LMFDB - Embedded newform 384.2.v.a.13.2

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			13.2
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39658 - 0.222610i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.90089 + 0.621788i) q^{4} +(0.0409738 + 0.416014i) q^{5} +(0.192382 + 1.40107i) q^{6} +(-0.338624 + 0.506787i) q^{7} +(-2.51633 - 1.29154i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-1.39658 - 0.222610i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.90089 + 0.621788i) q^{4} +(0.0409738 + 0.416014i) q^{5} +(0.192382 + 1.40107i) q^{6} +(-0.338624 + 0.506787i) q^{7} +(-2.51633 - 1.29154i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(0.0353857 - 0.590120i) q^{10} +(2.06540 - 1.10398i) q^{11} +(0.0432145 - 1.99953i) q^{12} +(6.13408 + 0.604154i) q^{13} +(0.585733 - 0.632389i) q^{14} +(0.386207 - 0.159972i) q^{15} +(3.22676 + 2.36390i) q^{16} +(-1.03287 - 0.427827i) q^{17} +(1.28489 - 0.590806i) q^{18} +(-2.98293 + 2.44803i) q^{19} +(-0.180786 + 0.816274i) q^{20} +(0.583262 + 0.176931i) q^{21} +(-3.13027 + 1.08202i) q^{22} +(0.814610 - 4.09532i) q^{23} +(-0.505469 + 2.78289i) q^{24} +(4.73254 - 0.941360i) q^{25} +(-8.43226 - 2.20926i) q^{26} +(0.773010 + 0.634393i) q^{27} +(-0.958801 + 0.752794i) q^{28} +(-0.734072 + 1.37335i) q^{29} +(-0.574981 + 0.137441i) q^{30} +(5.44942 - 5.44942i) q^{31} +(-3.98021 - 4.01969i) q^{32} +(-1.65600 - 1.65600i) q^{33} +(1.34724 + 0.827422i) q^{34} +(-0.224705 - 0.120107i) q^{35} +(-1.92598 + 0.539080i) q^{36} +(3.28325 - 4.00065i) q^{37} +(4.71087 - 2.75484i) q^{38} +(-1.20249 - 6.04532i) q^{39} +(0.434193 - 1.09975i) q^{40} +(8.27977 + 1.64695i) q^{41} +(-0.775188 - 0.376939i) q^{42} +(1.68787 - 5.56418i) q^{43} +(4.61255 - 0.814304i) q^{44} +(-0.265194 - 0.323139i) q^{45} +(-2.04933 + 5.53811i) q^{46} +(2.83461 - 6.84336i) q^{47} +(1.32543 - 3.77402i) q^{48} +(2.53662 + 6.12394i) q^{49} +(-6.81894 + 0.261176i) q^{50} +(-0.109580 + 1.11258i) q^{51} +(11.2845 + 4.96252i) q^{52} +(-0.184717 - 0.345582i) q^{53} +(-0.938351 - 1.05806i) q^{54} +(0.543899 + 0.814003i) q^{55} +(1.50662 - 0.837900i) q^{56} +(3.20852 + 2.14386i) q^{57} +(1.33091 - 1.75459i) q^{58} +(-10.7359 + 1.05739i) q^{59} +(0.833605 - 0.0639507i) q^{60} +(-11.3165 + 3.43284i) q^{61} +(-8.82367 + 6.39748i) q^{62} -0.609507i q^{63} +(4.66387 + 6.49987i) q^{64} +2.57662i q^{65} +(1.94410 + 2.68138i) q^{66} +(-7.58663 + 2.30138i) q^{67} +(-1.69735 - 1.45547i) q^{68} +(-4.15545 + 0.409276i) q^{69} +(0.287082 + 0.217762i) q^{70} +(6.87928 + 4.59659i) q^{71} +(2.80979 - 0.324128i) q^{72} +(0.422635 + 0.632519i) q^{73} +(-5.47591 + 4.85635i) q^{74} +(-2.27461 - 4.25549i) q^{75} +(-7.19237 + 2.79868i) q^{76} +(-0.139912 + 1.42055i) q^{77} +(0.333626 + 8.71048i) q^{78} +(-1.95015 - 4.70808i) q^{79} +(-0.851203 + 1.43924i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-11.1968 - 4.14326i) q^{82} +(5.03186 + 6.13134i) q^{83} +(0.998704 + 0.698991i) q^{84} +(0.135662 - 0.447216i) q^{85} +(-3.59590 + 7.39510i) q^{86} +(1.52731 + 0.303800i) q^{87} +(-6.62308 + 0.110443i) q^{88} +(1.92002 + 9.65260i) q^{89} +(0.298431 + 0.510326i) q^{90} +(-2.38332 + 2.90409i) q^{91} +(4.09490 - 7.27824i) q^{92} +(-6.79666 - 3.63289i) q^{93} +(-5.48218 + 8.92631i) q^{94} +(-1.14064 - 1.14064i) q^{95} +(-2.69121 + 4.97568i) q^{96} +(4.85430 - 4.85430i) q^{97} +(-2.17935 - 9.11726i) q^{98} +(-1.10398 + 2.06540i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−1.39658	−	0.222610i	−0.987533	−	0.157409i
$2$	−1.39658	−	0.222610i	−0.987533	−	0.157409i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$4$	1.90089	+	0.621788i	0.950445	+	0.310894i
$5$	0.0409738	+	0.416014i	0.0183240	+	0.186047i	0.999990	−	0.00456440i	$-0.00145290\pi$
$5$	0.0409738	+	0.416014i	0.0183240	+	0.186047i	−0.981666	+	0.190612i	$0.938953\pi$
$6$	0.192382	+	1.40107i	0.0785396	+	0.571983i
$7$	−0.338624	+	0.506787i	−0.127988	+	0.191547i	−0.889929	−	0.456099i	$-0.849246\pi$
$7$	−0.338624	+	0.506787i	−0.127988	+	0.191547i	0.761941	+	0.647646i	$0.224246\pi$
$8$	−2.51633	−	1.29154i	−0.889658	−	0.456627i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	0.0353857	−	0.590120i	0.0111899	−	0.186612i
$11$	2.06540	−	1.10398i	0.622743	−	0.332863i	−0.129668	−	0.991557i	$-0.541391\pi$
$11$	2.06540	−	1.10398i	0.622743	−	0.332863i	0.752410	+	0.658695i	$0.228891\pi$
$12$	0.0432145	−	1.99953i	0.0124750	−	0.577215i
$13$	6.13408	+	0.604154i	1.70129	+	0.167562i	0.901517	−	0.432744i	$-0.142455\pi$
$13$	6.13408	+	0.604154i	1.70129	+	0.167562i	0.799770	+	0.600306i	$0.204955\pi$
$14$	0.585733	−	0.632389i	0.156544	−	0.169013i
$15$	0.386207	−	0.159972i	0.0997181	−	0.0413046i
$16$	3.22676	+	2.36390i	0.806690	+	0.590975i
$17$	−1.03287	−	0.427827i	−0.250507	−	0.103763i	0.253897	−	0.967231i	$-0.418288\pi$
$17$	−1.03287	−	0.427827i	−0.250507	−	0.103763i	−0.504404	+	0.863468i	$0.668288\pi$
$18$	1.28489	−	0.590806i	0.302852	−	0.139254i
$19$	−2.98293	+	2.44803i	−0.684331	+	0.561616i	−0.911026	−	0.412350i	$-0.864708\pi$
$19$	−2.98293	+	2.44803i	−0.684331	+	0.561616i	0.226694	+	0.973966i	$0.427208\pi$
$20$	−0.180786	+	0.816274i	−0.0404249	+	0.182524i
$21$	0.583262	+	0.176931i	0.127278	+	0.0386094i
$22$	−3.13027	+	1.08202i	−0.667375	+	0.230688i
$23$	0.814610	−	4.09532i	0.169858	−	0.853933i	−0.798043	−	0.602601i	$-0.794131\pi$
$23$	0.814610	−	4.09532i	0.169858	−	0.853933i	0.967901	−	0.251333i	$-0.0808688\pi$
$24$	−0.505469	+	2.78289i	−0.103178	+	0.568056i
$25$	4.73254	−	0.941360i	0.946507	−	0.188272i
$26$	−8.43226	−	2.20926i	−1.65370	−	0.433271i
$27$	0.773010	+	0.634393i	0.148766	+	0.122089i
$28$	−0.958801	+	0.752794i	−0.181196	+	0.142265i
$29$	−0.734072	+	1.37335i	−0.136314	+	0.255025i	−0.940811	−	0.338931i	$-0.889935\pi$
$29$	−0.734072	+	1.37335i	−0.136314	+	0.255025i	0.804498	+	0.593956i	$0.202435\pi$
$30$	−0.574981	+	0.137441i	−0.104977	+	0.0250931i
$31$	5.44942	−	5.44942i	0.978745	−	0.978745i	−0.0210335	−	0.999779i	$-0.506696\pi$
$31$	5.44942	−	5.44942i	0.978745	−	0.978745i	0.999779	+	0.0210335i	$0.00669566\pi$
$32$	−3.98021	−	4.01969i	−0.703609	−	0.710588i
$33$	−1.65600	−	1.65600i	−0.288272	−	0.288272i
$34$	1.34724	+	0.827422i	0.231050	+	0.141902i
$35$	−0.224705	−	0.120107i	−0.0379821	−	0.0203019i
$36$	−1.92598	+	0.539080i	−0.320996	+	0.0898467i
$37$	3.28325	−	4.00065i	0.539763	−	0.657703i	−0.429691	−	0.902976i	$-0.641378\pi$
$37$	3.28325	−	4.00065i	0.539763	−	0.657703i	0.969454	+	0.245273i	$0.0788776\pi$
$38$	4.71087	−	2.75484i	0.764204	−	0.446895i
$39$	−1.20249	−	6.04532i	−0.192552	−	0.968026i
$40$	0.434193	−	1.09975i	0.0686520	−	0.173886i
$41$	8.27977	+	1.64695i	1.29308	+	0.257210i	0.793241	−	0.608907i	$-0.208392\pi$
$41$	8.27977	+	1.64695i	1.29308	+	0.257210i	0.499841	+	0.866117i	$0.333392\pi$
$42$	−0.775188	−	0.376939i	−0.119614	−	0.0581629i
$43$	1.68787	−	5.56418i	0.257398	−	0.848529i	−0.729050	−	0.684460i	$-0.760038\pi$
$43$	1.68787	−	5.56418i	0.257398	−	0.848529i	0.986449	−	0.164069i	$-0.0524619\pi$
$44$	4.61255	−	0.814304i	0.695367	−	0.122761i
$45$	−0.265194	−	0.323139i	−0.0395327	−	0.0481708i
$46$	−2.04933	+	5.53811i	−0.302157	+	0.816550i
$47$	2.83461	−	6.84336i	0.413471	−	0.998207i	−0.570728	−	0.821139i	$-0.693339\pi$
$47$	2.83461	−	6.84336i	0.413471	−	0.998207i	0.984199	−	0.177068i	$-0.0566612\pi$
$48$	1.32543	−	3.77402i	0.191309	−	0.544733i
$49$	2.53662	+	6.12394i	0.362374	+	0.874848i
$50$	−6.81894	+	0.261176i	−0.964344	+	0.0369359i
$51$	−0.109580	+	1.11258i	−0.0153442	+	0.155793i
$52$	11.2845	+	4.96252i	1.56489	+	0.688178i
$53$	−0.184717	−	0.345582i	−0.0253729	−	0.0474694i	0.868915	−	0.494961i	$-0.164818\pi$
$53$	−0.184717	−	0.345582i	−0.0253729	−	0.0474694i	−0.894288	+	0.447491i	$0.852318\pi$
$54$	−0.938351	−	1.05806i	−0.127693	−	0.143984i
$55$	0.543899	+	0.814003i	0.0733394	+	0.109760i
$56$	1.50662	−	0.837900i	0.201331	−	0.111969i
$57$	3.20852	+	2.14386i	0.424978	+	0.283961i
$58$	1.33091	−	1.75459i	0.174758	−	0.230389i
$59$	−10.7359	+	1.05739i	−1.39769	+	0.137661i	−0.768629	−	0.639695i	$-0.779061\pi$
$59$	−10.7359	+	1.05739i	−1.39769	+	0.137661i	−0.629062	+	0.777355i	$0.716561\pi$
$60$	0.833605	−	0.0639507i	0.107618	−	0.00825600i
$61$	−11.3165	+	3.43284i	−1.44894	+	0.439530i	−0.914121	−	0.405440i	$-0.867118\pi$
$61$	−11.3165	+	3.43284i	−1.44894	+	0.439530i	−0.534814	+	0.844970i	$0.679618\pi$
$62$	−8.82367	+	6.39748i	−1.12061	+	0.812480i
$63$		−	0.609507i		−	0.0767907i
$64$	4.66387	+	6.49987i	0.582984	+	0.812484i
$65$			2.57662i			0.319590i
$66$	1.94410	+	2.68138i	0.239302	+	0.330055i
$67$	−7.58663	+	2.30138i	−0.926854	+	0.281158i	−0.717401	−	0.696661i	$-0.754668\pi$
$67$	−7.58663	+	2.30138i	−0.926854	+	0.281158i	−0.209453	+	0.977819i	$0.567168\pi$
$68$	−1.69735	−	1.45547i	−0.205833	−	0.176502i
$69$	−4.15545	+	0.409276i	−0.500257	+	0.0492710i
$70$	0.287082	+	0.217762i	0.0343129	+	0.0260275i
$71$	6.87928	+	4.59659i	0.816421	+	0.545515i	0.892216	−	0.451609i	$-0.149150\pi$
$71$	6.87928	+	4.59659i	0.816421	+	0.545515i	−0.0757956	+	0.997123i	$0.524150\pi$
$72$	2.80979	−	0.324128i	0.331137	−	0.0381988i
$73$	0.422635	+	0.632519i	0.0494657	+	0.0740307i	0.855378	−	0.518004i	$-0.173325\pi$
$73$	0.422635	+	0.632519i	0.0494657	+	0.0740307i	−0.805912	+	0.592035i	$0.798325\pi$
$74$	−5.47591	+	4.85635i	−0.636562	+	0.564540i
$75$	−2.27461	−	4.25549i	−0.262649	−	0.491382i
$76$	−7.19237	+	2.79868i	−0.825022	+	0.321031i
