LMFDB - Embedded newform 384.3.u.a.235.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,3,Mod(19,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 23, 0]))

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

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

chi := DirichletCharacter("384.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	384.u (of order $32$, degree $16$, 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:	$10.4632421514$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			235.36
Character	$\chi$	$=$	384.235
Dual form			384.3.u.a.67.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.396081 - 1.96039i) q^{2} +(-1.09880 + 1.33889i) q^{3} +(-3.68624 - 1.55294i) q^{4} +(1.90299 + 6.27330i) q^{5} +(2.18954 + 2.68439i) q^{6} +(1.94643 - 9.78539i) q^{7} +(-4.50442 + 6.61137i) q^{8} +(-0.585271 - 2.94236i) q^{9} +O(q^{10})$	\(q+(0.396081 - 1.96039i) q^{2} +(-1.09880 + 1.33889i) q^{3} +(-3.68624 - 1.55294i) q^{4} +(1.90299 + 6.27330i) q^{5} +(2.18954 + 2.68439i) q^{6} +(1.94643 - 9.78539i) q^{7} +(-4.50442 + 6.61137i) q^{8} +(-0.585271 - 2.94236i) q^{9} +(13.0518 - 1.24585i) q^{10} +(-16.5164 - 1.62672i) q^{11} +(6.12967 - 3.22910i) q^{12} +(17.9126 + 5.43372i) q^{13} +(-18.4122 - 7.69157i) q^{14} +(-10.4903 - 4.34522i) q^{15} +(11.1767 + 11.4491i) q^{16} +(9.63304 + 23.2562i) q^{17} +(-5.99997 - 0.0180534i) q^{18} +(20.9732 - 11.2104i) q^{19} +(2.72723 - 26.0801i) q^{20} +(10.9628 + 13.3583i) q^{21} +(-9.73085 + 31.7342i) q^{22} +(27.9282 + 18.6610i) q^{23} +(-3.90245 - 13.2955i) q^{24} +(-14.9462 + 9.98676i) q^{25} +(17.7470 - 32.9634i) q^{26} +(4.58260 + 2.44945i) q^{27} +(-22.3712 + 33.0486i) q^{28} +(22.0253 - 2.16930i) q^{29} +(-12.6733 + 18.8440i) q^{30} +(-10.2095 + 10.2095i) q^{31} +(26.8715 - 17.3760i) q^{32} +(20.3263 - 20.3263i) q^{33} +(49.4067 - 9.67315i) q^{34} +(65.0907 - 6.41088i) q^{35} +(-2.41187 + 11.7551i) q^{36} +(50.9039 + 27.2087i) q^{37} +(-13.6697 - 45.5559i) q^{38} +(-26.9575 + 18.0124i) q^{39} +(-50.0470 - 15.6763i) q^{40} +(-48.2540 - 32.2423i) q^{41} +(30.5296 - 16.2005i) q^{42} +(-2.69034 - 3.27819i) q^{43} +(58.3572 + 31.6456i) q^{44} +(17.3445 - 9.27084i) q^{45} +(47.6447 - 47.3588i) q^{46} +(9.55675 + 23.0720i) q^{47} +(-27.6101 + 2.38421i) q^{48} +(-46.6951 - 19.3417i) q^{49} +(13.6580 + 33.2560i) q^{50} +(-41.7224 - 12.6564i) q^{51} +(-57.5917 - 47.8472i) q^{52} +(-15.2344 - 1.50046i) q^{53} +(6.61695 - 8.01349i) q^{54} +(-21.2256 - 106.708i) q^{55} +(55.9272 + 56.9461i) q^{56} +(-8.03585 + 40.3990i) q^{57} +(4.47113 - 44.0374i) q^{58} +(7.08556 + 23.3580i) q^{59} +(31.9218 + 32.3084i) q^{60} +(52.1586 - 63.5555i) q^{61} +(15.9707 + 24.0583i) q^{62} -29.9313 q^{63} +(-23.4203 - 59.5608i) q^{64} +122.711i q^{65} +(-31.7965 - 47.8982i) q^{66} +(84.7567 + 69.5580i) q^{67} +(0.605927 - 100.688i) q^{68} +(-55.6727 + 16.8881i) q^{69} +(13.2134 - 130.142i) q^{70} +(-64.9980 - 12.9289i) q^{71} +(22.0893 + 9.38418i) q^{72} +(-117.837 + 23.4392i) q^{73} +(73.5016 - 89.0145i) q^{74} +(3.05175 - 30.9849i) q^{75} +(-94.7216 + 8.75405i) q^{76} +(-48.0662 + 158.453i) q^{77} +(24.6340 + 59.9816i) q^{78} +(12.5240 - 30.2357i) q^{79} +(-50.5542 + 91.9024i) q^{80} +(-8.31492 + 3.44415i) q^{81} +(-82.3199 + 81.8260i) q^{82} +(-25.7348 - 48.1463i) q^{83} +(-19.6670 - 66.2665i) q^{84} +(-127.562 + 104.687i) q^{85} +(-7.49212 + 3.97568i) q^{86} +(-21.2970 + 31.8732i) q^{87} +(85.1518 - 101.869i) q^{88} +(45.8208 + 68.5757i) q^{89} +(-11.3046 - 37.6740i) q^{90} +(88.0367 - 164.705i) q^{91} +(-73.9705 - 112.160i) q^{92} +(-2.45121 - 24.8876i) q^{93} +(49.0154 - 9.59654i) q^{94} +(110.238 + 110.238i) q^{95} +(-6.26185 + 55.0708i) q^{96} +(48.2198 + 48.2198i) q^{97} +(-56.4123 + 83.8796i) q^{98} +(4.88017 + 49.5492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 1248 q^{50} + 1056 q^{52} + 288 q^{54} + 1568 q^{56} + 576 q^{60} + 192 q^{62} - 192 q^{64} - 576 q^{66} - 960 q^{68} - 1344 q^{70} - 2464 q^{74} - 416 q^{76} - 1440 q^{78} - 1632 q^{80}+O(q^{100}) $ 1024 * q + 1248 * q^50 + 1056 * q^52 + 288 * q^54 + 1568 * q^56 + 576 * q^60 + 192 * q^62 - 192 * q^64 - 576 * q^66 - 960 * q^68 - 1344 * q^70 - 2464 * q^74 - 416 * q^76 - 1440 * q^78 - 1632 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{13}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	0.396081	−	1.96039i	0.198041	−	0.980194i
$2$	0.396081	−	1.96039i	0.198041	−	0.980194i
$3$	−1.09880	+	1.33889i	−0.366267	+	0.446298i
$3$	−1.09880	+	1.33889i	−0.366267	+	0.446298i
$4$	−3.68624	−	1.55294i	−0.921560	−	0.388236i
$5$	1.90299	+	6.27330i	0.380597	+	1.25466i	0.912927	+	0.408124i	$0.133817\pi$
$5$	1.90299	+	6.27330i	0.380597	+	1.25466i	−0.532329	+	0.846537i	$0.678683\pi$
$6$	2.18954	+	2.68439i	0.364923	+	0.447398i
$7$	1.94643	−	9.78539i	0.278062	−	1.39791i	−0.549010	−	0.835816i	$-0.684995\pi$
$7$	1.94643	−	9.78539i	0.278062	−	1.39791i	0.827072	−	0.562096i	$-0.190005\pi$
$8$	−4.50442	+	6.61137i	−0.563053	+	0.826421i
$9$	−0.585271	−	2.94236i	−0.0650301	−	0.326928i
$10$	13.0518	−	1.24585i	1.30518	−	0.124585i
$11$	−16.5164	−	1.62672i	−1.50149	−	0.147884i	−0.686403	−	0.727221i	$-0.740812\pi$
$11$	−16.5164	−	1.62672i	−1.50149	−	0.147884i	−0.815088	+	0.579337i	$0.803312\pi$
$12$	6.12967	−	3.22910i	0.510806	−	0.269092i
$13$	17.9126	+	5.43372i	1.37789	+	0.417978i	0.890411	−	0.455157i	$-0.150417\pi$
$13$	17.9126	+	5.43372i	1.37789	+	0.417978i	0.487478	+	0.873135i	$0.337917\pi$
$14$	−18.4122	−	7.69157i	−1.31516	−	0.549398i
$15$	−10.4903	−	4.34522i	−0.699353	−	0.289681i
$16$	11.1767	+	11.4491i	0.698545	+	0.715566i
$17$	9.63304	+	23.2562i	0.566650	+	1.36801i	0.904363	+	0.426764i	$0.140347\pi$
$17$	9.63304	+	23.2562i	0.566650	+	1.36801i	−0.337713	+	0.941249i	$0.609653\pi$
$18$	−5.99997	−	0.0180534i	−0.333332	−	0.00100297i
$19$	20.9732	−	11.2104i	1.10385	−	0.590023i	0.184255	−	0.982879i	$-0.441013\pi$
$19$	20.9732	−	11.2104i	1.10385	−	0.590023i	0.919600	+	0.392856i	$0.128513\pi$
$20$	2.72723	−	26.0801i	0.136362	−	1.30401i
$21$	10.9628	+	13.3583i	0.522040	+	0.636108i
$22$	−9.73085	+	31.7342i	−0.442311	+	1.44247i
$23$	27.9282	+	18.6610i	1.21427	+	0.811349i	0.986722	−	0.162418i	$-0.0519292\pi$
$23$	27.9282	+	18.6610i	1.21427	+	0.811349i	0.227548	+	0.973767i	$0.426929\pi$
$24$	−3.90245	−	13.2955i	−0.162602	−	0.553980i
$25$	−14.9462	+	9.98676i	−0.597850	+	0.399471i
$26$	17.7470	−	32.9634i	0.682578	−	1.26782i
$27$	4.58260	+	2.44945i	0.169726	+	0.0907203i
$28$	−22.3712	+	33.0486i	−0.798971	+	1.18031i
$29$	22.0253	−	2.16930i	0.759493	−	0.0748036i	0.289146	−	0.957285i	$-0.406629\pi$
$29$	22.0253	−	2.16930i	0.759493	−	0.0748036i	0.470347	+	0.882481i	$0.344129\pi$
$30$	−12.6733	+	18.8440i	−0.422444	+	0.628132i
$31$	−10.2095	+	10.2095i	−0.329338	+	0.329338i	−0.852335	−	0.522997i	$-0.824814\pi$
$31$	−10.2095	+	10.2095i	−0.329338	+	0.329338i	0.522997	+	0.852335i	$0.324814\pi$
$32$	26.8715	−	17.3760i	0.839734	−	0.542999i
$33$	20.3263	−	20.3263i	0.615947	−	0.615947i
$34$	49.4067	−	9.67315i	1.45314	−	0.284504i
$35$	65.0907	−	6.41088i	1.85974	−	0.183168i
$36$	−2.41187	+	11.7551i	−0.0669963	+	0.326531i
$37$	50.9039	+	27.2087i	1.37578	+	0.735370i	0.982886	−	0.184214i	$-0.0589740\pi$
$37$	50.9039	+	27.2087i	1.37578	+	0.735370i	0.392894	+	0.919584i	$0.371474\pi$
$38$	−13.6697	−	45.5559i	−0.359729	−	1.19884i
$39$	−26.9575	+	18.0124i	−0.691218	+	0.461857i
$40$	−50.0470	−	15.6763i	−1.25117	−	0.391907i
$41$	−48.2540	−	32.2423i	−1.17693	−	0.786398i	−0.195968	−	0.980610i	$-0.562785\pi$
$41$	−48.2540	−	32.2423i	−1.17693	−	0.786398i	−0.980959	+	0.194213i	$0.937785\pi$
$42$	30.5296	−	16.2005i	0.726894	−	0.385725i
$43$	−2.69034	−	3.27819i	−0.0625661	−	0.0762370i	0.740787	−	0.671740i	$-0.234453\pi$
$43$	−2.69034	−	3.27819i	−0.0625661	−	0.0762370i	−0.803353	+	0.595503i	$0.796953\pi$
$44$	58.3572	+	31.6456i	1.32630	+	0.719217i
$45$	17.3445	−	9.27084i	0.385434	−	0.206019i
$46$	47.6447	−	47.3588i	1.03575	−	1.02954i
$47$	9.55675	+	23.0720i	0.203335	+	0.490895i	0.992347	−	0.123484i	$-0.0394068\pi$
$47$	9.55675	+	23.0720i	0.203335	+	0.490895i	−0.789011	+	0.614379i	$0.789407\pi$
$48$	−27.6101	+	2.38421i	−0.575210	+	0.0496710i
$49$	−46.6951	−	19.3417i	−0.952961	−	0.394729i
$50$	13.6580	+	33.2560i	0.273160	+	0.665120i
$51$	−41.7224	−	12.6564i	−0.818086	−	0.248164i
$52$	−57.5917	−	47.8472i	−1.10753	−	0.920139i
$53$	−15.2344	−	1.50046i	−0.287442	−	0.0283105i	−0.0467312	−	0.998908i	$-0.514880\pi$
$53$	−15.2344	−	1.50046i	−0.287442	−	0.0283105i	−0.240710	+	0.970597i	$0.577380\pi$
$54$	6.61695	−	8.01349i	0.122536	−	0.148398i
$55$	−21.2256	−	106.708i	−0.385919	−	1.94015i
$56$	55.9272	+	56.9461i	0.998700	+	1.01689i
$57$	−8.03585	+	40.3990i	−0.140980	+	0.708754i
$58$	4.47113	−	44.0374i	0.0770885	−	0.759265i
$59$	7.08556	+	23.3580i	0.120094	+	0.395898i	0.996290	−	0.0860573i	$-0.0274268\pi$
$59$	7.08556	+	23.3580i	0.120094	+	0.395898i	−0.876196	+	0.481955i	$0.839927\pi$
$60$	31.9218	+	32.3084i	0.532031	+	0.538473i
$61$	52.1586	−	63.5555i	0.855059	−	1.04189i	−0.143575	−	0.989639i	$-0.545860\pi$
$61$	52.1586	−	63.5555i	0.855059	−	1.04189i	0.998634	−	0.0522532i	$-0.0166403\pi$
$62$	15.9707	+	24.0583i	0.257593	+	0.388037i
$63$	−29.9313			−0.475100
$64$	−23.4203	−	59.5608i	−0.365943	−	0.930637i
$65$			122.711i			1.88787i
$66$	−31.7965	−	47.8982i	−0.481765	−	0.725730i
$67$	84.7567	+	69.5580i	1.26503	+	1.03818i	0.997205	+	0.0747103i	$0.0238032\pi$
