LMFDB - Embedded newform 280.3.bi.c.179.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,3,Mod(179,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))

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

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

chi := DirichletCharacter("280.179");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	280.bi (of order $6$, 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:	$7.62944740209$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$88$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.1
Character	$\chi$	$=$	280.179
Dual form			280.3.bi.c.219.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.99950 + 0.0446276i) q^{2} +(2.20583 + 1.27354i) q^{3} +(3.99602 - 0.178466i) q^{4} +(-4.70583 - 1.68971i) q^{5} +(-4.46740 - 2.44800i) q^{6} +(-0.0496201 + 6.99982i) q^{7} +(-7.98208 + 0.535176i) q^{8} +(-1.25621 - 2.17582i) q^{9} +O(q^{10})$	\(q+(-1.99950 + 0.0446276i) q^{2} +(2.20583 + 1.27354i) q^{3} +(3.99602 - 0.178466i) q^{4} +(-4.70583 - 1.68971i) q^{5} +(-4.46740 - 2.44800i) q^{6} +(-0.0496201 + 6.99982i) q^{7} +(-7.98208 + 0.535176i) q^{8} +(-1.25621 - 2.17582i) q^{9} +(9.48473 + 3.16858i) q^{10} +(5.26267 - 9.11521i) q^{11} +(9.04182 + 4.69541i) q^{12} -22.3239 q^{13} +(-0.213170 - 13.9984i) q^{14} +(-8.22836 - 9.72027i) q^{15} +(15.9363 - 1.42631i) q^{16} +(-14.4854 - 8.36313i) q^{17} +(2.60889 + 4.29449i) q^{18} +(-1.44806 - 2.50812i) q^{19} +(-19.1061 - 5.91229i) q^{20} +(-9.02399 + 15.3772i) q^{21} +(-10.1159 + 18.4608i) q^{22} +(5.72017 + 9.90763i) q^{23} +(-18.2887 - 8.98497i) q^{24} +(19.2897 + 15.9030i) q^{25} +(44.6367 - 0.996263i) q^{26} -29.3230i q^{27} +(1.05095 + 27.9803i) q^{28} -13.9323i q^{29} +(16.8864 + 19.0685i) q^{30} +(-14.0310 - 8.10081i) q^{31} +(-31.8010 + 3.56310i) q^{32} +(23.2171 - 13.4044i) q^{33} +(29.3367 + 16.0756i) q^{34} +(12.0612 - 32.8562i) q^{35} +(-5.40814 - 8.47040i) q^{36} +(-20.8814 - 36.1677i) q^{37} +(3.00734 + 4.95037i) q^{38} +(-49.2428 - 28.4303i) q^{39} +(38.4666 + 10.9690i) q^{40} -60.6840 q^{41} +(17.3572 - 31.1495i) q^{42} +75.6609i q^{43} +(19.4030 - 37.3638i) q^{44} +(2.23500 + 12.3617i) q^{45} +(-11.8796 - 19.5550i) q^{46} +(-30.4013 - 52.6566i) q^{47} +(36.9692 + 17.1493i) q^{48} +(-48.9951 - 0.694664i) q^{49} +(-39.2796 - 30.9373i) q^{50} +(-21.3015 - 36.8953i) q^{51} +(-89.2068 + 3.98406i) q^{52} +(35.7027 - 61.8390i) q^{53} +(1.30861 + 58.6313i) q^{54} +(-40.1674 + 34.0023i) q^{55} +(-3.35006 - 55.8997i) q^{56} -7.37665i q^{57} +(0.621767 + 27.8577i) q^{58} +(9.89755 - 17.1431i) q^{59} +(-34.6154 - 37.3739i) q^{60} +(-20.0849 + 11.5960i) q^{61} +(28.4166 + 15.5714i) q^{62} +(15.2927 - 8.68527i) q^{63} +(63.4272 - 8.54363i) q^{64} +(105.053 + 37.7210i) q^{65} +(-45.8245 + 27.8383i) q^{66} +(-52.3532 - 30.2261i) q^{67} +(-59.3763 - 30.8340i) q^{68} +29.1394i q^{69} +(-22.6501 + 66.2342i) q^{70} +103.573i q^{71} +(11.1916 + 16.6952i) q^{72} +(70.8642 + 40.9135i) q^{73} +(43.3666 + 71.3855i) q^{74} +(22.2968 + 59.6456i) q^{75} +(-6.23410 - 9.76406i) q^{76} +(63.5438 + 37.2901i) q^{77} +(99.7298 + 54.6489i) q^{78} +(-41.3158 + 23.8537i) q^{79} +(-77.4036 - 20.2158i) q^{80} +(26.0380 - 45.0992i) q^{81} +(121.338 - 2.70818i) q^{82} -93.0788i q^{83} +(-33.3157 + 63.0582i) q^{84} +(54.0344 + 63.8316i) q^{85} +(-3.37657 - 151.284i) q^{86} +(17.7433 - 30.7324i) q^{87} +(-37.1288 + 75.5748i) q^{88} +(26.0769 + 45.1666i) q^{89} +(-5.02056 - 24.6174i) q^{90} +(1.10771 - 156.264i) q^{91} +(24.6261 + 38.5702i) q^{92} +(-20.6334 - 35.7380i) q^{93} +(63.1374 + 103.930i) q^{94} +(2.57634 + 14.2496i) q^{95} +(-74.6854 - 32.6402i) q^{96} +18.0979i q^{97} +(97.9968 - 0.797551i) q^{98} -26.4440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 14 q^{4} - 24 q^{6} + 284 q^{9}+O(q^{10}) $ 176 * q + 14 * q^4 - 24 * q^6 + 284 * q^9	$ 176 q + 14 q^{4} - 24 q^{6} + 284 q^{9} - 24 q^{10} + 32 q^{11} + 2 q^{14} + 50 q^{16} + 48 q^{20} + 16 q^{24} + 98 q^{25} - 90 q^{26} - 32 q^{30} - 256 q^{34} + 154 q^{35} - 68 q^{36} - 84 q^{40} - 328 q^{41} + 174 q^{44} - 26 q^{46} + 240 q^{49} - 96 q^{50} - 76 q^{51} - 116 q^{54} + 228 q^{56} + 244 q^{59} + 90 q^{60} - 268 q^{64} + 8 q^{65} - 304 q^{66} + 98 q^{70} - 98 q^{74} - 38 q^{75} - 612 q^{76} + 112 q^{80} - 168 q^{81} - 20 q^{84} - 16 q^{86} + 20 q^{89} + 800 q^{90} - 280 q^{91} + 226 q^{94} - 408 q^{96} - 88 q^{99}+O(q^{100}) $ 176 * q + 14 * q^4 - 24 * q^6 + 284 * q^9 - 24 * q^10 + 32 * q^11 + 2 * q^14 + 50 * q^16 + 48 * q^20 + 16 * q^24 + 98 * q^25 - 90 * q^26 - 32 * q^30 - 256 * q^34 + 154 * q^35 - 68 * q^36 - 84 * q^40 - 328 * q^41 + 174 * q^44 - 26 * q^46 + 240 * q^49 - 96 * q^50 - 76 * q^51 - 116 * q^54 + 228 * q^56 + 244 * q^59 + 90 * q^60 - 268 * q^64 + 8 * q^65 - 304 * q^66 + 98 * q^70 - 98 * q^74 - 38 * q^75 - 612 * q^76 + 112 * q^80 - 168 * q^81 - 20 * q^84 - 16 * q^86 + 20 * q^89 + 800 * q^90 - 280 * q^91 + 226 * q^94 - 408 * q^96 - 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.99950	+	0.0446276i	−0.999751	+	0.0223138i
$2$	−1.99950	+	0.0446276i	−0.999751	+	0.0223138i
$3$	2.20583	+	1.27354i	0.735277	+	0.424512i	0.820350	−	0.571862i	$-0.193779\pi$
$3$	2.20583	+	1.27354i	0.735277	+	0.424512i	−0.0850726	+	0.996375i	$0.527112\pi$
$4$	3.99602	−	0.178466i	0.999004	−	0.0446165i
$5$	−4.70583	−	1.68971i	−0.941167	−	0.337943i
$5$	−4.70583	−	1.68971i	−0.941167	−	0.337943i
$6$	−4.46740	−	2.44800i	−0.744566	−	0.408000i
$7$	−0.0496201	+	6.99982i	−0.00708858	+	0.999975i
$7$	−0.0496201	+	6.99982i	−0.00708858	+	0.999975i
$8$	−7.98208	+	0.535176i	−0.997760	+	0.0668970i
$9$	−1.25621	−	2.17582i	−0.139579	−	0.241757i
$10$	9.48473	+	3.16858i	0.948473	+	0.316858i
$11$	5.26267	−	9.11521i	0.478425	−	0.828656i	−0.521269	−	0.853392i	$-0.674541\pi$
$11$	5.26267	−	9.11521i	0.478425	−	0.828656i	0.999694	+	0.0247363i	$0.00787463\pi$
$12$	9.04182	+	4.69541i	0.753485	+	0.391284i
$13$	−22.3239			−1.71722			−0.858612	−	0.512626i	$-0.828673\pi$
$13$	−22.3239			−1.71722			−0.858612	+	0.512626i	$0.828673\pi$
$14$	−0.213170	−	13.9984i	−0.0152264	−	0.999884i
$15$	−8.22836	−	9.72027i	−0.548557	−	0.648018i
$16$	15.9363	−	1.42631i	0.996019	−	0.0891441i
$17$	−14.4854	−	8.36313i	−0.852080	−	0.491949i	0.00927215	−	0.999957i	$-0.497049\pi$
$17$	−14.4854	−	8.36313i	−0.852080	−	0.491949i	−0.861352	+	0.508008i	$0.830382\pi$
$18$	2.60889	+	4.29449i	0.144938	+	0.238583i
$19$	−1.44806	−	2.50812i	−0.0762139	−	0.132006i	0.825400	−	0.564549i	$-0.190950\pi$
$19$	−1.44806	−	2.50812i	−0.0762139	−	0.132006i	−0.901614	+	0.432543i	$0.857617\pi$
$20$	−19.1061	−	5.91229i	−0.955307	−	0.295615i
$21$	−9.02399	+	15.3772i	−0.429714	+	0.732249i
$22$	−10.1159	+	18.4608i	−0.459815	+	0.839125i
$23$	5.72017	+	9.90763i	0.248703	+	0.430766i	0.963166	−	0.268907i	$-0.0866623\pi$
$23$	5.72017	+	9.90763i	0.248703	+	0.430766i	−0.714463	+	0.699673i	$0.753329\pi$
$24$	−18.2887	−	8.98497i	−0.762028	−	0.374374i
$25$	19.2897	+	15.9030i	0.771589	+	0.636121i
$26$	44.6367	−	0.996263i	1.71680	−	0.0383178i
$27$		−	29.3230i		−	1.08604i
$28$	1.05095	+	27.9803i	0.0375338	+	0.999295i
$29$		−	13.9323i		−	0.480426i	−0.970720	−	0.240213i	$-0.922783\pi$
$29$		−	13.9323i		−	0.480426i	0.970720	−	0.240213i	$-0.0772172\pi$
$30$	16.8864	+	19.0685i	0.562880	+	0.635617i
$31$	−14.0310	−	8.10081i	−0.452613	−	0.261316i	0.256320	−	0.966592i	$-0.417490\pi$
$31$	−14.0310	−	8.10081i	−0.452613	−	0.261316i	−0.708933	+	0.705276i	$0.750823\pi$
$32$	−31.8010	+	3.56310i	−0.993782	+	0.111347i
$33$	23.2171	−	13.4044i	0.703549	−	0.406194i
$34$	29.3367	+	16.0756i	0.862845	+	0.472813i
$35$	12.0612	−	32.8562i	0.344606	−	0.938748i
$36$	−5.40814	−	8.47040i	−0.150226	−	0.235289i
$37$	−20.8814	−	36.1677i	−0.564363	−	0.977506i	−0.997109	−	0.0759895i	$-0.975788\pi$
$37$	−20.8814	−	36.1677i	−0.564363	−	0.977506i	0.432745	−	0.901516i	$-0.357545\pi$
$38$	3.00734	+	4.95037i	0.0791405	+	0.130273i
$39$	−49.2428	−	28.4303i	−1.26264	−	0.728983i
$40$	38.4666	+	10.9690i	0.961666	+	0.274224i
$41$	−60.6840			−1.48010			−0.740048	−	0.672554i	$-0.765197\pi$
$41$	−60.6840			−1.48010			−0.740048	+	0.672554i	$0.765197\pi$
$42$	17.3572	−	31.1495i	0.413267	−	0.741655i
$43$			75.6609i			1.75956i	0.475384	+	0.879778i	$0.342309\pi$
$43$			75.6609i			1.75956i	−0.475384	+	0.879778i	$0.657691\pi$
$44$	19.4030	−	37.3638i	0.440977	−	0.849176i
$45$	2.23500	+	12.3617i	0.0496666	+	0.274703i
$46$	−11.8796	−	19.5550i	−0.258253	−	0.425110i
$47$	−30.4013	−	52.6566i	−0.646836	−	1.12035i	−0.983874	−	0.178862i	$-0.942758\pi$
$47$	−30.4013	−	52.6566i	−0.646836	−	1.12035i	0.337038	−	0.941491i	$-0.390575\pi$
$48$	36.9692	+	17.1493i	0.770192	+	0.357277i
$49$	−48.9951	−	0.694664i	−0.999900	−	0.0141768i
$50$	−39.2796	−	30.9373i	−0.785592	−	0.618745i
$51$	−21.3015	−	36.8953i	−0.417676	−	0.723437i
$52$	−89.2068	+	3.98406i	−1.71551	+	0.0766165i
$53$	35.7027	−	61.8390i	0.673637	−	1.16677i	−0.303229	−	0.952918i	$-0.598065\pi$
$53$	35.7027	−	61.8390i	0.673637	−	1.16677i	0.976865	−	0.213855i	$-0.0686021\pi$
$54$	1.30861	+	58.6313i	0.0242336	+	1.08577i
$55$	−40.1674	+	34.0023i	−0.730316	+	0.618223i
$56$	−3.35006	−	55.8997i	−0.0598226	−	0.998209i
$57$		−	7.37665i		−	0.129415i
$58$	0.621767	+	27.8577i	0.0107201	+	0.480306i
$59$	9.89755	−	17.1431i	0.167755	−	0.290560i	−0.769875	−	0.638195i	$-0.779682\pi$
$59$	9.89755	−	17.1431i	0.167755	−	0.290560i	0.937630	+	0.347634i	$0.113015\pi$
