LMFDB - Embedded newform 1020.3.bc.a.701.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1020,3,Mod(701,1020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1020, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 0, 3]))

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

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

chi := DirichletCharacter("1020.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1020.bc (of order $4$, degree $2$, 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:	$27.7929869648$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			701.17
Character	$\chi$	$=$	1020.701
Dual form			1020.3.bc.a.761.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23515 - 2.73394i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-3.40115 - 3.40115i) q^{7} +(-5.94881 + 6.75364i) q^{9} +O(q^{10})$	\(q+(-1.23515 - 2.73394i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-3.40115 - 3.40115i) q^{7} +(-5.94881 + 6.75364i) q^{9} +(-6.68330 + 6.68330i) q^{11} -15.8950 q^{13} +(2.36979 - 6.27568i) q^{15} +(16.0006 + 5.74283i) q^{17} -9.36536i q^{19} +(-5.09760 + 13.4995i) q^{21} +(18.2346 - 18.2346i) q^{23} +5.00000i q^{25} +(25.8117 + 7.92192i) q^{27} +(37.2023 + 37.2023i) q^{29} +(-4.34120 + 4.34120i) q^{31} +(26.5266 + 10.0168i) q^{33} -10.7554i q^{35} +(3.75111 - 3.75111i) q^{37} +(19.6327 + 43.4558i) q^{39} +(-22.1735 + 22.1735i) q^{41} +24.6675i q^{43} +(-20.0843 + 1.27254i) q^{45} -17.0190i q^{47} -25.8643i q^{49} +(-4.06262 - 50.8379i) q^{51} +66.1749 q^{53} -21.1344 q^{55} +(-25.6043 + 11.5676i) q^{57} +56.5082 q^{59} +(-1.23922 - 1.23922i) q^{61} +(43.2030 - 2.73734i) q^{63} +(-25.1322 - 25.1322i) q^{65} +47.5698 q^{67} +(-72.3745 - 27.3297i) q^{69} +(35.3401 + 35.3401i) q^{71} +(-31.7795 + 31.7795i) q^{73} +(13.6697 - 6.17575i) q^{75} +45.4618 q^{77} +(-72.8403 - 72.8403i) q^{79} +(-10.2233 - 80.3523i) q^{81} +32.3295 q^{83} +(16.2190 + 34.3794i) q^{85} +(55.7583 - 147.659i) q^{87} +141.035i q^{89} +(54.0612 + 54.0612i) q^{91} +(17.2306 + 6.50654i) q^{93} +(14.8079 - 14.8079i) q^{95} +(33.1883 - 33.1883i) q^{97} +(-5.37890 - 84.8942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 8 q^{3}+O(q^{10}) $ 96 * q - 8 * q^3	$ 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) $ 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.23515	−	2.73394i	−0.411717	−	0.911312i
$3$	−1.23515	−	2.73394i	−0.411717	−	0.911312i
$4$		0			0
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$5$	1.58114	+	1.58114i	0.316228	+	0.316228i
$6$		0			0
$7$	−3.40115	−	3.40115i	−0.485879	−	0.485879i	0.421124	−	0.907003i	$-0.361636\pi$
$7$	−3.40115	−	3.40115i	−0.485879	−	0.485879i	−0.907003	+	0.421124i	$0.861636\pi$
$8$		0			0
$9$	−5.94881	+	6.75364i	−0.660979	+	0.750404i
$10$		0			0
$11$	−6.68330	+	6.68330i	−0.607572	+	0.607572i	−0.942311	−	0.334739i	$-0.891352\pi$
$11$	−6.68330	+	6.68330i	−0.607572	+	0.607572i	0.334739	+	0.942311i	$0.391352\pi$
$12$		0			0
$13$	−15.8950			−1.22269			−0.611345	−	0.791364i	$-0.709371\pi$
$13$	−15.8950			−1.22269			−0.611345	+	0.791364i	$0.709371\pi$
$14$		0			0
$15$	2.36979	−	6.27568i	0.157986	−	0.418378i
$16$		0			0
$17$	16.0006	+	5.74283i	0.941213	+	0.337814i
$17$	16.0006	+	5.74283i	0.941213	+	0.337814i
$18$		0			0
$19$		−	9.36536i		−	0.492914i	−0.969154	−	0.246457i	$-0.920734\pi$
$19$		−	9.36536i		−	0.492914i	0.969154	−	0.246457i	$-0.0792664\pi$
$20$		0			0
$21$	−5.09760	+	13.4995i	−0.242743	+	0.642832i
$22$		0			0
$23$	18.2346	−	18.2346i	0.792807	−	0.792807i	−0.189143	−	0.981950i	$-0.560571\pi$
$23$	18.2346	−	18.2346i	0.792807	−	0.792807i	0.981950	+	0.189143i	$0.0605708\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	25.8117	+	7.92192i	0.955988	+	0.293404i
$28$		0			0
$29$	37.2023	+	37.2023i	1.28284	+	1.28284i	0.939046	+	0.343790i	$0.111711\pi$
$29$	37.2023	+	37.2023i	1.28284	+	1.28284i	0.343790	+	0.939046i	$0.388289\pi$
$30$		0			0
$31$	−4.34120	+	4.34120i	−0.140039	+	0.140039i	−0.773651	−	0.633612i	$-0.781572\pi$
$31$	−4.34120	+	4.34120i	−0.140039	+	0.140039i	0.633612	+	0.773651i	$0.281572\pi$
$32$		0			0
$33$	26.5266	+	10.0168i	0.803836	+	0.303540i
$34$		0			0
$35$		−	10.7554i		−	0.307297i
$36$		0			0
$37$	3.75111	−	3.75111i	0.101381	−	0.101381i	−0.654597	−	0.755978i	$-0.727162\pi$
$37$	3.75111	−	3.75111i	0.101381	−	0.101381i	0.755978	+	0.654597i	$0.227162\pi$
$38$		0			0
$39$	19.6327	+	43.4558i	0.503402	+	1.11425i
$40$		0			0
$41$	−22.1735	+	22.1735i	−0.540818	+	0.540818i	−0.923769	−	0.382951i	$-0.874908\pi$
$41$	−22.1735	+	22.1735i	−0.540818	+	0.540818i	0.382951	+	0.923769i	$0.374908\pi$
$42$		0			0
$43$			24.6675i			0.573664i	0.957981	+	0.286832i	$0.0926021\pi$
$43$			24.6675i			0.573664i	−0.957981	+	0.286832i	$0.907398\pi$
$44$		0			0
$45$	−20.0843	+	1.27254i	−0.446319	+	0.0282788i
$46$		0			0
$47$		−	17.0190i		−	0.362106i	−0.983473	−	0.181053i	$-0.942049\pi$
$47$		−	17.0190i		−	0.362106i	0.983473	−	0.181053i	$-0.0579506\pi$
$48$		0			0
$49$		−	25.8643i		−	0.527843i
$50$		0			0
$51$	−4.06262	−	50.8379i	−0.0796592	−	0.996822i
$52$		0			0
$53$	66.1749			1.24858			0.624291	−	0.781192i	$-0.285388\pi$
$53$	66.1749			1.24858			0.624291	+	0.781192i	$0.285388\pi$
$54$		0			0
$55$	−21.1344			−0.384263
$56$		0			0
$57$	−25.6043	+	11.5676i	−0.449198	+	0.202941i
$58$		0			0
$59$	56.5082			0.957767			0.478883	−	0.877879i	$-0.341042\pi$
$59$	56.5082			0.957767			0.478883	+	0.877879i	$0.341042\pi$
$60$		0			0
$61$	−1.23922	−	1.23922i	−0.0203151	−	0.0203151i	0.696876	−	0.717191i	$-0.254573\pi$
$61$	−1.23922	−	1.23922i	−0.0203151	−	0.0203151i	−0.717191	+	0.696876i	$0.754573\pi$
$62$		0			0
$63$	43.2030	−	2.73734i	0.685762	−	0.0434499i
$64$		0			0
$65$	−25.1322	−	25.1322i	−0.386649	−	0.386649i
$66$		0			0
$67$	47.5698			0.709997			0.354998	−	0.934867i	$-0.384481\pi$
$67$	47.5698			0.709997			0.354998	+	0.934867i	$0.384481\pi$
$68$		0			0
$69$	−72.3745	−	27.3297i	−1.04891	−	0.396083i
$70$		0			0
$71$	35.3401	+	35.3401i	0.497747	+	0.497747i	0.910736	−	0.412989i	$-0.135515\pi$
$71$	35.3401	+	35.3401i	0.497747	+	0.497747i	−0.412989	+	0.910736i	$0.635515\pi$
$72$		0			0
$73$	−31.7795	+	31.7795i	−0.435336	+	0.435336i	−0.890439	−	0.455103i	$-0.849603\pi$
$73$	−31.7795	+	31.7795i	−0.435336	+	0.435336i	0.455103	+	0.890439i	$0.349603\pi$
$74$		0			0
