LMFDB - Embedded newform 320.3.t.a.17.12

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			17.12
Character	$\chi$	$=$	320.17
Dual form			320.3.t.a.113.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.616720 q^{3} +(-4.57731 + 2.01201i) q^{5} +(3.63369 - 3.63369i) q^{7} -8.61966 q^{9} +O(q^{10})$	\(q+0.616720 q^{3} +(-4.57731 + 2.01201i) q^{5} +(3.63369 - 3.63369i) q^{7} -8.61966 q^{9} +(7.78746 - 7.78746i) q^{11} +20.9042 q^{13} +(-2.82292 + 1.24085i) q^{15} +(-10.7894 - 10.7894i) q^{17} +(23.2855 - 23.2855i) q^{19} +(2.24097 - 2.24097i) q^{21} +(20.2919 + 20.2919i) q^{23} +(16.9036 - 18.4192i) q^{25} -10.8664 q^{27} +(6.35745 - 6.35745i) q^{29} -2.17692 q^{31} +(4.80268 - 4.80268i) q^{33} +(-9.32151 + 23.9436i) q^{35} -2.31411 q^{37} +12.8920 q^{39} +0.335796i q^{41} -66.6501i q^{43} +(39.4549 - 17.3429i) q^{45} +(-31.1488 - 31.1488i) q^{47} +22.5926i q^{49} +(-6.65403 - 6.65403i) q^{51} -6.42977i q^{53} +(-19.9772 + 51.3141i) q^{55} +(14.3606 - 14.3606i) q^{57} +(2.51863 + 2.51863i) q^{59} +(59.4999 + 59.4999i) q^{61} +(-31.3211 + 31.3211i) q^{63} +(-95.6849 + 42.0594i) q^{65} +5.43449i q^{67} +(12.5144 + 12.5144i) q^{69} -21.9460i q^{71} +(-68.0765 - 68.0765i) q^{73} +(10.4248 - 11.3595i) q^{75} -56.5944i q^{77} +29.6860i q^{79} +70.8754 q^{81} +74.6461 q^{83} +(71.0948 + 27.6781i) q^{85} +(3.92077 - 3.92077i) q^{87} -82.9075 q^{89} +(75.9592 - 75.9592i) q^{91} -1.34255 q^{93} +(-59.7343 + 153.436i) q^{95} +(-2.47116 - 2.47116i) q^{97} +(-67.1252 + 67.1252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

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

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
$3$	0.616720			0.205573			0.102787	−	0.994703i	$-0.467224\pi$
$3$	0.616720			0.205573			0.102787	+	0.994703i	$0.467224\pi$
$4$		0			0
$5$	−4.57731	+	2.01201i	−0.915463	+	0.402402i
$5$	−4.57731	+	2.01201i	−0.915463	+	0.402402i
$6$		0			0
$7$	3.63369	−	3.63369i	0.519098	−	0.519098i	−0.398200	−	0.917299i	$-0.630365\pi$
$7$	3.63369	−	3.63369i	0.519098	−	0.519098i	0.917299	+	0.398200i	$0.130365\pi$
$8$		0			0
$9$	−8.61966			−0.957740
$10$		0			0
$11$	7.78746	−	7.78746i	0.707951	−	0.707951i	−0.258153	−	0.966104i	$-0.583114\pi$
$11$	7.78746	−	7.78746i	0.707951	−	0.707951i	0.966104	+	0.258153i	$0.0831139\pi$
$12$		0			0
$13$	20.9042			1.60801			0.804006	−	0.594621i	$-0.202698\pi$
$13$	20.9042			1.60801			0.804006	+	0.594621i	$0.202698\pi$
$14$		0			0
$15$	−2.82292	+	1.24085i	−0.188195	+	0.0827232i
$16$		0			0
$17$	−10.7894	−	10.7894i	−0.634670	−	0.634670i	0.314566	−	0.949236i	$-0.398141\pi$
$17$	−10.7894	−	10.7894i	−0.634670	−	0.634670i	−0.949236	+	0.314566i	$0.898141\pi$
$18$		0			0
$19$	23.2855	−	23.2855i	1.22555	−	1.22555i	0.259921	−	0.965630i	$-0.416303\pi$
$19$	23.2855	−	23.2855i	1.22555	−	1.22555i	0.965630	−	0.259921i	$-0.0836967\pi$
$20$		0			0
$21$	2.24097	−	2.24097i	0.106713	−	0.106713i
$22$		0			0
$23$	20.2919	+	20.2919i	0.882255	+	0.882255i	0.993763	−	0.111508i	$-0.0355682\pi$
$23$	20.2919	+	20.2919i	0.882255	+	0.882255i	−0.111508	+	0.993763i	$0.535568\pi$
$24$		0			0
$25$	16.9036	−	18.4192i	0.676145	−	0.736769i
$26$		0			0
$27$	−10.8664			−0.402459
$28$		0			0
$29$	6.35745	−	6.35745i	0.219222	−	0.219222i	−0.588948	−	0.808171i	$-0.700458\pi$
$29$	6.35745	−	6.35745i	0.219222	−	0.219222i	0.808171	+	0.588948i	$0.200458\pi$
$30$		0			0
$31$	−2.17692			−0.0702232			−0.0351116	−	0.999383i	$-0.511179\pi$
$31$	−2.17692			−0.0702232			−0.0351116	+	0.999383i	$0.511179\pi$
$32$		0			0
$33$	4.80268	−	4.80268i	0.145536	−	0.145536i
$34$		0			0
$35$	−9.32151	+	23.9436i	−0.266329	+	0.684102i
$36$		0			0
$37$	−2.31411			−0.0625435			−0.0312718	−	0.999511i	$-0.509956\pi$
$37$	−2.31411			−0.0625435			−0.0312718	+	0.999511i	$0.509956\pi$
$38$		0			0
$39$	12.8920			0.330564
$40$		0			0
$41$			0.335796i			0.00819015i	0.999992	+	0.00409508i	$0.00130351\pi$
$41$			0.335796i			0.00819015i	−0.999992	+	0.00409508i	$0.998696\pi$
$42$		0			0
$43$		−	66.6501i		−	1.55000i	−0.631959	−	0.775002i	$-0.717749\pi$
$43$		−	66.6501i		−	1.55000i	0.631959	−	0.775002i	$-0.282251\pi$
$44$		0			0
$45$	39.4549	−	17.3429i	0.876775	−	0.385397i
$46$		0			0
$47$	−31.1488	−	31.1488i	−0.662741	−	0.662741i	0.293285	−	0.956025i	$-0.405252\pi$
$47$	−31.1488	−	31.1488i	−0.662741	−	0.662741i	−0.956025	+	0.293285i	$0.905252\pi$
$48$		0			0
$49$			22.5926i			0.461074i
$50$		0			0
$51$	−6.65403	−	6.65403i	−0.130471	−	0.130471i
$52$		0			0
$53$		−	6.42977i		−	0.121316i	−0.998159	−	0.0606582i	$-0.980680\pi$
$53$		−	6.42977i		−	0.121316i	0.998159	−	0.0606582i	$-0.0193200\pi$
$54$		0			0
$55$	−19.9772	+	51.3141i	−0.363222	+	0.932984i
$56$		0			0
$57$	14.3606	−	14.3606i	0.251941	−	0.251941i
$58$		0			0
$59$	2.51863	+	2.51863i	0.0426887	+	0.0426887i	0.728129	−	0.685440i	$-0.240390\pi$
$59$	2.51863	+	2.51863i	0.0426887	+	0.0426887i	−0.685440	+	0.728129i	$0.740390\pi$
$60$		0			0
$61$	59.4999	+	59.4999i	0.975408	+	0.975408i	0.999705	−	0.0242966i	$-0.00773462\pi$
$61$	59.4999	+	59.4999i	0.975408	+	0.975408i	−0.0242966	+	0.999705i	$0.507735\pi$
$62$		0			0
$63$	−31.3211	+	31.3211i	−0.497161	+	0.497161i
$64$		0			0
$65$	−95.6849	+	42.0594i	−1.47208	+	0.647068i
$66$		0			0
$67$			5.43449i			0.0811118i	0.999177	+	0.0405559i	$0.0129129\pi$
$67$			5.43449i			0.0811118i	−0.999177	+	0.0405559i	$0.987087\pi$
$68$		0			0
$69$	12.5144	+	12.5144i	0.181368	+	0.181368i
$70$		0			0
$71$		−	21.9460i		−	0.309098i	−0.987985	−	0.154549i	$-0.950607\pi$
$71$		−	21.9460i		−	0.309098i	0.987985	−	0.154549i	$-0.0493925\pi$
$72$		0			0
$73$	−68.0765	−	68.0765i	−0.932555	−	0.932555i	0.0653096	−	0.997865i	$-0.479197\pi$
$73$	−68.0765	−	68.0765i	−0.932555	−	0.932555i	−0.997865	+	0.0653096i	$0.979197\pi$
$74$		0			0
$75$	10.4248	−	11.3595i	0.138997	−	0.151460i
$76$		0			0
$77$		−	56.5944i		−	0.734992i
$78$		0			0
$79$			29.6860i			0.375772i	0.982191	+	0.187886i	$0.0601635\pi$
$79$			29.6860i			0.375772i	−0.982191	+	0.187886i	$0.939837\pi$
$80$		0			0
$81$	70.8754			0.875005
$82$		0			0
$83$	74.6461			0.899351			0.449676	−	0.893192i	$-0.351540\pi$
$83$	74.6461			0.899351			0.449676	+	0.893192i	$0.351540\pi$
$84$		0			0
$85$	71.0948	+	27.6781i	0.836410	+	0.325624i
$86$		0			0
$87$	3.92077	−	3.92077i	0.0450663	−	0.0450663i
