LMFDB - Embedded newform 192.2.r.a.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

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("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	192.61
Dual form			192.2.r.a.85.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.796251 - 1.16875i) q^{2} +(0.195090 - 0.980785i) q^{3} +(-0.731968 + 1.86124i) q^{4} +(2.41595 + 1.61429i) q^{5} +(-1.30164 + 0.552939i) q^{6} +(1.09455 - 0.453379i) q^{7} +(2.75816 - 0.626527i) q^{8} +(-0.923880 - 0.382683i) q^{9} +O(q^{10})$	\(q+(-0.796251 - 1.16875i) q^{2} +(0.195090 - 0.980785i) q^{3} +(-0.731968 + 1.86124i) q^{4} +(2.41595 + 1.61429i) q^{5} +(-1.30164 + 0.552939i) q^{6} +(1.09455 - 0.453379i) q^{7} +(2.75816 - 0.626527i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(-0.0370012 - 4.10903i) q^{10} +(5.11927 - 1.01829i) q^{11} +(1.68268 + 1.08101i) q^{12} +(-3.73023 + 2.49246i) q^{13} +(-1.40143 - 0.918260i) q^{14} +(2.05460 - 2.05460i) q^{15} +(-2.92845 - 2.72474i) q^{16} +(-0.516827 - 0.516827i) q^{17} +(0.288378 + 1.38450i) q^{18} +(-2.92098 - 4.37155i) q^{19} +(-4.77298 + 3.31506i) q^{20} +(-0.231131 - 1.16197i) q^{21} +(-5.26635 - 5.17235i) q^{22} +(1.18470 - 2.86013i) q^{23} +(-0.0763975 - 2.82740i) q^{24} +(1.31748 + 3.18067i) q^{25} +(5.88328 + 2.37510i) q^{26} +(-0.555570 + 0.831470i) q^{27} +(0.0426702 + 2.36909i) q^{28} +(0.523666 + 0.104164i) q^{29} +(-4.03729 - 0.765341i) q^{30} +9.33809i q^{31} +(-0.852768 + 5.59221i) q^{32} -5.21956i q^{33} +(-0.192519 + 1.01557i) q^{34} +(3.37627 + 0.671583i) q^{35} +(1.38852 - 1.43945i) q^{36} +(3.58808 - 5.36994i) q^{37} +(-2.78343 + 6.89475i) q^{38} +(1.71684 + 4.14481i) q^{39} +(7.67498 + 2.93881i) q^{40} +(-3.54350 + 8.55477i) q^{41} +(-1.17402 + 1.19536i) q^{42} +(-0.828267 - 4.16398i) q^{43} +(-1.85186 + 10.2736i) q^{44} +(-1.61429 - 2.41595i) q^{45} +(-4.28611 + 0.892755i) q^{46} +(-1.07095 - 1.07095i) q^{47} +(-3.24370 + 2.34061i) q^{48} +(-3.95725 + 3.95725i) q^{49} +(2.66838 - 4.07242i) q^{50} +(-0.607724 + 0.406068i) q^{51} +(-1.90867 - 8.76727i) q^{52} +(3.79893 - 0.755654i) q^{53} +(1.41416 - 0.0127343i) q^{54} +(14.0117 + 5.80384i) q^{55} +(2.73491 - 1.93626i) q^{56} +(-4.85740 + 2.01200i) q^{57} +(-0.295228 - 0.694976i) q^{58} +(-10.0034 - 6.68404i) q^{59} +(2.32020 + 5.32800i) q^{60} +(-2.46666 + 12.4007i) q^{61} +(10.9139 - 7.43547i) q^{62} -1.18474 q^{63} +(7.21493 - 3.45613i) q^{64} -13.0356 q^{65} +(-6.10038 + 4.15608i) q^{66} +(-0.394189 + 1.98172i) q^{67} +(1.34024 - 0.583640i) q^{68} +(-2.57405 - 1.71992i) q^{69} +(-1.90345 - 4.48078i) q^{70} +(-0.0704826 + 0.0291948i) q^{71} +(-2.78797 - 0.476668i) q^{72} +(-10.6599 - 4.41547i) q^{73} +(-9.13314 + 0.0822428i) q^{74} +(3.37659 - 0.671645i) q^{75} +(10.2746 - 2.23681i) q^{76} +(5.14165 - 3.43554i) q^{77} +(3.47723 - 5.30687i) q^{78} +(-3.83034 + 3.83034i) q^{79} +(-2.67647 - 11.3102i) q^{80} +(0.707107 + 0.707107i) q^{81} +(12.8199 - 2.67027i) q^{82} +(-8.97007 - 13.4247i) q^{83} +(2.33189 + 0.420336i) q^{84} +(-0.414322 - 2.08294i) q^{85} +(-4.20716 + 4.28361i) q^{86} +(0.204324 - 0.493282i) q^{87} +(13.4818 - 6.01596i) q^{88} +(5.65060 + 13.6417i) q^{89} +(-1.53827 + 3.81041i) q^{90} +(-2.95291 + 4.41935i) q^{91} +(4.45623 + 4.29854i) q^{92} +(9.15866 + 1.82177i) q^{93} +(-0.398931 + 2.10442i) q^{94} -15.2767i q^{95} +(5.31839 + 1.92737i) q^{96} -3.93894i q^{97} +(7.77601 + 1.47408i) q^{98} +(-5.11927 - 1.01829i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	−0.796251	−	1.16875i	−0.563035	−	0.826433i
$2$	−0.796251	−	1.16875i	−0.563035	−	0.826433i
$3$	0.195090	−	0.980785i	0.112635	−	0.566257i
$3$	0.195090	−	0.980785i	0.112635	−	0.566257i
$4$	−0.731968	+	1.86124i	−0.365984	+	0.930621i
$5$	2.41595	+	1.61429i	1.08045	+	0.721931i	0.962552	−	0.271095i	$-0.0873859\pi$
$5$	2.41595	+	1.61429i	1.08045	+	0.721931i	0.117893	+	0.993026i	$0.462386\pi$
$6$	−1.30164	+	0.552939i	−0.531391	+	0.225736i
$7$	1.09455	−	0.453379i	0.413703	−	0.171361i	−0.166117	−	0.986106i	$-0.553123\pi$
$7$	1.09455	−	0.453379i	0.413703	−	0.171361i	0.579820	+	0.814745i	$0.303123\pi$
$8$	2.75816	−	0.626527i	0.975158	−	0.221511i
$9$	−0.923880	−	0.382683i	−0.307960	−	0.127561i
$10$	−0.0370012	−	4.10903i	−0.0117008	−	1.29939i