$75$	13.6697	−	6.17575i	0.182262	−	0.0823433i
$76$		0			0
$77$	45.4618			0.590413
$78$		0			0
$79$	−72.8403	−	72.8403i	−0.922029	−	0.922029i	0.0751434	−	0.997173i	$-0.476059\pi$
$79$	−72.8403	−	72.8403i	−0.922029	−	0.922029i	−0.997173	+	0.0751434i	$0.976059\pi$
$80$		0			0
$81$	−10.2233	−	80.3523i	−0.126213	−	0.992003i
$82$		0			0
$83$	32.3295			0.389511			0.194756	−	0.980852i	$-0.437609\pi$
$83$	32.3295			0.389511			0.194756	+	0.980852i	$0.437609\pi$
$84$		0			0
$85$	16.2190	+	34.3794i	0.190812	+	0.404464i
$86$		0			0
$87$	55.7583	−	147.659i	0.640899	−	1.69723i
$88$		0			0
$89$			141.035i			1.58466i	0.610093	+	0.792330i	$0.291132\pi$
$89$			141.035i			1.58466i	−0.610093	+	0.792330i	$0.708868\pi$
$90$		0			0
$91$	54.0612	+	54.0612i	0.594080	+	0.594080i
$92$		0			0
$93$	17.2306	+	6.50654i	0.185275	+	0.0699628i
$94$		0			0
$95$	14.8079	−	14.8079i	0.155873	−	0.155873i
$96$		0			0
$97$	33.1883	−	33.1883i	0.342148	−	0.342148i	−0.515027	−	0.857174i	$-0.672218\pi$
$97$	33.1883	−	33.1883i	0.342148	−	0.342148i	0.857174	+	0.515027i	$0.172218\pi$
$98$		0			0
$99$	−5.37890	−	84.8942i	−0.0543324	−	0.857518i
$100$		0			0
$101$		−	15.5300i		−	0.153762i	−0.997040	−	0.0768810i	$-0.975504\pi$
$101$		−	15.5300i		−	0.153762i	0.997040	−	0.0768810i	$-0.0244961\pi$
$102$		0			0
$103$	173.857			1.68793			0.843967	−	0.536394i	$-0.180214\pi$
$103$	173.857			1.68793			0.843967	+	0.536394i	$0.180214\pi$
$104$		0			0
$105$	−29.4046	+	13.2845i	−0.280043	+	0.126519i
$106$		0			0
$107$	85.2326	+	85.2326i	0.796566	+	0.796566i	0.982552	−	0.185986i	$-0.0595480\pi$
$107$	85.2326	+	85.2326i	0.796566	+	0.796566i	−0.185986	+	0.982552i	$0.559548\pi$
$108$		0			0
$109$	88.5254	+	88.5254i	0.812160	+	0.812160i	0.984957	−	0.172798i	$-0.0552807\pi$
$109$	88.5254	+	88.5254i	0.812160	+	0.812160i	−0.172798	+	0.984957i	$0.555281\pi$
$110$		0			0
$111$	−14.8885	−	5.62211i	−0.134130	−	0.0506497i
$112$		0			0
$113$	−15.5934	+	15.5934i	−0.137995	+	0.137995i	−0.772730	−	0.634735i	$-0.781109\pi$
$113$	−15.5934	+	15.5934i	−0.137995	+	0.137995i	0.634735	+	0.772730i	$0.281109\pi$
$114$		0			0
$115$	57.6627			0.501415
$116$		0			0
$117$	94.5562	−	107.349i	0.808173	−	0.917512i
$118$		0			0
$119$	−34.8883	−	73.9528i	−0.293179	−	0.621452i
$120$		0			0
$121$			31.6671i			0.261712i
$122$		0			0
$123$	88.0086	+	33.2334i	0.715517	+	0.270190i
$124$		0			0
$125$	−7.90569	+	7.90569i	−0.0632456	+	0.0632456i
$126$		0			0
$127$		−	92.2512i		−	0.726388i	−0.931714	−	0.363194i	$-0.881686\pi$
$127$		−	92.2512i		−	0.726388i	0.931714	−	0.363194i	$-0.118314\pi$
$128$		0			0
$129$	67.4395	−	30.4681i	0.522786	−	0.236187i
$130$		0			0
$131$	−61.0653	−	61.0653i	−0.466147	−	0.466147i	0.434517	−	0.900664i	$-0.356919\pi$
$131$	−61.0653	−	61.0653i	−0.466147	−	0.466147i	−0.900664	+	0.434517i	$0.856919\pi$
$132$		0			0
$133$	−31.8530	+	31.8530i	−0.239497	+	0.239497i
$134$		0			0
$135$	28.2862	+	53.3375i	0.209528	+	0.395093i
$136$		0			0
$137$		−	33.2346i		−	0.242589i	−0.992617	−	0.121294i	$-0.961296\pi$
$137$		−	33.2346i		−	0.242589i	0.992617	−	0.121294i	$-0.0387045\pi$
$138$		0			0
$139$	136.159	−	136.159i	0.979559	−	0.979559i	−0.0202361	−	0.999795i	$-0.506442\pi$
$139$	136.159	−	136.159i	0.979559	−	0.979559i	0.999795	+	0.0202361i	$0.00644178\pi$
$140$		0			0
$141$	−46.5288	+	21.0210i	−0.329992	+	0.149085i
$142$		0			0
$143$	106.231	−	106.231i	0.742873	−	0.742873i
$144$		0			0
$145$			117.644i			0.811337i
$146$		0			0
$147$	−70.7114	+	31.9463i	−0.481030	+	0.217322i
$148$		0			0
$149$		−	40.6409i		−	0.272758i	−0.990657	−	0.136379i	$-0.956454\pi$
$149$		−	40.6409i		−	0.272758i	0.990657	−	0.136379i	$-0.0435465\pi$
$150$		0			0
$151$			109.162i			0.722926i	0.932386	+	0.361463i	$0.117723\pi$
$151$			109.162i			0.722926i	−0.932386	+	0.361463i	$0.882277\pi$
$152$		0			0
$153$	−133.970	+	73.8994i	−0.875619	+	0.483003i
$154$		0			0
$155$	−13.7281			−0.0885683
$156$		0			0
$157$	15.5237			0.0988771			0.0494385	−	0.998777i	$-0.484257\pi$
$157$	15.5237			0.0988771			0.0494385	+	0.998777i	$0.484257\pi$
$158$		0			0
$159$	−81.7358	−	180.918i	−0.514062	−	1.13785i
$160$		0			0
$161$	−124.037			−0.770417
$162$		0			0
$163$	15.3124	+	15.3124i	0.0939410	+	0.0939410i	0.752516	−	0.658575i	$-0.228840\pi$
$163$	15.3124	+	15.3124i	0.0939410	+	0.0939410i	−0.658575	+	0.752516i	$0.728840\pi$
$164$		0			0
$165$	26.1042	+	57.7802i	0.158207	+	0.350183i
$166$		0			0
$167$	48.7483	+	48.7483i	0.291906	+	0.291906i	0.837833	−	0.545927i	$-0.183822\pi$
$167$	48.7483	+	48.7483i	0.291906	+	0.291906i	−0.545927	+	0.837833i	$0.683822\pi$
$168$		0			0
$169$	83.6501			0.494971
$170$		0			0
$171$	63.2503	+	55.7128i	0.369885	+	0.325806i
$172$		0			0
$173$	60.3305	+	60.3305i	0.348731	+	0.348731i	0.859637	−	0.510906i	$-0.170690\pi$
$173$	60.3305	+	60.3305i	0.348731	+	0.348731i	−0.510906	+	0.859637i	$0.670690\pi$
$174$		0			0
$175$	17.0058	−	17.0058i	0.0971758	−	0.0971758i
$176$		0			0
$177$	−69.7961	−	154.490i	−0.394328	−	0.872824i
$178$		0			0
$179$	150.532			0.840960			0.420480	−	0.907302i	$-0.361862\pi$
$179$	150.532			0.840960			0.420480	+	0.907302i	$0.361862\pi$
$180$		0			0
$181$	−231.615	−	231.615i	−1.27964	−	1.27964i	−0.940868	−	0.338774i	$-0.889988\pi$
$181$	−231.615	−	231.615i	−1.27964	−	1.27964i	−0.338774	−	0.940868i	$-0.610012\pi$
$182$		0			0
$183$	−1.85733	+	4.91857i	−0.0101493	+	0.0268774i
$184$		0			0
$185$	11.8620			0.0641192
$186$		0			0
$187$	−145.318	+	68.5558i	−0.777101	+	0.366609i
$188$		0			0
$189$	−60.8459	−	114.733i	−0.321936	−	0.607054i
$190$		0			0
$191$			106.810i			0.559214i	0.960114	+	0.279607i	$0.0902042\pi$
$191$			106.810i			0.559214i	−0.960114	+	0.279607i	$0.909796\pi$
$192$		0			0
$193$	127.373	+	127.373i	0.659965	+	0.659965i	0.955372	−	0.295406i	$-0.0954550\pi$
$193$	127.373	+	127.373i	0.659965	+	0.659965i	−0.295406	+	0.955372i	$0.595455\pi$
$194$		0			0
$195$	−37.6677	+	99.7517i	−0.193168	+	0.511547i
$196$		0			0
$197$	134.138	−	134.138i	0.680902	−	0.680902i	−0.279302	−	0.960203i	$-0.590103\pi$
$197$	134.138	−	134.138i	0.680902	−	0.680902i	0.960203	+	0.279302i	$0.0901029\pi$
$198$		0			0
$199$	99.4340	−	99.4340i	0.499668	−	0.499668i	−0.411666	−	0.911335i	$-0.635053\pi$
$199$	99.4340	−	99.4340i	0.499668	−	0.499668i	0.911335	+	0.411666i	$0.135053\pi$
$200$		0			0
$201$	−58.7558	−	130.053i	−0.292317	−	0.647029i
