LMFDB - Embedded newform 384.2.v.a.181.23

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			181.23
Character	$\chi$	$=$	384.181
Dual form			384.2.v.a.157.23

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{5}{32}\right)$	$1$

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	−0.378781	−	0.925487i	$-0.623656\pi$
$5$	−3.03822	−	1.62396i	−1.35873	−	0.726258i	−0.979953	+	0.199228i	$0.936156\pi$
$6$	1.18347	+	0.774212i	0.483149	+	0.316071i
$7$	−0.0609552	+	0.306443i	−0.0230389	+	0.115824i	−0.990593	−	0.136838i	$-0.956306\pi$
$7$	−0.0609552	+	0.306443i	−0.0230389	+	0.115824i	0.967555	+	0.252662i	$0.0813061\pi$
$8$	−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	−0.952992	−	0.302997i	$-0.902013\pi$
$11$	−3.52971	−	4.30096i	−1.06425	−	1.29679i	−0.111256	−	0.993792i	$-0.535487\pi$
$12$	1.90222	−	0.617717i	0.549122	−	0.178320i
$13$	0.800729	+	1.49806i	0.222082	+	0.415487i	0.968145	−	0.250389i	$-0.0805584\pi$
$13$	0.800729	+	1.49806i	0.222082	+	0.415487i	−0.746063	+	0.665875i	$0.768058\pi$
$14$	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	0.801190	−	0.598410i	$-0.204201\pi$
$17$	−0.777110	−	1.87611i	−0.188477	−	0.455023i	−0.989667	+	0.143387i	$0.954201\pi$
$18$	−0.654484	+	1.25366i	−0.154263	+	0.295489i
$19$	1.40624	−	4.63574i	0.322613	−	1.06351i	−0.634288	−	0.773097i	$-0.718707\pi$
$19$	1.40624	−	4.63574i	0.322613	−	1.06351i	0.956901	−	0.290415i	$-0.0937933\pi$
$20$	−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	0.750226	−	0.661181i	$-0.229945\pi$
$23$	2.04529	+	1.36662i	0.426473	+	0.284960i	−0.323753	+	0.946142i	$0.604945\pi$
$24$	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	0.831522	−	0.555491i	$-0.187470\pi$
$29$	2.41755	+	1.98403i	0.448927	+	0.368425i	−0.382596	+	0.923916i	$0.624970\pi$
$30$	−2.33835	−	4.27413i	−0.426922	−	0.780347i
$31$	1.08390	+	1.08390i	0.194675	+	0.194675i	0.797713	−	0.603038i	$-0.206043\pi$
$31$	1.08390	+	1.08390i	0.194675	+	0.194675i	−0.603038	+	0.797713i	$0.706043\pi$
$32$	−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	−0.691046	−	0.722811i	$-0.742850\pi$
$37$	−5.25585	+	1.59435i	−0.864057	+	0.262109i	−0.173011	+	0.984920i	$0.555350\pi$
$38$	−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	−0.138173	−	0.990408i	$-0.544123\pi$
$41$	5.31281	−	7.95118i	0.829721	−	1.24177i	0.967894	−	0.251357i	$-0.0808769\pi$
$42$	−0.309390	+	0.315473i	−0.0477399	+	0.0486785i
$43$	1.10705	−	11.2400i	0.168823	−	1.71409i	−0.421422	−	0.906864i	$-0.638469\pi$
$43$	1.10705	−	11.2400i	0.168823	−	1.71409i	0.590245	−	0.807224i	$-0.299031\pi$
$44$	−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	−0.845671	−	0.533704i	$-0.820800\pi$
$47$	−7.30995	+	3.02788i	−1.06627	+	0.441662i	−0.220594	+	0.975366i	$0.570800\pi$
$48$	−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	−0.552219	−	0.833699i	$-0.686219\pi$
$53$	1.14828	−	0.942371i	0.157729	−	0.129445i	0.709947	+	0.704255i	$0.248719\pi$
$54$	−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	−0.899396	−	0.437136i	$-0.855993\pi$
$59$	−0.278466	+	0.520974i	−0.0362532	+	0.0678250i	0.863142	+	0.504961i	$0.168493\pi$
$60$	−6.78250	−	1.21237i	−0.875617	−	0.156516i
$61$	14.9424	−	1.47170i	1.91318	−	0.188432i	0.929558	−	0.368677i	$-0.120189\pi$
$61$	14.9424	−	1.47170i	1.91318	−	0.188432i	0.983622	+	0.180245i	$0.0576891\pi$
$62$	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	−0.730520	−	0.682891i	$-0.760722\pi$
$67$	−10.7537	+	1.05915i	−1.31378	+	0.129396i	−0.583258	+	0.812287i	$0.698222\pi$
$68$	−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	0.368442	−	0.929651i	$-0.379891\pi$
$71$	2.97508	+	0.591780i	0.353077	+	0.0702314i	−0.0153654	+	0.999882i	$0.504891\pi$
$72$	2.72946	+	0.741670i	0.321669	+	0.0874066i
$73$	1.34471	+	6.76030i	0.157386	+	0.791234i	0.976149	+	0.217102i	$0.0696604\pi$
$73$	1.34471	+	6.76030i	0.157386	+	0.791234i	−0.818763	+	0.574132i	$0.805340\pi$
