LMFDB - Embedded newform 384.2.v.a.37.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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([0, 15, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			37.18
Character	$\chi$	$=$	384.37
Dual form			384.2.v.a.301.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.146373 - 1.40662i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.95715 - 0.411783i) q^{4} +(-1.38486 + 1.13652i) q^{5} +(-1.30953 + 0.533986i) q^{6} +(-0.955768 + 0.638624i) q^{7} +(-0.865695 + 2.69269i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(0.146373 - 1.40662i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.95715 - 0.411783i) q^{4} +(-1.38486 + 1.13652i) q^{5} +(-1.30953 + 0.533986i) q^{6} +(-0.955768 + 0.638624i) q^{7} +(-0.865695 + 2.69269i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(1.39595 + 2.11433i) q^{10} +(-0.00975057 - 0.0321433i) q^{11} +(0.559434 + 1.92016i) q^{12} +(-3.12625 + 3.80934i) q^{13} +(0.758401 + 1.43788i) q^{14} +(1.65514 + 0.685583i) q^{15} +(3.66087 + 1.61184i) q^{16} +(0.317933 - 0.131692i) q^{17} +(1.08824 + 0.903180i) q^{18} +(-0.119838 + 0.0118030i) q^{19} +(3.17838 - 1.65409i) q^{20} +(1.01376 + 0.541867i) q^{21} +(-0.0466406 + 0.00901041i) q^{22} +(-1.37784 + 0.274068i) q^{23} +(2.78283 - 0.505850i) q^{24} +(-0.349304 + 1.75607i) q^{25} +(4.90069 + 4.95502i) q^{26} +(0.995185 + 0.0980171i) q^{27} +(2.13356 - 0.856314i) q^{28} +(-8.24412 - 2.50082i) q^{29} +(1.20662 - 2.22780i) q^{30} +(2.27493 + 2.27493i) q^{31} +(2.80310 - 4.91352i) q^{32} +(-0.0237515 + 0.0237515i) q^{33} +(-0.138704 - 0.466486i) q^{34} +(0.597793 - 1.97066i) q^{35} +(1.42972 - 1.39854i) q^{36} +(-0.701998 + 7.12751i) q^{37} +(-0.000938741 + 0.170294i) q^{38} +(4.83324 + 0.961392i) q^{39} +(-1.86144 - 4.71288i) q^{40} +(-1.71742 - 8.63403i) q^{41} +(0.910588 - 1.34666i) q^{42} +(0.964303 - 1.80408i) q^{43} +(0.00584727 + 0.0669244i) q^{44} +(-0.175599 - 1.78289i) q^{45} +(0.183832 + 1.97820i) q^{46} +(-2.30707 - 5.56976i) q^{47} +(-0.304206 - 3.98842i) q^{48} +(-2.17313 + 5.24640i) q^{49} +(2.41899 + 0.748380i) q^{50} +(-0.266015 - 0.218312i) q^{51} +(7.68716 - 6.16812i) q^{52} +(-6.17064 + 1.87184i) q^{53} +(0.283541 - 1.38550i) q^{54} +(0.0500349 + 0.0334322i) q^{55} +(-0.892211 - 3.12644i) q^{56} +(0.0669005 + 0.100124i) q^{57} +(-4.72442 + 11.2303i) q^{58} +(0.0354888 + 0.0432432i) q^{59} +(-2.95705 - 2.02335i) q^{60} +(-5.90186 + 3.15461i) q^{61} +(3.53295 - 2.86697i) q^{62} -1.14949i q^{63} +(-6.50114 - 4.66209i) q^{64} -8.82847i q^{65} +(0.0299327 + 0.0368859i) q^{66} +(-9.08018 + 4.85346i) q^{67} +(-0.676471 + 0.126822i) q^{68} +(0.891214 + 1.08595i) q^{69} +(-2.68446 - 1.12932i) q^{70} +(7.07509 + 10.5886i) q^{71} +(-1.75793 - 2.21578i) q^{72} +(2.92088 + 1.95167i) q^{73} +(9.92293 + 2.03072i) q^{74} +(1.71338 - 0.519747i) q^{75} +(0.239401 + 0.0262469i) q^{76} +(0.0298468 + 0.0244946i) q^{77} +(2.05977 - 6.65781i) q^{78} +(4.64586 - 11.2161i) q^{79} +(-6.90169 + 1.92850i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-12.3962 + 1.15196i) q^{82} +(-0.444833 - 4.51647i) q^{83} +(-1.76095 - 1.47796i) q^{84} +(-0.290621 + 0.543714i) q^{85} +(-2.39651 - 1.62048i) q^{86} +(1.68072 + 8.44954i) q^{87} +(0.0949930 + 0.00157107i) q^{88} +(-6.64333 - 1.32144i) q^{89} +(-2.53355 - 0.0139661i) q^{90} +(0.555230 - 5.63735i) q^{91} +(2.80949 + 0.0309754i) q^{92} +(0.933915 - 3.07871i) q^{93} +(-8.17222 + 2.42990i) q^{94} +(0.152544 - 0.152544i) q^{95} +(-5.65471 - 0.155895i) q^{96} +(-1.40195 - 1.40195i) q^{97} +(7.06160 + 3.82470i) q^{98} +(0.0321433 + 0.00975057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{25}{32}\right)$	$1$

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 $

$2$	0.146373	−	1.40662i	0.103502	−	0.994629i
$2$	0.146373	−	1.40662i	0.103502	−	0.994629i
$3$	−0.471397	−	0.881921i	−0.272161	−	0.509177i
$3$	−0.471397	−	0.881921i	−0.272161	−	0.509177i
$4$	−1.95715	−	0.411783i	−0.978575	−	0.205891i
$5$	−1.38486	+	1.13652i	−0.619328	+	0.508269i	−0.890930	−	0.454140i	$-0.849947\pi$
$5$	−1.38486	+	1.13652i	−0.619328	+	0.508269i	0.271602	+	0.962410i	$0.412447\pi$
$6$	−1.30953	+	0.533986i	−0.534612	+	0.217999i
$7$	−0.955768	+	0.638624i	−0.361246	+	0.241377i	−0.722926	−	0.690925i	$-0.757203\pi$
$7$	−0.955768	+	0.638624i	−0.361246	+	0.241377i	0.361680	+	0.932302i	$0.382203\pi$
$8$	−0.865695	+	2.69269i	−0.306069	+	0.952009i
$9$	−0.555570	+	0.831470i	−0.185190	+	0.277157i
$10$	1.39595	+	2.11433i	0.441438	+	0.668608i
$11$	−0.00975057	−	0.0321433i	−0.00293991	−	0.00969158i	0.955458	−	0.295127i	$-0.0953619\pi$
$11$	−0.00975057	−	0.0321433i	−0.00293991	−	0.00969158i	−0.958398	+	0.285435i	$0.907862\pi$
$12$	0.559434	+	1.92016i	0.161495	+	0.554304i
$13$	−3.12625	+	3.80934i	−0.867065	+	1.05652i	0.130813	+	0.991407i	$0.458241\pi$
$13$	−3.12625	+	3.80934i	−0.867065	+	1.05652i	−0.997878	+	0.0651149i	$0.979259\pi$
$14$	0.758401	+	1.43788i	0.202691	+	0.384289i
$15$	1.65514	+	0.685583i	0.427356	+	0.177017i
$16$	3.66087	+	1.61184i	0.915218	+	0.402960i
$17$	0.317933	−	0.131692i	0.0771100	−	0.0319400i	−0.343795	−	0.939045i	$-0.611713\pi$
$17$	0.317933	−	0.131692i	0.0771100	−	0.0319400i	0.420905	+	0.907105i	$0.361713\pi$
$18$	1.08824	+	0.903180i	0.256501	+	0.212882i
$19$	−0.119838	+	0.0118030i	−0.0274927	+	0.00270779i	−0.111754	−	0.993736i	$-0.535647\pi$
$19$	−0.119838	+	0.0118030i	−0.0274927	+	0.00270779i	0.0842614	+	0.996444i	$0.473147\pi$
$20$	3.17838	−	1.65409i	0.710707	−	0.369865i
$21$	1.01376	+	0.541867i	0.221221	+	0.118245i
$22$	−0.0466406	+	0.00901041i	−0.00994381	+	0.00192103i
$23$	−1.37784	+	0.274068i	−0.287299	+	0.0571472i	−0.336636	−	0.941635i	$-0.609289\pi$
$23$	−1.37784	+	0.274068i	−0.287299	+	0.0571472i	0.0493372	+	0.998782i	$0.484289\pi$
$24$	2.78283	−	0.505850i	0.568042	−	0.103256i
$25$	−0.349304	+	1.75607i	−0.0698609	+	0.351214i
$26$	4.90069	+	4.95502i	0.961105	+	0.971760i
$27$	0.995185	+	0.0980171i	0.191523	+	0.0188634i
$28$	2.13356	−	0.856314i	0.403204	−	0.161828i
$29$	−8.24412	−	2.50082i	−1.53089	−	0.464392i	−0.591233	−	0.806500i	$-0.701359\pi$
$29$	−8.24412	−	2.50082i	−1.53089	−	0.464392i	−0.939660	+	0.342109i	$0.888859\pi$
$30$	1.20662	−	2.22780i	0.220298	−	0.406740i
$31$	2.27493	+	2.27493i	0.408590	+	0.408590i	0.881247	−	0.472657i	$-0.156705\pi$
$31$	2.27493	+	2.27493i	0.408590	+	0.408590i	−0.472657	+	0.881247i	$0.656705\pi$
$32$	2.80310	−	4.91352i	0.495522	−	0.868595i
$33$	−0.0237515	+	0.0237515i	−0.00413461	+	0.00413461i
$34$	−0.138704	−	0.466486i	−0.0237875	−	0.0800017i
$35$	0.597793	−	1.97066i	0.101045	−	0.333102i
$36$	1.42972	−	1.39854i	0.238286	−	0.233089i
$37$	−0.701998	+	7.12751i	−0.115408	+	1.17176i	0.746746	+	0.665109i	$0.231615\pi$
$37$	−0.701998	+	7.12751i	−0.115408	+	1.17176i	−0.862154	+	0.506646i	$0.830885\pi$
$38$	−0.000938741		0.170294i	−0.000152284		0.0276253i
$39$	4.83324	+	0.961392i	0.773939	+	0.153946i
$40$	−1.86144	−	4.71288i	−0.294320	−	0.745172i
$41$	−1.71742	−	8.63403i	−0.268215	−	1.34841i	−0.846419	−	0.532517i	$-0.821246\pi$
$41$	−1.71742	−	8.63403i	−0.268215	−	1.34841i	0.578204	−	0.815892i	$-0.303754\pi$
$42$	0.910588	−	1.34666i	0.140507	−	0.207794i
$43$	0.964303	−	1.80408i	0.147055	−	0.275120i	−0.797600	−	0.603187i	$-0.793897\pi$
$43$	0.964303	−	1.80408i	0.147055	−	0.275120i	0.944654	+	0.328067i	$0.106397\pi$
$44$	0.00584727	+	0.0669244i	0.000881509	+	0.0100892i
$45$	−0.175599	−	1.78289i	−0.0261768	−	0.265777i
$46$	0.183832	+	1.97820i	0.0271045	+	0.291670i
$47$	−2.30707	−	5.56976i	−0.336521	−	0.812434i	−0.998044	−	0.0625090i	$-0.980090\pi$
$47$	−2.30707	−	5.56976i	−0.336521	−	0.812434i	0.661523	−	0.749925i	$-0.269910\pi$
$48$	−0.304206	−	3.98842i	−0.0439084	−	0.575678i
$49$	−2.17313	+	5.24640i	−0.310447	+	0.749486i
$50$	2.41899	+	0.748380i	0.342097	+	0.105837i
$51$	−0.266015	−	0.218312i	−0.0372495	−	0.0305699i
$52$	7.68716	−	6.16812i	1.06602	−	0.855365i
$53$	−6.17064	+	1.87184i	−0.847603	+	0.257118i	−0.684067	−	0.729420i	$-0.739790\pi$
$53$	−6.17064	+	1.87184i	−0.847603	+	0.257118i	−0.163537	+	0.986537i	$0.552290\pi$
$54$	0.283541	−	1.38550i	0.0385851	−	0.188542i
$55$	0.0500349	+	0.0334322i	0.00674670	+	0.00450800i
$56$	−0.892211	−	3.12644i	−0.119227	−	0.417788i
$57$	0.0669005	+	0.100124i	0.00886119	+	0.0132617i
$58$	−4.72442	+	11.2303i	−0.620347	+	1.47461i
$59$	0.0354888	+	0.0432432i	0.00462024	+	0.00562978i	0.775315	−	0.631574i	$-0.217591\pi$
$59$	0.0354888	+	0.0432432i	0.00462024	+	0.00562978i	−0.770695	+	0.637204i	$0.780091\pi$
$60$	−2.95705	−	2.02335i	−0.381754	−	0.261213i
$61$	−5.90186	+	3.15461i	−0.755655	+	0.403906i	−0.803774	−	0.594935i	$-0.797178\pi$
$61$	−5.90186	+	3.15461i	−0.755655	+	0.403906i	0.0481181	+	0.998842i	$0.484678\pi$
$62$	3.53295	−	2.86697i	0.448685	−	0.364106i
$63$		−	1.14949i		−	0.144822i
$64$	−6.50114	−	4.66209i	−0.812643	−	0.582762i
$65$		−	8.82847i		−	1.09504i
$66$	0.0299327	+	0.0368859i	0.00368446	+	0.00454034i
$67$	−9.08018	+	4.85346i	−1.10932	+	0.592944i	−0.921156	−	0.389193i	$-0.872754\pi$
$67$	−9.08018	+	4.85346i	−1.10932	+	0.592944i	−0.188165	+	0.982138i	$0.560254\pi$
$68$	−0.676471	+	0.126822i	−0.0820341	+	0.0153794i
$69$	0.891214	+	1.08595i	0.107290	+	0.130733i
$70$	−2.68446	−	1.12932i	−0.320855	−	0.134979i
$71$	7.07509	+	10.5886i	0.839658	+	1.25664i	0.964400	+	0.264448i	$0.0851897\pi$
$71$	7.07509	+	10.5886i	0.839658	+	1.25664i	−0.124742	+	0.992189i	$0.539810\pi$
$72$	−1.75793	−	2.21578i	−0.207175	−	0.261132i
$73$	2.92088	+	1.95167i	0.341863	+	0.228426i	0.714635	−	0.699497i	$-0.246593\pi$