$67$	84.7567	+	69.5580i	1.26503	+	1.03818i	0.267820	+	0.963469i	$0.413697\pi$
$68$	0.605927	−	100.688i	0.00891069	−	1.48070i
$69$	−55.6727	+	16.8881i	−0.806850	+	0.244755i
$70$	13.2134	−	130.142i	0.188763	−	1.85918i
$71$	−64.9980	−	12.9289i	−0.915464	−	0.182097i	−0.285191	−	0.958471i	$-0.592057\pi$
$71$	−64.9980	−	12.9289i	−0.915464	−	0.182097i	−0.630273	+	0.776374i	$0.717057\pi$
$72$	22.0893	+	9.38418i	0.306796	+	0.130336i
$73$	−117.837	+	23.4392i	−1.61420	+	0.321085i	−0.917946	−	0.396706i	$-0.870153\pi$
$73$	−117.837	+	23.4392i	−1.61420	+	0.321085i	−0.696258	+	0.717791i	$0.745153\pi$
$74$	73.5016	−	89.0145i	0.993265	−	1.20290i
$75$	3.05175	−	30.9849i	0.0406900	−	0.413132i
$76$	−94.7216	+	8.75405i	−1.24634	+	0.115185i
$77$	−48.0662	+	158.453i	−0.624237	+	2.05783i
$78$	24.6340	+	59.9816i	0.315821	+	0.768995i
$79$	12.5240	−	30.2357i	0.158532	−	0.382730i	−0.824577	−	0.565749i	$-0.808587\pi$
$79$	12.5240	−	30.2357i	0.158532	−	0.382730i	0.983109	+	0.183019i	$0.0585871\pi$
$80$	−50.5542	+	91.9024i	−0.631928	+	1.14878i
$81$	−8.31492	+	3.44415i	−0.102653	+	0.0425204i
$82$	−82.3199	+	81.8260i	−1.00390	+	0.997878i
$83$	−25.7348	−	48.1463i	−0.310057	−	0.580076i	0.677836	−	0.735213i	$-0.262918\pi$
$83$	−25.7348	−	48.1463i	−0.310057	−	0.580076i	−0.987893	+	0.155137i	$0.950418\pi$
$84$	−19.6670	−	66.2665i	−0.234131	−	0.788886i
$85$	−127.562	+	104.687i	−1.50073	+	1.23161i
$86$	−7.49212	+	3.97568i	−0.0871177	+	0.0462289i
$87$	−21.2970	+	31.8732i	−0.244793	+	0.366358i
$88$	85.1518	−	101.869i	0.967634	−	1.15760i
$89$	45.8208	+	68.5757i	0.514841	+	0.770514i	0.994251	−	0.107077i	$-0.0341492\pi$
$89$	45.8208	+	68.5757i	0.514841	+	0.770514i	−0.479410	+	0.877591i	$0.659149\pi$
$90$	−11.3046	−	37.6740i	−0.125607	−	0.418600i
$91$	88.0367	−	164.705i	0.967436	−	1.80995i
$92$	−73.9705	−	112.160i	−0.804027	−	1.21913i
$93$	−2.45121	−	24.8876i	−0.0263571	−	0.267608i
$94$	49.0154	−	9.59654i	0.521440	−	0.102091i
$95$	110.238	+	110.238i	1.16040	+	1.16040i
$96$	−6.26185	+	55.0708i	−0.0652276	+	0.573654i
$97$	48.2198	+	48.2198i	0.497111	+	0.497111i	0.910537	−	0.413427i	$-0.135668\pi$
$97$	48.2198	+	48.2198i	0.497111	+	0.497111i	−0.413427	+	0.910537i	$0.635668\pi$
$98$	−56.4123	+	83.8796i	−0.575636	+	0.855914i
$99$	4.88017	+	49.5492i	0.0492947	+	0.500497i
$100$	70.6043	−	13.6029i	0.706043	−	0.136029i
$101$	−5.64311	+	10.5575i	−0.0558723	+	0.104530i	−0.908307	−	0.418303i	$-0.862625\pi$
$101$	−5.64311	+	10.5575i	−0.0558723	+	0.104530i	0.852435	+	0.522833i	$0.175125\pi$
$102$	−41.3368	+	76.7791i	−0.405263	+	0.752737i
$103$	2.04716	+	3.06379i	0.0198753	+	0.0297455i	0.841274	−	0.540609i	$-0.181806\pi$
$103$	2.04716	+	3.06379i	0.0198753	+	0.0297455i	−0.821399	+	0.570354i	$0.806806\pi$
$104$	−116.610	+	93.9508i	−1.12125	+	0.903373i
$105$	−62.9383	+	94.1938i	−0.599413	+	0.897084i
$106$	−8.97554	+	29.2710i	−0.0846749	+	0.276142i
$107$	91.4425	−	75.0449i	0.854603	−	0.701355i	−0.101357	−	0.994850i	$-0.532319\pi$
$107$	91.4425	−	75.0449i	0.854603	−	0.701355i	0.955960	+	0.293495i	$0.0948186\pi$
$108$	−13.0887	−	16.1458i	−0.121192	−	0.149498i
$109$	−37.5182	−	70.1917i	−0.344204	−	0.643961i	0.648942	−	0.760838i	$-0.275212\pi$
$109$	−37.5182	−	70.1917i	−0.344204	−	0.643961i	−0.993146	+	0.116877i	$0.962712\pi$
$110$	−217.596	−	0.654729i	−1.97815	−	0.00595209i
$111$	−92.3628	+	38.2579i	−0.832097	+	0.344666i
$112$	133.788	−	87.0837i	1.19454	−	0.777533i
$113$	9.59312	−	23.1598i	0.0848949	−	0.204954i	−0.875731	−	0.482799i	$-0.839620\pi$
$113$	9.59312	−	23.1598i	0.0848949	−	0.204954i	0.960626	+	0.277845i	$0.0896201\pi$
$114$	76.0148	+	31.7547i	0.666796	+	0.278550i
$115$	−63.9193	+	210.714i	−0.555820	+	1.83229i
$116$	−84.5594	−	26.2075i	−0.728960	−	0.225927i
$117$	5.50423	−	55.8853i	0.0470447	−	0.477652i
$118$	48.5971	−	4.63880i	0.411840	−	0.0393119i
$119$	246.321	−	48.9963i	2.06993	−	0.411734i
$120$	75.9805	−	49.7824i	0.633171	−	0.414854i
$121$	151.470	+	30.1294i	1.25182	+	0.249003i
$122$	−103.934	−	127.424i	−0.851920	−	1.04446i
$123$	96.1906	−	29.1791i	0.782037	−	0.237228i
$124$	53.4893	−	21.7798i	0.431365	−	0.175644i
$125$	35.5959	+	29.2128i	0.284767	+	0.233702i
$126$	−11.8552	+	58.6769i	−0.0940890	+	0.465690i
$127$			24.7740i			0.195071i	0.995232	+	0.0975355i	$0.0310960\pi$
$127$			24.7740i			0.195071i	−0.995232	+	0.0975355i	$0.968904\pi$
$128$	−126.039	+	22.3220i	−0.984676	+	0.174391i
$129$	7.34530			0.0569403
$130$	240.562	+	48.6036i	1.85047	+	0.373874i
$131$	−39.0403	+	47.5707i	−0.298017	+	0.363135i	−0.900393	−	0.435077i	$-0.856721\pi$
$131$	−39.0403	+	47.5707i	−0.298017	+	0.363135i	0.602376	+	0.798213i	$0.294221\pi$
$132$	−106.493	+	43.3619i	−0.806765	+	0.328499i
$133$	−68.8753	−	227.052i	−0.517860	−	1.70715i
$134$	169.931	−	138.605i	1.26814	−	1.03437i
$135$	−6.64552	+	33.4093i	−0.0492261	+	0.247476i
$136$	−197.147	−	41.0683i	−1.44961	−	0.301973i
$137$	−12.6183	−	63.4363i	−0.0921041	−	0.463038i	−0.999120	−	0.0419422i	$-0.986645\pi$
$137$	−12.6183	−	63.4363i	−0.0921041	−	0.463038i	0.907016	−	0.421096i	$-0.138355\pi$
$138$	11.0564	+	115.829i	0.0801186	+	0.839341i
$139$	−100.616	−	9.90979i	−0.723854	−	0.0712934i	−0.270622	−	0.962686i	$-0.587229\pi$
$139$	−100.616	−	9.90979i	−0.723854	−	0.0712934i	−0.453233	+	0.891392i	$0.649729\pi$
$140$	−249.896	−	77.4503i	−1.78497	−	0.553216i
$141$	−41.3920	−	12.5561i	−0.293560	−	0.0890505i
$142$	−51.0901	+	122.300i	−0.359789	+	0.861270i
$143$	−287.012	−	118.884i	−2.00708	−	0.831359i
$144$	27.1458	−	39.5867i	0.188512	−	0.274908i
$145$	55.5226	+	134.043i	0.382914	+	0.924437i
$146$	−0.723013	+	240.290i	−0.00495214	+	1.64582i
$147$	77.2052	−	41.2670i	0.525205	−	0.280728i
$148$	−145.390	−	179.349i	−0.982367	−	1.21181i
$149$	109.824	+	133.821i	0.737076	+	0.898130i	0.997733	−	0.0673015i	$-0.0214389\pi$
$149$	109.824	+	133.821i	0.737076	+	0.898130i	−0.260656	+	0.965432i	$0.583939\pi$
$150$	−59.5337	−	18.2551i	−0.396891	−	0.121701i
$151$	−166.984	−	111.575i	−1.10585	−	0.738908i	−0.138003	−	0.990432i	$-0.544068\pi$
$151$	−166.984	−	111.575i	−1.10585	−	0.738908i	−0.967851	+	0.251524i	$0.919068\pi$
$152$	−20.3561	+	189.158i	−0.133922	+	1.24446i
$153$	62.7901	−	41.9550i	0.410393	−	0.274216i
$154$	291.591	+	156.989i	1.89345	+	1.01941i
$155$	−83.4756	−	44.6186i	−0.538552	−	0.287862i
$156$	127.344	−	24.5346i	0.816309	−	0.157273i
$157$	−137.102	+	13.5034i	−0.873263	+	0.0860089i	−0.524711	−	0.851281i	$-0.675826\pi$
$157$	−137.102	+	13.5034i	−0.873263	+	0.0860089i	−0.348552	+	0.937289i	$0.613326\pi$
$158$	−54.3131	−	36.5277i	−0.343754	−	0.231188i
$159$	18.7485	−	18.7485i	0.117915	−	0.117915i
$160$	160.141	+	135.507i	1.00088	+	0.846917i
$161$	236.966	−	236.966i	1.47184	−	1.47184i
$162$	3.45849	+	17.6646i	0.0213487	+	0.109041i
$163$	−126.635	+	12.4725i	−0.776901	+	0.0765181i	−0.478693	−	0.877983i	$-0.658889\pi$
$163$	−126.635	+	12.4725i	−0.776901	+	0.0765181i	−0.298209	+	0.954501i	$0.596389\pi$
$164$	127.805	+	193.789i	0.779301	+	1.18164i
$165$	166.193	+	88.8322i	1.00723	+	0.538377i
$166$	−104.579	+	31.3802i	−0.629991	+	0.189038i
$167$	−58.5353	+	39.1120i	−0.350511	+	0.234204i	−0.718344	−	0.695688i	$-0.755100\pi$
$167$	−58.5353	+	39.1120i	−0.350511	+	0.234204i	0.367833	+	0.929892i	$0.380100\pi$
$168$	−137.698	+	12.3081i	−0.819629	+	0.0732625i
$169$	150.816	+	100.772i	0.892404	+	0.596286i
$170$	154.703	+	291.535i	0.910017	+	1.71491i
$171$	−45.2601	−	55.1496i	−0.264679	−	0.322512i
$172$	4.82640	+	16.2622i	0.0280604	+	0.0945474i
$173$	−155.654	+	83.1987i	−0.899733	+	0.480918i	−0.855323	−	0.518096i	$-0.826641\pi$
$173$	−155.654	+	83.1987i	−0.899733	+	0.480918i	−0.0444108	+	0.999013i	$0.514141\pi$
$174$	54.0485	+	54.3747i	0.310623	+	0.312498i
$175$	68.6325	+	165.693i	0.392185	+	0.946819i
$176$	−165.975	−	207.279i	−0.943039	−	1.17772i
$177$	−39.0595	−	16.1790i	−0.220675	−	0.0914065i
$178$	152.584	−	62.6651i	0.857212	−	0.352051i
$179$	130.580	+	39.6110i	0.729496	+	0.221290i	0.633119	−	0.774055i	$-0.281774\pi$
$179$	130.580	+	39.6110i	0.729496	+	0.221290i	0.0963775	+	0.995345i	$0.469274\pi$
$180$	−78.3332	+	7.23946i	−0.435184	+	0.0402192i
$181$	−308.347	−	30.3695i	−1.70358	−	0.167787i	−0.801100	−	0.598530i	$-0.795752\pi$
$181$	−308.347	−	30.3695i	−1.70358	−	0.167787i	−0.902475	+	0.430743i	$0.858252\pi$
$182$	−288.016	−	237.823i	−1.58251	−	1.30672i
$183$	27.7820	+	139.670i	0.151814	+	0.763222i
$184$	−249.175	+	100.586i	−1.35421	+	0.546665i
$185$	−73.8190	+	371.113i	−0.399022	+	2.00602i
$186$	−49.7602	−	5.05217i	−0.267528	−	0.0271622i
$187$	−121.272	−	399.780i	−0.648512	−	2.13786i
$188$	0.601129	−	99.8902i	0.00319749	−	0.531331i
$189$	32.8885	−	40.0748i	0.174013	−	0.212036i
$190$	259.773	−	172.446i	1.36723	−	0.907612i
$191$	−219.935			−1.15149			−0.575745	−	0.817629i	$-0.695288\pi$
$191$	−219.935			−1.15149			−0.575745	+	0.817629i	$0.695288\pi$
$192$	105.480	+	34.0881i	0.549374	+	0.177542i
$193$			81.9126i			0.424417i	0.977224	+	0.212209i	$0.0680657\pi$
$193$			81.9126i			0.424417i	−0.977224	+	0.212209i	$0.931934\pi$
$194$	113.628	−	75.4305i	0.585713	−	0.388817i
$195$	−164.297	−	134.835i	−0.842550	−	0.691463i
$196$	142.093	+	143.813i	0.724962	+	0.733741i
$197$	299.627	−	90.8910i	1.52095	−	0.461376i	0.584270	−	0.811559i	$-0.301381\pi$
$197$	299.627	−	90.8910i	1.52095	−	0.461376i	0.936681	+	0.350184i	$0.113881\pi$
$198$	99.0686	+	10.0585i	0.500347	+	0.0508004i
$199$	−50.2247	−	9.99032i	−0.252385	−	0.0502026i	0.0672760	−	0.997734i	$-0.478569\pi$
