LMFDB - Embedded newform 384.2.v.a.157.23

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			157.23
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.886484 + 1.10188i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-0.428293 + 1.95360i) q^{4} +(-3.03822 + 1.62396i) q^{5} +(1.18347 - 0.774212i) q^{6} +(-0.0609552 - 0.306443i) q^{7} +(-2.53232 + 1.25991i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(0.886484 + 1.10188i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-0.428293 + 1.95360i) q^{4} +(-3.03822 + 1.62396i) q^{5} +(1.18347 - 0.774212i) q^{6} +(-0.0609552 - 0.306443i) q^{7} +(-2.53232 + 1.25991i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-4.48275 - 1.90815i) q^{10} +(-3.52971 + 4.30096i) q^{11} +(1.90222 + 0.617717i) q^{12} +(0.800729 - 1.49806i) q^{13} +(0.283628 - 0.338822i) q^{14} +(1.31835 + 3.18277i) q^{15} +(-3.63313 - 1.67343i) q^{16} +(-0.777110 + 1.87611i) q^{17} +(-0.654484 - 1.25366i) q^{18} +(1.40624 + 4.63574i) q^{19} +(-1.87133 - 6.63101i) q^{20} +(-0.310942 + 0.0306251i) q^{21} +(-7.86819 - 0.0765928i) q^{22} +(2.04529 - 1.36662i) q^{23} +(1.00563 + 2.64362i) q^{24} +(3.81568 - 5.71057i) q^{25} +(2.36052 - 0.445695i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(0.624774 + 0.0121649i) q^{28} +(2.41755 - 1.98403i) q^{29} +(-2.33835 + 4.27413i) q^{30} +(1.08390 - 1.08390i) q^{31} +(-1.37679 - 5.48675i) q^{32} +(3.93428 + 3.93428i) q^{33} +(-2.75615 + 0.806856i) q^{34} +(0.682847 + 0.832051i) q^{35} +(0.801192 - 1.83251i) q^{36} +(-5.25585 - 1.59435i) q^{37} +(-3.86144 + 5.65902i) q^{38} +(-1.41236 - 0.943708i) q^{39} +(5.64769 - 7.94027i) q^{40} +(5.31281 + 7.95118i) q^{41} +(-0.309390 - 0.315473i) q^{42} +(1.10705 + 11.2400i) q^{43} +(-6.89062 - 8.73772i) q^{44} +(3.29666 - 1.00003i) q^{45} +(3.31898 + 1.04219i) q^{46} +(-7.30995 - 3.02788i) q^{47} +(-2.02148 + 3.45161i) q^{48} +(6.37697 - 2.64143i) q^{49} +(9.67491 - 0.857893i) q^{50} +(1.79091 + 0.957259i) q^{51} +(2.58366 + 2.20591i) q^{52} +(1.14828 + 0.942371i) q^{53} +(-1.31177 + 0.528452i) q^{54} +(3.73943 - 18.7994i) q^{55} +(0.540448 + 0.699212i) q^{56} +(4.75125 - 0.945083i) q^{57} +(4.32928 + 0.905044i) q^{58} +(-0.278466 - 0.520974i) q^{59} +(-6.78250 + 1.21237i) q^{60} +(14.9424 + 1.47170i) q^{61} +(2.15520 + 0.233472i) q^{62} +0.312446i q^{63} +(4.82526 - 6.38098i) q^{64} +5.85178i q^{65} +(-0.847441 + 7.82279i) q^{66} +(-10.7537 - 1.05915i) q^{67} +(-3.33234 - 2.32169i) q^{68} +(-1.15957 - 2.16940i) q^{69} +(-0.311491 + 1.49002i) q^{70} +(2.97508 - 0.591780i) q^{71} +(2.72946 - 0.741670i) q^{72} +(1.34471 - 6.76030i) q^{73} +(-2.90245 - 7.20470i) q^{74} +(-5.30907 - 4.35704i) q^{75} +(-9.65867 + 0.761773i) q^{76} +(1.53315 + 0.819487i) q^{77} +(-0.212177 - 2.39284i) q^{78} +(-10.0620 + 4.16781i) q^{79} +(13.7558 - 0.815823i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-4.05155 + 12.9027i) q^{82} +(-3.38393 + 1.02650i) q^{83} +(0.0733449 - 0.620573i) q^{84} +(-0.685700 - 6.96203i) q^{85} +(-11.4038 + 11.1839i) q^{86} +(-1.73751 - 2.60037i) q^{87} +(3.51952 - 15.3385i) q^{88} +(9.10601 + 6.08444i) q^{89} +(4.02435 + 2.74602i) q^{90} +(-0.507877 - 0.154063i) q^{91} +(1.79385 + 4.58101i) q^{92} +(-0.972442 - 1.18492i) q^{93} +(-3.14378 - 10.7389i) q^{94} +(-11.8007 - 11.8007i) q^{95} +(-5.59528 + 0.832363i) q^{96} +(-1.18315 + 1.18315i) q^{97} +(8.56362 + 4.68509i) q^{98} +(4.30096 - 3.52971i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

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 $

$2$	0.886484	+	1.10188i	0.626839	+	0.779149i
$2$	0.886484	+	1.10188i	0.626839	+	0.779149i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$4$	−0.428293	+	1.95360i	−0.214146	+	0.976802i
$5$	−3.03822	+	1.62396i	−1.35873	+	0.726258i	−0.979953	−	0.199228i	$-0.936156\pi$
$5$	−3.03822	+	1.62396i	−1.35873	+	0.726258i	−0.378781	+	0.925487i	$0.623656\pi$
$6$	1.18347	−	0.774212i	0.483149	−	0.316071i
$7$	−0.0609552	−	0.306443i	−0.0230389	−	0.115824i	0.967555	−	0.252662i	$-0.0813061\pi$
$7$	−0.0609552	−	0.306443i	−0.0230389	−	0.115824i	−0.990593	+	0.136838i	$0.956306\pi$
$8$	−2.53232	+	1.25991i	−0.895309	+	0.445445i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	−4.48275	−	1.90815i	−1.41757	−	0.603409i
$11$	−3.52971	+	4.30096i	−1.06425	+	1.29679i	−0.111256	+	0.993792i	$0.535487\pi$
$11$	−3.52971	+	4.30096i	−1.06425	+	1.29679i	−0.952992	+	0.302997i	$0.902013\pi$
$12$	1.90222	+	0.617717i	0.549122	+	0.178320i
$13$	0.800729	−	1.49806i	0.222082	−	0.415487i	−0.746063	−	0.665875i	$-0.768058\pi$
$13$	0.800729	−	1.49806i	0.222082	−	0.415487i	0.968145	+	0.250389i	$0.0805584\pi$
$14$	0.283628	−	0.338822i	0.0758028	−	0.0905540i
$15$	1.31835	+	3.18277i	0.340395	+	0.821787i
$16$	−3.63313	−	1.67343i	−0.908283	−	0.418357i
$17$	−0.777110	+	1.87611i	−0.188477	+	0.455023i	−0.989667	−	0.143387i	$-0.954201\pi$
$17$	−0.777110	+	1.87611i	−0.188477	+	0.455023i	0.801190	+	0.598410i	$0.204201\pi$
$18$	−0.654484	−	1.25366i	−0.154263	−	0.295489i
$19$	1.40624	+	4.63574i	0.322613	+	1.06351i	0.956901	+	0.290415i	$0.0937933\pi$
$19$	1.40624	+	4.63574i	0.322613	+	1.06351i	−0.634288	+	0.773097i	$0.718707\pi$
$20$	−1.87133	−	6.63101i	−0.418442	−	1.48274i
$21$	−0.310942	+	0.0306251i	−0.0678530	+	0.00668294i
$22$	−7.86819	−	0.0765928i	−1.67750	−	0.0163296i
$23$	2.04529	−	1.36662i	0.426473	−	0.284960i	−0.323753	−	0.946142i	$-0.604945\pi$
$23$	2.04529	−	1.36662i	0.426473	−	0.284960i	0.750226	+	0.661181i	$0.229945\pi$
$24$	1.00563	+	2.64362i	0.205274	+	0.539626i
$25$	3.81568	−	5.71057i	0.763136	−	1.14211i
$26$	2.36052	−	0.445695i	0.462936	−	0.0874079i
$27$	−0.290285	+	0.956940i	−0.0558653	+	0.184163i
$28$	0.624774	+	0.0121649i	0.118071	+	0.00229894i
$29$	2.41755	−	1.98403i	0.448927	−	0.368425i	−0.382596	−	0.923916i	$-0.624970\pi$
$29$	2.41755	−	1.98403i	0.448927	−	0.368425i	0.831522	+	0.555491i	$0.187470\pi$
$30$	−2.33835	+	4.27413i	−0.426922	+	0.780347i
$31$	1.08390	−	1.08390i	0.194675	−	0.194675i	−0.603038	−	0.797713i	$-0.706043\pi$
$31$	1.08390	−	1.08390i	0.194675	−	0.194675i	0.797713	+	0.603038i	$0.206043\pi$
$32$	−1.37679	−	5.48675i	−0.243384	−	0.969930i
$33$	3.93428	+	3.93428i	0.684870	+	0.684870i
$34$	−2.75615	+	0.806856i	−0.472676	+	0.138375i
$35$	0.682847	+	0.832051i	0.115422	+	0.140642i
$36$	0.801192	−	1.83251i	0.133532	−	0.305418i
$37$	−5.25585	−	1.59435i	−0.864057	−	0.262109i	−0.173011	−	0.984920i	$-0.555350\pi$
$37$	−5.25585	−	1.59435i	−0.864057	−	0.262109i	−0.691046	+	0.722811i	$0.742850\pi$
$38$	−3.86144	+	5.65902i	−0.626408	+	0.918013i
$39$	−1.41236	−	0.943708i	−0.226158	−	0.151114i
$40$	5.64769	−	7.94027i	0.892979	−	1.25547i
$41$	5.31281	+	7.95118i	0.829721	+	1.24177i	0.967894	+	0.251357i	$0.0808769\pi$
$41$	5.31281	+	7.95118i	0.829721	+	1.24177i	−0.138173	+	0.990408i	$0.544123\pi$
$42$	−0.309390	−	0.315473i	−0.0477399	−	0.0486785i
$43$	1.10705	+	11.2400i	0.168823	+	1.71409i	0.590245	+	0.807224i	$0.299031\pi$
$43$	1.10705	+	11.2400i	0.168823	+	1.71409i	−0.421422	+	0.906864i	$0.638469\pi$
$44$	−6.89062	−	8.73772i	−1.03880	−	1.31726i
$45$	3.29666	−	1.00003i	0.491437	−	0.149076i
$46$	3.31898	+	1.04219i	0.489357	+	0.153662i
$47$	−7.30995	−	3.02788i	−1.06627	−	0.441662i	−0.220594	−	0.975366i	$-0.570800\pi$
$47$	−7.30995	−	3.02788i	−1.06627	−	0.441662i	−0.845671	+	0.533704i	$0.820800\pi$
$48$	−2.02148	+	3.45161i	−0.291775	+	0.498197i
$49$	6.37697	−	2.64143i	0.910995	−	0.377346i
$50$	9.67491	−	0.857893i	1.36824	−	0.121324i
$51$	1.79091	+	0.957259i	0.250777	+	0.134043i
$52$	2.58366	+	2.20591i	0.358290	+	0.305905i
$53$	1.14828	+	0.942371i	0.157729	+	0.129445i	0.709947	−	0.704255i	$-0.248719\pi$
$53$	1.14828	+	0.942371i	0.157729	+	0.129445i	−0.552219	+	0.833699i	$0.686219\pi$
$54$	−1.31177	+	0.528452i	−0.178509	+	0.0719133i
$55$	3.73943	−	18.7994i	0.504225	−	2.53491i
$56$	0.540448	+	0.699212i	0.0722204	+	0.0934361i
$57$	4.75125	−	0.945083i	0.629319	−	0.125179i
$58$	4.32928	+	0.905044i	0.568463	+	0.118838i
$59$	−0.278466	−	0.520974i	−0.0362532	−	0.0678250i	0.863142	−	0.504961i	$-0.168493\pi$
$59$	−0.278466	−	0.520974i	−0.0362532	−	0.0678250i	−0.899396	+	0.437136i	$0.855993\pi$
$60$	−6.78250	+	1.21237i	−0.875617	+	0.156516i
$61$	14.9424	+	1.47170i	1.91318	+	0.188432i	0.983622	−	0.180245i	$-0.0576891\pi$
$61$	14.9424	+	1.47170i	1.91318	+	0.188432i	0.929558	+	0.368677i	$0.120189\pi$
$62$	2.15520	+	0.233472i	0.273710	+	0.0296509i
$63$			0.312446i			0.0393645i
$64$	4.82526	−	6.38098i	0.603157	−	0.797622i
$65$			5.85178i			0.725825i
$66$	−0.847441	+	7.82279i	−0.104313	+	0.962919i
$67$	−10.7537	−	1.05915i	−1.31378	−	0.129396i	−0.583258	−	0.812287i	$-0.698222\pi$
$67$	−10.7537	−	1.05915i	−1.31378	−	0.129396i	−0.730520	+	0.682891i	$0.760722\pi$
$68$	−3.33234	−	2.32169i	−0.404106	−	0.281546i
$69$	−1.15957	−	2.16940i	−0.139596	−	0.261165i
$70$	−0.311491	+	1.49002i	−0.0372303	+	0.178091i
$71$	2.97508	−	0.591780i	0.353077	−	0.0702314i	−0.0153654	−	0.999882i	$-0.504891\pi$
$71$	2.97508	−	0.591780i	0.353077	−	0.0702314i	0.368442	+	0.929651i	$0.379891\pi$
$72$	2.72946	−	0.741670i	0.321669	−	0.0874066i
$73$	1.34471	−	6.76030i	0.157386	−	0.791234i	−0.818763	−	0.574132i	$-0.805340\pi$
$73$	1.34471	−	6.76030i	0.157386	−	0.791234i	0.976149	−	0.217102i	$-0.0696604\pi$
$74$	−2.90245	−	7.20470i	−0.337402	−	0.837529i
$75$	−5.30907	−	4.35704i	−0.613038	−	0.503107i
