LMFDB - Embedded newform 50.4.d.b.21.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,4,Mod(11,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("50.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	50.d (of order $5$, degree $4$, 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:	$2.95009550029$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 135 x^{14} + 7296 x^{12} + 200295 x^{10} + 2912021 x^{8} + 20937420 x^{6} + 57578496 x^{4} + \cdots + 952576 $ x^16 + 135x^14 + 7296x^12 + 200295x^10 + 2912021x^8 + 20937420x^6 + 57578496x^4 + 16724160*x^2 + 952576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			21.3
Root			$-2.36461i$ of defining polynomial
Character	$\chi$	$=$	50.21
Dual form			50.4.d.b.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.618034 - 1.90211i) q^{2} +(3.55790 + 2.58496i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(-0.591780 - 11.1647i) q^{5} +(7.11579 - 5.16993i) q^{6} +32.4633 q^{7} +(-6.47214 + 4.70228i) q^{8} +(-2.36687 - 7.28447i) q^{9} +(-21.6022 - 5.77451i) q^{10} +(-13.6751 + 42.0875i) q^{11} +(-5.43598 - 16.7302i) q^{12} +(-6.12486 - 18.8504i) q^{13} +(20.0634 - 61.7488i) q^{14} +(26.7548 - 41.2524i) q^{15} +(4.94427 + 15.2169i) q^{16} +(-66.6454 + 48.4207i) q^{17} -15.3187 q^{18} +(-8.36319 + 6.07621i) q^{19} +(-24.3347 + 37.5210i) q^{20} +(115.501 + 83.9163i) q^{21} +(71.6036 + 52.0231i) q^{22} +(-60.0803 + 184.908i) q^{23} -35.1824 q^{24} +(-124.300 + 13.2140i) q^{25} -39.6409 q^{26} +(47.1019 - 144.965i) q^{27} +(-105.053 - 76.3257i) q^{28} +(159.317 + 115.751i) q^{29} +(-61.9315 - 76.3860i) q^{30} +(68.1740 - 49.5313i) q^{31} +32.0000 q^{32} +(-157.449 + 114.394i) q^{33} +(50.9126 + 156.693i) q^{34} +(-19.2111 - 362.442i) q^{35} +(-9.46747 + 29.1379i) q^{36} +(-70.9588 - 218.389i) q^{37} +(6.38891 + 19.6630i) q^{38} +(26.9359 - 82.9003i) q^{39} +(56.3295 + 69.4765i) q^{40} +(-6.39296 - 19.6755i) q^{41} +(231.002 - 167.833i) q^{42} -36.8678 q^{43} +(143.207 - 104.046i) q^{44} +(-79.9280 + 30.7361i) q^{45} +(314.584 + 228.559i) q^{46} +(-343.561 - 249.612i) q^{47} +(-21.7439 + 66.9209i) q^{48} +710.864 q^{49} +(-51.6868 + 244.599i) q^{50} -362.283 q^{51} +(-24.4995 + 75.4016i) q^{52} +(4.23242 + 3.07504i) q^{53} +(-246.629 - 179.186i) q^{54} +(477.986 + 127.771i) q^{55} +(-210.107 + 152.651i) q^{56} -45.4621 q^{57} +(318.635 - 231.502i) q^{58} +(16.0299 + 49.3350i) q^{59} +(-183.571 + 70.5915i) q^{60} +(-38.3804 + 118.123i) q^{61} +(-52.0803 - 160.287i) q^{62} +(-76.8363 - 236.478i) q^{63} +(19.7771 - 60.8676i) q^{64} +(-206.834 + 79.5373i) q^{65} +(120.280 + 370.185i) q^{66} +(630.360 - 457.984i) q^{67} +329.513 q^{68} +(-691.740 + 502.578i) q^{69} +(-701.278 - 187.460i) q^{70} +(-496.268 - 360.560i) q^{71} +(49.5723 + 36.0164i) q^{72} +(-280.603 + 863.608i) q^{73} -459.255 q^{74} +(-476.403 - 274.296i) q^{75} +41.3499 q^{76} +(-443.937 + 1366.30i) q^{77} +(-141.038 - 102.470i) q^{78} +(500.100 + 363.344i) q^{79} +(166.966 - 64.2062i) q^{80} +(375.005 - 272.457i) q^{81} -41.3761 q^{82} +(365.730 - 265.719i) q^{83} +(-176.470 - 543.118i) q^{84} +(580.041 + 715.420i) q^{85} +(-22.7855 + 70.1266i) q^{86} +(267.623 + 823.659i) q^{87} +(-109.401 - 336.700i) q^{88} +(266.987 - 821.703i) q^{89} +(9.06529 + 171.028i) q^{90} +(-198.833 - 611.945i) q^{91} +(629.169 - 457.118i) q^{92} +370.592 q^{93} +(-687.123 + 499.224i) q^{94} +(72.7880 + 89.7764i) q^{95} +(113.853 + 82.7188i) q^{96} +(-528.660 - 384.094i) q^{97} +(439.338 - 1352.14i) q^{98} +338.953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 7 q^{3} - 16 q^{4} + 15 q^{5} + 14 q^{6} - 54 q^{7} - 32 q^{8} - 83 q^{9} - 50 q^{10} + 152 q^{11} - 12 q^{12} + 77 q^{13} + 52 q^{14} - 70 q^{15} - 64 q^{16} + 76 q^{17} + 304 q^{18} - 20 q^{19}+ \cdots - 1786 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 7 * q^3 - 16 * q^4 + 15 * q^5 + 14 * q^6 - 54 * q^7 - 32 * q^8 - 83 * q^9 - 50 * q^10 + 152 * q^11 - 12 * q^12 + 77 * q^13 + 52 * q^14 - 70 * q^15 - 64 * q^16 + 76 * q^17 + 304 * q^18 - 20 * q^19 + 20 * q^20 + 257 * q^21 - 226 * q^22 - 383 * q^23 - 64 * q^24 - 215 * q^25 - 716 * q^26 + 415 * q^27 + 4 * q^28 + 105 * q^29 + 140 * q^30 + 177 * q^31 + 512 * q^32 + 64 * q^33 + 342 * q^34 - 210 * q^35 - 332 * q^36 + 446 * q^37 + 90 * q^38 - 146 * q^39 - 40 * q^40 + 462 * q^41 + 514 * q^42 - 1058 * q^43 - 452 * q^44 - 865 * q^45 + 1124 * q^46 - 1114 * q^47 - 48 * q^48 + 1698 * q^49 - 550 * q^50 - 3608 * q^51 + 308 * q^52 + 567 * q^53 + 390 * q^54 - 210 * q^55 + 8 * q^56 - 1520 * q^57 + 210 * q^58 + 1275 * q^59 + 1260 * q^60 + 252 * q^61 - 176 * q^62 + 5402 * q^63 - 256 * q^64 + 2645 * q^65 + 998 * q^66 + 3296 * q^67 - 1976 * q^68 - 5491 * q^69 - 1750 * q^70 + 3712 * q^71 + 56 * q^72 - 1688 * q^73 - 1148 * q^74 - 6315 * q^75 - 200 * q^76 - 5453 * q^77 - 1152 * q^78 + 1750 * q^79 + 160 * q^80 + 4106 * q^81 - 1576 * q^82 - 2153 * q^83 - 612 * q^84 + 5860 * q^85 + 1074 * q^86 - 1255 * q^87 + 1216 * q^88 + 5660 * q^89 + 820 * q^90 - 493 * q^91 + 2248 * q^92 - 256 * q^93 - 2228 * q^94 - 1420 * q^95 + 224 * q^96 - 429 * q^97 - 674 * q^98 - 1786 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.618034	−	1.90211i	0.218508	−	0.672499i
$2$	0.618034	−	1.90211i	0.218508	−	0.672499i
$3$	3.55790	+	2.58496i	0.684717	+	0.497476i	0.874919	−	0.484269i	$-0.160914\pi$
$3$	3.55790	+	2.58496i	0.684717	+	0.497476i	−0.190202	+	0.981745i	$0.560914\pi$
$4$	−3.23607	−	2.35114i	−0.404508	−	0.293893i
$5$	−0.591780	−	11.1647i	−0.0529304	−	0.998598i
$5$	−0.591780	−	11.1647i	−0.0529304	−	0.998598i
$6$	7.11579	−	5.16993i	0.484168	−	0.351769i
$7$	32.4633			1.75285			0.876426	−	0.481537i	$-0.159921\pi$
$7$	32.4633			1.75285			0.876426	+	0.481537i	$0.159921\pi$
$8$	−6.47214	+	4.70228i	−0.286031	+	0.207813i
$9$	−2.36687	−	7.28447i	−0.0876618	−	0.269795i
$10$	−21.6022	−	5.77451i	−0.683122	−	0.182606i
$11$	−13.6751	+	42.0875i	−0.374835	+	1.15362i	0.568754	+	0.822507i	$0.307425\pi$
$11$	−13.6751	+	42.0875i	−0.374835	+	1.15362i	−0.943590	+	0.331117i	$0.892575\pi$
$12$	−5.43598	−	16.7302i	−0.130769	−	0.402467i
$13$	−6.12486	−	18.8504i	−0.130672	−	0.402166i	0.864220	−	0.503114i	$-0.167812\pi$
$13$	−6.12486	−	18.8504i	−0.130672	−	0.402166i	−0.994892	+	0.100948i	$0.967812\pi$
$14$	20.0634	−	61.7488i	0.383012	−	1.17879i
$15$	26.7548	−	41.2524i	0.460537	−	0.710089i
$16$	4.94427	+	15.2169i	0.0772542	+	0.237764i
$17$	−66.6454	+	48.4207i	−0.950817	+	0.690809i	−0.951000	−	0.309191i	$-0.899942\pi$
$17$	−66.6454	+	48.4207i	−0.950817	+	0.690809i	0.000182954		1.00000i	$0.499942\pi$
$18$	−15.3187			−0.200592
$19$	−8.36319	+	6.07621i	−0.100981	+	0.0733673i	−0.637130	−	0.770756i	$-0.719879\pi$
$19$	−8.36319	+	6.07621i	−0.100981	+	0.0733673i	0.536149	+	0.844124i	$0.319879\pi$
$20$	−24.3347	+	37.5210i	−0.272070	+	0.419497i
$21$	115.501	+	83.9163i	1.20021	+	0.872002i
$22$	71.6036	+	52.0231i	0.693906	+	0.504152i
$23$	−60.0803	+	184.908i	−0.544678	+	1.67635i	0.177075	+	0.984197i	$0.443337\pi$
$23$	−60.0803	+	184.908i	−0.544678	+	1.67635i	−0.721753	+	0.692151i	$0.756663\pi$
$24$	−35.1824			−0.299232
$25$	−124.300	+	13.2140i	−0.994397	+	0.105712i
$26$	−39.6409			−0.299009
$27$	47.1019	−	144.965i	0.335732	−	1.03328i
$28$	−105.053	−	76.3257i	−0.709043	−	0.515150i
$29$	159.317	+	115.751i	1.02016	+	0.741186i	0.966315	−	0.257363i	$-0.0828538\pi$
$29$	159.317	+	115.751i	1.02016	+	0.741186i	0.0538405	+	0.998550i	$0.482854\pi$
$30$	−61.9315	−	76.3860i	−0.376903	−	0.464870i
$31$	68.1740	−	49.5313i	0.394981	−	0.286970i	−0.372513	−	0.928027i	$-0.621504\pi$
$31$	68.1740	−	49.5313i	0.394981	−	0.286970i	0.767493	+	0.641057i	$0.221504\pi$
$32$	32.0000			0.176777
$33$	−157.449	+	114.394i	−0.830557	+	0.603435i
$34$	50.9126	+	156.693i	0.256807	+	0.790370i
$35$	−19.2111	−	362.442i	−0.0927791	−	1.75039i
$36$	−9.46747	+	29.1379i	−0.0438309	+	0.134898i
$37$	−70.9588	−	218.389i	−0.315285	−	0.970348i	−0.975637	−	0.219391i	$-0.929593\pi$
$37$	−70.9588	−	218.389i	−0.315285	−	0.970348i	0.660352	−	0.750956i	$-0.270407\pi$
$38$	6.38891	+	19.6630i	0.0272741	+	0.0839412i
$39$	26.9359	−	82.9003i	0.110595	−	0.340376i
$40$	56.3295	+	69.4765i	0.222662	+	0.274630i
$41$	−6.39296	−	19.6755i	−0.0243515	−	0.0749463i	0.938142	−	0.346250i	$-0.112545\pi$
$41$	−6.39296	−	19.6755i	−0.0243515	−	0.0749463i	−0.962494	+	0.271304i	$0.912545\pi$
$42$	231.002	−	167.833i	0.848675	−	0.616599i
$43$	−36.8678			−0.130751			−0.0653753	−	0.997861i	$-0.520824\pi$
$43$	−36.8678			−0.130751			−0.0653753	+	0.997861i	$0.520824\pi$
$44$	143.207	−	104.046i	0.490666	−	0.356490i
$45$	−79.9280	+	30.7361i	−0.264777	+	0.101819i
$46$	314.584	+	228.559i	1.00832	+	0.732591i
$47$	−343.561	−	249.612i	−1.06625	−	0.774673i	−0.0910123	−	0.995850i	$-0.529010\pi$
$47$	−343.561	−	249.612i	−1.06625	−	0.774673i	−0.975234	+	0.221177i	$0.929010\pi$
$48$	−21.7439	+	66.9209i	−0.0653847	+	0.201233i
$49$	710.864			2.07249
$50$	−51.6868	+	244.599i	−0.146192	+	0.691829i
$51$	−362.283			−0.994702
$52$	−24.4995	+	75.4016i	−0.0653358	+	0.201083i
$53$	4.23242	+	3.07504i	0.0109692	+	0.00796960i	0.593256	−	0.805014i	$-0.297842\pi$
$53$	4.23242	+	3.07504i	0.0109692	+	0.00796960i	−0.582287	+	0.812983i	$0.697842\pi$
$54$	−246.629	−	179.186i	−0.621517	−	0.451558i
$55$	477.986	+	127.771i	1.17185	+	0.313248i
$56$	−210.107	+	152.651i	−0.501369	+	0.364266i
