LMFDB - Embedded newform 1020.3.bc.a.701.4

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			701.4
Character	$\chi$	$=$	1020.701
Dual form			1020.3.bc.a.761.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.91510 + 0.708668i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(-3.70850 - 3.70850i) q^{7} +(7.99558 - 4.13167i) q^{9} +O(q^{10})$	\(q+(-2.91510 + 0.708668i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(-3.70850 - 3.70850i) q^{7} +(7.99558 - 4.13167i) q^{9} +(12.0865 - 12.0865i) q^{11} +2.48655 q^{13} +(5.72968 + 3.48867i) q^{15} +(14.2170 + 9.32085i) q^{17} +6.60046i q^{19} +(13.4387 + 8.18254i) q^{21} +(-25.9693 + 25.9693i) q^{23} +5.00000i q^{25} +(-20.3799 + 17.7104i) q^{27} +(-3.09427 - 3.09427i) q^{29} +(35.6679 - 35.6679i) q^{31} +(-26.6680 + 43.7986i) q^{33} +11.7273i q^{35} +(-35.4487 + 35.4487i) q^{37} +(-7.24854 + 1.76214i) q^{39} +(-3.22686 + 3.22686i) q^{41} -57.6447i q^{43} +(-19.1749 - 6.10938i) q^{45} -54.0929i q^{47} -21.4941i q^{49} +(-48.0492 - 17.0961i) q^{51} +65.1682 q^{53} -38.2208 q^{55} +(-4.67753 - 19.2410i) q^{57} -42.8603 q^{59} +(-47.2212 - 47.2212i) q^{61} +(-44.9739 - 14.3293i) q^{63} +(-3.93158 - 3.93158i) q^{65} +101.077 q^{67} +(57.2995 - 94.1068i) q^{69} +(43.8770 + 43.8770i) q^{71} +(83.0253 - 83.0253i) q^{73} +(-3.54334 - 14.5755i) q^{75} -89.6454 q^{77} +(-104.380 - 104.380i) q^{79} +(46.8586 - 66.0702i) q^{81} -72.1519 q^{83} +(-7.74141 - 37.2165i) q^{85} +(11.2129 + 6.82730i) q^{87} +62.3777i q^{89} +(-9.22137 - 9.22137i) q^{91} +(-78.6986 + 129.252i) q^{93} +(10.4362 - 10.4362i) q^{95} +(-89.3401 + 89.3401i) q^{97} +(46.7011 - 146.576i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.91510	+	0.708668i	−0.971699	+	0.236223i
$3$	−2.91510	+	0.708668i	−0.971699	+	0.236223i
$4$		0			0
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$6$		0			0
$7$	−3.70850	−	3.70850i	−0.529786	−	0.529786i	0.390723	−	0.920508i	$-0.372225\pi$
$7$	−3.70850	−	3.70850i	−0.529786	−	0.529786i	−0.920508	+	0.390723i	$0.872225\pi$
$8$		0			0
$9$	7.99558	−	4.13167i	0.888398	−	0.459075i
$10$		0			0
$11$	12.0865	−	12.0865i	1.09877	−	1.09877i	0.104217	−	0.994555i	$-0.466766\pi$
$11$	12.0865	−	12.0865i	1.09877	−	1.09877i	0.994555	−	0.104217i	$-0.0332336\pi$
$12$		0			0
$13$	2.48655			0.191273			0.0956366	−	0.995416i	$-0.469511\pi$
$13$	2.48655			0.191273			0.0956366	+	0.995416i	$0.469511\pi$
$14$		0			0
$15$	5.72968	+	3.48867i	0.381978	+	0.232578i
$16$		0			0
$17$	14.2170	+	9.32085i	0.836291	+	0.548285i
$17$	14.2170	+	9.32085i	0.836291	+	0.548285i
$18$		0			0
$19$			6.60046i			0.347393i	0.984799	+	0.173696i	$0.0555711\pi$
$19$			6.60046i			0.347393i	−0.984799	+	0.173696i	$0.944429\pi$
$20$		0			0
$21$	13.4387	+	8.18254i	0.639940	+	0.389645i
$22$		0			0
$23$	−25.9693	+	25.9693i	−1.12910	+	1.12910i	−0.138778	+	0.990323i	$0.544318\pi$
$23$	−25.9693	+	25.9693i	−1.12910	+	1.12910i	−0.990323	+	0.138778i	$0.955682\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	−20.3799	+	17.7104i	−0.754811	+	0.655942i
$28$		0			0
$29$	−3.09427	−	3.09427i	−0.106699	−	0.106699i	0.651742	−	0.758441i	$-0.274039\pi$
$29$	−3.09427	−	3.09427i	−0.106699	−	0.106699i	−0.758441	+	0.651742i	$0.774039\pi$
$30$		0			0
$31$	35.6679	−	35.6679i	1.15058	−	1.15058i	0.164139	−	0.986437i	$-0.447516\pi$
$31$	35.6679	−	35.6679i	1.15058	−	1.15058i	0.986437	−	0.164139i	$-0.0524844\pi$
$32$		0			0
$33$	−26.6680	+	43.7986i	−0.808120	+	1.32723i
$34$		0			0
$35$			11.7273i			0.335066i
$36$		0			0
$37$	−35.4487	+	35.4487i	−0.958074	+	0.958074i	−0.999156	−	0.0410817i	$-0.986920\pi$
$37$	−35.4487	+	35.4487i	−0.958074	+	0.958074i	0.0410817	+	0.999156i	$0.486920\pi$
$38$		0			0
$39$	−7.24854	+	1.76214i	−0.185860	+	0.0451831i
$40$		0			0
$41$	−3.22686	+	3.22686i	−0.0787038	+	0.0787038i	−0.745363	−	0.666659i	$-0.767724\pi$
$41$	−3.22686	+	3.22686i	−0.0787038	+	0.0787038i	0.666659	+	0.745363i	$0.267724\pi$
$42$		0			0
$43$		−	57.6447i		−	1.34057i	−0.742102	−	0.670287i	$-0.766171\pi$
$43$		−	57.6447i		−	1.34057i	0.742102	−	0.670287i	$-0.233829\pi$
$44$		0			0
$45$	−19.1749	−	6.10938i	−0.426108	−	0.135764i
$46$		0			0
$47$		−	54.0929i		−	1.15091i	−0.817832	−	0.575457i	$-0.804824\pi$
$47$		−	54.0929i		−	1.15091i	0.817832	−	0.575457i	$-0.195176\pi$
$48$		0			0
$49$		−	21.4941i		−	0.438654i
$50$		0			0
$51$	−48.0492	−	17.0961i	−0.942141	−	0.335217i
$52$		0			0
$53$	65.1682			1.22959			0.614794	−	0.788688i	$-0.289239\pi$
$53$	65.1682			1.22959			0.614794	+	0.788688i	$0.289239\pi$
$54$		0			0
$55$	−38.2208			−0.694924
$56$		0			0
$57$	−4.67753	−	19.2410i	−0.0820620	−	0.337561i
$58$		0			0
$59$	−42.8603			−0.726446			−0.363223	−	0.931702i	$-0.618324\pi$
$59$	−42.8603			−0.726446			−0.363223	+	0.931702i	$0.618324\pi$
$60$		0			0
$61$	−47.2212	−	47.2212i	−0.774118	−	0.774118i	0.204706	−	0.978824i	$-0.434376\pi$
$61$	−47.2212	−	47.2212i	−0.774118	−	0.774118i	−0.978824	+	0.204706i	$0.934376\pi$
$62$		0			0
$63$	−44.9739	−	14.3293i	−0.713871	−	0.227449i
$64$		0			0
$65$	−3.93158	−	3.93158i	−0.0604859	−	0.0604859i
$66$		0			0
$67$	101.077			1.50861			0.754306	−	0.656523i	$-0.227974\pi$
$67$	101.077			1.50861			0.754306	+	0.656523i	$0.227974\pi$
$68$		0			0
$69$	57.2995	−	94.1068i	0.830428	−	1.36387i
$70$		0			0
$71$	43.8770	+	43.8770i	0.617986	+	0.617986i	0.945015	−	0.327028i	$-0.106047\pi$
$71$	43.8770	+	43.8770i	0.617986	+	0.617986i	−0.327028	+	0.945015i	$0.606047\pi$
$72$		0			0
$73$	83.0253	−	83.0253i	1.13733	−	1.13733i	0.148407	−	0.988926i	$-0.452586\pi$
$73$	83.0253	−	83.0253i	1.13733	−	1.13733i	0.988926	−	0.148407i	$-0.0474145\pi$
$74$		0			0
$75$	−3.54334	−	14.5755i	−0.0472445	−	0.194340i
$76$		0			0
$77$	−89.6454			−1.16423
$78$		0			0
$79$	−104.380	−	104.380i	−1.32126	−	1.32126i	−0.912757	−	0.408503i	$-0.866051\pi$
$79$	−104.380	−	104.380i	−1.32126	−	1.32126i	−0.408503	−	0.912757i	$-0.633949\pi$
$80$		0			0
$81$	46.8586	−	66.0702i	0.578501	−	0.815682i
$82$		0			0
$83$	−72.1519			−0.869300			−0.434650	−	0.900599i	$-0.643128\pi$
$83$	−72.1519			−0.869300			−0.434650	+	0.900599i	$0.643128\pi$
$84$		0			0
$85$	−7.74141	−	37.2165i	−0.0910755	−	0.437842i
$86$		0			0
$87$	11.2129	+	6.82730i	0.128884	+	0.0784747i
$88$		0			0
