LMFDB - Embedded newform 40.3.i.a.13.9

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			13.9
Root			$-0.541828 - 1.30630i$ of defining polynomial
Character	$\chi$	$=$	40.13
Dual form			40.3.i.a.37.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.84813 - 0.764474i) 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} +(3.07218 - 7.38659i) q^{8} +8.96579i q^{9} +(-6.27494 + 7.78621i) q^{10} -11.9427i q^{11} +(0.000715350 - 0.739867i) 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} +(6.85411 + 16.5699i) q^{18} +20.5611 q^{19} +(-5.64454 + 19.1870i) q^{20} +0.417782i q^{21} +(-9.12986 - 22.0716i) 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} +(-0.00873536 + 9.03474i) q^{28} +27.3404 q^{29} +(0.197662 + 1.83908i) q^{30} +40.0267 q^{31} +(-12.1744 - 29.5937i) 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} +(37.9996 - 15.7184i) q^{38} +2.51044i q^{39} +(4.23607 + 39.7751i) q^{40} -37.5504 q^{41} +(0.319383 + 0.772115i) 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} +(-2.08861 - 2.09670i) q^{48} +43.8983i q^{49} +(8.85703 - 49.2093i) q^{50} -0.224252i q^{51} +(-0.0524906 + 54.2896i) 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} +(50.5285 - 20.9010i) q^{58} -92.7071 q^{59} +(1.77123 + 3.24774i) q^{60} +4.82618i q^{61} +(73.9744 - 30.5993i) 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} +(0.00468885 - 4.84955i) q^{68} -5.79564 q^{69} +(-2.41371 - 22.4575i) q^{70} +59.2198 q^{71} +(66.2266 + 27.5445i) 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} +(1.91917 + 4.63963i) q^{78} -96.2455i q^{79} +(38.2358 + 70.2711i) q^{80} -80.0774 q^{81} +(-69.3980 + 28.7063i) 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} +(-88.2156 - 36.6901i) q^{88} -3.68406i q^{89} +(-69.8095 - 56.2598i) q^{90} -30.6558i q^{91} +(-125.333 - 0.121180i) 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} +(33.5591 + 81.1298i) 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} + 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}+ \cdots + 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

Character values

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

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	1.84813	−	0.764474i	0.924064	−	0.382237i
$2$	1.84813	−	0.764474i	0.924064	−	0.382237i
$3$	0.130791	−	0.130791i	0.0435971	−	0.0435971i	−0.684972	−	0.728569i	$-0.740186\pi$
$3$	0.130791	−	0.130791i	0.0435971	−	0.0435971i	0.728569	+	0.684972i	$0.240186\pi$
$4$	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	−0.811924	−	0.583763i	$-0.801580\pi$
$7$	−1.59713	+	1.59713i	−0.228162	+	0.228162i	0.583763	+	0.811924i	$0.301580\pi$
$8$	3.07218	−	7.38659i	0.384023	−	0.923324i
$9$			8.96579i			0.996199i
$10$	−6.27494	+	7.78621i	−0.627494	+	0.778621i
$11$		−	11.9427i		−	1.08570i	−0.839831	−	0.542849i	$-0.817346\pi$
$11$		−	11.9427i		−	1.08570i	0.839831	−	0.542849i	$-0.182654\pi$
$12$	0.000715350	−	0.739867i	5.96125e−5	−	0.0616556i
$13$	−9.59714	+	9.59714i	−0.738241	+	0.738241i	−0.972238	−	0.233996i	$-0.924820\pi$
$13$	−9.59714	+	9.59714i	−0.738241	+	0.738241i	0.233996	+	0.972238i	$0.424820\pi$
$14$	−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	−0.681443	−	0.731871i	$-0.738647\pi$
$17$	0.857288	−	0.857288i	0.0504287	−	0.0504287i	0.731871	+	0.681443i	$0.238647\pi$
$18$	6.85411	+	16.5699i	0.380784	+	0.920552i
$19$	20.5611			1.08216			0.541082	−	0.840970i	$-0.318015\pi$
$19$	20.5611			1.08216			0.541082	+	0.840970i	$0.318015\pi$
$20$	−5.64454	+	19.1870i	−0.282227	+	0.959348i
$21$			0.417782i			0.0198944i
$22$	−9.12986	−	22.0716i	−0.414993	−	1.00325i
$23$	−22.1560	−	22.1560i	−0.963306	−	0.963306i	0.0360441	−	0.999350i	$-0.488524\pi$
$23$	−22.1560	−	22.1560i	−0.963306	−	0.963306i	−0.999350	+	0.0360441i	$0.988524\pi$
$24$	−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
$28$	−0.00873536	+	9.03474i	−0.000311977	+	0.322669i
$29$	27.3404			0.942771			0.471385	−	0.881927i	$-0.343754\pi$
$29$	27.3404			0.942771			0.471385	+	0.881927i	$0.343754\pi$
$30$	0.197662	+	1.83908i	0.00658872	+	0.0613026i
$31$	40.0267			1.29118			0.645591	−	0.763683i	$-0.276611\pi$
$31$	40.0267			1.29118			0.645591	+	0.763683i	$0.276611\pi$
$32$	−12.1744	−	29.5937i	−0.380449	−	0.924802i
$33$	−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	$-0.240440\pi$
$37$	1.57131	+	1.57131i	0.0424677	+	0.0424677i	−0.685554	+	0.728022i	$0.740440\pi$
$38$	37.9996	−	15.7184i	0.999988	−	0.413642i
$39$			2.51044i			0.0643704i
$40$	4.23607	+	39.7751i	0.105902	+	0.994377i
$41$	−37.5504			−0.915864			−0.457932	−	0.888987i	$-0.651410\pi$
$41$	−37.5504			−0.915864			−0.457932	+	0.888987i	$0.651410\pi$
$42$	0.319383	+	0.772115i	0.00760437	+	0.0183837i
$43$	−49.2602	+	49.2602i	−1.14558	+	1.14558i	−0.158174	+	0.987411i	$0.550561\pi$
$43$	−49.2602	+	49.2602i	−1.14558	+	1.14558i	−0.987411	+	0.158174i	$0.949439\pi$
$44$	−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	−0.969673	−	0.244405i	$-0.921407\pi$
$47$	−34.0876	+	34.0876i	−0.725268	+	0.725268i	0.244405	+	0.969673i	$0.421407\pi$
$48$	−2.08861	−	2.09670i	−0.0435127	−	0.0436813i
$49$			43.8983i			0.895884i
$50$	8.85703	−	49.2093i	0.177141	−	0.984186i
$51$		−	0.224252i		−	0.00439709i
$52$	−0.0524906	+	54.2896i	−0.00100943	+	1.04403i
$53$	28.8002	−	28.8002i	0.543401	−	0.543401i	−0.381124	−	0.924524i	$-0.624463\pi$
$53$	28.8002	−	28.8002i	0.543401	−	0.543401i	0.924524	+	0.381124i	$0.124463\pi$
$54$	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
$58$	50.5285	−	20.9010i	0.871181	−	0.360362i
$59$	−92.7071			−1.57131			−0.785653	−	0.618667i	$-0.787673\pi$
$59$	−92.7071			−1.57131			−0.785653	+	0.618667i	$0.787673\pi$
$60$	1.77123	+	3.24774i	0.0295205	+	0.0541291i
$61$			4.82618i			0.0791176i	0.999217	+	0.0395588i	$0.0125952\pi$
$61$			4.82618i			0.0791176i	−0.999217	+	0.0395588i	$0.987405\pi$
$62$	73.9744	−	30.5993i	1.19314	−	0.493537i
$63$	−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	$-0.0544998\pi$
$67$	54.6048	+	54.6048i	0.814997	+	0.814997i	−0.170381	+	0.985378i	$0.554500\pi$
$68$	0.00468885	−	4.84955i	6.89537e−5	−	0.0713169i
$69$	−5.79564			−0.0839947
$70$	−2.41371	−	22.4575i	−0.0344815	−	0.320822i
$71$	59.2198			0.834082			0.417041	−	0.908888i	$-0.363067\pi$
$71$	59.2198			0.834082			0.417041	+	0.908888i	$0.363067\pi$
$72$	66.2266	+	27.5445i	0.919814	+	0.382563i
$73$	34.1124	+	34.1124i	0.467293	+	0.467293i	0.901037	−	0.433743i	$-0.142807\pi$