$73$	2.92088	+	1.95167i	0.341863	+	0.228426i	−0.372772	+	0.927923i	$0.621593\pi$
$74$	9.92293	+	2.03072i	1.15352	+	0.236066i
$75$	1.71338	−	0.519747i	0.197844	−	0.0600153i
$76$	0.239401	+	0.0262469i	0.0274612	+	0.00301073i
$77$	0.0298468	+	0.0244946i	0.00340136	+	0.00279142i
$78$	2.05977	−	6.65781i	0.233223	−	0.753848i
$79$	4.64586	−	11.2161i	0.522701	−	1.26191i	−0.413519	−	0.910495i	$-0.635700\pi$
$79$	4.64586	−	11.2161i	0.522701	−	1.26191i	0.936220	−	0.351415i	$-0.114300\pi$
$80$	−6.90169	+	1.92850i	−0.771632	+	0.215613i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−12.3962	+	1.15196i	−1.36893	+	0.127212i
$83$	−0.444833	−	4.51647i	−0.0488268	−	0.495747i	−0.988235	−	0.152945i	$-0.951124\pi$
$83$	−0.444833	−	4.51647i	−0.0488268	−	0.495747i	0.939408	−	0.342801i	$-0.111376\pi$
$84$	−1.76095	−	1.47796i	−0.192136	−	0.161259i
$85$	−0.290621	+	0.543714i	−0.0315223	+	0.0589740i
$86$	−2.39651	−	1.62048i	−0.258422	−	0.174740i
$87$	1.68072	+	8.44954i	0.180192	+	0.905886i
$88$	0.0949930	+	0.00157107i	0.0101263	+	0.000167476i
$89$	−6.64333	−	1.32144i	−0.704192	−	0.140072i	−0.170010	−	0.985442i	$-0.554380\pi$
$89$	−6.64333	−	1.32144i	−0.704192	−	0.140072i	−0.534181	+	0.845370i	$0.679380\pi$
$90$	−2.53355	−	0.0139661i	−0.267059	−	0.00147216i
$91$	0.555230	−	5.63735i	0.0582039	−	0.590955i
$92$	2.80949	+	0.0309754i	0.292909	+	0.00322941i
$93$	0.933915	−	3.07871i	0.0968425	−	0.319247i
$94$	−8.17222	+	2.42990i	−0.842901	+	0.250626i
$95$	0.152544	−	0.152544i	0.0156507	−	0.0156507i
$96$	−5.65471	−	0.155895i	−0.577131	−	0.0159110i
$97$	−1.40195	−	1.40195i	−0.142346	−	0.142346i	0.632343	−	0.774689i	$-0.282094\pi$
$97$	−1.40195	−	1.40195i	−0.142346	−	0.142346i	−0.774689	+	0.632343i	$0.782094\pi$
$98$	7.06160	+	3.82470i	0.713329	+	0.386353i
$99$	0.0321433	+	0.00975057i	0.00323053	+	0.000979969i
$100$	1.40676	−	3.29306i	0.140676	−	0.329306i
$101$	−6.30707	−	0.621192i	−0.627577	−	0.0618109i	−0.220771	−	0.975326i	$-0.570857\pi$
$101$	−6.30707	−	0.621192i	−0.627577	−	0.0618109i	−0.406806	+	0.913515i	$0.633357\pi$
$102$	−0.346020	+	0.342226i	−0.0342611	+	0.0338854i
$103$	−0.524693	+	2.63781i	−0.0516995	+	0.259911i	−0.997987	−	0.0634147i	$-0.979801\pi$
$103$	−0.524693	+	2.63781i	−0.0516995	+	0.259911i	0.946288	+	0.323326i	$0.104801\pi$
$104$	−7.55100	−	11.7157i	−0.740436	−	1.14882i
$105$	−2.01976	+	0.401756i	−0.197109	+	0.0392074i
$106$	1.72975	+	8.95373i	0.168009	+	0.869663i
$107$	13.7003	+	7.32294i	1.32445	+	0.707935i	0.973549	−	0.228476i	$-0.0733743\pi$
$107$	13.7003	+	7.32294i	1.32445	+	0.707935i	0.350904	+	0.936411i	$0.385874\pi$
$108$	−1.90736	−	0.601634i	−0.183536	−	0.0578922i
$109$	−8.98053	+	0.884505i	−0.860178	+	0.0847202i	−0.518480	−	0.855090i	$-0.673502\pi$
$109$	−8.98053	+	0.884505i	−0.860178	+	0.0847202i	−0.341698	+	0.939810i	$0.611002\pi$
$110$	0.0543502	−	0.0654864i	0.00518208	−	0.00624388i
$111$	6.61682	−	2.74078i	0.628041	−	0.260143i
$112$	−4.52830	+	0.797374i	−0.427884	+	0.0753447i
$113$	5.17388	+	2.14309i	0.486717	+	0.201605i	0.612527	−	0.790449i	$-0.290153\pi$
$113$	5.17388	+	2.14309i	0.486717	+	0.201605i	−0.125810	+	0.992054i	$0.540153\pi$
$114$	0.150628	−	0.0794480i	0.0141076	−	0.00744099i
$115$	1.59662	−	1.94549i	0.148886	−	0.181418i
$116$	15.1052	+	8.28927i	1.40248	+	0.769640i
$117$	−1.43050	−	4.71574i	−0.132250	−	0.435970i
$118$	0.0660212	−	0.0435895i	0.00607775	−	0.00401274i
$119$	−0.219768	+	0.328907i	−0.0201461	+	0.0301508i
$120$	−3.27891	+	3.86328i	−0.299322	+	0.352668i
$121$	9.14523	−	6.11065i	0.831384	−	0.555513i
$122$	3.57346	+	8.76341i	0.323525	+	0.793402i
$123$	−6.80495	+	5.58468i	−0.613582	+	0.503554i
$124$	−3.51561	−	5.38916i	−0.315711	−	0.483961i
$125$	−5.73465	−	10.7288i	−0.512923	−	0.959611i
$126$	−1.61690	−	0.168255i	−0.144045	−	0.0149893i
$127$	12.2956			1.09106			0.545529	−	0.838092i	$-0.316329\pi$
$127$	12.2956			1.09106			0.545529	+	0.838092i	$0.316329\pi$
$128$	−7.50938	+	8.46222i	−0.663742	+	0.747962i
$129$	−2.04563			−0.180108
$130$	−12.4183	−	1.29225i	−1.08916	−	0.113338i
$131$	−7.82133	−	14.6327i	−0.683353	−	1.27846i	−0.949268	−	0.314467i	$-0.898174\pi$
$131$	−7.82133	−	14.6327i	−0.683353	−	1.27846i	0.265915	−	0.963996i	$-0.414326\pi$
$132$	0.0562657	−	0.0367048i	0.00489730	−	0.00319474i
$133$	0.107000	−	0.0878122i	0.00927804	−	0.00761429i
$134$	5.49787	+	13.4828i	0.474943	+	1.16473i
$135$	−1.48959	+	0.995312i	−0.128204	+	0.0856628i
$136$	0.0793729	+	0.970099i	0.00680617	+	0.0831853i
$137$	2.74183	−	4.10343i	0.234250	−	0.350580i	−0.695657	−	0.718374i	$-0.744887\pi$
$137$	2.74183	−	4.10343i	0.234250	−	0.350580i	0.929907	+	0.367794i	$0.119887\pi$
$138$	1.65796	−	1.09464i	0.141135	−	0.0931823i
$139$	−3.33574	−	10.9964i	−0.282933	−	0.932706i	−0.977080	−	0.212873i	$-0.931718\pi$
$139$	−3.33574	−	10.9964i	−0.282933	−	0.932706i	0.694147	−	0.719834i	$-0.255782\pi$
$140$	−1.98145	+	3.61071i	−0.167463	+	0.305161i
$141$	−3.82455	+	4.66022i	−0.322085	+	0.392462i
$142$	15.9297	−	8.40205i	1.33679	−	0.705085i
$143$	0.152928	+	0.0633447i	0.0127885	+	0.00529715i
$144$	−3.37407	+	2.14841i	−0.281172	+	0.179034i
$145$	14.2592	−	5.90635i	1.18416	−	0.490496i
$146$	3.17280	−	3.82289i	0.262582	−	0.316385i
$147$	5.65132	−	0.556607i	0.466113	−	0.0459081i
$148$	4.30890	−	13.6605i	0.354189	−	1.12289i
$149$	14.8329	+	7.92836i	1.21516	+	0.649516i	0.949262	−	0.314485i	$-0.101832\pi$
$149$	14.8329	+	7.92836i	1.21516	+	0.649516i	0.265897	+	0.964001i	$0.414332\pi$
$150$	−0.480294	−	2.48615i	−0.0392158	−	0.202993i
$151$	−6.87739	+	1.36800i	−0.559674	+	0.111326i	−0.466818	−	0.884353i	$-0.654600\pi$
$151$	−6.87739	+	1.36800i	−0.559674	+	0.111326i	−0.0928563	+	0.995680i	$0.529600\pi$
$152$	0.0719612	−	0.332904i	0.00583683	−	0.0270021i
$153$	−0.0671360	+	0.337516i	−0.00542763	+	0.0272865i
$154$	0.0388234	−	0.0383977i	0.00312848	−	0.00309417i
$155$	−5.73598	−	0.564945i	−0.460725	−	0.0453774i
$156$	−9.06350	−	3.87183i	−0.725661	−	0.309995i
$157$	9.41002	+	2.85450i	0.751002	+	0.227814i	0.642503	−	0.766283i	$-0.277896\pi$
$157$	9.41002	+	2.85450i	0.751002	+	0.227814i	0.108498	+	0.994097i	$0.465396\pi$
$158$	−15.0968	−	8.17670i	−1.20103	−	0.650503i
$159$	4.55964	+	4.55964i	0.361603	+	0.361603i
$160$	1.70244	+	9.99032i	0.134590	+	0.789804i
$161$	1.14186	−	1.14186i	0.0899915	−	0.0899915i
$162$	−1.35556	+	0.403058i	−0.106503	+	0.0316672i
$163$	−3.29693	+	10.8685i	−0.258236	+	0.851289i	0.727948	+	0.685632i	$0.240474\pi$
$163$	−3.29693	+	10.8685i	−0.258236	+	0.851289i	−0.986184	+	0.165656i	$0.947026\pi$
$164$	−0.194104	+	17.6053i	−0.0151569	+	1.37474i
$165$	0.00589832	−	0.0598867i	0.000459184	−	0.00466217i
$166$	−6.41806	−	0.0353794i	−0.498138	−	0.00274597i
$167$	9.50435	+	1.89053i	0.735469	+	0.146294i	0.548593	−	0.836090i	$-0.315164\pi$
$167$	9.50435	+	1.89053i	0.735469	+	0.146294i	0.186876	+	0.982384i	$0.440164\pi$
$168$	−2.33669	+	2.26065i	−0.180279	+	0.174413i
$169$	−2.20150	−	11.0677i	−0.169346	−	0.851362i
$170$	0.722258	+	0.488378i	0.0553947	+	0.0374569i
$171$	0.0567645	−	0.106199i	0.00434089	−	0.00812123i
$172$	−2.63017	+	3.13378i	−0.200549	+	0.238948i
$173$	1.78949	+	18.1690i	0.136053	+	1.38137i	0.784511	+	0.620115i	$0.212914\pi$
$173$	1.78949	+	18.1690i	0.136053	+	1.38137i	−0.648458	+	0.761251i	$0.724586\pi$
$174$	12.1313	−	1.12734i	0.919671	−	0.0854636i
$175$	−0.787615	−	1.90147i	−0.0595381	−	0.143738i
$176$	0.0161143	−	0.133389i	0.00121466	−	0.0100546i
$177$	0.0214078	−	0.0516830i	0.00160911	−	0.00388473i
$178$	−2.83117	+	9.15121i	−0.212205	+	0.685912i
$179$	−2.20982	−	1.81356i	−0.165170	−	0.135552i	0.548177	−	0.836362i	$-0.315322\pi$
$179$	−2.20982	−	1.81356i	−0.165170	−	0.135552i	−0.713347	+	0.700811i	$0.752822\pi$
$180$	−0.390488	+	3.56169i	−0.0291053	+	0.265473i
$181$	23.5919	−	7.15654i	1.75358	−	0.531941i	0.760492	−	0.649348i	$-0.224958\pi$
$181$	23.5919	−	7.15654i	1.75358	−	0.531941i	0.993084	+	0.117406i	$0.0374579\pi$
$182$	−7.84832	−	1.60615i	−0.581756	−	0.119056i
$183$	5.56423	+	3.71790i	0.411320	+	0.274835i
$184$	0.454804	−	3.94734i	0.0335286	−	0.291002i
$185$	−7.12842	−	10.6684i	−0.524092	−	0.784359i
$186$	−4.19386	−	1.76430i	−0.307509	−	0.129365i
$187$	−0.00733305	−	0.00893535i	−0.000536246	−	0.000653417i
$188$	2.22175	+	11.8509i	0.162038	+	0.864314i
$189$	−1.01376	+	0.541867i	−0.0737403	+	0.0394150i
$190$	−0.192243	−	0.236900i	−0.0139468	−	0.0171865i
$191$		−	7.74946i		−	0.560731i	−0.959893	−	0.280366i	$-0.909544\pi$
$191$		−	7.74946i		−	0.560731i	0.959893	−	0.280366i	$-0.0904557\pi$
$192$	−1.04698	+	7.93119i	−0.0755595	+	0.572385i
$193$			23.3761i			1.68265i	0.540529	+	0.841326i	$0.318224\pi$
$193$			23.3761i			1.68265i	−0.540529	+	0.841326i	$0.681776\pi$
$194$	−2.17721	+	1.76680i	−0.156315	+	0.126849i
$195$	−7.78601	+	4.16171i	−0.557568	+	0.298026i
$196$	6.41352	−	9.37314i	0.458109	−	0.669510i
$197$	9.25612	+	11.2786i	0.659471	+	0.803568i	0.990125	−	0.140184i	$-0.0447694\pi$
$197$	9.25612	+	11.2786i	0.659471	+	0.803568i	−0.330654	+	0.943752i	$0.607269\pi$
$198$	0.0184203	−	0.0437862i	0.00130907	−	0.00311175i
$199$	2.11687	+	3.16812i	0.150061	+	0.224582i	0.898883	−	0.438189i	$-0.144380\pi$
$199$	2.11687	+	3.16812i	0.150061	+	0.224582i	−0.748822	+	0.662772i	$0.769380\pi$
$200$	−4.42616	−	2.46079i	−0.312977	−	0.174004i
$201$	8.56074	+	5.72010i	0.603828	+	0.403465i
$202$	−1.79697	+	8.78071i	−0.126434	+	0.617809i
$203$	9.47655	−	2.87468i	0.665123	−	0.201763i
$204$	0.430733	+	0.536810i	0.0301573	+	0.0375842i
$205$	12.1912	+	10.0050i	0.851469	+	0.698782i