$89$			62.3777i			0.700873i	0.936587	+	0.350436i	$0.113967\pi$
$89$			62.3777i			0.700873i	−0.936587	+	0.350436i	$0.886033\pi$
$90$		0			0
$91$	−9.22137	−	9.22137i	−0.101334	−	0.101334i
$92$		0			0
$93$	−78.6986	+	129.252i	−0.846221	+	1.38981i
$94$		0			0
$95$	10.4362	−	10.4362i	0.109855	−	0.109855i
$96$		0			0
$97$	−89.3401	+	89.3401i	−0.921032	+	0.921032i	−0.997102	−	0.0760707i	$-0.975763\pi$
$97$	−89.3401	+	89.3401i	−0.921032	+	0.921032i	0.0760707	+	0.997102i	$0.475763\pi$
$98$		0			0
$99$	46.7011	−	146.576i	0.471728	−	1.48056i
$100$		0			0
$101$		−	78.8147i		−	0.780344i	−0.920742	−	0.390172i	$-0.872416\pi$
$101$		−	78.8147i		−	0.780344i	0.920742	−	0.390172i	$-0.127584\pi$
$102$		0			0
$103$	37.6382			0.365420			0.182710	−	0.983167i	$-0.441513\pi$
$103$	37.6382			0.365420			0.182710	+	0.983167i	$0.441513\pi$
$104$		0			0
$105$	−8.31076	−	34.1862i	−0.0791501	−	0.325583i
$106$		0			0
$107$	−101.603	−	101.603i	−0.949560	−	0.949560i	0.0492275	−	0.998788i	$-0.484324\pi$
$107$	−101.603	−	101.603i	−0.949560	−	0.949560i	−0.998788	+	0.0492275i	$0.984324\pi$
$108$		0			0
$109$	19.2118	+	19.2118i	0.176255	+	0.176255i	0.789721	−	0.613466i	$-0.210225\pi$
$109$	19.2118	+	19.2118i	0.176255	+	0.176255i	−0.613466	+	0.789721i	$0.710225\pi$
$110$		0			0
$111$	78.2151	−	128.458i	0.704641	−	1.15728i
$112$		0			0
$113$	−126.374	+	126.374i	−1.11836	+	1.11836i	−0.126373	+	0.991983i	$0.540333\pi$
$113$	−126.374	+	126.374i	−1.11836	+	1.11836i	−0.991983	+	0.126373i	$0.959667\pi$
$114$		0			0
$115$	82.1223			0.714107
$116$		0			0
$117$	19.8814	−	10.2736i	0.169927	−	0.0878087i
$118$		0			0
$119$	−18.1572	−	87.2899i	−0.152581	−	0.733529i
$120$		0			0
$121$		−	171.166i		−	1.41460i
$122$		0			0
$123$	7.11983	−	11.6934i	0.0578848	−	0.0950681i
$124$		0			0
$125$	7.90569	−	7.90569i	0.0632456	−	0.0632456i
$126$		0			0
$127$		−	185.491i		−	1.46056i	−0.683147	−	0.730281i	$-0.739389\pi$
$127$		−	185.491i		−	1.46056i	0.683147	−	0.730281i	$-0.260611\pi$
$128$		0			0
$129$	40.8509	+	168.040i	0.316674	+	1.30263i
$130$		0			0
$131$	−27.9579	−	27.9579i	−0.213419	−	0.213419i	0.592299	−	0.805718i	$-0.298220\pi$
$131$	−27.9579	−	27.9579i	−0.213419	−	0.213419i	−0.805718	+	0.592299i	$0.798220\pi$
$132$		0			0
$133$	24.4778	−	24.4778i	0.184044	−	0.184044i
$134$		0			0
$135$	60.2261	+	4.22081i	0.446119	+	0.0312652i
$136$		0			0
$137$			257.387i			1.87873i	0.342913	+	0.939367i	$0.388586\pi$
$137$			257.387i			1.87873i	−0.342913	+	0.939367i	$0.611414\pi$
$138$		0			0
$139$	−107.587	+	107.587i	−0.774007	+	0.774007i	−0.978804	−	0.204797i	$-0.934346\pi$
$139$	−107.587	+	107.587i	−0.774007	+	0.774007i	0.204797	+	0.978804i	$0.434346\pi$
$140$		0			0
$141$	38.3339	+	157.686i	0.271872	+	1.11834i
$142$		0			0
$143$	30.0537	−	30.0537i	0.210165	−	0.210165i
$144$		0			0
$145$			9.78496i			0.0674825i
$146$		0			0
$147$	15.2322	+	62.6573i	0.103620	+	0.426240i
$148$		0			0
$149$		−	54.7126i		−	0.367198i	−0.983001	−	0.183599i	$-0.941225\pi$
$149$		−	54.7126i		−	0.367198i	0.983001	−	0.183599i	$-0.0587748\pi$
$150$		0			0
$151$		−	288.939i		−	1.91350i	−0.290910	−	0.956751i	$-0.593958\pi$
$151$		−	288.939i		−	1.91350i	0.290910	−	0.956751i	$-0.406042\pi$
$152$		0			0
$153$	152.183	+	15.7858i	0.994663	+	0.103175i
$154$		0			0
$155$	−112.792			−0.727688
$156$		0			0
$157$	−185.163			−1.17938			−0.589690	−	0.807630i	$-0.700750\pi$
$157$	−185.163			−1.17938			−0.589690	+	0.807630i	$0.700750\pi$
$158$		0			0
$159$	−189.972	+	46.1826i	−1.19479	+	0.290457i
$160$		0			0
$161$	192.615			1.19636
$162$		0			0
$163$	−57.3312	−	57.3312i	−0.351725	−	0.351725i	0.509026	−	0.860751i	$-0.330006\pi$
$163$	−57.3312	−	57.3312i	−0.351725	−	0.351725i	−0.860751	+	0.509026i	$0.830006\pi$
$164$		0			0
$165$	111.417	−	27.0859i	0.675257	−	0.164157i
$166$		0			0
$167$	−161.608	−	161.608i	−0.967711	−	0.967711i	0.0317840	−	0.999495i	$-0.489881\pi$
$167$	−161.608	−	161.608i	−0.967711	−	0.967711i	−0.999495	+	0.0317840i	$0.989881\pi$
$168$		0			0
$169$	−162.817			−0.963415
$170$		0			0
$171$	27.2709	+	52.7745i	0.159479	+	0.308623i
$172$		0			0
$173$	−118.558	−	118.558i	−0.685307	−	0.685307i	0.275884	−	0.961191i	$-0.411030\pi$
$173$	−118.558	−	118.558i	−0.685307	−	0.685307i	−0.961191	+	0.275884i	$0.911030\pi$
$174$		0			0
$175$	18.5425	−	18.5425i	0.105957	−	0.105957i
$176$		0			0
$177$	124.942	−	30.3737i	0.705887	−	0.171603i
$178$		0			0
$179$	108.016			0.603441			0.301720	−	0.953396i	$-0.402439\pi$
$179$	108.016			0.603441			0.301720	+	0.953396i	$0.402439\pi$
$180$		0			0
$181$	−176.726	−	176.726i	−0.976386	−	0.976386i	0.0233414	−	0.999728i	$-0.492570\pi$
$181$	−176.726	−	176.726i	−0.976386	−	0.976386i	−0.999728	+	0.0233414i	$0.992570\pi$
$182$		0			0
$183$	171.118	+	104.190i	0.935074	+	0.569345i
$184$		0			0
$185$	112.099			0.605939
$186$		0			0
$187$	284.489	−	59.1766i	1.52133	−	0.316453i
$188$		0			0
$189$	141.258	+	9.89974i	0.747397	+	0.0523796i
$190$		0			0
$191$		−	112.767i		−	0.590405i	−0.955435	−	0.295203i	$-0.904613\pi$
$191$		−	112.767i		−	0.590405i	0.955435	−	0.295203i	$-0.0953872\pi$
$192$		0			0
$193$	61.8902	+	61.8902i	0.320675	+	0.320675i	0.849026	−	0.528351i	$-0.177190\pi$
$193$	61.8902	+	61.8902i	0.320675	+	0.320675i	−0.528351	+	0.849026i	$0.677190\pi$
$194$		0			0
$195$	14.2471	+	8.67476i	0.0730622	+	0.0444859i
$196$		0			0
$197$	165.057	−	165.057i	0.837853	−	0.837853i	−0.150723	−	0.988576i	$-0.548160\pi$
$197$	165.057	−	165.057i	0.837853	−	0.837853i	0.988576	+	0.150723i	$0.0481602\pi$
$198$		0			0
$199$	−118.658	+	118.658i	−0.596271	+	0.596271i	−0.939318	−	0.343048i	$-0.888541\pi$
$199$	−118.658	+	118.658i	−0.596271	+	0.596271i	0.343048	+	0.939318i	$0.388541\pi$
$200$		0			0
$201$	−294.649	+	71.6300i	−1.46592	+	0.356368i
$202$		0			0
$203$			22.9502i			0.113055i
$204$		0			0
$205$	10.2042			0.0497767
$206$		0			0
$207$	−100.343	+	314.937i	−0.484749	+	1.52143i
$208$		0			0
$209$	79.7763	+	79.7763i	0.381705	+	0.381705i
$210$		0			0
$211$	−103.189	−	103.189i	−0.489046	−	0.489046i	0.418959	−	0.908005i	$-0.362395\pi$
$211$	−103.189	−	103.189i	−0.489046	−	0.489046i	−0.908005	+	0.418959i	$0.862395\pi$
$212$		0			0
$213$	−159.000	−	96.8115i	−0.746479	−	0.454514i
$214$		0			0