$57$	−45.4621			−0.105642
$58$	318.635	−	231.502i	0.721359	−	0.524098i
$59$	16.0299	+	49.3350i	0.0353715	+	0.108862i	0.967183	−	0.254079i	$-0.0817724\pi$
$59$	16.0299	+	49.3350i	0.0353715	+	0.108862i	−0.931812	+	0.362942i	$0.881772\pi$
$60$	−183.571	+	70.5915i	−0.394981	+	0.151889i
$61$	−38.3804	+	118.123i	−0.0805592	+	0.247936i	−0.983222	−	0.182413i	$-0.941609\pi$
$61$	−38.3804	+	118.123i	−0.0805592	+	0.247936i	0.902663	+	0.430348i	$0.141609\pi$
$62$	−52.0803	−	160.287i	−0.106681	−	0.328329i
$63$	−76.8363	−	236.478i	−0.153658	−	0.472911i
$64$	19.7771	−	60.8676i	0.0386271	−	0.118882i
$65$	−206.834	+	79.5373i	−0.394686	+	0.151775i
$66$	120.280	+	370.185i	0.224326	+	0.690404i
$67$	630.360	−	457.984i	1.14941	−	0.835098i	0.161011	−	0.986953i	$-0.448524\pi$
$67$	630.360	−	457.984i	1.14941	−	0.835098i	0.988403	+	0.151854i	$0.0485244\pi$
$68$	329.513			0.587637
$69$	−691.740	+	502.578i	−1.20689	+	0.876860i
$70$	−701.278	−	187.460i	−1.19741	−	0.320081i
$71$	−496.268	−	360.560i	−0.829523	−	0.602684i	0.0899013	−	0.995951i	$-0.471345\pi$
$71$	−496.268	−	360.560i	−0.829523	−	0.602684i	−0.919424	+	0.393267i	$0.871345\pi$
$72$	49.5723	+	36.0164i	0.0811411	+	0.0589524i
$73$	−280.603	+	863.608i	−0.449892	+	1.38463i	0.427136	+	0.904187i	$0.359523\pi$
$73$	−280.603	+	863.608i	−0.449892	+	1.38463i	−0.877028	+	0.480439i	$0.840477\pi$
$74$	−459.255			−0.721450
$75$	−476.403	−	274.296i	−0.733470	−	0.422306i
$76$	41.3499			0.0624099
$77$	−443.937	+	1366.30i	−0.657031	+	2.02213i
$78$	−141.038	−	102.470i	−0.204737	−	0.148750i
$79$	500.100	+	363.344i	0.712224	+	0.517461i	0.883890	−	0.467694i	$-0.154915\pi$
$79$	500.100	+	363.344i	0.712224	+	0.517461i	−0.171667	+	0.985155i	$0.554915\pi$
$80$	166.966	−	64.2062i	0.233342	−	0.0897309i
$81$	375.005	−	272.457i	0.514411	−	0.373741i
$82$	−41.3761			−0.0557223
$83$	365.730	−	265.719i	0.483664	−	0.351403i	−0.319078	−	0.947728i	$-0.603373\pi$
$83$	365.730	−	265.719i	0.483664	−	0.351403i	0.802743	+	0.596326i	$0.203373\pi$
$84$	−176.470	−	543.118i	−0.229219	−	0.705465i
$85$	580.041	+	715.420i	0.740168	+	0.912919i
$86$	−22.7855	+	70.1266i	−0.0285701	+	0.0879296i
$87$	267.623	+	823.659i	0.329795	+	1.01501i
$88$	−109.401	−	336.700i	−0.132524	−	0.407868i
$89$	266.987	−	821.703i	0.317984	−	0.978656i	−0.656524	−	0.754305i	$-0.727974\pi$
$89$	266.987	−	821.703i	0.317984	−	0.978656i	0.974509	−	0.224350i	$-0.0720260\pi$
$90$	9.06529	+	171.028i	0.0106174	+	0.200311i
$91$	−198.833	−	611.945i	−0.229048	−	0.704937i
$92$	629.169	−	457.118i	0.712993	−	0.518020i
$93$	370.592			0.413211
$94$	−687.123	+	499.224i	−0.753950	+	0.547777i
$95$	72.7880	+	89.7764i	0.0786094	+	0.0969565i
$96$	113.853	+	82.7188i	0.121042	+	0.0879422i
$97$	−528.660	−	384.094i	−0.553374	−	0.402050i	0.275654	−	0.961257i	$-0.411106\pi$
$97$	−528.660	−	384.094i	−0.553374	−	0.402050i	−0.829028	+	0.559207i	$0.811106\pi$
$98$	439.338	−	1352.14i	0.452856	−	1.39375i
$99$	338.953			0.344101
$100$	433.310	+	249.484i	0.433310	+	0.249484i
$101$	684.563			0.674421			0.337211	−	0.941429i	$-0.390517\pi$
$101$	684.563			0.674421			0.337211	+	0.941429i	$0.390517\pi$
$102$	−223.903	+	689.104i	−0.217350	+	0.668936i
$103$	−3.12140	−	2.26783i	−0.00298603	−	0.00216948i	0.586291	−	0.810100i	$-0.300587\pi$
$103$	−3.12140	−	2.26783i	−0.00298603	−	0.00216948i	−0.589277	+	0.807931i	$0.700587\pi$
$104$	128.281	+	93.2015i	0.120952	+	0.0878765i
$105$	868.547	−	1339.19i	0.807252	−	1.24468i
$106$	8.46485	−	6.15007i	0.00775640	−	0.00563536i
$107$	−1045.89			−0.944951			−0.472476	−	0.881344i	$-0.656640\pi$
$107$	−1045.89			−0.944951			−0.472476	+	0.881344i	$0.656640\pi$
$108$	−493.257	+	358.372i	−0.439479	+	0.319300i
$109$	−356.163	−	1096.16i	−0.312974	−	0.963236i	−0.976580	−	0.215153i	$-0.930975\pi$
$109$	−356.163	−	1096.16i	−0.312974	−	0.963236i	0.663606	−	0.748082i	$-0.269025\pi$
$110$	538.447	−	830.216i	0.466717	−	0.719618i
$111$	312.063	−	960.430i	0.266844	−	0.821261i
$112$	160.507	+	493.990i	0.135415	+	0.416765i
$113$	41.9853	+	129.218i	0.0349526	+	0.107573i	0.967011	−	0.254736i	$-0.0819885\pi$
$113$	41.9853	+	129.218i	0.0349526	+	0.107573i	−0.932058	+	0.362309i	$0.881989\pi$
$114$	−28.0971	+	86.4741i	−0.0230837	+	0.0710442i
$115$	2099.99	+	561.352i	1.70283	+	0.455185i
$116$	−243.415	−	749.155i	−0.194832	−	0.599632i
$117$	−122.818	+	89.2328i	−0.0970476	+	0.0705092i
$118$	103.748			0.0809387
$119$	−2163.53	+	1571.90i	−1.66664	+	1.21089i
$120$	20.8202	+	392.800i	0.0158385	+	0.298813i
$121$	−507.551	−	368.758i	−0.381331	−	0.277053i
$122$	200.963	+	146.008i	0.149134	+	0.108352i
$123$	28.1150	−	86.5290i	0.0206101	−	0.0634314i
$124$	−337.071			−0.244112
$125$	221.088	+	1379.94i	0.158198	+	0.987407i
$126$	−497.295			−0.351608
$127$	−505.692	+	1556.36i	−0.353330	+	1.08744i	0.603641	+	0.797256i	$0.293716\pi$
$127$	−505.692	+	1556.36i	−0.353330	+	1.08744i	−0.956971	+	0.290182i	$0.906284\pi$
$128$	−103.554	−	75.2365i	−0.0715077	−	0.0519534i
$129$	−131.172	−	95.3018i	−0.0895273	−	0.0650454i
$130$	23.4587	+	442.578i	0.0158266	+	0.298590i
$131$	874.934	−	635.677i	0.583537	−	0.423964i	−0.256461	−	0.966555i	$-0.582556\pi$
$131$	874.934	−	635.677i	0.583537	−	0.423964i	0.839997	+	0.542590i	$0.182556\pi$
$132$	778.471			0.513312
$133$	−271.496	+	197.254i	−0.177005	+	0.128602i
$134$	−481.552	−	1482.07i	−0.310446	−	0.955455i
$135$	−1646.36	−	440.090i	−1.04960	−	0.280570i
$136$	203.650	−	626.771i	0.128403	−	0.395185i
$137$	−716.275	−	2204.47i	−0.446683	−	1.37475i	−0.880628	−	0.473809i	$-0.842879\pi$
$137$	−716.275	−	2204.47i	−0.446683	−	1.37475i	0.433945	−	0.900939i	$-0.357121\pi$
$138$	528.442	+	1626.38i	0.325971	+	1.00324i
$139$	−327.762	+	1008.75i	−0.200003	+	0.615546i	0.799879	+	0.600162i	$0.204897\pi$
$139$	−327.762	+	1008.75i	−0.200003	+	0.615546i	−0.999882	+	0.0153844i	$0.995103\pi$
$140$	−789.983	+	1218.05i	−0.476898	+	0.735317i
$141$	−577.118	−	1776.19i	−0.344696	−	1.06086i
$142$	−992.535	+	721.119i	−0.586561	+	0.426162i
$143$	877.124			0.512929
$144$	99.1447	−	72.0328i	0.0573754	−	0.0416857i
$145$	1198.04	−	1847.22i	0.686150	−	1.05796i
$146$	1469.26	+	1067.48i	0.832854	+	0.605104i
$147$	2529.18	+	1837.56i	1.41907	+	1.03101i
$148$	−283.835	+	873.554i	−0.157643	+	0.485174i
$149$	−1830.45			−1.00642			−0.503209	−	0.864165i	$-0.667848\pi$
$149$	−1830.45			−1.00642			−0.503209	+	0.864165i	$0.667848\pi$
$150$	−816.174	+	736.648i	−0.444269	+	0.400980i
$151$	−1585.52			−0.854491			−0.427246	−	0.904136i	$-0.640516\pi$
$151$	−1585.52			−0.854491			−0.427246	+	0.904136i	$0.640516\pi$
$152$	25.5556	−	78.6521i	0.0136371	−	0.0419706i
$153$	510.460	+	370.871i	0.269727	+	0.195968i
$154$	2324.49	+	1688.84i	1.21631	+	0.883704i
$155$	−593.344	−	731.828i	−0.307475	−	0.379238i
$156$	−282.077	+	204.941i	−0.144771	+	0.105182i
$157$	−1535.51			−0.780554			−0.390277	−	0.920698i	$-0.627621\pi$
$157$	−1535.51			−0.780554			−0.390277	+	0.920698i	$0.627621\pi$
$158$	1000.20	−	726.688i	0.503618	−	0.365900i
$159$	7.10967	+	21.8813i	0.00354612	+	0.0109138i
$160$	−18.9369	−	357.269i	−0.00935686	−	0.176529i
$161$	−1950.40	+	6002.72i	−0.954741	+	2.93839i
$162$	−286.479	−	881.690i	−0.138938	−	0.427606i
$163$	−517.820	−	1593.69i	−0.248827	−	0.765811i	−0.994983	−	0.100040i	$-0.968103\pi$
$163$	−517.820	−	1593.69i	−0.248827	−	0.765811i	0.746156	−	0.665771i	$-0.231897\pi$
$164$	−25.5719	+	78.7021i	−0.0121758	+	0.0374732i
$165$	1370.34	+	1690.17i	0.646551	+	0.797453i
$166$	−279.393	−	859.884i	−0.130633	−	0.402048i
$167$	1664.99	−	1209.69i	0.771503	−	0.560530i	−0.130914	−	0.991394i	$-0.541791\pi$
$167$	1664.99	−	1209.69i	0.771503	−	0.560530i	0.902417	+	0.430864i	$0.141791\pi$
$168$	−1142.14			−0.524510
$169$	1459.59	−	1060.45i	0.664355	−	0.482682i
$170$	1719.29	−	661.150i	0.775670	−	0.298281i
$171$	64.0566	+	46.5398i	0.0286464	+	0.0208128i
$172$	119.307	+	86.6813i	0.0528898	+	0.0384267i
$173$	1331.88	−	4099.10i	0.585323	−	1.80144i	−0.0126483	−	0.999920i	$-0.504026\pi$
$173$	1331.88	−	4099.10i	0.585323	−	1.80144i	0.597971	−	0.801518i	$-0.295974\pi$
$174$	1732.09			0.754653
$175$	−4035.17	+	428.971i	−1.74303	+	0.185298i
$176$	−708.055			−0.303248
$177$	−70.4964	+	216.966i	−0.0299369	+	0.0921364i
$178$	−1397.96	−	1015.68i	−0.588662	−	0.427688i
$179$	2202.60	+	1600.28i	0.919719	+	0.668215i	0.943454	−	0.331503i	$-0.107556\pi$
$179$	2202.60	+	1600.28i	0.919719	+	0.668215i	−0.0237350	+	0.999718i	$0.507556\pi$
$180$	330.917	+	88.4580i	0.137029	+	0.0366293i
$181$	1056.07	−	767.281i	0.433686	−	0.315091i	−0.349435	−	0.936961i	$-0.613626\pi$
$181$	1056.07	−	767.281i	0.433686	−	0.315091i	0.783121	+	0.621869i	$0.213626\pi$
$182$	−1286.87			−0.524118
$183$	−441.897	+	321.057i	−0.178502	+	0.129690i
$184$	−480.642	−	1479.26i	−0.192573	−	0.592679i
$185$	−2396.24	+	921.469i	−0.952299	+	0.366204i
$186$	229.039	−	704.909i	0.0902900	−	0.277884i
$187$	−1126.53	−	3467.10i	−0.440534	−	1.35583i
$188$	524.915	+	1615.52i	0.203635	+	0.626724i
$189$	1529.08	−	4706.03i	0.588488	−	1.81118i
$190$	215.750	−	82.9662i	0.0823799	−	0.0316790i
$191$	1225.39	+	3771.37i	0.464221	+	1.42872i	0.859960	+	0.510362i	$0.170489\pi$
$191$	1225.39	+	3771.37i	0.464221	+	1.42872i	−0.395739	+	0.918363i	$0.629511\pi$
$192$	227.705	−	165.438i	0.0855897	−	0.0621845i
$193$	−1941.18			−0.723986			−0.361993	−	0.932181i	$-0.617904\pi$