$202$		0			0
$203$		−	253.061i		−	1.24661i
$204$		0			0
$205$	−70.1189			−0.342043
$206$		0			0
$207$	14.6757	+	231.624i	0.0708970	+	1.11895i
$208$		0			0
$209$	62.5915	+	62.5915i	0.299481	+	0.299481i
$210$		0			0
$211$	−49.2465	−	49.2465i	−0.233396	−	0.233396i	0.580713	−	0.814108i	$-0.302774\pi$
$211$	−49.2465	−	49.2465i	−0.233396	−	0.233396i	−0.814108	+	0.580713i	$0.802774\pi$
$212$		0			0
$213$	52.9672	−	140.268i	0.248672	−	0.658534i
$214$		0			0
$215$	−39.0028	+	39.0028i	−0.181408	+	0.181408i
$216$		0			0
$217$	29.5302			0.136084
$218$		0			0
$219$	126.136	+	47.6307i	0.575962	+	0.217492i
$220$		0			0
$221$	−254.329	−	91.2822i	−1.15081	−	0.413041i
$222$		0			0
$223$			407.873i			1.82903i	0.404557	+	0.914513i	$0.367426\pi$
$223$			407.873i			1.82903i	−0.404557	+	0.914513i	$0.632574\pi$
$224$		0			0
$225$	−33.7682	−	29.7441i	−0.150081	−	0.132196i
$226$		0			0
$227$	−136.081	+	136.081i	−0.599476	+	0.599476i	−0.940173	−	0.340697i	$-0.889337\pi$
$227$	−136.081	+	136.081i	−0.599476	+	0.599476i	0.340697	+	0.940173i	$0.389337\pi$
$228$		0			0
$229$			429.462i			1.87538i	0.347470	+	0.937691i	$0.387041\pi$
$229$			429.462i			1.87538i	−0.347470	+	0.937691i	$0.612959\pi$
$230$		0			0
$231$	−56.1522	−	124.290i	−0.243083	−	0.538051i
$232$		0			0
$233$	118.313	+	118.313i	0.507783	+	0.507783i	0.913845	−	0.406062i	$-0.133098\pi$
$233$	118.313	+	118.313i	0.507783	+	0.507783i	−0.406062	+	0.913845i	$0.633098\pi$
$234$		0			0
$235$	26.9094	−	26.9094i	0.114508	−	0.114508i
$236$		0			0
$237$	−109.172	+	289.109i	−0.460642	+	1.21987i
$238$		0			0
$239$			275.021i			1.15071i	0.817902	+	0.575357i	$0.195137\pi$
$239$			275.021i			1.15071i	−0.817902	+	0.575357i	$0.804863\pi$
$240$		0			0
$241$	−222.005	+	222.005i	−0.921182	+	0.921182i	−0.997113	−	0.0759315i	$-0.975807\pi$
$241$	−222.005	+	222.005i	−0.921182	+	0.921182i	0.0759315	+	0.997113i	$0.475807\pi$
$242$		0			0
$243$	−207.051	+	127.197i	−0.852060	+	0.523444i
$244$		0			0
$245$	40.8951	−	40.8951i	0.166919	−	0.166919i
$246$		0			0
$247$			148.862i			0.602681i
$248$		0			0
$249$	−39.9317	−	88.3866i	−0.160368	−	0.354966i
$250$		0			0
$251$		−	100.495i		−	0.400380i	−0.979757	−	0.200190i	$-0.935844\pi$
$251$		−	100.495i		−	0.400380i	0.979757	−	0.200190i	$-0.0641559\pi$
$252$		0			0
$253$			243.734i			0.963375i
$254$		0			0
$255$	73.9583	−	86.8054i	0.290032	−	0.340413i
$256$		0			0
$257$	−469.288			−1.82602			−0.913011	−	0.407935i	$-0.866249\pi$
$257$	−469.288			−1.82602			−0.913011	+	0.407935i	$0.866249\pi$
$258$		0			0
$259$	−25.5162			−0.0985181
$260$		0			0
$261$	−472.560	+	29.9414i	−1.81057	+	0.114718i
$262$		0			0
$263$	−347.734			−1.32218			−0.661092	−	0.750305i	$-0.729907\pi$
$263$	−347.734			−1.32218			−0.661092	+	0.750305i	$0.729907\pi$
$264$		0			0
$265$	104.632	+	104.632i	0.394836	+	0.394836i
$266$		0			0
$267$	385.580	−	174.199i	1.44412	−	0.652430i
$268$		0			0
$269$	−298.586	−	298.586i	−1.10999	−	1.10999i	−0.993151	−	0.116835i	$-0.962725\pi$
$269$	−298.586	−	298.586i	−1.10999	−	1.10999i	−0.116835	−	0.993151i	$-0.537275\pi$
$270$		0			0
$271$	−180.445			−0.665849			−0.332924	−	0.942954i	$-0.608035\pi$
$271$	−180.445			−0.665849			−0.332924	+	0.942954i	$0.608035\pi$
$272$		0			0
$273$	81.0263	−	214.574i	0.296799	−	0.785984i
$274$		0			0
$275$	−33.4165	−	33.4165i	−0.121514	−	0.121514i
$276$		0			0
$277$	51.8512	−	51.8512i	0.187189	−	0.187189i	−0.607291	−	0.794480i	$-0.707744\pi$
$277$	51.8512	−	51.8512i	0.187189	−	0.187189i	0.794480	+	0.607291i	$0.207744\pi$
$278$		0			0
$279$	−3.49392	−	55.1439i	−0.0125230	−	0.197648i
$280$		0			0
$281$	−202.969			−0.722309			−0.361155	−	0.932506i	$-0.617617\pi$
$281$	−202.969			−0.722309			−0.361155	+	0.932506i	$0.617617\pi$
$282$		0			0
$283$	−6.20394	−	6.20394i	−0.0219221	−	0.0219221i	0.696061	−	0.717983i	$-0.254934\pi$
$283$	−6.20394	−	6.20394i	−0.0219221	−	0.0219221i	−0.717983	+	0.696061i	$0.754934\pi$
$284$		0			0
$285$	−58.7740	−	22.1939i	−0.206224	−	0.0778735i
$286$		0			0
$287$	150.831			0.525544
$288$		0			0
$289$	223.040	+	183.778i	0.771764	+	0.635909i
$290$		0			0
$291$	−131.727	−	49.7422i	−0.452671	−	0.170935i
$292$		0			0
$293$			269.971i			0.921403i	0.887555	+	0.460701i	$0.152402\pi$
$293$			269.971i			0.921403i	−0.887555	+	0.460701i	$0.847598\pi$
$294$		0			0
$295$	89.3474	+	89.3474i	0.302872	+	0.302872i
$296$		0			0
$297$	−225.452	+	119.563i	−0.759097	+	0.402568i
$298$		0			0
$299$	−289.838	+	289.838i	−0.969357	+	0.969357i
$300$		0			0
$301$	83.8981	−	83.8981i	0.278731	−	0.278731i
$302$		0			0
$303$	−42.4579	+	19.1818i	−0.140125	+	0.0633063i
$304$		0			0
$305$		−	3.91876i		−	0.0128484i
$306$		0			0
$307$	−147.024			−0.478906			−0.239453	−	0.970908i	$-0.576968\pi$
$307$	−147.024			−0.478906			−0.239453	+	0.970908i	$0.576968\pi$
$308$		0			0
$309$	−214.740	−	475.315i	−0.694951	−	1.53824i
$310$		0			0
$311$	194.171	+	194.171i	0.624345	+	0.624345i	0.946639	−	0.322294i	$-0.104454\pi$
$311$	194.171	+	194.171i	0.624345	+	0.624345i	−0.322294	+	0.946639i	$0.604454\pi$
$312$		0			0
$313$	302.278	+	302.278i	0.965743	+	0.965743i	0.999432	−	0.0336894i	$-0.0107257\pi$
$313$	302.278	+	302.278i	0.965743	+	0.965743i	−0.0336894	+	0.999432i	$0.510726\pi$
$314$		0			0
$315$	72.6380	+	63.9818i	0.230597	+	0.203117i
$316$		0			0
$317$	226.622	−	226.622i	0.714896	−	0.714896i	−0.252659	−	0.967555i	$-0.581305\pi$
$317$	226.622	−	226.622i	0.714896	−	0.714896i	0.967555	+	0.252659i	$0.0813051\pi$
$318$		0			0
$319$	−497.268			−1.55883
$320$		0			0
$321$	127.745	−	338.295i	0.397961	−	1.05388i
$322$		0			0
$323$	53.7837	−	149.852i	0.166513	−	0.463937i
$324$		0			0
$325$		−	79.4749i		−	0.244538i
$326$		0			0
$327$	132.681	−	351.365i	0.405751	−	1.07451i
$328$		0			0
$329$	−57.8842	+	57.8842i	−0.175940	+	0.175940i
$330$		0			0
$331$		−	184.854i		−	0.558472i	−0.960222	−	0.279236i	$-0.909919\pi$
$331$		−	184.854i		−	0.558472i	0.960222	−	0.279236i	$-0.0900812\pi$
$332$		0			0
$333$	3.01900	+	47.6483i	0.00906606	+	0.143088i
$334$		0			0
$335$	75.2144	+	75.2144i	0.224521	+	0.224521i
$336$		0			0
$337$	231.436	−	231.436i	0.686754	−	0.686754i	−0.274759	−	0.961513i	$-0.588598\pi$
$337$	231.436	−	231.436i	0.686754	−	0.686754i	0.961513	+	0.274759i	$0.0885982\pi$
$338$		0			0
$339$	61.8915	+	23.3712i	0.182571	+	0.0689415i
$340$		0			0