$76$	−9.65867	+	0.761773i	−1.10793	+	0.0873814i
$77$	1.53315	+	0.819487i	0.174719	+	0.0933892i
$78$	−0.212177	−	2.39284i	−0.0240244	−	0.270935i
$79$	−10.0620	+	4.16781i	−1.13206	+	0.468915i	−0.868481	−	0.495722i	$-0.834903\pi$
$79$	−10.0620	+	4.16781i	−1.13206	+	0.468915i	−0.263580	+	0.964637i	$0.584903\pi$
$80$	13.7558	−	0.815823i	1.53795	−	0.0912118i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	−4.05155	+	12.9027i	−0.447419	+	1.42486i
$83$	−3.38393	+	1.02650i	−0.371435	+	0.112673i	−0.470483	−	0.882409i	$-0.655920\pi$
$83$	−3.38393	+	1.02650i	−0.371435	+	0.112673i	0.0990481	+	0.995083i	$0.468420\pi$
$84$	0.0733449	−	0.620573i	0.00800258	−	0.0677101i
$85$	−0.685700	−	6.96203i	−0.0743746	−	0.755138i
$86$	−11.4038	+	11.1839i	−1.22971	+	1.20600i
$87$	−1.73751	−	2.60037i	−0.186281	−	0.278789i
$88$	3.51952	−	15.3385i	0.375182	−	1.63509i
$89$	9.10601	+	6.08444i	0.965235	+	0.644949i	0.935020	−	0.354594i	$-0.115381\pi$
$89$	9.10601	+	6.08444i	0.965235	+	0.644949i	0.0302145	+	0.999543i	$0.490381\pi$
$90$	4.02435	+	2.74602i	0.424204	+	0.289456i
$91$	−0.507877	−	0.154063i	−0.0532400	−	0.0161502i
$92$	1.79385	+	4.58101i	0.187022	+	0.477603i
$93$	−0.972442	−	1.18492i	−0.100838	−	0.122871i
$94$	−3.14378	−	10.7389i	−0.324256	−	1.10763i
$95$	−11.8007	−	11.8007i	−1.21073	−	1.21073i
$96$	−5.59528	+	0.832363i	−0.571066	+	0.0849527i
$97$	−1.18315	+	1.18315i	−0.120131	+	0.120131i	−0.764617	−	0.644486i	$-0.777072\pi$
$97$	−1.18315	+	1.18315i	−0.120131	+	0.120131i	0.644486	+	0.764617i	$0.277072\pi$
$98$	8.56362	+	4.68509i	0.865056	+	0.473265i
$99$	4.30096	−	3.52971i	0.432263	−	0.354749i
$100$	9.52195	+	9.90012i	0.952195	+	0.990012i
$101$	−4.51399	+	14.8806i	−0.449159	+	1.48068i	0.381747	+	0.924267i	$0.375323\pi$
$101$	−4.51399	+	14.8806i	−0.449159	+	1.48068i	−0.830906	+	0.556413i	$0.812177\pi$
$102$	0.532821	+	2.82196i	0.0527572	+	0.279416i
$103$	−3.67892	+	5.50589i	−0.362495	+	0.542512i	−0.967226	−	0.253918i	$-0.918281\pi$
$103$	−3.67892	+	5.50589i	−0.362495	+	0.542512i	0.604731	+	0.796430i	$0.293281\pi$
$104$	−0.140282	+	4.80240i	−0.0137558	+	0.470914i
$105$	0.894976	−	0.598004i	0.0873407	−	0.0583592i
$106$	−0.0204489	+	2.10067i	−0.00198618	+	0.204035i
$107$	12.6640	−	1.24729i	1.22427	−	0.120580i	0.534855	−	0.844944i	$-0.320366\pi$
$107$	12.6640	−	1.24729i	1.22427	−	0.120580i	0.689418	+	0.724364i	$0.257866\pi$
$108$	−1.74515	−	0.976952i	−0.167928	−	0.0940072i
$109$	−0.574253	−	1.89306i	−0.0550035	−	0.181322i	0.925134	−	0.379640i	$-0.123952\pi$
$109$	−0.574253	−	1.89306i	−0.0550035	−	0.181322i	−0.980138	+	0.198318i	$0.936452\pi$
$110$	24.0297	−	12.5449i	2.29114	−	1.19611i
$111$	−2.10183	+	5.07427i	−0.199497	+	0.481628i
$112$	−0.291352	+	1.21535i	−0.0275301	+	0.114840i
$113$	−2.24754	−	5.42604i	−0.211431	−	0.510439i	0.782213	−	0.623011i	$-0.214091\pi$
$113$	−2.24754	−	5.42604i	−0.211431	−	0.510439i	−0.993644	+	0.112572i	$0.964091\pi$
$114$	5.25328	+	4.39752i	0.492015	+	0.411866i
$115$	−3.99471	+	7.47358i	−0.372509	+	0.696915i
$116$	2.84059	+	5.57267i	0.263742	+	0.517409i
$117$	−1.07760	+	1.31306i	−0.0996241	+	0.121392i
$118$	0.327196	−	0.768672i	0.0301209	−	0.0707620i
$119$	0.622289	+	0.123781i	0.0570451	+	0.0113470i
$120$	−7.34846	−	6.39878i	−0.670820	−	0.584126i
$121$	−3.89344	−	19.5736i	−0.353949	−	1.77942i
$122$	11.6246	+	17.7694i	1.05244	+	1.60877i
$123$	8.43364	−	4.50787i	0.760435	−	0.406461i
$124$	1.65329	+	2.58174i	0.148470	+	0.231847i
$125$	−0.630780	+	6.40441i	−0.0564187	+	0.572828i
$126$	−0.344279	+	0.276979i	−0.0306708	+	0.0246752i
$127$	21.5459			1.91189			0.955943	−	0.293552i	$-0.0948373\pi$
$127$	21.5459			1.91189			0.955943	+	0.293552i	$0.0948373\pi$
$128$	11.3086	−	0.339762i	0.999549	−	0.0300310i
$129$	11.2944			0.994418
$130$	−6.44798	+	5.18751i	−0.565525	+	0.454975i
$131$	−1.61917	+	16.4397i	−0.141467	+	1.43634i	0.618194	+	0.786025i	$0.287864\pi$
$131$	−1.61917	+	16.4397i	−0.141467	+	1.43634i	−0.759662	+	0.650318i	$0.774636\pi$
$132$	−9.37105	+	6.00100i	−0.815645	+	0.522320i
$133$	1.33487	−	0.713503i	0.115748	−	0.0618686i
$134$	−8.36595	−	12.7883i	−0.722708	−	1.10474i
$135$	−0.672087	−	3.37881i	−0.0578440	−	0.290801i
$136$	−0.395838	−	5.72999i	−0.0339428	−	0.491343i
$137$	−21.7227	−	4.32091i	−1.85589	−	0.369160i	−0.864776	−	0.502158i	$-0.832540\pi$
$137$	−21.7227	−	4.32091i	−1.85589	−	0.369160i	−0.991116	+	0.132998i	$0.957540\pi$
$138$	1.36249	−	3.20084i	0.115982	−	0.272474i
$139$	−0.654000	+	0.796901i	−0.0554716	+	0.0675923i	−0.800007	−	0.599991i	$-0.795171\pi$
$139$	−0.654000	+	0.796901i	−0.0554716	+	0.0675923i	0.744536	+	0.667583i	$0.232671\pi$
$140$	−1.91796	+	0.977650i	−0.162097	+	0.0826265i
$141$	−3.72980	+	6.97796i	−0.314106	+	0.587651i
$142$	3.28943	+	2.75359i	0.276043	+	0.231076i
$143$	3.61675	+	8.73161i	0.302448	+	0.730174i
$144$	3.23685	+	2.35006i	0.269738	+	0.195839i
$145$	−4.12305	+	9.95392i	−0.342401	+	0.826628i
$146$	8.64113	−	4.51119i	0.715145	−	0.373349i
$147$	−2.00365	−	6.60516i	−0.165259	−	0.544785i
$148$	5.36576	−	9.58500i	0.441063	−	0.787882i
$149$	1.63105	−	0.160645i	0.133621	−	0.0131605i	−0.0309856	−	0.999520i	$-0.509865\pi$
$149$	1.63105	−	0.160645i	0.133621	−	0.0131605i	0.164606	+	0.986359i	$0.447365\pi$
$150$	0.0945454	−	9.71242i	0.00771960	−	0.793015i
$151$	−19.4635	+	13.0051i	−1.58391	+	1.05834i	−0.622729	+	0.782438i	$0.713976\pi$
$151$	−19.4635	+	13.0051i	−1.58391	+	1.05834i	−0.961186	+	0.275900i	$0.911024\pi$
$152$	−9.40164	−	9.96743i	−0.762574	−	0.808465i
$153$	1.12819	−	1.68845i	0.0912087	−	0.136503i
$154$	0.456136	+	2.41582i	0.0367565	+	0.194672i
$155$	−1.53292	+	5.05335i	−0.123127	+	0.405895i
$156$	2.44853	−	2.35501i	0.196040	−	0.188551i
$157$	−12.1710	+	9.98848i	−0.971352	+	0.797168i	−0.979220	−	0.202801i	$-0.934995\pi$
$157$	−12.1710	+	9.98848i	−0.971352	+	0.797168i	0.00786830	+	0.999969i	$0.497495\pi$
$158$	−13.5122	−	7.39243i	−1.07497	−	0.588110i
$159$	1.05038	−	1.05038i	0.0833009	−	0.0833009i
$160$	13.0933	+	14.4341i	1.03511	+	1.14112i
$161$	−0.543463	−	0.543463i	−0.0428309	−	0.0428309i
$162$	0.397332	+	1.35725i	0.0312173	+	0.106636i
$163$	−5.16398	−	6.29233i	−0.404474	−	0.492854i	0.530442	−	0.847721i	$-0.322026\pi$
$163$	−5.16398	−	6.29233i	−0.404474	−	0.492854i	−0.934917	+	0.354868i	$0.884526\pi$
$164$	−17.8089	+	6.97368i	−1.39064	+	0.544553i
$165$	−18.3423	−	5.56409i	−1.42795	−	0.433164i
$166$	−4.13089	−	2.81872i	−0.320619	−	0.218775i
$167$	8.29891	+	5.54515i	0.642189	+	0.429097i	0.833566	−	0.552420i	$-0.186295\pi$
$167$	8.29891	+	5.54515i	0.642189	+	0.429097i	−0.191377	+	0.981517i	$0.561295\pi$
$168$	0.748818	−	0.469311i	0.0577726	−	0.0362081i
$169$	5.61940	+	8.41003i	0.432262	+	0.646925i
$170$	7.06348	−	6.92729i	0.541744	−	0.531299i
$171$	−0.474828	−	4.82101i	−0.0363110	−	0.368672i
$172$	−22.4327	−	2.65130i	−1.71048	−	0.202159i
$173$	6.37487	−	1.93379i	0.484672	−	0.147024i	−0.0384864	−	0.999259i	$-0.512254\pi$
$173$	6.37487	−	1.93379i	0.484672	−	0.147024i	0.523158	+	0.852235i	$0.324754\pi$
$174$	1.32503	−	4.21973i	0.100450	−	0.319897i
$175$	−1.98255	−	0.821198i	−0.149866	−	0.0620767i
$176$	20.0212	−	9.71924i	1.50916	−	0.732615i
$177$	−0.545760	+	0.226061i	−0.0410218	+	0.0169918i
$178$	1.36799	+	15.4275i	0.102535	+	1.15634i
$179$	−17.0357	−	9.10576i	−1.27331	−	0.680596i	−0.310444	−	0.950592i	$-0.600478\pi$
$179$	−17.0357	−	9.10576i	−1.27331	−	0.680596i	−0.962862	+	0.269995i	$0.912978\pi$
$180$	0.541728	+	6.86867i	0.0403780	+	0.511961i
$181$	−2.91551	−	2.39270i	−0.216708	−	0.177848i	0.519776	−	0.854303i	$-0.326015\pi$
$181$	−2.91551	−	2.39270i	−0.216708	−	0.177848i	−0.736484	+	0.676455i	$0.763515\pi$
$182$	−0.280466	−	0.696196i	−0.0207895	−	0.0516055i
$183$	2.92922	−	14.7262i	0.216534	−	1.08859i
$184$	−3.45751	+	6.03761i	−0.254891	+	0.445098i
$185$	18.5576	−	3.69134i	1.36438	−	0.271392i
$186$	0.443594	−	2.12193i	0.0325259	−	0.155588i
$187$	−5.32610	−	9.96444i	−0.389483	−	0.728672i
$188$	9.04607	−	12.9839i	0.659753	−	0.946949i
$189$	0.310942	+	0.0306251i	0.0226177	+	0.00222765i
$190$	2.54187	−	23.4642i	0.184406	−	1.70227i
$191$		−	3.12776i		−	0.226317i	−0.993577	−	0.113158i	$-0.963903\pi$
$191$		−	3.12776i		−	0.226317i	0.993577	−	0.113158i	$-0.0360968\pi$
$192$	−5.87729	−	5.42747i	−0.424157	−	0.391694i
$193$		−	9.41148i		−	0.677453i	−0.940885	−	0.338727i	$-0.890004\pi$
$193$		−	9.41148i		−	0.677453i	0.940885	−	0.338727i	$-0.109996\pi$
$194$	−2.35254	−	0.254850i	−0.168903	−	0.0182972i
$195$	5.82361	+	0.573575i	0.417037	+	0.0410746i
$196$	2.42909	+	13.5894i	0.173506	+	0.970669i
$197$	−10.5682	−	19.7718i	−0.752955	−	1.40868i	−0.907223	−	0.420650i	$-0.861802\pi$
$197$	−10.5682	−	19.7718i	−0.752955	−	1.40868i	0.154268	−	0.988029i	$-0.450698\pi$
$198$	7.70206	+	1.61013i	0.547362	+	0.114427i
$199$	1.11250	−	0.221289i	0.0788628	−	0.0156868i	−0.155501	−	0.987836i	$-0.549699\pi$
$199$	1.11250	−	0.221289i	0.0788628	−	0.0156868i	0.234364	+	0.972149i	$0.424699\pi$
$200$	−2.46771	+	19.2684i	−0.174494	+	1.36248i
$201$	−2.10810	+	10.5981i	−0.148694	+	0.747535i
$202$	−20.3983	+	8.21756i	−1.43522	+	0.578185i
$203$	−0.755353	−	0.619902i	−0.0530154	−	0.0435086i
$204$	−2.63714	+	3.08873i	−0.184636	+	0.216254i
$205$	−29.0539	−	15.5296i	−2.02921	−	1.08464i
$206$	−9.32816	+	0.827145i	−0.649923	+	0.0576299i
$207$	−2.27261	+	0.941346i	−0.157957	+	0.0654281i
$208$	−5.41604	+	4.10268i	−0.375535	+	0.284470i