$193$	−1941.18			−0.723986			−0.361993	+	0.932181i	$0.617904\pi$
$194$	−1057.32	+	768.188i	−0.391295	+	0.284292i
$195$	−941.494	−	251.672i	−0.345753	−	0.0924236i
$196$	−2300.40	−	1671.34i	−0.838340	−	0.609089i
$197$	1633.01	+	1186.45i	0.590595	+	0.429092i	0.842528	−	0.538652i	$-0.181066\pi$
$197$	1633.01	+	1186.45i	0.590595	+	0.429092i	−0.251933	+	0.967745i	$0.581066\pi$
$198$	209.484	−	644.726i	0.0751889	−	0.231408i
$199$	985.509			0.351060			0.175530	−	0.984474i	$-0.443836\pi$
$199$	985.509			0.351060			0.175530	+	0.984474i	$0.443836\pi$
$200$	742.348	−	670.015i	0.262460	−	0.236886i
$201$	3426.63			1.20247
$202$	423.083	−	1302.12i	0.147366	−	0.453547i
$203$	5171.96	+	3757.65i	1.78818	+	1.29919i
$204$	1172.37	+	851.779i	0.402365	+	0.292336i
$205$	−215.887	+	83.0189i	−0.0735523	+	0.0282843i
$206$	−6.24281	+	4.53567i	−0.00211144	+	0.00153405i
$207$	1489.16			0.500018
$208$	256.562	−	186.403i	0.0855257	−	0.0621381i
$209$	−141.366	−	435.079i	−0.0467869	−	0.143995i
$210$	−2010.50	−	2479.74i	−0.660655	−	0.814849i
$211$	1338.94	−	4120.84i	0.436856	−	1.34450i	−0.454317	−	0.890840i	$-0.650116\pi$
$211$	1338.94	−	4120.84i	0.436856	−	1.34450i	0.891173	−	0.453664i	$-0.149884\pi$
$212$	−6.46657	−	19.9021i	−0.00209493	−	0.00644754i
$213$	−833.636	−	2565.67i	−0.268168	−	0.825336i
$214$	−646.394	+	1989.40i	−0.206479	+	0.635478i
$215$	21.8176	+	411.616i	0.00692068	+	0.130567i
$216$	376.815	+	1159.72i	0.118699	+	0.365318i
$217$	2213.15	−	1607.95i	0.692343	−	0.503017i
$218$	−2305.13			−0.716162
$219$	−3230.75	+	2347.28i	−0.996868	+	0.724267i
$220$	−1246.39	−	1537.29i	−0.381961	−	0.471109i
$221$	1320.94	+	959.722i	0.402065	+	0.292117i
$222$	−1633.98	−	1187.16i	−0.493989	−	0.358904i
$223$	−1606.36	+	4943.88i	−0.482377	+	1.48460i	0.353367	+	0.935485i	$0.385037\pi$
$223$	−1606.36	+	4943.88i	−0.482377	+	1.48460i	−0.835744	+	0.549119i	$0.814963\pi$
$224$	1038.82			0.309863
$225$	390.458	+	874.181i	0.115691	+	0.259017i
$226$	271.735			0.0799802
$227$	1157.17	−	3561.42i	0.338345	−	1.04132i	−0.626705	−	0.779256i	$-0.715597\pi$
$227$	1157.17	−	3561.42i	0.338345	−	1.04132i	0.965051	−	0.262064i	$-0.0844030\pi$
$228$	147.119	+	106.888i	0.0427332	+	0.0310475i
$229$	3401.89	+	2471.62i	0.981673	+	0.713227i	0.958082	−	0.286494i	$-0.0924900\pi$
$229$	3401.89	+	2471.62i	0.981673	+	0.713227i	0.0235912	+	0.999722i	$0.492490\pi$
$230$	2365.62	−	3647.49i	0.678193	−	1.04569i
$231$	−5111.31	+	3713.59i	−1.45584	+	1.05773i
$232$	−1575.42			−0.445824
$233$	−5028.05	+	3653.09i	−1.41373	+	1.02713i	−0.420961	+	0.907079i	$0.638307\pi$
$233$	−5028.05	+	3653.09i	−1.41373	+	1.02713i	−0.992767	+	0.120055i	$0.961693\pi$
$234$	93.8249	+	288.763i	0.0262116	+	0.0806712i
$235$	−2583.52	+	3983.46i	−0.717150	+	1.10576i
$236$	64.1197	−	197.340i	0.0176857	−	0.0544311i
$237$	840.073	+	2585.48i	0.230247	+	0.708629i
$238$	1652.79	+	5086.76i	0.450144	+	1.38540i
$239$	262.864	−	809.011i	0.0711432	−	0.218956i	−0.909163	−	0.416441i	$-0.863277\pi$
$239$	262.864	−	809.011i	0.0711432	−	0.218956i	0.980306	+	0.197485i	$0.0632773\pi$
$240$	760.017	+	203.161i	0.204412	+	0.0546417i
$241$	1457.32	+	4485.16i	0.389518	+	1.19881i	0.933149	+	0.359490i	$0.117049\pi$
$241$	1457.32	+	4485.16i	0.389518	+	1.19881i	−0.543631	+	0.839325i	$0.682951\pi$
$242$	−1015.10	+	737.515i	−0.269642	+	0.195906i
$243$	−2076.95			−0.548298
$244$	401.925	−	292.016i	0.105453	−	0.0766164i
$245$	−420.675	−	7936.56i	−0.109698	−	2.06958i
$246$	−147.212	−	106.956i	−0.0381540	−	0.0277205i
$247$	165.762	+	120.433i	0.0427012	+	0.0310243i
$248$	−208.321	+	641.146i	−0.0533403	+	0.164165i
$249$	1988.10			0.505988
$250$	2761.45	+	432.317i	0.698598	+	0.109369i
$251$	619.865			0.155879			0.0779393	−	0.996958i	$-0.475166\pi$
$251$	619.865			0.155879			0.0779393	+	0.996958i	$0.475166\pi$
$252$	−307.345	+	945.911i	−0.0768291	+	0.236456i
$253$	−6960.72	−	5057.26i	−1.72971	−	1.25671i
$254$	2647.84	+	1923.77i	0.654095	+	0.475228i
$255$	214.392	+	4044.77i	0.0526499	+	0.993308i
$256$	−207.108	+	150.473i	−0.0505636	+	0.0367366i
$257$	−3006.52			−0.729733			−0.364867	−	0.931060i	$-0.618885\pi$
$257$	−3006.52			−0.729733			−0.364867	+	0.931060i	$0.618885\pi$
$258$	−262.343	+	190.604i	−0.0633053	+	0.0459940i
$259$	−2303.55	−	7089.61i	−0.552648	−	1.70088i
$260$	856.332	+	228.907i	0.204259	+	0.0546008i
$261$	466.101	−	1434.51i	0.110540	−	0.340207i
$262$	−668.390	−	2057.09i	−0.157608	−	0.485067i
$263$	149.072	+	458.796i	0.0349512	+	0.107569i	0.967010	−	0.254738i	$-0.0819893\pi$
$263$	149.072	+	458.796i	0.0349512	+	0.107569i	−0.932059	+	0.362307i	$0.881989\pi$
$264$	481.122	−	1480.74i	0.112163	−	0.345202i
$265$	31.8271	−	49.0734i	0.00737782	−	0.0113757i
$266$	207.405	+	638.326i	0.0478075	+	0.147136i
$267$	3073.99	−	2233.38i	0.704587	−	0.511913i
$268$	−3116.67			−0.710377
$269$	−4209.63	+	3058.48i	−0.954148	+	0.693229i	−0.951784	−	0.306768i	$-0.900752\pi$
$269$	−4209.63	+	3058.48i	−0.954148	+	0.693229i	−0.00236368	+	0.999997i	$0.500752\pi$
$270$	−1854.60	+	2859.57i	−0.418028	+	0.644547i
$271$	1750.36	+	1271.71i	0.392351	+	0.285059i	0.766418	−	0.642342i	$-0.222037\pi$
$271$	1750.36	+	1271.71i	0.392351	+	0.285059i	−0.374067	+	0.927402i	$0.622037\pi$
$272$	−1066.33	−	774.732i	−0.237704	−	0.172702i
$273$	874.428	−	2691.21i	0.193856	−	0.596629i
$274$	−4635.83			−1.02212
$275$	1143.66	−	5412.17i	0.250783	−	1.18679i
$276$	3420.15			0.745902
$277$	−1542.39	+	4746.99i	−0.334561	+	1.02967i	0.632377	+	0.774660i	$0.282079\pi$
$277$	−1542.39	+	4746.99i	−0.334561	+	1.02967i	−0.966938	+	0.255011i	$0.917921\pi$
$278$	1716.19	+	1246.88i	0.370252	+	0.269004i
$279$	−522.168	−	379.377i	−0.112048	−	0.0814076i
$280$	1828.64	+	2255.44i	0.390293	+	0.481386i
$281$	−355.968	+	258.626i	−0.0755704	+	0.0549051i	−0.624929	−	0.780682i	$-0.714872\pi$
$281$	−355.968	+	258.626i	−0.0755704	+	0.0549051i	0.549359	+	0.835587i	$0.314872\pi$
$282$	−3735.19			−0.788748
$283$	2941.14	−	2136.86i	0.617783	−	0.448845i	−0.234364	−	0.972149i	$-0.575301\pi$
$283$	2941.14	−	2136.86i	0.617783	−	0.448845i	0.852146	+	0.523304i	$0.175301\pi$
$284$	758.229	+	2333.59i	0.158425	+	0.487581i
$285$	26.9036	+	507.570i	0.00559168	+	0.105494i
$286$	542.093	−	1668.39i	0.112079	−	0.344944i
$287$	−207.537	−	638.732i	−0.0426846	−	0.131370i
$288$	−75.7398	−	233.103i	−0.0154966	−	0.0476935i
$289$	578.844	−	1781.50i	0.117819	−	0.362609i
$290$	−2773.20	−	3420.45i	−0.561545	−	0.692607i
$291$	−888.049	−	2733.13i	−0.178895	−	0.550581i
$292$	2938.52	−	2134.96i	0.588917	−	0.427873i
$293$	7040.42			1.40377			0.701887	−	0.712288i	$-0.252341\pi$
$293$	7040.42			1.40377			0.701887	+	0.712288i	$0.252341\pi$
$294$	5058.36	−	3675.11i	1.00343	−	0.729037i
$295$	541.323	−	208.164i	0.106837	−	0.0410840i
$296$	1486.18	+	1079.77i	0.291833	+	0.212029i
$297$	5457.09	+	3964.80i	1.06617	+	0.774617i
$298$	−1131.28	+	3481.72i	−0.219911	+	0.676815i
$299$	3853.57			0.745344
$300$	896.764	+	2007.73i	0.172582	+	0.386388i
$301$	−1196.85			−0.229187
$302$	−979.908	+	3015.85i	−0.186713	+	0.574644i
$303$	2435.60	+	1769.57i	0.461788	+	0.335509i
$304$	−133.811	−	97.2194i	−0.0252454	−	0.0183418i
$305$	1341.52	+	358.602i	0.251852	+	0.0673230i
$306$	1020.92	−	741.742i	0.190726	−	0.138571i
$307$	3985.50			0.740927			0.370463	−	0.928847i	$-0.379199\pi$
$307$	3985.50			0.740927			0.370463	+	0.928847i	$0.379199\pi$
$308$	4648.97	−	3377.68i	0.860064	−	0.624873i
$309$	−5.24337	−	16.1374i	−0.000965323	−	0.00297096i
$310$	−1758.73	+	676.313i	−0.322222	+	0.123910i
$311$	1984.51	−	6107.70i	0.361837	−	1.11362i	−0.590101	−	0.807329i	$-0.700912\pi$
$311$	1984.51	−	6107.70i	0.361837	−	1.11362i	0.951938	−	0.306290i	$-0.0990878\pi$
$312$	215.487	+	663.202i	0.0391012	+	0.120341i
$313$	−2142.09	−	6592.67i	−0.386831	−	1.19054i	−0.935143	−	0.354269i	$-0.884730\pi$
$313$	−2142.09	−	6592.67i	−0.386831	−	1.19054i	0.548313	−	0.836273i	$-0.315270\pi$
$314$	−948.996	+	2920.71i	−0.170557	+	0.524921i
$315$	−2594.73	+	997.794i	−0.464115	+	0.178474i
$316$	−764.085	−	2351.61i	−0.136023	−	0.418634i
$317$	−5346.35	+	3884.35i	−0.947258	+	0.688223i	−0.950157	−	0.311773i	$-0.899077\pi$
$317$	−5346.35	+	3884.35i	−0.947258	+	0.688223i	0.00289895	+	0.999996i	$0.499077\pi$
$318$	46.0148			0.00811440
$319$	−7050.35	+	5122.38i	−1.23744	+	0.899053i
$320$	−691.270	−	184.784i	−0.120760	−	0.0322805i
$321$	−3721.16	−	2703.58i	−0.647024	−	0.470091i
$322$	10212.4	+	7419.77i	1.76744	+	1.28412i
$323$	263.154	−	809.903i	0.0453321	−	0.139518i
$324$	−1854.13			−0.317923
$325$	1010.41	+	2262.16i	0.172453	+	0.386099i
$326$	−3351.40			−0.569378
$327$	1566.33	−	4820.68i	0.264888	−	0.815241i
$328$	133.896	+	97.2811i	0.0225401	+	0.0163764i
$329$	−11153.1	−	8103.22i	−1.86897	−	1.35789i
$330$	4061.81	−	1561.96i	0.677562	−	0.260555i
$331$	3033.15	−	2203.71i	0.503676	−	0.365942i	−0.306743	−	0.951792i	$-0.599239\pi$
$331$	3033.15	−	2203.71i	0.503676	−	0.365942i	0.810420	+	0.585850i	$0.199239\pi$
$332$	−1808.27			−0.298921
$333$	−1422.90	+	1033.79i	−0.234157	+	0.170125i
$334$	−1271.94	−	3914.63i	−0.208376	−	0.641315i
$335$	−5486.27	−	6766.74i	−0.894767	−	1.10360i
$336$	−705.879	+	2172.47i	−0.114610	+	0.352732i
$337$	97.7299	+	300.782i	0.0157973	+	0.0486191i	0.958644	−	0.284606i	$-0.0918629\pi$
$337$	97.7299	+	300.782i	0.0157973	+	0.0486191i	−0.942847	+	0.333226i	$0.891863\pi$
