LMFDB - Embedded newform 40.3.i.a.37.7

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			37.7
Root			$0.541828 + 1.30630i$ of defining polynomial
Character	$\chi$	$=$	40.37
Dual form			40.3.i.a.13.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.764474 + 1.84813i) q^{2} +(-0.130791 - 0.130791i) q^{3} +(-2.83116 + 2.82569i) q^{4} +(4.38731 + 2.39823i) q^{5} +(0.141733 - 0.341706i) q^{6} +(-1.59713 - 1.59713i) q^{7} +(-7.38659 - 3.07218i) q^{8} -8.96579i q^{9} +O(q^{10})$	\(q+(0.764474 + 1.84813i) q^{2} +(-0.130791 - 0.130791i) q^{3} +(-2.83116 + 2.82569i) q^{4} +(4.38731 + 2.39823i) q^{5} +(0.141733 - 0.341706i) q^{6} +(-1.59713 - 1.59713i) q^{7} +(-7.38659 - 3.07218i) q^{8} -8.96579i q^{9} +(-1.07825 + 9.94170i) q^{10} -11.9427i q^{11} +(0.739867 + 0.000715350i) q^{12} +(9.59714 + 9.59714i) q^{13} +(1.73074 - 4.17267i) q^{14} +(-0.260155 - 0.887490i) q^{15} +(0.0309396 - 16.0000i) q^{16} +(0.857288 + 0.857288i) q^{17} +(16.5699 - 6.85411i) q^{18} -20.5611 q^{19} +(-19.1978 + 5.60743i) q^{20} +0.417782i q^{21} +(22.0716 - 9.12986i) q^{22} +(-22.1560 + 22.1560i) q^{23} +(0.564287 + 1.36792i) q^{24} +(13.4970 + 21.0435i) q^{25} +(-10.4000 + 25.0735i) q^{26} +(-2.34977 + 2.34977i) q^{27} +(9.03474 + 0.00873536i) q^{28} -27.3404 q^{29} +(1.44131 - 1.15926i) q^{30} +40.0267 q^{31} +(29.5937 - 12.1744i) q^{32} +(-1.56200 + 1.56200i) q^{33} +(-0.929005 + 2.23975i) q^{34} +(-3.17684 - 10.8374i) q^{35} +(25.3345 + 25.3836i) q^{36} +(-1.57131 + 1.57131i) q^{37} +(-15.7184 - 37.9996i) q^{38} -2.51044i q^{39} +(-25.0395 - 31.1933i) q^{40} -37.5504 q^{41} +(-0.772115 + 0.319383i) q^{42} +(49.2602 + 49.2602i) q^{43} +(33.7463 + 33.8116i) q^{44} +(21.5020 - 39.3357i) q^{45} +(-57.8849 - 24.0095i) q^{46} +(-34.0876 - 34.0876i) q^{47} +(-2.09670 + 2.08861i) q^{48} -43.8983i q^{49} +(-28.5730 + 41.0315i) q^{50} -0.224252i q^{51} +(-54.2896 - 0.0524906i) q^{52} +(-28.8002 - 28.8002i) q^{53} +(-6.13901 - 2.54634i) q^{54} +(28.6412 - 52.3962i) q^{55} +(6.89068 + 16.7040i) q^{56} +(2.68921 + 2.68921i) q^{57} +(-20.9010 - 50.5285i) q^{58} +92.7071 q^{59} +(3.24431 + 1.77751i) q^{60} +4.82618i q^{61} +(30.5993 + 73.9744i) q^{62} +(-14.3196 + 14.3196i) q^{63} +(45.1234 + 45.3859i) q^{64} +(19.0895 + 65.1217i) q^{65} +(-4.08088 - 1.69267i) q^{66} +(-54.6048 + 54.6048i) q^{67} +(-4.84955 - 0.00468885i) q^{68} +5.79564 q^{69} +(17.6003 - 14.1561i) q^{70} +59.2198 q^{71} +(-27.5445 + 66.2266i) q^{72} +(34.1124 - 34.1124i) q^{73} +(-4.10520 - 1.70275i) q^{74} +(0.987017 - 4.51761i) q^{75} +(58.2118 - 58.0993i) q^{76} +(-19.0740 + 19.0740i) q^{77} +(4.63963 - 1.91917i) q^{78} +96.2455i q^{79} +(38.5073 - 70.1227i) q^{80} -80.0774 q^{81} +(-28.7063 - 69.3980i) q^{82} +(-63.6959 - 63.6959i) q^{83} +(-1.18052 - 1.18281i) q^{84} +(1.70522 + 5.81716i) q^{85} +(-53.3810 + 128.697i) q^{86} +(3.57588 + 3.57588i) q^{87} +(-36.6901 + 88.2156i) q^{88} +3.68406i q^{89} +(89.1352 + 9.66732i) q^{90} -30.6558i q^{91} +(0.121180 - 125.333i) q^{92} +(-5.23514 - 5.23514i) q^{93} +(36.9392 - 89.0574i) q^{94} +(-90.2080 - 49.3101i) q^{95} +(-5.46290 - 2.27829i) q^{96} +(46.0410 + 46.0410i) q^{97} +(81.1298 - 33.5591i) q^{98} -107.075 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 $

$2$	0.764474	+	1.84813i	0.382237	+	0.924064i
$2$	0.764474	+	1.84813i	0.382237	+	0.924064i
$3$	−0.130791	−	0.130791i	−0.0435971	−	0.0435971i	0.684972	−	0.728569i	$-0.259814\pi$
$3$	−0.130791	−	0.130791i	−0.0435971	−	0.0435971i	−0.728569	+	0.684972i	$0.759814\pi$
$4$	−2.83116	+	2.82569i	−0.707790	+	0.706423i
$5$	4.38731	+	2.39823i	0.877463	+	0.479645i
$5$	4.38731	+	2.39823i	0.877463	+	0.479645i
$6$	0.141733	−	0.341706i	0.0236221	−	0.0569510i
$7$	−1.59713	−	1.59713i	−0.228162	−	0.228162i	0.583763	−	0.811924i	$-0.301580\pi$
$7$	−1.59713	−	1.59713i	−0.228162	−	0.228162i	−0.811924	+	0.583763i	$0.801580\pi$
$8$	−7.38659	−	3.07218i	−0.923324	−	0.384023i
$9$		−	8.96579i		−	0.996199i
$10$	−1.07825	+	9.94170i	−0.107825	+	0.994170i
$11$		−	11.9427i		−	1.08570i	−0.839831	−	0.542849i	$-0.817346\pi$
$11$		−	11.9427i		−	1.08570i	0.839831	−	0.542849i	$-0.182654\pi$
$12$	0.739867		0.000715350i	0.0616556		5.96125e-5i
$13$	9.59714	+	9.59714i	0.738241	+	0.738241i	0.972238	−	0.233996i	$-0.0751803\pi$
$13$	9.59714	+	9.59714i	0.738241	+	0.738241i	−0.233996	+	0.972238i	$0.575180\pi$
$14$	1.73074	−	4.17267i	0.123624	−	0.298048i
$15$	−0.260155	−	0.887490i	−0.0173437	−	0.0591660i
$16$	0.0309396	−	16.0000i	0.00193372	−	0.999998i
$17$	0.857288	+	0.857288i	0.0504287	+	0.0504287i	0.731871	−	0.681443i	$-0.238647\pi$
$17$	0.857288	+	0.857288i	0.0504287	+	0.0504287i	−0.681443	+	0.731871i	$0.738647\pi$
$18$	16.5699	−	6.85411i	0.920552	−	0.380784i
$19$	−20.5611			−1.08216			−0.541082	−	0.840970i	$-0.681985\pi$
$19$	−20.5611			−1.08216			−0.541082	+	0.840970i	$0.681985\pi$
$20$	−19.1978	+	5.60743i	−0.959892	+	0.280371i
$21$			0.417782i			0.0198944i
$22$	22.0716	−	9.12986i	1.00325	−	0.414993i
$23$	−22.1560	+	22.1560i	−0.963306	+	0.963306i	−0.999350	−	0.0360441i	$-0.988524\pi$
$23$	−22.1560	+	22.1560i	−0.963306	+	0.963306i	0.0360441	+	0.999350i	$0.488524\pi$
$24$	0.564287	+	1.36792i	0.0235119	+	0.0569965i
$25$	13.4970	+	21.0435i	0.539881	+	0.841741i
$26$	−10.4000	+	25.0735i	−0.400000	+	0.964366i
$27$	−2.34977	+	2.34977i	−0.0870285	+	0.0870285i
$28$	9.03474	+	0.00873536i	0.322669	+	0.000311977i
$29$	−27.3404			−0.942771			−0.471385	−	0.881927i	$-0.656246\pi$
$29$	−27.3404			−0.942771			−0.471385	+	0.881927i	$0.656246\pi$
$30$	1.44131	−	1.15926i	0.0480438	−	0.0386421i
$31$	40.0267			1.29118			0.645591	−	0.763683i	$-0.276611\pi$
$31$	40.0267			1.29118			0.645591	+	0.763683i	$0.276611\pi$
$32$	29.5937	−	12.1744i	0.924802	−	0.380449i
$33$	−1.56200	+	1.56200i	−0.0473333	+	0.0473333i
$34$	−0.929005	+	2.23975i	−0.0273237	+	0.0658751i
$35$	−3.17684	−	10.8374i	−0.0907668	−	0.309640i
$36$	25.3345	+	25.3836i	0.703737	+	0.705100i
$37$	−1.57131	+	1.57131i	−0.0424677	+	0.0424677i	−0.728022	−	0.685554i	$-0.759560\pi$
$37$	−1.57131	+	1.57131i	−0.0424677	+	0.0424677i	0.685554	+	0.728022i	$0.259560\pi$
$38$	−15.7184	−	37.9996i	−0.413642	−	0.999988i
$39$		−	2.51044i		−	0.0643704i
$40$	−25.0395	−	31.1933i	−0.625987	−	0.779833i
$41$	−37.5504			−0.915864			−0.457932	−	0.888987i	$-0.651410\pi$
$41$	−37.5504			−0.915864			−0.457932	+	0.888987i	$0.651410\pi$
$42$	−0.772115	+	0.319383i	−0.0183837	+	0.00760437i
$43$	49.2602	+	49.2602i	1.14558	+	1.14558i	0.987411	+	0.158174i	$0.0505606\pi$
$43$	49.2602	+	49.2602i	1.14558	+	1.14558i	0.158174	+	0.987411i	$0.449439\pi$
$44$	33.7463	+	33.8116i	0.766961	+	0.768446i
$45$	21.5020	−	39.3357i	0.477822	−	0.874127i
$46$	−57.8849	−	24.0095i	−1.25837	−	0.521946i
$47$	−34.0876	−	34.0876i	−0.725268	−	0.725268i	0.244405	−	0.969673i	$-0.421407\pi$
$47$	−34.0876	−	34.0876i	−0.725268	−	0.725268i	−0.969673	+	0.244405i	$0.921407\pi$
$48$	−2.09670	+	2.08861i	−0.0436813	+	0.0435127i
$49$		−	43.8983i		−	0.895884i
$50$	−28.5730	+	41.0315i	−0.571461	+	0.820629i
$51$		−	0.224252i		−	0.00439709i
$52$	−54.2896	−	0.0524906i	−1.04403	−	0.00100943i
$53$	−28.8002	−	28.8002i	−0.543401	−	0.543401i	0.381124	−	0.924524i	$-0.375537\pi$
$53$	−28.8002	−	28.8002i	−0.543401	−	0.543401i	−0.924524	+	0.381124i	$0.875537\pi$
$54$	−6.13901	−	2.54634i	−0.113685	−	0.0471544i
$55$	28.6412	−	52.3962i	0.520749	−	0.952659i
$56$	6.89068	+	16.7040i	0.123048	+	0.298287i
$57$	2.68921	+	2.68921i	0.0471792	+	0.0471792i
$58$	−20.9010	−	50.5285i	−0.360362	−	0.871181i
$59$	92.7071			1.57131			0.785653	−	0.618667i	$-0.212327\pi$
$59$	92.7071			1.57131			0.785653	+	0.618667i	$0.212327\pi$
$60$	3.24431	+	1.77751i	0.0540719	+	0.0296251i
$61$			4.82618i			0.0791176i	0.999217	+	0.0395588i	$0.0125952\pi$
$61$			4.82618i			0.0791176i	−0.999217	+	0.0395588i	$0.987405\pi$
$62$	30.5993	+	73.9744i	0.493537	+	1.19314i
$63$	−14.3196	+	14.3196i	−0.227294	+	0.227294i
$64$	45.1234	+	45.3859i	0.705053	+	0.709155i
$65$	19.0895	+	65.1217i	0.293685	+	1.00187i
$66$	−4.08088	−	1.69267i	−0.0618315	−	0.0256465i
$67$	−54.6048	+	54.6048i	−0.814997	+	0.814997i	−0.985378	−	0.170381i	$-0.945500\pi$
$67$	−54.6048	+	54.6048i	−0.814997	+	0.814997i	0.170381	+	0.985378i	$0.445500\pi$
$68$	−4.84955	−	0.00468885i	−0.0713169	−	6.89537e-5i
$69$	5.79564			0.0839947
$70$	17.6003	−	14.1561i	0.251433	−	0.202230i
$71$	59.2198			0.834082			0.417041	−	0.908888i	$-0.363067\pi$
$71$	59.2198			0.834082			0.417041	+	0.908888i	$0.363067\pi$
$72$	−27.5445	+	66.2266i	−0.382563	+	0.919814i
$73$	34.1124	−	34.1124i	0.467293	−	0.467293i	−0.433743	−	0.901037i	$-0.642807\pi$
$73$	34.1124	−	34.1124i	0.467293	−	0.467293i	0.901037	+	0.433743i	$0.142807\pi$
$74$	−4.10520	−	1.70275i	−0.0554756	−	0.0230102i
$75$	0.987017	−	4.51761i	0.0131602	−	0.0602347i
$76$	58.2118	−	58.0993i	0.765944	−	0.764465i
$77$	−19.0740	+	19.0740i	−0.247715	+	0.247715i
$78$	4.63963	−	1.91917i	0.0594824	−	0.0246047i