$11$	5.11927	−	1.01829i	1.54352	−	0.307025i	0.651367	−	0.758763i	$-0.274196\pi$
$11$	5.11927	−	1.01829i	1.54352	−	0.307025i	0.892151	+	0.451738i	$0.149196\pi$
$12$	1.68268	+	1.08101i	0.485748	+	0.312062i
$13$	−3.73023	+	2.49246i	−1.03458	+	0.691285i	−0.952250	−	0.305320i	$-0.901236\pi$
$13$	−3.73023	+	2.49246i	−1.03458	+	0.691285i	−0.0823310	+	0.996605i	$0.526236\pi$
$14$	−1.40143	−	0.918260i	−0.374548	−	0.245415i
$15$	2.05460	−	2.05460i	0.530495	−	0.530495i
$16$	−2.92845	−	2.72474i	−0.732112	−	0.681185i
$17$	−0.516827	−	0.516827i	−0.125349	−	0.125349i	0.641649	−	0.766998i	$-0.278250\pi$
$17$	−0.516827	−	0.516827i	−0.125349	−	0.125349i	−0.766998	+	0.641649i	$0.778250\pi$
$18$	0.288378	+	1.38450i	0.0679713	+	0.326330i
$19$	−2.92098	−	4.37155i	−0.670118	−	1.00290i	−0.998300	−	0.0582875i	$-0.981436\pi$
$19$	−2.92098	−	4.37155i	−0.670118	−	1.00290i	0.328182	−	0.944614i	$-0.393564\pi$
$20$	−4.77298	+	3.31506i	−1.06727	+	0.741271i
$21$	−0.231131	−	1.16197i	−0.0504369	−	0.253563i
$22$	−5.26635	−	5.17235i	−1.12279	−	1.10275i
$23$	1.18470	−	2.86013i	0.247028	−	0.596378i	−0.750921	−	0.660392i	$-0.770390\pi$
$23$	1.18470	−	2.86013i	0.247028	−	0.596378i	0.997949	+	0.0640137i	$0.0203901\pi$
$24$	−0.0763975	−	2.82740i	−0.0155946	−	0.577140i
$25$	1.31748	+	3.18067i	0.263496	+	0.636135i
$26$	5.88328	+	2.37510i	1.15381	+	0.465795i
$27$	−0.555570	+	0.831470i	−0.106920	+	0.160016i
$28$	0.0426702	+	2.36909i	0.00806390	+	0.447716i
$29$	0.523666	+	0.104164i	0.0972423	+	0.0193427i	0.243472	−	0.969908i	$-0.421714\pi$
$29$	0.523666	+	0.104164i	0.0972423	+	0.0193427i	−0.146229	+	0.989251i	$0.546714\pi$
$30$	−4.03729	−	0.765341i	−0.737105	−	0.139732i
$31$			9.33809i			1.67717i	0.544770	+	0.838585i	$0.316617\pi$
$31$			9.33809i			1.67717i	−0.544770	+	0.838585i	$0.683383\pi$
$32$	−0.852768	+	5.59221i	−0.150750	+	0.988572i
$33$		−	5.21956i		−	0.908609i
$34$	−0.192519	+	1.01557i	−0.0330167	+	0.174168i
$35$	3.37627	+	0.671583i	0.570694	+	0.113518i
$36$	1.38852	−	1.43945i	0.231419	−	0.239909i
$37$	3.58808	−	5.36994i	0.589876	−	0.882812i	−0.409691	−	0.912224i	$-0.634363\pi$
$37$	3.58808	−	5.36994i	0.589876	−	0.882812i	0.999567	+	0.0294119i	$0.00936346\pi$
$38$	−2.78343	+	6.89475i	−0.451532	+	1.11848i
$39$	1.71684	+	4.14481i	0.274914	+	0.663701i
$40$	7.67498	+	2.93881i	1.21352	+	0.464666i
$41$	−3.54350	+	8.55477i	−0.553402	+	1.33603i	0.361507	+	0.932369i	$0.382262\pi$
$41$	−3.54350	+	8.55477i	−0.553402	+	1.33603i	−0.914909	+	0.403661i	$0.867738\pi$
$42$	−1.17402	+	1.19536i	−0.181155	+	0.184448i
$43$	−0.828267	−	4.16398i	−0.126310	−	0.635001i	−0.991127	−	0.132915i	$-0.957566\pi$
$43$	−0.828267	−	4.16398i	−0.126310	−	0.635001i	0.864818	−	0.502086i	$-0.167434\pi$
$44$	−1.85186	+	10.2736i	−0.279179	+	1.54880i
$45$	−1.61429	−	2.41595i	−0.240644	−	0.360149i
$46$	−4.28611	+	0.892755i	−0.631952	+	0.131630i
$47$	−1.07095	−	1.07095i	−0.156214	−	0.156214i	0.624673	−	0.780887i	$-0.285232\pi$
$47$	−1.07095	−	1.07095i	−0.156214	−	0.156214i	−0.780887	+	0.624673i	$0.785232\pi$
$48$	−3.24370	+	2.34061i	−0.468187	+	0.337837i
$49$	−3.95725	+	3.95725i	−0.565321	+	0.565321i
$50$	2.66838	−	4.07242i	0.377366	−	0.575927i
$51$	−0.607724	+	0.406068i	−0.0850984	+	0.0568609i
$52$	−1.90867	−	8.76727i	−0.264684	−	1.21580i
$53$	3.79893	−	0.755654i	0.521823	−	0.103797i	0.0728510	−	0.997343i	$-0.476790\pi$
$53$	3.79893	−	0.755654i	0.521823	−	0.103797i	0.448972	+	0.893546i	$0.351790\pi$
$54$	1.41416	−	0.0127343i	0.192442	−	0.00173292i
$55$	14.0117	+	5.80384i	1.88934	+	0.782589i
$56$	2.73491	−	1.93626i	0.365467	−	0.258744i
$57$	−4.85740	+	2.01200i	−0.643379	+	0.266496i
$58$	−0.295228	−	0.694976i	−0.0387653	−	0.0912549i
$59$	−10.0034	−	6.68404i	−1.30233	−	0.870187i	−0.305690	−	0.952131i	$-0.598887\pi$
$59$	−10.0034	−	6.68404i	−1.30233	−	0.870187i	−0.996637	+	0.0819436i	$0.973887\pi$
$60$	2.32020	+	5.32800i	0.299537	+	0.687842i
$61$	−2.46666	+	12.4007i	−0.315823	+	1.58775i	0.418024	+	0.908436i	$0.362723\pi$
$61$	−2.46666	+	12.4007i	−0.315823	+	1.58775i	−0.733847	+	0.679314i	$0.762277\pi$
$62$	10.9139	−	7.43547i	1.38607	−	0.944305i
$63$	−1.18474			−0.149263
$64$	7.21493	−	3.45613i	0.901866	−	0.432016i
$65$	−13.0356			−1.61687
$66$	−6.10038	+	4.15608i	−0.750905	+	0.511578i