$199$	−50.2247	−	9.99032i	−0.252385	−	0.0502026i	−0.319661	+	0.947532i	$0.603569\pi$
$200$	1.29808	−	143.800i	0.00649038	−	0.718999i
$201$	−186.262	+	37.0497i	−0.926674	+	0.184327i
$202$	18.4617	+	15.2443i	0.0913945	+	0.0754669i
$203$	21.6433	−	219.749i	0.106617	−	1.08251i
$204$	134.144	+	111.447i	0.657569	+	0.546309i
$205$	110.439	−	364.069i	0.538727	−	1.77595i
$206$	6.81706	−	2.79972i	0.0330925	−	0.0135909i
$207$	38.5618	−	93.0965i	0.186289	−	0.449741i
$208$	137.993	+	265.813i	0.663427	+	1.27795i
$209$	−364.639	+	151.038i	−1.74468	+	0.722671i
$210$	159.728	+	160.692i	0.760608	+	0.765200i
$211$	112.223	+	209.955i	0.531863	+	0.995046i	0.994118	+	0.108299i	$0.0345404\pi$
$211$	112.223	+	209.955i	0.531863	+	0.995046i	−0.462255	+	0.886747i	$0.652960\pi$
$212$	53.8275	+	29.1892i	0.253903	+	0.137685i
$213$	88.7303	−	72.8190i	0.416574	−	0.341873i
$214$	−110.899	−	208.987i	−0.518217	−	0.976573i
$215$	15.4454	−	23.1157i	0.0718391	−	0.107515i
$216$	−36.8362	+	19.2639i	−0.170538	+	0.0891846i
$217$	80.0316	+	119.776i	0.368809	+	0.551962i
$218$	−152.463	+	45.7487i	−0.699373	+	0.209856i
$219$	98.0967	−	183.526i	0.447930	−	0.838019i
$220$	−87.4693	+	426.314i	−0.397588	+	1.93779i
$221$	46.1848	+	468.922i	0.208981	+	2.12182i
$222$	38.4172	+	196.220i	0.173050	+	0.883874i
$223$	151.492	+	151.492i	0.679337	+	0.679337i	0.959850	−	0.280513i	$-0.0905046\pi$
$223$	151.492	+	151.492i	0.679337	+	0.679337i	−0.280513	+	0.959850i	$0.590505\pi$
$224$	−117.727	−	296.769i	−0.525567	−	1.32486i
$225$	38.1322	+	38.1322i	0.169477	+	0.169477i
$226$	−41.6026	−	27.9794i	−0.184082	−	0.123803i
$227$	−39.7102	−	403.185i	−0.174935	−	1.77614i	−0.536600	−	0.843837i	$-0.680292\pi$
$227$	−39.7102	−	403.185i	−0.174935	−	1.77614i	0.361665	−	0.932308i	$-0.382208\pi$
$228$	92.3594	−	136.441i	0.405085	−	0.598426i
$229$	144.992	−	271.260i	0.633151	−	1.18454i	−0.336877	−	0.941549i	$-0.609371\pi$
$229$	144.992	−	271.260i	0.633151	−	1.18454i	0.970028	−	0.242993i	$-0.0781293\pi$
$230$	387.763	+	208.766i	1.68593	+	0.907680i
$231$	−159.337	−	238.464i	−0.689769	−	1.03231i
$232$	−84.8693	+	155.389i	−0.365816	+	0.669780i
$233$	136.743	−	204.650i	0.586878	−	0.878325i	−0.412591	−	0.910916i	$-0.635376\pi$
$233$	136.743	−	204.650i	0.586878	−	0.878325i	0.999469	+	0.0325917i	$0.0103761\pi$
$234$	−107.377	−	32.9255i	−0.458875	−	0.140707i
$235$	−126.552	+	103.858i	−0.538517	+	0.441950i
$236$	10.1546	−	97.1066i	0.0430278	−	0.411468i
$237$	26.7209	+	49.9913i	0.112746	+	0.210934i
$238$	1.51135	−	502.292i	0.00635023	−	2.11047i
$239$	−27.2720	+	11.2965i	−0.114109	+	0.0472655i	−0.439008	−	0.898483i	$-0.644670\pi$
$239$	−27.2720	+	11.2965i	−0.114109	+	0.0472655i	0.324899	+	0.945749i	$0.394670\pi$
$240$	−67.4984	−	168.669i	−0.281243	−	0.702788i
$241$	128.684	−	310.671i	0.533958	−	1.28909i	−0.394924	−	0.918714i	$-0.629229\pi$
$241$	128.684	−	310.671i	0.533958	−	1.28909i	0.928882	−	0.370376i	$-0.120771\pi$
$242$	119.060	−	285.007i	0.491983	−	1.17772i
$243$	4.52509	−	14.9172i	0.0186218	−	0.0613878i
$244$	−290.967	+	153.281i	−1.19249	+	0.628202i
$245$	32.4765	−	329.740i	0.132557	−	1.34588i
$246$	−19.1031	−	200.128i	−0.0776548	−	0.813529i
$247$	436.599	−	86.8449i	1.76761	−	0.351599i
$248$	−21.5108	−	113.486i	−0.0867370	−	0.457606i
$249$	92.7402	+	18.4472i	0.372451	+	0.0740850i
$250$	71.3673	−	58.2111i	0.285469	−	0.232844i
$251$	137.413	−	41.6838i	0.547462	−	0.166071i	−0.00442409	−	0.999990i	$-0.501408\pi$
$251$	137.413	−	41.6838i	0.547462	−	0.166071i	0.551886	+	0.833919i	$0.313908\pi$
$252$	110.334	+	46.4816i	0.437833	+	0.184451i
$253$	−430.917	−	353.645i	−1.70323	−	1.39780i
$254$	48.5667	+	9.81252i	0.191207	+	0.0386320i
$255$		−	285.822i		−	1.12087i
$256$	−6.16165	+	255.926i	−0.0240690	+	0.999710i
$257$	64.2469			0.249988			0.124994	−	0.992158i	$-0.460109\pi$
$257$	64.2469			0.249988			0.124994	+	0.992158i	$0.460109\pi$
$258$	2.90933	−	14.3996i	0.0112765	−	0.0558125i
$259$	365.328	−	445.154i	1.41053	−	1.71874i
$260$	190.564	−	452.343i	0.732938	−	1.73978i
$261$	−19.2736	−	63.5367i	−0.0738454	−	0.243436i
$262$	77.7940	+	95.3760i	0.296923	+	0.364030i
$263$	23.1876	−	116.572i	0.0881657	−	0.443239i	−0.911336	−	0.411664i	$-0.864948\pi$
$263$	23.1876	−	116.572i	0.0881657	−	0.443239i	0.999501	−	0.0315749i	$-0.0100523\pi$
$264$	42.8263	+	225.942i	0.162221	+	0.855843i
$265$	−19.5780	−	98.4254i	−0.0738794	−	0.371417i
$266$	−472.389	+	45.0915i	−1.77590	+	0.169517i
$267$	−142.164	−	14.0019i	−0.532448	−	0.0524415i
$268$	−204.414	−	388.030i	−0.762738	−	1.44787i
$269$	−285.701	−	86.6666i	−1.06209	−	0.322181i	−0.289558	−	0.957160i	$-0.593508\pi$
$269$	−285.701	−	86.6666i	−1.06209	−	0.322181i	−0.772529	+	0.634980i	$0.781008\pi$
$270$	62.8630	+	26.2606i	0.232826	+	0.0972614i
$271$	−59.9514	−	24.8327i	−0.221223	−	0.0916336i	0.269319	−	0.963051i	$-0.413201\pi$
$271$	−59.9514	−	24.8327i	−0.221223	−	0.0916336i	−0.490542	+	0.871417i	$0.663201\pi$
$272$	−158.596	+	370.218i	−0.583073	+	1.36109i
$273$	123.788	+	298.850i	0.453435	+	1.09469i
$274$	−129.358	−	0.389226i	−0.472108	−	0.00142053i
$275$	263.104	−	140.632i	0.956742	−	0.511389i
$276$	231.449	+	24.2029i	0.838584	+	0.0876918i
$277$	131.816	+	160.618i	0.475870	+	0.579849i	0.954516	−	0.298159i	$-0.0963724\pi$
$277$	131.816	+	160.618i	0.475870	+	0.579849i	−0.478646	+	0.878008i	$0.658872\pi$
$278$	−59.2790	+	193.321i	−0.213234	+	0.695399i
$279$	36.0152	+	24.0646i	0.129087	+	0.0862530i
$280$	−250.812	+	459.216i	−0.895756	+	1.64006i
$281$	308.937	−	206.425i	1.09942	−	0.734609i	0.132882	−	0.991132i	$-0.457577\pi$
$281$	308.937	−	206.425i	1.09942	−	0.734609i	0.966538	+	0.256523i	$0.0825769\pi$
$282$	−41.0094	+	76.1711i	−0.145424	+	0.270110i
$283$	388.691	+	207.760i	1.37347	+	0.734133i	0.982498	−	0.186271i	$-0.0596401\pi$
$283$	388.691	+	207.760i	1.37347	+	0.734133i	0.390969	+	0.920404i	$0.372140\pi$
$284$	219.520	+	148.597i	0.772958	+	0.523230i
$285$	−268.727	+	26.4673i	−0.942902	+	0.0928677i
$286$	−346.739	+	515.567i	−1.21238	+	1.80268i
$287$	−409.427	+	409.427i	−1.42657	+	1.42657i
$288$	−66.8533	−	68.8958i	−0.232130	−	0.239221i
$289$	−243.702	+	243.702i	−0.843261	+	0.843261i
$290$	284.768	−	55.7537i	0.981960	−	0.192254i
$291$	−117.545	+	11.5772i	−0.403935	+	0.0397841i
$292$	470.775	+	96.5916i	1.61224	+	0.330793i
$293$	176.520	+	94.3519i	0.602458	+	0.322020i	0.744276	−	0.667872i	$-0.232795\pi$
$293$	176.520	+	94.3519i	0.602458	+	0.322020i	−0.141818	+	0.989893i	$0.545295\pi$
$294$	−50.3198	−	167.697i	−0.171156	−	0.570398i
$295$	−133.048	+	88.8998i	−0.451010	+	0.301355i
$296$	−409.179	+	213.985i	−1.38236	+	0.722921i
$297$	−71.7035	−	47.9107i	−0.241426	−	0.161316i
$298$	305.841	−	162.294i	1.02631	−	0.544612i
$299$	398.867	+	486.021i	1.33400	+	1.62549i
$300$	−59.3673	+	109.479i	−0.197891	+	0.364929i
$301$	−37.3149	+	19.9453i	−0.123970	+	0.0662633i
$302$	−284.870	+	283.161i	−0.943277	+	0.937618i
$303$	−7.93473	−	19.1561i	−0.0261872	−	0.0632215i
$304$	362.761	+	114.828i	1.19329	+	0.377723i
$305$	497.960	+	206.262i	1.63266	+	0.676268i
$306$	−57.3781	−	139.711i	−0.187510	−	0.456571i
$307$	300.722	+	91.2231i	0.979551	+	0.297144i	0.739158	−	0.673532i	$-0.235224\pi$
$307$	300.722	+	91.2231i	0.979551	+	0.297144i	0.240393	+	0.970676i	$0.422724\pi$
$308$	423.253	−	509.452i	1.37420	−	1.65406i
$309$	−6.35151	−	0.625569i	−0.0205551	−	0.00202450i
$310$	−120.533	+	145.972i	−0.388816	+	0.470877i
$311$	−37.3246	−	187.643i	−0.120015	−	0.603355i	−0.993244	−	0.116045i	$-0.962978\pi$
$311$	−37.3246	−	187.643i	−0.120015	−	0.603355i	0.873229	−	0.487310i	$-0.162022\pi$
$312$	2.34125	−	259.362i	0.00750401	−	0.831287i
$313$	1.80988	−	9.09889i	0.00578237	−	0.0290699i	−0.977786	−	0.209604i	$-0.932783\pi$
$313$	1.80988	−	9.09889i	0.00578237	−	0.0290699i	0.983569	+	0.180534i	$0.0577826\pi$
$314$	−27.8317	+	274.122i	−0.0886360	+	0.873000i
$315$	−56.9588	−	187.768i	−0.180822	−	0.596089i
$316$	−93.1209	+	92.0068i	−0.294686	+	0.291161i
$317$	−167.003	+	203.494i	−0.526823	+	0.641936i	−0.966636	−	0.256154i	$-0.917545\pi$
$317$	−167.003	+	203.494i	−0.526823	+	0.641936i	0.439813	+	0.898089i	$0.355045\pi$
$318$	−29.3285	−	44.1803i	−0.0922279	−	0.138932i
$319$	−367.308			−1.15144
$320$	329.074	−	260.266i	1.02836	−	0.813332i
$321$			204.891i			0.638291i
$322$	−370.687	−	558.403i	−1.15120	−	1.73417i
$323$	462.748	+	379.768i	1.43266	+	1.17575i
$324$	35.9993	+	0.216640i	0.111109	+	0.000668643i
$325$	−321.991	+	97.6749i	−0.990741	+	0.300538i
$326$	−25.7069	+	253.194i	−0.0788554	+	0.776668i
$327$	135.204	+	26.8938i	0.413469	+	0.0822441i
$328$	430.522	−	173.792i	1.31257	−	0.529854i
$329$	244.370	−	48.6083i	0.742767	−	0.147746i
$330$	239.972	−	290.619i	0.727187	−	0.880663i
$331$	−56.3557	+	572.189i	−0.170259	+	1.72867i	0.408144	+	0.912917i	$0.366176\pi$
$331$	−56.3557	+	572.189i	−0.170259	+	1.72867i	−0.578403	+	0.815751i	$0.696324\pi$
$332$	20.0959	+	217.444i	0.0605297	+	0.654951i
$333$	50.2651	−	165.702i	0.150946	−	0.497603i
$334$	53.4900	+	130.243i	0.160150	+	0.389950i
$335$	−275.068	+	664.072i	−0.821098	+	1.98231i
$336$	−30.4108	+	274.816i	−0.0905083	+	0.817904i
$337$	60.7563	−	25.1661i	0.180286	−	0.0746769i	−0.290715	−	0.956810i	$-0.593893\pi$
$337$	60.7563	−	25.1661i	0.180286	−	0.0746769i	0.471000	+	0.882133i	$0.343893\pi$
$338$	257.288	−	255.745i	0.761208	−	0.756641i
$339$	20.4676	+	38.2922i	0.0603765	+	0.112956i
$340$	632.797	−	187.806i	1.86117	−	0.552370i
$341$	185.232	−	152.016i	0.543202	−	0.445794i
