LMFDB - Embedded newform 320.3.t.a.113.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(17,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("320.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.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:	$8.71936845953$
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			113.8
Character	$\chi$	$=$	320.113
Dual form			320.3.t.a.17.8

$q$-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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			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	0.963401	+	0.268063i	$0.0863836\pi$
$7$	8.62025	+	8.62025i	1.23146	+	1.23146i	0.268063	+	0.963401i	$0.413616\pi$
$8$		0			0
$9$	−5.35728			−0.595254
$10$		0			0
$11$	−6.35145	−	6.35145i	−0.577404	−	0.577404i	0.356783	−	0.934187i	$-0.383874\pi$
$11$	−6.35145	−	6.35145i	−0.577404	−	0.577404i	−0.934187	+	0.356783i	$0.883874\pi$
$12$		0			0
$13$	6.65056			0.511581			0.255791	−	0.966732i	$-0.417664\pi$
$13$	6.65056			0.511581			0.255791	+	0.966732i	$0.417664\pi$
$14$		0			0
$15$	−9.48903	+	1.01300i	−0.632602	+	0.0675334i
$16$		0			0
$17$	−5.36508	+	5.36508i	−0.315593	+	0.315593i	−0.847072	−	0.531479i	$-0.821637\pi$
$17$	−5.36508	+	5.36508i	−0.315593	+	0.315593i	0.531479	+	0.847072i	$0.321637\pi$
$18$		0			0
$19$	18.1009	+	18.1009i	0.952677	+	0.952677i	0.998930	−	0.0462531i	$-0.0147281\pi$
$19$	18.1009	+	18.1009i	0.952677	+	0.952677i	−0.0462531	+	0.998930i	$0.514728\pi$
$20$		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	$-0.915645\pi$
$23$	−16.1730	+	16.1730i	−0.703172	+	0.703172i	0.261918	+	0.965090i	$0.415645\pi$
$24$		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	$-0.151565\pi$
$29$	12.4816	+	12.4816i	0.430400	+	0.430400i	−0.458365	+	0.888764i	$0.651565\pi$
$30$		0			0
$31$	18.5625			0.598792			0.299396	−	0.954129i	$-0.403215\pi$
$31$	18.5625			0.598792			0.299396	+	0.954129i	$0.403215\pi$
$32$		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	$-0.264969\pi$
$37$	49.8083			1.34617			0.673085	+	0.739565i	$0.264969\pi$
$38$		0			0
$39$	−12.6932			−0.325466
$40$		0			0
$41$			62.1433i			1.51569i	0.652434	+	0.757846i	$0.273748\pi$
$41$			62.1433i			1.51569i	−0.652434	+	0.757846i	$0.726252\pi$
$42$		0			0
$43$		−	32.2720i		−	0.750511i	−0.926921	−	0.375255i	$-0.877555\pi$
$43$		−	32.2720i		−	0.750511i	0.926921	−	0.375255i	$-0.122445\pi$
$44$		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	$-0.813947\pi$
$47$	−13.2635	+	13.2635i	−0.282202	+	0.282202i	0.551785	+	0.833986i	$0.313947\pi$
$48$		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	−0.728468	−	0.685080i	$-0.759767\pi$
$59$	−2.55993	+	2.55993i	−0.0433887	+	0.0433887i	0.685080	+	0.728468i	$0.259767\pi$
$60$		0			0
$61$	−52.5270	+	52.5270i	−0.861098	+	0.861098i	−0.991466	−	0.130367i	$-0.958384\pi$
$61$	−52.5270	+	52.5270i	−0.861098	+	0.861098i	0.130367	+	0.991466i	$0.458384\pi$
$62$		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	$-0.818813\pi$
$67$		−	72.2222i		−	1.07794i	0.842324	−	0.538972i	$-0.181187\pi$
$68$		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	−0.697464	−	0.716620i	$-0.745688\pi$
$73$	1.39841	−	1.39841i	0.0191563	−	0.0191563i	0.716620	+	0.697464i	$0.245688\pi$
$74$		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	0.0659075	−	0.997826i	$-0.479006\pi$
$97$	103.182	−	103.182i	1.06373	−	1.06373i	0.997826	−	0.0659075i	$-0.0209942\pi$