$341$		−	58.0271i		−	0.170167i
$342$		0			0
$343$	−254.625	+	254.625i	−0.742347	+	0.742347i
$344$		0			0
$345$	−71.2221	−	157.646i	−0.206441	−	0.456946i
$346$		0			0
$347$	−138.101	+	138.101i	−0.397985	+	0.397985i	−0.877522	−	0.479537i	$-0.840805\pi$
$347$	−138.101	+	138.101i	−0.397985	+	0.397985i	0.479537	+	0.877522i	$0.340805\pi$
$348$		0			0
$349$			515.588i			1.47733i	0.674073	+	0.738665i	$0.264543\pi$
$349$			515.588i			1.47733i	−0.674073	+	0.738665i	$0.735457\pi$
$350$		0			0
$351$	−410.276	−	125.919i	−1.16888	−	0.358743i
$352$		0			0
$353$		−	354.351i		−	1.00383i	−0.864918	−	0.501913i	$-0.832630\pi$
$353$		−	354.351i		−	1.00383i	0.864918	−	0.501913i	$-0.167370\pi$
$354$		0			0
$355$			111.755i			0.314803i
$356$		0			0
$357$	−159.090	+	186.725i	−0.445630	+	0.523040i
$358$		0			0
$359$	532.923			1.48446			0.742232	−	0.670143i	$-0.233767\pi$
$359$	532.923			1.48446			0.742232	+	0.670143i	$0.233767\pi$
$360$		0			0
$361$	273.290			0.757036
$362$		0			0
$363$	86.5758	−	39.1136i	0.238501	−	0.107751i
$364$		0			0
$365$	−100.496			−0.275331
$366$		0			0
$367$	−266.703	−	266.703i	−0.726712	−	0.726712i	0.243251	−	0.969963i	$-0.421786\pi$
$367$	−266.703	−	266.703i	−0.726712	−	0.726712i	−0.969963	+	0.243251i	$0.921786\pi$
$368$		0			0
$369$	−17.8459	−	281.658i	−0.0483628	−	0.763301i
$370$		0			0
$371$	−225.071	−	225.071i	−0.606660	−	0.606660i
$372$		0			0
$373$	258.112			0.691990			0.345995	−	0.938236i	$-0.387541\pi$
$373$	258.112			0.691990			0.345995	+	0.938236i	$0.387541\pi$
$374$		0			0
$375$	31.3784	+	11.8489i	0.0836757	+	0.0315972i
$376$		0			0
$377$	−591.329	−	591.329i	−1.56851	−	1.56851i
$378$		0			0
$379$	466.986	−	466.986i	1.23215	−	1.23215i	0.269017	−	0.963136i	$-0.413301\pi$
$379$	466.986	−	466.986i	1.23215	−	1.23215i	0.963136	−	0.269017i	$-0.0866986\pi$
$380$		0			0
$381$	−252.209	+	113.944i	−0.661966	+	0.299066i
$382$		0			0
$383$	676.746			1.76696			0.883480	−	0.468469i	$-0.155194\pi$
$383$	676.746			1.76696			0.883480	+	0.468469i	$0.155194\pi$
$384$		0			0
$385$	71.8815	+	71.8815i	0.186705	+	0.186705i
$386$		0			0
$387$	−166.596	−	146.743i	−0.430480	−	0.379180i
$388$		0			0
$389$	−603.542			−1.55152			−0.775761	−	0.631027i	$-0.782634\pi$
$389$	−603.542			−1.55152			−0.775761	+	0.631027i	$0.782634\pi$
$390$		0			0
$391$	396.482	−	187.046i	1.01402	−	0.478379i
$392$		0			0
$393$	−91.5238	+	242.373i	−0.232885	+	0.616726i
$394$		0			0
$395$		−	230.341i		−	0.583143i
$396$		0			0
$397$	195.551	+	195.551i	0.492572	+	0.492572i	0.909116	−	0.416544i	$-0.136759\pi$
$397$	195.551	+	195.551i	0.492572	+	0.492572i	−0.416544	+	0.909116i	$0.636759\pi$
$398$		0			0
$399$	126.427	+	47.7409i	0.316861	+	0.119651i
$400$		0			0
$401$	−103.092	+	103.092i	−0.257086	+	0.257086i	−0.823868	−	0.566782i	$-0.808188\pi$
$401$	−103.092	+	103.092i	−0.257086	+	0.257086i	0.566782	+	0.823868i	$0.308188\pi$
$402$		0			0
$403$	69.0033	−	69.0033i	0.171224	−	0.171224i
$404$		0			0
$405$	110.884	−	143.213i	0.273787	−	0.353611i
$406$		0			0
$407$			50.1396i			0.123193i
$408$		0			0
$409$	−449.199			−1.09828			−0.549142	−	0.835729i	$-0.685046\pi$
$409$	−449.199			−1.09828			−0.549142	+	0.835729i	$0.685046\pi$
$410$		0			0
$411$	−90.8614	+	41.0498i	−0.221074	+	0.0998778i
$412$		0			0
$413$	−192.193	−	192.193i	−0.465359	−	0.465359i
$414$		0			0
$415$	51.1174	+	51.1174i	0.123174	+	0.123174i
$416$		0			0
$417$	−540.426	−	204.073i	−1.29598	−	0.489383i
$418$		0			0
$419$	129.595	−	129.595i	0.309297	−	0.309297i	−0.535340	−	0.844637i	$-0.679816\pi$
$419$	129.595	−	129.595i	0.309297	−	0.309297i	0.844637	+	0.535340i	$0.179816\pi$
$420$		0			0
$421$	−132.726			−0.315263			−0.157631	−	0.987498i	$-0.550386\pi$
$421$	−132.726			−0.315263			−0.157631	+	0.987498i	$0.550386\pi$
$422$		0			0
$423$	114.940	+	101.243i	0.271726	+	0.239345i
$424$		0			0
$425$	−28.7142	+	80.0031i	−0.0675627	+	0.188243i
$426$		0			0
$427$			8.42956i			0.0197414i
$428$		0			0
$429$	−421.639	−	159.217i	−0.982842	−	0.371136i
$430$		0			0
$431$	−90.3653	+	90.3653i	−0.209664	+	0.209664i	−0.804125	−	0.594460i	$-0.797366\pi$
$431$	−90.3653	+	90.3653i	−0.209664	+	0.209664i	0.594460	+	0.804125i	$0.297366\pi$
$432$		0			0
$433$			358.954i			0.828993i	0.910051	+	0.414496i	$0.136042\pi$
$433$			358.954i			0.828993i	−0.910051	+	0.414496i	$0.863958\pi$
$434$		0			0
$435$	321.631	−	145.308i	0.739381	−	0.334041i
$436$		0			0
$437$	−170.773	−	170.773i	−0.390786	−	0.390786i
$438$		0			0
$439$	−390.728	+	390.728i	−0.890041	+	0.890041i	−0.994526	−	0.104485i	$-0.966680\pi$
$439$	−390.728	+	390.728i	−0.890041	+	0.890041i	0.104485	+	0.994526i	$0.466680\pi$
$440$		0			0
$441$	174.678	+	153.862i	0.396096	+	0.348893i
$442$		0			0
$443$		−	101.462i		−	0.229034i	−0.993421	−	0.114517i	$-0.963468\pi$
$443$		−	101.462i		−	0.229034i	0.993421	−	0.114517i	$-0.0365320\pi$
$444$		0			0
$445$	−222.995	+	222.995i	−0.501113	+	0.501113i
$446$		0			0
$447$	−111.110	+	50.1976i	−0.248568	+	0.112299i
$448$		0			0
$449$	−328.239	+	328.239i	−0.731045	+	0.731045i	−0.970827	−	0.239782i	$-0.922924\pi$
$449$	−328.239	+	328.239i	−0.731045	+	0.731045i	0.239782	+	0.970827i	$0.422924\pi$
$450$		0			0
$451$		−	296.385i		−	0.657172i
$452$		0			0
$453$	298.442	−	134.831i	0.658812	−	0.297641i
$454$		0			0
$455$			170.957i			0.375729i
$456$		0			0
$457$		−	556.123i		−	1.21690i	−0.793593	−	0.608449i	$-0.791792\pi$
$457$		−	556.123i		−	1.21690i	0.793593	−	0.608449i	$-0.208208\pi$
$458$		0			0
$459$	367.509	+	274.988i	0.800673	+	0.599102i
$460$		0			0
$461$	322.819			0.700259			0.350129	−	0.936701i	$-0.386138\pi$
$461$	322.819			0.700259			0.350129	+	0.936701i	$0.386138\pi$
$462$		0			0
$463$	885.611			1.91277			0.956383	−	0.292115i	$-0.0943591\pi$
$463$	885.611			1.91277			0.956383	+	0.292115i	$0.0943591\pi$
$464$		0			0
$465$	16.9562	+	37.5317i	0.0364650	+	0.0807134i
$466$		0			0
$467$	−403.791			−0.864649			−0.432324	−	0.901718i	$-0.642306\pi$
$467$	−403.791			−0.864649			−0.432324	+	0.901718i	$0.642306\pi$
$468$		0			0
$469$	−161.792	−	161.792i	−0.344973	−	0.344973i
$470$		0			0
$471$	−19.1741	−	42.4408i	−0.0407093	−	0.0901079i
$472$		0			0
$473$	−164.860	−	164.860i	−0.348542	−	0.348542i
$474$		0			0
$475$	46.8268			0.0985828
$476$		0			0
$477$	−393.662	+	446.921i	−0.825287	+	0.936942i
$478$		0			0
$479$	−155.444	−	155.444i	−0.324519	−	0.324519i	0.525979	−	0.850498i	$-0.323699\pi$