$79$			96.2455i			1.21830i	0.793056	+	0.609149i	$0.208489\pi$
$79$			96.2455i			1.21830i	−0.793056	+	0.609149i	$0.791511\pi$
$80$	38.5073	−	70.1227i	0.481341	−	0.876533i
$81$	−80.0774			−0.988610
$82$	−28.7063	−	69.3980i	−0.350077	−	0.846317i
$83$	−63.6959	−	63.6959i	−0.767421	−	0.767421i	0.210231	−	0.977652i	$-0.432578\pi$
$83$	−63.6959	−	63.6959i	−0.767421	−	0.767421i	−0.977652	+	0.210231i	$0.932578\pi$
$84$	−1.18052	−	1.18281i	−0.0140539	−	0.0140811i
$85$	1.70522	+	5.81716i	0.0200614	+	0.0684372i
$86$	−53.3810	+	128.697i	−0.620710	+	1.49648i
$87$	3.57588	+	3.57588i	0.0411021	+	0.0411021i
$88$	−36.6901	+	88.2156i	−0.416933	+	1.00245i
$89$			3.68406i			0.0413939i	0.999786	+	0.0206970i	$0.00658852\pi$
$89$			3.68406i			0.0413939i	−0.999786	+	0.0206970i	$0.993411\pi$
$90$	89.1352	+	9.66732i	0.990391	+	0.107415i
$91$		−	30.6558i		−	0.336877i
$92$	0.121180	−	125.333i	0.00131718	−	1.36232i
$93$	−5.23514	−	5.23514i	−0.0562918	−	0.0562918i
$94$	36.9392	−	89.0574i	0.392970	−	0.947419i
$95$	−90.2080	−	49.3101i	−0.949558	−	0.519054i
$96$	−5.46290	−	2.27829i	−0.0569052	−	0.0237322i
$97$	46.0410	+	46.0410i	0.474650	+	0.474650i	0.903416	−	0.428766i	$-0.141051\pi$
$97$	46.0410	+	46.0410i	0.474650	+	0.474650i	−0.428766	+	0.903416i	$0.641051\pi$
$98$	81.1298	−	33.5591i	0.827855	−	0.342440i
$99$	−107.075			−1.08157
$100$	−97.6748	−	21.4392i	−0.976748	−	0.214392i
$101$			108.173i			1.07102i	0.844529	+	0.535510i	$0.179880\pi$
$101$			108.173i			1.07102i	−0.844529	+	0.535510i	$0.820120\pi$
$102$	0.414446	−	0.171434i	0.00406320	−	0.00168073i
$103$	−50.9112	+	50.9112i	−0.494284	+	0.494284i	−0.909653	−	0.415369i	$-0.863652\pi$
$103$	−50.9112	+	50.9112i	−0.494284	+	0.494284i	0.415369	+	0.909653i	$0.363652\pi$
$104$	−41.4059	−	100.374i	−0.398134	−	0.965137i
$105$	−1.00194	+	1.83294i	−0.00954225	+	0.0174566i
$106$	31.2095	−	75.2435i	0.294429	−	0.709845i
$107$	95.4147	−	95.4147i	0.891726	−	0.891726i	−0.102960	−	0.994686i	$-0.532831\pi$
$107$	95.4147	−	95.4147i	0.891726	−	0.891726i	0.994686	+	0.102960i	$0.0328312\pi$
$108$	0.0128518	−	13.2923i	0.000118998	−	0.123077i
$109$	46.5432			0.427002			0.213501	−	0.976943i	$-0.431513\pi$
$109$	46.5432			0.427002			0.213501	+	0.976943i	$0.431513\pi$
$110$	118.730	+	12.8771i	1.07937	+	0.117065i
$111$	0.411026			0.00370294
$112$	−25.6035	+	25.5047i	−0.228603	+	0.227720i
$113$	88.0400	−	88.0400i	0.779115	−	0.779115i	−0.200565	−	0.979680i	$-0.564278\pi$
$113$	88.0400	−	88.0400i	0.779115	−	0.779115i	0.979680	+	0.200565i	$0.0642779\pi$
$114$	−2.91418	+	7.02585i	−0.0255630	+	0.0616302i
$115$	−150.341	+	44.0703i	−1.30731	+	0.383220i
$116$	77.4049	−	77.2554i	0.667284	−	0.665995i
$117$	86.0459	−	86.0459i	0.735435	−	0.735435i
$118$	70.8721	+	171.335i	0.600611	+	1.45199i
$119$		−	2.73841i		−	0.0230118i
$120$	−0.804870	+	7.35477i	−0.00670725	+	0.0612897i
$121$	−21.6274			−0.178739
$122$	−8.91939	+	3.68948i	−0.0731098	+	0.0302417i
$123$	4.91127	+	4.91127i	0.0399290	+	0.0399290i
$124$	−113.322	+	113.103i	−0.913886	+	0.912121i
$125$	8.74856	+	124.693i	0.0699885	+	0.997548i
$126$	−37.4113	−	15.5175i	−0.296915	−	0.123154i
$127$	44.3246	+	44.3246i	0.349012	+	0.349012i	0.859742	−	0.510729i	$-0.170625\pi$
$127$	44.3246	+	44.3246i	0.349012	+	0.349012i	−0.510729	+	0.859742i	$0.670625\pi$
$128$	−49.3834	+	118.090i	−0.385808	+	0.922579i
$129$		−	12.8856i		−	0.0998884i
$130$	−105.760	+	85.0638i	−0.813538	+	0.654337i
$131$		−	82.8025i		−	0.632080i	−0.948746	−	0.316040i	$-0.897647\pi$
$131$		−	82.8025i		−	0.632080i	0.948746	−	0.316040i	$-0.102353\pi$
$132$	0.00854319	−	8.83599i	6.47212e−5	−	0.0669393i
$133$	32.8388	+	32.8388i	0.246908	+	0.246908i
$134$	−142.661	−	59.1728i	−1.06463	−	0.441588i
$135$	−15.9444	+	4.67390i	−0.118107	+	0.0346215i
$136$	−3.69869	−	8.96618i	−0.0271962	−	0.0659278i
$137$	25.0030	+	25.0030i	0.182503	+	0.182503i	0.792446	−	0.609942i	$-0.208807\pi$
$137$	25.0030	+	25.0030i	0.182503	+	0.182503i	−0.609942	+	0.792446i	$0.708807\pi$
$138$	4.43061	+	10.7111i	0.0321059	+	0.0776165i
$139$	104.684			0.753121			0.376561	−	0.926392i	$-0.377107\pi$
$139$	104.684			0.753121			0.376561	+	0.926392i	$0.377107\pi$
$140$	39.6173	+	21.7057i	0.282981	+	0.155041i
$141$			8.91673i			0.0632392i
$142$	45.2720	+	109.446i	0.318817	+	0.770745i
$143$	114.615	−	114.615i	0.801507	−	0.801507i
$144$	−143.452	−	0.277398i	−0.996197	−	0.00192637i
$145$	−119.951	−	65.5683i	−0.827246	−	0.452195i
$146$	89.1222	+	36.9661i	0.610426	+	0.253193i
$147$	−5.74152	+	5.74152i	−0.0390580	+	0.0390580i
$148$	0.00859410	−	8.88864i	5.80682e−5	−	0.0600584i
$149$	−49.3481			−0.331196			−0.165598	−	0.986193i	$-0.552955\pi$
$149$	−49.3481			−0.331196			−0.165598	+	0.986193i	$0.552955\pi$
$150$	9.10367	−	1.62946i	0.0606911	−	0.0108630i
$151$	−22.1078			−0.146409			−0.0732047	−	0.997317i	$-0.523323\pi$
$151$	−22.1078			−0.146409			−0.0732047	+	0.997317i	$0.523323\pi$
$152$	151.876	+	63.1675i	0.999187	+	0.415575i
$153$	7.68626	−	7.68626i	0.0502370	−	0.0502370i
$154$	−49.8329	−	20.6697i	−0.323590	−	0.134219i
$155$	175.609	+	95.9930i	1.13296	+	0.619309i
$156$	7.09374	+	7.10747i	0.0454727	+	0.0455607i
$157$	64.7264	−	64.7264i	0.412270	−	0.412270i	−0.470258	−	0.882529i	$-0.655839\pi$
$157$	64.7264	−	64.7264i	0.412270	−	0.412270i	0.882529	+	0.470258i	$0.155839\pi$
$158$	−177.874	+	73.5771i	−1.12579	+	0.465678i
$159$			7.53364i			0.0473814i
$160$	159.034	+	17.5595i	0.993960	+	0.109747i
$161$	70.7723			0.439579
$162$	−61.2171	−	147.993i	−0.377883	−	0.913540i
$163$	−25.7888	−	25.7888i	−0.158213	−	0.158213i	0.623561	−	0.781775i	$-0.285685\pi$
$163$	−25.7888	−	25.7888i	−0.158213	−	0.158213i	−0.781775	+	0.623561i	$0.785685\pi$
$164$	106.311	−	106.106i	0.648240	−	0.646987i
$165$	−10.5990	+	3.10695i	−0.0642363	+	0.0188300i
$166$	69.0244	−	166.412i	0.415810	−	1.00248i
$167$	−56.4754	−	56.4754i	−0.338176	−	0.338176i	0.517504	−	0.855681i	$-0.326861\pi$
$167$	−56.4754	−	56.4754i	−0.338176	−	0.338176i	−0.855681	+	0.517504i	$0.826861\pi$
$168$	1.28350	−	3.08599i	0.00763990	−	0.0183690i
$169$			15.2101i			0.0900005i
$170$	−9.44727	+	7.59853i	−0.0555722	+	0.0446973i
$171$			184.346i			1.07805i
$172$	−278.657	−	0.269424i	−1.62010	−	0.00156642i
$173$	−135.496	−	135.496i	−0.783216	−	0.783216i	0.197156	−	0.980372i	$-0.436829\pi$
$173$	−135.496	−	135.496i	−0.783216	−	0.783216i	−0.980372	+	0.197156i	$0.936829\pi$
$174$	−3.87502	+	9.34236i	−0.0222702	+	0.0536917i
$175$	12.0528	−	55.1659i	0.0688729	−	0.315233i
$176$	−191.082	−	0.369501i	−1.08570	−	0.00209944i
$177$	−12.1253	−	12.1253i	−0.0685044	−	0.0685044i
$178$	−6.80861	+	2.81636i	−0.0382506	+	0.0158223i
$179$	−15.5036			−0.0866121			−0.0433061	−	0.999062i	$-0.513789\pi$
$179$	−15.5036			−0.0866121			−0.0433061	+	0.999062i	$0.513789\pi$
$180$	50.2750	+	172.124i	0.279306	+	0.956243i
$181$		−	263.672i		−	1.45675i	−0.685179	−	0.728375i	$-0.740276\pi$
$181$		−	263.672i		−	1.45675i	0.685179	−	0.728375i	$-0.259724\pi$
$182$	56.6559	−	23.4355i	0.311296	−	0.128767i
$183$	0.631222	−	0.631222i	0.00344930	−	0.00344930i
$184$	231.725	−	95.5901i	1.25937	−	0.519512i
$185$	−10.6622	+	3.12546i	−0.0576333	+	0.0168944i
$186$	5.67309	−	13.6773i	0.0305005	−	0.0735341i
$187$	10.2383	−	10.2383i	0.0547503	−	0.0547503i
$188$	192.829	+	0.186439i	1.02568	+	0.000991696i
$189$	7.50579			0.0397132
$190$	22.1699	−	204.412i	0.116684	−	1.07585i
$191$	−120.714			−0.632010			−0.316005	−	0.948758i	$-0.602342\pi$
$191$	−120.714			−0.632010			−0.316005	+	0.948758i	$0.602342\pi$
$192$	0.0343368	−	11.8378i	0.000178837	−	0.0616554i
$193$	−182.404	+	182.404i	−0.945098	+	0.945098i	−0.998569	−	0.0534716i	$-0.982971\pi$
$193$	−182.404	+	182.404i	−0.945098	+	0.945098i	0.0534716	+	0.998569i	$0.482971\pi$
$194$	−49.8926	+	120.287i	−0.257178	+	0.620036i
$195$	6.02061	−	11.0141i	0.0308749	−	0.0564826i
$196$	124.043	+	124.283i	0.632873	+	0.634098i
$197$	−224.288	+	224.288i	−1.13852	+	1.13852i	−0.149799	+	0.988716i	$0.547863\pi$
$197$	−224.288	+	224.288i	−1.13852	+	1.13852i	−0.988716	+	0.149799i	$0.952137\pi$
$198$	−81.8563	−	197.889i	−0.413416	−	0.999441i
$199$		−	87.9089i		−	0.441753i	−0.975302	−	0.220877i	$-0.929108\pi$
$199$		−	87.9089i		−	0.441753i	0.975302	−	0.220877i	$-0.0708918\pi$
$200$	−35.0474	−	196.905i	−0.175237	−	0.984526i
$201$	14.2837			0.0710631
$202$	−199.918	+	82.6954i	−0.989691	+	0.409383i
$203$	43.6662	+	43.6662i	0.215104	+	0.215104i
$204$	0.633666	+	0.634892i	0.00310621	+	0.00311222i
$205$	−164.745	−	90.0544i	−0.803636	−	0.439290i
$206$	−133.011	−	55.1702i	−0.645684	−	0.267817i
$207$	198.646	+	198.646i	0.959644	+	0.959644i
$208$	153.851	−	153.257i	0.739667	−	0.736812i
$209$			245.554i			1.17490i
$210$	−4.15347	−	0.450472i	−0.0197784	−	0.00214510i
$211$			119.117i			0.564534i	0.959336	+	0.282267i	$0.0910864\pi$
$211$			119.117i			0.564534i	−0.959336	+	0.282267i	$0.908914\pi$
$212$	162.919	+	0.157520i	0.768484	+	0.000743019i
