	−0.893297	+	0.449468i	$0.851614\pi$
$770$	167.001	−	120.259i	0.216884	−	0.156181i
$771$		0			0
$772$	465.887	+	465.887i	0.603480	+	0.603480i
$773$	−109.539	+	109.539i	−0.141706	+	0.141706i	−0.774401	−	0.632695i	$-0.781949\pi$
$773$	−109.539	+	109.539i	−0.141706	+	0.141706i	0.632695	+	0.774401i	$0.281949\pi$
$774$		0			0
$775$	−79.4899	+	237.793i	−0.102568	+	0.306830i
$776$	170.624			0.219876
$777$		0			0
$778$	359.148	−	359.148i	0.461630	−	0.461630i
$779$			294.561i			0.378127i
$780$		0			0
$781$	−259.537			−0.332314
$782$	441.982	+	441.982i	0.565194	+	0.565194i
$783$		0			0
$784$		−	261.848i		−	0.333990i
$785$	140.612	−	864.159i	0.179124	−	1.10084i
$786$		0			0
$787$	265.219	+	265.219i	0.337000	+	0.337000i	0.855237	−	0.518237i	$-0.173412\pi$
$787$	265.219	+	265.219i	0.337000	+	0.337000i	−0.518237	+	0.855237i	$0.673412\pi$
$788$	483.210	−	483.210i	0.613210	−	0.613210i
$789$		0			0
$790$	226.012	+	36.7757i	0.286092	+	0.0465515i
$791$	1726.87			2.18315
$792$		0			0
$793$	19.3370	−	19.3370i	0.0243846	−	0.0243846i
$794$			67.7016i			0.0852665i
$795$		0			0
$796$	217.750			0.273555
$797$	−90.0704	−	90.0704i	−0.113012	−	0.113012i	0.648340	−	0.761351i	$-0.275464\pi$
$797$	−90.0704	−	90.0704i	−0.113012	−	0.113012i	−0.761351	+	0.648340i	$0.775464\pi$
$798$		0			0
$799$			865.304i			1.08298i
$800$	741.434	−	369.927i	0.926793	−	0.462409i
$801$		0			0
$802$	−26.5637	−	26.5637i	−0.0331218	−	0.0331218i
$803$	−134.217	+	134.217i	−0.167145	+	0.167145i
$804$		0			0
$805$	1274.86	+	1770.37i	1.58368	+	2.19921i
$806$	−247.921			−0.307594
$807$		0			0
$808$	304.188	−	304.188i	0.376470	−	0.376470i
$809$		−	95.4868i		−	0.118031i	−0.998257	−	0.0590153i	$-0.981204\pi$
$809$		−	95.4868i		−	0.118031i	0.998257	−	0.0590153i	$-0.0187961\pi$
$810$		0			0
$811$	746.247			0.920157			0.460078	−	0.887878i	$-0.347821\pi$
$811$	746.247			0.920157			0.460078	+	0.887878i	$0.347821\pi$
$812$	−75.3130	−	75.3130i	−0.0927500	−	0.0927500i
$813$		0			0
$814$		−	213.218i		−	0.261938i
$815$	−604.617	−	98.3805i	−0.741861	−	0.120712i
$816$		0			0
$817$	131.771	+	131.771i	0.161287	+	0.161287i
$818$	−12.1934	+	12.1934i	−0.0149063	+	0.0149063i
$819$		0			0
$820$	−614.551	+	442.545i	−0.749453	+	0.539689i
$821$	318.502			0.387944			0.193972	−	0.981007i	$-0.437863\pi$
$821$	318.502			0.387944			0.193972	+	0.981007i	$0.437863\pi$
$822$		0			0
$823$	−491.401	+	491.401i	−0.597085	+	0.597085i	−0.939536	−	0.342451i	$-0.888743\pi$
$823$	−491.401	+	491.401i	−0.597085	+	0.597085i	0.342451	+	0.939536i	$0.388743\pi$
$824$		−	109.326i		−	0.132677i
$825$		0			0
$826$	934.620			1.13150
$827$	612.865	+	612.865i	0.741071	+	0.741071i	0.972784	−	0.231713i	$-0.0744332\pi$
