LMFDB - Embedded newform 200.3.i.b.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,3,Mod(93,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("200.93");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$N$	$=$	$200 = 2^{3} \cdot 5^{2}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	200.i (of order $4$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.44960528721$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024$ x^20 - x^18 - 3x^16 + 11x^14 + x^12 - 40x^10 + 4x^8 + 176x^6 - 192x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$2^{21}$
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.3
Root			$1.39859 - 0.209644i$ of defining polynomial
Character	$\chi$	$=$	200.157
Dual form			200.3.i.b.93.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18894 + 1.60823i) q^{2} +(-2.52630 - 2.52630i) q^{3} +(-1.17282 - 3.82420i) q^{4} +(7.06650 - 1.05925i) q^{6} +(5.20520 + 5.20520i) q^{7} +(7.54462 + 2.66059i) q^{8} +3.76437i q^{9} -2.49236i q^{11} +(-6.69817 + 12.6240i) q^{12} +(-6.65988 - 6.65988i) q^{13} +(-14.5599 + 2.18248i) q^{14} +(-13.2490 + 8.97020i) q^{16} +(-21.9428 - 21.9428i) q^{17} +(-6.05398 - 4.47563i) q^{18} -17.5567 q^{19} -26.2998i q^{21} +(4.00830 + 2.96328i) q^{22} +(-20.1791 + 20.1791i) q^{23} +(-12.3385 - 25.7814i) q^{24} +(18.6289 - 2.79240i) q^{26} +(-13.2268 + 13.2268i) q^{27} +(13.8010 - 26.0105i) q^{28} -1.04754 q^{29} -2.47263 q^{31} +(1.32614 - 31.9725i) q^{32} +(-6.29646 + 6.29646i) q^{33} +(61.3780 - 9.20035i) q^{34} +(14.3957 - 4.41493i) q^{36} +(19.2786 - 19.2786i) q^{37} +(20.8740 - 28.2353i) q^{38} +33.6497i q^{39} -43.9414 q^{41} +(42.2962 + 31.2690i) q^{42} +(32.9394 + 32.9394i) q^{43} +(-9.53129 + 2.92310i) q^{44} +(-8.46086 - 56.4446i) q^{46} +(-33.7079 - 33.7079i) q^{47} +(56.1323 + 10.8095i) q^{48} +5.18827i q^{49} +110.868i q^{51} +(-17.6578 + 33.2795i) q^{52} +(-36.4034 - 36.4034i) q^{53} +(-5.54582 - 36.9976i) q^{54} +(25.4224 + 53.1202i) q^{56} +(44.3536 + 44.3536i) q^{57} +(1.24547 - 1.68469i) q^{58} -30.5963 q^{59} -23.8366i q^{61} +(2.93982 - 3.97657i) q^{62} +(-19.5943 + 19.5943i) q^{63} +(49.8425 + 40.1463i) q^{64} +(-2.64003 - 17.6123i) q^{66} +(19.9932 - 19.9932i) q^{67} +(-58.1787 + 109.649i) q^{68} +101.957 q^{69} -21.8350 q^{71} +(-10.0154 + 28.4007i) q^{72} +(-32.6450 + 32.6450i) q^{73} +(8.08328 + 53.9257i) q^{74} +(20.5909 + 67.1405i) q^{76} +(12.9733 - 12.9733i) q^{77} +(-54.1165 - 40.0076i) q^{78} -16.4124i q^{79} +100.709 q^{81} +(52.2439 - 70.6680i) q^{82} +(-0.343799 - 0.343799i) q^{83} +(-100.576 + 30.8450i) q^{84} +(-92.1373 + 13.8111i) q^{86} +(2.64640 + 2.64640i) q^{87} +(6.63116 - 18.8039i) q^{88} +84.4631i q^{89} -69.3320i q^{91} +(100.836 + 53.5025i) q^{92} +(6.24661 + 6.24661i) q^{93} +(94.2869 - 14.1333i) q^{94} +(-84.1223 + 77.4219i) q^{96} +(24.1311 + 24.1311i) q^{97} +(-8.34394 - 6.16856i) q^{98} +9.38218 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 2 q^{2} - 16 q^{6} + 4 q^{7} - 4 q^{8} + 44 q^{12} - 56 q^{16} + 12 q^{17} - 10 q^{18} - 92 q^{22} + 4 q^{23} + 100 q^{26} - 68 q^{28} - 136 q^{31} - 128 q^{32} - 32 q^{33} + 220 q^{36} + 188 q^{38}+ \cdots - 546 q^{98}+O(q^{100})$ 20 * q + 2 * q^2 - 16 * q^6 + 4 * q^7 - 4 * q^8 + 44 * q^12 - 56 * q^16 + 12 * q^17 - 10 * q^18 - 92 * q^22 + 4 * q^23 + 100 * q^26 - 68 * q^28 - 136 * q^31 - 128 * q^32 - 32 * q^33 + 220 * q^36 + 188 * q^38 - 8 * q^41 + 284 * q^42 - 240 * q^46 - 188 * q^47 + 256 * q^48 + 332 * q^52 - 360 * q^56 + 40 * q^57 - 268 * q^58 - 336 * q^62 - 228 * q^63 + 616 * q^66 - 396 * q^68 + 248 * q^71 - 668 * q^72 + 124 * q^73 + 424 * q^76 + 368 * q^78 + 132 * q^81 + 676 * q^82 - 672 * q^86 + 488 * q^87 + 304 * q^88 + 628 * q^92 - 1024 * q^96 - 100 * q^97 - 546 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$ .

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.18894	+	1.60823i	−0.594472	+	0.804116i
$2$	−1.18894	+	1.60823i	−0.594472	+	0.804116i
$3$	−2.52630	−	2.52630i	−0.842100	−	0.842100i	0.147032	−	0.989132i	$-0.453028\pi$
$3$	−2.52630	−	2.52630i	−0.842100	−	0.842100i	−0.989132	+	0.147032i	$0.953028\pi$
$4$	−1.17282	−	3.82420i	−0.293205	−	0.956049i
$5$		0			0
$5$		0			0
$6$	7.06650	−	1.05925i	1.17775	−	0.176541i
$7$	5.20520	+	5.20520i	0.743600	+	0.743600i	0.973269	−	0.229669i	$-0.0737642\pi$
$7$	5.20520	+	5.20520i	0.743600	+	0.743600i	−0.229669	+	0.973269i	$0.573764\pi$
$8$	7.54462	+	2.66059i	0.943077	+	0.332574i
$9$			3.76437i			0.418263i
$10$		0			0
$11$		−	2.49236i		−	0.226579i	−0.993562	−	0.113289i	$-0.963861\pi$
$11$		−	2.49236i		−	0.226579i	0.993562	−	0.113289i	$-0.0361387\pi$
$12$	−6.69817	+	12.6240i	−0.558181	+	1.05200i
$13$	−6.65988	−	6.65988i	−0.512298	−	0.512298i	0.402932	−	0.915230i	$-0.367991\pi$
$13$	−6.65988	−	6.65988i	−0.512298	−	0.512298i	−0.915230	+	0.402932i	$0.867991\pi$
$14$	−14.5599	+	2.18248i	−1.03999	+	0.155891i
$15$		0			0
$16$	−13.2490	+	8.97020i	−0.828061	+	0.560638i
$17$	−21.9428	−	21.9428i	−1.29075	−	1.29075i	−0.934320	−	0.356434i	$-0.883992\pi$
$17$	−21.9428	−	21.9428i	−1.29075	−	1.29075i	−0.356434	−	0.934320i	$-0.616008\pi$
$18$	−6.05398	−	4.47563i	−0.336332	−	0.248646i
$19$	−17.5567			−0.924039			−0.462020	−	0.886870i	$-0.652875\pi$
$19$	−17.5567			−0.924039			−0.462020	+	0.886870i	$0.652875\pi$
$20$		0			0
$21$		−	26.2998i		−	1.25237i
$22$	4.00830	+	2.96328i	0.182195	+	0.134695i
$23$	−20.1791	+	20.1791i	−0.877354	+	0.877354i	−0.993260	−	0.115906i	$-0.963023\pi$
$23$	−20.1791	+	20.1791i	−0.877354	+	0.877354i	0.115906	+	0.993260i	$0.463023\pi$
$24$	−12.3385	−	25.7814i	−0.514105	−	1.07423i
$25$		0			0
$26$	18.6289	−	2.79240i	0.716495	−	0.107400i
$27$	−13.2268	+	13.2268i	−0.489880	+	0.489880i
$28$	13.8010	−	26.0105i	0.492891	−	0.928946i
$29$	−1.04754			−0.0361220			−0.0180610	−	0.999837i	$-0.505749\pi$
$29$	−1.04754			−0.0361220			−0.0180610	+	0.999837i	$0.505749\pi$
$30$		0			0
$31$	−2.47263			−0.0797623			−0.0398812	−	0.999204i	$-0.512698\pi$
$31$	−2.47263			−0.0797623			−0.0398812	+	0.999204i	$0.512698\pi$
$32$	1.32614	−	31.9725i	0.0414418	−	0.999141i
$33$	−6.29646	+	6.29646i	−0.190802	+	0.190802i
$34$	61.3780	−	9.20035i	1.80523	−	0.270599i
$35$		0			0
$36$	14.3957	−	4.41493i	0.399880	−	0.122637i
$37$	19.2786	−	19.2786i	0.521043	−	0.521043i	−0.396843	−	0.917886i	$-0.629894\pi$
$37$	19.2786	−	19.2786i	0.521043	−	0.521043i	0.917886	+	0.396843i	$0.129894\pi$
$38$	20.8740	−	28.2353i	0.549316	−	0.743035i
$39$			33.6497i			0.862813i
$40$		0			0
$41$	−43.9414			−1.07174			−0.535871	−	0.844300i	$-0.680017\pi$
$41$	−43.9414			−1.07174			−0.535871	+	0.844300i	$0.680017\pi$
$42$	42.2962	+	31.2690i	1.00705	+	0.744500i
$43$	32.9394	+	32.9394i	0.766032	+	0.766032i	0.977405	−	0.211373i	$-0.0677936\pi$
$43$	32.9394	+	32.9394i	0.766032	+	0.766032i	−0.211373	+	0.977405i	$0.567794\pi$
$44$	−9.53129	+	2.92310i	−0.216620	+	0.0664340i
$45$		0			0
$46$	−8.46086	−	56.4446i	−0.183932	−	1.22706i
$47$	−33.7079	−	33.7079i	−0.717189	−	0.717189i	0.250840	−	0.968029i	$-0.419293\pi$
$47$	−33.7079	−	33.7079i	−0.717189	−	0.717189i	−0.968029	+	0.250840i	$0.919293\pi$
$48$	56.1323	+	10.8095i	1.16942	+	0.225197i
$49$			5.18827i			0.105883i
$50$		0			0
$51$			110.868i			2.17389i
$52$	−17.6578	+	33.2795i	−0.339574	+	0.639991i
$53$	−36.4034	−	36.4034i	−0.686856	−	0.686856i	0.274679	−	0.961536i	$-0.411428\pi$
$53$	−36.4034	−	36.4034i	−0.686856	−	0.686856i	−0.961536	+	0.274679i	$0.911428\pi$
$54$	−5.54582	−	36.9976i	−0.102700	−	0.685141i
$55$		0			0
$56$	25.4224	+	53.1202i	0.453971	+	0.948575i
$57$	44.3536	+	44.3536i	0.778133	+	0.778133i
$58$	1.24547	−	1.68469i	0.0214736	−	0.0290463i
$59$	−30.5963			−0.518581			−0.259291	−	0.965799i	$-0.583489\pi$
