LMFDB - Embedded newform 40.3.i.a.13.6

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			13.6
Root			$-1.17039 + 0.793843i$ of defining polynomial
Character	$\chi$	$=$	40.13
Dual form			40.3.i.a.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.376547 + 1.96423i) q^{2} +(-0.977390 + 0.977390i) q^{3} +(-3.71643 + 1.47925i) q^{4} +(0.801246 + 4.93538i) q^{5} +(-2.28785 - 1.55179i) q^{6} +(8.39950 - 8.39950i) q^{7} +(-4.30500 - 6.74292i) q^{8} +7.08942i q^{9} +O(q^{10})$	\(q+(0.376547 + 1.96423i) q^{2} +(-0.977390 + 0.977390i) q^{3} +(-3.71643 + 1.47925i) q^{4} +(0.801246 + 4.93538i) q^{5} +(-2.28785 - 1.55179i) q^{6} +(8.39950 - 8.39950i) q^{7} +(-4.30500 - 6.74292i) q^{8} +7.08942i q^{9} +(-9.39254 + 3.43224i) q^{10} -4.01590i q^{11} +(2.18659 - 5.07820i) q^{12} +(11.0839 - 11.0839i) q^{13} +(19.6614 + 13.3358i) q^{14} +(-5.60692 - 4.04066i) q^{15} +(11.6236 - 10.9951i) q^{16} +(-3.79258 + 3.79258i) q^{17} +(-13.9253 + 2.66950i) q^{18} -15.9605 q^{19} +(-10.2784 - 17.1567i) q^{20} +16.4192i q^{21} +(7.88816 - 1.51217i) q^{22} +(1.86825 + 1.86825i) q^{23} +(10.7981 + 2.38279i) q^{24} +(-23.7160 + 7.90891i) q^{25} +(25.9449 + 17.5977i) q^{26} +(-15.7256 - 15.7256i) q^{27} +(-18.7911 + 43.6411i) q^{28} +0.468098 q^{29} +(5.82554 - 12.5348i) q^{30} -17.3217 q^{31} +(25.9737 + 18.6914i) q^{32} +(3.92510 + 3.92510i) q^{33} +(-8.87759 - 6.02143i) q^{34} +(48.1848 + 34.7247i) q^{35} +(-10.4870 - 26.3473i) q^{36} +(-22.1558 - 22.1558i) q^{37} +(-6.00989 - 31.3502i) q^{38} +21.6665i q^{39} +(29.8295 - 26.6496i) q^{40} +37.0776 q^{41} +(-32.2511 + 6.18259i) q^{42} +(17.1423 - 17.1423i) q^{43} +(5.94052 + 14.9248i) q^{44} +(-34.9890 + 5.68037i) q^{45} +(-2.96620 + 4.37316i) q^{46} +(-6.31059 + 6.31059i) q^{47} +(-0.614364 + 22.1073i) q^{48} -92.1033i q^{49} +(-24.4651 - 43.6057i) q^{50} -7.41366i q^{51} +(-24.7965 + 57.5881i) q^{52} +(39.8935 - 39.8935i) q^{53} +(24.9674 - 36.8102i) q^{54} +(19.8200 - 3.21772i) q^{55} +(-92.7970 - 20.4773i) q^{56} +(15.5997 - 15.5997i) q^{57} +(0.176261 + 0.919455i) q^{58} -50.6555 q^{59} +(26.8149 + 6.72277i) q^{60} +73.6559i q^{61} +(-6.52241 - 34.0238i) q^{62} +(59.5476 + 59.5476i) q^{63} +(-26.9339 + 58.0566i) q^{64} +(63.5839 + 45.8222i) q^{65} +(-6.23183 + 9.18779i) q^{66} +(77.6780 + 77.6780i) q^{67} +(8.48466 - 19.7050i) q^{68} -3.65202 q^{69} +(-50.0636 + 107.722i) q^{70} -78.3775 q^{71} +(47.8034 - 30.5200i) q^{72} +(-46.0027 - 46.0027i) q^{73} +(35.1765 - 51.8619i) q^{74} +(15.4497 - 30.9099i) q^{75} +(59.3162 - 23.6097i) q^{76} +(-33.7315 - 33.7315i) q^{77} +(-42.5580 + 8.15844i) q^{78} -31.6724i q^{79} +(63.5782 + 48.5573i) q^{80} -33.0646 q^{81} +(13.9614 + 72.8290i) q^{82} +(-84.9971 + 84.9971i) q^{83} +(-24.2881 - 61.0206i) q^{84} +(-21.7566 - 15.6790i) q^{85} +(40.1264 + 27.2166i) q^{86} +(-0.457515 + 0.457515i) q^{87} +(-27.0789 + 17.2885i) q^{88} +92.8102i q^{89} +(-24.3326 - 66.5876i) q^{90} -186.198i q^{91} +(-9.70682 - 4.17960i) q^{92} +(16.9300 - 16.9300i) q^{93} +(-14.7717 - 10.0192i) q^{94} +(-12.7883 - 78.7714i) q^{95} +(-43.6552 + 7.11767i) q^{96} +(-85.3107 + 85.3107i) q^{97} +(180.912 - 34.6812i) q^{98} +28.4704 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 $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.376547	+	1.96423i	0.188273	+	0.982117i
$2$	0.376547	+	1.96423i	0.188273	+	0.982117i
$3$	−0.977390	+	0.977390i	−0.325797	+	0.325797i	−0.850986	−	0.525189i	$-0.823995\pi$
$3$	−0.977390	+	0.977390i	−0.325797	+	0.325797i	0.525189	+	0.850986i	$0.323995\pi$
$4$	−3.71643	+	1.47925i	−0.929106	+	0.369813i
$5$	0.801246	+	4.93538i	0.160249	+	0.987077i
$5$	0.801246	+	4.93538i	0.160249	+	0.987077i
$6$	−2.28785	−	1.55179i	−0.381309	−	0.258631i
$7$	8.39950	−	8.39950i	1.19993	−	1.19993i	0.225742	−	0.974187i	$-0.427519\pi$
$7$	8.39950	−	8.39950i	1.19993	−	1.19993i	0.974187	−	0.225742i	$-0.0724805\pi$
$8$	−4.30500	−	6.74292i	−0.538125	−	0.842865i
$9$			7.08942i			0.787713i
$10$	−9.39254	+	3.43224i	−0.939254	+	0.343224i
$11$		−	4.01590i		−	0.365082i	−0.983198	−	0.182541i	$-0.941568\pi$
$11$		−	4.01590i		−	0.365082i	0.983198	−	0.182541i	$-0.0584322\pi$
$12$	2.18659	−	5.07820i	0.182216	−	0.423183i
$13$	11.0839	−	11.0839i	0.852604	−	0.852604i	−0.137849	−	0.990453i	$-0.544019\pi$
$13$	11.0839	−	11.0839i	0.852604	−	0.852604i	0.990453	+	0.137849i	$0.0440190\pi$
$14$	19.6614	+	13.3358i	1.40438	+	0.952555i
$15$	−5.60692	−	4.04066i	−0.373795	−	0.269378i
$16$	11.6236	−	10.9951i	0.726477	−	0.687191i
$17$	−3.79258	+	3.79258i	−0.223093	+	0.223093i	−0.809800	−	0.586707i	$-0.800424\pi$
$17$	−3.79258	+	3.79258i	−0.223093	+	0.223093i	0.586707	+	0.809800i	$0.300424\pi$
$18$	−13.9253	+	2.66950i	−0.773626	+	0.148305i
$19$	−15.9605			−0.840029			−0.420014	−	0.907517i	$-0.637975\pi$
$19$	−15.9605			−0.840029			−0.420014	+	0.907517i	$0.637975\pi$
$20$	−10.2784	−	17.1567i	−0.513922	−	0.857837i
$21$			16.4192i			0.781865i
$22$	7.88816	−	1.51217i	0.358553	−	0.0687352i
$23$	1.86825	+	1.86825i	0.0812283	+	0.0812283i	0.746554	−	0.665325i	$-0.231707\pi$
$23$	1.86825	+	1.86825i	0.0812283	+	0.0812283i	−0.665325	+	0.746554i	$0.731707\pi$
$24$	10.7981	+	2.38279i	0.449922	+	0.0992831i
$25$	−23.7160	+	7.90891i	−0.948640	+	0.316357i
$26$	25.9449	+	17.5977i	0.997879	+	0.676834i
$27$	−15.7256	−	15.7256i	−0.582431	−	0.582431i
$28$	−18.7911	+	43.6411i	−0.671112	+	1.55861i
$29$	0.468098			0.0161413			0.00807066	−	0.999967i	$-0.497431\pi$
$29$	0.468098			0.0161413			0.00807066	+	0.999967i	$0.497431\pi$
$30$	5.82554	−	12.5348i	0.194185	−	0.417827i
$31$	−17.3217			−0.558763			−0.279382	−	0.960180i	$-0.590129\pi$
$31$	−17.3217			−0.558763			−0.279382	+	0.960180i	$0.590129\pi$
$32$	25.9737	+	18.6914i	0.811678	+	0.584105i
$33$	3.92510	+	3.92510i	0.118942	+	0.118942i
$34$	−8.87759	−	6.02143i	−0.261106	−	0.177101i
$35$	48.1848	+	34.7247i	1.37671	+	0.992134i
$36$	−10.4870	−	26.3473i	−0.291306	−	0.731869i
$37$	−22.1558	−	22.1558i	−0.598805	−	0.598805i	0.341189	−	0.939995i	$-0.389170\pi$
$37$	−22.1558	−	22.1558i	−0.598805	−	0.598805i	−0.939995	+	0.341189i	$0.889170\pi$
$38$	−6.00989	−	31.3502i	−0.158155	−	0.825006i
$39$			21.6665i			0.555551i
$40$	29.8295	−	26.6496i	0.745738	−	0.666239i
$41$	37.0776			0.904331			0.452165	−	0.891934i	$-0.350652\pi$
$41$	37.0776			0.904331			0.452165	+	0.891934i	$0.350652\pi$
$42$	−32.2511	+	6.18259i	−0.767883	+	0.147204i
$43$	17.1423	−	17.1423i	0.398658	−	0.398658i	−0.479101	−	0.877760i	$-0.659037\pi$
$43$	17.1423	−	17.1423i	0.398658	−	0.398658i	0.877760	+	0.479101i	$0.159037\pi$
$44$	5.94052	+	14.9248i	0.135012	+	0.339200i
$45$	−34.9890	+	5.68037i	−0.777533	+	0.126230i
$46$	−2.96620	+	4.37316i	−0.0644825	+	0.0950688i
$47$	−6.31059	+	6.31059i	−0.134268	+	0.134268i	−0.771047	−	0.636779i	$-0.780266\pi$
$47$	−6.31059	+	6.31059i	−0.134268	+	0.134268i	0.636779	+	0.771047i	$0.280266\pi$
$48$	−0.614364	+	22.1073i	−0.0127992	+	0.460568i
$49$		−	92.1033i		−	1.87966i
$50$	−24.4651	−	43.6057i	−0.489303	−	0.872114i
$51$		−	7.41366i		−	0.145366i
$52$	−24.7965	+	57.5881i	−0.476856	+	1.10746i
$53$	39.8935	−	39.8935i	0.752708	−	0.752708i	−0.222276	−	0.974984i	$-0.571348\pi$
$53$	39.8935	−	39.8935i	0.752708	−	0.752708i	0.974984	+	0.222276i	$0.0713485\pi$
$54$	24.9674	−	36.8102i	0.462359	−	0.681671i
$55$	19.8200	−	3.21772i	0.360364	−	0.0585041i
$56$	−92.7970	−	20.4773i	−1.65709	−	0.365666i
$57$	15.5997	−	15.5997i	0.273679	−	0.273679i
$58$	0.176261	+	0.919455i	0.00303898	+	0.0158527i
$59$	−50.6555			−0.858567			−0.429284	−	0.903170i	$-0.641234\pi$
$59$	−50.6555			−0.858567			−0.429284	+	0.903170i	$0.641234\pi$
$60$	26.8149	+	6.72277i	0.446914	+	0.112046i
$61$			73.6559i			1.20747i	0.797183	+	0.603737i	$0.206322\pi$
$61$			73.6559i			1.20747i	−0.797183	+	0.603737i	$0.793678\pi$
$62$	−6.52241	−	34.0238i	−0.105200	−	0.548771i
$63$	59.5476	+	59.5476i	0.945200	+	0.945200i
$64$	−26.9339	+	58.0566i	−0.420842	+	0.907134i
$65$	63.5839	+	45.8222i	0.978214	+	0.704956i
$66$	−6.23183	+	9.18779i	−0.0944216	+	0.139209i
$67$	77.6780	+	77.6780i	1.15937	+	1.15937i	0.984611	+	0.174763i	$0.0559159\pi$
$67$	77.6780	+	77.6780i	1.15937	+	1.15937i	0.174763	+	0.984611i	$0.444084\pi$
$68$	8.48466	−	19.7050i	0.124774	−	0.289780i
$69$	−3.65202			−0.0529278
$70$	−50.0636	+	107.722i	−0.715194	+	1.53888i
$71$	−78.3775			−1.10391			−0.551954	−	0.833874i	$-0.686118\pi$
$71$	−78.3775			−1.10391			−0.551954	+	0.833874i	$0.686118\pi$
$72$	47.8034	−	30.5200i	0.663936	−	0.423888i
$73$	−46.0027	−	46.0027i	−0.630173	−	0.630173i	0.317938	−	0.948111i	$-0.397010\pi$
$73$	−46.0027	−	46.0027i	−0.630173	−	0.630173i	−0.948111	+	0.317938i	$0.897010\pi$
$74$	35.1765	−	51.8619i	0.475358	−	0.700836i
$75$	15.4497	−	30.9099i	0.205996	−	0.412132i
$76$	59.3162	−	23.6097i	0.780476	−	0.310653i
$77$	−33.7315	−	33.7315i	−0.438072	−	0.438072i