$74$	−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	−0.263580	−	0.964637i	$-0.584903\pi$
$79$	−10.0620	−	4.16781i	−1.13206	−	0.468915i	−0.868481	+	0.495722i	$0.834903\pi$
$80$	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	0.0990481	−	0.995083i	$-0.468420\pi$
$83$	−3.38393	−	1.02650i	−0.371435	−	0.112673i	−0.470483	+	0.882409i	$0.655920\pi$
$84$	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	0.0302145	−	0.999543i	$-0.490381\pi$
$89$	9.10601	−	6.08444i	0.965235	−	0.644949i	0.935020	+	0.354594i	$0.115381\pi$
$90$	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	0.644486	−	0.764617i	$-0.277072\pi$
$97$	−1.18315	−	1.18315i	−0.120131	−	0.120131i	−0.764617	+	0.644486i	$0.777072\pi$
$98$	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	−0.830906	−	0.556413i	$-0.812177\pi$
$101$	−4.51399	−	14.8806i	−0.449159	−	1.48068i	0.381747	−	0.924267i	$-0.375323\pi$
$102$	0.532821	−	2.82196i	0.0527572	−	0.279416i
$103$	−3.67892	−	5.50589i	−0.362495	−	0.542512i	0.604731	−	0.796430i	$-0.293281\pi$
$103$	−3.67892	−	5.50589i	−0.362495	−	0.542512i	−0.967226	+	0.253918i	$0.918281\pi$
$104$	−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	0.689418	−	0.724364i	$-0.257866\pi$
$107$	12.6640	+	1.24729i	1.22427	+	0.120580i	0.534855	+	0.844944i	$0.320366\pi$
$108$	−1.74515	+	0.976952i	−0.167928	+	0.0940072i
$109$	−0.574253	+	1.89306i	−0.0550035	+	0.181322i	−0.980138	−	0.198318i	$-0.936452\pi$
$109$	−0.574253	+	1.89306i	−0.0550035	+	0.181322i	0.925134	+	0.379640i	$0.123952\pi$
$110$	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	−0.993644	−	0.112572i	$-0.964091\pi$
$113$	−2.24754	+	5.42604i	−0.211431	+	0.510439i	0.782213	+	0.623011i	$0.214091\pi$
$114$	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	−0.759662	−	0.650318i	$-0.774636\pi$
$131$	−1.61917	−	16.4397i	−0.141467	−	1.43634i	0.618194	−	0.786025i	$-0.287864\pi$
$132$	−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	−0.991116	−	0.132998i	$-0.957540\pi$
$137$	−21.7227	+	4.32091i	−1.85589	+	0.369160i	−0.864776	+	0.502158i	$0.832540\pi$
$138$	1.36249	+	3.20084i	0.115982	+	0.272474i
$139$	−0.654000	−	0.796901i	−0.0554716	−	0.0675923i	0.744536	−	0.667583i	$-0.232671\pi$
$139$	−0.654000	−	0.796901i	−0.0554716	−	0.0675923i	−0.800007	+	0.599991i	$0.795171\pi$
$140$	−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	0.164606	−	0.986359i	$-0.447365\pi$
$149$	1.63105	+	0.160645i	0.133621	+	0.0131605i	−0.0309856	+	0.999520i	$0.509865\pi$
$150$	0.0945454	+	9.71242i	0.00771960	+	0.793015i
$151$	−19.4635	−	13.0051i	−1.58391	−	1.05834i	−0.961186	−	0.275900i	$-0.911024\pi$
$151$	−19.4635	−	13.0051i	−1.58391	−	1.05834i	−0.622729	−	0.782438i	$-0.713976\pi$
$152$	−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	0.00786830	−	0.999969i	$-0.497495\pi$
$157$	−12.1710	−	9.98848i	−0.971352	−	0.797168i	−0.979220	+	0.202801i	$0.934995\pi$
$158$	−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	−0.934917	−	0.354868i	$-0.884526\pi$
$163$	−5.16398	+	6.29233i	−0.404474	+	0.492854i	0.530442	+	0.847721i	$0.322026\pi$
$164$	−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	−0.191377	−	0.981517i	$-0.561295\pi$
$167$	8.29891	−	5.54515i	0.642189	−	0.429097i	0.833566	+	0.552420i	$0.186295\pi$
$168$	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	0.523158	−	0.852235i	$-0.324754\pi$
$173$	6.37487	+	1.93379i	0.484672	+	0.147024i	−0.0384864	+	0.999259i	$0.512254\pi$
$174$	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	−0.962862	−	0.269995i	$-0.912978\pi$
$179$	−17.0357	+	9.10576i	−1.27331	+	0.680596i	−0.310444	+	0.950592i	$0.600478\pi$
$180$	0.541728	−	6.86867i	0.0403780	−	0.511961i
$181$	−2.91551	+	2.39270i	−0.216708	+	0.177848i	−0.736484	−	0.676455i	$-0.763515\pi$
$181$	−2.91551	+	2.39270i	−0.216708	+	0.177848i	0.519776	+	0.854303i	$0.326015\pi$
