LMFDB - Embedded newform 40.3.i.a.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,3,Mod(13,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, 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("40.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	40.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:	$1.08992105744$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.8
Root			$-1.39859 - 0.209644i$ of defining polynomial
Character	$\chi$	$=$	40.37
Dual form			40.3.i.a.13.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18894 - 1.60823i) q^{2} +(2.52630 + 2.52630i) q^{3} +(-1.17282 - 3.82420i) q^{4} +(-3.09141 + 3.92978i) q^{5} +(7.06650 - 1.05925i) q^{6} +(-5.20520 - 5.20520i) q^{7} +(-7.54462 - 2.66059i) q^{8} +3.76437i q^{9} +O(q^{10})$	\(q+(1.18894 - 1.60823i) q^{2} +(2.52630 + 2.52630i) q^{3} +(-1.17282 - 3.82420i) q^{4} +(-3.09141 + 3.92978i) q^{5} +(7.06650 - 1.05925i) q^{6} +(-5.20520 - 5.20520i) q^{7} +(-7.54462 - 2.66059i) q^{8} +3.76437i q^{9} +(2.64449 + 9.64400i) q^{10} -2.49236i q^{11} +(6.69817 - 12.6240i) q^{12} +(6.65988 + 6.65988i) q^{13} +(-14.5599 + 2.18248i) q^{14} +(-17.7376 + 2.11798i) q^{15} +(-13.2490 + 8.97020i) q^{16} +(21.9428 + 21.9428i) q^{17} +(6.05398 + 4.47563i) q^{18} -17.5567 q^{19} +(18.6539 + 7.21322i) q^{20} -26.2998i q^{21} +(-4.00830 - 2.96328i) q^{22} +(20.1791 - 20.1791i) q^{23} +(-12.3385 - 25.7814i) q^{24} +(-5.88639 - 24.2971i) q^{25} +(18.6289 - 2.79240i) q^{26} +(13.2268 - 13.2268i) q^{27} +(-13.8010 + 26.0105i) q^{28} -1.04754 q^{29} +(-17.6828 + 31.0444i) q^{30} -2.47263 q^{31} +(-1.32614 + 31.9725i) q^{32} +(6.29646 - 6.29646i) q^{33} +(61.3780 - 9.20035i) q^{34} +(36.5467 - 4.36391i) q^{35} +(14.3957 - 4.41493i) q^{36} +(-19.2786 + 19.2786i) q^{37} +(-20.8740 + 28.2353i) q^{38} +33.6497i q^{39} +(33.7790 - 21.4237i) q^{40} -43.9414 q^{41} +(-42.2962 - 31.2690i) q^{42} +(-32.9394 - 32.9394i) q^{43} +(-9.53129 + 2.92310i) q^{44} +(-14.7932 - 11.6372i) q^{45} +(-8.46086 - 56.4446i) q^{46} +(33.7079 + 33.7079i) q^{47} +(-56.1323 - 10.8095i) q^{48} +5.18827i q^{49} +(-46.0740 - 19.4213i) q^{50} +110.868i q^{51} +(17.6578 - 33.2795i) q^{52} +(36.4034 + 36.4034i) q^{53} +(-5.54582 - 36.9976i) q^{54} +(9.79445 + 7.70491i) q^{55} +(25.4224 + 53.1202i) q^{56} +(-44.3536 - 44.3536i) q^{57} +(-1.24547 + 1.68469i) q^{58} -30.5963 q^{59} +(28.9027 + 65.3482i) q^{60} -23.8366i q^{61} +(-2.93982 + 3.97657i) q^{62} +(19.5943 - 19.5943i) q^{63} +(49.8425 + 40.1463i) q^{64} +(-46.7603 + 5.58347i) q^{65} +(-2.64003 - 17.6123i) q^{66} +(-19.9932 + 19.9932i) q^{67} +(58.1787 - 109.649i) q^{68} +101.957 q^{69} +(36.4339 - 63.9641i) q^{70} -21.8350 q^{71} +(10.0154 - 28.4007i) q^{72} +(32.6450 - 32.6450i) q^{73} +(8.08328 + 53.9257i) q^{74} +(46.5110 - 76.2526i) q^{75} +(20.5909 + 67.1405i) q^{76} +(-12.9733 + 12.9733i) q^{77} +(54.1165 + 40.0076i) q^{78} -16.4124i q^{79} +(5.70706 - 79.7962i) q^{80} +100.709 q^{81} +(-52.2439 + 70.6680i) q^{82} +(0.343799 + 0.343799i) q^{83} +(-100.576 + 30.8450i) q^{84} +(-154.065 + 18.3963i) q^{85} +(-92.1373 + 13.8111i) q^{86} +(-2.64640 - 2.64640i) q^{87} +(-6.63116 + 18.8039i) q^{88} +84.4631i q^{89} +(-36.3036 + 9.95483i) q^{90} -69.3320i q^{91} +(-100.836 - 53.5025i) q^{92} +(-6.24661 - 6.24661i) q^{93} +(94.2869 - 14.1333i) q^{94} +(54.2751 - 68.9942i) q^{95} +(-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}+O(q^{10}) $ 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8	$ 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31} + 128 q^{32} + 32 q^{33} + 220 q^{36} - 188 q^{38} + 156 q^{40} - 8 q^{41} - 284 q^{42} - 240 q^{46} + 188 q^{47} - 256 q^{48} - 274 q^{50} - 332 q^{52} + 96 q^{55} - 360 q^{56} - 40 q^{57} + 268 q^{58} - 340 q^{60} + 336 q^{62} + 228 q^{63} - 60 q^{65} + 616 q^{66} + 396 q^{68} + 300 q^{70} + 248 q^{71} + 668 q^{72} - 124 q^{73} + 424 q^{76} - 368 q^{78} + 496 q^{80} + 132 q^{81} - 676 q^{82} - 672 q^{86} - 488 q^{87} - 304 q^{88} - 474 q^{90} - 628 q^{92} - 488 q^{95} - 1024 q^{96} + 100 q^{97} + 546 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8 + 6 * q^10 - 44 * q^12 - 4 * q^15 - 56 * q^16 - 12 * q^17 + 10 * q^18 - 24 * q^20 + 92 * q^22 - 4 * q^23 - 28 * q^25 + 100 * q^26 + 68 * q^28 + 100 * q^30 - 136 * q^31 + 128 * q^32 + 32 * q^33 + 220 * q^36 - 188 * q^38 + 156 * q^40 - 8 * q^41 - 284 * q^42 - 240 * q^46 + 188 * q^47 - 256 * q^48 - 274 * q^50 - 332 * q^52 + 96 * q^55 - 360 * q^56 - 40 * q^57 + 268 * q^58 - 340 * q^60 + 336 * q^62 + 228 * q^63 - 60 * q^65 + 616 * q^66 + 396 * q^68 + 300 * q^70 + 248 * q^71 + 668 * q^72 - 124 * q^73 + 424 * q^76 - 368 * q^78 + 496 * q^80 + 132 * q^81 - 676 * q^82 - 672 * q^86 - 488 * q^87 - 304 * q^88 - 474 * q^90 - 628 * q^92 - 488 * q^95 - 1024 * q^96 + 100 * q^97 + 546 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	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	0.989132	−	0.147032i	$-0.0469721\pi$
$3$	2.52630	+	2.52630i	0.842100	+	0.842100i	−0.147032	+	0.989132i	$0.546972\pi$
$4$	−1.17282	−	3.82420i	−0.293205	−	0.956049i
$5$	−3.09141	+	3.92978i	−0.618282	+	0.785957i
$5$	−3.09141	+	3.92978i	−0.618282	+	0.785957i
$6$	7.06650	−	1.05925i	1.17775	−	0.176541i
$7$	−5.20520	−	5.20520i	−0.743600	−	0.743600i	0.229669	−	0.973269i	$-0.426236\pi$
$7$	−5.20520	−	5.20520i	−0.743600	−	0.743600i	−0.973269	+	0.229669i	$0.926236\pi$
$8$	−7.54462	−	2.66059i	−0.943077	−	0.332574i
$9$			3.76437i			0.418263i
$10$	2.64449	+	9.64400i	0.264449	+	0.964400i
$11$		−	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	0.915230	−	0.402932i	$-0.132009\pi$
$13$	6.65988	+	6.65988i	0.512298	+	0.512298i	−0.402932	+	0.915230i	$0.632009\pi$
$14$	−14.5599	+	2.18248i	−1.03999	+	0.155891i
$15$	−17.7376	+	2.11798i	−1.18251	+	0.141199i
$16$	−13.2490	+	8.97020i	−0.828061	+	0.560638i
$17$	21.9428	+	21.9428i	1.29075	+	1.29075i	0.934320	+	0.356434i	$0.116008\pi$
$17$	21.9428	+	21.9428i	1.29075	+	1.29075i	0.356434	+	0.934320i	$0.383992\pi$
$18$	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	$0.652875\pi$
$20$	18.6539	+	7.21322i	0.932697	+	0.360661i
$21$		−	26.2998i		−	1.25237i
$22$	−4.00830	−	2.96328i	−0.182195	−	0.134695i
$23$	20.1791	−	20.1791i	0.877354	−	0.877354i	−0.115906	−	0.993260i	$-0.536977\pi$
$23$	20.1791	−	20.1791i	0.877354	−	0.877354i	0.993260	+	0.115906i	$0.0369772\pi$
$24$	−12.3385	−	25.7814i	−0.514105	−	1.07423i
$25$	−5.88639	−	24.2971i	−0.235455	−	0.971885i
