LMFDB - Embedded newform 320.3.i.a.273.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(177,320)]

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, 1, 1]))

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

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

chi := DirichletCharacter("320.177");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.i (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			273.8
Character	$\chi$	$=$	320.273
Dual form			320.3.i.a.177.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90859i q^{3} +(-0.530759 - 4.97175i) q^{5} +(-8.62025 - 8.62025i) q^{7} +5.35728 q^{9} +O(q^{10})$	\(q-1.90859i q^{3} +(-0.530759 - 4.97175i) q^{5} +(-8.62025 - 8.62025i) q^{7} +5.35728 q^{9} +(-6.35145 + 6.35145i) q^{11} +6.65056i q^{13} +(-9.48903 + 1.01300i) q^{15} +(-5.36508 + 5.36508i) q^{17} +(-18.1009 + 18.1009i) q^{19} +(-16.4525 + 16.4525i) q^{21} +(16.1730 - 16.1730i) q^{23} +(-24.4366 + 5.27760i) q^{25} -27.4022i q^{27} +(-12.4816 + 12.4816i) q^{29} +18.5625 q^{31} +(12.1223 + 12.1223i) q^{33} +(-38.2825 + 47.4330i) q^{35} -49.8083i q^{37} +12.6932 q^{39} -62.1433i q^{41} -32.2720 q^{43} +(-2.84343 - 26.6351i) q^{45} +(-13.2635 + 13.2635i) q^{47} +99.6175i q^{49} +(10.2397 + 10.2397i) q^{51} -64.2436 q^{53} +(34.9489 + 28.2067i) q^{55} +(34.5471 + 34.5471i) q^{57} +(2.55993 + 2.55993i) q^{59} +(-52.5270 - 52.5270i) q^{61} +(-46.1811 - 46.1811i) q^{63} +(33.0649 - 3.52984i) q^{65} +72.2222 q^{67} +(-30.8676 - 30.8676i) q^{69} -24.3819i q^{71} +(-1.39841 + 1.39841i) q^{73} +(10.0728 + 46.6394i) q^{75} +109.502 q^{77} -90.0709i q^{79} -4.08398 q^{81} -3.78386i q^{83} +(29.5214 + 23.8263i) q^{85} +(23.8222 + 23.8222i) q^{87} +61.3939 q^{89} +(57.3295 - 57.3295i) q^{91} -35.4283i q^{93} +(99.6001 + 80.3857i) q^{95} +(103.182 - 103.182i) q^{97} +(-34.0265 + 34.0265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{5} - 108 q^{9}+O(q^{10}) $ 44 * q - 2 * q^5 - 108 * q^9	$ 44 q - 2 q^{5} - 108 q^{9} + 4 q^{11} + 4 q^{15} - 4 q^{17} - 32 q^{19} - 4 q^{21} + 8 q^{31} - 4 q^{33} - 96 q^{35} - 72 q^{39} - 124 q^{43} - 34 q^{45} + 4 q^{47} + 100 q^{51} - 4 q^{53} + 36 q^{57} - 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 292 q^{67} - 60 q^{69} + 48 q^{73} - 96 q^{75} + 192 q^{77} + 100 q^{81} + 48 q^{85} - 36 q^{87} - 188 q^{91} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) $ 44 * q - 2 * q^5 - 108 * q^9 + 4 * q^11 + 4 * q^15 - 4 * q^17 - 32 * q^19 - 4 * q^21 + 8 * q^31 - 4 * q^33 - 96 * q^35 - 72 * q^39 - 124 * q^43 - 34 * q^45 + 4 * q^47 + 100 * q^51 - 4 * q^53 + 36 * q^57 - 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 292 * q^67 - 60 * q^69 + 48 * q^73 - 96 * q^75 + 192 * q^77 + 100 * q^81 + 48 * q^85 - 36 * q^87 - 188 * q^91 - 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

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

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
$3$		−	1.90859i		−	0.636197i	−0.948058	−	0.318098i	$-0.896956\pi$
$3$		−	1.90859i		−	0.636197i	0.948058	−	0.318098i	$-0.103044\pi$
$4$		0			0
$5$	−0.530759	−	4.97175i	−0.106152	−	0.994350i
$5$	−0.530759	−	4.97175i	−0.106152	−	0.994350i
$6$		0			0
$7$	−8.62025	−	8.62025i	−1.23146	−	1.23146i	−0.963401	−	0.268063i	$-0.913616\pi$
$7$	−8.62025	−	8.62025i	−1.23146	−	1.23146i	−0.268063	−	0.963401i	$-0.586384\pi$
$8$		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
$13$			6.65056i			0.511581i	0.966732	+	0.255791i	$0.0823358\pi$
$13$			6.65056i			0.511581i	−0.966732	+	0.255791i	$0.917664\pi$
$14$		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	$-0.985272\pi$
$19$	−18.1009	+	18.1009i	−0.952677	+	0.952677i	0.0462531	+	0.998930i	$0.485272\pi$
$20$		0			0
$21$	−16.4525	+	16.4525i	−0.783454	+	0.783454i
$22$		0			0
$23$	16.1730	−	16.1730i	0.703172	−	0.703172i	−0.261918	−	0.965090i	$-0.584355\pi$
$23$	16.1730	−	16.1730i	0.703172	−	0.703172i	0.965090	+	0.261918i	$0.0843549\pi$
$24$		0			0
$25$	−24.4366	+	5.27760i	−0.977464	+	0.211104i
$26$		0			0
$27$		−	27.4022i		−	1.01490i
$28$		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	$-0.403215\pi$
$31$	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
$35$	−38.2825	+	47.4330i	−1.09378	+	1.35523i