$338$	−1115.03	−	3431.70i	−0.179436	−	0.552247i
$339$	−184.643	+	568.273i	−0.0295824	+	0.0910453i
$340$	−194.999	−	3678.90i	−0.0311039	−	0.586813i
$341$	1152.37	+	3546.62i	0.183003	+	0.563226i
$342$	128.113	−	93.0796i	0.0202560	−	0.0147169i
$343$	11942.1			1.87992
$344$	238.613	−	173.363i	0.0373987	−	0.0271718i
$345$	6020.48	+	7425.63i	0.939512	+	1.15879i
$346$	−6973.80	−	5066.77i	−1.08357	−	0.787257i
$347$	−4798.35	−	3486.20i	−0.742331	−	0.539335i	0.151109	−	0.988517i	$-0.451715\pi$
$347$	−4798.35	−	3486.20i	−0.742331	−	0.539335i	−0.893440	+	0.449182i	$0.851715\pi$
$348$	1070.49	−	3294.64i	0.164898	−	0.507503i
$349$	8313.16			1.27505			0.637526	−	0.770429i	$-0.279958\pi$
$349$	8313.16			1.27505			0.637526	+	0.770429i	$0.279958\pi$
$350$	−1677.92	+	7940.47i	−0.256253	+	1.21267i
$351$	−3021.13			−0.459419
$352$	−437.602	+	1346.80i	−0.0662621	+	0.203934i
$353$	2915.82	+	2118.46i	0.439641	+	0.319418i	0.785492	−	0.618872i	$-0.212410\pi$
$353$	2915.82	+	2118.46i	0.439641	+	0.319418i	−0.345851	+	0.938289i	$0.612410\pi$
$354$	369.124	+	268.184i	0.0554201	+	0.0402651i
$355$	−3731.85	+	5754.03i	−0.557932	+	0.860260i
$356$	−2795.93	+	2031.36i	−0.416247	+	0.302421i
$357$	−11760.9			−1.74357
$358$	4405.19	−	3200.56i	0.650340	−	0.472499i
$359$	2483.37	+	7643.04i	0.365090	+	1.12363i	0.949924	+	0.312480i	$0.101160\pi$
$359$	2483.37	+	7643.04i	0.365090	+	1.12363i	−0.584834	+	0.811153i	$0.698840\pi$
$360$	372.775	−	574.772i	0.0545750	−	0.0841477i
$361$	−2086.53	+	6421.66i	−0.304203	+	0.936239i
$362$	−806.767	−	2482.97i	−0.117135	−	0.360503i
$363$	−852.590	−	2624.00i	−0.123277	−	0.379406i
$364$	−795.332	+	2447.78i	−0.114524	+	0.352469i
$365$	9807.95	+	2621.78i	1.40650	+	0.375973i
$366$	337.579	+	1038.96i	0.0482119	+	0.148381i
$367$	−10517.3	+	7641.29i	−1.49591	+	1.08684i	−0.523940	+	0.851755i	$0.675538\pi$
$367$	−10517.3	+	7641.29i	−1.49591	+	1.08684i	−0.971974	+	0.235090i	$0.924462\pi$
$368$	−3110.78			−0.440654
$369$	−128.194	+	93.1387i	−0.0180855	+	0.0131399i
$370$	271.778	+	5127.43i	0.0381866	+	0.720438i
$371$	137.398	+	99.8257i	0.0192274	+	0.0139695i
$372$	−1199.26	−	871.315i	−0.167147	−	0.121440i
$373$	−2157.81	+	6641.04i	−0.299536	+	0.921877i	0.682124	+	0.731237i	$0.261056\pi$
$373$	−2157.81	+	6641.04i	−0.299536	+	0.921877i	−0.981660	+	0.190641i	$0.938944\pi$
$374$	−7291.05			−1.00805
$375$	−2780.49	+	5481.20i	−0.382891	+	0.754795i
$376$	3397.32			0.465967
$377$	1206.15	−	3712.15i	0.164774	−	0.507124i
$378$	−8006.37	−	5816.97i	−1.08943	−	0.791515i
$379$	741.524	+	538.749i	0.100500	+	0.0730176i	0.636900	−	0.770946i	$-0.280216\pi$
$379$	741.524	+	538.749i	0.100500	+	0.0730176i	−0.536400	+	0.843964i	$0.680216\pi$
$380$	−24.4700	−	461.658i	−0.00330338	−	0.0623225i
$381$	−5822.33	+	4230.17i	−0.782906	+	0.568814i
$382$	7930.90			1.06225
$383$	−453.273	+	329.322i	−0.0604730	+	0.0439362i	−0.617611	−	0.786484i	$-0.711899\pi$
$383$	−453.273	+	329.322i	−0.0604730	+	0.0439362i	0.557138	+	0.830420i	$0.311899\pi$
$384$	−173.951	−	535.367i	−0.0231170	−	0.0711467i
$385$	15517.0	+	4147.87i	2.05408	+	0.549078i
$386$	−1199.72	+	3692.35i	−0.158197	+	0.486880i
$387$	87.2611	+	268.562i	0.0114618	+	0.0352759i
$388$	807.721	+	2485.91i	0.105685	+	0.325265i
$389$	−917.355	+	2823.33i	−0.119567	+	0.367991i	−0.992872	−	0.119183i	$-0.961972\pi$
$389$	−917.355	+	2823.33i	−0.119567	+	0.367991i	0.873305	+	0.487174i	$0.161972\pi$
$390$	−1060.58	+	1635.29i	−0.137704	+	0.212323i
$391$	−4949.31	−	15232.4i	−0.640147	−	1.97017i
$392$	−4600.81	+	3342.68i	−0.592796	+	0.430691i
$393$	4756.12			0.610470
$394$	3266.02	−	2372.90i	0.417613	−	0.303414i
$395$	3760.67	−	5798.47i	0.479037	−	0.738615i
$396$	−1096.87	−	796.925i	−0.139192	−	0.101129i
$397$	5115.40	+	3716.55i	0.646686	+	0.469845i	0.862141	−	0.506669i	$-0.169123\pi$
$397$	5115.40	+	3716.55i	0.646686	+	0.469845i	−0.215455	+	0.976514i	$0.569123\pi$
$398$	609.078	−	1874.55i	0.0767094	−	0.236087i
$399$	−1475.85			−0.185175
$400$	−815.648	−	1826.12i	−0.101956	−	0.228265i
$401$	−3008.68			−0.374679			−0.187339	−	0.982295i	$-0.559986\pi$
$401$	−3008.68			−0.374679			−0.187339	+	0.982295i	$0.559986\pi$
$402$	2117.77	−	6517.83i	0.262748	−	0.808656i
$403$	−1351.24	−	981.734i	−0.167023	−	0.121349i
$404$	−2215.29	−	1609.50i	−0.272809	−	0.198207i
$405$	−3263.82	−	4025.57i	−0.400445	−	0.493907i
$406$	10343.9	−	7515.30i	1.26443	−	0.918666i
$407$	10161.8			1.23760
$408$	2344.75	−	1703.56i	0.284515	−	0.206712i
$409$	3472.20	+	10686.3i	0.419778	+	1.29194i	0.907907	+	0.419172i	$0.137680\pi$
$409$	3472.20	+	10686.3i	0.419778	+	1.29194i	−0.488129	+	0.872771i	$0.662320\pi$
$410$	24.4855	+	461.951i	0.00294940	+	0.0556442i
$411$	3150.04	−	9694.82i	0.378053	−	1.16353i
$412$	4.76908	+	14.6777i	0.000570281	+	0.00175514i
$413$	520.384	+	1601.58i	0.0620010	+	0.190819i
$414$	920.352	−	2832.55i	0.109258	−	0.336262i
$415$	−3183.09	−	3926.01i	−0.376511	−	0.464386i
$416$	−195.996	−	603.212i	−0.0230997	−	0.0710936i
$417$	−3773.72	+	2741.77i	−0.443165	+	0.321978i
$418$	−914.937			−0.107060
$419$	−3609.66	+	2622.57i	−0.420867	+	0.305778i	−0.777987	−	0.628281i	$-0.783759\pi$
$419$	−3609.66	+	2622.57i	−0.420867	+	0.305778i	0.357119	+	0.934059i	$0.383759\pi$
$420$	−5959.30	+	2291.63i	−0.692343	+	0.266239i
$421$	4617.41	+	3354.74i	0.534534	+	0.388361i	0.822051	−	0.569414i	$-0.192830\pi$
$421$	4617.41	+	3354.74i	0.534534	+	0.388361i	−0.287517	+	0.957775i	$0.592830\pi$
$422$	−7010.80	−	5093.64i	−0.808721	−	0.587570i
$423$	−1005.13	+	3093.46i	−0.115534	+	0.355577i
$424$	−41.8525			−0.00479372
$425$	7644.17	−	6899.33i	0.872462	−	0.787451i
$426$	−5395.40			−0.613634
$427$	−1245.95	+	3834.65i	−0.141208	+	0.434595i
$428$	3384.56	+	2459.03i	0.382241	+	0.277714i
$429$	3120.72	+	2267.33i	0.351211	+	0.255170i
$430$	796.425	+	212.893i	0.0893186	+	0.0238759i
$431$	6487.97	−	4713.79i	0.725092	−	0.526810i	−0.162915	−	0.986640i	$-0.552090\pi$
$431$	6487.97	−	4713.79i	0.725092	−	0.526810i	0.888007	+	0.459830i	$0.152090\pi$
$432$	2438.80			0.271613
$433$	−4678.75	+	3399.31i	−0.519276	+	0.377276i	−0.816331	−	0.577584i	$-0.803995\pi$
$433$	−4678.75	+	3399.31i	−0.519276	+	0.377276i	0.297055	+	0.954860i	$0.403995\pi$
$434$	−1690.70	−	5203.43i	−0.186995	−	0.575513i
$435$	9037.51	−	3475.35i	0.996127	−	0.383058i
$436$	−1424.65	+	4384.62i	−0.156487	+	0.481618i
$437$	−621.078	−	1911.48i	−0.0679867	−	0.209242i
$438$	2468.08	+	7595.95i	0.269245	+	0.828650i
$439$	3630.68	−	11174.1i	0.394721	−	1.21483i	−0.534457	−	0.845196i	$-0.679484\pi$
$439$	3630.68	−	11174.1i	0.394721	−	1.21483i	0.929178	−	0.369632i	$-0.120516\pi$
$440$	−3694.41	+	1420.67i	−0.400282	+	0.153927i
$441$	−1682.52	−	5178.27i	−0.181678	−	0.559148i
$442$	2641.89	−	1919.44i	0.284303	−	0.206558i
$443$	3568.50			0.382719			0.191360	−	0.981520i	$-0.438710\pi$
$443$	3568.50			0.382719			0.191360	+	0.981520i	$0.438710\pi$
$444$	−3267.96	+	2374.31i	−0.349303	+	0.253784i
$445$	−9332.04	−	2494.56i	−0.994115	−	0.265738i
$446$	8411.03	+	6110.97i	0.892990	+	0.648795i
$447$	−6512.55	−	4731.65i	−0.689112	−	0.500669i
$448$	642.029	−	1975.96i	0.0677076	−	0.208383i
$449$	−14369.1			−1.51029			−0.755145	−	0.655558i	$-0.772434\pi$
$449$	−14369.1			−1.51029			−0.755145	+	0.655558i	$0.772434\pi$
$450$	1904.11	−	202.422i	0.199468	−	0.0212050i
$451$	915.518			0.0955878
$452$	167.941	−	516.870i	0.0174763	−	0.0537866i
$453$	−5641.13	−	4098.52i	−0.585085	−	0.425089i
$454$	−6059.05	−	4402.15i	−0.626355	−	0.455073i
$455$	−6714.50	+	2582.04i	−0.691826	+	0.266040i
$456$	294.237	−	213.776i	0.0302169	−	0.0219539i
$457$	−402.073			−0.0411558			−0.0205779	−	0.999788i	$-0.506551\pi$
$457$	−402.073			−0.0411558			−0.0205779	+	0.999788i	$0.506551\pi$
$458$	6803.78	−	4943.23i	0.694148	−	0.504328i
$459$	3880.17	+	11941.9i	0.394577	+	1.21438i
$460$	−5475.90	−	6753.95i	−0.555033	−	0.684575i
$461$	2232.00	−	6869.38i	0.225498	−	0.694010i	−0.772743	−	0.634719i	$-0.781116\pi$
$461$	2232.00	−	6869.38i	0.225498	−	0.694010i	0.998241	−	0.0592914i	$-0.0188841\pi$
$462$	3904.70	+	12017.4i	0.393210	+	1.21018i
$463$	−1012.67	−	3116.67i	−0.101647	−	0.312838i	0.887282	−	0.461228i	$-0.152591\pi$
$463$	−1012.67	−	3116.67i	−0.101647	−	0.312838i	−0.988929	+	0.148390i	$0.952591\pi$
$464$	−973.661	+	2996.62i	−0.0974162	+	0.299816i
$465$	−219.309	−	4137.54i	−0.0218714	−	0.412632i
$466$	3841.09	+	11821.7i	0.381835	+	1.17517i
$467$	4679.36	−	3399.75i	0.463672	−	0.336877i	−0.331298	−	0.943526i	$-0.607487\pi$
$467$	4679.36	−	3399.75i	0.463672	−	0.336877i	0.794970	+	0.606649i	$0.207487\pi$
$468$	607.248			0.0599787
$469$	20463.6	−	14867.6i	2.01475	−	1.46380i
$470$	5980.29	+	7376.06i	0.586916	+	0.723899i
$471$	−5463.18	−	3969.23i	−0.534459	−	0.388307i
$472$	−335.735	−	243.926i	−0.0327404	−	0.0237873i
$473$	504.169	−	1551.67i	0.0490100	−	0.150837i
$474$	5437.07			0.526863
$475$	959.250	−	865.782i	0.0926598	−	0.0836312i
$476$	10697.1			1.03004
$477$	12.3824	−	38.1092i	0.00118858	−	0.00365807i
$478$	−1376.37	−	999.992i	−0.131702	−	0.0956874i
$479$	−1896.17	−	1377.64i	−0.180873	−	0.131412i	0.493665	−	0.869652i	$-0.335657\pi$
$479$	−1896.17	−	1377.64i	−0.180873	−	0.131412i	−0.674538	+	0.738241i	$0.735657\pi$
$480$	856.152	−	1320.08i	0.0814121	−	0.125527i
$481$	−3682.10	+	2675.20i	−0.349042	+	0.253594i
$482$	9431.94			0.891314
$483$	−22456.1	+	16315.3i	−2.11551	+	1.53701i