$209$	−24.9017	−	10.3146i	−1.72249	−	0.713478i
$210$	1.45231	+	0.456038i	0.100219	+	0.0314696i
$211$	10.2862	−	3.12029i	0.708133	−	0.214810i	0.0843826	−	0.996433i	$-0.473108\pi$
$211$	10.2862	−	3.12029i	0.708133	−	0.214810i	0.623750	+	0.781624i	$0.285608\pi$
$212$	−2.33282	+	1.83968i	−0.160219	+	0.126350i
$213$	−0.297322	−	3.01876i	−0.0203722	−	0.206842i
$214$	12.6008	+	12.8485i	0.861372	+	0.878307i
$215$	−21.6168	−	32.3519i	−1.47426	−	2.20638i
$216$	−0.470565	−	2.78901i	−0.0320179	−	0.189768i
$217$	−0.398223	−	0.266084i	−0.0270332	−	0.0180630i
$218$	1.57686	−	2.31093i	0.106799	−	0.156516i
$219$	−6.59595	−	2.00086i	−0.445713	−	0.135206i
$220$	35.1250	+	15.3570i	2.36812	+	1.03537i
$221$	2.18827	+	2.66641i	0.147199	+	0.179362i
$222$	−7.45449	+	2.18229i	−0.500313	+	0.146465i
$223$	13.9388	+	13.9388i	0.933413	+	0.933413i	0.997917	−	0.0645041i	$-0.0205466\pi$
$223$	13.9388	+	13.9388i	0.933413	+	0.933413i	−0.0645041	+	0.997917i	$0.520547\pi$
$224$	−1.59745	+	0.756353i	−0.106734	+	0.0505360i
$225$	−4.85644	+	4.85644i	−0.323763	+	0.323763i
$226$	3.98646	−	7.28663i	0.265175	−	0.484699i
$227$	−14.9210	+	12.2453i	−0.990340	+	0.812751i	−0.982319	−	0.187217i	$-0.940053\pi$
$227$	−14.9210	+	12.2453i	−0.990340	+	0.812751i	−0.00802138	+	0.999968i	$0.502553\pi$
$228$	−0.188611	+	9.68683i	−0.0124910	+	0.641526i
$229$	5.32186	−	17.5438i	0.351679	−	1.15933i	−0.585557	−	0.810631i	$-0.699124\pi$
$229$	5.32186	−	17.5438i	0.351679	−	1.15933i	0.937235	−	0.348697i	$-0.113376\pi$
$230$	−11.7763	+	2.22350i	−0.776504	+	0.146613i
$231$	0.965816	−	1.44545i	0.0635460	−	0.0951034i
$232$	−3.62230	+	8.07007i	−0.237815	+	0.529826i
$233$	24.5253	−	16.3873i	1.60670	−	1.07357i	0.660095	−	0.751182i	$-0.270516\pi$
$233$	24.5253	−	16.3873i	1.60670	−	1.07357i	0.946609	−	0.322384i	$-0.104484\pi$
$234$	−2.40211	−	0.0233833i	−0.157031	−	0.00152862i
$235$	27.1264	−	2.67172i	1.76953	−	0.174284i
$236$	1.13704	−	0.320883i	0.0740151	−	0.0208877i
$237$	3.16149	+	10.4220i	0.205361	+	0.676985i
$238$	0.415257	+	0.795420i	0.0269171	+	0.0515594i
$239$	−2.47822	+	5.98294i	−0.160303	+	0.387005i	−0.983539	−	0.180693i	$-0.942166\pi$
$239$	−2.47822	+	5.98294i	−0.160303	+	0.387005i	0.823237	+	0.567698i	$0.192166\pi$
$240$	0.536413	−	13.7696i	0.0346253	−	0.888822i
$241$	3.95964	+	9.55942i	0.255063	+	0.615776i	0.998599	−	0.0529199i	$-0.0168528\pi$
$241$	3.95964	+	9.55942i	0.255063	+	0.615776i	−0.743536	+	0.668696i	$0.766853\pi$
$242$	18.1164	−	21.6418i	1.16457	−	1.39119i
$243$	0.471397	−	0.881921i	0.0302401	−	0.0565753i
$244$	−9.27484	+	28.5612i	−0.593761	+	1.82844i
$245$	−15.0851	+	18.3812i	−0.963749	+	1.17433i
$246$	12.4434	+	5.29673i	0.793364	+	0.337707i
$247$	8.07062	+	1.60535i	0.513521	+	0.102146i
$248$	−1.37917	+	4.11040i	−0.0875771	+	0.261011i
$249$	0.689878	+	3.46825i	0.0437192	+	0.219791i
$250$	−7.61609	+	4.98236i	−0.481684	+	0.315112i
$251$	−1.31105	+	0.700770i	−0.0827526	+	0.0442322i	−0.512254	−	0.858834i	$-0.671189\pi$
$251$	−1.31105	+	0.700770i	−0.0827526	+	0.0442322i	0.429501	+	0.903066i	$0.358689\pi$
$252$	−0.610396	−	0.133818i	−0.0384513	−	0.00842977i
$253$	−1.34150	+	13.6205i	−0.0843396	+	0.856314i
$254$	19.1001	+	23.7410i	1.19844	+	1.48964i
$255$	−6.99572			−0.438089
$256$	10.3993	+	12.1596i	0.649955	+	0.759973i
$257$	13.3349			0.831810			0.415905	−	0.909408i	$-0.363465\pi$
$257$	13.3349			0.831810			0.415905	+	0.909408i	$0.363465\pi$
$258$	10.0123	+	12.4451i	0.623340	+	0.774800i
$259$	−0.168204	+	1.70780i	−0.0104517	+	0.106118i
$260$	−11.4321	−	2.50628i	−0.708987	−	0.155433i
$261$	−2.75816	+	1.47427i	−0.170726	+	0.0912548i
$262$	−19.5500	+	12.7894i	−1.20780	+	0.790131i
$263$	−2.65226	−	13.3338i	−0.163546	−	0.822199i	−0.972243	−	0.233974i	$-0.924827\pi$
$263$	−2.65226	−	13.3338i	−0.163546	−	0.822199i	0.808697	−	0.588225i	$-0.200173\pi$
$264$	−14.9197	−	5.00601i	−0.918243	−	0.308099i
$265$	−5.01911	−	0.998363i	−0.308322	−	0.0613290i
$266$	1.96954	+	0.838362i	0.120760	+	0.0514033i
$267$	6.94769	−	8.46578i	0.425191	−	0.518097i
$268$	6.67491	−	20.5549i	0.407735	−	1.25559i
$269$	12.5975	−	23.5683i	0.768085	−	1.43699i	−0.127381	−	0.991854i	$-0.540657\pi$
$269$	12.5975	−	23.5683i	0.768085	−	1.43699i	0.895465	−	0.445131i	$-0.146843\pi$
$270$	3.12726	−	3.73582i	0.190319	−	0.227355i
$271$	2.20593	+	5.32559i	0.134001	+	0.323507i	0.976610	−	0.215019i	$-0.0689814\pi$
$271$	2.20593	+	5.32559i	0.134001	+	0.323507i	−0.842609	+	0.538526i	$0.818981\pi$
$272$	5.96288	−	5.51571i	0.361553	−	0.334439i
$273$	−0.203102	+	0.490331i	−0.0122923	+	0.0296762i
$274$	−14.4957	−	27.7663i	−0.875715	−	1.67742i
$275$	11.0927	+	36.5677i	0.668915	+	2.20512i
$276$	4.73478	−	1.33620i	0.285000	−	0.0804296i
$277$	2.91834	−	0.287431i	0.175346	−	0.0172701i	−0.00996315	−	0.999950i	$-0.503171\pi$
$277$	2.91834	−	0.287431i	0.175346	−	0.0172701i	0.185309	+	0.982680i	$0.440671\pi$
$278$	−1.45785	−	0.0141914i	−0.0874362	−	0.000851147i
$279$	−1.27453	+	0.851616i	−0.0763044	+	0.0509849i
$280$	−2.77749	−	1.24669i	−0.165987	−	0.0745042i
$281$	−9.56299	+	14.3120i	−0.570480	+	0.853784i	−0.998756	−	0.0498640i	$-0.984121\pi$
$281$	−9.56299	+	14.3120i	−0.570480	+	0.853784i	0.428276	+	0.903648i	$0.359121\pi$
$282$	−10.9953	+	2.07605i	−0.654761	+	0.123627i
$283$	−6.17113	+	20.3435i	−0.366836	+	1.20929i	0.558294	+	0.829643i	$0.311456\pi$
$283$	−6.17113	+	20.3435i	−0.366836	+	1.20929i	−0.925130	+	0.379652i	$0.876044\pi$
$284$	−0.118102	+	6.06558i	−0.00700806	+	0.359926i
$285$	−12.9006	+	10.5872i	−0.764164	+	0.627133i
$286$	−6.41502	+	11.7257i	−0.379328	+	0.693353i
$287$	2.11274	−	2.11274i	0.124711	−	0.124711i
$288$	0.279922	+	5.64992i	0.0164945	+	0.332925i
$289$	9.10493	+	9.10493i	0.535584	+	0.535584i
$290$	−14.6231	+	4.28087i	−0.858696	+	0.251381i
$291$	1.06149	+	1.29343i	0.0622255	+	0.0758219i
$292$	12.6310	+	5.52242i	0.739175	+	0.323175i
$293$	−13.8648	−	4.20584i	−0.809990	−	0.245708i	−0.141989	−	0.989868i	$-0.545350\pi$
$293$	−13.8648	−	4.20584i	−0.809990	−	0.245708i	−0.668001	+	0.744161i	$0.732850\pi$
$294$	5.50191	−	8.06316i	0.320878	−	0.470253i
$295$	1.69208	+	1.13061i	0.0985169	+	0.0658269i
$296$	15.3182	−	2.58451i	0.890353	−	0.150221i
$297$	−3.09114	−	4.62622i	−0.179366	−	0.268441i
$298$	1.62291	+	1.65482i	0.0940128	+	0.0958611i
$299$	−0.409553	−	4.15826i	−0.0236851	−	0.240479i
$300$	10.7858	−	8.50572i	0.622716	−	0.491078i
$301$	3.37694	−	1.02438i	0.194644	−	0.0590446i
$302$	−31.5841	−	9.91768i	−1.81746	−	0.570698i
$303$	14.3665	+	5.95082i	0.825336	+	0.341865i
$304$	2.64854	−	19.1955i	0.151904	−	1.10094i
$305$	−47.7883	+	19.7946i	−2.73635	+	1.13343i
$306$	2.86060	−	0.253655i	0.163530	−	0.0145005i
$307$	12.2119	+	6.52741i	0.696971	+	0.372539i	0.781520	−	0.623881i	$-0.214445\pi$
$307$	12.2119	+	6.52741i	0.696971	+	0.372539i	−0.0845486	+	0.996419i	$0.526945\pi$
$308$	−2.25759	+	2.64419i	−0.128638	+	0.150667i
$309$	5.11879	+	4.20088i	0.291198	+	0.238980i
$310$	−6.92711	+	2.79062i	−0.393433	+	0.158496i
$311$	4.07429	−	20.4828i	0.231032	−	1.16148i	−0.674853	−	0.737952i	$-0.735793\pi$
$311$	4.07429	−	20.4828i	0.231032	−	1.16148i	0.905885	−	0.423524i	$-0.139207\pi$
$312$	4.76553	+	0.610325i	0.269795	+	0.0345528i
$313$	27.5256	−	5.47519i	1.55584	−	0.309476i	0.659108	−	0.752049i	$-0.270934\pi$
$313$	27.5256	−	5.47519i	1.55584	−	0.309476i	0.896733	+	0.442573i	$0.145934\pi$
$314$	−21.7955	−	4.55639i	−1.22999	−	0.257132i
$315$	−0.507401	−	0.949281i	−0.0285888	−	0.0534859i
$316$	−3.83277	−	21.4422i	−0.215610	−	1.20622i
$317$	11.4709	+	1.12979i	0.644271	+	0.0634552i	0.414876	−	0.909878i	$-0.363825\pi$
$317$	11.4709	+	1.12979i	0.644271	+	0.0634552i	0.229396	+	0.973333i	$0.426325\pi$
$318$	2.08855	+	0.226252i	0.117120	+	0.0126876i
$319$			17.4008i			0.974258i
$320$	−4.29773	+	27.2229i	−0.240251	+	1.52180i
$321$		−	12.7253i		−	0.710254i
$322$	0.117062	−	1.08060i	0.00652358	−	0.0602197i
$323$	−9.78995	−	0.964226i	−0.544728	−	0.0536510i
$324$	−1.14330	+	1.64099i	−0.0635168	+	0.0911663i
$325$	−5.49944	−	10.2887i	−0.305054	−	0.570716i
$326$	2.35563	−	11.2682i	0.130466	−	0.624086i
$327$	−1.94023	+	0.385936i	−0.107295	+	0.0213423i
$328$	−23.4715	−	13.4412i	−1.29600	−	0.742169i
$329$	−0.482292	+	2.42464i	−0.0265896	+	0.133675i
$330$	−10.1292	−	25.1436i	−0.557595	−	1.38411i
$331$	5.06819	+	4.15936i	0.278573	+	0.228619i	0.763296	−	0.646049i	$-0.223580\pi$
$331$	5.06819	+	4.15936i	0.278573	+	0.228619i	−0.484723	+	0.874668i	$0.661080\pi$
$332$	−0.556068	−	7.05050i	−0.0305182	−	0.386947i
$333$	4.84382	+	2.58908i	0.265440	+	0.141881i
$334$	1.24674	+	14.0601i	0.0682184	+	0.769336i
$335$	34.3922	−	14.2457i	1.87905	−	0.778328i
$336$	1.18094	+	0.409074i	0.0644256	+	0.0223168i
$337$	23.9316	+	9.91280i	1.30364	+	0.539985i	0.923022	−	0.384748i	$-0.125712\pi$
$337$	23.9316	+	9.91280i	1.30364	+	0.539985i	0.380617	+	0.924733i	$0.375712\pi$
$338$	−4.28536	+	13.6473i	−0.233093	+	0.742314i
$339$	−5.62021	+	1.70487i	−0.305248	+	0.0925960i
$340$	13.8947	+	1.64220i	0.753547	+	0.0890609i
$341$	0.835964	+	8.48768i	0.0452700	+	0.459634i
$342$	4.89126	−	4.79695i	0.264489	−	0.259389i
$343$	−2.41326	−	3.61169i	−0.130304	−	0.195013i
$344$	−16.9648	−	27.0685i	−0.914681	−	1.45944i
$345$	7.04604	+	4.70802i	0.379346	+	0.253471i
$346$	7.78203	+	5.31008i	0.418365	+	0.285472i
$347$	25.9122	+	7.86037i	1.39104	+	0.421967i	0.894896	−	0.446275i	$-0.147250\pi$
$347$	25.9122	+	7.86037i	1.39104	+	0.421967i	0.496142	+	0.868242i	$0.334750\pi$