$827$	612.865	+	612.865i	0.741071	+	0.741071i	−0.231713	+	0.972784i	$0.574433\pi$
$828$		0			0
$829$			164.834i			0.198835i	0.995046	+	0.0994176i	$0.0316980\pi$
$829$			164.834i			0.198835i	−0.995046	+	0.0994176i	$0.968302\pi$
$830$	−42.4663	−	58.9718i	−0.0511642	−	0.0710504i
$831$		0			0
$832$	372.306	+	372.306i	0.447483	+	0.447483i
$833$	−865.643	+	865.643i	−1.03919	+	1.03919i
$834$		0			0
$835$	−37.1704	+	228.438i	−0.0445154	+	0.273578i
$836$	51.2418			0.0612940
$837$		0			0
$838$	−587.557	+	587.557i	−0.701142	+	0.701142i
$839$			644.662i			0.768369i	0.923256	+	0.384184i	$0.125517\pi$
$839$			644.662i			0.768369i	−0.923256	+	0.384184i	$0.874483\pi$
$840$		0			0
$841$	830.046			0.986975
$842$	−295.577	−	295.577i	−0.351041	−	0.351041i
$843$		0			0
$844$			980.566i			1.16181i
$845$	1412.97	−	1017.50i	1.67215	−	1.20414i
$846$		0			0
$847$	88.8058	+	88.8058i	0.104848	+	0.104848i
$848$	−61.5463	+	61.5463i	−0.0725782	+	0.0725782i
$849$		0			0
$850$	−387.803	−	129.636i	−0.456239	−	0.152512i
$851$	2260.31			2.65606
$852$		0			0
$853$	237.329	−	237.329i	0.278229	−	0.278229i	−0.554173	−	0.832402i	$-0.686965\pi$
$853$	237.329	−	237.329i	0.278229	−	0.278229i	0.832402	+	0.554173i	$0.186965\pi$
$854$		−	14.9219i		−	0.0174730i
$855$		0			0
$856$	−1391.28			−1.62533
$857$	644.178	+	644.178i	0.751666	+	0.751666i	0.974790	−	0.223124i	$-0.0716254\pi$
$857$	644.178	+	644.178i	0.751666	+	0.751666i	−0.223124	+	0.974790i	$0.571625\pi$
$858$		0			0
$859$			355.700i			0.414086i	0.978332	+	0.207043i	$0.0663841\pi$
$859$			355.700i			0.414086i	−0.978332	+	0.207043i	$0.933616\pi$
$860$	−76.9466	+	472.890i	−0.0894728	+	0.549873i
$861$		0			0
$862$	181.053	+	181.053i	0.210038	+	0.210038i
$863$	−266.848	+	266.848i	−0.309210	+	0.309210i	−0.844603	−	0.535393i	$-0.820164\pi$
$863$	−266.848	+	266.848i	−0.309210	+	0.309210i	0.535393	+	0.844603i	$0.320164\pi$
$864$		0			0
$865$	−236.951	−	38.5556i	−0.273932	−	0.0445730i
$866$	188.042			0.217138
$867$		0			0
$868$	228.212	−	228.212i	0.262918	−	0.262918i
$869$			139.742i			0.160808i
$870$		0			0
$871$	7.11527			0.00816908
$872$	−715.100	−	715.100i	−0.820069	−	0.820069i
$873$		0			0
$874$		−	227.693i		−	0.260518i
$875$	−1263.30	−	663.973i	−1.44378	−	0.758827i
$876$		0			0
$877$	849.238	+	849.238i	0.968344	+	0.968344i	0.999514	−	0.0311697i	$-0.00992322\pi$
$877$	849.238	+	849.238i	0.968344	+	0.968344i	−0.0311697	+	0.999514i	$0.509923\pi$
$878$	−447.176	+	447.176i	−0.509312	+	0.509312i
$879$		0			0
$880$	31.1900	+	43.3127i	0.0354431	+	0.0492190i
$881$	−371.329			−0.421485			−0.210743	−	0.977542i	$-0.567588\pi$
$881$	−371.329			−0.421485			−0.210743	+	0.977542i	$0.567588\pi$
$882$		0			0
$883$	−114.399	+	114.399i	−0.129558	+	0.129558i	−0.768912	−	0.639354i	$-0.779202\pi$