$59$	−30.5963			−0.518581			−0.259291	+	0.965799i	$0.583489\pi$
$60$		0			0
$61$		−	23.8366i		−	0.390764i	−0.980727	−	0.195382i	$-0.937405\pi$
$61$		−	23.8366i		−	0.390764i	0.980727	−	0.195382i	$-0.0625947\pi$
$62$	2.93982	−	3.97657i	0.0474165	−	0.0641382i
$63$	−19.5943	+	19.5943i	−0.311021	+	0.311021i
$64$	49.8425	+	40.1463i	0.778789	+	0.627286i
$65$		0			0
$66$	−2.64003	−	17.6123i	−0.0400004	−	0.266853i
$67$	19.9932	−	19.9932i	0.298407	−	0.298407i	−0.541983	−	0.840390i	$-0.682326\pi$
$67$	19.9932	−	19.9932i	0.298407	−	0.298407i	0.840390	+	0.541983i	$0.182326\pi$
$68$	−58.1787	+	109.649i	−0.855569	+	1.61248i
$69$	101.957			1.47764
$70$		0			0
$71$	−21.8350			−0.307535			−0.153767	−	0.988107i	$-0.549141\pi$
$71$	−21.8350			−0.307535			−0.153767	+	0.988107i	$0.549141\pi$
$72$	−10.0154	+	28.4007i	−0.139103	+	0.394454i
$73$	−32.6450	+	32.6450i	−0.447191	+	0.447191i	−0.894420	−	0.447228i	$-0.852411\pi$
$73$	−32.6450	+	32.6450i	−0.447191	+	0.447191i	0.447228	+	0.894420i	$0.352411\pi$
$74$	8.08328	+	53.9257i	0.109233	+	0.728725i
$75$		0			0
$76$	20.5909	+	67.1405i	0.270933	+	0.883427i
$77$	12.9733	−	12.9733i	0.168484	−	0.168484i
$78$	−54.1165	−	40.0076i	−0.693801	−	0.512918i
$79$		−	16.4124i		−	0.207753i	−0.994590	−	0.103876i	$-0.966875\pi$
$79$		−	16.4124i		−	0.207753i	0.994590	−	0.103876i	$-0.0331246\pi$
$80$		0			0
$81$	100.709			1.24332
$82$	52.2439	−	70.6680i	0.637121	−	0.861805i
$83$	−0.343799	−	0.343799i	−0.00414216	−	0.00414216i	0.705033	−	0.709175i	$-0.250932\pi$
$83$	−0.343799	−	0.343799i	−0.00414216	−	0.00414216i	−0.709175	+	0.705033i	$0.750932\pi$
$84$	−100.576	+	30.8450i	−1.19733	+	0.367202i
$85$		0			0
$86$	−92.1373	+	13.8111i	−1.07136	+	0.160594i
$87$	2.64640	+	2.64640i	0.0304184	+	0.0304184i
$88$	6.63116	−	18.8039i	0.0753541	−	0.213681i
$89$			84.4631i			0.949024i	0.880249	+	0.474512i	$0.157375\pi$
$89$			84.4631i			0.949024i	−0.880249	+	0.474512i	$0.842625\pi$
$90$		0			0
$91$		−	69.3320i		−	0.761891i
$92$	100.836	+	53.5025i	1.09604	+	0.581549i
$93$	6.24661	+	6.24661i	0.0671678	+	0.0671678i
$94$	94.2869	−	14.1333i	1.00305	−	0.150354i
$95$		0			0
$96$	−84.1223	+	77.4219i	−0.876274	+	0.806478i
$97$	24.1311	+	24.1311i	0.248774	+	0.248774i	0.820467	−	0.571693i	$-0.193713\pi$
$97$	24.1311	+	24.1311i	0.248774	+	0.248774i	−0.571693	+	0.820467i	$0.693713\pi$
$98$	−8.34394	−	6.16856i	−0.0851422	−	0.0629445i
$99$	9.38218			0.0947695
$100$		0			0
$101$		−	152.095i		−	1.50589i	−0.658085	−	0.752944i	$-0.728633\pi$
$101$		−	152.095i		−	1.50589i	0.658085	−	0.752944i	$-0.271367\pi$
$102$	−178.302	−	131.816i	−1.74806	−	1.29232i
$103$	120.657	−	120.657i	1.17143	−	1.17143i	0.189558	−	0.981870i	$-0.439295\pi$
$103$	120.657	−	120.657i	1.17143	−	1.17143i	0.981870	−	0.189558i	$-0.0607054\pi$
$104$	−32.5270	−	67.9655i	−0.312760	−	0.653514i
$105$		0			0
$106$	101.827	−	15.2635i	0.960629	−	0.143995i
$107$	−75.2789	+	75.2789i	−0.703541	+	0.703541i	−0.965169	−	0.261628i	$-0.915741\pi$
$107$	−75.2789	+	75.2789i	−0.703541	+	0.703541i	0.261628	+	0.965169i	$0.415741\pi$
$108$	66.0944	+	35.0691i	0.611985	+	0.324714i
$109$	−11.8614			−0.108820			−0.0544100	−	0.998519i	$-0.517328\pi$
$109$	−11.8614			−0.108820			−0.0544100	+	0.998519i	$0.517328\pi$
$110$		0			0
$111$	−97.4070			−0.877541
$112$	−115.655	−	22.2719i	−1.03264	−	0.198856i
$113$	82.0090	−	82.0090i	0.725743	−	0.725743i	−0.244025	−	0.969769i	$-0.578468\pi$
$113$	82.0090	−	82.0090i	0.725743	−	0.725743i	0.969769	+	0.244025i	$0.0784680\pi$
$114$	−124.065	+	18.5969i	−1.08829	+	0.163131i
$115$		0			0
$116$	1.22858	+	4.00600i	0.0105912	+	0.0345345i
$117$	25.0702	−	25.0702i	0.214276	−	0.214276i
$118$	36.3773	−	49.2059i	0.308282	−	0.416999i
$119$		−	228.434i		−	1.91961i
$120$		0			0
$121$	114.788			0.948662
$122$	38.3348	+	28.3404i	0.314220	+	0.232299i
$123$	111.009	+	111.009i	0.902513	+	0.902513i
$124$	2.89996	+	9.45584i	0.0233867	+	0.0762567i
$125$		0			0
$126$	−8.21565	−	54.8087i	−0.0652035	−	0.434990i
$127$	55.8589	+	55.8589i	0.439834	+	0.439834i	0.891956	−	0.452122i	$-0.149333\pi$
$127$	55.8589	+	55.8589i	0.439834	+	0.439834i	−0.452122	+	0.891956i	$0.649333\pi$
$128$	−123.825	+	32.4266i	−0.967379	+	0.253333i
$129$		−	166.429i		−	1.29015i
$130$		0			0
$131$			151.619i			1.15740i	0.815541	+	0.578700i	$0.196440\pi$
$131$			151.619i			1.15740i	−0.815541	+	0.578700i	$0.803560\pi$
$132$	31.4635	+	16.6943i	0.238360	+	0.126472i
$133$	−91.3864	−	91.3864i	−0.687116	−	0.687116i
$134$	8.38292	+	55.9246i	0.0625591	+	0.417348i
$135$		0			0
$136$	−107.169	−	223.931i	−0.788010	−	1.64655i
$137$	−68.2473	−	68.2473i	−0.498156	−	0.498156i	0.412708	−	0.910863i	$-0.364583\pi$
$137$	−68.2473	−	68.2473i	−0.498156	−	0.498156i	−0.910863	+	0.412708i	$0.864583\pi$
$138$	−121.221	+	163.971i	−0.878415	+	1.18819i
$139$	−69.7245			−0.501615			−0.250807	−	0.968037i	$-0.580696\pi$
$139$	−69.7245			−0.501615			−0.250807	+	0.968037i	$0.580696\pi$
$140$		0			0
$141$			170.312i			1.20789i
$142$	25.9606	−	35.1157i	0.182821	−	0.247294i
$143$	−16.5988	+	16.5988i	−0.116076	+	0.116076i
$144$	−33.7671	−	49.8740i	−0.234494	−	0.346348i
$145$		0			0
$146$	−13.6876	−	91.3138i	−0.0937509	−	0.625437i
$147$	13.1071	−	13.1071i	0.0891640	−	0.0891640i
$148$	−96.3355	−	51.1148i	−0.650916	−	0.345370i
$149$	−78.9012			−0.529538			−0.264769	−	0.964312i	$-0.585296\pi$
$149$	−78.9012			−0.529538			−0.264769	+	0.964312i	$0.585296\pi$
$150$		0			0
$151$	197.562			1.30835			0.654177	−	0.756341i	$-0.273015\pi$
$151$	197.562			1.30835			0.654177	+	0.756341i	$0.273015\pi$
$152$	−132.459	−	46.7113i	−0.871440	−	0.307311i
$153$	82.6009	−	82.6009i	0.539875	−	0.539875i
$154$	5.43953	+	36.2885i	0.0353216	+	0.235640i
$155$		0			0
$156$	128.683	−	39.4651i	0.824891	−	0.252981i
$157$	−94.1106	+	94.1106i	−0.599431	+	0.599431i	−0.940161	−	0.340730i	$-0.889326\pi$
$157$	−94.1106	+	94.1106i	−0.599431	+	0.599431i	0.340730	+	0.940161i	$0.389326\pi$
$158$	26.3950	+	19.5135i	0.167057	+	0.123503i
$159$			183.932i			1.15680i
$160$		0			0
$161$	−210.073			−1.30480
$162$	−119.737	+	161.963i	−0.739119	+	0.999773i
$163$	−132.980	−	132.980i	−0.815827	−	0.815827i	0.169673	−	0.985500i	$-0.445729\pi$
$163$	−132.980	−	132.980i	−0.815827	−	0.815827i	−0.985500	+	0.169673i	$0.945729\pi$
$164$	51.5354	+	168.041i	0.314240	+	1.02464i
$165$		0			0
$166$	0.961668	−	0.144151i	0.00579318	−	0.000868378i
$167$	51.4111	+	51.4111i	0.307851	+	0.307851i	0.844075	−	0.536225i	$-0.180150\pi$
$167$	51.4111	+	51.4111i	0.307851	+	0.307851i	−0.536225	+	0.844075i	$0.680150\pi$
$168$	69.9730	−	198.422i	0.416506	−	1.18108i
$169$		−	80.2920i		−	0.475101i
$170$		0			0
$171$		−	66.0900i		−	0.386492i
$172$	87.3347	−	164.599i	0.507760	−	0.956969i
$173$	183.164	+	183.164i	1.05875	+	1.05875i	0.998163	+	0.0605880i	$0.0192976\pi$
$173$	183.164	+	183.164i	1.05875	+	1.05875i	0.0605880	+	0.998163i	$0.480702\pi$
$174$	−7.40244	+	1.10960i	−0.0425428	+	0.00637702i
$175$		0			0
$176$	22.3570	+	33.0213i	0.127028	+	0.187621i
$177$	77.2954	+	77.2954i	0.436697	+	0.436697i
$178$	−135.836	−	100.422i	−0.763125	−	0.564168i
$179$	31.3468			0.175122			0.0875610	−	0.996159i	$-0.472093\pi$
$179$	31.3468			0.175122			0.0875610	+	0.996159i	$0.472093\pi$
$180$		0			0
$181$		−	57.4156i		−	0.317214i	−0.987342	−	0.158607i	$-0.949300\pi$
$181$		−	57.4156i		−	0.317214i	0.987342	−	0.158607i	$-0.0507002\pi$
$182$	111.502	+	82.4320i	0.612648	+	0.452923i
$183$	−60.2184	+	60.2184i	−0.329063	+	0.329063i
$184$	−205.932	+	98.5555i	−1.11920	+	0.535628i
$185$		0			0
$186$	−17.4729	+	2.61912i	−0.0939401	+	0.0140813i
$187$	−54.6895	+	54.6895i	−0.292457	+	0.292457i