$215$	−91.1442	+	91.1442i	−0.423927	+	0.423927i
$216$		0			0
$217$	−264.548			−1.21912
$218$		0			0
$219$	−183.189	+	300.864i	−0.836482	+	1.37381i
$220$		0			0
$221$	35.3512	+	23.1768i	0.159960	+	0.104872i
$222$		0			0
$223$			106.104i			0.475802i	0.971289	+	0.237901i	$0.0764594\pi$
$223$			106.104i			0.475802i	−0.971289	+	0.237901i	$0.923541\pi$
$224$		0			0
$225$	20.6584	+	39.9779i	0.0918149	+	0.177680i
$226$		0			0
$227$	84.8050	−	84.8050i	0.373590	−	0.373590i	−0.495193	−	0.868783i	$-0.664903\pi$
$227$	84.8050	−	84.8050i	0.373590	−	0.373590i	0.868783	+	0.495193i	$0.164903\pi$
$228$		0			0
$229$			7.33852i			0.0320460i	0.999872	+	0.0160230i	$0.00510049\pi$
$229$			7.33852i			0.0320460i	−0.999872	+	0.0160230i	$0.994900\pi$
$230$		0			0
$231$	261.325	−	63.5289i	1.13128	−	0.275017i
$232$		0			0
$233$	143.383	+	143.383i	0.615377	+	0.615377i	0.944342	−	0.328965i	$-0.106700\pi$
$233$	143.383	+	143.383i	0.615377	+	0.615377i	−0.328965	+	0.944342i	$0.606700\pi$
$234$		0			0
$235$	−85.5284	+	85.5284i	−0.363951	+	0.363951i
$236$		0			0
$237$	378.247	+	230.306i	1.59598	+	0.971755i
$238$		0			0
$239$			392.344i			1.64161i	0.571211	+	0.820803i	$0.306474\pi$
$239$			392.344i			1.64161i	−0.571211	+	0.820803i	$0.693526\pi$
$240$		0			0
$241$	−24.9345	+	24.9345i	−0.103463	+	0.103463i	−0.756943	−	0.653481i	$-0.773308\pi$
$241$	−24.9345	+	24.9345i	−0.103463	+	0.103463i	0.653481	+	0.756943i	$0.273308\pi$
$242$		0			0
$243$	−89.7755	+	225.808i	−0.369446	+	0.929252i
$244$		0			0
$245$	−33.9851	+	33.9851i	−0.138715	+	0.138715i
$246$		0			0
$247$			16.4124i			0.0664469i
$248$		0			0
$249$	210.330	−	51.1318i	0.844698	−	0.205348i
$250$		0			0
$251$		−	94.3684i		−	0.375970i	−0.982172	−	0.187985i	$-0.939804\pi$
$251$		−	94.3684i		−	0.375970i	0.982172	−	0.187985i	$-0.0601956\pi$
$252$		0			0
$253$			627.756i			2.48125i
$254$		0			0
$255$	48.9411	+	103.004i	0.191926	+	0.403936i
$256$		0			0
$257$	−21.1723			−0.0823826			−0.0411913	−	0.999151i	$-0.513115\pi$
$257$	−21.1723			−0.0823826			−0.0411913	+	0.999151i	$0.513115\pi$
$258$		0			0
$259$	262.923			1.01515
$260$		0			0
$261$	−37.5250	−	11.9560i	−0.143774	−	0.0458084i
$262$		0			0
$263$	−463.683			−1.76305			−0.881526	−	0.472136i	$-0.843483\pi$
$263$	−463.683			−1.76305			−0.881526	+	0.472136i	$0.843483\pi$
$264$		0			0
$265$	−103.040	−	103.040i	−0.388830	−	0.388830i
$266$		0			0
$267$	−44.2050	−	181.837i	−0.165562	−	0.681037i
$268$		0			0
$269$	159.593	+	159.593i	0.593283	+	0.593283i	0.938517	−	0.345234i	$-0.112200\pi$
$269$	159.593	+	159.593i	0.593283	+	0.593283i	−0.345234	+	0.938517i	$0.612200\pi$
$270$		0			0
$271$	265.026			0.977956			0.488978	−	0.872296i	$-0.337370\pi$
$271$	265.026			0.977956			0.488978	+	0.872296i	$0.337370\pi$
$272$		0			0
$273$	33.4161	+	20.3463i	0.122403	+	0.0745286i
$274$		0			0
$275$	60.4324	+	60.4324i	0.219754	+	0.219754i
$276$		0			0
$277$	20.6034	−	20.6034i	0.0743805	−	0.0743805i	−0.668938	−	0.743318i	$-0.733251\pi$
$277$	20.6034	−	20.6034i	0.0743805	−	0.0743805i	0.743318	+	0.668938i	$0.233251\pi$
$278$		0			0
$279$	137.817	−	432.553i	0.493969	−	1.55037i
$280$		0			0
$281$	468.021			1.66556			0.832778	−	0.553607i	$-0.186749\pi$
$281$	468.021			1.66556			0.832778	+	0.553607i	$0.186749\pi$
$282$		0			0
$283$	−358.375	−	358.375i	−1.26634	−	1.26634i	−0.947964	−	0.318378i	$-0.896862\pi$
$283$	−358.375	−	358.375i	−1.26634	−	1.26634i	−0.318378	−	0.947964i	$-0.603138\pi$
$284$		0			0
$285$	−23.0268	+	37.8185i	−0.0807959	+	0.132696i
$286$		0			0
$287$	23.9336			0.0833923
$288$		0			0
$289$	115.243	+	265.028i	0.398766	+	0.917053i
$290$		0			0
$291$	197.123	−	323.747i	0.677397	−	1.11253i
$292$		0			0
$293$			98.5866i			0.336473i	0.985747	+	0.168237i	$0.0538073\pi$
$293$			98.5866i			0.336473i	−0.985747	+	0.168237i	$0.946193\pi$
$294$		0			0
$295$	67.7681	+	67.7681i	0.229722	+	0.229722i
$296$		0			0
$297$	−32.2645	+	460.378i	−0.108635	+	1.55010i
$298$		0			0
$299$	−64.5741	+	64.5741i	−0.215967	+	0.215967i
$300$		0			0
$301$	−213.775	+	213.775i	−0.710217	+	0.710217i
$302$		0			0
$303$	55.8535	+	229.753i	0.184335	+	0.758259i
$304$		0			0
$305$			149.327i			0.489595i
$306$		0			0
$307$	−119.701			−0.389905			−0.194953	−	0.980813i	$-0.562455\pi$
$307$	−119.701			−0.389905			−0.194953	+	0.980813i	$0.562455\pi$
$308$		0			0
$309$	−109.719	+	26.6730i	−0.355078	+	0.0863204i
$310$		0			0
$311$	303.676	+	303.676i	0.976452	+	0.976452i	0.999729	−	0.0232773i	$-0.00741008\pi$
$311$	303.676	+	303.676i	0.976452	+	0.976452i	−0.0232773	+	0.999729i	$0.507410\pi$
$312$		0			0
$313$	−22.6987	−	22.6987i	−0.0725199	−	0.0725199i	0.669917	−	0.742436i	$-0.266330\pi$
$313$	−22.6987	−	22.6987i	−0.0725199	−	0.0725199i	−0.742436	+	0.669917i	$0.766330\pi$
$314$		0			0
$315$	48.4534	+	93.7666i	0.153820	+	0.297672i
$316$		0			0
$317$	384.713	−	384.713i	1.21360	−	1.21360i	0.243772	−	0.969833i	$-0.421615\pi$
$317$	384.713	−	384.713i	1.21360	−	1.21360i	0.969833	−	0.243772i	$-0.0783848\pi$
$318$		0			0
$319$	−74.7978			−0.234476
$320$		0			0
$321$	368.185	+	224.180i	1.14699	+	0.698379i
$322$		0			0
$323$	−61.5219	+	93.8384i	−0.190470	+	0.290521i
$324$		0			0
$325$			12.4328i			0.0382546i
$326$		0			0
$327$	−69.6190	−	42.3895i	−0.212902	−	0.129631i
$328$		0			0
$329$	−200.604	+	200.604i	−0.609737	+	0.609737i
$330$		0			0
$331$		−	8.23630i		−	0.0248831i	−0.999923	−	0.0124415i	$-0.996040\pi$
$331$		−	8.23630i		−	0.0248831i	0.999923	−	0.0124415i	$-0.00396037\pi$
$332$		0			0
$333$	−136.971	+	429.896i	−0.411323	+	1.29098i
$334$		0			0
$335$	−159.817	−	159.817i	−0.477065	−	0.477065i
$336$		0			0
$337$	−15.8240	+	15.8240i	−0.0469556	+	0.0469556i	−0.730195	−	0.683239i	$-0.760571\pi$
$337$	−15.8240	+	15.8240i	−0.0469556	+	0.0469556i	0.683239	+	0.730195i	$0.260571\pi$
$338$		0			0
$339$	278.836	−	457.950i	0.822524	−	1.35089i
$340$		0			0
$341$		−	862.198i		−	2.52844i
$342$		0			0
$343$	−261.427	+	261.427i	−0.762178	+	0.762178i
$344$		0			0
$345$	−239.394	+	58.1974i	−0.693897	+	0.168688i
$346$		0			0
$347$	187.804	−	187.804i	0.541222	−	0.541222i	−0.382665	−	0.923887i	$-0.624994\pi$
$347$	187.804	−	187.804i	0.541222	−	0.541222i	0.923887	+	0.382665i	$0.124994\pi$
$348$		0			0
$349$		−	545.612i		−	1.56336i	−0.623680	−	0.781680i	$-0.714363\pi$