$60$	−34.6154	−	37.3739i	−0.576923	−	0.622898i
$61$	−20.0849	+	11.5960i	−0.329261	+	0.190099i	−0.655513	−	0.755184i	$-0.727548\pi$
$61$	−20.0849	+	11.5960i	−0.329261	+	0.190099i	0.326252	+	0.945283i	$0.394214\pi$
$62$	28.4166	+	15.5714i	0.458332	+	0.251152i
$63$	15.2927	−	8.68527i	0.242741	−	0.137861i
$64$	63.4272	−	8.54363i	0.991050	−	0.133494i
$65$	105.053	+	37.7210i	1.61619	+	0.580324i
$66$	−45.8245	+	27.8383i	−0.694310	+	0.421792i
$67$	−52.3532	−	30.2261i	−0.781391	−	0.451136i	0.0555319	−	0.998457i	$-0.482315\pi$
$67$	−52.3532	−	30.2261i	−0.781391	−	0.451136i	−0.836923	+	0.547321i	$0.815648\pi$
$68$	−59.3763	−	30.8340i	−0.873180	−	0.453442i
$69$			29.1394i			0.422310i
$70$	−22.6501	+	66.2342i	−0.323573	+	0.946203i
$71$			103.573i			1.45878i	0.684100	+	0.729388i	$0.260195\pi$
$71$			103.573i			1.45878i	−0.684100	+	0.729388i	$0.739805\pi$
$72$	11.1916	+	16.6952i	0.155439	+	0.231878i
$73$	70.8642	+	40.9135i	0.970742	+	0.560458i	0.899462	−	0.436998i	$-0.143958\pi$
$73$	70.8642	+	40.9135i	0.970742	+	0.560458i	0.0712797	+	0.997456i	$0.477292\pi$
$74$	43.3666	+	71.3855i	0.586035	+	0.964669i
$75$	22.2968	+	59.6456i	0.297291	+	0.795274i
$76$	−6.23410	−	9.76406i	−0.0820277	−	0.128474i
$77$	63.5438	+	37.2901i	0.825244	+	0.484287i
$78$	99.7298	+	54.6489i	1.27859	+	0.700627i
$79$	−41.3158	+	23.8537i	−0.522985	+	0.301945i	−0.738155	−	0.674631i	$-0.764303\pi$
$79$	−41.3158	+	23.8537i	−0.522985	+	0.301945i	0.215170	+	0.976577i	$0.430969\pi$
$80$	−77.4036	−	20.2158i	−0.967545	−	0.252698i
$81$	26.0380	−	45.0992i	0.321457	−	0.556780i
$82$	121.338	−	2.70818i	1.47973	−	0.0330266i
$83$		−	93.0788i		−	1.12143i	−0.828008	−	0.560716i	$-0.810526\pi$
$83$		−	93.0788i		−	1.12143i	0.828008	−	0.560716i	$-0.189474\pi$
$84$	−33.3157	+	63.0582i	−0.396615	+	0.750692i
$85$	54.0344	+	63.8316i	0.635699	+	0.750960i
$86$	−3.37657	−	151.284i	−0.0392624	−	1.75912i
$87$	17.7433	−	30.7324i	0.203947	−	0.353246i
$88$	−37.1288	+	75.5748i	−0.421918	+	0.858805i
$89$	26.0769	+	45.1666i	0.292999	+	0.507490i	0.974517	−	0.224312i	$-0.0720133\pi$
$89$	26.0769	+	45.1666i	0.292999	+	0.507490i	−0.681518	+	0.731801i	$0.738680\pi$
$90$	−5.02056	−	24.6174i	−0.0557840	−	0.273527i
$91$	1.10771	−	156.264i	0.0121727	−	1.71718i
$92$	24.6261	+	38.5702i	0.267675	+	0.419241i
$93$	−20.6334	−	35.7380i	−0.221864	−	0.384280i
$94$	63.1374	+	103.930i	0.671675	+	1.10564i
$95$	2.57634	+	14.2496i	0.0271194	+	0.149996i
$96$	−74.6854	−	32.6402i	−0.777973	−	0.340002i
$97$			18.0979i			0.186576i	0.995639	+	0.0932881i	$0.0297378\pi$
$97$			18.0979i			0.186576i	−0.995639	+	0.0932881i	$0.970262\pi$
$98$	97.9968	−	0.797551i	0.999967	−	0.00813828i
$99$	−26.4440			−0.267111
$100$	79.9203	+	60.1062i	0.799203	+	0.601062i
$101$	70.2765	+	40.5741i	0.695807	+	0.401724i	0.805784	−	0.592210i	$-0.201744\pi$
$101$	70.2765	+	40.5741i	0.695807	+	0.401724i	−0.109977	+	0.993934i	$0.535078\pi$
$102$	44.2389	+	72.8216i	0.433715	+	0.713937i
$103$	64.3871	+	111.522i	0.625118	+	1.08274i	0.988518	+	0.151103i	$0.0482824\pi$
$103$	64.3871	+	111.522i	0.625118	+	1.08274i	−0.363400	+	0.931633i	$0.618384\pi$
$104$	178.191	−	11.9472i	1.71338	−	0.114877i
$105$	68.4485	−	57.1147i	0.651890	−	0.543950i
$106$	−68.6280	+	125.240i	−0.647434	+	1.18151i
$107$	−16.1943	+	9.34976i	−0.151348	+	0.0873809i	−0.573762	−	0.819022i	$-0.694516\pi$
$107$	−16.1943	+	9.34976i	−0.151348	+	0.0873809i	0.422413	+	0.906403i	$0.361183\pi$
$108$	−5.23315	−	117.175i	−0.0484551	−	1.08495i
$109$	95.0225	+	54.8613i	0.871766	+	0.503315i	0.867935	−	0.496678i	$-0.165447\pi$
$109$	95.0225	+	54.8613i	0.871766	+	0.503315i	0.00383150	+	0.999993i	$0.498780\pi$
$110$	78.7973	−	69.7802i	0.716339	−	0.634365i
$111$		−	106.373i		−	0.958316i
$112$	9.19313	+	111.622i	0.0820815	+	0.996626i
$113$			203.210i			1.79832i	0.437620	+	0.899160i	$0.355821\pi$
$113$			203.210i			1.79832i	−0.437620	+	0.899160i	$0.644179\pi$
$114$	0.329202	+	14.7496i	0.00288774	+	0.129383i
$115$	−10.1771	−	56.2891i	−0.0884967	−	0.489470i
$116$	−2.48645	−	55.6739i	−0.0214349	−	0.479947i
$117$	28.0435	+	48.5727i	0.239688	+	0.415151i
$118$	−19.0251	+	34.7193i	−0.161230	+	0.294231i
$119$	59.2592	−	100.980i	0.497976	−	0.848571i
$120$	70.8815	+	73.1844i	0.590679	+	0.609870i
$121$	5.10857	+	8.84831i	0.0422196	+	0.0731265i
$122$	39.6423	−	24.0826i	0.324937	−	0.197399i
$123$	−133.859	−	77.2833i	−1.08828	−	0.628319i
$124$	−57.5139	−	29.8669i	−0.463822	−	0.240862i
$125$	−63.9027	−	107.431i	−0.511222	−	0.859449i
$126$	−30.1901	+	18.0487i	−0.239604	+	0.143244i
$127$	−65.1473			−0.512971			−0.256486	−	0.966548i	$-0.582565\pi$
$127$	−65.1473			−0.512971			−0.256486	+	0.966548i	$0.582565\pi$
$128$	−126.441	+	19.9136i	−0.987824	+	0.155575i
$129$	−96.3570	+	166.895i	−0.746953	+	1.29376i
$130$	−211.736	−	70.7350i	−1.62874	−	0.544116i
$131$	21.7029	+	37.5905i	0.165671	+	0.286950i	0.936893	−	0.349615i	$-0.113688\pi$
$131$	21.7029	+	37.5905i	0.165671	+	0.286950i	−0.771223	+	0.636566i	$0.780354\pi$
$132$	90.3838	−	57.7077i	0.684726	−	0.437180i
$133$	17.6283	−	10.0117i	0.132543	−	0.0752762i
$134$	106.029	+	58.1008i	0.791263	+	0.433588i
$135$	−49.5474	+	137.989i	−0.367018	+	1.02214i
$136$	120.099	+	59.0029i	0.883081	+	0.433845i
$137$	−61.4643	−	35.4865i	−0.448645	−	0.259025i	0.258613	−	0.965981i	$-0.416735\pi$
$137$	−61.4643	−	35.4865i	−0.448645	−	0.259025i	−0.707258	+	0.706956i	$0.750068\pi$
$138$	−1.30042	−	58.2643i	−0.00942334	−	0.422205i
$139$	−150.915			−1.08572			−0.542861	−	0.839823i	$-0.682659\pi$
$139$	−150.915			−1.08572			−0.542861	+	0.839823i	$0.682659\pi$
$140$	42.3331	−	133.446i	0.302379	−	0.953188i
$141$		−	154.869i		−	1.09836i
$142$	−4.62222	−	207.095i	−0.0325509	−	1.45841i
$143$	−117.483	+	203.487i	−0.821563	+	1.42299i
$144$	−23.1227	−	32.8827i	−0.160574	−	0.228352i
$145$	−23.5417	+	65.5633i	−0.162356	+	0.452161i
$146$	−143.519	−	78.6440i	−0.983006	−	0.538658i
$147$	−107.190	−	63.9293i	−0.729185	−	0.434894i
$148$	−89.8973	−	140.800i	−0.607414	−	0.951352i
$149$	−115.314	+	66.5765i	−0.773918	+	0.446822i	−0.834271	−	0.551355i	$-0.814111\pi$
$149$	−115.314	+	66.5765i	−0.773918	+	0.446822i	0.0603522	+	0.998177i	$0.480778\pi$
$150$	−47.2444	−	118.266i	−0.314962	−	0.788442i
$151$	−46.2732	−	26.7158i	−0.306445	−	0.176926i	0.338890	−	0.940826i	$-0.389949\pi$
$151$	−46.2732	−	26.7158i	−0.306445	−	0.176926i	−0.645335	+	0.763900i	$0.723282\pi$
$152$	12.9008	+	19.2450i	0.0848740	+	0.126612i
$153$			42.0233i			0.274662i
$154$	−128.720	−	71.7258i	−0.835845	−	0.465752i
$155$	52.3396	+	61.8295i	0.337675	+	0.398900i
$156$	−201.849	−	104.820i	−1.29390	−	0.671923i
$157$	111.987	−	193.967i	0.713293	−	1.23546i	−0.250321	−	0.968163i	$-0.580536\pi$
$157$	111.987	−	193.967i	0.713293	−	1.23546i	0.963614	−	0.267297i	$-0.0861306\pi$
$158$	81.5465	−	49.5393i	0.516117	−	0.313540i
$159$	157.508	−	90.9375i	0.990619	−	0.571934i
$160$	155.671	+	36.9672i	0.972943	+	0.231045i
$161$	−69.6355	+	39.5486i	−0.432519	+	0.245643i
$162$	−50.0504	+	91.3379i	−0.308953	+	0.563814i
$163$	185.513	−	107.106i	1.13812	−	0.657092i	0.192153	−	0.981365i	$-0.438453\pi$
$163$	185.513	−	107.106i	1.13812	−	0.657092i	0.945963	+	0.324273i	$0.105120\pi$
$164$	−242.494	+	10.8300i	−1.47862	+	0.0660367i
$165$	−131.906	+	23.8486i	−0.799428	+	0.144537i
$166$	4.15388	+	186.111i	0.0250234	+	1.12115i
$167$	134.838			0.807416			0.403708	−	0.914888i	$-0.367721\pi$
$167$	134.838			0.807416			0.403708	+	0.914888i	$0.367721\pi$
$168$	63.8007	−	127.572i	0.379766	−	0.759355i
$169$	329.357			1.94886
$170$	−110.891	−	125.220i	−0.652297	−	0.736588i
$171$	−3.63814	+	6.30144i	−0.0212757	+	0.0368505i
$172$	13.5029	+	302.342i	0.0785052	+	1.75780i
$173$	−77.9902	−	135.083i	−0.450811	−	0.780827i	0.547626	−	0.836723i	$-0.315532\pi$
$173$	−77.9902	−	135.083i	−0.450811	−	0.780827i	−0.998437	+	0.0558964i	$0.982198\pi$
$174$	−34.1064	+	62.2413i	−0.196014	+	0.357709i
$175$	−112.276	+	134.236i	−0.641574	+	0.767061i
$176$	70.8664	−	152.769i	0.402650	−	0.868006i
$177$	43.6646	−	25.2098i	0.246693	−	0.142428i
$178$	−54.1566	−	89.1469i	−0.304250	−	0.500825i
$179$	1.92040	−	3.32624i	0.0107285	−	0.0185823i	−0.860611	−	0.509262i	$-0.829918\pi$
$179$	1.92040	−	3.32624i	0.0107285	−	0.0185823i	0.871340	+	0.490680i	$0.163252\pi$
$180$	11.1372	+	48.9985i	0.0618735	+	0.272214i
$181$		−	212.490i		−	1.17398i	−0.809596	−	0.586988i	$-0.800314\pi$
$181$		−	212.490i		−	1.17398i	0.809596	−	0.586988i	$-0.199686\pi$
$182$	4.75879	+	312.499i	0.0261472	+	1.71703i
$183$	−59.0719			−0.322797
$184$	−50.9612	−	76.0222i	−0.276963	−	0.413164i
$185$	37.1515	+	205.483i	0.200819	+	1.11072i
$186$	42.8513	+	70.5374i	0.230384	+	0.379234i
$187$	−152.463	+	88.0248i	−0.815312	+	0.470721i
$188$	−130.882	−	204.991i	−0.696178	−	1.09038i
$189$	205.256	+	1.45501i	1.08601	+	0.00769846i
$190$	−5.78733	−	28.3772i	−0.0304596	−	0.149353i
$191$	56.9172	−	32.8611i	0.297996	−	0.172048i	−0.343546	−	0.939136i	$-0.611628\pi$
$191$	56.9172	−	32.8611i	0.297996	−	0.172048i	0.641542	+	0.767088i	$0.278295\pi$
$192$	150.790	+	61.9310i	0.785366	+	0.322558i
$193$	−194.968	−	112.565i	−1.01020	−	0.583238i	−0.0989485	−	0.995093i	$-0.531548\pi$
$193$	−194.968	−	112.565i	−1.01020	−	0.583238i	−0.911250	+	0.411854i	$0.864881\pi$
$194$	−0.807666	−	36.1868i	−0.00416323	−	0.186530i
$195$	183.689	+	216.995i	0.941996	+	1.11279i
$196$	−195.909	+	5.96806i	−0.999536	+	0.0304493i