$342$	−126.041	+	66.8836i	−0.368542	+	0.195566i
$343$	−8.54949	+	12.7952i	−0.0249256	+	0.0373038i
$344$	33.7918	−	3.02048i	0.0982319	−	0.00878045i
$345$	−211.889	−	317.114i	−0.614170	−	0.919170i
$346$	101.450	+	338.095i	0.293209	+	0.977154i
$347$	100.199	−	187.460i	0.288759	−	0.540229i	−0.695158	−	0.718857i	$-0.744666\pi$
$347$	100.199	−	187.460i	0.288759	−	0.540229i	0.983917	+	0.178627i	$0.0571657\pi$
$348$	128.003	−	84.4191i	0.367825	−	0.242584i
$349$	−20.3862	−	206.985i	−0.0584132	−	0.593079i	−0.979184	−	0.202975i	$-0.934939\pi$
$349$	−20.3862	−	206.985i	−0.0584132	−	0.593079i	0.920771	−	0.390104i	$-0.127561\pi$
$350$	352.007	−	68.9182i	1.00574	−	0.196909i
$351$	68.7765	+	68.7765i	0.195944	+	0.195944i
$352$	−472.086	+	243.276i	−1.34115	+	0.691125i
$353$	−184.698	−	184.698i	−0.523224	−	0.523224i	0.395320	−	0.918544i	$-0.370634\pi$
$353$	−184.698	−	184.698i	−0.523224	−	0.523224i	−0.918544	+	0.395320i	$0.870634\pi$
$354$	−47.1877	+	70.1635i	−0.133299	+	0.198202i
$355$	−42.5833	−	432.355i	−0.119953	−	1.21790i
$356$	−62.4123	−	323.944i	−0.175315	−	0.909955i
$357$	−205.057	+	383.635i	−0.574390	+	1.07461i
$358$	129.373	−	240.298i	0.361377	−	0.671223i
$359$	−130.822	−	195.789i	−0.364408	−	0.545375i	0.603279	−	0.797530i	$-0.293861\pi$
$359$	−130.822	−	195.789i	−0.364408	−	0.545375i	−0.967687	+	0.252156i	$0.918861\pi$
$360$	−16.8342	+	156.431i	−0.0467616	+	0.434530i
$361$	113.642	−	170.077i	0.314798	−	0.471129i
$362$	−181.667	+	592.451i	−0.501841	+	1.63661i
$363$	−206.776	+	169.697i	−0.569631	+	0.467484i
$364$	−580.302	+	470.426i	−1.59424	+	1.29238i
$365$	−371.283	−	694.622i	−1.01721	−	1.90307i
$366$	284.811	+	0.856972i	0.778171	+	0.00234145i
$367$	313.141	−	129.707i	0.853245	−	0.353426i	0.0871831	−	0.996192i	$-0.472213\pi$
$367$	313.141	−	129.707i	0.853245	−	0.353426i	0.766062	+	0.642767i	$0.222213\pi$
$368$	98.4947	+	528.321i	0.267649	+	1.43565i
$369$	−66.6267	+	160.851i	−0.180560	+	0.435911i
$370$	698.287	+	291.705i	1.88726	+	0.788391i
$371$	−44.3353	+	146.154i	−0.119502	+	0.393946i
$372$	−29.6133	+	95.5482i	−0.0796056	+	0.256850i
$373$	−26.6794	+	270.881i	−0.0715267	+	0.726222i	0.890813	+	0.454371i	$0.150136\pi$
$373$	−26.6794	+	270.881i	−0.0715267	+	0.726222i	−0.962339	+	0.271851i	$0.912364\pi$
$374$	−831.756	+	79.3946i	−2.22395	+	0.212285i
$375$	−78.2256	+	15.5600i	−0.208602	+	0.0414935i
$376$	−195.585	−	40.7431i	−0.520174	−	0.108359i
$377$	406.317	+	80.8215i	1.07776	+	0.214381i
$378$	−65.5356	−	80.3471i	−0.173375	−	0.212559i
$379$	−87.1450	+	26.4351i	−0.229934	+	0.0697497i	−0.403149	−	0.915134i	$-0.632084\pi$
$379$	−87.1450	+	26.4351i	−0.229934	+	0.0697497i	0.173215	+	0.984884i	$0.444584\pi$
$380$	−235.171	−	577.558i	−0.618870	−	1.51989i
$381$	−33.1698	−	27.2217i	−0.0870598	−	0.0714481i
$382$	−87.1120	+	431.157i	−0.228042	+	1.12868i
$383$		−	299.546i		−	0.782104i	−0.920369	−	0.391052i	$-0.872111\pi$
$383$		−	299.546i		−	0.782104i	0.920369	−	0.391052i	$-0.127889\pi$
$384$	108.605	−	193.280i	0.282824	−	0.503333i
$385$	−1085.49			−2.81946
$386$	160.580	+	32.4440i	0.416011	+	0.0840519i
$387$	−8.07103	+	9.83457i	−0.0208554	+	0.0254123i
$388$	−102.867	−	252.632i	−0.265121	−	0.651114i
$389$	6.14740	+	20.2653i	0.0158031	+	0.0520958i	0.964487	−	0.264129i	$-0.0850845\pi$
$389$	6.14740	+	20.2653i	0.0158031	+	0.0520958i	−0.948684	+	0.316225i	$0.897585\pi$
$390$	−329.405	+	268.681i	−0.844627	+	0.688925i
$391$	−164.951	+	829.267i	−0.421871	+	2.12089i
$392$	338.210	−	221.595i	0.862780	−	0.565293i
$393$	−20.7946	−	104.542i	−0.0529125	−	0.266009i
$394$	−59.5048	−	623.386i	−0.151027	−	1.58220i
$395$	213.511	+	21.0290i	0.540533	+	0.0532379i
$396$	58.9577	−	190.229i	0.148883	−	0.480376i
$397$	−535.257	−	162.368i	−1.34825	−	0.408989i	−0.468100	−	0.883675i	$-0.655061\pi$
$397$	−535.257	−	162.368i	−1.34825	−	0.408989i	−0.880155	+	0.474687i	$0.842561\pi$
$398$	−39.4779	+	94.5029i	−0.0991908	+	0.237445i
$399$	379.678	+	157.268i	0.951574	+	0.394155i
$400$	−281.389	−	59.5011i	−0.703473	−	0.148753i
$401$	22.9854	+	55.4917i	0.0573203	+	0.138383i	0.949945	−	0.312417i	$-0.101139\pi$
$401$	22.9854	+	55.4917i	0.0573203	+	0.138383i	−0.892625	+	0.450800i	$0.851139\pi$
$402$	−1.14285	+	379.819i	−0.00284290	+	0.944825i
$403$	−238.353	+	127.402i	−0.591447	+	0.316135i
$404$	37.1971	−	30.1541i	0.0920720	−	0.0746388i
$405$	−37.4294	−	45.6078i	−0.0924182	−	0.112612i
$406$	−422.220	−	129.468i	−1.03995	−	0.318886i
$407$	−796.488	−	532.196i	−1.95697	−	1.30761i
$408$	271.611	−	218.833i	0.665714	−	0.536354i
$409$	320.607	−	214.223i	0.783880	−	0.523772i	−0.0980337	−	0.995183i	$-0.531255\pi$
$409$	320.607	−	214.223i	0.783880	−	0.523772i	0.881913	+	0.471411i	$0.156255\pi$
$410$	−669.973	−	360.704i	−1.63408	−	0.879766i
$411$	98.7993	+	52.8093i	0.240388	+	0.128490i
$412$	−2.78842	−	14.4730i	−0.00676802	−	0.0351286i
$413$	242.358	−	23.8702i	0.586824	−	0.0577971i
$414$	−167.232	−	112.470i	−0.403941	−	0.271666i
$415$	253.064	−	253.064i	0.609792	−	0.609792i
$416$	575.753	−	165.236i	1.38402	−	0.397202i
$417$	123.825	−	123.825i	0.296942	−	0.296942i
$418$	151.667	+	774.657i	0.362840	+	1.85325i
$419$	−721.513	+	71.0628i	−1.72199	+	0.169601i	−0.910149	−	0.414281i	$-0.864033\pi$
$419$	−721.513	+	71.0628i	−1.72199	+	0.169601i	−0.811839	+	0.583882i	$0.801533\pi$
$420$	378.284	−	249.481i	0.900675	−	0.594003i
$421$	208.470	+	111.430i	0.495179	+	0.264679i	0.700029	−	0.714115i	$-0.253171\pi$
$421$	208.470	+	111.430i	0.495179	+	0.264679i	−0.204850	+	0.978793i	$0.565671\pi$
$422$	456.042	−	136.842i	1.08067	−	0.324270i
$423$	62.2929	−	41.6228i	0.147264	−	0.0983990i
$424$	78.5423	−	93.9615i	0.185241	−	0.221607i
$425$	−376.232	−	251.390i	−0.885252	−	0.591507i
$426$	−107.609	−	202.788i	−0.252604	−	0.476028i
$427$	−520.391	−	634.099i	−1.21872	−	1.48501i
$428$	−453.620	+	134.628i	−1.05986	+	0.314552i
$429$	474.543	−	253.648i	1.10616	−	0.591255i
$430$	−39.1981	−	39.4347i	−0.0911583	−	0.0917085i
$431$	−204.984	−	494.875i	−0.475601	−	1.14820i	−0.961652	−	0.274271i	$-0.911563\pi$
$431$	−204.984	−	494.875i	−0.475601	−	1.14820i	0.486052	−	0.873930i	$-0.338437\pi$
$432$	23.1746	+	79.8432i	0.0536448	+	0.184822i
$433$	−591.006	−	244.803i	−1.36491	−	0.565364i	−0.424506	−	0.905425i	$-0.639552\pi$
$433$	−591.006	−	244.803i	−1.36491	−	0.565364i	−0.940403	+	0.340061i	$0.889552\pi$
$434$	266.506	−	109.452i	0.614069	−	0.252194i
$435$	−240.478	−	72.9482i	−0.552823	−	0.167697i
$436$	29.2974	+	317.007i	0.0671959	+	0.727081i
$437$	794.943	+	78.2950i	1.81909	+	0.179165i
$438$	−320.928	−	264.999i	−0.732712	−	0.605020i
$439$	−28.9883	−	145.734i	−0.0660327	−	0.331969i	0.933622	−	0.358261i	$-0.116630\pi$
$439$	−28.9883	−	145.734i	−0.0660327	−	0.331969i	−0.999654	+	0.0262919i	$0.991630\pi$
$440$	801.095	+	340.328i	1.82067	+	0.773474i
$441$	−29.5810	+	148.714i	−0.0670771	+	0.337219i
$442$	937.561	+	95.1910i	2.12118	+	0.215364i
$443$	134.738	+	444.173i	0.304150	+	1.00265i	0.967188	+	0.254062i	$0.0817667\pi$
$443$	134.738	+	444.173i	0.304150	+	1.00265i	−0.663038	+	0.748586i	$0.730733\pi$
$444$	399.884	+	2.40646i	0.900639	+	0.00541995i
$445$	−343.000	+	417.947i	−0.770787	+	0.939206i
$446$	356.987	−	236.980i	0.800418	−	0.531346i
$447$	−299.848			−0.670800
$448$	−628.412	+	113.246i	−1.40270	+	0.252781i
$449$			739.430i			1.64684i	0.567435	+	0.823419i	$0.307936\pi$
$449$			739.430i			1.64684i	−0.567435	+	0.823419i	$0.692064\pi$
$450$	89.8574	−	59.6505i	0.199683	−	0.132557i
$451$	744.534	+	611.023i	1.65085	+	1.35482i
$452$	−71.3285	+	70.4751i	−0.157806	+	0.155918i
$453$	332.869	−	100.975i	0.734811	−	0.222903i
$454$	−806.127	−	81.8464i	−1.77561	−	0.180278i
$455$	1200.78	+	238.849i	2.63907	+	0.524944i
$456$	−230.895	−	235.102i	−0.506350	−	0.515575i
$457$	−552.375	+	109.874i	−1.20870	+	0.240425i	−0.758002	−	0.652253i	$-0.773824\pi$
$457$	−552.375	+	109.874i	−1.20870	+	0.240425i	−0.450696	+	0.892678i	$0.648824\pi$
$458$	−474.347	−	391.681i	−1.03569	−	0.855198i
$459$	−12.8206	+	130.170i	−0.0279315	+	0.283594i
$460$	562.849	−	677.478i	1.22358	−	1.47278i
$461$	167.879	−	553.422i	0.364162	−	1.20048i	−0.563201	−	0.826320i	$-0.690430\pi$
$461$	167.879	−	553.422i	0.364162	−	1.20048i	0.927363	−	0.374162i	$-0.122070\pi$
$462$	−530.592	+	217.910i	−1.14847	+	0.471668i
$463$	−115.934	+	279.890i	−0.250398	+	0.604514i	−0.998236	−	0.0593666i	$-0.981092\pi$
$463$	−115.934	+	279.890i	−0.250398	+	0.604514i	0.747838	+	0.663881i	$0.231092\pi$
$464$	271.007	+	227.923i	0.584067	+	0.491214i
$465$	151.463	−	62.7379i	0.325726	−	0.134920i
$466$	−347.032	−	349.126i	−0.744703	−	0.749198i
$467$	−86.4305	−	161.700i	−0.185076	−	0.346253i	0.772223	−	0.635351i	$-0.219145\pi$
$467$	−86.4305	−	161.700i	−0.185076	−	0.346253i	−0.957299	+	0.289098i	$0.906645\pi$
$468$	−107.077	+	197.459i	−0.228796	+	0.421921i
$469$	845.625	−	693.987i	1.80304	−	1.47972i
$470$	153.478	+	289.226i	0.326548	+	0.615375i
$471$	132.569	−	198.403i	0.281462	−	0.421237i
$472$	−186.344	−	58.3689i	−0.394798	−	0.123663i
$473$	39.1021	+	58.5204i	0.0826682	+	0.123722i
$474$	108.586	−	32.5827i	0.229084	−	0.0687400i
$475$	−201.515	+	377.009i	−0.424243	+	0.793702i
$476$	−984.088	−	201.911i	−2.06741	−	0.424183i
$477$	4.50137	+	45.7032i	0.00943684	+	0.0958139i
$478$	11.3435	+	57.9381i	0.0237311	+	0.121209i
$479$	−67.6561	−	67.6561i	−0.141245	−	0.141245i	0.632949	−	0.774194i	$-0.281844\pi$
$479$	−67.6561	−	67.6561i	−0.141245	−	0.141245i	−0.774194	+	0.632949i	$0.781844\pi$
$480$	−357.392	+	65.5164i	−0.744566	+	0.136492i