$78$	−42.5580	+	8.15844i	−0.545616	+	0.104595i
$79$		−	31.6724i		−	0.400916i	−0.979702	−	0.200458i	$-0.935757\pi$
$79$		−	31.6724i		−	0.400916i	0.979702	−	0.200458i	$-0.0642430\pi$
$80$	63.5782	+	48.5573i	0.794727	+	0.606967i
$81$	−33.0646			−0.408205
$82$	13.9614	+	72.8290i	0.170261	+	0.888158i
$83$	−84.9971	+	84.9971i	−1.02406	+	1.02406i	−0.0243583	+	0.999703i	$0.507754\pi$
$83$	−84.9971	+	84.9971i	−1.02406	+	1.02406i	−0.999703	+	0.0243583i	$0.992246\pi$
$84$	−24.2881	−	61.0206i	−0.289144	−	0.726436i
$85$	−21.7566	−	15.6790i	−0.255960	−	0.184459i
$86$	40.1264	+	27.2166i	0.466586	+	0.316472i
$87$	−0.457515	+	0.457515i	−0.00525879	+	0.00525879i
$88$	−27.0789	+	17.2885i	−0.307715	+	0.196460i
$89$			92.8102i			1.04281i	0.853309	+	0.521406i	$0.174592\pi$
$89$			92.8102i			1.04281i	−0.853309	+	0.521406i	$0.825408\pi$
$90$	−24.3326	−	66.5876i	−0.270362	−	0.739863i
$91$		−	186.198i		−	2.04613i
$92$	−9.70682	−	4.17960i	−0.105509	−	0.0454304i
$93$	16.9300	−	16.9300i	0.182043	−	0.182043i
$94$	−14.7717	−	10.0192i	−0.157146	−	0.106588i
$95$	−12.7883	−	78.7714i	−0.134614	−	0.829173i
$96$	−43.6552	+	7.11767i	−0.454741	+	0.0741424i
$97$	−85.3107	+	85.3107i	−0.879492	+	0.879492i	−0.993482	−	0.113990i	$-0.963637\pi$
$97$	−85.3107	+	85.3107i	−0.879492	+	0.879492i	0.113990	+	0.993482i	$0.463637\pi$
$98$	180.912	−	34.6812i	1.84604	−	0.353890i
$99$	28.4704			0.287580
$100$	76.4395	−	64.4748i	0.764395	−	0.644748i
$101$			20.4248i			0.202226i	0.994875	+	0.101113i	$0.0322404\pi$
$101$			20.4248i			0.202226i	−0.994875	+	0.101113i	$0.967760\pi$
$102$	14.5622	−	2.79159i	0.142766	−	0.0273685i
$103$	−38.9743	−	38.9743i	−0.378391	−	0.378391i	0.492130	−	0.870521i	$-0.336218\pi$
$103$	−38.9743	−	38.9743i	−0.378391	−	0.378391i	−0.870521	+	0.492130i	$0.836218\pi$
$104$	−122.454	−	27.0215i	−1.17744	−	0.259822i
$105$	−81.0349	+	13.1558i	−0.771761	+	0.125293i
$106$	93.3820	+	63.3384i	0.880962	+	0.597532i
$107$	−70.1663	−	70.1663i	−0.655760	−	0.655760i	0.298614	−	0.954374i	$-0.403476\pi$
$107$	−70.1663	−	70.1663i	−0.655760	−	0.655760i	−0.954374	+	0.298614i	$0.903476\pi$
$108$	81.7053	+	35.1810i	0.756531	+	0.325750i
$109$	160.230			1.47000			0.735001	−	0.678066i	$-0.237182\pi$
$109$	160.230			1.47000			0.735001	+	0.678066i	$0.237182\pi$
$110$	13.7835	+	37.7195i	0.125305	+	0.342904i
$111$	43.3097			0.390178
$112$	5.27973	−	189.986i	0.0471404	−	1.69630i
$113$	9.77907	+	9.77907i	0.0865404	+	0.0865404i	0.749052	−	0.662511i	$-0.230509\pi$
$113$	9.77907	+	9.77907i	0.0865404	+	0.0865404i	−0.662511	+	0.749052i	$0.730509\pi$
$114$	36.5154	+	24.7674i	0.320311	+	0.217258i
$115$	−7.72360	+	10.7175i	−0.0671618	+	0.0931953i
$116$	−1.73965	+	0.692435i	−0.0149970	+	0.00596927i
$117$	78.5781	+	78.5781i	0.671607	+	0.671607i
$118$	−19.0742	−	99.4992i	−0.161645	−	0.843213i
$119$			63.7116i			0.535391i
$120$	−3.10804	+	55.2021i	−0.0259004	+	0.460017i
$121$	104.873			0.866715
$122$	−144.677	+	27.7349i	−1.18588	+	0.227335i
$123$	−36.2392	+	36.2392i	−0.294628	+	0.294628i
$124$	64.3746	−	25.6231i	0.519150	−	0.206638i
$125$	−58.0359	−	110.711i	−0.464287	−	0.885685i
$126$	−94.5429	+	139.388i	−0.750340	+	1.10625i
$127$	59.0310	−	59.0310i	0.464811	−	0.464811i	−0.435418	−	0.900229i	$-0.643399\pi$
$127$	59.0310	−	59.0310i	0.464811	−	0.464811i	0.900229	+	0.435418i	$0.143399\pi$
$128$	−124.179	−	31.0435i	−0.970145	−	0.242527i
$129$			33.5094i			0.259763i
$130$	−66.0631	+	142.148i	−0.508178	+	1.09345i
$131$			144.850i			1.10572i	0.833274	+	0.552861i	$0.186464\pi$
$131$			144.850i			1.10572i	−0.833274	+	0.552861i	$0.813536\pi$
$132$	−20.3935	−	8.78113i	−0.154497	−	0.0665237i
$133$	−134.061	+	134.061i	−1.00797	+	1.00797i
$134$	−123.328	+	181.827i	−0.920361	+	1.35692i
$135$	65.0119	−	90.2121i	0.481570	−	0.668238i
$136$	41.9001	+	9.24599i	0.308089	+	0.0679852i
$137$	72.4869	−	72.4869i	0.529101	−	0.529101i	−0.391203	−	0.920304i	$-0.627941\pi$
$137$	72.4869	−	72.4869i	0.529101	−	0.529101i	0.920304	+	0.391203i	$0.127941\pi$
$138$	−1.37516	−	7.17341i	−0.00996489	−	0.0519813i
$139$	−55.4318			−0.398790			−0.199395	−	0.979919i	$-0.563898\pi$
$139$	−55.4318			−0.398790			−0.199395	+	0.979919i	$0.563898\pi$
$140$	−230.442	−	57.7742i	−1.64601	−	0.412673i
$141$		−	12.3358i		−	0.0874880i
$142$	−29.5128	−	153.952i	−0.207837	−	1.08417i
$143$	−44.5116	−	44.5116i	−0.311270	−	0.311270i
$144$	77.9485	+	82.4048i	0.541309	+	0.572255i
$145$	0.375062	+	2.31025i	0.00258664	+	0.0159327i
$146$	73.0378	−	107.682i	0.500259	−	0.737549i
$147$	90.0208	+	90.0208i	0.612386	+	0.612386i
$148$	115.114	+	49.5664i	0.777800	+	0.334908i
$149$	65.9772			0.442800			0.221400	−	0.975183i	$-0.428937\pi$
$149$	65.9772			0.442800			0.221400	+	0.975183i	$0.428937\pi$
$150$	66.5317	+	18.7078i	0.443545	+	0.124719i
$151$	188.113			1.24578			0.622891	−	0.782308i	$-0.285958\pi$
$151$	188.113			1.24578			0.622891	+	0.782308i	$0.285958\pi$
$152$	68.7102	+	107.621i	0.452041	+	0.708031i
$153$	−26.8872	−	26.8872i	−0.175733	−	0.175733i
$154$	53.5551	−	78.9581i	0.347761	−	0.512715i
$155$	−13.8789	−	85.4890i	−0.0895414	−	0.551542i
$156$	−32.0502	−	80.5219i	−0.205450	−	0.516166i
$157$	19.7604	+	19.7604i	0.125862	+	0.125862i	0.767232	−	0.641370i	$-0.221633\pi$
$157$	19.7604	+	19.7604i	0.125862	+	0.125862i	−0.641370	+	0.767232i	$0.721633\pi$
$158$	62.2119	−	11.9261i	0.393746	−	0.0754818i
$159$			77.9831i			0.490460i
$160$	−71.4377	+	143.167i	−0.446486	+	0.894791i
$161$	31.3847			0.194936
$162$	−12.4504	−	64.9466i	−0.0768542	−	0.400905i
$163$	27.8219	−	27.8219i	0.170686	−	0.170686i	−0.616595	−	0.787281i	$-0.711488\pi$
$163$	27.8219	−	27.8219i	0.170686	−	0.170686i	0.787281	+	0.616595i	$0.211488\pi$
$164$	−137.796	+	54.8470i	−0.840219	+	0.334433i
$165$	−16.2269	+	22.5168i	−0.0983448	+	0.136466i
$166$	−198.960	−	134.949i	−1.19855	−	0.812944i
$167$	−61.7394	+	61.7394i	−0.369697	+	0.369697i	−0.867367	−	0.497670i	$-0.834189\pi$
$167$	−61.7394	+	61.7394i	−0.369697	+	0.369697i	0.497670	+	0.867367i	$0.334189\pi$
$168$	110.713	−	70.6846i	0.659007	−	0.420742i
$169$		−	76.7035i		−	0.453867i
$170$	22.6049	−	48.6390i	0.132970	−	0.286112i
$171$		−	113.151i		−	0.661702i
$172$	−38.3503	+	89.0659i	−0.222967	+	0.517825i
$173$	6.43250	−	6.43250i	0.0371821	−	0.0371821i	−0.688271	−	0.725453i	$-0.741630\pi$
$173$	6.43250	−	6.43250i	0.0371821	−	0.0371821i	0.725453	+	0.688271i	$0.241630\pi$
$174$	−1.07094	−	0.726390i	−0.00615483	−	0.00417465i
$175$	−132.772	+	265.634i	−0.758696	+	1.51791i
$176$	−44.1550	−	46.6793i	−0.250881	−	0.265223i
$177$	49.5101	−	49.5101i	0.279718	−	0.279718i
$178$	−182.301	+	34.9474i	−1.02416	+	0.196334i
$179$	261.438			1.46055			0.730273	−	0.683155i	$-0.239393\pi$
$179$	261.438			1.46055			0.730273	+	0.683155i	$0.239393\pi$
$180$	121.631	−	72.8682i	0.675729	−	0.404823i
$181$		−	264.352i		−	1.46051i	−0.683174	−	0.730255i	$-0.739401\pi$
$181$		−	264.352i		−	1.46051i	0.683174	−	0.730255i	$-0.260599\pi$
$182$	365.736	−	70.1121i	2.00954	−	0.385231i
$183$	−71.9905	−	71.9905i	−0.393391	−	0.393391i
$184$	4.55464	−	20.6403i	0.0247535	−	0.112175i
$185$	91.5951	−	127.100i	0.495109	−	0.687025i
$186$	39.6294	+	26.8796i	0.213061	+	0.144514i
$187$	15.2306	+	15.2306i	0.0814471	+	0.0814471i
$188$	14.1179	−	32.7878i	0.0750951	−	0.174403i
$189$	−264.175			−1.39775
$190$	149.910	−	54.7804i	0.789000	−	0.288318i
$191$	−298.972			−1.56530			−0.782650	−	0.622463i	$-0.786132\pi$
$191$	−298.972			−1.56530			−0.782650	+	0.622463i	$0.786132\pi$
$192$	−30.4190	−	83.0688i	−0.158432	−	0.432650i
$193$	−33.8808	−	33.8808i	−0.175548	−	0.175548i	0.613864	−	0.789412i	$-0.289614\pi$
$193$	−33.8808	−	33.8808i	−0.175548	−	0.175548i	−0.789412	+	0.613864i	$0.789614\pi$
$194$	−199.694	−	135.447i	−1.02935	−	0.698178i
$195$	−106.932	+	17.3602i	−0.548371	+	0.0890266i
$196$	136.244	+	342.295i	0.695122	+	1.74640i
$197$	−62.3903	−	62.3903i	−0.316702	−	0.316702i	0.530797	−	0.847499i	$-0.321893\pi$
$197$	−62.3903	−	62.3903i	−0.316702	−	0.316702i	−0.847499	+	0.530797i	$0.821893\pi$
$198$	10.7204	+	55.9225i	0.0541436	+	0.282437i
$199$			53.5973i			0.269333i	0.990891	+	0.134666i	$0.0429963\pi$
$199$			53.5973i			0.269333i	−0.990891	+	0.134666i	$0.957004\pi$
$200$	155.427	+	125.867i	0.777133	+	0.629336i
$201$	−151.843			−0.755440
$202$	−40.1191	+	7.69090i	−0.198610	+	0.0380738i
$203$	3.93179	−	3.93179i	0.0193684	−	0.0193684i
$204$	10.9667	+	27.5523i	0.0537581	+	0.135060i
$205$	29.7083	+	182.992i	0.144918	+	0.892644i
$206$	61.8789	−	91.2302i	0.300383	−	0.442865i
$207$	−13.2448	+	13.2448i	−0.0639846	+	0.0639846i
$208$	6.96704	−	250.702i	0.0334954	−	1.20530i
$209$			64.0959i			0.306679i
$210$	−56.3545	−	154.218i	−0.268355	−	0.734370i
$211$			242.335i			1.14851i	0.818677	+	0.574254i	$0.194708\pi$
$211$			242.335i			1.14851i	−0.818677	+	0.574254i	$0.805292\pi$
$212$	−89.2488	+	207.274i	−0.420985	+	0.977707i