$484$	775.469	+	2386.65i	0.0728277	+	0.224141i
$485$	−3975.43	+	6129.61i	−0.372196	+	0.573879i
$486$	−1283.63	+	3950.60i	−0.119808	+	0.368730i
$487$	3635.26	+	11188.2i	0.338253	+	1.04104i	0.965097	+	0.261892i	$0.0843463\pi$
$487$	3635.26	+	11188.2i	0.338253	+	1.04104i	−0.626844	+	0.779145i	$0.715654\pi$
$488$	−307.044	−	944.983i	−0.0284820	−	0.0876585i
$489$	2277.27	−	7008.72i	0.210597	−	0.648150i
$490$	−15356.2	−	4104.89i	−1.41576	−	0.378449i
$491$	3398.57	+	10459.7i	0.312374	+	0.961387i	0.976822	+	0.214053i	$0.0686666\pi$
$491$	3398.57	+	10459.7i	0.312374	+	0.961387i	−0.664448	+	0.747334i	$0.731333\pi$
$492$	−294.424	+	213.912i	−0.0269790	+	0.0196014i
$493$	−16222.5			−1.48200
$494$	331.525	−	240.867i	0.0301943	−	0.0219375i
$495$	−200.585	−	3784.29i	−0.0182134	−	0.343619i
$496$	1090.78	+	792.501i	0.0987452	+	0.0717426i
$497$	−16110.5	−	11704.9i	−1.45403	−	1.05642i
$498$	1228.72	−	3781.60i	0.110562	−	0.340276i
$499$	12608.1			1.13109			0.565545	−	0.824717i	$-0.308666\pi$
$499$	12608.1			1.13109			0.565545	+	0.824717i	$0.308666\pi$
$500$	2528.99	−	4985.40i	0.226199	−	0.445908i
$501$	9050.87			0.807112
$502$	383.098	−	1179.05i	0.0340607	−	0.104828i
$503$	2621.20	+	1904.41i	0.232353	+	0.168814i	0.697870	−	0.716225i	$-0.254131\pi$
$503$	2621.20	+	1904.41i	0.232353	+	0.168814i	−0.465517	+	0.885039i	$0.654131\pi$
$504$	1609.28	+	1169.21i	0.142228	+	0.103335i
$505$	−405.110	−	7642.92i	−0.0356974	−	0.673476i
$506$	−13921.4	+	10114.5i	−1.22309	+	0.888627i
$507$	7934.29			0.695018
$508$	5295.68	−	3847.53i	0.462515	−	0.336037i
$509$	1458.15	+	4487.74i	0.126977	+	0.390797i	0.994256	−	0.107026i	$-0.0341329\pi$
$509$	1458.15	+	4487.74i	0.126977	+	0.390797i	−0.867279	+	0.497823i	$0.834133\pi$
$510$	7826.11	+	2092.01i	0.679502	+	0.181639i
$511$	−9109.30	+	28035.6i	−0.788595	+	2.42704i
$512$	158.217	+	486.941i	0.0136568	+	0.0420312i
$513$	486.914	+	1498.57i	0.0419060	+	0.128973i
$514$	−1858.13	+	5718.74i	−0.159453	+	0.490744i
$515$	−23.4724	+	36.1915i	−0.00200838	+	0.00309668i
$516$	200.412	+	616.806i	0.0170982	+	0.0526228i
$517$	15203.8	−	11046.2i	1.29335	−	0.939673i
$518$	−14908.9			−1.26459
$519$	15334.7	−	11141.3i	1.29695	−	0.942292i
$520$	964.649	−	1487.37i	0.0813513	−	0.125433i
$521$	7016.16	+	5097.54i	0.589987	+	0.428651i	0.842311	−	0.538992i	$-0.181195\pi$
$521$	7016.16	+	5097.54i	0.589987	+	0.428651i	−0.252324	+	0.967643i	$0.581195\pi$
$522$	−2440.53	−	1773.15i	−0.204635	−	0.148676i
$523$	1447.19	−	4454.00i	0.120997	−	0.372390i	−0.872154	−	0.489232i	$-0.837277\pi$
$523$	1447.19	−	4454.00i	0.120997	−	0.372390i	0.993150	+	0.116842i	$0.0372772\pi$
$524$	−4325.91			−0.360646
$525$	−15465.6	−	8904.53i	−1.28566	−	0.740239i
$526$	964.814			0.0799769
$527$	−2145.14	+	6602.07i	−0.177313	+	0.545713i
$528$	−2519.19	−	1830.30i	−0.207639	−	0.150859i
$529$	−20738.1	−	15067.1i	−1.70445	−	1.23836i
$530$	−73.6728	−	90.8677i	−0.00603801	−	0.00744725i
$531$	321.439	−	233.539i	0.0262698	−	0.0190861i
$532$	1342.35			0.109395
$533$	−331.735	+	241.020i	−0.0269588	+	0.0195867i
$534$	−2348.32	−	7227.37i	−0.190303	−	0.585691i
$535$	618.935	+	11677.0i	0.0500166	+	0.943626i
$536$	−1926.21	+	5928.26i	−0.155223	+	0.477728i
$537$	3699.94	+	11387.3i	0.297327	+	0.915077i
$538$	3215.87	+	9897.44i	0.257707	+	0.793139i
$539$	−9721.11	+	29918.5i	−0.776842	+	2.39087i
$540$	4293.01	+	5294.98i	0.342114	+	0.421962i
$541$	1143.80	+	3520.25i	0.0908980	+	0.279755i	0.986163	−	0.165779i	$-0.0530138\pi$
$541$	1143.80	+	3520.25i	0.0908980	+	0.279755i	−0.895265	+	0.445534i	$0.853014\pi$
$542$	3500.73	−	2543.43i	0.277434	−	0.201567i
$543$	5740.78			0.453703
$544$	−2132.65	+	1549.46i	−0.168082	+	0.122119i
$545$	−12027.4	+	4625.12i	−0.945320	+	0.363520i
$546$	−4578.57	−	3326.52i	−0.358873	−	0.260736i
$547$	−15680.7	−	11392.7i	−1.22570	−	0.890524i	−0.229141	−	0.973393i	$-0.573592\pi$
$547$	−15680.7	−	11392.7i	−1.22570	−	0.890524i	−0.996560	+	0.0828689i	$0.973592\pi$
$548$	−2865.10	+	8817.88i	−0.223341	+	0.687374i
$549$	951.304			0.0739539
$550$	−9587.73	−	5520.27i	−0.743313	−	0.427973i
$551$	−2035.73			−0.157396
$552$	2113.77	−	6505.51i	0.162985	−	0.501618i
$553$	16234.9	+	11795.3i	1.24842	+	0.907032i
$554$	8076.06	+	5867.60i	0.619348	+	0.449983i
$555$	−10907.5	−	2915.71i	−0.834234	−	0.223000i
$556$	3432.37	−	2493.76i	0.261807	−	0.190214i
$557$	−4428.74			−0.336897			−0.168448	−	0.985710i	$-0.553876\pi$
$557$	−4428.74			−0.336897			−0.168448	+	0.985710i	$0.553876\pi$
$558$	−1044.34	+	758.755i	−0.0792299	+	0.0575639i
$559$	225.810	+	694.972i	0.0170854	+	0.0525835i
$560$	5420.25	−	2084.34i	0.409014	−	0.157285i
$561$	4954.25	−	15247.6i	0.372849	−	1.14751i
$562$	271.936	+	836.932i	0.0204109	+	0.0628182i
$563$	3421.90	+	10531.5i	0.256156	+	0.788367i	0.993600	+	0.112959i	$0.0360327\pi$
$563$	3421.90	+	10531.5i	0.256156	+	0.788367i	−0.737444	+	0.675409i	$0.763967\pi$
$564$	−2308.47	+	7104.74i	−0.172348	+	0.530432i
$565$	1417.82	−	545.220i	0.105572	−	0.0405975i
$566$	−2246.83	−	6915.03i	−0.166857	−	0.513534i
$567$	12173.9	−	8844.85i	0.901685	−	0.655113i
$568$	4907.36			0.362515
$569$	21829.5	−	15860.1i	1.60833	−	1.16852i	0.739903	−	0.672714i	$-0.234872\pi$
$569$	21829.5	−	15860.1i	1.60833	−	1.16852i	0.868432	−	0.495809i	$-0.165128\pi$
$570$	982.082	+	262.522i	0.0721665	+	0.0192909i
$571$	−10821.3	−	7862.17i	−0.793099	−	0.576220i	0.115783	−	0.993275i	$-0.463062\pi$
$571$	−10821.3	−	7862.17i	−0.793099	−	0.576220i	−0.908881	+	0.417055i	$0.863062\pi$
$572$	−2838.43	−	2062.24i	−0.207484	−	0.150746i
$573$	−5389.03	+	16585.7i	−0.392897	+	1.20921i
$574$	−1343.20			−0.0976730
$575$	5024.57	−	23777.9i	0.364416	−	1.72453i
$576$	−490.198			−0.0354599
$577$	3221.69	−	9915.34i	0.232445	−	0.715391i	−0.765005	−	0.644024i	$-0.777264\pi$
$577$	3221.69	−	9915.34i	0.232445	−	0.715391i	0.997450	−	0.0713674i	$-0.0227363\pi$
$578$	−3030.87	−	2202.05i	−0.218110	−	0.158466i
$579$	−6906.52	−	5017.88i	−0.495726	−	0.360166i
$580$	−8220.02	+	3160.99i	−0.588479	+	0.226298i
$581$	11872.8	−	8626.10i	0.847792	−	0.615957i
$582$	−5747.57			−0.409355
$583$	−187.299	+	136.081i	−0.0133056	+	0.00966706i
$584$	−2244.83	−	6908.87i	−0.159061	−	0.489539i
$585$	1068.94	+	1318.42i	0.0755471	+	0.0931794i
$586$	4351.22	−	13391.7i	0.306736	−	0.944036i
$587$	−4132.00	−	12717.0i	−0.290538	−	0.894184i	−0.984684	−	0.174350i	$-0.944218\pi$
$587$	−4132.00	−	12717.0i	−0.290538	−	0.894184i	0.694146	−	0.719835i	$-0.255782\pi$
$588$	−3864.24	−	11892.9i	−0.271018	−	0.834108i
$589$	−269.189	+	828.479i	−0.0188315	+	0.0579573i
$590$	−61.3959	−	1158.31i	−0.00428411	−	0.0808252i
$591$	2743.15	+	8442.54i	0.190927	+	0.587614i
$592$	2972.36	−	2159.55i	0.206357	−	0.149927i
$593$	−2768.13			−0.191693			−0.0958463	−	0.995396i	$-0.530556\pi$
$593$	−2768.13			−0.191693			−0.0958463	+	0.995396i	$0.530556\pi$
$594$	10914.2	−	7929.61i	0.753895	−	0.547737i
$595$	18830.0	+	23224.9i	1.29740	+	1.60021i
$596$	5923.46	+	4303.65i	0.407105	+	0.295779i
$597$	3506.34	+	2547.50i	0.240377	+	0.174644i
$598$	2381.64	−	7329.93i	0.162864	−	0.501243i
$599$	4098.71			0.279580			0.139790	−	0.990181i	$-0.455357\pi$
$599$	4098.71			0.279580			0.139790	+	0.990181i	$0.455357\pi$
$600$	4373.16	−	464.902i	0.297556	−	0.0316326i
$601$	−17523.5			−1.18935			−0.594673	−	0.803968i	$-0.702718\pi$
$601$	−17523.5			−1.18935			−0.594673	+	0.803968i	$0.702718\pi$
$602$	−739.693	+	2276.54i	−0.0500791	+	0.154128i
$603$	−4828.15	−	3507.85i	−0.326065	−	0.236900i
$604$	5130.87	+	3727.79i	0.345649	+	0.251129i
$605$	−3816.70	+	5884.87i	−0.256481	+	0.395461i
$606$	4871.21	−	3539.14i	0.326533	−	0.237240i
$607$	14982.0			1.00182			0.500908	−	0.865501i	$-0.333000\pi$
$607$	14982.0			1.00182			0.500908	+	0.865501i	$0.333000\pi$
$608$	−267.622	+	194.439i	−0.0178512	+	0.0129696i
$609$	8687.92	+	26738.7i	0.578083	+	1.77916i
$610$	1511.20	−	2330.09i	0.100306	−	0.154660i
$611$	−2601.02	+	8005.10i	−0.172219	+	0.530036i
$612$	−779.914	−	2400.33i	−0.0515133	−	0.158542i
$613$	−9223.52	−	28387.1i	−0.607723	−	1.87038i	−0.476859	−	0.878980i	$-0.658225\pi$
$613$	−9223.52	−	28387.1i	−0.607723	−	1.87038i	−0.130864	−	0.991400i	$-0.541775\pi$
$614$	2463.17	−	7580.87i	0.161898	−	0.498272i
$615$	−982.706	−	262.688i	−0.0644334	−	0.0172238i
$616$	−3551.50	−	10930.4i	−0.232295	−	0.714932i
$617$	−15515.7	+	11272.8i	−1.01238	+	0.735538i	−0.964707	−	0.263325i	$-0.915181\pi$
$617$	−15515.7	+	11272.8i	−1.01238	+	0.735538i	−0.0476742	+	0.998863i	$0.515181\pi$
$618$	−33.9358			−0.00220890
$619$	−12120.6	+	8806.12i	−0.787023	+	0.571806i	−0.907079	−	0.420961i	$-0.861693\pi$
$619$	−12120.6	+	8806.12i	−0.787023	+	0.571806i	0.120055	+	0.992767i	$0.461693\pi$
$620$	199.471	+	3763.28i	0.0129209	+	0.243769i
$621$	23975.3	+	17419.0i	1.54927	+	1.12561i
$622$	−10391.0	−	7549.53i	−0.669843	−	0.486670i
$623$	8667.29	−	26675.2i	0.557380	−	1.71544i
$624$	1394.66			0.0894731
$625$	15275.8	−	3285.00i	0.977650	−	0.210240i
$626$	−13863.9			−0.885164
$627$	621.698	−	1913.39i	0.0395984	−	0.121871i
$628$	4969.01	+	3610.20i	0.315741	+	0.229399i
$629$	15303.6	+	11118.7i	0.970103	+	0.704821i
$630$	294.289	+	5552.13i	0.0186107	+	0.351115i
$631$	−15151.7	+	11008.3i	−0.955908	+	0.694508i	−0.952197	−	0.305485i	$-0.901181\pi$
$631$	−15151.7	+	11008.3i	−0.955908	+	0.694508i	−0.00371118	+	0.999993i	$0.501181\pi$
$632$	−4945.26			−0.311253