$77$	−0.139912	+	1.42055i	−0.0159445	+	0.161887i
$78$	0.333626	+	8.71048i	0.0377757	+	0.986268i
$79$	−1.95015	−	4.70808i	−0.219409	−	0.529700i	0.775399	−	0.631472i	$-0.217549\pi$
$79$	−1.95015	−	4.70808i	−0.219409	−	0.529700i	−0.994808	+	0.101772i	$0.967549\pi$
$80$	−0.851203	+	1.43924i	−0.0951673	+	0.160911i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−11.1968	−	4.14326i	−1.23647	−	0.457547i
$83$	5.03186	+	6.13134i	0.552318	+	0.673002i	0.972085	−	0.234631i	$-0.0753880\pi$
$83$	5.03186	+	6.13134i	0.552318	+	0.673002i	−0.419767	+	0.907632i	$0.637888\pi$
$84$	0.998704	+	0.698991i	0.108968	+	0.0762662i
$85$	0.135662	−	0.447216i	0.0147146	−	0.0485074i
$86$	−3.59590	+	7.39510i	−0.387756	+	0.797434i
$87$	1.52731	+	0.303800i	0.163744	+	0.0325708i
$88$	−6.62308	+	0.110443i	−0.706022	+	0.0117733i
$89$	1.92002	+	9.65260i	0.203522	+	1.02317i	0.938552	+	0.345139i	$0.112168\pi$
$89$	1.92002	+	9.65260i	0.203522	+	1.02317i	−0.735030	+	0.678035i	$0.762832\pi$
$90$	0.298431	+	0.510326i	0.0314574	+	0.0537931i
$91$	−2.38332	+	2.90409i	−0.249840	+	0.304431i
$92$	4.09490	−	7.27824i	0.426923	−	0.758809i
$93$	−6.79666	−	3.63289i	−0.704780	−	0.376713i
$94$	−5.48218	+	8.92631i	−0.565443	+	0.920679i
$95$	−1.14064	−	1.14064i	−0.117027	−	0.117027i
$96$	−2.69121	+	4.97568i	−0.274670	+	0.507828i
$97$	4.85430	−	4.85430i	0.492880	−	0.492880i	−0.416333	−	0.909212i	$-0.636685\pi$
$97$	4.85430	−	4.85430i	0.492880	−	0.492880i	0.909212	+	0.416333i	$0.136685\pi$
$98$	−2.17935	−	9.11726i	−0.220147	−	0.920983i
$99$	−1.10398	+	2.06540i	−0.110954	+	0.207581i
$100$	9.58136	+	1.15321i	0.958136	+	0.115321i
$101$	7.15808	+	5.87448i	0.712255	+	0.584533i	0.919186	−	0.393823i	$-0.128848\pi$
$101$	7.15808	+	5.87448i	0.712255	+	0.584533i	−0.206931	+	0.978356i	$0.566348\pi$
$102$	0.400709	−	1.52942i	0.0396762	−	0.151435i
$103$	−5.46101	+	1.08626i	−0.538089	+	0.107033i	−0.456651	−	0.889646i	$-0.650951\pi$
$103$	−5.46101	+	1.08626i	−0.538089	+	0.107033i	−0.0814381	+	0.996678i	$0.525951\pi$
$104$	−14.6551	−	9.44263i	−1.43705	−	0.925926i
$105$	−0.0497072	+	0.249895i	−0.00485092	+	0.0243872i
$106$	0.181043	+	0.523754i	0.0175845	+	0.0508715i
$107$	2.25225	+	0.683212i	0.217733	+	0.0660486i	0.397267	−	0.917703i	$-0.369959\pi$
$107$	2.25225	+	0.683212i	0.217733	+	0.0660486i	−0.179533	+	0.983752i	$0.557459\pi$
$108$	1.07495	+	1.68656i	0.103437	+	0.162289i
$109$	−5.96616	+	4.89630i	−0.571454	+	0.468980i	−0.875192	−	0.483775i	$-0.839265\pi$
$109$	−5.96616	+	4.89630i	−0.571454	+	0.468980i	0.303738	+	0.952756i	$0.401765\pi$
$110$	−0.578395	−	1.25790i	−0.0551478	−	0.119936i
$111$	−4.78146	−	1.98055i	−0.453836	−	0.187985i
$112$	−2.29065	+	0.834807i	−0.216446	+	0.0788818i
$113$	−16.1462	+	6.68799i	−1.51891	+	0.629153i	−0.977373	−	0.211524i	$-0.932157\pi$
$113$	−16.1462	+	6.68799i	−1.51891	+	0.629153i	−0.541537	+	0.840677i	$0.682157\pi$
$114$	−4.00371	−	3.70833i	−0.374982	−	0.347317i
$115$	1.73709	+	0.171088i	0.161984	+	0.0159541i
$116$	−2.24932	+	2.15415i	−0.208844	+	0.200008i
$117$	−5.43595	+	2.90558i	−0.502554	+	0.268621i
$118$	15.2289	+	0.913180i	1.40194	+	0.0840650i
$119$	0.566570	−	0.378570i	0.0519374	−	0.0347035i
$120$	−1.17843	−	0.0962565i	−0.107576	−	0.00878698i
$121$	−3.06416	+	4.58583i	−0.278560	+	0.416894i
$122$	16.5687	−	2.27506i	1.50006	−	0.205974i
$123$	−0.827458	−	8.40133i	−0.0746094	−	0.757522i
$124$	13.7471	−	6.97037i	1.23453	−	0.625957i
$125$	1.19226	+	3.93037i	0.106639	+	0.351543i
$126$	−0.135683	+	0.851228i	−0.0120876	+	0.0758334i
$127$	−4.84433			−0.429864			−0.214932	−	0.976629i	$-0.568953\pi$
$127$	−4.84433			−0.429864			−0.214932	+	0.976629i	$0.568953\pi$
$128$	−5.06655	−	10.1158i	−0.447824	−	0.894122i
$129$	−5.81455			−0.511942
$130$	0.573582	−	3.59846i	0.0503064	−	0.315606i
$131$	2.68374	+	8.84711i	0.234480	+	0.772975i	0.992661	+	0.120932i	$0.0385882\pi$
$131$	2.68374	+	8.84711i	0.234480	+	0.772975i	−0.758181	+	0.652044i	$0.773912\pi$
$132$	−2.11819	−	4.17755i	−0.184365	−	0.363609i
$133$	−0.230536	−	2.34067i	−0.0199900	−	0.202962i
$134$	11.1077	−	1.52520i	0.959556	−	0.131758i
$135$	−0.232243	+	0.347577i	−0.0199883	+	0.0299146i
$136$	2.04648	+	2.41054i	0.175484	+	0.206702i
$137$	0.482280	−	0.322249i	0.0412040	−	0.0275316i	−0.534798	−	0.844980i	$-0.679612\pi$
$137$	0.482280	−	0.322249i	0.0412040	−	0.0275316i	0.576002	+	0.817449i	$0.304612\pi$
$138$	5.89453	+	0.353457i	0.501776	+	0.0300883i
$139$	−11.8735	+	6.34650i	−1.00709	+	0.538303i	−0.890551	−	0.454882i	$-0.849681\pi$
$139$	−11.8735	+	6.34650i	−1.00709	+	0.538303i	−0.116543	+	0.993186i	$0.537181\pi$
$140$	−0.352459	−	0.368030i	−0.0297882	−	0.0311042i
$141$	−7.37154	−	0.726033i	−0.620795	−	0.0611430i
$142$	−8.58424	−	7.95092i	−0.720374	−	0.667226i
$143$	13.3363	−	5.52408i	1.11524	−	0.461947i
$144$	−3.99627	−	0.172818i	−0.333022	−	0.0144015i
$145$	−0.601411	−	0.249113i	−0.0499445	−	0.0206877i
$146$	−0.449440	−	0.977448i	−0.0371959	−	0.0808942i
$147$	5.12390	−	4.20508i	0.422612	−	0.346829i
$148$	8.72864	−	5.56331i	0.717490	−	0.457301i
$149$	−0.177772	−	0.0539265i	−0.0145636	−	0.00441783i	0.282994	−	0.959122i	$-0.408672\pi$
$149$	−0.177772	−	0.0539265i	−0.0145636	−	0.00441783i	−0.297558	+	0.954704i	$0.596172\pi$
$150$	2.22936	+	6.44950i	0.182027	+	0.526600i
$151$	−1.71263	+	8.60995i	−0.139371	+	0.700668i	0.846396	+	0.532554i	$0.178768\pi$
$151$	−1.71263	+	8.60995i	−0.139371	+	0.700668i	−0.985768	+	0.168114i	$0.946232\pi$
$152$	10.6678	−	2.30749i	0.865270	−	0.187163i
$153$	1.09648	−	0.218104i	0.0886455	−	0.0176327i
$154$	0.511629	−	1.95278i	0.0412283	−	0.157359i
$155$	2.49032	+	2.04375i	0.200027	+	0.164158i
$156$	1.47311	−	12.2392i	0.117943	−	0.979919i
$157$	4.42119	−	8.27146i	0.352849	−	0.660134i	−0.641402	−	0.767205i	$-0.721647\pi$
$157$	4.42119	−	8.27146i	0.352849	−	0.660134i	0.994251	+	0.107070i	$0.0341470\pi$
$158$	1.67548	+	7.00935i	0.133294	+	0.557634i
$159$	−0.277081	+	0.277081i	−0.0219739	+	0.0219739i
$160$	1.50916	−	1.82053i	0.119310	−	0.143925i
$161$	1.79961	+	1.79961i	0.141829	+	0.141829i
$162$	−0.740114	+	1.20509i	−0.0581489	+	0.0946804i
$163$	−0.669026	−	0.357602i	−0.0524022	−	0.0280096i	0.444988	−	0.895537i	$-0.353208\pi$
$163$	−0.669026	−	0.357602i	−0.0524022	−	0.0280096i	−0.497390	+	0.867527i	$0.665708\pi$
$164$	14.7149	+	8.27892i	1.14904	+	0.646475i
$165$	0.621066	−	0.756772i	0.0483500	−	0.0589146i
$166$	−5.66251	−	9.68306i	−0.439496	−	0.751552i
$167$	−3.61584	−	18.1780i	−0.279802	−	1.40666i	−0.823471	−	0.567359i	$-0.807965\pi$
$167$	−3.61584	−	18.1780i	−0.279802	−	1.40666i	0.543669	−	0.839300i	$-0.317035\pi$
$168$	−1.23917	−	1.19852i	−0.0956041	−	0.0924679i
$169$	24.5117	+	4.87568i	1.88552	+	0.375052i
$170$	−0.289018	+	0.594375i	−0.0221666	+	0.0455865i
$171$	1.12016	−	3.69269i	0.0856611	−	0.282387i
$172$	6.66820	−	9.52738i	0.508445	−	0.726456i
$173$	2.77486	+	3.38117i	0.210969	+	0.257066i	0.867734	−	0.497029i	$-0.165576\pi$
$173$	2.77486	+	3.38117i	0.210969	+	0.257066i	−0.656765	+	0.754095i	$0.728076\pi$
$174$	−2.06538	−	0.764276i	−0.156576	−	0.0579396i
$175$	−1.12548	+	2.71716i	−0.0850785	+	0.205398i
$176$	9.27426	+	1.32012i	0.699074	+	0.0995079i
$177$	4.12832	+	9.96664i	0.310303	+	0.749138i
$178$	−0.532702	−	13.9081i	−0.0399277	−	1.04245i
$179$	−1.16050	+	11.7827i	−0.0867398	+	0.880684i	0.849094	+	0.528242i	$0.177149\pi$
$179$	−1.16050	+	11.7827i	−0.0867398	+	0.880684i	−0.935834	+	0.352442i	$0.885351\pi$
$180$	−0.303180	−	0.779146i	−0.0225977	−	0.0580741i
$181$	−8.96137	−	16.7656i	−0.666094	−	1.24617i	−0.957185	−	0.289478i	$-0.906518\pi$
$181$	−8.96137	−	16.7656i	−0.666094	−	1.24617i	0.291091	−	0.956695i	$-0.405982\pi$
$182$	3.97499	−	3.52525i	0.294646	−	0.261309i
$183$	6.57004	+	9.83276i	0.485671	+	0.726858i
$184$	−7.33908	+	9.25310i	−0.541044	+	0.682147i
$185$	1.79885	+	1.20196i	0.132254	+	0.0883695i
$186$	8.68338	+	6.58664i	0.636696	+	0.482956i
$187$	−2.60560	+	0.256629i	−0.190540	+	0.0187666i
$188$	9.64341	−	11.2460i	0.703318	−	0.820195i
$189$	−0.583262	+	0.176931i	−0.0424261	+	0.0128698i
$190$	1.33908	+	1.84691i	0.0971468	+	0.133989i
$191$		−	19.9430i		−	1.44302i	−0.692403	−	0.721511i	$-0.743448\pi$
$191$		−	19.9430i		−	1.44302i	0.692403	−	0.721511i	$-0.256552\pi$
$192$	4.86614	−	6.34986i	0.351183	−	0.458262i
$193$		−	15.8427i		−	1.14038i	−0.821512	−	0.570191i	$-0.806869\pi$
$193$		−	15.8427i		−	1.14038i	0.821512	−	0.570191i	$-0.193131\pi$
$194$	−7.86006	+	5.69882i	−0.564319	+	0.409152i
$195$	2.46567	−	0.747953i	0.176570	−	0.0535620i
$196$	1.01404	+	13.2182i	0.0724316	+	0.944154i
$197$	1.21870	−	0.120031i	0.0868287	−	0.00855188i	−0.0545095	−	0.998513i	$-0.517360\pi$
$197$	1.21870	−	0.120031i	0.0868287	−	0.00855188i	0.141338	+	0.989961i	$0.454860\pi$
$198$	2.00158	−	2.63875i	0.142246	−	0.187528i
$199$	−20.4761	−	13.6817i	−1.45152	−	0.969872i	−0.996858	−	0.0792050i	$-0.974762\pi$
$199$	−20.4761	−	13.6817i	−1.45152	−	0.969872i	−0.454657	−	0.890667i	$-0.650238\pi$
$200$	−13.1244	−	3.74346i	−0.928038	−	0.264703i
$201$	4.40456	+	6.59189i	0.310674	+	0.464956i
$202$	−8.68913	−	9.79766i	−0.611365	−	0.689361i
$203$	−0.447422	−	0.837068i	−0.0314029	−	0.0587507i
$204$	−0.900089	+	2.04676i	−0.0630188	+	0.143302i
$205$	−0.345900	+	3.51198i	−0.0241587	+	0.245287i
$206$	7.86857	−	0.301379i	0.548229	−	0.0209981i
$207$	1.59791	+	3.85771i	0.111063	+	0.268129i
$208$	18.3650	+	16.4498i	1.27339	+	1.14059i
$209$	−3.45838	+	8.34927i	−0.239221	+	0.577531i