$206$	3.63359	+	1.12415i	0.253164	+	0.0783230i
$207$	0.537605	−	1.29789i	0.0373661	−	0.0902098i
$208$	−17.5848	+	8.90650i	−1.21929	+	0.617555i
$209$	0.00154788	+	0.00373690i	0.000107069	+	0.000258487i
$210$	0.269478	+	2.89984i	0.0185957	+	0.200108i
$211$	−1.52653	−	15.4991i	−0.105091	−	1.06701i	−0.892645	−	0.450760i	$-0.851153\pi$
$211$	−1.52653	−	15.4991i	−0.105091	−	1.06701i	0.787554	−	0.616245i	$-0.211347\pi$
$212$	12.8477	−	1.12252i	0.882381	−	0.0770948i
$213$	6.00315	−	11.2311i	0.411329	−	0.769543i
$214$	12.3059	−	18.1991i	0.841216	−	1.24407i
$215$	0.714962	+	3.59436i	0.0487600	+	0.245133i
$216$	−1.12546	+	2.59487i	−0.0765776	+	0.176559i
$217$	−3.62713	−	0.721482i	−0.246226	−	0.0489774i
$218$	−0.0703483	+	12.7616i	−0.00476459	+	0.864327i
$219$	0.344326	−	3.49600i	0.0232674	−	0.236238i
$220$	−0.0841589	−	0.0860354i	−0.00567399	−	0.00580050i
$221$	−0.492276	+	1.62282i	−0.0331141	+	0.109163i
$222$	−2.88670	−	9.70852i	−0.193743	−	0.651593i
$223$	−3.10221	+	3.10221i	−0.207739	+	0.207739i	−0.803306	−	0.595567i	$-0.796928\pi$
$223$	−3.10221	+	3.10221i	−0.207739	+	0.207739i	0.595567	+	0.803306i	$0.296928\pi$
$224$	0.458778	+	6.48631i	0.0306534	+	0.433385i
$225$	−1.26606	−	1.26606i	−0.0844038	−	0.0844038i
$226$	3.77183	−	6.96398i	0.250898	−	0.463237i
$227$	12.2525	+	3.71677i	0.813230	+	0.246691i	0.669391	−	0.742910i	$-0.266555\pi$
$227$	12.2525	+	3.71677i	0.813230	+	0.246691i	0.143839	+	0.989601i	$0.454055\pi$
$228$	−0.0897051	−	0.223505i	−0.00594087	−	0.0148020i
$229$	−10.8661	−	1.07021i	−0.718050	−	0.0707218i	−0.267609	−	0.963528i	$-0.586233\pi$
$229$	−10.8661	−	1.07021i	−0.718050	−	0.0707218i	−0.450441	+	0.892806i	$0.648733\pi$
$230$	−2.50286	−	2.53061i	−0.165034	−	0.166863i
$231$	0.00753265	−	0.0378692i	0.000495612	−	0.00249161i
$232$	13.8708	−	20.0339i	0.910665	−	1.31529i
$233$	−11.6156	+	2.31049i	−0.760965	+	0.151365i	−0.560294	−	0.828294i	$-0.689312\pi$
$233$	−11.6156	+	2.31049i	−0.760965	+	0.151365i	−0.200670	+	0.979659i	$0.564312\pi$
$234$	−6.84263	+	1.32191i	−0.447317	+	0.0864163i
$235$	9.52515	+	5.09130i	0.621352	+	0.332120i
$236$	−0.0516500	−	0.0992470i	−0.00336213	−	0.00646043i
$237$	−12.0818	+	1.18995i	−0.784795	+	0.0772956i
$238$	0.430478	+	0.357273i	0.0279037	+	0.0231586i
$239$	−9.03654	+	3.74306i	−0.584525	+	0.242118i	−0.655293	−	0.755375i	$-0.727455\pi$
$239$	−9.03654	+	3.74306i	−0.584525	+	0.242118i	0.0707681	+	0.997493i	$0.477455\pi$
$240$	4.95422	+	5.17766i	0.319793	+	0.334216i
$241$	23.1115	+	9.57310i	1.48874	+	0.616657i	0.971043	−	0.238905i	$-0.0767885\pi$
$241$	23.1115	+	9.57310i	1.48874	+	0.616657i	0.517700	+	0.855562i	$0.326789\pi$
$242$	−7.25673	−	13.7583i	−0.466480	−	0.884416i
$243$	−0.634393	+	0.773010i	−0.0406963	+	0.0495886i
$244$	12.8498	−	3.74376i	0.822626	−	0.239670i
$245$	−2.95319	−	9.73535i	−0.188672	−	0.621969i
$246$	6.85945	+	10.3894i	0.437343	+	0.662405i
$247$	0.329681	−	0.493403i	0.0209771	−	0.0313945i
$248$	−8.09508	+	4.15629i	−0.514038	+	0.263924i
$249$	−3.77348	+	2.52136i	−0.239134	+	0.159784i
$250$	−15.9307	+	6.49606i	−1.00755	+	0.410847i
$251$	−11.7293	+	9.62599i	−0.740347	+	0.607587i	−0.927098	−	0.374820i	$-0.877704\pi$
$251$	−11.7293	+	9.62599i	−0.740347	+	0.607587i	0.186750	+	0.982407i	$0.440204\pi$
$252$	−0.473341	+	2.24973i	−0.0298177	+	0.141720i
$253$	0.0222442	+	0.0416159i	0.00139848	+	0.00261637i
$254$	1.79975	−	17.2952i	0.112926	−	1.08520i
$255$	0.616510			0.0386074
$256$	10.8039	+	11.8015i	0.675246	+	0.737592i
$257$	9.87366			0.615902			0.307951	−	0.951402i	$-0.400357\pi$
$257$	9.87366			0.615902			0.307951	+	0.951402i	$0.400357\pi$
$258$	−0.299425	+	2.87742i	−0.0186414	+	0.179140i
$259$	−3.88085	−	7.26056i	−0.241144	−	0.451149i
$260$	−3.63541	+	17.2786i	−0.225458	+	1.07158i
$261$	6.65954	−	5.46535i	0.412215	−	0.338297i
$262$	−21.7274	+	8.85980i	−1.34233	+	0.547360i
$263$	−21.8883	+	14.6253i	−1.34969	+	0.901835i	−0.999394	−	0.0348035i	$-0.988919\pi$
$263$	−21.8883	+	14.6253i	−1.34969	+	0.901835i	−0.350297	+	0.936639i	$0.613919\pi$
$264$	−0.0433938	−	0.0845170i	−0.00267071	−	0.00520166i
$265$	6.41808	−	9.60533i	0.394259	−	0.590051i
$266$	−0.107856	−	0.163361i	−0.00661310	−	0.0100163i
$267$	1.96624	+	6.48182i	0.120332	+	0.396681i
$268$	19.7698	−	5.75988i	1.20764	−	0.351841i
$269$	−11.9314	+	14.5384i	−0.727467	+	0.886422i	−0.997066	−	0.0765512i	$-0.975609\pi$
$269$	−11.9314	+	14.5384i	−0.727467	+	0.886422i	0.269598	+	0.962973i	$0.413109\pi$
$270$	1.18199	+	2.24097i	0.0719335	+	0.136381i
$271$	21.3762	+	8.85433i	1.29851	+	0.537862i	0.921512	−	0.388350i	$-0.126955\pi$
$271$	21.3762	+	8.85433i	1.29851	+	0.537862i	0.377002	+	0.926212i	$0.376955\pi$
$272$	1.37618	+	0.0303492i	0.0834430	+	0.00184019i
$273$	−5.23343	+	2.16776i	−0.316742	+	0.131199i
$274$	−5.37063	−	4.45734i	−0.324452	−	0.269277i
$275$	0.0598519	−	0.00589490i	0.00360921	−	0.000355476i
$276$	−1.29706	−	2.49235i	−0.0780741	−	0.150022i
$277$	6.12145	+	3.27198i	0.367802	+	0.196594i	0.644935	−	0.764237i	$-0.276884\pi$
$277$	6.12145	+	3.27198i	0.367802	+	0.196594i	−0.277133	+	0.960832i	$0.589384\pi$
$278$	−15.9561	+	3.08252i	−0.956981	+	0.184877i
$279$	−3.15542	+	0.627652i	−0.188910	+	0.0375766i
$280$	4.78886	+	3.31566i	0.286189	+	0.198149i
$281$	3.81188	−	19.1636i	0.227397	−	1.14320i	−0.683303	−	0.730135i	$-0.739457\pi$
$281$	3.81188	−	19.1636i	0.227397	−	1.14320i	0.910700	−	0.413069i	$-0.135543\pi$
$282$	5.99534	+	6.06181i	0.357018	+	0.360976i
$283$	−23.1433	−	2.27942i	−1.37573	−	0.135497i	−0.617029	−	0.786940i	$-0.711664\pi$
$283$	−23.1433	−	2.27942i	−1.37573	−	0.135497i	−0.758697	+	0.651443i	$0.774164\pi$
$284$	−9.48680	−	23.6369i	−0.562938	−	1.40259i
$285$	−0.206441	−	0.0626231i	−0.0122285	−	0.00370947i
$286$	0.111486	−	0.205839i	0.00659233	−	0.0121715i
$287$	7.15535	+	7.15535i	0.422367	+	0.422367i
$288$	2.52812	+	5.06049i	0.148971	+	0.298192i
$289$	−11.9371	+	11.9371i	−0.702181	+	0.702181i
$290$	−6.22082	−	20.9218i	−0.365299	−	1.22857i
$291$	−0.575534	+	1.89728i	−0.0337384	+	0.111221i
$292$	−4.91294	−	5.02248i	−0.287508	−	0.293918i
$293$	0.0892229	−	0.905896i	0.00521246	−	0.0529230i	−0.992227	−	0.124444i	$-0.960285\pi$
$293$	0.0892229	−	0.905896i	0.00521246	−	0.0529230i	0.997439	+	0.0715210i	$0.0227853\pi$
$294$	0.0442692	−	8.03073i	0.00258183	−	0.468361i
$295$	−0.0982939	−	0.0195519i	−0.00572289	−	0.00113835i
$296$	−18.5844	−	8.06051i	−1.08020	−	0.468508i
$297$	−0.00655302	−	0.0329443i	−0.000380245	−	0.00191162i
$298$	13.3233	−	19.7038i	0.771799	−	1.14141i
$299$	3.26343	−	6.10545i	0.188729	−	0.353088i
$300$	−3.56736	+	0.311685i	−0.205962	+	0.0179951i
$301$	0.230481	+	2.34011i	0.0132847	+	0.134882i
$302$	0.917586	+	9.87411i	0.0528011	+	0.568191i
$303$	2.42529	+	5.85517i	0.139329	+	0.336371i
$304$	−0.457735	−	0.149950i	−0.0262529	−	0.00860023i
$305$	4.58795	−	11.0763i	0.262705	−	0.634227i
$306$	0.464929	+	0.143838i	0.0265782	+	0.00822267i
$307$	−26.6876	−	21.9019i	−1.52314	−	1.25001i	−0.870310	−	0.492505i	$-0.836081\pi$
$307$	−26.6876	−	21.9019i	−1.52314	−	1.25001i	−0.652830	−	0.757504i	$-0.726419\pi$
$308$	−0.0483282	−	0.0602300i	−0.00275375	−	0.00343192i
$309$	2.57368	−	0.780717i	0.146411	−	0.0444134i
$310$	−1.63426	+	7.98564i	−0.0928195	+	0.453554i
$311$	−20.7522	−	13.8662i	−1.17675	−	0.786278i	−0.195818	−	0.980640i	$-0.562736\pi$
$311$	−20.7522	−	13.8662i	−1.17675	−	0.786278i	−0.980930	+	0.194363i	$0.937736\pi$
$312$	−6.77285	+	12.1822i	−0.383437	+	0.689678i
$313$	−3.40315	−	5.09317i	−0.192357	−	0.287883i	0.722737	−	0.691123i	$-0.242884\pi$
$313$	−3.40315	−	5.09317i	−0.192357	−	0.287883i	−0.915094	+	0.403240i	$0.867884\pi$
$314$	5.39257	−	12.8185i	0.304320	−	0.723389i
$315$	1.30643	+	1.59189i	0.0736088	+	0.0896926i
$316$	−13.7113	+	20.0385i	−0.771318	+	1.12725i
$317$	−22.3753	+	11.9598i	−1.25672	+	0.671731i	−0.959131	−	0.282963i	$-0.908683\pi$
$317$	−22.3753	+	11.9598i	−1.25672	+	0.671731i	−0.297590	+	0.954694i	$0.596183\pi$
$318$	7.08108	−	5.74627i	0.397087	−	0.322235i
$319$			0.289378i			0.0162020i
$320$	14.3018	−	0.932365i	0.799493	−	0.0521208i
$321$		−	15.5346i		−	0.867054i
$322$	−1.43903	−	1.77331i	−0.0801939	−	0.0988225i
$323$	−0.0365460	+	0.0195343i	−0.00203347	+	0.00108691i
$324$	0.368531	+	1.96575i	0.0204740	+	0.109208i
$325$	−5.59747	−	6.82053i	−0.310492	−	0.378335i
$326$	14.8053	+	6.22838i	0.819989	+	0.344958i
$327$	5.01345	+	7.50317i	0.277245	+	0.414926i
$328$	24.7355	+	2.84997i	1.36579	+	0.157364i
$329$	5.76201	+	3.85005i	0.317670	+	0.212260i
$330$	−0.0833743	−	0.0170625i	−0.00458961	−	0.000939259i
$331$	0.740861	−	0.224738i	0.0407214	−	0.0123527i	−0.269858	−	0.962900i	$-0.586977\pi$
$331$	0.740861	−	0.224738i	0.0407214	−	0.0123527i	0.310580	+	0.950547i	$0.399477\pi$
$332$	−0.989197	+	9.02258i	−0.0542892	+	0.495178i
$333$	−5.53630	−	4.54352i	−0.303387	−	0.248983i
$334$	4.05044	−	13.0923i	0.221630	−	0.716377i
$335$	7.05870	−	17.0412i	0.385658	−	0.931061i
$336$	2.83785	+	3.61773i	0.154817	+	0.197363i
$337$	13.2047	+	31.8791i	0.719309	+	1.73656i	0.675311	+	0.737533i	$0.264009\pi$
$337$	13.2047	+	31.8791i	0.719309	+	1.73656i	0.0439972	+	0.999032i	$0.485991\pi$
$338$	−15.8903	+	1.47666i	−0.864317	+	0.0803196i
$339$	−0.548912	−	5.57320i	−0.0298128	−	0.302695i
$340$	0.792680	−	0.944456i	0.0429891	−	0.0512203i
$341$	0.0509420	−	0.0953058i	0.00275866	−	0.00516110i
$342$	−0.141073	−	0.0953907i	−0.00762833	−	0.00515814i
$343$	−2.84325	−	14.2940i	−0.153521	−	0.771803i
$344$	4.02304	+	4.15835i	0.216908	+	0.224203i
$345$	−2.46841	−	0.490998i	−0.132895	−	0.0264344i