$88$		0			0
$89$	−82.9075			−0.931545			−0.465772	−	0.884905i	$-0.654223\pi$
$89$	−82.9075			−0.931545			−0.465772	+	0.884905i	$0.654223\pi$
$90$		0			0
$91$	75.9592	−	75.9592i	0.834717	−	0.834717i
$92$		0			0
$93$	−1.34255			−0.0144360
$94$		0			0
$95$	−59.7343	+	153.436i	−0.628782	+	1.61511i
$96$		0			0
$97$	−2.47116	−	2.47116i	−0.0254759	−	0.0254759i	0.694254	−	0.719730i	$-0.255734\pi$
$97$	−2.47116	−	2.47116i	−0.0254759	−	0.0254759i	−0.719730	+	0.694254i	$0.755734\pi$
$98$		0			0
$99$	−67.1252	+	67.1252i	−0.678032	+	0.678032i
$100$		0			0
$101$	−30.4976	+	30.4976i	−0.301956	+	0.301956i	−0.841779	−	0.539822i	$-0.818491\pi$
$101$	−30.4976	+	30.4976i	−0.301956	+	0.301956i	0.539822	+	0.841779i	$0.318491\pi$
$102$		0			0
$103$	31.0112	+	31.0112i	0.301080	+	0.301080i	0.841436	−	0.540356i	$-0.181711\pi$
$103$	31.0112	+	31.0112i	0.301080	+	0.301080i	−0.540356	+	0.841436i	$0.681711\pi$
$104$		0			0
$105$	−5.74876	+	14.7665i	−0.0547501	+	0.140633i
$106$		0			0
$107$	−107.260			−1.00243			−0.501217	−	0.865322i	$-0.667114\pi$
$107$	−107.260			−1.00243			−0.501217	+	0.865322i	$0.667114\pi$
$108$		0			0
$109$	−113.752	+	113.752i	−1.04359	+	1.04359i	−0.0445889	+	0.999005i	$0.514198\pi$
$109$	−113.752	+	113.752i	−1.04359	+	1.04359i	−0.999005	+	0.0445889i	$0.985802\pi$
$110$		0			0
$111$	−1.42716			−0.0128573
$112$		0			0
$113$	−66.0483	+	66.0483i	−0.584498	+	0.584498i	−0.936136	−	0.351638i	$-0.885625\pi$
$113$	−66.0483	+	66.0483i	−0.584498	+	0.584498i	0.351638	+	0.936136i	$0.385625\pi$
$114$		0			0
$115$	−133.710	−	52.0548i	−1.16269	−	0.452650i
$116$		0			0
$117$	−180.187			−1.54006
$118$		0			0
$119$	−78.4106			−0.658912
$120$		0			0
$121$		−	0.289010i		−	0.00238852i
$122$		0			0
$123$			0.207092i			0.00168368i
$124$		0			0
$125$	−40.3135	+	118.321i	−0.322508	+	0.946567i
$126$		0			0
$127$	9.83801	+	9.83801i	0.0774646	+	0.0774646i	0.744777	−	0.667313i	$-0.232556\pi$
$127$	9.83801	+	9.83801i	0.0774646	+	0.0774646i	−0.667313	+	0.744777i	$0.732556\pi$
$128$		0			0
$129$		−	41.1045i		−	0.318639i
$130$		0			0
$131$	42.7566	+	42.7566i	0.326386	+	0.326386i	0.851211	−	0.524824i	$-0.175869\pi$
$131$	42.7566	+	42.7566i	0.326386	+	0.326386i	−0.524824	+	0.851211i	$0.675869\pi$
$132$		0			0
$133$		−	169.224i		−	1.27236i
$134$		0			0
$135$	49.7389	−	21.8633i	0.368436	−	0.161950i
$136$		0			0
$137$	−55.9231	+	55.9231i	−0.408198	+	0.408198i	−0.881110	−	0.472912i	$-0.843203\pi$
$137$	−55.9231	+	55.9231i	−0.408198	+	0.408198i	0.472912	+	0.881110i	$0.343203\pi$
$138$		0			0
$139$	185.038	+	185.038i	1.33121	+	1.33121i	0.904288	+	0.426924i	$0.140403\pi$
$139$	185.038	+	185.038i	1.33121	+	1.33121i	0.426924	+	0.904288i	$0.359597\pi$
$140$		0			0
$141$	−19.2101	−	19.2101i	−0.136242	−	0.136242i
$142$		0			0
$143$	162.790	−	162.790i	1.13839	−	1.13839i
$144$		0			0
$145$	−16.3088	+	41.8913i	−0.112474	+	0.288906i
$146$		0			0
$147$			13.9333i			0.0947844i
$148$		0			0
$149$	126.380	+	126.380i	0.848191	+	0.848191i	0.989907	−	0.141717i	$-0.0452621\pi$
$149$	126.380	+	126.380i	0.848191	+	0.848191i	−0.141717	+	0.989907i	$0.545262\pi$
$150$		0			0
$151$		−	217.779i		−	1.44225i	−0.692807	−	0.721123i	$-0.743626\pi$
$151$		−	217.779i		−	1.44225i	0.692807	−	0.721123i	$-0.256374\pi$
$152$		0			0
$153$	93.0009	+	93.0009i	0.607849	+	0.607849i
$154$		0			0
$155$	9.96444	−	4.37999i	0.0642867	−	0.0282580i
$156$		0			0
$157$		−	260.123i		−	1.65683i	−0.560113	−	0.828416i	$-0.689242\pi$
$157$		−	260.123i		−	1.65683i	0.560113	−	0.828416i	$-0.310758\pi$
$158$		0			0
$159$		−	3.96537i		−	0.0249394i
$160$		0			0
$161$	147.469			0.915954
$162$		0			0
$163$	−131.093			−0.804251			−0.402126	−	0.915585i	$-0.631728\pi$
$163$	−131.093			−0.804251			−0.402126	+	0.915585i	$0.631728\pi$
$164$		0			0
$165$	−12.3203	+	31.6464i	−0.0746686	+	0.191797i
$166$		0			0
$167$	−65.6476	+	65.6476i	−0.393099	+	0.393099i	−0.875791	−	0.482691i	$-0.839659\pi$
$167$	−65.6476	+	65.6476i	−0.393099	+	0.393099i	0.482691	+	0.875791i	$0.339659\pi$
$168$		0			0
$169$	267.984			1.58571
$170$		0			0
$171$	−200.713	+	200.713i	−1.17376	+	1.17376i
$172$		0			0
$173$	−23.8542			−0.137886			−0.0689428	−	0.997621i	$-0.521963\pi$
$173$	−23.8542			−0.137886			−0.0689428	+	0.997621i	$0.521963\pi$
$174$		0			0
$175$	−5.50725	−	128.352i	−0.0314700	−	0.733441i
$176$		0			0
$177$	1.55329	+	1.55329i	0.00877566	+	0.00877566i
$178$		0			0
$179$	187.766	−	187.766i	1.04897	−	1.04897i	0.0502349	−	0.998737i	$-0.484003\pi$
$179$	187.766	−	187.766i	1.04897	−	1.04897i	0.998737	−	0.0502349i	$-0.0159970\pi$
$180$		0			0
$181$	92.8536	−	92.8536i	0.513003	−	0.513003i	−0.402442	−	0.915445i	$-0.631839\pi$
$181$	92.8536	−	92.8536i	0.513003	−	0.513003i	0.915445	+	0.402442i	$0.131839\pi$
$182$		0			0
$183$	36.6948	+	36.6948i	0.200518	+	0.200518i
$184$		0			0
$185$	10.5924	−	4.65602i	0.0572563	−	0.0251677i
$186$		0			0
$187$	−168.044			−0.898630
$188$		0			0
$189$	−39.4851	+	39.4851i	−0.208916	+	0.208916i
$190$		0			0
$191$	274.168			1.43544			0.717718	−	0.696334i	$-0.245187\pi$
$191$	274.168			1.43544			0.717718	+	0.696334i	$0.245187\pi$
$192$		0			0
$193$	166.098	−	166.098i	0.860610	−	0.860610i	−0.130799	−	0.991409i	$-0.541754\pi$
$193$	166.098	−	166.098i	0.860610	−	0.860610i	0.991409	+	0.130799i	$0.0417543\pi$
$194$		0			0
$195$	−59.0108	+	25.9389i	−0.302620	+	0.133020i
$196$		0			0
$197$	25.1810			0.127823			0.0639113	−	0.997956i	$-0.479643\pi$
$197$	25.1810			0.127823			0.0639113	+	0.997956i	$0.479643\pi$
$198$		0			0
$199$	−318.400			−1.60000			−0.799999	−	0.600001i	$-0.795167\pi$
$199$	−318.400			−1.60000			−0.799999	+	0.600001i	$0.795167\pi$
$200$		0			0
$201$			3.35156i			0.0166744i
$202$		0			0
$203$		−	46.2020i		−	0.227596i
$204$		0			0
$205$	−0.675626	−	1.53705i	−0.00329574	−	0.00749778i
$206$		0			0
$207$	−174.909	−	174.909i	−0.844971	−	0.844971i
$208$		0			0
$209$		−	362.669i		−	1.73526i
$210$		0			0
$211$	192.005	+	192.005i	0.909977	+	0.909977i	0.996270	−	0.0862926i	$-0.0275020\pi$
$211$	192.005	+	192.005i	0.909977	+	0.909977i	−0.0862926	+	0.996270i	$0.527502\pi$
$212$		0			0
$213$		−	13.5345i		−	0.0635424i
$214$		0			0
$215$	134.101	+	305.079i	0.623725	+	1.41897i
$216$		0			0
$217$	−7.91025	+	7.91025i	−0.0364527	+	0.0364527i