$67$	−0.394189	+	1.98172i	−0.0481578	+	0.242106i	−0.997365	−	0.0725458i	$-0.976888\pi$
$67$	−0.394189	+	1.98172i	−0.0481578	+	0.242106i	0.949207	+	0.314652i	$0.101888\pi$
$68$	1.34024	−	0.583640i	0.162528	−	0.0707767i
$69$	−2.57405	−	1.71992i	−0.309879	−	0.207055i
$70$	−1.90345	−	4.48078i	−0.227506	−	0.535556i
$71$	−0.0704826	+	0.0291948i	−0.00836474	+	0.00346479i	−0.386862	−	0.922138i	$-0.626441\pi$
$71$	−0.0704826	+	0.0291948i	−0.00836474	+	0.00346479i	0.378497	+	0.925602i	$0.376441\pi$
$72$	−2.78797	−	0.476668i	−0.328566	−	0.0561759i
$73$	−10.6599	−	4.41547i	−1.24765	−	0.516792i	−0.341550	−	0.939864i	$-0.610952\pi$
$73$	−10.6599	−	4.41547i	−1.24765	−	0.516792i	−0.906096	+	0.423072i	$0.860952\pi$
$74$	−9.13314	+	0.0822428i	−1.06171	+	0.00956053i
$75$	3.37659	−	0.671645i	0.389894	−	0.0775548i
$76$	10.2746	−	2.23681i	1.17857	−	0.256580i
$77$	5.14165	−	3.43554i	0.585945	−	0.391516i
$78$	3.47723	−	5.30687i	0.393719	−	0.600885i
$79$	−3.83034	+	3.83034i	−0.430947	+	0.430947i	−0.888950	−	0.458004i	$-0.848565\pi$
$79$	−3.83034	+	3.83034i	−0.430947	+	0.430947i	0.458004	+	0.888950i	$0.348565\pi$
$80$	−2.67647	−	11.3102i	−0.299239	−	1.26452i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	12.8199	−	2.67027i	1.41572	−	0.294882i
$83$	−8.97007	−	13.4247i	−0.984593	−	1.47355i	−0.877662	−	0.479281i	$-0.840898\pi$
$83$	−8.97007	−	13.4247i	−0.984593	−	1.47355i	−0.106931	−	0.994266i	$-0.534102\pi$
$84$	2.33189	+	0.420336i	0.254430	+	0.0458625i
$85$	−0.414322	−	2.08294i	−0.0449395	−	0.225926i
$86$	−4.20716	+	4.28361i	−0.453669	+	0.461914i
$87$	0.204324	−	0.493282i	0.0219059	−	0.0528854i
$88$	13.4818	−	6.01596i	1.43716	−	0.641303i
$89$	5.65060	+	13.6417i	0.598962	+	1.44602i	0.874640	+	0.484772i	$0.161098\pi$
$89$	5.65060	+	13.6417i	0.598962	+	1.44602i	−0.275678	+	0.961250i	$0.588902\pi$
$90$	−1.53827	+	3.81041i	−0.162148	+	0.401652i
$91$	−2.95291	+	4.41935i	−0.309549	+	0.463274i
$92$	4.45623	+	4.29854i	0.464594	+	0.448154i
$93$	9.15866	+	1.82177i	0.949709	+	0.188909i
$94$	−0.398931	+	2.10442i	−0.0411466	+	0.217055i
$95$		−	15.2767i		−	1.56736i
$96$	5.31839	+	1.92737i	0.542806	+	0.196711i
$97$		−	3.93894i		−	0.399939i	−0.979802	−	0.199970i	$-0.935916\pi$
$97$		−	3.93894i		−	0.399939i	0.979802	−	0.199970i	$-0.0640843\pi$
$98$	7.77601	+	1.47408i	0.785496	+	0.148905i
$99$	−5.11927	−	1.01829i	−0.514506	−	0.102342i
$100$	−6.88436	+	0.123995i	−0.688436	+	0.0123995i
$101$	6.13787	−	9.18598i	0.610741	−	0.914039i	−0.389233	−	0.921139i	$-0.627260\pi$
$101$	6.13787	−	9.18598i	0.610741	−	0.914039i	0.999975	+	0.00710011i	$0.00226005\pi$
$102$	0.958495	+	0.386947i	0.0949051	+	0.0383135i
$103$	2.83230	+	6.83778i	0.279075	+	0.673746i	0.999811	−	0.0194638i	$-0.00619591\pi$
$103$	2.83230	+	6.83778i	0.279075	+	0.673746i	−0.720736	+	0.693210i	$0.756196\pi$
$104$	−8.72700	+	9.21171i	−0.855753	+	0.903283i
$105$	1.31736	−	3.18038i	0.128561	−	0.310373i
$106$	−3.90808	−	3.83832i	−0.379586	−	0.372811i
$107$	2.01439	+	10.1270i	0.194738	+	0.979016i	0.947264	+	0.320454i	$0.103835\pi$
$107$	2.01439	+	10.1270i	0.194738	+	0.979016i	−0.752526	+	0.658563i	$0.771165\pi$
$108$	−1.14091	−	1.64266i	−0.109784	−	0.158065i
$109$	−8.37442	−	12.5332i	−0.802124	−	1.20046i	−0.976443	−	0.215774i	$-0.930772\pi$
$109$	−8.37442	−	12.5332i	−0.802124	−	1.20046i	0.174319	−	0.984689i	$-0.444228\pi$
$110$	−4.37358	−	20.9975i	−0.417005	−	2.00204i
$111$	−4.56676	−	4.56676i	−0.433457	−	0.433457i
$112$	−4.44069	−	1.65468i	−0.419605	−	0.156352i
$113$	−0.125336	+	0.125336i	−0.0117907	+	0.0117907i	−0.712978	−	0.701187i	$-0.752654\pi$
$113$	−0.125336	+	0.125336i	−0.0117907	+	0.0117907i	0.701187	+	0.712978i	$0.252654\pi$
$114$	6.21925	+	4.07505i	0.582486	+	0.381663i
$115$	7.47926	−	4.99748i	0.697444	−	0.466017i
$116$	−0.577180	+	0.898425i	−0.0535898	+	0.0834166i
$117$	4.40011	−	0.875236i	0.406790	−	0.0809156i
$118$	0.153206	+	17.0136i	0.0141037	+	1.56623i
$119$	−0.800014	−	0.331377i	−0.0733372	−	0.0303773i
$120$	4.37965	−	6.95417i	0.399806	−	0.634826i
$121$	15.0073	−	6.21624i	1.36430	−	0.565113i
$122$	16.4575	−	6.99118i	1.48999	−	0.632952i
$123$	7.69909	+	5.14437i	0.694203	+	0.463852i
$124$	−17.3805	−	6.83518i	−1.56081	−	0.613818i
$125$	0.882754	−	4.43790i	0.0789559	−	0.396938i