$346$	25.8188	+	0.142326i	1.38803	+	0.00765148i
$347$	−0.718158	+	7.29158i	−0.0385527	+	0.391432i	0.956474	+	0.291819i	$0.0942605\pi$
$347$	−0.718158	+	7.29158i	−0.0385527	+	0.391432i	−0.995026	+	0.0996132i	$0.968239\pi$
$348$	0.189956	−	17.2291i	0.0101827	−	0.923577i
$349$	1.40214	−	4.62223i	0.0750547	−	0.247422i	−0.911383	−	0.411560i	$-0.864984\pi$
$349$	1.40214	−	4.62223i	0.0750547	−	0.247422i	0.986437	+	0.164138i	$0.0524841\pi$
$350$	−2.78993	+	0.829549i	−0.149128	+	0.0443413i
$351$	−3.48458	+	3.48458i	−0.185993	+	0.185993i
$352$	−0.185269	−	0.0421913i	−0.00987485	−	0.00224880i
$353$	−10.7039	−	10.7039i	−0.569711	−	0.569711i	0.362337	−	0.932047i	$-0.381979\pi$
$353$	−10.7039	−	10.7039i	−0.569711	−	0.569711i	−0.932047	+	0.362337i	$0.881979\pi$
$354$	−0.0695647	−	0.0376776i	−0.00369732	−	0.00200254i
$355$	−21.8322	−	6.62273i	−1.15873	−	0.351498i
$356$	12.4578	+	5.32187i	0.660265	+	0.282058i
$357$	0.393668	+	0.0387729i	0.0208351	+	0.00205208i
$358$	−2.87444	+	2.84292i	−0.151919	+	0.150253i
$359$	−2.02227	+	10.1666i	−0.106731	+	0.536574i	0.890012	+	0.455937i	$0.150696\pi$
$359$	−2.02227	+	10.1666i	−0.106731	+	0.536574i	−0.996743	+	0.0806375i	$0.974304\pi$
$360$	4.95278	+	1.07060i	0.261034	+	0.0564258i
$361$	−18.6207	+	3.70389i	−0.980037	+	0.194941i
$362$	−6.61329	−	34.2324i	−0.347587	−	1.79921i
$363$	−9.70014	−	5.18483i	−0.509125	−	0.272133i
$364$	−3.40803	+	10.8045i	−0.178629	+	0.566310i
$365$	−6.26313	+	0.616865i	−0.327827	+	0.0322882i
$366$	6.04412	−	7.28255i	0.315931	−	0.380665i
$367$	−23.0002	+	9.52700i	−1.20060	+	0.497305i	−0.891193	−	0.453624i	$-0.850131\pi$
$367$	−23.0002	+	9.52700i	−1.20060	+	0.497305i	−0.309408	+	0.950929i	$0.600131\pi$
$368$	−5.48583	−	1.21752i	−0.285969	−	0.0634677i
$369$	8.13308	+	3.36883i	0.423391	+	0.175374i
$370$	−16.0498	+	8.46539i	−0.834391	+	0.440095i
$371$	4.70230	−	5.72977i	0.244131	−	0.297475i
$372$	−3.09557	+	5.64092i	−0.160498	+	0.292468i
$373$	−6.05758	−	19.9692i	−0.313650	−	1.03396i	−0.962098	−	0.272706i	$-0.912082\pi$
$373$	−6.05758	−	19.9692i	−0.313650	−	1.03396i	0.648448	−	0.761259i	$-0.275418\pi$
$374$	−0.0136420	+	0.00900691i	−0.000705410	+	0.000465736i
$375$	−6.75864	+	10.1150i	−0.349015	+	0.522338i
$376$	16.9949	−	1.39051i	0.876443	−	0.0717100i
$377$	35.2997	−	23.5865i	1.81802	−	1.21477i
$378$	0.613812	+	1.50529i	0.0315711	+	0.0774238i
$379$	22.7931	−	18.7058i	1.17080	−	0.960852i	0.171099	−	0.985254i	$-0.445268\pi$
$379$	22.7931	−	18.7058i	1.17080	−	0.960852i	0.999702	+	0.0244022i	$0.00776822\pi$
$380$	−0.361367	+	0.235737i	−0.0185377	+	0.0120930i
$381$	−5.79610	−	10.8437i	−0.296943	−	0.555542i
$382$	−10.9005	−	1.13431i	−0.557720	−	0.0580365i
$383$	−28.4979			−1.45617			−0.728087	−	0.685485i	$-0.759590\pi$
$383$	−28.4979			−1.45617			−0.728087	+	0.685485i	$0.759590\pi$
$384$	11.0029	+	2.63362i	0.561490	+	0.134396i
$385$	−0.0691724			−0.00352535
$386$	32.8813	+	3.42164i	1.67361	+	0.174157i
$387$	0.964303	+	1.80408i	0.0490183	+	0.0917067i
$388$	2.16653	+	3.32112i	0.109989	+	0.168604i
$389$	4.60517	−	3.77937i	0.233491	−	0.191621i	−0.510371	−	0.859954i	$-0.670492\pi$
$389$	4.60517	−	3.77937i	0.233491	−	0.191621i	0.743862	+	0.668333i	$0.232992\pi$
$390$	4.71427	+	11.5611i	0.238717	+	0.585420i
$391$	−0.401966	+	0.268585i	−0.0203283	+	0.0135829i
$392$	−12.2457	−	10.3934i	−0.618499	−	0.524944i
$393$	−9.21792	+	13.7956i	−0.464983	+	0.695896i
$394$	17.2196	−	11.3689i	0.867508	−	0.572759i
$395$	6.31352	+	20.8129i	0.317668	+	1.04721i
$396$	−0.0588942	−	0.0323194i	−0.00295954	−	0.00162411i
$397$	20.0022	−	24.3728i	1.00388	−	1.22324i	0.0292174	−	0.999573i	$-0.490698\pi$
$397$	20.0022	−	24.3728i	1.00388	−	1.22324i	0.974667	−	0.223663i	$-0.0718015\pi$
$398$	4.76619	−	2.51390i	0.238908	−	0.126011i
$399$	−0.127883	−	0.0529708i	−0.00640214	−	0.00265185i
$400$	−4.10926	+	5.86573i	−0.205463	+	0.293286i
$401$	14.2438	−	5.89997i	0.711301	−	0.294631i	0.00245841	−	0.999997i	$-0.499217\pi$
$401$	14.2438	−	5.89997i	0.711301	−	0.294631i	0.708843	+	0.705366i	$0.249217\pi$
$402$	9.29906	−	11.2044i	0.463795	−	0.558826i
$403$	−15.7780	+	1.55400i	−0.785958	+	0.0774101i
$404$	12.0881	+	3.81291i	0.601405	+	0.189699i
$405$	1.57997	+	0.844514i	0.0785096	+	0.0419642i
$406$	−2.65646	−	13.7507i	−0.131838	−	0.682434i
$407$	0.235947	−	0.0469327i	0.0116954	−	0.00232637i
$408$	0.818135	−	0.527302i	0.0405037	−	0.0261053i
$409$	1.48731	−	7.47724i	0.0735430	−	0.369726i	−0.926434	−	0.376456i	$-0.877142\pi$
$409$	1.48731	−	7.47724i	0.0735430	−	0.369726i	0.999977	+	0.00673080i	$0.00214250\pi$
$410$	15.8577	−	15.6839i	0.783158	−	0.774571i
$411$	−4.91139	−	0.483730i	−0.242261	−	0.0238606i
$412$	2.11311	−	4.94653i	0.104105	−	0.243698i
$413$	−0.0615352	−	0.0186665i	−0.00302795	−	0.000918518i
$414$	−1.74695	−	0.946181i	−0.0858578	−	0.0465023i
$415$	5.74911	+	5.74911i	0.282213	+	0.282213i
$416$	9.95410	+	26.0388i	0.488040	+	1.27666i
$417$	−8.12555	+	8.12555i	−0.397910	+	0.397910i
$418$	0.00548296	−	0.00163029i	0.000268180	−	7.97400e-5i
$419$	−3.67114	+	12.1021i	−0.179347	+	0.591228i	0.820462	+	0.571701i	$0.193716\pi$
$419$	−3.67114	+	12.1021i	−0.179347	+	0.591228i	−0.999809	+	0.0195273i	$0.993784\pi$
$420$	4.11842	+	0.0454067i	0.200958	+	0.00221562i
$421$	−1.64601	+	16.7122i	−0.0802217	+	0.814505i	0.867930	+	0.496687i	$0.165450\pi$
$421$	−1.64601	+	16.7122i	−0.0802217	+	0.814505i	−0.948152	+	0.317818i	$0.897050\pi$
$422$	−22.0248	−	0.121411i	−1.07215	−	0.00591022i
$423$	5.91283	+	1.17613i	0.287492	+	0.0571856i
$424$	0.301602	−	18.2361i	0.0146471	−	0.885622i
$425$	0.120205	+	0.604313i	0.00583082	+	0.0293135i
$426$	−14.9192	−	10.0881i	−0.722837	−	0.488769i
$427$	3.62620	−	6.78414i	0.175484	−	0.328308i
$428$	−23.7980	−	19.9736i	−1.15032	−	0.965461i
$429$	−0.0162246	−	0.164731i	−0.000783329	−	0.00795327i
$430$	5.16054	−	0.479561i	0.248863	−	0.0231265i
$431$	−7.98291	−	19.2724i	−0.384523	−	0.928321i	−0.991078	−	0.133280i	$-0.957449\pi$
$431$	−7.98291	−	19.2724i	−0.384523	−	0.928321i	0.606555	−	0.795041i	$-0.292551\pi$
$432$	3.48525	+	1.96291i	0.167684	+	0.0944404i
$433$	−5.56598	+	13.4375i	−0.267484	+	0.645764i	−0.999364	−	0.0356703i	$-0.988643\pi$
$433$	−5.56598	+	13.4375i	−0.267484	+	0.645764i	0.731879	+	0.681434i	$0.238643\pi$
$434$	−1.54576	+	4.99639i	−0.0741991	+	0.239834i
$435$	−11.9307	−	9.79125i	−0.572032	−	0.469455i
$436$	17.9405	+	1.96692i	0.859192	+	0.0941982i
$437$	0.161882	−	0.0491064i	0.00774386	−	0.00234908i
$438$	−4.86714	−	0.996056i	−0.232561	−	0.0475934i
$439$	−21.5367	−	14.3903i	−1.02789	−	0.686814i	−0.0772180	−	0.997014i	$-0.524604\pi$
$439$	−21.5367	−	14.3903i	−1.02789	−	0.686814i	−0.950671	+	0.310201i	$0.899604\pi$
$440$	−0.133338	+	0.105786i	−0.00635662	+	0.00504316i
$441$	−3.15490	−	4.72164i	−0.150233	−	0.224840i
$442$	2.21063	+	0.929982i	0.105149	+	0.0442347i
$443$	20.0917	+	24.4817i	0.954583	+	1.16316i	0.986515	+	0.163673i	$0.0523341\pi$
$443$	20.0917	+	24.4817i	0.954583	+	1.16316i	−0.0319316	+	0.999490i	$0.510166\pi$
$444$	−14.0787	+	2.63942i	−0.668146	+	0.125261i
$445$	10.7019	−	5.72030i	0.507320	−	0.271168i
$446$	3.90954	+	4.81770i	0.185122	+	0.228125i
$447$		−	16.8189i		−	0.795505i
$448$	9.19091	+	0.304096i	0.434230	+	0.0143672i
$449$			26.0602i			1.22986i	0.788583	+	0.614928i	$0.210815\pi$
$449$			26.0602i			1.22986i	−0.788583	+	0.614928i	$0.789185\pi$
$450$	−1.96618	+	1.59554i	−0.0926864	+	0.0752146i
$451$	−0.260781	+	0.139390i	−0.0122797	+	0.00656363i
$452$	−9.24356	−	6.32486i	−0.434781	−	0.297496i
$453$	4.44845	+	5.42045i	0.209006	+	0.254675i
$454$	7.02152	−	16.6906i	0.329536	−	0.783330i
$455$	5.63807	+	8.43797i	0.264317	+	0.395578i
$456$	−0.327517	+	0.0934656i	−0.0153374	+	0.00437693i
$457$	0.191156	+	0.127726i	0.00894189	+	0.00597478i	0.560033	−	0.828470i	$-0.310788\pi$
$457$	0.191156	+	0.127726i	0.00894189	+	0.00597478i	−0.551091	+	0.834445i	$0.685788\pi$
$458$	−3.09588	+	15.1278i	−0.144661	+	0.706874i
$459$	0.329310	−	0.0998951i	0.0153709	−	0.00466270i
$460$	−3.92595	+	3.15015i	−0.183048	+	0.146877i
$461$	21.3981	+	17.5610i	0.996611	+	0.817898i	0.983296	−	0.182014i	$-0.0582616\pi$
$461$	21.3981	+	17.5610i	0.996611	+	0.817898i	0.0133151	+	0.999911i	$0.495762\pi$
$462$	−0.0521649	−	0.0161386i	−0.00242693	−	0.000750836i
$463$	14.2306	−	34.3557i	0.661352	−	1.59665i	−0.134334	−	0.990936i	$-0.542889\pi$
$463$	14.2306	−	34.3557i	0.661352	−	1.59665i	0.795686	−	0.605709i	$-0.207111\pi$
$464$	−26.1497	−	22.4434i	−1.21397	−	1.04191i
$465$	2.20569	+	5.32499i	0.102286	+	0.246941i
$466$	1.54976	+	16.6769i	0.0717914	+	0.772544i
$467$	3.08850	+	31.3581i	0.142919	+	1.45108i	0.752623	+	0.658451i	$0.228788\pi$
$467$	3.08850	+	31.3581i	0.142919	+	1.45108i	−0.609705	+	0.792629i	$0.708712\pi$
$468$	0.857851	+	9.81846i	0.0396542	+	0.453859i
$469$	5.57901	−	10.4376i	0.257615	−	0.481964i
$470$	8.55574	−	12.6530i	0.394647	−	0.583640i
$471$	−1.91841	−	9.64450i	−0.0883957	−	0.444395i
$472$	−0.147163	+	0.0581248i	−0.00677372	+	0.00267541i
$473$	−0.0673918	−	0.0134051i	−0.00309868	−	0.000616365i
$474$	−0.0946417	+	17.1686i	−0.00434704	+	0.788581i
$475$	0.0211330	−	0.214567i	0.000969647	−	0.00984499i
$476$	0.565558	−	0.553223i	0.0259223	−	0.0253569i
$477$	1.87184	−	6.17064i	0.0857059	−	0.282534i
$478$	3.94234	+	13.2588i	0.180319	+	0.606445i
$479$	−18.4958	+	18.4958i	−0.845095	+	0.845095i	−0.989516	−	0.144422i	$-0.953868\pi$
$479$	−18.4958	+	18.4958i	−0.845095	+	0.845095i	0.144422	+	0.989516i	$0.453868\pi$
$480$	8.00815	−	6.21082i	0.365520	−	0.283484i
$481$	−24.9565	−	24.9565i	−1.13792	−	1.13792i