$348$	5.82426	−	2.28069i	0.312213	−	0.122258i
$349$	−0.824480	−	1.00463i	−0.0441334	−	0.0537767i	0.750476	−	0.660898i	$-0.229824\pi$
$349$	−0.824480	−	1.00463i	−0.0441334	−	0.0537767i	−0.794609	+	0.607121i	$0.792324\pi$
$350$	−0.852632	−	2.91251i	−0.0455751	−	0.155680i
$351$	1.20111	+	1.20111i	0.0641107	+	0.0641107i
$352$	28.4580	+	13.4451i	1.51682	+	0.716627i
$353$	4.10908	−	4.10908i	0.218704	−	0.218704i	−0.589248	−	0.807952i	$-0.700576\pi$
$353$	4.10908	−	4.10908i	0.218704	−	0.218704i	0.807952	+	0.589248i	$0.200576\pi$
$354$	−0.732900	−	0.400964i	−0.0389532	−	0.0213110i
$355$	−8.07792	+	6.62938i	−0.428731	+	0.351851i
$356$	−15.7866	+	15.1836i	−0.836689	+	0.804729i
$357$	0.184180	−	0.607160i	0.00974783	−	0.0321343i
$358$	−5.06837	−	26.8434i	−0.267872	−	1.41872i
$359$	−6.21064	+	9.29487i	−0.327785	+	0.490565i	−0.958360	−	0.285564i	$-0.907819\pi$
$359$	−6.21064	+	9.29487i	−0.327785	+	0.490565i	0.630575	+	0.776128i	$0.282819\pi$
$360$	−7.08824	+	6.68589i	−0.373583	+	0.352377i
$361$	−3.71465	+	2.48205i	−0.195508	+	0.130634i
$362$	0.0519202	−	5.33364i	0.00272887	−	0.280330i
$363$	−19.8610	+	1.95614i	−1.04243	+	0.102671i
$364$	0.518498	−	0.926207i	0.0271767	−	0.0485464i
$365$	6.89296	+	22.7231i	0.360794	+	1.18938i
$366$	18.8233	−	9.82688i	0.983908	−	0.513659i
$367$	−1.01789	+	2.45739i	−0.0531332	+	0.128275i	−0.948217	−	0.317623i	$-0.897115\pi$
$367$	−1.01789	+	2.45739i	−0.0531332	+	0.128275i	0.895084	+	0.445898i	$0.147115\pi$
$368$	−9.71777	+	1.54246i	−0.506574	+	0.0804064i
$369$	−3.65952	−	8.83487i	−0.190507	−	0.459925i
$370$	20.5184	+	17.1760i	1.06670	+	0.892937i
$371$	0.218789	−	0.409325i	0.0113590	−	0.0212511i
$372$	2.73136	−	1.39227i	0.141614	−	0.0721859i
$373$	−5.83989	+	7.11592i	−0.302378	+	0.368449i	−0.901926	−	0.431890i	$-0.857847\pi$
$373$	−5.83989	+	7.11592i	−0.302378	+	0.368449i	0.599548	+	0.800339i	$0.295347\pi$
$374$	6.25814	−	14.7021i	0.323601	−	0.760225i
$375$	6.31175	+	1.25548i	0.325937	+	0.0648330i
$376$	22.3260	−	1.54232i	1.15137	−	0.0795389i
$377$	−1.03639	−	5.21029i	−0.0533769	−	0.268344i
$378$	0.241900	+	0.369770i	0.0124420	+	0.0190189i
$379$	22.2573	−	11.8968i	1.14328	−	0.611095i	0.212675	−	0.977123i	$-0.431782\pi$
$379$	22.2573	−	11.8968i	1.14328	−	0.611095i	0.930604	+	0.366028i	$0.119282\pi$
$380$	28.1081	−	17.9998i	1.44191	−	0.923368i
$381$	2.11186	−	21.4421i	0.108194	−	1.09851i
$382$	3.44643	−	2.77271i	0.176335	−	0.141864i
$383$	27.9281			1.42706			0.713529	−	0.700626i	$-0.247096\pi$
$383$	27.9281			1.42706			0.713529	+	0.700626i	$0.247096\pi$
$384$	0.770311	−	11.2875i	0.0393098	−	0.576010i
$385$	−5.98887			−0.305221
$386$	10.3704	−	8.34313i	0.527837	−	0.424654i
$387$	1.10705	−	11.2400i	0.0562743	−	0.571363i
$388$	−1.80468	−	2.81815i	−0.0916185	−	0.143070i
$389$	26.7851	−	14.3169i	1.35806	−	0.725897i	0.378225	−	0.925714i	$-0.376535\pi$
$389$	26.7851	−	14.3169i	1.35806	−	0.725897i	0.979833	+	0.199817i	$0.0640347\pi$
$390$	4.53052	+	6.92540i	0.229412	+	0.350681i
$391$	0.974514	+	4.89921i	0.0492833	+	0.247764i
$392$	−12.8205	+	14.7233i	−0.647535	+	0.743640i
$393$	16.2018	+	3.22275i	0.817274	+	0.162566i
$394$	12.4176	−	29.1723i	0.625590	−	1.46968i
$395$	23.8022	−	29.0030i	1.19762	−	1.45930i
$396$	5.05358	+	9.91412i	0.253952	+	0.498203i
$397$	−7.50956	+	14.0494i	−0.376894	+	0.705119i	−0.996832	−	0.0795313i	$-0.974658\pi$
$397$	−7.50956	+	14.0494i	−0.376894	+	0.705119i	0.619938	+	0.784651i	$0.287158\pi$
$398$	1.23005	+	1.02967i	0.0616566	+	0.0516128i
$399$	−0.579227	−	1.39838i	−0.0289976	−	0.0700065i
$400$	−23.4191	+	14.3620i	−1.17095	+	0.718098i
$401$	1.16206	−	2.80546i	0.0580305	−	0.140098i	−0.892205	−	0.451631i	$-0.850842\pi$
$401$	1.16206	−	2.80546i	0.0580305	−	0.140098i	0.950235	+	0.311533i	$0.100842\pi$
$402$	−13.5467	+	7.07220i	−0.675648	+	0.352729i
$403$	−0.755837	−	2.49166i	−0.0376509	−	0.124118i
$404$	−27.1376	−	15.1918i	−1.35014	−	0.755822i
$405$	−3.42841	+	0.337669i	−0.170359	+	0.0167789i
$406$	0.0134515	−	1.38184i	0.000667589	−	0.0685798i
$407$	25.4088	−	16.9776i	1.25947	−	0.841551i
$408$	−5.74120	−	0.167705i	−0.284232	−	0.00830265i
$409$	7.30195	−	10.9281i	0.361058	−	0.540362i	−0.605819	−	0.795602i	$-0.707155\pi$
$409$	7.30195	−	10.9281i	0.361058	−	0.540362i	0.966878	+	0.255240i	$0.0821546\pi$
$410$	−8.64397	−	45.7808i	−0.426895	−	2.26095i
$411$	−6.42929	+	21.1945i	−0.317134	+	1.04545i
$412$	−9.18068	−	9.54529i	−0.452300	−	0.470263i
$413$	−0.142675	+	0.117090i	−0.00702056	+	0.00576162i
$414$	−3.05188	−	1.66966i	−0.149992	−	0.0820594i
$415$	8.61412	−	8.61412i	0.422851	−	0.422851i
$416$	−9.32191	−	2.33089i	−0.457044	−	0.114281i
$417$	0.728961	+	0.728961i	0.0356974	+	0.0356974i
$418$	−10.7095	−	36.5826i	−0.523817	−	1.78931i
$419$	−3.41666	−	4.16321i	−0.166915	−	0.203386i	0.682835	−	0.730573i	$-0.260747\pi$
$419$	−3.41666	−	4.16321i	−0.166915	−	0.203386i	−0.849750	+	0.527187i	$0.823247\pi$
$420$	0.784950	+	2.00455i	0.0383016	+	0.0978119i
$421$	−34.4767	−	10.4584i	−1.68029	−	0.509711i	−0.701171	−	0.712994i	$-0.747339\pi$
$421$	−34.4767	−	10.4584i	−1.68029	−	0.509711i	−0.979120	+	0.203283i	$0.934839\pi$
$422$	12.5568	+	8.56813i	0.611254	+	0.417090i
$423$	6.57878	+	4.39580i	0.319871	+	0.213731i
$424$	−4.09512	−	0.939651i	−0.198876	−	0.0456335i
$425$	7.74845	+	11.5964i	0.375855	+	0.562507i
$426$	3.06275	−	3.00369i	0.148391	−	0.145529i
$427$	−0.459827	−	4.66870i	−0.0222526	−	0.225934i
$428$	−2.98718	+	25.2746i	−0.144391	+	1.22169i
$429$	9.04407	−	2.74349i	0.436652	−	0.132457i
$430$	16.4850	−	52.4987i	0.794978	−	2.53171i
$431$	−14.1731	−	5.87069i	−0.682695	−	0.282781i	0.0142582	−	0.999898i	$-0.495461\pi$
$431$	−14.1731	−	5.87069i	−0.682695	−	0.282781i	−0.696953	+	0.717117i	$0.745461\pi$
$432$	2.65601	−	2.99092i	0.127788	−	0.143901i
$433$	−10.6169	+	4.39765i	−0.510214	+	0.211338i	−0.622912	−	0.782292i	$-0.714051\pi$
$433$	−10.6169	+	4.39765i	−0.510214	+	0.211338i	0.112698	+	0.993629i	$0.464051\pi$
$434$	−0.0598247	−	0.674675i	−0.00287168	−	0.0323854i
$435$	9.50186	+	5.07885i	0.455579	+	0.243512i
$436$	3.94423	−	0.311079i	0.188895	−	0.0148980i
$437$	9.21147	+	7.55966i	0.440644	+	0.361627i
$438$	−3.64249	−	9.04169i	−0.174045	−	0.432029i
$439$	−5.39591	+	27.1270i	−0.257532	+	1.29470i	0.608035	+	0.793910i	$0.291958\pi$
$439$	−5.39591	+	27.1270i	−0.257532	+	1.29470i	−0.865567	+	0.500793i	$0.833042\pi$
$440$	14.2161	+	52.3173i	0.677726	+	2.49413i
$441$	−6.76975	+	1.34659i	−0.322369	+	0.0641232i
$442$	−0.998210	+	4.77494i	−0.0474800	+	0.227121i
$443$	−9.33466	−	17.4639i	−0.443503	−	0.829736i	0.556496	−	0.830850i	$-0.312145\pi$
$443$	−9.33466	−	17.4639i	−0.443503	−	0.829736i	−0.999999	+	0.00111419i	$0.999645\pi$
$444$	−9.01291	−	6.27942i	−0.427734	−	0.298008i
$445$	−37.5470	−	3.69805i	−1.77990	−	0.175305i
$446$	−3.00242	+	27.7155i	−0.142168	+	1.31237i
$447$		−	1.63894i		−	0.0775193i
$448$	−2.24953	−	1.08971i	−0.106280	−	0.0514840i
$449$			19.5943i			0.924715i	0.886694	+	0.462357i	$0.152996\pi$
$449$			19.5943i			0.924715i	−0.886694	+	0.462357i	$0.847004\pi$
$450$	−9.65638	−	1.04607i	−0.455206	−	0.0493124i
$451$	−52.9504	−	5.21516i	−2.49334	−	0.245572i
$452$	11.5629	−	2.06687i	0.543875	−	0.0972172i
$453$	11.0347	+	20.6445i	0.518455	+	0.969962i
$454$	−26.7201	−	5.58589i	−1.25404	−	0.262159i
$455$	1.79324	−	0.356697i	0.0840682	−	0.0167222i
$456$	−10.8410	+	8.37939i	−0.507674	+	0.392401i
$457$	−2.00972	+	10.1035i	−0.0940105	+	0.472623i	0.904886	+	0.425654i	$0.139956\pi$
$457$	−2.00972	+	10.1035i	−0.0940105	+	0.472623i	−0.998896	+	0.0469685i	$0.985044\pi$
$458$	24.0490	−	9.68825i	1.12374	−	0.452702i
$459$	−1.56974	−	1.28825i	−0.0732693	−	0.0601305i
$460$	−12.8895	−	11.0050i	−0.600976	−	0.513109i
$461$	21.2868	+	11.3780i	0.991426	+	0.529928i	0.885596	−	0.464456i	$-0.153750\pi$
$461$	21.2868	+	11.3780i	0.991426	+	0.529928i	0.105830	+	0.994384i	$0.466250\pi$
$462$	2.44889	−	0.217148i	0.113933	−	0.0101026i
$463$	−20.2481	+	8.38704i	−0.941009	+	0.389779i	−0.799844	−	0.600207i	$-0.795085\pi$
$463$	−20.2481	+	8.38704i	−0.941009	+	0.389779i	−0.141165	+	0.989986i	$0.545085\pi$
$464$	−12.1034	+	3.16264i	−0.561886	+	0.146822i
$465$	4.87877	+	2.02085i	0.226247	+	0.0937147i
$466$	39.7981	+	12.4969i	1.84361	+	0.578910i
$467$	25.3118	−	7.67826i	1.17129	−	0.355307i	0.356071	−	0.934459i	$-0.384116\pi$
$467$	25.3118	−	7.67826i	1.17129	−	0.355307i	0.815220	+	0.579152i	$0.196616\pi$
$468$	−2.10367	−	2.66758i	−0.0972421	−	0.123309i
$469$	0.330928	+	3.35996i	0.0152808	+	0.155149i
$470$	26.9910	+	27.5217i	1.24500	+	1.26948i
$471$	8.74742	+	13.0914i	0.403060	+	0.603222i
$472$	1.36154	+	0.968428i	0.0626701	+	0.0445755i
$473$	−52.2505	−	34.9127i	−2.40248	−	1.60529i
$474$	−8.68126	+	12.7226i	−0.398744	+	0.584367i
$475$	31.8384	+	9.65809i	1.46085	+	0.443143i
$476$	−0.508341	+	1.16269i	−0.0232998	+	0.0532919i
$477$	−0.942371	−	1.14828i	−0.0431482	−	0.0525762i
$478$	−8.78941	+	2.57308i	−0.402018	+	0.117690i
$479$	4.96815	+	4.96815i	0.227001	+	0.227001i	0.811438	−	0.584438i	$-0.198685\pi$
$479$	4.96815	+	4.96815i	0.227001	+	0.227001i	−0.584438	+	0.811438i	$0.698685\pi$
$480$	15.6480	−	11.6154i	0.714229	−	0.530170i
$481$	−6.59693	+	6.59693i	−0.300794	+	0.300794i
$482$	−7.02320	+	12.8373i	−0.319898	+	0.584724i
$483$	−0.594115	+	0.487577i	−0.0270331	+	0.0221855i
$484$	39.9067	+	0.777016i	1.81394	+	0.0353189i
$485$	1.67328	−	5.51608i	0.0759799	−	0.250472i
