LMFDB - Embedded newform 640.3.t.b.417.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,3,Mod(353,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("640.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	640.t (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$17.4387369191$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			417.8
Character	$\chi$	$=$	640.417
Dual form			640.3.t.b.353.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90859 q^{3} +(-4.97175 - 0.530759i) q^{5} +(-8.62025 + 8.62025i) q^{7} -5.35728 q^{9} +O(q^{10})$	\(q-1.90859 q^{3} +(-4.97175 - 0.530759i) q^{5} +(-8.62025 + 8.62025i) q^{7} -5.35728 q^{9} +(-6.35145 + 6.35145i) q^{11} -6.65056 q^{13} +(9.48903 + 1.01300i) q^{15} +(-5.36508 - 5.36508i) q^{17} +(18.1009 - 18.1009i) q^{19} +(16.4525 - 16.4525i) q^{21} +(16.1730 + 16.1730i) q^{23} +(24.4366 + 5.27760i) q^{25} +27.4022 q^{27} +(-12.4816 + 12.4816i) q^{29} -18.5625 q^{31} +(12.1223 - 12.1223i) q^{33} +(47.4330 - 38.2825i) q^{35} -49.8083 q^{37} +12.6932 q^{39} -62.1433i q^{41} +32.2720i q^{43} +(26.6351 + 2.84343i) q^{45} +(13.2635 + 13.2635i) q^{47} -99.6175i q^{49} +(10.2397 + 10.2397i) q^{51} -64.2436i q^{53} +(34.9489 - 28.2067i) q^{55} +(-34.5471 + 34.5471i) q^{57} +(-2.55993 - 2.55993i) q^{59} +(52.5270 + 52.5270i) q^{61} +(46.1811 - 46.1811i) q^{63} +(33.0649 + 3.52984i) q^{65} +72.2222i q^{67} +(-30.8676 - 30.8676i) q^{69} +24.3819i q^{71} +(1.39841 + 1.39841i) q^{73} +(-46.6394 - 10.0728i) q^{75} -109.502i q^{77} -90.0709i q^{79} -4.08398 q^{81} -3.78386 q^{83} +(23.8263 + 29.5214i) q^{85} +(23.8222 - 23.8222i) q^{87} -61.3939 q^{89} +(57.3295 - 57.3295i) q^{91} +35.4283 q^{93} +(-99.6001 + 80.3857i) q^{95} +(103.182 + 103.182i) q^{97} +(34.0265 - 34.0265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 2 q^{5} + 108 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 + 2 * q^5 + 108 * q^9	$ 44 q + 4 q^{3} + 2 q^{5} + 108 q^{9} + 4 q^{11} + 4 q^{13} - 4 q^{15} - 4 q^{17} + 32 q^{19} + 4 q^{21} + 40 q^{27} - 8 q^{31} - 4 q^{33} + 4 q^{35} + 4 q^{37} - 72 q^{39} + 70 q^{45} - 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} + 36 q^{61} - 200 q^{63} - 4 q^{65} - 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} + 52 q^{85} - 36 q^{87} - 188 q^{91} + 40 q^{93} + 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 2 * q^5 + 108 * q^9 + 4 * q^11 + 4 * q^13 - 4 * q^15 - 4 * q^17 + 32 * q^19 + 4 * q^21 + 40 * q^27 - 8 * q^31 - 4 * q^33 + 4 * q^35 + 4 * q^37 - 72 * q^39 + 70 * q^45 - 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 + 36 * q^61 - 200 * q^63 - 4 * q^65 - 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 + 52 * q^85 - 36 * q^87 - 188 * q^91 + 40 * q^93 + 380 * q^95 - 4 * q^97 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−1.90859			−0.636197			−0.318098	−	0.948058i	$-0.603044\pi$
$3$	−1.90859			−0.636197			−0.318098	+	0.948058i	$0.603044\pi$
$4$		0			0
$5$	−4.97175	−	0.530759i	−0.994350	−	0.106152i
$5$	−4.97175	−	0.530759i	−0.994350	−	0.106152i
$6$		0			0
$7$	−8.62025	+	8.62025i	−1.23146	+	1.23146i	−0.268063	+	0.963401i	$0.586384\pi$
$7$	−8.62025	+	8.62025i	−1.23146	+	1.23146i	−0.963401	+	0.268063i	$0.913616\pi$
$8$		0			0
$9$	−5.35728			−0.595254
$10$		0			0
$11$	−6.35145	+	6.35145i	−0.577404	+	0.577404i	−0.934187	−	0.356783i	$-0.883874\pi$
$11$	−6.35145	+	6.35145i	−0.577404	+	0.577404i	0.356783	+	0.934187i	$0.383874\pi$
$12$		0			0
$13$	−6.65056			−0.511581			−0.255791	−	0.966732i	$-0.582336\pi$
$13$	−6.65056			−0.511581			−0.255791	+	0.966732i	$0.582336\pi$
$14$		0			0
$15$	9.48903	+	1.01300i	0.632602	+	0.0675334i
$16$		0			0
$17$	−5.36508	−	5.36508i	−0.315593	−	0.315593i	0.531479	−	0.847072i	$-0.321637\pi$
$17$	−5.36508	−	5.36508i	−0.315593	−	0.315593i	−0.847072	+	0.531479i	$0.821637\pi$
$18$		0			0
$19$	18.1009	−	18.1009i	0.952677	−	0.952677i	−0.0462531	−	0.998930i	$-0.514728\pi$
$19$	18.1009	−	18.1009i	0.952677	−	0.952677i	0.998930	+	0.0462531i	$0.0147281\pi$
$20$		0			0
$21$	16.4525	−	16.4525i	0.783454	−	0.783454i
$22$		0			0
$23$	16.1730	+	16.1730i	0.703172	+	0.703172i	0.965090	−	0.261918i	$-0.0843549\pi$
$23$	16.1730	+	16.1730i	0.703172	+	0.703172i	−0.261918	+	0.965090i	$0.584355\pi$
$24$		0			0
$25$	24.4366	+	5.27760i	0.977464	+	0.211104i
$26$		0			0
$27$	27.4022			1.01490
$28$		0			0
$29$	−12.4816	+	12.4816i	−0.430400	+	0.430400i	−0.888764	−	0.458365i	$-0.848435\pi$
$29$	−12.4816	+	12.4816i	−0.430400	+	0.430400i	0.458365	+	0.888764i	$0.348435\pi$
$30$		0			0
$31$	−18.5625			−0.598792			−0.299396	−	0.954129i	$-0.596785\pi$
$31$	−18.5625			−0.598792			−0.299396	+	0.954129i	$0.596785\pi$
$32$		0			0
$33$	12.1223	−	12.1223i	0.367343	−	0.367343i
$34$		0			0
$35$	47.4330	−	38.2825i	1.35523	−	1.09378i
$36$		0			0
$37$	−49.8083			−1.34617			−0.673085	−	0.739565i	$-0.735031\pi$
$37$	−49.8083			−1.34617			−0.673085	+	0.739565i	$0.735031\pi$
$38$		0			0
$39$	12.6932			0.325466
$40$		0			0
$41$		−	62.1433i		−	1.51569i	−0.652434	−	0.757846i	$-0.726252\pi$
$41$		−	62.1433i		−	1.51569i	0.652434	−	0.757846i	$-0.273748\pi$
$42$		0			0
$43$			32.2720i			0.750511i	0.926921	+	0.375255i	$0.122445\pi$
$43$			32.2720i			0.750511i	−0.926921	+	0.375255i	$0.877555\pi$
$44$		0			0
$45$	26.6351	+	2.84343i	0.591890	+	0.0631872i
$46$		0			0
$47$	13.2635	+	13.2635i	0.282202	+	0.282202i	0.833986	−	0.551785i	$-0.186053\pi$
$47$	13.2635	+	13.2635i	0.282202	+	0.282202i	−0.551785	+	0.833986i	$0.686053\pi$
$48$		0			0
$49$		−	99.6175i		−	2.03301i
$50$		0			0
$51$	10.2397	+	10.2397i	0.200779	+	0.200779i
$52$		0			0
$53$		−	64.2436i		−	1.21214i	−0.795410	−	0.606071i	$-0.792745\pi$
$53$		−	64.2436i		−	1.21214i	0.795410	−	0.606071i	$-0.207255\pi$
$54$		0			0
$55$	34.9489	−	28.2067i	0.635435	−	0.512850i
$56$		0			0
$57$	−34.5471	+	34.5471i	−0.606090	+	0.606090i
$58$		0			0
$59$	−2.55993	−	2.55993i	−0.0433887	−	0.0433887i	0.685080	−	0.728468i	$-0.259767\pi$
$59$	−2.55993	−	2.55993i	−0.0433887	−	0.0433887i	−0.728468	+	0.685080i	$0.759767\pi$
$60$		0			0
$61$	52.5270	+	52.5270i	0.861098	+	0.861098i	0.991466	−	0.130367i	$-0.0416157\pi$
$61$	52.5270	+	52.5270i	0.861098	+	0.861098i	−0.130367	+	0.991466i	$0.541616\pi$
$62$		0			0
$63$	46.1811	−	46.1811i	0.733034	−	0.733034i
$64$		0			0
$65$	33.0649	+	3.52984i	0.508691	+	0.0543053i
$66$		0			0
$67$			72.2222i			1.07794i	0.842324	+	0.538972i	$0.181187\pi$
$67$			72.2222i			1.07794i	−0.842324	+	0.538972i	$0.818813\pi$
$68$		0			0