$482$	16.8486	−	31.1078i	0.767433	−	1.41692i
$483$	−1.54531	−	0.468763i	−0.0703138	−	0.0213295i
$484$	−20.4148	+	8.19360i	−0.927947	+	0.372437i
$485$	3.53485	+	0.348153i	0.160509	+	0.0158088i
$486$	0.994472	+	1.00550i	0.0451102	+	0.0456103i
$487$	−3.68367	+	18.5191i	−0.166923	+	0.839180i	0.803039	+	0.595926i	$0.203215\pi$
$487$	−3.68367	+	18.5191i	−0.166923	+	0.839180i	−0.969963	+	0.243254i	$0.921785\pi$
$488$	−3.38517	−	18.6228i	−0.153239	−	0.843014i
$489$	11.1393	−	2.21575i	0.503739	−	0.100200i
$490$	−14.1262	+	2.72901i	−0.638156	+	0.123284i
$491$	22.8861	+	12.2329i	1.03284	+	0.552062i	0.898546	−	0.438880i	$-0.144625\pi$
$491$	22.8861	+	12.2329i	1.03284	+	0.552062i	0.134290	+	0.990942i	$0.457125\pi$
$492$	15.6180	−	8.12790i	0.704113	−	0.366434i
$493$	−2.95041	+	0.290590i	−0.132880	+	0.0130875i
$494$	−0.645773	−	0.535956i	−0.0290547	−	0.0241138i
$495$	−0.0555958	+	0.0230285i	−0.00249884	+	0.00103506i
$496$	4.66140	+	11.9951i	0.209303	+	0.538594i
$497$	−13.5243	−	5.60194i	−0.606647	−	0.251281i
$498$	2.99425	+	5.67690i	0.134176	+	0.254388i
$499$	−14.6295	+	17.8261i	−0.654907	+	0.798007i	−0.989527	−	0.144347i	$-0.953892\pi$
$499$	−14.6295	+	17.8261i	−0.654907	+	0.798007i	0.334620	+	0.942353i	$0.391392\pi$
$500$	6.80565	+	23.3593i	0.304358	+	1.04466i
$501$	−2.81302	−	9.27328i	−0.125676	−	0.414300i
$502$	11.8232	+	17.9076i	0.527697	+	0.799257i
$503$	5.79686	−	8.67561i	0.258469	−	0.386826i	−0.679427	−	0.733743i	$-0.737771\pi$
$503$	5.79686	−	8.67561i	0.258469	−	0.386826i	0.937896	+	0.346917i	$0.112771\pi$
$504$	3.09523	+	0.995110i	0.137872	+	0.0443257i
$505$	9.44041	−	6.30788i	0.420093	−	0.280697i
$506$	0.0617936	−	0.0251976i	0.00274706	−	0.00112017i
$507$	−8.72306	+	7.15883i	−0.387405	+	0.317935i
$508$	−24.0643	−	5.06311i	−1.06768	−	0.224639i
$509$	−8.98691	−	16.8133i	−0.398338	−	0.745238i	0.600168	−	0.799874i	$-0.295100\pi$
$509$	−8.98691	−	16.8133i	−0.398338	−	0.745238i	−0.998506	+	0.0546358i	$0.982600\pi$
$510$	0.0902406	−	0.867195i	0.00399592	−	0.0384000i
$511$	−4.03807			−0.178634
$512$	18.1816	−	13.4696i	0.803520	−	0.595278i
$513$	−0.120418			−0.00531657
$514$	1.44524	−	13.8885i	0.0637468	−	0.612594i
$515$	−2.27131	−	4.24932i	−0.100086	−	0.187247i
$516$	4.00360	+	0.842354i	0.176249	+	0.0370826i
$517$	−0.156535	+	0.128465i	−0.00688442	+	0.00564990i
$518$	−10.7809	+	4.39612i	−0.473685	+	0.193154i
$519$	15.1801	−	10.1430i	0.666332	−	0.445229i
$520$	23.7723	+	7.64276i	1.04248	+	0.335157i
$521$	−15.8239	+	23.6822i	−0.693258	+	1.03753i	0.303157	+	0.952941i	$0.401959\pi$
$521$	−15.8239	+	23.6822i	−0.693258	+	1.03753i	−0.996416	+	0.0845937i	$0.973041\pi$
$522$	−6.71288	−	10.1674i	−0.293815	−	0.445016i
$523$	0.582836	+	1.92135i	0.0254856	+	0.0840149i	0.968761	−	0.247997i	$-0.0797724\pi$
$523$	0.582836	+	1.92135i	0.0254856	+	0.0840149i	−0.943275	+	0.332012i	$0.892272\pi$
$524$	9.28204	+	31.8590i	0.405488	+	1.39177i
$525$	−1.30567	+	1.59096i	−0.0569841	+	0.0694353i
$526$	17.3684	+	32.9293i	0.757296	+	1.43578i
$527$	1.02287	+	0.423685i	0.0445567	+	0.0184560i
$528$	−0.125235	+	0.0486675i	−0.00545014	+	0.00211798i
$529$	−19.4259	+	8.04648i	−0.844605	+	0.349847i
$530$	−12.5716	−	10.4338i	−0.546076	−	0.453213i
$531$	−0.0556719	+	0.00548320i	−0.00241595	+	0.000237951i
$532$	−0.245574	+	0.127801i	−0.0106470	+	0.00554088i
$533$	38.2591	+	20.4499i	1.65718	+	0.885784i
$534$	9.40525	−	1.81698i	0.407005	−	0.0786285i
$535$	−27.2956	+	5.42944i	−1.18009	+	0.234735i
$536$	−5.20818	−	28.6517i	−0.224959	−	1.23757i
$537$	−0.557709	+	2.80379i	−0.0240669	+	0.120993i
$538$	18.7035	+	18.9109i	0.806367	+	0.815306i
$539$	0.189826	+	0.0186962i	0.00817639	+	0.000805304i
$540$	3.32520	−	1.33459i	0.143094	−	0.0574315i
$541$	16.7944	+	5.09454i	0.722049	+	0.219031i	0.629858	−	0.776710i	$-0.283113\pi$
$541$	16.7944	+	5.09454i	0.722049	+	0.219031i	0.0921909	+	0.995741i	$0.470613\pi$
$542$	15.5836	−	28.7722i	0.669372	−	1.23587i
$543$	−17.4327	−	17.4327i	−0.748108	−	0.748108i
$544$	0.244125	−	1.93131i	0.0104668	−	0.0828044i
$545$	11.4315	−	11.4315i	0.489672	−	0.489672i
$546$	2.28317	+	7.67874i	0.0977108	+	0.328620i
$547$	−12.8042	+	42.2098i	−0.547468	+	1.80476i	0.0447703	+	0.998997i	$0.485744\pi$
$547$	−12.8042	+	42.2098i	−0.547468	+	1.80476i	−0.592238	+	0.805763i	$0.701756\pi$
$548$	−7.05589	+	6.90200i	−0.301413	+	0.294839i
$549$	0.655935	−	6.65982i	0.0279946	−	0.284234i
$550$	0.000468845	−	0.0850516i	1.99916e−5	−	0.00362661i
$551$	1.01747	+	0.202388i	0.0433459	+	0.00862203i
$552$	−3.69564	+	1.45966i	−0.157297	+	0.0621273i
$553$	2.72251	+	13.6870i	0.115773	+	0.582029i
$554$	5.49845	−	8.13161i	0.233607	−	0.345479i
$555$	−6.04841	+	11.3158i	−0.256741	+	0.480328i
$556$	2.00039	+	22.8953i	0.0848354	+	0.970977i
$557$	0.675085	+	6.85425i	0.0286043	+	0.290424i	0.998836	+	0.0482438i	$0.0153625\pi$
$557$	0.675085	+	6.85425i	0.0286043	+	0.290424i	−0.970231	+	0.242180i	$0.922138\pi$
$558$	0.420998	+	4.53035i	0.0178223	+	0.191785i
$559$	3.85773	+	9.31337i	0.163164	+	0.393914i
$560$	5.36483	−	6.25078i	0.226705	−	0.264144i
$561$	−0.00442350	+	0.0106793i	−0.000186760	+	0.000450879i
$562$	−26.3979	−	8.16689i	−1.11353	−	0.344499i
$563$	−8.72134	−	7.15742i	−0.367561	−	0.301649i	0.432423	−	0.901671i	$-0.357659\pi$
$563$	−8.72134	−	7.15742i	−0.367561	−	0.301649i	−0.799984	+	0.600021i	$0.795159\pi$
$564$	9.40421	−	7.54587i	0.395989	−	0.317739i
$565$	−9.60077	+	2.91236i	−0.403907	+	0.122524i
$566$	−6.59383	+	32.2201i	−0.277159	+	1.35431i
$567$	0.955768	+	0.638624i	0.0401385	+	0.0268197i
$568$	−34.6367	+	9.88449i	−1.45332	+	0.414744i
$569$	9.07969	+	13.5887i	0.380641	+	0.569669i	0.971480	−	0.237120i	$-0.0762035\pi$
$569$	9.07969	+	13.5887i	0.380641	+	0.569669i	−0.590840	+	0.806789i	$0.701203\pi$
$570$	−0.118304	+	0.281217i	−0.00495522	+	0.0117789i
$571$	17.9943	+	21.9262i	0.753039	+	0.917581i	0.998658	−	0.0517854i	$-0.0164912\pi$
$571$	17.9943	+	21.9262i	0.753039	+	0.917581i	−0.245619	+	0.969366i	$0.578991\pi$
$572$	−0.273218	−	0.186948i	−0.0114238	−	0.00781669i
$573$	−6.83441	+	3.65307i	−0.285512	+	0.152609i
$574$	11.1122	−	9.01750i	0.463814	−	0.376383i
$575$		−	2.51531i		−	0.104896i
$576$	7.48823	−	2.81538i	0.312010	−	0.117308i
$577$			11.7257i			0.488149i	0.969756	+	0.244075i	$0.0784842\pi$
$577$			11.7257i			0.488149i	−0.969756	+	0.244075i	$0.921516\pi$
$578$	15.0436	+	18.5382i	0.625733	+	0.771087i
$579$	20.6159	−	11.0194i	0.856768	−	0.457952i
$580$	−30.3395	+	5.68793i	−1.25978	+	0.236178i
$581$	3.30948	+	4.03261i	0.137300	+	0.167301i
$582$	2.58451	+	1.08727i	0.107131	+	0.0450687i
$583$	0.120335	+	0.180094i	0.00498375	+	0.00745871i
$584$	−7.78384	+	6.17547i	−0.322097	+	0.255543i
$585$	7.34060	+	4.90483i	0.303497	+	0.202790i
$586$	−1.26119	−	0.258101i	−0.0520993	−	0.0106621i
$587$	27.7541	−	8.41912i	1.14554	−	0.347494i	0.340223	−	0.940345i	$-0.389498\pi$
$587$	27.7541	−	8.41912i	1.14554	−	0.347494i	0.805312	+	0.592851i	$0.201998\pi$
$588$	−11.2897	−	1.23775i	−0.465579	−	0.0510441i
$589$	−0.299474	−	0.245772i	−0.0123396	−	0.0101269i
$590$	−0.0418896	+	0.135400i	−0.00172457	+	0.00557433i
$591$	5.58354	−	13.4799i	0.229676	−	0.554488i
$592$	−14.0583	+	24.9614i	−0.577794	+	1.02591i
$593$	5.62069	+	13.5695i	0.230814	+	0.557234i	0.996274	−	0.0862496i	$-0.0274883\pi$
$593$	5.62069	+	13.5695i	0.230814	+	0.557234i	−0.765459	+	0.643484i	$0.777488\pi$
$594$	−0.0472992	+	0.00439544i	−0.00194071	+	0.000180347i
$595$	−0.0694622	−	0.705262i	−0.00284767	−	0.0289129i
$596$	−25.7655	−	21.6249i	−1.05540	−	0.885791i
$597$	1.79615	−	3.36036i	0.0735114	−	0.137530i
$598$	−8.11036	−	5.48408i	−0.331657	−	0.224261i
$599$	−3.02971	−	15.2314i	−0.123791	−	0.622337i	−0.992010	−	0.126157i	$-0.959736\pi$
$599$	−3.02971	−	15.2314i	−0.123791	−	0.622337i	0.868220	−	0.496180i	$-0.165264\pi$
$600$	−0.0837447	+	5.06353i	−0.00341886	+	0.206718i
$601$	−21.1620	−	4.20938i	−0.863216	−	0.171704i	−0.256423	−	0.966565i	$-0.582544\pi$
$601$	−21.1620	−	4.20938i	−0.863216	−	0.171704i	−0.606792	+	0.794860i	$0.707544\pi$
$602$	3.32538	+	0.0183311i	0.135532	+	0.000747120i
$603$	1.00918	−	10.2463i	0.0410968	−	0.417263i
$604$	14.0234	+	0.154612i	0.570604	+	0.00629108i
$605$	−5.71996	+	18.8562i	−0.232549	+	0.766612i
$606$	8.59098	−	2.55442i	0.348985	−	0.103766i
$607$	−9.72985	+	9.72985i	−0.394922	+	0.394922i	−0.876438	−	0.481515i	$-0.840087\pi$
$607$	−9.72985	+	9.72985i	−0.394922	+	0.394922i	0.481515	+	0.876438i	$0.340087\pi$
$608$	−0.277923	+	0.621910i	−0.0112713	+	0.0252218i
$609$	−7.00246	−	7.00246i	−0.283754	−	0.283754i
$610$	−14.9086	−	8.07477i	−0.603630	−	0.326938i
$611$	28.4296	+	8.62403i	1.15014	+	0.348891i
$612$	0.270378	−	0.632923i	0.0109294	−	0.0255844i
$613$	−21.5727	−	2.12472i	−0.871312	−	0.0858167i	−0.347530	−	0.937669i	$-0.612979\pi$
$613$	−21.5727	−	2.12472i	−0.871312	−	0.0858167i	−0.523782	+	0.851852i	$0.675479\pi$
$614$	−34.7140	+	34.3334i	−1.40094	+	1.38558i
$615$	3.07678	−	15.4680i	0.124068	−	0.623730i
$616$	−0.0917946	+	0.0591632i	−0.00369851	+	0.00238375i
$617$	−17.1713	+	3.41559i	−0.691293	+	0.137507i	−0.528220	−	0.849107i	$-0.677140\pi$
$617$	−17.1713	+	3.41559i	−0.691293	+	0.137507i	−0.163072	+	0.986614i	$0.552140\pi$
$618$	−0.721453	−	3.73446i	−0.0290211	−	0.150222i
$619$	11.0818	+	5.92332i	0.445413	+	0.238078i	0.678826	−	0.734299i	$-0.262489\pi$
$619$	11.0818	+	5.92332i	0.445413	+	0.238078i	−0.233412	+	0.972378i	$0.574989\pi$
$620$	10.9935	+	3.46766i	0.441511	+	0.139264i
$621$	−1.39806	+	0.137697i	−0.0561024	+	0.00552560i
$622$	−22.5420	+	27.1607i	−0.903850	+	1.08905i