$188$	−89.3723	+	168.439i	−0.475385	+	0.895952i
$189$	−137.696			−0.728550
$190$		0			0
$191$	161.923			0.847767			0.423884	−	0.905717i	$-0.360667\pi$
$191$	161.923			0.847767			0.423884	+	0.905717i	$0.360667\pi$
$192$	−24.4956	−	227.339i	−0.127581	−	1.18405i
$193$	−63.0037	+	63.0037i	−0.326444	+	0.326444i	−0.851233	−	0.524789i	$-0.824144\pi$
$193$	−63.0037	+	63.0037i	−0.326444	+	0.326444i	0.524789	+	0.851233i	$0.324144\pi$
$194$	−67.4989	+	10.1179i	−0.347933	+	0.0521540i
$195$		0			0
$196$	19.8410	−	6.08491i	0.101229	−	0.0310455i
$197$	−3.96178	+	3.96178i	−0.0201106	+	0.0201106i	−0.717091	−	0.696980i	$-0.754527\pi$
$197$	−3.96178	+	3.96178i	−0.0201106	+	0.0201106i	0.696980	+	0.717091i	$0.254527\pi$
$198$	−11.1549	+	15.0887i	−0.0563378	+	0.0762056i
$199$			123.026i			0.618221i	0.951026	+	0.309110i	$0.100031\pi$
$199$			123.026i			0.618221i	−0.951026	+	0.309110i	$0.899969\pi$
$200$		0			0
$201$	−101.018			−0.502576
$202$	244.603	+	180.832i	1.21091	+	0.895208i
$203$	−5.45265	−	5.45265i	−0.0268604	−	0.0268604i
$204$	423.982	−	130.029i	2.07834	−	0.637395i
$205$		0			0
$206$	50.5900	+	337.499i	0.245582	+	1.63834i
$207$	−75.9617	−	75.9617i	−0.366965	−	0.366965i
$208$	147.977	+	28.4961i	0.711428	+	0.137001i
$209$			43.7578i			0.209367i
$210$		0			0
$211$		−	273.854i		−	1.29789i	−0.760837	−	0.648943i	$-0.775211\pi$
$211$		−	273.854i		−	1.29789i	0.760837	−	0.648943i	$-0.224789\pi$
$212$	−96.5191	+	181.908i	−0.455279	+	0.858059i
$213$	55.1617	+	55.1617i	0.258975	+	0.258975i
$214$	−31.5635	−	210.568i	−0.147493	−	0.983964i
$215$		0			0
$216$	−134.982	+	64.5999i	−0.624916	+	0.299074i
$217$	−12.8706	−	12.8706i	−0.0593113	−	0.0593113i
$218$	14.1025	−	19.0759i	0.0646905	−	0.0875040i
$219$	164.942			0.753159
$220$		0			0
$221$			292.273i			1.32250i
$222$	115.812	−	156.653i	0.521674	−	0.705644i
$223$	−128.870	+	128.870i	−0.577894	+	0.577894i	−0.934323	−	0.356429i	$-0.883994\pi$
$223$	−128.870	+	128.870i	−0.577894	+	0.577894i	0.356429	+	0.934323i	$0.383994\pi$
$224$	173.326	−	159.521i	0.773778	−	0.712145i
$225$		0			0
$226$	34.3854	+	229.394i	0.152148	+	1.01502i
$227$	242.455	−	242.455i	1.06808	−	1.06808i	0.0705768	−	0.997506i	$-0.477516\pi$
$227$	242.455	−	242.455i	1.06808	−	1.06808i	0.997506	−	0.0705768i	$-0.0224840\pi$
$228$	117.598	−	221.636i	0.515781	−	0.972086i
$229$	385.669			1.68414			0.842072	−	0.539365i	$-0.181336\pi$
$229$	385.669			1.68414			0.842072	+	0.539365i	$0.181336\pi$
$230$		0			0
$231$	−65.5487			−0.283760
$232$	−7.90328	−	2.78707i	−0.0340659	−	0.0120132i
$233$	−9.90826	+	9.90826i	−0.0425247	+	0.0425247i	−0.728049	−	0.685525i	$-0.759573\pi$
$233$	−9.90826	+	9.90826i	−0.0425247	+	0.0425247i	0.685525	+	0.728049i	$0.259573\pi$
$234$	10.5116	+	70.1259i	0.0449215	+	0.299683i
$235$		0			0
$236$	35.8840	+	117.006i	0.152051	+	0.495789i
$237$	−41.4627	+	41.4627i	−0.174948	+	0.174948i
$238$	367.374	+	271.595i	1.54359	+	1.14116i
$239$			44.7391i			0.187193i	0.995610	+	0.0935965i	$0.0298364\pi$
$239$			44.7391i			0.187193i	−0.995610	+	0.0935965i	$0.970164\pi$
$240$		0			0
$241$	−21.4785			−0.0891223			−0.0445611	−	0.999007i	$-0.514189\pi$
$241$	−21.4785			−0.0891223			−0.0445611	+	0.999007i	$0.514189\pi$
$242$	−136.477	+	184.606i	−0.563953	+	0.762835i
$243$	−135.380	−	135.380i	−0.557118	−	0.557118i
$244$	−91.1560	+	27.9561i	−0.373590	+	0.114574i
$245$		0			0
$246$	−310.512	+	46.5448i	−1.26224	+	0.189206i
$247$	116.926	+	116.926i	0.473384	+	0.473384i
$248$	−18.6551	−	6.57866i	−0.0752220	−	0.0265269i
$249$			1.73708i			0.00697623i
$250$		0			0
$251$		−	149.651i		−	0.596218i	−0.954532	−	0.298109i	$-0.903644\pi$
$251$		−	149.651i		−	0.596218i	0.954532	−	0.298109i	$-0.0963560\pi$
$252$	97.9131	+	51.9519i	0.388544	+	0.206158i
$253$	50.2938	+	50.2938i	0.198790	+	0.198790i
$254$	−156.247	+	23.4209i	−0.615146	+	0.0922084i
$255$		0			0
$256$	95.0710	−	237.692i	0.371371	−	0.928485i
$257$	−244.045	−	244.045i	−0.949590	−	0.949590i	0.0491992	−	0.998789i	$-0.484333\pi$
$257$	−244.045	−	244.045i	−0.949590	−	0.949590i	−0.998789	+	0.0491992i	$0.984333\pi$
$258$	267.657	+	197.875i	1.03743	+	0.766959i
$259$	200.698			0.774896
$260$		0			0
$261$		−	3.94332i		−	0.0151085i
$262$	−243.839	−	180.267i	−0.930683	−	0.688042i
$263$	241.557	−	241.557i	0.918467	−	0.918467i	−0.0784512	−	0.996918i	$-0.524997\pi$
$263$	241.557	−	241.557i	0.918467	−	0.918467i	0.996918	+	0.0784512i	$0.0249975\pi$
$264$	−64.2566	+	30.7521i	−0.243396	+	0.116485i
$265$		0			0
$266$	255.624	−	38.3172i	0.960992	−	0.144050i
$267$	213.379	−	213.379i	0.799172	−	0.799172i
$268$	−99.9066	−	53.0096i	−0.372786	−	0.197797i
$269$	−350.619			−1.30342			−0.651708	−	0.758470i	$-0.725947\pi$
$269$	−350.619			−1.30342			−0.651708	+	0.758470i	$0.725947\pi$
$270$		0			0
$271$	−298.610			−1.10188			−0.550940	−	0.834545i	$-0.685731\pi$
$271$	−298.610			−1.10188			−0.550940	+	0.834545i	$0.685731\pi$
$272$	487.552	+	93.8885i	1.79247	+	0.345178i
$273$	−175.153	+	175.153i	−0.641588	+	0.641588i
$274$	190.900	−	28.6153i	0.696715	−	0.104435i
$275$		0			0
$276$	−119.577	−	389.904i	−0.433252	−	1.41270i
$277$	275.798	−	275.798i	0.995660	−	0.995660i	−0.00433109	−	0.999991i	$-0.501379\pi$
$277$	275.798	−	275.798i	0.995660	−	0.995660i	0.999991	+	0.00433109i	$0.00137863\pi$
$278$	82.8985	−	112.133i	0.298196	−	0.403357i
$279$		−	9.30790i		−	0.0333617i
$280$		0			0
$281$	13.2859			0.0472808			0.0236404	−	0.999721i	$-0.492474\pi$
$281$	13.2859			0.0472808			0.0236404	+	0.999721i	$0.492474\pi$
$282$	−273.902	−	202.492i	−0.971283	−	0.718057i
$283$	−253.189	−	253.189i	−0.894662	−	0.894662i	0.100296	−	0.994958i	$-0.468021\pi$
$283$	−253.189	−	253.189i	−0.894662	−	0.894662i	−0.994958	+	0.100296i	$0.968021\pi$
$284$	25.6085	+	83.5013i	0.0901709	+	0.294019i
$285$		0			0
$286$	−6.95969	−	46.4299i	−0.0243346	−	0.162342i
$287$	−228.724	−	228.724i	−0.796948	−	0.796948i
$288$	120.356	+	4.99207i	0.417904	+	0.0173336i
$289$			673.975i			2.33209i
$290$		0			0
$291$		−	121.925i		−	0.418985i
$292$	163.128	+	86.5541i	0.558656	+	0.296418i
$293$	−143.408	−	143.408i	−0.489447	−	0.489447i	0.418685	−	0.908132i	$-0.362491\pi$
$293$	−143.408	−	143.408i	−0.489447	−	0.489447i	−0.908132	+	0.418685i	$0.862491\pi$
$294$	5.49565	+	36.6629i	0.0186927	+	0.124704i
$295$		0			0
$296$	196.742	−	94.1572i	0.664669	−	0.318099i
$297$	32.9659	+	32.9659i	0.110996	+	0.110996i
$298$	93.8092	−	126.891i	0.314796	−	0.425810i
$299$	268.781			0.898934
$300$		0			0
$301$			342.912i			1.13924i
$302$	−234.890	+	317.725i	−0.777781	+	1.05207i
$303$	−384.236	+	384.236i	−1.26811	+	1.26811i
$304$	232.609	−	157.488i	0.765161	−	0.518051i
$305$		0			0
$306$	34.6335	+	231.049i	0.113181	+	0.755063i
$307$	−357.761	+	357.761i	−1.16535	+	1.16535i	−0.182059	+	0.983288i	$0.558276\pi$
$307$	−357.761	+	357.761i	−1.16535	+	1.16535i	−0.983288	+	0.182059i	$0.941724\pi$
$308$	−64.8276	−	34.3970i	−0.210479	−	0.111679i
$309$	−609.631			−1.97292
$310$		0			0
$311$	−380.204			−1.22252			−0.611261	−	0.791429i	$-0.709337\pi$
$311$	−380.204			−1.22252			−0.611261	+	0.791429i	$0.709337\pi$
$312$	−89.5280	+	253.874i	−0.286949	+	0.813699i
$313$	−270.798	+	270.798i	−0.865169	+	0.865169i	−0.991933	−	0.126764i	$-0.959541\pi$
$313$	−270.798	+	270.798i	−0.865169	+	0.865169i	0.126764	+	0.991933i	$0.459541\pi$
$314$	−39.4594	−	263.244i	−0.125667	−	0.838357i
$315$		0			0
$316$	−62.7645	+	19.2489i	−0.198622	+	0.0609141i
$317$	−238.939	+	238.939i	−0.753752	+	0.753752i	−0.975177	−	0.221426i	$-0.928929\pi$
$317$	−238.939	+	238.939i	−0.753752	+	0.753752i	0.221426	+	0.975177i	$0.428929\pi$
$318$	−295.805	−	218.685i	−0.930204	−	0.687687i
$319$			2.61085i			0.00818448i
$320$		0			0
$321$	380.354			1.18490