$218$		0			0
$219$	−41.9842	−	41.9842i	−0.191708	−	0.191708i
$220$		0			0
$221$	−225.543	−	225.543i	−1.02056	−	1.02056i
$222$		0			0
$223$	−6.55254	+	6.55254i	−0.0293836	+	0.0293836i	−0.721646	−	0.692262i	$-0.756614\pi$
$223$	−6.55254	+	6.55254i	−0.0293836	+	0.0293836i	0.692262	+	0.721646i	$0.256614\pi$
$224$		0			0
$225$	−145.703	+	158.767i	−0.647570	+	0.705633i
$226$		0			0
$227$		−	139.078i		−	0.612679i	−0.951922	−	0.306339i	$-0.900896\pi$
$227$		−	139.078i		−	0.612679i	0.951922	−	0.306339i	$-0.0991042\pi$
$228$		0			0
$229$	51.3813	+	51.3813i	0.224373	+	0.224373i	0.810337	−	0.585964i	$-0.199284\pi$
$229$	51.3813	+	51.3813i	0.224373	+	0.224373i	−0.585964	+	0.810337i	$0.699284\pi$
$230$		0			0
$231$		−	34.9029i		−	0.151095i
$232$		0			0
$233$	105.735	+	105.735i	0.453799	+	0.453799i	0.896613	−	0.442814i	$-0.146020\pi$
$233$	105.735	+	105.735i	0.453799	+	0.453799i	−0.442814	+	0.896613i	$0.646020\pi$
$234$		0			0
$235$	205.250	+	79.9061i	0.873403	+	0.340026i
$236$		0			0
$237$			18.3079i			0.0772486i
$238$		0			0
$239$		−	19.0622i		−	0.0797582i	−0.999205	−	0.0398791i	$-0.987303\pi$
$239$		−	19.0622i		−	0.0797582i	0.999205	−	0.0398791i	$-0.0126973\pi$
$240$		0			0
$241$	236.326			0.980607			0.490303	−	0.871552i	$-0.336886\pi$
$241$	236.326			0.980607			0.490303	+	0.871552i	$0.336886\pi$
$242$		0			0
$243$	141.508			0.582337
$244$		0			0
$245$	−45.4566	−	103.414i	−0.185537	−	0.422096i
$246$		0			0
$247$	486.763	−	486.763i	1.97070	−	1.97070i
$248$		0			0
$249$	46.0358			0.184883
$250$		0			0
$251$	−111.828	+	111.828i	−0.445529	+	0.445529i	−0.893865	−	0.448336i	$-0.852017\pi$
$251$	−111.828	+	111.828i	−0.445529	+	0.445529i	0.448336	+	0.893865i	$0.352017\pi$
$252$		0			0
$253$	316.044			1.24919
$254$		0			0
$255$	43.8456	+	17.0696i	0.171943	+	0.0669396i
$256$		0			0
$257$	27.2119	+	27.2119i	0.105883	+	0.105883i	0.758064	−	0.652181i	$-0.226146\pi$
$257$	27.2119	+	27.2119i	0.105883	+	0.105883i	−0.652181	+	0.758064i	$0.726146\pi$
$258$		0			0
$259$	−8.40876	+	8.40876i	−0.0324662	+	0.0324662i
$260$		0			0
$261$	−54.7990	+	54.7990i	−0.209958	+	0.209958i
$262$		0			0
$263$	−255.406	−	255.406i	−0.971124	−	0.971124i	0.0284707	−	0.999595i	$-0.490936\pi$
$263$	−255.406	−	255.406i	−0.971124	−	0.971124i	−0.999595	+	0.0284707i	$0.990936\pi$
$264$		0			0
$265$	12.9368	+	29.4311i	0.0488180	+	0.111061i
$266$		0			0
$267$	−51.1307			−0.191501
$268$		0			0
$269$	−70.7092	+	70.7092i	−0.262859	+	0.262859i	−0.826215	−	0.563355i	$-0.809510\pi$
$269$	−70.7092	+	70.7092i	−0.262859	+	0.262859i	0.563355	+	0.826215i	$0.309510\pi$
$270$		0			0
$271$	151.732			0.559897			0.279949	−	0.960015i	$-0.409683\pi$
$271$	151.732			0.559897			0.279949	+	0.960015i	$0.409683\pi$
$272$		0			0
$273$	46.8456	−	46.8456i	0.171595	−	0.171595i
$274$		0			0
$275$	−11.8027	−	275.075i	−0.0429191	−	1.00027i
$276$		0			0
$277$	−328.029			−1.18422			−0.592111	−	0.805857i	$-0.701705\pi$
$277$	−328.029			−1.18422			−0.592111	+	0.805857i	$0.701705\pi$
$278$		0			0
$279$	18.7643			0.0672555
$280$		0			0
$281$			323.066i			1.14970i	0.818259	+	0.574850i	$0.194940\pi$
$281$			323.066i			1.14970i	−0.818259	+	0.574850i	$0.805060\pi$
$282$		0			0
$283$		−	54.8578i		−	0.193844i	−0.995292	−	0.0969219i	$-0.969100\pi$
$283$		−	54.8578i		−	0.193844i	0.995292	−	0.0969219i	$-0.0308997\pi$
$284$		0			0
$285$	−36.8393	+	94.6268i	−0.129261	+	0.332024i
$286$		0			0
$287$	1.22018	+	1.22018i	0.00425149	+	0.00425149i
$288$		0			0
$289$		−	56.1781i		−	0.194388i
$290$		0			0
$291$	−1.52401	−	1.52401i	−0.00523716	−	0.00523716i
$292$		0			0
$293$			146.787i			0.500978i	0.968119	+	0.250489i	$0.0805915\pi$
$293$			146.787i			0.500978i	−0.968119	+	0.250489i	$0.919409\pi$
$294$		0			0
$295$	−16.5961	−	6.46106i	−0.0562580	−	0.0219019i
$296$		0			0
$297$	−84.6216	+	84.6216i	−0.284921	+	0.284921i
$298$		0			0
$299$	424.185	+	424.185i	1.41868	+	1.41868i
$300$		0			0
$301$	−242.186	−	242.186i	−0.804604	−	0.804604i
$302$		0			0
$303$	−18.8085	+	18.8085i	−0.0620742	+	0.0620742i
$304$		0			0
$305$	−392.064	−	152.635i	−1.28546	−	0.500443i
$306$		0			0
$307$			171.615i			0.559005i	0.960145	+	0.279503i	$0.0901695\pi$
$307$			171.615i			0.559005i	−0.960145	+	0.279503i	$0.909830\pi$
$308$		0			0
$309$	19.1252	+	19.1252i	0.0618940	+	0.0618940i
$310$		0			0
$311$			368.122i			1.18367i	0.806058	+	0.591837i	$0.201597\pi$
$311$			368.122i			1.18367i	−0.806058	+	0.591837i	$0.798403\pi$
$312$		0			0
$313$	−86.8729	−	86.8729i	−0.277549	−	0.277549i	0.554581	−	0.832130i	$-0.312879\pi$
$313$	−86.8729	−	86.8729i	−0.277549	−	0.277549i	−0.832130	+	0.554581i	$0.812879\pi$
$314$		0			0
$315$	80.3482	−	206.385i	0.255074	−	0.655191i
$316$		0			0
$317$			165.093i			0.520797i	0.965501	+	0.260398i	$0.0838539\pi$
$317$			165.093i			0.520797i	−0.965501	+	0.260398i	$0.916146\pi$
$318$		0			0
$319$		−	99.0167i		−	0.310397i
$320$		0			0
$321$	−66.1497			−0.206074
$322$		0			0
$323$	−502.472			−1.55564
$324$		0			0
$325$	353.356	−	385.039i	1.08725	−	1.18473i
$326$		0			0
$327$	−70.1530	+	70.1530i	−0.214535	+	0.214535i
$328$		0			0
$329$	−226.370			−0.688055
$330$		0			0
$331$	103.932	−	103.932i	0.313993	−	0.313993i	−0.532461	−	0.846454i	$-0.678733\pi$
$331$	103.932	−	103.932i	0.313993	−	0.313993i	0.846454	+	0.532461i	$0.178733\pi$
$332$		0			0
$333$	19.9468			0.0599004
$334$		0			0
$335$	−10.9343	−	24.8754i	−0.0326396	−	0.0742548i
$336$		0			0
$337$	352.333	+	352.333i	1.04550	+	1.04550i	0.998914	+	0.0465846i	$0.0148337\pi$
$337$	352.333	+	352.333i	1.04550	+	1.04550i	0.0465846	+	0.998914i	$0.485166\pi$
$338$		0			0
$339$	−40.7333	+	40.7333i	−0.120157	+	0.120157i
$340$		0			0
$341$	−16.9527	+	16.9527i	−0.0497146	+	0.0497146i
$342$		0			0
$343$	260.145	+	260.145i	0.758441	+	0.758441i
$344$		0			0
$345$	−82.4614	−	32.1032i	−0.239019	−	0.0930528i
$346$		0			0
$347$	−288.705			−0.832004			−0.416002	−	0.909364i	$-0.636569\pi$
$347$	−288.705			−0.832004			−0.416002	+	0.909364i	$0.636569\pi$
$348$		0			0
$349$	−285.061	+	285.061i	−0.816794	+	0.816794i	−0.985642	−	0.168848i	$-0.945995\pi$
$349$	−285.061	+	285.061i	−0.816794	+	0.816794i	0.168848	+	0.985642i	$0.445995\pi$
$350$		0			0
$351$	−227.153			−0.647159
$352$		0			0
$353$	−290.958	+	290.958i	−0.824245	+	0.824245i	−0.986714	−	0.162469i	$-0.948054\pi$