$197$	−5.30573			−0.0269326			−0.0134663	−	0.999909i	$-0.504287\pi$
$197$	−5.30573			−0.0269326			−0.0134663	+	0.999909i	$0.504287\pi$
$198$	52.8749	−	1.18013i	0.267045	−	0.00596027i
$199$	−97.9447	−	56.5484i	−0.492184	−	0.284163i	0.233296	−	0.972406i	$-0.425049\pi$
$199$	−97.9447	−	56.5484i	−0.492184	−	0.284163i	−0.725480	+	0.688243i	$0.758382\pi$
$200$	−162.483	−	116.616i	−0.812416	−	0.583079i
$201$	−76.9882	−	133.347i	−0.383026	−	0.663420i
$202$	−142.329	−	77.9918i	−0.704597	−	0.386098i
$203$	97.5239	+	0.691324i	0.480413	+	0.00340554i
$204$	−91.7057	−	143.633i	−0.449538	−	0.704081i
$205$	285.569	+	102.539i	1.39302	+	0.500188i
$206$	−133.719	−	220.115i	−0.649122	−	1.06852i
$207$	14.3714	−	24.8921i	0.0694273	−	0.120252i
$208$	−355.761	+	31.8407i	−1.71039	+	0.153080i
$209$	−30.4827			−0.145850
$210$	−134.314	+	117.256i	−0.639591	+	0.558361i
$211$	213.135			1.01012			0.505059	−	0.863085i	$-0.331471\pi$
$211$	213.135			1.01012			0.505059	+	0.863085i	$0.331471\pi$
$212$	131.633	−	253.481i	0.620909	−	1.19567i
$213$	−131.904	+	228.465i	−0.619269	+	1.07260i
$214$	31.9632	−	19.4176i	0.149361	−	0.0907363i
$215$	127.845	−	356.048i	0.594629	−	1.65604i
$216$	15.6929	+	234.058i	0.0726525	+	1.08360i
$217$	57.4005	−	97.8127i	0.264518	−	0.450750i
$218$	−192.446	−	105.455i	−0.882780	−	0.483737i
$219$	104.210	+	180.496i	0.475843	+	0.824184i
$220$	−154.441	+	143.042i	−0.702005	+	0.650192i
$221$	323.370	+	186.698i	1.46321	+	0.844786i
$222$	4.74718	+	212.693i	0.0213837	+	0.958078i
$223$	174.444			0.782260			0.391130	−	0.920336i	$-0.372084\pi$
$223$	174.444			0.782260			0.391130	+	0.920336i	$0.372084\pi$
$224$	−23.3631	−	222.778i	−0.104300	−	0.994546i
$225$	10.3701	−	61.9484i	0.0460894	−	0.275326i
$226$	−9.06878	−	406.319i	−0.0401273	−	1.79787i
$227$	−233.714	−	134.935i	−1.02958	−	0.594426i	−0.112713	−	0.993628i	$-0.535954\pi$
$227$	−233.714	−	134.935i	−1.02958	−	0.594426i	−0.916863	+	0.399202i	$0.869287\pi$
$228$	−1.31648	−	29.4772i	−0.00577404	−	0.129286i
$229$	−267.526	+	154.456i	−1.16824	+	0.674481i	−0.953264	−	0.302139i	$-0.902299\pi$
$229$	−267.526	+	154.456i	−1.16824	+	0.674481i	−0.214972	+	0.976620i	$0.568966\pi$
$230$	22.8612	+	112.096i	0.0993966	+	0.487374i
$231$	92.6765	+	163.181i	0.401197	+	0.706411i
$232$	7.45625	+	111.209i	0.0321390	+	0.479349i
$233$	61.8899	−	35.7322i	0.265622	−	0.153357i	−0.361274	−	0.932460i	$-0.617658\pi$
$233$	61.8899	−	35.7322i	0.265622	−	0.153357i	0.626896	+	0.779103i	$0.284325\pi$
$234$	−58.2407	−	95.8697i	−0.248892	−	0.409700i
$235$	54.0889	+	299.163i	0.230166	+	1.27303i
$236$	36.4913	−	70.2703i	0.154624	−	0.297756i
$237$	−121.514			−0.512718
$238$	−113.982	+	204.554i	−0.478917	+	0.859472i
$239$		−	341.910i		−	1.43059i	−0.698824	−	0.715294i	$-0.746293\pi$
$239$		−	341.910i		−	1.43059i	0.698824	−	0.715294i	$-0.253707\pi$
$240$	−144.994	−	143.169i	−0.604140	−	0.596538i
$241$	−31.1312	+	53.9208i	−0.129175	+	0.223738i	−0.923357	−	0.383942i	$-0.874566\pi$
$241$	−31.1312	+	53.9208i	−0.129175	+	0.223738i	0.794182	+	0.607680i	$0.207900\pi$
$242$	−10.6095	−	17.4642i	−0.0438408	−	0.0721662i
$243$	−113.679	+	65.6326i	−0.467815	+	0.270093i
$244$	−78.1901	+	49.9224i	−0.320451	+	0.204600i
$245$	229.389	+	86.0566i	0.936281	+	0.351251i
$246$	271.099	+	148.554i	1.10203	+	0.603879i
$247$	32.3265	+	55.9911i	0.130876	+	0.226685i
$248$	116.332	+	57.1522i	0.469081	+	0.230453i
$249$	118.539	−	205.316i	0.476061	−	0.824563i
$250$	132.568	+	211.957i	0.530272	+	0.847827i
$251$	−383.203			−1.52670			−0.763352	−	0.645982i	$-0.776448\pi$
$251$	−383.203			−1.52670			−0.763352	+	0.645982i	$0.776448\pi$
$252$	59.5597	−	37.4357i	0.236348	−	0.148554i
$253$	120.414			0.475943
$254$	130.262	−	2.90737i	0.512844	−	0.0114463i
$255$	37.8989	+	209.616i	0.148623	+	0.822025i
$256$	251.931	−	45.4601i	0.984107	−	0.177578i
$257$	−302.947	+	174.906i	−1.17878	+	0.680569i	−0.955732	−	0.294238i	$-0.904934\pi$
$257$	−302.947	+	174.906i	−1.17878	+	0.680569i	−0.223049	+	0.974807i	$0.571601\pi$
$258$	185.218	−	338.007i	0.717899	−	1.31011i
$259$	254.204	−	144.372i	0.981482	−	0.557420i
$260$	426.524	+	131.986i	1.64048	+	0.507637i
$261$	−30.3142	+	17.5019i	−0.116146	+	0.0670571i
$262$	−45.0725	−	74.1937i	−0.172032	−	0.283182i
$263$	35.6986	−	61.8318i	0.135736	−	0.235102i	−0.790142	−	0.612923i	$-0.789993\pi$
$263$	35.6986	−	61.8318i	0.135736	−	0.235102i	0.925878	+	0.377822i	$0.123327\pi$
$264$	−178.147	+	119.420i	−0.674800	+	0.452350i
$265$	−272.501	+	230.676i	−1.02831	+	0.870477i
$266$	−34.8009	+	20.8052i	−0.130831	+	0.0782150i
$267$			132.840i			0.497527i
$268$	−214.599	−	111.441i	−0.800741	−	0.415824i
$269$	18.1246	+	10.4642i	0.0673776	+	0.0389004i	0.533310	−	0.845920i	$-0.320948\pi$
$269$	18.1246	+	10.4642i	0.0673776	+	0.0389004i	−0.465933	+	0.884820i	$0.654281\pi$
$270$	92.9120	−	278.121i	0.344119	−	1.03008i
$271$	−43.3246	+	25.0135i	−0.159869	+	0.0923006i	−0.577800	−	0.816178i	$-0.696089\pi$
$271$	−43.3246	+	25.0135i	−0.159869	+	0.0923006i	0.417931	+	0.908479i	$0.362755\pi$
$272$	−242.771	−	112.617i	−0.892542	−	0.414032i
$273$	201.451	−	343.280i	0.737915	−	1.25744i
$274$	124.482	+	68.2122i	0.454313	+	0.248950i
$275$	246.475	−	92.1377i	0.896273	−	0.335046i
$276$	5.20039	+	116.442i	0.0188420	+	0.421890i
$277$	61.9940	−	107.377i	0.223805	−	0.387642i	−0.732155	−	0.681138i	$-0.761485\pi$
$277$	61.9940	−	107.377i	0.223805	−	0.387642i	0.955960	+	0.293496i	$0.0948187\pi$
$278$	301.755	−	6.73499i	1.08545	−	0.0242266i
$279$			40.7052i			0.145897i
$280$	−78.6896	+	268.715i	−0.281034	+	0.959698i
$281$	−123.606			−0.439880			−0.219940	−	0.975513i	$-0.570586\pi$
$281$	−123.606			−0.439880			−0.219940	+	0.975513i	$0.570586\pi$
$282$	6.91142	+	309.660i	0.0245086	+	1.09809i
$283$	450.416	+	260.048i	1.59158	+	0.918897i	0.993037	+	0.117805i	$0.0375857\pi$
$283$	450.416	+	260.048i	1.59158	+	0.918897i	0.598540	+	0.801093i	$0.295748\pi$
$284$	18.4843	+	413.880i	0.0650855	+	1.45732i
$285$	−12.4644	+	34.7133i	−0.0437348	+	0.121801i
$286$	225.827	−	412.116i	0.789606	−	1.44097i
$287$	3.01114	−	424.777i	0.0104918	−	1.48006i
$288$	47.7013	+	64.7171i	0.165630	+	0.224712i
$289$	−4.61625	−	7.99558i	−0.0159732	−	0.0276664i
$290$	44.1457	−	132.145i	0.152226	−	0.455671i
$291$	−23.0483	+	39.9209i	−0.0792039	+	0.137185i
$292$	290.476	+	150.844i	0.994781	+	0.516589i
$293$	−304.497			−1.03924			−0.519619	−	0.854398i	$-0.673926\pi$
$293$	−304.497			−1.03924			−0.519619	+	0.854398i	$0.673926\pi$
$294$	217.180	+	123.043i	0.738707	+	0.418514i
$295$	−75.5431	+	63.9484i	−0.256078	+	0.216774i
$296$	186.033	+	277.518i	0.628491	+	0.937562i
$297$	−267.285	−	154.317i	−0.899950	−	0.519586i
$298$	227.599	−	138.266i	0.763755	−	0.463980i
$299$	−127.697	−	221.177i	−0.427079	−	0.739723i
$300$	99.7431	+	234.365i	0.332477	+	0.781218i
$301$	−529.613	−	3.75430i	−1.75951	−	0.0124728i
$302$	93.7156	+	51.3533i	0.310316	+	0.170044i
$303$	103.345	+	178.999i	0.341074	+	0.590757i
$304$	−26.6541	−	37.9048i	−0.0876781	−	0.124687i
$305$	114.110	−	20.6312i	0.374132	−	0.0676434i
$306$	−1.87540	−	84.0256i	−0.00612875	−	0.274594i
$307$			61.5844i			0.200601i	0.994957	+	0.100300i	$0.0319803\pi$
$307$			61.5844i			0.200601i	−0.994957	+	0.100300i	$0.968020\pi$
$308$	260.577	+	137.671i	0.846029	+	0.446985i
$309$			327.998i			1.06148i
$310$	−107.412	−	121.292i	−0.346492	−	0.391266i
$311$	−34.1410	−	19.7113i	−0.109778	−	0.0633804i	0.444106	−	0.895974i	$-0.353521\pi$
$311$	−34.1410	−	19.7113i	−0.109778	−	0.0633804i	−0.553884	+	0.832594i	$0.686855\pi$
$312$	408.275	+	200.580i	1.30857	+	0.642883i
$313$	−58.2627	+	33.6380i	−0.186143	+	0.107470i	−0.590176	−	0.807275i	$-0.700941\pi$
$313$	−58.2627	+	33.6380i	−0.186143	+	0.107470i	0.404033	+	0.914744i	$0.367608\pi$
$314$	−215.262	+	392.836i	−0.685548	+	1.25107i
$315$	−86.6403	+	15.0312i	−0.275049	+	0.0477181i
$316$	−160.842	+	102.693i	−0.508992	+	0.324979i
$317$	37.0622	+	64.1936i	0.116915	+	0.202503i	0.918544	−	0.395319i	$-0.129366\pi$
$317$	37.0622	+	64.1936i	0.116915	+	0.202503i	−0.801628	+	0.597823i	$0.796033\pi$
$318$	−310.880	+	188.859i	−0.977610	+	0.593896i
$319$	−126.996	−	73.3213i	−0.398107	−	0.229847i
$320$	−312.914	−	66.9689i	−0.977856	−	0.209278i
$321$	−47.6291			−0.148377
$322$	137.471	−	82.1851i	0.426930	−	0.255233i
$323$			48.4414i			0.149973i
$324$	95.9997	−	184.864i	0.296295	−	0.570568i
$325$	−430.623	−	355.018i	−1.32499	−	1.09236i
$326$	−366.154	+	222.438i	−1.12317	+	0.682324i
$327$	139.736	+	242.029i	0.427326	+	0.740151i
$328$	484.384	−	32.4766i	1.47678	−	0.0990140i
$329$	370.096	−	210.191i	1.12491	−	0.638878i
$330$	262.681	−	53.5720i	0.796003	−	0.162340i
$331$	85.4653	+	148.030i	0.258203	+	0.447221i	0.965761	−	0.259435i	$-0.0835362\pi$
$331$	85.4653	+	148.030i	0.258203	+	0.447221i	−0.707557	+	0.706656i	$0.750203\pi$
$332$	−16.6114	−	371.944i	−0.0500343	−	1.12031i
$333$	−52.4628	+	90.8683i	−0.157546	+	0.272878i
$334$	−269.610	+	6.01752i	−0.807215	+	0.0180165i
$335$	195.292	+	230.701i	0.582961	+	0.688660i
$336$	−121.876	+	257.927i	−0.362727	+	0.767640i
$337$		−	493.865i		−	1.46547i	−0.680512	−	0.732737i	$-0.738242\pi$
$337$		−	493.865i		−	1.46547i	0.680512	−	0.732737i	$-0.261758\pi$
$338$	−658.551	+	14.6984i	−1.94838	+	0.0434865i
$339$	−258.796	+	448.247i	−0.763409	+	1.32226i
$340$	227.314	+	245.429i	0.668571	+	0.721849i
$341$	−147.681	+	85.2638i	−0.433083	+	0.250040i