$479$	−155.444	−	155.444i	−0.324519	−	0.324519i	−0.850498	+	0.525979i	$0.823699\pi$
$480$		0			0
$481$	−59.6238	+	59.6238i	−0.123958	+	0.123958i
$482$		0			0
$483$	153.204	+	339.109i	0.317193	+	0.702090i
$484$		0			0
$485$	104.951			0.216393
$486$		0			0
$487$	241.599	+	241.599i	0.496097	+	0.496097i	0.910221	−	0.414123i	$-0.135912\pi$
$487$	241.599	+	241.599i	0.496097	+	0.496097i	−0.414123	+	0.910221i	$0.635912\pi$
$488$		0			0
$489$	22.9500	−	60.7762i	0.0469325	−	0.124287i
$490$		0			0
$491$	143.388			0.292033			0.146016	−	0.989282i	$-0.453355\pi$
$491$	143.388			0.292033			0.146016	+	0.989282i	$0.453355\pi$
$492$		0			0
$493$	381.613	+	808.906i	0.774063	+	1.64078i
$494$		0			0
$495$	125.725	−	142.734i	0.253989	−	0.288352i
$496$		0			0
$497$		−	240.394i		−	0.483690i
$498$		0			0
$499$	−285.260	−	285.260i	−0.571664	−	0.571664i	0.360930	−	0.932593i	$-0.382459\pi$
$499$	−285.260	−	285.260i	−0.571664	−	0.571664i	−0.932593	+	0.360930i	$0.882459\pi$
$500$		0			0
$501$	73.0633	−	193.486i	0.145835	−	0.386200i
$502$		0			0
$503$	−559.292	+	559.292i	−1.11191	+	1.11191i	−0.119020	+	0.992892i	$0.537975\pi$
$503$	−559.292	+	559.292i	−1.11191	+	1.11191i	−0.992892	+	0.119020i	$0.962025\pi$
$504$		0			0
$505$	24.5550	−	24.5550i	0.0486238	−	0.0486238i
$506$		0			0
$507$	−103.320	−	228.694i	−0.203788	−	0.451073i
$508$		0			0
$509$			402.687i			0.791133i	0.918437	+	0.395567i	$0.129452\pi$
$509$			402.687i			0.791133i	−0.918437	+	0.395567i	$0.870548\pi$
$510$		0			0
$511$	216.174			0.423041
$512$		0			0
$513$	74.1916	−	241.736i	0.144623	−	0.471220i
$514$		0			0
$515$	274.893	+	274.893i	0.533772	+	0.533772i
$516$		0			0
$517$	113.743	+	113.743i	0.220006	+	0.220006i
$518$		0			0
$519$	90.4225	−	239.457i	0.174225	−	0.461381i
$520$		0			0
$521$	566.737	−	566.737i	1.08779	−	1.08779i	0.0920308	−	0.995756i	$-0.470664\pi$
$521$	566.737	−	566.737i	1.08779	−	1.08779i	0.995756	−	0.0920308i	$-0.0293358\pi$
$522$		0			0
$523$	−153.194			−0.292915			−0.146457	−	0.989217i	$-0.546787\pi$
$523$	−153.194			−0.292915			−0.146457	+	0.989217i	$0.546787\pi$
$524$		0			0
$525$	−67.4973	−	25.4880i	−0.128566	−	0.0485486i
$526$		0			0
$527$	−94.3928	+	44.5311i	−0.179113	+	0.0844993i
$528$		0			0
$529$		−	135.999i		−	0.257086i
$530$		0			0
$531$	−336.157	+	381.636i	−0.633064	+	0.718712i
$532$		0			0
$533$	352.448	−	352.448i	0.661253	−	0.661253i
$534$		0			0
$535$			269.529i			0.503793i
$536$		0			0
$537$	−185.929	−	411.544i	−0.346237	−	0.766377i
$538$		0			0
$539$	172.859	+	172.859i	0.320703	+	0.320703i
$540$		0			0
$541$	603.139	−	603.139i	1.11486	−	1.11486i	0.122375	−	0.992484i	$-0.460949\pi$
$541$	603.139	−	603.139i	1.11486	−	1.11486i	0.992484	−	0.122375i	$-0.0390511\pi$
$542$		0			0
$543$	−347.142	+	919.300i	−0.639303	+	1.69300i
$544$		0			0
$545$			279.942i			0.513655i
$546$		0			0
$547$	−424.515	+	424.515i	−0.776078	+	0.776078i	−0.979161	−	0.203083i	$-0.934904\pi$
$547$	−424.515	+	424.515i	−0.776078	+	0.776078i	0.203083	+	0.979161i	$0.434904\pi$
$548$		0			0
$549$	15.7411	−	0.997359i	0.0286724	−	0.00181668i
$550$		0			0
$551$	348.413	−	348.413i	0.632328	−	0.632328i
$552$		0			0
$553$			495.482i			0.895990i
$554$		0			0
$555$	−14.6514	−	32.4301i	−0.0263989	−	0.0584326i
$556$		0			0
$557$			716.580i			1.28650i	0.765657	+	0.643249i	$0.222414\pi$
$557$			716.580i			1.28650i	−0.765657	+	0.643249i	$0.777586\pi$
$558$		0			0
$559$		−	392.090i		−	0.701413i
$560$		0			0
$561$	366.917	+	312.613i	0.654040	+	0.557243i
$562$		0			0
$563$	495.495			0.880097			0.440048	−	0.897974i	$-0.354961\pi$
$563$	495.495			0.880097			0.440048	+	0.897974i	$0.354961\pi$
$564$		0			0
$565$	−49.3106			−0.0872755
$566$		0			0
$567$	−238.519	+	308.061i	−0.420669	+	0.543318i
$568$		0			0
$569$	196.098			0.344636			0.172318	−	0.985041i	$-0.444874\pi$
$569$	196.098			0.344636			0.172318	+	0.985041i	$0.444874\pi$
$570$		0			0
$571$	−510.530	−	510.530i	−0.894098	−	0.894098i	0.100808	−	0.994906i	$-0.467857\pi$
$571$	−510.530	−	510.530i	−0.894098	−	0.894098i	−0.994906	+	0.100808i	$0.967857\pi$
$572$		0			0
$573$	292.012	−	131.926i	0.509619	−	0.230238i
$574$		0			0
$575$	91.1728	+	91.1728i	0.158561	+	0.158561i
$576$		0			0
$577$	−717.661			−1.24378			−0.621890	−	0.783105i	$-0.713635\pi$
$577$	−717.661			−1.24378			−0.621890	+	0.783105i	$0.713635\pi$
$578$		0			0
$579$	190.905	−	505.556i	0.329716	−	0.873153i
$580$		0			0
$581$	−109.957	−	109.957i	−0.189255	−	0.189255i
$582$		0			0
$583$	−442.266	+	442.266i	−0.758604	+	0.758604i
$584$		0			0
$585$	319.240	−	20.2271i	0.545709	−	0.0345762i
$586$		0			0
$587$	1127.16			1.92021			0.960105	−	0.279640i	$-0.0902151\pi$
$587$	1127.16			1.92021			0.960105	+	0.279640i	$0.0902151\pi$
$588$		0			0
$589$	40.6569	+	40.6569i	0.0690271	+	0.0690271i
$590$		0			0
$591$	−532.404	−	201.044i	−0.900853	−	0.340176i
$592$		0			0
$593$	86.8276			0.146421			0.0732105	−	0.997317i	$-0.476676\pi$
$593$	86.8276			0.146421			0.0732105	+	0.997317i	$0.476676\pi$
$594$		0			0
$595$	61.7664	−	172.093i	0.103809	−	0.289232i
$596$		0			0
$597$	−394.662	−	149.030i	−0.661075	−	0.249632i
$598$		0			0
$599$			895.776i			1.49545i	0.664007	+	0.747726i	$0.268854\pi$
$599$			895.776i			1.49545i	−0.664007	+	0.747726i	$0.731146\pi$
$600$		0			0
$601$	−735.170	−	735.170i	−1.22324	−	1.22324i	−0.966472	−	0.256773i	$-0.917341\pi$
$601$	−735.170	−	735.170i	−1.22324	−	1.22324i	−0.256773	−	0.966472i	$-0.582659\pi$
$602$		0			0
$603$	−282.984	+	321.269i	−0.469293	+	0.532785i
$604$		0			0
$605$	−50.0701	+	50.0701i	−0.0827605	+	0.0827605i
$606$		0			0
$607$	−308.131	+	308.131i	−0.507630	+	0.507630i	−0.913798	−	0.406168i	$-0.866865\pi$
$607$	−308.131	+	308.131i	−0.507630	+	0.507630i	0.406168	+	0.913798i	$0.366865\pi$
$608$		0			0
$609$	−691.853	+	312.568i	−1.13605	+	0.513249i
$610$		0			0
$611$			270.516i			0.442744i
$612$		0			0
$613$	431.738			0.704304			0.352152	−	0.935943i	$-0.385450\pi$
$613$	431.738			0.704304			0.352152	+	0.935943i	$0.385450\pi$
$614$		0			0
$615$	86.6073	+	191.700i	0.140825	+	0.311708i
$616$		0			0
$617$	205.274	+	205.274i	0.332696	+	0.332696i	0.853610	−	0.520913i	$-0.174409\pi$
$617$	205.274	+	205.274i	0.332696	+	0.332696i	−0.520913	+	0.853610i	$0.674409\pi$
$618$		0			0
$619$	706.315	+	706.315i	1.14106	+	1.14106i	0.988257	+	0.152802i	$0.0488296\pi$