$481$	763.974	+	763.974i	1.58830	+	1.58830i
$482$	−558.066	−	375.321i	−1.15781	−	0.778675i
$483$	56.8936	+	577.650i	0.117792	+	1.19596i
$484$	−511.567	−	346.289i	−1.05696	−	0.715474i
$485$	−210.736	+	394.259i	−0.434507	+	0.812905i
$486$	−27.4512	−	14.7794i	−0.0564840	−	0.0304102i
$487$	71.4821	+	106.980i	0.146780	+	0.219672i	0.897573	−	0.440865i	$-0.145328\pi$
$487$	71.4821	+	106.980i	0.146780	+	0.219672i	−0.750793	+	0.660538i	$0.770328\pi$
$488$	185.244	+	631.120i	0.379598	+	1.29328i
$489$	122.447	−	183.255i	0.250404	−	0.374755i
$490$	−633.554	−	194.270i	−1.29297	−	0.396470i
$491$	−219.173	+	179.871i	−0.446381	+	0.366335i	−0.830565	−	0.556921i	$-0.811983\pi$
$491$	−219.173	+	179.871i	−0.446381	+	0.366335i	0.384185	+	0.923256i	$0.374483\pi$
$492$	−399.895	−	41.8175i	−0.812795	−	0.0849950i
$493$	262.621	+	491.328i	0.532699	+	0.996609i
$494$	2.67884	−	890.300i	0.00542276	−	1.80223i
$495$	−301.550	+	124.906i	−0.609193	+	0.252336i
$496$	−230.997	−	2.78033i	−0.465720	−	0.00560551i
$497$	−253.029	+	610.865i	−0.509112	+	1.22910i
$498$	72.8962	−	174.500i	0.146378	−	0.350402i
$499$	−94.0417	+	310.014i	−0.188460	+	0.621270i	0.810889	+	0.585200i	$0.198984\pi$
$499$	−94.0417	+	310.014i	−0.188460	+	0.621270i	−0.999349	+	0.0360703i	$0.988516\pi$
$500$	−85.8491	−	162.964i	−0.171698	−	0.325928i
$501$	11.9518	−	121.349i	0.0238559	−	0.242213i
$502$	−27.2897	−	285.893i	−0.0543619	−	0.569508i
$503$	−505.830	+	100.616i	−1.00563	+	0.200031i	−0.670316	−	0.742076i	$-0.733841\pi$
$503$	−505.830	+	100.616i	−1.00563	+	0.200031i	−0.335311	+	0.942108i	$0.608841\pi$
$504$	134.823	−	197.887i	0.267506	−	0.392632i
$505$	−76.9692	−	15.3101i	−0.152414	−	0.0303171i
$506$	−863.959	+	704.693i	−1.70743	+	1.39267i
$507$	−300.641	+	91.1983i	−0.592979	+	0.179878i
$508$	38.4727	−	91.3230i	0.0757336	−	0.179770i
$509$	−373.184	−	306.264i	−0.733170	−	0.601697i	0.191935	−	0.981408i	$-0.438524\pi$
$509$	−373.184	−	306.264i	−0.733170	−	0.601697i	−0.925105	+	0.379710i	$0.876024\pi$
$510$	−560.322	−	113.209i	−1.09867	−	0.221978i
$511$			1198.70i			2.34580i
$512$	499.273	+	113.447i	0.975143	+	0.221575i
$513$	123.571			0.240880
$514$	25.4470	−	125.949i	0.0495077	−	0.245037i
$515$	−15.3244	+	18.6728i	−0.0297561	+	0.0362579i
$516$	−27.0765	−	11.4068i	−0.0524739	−	0.0221063i
$517$	−120.311	−	396.614i	−0.232711	−	0.767144i
$518$	−727.975	−	892.503i	−1.40536	−	1.72298i
$519$	59.6385	−	299.823i	0.114910	−	0.577693i
$520$	−811.289	−	552.743i	−1.56017	−	1.06297i
$521$	−110.412	−	555.079i	−0.211923	−	1.06541i	−0.929469	−	0.368900i	$-0.879735\pi$
$521$	−110.412	−	555.079i	−0.211923	−	1.06541i	0.717546	−	0.696511i	$-0.245265\pi$
$522$	−132.190	+	12.6181i	−0.253238	+	0.0241727i
$523$	−323.495	−	31.8614i	−0.618537	−	0.0609205i	−0.216104	−	0.976370i	$-0.569335\pi$
$523$	−323.495	−	31.8614i	−0.618537	−	0.0609205i	−0.402432	+	0.915450i	$0.631835\pi$
$524$	217.787	−	114.730i	0.415623	−	0.218950i
$525$	−297.259	−	90.1726i	−0.566208	−	0.171757i
$526$	−219.342	−	91.6285i	−0.417000	−	0.174199i
$527$	−335.782	−	139.085i	−0.637158	−	0.263919i
$528$	459.897	+	5.53543i	0.871018	+	0.0104838i
$529$	229.311	+	553.606i	0.433480	+	1.04651i
$530$	−200.706	−	0.603909i	−0.378691	−	0.00113945i
$531$	64.5805	−	34.5190i	0.121620	−	0.0650075i
$532$	−98.7076	+	943.926i	−0.185541	+	1.77430i
$533$	−689.158	−	839.741i	−1.29298	−	1.57550i
$534$	−83.7575	+	273.150i	−0.156849	+	0.511517i
$535$	644.794	+	430.837i	1.20522	+	0.805303i
$536$	−841.654	+	247.039i	−1.57025	+	0.460893i
$537$	−196.516	+	131.308i	−0.365952	+	0.244521i
$538$	−283.061	+	525.759i	−0.526136	+	0.977247i
$539$	739.771	+	395.416i	1.37249	+	0.733611i
$540$	76.3798	−	112.835i	0.141444	−	0.208953i
$541$	510.536	−	50.2834i	0.943689	−	0.0929453i	0.385545	−	0.922689i	$-0.374013\pi$
$541$	510.536	−	50.2834i	0.943689	−	0.0929453i	0.558145	+	0.829744i	$0.311513\pi$
$542$	−72.4273	+	107.692i	−0.133630	+	0.198694i
$543$	379.474	−	379.474i	0.698847	−	0.698847i
$544$	662.953	+	457.546i	1.21866	+	0.841076i
$545$	368.937	−	368.937i	0.676949	−	0.676949i
$546$	634.891	−	124.303i	1.16280	−	0.227661i
$547$	218.986	−	21.5683i	0.400341	−	0.0394301i	0.104156	−	0.994561i	$-0.466786\pi$
$547$	218.986	−	21.5683i	0.400341	−	0.0394301i	0.296184	+	0.955131i	$0.404286\pi$
$548$	−51.9991	+	253.437i	−0.0948889	+	0.462476i
$549$	−217.530	−	116.272i	−0.396229	−	0.211789i
$550$	−171.483	−	571.488i	−0.311787	−	1.03907i
$551$	437.623	−	292.410i	0.794234	−	0.530691i
$552$	139.120	−	444.144i	0.252029	−	0.804608i
$553$	−271.490	−	181.404i	−0.490941	−	0.328036i
$554$	367.084	−	194.793i	0.662606	−	0.351611i
$555$	−415.769	−	506.615i	−0.749132	−	0.912821i
$556$	355.504	+	192.781i	0.639397	+	0.346728i
$557$	−34.9481	+	18.6802i	−0.0627435	+	0.0335371i	−0.502470	−	0.864595i	$-0.667575\pi$
$557$	−34.9481	+	18.6802i	−0.0627435	+	0.0335371i	0.439727	+	0.898132i	$0.355075\pi$
$558$	61.4409	−	61.0722i	0.110109	−	0.109448i
$559$	−30.3782	−	73.3394i	−0.0543438	−	0.131197i
$560$	800.900	+	673.575i	1.43018	+	1.20281i
$561$	668.516	+	276.908i	1.19165	+	0.493598i
$562$	−282.309	−	687.397i	−0.502330	−	1.22313i
$563$	−34.9916	−	10.6146i	−0.0621521	−	0.0188536i	0.259056	−	0.965862i	$-0.416589\pi$
$563$	−34.9916	−	10.6146i	−0.0621521	−	0.0188536i	−0.321208	+	0.947009i	$0.604089\pi$
$564$	133.082	+	110.564i	0.235961	+	0.196036i
$565$	163.544	+	16.1077i	0.289459	+	0.0285092i
$566$	561.243	−	679.696i	0.991595	−	1.20088i
$567$	17.5179	+	88.0685i	0.0308958	+	0.155324i
$568$	378.256	−	371.488i	0.665944	−	0.654028i
$569$	−99.0568	+	497.992i	−0.174089	+	0.875206i	0.790705	+	0.612198i	$0.209714\pi$
$569$	−99.0568	+	497.992i	−0.174089	+	0.875206i	−0.964794	+	0.263008i	$0.915286\pi$
$570$	−54.5515	+	537.292i	−0.0957044	+	0.942618i
$571$	−267.633	−	882.268i	−0.468709	−	1.54513i	−0.799049	−	0.601265i	$-0.794663\pi$
$571$	−267.633	−	882.268i	−0.468709	−	1.54513i	0.330340	−	0.943862i	$-0.392837\pi$
$572$	873.374	+	883.950i	1.52688	+	1.54537i
$573$	241.665	−	294.469i	0.421753	−	0.513908i
$574$	640.469	+	964.801i	1.11580	+	1.68084i
$575$	−603.785			−1.05006
$576$	−161.542	+	103.770i	−0.280455	+	0.180157i
$577$		−	621.867i		−	1.07776i	−0.842383	−	0.538879i	$-0.818848\pi$
$577$		−	621.867i		−	1.07776i	0.842383	−	0.538879i	$-0.181152\pi$
$578$	381.225	+	574.277i	0.659560	+	0.993559i
$579$	−109.672	−	90.0056i	−0.189417	−	0.155450i
$580$	3.49242	−	580.339i	0.00602141	−	1.00058i
$581$	−521.222	+	158.111i	−0.897111	+	0.272136i
$582$	−23.8616	+	235.019i	−0.0409993	+	0.403813i
$583$	249.177	+	49.5643i	0.427404	+	0.0850160i
$584$	375.822	−	884.643i	0.643531	−	1.51480i
$585$	361.060	−	71.8193i	0.617197	−	0.122768i
$586$	254.883	−	308.677i	0.434953	−	0.526752i
$587$	74.2901	−	754.280i	0.126559	−	1.28497i	−0.696723	−	0.717341i	$-0.745359\pi$
$587$	74.2901	−	754.280i	0.126559	−	1.28497i	0.823282	−	0.567633i	$-0.192141\pi$
$588$	−348.682	+	32.2248i	−0.592997	+	0.0548040i
$589$	−99.6731	+	328.578i	−0.169224	+	0.557858i
$590$	121.580	+	296.037i	0.206068	+	0.501758i
$591$	−207.538	+	501.040i	−0.351164	+	0.847784i
$592$	257.425	+	886.905i	0.434839	+	1.49815i
$593$	−332.287	+	137.638i	−0.560350	+	0.232104i	−0.644837	−	0.764320i	$-0.723075\pi$
$593$	−332.287	+	137.638i	−0.560350	+	0.232104i	0.0844873	+	0.996425i	$0.473075\pi$
$594$	−122.324	+	121.590i	−0.205933	+	0.204697i
$595$	776.115	+	1452.01i	1.30439	+	2.44035i
$596$	−197.022	−	663.849i	−0.330573	−	1.11384i
$597$	68.5630	−	56.2682i	0.114846	−	0.0942515i
$598$	1110.77	−	589.430i	1.85748	−	0.985669i
$599$	−469.809	+	703.119i	−0.784322	+	1.17382i	0.196802	+	0.980443i	$0.436944\pi$
$599$	−469.809	+	703.119i	−0.784322	+	1.17382i	−0.981124	+	0.193378i	$0.938056\pi$
$600$	191.106	+	159.745i	0.318510	+	0.266242i
$601$	−375.166	−	561.475i	−0.624236	−	0.934235i	−0.999972	−	0.00750797i	$-0.997610\pi$
$601$	−375.166	−	561.475i	−0.624236	−	0.934235i	0.375736	−	0.926727i	$-0.377390\pi$
$602$	24.3207	+	81.0517i	0.0403998	+	0.134637i
$603$	155.059	−	290.095i	0.257146	−	0.481086i
$604$	442.273	+	670.610i	0.732240	+	1.11028i
$605$	99.2356	+	1007.56i	0.164026	+	1.66538i
$606$	−40.6962	+	7.96776i	−0.0671555	+	0.0131481i
$607$	27.3728	+	27.3728i	0.0450953	+	0.0450953i	0.729295	−	0.684200i	$-0.239848\pi$
$607$	27.3728	+	27.3728i	0.0450953	+	0.0450953i	−0.684200	+	0.729295i	$0.739848\pi$
$608$	368.790	−	665.671i	0.606562	−	1.09485i
$609$	270.438	+	270.438i	0.444069	+	0.444069i
$610$	601.585	−	894.498i	0.986205	−	1.46639i
$611$	45.8190	+	465.208i	0.0749902	+	0.761388i
$612$	−296.613	+	57.1467i	−0.484662	+	0.0933769i
$613$	119.828	−	224.182i	0.195478	−	0.365714i	−0.765017	−	0.644010i	$-0.777270\pi$
$613$	119.828	−	224.182i	0.195478	−	0.365714i	0.960495	+	0.278296i	$0.0897696\pi$
$614$	297.943	−	553.400i	0.485249	−	0.901304i
$615$	366.099	+	547.905i	0.595283	+	0.890903i
$616$	−831.081	−	1031.52i	−1.34916	−	1.67455i
$617$	338.872	−	507.157i	0.549224	−	0.821973i	−0.448182	−	0.893942i	$-0.647928\pi$
$617$	338.872	−	507.157i	0.549224	−	0.821973i	0.997407	+	0.0719696i	$0.0229285\pi$
$618$	−3.74207	+	12.2036i	−0.00605513	+	0.0197470i
$619$	−536.660	+	440.425i	−0.866979	+	0.711511i	−0.958744	−	0.284270i	$-0.908249\pi$
$619$	−536.660	+	440.425i	−0.866979	+	0.711511i	0.0917656	+	0.995781i	$0.470749\pi$
$620$	238.421	+	294.108i	0.384550	+	0.474368i
$621$	82.2745	+	153.925i	0.132487	+	0.247866i
$622$	−382.638	−	1.15133i	−0.615173	−	0.00185101i
$623$	760.227	−	314.896i	1.22027	−	0.505452i