$26$	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	$0.505749\pi$
$30$	−17.6828	+	31.0444i	−0.589428	+	1.03481i
$31$	−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
$35$	36.5467	−	4.36391i	1.04419	−	0.124683i
$36$	14.3957	−	4.41493i	0.399880	−	0.122637i
$37$	−19.2786	+	19.2786i	−0.521043	+	0.521043i	−0.917886	−	0.396843i	$-0.870106\pi$
$37$	−19.2786	+	19.2786i	−0.521043	+	0.521043i	0.396843	+	0.917886i	$0.370106\pi$
$38$	−20.8740	+	28.2353i	−0.549316	+	0.743035i
$39$			33.6497i			0.862813i
$40$	33.7790	−	21.4237i	0.844476	−	0.535593i
$41$	−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	0.211373	−	0.977405i	$-0.432206\pi$
$43$	−32.9394	−	32.9394i	−0.766032	−	0.766032i	−0.977405	+	0.211373i	$0.932206\pi$
$44$	−9.53129	+	2.92310i	−0.216620	+	0.0664340i
$45$	−14.7932	−	11.6372i	−0.328737	−	0.258604i
$46$	−8.46086	−	56.4446i	−0.183932	−	1.22706i
$47$	33.7079	+	33.7079i	0.717189	+	0.717189i	0.968029	−	0.250840i	$-0.0807067\pi$
$47$	33.7079	+	33.7079i	0.717189	+	0.717189i	−0.250840	+	0.968029i	$0.580707\pi$
$48$	−56.1323	−	10.8095i	−1.16942	−	0.225197i
$49$			5.18827i			0.105883i
$50$	−46.0740	−	19.4213i	−0.921480	−	0.388425i
$51$			110.868i			2.17389i
$52$	17.6578	−	33.2795i	0.339574	−	0.639991i
$53$	36.4034	+	36.4034i	0.686856	+	0.686856i	0.961536	−	0.274679i	$-0.0885717\pi$
$53$	36.4034	+	36.4034i	0.686856	+	0.686856i	−0.274679	+	0.961536i	$0.588572\pi$
$54$	−5.54582	−	36.9976i	−0.102700	−	0.685141i
$55$	9.79445	+	7.70491i	0.178081	+	0.140089i
$56$	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	$0.583489\pi$
$60$	28.9027	+	65.3482i	0.481711	+	1.08914i
$61$		−	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
$65$	−46.7603	+	5.58347i	−0.719389	+	0.0858996i
$66$	−2.64003	−	17.6123i	−0.0400004	−	0.266853i
$67$	−19.9932	+	19.9932i	−0.298407	+	0.298407i	−0.840390	−	0.541983i	$-0.817674\pi$
$67$	−19.9932	+	19.9932i	−0.298407	+	0.298407i	0.541983	+	0.840390i	$0.317674\pi$
$68$	58.1787	−	109.649i	0.855569	−	1.61248i
$69$	101.957			1.47764
$70$	36.4339	−	63.9641i	0.520484	−	0.913772i
$71$	−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	−0.447228	−	0.894420i	$-0.647589\pi$
$73$	32.6450	−	32.6450i	0.447191	−	0.447191i	0.894420	+	0.447228i	$0.147589\pi$
$74$	8.08328	+	53.9257i	0.109233	+	0.728725i
$75$	46.5110	−	76.2526i	0.620147	−	1.01670i
$76$	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	$-0.0331246\pi$
$80$	5.70706	−	79.7962i	0.0713383	−	0.997452i
$81$	100.709			1.24332
$82$	−52.2439	+	70.6680i	−0.637121	+	0.861805i
$83$	0.343799	+	0.343799i	0.00414216	+	0.00414216i	0.709175	−	0.705033i	$-0.249068\pi$
$83$	0.343799	+	0.343799i	0.00414216	+	0.00414216i	−0.705033	+	0.709175i	$0.749068\pi$
$84$	−100.576	+	30.8450i	−1.19733	+	0.367202i
$85$	−154.065	+	18.3963i	−1.81253	+	0.216427i
$86$	−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	$0.842625\pi$
$90$	−36.3036	+	9.95483i	−0.403373	+	0.110609i
$91$		−	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
$95$	54.2751	−	68.9942i	0.571316	−	0.726255i
$96$	−84.1223	+	77.4219i	−0.876274	+	0.806478i
$97$	−24.1311	−	24.1311i	−0.248774	−	0.248774i	0.571693	−	0.820467i	$-0.306287\pi$
$97$	−24.1311	−	24.1311i	−0.248774	−	0.248774i	−0.820467	+	0.571693i	$0.806287\pi$
$98$	8.34394	+	6.16856i	0.0851422	+	0.0629445i
$99$	9.38218			0.0947695
$100$	−86.0133	+	51.0069i	−0.860133	+	0.510069i
$101$		−	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	$0.560705\pi$
$103$	−120.657	+	120.657i	−1.17143	+	1.17143i	−0.981870	+	0.189558i	$0.939295\pi$
$104$	−32.5270	−	67.9655i	−0.312760	−	0.653514i
$105$	103.352	+	81.3034i	0.984309	+	0.774318i
$106$	101.827	−	15.2635i	0.960629	−	0.143995i
$107$	75.2789	−	75.2789i	0.703541	−	0.703541i	−0.261628	−	0.965169i	$-0.584259\pi$
$107$	75.2789	−	75.2789i	0.703541	−	0.703541i	0.965169	+	0.261628i	$0.0842594\pi$
$108$	−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	$0.517328\pi$
$110$	24.0363	−	6.59103i	0.218512	−	0.0599185i
$111$	−97.4070			−0.877541
$112$	115.655	+	22.2719i	1.03264	+	0.198856i
$113$	−82.0090	+	82.0090i	−0.725743	+	0.725743i	−0.969769	−	0.244025i	$-0.921532\pi$
$113$	−82.0090	+	82.0090i	−0.725743	+	0.725743i	0.244025	+	0.969769i	$0.421532\pi$
$114$	−124.065	+	18.5969i	−1.08829	+	0.163131i
$115$	16.9177	+	141.682i	0.147110	+	1.23201i
$116$	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
$120$	139.459	+	31.2132i	1.16216	+	0.260110i
$121$	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
$125$	113.680	+	51.9801i	0.909437	+	0.415841i
$126$	−8.21565	−	54.8087i	−0.0652035	−	0.434990i
$127$	−55.8589	−	55.8589i	−0.439834	−	0.439834i	0.452122	−	0.891956i	$-0.350667\pi$
$127$	−55.8589	−	55.8589i	−0.439834	−	0.439834i	−0.891956	+	0.452122i	$0.850667\pi$
$128$	123.825	−	32.4266i	0.967379	−	0.253333i
$129$		−	166.429i		−	1.29015i
$130$	−46.6159	+	81.8398i	−0.358584	+	0.629537i
$131$			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
$135$	11.0890	+	92.8677i	0.0821406	+	0.687909i
$136$	−107.169	−	223.931i	−0.788010	−	1.64655i
$137$	68.2473	+	68.2473i	0.498156	+	0.498156i	0.910863	−	0.412708i	$-0.135417\pi$
$137$	68.2473	+	68.2473i	0.498156	+	0.498156i	−0.412708	+	0.910863i	$0.635417\pi$
$138$	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	$0.580696\pi$
$140$	−59.5512	−	134.644i	−0.425366	−	0.961742i
$141$			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
$145$	3.23837	−	4.11660i	0.0223336	−	0.0283904i
$146$	−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	$0.585296\pi$
$150$	−67.3328	−	165.461i	−0.448885	−	1.10307i
$151$	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
$155$	7.64392	−	9.71691i	0.0493156	−	0.0626897i
$156$	128.683	−	39.4651i	0.824891	−	0.252981i
$157$	94.1106	−	94.1106i	0.599431	−	0.599431i	−0.340730	−	0.940161i	$-0.610674\pi$
$157$	94.1106	−	94.1106i	0.599431	−	0.599431i	0.940161	+	0.340730i	$0.110674\pi$
$158$	−26.3950	−	19.5135i	−0.167057	−	0.123503i
$159$			183.932i			1.15680i
$160$	−121.545	−	104.052i	−0.759659	−	0.650322i
$161$	−210.073			−1.30480
$162$	119.737	−	161.963i	0.739119	−	0.999773i
$163$	132.980	+	132.980i	0.815827	+	0.815827i	0.985500	−	0.169673i	$-0.0542712\pi$
$163$	132.980	+	132.980i	0.815827	+	0.815827i	−0.169673	+	0.985500i	$0.554271\pi$
$164$	51.5354	+	168.041i	0.314240	+	1.02464i
$165$	5.27879	+	44.2086i	0.0319926	+	0.267931i
$166$	0.961668	−	0.144151i	0.00579318	−	0.000868378i
$167$	−51.4111	−	51.4111i	−0.307851	−	0.307851i	0.536225	−	0.844075i	$-0.319850\pi$