$182$	−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	$0.0360968\pi$
$191$			3.12776i			0.226317i	−0.993577	+	0.113158i	$0.963903\pi$
$192$	−5.87729	+	5.42747i	−0.424157	+	0.391694i
$193$			9.41148i			0.677453i	0.940885	+	0.338727i	$0.109996\pi$
$193$			9.41148i			0.677453i	−0.940885	+	0.338727i	$0.890004\pi$
$194$	−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	0.154268	+	0.988029i	$0.450698\pi$
$197$	−10.5682	+	19.7718i	−0.752955	+	1.40868i	−0.907223	+	0.420650i	$0.861802\pi$
$198$	7.70206	−	1.61013i	0.547362	−	0.114427i
$199$	1.11250	+	0.221289i	0.0788628	+	0.0156868i	0.234364	−	0.972149i	$-0.424699\pi$
$199$	1.11250	+	0.221289i	0.0788628	+	0.0156868i	−0.155501	+	0.987836i	$0.549699\pi$
$200$	−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	0.623750	−	0.781624i	$-0.285608\pi$
$211$	10.2862	+	3.12029i	0.708133	+	0.214810i	0.0843826	+	0.996433i	$0.473108\pi$
$212$	−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	−0.0645041	−	0.997917i	$-0.520547\pi$
$223$	13.9388	−	13.9388i	0.933413	−	0.933413i	0.997917	+	0.0645041i	$0.0205466\pi$
$224$	−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	−0.00802138	−	0.999968i	$-0.502553\pi$
$227$	−14.9210	−	12.2453i	−0.990340	−	0.812751i	−0.982319	+	0.187217i	$0.940053\pi$
$228$	−0.188611	−	9.68683i	−0.0124910	−	0.641526i
$229$	5.32186	+	17.5438i	0.351679	+	1.15933i	0.937235	+	0.348697i	$0.113376\pi$
$229$	5.32186	+	17.5438i	0.351679	+	1.15933i	−0.585557	+	0.810631i	$0.699124\pi$
$230$	−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	0.946609	+	0.322384i	$0.104484\pi$
$233$	24.5253	+	16.3873i	1.60670	+	1.07357i	0.660095	+	0.751182i	$0.270516\pi$
$234$	−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	0.823237	−	0.567698i	$-0.192166\pi$
$239$	−2.47822	−	5.98294i	−0.160303	−	0.387005i	−0.983539	+	0.180693i	$0.942166\pi$
$240$	0.536413	+	13.7696i	0.0346253	+	0.888822i
$241$	3.95964	−	9.55942i	0.255063	−	0.615776i	−0.743536	−	0.668696i	$-0.766853\pi$
$241$	3.95964	−	9.55942i	0.255063	−	0.615776i	0.998599	+	0.0529199i	$0.0168528\pi$
$242$	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	0.429501	−	0.903066i	$-0.358689\pi$
$251$	−1.31105	−	0.700770i	−0.0827526	−	0.0442322i	−0.512254	+	0.858834i	$0.671189\pi$
$252$	−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	0.808697	+	0.588225i	$0.200173\pi$
$263$	−2.65226	+	13.3338i	−0.163546	+	0.822199i	−0.972243	+	0.233974i	$0.924827\pi$
$264$	−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	0.895465	+	0.445131i	$0.146843\pi$
$269$	12.5975	+	23.5683i	0.768085	+	1.43699i	−0.127381	+	0.991854i	$0.540657\pi$
$270$	3.12726	+	3.73582i	0.190319	+	0.227355i
$271$	2.20593	−	5.32559i	0.134001	−	0.323507i	−0.842609	−	0.538526i	$-0.818981\pi$
$271$	2.20593	−	5.32559i	0.134001	−	0.323507i	0.976610	+	0.215019i	$0.0689814\pi$
$272$	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	0.185309	−	0.982680i	$-0.440671\pi$
$277$	2.91834	+	0.287431i	0.175346	+	0.0172701i	−0.00996315	+	0.999950i	$0.503171\pi$
$278$	−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	0.428276	−	0.903648i	$-0.359121\pi$
$281$	−9.56299	−	14.3120i	−0.570480	−	0.853784i	−0.998756	+	0.0498640i	$0.984121\pi$
$282$	−10.9953	−	2.07605i	−0.654761	−	0.123627i
$283$	−6.17113	−	20.3435i	−0.366836	−	1.20929i	−0.925130	−	0.379652i	$-0.876044\pi$
$283$	−6.17113	−	20.3435i	−0.366836	−	1.20929i	0.558294	−	0.829643i	$-0.311456\pi$
$284$	−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	−0.668001	−	0.744161i	$-0.732850\pi$
$293$	−13.8648	+	4.20584i	−0.809990	+	0.245708i	−0.141989	+	0.989868i	$0.545350\pi$
$294$	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	−0.0845486	−	0.996419i	$-0.526945\pi$
$307$	12.2119	−	6.52741i	0.696971	−	0.372539i	0.781520	+	0.623881i	$0.214445\pi$
$308$	−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	0.905885	+	0.423524i	$0.139207\pi$