$349$		−	545.612i		−	1.56336i	0.623680	−	0.781680i	$-0.285637\pi$
$350$		0			0
$351$	−50.6757	+	44.0379i	−0.144375	+	0.125464i
$352$		0			0
$353$			191.102i			0.541365i	0.962669	+	0.270683i	$0.0872494\pi$
$353$			191.102i			0.541365i	−0.962669	+	0.270683i	$0.912751\pi$
$354$		0			0
$355$		−	138.751i		−	0.390849i
$356$		0			0
$357$	114.790	+	241.591i	0.321539	+	0.676726i
$358$		0			0
$359$	−75.9874			−0.211664			−0.105832	−	0.994384i	$-0.533751\pi$
$359$	−75.9874			−0.211664			−0.105832	+	0.994384i	$0.533751\pi$
$360$		0			0
$361$	317.434			0.879318
$362$		0			0
$363$	121.300	+	498.966i	0.334160	+	1.37456i
$364$		0			0
$365$	−262.549			−0.719313
$366$		0			0
$367$	−262.496	−	262.496i	−0.715249	−	0.715249i	0.252380	−	0.967628i	$-0.418787\pi$
$367$	−262.496	−	262.496i	−0.715249	−	0.715249i	−0.967628	+	0.252380i	$0.918787\pi$
$368$		0			0
$369$	−12.4683	+	39.1329i	−0.0337894	+	0.106051i
$370$		0			0
$371$	−241.676	−	241.676i	−0.651418	−	0.651418i
$372$		0			0
$373$	191.625			0.513739			0.256870	−	0.966446i	$-0.417309\pi$
$373$	191.625			0.513739			0.256870	+	0.966446i	$0.417309\pi$
$374$		0			0
$375$	−17.4434	+	28.6484i	−0.0465156	+	0.0763957i
$376$		0			0
$377$	−7.69407	−	7.69407i	−0.0204087	−	0.0204087i
$378$		0			0
$379$	418.754	−	418.754i	1.10489	−	1.10489i	0.111079	−	0.993812i	$-0.464569\pi$
$379$	418.754	−	418.754i	1.10489	−	1.10489i	0.993812	−	0.111079i	$-0.0354306\pi$
$380$		0			0
$381$	131.452	+	540.725i	0.345018	+	1.41923i
$382$		0			0
$383$	285.393			0.745151			0.372575	−	0.928002i	$-0.378475\pi$
$383$	285.393			0.745151			0.372575	+	0.928002i	$0.378475\pi$
$384$		0			0
$385$	141.742	+	141.742i	0.368161	+	0.368161i
$386$		0			0
$387$	−238.169	−	460.903i	−0.615423	−	1.19096i
$388$		0			0
$389$	−2.70933			−0.00696485			−0.00348242	−	0.999994i	$-0.501108\pi$
$389$	−2.70933			−0.00696485			−0.00348242	+	0.999994i	$0.501108\pi$
$390$		0			0
$391$	−611.261	+	127.148i	−1.56333	+	0.325188i
$392$		0			0
$393$	101.313	+	61.6872i	0.257794	+	0.156965i
$394$		0			0
$395$			330.077i			0.835638i
$396$		0			0
$397$	−39.2414	−	39.2414i	−0.0988448	−	0.0988448i	0.655955	−	0.754800i	$-0.272266\pi$
$397$	−39.2414	−	39.2414i	−0.0988448	−	0.0988448i	−0.754800	+	0.655955i	$0.772266\pi$
$398$		0			0
$399$	−54.0085	+	88.7018i	−0.135360	+	0.222310i
$400$		0			0
$401$	158.403	−	158.403i	0.395019	−	0.395019i	−0.481453	−	0.876472i	$-0.659891\pi$
$401$	158.403	−	158.403i	0.395019	−	0.395019i	0.876472	+	0.481453i	$0.159891\pi$
$402$		0			0
$403$	88.6899	−	88.6899i	0.220074	−	0.220074i
$404$		0			0
$405$	−178.556	+	30.3763i	−0.440879	+	0.0750031i
$406$		0			0
$407$			856.901i			2.10541i
$408$		0			0
$409$	220.196			0.538376			0.269188	−	0.963088i	$-0.413245\pi$
$409$	220.196			0.538376			0.269188	+	0.963088i	$0.413245\pi$
$410$		0			0
$411$	−182.402	−	750.307i	−0.443800	−	1.82556i
$412$		0			0
$413$	158.947	+	158.947i	0.384861	+	0.384861i
$414$		0			0
$415$	114.082	+	114.082i	0.274897	+	0.274897i
$416$		0			0
$417$	237.383	−	389.870i	0.569264	−	0.934940i
$418$		0			0
$419$	221.215	−	221.215i	0.527959	−	0.527959i	−0.392004	−	0.919963i	$-0.628218\pi$
$419$	221.215	−	221.215i	0.527959	−	0.527959i	0.919963	+	0.392004i	$0.128218\pi$
$420$		0			0
$421$	−254.799			−0.605224			−0.302612	−	0.953114i	$-0.597859\pi$
$421$	−254.799			−0.605224			−0.302612	+	0.953114i	$0.597859\pi$
$422$		0			0
$423$	−223.494	−	432.504i	−0.528355	−	1.02247i
$424$		0			0
$425$	−46.6043	+	71.0848i	−0.109657	+	0.167258i
$426$		0			0
$427$			350.240i			0.820233i
$428$		0			0
$429$	−66.3113	+	108.907i	−0.154572	+	0.253863i
$430$		0			0
$431$	63.1928	−	63.1928i	0.146619	−	0.146619i	−0.629987	−	0.776606i	$-0.716940\pi$
$431$	63.1928	−	63.1928i	0.146619	−	0.146619i	0.776606	+	0.629987i	$0.216940\pi$
$432$		0			0
$433$			417.526i			0.964263i	0.876099	+	0.482132i	$0.160137\pi$
$433$			417.526i			0.964263i	−0.876099	+	0.482132i	$0.839863\pi$
$434$		0			0
$435$	−6.93428	−	28.5241i	−0.0159409	−	0.0655726i
$436$		0			0
$437$	−171.410	−	171.410i	−0.392241	−	0.392241i
$438$		0			0
$439$	−411.709	+	411.709i	−0.937834	+	0.937834i	−0.998178	−	0.0603435i	$-0.980780\pi$
$439$	−411.709	+	411.709i	−0.937834	+	0.937834i	0.0603435	+	0.998178i	$0.480780\pi$
$440$		0			0
$441$	−88.8064	−	171.857i	−0.201375	−	0.389700i
$442$		0			0
$443$			126.684i			0.285969i	0.989725	+	0.142985i	$0.0456699\pi$
$443$			126.684i			0.285969i	−0.989725	+	0.142985i	$0.954330\pi$
$444$		0			0
$445$	98.6277	−	98.6277i	0.221635	−	0.221635i
$446$		0			0
$447$	38.7730	+	159.492i	0.0867406	+	0.356806i
$448$		0			0
$449$	378.300	−	378.300i	0.842539	−	0.842539i	−0.146649	−	0.989189i	$-0.546849\pi$
$449$	378.300	−	378.300i	0.842539	−	0.842539i	0.989189	+	0.146649i	$0.0468489\pi$
$450$		0			0
$451$			78.0027i			0.172955i
$452$		0			0
$453$	204.762	+	842.284i	0.452012	+	1.85935i
$454$		0			0
$455$			29.1605i			0.0640891i
$456$		0			0
$457$			274.066i			0.599708i	0.953985	+	0.299854i	$0.0969379\pi$
$457$			274.066i			0.599708i	−0.953985	+	0.299854i	$0.903062\pi$
$458$		0			0
$459$	−454.816	+	61.8303i	−0.990886	+	0.134707i
$460$		0			0
$461$	−410.066			−0.889514			−0.444757	−	0.895651i	$-0.646710\pi$
$461$	−410.066			−0.889514			−0.444757	+	0.895651i	$0.646710\pi$
$462$		0			0
$463$	883.786			1.90883			0.954413	−	0.298489i	$-0.0964827\pi$
$463$	883.786			1.90883			0.954413	+	0.298489i	$0.0964827\pi$
$464$		0			0
$465$	328.799	−	79.9318i	0.707094	−	0.171896i
$466$		0			0
$467$	35.2137			0.0754042			0.0377021	−	0.999289i	$-0.487996\pi$
$467$	35.2137			0.0754042			0.0377021	+	0.999289i	$0.487996\pi$
$468$		0			0
$469$	−374.844	−	374.844i	−0.799241	−	0.799241i
$470$		0			0
$471$	539.767	−	131.219i	1.14600	−	0.278596i
$472$		0			0
$473$	−696.722	−	696.722i	−1.47298	−	1.47298i
$474$		0			0
$475$	−33.0023			−0.0694785
$476$		0			0
$477$	521.057	−	269.253i	1.09236	−	0.564473i
$478$		0			0
$479$	−145.662	−	145.662i	−0.304096	−	0.304096i	0.538518	−	0.842614i	$-0.318984\pi$
$479$	−145.662	−	145.662i	−0.304096	−	0.304096i	−0.842614	+	0.538518i	$0.818984\pi$
$480$		0			0
$481$	−88.1451	+	88.1451i	−0.183254	+	0.183254i
$482$		0			0
$483$	−561.490	+	136.500i	−1.16251	+	0.282608i
$484$		0			0
$485$	282.518			0.582512