$213$	−7.74544	−	7.74544i	−0.0363636	−	0.0363636i
$214$	249.281	+	103.397i	1.16486	+	0.483162i
$215$	97.9828	+	334.257i	0.455734	+	1.55468i
$216$	24.5757	−	10.1379i	0.113776	−	0.0469345i
$217$	−63.9279	−	63.9279i	−0.294599	−	0.294599i
$218$	35.5811	+	86.0179i	0.163216	+	0.394577i
$219$	−8.92322			−0.0407453
$220$	66.9677	+	229.273i	0.304399	+	1.04215i
$221$			16.4550i			0.0744571i
$222$	0.314219	+	0.759629i	0.00141540	+	0.00342175i
$223$	111.993	−	111.993i	0.502212	−	0.502212i	−0.409913	−	0.912125i	$-0.634441\pi$
$223$	111.993	−	111.993i	0.502212	−	0.502212i	0.912125	+	0.409913i	$0.134441\pi$
$224$	−66.7091	−	27.8209i	−0.297808	−	0.124200i
$225$	188.672	−	121.011i	0.838541	−	0.537829i
$226$	230.013	+	95.4050i	1.01776	+	0.422146i
$227$	−85.8837	+	85.8837i	−0.378342	+	0.378342i	−0.870504	−	0.492162i	$-0.836207\pi$
$227$	−85.8837	+	85.8837i	−0.378342	+	0.378342i	0.492162	+	0.870504i	$0.336207\pi$
$228$	−15.2125	−	0.0147084i	−0.0667214	−	6.45105e-5i
$229$	26.5156			0.115789			0.0578943	−	0.998323i	$-0.481561\pi$
$229$	26.5156			0.115789			0.0578943	+	0.998323i	$0.481561\pi$
$230$	−196.379	−	244.158i	−0.853822	−	1.06156i
$231$	4.98944			0.0215993
$232$	201.952	+	83.9946i	0.870482	+	0.362046i
$233$	−71.6569	+	71.6569i	−0.307541	+	0.307541i	−0.843955	−	0.536414i	$-0.819778\pi$
$233$	−71.6569	+	71.6569i	−0.307541	+	0.307541i	0.536414	+	0.843955i	$0.319778\pi$
$234$	224.804	+	93.2441i	0.960700	+	0.398479i
$235$	−67.8033	−	231.303i	−0.288524	−	0.984267i
$236$	−262.469	+	261.962i	−1.11215	+	1.11001i
$237$	12.5881	−	12.5881i	0.0531143	−	0.0531143i
$238$	5.06093	−	2.09344i	0.0212644	−	0.00879596i
$239$		−	114.913i		−	0.480809i	−0.970673	−	0.240405i	$-0.922720\pi$
$239$		−	114.913i		−	0.480809i	0.970673	−	0.240405i	$-0.0772801\pi$
$240$	−14.2079	+	4.13502i	−0.0591994	+	0.0172293i
$241$	219.080			0.909045			0.454522	−	0.890735i	$-0.349810\pi$
$241$	219.080			0.909045			0.454522	+	0.890735i	$0.349810\pi$
$242$	−16.5336	−	39.9702i	−0.0683205	−	0.165166i
$243$	31.6214	+	31.6214i	0.130129	+	0.130129i
$244$	−13.6373	−	13.6637i	−0.0558905	−	0.0559987i
$245$	105.278	−	192.596i	0.429707	−	0.786105i
$246$	−5.32212	+	12.8312i	−0.0216347	+	0.0521593i
$247$	−197.328	−	197.328i	−0.798897	−	0.798897i
$248$	−295.660	−	122.969i	−1.19218	−	0.495844i
$249$			16.6618i			0.0669147i
$250$	−223.762	+	111.493i	−0.895046	+	0.445973i
$251$		−	95.0552i		−	0.378706i	−0.981909	−	0.189353i	$-0.939361\pi$
$251$		−	95.0552i		−	0.378706i	0.981909	−	0.189353i	$-0.0606390\pi$
$252$	0.0783194	−	81.0036i	0.000310791	−	0.321443i
$253$	264.602	+	264.602i	1.04586	+	1.04586i
$254$	−48.0326	+	115.802i	−0.189105	+	0.455915i
$255$	0.537806	−	0.983862i	0.00210904	−	0.00385828i
$256$	−255.998	−	0.990065i	−0.999993	−	0.00386744i
$257$	−249.128	−	249.128i	−0.969369	−	0.969369i	0.0301755	−	0.999545i	$-0.490393\pi$
$257$	−249.128	−	249.128i	−0.969369	−	0.969369i	−0.999545	+	0.0301755i	$0.990393\pi$
$258$	23.8143	−	9.85070i	0.0923033	−	0.0381810i
$259$	5.01917			0.0193790
$260$	−238.059	−	130.429i	−0.915613	−	0.501650i
$261$			245.128i			0.939187i
$262$	153.030	−	63.3003i	0.584082	−	0.241604i
$263$	−85.6095	+	85.6095i	−0.325511	+	0.325511i	−0.850877	−	0.525365i	$-0.823929\pi$
$263$	−85.6095	+	85.6095i	−0.325511	+	0.325511i	0.525365	+	0.850877i	$0.323929\pi$
$264$	16.3366	−	6.73909i	0.0618810	−	0.0255269i
$265$	−57.2862	−	195.425i	−0.216174	−	0.737453i
$266$	−35.5859	+	85.7947i	−0.133782	+	0.322537i
$267$	0.481843	−	0.481843i	0.00180465	−	0.00180465i
$268$	0.298656	−	308.891i	0.00111439	−	1.15258i
$269$	192.119			0.714196			0.357098	−	0.934067i	$-0.383766\pi$
$269$	192.119			0.714196			0.357098	+	0.934067i	$0.383766\pi$
$270$	−20.8271	−	25.8943i	−0.0771373	−	0.0959049i
$271$	−485.780			−1.79255			−0.896274	−	0.443501i	$-0.853736\pi$
$271$	−485.780			−1.79255			−0.896274	+	0.443501i	$0.853736\pi$
$272$	13.7431	−	13.6901i	0.0505261	−	0.0503311i
$273$	−4.00951	+	4.00951i	−0.0146869	+	0.0146869i
$274$	−27.0946	+	65.3228i	−0.0988853	+	0.238404i
$275$	251.316	−	161.191i	0.913876	−	0.586148i
$276$	−16.4084	+	16.3767i	−0.0594506	+	0.0593358i
$277$	88.8551	−	88.8551i	0.320777	−	0.320777i	−0.528288	−	0.849065i	$-0.677166\pi$
$277$	88.8551	−	88.8551i	0.320777	−	0.320777i	0.849065	+	0.528288i	$0.177166\pi$
$278$	80.0280	+	193.469i	0.287871	+	0.695933i
$279$		−	358.871i		−	1.28627i
$280$	−9.82851	+	89.8113i	−0.0351018	+	0.320755i
$281$	390.006			1.38792			0.693961	−	0.720012i	$-0.255864\pi$
$281$	390.006			1.38792			0.693961	+	0.720012i	$0.255864\pi$
$282$	−16.4793	+	6.81660i	−0.0584371	+	0.0241724i
$283$	−121.062	−	121.062i	−0.427779	−	0.427779i	0.460092	−	0.887871i	$-0.347816\pi$
$283$	−121.062	−	121.062i	−0.427779	−	0.427779i	−0.887871	+	0.460092i	$0.847816\pi$
$284$	−167.661	+	167.337i	−0.590355	+	0.589214i
$285$	5.34908	+	18.2478i	0.0187687	+	0.0640272i
$286$	299.445	+	124.204i	1.04701	+	0.434278i
$287$	59.9730	+	59.9730i	0.208965	+	0.208965i
$288$	−109.153	−	265.330i	−0.379003	−	0.921286i
$289$		−	287.530i		−	0.994914i
$290$	29.4796	−	271.810i	0.101654	−	0.937274i
$291$		−	12.0435i		−	0.0413867i
$292$	−0.186575	+	192.969i	−0.000638954	+	0.660852i
$293$	244.956	+	244.956i	0.836026	+	0.836026i	0.988333	−	0.152307i	$-0.0486702\pi$
$293$	244.956	+	244.956i	0.836026	+	0.836026i	−0.152307	+	0.988333i	$0.548670\pi$
$294$	−15.0003	−	6.22183i	−0.0510215	−	0.0211627i
$295$	406.735	+	222.332i	1.37876	+	0.753669i
$296$	16.4339	−	6.77925i	0.0555200	−	0.0229029i
$297$	28.0625	+	28.0625i	0.0944866	+	0.0944866i
$298$	−37.7253	−	91.2017i	−0.126595	−	0.306046i
$299$	−425.269			−1.42230
$300$	9.97096	+	15.5791i	0.0332365	+	0.0519302i
$301$		−	157.350i		−	0.522757i
$302$	−16.9008	−	40.8581i	−0.0559630	−	0.135292i
$303$	14.1481	−	14.1481i	0.0466934	−	0.0466934i
$304$	−0.636152	+	328.977i	−0.00209260	+	1.08216i
$305$	−11.5743	+	21.1739i	−0.0379484	+	0.0694228i
$306$	20.0811	+	8.32926i	0.0656247	+	0.0272198i
$307$	135.324	−	135.324i	0.440796	−	0.440796i	−0.451483	−	0.892280i	$-0.649105\pi$
$307$	135.324	−	135.324i	0.440796	−	0.440796i	0.892280	+	0.451483i	$0.149105\pi$
$308$	0.104324	−	107.899i	0.000338713	−	0.350321i
$309$	13.3175			0.0430987
$310$	−43.1585	+	397.933i	−0.139221	+	1.28365i
$311$	225.951			0.726531			0.363266	−	0.931686i	$-0.381662\pi$
$311$	225.951			0.726531			0.363266	+	0.931686i	$0.381662\pi$
$312$	−7.71255	+	18.5436i	−0.0247197	+	0.0594347i
$313$	−230.622	+	230.622i	−0.736812	+	0.736812i	−0.971960	−	0.235148i	$-0.924443\pi$
$313$	−230.622	+	230.622i	−0.736812	+	0.736812i	0.235148	+	0.971960i	$0.424443\pi$
$314$	169.104	+	70.1411i	0.538549	+	0.223379i
$315$	−97.1659	+	28.4828i	−0.308463	+	0.0904217i
$316$	−271.960	−	272.486i	−0.860633	−	0.862299i
$317$	−221.563	+	221.563i	−0.698938	+	0.698938i	−0.964182	−	0.265243i	$-0.914548\pi$
$317$	−221.563	+	221.563i	−0.698938	+	0.698938i	0.265243	+	0.964182i	$0.414548\pi$
$318$	−13.9231	+	5.75927i	−0.0437835	+	0.0181109i
$319$			326.517i			1.02356i
$320$	89.1247	+	307.338i	0.278515	+	0.960432i
$321$	−24.9588			−0.0777534
$322$	54.1035	+	130.796i	0.168023	+	0.406200i
$323$	−17.6268	−	17.6268i	−0.0545721	−	0.0545721i
$324$	226.712	−	226.274i	0.699729	−	0.698377i
$325$	−72.4248	+	331.490i	−0.222846	+	1.01997i
$326$	27.9462	−	67.3759i	0.0857244	−	0.206674i
$327$	−6.08745	−	6.08745i	−0.0186161	−	0.0186161i
$328$	277.370	+	115.362i	0.845639	+	0.351713i
$329$			108.885i			0.330957i
$330$	−13.8447	−	17.2131i	−0.0419536	−	0.0521610i
$331$		−	141.212i		−	0.426624i	−0.976984	−	0.213312i	$-0.931575\pi$
$331$		−	141.212i		−	0.426624i	0.976984	−	0.213312i	$-0.0684250\pi$
$332$	360.318	+	0.348379i	1.08530	+	0.00104933i
$333$	14.0880	+	14.0880i	0.0423063	+	0.0423063i
$334$	61.1999	−	147.548i	0.183233	−	0.441760i
$335$	−370.523	+	108.614i	−1.10604	+	0.324220i
$336$	6.68450	+	0.0129260i	0.0198944	+	3.84703e-5i
$337$	225.465	+	225.465i	0.669035	+	0.669035i	0.957493	−	0.288458i	$-0.0931424\pi$
$337$	225.465	+	225.465i	0.669035	+	0.669035i	−0.288458	+	0.957493i	$0.593142\pi$
$338$	−28.1102	+	11.6277i	−0.0831663	+	0.0344015i
$339$	−23.0297			−0.0679343
$340$	−21.2653	−	11.6509i	−0.0625449	−	0.0342673i
$341$		−	478.025i		−	1.40183i
$342$	−340.696	+	140.928i	−0.996187	+	0.412070i
$343$	−148.371	+	148.371i	−0.432568	+	0.432568i
$344$	−212.528	−	515.201i	−0.617815	−	1.49768i
$345$	25.4273	+	13.8992i	0.0737022	+	0.0402877i
$346$	146.831	−	353.998i	0.424368	−	1.02312i
$347$	−346.013	+	346.013i	−0.997155	+	0.997155i	−0.999996	−	0.00284067i	$-0.999096\pi$
$347$	−346.013	+	346.013i	−0.997155	+	0.997155i	0.00284067	+	0.999996i	$0.499096\pi$
$348$	−20.2282	−	0.0195579i	−0.0581271	−	5.62009e-5i
$349$	−428.411			−1.22754			−0.613769	−	0.789486i	$-0.710347\pi$
$349$	−428.411			−1.22754			−0.613769	+	0.789486i	$0.710347\pi$
$350$	111.168	−	19.8978i	0.317622	−	0.0568508i
$351$	−45.1021			−0.128496
$352$	−145.395	−	353.427i	−0.413053	−	1.00405i