$342$	6.99325	−	12.7621i	0.0204481	−	0.0373161i
$343$	7.29366	−	342.922i	0.0212643	−	0.999774i
$344$	−40.4919	−	603.932i	−0.117709	−	1.75562i
$345$	49.2372	−	137.125i	0.142717	−	0.397464i
$346$	161.970	+	266.618i	0.468122	+	0.770573i
$347$	−328.129	−	189.446i	−0.945618	−	0.545953i	−0.0539011	−	0.998546i	$-0.517166\pi$
$347$	−328.129	−	189.446i	−0.945618	−	0.545953i	−0.891717	+	0.452593i	$0.850499\pi$
$348$	65.4180	−	125.974i	0.187983	−	0.361993i
$349$			325.737i			0.933345i	0.884430	+	0.466672i	$0.154547\pi$
$349$			325.737i			0.933345i	−0.884430	+	0.466672i	$0.845453\pi$
$350$	218.504	−	273.415i	0.624299	−	0.781186i
$351$			654.604i			1.86497i
$352$	−134.880	+	308.624i	−0.383181	+	0.876774i
$353$	−438.688	−	253.276i	−1.24274	−	0.717497i	−0.273090	−	0.961989i	$-0.588046\pi$
$353$	−438.688	−	253.276i	−1.24274	−	0.717497i	−0.969651	+	0.244491i	$0.921379\pi$
$354$	−86.1825	+	52.3557i	−0.243453	+	0.147897i
$355$	175.009	−	487.398i	0.492983	−	1.37295i
$356$	112.265	+	175.833i	0.315350	+	0.493912i
$357$	259.317	−	147.276i	0.726379	−	0.412538i
$358$	−3.69141	+	6.73652i	−0.0103112	+	0.0188171i
$359$	−171.795	+	99.1859i	−0.478537	+	0.276284i	−0.719807	−	0.694174i	$-0.755770\pi$
$359$	−171.795	+	99.1859i	−0.478537	+	0.276284i	0.241269	+	0.970458i	$0.422436\pi$
$360$	−24.4556	−	97.4756i	−0.0679322	−	0.270766i
$361$	176.306	−	305.371i	0.488383	−	0.845904i
$362$	9.48290	+	424.874i	0.0261959	+	1.17368i
$363$			26.0238i			0.0716910i
$364$	−23.4613	−	624.629i	−0.0644540	−	1.71601i
$365$	−264.343	−	312.272i	−0.724227	−	0.855540i
$366$	118.114	−	2.63624i	0.322717	−	0.00720283i
$367$	231.240	−	400.519i	0.630081	−	1.09133i	−0.357454	−	0.933931i	$-0.616355\pi$
$367$	231.240	−	400.519i	0.630081	−	1.09133i	0.987535	−	0.157401i	$-0.0503115\pi$
$368$	105.290	+	149.732i	0.286113	+	0.406881i
$369$	76.2317	+	132.037i	0.206590	+	0.357824i
$370$	−83.4547	−	409.205i	−0.225553	−	1.10596i
$371$	431.090	+	252.981i	1.16197	+	0.681891i
$372$	−88.8293	−	139.127i	−0.238788	−	0.373998i
$373$	−15.8596	−	27.4696i	−0.0425190	−	0.0736451i	0.843983	−	0.536370i	$-0.180205\pi$
$373$	−15.8596	−	27.4696i	−0.0425190	−	0.0736451i	−0.886502	+	0.462725i	$0.846872\pi$
$374$	300.923	−	182.810i	0.804606	−	0.488796i
$375$	−4.14116	−	318.357i	−0.0110431	−	0.848953i
$376$	270.846	+	404.039i	0.720336	+	1.07457i
$377$			311.024i			0.824999i
$378$	−410.474	+	6.25077i	−1.08591	+	0.0165364i
$379$	−382.893			−1.01027			−0.505135	−	0.863040i	$-0.668557\pi$
$379$	−382.893			−1.01027			−0.505135	+	0.863040i	$0.668557\pi$
$380$	12.8382	+	56.4819i	0.0337847	+	0.148637i
$381$	−143.704	−	82.9676i	−0.377176	−	0.217763i
$382$	−112.339	+	68.2460i	−0.294082	+	0.178654i
$383$	−90.4747	−	156.707i	−0.236226	−	0.409156i	0.723402	−	0.690427i	$-0.242577\pi$
$383$	−90.4747	−	156.707i	−0.236226	−	0.409156i	−0.959628	+	0.281271i	$0.909244\pi$
$384$	−304.269	−	117.102i	−0.792368	−	0.304953i
$385$	−236.017	−	282.852i	−0.613031	−	0.734680i
$386$	394.863	+	216.373i	1.02296	+	0.560552i
$387$	164.624	−	95.0458i	0.425386	−	0.245596i
$388$	3.22986	+	72.3195i	0.00832438	+	0.186390i
$389$	582.323	+	336.205i	1.49698	+	0.864279i	0.999994	−	0.00348212i	$-0.00110840\pi$
$389$	582.323	+	336.205i	1.49698	+	0.864279i	0.496981	+	0.867761i	$0.334442\pi$
$390$	−376.971	−	425.684i	−0.966592	−	1.09150i
$391$		−	191.354i		−	0.489397i
$392$	391.454	−	20.6761i	0.998608	−	0.0527452i
$393$			110.558i			0.281317i
$394$	10.6088	−	0.236782i	0.0269259	−	0.000600970i
$395$	234.731	−	42.4396i	0.594256	−	0.107442i
$396$	−105.671	+	4.71936i	−0.266845	+	0.0119176i
$397$	−45.1868	−	78.2658i	−0.113821	−	0.197143i	0.803487	−	0.595322i	$-0.202976\pi$
$397$	−45.1868	−	78.2658i	−0.113821	−	0.197143i	−0.917308	+	0.398179i	$0.869642\pi$
$398$	198.364	+	108.698i	0.498403	+	0.273110i
$399$	51.6353	+	0.366030i	0.129412	+	0.000917369i
$400$	330.090	+	225.922i	0.825224	+	0.564806i
$401$	84.6736	+	146.659i	0.211156	+	0.365733i	0.952077	−	0.305860i	$-0.0989438\pi$
$401$	84.6736	+	146.659i	0.211156	+	0.365733i	−0.740920	+	0.671593i	$0.765610\pi$
$402$	159.889	+	263.193i	0.397734	+	0.654708i
$403$	313.227	+	180.842i	0.777239	+	0.448739i
$404$	288.067	+	149.593i	0.713037	+	0.370280i
$405$	−198.735	+	168.232i	−0.490704	+	0.415389i
$406$	−195.030	+	2.96996i	−0.480370	+	0.00731516i
$407$	−439.569			−1.08002
$408$	189.776	+	283.101i	0.465137	+	0.693875i
$409$	308.816	−	534.886i	0.755052	−	1.30779i	−0.190296	−	0.981727i	$-0.560945\pi$
$409$	308.816	−	534.886i	0.755052	−	1.30779i	0.945348	−	0.326062i	$-0.105722\pi$
$410$	−575.571	−	192.282i	−1.40383	−	0.468980i
$411$	−90.3866	−	156.554i	−0.219919	−	0.380910i
$412$	277.195	+	434.152i	0.672803	+	1.05377i
$413$	119.507	+	70.1318i	0.289364	+	0.169811i
$414$	−27.6249	+	50.4131i	−0.0667267	+	0.121771i
$415$	−157.277	+	438.013i	−0.378980	+	1.05545i
$416$	709.923	−	79.5424i	1.70655	−	0.191208i
$417$	−332.894	−	192.196i	−0.798306	−	0.460902i
$418$	60.9503	−	1.36037i	0.145814	−	0.00325448i
$419$	−74.5350			−0.177888			−0.0889440	−	0.996037i	$-0.528349\pi$
$419$	−74.5350			−0.177888			−0.0889440	+	0.996037i	$0.528349\pi$
$420$	263.328	−	240.447i	0.626972	−	0.572493i
$421$		−	617.258i		−	1.46617i	−0.680137	−	0.733085i	$-0.738080\pi$
$421$		−	617.258i		−	1.46617i	0.680137	−	0.733085i	$-0.261920\pi$
$422$	−426.164	+	9.51170i	−1.00987	+	0.0225396i
$423$	−76.3807	+	132.295i	−0.180569	+	0.312755i
$424$	−251.887	+	512.711i	−0.594074	+	1.20922i
$425$	−146.420	−	391.683i	−0.344517	−	0.921608i
$426$	253.547	−	462.702i	0.595181	−	1.08616i
$427$	−80.1736	−	141.166i	−0.187760	−	0.330600i
$428$	−63.0439	+	40.2519i	−0.147299	+	0.0940466i
$429$	−518.297	+	299.239i	−1.20815	+	0.697527i
$430$	−239.737	+	717.624i	−0.557529	+	1.66889i
$431$	−50.4039	−	29.1007i	−0.116946	−	0.0675190i	0.440386	−	0.897809i	$-0.354842\pi$
$431$	−50.4039	−	29.1007i	−0.116946	−	0.0675190i	−0.557332	+	0.830290i	$0.688175\pi$
$432$	−41.8235	−	467.300i	−0.0968137	−	1.08171i
$433$			597.376i			1.37962i	0.723990	+	0.689811i	$0.242306\pi$
$433$			597.376i			1.37962i	−0.723990	+	0.689811i	$0.757694\pi$
$434$	−110.407	+	198.138i	−0.254394	+	0.456540i
$435$	−135.426	+	114.640i	−0.311325	+	0.263541i
$436$	389.502	+	202.268i	0.893354	+	0.463918i
$437$	16.5664	−	28.6938i	0.0379093	−	0.0656608i
$438$	−216.422	−	356.252i	−0.494115	−	0.813361i
$439$	175.474	−	101.310i	0.399712	−	0.230774i	−0.286648	−	0.958036i	$-0.592541\pi$
$439$	175.474	−	101.310i	0.399712	−	0.230774i	0.686360	+	0.727262i	$0.259208\pi$
$440$	302.422	−	292.905i	0.687322	−	0.665694i
$441$	60.0365	+	107.477i	0.136137	+	0.243712i
$442$	−654.911	−	358.871i	−1.48170	−	0.811926i
$443$	398.924	−	230.319i	0.900505	−	0.519907i	0.0231409	−	0.999732i	$-0.492633\pi$
$443$	398.924	−	230.319i	0.900505	−	0.519907i	0.877364	+	0.479826i	$0.159300\pi$
$444$	−18.9840	−	425.069i	−0.0427567	−	0.957362i
$445$	−46.3951	−	256.609i	−0.104259	−	0.576649i
$446$	−348.801	+	7.78501i	−0.782065	+	0.0174552i
$447$	−339.150			−0.758726
$448$	56.6566	+	444.403i	0.126466	+	0.991971i
$449$	−705.122			−1.57043			−0.785213	−	0.619225i	$-0.787447\pi$
$449$	−705.122			−1.57043			−0.785213	+	0.619225i	$0.787447\pi$
$450$	−17.9705	+	124.329i	−0.0399344	+	0.276286i
$451$	−319.360	+	553.147i	−0.708115	+	1.22649i
$452$	36.2661	+	812.031i	0.0802347	+	1.79653i
$453$	−68.0472	−	117.861i	−0.150215	−	0.260179i
$454$	473.333	+	259.372i	1.04258	+	0.571304i
$455$	−269.253	+	733.478i	−0.591765	+	1.61204i
$456$	3.94780	+	58.8810i	0.00865747	+	0.129125i
$457$	336.247	−	194.132i	0.735770	−	0.424797i	−0.0847593	−	0.996401i	$-0.527012\pi$
$457$	336.247	−	194.132i	0.735770	−	0.424797i	0.820529	+	0.571604i	$0.193679\pi$
$458$	528.026	−	320.774i	1.15289	−	0.700381i
$459$	−245.232	+	424.754i	−0.534274	+	0.925389i
$460$	−50.7136	−	223.116i	−0.110247	−	0.485035i
$461$		−	401.436i		−	0.870795i	−0.900238	−	0.435397i	$-0.856608\pi$
$461$		−	401.436i		−	0.870795i	0.900238	−	0.435397i	$-0.143392\pi$
$462$	−192.589	−	322.145i	−0.416860	−	0.697283i
$463$	83.3995			0.180129			0.0900643	−	0.995936i	$-0.471293\pi$
$463$	83.3995			0.180129			0.0900643	+	0.995936i	$0.471293\pi$
$464$	−19.8718	−	222.030i	−0.0428271	−	0.478513i
$465$	36.7101	+	203.042i	0.0789465	+	0.436649i
$466$	−122.154	+	74.2085i	−0.262134	+	0.159246i
$467$	534.075	−	308.348i	1.14363	−	0.660275i	0.196303	−	0.980543i	$-0.437106\pi$
$467$	534.075	−	308.348i	1.14363	−	0.660275i	0.947327	+	0.320268i	$0.103773\pi$
$468$	120.731	+	189.093i	0.257972	+	0.404044i
$469$	214.175	−	364.963i	0.456664	−	0.778174i
$470$	−121.502	−	595.763i	−0.258514	−	1.26758i
$471$	494.049	−	285.239i	1.04894	−	0.605604i
$472$	−69.8285	+	142.134i	−0.147942	+	0.301132i
$473$	689.666	+	398.179i	1.45807	+	0.841815i
$474$	242.968	−	5.42289i	0.512591	−	0.0114407i
$475$	11.9539	−	71.4096i	0.0251661	−	0.150336i
$476$	218.779	−	414.093i	0.459620	−	0.869944i
$477$	−179.400			−0.376101
$478$	15.2586	+	683.651i	0.0319218	+	1.43023i
$479$	252.305	+	145.668i	0.526733	+	0.304109i	0.739685	−	0.672953i	$-0.234975\pi$
$479$	252.305	+	145.668i	0.526733	+	0.304109i	−0.212952	+	0.977063i	$0.568308\pi$
$480$	296.304	+	279.796i	0.617301	+	0.582909i
$481$	466.156	+	807.405i	0.969138	+	1.67860i
$482$	59.8405	−	109.204i	0.124150	−	0.226564i
$483$	−203.971	−	1.44590i	−0.422300	−	0.00299358i
$484$	21.9931	+	34.4463i	0.0454402	+	0.0711700i
$485$	30.5803	−	85.1657i	0.0630521	−	0.175599i