$311$	4.07429	+	20.4828i	0.231032	+	1.16148i	−0.674853	+	0.737952i	$0.735793\pi$
$312$	4.76553	−	0.610325i	0.269795	−	0.0345528i
$313$	27.5256	+	5.47519i	1.55584	+	0.309476i	0.896733	−	0.442573i	$-0.145934\pi$
$313$	27.5256	+	5.47519i	1.55584	+	0.309476i	0.659108	+	0.752049i	$0.270934\pi$
$314$	−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	0.229396	−	0.973333i	$-0.426325\pi$
$317$	11.4709	−	1.12979i	0.644271	−	0.0634552i	0.414876	+	0.909878i	$0.363825\pi$
$318$	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	−0.484723	−	0.874668i	$-0.661080\pi$
$331$	5.06819	−	4.15936i	0.278573	−	0.228619i	0.763296	+	0.646049i	$0.223580\pi$
$332$	−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	0.380617	−	0.924733i	$-0.375712\pi$
$337$	23.9316	−	9.91280i	1.30364	−	0.539985i	0.923022	+	0.384748i	$0.125712\pi$
$338$	−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	0.496142	−	0.868242i	$-0.334750\pi$
$347$	25.9122	−	7.86037i	1.39104	−	0.421967i	0.894896	+	0.446275i	$0.147250\pi$
$348$	5.82426	+	2.28069i	0.312213	+	0.122258i
$349$	−0.824480	+	1.00463i	−0.0441334	+	0.0537767i	−0.794609	−	0.607121i	$-0.792324\pi$
$349$	−0.824480	+	1.00463i	−0.0441334	+	0.0537767i	0.750476	+	0.660898i	$0.229824\pi$
$350$	−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	0.807952	−	0.589248i	$-0.200576\pi$
$353$	4.10908	+	4.10908i	0.218704	+	0.218704i	−0.589248	+	0.807952i	$0.700576\pi$
$354$	−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	0.630575	−	0.776128i	$-0.282819\pi$
$359$	−6.21064	−	9.29487i	−0.327785	−	0.490565i	−0.958360	+	0.285564i	$0.907819\pi$
$360$	−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	0.895084	−	0.445898i	$-0.147115\pi$
$367$	−1.01789	−	2.45739i	−0.0531332	−	0.128275i	−0.948217	+	0.317623i	$0.897115\pi$
$368$	−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	0.599548	−	0.800339i	$-0.295347\pi$
$373$	−5.83989	−	7.11592i	−0.302378	−	0.368449i	−0.901926	+	0.431890i	$0.857847\pi$
$374$	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	0.930604	−	0.366028i	$-0.119282\pi$
$379$	22.2573	+	11.8968i	1.14328	+	0.611095i	0.212675	+	0.977123i	$0.431782\pi$
$380$	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	0.979833	−	0.199817i	$-0.0640347\pi$
$389$	26.7851	+	14.3169i	1.35806	+	0.725897i	0.378225	+	0.925714i	$0.376535\pi$
$390$	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	0.619938	−	0.784651i	$-0.287158\pi$
$397$	−7.50956	−	14.0494i	−0.376894	−	0.705119i	−0.996832	+	0.0795313i	$0.974658\pi$
$398$	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	0.950235	−	0.311533i	$-0.100842\pi$
$401$	1.16206	+	2.80546i	0.0580305	+	0.140098i	−0.892205	+	0.451631i	$0.850842\pi$
$402$	−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	0.966878	−	0.255240i	$-0.0821546\pi$
$409$	7.30195	+	10.9281i	0.361058	+	0.540362i	−0.605819	+	0.795602i	$0.707155\pi$
$410$	−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	−0.849750	−	0.527187i	$-0.823247\pi$
$419$	−3.41666	+	4.16321i	−0.166915	+	0.203386i	0.682835	+	0.730573i	$0.260747\pi$
$420$	0.784950	−	2.00455i	0.0383016	−	0.0978119i
$421$	−34.4767	+	10.4584i	−1.68029	+	0.509711i	−0.979120	−	0.203283i	$-0.934839\pi$
$421$	−34.4767	+	10.4584i	−1.68029	+	0.509711i	−0.701171	+	0.712994i	$0.747339\pi$
$422$	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	−0.696953	−	0.717117i	$-0.745461\pi$
$431$	−14.1731	+	5.87069i	−0.682695	+	0.282781i	0.0142582	+	0.999898i	$0.495461\pi$
$432$	2.65601	+	2.99092i	0.127788	+	0.143901i
$433$	−10.6169	−	4.39765i	−0.510214	−	0.211338i	0.112698	−	0.993629i	$-0.464051\pi$
$433$	−10.6169	−	4.39765i	−0.510214	−	0.211338i	−0.622912	+	0.782292i	$0.714051\pi$
$434$	−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	−0.865567	−	0.500793i	$-0.833042\pi$
$439$	−5.39591	−	27.1270i	−0.257532	−	1.29470i	0.608035	−	0.793910i	$-0.291958\pi$