$126$	0.943349	+	1.38467i	0.0840402	+	0.123356i
$127$	−11.1669			−0.990901			−0.495450	−	0.868636i	$-0.664997\pi$
$127$	−11.1669			−0.990901			−0.495450	+	0.868636i	$0.664997\pi$
$128$	−9.78426	−	5.68052i	−0.864814	−	0.502092i
$129$	−4.24556			−0.373801
$130$	10.3796	+	15.2354i	0.910353	+	1.33623i
$131$	2.53280	−	12.7332i	0.221292	−	1.11251i	−0.697142	−	0.716933i	$-0.745545\pi$
$131$	2.53280	−	12.7332i	0.221292	−	1.11251i	0.918433	−	0.395576i	$-0.129455\pi$
$132$	9.71487	+	3.82055i	0.845571	+	0.332536i
$133$	−5.17914	−	3.46059i	−0.449088	−	0.300071i
$134$	2.63002	−	1.11724i	0.227199	−	0.0965147i
$135$	−2.68446	+	1.11194i	−0.231042	+	0.0957005i
$136$	−1.74930	−	1.10169i	−0.150001	−	0.0944689i
$137$	2.23903	+	0.927436i	0.191293	+	0.0792362i	0.476274	−	0.879297i	$-0.341987\pi$
$137$	2.23903	+	0.927436i	0.191293	+	0.0792362i	−0.284981	+	0.958533i	$0.591987\pi$
$138$	0.0394226	+	4.37792i	0.00335587	+	0.372673i
$139$	−2.95706	+	0.588197i	−0.250815	+	0.0498902i	−0.318896	−	0.947790i	$-0.603312\pi$
$139$	−2.95706	+	0.588197i	−0.250815	+	0.0498902i	0.0680815	+	0.997680i	$0.478312\pi$
$140$	−3.72130	+	5.79249i	−0.314507	+	0.489555i
$141$	−1.25930	+	0.841440i	−0.106053	+	0.0708620i
$142$	0.0902434	+	0.0591303i	0.00757306	+	0.00496210i
$143$	−16.5580	+	16.5580i	−1.38465	+	1.38465i
$144$	1.66282	+	3.63800i	0.138568	+	0.303167i
$145$	1.09700	+	1.09700i	0.0911009	+	0.0911009i
$146$	3.32736	+	15.9746i	0.275374	+	1.32207i
$147$	3.10919	+	4.65323i	0.256442	+	0.383792i
$148$	7.36840	+	10.6089i	0.605679	+	0.872047i
$149$	3.75414	+	18.8734i	0.307551	+	1.54617i	0.757334	+	0.653027i	$0.226501\pi$
$149$	3.75414	+	18.8734i	0.307551	+	1.54617i	−0.449783	+	0.893138i	$0.648499\pi$
$150$	−3.47360	−	3.41160i	−0.283618	−	0.278556i
$151$	−4.40228	+	10.6281i	−0.358253	+	0.864899i	0.637293	+	0.770621i	$0.280054\pi$
$151$	−4.40228	+	10.6281i	−0.358253	+	0.864899i	−0.995546	+	0.0942773i	$0.969946\pi$
$152$	−10.7954	−	10.2274i	−0.875624	−	0.829550i
$153$	0.279705	+	0.675267i	0.0226128	+	0.0545921i
$154$	−8.10934	−	3.27377i	−0.653470	−	0.263808i
$155$	−15.0744	+	22.5604i	−1.21080	+	1.81209i
$156$	−8.97117	+	0.161582i	−0.718269	+	0.0129369i
$157$	1.73052	+	0.344221i	0.138110	+	0.0274719i	0.263661	−	0.964615i	$-0.415070\pi$
$157$	1.73052	+	0.344221i	0.138110	+	0.0274719i	−0.125551	+	0.992087i	$0.540070\pi$
$158$	7.52663	+	1.42681i	0.598786	+	0.113511i
$159$		−	3.87336i		−	0.307177i
$160$	−11.0877	+	12.1339i	−0.876557	+	0.959268i
$161$		−	3.66769i		−	0.289054i
$162$	0.263399	−	1.38947i	0.0206945	−	0.109167i
$163$	7.45340	+	1.48257i	0.583796	+	0.116124i	0.478148	−	0.878279i	$-0.341308\pi$
$163$	7.45340	+	1.48257i	0.583796	+	0.116124i	0.105648	+	0.994404i	$0.466308\pi$
$164$	−13.3288	−	12.8571i	−1.04080	−	1.00397i
$165$	8.42587	−	12.6102i	0.655953	−	0.981703i
$166$	−8.54768	+	21.1732i	−0.663428	+	1.64336i
$167$	−4.28493	−	10.3447i	−0.331578	−	0.800500i	−0.998467	−	0.0553433i	$-0.982375\pi$
$167$	−4.28493	−	10.3447i	−0.331578	−	0.800500i	0.666889	−	0.745157i	$-0.267625\pi$
$168$	−1.36550	−	3.06010i	−0.105351	−	0.236092i
$169$	2.72739	−	6.58450i	0.209799	−	0.506500i
$170$	−2.10453	+	2.14278i	−0.161410	+	0.164344i
$171$	1.02571	+	5.15659i	0.0784380	+	0.394335i
$172$	8.35644	+	1.50629i	0.637173	+	0.114854i
$173$	8.84846	+	13.2427i	0.672736	+	1.00682i	0.998123	+	0.0612394i	$0.0195053\pi$
$173$	8.84846	+	13.2427i	0.672736	+	1.00682i	−0.325387	+	0.945581i	$0.605495\pi$
$174$	−0.739219	+	0.153972i	−0.0560400	+	0.0116726i
$175$	2.88410	+	2.88410i	0.218018	+	0.218018i
$176$	−17.7661	−	10.9667i	−1.33917	−	0.826644i
$177$	−8.50716	+	8.50716i	−0.639438	+	0.639438i
$178$	11.4445	−	17.4664i	0.857804	−	1.30916i
$179$	4.13382	−	2.76213i	0.308976	−	0.206451i	−0.391408	−	0.920217i	$-0.628012\pi$
$179$	4.13382	−	2.76213i	0.308976	−	0.206451i	0.700384	+	0.713766i	$0.253012\pi$
$180$	5.67827	−	1.23618i	0.423234	−	0.0921394i
$181$	21.1385	−	4.20472i	1.57121	−	0.312534i	0.668813	−	0.743430i	$-0.266803\pi$
$181$	21.1385	−	4.20472i	1.57121	−	0.312534i	0.902401	+	0.430896i	$0.141803\pi$
$182$	7.51639	−	0.0676841i	0.557152	−	0.00501708i
$183$	11.6812	+	4.83852i	0.863501	+	0.357674i
$184$	1.47566	−	8.63095i	0.108787	−	0.636282i
$185$	17.3372	−	7.18132i	1.27466	−	0.527981i