$210$	0.125049	−	0.337934i	0.00862923	−	0.0233196i
$211$	−0.918023	−	1.11861i	−0.0631993	−	0.0770086i	0.740451	−	0.672110i	$-0.234612\pi$
$211$	−0.918023	−	1.11861i	−0.0631993	−	0.0770086i	−0.803651	+	0.595101i	$0.797112\pi$
$212$	−0.136249	−	0.771768i	−0.00935761	−	0.0530053i
$213$	2.40171	−	7.91738i	0.164563	−	0.542490i
$214$	−2.99336	−	1.45554i	−0.204622	−	0.0994984i
$215$	2.38393	+	0.474194i	0.162583	+	0.0323398i
$216$	−1.12581	−	2.59472i	−0.0766017	−	0.176548i
$217$	0.916390	+	4.60700i	0.0622086	+	0.312744i
$218$	9.42220	−	5.50996i	0.638152	−	0.373182i
$219$	0.482598	−	0.588047i	0.0326109	−	0.0397366i
$220$	0.527756	+	1.88552i	0.0355813	+	0.127122i
$221$	−6.07720	−	3.24833i	−0.408797	−	0.218507i
$222$	6.23682	+	3.83040i	0.418588	+	0.257079i
$223$	15.6533	+	15.6533i	1.04822	+	1.04822i	0.998777	+	0.0494474i	$0.0157460\pi$
$223$	15.6533	+	15.6533i	1.04822	+	1.04822i	0.0494474	+	0.998777i	$0.484254\pi$
$224$	3.38492	−	0.655955i	0.226165	−	0.0438278i
$225$	−3.41197	+	3.41197i	−0.227465	+	0.227465i
$226$	24.0384	−	5.74602i	1.59901	−	0.382219i
$227$	−13.8127	+	25.8418i	−0.916784	+	1.71518i	−0.252666	+	0.967554i	$0.581307\pi$
$227$	−13.8127	+	25.8418i	−0.916784	+	1.71518i	−0.664118	+	0.747628i	$0.731193\pi$
$228$	4.76601	+	6.07026i	0.315637	+	0.402013i
$229$	−21.5818	−	17.7117i	−1.42617	−	1.17042i	−0.957994	−	0.286787i	$-0.907413\pi$
$229$	−21.5818	−	17.7117i	−1.42617	−	1.17042i	−0.468172	−	0.883637i	$-0.655087\pi$
$230$	−2.38790	−	0.625633i	−0.157454	−	0.0412530i
$231$	1.40000	−	0.278477i	0.0921132	−	0.0183225i
$232$	3.62090	−	2.50773i	0.237724	−	0.164641i
$233$	3.35240	−	16.8537i	0.219623	−	1.10412i	−0.700848	−	0.713310i	$-0.747195\pi$
$233$	3.35240	−	16.8537i	0.219623	−	1.10412i	0.920471	−	0.390810i	$-0.127805\pi$
$234$	8.23857	−	2.84778i	0.538572	−	0.186165i
$235$	2.96308	+	0.898841i	0.193290	+	0.0586339i
$236$	−21.0652	−	4.66544i	−1.37123	−	0.303695i
$237$	−3.93925	+	3.23286i	−0.255882	+	0.209997i
$238$	−0.875536	+	0.402580i	−0.0567526	+	0.0260954i
$239$	15.9379	+	6.60171i	1.03094	+	0.427029i	0.833052	−	0.553195i	$-0.186592\pi$
$239$	15.9379	+	6.60171i	1.03094	+	0.427029i	0.197888	+	0.980225i	$0.436592\pi$
$240$	1.62435	+	0.396762i	0.104852	+	0.0256109i
$241$	23.6164	−	9.78225i	1.52127	−	0.630130i	0.543423	−	0.839459i	$-0.317128\pi$
$241$	23.6164	−	9.78225i	1.52127	−	0.630130i	0.977845	+	0.209329i	$0.0671280\pi$
$242$	5.30020	−	5.72238i	0.340710	−	0.367849i
$243$	−0.995185	−	0.0980171i	−0.0638411	−	0.00628780i
$244$	−23.6460	−	0.511044i	−1.51378	−	0.0327163i
$245$	−2.44371	+	1.30619i	−0.156123	+	0.0834494i
$246$	−0.714607	+	11.9174i	−0.0455617	+	0.759823i
$247$	−19.7765	+	13.2142i	−1.25835	+	0.840802i
$248$	−20.7507	+	6.67444i	−1.31767	+	0.423828i
$249$	4.40665	−	6.59502i	0.279260	−	0.417942i
$250$	−0.790155	−	5.75449i	−0.0499738	−	0.363946i
$251$	0.770247	+	7.82045i	0.0486176	+	0.493622i	0.988403	+	0.151856i	$0.0485251\pi$
$251$	0.770247	+	7.82045i	0.0486176	+	0.493622i	−0.939785	+	0.341766i	$0.888975\pi$
$252$	0.378984	−	1.15861i	0.0238738	−	0.0729853i
$253$	−2.83866	−	9.35780i	−0.178465	−	0.588320i
$254$	6.76550	+	1.07840i	0.424505	+	0.0676646i
$255$	−0.467340			−0.0292660
$256$	4.82397	+	15.2555i	0.301498	+	0.953467i
$257$	−18.6111			−1.16093			−0.580464	−	0.814286i	$-0.697129\pi$
$257$	−18.6111			−1.16093			−0.580464	+	0.814286i	$0.697129\pi$
$258$	8.12050	+	1.29438i	0.505560	+	0.0805845i
$259$	0.915690	+	3.01862i	0.0568982	+	0.187568i
$260$	−1.60211	+	4.89786i	−0.0993586	+	0.303753i
$261$	−0.152635	−	1.54973i	−0.00944787	−	0.0959258i
$262$	−1.77861	−	12.9532i	−0.109883	−	0.800248i
$263$	−0.981916	+	1.46954i	−0.0605475	+	0.0906158i	−0.860508	−	0.509437i	$-0.829854\pi$
$263$	−0.981916	+	1.46954i	−0.0605475	+	0.0906158i	0.799960	+	0.600053i	$0.204854\pi$
$264$	2.02827	+	6.30583i	0.124831	+	0.388097i
$265$	0.136198	−	0.0910049i	0.00836661	−	0.00559039i
$266$	−0.199095	+	3.32026i	−0.0122073	+	0.203578i
$267$	8.67961	−	4.63935i	0.531183	−	0.283923i
$268$	−15.8523	−	0.342605i	−0.968334	−	0.0209279i
$269$	12.5169	+	1.23280i	0.763166	+	0.0751653i	0.472109	−	0.881540i	$-0.343493\pi$
$269$	12.5169	+	1.23280i	0.763166	+	0.0751653i	0.291058	+	0.956706i	$0.405993\pi$
$270$	0.401721	−	0.433720i	0.0244480	−	0.0263954i
$271$	4.47825	−	1.85495i	0.272034	−	0.112680i	−0.242496	−	0.970152i	$-0.577966\pi$
$271$	4.47825	−	1.85495i	0.272034	−	0.112680i	0.514530	+	0.857472i	$0.327966\pi$
$272$	−2.32147	−	3.82208i	−0.140760	−	0.231748i
$273$	3.47088	+	1.43769i	0.210067	+	0.0870128i
$274$	−0.745280	+	0.342687i	−0.0450240	+	0.0207025i
$275$	8.73536	−	7.16892i	0.526762	−	0.432302i
$276$	−8.15353	−	1.80582i	−0.490785	−	0.108697i
$277$	−8.60193	−	2.60937i	−0.516840	−	0.156782i	0.0210799	−	0.999778i	$-0.493290\pi$
$277$	−8.60193	−	2.60937i	−0.516840	−	0.156782i	−0.537920	+	0.842996i	$0.680790\pi$
$278$	17.9951	−	6.22026i	1.07927	−	0.373066i
$279$	−1.50349	+	7.55857i	−0.0900117	+	0.452520i
$280$	0.410310	+	0.592445i	0.0245207	+	0.0354054i
$281$	−4.72946	+	0.940748i	−0.282136	+	0.0561203i	−0.334130	−	0.942527i	$-0.608442\pi$
$281$	−4.72946	+	0.940748i	−0.282136	+	0.0561203i	0.0519939	+	0.998647i	$0.483442\pi$
$282$	10.1333	+	2.65494i	0.603432	+	0.158100i
$283$	−14.0344	−	11.5177i	−0.834259	−	0.684658i	0.116973	−	0.993135i	$-0.462681\pi$
$283$	−14.0344	−	11.5177i	−0.834259	−	0.684658i	−0.951232	+	0.308477i	$0.900181\pi$
$284$	10.2187	+	13.0151i	0.606365	+	0.772302i
$285$	−0.760412	+	1.42263i	−0.0450429	+	0.0842693i
$286$	−19.8550	+	4.74604i	−1.17405	+	0.280639i
$287$	−3.63838	+	3.63838i	−0.214767	+	0.214767i
$288$	5.54265	+	1.13096i	0.326604	+	0.0666427i
$289$	−11.1370	−	11.1370i	−0.655120	−	0.655120i
$290$	0.784466	+	0.481787i	0.0460654	+	0.0282915i
$291$	−6.05441	−	3.23615i	−0.354916	−	0.189706i
$292$	0.410091	+	1.46514i	0.0239988	+	0.0857407i
$293$	10.1985	−	12.4270i	0.595805	−	0.725991i	−0.384578	−	0.923093i	$-0.625653\pi$
$293$	10.1985	−	12.4270i	0.595805	−	0.725991i	0.980383	+	0.197102i	$0.0631529\pi$
$294$	−8.09205	+	4.73211i	−0.471938	+	0.275982i
$295$	−0.879779	−	4.42295i	−0.0512227	−	0.257514i
$296$	−13.4287	+	5.82654i	−0.780529	+	0.338661i
$297$	2.29694	+	0.456889i	0.133282	+	0.0265114i
$298$	0.236269	+	0.114887i	0.0136867	+	0.00665521i
$299$	7.47108	−	24.6289i	0.432064	−	1.42432i
$300$	−1.67777	−	9.50355i	−0.0968659	−	0.548687i
$301$	2.24830	+	2.73956i	0.129590	+	0.157905i
$302$	4.30849	−	11.6433i	0.247926	−	0.669995i
$303$	3.54365	−	8.55513i	0.203577	−	0.491479i
$304$	−15.4121	+	0.847855i	−0.883944	+	0.0486278i
$305$	−1.89179	−	4.56719i	−0.108324	−	0.261516i
$306$	−1.57988	+	0.0605121i	−0.0903159	+	0.00345925i
$307$	−1.69690	+	17.2289i	−0.0968474	+	0.983308i	0.816833	+	0.576874i	$0.195728\pi$
$307$	−1.69690	+	17.2289i	−0.0968474	+	0.983308i	−0.913680	+	0.406434i	$0.866772\pi$
$308$	−1.14924	+	2.61332i	−0.0654841	+	0.148908i
$309$	2.62474	+	4.91054i	0.149316	+	0.279351i
$310$	−3.02298	−	3.40864i	−0.171694	−	0.193598i
$311$	9.06083	+	13.5605i	0.513793	+	0.768945i	0.994136	−	0.108135i	$-0.0344880\pi$
$311$	9.06083	+	13.5605i	0.513793	+	0.768945i	−0.480344	+	0.877080i	$0.659488\pi$
$312$	−4.78188	+	16.7651i	−0.270721	+	0.949137i
$313$	−1.76224	−	1.17749i	−0.0996075	−	0.0665556i	0.504769	−	0.863254i	$-0.331578\pi$
$313$	−1.76224	−	1.17749i	−0.0996075	−	0.0665556i	−0.604376	+	0.796699i	$0.706578\pi$
$314$	−8.01587	+	10.5676i	−0.452362	+	0.596363i
$315$	0.253564	−	0.0249738i	0.0142867	−	0.00140712i
$316$	−0.779595	−	10.1621i	−0.0438556	−	0.571664i
$317$	−30.4668	+	9.24201i	−1.71119	+	0.519083i	−0.985607	−	0.169055i	$-0.945929\pi$
$317$	−30.4668	+	9.24201i	−1.71119	+	0.519083i	−0.725580	+	0.688138i	$0.758429\pi$
$318$	0.448647	−	0.325285i	0.0251589	−	0.0182411i
$319$			3.64693i			0.204189i
$320$	−2.51294	+	2.20656i	−0.140478	+	0.123351i
$321$		−	2.35359i		−	0.131365i
$322$	−2.11269	−	2.91391i	−0.117736	−	0.162386i
$323$	4.12830	−	1.25231i	0.229705	−	0.0696801i
$324$	1.30190	−	1.51824i	0.0723275	−	0.0843469i
$325$	29.5985	−	2.91520i	1.64183	−	0.161706i
$326$	0.854745	+	0.648353i	0.0473400	+	0.0359090i
$327$	6.41735	+	4.28794i	0.354880	+	0.237123i
$328$	−18.7076	−	14.8379i	−1.03295	−	0.819285i
$329$	2.50826	+	3.75387i	0.138285	+	0.206958i
$330$	−1.03584	+	0.918639i	−0.0570209	+	0.0505694i
$331$	−1.97375	−	3.69262i	−0.108487	−	0.202965i	0.821820	−	0.569748i	$-0.192959\pi$
$331$	−1.97375	−	3.69262i	−0.108487	−	0.202965i	−0.930307	+	0.366783i	$0.880459\pi$
$332$	5.75262	+	14.7837i	0.315716	+	0.811363i
$333$	−0.507279	+	5.15049i	−0.0277987	+	0.282245i
$334$	1.00320	+	26.1921i	0.0548926	+	1.43317i
$335$	−1.26826	−	3.06185i	−0.0692924	−	0.167287i
$336$	1.46380	+	1.94969i	0.0798569	+	0.106364i
$337$	−10.7330	+	25.9119i	−0.584666	+	1.41151i	0.303875	+	0.952712i	$0.401719\pi$
$337$	−10.7330	+	25.9119i	−0.584666	+	1.41151i	−0.888541	+	0.458797i	$0.848281\pi$
$338$	−33.1472	−	12.2658i	−1.80297	−	0.667174i
$339$	11.0870	+	13.5096i	0.602164	+	0.733739i
$340$	0.535951	−	0.765756i	0.0290660	−	0.0415290i
$341$	5.23920	−	17.2713i	0.283718	−	0.935294i
$342$	−2.38643	+	4.90779i	−0.129044	+	0.265383i
$343$	−8.14706	−	1.62055i	−0.439900	−	0.0875016i
$344$	−11.4336	+	11.8214i	−0.616458	+	0.637366i
$345$	−0.340529	−	1.71195i	−0.0183335	−	0.0921685i
$346$	−3.12264	−	5.33980i	−0.167874	−	0.287070i
$347$	−14.3509	+	17.4867i	−0.770398	+	0.938733i	−0.999398	−	0.0346937i	$-0.988954\pi$
$347$	−14.3509	+	17.4867i	−0.770398	+	0.938733i	0.229000	+	0.973426i	$0.426454\pi$