$213$	76.6054	−	76.6054i	0.359650	−	0.359650i
$214$	111.402	−	164.244i	0.520571	−	0.767495i
$215$	98.3391	+	70.8687i	0.457391	+	0.329622i
$216$	−38.3378	+	173.736i	−0.177490	+	0.804331i
$217$	−145.493	+	145.493i	−0.670476	+	0.670476i
$218$	60.3342	+	314.730i	0.276762	+	1.44371i
$219$	89.9251			0.410617
$220$	−68.8997	+	41.2772i	−0.313181	+	0.187624i
$221$			84.0728i			0.380420i
$222$	16.3081	+	85.0704i	0.0734601	+	0.383200i
$223$	181.009	+	181.009i	0.811701	+	0.811701i	0.984889	−	0.173188i	$-0.0554068\pi$
$223$	181.009	+	181.009i	0.811701	+	0.811701i	−0.173188	+	0.984889i	$0.555407\pi$
$224$	375.164	−	61.1679i	1.67484	−	0.273071i
$225$	−56.0696	−	168.133i	−0.249198	−	0.747257i
$226$	−15.5261	+	22.8907i	−0.0686995	+	0.101286i
$227$	−162.883	−	162.883i	−0.717545	−	0.717545i	0.250557	−	0.968102i	$-0.419386\pi$
$227$	−162.883	−	162.883i	−0.717545	−	0.717545i	−0.968102	+	0.250557i	$0.919386\pi$
$228$	−34.8992	+	81.0509i	−0.153067	+	0.355486i
$229$	−285.470			−1.24660			−0.623298	−	0.781984i	$-0.714208\pi$
$229$	−285.470			−1.24660			−0.623298	+	0.781984i	$0.714208\pi$
$230$	−23.9599	−	11.1353i	−0.104173	−	0.0484145i
$231$	65.9377			0.285445
$232$	−2.01517	−	3.15635i	−0.00868606	−	0.0136050i
$233$	178.054	+	178.054i	0.764180	+	0.764180i	0.977075	−	0.212895i	$-0.0682893\pi$
$233$	178.054	+	178.054i	0.764180	+	0.764180i	−0.212895	+	0.977075i	$0.568289\pi$
$234$	−124.757	+	183.934i	−0.533151	+	0.786043i
$235$	−36.2015	−	26.0888i	−0.154049	−	0.111016i
$236$	188.257	−	74.9322i	0.797700	−	0.317509i
$237$	30.9562	+	30.9562i	0.130617	+	0.130617i
$238$	−125.144	+	23.9904i	−0.525817	+	0.100800i
$239$		−	452.291i		−	1.89243i	−0.323540	−	0.946214i	$-0.604873\pi$
$239$		−	452.291i		−	1.89243i	0.323540	−	0.946214i	$-0.395127\pi$
$240$	−109.600	+	14.6812i	−0.456667	+	0.0611719i
$241$	−83.8188			−0.347796			−0.173898	−	0.984764i	$-0.555636\pi$
$241$	−83.8188			−0.347796			−0.173898	+	0.984764i	$0.555636\pi$
$242$	39.4894	+	205.994i	0.163179	+	0.851216i
$243$	173.848	−	173.848i	0.715423	−	0.715423i
$244$	−108.956	−	273.737i	−0.446539	−	1.12187i
$245$	454.565	−	73.7974i	1.85537	−	0.301214i
$246$	−84.8281	−	57.5365i	−0.344830	−	0.233888i
$247$	−176.904	+	176.904i	−0.716212	+	0.716212i
$248$	74.5698	+	116.799i	0.300685	+	0.470962i
$249$		−	166.151i		−	0.667272i
$250$	195.608	−	155.684i	0.782433	−	0.622735i
$251$			343.010i			1.36657i	0.730150	+	0.683287i	$0.239450\pi$
$251$			343.010i			1.36657i	−0.730150	+	0.683287i	$0.760550\pi$
$252$	−309.390	−	133.218i	−1.22774	−	0.528644i
$253$	7.50270	−	7.50270i	0.0296550	−	0.0296550i
$254$	138.179	+	93.7227i	0.544010	+	0.368987i
$255$	36.5892	−	5.94016i	0.143487	−	0.0232948i
$256$	14.2176	−	255.605i	0.0555374	−	0.998457i
$257$	171.974	−	171.974i	0.669159	−	0.669159i	−0.288363	−	0.957521i	$-0.593111\pi$
$257$	171.974	−	171.974i	0.669159	−	0.669159i	0.957521	+	0.288363i	$0.0931108\pi$
$258$	−65.8204	+	12.6179i	−0.255118	+	0.0489065i
$259$	−372.195			−1.43705
$260$	−304.087	−	76.2380i	−1.16957	−	0.293223i
$261$			3.31855i			0.0127147i
$262$	−284.518	+	54.5426i	−1.08595	+	0.208178i
$263$	−109.775	−	109.775i	−0.417396	−	0.417396i	0.466909	−	0.884305i	$-0.345367\pi$
$263$	−109.775	−	109.775i	−0.417396	−	0.417396i	−0.884305	+	0.466909i	$0.845367\pi$
$264$	9.56906	−	43.3642i	0.0362464	−	0.164258i
$265$	228.854	+	164.925i	0.863602	+	0.622360i
$266$	−313.806	−	212.846i	−1.17972	−	0.800174i
$267$	−90.7117	−	90.7117i	−0.339744	−	0.339744i
$268$	−403.590	−	173.779i	−1.50593	−	0.648430i
$269$	126.610			0.470668			0.235334	−	0.971915i	$-0.424382\pi$
$269$	126.610			0.470668			0.235334	+	0.971915i	$0.424382\pi$
$270$	201.678	+	93.7295i	0.746954	+	0.347146i
$271$	341.904			1.26164			0.630819	−	0.775930i	$-0.282719\pi$
$271$	341.904			1.26164			0.630819	+	0.775930i	$0.282719\pi$
$272$	−2.38392	+	85.7832i	−0.00876443	+	0.315379i
$273$	181.988	+	181.988i	0.666622	+	0.666622i
$274$	169.676	+	115.086i	0.619255	+	0.420023i
$275$	31.7614	+	95.2411i	0.115496	+	0.346331i
$276$	13.5724	−	5.40225i	0.0491755	−	0.0195734i
$277$	125.838	+	125.838i	0.454287	+	0.454287i	0.896775	−	0.442487i	$-0.145904\pi$
$277$	125.838	+	125.838i	0.454287	+	0.454287i	−0.442487	+	0.896775i	$0.645904\pi$
$278$	−20.8727	−	108.881i	−0.0750816	−	0.391659i
$279$		−	122.800i		−	0.440145i
$280$	26.7099	−	474.396i	0.0953926	−	1.69427i
$281$	−375.014			−1.33457			−0.667285	−	0.744802i	$-0.732544\pi$
$281$	−375.014			−1.33457			−0.667285	+	0.744802i	$0.732544\pi$
$282$	24.2304	−	4.64501i	0.0859234	−	0.0164717i
$283$	289.819	−	289.819i	1.02409	−	1.02409i	0.0243913	−	0.999702i	$-0.492235\pi$
$283$	289.819	−	289.819i	1.02409	−	1.02409i	0.999702	−	0.0243913i	$-0.00776478\pi$
$284$	291.284	−	115.940i	1.02565	−	0.408239i
$285$	89.4896	+	64.4912i	0.313998	+	0.226285i
$286$	70.6705	−	104.192i	0.247100	−	0.364307i
$287$	311.433	−	311.433i	1.08513	−	1.08513i
$288$	−132.511	+	184.138i	−0.460107	+	0.639369i
$289$			260.233i			0.900459i
$290$	−4.39663	+	1.60662i	−0.0151608	+	0.00554009i
$291$		−	166.764i		−	0.573071i
$292$	239.015	+	102.916i	0.818544	+	0.352452i
$293$	−254.820	+	254.820i	−0.869693	+	0.869693i	−0.992438	−	0.122745i	$-0.960830\pi$
$293$	−254.820	+	254.820i	−0.869693	+	0.869693i	0.122745	+	0.992438i	$0.460830\pi$
$294$	−142.925	+	210.719i	−0.486139	+	0.716731i
$295$	−40.5875	−	250.004i	−0.137585	−	0.847472i
$296$	−54.0140	+	244.776i	−0.182480	+	0.826944i
$297$	−63.1525	+	63.1525i	−0.212635	+	0.212635i
$298$	24.8435	+	129.595i	0.0833674	+	0.434881i
$299$	41.4148			0.138511
$300$	−11.6942	+	137.728i	−0.0389805	+	0.459094i
$301$		−	287.974i		−	0.956724i
$302$	70.8334	+	369.498i	0.234548	+	1.22350i
$303$	−19.9630	−	19.9630i	−0.0658845	−	0.0658845i
$304$	−185.519	+	175.487i	−0.610262	+	0.577260i
$305$	−363.520	+	59.0165i	−1.19187	+	0.193497i
$306$	42.6884	−	62.9370i	0.139505	−	0.205676i
$307$	−157.959	−	157.959i	−0.514526	−	0.514526i	0.401384	−	0.915910i	$-0.368529\pi$
$307$	−157.959	−	157.959i	−0.514526	−	0.514526i	−0.915910	+	0.401384i	$0.868529\pi$
$308$	175.258	+	75.4633i	0.569020	+	0.245011i
$309$	76.1861			0.246557
$310$	162.694	−	59.4520i	0.524820	−	0.191781i
$311$	288.646			0.928122			0.464061	−	0.885803i	$-0.346392\pi$
$311$	288.646			0.928122			0.464061	+	0.885803i	$0.346392\pi$
$312$	146.095	−	93.2743i	0.468254	−	0.298956i
$313$	138.120	+	138.120i	0.441279	+	0.441279i	0.892442	−	0.451163i	$-0.148991\pi$
$313$	138.120	+	138.120i	0.441279	+	0.441279i	−0.451163	+	0.892442i	$0.648991\pi$
$314$	−31.3733	+	46.2548i	−0.0999151	+	0.147308i
$315$	−246.178	+	341.602i	−0.781517	+	1.08445i
$316$	46.8514	+	117.708i	0.148264	+	0.372494i
$317$	−79.5178	−	79.5178i	−0.250845	−	0.250845i	0.570472	−	0.821317i	$-0.306760\pi$
$317$	−79.5178	−	79.5178i	−0.250845	−	0.250845i	−0.821317	+	0.570472i	$0.806760\pi$
$318$	−153.177	+	29.3643i	−0.481688	+	0.0923405i
$319$		−	1.87984i		−	0.00589290i
$320$	−308.112	−	86.4115i	−0.962850	−	0.270036i
$321$	137.160			0.427289
$322$	11.8178	+	61.6470i	0.0367013	+	0.191450i
$323$	60.5316	−	60.5316i	0.187404	−	0.187404i
$324$	122.882	−	48.9109i	0.379266	−	0.150960i
$325$	−175.203	+	350.526i	−0.539088	+	1.07854i
$326$	65.1249	+	44.1724i	0.199770	+	0.135498i
$327$	−156.607	+	156.607i	−0.478922	+	0.478922i
$328$	−159.619	−	250.011i	−0.486643	−	0.762229i
$329$			106.012i			0.322224i
$330$	−50.3385	−	23.3948i	−0.152541	−	0.0708932i
$331$			515.252i			1.55665i	0.627859	+	0.778327i	$0.283931\pi$
$331$			515.252i			1.55665i	−0.627859	+	0.778327i	$0.716069\pi$
$332$	190.153	−	441.617i	0.572751	−	1.33017i
$333$	157.072	−	157.072i	0.471687	−	0.471687i
$334$	−144.518	−	98.0228i	−0.432690	−	0.293481i
$335$	−321.132	+	445.610i	−0.958602	+	1.33018i
$336$	180.530	+	190.850i	0.537291	+	0.568007i
$337$	174.049	−	174.049i	0.516466	−	0.516466i	−0.400034	−	0.916500i	$-0.631002\pi$
$337$	174.049	−	174.049i	0.516466	−	0.516466i	0.916500	+	0.400034i	$0.131002\pi$
$338$	150.664	−	28.8825i	0.445750	−	0.0854510i
$339$	−19.1159			−0.0563892
$340$	104.050	+	26.0865i	0.306030	+	0.0767249i
$341$			69.5620i			0.203994i
$342$	222.255	−	42.6066i	0.649868	−	0.124581i
$343$	−362.046	−	362.046i	−1.05553	−	1.05553i
$344$	−189.387	−	41.7915i	−0.550543	−	0.121487i
$345$	−2.92616	−	18.0241i	−0.00848164	−	0.0522438i
$346$	15.0571	+	10.2128i	0.0435175	+	0.0295167i
$347$	45.0127	+	45.0127i	0.129720	+	0.129720i	0.768986	−	0.639266i	$-0.220762\pi$
$347$	45.0127	+	45.0127i	0.129720	+	0.129720i	−0.639266	+	0.768986i	$0.720762\pi$
$348$	1.02354	−	2.37710i	0.00294121	−	0.00683074i
$349$	−57.5715			−0.164961			−0.0824806	−	0.996593i	$-0.526284\pi$
$349$	−57.5715			−0.164961			−0.0824806	+	0.996593i	$0.526284\pi$
$350$	−571.761	−	160.771i	−1.63360	−	0.459346i
$351$	−348.601			−0.993166
$352$	75.0626	−	104.308i	0.213246	−	0.296329i