$73$	34.1124	+	34.1124i	0.467293	+	0.467293i	−0.433743	+	0.901037i	$0.642807\pi$
$74$	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
$78$	1.91917	+	4.63963i	0.0246047	+	0.0594824i
$79$		−	96.2455i		−	1.21830i	−0.793056	−	0.609149i	$-0.791511\pi$
$79$		−	96.2455i		−	1.21830i	0.793056	−	0.609149i	$-0.208489\pi$
$80$	38.2358	+	70.2711i	0.477947	+	0.878388i
$81$	−80.0774			−0.988610
$82$	−69.3980	+	28.7063i	−0.846317	+	0.350077i
$83$	63.6959	−	63.6959i	0.767421	−	0.767421i	−0.210231	−	0.977652i	$-0.567422\pi$
$83$	63.6959	−	63.6959i	0.767421	−	0.767421i	0.977652	+	0.210231i	$0.0674216\pi$
$84$	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
$88$	−88.2156	−	36.6901i	−1.00245	−	0.416933i
$89$		−	3.68406i		−	0.0413939i	−0.999786	−	0.0206970i	$-0.993411\pi$
$89$		−	3.68406i		−	0.0413939i	0.999786	−	0.0206970i	$-0.00658852\pi$
$90$	−69.8095	−	56.2598i	−0.775662	−	0.625109i
$91$		−	30.6558i		−	0.336877i
$92$	−125.333	−	0.121180i	−1.36232	−	0.00131718i
$93$	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	−0.428766	−	0.903416i	$-0.641051\pi$
$97$	46.0410	−	46.0410i	0.474650	−	0.474650i	0.903416	+	0.428766i	$0.141051\pi$
$98$	33.5591	+	81.1298i	0.342440	+	0.827855i
$99$	107.075			1.08157
$100$	−21.2503	−	97.7160i	−0.212503	−	0.977160i
$101$			108.173i			1.07102i	0.844529	+	0.535510i	$0.179880\pi$
$101$			108.173i			1.07102i	−0.844529	+	0.535510i	$0.820120\pi$
$102$	−0.171434	−	0.414446i	−0.00168073	−	0.00406320i
$103$	−50.9112	−	50.9112i	−0.494284	−	0.494284i	0.415369	−	0.909653i	$-0.363652\pi$
$103$	−50.9112	−	50.9112i	−0.494284	−	0.494284i	−0.909653	+	0.415369i	$0.863652\pi$
$104$	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	$-0.467169\pi$
$107$	−95.4147	−	95.4147i	−0.891726	−	0.891726i	−0.994686	+	0.102960i	$0.967169\pi$
$108$	13.2923	+	0.0128518i	0.123077	+	0.000118998i
$109$	−46.5432			−0.427002			−0.213501	−	0.976943i	$-0.568487\pi$
$109$	−46.5432			−0.427002			−0.213501	+	0.976943i	$0.568487\pi$
$110$	92.9882	+	74.9395i	0.845347	+	0.681269i
$111$	0.411026			0.00370294
$112$	25.5047	+	25.6035i	0.227720	+	0.228603i
$113$	88.0400	+	88.0400i	0.779115	+	0.779115i	0.979680	−	0.200565i	$-0.0642779\pi$
$113$	88.0400	+	88.0400i	0.779115	+	0.779115i	−0.200565	+	0.979680i	$0.564278\pi$
$114$	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
$118$	−171.335	+	70.8721i	−1.45199	+	0.600611i
$119$			2.73841i			0.0230118i
$120$	5.75628	+	4.64819i	0.0479690	+	0.0387349i
$121$	−21.6274			−0.178739
$122$	3.68948	+	8.91939i	0.0302417	+	0.0731098i
$123$	−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	−0.510729	−	0.859742i	$-0.670625\pi$
$127$	44.3246	−	44.3246i	0.349012	−	0.349012i	0.859742	+	0.510729i	$0.170625\pi$
$128$	−118.090	−	49.3834i	−0.922579	−	0.385808i
$129$			12.8856i			0.0998884i
$130$	−14.5039	−	134.947i	−0.111569	−	1.03805i
$131$		−	82.8025i		−	0.632080i	−0.948746	−	0.316040i	$-0.897647\pi$
$131$		−	82.8025i		−	0.632080i	0.948746	−	0.316040i	$-0.102353\pi$
$132$	−8.83599	−	0.00854319i	−0.0669393	−	6.47212e-5i
$133$	−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	−0.609942	−	0.792446i	$-0.708807\pi$
$137$	25.0030	−	25.0030i	0.182503	−	0.182503i	0.792446	+	0.609942i	$0.208807\pi$
$138$	−10.7111	+	4.43061i	−0.0776165	+	0.0321059i
$139$	−104.684			−0.753121			−0.376561	−	0.926392i	$-0.622893\pi$
$139$	−104.684			−0.753121			−0.376561	+	0.926392i	$0.622893\pi$
$140$	−21.6290	−	39.6592i	−0.154493	−	0.283280i
$141$			8.91673i			0.0632392i
$142$	109.446	−	45.2720i	0.770745	−	0.318817i
$143$	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
$148$	8.88864	+	0.00859410i	0.0600584	+	5.80682e-5i
$149$	49.3481			0.331196			0.165598	−	0.986193i	$-0.447045\pi$
$149$	49.3481			0.331196			0.165598	+	0.986193i	$0.447045\pi$
$150$	−5.27772	−	7.59457i	−0.0351848	−	0.0506305i
$151$	−22.1078			−0.146409			−0.0732047	−	0.997317i	$-0.523323\pi$
$151$	−22.1078			−0.146409			−0.0732047	+	0.997317i	$0.523323\pi$
$152$	63.1675	−	151.876i	0.415575	−	0.999187i
$153$	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	$-0.344161\pi$
$157$	−64.7264	−	64.7264i	−0.412270	−	0.412270i	−0.882529	+	0.470258i	$0.844161\pi$
$158$	−73.5771	−	177.874i	−0.465678	−	1.12579i
$159$		−	7.53364i		−	0.0473814i
$160$	124.385	+	100.640i	0.777407	+	0.628998i
$161$	70.7723			0.439579
$162$	−147.993	+	61.2171i	−0.913540	+	0.377883i
$163$	25.7888	−	25.7888i	0.158213	−	0.158213i	−0.623561	−	0.781775i	$-0.714315\pi$
$163$	25.7888	−	25.7888i	0.158213	−	0.158213i	0.781775	+	0.623561i	$0.214315\pi$
$164$	−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	−0.855681	−	0.517504i	$-0.826861\pi$
$167$	−56.4754	+	56.4754i	−0.338176	+	0.338176i	0.517504	+	0.855681i	$0.326861\pi$
$168$	3.08599	+	1.28350i	0.0183690	+	0.00763990i
$169$		−	15.2101i		−	0.0900005i
$170$	1.29560	+	12.0545i	0.00762116	+	0.0709086i
$171$			184.346i			1.07805i
$172$	−0.269424	+	278.657i	−0.00156642	+	1.62010i
$173$	135.496	−	135.496i	0.783216	−	0.783216i	−0.197156	−	0.980372i	$-0.563171\pi$
$173$	135.496	−	135.496i	0.783216	−	0.783216i	0.980372	+	0.197156i	$0.0631706\pi$
$174$	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
$178$	−2.81636	−	6.80861i	−0.0158223	−	0.0382506i
$179$	15.5036			0.0866121			0.0433061	−	0.999062i	$-0.486211\pi$
$179$	15.5036			0.0866121			0.0433061	+	0.999062i	$0.486211\pi$
$180$	−172.026	−	50.6078i	−0.955701	−	0.281154i
$181$		−	263.672i		−	1.45675i	−0.685179	−	0.728375i	$-0.740276\pi$
$181$		−	263.672i		−	1.45675i	0.685179	−	0.728375i	$-0.259724\pi$
$182$	−23.4355	−	56.6559i	−0.128767	−	0.311296i
$183$	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
$188$	−0.186439	+	192.829i	−0.000991696	+	1.02568i
$189$	−7.50579			−0.0397132
$190$	−129.020	+	160.093i	−0.679051	+	0.842595i
$191$	−120.714			−0.632010			−0.316005	−	0.948758i	$-0.602342\pi$
$191$	−120.714			−0.632010			−0.316005	+	0.948758i	$0.602342\pi$
$192$	−11.8378	−	0.0343368i	−0.0616554	−	0.000178837i
$193$	−182.404	−	182.404i	−0.945098	−	0.945098i	0.0534716	−	0.998569i	$-0.482971\pi$
$193$	−182.404	−	182.404i	−0.945098	−	0.945098i	−0.998569	+	0.0534716i	$0.982971\pi$
$194$	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	0.988716	+	0.149799i	$0.0478626\pi$
$197$	224.288	+	224.288i	1.13852	+	1.13852i	0.149799	+	0.988716i	$0.452137\pi$
$198$	197.889	−	81.8563i	0.999441	−	0.413416i
$199$			87.9089i			0.441753i	0.975302	+	0.220877i	$0.0708918\pi$
$199$			87.9089i			0.441753i	−0.975302	+	0.220877i	$0.929108\pi$