$353$	25.9724	−	25.9724i	0.0735762	−	0.0735762i	−0.669361	−	0.742937i	$-0.733432\pi$
$353$	25.9724	−	25.9724i	0.0735762	−	0.0735762i	0.742937	+	0.669361i	$0.233432\pi$
$354$	13.1396	−	31.6785i	0.0371176	−	0.0894874i
$355$	259.816	+	142.022i	0.731876	+	0.400063i
$356$	−10.4100	−	10.4302i	−0.0292416	−	0.0292982i
$357$	−0.358160	+	0.358160i	−0.00100325	+	0.00100325i
$358$	−11.8521	−	28.6526i	−0.0331063	−	0.0800352i
$359$		−	288.043i		−	0.802348i	−0.916002	−	0.401174i	$-0.868602\pi$
$359$		−	288.043i		−	0.802348i	0.916002	−	0.401174i	$-0.131398\pi$
$360$	−279.673	+	224.499i	−0.776869	+	0.623608i
$361$	61.7587			0.171077
$362$	487.299	−	201.570i	1.34613	−	0.556823i
$363$	2.82868	+	2.82868i	0.00779249	+	0.00779249i
$364$	86.6238	+	86.7915i	0.237978	+	0.238438i
$365$	231.471	−	67.8526i	0.634168	−	0.185898i
$366$	1.64913	+	0.684027i	0.00450583	+	0.00186893i
$367$	160.854	+	160.854i	0.438295	+	0.438295i	0.891438	−	0.453143i	$-0.149697\pi$
$367$	160.854	+	160.854i	0.438295	+	0.438295i	−0.453143	+	0.891438i	$0.649697\pi$
$368$	353.810	+	355.181i	0.961442	+	0.965167i
$369$			336.669i			0.912382i
$370$	−13.9272	−	17.3157i	−0.0376411	−	0.0467992i
$371$			91.9956i			0.247966i
$372$	29.6144	+	0.0286331i	0.0796086	+	7.69706e-5i
$373$	−360.121	−	360.121i	−0.965471	−	0.965471i	0.0339529	−	0.999423i	$-0.489190\pi$
$373$	−360.121	−	360.121i	−0.965471	−	0.965471i	−0.999423	+	0.0339529i	$0.989190\pi$
$374$	26.7486	+	11.0948i	0.0715204	+	0.0296652i
$375$	15.1646	−	17.4531i	0.0404389	−	0.0465415i
$376$	147.068	+	356.515i	0.391138	+	0.948177i
$377$	−262.389	−	262.389i	−0.695992	−	0.695992i
$378$	5.73797	+	13.8717i	0.0151798	+	0.0366975i
$379$	−64.1572			−0.169280			−0.0846402	−	0.996412i	$-0.526974\pi$
$379$	−64.1572			−0.169280			−0.0846402	+	0.996412i	$0.526974\pi$
$380$	394.728	−	115.295i	1.03876	−	0.303408i
$381$		−	11.5945i		−	0.0304319i
$382$	−92.2826	−	223.095i	−0.241577	−	0.584018i
$383$	376.877	−	376.877i	0.984014	−	0.984014i	−0.0158604	−	0.999874i	$-0.505049\pi$
$383$	376.877	−	376.877i	0.984014	−	0.984014i	0.999874	+	0.0158604i	$0.00504875\pi$
$384$	21.9041	−	8.98625i	0.0570419	−	0.0234017i
$385$	−129.428	+	37.9399i	−0.336175	+	0.0985452i
$386$	−476.549	−	197.663i	−1.23458	−	0.512080i
$387$	441.656	−	441.656i	1.14123	−	1.14123i
$388$	−260.447	−	0.251817i	−0.671256	−	0.000649013i
$389$	10.3794			0.0266823			0.0133411	−	0.999911i	$-0.495753\pi$
$389$	10.3794			0.0266823			0.0133411	+	0.999911i	$0.495753\pi$
$390$	24.9581	+	2.70687i	0.0639951	+	0.00694070i
$391$	−37.9882			−0.0971566
$392$	−134.864	+	324.259i	−0.344040	+	0.827191i
$393$	−10.8298	+	10.8298i	−0.0275569	+	0.0275569i
$394$	−585.974	−	243.050i	−1.48724	−	0.616879i
$395$	−230.818	+	422.259i	−0.584350	+	1.06901i
$396$	303.148	−	302.562i	0.765525	−	0.764046i
$397$	184.458	−	184.458i	0.464630	−	0.464630i	−0.435540	−	0.900169i	$-0.643442\pi$
$397$	184.458	−	184.458i	0.464630	−	0.464630i	0.900169	+	0.435540i	$0.143442\pi$
$398$	162.467	−	67.2040i	0.408208	−	0.168854i
$399$		−	8.59006i		−	0.0215290i
$400$	337.113	−	215.301i	0.842784	−	0.538252i
$401$	−262.943			−0.655719			−0.327859	−	0.944727i	$-0.606327\pi$
$401$	−262.943			−0.655719			−0.327859	+	0.944727i	$0.606327\pi$
$402$	10.9195	+	26.3981i	0.0271629	+	0.0656669i
$403$	384.141	+	384.141i	0.953204	+	0.953204i
$404$	−305.663	−	306.255i	−0.756593	−	0.758057i
$405$	−351.325	−	192.044i	−0.867468	−	0.474182i
$406$	−47.3191	+	114.082i	−0.116549	+	0.280991i
$407$	18.7656	+	18.7656i	0.0461071	+	0.0461071i
$408$	−0.688942	+	1.65645i	−0.00168858	+	0.00405994i
$409$		−	245.618i		−	0.600532i	−0.953855	−	0.300266i	$-0.902925\pi$
$409$		−	245.618i		−	0.600532i	0.953855	−	0.300266i	$-0.0970755\pi$
$410$	40.4886	−	373.315i	0.0987526	−	0.910525i
$411$		−	6.54034i		−	0.0159132i
$412$	0.278454	−	287.997i	0.000675859	−	0.699023i
$413$	−148.065	−	148.065i	−0.358512	−	0.358512i
$414$	−215.264	+	518.984i	−0.519962	+	1.25358i
$415$	−126.697	−	432.211i	−0.305293	−	1.04147i
$416$	400.854	+	167.175i	0.963590	+	0.401864i
$417$	−13.6917	−	13.6917i	−0.0328339	−	0.0328339i
$418$	−453.816	+	187.720i	−1.08568	+	0.449091i
$419$	673.011			1.60623			0.803116	−	0.595823i	$-0.203174\pi$
$419$	673.011			1.60623			0.803116	+	0.595823i	$0.203174\pi$
$420$	−2.34268	−	8.02051i	−0.00557782	−	0.0190965i
$421$			701.227i			1.66562i	0.553557	+	0.832811i	$0.313270\pi$
$421$			701.227i			1.66562i	−0.553557	+	0.832811i	$0.686730\pi$
$422$	−220.143	+	91.0615i	−0.521666	+	0.215786i
$423$	−305.622	+	305.622i	−0.722511	+	0.722511i
$424$	124.256	+	301.215i	0.293056	+	0.710413i
$425$	−6.46952	+	29.6112i	−0.0152224	+	0.0696734i
$426$	8.39339	−	20.2358i	0.0197028	−	0.0475018i
$427$	7.70804	−	7.70804i	0.0180516	−	0.0180516i
$428$	−0.521861	+	539.747i	−0.00121930	+	1.26109i
$429$	−29.9814			−0.0698868
$430$	−542.844	+	436.615i	−1.26243	+	1.01538i
$431$	405.559			0.940973			0.470486	−	0.882407i	$-0.344078\pi$
$431$	405.559			0.940973			0.470486	+	0.882407i	$0.344078\pi$
$432$	37.5235	+	37.6689i	0.0868600	+	0.0871966i
$433$	145.764	−	145.764i	0.336638	−	0.336638i	−0.518462	−	0.855100i	$-0.673495\pi$
$433$	145.764	−	145.764i	0.336638	−	0.336638i	0.855100	+	0.518462i	$0.173495\pi$
$434$	69.2758	−	167.018i	0.159622	−	0.384834i
$435$	7.11274	+	24.2643i	0.0163511	+	0.0557800i
$436$	−131.771	+	131.517i	−0.302228	+	0.301644i
$437$	455.553	−	455.553i	1.04245	−	1.04245i
$438$	−6.82156	−	16.4913i	−0.0155743	−	0.0376513i
$439$			62.3888i			0.142116i	0.997472	+	0.0710579i	$0.0226375\pi$
$439$			62.3888i			0.142116i	−0.997472	+	0.0710579i	$0.977362\pi$
$440$	−372.532	+	299.038i	−0.846663	+	0.679633i
$441$	−393.583			−0.892479
$442$	−30.4110	+	12.5794i	−0.0688032	+	0.0284602i
$443$	−169.632	−	169.632i	−0.382918	−	0.382918i	0.489235	−	0.872152i	$-0.337276\pi$
$443$	−169.632	−	169.632i	−0.382918	−	0.382918i	−0.872152	+	0.489235i	$0.837276\pi$
$444$	−1.16368	+	1.16143i	−0.00262090	+	0.00261584i
$445$	−8.83520	+	16.1631i	−0.0198544	+	0.0363216i
$446$	292.594	+	121.362i	0.656040	+	0.272112i
$447$	6.45431	+	6.45431i	0.0144392	+	0.0144392i
$448$	0.419297	−	144.555i	0.000935930	−	0.322668i
$449$			17.0056i			0.0378743i	0.999821	+	0.0189371i	$0.00602824\pi$
$449$			17.0056i			0.0378743i	−0.999821	+	0.0189371i	$0.993972\pi$
$450$	367.879	+	256.180i	0.817510	+	0.569288i
$451$			448.452i			0.994351i
$452$	−0.481526	+	498.029i	−0.00106532	+	1.10183i
$453$	2.89151	+	2.89151i	0.00638303	+	0.00638303i
$454$	−224.380	−	93.0683i	−0.494229	−	0.204996i
$455$	73.5195	−	134.497i	0.161581	−	0.295597i
$456$	−11.6024	−	28.1259i	−0.0254438	−	0.0616795i
$457$	559.163	+	559.163i	1.22355	+	1.22355i	0.966360	+	0.257191i	$0.0827971\pi$
$457$	559.163	+	559.163i	1.22355	+	1.22355i	0.257191	+	0.966360i	$0.417203\pi$
$458$	20.2705	+	49.0042i	0.0442586	+	0.106996i
$459$	−4.02886			−0.00877747
$460$	301.109	−	549.586i	0.654586	−	1.19475i
$461$		−	327.625i		−	0.710683i	−0.934737	−	0.355341i	$-0.884365\pi$
$461$		−	327.625i		−	0.710683i	0.934737	−	0.355341i	$-0.115635\pi$
$462$	3.81429	+	9.22112i	0.00825604	+	0.0199591i
$463$	605.934	−	605.934i	1.30871	−	1.30871i	0.386367	−	0.922345i	$-0.373730\pi$
$463$	605.934	−	605.934i	1.30871	−	1.30871i	0.922345	−	0.386367i	$-0.126270\pi$
$464$	−0.845899	+	437.445i	−0.00182306	+	0.942769i
$465$	−10.4132	−	35.5232i	−0.0223939	−	0.0763941i
$466$	−187.211	−	77.6514i	−0.401741	−	0.166634i
$467$	−83.9231	+	83.9231i	−0.179707	+	0.179707i	−0.791228	−	0.611521i	$-0.790558\pi$
$467$	−83.9231	+	83.9231i	−0.179707	+	0.179707i	0.611521	+	0.791228i	$0.290558\pi$
$468$	−0.470619	+	486.749i	−0.00100560	+	1.04006i
$469$	174.422			0.371903
$470$	375.644	−	302.134i	0.799242	−	0.642838i
$471$	−16.9313			−0.0359476
$472$	−684.789	−	284.813i	−1.45082	−	0.603418i
$473$	588.298	−	588.298i	1.24376	−	1.24376i
$474$	32.8876	+	13.6411i	0.0693832	+	0.0287788i
$475$	−277.514	−	432.678i	−0.584239	−	0.910901i
$476$	7.73789	+	7.75286i	0.0162561	+	0.0162875i
$477$	−258.217	+	258.217i	−0.541335	+	0.541335i
$478$	212.375	−	87.8483i	0.444299	−	0.183783i
$479$			831.992i			1.73694i	0.495746	+	0.868468i	$0.334895\pi$
$479$			831.992i			1.73694i	−0.495746	+	0.868468i	$0.665105\pi$
$480$	−18.5036	−	23.0968i	−0.0385491	−	0.0481184i
$481$	−30.1601			−0.0627028
$482$	167.481	+	404.888i	0.347470	+	0.840016i
$483$	−9.25640	−	9.25640i	−0.0191644	−	0.0191644i
$484$	61.2306	−	61.1123i	0.126510	−	0.126265i
$485$	91.5797	+	312.413i	0.188824	+	0.644151i
$486$	−34.2667	+	82.6140i	−0.0705075	+	0.169988i
$487$	−373.676	−	373.676i	−0.767301	−	0.767301i	0.210329	−	0.977631i	$-0.432546\pi$
$487$	−373.676	−	373.676i	−0.767301	−	0.767301i	−0.977631	+	0.210329i	$0.932546\pi$
$488$	14.8269	−	35.6490i	0.0303830	−	0.0730512i
$489$			6.74590i			0.0137953i
$490$	436.424	+	47.3332i	0.890661	+	0.0965983i
$491$			42.8051i			0.0871795i	0.999050	+	0.0435898i	$0.0138794\pi$
$491$			42.8051i			0.0871795i	−0.999050	+	0.0435898i	$0.986121\pi$