$353$	−452.340	−	452.340i	−1.28142	−	1.28142i	−0.939863	−	0.341553i	$-0.889047\pi$
$353$	−452.340	−	452.340i	−1.28142	−	1.28142i	−0.341553	−	0.939863i	$-0.610953\pi$
$354$	115.892	+	78.6066i	0.327380	+	0.222052i
$355$	−62.7997	−	386.823i	−0.176900	−	1.08964i
$356$	−137.290	−	344.922i	−0.385645	−	0.968883i
$357$	−62.2710	−	62.2710i	−0.174429	−	0.174429i
$358$	98.4435	+	513.525i	0.274982	+	1.43443i
$359$			492.146i			1.37088i	0.728129	+	0.685440i	$0.240390\pi$
$359$			492.146i			1.37088i	−0.728129	+	0.685440i	$0.759610\pi$
$360$	188.930	+	211.474i	0.524806	+	0.587428i
$361$	−106.261			−0.294352
$362$	519.250	−	99.5411i	1.43439	−	0.274975i
$363$	−102.501	+	102.501i	−0.282373	+	0.282373i
$364$	275.433	+	691.990i	0.756684	+	1.90107i
$365$	190.181	−	263.900i	0.521045	−	0.723014i
$366$	114.298	−	168.514i	0.312291	−	0.460421i
$367$	2.84592	−	2.84592i	0.00775455	−	0.00775455i	−0.703219	−	0.710973i	$-0.748255\pi$
$367$	2.84592	−	2.84592i	0.00775455	−	0.00775455i	0.710973	+	0.703219i	$0.248255\pi$
$368$	42.2574	+	1.17434i	0.114830	+	0.00319113i
$369$			262.858i			0.712353i
$370$	284.143	+	132.055i	0.767954	+	0.356906i
$371$		−	670.172i		−	1.80639i
$372$	−37.8754	+	87.9629i	−0.101816	+	0.236459i
$373$	309.505	−	309.505i	0.829773	−	0.829773i	−0.157712	−	0.987485i	$-0.550412\pi$
$373$	309.505	−	309.505i	0.829773	−	0.829773i	0.987485	+	0.157712i	$0.0504117\pi$
$374$	−24.1814	+	35.6515i	−0.0646563	+	0.0953249i
$375$	164.931	+	51.4837i	0.439816	+	0.137290i
$376$	69.7189	+	15.3847i	0.185423	+	0.0409167i
$377$	5.18833	−	5.18833i	0.0137622	−	0.0137622i
$378$	−99.4742	−	518.901i	−0.263159	−	1.37275i
$379$	298.281			0.787022			0.393511	−	0.919320i	$-0.371260\pi$
$379$	298.281			0.787022			0.393511	+	0.919320i	$0.371260\pi$
$380$	164.050	+	273.831i	0.431709	+	0.720608i
$381$			115.393i			0.302868i
$382$	−112.577	−	587.251i	−0.294704	−	1.53731i
$383$	507.746	+	507.746i	1.32571	+	1.32571i	0.909075	+	0.416633i	$0.136790\pi$
$383$	507.746	+	507.746i	1.32571	+	1.32571i	0.416633	+	0.909075i	$0.363210\pi$
$384$	151.712	−	91.0293i	0.395084	−	0.237055i
$385$	139.451	−	193.505i	0.362210	−	0.502611i
$386$	53.7921	−	79.3075i	0.139358	−	0.205460i
$387$	121.529	+	121.529i	0.314029	+	0.314029i
$388$	190.855	−	443.247i	0.491894	−	1.14239i
$389$	−506.443			−1.30191			−0.650956	−	0.759116i	$-0.725632\pi$
$389$	−506.443			−1.30191			−0.650956	+	0.759116i	$0.725632\pi$
$390$	−74.3645	−	203.503i	−0.190678	−	0.521803i
$391$	−14.1710			−0.0362429
$392$	−621.045	+	396.505i	−1.58430	+	1.01149i
$393$	−141.574	−	141.574i	−0.360240	−	0.360240i
$394$	99.0563	−	146.042i	0.251412	−	0.370665i
$395$	156.315	−	25.3774i	0.395735	−	0.0642465i
$396$	−105.808	+	42.1149i	−0.267192	+	0.106351i
$397$	−77.8603	−	77.8603i	−0.196122	−	0.196122i	0.602213	−	0.798335i	$-0.294286\pi$
$397$	−77.8603	−	77.8603i	−0.196122	−	0.196122i	−0.798335	+	0.602213i	$0.794286\pi$
$398$	−105.278	+	20.1819i	−0.264516	+	0.0507082i
$399$		−	262.059i		−	0.656789i
$400$	−188.707	+	352.689i	−0.471768	+	0.881723i
$401$	366.451			0.913844			0.456922	−	0.889507i	$-0.348952\pi$
$401$	366.451			0.913844			0.456922	+	0.889507i	$0.348952\pi$
$402$	−57.1761	−	298.256i	−0.142229	−	0.741930i
$403$	−191.991	+	191.991i	−0.476404	+	0.476404i
$404$	−30.2135	−	75.9073i	−0.0747858	−	0.187889i
$405$	−26.4929	−	163.187i	−0.0654146	−	0.402930i
$406$	9.20346	+	6.24246i	0.0226686	+	0.0153755i
$407$	−88.9755	+	88.9755i	−0.218613	+	0.218613i
$408$	−49.9897	+	31.9158i	−0.122524	+	0.0782250i
$409$		−	390.914i		−	0.955779i	−0.878420	−	0.477889i	$-0.841402\pi$
$409$		−	390.914i		−	0.955779i	0.878420	−	0.477889i	$-0.158598\pi$
$410$	−348.252	+	127.259i	−0.849396	+	0.310388i
$411$			141.696i			0.344759i
$412$	202.498	+	87.1922i	0.491499	+	0.211632i
$413$	−425.481	+	425.481i	−1.03022	+	1.03022i
$414$	−31.0032	−	21.0286i	−0.0748869	−	0.0507937i
$415$	−487.597	−	351.390i	−1.17493	−	0.846722i
$416$	495.061	−	80.7162i	1.19005	−	0.194029i
$417$	54.1785	−	54.1785i	0.129924	−	0.129924i
$418$	−125.899	+	24.1351i	−0.301195	+	0.0577395i
$419$	356.953			0.851917			0.425959	−	0.904743i	$-0.359937\pi$
$419$	356.953			0.851917			0.425959	+	0.904743i	$0.359937\pi$
$420$	281.699	−	168.764i	0.670713	−	0.401818i
$421$		−	174.212i		−	0.413806i	−0.978361	−	0.206903i	$-0.933661\pi$
$421$		−	174.212i		−	0.413806i	0.978361	−	0.206903i	$-0.0663385\pi$
$422$	−476.003	+	91.2505i	−1.12797	+	0.216233i
$423$	−44.7384	−	44.7384i	−0.105765	−	0.105765i
$424$	−440.741	−	97.2571i	−1.03948	−	0.229380i
$425$	59.9497	−	119.940i	0.141058	−	0.282212i
$426$	179.316	+	121.625i	0.420930	+	0.285505i
$427$	618.673	+	618.673i	1.44888	+	1.44888i
$428$	364.562	+	156.974i	0.851779	+	0.366762i
$429$	87.0104			0.202821
$430$	−102.173	+	219.846i	−0.237612	+	0.511270i
$431$	48.7663			0.113147			0.0565734	−	0.998398i	$-0.481983\pi$
$431$	48.7663			0.113147			0.0565734	+	0.998398i	$0.481983\pi$
$432$	−355.693	−	9.88476i	−0.823364	−	0.0228814i
$433$	215.414	+	215.414i	0.497492	+	0.497492i	0.910656	−	0.413165i	$-0.135577\pi$
$433$	215.414	+	215.414i	0.497492	+	0.497492i	−0.413165	+	0.910656i	$0.635577\pi$
$434$	−340.568	−	230.998i	−0.784718	−	0.532253i
$435$	−2.62459	−	1.89143i	−0.00603354	−	0.00434811i
$436$	−595.484	+	237.021i	−1.36579	+	0.543626i
$437$	−29.8183	−	29.8183i	−0.0682341	−	0.0682341i
$438$	33.8610	+	176.634i	0.0773082	+	0.403274i
$439$			466.896i			1.06354i	0.846887	+	0.531772i	$0.178474\pi$
$439$			466.896i			1.06354i	−0.846887	+	0.531772i	$0.821526\pi$
$440$	−107.022	−	119.792i	−0.243232	−	0.272255i
$441$	652.959			1.48063
$442$	−165.139	+	31.6573i	−0.373617	+	0.0716229i
$443$	−423.624	+	423.624i	−0.956263	+	0.956263i	−0.999083	−	0.0428200i	$-0.986366\pi$
$443$	−423.624	+	423.624i	−0.956263	+	0.956263i	0.0428200	+	0.999083i	$0.486366\pi$
$444$	−160.957	+	64.0660i	−0.362516	+	0.144293i
$445$	−458.054	+	74.3638i	−1.02933	+	0.167110i
$446$	−287.386	+	423.703i	−0.644363	+	0.950006i
$447$	−64.4854	+	64.4854i	−0.144263	+	0.144263i
$448$	261.415	+	713.878i	0.583515	+	1.59348i
$449$		−	255.859i		−	0.569841i	−0.958551	−	0.284921i	$-0.908033\pi$
$449$		−	255.859i		−	0.569841i	0.958551	−	0.284921i	$-0.0919673\pi$
$450$	309.139	−	173.444i	0.686976	−	0.385430i
$451$		−	148.900i		−	0.330155i
$452$	−50.8089	−	21.8775i	−0.112409	−	0.0484015i
$453$	−183.860	+	183.860i	−0.405872	+	0.405872i
$454$	258.607	−	381.273i	0.569619	−	0.839808i
$455$	918.957	−	149.190i	2.01969	−	0.327890i
$456$	−172.344	−	38.0307i	−0.377947	−	0.0834006i
$457$	53.0785	−	53.0785i	0.116145	−	0.116145i	−0.646645	−	0.762791i	$-0.723829\pi$
$457$	53.0785	−	53.0785i	0.116145	−	0.116145i	0.762791	+	0.646645i	$0.223829\pi$
$458$	−107.493	−	560.731i	−0.234701	−	1.22430i
$459$	119.281			0.259872
$460$	12.8504	−	51.2558i	0.0279356	−	0.111426i
$461$			395.425i			0.857755i	0.903363	+	0.428877i	$0.141091\pi$
$461$			395.425i			0.857755i	−0.903363	+	0.428877i	$0.858909\pi$
$462$	24.8286	+	129.517i	0.0537417	+	0.280340i
$463$	87.9974	+	87.9974i	0.190059	+	0.190059i	0.795722	−	0.605662i	$-0.207092\pi$
$463$	87.9974	+	87.9974i	0.190059	+	0.190059i	−0.605662	+	0.795722i	$0.707092\pi$
$464$	5.44100	−	5.14677i	0.0117263	−	0.0110922i
$465$	97.1212	+	69.9910i	0.208863	+	0.150518i
$466$	−282.694	+	416.785i	−0.606639	+	0.894389i
$467$	−538.709	−	538.709i	−1.15355	−	1.15355i	−0.985835	−	0.167717i	$-0.946361\pi$
$467$	−538.709	−	538.709i	−1.15355	−	1.15355i	−0.167717	−	0.985835i	$-0.553639\pi$
$468$	−408.266	−	175.793i	−0.872364	−	0.375626i
$469$	1304.91			2.78233
$470$	37.6130	−	80.9318i	0.0800276	−	0.172195i
$471$	−38.6272			−0.0820111
$472$	218.072	+	341.566i	0.462017	+	0.723656i
$473$	−68.8418	−	68.8418i	−0.145543	−	0.145543i
$474$	−49.1488	+	72.4618i	−0.103689	+	0.152873i
$475$	378.520	−	126.231i	0.796885	−	0.265749i
$476$	−94.2454	−	236.779i	−0.197995	−	0.497435i
$477$	282.822	+	282.822i	0.592918	+	0.592918i
$478$	888.404	−	170.309i	1.85859	−	0.356294i
$479$		−	52.4501i		−	0.109499i	−0.998500	−	0.0547496i	$-0.982564\pi$
$479$		−	52.4501i		−	0.109499i	0.998500	−	0.0547496i	$-0.0174361\pi$
$480$	−70.1070	−	209.752i	−0.146056	−	0.436983i
$481$	−491.143			−1.02109
$482$	−31.5617	−	164.640i	−0.0654807	−	0.341576i
$483$	−30.6751	+	30.6751i	−0.0635096	+	0.0635096i
$484$	−389.751	+	155.133i	−0.805271	+	0.320522i
$485$	−489.396	−	352.686i	−1.00906	−	0.727188i
$486$	406.939	+	276.016i	0.837324	+	0.567934i
$487$	239.841	−	239.841i	0.492486	−	0.492486i	−0.416602	−	0.909089i	$-0.636779\pi$
$487$	239.841	−	239.841i	0.492486	−	0.492486i	0.909089	+	0.416602i	$0.136779\pi$
$488$	496.656	−	317.089i	1.01774	−	0.649772i
$489$			54.3856i			0.111218i
$490$	316.120	+	865.083i	0.645143	+	1.76548i
$491$		−	170.797i		−	0.347855i	−0.984758	−	0.173927i	$-0.944354\pi$
$491$		−	170.797i		−	0.347855i	0.984758	−	0.173927i	$-0.0556458\pi$
$492$	81.0734	−	188.287i	0.164783	−	0.382698i