$322$	249.765	−	337.846i	0.775668	−	1.04921i
$323$	385.245	+	385.245i	1.19271	+	1.19271i
$324$	−118.113	−	385.131i	−0.364548	−	1.18867i
$325$		0			0
$326$	371.968	−	55.7568i	1.14101	−	0.171033i
$327$	29.9654	+	29.9654i	0.0916373	+	0.0916373i
$328$	−331.521	−	116.910i	−1.01074	−	0.356433i
$329$		−	350.913i		−	1.06660i
$330$		0			0
$331$			73.0725i			0.220763i	0.993889	+	0.110381i	$0.0352072\pi$
$331$			73.0725i			0.220763i	−0.993889	+	0.110381i	$0.964793\pi$
$332$	−0.911542	+	1.71797i	−0.00274561	+	0.00517462i
$333$	72.5718	+	72.5718i	0.217933	+	0.217933i
$334$	−143.806	+	21.5560i	−0.430557	+	0.0645390i
$335$		0			0
$336$	235.914	+	348.445i	0.702126	+	1.03704i
$337$	207.932	+	207.932i	0.617008	+	0.617008i	0.944763	−	0.327755i	$-0.106292\pi$
$337$	207.932	+	207.932i	0.617008	+	0.617008i	−0.327755	+	0.944763i	$0.606292\pi$
$338$	129.128	+	95.4627i	0.382036	+	0.282434i
$339$	−414.358			−1.22230
$340$		0			0
$341$			6.16270i			0.0180724i
$342$	106.288	+	78.5774i	0.310784	+	0.229759i
$343$	228.049	−	228.049i	0.664866	−	0.664866i
$344$	160.877	+	336.153i	0.467665	+	0.977189i
$345$		0			0
$346$	−512.342	+	76.7983i	−1.48076	+	0.221961i
$347$	150.516	−	150.516i	0.433765	−	0.433765i	−0.456142	−	0.889907i	$-0.650769\pi$
$347$	150.516	−	150.516i	0.433765	−	0.433765i	0.889907	+	0.456142i	$0.150769\pi$
$348$	7.01659	−	13.2241i	0.0201626	−	0.0380003i
$349$	159.797			0.457871			0.228935	−	0.973442i	$-0.426476\pi$
$349$	159.797			0.457871			0.228935	+	0.973442i	$0.426476\pi$
$350$		0			0
$351$	176.177			0.501930
$352$	−79.6871	−	3.30521i	−0.226384	−	0.00938981i
$353$	−31.8920	+	31.8920i	−0.0903455	+	0.0903455i	−0.750835	−	0.660490i	$-0.770349\pi$
$353$	−31.8920	+	31.8920i	−0.0903455	+	0.0903455i	0.660490	+	0.750835i	$0.270349\pi$
$354$	−216.209	+	32.4090i	−0.610759	+	0.0915508i
$355$		0			0
$356$	323.004	−	99.0601i	0.907314	−	0.278259i
$357$	−577.092	+	577.092i	−1.61650	+	1.61650i
$358$	−37.2697	+	50.4130i	−0.104105	+	0.140818i
$359$		−	374.114i		−	1.04210i	−0.853526	−	0.521050i	$-0.825541\pi$
$359$		−	374.114i		−	1.04210i	0.853526	−	0.521050i	$-0.174459\pi$
$360$		0			0
$361$	−52.7608			−0.146152
$362$	92.3377	+	68.2640i	0.255076	+	0.188575i
$363$	−289.989	−	289.989i	−0.798868	−	0.798868i
$364$	−265.139	+	81.3141i	−0.728405	+	0.223390i
$365$		0			0
$366$	−25.2488	−	168.442i	−0.0689859	−	0.460223i
$367$	−195.775	−	195.775i	−0.533446	−	0.533446i	0.388150	−	0.921596i	$-0.373114\pi$
$367$	−195.775	−	195.775i	−0.533446	−	0.533446i	−0.921596	+	0.388150i	$0.873114\pi$
$368$	86.3421	−	448.364i	0.234625	−	1.21838i
$369$		−	165.412i		−	0.448270i
$370$		0			0
$371$		−	378.974i		−	1.02149i
$372$	16.5621	−	31.2144i	0.0445218	−	0.0839097i
$373$	342.423	+	342.423i	0.918023	+	0.918023i	0.996885	−	0.0788627i	$-0.0251289\pi$
$373$	342.423	+	342.423i	0.918023	+	0.918023i	−0.0788627	+	0.996885i	$0.525129\pi$
$374$	−22.9306	−	152.976i	−0.0613118	−	0.409027i
$375$		0			0
$376$	−164.630	−	343.996i	−0.437846	−	0.914883i
$377$	6.97649	+	6.97649i	0.0185053	+	0.0185053i
$378$	163.713	−	221.447i	0.433103	−	0.585839i
$379$	−607.050			−1.60171			−0.800857	−	0.598855i	$-0.795622\pi$
$379$	−607.050			−1.60171			−0.800857	+	0.598855i	$0.795622\pi$
$380$		0			0
$381$		−	282.232i		−	0.740767i
$382$	−192.518	+	260.411i	−0.503974	+	0.681703i
$383$	154.687	−	154.687i	0.403882	−	0.403882i	−0.475717	−	0.879599i	$-0.657811\pi$
$383$	154.687	−	154.687i	0.403882	−	0.403882i	0.879599	+	0.475717i	$0.157811\pi$
$384$	394.737	+	230.898i	1.02796	+	0.601298i
$385$		0			0
$386$	−26.4167	−	176.233i	−0.0684370	−	0.456561i
$387$	−123.996	+	123.996i	−0.320403	+	0.320403i
$388$	63.9806	−	120.584i	0.164899	−	0.310782i
$389$	323.730			0.832210			0.416105	−	0.909317i	$-0.363395\pi$
$389$	323.730			0.832210			0.416105	+	0.909317i	$0.363395\pi$
$390$		0			0
$391$	885.575			2.26490
$392$	−13.8039	+	39.1435i	−0.0352139	+	0.0998559i
$393$	383.036	−	383.036i	0.974645	−	0.974645i
$394$	−1.66113	−	11.0818i	−0.00421605	−	0.0281264i
$395$		0			0
$396$	−11.0036	−	35.8793i	−0.0277869	−	0.0906043i
$397$	376.174	−	376.174i	0.947543	−	0.947543i	−0.0511485	−	0.998691i	$-0.516288\pi$
$397$	376.174	−	376.174i	0.947543	−	0.947543i	0.998691	+	0.0511485i	$0.0162882\pi$
$398$	−197.854	−	146.271i	−0.497121	−	0.367515i
$399$			461.739i			1.15724i
$400$		0			0
$401$	−401.761			−1.00190			−0.500948	−	0.865477i	$-0.667015\pi$
$401$	−401.761			−1.00190			−0.500948	+	0.865477i	$0.667015\pi$
$402$	120.105	−	162.460i	0.298768	−	0.404130i
$403$	16.4674	+	16.4674i	0.0408621	+	0.0408621i
$404$	−581.640	+	178.380i	−1.43970	+	0.441534i
$405$		0			0
$406$	15.2520	−	2.28623i	0.0375666	−	0.00563111i
$407$	−48.0493	−	48.0493i	−0.118057	−	0.118057i
$408$	−294.975	+	836.459i	−0.722978	+	2.05014i
$409$		−	166.880i		−	0.408020i	−0.978969	−	0.204010i	$-0.934603\pi$
$409$		−	166.880i		−	0.408020i	0.978969	−	0.204010i	$-0.0653974\pi$
$410$		0			0
$411$			344.826i			0.838993i
$412$	−602.925	−	319.907i	−1.46341	−	0.776474i
$413$	−159.260	−	159.260i	−0.385617	−	0.385617i
$414$	212.478	−	31.8498i	0.513233	−	0.0769319i
$415$		0			0
$416$	−221.765	+	204.101i	−0.533089	+	0.490628i
$417$	176.145	+	176.145i	0.422410	+	0.422410i
$418$	−70.3727	−	52.0256i	−0.168356	−	0.124463i
$419$	533.694			1.27373			0.636866	−	0.770974i	$-0.280230\pi$
$419$	533.694			1.27373			0.636866	+	0.770974i	$0.280230\pi$
$420$		0			0
$421$			214.523i			0.509556i	0.967000	+	0.254778i	$0.0820023\pi$
$421$			214.523i			0.509556i	−0.967000	+	0.254778i	$0.917998\pi$
$422$	440.421	+	325.597i	1.04365	+	0.771558i
$423$	126.889	−	126.889i	0.299974	−	0.299974i
$424$	−177.795	−	371.504i	−0.419328	−	0.876189i
$425$		0			0
$426$	−154.297	+	23.1286i	−0.362199	+	0.0542925i
$427$	124.074	−	124.074i	0.290573	−	0.290573i
$428$	376.170	+	199.593i	0.878902	+	0.466338i
$429$	83.8673			0.195495
$430$		0			0
$431$	−525.371			−1.21896			−0.609479	−	0.792802i	$-0.708621\pi$
$431$	−525.371			−1.21896			−0.609479	+	0.792802i	$0.708621\pi$
$432$	56.5944	−	293.888i	0.131006	−	0.680296i
$433$	262.829	−	262.829i	0.606994	−	0.606994i	−0.335165	−	0.942159i	$-0.608792\pi$
$433$	262.829	−	262.829i	0.606994	−	0.606994i	0.942159	+	0.335165i	$0.108792\pi$
$434$	36.0012	−	5.39646i	0.0829521	−	0.0124342i
$435$		0			0
$436$	13.9113	+	45.3603i	0.0319066	+	0.104037i
$437$	354.280	−	354.280i	0.810709	−	0.810709i
$438$	−196.107	+	265.265i	−0.447732	+	0.605627i
$439$		−	419.145i		−	0.954771i	−0.878694	−	0.477386i	$-0.841584\pi$
$439$		−	419.145i		−	0.954771i	0.878694	−	0.477386i	$-0.158416\pi$
$440$		0			0
$441$	−19.5306			−0.0442870
$442$	−470.043	−	347.497i	−1.06345	−	0.786191i
$443$	−119.234	−	119.234i	−0.269152	−	0.269152i	0.559606	−	0.828758i	$-0.310952\pi$
$443$	−119.234	−	119.234i	−0.269152	−	0.269152i	−0.828758	+	0.559606i	$0.810952\pi$
$444$	114.241	+	372.504i	0.257300	+	0.838972i
$445$		0			0
$446$	−54.0337	−	360.473i	−0.121152	−	0.808236i
$447$	199.328	+	199.328i	0.445924	+	0.445924i
$448$	50.4709	+	468.410i	0.112658	+	1.04556i
$449$		−	596.070i		−	1.32755i	−0.747932	−	0.663775i	$-0.768953\pi$
$449$		−	596.070i		−	1.32755i	0.747932	−	0.663775i	$-0.231047\pi$
$450$		0			0
$451$			109.518i			0.242834i
$452$	−409.801	−	217.437i	−0.906639	−	0.481055i
$453$	−499.099	−	499.099i	−1.10176	−	1.10176i
$454$	101.658	+	678.189i	0.223917	+	1.49381i
$455$		0			0
$456$	216.624	+	452.637i	0.475053	+	0.992626i
$457$	−144.279	−	144.279i	−0.315708	−	0.315708i	0.531408	−	0.847116i	$-0.321663\pi$
$457$	−144.279	−	144.279i	−0.315708	−	0.315708i	−0.847116	+	0.531408i	$0.821663\pi$
$458$	−458.539	+	620.245i	−1.00118	+	1.35425i
$459$	580.465			1.26463
$460$		0			0