$624$	−507.522	−	107.318i	−0.813337	−	0.171984i
$625$	−287.497	+	694.080i	−0.459996	+	1.11053i
$626$	−17.1205	−	7.15197i	−0.0273490	−	0.0114249i
$627$	198.441	−	654.174i	0.316493	−	1.04334i
$628$	526.362	+	163.135i	0.838156	+	0.259770i
$629$	−142.412	+	1445.93i	−0.226410	+	2.29878i
$630$	−390.658	+	37.2900i	−0.620093	+	0.0591905i
$631$	−682.090	+	135.676i	−1.08097	+	0.215018i	−0.703278	−	0.710915i	$-0.748281\pi$
$631$	−682.090	+	135.676i	−1.08097	+	0.215018i	−0.377689	+	0.925933i	$0.623281\pi$
$632$	143.486	+	218.995i	0.227034	+	0.346511i
$633$	−404.418	−	80.4437i	−0.638891	−	0.127083i
$634$	332.780	+	407.990i	0.524889	+	0.643518i
$635$	−155.415	+	47.1446i	−0.244748	+	0.0742435i
$636$	−98.2270	+	39.9962i	−0.154445	+	0.0628870i
$637$	−731.331	−	600.188i	−1.14809	−	0.942210i
$638$	−145.484	+	720.066i	−0.228031	+	1.12863i
$639$			198.814i			0.311133i
$640$	−379.883	−	748.200i	−0.593567	−	1.16906i
$641$	776.937			1.21207			0.606035	−	0.795438i	$-0.292759\pi$
$641$	776.937			1.21207			0.606035	+	0.795438i	$0.292759\pi$
$642$	401.666	+	81.1536i	0.625649	+	0.126407i
$643$	−381.234	+	464.535i	−0.592899	+	0.722450i	−0.979869	−	0.199643i	$-0.936022\pi$
$643$	−381.234	+	464.535i	−0.592899	+	0.722450i	0.386970	+	0.922092i	$0.373522\pi$
$644$	−1241.51	+	505.518i	−1.92781	+	0.784966i
$645$	13.9780	+	46.0793i	0.0216713	+	0.0714408i
$646$	927.778	−	756.747i	1.43619	−	1.17144i
$647$	−232.255	+	1167.62i	−0.358971	+	1.80467i	0.204871	+	0.978789i	$0.434322\pi$
$647$	−232.255	+	1167.62i	−0.358971	+	1.80467i	−0.563843	+	0.825882i	$0.690678\pi$
$648$	14.6834	−	70.4869i	0.0226595	−	0.108776i
$649$	−79.0311	−	397.316i	−0.121774	−	0.612197i
$650$	63.9461	+	669.914i	0.0983786	+	1.03064i
$651$	−248.306	−	24.4560i	−0.381422	−	0.0375668i
$652$	486.176	+	150.681i	0.745668	+	0.231105i
$653$	618.259	+	187.547i	0.946798	+	0.287208i	0.725675	−	0.688038i	$-0.241528\pi$
$653$	618.259	+	187.547i	0.946798	+	0.287208i	0.221123	+	0.975246i	$0.429028\pi$
$654$	106.274	−	254.401i	0.162499	−	0.388992i
$655$	−372.719	−	154.385i	−0.569036	−	0.235703i
$656$	−170.178	−	912.826i	−0.259418	−	1.39150i
$657$	137.933	+	333.000i	0.209944	+	0.506849i
$658$	1.49939	−	498.314i	0.00227870	−	0.757316i
$659$	−198.058	+	105.864i	−0.300543	+	0.160643i	−0.614775	−	0.788703i	$-0.710753\pi$
$659$	−198.058	+	105.864i	−0.300543	+	0.160643i	0.314232	+	0.949346i	$0.398253\pi$
$660$	−474.677	−	585.546i	−0.719208	−	0.887191i
$661$	−375.767	−	457.874i	−0.568483	−	0.692698i	0.406836	−	0.913501i	$-0.366632\pi$
$661$	−375.767	−	457.874i	−0.568483	−	0.692698i	−0.975318	+	0.220803i	$0.929132\pi$
$662$	1099.39	+	337.112i	1.66071	+	0.509233i
$663$	−678.584	−	453.415i	−1.02351	−	0.683885i
$664$	434.233	+	46.7296i	0.653966	+	0.0703759i
$665$	1293.29	−	864.152i	1.94480	−	1.29948i
$666$	−304.931	−	164.170i	−0.457854	−	0.246502i
$667$	655.609	+	350.430i	0.982922	+	0.525383i
$668$	276.514	−	53.2743i	0.413943	−	0.0797519i
$669$	−369.292	+	36.3721i	−0.552005	+	0.0543678i
$670$	1192.89	+	802.266i	1.78043	+	1.19741i
$671$	−964.860	+	964.860i	−1.43794	+	1.43794i
$672$	526.700	+	168.466i	0.783780	+	0.250694i
$673$	241.041	−	241.041i	0.358159	−	0.358159i	−0.504975	−	0.863134i	$-0.668498\pi$
$673$	241.041	−	241.041i	0.358159	−	0.358159i	0.863134	+	0.504975i	$0.168498\pi$
$674$	−25.2709	−	129.074i	−0.0374939	−	0.191504i
$675$	−92.9547	+	9.15524i	−0.137711	+	0.0135633i
$676$	−399.451	−	605.680i	−0.590904	−	0.895977i
$677$	193.342	+	103.343i	0.285586	+	0.152649i	0.607970	−	0.793960i	$-0.291984\pi$
$677$	193.342	+	103.343i	0.285586	+	0.152649i	−0.322384	+	0.946609i	$0.604484\pi$
$678$	83.1744	−	24.9576i	0.122676	−	0.0368107i
$679$	565.706	−	377.992i	0.833145	−	0.556690i
$680$	−117.534	−	1314.91i	−0.172843	−	1.93370i
$681$	583.455	+	389.852i	0.856762	+	0.572470i
$682$	−224.643	−	423.337i	−0.329389	−	0.620728i
$683$	−387.959	−	472.730i	−0.568023	−	0.692138i	0.407206	−	0.913336i	$-0.366503\pi$
$683$	−387.959	−	472.730i	−0.568023	−	0.692138i	−0.975229	+	0.221199i	$0.929003\pi$
$684$	81.1953	+	273.581i	0.118707	+	0.399972i
$685$	373.943	−	199.876i	0.545902	−	0.291790i
$686$	21.6973	+	21.8282i	0.0316287	+	0.0318196i
$687$	203.871	+	492.189i	0.296756	+	0.716433i
$688$	7.46298	−	67.4413i	0.0108473	−	0.0980252i
$689$	−264.734	−	109.656i	−0.384230	−	0.159153i
$690$	−705.591	+	289.781i	−1.02260	+	0.419973i
$691$	461.638	+	140.036i	0.668072	+	0.202657i	0.606061	−	0.795418i	$-0.292749\pi$
$691$	461.638	+	140.036i	0.668072	+	0.202657i	0.0620108	+	0.998075i	$0.480249\pi$
$692$	702.981	−	64.9686i	1.01587	−	0.0938852i
$693$	494.357	+	48.6899i	0.713358	+	0.0702597i
$694$	−327.806	−	270.679i	−0.472344	−	0.390027i
$695$	−129.303	−	650.051i	−0.186048	−	0.935326i
$696$	−114.795	−	284.372i	−0.164935	−	0.408581i
$697$	285.001	−	1432.80i	0.408897	−	2.05566i
$698$	−413.845	−	42.0178i	−0.592901	−	0.0601975i
$699$	123.751	+	407.953i	0.177040	+	0.583624i
$700$	4.31704	−	717.368i	0.00616721	−	1.02481i
$701$	−339.936	+	414.213i	−0.484930	+	0.590889i	−0.956788	−	0.290786i	$-0.906083\pi$
$701$	−339.936	+	414.213i	−0.484930	+	0.590889i	0.471858	+	0.881674i	$0.343583\pi$
$702$	162.070	−	107.587i	0.230868	−	0.153258i
$703$	1372.64			1.95255
$704$	289.931	+	1021.83i	0.411834	+	1.45146i
$705$		−	283.559i		−	0.402211i
$706$	−435.235	+	288.924i	−0.616481	+	0.409241i
$707$	92.3254	+	75.7695i	0.130588	+	0.107170i
$708$	118.857	+	120.297i	0.167878	+	0.169911i
$709$	838.106	−	254.237i	1.18210	−	0.358585i	0.362751	−	0.931886i	$-0.381837\pi$
$709$	838.106	−	254.237i	1.18210	−	0.358585i	0.819345	+	0.573301i	$0.194337\pi$
$710$	−864.451	−	87.7680i	−1.21754	−	0.123617i
$711$	−96.2940	−	19.1541i	−0.135435	−	0.0269396i
$712$	−659.776	−	5.95578i	−0.926651	−	0.00836486i
$713$	−475.652	+	94.6130i	−0.667113	+	0.132697i
$714$	670.854	+	553.942i	0.939572	+	0.775829i
$715$	199.617	−	2026.75i	0.279185	−	2.83461i
$716$	−419.835	−	348.799i	−0.586362	−	0.487149i
$717$	14.8418	−	48.9269i	0.0206999	−	0.0682384i
$718$	−435.639	+	178.914i	−0.606740	+	0.249184i
$719$	236.668	−	571.367i	0.329163	−	0.794669i	−0.669492	−	0.742819i	$-0.733488\pi$
$719$	236.668	−	571.367i	0.329163	−	0.794669i	0.998655	−	0.0518498i	$-0.0165117\pi$
$720$	299.997	+	94.9608i	0.416663	+	0.131890i
$721$	33.9650	−	14.0688i	0.0471082	−	0.0195129i
$722$	−288.406	−	290.147i	−0.399454	−	0.401866i
$723$	274.557	+	513.659i	0.379746	+	0.710456i
$724$	1089.48	+	590.795i	1.50481	+	0.816016i
$725$	−307.531	+	252.385i	−0.424181	+	0.348117i
$726$	250.771	+	472.575i	0.345415	+	0.650929i
$727$	−162.219	+	242.778i	−0.223135	+	0.333945i	−0.926099	−	0.377280i	$-0.876859\pi$
$727$	−162.219	+	242.778i	−0.223135	+	0.333945i	0.702964	+	0.711225i	$0.251859\pi$
$728$	692.371	+	1323.94i	0.951059	+	1.81860i
$729$	15.0004	+	22.4497i	0.0205767	+	0.0307952i
$730$	−1508.79	+	452.733i	−2.06683	+	0.620182i
$731$	50.3222	−	94.1461i	0.0688402	−	0.128791i
$732$	114.488	−	558.000i	0.156404	−	0.762295i
$733$	39.5882	+	401.946i	0.0540085	+	0.548357i	0.983675	+	0.179955i	$0.0575952\pi$
$733$	39.5882	+	401.946i	0.0540085	+	0.548357i	−0.929666	+	0.368403i	$0.879905\pi$
$734$	−130.247	−	665.252i	−0.177449	−	0.906338i
$735$	405.801	+	405.801i	0.552110	+	0.552110i
$736$	1074.73	+	16.1700i	1.46022	+	0.0219701i
$737$	−1286.72	−	1286.72i	−1.74589	−	1.74589i
$738$	288.941	+	194.324i	0.391519	+	0.263312i
$739$	−11.1230	−	112.934i	−0.0150515	−	0.152820i	0.984721	−	0.174138i	$-0.0557138\pi$
$739$	−11.1230	−	112.934i	−0.0150515	−	0.152820i	−0.999773	+	0.0213177i	$0.993214\pi$
$740$	848.433	−	1253.38i	1.14653	−	1.69375i
$741$	−363.459	+	679.984i	−0.490498	+	0.917658i
$742$	268.958	+	144.803i	0.362477	+	0.195153i
$743$	−724.589	−	1084.42i	−0.975221	−	1.45952i	−0.886096	−	0.463501i	$-0.846593\pi$
$743$	−724.589	−	1084.42i	−0.975221	−	1.45952i	−0.0891252	−	0.996020i	$-0.528407\pi$
$744$	175.582	+	95.8983i	0.235998	+	0.128896i
$745$	−630.508	+	943.622i	−0.846320	+	1.26661i
$746$	520.464	+	159.593i	0.697673	+	0.213931i
$747$	−126.602	+	103.899i	−0.169480	+	0.139089i
$748$	−173.799	+	1662.01i	−0.232351	+	2.22194i
$749$	−556.357	−	1040.87i	−0.742800	−	1.38968i
$750$	−0.479970	+	159.516i	−0.000639959	+	0.212687i
$751$	−162.341	+	67.2437i	−0.216166	+	0.0895389i	−0.488139	−	0.872766i	$-0.662324\pi$
$751$	−162.341	+	67.2437i	−0.216166	+	0.0895389i	0.271973	+	0.962305i	$0.412324\pi$
$752$	−157.340	+	367.286i	−0.209229	+	0.488412i
$753$	−95.1795	+	229.784i	−0.126400	+	0.305157i
$754$	319.376	−	764.527i	0.423576	−	1.01396i
$755$	382.177	−	1259.87i	0.506194	−	1.66870i
$756$	−183.469	+	96.6512i	−0.242684	+	0.127846i
$757$	76.3038	−	774.725i	0.100798	−	1.02342i	−0.803151	−	0.595775i	$-0.796845\pi$
$757$	76.3038	−	774.725i	0.100798	−	1.02342i	0.903949	−	0.427640i	$-0.140655\pi$
$758$	17.3067	+	181.308i	0.0228320	+	0.239193i
$759$	946.985	−	188.367i	1.24767	−	0.248178i
$760$	−1225.38	+	232.266i	−1.61235	+	0.305613i
$761$	−1222.79	−	243.227i	−1.60681	−	0.319615i	−0.691506	−	0.722371i	$-0.743053\pi$
$761$	−1222.79	−	243.227i	−1.60681	−	0.319615i	−0.915308	+	0.402755i	$0.868053\pi$
$762$	−66.5031	+	54.2436i	−0.0872743	+	0.0711858i
$763$	−759.880	+	230.507i	−0.995911	+	0.302106i
$764$	810.732	+	341.546i	1.06117	+	0.447050i
$765$	382.685	+	314.062i	0.500242	+	0.410538i
$766$	−587.226	−	118.644i	−0.766614	−	0.154888i
$767$			456.902i			0.595700i
$768$	−335.887	−	289.461i	−0.437353	−	0.376903i
$769$	133.032			0.172993			0.0864967	−	0.996252i	$-0.472433\pi$