$623$	7.19339	−	2.97960i	0.288197	−	0.119375i
$624$	16.1443	+	11.3099i	0.646288	+	0.452760i
$625$	11.8643	+	4.91435i	0.474572	+	0.196574i
$626$	−7.66228	+	4.04143i	−0.306246	+	0.161528i
$627$	0.00256599	−	0.00312667i	0.000102476	−	0.000124867i
$628$	−17.2414	−	9.46157i	−0.688006	−	0.377558i
$629$	0.715448	+	2.35852i	0.0285268	+	0.0940402i
$630$	2.43040	−	1.60463i	0.0968295	−	0.0639302i
$631$	16.8449	−	25.2102i	0.670587	−	1.00360i	−0.327682	−	0.944788i	$-0.606267\pi$
$631$	16.8449	−	25.2102i	0.670587	−	1.00360i	0.998269	−	0.0588160i	$-0.0187325\pi$
$632$	26.1796	+	22.2196i	1.04137	+	0.883848i
$633$	−12.9494	+	8.65253i	−0.514693	+	0.343907i
$634$	13.5478	+	33.2241i	0.538051	+	1.31950i
$635$	−17.0277	+	13.9742i	−0.675722	+	0.554551i
$636$	−7.04632	−	10.8015i	−0.279405	−	0.428307i
$637$	−13.1916	−	24.6798i	−0.522671	−	0.977848i
$638$	0.407044	+	0.0423572i	0.0161150	+	0.00167694i
$639$	−12.7348			−0.503782
$640$	0.781913	−	20.2536i	0.0309078	−	0.800593i
$641$	−16.6311			−0.656891			−0.328445	−	0.944523i	$-0.606525\pi$
$641$	−16.6311			−0.656891			−0.328445	+	0.944523i	$0.606525\pi$
$642$	−21.8512	−	2.27384i	−0.862398	−	0.0897414i
$643$	18.3837	+	34.3934i	0.724981	+	1.35634i	0.926288	+	0.376816i	$0.122981\pi$
$643$	18.3837	+	34.3934i	0.724981	+	1.35634i	−0.201307	+	0.979528i	$0.564519\pi$
$644$	−2.70500	+	1.76460i	−0.106592	+	0.0695350i
$645$	2.83291	−	2.32491i	0.111546	−	0.0915432i
$646$	0.0221279	+	0.0542656i	0.000870610	+	0.00213505i
$647$	−21.1428	+	14.1272i	−0.831210	+	0.555397i	−0.896793	−	0.442450i	$-0.854109\pi$
$647$	−21.1428	+	14.1272i	−0.831210	+	0.555397i	0.0655829	+	0.997847i	$0.479109\pi$
$648$	2.81901	−	0.230649i	0.110741	−	0.00906076i
$649$	0.00104394	−	0.00156237i	4.09784e−5	−	6.13285e-5i
$650$	−10.4132	+	6.87516i	−0.408440	+	0.269666i
$651$	1.07353	+	3.53895i	0.0420749	+	0.138702i
$652$	10.9281	−	19.9137i	0.427976	−	0.779881i
$653$	18.9973	−	23.1482i	0.743420	−	0.905860i	−0.254708	−	0.967018i	$-0.581979\pi$
$653$	18.9973	−	23.1482i	0.743420	−	0.905860i	0.998128	+	0.0611578i	$0.0194793\pi$
$654$	11.2879	−	5.95375i	0.441393	−	0.232810i
$655$	27.4619	+	11.3751i	1.07302	+	0.444461i
$656$	7.62945	−	34.3763i	0.297880	−	1.34217i
$657$	−3.24551	+	1.34433i	−0.126619	+	0.0524475i
$658$	6.25896	−	7.54140i	0.244000	−	0.293995i
$659$	47.8799	−	4.71576i	1.86513	−	0.183700i	0.898348	−	0.439284i	$-0.144768\pi$
$659$	47.8799	−	4.71576i	1.86513	−	0.183700i	0.966787	+	0.255584i	$0.0822679\pi$
$660$	−0.0362042	+	0.114778i	−0.00140925	+	0.00446774i
$661$	−8.97187	−	4.79557i	−0.348965	−	0.186526i	0.287596	−	0.957752i	$-0.407144\pi$
$661$	−8.97187	−	4.79557i	−0.348965	−	0.186526i	−0.636562	+	0.771226i	$0.719644\pi$
$662$	−0.207678	−	1.07500i	−0.00807163	−	0.0417812i
$663$	1.66325	−	0.330842i	0.0645955	−	0.0128488i
$664$	12.5465	+	2.71209i	0.486900	+	0.105249i
$665$	−0.0483785	+	0.243215i	−0.00187604	+	0.00943148i
$666$	−7.20137	+	7.12241i	−0.279047	+	0.275988i
$667$	12.0444	+	1.18627i	0.466362	+	0.0459327i
$668$	−17.8230	−	7.61378i	−0.689591	−	0.294586i
$669$	4.19827	+	1.27353i	0.162315	+	0.0492376i
$670$	−22.9373	−	12.4233i	−0.886144	−	0.479953i
$671$	0.158946	+	0.158946i	0.00613605	+	0.00613605i
$672$	5.50415	−	3.46223i	0.212327	−	0.133558i
$673$	−31.5607	+	31.5607i	−1.21657	+	1.21657i	−0.247751	+	0.968824i	$0.579692\pi$
$673$	−31.5607	+	31.5607i	−1.21657	+	1.21657i	−0.968824	+	0.247751i	$0.920308\pi$
$674$	46.7745	−	13.9078i	1.80169	−	0.535708i
$675$	−0.519747	+	1.71338i	−0.0200051	+	0.0659479i
$676$	−0.248815	+	22.5677i	−0.00956982	+	0.867988i
$677$	0.846821	−	8.59791i	0.0325460	−	0.330445i	−0.965101	−	0.261879i	$-0.915658\pi$
$677$	0.846821	−	8.59791i	0.0325460	−	0.330445i	0.997647	−	0.0685655i	$-0.0218422\pi$
$678$	−7.91971	−	0.0436572i	−0.304155	−	0.00167665i
$679$	2.23526	+	0.444620i	0.0857813	+	0.0170630i
$680$	−1.21246	−	1.25324i	−0.0464958	−	0.0480596i
$681$	−2.49791	−	12.5579i	−0.0957202	−	0.481218i
$682$	−0.126602	−	0.0856062i	−0.00484785	−	0.00327803i
$683$	23.5531	−	44.0647i	0.901234	−	1.68609i	0.191657	−	0.981462i	$-0.438614\pi$
$683$	23.5531	−	44.0647i	0.901234	−	1.68609i	0.709577	−	0.704628i	$-0.248886\pi$
$684$	−0.154827	+	0.184473i	−0.00591998	+	0.00705348i
$685$	0.866609	+	8.79883i	0.0331114	+	0.336186i
$686$	−20.5224	+	1.90711i	−0.783548	+	0.0728139i
$687$	4.17838	+	10.0875i	0.159415	+	0.384863i
$688$	6.43808	−	5.05021i	0.245450	−	0.192538i
$689$	12.1605	−	29.3580i	0.463277	−	1.11845i
$690$	−1.05196	+	3.40024i	−0.0400473	+	0.129445i
$691$	−21.3485	−	17.5203i	−0.812135	−	0.666502i	0.133746	−	0.991016i	$-0.457299\pi$
$691$	−21.3485	−	17.5203i	−0.812135	−	0.666502i	−0.945881	+	0.324513i	$0.894799\pi$
$692$	3.97938	−	36.2964i	0.151273	−	1.37978i
$693$	−0.0369485	+	0.0112082i	−0.00140356	+	0.000425765i
$694$	10.1513	+	2.07747i	0.385340	+	0.0788595i
$695$	17.1173	+	11.4374i	0.649295	+	0.433845i
$696$	−24.2070	−	2.78908i	−0.917563	−	0.105720i
$697$	−1.68306	−	2.51887i	−0.0637503	−	0.0954091i
$698$	−6.29648	−	2.64884i	−0.238325	−	0.100260i
$699$	7.51324	+	9.15491i	0.284177	+	0.346270i
$700$	0.758488	+	4.04579i	0.0286682	+	0.152916i
$701$	12.0246	−	6.42726i	0.454162	−	0.242754i	−0.228422	−	0.973562i	$-0.573356\pi$
$701$	12.0246	−	6.42726i	0.454162	−	0.242754i	0.682583	+	0.730808i	$0.260856\pi$
$702$	4.39142	+	5.41152i	0.165743	+	0.204245i
$703$		−	0.862431i		−	0.0325272i
$704$	−0.0864654	+	0.254427i	−0.00325879	+	0.00958906i
$705$		−	10.8004i		−	0.406768i
$706$	−16.6231	+	13.4895i	−0.625617	+	0.507685i
$707$	6.42480	−	3.43413i	0.241630	−	0.129154i
$708$	−0.0631804	+	0.0923360i	−0.00237447	+	0.00347020i
$709$	−20.7755	−	25.3150i	−0.780240	−	0.950726i	0.219450	−	0.975624i	$-0.429574\pi$
$709$	−20.7755	−	25.3150i	−0.780240	−	0.950726i	−0.999690	+	0.0248982i	$0.992074\pi$
$710$	−12.5113	+	29.7402i	−0.469541	+	1.11613i
$711$	6.74475	+	10.0942i	0.252948	+	0.378563i
$712$	9.30933	−	16.7445i	0.348882	−	0.627525i
$713$	−3.75797	−	2.51099i	−0.140737	−	0.0940375i
$714$	0.112161	−	0.548065i	0.00419752	−	0.0205108i
$715$	−0.283776	+	0.0860826i	−0.0106126	+	0.00321931i
$716$	3.57817	+	4.45937i	0.133722	+	0.166654i
$717$	7.56088	+	6.20505i	0.282366	+	0.231732i
$718$	14.0046	+	4.33268i	0.522645	+	0.161694i
$719$	7.40389	−	17.8746i	0.276119	−	0.666609i	−0.723603	−	0.690217i	$-0.757515\pi$
$719$	7.40389	−	17.8746i	0.276119	−	0.666609i	0.999721	+	0.0236075i	$0.00751518\pi$
$720$	2.23088	−	6.80996i	0.0831402	−	0.253792i
$721$	−1.18308	−	2.85621i	−0.0440603	−	0.106371i
$722$	2.48438	+	26.7344i	0.0924592	+	0.994950i
$723$	−2.45197	−	24.8952i	−0.0911897	−	0.925864i
$724$	−49.1199	+	4.29167i	−1.82553	+	0.159499i
$725$	7.27133	−	13.6037i	0.270050	−	0.505229i
$726$	−8.71292	+	12.8855i	−0.323367	+	0.478225i
$727$	−2.28380	−	11.4814i	−0.0847015	−	0.425823i	−0.999747	−	0.0224736i	$-0.992846\pi$
$727$	−2.28380	−	11.4814i	−0.0847015	−	0.425823i	0.915046	−	0.403350i	$-0.132154\pi$
$728$	14.6990	+	6.37529i	0.544780	+	0.236284i
$729$	0.980785	+	0.195090i	0.0363254	+	0.00722557i
$730$	−0.0490618	+	8.90013i	−0.00181586	+	0.329409i
$731$	0.0690000	−	0.700568i	0.00255206	−	0.0259115i
$732$	−9.35907	−	9.56774i	−0.345921	−	0.353634i
$733$	−3.20067	+	10.5512i	−0.118220	+	0.389717i	−0.996001	−	0.0893441i	$-0.971523\pi$
$733$	−3.20067	+	10.5512i	−0.118220	+	0.389717i	0.877781	+	0.479062i	$0.159023\pi$
$734$	10.0342	+	33.7470i	0.370370	+	1.24562i
$735$	−7.19369	+	7.19369i	−0.265343	+	0.265343i
$736$	−2.51557	+	7.53826i	−0.0927250	+	0.277864i
$737$	0.244543	+	0.244543i	0.00900787	+	0.00900787i
$738$	5.92913	−	10.9470i	0.218254	−	0.402966i
$739$	42.7260	+	12.9608i	1.57170	+	0.476771i	0.951494	−	0.307666i	$-0.0995480\pi$
$739$	42.7260	+	12.9608i	1.57170	+	0.476771i	0.620208	+	0.784437i	$0.287048\pi$
$740$	9.55831	+	23.8151i	0.351371	+	0.875460i
$741$	−0.590553	−	0.0581644i	−0.0216945	−	0.00213672i
$742$	−7.37131	−	7.45303i	−0.270609	−	0.273609i
$743$	8.00632	−	40.2505i	0.293724	−	1.47665i	−0.498752	−	0.866745i	$-0.666208\pi$
$743$	8.00632	−	40.2505i	0.293724	−	1.47665i	0.792476	−	0.609903i	$-0.208792\pi$
$744$	7.48151	+	5.17996i	0.274286	+	0.189907i
$745$	−29.5523	+	5.87832i	−1.08271	+	0.215365i
$746$	−28.9757	+	5.59775i	−1.06087	+	0.204948i
$747$	4.00244	+	2.13935i	0.146442	+	0.0782747i
$748$	0.0106725	+	0.0205074i	0.000390224	+	0.000749826i
$749$	−17.7709	+	1.75028i	−0.649333	+	0.0639538i
$750$	13.2387	+	10.9874i	0.483409	+	0.401203i
$751$	26.3862	−	10.9295i	0.962846	−	0.398824i	0.154802	−	0.987946i	$-0.450526\pi$
$751$	26.3862	−	10.9295i	0.962846	−	0.398824i	0.808044	+	0.589122i	$0.200526\pi$
$752$	0.531678	−	24.1088i	0.0193883	−	0.879158i
$753$	14.0185	+	5.80666i	0.510863	+	0.211607i
$754$	−28.0102	−	53.1056i	−1.02007	−	1.93399i
$755$	7.96946	−	9.71082i	0.290038	−	0.353413i
$756$	2.20722	−	0.643066i	0.0802756	−	0.0233881i
$757$	−0.518684	−	1.70987i	−0.0188519	−	0.0621464i	0.947010	−	0.321205i	$-0.104088\pi$
$757$	−0.518684	−	1.70987i	−0.0188519	−	0.0621464i	−0.965862	+	0.259058i	$0.916588\pi$
$758$	−22.9756	−	34.7992i	−0.834512	−	1.26396i
$759$	0.0262161	−	0.0392352i	0.000951585	−	0.00142415i
$760$	0.278697	+	0.542811i	0.0101094	+	0.0196898i
$761$	29.9683	−	20.0242i	1.08635	−	0.725876i	0.122539	−	0.992464i	$-0.460896\pi$
$761$	29.9683	−	20.0242i	1.08635	−	0.725876i	0.963811	+	0.266588i	$0.0858963\pi$
$762$	−16.1014	+	6.56567i	−0.583292	+	0.237849i
$763$	8.01844	−	6.58056i	0.290287	−	0.238232i
$764$	−3.19109	+	15.1669i	−0.115450	+	0.548718i
$765$	−0.290621	−	0.543714i	−0.0105074	−	0.0196580i
$766$	−4.17133	+	40.0856i	−0.150716	+	1.44835i