$36$		0			0
$37$		−	49.8083i		−	1.34617i	−0.739565	−	0.673085i	$-0.764969\pi$
$37$		−	49.8083i		−	1.34617i	0.739565	−	0.673085i	$-0.235031\pi$
$38$		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
$43$	−32.2720			−0.750511			−0.375255	−	0.926921i	$-0.622445\pi$
$43$	−32.2720			−0.750511			−0.375255	+	0.926921i	$0.622445\pi$
$44$		0			0
$45$	−2.84343	−	26.6351i	−0.0631872	−	0.591890i
$46$		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
$53$	−64.2436			−1.21214			−0.606071	−	0.795410i	$-0.707255\pi$
$53$	−64.2436			−1.21214			−0.606071	+	0.795410i	$0.707255\pi$
$54$		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	$-0.240233\pi$
$59$	2.55993	+	2.55993i	0.0433887	+	0.0433887i	−0.685080	+	0.728468i	$0.740233\pi$
$60$		0			0
$61$	−52.5270	−	52.5270i	−0.861098	−	0.861098i	0.130367	−	0.991466i	$-0.458384\pi$
$61$	−52.5270	−	52.5270i	−0.861098	−	0.861098i	−0.991466	+	0.130367i	$0.958384\pi$
$62$		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
$67$	72.2222			1.07794			0.538972	−	0.842324i	$-0.318813\pi$
$67$	72.2222			1.07794			0.538972	+	0.842324i	$0.318813\pi$
$68$		0			0
$69$	−30.8676	−	30.8676i	−0.447356	−	0.447356i
$70$		0			0
$71$		−	24.3819i		−	0.343407i	−0.985149	−	0.171703i	$-0.945073\pi$
$71$		−	24.3819i		−	0.343407i	0.985149	−	0.171703i	$-0.0549270\pi$
$72$		0			0
$73$	−1.39841	+	1.39841i	−0.0191563	+	0.0191563i	−0.716620	−	0.697464i	$-0.754312\pi$
$73$	−1.39841	+	1.39841i	−0.0191563	+	0.0191563i	0.697464	+	0.716620i	$0.254312\pi$
$74$		0			0
$75$	10.0728	+	46.6394i	0.134304	+	0.621859i
$76$		0			0
$77$	109.502			1.42211
$78$		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
$83$		−	3.78386i		−	0.0455886i	−0.999740	−	0.0227943i	$-0.992744\pi$
$83$		−	3.78386i		−	0.0455886i	0.999740	−	0.0227943i	$-0.00725628\pi$
$84$		0			0
$85$	29.5214	+	23.8263i	0.347311	+	0.280309i
$86$		0			0
$87$	23.8222	+	23.8222i	0.273819	+	0.273819i
$88$		0			0
$89$	61.3939			0.689819			0.344910	−	0.938636i	$-0.387910\pi$
$89$	61.3939			0.689819			0.344910	+	0.938636i	$0.387910\pi$
$90$		0			0
$91$	57.3295	−	57.3295i	0.629994	−	0.629994i
$92$		0			0
$93$		−	35.4283i		−	0.380949i
$94$		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	−0.996471	−	0.0839323i	$-0.973252\pi$
$101$	−92.1665	+	92.1665i	−0.912539	+	0.912539i	0.0839323	+	0.996471i	$0.473252\pi$
$102$		0			0
$103$	73.2115	−	73.2115i	0.710791	−	0.710791i	−0.255909	−	0.966701i	$-0.582375\pi$
$103$	73.2115	−	73.2115i	0.710791	−	0.710791i	0.966701	+	0.255909i	$0.0823749\pi$
$104$		0			0
$105$	90.5302	+	73.0655i	0.862192	+	0.695862i
$106$		0			0
$107$			17.7853i			0.166218i	0.996540	+	0.0831089i	$0.0264849\pi$
$107$			17.7853i			0.166218i	−0.996540	+	0.0831089i	$0.973515\pi$
$108$		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	0.374276	−	0.927317i	$-0.377891\pi$
$113$	−62.4937	−	62.4937i	−0.553042	−	0.553042i	−0.927317	+	0.374276i	$0.877891\pi$
$114$		0			0
$115$	−88.9919	−	71.8240i	−0.773842	−	0.624556i
$116$		0			0
$117$			35.6289i			0.304521i
$118$		0			0
$119$	92.4967			0.777283
$120$		0			0
$121$			40.3182i			0.333208i
$122$		0			0
$123$	−118.606			−0.964278
$124$		0			0
$125$	39.2089	+	118.691i	0.313671	+	0.949532i
$126$		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	0.786404	−	0.617712i	$-0.211940\pi$
$131$	22.0987	+	22.0987i	0.168693	+	0.168693i	−0.617712	+	0.786404i	$0.711940\pi$
$132$		0			0
$133$	312.068			2.34637
$134$		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	$-0.427094\pi$
$137$	−102.317	−	102.317i	−0.746841	−	0.746841i	−0.973885	+	0.227043i	$0.927094\pi$
$138$		0			0
$139$	83.0087	+	83.0087i	0.597185	+	0.597185i	0.939562	−	0.342378i	$-0.111232\pi$
$139$	83.0087	+	83.0087i	0.597185	+	0.597185i	−0.342378	+	0.939562i	$0.611232\pi$
$140$		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
$147$	190.129			1.29339
$148$		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	$0.0514334\pi$
$151$			48.5859i			0.321761i	−0.986974	+	0.160881i	$0.948567\pi$
$152$		0			0
$153$	−28.7423	+	28.7423i	−0.187858	+	0.187858i
$154$		0			0
$155$	−9.85223	−	92.2883i	−0.0635628	−	0.595408i
$156$		0			0
$157$	140.992			0.898038			0.449019	−	0.893522i	$-0.351774\pi$
$157$	140.992			0.898038			0.449019	+	0.893522i	$0.351774\pi$
