LMFDB - Embedded newform 40.3.i.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("40.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.08992105744$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024 $ x^20 - x^18 - 3x^16 + 11x^14 + x^12 - 40x^10 + 4x^8 + 176x^6 - 192x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Root			$1.17039 - 0.793843i$ of defining polynomial
Character	$\chi$	$=$	40.37
Dual form			40.3.i.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96423 + 0.376547i) q^{2} +(0.977390 + 0.977390i) q^{3} +(3.71643 - 1.47925i) q^{4} +(-0.801246 + 4.93538i) q^{5} +(-2.28785 - 1.55179i) q^{6} +(8.39950 + 8.39950i) q^{7} +(-6.74292 + 4.30500i) q^{8} -7.08942i q^{9} +O(q^{10})$	\(q+(-1.96423 + 0.376547i) 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} +(-6.74292 + 4.30500i) q^{8} -7.08942i q^{9} +(-0.284568 - 9.99595i) q^{10} -4.01590i q^{11} +(5.07820 + 2.18659i) 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} +(2.66950 + 13.9253i) q^{18} +15.9605 q^{19} +(4.32290 + 19.5272i) q^{20} +16.4192i q^{21} +(1.51217 + 7.88816i) 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} +(43.6411 + 18.7911i) q^{28} -0.468098 q^{29} +(9.49181 - 10.0481i) q^{30} -17.3217 q^{31} +(-18.6914 + 25.9737i) 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} +(-31.3502 + 6.00989i) q^{38} -21.6665i q^{39} +(-15.8441 - 36.7283i) q^{40} +37.0776 q^{41} +(-6.18259 - 32.2511i) 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} +(22.1073 + 0.614364i) q^{48} +92.1033i q^{49} +(49.5619 + 6.60476i) q^{50} -7.41366i q^{51} +(-57.5881 - 24.7965i) 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} +(0.919455 - 0.176261i) q^{58} +50.6555 q^{59} +(-14.8606 + 23.3109i) q^{60} +73.6559i q^{61} +(34.0238 - 6.52241i) 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} +(-19.7050 - 8.48466i) q^{68} +3.65202 q^{69} +(81.5708 - 86.3512i) q^{70} -78.3775 q^{71} +(30.5200 + 47.8034i) 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} +(8.15844 + 42.5580i) q^{78} +31.6724i q^{79} +(44.9514 + 66.1768i) q^{80} -33.0646 q^{81} +(-72.8290 + 13.9614i) 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} +(17.2885 + 27.0789i) q^{88} -92.8102i q^{89} +(-70.8655 + 2.01742i) q^{90} -186.198i q^{91} +(4.17960 - 9.70682i) 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} +(-34.6812 - 180.912i) 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 $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.96423	+	0.376547i	−0.982117	+	0.188273i
$2$	−1.96423	+	0.376547i	−0.982117	+	0.188273i
$3$	0.977390	+	0.977390i	0.325797	+	0.325797i	0.850986	−	0.525189i	$-0.176005\pi$
$3$	0.977390	+	0.977390i	0.325797	+	0.325797i	−0.525189	+	0.850986i	$0.676005\pi$
$4$	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	0.974187	+	0.225742i	$0.0724805\pi$
$7$	8.39950	+	8.39950i	1.19993	+	1.19993i	0.225742	+	0.974187i	$0.427519\pi$
$8$	−6.74292	+	4.30500i	−0.842865	+	0.538125i
$9$		−	7.08942i		−	0.787713i
$10$	−0.284568	−	9.99595i	−0.0284568	−	0.999595i
$11$		−	4.01590i		−	0.365082i	−0.983198	−	0.182541i	$-0.941568\pi$
$11$		−	4.01590i		−	0.365082i	0.983198	−	0.182541i	$-0.0584322\pi$
$12$	5.07820	+	2.18659i	0.423183	+	0.182216i
$13$	−11.0839	−	11.0839i	−0.852604	−	0.852604i	0.137849	−	0.990453i	$-0.455981\pi$
$13$	−11.0839	−	11.0839i	−0.852604	−	0.852604i	−0.990453	+	0.137849i	$0.955981\pi$
$14$	−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	0.586707	−	0.809800i	$-0.300424\pi$
$17$	−3.79258	−	3.79258i	−0.223093	−	0.223093i	−0.809800	+	0.586707i	$0.800424\pi$
$18$	2.66950	+	13.9253i	0.148305	+	0.773626i
$19$	15.9605			0.840029			0.420014	−	0.907517i	$-0.362025\pi$
$19$	15.9605			0.840029			0.420014	+	0.907517i	$0.362025\pi$
$20$	4.32290	+	19.5272i	0.216145	+	0.976361i
$21$			16.4192i			0.781865i
$22$	1.51217	+	7.88816i	0.0687352	+	0.358553i
$23$	1.86825	−	1.86825i	0.0812283	−	0.0812283i	−0.665325	−	0.746554i	$-0.731707\pi$
$23$	1.86825	−	1.86825i	0.0812283	−	0.0812283i	0.746554	+	0.665325i	$0.231707\pi$
$24$	−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
$28$	43.6411	+	18.7911i	1.55861	+	0.671112i
$29$	−0.468098			−0.0161413			−0.00807066	−	0.999967i	$-0.502569\pi$
$29$	−0.468098			−0.0161413			−0.00807066	+	0.999967i	$0.502569\pi$
$30$	9.49181	−	10.0481i	0.316394	−	0.334936i
$31$	−17.3217			−0.558763			−0.279382	−	0.960180i	$-0.590129\pi$
$31$	−17.3217			−0.558763			−0.279382	+	0.960180i	$0.590129\pi$
$32$	−18.6914	+	25.9737i	−0.584105	+	0.811678i
$33$	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	$-0.610830\pi$
$37$	22.1558	−	22.1558i	0.598805	−	0.598805i	0.939995	+	0.341189i	$0.110830\pi$
$38$	−31.3502	+	6.00989i	−0.825006	+	0.158155i
$39$		−	21.6665i		−	0.555551i
$40$	−15.8441	−	36.7283i	−0.396102	−	0.918206i
$41$	37.0776			0.904331			0.452165	−	0.891934i	$-0.350652\pi$
$41$	37.0776			0.904331			0.452165	+	0.891934i	$0.350652\pi$
$42$	−6.18259	−	32.2511i	−0.147204	−	0.767883i
$43$	−17.1423	−	17.1423i	−0.398658	−	0.398658i	0.479101	−	0.877760i	$-0.340963\pi$
$43$	−17.1423	−	17.1423i	−0.398658	−	0.398658i	−0.877760	+	0.479101i	$0.840963\pi$
$44$	−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	0.636779	−	0.771047i	$-0.280266\pi$
$47$	−6.31059	−	6.31059i	−0.134268	−	0.134268i	−0.771047	+	0.636779i	$0.780266\pi$
$48$	22.1073	+	0.614364i	0.460568	+	0.0127992i
$49$			92.1033i			1.87966i
$50$	49.5619	+	6.60476i	0.991237	+	0.132095i
$51$		−	7.41366i		−	0.145366i
$52$	−57.5881	−	24.7965i	−1.10746	−	0.476856i
$53$	−39.8935	−	39.8935i	−0.752708	−	0.752708i	0.222276	−	0.974984i	$-0.428652\pi$
$53$	−39.8935	−	39.8935i	−0.752708	−	0.752708i	−0.974984	+	0.222276i	$0.928652\pi$
$54$	−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
$58$	0.919455	−	0.176261i	0.0158527	−	0.00303898i
$59$	50.6555			0.858567			0.429284	−	0.903170i	$-0.358766\pi$
$59$	50.6555			0.858567			0.429284	+	0.903170i	$0.358766\pi$
$60$	−14.8606	+	23.3109i	−0.247676	+	0.388514i
$61$			73.6559i			1.20747i	0.797183	+	0.603737i	$0.206322\pi$
$61$			73.6559i			1.20747i	−0.797183	+	0.603737i	$0.793678\pi$
$62$	34.0238	−	6.52241i	0.548771	−	0.105200i
$63$	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	−0.174763	+	0.984611i	$0.555916\pi$
$67$	−77.6780	+	77.6780i	−1.15937	+	1.15937i	−0.984611	+	0.174763i	$0.944084\pi$
$68$	−19.7050	−	8.48466i	−0.289780	−	0.124774i
$69$	3.65202			0.0529278
$70$	81.5708	−	86.3512i	1.16530	−	1.23359i