$619$	706.315	+	706.315i	1.14106	+	1.14106i	0.152802	+	0.988257i	$0.451170\pi$
$620$		0			0
$621$	615.117	−	326.212i	0.990527	−	0.525301i
$622$		0			0
$623$	479.681	−	479.681i	0.769953	−	0.769953i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	93.8113	−	248.431i	0.149619	−	0.396222i
$628$		0			0
$629$	81.5621	−	38.4781i	0.129669	−	0.0611734i
$630$		0			0
$631$		−	441.576i		−	0.699804i	−0.936786	−	0.349902i	$-0.886215\pi$
$631$		−	441.576i		−	0.699804i	0.936786	−	0.349902i	$-0.113785\pi$
$632$		0			0
$633$	−73.8099	+	195.463i	−0.116603	+	0.308789i
$634$		0			0
$635$	145.862	−	145.862i	0.229704	−	0.229704i
$636$		0			0
$637$			411.112i			0.645388i
$638$		0			0
$639$	−448.905	+	28.4427i	−0.702512	+	0.0445112i
$640$		0			0
$641$	−94.9083	−	94.9083i	−0.148063	−	0.148063i	0.629189	−	0.777252i	$-0.283387\pi$
$641$	−94.9083	−	94.9083i	−0.148063	−	0.148063i	−0.777252	+	0.629189i	$0.783387\pi$
$642$		0			0
$643$	201.062	−	201.062i	0.312694	−	0.312694i	−0.533259	−	0.845952i	$-0.679033\pi$
$643$	201.062	−	201.062i	0.312694	−	0.312694i	0.845952	+	0.533259i	$0.179033\pi$
$644$		0			0
$645$	154.805	+	58.4569i	0.240008	+	0.0906308i
$646$		0			0
$647$			177.832i			0.274856i	0.990512	+	0.137428i	$0.0438835\pi$
$647$			177.832i			0.274856i	−0.990512	+	0.137428i	$0.956116\pi$
$648$		0			0
$649$	−377.661	+	377.661i	−0.581913	+	0.581913i
$650$		0			0
$651$	−36.4742	−	80.7337i	−0.0560280	−	0.124015i
$652$		0			0
$653$	688.305	−	688.305i	1.05407	−	1.05407i	0.0556131	−	0.998452i	$-0.482289\pi$
$653$	688.305	−	688.305i	1.05407	−	1.05407i	0.998452	−	0.0556131i	$-0.0177113\pi$
$654$		0			0
$655$		−	193.105i		−	0.294817i
$656$		0			0
$657$	−25.5771	−	403.678i	−0.0389301	−	0.614426i
$658$		0			0
$659$		−	373.864i		−	0.567319i	−0.958925	−	0.283660i	$-0.908451\pi$
$659$		−	373.864i		−	0.567319i	0.958925	−	0.283660i	$-0.0915486\pi$
$660$		0			0
$661$		−	241.019i		−	0.364628i	−0.983240	−	0.182314i	$-0.941641\pi$
$661$		−	241.019i		−	0.364628i	0.983240	−	0.182314i	$-0.0583587\pi$
$662$		0			0
$663$	64.5753	+	808.067i	0.0973986	+	1.21880i
$664$		0			0
$665$	−100.728			−0.151471
$666$		0			0
$667$	1356.73			2.03408
$668$		0			0
$669$	1115.10	−	503.784i	1.66681	−	0.753040i
$670$		0			0
$671$	16.5642			0.0246858
$672$		0			0
$673$	16.0911	+	16.0911i	0.0239095	+	0.0239095i	0.718960	−	0.695051i	$-0.244618\pi$
$673$	16.0911	+	16.0911i	0.0239095	+	0.0239095i	−0.695051	+	0.718960i	$0.744618\pi$
$674$		0			0
$675$	−39.6096	+	129.058i	−0.0586809	+	0.191198i
$676$		0			0
$677$	722.909	+	722.909i	1.06781	+	1.06781i	0.997527	+	0.0702855i	$0.0223910\pi$
$677$	722.909	+	722.909i	1.06781	+	1.06781i	0.0702855	+	0.997527i	$0.477609\pi$
$678$		0			0
$679$	−225.757			−0.332485
$680$		0			0
$681$	540.118	+	203.957i	0.793124	+	0.299496i
$682$		0			0
$683$	−340.626	−	340.626i	−0.498721	−	0.498721i	0.412319	−	0.911040i	$-0.364719\pi$
$683$	−340.626	−	340.626i	−0.498721	−	0.498721i	−0.911040	+	0.412319i	$0.864719\pi$
$684$		0			0
$685$	52.5486	−	52.5486i	0.0767133	−	0.0767133i
$686$		0			0
$687$	1174.12	−	530.450i	1.70906	−	0.772126i
$688$		0			0
$689$	−1051.85			−1.52663
$690$		0			0
$691$	−704.110	−	704.110i	−1.01897	−	1.01897i	−0.999817	−	0.0191555i	$-0.993902\pi$
$691$	−704.110	−	704.110i	−1.01897	−	1.01897i	−0.0191555	−	0.999817i	$-0.506098\pi$
$692$		0			0
$693$	−270.444	+	307.033i	−0.390251	+	0.443049i
$694$		0			0
$695$	430.572			0.619528
$696$		0			0
$697$	−482.129	+	227.451i	−0.691720	+	0.326329i
$698$		0			0
$699$	177.327	−	469.596i	0.253686	−	0.671811i
$700$		0			0
$701$			1099.24i			1.56810i	0.620697	+	0.784051i	$0.286850\pi$
$701$			1099.24i			1.56810i	−0.620697	+	0.784051i	$0.713150\pi$
$702$		0			0
$703$	−35.1305	−	35.1305i	−0.0499723	−	0.0499723i
$704$		0			0
$705$	−106.806	−	40.3314i	−0.151497	−	0.0572077i
$706$		0			0
$707$	−52.8198	+	52.8198i	−0.0747097	+	0.0747097i
$708$		0			0
$709$	669.744	−	669.744i	0.944632	−	0.944632i	−0.0539135	−	0.998546i	$-0.517170\pi$
$709$	669.744	−	669.744i	0.944632	−	0.944632i	0.998546	+	0.0539135i	$0.0171695\pi$
$710$		0			0
$711$	925.251	−	58.6239i	1.30134	−	0.0824528i
$712$		0			0
$713$			158.320i			0.222048i
$714$		0			0
$715$	335.931			0.469834
$716$		0			0
$717$	751.889	−	339.692i	1.04866	−	0.473768i
$718$		0			0
$719$	135.921	+	135.921i	0.189041	+	0.189041i	0.795281	−	0.606240i	$-0.207323\pi$
$719$	135.921	+	135.921i	0.189041	+	0.189041i	−0.606240	+	0.795281i	$0.707323\pi$
$720$		0			0
$721$	−591.315	−	591.315i	−0.820132	−	0.820132i
$722$		0			0
$723$	881.156	+	332.738i	1.21875	+	0.460218i
$724$		0			0
$725$	−186.011	+	186.011i	−0.256567	+	0.256567i
$726$		0			0
$727$	−828.671			−1.13985			−0.569925	−	0.821697i	$-0.693028\pi$
$727$	−828.671			−1.13985			−0.569925	+	0.821697i	$0.693028\pi$
$728$		0			0
$729$	603.487	+	408.956i	0.827828	+	0.560982i
$730$		0			0
$731$	−141.662	+	394.696i	−0.193791	+	0.539940i
$732$		0			0
$733$		−	546.632i		−	0.745747i	−0.927882	−	0.372873i	$-0.878373\pi$
$733$		−	546.632i		−	0.745747i	0.927882	−	0.372873i	$-0.121627\pi$
$734$		0			0
$735$	−162.316	−	61.2930i	−0.220838	−	0.0833918i
$736$		0			0
$737$	−317.923	+	317.923i	−0.431374	+	0.431374i
$738$		0			0
$739$		−	748.088i		−	1.01230i	−0.862446	−	0.506149i	$-0.831069\pi$
$739$		−	748.088i		−	1.01230i	0.862446	−	0.506149i	$-0.168931\pi$
$740$		0			0
$741$	406.980	−	183.867i	0.549230	−	0.248134i
$742$		0			0
$743$	−208.399	−	208.399i	−0.280484	−	0.280484i	0.552818	−	0.833302i	$-0.313552\pi$
$743$	−208.399	−	208.399i	−0.280484	−	0.280484i	−0.833302	+	0.552818i	$0.813552\pi$
$744$		0			0
$745$	64.2589	−	64.2589i	0.0862536	−	0.0862536i
$746$		0			0
$747$	−192.322	+	218.341i	−0.257459	+	0.292291i
$748$		0			0
$749$		−	579.778i		−	0.774070i
$750$		0			0
$751$	430.725	−	430.725i	0.573535	−	0.573535i	−0.359580	−	0.933114i	$-0.617080\pi$
$751$	430.725	−	430.725i	0.573535	−	0.573535i	0.933114	+	0.359580i	$0.117080\pi$
$752$		0			0
$753$	−274.748	+	124.127i	−0.364871	+	0.164843i
$754$		0			0
$755$	−172.600	+	172.600i	−0.228609	+	0.228609i
$756$		0			0
$757$		−	62.1302i		−	0.0820743i	−0.999158	−	0.0410371i	$-0.986934\pi$
$757$		−	62.1302i		−	0.0820743i	0.999158	−	0.0410371i	$-0.0130662\pi$
$758$		0			0
$759$	666.353	−	301.048i	0.877936	−	0.396638i
$760$		0			0
$761$			567.820i			0.746149i	0.927801	+	0.373075i	$0.121696\pi$