$486$	1.38966	−	0.262385i	0.0630362	−	0.0119020i
$487$	−4.96578	+	7.43181i	−0.225021	+	0.336768i	−0.926752	−	0.375675i	$-0.877411\pi$
$487$	−4.96578	+	7.43181i	−0.225021	+	0.336768i	0.701731	+	0.712442i	$0.252411\pi$
$488$	−39.6931	+	15.0993i	−1.79682	+	0.683512i
$489$	−6.76819	+	4.52236i	−0.306068	+	0.204508i
$490$	−33.6266	−	0.327338i	−1.51909	−	0.0147876i
$491$	27.8224	−	2.74026i	1.25561	−	0.123666i	0.551750	−	0.834009i	$-0.313960\pi$
$491$	27.8224	−	2.74026i	1.25561	−	0.123666i	0.703856	+	0.710343i	$0.251460\pi$
$492$	5.19453	+	18.4067i	0.234187	+	0.829837i
$493$	1.84356	+	6.07739i	0.0830296	+	0.273712i
$494$	5.38557	+	10.3160i	0.242308	+	0.464138i
$495$	−7.33516	+	17.7086i	−0.329691	+	0.795944i
$496$	−5.75179	+	2.12412i	−0.258263	+	0.0953760i
$497$	−0.362693	−	0.875619i	−0.0162690	−	0.0392769i
$498$	−3.21004	+	3.83471i	−0.143845	+	0.171838i
$499$	13.4112	−	25.0905i	0.600366	−	1.12321i	−0.379808	−	0.925065i	$-0.624010\pi$
$499$	13.4112	−	25.0905i	0.600366	−	1.12321i	0.980174	−	0.198140i	$-0.0634900\pi$
$500$	−12.2415	−	3.97526i	−0.547458	−	0.177779i
$501$	6.33189	−	7.71543i	0.282888	−	0.344700i
$502$	−1.93439	−	0.823401i	−0.0863360	−	0.0367502i
$503$	10.8294	+	2.15410i	0.482858	+	0.0960464i	0.430516	−	0.902583i	$-0.358332\pi$
$503$	10.8294	+	2.15410i	0.482858	+	0.0960464i	0.0523417	+	0.998629i	$0.483332\pi$
$504$	−0.393654	−	0.791213i	−0.0175347	−	0.0352434i
$505$	−10.4511	−	52.5412i	−0.465068	−	2.33805i
$506$	−16.1974	+	10.5962i	−0.720064	+	0.471058i
$507$	8.92033	−	4.76802i	0.396166	−	0.211755i
$508$	−9.22794	+	42.0921i	−0.409424	+	1.86753i
$509$	−0.445462	+	4.52285i	−0.0197448	+	0.200472i	0.980252	+	0.197755i	$0.0633649\pi$
$509$	−0.445462	+	4.52285i	−0.0197448	+	0.200472i	−0.999996	+	0.00271731i	$0.999135\pi$
$510$	−6.20159	−	7.70846i	−0.274611	−	0.341337i
$511$	−2.15361			−0.0952702
$512$	−4.17964	+	22.2380i	−0.184716	+	0.982792i
$513$	−4.84433			−0.213883
$514$	11.8212	+	14.6935i	0.521410	+	0.648104i
$515$	2.23601	−	22.7026i	0.0985302	−	1.00039i
$516$	−4.83732	+	22.0648i	−0.212951	+	0.971349i
$517$	38.8248	−	20.7523i	1.70751	−	0.912684i
$518$	−2.03091	+	1.32860i	−0.0892329	+	0.0583752i
$519$	−1.29964	−	6.53371i	−0.0570477	−	0.286798i
$520$	−7.37272	−	14.8186i	−0.323315	−	0.649837i
$521$	−30.7751	−	6.12155i	−1.34828	−	0.268190i	−0.532442	−	0.846466i	$-0.678726\pi$
$521$	−30.7751	−	6.12155i	−1.34828	−	0.268190i	−0.815841	+	0.578276i	$0.803726\pi$
$522$	−4.06953	−	1.73225i	−0.178119	−	0.0758187i
$523$	5.97612	−	7.28193i	0.261318	−	0.318416i	−0.625779	−	0.780001i	$-0.715219\pi$
$523$	5.97612	−	7.28193i	0.261318	−	0.318416i	0.887096	+	0.461584i	$0.152719\pi$
$524$	−31.4232	−	10.2042i	−1.37273	−	0.445773i
$525$	−1.01157	+	1.89251i	−0.0441484	+	0.0825959i
$526$	12.3411	−	14.7427i	0.538099	−	0.642813i
$527$	1.19121	+	2.87583i	0.0518898	+	0.125273i
$528$	−7.71002	−	20.8775i	−0.335535	−	0.908576i
$529$	−6.48615	+	15.6589i	−0.282006	+	0.680823i
$530$	−3.34928	−	6.41551i	−0.145483	−	0.278672i
$531$	0.171479	+	0.565289i	0.00744154	+	0.0245315i
$532$	0.822187	+	2.91340i	0.0356463	+	0.126312i
$533$	16.1654	−	1.59216i	0.700203	−	0.0689640i
$534$	15.4873	+	0.150761i	0.670201	+	0.00652407i
$535$	−36.4504	+	24.3554i	−1.57589	+	1.05297i
$536$	28.5663	−	10.8666i	1.23388	−	0.469367i
$537$	−10.7317	+	16.0611i	−0.463107	+	0.693088i
$538$	37.1370	−	7.01193i	1.60109	−	0.302306i
$539$	−11.1482	+	36.7505i	−0.480185	+	1.58296i
$540$	6.88870	+	0.134129i	0.296442	+	0.00577198i
$541$	−7.46576	+	6.12699i	−0.320978	+	0.263420i	−0.781059	−	0.624457i	$-0.785320\pi$
$541$	−7.46576	+	6.12699i	−0.320978	+	0.263420i	0.460081	+	0.887877i	$0.347820\pi$
$542$	−3.91266	+	7.15173i	−0.168063	+	0.307193i
$543$	−2.66695	+	2.66695i	−0.114450	+	0.114450i
$544$	11.3637	+	1.68080i	0.487213	+	0.0720639i
$545$	4.81896	+	4.81896i	0.206422	+	0.206422i
$546$	−0.720334	+	0.210876i	−0.0308275	+	0.00902467i
$547$	−14.6906	−	17.9006i	−0.628126	−	0.765374i	0.357574	−	0.933885i	$-0.383604\pi$
$547$	−14.6906	−	17.9006i	−0.628126	−	0.765374i	−0.985700	+	0.168511i	$0.946104\pi$
$548$	17.7450	−	40.5869i	0.758029	−	1.73378i
$549$	−14.3682	−	4.35854i	−0.613219	−	0.186018i
$550$	−30.4599	+	44.6396i	−1.29881	+	1.90344i
$551$	12.5971	+	8.41710i	0.536653	+	0.358580i
$552$	5.66964	+	4.03265i	0.241316	+	0.171641i
$553$	1.89052	+	2.82937i	0.0803933	+	0.120317i
$554$	2.90377	+	2.96086i	0.123369	+	0.125795i
$555$	−1.85460	−	18.8300i	−0.0787233	−	0.799291i
$556$	−1.27673	−	1.61896i	−0.0541452	−	0.0686593i
$557$	35.6824	−	10.8241i	1.51191	−	0.458633i	0.577968	−	0.816059i	$-0.303846\pi$
$557$	35.6824	−	10.8241i	1.51191	−	0.458633i	0.933941	+	0.357426i	$0.116346\pi$
$558$	−2.06824	−	0.649443i	−0.0875554	−	0.0274931i
$559$	17.7247	+	7.34179i	0.749673	+	0.310525i
$560$	−1.08849	−	4.16565i	−0.0459972	−	0.176031i
$561$	−10.4385	+	4.32377i	−0.440714	+	0.182550i
$562$	−24.2476	+	2.15008i	−1.02282	+	0.0906958i
$563$	3.31356	+	1.77114i	0.139650	+	0.0746445i	0.539742	−	0.841831i	$-0.318522\pi$
$563$	3.31356	+	1.77114i	0.139650	+	0.0746445i	−0.400092	+	0.916475i	$0.631022\pi$
$564$	−12.0347	−	10.2752i	−0.506753	−	0.432662i
$565$	15.6402	+	12.8356i	0.657989	+	0.539997i
$566$	−27.8867	+	11.2343i	−1.17217	+	0.472213i
$567$	0.0609552	−	0.306443i	0.00255988	−	0.0128694i
$568$	−6.78826	+	5.24690i	−0.284829	+	0.220155i
$569$	−28.5480	+	5.67856i	−1.19680	+	0.238058i	−0.752970	−	0.658055i	$-0.771379\pi$
$569$	−28.5480	+	5.67856i	−1.19680	+	0.238058i	−0.443826	+	0.896113i	$0.646379\pi$
$570$	−23.1020	−	4.82952i	−0.967638	−	0.202286i
$571$	7.50330	+	14.0377i	0.314003	+	0.587459i	0.988571	−	0.150754i	$-0.0481701\pi$
$571$	7.50330	+	14.0377i	0.314003	+	0.587459i	−0.674568	+	0.738213i	$0.735670\pi$
$572$	−18.6071	+	3.32601i	−0.778003	+	0.139068i
$573$	−3.11270	−	0.306574i	−0.130035	−	0.0128073i
$574$	4.20090	+	0.455082i	0.175342	+	0.0189948i
$575$		−	16.8944i		−	0.704544i
$576$	−5.97741	+	5.31701i	−0.249059	+	0.221542i
$577$			32.1764i			1.33952i	0.742577	+	0.669761i	$0.233603\pi$
$577$			32.1764i			1.33952i	−0.742577	+	0.669761i	$0.766397\pi$
$578$	−1.96120	+	18.1039i	−0.0815750	+	0.753025i
$579$	−9.36617	−	0.922487i	−0.389245	−	0.0383372i
$580$	−17.6801	−	12.3180i	−0.734128	−	0.511477i
$581$	0.520833	+	0.974410i	0.0216078	+	0.0404253i
$582$	−0.484213	+	2.31623i	−0.0200713	+	0.0960110i
$583$	−8.10620	+	1.61242i	−0.335725	+	0.0667798i
$584$	5.11214	+	18.8134i	0.211542	+	0.778506i
$585$	1.14163	−	5.73934i	0.0472004	−	0.237293i
$586$	−7.65657	−	19.0058i	−0.316290	−	0.785122i
$587$	−15.4559	−	12.6843i	−0.637933	−	0.523538i	0.258901	−	0.965904i	$-0.416639\pi$
$587$	−15.4559	−	12.6843i	−0.637933	−	0.523538i	−0.896835	+	0.442365i	$0.854139\pi$
$588$	13.7620	−	1.08540i	0.567536	−	0.0447612i
$589$	6.54891	+	3.50046i	0.269843	+	0.144234i
$590$	0.254200	+	2.86675i	0.0104653	+	0.118022i
$591$	−20.7124	+	8.57936i	−0.851995	+	0.352908i
$592$	16.4272	+	14.5878i	0.675153	+	0.599553i
$593$	4.02668	+	1.66791i	0.165356	+	0.0684927i	0.463826	−	0.885926i	$-0.346476\pi$
$593$	4.02668	+	1.66791i	0.165356	+	0.0684927i	−0.298470	+	0.954419i	$0.596476\pi$
$594$	2.35731	−	7.50715i	0.0967216	−	0.308022i
$595$	−2.09167	+	0.634500i	−0.0857500	+	0.0260120i
$596$	−0.384732	+	3.25523i	−0.0157592	+	0.133339i
$597$	−0.111180	−	1.12883i	−0.00455030	−	0.0461999i
$598$	4.21886	−	4.13751i	0.172522	−	0.169195i
$599$	−15.9120	−	23.8140i	−0.650146	−	0.973013i	−0.999353	−	0.0359669i	$-0.988549\pi$
$599$	−15.9120	−	23.8140i	−0.650146	−	0.973013i	0.349207	−	0.937046i	$-0.386451\pi$
$600$	18.9337	+	4.34446i	0.772966	+	0.177362i
$601$	−19.3296	−	12.9156i	−0.788469	−	0.526838i	0.0949164	−	0.995485i	$-0.469742\pi$
$601$	−19.3296	−	12.9156i	−0.788469	−	0.526838i	−0.883386	+	0.468647i	$0.844742\pi$
$602$	4.12236	+	2.81290i	0.168015	+	0.114645i
$603$	10.3405	+	3.13675i	0.421097	+	0.127738i
$604$	−17.0707	−	43.5939i	−0.694597	−	1.77381i
$605$	43.6160	+	53.1462i	1.77324	+	2.16070i
$606$	6.17860	+	21.1056i	0.250989	+	0.857354i
$607$	−10.5714	−	10.5714i	−0.429078	−	0.429078i	0.459236	−	0.888314i	$-0.348123\pi$
$607$	−10.5714	−	10.5714i	−0.429078	−	0.429078i	−0.888314	+	0.459236i	$0.848123\pi$
$608$	23.4991	−	14.0981i	0.953013	−	0.571754i
$609$	−0.690955	+	0.690955i	−0.0279989	+	0.0279989i
$610$	−64.1749	−	35.1096i	−2.59836	−	1.42155i
$611$	−10.3892	+	8.52621i	−0.420303	+	0.344934i
$612$	2.81537	+	2.92719i	0.113805	+	0.118324i
$613$	−0.666110	+	2.19587i	−0.0269039	+	0.0886903i	−0.969364	−	0.245628i	$-0.921006\pi$
$613$	−0.666110	+	2.19587i	−0.0269039	+	0.0886903i	0.942460	+	0.334318i	$0.108506\pi$
$614$	3.63323	+	19.2425i	0.146625	+	0.776566i
$615$	−18.3026	+	27.3918i	−0.738033	+	1.10454i
$616$	−4.91491	−	0.143569i	−0.198027	−	0.00578454i
$617$	14.7954	−	9.88595i	0.595639	−	0.397993i	−0.220889	−	0.975299i	$-0.570896\pi$
$617$	14.7954	−	9.88595i	0.595639	−	0.397993i	0.816528	+	0.577306i	$0.195896\pi$
$618$	−0.0911568	+	9.36431i	−0.00366686	+	0.376688i
$619$	−0.383689	+	0.0377900i	−0.0154217	+	0.00151891i	−0.105725	−	0.994395i	$-0.533716\pi$
$619$	−0.383689	+	0.0377900i	−0.0154217	+	0.00151891i	0.0903033	+	0.995914i	$0.471216\pi$
$620$	−9.21570	−	5.15903i	−0.370112	−	0.207191i
$621$	0.714058	+	2.35393i	0.0286542	+	0.0944601i
$622$	26.1815	−	13.6683i	1.04978	−	0.548050i
$623$	1.30947	−	3.16135i	0.0524629	−	0.126657i
$624$	3.55206	+	5.79210i	0.142196	+	0.231869i