$486$	224.372	−	136.306i	0.461672	−	0.280465i
$487$	299.137	−	518.121i	0.614245	−	1.06390i	−0.376272	−	0.926509i	$-0.622794\pi$
$487$	299.137	−	518.121i	0.614245	−	1.06390i	0.990517	−	0.137394i	$-0.0438725\pi$
$488$	154.113	−	103.309i	0.315806	−	0.211700i
$489$	545.613			1.11577
$490$	−462.504	−	161.833i	−0.943886	−	0.330272i
$491$	443.152			0.902550			0.451275	−	0.892385i	$-0.350969\pi$
$491$	443.152			0.902550			0.451275	+	0.892385i	$0.350969\pi$
$492$	−548.694	−	284.936i	−1.11523	−	0.579138i
$493$	−116.518	+	201.815i	−0.236345	+	0.409361i
$494$	−67.1356	−	110.512i	−0.135902	−	0.223708i
$495$	124.441	+	44.6828i	0.251396	+	0.0902684i
$496$	−235.157	−	109.084i	−0.474106	−	0.219928i
$497$	−724.994	−	5.13931i	−1.45874	−	0.0103407i
$498$	−227.857	+	415.820i	−0.457544	+	0.834980i
$499$	−425.717	−	737.364i	−0.853141	−	1.47768i	−0.878359	−	0.478002i	$-0.841361\pi$
$499$	−425.717	−	737.364i	−0.853141	−	1.47768i	0.0252177	−	0.999682i	$-0.491972\pi$
$500$	−274.529	−	417.892i	−0.549058	−	0.835784i
$501$	297.431	+	171.722i	0.593674	+	0.342758i
$502$	766.215	−	17.1014i	1.52632	−	0.0340666i
$503$	−587.689			−1.16837			−0.584184	−	0.811621i	$-0.698585\pi$
$503$	−587.689			−1.16837			−0.584184	+	0.811621i	$0.698585\pi$
$504$	−117.419	+	77.5107i	−0.232974	+	0.153791i
$505$	−262.151	−	309.682i	−0.519110	−	0.613232i
$506$	−240.767	+	5.37377i	−0.475824	+	0.0106201i
$507$	726.507	+	419.449i	1.43295	+	0.827315i
$508$	−260.330	+	11.6266i	−0.512460	+	0.0228870i
$509$	−559.697	+	323.141i	−1.09960	+	0.634855i	−0.936116	−	0.351691i	$-0.885607\pi$
$509$	−559.697	+	323.141i	−1.09960	+	0.634855i	−0.163485	+	0.986546i	$0.552273\pi$
$510$	−85.1335	−	417.437i	−0.166928	−	0.818504i
$511$	−289.903	+	494.007i	−0.567325	+	0.966745i
$512$	−501.708	+	102.141i	−0.979899	+	0.199493i
$513$	−73.5455	+	42.4615i	−0.143364	+	0.0827710i
$514$	597.937	−	363.245i	1.16330	−	0.706703i
$515$	−114.555	−	633.599i	−0.222437	−	1.23029i
$516$	−355.259	+	684.112i	−0.688487	+	1.32580i
$517$	−639.968			−1.23785
$518$	−501.838	+	300.016i	−0.968799	+	0.579182i
$519$		−	397.294i		−	0.765499i
$520$	−858.726	−	244.871i	−1.65140	−	0.470905i
$521$	178.119	−	308.511i	0.341879	−	0.592151i	−0.642903	−	0.765948i	$-0.722270\pi$
$521$	178.119	−	308.511i	0.341879	−	0.592151i	0.984782	+	0.173797i	$0.0556035\pi$
$522$	59.8322	−	36.3480i	0.114621	−	0.0696321i
$523$	−618.448	+	357.061i	−1.18250	+	0.682717i	−0.956592	−	0.291431i	$-0.905869\pi$
$523$	−618.448	+	357.061i	−1.18250	+	0.682717i	−0.225909	+	0.974148i	$0.572535\pi$
$524$	93.4337	+	146.339i	0.178308	+	0.279273i
$525$	−418.615	+	153.114i	−0.797362	+	0.291646i
$526$	−68.6200	+	125.226i	−0.130456	+	0.238072i
$527$	135.496	+	234.686i	0.257109	+	0.445325i
$528$	350.876	−	246.731i	0.664538	−	0.467294i
$529$	199.059	−	344.781i	0.376294	−	0.651759i
$530$	534.572	−	473.399i	1.00863	−	0.893206i
$531$	−49.7335			−0.0936601
$532$	68.6561	−	43.1531i	0.129053	−	0.0811149i
$533$	1354.70			2.54166
$534$	−5.92832	−	265.613i	−0.0111017	−	0.497403i
$535$	92.0059	−	16.6348i	0.171974	−	0.0310930i
$536$	434.064	+	213.249i	0.809820	+	0.397853i
$537$	8.47217	−	4.89141i	0.0157769	−	0.00910877i
$538$	−36.7071	−	20.1144i	−0.0682288	−	0.0373873i
$539$	−264.177	+	442.945i	−0.490124	+	0.821790i
$540$	−173.366	+	560.249i	−0.321048	+	1.03750i
$541$	−310.573	+	179.309i	−0.574072	+	0.331440i	−0.758774	−	0.651354i	$-0.774201\pi$
$541$	−310.573	+	179.309i	−0.574072	+	0.331440i	0.184702	+	0.982795i	$0.440868\pi$
$542$	85.5113	−	51.9479i	0.157770	−	0.0958449i
$543$	270.613	−	468.716i	0.498367	−	0.863197i
$544$	490.448	+	214.343i	0.901558	+	0.394013i
$545$	−354.460	−	418.729i	−0.650386	−	0.768310i
$546$	−387.481	+	695.380i	−0.709673	+	1.27359i
$547$			34.7057i			0.0634474i	0.999497	+	0.0317237i	$0.0100997\pi$
$547$			34.7057i			0.0634474i	−0.999497	+	0.0317237i	$0.989900\pi$
$548$	−251.946	−	130.835i	−0.459755	−	0.238750i
$549$	50.4616	+	29.1340i	0.0919155	+	0.0530675i
$550$	−488.715	+	195.229i	−0.888573	+	0.354962i
$551$	−34.9440	+	20.1749i	−0.0634192	+	0.0366151i
$552$	−15.5947	−	232.593i	−0.0282513	−	0.421364i
$553$	−164.922	−	290.387i	−0.298231	−	0.525112i
$554$	−119.165	+	217.467i	−0.215100	+	0.392539i
$555$	−179.740	+	500.574i	−0.323856	+	0.901935i
$556$	−603.060	+	26.9332i	−1.08464	+	0.0484411i
$557$	−382.407	+	662.349i	−0.686548	+	1.18914i	0.286400	+	0.958110i	$0.407541\pi$
$557$	−382.407	+	662.349i	−0.686548	+	1.18914i	−0.972948	+	0.231026i	$0.925792\pi$
$558$	−1.81657	−	81.3901i	−0.00325551	−	0.145860i
$559$		−	1689.05i		−	3.02155i
$560$	145.348	−	540.809i	0.259550	−	0.965730i
$561$	−448.411			−0.799307
$562$	247.151	−	5.51625i	0.439770	−	0.00981538i
$563$	−712.800	−	411.535i	−1.26607	−	0.730968i	−0.291831	−	0.956470i	$-0.594265\pi$
$563$	−712.800	−	411.535i	−1.26607	−	0.730968i	−0.974243	+	0.225501i	$0.927598\pi$
$564$	−27.6388	−	618.858i	−0.0490050	−	1.09727i
$565$	343.367	−	956.273i	0.607729	−	1.69252i
$566$	−912.214	−	499.865i	−1.61168	−	0.883155i
$567$	314.394	+	184.499i	0.554487	+	0.325396i
$568$	−55.4298	−	826.729i	−0.0975877	−	1.45551i
$569$	222.695	+	385.719i	0.391379	+	0.677889i	0.992632	−	0.121170i	$-0.0386647\pi$
$569$	222.695	+	385.719i	0.391379	+	0.677889i	−0.601252	+	0.799059i	$0.705331\pi$
$570$	23.3735	−	69.9656i	0.0410061	−	0.122747i
$571$	286.811	−	496.771i	0.502296	−	0.870002i	−0.497701	−	0.867349i	$-0.665822\pi$
$571$	286.811	−	496.771i	0.502296	−	0.870002i	0.999996	−	0.00265287i	$-0.000844435\pi$
$572$	−433.150	+	834.106i	−0.757256	+	1.45823i
$573$	167.399			0.292146
$574$	12.9360	+	849.477i	0.0225366	+	1.47993i
$575$	−47.2206	+	282.084i	−0.0821228	+	0.490580i
$576$	−98.2670	−	127.273i	−0.170603	−	0.220960i
$577$	351.547	+	202.966i	0.609268	+	0.351761i	0.772679	−	0.634797i	$-0.218916\pi$
$577$	351.547	+	202.966i	0.609268	+	0.351761i	−0.163411	+	0.986558i	$0.552250\pi$
$578$	9.58702	+	15.7812i	0.0165865	+	0.0273030i
$579$	−286.711	−	496.599i	−0.495184	−	0.857683i
$580$	−82.3721	+	266.193i	−0.142021	+	0.458954i
$581$	651.535	+	4.61858i	1.12140	+	0.00794936i
$582$	44.3036	−	80.8505i	0.0761231	−	0.138918i
$583$	−375.784	−	650.876i	−0.644569	−	1.11643i
$584$	−587.539	−	288.650i	−1.00606	−	0.494263i
$585$	−49.8939	−	275.961i	−0.0852888	−	0.471727i
$586$	608.841	−	13.5890i	1.03898	−	0.0231893i
$587$			216.676i			0.369124i	0.982821	+	0.184562i	$0.0590866\pi$
$587$			216.676i			0.369124i	−0.982821	+	0.184562i	$0.940913\pi$
$588$	−439.743	−	236.333i	−0.747862	−	0.401927i
$589$			46.9220i			0.0796638i
$590$	148.195	−	131.236i	0.251177	−	0.222434i
$591$	−11.7035	−	6.75704i	−0.0198030	−	0.0114332i
$592$	−384.359	−	546.596i	−0.649255	−	0.923304i
$593$	149.101	−	86.0835i	0.251435	−	0.145166i	−0.368986	−	0.929435i	$-0.620295\pi$
$593$	149.101	−	86.0835i	0.251435	−	0.145166i	0.620421	+	0.784269i	$0.286962\pi$
$594$	541.324	+	296.629i	0.911320	+	0.499376i
$595$	−449.491	+	375.064i	−0.755447	+	0.630360i
$596$	−448.914	+	286.620i	−0.753212	+	0.480907i
$597$	−144.033	−	249.472i	−0.241261	−	0.417877i
$598$	265.200	+	436.545i	0.443479	+	0.730009i
$599$	−807.571	−	466.252i	−1.34820	−	0.778383i	−0.360205	−	0.932873i	$-0.617293\pi$
$599$	−807.571	−	466.252i	−1.34820	−	0.778383i	−0.987994	+	0.154490i	$0.950627\pi$
$600$	−209.896	−	464.163i	−0.349826	−	0.773605i
$601$	167.993			0.279523			0.139761	−	0.990185i	$-0.455366\pi$
$601$	167.993			0.279523			0.139761	+	0.990185i	$0.455366\pi$
$602$	1059.13	−	16.1286i	1.75935	−	0.0267917i
$603$			151.881i			0.251876i
$604$	−189.676	−	98.4987i	−0.314034	−	0.163077i
$605$	−9.08899	−	50.2707i	−0.0150231	−	0.0830921i
$606$	−214.628	−	353.298i	−0.354171	−	0.582999i
$607$	407.180	+	705.257i	0.670808	+	1.16187i	0.977675	+	0.210121i	$0.0673859\pi$
$607$	407.180	+	705.257i	0.670808	+	1.16187i	−0.306867	+	0.951752i	$0.599281\pi$
$608$	54.9866	+	74.6012i	0.0904385	+	0.122699i
$609$	214.241	+	125.725i	0.351791	+	0.206445i
$610$	−227.243	+	46.3447i	−0.372529	+	0.0759749i
$611$	678.676	+	1175.50i	1.11076	+	1.92390i
$612$	7.49973	+	167.926i	0.0122545	+	0.274388i
$613$	−490.009	+	848.721i	−0.799363	+	1.38454i	0.120669	+	0.992693i	$0.461496\pi$
$613$	−490.009	+	848.721i	−0.799363	+	1.38454i	−0.920032	+	0.391844i	$0.871837\pi$
$614$	−2.74836	−	123.138i	−0.00447616	−	0.200551i
$615$	499.330	+	589.865i	0.811918	+	0.959130i
$616$	−527.168	−	263.645i	−0.855792	−	0.427996i
$617$			624.945i			1.01288i	0.862276	+	0.506439i	$0.169038\pi$
$617$			624.945i			1.01288i	−0.862276	+	0.506439i	$0.830962\pi$
$618$	−14.6377	−	655.832i	−0.0236857	−	1.06122i
$619$	193.068	−	334.403i	0.311903	−	0.540232i	−0.666871	−	0.745173i	$-0.732367\pi$
$619$	193.068	−	334.403i	0.311903	−	0.540232i	0.978774	+	0.204941i	$0.0657003\pi$
$620$	220.184	+	237.731i	0.355136	+	0.383437i
$621$	290.521	−	167.732i	0.467828	−	0.270101i
$622$	69.1446	+	37.8892i	0.111165	+	0.0609151i
$623$	−317.452	+	180.293i	−0.509554	+	0.289395i
$624$	−825.298	−	382.839i	−1.32259	−	0.613524i
$625$	119.188	+	613.530i	0.190701	+	0.981648i
$626$	114.995	−	69.8593i	0.183698	−	0.111596i
$627$	−67.2398	−	38.8209i	−0.107240	−	0.0619153i
$628$	412.886	−	795.082i	0.657461	−	1.26605i
$629$			698.536i			1.11055i
$630$	172.567	−	33.9215i	0.273915	−	0.0538436i
$631$			146.516i			0.232197i	0.993238	+	0.116098i	$0.0370388\pi$
$631$			146.516i			0.232197i	−0.993238	+	0.116098i	$0.962961\pi$
$632$	317.020	−	212.513i	0.501614	−	0.336255i