$883$	−114.399	+	114.399i	−0.129558	+	0.129558i	0.639354	+	0.768912i	$0.279202\pi$
$884$			964.593i			1.09117i
$885$		0			0
$886$	−104.683			−0.118152
$887$	428.972	+	428.972i	0.483622	+	0.483622i	0.906286	−	0.422665i	$-0.138905\pi$
$887$	428.972	+	428.972i	0.483622	+	0.483622i	−0.422665	+	0.906286i	$0.638905\pi$
$888$		0			0
$889$		−	2169.01i		−	2.43983i
$890$	6.65782	+	1.08333i	0.00748069	+	0.00121722i
$891$		0			0
$892$	−790.579	−	790.579i	−0.886299	−	0.886299i
$893$	222.886	−	222.886i	0.249593	−	0.249593i
$894$		0			0
$895$	111.660	−	80.4079i	0.124760	−	0.0898412i
$896$	−1226.35			−1.36870
$897$		0			0
$898$	−220.482	+	220.482i	−0.245526	+	0.245526i
$899$		−	33.1936i		−	0.0369228i
$900$		0			0
$901$	406.931			0.451644
$902$	136.981	+	136.981i	0.151864	+	0.151864i
$903$		0			0
$904$		−	1120.97i		−	1.24001i
$905$	−742.984	−	1031.76i	−0.820977	−	1.14007i
$906$		0			0
$907$	124.993	+	124.993i	0.137810	+	0.137810i	0.772646	−	0.634837i	$-0.218933\pi$
$907$	124.993	+	124.993i	0.137810	+	0.137810i	−0.634837	+	0.772646i	$0.718933\pi$
$908$	−179.145	+	179.145i	−0.197296	+	0.197296i
$909$		0			0
$910$	226.641	−	1392.87i	0.249056	−	1.53062i
$911$	−950.607			−1.04348			−0.521738	−	0.853106i	$-0.674716\pi$
$911$	−950.607			−1.04348			−0.521738	+	0.853106i	$0.674716\pi$
$912$		0			0
$913$	31.3594	−	31.3594i	0.0343476	−	0.0343476i
$914$		−	127.512i		−	0.139510i
$915$		0			0
$916$	734.795			0.802178
$917$	331.777	+	331.777i	0.361807	+	0.361807i
$918$		0			0
$919$			883.245i			0.961093i	0.876969	+	0.480547i	$0.159562\pi$
$919$			883.245i			0.961093i	−0.876969	+	0.480547i	$0.840438\pi$
$920$	1149.20	−	827.554i	1.24913	−	0.899515i
$921$		0			0
$922$	−139.415	−	139.415i	−0.151209	−	0.151209i
$923$	−1258.45	+	1258.45i	−1.36343	+	1.36343i
$924$		0			0
$925$	−1323.10	+	660.139i	−1.43038	+	0.713663i
$926$	223.945			0.241842
$927$		0			0
$928$	−77.5676	+	77.5676i	−0.0835858	+	0.0835858i
$929$		−	48.5749i		−	0.0522872i	−0.999658	−	0.0261436i	$-0.991677\pi$
$929$		−	48.5749i		−	0.0522872i	0.999658	−	0.0261436i	$-0.00832272\pi$
$930$		0			0
$931$	445.947			0.478998
$932$	405.490	+	405.490i	0.435075	+	0.435075i
$933$		0			0
$934$			982.791i			1.05224i
$935$	40.0765	−	246.298i	0.0428626	−	0.263421i
$936$		0			0
$937$	−151.449	−	151.449i	−0.161632	−	0.161632i	0.621658	−	0.783289i	$-0.286460\pi$
$937$	−151.449	−	151.449i	−0.161632	−	0.161632i	−0.783289	+	0.621658i	$0.786460\pi$
$938$	2.74535	−	2.74535i	0.00292682	−	0.00292682i
$939$		0			0
$940$	799.877	+	130.152i	0.850933	+	0.138460i
$941$	−1424.35			−1.51365			−0.756827	−	0.653615i	$-0.773252\pi$
$941$	−1424.35			−1.51365			−0.756827	+	0.653615i	$0.773252\pi$
$942$		0			0