$625$	4.65734	+	11.2438i	0.186294	+	0.449753i
$626$	30.4340	+	25.4764i	1.21639	+	1.01824i
$627$	−12.7058	+	23.7708i	−0.507419	+	0.949315i
$628$	−14.3008	−	28.0553i	−0.570663	−	1.11953i
$629$	7.07554	−	8.62157i	0.282120	−	0.343765i
$630$	0.596193	−	1.40062i	0.0237529	−	0.0558020i
$631$	13.7185	+	2.72878i	0.546126	+	0.108631i	0.460440	−	0.887691i	$-0.347692\pi$
$631$	13.7185	+	2.72878i	0.546126	+	0.108631i	0.0856862	+	0.996322i	$0.472692\pi$
$632$	20.2291	−	23.2314i	0.804669	−	0.924095i
$633$	−2.09704	−	10.5425i	−0.0833499	−	0.419028i
$634$	8.92390	+	13.6412i	0.354413	+	0.541760i
$635$	−65.4611	+	34.9897i	−2.59774	+	1.38852i
$636$	1.60216	+	2.50191i	0.0635299	+	0.0992071i
$637$	1.14921	−	11.6681i	0.0455334	−	0.462308i
$638$	−19.1737	+	15.4255i	−0.759092	+	0.610703i
$639$	−3.03337			−0.119998
$640$	−33.8063	+	19.3970i	−1.33631	+	0.766735i
$641$	−22.0554			−0.871134			−0.435567	−	0.900156i	$-0.643452\pi$
$641$	−22.0554			−0.871134			−0.435567	+	0.900156i	$0.643452\pi$
$642$	14.0217	−	11.2807i	0.553394	−	0.445215i
$643$	4.74273	−	48.1537i	0.187035	−	1.89900i	−0.204550	−	0.978856i	$-0.565573\pi$
$643$	4.74273	−	48.1537i	0.187035	−	1.89900i	0.391585	−	0.920142i	$-0.371927\pi$
$644$	1.29447	−	0.828949i	0.0510093	−	0.0326652i
$645$	−34.3149	+	18.3417i	−1.35115	+	0.722204i
$646$	−7.61617	−	11.6422i	−0.299654	−	0.458054i
$647$	−1.43690	−	7.22376i	−0.0564902	−	0.283995i	0.942207	−	0.335033i	$-0.108747\pi$
$647$	−1.43690	−	7.22376i	−0.0564902	−	0.283995i	−0.998697	+	0.0510372i	$0.983747\pi$
$648$	−2.82170	+	0.194928i	−0.110847	+	0.00765751i
$649$	3.22359	+	0.641212i	0.126537	+	0.0251698i
$650$	6.46181	−	15.1805i	0.253453	−	0.595429i
$651$	−0.303836	+	0.370225i	−0.0119083	+	0.0145103i
$652$	14.5044	−	7.39341i	0.568037	−	0.289548i
$653$	20.7155	−	38.7561i	0.810662	−	1.51664i	−0.0449298	−	0.998990i	$-0.514306\pi$
$653$	20.7155	−	38.7561i	0.810662	−	1.51664i	0.855592	−	0.517651i	$-0.173194\pi$
$654$	−2.14524	−	1.79578i	−0.0838854	−	0.0702206i
$655$	−21.7781	−	52.5769i	−0.850940	−	2.05435i
$656$	−5.99639	−	37.7783i	−0.234120	−	1.47499i
$657$	−2.63774	+	6.36807i	−0.102908	+	0.248442i
$658$	−3.09922	+	1.61798i	−0.120820	+	0.0630754i
$659$	7.96911	+	26.2706i	0.310432	+	1.02336i	0.963869	+	0.266377i	$0.0858266\pi$
$659$	7.96911	+	26.2706i	0.310432	+	1.02336i	−0.653437	+	0.756981i	$0.726673\pi$
$660$	18.7259	−	33.4506i	0.728905	−	1.30206i
$661$	27.3706	−	2.69577i	1.06459	−	0.104853i	0.449479	−	0.893291i	$-0.351610\pi$
$661$	27.3706	−	2.69577i	1.06459	−	0.104853i	0.615115	+	0.788438i	$0.289110\pi$
$662$	−0.0902558	+	9.27176i	−0.00350789	+	0.360357i
$663$	2.86806	−	1.91638i	0.111386	−	0.0744259i
$664$	7.27588	−	6.86288i	0.282359	−	0.266331i
$665$	−2.89693	+	4.33556i	−0.112338	+	0.168126i
$666$	1.44111	+	7.63250i	0.0558419	+	0.295753i
$667$	2.23318	−	7.36179i	0.0864689	−	0.285050i
$668$	−14.3874	+	13.8378i	−0.556665	+	0.535402i
$669$	15.2380	−	12.5055i	0.589134	−	0.483489i
$670$	46.1853	+	25.2676i	1.78429	+	0.976173i
$671$	−59.0721	+	59.0721i	−2.28045	+	2.28045i
$672$	0.596133	+	1.66390i	0.0229963	+	0.0641862i
$673$	−23.4780	−	23.4780i	−0.905011	−	0.905011i	0.0908536	−	0.995864i	$-0.471040\pi$
$673$	−23.4780	−	23.4780i	−0.905011	−	0.905011i	−0.995864	+	0.0908536i	$0.971040\pi$
$674$	10.2922	+	35.1574i	0.396442	+	1.35421i
$675$	4.35704	+	5.30907i	0.167702	+	0.204346i
$676$	−18.8366	+	7.37613i	−0.724485	+	0.283697i
$677$	17.9682	+	5.45060i	0.690575	+	0.209484i	0.616017	−	0.787733i	$-0.288745\pi$
$677$	17.9682	+	5.45060i	0.690575	+	0.209484i	0.0745583	+	0.997217i	$0.476245\pi$
$678$	−6.86080	−	4.68147i	−0.263487	−	0.179791i
$679$	0.434688	+	0.290449i	0.0166818	+	0.0111464i
$680$	10.5079	+	16.7662i	0.402961	+	0.642953i
$681$	10.7239	+	16.0494i	0.410939	+	0.615014i
$682$	−8.61136	+	8.44532i	−0.329746	+	0.323388i
$683$	−1.39650	−	14.1789i	−0.0534356	−	0.542540i	−0.984217	−	0.176965i	$-0.943372\pi$
$683$	−1.39650	−	14.1789i	−0.0534356	−	0.542540i	0.930782	−	0.365576i	$-0.119128\pi$
$684$	9.62170	+	1.13718i	0.367895	+	0.0434811i
$685$	73.0152	−	22.1489i	2.78977	−	0.846267i
$686$	1.84035	−	5.86083i	0.0702649	−	0.223768i
$687$	−16.9377	−	7.01583i	−0.646214	−	0.267671i
$688$	14.7873	−	42.6891i	0.563762	−	1.62750i
$689$	2.33119	−	0.965610i	0.0888112	−	0.0367868i
$690$	1.05852	+	11.9375i	0.0402972	+	0.454453i
$691$	−18.9160	−	10.1108i	−0.719598	−	0.384633i	0.0705836	−	0.997506i	$-0.477514\pi$
$691$	−18.9160	−	10.1108i	−0.719598	−	0.384633i	−0.790182	+	0.612873i	$0.790014\pi$
$692$	1.04756	+	13.2822i	0.0398221	+	0.504913i
$693$	−1.34382	−	1.10284i	−0.0510475	−	0.0418936i
$694$	14.3095	+	35.5203i	0.543181	+	1.34833i
$695$	0.692858	−	3.48323i	0.0262816	−	0.132127i
$696$	7.67617	+	4.39586i	0.290964	+	0.166625i
$697$	−19.0459	+	3.78847i	−0.721415	+	0.143498i
$698$	0.376099	−	1.79907i	0.0142355	−	0.0680958i
$699$	−13.9045	−	26.0134i	−0.525915	−	0.983918i
$700$	2.45341	−	3.52140i	0.0927300	−	0.133096i
$701$	−46.6997	−	4.59951i	−1.76382	−	0.173721i	−0.836495	−	0.547974i	$-0.815399\pi$
$701$	−46.6997	−	4.59951i	−1.76382	−	0.173721i	−0.927327	+	0.374253i	$0.877899\pi$
$702$	−0.258719	+	2.38825i	−0.00976471	+	0.0901388i
$703$		−	26.6068i		−	1.00349i
$704$	10.4126	+	43.2762i	0.392439	+	1.63103i
$705$		−	27.2576i		−	1.02658i
$706$	8.17036	+	0.885093i	0.307496	+	0.0333109i
$707$	4.83522	+	0.476227i	0.181847	+	0.0179104i
$708$	−0.207889	−	1.16302i	−0.00781293	−	0.0437089i
$709$	13.1928	+	24.6820i	0.495466	+	0.926951i	0.998050	+	0.0624226i	$0.0198826\pi$
$709$	13.1928	+	24.6820i	0.495466	+	0.926951i	−0.502584	+	0.864528i	$0.667617\pi$
$710$	−14.4657	−	3.02409i	−0.542890	−	0.113492i
$711$	10.6817	−	2.12473i	0.400597	−	0.0796836i
$712$	−30.7251	−	3.93499i	−1.15147	−	0.147470i
$713$	0.735614	−	3.69818i	0.0275490	−	0.138498i
$714$	0.832292	−	0.335293i	0.0311477	−	0.0125480i
$715$	−25.1683	−	20.6551i	−0.941241	−	0.772457i
$716$	25.0853	−	29.3810i	0.937481	−	1.09802i
$717$	5.71123	+	3.05271i	0.213290	+	0.114006i
$718$	−15.7475	+	1.39636i	−0.587691	+	0.0521117i
$719$	−33.2563	+	13.7752i	−1.24025	+	0.513728i	−0.903793	−	0.427970i	$-0.859229\pi$
$719$	−33.2563	+	13.7752i	−1.24025	+	0.513728i	−0.336457	+	0.941699i	$0.609229\pi$
$720$	−13.6507	−	1.88348i	−0.508731	−	0.0701933i
$721$	1.91149	+	0.791765i	0.0711876	+	0.0294869i
$722$	−6.02791	−	1.89281i	−0.224336	−	0.0704432i
$723$	9.90150	−	3.00359i	0.368241	−	0.111705i
$724$	5.92307	−	4.67097i	0.220129	−	0.173595i
$725$	−2.10535	−	21.3760i	−0.0781907	−	0.793884i
$726$	−19.7619	−	20.1504i	−0.733433	−	0.747853i
$727$	18.1985	+	27.2360i	0.674946	+	1.01013i	0.997967	+	0.0637367i	$0.0203018\pi$
$727$	18.1985	+	27.2360i	0.674946	+	1.01013i	−0.323020	+	0.946392i	$0.604698\pi$
$728$	1.48021	−	0.249743i	0.0548603	−	0.00925610i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−18.9276	+	27.7389i	−0.700544	+	1.02666i
$731$	−21.9478	−	6.65780i	−0.811770	−	0.246248i
$732$	27.5146	+	12.0297i	1.01697	+	0.444629i
$733$	−21.3455	−	26.0096i	−0.788415	−	0.960686i	0.211445	−	0.977390i	$-0.432183\pi$
$733$	−21.3455	−	26.0096i	−0.788415	−	0.960686i	−0.999860	+	0.0167033i	$0.994683\pi$
$734$	−3.61010	+	1.05685i	−0.133251	+	0.0390090i
$735$	16.8141	+	16.8141i	0.620197	+	0.620197i
$736$	−10.3143	−	9.34048i	−0.380189	−	0.344294i
$737$	42.5129	−	42.5129i	1.56598	−	1.56598i
$738$	6.49089	−	11.8643i	0.238933	−	0.436732i
$739$	14.7811	−	12.1305i	0.543732	−	0.446229i	−0.321998	−	0.946740i	$-0.604355\pi$
$739$	14.7811	−	12.1305i	0.543732	−	0.446229i	0.865730	+	0.500511i	$0.166855\pi$
$740$	−0.736682	+	37.8351i	−0.0270810	+	1.39085i
$741$	2.38867	−	7.87441i	0.0877502	−	0.289274i
$742$	0.644981	−	0.121780i	0.0236780	−	0.00447070i
$743$	−7.91652	+	11.8479i	−0.290429	+	0.434658i	−0.947779	−	0.318928i	$-0.896677\pi$
$743$	−7.91652	+	11.8479i	−0.290429	+	0.434658i	0.657350	+	0.753585i	$0.271677\pi$
$744$	3.95543	+	1.77541i	0.145013	+	0.0650899i
$745$	−4.69461	+	3.13684i	−0.171997	+	0.114925i
$746$	−13.0179	−	0.126722i	−0.476619	−	0.00463964i
$747$	3.51917	−	0.346608i	0.128760	−	0.0126817i
$748$	21.7477	−	6.13740i	0.795174	−	0.224405i
$749$	−1.15416	−	3.80475i	−0.0421721	−	0.139023i
$750$	4.21187	+	8.06778i	0.153796	+	0.294594i
$751$	−11.5884	+	27.9770i	−0.422868	+	1.02089i	0.558629	+	0.829418i	$0.311328\pi$
$751$	−11.5884	+	27.9770i	−0.422868	+	1.02089i	−0.981497	+	0.191477i	$0.938672\pi$
$752$	21.4911	+	23.2334i	0.783698	+	0.847233i
$753$	0.568890	+	1.37342i	0.0207315	+	0.0500503i
$754$	4.82239	−	5.76082i	0.175621	−	0.209797i
$755$	38.0146	−	71.1202i	1.38349	−	2.58833i
$756$	−0.193003	+	0.594340i	−0.00701947	+	0.0216159i
$757$	−15.5548	+	18.9536i	−0.565350	+	0.688880i	−0.974705	−	0.223494i	$-0.928254\pi$
$757$	−15.5548	+	18.9536i	−0.565350	+	0.688880i	0.409356	+	0.912375i	$0.365754\pi$
$758$	32.8395	+	13.9786i	1.19279	+	0.507726i
$759$	13.4234	+	2.67009i	0.487240	+	0.0969180i
$760$	44.7510	+	15.0153i	1.62329	+	0.544663i
$761$	3.97875	+	20.0025i	0.144230	+	0.725091i	0.983433	+	0.181273i	$0.0580218\pi$
$761$	3.97875	+	20.0025i	0.144230	+	0.725091i	−0.839203	+	0.543818i	$0.816978\pi$
$762$	25.4988	−	16.6811i	0.923725	−	0.604291i
$763$	−0.545110	+	0.291367i	−0.0197343	+	0.0105482i
$764$	6.11040	+	1.33960i	0.221067	+	0.0484649i
$765$	−0.685700	+	6.96203i	−0.0247915	+	0.251713i
$766$	24.7578	+	30.7735i	0.894535	+	1.11189i
$767$	−1.00342			−0.0362316
$768$	13.1203	−	9.15735i	0.473439	−	0.330437i