$98$		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	$-0.473252\pi$
$101$	−92.1665	−	92.1665i	−0.912539	−	0.912539i	−0.996471	+	0.0839323i	$0.973252\pi$
$102$		0			0
$103$	−73.2115	+	73.2115i	−0.710791	+	0.710791i	−0.966701	−	0.255909i	$-0.917625\pi$
$103$	−73.2115	+	73.2115i	−0.710791	+	0.710791i	0.255909	+	0.966701i	$0.417625\pi$
$104$		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	$-0.269920\pi$
$109$	−9.64065	−	9.64065i	−0.0884463	−	0.0884463i	−0.749946	+	0.661499i	$0.769920\pi$
$110$		0			0
$111$	−95.0636			−0.856429
$112$		0			0
$113$	−62.4937	−	62.4937i	−0.553042	−	0.553042i	0.374276	−	0.927317i	$-0.377891\pi$
$113$	−62.4937	−	62.4937i	−0.553042	−	0.553042i	−0.927317	+	0.374276i	$0.877891\pi$
$114$		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	$-0.659091\pi$
$127$	50.6008	−	50.6008i	0.398432	−	0.398432i	0.877680	+	0.479248i	$0.159091\pi$
$128$		0			0
$129$			61.5939i			0.477472i
$130$		0			0
$131$	22.0987	−	22.0987i	0.168693	−	0.168693i	−0.617712	−	0.786404i	$-0.711940\pi$
$131$	22.0987	−	22.0987i	0.168693	−	0.168693i	0.786404	+	0.617712i	$0.211940\pi$
$132$		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	0.973885	−	0.227043i	$-0.0729059\pi$
$137$	102.317	+	102.317i	0.746841	+	0.746841i	−0.227043	+	0.973885i	$0.572906\pi$
$138$		0			0
$139$	−83.0087	+	83.0087i	−0.597185	+	0.597185i	−0.939562	−	0.342378i	$-0.888768\pi$
$139$	−83.0087	+	83.0087i	−0.597185	+	0.597185i	0.342378	+	0.939562i	$0.388768\pi$
$140$		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	$-0.530328\pi$
$149$	134.149	−	134.149i	0.900331	−	0.900331i	0.995465	+	0.0951332i	$0.0303277\pi$
$150$		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	$-0.237073\pi$
$167$	9.58867	+	9.58867i	0.0574172	+	0.0574172i	−0.677815	+	0.735232i	$0.737073\pi$
$168$		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	$-0.666566\pi$
$173$	−172.905			−0.999452			−0.499726	+	0.866184i	$0.666566\pi$
$174$		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	0.562920	−	0.826511i	$-0.309678\pi$
$179$	−47.1828	−	47.1828i	−0.263591	−	0.263591i	−0.826511	+	0.562920i	$0.809678\pi$
$180$		0			0
$181$	50.7180	+	50.7180i	0.280210	+	0.280210i	0.833193	−	0.552983i	$-0.186511\pi$
$181$	50.7180	+	50.7180i	0.280210	+	0.280210i	−0.552983	+	0.833193i	$0.686511\pi$
$182$		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	$-0.832181\pi$
$191$	−330.128			−1.72842			−0.864210	+	0.503132i	$0.832181\pi$
$192$		0			0
$193$	−150.560	−	150.560i	−0.780103	−	0.780103i	0.199745	−	0.979848i	$-0.435989\pi$
$193$	−150.560	−	150.560i	−0.780103	−	0.780103i	−0.979848	+	0.199745i	$0.935989\pi$
$194$		0			0
$195$	−63.1074	+	6.73702i	−0.323627	+	0.0345488i
$196$		0			0
$197$	−257.794			−1.30860			−0.654299	−	0.756236i	$-0.727036\pi$
$197$	−257.794			−1.30860			−0.654299	+	0.756236i	$0.727036\pi$
$198$		0			0
$199$	328.501			1.65076			0.825378	−	0.564580i	$-0.190962\pi$
$199$	328.501			1.65076			0.825378	+	0.564580i	$0.190962\pi$
$200$		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	−0.818322	−	0.574760i	$-0.805095\pi$
$211$	−51.3916	+	51.3916i	−0.243562	+	0.243562i	0.574760	+	0.818322i	$0.305095\pi$
$212$		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	$-0.0313139\pi$
$223$	200.019	+	200.019i	0.896948	+	0.896948i	−0.0982168	+	0.995165i	$0.531314\pi$
$224$		0			0
$225$	−130.914	+	28.2736i	−0.581839	+	0.125660i
$226$		0			0