$461$		−	743.994i		−	1.61387i	−0.590640	−	0.806935i	$-0.701125\pi$
$461$		−	743.994i		−	1.61387i	0.590640	−	0.806935i	$-0.298875\pi$
$462$	77.9337	−	105.417i	0.168688	−	0.228176i
$463$	−446.519	+	446.519i	−0.964404	+	0.964404i	−0.999388	−	0.0349842i	$-0.988862\pi$
$463$	−446.519	+	446.519i	−0.964404	+	0.964404i	0.0349842	+	0.999388i	$0.488862\pi$
$464$	13.8788	−	9.39664i	0.0299113	−	0.0202514i
$465$		0			0
$466$	−4.15441	−	27.7152i	−0.00891504	−	0.0594746i
$467$	5.61916	−	5.61916i	0.0120325	−	0.0120325i	−0.701065	−	0.713097i	$-0.747292\pi$
$467$	5.61916	−	5.61916i	0.0120325	−	0.0120325i	0.713097	+	0.701065i	$0.247292\pi$
$468$	−125.276	−	66.4707i	−0.267685	−	0.142031i
$469$	208.138			0.443791
$470$		0			0
$471$	475.503			1.00956
$472$	−230.837	−	81.4042i	−0.489062	−	0.172467i
$473$	82.0969	−	82.0969i	0.173566	−	0.173566i
$474$	−17.3848	−	115.979i	−0.0366768	−	0.244681i
$475$		0			0
$476$	−873.576	+	267.912i	−1.83524	+	0.562840i
$477$	137.036	−	137.036i	0.287287	−	0.287287i
$478$	−71.9509	−	53.1923i	−0.150525	−	0.111281i
$479$			765.340i			1.59779i	0.601472	+	0.798894i	$0.294581\pi$
$479$			765.340i			1.59779i	−0.601472	+	0.798894i	$0.705419\pi$
$480$		0			0
$481$	−256.786			−0.533859
$482$	25.5367	−	34.5424i	0.0529807	−	0.0716647i
$483$	530.707	+	530.707i	1.09877	+	1.09877i
$484$	−134.626	−	438.973i	−0.278153	−	0.906968i
$485$		0			0
$486$	378.681	−	56.7630i	0.779179	−	0.116796i
$487$	611.323	+	611.323i	1.25528	+	1.25528i	0.953320	+	0.301963i	$0.0976420\pi$
$487$	611.323	+	611.323i	1.25528	+	1.25528i	0.301963	+	0.953320i	$0.402358\pi$
$488$	63.4195	−	179.838i	0.129958	−	0.368521i
$489$			671.893i			1.37402i
$490$		0			0
$491$			899.211i			1.83139i	0.401877	+	0.915694i	$0.368358\pi$
$491$			899.211i			1.83139i	−0.401877	+	0.915694i	$0.631642\pi$
$492$	294.327	−	554.715i	0.598226	−	1.12747i
$493$	22.9860	+	22.9860i	0.0466247	+	0.0466247i
$494$	−327.062	+	49.0255i	−0.662069	+	0.0992419i
$495$		0			0
$496$	32.7599	−	22.1800i	0.0660481	−	0.0447178i
$497$	−113.655	−	113.655i	−0.228683	−	0.228683i
$498$	−2.79363	−	2.06529i	−0.00560969	−	0.00414717i
$499$	−755.350			−1.51373			−0.756864	−	0.653572i	$-0.773270\pi$
$499$	−755.350			−1.51373			−0.756864	+	0.653572i	$0.773270\pi$
$500$		0			0
$501$		−	259.760i		−	0.518482i
$502$	240.673	+	177.927i	0.479429	+	0.354435i
$503$	505.226	−	505.226i	1.00443	−	1.00443i	0.00443600	−	0.999990i	$-0.498588\pi$
$503$	505.226	−	505.226i	1.00443	−	1.00443i	0.999990	−	0.00443600i	$-0.00141203\pi$
$504$	−199.964	+	95.6991i	−0.396754	+	0.189879i
$505$		0			0
$506$	−140.681	+	21.0876i	−0.278025	+	0.0416750i
$507$	−202.842	+	202.842i	−0.400082	+	0.400082i
$508$	148.103	−	279.128i	0.291541	−	0.549464i
$509$	594.029			1.16705			0.583526	−	0.812095i	$-0.301673\pi$
$509$	594.029			1.16705			0.583526	+	0.812095i	$0.301673\pi$
$510$		0			0
$511$	−339.847			−0.665063
$512$	269.230	+	435.499i	0.525840	+	0.850584i
$513$	232.219	−	232.219i	0.452668	−	0.452668i
$514$	682.636	−	102.325i	1.32809	−	0.199076i
$515$		0			0
$516$	−636.459	+	195.192i	−1.23345	+	0.378279i
$517$	−84.0123	+	84.0123i	−0.162500	+	0.162500i
$518$	−238.619	+	322.769i	−0.460654	+	0.623106i
$519$		−	925.453i		−	1.78315i
$520$		0			0
$521$	871.615			1.67297			0.836483	−	0.547993i	$-0.184608\pi$
$521$	871.615			1.67297			0.836483	+	0.547993i	$0.184608\pi$
$522$	6.34178	+	4.68839i	0.0121490	+	0.00898160i
$523$	601.907	+	601.907i	1.15087	+	1.15087i	0.986378	+	0.164497i	$0.0526001\pi$
$523$	601.907	+	601.907i	1.15087	+	1.15087i	0.164497	+	0.986378i	$0.447400\pi$
$524$	579.822	−	177.822i	1.10653	−	0.339356i
$525$		0			0
$526$	101.282	+	675.677i	0.192551	+	1.28456i
$527$	54.2566	+	54.2566i	0.102954	+	0.102954i
$528$	26.9411	−	139.902i	0.0510249	−	0.264966i
$529$		−	285.396i		−	0.539500i
$530$		0			0
$531$		−	115.176i		−	0.216903i
$532$	−242.300	+	456.660i	−0.455451	+	0.858383i
$533$	292.645	+	292.645i	0.549052	+	0.549052i
$534$	89.4672	+	596.859i	0.167542	+	1.11771i
$535$		0			0
$536$	204.035	−	97.6475i	0.380663	−	0.182178i
$537$	−79.1915	−	79.1915i	−0.147470	−	0.147470i
$538$	416.867	−	563.877i	0.774845	−	1.04810i
$539$	12.9311			0.0239908
$540$		0			0
$541$			109.548i			0.202492i	0.994861	+	0.101246i	$0.0322830\pi$
$541$			109.548i			0.202492i	−0.994861	+	0.101246i	$0.967717\pi$
$542$	355.030	−	480.233i	0.655037	−	0.886040i
$543$	−145.049	+	145.049i	−0.267125	+	0.267125i
$544$	−730.666	+	672.468i	−1.34314	+	1.23615i
$545$		0			0
$546$	−73.4397	−	489.935i	−0.134505	−	0.897317i
$547$	−330.968	+	330.968i	−0.605060	+	0.605060i	−0.941651	−	0.336591i	$-0.890726\pi$
$547$	−330.968	+	330.968i	−0.605060	+	0.605060i	0.336591	+	0.941651i	$0.390726\pi$
$548$	−180.949	+	341.033i	−0.330200	+	0.622323i
$549$	89.7299			0.163442
$550$		0			0
$551$	18.3914			0.0333782
$552$	769.227	+	271.266i	1.39353	+	0.491424i
$553$	85.4301	−	85.4301i	0.154485	−	0.154485i
$554$	115.639	+	771.455i	0.208734	+	1.39252i
$555$		0			0
$556$	81.7744	+	266.640i	0.147076	+	0.479569i
$557$	−62.7080	+	62.7080i	−0.112582	+	0.112582i	−0.761153	−	0.648572i	$-0.775367\pi$
$557$	−62.7080	+	62.7080i	−0.112582	+	0.112582i	0.648572	+	0.761153i	$0.275367\pi$
$558$	14.9693	+	11.0666i	0.0268266	+	0.0198326i
$559$		−	438.745i		−	0.784874i
$560$		0			0
$561$	276.324			0.492556
$562$	−15.7962	+	21.3668i	−0.0281071	+	0.0380193i
$563$	−116.120	−	116.120i	−0.206252	−	0.206252i	0.596420	−	0.802672i	$-0.296589\pi$
$563$	−116.120	−	116.120i	−0.206252	−	0.206252i	−0.802672	+	0.596420i	$0.796589\pi$
$564$	651.308	−	199.746i	1.15480	−	0.354159i
$565$		0			0
$566$	708.215	−	106.159i	1.25126	−	0.187560i
$567$	524.210	+	524.210i	0.924533	+	0.924533i
$568$	−164.737	−	58.0939i	−0.290029	−	0.102278i
$569$			323.733i			0.568950i	0.958683	+	0.284475i	$0.0918193\pi$
$569$			323.733i			0.568950i	−0.958683	+	0.284475i	$0.908181\pi$
$570$		0			0
$571$			433.708i			0.759558i	0.925077	+	0.379779i	$0.124000\pi$
$571$			433.708i			0.759558i	−0.925077	+	0.379779i	$0.876000\pi$
$572$	82.9447	+	44.0098i	0.145008	+	0.0769402i
$573$	−409.067	−	409.067i	−0.713904	−	0.713904i
$574$	639.782	−	95.9011i	1.11460	−	0.167075i
$575$		0			0
$576$	−151.125	+	187.626i	−0.262370	+	0.325739i
$577$	−27.1282	−	27.1282i	−0.0470159	−	0.0470159i	0.683208	−	0.730224i	$-0.260584\pi$
$577$	−27.1282	−	27.1282i	−0.0470159	−	0.0470159i	−0.730224	+	0.683208i	$0.760584\pi$
$578$	−1083.91	−	801.319i	−1.87527	−	1.38637i
$579$	318.332			0.549797
$580$		0			0
$581$		−	3.57909i		−	0.00616023i
$582$	196.083	+	144.962i	0.336913	+	0.249075i
$583$	−90.7305	+	90.7305i	−0.155627	+	0.155627i
$584$	−333.149	+	159.439i	−0.570460	+	0.273012i
$585$		0			0
$586$	401.137	−	60.1291i	0.684535	−	0.102609i
$587$	−163.733	+	163.733i	−0.278932	+	0.278932i	−0.832682	−	0.553751i	$-0.813196\pi$
$587$	−163.733	+	163.733i	−0.278932	+	0.278932i	0.553751	+	0.832682i	$0.313196\pi$
$588$	−65.4965	−	34.7519i	−0.111389	−	0.0591019i
$589$	43.4114			0.0737035
$590$		0			0
$591$	20.0173			0.0338702
$592$	−82.4889	+	428.355i	−0.139339	+	0.723572i
$593$	−280.606	+	280.606i	−0.473198	+	0.473198i	−0.902948	−	0.429750i	$-0.858602\pi$
$593$	−280.606	+	280.606i	−0.473198	+	0.473198i	0.429750	+	0.902948i	$0.358602\pi$
$594$	−92.2115	+	13.8222i	−0.155238	+	0.0232697i
$595$		0			0
$596$	92.5370	+	301.734i	0.155263	+	0.506265i
$597$	310.800	−	310.800i	0.520603	−	0.520603i
$598$	−319.566	+	432.263i	−0.534392	+	0.722848i
$599$			639.232i			1.06716i	0.845748	+	0.533582i	$0.179155\pi$
$599$			639.232i			1.06716i	−0.845748	+	0.533582i	$0.820845\pi$
$600$		0			0
$601$	−332.979			−0.554041			−0.277021	−	0.960864i	$-0.589347\pi$
$601$	−332.979			−0.554041			−0.277021	+	0.960864i	$0.589347\pi$