$633$	15416.0	−	11200.4i	0.967982	−	0.703280i
$634$	4084.24	+	12570.0i	0.255846	+	0.787412i
$635$	17675.5	+	4724.86i	1.10462	+	0.295276i
$636$	28.4387	−	87.5253i	0.00177306	−	0.00545692i
$637$	−4353.94	−	13400.1i	−0.270816	−	0.833485i
$638$	5385.98	+	16576.4i	0.334221	+	1.02863i
$639$	−1451.89	+	4468.44i	−0.0898837	+	0.276634i
$640$	−778.709	+	1200.67i	−0.0480956	+	0.0741573i
$641$	−5889.14	−	18124.9i	−0.362881	−	1.11683i	−0.951297	−	0.308275i	$-0.900248\pi$
$641$	−5889.14	−	18124.9i	−0.362881	−	1.11683i	0.588416	−	0.808558i	$-0.299752\pi$
$642$	−7442.32	+	5407.16i	−0.457515	+	0.332404i
$643$	−10953.1			−0.671768			−0.335884	−	0.941903i	$-0.609035\pi$
$643$	−10953.1			−0.671768			−0.335884	+	0.941903i	$0.609035\pi$
$644$	20424.9	−	14839.5i	1.24977	−	0.908012i
$645$	−986.388	+	1520.89i	−0.0602155	+	0.0928446i
$646$	−1377.89	−	1001.10i	−0.0839201	−	0.0609715i
$647$	8682.80	+	6308.42i	0.527598	+	0.383323i	0.819459	−	0.573138i	$-0.194274\pi$
$647$	8682.80	+	6308.42i	0.527598	+	0.383323i	−0.291860	+	0.956461i	$0.594274\pi$
$648$	−1145.91	+	3526.76i	−0.0694688	+	0.213803i
$649$	−2295.60			−0.138845
$650$	4927.35	−	523.817i	0.297333	−	0.0316089i
$651$	12030.6			0.724298
$652$	−2071.28	+	6374.75i	−0.124414	+	0.382906i
$653$	6391.92	+	4644.00i	0.383055	+	0.278306i	0.762604	−	0.646866i	$-0.223921\pi$
$653$	6391.92	+	4644.00i	0.383055	+	0.278306i	−0.379548	+	0.925172i	$0.623921\pi$
$654$	−8201.42	−	5958.68i	−0.490368	−	0.356274i
$655$	−7614.89	−	9392.17i	−0.454257	−	0.560278i
$656$	267.792	−	194.562i	0.0159383	−	0.0115798i
$657$	6955.08			0.413004
$658$	−22306.2	+	16206.4i	−1.32156	+	0.960171i
$659$	−4537.13	−	13963.8i	−0.268196	−	0.825423i	−0.990940	−	0.134307i	$-0.957119\pi$
$659$	−4537.13	−	13963.8i	−0.268196	−	0.825423i	0.722743	−	0.691116i	$-0.242881\pi$
$660$	−460.683	−	8691.38i	−0.0271698	−	0.512593i
$661$	−3412.01	+	10501.1i	−0.200774	+	0.617919i	0.799086	+	0.601216i	$0.205317\pi$
$661$	−3412.01	+	10501.1i	−0.200774	+	0.617919i	−0.999860	+	0.0167028i	$0.994683\pi$
$662$	−2317.12	−	7131.36i	−0.136038	−	0.418683i
$663$	2218.94	+	6829.18i	0.129979	+	0.400035i
$664$	−1117.57	+	3439.54i	−0.0653166	+	0.201024i
$665$	2362.94	+	2914.44i	0.137791	+	0.169950i
$666$	1087.00	+	3345.43i	0.0632436	+	0.194644i
$667$	−30975.1	+	22504.7i	−1.79814	+	1.30643i
$668$	−8232.18			−0.476815
$669$	−18495.0	+	13437.4i	−1.06885	+	0.776563i
$670$	−16261.8	+	6253.43i	−0.937684	+	0.360584i
$671$	−4446.64	−	3230.68i	−0.255828	−	0.185870i
$672$	3696.03	+	2685.32i	0.212169	+	0.154150i
$673$	4257.81	−	13104.2i	0.243873	−	0.750564i	−0.751947	−	0.659224i	$-0.770885\pi$
$673$	4257.81	−	13104.2i	0.243873	−	0.750564i	0.995820	−	0.0913399i	$-0.0291150\pi$
$674$	632.521			0.0361481
$675$	−3939.18	+	18641.5i	−0.224621	+	1.06298i
$676$	−7216.60			−0.410594
$677$	1996.34	−	6144.11i	0.113332	−	0.348799i	−0.878264	−	0.478177i	$-0.841298\pi$
$677$	1996.34	−	6144.11i	0.113332	−	0.348799i	0.991595	+	0.129377i	$0.0412978\pi$
$678$	966.804	+	702.424i	0.0547638	+	0.0397882i
$679$	−17162.0	−	12468.9i	−0.969983	−	0.704734i
$680$	−7118.21	−	1902.78i	−0.401428	−	0.107306i
$681$	13323.2	−	9679.90i	0.749703	−	0.544691i
$682$	7458.27			0.418756
$683$	9137.33	−	6638.66i	0.511904	−	0.371920i	−0.301641	−	0.953421i	$-0.597535\pi$
$683$	9137.33	−	6638.66i	0.511904	−	0.371920i	0.813545	+	0.581501i	$0.197535\pi$
$684$	−97.8697	−	301.212i	−0.00547097	−	0.0168379i
$685$	−24188.3	+	9301.54i	−1.34918	+	0.518823i
$686$	7380.60	−	22715.2i	0.410777	−	1.26424i
$687$	5714.53	+	17587.5i	0.317355	+	0.976718i
$688$	−182.284	−	561.013i	−0.0101010	−	0.0310878i
$689$	32.0426	−	98.6170i	0.00177174	−	0.00545284i
$690$	17845.2	−	6862.34i	0.984575	−	0.378616i
$691$	828.470	+	2549.77i	0.0456100	+	0.140373i	0.971268	−	0.237988i	$-0.0764878\pi$
$691$	828.470	+	2549.77i	0.0456100	+	0.140373i	−0.925658	+	0.378361i	$0.876488\pi$
$692$	−13947.6	+	10133.5i	−0.766197	+	0.556675i
$693$	11003.5			0.603158
$694$	−9596.70	+	6972.41i	−0.524907	+	0.381367i
$695$	11456.3	+	3062.40i	0.625270	+	0.167142i
$696$	−5605.17	−	4072.39i	−0.305264	−	0.221787i
$697$	1378.76	+	1001.73i	0.0749275	+	0.0544380i
$698$	5137.82	−	15812.6i	0.278609	−	0.857471i
$699$	−27332.4			−1.47898
$700$	14066.7	+	8099.08i	0.759528	+	0.437309i
$701$	−34520.6			−1.85995			−0.929976	−	0.367620i	$-0.880173\pi$
$701$	−34520.6			−1.85995			−0.929976	+	0.367620i	$0.880173\pi$
$702$	−1867.16	+	5746.54i	−0.100387	+	0.308959i
$703$	1920.42	+	1395.26i	0.103030	+	0.0748555i
$704$	2291.31	+	1664.74i	0.122666	+	0.0891224i
$705$	−19489.0	+	7494.44i	−1.04113	+	0.400364i
$706$	5831.63	−	4236.93i	0.310873	−	0.225862i
$707$	22223.1			1.18216
$708$	738.248	−	536.369i	0.0391879	−	0.0284717i
$709$	−6361.25	−	19577.9i	−0.336956	−	1.03704i	−0.965751	−	0.259472i	$-0.916451\pi$
$709$	−6361.25	−	19577.9i	−0.336956	−	1.03704i	0.628794	−	0.777572i	$-0.283549\pi$
$710$	8638.42	+	10654.6i	0.456611	+	0.563182i
$711$	1463.10	−	4502.95i	0.0771736	−	0.237516i
$712$	2135.90	+	6573.62i	0.112424	+	0.346007i
$713$	5062.82	+	15581.8i	0.265925	+	0.818432i
$714$	−7268.64	+	22370.6i	−0.380983	+	1.17255i
$715$	−519.064	−	9792.80i	−0.0271495	−	0.512210i
$716$	−3365.27	−	10357.2i	−0.175651	−	0.540597i
$717$	3026.50	−	2198.88i	0.157639	−	0.114531i
$718$	16072.7			0.835417
$719$	8049.33	−	5848.18i	0.417510	−	0.303339i	−0.359125	−	0.933289i	$-0.616925\pi$
$719$	8049.33	−	5848.18i	0.417510	−	0.303339i	0.776635	+	0.629951i	$0.216925\pi$
$720$	−862.894	−	1064.29i	−0.0446641	−	0.0550885i
$721$	−101.331	−	73.6213i	−0.00523407	−	0.00380277i
$722$	10925.2	+	7937.61i	0.563149	+	0.409151i
$723$	−6408.98	+	19724.8i	−0.329672	+	1.01463i
$724$	−5221.50			−0.268033
$725$	−21332.6	−	12282.6i	−1.09279	−	0.629190i
$726$	−5518.08			−0.282087
$727$	−2960.41	+	9111.21i	−0.151026	+	0.464809i	−0.997737	−	0.0672442i	$-0.978579\pi$
$727$	−2960.41	+	9111.21i	−0.151026	+	0.464809i	0.846711	+	0.532053i	$0.178579\pi$
$728$	4164.41	+	3025.62i	0.212010	+	0.154034i
$729$	−17514.7	−	12725.2i	−0.889840	−	0.646506i
$730$	11048.6	−	17035.5i	0.560172	−	0.863715i
$731$	2457.07	−	1785.16i	0.124320	−	0.0903238i
$732$	2184.86			0.110321
$733$	25696.8	−	18669.8i	1.29486	−	0.940772i	0.294970	−	0.955507i	$-0.404690\pi$
$733$	25696.8	−	18669.8i	1.29486	−	0.940772i	0.999891	+	0.0147351i	$0.00469049\pi$
$734$	8034.53	+	24727.7i	0.404032	+	1.24348i
$735$	19019.0	−	29324.9i	0.954457	−	1.47165i
$736$	−1922.57	+	5917.06i	−0.0962865	+	0.296339i
$737$	10655.2	+	32793.3i	0.532549	+	1.63902i
$738$	97.9319	+	301.403i	0.00488472	+	0.0150336i
$739$	4249.28	−	13077.9i	0.211519	−	0.650987i	−0.787864	−	0.615849i	$-0.788813\pi$
$739$	4249.28	−	13077.9i	0.211519	−	0.650987i	0.999382	−	0.0351378i	$-0.0111870\pi$
$740$	9920.91	+	2651.97i	0.492838	+	0.131741i
$741$	278.449	+	856.979i	0.0138044	+	0.0424857i
$742$	274.797	−	199.651i	0.0135958	−	0.00987795i
$743$	−6312.16			−0.311670			−0.155835	−	0.987783i	$-0.549807\pi$
$743$	−6312.16			−0.311670			−0.155835	+	0.987783i	$0.549807\pi$
$744$	−2398.52	+	1742.63i	−0.118191	+	0.0858708i
$745$	1083.22	+	20436.4i	0.0532701	+	1.00501i
$746$	11298.4	+	8208.78i	0.554510	+	0.402875i
$747$	−2801.26	−	2035.23i	−0.137206	−	0.0996857i
$748$	−4506.11	+	13868.4i	−0.220267	+	0.677913i
$749$	−33952.9			−1.65636
$750$	8707.42	+	8676.38i	0.423934	+	0.422422i
$751$	40114.6			1.94914			0.974569	−	0.224087i	$-0.0719400\pi$
$751$	40114.6			1.94914			0.974569	+	0.224087i	$0.0719400\pi$
$752$	2099.66	−	6462.09i	0.101817	−	0.313362i
$753$	2205.42	+	1602.33i	0.106733	+	0.0775459i
$754$	−6315.49	−	4588.47i	−0.305035	−	0.221621i
$755$	938.281	+	17701.9i	0.0452285	+	0.853293i
$756$	−16012.7	+	11633.9i	−0.770341	+	0.559686i
$757$	−8151.37			−0.391369			−0.195685	−	0.980667i	$-0.562693\pi$
$757$	−8151.37			−0.391369			−0.195685	+	0.980667i	$0.562693\pi$
$758$	1483.05	−	1077.50i	0.0710643	−	0.0516312i
$759$	−11692.7	−	35986.4i	−0.559181	−	1.72098i
$760$	−893.248	−	238.775i	−0.0426336	−	0.0113964i
$761$	−1730.96	+	5327.36i	−0.0824538	+	0.253767i	−0.983781	−	0.179371i	$-0.942594\pi$
$761$	−1730.96	+	5327.36i	−0.0824538	+	0.253767i	0.901328	+	0.433138i	$0.142594\pi$
$762$	4447.87	+	13689.1i	0.211456	+	0.650793i
$763$	−11562.2	−	35584.8i	−0.548597	−	1.68841i
$764$	4901.56	−	15085.5i	0.232110	−	0.714362i
$765$	3838.57	−	5918.59i	0.181417	−	0.279722i
$766$	346.270	+	1065.71i	0.0163332	+	0.0502684i
$767$	831.804	−	604.341i	0.0391587	−	0.0284504i
$768$	−1125.84			−0.0528973
$769$	−2973.61	+	2160.45i	−0.139442	+	0.101311i	−0.655320	−	0.755352i	$-0.727466\pi$
$769$	−2973.61	+	2160.45i	−0.139442	+	0.101311i	0.515877	+	0.856662i	$0.327466\pi$
$770$	17479.7	−	26951.5i	0.818086	−	1.26138i
$771$	−10696.9	−	7771.73i	−0.499661	−	0.363025i
$772$	6281.80	+	4563.99i	0.292859	+	0.212774i
$773$	−2094.03	+	6444.75i	−0.0974345	+	0.299873i	−0.987881	−	0.155216i	$-0.950393\pi$
$773$	−2094.03	+	6444.75i	−0.0974345	+	0.299873i	0.890446	+	0.455089i	$0.150393\pi$
$774$	564.766			0.0262275
$775$	−7819.49	+	7057.57i	−0.362431	+	0.327117i
$776$	5227.68			0.241833
$777$	10130.6	−	31178.7i	0.467738	−	1.43955i
$778$	4803.33	+	3489.83i	0.221347	+	0.160818i
$779$	173.018	+	125.705i	0.00795766	+	0.00578158i
$780$	2455.02	+	3028.01i	0.112697	+	0.139000i
$781$	21961.6	−	15956.0i	1.00621	−	0.731051i
$782$	−32032.6			−1.46481
$783$	24283.9	−	17643.3i	1.10835	−	0.805263i