$486$		0			0
$487$	−414.175	−	414.175i	−0.850463	−	0.850463i	0.139727	−	0.990190i	$-0.455377\pi$
$487$	−414.175	−	414.175i	−0.850463	−	0.850463i	−0.990190	+	0.139727i	$0.955377\pi$
$488$		0			0
$489$	207.755	+	126.497i	0.424856	+	0.258685i
$490$		0			0
$491$	849.887			1.73093			0.865466	−	0.500968i	$-0.167023\pi$
$491$	849.887			1.73093			0.865466	+	0.500968i	$0.167023\pi$
$492$		0			0
$493$	−15.1499	−	72.8324i	−0.0307300	−	0.147733i
$494$		0			0
$495$	−305.598	+	157.916i	−0.617369	+	0.319022i
$496$		0			0
$497$		−	325.436i		−	0.654801i
$498$		0			0
$499$	110.052	+	110.052i	0.220545	+	0.220545i	0.808728	−	0.588183i	$-0.200157\pi$
$499$	110.052	+	110.052i	0.220545	+	0.220545i	−0.588183	+	0.808728i	$0.700157\pi$
$500$		0			0
$501$	585.628	+	356.576i	1.16892	+	0.711728i
$502$		0			0
$503$	−275.657	+	275.657i	−0.548027	+	0.548027i	−0.925870	−	0.377843i	$-0.876666\pi$
$503$	−275.657	+	275.657i	−0.548027	+	0.548027i	0.377843	+	0.925870i	$0.376666\pi$
$504$		0			0
$505$	−124.617	+	124.617i	−0.246766	+	0.246766i
$506$		0			0
$507$	474.628	−	115.383i	0.936149	−	0.227580i
$508$		0			0
$509$			370.713i			0.728316i	0.931337	+	0.364158i	$0.118643\pi$
$509$			370.713i			0.728316i	−0.931337	+	0.364158i	$0.881357\pi$
$510$		0			0
$511$	−615.799			−1.20509
$512$		0			0
$513$	−116.897	−	134.517i	−0.227869	−	0.262216i
$514$		0			0
$515$	−59.5113	−	59.5113i	−0.115556	−	0.115556i
$516$		0			0
$517$	−653.793	−	653.793i	−1.26459	−	1.26459i
$518$		0			0
$519$	429.627	+	261.590i	0.827797	+	0.504027i
$520$		0			0
$521$	−93.7463	+	93.7463i	−0.179935	+	0.179935i	−0.791328	−	0.611392i	$-0.790610\pi$
$521$	−93.7463	+	93.7463i	−0.179935	+	0.179935i	0.611392	+	0.791328i	$0.290610\pi$
$522$		0			0
$523$	247.501			0.473233			0.236616	−	0.971603i	$-0.423962\pi$
$523$	247.501			0.473233			0.236616	+	0.971603i	$0.423962\pi$
$524$		0			0
$525$	−40.9127	+	67.1936i	−0.0779290	+	0.127988i
$526$		0			0
$527$	839.543	−	174.633i	1.59306	−	0.331373i
$528$		0			0
$529$		−	819.813i		−	1.54974i
$530$		0			0
$531$	−342.693	+	177.085i	−0.645373	+	0.333493i
$532$		0			0
$533$	−8.02375	+	8.02375i	−0.0150539	+	0.0150539i
$534$		0			0
$535$			321.297i			0.600555i
$536$		0			0
$537$	−314.877	+	76.5474i	−0.586363	+	0.142546i
$538$		0			0
$539$	−259.788	−	259.788i	−0.481981	−	0.481981i
$540$		0			0
$541$	−229.311	+	229.311i	−0.423864	+	0.423864i	−0.886532	−	0.462668i	$-0.846892\pi$
$541$	−229.311	+	229.311i	−0.423864	+	0.423864i	0.462668	+	0.886532i	$0.346892\pi$
$542$		0			0
$543$	640.413	+	389.933i	1.17940	+	0.718109i
$544$		0			0
$545$		−	60.7530i		−	0.111473i
$546$		0			0
$547$	273.322	−	273.322i	0.499674	−	0.499674i	−0.411663	−	0.911336i	$-0.635052\pi$
$547$	273.322	−	273.322i	0.499674	−	0.499674i	0.911336	+	0.411663i	$0.135052\pi$
$548$		0			0
$549$	−572.663	−	182.458i	−1.04310	−	0.332347i
$550$		0			0
$551$	20.4236	−	20.4236i	0.0370665	−	0.0370665i
$552$		0			0
$553$			774.183i			1.39997i
$554$		0			0
$555$	−326.779	+	79.4408i	−0.588791	+	0.143137i
$556$		0			0
$557$		−	302.784i		−	0.543597i	−0.962354	−	0.271799i	$-0.912382\pi$
$557$		−	302.784i		−	0.543597i	0.962354	−	0.271799i	$-0.0876185\pi$
$558$		0			0
$559$		−	143.336i		−	0.256416i
$560$		0			0
$561$	−787.377	+	374.114i	−1.40352	+	0.666870i
$562$		0			0
$563$	−268.963			−0.477731			−0.238866	−	0.971053i	$-0.576776\pi$
$563$	−268.963			−0.477731			−0.238866	+	0.971053i	$0.576776\pi$
$564$		0			0
$565$	399.630			0.707310
$566$		0			0
$567$	−418.796	+	71.2463i	−0.738618	+	0.125655i
$568$		0			0
$569$	929.694			1.63391			0.816954	−	0.576703i	$-0.195661\pi$
$569$	929.694			1.63391			0.816954	+	0.576703i	$0.195661\pi$
$570$		0			0
$571$	−512.353	−	512.353i	−0.897290	−	0.897290i	0.0979054	−	0.995196i	$-0.468786\pi$
$571$	−512.353	−	512.353i	−0.897290	−	0.897290i	−0.995196	+	0.0979054i	$0.968786\pi$
$572$		0			0
$573$	79.9147	+	328.728i	0.139467	+	0.573696i
$574$		0			0
$575$	−129.847	−	129.847i	−0.225820	−	0.225820i
$576$		0			0
$577$	501.812			0.869691			0.434846	−	0.900505i	$-0.356803\pi$
$577$	501.812			0.869691			0.434846	+	0.900505i	$0.356803\pi$
$578$		0			0
$579$	−224.275	−	136.556i	−0.387350	−	0.235849i
$580$		0			0
$581$	267.575	+	267.575i	0.460543	+	0.460543i
$582$		0			0
$583$	787.654	−	787.654i	1.35104	−	1.35104i
$584$		0			0
$585$	−47.6793	−	15.1913i	−0.0815031	−	0.0259680i
$586$		0			0
$587$	−469.870			−0.800460			−0.400230	−	0.916415i	$-0.631070\pi$
$587$	−469.870			−0.800460			−0.400230	+	0.916415i	$0.631070\pi$
$588$		0			0
$589$	235.424	+	235.424i	0.399701	+	0.399701i
$590$		0			0
$591$	−364.187	+	598.128i	−0.616221	+	1.01206i
$592$		0			0
$593$	−939.727			−1.58470			−0.792350	−	0.610067i	$-0.791143\pi$
$593$	−939.727			−1.58470			−0.792350	+	0.610067i	$0.791143\pi$
$594$		0			0
$595$	−109.308	+	166.727i	−0.183712	+	0.280213i
$596$		0			0
$597$	261.810	−	429.988i	0.438543	−	0.720248i
$598$		0			0
$599$			317.831i			0.530603i	0.964166	+	0.265301i	$0.0854714\pi$
$599$			317.831i			0.530603i	−0.964166	+	0.265301i	$0.914529\pi$
$600$		0			0
$601$	99.9453	+	99.9453i	0.166298	+	0.166298i	0.785350	−	0.619052i	$-0.212483\pi$
$601$	99.9453	+	99.9453i	0.166298	+	0.166298i	−0.619052	+	0.785350i	$0.712483\pi$
$602$		0			0
$603$	808.169	−	417.617i	1.34025	−	0.692565i
$604$		0			0
$605$	−270.638	+	270.638i	−0.447335	+	0.447335i
$606$		0			0
$607$	321.780	−	321.780i	0.530115	−	0.530115i	−0.390492	−	0.920606i	$-0.627695\pi$
$607$	321.780	−	321.780i	0.530115	−	0.530115i	0.920606	+	0.390492i	$0.127695\pi$
$608$		0			0
$609$	−16.2641	−	66.9021i	−0.0267062	−	0.109856i
$610$		0			0
$611$		−	134.505i		−	0.220139i
$612$		0			0
$613$	−776.333			−1.26645			−0.633224	−	0.773968i	$-0.718269\pi$
$613$	−776.333			−1.26645			−0.633224	+	0.773968i	$0.718269\pi$
$614$		0			0
$615$	−29.7463	+	7.23140i	−0.0483679	+	0.0117584i
$616$		0			0
$617$	334.721	+	334.721i	0.542498	+	0.542498i	0.924261	−	0.381762i	$-0.124683\pi$
$617$	334.721	+	334.721i	0.542498	+	0.542498i	−0.381762	+	0.924261i	$0.624683\pi$
$618$		0			0
$619$	−533.463	−	533.463i	−0.861815	−	0.861815i	0.129734	−	0.991549i	$-0.458588\pi$
$619$	−533.463	−	533.463i	−0.861815	−	0.861815i	−0.991549	+	0.129734i	$0.958588\pi$
$620$		0			0