$348$	2.71434	+	1.52715i	0.145504	+	0.0818638i
$349$	17.1181	+	9.14984i	0.916313	+	0.489779i	0.860952	−	0.508687i	$-0.169869\pi$
$349$	17.1181	+	9.14984i	0.916313	+	0.489779i	0.0553613	+	0.998466i	$0.482369\pi$
$350$	2.17670	−	3.54419i	0.116349	−	0.189445i
$351$	4.35843	+	4.35843i	0.232636	+	0.232636i
$352$	−12.6584	−	3.90821i	−0.674695	−	0.208308i
$353$	15.1681	−	15.1681i	0.807319	−	0.807319i	−0.176909	−	0.984227i	$-0.556610\pi$
$353$	15.1681	−	15.1681i	0.807319	−	0.807319i	0.984227	+	0.176909i	$0.0566097\pi$
$354$	−3.54686	−	14.8382i	−0.188514	−	0.788644i
$355$	−1.63038	+	3.05022i	−0.0865314	+	0.161889i
$356$	−2.35212	+	19.5424i	−0.124662	+	1.03574i
$357$	−0.526736	−	0.432281i	−0.0278778	−	0.0228787i
$358$	4.24370	−	16.1973i	0.224286	−	0.856051i
$359$	−23.9405	+	4.76206i	−1.26353	+	0.251332i	−0.780991	−	0.624542i	$-0.785286\pi$
$359$	−23.9405	+	4.76206i	−1.26353	+	0.251332i	−0.482540	+	0.875874i	$0.660286\pi$
$360$	0.249970	+	1.15563i	0.0131746	+	0.0609072i
$361$	−0.801682	+	4.03033i	−0.0421938	+	0.212122i
$362$	8.78312	+	25.4094i	0.461631	+	1.33549i
$363$	5.27785	+	1.60102i	0.277015	+	0.0840316i
$364$	−6.33616	+	4.03843i	−0.332105	+	0.211671i
$365$	−0.245820	+	0.201739i	−0.0128668	+	0.0105595i
$366$	−6.98673	−	15.1948i	−0.365202	−	0.794246i
$367$	24.9908	+	10.3515i	1.30451	+	0.540346i	0.923277	−	0.384134i	$-0.125500\pi$
$367$	24.9908	+	10.3515i	1.30451	+	0.540346i	0.381232	+	0.924479i	$0.375500\pi$
$368$	12.3095	−	11.2890i	0.641676	−	0.588478i
$369$	−7.79937	+	3.23060i	−0.406019	+	0.168179i
$370$	−2.24468	−	2.07907i	−0.116695	−	0.108086i
$371$	0.237686	+	0.0234101i	0.0123401	+	0.00121539i
$372$	−10.6608	−	11.1318i	−0.552737	−	0.577157i
$373$	−19.4855	+	10.4152i	−1.00892	+	0.539279i	−0.891125	−	0.453758i	$-0.850083\pi$
$373$	−19.4855	+	10.4152i	−1.00892	+	0.539279i	−0.117796	+	0.993038i	$0.537583\pi$
$374$	3.69606	+	0.221629i	0.191119	+	0.0114602i
$375$	3.41503	−	2.28185i	0.176351	−	0.117834i
$376$	−15.9713	+	13.5592i	−0.823656	+	0.699262i
$377$	−5.33257	+	7.98075i	−0.274641	+	0.411030i
$378$	0.853961	−	0.117258i	0.0439230	−	0.00603111i
$379$	1.83099	+	18.5904i	0.0940516	+	0.954922i	0.920194	+	0.391462i	$0.128030\pi$
$379$	1.83099	+	18.5904i	0.0940516	+	0.954922i	−0.826143	+	0.563461i	$0.809470\pi$
$380$	−1.45899	−	2.87746i	−0.0748446	−	0.147610i
$381$	1.40623	+	4.63573i	0.0720435	+	0.237496i
$382$	−4.43951	+	27.8520i	−0.227145	+	1.42503i
$383$	−8.20885			−0.419453			−0.209726	−	0.977760i	$-0.567257\pi$
$383$	−8.20885			−0.419453			−0.209726	+	0.977760i	$0.567257\pi$
$384$	−8.20951	+	7.78486i	−0.418940	+	0.397269i
$385$	−0.596703			−0.0304108
$386$	−3.52675	+	22.1256i	−0.179507	+	1.12617i
$387$	1.68787	+	5.56418i	0.0857995	+	0.282843i
$388$	12.2458	−	6.20915i	0.621688	−	0.315222i
$389$	−1.05951	−	10.7574i	−0.0537194	−	0.545422i	−0.983950	−	0.178446i	$-0.942893\pi$
$389$	−1.05951	−	10.7574i	−0.0537194	−	0.545422i	0.930230	−	0.366976i	$-0.119607\pi$
$390$	−3.61001	+	0.495695i	−0.182800	+	0.0251005i
$391$	−2.59347	+	3.88140i	−0.131157	+	0.196291i
$392$	1.52630	−	18.6860i	0.0770900	−	0.943785i
$393$	7.68711	−	5.13636i	0.387763	−	0.259095i
$394$	−1.72873	−	0.103661i	−0.0870923	−	0.00522237i
$395$	1.87872	−	1.00420i	0.0945288	−	0.0505267i
$396$	−3.38279	+	3.23966i	−0.169992	+	0.162799i
$397$	20.4277	+	2.01195i	1.02524	+	0.100977i	0.596632	−	0.802515i	$-0.296505\pi$
$397$	20.4277	+	2.01195i	1.02524	+	0.100977i	0.428605	+	0.903492i	$0.359005\pi$
$398$	25.5509	+	23.6659i	1.28075	+	1.18626i
$399$	−2.17296	+	0.900070i	−0.108784	+	0.0450599i
$400$	17.4960	+	8.14969i	0.874802	+	0.407485i
$401$	−21.9440	−	9.08949i	−1.09583	−	0.453907i	−0.239793	−	0.970824i	$-0.577080\pi$
$401$	−21.9440	−	9.08949i	−1.09583	−	0.453907i	−0.856036	+	0.516917i	$0.827080\pi$
$402$	−4.68392	−	10.1866i	−0.233612	−	0.508063i
$403$	36.7195	−	30.1349i	1.82913	−	1.50113i
$404$	9.95403	+	15.6175i	0.495232	+	0.777002i
$405$	0.400027	+	0.121347i	0.0198775	+	0.00602977i
$406$	0.438522	+	1.26864i	0.0217635	+	0.0629613i
$407$	2.36459	−	11.8876i	0.117208	−	0.589246i
$408$	1.71268	−	2.65810i	0.0847902	−	0.131596i
$409$	−3.22902	+	0.642292i	−0.159665	+	0.0317593i	−0.274275	−	0.961651i	$-0.588438\pi$
$409$	−3.22902	+	0.642292i	−0.159665	+	0.0317593i	0.114611	+	0.993410i	$0.463438\pi$
$410$	1.26488	−	4.82777i	0.0624680	−	0.238427i
$411$	−0.448372	−	0.367969i	−0.0221165	−	0.0181506i
$412$	−11.0562	−	1.33072i	−0.544700	−	0.0655600i
$413$	3.09955	−	5.79885i	0.152519	−	0.285343i
$414$	−1.37286	−	5.74332i	−0.0674722	−	0.282269i
$415$	−2.34455	+	2.34455i	−0.115089	+	0.115089i
$416$	−21.9864	−	27.0618i	−1.07797	−	1.32681i
$417$	9.51991	+	9.51991i	0.466192	+	0.466192i
$418$	6.68855	−	10.8906i	0.327147	−	0.532675i
$419$	−8.07165	−	4.31439i	−0.394326	−	0.210772i	0.262303	−	0.964986i	$-0.415518\pi$
$419$	−8.07165	−	4.31439i	−0.394326	−	0.210772i	−0.656629	+	0.754214i	$0.728018\pi$
$420$	−0.249869	+	0.444115i	−0.0121924	+	0.0216706i
$421$	14.5215	−	17.6944i	0.707732	−	0.862375i	−0.287712	−	0.957717i	$-0.592895\pi$
$421$	14.5215	−	17.6944i	0.707732	−	0.862375i	0.995445	+	0.0953425i	$0.0303946\pi$
$422$	1.03308	+	1.76660i	0.0502896	+	0.0859967i
$423$	1.44507	+	7.26488i	0.0702619	+	0.353230i
$424$	0.0184793	+	1.10817i	0.000897435	+	0.0538175i
$425$	−5.29081	−	1.05241i	−0.256642	−	0.0510493i
$426$	−5.11668	+	10.5226i	−0.247904	+	0.509823i
$427$	2.09234	−	6.89752i	0.101255	−	0.333794i
$428$	3.85646	+	2.69913i	0.186409	+	0.130467i
$429$	−9.15755	−	11.1585i	−0.442131	−	0.538738i
$430$	−3.22380	−	1.19294i	−0.155466	−	0.0575287i
$431$	8.56771	−	20.6843i	0.412692	−	0.996327i	−0.571720	−	0.820449i	$-0.693724\pi$
$431$	8.56771	−	20.6843i	0.412692	−	0.996327i	0.984412	−	0.175878i	$-0.0562764\pi$
$432$	0.994678	+	3.87435i	0.0478565	+	0.186405i
$433$	−11.5356	−	27.8494i	−0.554365	−	1.33836i	−0.914171	−	0.405329i	$-0.867157\pi$
$433$	−11.5356	−	27.8494i	−0.554365	−	1.33836i	0.359806	−	0.933027i	$-0.382843\pi$
$434$	−0.254249	−	6.63806i	−0.0122043	−	0.318637i
$435$	−0.0638055	+	0.647828i	−0.00305924	+	0.0310610i
$436$	−14.3855	+	5.59764i	−0.688939	+	0.268078i
$437$	7.59553	+	14.2102i	0.363344	+	0.679768i
$438$	−0.804894	+	0.713826i	−0.0384593	+	0.0341079i
$439$	17.2069	+	25.7520i	0.821243	+	1.22908i	0.970697	+	0.240308i	$0.0772484\pi$
$439$	17.2069	+	25.7520i	0.821243	+	1.22908i	−0.149454	+	0.988769i	$0.547752\pi$
$440$	−0.317319	−	2.75077i	−0.0151276	−	0.131138i
$441$	−5.51140	−	3.68260i	−0.262447	−	0.175362i
$442$	7.76421	+	5.88941i	0.369306	+	0.280131i
$443$	12.0436	−	1.18619i	0.572207	−	0.0563575i	0.192224	−	0.981351i	$-0.438430\pi$
$443$	12.0436	−	1.18619i	0.572207	−	0.0563575i	0.379983	+	0.924994i	$0.375930\pi$
$444$	−7.85755	−	6.73785i	−0.372903	−	0.319764i
$445$	−3.93695	+	1.19426i	−0.186629	+	0.0566134i
$446$	−18.3766	−	25.3458i	−0.870156	−	1.20016i
$447$			0.185771i			0.00878667i
$448$	−4.87335	+	0.162577i	−0.230244	+	0.00768102i
$449$		−	37.2145i		−	1.75626i	−0.478421	−	0.878130i	$-0.658791\pi$
$449$		−	37.2145i		−	1.75626i	0.478421	−	0.878130i	$-0.341209\pi$
$450$	5.52464	−	4.00556i	0.260434	−	0.188824i
$451$	18.9193	−	5.73909i	0.890873	−	0.270243i
$452$	−34.8507	+	2.67360i	−1.63924	+	0.125756i
$453$	8.73636	−	0.860456i	0.410470	−	0.0404278i
$454$	25.0433	−	33.0154i	1.17534	−	1.54949i
$455$	−1.30580	−	0.872505i	−0.0612167	−	0.0409037i
$456$	−5.30482	−	9.53858i	−0.248421	−	0.446685i
$457$	3.80698	+	5.69755i	0.178083	+	0.266520i	0.909763	−	0.415128i	$-0.136263\pi$
$457$	3.80698	+	5.69755i	0.178083	+	0.266520i	−0.731680	+	0.681649i	$0.761263\pi$
$458$	26.1980	+	29.5402i	1.22415	+	1.38033i
$459$	−0.527005	−	0.985958i	−0.0245985	−	0.0460206i
$460$	3.19563	+	1.40532i	0.148997	+	0.0655234i
$461$	−2.29273	+	23.2785i	−0.106783	+	1.08419i	0.781191	+	0.624292i	$0.214613\pi$
$461$	−2.29273	+	23.2785i	−0.106783	+	1.08419i	−0.887974	+	0.459894i	$0.847887\pi$
$462$	−2.01721	+	0.0772624i	−0.0938490	+	0.00359457i
$463$	6.25907	+	15.1107i	0.290884	+	0.702255i	0.999996	−	0.00284016i	$-0.000904054\pi$
$463$	6.25907	+	15.1107i	0.290884	+	0.702255i	−0.709112	+	0.705096i	$0.750904\pi$
$464$	−5.61514	+	2.69621i	−0.260676	+	0.125168i
$465$	1.23285	−	2.97636i	0.0571720	−	0.138025i
$466$	−8.43371	+	22.7913i	−0.390684	+	1.05578i
$467$	7.35742	+	8.96504i	0.340461	+	0.414853i	0.914891	−	0.403701i	$-0.132276\pi$
$467$	7.35742	+	8.96504i	0.340461	+	0.414853i	−0.574430	+	0.818554i	$0.694776\pi$
$468$	−12.1398	+	2.14317i	−0.561162	+	0.0990682i
$469$	1.40271	−	4.62411i	0.0647710	−	0.213521i
$470$	−3.93810	−	1.91492i	−0.181651	−	0.0883286i
$471$	−9.19870	−	1.82973i	−0.423854	−	0.0843097i
$472$	28.3807	+	11.2050i	1.30633	+	0.515752i
$473$	−2.65660	−	13.3556i	−0.122151	−	0.614093i
$474$	6.22116	−	3.63804i	0.285747	−	0.167101i
$475$	−11.8124	+	14.3934i	−0.541988	+	0.660414i
$476$	1.31238	−	0.367334i	0.0601527	−	0.0168367i
$477$	0.345582	+	0.184717i	0.0158231	+	0.00845763i
$478$	−20.7891	−	12.7678i	−0.950869	−	0.583985i
$479$	10.3486	+	10.3486i	0.472840	+	0.472840i	0.902832	−	0.429993i	$-0.141484\pi$
$479$	10.3486	+	10.3486i	0.472840	+	0.472840i	−0.429993	+	0.902832i	$0.641484\pi$
$480$	−2.18022	−	0.915709i	−0.0995131	−	0.0417962i
$481$	22.5567	−	22.5567i	1.02850	−	1.02850i
$482$	−35.1599	+	8.40446i	−1.60149	+	0.382813i
$483$	1.19972	−	2.24452i	0.0545891	−	0.102129i
$484$	−8.67603	+	6.81191i	−0.394365	+	0.309632i
$485$	2.21836	+	1.82056i	0.100730	+	0.0826674i