$186$	−5.16340	−	12.1548i	−0.378599	−	0.891233i
$187$	−3.17205	−	2.11950i	−0.231964	−	0.154993i
$188$	2.77720	−	1.20940i	0.202548	−	0.0882043i
$189$	−0.231131	+	1.16197i	−0.0168123	+	0.0845211i
$190$	−17.8547	+	12.1641i	−1.29532	+	0.882478i
$191$	10.3424			0.748353			0.374177	−	0.927357i	$-0.377925\pi$
$191$	10.3424			0.748353			0.374177	+	0.927357i	$0.377925\pi$
$192$	−1.98216	−	7.75055i	−0.143050	−	0.559348i
$193$	17.5764			1.26517			0.632587	−	0.774489i	$-0.281993\pi$
$193$	17.5764			1.26517			0.632587	+	0.774489i	$0.281993\pi$
$194$	−4.60365	+	3.13639i	−0.330523	+	0.225180i
$195$	−2.54312	+	12.7851i	−0.182117	+	0.915562i
$196$	−4.46882	−	10.2620i	−0.319202	−	0.732999i
$197$	−5.63403	−	3.76454i	−0.401408	−	0.268212i	0.338438	−	0.940989i	$-0.390101\pi$
$197$	−5.63403	−	3.76454i	−0.401408	−	0.268212i	−0.739846	+	0.672777i	$0.765101\pi$
$198$	2.88610	+	6.79397i	0.205106	+	0.482827i
$199$	−5.40441	+	2.23858i	−0.383108	+	0.158689i	−0.565922	−	0.824459i	$-0.691480\pi$
$199$	−5.40441	+	2.23858i	−0.383108	+	0.158689i	0.182813	+	0.983148i	$0.441480\pi$
$200$	5.62660	+	7.94738i	0.397861	+	0.561965i
$201$	1.86674	+	0.773229i	0.131670	+	0.0545394i
$202$	−15.6234	+	0.140687i	−1.09926	+	0.00989870i
$203$	0.620407	−	0.123407i	0.0435440	−	0.00866144i
$204$	−0.310957	−	1.42835i	−0.0217713	−	0.100005i
$205$	−22.3708	+	14.9477i	−1.56244	+	1.04399i
$206$	5.73645	−	8.75485i	0.399677	−	0.609979i
$207$	−2.18905	+	2.18905i	−0.152149	+	0.152149i
$208$	17.7151	+	2.86487i	1.22832	+	0.198643i
$209$	−19.4047	−	19.4047i	−1.34225	−	1.34225i
$210$	−4.76603	+	0.992717i	−0.328887	+	0.0685040i
$211$	−10.2397	−	15.3248i	−0.704931	−	1.05500i	−0.995181	−	0.0980534i	$-0.968738\pi$
$211$	−10.2397	−	15.3248i	−0.704931	−	1.05500i	0.290250	−	0.956951i	$-0.406262\pi$
$212$	−1.37424	+	7.62384i	−0.0943831	+	0.523608i
$213$	0.0148834	+	0.0748239i	0.00101979	+	0.00512685i
$214$	10.2320	−	10.4180i	0.699447	−	0.712159i
$215$	4.72080	−	11.3970i	0.321956	−	0.777271i
$216$	−1.01142	+	2.64141i	−0.0688181	+	0.179725i
$217$	4.23370	+	10.2211i	0.287402	+	0.693850i
$218$	−7.98008	+	19.7672i	−0.540479	+	1.33880i
$219$	−6.41027	+	9.59365i	−0.433166	+	0.648279i
$220$	−21.0585	+	21.8310i	−1.41976	+	1.47184i
$221$	3.21606	+	0.639714i	0.216335	+	0.0430318i
$222$	−1.70113	+	8.97370i	−0.114172	+	0.602275i
$223$		−	16.9141i		−	1.13265i	−0.824181	−	0.566326i	$-0.808364\pi$
$223$		−	16.9141i		−	1.13265i	0.824181	−	0.566326i	$-0.191636\pi$
$224$	1.60199	+	6.50760i	0.107037	+	0.434808i
$225$		−	3.44274i		−	0.229516i
$226$	0.246286	+	0.0466880i	0.0163827	+	0.00310564i
$227$	13.5902	+	2.70326i	0.902015	+	0.179422i	0.624248	−	0.781227i	$-0.285406\pi$
$227$	13.5902	+	2.70326i	0.902015	+	0.179422i	0.277767	+	0.960648i	$0.410406\pi$
$228$	−0.189361	−	10.5135i	−0.0125408	−	0.696275i
$229$	−7.54671	+	11.2944i	−0.498700	+	0.746358i	−0.992371	−	0.123291i	$-0.960655\pi$
$229$	−7.54671	+	11.2944i	−0.498700	+	0.746358i	0.493670	+	0.869649i	$0.335655\pi$
$230$	−11.7962	−	4.76215i	−0.777817	−	0.314007i
$231$	−2.36644	−	5.71310i	−0.155700	−	0.375894i
$232$	1.50962	−	0.0407905i	0.0991112	−	0.00267803i
$233$	6.82763	−	16.4834i	0.447293	−	1.07986i	−0.526039	−	0.850460i	$-0.676323\pi$
$233$	6.82763	−	16.4834i	0.447293	−	1.07986i	0.973332	−	0.229401i	$-0.0736766\pi$
$234$	−4.52653	−	4.44574i	−0.295908	−	0.290627i
$235$	−0.858542	−	4.31618i	−0.0560051	−	0.281557i
$236$	19.7628	−	13.7262i	1.28645	−	0.893499i
$237$	3.00948	+	4.50400i	0.195486	+	0.292566i
$238$	0.249715	+	1.19888i	0.0161866	+	0.0777117i
$239$	9.36327	+	9.36327i	0.605660	+	0.605660i	0.941809	−	0.336149i	$-0.109125\pi$
$239$	9.36327	+	9.36327i	0.605660	+	0.605660i	−0.336149	+	0.941809i	$0.609125\pi$
$240$	−11.6150	+	0.418536i	−0.749746	+	0.0270164i
$241$	14.2158	−	14.2158i	0.915718	−	0.915718i	−0.0809960	−	0.996714i	$-0.525810\pi$
$241$	14.2158	−	14.2158i	0.915718	−	0.915718i	0.996714	+	0.0809960i	$0.0258101\pi$
$242$	−19.2149	−	12.5902i	−1.23518	−	0.809327i
$243$	0.831470	−	0.555570i	0.0533388	−	0.0356398i
$244$	−21.2752	−	13.6680i	−1.36201	−	0.875003i
$245$	−15.9487	+	3.17238i	−1.01892	+	0.202676i
$246$	−0.117915	−	13.0945i	−0.00751796	−	0.834877i
$247$	21.7918	+	9.02648i	1.38658	+	0.574341i
$248$	5.85057	+	25.7560i	0.371511	+	1.63551i