$71$	−78.3775			−1.10391			−0.551954	−	0.833874i	$-0.686118\pi$
$71$	−78.3775			−1.10391			−0.551954	+	0.833874i	$0.686118\pi$
$72$	30.5200	+	47.8034i	0.423888	+	0.663936i
$73$	−46.0027	+	46.0027i	−0.630173	+	0.630173i	−0.948111	−	0.317938i	$-0.897010\pi$
$73$	−46.0027	+	46.0027i	−0.630173	+	0.630173i	0.317938	+	0.948111i	$0.397010\pi$
$74$	−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
$78$	8.15844	+	42.5580i	0.104595	+	0.545616i
$79$			31.6724i			0.400916i	0.979702	+	0.200458i	$0.0642430\pi$
$79$			31.6724i			0.400916i	−0.979702	+	0.200458i	$0.935757\pi$
$80$	44.9514	+	66.1768i	0.561893	+	0.827210i
$81$	−33.0646			−0.408205
$82$	−72.8290	+	13.9614i	−0.888158	+	0.170261i
$83$	84.9971	+	84.9971i	1.02406	+	1.02406i	0.999703	+	0.0243583i	$0.00775424\pi$
$83$	84.9971	+	84.9971i	1.02406	+	1.02406i	0.0243583	+	0.999703i	$0.492246\pi$
$84$	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
$88$	17.2885	+	27.0789i	0.196460	+	0.307715i
$89$		−	92.8102i		−	1.04281i	−0.853309	−	0.521406i	$-0.825408\pi$
$89$		−	92.8102i		−	1.04281i	0.853309	−	0.521406i	$-0.174592\pi$
$90$	−70.8655	+	2.01742i	−0.787394	+	0.0224158i
$91$		−	186.198i		−	2.04613i
$92$	4.17960	−	9.70682i	0.0454304	−	0.105509i
$93$	−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	0.113990	−	0.993482i	$-0.463637\pi$
$97$	−85.3107	−	85.3107i	−0.879492	−	0.879492i	−0.993482	+	0.113990i	$0.963637\pi$
$98$	−34.6812	−	180.912i	−0.353890	−	1.84604i
$99$	−28.4704			−0.287580
$100$	−99.8380	+	5.68906i	−0.998380	+	0.0568906i
$101$			20.4248i			0.202226i	0.994875	+	0.101113i	$0.0322404\pi$
$101$			20.4248i			0.202226i	−0.994875	+	0.101113i	$0.967760\pi$
$102$	2.79159	+	14.5622i	0.0273685	+	0.142766i
$103$	−38.9743	+	38.9743i	−0.378391	+	0.378391i	−0.870521	−	0.492130i	$-0.836218\pi$
$103$	−38.9743	+	38.9743i	−0.378391	+	0.378391i	0.492130	+	0.870521i	$0.336218\pi$
$104$	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	$-0.596524\pi$
$107$	70.1663	−	70.1663i	0.655760	−	0.655760i	0.954374	+	0.298614i	$0.0965243\pi$
$108$	35.1810	−	81.7053i	0.325750	−	0.756531i
$109$	−160.230			−1.47000			−0.735001	−	0.678066i	$-0.762818\pi$
$109$	−160.230			−1.47000			−0.735001	+	0.678066i	$0.762818\pi$
$110$	−40.1427	+	1.14280i	−0.364934	+	0.0103891i
$111$	43.3097			0.390178
$112$	189.986	+	5.27973i	1.69630	+	0.0471404i
$113$	9.77907	−	9.77907i	0.0865404	−	0.0865404i	−0.662511	−	0.749052i	$-0.730509\pi$
$113$	9.77907	−	9.77907i	0.0865404	−	0.0865404i	0.749052	+	0.662511i	$0.230509\pi$
$114$	−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
$118$	−99.4992	+	19.0742i	−0.843213	+	0.161645i
$119$		−	63.7116i		−	0.535391i
$120$	20.4120	−	51.3837i	0.170100	−	0.428197i
$121$	104.873			0.866715
$122$	−27.7349	−	144.677i	−0.227335	−	1.18588i
$123$	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	0.900229	−	0.435418i	$-0.143399\pi$
$127$	59.0310	+	59.0310i	0.464811	+	0.464811i	−0.435418	+	0.900229i	$0.643399\pi$
$128$	−31.0435	+	124.179i	−0.242527	+	0.970145i
$129$		−	33.5094i		−	0.259763i
$130$	−107.640	+	113.948i	−0.827996	+	0.876521i
$131$			144.850i			1.10572i	0.833274	+	0.552861i	$0.186464\pi$
$131$			144.850i			1.10572i	−0.833274	+	0.552861i	$0.813536\pi$
$132$	8.78113	−	20.3935i	0.0665237	−	0.154497i
$133$	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	0.920304	−	0.391203i	$-0.127941\pi$
$137$	72.4869	+	72.4869i	0.529101	+	0.529101i	−0.391203	+	0.920304i	$0.627941\pi$
$138$	−7.17341	+	1.37516i	−0.0519813	+	0.00996489i
$139$	55.4318			0.398790			0.199395	−	0.979919i	$-0.436102\pi$
$139$	55.4318			0.398790			0.199395	+	0.979919i	$0.436102\pi$
$140$	−127.709	+	200.329i	−0.912205	+	1.43092i
$141$		−	12.3358i		−	0.0874880i
$142$	153.952	−	29.5128i	1.08417	−	0.207837i
$143$	−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
$148$	49.5664	−	115.114i	0.334908	−	0.777800i
$149$	−65.9772			−0.442800			−0.221400	−	0.975183i	$-0.571063\pi$
$149$	−65.9772			−0.442800			−0.221400	+	0.975183i	$0.571063\pi$
$150$	41.9858	+	54.8967i	0.279905	+	0.365978i
$151$	188.113			1.24578			0.622891	−	0.782308i	$-0.285958\pi$
$151$	188.113			1.24578			0.622891	+	0.782308i	$0.285958\pi$
$152$	−107.621	+	68.7102i	−0.708031	+	0.452041i
$153$	−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	$-0.778367\pi$
$157$	−19.7604	+	19.7604i	−0.125862	+	0.125862i	0.641370	+	0.767232i	$0.278367\pi$
$158$	−11.9261	−	62.2119i	−0.0754818	−	0.393746i
$159$		−	77.9831i		−	0.490460i
$160$	−113.214	−	113.060i	−0.707586	−	0.706627i
$161$	31.3847			0.194936
$162$	64.9466	−	12.4504i	0.400905	−	0.0768542i
$163$	−27.8219	−	27.8219i	−0.170686	−	0.170686i	0.616595	−	0.787281i	$-0.288512\pi$
$163$	−27.8219	−	27.8219i	−0.170686	−	0.170686i	−0.787281	+	0.616595i	$0.788512\pi$
$164$	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	0.497670	−	0.867367i	$-0.334189\pi$
$167$	−61.7394	−	61.7394i	−0.369697	−	0.369697i	−0.867367	+	0.497670i	$0.834189\pi$
$168$	−70.6846	−	110.713i	−0.420742	−	0.659007i
$169$			76.7035i			0.453867i
$170$	−36.8312	+	38.9897i	−0.216654	+	0.229351i
$171$		−	113.151i		−	0.661702i
$172$	−89.0659	−	38.3503i	−0.517825	−	0.222967i
$173$	−6.43250	−	6.43250i	−0.0371821	−	0.0371821i	0.688271	−	0.725453i	$-0.258370\pi$
$173$	−6.43250	−	6.43250i	−0.0371821	−	0.0371821i	−0.725453	+	0.688271i	$0.758370\pi$
$174$	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
$178$	34.9474	+	182.301i	0.196334	+	1.02416i
$179$	−261.438			−1.46055			−0.730273	−	0.683155i	$-0.760607\pi$
$179$	−261.438			−1.46055			−0.730273	+	0.683155i	$0.760607\pi$
$180$	138.437	−	30.6469i	0.769093	−	0.170260i
$181$		−	264.352i		−	1.46051i	−0.683174	−	0.730255i	$-0.739401\pi$
$181$		−	264.352i		−	1.46051i	0.683174	−	0.730255i	$-0.260599\pi$
$182$	70.1121	+	365.736i	0.385231	+	2.00954i
$183$	−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
$188$	−32.7878	−	14.1179i	−0.174403	−	0.0750951i
$189$	264.175			1.39775
$190$	−4.54186	−	159.541i	−0.0239045	−	0.839689i
$191$	−298.972			−1.56530			−0.782650	−	0.622463i	$-0.786132\pi$
$191$	−298.972			−1.56530			−0.782650	+	0.622463i	$0.786132\pi$
$192$	83.0688	−	30.4190i	0.432650	−	0.158432i
$193$	−33.8808	+	33.8808i	−0.175548	+	0.175548i	−0.789412	−	0.613864i	$-0.789614\pi$
$193$	−33.8808	+	33.8808i	−0.175548	+	0.175548i	0.613864	+	0.789412i	$0.289614\pi$
$194$	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	$-0.678107\pi$
$197$	62.3903	−	62.3903i	0.316702	−	0.316702i	0.847499	+	0.530797i	$0.178107\pi$