$943$	−1452.13	+	1452.13i	−1.53991	+	1.53991i
$944$			242.399i			0.256779i
$945$		0			0
$946$	122.557			0.129553
$947$	79.1217	+	79.1217i	0.0835498	+	0.0835498i	0.747647	−	0.664097i	$-0.231184\pi$
$947$	79.1217	+	79.1217i	0.0835498	+	0.0835498i	−0.664097	+	0.747647i	$0.731184\pi$
$948$		0			0
$949$			1301.59i			1.37154i
$950$	66.4993	+	133.283i	0.0699993	+	0.140298i
$951$		0			0
$952$	900.360	+	900.360i	0.945756	+	0.945756i
$953$	−792.426	+	792.426i	−0.831506	+	0.831506i	−0.987723	−	0.156217i	$-0.950070\pi$
$953$	−792.426	+	792.426i	−0.831506	+	0.831506i	0.156217	+	0.987723i	$0.450070\pi$
$954$		0			0
$955$	694.083	+	963.856i	0.726789	+	1.00927i
$956$	705.913			0.738402
$957$		0			0
$958$	324.660	−	324.660i	0.338893	−	0.338893i
$959$		−	2213.29i		−	2.30791i
$960$		0			0
$961$	−860.417			−0.895335
$962$	−1033.85	−	1033.85i	−1.07469	−	1.07469i
$963$		0			0
$964$		−	1143.72i		−	1.18643i
$965$	−1153.62	−	187.712i	−1.19546	−	0.194520i
$966$		0			0
$967$	−807.667	−	807.667i	−0.835230	−	0.835230i	0.152997	−	0.988227i	$-0.451108\pi$
$967$	−807.667	−	807.667i	−0.835230	−	0.835230i	−0.988227	+	0.152997i	$0.951108\pi$
$968$	57.6468	−	57.6468i	0.0595525	−	0.0595525i
$969$		0			0
$970$	−101.531	+	73.1139i	−0.104671	+	0.0753751i
$971$	226.305			0.233064			0.116532	−	0.993187i	$-0.462822\pi$
$971$	226.305			0.233064			0.116532	+	0.993187i	$0.462822\pi$
$972$		0			0
$973$	−759.509	+	759.509i	−0.780584	+	0.780584i
$974$			247.873i			0.254490i
$975$		0			0
$976$	3.87010			0.00396527
$977$	608.799	+	608.799i	0.623131	+	0.623131i	0.946331	−	0.323200i	$-0.104759\pi$
$977$	608.799	+	608.799i	0.623131	+	0.623131i	−0.323200	+	0.946331i	$0.604759\pi$
$978$		0			0
$979$			4.11650i			0.00420480i
$980$	669.987	+	930.393i	0.683660	+	0.949381i
$981$		0			0
$982$	−328.990	−	328.990i	−0.335020	−	0.335020i
$983$	997.652	−	997.652i	1.01491	−	1.01491i	0.0150182	−	0.999887i	$-0.495219\pi$
$983$	997.652	−	997.652i	1.01491	−	1.01491i	0.999887	−	0.0150182i	$-0.00478063\pi$
$984$		0			0
$985$	−194.691	+	1196.51i	−0.197656	+	1.21474i
$986$	54.1336			0.0549022
$987$		0			0
$988$	248.461	−	248.461i	0.251479	−	0.251479i
$989$			1299.22i			1.31367i
$990$		0			0
$991$	−706.711			−0.713129			−0.356564	−	0.934271i	$-0.616052\pi$
$991$	−706.711			−0.713129			−0.356564	+	0.934271i	$0.616052\pi$
$992$	−235.044	−	235.044i	−0.236940	−	0.236940i
$993$		0			0
$994$			971.118i			0.976980i
$995$	−313.461	+	225.726i	−0.315036	+	0.226861i
$996$		0			0
$997$	517.768	+	517.768i	0.519326	+	0.519326i	0.917367	−	0.398042i	$-0.130310\pi$
$997$	517.768	+	517.768i	0.519326	+	0.519326i	−0.398042	+	0.917367i	$0.630310\pi$
$998$	−5.70452	+	5.70452i	−0.00571595	+	0.00571595i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.3.j.c.397.14	yes	40