$493$	−1.77530	+	1.77530i	−0.00360102	+	0.00360102i
$494$	−414.094	−	280.869i	−0.838247	−	0.568560i
$495$	22.8118	+	140.512i	0.0460844	+	0.283863i
$496$	−201.341	+	190.453i	−0.405929	+	0.383977i
$497$	−658.332	+	658.332i	−1.32461	+	1.32461i
$498$	326.359	−	62.5635i	0.655338	−	0.125629i
$499$	−878.181			−1.75988			−0.879941	−	0.475083i	$-0.842418\pi$
$499$	−878.181			−1.75988			−0.879941	+	0.475083i	$0.842418\pi$
$500$	379.455	+	325.598i	0.758910	+	0.651196i
$501$		−	120.687i		−	0.240892i
$502$	−673.751	+	129.159i	−1.34213	+	0.257289i
$503$	−476.137	−	476.137i	−0.946595	−	0.946595i	0.0520493	−	0.998645i	$-0.483425\pi$
$503$	−476.137	−	476.137i	−0.946595	−	0.946595i	−0.998645	+	0.0520493i	$0.983425\pi$
$504$	145.172	−	657.877i	0.288040	−	1.30531i
$505$	−100.804	+	16.3653i	−0.199613	+	0.0324066i
$506$	17.5622	+	11.9119i	0.0347079	+	0.0235414i
$507$	74.9692	+	74.9692i	0.147868	+	0.147868i
$508$	−132.063	+	306.706i	−0.259966	+	0.603752i
$509$	176.377			0.346516			0.173258	−	0.984876i	$-0.444571\pi$
$509$	176.377			0.346516			0.173258	+	0.984876i	$0.444571\pi$
$510$	25.4454	+	69.6330i	0.0498930	+	0.136535i
$511$	−772.799			−1.51233
$512$	507.421	−	68.3206i	0.991057	−	0.133439i
$513$	250.990	+	250.990i	0.489259	+	0.489259i
$514$	402.553	+	273.040i	0.783177	+	0.531207i
$515$	161.125	−	223.581i	0.312864	−	0.434138i
$516$	−49.5689	−	124.535i	−0.0960637	−	0.241348i
$517$	25.3427	+	25.3427i	0.0490187	+	0.0490187i
$518$	−140.149	−	731.079i	−0.270558	−	1.41135i
$519$			12.5741i			0.0242276i
$520$	35.2460	−	626.006i	0.0677808	−	1.20386i
$521$	−209.641			−0.402381			−0.201191	−	0.979552i	$-0.564481\pi$
$521$	−209.641			−0.402381			−0.201191	+	0.979552i	$0.564481\pi$
$522$	−6.51840	+	1.24959i	−0.0124874	+	0.00239385i
$523$	−115.800	+	115.800i	−0.221415	+	0.221415i	−0.809094	−	0.587679i	$-0.800042\pi$
$523$	−115.800	+	115.800i	−0.221415	+	0.221415i	0.587679	+	0.809094i	$0.300042\pi$
$524$	−214.269	−	538.322i	−0.408910	−	1.02733i
$525$	−129.858	−	389.397i	−0.247348	−	0.741709i
$526$	174.288	−	256.959i	0.331347	−	0.488516i
$527$	65.6938	−	65.6938i	0.124656	−	0.124656i
$528$	88.7806	+	2.46722i	0.168145	+	0.00467277i
$529$		−	522.019i		−	0.986804i
$530$	−237.777	+	511.626i	−0.448637	+	0.965331i
$531$		−	359.118i		−	0.676305i
$532$	299.917	−	696.536i	0.563754	−	1.30928i
$533$	410.962	−	410.962i	0.771036	−	0.771036i
$534$	144.022	−	212.336i	0.269704	−	0.397633i
$535$	290.077	−	402.518i	0.542200	−	0.752370i
$536$	189.372	−	858.181i	0.353307	−	1.60108i
$537$	−255.527	+	255.527i	−0.475841	+	0.475841i
$538$	47.6744	+	248.691i	0.0886142	+	0.462251i
$539$	−369.877			−0.686229
$540$	−108.166	+	431.436i	−0.200306	+	0.798955i
$541$		−	299.624i		−	0.553833i	−0.960894	−	0.276917i	$-0.910687\pi$
$541$		−	299.624i		−	0.553833i	0.960894	−	0.276917i	$-0.0893126\pi$
$542$	128.743	+	671.580i	0.237533	+	1.23908i
$543$	258.375	+	258.375i	0.475829	+	0.475829i
$544$	−169.396	+	27.6188i	−0.311389	+	0.0507698i
$545$	128.384	+	790.798i	0.235567	+	1.45100i
$546$	−288.939	+	425.993i	−0.529193	+	0.780207i
$547$	282.004	+	282.004i	0.515546	+	0.515546i	0.916220	−	0.400674i	$-0.131224\pi$
$547$	282.004	+	282.004i	0.515546	+	0.515546i	−0.400674	+	0.916220i	$0.631224\pi$
$548$	−162.166	+	376.618i	−0.295923	+	0.687260i
$549$	−522.178			−0.951143
$550$	−175.116	+	98.2495i	−0.318393	+	0.178635i
$551$	−7.47111			−0.0135592
$552$	15.7219	+	24.6253i	0.0284818	+	0.0446110i
$553$	−266.032	−	266.032i	−0.481071	−	0.481071i
$554$	−199.791	+	294.558i	−0.360633	+	0.531693i
$555$	34.7017	+	213.750i	0.0625257	+	0.385135i
$556$	206.008	−	81.9976i	0.370518	−	0.147478i
$557$	275.294	+	275.294i	0.494245	+	0.494245i	0.909641	−	0.415396i	$-0.136357\pi$
$557$	275.294	+	275.294i	0.494245	+	0.494245i	−0.415396	+	0.909641i	$0.636357\pi$
$558$	241.209	−	46.2401i	0.432274	−	0.0828676i
$559$		−	380.006i		−	0.679796i
$560$	941.882	−	126.168i	1.68193	−	0.225300i
$561$	−29.7725			−0.0530704
$562$	−141.210	−	736.616i	−0.251264	−	1.31070i
$563$	122.106	−	122.106i	0.216884	−	0.216884i	−0.590300	−	0.807184i	$-0.700991\pi$
$563$	122.106	−	122.106i	0.216884	−	0.216884i	0.807184	+	0.590300i	$0.200991\pi$
$564$	18.2478	+	45.8451i	0.0323542	+	0.0812856i
$565$	−40.4280	+	56.0989i	−0.0715540	+	0.0992901i
$566$	678.402	+	460.141i	1.19859	+	0.812970i
$567$	−277.726	+	277.726i	−0.489817	+	0.489817i
$568$	337.415	+	528.493i	0.594041	+	0.930445i
$569$			639.803i			1.12443i	0.826990	+	0.562217i	$0.190051\pi$
$569$			639.803i			1.12443i	−0.826990	+	0.562217i	$0.809949\pi$
$570$	−92.9787	+	200.062i	−0.163121	+	0.350987i
$571$		−	692.275i		−	1.21239i	−0.795316	−	0.606195i	$-0.792695\pi$
$571$		−	692.275i		−	1.21239i	0.795316	−	0.606195i	$-0.207305\pi$
$572$	231.268	+	99.5802i	0.404315	+	0.174091i
$573$	292.212	−	292.212i	0.509969	−	0.509969i
$574$	728.996	+	494.458i	1.27003	+	0.861425i
$575$	−59.0833	−	29.5316i	−0.102754	−	0.0513593i
$576$	−411.587	−	190.946i	−0.714561	−	0.331503i
$577$	−302.068	+	302.068i	−0.523515	+	0.523515i	−0.918631	−	0.395116i	$-0.870704\pi$
$577$	−302.068	+	302.068i	−0.523515	+	0.523515i	0.395116	+	0.918631i	$0.370704\pi$
$578$	−511.158	+	97.9898i	−0.884356	+	0.169532i
$579$	66.2295			0.114386
$580$	−4.81132	−	8.03104i	−0.00829539	−	0.0138466i
$581$			1427.87i			2.45760i
$582$	327.563	−	62.7943i	0.562822	−	0.107894i
$583$	−160.208	−	160.208i	−0.274800	−	0.274800i
$584$	−112.151	+	508.234i	−0.192039	+	0.870263i
$585$	−324.852	+	450.773i	−0.555303	+	0.770552i
$586$	−596.478	−	404.574i	−1.01788	−	0.690400i
$587$	53.0146	+	53.0146i	0.0903144	+	0.0903144i	0.750821	−	0.660506i	$-0.229658\pi$
$587$	53.0146	+	53.0146i	0.0903144	+	0.0903144i	−0.660506	+	0.750821i	$0.729658\pi$
$588$	−467.719	−	201.392i	−0.795440	−	0.342504i
$589$	276.463			0.469377
$590$	475.783	−	173.862i	0.806412	−	0.294681i
$591$	121.959			0.206361
$592$	−501.135	−	13.9266i	−0.846512	−	0.0235247i
$593$	−401.453	−	401.453i	−0.676986	−	0.676986i	0.282331	−	0.959317i	$-0.408892\pi$
$593$	−401.453	−	401.453i	−0.676986	−	0.676986i	−0.959317	+	0.282331i	$0.908892\pi$
$594$	−147.826	−	100.266i	−0.248866	−	0.168799i
$595$	−314.441	+	51.0486i	−0.528472	+	0.0857960i
$596$	−245.199	+	97.5968i	−0.411408	+	0.163753i
$597$	−52.3854	−	52.3854i	−0.0877478	−	0.0877478i
$598$	15.5946	+	81.3484i	0.0260779	+	0.136034i
$599$			152.120i			0.253956i	0.991906	+	0.126978i	$0.0405277\pi$
$599$			152.120i			0.253956i	−0.991906	+	0.126978i	$0.959472\pi$
$600$	−274.934	+	28.8911i	−0.458223	+	0.0481518i
$601$	743.521			1.23714			0.618570	−	0.785730i	$-0.287712\pi$
$601$	743.521			1.23714			0.618570	+	0.785730i	$0.287712\pi$
$602$	565.648	−	108.436i	0.939614	−	0.180126i
$603$	−550.692	+	550.692i	−0.913254	+	0.913254i
$604$	−699.109	+	278.267i	−1.15746	+	0.460706i
$605$	84.0287	+	517.586i	0.138890	+	0.855514i
$606$	31.6950	−	46.7290i	0.0523020	−	0.0771106i
$607$	671.938	−	671.938i	1.10698	−	1.10698i	0.113437	−	0.993545i	$-0.463814\pi$
$607$	671.938	−	671.938i	1.10698	−	1.10698i	0.993545	−	0.113437i	$-0.0361859\pi$
$608$	−414.554	−	298.324i	−0.681833	−	0.490665i
$609$			7.68579i			0.0126203i
$610$	−252.805	−	691.816i	−0.414434	−	1.13412i
$611$			139.891i			0.228955i
$612$	139.697	+	60.1513i	0.228263	+	0.0982864i
$613$	−232.793	+	232.793i	−0.379761	+	0.379761i	−0.871016	−	0.491255i	$-0.836538\pi$
$613$	−232.793	+	232.793i	−0.379761	+	0.379761i	0.491255	+	0.871016i	$0.336538\pi$
$614$	250.790	−	369.748i	0.408453	−	0.602196i
$615$	−207.891	−	149.818i	−0.338034	−	0.243606i
$616$	−82.2347	+	372.663i	−0.133498	+	0.604973i
$617$	801.371	−	801.371i	1.29882	−	1.29882i	0.369645	−	0.929173i	$-0.379479\pi$
$617$	801.371	−	801.371i	1.29882	−	1.29882i	0.929173	−	0.369645i	$-0.120521\pi$
$618$	28.6876	+	149.647i	0.0464201	+	0.242148i
$619$	−111.616			−0.180317			−0.0901583	−	0.995927i	$-0.528737\pi$
$619$	−111.616			−0.180317			−0.0901583	+	0.995927i	$0.528737\pi$
$620$	178.040	+	297.183i	0.287161	+	0.479328i
$621$		−	58.7588i		−	0.0946197i
$622$	108.689	+	566.968i	0.174741	+	0.911524i
$623$	779.559	+	779.559i	1.25130	+	1.25130i
$624$	238.224	+	251.843i	0.381770	+	0.403595i
$625$	499.898	−	375.136i	0.799837	−	0.600217i
$626$	−219.292	+	323.309i	−0.350306	+	0.516469i
$627$	−62.6467	−	62.6467i	−0.0999150	−	0.0999150i
$628$	−102.669	−	44.2075i	−0.163485	−	0.0703940i
$629$	168.055			0.267178
$630$	−763.684	−	354.921i	−1.21220	−	0.563367i
$631$	−24.4343			−0.0387231			−0.0193615	−	0.999813i	$-0.506163\pi$
$631$	−24.4343			−0.0387231			−0.0193615	+	0.999813i	$0.506163\pi$
$632$	−213.564	+	136.350i	−0.337918	+	0.215743i
$633$	−236.856	−	236.856i	−0.374180	−	0.374180i
$634$	126.249	−	186.134i	0.199131	−	0.293586i
$635$	338.639	+	244.042i	0.533289	+	0.384318i
$636$	−115.357	−	289.818i	−0.181378	−	0.455689i
$637$	−1020.86	−	1020.86i	−1.60260	−	1.60260i
$638$	3.69244	−	0.707846i	0.00578752	−	0.00110948i