$486$	1.36804	+	0.358427i	0.0620555	+	0.0162586i
$487$	−16.5317	+	3.28836i	−0.749124	+	0.149010i	−0.554865	−	0.831940i	$-0.687230\pi$
$487$	−16.5317	+	3.28836i	−0.749124	+	0.149010i	−0.194259	+	0.980950i	$0.562230\pi$
$488$	32.9098	+	5.97756i	1.48976	+	0.270591i
$489$	−0.147996	+	0.744025i	−0.00669260	+	0.0336460i
$490$	3.70361	−	1.28021i	0.167312	−	0.0578339i
$491$	−17.3577	−	5.26541i	−0.783344	−	0.237625i	−0.126816	−	0.991926i	$-0.540476\pi$
$491$	−17.3577	−	5.26541i	−0.783344	−	0.237625i	−0.656528	+	0.754302i	$0.727976\pi$
$492$	3.65093	−	16.4845i	0.164597	−	0.743178i
$493$	1.34575	−	1.10443i	0.0606097	−	0.0497411i
$494$	30.5612	−	14.0523i	1.37501	−	0.632244i
$495$	−0.904471	−	0.374644i	−0.0406530	−	0.0168390i
$496$	30.4659	−	4.70210i	1.36796	−	0.211131i
$497$	−4.65898	+	1.92981i	−0.208984	+	0.0865640i
$498$	−7.62237	+	8.22953i	−0.341567	+	0.368774i
$499$	15.8508	+	1.56117i	0.709578	+	0.0698874i	0.446366	−	0.894851i	$-0.352718\pi$
$499$	15.8508	+	1.56117i	0.709578	+	0.0698874i	0.263212	+	0.964738i	$0.415218\pi$
$500$	−0.177492	+	8.21253i	−0.00793766	+	0.367275i
$501$	−16.3457	+	8.73695i	−0.730271	+	0.390338i
$502$	0.665198	−	11.0934i	0.0296892	−	0.495121i
$503$	23.7973	−	15.9009i	1.06107	−	0.708985i	0.102758	−	0.994706i	$-0.467233\pi$
$503$	23.7973	−	15.9009i	1.06107	−	0.708985i	0.958313	+	0.285722i	$0.0922333\pi$
$504$	−0.787201	+	1.53372i	−0.0350647	+	0.0683175i
$505$	−2.15057	+	3.21856i	−0.0956993	+	0.143224i
$506$	1.88128	+	13.7009i	0.0836331	+	0.609078i
$507$	−2.44964	−	24.8716i	−0.108792	−	1.10458i
$508$	−9.20853	−	3.01214i	−0.408562	−	0.133642i
$509$	−12.3609	−	40.7483i	−0.547886	−	1.80614i	−0.590488	−	0.807046i	$-0.701065\pi$
$509$	−12.3609	−	40.7483i	−0.547886	−	1.80614i	0.0426019	−	0.999092i	$-0.486435\pi$
$510$	0.652679	+	0.104035i	0.0289011	+	0.00460673i
$511$	−0.463667			−0.0205114
$512$	−3.34105	−	22.3794i	−0.147655	−	0.989039i
$513$	−3.85885			−0.170372
$514$	25.9919	+	4.14302i	1.14645	+	0.182741i
$515$	−0.675659	−	2.22735i	−0.0297731	−	0.0981487i
$516$	−11.0528	−	3.61541i	−0.486573	−	0.159160i
$517$	−1.70032	−	17.2637i	−0.0747801	−	0.759255i
$518$	−0.606860	−	4.41960i	−0.0266639	−	0.194186i
$519$	2.43008	−	3.63688i	0.106669	−	0.159641i
$520$	3.32779	−	6.48363i	0.145933	−	0.284326i
$521$	−11.3479	+	7.58242i	−0.497160	+	0.332192i	−0.778741	−	0.627346i	$-0.784141\pi$
$521$	−11.3479	+	7.58242i	−0.497160	+	0.332192i	0.281581	+	0.959538i	$0.409141\pi$
$522$	−0.131818	+	2.19830i	−0.00576952	+	0.0962171i
$523$	−9.96630	+	5.32710i	−0.435796	+	0.232938i	−0.674680	−	0.738110i	$-0.735718\pi$
$523$	−9.96630	+	5.32710i	−0.435796	+	0.232938i	0.238884	+	0.971048i	$0.423218\pi$
$524$	−0.399527	+	18.4861i	−0.0174534	+	0.807569i
$525$	2.92687	+	0.288271i	0.127739	+	0.0125812i
$526$	1.69846	−	1.83375i	0.0740565	−	0.0799554i
$527$	−7.95993	+	3.29711i	−0.346740	+	0.143624i
$528$	−1.42890	−	9.25813i	−0.0621848	−	0.402908i
$529$	5.14117	+	2.12954i	0.223529	+	0.0925888i
$530$	−0.210471	+	0.0967768i	−0.00914228	+	0.00420371i
$531$	8.33909	−	6.84372i	0.361886	−	0.296992i
$532$	1.01718	−	4.59270i	0.0441002	−	0.199119i
$533$	49.7937	+	15.1048i	2.15681	+	0.654260i
$534$	−13.1546	+	4.54707i	−0.569254	+	0.196771i
$535$	−0.191943	+	0.964961i	−0.00829841	+	0.0417189i
$536$	22.0628	+	4.00736i	0.952968	+	0.173092i
$537$	11.6123	−	2.30982i	0.501106	−	0.0996762i
$538$	−17.2064	−	4.50809i	−0.741821	−	0.194358i
$539$	11.9998	+	9.84802i	0.516870	+	0.424184i
$540$	−0.657588	+	0.516299i	−0.0282981	+	0.0222180i
$541$	−13.9503	+	26.0993i	−0.599772	+	1.12209i	0.380563	+	0.924755i	$0.375730\pi$
$541$	−13.9503	+	26.0993i	−0.599772	+	1.12209i	−0.980335	+	0.197340i	$0.936770\pi$
$542$	−6.66718	+	1.59369i	−0.286380	+	0.0684548i
$543$	−13.4423	+	13.4423i	−0.576864	+	0.576864i
$544$	2.39129	+	5.85464i	0.102526	+	0.251016i
$545$	−2.28139	−	2.28139i	−0.0977238	−	0.0977238i
$546$	−4.52733	−	2.78050i	−0.193752	−	0.118995i
$547$	−34.4733	−	18.4263i	−1.47397	−	0.787854i	−0.478071	−	0.878321i	$-0.658664\pi$
$547$	−34.4733	−	18.4263i	−1.47397	−	0.787854i	−0.995899	+	0.0904677i	$0.971164\pi$
$548$	1.11713	−	0.312684i	0.0477215	−	0.0133572i
$549$	7.50218	−	9.14143i	0.320185	−	0.390147i
$550$	−13.7955	+	8.06742i	−0.588243	+	0.343996i
$551$	−1.17232	−	5.89364i	−0.0499424	−	0.251078i
$552$	10.9851	+	4.33703i	0.467556	+	0.184596i
$553$	3.04636	+	0.605959i	0.129544	+	0.0257680i
$554$	11.4324	+	5.55907i	0.485718	+	0.236182i
$555$	0.628020	−	2.07031i	0.0266580	−	0.0878796i
$556$	−26.5163	+	4.68122i	−1.12454	+	0.198528i
$557$	23.9379	+	29.1684i	1.01428	+	1.23591i	0.971554	+	0.236819i	$0.0761047\pi$
$557$	23.9379	+	29.1684i	1.01428	+	1.23591i	0.0427275	+	0.999087i	$0.486395\pi$
$558$	3.78237	−	10.2215i	0.160120	−	0.432710i
$559$	13.7152	−	33.1113i	0.580090	−	1.40046i
$560$	−0.441148	−	0.918739i	−0.0186419	−	0.0388238i
$561$	1.00194	+	2.41891i	0.0423021	+	0.102126i
$562$	6.81450	−	0.261007i	0.287452	−	0.0110099i
$563$	−4.30399	+	43.6992i	−0.181392	+	1.84170i	0.286699	+	0.958021i	$0.407442\pi$
$563$	−4.30399	+	43.6992i	−0.181392	+	1.84170i	−0.468091	+	0.883680i	$0.655058\pi$
$564$	−13.5610	−	5.96364i	−0.571023	−	0.251114i
$565$	−3.44387	−	6.44303i	−0.144885	−	0.271060i
$566$	17.0362	+	19.2097i	0.716087	+	0.807443i
$567$	0.338624	+	0.506787i	0.0142209	+	0.0212831i
$568$	−11.3739	−	20.4514i	−0.477239	−	0.858121i
$569$	−32.6635	−	21.8250i	−1.36932	−	0.914953i	−0.369427	−	0.929260i	$-0.620446\pi$
$569$	−32.6635	−	21.8250i	−1.36932	−	0.914953i	−0.999898	+	0.0143066i	$0.995446\pi$
$570$	1.37867	−	1.81755i	0.0577461	−	0.0761286i
$571$	11.5810	−	1.14063i	0.484651	−	0.0477340i	0.147259	−	0.989098i	$-0.452955\pi$
$571$	11.5810	−	1.14063i	0.484651	−	0.0477340i	0.337393	+	0.941364i	$0.390455\pi$
$572$	28.7857	−	2.20832i	1.20359	−	0.0923343i
$573$	−19.0842	+	5.78913i	−0.797255	+	0.241845i
$574$	5.89124	−	4.27136i	0.245896	−	0.178283i
$575$		−	20.1481i		−	0.840234i
$576$	−7.48900	−	2.81333i	−0.312042	−	0.117222i
$577$			28.8153i			1.19960i	0.800151	+	0.599799i	$0.204753\pi$
$577$			28.8153i			1.19960i	−0.800151	+	0.599799i	$0.795247\pi$
$578$	13.0746	+	18.0330i	0.543831	+	0.750075i
$579$	−15.1605	+	4.59889i	−0.630050	+	0.191123i
$580$	−0.988321	−	0.847486i	−0.0410378	−	0.0351899i
$581$	−4.81119	+	0.473861i	−0.199602	+	0.0196591i
$582$	7.73509	+	5.86733i	0.320630	+	0.243208i
$583$	−0.763032	−	0.509842i	−0.0316016	−	0.0211155i
$584$	−0.246572	−	2.13748i	−0.0102032	−	0.0884494i
$585$	−1.43149	−	2.14238i	−0.0591849	−	0.0885765i
$586$	−17.0095	+	15.0850i	−0.702655	+	0.623155i
$587$	−18.4032	−	34.4300i	−0.759582	−	1.42108i	−0.902208	−	0.431301i	$-0.858055\pi$
$587$	−18.4032	−	34.4300i	−0.759582	−	1.42108i	0.142626	−	0.989777i	$-0.454445\pi$
$588$	12.3546	−	4.80741i	0.509496	−	0.198254i
$589$	−2.91491	+	29.5956i	−0.120107	+	1.21947i
$590$	0.244091	+	6.37286i	0.0100491	+	0.262367i
$591$	−0.468632	−	1.13138i	−0.0192770	−	0.0465387i
$592$	20.0514	−	5.14787i	0.824107	−	0.211576i
$593$	−16.3369	+	39.4407i	−0.670875	+	1.61964i	0.109251	+	0.994014i	$0.465155\pi$
$593$	−16.3369	+	39.4407i	−0.670875	+	1.61964i	−0.780126	+	0.625622i	$0.784845\pi$
$594$	−3.10616	−	1.14941i	−0.127447	−	0.0471607i
$595$	0.180705	+	0.220190i	0.00740819	+	0.00902690i
$596$	−0.304394	−	0.213045i	−0.0124685	−	0.00872665i
$597$	−7.14868	+	23.5660i	−0.292576	+	0.964494i
$598$	−15.9166	+	32.7331i	−0.650879	+	1.33856i
$599$	−10.9243	−	2.17298i	−0.446355	−	0.0887856i	−0.0332053	−	0.999449i	$-0.510572\pi$
$599$	−10.9243	−	2.17298i	−0.446355	−	0.0887856i	−0.413150	+	0.910663i	$0.635572\pi$
$600$	0.227554	+	13.6460i	0.00928985	+	0.557095i
$601$	0.792285	+	3.98309i	0.0323180	+	0.162473i	0.993574	−	0.113183i	$-0.0361047\pi$
$601$	0.792285	+	3.98309i	0.0323180	+	0.162473i	−0.961256	+	0.275657i	$0.911105\pi$
$602$	−2.53008	−	4.32651i	−0.103118	−	0.176336i
$603$	5.02947	−	6.12843i	0.204816	−	0.249569i
$604$	−8.60907	+	15.3017i	−0.350298	+	0.622616i
$605$	−2.03332	−	1.08683i	−0.0826663	−	0.0441860i
$606$	−6.85346	+	11.1591i	−0.278403	+	0.453307i
$607$	0.665676	+	0.665676i	0.0270190	+	0.0270190i	0.720487	−	0.693468i	$-0.243918\pi$
$607$	0.665676	+	0.665676i	0.0270190	+	0.0270190i	−0.693468	+	0.720487i	$0.743918\pi$
$608$	21.7130	+	2.24679i	0.880579	+	0.0911194i
$609$	−0.671144	+	0.671144i	−0.0271961	+	0.0271961i
$610$	1.62534	+	6.79959i	0.0658081	+	0.275307i
$611$	21.5222	−	40.2652i	0.870695	−	1.62895i
$612$	2.21991	+	0.267188i	0.0897345	+	0.0108004i
$613$	−2.67832	−	2.19804i	−0.108176	−	0.0887780i	0.578750	−	0.815505i	$-0.303541\pi$
$613$	−2.67832	−	2.19804i	−0.108176	−	0.0887780i	−0.686927	+	0.726727i	$0.741041\pi$
$614$	6.20521	−	23.6839i	0.250422	−	0.955805i
$615$	3.46117	−	0.688469i	0.139568	−	0.0277617i
$616$	2.18676	−	3.39389i	0.0881072	−	0.136744i
$617$	6.45664	−	32.4597i	0.259934	−	1.30678i	−0.601485	−	0.798884i	$-0.705424\pi$
$617$	6.45664	−	32.4597i	0.259934	−	1.30678i	0.861419	−	0.507895i	$-0.169576\pi$
$618$	−2.57253	−	7.44226i	−0.103482	−	0.299372i
$619$	44.3891	+	13.4653i	1.78415	+	0.541215i	0.997130	−	0.0757144i	$-0.0241237\pi$
$619$	44.3891	+	13.4653i	1.78415	+	0.541215i	0.787018	+	0.616930i	$0.211624\pi$
$620$	3.46304	+	5.43340i	0.139079	+	0.218211i
$621$	3.22775	−	2.64894i	0.129525	−	0.106298i
$622$	−9.63550	−	20.9554i	−0.386348	−	0.840235i
$623$	−5.54198	−	2.29556i	−0.222035	−	0.0919698i
$624$	10.4104	−	22.3494i	0.416749	−	0.894691i
$625$	20.7035	−	8.57568i	0.828141	−	0.343027i