$353$	−290.958	+	290.958i	−0.824245	+	0.824245i	0.162469	+	0.986714i	$0.448054\pi$
$354$		0			0
$355$	44.1556	+	100.454i	0.124382	+	0.282968i
$356$		0			0
$357$	−48.3574			−0.135455
$358$		0			0
$359$	−556.324			−1.54965			−0.774825	−	0.632176i	$-0.782162\pi$
$359$	−556.324			−1.54965			−0.774825	+	0.632176i	$0.782162\pi$
$360$		0			0
$361$		−	723.427i		−	2.00395i
$362$		0			0
$363$		−	0.178238i		−	0.000491015i
$364$		0			0
$365$	448.579	+	174.637i	1.22898	+	0.478457i
$366$		0			0
$367$	415.205	+	415.205i	1.13135	+	1.13135i	0.989953	+	0.141396i	$0.0451590\pi$
$367$	415.205	+	415.205i	1.13135	+	1.13135i	0.141396	+	0.989953i	$0.454841\pi$
$368$		0			0
$369$		−	2.89445i		−	0.00784403i
$370$		0			0
$371$	−23.3638	−	23.3638i	−0.0629751	−	0.0629751i
$372$		0			0
$373$		−	46.4943i		−	0.124650i	−0.998056	−	0.0623248i	$-0.980149\pi$
$373$		−	46.4943i		−	0.124650i	0.998056	−	0.0623248i	$-0.0198515\pi$
$374$		0			0
$375$	−24.8621	+	72.9708i	−0.0662990	+	0.194589i
$376$		0			0
$377$	132.897	−	132.897i	0.352512	−	0.352512i
$378$		0			0
$379$	−477.500	−	477.500i	−1.25990	−	1.25990i	−0.951142	−	0.308753i	$-0.900088\pi$
$379$	−477.500	−	477.500i	−1.25990	−	1.25990i	−0.308753	−	0.951142i	$-0.599912\pi$
$380$		0			0
$381$	6.06729	+	6.06729i	0.0159247	+	0.0159247i
$382$		0			0
$383$	−457.761	+	457.761i	−1.19520	+	1.19520i	−0.219609	+	0.975588i	$0.570478\pi$
$383$	−457.761	+	457.761i	−1.19520	+	1.19520i	−0.975588	+	0.219609i	$0.929522\pi$
$384$		0			0
$385$	113.869	+	259.050i	0.295763	+	0.672858i
$386$		0			0
$387$			574.501i			1.48450i
$388$		0			0
$389$	183.479	+	183.479i	0.471668	+	0.471668i	0.902454	−	0.430786i	$-0.141764\pi$
$389$	183.479	+	183.479i	0.471668	+	0.471668i	−0.430786	+	0.902454i	$0.641764\pi$
$390$		0			0
$391$		−	437.874i		−	1.11988i
$392$		0			0
$393$	26.3688	+	26.3688i	0.0670963	+	0.0670963i
$394$		0			0
$395$	−59.7285	−	135.882i	−0.151211	−	0.344005i
$396$		0			0
$397$		−	100.070i		−	0.252067i	−0.992026	−	0.126033i	$-0.959775\pi$
$397$		−	100.070i		−	0.252067i	0.992026	−	0.126033i	$-0.0402246\pi$
$398$		0			0
$399$		−	104.364i		−	0.261564i
$400$		0			0
$401$	−92.8038			−0.231431			−0.115716	−	0.993282i	$-0.536916\pi$
$401$	−92.8038			−0.231431			−0.115716	+	0.993282i	$0.536916\pi$
$402$		0			0
$403$	−45.5067			−0.112920
$404$		0			0
$405$	−324.419	+	142.602i	−0.801034	+	0.352104i
$406$		0			0
$407$	−18.0210	+	18.0210i	−0.0442777	+	0.0442777i
$408$		0			0
$409$	91.9271			0.224761			0.112380	−	0.993665i	$-0.464153\pi$
$409$	91.9271			0.224761			0.112380	+	0.993665i	$0.464153\pi$
$410$		0			0
$411$	−34.4889	+	34.4889i	−0.0839145	+	0.0839145i
$412$		0			0
$413$	18.3039			0.0443193
$414$		0			0
$415$	−341.679	+	150.189i	−0.823323	+	0.361901i
$416$		0			0
$417$	114.117	+	114.117i	0.273661	+	0.273661i
$418$		0			0
$419$	168.099	−	168.099i	0.401191	−	0.401191i	−0.477461	−	0.878653i	$-0.658443\pi$
$419$	168.099	−	168.099i	0.401191	−	0.401191i	0.878653	+	0.477461i	$0.158443\pi$
$420$		0			0
$421$	−458.850	+	458.850i	−1.08990	+	1.08990i	−0.0943673	+	0.995537i	$0.530083\pi$
$421$	−458.850	+	458.850i	−1.08990	+	1.08990i	−0.995537	+	0.0943673i	$0.969917\pi$
$422$		0			0
$423$	268.492	+	268.492i	0.634733	+	0.634733i
$424$		0			0
$425$	−381.112	+	16.3525i	−0.896734	+	0.0384765i
$426$		0			0
$427$	432.408			1.01267
$428$		0			0
$429$	100.396	−	100.396i	0.234023	−	0.234023i
$430$		0			0
$431$	−565.514			−1.31210			−0.656048	−	0.754719i	$-0.727773\pi$
$431$	−565.514			−1.31210			−0.656048	+	0.754719i	$0.727773\pi$
$432$		0			0
$433$	−500.249	+	500.249i	−1.15531	+	1.15531i	−0.169837	+	0.985472i	$0.554324\pi$
$433$	−500.249	+	500.249i	−1.15531	+	1.15531i	−0.985472	+	0.169837i	$0.945676\pi$
$434$		0			0
$435$	−10.0579	+	25.8352i	−0.0231217	+	0.0593913i
$436$		0			0
$437$	945.011			2.16250
$438$		0			0
$439$	231.157			0.526553			0.263276	−	0.964720i	$-0.415197\pi$
$439$	231.157			0.526553			0.263276	+	0.964720i	$0.415197\pi$
$440$		0			0
$441$		−	194.741i		−	0.441589i
$442$		0			0
$443$		−	502.257i		−	1.13376i	−0.823799	−	0.566881i	$-0.808150\pi$
$443$		−	502.257i		−	1.13376i	0.823799	−	0.566881i	$-0.191850\pi$
$444$		0			0
$445$	379.494	−	166.811i	0.852795	−	0.374856i
$446$		0			0
$447$	77.9413	+	77.9413i	0.174365	+	0.174365i
$448$		0			0
$449$		−	654.267i		−	1.45716i	−0.684959	−	0.728582i	$-0.740180\pi$
$449$		−	654.267i		−	1.45716i	0.684959	−	0.728582i	$-0.259820\pi$
$450$		0			0
$451$	2.61500	+	2.61500i	0.00579822	+	0.00579822i
$452$		0			0
$453$		−	134.309i		−	0.296487i
$454$		0			0
$455$	−194.858	+	500.520i	−0.428260	+	1.10004i
$456$		0			0
$457$	−21.8008	+	21.8008i	−0.0477041	+	0.0477041i	−0.730556	−	0.682852i	$-0.760739\pi$
$457$	−21.8008	+	21.8008i	−0.0477041	+	0.0477041i	0.682852	+	0.730556i	$0.260739\pi$
$458$		0			0
$459$	117.242	+	117.242i	0.255429	+	0.255429i
$460$		0			0
$461$	537.362	+	537.362i	1.16564	+	1.16564i	0.983220	+	0.182423i	$0.0583942\pi$
$461$	537.362	+	537.362i	1.16564	+	1.16564i	0.182423	+	0.983220i	$0.441606\pi$
$462$		0			0
$463$	239.631	−	239.631i	0.517561	−	0.517561i	−0.399272	−	0.916833i	$-0.630737\pi$
$463$	239.631	−	239.631i	0.517561	−	0.517561i	0.916833	+	0.399272i	$0.130737\pi$
$464$		0			0
$465$	6.14527	−	2.70123i	0.0132156	−	0.00580909i
$466$		0			0
$467$		−	507.389i		−	1.08649i	−0.839576	−	0.543243i	$-0.817196\pi$
$467$		−	507.389i		−	1.08649i	0.839576	−	0.543243i	$-0.182804\pi$
$468$		0			0
$469$	19.7472	+	19.7472i	0.0421050	+	0.0421050i
$470$		0			0
$471$		−	160.423i		−	0.340601i
$472$		0			0
$473$	−519.035	−	519.035i	−1.09733	−	1.09733i
$474$		0			0
$475$	−35.2917	−	822.509i	−0.0742983	−	1.73160i
$476$		0			0
$477$			55.4224i			0.116190i
$478$		0			0
$479$			880.902i			1.83904i	0.393039	+	0.919522i	$0.371424\pi$
$479$			880.902i			1.83904i	−0.393039	+	0.919522i	$0.628576\pi$
$480$		0			0
$481$	−48.3746			−0.100571
$482$		0			0
$483$	90.9468			0.188296
$484$		0			0
$485$	16.2833	+	6.33928i	0.0335738	+	0.0130707i
$486$		0			0
$487$	−163.790	+	163.790i	−0.336324	+	0.336324i	−0.854982	−	0.518658i	$-0.826432\pi$
$487$	−163.790	+	163.790i	−0.336324	+	0.336324i	0.518658	+	0.854982i	$0.326432\pi$
$488$		0			0
$489$	−80.8476			−0.165333
$490$		0			0