$769$	133.032			0.172993			0.0864967	+	0.996252i	$0.472433\pi$
$770$	−429.944	+	2127.99i	−0.558368	+	2.76362i
$771$	−70.5946	+	86.0197i	−0.0915623	+	0.111569i
$772$	127.206	−	301.949i	0.164774	−	0.391126i
$773$	332.656	+	1096.62i	0.430344	+	1.41865i	0.857504	+	0.514478i	$0.172014\pi$
$773$	332.656	+	1096.62i	0.430344	+	1.41865i	−0.427160	+	0.904176i	$0.640486\pi$
$774$	16.0828	+	19.7176i	0.0207788	+	0.0254750i
$775$	50.6337	−	254.553i	0.0653338	−	0.328455i
$776$	−536.001	+	101.596i	−0.690723	+	0.130923i
$777$	194.590	+	978.272i	0.250438	+	1.25904i
$778$	42.1626	−	4.02460i	0.0541936	−	0.00517301i
$779$	−1373.49	−	135.277i	−1.76315	−	0.173655i
$780$	396.247	+	752.180i	0.508009	+	0.964333i
$781$	1052.50	+	319.273i	1.34763	+	0.408800i
$782$	1560.35	+	651.826i	1.99533	+	0.833537i
$783$	106.247	+	44.0088i	0.135692	+	0.0562054i
$784$	−300.454	−	750.792i	−0.383232	−	0.957643i
$785$	−345.614	−	834.387i	−0.440273	−	1.06291i
$786$	−213.178	−	0.641436i	−0.271219	−	0.000816077i
$787$	−388.305	+	207.553i	−0.493399	+	0.263727i	−0.699277	−	0.714850i	$-0.746495\pi$
$787$	−388.305	+	207.553i	−0.493399	+	0.263727i	0.205879	+	0.978578i	$0.433995\pi$
$788$	−1245.65	−	130.259i	−1.58077	−	0.165303i
$789$	130.599	+	159.135i	0.165524	+	0.201692i
$790$	125.792	−	410.234i	0.159231	−	0.519284i
$791$	−207.956	−	138.951i	−0.262902	−	0.175666i
$792$	−349.570	−	190.926i	−0.441377	−	0.241068i
$793$	1279.64	−	855.026i	1.61367	−	1.07822i
$794$	−530.310	+	985.000i	−0.667897	+	1.24055i
$795$	153.293	+	81.9371i	0.192822	+	0.103066i
$796$	169.626	+	114.823i	0.213098	+	0.144250i
$797$	−398.041	+	39.2036i	−0.499424	+	0.0491890i	−0.344593	−	0.938752i	$-0.611983\pi$
$797$	−398.041	+	39.2036i	−0.499424	+	0.0491890i	−0.154831	+	0.987941i	$0.549483\pi$
$798$	458.689	−	682.026i	0.574799	−	0.854669i
$799$	−444.508	+	444.508i	−0.556330	+	0.556330i
$800$	−228.098	+	528.064i	−0.285123	+	0.660081i
$801$	174.957	−	174.957i	0.218423	−	0.218423i
$802$	117.889	−	23.0811i	0.146994	−	0.0287795i
$803$	1984.37	−	195.444i	2.47120	−	0.243392i
$804$	744.141	+	152.680i	0.925548	+	0.189900i
$805$	1937.50	+	1035.62i	2.40683	+	1.28648i
$806$	155.351	+	517.726i	0.192743	+	0.642341i
$807$	429.966	−	287.294i	0.532796	−	0.356003i
$808$	−44.3806	−	84.8641i	−0.0549265	−	0.105030i
$809$	216.492	+	144.655i	0.267604	+	0.178807i	0.682132	−	0.731229i	$-0.261053\pi$
$809$	216.492	+	144.655i	0.267604	+	0.178807i	−0.414527	+	0.910037i	$0.636053\pi$
$810$	−104.234	+	55.3117i	−0.128684	+	0.0682860i
$811$	12.1042	+	14.7490i	0.0149250	+	0.0181862i	0.780419	−	0.625256i	$-0.215006\pi$
$811$	12.1042	+	14.7490i	0.0149250	+	0.0181862i	−0.765494	+	0.643442i	$0.777506\pi$
$812$	−421.040	+	776.435i	−0.518522	+	0.956201i
$813$	99.1230	−	52.9824i	0.121923	−	0.0651690i
$814$	−1358.78	+	1350.63i	−1.66927	+	1.65925i
$815$	−319.228	−	770.684i	−0.391691	−	0.945625i
$816$	−321.417	−	619.139i	−0.393893	−	0.758748i
$817$	−93.1751	−	38.5944i	−0.114045	−	0.0472392i
$818$	−292.973	−	713.363i	−0.358158	−	0.872082i
$819$	−536.146	−	162.638i	−0.654635	−	0.198581i
$820$	−972.484	+	1170.54i	−1.18596	+	1.42749i
$821$	−1511.55	−	148.875i	−1.84111	−	0.181334i	−0.883314	−	0.468781i	$-0.844693\pi$
$821$	−1511.55	−	148.875i	−1.84111	−	0.181334i	−0.957796	+	0.287447i	$0.907193\pi$
$822$	142.659	−	172.768i	0.173552	−	0.210180i
$823$	−193.036	−	970.460i	−0.234552	−	1.17917i	−0.901066	−	0.433681i	$-0.857214\pi$
$823$	−193.036	−	970.460i	−0.234552	−	1.17917i	0.666514	−	0.745492i	$-0.267786\pi$
$824$	−29.4771	−	0.266089i	−0.0357732	−	0.000322924i
$825$	−100.808	+	506.795i	−0.122191	+	0.614297i
$826$	49.1987	−	484.571i	0.0595626	−	0.586647i
$827$	−164.866	−	543.491i	−0.199355	−	0.657184i	−0.998433	−	0.0559575i	$-0.982179\pi$
$827$	−164.866	−	543.491i	−0.199355	−	0.657184i	0.799078	−	0.601227i	$-0.205321\pi$
$828$	−286.722	+	283.292i	−0.346282	+	0.342140i
$829$	−296.472	+	361.252i	−0.357626	+	0.435768i	−0.920481	−	0.390787i	$-0.872203\pi$
$829$	−296.472	+	361.252i	−0.357626	+	0.435768i	0.562855	+	0.826555i	$0.309703\pi$
$830$	−395.869	−	596.337i	−0.476951	−	0.718478i
$831$	−359.890			−0.433081
$832$	−95.8818	−	1194.15i	−0.115243	−	1.43527i
$833$		−	1272.27i		−	1.52734i
$834$	−193.700	−	291.789i	−0.232254	−	0.349867i
$835$	−356.754	−	292.780i	−0.427250	−	0.350635i
$836$	1578.70	+	9.50045i	1.88840	+	0.0113642i
$837$	−71.7935	+	21.7783i	−0.0857748	+	0.0260195i
$838$	−146.467	+	1442.59i	−0.174781	+	1.72147i
$839$	1563.56	+	311.012i	1.86360	+	0.370693i	0.992685	−	0.120736i	$-0.0385254\pi$
$839$	1563.56	+	311.012i	1.86360	+	0.370693i	0.870917	+	0.491429i	$0.163525\pi$
$840$	−339.249	−	840.397i	−0.403868	−	1.00047i
$841$	−344.432	+	68.5118i	−0.409551	+	0.0814647i
$842$	301.017	−	364.547i	0.357502	−	0.432954i
$843$	−63.0792	+	640.454i	−0.0748271	+	0.759732i
$844$	−87.6333	−	948.220i	−0.103831	−	1.12348i
$845$	−345.174	+	1137.88i	−0.408489	+	1.34661i
$846$	−56.9237	−	138.604i	−0.0672857	−	0.163835i
$847$	589.655	−	1423.55i	0.696168	−	1.68070i
$848$	−153.092	−	191.190i	−0.180533	−	0.225460i
$849$	−705.263	+	292.129i	−0.830698	+	0.344086i
$850$	−641.841	+	637.990i	−0.755107	+	0.750577i
$851$	913.911	+	1709.81i	1.07393	+	2.00918i
$852$	−440.165	+	130.635i	−0.516625	+	0.153328i
$853$	1160.67	−	952.536i	1.36069	−	1.11669i	0.379170	−	0.925327i	$-0.376209\pi$
$853$	1160.67	−	952.536i	1.36069	−	1.11669i	0.981519	−	0.191363i	$-0.0612906\pi$
$854$	−1449.20	+	769.014i	−1.69695	+	0.900485i
$855$	259.841	−	388.879i	0.303907	−	0.454830i
$856$	84.2537	+	942.594i	0.0984273	+	1.10116i
$857$	−395.602	−	592.060i	−0.461613	−	0.690852i	0.525515	−	0.850784i	$-0.323873\pi$
$857$	−395.602	−	592.060i	−0.461613	−	0.690852i	−0.987128	+	0.159932i	$0.948873\pi$
$858$	−309.292	−	1030.75i	−0.360480	−	1.20134i
$859$	447.666	−	837.524i	0.521148	−	0.974999i	−0.474361	−	0.880330i	$-0.657321\pi$
$859$	447.666	−	837.524i	0.521148	−	0.974999i	0.995509	−	0.0946687i	$-0.0301792\pi$
$860$	−92.8329	+	61.2241i	−0.107945	+	0.0711908i
$861$	−98.3001	−	998.057i	−0.114170	−	1.15918i
$862$	−1051.34	+	205.837i	−1.21965	+	0.238790i
$863$	−425.626	−	425.626i	−0.493193	−	0.493193i	0.416118	−	0.909311i	$-0.363390\pi$
$863$	−425.626	−	425.626i	−0.493193	−	0.493193i	−0.909311	+	0.416118i	$0.863390\pi$
$864$	165.703	−	13.8067i	0.191785	−	0.0159800i
$865$	−818.138	−	818.138i	−0.945824	−	0.945824i
$866$	−713.994	+	1061.64i	−0.824473	+	1.22591i
$867$	−58.5110	−	594.072i	−0.0674867	−	0.685204i
$868$	−109.010	−	565.807i	−0.125588	−	0.651851i
$869$	−256.037	+	479.011i	−0.294634	+	0.551221i
$870$	−238.256	+	442.537i	−0.273857	+	0.508663i
$871$	1140.25	+	1706.51i	1.30913	+	1.95925i
$872$	633.061	+	68.1263i	0.725988	+	0.0781265i
$873$	113.658	−	170.101i	0.130193	−	0.194847i
$874$	468.350	−	1527.39i	0.535870	−	1.74758i
$875$	355.144	−	291.459i	0.405878	−	0.333096i
$876$	−646.614	+	524.182i	−0.738144	+	0.598382i
$877$	122.513	+	229.205i	0.139695	+	0.261351i	0.942034	−	0.335518i	$-0.108911\pi$
$877$	122.513	+	229.205i	0.139695	+	0.261351i	−0.802339	+	0.596869i	$0.796411\pi$
$878$	−297.177	−	0.894183i	−0.338471	−	0.00101843i
$879$	−320.288	+	132.668i	−0.364377	+	0.150930i
$880$	984.474	−	1435.66i	1.11872	−	1.63143i
$881$	−124.954	+	301.667i	−0.141833	+	0.342414i	−0.978794	−	0.204848i	$-0.934330\pi$
$881$	−124.954	+	301.667i	−0.141833	+	0.342414i	0.836961	+	0.547262i	$0.184330\pi$
$882$	279.820	+	116.893i	0.317256	+	0.132532i
$883$	278.188	−	917.063i	0.315049	−	1.03858i	−0.646263	−	0.763115i	$-0.723669\pi$
$883$	278.188	−	917.063i	0.315049	−	1.03858i	0.961312	−	0.275462i	$-0.0888309\pi$
$884$	557.962	−	1800.28i	0.631178	−	2.03652i
$885$	27.1659	−	275.820i	0.0306959	−	0.311661i
$886$	924.118	−	88.2110i	1.04302	−	0.0995609i
$887$	−164.954	+	32.8114i	−0.185968	+	0.0369914i	−0.287196	−	0.957872i	$-0.592723\pi$
$887$	−164.954	+	32.8114i	−0.185968	+	0.0369914i	0.101227	+	0.994863i	$0.467723\pi$
$888$	163.104	−	782.974i	0.183676	−	0.881727i
$889$	242.423	+	48.2210i	0.272692	+	0.0542418i
$890$	683.482	+	837.954i	0.767957	+	0.941521i
$891$	142.935	−	43.3589i	0.160421	−	0.0486632i
$892$	−323.177	−	793.695i	−0.362307	−	0.889793i
$893$	459.084	+	376.760i	0.514091	+	0.421904i
$894$	−118.764	+	587.818i	−0.132846	+	0.657514i
$895$			894.546i			0.999493i
$896$	−26.8961	+	1276.78i	−0.0300180	+	1.42498i
$897$	−1089.01			−1.21405
$898$	1449.57	+	292.874i	1.61422	+	0.326140i
$899$	−202.719	+	247.014i	−0.225494	+	0.274766i
$900$	−81.3473	−	199.782i	−0.0903858	−	0.221980i
$901$	−111.859	−	368.749i	−0.124149	−	0.409266i
$902$	1492.74	−	1217.56i	1.65492	−	1.34985i
$903$	14.2971	−	71.8766i	0.0158329	−	0.0795976i
$904$	109.907	+	167.745i	0.121578	+	0.185559i
$905$	−396.263	−	1992.15i	−0.437859	−	2.20127i
$906$	−66.1066	−	692.547i	−0.0729653	−	0.764401i
$907$	1056.89	+	104.095i	1.16526	+	0.114769i	0.662096	−	0.749419i	$-0.269667\pi$
$907$	1056.89	+	104.095i	1.16526	+	0.114769i	0.503169	+	0.864188i	$0.332167\pi$
$908$	−479.742	+	1547.90i	−0.528351	+	1.70474i
$909$	34.3667	+	10.4250i	0.0378071	+	0.0114687i
$910$	943.843	−	2259.38i	1.03719	−	2.48284i
$911$	39.1148	+	16.2019i	0.0429362	+	0.0177847i	0.404048	−	0.914738i	$-0.367603\pi$
$911$	39.1148	+	16.2019i	0.0429362	+	0.0177847i	−0.361112	+	0.932522i	$0.617603\pi$
$912$	−552.344	+	359.525i	−0.605641	+	0.394216i
$913$	346.725	+	837.068i	0.379764	+	0.916832i
$914$	−3.38921	+	1126.39i	−0.00370811	+	1.23237i
$915$	−823.321	+	440.074i	−0.899805	+	0.480956i
$916$	−955.726	+	774.766i	−1.04337	+	0.845814i