$784$	3514.70	+	10817.1i	0.160109	+	0.492764i
$785$	908.682	+	17143.4i	0.0413150	+	0.779459i
$786$	2939.45	−	9046.69i	0.133393	−	0.410540i
$787$	1608.89	+	4951.65i	0.0728725	+	0.224278i	0.980858	−	0.194722i	$-0.0623805\pi$
$787$	1608.89	+	4951.65i	0.0728725	+	0.224278i	−0.907986	+	0.419001i	$0.862381\pi$
$788$	−2495.02	−	7678.87i	−0.112794	−	0.347143i
$789$	−655.588	+	2017.69i	−0.0295812	+	0.0910416i
$790$	−8705.13	−	10736.9i	−0.392044	−	0.483545i
$791$	1362.98	+	4194.82i	0.0612668	+	0.188560i
$792$	−2193.75	+	1593.85i	−0.0984235	+	0.0715089i
$793$	2461.74			0.110238
$794$	10230.8	−	7433.11i	0.457276	−	0.332231i
$795$	240.090	−	92.3260i	0.0107108	−	0.00411883i
$796$	−3189.17	−	2317.07i	−0.142007	−	0.103174i
$797$	26265.4	+	19082.9i	1.16734	+	0.848121i	0.990688	−	0.136153i	$-0.0434738\pi$
$797$	26265.4	+	19082.9i	1.16734	+	0.848121i	0.176650	+	0.984274i	$0.443474\pi$
$798$	−912.125	+	2807.23i	−0.0404623	+	0.124530i
$799$	34983.2			1.54896
$800$	−3977.59	+	422.849i	−0.175786	+	0.0186875i
$801$	−6617.60			−0.291912
$802$	−1859.47	+	5722.85i	−0.0818703	+	0.251971i
$803$	−32509.9	−	23619.8i	−1.42870	−	1.03801i
$804$	−11088.8	−	8056.48i	−0.486408	−	0.353396i
$805$	68172.6	+	18223.3i	2.98481	+	0.797872i
$806$	−2702.48	+	1963.47i	−0.118103	+	0.0858067i
$807$	−22883.5			−0.998187
$808$	−4430.58	+	3219.01i	−0.192905	+	0.140154i
$809$	4880.74	+	15021.4i	0.212111	+	0.652811i	0.999346	+	0.0361575i	$0.0115118\pi$
$809$	4880.74	+	15021.4i	0.212111	+	0.652811i	−0.787235	+	0.616653i	$0.788488\pi$
$810$	−9674.25	+	3720.20i	−0.419652	+	0.161376i
$811$	1468.40	−	4519.27i	0.0635789	−	0.195676i	−0.914221	−	0.405215i	$-0.867197\pi$
$811$	1468.40	−	4519.27i	0.0635789	−	0.195676i	0.977800	+	0.209540i	$0.0671965\pi$
$812$	−7902.06	−	24320.0i	−0.341512	−	1.05107i
$813$	2940.28	+	9049.25i	0.126839	+	0.390370i
$814$	6280.34	−	19328.9i	0.270425	−	0.832282i
$815$	−17486.6	+	6724.40i	−0.751567	+	0.289013i
$816$	−1791.23	−	5512.83i	−0.0768450	−	0.236504i
$817$	308.332	−	224.016i	0.0132034	−	0.00959282i
$818$	22472.5			0.960555
$819$	−3987.09	+	2896.79i	−0.170110	+	0.123592i
$820$	893.815	+	238.927i	0.0380651	+	0.0101752i
$821$	−33068.5	−	24025.6i	−1.40572	−	1.02132i	−0.993927	−	0.110039i	$-0.964902\pi$
$821$	−33068.5	−	24025.6i	−1.40572	−	1.02132i	−0.411794	−	0.911277i	$-0.635098\pi$
$822$	−16493.8	−	11983.5i	−0.699863	−	0.508480i
$823$	4691.60	−	14439.2i	0.198710	−	0.611568i	−0.801203	−	0.598393i	$-0.795806\pi$
$823$	4691.60	−	14439.2i	0.198710	−	0.611568i	0.999913	−	0.0131750i	$-0.00419385\pi$
$824$	30.8661			0.00130494
$825$	18059.3	−	16299.6i	0.762113	−	0.687854i
$826$	3367.99			0.141874
$827$	−4888.31	+	15044.7i	−0.205542	+	0.632593i	0.794149	+	0.607723i	$0.207917\pi$
$827$	−4888.31	+	15044.7i	−0.205542	+	0.632593i	−0.999691	+	0.0248693i	$0.992083\pi$
$828$	−4819.02	−	3501.23i	−0.202262	−	0.146952i
$829$	−1.67554	−	1.21735i	−7.01976e−5	−	5.10015e-5i	0.587750	−	0.809042i	$-0.300014\pi$
$829$	−1.67554	−	1.21735i	−7.01976e−5	−	5.10015e-5i	−0.587820	+	0.808991i	$0.700014\pi$
$830$	−9434.98	+	3628.19i	−0.394570	+	0.151731i
$831$	−17758.5	+	12902.3i	−0.741317	+	0.538598i
$832$	−1268.51			−0.0528578
$833$	−47375.8	+	34420.6i	−1.97056	+	1.43169i
$834$	2882.87	+	8872.55i	0.119695	+	0.368383i
$835$	−14491.1	−	17873.2i	−0.600580	−	0.740753i
$836$	−565.462	+	1740.31i	−0.0233935	+	0.0719976i
$837$	−3969.17	−	12215.8i	−0.163912	−	0.504470i
$838$	2757.53	+	8486.82i	0.113672	+	0.349848i
$839$	5938.00	−	18275.3i	0.244341	−	0.752005i	−0.751403	−	0.659844i	$-0.770622\pi$
$839$	5938.00	−	18275.3i	0.244341	−	0.752005i	0.995744	−	0.0921615i	$-0.0293776\pi$
$840$	675.893	+	12751.6i	0.0277625	+	0.523775i
$841$	4447.16	+	13686.9i	0.182343	+	0.561193i
$842$	9234.81	−	6709.49i	0.377972	−	0.274613i
$843$	−1935.04			−0.0790584
$844$	−14021.6	+	10187.3i	−0.571852	+	0.415475i
$845$	−12703.3	−	15668.3i	−0.517170	−	0.637875i
$846$	5262.91	+	3823.73i	0.213880	+	0.155393i
$847$	−16476.8	−	11971.1i	−0.668416	−	0.485633i
$848$	−25.8663	+	79.6082i	−0.00104747	+	0.00322377i
$849$	15988.0			0.646296
$850$	−8398.96	−	18804.1i	−0.338920	−	0.758794i
$851$	44645.0			1.79837
$852$	−3334.54	+	10262.7i	−0.134084	+	0.412668i
$853$	20360.1	+	14792.5i	0.817253	+	0.593769i	0.915924	−	0.401351i	$-0.131459\pi$
$853$	20360.1	+	14792.5i	0.817253	+	0.593769i	−0.0986714	+	0.995120i	$0.531459\pi$
$854$	6523.90	+	4739.89i	0.261409	+	0.189925i
$855$	481.694	−	742.711i	0.0192674	−	0.0297078i
$856$	6769.13	−	4918.06i	0.270285	−	0.196374i
$857$	32539.4			1.29699			0.648497	−	0.761217i	$-0.275398\pi$
$857$	32539.4			1.29699			0.648497	+	0.761217i	$0.275398\pi$
$858$	6241.43	−	4534.67i	0.248344	−	0.180432i
$859$	14076.7	+	43323.7i	0.559129	+	1.72082i	0.684783	+	0.728747i	$0.259897\pi$
$859$	14076.7	+	43323.7i	0.559129	+	1.72082i	−0.125654	+	0.992074i	$0.540103\pi$
$860$	897.165	−	1383.31i	0.0355733	−	0.0548496i
$861$	912.704	−	2809.02i	0.0361265	−	0.111186i
$862$	−4956.37	−	15254.1i	−0.195841	−	0.602735i
$863$	1234.72	+	3800.08i	0.0487027	+	0.149892i	0.972450	−	0.233110i	$-0.0748903\pi$
$863$	1234.72	+	3800.08i	0.0487027	+	0.149892i	−0.923748	+	0.383002i	$0.874890\pi$
$864$	1507.26	−	4638.87i	0.0593496	−	0.182659i
$865$	−46553.3	−	12444.2i	−1.82989	−	0.489151i
$866$	3574.25	+	11000.4i	0.140252	+	0.431650i
$867$	6664.58	−	4842.10i	0.261062	−	0.189673i
$868$	−10942.4			−0.427891
$869$	−22131.2	+	16079.2i	−0.863922	+	0.627676i
$870$	−1025.02	−	19338.2i	−0.0399441	−	0.753595i
$871$	−12494.0	−	9077.45i	−0.486044	−	0.353132i
$872$	7459.57	+	5419.69i	0.289694	+	0.210475i
$873$	−1546.65	+	4760.11i	−0.0599614	+	0.184542i
$874$	−4019.70			−0.155570
$875$	7177.25	+	44797.5i	0.277298	+	1.73078i
$876$	15973.7			0.616098
$877$	−757.438	+	2331.16i	−0.0291641	+	0.0897577i	−0.964579	−	0.263794i	$-0.915026\pi$
$877$	−757.438	+	2331.16i	−0.0291641	+	0.0897577i	0.935415	+	0.353552i	$0.115026\pi$
$878$	−19010.5	−	13811.9i	−0.730720	−	0.530899i
$879$	25049.1	+	18199.2i	0.961189	+	0.698345i
$880$	419.013	+	7905.20i	0.0160510	+	0.302823i
$881$	−28818.0	+	20937.5i	−1.10205	+	0.800684i	−0.981393	−	0.192011i	$-0.938499\pi$
$881$	−28818.0	+	20937.5i	−1.10205	+	0.800684i	−0.120654	+	0.992695i	$0.538499\pi$
$882$	−10889.5			−0.415724
$883$	−16992.6	+	12345.8i	−0.647617	+	0.470521i	−0.862459	−	0.506128i	$-0.831076\pi$
$883$	−16992.6	+	12345.8i	−0.647617	+	0.470521i	0.214842	+	0.976649i	$0.431076\pi$
$884$	−2018.22	−	6211.45i	−0.0767875	−	0.236328i
$885$	2464.07	+	658.673i	0.0935918	+	0.0250181i
$886$	2205.45	−	6787.69i	0.0836272	−	0.257378i
$887$	3762.96	+	11581.2i	0.142444	+	0.438398i	0.996673	−	0.0814984i	$-0.0259705\pi$
$887$	3762.96	+	11581.2i	0.142444	+	0.438398i	−0.854229	+	0.519896i	$0.825971\pi$
$888$	2496.50	+	7683.44i	0.0943435	+	0.290360i
$889$	−16416.4	+	50524.5i	−0.619335	+	1.90612i
$890$	−10512.5	+	16208.9i	−0.395931	+	0.610475i
$891$	6338.83	+	19508.9i	0.238338	+	0.733528i
$892$	16822.1	−	12221.9i	0.631440	−	0.458768i
$893$	4389.96			0.164507
$894$	−13025.1	+	9463.29i	−0.487276	+	0.354027i
$895$	16563.1	−	25538.3i	0.618597	−	0.953799i
$896$	−3361.71	−	2442.42i	−0.125342	−	0.0910666i
$897$	13710.6	+	9961.34i	0.510350	+	0.370791i
$898$	−8880.60	+	27331.7i	−0.330011	+	1.01567i
$899$	16594.6			0.615640
$900$	791.774	−	3746.93i	0.0293250	−	0.138775i
$901$	−430.967			−0.0159352
$902$	565.821	−	1741.42i	0.0208867	−	0.0642826i
$903$	−4258.26	−	3093.81i	−0.156928	−	0.114015i
$904$	−879.352	−	638.887i	−0.0323527	−	0.0235056i
$905$	−9191.40	−	11336.6i	−0.337605	−	0.416400i
$906$	−11282.3	+	8197.04i	−0.413718	+	0.300583i
$907$	−33352.4			−1.22100			−0.610501	−	0.792015i	$-0.709032\pi$
$907$	−33352.4			−1.22100			−0.610501	+	0.792015i	$0.709032\pi$
$908$	−12118.1	+	8804.31i	−0.442900	+	0.321786i
$909$	−1620.27	−	4986.68i	−0.0591210	−	0.181956i
$910$	761.546	+	14367.5i	0.0277418	+	0.523383i
$911$	5604.85	−	17249.9i	0.203839	−	0.627350i	−0.795921	−	0.605401i	$-0.793013\pi$
$911$	5604.85	−	17249.9i	0.203839	−	0.627350i	0.999759	−	0.0219494i	$-0.00698727\pi$
$912$	−224.777	−	691.793i	−0.00816131	−	0.0251179i
$913$	6182.06	+	19026.4i	0.224092	+	0.689685i
$914$	−248.495	+	764.789i	−0.00899287	+	0.0276772i
$915$	3846.00	+	4743.64i	0.138956	+	0.171388i
$916$	−5197.62	−	15996.6i	−0.187483	−	0.577013i
$917$	28403.2	−	20636.1i	1.02285	−	0.743147i
$918$	25113.0			0.902889
$919$	25633.4	−	18623.8i	0.920096	−	0.668489i	−0.0234522	−	0.999725i	$-0.507466\pi$
$919$	25633.4	−	18623.8i	0.920096	−	0.668489i	0.943548	+	0.331236i	$0.107466\pi$
$920$	−16231.1	+	6241.61i	−0.581655	+	0.223674i
$921$	14180.0	+	10302.4i	0.507325	+	0.368593i
$922$	−11686.9	−	8491.02i	−0.417448	−	0.303294i
$923$	−3757.12	+	11563.2i	−0.133984	+	0.412360i
$924$	25271.7			0.899761
$925$	11705.9	+	26208.0i	0.416096	+	0.931581i
$926$	−6554.13			−0.232594
$927$	−9.13201	+	28.1054i	−0.000323554	+	0.000995797i
$928$	5098.16	+	3704.03i	0.180340	+	0.131024i
$929$	22563.0	+	16393.0i	0.796844	+	0.578941i	0.909987	−	0.414638i	$-0.136092\pi$
$929$	22563.0	+	16393.0i	0.796844	+	0.578941i	−0.113143	+	0.993579i	$0.536092\pi$
$930$	−8005.61	−	2139.99i	−0.282273	−	0.0754549i
$931$	−5945.09	+	4319.36i	−0.209283	+	0.152053i
$932$	24860.1			0.873732
$933$	22848.8	−	16600.7i	0.801755	−	0.582509i
$934$	−3574.71	−	11001.8i	−0.125234	−	0.385429i
$935$	−38042.3	+	14629.1i	−1.33061	+	0.511681i