$639$		−	555.651i		−	0.869563i
$640$	53.7138	−	637.742i	0.0839278	−	0.996472i
$641$	416.342			0.649519			0.324759	−	0.945797i	$-0.394717\pi$
$641$	416.342			0.649519			0.324759	+	0.945797i	$0.394717\pi$
$642$	51.6470	+	269.414i	0.0804471	+	0.419647i
$643$	86.0053	−	86.0053i	0.133756	−	0.133756i	−0.637059	−	0.770815i	$-0.719849\pi$
$643$	86.0053	−	86.0053i	0.133756	−	0.133756i	0.770815	+	0.637059i	$0.219849\pi$
$644$	−116.639	+	46.4259i	−0.181117	+	0.0720899i
$645$	−165.382	+	26.8493i	−0.256406	+	0.0416268i
$646$	141.691	+	96.1053i	0.219336	+	0.148770i
$647$	−323.159	+	323.159i	−0.499472	+	0.499472i	−0.911274	−	0.411801i	$-0.864900\pi$
$647$	−323.159	+	323.159i	−0.499472	+	0.499472i	0.411801	+	0.911274i	$0.364900\pi$
$648$	142.343	+	222.952i	0.219666	+	0.344062i
$649$			203.427i			0.313447i
$650$	−754.487	−	212.151i	−1.16075	−	0.326386i
$651$		−	284.407i		−	0.436878i
$652$	−62.2423	+	144.553i	−0.0954637	+	0.221708i
$653$	635.931	−	635.931i	0.973860	−	0.973860i	−0.0258069	−	0.999667i	$-0.508216\pi$
$653$	635.931	−	635.931i	0.973860	−	0.973860i	0.999667	+	0.0258069i	$0.00821552\pi$
$654$	−366.583	−	248.643i	−0.560525	−	0.380189i
$655$	−714.888	+	116.060i	−1.09143	+	0.177191i
$656$	430.976	−	407.670i	0.656975	−	0.621448i
$657$	326.132	−	326.132i	0.496396	−	0.496396i
$658$	−208.231	+	39.9183i	−0.316461	+	0.0606661i
$659$	1040.90			1.57952			0.789759	−	0.613417i	$-0.210206\pi$
$659$	1040.90			1.57952			0.789759	+	0.613417i	$0.210206\pi$
$660$	26.9980	−	107.686i	0.0409060	−	0.163160i
$661$			325.566i			0.492536i	0.969202	+	0.246268i	$0.0792043\pi$
$661$			325.566i			0.492536i	−0.969202	+	0.246268i	$0.920796\pi$
$662$	−1012.08	+	194.017i	−1.52882	+	0.293077i
$663$	−82.1719	−	82.1719i	−0.123939	−	0.123939i
$664$	939.041	+	207.216i	1.41422	+	0.312072i
$665$	−769.056	−	554.225i	−1.15648	−	0.833421i
$666$	367.670	+	249.381i	0.552058	+	0.374446i
$667$	0.874525	+	0.874525i	0.00131113	+	0.00131113i
$668$	138.122	−	320.778i	0.206769	−	0.480206i
$669$	−353.833			−0.528899
$670$	−996.203	−	462.984i	−1.48687	−	0.691021i
$671$	295.795			0.440827
$672$	−306.897	+	426.467i	−0.456692	+	0.634623i
$673$	469.880	+	469.880i	0.698187	+	0.698187i	0.964019	−	0.265832i	$-0.0856468\pi$
$673$	469.880	+	469.880i	0.698187	+	0.698187i	−0.265832	+	0.964019i	$0.585647\pi$
$674$	407.411	+	276.335i	0.604467	+	0.409993i
$675$	497.322	+	248.577i	0.736773	+	0.368262i
$676$	113.464	+	285.063i	0.167846	+	0.421690i
$677$	−435.841	−	435.841i	−0.643783	−	0.643783i	0.307700	−	0.951483i	$-0.400441\pi$
$677$	−435.841	−	435.841i	−0.643783	−	0.643783i	−0.951483	+	0.307700i	$0.900441\pi$
$678$	−7.19804	−	37.5481i	−0.0106166	−	0.0553807i
$679$			1433.13i			2.11065i
$680$	−12.0602	+	214.201i	−0.0177356	+	0.315002i
$681$	318.400			0.467548
$682$	−136.636	+	26.1934i	−0.200346	+	0.0384067i
$683$	311.279	−	311.279i	0.455752	−	0.455752i	−0.441506	−	0.897258i	$-0.645556\pi$
$683$	311.279	−	311.279i	0.455752	−	0.455752i	0.897258	+	0.441506i	$0.145556\pi$
$684$	167.379	+	420.517i	0.244706	+	0.614791i
$685$	415.830	+	299.671i	0.607051	+	0.437475i
$686$	574.815	−	847.470i	0.837923	−	1.23538i
$687$	279.016	−	279.016i	0.406137	−	0.406137i
$688$	10.7752	−	387.737i	0.0156617	−	0.563571i
$689$		−	884.348i		−	1.28352i
$690$	34.3017	−	12.5346i	0.0497126	−	0.0181661i
$691$			726.094i			1.05079i	0.850859	+	0.525394i	$0.176082\pi$
$691$			726.094i			1.05079i	−0.850859	+	0.525394i	$0.823918\pi$
$692$	−14.3906	+	33.4212i	−0.0207957	+	0.0482965i
$693$	239.137	−	239.137i	0.345075	−	0.345075i
$694$	−71.4661	+	105.365i	−0.102977	+	0.151823i
$695$	−44.4145	−	273.577i	−0.0639058	−	0.393636i
$696$	5.05459	+	1.11538i	0.00726234	+	0.00160256i
$697$	−140.620	+	140.620i	−0.201750	+	0.201750i
$698$	−21.6784	−	113.084i	−0.0310578	−	0.162011i
$699$	−348.056			−0.497934
$700$	100.497	−	1183.61i	0.143568	−	1.69087i
$701$		−	286.170i		−	0.408232i	−0.978947	−	0.204116i	$-0.934568\pi$
$701$		−	286.170i		−	0.408232i	0.978947	−	0.204116i	$-0.0654319\pi$
$702$	−131.265	−	684.734i	−0.186987	−	0.975405i
$703$	353.619	+	353.619i	0.503014	+	0.503014i
$704$	233.149	+	108.164i	0.331178	+	0.153642i
$705$	60.8819	−	9.88402i	0.0863573	−	0.0140199i
$706$	718.173	−	1058.83i	1.01724	−	1.49976i
$707$	171.558	+	171.558i	0.242657	+	0.242657i
$708$	−110.763	+	257.239i	−0.156445	+	0.363331i
$709$	36.2751			0.0511638			0.0255819	−	0.999673i	$-0.491856\pi$
$709$	36.2751			0.0511638			0.0255819	+	0.999673i	$0.491856\pi$
$710$	736.163	−	269.010i	1.03685	−	0.378887i
$711$	224.539			0.315807
$712$	625.812	−	399.548i	0.878949	−	0.561163i
$713$	−32.3612	−	32.3612i	−0.0453874	−	0.0453874i
$714$	98.8669	−	145.763i	0.138469	−	0.204150i
$715$	184.017	−	255.347i	0.257367	−	0.357128i
$716$	−971.614	+	386.732i	−1.35700	+	0.540129i
$717$	442.064	+	442.064i	0.616547	+	0.616547i
$718$	−966.689	+	185.316i	−1.34636	+	0.258100i
$719$			103.315i			0.143693i	0.997416	+	0.0718464i	$0.0228891\pi$
$719$			103.315i			0.143693i	−0.997416	+	0.0718464i	$0.977111\pi$
$720$	−344.243	+	450.732i	−0.478116	+	0.626017i
$721$	−654.729			−0.908085
$722$	−40.0122	−	208.721i	−0.0554186	−	0.289088i
$723$	81.9236	−	81.9236i	0.113311	−	0.113311i
$724$	391.044	+	982.446i	0.540116	+	1.35697i
$725$	−11.1014	+	3.70215i	−0.0153123	+	0.00510641i
$726$	−239.933	−	162.740i	−0.330486	−	0.224160i
$727$	−328.631	+	328.631i	−0.452037	+	0.452037i	−0.896030	−	0.443993i	$-0.853561\pi$
$727$	−328.631	+	328.631i	−0.452037	+	0.452037i	0.443993	+	0.896030i	$0.353561\pi$
$728$	−1255.52	+	801.581i	−1.72461	+	1.10107i
$729$			42.2524i			0.0579594i
$730$	589.974	+	274.190i	0.808183	+	0.375602i
$731$			130.027i			0.177876i
$732$	374.040	+	161.055i	0.510983	+	0.220021i
$733$	−676.211	+	676.211i	−0.922525	+	0.922525i	−0.997207	−	0.0746826i	$-0.976206\pi$
$733$	−676.211	+	676.211i	−0.922525	+	0.922525i	0.0746826	+	0.997207i	$0.476206\pi$
$734$	6.66168	+	4.51843i	0.00907585	+	0.00615590i
$735$	−372.158	+	516.416i	−0.506338	+	0.702607i
$736$	13.6052	+	83.4455i	0.0184853	+	0.113377i
$737$	311.947	−	311.947i	0.423266	−	0.423266i
$738$	−516.315	+	98.9785i	−0.699614	+	0.134117i
$739$	−1456.68			−1.97115			−0.985576	−	0.169235i	$-0.945870\pi$
$739$	−1456.68			−1.97115			−0.985576	+	0.169235i	$0.945870\pi$
$740$	−152.394	+	607.848i	−0.205938	+	0.821417i
$741$		−	345.809i		−	0.466679i
$742$	1316.37	−	252.351i	1.77409	−	0.340096i
$743$	−544.329	−	544.329i	−0.732610	−	0.732610i	0.238526	−	0.971136i	$-0.423336\pi$
$743$	−544.329	−	544.329i	−0.732610	−	0.732610i	−0.971136	+	0.238526i	$0.923336\pi$
$744$	−187.041	−	41.2739i	−0.251400	−	0.0554757i
$745$	52.8640	+	325.623i	0.0709583	+	0.437077i
$746$	724.484	+	491.398i	0.971158	+	0.658710i
$747$	−602.580	−	602.580i	−0.806667	−	0.806667i
$748$	−79.1333	−	34.0735i	−0.105793	−	0.0455528i
$749$	−1178.72			−1.57373
$750$	−39.0218	+	343.349i	−0.0520291	+	0.457799i
$751$	−789.079			−1.05070			−0.525352	−	0.850885i	$-0.676066\pi$
$751$	−789.079			−1.05070			−0.525352	+	0.850885i	$0.676066\pi$
$752$	−3.96668	+	142.737i	−0.00527485	+	0.189810i
$753$	−335.254	−	335.254i	−0.445225	−	0.445225i
$754$	12.1447	+	8.23745i	0.0161071	+	0.0109250i
$755$	150.725	+	928.411i	0.199636	+	1.22968i
$756$	981.786	−	390.781i	1.29866	−	0.516906i
$757$	−190.261	−	190.261i	−0.251336	−	0.251336i	0.570182	−	0.821518i	$-0.306873\pi$
$757$	−190.261	−	190.261i	−0.251336	−	0.251336i	−0.821518	+	0.570182i	$0.806873\pi$
$758$	112.317	+	585.894i	0.148175	+	0.772947i
$759$			14.6661i			0.0193230i
$760$	−476.095	+	425.342i	−0.626441	+	0.559660i
$761$	−467.711			−0.614600			−0.307300	−	0.951613i	$-0.599425\pi$
$761$	−467.711			−0.614600			−0.307300	+	0.951613i	$0.599425\pi$
$762$	−226.658	+	43.4507i	−0.297451	+	0.0570219i
$763$	1345.85	−	1345.85i	1.76390	−	1.76390i
$764$	1111.11	−	442.255i	1.45433	−	0.578868i
$765$	111.155	−	154.242i	0.145301	−	0.201623i
$766$	−806.142	+	1188.52i	−1.05240	+	1.55160i
$767$	−561.458	+	561.458i	−0.732018	+	0.732018i
$768$	235.930	+	263.722i	0.307200	+	0.343388i
$769$		−	174.539i		−	0.226969i	−0.993540	−	0.113485i	$-0.963799\pi$
$769$		−	174.539i		−	0.226969i	0.993540	−	0.113485i	$-0.0362012\pi$
$770$	432.599	+	201.050i	0.561818	+	0.261104i
$771$			336.171i			0.436019i
$772$	176.034	+	75.7972i	0.228023	+	0.0981829i
$773$	180.738	−	180.738i	0.233814	−	0.233814i	−0.580469	−	0.814283i	$-0.697131\pi$
$773$	180.738	−	180.738i	0.233814	−	0.233814i	0.814283	+	0.580469i	$0.197131\pi$
$774$	−192.950	+	284.473i	−0.249289	+	0.367536i
$775$	410.801	−	136.995i	0.530065	−	0.176768i
$776$	942.506	+	207.980i	1.21457	+	0.268016i
$777$	363.780	−	363.780i	0.468185	−	0.468185i
$778$	−190.700	−	994.773i	−0.245115	−	1.27863i
$779$	−591.778			−0.759664
$780$	371.726	−	222.698i	0.476572	−	0.285510i
$781$			314.756i			0.403017i
$782$	−5.33603	−	27.8351i	−0.00682357	−	0.0355948i