$167$	−51.4111	−	51.4111i	−0.307851	−	0.307851i	−0.844075	+	0.536225i	$0.819850\pi$
$168$	−69.9730	+	198.422i	−0.416506	+	1.18108i
$169$		−	80.2920i		−	0.475101i
$170$	−153.589	+	269.644i	−0.903465	+	1.58614i
$171$		−	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	$-0.980702\pi$
$173$	−183.164	−	183.164i	−1.05875	−	1.05875i	−0.0605880	−	0.998163i	$-0.519298\pi$
$174$	−7.40244	+	1.10960i	−0.0425428	+	0.00637702i
$175$	−95.8316	+	157.111i	−0.547609	+	0.897779i
$176$	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	$0.472093\pi$
$180$	−27.1532	+	70.2203i	−0.150851	+	0.390113i
$181$		−	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
$185$	−16.1627	−	135.359i	−0.0873659	−	0.731669i
$186$	−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
$190$	−46.4286	−	169.317i	−0.244361	−	0.891143i
$191$	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	−0.524789	−	0.851233i	$-0.675856\pi$
$193$	63.0037	−	63.0037i	0.326444	−	0.326444i	0.851233	+	0.524789i	$0.175856\pi$
$194$	−67.4989	+	10.1179i	−0.347933	+	0.0521540i
$195$	−132.236	−	104.025i	−0.678133	−	0.533461i
$196$	19.8410	−	6.08491i	0.101229	−	0.0310455i
$197$	3.96178	−	3.96178i	0.0201106	−	0.0201106i	−0.696980	−	0.717091i	$-0.745473\pi$
$197$	3.96178	−	3.96178i	0.0201106	−	0.0201106i	0.717091	+	0.696980i	$0.245473\pi$
$198$	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	$0.899969\pi$
$200$	−20.2342	+	198.974i	−0.101171	+	0.994869i
$201$	−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
$205$	135.841	−	172.680i	0.662639	−	0.842343i
$206$	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
$210$	253.635	−	69.5495i	1.20779	−	0.331188i
$211$		−	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
$215$	231.274	−	27.6155i	1.07569	−	0.128444i
$216$	−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
$220$	17.9780	−	46.4924i	0.0817181	−	0.211329i
$221$			292.273i			1.32250i
$222$	−115.812	+	156.653i	−0.521674	+	0.705644i
$223$	128.870	−	128.870i	0.577894	−	0.577894i	−0.356429	−	0.934323i	$-0.616006\pi$
$223$	128.870	−	128.870i	0.577894	−	0.577894i	0.934323	+	0.356429i	$0.116006\pi$
$224$	173.326	−	159.521i	0.773778	−	0.712145i
$225$	91.4634	−	22.1585i	0.406504	−	0.0984824i
$226$	34.3854	+	229.394i	0.152148	+	1.01502i
$227$	−242.455	+	242.455i	−1.06808	+	1.06808i	−0.0705768	+	0.997506i	$0.522484\pi$
$227$	−242.455	+	242.455i	−1.06808	+	1.06808i	−0.997506	+	0.0705768i	$0.977516\pi$
$228$	−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	$0.181336\pi$
$230$	247.971	+	141.244i	1.07814	+	0.614105i
$231$	−65.5487			−0.283760
$232$	7.90328	+	2.78707i	0.0340659	+	0.0120132i
$233$	9.90826	−	9.90826i	0.0425247	−	0.0425247i	−0.685525	−	0.728049i	$-0.740427\pi$
$233$	9.90826	−	9.90826i	0.0425247	−	0.0425247i	0.728049	+	0.685525i	$0.240427\pi$
$234$	10.5116	+	70.1259i	0.0449215	+	0.299683i
$235$	−236.669	+	28.2598i	−1.00710	+	0.120255i
$236$	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	$0.970164\pi$
$240$	216.007	−	187.171i	0.900028	−	0.779880i
$241$	−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
$245$	−20.3888	−	16.0391i	−0.0832194	−	0.0654655i
$246$	−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
$250$	218.755	−	121.022i	0.875020	−	0.484087i
$251$		−	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
$255$	−435.688	−	342.739i	−1.70858	−	1.34407i
$256$	95.0710	−	237.692i	0.371371	−	0.928485i
$257$	244.045	+	244.045i	0.949590	+	0.949590i	0.998789	−	0.0491992i	$-0.0156669\pi$
$257$	244.045	+	244.045i	0.949590	+	0.949590i	−0.0491992	+	0.998789i	$0.515667\pi$
$258$	−267.657	−	197.875i	−1.03743	−	0.766959i
$259$	200.698			0.774896
$260$	76.1938	+	172.272i	0.293053	+	0.662585i
$261$		−	3.94332i		−	0.0151085i
$262$	243.839	+	180.267i	0.930683	+	0.688042i
$263$	−241.557	+	241.557i	−0.918467	+	0.918467i	−0.996918	−	0.0784512i	$-0.975003\pi$
$263$	−241.557	+	241.557i	−0.918467	+	0.918467i	0.0784512	+	0.996918i	$0.475003\pi$
$264$	−64.2566	+	30.7521i	−0.243396	+	0.116485i
$265$	−255.595	+	30.5197i	−0.964510	+	0.115169i
$266$	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	$0.725947\pi$
$270$	162.537	+	92.5809i	0.601989	+	0.342892i
$271$	−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
$275$	−60.5573	+	14.6710i	−0.220208	+	0.0533492i
$276$	−119.577	−	389.904i	−0.433252	−	1.41270i
$277$	−275.798	+	275.798i	−0.995660	+	0.995660i	−0.999991	−	0.00433109i	$-0.998621\pi$
$277$	−275.798	+	275.798i	−0.995660	+	0.995660i	0.00433109	+	0.999991i	$0.498621\pi$
$278$	−82.8985	+	112.133i	−0.298196	+	0.403357i
$279$		−	9.30790i		−	0.0333617i
$280$	−287.342	−	64.3118i	−1.02622	−	0.229685i
$281$	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	0.994958	−	0.100296i	$-0.0319789\pi$
$283$	253.189	+	253.189i	0.894662	+	0.894662i	−0.100296	+	0.994958i	$0.531979\pi$
$284$	25.6085	+	83.5013i	0.0901709	+	0.294019i
$285$	311.415	−	37.1849i	1.09268	−	0.130473i
$286$	−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
$290$	−2.77021	−	10.1025i	−0.00955244	−	0.0348361i
$291$		−	121.925i		−	0.418985i
$292$	−163.128	−	86.5541i	−0.558656	−	0.296418i
$293$	143.408	+	143.408i	0.489447	+	0.489447i	0.908132	−	0.418685i	$-0.137509\pi$
$293$	143.408	+	143.408i	0.489447	+	0.489447i	−0.418685	+	0.908132i	$0.637509\pi$
$294$	5.49565	+	36.6629i	0.0186927	+	0.124704i
$295$	94.5856	−	120.237i	0.320629	−	0.407582i
$296$	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
$300$	−346.154	−	88.4367i	−1.15385	−	0.294789i
$301$			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
$305$	93.6728	+	73.6888i	0.307124	+	0.241602i
$306$	34.6335	+	231.049i	0.113181	+	0.755063i
$307$	357.761	−	357.761i	1.16535	−	1.16535i	0.182059	−	0.983288i	$-0.441724\pi$
$307$	357.761	−	357.761i	1.16535	−	1.16535i	0.983288	−	0.182059i	$-0.0582762\pi$
$308$	64.8276	+	34.3970i	0.210479	+	0.111679i
$309$	−609.631			−1.97292
$310$	−6.53885	−	23.8461i	−0.0210931	−	0.0769228i
$311$	−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	−0.126764	−	0.991933i	$-0.540459\pi$
$313$	270.798	−	270.798i	0.865169	−	0.865169i	0.991933	+	0.126764i	$0.0404591\pi$
$314$	−39.4594	−	263.244i	−0.125667	−	0.838357i
$315$	16.4274	+	137.575i	0.0521503	+	0.436747i
$316$	−62.7645	+	19.2489i	−0.198622	+	0.0609141i
$317$	238.939	−	238.939i	0.753752	−	0.753752i	−0.221426	−	0.975177i	$-0.571071\pi$
$317$	238.939	−	238.939i	0.753752	−	0.753752i	0.975177	+	0.221426i	$0.0710710\pi$
$318$	295.805	+	218.685i	0.930204	+	0.687687i
$319$			2.61085i			0.00818448i