$761$			567.820i			0.746149i	−0.927801	+	0.373075i	$0.878304\pi$
$762$		0			0
$763$		−	602.177i		−	0.789223i
$764$		0			0
$765$	−328.670	−	94.9795i	−0.429634	−	0.124156i
$766$		0			0
$767$	−898.197			−1.17105
$768$		0			0
$769$	−280.257			−0.364444			−0.182222	−	0.983257i	$-0.558329\pi$
$769$	−280.257			−0.364444			−0.182222	+	0.983257i	$0.558329\pi$
$770$		0			0
$771$	579.640	+	1283.00i	0.751803	+	1.66408i
$772$		0			0
$773$	1514.10			1.95873			0.979367	−	0.202089i	$-0.0647731\pi$
$773$	1514.10			1.95873			0.979367	+	0.202089i	$0.0647731\pi$
$774$		0			0
$775$	−21.7060	−	21.7060i	−0.0280078	−	0.0280078i
$776$		0			0
$777$	31.5163	+	69.7597i	0.0405615	+	0.0897808i
$778$		0			0
$779$	207.663	+	207.663i	0.266577	+	0.266577i
$780$		0			0
$781$	−472.376			−0.604835
$782$		0			0
$783$	665.540	+	1254.97i	0.849987	+	1.60277i
$784$		0			0
$785$	24.5451	+	24.5451i	0.0312677	+	0.0312677i
$786$		0			0
$787$	463.218	−	463.218i	0.588586	−	0.588586i	−0.348662	−	0.937249i	$-0.613364\pi$
$787$	463.218	−	463.218i	0.588586	−	0.588586i	0.937249	+	0.348662i	$0.113364\pi$
$788$		0			0
$789$	429.504	+	950.683i	0.544365	+	1.20492i
$790$		0			0
$791$	106.071			0.134097
$792$		0			0
$793$	19.6974	+	19.6974i	0.0248391	+	0.0248391i
$794$		0			0
$795$	156.820	−	415.292i	0.197258	−	0.522380i
$796$		0			0
$797$	−1018.66			−1.27812			−0.639061	−	0.769156i	$-0.720677\pi$
$797$	−1018.66			−1.27812			−0.639061	+	0.769156i	$0.720677\pi$
$798$		0			0
$799$	97.7372	−	272.314i	0.122324	−	0.340819i
$800$		0			0
$801$	−952.497	−	838.989i	−1.18914	−	1.04743i
$802$		0			0
$803$		−	424.784i		−	0.528996i
$804$		0			0
$805$	−196.120	−	196.120i	−0.243627	−	0.243627i
$806$		0			0
$807$	−447.517	+	1185.11i	−0.554544	+	1.46854i
$808$		0			0
$809$	−41.1120	+	41.1120i	−0.0508183	+	0.0508183i	−0.732059	−	0.681241i	$-0.761441\pi$
$809$	−41.1120	+	41.1120i	−0.0508183	+	0.0508183i	0.681241	+	0.732059i	$0.261441\pi$
$810$		0			0
$811$	518.776	−	518.776i	0.639674	−	0.639674i	−0.310801	−	0.950475i	$-0.600597\pi$
$811$	518.776	−	518.776i	0.639674	−	0.639674i	0.950475	+	0.310801i	$0.100597\pi$
$812$		0			0
$813$	222.877	+	493.325i	0.274141	+	0.606796i
$814$		0			0
$815$			48.4220i			0.0594135i
$816$		0			0
$817$	231.020			0.282767
$818$		0			0
$819$	−686.710	+	43.5100i	−0.838474	+	0.0531258i
$820$		0			0
$821$	634.532	+	634.532i	0.772877	+	0.772877i	0.978608	−	0.205732i	$-0.0659574\pi$
$821$	634.532	+	634.532i	0.772877	+	0.772877i	−0.205732	+	0.978608i	$0.565957\pi$
$822$		0			0
$823$	−355.730	−	355.730i	−0.432236	−	0.432236i	0.457153	−	0.889388i	$-0.348869\pi$
$823$	−355.730	−	355.730i	−0.432236	−	0.432236i	−0.889388	+	0.457153i	$0.848869\pi$
$824$		0			0
$825$	−50.0842	+	132.633i	−0.0607081	+	0.160767i
$826$		0			0
$827$	876.393	−	876.393i	1.05973	−	1.05973i	0.0616267	−	0.998099i	$-0.480371\pi$
$827$	876.393	−	876.393i	1.05973	−	1.05973i	0.998099	−	0.0616267i	$-0.0196288\pi$
$828$		0			0
$829$	471.985			0.569342			0.284671	−	0.958625i	$-0.408116\pi$
$829$	471.985			0.569342			0.284671	+	0.958625i	$0.408116\pi$
$830$		0			0
$831$	−205.802	−	77.7139i	−0.247656	−	0.0935186i
$832$		0			0
$833$	148.534	−	413.845i	0.178313	−	0.496813i
$834$		0			0
$835$			154.156i			0.184618i
$836$		0			0
$837$	−146.444	+	77.6631i	−0.174963	+	0.0927875i
$838$		0			0
$839$	−426.491	+	426.491i	−0.508332	+	0.508332i	−0.914014	−	0.405682i	$-0.867034\pi$
$839$	−426.491	+	426.491i	−0.508332	+	0.508332i	0.405682	+	0.914014i	$0.367034\pi$
$840$		0			0
$841$			1927.02i			2.29134i
$842$		0			0
$843$	250.697	+	554.904i	0.297387	+	0.658249i
$844$		0			0
$845$	132.262	+	132.262i	0.156524	+	0.156524i
$846$		0			0
$847$	107.705	−	107.705i	0.127160	−	0.127160i
$848$		0			0
$849$	−9.29838	+	24.6240i	−0.0109522	+	0.0290035i
$850$		0			0
$851$		−	136.800i		−	0.160752i
$852$		0			0
$853$	984.717	−	984.717i	1.15442	−	1.15442i	0.168759	−	0.985657i	$-0.446024\pi$
$853$	984.717	−	984.717i	1.15442	−	1.15442i	0.985657	−	0.168759i	$-0.0539760\pi$
$854$		0			0
$855$	11.9178	+	188.097i	0.0139390	+	0.219997i
$856$		0			0
$857$	233.487	−	233.487i	0.272447	−	0.272447i	−0.557638	−	0.830084i	$-0.688292\pi$
$857$	233.487	−	233.487i	0.272447	−	0.272447i	0.830084	+	0.557638i	$0.188292\pi$
$858$		0			0
$859$		−	596.880i		−	0.694854i	−0.937707	−	0.347427i	$-0.887055\pi$
$859$		−	596.880i		−	0.694854i	0.937707	−	0.347427i	$-0.112945\pi$
$860$		0			0
$861$	−186.299	−	412.363i	−0.216375	−	0.478935i
$862$		0			0
$863$		−	1304.23i		−	1.51127i	−0.654994	−	0.755634i	$-0.727329\pi$
$863$		−	1304.23i		−	1.51127i	0.654994	−	0.755634i	$-0.272671\pi$
$864$		0			0
$865$			190.782i			0.220557i
$866$		0			0
$867$	226.949	−	836.769i	0.261764	−	0.965132i
$868$		0			0
$869$	973.627			1.12040
$870$		0			0
$871$	−756.120			−0.868106
$872$		0			0
$873$	26.7109	+	421.573i	0.0305967	+	0.482901i
$874$		0			0
$875$	53.7770			0.0614594
$876$		0			0
$877$	−809.030	−	809.030i	−0.922497	−	0.922497i	0.0747086	−	0.997205i	$-0.476197\pi$
$877$	−809.030	−	809.030i	−0.922497	−	0.922497i	−0.997205	+	0.0747086i	$0.976197\pi$
$878$		0			0
$879$	738.083	−	333.455i	0.839685	−	0.379357i
$880$		0			0
$881$	−1191.37	−	1191.37i	−1.35229	−	1.35229i	−0.883090	−	0.469204i	$-0.844541\pi$
$881$	−1191.37	−	1191.37i	−1.35229	−	1.35229i	−0.469204	−	0.883090i	$-0.655459\pi$
$882$		0			0
$883$	−1644.44			−1.86233			−0.931167	−	0.364593i	$-0.881208\pi$
$883$	−1644.44			−1.86233			−0.931167	+	0.364593i	$0.881208\pi$
$884$		0			0
$885$	133.913	−	354.627i	0.151314	−	0.400709i
$886$		0			0
$887$	51.8651	+	51.8651i	0.0584725	+	0.0584725i	0.735738	−	0.677266i	$-0.236835\pi$
$887$	51.8651	+	51.8651i	0.0584725	+	0.0584725i	−0.677266	+	0.735738i	$0.736835\pi$
$888$		0			0
$889$	−313.761	+	313.761i	−0.352937	+	0.352937i
$890$		0			0
$891$	605.343	+	468.693i	0.679397	+	0.526030i
$892$		0			0
$893$	−159.389			−0.178487
$894$		0			0
$895$	238.012	+	238.012i	0.265935	+	0.265935i
$896$		0			0
$897$	1150.39	+	434.405i	1.28249	+	0.484287i
$898$		0			0
$899$	−323.005			−0.359294
$900$		0			0
$901$	1058.84	+	380.031i	1.17518	+	0.421788i
$902$		0			0
$903$	−332.999	−	125.745i	−0.368769	−	0.139253i
$904$		0			0
$905$		−	732.431i		−	0.809316i
$906$		0			0
$907$	−778.493	−	778.493i	−0.858316	−	0.858316i	0.132823	−	0.991140i	$-0.457596\pi$