$158$		0			0
$159$			122.615i			0.771162i
$160$		0			0
$161$	−278.830			−1.73186
$162$		0			0
$163$		−	98.2045i		−	0.602482i	−0.953548	−	0.301241i	$-0.902599\pi$
$163$		−	98.2045i		−	0.602482i	0.953548	−	0.301241i	$-0.0974008\pi$
$164$		0			0
$165$	53.8351	−	66.7031i	0.326273	−	0.404261i
$166$		0			0
$167$	−9.58867	−	9.58867i	−0.0574172	−	0.0574172i	0.677815	−	0.735232i	$-0.262927\pi$
$167$	−9.58867	−	9.58867i	−0.0574172	−	0.0574172i	−0.735232	+	0.677815i	$0.762927\pi$
$168$		0			0
$169$	124.770			0.738285
$170$		0			0
$171$	−96.9714	+	96.9714i	−0.567084	+	0.567084i
$172$		0			0
$173$		−	172.905i		−	0.999452i	−0.866184	−	0.499726i	$-0.833434\pi$
$173$		−	172.905i		−	0.999452i	0.866184	−	0.499726i	$-0.166566\pi$
$174$		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	$-0.690322\pi$
$179$	47.1828	−	47.1828i	0.263591	−	0.263591i	0.826511	+	0.562920i	$0.190322\pi$
$180$		0			0
$181$	50.7180	−	50.7180i	0.280210	−	0.280210i	−0.552983	−	0.833193i	$-0.686511\pi$
$181$	50.7180	−	50.7180i	0.280210	−	0.280210i	0.833193	+	0.552983i	$0.186511\pi$
$182$		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
$187$		−	68.1521i		−	0.364450i
$188$		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
$195$	−6.73702	−	63.1074i	−0.0345488	−	0.323627i
$196$		0			0
$197$			257.794i			1.30860i	0.756236	+	0.654299i	$0.227036\pi$
$197$			257.794i			1.30860i	−0.756236	+	0.654299i	$0.772964\pi$
$198$		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
$203$	215.189			1.06004
$204$		0			0
$205$	−308.961	+	32.9831i	−1.50713	+	0.160893i
$206$		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
$213$	−46.5350			−0.218474
$214$		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
$227$	−47.5480			−0.209462			−0.104731	−	0.994501i	$-0.533398\pi$
$227$	−47.5480			−0.209462			−0.104731	+	0.994501i	$0.533398\pi$
$228$		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	$-0.958934\pi$
$233$	−201.087	+	201.087i	−0.863035	+	0.863035i	0.128655	+	0.991689i	$0.458934\pi$
$234$		0			0
$235$	72.9824	+	58.9030i	0.310563	+	0.250651i
$236$		0			0
$237$	−171.908			−0.725352
$238$		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
$243$		−	238.825i		−	0.982819i
$244$		0			0
$245$	495.273	−	52.8729i	2.02152	−	0.215808i
$246$		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
$253$			205.444i			0.812030i
$254$		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	$0.643686\pi$
$263$	−351.385	+	351.385i	−1.33606	+	1.33606i	−0.899836	+	0.436228i	$0.856314\pi$
$264$		0			0
$265$	34.0979	+	319.403i	0.128671	+	1.20529i
$266$		0			0
$267$		−	117.176i		−	0.438861i
$268$		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	$-0.525403\pi$
$271$	−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
$275$	121.687	−	188.728i	0.442499	−	0.686284i
$276$		0			0
$277$			53.1202i			0.191770i	0.995392	+	0.0958849i	$0.0305681\pi$
$277$			53.1202i			0.191770i	−0.995392	+	0.0958849i	$0.969432\pi$
$278$		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
$283$	−87.7034			−0.309906			−0.154953	−	0.987922i	$-0.549523\pi$
$283$	−87.7034			−0.309906			−0.154953	+	0.987922i	$0.549523\pi$
$284$		0			0
$285$	153.423	−	190.096i	0.538328	−	0.667003i
$286$		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
$293$	−257.077			−0.877395			−0.438697	−	0.898635i	$-0.644560\pi$
$293$	−257.077			−0.877395			−0.438697	+	0.898635i	$0.644560\pi$
$294$		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
$307$	601.105			1.95800			0.978998	−	0.203870i	$-0.0653519\pi$
$307$	601.105			1.95800			0.978998	+	0.203870i	$0.0653519\pi$
$308$		0			0
$309$	−139.731	−	139.731i	−0.452203	−	0.452203i
$310$		0			0
$311$		−	7.34424i		−	0.0236149i	−0.999930	−	0.0118075i	$-0.996241\pi$
$311$		−	7.34424i		−	0.0236149i	0.999930	−	0.0118075i	$-0.00375852\pi$
$312$		0			0
$313$	170.573	−	170.573i	0.544962	−	0.544962i	−0.380017	−	0.924979i	$-0.624082\pi$
$313$	170.573	−	170.573i	0.544962	−	0.544962i	0.924979	+	0.380017i	$0.124082\pi$
$314$		0			0
$315$	−205.090	+	254.112i	−0.651079	+	0.806705i
$316$		0			0
$317$	266.389			0.840345			0.420172	−	0.907444i	$-0.361970\pi$
$317$	266.389			0.840345			0.420172	+	0.907444i	$0.361970\pi$
$318$		0			0