$769$	44.0643			1.58900			0.794500	−	0.607264i	$-0.207733\pi$
$769$	44.0643			1.58900			0.794500	+	0.607264i	$0.207733\pi$
$770$	−5.30904	−	6.59904i	−0.191324	−	0.237813i
$771$	1.30705	−	13.2707i	0.0470723	−	0.477933i
$772$	18.3863	+	4.03087i	0.661738	+	0.145074i
$773$	−17.9619	+	9.60085i	−0.646045	+	0.345319i	−0.761661	−	0.647976i	$-0.775616\pi$
$773$	−17.9619	+	9.60085i	−0.646045	+	0.345319i	0.115616	+	0.993294i	$0.463116\pi$
$774$	13.3666	−	8.74427i	0.480452	−	0.314306i
$775$	−2.05387	−	10.3255i	−0.0737773	−	0.370904i
$776$	1.50545	−	4.48678i	0.0540426	−	0.161066i
$777$	1.68309	+	0.334788i	0.0603805	+	0.0120104i
$778$	39.5201	+	16.8223i	1.41687	+	0.603109i
$779$	−29.3885	+	35.8100i	−1.05295	+	1.28303i
$780$	−3.61475	+	11.1314i	−0.129429	+	0.398567i
$781$	−7.95594	+	14.8845i	−0.284686	+	0.532610i
$782$	−4.53447	+	5.41687i	−0.162152	+	0.193707i
$783$	1.19682	+	2.88938i	0.0427709	+	0.103258i
$784$	−27.5886	−	1.07475i	−0.985307	−	0.0383840i
$785$	20.7573	−	50.1125i	0.740858	−	1.78859i
$786$	10.8116	+	20.7094i	0.385636	+	0.738681i
$787$	−8.43333	−	27.8009i	−0.300616	−	0.990997i	−0.968975	−	0.247158i	$-0.920503\pi$
$787$	−8.43333	−	27.8009i	−0.300616	−	0.990997i	0.668360	−	0.743838i	$-0.266997\pi$
$788$	43.1525	−	12.1780i	1.53724	−	0.433824i
$789$	−13.5296	+	1.33255i	−0.481666	+	0.0474400i
$790$	53.0581	+	0.516494i	1.88772	+	0.0183760i
$791$	−1.52577	+	1.01949i	−0.0542502	+	0.0362488i
$792$	−6.44429	+	14.3572i	−0.228988	+	0.510159i
$793$	14.1695	−	21.2062i	0.503174	−	0.753053i
$794$	−22.1379	+	4.17991i	−0.785645	+	0.148339i
$795$	−1.48551	+	4.89709i	−0.0526858	+	0.173682i
$796$	−0.0441628	+	2.26815i	−0.00156531	+	0.0803926i
$797$	−6.06825	+	4.98009i	−0.214949	+	0.176404i	−0.735706	−	0.677301i	$-0.763150\pi$
$797$	−6.06825	+	4.98009i	−0.214949	+	0.176404i	0.520758	+	0.853705i	$0.325650\pi$
$798$	1.02737	−	1.87788i	0.0363686	−	0.0664763i
$799$	11.3613	−	11.3613i	0.401933	−	0.401933i
$800$	−36.5859	−	13.0734i	−1.29351	−	0.462216i
$801$	−7.74402	−	7.74402i	−0.273622	−	0.273622i
$802$	4.12144	−	1.20654i	0.145533	−	0.0426044i
$803$	24.3294	+	29.6454i	0.858565	+	1.04616i
$804$	−19.8017	−	8.65750i	−0.698351	−	0.305326i
$805$	2.53372	+	0.768597i	0.0893020	+	0.0270895i
$806$	2.07548	−	3.04166i	0.0731057	−	0.107138i
$807$	−22.2200	−	14.8470i	−0.782183	−	0.522638i
$808$	−7.31739	−	43.3697i	−0.257425	−	1.52574i
$809$	8.50657	+	12.7310i	0.299075	+	0.447597i	0.950322	−	0.311268i	$-0.100754\pi$
$809$	8.50657	+	12.7310i	0.299075	+	0.447597i	−0.651247	+	0.758866i	$0.725754\pi$
$810$	−3.41131	−	3.47837i	−0.119861	−	0.122218i
$811$	−1.49718	−	15.2011i	−0.0525730	−	0.533783i	−0.985016	−	0.172465i	$-0.944827\pi$
$811$	−1.49718	−	15.2011i	−0.0525730	−	0.533783i	0.932443	−	0.361318i	$-0.117673\pi$
$812$	1.53455	−	1.21016i	0.0538523	−	0.0424683i
$813$	5.51616	−	1.67331i	0.193460	−	0.0586856i
$814$	41.2319	+	12.9472i	1.44518	+	0.453798i
$815$	25.9078	+	10.7314i	0.907512	+	0.375904i
$816$	−4.90469	−	6.47480i	−0.171698	−	0.226663i
$817$	−50.5491	+	20.9381i	−1.76849	+	0.732532i
$818$	18.5146	−	1.64172i	0.647348	−	0.0574015i
$819$	0.468063	+	0.250185i	0.0163554	+	0.00874216i
$820$	42.7823	−	50.1085i	1.49402	−	1.74987i
$821$	−14.2740	−	11.7144i	−0.498166	−	0.408834i	0.351474	−	0.936198i	$-0.385681\pi$
$821$	−14.2740	−	11.7144i	−0.498166	−	0.408834i	−0.849640	+	0.527364i	$0.823181\pi$
$822$	−29.0534	+	11.7043i	−1.01335	+	0.408234i
$823$	−2.24759	+	11.2994i	−0.0783461	+	0.393872i	0.921637	+	0.388053i	$0.126852\pi$
$823$	−2.24759	+	11.2994i	−0.0783461	+	0.393872i	−0.999983	+	0.00581920i	$0.998148\pi$
$824$	2.37927	−	18.5778i	0.0828858	−	0.647188i
$825$	37.4789	−	7.45502i	1.30485	−	0.259550i
$826$	−0.255498	−	0.0534123i	−0.00888992	−	0.00185845i
$827$	3.31851	+	6.20850i	0.115396	+	0.215891i	0.932988	−	0.359907i	$-0.117192\pi$
$827$	3.31851	+	6.20850i	0.115396	+	0.215891i	−0.817592	+	0.575798i	$0.804692\pi$
$828$	−0.865673	−	4.84295i	−0.0300842	−	0.168304i
$829$	22.1923	+	2.18575i	0.770769	+	0.0759141i	0.475754	−	0.879579i	$-0.342175\pi$
$829$	22.1923	+	2.18575i	0.770769	+	0.0759141i	0.295015	+	0.955493i	$0.404675\pi$
$830$	17.1280	+	1.85548i	0.594523	+	0.0644045i
$831$		−	2.93246i		−	0.101726i
$832$	−5.69535	−	12.3379i	−0.197451	−	0.427741i
$833$			14.0166i			0.485645i
$834$	−0.157018	+	1.44944i	−0.00543708	+	0.0501901i
$835$	−34.2190	−	3.37028i	−1.18420	−	0.116633i
$836$	30.8159	−	44.2304i	1.06579	−	1.52974i
$837$	0.722589	+	1.35187i	0.0249763	+	0.0467275i
$838$	1.55856	−	7.45538i	0.0538395	−	0.257542i
$839$	21.0333	−	4.18378i	0.726150	−	0.144440i	0.181845	−	0.983327i	$-0.441793\pi$
$839$	21.0333	−	4.18378i	0.726150	−	0.144440i	0.544306	+	0.838887i	$0.316793\pi$
$840$	−1.51293	+	2.64192i	−0.0522011	+	0.0911550i
$841$	−3.74946	+	18.8498i	−0.129292	+	0.649994i
$842$	−19.0391	−	47.2605i	−0.656131	−	1.62870i
$843$	13.3058	+	10.9198i	0.458275	+	0.376097i
$844$	1.69030	+	21.4316i	0.0581824	+	0.737706i
$845$	−30.7306	−	16.4258i	−1.05716	−	0.565066i
$846$	0.988324	+	11.1458i	0.0339793	+	0.383202i
$847$	−5.76087	+	2.38623i	−0.197946	+	0.0819919i
$848$	−2.59487	−	5.34533i	−0.0891082	−	0.183559i
$849$	19.6406	+	8.13542i	0.674065	+	0.279207i
$850$	−5.90897	+	18.8179i	−0.202676	+	0.645448i
$851$	−12.9286	+	3.92186i	−0.443188	+	0.134440i
$852$	6.02480	+	0.712064i	0.206406	+	0.0243949i
$853$	5.26341	+	53.4403i	0.180216	+	1.82976i	0.481754	+	0.876306i	$0.340000\pi$
$853$	5.26341	+	53.4403i	0.180216	+	1.82976i	−0.301539	+	0.953454i	$0.597500\pi$
$854$	4.73673	−	4.64540i	0.162088	−	0.158962i
$855$	9.27177	+	13.8762i	0.317088	+	0.474555i
$856$	−30.4977	+	19.1140i	−1.04239	+	0.653303i
$857$	8.24478	+	5.50899i	0.281636	+	0.188183i	0.688363	−	0.725367i	$-0.258330\pi$
$857$	8.24478	+	5.50899i	0.281636	+	0.188183i	−0.406726	+	0.913550i	$0.633330\pi$
$858$	11.0404	+	7.53345i	0.376914	+	0.257188i
$859$	−11.7240	−	3.55644i	−0.400018	−	0.121344i	0.0838645	−	0.996477i	$-0.473274\pi$
$859$	−11.7240	−	3.55644i	−0.400018	−	0.121344i	−0.483882	+	0.875133i	$0.660774\pi$
$860$	72.4611	−	28.3746i	2.47090	−	0.967567i
$861$	−1.89548	−	2.30965i	−0.0645977	−	0.0787126i
$862$	−6.09541	−	20.8214i	−0.207611	−	0.709179i
$863$	13.6342	+	13.6342i	0.464115	+	0.464115i	0.900002	−	0.435887i	$-0.143565\pi$
$863$	13.6342	+	13.6342i	0.464115	+	0.464115i	−0.435887	+	0.900002i	$0.643565\pi$
$864$	5.65016	+	0.275216i	0.192222	+	0.00936302i
$865$	−16.2278	+	16.2278i	−0.551763	+	0.551763i
$866$	−14.2574	−	7.80011i	−0.484486	−	0.265058i
$867$	9.95352	−	8.16865i	0.338039	−	0.277422i
$868$	0.690379	−	0.664008i	0.0234330	−	0.0225379i
$869$	17.5903	−	57.9873i	0.596709	−	1.96709i
$870$	2.82695	+	14.9723i	0.0958424	+	0.507607i
$871$	−10.1975	+	15.2616i	−0.345529	+	0.517121i
$872$	3.83927	+	4.07032i	0.130014	+	0.137838i
$873$	1.39124	−	0.929598i	0.0470864	−	0.0314621i
$874$	−0.164041	+	16.8515i	−0.00554875	+	0.570010i
$875$	2.00104	−	0.197085i	0.0676473	−	0.00666268i
$876$	6.73388	−	12.0289i	0.227517	−	0.406419i
$877$	−10.8128	−	35.6450i	−0.365122	−	1.20365i	−0.926566	−	0.376131i	$-0.877254\pi$
$877$	−10.8128	−	35.6450i	−0.365122	−	1.20365i	0.561445	−	0.827514i	$-0.310246\pi$
$878$	−34.6742	+	18.1020i	−1.17020	+	0.610914i
$879$	−5.54457	+	13.3858i	−0.187014	+	0.451491i
$880$	−45.0453	+	62.0430i	−1.51848	+	2.09147i
$881$	−0.200823	−	0.484831i	−0.00676592	−	0.0163344i	0.920460	−	0.390836i	$-0.127814\pi$
$881$	−0.200823	−	0.484831i	−0.00676592	−	0.0163344i	−0.927226	+	0.374501i	$0.877814\pi$
$882$	−7.48506	−	6.26575i	−0.252035	−	0.210979i
$883$	−12.4421	+	23.2776i	−0.418711	+	0.783353i	−0.999529	−	0.0306799i	$-0.990233\pi$
$883$	−12.4421	+	23.2776i	−0.418711	+	0.783353i	0.580818	+	0.814033i	$0.302733\pi$
$884$	−6.14633	+	3.13300i	−0.206723	+	0.105374i
$885$	1.29102	−	1.57312i	0.0433973	−	0.0528797i
$886$	10.9682	−	25.7672i	0.368483	−	0.865666i
$887$	−36.0021	−	7.16127i	−1.20883	−	0.240452i	−0.450774	−	0.892638i	$-0.648852\pi$
$887$	−36.0021	−	7.16127i	−1.20883	−	0.240452i	−0.758059	+	0.652186i	$0.773852\pi$
$888$	−1.07061	−	15.4978i	−0.0359275	−	0.520071i
$889$	−1.31333	−	6.60257i	−0.0440478	−	0.221443i
$890$	−29.2100	−	44.6506i	−0.979120	−	1.49669i
$891$	−4.90693	+	2.62281i	−0.164388	+	0.0878674i
$892$	−33.2009	+	21.2610i	−1.11165	+	0.711872i
$893$	3.75695	−	38.1449i	0.125721	−	1.27647i
$894$	1.80592	−	1.45290i	0.0603991	−	0.0485921i
$895$	66.5455			2.22437
$896$	−0.793436	−	3.44473i	−0.0265068	−	0.115080i
$897$	−4.17838			−0.139512
$898$	−21.5907	+	17.3701i	−0.720490	+	0.579647i
$899$	0.469890	−	4.77087i	0.0156717	−	0.159118i
$900$	−7.40757	−	11.5675i	−0.246919	−	0.385584i
$901$	−2.66033	+	1.42198i	−0.0886285	+	0.0473729i
$902$	−41.1931	−	62.9683i	−1.37158	−	2.09661i
$903$	−0.688454	−	3.46109i	−0.0229103	−	0.115178i
$904$	12.5278	+	10.9088i	0.416669	+	0.362820i
$905$	12.7436	+	2.53486i	0.423612	+	0.0842617i
$906$	−12.9657	+	30.4599i	−0.430757	+	1.01196i
$907$	2.35314	−	2.86731i	0.0781348	−	0.0952076i	−0.732476	−	0.680793i	$-0.761635\pi$
$907$	2.35314	−	2.86731i	0.0781348	−	0.0952076i	0.810611	+	0.585585i	$0.199135\pi$
$908$	−17.5320	−	34.3943i	−0.581819	−	1.14141i
$909$	7.33033	−	13.7141i	0.243132	−	0.454867i
$910$	1.98271	+	1.65973i	0.0657263	+	0.0550195i
$911$	−11.9857	−	28.9360i	−0.397104	−	0.958694i	−0.988349	−	0.152202i	$-0.951364\pi$
$911$	−11.9857	−	28.9360i	−0.397104	−	0.958694i	0.591246	−	0.806492i	$-0.298636\pi$
$912$	−18.8434	−	4.51727i	−0.623969	−	0.149582i