$227$			47.5480i			0.209462i	0.994501	+	0.104731i	$0.0333982\pi$
$227$			47.5480i			0.209462i	−0.994501	+	0.104731i	$0.966602\pi$
$228$		0			0
$229$	−65.5550	+	65.5550i	−0.286266	+	0.286266i	−0.835602	−	0.549336i	$-0.814881\pi$
$229$	−65.5550	+	65.5550i	−0.286266	+	0.286266i	0.549336	+	0.835602i	$0.314881\pi$
$230$		0			0
$231$			208.995i			0.904739i
$232$		0			0
$233$	201.087	−	201.087i	0.863035	−	0.863035i	−0.128655	−	0.991689i	$-0.541066\pi$
$233$	201.087	−	201.087i	0.863035	−	0.863035i	0.991689	+	0.128655i	$0.0410659\pi$
$234$		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	0.805698	−	0.592326i	$-0.201790\pi$
$251$	53.5564	+	53.5564i	0.213372	+	0.213372i	−0.592326	+	0.805698i	$0.701790\pi$
$252$		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	−0.411374	−	0.911466i	$-0.634951\pi$
$257$	128.524	−	128.524i	0.500092	−	0.500092i	0.911466	+	0.411374i	$0.134951\pi$
$258$		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	0.436228	−	0.899836i	$-0.356314\pi$
$263$	351.385	−	351.385i	1.33606	−	1.33606i	0.899836	−	0.436228i	$-0.143686\pi$
$264$		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	$-0.288125\pi$
$269$	−45.4562	−	45.4562i	−0.168982	−	0.168982i	−0.786532	+	0.617550i	$0.788125\pi$
$270$		0			0
$271$	−43.2087			−0.159442			−0.0797209	−	0.996817i	$-0.525403\pi$
$271$	−43.2087			−0.159442			−0.0797209	+	0.996817i	$0.525403\pi$
$272$		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	$-0.530568\pi$
$277$	−53.1202			−0.191770			−0.0958849	+	0.995392i	$0.530568\pi$
$278$		0			0
$279$	−99.4448			−0.356433
$280$		0			0
$281$			146.320i			0.520712i	0.965513	+	0.260356i	$0.0838399\pi$
$281$			146.320i			0.520712i	−0.965513	+	0.260356i	$0.916160\pi$
$282$		0			0
$283$		−	87.7034i		−	0.309906i	−0.987922	−	0.154953i	$-0.950477\pi$
$283$		−	87.7034i		−	0.309906i	0.987922	−	0.154953i	$-0.0495226\pi$
$284$		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	$-0.565352\pi$
$307$		−	601.105i		−	1.95800i	0.203870	−	0.978998i	$-0.434648\pi$
$308$		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	−0.924979	−	0.380017i	$-0.875918\pi$
$313$	−170.573	+	170.573i	−0.544962	+	0.544962i	0.380017	+	0.924979i	$0.375918\pi$
$314$		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	0.801018	−	0.598641i	$-0.204292\pi$
$331$	66.9868	+	66.9868i	0.202377	+	0.202377i	−0.598641	+	0.801018i	$0.704292\pi$
$332$		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	−0.910753	−	0.412952i	$-0.864498\pi$
$337$	−167.759	+	167.759i	−0.497801	+	0.497801i	0.412952	+	0.910753i	$0.364498\pi$
$338$		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	$-0.395838\pi$
$349$	−218.302	−	218.302i	−0.625508	−	0.625508i	−0.946935	+	0.321426i	$0.895838\pi$
$350$		0			0
$351$	182.240			0.519201
$352$		0			0
$353$	194.122	+	194.122i	0.549920	+	0.549920i	0.926418	−	0.376498i	$-0.122872\pi$
$353$	194.122	+	194.122i	0.549920	+	0.549920i	−0.376498	+	0.926418i	$0.622872\pi$
$354$		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	$-0.774918\pi$
$359$	−545.851			−1.52048			−0.760238	+	0.649644i	$0.774918\pi$
$360$		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	$-0.553207\pi$
$367$	300.825	−	300.825i	0.819686	−	0.819686i	0.986062	+	0.166376i	$0.0532065\pi$
$368$		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	−0.819637	−	0.572883i	$-0.805825\pi$
$379$	−93.5200	+	93.5200i	−0.246755	+	0.246755i	0.572883	+	0.819637i	$0.305825\pi$