$320$	−311.850	+	71.7617i	−0.974530	+	0.224255i
$321$	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
$325$	122.613	−	201.019i	0.377272	−	0.618519i
$326$	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
$330$	77.3739	+	44.0721i	0.234466	+	0.133552i
$331$			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
$335$	−16.7618	−	140.376i	−0.0500353	−	0.419034i
$336$	235.914	+	348.445i	0.702126	+	1.03704i
$337$	−207.932	−	207.932i	−0.617008	−	0.617008i	0.327755	−	0.944763i	$-0.393708\pi$
$337$	−207.932	−	207.932i	−0.617008	−	0.617008i	−0.944763	+	0.327755i	$0.893708\pi$
$338$	−129.128	−	95.4627i	−0.382036	−	0.282434i
$339$	−414.358			−1.22230
$340$	251.042	+	567.599i	0.738358	+	1.66941i
$341$			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
$345$	−315.191	+	400.669i	−0.913597	+	1.16136i
$346$	−512.342	+	76.7983i	−1.48076	+	0.221961i
$347$	−150.516	+	150.516i	−0.433765	+	0.433765i	−0.889907	−	0.456142i	$-0.849231\pi$
$347$	−150.516	+	150.516i	−0.433765	+	0.433765i	0.456142	+	0.889907i	$0.349231\pi$
$348$	−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	$0.426476\pi$
$350$	138.733	+	340.916i	0.396380	+	0.974046i
$351$	176.177			0.501930
$352$	79.6871	+	3.30521i	0.226384	+	0.00938981i
$353$	31.8920	−	31.8920i	0.0903455	−	0.0903455i	−0.660490	−	0.750835i	$-0.729651\pi$
$353$	31.8920	−	31.8920i	0.0903455	−	0.0903455i	0.750835	+	0.660490i	$0.229651\pi$
$354$	−216.209	+	32.4090i	−0.610759	+	0.0915508i
$355$	67.5008	−	85.8067i	0.190143	−	0.241709i
$356$	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	$-0.174459\pi$
$360$	80.6468	+	127.157i	0.224019	+	0.353213i
$361$	−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
$365$	27.3687	+	229.207i	0.0749828	+	0.627963i
$366$	−25.2488	−	168.442i	−0.0689859	−	0.460223i
$367$	195.775	+	195.775i	0.533446	+	0.533446i	0.921596	−	0.388150i	$-0.126886\pi$
$367$	195.775	+	195.775i	0.533446	+	0.533446i	−0.388150	+	0.921596i	$0.626886\pi$
$368$	−86.3421	+	448.364i	−0.234625	+	1.21838i
$369$		−	165.412i		−	0.448270i
$370$	−236.905	−	134.941i	−0.640283	−	0.364705i
$371$		−	378.974i		−	1.02149i
$372$	−16.5621	+	31.2144i	−0.0445218	+	0.0839097i
$373$	−342.423	−	342.423i	−0.918023	−	0.918023i	0.0788627	−	0.996885i	$-0.474871\pi$
$373$	−342.423	−	342.423i	−0.918023	−	0.918023i	−0.996885	+	0.0788627i	$0.974871\pi$
$374$	−22.9306	−	152.976i	−0.0613118	−	0.409027i
$375$	155.871	+	418.506i	0.415657	+	1.11602i
$376$	−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	$0.795622\pi$
$380$	−327.502	−	126.641i	−0.861848	−	0.333265i
$381$		−	282.232i		−	0.740767i
$382$	192.518	−	260.411i	0.503974	−	0.681703i
$383$	−154.687	+	154.687i	−0.403882	+	0.403882i	−0.879599	−	0.475717i	$-0.842189\pi$
$383$	−154.687	+	154.687i	−0.403882	+	0.403882i	0.475717	+	0.879599i	$0.342189\pi$
$384$	394.737	+	230.898i	1.02796	+	0.601298i
$385$	−10.8764	−	91.0877i	−0.0282505	−	0.236592i
$386$	−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	$0.363395\pi$
$390$	−324.517	+	88.9863i	−0.832096	+	0.228170i
$391$	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
$395$	64.4974	+	50.7376i	0.163284	+	0.128450i
$396$	−11.0036	−	35.8793i	−0.0277869	−	0.0906043i
$397$	−376.174	+	376.174i	−0.947543	+	0.947543i	−0.998691	−	0.0511485i	$-0.983712\pi$
$397$	−376.174	+	376.174i	−0.947543	+	0.947543i	0.0511485	+	0.998691i	$0.483712\pi$
$398$	197.854	+	146.271i	0.497121	+	0.367515i
$399$			461.739i			1.15724i
$400$	295.939	+	269.110i	0.739847	+	0.672775i
$401$	−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
$405$	−311.332	+	395.764i	−0.768721	+	0.977195i
$406$	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	$-0.0653974\pi$
$410$	−116.203	−	423.771i	−0.283421	−	1.03359i
$411$			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
$415$	−2.41388	+	0.288233i	−0.00581658	+	0.000694536i
$416$	−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	$0.280230\pi$
$420$	189.706	−	490.595i	0.451682	−	1.16808i
$421$			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
$425$	403.984	−	662.312i	0.950550	−	1.55838i
$426$	−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
$430$	230.559	−	404.775i	0.536185	−	0.941337i
$431$	−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	−0.942159	−	0.335165i	$-0.891208\pi$
$433$	−262.829	+	262.829i	−0.606994	+	0.606994i	0.335165	+	0.942159i	$0.391208\pi$
$434$	36.0012	−	5.39646i	0.0829521	−	0.0124342i
$435$	18.5809	−	2.21867i	0.0427146	−	0.00510039i
$436$	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	$-0.158416\pi$
$440$	−53.3957	−	84.1897i	−0.121354	−	0.191340i
$441$	−19.5306			−0.0442870
$442$	470.043	+	347.497i	1.06345	+	0.786191i
$443$	119.234	+	119.234i	0.269152	+	0.269152i	0.828758	−	0.559606i	$-0.189048\pi$
$443$	119.234	+	119.234i	0.269152	+	0.269152i	−0.559606	+	0.828758i	$0.689048\pi$
$444$	114.241	+	372.504i	0.257300	+	0.838972i
$445$	−331.922	−	261.110i	−0.745891	−	0.586764i
$446$	−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	$-0.231047\pi$
$450$	73.1088	−	173.440i	0.162464	−	0.385421i
$451$			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
$455$	272.460	+	214.334i	0.598813	+	0.471063i
$456$	216.624	+	452.637i	0.475053	+	0.992626i
$457$	144.279	+	144.279i	0.315708	+	0.315708i	0.847116	−	0.531408i	$-0.178337\pi$
$457$	144.279	+	144.279i	0.315708	+	0.315708i	−0.531408	+	0.847116i	$0.678337\pi$
$458$	458.539	−	620.245i	1.00118	−	1.35425i
$459$	580.465			1.26463
$460$	521.977	−	230.864i	1.13473	−	0.501878i
$461$		−	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	−0.0349842	−	0.999388i	$-0.511138\pi$
$463$	446.519	−	446.519i	0.964404	−	0.964404i	0.999388	+	0.0349842i	$0.0111381\pi$
$464$	13.8788	−	9.39664i	0.0299113	−	0.0202514i
$465$	43.8586	−	5.23700i	0.0943196	−	0.0112624i
$466$	−4.15441	−	27.7152i	−0.00891504	−	0.0594746i
$467$	−5.61916	+	5.61916i	−0.0120325	+	0.0120325i	−0.713097	−	0.701065i	$-0.752708\pi$
$467$	−5.61916	+	5.61916i	−0.0120325	+	0.0120325i	0.701065	+	0.713097i	$0.252708\pi$
$468$	125.276	+	66.4707i	0.267685	+	0.142031i
$469$	208.138			0.443791
$470$	−235.939	+	414.219i	−0.501997	+	0.881317i
$471$	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
$475$	103.346	+	426.578i	0.217570	+	0.898060i
$476$	−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	$0.705419\pi$
$480$	−44.1947	−	569.925i	−0.0920724	−	1.18734i
$481$	−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
$485$	169.429	−	20.2309i	0.349338	−	0.0417132i
$486$	378.681	−	56.7630i	0.779179	−	0.116796i