$621$	69.3244	−	989.181i	0.111634	−	1.59288i
$622$		0			0
$623$	231.328	−	231.328i	0.371312	−	0.371312i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	−289.091	−	176.021i	−0.461070	−	0.280735i
$628$		0			0
$629$	−834.385	+	173.561i	−1.32653	+	0.275931i
$630$		0			0
$631$			747.936i			1.18532i	0.805453	+	0.592659i	$0.201922\pi$
$631$			747.936i			1.18532i	−0.805453	+	0.592659i	$0.798078\pi$
$632$		0			0
$633$	373.931	+	227.678i	0.590729	+	0.359681i
$634$		0			0
$635$	−293.288	+	293.288i	−0.461870	+	0.461870i
$636$		0			0
$637$		−	53.4461i		−	0.0839028i
$638$		0			0
$639$	532.108	+	169.537i	0.832719	+	0.265316i
$640$		0			0
$641$	−435.153	−	435.153i	−0.678865	−	0.678865i	0.280878	−	0.959743i	$-0.409374\pi$
$641$	−435.153	−	435.153i	−0.678865	−	0.678865i	−0.959743	+	0.280878i	$0.909374\pi$
$642$		0			0
$643$	−298.312	+	298.312i	−0.463937	+	0.463937i	−0.899944	−	0.436006i	$-0.856393\pi$
$643$	−298.312	+	298.312i	−0.463937	+	0.463937i	0.436006	+	0.899944i	$0.356393\pi$
$644$		0			0
$645$	201.103	−	330.285i	0.311788	−	0.512070i
$646$		0			0
$647$			562.517i			0.869423i	0.900570	+	0.434711i	$0.143150\pi$
$647$			562.517i			0.869423i	−0.900570	+	0.434711i	$0.856850\pi$
$648$		0			0
$649$	−518.031	+	518.031i	−0.798198	+	0.798198i
$650$		0			0
$651$	771.184	−	187.477i	1.18461	−	0.287983i
$652$		0			0
$653$	−57.9563	+	57.9563i	−0.0887538	+	0.0887538i	−0.750090	−	0.661336i	$-0.769990\pi$
$653$	−57.9563	+	57.9563i	−0.0887538	+	0.0887538i	0.661336	+	0.750090i	$0.269990\pi$
$654$		0			0
$655$			88.4108i			0.134978i
$656$		0			0
$657$	320.802	−	1006.87i	0.488283	−	1.53253i
$658$		0			0
$659$			567.798i			0.861606i	0.902446	+	0.430803i	$0.141770\pi$
$659$			567.798i			0.861606i	−0.902446	+	0.430803i	$0.858230\pi$
$660$		0			0
$661$		−	845.468i		−	1.27907i	−0.768760	−	0.639537i	$-0.779126\pi$
$661$		−	845.468i		−	1.27907i	0.768760	−	0.639537i	$-0.220874\pi$
$662$		0			0
$663$	−119.477	−	42.5103i	−0.180206	−	0.0641181i
$664$		0			0
$665$	−77.4056			−0.116399
$666$		0			0
$667$	160.713			0.240948
$668$		0			0
$669$	−75.1924	−	309.303i	−0.112395	−	0.462336i
$670$		0			0
$671$	−1141.48			−1.70116
$672$		0			0
$673$	−66.6395	−	66.6395i	−0.0990185	−	0.0990185i	0.655862	−	0.754881i	$-0.272305\pi$
$673$	−66.6395	−	66.6395i	−0.0990185	−	0.0990185i	−0.754881	+	0.655862i	$0.772305\pi$
$674$		0			0
$675$	−88.5522	−	101.900i	−0.131188	−	0.150962i
$676$		0			0
$677$	348.318	+	348.318i	0.514502	+	0.514502i	0.915903	−	0.401400i	$-0.131476\pi$
$677$	348.318	+	348.318i	0.514502	+	0.514502i	−0.401400	+	0.915903i	$0.631476\pi$
$678$		0			0
$679$	662.635			0.975899
$680$		0			0
$681$	−187.116	+	307.313i	−0.274767	+	0.451268i
$682$		0			0
$683$	−559.482	−	559.482i	−0.819153	−	0.819153i	0.166832	−	0.985985i	$-0.446646\pi$
$683$	−559.482	−	559.482i	−0.819153	−	0.819153i	−0.985985	+	0.166832i	$0.946646\pi$
$684$		0			0
$685$	406.964	−	406.964i	0.594108	−	0.594108i
$686$		0			0
$687$	−5.20058	−	21.3925i	−0.00756998	−	0.0311390i
$688$		0			0
$689$	162.044			0.235187
$690$		0			0
$691$	797.399	+	797.399i	1.15398	+	1.15398i	0.985748	+	0.168230i	$0.0538051\pi$
$691$	797.399	+	797.399i	1.15398	+	1.15398i	0.168230	+	0.985748i	$0.446195\pi$
$692$		0			0
$693$	−716.767	+	370.386i	−1.03430	+	0.534467i
$694$		0			0
$695$	340.220			0.489525
$696$		0			0
$697$	−75.9531	+	15.7990i	−0.108972	+	0.0226672i
$698$		0			0
$699$	−519.585	−	316.364i	−0.743327	−	0.452595i
$700$		0			0
$701$		−	158.435i		−	0.226013i	−0.993594	−	0.113006i	$-0.963952\pi$
$701$		−	158.435i		−	0.226013i	0.993594	−	0.113006i	$-0.0360480\pi$
$702$		0			0
$703$	−233.978	−	233.978i	−0.332828	−	0.332828i
$704$		0			0
$705$	188.712	−	309.935i	0.267677	−	0.439624i
$706$		0			0
$707$	−292.284	+	292.284i	−0.413415	+	0.413415i
$708$		0			0
$709$	342.014	−	342.014i	0.482389	−	0.482389i	−0.423505	−	0.905894i	$-0.639200\pi$
$709$	342.014	−	342.014i	0.482389	−	0.482389i	0.905894	+	0.423505i	$0.139200\pi$
$710$		0			0
$711$	−1265.84	−	403.313i	−1.78036	−	0.567247i
$712$		0			0
$713$			1852.54i			2.59823i
$714$		0			0
$715$	−95.0380			−0.132920
$716$		0			0
$717$	−278.042	−	1143.72i	−0.387785	−	1.59515i
$718$		0			0
$719$	−27.8019	−	27.8019i	−0.0386675	−	0.0386675i	0.687509	−	0.726176i	$-0.258704\pi$
$719$	−27.8019	−	27.8019i	−0.0386675	−	0.0386675i	−0.726176	+	0.687509i	$0.758704\pi$
$720$		0			0
$721$	−139.581	−	139.581i	−0.193594	−	0.193594i
$722$		0			0
$723$	55.0162	−	90.3568i	0.0760944	−	0.124975i
$724$		0			0
$725$	15.4714	−	15.4714i	0.0213398	−	0.0213398i
$726$		0			0
$727$	656.992			0.903703			0.451851	−	0.892093i	$-0.350764\pi$
$727$	656.992			0.903703			0.451851	+	0.892093i	$0.350764\pi$
$728$		0			0
$729$	101.681	−	721.874i	0.139480	−	0.990225i
$730$		0			0
$731$	537.298	−	819.532i	0.735017	−	1.12111i
$732$		0			0
$733$		−	123.738i		−	0.168810i	−0.996432	−	0.0844050i	$-0.973101\pi$
$733$		−	123.738i		−	0.168810i	0.996432	−	0.0844050i	$-0.0268989\pi$
$734$		0			0
$735$	74.9857	−	123.154i	0.102021	−	0.167556i
$736$		0			0
$737$	1221.67	−	1221.67i	1.65762	−	1.65762i
$738$		0			0
$739$			99.8014i			0.135049i	0.997718	+	0.0675246i	$0.0215101\pi$
$739$			99.8014i			0.135049i	−0.997718	+	0.0675246i	$0.978490\pi$
$740$		0			0
$741$	−11.6309	−	47.8437i	−0.0156963	−	0.0645663i
$742$		0			0
$743$	296.225	+	296.225i	0.398688	+	0.398688i	0.877770	−	0.479082i	$-0.159030\pi$
$743$	296.225	+	296.225i	0.398688	+	0.398688i	−0.479082	+	0.877770i	$0.659030\pi$
$744$		0			0
$745$	−86.5081	+	86.5081i	−0.116118	+	0.116118i
$746$		0			0
$747$	−576.897	+	298.108i	−0.772285	+	0.399074i
$748$		0			0
$749$			753.589i			1.00613i
$750$		0			0
$751$	−313.884	+	313.884i	−0.417954	+	0.417954i	−0.884498	−	0.466544i	$-0.845499\pi$
$751$	−313.884	+	313.884i	−0.417954	+	0.417954i	0.466544	+	0.884498i	$0.345499\pi$
$752$		0			0
$753$	66.8759	+	275.093i	0.0888126	+	0.365329i
$754$		0			0
$755$	−456.852	+	456.852i	−0.605102	+	0.605102i
$756$		0			0
$757$		−	1476.20i		−	1.95007i	−0.222053	−	0.975035i	$-0.571276\pi$
$757$		−	1476.20i		−	1.95007i	0.222053	−	0.975035i	$-0.428724\pi$
$758$		0			0
$759$	−444.871	−	1829.97i	−0.586127	−	2.41103i
$760$		0			0
$761$			434.172i			0.570528i	0.958449	+	0.285264i	$0.0920813\pi$