$249$	−14.9167	+	6.17869i	−0.945306	+	0.391558i
$250$	−5.88971	+	2.50196i	−0.372498	+	0.158238i
$251$	−5.62659	−	3.75956i	−0.355147	−	0.237302i	0.365179	−	0.930937i	$-0.381008\pi$
$251$	−5.62659	−	3.75956i	−0.355147	−	0.237302i	−0.720326	+	0.693636i	$0.756008\pi$
$252$	0.867190	−	2.20508i	0.0546278	−	0.138907i
$253$	3.15239	−	15.8481i	0.198189	−	0.996364i
$254$	8.89165	+	13.0513i	0.557912	+	0.818914i
$255$	−2.12374			−0.132994
$256$	1.15160	+	15.9585i	0.0719747	+	0.997406i
$257$	19.0646			1.18922			0.594609	−	0.804015i	$-0.297307\pi$
$257$	19.0646			1.18922			0.594609	+	0.804015i	$0.297307\pi$
$258$	3.38053	+	4.96201i	0.210463	+	0.308921i
$259$	1.49273	−	7.50445i	0.0927536	−	0.466304i
$260$	9.54165	−	24.2624i	0.591748	−	1.50469i
$261$	−0.443942	−	0.296633i	−0.0274793	−	0.0183611i
$262$	−16.8988	+	7.17865i	−1.04401	+	0.443498i
$263$	−1.51777	+	0.628681i	−0.0935898	+	0.0387662i	−0.428987	−	0.903311i	$-0.641129\pi$
$263$	−1.51777	+	0.628681i	−0.0935898	+	0.0387662i	0.335397	+	0.942077i	$0.391129\pi$
$264$	−3.27020	−	14.3964i	−0.201267	−	0.886037i
$265$	10.3979	+	4.30694i	0.638736	+	0.264573i
$266$	0.0793206	+	8.80863i	0.00486346	+	0.540092i
$267$	14.4820	−	2.88065i	0.886284	−	0.176293i
$268$	−3.39993	−	2.18424i	−0.207684	−	0.133424i
$269$	−15.0009	+	10.0233i	−0.914622	+	0.611131i	−0.921303	−	0.388847i	$-0.872874\pi$
$269$	−15.0009	+	10.0233i	−0.914622	+	0.611131i	0.00668013	+	0.999978i	$0.497874\pi$
$270$	3.43709	+	2.25209i	0.209175	+	0.137058i
$271$	−1.07768	+	1.07768i	−0.0654641	+	0.0654641i	−0.739081	−	0.673617i	$-0.764740\pi$
$271$	−1.07768	+	1.07768i	−0.0654641	+	0.0654641i	0.673617	+	0.739081i	$0.264740\pi$
$272$	0.105281	+	2.92172i	0.00638363	+	0.177155i
$273$	3.75835	+	3.75835i	0.227465	+	0.227465i
$274$	−0.698886	−	3.35534i	−0.0422212	−	0.202704i
$275$	9.98336	+	14.9412i	0.602019	+	0.900985i
$276$	5.08532	−	3.53200i	0.306100	−	0.212601i
$277$	−2.53645	−	12.7516i	−0.152400	−	0.766168i	−0.979077	−	0.203491i	$-0.934771\pi$
$277$	−2.53645	−	12.7516i	−0.152400	−	0.766168i	0.826677	−	0.562677i	$-0.190229\pi$
$278$	3.04202	+	2.98773i	0.182448	+	0.179192i
$279$	3.57353	−	8.62727i	0.213942	−	0.516501i
$280$	9.73308	−	0.262992i	0.581663	−	0.0157168i
$281$	8.89914	+	21.4844i	0.530878	+	1.28165i	0.930943	+	0.365166i	$0.118988\pi$
$281$	8.89914	+	21.4844i	0.530878	+	1.28165i	−0.400065	+	0.916487i	$0.631012\pi$
$282$	1.98616	+	0.801818i	0.118274	+	0.0477476i
$283$	9.44146	−	14.1301i	0.561237	−	0.839950i	−0.436991	−	0.899466i	$-0.643956\pi$
$283$	9.44146	−	14.1301i	0.561237	−	0.839950i	0.998227	+	0.0595160i	$0.0189557\pi$
$284$	−0.00274769	−	0.152555i	−0.000163046	−	0.00905246i
$285$	−14.9832	−	2.98034i	−0.887528	−	0.176540i
$286$	32.5366	+	6.16790i	1.92393	+	0.364715i
$287$			10.9702i			0.647551i
$288$	2.92790	−	4.84019i	0.172528	−	0.285211i
$289$		−	16.4658i		−	0.968575i
$290$	0.408635	−	2.15561i	0.0239959	−	0.126582i
$291$	−3.86326	−	0.768450i	−0.226468	−	0.0450473i
$292$	16.0210	−	16.6087i	0.937556	−	0.971949i
$293$	4.51563	−	6.75812i	0.263806	−	0.394813i	−0.675793	−	0.737092i	$-0.736199\pi$
$293$	4.51563	−	6.75812i	0.263806	−	0.394813i	0.939599	+	0.342278i	$0.111199\pi$
$294$	2.96278	−	7.33902i	0.172793	−	0.428020i
$295$	−13.3777	−	32.2966i	−0.778879	−	1.88038i
$296$	6.53209	−	17.0592i	0.379670	−	0.991546i
$297$	−1.99744	+	4.82225i	−0.115903	+	0.279815i
$298$	19.0690	−	19.4156i	1.10464	−	1.12472i
$299$	2.70954	+	13.6218i	0.156697	+	0.787768i
$300$	−1.22146	+	6.77627i	−0.0705209	+	0.391228i
$301$	−2.79445	−	4.18219i	−0.161069	−	0.241057i
$302$	15.9269	−	3.31742i	0.916490	−	0.190896i
$303$	−7.81203	−	7.81203i	−0.448790	−	0.448790i
$304$	−3.35741	+	20.7607i	−0.192561	+	1.19071i
$305$	−25.9776	+	25.9776i	−1.48748	+	1.48748i
$306$	0.566505	−	0.864588i	0.0323849	−	0.0494252i
$307$	−21.5889	+	14.4252i	−1.23214	+	0.823292i	−0.989175	−	0.146742i	$-0.953121\pi$
$307$	−21.5889	+	14.4252i	−1.23214	+	0.823292i	−0.242969	+	0.970034i	$0.578121\pi$
$308$	2.63085	+	12.0846i	0.149907	+	0.688582i
$309$	7.25894	−	1.44389i	0.412947	−	0.0821402i
$310$	38.3705	−	0.345521i	2.17930	−	0.0196243i
$311$	−3.61751	−	1.49842i	−0.205130	−	0.0849678i	0.277753	−	0.960653i	$-0.410410\pi$
$311$	−3.61751	−	1.49842i	−0.205130	−	0.0849678i	−0.482883	+	0.875685i	$0.660410\pi$