3.2	odd	2	inner	495.3.j.c.397.7	yes	40
5.3	odd	4	inner	495.3.j.c.298.14	yes	40
15.8	even	4	inner	495.3.j.c.298.7	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.3.j.c.298.7	✓	40	15.8	even	4	inner
495.3.j.c.298.14	yes	40	5.3	odd	4	inner
495.3.j.c.397.7	yes	40	3.2	odd	2	inner
495.3.j.c.397.14	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	495.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.768581 + 0.768581i) q^{2} -2.81857i q^{4} +(2.92182 + 4.05746i) q^{5} +(8.07326 + 8.07326i) q^{7} +(5.24062 - 5.24062i) q^{8} +(-0.872829 + 5.36414i) q^{10} -3.31662 q^{11} +(-16.0817 + 16.0817i) q^{13} +12.4099i q^{14} -3.21859 q^{16} +(10.6403 + 10.6403i) q^{17} -5.48150i q^{19} +(11.4362 - 8.23535i) q^{20} +(-2.54909 - 2.54909i) q^{22} +(27.0228 - 27.0228i) q^{23} +(-7.92592 + 23.7103i) q^{25} -24.7201 q^{26} +(22.7550 - 22.7550i) q^{28} -3.30973i q^{29} +10.0291 q^{31} +(-23.4362 - 23.4362i) q^{32} +16.3559i q^{34} +(-9.16829 + 56.3455i) q^{35} +(41.8222 + 41.8222i) q^{37} +(4.21298 - 4.21298i) q^{38} +(36.5757 + 5.95144i) q^{40} -53.7373 q^{41} +(-24.0393 + 24.0393i) q^{43} +9.34813i q^{44} +41.5384 q^{46} +(40.6616 + 40.6616i) q^{47} +81.3550i q^{49} +(-24.3150 + 12.1316i) q^{50} +(45.3273 + 45.3273i) q^{52} +(19.1222 - 19.1222i) q^{53} +(-9.69058 - 13.4571i) q^{55} +84.6178 q^{56} +(2.54380 - 2.54380i) q^{58} -75.3124i q^{59} -1.20242 q^{61} +(7.70818 + 7.70818i) q^{62} -23.1509i q^{64} +(-112.238 - 18.2629i) q^{65} +(-0.221223 - 0.221223i) q^{67} +(29.9904 - 29.9904i) q^{68} +(-50.3527 + 36.2595i) q^{70} +78.2535 q^{71} +(40.4681 - 40.4681i) q^{73} +64.2875i q^{74} -15.4500 q^{76} +(-26.7760 - 26.7760i) q^{77} -42.1339i q^{79} +(-9.40413 - 13.0593i) q^{80} +(-41.3015 - 41.3015i) q^{82} +(-9.45520 + 9.45520i) q^{83} +(-12.0835 + 74.2617i) q^{85} -36.9523 q^{86} +(-17.3812 + 17.3812i) q^{88} -1.24117i q^{89} -259.663 q^{91} +(-76.1655 - 76.1655i) q^{92} +62.5034i q^{94} +(22.2410 - 16.0160i) q^{95} +(16.2790 + 16.2790i) q^{97} +(-62.5279 + 62.5279i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{10} - 88 q^{13} - 296 q^{16} + 168 q^{25} + 248 q^{28} - 32 q^{31} - 24 q^{37} + 296 q^{40} - 48 q^{43} + 48 q^{46} + 64 q^{52} + 104 q^{58} + 576 q^{61} - 544 q^{67} - 1048 q^{70} - 408 q^{73}+ \cdots + 712 q^{97}+O(q^{100}) \) 40 * q + 24 * q^10 - 88 * q^13 - 296 * q^16 + 168 * q^25 + 248 * q^28 - 32 * q^31 - 24 * q^37 + 296 * q^40 - 48 * q^43 + 48 * q^46 + 64 * q^52 + 104 * q^58 + 576 * q^61 - 544 * q^67 - 1048 * q^70 - 408 * q^73 - 96 * q^76 - 280 * q^82 + 160 * q^85 + 264 * q^88 + 528 * q^91 + 712 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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