$633$	470.140	+	271.435i	0.742717	+	0.428808i
$634$	−76.9707	−	126.701i	−0.121405	−	0.199844i
$635$	306.573	+	110.080i	0.482791	+	0.173355i
$636$	613.177	−	391.498i	0.964115	−	0.615563i
$637$	1093.76	+	15.5076i	1.71705	+	0.0243448i
$638$	257.201	+	140.939i	0.403137	+	0.220907i
$639$	225.356	−	130.109i	0.352670	−	0.203614i
$640$	628.661	+	119.940i	0.982283	+	0.187406i
$641$	−247.696	+	429.022i	−0.386422	+	0.669302i	−0.991965	−	0.126510i	$-0.959622\pi$
$641$	−247.696	+	429.022i	−0.386422	+	0.669302i	0.605544	+	0.795812i	$0.292956\pi$
$642$	95.2344	−	2.12557i	0.148340	−	0.00331086i
$643$			335.746i			0.522156i	0.965318	+	0.261078i	$0.0840780\pi$
$643$			335.746i			0.522156i	−0.965318	+	0.261078i	$0.915922\pi$
$644$	−271.207	+	170.464i	−0.421128	+	0.264696i
$645$	735.445	−	622.565i	1.14022	−	0.965218i
$646$	−2.16182	−	96.8586i	−0.00334647	−	0.149936i
$647$	−304.061	+	526.649i	−0.469955	+	0.813986i	−0.999410	−	0.0343524i	$-0.989063\pi$
$647$	−304.061	+	526.649i	−0.469955	+	0.813986i	0.529455	+	0.848338i	$0.322396\pi$
$648$	−183.702	+	373.920i	−0.283490	+	0.577037i
$649$	−104.175	−	180.437i	−0.160516	−	0.278023i
$650$	876.874	+	690.641i	1.34904	+	1.06252i
$651$	251.184	−	142.657i	0.385843	−	0.219135i
$652$	722.198	−	461.105i	1.10767	−	0.707216i
$653$	213.064	+	369.038i	0.326285	+	0.565143i	0.981772	−	0.190064i	$-0.0608696\pi$
$653$	213.064	+	369.038i	0.326285	+	0.565143i	−0.655486	+	0.755207i	$0.727536\pi$
$654$	−290.203	−	477.702i	−0.443736	−	0.730431i
$655$	−38.6130	−	213.566i	−0.0589511	−	0.326055i
$656$	−967.078	+	86.5539i	−1.47420	+	0.131942i
$657$		−	205.583i		−	0.312912i
$658$	−730.626	+	436.794i	−1.11037	+	0.663820i
$659$	171.388			0.260073			0.130036	−	0.991509i	$-0.458491\pi$
$659$	171.388			0.260073			0.130036	+	0.991509i	$0.458491\pi$
$660$	−522.841	+	118.840i	−0.792183	+	0.180061i
$661$	−523.158	−	302.046i	−0.791465	−	0.456953i	0.0490130	−	0.998798i	$-0.484392\pi$
$661$	−523.158	−	302.046i	−0.791465	−	0.456953i	−0.840478	+	0.541846i	$0.817726\pi$
$662$	−177.494	−	292.173i	−0.268118	−	0.441348i
$663$	475.533	+	823.647i	0.717244	+	1.24230i
$664$	49.8135	+	742.962i	0.0750204	+	1.11892i
$665$	−99.8726	+	17.3269i	−0.150184	+	0.0260555i
$666$	100.844	−	184.033i	0.151418	−	0.276325i
$667$	138.036	−	79.6954i	0.206951	−	0.119483i
$668$	538.817	−	24.0641i	0.806612	−	0.0360241i
$669$	384.794	+	222.161i	0.575177	+	0.332079i
$670$	−400.782	−	452.572i	−0.598183	−	0.675480i
$671$			244.104i			0.363792i
$672$	232.181	−	521.165i	0.345508	−	0.775543i
$673$		−	776.249i		−	1.15342i	−0.816950	−	0.576708i	$-0.804337\pi$
$673$		−	776.249i		−	1.15342i	0.816950	−	0.576708i	$-0.195663\pi$
$674$	22.0400	+	987.484i	0.0327003	+	1.46511i
$675$	466.324	−	565.632i	0.690850	−	0.837974i
$676$	1316.12	−	58.7791i	1.94692	−	0.0869513i
$677$	270.270	+	468.121i	0.399217	+	0.691463i	0.993629	−	0.112697i	$-0.0359488\pi$
$677$	270.270	+	468.121i	0.399217	+	0.691463i	−0.594413	+	0.804160i	$0.702616\pi$
$678$	497.458	−	907.820i	0.733714	−	1.33897i
$679$	−126.682	−	0.898019i	−0.186572	−	0.00132256i
$680$	−465.468	−	480.591i	−0.684512	−	0.706751i
$681$	−343.689	−	595.286i	−0.504682	−	0.874135i
$682$	291.484	−	177.076i	0.427396	−	0.259642i
$683$	−747.740	−	431.708i	−1.09479	−	0.632076i	−0.159940	−	0.987127i	$-0.551130\pi$
$683$	−747.740	−	431.708i	−1.09479	−	0.632076i	−0.934847	+	0.355051i	$0.884464\pi$
$684$	−13.4135	+	25.8299i	−0.0196103	+	0.0377631i
$685$	229.279	+	270.850i	0.334714	+	0.395402i
$686$	0.720110	+	686.000i	0.00104972	+	0.999999i
$687$	−786.822			−1.14530
$688$	107.916	+	1205.76i	0.156854	+	1.75255i
$689$	−797.025	+	1380.49i	−1.15679	+	2.00361i
$690$	−92.3304	+	276.379i	−0.133812	+	0.400550i
$691$	−210.216	−	364.104i	−0.304219	−	0.526924i	0.672868	−	0.739763i	$-0.265062\pi$
$691$	−210.216	−	364.104i	−0.304219	−	0.526924i	−0.977087	+	0.212839i	$0.931729\pi$
$692$	−335.758	−	525.876i	−0.485199	−	0.759936i
$693$	1.31215	−	185.104i	0.00189344	−	0.267105i
$694$	664.550	+	364.153i	0.957565	+	0.524717i
$695$	710.182	+	255.004i	1.02185	+	0.366912i
$696$	−125.182	+	254.804i	−0.179859	+	0.366098i
$697$	879.029	+	507.508i	1.26116	+	0.728132i
$698$	−14.5369	−	651.312i	−0.0208265	−	0.933112i
$699$	182.025			0.260408
$700$	−424.698	+	556.445i	−0.606712	+	0.794922i
$701$			391.074i			0.557880i	0.960308	+	0.278940i	$0.0899831\pi$
$701$			391.074i			0.557880i	−0.960308	+	0.278940i	$0.910017\pi$
$702$	−29.2134	−	1308.88i	−0.0416145	−	1.86450i
$703$	−60.4753	+	104.746i	−0.0860246	+	0.148999i
$704$	255.919	−	623.115i	0.363522	−	0.885106i
$705$	−261.684	+	728.787i	−0.371183	+	1.03374i
$706$	888.460	+	486.849i	1.25844	+	0.689588i
$707$	−287.499	+	489.910i	−0.406646	+	0.692942i
$708$	169.986	−	108.531i	0.240093	−	0.153293i
$709$	160.012	−	92.3832i	0.225687	−	0.130301i	−0.382894	−	0.923792i	$-0.625072\pi$
$709$	160.012	−	92.3832i	0.225687	−	0.130301i	0.608581	+	0.793492i	$0.291739\pi$
$710$	−328.179	+	982.363i	−0.462224	+	1.38361i
$711$	103.802	+	59.9304i	0.145995	+	0.0842902i
$712$	−232.320	−	346.567i	−0.326292	−	0.486752i
$713$		−	185.352i		−	0.259961i
$714$	−511.933	+	306.051i	−0.716993	+	0.428643i
$715$	896.693	−	759.064i	1.25412	−	1.06163i
$716$	7.08035	−	13.6344i	0.00988875	−	0.0190425i
$717$	435.436	−	754.197i	0.607302	−	1.05188i
$718$	339.078	−	205.989i	0.472253	−	0.286893i
$719$	841.418	−	485.793i	1.17026	−	0.675651i	0.216520	−	0.976278i	$-0.430529\pi$
$719$	841.418	−	485.793i	1.17026	−	0.675651i	0.953742	+	0.300627i	$0.0971961\pi$
$720$	53.2491	+	193.811i	0.0739571	+	0.269182i
$721$	−783.828	+	445.165i	−1.08714	+	0.617427i
$722$	−338.897	+	618.459i	−0.469386	+	0.856591i
$723$	−137.340	+	79.2934i	−0.189959	+	0.109673i
$724$	−37.9222	−	849.112i	−0.0523787	−	1.17281i
$725$	221.566	−	268.751i	0.305609	−	0.370691i
$726$	−1.16138	−	52.0347i	−0.00159970	−	0.0716731i
$727$	472.474			0.649895			0.324948	−	0.945732i	$-0.394653\pi$
$727$	472.474			0.649895			0.324948	+	0.945732i	$0.394653\pi$
$728$	74.7866	+	1247.90i	0.102729	+	1.71415i
$729$	−803.027			−1.10155
$730$	542.490	+	612.592i	0.743137	+	0.839167i
$731$	632.762	−	1095.98i	0.865611	−	1.49928i
$732$	−236.052	+	10.5423i	−0.322476	+	0.0144021i
$733$	−412.237	−	714.016i	−0.562397	−	0.974100i	−0.997287	−	0.0736165i	$-0.976546\pi$
$733$	−412.237	−	714.016i	−0.562397	−	0.974100i	0.434890	−	0.900484i	$-0.356787\pi$
$734$	−444.490	+	811.158i	−0.605572	+	1.10512i
$735$	396.397	+	481.962i	0.539315	+	0.655730i
$736$	−217.209	−	294.691i	−0.295121	−	0.400395i
$737$	−551.036	+	318.140i	−0.747674	+	0.431670i
$738$	−158.318	−	260.606i	−0.214523	−	0.353125i
$739$	−74.3888	+	128.845i	−0.100661	+	0.174351i	−0.911957	−	0.410285i	$-0.865429\pi$
$739$	−74.3888	+	128.845i	−0.100661	+	0.174351i	0.811296	+	0.584636i	$0.198763\pi$
$740$	185.130	+	814.483i	0.250175	+	1.10065i
$741$			164.676i			0.222235i
$742$	−873.256	−	486.598i	−1.17689	−	0.655793i
$743$	996.184			1.34076			0.670380	−	0.742018i	$-0.266131\pi$
$743$	996.184			1.34076			0.670380	+	0.742018i	$0.266131\pi$
$744$	183.823	+	274.221i	0.247074	+	0.368577i
$745$	655.143	−	118.450i	0.879387	−	0.158994i
$746$	32.9372	+	54.2178i	0.0441517	+	0.0726780i
$747$	−202.522	+	116.926i	−0.271114	+	0.156528i
$748$	−593.537	+	378.958i	−0.793498	+	0.506628i
$749$	−64.6431	−	113.821i	−0.0863059	−	0.151964i
$750$	22.4878	+	636.371i	0.0299837	+	0.848495i
$751$	148.810	−	85.9154i	0.198149	−	0.114401i	−0.397643	−	0.917540i	$-0.630172\pi$
$751$	148.810	−	85.9154i	0.198149	−	0.114401i	0.595792	+	0.803139i	$0.296838\pi$
$752$	−559.589	−	795.790i	−0.744134	−	1.05823i
$753$	−845.281	−	488.023i	−1.12255	−	0.648105i
$754$	−13.8803	−	621.894i	−0.0184089	−	0.824793i
$755$	172.612	+	203.909i	0.228625	+	0.270078i
$756$	820.465	−	30.8169i	1.08527	−	0.0407631i
$757$	−1237.36			−1.63456			−0.817279	−	0.576243i	$-0.804518\pi$
$757$	−1237.36			−1.63456			−0.817279	+	0.576243i	$0.804518\pi$
$758$	765.595	−	17.0876i	1.01002	−	0.0225430i
$759$	265.612	+	153.351i	0.349950	+	0.202044i
$760$	−28.1906	−	112.363i	−0.0370929	−	0.147846i
$761$	110.973	+	192.211i	0.145825	+	0.252576i	0.929680	−	0.368367i	$-0.120083\pi$
$761$	110.973	+	192.211i	0.145825	+	0.252576i	−0.783855	+	0.620943i	$0.786750\pi$
$762$	291.039	+	159.481i	0.381941	+	0.209292i
$763$	−388.734	+	662.419i	−0.509481	+	0.868177i
$764$	221.577	−	141.471i	0.290023	−	0.185172i
$765$	71.0073	−	197.755i	0.0928200	−	0.258503i
$766$	187.898	+	309.298i	0.245298	+	0.403783i
$767$	−220.952	+	382.700i	−0.288073	+	0.498957i
$768$	613.613	+	220.567i	0.798975	+	0.287196i
$769$	442.458			0.575367			0.287684	−	0.957725i	$-0.407115\pi$
$769$	442.458			0.575367			0.287684	+	0.957725i	$0.407115\pi$
$770$	484.539	+	555.030i	0.629272	+	0.720818i
$771$	−890.999			−1.15564
$772$	−799.185	−	415.016i	−1.03521	−	0.537586i
$773$	216.133	−	374.353i	0.279602	−	0.484285i	−0.691684	−	0.722201i	$-0.743131\pi$
$773$	216.133	−	374.353i	0.279602	−	0.484285i	0.971286	+	0.237915i	$0.0764641\pi$
$774$	−324.925	+	197.391i	−0.419799	+	0.255027i
$775$	−141.827	−	379.398i	−0.183003	−	0.489546i
$776$	−9.68556	−	144.459i	−0.0124814	−	0.186158i
$777$	744.593	+	5.27824i	0.958292	+	0.00679311i
$778$	−1179.36	−	646.254i	−1.51589	−	0.830661i
$779$	87.8743	+	152.203i	0.112804	+	0.195382i
$780$	772.751	+	834.332i	0.990707	+	1.06966i
$781$	944.091	+	545.071i	1.20882	+	0.697915i
$782$	8.53967	+	382.613i	0.0109203	+	0.489275i
$783$	−408.538			−0.521759