$380$		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	$-0.203151\pi$
$383$	79.4324	+	79.4324i	0.207395	+	0.207395i	−0.595764	+	0.803159i	$0.703151\pi$
$384$		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	$-0.806775\pi$
$389$	−97.6035	+	97.6035i	−0.250909	+	0.250909i	0.570434	+	0.821343i	$0.306775\pi$
$390$		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	0.858800	−	0.512311i	$-0.171210\pi$
$419$	145.179	+	145.179i	0.346489	+	0.346489i	−0.512311	+	0.858800i	$0.671210\pi$
$420$		0			0
$421$	−19.6145	−	19.6145i	−0.0465904	−	0.0465904i	0.683428	−	0.730018i	$-0.260488\pi$
$421$	−19.6145	−	19.6145i	−0.0465904	−	0.0465904i	−0.730018	+	0.683428i	$0.760488\pi$
$422$		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	$-0.568545\pi$
$431$	−184.193			−0.427362			−0.213681	+	0.976903i	$0.568545\pi$
$432$		0			0
$433$	401.221	+	401.221i	0.926607	+	0.926607i	0.997485	−	0.0708779i	$-0.0225801\pi$
$433$	401.221	+	401.221i	0.926607	+	0.926607i	−0.0708779	+	0.997485i	$0.522580\pi$
$434$		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	$-0.797064\pi$
$439$	−705.526			−1.60712			−0.803561	+	0.595223i	$0.797064\pi$
$440$		0			0
$441$		−	533.679i		−	1.21016i
$442$		0			0
$443$		−	499.336i		−	1.12717i	−0.826058	−	0.563585i	$-0.809422\pi$
$443$		−	499.336i		−	1.12717i	0.826058	−	0.563585i	$-0.190578\pi$
$444$		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	$0.339413\pi$
$449$			786.125i			1.75083i	−0.483368	+	0.875417i	$0.660587\pi$
$450$		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	0.995387	−	0.0959440i	$-0.0305870\pi$
$457$	411.045	+	411.045i	0.899443	+	0.899443i	−0.0959440	+	0.995387i	$0.530587\pi$
$458$		0			0
$459$	−147.015	+	147.015i	−0.320294	+	0.320294i
$460$		0			0
$461$	544.187	−	544.187i	1.18045	−	1.18045i	0.200821	−	0.979628i	$-0.435639\pi$
$461$	544.187	−	544.187i	1.18045	−	1.18045i	0.979628	−	0.200821i	$-0.0643610\pi$
$462$		0			0
$463$	−109.453	−	109.453i	−0.236400	−	0.236400i	0.578957	−	0.815358i	$-0.303460\pi$
$463$	−109.453	−	109.453i	−0.236400	−	0.236400i	−0.815358	+	0.578957i	$0.803460\pi$
$464$		0			0
$465$	−176.141	+	18.8039i	−0.378797	+	0.0404384i
$466$		0			0
$467$			462.541i			0.990452i	0.868764	+	0.495226i	$0.164915\pi$
$467$			462.541i			0.990452i	−0.868764	+	0.495226i	$0.835085\pi$
$468$		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	$-0.0658165\pi$
$487$	376.646	+	376.646i	0.773401	+	0.773401i	−0.205299	+	0.978699i	$0.565817\pi$
$488$		0			0
$489$	187.432			0.383297
$490$		0			0
$491$	552.932	+	552.932i	1.12613	+	1.12613i	0.990800	+	0.135334i	$0.0432107\pi$
$491$	552.932	+	552.932i	1.12613	+	1.12613i	0.135334	+	0.990800i	$0.456789\pi$
$492$		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	0.326314	−	0.945261i	$-0.394193\pi$
$499$	−308.855	−	308.855i	−0.618947	−	0.618947i	−0.945261	+	0.326314i	$0.894193\pi$
$500$		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	$-0.588440\pi$
$503$	345.746	−	345.746i	0.687368	−	0.687368i	0.961650	+	0.274281i	$0.0884399\pi$
$504$		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	$-0.180336\pi$
$509$	156.286	+	156.286i	0.307046	+	0.307046i	−0.536717	+	0.843762i	$0.680336\pi$
$510$		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	$0.153651\pi$
$521$			483.674i			0.928358i	−0.885741	+	0.464179i	$0.846349\pi$
$522$		0			0
$523$			114.482i			0.218895i	0.993993	+	0.109448i	$0.0349082\pi$