$491$	47.6692	−	47.6692i	0.0970859	−	0.0970859i	−0.656896	−	0.753982i	$-0.728131\pi$
$491$	47.6692	−	47.6692i	0.0970859	−	0.0970859i	0.753982	+	0.656896i	$0.228131\pi$
$492$		0			0
$493$	−137.186			−0.278268
$494$		0			0
$495$	172.196	−	442.310i	0.347872	−	0.893555i
$496$		0			0
$497$	−79.7449	−	79.7449i	−0.160453	−	0.160453i
$498$		0			0
$499$	187.062	−	187.062i	0.374875	−	0.374875i	−0.494374	−	0.869249i	$-0.664603\pi$
$499$	187.062	−	187.062i	0.374875	−	0.374875i	0.869249	+	0.494374i	$0.164603\pi$
$500$		0			0
$501$	−40.4862	+	40.4862i	−0.0808107	+	0.0808107i
$502$		0			0
$503$	250.999	+	250.999i	0.499003	+	0.499003i	0.911128	−	0.412124i	$-0.135213\pi$
$503$	250.999	+	250.999i	0.499003	+	0.499003i	−0.412124	+	0.911128i	$0.635213\pi$
$504$		0			0
$505$	78.2356	−	200.959i	0.154922	−	0.397938i
$506$		0			0
$507$	165.271			0.325979
$508$		0			0
$509$	293.617	−	293.617i	0.576850	−	0.576850i	−0.357184	−	0.934034i	$-0.616263\pi$
$509$	293.617	−	293.617i	0.576850	−	0.576850i	0.934034	+	0.357184i	$0.116263\pi$
$510$		0			0
$511$	−494.738			−0.968176
$512$		0			0
$513$	−253.029	+	253.029i	−0.493234	+	0.493234i
$514$		0			0
$515$	−204.343	−	79.5532i	−0.396783	−	0.154472i
$516$		0			0
$517$	−485.140			−0.938375
$518$		0			0
$519$	−14.7114			−0.0283456
$520$		0			0
$521$			1029.93i			1.97683i	0.151767	+	0.988416i	$0.451504\pi$
$521$			1029.93i			1.97683i	−0.151767	+	0.988416i	$0.548496\pi$
$522$		0			0
$523$			725.274i			1.38676i	0.720574	+	0.693378i	$0.243879\pi$
$523$			725.274i			1.38676i	−0.720574	+	0.693378i	$0.756121\pi$
$524$		0			0
$525$	−3.39643	−	79.1573i	−0.00646940	−	0.150776i
$526$		0			0
$527$	23.4876	+	23.4876i	0.0445686	+	0.0445686i
$528$		0			0
$529$			294.520i			0.556748i
$530$		0			0
$531$	−21.7098	−	21.7098i	−0.0408847	−	0.0408847i
$532$		0			0
$533$			7.01954i			0.0131699i
$534$		0			0
$535$	490.965	−	215.809i	0.917691	−	0.403382i
$536$		0			0
$537$	115.799	−	115.799i	0.215641	−	0.215641i
$538$		0			0
$539$	175.939	+	175.939i	0.326418	+	0.326418i
$540$		0			0
$541$	−9.05009	−	9.05009i	−0.0167285	−	0.0167285i	0.698693	−	0.715422i	$-0.253765\pi$
$541$	−9.05009	−	9.05009i	−0.0167285	−	0.0167285i	−0.715422	+	0.698693i	$0.753765\pi$
$542$		0			0
$543$	57.2646	−	57.2646i	0.105460	−	0.105460i
$544$		0			0
$545$	291.808	−	749.548i	0.535427	−	1.37532i
$546$		0			0
$547$			850.042i			1.55401i	0.629496	+	0.777004i	$0.283261\pi$
$547$			850.042i			1.55401i	−0.629496	+	0.777004i	$0.716739\pi$
$548$		0			0
$549$	−512.869	−	512.869i	−0.934187	−	0.934187i
$550$		0			0
$551$		−	296.072i		−	0.537337i
$552$		0			0
$553$	107.870	+	107.870i	0.195062	+	0.195062i
$554$		0			0
$555$	6.53255	−	2.87146i	0.0117704	−	0.00517380i
$556$		0			0
$557$		−	392.785i		−	0.705180i	−0.935778	−	0.352590i	$-0.885301\pi$
$557$		−	392.785i		−	0.705180i	0.935778	−	0.352590i	$-0.114699\pi$
$558$		0			0
$559$		−	1393.27i		−	2.49243i
$560$		0			0
$561$	−103.636			−0.184734
$562$		0			0
$563$	807.064			1.43351			0.716753	−	0.697327i	$-0.245627\pi$
$563$	807.064			1.43351			0.716753	+	0.697327i	$0.245627\pi$
$564$		0			0
$565$	169.434	−	435.214i	0.299883	−	0.770289i
$566$		0			0
$567$	257.539	−	257.539i	0.454214	−	0.454214i
$568$		0			0
$569$	−59.3092			−0.104234			−0.0521170	−	0.998641i	$-0.516597\pi$
$569$	−59.3092			−0.104234			−0.0521170	+	0.998641i	$0.516597\pi$
$570$		0			0
$571$	−170.458	+	170.458i	−0.298525	+	0.298525i	−0.840436	−	0.541911i	$-0.817701\pi$
$571$	−170.458	+	170.458i	−0.298525	+	0.298525i	0.541911	+	0.840436i	$0.317701\pi$
$572$		0			0
$573$	169.085			0.295087
$574$		0			0
$575$	716.766	−	30.7546i	1.24655	−	0.0534862i
$576$		0			0
$577$	118.008	+	118.008i	0.204519	+	0.204519i	0.801933	−	0.597414i	$-0.203805\pi$
$577$	118.008	+	118.008i	0.204519	+	0.204519i	−0.597414	+	0.801933i	$0.703805\pi$
$578$		0			0
$579$	102.436	−	102.436i	0.176918	−	0.176918i
$580$		0			0
$581$	271.241	−	271.241i	0.466852	−	0.466852i
$582$		0			0
$583$	−50.0716	−	50.0716i	−0.0858860	−	0.0858860i
$584$		0			0
$585$	824.771	−	362.538i	1.40987	−	0.619723i
$586$		0			0
$587$	181.184			0.308660			0.154330	−	0.988019i	$-0.450678\pi$
$587$	181.184			0.308660			0.154330	+	0.988019i	$0.450678\pi$
$588$		0			0
$589$	−50.6906	+	50.6906i	−0.0860621	+	0.0860621i
$590$		0			0
$591$	15.5296			0.0262769
$592$		0			0
$593$	410.254	−	410.254i	0.691828	−	0.691828i	−0.270806	−	0.962634i	$-0.587290\pi$
$593$	410.254	−	410.254i	0.691828	−	0.691828i	0.962634	+	0.270806i	$0.0872902\pi$
$594$		0			0
$595$	358.910	−	157.763i	0.603210	−	0.265148i
$596$		0			0
$597$	−196.363			−0.328917
$598$		0			0
$599$	481.579			0.803971			0.401986	−	0.915646i	$-0.368320\pi$
$599$	481.579			0.803971			0.401986	+	0.915646i	$0.368320\pi$
$600$		0			0
$601$			390.141i			0.649154i	0.945859	+	0.324577i	$0.105222\pi$
$601$			390.141i			0.649154i	−0.945859	+	0.324577i	$0.894778\pi$
$602$		0			0
$603$		−	46.8434i		−	0.0776840i
$604$		0			0
$605$	0.581492	+	1.32289i	0.000961144	+	0.00218660i
$606$		0			0
$607$	36.3213	+	36.3213i	0.0598374	+	0.0598374i	0.736392	−	0.676555i	$-0.236528\pi$
$607$	36.3213	+	36.3213i	0.0598374	+	0.0598374i	−0.676555	+	0.736392i	$0.736528\pi$
$608$		0			0
$609$		−	28.4937i		−	0.0467877i
$610$		0			0
$611$	−651.140	−	651.140i	−1.06570	−	1.06570i
$612$		0			0
$613$			397.738i			0.648838i	0.945913	+	0.324419i	$0.105169\pi$
$613$			397.738i			0.648838i	−0.945913	+	0.324419i	$0.894831\pi$
$614$		0			0
$615$	−0.416672	−	0.947926i	−0.000677516	−	0.00154134i
$616$		0			0
$617$	124.670	−	124.670i	0.202058	−	0.202058i	−0.598823	−	0.800881i	$-0.704365\pi$
$617$	124.670	−	124.670i	0.202058	−	0.202058i	0.800881	+	0.598823i	$0.204365\pi$
$618$		0			0
$619$	−345.559	−	345.559i	−0.558254	−	0.558254i	0.370556	−	0.928810i	$-0.379167\pi$
$619$	−345.559	−	345.559i	−0.558254	−	0.558254i	−0.928810	+	0.370556i	$0.879167\pi$
$620$		0			0
$621$	−220.499	−	220.499i	−0.355071	−	0.355071i
$622$		0			0
$623$	−301.260	+	301.260i	−0.483563	+	0.483563i
$624$		0			0
$625$	−53.5356	−	622.703i	−0.0856570	−	0.996325i
$626$		0			0
$627$		−	223.665i		−	0.356723i
$628$		0			0
$629$	24.9678	+	24.9678i	0.0396945	+	0.0396945i
$630$		0			0
$631$			502.145i			0.795793i	0.917430	+	0.397896i	$0.130260\pi$
$631$			502.145i			0.795793i	−0.917430	+	0.397896i	$0.869740\pi$