$913$	7.52933	−	18.1774i	0.249185	−	0.601585i
$914$	−12.9145	+	6.74214i	−0.427173	+	0.223010i
$915$	15.0152	+	49.4984i	0.496387	+	1.63637i
$916$	31.9944	+	17.9107i	1.05712	+	0.591786i
$917$	5.13652	−	0.505903i	0.169623	−	0.0167064i
$918$	0.0279544	−	2.87169i	0.000922633	−	0.0947798i
$919$	−0.0282128	+	0.0188512i	−0.000930655	+	0.000621844i	−0.556035	−	0.831159i	$-0.687678\pi$
$919$	−0.0282128	+	0.0188512i	−0.000930655	+	0.000621844i	0.555105	+	0.831780i	$0.312678\pi$
$920$	0.699847	−	23.9585i	0.0230733	−	0.789887i
$921$	7.69295	−	11.5133i	0.253491	−	0.379377i
$922$	6.33315	+	33.5420i	0.208571	+	1.10465i
$923$	1.49571	−	4.93070i	0.0492319	−	0.162296i
$924$	2.41018	+	2.50590i	0.0792890	+	0.0824379i
$925$	−29.1593	+	23.9304i	−0.958750	+	0.786826i
$926$	−27.1912	−	14.8761i	−0.893557	−	0.488858i
$927$	4.68238	−	4.68238i	0.153789	−	0.153789i
$928$	−14.2143	−	10.5329i	−0.466608	−	0.345759i
$929$	−19.5863	−	19.5863i	−0.642606	−	0.642606i	0.308589	−	0.951195i	$-0.400143\pi$
$929$	−19.5863	−	19.5863i	−0.642606	−	0.642606i	−0.951195	+	0.308589i	$0.900143\pi$
$930$	2.09821	+	7.16728i	0.0688029	+	0.235024i
$931$	21.2125	+	25.8475i	0.695211	+	0.847117i
$932$	21.5102	+	54.9312i	0.704590	+	1.79933i
$933$	−19.9849	−	6.06234i	−0.654275	−	0.198472i
$934$	30.8991	+	21.0840i	1.01105	+	0.689890i
$935$	32.3638	+	21.6248i	1.05841	+	0.707206i
$936$	1.07449	−	4.68276i	0.0351208	−	0.153061i
$937$	6.59852	+	9.87538i	0.215564	+	0.322615i	0.923455	−	0.383708i	$-0.125353\pi$
$937$	6.59852	+	9.87538i	0.215564	+	0.322615i	−0.707890	+	0.706322i	$0.750353\pi$
$938$	−3.40893	+	3.34320i	−0.111305	+	0.109159i
$939$	−2.75084	−	27.9297i	−0.0897702	−	0.911453i
$940$	−6.39857	+	54.1385i	−0.208698	+	1.76580i
$941$	−26.3707	+	7.99946i	−0.859659	+	0.260775i	−0.689183	−	0.724587i	$-0.742031\pi$
$941$	−26.3707	+	7.99946i	−0.859659	+	0.260775i	−0.170476	+	0.985362i	$0.554531\pi$
$942$	−6.67079	+	21.2440i	−0.217346	+	0.692166i
$943$	21.7325	+	9.00190i	0.707708	+	0.293142i
$944$	0.139892	+	2.35876i	0.00455309	+	0.0767711i
$945$	−0.994444	+	0.411912i	−0.0323493	+	0.0133995i
$946$	−7.84954	−	88.5234i	−0.255211	−	2.87815i
$947$	−0.220973	−	0.118113i	−0.00718066	−	0.00383814i	0.467802	−	0.883833i	$-0.345046\pi$
$947$	−0.220973	−	0.118113i	−0.00718066	−	0.00383814i	−0.474983	+	0.879995i	$0.657546\pi$
$948$	−21.7146	+	1.71261i	−0.705257	+	0.0556231i
$949$	−9.05058	−	7.42762i	−0.293794	−	0.241111i
$950$	17.5822	+	43.6440i	0.570441	+	1.41600i
$951$	2.24869	−	11.3050i	0.0729189	−	0.366588i
$952$	−1.73179	+	0.470575i	−0.0561275	+	0.0152514i
$953$	−15.2690	+	3.03718i	−0.494610	+	0.0983840i	−0.436092	−	0.899902i	$-0.643638\pi$
$953$	−15.2690	+	3.03718i	−0.494610	+	0.0983840i	−0.0585184	+	0.998286i	$0.518638\pi$
$954$	0.429876	−	2.05632i	0.0139178	−	0.0665757i
$955$	5.07937	+	9.50283i	0.164364	+	0.307504i
$956$	−10.6269	−	7.40391i	−0.343698	−	0.239459i
$957$	17.3170	+	1.70558i	0.559780	+	0.0551335i
$958$	−1.07014	+	9.87851i	−0.0345745	+	0.319160i
$959$			6.92013i			0.223463i
$960$	26.6705	+	6.94534i	0.860787	+	0.224160i
$961$			28.6503i			0.924204i
$962$	−13.1171	−	1.42097i	−0.422913	−	0.0458141i
$963$	−12.6640	−	1.24729i	−0.408091	−	0.0401934i
$964$	−20.3712	+	3.64133i	−0.656112	+	0.117279i
$965$	15.2839	+	28.5942i	0.492006	+	0.920479i
$966$	−1.06393	−	0.222415i	−0.0342313	−	0.00715610i
$967$	40.6206	−	8.07994i	1.30627	−	0.259833i	0.507596	−	0.861595i	$-0.330534\pi$
$967$	40.6206	−	8.07994i	1.30627	−	0.259833i	0.798675	+	0.601762i	$0.205534\pi$
$968$	34.5204	+	44.6613i	1.10953	+	1.43547i
$969$	−1.91917	+	9.64830i	−0.0616525	+	0.309948i
$970$	7.56141	−	3.04615i	0.242782	−	0.0978060i
$971$	2.75082	+	2.25754i	0.0882779	+	0.0724478i	0.677497	−	0.735525i	$-0.263065\pi$
$971$	2.75082	+	2.25754i	0.0882779	+	0.0724478i	−0.589219	+	0.807973i	$0.700565\pi$
$972$	1.52103	+	1.29864i	0.0487870	+	0.0416540i
$973$	0.284069	+	0.151838i	0.00910684	+	0.00486771i
$974$	−12.5911	+	1.11647i	−0.403444	+	0.0357741i
$975$	−10.7782	+	4.46448i	−0.345179	+	0.142978i
$976$	−51.8249	−	30.3519i	−1.65888	−	0.971542i
$977$	−27.2419	−	11.2840i	−0.871545	−	0.361006i	−0.0983333	−	0.995154i	$-0.531351\pi$
$977$	−27.2419	−	11.2840i	−0.871545	−	0.361006i	−0.773212	+	0.634148i	$0.781351\pi$
$978$	−10.9830	−	3.44876i	−0.351198	−	0.110279i
$979$	−58.3105	+	17.6883i	−1.86361	+	0.565320i
$980$	−29.4487	−	37.3427i	−0.940705	−	1.19287i
$981$	0.193902	+	1.96871i	0.00619080	+	0.0628562i
$982$	27.6835	+	28.2278i	0.883417	+	0.900785i
$983$	−17.4570	−	26.1262i	−0.556792	−	0.833298i	0.441149	−	0.897434i	$-0.354571\pi$
$983$	−17.4570	−	26.1262i	−0.556792	−	0.833298i	−0.997941	+	0.0641358i	$0.979571\pi$
$984$	−15.6771	+	22.0410i	−0.499769	+	0.702641i
$985$	64.2172	+	42.9086i	2.04613	+	1.36718i
$986$	−5.06229	+	7.41889i	−0.161216	+	0.236266i
$987$	2.36570	+	0.717626i	0.0753009	+	0.0228423i
$988$	−6.59280	+	15.0792i	−0.209745	+	0.479734i
$989$	17.6251	+	21.4763i	0.560446	+	0.682905i
$990$	−26.0153	+	7.61593i	−0.826822	+	0.242050i
$991$	−27.5282	−	27.5282i	−0.874461	−	0.874461i	0.118494	−	0.992955i	$-0.462193\pi$
$991$	−27.5282	−	27.5282i	−0.874461	−	0.874461i	−0.992955	+	0.118494i	$0.962193\pi$
$992$	−7.43941	−	4.45480i	−0.236201	−	0.141440i
$993$	4.63610	−	4.63610i	0.147122	−	0.147122i
$994$	0.643308	−	1.17587i	0.0204045	−	0.0372963i
$995$	−3.02065	+	2.47898i	−0.0957609	+	0.0785889i
$996$	−7.07106	−	0.137679i	−0.224055	−	0.00436254i
$997$	1.42030	−	4.68211i	0.0449814	−	0.148284i	−0.931573	−	0.363554i	$-0.881563\pi$
$997$	1.42030	−	4.68211i	0.0449814	−	0.148284i	0.976555	+	0.215270i	$0.0690632\pi$
$998$	39.5356	−	7.46480i	1.25148	−	0.236294i
$999$	3.05139	−	4.56672i	0.0965416	−	0.144485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.23	✓	512
128.53	even	32	inner	384.2.v.a.181.23	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.23	✓	512	1.1	even	1	trivial
384.2.v.a.181.23	yes	512	128.53	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)

\(f(q)\)	\(=\)	\(q+(0.886484 + 1.10188i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-0.428293 + 1.95360i) q^{4} +(-3.03822 + 1.62396i) q^{5} +(1.18347 - 0.774212i) q^{6} +(-0.0609552 - 0.306443i) q^{7} +(-2.53232 + 1.25991i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(0.886484 + 1.10188i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-0.428293 + 1.95360i) q^{4} +(-3.03822 + 1.62396i) q^{5} +(1.18347 - 0.774212i) q^{6} +(-0.0609552 - 0.306443i) q^{7} +(-2.53232 + 1.25991i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-4.48275 - 1.90815i) q^{10} +(-3.52971 + 4.30096i) q^{11} +(1.90222 + 0.617717i) q^{12} +(0.800729 - 1.49806i) q^{13} +(0.283628 - 0.338822i) q^{14} +(1.31835 + 3.18277i) q^{15} +(-3.63313 - 1.67343i) q^{16} +(-0.777110 + 1.87611i) q^{17} +(-0.654484 - 1.25366i) q^{18} +(1.40624 + 4.63574i) q^{19} +(-1.87133 - 6.63101i) q^{20} +(-0.310942 + 0.0306251i) q^{21} +(-7.86819 - 0.0765928i) q^{22} +(2.04529 - 1.36662i) q^{23} +(1.00563 + 2.64362i) q^{24} +(3.81568 - 5.71057i) q^{25} +(2.36052 - 0.445695i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(0.624774 + 0.0121649i) q^{28} +(2.41755 - 1.98403i) q^{29} +(-2.33835 + 4.27413i) q^{30} +(1.08390 - 1.08390i) q^{31} +(-1.37679 - 5.48675i) q^{32} +(3.93428 + 3.93428i) q^{33} +(-2.75615 + 0.806856i) q^{34} +(0.682847 + 0.832051i) q^{35} +(0.801192 - 1.83251i) q^{36} +(-5.25585 - 1.59435i) q^{37} +(-3.86144 + 5.65902i) q^{38} +(-1.41236 - 0.943708i) q^{39} +(5.64769 - 7.94027i) q^{40} +(5.31281 + 7.95118i) q^{41} +(-0.309390 - 0.315473i) q^{42} +(1.10705 + 11.2400i) q^{43} +(-6.89062 - 8.73772i) q^{44} +(3.29666 - 1.00003i) q^{45} +(3.31898 + 1.04219i) q^{46} +(-7.30995 - 3.02788i) q^{47} +(-2.02148 + 3.45161i) q^{48} +(6.37697 - 2.64143i) q^{49} +(9.67491 - 0.857893i) q^{50} +(1.79091 + 0.957259i) q^{51} +(2.58366 + 2.20591i) q^{52} +(1.14828 + 0.942371i) q^{53} +(-1.31177 + 0.528452i) q^{54} +(3.73943 - 18.7994i) q^{55} +(0.540448 + 0.699212i) q^{56} +(4.75125 - 0.945083i) q^{57} +(4.32928 + 0.905044i) q^{58} +(-0.278466 - 0.520974i) q^{59} +(-6.78250 + 1.21237i) q^{60} +(14.9424 + 1.47170i) q^{61} +(2.15520 + 0.233472i) q^{62} +0.312446i q^{63} +(4.82526 - 6.38098i) q^{64} +5.85178i q^{65} +(-0.847441 + 7.82279i) q^{66} +(-10.7537 - 1.05915i) q^{67} +(-3.33234 - 2.32169i) q^{68} +(-1.15957 - 2.16940i) q^{69} +(-0.311491 + 1.49002i) q^{70} +(2.97508 - 0.591780i) q^{71} +(2.72946 - 0.741670i) q^{72} +(1.34471 - 6.76030i) q^{73} +(-2.90245 - 7.20470i) q^{74} +(-5.30907 - 4.35704i) q^{75} +(-9.65867 + 0.761773i) q^{76} +(1.53315 + 0.819487i) q^{77} +(-0.212177 - 2.39284i) q^{78} +(-10.0620 + 4.16781i) q^{79} +(13.7558 - 0.815823i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-4.05155 + 12.9027i) q^{82} +(-3.38393 + 1.02650i) q^{83} +(0.0733449 - 0.620573i) q^{84} +(-0.685700 - 6.96203i) q^{85} +(-11.4038 + 11.1839i) q^{86} +(-1.73751 - 2.60037i) q^{87} +(3.51952 - 15.3385i) q^{88} +(9.10601 + 6.08444i) q^{89} +(4.02435 + 2.74602i) q^{90} +(-0.507877 - 0.154063i) q^{91} +(1.79385 + 4.58101i) q^{92} +(-0.972442 - 1.18492i) q^{93} +(-3.14378 - 10.7389i) q^{94} +(-11.8007 - 11.8007i) q^{95} +(-5.59528 + 0.832363i) q^{96} +(-1.18315 + 1.18315i) q^{97} +(8.56362 + 4.68509i) q^{98} +(4.30096 - 3.52971i) 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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