$200$	−113.975	−	164.347i	−0.569873	−	0.821733i
$201$	14.2837			0.0710631
$202$	82.6954	+	199.918i	0.409383	+	0.989691i
$203$	−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
$208$	153.257	+	153.851i	0.736812	+	0.739667i
$209$		−	245.554i		−	1.17490i
$210$	−3.25294	−	2.62156i	−0.0154902	−	0.0124836i
$211$			119.117i			0.564534i	0.959336	+	0.282267i	$0.0910864\pi$
$211$			119.117i			0.564534i	−0.959336	+	0.282267i	$0.908914\pi$
$212$	0.157520	−	162.919i	0.000743019	−	0.768484i
$213$	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
$218$	−86.0179	+	35.5811i	−0.394577	+	0.163216i
$219$	8.92322			0.0407453
$220$	229.143	+	67.4109i	1.04156	+	0.306413i
$221$			16.4550i			0.0744571i
$222$	0.759629	−	0.314219i	0.00342175	−	0.00141540i
$223$	111.993	+	111.993i	0.502212	+	0.502212i	0.912125	−	0.409913i	$-0.134441\pi$
$223$	111.993	+	111.993i	0.502212	+	0.502212i	−0.409913	+	0.912125i	$0.634441\pi$
$224$	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	$-0.163793\pi$
$227$	85.8837	+	85.8837i	0.378342	+	0.378342i	−0.492162	+	0.870504i	$0.663793\pi$
$228$	0.0147084	−	15.2125i	6.45105e−5	−	0.0667214i
$229$	−26.5156			−0.115789			−0.0578943	−	0.998323i	$-0.518439\pi$
$229$	−26.5156			−0.115789			−0.0578943	+	0.998323i	$0.518439\pi$
$230$	311.540	−	33.4839i	1.35452	−	0.145582i
$231$	4.98944			0.0215993
$232$	83.9946	−	201.952i	0.362046	−	0.870482i
$233$	−71.6569	−	71.6569i	−0.307541	−	0.307541i	0.536414	−	0.843955i	$-0.319778\pi$
$233$	−71.6569	−	71.6569i	−0.307541	−	0.307541i	−0.843955	+	0.536414i	$0.819778\pi$
$234$	−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
$238$	2.09344	+	5.06093i	0.00879596	+	0.0212644i
$239$			114.913i			0.480809i	0.970673	+	0.240405i	$0.0772801\pi$
$239$			114.913i			0.480809i	−0.970673	+	0.240405i	$0.922720\pi$
$240$	14.1918	+	4.18994i	0.0591323	+	0.0174581i
$241$	219.080			0.909045			0.454522	−	0.890735i	$-0.349810\pi$
$241$	219.080			0.909045			0.454522	+	0.890735i	$0.349810\pi$
$242$	−39.9702	+	16.5336i	−0.165166	+	0.0683205i
$243$	−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
$248$	122.969	−	295.660i	0.495844	−	1.19218i
$249$		−	16.6618i		−	0.0669147i
$250$	79.1564	+	237.138i	0.316626	+	0.948551i
$251$		−	95.0552i		−	0.378706i	−0.981909	−	0.189353i	$-0.939361\pi$
$251$		−	95.0552i		−	0.378706i	0.981909	−	0.189353i	$-0.0606390\pi$
$252$	−81.0036	−	0.0783194i	−0.321443	−	0.000310791i
$253$	−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	−0.999545	−	0.0301755i	$-0.990393\pi$
$257$	−249.128	+	249.128i	−0.969369	+	0.969369i	0.0301755	+	0.999545i	$0.490393\pi$
$258$	9.85070	+	23.8143i	0.0381810	+	0.0923033i
$259$	−5.01917			−0.0193790
$260$	−129.968	−	238.311i	−0.499878	−	0.916582i
$261$			245.128i			0.939187i
$262$	−63.3003	−	153.030i	−0.241604	−	0.584082i
$263$	−85.6095	−	85.6095i	−0.325511	−	0.325511i	0.525365	−	0.850877i	$-0.323929\pi$
$263$	−85.6095	−	85.6095i	−0.325511	−	0.325511i	−0.850877	+	0.525365i	$0.823929\pi$
$264$	−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
$268$	308.891	+	0.298656i	1.15258	+	0.00111439i
$269$	−192.119			−0.714196			−0.357098	−	0.934067i	$-0.616234\pi$
$269$	−192.119			−0.714196			−0.357098	+	0.934067i	$0.616234\pi$
$270$	−33.0405	+	3.55115i	−0.122372	+	0.0131524i
$271$	−485.780			−1.79255			−0.896274	−	0.443501i	$-0.853736\pi$
$271$	−485.780			−1.79255			−0.896274	+	0.443501i	$0.853736\pi$
$272$	−13.6901	−	13.7431i	−0.0503311	−	0.0505261i
$273$	−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	$-0.322834\pi$
$277$	−88.8551	−	88.8551i	−0.320777	−	0.320777i	−0.849065	+	0.528288i	$0.822834\pi$
$278$	−193.469	+	80.0280i	−0.695933	+	0.287871i
$279$			358.871i			1.28627i
$280$	−70.2916	−	56.7605i	−0.251042	−	0.202716i
$281$	390.006			1.38792			0.693961	−	0.720012i	$-0.255864\pi$
$281$	390.006			1.38792			0.693961	+	0.720012i	$0.255864\pi$
$282$	6.81660	+	16.4793i	0.0241724	+	0.0584371i
$283$	121.062	−	121.062i	0.427779	−	0.427779i	−0.460092	−	0.887871i	$-0.652184\pi$
$283$	121.062	−	121.062i	0.427779	−	0.427779i	0.887871	+	0.460092i	$0.152184\pi$
$284$	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
$288$	265.330	−	109.153i	0.921286	−	0.379003i
$289$			287.530i			0.994914i
$290$	−171.559	+	212.878i	−0.591583	+	0.734061i
$291$		−	12.0435i		−	0.0413867i
$292$	192.969	+	0.186575i	0.660852	+	0.000638954i
$293$	−244.956	+	244.956i	−0.836026	+	0.836026i	−0.988333	−	0.152307i	$-0.951330\pi$
$293$	−244.956	+	244.956i	−0.836026	+	0.836026i	0.152307	+	0.988333i	$0.451330\pi$
$294$	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
$298$	91.2017	−	37.7253i	0.306046	−	0.126595i
$299$	425.269			1.42230
$300$	−15.5598	−	10.0011i	−0.0518659	−	0.0333369i
$301$		−	157.350i		−	0.522757i
$302$	−40.8581	+	16.9008i	−0.135292	+	0.0559630i
$303$	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	$-0.350895\pi$
$307$	−135.324	−	135.324i	−0.440796	−	0.440796i	−0.892280	+	0.451483i	$0.850895\pi$
$308$	107.899	+	0.104324i	0.350321	+	0.000338713i
$309$	−13.3175			−0.0430987
$310$	−251.165	+	311.656i	−0.810209	+	1.00534i
$311$	225.951			0.726531			0.363266	−	0.931686i	$-0.381662\pi$
$311$	225.951			0.726531			0.363266	+	0.931686i	$0.381662\pi$
$312$	18.5436	+	7.71255i	0.0594347	+	0.0247197i
$313$	−230.622	−	230.622i	−0.736812	−	0.736812i	0.235148	−	0.971960i	$-0.424443\pi$
$313$	−230.622	−	230.622i	−0.736812	−	0.736812i	−0.971960	+	0.235148i	$0.924443\pi$
$314$	−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	$-0.0854522\pi$
$317$	221.563	+	221.563i	0.698938	+	0.698938i	−0.265243	+	0.964182i	$0.585452\pi$
$318$	−5.75927	−	13.9231i	−0.0181109	−	0.0437835i
$319$		−	326.517i		−	1.02356i
$320$	306.816	+	90.9062i	0.958800	+	0.284082i
$321$	−24.9588			−0.0777534
$322$	130.796	−	54.1035i	0.406200	−	0.168023i
$323$	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
$328$	−115.362	+	277.370i	−0.351713	+	0.845639i
$329$		−	108.885i		−	0.330957i
$330$	21.9635	−	2.36061i	0.0665560	−	0.00715336i
$331$		−	141.212i		−	0.426624i	−0.976984	−	0.213312i	$-0.931575\pi$
$331$		−	141.212i		−	0.426624i	0.976984	−	0.213312i	$-0.0684250\pi$
$332$	0.348379	−	360.318i	0.00104933	−	1.08530i
$333$	−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	−0.288458	−	0.957493i	$-0.593142\pi$
$337$	225.465	−	225.465i	0.669035	−	0.669035i	0.957493	+	0.288458i	$0.0931424\pi$
$338$	−11.6277	−	28.1102i	−0.0344015	−	0.0831663i
$339$	23.0297			0.0679343