$69$	−30.8676	−	30.8676i	−0.447356	−	0.447356i
$70$		0			0
$71$			24.3819i			0.343407i	0.985149	+	0.171703i	$0.0549270\pi$
$71$			24.3819i			0.343407i	−0.985149	+	0.171703i	$0.945073\pi$
$72$		0			0
$73$	1.39841	+	1.39841i	0.0191563	+	0.0191563i	0.716620	−	0.697464i	$-0.245688\pi$
$73$	1.39841	+	1.39841i	0.0191563	+	0.0191563i	−0.697464	+	0.716620i	$0.745688\pi$
$74$		0			0
$75$	−46.6394	−	10.0728i	−0.621859	−	0.134304i
$76$		0			0
$77$		−	109.502i		−	1.42211i
$78$		0			0
$79$		−	90.0709i		−	1.14014i	−0.821597	−	0.570069i	$-0.806917\pi$
$79$		−	90.0709i		−	1.14014i	0.821597	−	0.570069i	$-0.193083\pi$
$80$		0			0
$81$	−4.08398			−0.0504195
$82$		0			0
$83$	−3.78386			−0.0455886			−0.0227943	−	0.999740i	$-0.507256\pi$
$83$	−3.78386			−0.0455886			−0.0227943	+	0.999740i	$0.507256\pi$
$84$		0			0
$85$	23.8263	+	29.5214i	0.280309	+	0.347311i
$86$		0			0
$87$	23.8222	−	23.8222i	0.273819	−	0.273819i
$88$		0			0
$89$	−61.3939			−0.689819			−0.344910	−	0.938636i	$-0.612090\pi$
$89$	−61.3939			−0.689819			−0.344910	+	0.938636i	$0.612090\pi$
$90$		0			0
$91$	57.3295	−	57.3295i	0.629994	−	0.629994i
$92$		0			0
$93$	35.4283			0.380949
$94$		0			0
$95$	−99.6001	+	80.3857i	−1.04842	+	0.846166i
$96$		0			0
$97$	103.182	+	103.182i	1.06373	+	1.06373i	0.997826	+	0.0659075i	$0.0209942\pi$
$97$	103.182	+	103.182i	1.06373	+	1.06373i	0.0659075	+	0.997826i	$0.479006\pi$
$98$		0			0
$99$	34.0265	−	34.0265i	0.343702	−	0.343702i
$100$		0			0
$101$	92.1665	−	92.1665i	0.912539	−	0.912539i	−0.0839323	−	0.996471i	$-0.526748\pi$
$101$	92.1665	−	92.1665i	0.912539	−	0.912539i	0.996471	+	0.0839323i	$0.0267479\pi$
$102$		0			0
$103$	73.2115	+	73.2115i	0.710791	+	0.710791i	0.966701	−	0.255909i	$-0.0823749\pi$
$103$	73.2115	+	73.2115i	0.710791	+	0.710791i	−0.255909	+	0.966701i	$0.582375\pi$
$104$		0			0
$105$	−90.5302	+	73.0655i	−0.862192	+	0.695862i
$106$		0			0
$107$	−17.7853			−0.166218			−0.0831089	−	0.996540i	$-0.526485\pi$
$107$	−17.7853			−0.166218			−0.0831089	+	0.996540i	$0.526485\pi$
$108$		0			0
$109$	9.64065	−	9.64065i	0.0884463	−	0.0884463i	−0.661499	−	0.749946i	$-0.730080\pi$
$109$	9.64065	−	9.64065i	0.0884463	−	0.0884463i	0.749946	+	0.661499i	$0.230080\pi$
$110$		0			0
$111$	95.0636			0.856429
$112$		0			0
$113$	−62.4937	+	62.4937i	−0.553042	+	0.553042i	−0.927317	−	0.374276i	$-0.877891\pi$
$113$	−62.4937	+	62.4937i	−0.553042	+	0.553042i	0.374276	+	0.927317i	$0.377891\pi$
$114$		0			0
$115$	−71.8240	−	88.9919i	−0.624556	−	0.773842i
$116$		0			0
$117$	35.6289			0.304521
$118$		0			0
$119$	92.4967			0.777283
$120$		0			0
$121$			40.3182i			0.333208i
$122$		0			0
$123$			118.606i			0.964278i
$124$		0			0
$125$	−118.691	−	39.2089i	−0.949532	−	0.313671i
$126$		0			0
$127$	−50.6008	−	50.6008i	−0.398432	−	0.398432i	0.479248	−	0.877680i	$-0.340909\pi$
$127$	−50.6008	−	50.6008i	−0.398432	−	0.398432i	−0.877680	+	0.479248i	$0.840909\pi$
$128$		0			0
$129$		−	61.5939i		−	0.477472i
$130$		0			0
$131$	22.0987	+	22.0987i	0.168693	+	0.168693i	0.786404	−	0.617712i	$-0.211940\pi$
$131$	22.0987	+	22.0987i	0.168693	+	0.168693i	−0.617712	+	0.786404i	$0.711940\pi$
$132$		0			0
$133$			312.068i			2.34637i
$134$		0			0
$135$	−136.237	−	14.5440i	−1.00916	−	0.107733i
$136$		0			0
$137$	102.317	−	102.317i	0.746841	−	0.746841i	−0.227043	−	0.973885i	$-0.572906\pi$
$137$	102.317	−	102.317i	0.746841	−	0.746841i	0.973885	+	0.227043i	$0.0729059\pi$
$138$		0			0
$139$	−83.0087	−	83.0087i	−0.597185	−	0.597185i	0.342378	−	0.939562i	$-0.388768\pi$
$139$	−83.0087	−	83.0087i	−0.597185	−	0.597185i	−0.939562	+	0.342378i	$0.888768\pi$
$140$		0			0
$141$	−25.3145	−	25.3145i	−0.179536	−	0.179536i
$142$		0			0
$143$	42.2407	−	42.2407i	0.295389	−	0.295389i
$144$		0			0
$145$	68.6800	−	55.4306i	0.473656	−	0.382280i
$146$		0			0
$147$			190.129i			1.29339i
$148$		0			0
$149$	−134.149	−	134.149i	−0.900331	−	0.900331i	0.0951332	−	0.995465i	$-0.469672\pi$
$149$	−134.149	−	134.149i	−0.900331	−	0.900331i	−0.995465	+	0.0951332i	$0.969672\pi$
$150$		0			0
$151$		−	48.5859i		−	0.321761i	−0.986974	−	0.160881i	$-0.948567\pi$
$151$		−	48.5859i		−	0.321761i	0.986974	−	0.160881i	$-0.0514334\pi$
$152$		0			0
$153$	28.7423	+	28.7423i	0.187858	+	0.187858i
$154$		0			0
$155$	92.2883	+	9.85223i	0.595408	+	0.0635628i
$156$		0			0
$157$		−	140.992i		−	0.898038i	−0.893522	−	0.449019i	$-0.851774\pi$
$157$		−	140.992i		−	0.898038i	0.893522	−	0.449019i	$-0.148226\pi$
$158$		0			0
$159$			122.615i			0.771162i
$160$		0			0
$161$	−278.830			−1.73186
$162$		0			0
$163$	−98.2045			−0.602482			−0.301241	−	0.953548i	$-0.597401\pi$
$163$	−98.2045			−0.602482			−0.301241	+	0.953548i	$0.597401\pi$
$164$		0			0
$165$	−66.7031	+	53.8351i	−0.404261	+	0.326273i
$166$		0			0
$167$	−9.58867	+	9.58867i	−0.0574172	+	0.0574172i	−0.735232	−	0.677815i	$-0.762927\pi$
$167$	−9.58867	+	9.58867i	−0.0574172	+	0.0574172i	0.677815	+	0.735232i	$0.262927\pi$
$168$		0			0
$169$	−124.770			−0.738285
$170$		0			0
$171$	−96.9714	+	96.9714i	−0.567084	+	0.567084i
$172$		0			0
$173$	172.905			0.999452			0.499726	−	0.866184i	$-0.333434\pi$
$173$	172.905			0.999452			0.499726	+	0.866184i	$0.333434\pi$
$174$		0			0
$175$	−256.144	+	165.155i	−1.46368	+	0.943744i
$176$		0			0
$177$	4.88586	+	4.88586i	0.0276037	+	0.0276037i
$178$		0			0
$179$	−47.1828	+	47.1828i	−0.263591	+	0.263591i	−0.826511	−	0.562920i	$-0.809678\pi$
$179$	−47.1828	+	47.1828i	−0.263591	+	0.263591i	0.562920	+	0.826511i	$0.309678\pi$
$180$		0			0
$181$	−50.7180	+	50.7180i	−0.280210	+	0.280210i	−0.833193	−	0.552983i	$-0.813489\pi$
$181$	−50.7180	+	50.7180i	−0.280210	+	0.280210i	0.552983	+	0.833193i	$0.313489\pi$
$182$		0			0
$183$	−100.253	−	100.253i	−0.547828	−	0.547828i
$184$		0			0
$185$	247.634	+	26.4362i	1.33856	+	0.142898i
$186$		0			0
$187$	68.1521			0.364450
$188$		0			0
$189$	−236.214	+	236.214i	−1.24981	+	1.24981i
$190$		0			0
$191$	330.128			1.72842			0.864210	−	0.503132i	$-0.167819\pi$
$191$	330.128			1.72842			0.864210	+	0.503132i	$0.167819\pi$
$192$		0			0
$193$	−150.560	+	150.560i	−0.780103	+	0.780103i	−0.979848	−	0.199745i	$-0.935989\pi$
$193$	−150.560	+	150.560i	−0.780103	+	0.780103i	0.199745	+	0.979848i	$0.435989\pi$
$194$		0			0
$195$	−63.1074	−	6.73702i	−0.323627	−	0.0345488i
$196$		0			0
$197$	257.794			1.30860			0.654299	−	0.756236i	$-0.272964\pi$
$197$	257.794			1.30860			0.654299	+	0.756236i	$0.272964\pi$
$198$		0			0
$199$	−328.501			−1.65076			−0.825378	−	0.564580i	$-0.809038\pi$
$199$	−328.501			−1.65076			−0.825378	+	0.564580i	$0.809038\pi$