$198$	55.9225	−	10.7204i	0.282437	−	0.0541436i
$199$		−	53.5973i		−	0.269333i	−0.990891	−	0.134666i	$-0.957004\pi$
$199$		−	53.5973i		−	0.269333i	0.990891	−	0.134666i	$-0.0429963\pi$
$200$	193.963	−	48.7683i	0.969815	−	0.243842i
$201$	−151.843			−0.755440
$202$	−7.69090	−	40.1191i	−0.0380738	−	0.198610i
$203$	−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
$208$	−250.702	−	6.96704i	−1.20530	−	0.0334954i
$209$		−	64.0959i		−	0.306679i
$210$	164.125	−	4.67237i	0.781549	−	0.0222494i
$211$			242.335i			1.14851i	0.818677	+	0.574254i	$0.194708\pi$
$211$			242.335i			1.14851i	−0.818677	+	0.574254i	$0.805292\pi$
$212$	−207.274	−	89.2488i	−0.977707	−	0.420985i
$213$	−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
$218$	314.730	−	60.3342i	1.44371	−	0.276762i
$219$	−89.9251			−0.410617
$220$	78.4194	−	17.3603i	0.356452	−	0.0789106i
$221$			84.0728i			0.380420i
$222$	−85.0704	+	16.3081i	−0.383200	+	0.0734601i
$223$	181.009	−	181.009i	0.811701	−	0.811701i	−0.173188	−	0.984889i	$-0.555407\pi$
$223$	181.009	−	181.009i	0.811701	−	0.811701i	0.984889	+	0.173188i	$0.0554068\pi$
$224$	−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	$-0.580614\pi$
$227$	162.883	−	162.883i	0.717545	−	0.717545i	0.968102	+	0.250557i	$0.0806136\pi$
$228$	81.0509	+	34.8992i	0.355486	+	0.153067i
$229$	285.470			1.24660			0.623298	−	0.781984i	$-0.285792\pi$
$229$	285.470			1.24660			0.623298	+	0.781984i	$0.285792\pi$
$230$	−19.2066	−	18.1433i	−0.0835069	−	0.0788839i
$231$	65.9377			0.285445
$232$	3.15635	−	2.01517i	0.0136050	−	0.00868606i
$233$	178.054	−	178.054i	0.764180	−	0.764180i	−0.212895	−	0.977075i	$-0.568289\pi$
$233$	178.054	−	178.054i	0.764180	−	0.764180i	0.977075	+	0.212895i	$0.0682893\pi$
$234$	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
$238$	23.9904	+	125.144i	0.100800	+	0.525817i
$239$			452.291i			1.89243i	0.323540	+	0.946214i	$0.395127\pi$
$239$			452.291i			1.89243i	−0.323540	+	0.946214i	$0.604873\pi$
$240$	−20.7455	+	108.616i	−0.0864395	+	0.452565i
$241$	−83.8188			−0.347796			−0.173898	−	0.984764i	$-0.555636\pi$
$241$	−83.8188			−0.347796			−0.173898	+	0.984764i	$0.555636\pi$
$242$	−205.994	+	39.4894i	−0.851216	+	0.163179i
$243$	−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
$248$	116.799	−	74.5698i	0.470962	−	0.300685i
$249$			166.151i			0.667272i
$250$	−72.3083	+	239.315i	−0.289233	+	0.957259i
$251$			343.010i			1.36657i	0.730150	+	0.683287i	$0.239450\pi$
$251$			343.010i			1.36657i	−0.730150	+	0.683287i	$0.760550\pi$
$252$	133.218	−	309.390i	0.528644	−	1.22774i
$253$	−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	0.957521	−	0.288363i	$-0.0931108\pi$
$257$	171.974	+	171.974i	0.669159	+	0.669159i	−0.288363	+	0.957521i	$0.593111\pi$
$258$	12.6179	+	65.8204i	0.0489065	+	0.255118i
$259$	372.195			1.43705
$260$	168.522	−	264.351i	0.648163	−	1.01674i
$261$			3.31855i			0.0127147i
$262$	−54.5426	−	284.518i	−0.208178	−	1.08595i
$263$	−109.775	+	109.775i	−0.417396	+	0.417396i	−0.884305	−	0.466909i	$-0.845367\pi$
$263$	−109.775	+	109.775i	−0.417396	+	0.417396i	0.466909	+	0.884305i	$0.345367\pi$
$264$	−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
$268$	−173.779	+	403.590i	−0.648430	+	1.50593i
$269$	−126.610			−0.470668			−0.235334	−	0.971915i	$-0.575618\pi$
$269$	−126.610			−0.470668			−0.235334	+	0.971915i	$0.575618\pi$
$270$	−161.668	−	152.718i	−0.598769	−	0.565621i
$271$	341.904			1.26164			0.630819	−	0.775930i	$-0.282719\pi$
$271$	341.904			1.26164			0.630819	+	0.775930i	$0.282719\pi$
$272$	−85.7832	−	2.38392i	−0.315379	−	0.00876443i
$273$	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	$-0.854096\pi$
$277$	−125.838	+	125.838i	−0.454287	+	0.454287i	0.442487	+	0.896775i	$0.354096\pi$
$278$	−108.881	+	20.8727i	−0.391659	+	0.0750816i
$279$			122.800i			0.440145i
$280$	175.416	−	441.582i	0.626487	−	1.57708i
$281$	−375.014			−1.33457			−0.667285	−	0.744802i	$-0.732544\pi$
$281$	−375.014			−1.33457			−0.667285	+	0.744802i	$0.732544\pi$
$282$	4.64501	+	24.2304i	0.0164717	+	0.0859234i
$283$	−289.819	−	289.819i	−1.02409	−	1.02409i	−0.999702	−	0.0243913i	$-0.992235\pi$
$283$	−289.819	−	289.819i	−1.02409	−	1.02409i	−0.0243913	−	0.999702i	$-0.507765\pi$
$284$	−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
$288$	184.138	+	132.511i	0.639369	+	0.460107i
$289$		−	260.233i		−	0.900459i
$290$	0.133206	+	4.67909i	0.000459331	+	0.0161348i
$291$		−	166.764i		−	0.573071i
$292$	−102.916	+	239.015i	−0.352452	+	0.818544i
$293$	254.820	+	254.820i	0.869693	+	0.869693i	0.992438	−	0.122745i	$-0.0391698\pi$
$293$	254.820	+	254.820i	0.869693	+	0.869693i	−0.122745	+	0.992438i	$0.539170\pi$
$294$	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
$298$	129.595	−	24.8435i	0.434881	−	0.0833674i
$299$	−41.4148			−0.138511
$300$	−103.141	−	92.0203i	−0.343804	−	0.306734i
$301$		−	287.974i		−	0.956724i
$302$	−369.498	+	70.8334i	−1.22350	+	0.234548i
$303$	−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	$-0.631471\pi$
$307$	157.959	−	157.959i	0.514526	−	0.514526i	0.915910	+	0.401384i	$0.131471\pi$
$308$	75.4633	−	175.258i	0.245011	−	0.569020i
$309$	−76.1861			−0.246557
$310$	4.92919	+	173.146i	0.0159006	+	0.558537i
$311$	288.646			0.928122			0.464061	−	0.885803i	$-0.346392\pi$
$311$	288.646			0.928122			0.464061	+	0.885803i	$0.346392\pi$
$312$	93.2743	+	146.095i	0.298956	+	0.468254i
$313$	138.120	−	138.120i	0.441279	−	0.441279i	−0.451163	−	0.892442i	$-0.648991\pi$
$313$	138.120	−	138.120i	0.441279	−	0.441279i	0.892442	+	0.451163i	$0.148991\pi$
$314$	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	$-0.693240\pi$
$317$	79.5178	−	79.5178i	0.250845	−	0.250845i	0.821317	+	0.570472i	$0.193240\pi$
$318$	29.3643	+	153.177i	0.0923405	+	0.481688i
$319$			1.87984i			0.00589290i
$320$	264.951	+	179.447i	0.827971	+	0.560771i
$321$	137.160			0.427289
$322$	−61.6470	+	11.8178i	−0.191450	+	0.0367013i
$323$	−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
$328$	−250.011	+	159.619i	−0.762229	+	0.486643i
$329$		−	106.012i		−	0.322224i
$330$	−40.3520	−	38.1181i	−0.122279	−	0.115509i
$331$			515.252i			1.55665i	0.627859	+	0.778327i	$0.283931\pi$
$331$			515.252i			1.55665i	−0.627859	+	0.778327i	$0.716069\pi$
$332$	441.617	+	190.153i	1.33017	+	0.572751i
$333$	−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	0.916500	−	0.400034i	$-0.131002\pi$
$337$	174.049	+	174.049i	0.516466	+	0.516466i	−0.400034	+	0.916500i	$0.631002\pi$
$338$	−28.8825	−	150.664i	−0.0854510	−	0.445750i