$312$	7.33216	+	10.3564i	0.415102	+	0.586317i
$313$	−6.92151	+	2.86698i	−0.391227	+	0.162052i	−0.569621	−	0.821908i	$-0.692910\pi$
$313$	−6.92151	+	2.86698i	−0.391227	+	0.162052i	0.178394	+	0.983959i	$0.442910\pi$
$314$	−0.975617	−	2.29664i	−0.0550573	−	0.129607i
$315$	−2.86227	−	1.91251i	−0.161270	−	0.107757i
$316$	−4.32550	−	9.93287i	−0.243328	−	0.558767i
$317$	4.76778	−	23.9692i	0.267785	−	1.34625i	−0.579441	−	0.815014i	$-0.696729\pi$
$317$	4.76778	−	23.9692i	0.267785	−	1.34625i	0.847226	−	0.531232i	$-0.178271\pi$
$318$	−4.52700	+	3.08416i	−0.253861	+	0.172951i
$319$	2.78685			0.156034
$320$	23.0101	+	3.29713i	1.28630	+	0.184315i
$321$	10.3254			0.576309
$322$	−4.28662	+	2.92040i	−0.238884	+	0.162748i
$323$	−0.749695	+	3.76897i	−0.0417142	+	0.209711i
$324$	−1.83368	+	0.798518i	−0.101871	+	0.0443621i
$325$	−12.8422	−	8.58089i	−0.712358	−	0.475982i
$326$	−4.20202	−	9.89169i	−0.232728	−	0.547850i
$327$	−13.9262	+	5.76840i	−0.770118	+	0.318993i
$328$	−4.41376	+	25.8155i	−0.243709	+	1.42542i
$329$	−1.65776	−	0.686667i	−0.0913953	−	0.0378572i
$330$	−21.4473	+	0.193130i	−1.18064	+	0.0106315i
$331$	9.53588	−	1.89680i	0.524139	−	0.104258i	0.0740728	−	0.997253i	$-0.476400\pi$
$331$	9.53588	−	1.89680i	0.524139	−	0.104258i	0.450066	+	0.892995i	$0.351400\pi$
$332$	31.5523	−	6.86905i	1.73166	−	0.376988i
$333$	−5.36994	+	3.58808i	−0.294271	+	0.196625i
$334$	−8.67856	+	13.2450i	−0.474870	+	0.724736i
$335$	−4.15141	+	4.15141i	−0.226816	+	0.226816i
$336$	−2.48922	+	4.03255i	−0.135798	+	0.219993i
$337$	−9.94514	−	9.94514i	−0.541746	−	0.541746i	0.382294	−	0.924041i	$-0.375134\pi$
$337$	−9.94514	−	9.94514i	−0.541746	−	0.541746i	−0.924041	+	0.382294i	$0.875134\pi$
$338$	−9.86735	+	2.05527i	−0.536713	+	0.111792i
$339$	0.0984761	+	0.147380i	0.00534849	+	0.00800458i
$340$	4.18012	+	0.753489i	0.226699	+	0.0408637i
$341$	9.50885	+	47.8042i	0.514933	+	2.58874i
$342$	5.21006	−	5.30475i	0.281728	−	0.286848i
$343$	−5.71095	+	13.7874i	−0.308362	+	0.744452i
$344$	−4.89334	−	10.9660i	−0.263831	−	0.591247i
$345$	−3.44232	−	8.31050i	−0.185328	−	0.447422i
$346$	8.43180	−	20.8861i	0.453296	−	1.12285i
$347$	−0.240093	+	0.359325i	−0.0128889	+	0.0192896i	−0.837858	−	0.545888i	$-0.816192\pi$
$347$	−0.240093	+	0.359325i	−0.0128889	+	0.0192896i	0.824969	+	0.565178i	$0.191192\pi$
$348$	0.768559	+	0.741364i	0.0411991	+	0.0397413i
$349$	19.9217	+	3.96268i	1.06639	+	0.212117i	0.696936	−	0.717133i	$-0.254546\pi$
$349$	19.9217	+	3.96268i	1.06639	+	0.212117i	0.369450	+	0.929250i	$0.379546\pi$
$350$	1.07433	−	5.66728i	0.0574256	−	0.302929i
$351$		−	4.48631i		−	0.239462i
$352$	1.32892	+	29.4964i	0.0708315	+	1.57216i
$353$		−	9.26925i		−	0.493352i	−0.969098	−	0.246676i	$-0.920662\pi$
$353$		−	9.26925i		−	0.493352i	0.969098	−	0.246676i	$-0.0793384\pi$
$354$	16.7166	+	3.16893i	0.888478	+	0.168427i
$355$	−0.217411	−	0.0432458i	−0.0115390	−	0.00229525i
$356$	−29.5267	+	0.531810i	−1.56491	+	0.0281859i
$357$	−0.481084	+	0.719994i	−0.0254617	+	0.0381061i
$358$	−6.51981	−	2.63207i	−0.344583	−	0.139109i
$359$	−2.52748	−	6.10187i	−0.133395	−	0.322044i	0.843042	−	0.537848i	$-0.180763\pi$
$359$	−2.52748	−	6.10187i	−0.133395	−	0.322044i	−0.976437	+	0.215804i	$0.930763\pi$
$360$	−5.96612	−	5.65219i	−0.314442	−	0.297897i
$361$	−3.30735	+	7.98466i	−0.174071	+	0.420245i
$362$	−21.7459	−	21.3577i	−1.14294	−	1.12254i
$363$	−3.16901	−	15.9317i	−0.166330	−	0.836197i
$364$	−6.06404	−	8.73091i	−0.317842	−	0.457624i
$365$	−18.6259	−	27.8757i	−0.974926	−	1.45908i
$366$	−3.64615	−	17.5052i	−0.190587	−	0.915009i
$367$	12.1118	+	12.1118i	0.632231	+	0.632231i	0.948627	−	0.316396i	$-0.102473\pi$
$367$	12.1118	+	12.1118i	0.632231	+	0.632231i	−0.316396	+	0.948627i	$0.602473\pi$
$368$	−11.2624	+	5.14773i	−0.587096	+	0.268344i
$369$	6.54754	−	6.54754i	0.340851	−	0.340851i
$370$	−22.1980	−	14.5448i	−1.15402	−	0.756149i
$371$	3.81554	−	2.54946i	0.198093	−	0.132361i
$372$	−10.0946	+	15.7130i	−0.523381	+	0.814682i
$373$	−27.0116	+	5.37294i	−1.39861	+	0.278200i	−0.836093	−	0.548587i	$-0.815166\pi$
$373$	−27.0116	+	5.37294i	−1.39861	+	0.278200i	−0.562514	+	0.826788i	$0.690166\pi$
$374$	0.0485813	+	5.39500i	0.00251208	+	0.278969i
$375$	−4.18041	−	1.73158i	−0.215876	−	0.0894186i