$632$		0			0
$633$	118.413	+	118.413i	0.187067	+	0.187067i
$634$		0			0
$635$	−64.8258	−	25.2375i	−0.102088	−	0.0397440i
$636$		0			0
$637$			472.280i			0.741413i
$638$		0			0
$639$			189.167i			0.296036i
$640$		0			0
$641$	−675.484			−1.05380			−0.526899	−	0.849928i	$-0.676645\pi$
$641$	−675.484			−1.05380			−0.526899	+	0.849928i	$0.676645\pi$
$642$		0			0
$643$	−391.519			−0.608895			−0.304447	−	0.952529i	$-0.598472\pi$
$643$	−391.519			−0.608895			−0.304447	+	0.952529i	$0.598472\pi$
$644$		0			0
$645$	82.7027	+	188.148i	0.128221	+	0.291702i
$646$		0			0
$647$	−60.5768	+	60.5768i	−0.0936273	+	0.0936273i	−0.752369	−	0.658742i	$-0.771089\pi$
$647$	−60.5768	+	60.5768i	−0.0936273	+	0.0936273i	0.658742	+	0.752369i	$0.271089\pi$
$648$		0			0
$649$	39.2275			0.0604430
$650$		0			0
$651$	−4.87841	+	4.87841i	−0.00749371	+	0.00749371i
$652$		0			0
$653$	−240.996			−0.369059			−0.184529	−	0.982827i	$-0.559076\pi$
$653$	−240.996			−0.369059			−0.184529	+	0.982827i	$0.559076\pi$
$654$		0			0
$655$	−281.737	−	109.684i	−0.430133	−	0.167456i
$656$		0			0
$657$	586.796	+	586.796i	0.893145	+	0.893145i
$658$		0			0
$659$	416.085	−	416.085i	0.631389	−	0.631389i	−0.317028	−	0.948416i	$-0.602685\pi$
$659$	416.085	−	416.085i	0.631389	−	0.631389i	0.948416	+	0.317028i	$0.102685\pi$
$660$		0			0
$661$	−254.599	+	254.599i	−0.385172	+	0.385172i	−0.872962	−	0.487789i	$-0.837804\pi$
$661$	−254.599	+	254.599i	−0.385172	+	0.385172i	0.487789	+	0.872962i	$0.337804\pi$
$662$		0			0
$663$	−139.097	−	139.097i	−0.209799	−	0.209799i
$664$		0			0
$665$	340.481	+	774.593i	0.512002	+	1.16480i
$666$		0			0
$667$	258.009			0.386820
$668$		0			0
$669$	−4.04108	+	4.04108i	−0.00604048	+	0.00604048i
$670$		0			0
$671$	926.706			1.38108
$672$		0			0
$673$	382.676	−	382.676i	0.568612	−	0.568612i	−0.363127	−	0.931740i	$-0.618291\pi$
$673$	382.676	−	382.676i	0.568612	−	0.568612i	0.931740	+	0.363127i	$0.118291\pi$
$674$		0			0
$675$	−183.681	+	200.151i	−0.272120	+	0.296519i
$676$		0			0
$677$	738.283			1.09052			0.545261	−	0.838266i	$-0.316431\pi$
$677$	738.283			1.09052			0.545261	+	0.838266i	$0.316431\pi$
$678$		0			0
$679$	−17.9589			−0.0264490
$680$		0			0
$681$		−	85.7722i		−	0.125950i
$682$		0			0
$683$		−	43.0532i		−	0.0630355i	−0.999503	−	0.0315177i	$-0.989966\pi$
$683$		−	43.0532i		−	0.0630355i	0.999503	−	0.0315177i	$-0.0100341\pi$
$684$		0			0
$685$	143.460	−	368.495i	0.209430	−	0.537949i
$686$		0			0
$687$	31.6879	+	31.6879i	0.0461250	+	0.0461250i
$688$		0			0
$689$		−	134.409i		−	0.195078i
$690$		0			0
$691$	118.864	+	118.864i	0.172018	+	0.172018i	0.787865	−	0.615848i	$-0.211186\pi$
$691$	118.864	+	118.864i	0.172018	+	0.172018i	−0.615848	+	0.787865i	$0.711186\pi$
$692$		0			0
$693$			487.824i			0.703931i
$694$		0			0
$695$	−1219.28	−	474.679i	−1.75436	−	0.682992i
$696$		0			0
$697$	3.62304	−	3.62304i	0.00519805	−	0.00519805i
$698$		0			0
$699$	65.2090	+	65.2090i	0.0932890	+	0.0932890i
$700$		0			0
$701$	−279.697	−	279.697i	−0.398998	−	0.398998i	0.478882	−	0.877879i	$-0.341042\pi$
$701$	−279.697	−	279.697i	−0.398998	−	0.398998i	−0.877879	+	0.478882i	$0.841042\pi$
$702$		0			0
$703$	−53.8852	+	53.8852i	−0.0766503	+	0.0766503i
$704$		0			0
$705$	126.582	+	49.2797i	0.179548	+	0.0699003i
$706$		0			0
$707$			221.638i			0.313490i
$708$		0			0
$709$	270.217	+	270.217i	0.381124	+	0.381124i	0.871507	−	0.490383i	$-0.163143\pi$
$709$	270.217	+	270.217i	0.381124	+	0.381124i	−0.490383	+	0.871507i	$0.663143\pi$
$710$		0			0
$711$		−	255.883i		−	0.359891i
$712$		0			0
$713$	−44.1738	−	44.1738i	−0.0619548	−	0.0619548i
$714$		0			0
$715$	−417.606	+	1072.68i	−0.584065	+	1.50025i
$716$		0			0
$717$		−	11.7560i		−	0.0163962i
$718$		0			0
$719$		−	399.636i		−	0.555822i	−0.960607	−	0.277911i	$-0.910358\pi$
$719$		−	399.636i		−	0.555822i	0.960607	−	0.277911i	$-0.0896421\pi$
$720$		0			0
$721$	225.370			0.312580
$722$		0			0
$723$	145.747			0.201587
$724$		0			0
$725$	−9.63541	−	224.563i	−0.0132902	−	0.309742i
$726$		0			0
$727$	−427.676	+	427.676i	−0.588275	+	0.588275i	−0.937164	−	0.348889i	$-0.886559\pi$
$727$	−427.676	+	427.676i	−0.588275	+	0.588275i	0.348889	+	0.937164i	$0.386559\pi$
$728$		0			0
$729$	−550.608			−0.755292
$730$		0			0
$731$	−719.114	+	719.114i	−0.983741	+	0.983741i
$732$		0			0
$733$	−959.876			−1.30952			−0.654758	−	0.755838i	$-0.727230\pi$
$733$	−959.876			−1.30952			−0.654758	+	0.755838i	$0.727230\pi$
$734$		0			0
$735$	−28.0340	−	63.7772i	−0.0381415	−	0.0867716i
$736$		0			0
$737$	42.3209	+	42.3209i	0.0574231	+	0.0574231i
$738$		0			0
$739$	−685.455	+	685.455i	−0.927545	+	0.927545i	−0.997547	−	0.0700023i	$-0.977699\pi$
$739$	−685.455	+	685.455i	−0.927545	+	0.927545i	0.0700023	+	0.997547i	$0.477699\pi$
$740$		0			0
$741$	300.197	−	300.197i	0.405124	−	0.405124i
$742$		0			0
$743$	−922.769	−	922.769i	−1.24195	−	1.24195i	−0.959191	−	0.282760i	$-0.908750\pi$
$743$	−922.769	−	922.769i	−1.24195	−	1.24195i	−0.282760	−	0.959191i	$-0.591250\pi$
$744$		0			0
$745$	−832.762	−	324.204i	−1.11780	−	0.435173i
$746$		0			0
$747$	−643.424			−0.861344
$748$		0			0
$749$	−389.751	+	389.751i	−0.520362	+	0.520362i
$750$		0			0
$751$	240.264			0.319926			0.159963	−	0.987123i	$-0.448863\pi$
$751$	240.264			0.319926			0.159963	+	0.987123i	$0.448863\pi$
$752$		0			0
$753$	−68.9664	+	68.9664i	−0.0915889	+	0.0915889i
$754$		0			0
$755$	438.174	+	996.844i	0.580363	+	1.32032i
$756$		0			0
$757$	−81.0996			−0.107133			−0.0535664	−	0.998564i	$-0.517059\pi$
$757$	−81.0996			−0.107133			−0.0535664	+	0.998564i	$0.517059\pi$
$758$		0			0
$759$	194.911			0.256799
$760$		0			0
$761$		−	1126.31i		−	1.48004i	−0.672585	−	0.740020i	$-0.734816\pi$
$761$		−	1126.31i		−	1.48004i	0.672585	−	0.740020i	$-0.265184\pi$
$762$		0			0
$763$			826.677i			1.08346i
$764$		0			0
$765$	−612.813	−	238.575i	−0.801063	−	0.311863i
$766$		0			0
$767$	52.6499	+	52.6499i	0.0686440	+	0.0686440i
$768$		0			0
$769$			957.757i			1.24546i	0.782438	+	0.622729i	$0.213976\pi$
$769$			957.757i			1.24546i	−0.782438	+	0.622729i	$0.786024\pi$
$770$		0			0
$771$	16.7821	+	16.7821i	0.0217667	+	0.0217667i
$772$		0			0
$773$		−	566.715i		−	0.733137i	−0.930391	−	0.366568i	$-0.880533\pi$
$773$		−	566.715i		−	0.733137i	0.930391	−	0.366568i	$-0.119467\pi$