$783$	−7.36114	−	7.36114i	−0.00940121	−	0.00940121i
$784$	−1012.68	−	1070.57i	−1.29168	−	1.36553i
$785$	−81.6922	+	113.358i	−0.104067	+	0.144405i
$786$	224.776	−	331.395i	0.285974	−	0.421622i
$787$	578.023	+	578.023i	0.734464	+	0.734464i	0.971501	−	0.237037i	$-0.0761762\pi$
$787$	578.023	+	578.023i	0.734464	+	0.734464i	−0.237037	+	0.971501i	$0.576176\pi$
$788$	324.160	+	139.578i	0.411370	+	0.177129i
$789$	214.586			0.271972
$790$	108.707	+	297.484i	0.137604	+	0.376562i
$791$	164.279			0.207685
$792$	−122.565	−	191.974i	−0.154754	−	0.242391i
$793$	816.391	+	816.391i	1.02950	+	1.02950i
$794$	123.618	−	182.254i	0.155690	−	0.229539i
$795$	−384.876	+	62.4836i	−0.484121	+	0.0785958i
$796$	−79.2838	−	199.190i	−0.0996028	−	0.250239i
$797$	320.738	+	320.738i	0.402432	+	0.402432i	0.879089	−	0.476657i	$-0.158152\pi$
$797$	320.738	+	320.738i	0.402432	+	0.402432i	−0.476657	+	0.879089i	$0.658152\pi$
$798$	514.745	−	98.6775i	0.645044	−	0.123656i
$799$		−	47.8668i		−	0.0599084i
$800$	−763.821	−	237.861i	−0.954776	−	0.297326i
$801$	−657.970			−0.821436
$802$	137.986	+	719.796i	0.172053	+	0.897501i
$803$	−184.742	+	184.742i	−0.230065	+	0.230065i
$804$	564.315	−	224.615i	0.701884	−	0.279371i
$805$	25.1469	+	154.896i	0.0312384	+	0.192417i
$806$	−449.408	−	304.821i	−0.557578	−	0.378190i
$807$	−123.747	+	123.747i	−0.153342	+	0.153342i
$808$	137.723	−	87.9289i	0.170449	−	0.108823i
$809$			764.477i			0.944966i	0.881340	+	0.472483i	$0.156642\pi$
$809$			764.477i			0.944966i	−0.881340	+	0.472483i	$0.843358\pi$
$810$	310.561	−	113.486i	0.383408	−	0.140106i
$811$			189.765i			0.233989i	0.993133	+	0.116995i	$0.0373260\pi$
$811$			189.765i			0.233989i	−0.993133	+	0.116995i	$0.962674\pi$
$812$	−8.79611	+	20.4283i	−0.0108326	+	0.0251580i
$813$	−334.174	+	334.174i	−0.411038	+	0.411038i
$814$	−208.272	−	141.265i	−0.255862	−	0.173544i
$815$	159.604	+	115.019i	0.195833	+	0.141128i
$816$	−81.5136	−	86.1736i	−0.0998941	−	0.105605i
$817$	−273.601	+	273.601i	−0.334885	+	0.334885i
$818$	767.845	−	147.197i	0.938686	−	0.179948i
$819$	1320.03			1.61176
$820$	−381.100	−	636.130i	−0.464756	−	0.775768i
$821$		−	1526.85i		−	1.85974i	−0.367884	−	0.929872i	$-0.619918\pi$
$821$		−	1526.85i		−	1.85974i	0.367884	−	0.929872i	$-0.380082\pi$
$822$	−278.324	+	53.3551i	−0.338593	+	0.0649089i
$823$	23.3976	+	23.3976i	0.0284297	+	0.0284297i	0.721179	−	0.692749i	$-0.243601\pi$
$823$	23.3976	+	23.3976i	0.0284297	+	0.0284297i	−0.692749	+	0.721179i	$0.743601\pi$
$824$	−95.0160	+	430.585i	−0.115311	+	0.522554i
$825$	−124.131	−	62.0444i	−0.150462	−	0.0752053i
$826$	−995.957	−	675.530i	−1.20576	−	0.817833i
$827$	−876.833	−	876.833i	−1.06026	−	1.06026i	−0.998064	−	0.0621932i	$-0.980190\pi$
$827$	−876.833	−	876.833i	−1.06026	−	1.06026i	−0.0621932	−	0.998064i	$-0.519810\pi$
$828$	29.6309	−	68.8157i	0.0357862	−	0.0831108i
$829$	518.022			0.624876			0.312438	−	0.949938i	$-0.398854\pi$
$829$	518.022			0.624876			0.312438	+	0.949938i	$0.398854\pi$
$830$	506.608	−	1090.07i	0.610371	−	1.31334i
$831$	−245.985			−0.296010
$832$	344.959	+	942.022i	0.414614	+	1.13224i
$833$	349.309	+	349.309i	0.419338	+	0.419338i
$834$	126.820	+	86.0185i	0.152062	+	0.103140i
$835$	−354.176	−	255.239i	−0.424163	−	0.305675i
$836$	−94.8140	−	238.208i	−0.113414	−	0.284938i
$837$	272.394	+	272.394i	0.325441	+	0.325441i
$838$	134.410	+	701.140i	0.160393	+	0.836682i
$839$		−	1666.89i		−	1.98676i	−0.114858	−	0.993382i	$-0.536641\pi$
$839$		−	1666.89i		−	1.98676i	0.114858	−	0.993382i	$-0.463359\pi$
$840$	437.564	+	489.776i	0.520910	+	0.583067i
$841$	−840.781			−0.999739
$842$	342.194	−	65.5991i	0.406406	−	0.0779087i
$843$	366.535	−	366.535i	0.434799	−	0.434799i
$844$	−358.475	−	900.621i	−0.424733	−	1.06709i
$845$	378.561	−	61.4584i	0.448001	−	0.0727318i
$846$	71.0305	−	104.723i	0.0839605	−	0.123786i
$847$	880.877	−	880.877i	1.04000	−	1.04000i
$848$	25.0761	−	902.339i	0.0295709	−	1.06408i
$849$			566.531i			0.667293i
$850$	258.164	+	72.5921i	0.303722	+	0.0854025i
$851$		−	82.7852i		−	0.0972799i
$852$	−171.379	+	398.017i	−0.201150	+	0.467156i
$853$	238.631	−	238.631i	0.279755	−	0.279755i	−0.553256	−	0.833011i	$-0.686615\pi$
$853$	238.631	−	238.631i	0.279755	−	0.279755i	0.833011	+	0.553256i	$0.186615\pi$
$854$	−982.259	+	1448.18i	−1.15019	+	1.69576i
$855$	558.444	−	90.6618i	0.653150	−	0.106037i
$856$	−171.060	+	775.192i	−0.199836	+	0.905598i
$857$	−593.379	+	593.379i	−0.692390	+	0.692390i	−0.962757	−	0.270367i	$-0.912855\pi$
$857$	−593.379	+	593.379i	−0.692390	+	0.692390i	0.270367	+	0.962757i	$0.412855\pi$
$858$	32.7635	+	170.909i	0.0381859	+	0.199194i
$859$	1008.66			1.17423			0.587114	−	0.809504i	$-0.300264\pi$
$859$	1008.66			1.17423			0.587114	+	0.809504i	$0.300264\pi$
$860$	−470.302	−	117.910i	−0.546863	−	0.137104i
$861$			608.783i			0.707065i
$862$	18.3628	+	95.7884i	0.0213025	+	0.111123i
$863$	−655.271	−	655.271i	−0.759294	−	0.759294i	0.216900	−	0.976194i	$-0.430406\pi$
$863$	−655.271	−	655.271i	−0.759294	−	0.759294i	−0.976194	+	0.216900i	$0.930406\pi$
$864$	−114.519	−	702.386i	−0.132545	−	0.812947i
$865$	36.9009	+	26.5928i	0.0426599	+	0.0307431i
$866$	−342.010	+	504.237i	−0.394931	+	0.582260i
$867$	−254.349	−	254.349i	−0.293367	−	0.293367i
$868$	325.494	−	755.936i	0.374993	−	0.870894i
$869$	−127.193			−0.146367
$870$	2.72692	−	5.86752i	0.00313440	−	0.00674428i
$871$	1721.94			1.97697
$872$	−689.792	−	1080.42i	−0.791045	−	1.23901i
$873$	−604.803	−	604.803i	−0.692787	−	0.692787i
$874$	47.3421	−	69.7981i	0.0541672	−	0.0798605i
$875$	−1417.39	−	442.441i	−1.61987	−	0.505647i
$876$	−334.200	+	133.022i	−0.381507	+	0.151851i
$877$	119.801	+	119.801i	0.136604	+	0.136604i	0.772102	−	0.635498i	$-0.219205\pi$
$877$	119.801	+	119.801i	0.136604	+	0.136604i	−0.635498	+	0.772102i	$0.719205\pi$
$878$	−917.093	+	175.808i	−1.04452	+	0.200237i
$879$		−	498.117i		−	0.566686i
$880$	195.001	−	255.324i	0.221592	−	0.290140i
$881$	1243.40			1.41135			0.705673	−	0.708537i	$-0.250645\pi$
$881$	1243.40			1.41135			0.705673	+	0.708537i	$0.250645\pi$
$882$	245.869	+	1282.56i	0.278764	+	1.45415i
$883$	−955.712	+	955.712i	−1.08235	+	1.08235i	−0.0860557	+	0.996290i	$0.527426\pi$
$883$	−955.712	+	955.712i	−1.08235	+	1.08235i	−0.996290	+	0.0860557i	$0.972574\pi$
$884$	−124.365	−	312.450i	−0.140684	−	0.353450i
$885$	284.021	+	204.682i	0.320928	+	0.231279i
$886$	−991.612	−	672.583i	−1.11920	−	0.759123i
$887$	221.872	−	221.872i	0.250138	−	0.250138i	−0.570889	−	0.821027i	$-0.693401\pi$
$887$	221.872	−	221.872i	0.250138	−	0.250138i	0.821027	+	0.570889i	$0.193401\pi$
$888$	−186.448	−	292.034i	−0.209964	−	0.328867i
$889$		−	991.662i		−	1.11548i
$890$	−318.547	−	871.723i	−0.357918	−	0.979464i
$891$			132.784i			0.149028i
$892$	−940.466	−	404.949i	−1.05433	−	0.453979i
$893$	100.720	−	100.720i	0.112789	−	0.112789i
$894$	−150.946	−	102.383i	−0.168844	−	0.114522i
$895$	209.476	+	1290.30i	0.234051	+	1.44167i
$896$	−1303.79	+	782.288i	−1.45512	+	0.873089i
$897$	−40.4784	+	40.4784i	−0.0451264	+	0.0451264i
$898$	502.566	−	96.3428i	0.559651	−	0.107286i
$899$	−8.10824			−0.00901918
$900$	457.089	+	541.912i	0.507877	+	0.602124i
$901$			302.599i			0.335848i
$902$	292.474	−	56.0677i	0.324250	−	0.0621593i
$903$	281.463	+	281.463i	0.311697	+	0.311697i
$904$	23.8405	−	108.038i	0.0263723	−	0.119511i
$905$	1304.68	−	211.811i	1.44164	−	0.234046i
$906$	−430.376	−	291.912i	−0.475028	−	0.322199i
$907$	−432.864	−	432.864i	−0.477248	−	0.477248i	0.427002	−	0.904251i	$-0.359570\pi$
$907$	−432.864	−	432.864i	−0.477248	−	0.477248i	−0.904251	+	0.427002i	$0.859570\pi$
$908$	846.286	+	364.397i	0.932033	+	0.401318i
$909$	−144.800			−0.159296
$910$	639.074	+	1748.87i	0.702280	+	1.92183i
$911$	−820.509			−0.900668			−0.450334	−	0.892860i	$-0.648695\pi$
$911$	−820.509			−0.900668			−0.450334	+	0.892860i	$0.648695\pi$
$912$	9.80558	−	352.844i	0.0107517	−	0.386890i
$913$	341.340	+	341.340i	0.373866	+	0.373866i
$914$	124.245	+	84.2720i	0.135935	+	0.0922013i
$915$	297.619	−	412.983i	0.325266	−	0.451348i
$916$	1060.93	−	422.283i	1.15822	−	0.461007i
$917$	1216.66	+	1216.66i	1.32679	+	1.32679i
$918$	44.9150	+	234.297i	0.0489271	+	0.255225i
$919$		−	16.4894i		−	0.0179428i	−0.999960	−	0.00897139i	$-0.997144\pi$
$919$		−	16.4894i		−	0.0179428i	0.999960	−	0.00897139i	$-0.00285572\pi$
$920$	105.517	+	5.94093i	0.114692	+	0.00645753i
$921$	308.776			0.335262
$922$	−776.707	+	148.896i	−0.842415	+	0.161492i
$923$	−868.724	+	868.724i	−0.941197	+	0.941197i
$924$	−245.053	+	97.5385i	−0.265209	+	0.105561i
$925$	700.676	+	350.219i	0.757487	+	0.378615i
$926$	−139.712	+	205.983i	−0.150877	+	0.222443i
$927$	276.305	−	276.305i	0.298064	−	0.298064i
$928$	12.1582	+	8.74940i	0.0131016	+	0.00942823i
$929$			427.239i			0.459892i	0.973203	+	0.229946i	$0.0738549\pi$