$602$	−551.482	−	407.704i	−0.916084	−	0.677249i
$603$	75.2619	+	75.2619i	0.124812	+	0.124812i
$604$	−231.704	−	755.514i	−0.383617	−	1.25085i
$605$		0			0
$606$	−161.106	−	1074.78i	−0.265851	−	1.77356i
$607$	−681.745	−	681.745i	−1.12314	−	1.12314i	−0.991267	−	0.131873i	$-0.957901\pi$
$607$	−681.745	−	681.745i	−1.12314	−	1.12314i	−0.131873	−	0.991267i	$-0.542099\pi$
$608$	−23.2826	+	561.333i	−0.0382938	+	0.923245i
$609$			27.5501i			0.0452382i
$610$		0			0
$611$			448.981i			0.734830i
$612$	−412.758	−	219.006i	−0.674442	−	0.357853i
$613$	378.926	+	378.926i	0.618150	+	0.618150i	0.945057	−	0.326907i	$-0.106006\pi$
$613$	378.926	+	378.926i	0.618150	+	0.618150i	−0.326907	+	0.945057i	$0.606006\pi$
$614$	−150.005	−	1000.72i	−0.244308	−	1.62984i
$615$		0			0
$616$	132.395	−	63.3617i	0.214927	−	0.102860i
$617$	68.3041	+	68.3041i	0.110704	+	0.110704i	0.760289	−	0.649585i	$-0.225057\pi$
$617$	68.3041	+	68.3041i	0.110704	+	0.110704i	−0.649585	+	0.760289i	$0.725057\pi$
$618$	724.818	−	980.429i	1.17284	−	1.58645i
$619$	−1009.69			−1.63116			−0.815580	−	0.578645i	$-0.803582\pi$
$619$	−1009.69			−1.63116			−0.815580	+	0.578645i	$0.803582\pi$
$620$		0			0
$621$		−	533.810i		−	0.859597i
$622$	452.042	−	611.456i	0.726755	−	0.983049i
$623$	−439.648	+	439.648i	−0.705694	+	0.705694i
$624$	−301.845	−	445.824i	−0.483725	−	0.714462i
$625$		0			0
$626$	−113.542	−	757.470i	−0.181377	−	1.21002i
$627$	110.545	−	110.545i	0.176308	−	0.176308i
$628$	470.273	+	249.523i	0.748842	+	0.397329i
$629$	−846.054			−1.34508
$630$		0			0
$631$	−867.965			−1.37554			−0.687769	−	0.725929i	$-0.741410\pi$
$631$	−867.965			−1.37554			−0.687769	+	0.725929i	$0.741410\pi$
$632$	43.6668	−	123.826i	0.0690930	−	0.195927i
$633$	−691.837	+	691.837i	−1.09295	+	1.09295i
$634$	−100.184	−	668.355i	−0.158019	−	1.05419i
$635$		0			0
$636$	703.391	−	215.719i	1.10596	−	0.339181i
$637$	34.5532	−	34.5532i	0.0542437	−	0.0542437i
$638$	−4.19885	−	3.10415i	−0.00658127	−	0.00486545i
$639$		−	82.1949i		−	0.128631i
$640$		0			0
$641$	116.032			0.181017			0.0905083	−	0.995896i	$-0.471151\pi$
$641$	116.032			0.181017			0.0905083	+	0.995896i	$0.471151\pi$
$642$	−452.220	+	611.697i	−0.704392	+	0.952799i
$643$	−429.493	−	429.493i	−0.667951	−	0.667951i	0.289290	−	0.957241i	$-0.406581\pi$
$643$	−429.493	−	429.493i	−0.667951	−	0.667951i	−0.957241	+	0.289290i	$0.906581\pi$
$644$	246.378	+	803.361i	0.382575	+	1.24745i
$645$		0			0
$646$	−1077.60	+	161.528i	−1.66811	+	0.250044i
$647$	−511.695	−	511.695i	−0.790873	−	0.790873i	0.190763	−	0.981636i	$-0.438904\pi$
$647$	−511.695	−	511.695i	−0.790873	−	0.790873i	−0.981636	+	0.190763i	$0.938904\pi$
$648$	759.810	+	267.945i	1.17255	+	0.413495i
$649$			76.2571i			0.117499i
$650$		0			0
$651$			65.0297i			0.0998920i
$652$	−352.580	+	664.503i	−0.540766	+	1.01918i
$653$	−777.556	−	777.556i	−1.19074	−	1.19074i	−0.976859	−	0.213886i	$-0.931388\pi$
$653$	−777.556	−	777.556i	−1.19074	−	1.19074i	−0.213886	−	0.976859i	$-0.568612\pi$
$654$	−83.8186	+	12.5641i	−0.128163	+	0.0192112i
$655$		0			0
$656$	582.179	−	394.163i	0.887468	−	0.600859i
$657$	−122.888	−	122.888i	−0.187044	−	0.187044i
$658$	564.349	+	417.216i	0.857673	+	0.634067i
$659$	−734.265			−1.11421			−0.557105	−	0.830442i	$-0.688088\pi$
$659$	−734.265			−1.11421			−0.557105	+	0.830442i	$0.688088\pi$
$660$		0			0
$661$			799.237i			1.20913i	0.796555	+	0.604567i	$0.206654\pi$
$661$			799.237i			1.20913i	−0.796555	+	0.604567i	$0.793346\pi$
$662$	−117.518	−	86.8791i	−0.177519	−	0.131237i
$663$	738.369	−	738.369i	1.11368	−	1.11368i
$664$	−1.67913	−	3.50855i	−0.00252880	−	0.00528395i
$665$		0			0
$666$	−202.996	+	30.4284i	−0.304799	+	0.0456883i
$667$	21.1384	−	21.1384i	0.0316918	−	0.0316918i
$668$	136.310	−	256.902i	0.204057	−	0.384584i
$669$	651.130			0.973288
$670$		0			0
$671$	−59.4096			−0.0885388
$672$	−840.870	−	34.8771i	−1.25130	−	0.0519005i
$673$	185.806	−	185.806i	0.276087	−	0.276087i	−0.555458	−	0.831545i	$-0.687457\pi$
$673$	185.806	−	185.806i	0.276087	−	0.276087i	0.831545	+	0.555458i	$0.187457\pi$
$674$	−581.622	+	87.1832i	−0.862940	+	0.129352i
$675$		0			0
$676$	−307.053	+	94.1682i	−0.454220	+	0.139302i
$677$	−448.763	+	448.763i	−0.662870	+	0.662870i	−0.956055	−	0.293186i	$-0.905285\pi$
$677$	−448.763	+	448.763i	−0.662870	+	0.662870i	0.293186	+	0.956055i	$0.405285\pi$
$678$	492.649	−	666.385i	0.726621	−	0.982868i
$679$			251.214i			0.369977i
$680$		0			0
$681$	−1225.03			−1.79886
$682$	−9.91105	−	7.32711i	−0.0145323	−	0.0107436i
$683$	−67.1358	−	67.1358i	−0.0982955	−	0.0982955i	0.656249	−	0.754544i	$-0.272142\pi$
$683$	−67.1358	−	67.1358i	−0.0982955	−	0.0982955i	−0.754544	+	0.656249i	$0.772142\pi$
$684$	−252.741	+	77.5118i	−0.369505	+	0.113321i
$685$		0			0
$686$	95.6181	+	637.893i	0.139385	+	0.929873i
$687$	−974.315	−	974.315i	−1.41822	−	1.41822i
$688$	−731.886	−	140.940i	−1.06379	−	0.204855i
$689$			484.884i			0.703751i
$690$		0			0
$691$		−	533.282i		−	0.771753i	−0.922550	−	0.385877i	$-0.873899\pi$
$691$		−	533.282i		−	0.771753i	0.922550	−	0.385877i	$-0.126101\pi$
$692$	485.636	−	915.274i	0.701787	−	1.32265i
$693$	48.8361	+	48.8361i	0.0704706	+	0.0704706i
$694$	63.1097	+	421.021i	0.0909362	+	0.606659i
$695$		0			0
$696$	12.9251	+	27.0070i	0.0185705	+	0.0388032i
$697$	964.199	+	964.199i	1.38336	+	1.38336i
$698$	−189.990	+	256.991i	−0.272192	+	0.368181i
$699$	50.0625			0.0716201
$700$		0			0
$701$		−	1203.60i		−	1.71697i	−0.512835	−	0.858487i	$-0.671405\pi$
$701$		−	1203.60i		−	1.71697i	0.512835	−	0.858487i	$-0.328595\pi$
$702$	−209.465	+	283.334i	−0.298383	+	0.403610i
$703$	−338.469	+	338.469i	−0.481464	+	0.481464i
$704$	100.059	−	124.226i	0.142129	−	0.176457i
$705$		0			0
$706$	−13.3719	−	89.2075i	−0.0189404	−	0.126356i
$707$	791.683	−	791.683i	1.11978	−	1.11978i
$708$	204.939	−	386.246i	0.289462	−	0.545546i
$709$	456.445			0.643788			0.321894	−	0.946776i	$-0.395681\pi$
$709$	456.445			0.643788			0.321894	+	0.946776i	$0.395681\pi$
$710$		0			0
$711$	61.7825			0.0868952
$712$	−224.722	+	637.242i	−0.315620	+	0.895003i
$713$	49.8956	−	49.8956i	0.0699798	−	0.0699798i
$714$	−241.967	−	1614.23i	−0.338890	−	2.26082i
$715$		0			0
$716$	−36.7642	−	119.877i	−0.0513467	−	0.167425i
$717$	113.024	−	113.024i	0.157635	−	0.157635i
$718$	601.662	+	444.800i	0.837969	+	0.619499i
$719$		−	63.2841i		−	0.0880168i	−0.999031	−	0.0440084i	$-0.985987\pi$
$719$		−	63.2841i		−	0.0880168i	0.999031	−	0.0440084i	$-0.0140128\pi$
$720$		0			0
$721$	1256.09			1.74215
$722$	62.7297	−	84.8517i	0.0868833	−	0.117523i
$723$	54.2610	+	54.2610i	0.0750498	+	0.0750498i
$724$	−219.569	+	67.3383i	−0.303272	+	0.0930087i
$725$		0			0
$726$	811.151	−	121.589i	1.11729	−	0.167478i
$727$	−408.139	−	408.139i	−0.561401	−	0.561401i	0.368304	−	0.929705i	$-0.379939\pi$
$727$	−408.139	−	408.139i	−0.561401	−	0.561401i	−0.929705	+	0.368304i	$0.879939\pi$
$728$	184.464	−	523.084i	0.253385	−	0.718522i
$729$		−	222.361i		−	0.305021i
$730$		0			0
$731$		−	1445.57i		−	1.97752i
$732$	300.913	+	159.662i	0.411083	+	0.218117i
$733$	−90.0317	−	90.0317i	−0.122826	−	0.122826i	0.643022	−	0.765848i	$-0.277681\pi$
$733$	−90.0317	−	90.0317i	−0.122826	−	0.122826i	−0.765848	+	0.643022i	$0.777681\pi$
$734$	547.616	−	82.0858i	0.746071	−	0.111834i
$735$		0			0
$736$	618.418	+	671.938i	0.840241	+	0.912959i
$737$	−49.8304	−	49.8304i	−0.0676125	−	0.0676125i
$738$	266.020	+	196.665i	0.360461	+	0.266484i
$739$	875.498			1.18471			0.592353	−	0.805679i	$-0.298199\pi$
$739$	875.498			1.18471			0.592353	+	0.805679i	$0.298199\pi$
$740$		0			0
$741$		−	590.779i		−	0.797272i
$742$	609.478	+	450.579i	0.821399	+	0.607250i
$743$	−282.061	+	282.061i	−0.379624	+	0.379624i	−0.870967	−	0.491342i	$-0.836506\pi$