$340$	11.6097	+	21.2877i	0.0341463	+	0.0626110i
$341$		−	478.025i		−	1.40183i
$342$	140.928	+	340.696i	0.412070	+	0.996187i
$343$	−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	$-0.000904214\pi$
$347$	346.013	+	346.013i	0.997155	+	0.997155i	−0.00284067	+	0.999996i	$0.500904\pi$
$348$	0.0195579	−	20.2282i	5.62009e−5	−	0.0581271i
$349$	428.411			1.22754			0.613769	−	0.789486i	$-0.289653\pi$
$349$	428.411			1.22754			0.613769	+	0.789486i	$0.289653\pi$
$350$	64.4479	+	92.7396i	0.184137	+	0.264970i
$351$	−45.1021			−0.128496
$352$	−353.427	+	145.395i	−1.00405	+	0.413053i
$353$	25.9724	+	25.9724i	0.0735762	+	0.0735762i	0.742937	−	0.669361i	$-0.233432\pi$
$353$	25.9724	+	25.9724i	0.0735762	+	0.0735762i	−0.669361	+	0.742937i	$0.733432\pi$
$354$	−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
$358$	28.6526	−	11.8521i	0.0800352	−	0.0331063i
$359$			288.043i			0.802348i	0.916002	+	0.401174i	$0.131398\pi$
$359$			288.043i			0.802348i	−0.916002	+	0.401174i	$0.868602\pi$
$360$	−356.615	+	37.9797i	−0.990597	+	0.105499i
$361$	61.7587			0.171077
$362$	−201.570	−	487.299i	−0.556823	−	1.34613i
$363$	−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	−0.453143	−	0.891438i	$-0.649697\pi$
$367$	160.854	−	160.854i	0.438295	−	0.438295i	0.891438	+	0.453143i	$0.149697\pi$
$368$	−355.181	+	353.810i	−0.965167	+	0.961442i
$369$		−	336.669i		−	0.912382i
$370$	−22.0944	+	2.37467i	−0.0597145	+	0.00641804i
$371$			91.9956i			0.247966i
$372$	0.0286331	−	29.6144i	7.69706e−5	−	0.0796086i
$373$	360.121	−	360.121i	0.965471	−	0.965471i	−0.0339529	−	0.999423i	$-0.510810\pi$
$373$	360.121	−	360.121i	0.965471	−	0.965471i	0.999423	+	0.0339529i	$0.0108096\pi$
$374$	−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
$378$	−13.8717	+	5.73797i	−0.0366975	+	0.0151798i
$379$	64.1572			0.169280			0.0846402	−	0.996412i	$-0.473026\pi$
$379$	64.1572			0.169280			0.0846402	+	0.996412i	$0.473026\pi$
$380$	−116.058	+	394.505i	−0.305416	+	1.03817i
$381$		−	11.5945i		−	0.0304319i
$382$	−223.095	+	92.2826i	−0.584018	+	0.241577i
$383$	376.877	+	376.877i	0.984014	+	0.984014i	0.999874	−	0.0158604i	$-0.00504875\pi$
$383$	376.877	+	376.877i	0.984014	+	0.984014i	−0.0158604	+	0.999874i	$0.505049\pi$
$384$	−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
$388$	0.251817	−	260.447i	0.000649013	−	0.671256i
$389$	−10.3794			−0.0266823			−0.0133411	−	0.999911i	$-0.504247\pi$
$389$	−10.3794			−0.0266823			−0.0133411	+	0.999911i	$0.504247\pi$
$390$	−19.5469	−	15.7529i	−0.0501202	−	0.0403920i
$391$	−37.9882			−0.0971566
$392$	324.259	+	134.864i	0.827191	+	0.344040i
$393$	−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	$-0.356558\pi$
$397$	−184.458	−	184.458i	−0.464630	−	0.464630i	−0.900169	+	0.435540i	$0.856558\pi$
$398$	67.2040	+	162.467i	0.168854	+	0.408208i
$399$			8.59006i			0.0215290i
$400$	−336.278	−	216.603i	−0.840696	−	0.541508i
$401$	−262.943			−0.655719			−0.327859	−	0.944727i	$-0.606327\pi$
$401$	−262.943			−0.655719			−0.327859	+	0.944727i	$0.606327\pi$
$402$	26.3981	−	10.9195i	0.0656669	−	0.0271629i
$403$	−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
$408$	−1.65645	−	0.688942i	−0.00405994	−	0.00168858i
$409$			245.618i			0.600532i	0.953855	+	0.300266i	$0.0970755\pi$
$409$			245.618i			0.600532i	−0.953855	+	0.300266i	$0.902925\pi$
$410$	235.627	−	292.376i	0.574699	−	0.713111i
$411$		−	6.54034i		−	0.0159132i
$412$	−287.997	−	0.278454i	−0.699023	−	0.000675859i
$413$	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
$418$	−187.720	−	453.816i	−0.449091	−	1.08568i
$419$	−673.011			−1.60623			−0.803116	−	0.595823i	$-0.796826\pi$
$419$	−673.011			−1.60623			−0.803116	+	0.595823i	$0.796826\pi$
$420$	−8.01597	−	2.35819i	−0.0190856	−	0.00561474i
$421$			701.227i			1.66562i	0.553557	+	0.832811i	$0.313270\pi$
$421$			701.227i			1.66562i	−0.553557	+	0.832811i	$0.686730\pi$
$422$	91.0615	+	220.143i	0.215786	+	0.521666i
$423$	−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
$428$	−539.747	−	0.521861i	−1.26109	−	0.00121930i
$429$	29.9814			0.0698868
$430$	−74.4456	−	692.655i	−0.173129	−	1.61082i
$431$	405.559			0.940973			0.470486	−	0.882407i	$-0.344078\pi$
$431$	405.559			0.940973			0.470486	+	0.882407i	$0.344078\pi$
$432$	37.6689	−	37.5235i	0.0871966	−	0.0868600i
$433$	145.764	+	145.764i	0.336638	+	0.336638i	0.855100	−	0.518462i	$-0.173495\pi$
$433$	145.764	+	145.764i	0.336638	+	0.336638i	−0.518462	+	0.855100i	$0.673495\pi$
$434$	−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
$438$	16.4913	−	6.82156i	0.0376513	−	0.0155743i
$439$		−	62.3888i		−	0.142116i	−0.997472	−	0.0710579i	$-0.977362\pi$
$439$		−	62.3888i		−	0.142116i	0.997472	−	0.0710579i	$-0.0226375\pi$
$440$	475.020	−	50.5900i	1.07959	−	0.114977i
$441$	−393.583			−0.892479
$442$	12.5794	+	30.4110i	0.0284602	+	0.0688032i
$443$	169.632	−	169.632i	0.382918	−	0.382918i	−0.489235	−	0.872152i	$-0.662724\pi$
$443$	169.632	−	169.632i	0.382918	−	0.382918i	0.872152	+	0.489235i	$0.162724\pi$
$444$	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
$448$	144.555	+	0.419297i	0.322668	+	0.000935930i
$449$		−	17.0056i		−	0.0378743i	−0.999821	−	0.0189371i	$-0.993972\pi$
$449$		−	17.0056i		−	0.0378743i	0.999821	−	0.0189371i	$-0.00602824\pi$
$450$	441.200	+	79.4102i	0.980444	+	0.176467i
$451$			448.452i			0.994351i
$452$	498.029	+	0.481526i	1.10183	+	0.00106532i
$453$	−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	0.257191	−	0.966360i	$-0.417203\pi$
$457$	559.163	−	559.163i	1.22355	−	1.22355i	0.966360	−	0.257191i	$-0.0827971\pi$
$458$	−49.0042	+	20.2705i	−0.106996	+	0.0442586i
$459$	4.02886			0.00877747
$460$	550.168	−	300.046i	1.19602	−	0.652274i
$461$		−	327.625i		−	0.710683i	−0.934737	−	0.355341i	$-0.884365\pi$
$461$		−	327.625i		−	0.710683i	0.934737	−	0.355341i	$-0.115635\pi$
$462$	9.22112	−	3.81429i	0.0199591	−	0.00825604i
$463$	605.934	+	605.934i	1.30871	+	1.30871i	0.922345	+	0.386367i	$0.126270\pi$
$463$	605.934	+	605.934i	1.30871	+	1.30871i	0.386367	+	0.922345i	$0.373730\pi$
$464$	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	$-0.209442\pi$
$467$	83.9231	+	83.9231i	0.179707	+	0.179707i	−0.611521	+	0.791228i	$0.709442\pi$
$468$	−486.749	−	0.470619i	−1.04006	−	0.00100560i
$469$	−174.422			−0.371903
$470$	−51.5157	−	479.311i	−0.109608	−	1.01981i
$471$	−16.9313			−0.0359476
$472$	−284.813	+	684.789i	−0.603418	+	1.45082i
$473$	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
$478$	87.8483	+	212.375i	0.183783	+	0.444299i