$523$			114.482i			0.218895i	−0.993993	+	0.109448i	$0.965092\pi$
$524$		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	−0.0660852	+	0.997814i	$0.521051\pi$
$541$	−575.569	+	575.569i	−1.06390	+	1.06390i	−0.997814	+	0.0660852i	$0.978949\pi$
$542$		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	$0.413234\pi$
$547$			1053.61i			1.92616i	−0.269219	+	0.963079i	$0.586766\pi$
$548$		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	0.807528	−	0.589829i	$-0.200805\pi$
$571$	124.307	+	124.307i	0.217700	+	0.217700i	−0.589829	+	0.807528i	$0.700805\pi$
$572$		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	−0.919337	−	0.393471i	$-0.871274\pi$
$577$	−303.425	+	303.425i	−0.525866	+	0.525866i	0.393471	+	0.919337i	$0.371274\pi$
$578$		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	0.304970	−	0.952362i	$-0.401354\pi$
$593$	−383.903	−	383.903i	−0.647392	−	0.647392i	−0.952362	+	0.304970i	$0.901354\pi$
$594$		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	$-0.454712\pi$
$599$	169.873			0.283594			0.141797	+	0.989896i	$0.454712\pi$
$600$		0			0
$601$		−	283.673i		−	0.472002i	−0.971753	−	0.236001i	$-0.924163\pi$
$601$		−	283.673i		−	0.472002i	0.971753	−	0.236001i	$-0.0758369\pi$
$602$		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	$-0.920593\pi$
$607$	−438.351	+	438.351i	−0.722160	+	0.722160i	0.246885	+	0.969045i	$0.420593\pi$
$608$		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	0.862010	−	0.506892i	$-0.169206\pi$
$617$	219.108	+	219.108i	0.355118	+	0.355118i	−0.506892	+	0.862010i	$0.669206\pi$
$618$		0			0
$619$	365.140	−	365.140i	0.589888	−	0.589888i	−0.347713	−	0.937601i	$-0.613042\pi$
$619$	365.140	−	365.140i	0.589888	−	0.589888i	0.937601	+	0.347713i	$0.113042\pi$
$620$		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	$-0.228825\pi$
$647$	60.8229	+	60.8229i	0.0940075	+	0.0940075i	−0.658539	+	0.752547i	$0.728825\pi$
$648$		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	$-0.285288\pi$
$653$	815.643			1.24907			0.624536	+	0.780996i	$0.285288\pi$
$654$		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	−0.984192	−	0.177103i	$-0.943327\pi$
$659$	−765.294	−	765.294i	−1.16130	−	1.16130i	−0.177103	−	0.984192i	$-0.556673\pi$
$660$		0			0
$661$	423.035	+	423.035i	0.639993	+	0.639993i	0.950553	−	0.310561i	$-0.100517\pi$
$661$	423.035	+	423.035i	0.639993	+	0.639993i	−0.310561	+	0.950553i	$0.600517\pi$
$662$		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	0.374190	−	0.927352i	$-0.377921\pi$
$673$	−372.278	−	372.278i	−0.553162	−	0.553162i	−0.927352	+	0.374190i	$0.877921\pi$
$674$		0			0
$675$	669.616	−	144.618i	0.992023	−	0.214249i
$676$		0			0
$677$	244.469			0.361106			0.180553	−	0.983565i	$-0.442211\pi$
$677$	244.469			0.361106			0.180553	+	0.983565i	$0.442211\pi$
$678$		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	$0.103037\pi$
$683$			434.494i			0.636155i	−0.948065	+	0.318077i	$0.896963\pi$
$684$		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	−0.598424	−	0.801180i	$-0.704206\pi$
$691$	140.105	−	140.105i	0.202756	−	0.202756i	0.801180	+	0.598424i	$0.204206\pi$
$692$		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	$-0.640942\pi$
$701$	333.050	−	333.050i	0.475106	−	0.475106i	0.903563	+	0.428456i	$0.140942\pi$
$702$		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	$-0.949737\pi$