$743$	−282.061	+	282.061i	−0.379624	+	0.379624i	0.491342	+	0.870967i	$0.336506\pi$
$744$	30.5086	+	63.7479i	0.0410062	+	0.0856827i
$745$		0			0
$746$	−957.816	+	143.573i	−1.28394	+	0.192458i
$747$	1.29419	−	1.29419i	0.00173251	−	0.00173251i
$748$	273.285	+	145.002i	0.365354	+	0.193854i
$749$	−783.683			−1.04631
$750$		0			0
$751$	606.986			0.808237			0.404119	−	0.914707i	$-0.367578\pi$
$751$	606.986			0.808237			0.404119	+	0.914707i	$0.367578\pi$
$752$	748.962	+	144.229i	0.995960	+	0.191793i
$753$	−378.063	+	378.063i	−0.502075	+	0.502075i
$754$	−19.5145	+	2.92515i	−0.0258812	+	0.00387951i
$755$		0			0
$756$	161.493	+	526.577i	0.213615	+	0.696530i
$757$	−173.075	+	173.075i	−0.228633	+	0.228633i	−0.812121	−	0.583488i	$-0.801687\pi$
$757$	−173.075	+	173.075i	−0.228633	+	0.228633i	0.583488	+	0.812121i	$0.301687\pi$
$758$	721.749	−	976.277i	0.952175	−	1.28796i
$759$		−	254.114i		−	0.334801i
$760$		0			0
$761$	100.678			0.132297			0.0661483	−	0.997810i	$-0.478929\pi$
$761$	100.678			0.132297			0.0661483	+	0.997810i	$0.478929\pi$
$762$	453.895	+	335.559i	0.595663	+	0.440366i
$763$	−61.7409	−	61.7409i	−0.0809187	−	0.0809187i
$764$	−189.907	−	619.228i	−0.248570	−	0.810507i
$765$		0			0
$766$	64.8582	+	432.686i	0.0846713	+	0.564864i
$767$	203.768	+	203.768i	0.265668	+	0.265668i
$768$	−840.659	+	360.303i	−1.09461	+	0.469145i
$769$		−	370.732i		−	0.482097i	−0.970513	−	0.241048i	$-0.922509\pi$
$769$		−	370.732i		−	0.482097i	0.970513	−	0.241048i	$-0.0774913\pi$
$770$		0			0
$771$			1233.06i			1.59930i
$772$	314.831	+	167.047i	0.407812	+	0.216382i
$773$	−319.455	−	319.455i	−0.413267	−	0.413267i	0.469608	−	0.882875i	$-0.344395\pi$
$773$	−319.455	−	319.455i	−0.413267	−	0.413267i	−0.882875	+	0.469608i	$0.844395\pi$
$774$	−51.9900	−	346.839i	−0.0671705	−	0.448112i
$775$		0			0
$776$	117.857	+	246.263i	0.151877	+	0.317349i
$777$	−507.023	−	507.023i	−0.652539	−	0.652539i
$778$	−384.897	+	520.633i	−0.494726	+	0.669194i
$779$	771.468			0.990331
$780$		0			0
$781$			54.4207i			0.0696808i
$782$	−1052.90	+	1424.21i	−1.34642	+	1.82124i
$783$	13.8556	−	13.8556i	0.0176955	−	0.0176955i
$784$	−46.5398	−	68.7393i	−0.0593620	−	0.0876776i
$785$		0			0
$786$	160.602	+	1071.42i	0.204328	+	1.36313i
$787$	−1104.16	+	1104.16i	−1.40300	+	1.40300i	−0.612627	+	0.790372i	$0.709887\pi$
$787$	−1104.16	+	1104.16i	−1.40300	+	1.40300i	−0.790372	+	0.612627i	$0.790113\pi$
$788$	19.7971	+	10.5042i	0.0251232	+	0.0133302i
$789$	−1220.49			−1.54688
$790$		0			0
$791$	853.747			1.07933
$792$	70.7849	+	24.9621i	0.0893749	+	0.0315178i
$793$	−158.749	+	158.749i	−0.200188	+	0.200188i
$794$	157.725	+	1052.23i	0.198646	+	1.32522i
$795$		0			0
$796$	470.476	−	144.287i	0.591050	−	0.181266i
$797$	434.605	−	434.605i	0.545301	−	0.545301i	−0.379777	−	0.925078i	$-0.623999\pi$
$797$	434.605	−	434.605i	0.545301	−	0.545301i	0.925078	+	0.379777i	$0.123999\pi$
$798$	−742.583	−	548.982i	−0.930555	−	0.687947i
$799$			1479.29i			1.85143i
$800$		0			0
$801$	−317.950			−0.396942
$802$	477.671	−	646.124i	0.595600	−	0.805641i
$803$	81.3631	+	81.3631i	0.101324	+	0.101324i
$804$	118.476	+	386.312i	0.147358	+	0.480488i
$805$		0			0
$806$	−46.0623	+	6.90459i	−0.0571493	+	0.00856649i
$807$	885.768	+	885.768i	1.09761	+	1.09761i
$808$	404.662	−	1147.50i	0.500819	−	1.42017i
$809$		−	164.175i		−	0.202935i	−0.994839	−	0.101468i	$-0.967646\pi$
$809$		−	164.175i		−	0.202935i	0.994839	−	0.101468i	$-0.0323538\pi$
$810$		0			0
$811$		−	1283.08i		−	1.58210i	−0.611752	−	0.791049i	$-0.709535\pi$
$811$		−	1283.08i		−	1.58210i	0.611752	−	0.791049i	$-0.290465\pi$
$812$	−14.4570	+	27.2470i	−0.0178042	+	0.0335554i
$813$	754.377	+	754.377i	0.927893	+	0.927893i
$814$	134.402	−	20.1465i	0.165113	−	0.0247500i
$815$		0			0
$816$	−994.511	−	1468.89i	−1.21876	−	1.80011i
$817$	−578.308	−	578.308i	−0.707843	−	0.707843i
$818$	268.382	+	198.411i	0.328095	+	0.242556i
$819$	260.991			0.318671
$820$		0			0
$821$			1292.43i			1.57421i	0.616817	+	0.787106i	$0.288422\pi$
$821$			1292.43i			1.57421i	−0.616817	+	0.787106i	$0.711578\pi$
$822$	−554.561	−	409.979i	−0.674648	−	0.498758i
$823$	−38.6290	+	38.6290i	−0.0469368	+	0.0469368i	−0.730186	−	0.683249i	$-0.760566\pi$
$823$	−38.6290	+	38.6290i	−0.0469368	+	0.0469368i	0.683249	+	0.730186i	$0.260566\pi$
$824$	1231.33	−	589.292i	1.49433	−	0.715160i
$825$		0			0
$826$	445.478	−	66.7757i	0.539320	−	0.0808422i
$827$	−432.150	+	432.150i	−0.522552	+	0.522552i	−0.918341	−	0.395789i	$-0.870471\pi$
$827$	−432.150	+	432.150i	−0.522552	+	0.522552i	0.395789	+	0.918341i	$0.370471\pi$
$828$	−201.403	+	379.582i	−0.243241	+	0.458433i
$829$	684.217			0.825353			0.412676	−	0.910878i	$-0.364594\pi$
$829$	684.217			0.825353			0.412676	+	0.910878i	$0.364594\pi$
$830$		0			0
$831$	−1393.49			−1.67689
$832$	−64.5758	−	599.315i	−0.0776151	−	0.720330i
$833$	113.845	−	113.845i	0.136669	−	0.136669i
$834$	−492.708	+	73.8553i	−0.590777	+	0.0885556i
$835$		0			0
$836$	167.338	−	51.3201i	0.200166	−	0.0613876i
$837$	32.7049	−	32.7049i	0.0390740	−	0.0390740i
$838$	−634.533	+	858.304i	−0.757199	+	1.02423i
$839$		−	579.065i		−	0.690184i	−0.938569	−	0.345092i	$-0.887848\pi$
$839$		−	579.065i		−	0.690184i	0.938569	−	0.345092i	$-0.112152\pi$
$840$		0			0
$841$	−839.903			−0.998695
$842$	−345.003	−	255.056i	−0.409742	−	0.302917i
$843$	−33.5642	−	33.5642i	−0.0398151	−	0.0398151i
$844$	−1047.27	+	321.182i	−1.24084	+	0.380547i
$845$		0			0
$846$	53.2029	+	354.931i	0.0628876	+	0.419540i
$847$	597.495	+	597.495i	0.705426	+	0.705426i
$848$	808.854	+	155.762i	0.953837	+	0.183682i
$849$			1279.26i			1.50679i
$850$		0			0
$851$			778.051i			0.914279i
$852$	146.254	−	275.644i	0.171660	−	0.323526i
$853$	89.6610	+	89.6610i	0.105113	+	0.105113i	0.757707	−	0.652595i	$-0.226320\pi$
$853$	89.6610	+	89.6610i	0.105113	+	0.105113i	−0.652595	+	0.757707i	$0.726320\pi$
$854$	52.0229	+	347.058i	0.0609167	+	0.406391i
$855$		0			0
$856$	−768.237	+	367.664i	−0.897473	+	0.429514i
$857$	409.705	+	409.705i	0.478069	+	0.478069i	0.904514	−	0.426445i	$-0.140234\pi$
$857$	409.705	+	409.705i	0.478069	+	0.478069i	−0.426445	+	0.904514i	$0.640234\pi$
$858$	−99.7135	+	134.878i	−0.116216	+	0.157201i
$859$	−799.305			−0.930507			−0.465253	−	0.885178i	$-0.654037\pi$
$859$	−799.305			−0.930507			−0.465253	+	0.885178i	$0.654037\pi$
$860$		0			0
$861$			1155.65i			1.34222i
$862$	624.637	−	844.918i	0.724637	−	0.980184i
$863$	−1116.04	+	1116.04i	−1.29321	+	1.29321i	−0.360414	+	0.932793i	$0.617364\pi$
$863$	−1116.04	+	1116.04i	−1.29321	+	1.29321i	−0.932793	+	0.360414i	$0.882636\pi$
$864$	405.352	+	440.433i	0.469158	+	0.509761i
$865$		0			0
$866$	110.201	+	735.178i	0.127253	+	0.848935i
$867$	1702.66	−	1702.66i	1.96386	−	1.96386i
$868$	−34.1247	+	64.3144i	−0.0393142	+	0.0740949i
$869$	−40.9058			−0.0470723
$870$		0			0
$871$	−266.305			−0.305746
$872$	−89.4897	−	31.5583i	−0.102626	−	0.0361907i
$873$	−90.8383	+	90.8383i	−0.104053	+	0.104053i
$874$	148.545	+	990.984i	0.169960	+	1.13385i
$875$		0			0
$876$	−193.447	−	630.770i	−0.220830	−	0.720058i
$877$	−98.3606	+	98.3606i	−0.112156	+	0.112156i	−0.760957	−	0.648802i	$-0.775270\pi$
$877$	−98.3606	+	98.3606i	−0.112156	+	0.112156i	0.648802	+	0.760957i	$0.275270\pi$
$878$	674.082	+	498.340i	0.767747	+	0.567585i
$879$			724.582i			0.824326i
$880$		0			0
$881$	−654.962			−0.743430			−0.371715	−	0.928347i	$-0.621230\pi$
$881$	−654.962			−0.743430			−0.371715	+	0.928347i	$0.621230\pi$
$882$	23.2207	−	31.4097i	0.0263274	−	0.0356119i
$883$	−963.144	−	963.144i	−1.09076	−	1.09076i	−0.995447	−	0.0953158i	$-0.969614\pi$
$883$	−963.144	−	963.144i	−1.09076	−	1.09076i	−0.0953158	−	0.995447i	$-0.530386\pi$