$626$	2.19899	+	2.03675i	0.0878893	+	0.0814050i
$627$	8.99366	+	0.885798i	0.359172	+	0.0353754i
$628$	13.5473	−	12.9741i	0.540595	−	0.517723i
$629$	−5.10274	+	2.72747i	−0.203460	+	0.108751i
$630$	−0.359682	−	0.0215678i	−0.0143301	−	0.000859283i
$631$	−30.2892	+	20.2386i	−1.20579	+	0.805686i	−0.985488	−	0.169744i	$-0.945706\pi$
$631$	−30.2892	+	20.2386i	−1.20579	+	0.805686i	−0.220307	+	0.975431i	$0.570706\pi$
$632$	−1.17342	+	14.3658i	−0.0466762	+	0.571440i
$633$	−0.803959	+	1.20321i	−0.0319545	+	0.0478233i
$634$	44.6068	−	6.12501i	1.77156	−	0.243255i
$635$	−0.198491	−	2.01531i	−0.00787686	−	0.0799751i
$636$	−0.698985	+	0.354415i	−0.0277166	+	0.0140535i
$637$	11.8600	+	39.0972i	0.469911	+	1.54909i
$638$	0.811843	−	5.09324i	0.0321412	−	0.201643i
$639$	−8.27364			−0.327300
$640$	4.00073	−	2.52224i	0.158143	−	0.0997003i
$641$	−41.6297			−1.64428			−0.822138	−	0.569289i	$-0.807219\pi$
$641$	−41.6297			−1.64428			−0.822138	+	0.569289i	$0.807219\pi$
$642$	−0.523934	+	3.28699i	−0.0206780	+	0.129727i
$643$	−10.3052	−	33.9716i	−0.406396	−	1.33971i	−0.886594	−	0.462548i	$-0.846935\pi$
$643$	−10.3052	−	33.9716i	−0.406396	−	1.33971i	0.480198	−	0.877160i	$-0.340565\pi$
$644$	2.30188	+	4.53983i	0.0907069	+	0.178894i
$645$	−0.238244	−	2.41893i	−0.00938086	−	0.0952454i
$646$	−6.04429	+	0.829947i	−0.237809	+	0.0326538i
$647$	5.57193	−	8.33898i	0.219055	−	0.327839i	−0.705624	−	0.708586i	$-0.749333\pi$
$647$	5.57193	−	8.33898i	0.219055	−	0.327839i	0.924679	+	0.380747i	$0.124333\pi$
$648$	−2.15618	+	1.83054i	−0.0847028	+	0.0719104i
$649$	−21.0066	+	14.0361i	−0.824579	+	0.550966i
$650$	−41.9857	−	2.51761i	−1.64681	−	0.0987489i
$651$	4.14261	−	2.21427i	0.162362	−	0.0867842i
$652$	−1.04939	−	1.09575i	−0.0410974	−	0.0429130i
$653$	34.8828	+	3.43566i	1.36507	+	0.134448i	0.753868	−	0.657026i	$-0.228186\pi$
$653$	34.8828	+	3.43566i	1.36507	+	0.134448i	0.611203	+	0.791474i	$0.290686\pi$
$654$	−8.00782	−	7.41703i	−0.313131	−	0.290029i
$655$	−3.57056	+	1.47897i	−0.139513	+	0.0577883i
$656$	22.8236	+	24.8868i	0.891112	+	0.971668i
$657$	−0.702817	−	0.291116i	−0.0274195	−	0.0113575i
$658$	−2.66734	−	5.80096i	−0.103984	−	0.226145i
$659$	−29.2206	+	23.9807i	−1.13827	+	0.934156i	−0.998430	−	0.0560181i	$-0.982160\pi$
$659$	−29.2206	+	23.9807i	−1.13827	+	0.934156i	−0.139842	+	0.990174i	$0.544660\pi$
$660$	1.65113	−	1.05237i	0.0642701	−	0.0409634i
$661$	15.4591	+	4.68946i	0.601288	+	0.182399i	0.576231	−	0.817287i	$-0.304523\pi$
$661$	15.4591	+	4.68946i	0.601288	+	0.182399i	0.0250577	+	0.999686i	$0.492023\pi$
$662$	1.93449	+	5.59643i	0.0751860	+	0.217511i
$663$	−1.34434	+	6.75846i	−0.0522099	+	0.262477i
$664$	−4.74300	−	21.9273i	−0.184064	−	0.850945i
$665$	0.964307	−	0.191813i	0.0373942	−	0.00743817i
$666$	1.85501	−	7.08017i	0.0718802	−	0.274351i
$667$	5.02633	+	4.12500i	0.194620	+	0.159721i
$668$	4.42957	−	36.8027i	0.171385	−	1.42394i
$669$	10.4354	−	19.5232i	0.403455	−	0.754811i
$670$	1.08963	+	4.55845i	0.0420961	+	0.176108i
$671$	−19.5834	+	19.5834i	−0.756011	+	0.756011i
$672$	−1.61030	−	3.04876i	−0.0621187	−	0.117608i
$673$	0.465720	+	0.465720i	0.0179522	+	0.0179522i	0.716026	−	0.698074i	$-0.245959\pi$
$673$	0.465720	+	0.465720i	0.0179522	+	0.0179522i	−0.698074	+	0.716026i	$0.745959\pi$
$674$	20.7578	−	33.7988i	0.799562	−	1.30188i
$675$	4.25549	+	2.27461i	0.163794	+	0.0875497i
$676$	43.5624	+	24.5092i	1.67548	+	0.942661i
$677$	−5.39942	+	6.57921i	−0.207517	+	0.252860i	−0.866360	−	0.499421i	$-0.833546\pi$
$677$	−5.39942	+	6.57921i	−0.207517	+	0.252860i	0.658843	+	0.752280i	$0.271046\pi$
$678$	−12.4766	−	21.3353i	−0.479160	−	0.819378i
$679$	0.816313	+	4.10388i	0.0313272	+	0.157493i
$680$	−0.918966	+	0.950134i	−0.0352407	+	0.0364360i
$681$	28.7387	+	5.71648i	1.10127	+	0.219056i
$682$	−11.1617	+	22.9545i	−0.427405	+	0.878975i
$683$	6.67581	−	22.0072i	0.255443	−	0.842082i	−0.731615	−	0.681718i	$-0.761233\pi$
$683$	6.67581	−	22.0072i	0.255443	−	0.842082i	0.987058	−	0.160364i	$-0.0512668\pi$
$684$	4.42538	−	6.32289i	0.169209	−	0.241762i
$685$	0.153821	+	0.187432i	0.00587720	+	0.00716139i
$686$	11.0173	+	4.07685i	0.420642	+	0.155655i
$687$	−10.6842	+	25.7940i	−0.407628	+	0.984101i
$688$	18.5995	−	13.9643i	0.709100	−	0.532384i
$689$	−0.924287	−	2.23143i	−0.0352125	−	0.0850105i
$690$	0.0944784	+	2.46669i	0.00359673	+	0.0939054i
$691$	1.47751	−	15.0014i	0.0562072	−	0.570681i	−0.925297	−	0.379242i	$-0.876185\pi$
$691$	1.47751	−	15.0014i	0.0562072	−	0.570681i	0.981505	−	0.191439i	$-0.0613154\pi$
$692$	3.17233	+	8.15261i	0.120594	+	0.309916i
$693$	−0.672885	−	1.25888i	−0.0255608	−	0.0478209i
$694$	23.9350	−	21.2269i	0.908559	−	0.805762i
$695$	−3.12674	−	4.67949i	−0.118604	−	0.177503i
$696$	−3.45084	−	2.73703i	−0.130804	−	0.103747i
$697$	−7.84728	−	5.24338i	−0.297237	−	0.198607i
$698$	−21.8701	−	16.5892i	−0.827794	−	0.627910i
$699$	−17.1011	+	1.68431i	−0.646823	+	0.0637065i
$700$	−3.82891	+	4.46520i	−0.144719	+	0.168769i
$701$	12.3883	−	3.75795i	0.467900	−	0.141936i	−0.0475260	−	0.998870i	$-0.515134\pi$
$701$	12.3883	−	3.75795i	0.467900	−	0.141936i	0.515426	+	0.856934i	$0.327634\pi$
$702$	−5.11668	−	7.05715i	−0.193117	−	0.266355i
$703$			19.9711i			0.753226i
$704$	16.8085	+	8.27603i	0.633495	+	0.311914i
$705$		−	3.09641i		−	0.116618i
$706$	−24.5602	+	17.8070i	−0.924334	+	0.670175i
$707$	−5.40101	+	1.63838i	−0.203126	+	0.0616176i
$708$	1.65034	+	21.5124i	0.0620237	+	0.808486i
$709$	−6.56230	+	0.646331i	−0.246453	+	0.0242735i	−0.220489	−	0.975389i	$-0.570765\pi$
$709$	−6.56230	+	0.646331i	−0.246453	+	0.0242735i	−0.0259634	+	0.999663i	$0.508265\pi$
$710$	2.95597	−	3.89695i	0.110935	−	0.146250i
$711$	4.23716	+	2.83118i	0.158906	+	0.106178i
$712$	7.63526	−	26.7689i	0.286143	−	1.00321i
$713$	−17.8780	−	26.7563i	−0.669536	−	1.00203i
$714$	0.639400	+	0.720973i	0.0239289	+	0.0269817i
$715$	2.84454	+	5.32176i	0.106380	+	0.199022i
$716$	−9.53235	+	21.6761i	−0.356241	+	0.810075i
$717$	1.69090	−	17.1680i	0.0631480	−	0.641152i
$718$	34.4950	−	1.32121i	1.28734	−	0.0493073i
$719$	5.85763	+	14.1416i	0.218453	+	0.527391i	0.994674	−	0.103069i	$-0.0328662\pi$
$719$	5.85763	+	14.1416i	0.218453	+	0.527391i	−0.776222	+	0.630460i	$0.782866\pi$
$720$	−0.0918477	−	1.66958i	−0.00342296	−	0.0622217i
$721$	1.29873	−	3.13540i	0.0483671	−	0.116769i
$722$	2.01681	−	5.45022i	0.0750578	−	0.202836i
$723$	−16.2165	−	19.7599i	−0.603099	−	0.734878i
$724$	−6.60997	−	37.4415i	−0.245658	−	1.39150i
$725$	−2.18120	+	7.19046i	−0.0810079	+	0.267047i
$726$	−7.01455	−	3.41086i	−0.260334	−	0.126589i
$727$	−1.68224	−	0.334618i	−0.0623907	−	0.0124103i	0.163796	−	0.986494i	$-0.447626\pi$
$727$	−1.68224	−	0.334618i	−0.0623907	−	0.0124103i	−0.226187	+	0.974084i	$0.572626\pi$
$728$	9.74797	−	4.22951i	0.361284	−	0.156756i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	0.388217	−	0.227023i	0.0143685	−	0.00840251i
$731$	−4.12385	+	5.02493i	−0.152526	+	0.185854i
$732$	6.37503	+	22.7762i	0.235628	+	0.841831i
$733$	4.18935	+	2.23925i	0.154737	+	0.0827087i	0.546948	−	0.837167i	$-0.315790\pi$
$733$	4.18935	+	2.23925i	0.154737	+	0.0827087i	−0.392211	+	0.919875i	$0.628290\pi$
$734$	−32.5974	−	20.0200i	−1.20319	−	0.738951i
$735$	1.95932	+	1.95932i	0.0722705	+	0.0722705i
$736$	−19.7042	+	13.0258i	−0.726308	+	0.480136i
$737$	−13.1288	+	13.1288i	−0.483604	+	0.483604i
$738$	11.6116	−	2.77559i	0.427430	−	0.102171i
$739$	0.0881916	−	0.164995i	0.00324418	−	0.00606943i	−0.880294	−	0.474429i	$-0.842655\pi$
$739$	0.0881916	−	0.164995i	0.00324418	−	0.00606943i	0.883538	+	0.468359i	$0.155155\pi$
$740$	2.67206	+	3.40329i	0.0982269	+	0.125107i
$741$	18.3861	+	15.0891i	0.675429	+	0.554310i
$742$	−0.326737	−	0.0856055i	−0.0119949	−	0.00314268i
$743$	−3.36663	+	0.669664i	−0.123510	+	0.0245676i	−0.256458	−	0.966555i	$-0.582556\pi$
$743$	−3.36663	+	0.669664i	−0.123510	+	0.0245676i	0.132948	+	0.991123i	$0.457556\pi$
$744$	12.4107	+	17.9197i	0.454997	+	0.656967i
$745$	0.0151502	−	0.0761652i	0.000555060	−	0.00279048i
$746$	29.5317	−	10.2080i	1.08123	−	0.373743i
$747$	−7.59022	−	2.30247i	−0.277712	−	0.0842430i
$748$	−5.11252	−	1.13230i	−0.186932	−	0.0414012i
$749$	−1.10891	+	0.910058i	−0.0405187	+	0.0332528i
$750$	−5.27734	+	2.42657i	−0.192701	+	0.0886059i
$751$	18.9917	+	7.86662i	0.693017	+	0.287057i	0.701257	−	0.712909i	$-0.252623\pi$
$751$	18.9917	+	7.86662i	0.693017	+	0.287057i	−0.00823932	+	0.999966i	$0.502623\pi$
$752$	25.3236	−	15.3812i	0.923458	−	0.560893i
$753$	7.26011	−	3.00724i	0.264573	−	0.109590i
$754$	9.22397	−	9.95870i	0.335917	−	0.362674i
$755$	−3.65203	−	0.359694i	−0.132911	−	0.0130906i
$756$	−1.21873	−	0.0263396i	−0.0443248	−	0.000957960i
$757$	−33.6124	+	17.9662i	−1.22166	+	0.652993i	−0.950854	−	0.309640i	$-0.899792\pi$
$757$	−33.6124	+	17.9662i	−1.22166	+	0.652993i	−0.270810	+	0.962633i	$0.587292\pi$
$758$	1.58127	−	26.3706i	0.0574344	−	0.957822i
$759$	−8.13084	+	5.43285i	−0.295131	+	0.197200i
$760$	1.39705	+	4.34339i	0.0506763	+	0.157551i
$761$	−4.42430	+	6.62143i	−0.160381	+	0.240027i	−0.902953	−	0.429739i	$-0.858606\pi$
$761$	−4.42430	+	6.62143i	−0.160381	+	0.240027i	0.742572	+	0.669766i	$0.233606\pi$
$762$	−0.931961	−	6.78723i	−0.0337614	−	0.245875i
$763$	−0.461095	−	4.68158i	−0.0166928	−	0.169484i
$764$	12.4003	−	37.9093i	0.448626	−	1.37151i
$765$	0.135662	+	0.447216i	0.00490486	+	0.0161691i
$766$	11.4643	+	1.82738i	0.414224	+	0.0660258i
$767$	−66.4935			−2.40094
$768$	13.1982	−	9.04468i	0.476251	−	0.326372i