$492$	−27.7823	−	0.0268617i	−0.0564681	−	5.45970e-5i
$493$	−23.4386	−	23.4386i	−0.0475427	−	0.0475427i
$494$	213.835	−	515.539i	0.432865	−	1.04360i
$495$	−469.773	−	256.791i	−0.949037	−	0.518770i
$496$	1.23841	−	640.425i	0.00249679	−	1.29118i
$497$	−94.5819	−	94.5819i	−0.190306	−	0.190306i
$498$	−30.7931	+	12.7375i	−0.0618335	+	0.0255772i
$499$	485.100			0.972143			0.486072	−	0.873919i	$-0.338429\pi$
$499$	485.100			0.972143			0.486072	+	0.873919i	$0.338429\pi$
$500$	−377.114	−	328.307i	−0.754228	−	0.656613i
$501$			14.7730i			0.0294870i
$502$	175.674	−	72.6672i	0.349949	−	0.144755i
$503$	−666.926	+	666.926i	−1.32590	+	1.32590i	−0.416980	+	0.908916i	$0.636912\pi$
$503$	−666.926	+	666.926i	−1.32590	+	1.32590i	−0.908916	+	0.416980i	$0.863088\pi$
$504$	149.765	−	61.7803i	0.297153	−	0.122580i
$505$	−259.423	+	474.589i	−0.513709	+	0.939780i
$506$	−286.738	+	691.301i	−0.566675	+	1.36621i
$507$	1.98935	−	1.98935i	0.00392376	−	0.00392376i
$508$	−250.738	−	0.242429i	−0.493578	−	0.000477222i
$509$	779.971			1.53236			0.766180	−	0.642626i	$-0.222155\pi$
$509$	779.971			1.53236			0.766180	+	0.642626i	$0.222155\pi$
$510$	2.22944	+	0.241798i	0.00437146	+	0.000474114i
$511$	−108.964			−0.213237
$512$	−193.874	−	473.874i	−0.378660	−	0.925536i
$513$	48.3138	−	48.3138i	0.0941790	−	0.0941790i
$514$	269.969	−	650.872i	0.525231	−	1.26629i
$515$	−345.460	+	101.267i	−0.670796	+	0.196635i
$516$	36.4107	+	36.4812i	0.0705634	+	0.0707000i
$517$	−407.097	+	407.097i	−0.787422	+	0.787422i
$518$	3.83702	+	9.27606i	0.00740737	+	0.0179075i
$519$			35.4435i			0.0682919i
$520$	59.0593	−	539.674i	0.113576	−	1.03783i
$521$	−736.972			−1.41453			−0.707267	−	0.706947i	$-0.750072\pi$
$521$	−736.972			−1.41453			−0.707267	+	0.706947i	$0.750072\pi$
$522$	−453.028	+	187.394i	−0.867869	+	0.358992i
$523$	−671.690	−	671.690i	−1.28430	−	1.28430i	−0.938195	−	0.346108i	$-0.887503\pi$
$523$	−671.690	−	671.690i	−1.28430	−	1.28430i	−0.346108	−	0.938195i	$-0.612497\pi$
$524$	233.974	+	234.427i	0.446516	+	0.447380i
$525$	−8.79161	+	5.63882i	−0.0167459	+	0.0107406i
$526$	−223.664	−	92.7712i	−0.425216	−	0.176371i
$527$	34.3144	+	34.3144i	0.0651127	+	0.0651127i
$528$	24.9436	+	25.0402i	0.0472417	+	0.0474247i
$529$		−	452.780i		−	0.855917i
$530$	317.377	−	255.270i	0.598824	−	0.481641i
$531$		−	831.192i		−	1.56533i
$532$	−185.764	−	0.179609i	−0.349181	−	0.000337610i
$533$	−360.377	−	360.377i	−0.676129	−	0.676129i
$534$	1.25886	+	0.522152i	0.00235742	+	0.000977812i
$535$	647.440	−	189.788i	1.21017	−	0.354744i
$536$	571.099	−	235.587i	1.06548	−	0.439529i
$537$	2.02773	+	2.02773i	0.00377604	+	0.00377604i
$538$	146.870	+	355.060i	0.272992	+	0.659963i
$539$	−524.263			−0.972659
$540$	31.9343	−	58.2866i	0.0591376	−	0.107938i
$541$			1039.61i			1.92164i	0.277168	+	0.960822i	$0.410604\pi$
$541$			1039.61i			1.92164i	−0.277168	+	0.960822i	$0.589396\pi$
$542$	−371.366	−	897.785i	−0.685177	−	1.65643i
$543$	−34.4860	+	34.4860i	−0.0635101	+	0.0635101i
$544$	35.8072	+	14.9333i	0.0658221	+	0.0274510i
$545$	204.200	+	111.621i	0.374678	+	0.204809i
$546$	−10.4753	−	4.34493i	−0.0191855	−	0.00795775i
$547$	−238.506	+	238.506i	−0.436026	+	0.436026i	−0.890672	−	0.454646i	$-0.849766\pi$
$547$	−238.506	+	238.506i	−0.436026	+	0.436026i	0.454646	+	0.890672i	$0.349766\pi$
$548$	−141.438	−	0.136751i	−0.258099	−	0.000249546i
$549$	43.2705			0.0788169
$550$	490.025	+	341.238i	0.890955	+	0.620433i
$551$	562.148			1.02023
$552$	−42.8100	−	17.8053i	−0.0775543	−	0.0322559i
$553$	153.717	−	153.717i	0.277969	−	0.277969i
$554$	232.143	+	96.2883i	0.419031	+	0.173806i
$555$	1.80330	+	0.985734i	0.00324919	+	0.00177610i
$556$	−296.377	+	295.804i	−0.533052	+	0.532022i
$557$	263.387	−	263.387i	0.472867	−	0.472867i	−0.429974	−	0.902841i	$-0.641477\pi$
$557$	263.387	−	263.387i	0.472867	−	0.472867i	0.902841	+	0.429974i	$0.141477\pi$
$558$	663.239	−	274.347i	1.18860	−	0.491661i
$559$			945.513i			1.69144i
$560$	−173.496	+	50.4940i	−0.309815	+	0.0901678i
$561$	−2.67816			−0.00477391
$562$	298.149	+	720.782i	0.530515	+	1.28253i
$563$	−160.698	−	160.698i	−0.285431	−	0.285431i	0.549839	−	0.835270i	$-0.314689\pi$
$563$	−160.698	−	160.698i	−0.285431	−	0.285431i	−0.835270	+	0.549839i	$0.814689\pi$
$564$	−25.1959	−	25.2447i	−0.0446736	−	0.0447601i
$565$	597.399	−	175.119i	1.05734	−	0.309946i
$566$	131.189	−	316.286i	0.231783	−	0.558809i
$567$	127.894	+	127.894i	0.225563	+	0.225563i
$568$	−437.432	−	181.934i	−0.770127	−	0.320307i
$569$			407.195i			0.715633i	0.933792	+	0.357817i	$0.116479\pi$
$569$			407.195i			0.715633i	−0.933792	+	0.357817i	$0.883521\pi$
$570$	−29.6350	+	23.8357i	−0.0519912	+	0.0418171i
$571$			131.146i			0.229678i	0.993384	+	0.114839i	$0.0366351\pi$
$571$			131.146i			0.229678i	−0.993384	+	0.114839i	$0.963365\pi$
$572$	−0.626878	+	648.363i	−0.00109594	+	1.13350i
$573$	15.7883	+	15.7883i	0.0275538	+	0.0275538i
$574$	−64.9901	+	156.686i	−0.113223	+	0.272971i
$575$	−765.282	−	167.201i	−1.33093	−	0.290784i
$576$	406.920	−	404.567i	0.706459	−	0.702373i
$577$	417.933	+	417.933i	0.724321	+	0.724321i	0.969482	−	0.245162i	$-0.0788410\pi$
$577$	417.933	+	417.933i	0.724321	+	0.724321i	−0.245162	+	0.969482i	$0.578841\pi$
$578$	531.393	−	219.809i	0.919365	−	0.380293i
$579$	47.7137			0.0824071
$580$	524.875	−	153.309i	0.904958	−	0.264326i
$581$			203.462i			0.350192i
$582$	22.2580	−	9.20697i	0.0382440	−	0.0158195i
$583$	−343.952	+	343.952i	−0.589969	+	0.589969i
$584$	−356.774	+	147.175i	−0.610914	+	0.252012i
$585$	583.868	−	171.153i	0.998064	−	0.292569i
$586$	−265.448	+	639.972i	−0.452982	+	1.09210i
$587$	−212.882	+	212.882i	−0.362660	+	0.362660i	−0.864791	−	0.502131i	$-0.832549\pi$
$587$	−212.882	+	212.882i	−0.362660	+	0.362660i	0.502131	+	0.864791i	$0.332549\pi$
$588$	0.0314027	−	32.4789i	5.34059e−5	−	0.0552363i
$589$	−822.992			−1.39727
$590$	−99.9609	+	921.666i	−0.169425	+	1.56215i
$591$	58.6697			0.0992720
$592$	25.0922	+	25.1895i	0.0423855	+	0.0425498i
$593$	97.2530	−	97.2530i	0.164002	−	0.164002i	−0.620335	−	0.784337i	$-0.713003\pi$
$593$	97.2530	−	97.2530i	0.164002	−	0.164002i	0.784337	+	0.620335i	$0.213003\pi$
$594$	−30.4101	+	73.3162i	−0.0511955	+	0.123428i
$595$	6.56731	−	12.0142i	0.0110375	−	0.0201920i
$596$	139.712	−	139.443i	0.234417	−	0.233964i
$597$	−11.4977	+	11.4977i	−0.0192592	+	0.0192592i
$598$	−325.107	−	785.952i	−0.543657	−	1.31430i
$599$		−	712.479i		−	1.18945i	−0.803930	−	0.594723i	$-0.797262\pi$
$599$		−	712.479i		−	1.18945i	0.803930	−	0.594723i	$-0.202738\pi$
$600$	−21.1696	+	30.3374i	−0.0352827	+	0.0505623i
$601$	217.550			0.361980			0.180990	−	0.983485i	$-0.442070\pi$
$601$	217.550			0.361980			0.180990	+	0.983485i	$0.442070\pi$
$602$	290.803	−	120.290i	0.483062	−	0.199817i
$603$	489.575	+	489.575i	0.811899	+	0.811899i
$604$	62.5908	−	62.4699i	0.103627	−	0.103427i
$605$	−94.8861	−	51.8674i	−0.156837	−	0.0857312i
$606$	36.9633	+	15.3317i	0.0609956	+	0.0252998i
$607$	12.6560	+	12.6560i	0.0208501	+	0.0208501i	0.717455	−	0.696605i	$-0.245307\pi$
$607$	12.6560	+	12.6560i	0.0208501	+	0.0208501i	−0.696605	+	0.717455i	$0.745307\pi$
$608$	−608.478	+	250.318i	−1.00079	+	0.411708i
$609$		−	11.4223i		−	0.0187558i
$610$	−47.9804	−	5.20380i	−0.0786564	−	0.00853082i
$611$		−	654.287i		−	1.07085i
$612$	−0.0420392	+	43.4800i	−6.86916e−5	+	0.0710458i
$613$	523.841	+	523.841i	0.854552	+	0.854552i	0.990690	−	0.136138i	$-0.0434689\pi$
$613$	523.841	+	523.841i	0.854552	+	0.854552i	−0.136138	+	0.990690i	$0.543469\pi$
$614$	353.549	+	146.645i	0.575813	+	0.238836i
$615$	9.76895	+	33.3256i	0.0158845	+	0.0541880i
$616$	199.491	−	82.2931i	0.323849	−	0.133593i
$617$	−331.035	−	331.035i	−0.536523	−	0.536523i	0.385983	−	0.922506i	$-0.373862\pi$
$617$	−331.035	−	331.035i	−0.536523	−	0.536523i	−0.922506	+	0.385983i	$0.873862\pi$
$618$	10.1809	+	24.6125i	0.0164739	+	0.0398260i
$619$	277.907			0.448961			0.224481	−	0.974479i	$-0.427931\pi$
$619$	277.907			0.448961			0.224481	+	0.974479i	$0.427931\pi$
$620$	−768.425	+	224.447i	−1.23940	+	0.362011i
$621$		−	104.123i		−	0.167670i
$622$	172.734	+	417.587i	0.277707	+	0.671361i
$623$	5.88393	−	5.88393i	0.00944451	−	0.00944451i
$624$	−40.1670	−	0.0776721i	−0.0643703	−	0.000124475i
$625$	−260.660	+	568.050i	−0.417057	+	0.908881i
$626$	−602.524	−	249.915i	−0.962498	−	0.399225i
$627$	32.1164	−	32.1164i	0.0512223	−	0.0512223i
$628$	−0.354015	+	366.148i	−0.000563718	+	0.583038i
$629$	−2.69412			−0.00428318
$630$	−126.921	−	157.801i	−0.201461	−	0.250477i
$631$	425.237			0.673910			0.336955	−	0.941521i	$-0.390603\pi$
$631$	425.237			0.673910			0.336955	+	0.941521i	$0.390603\pi$
$632$	295.684	−	710.926i	0.467854	−	1.12488i
$633$	15.5794	−	15.5794i	0.0246121	−	0.0246121i
$634$	−578.857	−	240.098i	−0.913024	−	0.378704i
$635$	88.1655	+	300.766i	0.138843	+	0.473647i
$636$	−21.2877	−	21.3289i	−0.0334713	−	0.0335361i
$637$	421.298	−	421.298i	0.661379	−	0.661379i
$638$	−603.445	+	249.613i	−0.945839	+	0.391244i