$440$	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	−0.999999	−	0.00111419i	$-0.999645\pi$
$443$	−9.33466	+	17.4639i	−0.443503	+	0.829736i	0.556496	+	0.830850i	$0.312145\pi$
$444$	−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	$-0.847004\pi$
$449$		−	19.5943i		−	0.924715i	0.886694	−	0.462357i	$-0.152996\pi$
$450$	−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	−0.998896	−	0.0469685i	$-0.985044\pi$
$457$	−2.00972	−	10.1035i	−0.0940105	−	0.472623i	0.904886	−	0.425654i	$-0.139956\pi$
$458$	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	0.105830	−	0.994384i	$-0.466250\pi$
$461$	21.2868	−	11.3780i	0.991426	−	0.529928i	0.885596	+	0.464456i	$0.153750\pi$
$462$	2.44889	+	0.217148i	0.113933	+	0.0101026i
$463$	−20.2481	−	8.38704i	−0.941009	−	0.389779i	−0.141165	−	0.989986i	$-0.545085\pi$
$463$	−20.2481	−	8.38704i	−0.941009	−	0.389779i	−0.799844	+	0.600207i	$0.795085\pi$
$464$	−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	0.815220	−	0.579152i	$-0.196616\pi$
$467$	25.3118	+	7.67826i	1.17129	+	0.355307i	0.356071	+	0.934459i	$0.384116\pi$
$468$	−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	−0.584438	−	0.811438i	$-0.698685\pi$
$479$	4.96815	−	4.96815i	0.227001	−	0.227001i	0.811438	+	0.584438i	$0.198685\pi$
$480$	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	0.701731	−	0.712442i	$-0.252411\pi$
$487$	−4.96578	−	7.43181i	−0.225021	−	0.336768i	−0.926752	+	0.375675i	$0.877411\pi$
$488$	−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	0.703856	−	0.710343i	$-0.251460\pi$
$491$	27.8224	+	2.74026i	1.25561	+	0.123666i	0.551750	+	0.834009i	$0.313960\pi$
$492$	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	0.980174	+	0.198140i	$0.0634900\pi$
$499$	13.4112	+	25.0905i	0.600366	+	1.12321i	−0.379808	+	0.925065i	$0.624010\pi$
$500$	−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	0.0523417	−	0.998629i	$-0.483332\pi$
$503$	10.8294	−	2.15410i	0.482858	−	0.0960464i	0.430516	+	0.902583i	$0.358332\pi$
$504$	−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	−0.999996	−	0.00271731i	$-0.999135\pi$
$509$	−0.445462	−	4.52285i	−0.0197448	−	0.200472i	0.980252	−	0.197755i	$-0.0633649\pi$
$510$	−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	−0.815841	−	0.578276i	$-0.803726\pi$
$521$	−30.7751	+	6.12155i	−1.34828	+	0.268190i	−0.532442	+	0.846466i	$0.678726\pi$
$522$	−4.06953	+	1.73225i	−0.178119	+	0.0758187i
$523$	5.97612	+	7.28193i	0.261318	+	0.318416i	0.887096	−	0.461584i	$-0.152719\pi$
$523$	5.97612	+	7.28193i	0.261318	+	0.318416i	−0.625779	+	0.780001i	$0.715219\pi$
$524$	−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	0.460081	−	0.887877i	$-0.347820\pi$
$541$	−7.46576	−	6.12699i	−0.320978	−	0.263420i	−0.781059	+	0.624457i	$0.785320\pi$
$542$	−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	−0.985700	−	0.168511i	$-0.946104\pi$
$547$	−14.6906	+	17.9006i	−0.628126	+	0.765374i	0.357574	+	0.933885i	$0.383604\pi$
$548$	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	0.933941	−	0.357426i	$-0.116346\pi$
$557$	35.6824	+	10.8241i	1.51191	+	0.458633i	0.577968	+	0.816059i	$0.303846\pi$
$558$	−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	−0.400092	−	0.916475i	$-0.631022\pi$
$563$	3.31356	−	1.77114i	0.139650	−	0.0746445i	0.539742	+	0.841831i	$0.318522\pi$
$564$	−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	−0.443826	−	0.896113i	$-0.646379\pi$
$569$	−28.5480	−	5.67856i	−1.19680	−	0.238058i	−0.752970	+	0.658055i	$0.771379\pi$
$570$	−23.1020	+	4.82952i	−0.967638	+	0.202286i
$571$	7.50330	−	14.0377i	0.314003	−	0.587459i	−0.674568	−	0.738213i	$-0.735670\pi$
$571$	7.50330	−	14.0377i	0.314003	−	0.587459i	0.988571	+	0.150754i	$0.0481701\pi$
$572$	−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	$-0.766397\pi$
$577$		−	32.1764i		−	1.33952i	0.742577	−	0.669761i	$-0.233603\pi$