$487$	−611.323	−	611.323i	−1.25528	−	1.25528i	−0.953320	−	0.301963i	$-0.902358\pi$
$487$	−611.323	−	611.323i	−1.25528	−	1.25528i	−0.301963	−	0.953320i	$-0.597642\pi$
$488$	−63.4195	+	179.838i	−0.129958	+	0.368521i
$489$			671.893i			1.37402i
$490$	−50.0356	+	13.7203i	−0.102114	+	0.0280007i
$491$			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
$495$	−29.0041	+	36.8699i	−0.0585942	+	0.0744847i
$496$	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	$0.773270\pi$
$500$	65.4564	−	495.697i	0.130913	−	0.991394i
$501$		−	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	$0.501412\pi$
$503$	−505.226	+	505.226i	−1.00443	+	1.00443i	−0.999990	+	0.00443600i	$0.998588\pi$
$504$	−199.964	+	95.6991i	−0.396754	+	0.189879i
$505$	597.699	+	470.187i	1.18356	+	0.931063i
$506$	−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	$0.301673\pi$
$510$	−1069.21	+	293.190i	−2.09650	+	0.574882i
$511$	−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
$515$	−101.156	−	847.156i	−0.196419	−	1.64496i
$516$	−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
$520$	367.644	+	82.2848i	0.707007	+	0.158240i
$521$	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	$-0.947400\pi$
$523$	−601.907	−	601.907i	−1.15087	−	1.15087i	−0.164497	−	0.986378i	$-0.552600\pi$
$524$	579.822	−	177.822i	1.10653	−	0.339356i
$525$	−639.009	+	154.811i	−1.21716	+	0.294878i
$526$	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
$530$	−254.806	+	447.343i	−0.480766	+	0.844043i
$531$		−	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
$535$	63.1119	+	528.547i	0.117966	+	0.987939i
$536$	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
$540$	342.139	−	151.324i	0.633591	−	0.280229i
$541$			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
$545$	36.6684	−	46.6127i	0.0672815	−	0.0855279i
$546$	−73.4397	−	489.935i	−0.134505	−	0.897317i
$547$	330.968	−	330.968i	0.605060	−	0.605060i	−0.336591	−	0.941651i	$-0.609274\pi$
$547$	330.968	−	330.968i	0.605060	−	0.605060i	0.941651	+	0.336591i	$0.109274\pi$
$548$	180.949	−	341.033i	0.330200	−	0.622323i
$549$	89.7299			0.163442
$550$	−48.4049	+	114.833i	−0.0880088	+	0.208788i
$551$	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
$555$	301.125	−	382.788i	0.542567	−	0.689709i
$556$	81.7744	+	266.640i	0.147076	+	0.479569i
$557$	62.7080	−	62.7080i	0.112582	−	0.112582i	−0.648572	−	0.761153i	$-0.724633\pi$
$557$	62.7080	−	62.7080i	0.112582	−	0.112582i	0.761153	+	0.648572i	$0.224633\pi$
$558$	−14.9693	−	11.0666i	−0.0268266	−	0.0198326i
$559$		−	438.745i		−	0.784874i
$560$	−445.062	+	385.649i	−0.794753	+	0.688659i
$561$	276.324			0.492556
$562$	15.7962	−	21.3668i	0.0281071	−	0.0380193i
$563$	116.120	+	116.120i	0.206252	+	0.206252i	0.802672	−	0.596420i	$-0.203411\pi$
$563$	116.120	+	116.120i	0.206252	+	0.206252i	−0.596420	+	0.802672i	$0.703411\pi$
$564$	651.308	−	199.746i	1.15480	−	0.354159i
$565$	−68.7543	−	575.801i	−0.121689	−	1.01912i
$566$	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	$0.908181\pi$
$570$	310.453	−	545.038i	0.544655	−	0.956207i
$571$			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
$575$	−609.078	−	371.513i	−1.05927	−	0.646110i
$576$	−151.125	+	187.626i	−0.262370	+	0.325739i
$577$	27.1282	+	27.1282i	0.0470159	+	0.0470159i	0.730224	−	0.683208i	$-0.239416\pi$
$577$	27.1282	+	27.1282i	0.0470159	+	0.0470159i	−0.683208	+	0.730224i	$0.739416\pi$
$578$	1083.91	+	801.319i	1.87527	+	1.38637i
$579$	318.332			0.549797
$580$	−19.5407	−	7.55614i	−0.0336909	−	0.0130278i
$581$		−	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
$585$	−21.0182	−	176.023i	−0.0359286	−	0.300894i
$586$	401.137	−	60.1291i	0.684535	−	0.102609i
$587$	163.733	−	163.733i	0.278932	−	0.278932i	−0.553751	−	0.832682i	$-0.686804\pi$
$587$	163.733	−	163.733i	0.278932	−	0.278932i	0.832682	+	0.553751i	$0.186804\pi$
$588$	65.4965	+	34.7519i	0.111389	+	0.0591019i
$589$	43.4114			0.0737035
$590$	−80.9116	−	295.070i	−0.137138	−	0.500119i
$591$	20.0173			0.0338702
$592$	82.4889	−	428.355i	0.139339	−	0.723572i
$593$	280.606	−	280.606i	0.473198	−	0.473198i	−0.429750	−	0.902948i	$-0.641398\pi$
$593$	280.606	−	280.606i	0.473198	−	0.473198i	0.902948	+	0.429750i	$0.141398\pi$
$594$	−92.2115	+	13.8222i	−0.155238	+	0.0232697i
$595$	897.695	+	706.182i	1.50873	+	1.18686i
$596$	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	$0.820845\pi$
$600$	−553.785	+	451.550i	−0.922975	+	0.752583i
$601$	−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
$605$	−354.857	+	451.092i	−0.586540	+	0.745607i
$606$	−161.106	−	1074.78i	−0.265851	−	1.77356i
$607$	681.745	+	681.745i	1.12314	+	1.12314i	0.991267	+	0.131873i	$0.0420990\pi$
$607$	681.745	+	681.745i	1.12314	+	1.12314i	0.131873	+	0.991267i	$0.457901\pi$
$608$	23.2826	−	561.333i	0.0382938	−	0.923245i
$609$			27.5501i			0.0452382i
$610$	229.880	−	63.0357i	0.376853	−	0.103337i
$611$			448.981i			0.734830i
$612$	412.758	+	219.006i	0.674442	+	0.357853i
$613$	−378.926	−	378.926i	−0.618150	−	0.618150i	0.326907	−	0.945057i	$-0.393994\pi$
$613$	−378.926	−	378.926i	−0.618150	−	0.618150i	−0.945057	+	0.326907i	$0.893994\pi$
$614$	−150.005	−	1000.72i	−0.244308	−	1.62984i
$615$	779.417	−	93.0672i	1.26734	−	0.151329i
$616$	132.395	−	63.3617i	0.214927	−	0.102860i
$617$	−68.3041	−	68.3041i	−0.110704	−	0.110704i	0.649585	−	0.760289i	$-0.274943\pi$
$617$	−68.3041	−	68.3041i	−0.110704	−	0.110704i	−0.760289	+	0.649585i	$0.774943\pi$
$618$	−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	$0.803582\pi$
$620$	−46.1243	−	17.8357i	−0.0743941	−	0.0287672i
$621$		−	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
$625$	−555.701	+	286.045i	−0.889121	+	0.457671i
$626$	−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
$630$	240.784	+	137.150i	0.382197	+	0.217699i
$631$	−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
$635$	392.196	−	46.8307i	0.617631	−	0.0737491i
$636$	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
$640$	−255.363	+	586.847i	−0.399004	+	0.916949i
$641$	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	0.957241	−	0.289290i	$-0.0934193\pi$
$643$	429.493	+	429.493i	0.667951	+	0.667951i	−0.289290	+	0.957241i	$0.593419\pi$
$644$	246.378	+	803.361i	0.382575	+	1.24745i
$645$	654.031	+	514.501i	1.01400	+	0.797676i
$646$	−1077.60	+	161.528i	−1.66811	+	0.250044i
$647$	511.695	+	511.695i	0.790873	+	0.790873i	0.981636	−	0.190763i	$-0.0610963\pi$
$647$	511.695	+	511.695i	0.790873	+	0.790873i	−0.190763	+	0.981636i	$0.561096\pi$