$929$			427.239i			0.459892i	−0.973203	+	0.229946i	$0.926145\pi$
$930$	−100.908	+	217.124i	−0.108503	+	0.233466i
$931$			1470.02i			1.57897i
$932$	−925.111	−	398.338i	−0.992608	−	0.427401i
$933$	−282.120	+	282.120i	−0.302379	+	0.302379i
$934$	855.301	−	1261.00i	0.915740	−	1.35011i
$935$	−62.9654	+	87.3724i	−0.0673427	+	0.0934464i
$936$	191.567	−	868.124i	0.204665	−	0.927483i
$937$	−709.466	+	709.466i	−0.757168	+	0.757168i	−0.975806	−	0.218638i	$-0.929839\pi$
$937$	−709.466	+	709.466i	−0.757168	+	0.757168i	0.218638	+	0.975806i	$0.429839\pi$
$938$	491.361	+	2563.15i	0.523839	+	2.73257i
$939$	−269.995			−0.287534
$940$	173.132	+	43.4061i	0.184183	+	0.0461767i
$941$		−	1613.99i		−	1.71519i	−0.514328	−	0.857594i	$-0.671959\pi$
$941$		−	1613.99i		−	1.71519i	0.514328	−	0.857594i	$-0.328041\pi$
$942$	−14.5450	−	75.8729i	−0.0154405	−	0.0805445i
$943$	69.2702	+	69.2702i	0.0734572	+	0.0734572i
$944$	−588.800	+	556.960i	−0.623729	+	0.590000i
$945$	−211.669	−	1303.80i	−0.223989	−	1.37969i
$946$	109.299	−	161.144i	0.115538	−	0.170342i
$947$	1268.86	+	1268.86i	1.33987	+	1.33987i	0.896181	+	0.443688i	$0.146330\pi$
$947$	1268.86	+	1268.86i	1.33987	+	1.33987i	0.443688	+	0.896181i	$0.353670\pi$
$948$	−160.839	−	69.2545i	−0.169661	−	0.0730533i
$949$	−1019.77			−1.07458
$950$	390.477	+	695.971i	0.411028	+	0.732601i
$951$	155.440			0.163449
$952$	429.602	−	274.278i	0.451262	−	0.288108i
$953$	984.100	+	984.100i	1.03263	+	1.03263i	0.999449	+	0.0331842i	$0.0105648\pi$
$953$	984.100	+	984.100i	1.03263	+	1.03263i	0.0331842	+	0.999449i	$0.489435\pi$
$954$	−449.033	+	662.024i	−0.470684	+	0.693946i
$955$	−239.550	−	1475.54i	−0.250838	−	1.54507i
$956$	669.051	+	1680.90i	0.699845	+	1.75827i
$957$	1.83733	+	1.83733i	0.00191989	+	0.00191989i
$958$	103.024	−	19.7499i	0.107541	−	0.0206158i
$959$		−	1217.71i		−	1.26977i
$960$	385.603	−	216.688i	0.401670	−	0.225717i
$961$	−660.960			−0.687784
$962$	−184.938	−	964.720i	−0.192244	−	1.00283i
$963$	497.438	−	497.438i	0.516551	−	0.516551i
$964$	311.506	−	123.989i	0.323139	−	0.128619i
$965$	140.068	−	194.362i	0.145148	−	0.201411i
$966$	−71.8037	−	48.7025i	−0.0743310	−	0.0504166i
$967$	−960.198	+	960.198i	−0.992965	+	0.992965i	−0.999975	−	0.00701003i	$-0.997769\pi$
$967$	−960.198	+	960.198i	−0.992965	+	0.992965i	0.00701003	+	0.999975i	$0.497769\pi$
$968$	−451.477	−	707.147i	−0.466402	−	0.730524i
$969$			118.326i			0.122111i
$970$	508.477	−	1094.09i	0.524203	−	1.12793i
$971$		−	469.039i		−	0.483047i	−0.970395	−	0.241523i	$-0.922353\pi$
$971$		−	469.039i		−	0.483047i	0.970395	−	0.241523i	$-0.0776471\pi$
$972$	−388.928	+	903.257i	−0.400131	+	0.929276i
$973$	−465.600	+	465.600i	−0.478520	+	0.478520i
$974$	561.415	+	380.792i	0.576401	+	0.390957i
$975$	−171.358	−	513.843i	−0.175752	−	0.527018i
$976$	809.851	+	856.149i	0.829765	+	0.877202i
$977$	−162.956	+	162.956i	−0.166792	+	0.166792i	−0.785568	−	0.618776i	$-0.787629\pi$
$977$	−162.956	+	162.956i	−0.166792	+	0.166792i	0.618776	+	0.785568i	$0.287629\pi$
$978$	−106.826	+	20.4787i	−0.109229	+	0.0209394i
$979$	372.716			0.380711
$980$	−1580.19	+	946.678i	−1.61244	+	0.965998i
$981$			1135.94i			1.15794i
$982$	335.485	−	64.3129i	0.341634	−	0.0654918i
$983$	−421.256	−	421.256i	−0.428541	−	0.428541i	0.459590	−	0.888131i	$-0.347996\pi$
$983$	−421.256	−	421.256i	−0.428541	−	0.428541i	−0.888131	+	0.459590i	$0.847996\pi$
$984$	400.368	+	88.3482i	0.406878	+	0.0897847i
$985$	257.930	−	357.910i	0.261858	−	0.363360i
$986$	−4.15559	−	2.81862i	−0.00421459	−	0.00285864i
$987$	−103.615	−	103.615i	−0.104979	−	0.104979i
$988$	395.766	−	919.138i	0.400573	−	0.930301i
$989$	64.0523			0.0647647
$990$	−267.409	+	97.7171i	−0.270110	+	0.0987042i
$991$	1790.76			1.80703			0.903513	−	0.428561i	$-0.140979\pi$
$991$	1790.76			1.80703			0.903513	+	0.428561i	$0.140979\pi$
$992$	−449.907	−	323.766i	−0.453536	−	0.326377i
$993$	−503.602	−	503.602i	−0.507153	−	0.507153i
$994$	−1541.01	−	1045.22i	−1.55031	−	1.05153i
$995$	−264.523	+	42.9446i	−0.265852	+	0.0431604i
$996$	245.779	+	617.486i	0.246766	+	0.619966i
$997$	−651.402	−	651.402i	−0.653362	−	0.653362i	0.300439	−	0.953801i	$-0.402867\pi$
$997$	−651.402	−	651.402i	−0.653362	−	0.653362i	−0.953801	+	0.300439i	$0.902867\pi$
$998$	−330.676	−	1724.95i	−0.331339	−	1.72841i
$999$			696.828i			0.697526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.i.a.13.6	yes	20
3.2	odd	2		360.3.u.b.253.5		20
4.3	odd	2		160.3.m.a.113.7		20
5.2	odd	4	inner	40.3.i.a.37.1	yes	20
5.3	odd	4		200.3.i.b.157.10		20
5.4	even	2		200.3.i.b.93.5		20
8.3	odd	2		160.3.m.a.113.4		20
8.5	even	2	inner	40.3.i.a.13.1	✓	20
15.2	even	4		360.3.u.b.37.10		20
20.3	even	4		800.3.m.b.657.7		20
20.7	even	4		160.3.m.a.17.4		20
20.19	odd	2		800.3.m.b.593.4		20
24.5	odd	2		360.3.u.b.253.10		20
40.3	even	4		800.3.m.b.657.4		20
40.13	odd	4		200.3.i.b.157.5		20
40.19	odd	2		800.3.m.b.593.7		20
40.27	even	4		160.3.m.a.17.7		20
40.29	even	2		200.3.i.b.93.10		20
40.37	odd	4	inner	40.3.i.a.37.6	yes	20
120.77	even	4		360.3.u.b.37.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.1	✓	20	8.5	even	2	inner
40.3.i.a.13.6	yes	20	1.1	even	1	trivial
40.3.i.a.37.1	yes	20	5.2	odd	4	inner
40.3.i.a.37.6	yes	20	40.37	odd	4	inner
160.3.m.a.17.4		20	20.7	even	4
160.3.m.a.17.7		20	40.27	even	4
160.3.m.a.113.4		20	8.3	odd	2
160.3.m.a.113.7		20	4.3	odd	2
200.3.i.b.93.5		20	5.4	even	2
200.3.i.b.93.10		20	40.29	even	2
200.3.i.b.157.5		20	40.13	odd	4
200.3.i.b.157.10		20	5.3	odd	4
360.3.u.b.37.5		20	120.77	even	4
360.3.u.b.37.10		20	15.2	even	4
360.3.u.b.253.5		20	3.2	odd	2
360.3.u.b.253.10		20	24.5	odd	2
800.3.m.b.593.4		20	20.19	odd	2
800.3.m.b.593.7		20	40.19	odd	2
800.3.m.b.657.4		20	40.3	even	4
800.3.m.b.657.7		20	20.3	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)

\(f(q)\)	\(=\)	\(q+(0.376547 + 1.96423i) q^{2} +(-0.977390 + 0.977390i) q^{3} +(-3.71643 + 1.47925i) q^{4} +(0.801246 + 4.93538i) q^{5} +(-2.28785 - 1.55179i) q^{6} +(8.39950 - 8.39950i) q^{7} +(-4.30500 - 6.74292i) q^{8} +7.08942i q^{9} +O(q^{10})\)	\(q+(0.376547 + 1.96423i) q^{2} +(-0.977390 + 0.977390i) q^{3} +(-3.71643 + 1.47925i) q^{4} +(0.801246 + 4.93538i) q^{5} +(-2.28785 - 1.55179i) q^{6} +(8.39950 - 8.39950i) q^{7} +(-4.30500 - 6.74292i) q^{8} +7.08942i q^{9} +(-9.39254 + 3.43224i) q^{10} -4.01590i q^{11} +(2.18659 - 5.07820i) q^{12} +(11.0839 - 11.0839i) q^{13} +(19.6614 + 13.3358i) q^{14} +(-5.60692 - 4.04066i) q^{15} +(11.6236 - 10.9951i) q^{16} +(-3.79258 + 3.79258i) q^{17} +(-13.9253 + 2.66950i) q^{18} -15.9605 q^{19} +(-10.2784 - 17.1567i) q^{20} +16.4192i q^{21} +(7.88816 - 1.51217i) q^{22} +(1.86825 + 1.86825i) q^{23} +(10.7981 + 2.38279i) q^{24} +(-23.7160 + 7.90891i) q^{25} +(25.9449 + 17.5977i) q^{26} +(-15.7256 - 15.7256i) q^{27} +(-18.7911 + 43.6411i) q^{28} +0.468098 q^{29} +(5.82554 - 12.5348i) q^{30} -17.3217 q^{31} +(25.9737 + 18.6914i) q^{32} +(3.92510 + 3.92510i) q^{33} +(-8.87759 - 6.02143i) q^{34} +(48.1848 + 34.7247i) q^{35} +(-10.4870 - 26.3473i) q^{36} +(-22.1558 - 22.1558i) q^{37} +(-6.00989 - 31.3502i) q^{38} +21.6665i q^{39} +(29.8295 - 26.6496i) q^{40} +37.0776 q^{41} +(-32.2511 + 6.18259i) q^{42} +(17.1423 - 17.1423i) q^{43} +(5.94052 + 14.9248i) q^{44} +(-34.9890 + 5.68037i) q^{45} +(-2.96620 + 4.37316i) q^{46} +(-6.31059 + 6.31059i) q^{47} +(-0.614364 + 22.1073i) q^{48} -92.1033i q^{49} +(-24.4651 - 43.6057i) q^{50} -7.41366i q^{51} +(-24.7965 + 57.5881i) q^{52} +(39.8935 - 39.8935i) q^{53} +(24.9674 - 36.8102i) q^{54} +(19.8200 - 3.21772i) q^{55} +(-92.7970 - 20.4773i) q^{56} +(15.5997 - 15.5997i) q^{57} +(0.176261 + 0.919455i) q^{58} -50.6555 q^{59} +(26.8149 + 6.72277i) q^{60} +73.6559i q^{61} +(-6.52241 - 34.0238i) q^{62} +(59.5476 + 59.5476i) q^{63} +(-26.9339 + 58.0566i) q^{64} +(63.5839 + 45.8222i) q^{65} +(-6.23183 + 9.18779i) q^{66} +(77.6780 + 77.6780i) q^{67} +(8.48466 - 19.7050i) q^{68} -3.65202 q^{69} +(-50.0636 + 107.722i) q^{70} -78.3775 q^{71} +(47.8034 - 30.5200i) q^{72} +(-46.0027 - 46.0027i) q^{73} +(35.1765 - 51.8619i) q^{74} +(15.4497 - 30.9099i) q^{75} +(59.3162 - 23.6097i) q^{76} +(-33.7315 - 33.7315i) q^{77} +(-42.5580 + 8.15844i) q^{78} -31.6724i q^{79} +(63.5782 + 48.5573i) q^{80} -33.0646 q^{81} +(13.9614 + 72.8290i) q^{82} +(-84.9971 + 84.9971i) q^{83} +(-24.2881 - 61.0206i) q^{84} +(-21.7566 - 15.6790i) q^{85} +(40.1264 + 27.2166i) q^{86} +(-0.457515 + 0.457515i) q^{87} +(-27.0789 + 17.2885i) q^{88} +92.8102i q^{89} +(-24.3326 - 66.5876i) q^{90} -186.198i q^{91} +(-9.70682 - 4.17960i) q^{92} +(16.9300 - 16.9300i) q^{93} +(-14.7717 - 10.0192i) q^{94} +(-12.7883 - 78.7714i) q^{95} +(-43.6552 + 7.11767i) q^{96} +(-85.3107 + 85.3107i) q^{97} +(180.912 - 34.6812i) q^{98} +28.4704 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

L-functions

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