$784$	−781.791	+	58.8116i	−0.997182	+	0.0750148i
$785$	−854.742	+	723.552i	−1.08884	+	0.921722i
$786$	−4.93392	−	221.060i	−0.00627725	−	0.281247i
$787$	346.790	+	200.219i	0.440648	+	0.254408i	0.703873	−	0.710326i	$-0.251453\pi$
$787$	346.790	+	200.219i	0.440648	+	0.254408i	−0.263224	+	0.964735i	$0.584786\pi$
$788$	−21.2018	+	0.946892i	−0.0269058	+	0.00120164i
$789$	157.490	−	90.9270i	0.199607	−	0.115243i
$790$	−467.452	+	95.3336i	−0.591711	+	0.120675i
$791$	−1422.44	−	10.0833i	−1.79827	−	0.0127475i
$792$	211.078	−	14.1522i	0.266513	−	0.0178689i
$793$	448.374	−	258.869i	0.565415	−	0.326442i
$794$	93.8438	+	154.476i	0.118191	+	0.194554i
$795$	−894.867	+	161.793i	−1.12562	+	0.203513i
$796$	−401.481	−	208.489i	−0.504373	−	0.261920i
$797$	673.716			0.845315			0.422658	−	0.906289i	$-0.361097\pi$
$797$	673.716			0.845315			0.422658	+	0.906289i	$0.361097\pi$
$798$	−103.261	+	1.57248i	−0.129400	+	0.00197053i
$799$			1017.00i			1.27284i
$800$	−670.097	−	437.001i	−0.837621	−	0.546251i
$801$	65.5161	−	113.477i	0.0817929	−	0.141669i
$802$	−175.850	−	289.466i	−0.219264	−	0.360930i
$803$	745.870	−	430.628i	0.928854	−	0.536274i
$804$	−331.444	−	519.119i	−0.412244	−	0.645670i
$805$	394.519	−	68.4450i	0.490085	−	0.0850249i
$806$	−634.369	−	347.615i	−0.787058	−	0.431284i
$807$	26.6531	+	46.1646i	0.0330274	+	0.0572052i
$808$	−582.667	−	286.256i	−0.721122	−	0.354277i
$809$	419.904	−	727.296i	0.519041	−	0.899006i	−0.480714	−	0.876878i	$-0.659622\pi$
$809$	419.904	−	727.296i	0.519041	−	0.899006i	0.999755	−	0.0221284i	$-0.00704426\pi$
$810$	389.864	−	345.250i	0.481313	−	0.426235i
$811$	−545.334			−0.672422			−0.336211	−	0.941787i	$-0.609145\pi$
$811$	−545.334			−0.672422			−0.336211	+	0.941787i	$0.609145\pi$
$812$	389.831	−	14.6422i	0.480087	−	0.0180322i
$813$	−127.422			−0.156731
$814$	878.918	−	19.6169i	1.07975	−	0.0240994i
$815$	−1053.97	+	190.559i	−1.29322	+	0.233815i
$816$	−392.091	−	557.592i	−0.480504	−	0.683323i
$817$	189.767	−	109.562i	0.232273	−	0.134103i
$818$	−593.608	+	1083.29i	−0.725682	+	1.32431i
$819$	−341.392	+	193.889i	−0.416840	+	0.236739i
$820$	1159.44	+	358.781i	1.41395	+	0.437538i
$821$	61.5819	−	35.5543i	0.0750083	−	0.0433061i	−0.462027	−	0.886866i	$-0.652878\pi$
$821$	61.5819	−	35.5543i	0.0750083	−	0.0433061i	0.537035	+	0.843560i	$0.319544\pi$
$822$	187.715	+	308.997i	0.228364	+	0.375908i
$823$	233.563	−	404.543i	0.283795	−	0.491547i	−0.688522	−	0.725216i	$-0.741740\pi$
$823$	233.563	−	404.543i	0.283795	−	0.491547i	0.972316	+	0.233669i	$0.0750733\pi$
$824$	−573.627	−	855.717i	−0.696149	−	1.03849i
$825$	661.023	+	110.655i	0.801240	+	0.134127i
$826$	−242.085	−	134.895i	−0.293081	−	0.163311i
$827$		−	1118.58i		−	1.35257i	−0.736639	−	0.676286i	$-0.763588\pi$
$827$		−	1118.58i		−	1.35257i	0.736639	−	0.676286i	$-0.236412\pi$
$828$	52.9861	−	102.034i	0.0639929	−	0.123229i
$829$	1405.64	+	811.545i	1.69558	+	0.978944i	0.949854	+	0.312693i	$0.101231\pi$
$829$	1405.64	+	811.545i	1.69558	+	0.978944i	0.745727	+	0.666252i	$0.232102\pi$
$830$	294.927	−	882.828i	0.355334	−	1.06365i
$831$	273.497	−	157.903i	0.329118	−	0.190016i
$832$	−1415.94	+	190.727i	−1.70185	+	0.229240i
$833$	703.902	+	419.814i	0.845020	+	0.503979i
$834$	674.199	+	369.440i	0.808392	+	0.442974i
$835$	−634.527	−	227.838i	−0.759913	−	0.272860i
$836$	−121.810	+	5.44013i	−0.145705	+	0.00650733i
$837$	−237.540	+	411.431i	−0.283799	+	0.491554i
$838$	149.033	−	3.32632i	0.177844	−	0.00396936i
$839$		−	1049.61i		−	1.25102i	−0.780215	−	0.625511i	$-0.784890\pi$
$839$		−	1049.61i		−	1.25102i	0.780215	−	0.625511i	$-0.215110\pi$
$840$	−515.795	+	492.526i	−0.614042	+	0.586341i
$841$	646.890			0.769191
$842$	27.5467	+	1234.21i	0.0327158	+	1.46580i
$843$	−272.654	−	157.417i	−0.323433	−	0.186734i
$844$	851.691	−	38.0373i	1.00911	−	0.0450679i
$845$	−1549.90	−	556.520i	−1.83420	−	0.658603i
$846$	146.819	−	267.933i	0.173545	−	0.316706i
$847$	−62.1901	+	35.3201i	−0.0734240	+	0.0417002i
$848$	480.768	−	1036.41i	0.566944	−	1.22218i
$849$	662.361	+	1147.24i	0.780167	+	1.35129i
$850$	310.247	+	776.638i	0.364996	+	0.913691i
$851$	238.891	−	413.771i	0.280718	−	0.486217i
$852$	−486.318	+	936.490i	−0.570796	+	1.09917i
$853$	66.5146			0.0779773			0.0389886	−	0.999240i	$-0.487586\pi$
$853$	66.5146			0.0779773			0.0389886	+	0.999240i	$0.487586\pi$
$854$	166.607	+	278.684i	0.195090	+	0.326328i
$855$	27.7681	−	23.5061i	0.0324773	−	0.0274925i
$856$	124.260	−	83.2973i	0.145164	−	0.0973099i
$857$	1356.97	+	783.445i	1.58339	+	0.914172i	0.994360	+	0.106062i	$0.0338242\pi$
$857$	1356.97	+	783.445i	1.58339	+	0.914172i	0.589032	+	0.808110i	$0.299509\pi$
$858$	1022.98	−	621.459i	1.19229	−	0.724312i
$859$	−41.5782	−	72.0155i	−0.0484030	−	0.0838365i	0.840809	−	0.541332i	$-0.182080\pi$
$859$	−41.5782	−	72.0155i	−0.0484030	−	0.0838365i	−0.889212	+	0.457496i	$0.848747\pi$
$860$	447.330	−	1445.59i	0.520151	−	1.68092i
$861$	547.611	−	933.152i	0.636018	−	1.08380i
$862$	102.081	+	55.9375i	0.118424	+	0.0648927i
$863$	27.1503	+	47.0257i	0.0314604	+	0.0544910i	0.881327	−	0.472507i	$-0.156651\pi$
$863$	27.1503	+	47.0257i	0.0314604	+	0.0544910i	−0.849867	+	0.526998i	$0.823318\pi$
$864$	104.481	+	932.500i	0.120927	+	1.07928i
$865$	138.757	+	767.459i	0.160413	+	0.887236i
$866$	−26.6595	−	1194.45i	−0.0307846	−	1.37928i
$867$		−	23.5158i		−	0.0271232i
$868$	211.917	−	401.105i	0.244144	−	0.462103i
$869$			502.137i			0.577833i
$870$	265.669	−	235.267i	0.305366	−	0.270422i
$871$	1168.73	+	674.766i	1.34182	+	0.774703i
$872$	−787.838	−	387.053i	−0.903484	−	0.443869i
$873$	39.3777	−	22.7347i	0.0451062	−	0.0260421i
$874$	−31.8439	+	58.1126i	−0.0364347	+	0.0664903i
$875$	755.170	−	441.977i	0.863051	−	0.505117i
$876$	448.636	+	702.668i	0.512141	+	0.802133i
$877$	12.2064	+	21.1421i	0.0139184	+	0.0241073i	0.872901	−	0.487898i	$-0.162236\pi$
$877$	12.2064	+	21.1421i	0.0139184	+	0.0241073i	−0.858982	+	0.512005i	$0.828903\pi$
$878$	−346.339	+	210.400i	−0.394463	+	0.239636i
$879$	−671.668	−	387.788i	−0.764127	−	0.441169i
$880$	−591.621	+	599.161i	−0.672297	+	0.680865i
$881$	2.08057			0.00236160			0.00118080	−	0.999999i	$-0.499624\pi$
$881$	2.08057			0.00236160			0.00118080	+	0.999999i	$0.499624\pi$
$882$	−124.840	−	212.221i	−0.141541	−	0.240613i
$883$			727.936i			0.824390i	0.911096	+	0.412195i	$0.135238\pi$
$883$			727.936i			0.824390i	−0.911096	+	0.412195i	$0.864762\pi$
$884$	1325.51	+	688.337i	1.49945	+	0.778662i
$885$	−248.076	+	44.8524i	−0.280312	+	0.0506806i
$886$	−787.370	+	478.326i	−0.888679	+	0.539871i
$887$	468.238	+	811.012i	0.527890	+	0.914332i	0.999471	+	0.0325094i	$0.0103499\pi$
$887$	468.238	+	811.012i	0.527890	+	0.914332i	−0.471582	+	0.881822i	$0.656317\pi$
$888$	56.9283	+	849.079i	0.0641085	+	0.956170i
$889$	3.23262	−	456.020i	0.00363624	−	0.512958i
$890$	104.219	+	511.020i	0.117100	+	0.574179i
$891$	−274.059	−	474.684i	−0.307586	−	0.532754i
$892$	697.081	−	31.1323i	0.781481	−	0.0349017i
$893$	−88.0461	+	152.500i	−0.0985958	+	0.170773i
$894$	678.132	−	15.1355i	0.758537	−	0.0169301i
$895$	−14.6575	+	12.4078i	−0.0163771	+	0.0138635i
$896$	−133.118	−	886.056i	−0.148569	−	0.988902i
$897$		−	650.506i		−	0.725201i
$898$	1409.89	−	31.4679i	1.57004	−	0.0350422i
$899$	−112.863	+	195.485i	−0.125543	+	0.217447i
$900$	30.3835	−	249.398i	0.0337594	−	0.277108i
$901$	−1034.33	+	597.173i	−1.14798	+	0.662789i
$902$	613.875	−	1120.27i	0.680571	−	1.24199i
$903$	−1163.46	−	682.763i	−1.28843	−	0.756106i
$904$	−108.753	−	1622.04i	−0.120302	−	1.79429i
$905$	−359.047	+	999.941i	−0.396737	+	1.10491i
$906$	141.320	+	232.627i	0.155983	+	0.256763i
$907$	−481.672	−	278.094i	−0.531061	−	0.306608i	0.210387	−	0.977618i	$-0.432527\pi$
$907$	−481.672	−	278.094i	−0.531061	−	0.306608i	−0.741448	+	0.671010i	$0.765861\pi$
$908$	−958.005	−	497.491i	−1.05507	−	0.547898i
$909$		−	203.878i		−	0.224288i
$910$	505.639	−	1478.61i	0.555647	−	1.62484i
$911$		−	678.597i		−	0.744893i	−0.928054	−	0.372446i	$-0.878519\pi$
$911$		−	678.597i		−	0.744893i	0.928054	−	0.372446i	$-0.121481\pi$
$912$	−10.5214	−	117.557i	−0.0115366	−	0.128900i
$913$	−848.433	−	489.843i	−0.929281	−	0.536521i
$914$	−663.663	+	403.174i	−0.726108	+	0.441109i
$915$	277.982	+	99.8146i	0.303806	+	0.109087i
$916$	−1041.47	+	664.954i	−1.13698	+	0.725932i
$917$	−264.204	+	150.051i	−0.288117	+	0.163633i
$918$	471.386	−	860.240i	0.513492	−	0.937081i
$919$	−1269.77	+	733.104i	−1.38169	+	0.797720i	−0.992360	−	0.123378i	$-0.960627\pi$
$919$	−1269.77	+	733.104i	−1.38169	+	0.797720i	−0.389331	+	0.921098i	$0.627294\pi$
$920$	111.359	+	443.858i	0.121043	+	0.482454i
$921$	−78.4300	+	135.845i	−0.0851574	+	0.147497i
$922$	17.9151	+	802.673i	0.0194307	+	0.870578i
$923$		−	2312.16i		−	2.50505i
$924$	399.459	+	635.534i	0.432315	+	0.687807i
$925$	172.378	−	1029.74i	0.186355	−	1.11324i
$926$	−166.758	+	3.72192i	−0.180084	+	0.00401935i
$927$	161.767	−	280.189i	0.174506	−	0.302253i
$928$	49.6423	+	443.063i	0.0534939	+	0.477438i
$929$	−157.948	−	273.574i	−0.170020	−	0.294483i	0.768407	−	0.639962i	$-0.221050\pi$
$929$	−157.948	−	273.574i	−0.170020	−	0.294483i	−0.938426	+	0.345479i	$0.887716\pi$
$930$	−82.4632	−	404.344i	−0.0886702	−	0.434778i
$931$	69.2057	+	123.891i	0.0743348	+	0.133074i
$932$	240.936	−	153.832i	0.258515	−	0.165055i
$933$	−50.2062	−	86.9596i	−0.0538115	−	0.0932043i
$934$	−1054.12	+	640.378i	−1.12861	+	0.685629i