$319$		−	158.552i		−	0.497029i
$320$		0			0
$321$	33.9449			0.105747
$322$		0			0
$323$		−	194.225i		−	0.601316i
$324$		0			0
$325$	−35.0990	−	162.517i	−0.107997	−	0.500052i
$326$		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
$333$		−	266.837i		−	0.801312i
$334$		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
$347$		−	575.495i		−	1.65849i	−0.558888	−	0.829243i	$-0.688772\pi$
$347$		−	575.495i		−	1.65849i	0.558888	−	0.829243i	$-0.311228\pi$
$348$		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	0.926418	−	0.376498i	$-0.122872\pi$
$353$	194.122	+	194.122i	0.549920	+	0.549920i	−0.376498	+	0.926418i	$0.622872\pi$
$354$		0			0
$355$	−121.221	+	12.9409i	−0.341466	+	0.0364532i
$356$		0			0
$357$		−	176.538i		−	0.494505i
$358$		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
$363$	76.9509			0.211986
$364$		0			0
$365$	7.69477	+	6.21033i	0.0210816	+	0.0170146i
$366$		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
$373$	−73.3291			−0.196593			−0.0982963	−	0.995157i	$-0.531339\pi$
$373$	−73.3291			−0.196593			−0.0982963	+	0.995157i	$0.531339\pi$
$374$		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	$-0.194175\pi$
$379$	93.5200	+	93.5200i	0.246755	+	0.246755i	−0.572883	+	0.819637i	$0.694175\pi$
$380$		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
$387$	−172.890			−0.446744
$388$		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
$395$	−447.810	+	47.8059i	−1.13370	+	0.121028i
$396$		0			0
$397$	−299.500			−0.754407			−0.377204	−	0.926130i	$-0.623114\pi$
$397$	−299.500			−0.754407			−0.377204	+	0.926130i	$0.623114\pi$
$398$		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
$403$			123.451i			0.306331i
$404$		0			0
$405$	2.16761	+	20.3045i	0.00535212	+	0.0501346i
$406$		0			0
$407$	316.355	+	316.355i	0.777284	+	0.777284i
$408$		0			0
$409$	657.734			1.60815			0.804076	−	0.594526i	$-0.202660\pi$
$409$	657.734			1.60815			0.804076	+	0.594526i	$0.202660\pi$
$410$		0			0
$411$	−195.282	+	195.282i	−0.475138	+	0.475138i
$412$		0			0
$413$		−	44.1345i		−	0.106863i
$414$		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	$-0.828790\pi$
$419$	−145.179	+	145.179i	−0.346489	+	0.346489i	0.512311	+	0.858800i	$0.328790\pi$
$420$		0			0
$421$	−19.6145	+	19.6145i	−0.0465904	+	0.0465904i	−0.730018	−	0.683428i	$-0.760488\pi$
$421$	−19.6145	+	19.6145i	−0.0465904	+	0.0465904i	0.683428	+	0.730018i	$0.260488\pi$
$422$		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
$427$			905.592i			2.12082i
$428$		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
$435$	105.794	−	131.082i	0.243205	−	0.301338i
$436$		0			0
$437$			585.489i			1.33979i
$438$		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
$443$	−499.336			−1.12717			−0.563585	−	0.826058i	$-0.690578\pi$
$443$	−499.336			−1.12717			−0.563585	+	0.826058i	$0.690578\pi$
$444$		0			0
$445$	−32.5854	−	305.235i	−0.0732256	−	0.685922i
$446$		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
$453$	92.7306			0.204703
$454$		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	$-0.469413\pi$
$457$	−411.045	−	411.045i	−0.899443	−	0.899443i	−0.995387	+	0.0959440i	$0.969413\pi$
$458$		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	$0.0643610\pi$
$461$	544.187	+	544.187i	1.18045	+	1.18045i	0.200821	+	0.979628i	$0.435639\pi$
$462$		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
$467$	−462.541			−0.990452			−0.495226	−	0.868764i	$-0.664915\pi$
$467$	−462.541			−0.990452			−0.495226	+	0.868764i	$0.664915\pi$
$468$		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
$475$	346.794	−	537.852i	0.730093	−	1.13232i
$476$		0			0
$477$	−344.171			−0.721533
$478$		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
$483$			532.172i			1.10181i
$484$		0			0
$485$	−567.761	−	458.231i	−1.17064	−	0.944806i
$486$		0			0
$487$	−376.646	−	376.646i	−0.773401	−	0.773401i	0.205299	−	0.978699i	$-0.434183\pi$
$487$	−376.646	−	376.646i	−0.773401	−	0.773401i	−0.978699	+	0.205299i	$0.934183\pi$
$488$		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
$493$		−	133.929i		−	0.271662i
$494$		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	$-0.605807\pi$
$499$	308.855	−	308.855i	0.618947	−	0.618947i	0.945261	+	0.326314i	$0.105807\pi$