$767$	−0.275675			−0.00995404
$768$	5.31503	−	15.0914i	0.191790	−	0.544564i
$769$	21.4263			0.772651			0.386326	−	0.922363i	$-0.373744\pi$
$769$	21.4263			0.772651			0.386326	+	0.922363i	$0.373744\pi$
$770$	−0.0101250	+	0.0972991i	−0.000364879	+	0.00350642i
$771$	−4.65441	−	8.70779i	−0.167625	−	0.313604i
$772$	9.62588	−	45.7506i	0.346443	−	1.64660i
$773$	−0.234935	+	0.192806i	−0.00845004	+	0.00693477i	−0.638609	−	0.769532i	$-0.720490\pi$
$773$	−0.234935	+	0.192806i	−0.00845004	+	0.00693477i	0.630159	+	0.776466i	$0.282990\pi$
$774$	2.67880	−	1.09234i	0.0962876	−	0.0392632i
$775$	−4.78959	+	3.20030i	−0.172047	+	0.114958i
$776$	4.98867	−	2.56135i	0.179083	−	0.0919472i
$777$	−4.57382	+	6.84521i	−0.164085	+	0.245570i
$778$	−4.64205	−	7.03092i	−0.166426	−	0.252071i
$779$	0.307719	+	1.01441i	0.0110252	+	0.0363451i
$780$	16.9521	−	4.93895i	0.606983	−	0.176843i
$781$	0.271367	−	0.330662i	0.00971028	−	0.0118320i
$782$	0.318960	+	0.604727i	0.0114060	+	0.0216250i
$783$	−7.95929	−	3.29685i	−0.284442	−	0.117820i
$784$	−16.4119	+	15.7037i	−0.586140	+	0.560845i
$785$	−16.2758	+	6.74164i	−0.580907	+	0.240620i
$786$	18.0559	+	14.9854i	0.644032	+	0.534512i
$787$	41.8230	−	4.11920i	1.49083	−	0.146834i	0.680473	−	0.732773i	$-0.261774\pi$
$787$	41.8230	−	4.11920i	1.49083	−	0.146834i	0.810355	+	0.585940i	$0.199274\pi$
$788$	−13.4713	−	25.8854i	−0.479894	−	0.922131i
$789$	23.2165	+	12.4095i	0.826528	+	0.441788i
$790$	30.1999	−	5.83426i	1.07446	−	0.207574i
$791$	−6.31366	+	1.25586i	−0.224488	+	0.0446534i
$792$	−0.0540816	+	0.0781110i	−0.00192171	+	0.00277555i
$793$	6.43368	−	32.3443i	0.228467	−	1.14858i
$794$	−31.3554	−	31.7030i	−1.11276	−	1.12510i
$795$	−11.4966	−	1.13232i	−0.407743	−	0.0401592i
$796$	−2.83846	−	7.07218i	−0.100606	−	0.250667i
$797$	−28.4307	−	8.62435i	−1.00707	−	0.305490i	−0.256685	−	0.966495i	$-0.582630\pi$
$797$	−28.4307	−	8.62435i	−1.00707	−	0.305490i	−0.750382	+	0.661005i	$0.770130\pi$
$798$	−0.0932282	+	0.172129i	−0.00330024	+	0.00609329i
$799$	−1.46699	−	1.46699i	−0.0518983	−	0.0518983i
$800$	7.64935	+	6.63875i	0.270445	+	0.234715i
$801$	4.78958	−	4.78958i	0.169231	−	0.169231i
$802$	−6.21410	−	20.8992i	−0.219428	−	0.737976i
$803$	0.0342529	−	0.112917i	0.00120876	−	0.00398475i
$804$	−14.3992	−	14.7203i	−0.507821	−	0.519143i
$805$	−0.283565	+	2.87908i	−0.00999434	+	0.101474i
$806$	−0.123596	+	22.4211i	−0.00435348	+	0.789749i
$807$	18.4461	+	3.66916i	0.649334	+	0.129161i
$808$	7.13268	−	16.4452i	0.250927	−	0.578540i
$809$	10.8192	+	54.3920i	0.380384	+	1.91232i	0.408592	+	0.912717i	$0.366020\pi$
$809$	10.8192	+	54.3920i	0.380384	+	1.91232i	−0.0282081	+	0.999602i	$0.508980\pi$
$810$	1.41918	−	2.09881i	0.0498647	−	0.0737446i
$811$	13.5530	−	25.3560i	0.475912	−	0.890368i	−0.523356	−	0.852114i	$-0.675320\pi$
$811$	13.5530	−	25.3560i	0.475912	−	0.890368i	0.999268	−	0.0382542i	$-0.0121797\pi$
$812$	−19.7308	+	1.72390i	−0.692414	+	0.0604971i
$813$	−2.26787	−	23.0261i	−0.0795376	−	0.807559i
$814$	−0.0314801	−	0.338757i	−0.00110338	−	0.0118734i
$815$	−7.78656	−	18.7984i	−0.272751	−	0.658480i
$816$	−0.621960	−	1.22799i	−0.0217730	−	0.0429881i
$817$	−0.0942664	+	0.227579i	−0.00329796	+	0.00796199i
$818$	−10.2999	−	3.18655i	−0.360128	−	0.111415i
$819$	4.37881	+	3.59360i	0.153008	+	0.125571i
$820$	−19.7401	−	24.6015i	−0.689353	−	0.859121i
$821$	−15.7767	+	4.78580i	−0.550609	+	0.167025i	−0.553317	−	0.832971i	$-0.686638\pi$
$821$	−15.7767	+	4.78580i	−0.550609	+	0.167025i	0.00270772	+	0.999996i	$0.499138\pi$
$822$	−1.39932	+	6.83765i	−0.0488069	+	0.238490i
$823$	37.4340	+	25.0126i	1.30487	+	0.871885i	0.996836	−	0.0794909i	$-0.0253295\pi$
$823$	37.4340	+	25.0126i	1.30487	+	0.871885i	0.308032	+	0.951376i	$0.400329\pi$
$824$	−6.64857	−	3.69637i	−0.231614	−	0.128769i
$825$	−0.0334128	−	0.0500058i	−0.00116329	−	0.00174098i
$826$	−0.0352637	+	0.0838242i	−0.00122698	+	0.00291662i
$827$	−20.0577	−	24.4404i	−0.697476	−	0.849877i	0.296996	−	0.954879i	$-0.404015\pi$
$827$	−20.0577	−	24.4404i	−0.697476	−	0.849877i	−0.994472	+	0.105002i	$0.966515\pi$
$828$	−1.58662	+	2.31879i	−0.0551389	+	0.0805836i
$829$	41.7462	−	22.3138i	1.44991	−	0.774991i	0.456510	−	0.889718i	$-0.349099\pi$
$829$	41.7462	−	22.3138i	1.44991	−	0.774991i	0.993397	+	0.114727i	$0.0365993\pi$
$830$	8.92832	−	7.24529i	0.309906	−	0.251488i
$831$		−	6.94104i		−	0.240782i
$832$	38.0837	−	10.1902i	1.32032	−	0.353283i
$833$			1.95419i			0.0677086i
$834$	10.2402	+	12.6189i	0.354588	+	0.436957i
$835$	−15.3108	+	8.18381i	−0.529853	+	0.283212i
$836$	−0.00149063	−	0.00795106i	−5.15546e−5	−	0.000274993i
$837$	2.04100	+	2.48696i	0.0705471	+	0.0859619i
$838$	16.4857	+	6.93532i	0.569490	+	0.239577i
$839$	11.2546	+	16.8436i	0.388551	+	0.581507i	0.973252	−	0.229742i	$-0.0737882\pi$
$839$	11.2546	+	16.8436i	0.388551	+	0.581507i	−0.584701	+	0.811249i	$0.698788\pi$
$840$	0.666696	−	5.78639i	0.0230032	−	0.199650i
$841$	37.5987	+	25.1226i	1.29651	+	0.866298i
$842$	23.2668	+	4.76154i	0.801827	+	0.164093i
$843$	−18.6977	+	5.67188i	−0.643982	+	0.195350i
$844$	−3.39462	+	30.9628i	−0.116848	+	1.06578i
$845$	15.6275	+	12.8252i	0.537602	+	0.441199i
$846$	2.51985	−	8.14494i	0.0866343	−	0.280029i
$847$	−4.83831	+	11.6807i	−0.166246	+	0.401354i
$848$	−25.6070	−	3.09351i	−0.879349	−	0.106232i
$849$	8.89941	+	21.4851i	0.305427	+	0.737366i
$850$	0.867633	−	0.0806278i	0.0297596	−	0.00276551i
$851$	−0.986187	−	10.0129i	−0.0338061	−	0.343239i
$852$	−16.3738	+	19.5090i	−0.560958	+	0.668366i
$853$	−6.31898	+	11.8220i	−0.216358	+	0.404777i	−0.966563	−	0.256428i	$-0.917454\pi$
$853$	−6.31898	+	11.8220i	−0.216358	+	0.404777i	0.750206	+	0.661205i	$0.229954\pi$
$854$	−9.01192	−	6.09369i	−0.308382	−	0.208522i
$855$	0.0420868	+	0.211585i	0.00143934	+	0.00723605i
$856$	−31.5786	+	30.5511i	−1.07934	+	1.04421i
$857$	−7.60398	−	1.51253i	−0.259747	−	0.0516669i	0.0634988	−	0.997982i	$-0.479774\pi$
$857$	−7.60398	−	1.51253i	−0.259747	−	0.0516669i	−0.323246	+	0.946315i	$0.604774\pi$
$858$	−0.234088	−	0.00129041i	−0.00799164	−	4.40537e-5i
$859$	3.19396	−	32.4288i	0.108977	−	1.10646i	−0.772754	−	0.634705i	$-0.781122\pi$
$859$	3.19396	−	32.4288i	0.108977	−	1.10646i	0.881731	−	0.471753i	$-0.156378\pi$
$860$	0.0808055	−	7.32910i	0.00275545	−	0.249920i
$861$	2.93745	−	9.68347i	0.100108	−	0.330012i
$862$	−28.2774	+	8.40793i	−0.963134	+	0.286375i
$863$	6.50140	−	6.50140i	0.221310	−	0.221310i	−0.587740	−	0.809050i	$-0.699982\pi$
$863$	6.50140	−	6.50140i	0.221310	−	0.221310i	0.809050	+	0.587740i	$0.199982\pi$
$864$	3.27121	−	4.61511i	0.111289	−	0.157009i
$865$	−23.1278	−	23.1278i	−0.786367	−	0.786367i
$866$	18.0867	+	9.79610i	0.614611	+	0.332885i
$867$	16.1547	+	4.90046i	0.548641	+	0.166428i
$868$	6.80175	+	2.90564i	0.230866	+	0.0986238i
$869$	−0.405823	−	0.0399701i	−0.0137666	−	0.00135589i
$870$	−15.5189	+	15.3487i	−0.526139	+	0.520371i
$871$	9.89841	−	49.7626i	0.335395	−	1.68614i
$872$	5.39270	−	24.9475i	0.182620	−	0.844828i
$873$	1.94456	−	0.386797i	0.0658134	−	0.0130911i
$874$	−0.0453787	−	0.234894i	−0.00153496	−	0.00794541i
$875$	12.3327	+	6.59194i	0.416920	+	0.222848i
$876$	−2.11349	+	6.70041i	−0.0714082	+	0.226386i
$877$	19.3567	−	1.90646i	0.653628	−	0.0643767i	0.234233	−	0.972181i	$-0.424742\pi$
$877$	19.3567	−	1.90646i	0.653628	−	0.0643767i	0.419395	+	0.907804i	$0.362242\pi$
$878$	−23.3941	+	28.1875i	−0.789513	+	0.951282i
$879$	−0.840988	+	0.348349i	−0.0283658	+	0.0117495i
$880$	0.129284	+	0.203039i	0.00435816	+	0.00684445i
$881$	−45.7885	−	18.9662i	−1.54265	−	0.638988i	−0.560684	−	0.828030i	$-0.689462\pi$
$881$	−45.7885	−	18.9662i	−1.54265	−	0.638988i	−0.981969	+	0.189042i	$0.939462\pi$
$882$	−7.10334	+	3.74662i	−0.239182	+	0.126155i
$883$	−2.55426	+	3.11237i	−0.0859576	+	0.104740i	−0.814213	−	0.580566i	$-0.802831\pi$
$883$	−2.55426	+	3.11237i	−0.0859576	+	0.104740i	0.728256	+	0.685306i	$0.240331\pi$
$884$	1.63171	−	2.97339i	0.0548802	−	0.100006i
$885$	0.0290922	+	0.0959042i	0.000977924	+	0.00322378i
$886$	37.3774	−	24.6778i	1.25572	−	0.829067i
$887$	−6.59878	+	9.87578i	−0.221565	+	0.331596i	−0.925554	−	0.378615i	$-0.876400\pi$
$887$	−6.59878	+	9.87578i	−0.221565	+	0.331596i	0.703989	+	0.710211i	$0.251400\pi$
$888$	1.65191	+	20.1897i	0.0554344	+	0.677522i
$889$	−11.7517	+	7.85226i	−0.394141	+	0.263356i
$890$	−6.47981	−	15.8908i	−0.217204	−	0.532662i
$891$	−0.0259652	+	0.0213091i	−0.000869866	+	0.000713881i
$892$	7.34892	−	4.79405i	0.246060	−	0.160517i
$893$	0.342214	+	0.640238i	0.0114518	+	0.0214248i
$894$	−23.6577	−	2.46183i	−0.791233	−	0.0823360i
$895$	5.12145			0.171191
$896$	1.77305	−	12.8836i	0.0592335	−	0.430411i
$897$	−6.92290			−0.231149
$898$	36.6567	+	3.81451i	1.22325	+	0.127292i
$899$	−13.0656	−	24.4440i	−0.435762	−	0.815253i
$900$	1.95652	+	2.99920i	0.0652174	+	0.0999734i
$901$	−1.71534	+	1.40775i	−0.0571464	+	0.0468988i
$902$	0.157898	+	0.387222i	0.00525741	+	0.0128931i
$903$	1.95515	−	1.30639i	0.0650632	−	0.0434738i
$904$	−10.2497	+	12.0764i	−0.340899	+	0.401654i
$905$	−24.5380	+	36.7236i	−0.815669	+	1.22074i
$906$	8.27564	−	5.46386i	0.274940	−	0.181525i
$907$	7.68718	+	25.3413i	0.255249	+	0.841442i	0.987118	+	0.159997i	$0.0511484\pi$
$907$	7.68718	+	25.3413i	0.255249	+	0.841442i	−0.731869	+	0.681446i	$0.761352\pi$
$908$	−22.4496	−	12.3197i	−0.745015	−	0.408842i
$909$	4.02052	−	4.89902i	0.133352	−	0.162490i
$910$	12.6943	−	6.69552i	0.420811	−	0.221954i
$911$	−42.8658	−	17.7556i	−1.42021	−	0.588269i	−0.465294	−	0.885156i	$-0.654051\pi$
$911$	−42.8658	−	17.7556i	−1.42021	−	0.588269i	−0.954912	+	0.296888i	$0.904051\pi$