$200$		0			0
$201$		−	137.843i		−	0.685785i
$202$		0			0
$203$		−	215.189i		−	1.06004i
$204$		0			0
$205$	−32.9831	+	308.961i	−0.160893	+	1.50713i
$206$		0			0
$207$	−86.6431	−	86.6431i	−0.418566	−	0.418566i
$208$		0			0
$209$			229.933i			1.10016i
$210$		0			0
$211$	−51.3916	−	51.3916i	−0.243562	−	0.243562i	0.574760	−	0.818322i	$-0.305095\pi$
$211$	−51.3916	−	51.3916i	−0.243562	−	0.243562i	−0.818322	+	0.574760i	$0.805095\pi$
$212$		0			0
$213$		−	46.5350i		−	0.218474i
$214$		0			0
$215$	17.1286	−	160.448i	0.0796681	−	0.746270i
$216$		0			0
$217$	160.014	−	160.014i	0.737390	−	0.737390i
$218$		0			0
$219$	−2.66900	−	2.66900i	−0.0121872	−	0.0121872i
$220$		0			0
$221$	35.6808	+	35.6808i	0.161451	+	0.161451i
$222$		0			0
$223$	−200.019	+	200.019i	−0.896948	+	0.896948i	−0.995165	−	0.0982168i	$-0.968686\pi$
$223$	−200.019	+	200.019i	−0.896948	+	0.896948i	0.0982168	+	0.995165i	$0.468686\pi$
$224$		0			0
$225$	−130.914	−	28.2736i	−0.581839	−	0.125660i
$226$		0			0
$227$		−	47.5480i		−	0.209462i	−0.994501	−	0.104731i	$-0.966602\pi$
$227$		−	47.5480i		−	0.209462i	0.994501	−	0.104731i	$-0.0333982\pi$
$228$		0			0
$229$	65.5550	+	65.5550i	0.286266	+	0.286266i	0.835602	−	0.549336i	$-0.185119\pi$
$229$	65.5550	+	65.5550i	0.286266	+	0.286266i	−0.549336	+	0.835602i	$0.685119\pi$
$230$		0			0
$231$			208.995i			0.904739i
$232$		0			0
$233$	201.087	+	201.087i	0.863035	+	0.863035i	0.991689	−	0.128655i	$-0.0410659\pi$
$233$	201.087	+	201.087i	0.863035	+	0.863035i	−0.128655	+	0.991689i	$0.541066\pi$
$234$		0			0
$235$	−58.9030	−	72.9824i	−0.250651	−	0.310563i
$236$		0			0
$237$			171.908i			0.725352i
$238$		0			0
$239$		−	245.088i		−	1.02547i	−0.858546	−	0.512737i	$-0.828632\pi$
$239$		−	245.088i		−	1.02547i	0.858546	−	0.512737i	$-0.171368\pi$
$240$		0			0
$241$	462.483			1.91902			0.959508	−	0.281682i	$-0.0908922\pi$
$241$	462.483			1.91902			0.959508	+	0.281682i	$0.0908922\pi$
$242$		0			0
$243$	−238.825			−0.982819
$244$		0			0
$245$	−52.8729	+	495.273i	−0.215808	+	2.02152i
$246$		0			0
$247$	−120.381	+	120.381i	−0.487372	+	0.487372i
$248$		0			0
$249$	7.22183			0.0290033
$250$		0			0
$251$	53.5564	−	53.5564i	0.213372	−	0.213372i	−0.592326	−	0.805698i	$-0.701790\pi$
$251$	53.5564	−	53.5564i	0.213372	−	0.213372i	0.805698	+	0.592326i	$0.201790\pi$
$252$		0			0
$253$	−205.444			−0.812030
$254$		0			0
$255$	−45.4746	−	56.3443i	−0.178332	−	0.220958i
$256$		0			0
$257$	128.524	+	128.524i	0.500092	+	0.500092i	0.911466	−	0.411374i	$-0.134951\pi$
$257$	128.524	+	128.524i	0.500092	+	0.500092i	−0.411374	+	0.911466i	$0.634951\pi$
$258$		0			0
$259$	429.360	−	429.360i	1.65776	−	1.65776i
$260$		0			0
$261$	66.8674	−	66.8674i	0.256197	−	0.256197i
$262$		0			0
$263$	−351.385	−	351.385i	−1.33606	−	1.33606i	−0.899836	−	0.436228i	$-0.856314\pi$
$263$	−351.385	−	351.385i	−1.33606	−	1.33606i	−0.436228	−	0.899836i	$-0.643686\pi$
$264$		0			0
$265$	−34.0979	+	319.403i	−0.128671	+	1.20529i
$266$		0			0
$267$	117.176			0.438861
$268$		0			0
$269$	45.4562	−	45.4562i	0.168982	−	0.168982i	−0.617550	−	0.786532i	$-0.711875\pi$
$269$	45.4562	−	45.4562i	0.168982	−	0.168982i	0.786532	+	0.617550i	$0.211875\pi$
$270$		0			0
$271$	43.2087			0.159442			0.0797209	−	0.996817i	$-0.474597\pi$
$271$	43.2087			0.159442			0.0797209	+	0.996817i	$0.474597\pi$
$272$		0			0
$273$	−109.418	+	109.418i	−0.400800	+	0.400800i
$274$		0			0
$275$	−188.728	+	121.687i	−0.686284	+	0.442499i
$276$		0			0
$277$	53.1202			0.191770			0.0958849	−	0.995392i	$-0.469432\pi$
$277$	53.1202			0.191770			0.0958849	+	0.995392i	$0.469432\pi$
$278$		0			0
$279$	99.4448			0.356433
$280$		0			0
$281$		−	146.320i		−	0.520712i	−0.965513	−	0.260356i	$-0.916160\pi$
$281$		−	146.320i		−	0.520712i	0.965513	−	0.260356i	$-0.0838399\pi$
$282$		0			0
$283$			87.7034i			0.309906i	0.987922	+	0.154953i	$0.0495226\pi$
$283$			87.7034i			0.309906i	−0.987922	+	0.154953i	$0.950477\pi$
$284$		0			0
$285$	190.096	−	153.423i	0.667003	−	0.538328i
$286$		0			0
$287$	535.691	+	535.691i	1.86652	+	1.86652i
$288$		0			0
$289$		−	231.432i		−	0.800802i
$290$		0			0
$291$	−196.932	−	196.932i	−0.676744	−	0.676744i
$292$		0			0
$293$		−	257.077i		−	0.877395i	−0.898635	−	0.438697i	$-0.855440\pi$
$293$		−	257.077i		−	0.877395i	0.898635	−	0.438697i	$-0.144560\pi$
$294$		0			0
$295$	11.3686	+	14.0861i	0.0385378	+	0.0477493i
$296$		0			0
$297$	−174.044	+	174.044i	−0.586005	+	0.586005i
$298$		0			0
$299$	−107.559	−	107.559i	−0.359730	−	0.359730i
$300$		0			0
$301$	−278.192	−	278.192i	−0.924227	−	0.924227i
$302$		0			0
$303$	−175.908	+	175.908i	−0.580555	+	0.580555i
$304$		0			0
$305$	−233.272	−	289.030i	−0.764826	−	0.947640i
$306$		0			0
$307$			601.105i			1.95800i	0.203870	+	0.978998i	$0.434648\pi$
$307$			601.105i			1.95800i	−0.203870	+	0.978998i	$0.565352\pi$
$308$		0			0
$309$	−139.731	−	139.731i	−0.452203	−	0.452203i
$310$		0			0
$311$			7.34424i			0.0236149i	0.999930	+	0.0118075i	$0.00375852\pi$
$311$			7.34424i			0.0236149i	−0.999930	+	0.0118075i	$0.996241\pi$
$312$		0			0
$313$	−170.573	−	170.573i	−0.544962	−	0.544962i	0.380017	−	0.924979i	$-0.375918\pi$
$313$	−170.573	−	170.573i	−0.544962	−	0.544962i	−0.924979	+	0.380017i	$0.875918\pi$
$314$		0			0
$315$	−254.112	+	205.090i	−0.806705	+	0.651079i
$316$		0			0
$317$		−	266.389i		−	0.840345i	−0.907444	−	0.420172i	$-0.861970\pi$
$317$		−	266.389i		−	0.840345i	0.907444	−	0.420172i	$-0.138030\pi$
$318$		0			0
$319$		−	158.552i		−	0.497029i
$320$		0			0
$321$	33.9449			0.105747
$322$		0			0
$323$	−194.225			−0.601316
$324$		0			0
$325$	−162.517	−	35.0990i	−0.500052	−	0.107997i
$326$		0			0
$327$	−18.4000	+	18.4000i	−0.0562693	+	0.0562693i
$328$		0			0
$329$	−228.669			−0.695043
$330$		0			0
$331$	66.9868	−	66.9868i	0.202377	−	0.202377i	−0.598641	−	0.801018i	$-0.704292\pi$
$331$	66.9868	−	66.9868i	0.202377	−	0.202377i	0.801018	+	0.598641i	$0.204292\pi$
$332$		0			0
$333$	266.837			0.801312
$334$		0			0
$335$	38.3326	−	359.071i	0.114426	−	1.07185i
$336$		0			0
$337$	−167.759	−	167.759i	−0.497801	−	0.497801i	0.412952	−	0.910753i	$-0.364498\pi$
$337$	−167.759	−	167.759i	−0.497801	−	0.497801i	−0.910753	+	0.412952i	$0.864498\pi$
$338$		0			0
$339$	119.275	−	119.275i	0.351843	−	0.351843i
$340$		0			0
$341$	117.899	−	117.899i	0.345745	−	0.345745i
$342$		0			0
$343$	436.335	+	436.335i	1.27211	+	1.27211i
$344$		0			0
$345$	137.083	+	169.849i	0.397341	+	0.492316i
$346$		0			0
$347$	575.495			1.65849			0.829243	−	0.558888i	$-0.188772\pi$