$709$	−588.688	+	588.688i	−0.830308	+	0.830308i	0.157251	+	0.987559i	$0.449737\pi$
$710$		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	$-0.214086\pi$
$727$	115.757	+	115.757i	0.159225	+	0.159225i	−0.622998	+	0.782223i	$0.714086\pi$
$728$		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	$-0.526781\pi$
$733$	−123.197			−0.168073			−0.0840363	+	0.996463i	$0.526781\pi$
$734$		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	0.124166	−	0.992262i	$-0.460375\pi$
$739$	−641.523	−	641.523i	−0.868096	−	0.868096i	−0.992262	+	0.124166i	$0.960375\pi$
$740$		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	$-0.724294\pi$
$743$	84.7652	−	84.7652i	0.114085	−	0.114085i	0.761845	+	0.647760i	$0.224294\pi$
$744$		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	$-0.529191\pi$
$751$	−137.548			−0.183153			−0.0915766	+	0.995798i	$0.529191\pi$
$752$		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	$-0.308269\pi$
$757$	857.792			1.13315			0.566574	+	0.824011i	$0.308269\pi$
$758$		0			0
$759$	−392.108			−0.516611
$760$		0			0
$761$		−	353.070i		−	0.463956i	−0.972721	−	0.231978i	$-0.925480\pi$
$761$		−	353.070i		−	0.463956i	0.972721	−	0.231978i	$-0.0745197\pi$
$762$		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	$-0.916030\pi$
$769$		−	401.035i		−	0.521503i	0.965406	−	0.260751i	$-0.0839703\pi$
$770$		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	$0.0373917\pi$
$787$			184.472i			0.234399i	−0.993108	+	0.117200i	$0.962608\pi$
$788$		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	−0.995702	−	0.0926166i	$-0.970477\pi$
$811$	−882.626	−	882.626i	−1.08832	−	1.08832i	−0.0926166	−	0.995702i	$-0.529523\pi$
$812$		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	$-0.254927\pi$
$821$	−17.9719	−	17.9719i	−0.0218902	−	0.0218902i	−0.717967	+	0.696077i	$0.754927\pi$
$822$		0			0
$823$	−36.8905	+	36.8905i	−0.0448245	+	0.0448245i	−0.729164	−	0.684339i	$-0.760091\pi$
$823$	−36.8905	+	36.8905i	−0.0448245	+	0.0448245i	0.684339	+	0.729164i	$0.260091\pi$
$824$		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	−0.871116	−	0.491077i	$-0.836603\pi$
$829$	−1129.26	−	1129.26i	−1.36219	−	1.36219i	−0.491077	−	0.871116i	$-0.663397\pi$
$830$		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	$-0.691410\pi$
$839$	−949.313			−1.13148			−0.565741	+	0.824583i	$0.691410\pi$
$840$		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	0.211136	−	0.977457i	$-0.432284\pi$
$857$	−656.737	−	656.737i	−0.766321	−	0.766321i	−0.977457	+	0.211136i	$0.932284\pi$
$858$		0			0
$859$	1015.37	−	1015.37i	1.18203	−	1.18203i	0.202818	−	0.979217i	$-0.434990\pi$
$859$	1015.37	−	1015.37i	1.18203	−	1.18203i	0.979217	−	0.202818i	$-0.0650099\pi$
$860$		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	$-0.356333\pi$
$863$	−400.164	−	400.164i	−0.463689	−	0.463689i	−0.899863	+	0.436174i	$0.856333\pi$
$864$		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	$-0.183803\pi$
$887$	258.995	+	258.995i	0.291990	+	0.291990i	−0.545876	+	0.837866i	$0.683803\pi$
$888$		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	$-0.514205\pi$
$911$	−81.2821			−0.0892229			−0.0446114	+	0.999004i	$0.514205\pi$
$912$		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	$-0.445290\pi$
$919$	314.358			0.342065			0.171033	+	0.985265i	$0.445290\pi$
$920$		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	$-0.922567\pi$