$912$	0.0835307	+	0.474373i	0.00276598	+	0.0157080i
$913$	−0.140837	+	0.0583366i	−0.00466102	+	0.00193066i
$914$	0.207642	−	0.250188i	0.00686819	−	0.00827547i
$915$	−11.9312	+	1.17512i	−0.394432	+	0.0388482i
$916$	20.8258	+	6.56903i	0.688105	+	0.217047i
$917$	16.8202	+	8.99056i	0.555451	+	0.296895i
$918$	−0.0923121	−	0.477835i	−0.00304675	−	0.0157709i
$919$	−57.0590	+	11.3497i	−1.88220	+	0.374393i	−0.996034	−	0.0889711i	$-0.971642\pi$
$919$	−57.0590	+	11.3497i	−1.88220	+	0.374393i	−0.886168	+	0.463364i	$0.846642\pi$
$920$	3.85641	+	5.98341i	0.127142	+	0.197267i
$921$	−6.73534	+	33.8608i	−0.221937	+	1.11575i
$922$	27.8337	−	27.5286i	0.916656	−	0.906605i
$923$	−62.4541	−	6.15120i	−2.05570	−	0.202469i
$924$	−0.0303364	+	0.0710139i	−0.000997994	+	0.00233619i
$925$	−12.2712	−	3.72243i	−0.403475	−	0.122393i
$926$	−46.2424	−	25.0458i	−1.51962	−	0.823056i
$927$	−1.90175	−	1.90175i	−0.0624618	−	0.0624618i
$928$	−35.3969	+	33.4975i	−1.16196	+	1.09961i
$929$	−28.0818	+	28.0818i	−0.921335	+	0.921335i	−0.997124	−	0.0757891i	$-0.975852\pi$
$929$	−28.0818	+	28.0818i	−0.921335	+	0.921335i	0.0757891	+	0.997124i	$0.475852\pi$
$930$	7.81309	−	2.32312i	0.256201	−	0.0761781i
$931$	0.198500	−	0.654367i	0.00650558	−	0.0214460i
$932$	23.6849	+	0.261133i	0.775826	+	0.00855371i
$933$	−2.44635	+	24.8382i	−0.0800900	+	0.813168i
$934$	44.5610	+	0.245641i	1.45808	+	0.00803763i
$935$	0.0203105	+	0.00404001i	0.000664224	+	0.000132122i
$936$	13.9364	+	0.230491i	0.455525	+	0.00753383i
$937$	−10.9203	−	54.9000i	−0.356751	−	1.79351i	−0.575582	−	0.817744i	$-0.695225\pi$
$937$	−10.9203	−	54.9000i	−0.356751	−	1.79351i	0.218832	−	0.975763i	$-0.429775\pi$
$938$	−13.8651	−	9.37533i	−0.452712	−	0.306115i
$939$	−2.88754	+	5.40221i	−0.0942314	+	0.176295i
$940$	−16.5456	−	13.8867i	−0.539659	−	0.452935i
$941$	1.40084	+	14.2230i	0.0456662	+	0.463657i	0.990639	+	0.136508i	$0.0435879\pi$
$941$	1.40084	+	14.2230i	0.0456662	+	0.463657i	−0.944973	+	0.327149i	$0.893912\pi$
$942$	−13.8469	+	1.28677i	−0.451158	+	0.0419254i
$943$	4.73263	+	11.4256i	0.154116	+	0.372068i
$944$	0.0602187	+	0.215510i	0.00195995	+	0.00701425i
$945$	0.788073	−	1.90258i	0.0256360	−	0.0618908i
$946$	−0.0287201	+	0.0928323i	−0.000933772	+	0.00301824i
$947$	19.8823	+	16.3169i	0.646087	+	0.530230i	0.899384	−	0.437159i	$-0.144015\pi$
$947$	19.8823	+	16.3169i	0.646087	+	0.530230i	−0.253298	+	0.967388i	$0.581515\pi$
$948$	24.1358	+	2.64615i	0.783895	+	0.0859430i
$949$	−16.5660	+	5.02524i	−0.537755	+	0.163126i
$950$	−0.298720	−	0.0611328i	−0.00969176	−	0.00198341i
$951$	21.0953	+	14.0954i	0.684061	+	0.457075i
$952$	−0.695391	−	0.876501i	−0.0225377	−	0.0284075i
$953$	−3.12740	−	4.68049i	−0.101307	−	0.151616i	0.777353	−	0.629064i	$-0.216562\pi$
$953$	−3.12740	−	4.68049i	−0.101307	−	0.151616i	−0.878660	+	0.477448i	$0.841562\pi$
$954$	−8.40575	−	3.53619i	−0.272146	−	0.114488i
$955$	8.80746	+	10.7319i	0.285003	+	0.347277i
$956$	19.2272	−	3.60463i	0.621852	−	0.116582i
$957$	0.255208	−	0.136412i	0.00824972	−	0.00440957i
$958$	23.3092	+	28.7238i	0.753087	+	0.928024i
$959$			5.67293i			0.183188i
$960$	−7.56408	−	12.1735i	−0.244129	−	0.392898i
$961$		−	20.6494i		−	0.666109i
$962$	−38.7572	+	31.4513i	−1.24958	+	1.01403i
$963$	−13.7003	+	7.32294i	−0.441485	+	0.235978i
$964$	−41.2906	−	28.2529i	−1.32988	−	0.909964i
$965$	−26.5676	−	32.3727i	−0.855240	−	1.04211i
$966$	−0.885562	+	2.10504i	−0.0284925	+	0.0677286i
$967$	−16.3877	−	24.5259i	−0.526993	−	0.788701i	0.468507	−	0.883460i	$-0.344792\pi$
$967$	−16.3877	−	24.5259i	−0.526993	−	0.788701i	−0.995500	+	0.0947586i	$0.969792\pi$
$968$	8.53709	+	29.9152i	0.274392	+	0.961511i
$969$	0.0344553	+	0.0230223i	0.00110687	+	0.000739584i
$970$	1.00713	−	4.92123i	0.0323369	−	0.158011i
$971$	−40.0457	+	12.1477i	−1.28513	+	0.389839i	−0.857672	−	0.514198i	$-0.828090\pi$
$971$	−40.0457	+	12.1477i	−1.28513	+	0.389839i	−0.427455	+	0.904037i	$0.640590\pi$
$972$	1.55991	−	1.25167i	0.0500343	−	0.0401472i
$973$	10.2108	+	8.37977i	0.327343	+	0.268643i
$974$	25.5101	+	7.89222i	0.817396	+	0.252883i
$975$	−3.37655	+	8.15170i	−0.108136	+	0.261063i
$976$	−26.6907	+	2.03576i	−0.854347	+	0.0651632i
$977$	2.42624	+	5.85745i	0.0776222	+	0.187396i	0.957927	−	0.287012i	$-0.0926620\pi$
$977$	2.42624	+	5.85745i	0.0776222	+	0.187396i	−0.880305	+	0.474409i	$0.842662\pi$
$978$	−1.48622	−	15.9931i	−0.0475240	−	0.511404i
$979$	0.0223008	+	0.226424i	0.000712736	+	0.00723653i
$980$	1.77098	+	20.2696i	0.0565719	+	0.647489i
$981$	4.25387	−	7.95844i	0.135816	−	0.254093i
$982$	20.5569	−	30.4015i	0.655997	−	0.970149i
$983$	−7.05485	−	35.4671i	−0.225015	−	1.13123i	−0.913770	−	0.406231i	$-0.866843\pi$
$983$	−7.05485	−	35.4671i	−0.225015	−	1.13123i	0.688756	−	0.724994i	$-0.258157\pi$
$984$	−9.14679	−	23.1583i	−0.291589	−	0.738258i
$985$	−25.6369	−	5.09949i	−0.816858	−	0.162483i
$986$	−0.0231118	+	4.19264i	−0.000736031	+	0.133521i
$987$	0.679250	−	6.89654i	0.0216208	−	0.219519i
$988$	−0.848410	+	0.829906i	−0.0269915	+	0.0264028i
$989$	−0.834208	+	2.75001i	−0.0265263	+	0.0874454i
$990$	0.0242546	+	0.0815728i	0.000770862	+	0.00259255i
$991$	−3.33910	+	3.33910i	−0.106070	+	0.106070i	−0.758150	−	0.652080i	$-0.773897\pi$
$991$	−3.33910	+	3.33910i	−0.106070	+	0.106070i	0.652080	+	0.758150i	$0.273897\pi$
$992$	17.5548	−	4.80106i	0.557365	−	0.152434i
$993$	−0.547440	−	0.547440i	−0.0173725	−	0.0173725i
$994$	−9.85939	+	18.2035i	−0.312721	+	0.577381i
$995$	−6.53222	−	1.98153i	−0.207085	−	0.0628186i
$996$	8.42351	−	3.38082i	0.266909	−	0.107125i
$997$	−23.9323	−	2.35713i	−0.757945	−	0.0746511i	−0.288341	−	0.957528i	$-0.593104\pi$
$997$	−23.9323	−	2.35713i	−0.757945	−	0.0746511i	−0.469605	+	0.882877i	$0.655604\pi$
$998$	22.9332	+	23.1874i	0.725937	+	0.733985i
$999$	−1.39724	+	7.02438i	−0.0442066	+	0.222242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.37.18	✓	512
128.45	even	32	inner	384.2.v.a.301.18	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.37.18	✓	512	1.1	even	1	trivial
384.2.v.a.301.18	yes	512	128.45	even	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.146373 - 1.40662i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.95715 - 0.411783i) q^{4} +(-1.38486 + 1.13652i) q^{5} +(-1.30953 + 0.533986i) q^{6} +(-0.955768 + 0.638624i) q^{7} +(-0.865695 + 2.69269i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.146373 - 1.40662i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.95715 - 0.411783i) q^{4} +(-1.38486 + 1.13652i) q^{5} +(-1.30953 + 0.533986i) q^{6} +(-0.955768 + 0.638624i) q^{7} +(-0.865695 + 2.69269i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(1.39595 + 2.11433i) q^{10} +(-0.00975057 - 0.0321433i) q^{11} +(0.559434 + 1.92016i) q^{12} +(-3.12625 + 3.80934i) q^{13} +(0.758401 + 1.43788i) q^{14} +(1.65514 + 0.685583i) q^{15} +(3.66087 + 1.61184i) q^{16} +(0.317933 - 0.131692i) q^{17} +(1.08824 + 0.903180i) q^{18} +(-0.119838 + 0.0118030i) q^{19} +(3.17838 - 1.65409i) q^{20} +(1.01376 + 0.541867i) q^{21} +(-0.0466406 + 0.00901041i) q^{22} +(-1.37784 + 0.274068i) q^{23} +(2.78283 - 0.505850i) q^{24} +(-0.349304 + 1.75607i) q^{25} +(4.90069 + 4.95502i) q^{26} +(0.995185 + 0.0980171i) q^{27} +(2.13356 - 0.856314i) q^{28} +(-8.24412 - 2.50082i) q^{29} +(1.20662 - 2.22780i) q^{30} +(2.27493 + 2.27493i) q^{31} +(2.80310 - 4.91352i) q^{32} +(-0.0237515 + 0.0237515i) q^{33} +(-0.138704 - 0.466486i) q^{34} +(0.597793 - 1.97066i) q^{35} +(1.42972 - 1.39854i) q^{36} +(-0.701998 + 7.12751i) q^{37} +(-0.000938741 + 0.170294i) q^{38} +(4.83324 + 0.961392i) q^{39} +(-1.86144 - 4.71288i) q^{40} +(-1.71742 - 8.63403i) q^{41} +(0.910588 - 1.34666i) q^{42} +(0.964303 - 1.80408i) q^{43} +(0.00584727 + 0.0669244i) q^{44} +(-0.175599 - 1.78289i) q^{45} +(0.183832 + 1.97820i) q^{46} +(-2.30707 - 5.56976i) q^{47} +(-0.304206 - 3.98842i) q^{48} +(-2.17313 + 5.24640i) q^{49} +(2.41899 + 0.748380i) q^{50} +(-0.266015 - 0.218312i) q^{51} +(7.68716 - 6.16812i) q^{52} +(-6.17064 + 1.87184i) q^{53} +(0.283541 - 1.38550i) q^{54} +(0.0500349 + 0.0334322i) q^{55} +(-0.892211 - 3.12644i) q^{56} +(0.0669005 + 0.100124i) q^{57} +(-4.72442 + 11.2303i) q^{58} +(0.0354888 + 0.0432432i) q^{59} +(-2.95705 - 2.02335i) q^{60} +(-5.90186 + 3.15461i) q^{61} +(3.53295 - 2.86697i) q^{62} -1.14949i q^{63} +(-6.50114 - 4.66209i) q^{64} -8.82847i q^{65} +(0.0299327 + 0.0368859i) q^{66} +(-9.08018 + 4.85346i) q^{67} +(-0.676471 + 0.126822i) q^{68} +(0.891214 + 1.08595i) q^{69} +(-2.68446 - 1.12932i) q^{70} +(7.07509 + 10.5886i) q^{71} +(-1.75793 - 2.21578i) q^{72} +(2.92088 + 1.95167i) q^{73} +(9.92293 + 2.03072i) q^{74} +(1.71338 - 0.519747i) q^{75} +(0.239401 + 0.0262469i) q^{76} +(0.0298468 + 0.0244946i) q^{77} +(2.05977 - 6.65781i) q^{78} +(4.64586 - 11.2161i) q^{79} +(-6.90169 + 1.92850i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-12.3962 + 1.15196i) q^{82} +(-0.444833 - 4.51647i) q^{83} +(-1.76095 - 1.47796i) q^{84} +(-0.290621 + 0.543714i) q^{85} +(-2.39651 - 1.62048i) q^{86} +(1.68072 + 8.44954i) q^{87} +(0.0949930 + 0.00157107i) q^{88} +(-6.64333 - 1.32144i) q^{89} +(-2.53355 - 0.0139661i) q^{90} +(0.555230 - 5.63735i) q^{91} +(2.80949 + 0.0309754i) q^{92} +(0.933915 - 3.07871i) q^{93} +(-8.17222 + 2.42990i) q^{94} +(0.152544 - 0.152544i) q^{95} +(-5.65471 - 0.155895i) q^{96} +(-1.40195 - 1.40195i) q^{97} +(7.06160 + 3.82470i) q^{98} +(0.0321433 + 0.00975057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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