$648$	−759.810	−	267.945i	−1.17255	−	0.413495i
$649$			76.2571i			0.117499i
$650$	−177.504	−	436.191i	−0.273083	−	0.671063i
$651$			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	$0.0686120\pi$
$653$	777.556	+	777.556i	1.19074	+	1.19074i	0.213886	+	0.976859i	$0.431388\pi$
$654$	−83.8186	+	12.5641i	−0.128163	+	0.0192112i
$655$	−595.831	−	468.717i	−0.909666	−	0.715599i
$656$	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	$0.688088\pi$
$660$	162.871	−	72.0359i	0.246775	−	0.109145i
$661$			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
$665$	−641.641	+	76.6160i	−0.964874	+	0.115212i
$666$	−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
$670$	−245.687	−	139.943i	−0.366697	−	0.208870i
$671$	−59.4096			−0.0885388
$672$	840.870	+	34.8771i	1.25130	+	0.0519005i
$673$	−185.806	+	185.806i	−0.276087	+	0.276087i	−0.831545	−	0.555458i	$-0.812543\pi$
$673$	−185.806	+	185.806i	−0.276087	+	0.276087i	0.555458	+	0.831545i	$0.312543\pi$
$674$	−581.622	+	87.1832i	−0.862940	+	0.129352i
$675$	−399.230	−	243.515i	−0.591452	−	0.360762i
$676$	−307.053	+	94.1682i	−0.454220	+	0.139302i
$677$	448.763	−	448.763i	0.662870	−	0.662870i	−0.293186	−	0.956055i	$-0.594715\pi$
$677$	448.763	−	448.763i	0.662870	−	0.662870i	0.956055	+	0.293186i	$0.0947155\pi$
$678$	−492.649	+	666.385i	−0.726621	+	0.982868i
$679$			251.214i			0.369977i
$680$	1211.31	+	271.110i	1.78133	+	0.398692i
$681$	−1225.03			−1.79886
$682$	9.91105	+	7.32711i	0.0145323	+	0.0107436i
$683$	67.1358	+	67.1358i	0.0982955	+	0.0982955i	0.754544	−	0.656249i	$-0.227858\pi$
$683$	67.1358	+	67.1358i	0.0982955	+	0.0982955i	−0.656249	+	0.754544i	$0.727858\pi$
$684$	−252.741	+	77.5118i	−0.369505	+	0.113321i
$685$	−479.178	+	57.2168i	−0.699529	+	0.0835282i
$686$	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
$690$	269.624	+	983.274i	0.390760	+	1.42503i
$691$		−	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
$695$	215.547	−	274.002i	0.310139	−	0.394248i
$696$	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
$700$	713.218	+	182.216i	1.01888	+	0.260308i
$701$		−	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
$705$	−669.291	−	526.505i	−0.949348	−	0.746816i
$706$	−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	$0.395681\pi$
$710$	−57.7424	−	210.576i	−0.0813273	−	0.296587i
$711$	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
$715$	13.9160	+	116.544i	0.0194630	+	0.162998i
$716$	−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	$-0.0140128\pi$
$720$	300.382	+	21.4835i	0.417198	+	0.0298382i
$721$	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
$725$	6.16622	+	25.4522i	0.00850513	+	0.0351065i
$726$	811.151	−	121.589i	1.11729	−	0.167478i
$727$	408.139	+	408.139i	0.561401	+	0.561401i	0.929705	−	0.368304i	$-0.120061\pi$
$727$	408.139	+	408.139i	0.561401	+	0.561401i	−0.368304	+	0.929705i	$0.620061\pi$
$728$	−184.464	+	523.084i	−0.253385	+	0.718522i
$729$		−	222.361i		−	0.305021i
$730$	401.157	+	228.499i	0.549530	+	0.313012i
$731$		−	1445.57i		−	1.97752i
$732$	−300.913	−	159.662i	−0.411083	−	0.218117i
$733$	90.0317	+	90.0317i	0.122826	+	0.122826i	0.765848	−	0.643022i	$-0.222319\pi$
$733$	90.0317	+	90.0317i	0.122826	+	0.122826i	−0.643022	+	0.765848i	$0.722319\pi$
$734$	547.616	−	82.0858i	0.746071	−	0.111834i
$735$	−10.9887	−	92.0275i	−0.0149506	−	0.125208i
$736$	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	$0.298199\pi$
$740$	−498.683	+	220.561i	−0.673896	+	0.298055i
$741$		−	590.779i		−	0.797272i
$742$	−609.478	−	450.579i	−0.821399	−	0.607250i
$743$	282.061	−	282.061i	0.379624	−	0.379624i	−0.491342	−	0.870967i	$-0.663494\pi$
$743$	282.061	−	282.061i	0.379624	−	0.379624i	0.870967	+	0.491342i	$0.163494\pi$
$744$	30.5086	+	63.7479i	0.0410062	+	0.0856827i
$745$	243.916	−	310.065i	0.327404	−	0.416194i
$746$	−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
$750$	858.377	+	246.903i	1.14450	+	0.329204i
$751$	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
$755$	−610.743	+	776.374i	−0.808932	+	1.02831i
$756$	161.493	+	526.577i	0.213615	+	0.696530i
$757$	173.075	−	173.075i	0.228633	−	0.228633i	−0.583488	−	0.812121i	$-0.698313\pi$
$757$	173.075	−	173.075i	0.228633	−	0.228633i	0.812121	+	0.583488i	$0.198313\pi$
$758$	−721.749	+	976.277i	−0.952175	+	1.28796i
$759$		−	254.114i		−	0.334801i
$760$	−593.050	+	376.131i	−0.780329	+	0.494909i
$761$	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
$765$	−69.2505	−	579.957i	−0.0905235	−	0.758113i
$766$	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	$-0.0774913\pi$
$770$	−159.422	−	90.8064i	−0.207041	−	0.117930i
$771$			1233.06i			1.59930i
$772$	−314.831	−	167.047i	−0.407812	−	0.216382i
$773$	319.455	+	319.455i	0.413267	+	0.413267i	0.882875	−	0.469608i	$-0.155605\pi$
$773$	319.455	+	319.455i	0.413267	+	0.413267i	−0.469608	+	0.882875i	$0.655605\pi$
$774$	−51.9900	−	346.839i	−0.0671705	−	0.448112i
$775$	14.5549	+	60.0779i	0.0187805	+	0.0775198i
$776$	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
$780$	−242.723	+	627.699i	−0.311183	+	0.804743i
$781$			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
$785$	78.8999	+	660.769i	0.100509	+	0.841744i
$786$	160.602	+	1071.42i	0.204328	+	1.36313i
$787$	1104.16	−	1104.16i	1.40300	−	1.40300i	0.612627	−	0.790372i	$-0.290113\pi$
$787$	1104.16	−	1104.16i	1.40300	−	1.40300i	0.790372	−	0.612627i	$-0.209887\pi$
$788$	−19.7971	−	10.5042i	−0.0251232	−	0.0133302i
$789$	−1220.49			−1.54688
$790$	158.282	−	43.4025i	0.200356	−	0.0549399i
$791$	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
$795$	−722.811	−	568.608i	−0.909197	−	0.715230i
$796$	470.476	−	144.287i	0.591050	−	0.181266i
$797$	−434.605	+	434.605i	−0.545301	+	0.545301i	−0.925078	−	0.379777i	$-0.876001\pi$
$797$	−434.605	+	434.605i	−0.545301	+	0.545301i	0.379777	+	0.925078i	$0.376001\pi$
$798$	742.583	+	548.982i	0.930555	+	0.687947i
$799$			1479.29i			1.85143i
$800$	784.646	−	155.981i	0.980808	−	0.194977i
$801$	−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
$805$	649.422	−	825.542i	0.806735	−	1.02552i
$806$	−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	$-0.0323538\pi$
$810$	266.323	+	971.236i	0.328794	+	1.19906i
$811$		−	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
$815$	−933.677	+	111.487i	−1.14562	+	0.136794i
$816$	−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
$820$	−819.681	−	316.959i	−0.999610	−	0.386536i