$479$		−	831.992i		−	1.73694i	−0.495746	−	0.868468i	$-0.665105\pi$
$479$		−	831.992i		−	1.73694i	0.495746	−	0.868468i	$-0.334895\pi$
$480$	29.4313	−	3.10568i	0.0613152	−	0.00647017i
$481$	−30.1601			−0.0627028
$482$	404.888	−	167.481i	0.840016	−	0.347470i
$483$	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	−0.977631	−	0.210329i	$-0.932546\pi$
$487$	−373.676	+	373.676i	−0.767301	+	0.767301i	0.210329	+	0.977631i	$0.432546\pi$
$488$	35.6490	+	14.8269i	0.0730512	+	0.0303830i
$489$		−	6.74590i		−	0.0137953i
$490$	−341.802	−	275.459i	−0.697555	−	0.562162i
$491$			42.8051i			0.0871795i	0.999050	+	0.0435898i	$0.0138794\pi$
$491$			42.8051i			0.0871795i	−0.999050	+	0.0435898i	$0.986121\pi$
$492$	−0.0268617	+	27.7823i	−5.45970e−5	+	0.0564681i
$493$	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
$498$	−12.7375	−	30.7931i	−0.0255772	−	0.0618335i
$499$	−485.100			−0.972143			−0.486072	−	0.873919i	$-0.661571\pi$
$499$	−485.100			−0.972143			−0.486072	+	0.873919i	$0.661571\pi$
$500$	327.577	+	377.748i	0.655153	+	0.755496i
$501$			14.7730i			0.0294870i
$502$	−72.6672	−	175.674i	−0.144755	−	0.349949i
$503$	−666.926	−	666.926i	−1.32590	−	1.32590i	−0.908916	−	0.416980i	$-0.863088\pi$
$503$	−666.926	−	666.926i	−1.32590	−	1.32590i	−0.416980	−	0.908916i	$-0.636912\pi$
$504$	−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
$508$	0.242429	−	250.738i	0.000477222	−	0.493578i
$509$	−779.971			−1.53236			−0.766180	−	0.642626i	$-0.777845\pi$
$509$	−779.971			−1.53236			−0.766180	+	0.642626i	$0.777845\pi$
$510$	1.74607	+	1.40717i	0.00342367	+	0.00275915i
$511$	−108.964			−0.213237
$512$	−473.874	+	193.874i	−0.925536	+	0.378660i
$513$	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
$518$	−9.27606	+	3.83702i	−0.0179075	+	0.00740737i
$519$		−	35.4435i		−	0.0682919i
$520$	−422.381	−	341.073i	−0.812271	−	0.655909i
$521$	−736.972			−1.41453			−0.707267	−	0.706947i	$-0.750072\pi$
$521$	−736.972			−1.41453			−0.707267	+	0.706947i	$0.750072\pi$
$522$	187.394	+	453.028i	0.358992	+	0.867869i
$523$	671.690	−	671.690i	1.28430	−	1.28430i	0.346108	−	0.938195i	$-0.387503\pi$
$523$	671.690	−	671.690i	1.28430	−	1.28430i	0.938195	−	0.346108i	$-0.112497\pi$
$524$	−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
$528$	−25.0402	+	24.9436i	−0.0474247	+	0.0472417i
$529$			452.780i			0.855917i
$530$	43.5250	+	404.964i	0.0821227	+	0.764084i
$531$		−	831.192i		−	1.56533i
$532$	−0.179609	+	185.764i	−0.000337610	+	0.349181i
$533$	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
$538$	−355.060	+	146.870i	−0.659963	+	0.272992i
$539$	524.263			0.972659
$540$	−58.3483	+	31.8215i	−0.108052	+	0.0589288i
$541$			1039.61i			1.92164i	0.277168	+	0.960822i	$0.410604\pi$
$541$			1039.61i			1.92164i	−0.277168	+	0.960822i	$0.589396\pi$
$542$	−897.785	+	371.366i	−1.65643	+	0.685177i
$543$	−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	$-0.150234\pi$
$547$	238.506	+	238.506i	0.436026	+	0.436026i	−0.454646	+	0.890672i	$0.650234\pi$
$548$	0.136751	−	141.438i	0.000249546	−	0.258099i
$549$	−43.2705			−0.0788169
$550$	−587.690	−	105.777i	−1.06853	−	0.192321i
$551$	562.148			1.02023
$552$	−17.8053	+	42.8100i	−0.0322559	+	0.0775543i
$553$	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	$-0.358523\pi$
$557$	−263.387	−	263.387i	−0.472867	−	0.472867i	−0.902841	+	0.429974i	$0.858523\pi$
$558$	274.347	+	663.239i	0.491661	+	1.18860i
$559$		−	945.513i		−	1.69144i
$560$	−173.300	−	51.1646i	−0.309464	−	0.0913653i
$561$	−2.67816			−0.00477391
$562$	720.782	−	298.149i	1.28253	−	0.530515i
$563$	160.698	−	160.698i	0.285431	−	0.285431i	−0.549839	−	0.835270i	$-0.685311\pi$
$563$	160.698	−	160.698i	0.285431	−	0.285431i	0.835270	+	0.549839i	$0.185311\pi$
$564$	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
$568$	181.934	−	437.432i	0.320307	−	0.770127i
$569$		−	407.195i		−	0.715633i	−0.933792	−	0.357817i	$-0.883521\pi$
$569$		−	407.195i		−	0.715633i	0.933792	−	0.357817i	$-0.116479\pi$
$570$	4.06414	+	37.8134i	0.00713007	+	0.0663394i
$571$			131.146i			0.229678i	0.993384	+	0.114839i	$0.0366351\pi$
$571$			131.146i			0.229678i	−0.993384	+	0.114839i	$0.963365\pi$
$572$	648.363	+	0.626878i	1.13350	+	0.00109594i
$573$	−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	−0.245162	−	0.969482i	$-0.578841\pi$
$577$	417.933	−	417.933i	0.724321	−	0.724321i	0.969482	+	0.245162i	$0.0788410\pi$
$578$	219.809	+	531.393i	0.380293	+	0.919365i
$579$	−47.7137			−0.0824071
$580$	−154.324	+	524.578i	−0.266075	+	0.904445i
$581$			203.462i			0.350192i
$582$	−9.20697	−	22.2580i	−0.0158195	−	0.0382440i
$583$	−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	$-0.167451\pi$
$587$	212.882	+	212.882i	0.362660	+	0.362660i	−0.502131	+	0.864791i	$0.667451\pi$
$588$	32.4789	+	0.0314027i	0.0552363	+	5.34059e-5i
$589$	822.992			1.39727
$590$	581.731	−	721.837i	0.985985	−	1.22345i
$591$	58.6697			0.0992720
$592$	25.1895	−	25.0922i	0.0425498	−	0.0423855i
$593$	97.2530	+	97.2530i	0.164002	+	0.164002i	0.784337	−	0.620335i	$-0.213003\pi$
$593$	97.2530	+	97.2530i	0.164002	+	0.164002i	−0.620335	+	0.784337i	$0.713003\pi$
$594$	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
$598$	785.952	−	325.107i	1.31430	−	0.543657i
$599$			712.479i			1.18945i	0.803930	+	0.594723i	$0.202738\pi$
$599$			712.479i			1.18945i	−0.803930	+	0.594723i	$0.797262\pi$
$600$	−36.4020	−	6.58823i	−0.0606700	−	0.0109804i
$601$	217.550			0.361980			0.180990	−	0.983485i	$-0.442070\pi$
$601$	217.550			0.361980			0.180990	+	0.983485i	$0.442070\pi$
$602$	−120.290	−	290.803i	−0.199817	−	0.483062i
$603$	−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	−0.696605	−	0.717455i	$-0.745307\pi$
$607$	12.6560	−	12.6560i	0.0208501	−	0.0208501i	0.717455	+	0.696605i	$0.245307\pi$
$608$	−250.318	−	608.478i	−0.411708	−	1.00079i
$609$			11.4223i			0.0187558i
$610$	−37.5776	−	30.2840i	−0.0616027	−	0.0496458i
$611$		−	654.287i		−	1.07085i
$612$	43.4800	+	0.0420392i	0.0710458	+	6.86916e-5i
$613$	−523.841	+	523.841i	−0.854552	+	0.854552i	−0.990690	−	0.136138i	$-0.956531\pi$
$613$	−523.841	+	523.841i	−0.854552	+	0.854552i	0.136138	+	0.990690i	$0.456531\pi$
$614$	−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	−0.922506	−	0.385983i	$-0.873862\pi$
$617$	−331.035	+	331.035i	−0.536523	+	0.536523i	0.385983	+	0.922506i	$0.373862\pi$
$618$	−24.6125	+	10.1809i	−0.0398260	+	0.0164739i
$619$	−277.907			−0.448961			−0.224481	−	0.974479i	$-0.572069\pi$