$639$		−	530.952i		−	0.830911i
$640$	−499.867	+	399.666i	−0.781042	+	0.624478i
$641$	−474.056			−0.739558			−0.369779	−	0.929120i	$-0.620567\pi$
$641$	−474.056			−0.739558			−0.369779	+	0.929120i	$0.620567\pi$
$642$	−19.0804	−	46.1271i	−0.0297202	−	0.0718491i
$643$	490.408	+	490.408i	0.762687	+	0.762687i	0.976807	−	0.214121i	$-0.0686885\pi$
$643$	490.408	+	490.408i	0.762687	+	0.762687i	−0.214121	+	0.976807i	$0.568689\pi$
$644$	−200.368	+	199.981i	−0.311130	+	0.310529i
$645$	30.9026	−	56.5332i	0.0479110	−	0.0876483i
$646$	19.1014	−	46.0518i	0.0295687	−	0.0712876i
$647$	−319.187	−	319.187i	−0.493334	−	0.493334i	0.416021	−	0.909355i	$-0.363424\pi$
$647$	−319.187	−	319.187i	−0.493334	−	0.493334i	−0.909355	+	0.416021i	$0.863424\pi$
$648$	591.499	+	246.013i	0.912807	+	0.379649i
$649$		−	1107.17i		−	1.70596i
$650$	−668.004	+	119.565i	−1.02770	+	0.183947i
$651$			16.7224i			0.0256873i
$652$	145.883	+	0.141049i	0.223747	+	0.000216333i
$653$	−95.6351	−	95.6351i	−0.146455	−	0.146455i	0.630077	−	0.776532i	$-0.283023\pi$
$653$	−95.6351	−	95.6351i	−0.146455	−	0.146455i	−0.776532	+	0.630077i	$0.783023\pi$
$654$	6.59670	−	15.9041i	0.0100867	−	0.0243182i
$655$	198.579	−	363.280i	0.303174	−	0.554626i
$656$	−1.16179	+	600.806i	−0.00177103	+	0.915862i
$657$	−305.845	−	305.845i	−0.465517	−	0.465517i
$658$	−201.233	+	83.2396i	−0.305826	+	0.126504i
$659$	−295.703			−0.448715			−0.224358	−	0.974507i	$-0.572028\pi$
$659$	−295.703			−0.448715			−0.224358	+	0.974507i	$0.572028\pi$
$660$	21.2282	−	38.7458i	0.0321639	−	0.0587057i
$661$		−	1223.87i		−	1.85154i	−0.378088	−	0.925770i	$-0.623418\pi$
$661$		−	1223.87i		−	1.85154i	0.378088	−	0.925770i	$-0.376582\pi$
$662$	260.979	−	107.953i	0.394228	−	0.163071i
$663$	2.15217	−	2.15217i	0.00324611	−	0.00324611i
$664$	274.810	+	666.181i	0.413871	+	1.00328i
$665$	65.3192	+	222.829i	0.0982244	+	0.335081i
$666$	−15.2665	+	36.8063i	−0.0229227	+	0.0552647i
$667$	605.754	−	605.754i	0.908177	−	0.908177i
$668$	319.473	+	0.308887i	0.478253	+	0.000462405i
$669$	−29.2955			−0.0437900
$670$	−483.987	−	601.742i	−0.722369	−	0.898123i
$671$	57.6374			0.0858978
$672$	5.08624	+	12.3637i	0.00756880	+	0.0183984i
$673$	−95.3663	+	95.3663i	−0.141703	+	0.141703i	−0.774400	−	0.632697i	$-0.781948\pi$
$673$	−95.3663	+	95.3663i	−0.141703	+	0.141703i	0.632697	+	0.774400i	$0.281948\pi$
$674$	−244.326	+	589.050i	−0.362502	+	0.873961i
$675$	−81.1623	−	17.7325i	−0.120241	−	0.0262704i
$676$	−42.9790	−	43.0622i	−0.0635784	−	0.0637015i
$677$	−208.006	+	208.006i	−0.307247	+	0.307247i	−0.843841	−	0.536594i	$-0.819711\pi$
$677$	−208.006	+	208.006i	−0.307247	+	0.307247i	0.536594	+	0.843841i	$0.319711\pi$
$678$	−17.6056	−	42.5619i	−0.0259670	−	0.0627757i
$679$		−	147.067i		−	0.216594i
$680$	5.27562	−	48.2077i	0.00775826	−	0.0708937i
$681$	22.4657			0.0329892
$682$	883.452	−	365.438i	1.29538	−	0.535832i
$683$	704.881	+	704.881i	1.03204	+	1.03204i	0.999470	+	0.0325668i	$0.0103682\pi$
$683$	704.881	+	704.881i	1.03204	+	1.03204i	0.0325668	+	0.999470i	$0.489632\pi$
$684$	−520.906	−	521.914i	−0.761559	−	0.763033i
$685$	49.7331	+	169.658i	0.0726030	+	0.247677i
$686$	−387.634	−	160.783i	−0.565065	−	0.234378i
$687$	−3.46801	−	3.46801i	−0.00504805	−	0.00504805i
$688$	789.685	−	786.637i	1.14780	−	1.14337i
$689$		−	552.800i		−	0.802321i
$690$	−6.24912	+	57.6185i	−0.00905669	+	0.0835050i
$691$			814.437i			1.17864i	0.807901	+	0.589318i	$0.200603\pi$
$691$			814.437i			1.17864i	−0.807901	+	0.589318i	$0.799397\pi$
$692$	766.483	+	0.741084i	1.10763	+	0.00107093i
$693$	171.014	+	171.014i	0.246773	+	0.246773i
$694$	−903.994	−	374.959i	−1.30259	−	0.540286i
$695$	459.281	+	251.056i	0.660836	+	0.361231i
$696$	−15.4278	−	37.3993i	−0.0221664	−	0.0537347i
$697$	−32.1915	−	32.1915i	−0.0461858	−	0.0461858i
$698$	−327.509	−	791.758i	−0.469210	−	1.13432i
$699$	18.7442			0.0268158
$700$	121.758	+	190.241i	0.173941	+	0.271773i
$701$		−	39.4607i		−	0.0562920i	−0.999604	−	0.0281460i	$-0.991040\pi$
$701$		−	39.4607i		−	0.0562920i	0.999604	−	0.0281460i	$-0.00896033\pi$
$702$	−34.4794	−	83.3545i	−0.0491159	−	0.118739i
$703$	32.3078	−	32.3078i	0.0459570	−	0.0459570i
$704$	542.029	−	538.894i	0.769928	−	0.765474i
$705$	−21.3843	+	39.1205i	−0.0303324	+	0.0554900i
$706$	67.8556	+	28.1451i	0.0961127	+	0.0398656i
$707$	172.767	−	172.767i	0.244366	−	0.244366i
$708$	68.5909	+	0.0663180i	0.0968798	+	9.36695e-5i
$709$	−1177.86			−1.66130			−0.830648	−	0.556798i	$-0.812030\pi$
$709$	−1177.86			−1.66130			−0.830648	+	0.556798i	$0.812030\pi$
$710$	−63.8535	+	588.746i	−0.0899345	+	0.829219i
$711$	862.917			1.21367
$712$	11.3181	−	27.2126i	0.0158962	−	0.0382200i
$713$	−886.832	+	886.832i	−1.24380	+	1.24380i
$714$	−0.935729	−	0.388122i	−0.00131054	−	0.000543588i
$715$	777.728	−	227.980i	1.08773	−	0.318853i
$716$	43.8931	−	43.8083i	0.0613032	−	0.0611848i
$717$	−15.0297	+	15.0297i	−0.0209619	+	0.0209619i
$718$	532.341	−	220.201i	0.741422	−	0.306687i
$719$			242.835i			0.337740i	0.985638	+	0.168870i	$0.0540119\pi$
$719$			242.835i			0.337740i	−0.985638	+	0.168870i	$0.945988\pi$
$720$	−628.705	−	345.248i	−0.873201	−	0.479511i
$721$	162.624			0.225553
$722$	47.2129	+	114.138i	0.0653918	+	0.158086i
$723$	−28.6537	−	28.6537i	−0.0396317	−	0.0396317i
$724$	745.054	+	746.497i	1.02908	+	1.03107i
$725$	−369.014	−	575.338i	−0.508984	−	0.793569i
$726$	−3.06531	+	7.39020i	−0.00422219	+	0.0101793i
$727$	−619.622	−	619.622i	−0.852300	−	0.852300i	0.138116	−	0.990416i	$-0.455895\pi$
$727$	−619.622	−	619.622i	−0.852300	−	0.852300i	−0.990416	+	0.138116i	$0.955895\pi$
$728$	−94.1802	+	226.442i	−0.129368	+	0.311046i
$729$			712.425i			0.977264i
$730$	302.354	+	375.917i	0.414183	+	0.514955i
$731$			84.4603i			0.115541i
$732$	−0.00345241	+	3.57073i	−4.71640e−6	+	0.00487804i
$733$	−281.127	−	281.127i	−0.383529	−	0.383529i	0.488843	−	0.872372i	$-0.337419\pi$
$733$	−281.127	−	281.127i	−0.383529	−	0.383529i	−0.872372	+	0.488843i	$0.837419\pi$
$734$	−174.310	+	420.248i	−0.237480	+	0.572545i
$735$	−38.9593	+	11.4204i	−0.0530059	+	0.0155379i
$736$	−385.942	+	925.414i	−0.524378	+	1.25736i
$737$	652.127	+	652.127i	0.884841	+	0.884841i
$738$	−622.208	+	257.375i	−0.843100	+	0.348746i
$739$	−1109.74			−1.50168			−0.750839	−	0.660485i	$-0.770351\pi$
$739$	−1109.74			−1.50168			−0.750839	+	0.660485i	$0.770351\pi$
$740$	21.3547	−	38.9766i	0.0288577	−	0.0526711i
$741$			51.6175i			0.0696592i
$742$	−170.020	+	70.3282i	−0.229137	+	0.0947819i
$743$	−339.850	+	339.850i	−0.457403	+	0.457403i	−0.897802	−	0.440399i	$-0.854837\pi$
$743$	−339.850	+	339.850i	−0.457403	+	0.457403i	0.440399	+	0.897802i	$0.354837\pi$
$744$	22.5865	+	54.7531i	0.0303582	+	0.0735929i
$745$	−216.506	−	118.348i	−0.290612	−	0.158856i
$746$	390.247	−	940.852i	0.523119	−	1.26120i
$747$	−571.084	+	571.084i	−0.764504	+	0.764504i
$748$	−0.0559974	+	57.9166i	−7.48629e−5	+	0.0774286i
$749$	−304.780			−0.406916
$750$	43.8484	+	14.6837i	0.0584646	+	0.0195783i
$751$	−980.557			−1.30567			−0.652834	−	0.757501i	$-0.726420\pi$
$751$	−980.557			−1.30567			−0.652834	+	0.757501i	$0.726420\pi$
$752$	−546.455	+	544.346i	−0.726670	+	0.723865i
$753$	−12.4324	+	12.4324i	−0.0165105	+	0.0165105i
$754$	284.339	−	685.518i	0.377108	−	0.909176i
$755$	−96.9939	−	53.0195i	−0.128469	−	0.0702245i
$756$	−21.2501	+	21.2090i	−0.0281086	+	0.0280543i
$757$	101.564	−	101.564i	0.134166	−	0.134166i	−0.636834	−	0.771001i	$-0.719757\pi$
$757$	101.564	−	101.564i	0.134166	−	0.134166i	0.771001	+	0.636834i	$0.219757\pi$
$758$	−49.0465	−	118.571i	−0.0647052	−	0.156426i
$759$		−	69.2154i		−	0.0911929i
$760$	514.839	+	641.369i	0.677420	+	0.843907i
$761$	767.675			1.00877			0.504386	−	0.863478i	$-0.331719\pi$
$761$	767.675			1.00877			0.504386	+	0.863478i	$0.331719\pi$
$762$	21.4282	−	8.86372i	0.0281210	−	0.0116322i
$763$	−74.3357	−	74.3357i	−0.0974256	−	0.0974256i
$764$	341.760	−	341.100i	0.447330	−	0.446466i
$765$	52.1554	−	15.2886i	0.0681770	−	0.0199852i
$766$	984.630	+	408.405i	1.28542	+	0.533166i
$767$	889.722	+	889.722i	1.16000	+	1.16000i
$768$	33.3528	+	33.6118i	0.0434282	+	0.0437654i
$769$			331.840i			0.431522i	0.976446	+	0.215761i	$0.0692232\pi$
$769$			331.840i			0.431522i	−0.976446	+	0.215761i	$0.930777\pi$
$770$	−169.062	−	210.195i	−0.219561	−	0.272980i
$771$			65.1675i			0.0845234i
$772$	0.997640	−	1031.83i	0.00129228	−	1.33657i
$773$	180.328	+	180.328i	0.233283	+	0.233283i	0.814061	−	0.580779i	$-0.197252\pi$
$773$	180.328	+	180.328i	0.233283	+	0.233283i	−0.580779	+	0.814061i	$0.697252\pi$
$774$	1153.87	+	478.603i	1.49079	+	0.618350i
$775$	540.241	+	842.302i	0.697085	+	1.08684i
$776$	−198.640	−	481.533i	−0.255979	−	0.620532i
$777$	−0.656463	−	0.656463i	−0.000844869	−	0.000844869i
$778$	7.93478	+	19.1825i	0.0101989	+	0.0246561i
$779$	772.078			0.991114
$780$	14.0771	+	48.1951i	0.0180476	+	0.0617886i
$781$		−	707.243i		−	0.905561i