$774$		0			0
$775$	−36.7978	+	40.0972i	−0.0474810	+	0.0517383i
$776$		0			0
$777$	−5.18585	+	5.18585i	−0.00667419	+	0.00667419i
$778$		0			0
$779$	7.81917	+	7.81917i	0.0100375	+	0.0100375i
$780$		0			0
$781$	−170.904	−	170.904i	−0.218827	−	0.218827i
$782$		0			0
$783$	−69.0825	+	69.0825i	−0.0882280	+	0.0882280i
$784$		0			0
$785$	523.370	+	1190.66i	0.666714	+	1.51677i
$786$		0			0
$787$		−	1020.44i		−	1.29662i	−0.761375	−	0.648311i	$-0.775476\pi$
$787$		−	1020.44i		−	1.29662i	0.761375	−	0.648311i	$-0.224524\pi$
$788$		0			0
$789$	−157.514	−	157.514i	−0.199637	−	0.199637i
$790$		0			0
$791$			479.998i			0.606824i
$792$		0			0
$793$	1243.80	+	1243.80i	1.56847	+	1.56847i
$794$		0			0
$795$	7.97836	+	18.1507i	0.0100357	+	0.0228311i
$796$		0			0
$797$			354.401i			0.444669i	0.974970	+	0.222334i	$0.0713676\pi$
$797$			354.401i			0.444669i	−0.974970	+	0.222334i	$0.928632\pi$
$798$		0			0
$799$			672.153i			0.841243i
$800$		0			0
$801$	714.634			0.892177
$802$		0			0
$803$	−1060.29			−1.32041
$804$		0			0
$805$	−675.010	+	296.709i	−0.838522	+	0.368582i
$806$		0			0
$807$	−43.6077	+	43.6077i	−0.0540369	+	0.0540369i
$808$		0			0
$809$	691.662			0.854960			0.427480	−	0.904025i	$-0.359402\pi$
$809$	691.662			0.854960			0.427480	+	0.904025i	$0.359402\pi$
$810$		0			0
$811$	373.940	−	373.940i	0.461086	−	0.461086i	−0.437926	−	0.899011i	$-0.644287\pi$
$811$	373.940	−	373.940i	0.461086	−	0.461086i	0.899011	+	0.437926i	$0.144287\pi$
$812$		0			0
$813$	93.5762			0.115100
$814$		0			0
$815$	600.054	−	263.761i	0.736262	−	0.323633i
$816$		0			0
$817$	−1551.98	−	1551.98i	−1.89961	−	1.89961i
$818$		0			0
$819$	−654.742	+	654.742i	−0.799441	+	0.799441i
$820$		0			0
$821$	−131.961	+	131.961i	−0.160732	+	0.160732i	−0.782891	−	0.622159i	$-0.786256\pi$
$821$	−131.961	+	131.961i	−0.160732	+	0.160732i	0.622159	+	0.782891i	$0.286256\pi$
$822$		0			0
$823$	161.468	+	161.468i	0.196195	+	0.196195i	0.798366	−	0.602172i	$-0.205698\pi$
$823$	161.468	+	161.468i	0.196195	+	0.196195i	−0.602172	+	0.798366i	$0.705698\pi$
$824$		0			0
$825$	−7.27899	−	169.644i	−0.00882302	−	0.205629i
$826$		0			0
$827$	1018.39			1.23143			0.615713	−	0.787971i	$-0.288868\pi$
$827$	1018.39			1.23143			0.615713	+	0.787971i	$0.288868\pi$
$828$		0			0
$829$	248.048	−	248.048i	0.299213	−	0.299213i	−0.541492	−	0.840706i	$-0.682141\pi$
$829$	248.048	−	248.048i	0.299213	−	0.299213i	0.840706	+	0.541492i	$0.182141\pi$
$830$		0			0
$831$	−202.302			−0.243444
$832$		0			0
$833$	243.761	−	243.761i	0.292630	−	0.292630i
$834$		0			0
$835$	168.406	−	432.573i	0.201684	−	0.518052i
$836$		0			0
$837$	23.6553			0.0282620
$838$		0			0
$839$	585.727			0.698125			0.349063	−	0.937099i	$-0.386500\pi$
$839$	585.727			0.698125			0.349063	+	0.937099i	$0.386500\pi$
$840$		0			0
$841$			760.166i			0.903883i
$842$		0			0
$843$			199.241i			0.236348i
$844$		0			0
$845$	−1226.65	+	539.187i	−1.45165	+	0.638092i
$846$		0			0
$847$	−1.05017	−	1.05017i	−0.00123987	−	0.00123987i
$848$		0			0
$849$		−	33.8319i		−	0.0398491i
$850$		0			0
$851$	−46.9576	−	46.9576i	−0.0551793	−	0.0551793i
$852$		0			0
$853$		−	521.830i		−	0.611758i	−0.952070	−	0.305879i	$-0.901050\pi$
$853$		−	521.830i		−	0.611758i	0.952070	−	0.305879i	$-0.0989504\pi$
$854$		0			0
$855$	514.889	−	1322.56i	0.602209	−	1.54686i
$856$		0			0
$857$	−835.844	+	835.844i	−0.975314	+	0.975314i	−0.999703	−	0.0243886i	$-0.992236\pi$
$857$	−835.844	+	835.844i	−0.975314	+	0.975314i	0.0243886	+	0.999703i	$0.492236\pi$
$858$		0			0
$859$	274.532	+	274.532i	0.319595	+	0.319595i	0.848612	−	0.529017i	$-0.177439\pi$
$859$	274.532	+	274.532i	0.319595	+	0.319595i	−0.529017	+	0.848612i	$0.677439\pi$
$860$		0			0
$861$	0.752509	+	0.752509i	0.000873994	+	0.000873994i
$862$		0			0
$863$	975.977	−	975.977i	1.13091	−	1.13091i	0.140887	−	0.990026i	$-0.455005\pi$
$863$	975.977	−	975.977i	1.13091	−	1.13091i	0.990026	−	0.140887i	$-0.0449953\pi$
$864$		0			0
$865$	109.188	−	47.9949i	0.126229	−	0.0554855i
$866$		0			0
$867$		−	34.6461i		−	0.0399609i
$868$		0			0
$869$	231.178	+	231.178i	0.266028	+	0.266028i
$870$		0			0
$871$			113.603i			0.130429i
$872$		0			0
$873$	21.3006	+	21.3006i	0.0243993	+	0.0243993i
$874$		0			0
$875$	283.455	+	576.428i	0.323948	+	0.658774i
$876$		0			0
$877$			1112.04i			1.26800i	0.773333	+	0.633999i	$0.218588\pi$
$877$			1112.04i			1.26800i	−0.773333	+	0.633999i	$0.781412\pi$
$878$		0			0
$879$			90.5263i			0.102988i
$880$		0			0
$881$	−104.966			−0.119145			−0.0595723	−	0.998224i	$-0.518974\pi$
$881$	−104.966			−0.119145			−0.0595723	+	0.998224i	$0.518974\pi$
$882$		0			0
$883$	−502.488			−0.569069			−0.284535	−	0.958666i	$-0.591839\pi$
$883$	−502.488			−0.569069			−0.284535	+	0.958666i	$0.591839\pi$
$884$		0			0
$885$	−10.2351	−	3.98466i	−0.0115651	−	0.00450244i
$886$		0			0
$887$	148.430	−	148.430i	0.167340	−	0.167340i	−0.618469	−	0.785809i	$-0.712247\pi$
$887$	148.430	−	148.430i	0.167340	−	0.167340i	0.785809	+	0.618469i	$0.212247\pi$
$888$		0			0
$889$	71.4965			0.0804235
$890$		0			0
$891$	551.939	−	551.939i	0.619460	−	0.619460i
$892$		0			0
$893$	−1450.63			−1.62445
$894$		0			0
$895$	−481.677	+	1237.25i	−0.538186	+	1.38240i
$896$		0			0
$897$	261.603	+	261.603i	0.291642	+	0.291642i
$898$		0			0
$899$	−13.8397	+	13.8397i	−0.0153945	+	0.0153945i
$900$		0			0
$901$	−69.3733	+	69.3733i	−0.0769959	+	0.0769959i
$902$		0			0
$903$	−149.361	−	149.361i	−0.165405	−	0.165405i
$904$		0			0
$905$	−238.197	+	611.843i	−0.263202	+	0.676069i
$906$		0			0
$907$	−319.731			−0.352514			−0.176257	−	0.984344i	$-0.556399\pi$
$907$	−319.731			−0.352514			−0.176257	+	0.984344i	$0.556399\pi$
$908$		0			0
$909$	262.879	−	262.879i	0.289196	−	0.289196i
$910$		0			0
$911$	113.657			0.124761			0.0623804	−	0.998052i	$-0.480131\pi$
$911$	113.657			0.124761			0.0623804	+	0.998052i	$0.480131\pi$
$912$		0			0
$913$	581.304	−	581.304i	0.636696	−	0.636696i
$914$		0			0
$915$	−241.794	−	94.1332i	−0.264256	−	0.102878i
$916$		0			0
$917$	310.728			0.338853
$918$		0			0
$919$	−1118.61			−1.21720			−0.608602	−	0.793475i	$-0.708270\pi$
$919$	−1118.61			−1.21720			−0.608602	+	0.793475i	$0.708270\pi$
$920$		0			0
$921$			105.838i			0.114917i
$922$		0			0
$923$		−	458.763i		−	0.497034i
$924$		0			0