$339$	19.1159			0.0563892
$340$	57.6636	−	90.4535i	0.169599	−	0.266040i
$341$			69.5620i			0.203994i
$342$	42.6066	+	222.255i	0.124581	+	0.649868i
$343$	−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	$-0.779238\pi$
$347$	−45.0127	+	45.0127i	−0.129720	+	0.129720i	0.639266	+	0.768986i	$0.279238\pi$
$348$	−2.37710	−	1.02354i	−0.00683074	−	0.00294121i
$349$	57.5715			0.164961			0.0824806	−	0.996593i	$-0.473716\pi$
$349$	57.5715			0.164961			0.0824806	+	0.996593i	$0.473716\pi$
$350$	360.818	+	471.772i	1.03091	+	1.34792i
$351$	−348.601			−0.993166
$352$	104.308	+	75.0626i	0.296329	+	0.213246i
$353$	−452.340	+	452.340i	−1.28142	+	1.28142i	−0.341553	+	0.939863i	$0.610953\pi$
$353$	−452.340	+	452.340i	−1.28142	+	1.28142i	−0.939863	+	0.341553i	$0.889047\pi$
$354$	−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
$358$	513.525	−	98.4435i	1.43443	−	0.274982i
$359$		−	492.146i		−	1.37088i	−0.728129	−	0.685440i	$-0.759610\pi$
$359$		−	492.146i		−	1.37088i	0.728129	−	0.685440i	$-0.240390\pi$
$360$	−260.382	+	112.325i	−0.723283	+	0.312015i
$361$	−106.261			−0.294352
$362$	99.5411	+	519.250i	0.274975	+	1.43439i
$363$	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	0.710973	−	0.703219i	$-0.248255\pi$
$367$	2.84592	+	2.84592i	0.00775455	+	0.00775455i	−0.703219	+	0.710973i	$0.748255\pi$
$368$	1.17434	−	42.2574i	0.00319113	−	0.114830i
$369$		−	262.858i		−	0.712353i
$370$	−227.773	−	215.163i	−0.615603	−	0.581523i
$371$		−	670.172i		−	1.80639i
$372$	−87.9629	−	37.8754i	−0.236459	−	0.101816i
$373$	−309.505	−	309.505i	−0.829773	−	0.829773i	0.157712	−	0.987485i	$-0.449588\pi$
$373$	−309.505	−	309.505i	−0.829773	−	0.829773i	−0.987485	+	0.157712i	$0.949588\pi$
$374$	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
$378$	−518.901	+	99.4742i	−1.37275	+	0.263159i
$379$	−298.281			−0.787022			−0.393511	−	0.919320i	$-0.628740\pi$
$379$	−298.281			−0.787022			−0.393511	+	0.919320i	$0.628740\pi$
$380$	68.9959	+	311.665i	0.181568	+	0.820172i
$381$			115.393i			0.302868i
$382$	587.251	−	112.577i	1.53731	−	0.294704i
$383$	507.746	−	507.746i	1.32571	−	1.32571i	0.416633	−	0.909075i	$-0.363210\pi$
$383$	507.746	−	507.746i	1.32571	−	1.32571i	0.909075	−	0.416633i	$-0.136790\pi$
$384$	−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
$388$	−443.247	−	190.855i	−1.14239	−	0.491894i
$389$	506.443			1.30191			0.650956	−	0.759116i	$-0.274368\pi$
$389$	506.443			1.30191			0.650956	+	0.759116i	$0.274368\pi$
$390$	−216.577	+	6.16559i	−0.555326	+	0.0158092i
$391$	−14.1710			−0.0362429
$392$	−396.505	−	621.045i	−1.01149	−	1.58430i
$393$	−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	$-0.705714\pi$
$397$	77.8603	−	77.8603i	0.196122	−	0.196122i	0.798335	+	0.602213i	$0.205714\pi$
$398$	20.1819	+	105.278i	0.0507082	+	0.264516i
$399$			262.059i			0.656789i
$400$	−362.625	+	168.829i	−0.906563	+	0.422071i
$401$	366.451			0.913844			0.456922	−	0.889507i	$-0.348952\pi$
$401$	366.451			0.913844			0.456922	+	0.889507i	$0.348952\pi$
$402$	298.256	−	57.1761i	0.741930	−	0.142229i
$403$	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
$408$	31.9158	+	49.9897i	0.0782250	+	0.122524i
$409$			390.914i			0.955779i	0.878420	+	0.477889i	$0.158598\pi$
$409$			390.914i			0.955779i	−0.878420	+	0.477889i	$0.841402\pi$
$410$	−10.5511	−	370.625i	−0.0257344	−	0.903965i
$411$			141.696i			0.344759i
$412$	−87.1922	+	202.498i	−0.211632	+	0.491499i
$413$	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
$418$	24.1351	+	125.899i	0.0577395	+	0.301195i
$419$	−356.953			−0.851917			−0.425959	−	0.904743i	$-0.640063\pi$
$419$	−356.953			−0.851917			−0.425959	+	0.904743i	$0.640063\pi$
$420$	−320.621	+	70.9785i	−0.763383	+	0.168996i
$421$		−	174.212i		−	0.413806i	−0.978361	−	0.206903i	$-0.933661\pi$
$421$		−	174.212i		−	0.413806i	0.978361	−	0.206903i	$-0.0663385\pi$
$422$	−91.2505	−	476.003i	−0.216233	−	1.12797i
$423$	−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
$428$	156.974	−	364.562i	0.366762	−	0.851779i
$429$	−87.0104			−0.202821
$430$	−166.476	+	176.232i	−0.387152	+	0.409842i
$431$	48.7663			0.113147			0.0565734	−	0.998398i	$-0.481983\pi$
$431$	48.7663			0.113147			0.0565734	+	0.998398i	$0.481983\pi$
$432$	9.88476	−	355.693i	0.0228814	−	0.823364i
$433$	215.414	−	215.414i	0.497492	−	0.497492i	−0.413165	−	0.910656i	$-0.635577\pi$
$433$	215.414	−	215.414i	0.497492	−	0.497492i	0.910656	+	0.413165i	$0.135577\pi$
$434$	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
$438$	176.634	−	33.8610i	0.403274	−	0.0773082i
$439$		−	466.896i		−	1.06354i	−0.846887	−	0.531772i	$-0.821526\pi$
$439$		−	466.896i		−	1.06354i	0.846887	−	0.531772i	$-0.178474\pi$
$440$	−147.497	+	63.6283i	−0.335220	+	0.144610i
$441$	652.959			1.48063
$442$	−31.6573	−	165.139i	−0.0716229	−	0.373617i
$443$	423.624	+	423.624i	0.956263	+	0.956263i	0.999083	−	0.0428200i	$-0.0136342\pi$
$443$	423.624	+	423.624i	0.956263	+	0.956263i	−0.0428200	+	0.999083i	$0.513634\pi$
$444$	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
$448$	713.878	−	261.415i	1.59348	−	0.583515i
$449$			255.859i			0.569841i	0.958551	+	0.284921i	$0.0919673\pi$
$449$			255.859i			0.569841i	−0.958551	+	0.284921i	$0.908033\pi$
$450$	46.8239	−	351.365i	0.104053	−	0.780810i
$451$		−	148.900i		−	0.330155i
$452$	21.8775	−	50.8089i	0.0484015	−	0.112409i
$453$	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	0.762791	−	0.646645i	$-0.223829\pi$
$457$	53.0785	+	53.0785i	0.116145	+	0.116145i	−0.646645	+	0.762791i	$0.723829\pi$
$458$	−560.731	+	107.493i	−1.22430	+	0.234701i
$459$	−119.281			−0.259872
$460$	44.5580	+	28.4055i	0.0968652	+	0.0617510i
$461$			395.425i			0.857755i	0.903363	+	0.428877i	$0.141091\pi$
$461$			395.425i			0.857755i	−0.903363	+	0.428877i	$0.858909\pi$
$462$	−129.517	+	24.8286i	−0.280340	+	0.0537417i
$463$	87.9974	−	87.9974i	0.190059	−	0.190059i	−0.605662	−	0.795722i	$-0.707092\pi$
$463$	87.9974	−	87.9974i	0.190059	−	0.190059i	0.795722	+	0.605662i	$0.207092\pi$
$464$	−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	0.167717	−	0.985835i	$-0.446361\pi$
$467$	538.709	−	538.709i	1.15355	−	1.15355i	0.985835	−	0.167717i	$-0.0536394\pi$
$468$	−175.793	+	408.266i	−0.375626	+	0.872364i
$469$	−1304.91			−2.78233
$470$	−61.2845	+	64.8761i	−0.130393	+	0.138034i
$471$	−38.6272			−0.0820111
$472$	−341.566	+	218.072i	−0.723656	+	0.462017i
$473$	−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