$619$	−277.907			−0.448961			−0.224481	+	0.974479i	$0.572069\pi$
$620$	−225.932	+	767.990i	−0.364407	+	1.23869i
$621$		−	104.123i		−	0.167670i
$622$	417.587	−	172.734i	0.671361	−	0.277707i
$623$	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
$628$	−366.148	−	0.354015i	−0.583038	−	0.000563718i
$629$	2.69412			0.00428318
$630$	201.349	−	21.6408i	0.319602	−	0.0343504i
$631$	425.237			0.673910			0.336955	−	0.941521i	$-0.390603\pi$
$631$	425.237			0.673910			0.336955	+	0.941521i	$0.390603\pi$
$632$	−710.926	−	295.684i	−1.12488	−	0.467854i
$633$	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
$638$	−249.613	−	603.445i	−0.391244	−	0.945839i
$639$			530.952i			0.830911i
$640$	636.531	−	66.5464i	0.994580	−	0.103979i
$641$	−474.056			−0.739558			−0.369779	−	0.929120i	$-0.620567\pi$
$641$	−474.056			−0.739558			−0.369779	+	0.929120i	$0.620567\pi$
$642$	−46.1271	+	19.0804i	−0.0718491	+	0.0297202i
$643$	−490.408	+	490.408i	−0.762687	+	0.762687i	−0.976807	−	0.214121i	$-0.931311\pi$
$643$	−490.408	+	490.408i	−0.762687	+	0.762687i	0.214121	+	0.976807i	$0.431311\pi$
$644$	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	−0.909355	−	0.416021i	$-0.863424\pi$
$647$	−319.187	+	319.187i	−0.493334	+	0.493334i	0.416021	+	0.909355i	$0.363424\pi$
$648$	−246.013	+	591.499i	−0.379649	+	0.912807i
$649$			1107.17i			1.70596i
$650$	387.266	+	557.270i	0.595794	+	0.857339i
$651$			16.7224i			0.0256873i
$652$	0.141049	−	145.883i	0.000216333	−	0.223747i
$653$	95.6351	−	95.6351i	0.146455	−	0.146455i	−0.630077	−	0.776532i	$-0.716977\pi$
$653$	95.6351	−	95.6351i	0.146455	−	0.146455i	0.776532	+	0.630077i	$0.216977\pi$
$654$	−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
$658$	−83.2396	−	201.233i	−0.126504	−	0.305826i
$659$	295.703			0.448715			0.224358	−	0.974507i	$-0.427972\pi$
$659$	295.703			0.448715			0.224358	+	0.974507i	$0.427972\pi$
$660$	38.7867	−	21.1532i	0.0587678	−	0.0320503i
$661$		−	1223.87i		−	1.85154i	−0.378088	−	0.925770i	$-0.623418\pi$
$661$		−	1223.87i		−	1.85154i	0.378088	−	0.925770i	$-0.376582\pi$
$662$	−107.953	−	260.979i	−0.163071	−	0.394228i
$663$	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
$668$	−0.308887	+	319.473i	−0.000462405	+	0.478253i
$669$	29.2955			0.0437900
$670$	−767.807	+	82.5229i	−1.14598	+	0.123168i
$671$	57.6374			0.0858978
$672$	12.3637	−	5.08624i	0.0183984	−	0.00756880i
$673$	−95.3663	−	95.3663i	−0.141703	−	0.141703i	0.632697	−	0.774400i	$-0.281948\pi$
$673$	−95.3663	−	95.3663i	−0.141703	−	0.141703i	−0.774400	+	0.632697i	$0.781948\pi$
$674$	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	$-0.180289\pi$
$677$	208.006	+	208.006i	0.307247	+	0.307247i	−0.536594	+	0.843841i	$0.680289\pi$
$678$	42.5619	−	17.6056i	0.0627757	−	0.0259670i
$679$			147.067i			0.216594i
$680$	37.7302	+	30.4671i	0.0554856	+	0.0448046i
$681$	22.4657			0.0329892
$682$	−365.438	−	883.452i	−0.535832	−	1.29538i
$683$	−704.881	+	704.881i	−1.03204	+	1.03204i	−0.0325668	+	0.999470i	$0.510368\pi$
$683$	−704.881	+	704.881i	−1.03204	+	1.03204i	−0.999470	+	0.0325668i	$0.989632\pi$
$684$	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
$688$	786.637	+	789.685i	1.14337	+	1.14780i
$689$			552.800i			0.802321i
$690$	36.3673	−	45.1261i	0.0527062	−	0.0654001i
$691$			814.437i			1.17864i	0.807901	+	0.589318i	$0.200603\pi$
$691$			814.437i			1.17864i	−0.807901	+	0.589318i	$0.799397\pi$
$692$	0.741084	−	766.483i	0.00107093	−	1.10763i
$693$	−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
$698$	791.758	−	327.509i	1.13432	−	0.469210i
$699$	−18.7442			−0.0268158
$700$	190.005	+	122.126i	0.271436	+	0.174466i
$701$		−	39.4607i		−	0.0562920i	−0.999604	−	0.0281460i	$-0.991040\pi$
$701$		−	39.4607i		−	0.0562920i	0.999604	−	0.0281460i	$-0.00896033\pi$
$702$	−83.3545	+	34.4794i	−0.118739	+	0.0491159i
$703$	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
$708$	−0.0663180	+	68.5909i	−9.36695e−5	+	0.0968798i
$709$	1177.86			1.66130			0.830648	−	0.556798i	$-0.187970\pi$
$709$	1177.86			1.66130			0.830648	+	0.556798i	$0.187970\pi$
$710$	−371.601	+	461.098i	−0.523381	+	0.649434i
$711$	862.917			1.21367
$712$	−27.2126	−	11.3181i	−0.0382200	−	0.0158962i
$713$	−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
$718$	220.201	+	532.341i	0.306687	+	0.741422i
$719$		−	242.835i		−	0.337740i	−0.985638	−	0.168870i	$-0.945988\pi$
$719$		−	242.835i		−	0.337740i	0.985638	−	0.168870i	$-0.0540119\pi$
$720$	−630.036	+	342.814i	−0.875049	+	0.476131i
$721$	162.624			0.225553
$722$	114.138	−	47.2129i	0.158086	−	0.0653918i
$723$	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	−0.990416	−	0.138116i	$-0.955895\pi$
$727$	−619.622	+	619.622i	−0.852300	+	0.852300i	0.138116	+	0.990416i	$0.455895\pi$
$728$	−226.442	−	94.1802i	−0.311046	−	0.129368i
$729$		−	712.425i		−	0.977264i
$730$	−479.660	+	51.5532i	−0.657069	+	0.0706209i
$731$			84.4603i			0.115541i
$732$	3.57073	+	0.00345241i	0.00487804	+	4.71640e-6i
$733$	281.127	−	281.127i	0.383529	−	0.383529i	−0.488843	−	0.872372i	$-0.662581\pi$
$733$	281.127	−	281.127i	0.383529	−	0.383529i	0.872372	+	0.488843i	$0.162581\pi$
$734$	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
$738$	−257.375	−	622.208i	−0.348746	−	0.843100i
$739$	1109.74			1.50168			0.750839	−	0.660485i	$-0.229649\pi$
$739$	1109.74			1.50168			0.750839	+	0.660485i	$0.229649\pi$
$740$	−39.0179	+	21.2793i	−0.0527268	+	0.0287558i
$741$			51.6175i			0.0696592i
$742$	70.3282	+	170.020i	0.0947819	+	0.229137i
$743$	−339.850	−	339.850i	−0.457403	−	0.457403i	0.440399	−	0.897802i	$-0.354837\pi$
$743$	−339.850	−	339.850i	−0.457403	−	0.457403i	−0.897802	+	0.440399i	$0.854837\pi$
$744$	−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
$748$	−57.9166	−	0.0559974i	−0.0774286	−	7.48629e-5i
$749$	304.780			0.406916
$750$	41.3685	+	20.6626i	0.0551580	+	0.0275501i
$751$	−980.557			−1.30567			−0.652834	−	0.757501i	$-0.726420\pi$
$751$	−980.557			−1.30567			−0.652834	+	0.757501i	$0.726420\pi$
$752$	544.346	+	546.455i	0.723865	+	0.726670i
$753$	−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	$-0.280243\pi$
$757$	−101.564	−	101.564i	−0.134166	−	0.134166i	−0.771001	+	0.636834i	$0.780243\pi$
$758$	118.571	−	49.0465i	0.156426	−	0.0647052i
$759$			69.2154i			0.0911929i
$760$	87.0983	+	817.819i	0.114603	+	1.07608i
$761$	767.675			1.00877			0.504386	−	0.863478i	$-0.331719\pi$
$761$	767.675			1.00877			0.504386	+	0.863478i	$0.331719\pi$