$925$	−39.1168	+	42.6241i	−0.0422885	+	0.0460801i
$926$		0			0
$927$	−267.306	−	267.306i	−0.288356	−	0.288356i
$928$		0			0
$929$			883.130i			0.950624i	0.879817	+	0.475312i	$0.157665\pi$
$929$			883.130i			0.950624i	−0.879817	+	0.475312i	$0.842335\pi$
$930$		0			0
$931$	526.080	+	526.080i	0.565070	+	0.565070i
$932$		0			0
$933$			227.028i			0.243332i
$934$		0			0
$935$	769.190	−	338.106i	0.822663	−	0.361611i
$936$		0			0
$937$	−87.6373	+	87.6373i	−0.0935297	+	0.0935297i	−0.752324	−	0.658794i	$-0.771067\pi$
$937$	−87.6373	+	87.6373i	−0.0935297	+	0.0935297i	0.658794	+	0.752324i	$0.271067\pi$
$938$		0			0
$939$	−53.5762	−	53.5762i	−0.0570567	−	0.0570567i
$940$		0			0
$941$	24.9318	+	24.9318i	0.0264950	+	0.0264950i	0.720230	−	0.693735i	$-0.244036\pi$
$941$	24.9318	+	24.9318i	0.0264950	+	0.0264950i	−0.693735	+	0.720230i	$0.744036\pi$
$942$		0			0
$943$	−6.81393	+	6.81393i	−0.00722580	+	0.00722580i
$944$		0			0
$945$	101.291	−	260.180i	0.107186	−	0.275323i
$946$		0			0
$947$		−	966.607i		−	1.02070i	−0.859966	−	0.510352i	$-0.829515\pi$
$947$		−	966.607i		−	1.02070i	0.859966	−	0.510352i	$-0.170485\pi$
$948$		0			0
$949$	−1423.08	−	1423.08i	−1.49956	−	1.49956i
$950$		0			0
$951$			101.816i			0.107062i
$952$		0			0
$953$	−714.443	−	714.443i	−0.749678	−	0.749678i	0.224741	−	0.974419i	$-0.427846\pi$
$953$	−714.443	−	714.443i	−0.749678	−	0.749678i	−0.974419	+	0.224741i	$0.927846\pi$
$954$		0			0
$955$	−1254.95	+	551.630i	−1.31409	+	0.577623i
$956$		0			0
$957$		−	61.0656i		−	0.0638094i
$958$		0			0
$959$			406.414i			0.423789i
$960$		0			0
$961$	−956.261			−0.995069
$962$		0			0
$963$	924.548			0.960071
$964$		0			0
$965$	−426.091	+	1094.47i	−0.441545	+	1.13417i
$966$		0			0
$967$	−357.290	+	357.290i	−0.369483	+	0.369483i	−0.867289	−	0.497806i	$-0.834139\pi$
$967$	−357.290	+	357.290i	−0.369483	+	0.369483i	0.497806	+	0.867289i	$0.334139\pi$
$968$		0			0
$969$	−309.885			−0.319798
$970$		0			0
$971$	623.731	−	623.731i	0.642359	−	0.642359i	−0.308776	−	0.951135i	$-0.599919\pi$
$971$	623.731	−	623.731i	0.642359	−	0.642359i	0.951135	+	0.308776i	$0.0999193\pi$
$972$		0			0
$973$	1344.74			1.38206
$974$		0			0
$975$	217.922	−	237.461i	0.223509	−	0.243550i
$976$		0			0
$977$	−431.088	−	431.088i	−0.441236	−	0.441236i	0.451191	−	0.892427i	$-0.350999\pi$
$977$	−431.088	−	431.088i	−0.441236	−	0.441236i	−0.892427	+	0.451191i	$0.850999\pi$
$978$		0			0
$979$	−645.639	+	645.639i	−0.659488	+	0.659488i
$980$		0			0
$981$	980.501	−	980.501i	0.999492	−	0.999492i
$982$		0			0
$983$	265.362	+	265.362i	0.269951	+	0.269951i	0.829080	−	0.559130i	$-0.188865\pi$
$983$	265.362	+	265.362i	0.269951	+	0.269951i	−0.559130	+	0.829080i	$0.688865\pi$
$984$		0			0
$985$	−115.262	+	50.6646i	−0.117017	+	0.0514361i
$986$		0			0
$987$	−139.607			−0.141446
$988$		0			0
$989$	1352.46	−	1352.46i	1.36750	−	1.36750i
$990$		0			0
$991$	−863.519			−0.871362			−0.435681	−	0.900101i	$-0.643492\pi$
$991$	−863.519			−0.871362			−0.435681	+	0.900101i	$0.643492\pi$
$992$		0			0
$993$	64.0968	−	64.0968i	0.0645486	−	0.0645486i
$994$		0			0
$995$	1457.42	−	640.624i	1.46474	−	0.643843i
$996$		0			0
$997$	138.026			0.138442			0.0692208	−	0.997601i	$-0.477949\pi$
$997$	138.026			0.138442			0.0692208	+	0.997601i	$0.477949\pi$
$998$		0			0
$999$	25.1460			0.0251712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.t.a.17.12		44
4.3	odd	2		80.3.t.a.77.8	yes	44
5.3	odd	4		320.3.i.a.273.12		44
8.3	odd	2		640.3.t.b.417.12		44
8.5	even	2		640.3.t.a.417.11		44
16.3	odd	4		640.3.i.b.97.11		44
16.5	even	4		320.3.i.a.177.11		44
16.11	odd	4		80.3.i.a.37.5	yes	44
16.13	even	4		640.3.i.a.97.12		44
20.3	even	4		80.3.i.a.13.5	✓	44
20.7	even	4		400.3.i.b.93.18		44
20.19	odd	2		400.3.t.b.157.15		44
40.3	even	4		640.3.i.b.33.12		44
40.13	odd	4		640.3.i.a.33.11		44
80.3	even	4		640.3.t.b.353.12		44
80.13	odd	4		640.3.t.a.353.11		44
80.27	even	4		400.3.t.b.293.15		44
80.43	even	4		80.3.t.a.53.8	yes	44
80.53	odd	4	inner	320.3.t.a.113.12		44
80.59	odd	4		400.3.i.b.357.18		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.5	✓	44	20.3	even	4
80.3.i.a.37.5	yes	44	16.11	odd	4
80.3.t.a.53.8	yes	44	80.43	even	4
80.3.t.a.77.8	yes	44	4.3	odd	2
320.3.i.a.177.11		44	16.5	even	4
320.3.i.a.273.12		44	5.3	odd	4
320.3.t.a.17.12		44	1.1	even	1	trivial
320.3.t.a.113.12		44	80.53	odd	4	inner
400.3.i.b.93.18		44	20.7	even	4
400.3.i.b.357.18		44	80.59	odd	4
400.3.t.b.157.15		44	20.19	odd	2
400.3.t.b.293.15		44	80.27	even	4
640.3.i.a.33.11		44	40.13	odd	4
640.3.i.a.97.12		44	16.13	even	4
640.3.i.b.33.12		44	40.3	even	4
640.3.i.b.97.11		44	16.3	odd	4
640.3.t.a.353.11		44	80.13	odd	4
640.3.t.a.417.11		44	8.5	even	2
640.3.t.b.353.12		44	80.3	even	4
640.3.t.b.417.12		44	8.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+0.616720 q^{3} +(-4.57731 + 2.01201i) q^{5} +(3.63369 - 3.63369i) q^{7} -8.61966 q^{9} +O(q^{10})\)	\(q+0.616720 q^{3} +(-4.57731 + 2.01201i) q^{5} +(3.63369 - 3.63369i) q^{7} -8.61966 q^{9} +(7.78746 - 7.78746i) q^{11} +20.9042 q^{13} +(-2.82292 + 1.24085i) q^{15} +(-10.7894 - 10.7894i) q^{17} +(23.2855 - 23.2855i) q^{19} +(2.24097 - 2.24097i) q^{21} +(20.2919 + 20.2919i) q^{23} +(16.9036 - 18.4192i) q^{25} -10.8664 q^{27} +(6.35745 - 6.35745i) q^{29} -2.17692 q^{31} +(4.80268 - 4.80268i) q^{33} +(-9.32151 + 23.9436i) q^{35} -2.31411 q^{37} +12.8920 q^{39} +0.335796i q^{41} -66.6501i q^{43} +(39.4549 - 17.3429i) q^{45} +(-31.1488 - 31.1488i) q^{47} +22.5926i q^{49} +(-6.65403 - 6.65403i) q^{51} -6.42977i q^{53} +(-19.9772 + 51.3141i) q^{55} +(14.3606 - 14.3606i) q^{57} +(2.51863 + 2.51863i) q^{59} +(59.4999 + 59.4999i) q^{61} +(-31.3211 + 31.3211i) q^{63} +(-95.6849 + 42.0594i) q^{65} +5.43449i q^{67} +(12.5144 + 12.5144i) q^{69} -21.9460i q^{71} +(-68.0765 - 68.0765i) q^{73} +(10.4248 - 11.3595i) q^{75} -56.5944i q^{77} +29.6860i q^{79} +70.8754 q^{81} +74.6461 q^{83} +(71.0948 + 27.6781i) q^{85} +(3.92077 - 3.92077i) q^{87} -82.9075 q^{89} +(75.9592 - 75.9592i) q^{91} -1.34255 q^{93} +(-59.7343 + 153.436i) q^{95} +(-2.47116 - 2.47116i) q^{97} +(-67.1252 + 67.1252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) \) 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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