$478$	−170.309	−	888.404i	−0.356294	−	1.85859i
$479$			52.4501i			0.109499i	0.998500	+	0.0547496i	$0.0174361\pi$
$479$			52.4501i			0.109499i	−0.998500	+	0.0547496i	$0.982564\pi$
$480$	−0.149874	−	221.158i	−0.000312237	−	0.460746i
$481$	−491.143			−1.02109
$482$	164.640	−	31.5617i	0.341576	−	0.0654807i
$483$	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	0.909089	−	0.416602i	$-0.136779\pi$
$487$	239.841	+	239.841i	0.492486	+	0.492486i	−0.416602	+	0.909089i	$0.636779\pi$
$488$	−317.089	−	496.656i	−0.649772	−	1.01774i
$489$		−	54.3856i		−	0.111218i
$490$	920.660	−	26.2097i	1.87890	−	0.0534891i
$491$		−	170.797i		−	0.347855i	−0.984758	−	0.173927i	$-0.944354\pi$
$491$		−	170.797i		−	0.347855i	0.984758	−	0.173927i	$-0.0556458\pi$
$492$	188.287	+	81.0734i	0.382698	+	0.164783i
$493$	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
$498$	−62.5635	−	326.359i	−0.125629	−	0.655338i
$499$	878.181			1.75988			0.879941	−	0.475083i	$-0.157582\pi$
$499$	878.181			1.75988			0.879941	+	0.475083i	$0.157582\pi$
$500$	51.9172	−	497.297i	0.103834	−	0.994595i
$501$		−	120.687i		−	0.240892i
$502$	−129.159	−	673.751i	−0.257289	−	1.34213i
$503$	−476.137	+	476.137i	−0.946595	+	0.946595i	−0.998645	−	0.0520493i	$-0.983425\pi$
$503$	−476.137	+	476.137i	−0.946595	+	0.946595i	0.0520493	+	0.998645i	$0.483425\pi$
$504$	−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
$508$	306.706	+	132.063i	0.603752	+	0.259966i
$509$	−176.377			−0.346516			−0.173258	−	0.984876i	$-0.555429\pi$
$509$	−176.377			−0.346516			−0.173258	+	0.984876i	$0.555429\pi$
$510$	−74.1065	+	2.10969i	−0.145307	+	0.00413665i
$511$	−772.799			−1.51233
$512$	68.3206	+	507.421i	0.133439	+	0.991057i
$513$	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
$518$	−731.079	+	140.149i	−1.41135	+	0.270558i
$519$		−	12.5741i		−	0.0242276i
$520$	−231.477	+	582.704i	−0.445148	+	1.12058i
$521$	−209.641			−0.402381			−0.201191	−	0.979552i	$-0.564481\pi$
$521$	−209.641			−0.402381			−0.201191	+	0.979552i	$0.564481\pi$
$522$	−1.24959	−	6.51840i	−0.00239385	−	0.0124874i
$523$	115.800	+	115.800i	0.221415	+	0.221415i	0.809094	−	0.587679i	$-0.199958\pi$
$523$	115.800	+	115.800i	0.221415	+	0.221415i	−0.587679	+	0.809094i	$0.699958\pi$
$524$	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
$528$	2.46722	−	88.7806i	0.00467277	−	0.168145i
$529$			522.019i			0.986804i
$530$	−387.421	+	410.126i	−0.730984	+	0.773823i
$531$		−	359.118i		−	0.676305i
$532$	696.536	+	299.917i	1.30928	+	0.563754i
$533$	−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
$538$	248.691	−	47.6744i	0.462251	−	0.0886142i
$539$	369.877			0.686229
$540$	375.058	+	239.098i	0.694552	+	0.442773i
$541$		−	299.624i		−	0.553833i	−0.960894	−	0.276917i	$-0.910687\pi$
$541$		−	299.624i		−	0.553833i	0.960894	−	0.276917i	$-0.0893126\pi$
$542$	−671.580	+	128.743i	−1.23908	+	0.237533i
$543$	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	$-0.868776\pi$
$547$	−282.004	+	282.004i	−0.515546	+	0.515546i	0.400674	+	0.916220i	$0.368776\pi$
$548$	376.618	+	162.166i	0.687260	+	0.295923i
$549$	522.178			0.951143
$550$	26.5241	−	199.035i	0.0482256	−	0.361883i
$551$	−7.47111			−0.0135592
$552$	−24.6253	+	15.7219i	−0.0446110	+	0.0284818i
$553$	−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	$-0.863643\pi$
$557$	−275.294	+	275.294i	−0.494245	+	0.494245i	0.415396	+	0.909641i	$0.363643\pi$
$558$	−46.2401	−	241.209i	−0.0828676	−	0.432274i
$559$			380.006i			0.679796i
$560$	−178.283	+	933.422i	−0.318362	+	1.66682i
$561$	−29.7725			−0.0530704
$562$	736.616	−	141.210i	1.31070	−	0.251264i
$563$	−122.106	−	122.106i	−0.216884	−	0.216884i	0.590300	−	0.807184i	$-0.299009\pi$
$563$	−122.106	−	122.106i	−0.216884	−	0.216884i	−0.807184	+	0.590300i	$0.799009\pi$
$564$	−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
$568$	528.493	−	337.415i	0.930445	−	0.594041i
$569$		−	639.803i		−	1.12443i	−0.826990	−	0.562217i	$-0.809949\pi$
$569$		−	639.803i		−	1.12443i	0.826990	−	0.562217i	$-0.190051\pi$
$570$	151.494	−	160.373i	0.265780	−	0.281356i
$571$		−	692.275i		−	1.21239i	−0.795316	−	0.606195i	$-0.792695\pi$
$571$		−	692.275i		−	1.21239i	0.795316	−	0.606195i	$-0.207305\pi$
$572$	−99.5802	+	231.268i	−0.174091	+	0.404315i
$573$	−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	0.395116	−	0.918631i	$-0.370704\pi$
$577$	−302.068	−	302.068i	−0.523515	−	0.523515i	−0.918631	+	0.395116i	$0.870704\pi$
$578$	97.9898	+	511.158i	0.169532	+	0.884356i
$579$	−66.2295			−0.114386
$580$	−2.02354	−	9.14066i	−0.00348887	−	0.0157598i
$581$			1427.87i			2.45760i
$582$	62.7943	+	327.563i	0.107894	+	0.562822i
$583$	−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	$-0.770342\pi$
$587$	−53.0146	+	53.0146i	−0.0903144	+	0.0903144i	0.660506	+	0.750821i	$0.270342\pi$
$588$	−201.392	+	467.719i	−0.342504	+	0.795440i
$589$	−276.463			−0.469377
$590$	−14.4149	−	506.350i	−0.0244321	−	0.858220i
$591$	121.959			0.206361
$592$	13.9266	−	501.135i	0.0235247	−	0.846512i
$593$	−401.453	+	401.453i	−0.676986	+	0.676986i	−0.959317	−	0.282331i	$-0.908892\pi$
$593$	−401.453	+	401.453i	−0.676986	+	0.676986i	0.282331	+	0.959317i	$0.408892\pi$
$594$	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
$598$	81.3484	−	15.5946i	0.136034	−	0.0260779i
$599$		−	152.120i		−	0.253956i	−0.991906	−	0.126978i	$-0.959472\pi$
$599$		−	152.120i		−	0.253956i	0.991906	−	0.126978i	$-0.0405277\pi$
$600$	237.243	+	141.912i	0.395405	+	0.236520i
$601$	743.521			1.23714			0.618570	−	0.785730i	$-0.287712\pi$
$601$	743.521			1.23714			0.618570	+	0.785730i	$0.287712\pi$
$602$	108.436	+	565.648i	0.180126	+	0.939614i
$603$	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	0.993545	+	0.113437i	$0.0361859\pi$
$607$	671.938	+	671.938i	1.10698	+	1.10698i	0.113437	+	0.993545i	$0.463814\pi$
$608$	−298.324	+	414.554i	−0.490665	+	0.681833i
$609$		−	7.68579i		−	0.0126203i
$610$	736.261	−	20.9601i	1.20699	−	0.0343609i
$611$			139.891i			0.228955i
$612$	−60.1513	+	139.697i	−0.0982864	+	0.228263i
$613$	232.793	+	232.793i	0.379761	+	0.379761i	0.871016	−	0.491255i	$-0.163462\pi$
$613$	232.793	+	232.793i	0.379761	+	0.379761i	−0.491255	+	0.871016i	$0.663462\pi$
$614$	−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	0.929173	+	0.369645i	$0.120521\pi$
$617$	801.371	+	801.371i	1.29882	+	1.29882i	0.369645	+	0.929173i	$0.379479\pi$
$618$	149.647	−	28.6876i	0.242148	−	0.0464201i
$619$	111.616			0.180317			0.0901583	−	0.995927i	$-0.471263\pi$