$761$			434.172i			0.570528i	−0.958449	+	0.285264i	$0.907919\pi$
$762$		0			0
$763$		−	142.494i		−	0.186755i
$764$		0			0
$765$	−215.664	−	265.583i	−0.281913	−	0.347167i
$766$		0			0
$767$	−106.574			−0.138950
$768$		0			0
$769$	186.914			0.243061			0.121530	−	0.992588i	$-0.461220\pi$
$769$	186.914			0.243061			0.121530	+	0.992588i	$0.461220\pi$
$770$		0			0
$771$	61.7194	−	15.0041i	0.0800511	−	0.0194606i
$772$		0			0
$773$	−650.279			−0.841240			−0.420620	−	0.907237i	$-0.638187\pi$
$773$	−650.279			−0.841240			−0.420620	+	0.907237i	$0.638187\pi$
$774$		0			0
$775$	178.339	+	178.339i	0.230115	+	0.230115i
$776$		0			0
$777$	−766.447	+	186.325i	−0.986418	+	0.239801i
$778$		0			0
$779$	−21.2987	−	21.2987i	−0.0273411	−	0.0273411i
$780$		0			0
$781$	1060.64			1.35805
$782$		0			0
$783$	117.862	+	8.26008i	0.150526	+	0.0105493i
$784$		0			0
$785$	292.768	+	292.768i	0.372953	+	0.372953i
$786$		0			0
$787$	117.064	−	117.064i	0.148747	−	0.148747i	−0.628811	−	0.777558i	$-0.716458\pi$
$787$	117.064	−	117.064i	0.148747	−	0.148747i	0.777558	+	0.628811i	$0.216458\pi$
$788$		0			0
$789$	1351.68	−	328.597i	1.71316	−	0.416473i
$790$		0			0
$791$	937.317			1.18498
$792$		0			0
$793$	−117.418	−	117.418i	−0.148068	−	0.148068i
$794$		0			0
$795$	373.392	+	227.350i	0.469676	+	0.285975i
$796$		0			0
$797$	−642.384			−0.806003			−0.403002	−	0.915199i	$-0.632033\pi$
$797$	−642.384			−0.806003			−0.403002	+	0.915199i	$0.632033\pi$
$798$		0			0
$799$	504.192	−	769.037i	0.631029	−	0.962499i
$800$		0			0
$801$	257.724	+	498.746i	0.321753	+	0.622654i
$802$		0			0
$803$		−	2006.97i		−	2.49934i
$804$		0			0
$805$	−304.550	−	304.550i	−0.378323	−	0.378323i
$806$		0			0
$807$	−578.328	−	352.131i	−0.716639	−	0.436345i
$808$		0			0
$809$	−697.276	+	697.276i	−0.861899	+	0.861899i	−0.991559	−	0.129659i	$-0.958612\pi$
$809$	−697.276	+	697.276i	−0.861899	+	0.861899i	0.129659	+	0.991559i	$0.458612\pi$
$810$		0			0
$811$	1140.82	−	1140.82i	1.40668	−	1.40668i	0.630442	−	0.776236i	$-0.282874\pi$
$811$	1140.82	−	1140.82i	1.40668	−	1.40668i	0.776236	−	0.630442i	$-0.217126\pi$
$812$		0			0
$813$	−772.577	+	187.816i	−0.950279	+	0.231015i
$814$		0			0
$815$			181.297i			0.222450i
$816$		0			0
$817$	380.481			0.465705
$818$		0			0
$819$	−111.830	−	35.6305i	−0.136544	−	0.0435049i
$820$		0			0
$821$	−22.1943	−	22.1943i	−0.0270332	−	0.0270332i	0.693461	−	0.720494i	$-0.256085\pi$
$821$	−22.1943	−	22.1943i	−0.0270332	−	0.0270332i	−0.720494	+	0.693461i	$0.756085\pi$
$822$		0			0
$823$	949.378	+	949.378i	1.15356	+	1.15356i	0.985834	+	0.167723i	$0.0536415\pi$
$823$	949.378	+	949.378i	1.15356	+	1.15356i	0.167723	+	0.985834i	$0.446358\pi$
$824$		0			0
$825$	−218.993	−	133.340i	−0.265446	−	0.161624i
$826$		0			0
$827$	−616.172	+	616.172i	−0.745069	+	0.745069i	−0.973549	−	0.228480i	$-0.926624\pi$
$827$	−616.172	+	616.172i	−0.745069	+	0.745069i	0.228480	+	0.973549i	$0.426624\pi$
$828$		0			0
$829$	−683.788			−0.824835			−0.412418	−	0.910995i	$-0.635316\pi$
$829$	−683.788			−0.824835			−0.412418	+	0.910995i	$0.635316\pi$
$830$		0			0
$831$	−45.4599	+	74.6618i	−0.0547051	+	0.0898458i
$832$		0			0
$833$	200.343	−	305.580i	0.240508	−	0.366843i
$834$		0			0
$835$			511.048i			0.612034i
$836$		0			0
$837$	−95.2144	+	1358.60i	−0.113757	+	1.62318i
$838$		0			0
$839$	−404.564	+	404.564i	−0.482198	+	0.482198i	−0.905833	−	0.423635i	$-0.860754\pi$
$839$	−404.564	+	404.564i	−0.482198	+	0.482198i	0.423635	+	0.905833i	$0.360754\pi$
$840$		0			0
$841$		−	821.851i		−	0.977231i
$842$		0			0
$843$	−1364.33	+	331.672i	−1.61842	+	0.393442i
$844$		0			0
$845$	257.436	+	257.436i	0.304658	+	0.304658i
$846$		0			0
$847$	−634.770	+	634.770i	−0.749433	+	0.749433i
$848$		0			0
$849$	1298.67	+	790.728i	1.52964	+	0.931364i
$850$		0			0
$851$		−	1841.16i		−	2.16353i
$852$		0			0
$853$	36.2095	−	36.2095i	0.0424496	−	0.0424496i	−0.685563	−	0.728013i	$-0.740444\pi$
$853$	36.2095	−	36.2095i	0.0424496	−	0.0424496i	0.728013	+	0.685563i	$0.240444\pi$
$854$		0			0
$855$	40.3247	−	126.563i	0.0471634	−	0.148027i
$856$		0			0
$857$	658.476	−	658.476i	0.768351	−	0.768351i	−0.209465	−	0.977816i	$-0.567172\pi$
$857$	658.476	−	658.476i	0.768351	−	0.768351i	0.977816	+	0.209465i	$0.0671724\pi$
$858$		0			0
$859$			847.766i			0.986922i	0.869768	+	0.493461i	$0.164268\pi$
$859$			847.766i			0.986922i	−0.869768	+	0.493461i	$0.835732\pi$
$860$		0			0
$861$	−69.7688	+	16.9610i	−0.0810322	+	0.0196992i
$862$		0			0
$863$		−	1006.87i		−	1.16671i	−0.812216	−	0.583357i	$-0.801739\pi$
$863$		−	1006.87i		−	1.16671i	0.812216	−	0.583357i	$-0.198261\pi$
$864$		0			0
$865$			374.914i			0.433426i
$866$		0			0
$867$	−523.763	−	690.914i	−0.604109	−	0.796901i
$868$		0			0
$869$	−2523.16			−2.90353
$870$		0			0
$871$	251.333			0.288557
$872$		0			0
$873$	−345.202	+	1083.45i	−0.395420	+	1.24106i
$874$		0			0
$875$	−58.6365			−0.0670132
$876$		0			0
$877$	714.976	+	714.976i	0.815253	+	0.815253i	0.985416	−	0.170163i	$-0.0544295\pi$
$877$	714.976	+	714.976i	0.815253	+	0.815253i	−0.170163	+	0.985416i	$0.554430\pi$
$878$		0			0
$879$	−69.8652	−	287.390i	−0.0794826	−	0.326951i
$880$		0			0
$881$	−577.180	−	577.180i	−0.655141	−	0.655141i	0.299085	−	0.954226i	$-0.403319\pi$
$881$	−577.180	−	577.180i	−0.655141	−	0.655141i	−0.954226	+	0.299085i	$0.903319\pi$
$882$		0			0
$883$	−142.676			−0.161581			−0.0807906	−	0.996731i	$-0.525745\pi$
$883$	−142.676			−0.161581			−0.0807906	+	0.996731i	$0.525745\pi$
$884$		0			0
$885$	−245.576	−	149.526i	−0.277487	−	0.168955i
$886$		0			0
$887$	−846.549	−	846.549i	−0.954396	−	0.954396i	0.0446083	−	0.999005i	$-0.485796\pi$
$887$	−846.549	−	846.549i	−0.954396	−	0.954396i	−0.999005	+	0.0446083i	$0.985796\pi$
$888$		0			0
$889$	−687.895	+	687.895i	−0.773785	+	0.773785i
$890$		0			0
$891$	−232.201	−	1364.91i	−0.260607	−	1.53189i
$892$		0			0
$893$	357.038			0.399819
$894$		0			0
$895$	−170.788	−	170.788i	−0.190825	−	0.190825i
$896$		0			0
$897$	142.478	−	234.001i	0.158839	−	0.260871i
$898$		0			0
$899$	−220.732			−0.245531
$900$		0			0
$901$	926.493	+	607.423i	1.02829	+	0.674165i
$902$		0			0
$903$	471.680	−	774.671i	0.522348	−	0.857886i
$904$		0			0
$905$			558.856i			0.617521i
$906$		0			0
$907$	1029.98	+	1029.98i	1.13559	+	1.13559i	0.989231	+	0.146362i	$0.0467563\pi$