$762$	−8.86372	−	21.4282i	−0.0116322	−	0.0281210i
$763$	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
$768$	−33.6118	+	33.3528i	−0.0437654	+	0.0434282i
$769$		−	331.840i		−	0.431522i	−0.976446	−	0.215761i	$-0.930777\pi$
$769$		−	331.840i		−	0.431522i	0.976446	−	0.215761i	$-0.0692232\pi$
$770$	−268.203	+	28.8261i	−0.348315	+	0.0374365i
$771$			65.1675i			0.0845234i
$772$	−1031.83	−	0.997640i	−1.33657	−	0.00129228i
$773$	−180.328	+	180.328i	−0.233283	+	0.233283i	−0.814061	−	0.580779i	$-0.802748\pi$
$773$	−180.328	+	180.328i	−0.233283	+	0.233283i	0.580779	+	0.814061i	$0.302748\pi$
$774$	−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
$778$	−19.1825	+	7.93478i	−0.0246561	+	0.0101989i
$779$	−772.078			−0.991114
$780$	−48.1678	−	14.1703i	−0.0617536	−	0.0181671i
$781$		−	707.243i		−	0.905561i
$782$	−70.2071	+	29.0410i	−0.0897789	+	0.0371368i
$783$	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	0.973924	+	0.226876i	$0.0728513\pi$
$787$	945.029	+	945.029i	1.20080	+	1.20080i	0.226876	+	0.973924i	$0.427149\pi$
$788$	1268.76	+	1.22672i	1.61010	+	0.00155675i
$789$	−22.3940			−0.0283827
$790$	749.388	+	603.935i	0.948593	+	0.764474i
$791$	−281.223			−0.355529
$792$	328.955	−	790.922i	0.415348	−	0.998639i
$793$	−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	$-0.0435766\pi$
$797$	680.774	+	680.774i	0.854171	+	0.854171i	−0.136473	+	0.990644i	$0.543577\pi$
$798$	6.56687	+	15.8755i	0.00822917	+	0.0198942i
$799$			58.4458i			0.0731487i
$800$	−787.073	−	143.235i	−0.983841	−	0.179043i
$801$	33.0305			0.0412366
$802$	−485.953	+	201.013i	−0.605926	+	0.250640i
$803$	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
$808$	799.029	+	332.327i	0.988898	+	0.411296i
$809$		−	427.952i		−	0.528989i	−0.964387	−	0.264495i	$-0.914795\pi$
$809$		−	427.952i		−	0.528989i	0.964387	−	0.264495i	$-0.0852051\pi$
$810$	502.481	−	623.500i	0.620347	−	0.769753i
$811$		−	1222.46i		−	1.50735i	−0.657245	−	0.753677i	$-0.728278\pi$
$811$		−	1222.46i		−	1.50735i	0.657245	−	0.753677i	$-0.271722\pi$
$812$	−0.238828	+	247.013i	−0.000294123	+	0.304203i
$813$	−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
$818$	187.768	+	453.933i	0.229545	+	0.554930i
$819$	274.853			0.335596
$820$	211.955	−	720.478i	0.258482	−	0.878632i
$821$			1019.26i			1.24148i	0.784015	+	0.620742i	$0.213169\pi$
$821$			1019.26i			1.24148i	−0.784015	+	0.620742i	$0.786831\pi$
$822$	−4.99992	−	12.0874i	−0.00608262	−	0.0147049i
$823$	−158.477	−	158.477i	−0.192560	−	0.192560i	0.604241	−	0.796801i	$-0.293476\pi$
$823$	−158.477	−	158.477i	−0.192560	−	0.192560i	−0.796801	+	0.604241i	$0.793476\pi$
$824$	−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	$-0.413144\pi$
$827$	−573.534	−	573.534i	−0.693511	−	0.693511i	−0.963003	+	0.269492i	$0.913144\pi$
$828$	1.08648	−	1123.71i	0.00131217	−	1.35714i
$829$	−1133.71			−1.36756			−0.683782	−	0.729686i	$-0.739666\pi$
$829$	−1133.71			−1.36756			−0.683782	+	0.729686i	$0.739666\pi$
$830$	96.2620	+	895.638i	0.115978	+	1.07908i
$831$	−23.2430			−0.0279699
$832$	868.630	+	2.51955i	1.04403	+	0.00302830i
$833$	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
$838$	−1243.81	+	514.499i	−1.48426	+	0.613961i
$839$			1109.49i			1.32240i	0.750212	+	0.661198i	$0.229952\pi$
$839$			1109.49i			1.32240i	−0.750212	+	0.661198i	$0.770048\pi$
$840$	−16.6173	+	1.76976i	−0.0197825	+	0.00210685i
$841$	−93.5052			−0.111183
$842$	536.070	+	1295.96i	0.636662	+	1.53914i
$843$	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
$848$	−459.912	−	461.694i	−0.542349	−	0.544450i
$849$		−	31.6676i		−	0.0372999i
$850$	−34.5935	−	49.7795i	−0.0406982	−	0.0585642i
$851$		−	69.6278i		−	0.0818188i
$852$	0.0423629	−	43.8148i	4.97217e−5	−	0.0514258i
$853$	−1.51055	+	1.51055i	−0.00177087	+	0.00177087i	−0.707992	−	0.706221i	$-0.750399\pi$
$853$	−1.51055	+	1.51055i	−0.00177087	+	0.00177087i	0.706221	+	0.707992i	$0.250399\pi$
$854$	−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	−0.899676	−	0.436558i	$-0.856197\pi$
$857$	−396.892	+	396.892i	−0.463118	+	0.463118i	0.436558	+	0.899676i	$0.356197\pi$
$858$	55.4095	−	22.9200i	0.0645799	−	0.0267133i
$859$	−941.956			−1.09657			−0.548286	−	0.836291i	$-0.684720\pi$
$859$	−941.956			−1.09657			−0.548286	+	0.836291i	$0.684720\pi$
$860$	−667.101	−	1223.20i	−0.775699	−	1.42233i
$861$		−	15.6879i		−	0.0182206i
$862$	749.526	−	310.039i	0.869520	−	0.359674i
$863$	833.800	+	833.800i	0.966164	+	0.966164i	0.999446	−	0.0332818i	$-0.0105959\pi$
$863$	833.800	+	833.800i	0.966164	+	0.966164i	−0.0332818	+	0.999446i	$0.510596\pi$
$864$	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
$868$	−0.349647	+	361.631i	−0.000402819	+	0.416625i
$869$	−1149.43			−1.32270
$870$	5.40414	+	50.2810i	0.00621165	+	0.0577943i
$871$	−1048.10			−1.20333
$872$	−142.989	+	343.796i	−0.163979	+	0.394261i
$873$	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	$-0.258625\pi$
$877$	−33.6015	−	33.6015i	−0.0383142	−	0.0383142i	−0.726004	+	0.687690i	$0.758625\pi$
$878$	−47.6946	−	115.303i	−0.0543219	−	0.131324i
$879$			64.0762i			0.0728967i
$880$	839.224	−	456.638i	0.953664	−	0.518906i
$881$	1084.55			1.23104			0.615521	−	0.788121i	$-0.288946\pi$
$881$	1084.55			1.23104			0.615521	+	0.788121i	$0.288946\pi$
$882$	−727.392	+	300.884i	−0.824708	+	0.341138i
$883$	1165.53	−	1165.53i	1.31997	−	1.31997i	0.406174	−	0.913796i	$-0.366863\pi$
$883$	1165.53	−	1165.53i	1.31997	−	1.31997i	0.913796	−	0.406174i	$-0.133137\pi$
$884$	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	−0.888742	−	0.458409i	$-0.848420\pi$
$887$	−381.705	+	381.705i	−0.430333	+	0.430333i	0.458409	+	0.888742i	$0.348420\pi$
$888$	1.26275	−	3.03608i	0.00142201	−	0.00341901i
$889$			141.584i			0.159263i
$890$	28.6849	+	23.1172i	0.0322302	+	0.0259744i
$891$			956.338i			1.07333i
$892$	633.529	+	0.612536i	0.710234	+	0.000686699i
$893$	−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
$898$	−13.0003	−	31.4285i	−0.0144769	−	0.0349983i
$899$	1094.34			1.21729
$900$	876.101	−	190.525i	0.973446	−	0.211695i
$901$		−	49.3802i		−	0.0548060i
$902$	342.830	+	828.798i	0.380078	+	0.918845i
$903$	−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	$-0.366092\pi$
$907$	−457.511	−	457.511i	−0.504422	−	0.504422i	−0.912809	+	0.408387i	$0.866092\pi$
$908$	485.831	+	0.469732i	0.535056	+	0.000517326i
$909$	−969.856			−1.06695
$910$	238.693	+	192.363i	0.262300	+	0.211388i
$911$	−620.530			−0.681152			−0.340576	−	0.940217i	$-0.610622\pi$