$821$			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	−0.683249	−	0.730186i	$-0.739434\pi$
$823$	38.6290	−	38.6290i	0.0469368	−	0.0469368i	0.730186	+	0.683249i	$0.239434\pi$
$824$	1231.33	−	589.292i	1.49433	−	0.715160i
$825$	−190.049	−	115.922i	−0.230363	−	0.140512i
$826$	445.478	−	66.7757i	0.539320	−	0.0808422i
$827$	432.150	−	432.150i	0.522552	−	0.522552i	−0.395789	−	0.918341i	$-0.629529\pi$
$827$	432.150	−	432.150i	0.522552	−	0.522552i	0.918341	+	0.395789i	$0.129529\pi$
$828$	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	$0.364594\pi$
$830$	−2.40643	+	4.22477i	−0.00289931	+	0.00509009i
$831$	−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
$835$	360.967	−	43.1017i	0.432296	−	0.0516189i
$836$	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	$-0.112152\pi$
$840$	−563.440	−	888.382i	−0.670762	−	1.05760i
$841$	−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
$845$	315.530	+	248.215i	0.373408	+	0.293746i
$846$	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
$850$	−584.837	−	1437.15i	−0.688043	−	1.69077i
$851$			778.051i			0.914279i
$852$	−146.254	+	275.644i	−0.171660	+	0.323526i
$853$	−89.6610	−	89.6610i	−0.105113	−	0.105113i	0.652595	−	0.757707i	$-0.273680\pi$
$853$	−89.6610	−	89.6610i	−0.105113	−	0.105113i	−0.757707	+	0.652595i	$0.773680\pi$
$854$	52.0229	+	347.058i	0.0609167	+	0.406391i
$855$	259.720	+	204.311i	0.303766	+	0.238961i
$856$	−768.237	+	367.664i	−0.897473	+	0.429514i
$857$	−409.705	−	409.705i	−0.478069	−	0.478069i	0.426445	−	0.904514i	$-0.359766\pi$
$857$	−409.705	−	409.705i	−0.478069	−	0.478069i	−0.904514	+	0.426445i	$0.859766\pi$
$858$	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	$0.654037\pi$
$860$	−376.850	−	852.048i	−0.438198	−	0.990754i
$861$			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	$-0.382636\pi$
$863$	1116.04	−	1116.04i	1.29321	−	1.29321i	0.932793	−	0.360414i	$-0.117364\pi$
$864$	405.352	+	440.433i	0.469158	+	0.509761i
$865$	1286.03	−	153.560i	1.48674	−	0.177526i
$866$	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
$870$	18.5235	−	32.5202i	0.0212913	−	0.0373796i
$871$	−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
$875$	−321.159	−	862.293i	−0.367038	−	0.985477i
$876$	−193.447	−	630.770i	−0.220830	−	0.720058i
$877$	98.3606	−	98.3606i	0.112156	−	0.112156i	−0.648802	−	0.760957i	$-0.724730\pi$
$877$	98.3606	−	98.3606i	0.112156	−	0.112156i	0.760957	+	0.648802i	$0.224730\pi$
$878$	−674.082	−	498.340i	−0.767747	−	0.567585i
$879$			724.582i			0.824326i
$880$	−198.881	−	14.2241i	−0.226001	−	0.0161637i
$881$	−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	$0.0303861\pi$
$883$	963.144	+	963.144i	1.09076	+	1.09076i	0.0953158	+	0.995447i	$0.469614\pi$
$884$	1117.71	−	342.784i	1.26438	−	0.387765i
$885$	542.705	−	64.8024i	0.613227	−	0.0732231i
$886$	333.520	−	49.9935i	0.376433	−	0.0564260i
$887$	−588.066	−	588.066i	−0.662983	−	0.662983i	0.293099	−	0.956082i	$-0.405313\pi$
$887$	−588.066	−	588.066i	−0.662983	−	0.662983i	−0.956082	+	0.293099i	$0.905313\pi$
$888$	734.899	+	259.160i	0.827588	+	0.291847i
$889$			581.514i			0.654121i
$890$	−814.562	+	223.362i	−0.915238	+	0.250968i
$891$		−	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
$895$	−96.9059	+	123.186i	−0.108275	+	0.137638i
$896$	−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
$900$	−192.009	−	323.786i	−0.213343	−	0.359762i
$901$			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
$905$	225.631	+	177.495i	0.249316	+	0.196127i
$906$	1396.07	−	209.266i	1.54092	−	0.230978i
$907$	−692.104	+	692.104i	−0.763069	+	0.763069i	−0.976876	−	0.213807i	$-0.931414\pi$
$907$	−692.104	+	692.104i	−0.763069	+	0.763069i	0.213807	+	0.976876i	$0.431414\pi$
$908$	1211.55	+	642.839i	1.33431	+	0.707973i
$909$	572.540			0.629857
$910$	668.638	−	183.348i	0.734767	−	0.201481i
$911$	−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
$915$	50.4856	+	422.805i	0.0551755	+	0.462082i
$916$	−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	$-0.335667\pi$
$920$	249.319	−	1113.94i	0.270999	−	1.21081i
$921$	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
$925$	581.896	+	354.933i	0.629077	+	0.383712i
$926$	−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	$-0.158533\pi$
$930$	43.7232	−	76.7614i	0.0470142	−	0.0825391i
$931$		−	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
$935$	45.8503	+	383.986i	0.0490377	+	0.410680i
$936$	255.847	−	122.444i	0.273341	−	0.130816i
$937$	1241.34	+	1241.34i	1.32480	+	1.32480i	0.909841	+	0.414958i	$0.136204\pi$
$937$	1241.34	+	1241.34i	1.32480	+	1.32480i	0.414958	+	0.909841i	$0.363796\pi$
$938$	247.464	−	334.734i	0.263821	−	0.356859i
$939$	1368.23			1.45712
$940$	385.642	+	871.927i	0.410258	+	0.927582i
$941$			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
$945$	425.675	−	541.115i	0.450449	−	0.572609i
$946$	34.4222	+	229.640i	0.0363871	+	0.242748i
$947$	228.351	−	228.351i	0.241131	−	0.241131i	−0.576187	−	0.817318i	$-0.695460\pi$
$947$	228.351	−	228.351i	0.241131	−	0.241131i	0.817318	+	0.576187i	$0.195460\pi$
$948$	−207.190	−	109.933i	−0.218555	−	0.115963i
$949$	434.823			0.458191
$950$	808.909	+	340.974i	0.851484	+	0.358920i
$951$	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	$0.657715\pi$
$953$	−1291.50	+	1291.50i	−1.35519	+	1.35519i	−0.879742	+	0.475451i	$0.842285\pi$
$954$	57.4574	+	383.313i	0.0602279	+	0.401796i
$955$	−500.572	+	636.324i	−0.524159	+	0.666308i
$956$	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
$960$	−969.117	−	606.534i	−1.00950	−	0.631806i
$961$	−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
$965$	52.8207	+	442.361i	0.0547365	+	0.458405i
$966$	−1484.48	+	222.519i	−1.53673	+	0.230351i
$967$	486.969	+	486.969i	0.503588	+	0.503588i	0.912551	−	0.408963i	$-0.134110\pi$
$967$	486.969	+	486.969i	0.503588	+	0.503588i	−0.408963	+	0.912551i	$0.634110\pi$
$968$	−866.033	−	305.404i	−0.894662	−	0.315500i
$969$		−	1946.49i		−	2.00876i
$970$	168.906	−	296.535i	0.174130	−	0.305706i
$971$		−	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
$975$	817.591	−	198.075i	0.838555	−	0.203154i
$976$	213.819	+	315.811i	0.219077	+	0.323577i
$977$	−1073.65	−	1073.65i	−1.09892	−	1.09892i	−0.994537	−	0.104387i	$-0.966712\pi$
$977$	−1073.65	−	1073.65i	−1.09892	−	1.09892i	−0.104387	−	0.994537i	$-0.533288\pi$
$978$	1080.56	+	798.844i	1.10487	+	0.816814i
$979$	210.513			0.215028
$980$	−37.4241	+	96.7816i	−0.0381879	+	0.0987568i
$981$		−	44.6506i		−	0.0455154i
$982$	1446.14	+	1069.11i	1.47265	+	1.08871i