$769$	−3.28408			−0.118427			−0.0592135	−	0.998245i	$-0.518859\pi$
$769$	−3.28408			−0.118427			−0.0592135	+	0.998245i	$0.518859\pi$
$770$	0.833346	+	0.132832i	0.0300317	+	0.00478694i
$771$	5.40251	+	17.8097i	0.194567	+	0.641401i
$772$	9.85079	−	30.1152i	0.354538	−	1.08387i
$773$	4.33592	+	44.0233i	0.155952	+	1.58341i	0.680966	+	0.732315i	$0.261560\pi$
$773$	4.33592	+	44.0233i	0.155952	+	1.58341i	−0.525014	+	0.851094i	$0.675940\pi$
$774$	−1.11861	−	8.14657i	−0.0402078	−	0.292822i
$775$	20.6597	−	30.9195i	0.742119	−	1.11066i
$776$	−18.4846	+	5.94554i	−0.663557	+	0.213433i
$777$	2.62283	−	1.75252i	0.0940936	−	0.0628713i
$778$	−0.915013	+	15.2595i	−0.0328048	+	0.547079i
$779$	−28.7297	+	15.3564i	−1.02935	+	0.550199i
$780$	5.15203	+	0.111347i	0.184472	+	0.00398687i
$781$	19.2830	+	1.89921i	0.690001	+	0.0679592i
$782$	4.48604	−	4.84337i	0.160420	−	0.173199i
$783$	−1.43869	+	0.595925i	−0.0514146	+	0.0212966i
$784$	−6.29131	+	25.7568i	−0.224690	+	0.919885i
$785$	3.62220	+	1.50036i	0.129282	+	0.0535503i
$786$	−11.8791	+	5.46213i	−0.423713	+	0.194828i
$787$	39.2029	−	32.1730i	1.39743	−	1.14684i	0.427343	−	0.904090i	$-0.359450\pi$
$787$	39.2029	−	32.1730i	1.39743	−	1.14684i	0.970088	−	0.242752i	$-0.0780502\pi$
$788$	2.39124	+	0.529605i	0.0851846	+	0.0188664i
$789$	1.69130	+	0.513050i	0.0602118	+	0.0182651i
$790$	−2.84734	+	0.984223i	−0.101304	+	0.0350171i
$791$	2.07812	−	10.4474i	0.0738894	−	0.371467i
$792$	5.44553	−	3.77141i	0.193498	−	0.134011i
$793$	−71.4905	+	14.2203i	−2.53870	+	0.504979i
$794$	−28.0811	−	7.35728i	−0.996562	−	0.261100i
$795$	−0.126623	−	0.103916i	−0.00449084	−	0.00368554i
$796$	−30.4158	−	38.7393i	−1.07806	−	1.37308i
$797$	19.8260	−	37.0919i	0.702275	−	1.31386i	−0.237272	−	0.971443i	$-0.576253\pi$
$797$	19.8260	−	37.0919i	0.702275	−	1.31386i	0.939547	−	0.342420i	$-0.111247\pi$
$798$	3.23509	−	0.773300i	0.114521	−	0.0273745i
$799$	−5.85555	+	5.85555i	−0.207154	+	0.207154i
$800$	−22.6205	−	15.2765i	−0.799755	−	0.540107i
$801$	−6.95914	−	6.95914i	−0.245889	−	0.245889i
$802$	28.6232	+	17.5792i	1.01072	+	0.620742i
$803$	1.57120	+	0.839825i	0.0554465	+	0.0296368i
$804$	4.27383	+	15.2692i	0.150726	+	0.538502i
$805$	−0.674926	+	0.822399i	−0.0237880	+	0.0289858i
$806$	−57.9901	+	33.9118i	−2.04262	+	1.19449i
$807$	−2.45373	−	12.3358i	−0.0863755	−	0.434239i
$808$	−10.4250	−	24.0271i	−0.366751	−	0.845269i
$809$	55.2119	+	10.9823i	1.94115	+	0.386118i	0.998652	+	0.0518988i	$0.0165273\pi$
$809$	55.2119	+	10.9823i	1.94115	+	0.386118i	0.942495	+	0.334219i	$0.108473\pi$
$810$	−0.531658	−	0.258521i	−0.0186806	−	0.00908351i
$811$	10.4600	−	34.4819i	0.367300	−	1.21082i	−0.557438	−	0.830219i	$-0.688216\pi$
$811$	10.4600	−	34.4819i	0.367300	−	1.21082i	0.924737	−	0.380606i	$-0.124284\pi$
$812$	−0.330022	−	1.86938i	−0.0115815	−	0.0656022i
$813$	−3.07504	−	3.74695i	−0.107846	−	0.131411i
$814$	−5.94865	+	16.0756i	−0.208500	+	0.563451i
$815$	0.121355	−	0.292977i	0.00425088	−	0.0102625i
$816$	−2.98362	+	3.33100i	−0.104448	+	0.116608i
$817$	8.58645	+	20.7295i	0.300402	+	0.725234i
$818$	4.65258	−	0.178201i	0.162673	−	0.00623066i
$819$	0.368236	−	3.73877i	0.0128672	−	0.130643i
$820$	−2.84122	+	6.46081i	−0.0992199	+	0.225621i
$821$	−1.80417	−	3.37536i	−0.0629658	−	0.117801i	0.848469	−	0.529245i	$-0.177525\pi$
$821$	−1.80417	−	3.37536i	−0.0629658	−	0.117801i	−0.911435	+	0.411444i	$0.865025\pi$
$822$	0.544275	+	0.613712i	0.0189838	+	0.0214057i
$823$	−8.19287	−	12.2615i	−0.285585	−	0.427409i	0.660745	−	0.750611i	$-0.270241\pi$
$823$	−8.19287	−	12.2615i	−0.285585	−	0.427409i	−0.946330	+	0.323202i	$0.895241\pi$
$824$	15.1447	+	4.31969i	0.527590	+	0.150484i
$825$	−9.39597	−	6.27819i	−0.327126	−	0.218578i
$826$	−5.61967	+	7.40859i	−0.195533	+	0.257778i
$827$	−7.43798	+	0.732577i	−0.258644	+	0.0254742i	−0.226508	−	0.974009i	$-0.572731\pi$
$827$	−7.43798	+	0.732577i	−0.258644	+	0.0254742i	−0.0321360	+	0.999484i	$0.510231\pi$
$828$	0.638785	+	8.32664i	0.0221993	+	0.289371i
$829$	−7.27442	+	2.20667i	−0.252651	+	0.0766408i	−0.414070	−	0.910245i	$-0.635893\pi$
$829$	−7.27442	+	2.20667i	−0.252651	+	0.0766408i	0.161419	+	0.986886i	$0.448393\pi$
$830$	3.79628	−	2.75244i	0.131771	−	0.0955385i
$831$			8.98899i			0.311825i
$832$	24.6816	+	42.6884i	0.855682	+	1.47995i
$833$		−	7.41044i		−	0.256756i
$834$	−11.1761	−	15.4146i	−0.386997	−	0.533763i
$835$	7.41417	−	2.24906i	0.256578	−	0.0778320i
$836$	−11.7655	+	13.7207i	−0.406917	+	0.474539i
$837$	7.66954	−	0.755384i	0.265098	−	0.0261099i
$838$	10.3123	+	7.82224i	0.356233	+	0.270215i
$839$	4.67280	+	3.12227i	0.161323	+	0.107793i	0.633611	−	0.773652i	$-0.281572\pi$
$839$	4.67280	+	3.12227i	0.161323	+	0.107793i	−0.472288	+	0.881444i	$0.656572\pi$
$840$	0.447828	−	0.564620i	0.0154515	−	0.0194813i
$841$	14.7643	+	22.0963i	0.509114	+	0.761943i
$842$	−24.2194	+	21.4791i	−0.834655	+	0.740220i
$843$	2.27313	+	4.25273i	0.0782907	+	0.146472i
$844$	−1.04952	−	2.69718i	−0.0361260	−	0.0928407i
$845$	−1.02401	+	10.3970i	−0.0352271	+	0.357667i
$846$	−0.400930	−	10.4677i	−0.0137842	−	0.359887i
$847$	−1.28644	−	3.10575i	−0.0442027	−	0.106715i
$848$	0.220882	−	1.55176i	0.00758512	−	0.0532878i
$849$	−6.94782	+	16.7735i	−0.238448	+	0.575665i
$850$	7.15478	+	2.64757i	0.245407	+	0.0908107i
$851$	−13.7094	−	16.7049i	−0.469951	−	0.572637i
$852$	9.48832	−	13.5567i	0.325064	−	0.464445i
$853$	−9.33863	+	30.7853i	−0.319748	+	1.05407i	0.638856	+	0.769327i	$0.279408\pi$
$853$	−9.33863	+	30.7853i	−0.319748	+	1.05407i	−0.958604	+	0.284743i	$0.908092\pi$
$854$	−4.45758	+	9.16718i	−0.152535	+	0.313695i
$855$	1.58211	+	0.314701i	0.0541070	+	0.0107625i
$856$	−4.78502	−	4.62805i	−0.163549	−	0.158183i
$857$	10.9328	+	54.9630i	0.373458	+	1.87750i	0.470788	+	0.882247i	$0.343970\pi$
$857$	10.9328	+	54.9630i	0.373458	+	1.87750i	−0.0973298	+	0.995252i	$0.531030\pi$
$858$	10.3053	+	17.6223i	0.351816	+	0.601617i
$859$	−3.02464	+	3.68554i	−0.103200	+	0.125749i	−0.822049	−	0.569417i	$-0.807169\pi$
$859$	−3.02464	+	3.68554i	−0.103200	+	0.125749i	0.718849	+	0.695166i	$0.244669\pi$
$860$	4.23675	+	2.38369i	0.144472	+	0.0812832i
$861$	4.53788	+	2.42555i	0.154651	+	0.0826624i
$862$	−16.5701	+	26.9801i	−0.564378	+	0.918944i
$863$	−19.5914	−	19.5914i	−0.666899	−	0.666899i	0.290098	−	0.956997i	$-0.406312\pi$
$863$	−19.5914	−	19.5914i	−0.666899	−	0.666899i	−0.956997	+	0.290098i	$0.906312\pi$
$864$	−0.526680	−	5.63228i	−0.0179180	−	0.191614i
$865$	−1.29292	+	1.29292i	−0.0439606	+	0.0439606i
$866$	9.91086	+	41.4619i	0.336785	+	1.40893i
$867$	−7.42457	+	13.8904i	−0.252152	+	0.471743i
$868$	−1.12262	+	9.32720i	−0.0381042	+	0.316586i
$869$	−9.22548	−	7.57115i	−0.312953	−	0.256834i
$870$	0.233323	−	0.890543i	0.00791039	−	0.0301922i
$871$	−47.9273	+	9.53334i	−1.62396	+	0.323025i
$872$	21.3366	−	4.61522i	0.722548	−	0.156291i
$873$	−1.33930	+	6.73311i	−0.0453284	+	0.227881i
$874$	−7.44445	−	21.5366i	−0.251812	−	0.728487i
$875$	−2.39559	−	0.726694i	−0.0809856	−	0.0245667i
$876$	1.28301	−	0.817739i	0.0433487	−	0.0276289i
$877$	−20.9130	+	17.1629i	−0.706183	+	0.579549i	−0.917437	−	0.397882i	$-0.869745\pi$
$877$	−20.9130	+	17.1629i	−0.706183	+	0.579549i	0.211254	+	0.977431i	$0.432245\pi$
$878$	−18.2983	−	39.7953i	−0.617537	−	1.34303i
$879$	−14.8523	−	6.15204i	−0.500957	−	0.207503i
$880$	−0.169187	+	3.91231i	−0.00570330	+	0.131884i
$881$	−11.0955	+	4.59591i	−0.373817	+	0.154840i	−0.561679	−	0.827355i	$-0.689844\pi$
$881$	−11.0955	+	4.59591i	−0.373817	+	0.154840i	0.187862	+	0.982195i	$0.439844\pi$
$882$	6.87734	+	6.36995i	0.231572	+	0.214487i
$883$	−48.5536	−	4.78212i	−1.63396	−	0.160931i	−0.761010	−	0.648740i	$-0.775296\pi$
$883$	−48.5536	−	4.78212i	−1.63396	−	0.160931i	−0.872950	+	0.487809i	$0.837796\pi$
$884$	−9.53232	−	9.95345i	−0.320607	−	0.334771i
$885$	−3.97711	+	2.12581i	−0.133689	+	0.0714583i
$886$	−17.0839	−	1.02441i	−0.573945	−	0.0344158i
$887$	−36.0396	+	24.0809i	−1.21009	+	0.808556i	−0.986119	−	0.166039i	$-0.946902\pi$
$887$	−36.0396	+	24.0809i	−1.21009	+	0.808556i	−0.223971	+	0.974596i	$0.571902\pi$
$888$	9.47380	+	11.1591i	0.317920	+	0.374476i
$889$	1.64041	−	2.45504i	0.0550174	−	0.0823394i
$890$	5.76413	−	0.791479i	0.193214	−	0.0265304i
$891$	−0.229550	−	2.33066i	−0.00769021	−	0.0780800i
$892$	20.0222	+	39.4883i	0.670393	+	1.32217i
$893$	8.29729	+	27.3525i	0.277658	+	0.915316i
$894$	0.0413545	−	0.259445i	0.00138310	−	0.00867713i
$895$	−4.94934			−0.165438
$896$	6.84223	+	0.857806i	0.228583	+	0.0286573i
$897$	−25.7371			−0.859336
$898$	−8.28433	+	51.9731i	−0.276452	+	1.73437i
$899$	3.48371	+	11.4842i	0.116188	+	0.383021i
$900$	−8.60730	+	4.36426i	−0.286910	+	0.145475i
$901$	0.0429390	+	0.435967i	0.00143051	+	0.0145242i
$902$	−27.6999	+	3.80350i	−0.922306	+	0.126643i
$903$	1.96895	−	2.94674i	0.0655224	−	0.0980613i
$904$	49.2671	+	4.02422i	1.63860	+	0.133844i
$905$	6.60752	−	4.41501i	0.219642	−	0.146760i
$906$	−12.3926	−	0.743104i	−0.411716	−	0.0246880i
$907$	−9.72920	+	5.20037i	−0.323053	+	0.172675i	−0.624949	−	0.780665i	$-0.714880\pi$
$907$	−9.72920	+	5.20037i	−0.323053	+	0.172675i	0.301896	+	0.953341i	$0.402380\pi$
$908$	−42.3246	+	40.5338i	−1.40459	+	1.34516i
$909$	−9.21541	−	0.907639i	−0.305656	−	0.0301045i
$910$	1.62942	+	1.50921i	0.0540149	+	0.0500298i
$911$	14.0096	−	5.80297i	0.464159	−	0.192261i	−0.138333	−	0.990386i	$-0.544174\pi$
$911$	14.0096	−	5.80297i	0.464159	−	0.192261i	0.602492	+	0.798125i	$0.294174\pi$