$578$	−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	−0.896835	−	0.442365i	$-0.854139\pi$
$587$	−15.4559	+	12.6843i	−0.637933	+	0.523538i	0.258901	+	0.965904i	$0.416639\pi$
$588$	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	−0.298470	−	0.954419i	$-0.596476\pi$
$593$	4.02668	−	1.66791i	0.165356	−	0.0684927i	0.463826	+	0.885926i	$0.346476\pi$
$594$	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	0.349207	+	0.937046i	$0.386451\pi$
$599$	−15.9120	+	23.8140i	−0.650146	+	0.973013i	−0.999353	+	0.0359669i	$0.988549\pi$
$600$	18.9337	−	4.34446i	0.772966	−	0.177362i
$601$	−19.3296	+	12.9156i	−0.788469	+	0.526838i	−0.883386	−	0.468647i	$-0.844742\pi$
$601$	−19.3296	+	12.9156i	−0.788469	+	0.526838i	0.0949164	+	0.995485i	$0.469742\pi$
$602$	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	−0.888314	−	0.459236i	$-0.848123\pi$
$607$	−10.5714	+	10.5714i	−0.429078	+	0.429078i	0.459236	+	0.888314i	$0.348123\pi$
$608$	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	0.942460	−	0.334318i	$-0.108506\pi$
$613$	−0.666110	−	2.19587i	−0.0269039	−	0.0886903i	−0.969364	+	0.245628i	$0.921006\pi$
$614$	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	0.816528	−	0.577306i	$-0.195896\pi$
$617$	14.7954	+	9.88595i	0.595639	+	0.397993i	−0.220889	+	0.975299i	$0.570896\pi$
$618$	−0.0911568	−	9.36431i	−0.00366686	−	0.376688i
$619$	−0.383689	−	0.0377900i	−0.0154217	−	0.00151891i	0.0903033	−	0.995914i	$-0.471216\pi$
$619$	−0.383689	−	0.0377900i	−0.0154217	−	0.00151891i	−0.105725	+	0.994395i	$0.533716\pi$
$620$	−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	0.0856862	−	0.996322i	$-0.472692\pi$
$631$	13.7185	−	2.72878i	0.546126	−	0.108631i	0.460440	+	0.887691i	$0.347692\pi$
$632$	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	0.391585	+	0.920142i	$0.371927\pi$
$643$	4.74273	+	48.1537i	0.187035	+	1.89900i	−0.204550	+	0.978856i	$0.565573\pi$
$644$	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	−0.998697	−	0.0510372i	$-0.983747\pi$
$647$	−1.43690	+	7.22376i	−0.0564902	+	0.283995i	0.942207	+	0.335033i	$0.108747\pi$
$648$	−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	0.855592	+	0.517651i	$0.173194\pi$
$653$	20.7155	+	38.7561i	0.810662	+	1.51664i	−0.0449298	+	0.998990i	$0.514306\pi$
$654$	−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	−0.653437	−	0.756981i	$-0.726673\pi$
$659$	7.96911	−	26.2706i	0.310432	−	1.02336i	0.963869	−	0.266377i	$-0.0858266\pi$
$660$	18.7259	+	33.4506i	0.728905	+	1.30206i
$661$	27.3706	+	2.69577i	1.06459	+	0.104853i	0.615115	−	0.788438i	$-0.289110\pi$
$661$	27.3706	+	2.69577i	1.06459	+	0.104853i	0.449479	+	0.893291i	$0.351610\pi$
$662$	−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	−0.995864	−	0.0908536i	$-0.971040\pi$
$673$	−23.4780	+	23.4780i	−0.905011	+	0.905011i	0.0908536	+	0.995864i	$0.471040\pi$
$674$	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	0.0745583	−	0.997217i	$-0.476245\pi$
$677$	17.9682	−	5.45060i	0.690575	−	0.209484i	0.616017	+	0.787733i	$0.288745\pi$
$678$	−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	0.930782	+	0.365576i	$0.119128\pi$
$683$	−1.39650	+	14.1789i	−0.0534356	+	0.542540i	−0.984217	+	0.176965i	$0.943372\pi$
$684$	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	−0.790182	−	0.612873i	$-0.790014\pi$
$691$	−18.9160	+	10.1108i	−0.719598	+	0.384633i	0.0705836	+	0.997506i	$0.477514\pi$
$692$	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	−0.927327	−	0.374253i	$-0.877899\pi$
$701$	−46.6997	+	4.59951i	−1.76382	+	0.173721i	−0.836495	+	0.547974i	$0.815399\pi$
$702$	−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	−0.502584	−	0.864528i	$-0.667617\pi$
$709$	13.1928	−	24.6820i	0.495466	−	0.926951i	0.998050	−	0.0624226i	$-0.0198826\pi$
$710$	−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	−0.336457	−	0.941699i	$-0.609229\pi$