$500$		0			0
$501$	−18.3009	+	18.3009i	−0.0365286	+	0.0365286i
$502$		0			0
$503$	−345.746	+	345.746i	−0.687368	+	0.687368i	−0.961650	−	0.274281i	$-0.911560\pi$
$503$	−345.746	+	345.746i	−0.687368	+	0.687368i	0.274281	+	0.961650i	$0.411560\pi$
$504$		0			0
$505$	507.147	+	409.310i	1.00425	+	0.810516i
$506$		0			0
$507$		−	238.135i		−	0.469694i
$508$		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
$515$	−402.847	−	325.132i	−0.782227	−	0.631324i
$516$		0			0
$517$		−	168.485i		−	0.325889i
$518$		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
$523$	114.482			0.218895			0.109448	−	0.993993i	$-0.465092\pi$
$523$	114.482			0.218895			0.109448	+	0.993993i	$0.465092\pi$
$524$		0			0
$525$	315.214	−	488.874i	0.600407	−	0.931188i
$526$		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
$533$	413.288			0.775399
$534$		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	$-0.978949\pi$
$541$	−575.569	−	575.569i	−1.06390	−	1.06390i	−0.0660852	−	0.997814i	$-0.521051\pi$
$542$		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
$547$	−1053.61			−1.92616			−0.963079	−	0.269219i	$-0.913234\pi$
$547$	−1053.61			−1.92616			−0.963079	+	0.269219i	$0.913234\pi$
$548$		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
$555$	50.4559	+	472.632i	0.0909115	+	0.851590i
$556$		0			0
$557$	680.234			1.22125			0.610623	−	0.791922i	$-0.290919\pi$
$557$	680.234			1.22125			0.610623	+	0.791922i	$0.290919\pi$
$558$		0			0
$559$		−	214.626i		−	0.383947i
$560$		0			0
$561$	−130.074			−0.231862
$562$		0			0
$563$			408.818i			0.726142i	0.931761	+	0.363071i	$0.118272\pi$
$563$			408.818i			0.726142i	−0.931761	+	0.363071i	$0.881728\pi$
$564$		0			0
$565$	−277.534	+	343.872i	−0.491211	+	0.608623i
$566$		0			0
$567$	35.2049	+	35.2049i	0.0620898	+	0.0620898i
$568$		0			0
$569$	−324.426			−0.570169			−0.285084	−	0.958502i	$-0.592022\pi$
$569$	−324.426			−0.570169			−0.285084	+	0.958502i	$0.592022\pi$
$570$		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
$573$			630.079i			1.09962i
$574$		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
$587$			279.206i			0.475649i	0.971308	+	0.237824i	$0.0764343\pi$
$587$			279.206i			0.475649i	−0.971308	+	0.237824i	$0.923566\pi$
$588$		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
$595$	−49.0935	−	459.870i	−0.0825100	−	0.772892i
$596$		0			0
$597$			626.973i			1.05021i
$598$		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
$603$	386.915			0.641650
$604$		0			0
$605$	200.452	−	21.3992i	0.331325	−	0.0353706i
$606$		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
$613$	165.499			0.269981			0.134991	−	0.990847i	$-0.456900\pi$
$613$	165.499			0.269981			0.134991	+	0.990847i	$0.456900\pi$
$614$		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	$-0.330794\pi$
$617$	−219.108	−	219.108i	−0.355118	−	0.355118i	−0.862010	+	0.506892i	$0.830794\pi$
$618$		0			0
$619$	−365.140	−	365.140i	−0.589888	−	0.589888i	0.347713	−	0.937601i	$-0.386958\pi$
$619$	−365.140	−	365.140i	−0.589888	−	0.589888i	−0.937601	+	0.347713i	$0.886958\pi$
$620$		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
$627$	−438.849			−0.699918
$628$		0			0
$629$	267.225	+	267.225i	0.424842	+	0.424842i
$630$		0			0
$631$			1113.61i			1.76484i	0.470463	+	0.882420i	$0.344087\pi$
$631$			1113.61i			1.76484i	−0.470463	+	0.882420i	$0.655913\pi$
$632$		0			0
$633$	−98.0856	+	98.0856i	−0.154953	+	0.154953i
$634$		0			0
$635$	−278.431	−	224.718i	−0.438475	−	0.353886i
$636$		0			0
$637$	−662.511			−1.04005
$638$		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
$643$		−	68.4686i		−	0.106483i	−0.998582	−	0.0532415i	$-0.983045\pi$
$643$		−	68.4686i		−	0.106483i	0.998582	−	0.0532415i	$-0.0169553\pi$
$644$		0			0
$645$	306.230	−	32.6915i	0.474775	−	0.0506846i
$646$		0			0
$647$	−60.8229	−	60.8229i	−0.0940075	−	0.0940075i	0.658539	−	0.752547i	$-0.271175\pi$
$647$	−60.8229	−	60.8229i	−0.0940075	−	0.0940075i	−0.752547	+	0.658539i	$0.771175\pi$
$648$		0			0
$649$	−32.5186			−0.0501057
$650$		0			0
$651$	−305.401	+	305.401i	−0.469125	+	0.469125i
$652$		0			0
$653$			815.643i			1.24907i	0.780996	+	0.624536i	$0.214712\pi$
$653$			815.643i			1.24907i	−0.780996	+	0.624536i	$0.785288\pi$