$907$	1029.98	+	1029.98i	1.13559	+	1.13559i	0.146362	+	0.989231i	$0.453244\pi$
$908$		0			0
$909$	−325.637	−	630.169i	−0.358236	−	0.693256i
$910$		0			0
$911$	1048.46	−	1048.46i	1.15089	−	1.15089i	0.164519	−	0.986374i	$-0.447393\pi$
$911$	1048.46	−	1048.46i	1.15089	−	1.15089i	0.986374	−	0.164519i	$-0.0526073\pi$
$912$		0			0
$913$	−872.063	+	872.063i	−0.955162	+	0.955162i
$914$		0			0
$915$	−105.823	−	435.301i	−0.115653	−	0.475739i
$916$		0			0
$917$			207.364i			0.226133i
$918$		0			0
$919$	99.7759			0.108570			0.0542851	−	0.998525i	$-0.482712\pi$
$919$	99.7759			0.108570			0.0542851	+	0.998525i	$0.482712\pi$
$920$		0			0
$921$	348.940	−	84.8282i	0.378870	−	0.0921044i
$922$		0			0
$923$	109.102	+	109.102i	0.118204	+	0.118204i
$924$		0			0
$925$	−177.244	−	177.244i	−0.191615	−	0.191615i
$926$		0			0
$927$	300.939	−	155.509i	0.324638	−	0.167755i
$928$		0			0
$929$	307.916	−	307.916i	0.331449	−	0.331449i	−0.521687	−	0.853137i	$-0.674697\pi$
$929$	307.916	−	307.916i	0.331449	−	0.331449i	0.853137	+	0.521687i	$0.174697\pi$
$930$		0			0
$931$	141.871			0.152385
$932$		0			0
$933$	−1100.45	−	670.041i	−1.17948	−	0.718157i
$934$		0			0
$935$	−543.384	−	356.251i	−0.581159	−	0.381017i
$936$		0			0
$937$			59.5383i			0.0635414i	0.999495	+	0.0317707i	$0.0101146\pi$
$937$			59.5383i			0.0635414i	−0.999495	+	0.0317707i	$0.989885\pi$
$938$		0			0
$939$	82.2549	+	50.0831i	0.0875984	+	0.0533367i
$940$		0			0
$941$	−769.713	+	769.713i	−0.817973	+	0.817973i	−0.985814	−	0.167841i	$-0.946321\pi$
$941$	−769.713	+	769.713i	−0.817973	+	0.817973i	0.167841	+	0.985814i	$0.446321\pi$
$942$		0			0
$943$		−	167.599i		−	0.177729i
$944$		0			0
$945$	−207.696	−	239.001i	−0.219784	−	0.252912i
$946$		0			0
$947$	−498.195	−	498.195i	−0.526077	−	0.526077i	0.393323	−	0.919400i	$-0.371325\pi$
$947$	−498.195	−	498.195i	−0.526077	−	0.526077i	−0.919400	+	0.393323i	$0.871325\pi$
$948$		0			0
$949$	206.447	−	206.447i	0.217541	−	0.217541i
$950$		0			0
$951$	−848.841	+	1394.11i	−0.892577	+	1.46594i
$952$		0			0
$953$		−	1100.18i		−	1.15444i	−0.816589	−	0.577220i	$-0.804137\pi$
$953$		−	1100.18i		−	1.15444i	0.816589	−	0.577220i	$-0.195863\pi$
$954$		0			0
$955$	−178.301	+	178.301i	−0.186703	+	0.186703i
$956$		0			0
$957$	218.043	−	53.0068i	0.227840	−	0.0553885i
$958$		0			0
$959$	954.518	−	954.518i	0.995327	−	0.995327i
$960$		0			0
$961$		−	1583.39i		−	1.64765i
$962$		0			0
$963$	−1232.16	−	392.584i	−1.27951	−	0.407668i
$964$		0			0
$965$		−	195.714i		−	0.202812i
$966$		0			0
$967$			836.593i			0.865143i	0.901600	+	0.432571i	$0.142394\pi$
$967$			836.593i			0.865143i	−0.901600	+	0.432571i	$0.857606\pi$
$968$		0			0
$969$	112.842	−	317.147i	0.116452	−	0.327293i
$970$		0			0
$971$	33.5615			0.0345638			0.0172819	−	0.999851i	$-0.494499\pi$
$971$	33.5615			0.0345638			0.0172819	+	0.999851i	$0.494499\pi$
$972$		0			0
$973$	797.972			0.820116
$974$		0			0
$975$	−8.81070	−	36.2427i	−0.00903661	−	0.0371720i
$976$		0			0
$977$	1085.46			1.11102			0.555508	−	0.831511i	$-0.312524\pi$
$977$	1085.46			1.11102			0.555508	+	0.831511i	$0.312524\pi$
$978$		0			0
$979$	753.927	+	753.927i	0.770099	+	0.770099i
$980$		0			0
$981$	232.986	+	74.2326i	0.237499	+	0.0756703i
$982$		0			0
$983$	32.4945	+	32.4945i	0.0330565	+	0.0330565i	0.723442	−	0.690385i	$-0.242559\pi$
$983$	32.4945	+	32.4945i	0.0330565	+	0.0330565i	−0.690385	+	0.723442i	$0.742559\pi$
$984$		0			0
$985$	−521.956			−0.529905
$986$		0			0
$987$	442.618	−	726.940i	0.448447	−	0.736515i
$988$		0			0
$989$	1496.99	+	1496.99i	1.51364	+	1.51364i
$990$		0			0
$991$	−533.451	+	533.451i	−0.538296	+	0.538296i	−0.923028	−	0.384732i	$-0.874294\pi$
$991$	−533.451	+	533.451i	−0.538296	+	0.538296i	0.384732	+	0.923028i	$0.374294\pi$
$992$		0			0
$993$	5.83680	+	24.0096i	0.00587795	+	0.0241789i
$994$		0			0
$995$	375.229			0.377115
$996$		0			0
$997$	−666.131	−	666.131i	−0.668136	−	0.668136i	0.289149	−	0.957284i	$-0.406628\pi$
$997$	−666.131	−	666.131i	−0.668136	−	0.668136i	−0.957284	+	0.289149i	$0.906628\pi$
$998$		0			0
$999$	94.6295	−	1350.25i	0.0947242	−	1.35161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1020.3.bc.a.701.4	✓	96
3.2	odd	2	inner	1020.3.bc.a.701.23	yes	96
17.13	even	4	inner	1020.3.bc.a.761.23	yes	96
51.47	odd	4	inner	1020.3.bc.a.761.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1020.3.bc.a.701.4	✓	96	1.1	even	1	trivial
1020.3.bc.a.701.23	yes	96	3.2	odd	2	inner
1020.3.bc.a.761.4	yes	96	51.47	odd	4	inner
1020.3.bc.a.761.23	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)

\(f(q)\)	\(=\)	\(q+(-2.91510 + 0.708668i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(-3.70850 - 3.70850i) q^{7} +(7.99558 - 4.13167i) q^{9} +O(q^{10})\)	\(q+(-2.91510 + 0.708668i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(-3.70850 - 3.70850i) q^{7} +(7.99558 - 4.13167i) q^{9} +(12.0865 - 12.0865i) q^{11} +2.48655 q^{13} +(5.72968 + 3.48867i) q^{15} +(14.2170 + 9.32085i) q^{17} +6.60046i q^{19} +(13.4387 + 8.18254i) q^{21} +(-25.9693 + 25.9693i) q^{23} +5.00000i q^{25} +(-20.3799 + 17.7104i) q^{27} +(-3.09427 - 3.09427i) q^{29} +(35.6679 - 35.6679i) q^{31} +(-26.6680 + 43.7986i) q^{33} +11.7273i q^{35} +(-35.4487 + 35.4487i) q^{37} +(-7.24854 + 1.76214i) q^{39} +(-3.22686 + 3.22686i) q^{41} -57.6447i q^{43} +(-19.1749 - 6.10938i) q^{45} -54.0929i q^{47} -21.4941i q^{49} +(-48.0492 - 17.0961i) q^{51} +65.1682 q^{53} -38.2208 q^{55} +(-4.67753 - 19.2410i) q^{57} -42.8603 q^{59} +(-47.2212 - 47.2212i) q^{61} +(-44.9739 - 14.3293i) q^{63} +(-3.93158 - 3.93158i) q^{65} +101.077 q^{67} +(57.2995 - 94.1068i) q^{69} +(43.8770 + 43.8770i) q^{71} +(83.0253 - 83.0253i) q^{73} +(-3.54334 - 14.5755i) q^{75} -89.6454 q^{77} +(-104.380 - 104.380i) q^{79} +(46.8586 - 66.0702i) q^{81} -72.1519 q^{83} +(-7.74141 - 37.2165i) q^{85} +(11.2129 + 6.82730i) q^{87} +62.3777i q^{89} +(-9.22137 - 9.22137i) q^{91} +(-78.6986 + 129.252i) q^{93} +(10.4362 - 10.4362i) q^{95} +(-89.3401 + 89.3401i) q^{97} +(46.7011 - 146.576i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{3}+O(q^{10}) \) 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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