$782$	−29.0410	−	70.2071i	−0.0371368	−	0.0897789i
$783$	64.2435	−	64.2435i	0.0820479	−	0.0820479i
$784$	−702.372	−	1.35820i	−0.895883	−	0.00173239i
$785$	439.204	−	128.747i	0.559495	−	0.164008i
$786$	−28.2941	−	11.7358i	−0.0359976	−	0.0149311i
$787$	−945.029	+	945.029i	−1.20080	+	1.20080i	−0.226876	+	0.973924i	$0.572851\pi$
$787$	−945.029	+	945.029i	−1.20080	+	1.20080i	−0.973924	+	0.226876i	$0.927149\pi$
$788$	1.22672	−	1268.76i	0.00155675	−	1.61010i
$789$	22.3940			0.0283827
$790$	−956.844	−	103.776i	−1.21119	−	0.131362i
$791$	−281.223			−0.355529
$792$	790.922	+	328.955i	0.998639	+	0.415348i
$793$	−46.3175	+	46.3175i	−0.0584079	+	0.0584079i
$794$	481.915	+	199.889i	0.606946	+	0.251749i
$795$	−18.0674	+	33.0524i	−0.0227263	+	0.0415754i
$796$	248.403	+	248.884i	0.312065	+	0.312669i
$797$	−680.774	+	680.774i	−0.854171	+	0.854171i	−0.990644	−	0.136473i	$-0.956423\pi$
$797$	−680.774	+	680.774i	−0.854171	+	0.854171i	0.136473	+	0.990644i	$0.456423\pi$
$798$	15.8755	−	6.56687i	0.0198942	−	0.00822917i
$799$		−	58.4458i		−	0.0731487i
$800$	655.618	+	458.437i	0.819523	+	0.573047i
$801$	33.0305			0.0412366
$802$	−201.013	−	485.953i	−0.250640	−	0.605926i
$803$	−407.393	−	407.393i	−0.507339	−	0.507339i
$804$	−40.4394	+	40.3613i	−0.0502977	+	0.0502006i
$805$	310.500	+	169.728i	0.385714	+	0.210842i
$806$	−416.277	+	1003.61i	−0.516472	+	1.24517i
$807$	−25.1275	−	25.1275i	−0.0311369	−	0.0311369i
$808$	332.327	−	799.029i	0.411296	−	0.988898i
$809$			427.952i			0.528989i	0.964387	+	0.264495i	$0.0852051\pi$
$809$			427.952i			0.528989i	−0.964387	+	0.264495i	$0.914795\pi$
$810$	86.3431	−	796.106i	0.106596	−	0.982847i
$811$		−	1222.46i		−	1.50735i	−0.657245	−	0.753677i	$-0.728278\pi$
$811$		−	1222.46i		−	1.50735i	0.657245	−	0.753677i	$-0.271722\pi$
$812$	−247.013	−	0.238828i	−0.304203	−	0.000294123i
$813$	63.5359	+	63.5359i	0.0781499	+	0.0781499i
$814$	−20.3354	+	49.0270i	−0.0249821	+	0.0602297i
$815$	−51.2962	−	174.991i	−0.0629401	−	0.214713i
$816$	−3.58802	−	0.00693825i	−0.00439708	−	8.50276e-6i
$817$	−1012.84	−	1012.84i	−1.23971	−	1.23971i
$818$	453.933	−	187.768i	0.554930	−	0.229545i
$819$	−274.853			−0.335596
$820$	720.887	−	210.561i	0.879130	−	0.256782i
$821$			1019.26i			1.24148i	0.784015	+	0.620742i	$0.213169\pi$
$821$			1019.26i			1.24148i	−0.784015	+	0.620742i	$0.786831\pi$
$822$	12.0874	−	4.99992i	0.0147049	−	0.00608262i
$823$	−158.477	+	158.477i	−0.192560	+	0.192560i	−0.796801	−	0.604241i	$-0.793476\pi$
$823$	−158.477	+	158.477i	−0.192560	+	0.192560i	0.604241	+	0.796801i	$0.293476\pi$
$824$	532.469	−	219.652i	0.646200	−	0.266568i
$825$	−53.9523	−	11.7876i	−0.0653967	−	0.0142880i
$826$	160.452	−	386.836i	0.194252	−	0.468325i
$827$	573.534	−	573.534i	0.693511	−	0.693511i	−0.269492	−	0.963003i	$-0.586856\pi$
$827$	573.534	−	573.534i	0.693511	−	0.693511i	0.963003	+	0.269492i	$0.0868557\pi$
$828$	−1123.71	−	1.08648i	−1.35714	−	0.00131217i
$829$	1133.71			1.36756			0.683782	−	0.729686i	$-0.260334\pi$
$829$	1133.71			1.36756			0.683782	+	0.729686i	$0.260334\pi$
$830$	701.926	−	564.566i	0.845693	−	0.680200i
$831$	−23.2430			−0.0279699
$832$	−2.51955	+	868.630i	−0.00302830	+	1.04403i
$833$	37.6335	−	37.6335i	0.0451783	−	0.0451783i
$834$	14.8371	−	35.7711i	0.0177903	−	0.0428910i
$835$	−112.335	−	383.216i	−0.134532	−	0.458941i
$836$	−693.861	−	695.204i	−0.829977	−	0.831584i
$837$	−94.0534	+	94.0534i	−0.112370	+	0.112370i
$838$	514.499	+	1243.81i	0.613961	+	1.48426i
$839$		−	1109.49i		−	1.32240i	−0.750212	−	0.661198i	$-0.770048\pi$
$839$		−	1109.49i		−	1.32240i	0.750212	−	0.661198i	$-0.229952\pi$
$840$	13.0320	−	10.4611i	0.0155143	−	0.0124536i
$841$	−93.5052			−0.111183
$842$	−1295.96	+	536.070i	−1.53914	+	0.636662i
$843$	−51.0094	−	51.0094i	−0.0605094	−	0.0605094i
$844$	−336.587	−	337.238i	−0.398800	−	0.399572i
$845$	−36.4772	+	66.7314i	−0.0431683	+	0.0789721i
$846$	−798.470	−	331.189i	−0.943817	−	0.391477i
$847$	34.5418	+	34.5418i	0.0407814	+	0.0407814i
$848$	−461.694	+	459.912i	−0.544450	+	0.542349i
$849$			31.6676i			0.0372999i
$850$	−59.6711	+	10.6805i	−0.0702013	+	0.0125653i
$851$		−	69.6278i		−	0.0818188i
$852$	43.8148	+	0.0423629i	0.0514258	+	4.97217e-5i
$853$	1.51055	+	1.51055i	0.00177087	+	0.00177087i	0.707992	−	0.706221i	$-0.249601\pi$
$853$	1.51055	+	1.51055i	0.00177087	+	0.00177087i	−0.706221	+	0.707992i	$0.749601\pi$
$854$	20.1380	+	8.35286i	0.0235809	+	0.00978087i
$855$	−442.104	+	808.785i	−0.517081	+	0.945948i
$856$	−997.920	+	411.658i	−1.16579	+	0.480908i
$857$	−396.892	−	396.892i	−0.463118	−	0.463118i	0.436558	−	0.899676i	$-0.356197\pi$
$857$	−396.892	−	396.892i	−0.463118	−	0.463118i	−0.899676	+	0.436558i	$0.856197\pi$
$858$	−22.9200	−	55.4095i	−0.0267133	−	0.0645799i
$859$	941.956			1.09657			0.548286	−	0.836291i	$-0.315280\pi$
$859$	941.956			1.09657			0.548286	+	0.836291i	$0.315280\pi$
$860$	−1221.91	−	669.465i	−1.42083	−	0.778448i
$861$		−	15.6879i		−	0.0182206i
$862$	310.039	+	749.526i	0.359674	+	0.869520i
$863$	833.800	−	833.800i	0.966164	−	0.966164i	−0.0332818	−	0.999446i	$-0.510596\pi$
$863$	833.800	−	833.800i	0.966164	−	0.966164i	0.999446	+	0.0332818i	$0.0105959\pi$
$864$	−40.9313	+	98.1452i	−0.0473742	+	0.113594i
$865$	−269.514	−	919.416i	−0.311577	−	1.06291i
$866$	380.824	+	157.958i	0.439751	+	0.182400i
$867$	−37.6064	+	37.6064i	−0.0433754	+	0.0433754i
$868$	361.631	+	0.349647i	0.416625	+	0.000402819i
$869$	1149.43			1.32270
$870$	−39.4060	+	31.6947i	−0.0452943	+	0.0364306i
$871$	−1048.10			−1.20333
$872$	−343.796	−	142.989i	−0.394261	−	0.163979i
$873$	412.794	−	412.794i	0.472846	−	0.472846i
$874$	1190.18	+	493.662i	1.36176	+	0.564831i
$875$	185.179	−	213.125i	0.211634	−	0.243571i
$876$	25.2631	−	25.2143i	0.0288391	−	0.0287834i
$877$	33.6015	−	33.6015i	0.0383142	−	0.0383142i	−0.687690	−	0.726004i	$-0.741375\pi$
$877$	33.6015	−	33.6015i	0.0383142	−	0.0383142i	0.726004	+	0.687690i	$0.241375\pi$
$878$	−115.303	+	47.6946i	−0.131324	+	0.0543219i
$879$		−	64.0762i		−	0.0728967i
$880$	−837.452	−	459.880i	−0.951650	−	0.522591i
$881$	1084.55			1.23104			0.615521	−	0.788121i	$-0.288946\pi$
$881$	1084.55			1.23104			0.615521	+	0.788121i	$0.288946\pi$
$882$	−300.884	−	727.392i	−0.341138	−	0.824708i
$883$	−1165.53	−	1165.53i	−1.31997	−	1.31997i	−0.913796	−	0.406174i	$-0.866863\pi$
$883$	−1165.53	−	1165.53i	−1.31997	−	1.31997i	−0.406174	−	0.913796i	$-0.633137\pi$
$884$	−46.4968	−	46.5868i	−0.0525982	−	0.0527000i
$885$	−24.1182	−	82.2765i	−0.0272523	−	0.0929679i
$886$	183.823	−	443.182i	0.207475	−	0.500206i
$887$	−381.705	−	381.705i	−0.430333	−	0.430333i	0.458409	−	0.888742i	$-0.348420\pi$
$887$	−381.705	−	381.705i	−0.430333	−	0.430333i	−0.888742	+	0.458409i	$0.848420\pi$
$888$	−3.03608	−	1.26275i	−0.00341901	−	0.00142201i
$889$		−	141.584i		−	0.159263i
$890$	−36.6258	−	3.97232i	−0.0411526	−	0.00446328i
$891$			956.338i			1.07333i
$892$	−0.612536	+	633.529i	−0.000686699	+	0.710234i
$893$	700.879	+	700.879i	0.784859	+	0.784859i
$894$	−6.99425	+	16.8625i	−0.00782354	+	0.0188619i
$895$	−68.0190	−	37.1811i	−0.0759989	−	0.0415431i
$896$	267.477	−	109.734i	0.298524	−	0.122471i
$897$	55.6215	+	55.6215i	0.0620084	+	0.0620084i
$898$	−31.4285	+	13.0003i	−0.0349983	+	0.0144769i
$899$	−1094.34			−1.21729
$900$	−192.219	+	875.731i	−0.213577	+	0.973035i
$901$		−	49.3802i		−	0.0548060i
$902$	−828.798	+	342.830i	−0.918845	+	0.380078i
$903$	−20.5800	+	20.5800i	−0.0227907	+	0.0227907i
$904$	−920.790	+	379.840i	−1.01857	+	0.420177i
$905$	632.344	−	1156.81i	0.698723	−	1.27824i
$906$	−3.13340	+	7.55437i	−0.00345850	+	0.00833815i
$907$	457.511	−	457.511i	0.504422	−	0.504422i	−0.408387	−	0.912809i	$-0.633908\pi$
$907$	457.511	−	457.511i	0.504422	−	0.504422i	0.912809	+	0.408387i	$0.133908\pi$
$908$	0.469732	−	485.831i	0.000517326	−	0.535056i
$909$	969.856			1.06695
$910$	304.771	+	33.0545i	0.334913	+	0.0363236i
$911$	−620.530			−0.681152			−0.340576	−	0.940217i	$-0.610622\pi$
$911$	−620.530			−0.681152			−0.340576	+	0.940217i	$0.610622\pi$
$912$	43.1105	−	42.9441i	0.0472703	−	0.0470879i
$913$	−760.699	+	760.699i	−0.833187	+	0.833187i
$914$	−605.940	+	1460.87i	−0.662954	+	1.59833i
$915$	4.28318	−	1.25556i	0.00468107	−	0.00137219i
$916$	−75.0699	+	74.9248i	−0.0819540	+	0.0817957i
$917$	−132.247	+	132.247i	−0.144216	+	0.144216i
$918$	−3.07996	−	7.44585i	−0.00335507	−	0.00811095i
$919$			981.064i			1.06753i	0.845631	+	0.533767i	$0.179224\pi$
$919$			981.064i			1.06753i	−0.845631	+	0.533767i	$0.820776\pi$
$920$	1245.90	+	136.345i	1.35424	+	0.148201i
$921$	−35.3985			−0.0384349
$922$	605.493	−	250.460i	0.656717	−	0.271649i
$923$	568.341	+	568.341i	0.615754	+	0.615754i
$924$	−14.1259	+	14.0986i	−0.0152878	+	0.0152582i
$925$	−54.2738	−	11.8579i	−0.0586743	−	0.0128193i
$926$	1583.06	+	656.623i	1.70957	+	0.709096i
$927$	456.459	+	456.459i	0.492405	+	0.492405i
$928$	−809.101	+	332.852i	−0.871876	+	0.358676i
$929$			776.484i			0.835827i	0.908487	+	0.417914i	$0.137239\pi$