$654$		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	$-0.443327\pi$
$659$	765.294	−	765.294i	1.16130	−	1.16130i	0.984192	−	0.177103i	$-0.0566727\pi$
$660$		0			0
$661$	423.035	−	423.035i	0.639993	−	0.639993i	−0.310561	−	0.950553i	$-0.600517\pi$
$661$	423.035	−	423.035i	0.639993	−	0.639993i	0.950553	+	0.310561i	$0.100517\pi$
$662$		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
$667$			403.729i			0.605290i
$668$		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
$675$	144.618	+	669.616i	0.214249	+	0.992023i
$676$		0			0
$677$		−	244.469i		−	0.361106i	−0.983565	−	0.180553i	$-0.942211\pi$
$677$		−	244.469i		−	0.361106i	0.983565	−	0.180553i	$-0.0577888\pi$
$678$		0			0
$679$	−1778.91			−2.61990
$680$		0			0
$681$			90.7496i			0.133259i
$682$		0			0
$683$	434.494			0.636155			0.318077	−	0.948065i	$-0.396963\pi$
$683$	434.494			0.636155			0.318077	+	0.948065i	$0.396963\pi$
$684$		0			0
$685$	−454.390	+	563.002i	−0.663343	+	0.821900i
$686$		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
$693$	586.634			0.846514
$694$		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	0.903563	−	0.428456i	$-0.140942\pi$
$701$	333.050	+	333.050i	0.475106	+	0.475106i	−0.428456	+	0.903563i	$0.640942\pi$
$702$		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
$707$	1589.00			2.24752
$708$		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
$715$	−187.590	+	232.430i	−0.262364	+	0.325076i
$716$		0			0
$717$	−467.773			−0.652403
$718$		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
$723$		−	882.690i		−	1.22087i
$724$		0			0
$725$	239.135	−	370.880i	0.329841	−	0.511559i
$726$		0			0
$727$	−115.757	−	115.757i	−0.159225	−	0.159225i	0.622998	−	0.782223i	$-0.285914\pi$
$727$	−115.757	−	115.757i	−0.159225	−	0.159225i	−0.782223	+	0.622998i	$0.785914\pi$
$728$		0			0
$729$	−492.575			−0.675686
$730$		0			0
$731$	173.142	−	173.142i	0.236856	−	0.236856i
$732$		0			0
$733$		−	123.197i		−	0.168073i	−0.996463	−	0.0840363i	$-0.973219\pi$
$733$		−	123.197i		−	0.168073i	0.996463	−	0.0840363i	$-0.0267812\pi$
$734$		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	$-0.539625\pi$
$739$	641.523	−	641.523i	0.868096	−	0.868096i	0.992262	+	0.124166i	$0.0396254\pi$
$740$		0			0
$741$	−229.758	+	229.758i	−0.310064	+	0.310064i
$742$		0			0
$743$	−84.7652	+	84.7652i	−0.114085	+	0.114085i	−0.761845	−	0.647760i	$-0.775706\pi$
$743$	−84.7652	+	84.7652i	−0.114085	+	0.114085i	0.647760	+	0.761845i	$0.275706\pi$
$744$		0			0
$745$	−595.756	+	738.158i	−0.799673	+	0.990816i
$746$		0			0
$747$		−	20.2712i		−	0.0271368i
$748$		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
$755$	241.557	−	25.7874i	0.319943	−	0.0341555i
$756$		0			0
$757$		−	857.792i		−	1.13315i	−0.824011	−	0.566574i	$-0.808269\pi$
$757$		−	857.792i		−	1.13315i	0.824011	−	0.566574i	$-0.191731\pi$
$758$		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
$763$	−166.210			−0.217837
$764$		0			0
$765$	158.155	+	127.644i	0.206738	+	0.166855i
$766$		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
$773$	−396.076			−0.512388			−0.256194	−	0.966625i	$-0.582469\pi$
$773$	−396.076			−0.512388			−0.256194	+	0.966625i	$0.582469\pi$
$774$		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
$787$	−184.472			−0.234399			−0.117200	−	0.993108i	$-0.537392\pi$
$787$	−184.472			−0.234399			−0.117200	+	0.993108i	$0.537392\pi$
$788$		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
$795$	609.609	−	65.0788i	0.766804	−	0.0818602i
$796$		0			0
$797$	187.027			0.234664			0.117332	−	0.993093i	$-0.462566\pi$
$797$	187.027			0.234664			0.117332	+	0.993093i	$0.462566\pi$
$798$		0			0
$799$		−	142.319i		−	0.178122i
$800$		0			0
$801$	328.905			0.410617
$802$		0			0
$803$		−	17.7639i		−	0.0221219i
$804$		0			0
$805$	147.992	+	1386.27i	0.183840	+	1.72208i
$806$		0			0
$807$	−86.7572	−	86.7572i	−0.107506	−	0.107506i
$808$		0			0
$809$	356.858			0.441110			0.220555	−	0.975374i	$-0.429213\pi$
$809$	356.858			0.441110			0.220555	+	0.975374i	$0.429213\pi$
$810$		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
$813$			82.4677i			0.101436i
$814$		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	−0.717967	−	0.696077i	$-0.754927\pi$