$347$	575.495			1.65849			0.829243	+	0.558888i	$0.188772\pi$
$348$		0			0
$349$	218.302	−	218.302i	0.625508	−	0.625508i	−0.321426	−	0.946935i	$-0.604162\pi$
$349$	218.302	−	218.302i	0.625508	−	0.625508i	0.946935	+	0.321426i	$0.104162\pi$
$350$		0			0
$351$	−182.240			−0.519201
$352$		0			0
$353$	194.122	−	194.122i	0.549920	−	0.549920i	−0.376498	−	0.926418i	$-0.622872\pi$
$353$	194.122	−	194.122i	0.549920	−	0.549920i	0.926418	+	0.376498i	$0.122872\pi$
$354$		0			0
$355$	12.9409	−	121.221i	0.0364532	−	0.341466i
$356$		0			0
$357$	−176.538			−0.494505
$358$		0			0
$359$	545.851			1.52048			0.760238	−	0.649644i	$-0.225082\pi$
$359$	545.851			1.52048			0.760238	+	0.649644i	$0.225082\pi$
$360$		0			0
$361$		−	294.282i		−	0.815186i
$362$		0			0
$363$		−	76.9509i		−	0.211986i
$364$		0			0
$365$	−6.21033	−	7.69477i	−0.0170146	−	0.0210816i
$366$		0			0
$367$	−300.825	−	300.825i	−0.819686	−	0.819686i	0.166376	−	0.986062i	$-0.446793\pi$
$367$	−300.825	−	300.825i	−0.819686	−	0.819686i	−0.986062	+	0.166376i	$0.946793\pi$
$368$		0			0
$369$			332.919i			0.902221i
$370$		0			0
$371$	553.796	+	553.796i	1.49271	+	1.49271i
$372$		0			0
$373$		−	73.3291i		−	0.196593i	−0.995157	−	0.0982963i	$-0.968661\pi$
$373$		−	73.3291i		−	0.196593i	0.995157	−	0.0982963i	$-0.0313393\pi$
$374$		0			0
$375$	226.533	+	74.8336i	0.604089	+	0.199556i
$376$		0			0
$377$	83.0095	−	83.0095i	0.220184	−	0.220184i
$378$		0			0
$379$	−93.5200	−	93.5200i	−0.246755	−	0.246755i	0.572883	−	0.819637i	$-0.305825\pi$
$379$	−93.5200	−	93.5200i	−0.246755	−	0.246755i	−0.819637	+	0.572883i	$0.805825\pi$
$380$		0			0
$381$	96.5762	+	96.5762i	0.253481	+	0.253481i
$382$		0			0
$383$	−79.4324	+	79.4324i	−0.207395	+	0.207395i	−0.803159	−	0.595764i	$-0.796849\pi$
$383$	−79.4324	+	79.4324i	−0.207395	+	0.207395i	0.595764	+	0.803159i	$0.296849\pi$
$384$		0			0
$385$	−58.1193	+	544.417i	−0.150959	+	1.41407i
$386$		0			0
$387$		−	172.890i		−	0.446744i
$388$		0			0
$389$	97.6035	+	97.6035i	0.250909	+	0.250909i	0.821343	−	0.570434i	$-0.193225\pi$
$389$	97.6035	+	97.6035i	0.250909	+	0.250909i	−0.570434	+	0.821343i	$0.693225\pi$
$390$		0			0
$391$		−	173.539i		−	0.443833i
$392$		0			0
$393$	−42.1774	−	42.1774i	−0.107322	−	0.107322i
$394$		0			0
$395$	−47.8059	+	447.810i	−0.121028	+	1.13370i
$396$		0			0
$397$			299.500i			0.754407i	0.926130	+	0.377204i	$0.123114\pi$
$397$			299.500i			0.754407i	−0.926130	+	0.377204i	$0.876886\pi$
$398$		0			0
$399$		−	595.610i		−	1.49276i
$400$		0			0
$401$	−90.9226			−0.226740			−0.113370	−	0.993553i	$-0.536164\pi$
$401$	−90.9226			−0.226740			−0.113370	+	0.993553i	$0.536164\pi$
$402$		0			0
$403$	123.451			0.306331
$404$		0			0
$405$	20.3045	+	2.16761i	0.0501346	+	0.00535212i
$406$		0			0
$407$	316.355	−	316.355i	0.777284	−	0.777284i
$408$		0			0
$409$	−657.734			−1.60815			−0.804076	−	0.594526i	$-0.797340\pi$
$409$	−657.734			−1.60815			−0.804076	+	0.594526i	$0.797340\pi$
$410$		0			0
$411$	−195.282	+	195.282i	−0.475138	+	0.475138i
$412$		0			0
$413$	44.1345			0.106863
$414$		0			0
$415$	18.8124	+	2.00832i	0.0453310	+	0.00483931i
$416$		0			0
$417$	158.430	+	158.430i	0.379927	+	0.379927i
$418$		0			0
$419$	145.179	−	145.179i	0.346489	−	0.346489i	−0.512311	−	0.858800i	$-0.671210\pi$
$419$	145.179	−	145.179i	0.346489	−	0.346489i	0.858800	+	0.512311i	$0.171210\pi$
$420$		0			0
$421$	19.6145	−	19.6145i	0.0465904	−	0.0465904i	−0.683428	−	0.730018i	$-0.739512\pi$
$421$	19.6145	−	19.6145i	0.0465904	−	0.0465904i	0.730018	+	0.683428i	$0.239512\pi$
$422$		0			0
$423$	−71.0562	−	71.0562i	−0.167982	−	0.167982i
$424$		0			0
$425$	−102.790	−	159.419i	−0.241858	−	0.375104i
$426$		0			0
$427$	−905.592			−2.12082
$428$		0			0
$429$	−80.6201	+	80.6201i	−0.187926	+	0.187926i
$430$		0			0
$431$	184.193			0.427362			0.213681	−	0.976903i	$-0.431455\pi$
$431$	184.193			0.427362			0.213681	+	0.976903i	$0.431455\pi$
$432$		0			0
$433$	401.221	−	401.221i	0.926607	−	0.926607i	−0.0708779	−	0.997485i	$-0.522580\pi$
$433$	401.221	−	401.221i	0.926607	−	0.926607i	0.997485	+	0.0708779i	$0.0225801\pi$
$434$		0			0
$435$	−131.082	+	105.794i	−0.301338	+	0.243205i
$436$		0			0
$437$	585.489			1.33979
$438$		0			0
$439$	705.526			1.60712			0.803561	−	0.595223i	$-0.202936\pi$
$439$	705.526			1.60712			0.803561	+	0.595223i	$0.202936\pi$
$440$		0			0
$441$			533.679i			1.21016i
$442$		0			0
$443$			499.336i			1.12717i	0.826058	+	0.563585i	$0.190578\pi$
$443$			499.336i			1.12717i	−0.826058	+	0.563585i	$0.809422\pi$
$444$		0			0
$445$	305.235	+	32.5854i	0.685922	+	0.0732256i
$446$		0			0
$447$	256.036	+	256.036i	0.572788	+	0.572788i
$448$		0			0
$449$		−	786.125i		−	1.75083i	−0.483368	−	0.875417i	$-0.660587\pi$
$449$		−	786.125i		−	1.75083i	0.483368	−	0.875417i	$-0.339413\pi$
$450$		0			0
$451$	394.700	+	394.700i	0.875167	+	0.875167i
$452$		0			0
$453$			92.7306i			0.204703i
$454$		0			0
$455$	−315.456	+	254.600i	−0.693310	+	0.559560i
$456$		0			0
$457$	411.045	−	411.045i	0.899443	−	0.899443i	−0.0959440	−	0.995387i	$-0.530587\pi$
$457$	411.045	−	411.045i	0.899443	−	0.899443i	0.995387	+	0.0959440i	$0.0305870\pi$
$458$		0			0
$459$	−147.015	−	147.015i	−0.320294	−	0.320294i
$460$		0			0
$461$	−544.187	−	544.187i	−1.18045	−	1.18045i	−0.979628	−	0.200821i	$-0.935639\pi$
$461$	−544.187	−	544.187i	−1.18045	−	1.18045i	−0.200821	−	0.979628i	$-0.564361\pi$
$462$		0			0
$463$	109.453	−	109.453i	0.236400	−	0.236400i	−0.578957	−	0.815358i	$-0.696540\pi$
$463$	109.453	−	109.453i	0.236400	−	0.236400i	0.815358	+	0.578957i	$0.196540\pi$
$464$		0			0
$465$	−176.141	−	18.8039i	−0.378797	−	0.0404384i
$466$		0			0
$467$		−	462.541i		−	0.990452i	−0.868764	−	0.495226i	$-0.835085\pi$
$467$		−	462.541i		−	0.990452i	0.868764	−	0.495226i	$-0.164915\pi$
$468$		0			0
$469$	−622.574	−	622.574i	−1.32745	−	1.32745i
$470$		0			0
$471$			269.096i			0.571329i
$472$		0			0
$473$	−204.974	−	204.974i	−0.433348	−	0.433348i
$474$		0			0
$475$	537.852	−	346.794i	1.13232	−	0.730093i
$476$		0			0
$477$			344.171i			0.721533i
$478$		0			0
$479$			127.125i			0.265397i	0.991156	+	0.132698i	$0.0423642\pi$
$479$			127.125i			0.265397i	−0.991156	+	0.132698i	$0.957636\pi$
$480$		0			0
$481$	331.253			0.688675
$482$		0			0
$483$	532.172			1.10181
$484$		0			0
$485$	−458.231	−	567.761i	−0.944806	−	1.17064i
$486$		0			0
$487$	−376.646	+	376.646i	−0.773401	+	0.773401i	−0.978699	−	0.205299i	$-0.934183\pi$
$487$	−376.646	+	376.646i	−0.773401	+	0.773401i	0.205299	+	0.978699i	$0.434183\pi$