$884$	1117.71	−	342.784i	1.26438	−	0.387765i
$885$		0			0
$886$	333.520	−	49.9935i	0.376433	−	0.0564260i
$887$	588.066	+	588.066i	0.662983	+	0.662983i	0.956082	−	0.293099i	$-0.0946866\pi$
$887$	588.066	+	588.066i	0.662983	+	0.662983i	−0.293099	+	0.956082i	$0.594687\pi$
$888$	−734.899	−	259.160i	−0.827588	−	0.291847i
$889$			581.514i			0.654121i
$890$		0			0
$891$		−	251.003i		−	0.281709i
$892$	643.968	+	341.684i	0.721937	+	0.383054i
$893$	591.801	+	591.801i	0.662711	+	0.662711i
$894$	−557.556	+	83.5758i	−0.623664	+	0.0934852i
$895$		0			0
$896$	−813.319	−	475.745i	−0.907722	−	0.530965i
$897$	−679.022	−	679.022i	−0.756992	−	0.756992i
$898$	958.619	+	708.694i	1.06750	+	0.789192i
$899$	2.59018			0.00288118
$900$		0			0
$901$			1597.59i			1.77313i
$902$	−176.130	−	130.211i	−0.195267	−	0.144358i
$903$	866.299	−	866.299i	0.959356	−	0.959356i
$904$	836.919	−	400.534i	0.925795	−	0.443069i
$905$		0			0
$906$	1396.07	−	209.266i	1.54092	−	0.230978i
$907$	692.104	−	692.104i	0.763069	−	0.763069i	−0.213807	−	0.976876i	$-0.568586\pi$
$907$	692.104	−	692.104i	0.763069	−	0.763069i	0.976876	+	0.213807i	$0.0685863\pi$
$908$	−1211.55	−	642.839i	−1.33431	−	0.707973i
$909$	572.540			0.629857
$910$		0			0
$911$	−45.1707			−0.0495836			−0.0247918	−	0.999693i	$-0.507892\pi$
$911$	−45.1707			−0.0495836			−0.0247918	+	0.999693i	$0.507892\pi$
$912$	−985.500	−	189.779i	−1.08059	−	0.208091i
$913$	−0.856873	+	0.856873i	−0.000938525	+	0.000938525i
$914$	403.573	−	60.4943i	0.441546	−	0.0661863i
$915$		0			0
$916$	−452.321	−	1474.87i	−0.493800	−	1.61013i
$917$	−789.209	+	789.209i	−0.860643	+	0.860643i
$918$	−690.141	+	933.523i	−0.751788	+	1.01691i
$919$		−	1598.45i		−	1.73934i	−0.493637	−	0.869668i	$-0.664333\pi$
$919$		−	1598.45i		−	1.73934i	0.493637	−	0.869668i	$-0.335667\pi$
$920$		0			0
$921$	1807.62			1.96268
$922$	1196.52	+	884.568i	1.29774	+	0.959402i
$923$	145.418	+	145.418i	0.157550	+	0.157550i
$924$	76.8769	+	250.671i	0.0832001	+	0.271289i
$925$		0			0
$926$	−187.220	−	1248.99i	−0.202181	−	1.34880i
$927$	454.197	+	454.197i	0.489965	+	0.489965i
$928$	−1.38918	+	33.4925i	−0.00149696	+	0.0360910i
$929$		−	887.585i		−	0.955420i	−0.878518	−	0.477710i	$-0.841467\pi$
$929$		−	887.585i		−	0.955420i	0.878518	−	0.477710i	$-0.158533\pi$
$930$		0			0
$931$		−	91.0891i		−	0.0978400i
$932$	49.5118	+	26.2705i	0.0531242	+	0.0281873i
$933$	960.509	+	960.509i	1.02948	+	1.02948i
$934$	2.35604	+	15.7178i	0.00252253	+	0.0168285i
$935$		0			0
$936$	255.847	−	122.444i	0.273341	−	0.130816i
$937$	−1241.34	−	1241.34i	−1.32480	−	1.32480i	−0.909841	−	0.414958i	$-0.863796\pi$
$937$	−1241.34	−	1241.34i	−1.32480	−	1.32480i	−0.414958	−	0.909841i	$-0.636204\pi$
$938$	−247.464	+	334.734i	−0.263821	+	0.356859i
$939$	1368.23			1.45712
$940$		0			0
$941$			328.028i			0.348595i	0.984693	+	0.174298i	$0.0557654\pi$
$941$			328.028i			0.348595i	−0.984693	+	0.174298i	$0.944235\pi$
$942$	−565.347	+	764.719i	−0.600156	+	0.811804i
$943$	886.700	−	886.700i	0.940297	−	0.940297i
$944$	405.370	−	274.455i	0.429417	−	0.290736i
$945$		0			0
$946$	34.4222	+	229.640i	0.0363871	+	0.242748i
$947$	−228.351	+	228.351i	−0.241131	+	0.241131i	−0.817318	−	0.576187i	$-0.804540\pi$
$947$	−228.351	+	228.351i	−0.241131	+	0.241131i	0.576187	+	0.817318i	$0.304540\pi$
$948$	207.190	+	109.933i	0.218555	+	0.115963i
$949$	434.823			0.458191
$950$		0			0
$951$	1207.26			1.26947
$952$	607.769	−	1723.45i	0.638412	−	1.81034i
$953$	1291.50	−	1291.50i	1.35519	−	1.35519i	0.475451	−	0.879742i	$-0.342285\pi$
$953$	1291.50	−	1291.50i	1.35519	−	1.35519i	0.879742	−	0.475451i	$-0.157715\pi$
$954$	57.4574	+	383.313i	0.0602279	+	0.401796i
$955$		0			0
$956$	171.091	−	52.4710i	0.178966	−	0.0548860i
$957$	6.59578	−	6.59578i	0.00689215	−	0.00689215i
$958$	−1230.84	−	909.947i	−1.28481	−	0.949840i
$959$		−	710.482i		−	0.740857i
$960$		0			0
$961$	−954.886			−0.993638
$962$	305.305	−	412.972i	0.317365	−	0.429285i
$963$	−283.377	−	283.377i	−0.294265	−	0.294265i
$964$	25.1904	+	82.1379i	0.0261311	+	0.0852053i
$965$		0			0
$966$	−1484.48	+	222.519i	−1.53673	+	0.230351i
$967$	−486.969	−	486.969i	−0.503588	−	0.503588i	0.408963	−	0.912551i	$-0.365890\pi$
$967$	−486.969	−	486.969i	−0.503588	−	0.503588i	−0.912551	+	0.408963i	$0.865890\pi$
$968$	866.033	+	305.404i	0.894662	+	0.315500i
$969$		−	1946.49i		−	2.00876i
$970$		0			0
$971$		−	361.550i		−	0.372348i	−0.982517	−	0.186174i	$-0.940391\pi$
$971$		−	361.550i		−	0.372348i	0.982517	−	0.186174i	$-0.0596088\pi$
$972$	−358.943	+	676.495i	−0.369282	+	0.695983i
$973$	−362.930	−	362.930i	−0.373001	−	0.373001i
$974$	−1709.98	+	256.320i	−1.75562	+	0.263162i
$975$		0			0
$976$	213.819	+	315.811i	0.219077	+	0.323577i
$977$	1073.65	+	1073.65i	1.09892	+	1.09892i	0.994537	+	0.104387i	$0.0332881\pi$
$977$	1073.65	+	1073.65i	1.09892	+	1.09892i	0.104387	+	0.994537i	$0.466712\pi$
$978$	−1080.56	−	798.844i	−1.10487	−	0.816814i
$979$	210.513			0.215028
$980$		0			0
$981$		−	44.6506i		−	0.0455154i
$982$	−1446.14	−	1069.11i	−1.47265	−	1.08871i
$983$	−122.156	+	122.156i	−0.124269	+	0.124269i	−0.766506	−	0.642237i	$-0.778006\pi$
$983$	−122.156	+	122.156i	−0.124269	+	0.124269i	0.642237	+	0.766506i	$0.278006\pi$
$984$	542.172	+	1132.87i	0.550988	+	1.15129i
$985$		0			0
$986$	−64.2958	+	9.63773i	−0.0652088	+	0.00977458i
$987$	−886.510	+	886.510i	−0.898187	+	0.898187i
$988$	310.014	−	584.280i	0.313780	−	0.591377i
$989$	−1329.38			−1.34416
$990$		0			0
$991$	324.300			0.327245			0.163623	−	0.986523i	$-0.447682\pi$
$991$	324.300			0.327245			0.163623	+	0.986523i	$0.447682\pi$
$992$	−3.27905	+	79.0563i	−0.00330549	+	0.0796938i
$993$	184.603	−	184.603i	0.185904	−	0.185904i
$994$	317.914	−	47.6543i	0.319833	−	0.0479420i
$995$		0			0
$996$	6.64294	−	2.03728i	0.00666962	−	0.00204547i
$997$	743.909	−	743.909i	0.746148	−	0.746148i	−0.227606	−	0.973753i	$-0.573090\pi$
$997$	743.909	−	743.909i	0.746148	−	0.746148i	0.973753	+	0.227606i	$0.0730897\pi$
$998$	898.070	−	1214.78i	0.899869	−	1.21721i
$999$			509.987i			0.510498i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.3.i.b.157.3		20
4.3	odd	2		800.3.m.b.657.8		20
5.2	odd	4		40.3.i.a.13.2	✓	20
5.3	odd	4	inner	200.3.i.b.93.9		20
5.4	even	2		40.3.i.a.37.8	yes	20
8.3	odd	2		800.3.m.b.657.3		20
8.5	even	2	inner	200.3.i.b.157.9		20
15.2	even	4		360.3.u.b.253.9		20
15.14	odd	2		360.3.u.b.37.3		20
20.3	even	4		800.3.m.b.593.3		20
20.7	even	4		160.3.m.a.113.8		20
20.19	odd	2		160.3.m.a.17.3		20
40.3	even	4		800.3.m.b.593.8		20
40.13	odd	4	inner	200.3.i.b.93.3		20
40.19	odd	2		160.3.m.a.17.8		20
40.27	even	4		160.3.m.a.113.3		20
40.29	even	2		40.3.i.a.37.2	yes	20
40.37	odd	4		40.3.i.a.13.8	yes	20
120.29	odd	2		360.3.u.b.37.9		20
120.77	even	4		360.3.u.b.253.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.2	✓	20	5.2	odd	4
40.3.i.a.13.8	yes	20	40.37	odd	4
40.3.i.a.37.2	yes	20	40.29	even	2
40.3.i.a.37.8	yes	20	5.4	even	2
160.3.m.a.17.3		20	20.19	odd	2
160.3.m.a.17.8		20	40.19	odd	2
160.3.m.a.113.3		20	40.27	even	4
160.3.m.a.113.8		20	20.7	even	4
200.3.i.b.93.3		20	40.13	odd	4	inner
200.3.i.b.93.9		20	5.3	odd	4	inner
200.3.i.b.157.3		20	1.1	even	1	trivial
200.3.i.b.157.9		20	8.5	even	2	inner
360.3.u.b.37.3		20	15.14	odd	2
360.3.u.b.37.9		20	120.29	odd	2
360.3.u.b.253.3		20	120.77	even	4
360.3.u.b.253.9		20	15.2	even	4
800.3.m.b.593.3		20	20.3	even	4
800.3.m.b.593.8		20	40.3	even	4
800.3.m.b.657.3		20	8.3	odd	2
800.3.m.b.657.8		20	4.3	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	200.3.i.b.157.3

Level	$200$
Weight	$3$
Character	200.157
Analytic conductor	$5.450$
Analytic rank	$0$
Dimension	$20$
Inner twists	$4$