$821$	−17.9719	+	17.9719i	−0.0218902	+	0.0218902i	0.696077	+	0.717967i	$0.254927\pi$
$822$		0			0
$823$	36.8905	−	36.8905i	0.0448245	−	0.0448245i	−0.684339	−	0.729164i	$-0.739909\pi$
$823$	36.8905	−	36.8905i	0.0448245	−	0.0448245i	0.729164	+	0.684339i	$0.239909\pi$
$824$		0			0
$825$	−360.205	−	232.251i	−0.436612	−	0.281517i
$826$		0			0
$827$		−	837.787i		−	1.01304i	−0.862227	−	0.506522i	$-0.830931\pi$
$827$		−	837.787i		−	1.01304i	0.862227	−	0.506522i	$-0.169069\pi$
$828$		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
$835$	−42.5832	+	52.7618i	−0.0509979	+	0.0631877i
$836$		0			0
$837$		−	508.654i		−	0.607711i
$838$		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
$843$	−279.265			−0.331275
$844$		0			0
$845$	−66.2229	−	620.326i	−0.0783702	−	0.734113i
$846$		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
$853$	−293.712			−0.344329			−0.172164	−	0.985068i	$-0.555076\pi$
$853$	−293.712			−0.344329			−0.172164	+	0.985068i	$0.555076\pi$
$854$		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	$-0.0677162\pi$
$857$	656.737	+	656.737i	0.766321	+	0.766321i	−0.211136	+	0.977457i	$0.567716\pi$
$858$		0			0
$859$	−1015.37	−	1015.37i	−1.18203	−	1.18203i	−0.979217	−	0.202818i	$-0.934990\pi$
$859$	−1015.37	−	1015.37i	−1.18203	−	1.18203i	−0.202818	−	0.979217i	$-0.565010\pi$
$860$		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
$867$	441.709			0.509468
$868$		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
$875$	685.160	−	1361.14i	0.783040	−	1.55559i
$876$		0			0
$877$	532.291			0.606945			0.303472	−	0.952840i	$-0.401854\pi$
$877$	532.291			0.606945			0.303472	+	0.952840i	$0.401854\pi$
$878$		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
$883$			141.696i			0.160471i	0.996776	+	0.0802354i	$0.0255672\pi$
$883$			141.696i			0.160471i	−0.996776	+	0.0802354i	$0.974433\pi$
$884$		0			0
$885$	−26.8845	−	21.6981i	−0.0303780	−	0.0245176i
$886$		0			0
$887$	−258.995	−	258.995i	−0.291990	−	0.291990i	0.545876	−	0.837866i	$-0.316197\pi$
$887$	−258.995	−	258.995i	−0.291990	−	0.291990i	−0.837866	+	0.545876i	$0.816197\pi$
$888$		0			0
$889$	−872.383			−0.981309
$890$		0			0
$891$	25.9392	−	25.9392i	0.0291125	−	0.0291125i
$892$		0			0
$893$		−	480.161i		−	0.537694i
$894$		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
$907$			427.687i			0.471540i	0.971809	+	0.235770i	$0.0757613\pi$
$907$			427.687i			0.471540i	−0.971809	+	0.235770i	$0.924239\pi$
$908$		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
$915$	551.640	+	445.221i	0.602886	+	0.486580i
$916$		0			0
$917$		−	380.993i		−	0.415478i
$918$		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
$923$	162.153			0.175680
$924$		0			0
$925$	262.868	+	1217.14i	0.284182	+	1.31583i
$926$		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
$933$	−14.0171			−0.0150237
$934$		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	$-0.177361\pi$
$937$	299.777	+	299.777i	0.319932	+	0.319932i	−0.528809	+	0.848741i	$0.677361\pi$
$938$		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	$-0.982562\pi$
$941$	−991.114	−	991.114i	−1.05326	−	1.05326i	−0.0547565	−	0.998500i	$-0.517438\pi$
$942$		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
$947$	−22.1486			−0.0233882			−0.0116941	−	0.999932i	$-0.503722\pi$
$947$	−22.1486			−0.0233882			−0.0116941	+	0.999932i	$0.503722\pi$
$948$		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	$0.598206\pi$
$953$	−1197.38	+	1197.38i	−1.25643	+	1.25643i	−0.952783	+	0.303651i	$0.901794\pi$
$954$		0			0
$955$	175.218	+	1641.31i	0.183475	+	1.71865i
$956$		0			0
$957$	−302.612			−0.316208
$958$		0			0
$959$			1764.00i			1.83942i
$960$		0			0
$961$	−616.432			−0.641449
$962$		0			0
$963$			95.2809i			0.0989417i
$964$		0			0
$965$	−668.635	+	828.457i	−0.692886	+	0.858505i
$966$		0			0
$967$	937.022	+	937.022i	0.968998	+	0.968998i	0.999534	−	0.0305352i	$-0.00972117\pi$
$967$	937.022	+	937.022i	0.968998	+	0.968998i	−0.0305352	+	0.999534i	$0.509721\pi$
$968$		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
$973$		−	1431.11i		−	1.47082i
$974$		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	−0.959646	−	0.281209i	$-0.909265\pi$
$983$	−666.904	+	666.904i	−0.678437	+	0.678437i	0.281209	+	0.959646i	$0.409265\pi$