$929$		−	447.538i		−	0.481742i	0.970557	−	0.240871i	$-0.0774330\pi$
$930$		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	0.528809	−	0.848741i	$-0.322639\pi$
$937$	−299.777	−	299.777i	−0.319932	−	0.319932i	−0.848741	+	0.528809i	$0.822639\pi$
$938$		0			0
$939$	325.554	−	325.554i	0.346703	−	0.346703i
$940$		0			0
$941$	−991.114	+	991.114i	−1.05326	+	1.05326i	−0.0547565	+	0.998500i	$0.517438\pi$
$941$	−991.114	+	991.114i	−1.05326	+	1.05326i	−0.998500	+	0.0547565i	$0.982562\pi$
$942$		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	$0.00372243\pi$
$947$			22.1486i			0.0233882i	−0.999932	+	0.0116941i	$0.996278\pi$
$948$		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	0.303651	−	0.952783i	$-0.401794\pi$
$953$	1197.38	−	1197.38i	1.25643	−	1.25643i	0.952783	−	0.303651i	$-0.0982056\pi$
$954$		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	$-0.490279\pi$
$967$	−937.022	−	937.022i	−0.968998	−	0.968998i	−0.999534	+	0.0305352i	$0.990279\pi$
$968$		0			0
$969$	370.696			0.382555
$970$		0			0
$971$	1016.28	+	1016.28i	1.04663	+	1.04663i	0.998858	+	0.0477733i	$0.0152125\pi$
$971$	1016.28	+	1016.28i	1.04663	+	1.04663i	0.0477733	+	0.998858i	$0.484787\pi$
$972$		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	−0.938242	−	0.345980i	$-0.887546\pi$
$977$	−578.640	+	578.640i	−0.592262	+	0.592262i	0.345980	+	0.938242i	$0.387546\pi$
$978$		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	$-0.590735\pi$
$983$	666.904	−	666.904i	0.678437	−	0.678437i	0.959646	+	0.281209i	$0.0907355\pi$
$984$		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	$-0.593519\pi$
$991$	−573.966			−0.579178			−0.289589	+	0.957151i	$0.593519\pi$
$992$		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	$-0.452989\pi$
$997$	293.423			0.294306			0.147153	+	0.989114i	$0.452989\pi$
$998$		0			0
$999$	1364.85			1.36622

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.t.a.113.8		44
4.3	odd	2		80.3.t.a.53.17	yes	44
5.2	odd	4		320.3.i.a.177.15		44
8.3	odd	2		640.3.t.b.353.8		44
8.5	even	2		640.3.t.a.353.15		44
16.3	odd	4		80.3.i.a.13.7	✓	44
16.5	even	4		640.3.i.a.33.15		44
16.11	odd	4		640.3.i.b.33.8		44
16.13	even	4		320.3.i.a.273.8		44
20.3	even	4		400.3.i.b.357.16		44
20.7	even	4		80.3.i.a.37.7	yes	44
20.19	odd	2		400.3.t.b.293.6		44
40.27	even	4		640.3.i.b.97.15		44
40.37	odd	4		640.3.i.a.97.8		44
80.3	even	4		400.3.t.b.157.6		44
80.19	odd	4		400.3.i.b.93.16		44
80.27	even	4		640.3.t.b.417.8		44
80.37	odd	4		640.3.t.a.417.15		44
80.67	even	4		80.3.t.a.77.17	yes	44
80.77	odd	4	inner	320.3.t.a.17.8		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.7	✓	44	16.3	odd	4
80.3.i.a.37.7	yes	44	20.7	even	4
80.3.t.a.53.17	yes	44	4.3	odd	2
80.3.t.a.77.17	yes	44	80.67	even	4
320.3.i.a.177.15		44	5.2	odd	4
320.3.i.a.273.8		44	16.13	even	4
320.3.t.a.17.8		44	80.77	odd	4	inner
320.3.t.a.113.8		44	1.1	even	1	trivial
400.3.i.b.93.16		44	80.19	odd	4
400.3.i.b.357.16		44	20.3	even	4
400.3.t.b.157.6		44	80.3	even	4
400.3.t.b.293.6		44	20.19	odd	2
640.3.i.a.33.15		44	16.5	even	4
640.3.i.a.97.8		44	40.37	odd	4
640.3.i.b.33.8		44	16.11	odd	4
640.3.i.b.97.15		44	40.27	even	4
640.3.t.a.353.15		44	8.5	even	2
640.3.t.a.417.15		44	80.37	odd	4
640.3.t.b.353.8		44	8.3	odd	2
640.3.t.b.417.8		44	80.27	even	4

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.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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