$929$			776.484i			0.835827i	−0.908487	+	0.417914i	$0.862761\pi$
$930$	57.6910	−	46.4014i	0.0620333	−	0.0498940i
$931$			902.598i			0.969493i
$932$	0.391921	−	405.353i	0.000420516	−	0.434928i
$933$	−29.5525	−	29.5525i	−0.0316747	−	0.0316747i
$934$	−219.258	−	90.9437i	−0.234751	−	0.0973701i
$935$	69.4724	−	20.3649i	0.0743021	−	0.0217806i
$936$	−899.934	+	371.237i	−0.961468	+	0.396621i
$937$	759.800	+	759.800i	0.810885	+	0.810885i	0.984767	−	0.173881i	$-0.0556309\pi$
$937$	759.800	+	759.800i	0.810885	+	0.810885i	−0.173881	+	0.984767i	$0.555631\pi$
$938$	133.341	+	322.355i	0.142155	+	0.343662i
$939$	60.3267			0.0642457
$940$	845.552	+	463.264i	0.899524	+	0.492834i
$941$			759.500i			0.807120i	0.914953	+	0.403560i	$0.132227\pi$
$941$			759.500i			0.807120i	−0.914953	+	0.403560i	$0.867773\pi$
$942$	−12.9435	−	31.2912i	−0.0137405	−	0.0332179i
$943$	831.969	−	831.969i	0.882257	−	0.882257i
$944$	2.86832	−	1483.31i	0.00303847	−	1.57130i
$945$	32.9302	+	18.0006i	0.0348468	+	0.0190482i
$946$	1536.99	+	637.512i	1.62472	+	0.673903i
$947$	822.618	−	822.618i	0.868657	−	0.868657i	−0.123667	−	0.992324i	$-0.539465\pi$
$947$	822.618	−	822.618i	0.868657	−	0.868657i	0.992324	+	0.123667i	$0.0394653\pi$
$948$	−0.0688492	+	71.2089i	−7.26258e−5	+	0.0751149i
$949$	654.763			0.689951
$950$	587.493	−	843.652i	0.618414	−	0.888055i
$951$	57.9572			0.0609434
$952$	−8.41288	+	20.2275i	−0.00883706	+	0.0212473i
$953$	659.139	−	659.139i	0.691647	−	0.691647i	−0.270947	−	0.962594i	$-0.587337\pi$
$953$	659.139	−	659.139i	0.691647	−	0.691647i	0.962594	+	0.270947i	$0.0873369\pi$
$954$	−674.618	−	279.818i	−0.707146	−	0.293310i
$955$	−529.610	−	289.499i	−0.554565	−	0.303140i
$956$	324.710	+	325.338i	0.339655	+	0.340312i
$957$	42.7056	−	42.7056i	0.0446244	−	0.0446244i
$958$	−1537.63	+	636.036i	−1.60504	+	0.663920i
$959$		−	79.8661i		−	0.0832806i
$960$	28.5404	−	51.8539i	0.0297296	−	0.0540145i
$961$	641.133			0.667152
$962$	−23.0566	−	55.7397i	−0.0239673	−	0.0579415i
$963$	−855.468	−	855.468i	−0.888336	−	0.888336i
$964$	−620.250	+	619.052i	−0.643413	+	0.642170i
$965$	−1237.71	+	362.817i	−1.28260	+	0.375976i
$966$	10.0307	−	24.1833i	0.0103838	−	0.0250345i
$967$	332.005	+	332.005i	0.343335	+	0.343335i	0.857620	−	0.514284i	$-0.171942\pi$
$967$	332.005	+	332.005i	0.343335	+	0.343335i	−0.514284	+	0.857620i	$0.671942\pi$
$968$	159.753	+	66.4433i	0.165034	+	0.0686398i
$969$			4.61086i			0.00475837i
$970$	−507.370	+	408.083i	−0.523062	+	0.420704i
$971$			960.961i			0.989661i	0.868989	+	0.494831i	$0.164770\pi$
$971$			960.961i			0.989661i	−0.868989	+	0.494831i	$0.835230\pi$
$972$	−178.877	−	0.172950i	−0.184030	−	0.000177932i
$973$	−167.194	−	167.194i	−0.171834	−	0.171834i
$974$	404.936	−	976.266i	0.415745	−	1.00233i
$975$	52.8286	−	33.8835i	0.0541832	−	0.0347524i
$976$	77.2187	+	0.149320i	0.0791175	+	0.000152992i
$977$	69.4628	+	69.4628i	0.0710980	+	0.0710980i	0.741762	−	0.670664i	$-0.233991\pi$
$977$	69.4628	+	69.4628i	0.0710980	+	0.0710980i	−0.670664	+	0.741762i	$0.733991\pi$
$978$	−12.4673	+	5.15706i	−0.0127477	+	0.00527307i
$979$	43.9975			0.0449413
$980$	246.157	+	842.753i	0.251180	+	0.859952i
$981$		−	417.297i		−	0.425379i
$982$	−79.1094	+	32.7234i	−0.0805595	+	0.0333232i
$983$	234.943	−	234.943i	0.239006	−	0.239006i	−0.577433	−	0.816438i	$-0.695945\pi$
$983$	234.943	−	234.943i	0.239006	−	0.239006i	0.816438	+	0.577433i	$0.195945\pi$
$984$	−21.1892	−	51.3659i	−0.0215338	−	0.0522011i
$985$	−1521.91	+	446.128i	−1.54509	+	0.452921i
$986$	25.3993	−	61.2356i	0.0257600	−	0.0621051i
$987$	14.2412	−	14.2412i	0.0144288	−	0.0144288i
$988$	1116.25	+	1.07926i	1.12981	+	0.00109237i
$989$	−2182.82			−2.20710
$990$	115.454	−	1064.51i	0.116620	−	1.07526i
$991$	−919.592			−0.927944			−0.463972	−	0.885850i	$-0.653576\pi$
$991$	−919.592			−0.927944			−0.463972	+	0.885850i	$0.653576\pi$
$992$	1184.54	−	487.299i	1.19409	−	0.491229i
$993$	−18.4694	+	18.4694i	−0.0185996	+	0.0185996i
$994$	102.494	−	247.105i	0.103113	−	0.248596i
$995$	210.825	−	385.684i	0.211885	−	0.387622i
$996$	−47.0810	−	47.1721i	−0.0472700	−	0.0473615i
$997$	835.935	−	835.935i	0.838450	−	0.838450i	−0.150205	−	0.988655i	$-0.547993\pi$
$997$	835.935	−	835.935i	0.838450	−	0.838450i	0.988655	+	0.150205i	$0.0479932\pi$
$998$	370.846	+	896.526i	0.371589	+	0.898323i
$999$		−	7.38441i		−	0.00739180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.i.a.37.7	yes	20
3.2	odd	2		360.3.u.b.37.4		20
4.3	odd	2		160.3.m.a.17.6		20
5.2	odd	4		200.3.i.b.93.2		20
5.3	odd	4	inner	40.3.i.a.13.9	yes	20
5.4	even	2		200.3.i.b.157.4		20
8.3	odd	2		160.3.m.a.17.5		20
8.5	even	2	inner	40.3.i.a.37.9	yes	20
15.8	even	4		360.3.u.b.253.2		20
20.3	even	4		160.3.m.a.113.5		20
20.7	even	4		800.3.m.b.593.6		20
20.19	odd	2		800.3.m.b.657.5		20
24.5	odd	2		360.3.u.b.37.2		20
40.3	even	4		160.3.m.a.113.6		20
40.13	odd	4	inner	40.3.i.a.13.7	✓	20
40.19	odd	2		800.3.m.b.657.6		20
40.27	even	4		800.3.m.b.593.5		20
40.29	even	2		200.3.i.b.157.2		20
40.37	odd	4		200.3.i.b.93.4		20
120.53	even	4		360.3.u.b.253.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.7	✓	20	40.13	odd	4	inner
40.3.i.a.13.9	yes	20	5.3	odd	4	inner
40.3.i.a.37.7	yes	20	1.1	even	1	trivial
40.3.i.a.37.9	yes	20	8.5	even	2	inner
160.3.m.a.17.5		20	8.3	odd	2
160.3.m.a.17.6		20	4.3	odd	2
160.3.m.a.113.5		20	20.3	even	4
160.3.m.a.113.6		20	40.3	even	4
200.3.i.b.93.2		20	5.2	odd	4
200.3.i.b.93.4		20	40.37	odd	4
200.3.i.b.157.2		20	40.29	even	2
200.3.i.b.157.4		20	5.4	even	2
360.3.u.b.37.2		20	24.5	odd	2
360.3.u.b.37.4		20	3.2	odd	2
360.3.u.b.253.2		20	15.8	even	4
360.3.u.b.253.4		20	120.53	even	4
800.3.m.b.593.5		20	40.27	even	4
800.3.m.b.593.6		20	20.7	even	4
800.3.m.b.657.5		20	20.19	odd	2
800.3.m.b.657.6		20	40.19	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)

\(f(q)\)	\(=\)	\(q+(0.764474 + 1.84813i) q^{2} +(-0.130791 - 0.130791i) q^{3} +(-2.83116 + 2.82569i) q^{4} +(4.38731 + 2.39823i) q^{5} +(0.141733 - 0.341706i) q^{6} +(-1.59713 - 1.59713i) q^{7} +(-7.38659 - 3.07218i) q^{8} -8.96579i q^{9} +O(q^{10})\)	\(q+(0.764474 + 1.84813i) q^{2} +(-0.130791 - 0.130791i) q^{3} +(-2.83116 + 2.82569i) q^{4} +(4.38731 + 2.39823i) q^{5} +(0.141733 - 0.341706i) q^{6} +(-1.59713 - 1.59713i) q^{7} +(-7.38659 - 3.07218i) q^{8} -8.96579i q^{9} +(-1.07825 + 9.94170i) q^{10} -11.9427i q^{11} +(0.739867 + 0.000715350i) q^{12} +(9.59714 + 9.59714i) q^{13} +(1.73074 - 4.17267i) q^{14} +(-0.260155 - 0.887490i) q^{15} +(0.0309396 - 16.0000i) q^{16} +(0.857288 + 0.857288i) q^{17} +(16.5699 - 6.85411i) q^{18} -20.5611 q^{19} +(-19.1978 + 5.60743i) q^{20} +0.417782i q^{21} +(22.0716 - 9.12986i) q^{22} +(-22.1560 + 22.1560i) q^{23} +(0.564287 + 1.36792i) q^{24} +(13.4970 + 21.0435i) q^{25} +(-10.4000 + 25.0735i) q^{26} +(-2.34977 + 2.34977i) q^{27} +(9.03474 + 0.00873536i) q^{28} -27.3404 q^{29} +(1.44131 - 1.15926i) q^{30} +40.0267 q^{31} +(29.5937 - 12.1744i) q^{32} +(-1.56200 + 1.56200i) q^{33} +(-0.929005 + 2.23975i) q^{34} +(-3.17684 - 10.8374i) q^{35} +(25.3345 + 25.3836i) q^{36} +(-1.57131 + 1.57131i) q^{37} +(-15.7184 - 37.9996i) q^{38} -2.51044i q^{39} +(-25.0395 - 31.1933i) q^{40} -37.5504 q^{41} +(-0.772115 + 0.319383i) q^{42} +(49.2602 + 49.2602i) q^{43} +(33.7463 + 33.8116i) q^{44} +(21.5020 - 39.3357i) q^{45} +(-57.8849 - 24.0095i) q^{46} +(-34.0876 - 34.0876i) q^{47} +(-2.09670 + 2.08861i) q^{48} -43.8983i q^{49} +(-28.5730 + 41.0315i) q^{50} -0.224252i q^{51} +(-54.2896 - 0.0524906i) q^{52} +(-28.8002 - 28.8002i) q^{53} +(-6.13901 - 2.54634i) q^{54} +(28.6412 - 52.3962i) q^{55} +(6.89068 + 16.7040i) q^{56} +(2.68921 + 2.68921i) q^{57} +(-20.9010 - 50.5285i) q^{58} +92.7071 q^{59} +(3.24431 + 1.77751i) q^{60} +4.82618i q^{61} +(30.5993 + 73.9744i) q^{62} +(-14.3196 + 14.3196i) q^{63} +(45.1234 + 45.3859i) q^{64} +(19.0895 + 65.1217i) q^{65} +(-4.08088 - 1.69267i) q^{66} +(-54.6048 + 54.6048i) q^{67} +(-4.84955 - 0.00468885i) q^{68} +5.79564 q^{69} +(17.6003 - 14.1561i) q^{70} +59.2198 q^{71} +(-27.5445 + 66.2266i) q^{72} +(34.1124 - 34.1124i) q^{73} +(-4.10520 - 1.70275i) q^{74} +(0.987017 - 4.51761i) q^{75} +(58.2118 - 58.0993i) q^{76} +(-19.0740 + 19.0740i) q^{77} +(4.63963 - 1.91917i) q^{78} +96.2455i q^{79} +(38.5073 - 70.1227i) q^{80} -80.0774 q^{81} +(-28.7063 - 69.3980i) q^{82} +(-63.6959 - 63.6959i) q^{83} +(-1.18052 - 1.18281i) q^{84} +(1.70522 + 5.81716i) q^{85} +(-53.3810 + 128.697i) q^{86} +(3.57588 + 3.57588i) q^{87} +(-36.6901 + 88.2156i) q^{88} +3.68406i q^{89} +(89.1352 + 9.66732i) q^{90} -30.6558i q^{91} +(0.121180 - 125.333i) q^{92} +(-5.23514 - 5.23514i) q^{93} +(36.9392 - 89.0574i) q^{94} +(-90.2080 - 49.3101i) q^{95} +(-5.46290 - 2.27829i) q^{96} +(46.0410 + 46.0410i) q^{97} +(81.1298 - 33.5591i) q^{98} -107.075 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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