$936$	375.300	−	1155.05i	0.0131058	−	0.0403356i
$937$	−12599.7	−	38777.9i	−0.439290	−	1.35200i	−0.888626	−	0.458633i	$-0.848339\pi$
$937$	−12599.7	−	38777.9i	−0.439290	−	1.35200i	0.449336	−	0.893363i	$-0.351661\pi$
$938$	−15632.8	−	48112.7i	−0.544166	−	1.67477i
$939$	9420.48	−	28993.3i	0.327397	−	1.00762i
$940$	17726.1	−	6816.53i	0.615067	−	0.236522i
$941$	−7635.56	−	23499.8i	−0.264519	−	0.814105i	−0.991804	−	0.127769i	$-0.959218\pi$
$941$	−7635.56	−	23499.8i	−0.264519	−	0.814105i	0.727285	−	0.686335i	$-0.240782\pi$
$942$	−10926.4	+	7938.46i	−0.377919	+	0.274574i
$943$	4022.25			0.138900
$944$	−671.470	+	487.852i	−0.0231509	+	0.0168201i
$945$	−53446.1	−	14286.8i	−1.83979	−	0.491797i
$946$	−2639.86	−	1917.97i	−0.0907287	−	0.0659183i
$947$	−26803.1	−	19473.6i	−0.919730	−	0.668223i	0.0237270	−	0.999718i	$-0.492447\pi$
$947$	−26803.1	−	19473.6i	−0.919730	−	0.668223i	−0.943457	+	0.331496i	$0.892447\pi$
$948$	3360.29	−	10341.9i	0.115124	−	0.354314i
$949$	17998.0			0.615638
$950$	−1053.97	−	2359.68i	−0.0359949	−	0.0805876i
$951$	−29062.6			−0.990978
$952$	6611.15	−	20347.0i	0.225072	−	0.692701i
$953$	−26148.8	−	18998.2i	−0.888816	−	0.645763i	0.0467529	−	0.998906i	$-0.485113\pi$
$953$	−26148.8	−	18998.2i	−0.888816	−	0.645763i	−0.935569	+	0.353144i	$0.885113\pi$
$954$	−64.8352	−	47.1055i	−0.00220033	−	0.00159864i
$955$	41380.9	−	15912.9i	1.40215	−	0.539193i
$956$	−2752.74	+	1999.98i	−0.0931277	+	0.0676612i
$957$	−38325.5			−1.29455
$958$	−3792.33	+	2755.29i	−0.127896	+	0.0929221i
$959$	−23252.6	−	71564.3i	−0.782969	−	2.40973i
$960$	−1981.81	−	2444.35i	−0.0666277	−	0.0821782i
$961$	−7011.58	+	21579.4i	−0.235359	+	0.724361i
$962$	2812.87	+	8657.13i	0.0942730	+	0.290143i
$963$	2475.48	+	7618.74i	0.0828361	+	0.254943i
$964$	5829.26	−	17940.6i	0.194759	−	0.599407i
$965$	1148.75	+	21672.7i	0.0383209	+	0.722971i
$966$	17155.0	+	52797.6i	0.571379	+	1.75852i
$967$	−10355.3	+	7523.54i	−0.344367	+	0.250197i	−0.746502	−	0.665383i	$-0.768268\pi$
$967$	−10355.3	+	7523.54i	−0.344367	+	0.250197i	0.402135	+	0.915580i	$0.368268\pi$
$968$	5018.94			0.166648
$969$	3029.84	−	2201.31i	0.100446	−	0.0729786i
$970$	9202.26	+	11350.0i	0.304605	+	0.375698i
$971$	30611.3	+	22240.4i	1.01170	+	0.735046i	0.964566	−	0.263842i	$-0.0849898\pi$
$971$	30611.3	+	22240.4i	1.01170	+	0.735046i	0.0471385	+	0.998888i	$0.484990\pi$
$972$	6721.15	+	4883.20i	0.221791	+	0.161141i
$973$	−10640.2	+	32747.3i	−0.350576	+	1.07896i
$974$	23527.9			0.774006
$975$	−2252.68	+	10660.4i	−0.0739932	+	0.350160i
$976$	−1987.23			−0.0651738
$977$	9126.82	−	28089.5i	0.298867	−	0.919817i	−0.683028	−	0.730392i	$-0.739337\pi$
$977$	9126.82	−	28089.5i	0.298867	−	0.919817i	0.981895	−	0.189425i	$-0.0606625\pi$
$978$	−11923.9	−	8663.25i	−0.389863	−	0.283252i
$979$	30932.4	+	22473.7i	1.00981	+	0.733669i
$980$	−17298.6	+	26672.3i	−0.563862	+	0.869404i
$981$	−7141.93	+	5188.91i	−0.232441	+	0.168878i
$982$	21996.0			0.714788
$983$	859.475	−	624.445i	0.0278871	−	0.0202611i	−0.573754	−	0.819027i	$-0.694514\pi$
$983$	859.475	−	624.445i	0.0278871	−	0.0202611i	0.601641	+	0.798766i	$0.294514\pi$
$984$	224.920	+	692.232i	0.00728677	+	0.0224264i
$985$	12280.0	−	18934.1i	0.397230	−	0.612479i
$986$	−10026.1	+	30857.1i	−0.323829	+	0.996642i
$987$	−18735.1	−	57660.8i	−0.604200	−	1.85954i
$988$	−253.262	−	779.461i	−0.00815521	−	0.0250992i
$989$	2215.03	−	6817.15i	0.0712171	−	0.219184i
$990$	−7322.12	−	1957.29i	−0.235063	−	0.0628350i
$991$	15803.1	+	48637.0i	0.506561	+	1.55904i	0.798130	+	0.602486i	$0.205823\pi$
$991$	15803.1	+	48637.0i	0.506561	+	1.55904i	−0.291568	+	0.956550i	$0.594177\pi$
$992$	2181.57	−	1585.00i	0.0698234	−	0.0507297i
$993$	16488.1			0.526924
$994$	−32220.9	+	23409.9i	−1.02816	+	0.746998i
$995$	−583.204	−	11002.9i	−0.0185817	−	0.350568i
$996$	−6433.64	−	4674.31i	−0.204676	−	0.148706i
$997$	38107.1	+	27686.5i	1.21050	+	0.879477i	0.995276	−	0.0970879i	$-0.0309528\pi$
$997$	38107.1	+	27686.5i	1.21050	+	0.879477i	0.215221	+	0.976565i	$0.430953\pi$
$998$	7792.21	−	23982.0i	0.247152	−	0.760657i
$999$	−35000.9			−1.10849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.4.d.b.21.3	✓	16
5.2	odd	4		250.4.e.c.149.7		32
5.3	odd	4		250.4.e.c.149.2		32
5.4	even	2		250.4.d.b.101.2		16
25.6	even	5	inner	50.4.d.b.31.3	yes	16
25.8	odd	20		250.4.e.c.99.7		32
25.9	even	10		1250.4.a.g.1.6		8
25.16	even	5		1250.4.a.j.1.3		8
25.17	odd	20		250.4.e.c.99.2		32
25.19	even	10		250.4.d.b.151.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.4.d.b.21.3	✓	16	1.1	even	1	trivial
50.4.d.b.31.3	yes	16	25.6	even	5	inner
250.4.d.b.101.2		16	5.4	even	2
250.4.d.b.151.2		16	25.19	even	10
250.4.e.c.99.2		32	25.17	odd	20
250.4.e.c.99.7		32	25.8	odd	20
250.4.e.c.149.2		32	5.3	odd	4
250.4.e.c.149.7		32	5.2	odd	4
1250.4.a.g.1.6		8	25.9	even	10
1250.4.a.j.1.3		8	25.16	even	5

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.618034 - 1.90211i) q^{2} +(3.55790 + 2.58496i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(-0.591780 - 11.1647i) q^{5} +(7.11579 - 5.16993i) q^{6} +32.4633 q^{7} +(-6.47214 + 4.70228i) q^{8} +(-2.36687 - 7.28447i) q^{9} +(-21.6022 - 5.77451i) q^{10} +(-13.6751 + 42.0875i) q^{11} +(-5.43598 - 16.7302i) q^{12} +(-6.12486 - 18.8504i) q^{13} +(20.0634 - 61.7488i) q^{14} +(26.7548 - 41.2524i) q^{15} +(4.94427 + 15.2169i) q^{16} +(-66.6454 + 48.4207i) q^{17} -15.3187 q^{18} +(-8.36319 + 6.07621i) q^{19} +(-24.3347 + 37.5210i) q^{20} +(115.501 + 83.9163i) q^{21} +(71.6036 + 52.0231i) q^{22} +(-60.0803 + 184.908i) q^{23} -35.1824 q^{24} +(-124.300 + 13.2140i) q^{25} -39.6409 q^{26} +(47.1019 - 144.965i) q^{27} +(-105.053 - 76.3257i) q^{28} +(159.317 + 115.751i) q^{29} +(-61.9315 - 76.3860i) q^{30} +(68.1740 - 49.5313i) q^{31} +32.0000 q^{32} +(-157.449 + 114.394i) q^{33} +(50.9126 + 156.693i) q^{34} +(-19.2111 - 362.442i) q^{35} +(-9.46747 + 29.1379i) q^{36} +(-70.9588 - 218.389i) q^{37} +(6.38891 + 19.6630i) q^{38} +(26.9359 - 82.9003i) q^{39} +(56.3295 + 69.4765i) q^{40} +(-6.39296 - 19.6755i) q^{41} +(231.002 - 167.833i) q^{42} -36.8678 q^{43} +(143.207 - 104.046i) q^{44} +(-79.9280 + 30.7361i) q^{45} +(314.584 + 228.559i) q^{46} +(-343.561 - 249.612i) q^{47} +(-21.7439 + 66.9209i) q^{48} +710.864 q^{49} +(-51.6868 + 244.599i) q^{50} -362.283 q^{51} +(-24.4995 + 75.4016i) q^{52} +(4.23242 + 3.07504i) q^{53} +(-246.629 - 179.186i) q^{54} +(477.986 + 127.771i) q^{55} +(-210.107 + 152.651i) q^{56} -45.4621 q^{57} +(318.635 - 231.502i) q^{58} +(16.0299 + 49.3350i) q^{59} +(-183.571 + 70.5915i) q^{60} +(-38.3804 + 118.123i) q^{61} +(-52.0803 - 160.287i) q^{62} +(-76.8363 - 236.478i) q^{63} +(19.7771 - 60.8676i) q^{64} +(-206.834 + 79.5373i) q^{65} +(120.280 + 370.185i) q^{66} +(630.360 - 457.984i) q^{67} +329.513 q^{68} +(-691.740 + 502.578i) q^{69} +(-701.278 - 187.460i) q^{70} +(-496.268 - 360.560i) q^{71} +(49.5723 + 36.0164i) q^{72} +(-280.603 + 863.608i) q^{73} -459.255 q^{74} +(-476.403 - 274.296i) q^{75} +41.3499 q^{76} +(-443.937 + 1366.30i) q^{77} +(-141.038 - 102.470i) q^{78} +(500.100 + 363.344i) q^{79} +(166.966 - 64.2062i) q^{80} +(375.005 - 272.457i) q^{81} -41.3761 q^{82} +(365.730 - 265.719i) q^{83} +(-176.470 - 543.118i) q^{84} +(580.041 + 715.420i) q^{85} +(-22.7855 + 70.1266i) q^{86} +(267.623 + 823.659i) q^{87} +(-109.401 - 336.700i) q^{88} +(266.987 - 821.703i) q^{89} +(9.06529 + 171.028i) q^{90} +(-198.833 - 611.945i) q^{91} +(629.169 - 457.118i) q^{92} +370.592 q^{93} +(-687.123 + 499.224i) q^{94} +(72.7880 + 89.7764i) q^{95} +(113.853 + 82.7188i) q^{96} +(-528.660 - 384.094i) q^{97} +(439.338 - 1352.14i) q^{98} +338.953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 7 q^{3} - 16 q^{4} + 15 q^{5} + 14 q^{6} - 54 q^{7} - 32 q^{8} - 83 q^{9} - 50 q^{10} + 152 q^{11} - 12 q^{12} + 77 q^{13} + 52 q^{14} - 70 q^{15} - 64 q^{16} + 76 q^{17} + 304 q^{18} - 20 q^{19}+ \cdots - 1786 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 7 * q^3 - 16 * q^4 + 15 * q^5 + 14 * q^6 - 54 * q^7 - 32 * q^8 - 83 * q^9 - 50 * q^10 + 152 * q^11 - 12 * q^12 + 77 * q^13 + 52 * q^14 - 70 * q^15 - 64 * q^16 + 76 * q^17 + 304 * q^18 - 20 * q^19 + 20 * q^20 + 257 * q^21 - 226 * q^22 - 383 * q^23 - 64 * q^24 - 215 * q^25 - 716 * q^26 + 415 * q^27 + 4 * q^28 + 105 * q^29 + 140 * q^30 + 177 * q^31 + 512 * q^32 + 64 * q^33 + 342 * q^34 - 210 * q^35 - 332 * q^36 + 446 * q^37 + 90 * q^38 - 146 * q^39 - 40 * q^40 + 462 * q^41 + 514 * q^42 - 1058 * q^43 - 452 * q^44 - 865 * q^45 + 1124 * q^46 - 1114 * q^47 - 48 * q^48 + 1698 * q^49 - 550 * q^50 - 3608 * q^51 + 308 * q^52 + 567 * q^53 + 390 * q^54 - 210 * q^55 + 8 * q^56 - 1520 * q^57 + 210 * q^58 + 1275 * q^59 + 1260 * q^60 + 252 * q^61 - 176 * q^62 + 5402 * q^63 - 256 * q^64 + 2645 * q^65 + 998 * q^66 + 3296 * q^67 - 1976 * q^68 - 5491 * q^69 - 1750 * q^70 + 3712 * q^71 + 56 * q^72 - 1688 * q^73 - 1148 * q^74 - 6315 * q^75 - 200 * q^76 - 5453 * q^77 - 1152 * q^78 + 1750 * q^79 + 160 * q^80 + 4106 * q^81 - 1576 * q^82 - 2153 * q^83 - 612 * q^84 + 5860 * q^85 + 1074 * q^86 - 1255 * q^87 + 1216 * q^88 + 5660 * q^89 + 820 * q^90 - 493 * q^91 + 2248 * q^92 - 256 * q^93 - 2228 * q^94 - 1420 * q^95 + 224 * q^96 - 429 * q^97 - 674 * q^98 - 1786 * q^99

Introduction

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