$907$	−778.493	−	778.493i	−0.858316	−	0.858316i	−0.991140	+	0.132823i	$0.957596\pi$
$908$		0			0
$909$	104.884	+	92.3848i	0.115384	+	0.101633i
$910$		0			0
$911$	820.678	−	820.678i	0.900854	−	0.900854i	−0.0946561	−	0.995510i	$-0.530175\pi$
$911$	820.678	−	820.678i	0.900854	−	0.900854i	0.995510	+	0.0946561i	$0.0301751\pi$
$912$		0			0
$913$	−216.067	+	216.067i	−0.236656	+	0.236656i
$914$		0			0
$915$	−10.7136	+	4.84025i	−0.0117089	+	0.00528989i
$916$		0			0
$917$			415.385i			0.452982i
$918$		0			0
$919$	−247.034			−0.268807			−0.134404	−	0.990927i	$-0.542912\pi$
$919$	−247.034			−0.268807			−0.134404	+	0.990927i	$0.542912\pi$
$920$		0			0
$921$	181.597	+	401.954i	0.197173	+	0.436433i
$922$		0			0
$923$	−561.729	−	561.729i	−0.608591	−	0.608591i
$924$		0			0
$925$	18.7555	+	18.7555i	0.0202763	+	0.0202763i
$926$		0			0
$927$	−1034.24	+	1174.17i	−1.11569	+	1.26663i
$928$		0			0
$929$	−626.205	+	626.205i	−0.674064	+	0.674064i	−0.958650	−	0.284587i	$-0.908144\pi$
$929$	−626.205	+	626.205i	−0.674064	+	0.674064i	0.284587	+	0.958650i	$0.408144\pi$
$930$		0			0
$931$	−242.229			−0.260181
$932$		0			0
$933$	291.021	−	770.683i	0.311920	−	0.826026i
$934$		0			0
$935$	−338.164	−	121.372i	−0.361673	−	0.129809i
$936$		0			0
$937$		−	916.472i		−	0.978092i	−0.872258	−	0.489046i	$-0.837345\pi$
$937$		−	916.472i		−	0.978092i	0.872258	−	0.489046i	$-0.162655\pi$
$938$		0			0
$939$	453.050	−	1199.77i	0.482481	−	1.27771i
$940$		0			0
$941$	380.878	−	380.878i	0.404759	−	0.404759i	−0.475147	−	0.879906i	$-0.657605\pi$
$941$	380.878	−	380.878i	0.404759	−	0.404759i	0.879906	+	0.475147i	$0.157605\pi$
$942$		0			0
$943$			808.649i			0.857528i
$944$		0			0
$945$	85.2033	−	277.615i	0.0901622	−	0.293772i
$946$		0			0
$947$	668.575	+	668.575i	0.705993	+	0.705993i	0.965690	−	0.259697i	$-0.0836228\pi$
$947$	668.575	+	668.575i	0.705993	+	0.705993i	−0.259697	+	0.965690i	$0.583623\pi$
$948$		0			0
$949$	505.135	−	505.135i	0.532281	−	0.532281i
$950$		0			0
$951$	−899.483	−	339.658i	−0.945828	−	0.357159i
$952$		0			0
$953$		−	306.662i		−	0.321786i	−0.986972	−	0.160893i	$-0.948563\pi$
$953$		−	306.662i		−	0.321786i	0.986972	−	0.160893i	$-0.0514374\pi$
$954$		0			0
$955$	−168.881	+	168.881i	−0.176839	+	0.176839i
$956$		0			0
$957$	614.200	+	1359.50i	0.641797	+	1.42058i
$958$		0			0
$959$	−113.036	+	113.036i	−0.117869	+	0.117869i
$960$		0			0
$961$			923.308i			0.960778i
$962$		0			0
$963$	−1082.66	+	68.5976i	−1.12426	+	0.0712332i
$964$		0			0
$965$			402.790i			0.417399i
$966$		0			0
$967$		−	1820.59i		−	1.88272i	−0.337398	−	0.941362i	$-0.609547\pi$
$967$		−	1820.59i		−	1.88272i	0.337398	−	0.941362i	$-0.390453\pi$
$968$		0			0
$969$	−476.116	+	38.0479i	−0.491347	+	0.0392651i
$970$		0			0
$971$	413.403			0.425750			0.212875	−	0.977079i	$-0.431717\pi$
$971$	413.403			0.425750			0.212875	+	0.977079i	$0.431717\pi$
$972$		0			0
$973$	−926.193			−0.951895
$974$		0			0
$975$	−217.279	+	98.1633i	−0.222850	+	0.100680i
$976$		0			0
$977$	110.227			0.112822			0.0564108	−	0.998408i	$-0.482034\pi$
$977$	110.227			0.112822			0.0564108	+	0.998408i	$0.482034\pi$
$978$		0			0
$979$	−942.577	−	942.577i	−0.962795	−	0.962795i
$980$		0			0
$981$	−1124.49	+	71.2477i	−1.14627	+	0.0726276i
$982$		0			0
$983$	−247.727	−	247.727i	−0.252011	−	0.252011i	0.569784	−	0.821795i	$-0.307027\pi$
$983$	−247.727	−	247.727i	−0.252011	−	0.252011i	−0.821795	+	0.569784i	$0.807027\pi$
$984$		0			0
$985$	424.181			0.430640
$986$		0			0
$987$	229.747	+	86.7561i	0.232773	+	0.0878987i
$988$		0			0
$989$	449.802	+	449.802i	0.454805	+	0.454805i
$990$		0			0
$991$	−434.816	+	434.816i	−0.438765	+	0.438765i	−0.891596	−	0.452831i	$-0.850414\pi$
$991$	−434.816	+	434.816i	−0.438765	+	0.438765i	0.452831	+	0.891596i	$0.350414\pi$
$992$		0			0
$993$	−505.380	+	228.323i	−0.508942	+	0.229932i
$994$		0			0
$995$	314.438			0.316018
$996$		0			0
$997$	−557.285	−	557.285i	−0.558961	−	0.558961i	0.370050	−	0.929012i	$-0.379340\pi$
$997$	−557.285	−	557.285i	−0.558961	−	0.558961i	−0.929012	+	0.370050i	$0.879340\pi$
$998$		0			0
$999$	126.538	−	67.1065i	0.126665	−	0.0671737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1020.3.bc.a.701.17	✓	96
3.2	odd	2	inner	1020.3.bc.a.701.41	yes	96
17.13	even	4	inner	1020.3.bc.a.761.41	yes	96
51.47	odd	4	inner	1020.3.bc.a.761.17	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1020.3.bc.a.701.17	✓	96	1.1	even	1	trivial
1020.3.bc.a.701.41	yes	96	3.2	odd	2	inner
1020.3.bc.a.761.17	yes	96	51.47	odd	4	inner
1020.3.bc.a.761.41	yes	96	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1020.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23515 - 2.73394i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-3.40115 - 3.40115i) q^{7} +(-5.94881 + 6.75364i) q^{9} +O(q^{10})\)	\(q+(-1.23515 - 2.73394i) q^{3} +(1.58114 + 1.58114i) q^{5} +(-3.40115 - 3.40115i) q^{7} +(-5.94881 + 6.75364i) q^{9} +(-6.68330 + 6.68330i) q^{11} -15.8950 q^{13} +(2.36979 - 6.27568i) q^{15} +(16.0006 + 5.74283i) q^{17} -9.36536i q^{19} +(-5.09760 + 13.4995i) q^{21} +(18.2346 - 18.2346i) q^{23} +5.00000i q^{25} +(25.8117 + 7.92192i) q^{27} +(37.2023 + 37.2023i) q^{29} +(-4.34120 + 4.34120i) q^{31} +(26.5266 + 10.0168i) q^{33} -10.7554i q^{35} +(3.75111 - 3.75111i) q^{37} +(19.6327 + 43.4558i) q^{39} +(-22.1735 + 22.1735i) q^{41} +24.6675i q^{43} +(-20.0843 + 1.27254i) q^{45} -17.0190i q^{47} -25.8643i q^{49} +(-4.06262 - 50.8379i) q^{51} +66.1749 q^{53} -21.1344 q^{55} +(-25.6043 + 11.5676i) q^{57} +56.5082 q^{59} +(-1.23922 - 1.23922i) q^{61} +(43.2030 - 2.73734i) q^{63} +(-25.1322 - 25.1322i) q^{65} +47.5698 q^{67} +(-72.3745 - 27.3297i) q^{69} +(35.3401 + 35.3401i) q^{71} +(-31.7795 + 31.7795i) q^{73} +(13.6697 - 6.17575i) q^{75} +45.4618 q^{77} +(-72.8403 - 72.8403i) q^{79} +(-10.2233 - 80.3523i) q^{81} +32.3295 q^{83} +(16.2190 + 34.3794i) q^{85} +(55.7583 - 147.659i) q^{87} +141.035i q^{89} +(54.0612 + 54.0612i) q^{91} +(17.2306 + 6.50654i) q^{93} +(14.8079 - 14.8079i) q^{95} +(33.1883 - 33.1883i) q^{97} +(-5.37890 - 84.8942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{3}+O(q^{10}) \) 96 * q - 8 * q^3	\( 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) \) 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Introduction

L-functions

Modular forms

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