$917$	389.509	+	474.618i	0.424764	+	0.517576i
$918$	250.105	+	76.6910i	0.272445	+	0.0835414i
$919$	1137.59	+	760.111i	1.23785	+	0.827107i	0.989914	−	0.141669i	$-0.0452469\pi$
$919$	1137.59	+	760.111i	1.23785	+	0.827107i	0.247939	+	0.968776i	$0.420247\pi$
$920$	−1105.19	−	1371.74i	−1.20129	−	1.49102i
$921$	−452.572	+	302.399i	−0.491392	+	0.328338i
$922$	−1018.43	−	548.308i	−1.10459	−	0.594694i
$923$	−1094.03	−	584.770i	−1.18530	−	0.633554i
$924$	217.031	+	1126.48i	0.234882	+	1.21913i
$925$	−1032.55	+	101.697i	−1.11627	+	0.109943i
$926$	502.774	+	338.135i	0.542952	+	0.365157i
$927$	7.81662	−	7.81662i	0.00843217	−	0.00843217i
$928$	554.159	−	441.003i	0.597154	−	0.475219i
$929$	−515.246	+	515.246i	−0.554625	+	0.554625i	−0.927772	−	0.373147i	$-0.878279\pi$
$929$	−515.246	+	515.246i	−0.554625	+	0.554625i	0.373147	+	0.927772i	$0.378279\pi$
$930$	−62.9991	−	321.775i	−0.0677410	−	0.345995i
$931$	−1196.18	+	117.813i	−1.28483	+	0.126545i
$932$	−821.875	+	542.034i	−0.881840	+	0.581582i
$933$	292.247	+	156.209i	0.313234	+	0.167427i
$934$	−351.228	+	105.391i	−0.376047	+	0.112838i
$935$	2277.16	−	1521.55i	2.43547	−	1.62733i
$936$	344.685	+	288.122i	0.368253	+	0.307822i
$937$	300.326	+	200.672i	0.320519	+	0.214164i	0.705412	−	0.708797i	$-0.250762\pi$
$937$	300.326	+	200.672i	0.320519	+	0.214164i	−0.384893	+	0.922961i	$0.625762\pi$
$938$	−1025.55	−	1932.63i	−1.09333	−	2.06037i
$939$	10.1937	+	12.4211i	0.0108560	+	0.0132280i
$940$	627.786	−	186.319i	0.667857	−	0.198211i
$941$	442.938	−	236.755i	0.470710	−	0.251600i	−0.218946	−	0.975737i	$-0.570262\pi$
$941$	442.938	−	236.755i	0.470710	−	0.251600i	0.689656	+	0.724137i	$0.257762\pi$
$942$	−336.439	−	338.469i	−0.357153	−	0.359309i
$943$	−745.974	−	1800.94i	−0.791064	−	1.90980i
$944$	−188.233	+	342.189i	−0.199400	+	0.362488i
$945$	313.988	+	130.058i	0.332262	+	0.137628i
$946$	130.210	−	53.4764i	0.137643	−	0.0565290i
$947$	−1263.71	−	383.343i	−1.33444	−	0.404797i	−0.459132	−	0.888368i	$-0.651840\pi$
$947$	−1263.71	−	383.343i	−1.33444	−	0.404797i	−0.875305	+	0.483571i	$0.839340\pi$
$948$	−20.8659	−	225.776i	−0.0220105	−	0.238160i
$949$	−2238.12	−	220.436i	−2.35840	−	0.232282i
$950$	659.267	+	544.374i	0.693965	+	0.573025i
$951$	−88.9532	−	447.198i	−0.0935365	−	0.470240i
$952$	−785.602	+	1849.22i	−0.825213	+	1.94246i
$953$	244.471	−	1229.04i	0.256528	−	1.28965i	−0.610748	−	0.791825i	$-0.709131\pi$
$953$	244.471	−	1229.04i	0.256528	−	1.28965i	0.867276	−	0.497828i	$-0.165869\pi$
$954$	91.3789	+	9.27774i	0.0957850	+	0.00972509i
$955$	−418.533	−	1379.72i	−0.438254	−	1.44473i
$956$	118.074	+	0.710557i	0.123508	+	0.000743261i
$957$	403.598	−	491.786i	0.421733	−	0.513883i
$958$	−159.430	+	105.835i	−0.166419	+	0.110475i
$959$	−645.309			−0.672898
$960$	−13.1186	+	726.576i	−0.0136653	+	0.756850i
$961$			752.533i			0.783073i
$962$	1800.28	−	1195.09i	1.87139	−	1.24230i
$963$	−274.328	−	225.135i	−0.284868	−	0.233785i
$964$	−956.814	+	945.367i	−0.992546	+	0.980671i
$965$	−513.862	+	155.878i	−0.532500	+	0.161532i
$966$	1154.95	+	117.263i	1.19560	+	0.121390i
$967$	−1013.03	−	201.505i	−1.04760	−	0.208381i	−0.358863	−	0.933390i	$-0.616836\pi$
$967$	−1013.03	−	201.505i	−1.04760	−	0.208381i	−0.688739	+	0.725009i	$0.741836\pi$
$968$	−881.483	+	865.711i	−0.910623	+	0.894330i
$969$	−1016.94	+	202.281i	−1.04947	+	0.208753i
$970$	689.432	+	569.282i	0.710754	+	0.586889i
$971$	−187.772	+	1906.48i	−0.193380	+	1.96342i	0.0665139	+	0.997785i	$0.478812\pi$
$971$	−187.772	+	1906.48i	−0.193380	+	1.96342i	−0.259894	+	0.965637i	$0.583688\pi$
$972$	−39.8462	+	47.9612i	−0.0409940	+	0.0493428i
$973$	−292.813	+	965.275i	−0.300938	+	0.992061i
$974$	238.036	−	97.7596i	0.244390	−	0.100369i
$975$	223.028	−	538.437i	0.228746	−	0.552243i
$976$	1310.61	−	113.175i	1.34284	−	0.115958i
$977$	1291.90	−	535.122i	1.32231	−	0.547720i	0.393859	−	0.919171i	$-0.371140\pi$
$977$	1291.90	−	535.122i	1.32231	−	0.547720i	0.928453	+	0.371451i	$0.121140\pi$
$978$	−310.753	−	312.628i	−0.317743	−	0.319661i
$979$	−645.242	−	1207.16i	−0.659083	−	1.23306i
$980$	−631.784	+	1165.06i	−0.644677	+	1.18884i
$981$	−184.571	+	151.473i	−0.188145	+	0.154407i
$982$	265.806	+	500.907i	0.270678	+	0.510089i
$983$	−75.5095	+	113.008i	−0.0768153	+	0.114962i	−0.867888	−	0.496760i	$-0.834523\pi$
$983$	−75.5095	+	113.008i	−0.0768153	+	0.114962i	0.791073	+	0.611722i	$0.209523\pi$
$984$	−240.369	+	767.386i	−0.244278	+	0.779864i
$985$	1140.37	+	1706.69i	1.15774	+	1.73268i
$986$	1067.21	−	320.232i	1.08237	−	0.324779i
$987$	−203.433	+	380.597i	−0.206113	+	0.385610i
$988$	−1744.27	−	357.883i	−1.76546	−	0.362229i
$989$	−13.9620	−	141.759i	−0.0141173	−	0.143335i
$990$	125.426	+	640.629i	0.126693	+	0.647100i
$991$	−270.081	−	270.081i	−0.272534	−	0.272534i	0.557586	−	0.830119i	$-0.311728\pi$
$991$	−270.081	−	270.081i	−0.272534	−	0.272534i	−0.830119	+	0.557586i	$0.811728\pi$
$992$	−96.9442	+	451.743i	−0.0977260	+	0.455386i
$993$	−704.177	−	704.177i	−0.709141	−	0.709141i
$994$	1097.31	+	737.986i	1.10394	+	0.742441i
$995$	−32.9046	−	334.086i	−0.0330700	−	0.335765i
$996$	−313.215	−	212.021i	−0.314473	−	0.212873i
$997$	−726.753	+	1359.66i	−0.728940	+	1.36375i	0.194843	+	0.980834i	$0.437580\pi$
$997$	−726.753	+	1359.66i	−0.728940	+	1.36375i	−0.923783	+	0.382916i	$0.874920\pi$
$998$	570.499	+	307.149i	0.571643	+	0.307764i
$999$	166.626	+	249.373i	0.166792	+	0.249622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.3.u.a.235.36	yes	1024
128.67	odd	32	inner	384.3.u.a.67.36	✓	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.3.u.a.67.36	✓	1024	128.67	odd	32	inner
384.3.u.a.235.36	yes	1024	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	384.u (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.396081 - 1.96039i) q^{2} +(-1.09880 + 1.33889i) q^{3} +(-3.68624 - 1.55294i) q^{4} +(1.90299 + 6.27330i) q^{5} +(2.18954 + 2.68439i) q^{6} +(1.94643 - 9.78539i) q^{7} +(-4.50442 + 6.61137i) q^{8} +(-0.585271 - 2.94236i) q^{9} +O(q^{10})\)	\(q+(0.396081 - 1.96039i) q^{2} +(-1.09880 + 1.33889i) q^{3} +(-3.68624 - 1.55294i) q^{4} +(1.90299 + 6.27330i) q^{5} +(2.18954 + 2.68439i) q^{6} +(1.94643 - 9.78539i) q^{7} +(-4.50442 + 6.61137i) q^{8} +(-0.585271 - 2.94236i) q^{9} +(13.0518 - 1.24585i) q^{10} +(-16.5164 - 1.62672i) q^{11} +(6.12967 - 3.22910i) q^{12} +(17.9126 + 5.43372i) q^{13} +(-18.4122 - 7.69157i) q^{14} +(-10.4903 - 4.34522i) q^{15} +(11.1767 + 11.4491i) q^{16} +(9.63304 + 23.2562i) q^{17} +(-5.99997 - 0.0180534i) q^{18} +(20.9732 - 11.2104i) q^{19} +(2.72723 - 26.0801i) q^{20} +(10.9628 + 13.3583i) q^{21} +(-9.73085 + 31.7342i) q^{22} +(27.9282 + 18.6610i) q^{23} +(-3.90245 - 13.2955i) q^{24} +(-14.9462 + 9.98676i) q^{25} +(17.7470 - 32.9634i) q^{26} +(4.58260 + 2.44945i) q^{27} +(-22.3712 + 33.0486i) q^{28} +(22.0253 - 2.16930i) q^{29} +(-12.6733 + 18.8440i) q^{30} +(-10.2095 + 10.2095i) q^{31} +(26.8715 - 17.3760i) q^{32} +(20.3263 - 20.3263i) q^{33} +(49.4067 - 9.67315i) q^{34} +(65.0907 - 6.41088i) q^{35} +(-2.41187 + 11.7551i) q^{36} +(50.9039 + 27.2087i) q^{37} +(-13.6697 - 45.5559i) q^{38} +(-26.9575 + 18.0124i) q^{39} +(-50.0470 - 15.6763i) q^{40} +(-48.2540 - 32.2423i) q^{41} +(30.5296 - 16.2005i) q^{42} +(-2.69034 - 3.27819i) q^{43} +(58.3572 + 31.6456i) q^{44} +(17.3445 - 9.27084i) q^{45} +(47.6447 - 47.3588i) q^{46} +(9.55675 + 23.0720i) q^{47} +(-27.6101 + 2.38421i) q^{48} +(-46.6951 - 19.3417i) q^{49} +(13.6580 + 33.2560i) q^{50} +(-41.7224 - 12.6564i) q^{51} +(-57.5917 - 47.8472i) q^{52} +(-15.2344 - 1.50046i) q^{53} +(6.61695 - 8.01349i) q^{54} +(-21.2256 - 106.708i) q^{55} +(55.9272 + 56.9461i) q^{56} +(-8.03585 + 40.3990i) q^{57} +(4.47113 - 44.0374i) q^{58} +(7.08556 + 23.3580i) q^{59} +(31.9218 + 32.3084i) q^{60} +(52.1586 - 63.5555i) q^{61} +(15.9707 + 24.0583i) q^{62} -29.9313 q^{63} +(-23.4203 - 59.5608i) q^{64} +122.711i q^{65} +(-31.7965 - 47.8982i) q^{66} +(84.7567 + 69.5580i) q^{67} +(0.605927 - 100.688i) q^{68} +(-55.6727 + 16.8881i) q^{69} +(13.2134 - 130.142i) q^{70} +(-64.9980 - 12.9289i) q^{71} +(22.0893 + 9.38418i) q^{72} +(-117.837 + 23.4392i) q^{73} +(73.5016 - 89.0145i) q^{74} +(3.05175 - 30.9849i) q^{75} +(-94.7216 + 8.75405i) q^{76} +(-48.0662 + 158.453i) q^{77} +(24.6340 + 59.9816i) q^{78} +(12.5240 - 30.2357i) q^{79} +(-50.5542 + 91.9024i) q^{80} +(-8.31492 + 3.44415i) q^{81} +(-82.3199 + 81.8260i) q^{82} +(-25.7348 - 48.1463i) q^{83} +(-19.6670 - 66.2665i) q^{84} +(-127.562 + 104.687i) q^{85} +(-7.49212 + 3.97568i) q^{86} +(-21.2970 + 31.8732i) q^{87} +(85.1518 - 101.869i) q^{88} +(45.8208 + 68.5757i) q^{89} +(-11.3046 - 37.6740i) q^{90} +(88.0367 - 164.705i) q^{91} +(-73.9705 - 112.160i) q^{92} +(-2.45121 - 24.8876i) q^{93} +(49.0154 - 9.59654i) q^{94} +(110.238 + 110.238i) q^{95} +(-6.26185 + 55.0708i) q^{96} +(48.2198 + 48.2198i) q^{97} +(-56.4123 + 83.8796i) q^{98} +(4.88017 + 49.5492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 1248 q^{50} + 1056 q^{52} + 288 q^{54} + 1568 q^{56} + 576 q^{60} + 192 q^{62} - 192 q^{64} - 576 q^{66} - 960 q^{68} - 1344 q^{70} - 2464 q^{74} - 416 q^{76} - 1440 q^{78} - 1632 q^{80}+O(q^{100}) \) 1024 * q + 1248 * q^50 + 1056 * q^52 + 288 * q^54 + 1568 * q^56 + 576 * q^60 + 192 * q^62 - 192 * q^64 - 576 * q^66 - 960 * q^68 - 1344 * q^70 - 2464 * q^74 - 416 * q^76 - 1440 * q^78 - 1632 * q^80

Introduction

L-functions

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