$912$	5.28524	+	14.5023i	0.175012	+	0.480220i
$913$	17.1617	+	7.10861i	0.567969	+	0.235261i
$914$	−4.04843	−	8.80457i	−0.133910	−	0.291229i
$915$	−3.82137	+	3.13612i	−0.126331	+	0.103677i
$916$	−30.0117	−	47.0874i	−0.991615	−	1.55581i
$917$	−5.39238	−	1.63576i	−0.178072	−	0.0540176i
$918$	0.516522	+	1.49429i	0.0170478	+	0.0493189i
$919$	0.372810	−	1.87424i	0.0122979	−	0.0618255i	−0.974149	−	0.225906i	$-0.927466\pi$
$919$	0.372810	−	1.87424i	0.0122979	−	0.0618255i	0.986447	+	0.164081i	$0.0524657\pi$
$920$	−4.15013	−	2.67403i	−0.136826	−	0.0881601i
$921$	16.9797	−	3.37746i	0.559499	−	0.111291i
$922$	8.38401	−	31.9999i	0.276113	−	1.05386i
$923$	39.4210	+	32.3520i	1.29756	+	1.06488i
$924$	2.83440	+	0.341148i	0.0932449	+	0.0112229i
$925$	11.7720	−	22.0239i	0.387062	−	0.724143i
$926$	−5.37751	−	22.4967i	−0.176716	−	0.739289i
$927$	3.93717	−	3.93717i	0.129314	−	0.129314i
$928$	8.44221	−	2.51549i	0.277129	−	0.0825750i
$929$	22.8910	+	22.8910i	0.751029	+	0.751029i	0.974671	−	0.223642i	$-0.0717948\pi$
$929$	22.8910	+	22.8910i	0.751029	+	0.751029i	−0.223642	+	0.974671i	$0.571795\pi$
$930$	−2.38434	+	3.88229i	−0.0781857	+	0.127305i
$931$	−22.5581	−	12.0576i	−0.739313	−	0.395171i
$932$	16.8519	−	29.9525i	0.552004	−	0.981126i
$933$	10.3464	−	12.6071i	0.338725	−	0.412737i
$934$	−8.27954	−	14.1583i	−0.270915	−	0.463273i
$935$	−0.213523	−	1.07345i	−0.00698293	−	0.0351056i
$936$	17.4313	−	0.290677i	0.569760	−	0.00950106i
$937$	0.0857064	+	0.0170481i	0.00279991	+	0.000556936i	0.196490	−	0.980506i	$-0.437046\pi$
$937$	0.0857064	+	0.0170481i	0.00279991	+	0.000556936i	−0.193690	+	0.981063i	$0.562046\pi$
$938$	−2.98837	+	6.14569i	−0.0975738	+	0.200664i
$939$	−0.615236	+	2.02816i	−0.0200775	+	0.0661866i
$940$	5.07360	+	3.55100i	0.165483	+	0.115821i
$941$	−13.3378	−	16.2521i	−0.434798	−	0.529803i	0.508805	−	0.860882i	$-0.330087\pi$
$941$	−13.3378	−	16.2521i	−0.434798	−	0.529803i	−0.943603	+	0.331079i	$0.892587\pi$
$942$	12.4394	+	4.60310i	0.405298	+	0.149977i
$943$	13.4896	−	32.5667i	0.439280	−	1.06052i
$944$	−37.1416	−	21.9666i	−1.20886	−	0.714950i
$945$	−0.0975042	−	0.235396i	−0.00317181	−	0.00765743i
$946$	0.737064	+	19.2437i	0.0239640	+	0.625665i
$947$	1.60809	−	16.3272i	0.0522558	−	0.530562i	−0.933048	−	0.359752i	$-0.882861\pi$
$947$	1.60809	−	16.3272i	0.0522558	−	0.530562i	0.985304	−	0.170810i	$-0.0546386\pi$
$948$	−9.49823	+	3.69593i	−0.308488	+	0.120038i
$949$	2.21034	+	4.13525i	0.0717507	+	0.134236i
$950$	19.7011	−	17.4720i	0.639187	−	0.566867i
$951$	17.6881	+	26.4721i	0.573576	+	0.858417i
$952$	−1.91462	+	0.220863i	−0.0620531	+	0.00715822i
$953$	−20.9125	−	13.9733i	−0.677423	−	0.452640i	0.168672	−	0.985672i	$-0.446052\pi$
$953$	−20.9125	−	13.9733i	−0.677423	−	0.452640i	−0.846095	+	0.533033i	$0.821052\pi$
$954$	−0.441514	−	0.334903i	−0.0142945	−	0.0108429i
$955$	8.29655	−	0.817139i	0.268470	−	0.0264420i
$956$	26.1914	+	22.4591i	0.847091	+	0.726381i
$957$	3.48989	−	1.05865i	0.112812	−	0.0342212i
$958$	−12.1490	−	16.7564i	−0.392516	−	0.541374i
$959$			0.353535i			0.0114162i
$960$	2.84102	+	1.76420i	0.0916934	+	0.0569394i
$961$		−	28.3924i		−	0.915885i
$962$	−36.5237	+	26.4810i	−1.17757	+	0.853780i
$963$	−2.25225	+	0.683212i	−0.0725777	+	0.0220162i
$964$	50.9747	−	3.91057i	1.64178	−	0.125951i
$965$	6.59079	−	0.649136i	0.212165	−	0.0208964i
$966$	−2.17516	+	2.86758i	−0.0699846	+	0.0922630i
$967$	32.2960	+	21.5795i	1.03857	+	0.693949i	0.953182	−	0.302399i	$-0.0977874\pi$
$967$	32.2960	+	21.5795i	1.03857	+	0.693949i	0.0853869	+	0.996348i	$0.472787\pi$
$968$	13.6332	−	7.58202i	0.438188	−	0.243695i
$969$	−2.39676	−	3.58701i	−0.0769951	−	0.115231i
$970$	−2.69285	−	3.03639i	−0.0864621	−	0.0974927i
$971$	−4.21988	−	7.89484i	−0.135422	−	0.253357i	0.805065	−	0.593187i	$-0.202131\pi$
$971$	−4.21988	−	7.89484i	−0.135422	−	0.253357i	−0.940487	+	0.339830i	$0.889631\pi$
$972$	−1.83079	−	0.805113i	−0.0587226	−	0.0258240i
$973$	0.804320	−	8.16640i	0.0257853	−	0.261803i
$974$	23.8199	−	0.912343i	0.763240	−	0.0292333i
$975$	−11.3817	−	27.4777i	−0.364505	−	0.879992i
$976$	−44.6307	−	15.6742i	−1.42859	−	0.501720i
$977$	8.16450	−	19.7108i	0.261205	−	0.630606i	−0.737808	−	0.675010i	$-0.764139\pi$
$977$	8.16450	−	19.7108i	0.261205	−	0.630606i	0.999014	+	0.0444047i	$0.0141391\pi$
$978$	0.372316	−	1.00615i	0.0119053	−	0.0321730i
$979$	14.6219	+	17.8168i	0.467318	+	0.569429i
$980$	−5.45739	+	0.963454i	−0.174330	+	0.0307764i
$981$	2.24044	−	7.38574i	0.0715318	−	0.235809i
$982$	23.0694	+	11.2176i	0.736174	+	0.357968i
$983$	54.2494	+	10.7909i	1.73029	+	0.344175i	0.957046	−	0.289937i	$-0.0936344\pi$
$983$	54.2494	+	10.7909i	1.73029	+	0.344175i	0.773241	+	0.634113i	$0.218634\pi$
$984$	−8.76845	+	22.2092i	−0.279528	+	0.708005i
$985$	0.0998694	+	0.502078i	0.00318211	+	0.0159975i
$986$	−2.12532	+	1.24285i	−0.0676838	+	0.0395805i
$987$	2.86412	−	3.48995i	0.0911661	−	0.111086i
$988$	−45.8094	+	12.8220i	−1.45739	+	0.407923i
$989$	−21.4121	−	11.4450i	−0.680866	−	0.363930i
$990$	1.17977	+	0.724567i	0.0374956	+	0.0230282i
$991$	12.3819	+	12.3819i	0.393325	+	0.393325i	0.875871	−	0.482546i	$-0.160288\pi$
$991$	12.3819	+	12.3819i	0.393325	+	0.393325i	−0.482546	+	0.875871i	$0.660288\pi$
$992$	−43.5949	−	0.215140i	−1.38414	−	0.00683069i
$993$	−2.96067	+	2.96067i	−0.0939540	+	0.0939540i
$994$	6.93625	−	1.65801i	0.220005	−	0.0525888i
$995$	4.85280	−	9.07896i	0.153844	−	0.287822i
$996$	12.4773	−	9.79640i	0.395357	−	0.310411i
$997$	4.03709	+	3.31316i	0.127856	+	0.104929i	0.696148	−	0.717898i	$-0.254896\pi$
$997$	4.03709	+	3.31316i	0.127856	+	0.104929i	−0.568292	+	0.822827i	$0.692396\pi$
$998$	−21.7894	−	5.70884i	−0.689732	−	0.180710i
$999$	5.07597	−	1.00967i	0.160597	−	0.0319446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.2	✓	512
128.69	even	32	inner	384.2.v.a.325.2	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.2	✓	512	1.1	even	1	trivial
384.2.v.a.325.2	yes	512	128.69	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)

\(f(q)\)	\(=\)	\(q+(-1.39658 - 0.222610i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.90089 + 0.621788i) q^{4} +(0.0409738 + 0.416014i) q^{5} +(0.192382 + 1.40107i) q^{6} +(-0.338624 + 0.506787i) q^{7} +(-2.51633 - 1.29154i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-1.39658 - 0.222610i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.90089 + 0.621788i) q^{4} +(0.0409738 + 0.416014i) q^{5} +(0.192382 + 1.40107i) q^{6} +(-0.338624 + 0.506787i) q^{7} +(-2.51633 - 1.29154i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(0.0353857 - 0.590120i) q^{10} +(2.06540 - 1.10398i) q^{11} +(0.0432145 - 1.99953i) q^{12} +(6.13408 + 0.604154i) q^{13} +(0.585733 - 0.632389i) q^{14} +(0.386207 - 0.159972i) q^{15} +(3.22676 + 2.36390i) q^{16} +(-1.03287 - 0.427827i) q^{17} +(1.28489 - 0.590806i) q^{18} +(-2.98293 + 2.44803i) q^{19} +(-0.180786 + 0.816274i) q^{20} +(0.583262 + 0.176931i) q^{21} +(-3.13027 + 1.08202i) q^{22} +(0.814610 - 4.09532i) q^{23} +(-0.505469 + 2.78289i) q^{24} +(4.73254 - 0.941360i) q^{25} +(-8.43226 - 2.20926i) q^{26} +(0.773010 + 0.634393i) q^{27} +(-0.958801 + 0.752794i) q^{28} +(-0.734072 + 1.37335i) q^{29} +(-0.574981 + 0.137441i) q^{30} +(5.44942 - 5.44942i) q^{31} +(-3.98021 - 4.01969i) q^{32} +(-1.65600 - 1.65600i) q^{33} +(1.34724 + 0.827422i) q^{34} +(-0.224705 - 0.120107i) q^{35} +(-1.92598 + 0.539080i) q^{36} +(3.28325 - 4.00065i) q^{37} +(4.71087 - 2.75484i) q^{38} +(-1.20249 - 6.04532i) q^{39} +(0.434193 - 1.09975i) q^{40} +(8.27977 + 1.64695i) q^{41} +(-0.775188 - 0.376939i) q^{42} +(1.68787 - 5.56418i) q^{43} +(4.61255 - 0.814304i) q^{44} +(-0.265194 - 0.323139i) q^{45} +(-2.04933 + 5.53811i) q^{46} +(2.83461 - 6.84336i) q^{47} +(1.32543 - 3.77402i) q^{48} +(2.53662 + 6.12394i) q^{49} +(-6.81894 + 0.261176i) q^{50} +(-0.109580 + 1.11258i) q^{51} +(11.2845 + 4.96252i) q^{52} +(-0.184717 - 0.345582i) q^{53} +(-0.938351 - 1.05806i) q^{54} +(0.543899 + 0.814003i) q^{55} +(1.50662 - 0.837900i) q^{56} +(3.20852 + 2.14386i) q^{57} +(1.33091 - 1.75459i) q^{58} +(-10.7359 + 1.05739i) q^{59} +(0.833605 - 0.0639507i) q^{60} +(-11.3165 + 3.43284i) q^{61} +(-8.82367 + 6.39748i) q^{62} -0.609507i q^{63} +(4.66387 + 6.49987i) q^{64} +2.57662i q^{65} +(1.94410 + 2.68138i) q^{66} +(-7.58663 + 2.30138i) q^{67} +(-1.69735 - 1.45547i) q^{68} +(-4.15545 + 0.409276i) q^{69} +(0.287082 + 0.217762i) q^{70} +(6.87928 + 4.59659i) q^{71} +(2.80979 - 0.324128i) q^{72} +(0.422635 + 0.632519i) q^{73} +(-5.47591 + 4.85635i) q^{74} +(-2.27461 - 4.25549i) q^{75} +(-7.19237 + 2.79868i) q^{76} +(-0.139912 + 1.42055i) q^{77} +(0.333626 + 8.71048i) q^{78} +(-1.95015 - 4.70808i) q^{79} +(-0.851203 + 1.43924i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-11.1968 - 4.14326i) q^{82} +(5.03186 + 6.13134i) q^{83} +(0.998704 + 0.698991i) q^{84} +(0.135662 - 0.447216i) q^{85} +(-3.59590 + 7.39510i) q^{86} +(1.52731 + 0.303800i) q^{87} +(-6.62308 + 0.110443i) q^{88} +(1.92002 + 9.65260i) q^{89} +(0.298431 + 0.510326i) q^{90} +(-2.38332 + 2.90409i) q^{91} +(4.09490 - 7.27824i) q^{92} +(-6.79666 - 3.63289i) q^{93} +(-5.48218 + 8.92631i) q^{94} +(-1.14064 - 1.14064i) q^{95} +(-2.69121 + 4.97568i) q^{96} +(4.85430 - 4.85430i) q^{97} +(-2.17935 - 9.11726i) q^{98} +(-1.10398 + 2.06540i) 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

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