$911$	−620.530			−0.681152			−0.340576	+	0.940217i	$0.610622\pi$
$912$	−42.9441	−	43.1105i	−0.0470879	−	0.0472703i
$913$	−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
$918$	7.44585	−	3.07996i	0.00811095	−	0.00335507i
$919$		−	981.064i		−	1.06753i	−0.845631	−	0.533767i	$-0.820776\pi$
$919$		−	981.064i		−	1.06753i	0.845631	−	0.533767i	$-0.179224\pi$
$920$	787.403	−	975.113i	0.855873	−	1.05990i
$921$	−35.3985			−0.0384349
$922$	−250.460	−	605.493i	−0.271649	−	0.656717i
$923$	−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
$928$	−332.852	−	809.101i	−0.358676	−	0.871876i
$929$		−	776.484i		−	0.835827i	−0.908487	−	0.417914i	$-0.862761\pi$
$929$		−	776.484i		−	0.835827i	0.908487	−	0.417914i	$-0.137239\pi$
$930$	7.91173	+	73.6121i	0.00850724	+	0.0791528i
$931$			902.598i			0.969493i
$932$	−405.353	−	0.391921i	−0.434928	−	0.000420516i
$933$	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	−0.173881	−	0.984767i	$-0.555631\pi$
$937$	759.800	−	759.800i	0.810885	−	0.810885i	0.984767	+	0.173881i	$0.0556309\pi$
$938$	−322.355	+	133.341i	−0.343662	+	0.142155i
$939$	−60.3267			−0.0642457
$940$	−461.628	−	846.446i	−0.491094	−	0.900475i
$941$			759.500i			0.807120i	0.914953	+	0.403560i	$0.132227\pi$
$941$			759.500i			0.807120i	−0.914953	+	0.403560i	$0.867773\pi$
$942$	−31.2912	+	12.9435i	−0.0332179	+	0.0137405i
$943$	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	$-0.460535\pi$
$947$	−822.618	−	822.618i	−0.868657	−	0.868657i	−0.992324	+	0.123667i	$0.960535\pi$
$948$	−71.2089	−	0.0688492i	−0.0751149	−	7.26258e-5i
$949$	−654.763			−0.689951
$950$	182.110	−	1011.80i	0.191695	−	1.06505i
$951$	57.9572			0.0609434
$952$	20.2275	+	8.41288i	0.0212473	+	0.00883706i
$953$	659.139	+	659.139i	0.691647	+	0.691647i	0.962594	−	0.270947i	$-0.0873369\pi$
$953$	659.139	+	659.139i	0.691647	+	0.691647i	−0.270947	+	0.962594i	$0.587337\pi$
$954$	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
$958$	−636.036	−	1537.63i	−0.663920	−	1.60504i
$959$			79.8661i			0.0832806i
$960$	52.0186	−	28.2391i	0.0541861	−	0.0294158i
$961$	641.133			0.667152
$962$	−55.7397	+	23.0566i	−0.0579415	+	0.0239673i
$963$	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	−0.514284	−	0.857620i	$-0.671942\pi$
$967$	332.005	−	332.005i	0.343335	−	0.343335i	0.857620	+	0.514284i	$0.171942\pi$
$968$	−66.4433	+	159.753i	−0.0686398	+	0.165034i
$969$		−	4.61086i		−	0.00475837i
$970$	69.5807	+	647.390i	0.0717326	+	0.667413i
$971$			960.961i			0.989661i	0.868989	+	0.494831i	$0.164770\pi$
$971$			960.961i			0.989661i	−0.868989	+	0.494831i	$0.835230\pi$
$972$	−0.172950	+	178.877i	−0.000177932	+	0.184030i
$973$	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	−0.670664	−	0.741762i	$-0.733991\pi$
$977$	69.4628	−	69.4628i	0.0710980	−	0.0710980i	0.741762	+	0.670664i	$0.233991\pi$
$978$	−5.15706	−	12.4673i	−0.00527307	−	0.0127477i
$979$	−43.9975			−0.0449413
$980$	−842.275	−	247.786i	−0.859465	−	0.252843i
$981$		−	417.297i		−	0.425379i
$982$	32.7234	+	79.1094i	0.0333232	+	0.0805595i
$983$	234.943	+	234.943i	0.239006	+	0.239006i	0.816438	−	0.577433i	$-0.195945\pi$
$983$	234.943	+	234.943i	0.239006	+	0.239006i	−0.577433	+	0.816438i	$0.695945\pi$
$984$	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
$988$	−1.07926	+	1116.25i	−0.00109237	+	1.12981i
$989$	2182.82			2.20710
$990$	−671.892	+	833.712i	−0.678679	+	0.842134i
$991$	−919.592			−0.927944			−0.463972	−	0.885850i	$-0.653576\pi$
$991$	−919.592			−0.927944			−0.463972	+	0.885850i	$0.653576\pi$
$992$	−487.299	−	1184.54i	−0.491229	−	1.19409i
$993$	−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	$-0.452007\pi$
$997$	−835.935	−	835.935i	−0.838450	−	0.838450i	−0.988655	+	0.150205i	$0.952007\pi$
$998$	−896.526	+	370.846i	−0.898323	+	0.371589i
$999$			7.38441i			0.00739180i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.7	✓	20	8.5	even	2	inner
40.3.i.a.13.9	yes	20	1.1	even	1	trivial
40.3.i.a.37.7	yes	20	5.2	odd	4	inner
40.3.i.a.37.9	yes	20	40.37	odd	4	inner
160.3.m.a.17.5		20	40.27	even	4
160.3.m.a.17.6		20	20.7	even	4
160.3.m.a.113.5		20	4.3	odd	2
160.3.m.a.113.6		20	8.3	odd	2
200.3.i.b.93.2		20	5.4	even	2
200.3.i.b.93.4		20	40.29	even	2
200.3.i.b.157.2		20	40.13	odd	4
200.3.i.b.157.4		20	5.3	odd	4
360.3.u.b.37.2		20	120.77	even	4
360.3.u.b.37.4		20	15.2	even	4
360.3.u.b.253.2		20	3.2	odd	2
360.3.u.b.253.4		20	24.5	odd	2
800.3.m.b.593.5		20	40.19	odd	2
800.3.m.b.593.6		20	20.19	odd	2
800.3.m.b.657.5		20	20.3	even	4
800.3.m.b.657.6		20	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	40.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84813 - 0.764474i) 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} +(3.07218 - 7.38659i) q^{8} +8.96579i q^{9} +(-6.27494 + 7.78621i) q^{10} -11.9427i q^{11} +(0.000715350 - 0.739867i) 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} +(6.85411 + 16.5699i) q^{18} +20.5611 q^{19} +(-5.64454 + 19.1870i) q^{20} +0.417782i q^{21} +(-9.12986 - 22.0716i) 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} +(-0.00873536 + 9.03474i) q^{28} +27.3404 q^{29} +(0.197662 + 1.83908i) q^{30} +40.0267 q^{31} +(-12.1744 - 29.5937i) 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} +(37.9996 - 15.7184i) q^{38} +2.51044i q^{39} +(4.23607 + 39.7751i) q^{40} -37.5504 q^{41} +(0.319383 + 0.772115i) 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} +(-2.08861 - 2.09670i) q^{48} +43.8983i q^{49} +(8.85703 - 49.2093i) q^{50} -0.224252i q^{51} +(-0.0524906 + 54.2896i) 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} +(50.5285 - 20.9010i) q^{58} -92.7071 q^{59} +(1.77123 + 3.24774i) q^{60} +4.82618i q^{61} +(73.9744 - 30.5993i) 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} +(0.00468885 - 4.84955i) q^{68} -5.79564 q^{69} +(-2.41371 - 22.4575i) q^{70} +59.2198 q^{71} +(66.2266 + 27.5445i) 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} +(1.91917 + 4.63963i) q^{78} -96.2455i q^{79} +(38.2358 + 70.2711i) q^{80} -80.0774 q^{81} +(-69.3980 + 28.7063i) 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} +(-88.2156 - 36.6901i) q^{88} -3.68406i q^{89} +(-69.8095 - 56.2598i) q^{90} -30.6558i q^{91} +(-125.333 - 0.121180i) 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} +(33.5591 + 81.1298i) q^{98} +107.075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31}+ \cdots + 546 q^{98}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more