$619$	111.616			0.180317			0.0901583	+	0.995927i	$0.471263\pi$
$620$	−74.8798	−	338.244i	−0.120774	−	0.545555i
$621$		−	58.7588i		−	0.0946197i
$622$	−566.968	+	108.689i	−0.911524	+	0.174741i
$623$	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
$628$	−44.2075	+	102.669i	−0.0703940	+	0.163485i
$629$	−168.055			−0.267178
$630$	−612.180	−	578.289i	−0.971714	−	0.917920i
$631$	−24.4343			−0.0387231			−0.0193615	−	0.999813i	$-0.506163\pi$
$631$	−24.4343			−0.0387231			−0.0193615	+	0.999813i	$0.506163\pi$
$632$	−136.350	−	213.564i	−0.215743	−	0.337918i
$633$	−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
$638$	−0.707846	−	3.69244i	−0.00110948	−	0.00578752i
$639$			555.651i			0.869563i
$640$	−587.995	−	252.709i	−0.918742	−	0.394858i
$641$	416.342			0.649519			0.324759	−	0.945797i	$-0.394717\pi$
$641$	416.342			0.649519			0.324759	+	0.945797i	$0.394717\pi$
$642$	−269.414	+	51.6470i	−0.419647	+	0.0804471i
$643$	−86.0053	−	86.0053i	−0.133756	−	0.133756i	0.637059	−	0.770815i	$-0.280151\pi$
$643$	−86.0053	−	86.0053i	−0.133756	−	0.133756i	−0.770815	+	0.637059i	$0.780151\pi$
$644$	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	0.411801	−	0.911274i	$-0.364900\pi$
$647$	−323.159	−	323.159i	−0.499472	−	0.499472i	−0.911274	+	0.411801i	$0.864900\pi$
$648$	222.952	−	142.343i	0.344062	−	0.219666i
$649$		−	203.427i		−	0.313447i
$650$	−476.130	−	622.542i	−0.732508	−	0.957757i
$651$		−	284.407i		−	0.436878i
$652$	−144.553	−	62.2423i	−0.221708	−	0.0954637i
$653$	−635.931	−	635.931i	−0.973860	−	0.973860i	0.0258069	−	0.999667i	$-0.491784\pi$
$653$	−635.931	−	635.931i	−0.973860	−	0.973860i	−0.999667	+	0.0258069i	$0.991784\pi$
$654$	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
$658$	39.9183	+	208.231i	0.0606661	+	0.316461i
$659$	−1040.90			−1.57952			−0.789759	−	0.613417i	$-0.789794\pi$
$659$	−1040.90			−1.57952			−0.789759	+	0.613417i	$0.789794\pi$
$660$	93.6141	+	59.6785i	0.141840	+	0.0904219i
$661$			325.566i			0.492536i	0.969202	+	0.246268i	$0.0792043\pi$
$661$			325.566i			0.492536i	−0.969202	+	0.246268i	$0.920796\pi$
$662$	−194.017	−	1012.08i	−0.293077	−	1.52882i
$663$	−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
$668$	−320.778	−	138.122i	−0.480206	−	0.206769i
$669$	353.833			0.528899
$670$	798.570	+	754.361i	1.19190	+	1.12591i
$671$	295.795			0.440827
$672$	−426.467	−	306.897i	−0.634623	−	0.456692i
$673$	469.880	−	469.880i	0.698187	−	0.698187i	−0.265832	−	0.964019i	$-0.585647\pi$
$673$	469.880	−	469.880i	0.698187	−	0.698187i	0.964019	+	0.265832i	$0.0856468\pi$
$674$	−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	$-0.599559\pi$
$677$	435.841	−	435.841i	0.643783	−	0.643783i	0.951483	+	0.307700i	$0.0995595\pi$
$678$	−37.5481	+	7.19804i	−0.0553807	+	0.0106166i
$679$		−	1433.13i		−	2.11065i
$680$	−79.2048	+	199.385i	−0.116478	+	0.293213i
$681$	318.400			0.467548
$682$	−26.1934	−	136.636i	−0.0384067	−	0.200346i
$683$	−311.279	−	311.279i	−0.455752	−	0.455752i	0.441506	−	0.897258i	$-0.354444\pi$
$683$	−311.279	−	311.279i	−0.455752	−	0.455752i	−0.897258	+	0.441506i	$0.854444\pi$
$684$	−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
$688$	−387.737	−	10.7752i	−0.563571	−	0.0156617i
$689$			884.348i			1.28352i
$690$	−1.03925	−	36.5054i	−0.00150616	−	0.0529064i
$691$			726.094i			1.05079i	0.850859	+	0.525394i	$0.176082\pi$
$691$			726.094i			1.05079i	−0.850859	+	0.525394i	$0.823918\pi$
$692$	−33.4212	−	14.3906i	−0.0482965	−	0.0207957i
$693$	−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
$698$	−113.084	+	21.6784i	−0.162011	+	0.0310578i
$699$	348.056			0.497934
$700$	−886.375	−	790.805i	−1.26625	−	1.12972i
$701$		−	286.170i		−	0.408232i	−0.978947	−	0.204116i	$-0.934568\pi$
$701$		−	286.170i		−	0.408232i	0.978947	−	0.204116i	$-0.0654319\pi$
$702$	684.734	−	131.265i	0.975405	−	0.186987i
$703$	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
$708$	257.239	+	110.763i	0.363331	+	0.156445i
$709$	−36.2751			−0.0511638			−0.0255819	−	0.999673i	$-0.508144\pi$
$709$	−36.2751			−0.0511638			−0.0255819	+	0.999673i	$0.508144\pi$
$710$	22.3037	+	783.457i	0.0314137	+	1.10346i
$711$	224.539			0.315807
$712$	399.548	+	625.812i	0.561163	+	0.878949i
$713$	−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
$718$	185.316	+	966.689i	0.258100	+	1.34636i
$719$		−	103.315i		−	0.143693i	−0.997416	−	0.0718464i	$-0.977111\pi$
$719$		−	103.315i		−	0.143693i	0.997416	−	0.0718464i	$-0.0228891\pi$
$720$	469.155	−	318.679i	0.651604	−	0.442610i
$721$	−654.729			−0.908085
$722$	208.721	−	40.0122i	0.289088	−	0.0554186i
$723$	−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	0.443993	−	0.896030i	$-0.353561\pi$
$727$	−328.631	−	328.631i	−0.452037	−	0.452037i	−0.896030	+	0.443993i	$0.853561\pi$
$728$	801.581	+	1255.52i	1.10107	+	1.72461i
$729$		−	42.2524i		−	0.0579594i
$730$	472.931	+	446.749i	0.647851	+	0.611985i
$731$			130.027i			0.177876i
$732$	−161.055	+	374.040i	−0.220021	+	0.510983i
$733$	676.211	+	676.211i	0.922525	+	0.922525i	0.997207	−	0.0746826i	$-0.0237944\pi$
$733$	676.211	+	676.211i	0.922525	+	0.922525i	−0.0746826	+	0.997207i	$0.523794\pi$
$734$	−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
$738$	98.9785	+	516.315i	0.134117	+	0.699614i
$739$	1456.68			1.97115			0.985576	−	0.169235i	$-0.0541296\pi$
$739$	1456.68			1.97115			0.985576	+	0.169235i	$0.0541296\pi$
$740$	528.419	+	336.864i	0.714079	+	0.455222i
$741$		−	345.809i		−	0.466679i
$742$	252.351	+	1316.37i	0.340096	+	1.77409i
$743$	−544.329	+	544.329i	−0.732610	+	0.732610i	−0.971136	−	0.238526i	$-0.923336\pi$
$743$	−544.329	+	544.329i	−0.732610	+	0.732610i	0.238526	+	0.971136i	$0.423336\pi$
$744$	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
$748$	−34.0735	+	79.1333i	−0.0455528	+	0.105793i
$749$	1178.72			1.57373
$750$	−304.577	+	163.230i	−0.406103	+	0.217640i
$751$	−789.079			−1.05070			−0.525352	−	0.850885i	$-0.676066\pi$
$751$	−789.079			−1.05070			−0.525352	+	0.850885i	$0.676066\pi$
$752$	−142.737	−	3.96668i	−0.189810	−	0.00527485i
$753$	−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	$-0.693127\pi$
$757$	190.261	−	190.261i	0.251336	−	0.251336i	0.821518	+	0.570182i	$0.193127\pi$
$758$	585.894	−	112.317i	0.772947	−	0.148175i
$759$		−	14.6661i		−	0.0193230i
$760$	−252.881	−	586.203i	−0.332738	−	0.771320i
$761$	−467.711			−0.614600			−0.307300	−	0.951613i	$-0.599425\pi$
$761$	−467.711			−0.614600			−0.307300	+	0.951613i	$0.599425\pi$
$762$	−43.4507	−	226.658i	−0.0570219	−	0.297451i