$935$	866.204	−	156.610i	0.926421	−	0.167498i
$936$	−249.840	−	372.703i	−0.266923	−	0.398187i
$937$			216.315i			0.230859i	0.993316	+	0.115430i	$0.0368245\pi$
$937$			216.315i			0.230859i	−0.993316	+	0.115430i	$0.963176\pi$
$938$	−411.957	+	739.303i	−0.439186	+	0.788170i
$939$	−171.357			−0.182489
$940$	269.531	+	1185.81i	0.286735	+	1.26150i
$941$	−1013.91	−	585.380i	−1.07748	−	0.622083i	−0.147264	−	0.989097i	$-0.547047\pi$
$941$	−1013.91	−	585.380i	−1.07748	−	0.622083i	−0.930215	+	0.367014i	$0.880380\pi$
$942$	−975.122	+	592.385i	−1.03516	+	0.628859i
$943$	−347.123	−	601.234i	−0.368105	−	0.637576i
$944$	133.279	−	287.314i	0.141185	−	0.304358i
$945$	−963.440	−	353.670i	−1.01951	−	0.374254i
$946$	−1396.76	−	765.381i	−1.47649	−	0.809071i
$947$	−1407.98	+	812.898i	−1.48678	+	0.858393i	−0.999886	−	0.0150690i	$-0.995203\pi$
$947$	−1407.98	+	812.898i	−1.48678	+	0.858393i	−0.486893	+	0.873462i	$0.661870\pi$
$948$	−485.573	+	21.6861i	−0.512208	+	0.0228757i
$949$	−1581.97	−	913.349i	−1.66698	−	0.962433i
$950$	−20.7150	+	143.317i	−0.0218053	+	0.150860i
$951$			188.800i			0.198528i
$952$	−418.969	+	837.744i	−0.440094	+	0.879984i
$953$		−	14.0364i		−	0.0147286i	−0.999973	−	0.00736432i	$-0.997656\pi$
$953$		−	14.0364i		−	0.0147286i	0.999973	−	0.00736432i	$-0.00234416\pi$
$954$	358.711	−	8.00620i	0.376007	−	0.00839224i
$955$	−323.369	+	58.4654i	−0.338606	+	0.0612203i
$956$	−61.0194	−	1366.28i	−0.0638278	−	1.42916i
$957$	−186.755	−	323.469i	−0.195146	−	0.338003i
$958$	−510.985	−	280.004i	−0.533387	−	0.292280i
$959$	251.449	−	428.479i	0.262199	−	0.446797i
$960$	−604.948	−	546.229i	−0.630154	−	0.568989i
$961$	−349.254	−	604.925i	−0.363427	−	0.629475i
$962$	−968.111	−	1593.60i	−1.00635	−	1.65655i
$963$	40.6867	+	23.4905i	0.0422500	+	0.0243930i
$964$	−114.778	+	221.024i	−0.119064	+	0.229278i
$965$	727.286	+	859.152i	0.753664	+	0.890313i
$966$	407.904	−	6.21164i	0.422261	−	0.00643027i
$967$	−1658.44			−1.71504			−0.857518	−	0.514453i	$-0.827995\pi$
$967$	−1658.44			−1.71504			−0.857518	+	0.514453i	$0.827995\pi$
$968$	−45.5124	−	67.8939i	−0.0470170	−	0.0701383i
$969$	−61.6919	+	106.853i	−0.0636655	+	0.110272i
$970$	−57.3446	+	171.654i	−0.0591181	+	0.176963i
$971$	−141.104	−	244.399i	−0.145318	−	0.251698i	0.784174	−	0.620542i	$-0.213087\pi$
$971$	−141.104	−	244.399i	−0.145318	−	0.251698i	−0.929492	+	0.368843i	$0.879754\pi$
$972$	−442.550	+	282.557i	−0.455298	+	0.290696i
$973$	7.48843	−	1056.38i	0.00769623	−	1.08569i
$974$	−575.003	+	1049.33i	−0.590352	+	1.07734i
$975$	−497.752	−	1331.52i	−0.510515	−	1.36566i
$976$	−303.540	+	213.445i	−0.311004	+	0.218694i
$977$	1565.31	+	903.735i	1.60216	+	0.925010i	0.991053	+	0.133465i	$0.0426105\pi$
$977$	1565.31	+	903.735i	1.60216	+	0.925010i	0.611111	+	0.791545i	$0.290723\pi$
$978$	−1090.96	+	24.3494i	−1.11550	+	0.0248972i
$979$	548.937			0.560712
$980$	932.000	+	302.946i	0.951020	+	0.309128i
$981$		−	275.669i		−	0.281008i
$982$	−886.084	+	19.7768i	−0.902326	+	0.0201393i
$983$	−501.764	+	869.081i	−0.510442	+	0.884111i	0.489485	+	0.872012i	$0.337185\pi$
$983$	−501.764	+	869.081i	−0.510442	+	0.884111i	−0.999927	+	0.0120995i	$0.996149\pi$
$984$	1109.83	+	545.243i	1.12788	+	0.554109i
$985$	24.9679	+	8.96516i	0.0253481	+	0.00910169i
$986$	223.971	−	408.729i	0.227151	−	0.414533i
$987$	1084.05	+	7.68460i	1.09833	+	0.00778582i
$988$	139.170	+	217.972i	0.140860	+	0.220620i
$989$	−749.620	+	432.794i	−0.757958	+	0.437607i
$990$	−250.815	−	83.7899i	−0.253348	−	0.0846363i
$991$	−1157.63	−	668.356i	−1.16814	−	0.674426i	−0.214898	−	0.976636i	$-0.568942\pi$
$991$	−1157.63	−	668.356i	−1.16814	−	0.674426i	−0.953241	+	0.302211i	$0.902275\pi$
$992$	475.064	+	207.620i	0.478896	+	0.209294i
$993$			435.373i			0.438442i
$994$	1449.86	−	22.0787i	1.45861	−	0.0222119i
$995$	365.361	+	431.606i	0.367197	+	0.433775i
$996$	437.043	−	841.602i	0.438798	−	0.844982i
$997$	38.7611	−	67.1362i	0.0388778	−	0.0673383i	−0.845932	−	0.533291i	$-0.820955\pi$
$997$	38.7611	−	67.1362i	0.0388778	−	0.0673383i	0.884810	+	0.465953i	$0.154288\pi$
$998$	884.130	+	1455.36i	0.885901	+	1.45828i
$999$	−1060.54	+	612.306i	−1.06161	+	0.612919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.3.bi.c.179.1	✓	176
5.4	even	2	inner	280.3.bi.c.179.88	yes	176
7.2	even	3	inner	280.3.bi.c.219.59	yes	176
8.3	odd	2	inner	280.3.bi.c.179.30	yes	176
35.9	even	6	inner	280.3.bi.c.219.30	yes	176
40.19	odd	2	inner	280.3.bi.c.179.59	yes	176
56.51	odd	6	inner	280.3.bi.c.219.88	yes	176
280.219	odd	6	inner	280.3.bi.c.219.1	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.3.bi.c.179.1	✓	176	1.1	even	1	trivial
280.3.bi.c.179.30	yes	176	8.3	odd	2	inner
280.3.bi.c.179.59	yes	176	40.19	odd	2	inner
280.3.bi.c.179.88	yes	176	5.4	even	2	inner
280.3.bi.c.219.1	yes	176	280.219	odd	6	inner
280.3.bi.c.219.30	yes	176	35.9	even	6	inner
280.3.bi.c.219.59	yes	176	7.2	even	3	inner
280.3.bi.c.219.88	yes	176	56.51	odd	6	inner

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	280.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99950 + 0.0446276i) q^{2} +(2.20583 + 1.27354i) q^{3} +(3.99602 - 0.178466i) q^{4} +(-4.70583 - 1.68971i) q^{5} +(-4.46740 - 2.44800i) q^{6} +(-0.0496201 + 6.99982i) q^{7} +(-7.98208 + 0.535176i) q^{8} +(-1.25621 - 2.17582i) q^{9} +O(q^{10})\)	\(q+(-1.99950 + 0.0446276i) q^{2} +(2.20583 + 1.27354i) q^{3} +(3.99602 - 0.178466i) q^{4} +(-4.70583 - 1.68971i) q^{5} +(-4.46740 - 2.44800i) q^{6} +(-0.0496201 + 6.99982i) q^{7} +(-7.98208 + 0.535176i) q^{8} +(-1.25621 - 2.17582i) q^{9} +(9.48473 + 3.16858i) q^{10} +(5.26267 - 9.11521i) q^{11} +(9.04182 + 4.69541i) q^{12} -22.3239 q^{13} +(-0.213170 - 13.9984i) q^{14} +(-8.22836 - 9.72027i) q^{15} +(15.9363 - 1.42631i) q^{16} +(-14.4854 - 8.36313i) q^{17} +(2.60889 + 4.29449i) q^{18} +(-1.44806 - 2.50812i) q^{19} +(-19.1061 - 5.91229i) q^{20} +(-9.02399 + 15.3772i) q^{21} +(-10.1159 + 18.4608i) q^{22} +(5.72017 + 9.90763i) q^{23} +(-18.2887 - 8.98497i) q^{24} +(19.2897 + 15.9030i) q^{25} +(44.6367 - 0.996263i) q^{26} -29.3230i q^{27} +(1.05095 + 27.9803i) q^{28} -13.9323i q^{29} +(16.8864 + 19.0685i) q^{30} +(-14.0310 - 8.10081i) q^{31} +(-31.8010 + 3.56310i) q^{32} +(23.2171 - 13.4044i) q^{33} +(29.3367 + 16.0756i) q^{34} +(12.0612 - 32.8562i) q^{35} +(-5.40814 - 8.47040i) q^{36} +(-20.8814 - 36.1677i) q^{37} +(3.00734 + 4.95037i) q^{38} +(-49.2428 - 28.4303i) q^{39} +(38.4666 + 10.9690i) q^{40} -60.6840 q^{41} +(17.3572 - 31.1495i) q^{42} +75.6609i q^{43} +(19.4030 - 37.3638i) q^{44} +(2.23500 + 12.3617i) q^{45} +(-11.8796 - 19.5550i) q^{46} +(-30.4013 - 52.6566i) q^{47} +(36.9692 + 17.1493i) q^{48} +(-48.9951 - 0.694664i) q^{49} +(-39.2796 - 30.9373i) q^{50} +(-21.3015 - 36.8953i) q^{51} +(-89.2068 + 3.98406i) q^{52} +(35.7027 - 61.8390i) q^{53} +(1.30861 + 58.6313i) q^{54} +(-40.1674 + 34.0023i) q^{55} +(-3.35006 - 55.8997i) q^{56} -7.37665i q^{57} +(0.621767 + 27.8577i) q^{58} +(9.89755 - 17.1431i) q^{59} +(-34.6154 - 37.3739i) q^{60} +(-20.0849 + 11.5960i) q^{61} +(28.4166 + 15.5714i) q^{62} +(15.2927 - 8.68527i) q^{63} +(63.4272 - 8.54363i) q^{64} +(105.053 + 37.7210i) q^{65} +(-45.8245 + 27.8383i) q^{66} +(-52.3532 - 30.2261i) q^{67} +(-59.3763 - 30.8340i) q^{68} +29.1394i q^{69} +(-22.6501 + 66.2342i) q^{70} +103.573i q^{71} +(11.1916 + 16.6952i) q^{72} +(70.8642 + 40.9135i) q^{73} +(43.3666 + 71.3855i) q^{74} +(22.2968 + 59.6456i) q^{75} +(-6.23410 - 9.76406i) q^{76} +(63.5438 + 37.2901i) q^{77} +(99.7298 + 54.6489i) q^{78} +(-41.3158 + 23.8537i) q^{79} +(-77.4036 - 20.2158i) q^{80} +(26.0380 - 45.0992i) q^{81} +(121.338 - 2.70818i) q^{82} -93.0788i q^{83} +(-33.3157 + 63.0582i) q^{84} +(54.0344 + 63.8316i) q^{85} +(-3.37657 - 151.284i) q^{86} +(17.7433 - 30.7324i) q^{87} +(-37.1288 + 75.5748i) q^{88} +(26.0769 + 45.1666i) q^{89} +(-5.02056 - 24.6174i) q^{90} +(1.10771 - 156.264i) q^{91} +(24.6261 + 38.5702i) q^{92} +(-20.6334 - 35.7380i) q^{93} +(63.1374 + 103.930i) q^{94} +(2.57634 + 14.2496i) q^{95} +(-74.6854 - 32.6402i) q^{96} +18.0979i q^{97} +(97.9968 - 0.797551i) q^{98} -26.4440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 14 q^{4} - 24 q^{6} + 284 q^{9}+O(q^{10}) \) 176 * q + 14 * q^4 - 24 * q^6 + 284 * q^9	\( 176 q + 14 q^{4} - 24 q^{6} + 284 q^{9} - 24 q^{10} + 32 q^{11} + 2 q^{14} + 50 q^{16} + 48 q^{20} + 16 q^{24} + 98 q^{25} - 90 q^{26} - 32 q^{30} - 256 q^{34} + 154 q^{35} - 68 q^{36} - 84 q^{40} - 328 q^{41} + 174 q^{44} - 26 q^{46} + 240 q^{49} - 96 q^{50} - 76 q^{51} - 116 q^{54} + 228 q^{56} + 244 q^{59} + 90 q^{60} - 268 q^{64} + 8 q^{65} - 304 q^{66} + 98 q^{70} - 98 q^{74} - 38 q^{75} - 612 q^{76} + 112 q^{80} - 168 q^{81} - 20 q^{84} - 16 q^{86} + 20 q^{89} + 800 q^{90} - 280 q^{91} + 226 q^{94} - 408 q^{96} - 88 q^{99}+O(q^{100}) \) 176 * q + 14 * q^4 - 24 * q^6 + 284 * q^9 - 24 * q^10 + 32 * q^11 + 2 * q^14 + 50 * q^16 + 48 * q^20 + 16 * q^24 + 98 * q^25 - 90 * q^26 - 32 * q^30 - 256 * q^34 + 154 * q^35 - 68 * q^36 - 84 * q^40 - 328 * q^41 + 174 * q^44 - 26 * q^46 + 240 * q^49 - 96 * q^50 - 76 * q^51 - 116 * q^54 + 228 * q^56 + 244 * q^59 + 90 * q^60 - 268 * q^64 + 8 * q^65 - 304 * q^66 + 98 * q^70 - 98 * q^74 - 38 * q^75 - 612 * q^76 + 112 * q^80 - 168 * q^81 - 20 * q^84 - 16 * q^86 + 20 * q^89 + 800 * q^90 - 280 * q^91 + 226 * q^94 - 408 * q^96 - 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more