$984$		0			0
$985$	1281.69	−	136.826i	1.30120	−	0.138910i
$986$		0			0
$987$		−	436.435i		−	0.442184i
$988$		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
$995$	174.355	+	1633.22i	0.175231	+	1.64143i
$996$		0			0
$997$		−	293.423i		−	0.294306i	−0.989114	−	0.147153i	$-0.952989\pi$
$997$		−	293.423i		−	0.294306i	0.989114	−	0.147153i	$-0.0470110\pi$
$998$		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.i.a.273.8		44
4.3	odd	2		80.3.i.a.13.7	✓	44
5.2	odd	4		320.3.t.a.17.8		44
8.3	odd	2		640.3.i.b.33.8		44
8.5	even	2		640.3.i.a.33.15		44
16.3	odd	4		640.3.t.b.353.8		44
16.5	even	4		320.3.t.a.113.8		44
16.11	odd	4		80.3.t.a.53.17	yes	44
16.13	even	4		640.3.t.a.353.15		44
20.3	even	4		400.3.t.b.157.6		44
20.7	even	4		80.3.t.a.77.17	yes	44
20.19	odd	2		400.3.i.b.93.16		44
40.27	even	4		640.3.t.b.417.8		44
40.37	odd	4		640.3.t.a.417.15		44
80.27	even	4		80.3.i.a.37.7	yes	44
80.37	odd	4	inner	320.3.i.a.177.15		44
80.43	even	4		400.3.i.b.357.16		44
80.59	odd	4		400.3.t.b.293.6		44
80.67	even	4		640.3.i.b.97.15		44
80.77	odd	4		640.3.i.a.97.8		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.7	✓	44	4.3	odd	2
80.3.i.a.37.7	yes	44	80.27	even	4
80.3.t.a.53.17	yes	44	16.11	odd	4
80.3.t.a.77.17	yes	44	20.7	even	4
320.3.i.a.177.15		44	80.37	odd	4	inner
320.3.i.a.273.8		44	1.1	even	1	trivial
320.3.t.a.17.8		44	5.2	odd	4
320.3.t.a.113.8		44	16.5	even	4
400.3.i.b.93.16		44	20.19	odd	2
400.3.i.b.357.16		44	80.43	even	4
400.3.t.b.157.6		44	20.3	even	4
400.3.t.b.293.6		44	80.59	odd	4
640.3.i.a.33.15		44	8.5	even	2
640.3.i.a.97.8		44	80.77	odd	4
640.3.i.b.33.8		44	8.3	odd	2
640.3.i.b.97.15		44	80.67	even	4
640.3.t.a.353.15		44	16.13	even	4
640.3.t.a.417.15		44	40.37	odd	4
640.3.t.b.353.8		44	16.3	odd	4
640.3.t.b.417.8		44	40.27	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.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.90859i q^{3} +(-0.530759 - 4.97175i) q^{5} +(-8.62025 - 8.62025i) q^{7} +5.35728 q^{9} +O(q^{10})\)	\(q-1.90859i q^{3} +(-0.530759 - 4.97175i) q^{5} +(-8.62025 - 8.62025i) q^{7} +5.35728 q^{9} +(-6.35145 + 6.35145i) q^{11} +6.65056i q^{13} +(-9.48903 + 1.01300i) q^{15} +(-5.36508 + 5.36508i) q^{17} +(-18.1009 + 18.1009i) q^{19} +(-16.4525 + 16.4525i) q^{21} +(16.1730 - 16.1730i) q^{23} +(-24.4366 + 5.27760i) q^{25} -27.4022i q^{27} +(-12.4816 + 12.4816i) q^{29} +18.5625 q^{31} +(12.1223 + 12.1223i) q^{33} +(-38.2825 + 47.4330i) q^{35} -49.8083i q^{37} +12.6932 q^{39} -62.1433i q^{41} -32.2720 q^{43} +(-2.84343 - 26.6351i) q^{45} +(-13.2635 + 13.2635i) q^{47} +99.6175i q^{49} +(10.2397 + 10.2397i) q^{51} -64.2436 q^{53} +(34.9489 + 28.2067i) q^{55} +(34.5471 + 34.5471i) q^{57} +(2.55993 + 2.55993i) q^{59} +(-52.5270 - 52.5270i) q^{61} +(-46.1811 - 46.1811i) q^{63} +(33.0649 - 3.52984i) q^{65} +72.2222 q^{67} +(-30.8676 - 30.8676i) q^{69} -24.3819i q^{71} +(-1.39841 + 1.39841i) q^{73} +(10.0728 + 46.6394i) q^{75} +109.502 q^{77} -90.0709i q^{79} -4.08398 q^{81} -3.78386i q^{83} +(29.5214 + 23.8263i) q^{85} +(23.8222 + 23.8222i) q^{87} +61.3939 q^{89} +(57.3295 - 57.3295i) q^{91} -35.4283i q^{93} +(99.6001 + 80.3857i) q^{95} +(103.182 - 103.182i) q^{97} +(-34.0265 + 34.0265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{5} - 108 q^{9}+O(q^{10}) \) 44 * q - 2 * q^5 - 108 * q^9	\( 44 q - 2 q^{5} - 108 q^{9} + 4 q^{11} + 4 q^{15} - 4 q^{17} - 32 q^{19} - 4 q^{21} + 8 q^{31} - 4 q^{33} - 96 q^{35} - 72 q^{39} - 124 q^{43} - 34 q^{45} + 4 q^{47} + 100 q^{51} - 4 q^{53} + 36 q^{57} - 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 292 q^{67} - 60 q^{69} + 48 q^{73} - 96 q^{75} + 192 q^{77} + 100 q^{81} + 48 q^{85} - 36 q^{87} - 188 q^{91} - 380 q^{95} - 4 q^{97} + 92 q^{99}+O(q^{100}) \) 44 * q - 2 * q^5 - 108 * q^9 + 4 * q^11 + 4 * q^15 - 4 * q^17 - 32 * q^19 - 4 * q^21 + 8 * q^31 - 4 * q^33 - 96 * q^35 - 72 * q^39 - 124 * q^43 - 34 * q^45 + 4 * q^47 + 100 * q^51 - 4 * q^53 + 36 * q^57 - 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 292 * q^67 - 60 * q^69 + 48 * q^73 - 96 * q^75 + 192 * q^77 + 100 * q^81 + 48 * q^85 - 36 * q^87 - 188 * q^91 - 380 * q^95 - 4 * q^97 + 92 * q^99

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