$763$	−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
$768$	263.722	−	235.930i	0.343388	−	0.307200i
$769$			174.539i			0.226969i	0.993540	+	0.113485i	$0.0362012\pi$
$769$			174.539i			0.226969i	−0.993540	+	0.113485i	$0.963799\pi$
$770$	−346.778	−	327.580i	−0.450361	−	0.425429i
$771$			336.171i			0.436019i
$772$	−75.7972	+	176.034i	−0.0981829	+	0.228023i
$773$	−180.738	−	180.738i	−0.233814	−	0.233814i	0.580469	−	0.814283i	$-0.302869\pi$
$773$	−180.738	−	180.738i	−0.233814	−	0.233814i	−0.814283	+	0.580469i	$0.802869\pi$
$774$	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
$778$	−994.773	+	190.700i	−1.27863	+	0.245115i
$779$	591.778			0.759664
$780$	423.086	−	93.6621i	0.542418	−	0.120080i
$781$			314.756i			0.403017i
$782$	27.8351	−	5.33603i	0.0355948	−	0.00682357i
$783$	−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	$-0.923824\pi$
$787$	−578.023	+	578.023i	−0.734464	+	0.734464i	0.237037	+	0.971501i	$0.423824\pi$
$788$	139.578	−	324.160i	0.177129	−	0.411370i
$789$	−214.586			−0.271972
$790$	316.595	−	9.01295i	0.400754	−	0.0114088i
$791$	164.279			0.207685
$792$	191.974	−	122.565i	0.242391	−	0.154754i
$793$	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	$-0.841848\pi$
$797$	−320.738	+	320.738i	−0.402432	+	0.402432i	0.476657	+	0.879089i	$0.341848\pi$
$798$	−98.6775	−	514.745i	−0.123656	−	0.645044i
$799$			47.8668i			0.0599084i
$800$	648.708	−	468.164i	0.810885	−	0.585205i
$801$	−657.970			−0.821436
$802$	−719.796	+	137.986i	−0.897501	+	0.172053i
$803$	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
$808$	−87.9289	−	137.723i	−0.108823	−	0.170449i
$809$		−	764.477i		−	0.944966i	−0.881340	−	0.472483i	$-0.843358\pi$
$809$		−	764.477i		−	0.944966i	0.881340	−	0.472483i	$-0.156642\pi$
$810$	9.40914	+	330.512i	0.0116162	+	0.408040i
$811$			189.765i			0.233989i	0.993133	+	0.116995i	$0.0373260\pi$
$811$			189.765i			0.233989i	−0.993133	+	0.116995i	$0.962674\pi$
$812$	−20.4283	−	8.79611i	−0.0251580	−	0.0108326i
$813$	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
$818$	−147.197	−	767.845i	−0.179948	−	0.938686i
$819$	−1320.03			−1.61176
$820$	160.283	+	724.022i	0.195467	+	0.882954i
$821$		−	1526.85i		−	1.85974i	−0.367884	−	0.929872i	$-0.619918\pi$
$821$		−	1526.85i		−	1.85974i	0.367884	−	0.929872i	$-0.380082\pi$
$822$	−53.3551	−	278.324i	−0.0649089	−	0.338593i
$823$	23.3976	−	23.3976i	0.0284297	−	0.0284297i	−0.692749	−	0.721179i	$-0.743601\pi$
$823$	23.3976	−	23.3976i	0.0284297	−	0.0284297i	0.721179	+	0.692749i	$0.243601\pi$
$824$	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	0.0621932	−	0.998064i	$-0.480190\pi$
$827$	876.833	−	876.833i	1.06026	−	1.06026i	0.998064	−	0.0621932i	$-0.0198095\pi$
$828$	−68.8157	−	29.6309i	−0.0831108	−	0.0357862i
$829$	−518.022			−0.624876			−0.312438	−	0.949938i	$-0.601146\pi$
$829$	−518.022			−0.624876			−0.312438	+	0.949938i	$0.601146\pi$
$830$	825.439	−	873.814i	0.994505	−	1.05279i
$831$	−245.985			−0.296010
$832$	−942.022	+	344.959i	−1.13224	+	0.414614i
$833$	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
$838$	701.140	−	134.410i	0.836682	−	0.160393i
$839$			1666.89i			1.98676i	0.114858	+	0.993382i	$0.463359\pi$
$839$			1666.89i			1.98676i	−0.114858	+	0.993382i	$0.536641\pi$
$840$	603.048	−	260.147i	0.717914	−	0.309699i
$841$	−840.781			−0.999739
$842$	65.5991	+	342.194i	0.0779087	+	0.406406i
$843$	−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
$848$	−902.339	−	25.0761i	−1.06408	−	0.0295709i
$849$		−	566.531i		−	0.667293i
$850$	−162.918	−	213.016i	−0.191668	−	0.250607i
$851$		−	82.7852i		−	0.0972799i
$852$	−398.017	−	171.379i	−0.467156	−	0.201150i
$853$	−238.631	−	238.631i	−0.279755	−	0.279755i	0.553256	−	0.833011i	$-0.313385\pi$
$853$	−238.631	−	238.631i	−0.279755	−	0.279755i	−0.833011	+	0.553256i	$0.813385\pi$
$854$	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	0.270367	−	0.962757i	$-0.412855\pi$
$857$	−593.379	−	593.379i	−0.692390	−	0.692390i	−0.962757	+	0.270367i	$0.912855\pi$
$858$	170.909	−	32.7635i	0.199194	−	0.0381859i
$859$	−1008.66			−1.17423			−0.587114	−	0.809504i	$-0.699736\pi$
$859$	−1008.66			−1.17423			−0.587114	+	0.809504i	$0.699736\pi$
$860$	260.637	−	408.846i	0.303067	−	0.475403i
$861$			608.783i			0.707065i
$862$	−95.7884	+	18.3628i	−0.111123	+	0.0213025i
$863$	−655.271	+	655.271i	−0.759294	+	0.759294i	−0.976194	−	0.216900i	$-0.930406\pi$
$863$	−655.271	+	655.271i	−0.759294	+	0.759294i	0.216900	+	0.976194i	$0.430406\pi$
$864$	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
$868$	−755.936	−	325.494i	−0.870894	−	0.374993i
$869$	127.193			0.146367
$870$	−4.44310	+	4.70349i	−0.00510701	+	0.00540631i
$871$	1721.94			1.97697
$872$	1080.42	−	689.792i	1.23901	−	0.791045i
$873$	−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	$-0.780795\pi$
$877$	−119.801	+	119.801i	−0.136604	+	0.136604i	0.635498	+	0.772102i	$0.280795\pi$
$878$	175.808	+	917.093i	0.200237	+	1.04452i
$879$			498.117i			0.566686i
$880$	265.759	−	180.520i	0.301999	−	0.205137i
$881$	1243.40			1.41135			0.705673	−	0.708537i	$-0.250645\pi$
$881$	1243.40			1.41135			0.705673	+	0.708537i	$0.250645\pi$
$882$	−1282.56	+	245.869i	−1.45415	+	0.278764i
$883$	955.712	+	955.712i	1.08235	+	1.08235i	0.996290	+	0.0860557i	$0.0274263\pi$
$883$	955.712	+	955.712i	1.08235	+	1.08235i	0.0860557	+	0.996290i	$0.472574\pi$
$884$	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	0.821027	−	0.570889i	$-0.193401\pi$
$887$	221.872	+	221.872i	0.250138	+	0.250138i	−0.570889	+	0.821027i	$0.693401\pi$
$888$	−292.034	+	186.448i	−0.328867	+	0.209964i
$889$			991.662i			1.11548i
$890$	−927.726	+	26.4108i	−1.04239	+	0.0296751i
$891$			132.784i			0.149028i
$892$	404.949	−	940.466i	0.453979	−	1.05433i
$893$	−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
$898$	−96.3428	−	502.566i	−0.107286	−	0.559651i
$899$	8.10824			0.00901918
$900$	40.3321	+	707.794i	0.0448135	+	0.786437i
$901$			302.599i			0.335848i
$902$	56.0677	+	292.474i	0.0621593	+	0.324250i
$903$	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	$-0.640430\pi$
$907$	432.864	−	432.864i	0.477248	−	0.477248i	0.904251	+	0.427002i	$0.140430\pi$
$908$	364.397	−	846.286i	0.401318	−	0.932033i
$909$	144.800			0.159296
$910$	−1861.22	+	52.9859i	−2.04530	+	0.0582263i
$911$	−820.509			−0.900668			−0.450334	−	0.892860i	$-0.648695\pi$
$911$	−820.509			−0.900668			−0.450334	+	0.892860i	$0.648695\pi$