$719$	−33.2563	−	13.7752i	−1.24025	−	0.513728i	−0.903793	+	0.427970i	$0.859229\pi$
$720$	−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	−0.323020	−	0.946392i	$-0.604698\pi$
$727$	18.1985	−	27.2360i	0.674946	−	1.01013i	0.997967	−	0.0637367i	$-0.0203018\pi$
$728$	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	−0.999860	−	0.0167033i	$-0.994683\pi$
$733$	−21.3455	+	26.0096i	−0.788415	+	0.960686i	0.211445	+	0.977390i	$0.432183\pi$
$734$	−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	0.865730	−	0.500511i	$-0.166855\pi$
$739$	14.7811	+	12.1305i	0.543732	+	0.446229i	−0.321998	+	0.946740i	$0.604355\pi$
$740$	−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	0.657350	−	0.753585i	$-0.271677\pi$
$743$	−7.91652	−	11.8479i	−0.290429	−	0.434658i	−0.947779	+	0.318928i	$0.896677\pi$
$744$	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	−0.981497	−	0.191477i	$-0.938672\pi$
$751$	−11.5884	−	27.9770i	−0.422868	−	1.02089i	0.558629	−	0.829418i	$-0.311328\pi$
$752$	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	0.409356	−	0.912375i	$-0.365754\pi$
$757$	−15.5548	−	18.9536i	−0.565350	−	0.688880i	−0.974705	+	0.223494i	$0.928254\pi$
$758$	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	−0.839203	−	0.543818i	$-0.816978\pi$
$761$	3.97875	−	20.0025i	0.144230	−	0.725091i	0.983433	−	0.181273i	$-0.0580218\pi$
$762$	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	0.115616	−	0.993294i	$-0.463116\pi$
$773$	−17.9619	−	9.60085i	−0.646045	−	0.345319i	−0.761661	+	0.647976i	$0.775616\pi$
$774$	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	0.668360	+	0.743838i	$0.266997\pi$
$787$	−8.43333	+	27.8009i	−0.300616	+	0.990997i	−0.968975	+	0.247158i	$0.920503\pi$
$788$	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	0.520758	−	0.853705i	$-0.325650\pi$
$797$	−6.06825	−	4.98009i	−0.214949	−	0.176404i	−0.735706	+	0.677301i	$0.763150\pi$
$798$	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	−0.651247	−	0.758866i	$-0.725754\pi$
$809$	8.50657	−	12.7310i	0.299075	−	0.447597i	0.950322	+	0.311268i	$0.100754\pi$
$810$	−3.41131	+	3.47837i	−0.119861	+	0.122218i
$811$	−1.49718	+	15.2011i	−0.0525730	+	0.533783i	0.932443	+	0.361318i	$0.117673\pi$
$811$	−1.49718	+	15.2011i	−0.0525730	+	0.533783i	−0.985016	+	0.172465i	$0.944827\pi$
$812$	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	−0.849640	−	0.527364i	$-0.823181\pi$
$821$	−14.2740	+	11.7144i	−0.498166	+	0.408834i	0.351474	+	0.936198i	$0.385681\pi$
$822$	−29.0534	−	11.7043i	−1.01335	−	0.408234i
$823$	−2.24759	−	11.2994i	−0.0783461	−	0.393872i	−0.999983	−	0.00581920i	$-0.998148\pi$
$823$	−2.24759	−	11.2994i	−0.0783461	−	0.393872i	0.921637	−	0.388053i	$-0.126852\pi$
$824$	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	−0.817592	−	0.575798i	$-0.804692\pi$
$827$	3.31851	−	6.20850i	0.115396	−	0.215891i	0.932988	+	0.359907i	$0.117192\pi$
$828$	−0.865673	+	4.84295i	−0.0300842	+	0.168304i
$829$	22.1923	−	2.18575i	0.770769	−	0.0759141i	0.295015	−	0.955493i	$-0.404675\pi$
$829$	22.1923	−	2.18575i	0.770769	−	0.0759141i	0.475754	+	0.879579i	$0.342175\pi$
$830$	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	0.544306	−	0.838887i	$-0.316793\pi$
$839$	21.0333	+	4.18378i	0.726150	+	0.144440i	0.181845	+	0.983327i	$0.441793\pi$
$840$	−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	−0.301539	−	0.953454i	$-0.597500\pi$
$853$	5.26341	−	53.4403i	0.180216	−	1.82976i	0.481754	−	0.876306i	$-0.340000\pi$
$854$	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	−0.406726	−	0.913550i	$-0.633330\pi$
$857$	8.24478	−	5.50899i	0.281636	−	0.188183i	0.688363	+	0.725367i	$0.258330\pi$
$858$	11.0404	−	7.53345i	0.376914	−	0.257188i
$859$	−11.7240	+	3.55644i	−0.400018	+	0.121344i	−0.483882	−	0.875133i	$-0.660774\pi$
$859$	−11.7240	+	3.55644i	−0.400018	+	0.121344i	0.0838645	+	0.996477i	$0.473274\pi$