$488$		0			0
$489$	187.432			0.383297
$490$		0			0
$491$	552.932	−	552.932i	1.12613	−	1.12613i	0.135334	−	0.990800i	$-0.456789\pi$
$491$	552.932	−	552.932i	1.12613	−	1.12613i	0.990800	−	0.135334i	$-0.0432107\pi$
$492$		0			0
$493$	133.929			0.271662
$494$		0			0
$495$	−187.231	+	151.111i	−0.378245	+	0.305276i
$496$		0			0
$497$	−210.178	−	210.178i	−0.422893	−	0.422893i
$498$		0			0
$499$	−308.855	+	308.855i	−0.618947	+	0.618947i	−0.945261	−	0.326314i	$-0.894193\pi$
$499$	−308.855	+	308.855i	−0.618947	+	0.618947i	0.326314	+	0.945261i	$0.394193\pi$
$500$		0			0
$501$	18.3009	−	18.3009i	0.0365286	−	0.0365286i
$502$		0			0
$503$	−345.746	−	345.746i	−0.687368	−	0.687368i	0.274281	−	0.961650i	$-0.411560\pi$
$503$	−345.746	−	345.746i	−0.687368	−	0.687368i	−0.961650	+	0.274281i	$0.911560\pi$
$504$		0			0
$505$	−507.147	+	409.310i	−1.00425	+	0.810516i
$506$		0			0
$507$	238.135			0.469694
$508$		0			0
$509$	−156.286	+	156.286i	−0.307046	+	0.307046i	−0.843762	−	0.536717i	$-0.819664\pi$
$509$	−156.286	+	156.286i	−0.307046	+	0.307046i	0.536717	+	0.843762i	$0.319664\pi$
$510$		0			0
$511$	−24.1093			−0.0471807
$512$		0			0
$513$	496.003	−	496.003i	0.966867	−	0.966867i
$514$		0			0
$515$	−325.132	−	402.847i	−0.631324	−	0.782227i
$516$		0			0
$517$	−168.485			−0.325889
$518$		0			0
$519$	−330.005			−0.635848
$520$		0			0
$521$		−	483.674i		−	0.928358i	−0.885741	−	0.464179i	$-0.846349\pi$
$521$		−	483.674i		−	0.928358i	0.885741	−	0.464179i	$-0.153651\pi$
$522$		0			0
$523$		−	114.482i		−	0.218895i	−0.993993	−	0.109448i	$-0.965092\pi$
$523$		−	114.482i		−	0.218895i	0.993993	−	0.109448i	$-0.0349082\pi$
$524$		0			0
$525$	488.874	−	315.214i	0.931188	−	0.600407i
$526$		0			0
$527$	99.5895	+	99.5895i	0.188974	+	0.188974i
$528$		0			0
$529$		−	5.87038i		−	0.0110971i
$530$		0			0
$531$	13.7143	+	13.7143i	0.0258273	+	0.0258273i
$532$		0			0
$533$			413.288i			0.775399i
$534$		0			0
$535$	88.4241	+	9.43971i	0.165279	+	0.0176443i
$536$		0			0
$537$	90.0527	−	90.0527i	0.167696	−	0.167696i
$538$		0			0
$539$	632.715	+	632.715i	1.17387	+	1.17387i
$540$		0			0
$541$	575.569	+	575.569i	1.06390	+	1.06390i	0.997814	+	0.0660852i	$0.0210509\pi$
$541$	575.569	+	575.569i	1.06390	+	1.06390i	0.0660852	+	0.997814i	$0.478949\pi$
$542$		0			0
$543$	96.7998	−	96.7998i	0.178269	−	0.178269i
$544$		0			0
$545$	−53.0478	+	42.8140i	−0.0973353	+	0.0785579i
$546$		0			0
$547$		−	1053.61i		−	1.92616i	−0.269219	−	0.963079i	$-0.586766\pi$
$547$		−	1053.61i		−	1.92616i	0.269219	−	0.963079i	$-0.413234\pi$
$548$		0			0
$549$	−281.402	−	281.402i	−0.512572	−	0.512572i
$550$		0			0
$551$			451.855i			0.820063i
$552$		0			0
$553$	776.434	+	776.434i	1.40404	+	1.40404i
$554$		0			0
$555$	−472.632	−	50.4559i	−0.851590	−	0.0909115i
$556$		0			0
$557$		−	680.234i		−	1.22125i	−0.791922	−	0.610623i	$-0.790919\pi$
$557$		−	680.234i		−	1.22125i	0.791922	−	0.610623i	$-0.209081\pi$
$558$		0			0
$559$		−	214.626i		−	0.383947i
$560$		0			0
$561$	−130.074			−0.231862
$562$		0			0
$563$	408.818			0.726142			0.363071	−	0.931761i	$-0.381728\pi$
$563$	408.818			0.726142			0.363071	+	0.931761i	$0.381728\pi$
$564$		0			0
$565$	343.872	−	277.534i	0.608623	−	0.491211i
$566$		0			0
$567$	35.2049	−	35.2049i	0.0620898	−	0.0620898i
$568$		0			0
$569$	324.426			0.570169			0.285084	−	0.958502i	$-0.407978\pi$
$569$	324.426			0.570169			0.285084	+	0.958502i	$0.407978\pi$
$570$		0			0
$571$	124.307	−	124.307i	0.217700	−	0.217700i	−0.589829	−	0.807528i	$-0.700805\pi$
$571$	124.307	−	124.307i	0.217700	−	0.217700i	0.807528	+	0.589829i	$0.200805\pi$
$572$		0			0
$573$	−630.079			−1.09962
$574$		0			0
$575$	309.858	+	480.567i	0.538883	+	0.835768i
$576$		0			0
$577$	−303.425	−	303.425i	−0.525866	−	0.525866i	0.393471	−	0.919337i	$-0.371274\pi$
$577$	−303.425	−	303.425i	−0.525866	−	0.525866i	−0.919337	+	0.393471i	$0.871274\pi$
$578$		0			0
$579$	287.357	−	287.357i	0.496299	−	0.496299i
$580$		0			0
$581$	32.6178	−	32.6178i	0.0561408	−	0.0561408i
$582$		0			0
$583$	408.040	+	408.040i	0.699897	+	0.699897i
$584$		0			0
$585$	−177.138	−	18.9104i	−0.302800	−	0.0323254i
$586$		0			0
$587$	−279.206			−0.475649			−0.237824	−	0.971308i	$-0.576434\pi$
$587$	−279.206			−0.475649			−0.237824	+	0.971308i	$0.576434\pi$
$588$		0			0
$589$	−335.998	+	335.998i	−0.570455	+	0.570455i
$590$		0			0
$591$	−492.023			−0.832526
$592$		0			0
$593$	−383.903	+	383.903i	−0.647392	+	0.647392i	−0.952362	−	0.304970i	$-0.901354\pi$
$593$	−383.903	+	383.903i	−0.647392	+	0.647392i	0.304970	+	0.952362i	$0.401354\pi$
$594$		0			0
$595$	−459.870	−	49.0935i	−0.772892	−	0.0825100i
$596$		0			0
$597$	626.973			1.05021
$598$		0			0
$599$	−169.873			−0.283594			−0.141797	−	0.989896i	$-0.545288\pi$
$599$	−169.873			−0.283594			−0.141797	+	0.989896i	$0.545288\pi$
$600$		0			0
$601$			283.673i			0.472002i	0.971753	+	0.236001i	$0.0758369\pi$
$601$			283.673i			0.472002i	−0.971753	+	0.236001i	$0.924163\pi$
$602$		0			0
$603$		−	386.915i		−	0.641650i
$604$		0			0
$605$	21.3992	−	200.452i	0.0353706	−	0.331325i
$606$		0			0
$607$	438.351	+	438.351i	0.722160	+	0.722160i	0.969045	−	0.246885i	$-0.0794069\pi$
$607$	438.351	+	438.351i	0.722160	+	0.722160i	−0.246885	+	0.969045i	$0.579407\pi$
$608$		0			0
$609$			410.707i			0.674396i
$610$		0			0
$611$	−88.2095	−	88.2095i	−0.144369	−	0.144369i
$612$		0			0
$613$			165.499i			0.269981i	0.990847	+	0.134991i	$0.0431005\pi$
$613$			165.499i			0.269981i	−0.990847	+	0.134991i	$0.956900\pi$
$614$		0			0
$615$	62.9513	−	589.680i	0.102360	−	0.958830i
$616$		0			0
$617$	219.108	−	219.108i	0.355118	−	0.355118i	−0.506892	−	0.862010i	$-0.669206\pi$
$617$	219.108	−	219.108i	0.355118	−	0.355118i	0.862010	+	0.506892i	$0.169206\pi$
$618$		0			0
$619$	365.140	+	365.140i	0.589888	+	0.589888i	0.937601	−	0.347713i	$-0.113042\pi$
$619$	365.140	+	365.140i	0.589888	+	0.589888i	−0.347713	+	0.937601i	$0.613042\pi$
$620$		0			0
$621$	443.174	+	443.174i	0.713646	+	0.713646i
$622$		0			0
$623$	529.231	−	529.231i	0.849488	−	0.849488i
$624$		0			0
$625$	569.294	+	257.933i	0.910870	+	0.412693i
$626$		0			0
$627$		−	438.849i		−	0.699918i
$628$		0			0
$629$	267.225	+	267.225i	0.424842	+	0.424842i
$630$		0			0
$631$		−	1113.61i		−	1.76484i	−0.470463	−	0.882420i	$-0.655913\pi$
$631$		−	1113.61i		−	1.76484i	0.470463	−	0.882420i	$-0.344087\pi$
$632$		0			0
$633$	98.0856	+	98.0856i	0.154953	+	0.154953i
$634$		0			0
$635$	224.718	+	278.431i	0.353886	+	0.438475i
$636$		0			0
$637$			662.511i			1.04005i