$983$	122.156	−	122.156i	0.124269	−	0.124269i	−0.642237	−	0.766506i	$-0.721994\pi$
$983$	122.156	−	122.156i	0.124269	−	0.124269i	0.766506	+	0.642237i	$0.221994\pi$
$984$	542.172	+	1132.87i	0.550988	+	1.15129i
$985$	3.32146	+	27.8164i	0.00337204	+	0.0282400i
$986$	−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
$990$	24.8111	+	90.4817i	0.0250617	+	0.0913956i
$991$	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
$995$	−483.465	−	380.323i	−0.485895	−	0.382235i
$996$	6.64294	−	2.03728i	0.00666962	−	0.00204547i
$997$	−743.909	+	743.909i	−0.746148	+	0.746148i	−0.973753	−	0.227606i	$-0.926910\pi$
$997$	−743.909	+	743.909i	−0.746148	+	0.746148i	0.227606	+	0.973753i	$0.426910\pi$
$998$	−898.070	+	1214.78i	−0.899869	+	1.21721i
$999$			509.987i			0.510498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.i.a.37.8	yes	20
3.2	odd	2		360.3.u.b.37.3		20
4.3	odd	2		160.3.m.a.17.3		20
5.2	odd	4		200.3.i.b.93.9		20
5.3	odd	4	inner	40.3.i.a.13.2	✓	20
5.4	even	2		200.3.i.b.157.3		20
8.3	odd	2		160.3.m.a.17.8		20
8.5	even	2	inner	40.3.i.a.37.2	yes	20
15.8	even	4		360.3.u.b.253.9		20
20.3	even	4		160.3.m.a.113.8		20
20.7	even	4		800.3.m.b.593.3		20
20.19	odd	2		800.3.m.b.657.8		20
24.5	odd	2		360.3.u.b.37.9		20
40.3	even	4		160.3.m.a.113.3		20
40.13	odd	4	inner	40.3.i.a.13.8	yes	20
40.19	odd	2		800.3.m.b.657.3		20
40.27	even	4		800.3.m.b.593.8		20
40.29	even	2		200.3.i.b.157.9		20
40.37	odd	4		200.3.i.b.93.3		20
120.53	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	5.3	odd	4	inner
40.3.i.a.13.8	yes	20	40.13	odd	4	inner
40.3.i.a.37.2	yes	20	8.5	even	2	inner
40.3.i.a.37.8	yes	20	1.1	even	1	trivial
160.3.m.a.17.3		20	4.3	odd	2
160.3.m.a.17.8		20	8.3	odd	2
160.3.m.a.113.3		20	40.3	even	4
160.3.m.a.113.8		20	20.3	even	4
200.3.i.b.93.3		20	40.37	odd	4
200.3.i.b.93.9		20	5.2	odd	4
200.3.i.b.157.3		20	5.4	even	2
200.3.i.b.157.9		20	40.29	even	2
360.3.u.b.37.3		20	3.2	odd	2
360.3.u.b.37.9		20	24.5	odd	2
360.3.u.b.253.3		20	120.53	even	4
360.3.u.b.253.9		20	15.8	even	4
800.3.m.b.593.3		20	20.7	even	4
800.3.m.b.593.8		20	40.27	even	4
800.3.m.b.657.3		20	40.19	odd	2
800.3.m.b.657.8		20	20.19	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	40.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18894 - 1.60823i) q^{2} +(2.52630 + 2.52630i) q^{3} +(-1.17282 - 3.82420i) q^{4} +(-3.09141 + 3.92978i) q^{5} +(7.06650 - 1.05925i) q^{6} +(-5.20520 - 5.20520i) q^{7} +(-7.54462 - 2.66059i) q^{8} +3.76437i q^{9} +O(q^{10})\)	\(q+(1.18894 - 1.60823i) q^{2} +(2.52630 + 2.52630i) q^{3} +(-1.17282 - 3.82420i) q^{4} +(-3.09141 + 3.92978i) q^{5} +(7.06650 - 1.05925i) q^{6} +(-5.20520 - 5.20520i) q^{7} +(-7.54462 - 2.66059i) q^{8} +3.76437i q^{9} +(2.64449 + 9.64400i) q^{10} -2.49236i q^{11} +(6.69817 - 12.6240i) q^{12} +(6.65988 + 6.65988i) q^{13} +(-14.5599 + 2.18248i) q^{14} +(-17.7376 + 2.11798i) q^{15} +(-13.2490 + 8.97020i) q^{16} +(21.9428 + 21.9428i) q^{17} +(6.05398 + 4.47563i) q^{18} -17.5567 q^{19} +(18.6539 + 7.21322i) q^{20} -26.2998i q^{21} +(-4.00830 - 2.96328i) q^{22} +(20.1791 - 20.1791i) q^{23} +(-12.3385 - 25.7814i) q^{24} +(-5.88639 - 24.2971i) q^{25} +(18.6289 - 2.79240i) q^{26} +(13.2268 - 13.2268i) q^{27} +(-13.8010 + 26.0105i) q^{28} -1.04754 q^{29} +(-17.6828 + 31.0444i) q^{30} -2.47263 q^{31} +(-1.32614 + 31.9725i) q^{32} +(6.29646 - 6.29646i) q^{33} +(61.3780 - 9.20035i) q^{34} +(36.5467 - 4.36391i) q^{35} +(14.3957 - 4.41493i) q^{36} +(-19.2786 + 19.2786i) q^{37} +(-20.8740 + 28.2353i) q^{38} +33.6497i q^{39} +(33.7790 - 21.4237i) q^{40} -43.9414 q^{41} +(-42.2962 - 31.2690i) q^{42} +(-32.9394 - 32.9394i) q^{43} +(-9.53129 + 2.92310i) q^{44} +(-14.7932 - 11.6372i) q^{45} +(-8.46086 - 56.4446i) q^{46} +(33.7079 + 33.7079i) q^{47} +(-56.1323 - 10.8095i) q^{48} +5.18827i q^{49} +(-46.0740 - 19.4213i) q^{50} +110.868i q^{51} +(17.6578 - 33.2795i) q^{52} +(36.4034 + 36.4034i) q^{53} +(-5.54582 - 36.9976i) q^{54} +(9.79445 + 7.70491i) q^{55} +(25.4224 + 53.1202i) q^{56} +(-44.3536 - 44.3536i) q^{57} +(-1.24547 + 1.68469i) q^{58} -30.5963 q^{59} +(28.9027 + 65.3482i) q^{60} -23.8366i q^{61} +(-2.93982 + 3.97657i) q^{62} +(19.5943 - 19.5943i) q^{63} +(49.8425 + 40.1463i) q^{64} +(-46.7603 + 5.58347i) q^{65} +(-2.64003 - 17.6123i) q^{66} +(-19.9932 + 19.9932i) q^{67} +(58.1787 - 109.649i) q^{68} +101.957 q^{69} +(36.4339 - 63.9641i) q^{70} -21.8350 q^{71} +(10.0154 - 28.4007i) q^{72} +(32.6450 - 32.6450i) q^{73} +(8.08328 + 53.9257i) q^{74} +(46.5110 - 76.2526i) q^{75} +(20.5909 + 67.1405i) q^{76} +(-12.9733 + 12.9733i) q^{77} +(54.1165 + 40.0076i) q^{78} -16.4124i q^{79} +(5.70706 - 79.7962i) q^{80} +100.709 q^{81} +(-52.2439 + 70.6680i) q^{82} +(0.343799 + 0.343799i) q^{83} +(-100.576 + 30.8450i) q^{84} +(-154.065 + 18.3963i) q^{85} +(-92.1373 + 13.8111i) q^{86} +(-2.64640 - 2.64640i) q^{87} +(-6.63116 + 18.8039i) q^{88} +84.4631i q^{89} +(-36.3036 + 9.95483i) q^{90} -69.3320i q^{91} +(-100.836 - 53.5025i) q^{92} +(-6.24661 - 6.24661i) q^{93} +(94.2869 - 14.1333i) q^{94} +(54.2751 - 68.9942i) q^{95} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31} + 128 q^{32} + 32 q^{33} + 220 q^{36} - 188 q^{38} + 156 q^{40} - 8 q^{41} - 284 q^{42} - 240 q^{46} + 188 q^{47} - 256 q^{48} - 274 q^{50} - 332 q^{52} + 96 q^{55} - 360 q^{56} - 40 q^{57} + 268 q^{58} - 340 q^{60} + 336 q^{62} + 228 q^{63} - 60 q^{65} + 616 q^{66} + 396 q^{68} + 300 q^{70} + 248 q^{71} + 668 q^{72} - 124 q^{73} + 424 q^{76} - 368 q^{78} + 496 q^{80} + 132 q^{81} - 676 q^{82} - 672 q^{86} - 488 q^{87} - 304 q^{88} - 474 q^{90} - 628 q^{92} - 488 q^{95} - 1024 q^{96} + 100 q^{97} + 546 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8 + 6 * q^10 - 44 * q^12 - 4 * q^15 - 56 * q^16 - 12 * q^17 + 10 * q^18 - 24 * q^20 + 92 * q^22 - 4 * q^23 - 28 * q^25 + 100 * q^26 + 68 * q^28 + 100 * q^30 - 136 * q^31 + 128 * q^32 + 32 * q^33 + 220 * q^36 - 188 * q^38 + 156 * q^40 - 8 * q^41 - 284 * q^42 - 240 * q^46 + 188 * q^47 - 256 * q^48 - 274 * q^50 - 332 * q^52 + 96 * q^55 - 360 * q^56 - 40 * q^57 + 268 * q^58 - 340 * q^60 + 336 * q^62 + 228 * q^63 - 60 * q^65 + 616 * q^66 + 396 * q^68 + 300 * q^70 + 248 * q^71 + 668 * q^72 - 124 * q^73 + 424 * q^76 - 368 * q^78 + 496 * q^80 + 132 * q^81 - 676 * q^82 - 672 * q^86 - 488 * q^87 - 304 * q^88 - 474 * q^90 - 628 * q^92 - 488 * q^95 - 1024 * q^96 + 100 * q^97 + 546 * q^98

Introduction

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