$860$	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	−0.435887	−	0.900002i	$-0.643565\pi$
$863$	13.6342	−	13.6342i	0.464115	−	0.464115i	0.900002	+	0.435887i	$0.143565\pi$
$864$	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	0.561445	+	0.827514i	$0.310246\pi$
$877$	−10.8128	+	35.6450i	−0.365122	+	1.20365i	−0.926566	+	0.376131i	$0.877254\pi$
$878$	−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	−0.927226	−	0.374501i	$-0.877814\pi$
$881$	−0.200823	+	0.484831i	−0.00676592	+	0.0163344i	0.920460	+	0.390836i	$0.127814\pi$
$882$	−7.48506	+	6.26575i	−0.252035	+	0.210979i
$883$	−12.4421	−	23.2776i	−0.418711	−	0.783353i	0.580818	−	0.814033i	$-0.302733\pi$
$883$	−12.4421	−	23.2776i	−0.418711	−	0.783353i	−0.999529	+	0.0306799i	$0.990233\pi$
$884$	−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	−0.758059	−	0.652186i	$-0.773852\pi$
$887$	−36.0021	+	7.16127i	−1.20883	+	0.240452i	−0.450774	+	0.892638i	$0.648852\pi$
$888$	−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	0.810611	−	0.585585i	$-0.199135\pi$
$907$	2.35314	+	2.86731i	0.0781348	+	0.0952076i	−0.732476	+	0.680793i	$0.761635\pi$
$908$	−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	0.591246	+	0.806492i	$0.298636\pi$
$911$	−11.9857	+	28.9360i	−0.397104	+	0.958694i	−0.988349	+	0.152202i	$0.951364\pi$
$912$	−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	0.555105	−	0.831780i	$-0.312678\pi$
$919$	−0.0282128	−	0.0188512i	−0.000930655	−	0.000621844i	−0.556035	+	0.831159i	$0.687678\pi$
$920$	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	−0.951195	−	0.308589i	$-0.900143\pi$
$929$	−19.5863	+	19.5863i	−0.642606	+	0.642606i	0.308589	+	0.951195i	$0.400143\pi$
$930$	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	−0.707890	−	0.706322i	$-0.750353\pi$
$937$	6.59852	−	9.87538i	0.215564	−	0.322615i	0.923455	+	0.383708i	$0.125353\pi$
$938$	−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	−0.170476	−	0.985362i	$-0.554531\pi$
$941$	−26.3707	−	7.99946i	−0.859659	−	0.260775i	−0.689183	+	0.724587i	$0.742031\pi$
$942$	−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	−0.474983	−	0.879995i	$-0.657546\pi$
$947$	−0.220973	+	0.118113i	−0.00718066	+	0.00383814i	0.467802	+	0.883833i	$0.345046\pi$
$948$	−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	−0.0585184	−	0.998286i	$-0.518638\pi$
$953$	−15.2690	−	3.03718i	−0.494610	−	0.0983840i	−0.436092	+	0.899902i	$0.643638\pi$
$954$	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	0.798675	−	0.601762i	$-0.205534\pi$
$967$	40.6206	+	8.07994i	1.30627	+	0.259833i	0.507596	+	0.861595i	$0.330534\pi$
$968$	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	−0.589219	−	0.807973i	$-0.700565\pi$
$971$	2.75082	−	2.25754i	0.0882779	−	0.0724478i	0.677497	+	0.735525i	$0.263065\pi$
$972$	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	−0.773212	−	0.634148i	$-0.781351\pi$
$977$	−27.2419	+	11.2840i	−0.871545	+	0.361006i	−0.0983333	+	0.995154i	$0.531351\pi$
$978$	−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	−0.997941	−	0.0641358i	$-0.979571\pi$
$983$	−17.4570	+	26.1262i	−0.556792	+	0.833298i	0.441149	+	0.897434i	$0.354571\pi$
$984$	−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	−0.992955	−	0.118494i	$-0.962193\pi$
$991$	−27.5282	+	27.5282i	−0.874461	+	0.874461i	0.118494	+	0.992955i	$0.462193\pi$
$992$	−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	0.976555	−	0.215270i	$-0.0690632\pi$
$997$	1.42030	+	4.68211i	0.0449814	+	0.148284i	−0.931573	+	0.363554i	$0.881563\pi$
$998$	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.181.23	yes	512
128.29	even	32	inner	384.2.v.a.157.23	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.23	✓	512	128.29	even	32	inner
384.2.v.a.181.23	yes	512	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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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