$638$		0			0
$639$		−	130.621i		−	0.204414i
$640$		0			0
$641$	279.808			0.436518			0.218259	−	0.975891i	$-0.429962\pi$
$641$	279.808			0.436518			0.218259	+	0.975891i	$0.429962\pi$
$642$		0			0
$643$	−68.4686			−0.106483			−0.0532415	−	0.998582i	$-0.516955\pi$
$643$	−68.4686			−0.106483			−0.0532415	+	0.998582i	$0.516955\pi$
$644$		0			0
$645$	−32.6915	+	306.230i	−0.0506846	+	0.474775i
$646$		0			0
$647$	−60.8229	+	60.8229i	−0.0940075	+	0.0940075i	−0.752547	−	0.658539i	$-0.771175\pi$
$647$	−60.8229	+	60.8229i	−0.0940075	+	0.0940075i	0.658539	+	0.752547i	$0.271175\pi$
$648$		0			0
$649$	32.5186			0.0501057
$650$		0			0
$651$	−305.401	+	305.401i	−0.469125	+	0.469125i
$652$		0			0
$653$	−815.643			−1.24907			−0.624536	−	0.780996i	$-0.714712\pi$
$653$	−815.643			−1.24907			−0.624536	+	0.780996i	$0.714712\pi$
$654$		0			0
$655$	−98.1403	−	121.598i	−0.149832	−	0.185646i
$656$		0			0
$657$	−7.49169	−	7.49169i	−0.0114029	−	0.0114029i
$658$		0			0
$659$	−765.294	+	765.294i	−1.16130	+	1.16130i	−0.177103	+	0.984192i	$0.556673\pi$
$659$	−765.294	+	765.294i	−1.16130	+	1.16130i	−0.984192	+	0.177103i	$0.943327\pi$
$660$		0			0
$661$	−423.035	+	423.035i	−0.639993	+	0.639993i	−0.950553	−	0.310561i	$-0.899483\pi$
$661$	−423.035	+	423.035i	−0.639993	+	0.639993i	0.310561	+	0.950553i	$0.399483\pi$
$662$		0			0
$663$	−68.1000	−	68.1000i	−0.102715	−	0.102715i
$664$		0			0
$665$	165.633	−	1551.52i	0.249072	−	2.33312i
$666$		0			0
$667$	−403.729			−0.605290
$668$		0			0
$669$	381.755	−	381.755i	0.570636	−	0.570636i
$670$		0			0
$671$	−667.245			−0.994404
$672$		0			0
$673$	−372.278	+	372.278i	−0.553162	+	0.553162i	−0.927352	−	0.374190i	$-0.877921\pi$
$673$	−372.278	+	372.278i	−0.553162	+	0.553162i	0.374190	+	0.927352i	$0.377921\pi$
$674$		0			0
$675$	669.616	+	144.618i	0.992023	+	0.214249i
$676$		0			0
$677$	−244.469			−0.361106			−0.180553	−	0.983565i	$-0.557789\pi$
$677$	−244.469			−0.361106			−0.180553	+	0.983565i	$0.557789\pi$
$678$		0			0
$679$	−1778.91			−2.61990
$680$		0			0
$681$			90.7496i			0.133259i
$682$		0			0
$683$		−	434.494i		−	0.636155i	−0.948065	−	0.318077i	$-0.896963\pi$
$683$		−	434.494i		−	0.636155i	0.948065	−	0.318077i	$-0.103037\pi$
$684$		0			0
$685$	−563.002	+	454.390i	−0.821900	+	0.663343i
$686$		0			0
$687$	−125.118	−	125.118i	−0.182122	−	0.182122i
$688$		0			0
$689$			427.256i			0.620110i
$690$		0			0
$691$	140.105	+	140.105i	0.202756	+	0.202756i	0.801180	−	0.598424i	$-0.204206\pi$
$691$	140.105	+	140.105i	0.202756	+	0.202756i	−0.598424	+	0.801180i	$0.704206\pi$
$692$		0			0
$693$			586.634i			0.846514i
$694$		0			0
$695$	368.641	+	456.756i	0.530419	+	0.657203i
$696$		0			0
$697$	−333.404	+	333.404i	−0.478342	+	0.478342i
$698$		0			0
$699$	−383.793	−	383.793i	−0.549060	−	0.549060i
$700$		0			0
$701$	−333.050	−	333.050i	−0.475106	−	0.475106i	0.428456	−	0.903563i	$-0.359058\pi$
$701$	−333.050	−	333.050i	−0.475106	−	0.475106i	−0.903563	+	0.428456i	$0.859058\pi$
$702$		0			0
$703$	−901.572	+	901.572i	−1.28246	+	1.28246i
$704$		0			0
$705$	112.422	+	139.294i	0.159463	+	0.197579i
$706$		0			0
$707$			1589.00i			2.24752i
$708$		0			0
$709$	588.688	+	588.688i	0.830308	+	0.830308i	0.987559	−	0.157251i	$-0.0502632\pi$
$709$	588.688	+	588.688i	0.830308	+	0.830308i	−0.157251	+	0.987559i	$0.550263\pi$
$710$		0			0
$711$			482.535i			0.678671i
$712$		0			0
$713$	−300.211	−	300.211i	−0.421054	−	0.421054i
$714$		0			0
$715$	−232.430	+	187.590i	−0.325076	+	0.262364i
$716$		0			0
$717$			467.773i			0.652403i
$718$		0			0
$719$			837.132i			1.16430i	0.813081	+	0.582150i	$0.197788\pi$
$719$			837.132i			1.16430i	−0.813081	+	0.582150i	$0.802212\pi$
$720$		0			0
$721$	−1262.20			−1.75063
$722$		0			0
$723$	−882.690			−1.22087
$724$		0			0
$725$	−370.880	+	239.135i	−0.511559	+	0.329841i
$726$		0			0
$727$	−115.757	+	115.757i	−0.159225	+	0.159225i	−0.782223	−	0.622998i	$-0.785914\pi$
$727$	−115.757	+	115.757i	−0.159225	+	0.159225i	0.622998	+	0.782223i	$0.285914\pi$
$728$		0			0
$729$	492.575			0.675686
$730$		0			0
$731$	173.142	−	173.142i	0.236856	−	0.236856i
$732$		0			0
$733$	123.197			0.168073			0.0840363	−	0.996463i	$-0.473219\pi$
$733$	123.197			0.168073			0.0840363	+	0.996463i	$0.473219\pi$
$734$		0			0
$735$	100.913	−	945.273i	0.137296	−	1.28609i
$736$		0			0
$737$	−458.716	−	458.716i	−0.622410	−	0.622410i
$738$		0			0
$739$	−641.523	+	641.523i	−0.868096	+	0.868096i	−0.992262	−	0.124166i	$-0.960375\pi$
$739$	−641.523	+	641.523i	−0.868096	+	0.868096i	0.124166	+	0.992262i	$0.460375\pi$
$740$		0			0
$741$	229.758	−	229.758i	0.310064	−	0.310064i
$742$		0			0
$743$	−84.7652	−	84.7652i	−0.114085	−	0.114085i	0.647760	−	0.761845i	$-0.275706\pi$
$743$	−84.7652	−	84.7652i	−0.114085	−	0.114085i	−0.761845	+	0.647760i	$0.775706\pi$
$744$		0			0
$745$	595.756	+	738.158i	0.799673	+	0.990816i
$746$		0			0
$747$	20.2712			0.0271368
$748$		0			0
$749$	153.314	−	153.314i	0.204691	−	0.204691i
$750$		0			0
$751$	137.548			0.183153			0.0915766	−	0.995798i	$-0.470809\pi$
$751$	137.548			0.183153			0.0915766	+	0.995798i	$0.470809\pi$
$752$		0			0
$753$	−102.217	+	102.217i	−0.135747	+	0.135747i
$754$		0			0
$755$	−25.7874	+	241.557i	−0.0341555	+	0.319943i
$756$		0			0
$757$	−857.792			−1.13315			−0.566574	−	0.824011i	$-0.691731\pi$
$757$	−857.792			−1.13315			−0.566574	+	0.824011i	$0.691731\pi$
$758$		0			0
$759$	392.108			0.516611
$760$		0			0
$761$			353.070i			0.463956i	0.972721	+	0.231978i	$0.0745197\pi$
$761$			353.070i			0.463956i	−0.972721	+	0.231978i	$0.925480\pi$
$762$		0			0
$763$			166.210i			0.217837i
$764$		0			0
$765$	−127.644	−	158.155i	−0.166855	−	0.206738i
$766$		0			0
$767$	17.0250	+	17.0250i	0.0221968	+	0.0221968i
$768$		0			0
$769$			401.035i			0.521503i	0.965406	+	0.260751i	$0.0839703\pi$
$769$			401.035i			0.521503i	−0.965406	+	0.260751i	$0.916030\pi$
$770$		0			0
$771$	−245.299	−	245.299i	−0.318157	−	0.318157i
$772$		0			0
$773$		−	396.076i		−	0.512388i	−0.966625	−	0.256194i	$-0.917531\pi$
$773$		−	396.076i		−	0.512388i	0.966625	−	0.256194i	$-0.0824686\pi$
$774$		0			0
$775$	−453.605	−	97.9657i	−0.585297	−	0.126407i
$776$		0			0
$777$	−819.472	+	819.472i	−1.05466	+	1.05466i
$778$		0			0
$779$	−1124.85	−	1124.85i	−1.44396	−	1.44396i
$780$		0			0
$781$	−154.860	−	154.860i	−0.198285	−	0.198285i
$782$		0			0
$783$	−342.023	+	342.023i	−0.436811	+	0.436811i
$784$		0			0
$785$	−74.8328	+	700.977i	−0.0953284	+	0.892964i
$786$		0			0
$787$		−	184.472i		−	0.234399i	−0.993108	−	0.117200i	$-0.962608\pi$