$912$	352.844	+	9.80558i	0.386890	+	0.0107517i
$913$	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
$918$	234.297	−	44.9150i	0.255225	−	0.0489271i
$919$			16.4894i			0.0179428i	0.999960	+	0.00897139i	$0.00285572\pi$
$919$			16.4894i			0.0179428i	−0.999960	+	0.00897139i	$0.997144\pi$
$920$	−98.2183	−	39.0168i	−0.106759	−	0.0424096i
$921$	308.776			0.335262
$922$	−148.896	−	776.707i	−0.161492	−	0.842415i
$923$	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
$928$	8.74940	−	12.1582i	0.00942823	−	0.0131016i
$929$		−	427.239i		−	0.459892i	−0.973203	−	0.229946i	$-0.926145\pi$
$929$		−	427.239i		−	0.459892i	0.973203	−	0.229946i	$-0.0738549\pi$
$930$	−164.414	+	174.049i	−0.176789	+	0.187150i
$931$			1470.02i			1.57897i
$932$	398.338	−	925.111i	0.427401	−	0.992608i
$933$	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	0.218638	−	0.975806i	$-0.429839\pi$
$937$	−709.466	−	709.466i	−0.757168	−	0.757168i	−0.975806	+	0.218638i	$0.929839\pi$
$938$	2563.15	−	491.361i	2.73257	−	0.523839i
$939$	269.995			0.287534
$940$	95.9482	−	150.508i	0.102073	−	0.160115i
$941$		−	1613.99i		−	1.71519i	−0.514328	−	0.857594i	$-0.671959\pi$
$941$		−	1613.99i		−	1.71519i	0.514328	−	0.857594i	$-0.328041\pi$
$942$	75.8729	−	14.5450i	0.0805445	−	0.0154405i
$943$	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	−0.443688	+	0.896181i	$0.646330\pi$
$947$	−1268.86	+	1268.86i	−1.33987	+	1.33987i	−0.896181	+	0.443688i	$0.853670\pi$
$948$	−69.2545	+	160.839i	−0.0730533	+	0.169661i
$949$	1019.77			1.07458
$950$	791.034	+	105.416i	0.832668	+	0.110964i
$951$	155.440			0.163449
$952$	274.278	+	429.602i	0.288108	+	0.451262i
$953$	984.100	−	984.100i	1.03263	−	1.03263i	0.0331842	−	0.999449i	$-0.489435\pi$
$953$	984.100	−	984.100i	1.03263	−	1.03263i	0.999449	−	0.0331842i	$-0.0105648\pi$
$954$	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
$958$	−19.7499	−	103.024i	−0.0206158	−	0.107541i
$959$			1217.71i			1.26977i
$960$	83.5707	+	434.349i	0.0870528	+	0.452447i
$961$	−660.960			−0.687784
$962$	964.720	−	184.938i	1.00283	−	0.192244i
$963$	−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	0.00701003	−	0.999975i	$-0.497769\pi$
$967$	−960.198	−	960.198i	−0.992965	−	0.992965i	−0.999975	+	0.00701003i	$0.997769\pi$
$968$	−707.147	+	451.477i	−0.730524	+	0.466402i
$969$		−	118.326i		−	0.122111i
$970$	−828.485	+	877.038i	−0.854108	+	0.904163i
$971$		−	469.039i		−	0.483047i	−0.970395	−	0.241523i	$-0.922353\pi$
$971$		−	469.039i		−	0.483047i	0.970395	−	0.241523i	$-0.0776471\pi$
$972$	−903.257	−	388.928i	−0.929276	−	0.400131i
$973$	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	0.618776	−	0.785568i	$-0.287629\pi$
$977$	−162.956	−	162.956i	−0.166792	−	0.166792i	−0.785568	+	0.618776i	$0.787629\pi$
$978$	20.4787	+	106.826i	0.0209394	+	0.109229i
$979$	−372.716			−0.380711
$980$	−1798.52	+	398.153i	−1.83523	+	0.406279i
$981$			1135.94i			1.15794i
$982$	64.3129	+	335.485i	0.0654918	+	0.341634i
$983$	−421.256	+	421.256i	−0.428541	+	0.428541i	−0.888131	−	0.459590i	$-0.847996\pi$
$983$	−421.256	+	421.256i	−0.428541	+	0.428541i	0.459590	+	0.888131i	$0.347996\pi$
$984$	−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
$988$	−919.138	−	395.766i	−0.930301	−	0.400573i
$989$	−64.0523			−0.0647647
$990$	8.10176	+	284.589i	0.00818360	+	0.287463i
$991$	1790.76			1.80703			0.903513	−	0.428561i	$-0.140979\pi$
$991$	1790.76			1.80703			0.903513	+	0.428561i	$0.140979\pi$
$992$	323.766	−	449.907i	0.326377	−	0.453536i
$993$	−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	$-0.597133\pi$
$997$	651.402	−	651.402i	0.653362	−	0.653362i	0.953801	+	0.300439i	$0.0971331\pi$
$998$	−1724.95	+	330.676i	−1.72841	+	0.331339i
$999$		−	696.828i		−	0.697526i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.1	✓	20	40.13	odd	4	inner
40.3.i.a.13.6	yes	20	5.3	odd	4	inner
40.3.i.a.37.1	yes	20	1.1	even	1	trivial
40.3.i.a.37.6	yes	20	8.5	even	2	inner
160.3.m.a.17.4		20	4.3	odd	2
160.3.m.a.17.7		20	8.3	odd	2
160.3.m.a.113.4		20	40.3	even	4
160.3.m.a.113.7		20	20.3	even	4
200.3.i.b.93.5		20	5.2	odd	4
200.3.i.b.93.10		20	40.37	odd	4
200.3.i.b.157.5		20	40.29	even	2
200.3.i.b.157.10		20	5.4	even	2
360.3.u.b.37.5		20	24.5	odd	2
360.3.u.b.37.10		20	3.2	odd	2
360.3.u.b.253.5		20	15.8	even	4
360.3.u.b.253.10		20	120.53	even	4
800.3.m.b.593.4		20	20.7	even	4
800.3.m.b.593.7		20	40.27	even	4
800.3.m.b.657.4		20	40.19	odd	2
800.3.m.b.657.7		20	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.96423 + 0.376547i) q^{2} +(0.977390 + 0.977390i) q^{3} +(3.71643 - 1.47925i) q^{4} +(-0.801246 + 4.93538i) q^{5} +(-2.28785 - 1.55179i) q^{6} +(8.39950 + 8.39950i) q^{7} +(-6.74292 + 4.30500i) q^{8} -7.08942i q^{9} +O(q^{10})\)	\(q+(-1.96423 + 0.376547i) 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} +(-6.74292 + 4.30500i) q^{8} -7.08942i q^{9} +(-0.284568 - 9.99595i) q^{10} -4.01590i q^{11} +(5.07820 + 2.18659i) 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} +(2.66950 + 13.9253i) q^{18} +15.9605 q^{19} +(4.32290 + 19.5272i) q^{20} +16.4192i q^{21} +(1.51217 + 7.88816i) 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} +(43.6411 + 18.7911i) q^{28} -0.468098 q^{29} +(9.49181 - 10.0481i) q^{30} -17.3217 q^{31} +(-18.6914 + 25.9737i) 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} +(-31.3502 + 6.00989i) q^{38} -21.6665i q^{39} +(-15.8441 - 36.7283i) q^{40} +37.0776 q^{41} +(-6.18259 - 32.2511i) 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} +(22.1073 + 0.614364i) q^{48} +92.1033i q^{49} +(49.5619 + 6.60476i) q^{50} -7.41366i q^{51} +(-57.5881 - 24.7965i) 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} +(0.919455 - 0.176261i) q^{58} +50.6555 q^{59} +(-14.8606 + 23.3109i) q^{60} +73.6559i q^{61} +(34.0238 - 6.52241i) 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} +(-19.7050 - 8.48466i) q^{68} +3.65202 q^{69} +(81.5708 - 86.3512i) q^{70} -78.3775 q^{71} +(30.5200 + 47.8034i) 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} +(8.15844 + 42.5580i) q^{78} +31.6724i q^{79} +(44.9514 + 66.1768i) q^{80} -33.0646 q^{81} +(-72.8290 + 13.9614i) 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} +(17.2885 + 27.0789i) q^{88} -92.8102i q^{89} +(-70.8655 + 2.01742i) q^{90} -186.198i q^{91} +(4.17960 - 9.70682i) 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} +(-34.6812 - 180.912i) 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

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