$787$		−	184.472i		−	0.234399i	0.993108	−	0.117200i	$-0.0373917\pi$
$788$		0			0
$789$	670.650	+	670.650i	0.850000	+	0.850000i
$790$		0			0
$791$		−	1077.42i		−	1.36210i
$792$		0			0
$793$	−349.334	−	349.334i	−0.440522	−	0.440522i
$794$		0			0
$795$	65.0788	−	609.609i	0.0818602	−	0.766804i
$796$		0			0
$797$		−	187.027i		−	0.234664i	−0.993093	−	0.117332i	$-0.962566\pi$
$797$		−	187.027i		−	0.234664i	0.993093	−	0.117332i	$-0.0374341\pi$
$798$		0			0
$799$		−	142.319i		−	0.178122i
$800$		0			0
$801$	328.905			0.410617
$802$		0			0
$803$	−17.7639			−0.0221219
$804$		0			0
$805$	1386.27	+	147.992i	1.72208	+	0.183840i
$806$		0			0
$807$	−86.7572	+	86.7572i	−0.107506	+	0.107506i
$808$		0			0
$809$	−356.858			−0.441110			−0.220555	−	0.975374i	$-0.570787\pi$
$809$	−356.858			−0.441110			−0.220555	+	0.975374i	$0.570787\pi$
$810$		0			0
$811$	−882.626	+	882.626i	−1.08832	+	1.08832i	−0.0926166	+	0.995702i	$0.529523\pi$
$811$	−882.626	+	882.626i	−1.08832	+	1.08832i	−0.995702	+	0.0926166i	$0.970477\pi$
$812$		0			0
$813$	−82.4677			−0.101436
$814$		0			0
$815$	488.248	+	52.1229i	0.599078	+	0.0639545i
$816$		0			0
$817$	584.150	+	584.150i	0.714994	+	0.714994i
$818$		0			0
$819$	−307.130	+	307.130i	−0.375006	+	0.375006i
$820$		0			0
$821$	17.9719	−	17.9719i	0.0218902	−	0.0218902i	−0.696077	−	0.717967i	$-0.745073\pi$
$821$	17.9719	−	17.9719i	0.0218902	−	0.0218902i	0.717967	+	0.696077i	$0.245073\pi$
$822$		0			0
$823$	36.8905	+	36.8905i	0.0448245	+	0.0448245i	0.729164	−	0.684339i	$-0.239909\pi$
$823$	36.8905	+	36.8905i	0.0448245	+	0.0448245i	−0.684339	+	0.729164i	$0.739909\pi$
$824$		0			0
$825$	360.205	−	232.251i	0.436612	−	0.281517i
$826$		0			0
$827$	837.787			1.01304			0.506522	−	0.862227i	$-0.330931\pi$
$827$	837.787			1.01304			0.506522	+	0.862227i	$0.330931\pi$
$828$		0			0
$829$	1129.26	−	1129.26i	1.36219	−	1.36219i	0.491077	−	0.871116i	$-0.336603\pi$
$829$	1129.26	−	1129.26i	1.36219	−	1.36219i	0.871116	−	0.491077i	$-0.163397\pi$
$830$		0			0
$831$	−101.385			−0.122003
$832$		0			0
$833$	−534.456	+	534.456i	−0.641604	+	0.641604i
$834$		0			0
$835$	52.7618	−	42.5832i	0.0631877	−	0.0509979i
$836$		0			0
$837$	−508.654			−0.607711
$838$		0			0
$839$	949.313			1.13148			0.565741	−	0.824583i	$-0.308590\pi$
$839$	949.313			1.13148			0.565741	+	0.824583i	$0.308590\pi$
$840$		0			0
$841$			529.420i			0.629512i
$842$		0			0
$843$			279.265i			0.331275i
$844$		0			0
$845$	620.326	+	66.2229i	0.734113	+	0.0783702i
$846$		0			0
$847$	−347.553	−	347.553i	−0.410334	−	0.410334i
$848$		0			0
$849$		−	167.390i		−	0.197161i
$850$		0			0
$851$	−805.547	−	805.547i	−0.946589	−	0.946589i
$852$		0			0
$853$		−	293.712i		−	0.344329i	−0.985068	−	0.172164i	$-0.944924\pi$
$853$		−	293.712i		−	0.344329i	0.985068	−	0.172164i	$-0.0550760\pi$
$854$		0			0
$855$	533.586	−	430.649i	0.624077	−	0.503683i
$856$		0			0
$857$	−656.737	+	656.737i	−0.766321	+	0.766321i	−0.977457	−	0.211136i	$-0.932284\pi$
$857$	−656.737	+	656.737i	−0.766321	+	0.766321i	0.211136	+	0.977457i	$0.432284\pi$
$858$		0			0
$859$	1015.37	+	1015.37i	1.18203	+	1.18203i	0.979217	+	0.202818i	$0.0650099\pi$
$859$	1015.37	+	1015.37i	1.18203	+	1.18203i	0.202818	+	0.979217i	$0.434990\pi$
$860$		0			0
$861$	−1022.41	−	1022.41i	−1.18747	−	1.18747i
$862$		0			0
$863$	400.164	−	400.164i	0.463689	−	0.463689i	−0.436174	−	0.899863i	$-0.643667\pi$
$863$	400.164	−	400.164i	0.463689	−	0.463689i	0.899863	+	0.436174i	$0.143667\pi$
$864$		0			0
$865$	−859.641	−	91.7710i	−0.993805	−	0.106094i
$866$		0			0
$867$			441.709i			0.509468i
$868$		0			0
$869$	572.081	+	572.081i	0.658321	+	0.658321i
$870$		0			0
$871$		−	480.318i		−	0.551456i
$872$		0			0
$873$	−552.776	−	552.776i	−0.633191	−	0.633191i
$874$		0			0
$875$	1361.14	−	685.160i	1.55559	−	0.783040i
$876$		0			0
$877$		−	532.291i		−	0.606945i	−0.952840	−	0.303472i	$-0.901854\pi$
$877$		−	532.291i		−	0.606945i	0.952840	−	0.303472i	$-0.0981460\pi$
$878$		0			0
$879$			490.654i			0.558196i
$880$		0			0
$881$	1748.05			1.98417			0.992083	−	0.125586i	$-0.0400812\pi$
$881$	1748.05			1.98417			0.992083	+	0.125586i	$0.0400812\pi$
$882$		0			0
$883$	141.696			0.160471			0.0802354	−	0.996776i	$-0.474433\pi$
$883$	141.696			0.160471			0.0802354	+	0.996776i	$0.474433\pi$
$884$		0			0
$885$	−21.6981	−	26.8845i	−0.0245176	−	0.0303780i
$886$		0			0
$887$	−258.995	+	258.995i	−0.291990	+	0.291990i	−0.837866	−	0.545876i	$-0.816197\pi$
$887$	−258.995	+	258.995i	−0.291990	+	0.291990i	0.545876	+	0.837866i	$0.316197\pi$
$888$		0			0
$889$	872.383			0.981309
$890$		0			0
$891$	25.9392	−	25.9392i	0.0291125	−	0.0291125i
$892$		0			0
$893$	480.161			0.537694
$894$		0			0
$895$	259.624	−	209.538i	0.290083	−	0.234121i
$896$		0			0
$897$	205.286	+	205.286i	0.228859	+	0.228859i
$898$		0			0
$899$	231.690	−	231.690i	0.257720	−	0.257720i
$900$		0			0
$901$	−344.672	+	344.672i	−0.382544	+	0.382544i
$902$		0			0
$903$	530.955	+	530.955i	0.587990	+	0.587990i
$904$		0			0
$905$	279.076	−	225.238i	0.308371	−	0.248882i
$906$		0			0
$907$	−427.687			−0.471540			−0.235770	−	0.971809i	$-0.575761\pi$
$907$	−427.687			−0.471540			−0.235770	+	0.971809i	$0.575761\pi$
$908$		0			0
$909$	−493.762	+	493.762i	−0.543192	+	0.543192i
$910$		0			0
$911$	81.2821			0.0892229			0.0446114	−	0.999004i	$-0.485795\pi$
$911$	81.2821			0.0892229			0.0446114	+	0.999004i	$0.485795\pi$
$912$		0			0
$913$	24.0330	−	24.0330i	0.0263231	−	0.0263231i
$914$		0			0
$915$	445.221	+	551.640i	0.486580	+	0.602886i
$916$		0			0
$917$	−380.993			−0.415478
$918$		0			0
$919$	−314.358			−0.342065			−0.171033	−	0.985265i	$-0.554710\pi$
$919$	−314.358			−0.342065			−0.171033	+	0.985265i	$0.554710\pi$
$920$		0			0
$921$		−	1147.26i		−	1.24567i
$922$		0			0
$923$		−	162.153i		−	0.175680i
$924$		0			0
$925$	−1217.14	−	262.868i	−1.31583	−	0.284182i
$926$		0			0
$927$	−392.215	−	392.215i	−0.423101	−	0.423101i
$928$		0			0
$929$			447.538i			0.481742i	0.970557	+	0.240871i	$0.0774330\pi$
$929$			447.538i			0.481742i	−0.970557	+	0.240871i	$0.922567\pi$
$930$		0			0
$931$	−1803.16	−	1803.16i	−1.93680	−	1.93680i
$932$		0			0
$933$		−	14.0171i		−	0.0150237i
$934$		0			0
$935$	−338.835	−	36.1723i	−0.362391	−	0.0386870i
$936$		0			0
$937$	−299.777	+	299.777i	−0.319932	+	0.319932i	−0.848741	−	0.528809i	$-0.822639\pi$
$937$	−299.777	+	299.777i	−0.319932	+	0.319932i	0.528809	+	0.848741i	$0.322639\pi$
$938$		0			0
$939$	325.554	+	325.554i	0.346703	+	0.346703i
$940$		0			0
$941$	991.114	+	991.114i	1.05326	+	1.05326i	0.998500	+	0.0547565i	$0.0174382\pi$
$941$	991.114	+	991.114i	1.05326	+	1.05326i	0.0547565	+	0.998500i	$0.482562\pi$
$942$		0			0
$943$	1005.04	−	1005.04i	1.06579	−	1.06579i
$944$		0			0
$945$	1299.77	−	1049.02i	1.37542	−	1.11008i
$946$		0			0
$947$		−	22.1486i		−	0.0233882i	−0.999932	−	0.0116941i	$-0.996278\pi$
$947$		−	22.1486i		−	0.0233882i	0.999932	−	0.0116941i	$-0.00372243\pi$
$948$		0			0
$949$	−9.30022	−	9.30022i	−0.00980002	−	0.00980002i
$950$		0			0
$951$			508.428i			0.534625i
$952$		0			0
$953$	1197.38	+	1197.38i	1.25643	+	1.25643i	0.952783	+	0.303651i	$0.0982056\pi$
$953$	1197.38	+	1197.38i	1.25643	+	1.25643i	0.303651	+	0.952783i	$0.401794\pi$
$954$		0			0
$955$	−1641.31	−	175.218i	−1.71865	−	0.183475i
$956$		0			0
$957$			302.612i			0.316208i
$958$		0			0
$959$			1764.00i			1.83942i
$960$		0			0
$961$	−616.432			−0.641449
$962$		0			0
$963$	95.2809			0.0989417
$964$		0			0
$965$	828.457	−	668.635i	0.858505	−	0.692886i
$966$		0			0
$967$	937.022	−	937.022i	0.968998	−	0.968998i	−0.0305352	−	0.999534i	$-0.509721\pi$
$967$	937.022	−	937.022i	0.968998	−	0.968998i	0.999534	+	0.0305352i	$0.00972117\pi$
$968$		0			0
$969$	370.696			0.382555
$970$		0			0
$971$	1016.28	−	1016.28i	1.04663	−	1.04663i	0.0477733	−	0.998858i	$-0.484787\pi$
$971$	1016.28	−	1016.28i	1.04663	−	1.04663i	0.998858	−	0.0477733i	$-0.0152125\pi$
$972$		0			0
$973$	1431.11			1.47082
$974$		0			0
$975$	310.178	+	66.9896i	0.318132	+	0.0687073i
$976$		0			0
$977$	−578.640	−	578.640i	−0.592262	−	0.592262i	0.345980	−	0.938242i	$-0.387546\pi$
$977$	−578.640	−	578.640i	−0.592262	−	0.592262i	−0.938242	+	0.345980i	$0.887546\pi$
$978$		0			0
$979$	389.940	−	389.940i	0.398305	−	0.398305i
$980$		0			0
$981$	−51.6477	+	51.6477i	−0.0526480	+	0.0526480i
$982$		0			0
$983$	−666.904	−	666.904i	−0.678437	−	0.678437i	0.281209	−	0.959646i	$-0.409265\pi$
$983$	−666.904	−	666.904i	−0.678437	−	0.678437i	−0.959646	+	0.281209i	$0.909265\pi$
$984$		0			0
$985$	−1281.69	−	136.826i	−1.30120	−	0.138910i
$986$		0			0
$987$	436.435			0.442184
$988$		0			0
$989$	−521.933	+	521.933i	−0.527738	+	0.527738i
$990$		0			0
$991$	573.966			0.579178			0.289589	−	0.957151i	$-0.406481\pi$
$991$	573.966			0.579178			0.289589	+	0.957151i	$0.406481\pi$
$992$		0			0
$993$	−127.850	+	127.850i	−0.128752	+	0.128752i
$994$		0			0
$995$	1633.22	+	174.355i	1.64143	+	0.175231i
$996$		0			0
$997$	−293.423			−0.294306			−0.147153	−	0.989114i	$-0.547011\pi$
$997$	−293.423			−0.294306			−0.147153	+	0.989114i	$0.547011\pi$
$998$		0			0
$999$	−1364.85			−1.36622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.3.t.b.417.8		44
4.3	odd	2		640.3.t.a.417.15		44
5.3	odd	4		640.3.i.b.33.8		44
8.3	odd	2		320.3.t.a.17.8		44
8.5	even	2		80.3.t.a.77.17	yes	44
16.3	odd	4		320.3.i.a.177.15		44
16.5	even	4		640.3.i.b.97.15		44
16.11	odd	4		640.3.i.a.97.8		44
16.13	even	4		80.3.i.a.37.7	yes	44
20.3	even	4		640.3.i.a.33.15		44
40.3	even	4		320.3.i.a.273.8		44
40.13	odd	4		80.3.i.a.13.7	✓	44
40.29	even	2		400.3.t.b.157.6		44
40.37	odd	4		400.3.i.b.93.16		44
80.3	even	4		320.3.t.a.113.8		44
80.13	odd	4		80.3.t.a.53.17	yes	44
80.29	even	4		400.3.i.b.357.16		44
80.43	even	4		640.3.t.a.353.15		44
80.53	odd	4	inner	640.3.t.b.353.8		44
80.77	odd	4		400.3.t.b.293.6		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.7	✓	44	40.13	odd	4
80.3.i.a.37.7	yes	44	16.13	even	4
80.3.t.a.53.17	yes	44	80.13	odd	4
80.3.t.a.77.17	yes	44	8.5	even	2
320.3.i.a.177.15		44	16.3	odd	4
320.3.i.a.273.8		44	40.3	even	4
320.3.t.a.17.8		44	8.3	odd	2
320.3.t.a.113.8		44	80.3	even	4
400.3.i.b.93.16		44	40.37	odd	4
400.3.i.b.357.16		44	80.29	even	4
400.3.t.b.157.6		44	40.29	even	2
400.3.t.b.293.6		44	80.77	odd	4
640.3.i.a.33.15		44	20.3	even	4
640.3.i.a.97.8		44	16.11	odd	4
640.3.i.b.33.8		44	5.3	odd	4
640.3.i.b.97.15		44	16.5	even	4
640.3.t.a.353.15		44	80.43	even	4
640.3.t.a.417.15		44	4.3	odd	2
640.3.t.b.353.8		44	80.53	odd	4	inner
640.3.t.b.417.8		44	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	640.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.90859 q^{3} +(-4.97175 - 0.530759i) q^{5} +(-8.62025 + 8.62025i) q^{7} -5.35728 q^{9} +O(q^{10})\)	\(q-1.90859 q^{3} +(-4.97175 - 0.530759i) q^{5} +(-8.62025 + 8.62025i) q^{7} -5.35728 q^{9} +(-6.35145 + 6.35145i) q^{11} -6.65056 q^{13} +(9.48903 + 1.01300i) q^{15} +(-5.36508 - 5.36508i) q^{17} +(18.1009 - 18.1009i) q^{19} +(16.4525 - 16.4525i) q^{21} +(16.1730 + 16.1730i) q^{23} +(24.4366 + 5.27760i) q^{25} +27.4022 q^{27} +(-12.4816 + 12.4816i) q^{29} -18.5625 q^{31} +(12.1223 - 12.1223i) q^{33} +(47.4330 - 38.2825i) q^{35} -49.8083 q^{37} +12.6932 q^{39} -62.1433i q^{41} +32.2720i q^{43} +(26.6351 + 2.84343i) q^{45} +(13.2635 + 13.2635i) q^{47} -99.6175i q^{49} +(10.2397 + 10.2397i) q^{51} -64.2436i q^{53} +(34.9489 - 28.2067i) q^{55} +(-34.5471 + 34.5471i) q^{57} +(-2.55993 - 2.55993i) q^{59} +(52.5270 + 52.5270i) q^{61} +(46.1811 - 46.1811i) q^{63} +(33.0649 + 3.52984i) q^{65} +72.2222i q^{67} +(-30.8676 - 30.8676i) q^{69} +24.3819i q^{71} +(1.39841 + 1.39841i) q^{73} +(-46.6394 - 10.0728i) q^{75} -109.502i q^{77} -90.0709i q^{79} -4.08398 q^{81} -3.78386 q^{83} +(23.8263 + 29.5214i) q^{85} +(23.8222 - 23.8222i) q^{87} -61.3939 q^{89} +(57.3295 - 57.3295i) q^{91} +35.4283 q^{93} +(-99.6001 + 80.3857i) q^{95} +(103.182 + 103.182i) q^{97} +(34.0265 - 34.0265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 2 q^{5} + 108 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 + 2 * q^5 + 108 * q^9	\( 44 q + 4 q^{3} + 2 q^{5} + 108 q^{9} + 4 q^{11} + 4 q^{13} - 4 q^{15} - 4 q^{17} + 32 q^{19} + 4 q^{21} + 40 q^{27} - 8 q^{31} - 4 q^{33} + 4 q^{35} + 4 q^{37} - 72 q^{39} + 70 q^{45} - 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} + 36 q^{61} - 200 q^{63} - 4 q^{65} - 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} + 52 q^{85} - 36 q^{87} - 188 q^{91} + 40 q^{93} + 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 2 * q^5 + 108 * q^9 + 4 * q^11 + 4 * q^13 - 4 * q^15 - 4 * q^17 + 32 * q^19 + 4 * q^21 + 40 * q^27 - 8 * q^31 - 4 * q^33 + 4 * q^35 + 4 * q^37 - 72 * q^39 + 70 * q^45 - 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 + 36 * q^61 - 200 * q^63 - 4 * q^65 - 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 + 52 * q^85 - 36 * q^87 - 188 * q^91 + 40 * q^93 + 380 * q^95 - 4 * q^97 - 92 * q^99

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