$376$	−3.62483	−	2.28288i	−0.186937	−	0.117730i
$377$	−2.21302	+	0.916663i	−0.113976	+	0.0472105i
$378$	1.54210	−	0.655088i	0.0793170	−	0.0336941i
$379$	18.0856	+	12.0844i	0.928995	+	0.620735i	0.925291	−	0.379258i	$-0.123821\pi$
$379$	18.0856	+	12.0844i	0.928995	+	0.620735i	0.00370441	+	0.999993i	$0.498821\pi$
$380$	28.4337	+	11.1821i	1.45862	+	0.573628i
$381$	−2.17855	+	10.9523i	−0.111611	+	0.561104i
$382$	−8.23519	−	12.0878i	−0.421349	−	0.618464i
$383$	2.66021			0.135930			0.0679651	−	0.997688i	$-0.478349\pi$
$383$	2.66021			0.135930			0.0679651	+	0.997688i	$0.478349\pi$
$384$	−7.48019	+	8.48804i	−0.381722	+	0.433153i
$385$	17.9679			0.915730
$386$	−13.9952	−	20.5424i	−0.712337	−	1.04558i
$387$	−0.828267	+	4.16398i	−0.0421032	+	0.211667i
$388$	7.33133	+	2.88318i	0.372192	+	0.146371i
$389$	4.82813	+	3.22605i	0.244796	+	0.163567i	0.671916	−	0.740628i	$-0.265472\pi$
$389$	4.82813	+	3.22605i	0.244796	+	0.163567i	−0.427120	+	0.904195i	$0.640472\pi$
$390$	16.9676	−	7.20790i	0.859189	−	0.364986i
$391$	−2.09048	+	0.865905i	−0.105720	+	0.0437907i
$392$	−8.43542	+	13.3941i	−0.426053	+	0.676502i
$393$	−11.9945	−	4.96827i	−0.605040	−	0.250616i
$394$	0.0862874	+	9.58230i	0.00434709	+	0.482749i
$395$	−15.4372	+	3.07064i	−0.776728	+	0.154501i
$396$	5.64242	−	8.78285i	0.283542	−	0.441355i
$397$	−28.1488	+	18.8084i	−1.41275	+	0.943969i	−0.413306	+	0.910592i	$0.635626\pi$
$397$	−28.1488	+	18.8084i	−1.41275	+	0.943969i	−0.999443	+	0.0333765i	$0.989374\pi$
$398$	6.91961	+	4.53395i	0.346849	+	0.227266i
$399$	−4.40449	+	4.40449i	−0.220501	+	0.220501i
$400$	4.80834	−	12.9042i	0.240417	−	0.645211i
$401$	9.71914	+	9.71914i	0.485350	+	0.485350i	0.906835	−	0.421485i	$-0.138491\pi$
$401$	9.71914	+	9.71914i	0.485350	+	0.485350i	−0.421485	+	0.906835i	$0.638491\pi$
$402$	−0.582680	−	2.79744i	−0.0290615	−	0.139524i
$403$	−23.2748	−	34.8333i	−1.15940	−	1.73517i
$404$	12.6046	+	18.1479i	0.627103	+	0.902892i
$405$	0.566862	+	2.84981i	0.0281676	+	0.141608i
$406$	−0.638231	−	0.626839i	−0.0316749	−	0.0311095i
$407$	12.9002	−	31.1438i	0.639439	−	1.54374i
$408$	−1.42179	+	1.50076i	−0.0703891	+	0.0742986i
$409$	−2.47741	−	5.98100i	−0.122500	−	0.295742i	0.850719	−	0.525621i	$-0.176167\pi$
$409$	−2.47741	−	5.98100i	−0.122500	−	0.295742i	−0.973219	+	0.229879i	$0.926167\pi$
$410$	35.2829	+	14.2438i	1.74250	+	0.703451i
$411$	1.34643	−	2.01507i	0.0664144	−	0.0993962i
$412$	−14.7999	+	0.266564i	−0.729139	+	0.0131327i
$413$	−13.9796	−	2.78072i	−0.687893	−	0.136830i
$414$	4.30149	+	0.815425i	0.211407	+	0.0400759i
$415$		−	46.9135i		−	2.30290i
$416$	−10.7573	−	22.9857i	−0.527422	−	1.12697i
$417$			3.01500i			0.147645i
$418$	−7.22830	+	38.1304i	−0.353548	+	1.86502i
$419$	14.4757	+	2.87940i	0.707184	+	0.140668i	0.535563	−	0.844495i	$-0.320099\pi$
$419$	14.4757	+	2.87940i	0.707184	+	0.140668i	0.171621	+	0.985163i	$0.445099\pi$
$420$	4.95520	+	4.77986i	0.241789	+	0.233233i
$421$	−11.6193	+	17.3895i	−0.566290	+	0.847513i	−0.998528	−	0.0542468i	$-0.982724\pi$
$421$	−11.6193	+	17.3895i	−0.566290	+	0.847513i	0.432237	+	0.901760i	$0.357724\pi$
$422$	−9.75754	+	24.1701i	−0.474990	+	1.17658i
$423$	0.579594	+	1.39926i	0.0281808	+	0.0680345i
$424$	10.0046	−	4.46435i	0.485868	−	0.216808i
$425$	0.962950	−	2.32477i	0.0467099	−	0.112768i
$426$	0.0755997	−	0.0769736i	0.00366282	−	0.00372938i
$427$	2.92234	+	14.6916i	0.141422	+	0.710977i
$428$	−20.3233	−	3.66339i	−0.982365	−	0.177076i
$429$	13.0096	+	19.4702i	0.628107	+	0.940029i
$430$	−17.0793	+	3.55745i	−0.823635	+	0.171555i
$431$	−1.71192	−	1.71192i	−0.0824605	−	0.0824605i	0.664673	−	0.747134i	$-0.268571\pi$
$431$	−1.71192	−	1.71192i	−0.0824605	−	0.0824605i	−0.747134	+	0.664673i	$0.768571\pi$
$432$	3.89250	−	0.921130i	0.187278	−	0.0443179i
$433$	−14.2129	+	14.2129i	−0.683030	+	0.683030i	−0.960682	−	0.277652i	$-0.910444\pi$
$433$	−14.2129	+	14.2129i	−0.683030	+	0.683030i	0.277652	+	0.960682i	$0.410444\pi$
$434$	8.57480	−	13.0867i	0.411604	−	0.628180i
$435$	1.28994	−	0.861908i	0.0618477	−	0.0413253i
$436$	29.4571	−	6.41292i	1.41074	−	0.307123i
$437$	−15.9637	+	3.17537i	−0.763647	+	0.151899i
$438$	16.3168	−	0.146931i	0.779647	−	0.00702062i
$439$	−9.27423	−	3.84151i	−0.442635	−	0.183345i	0.150224	−	0.988652i	$-0.452001\pi$
$439$	−9.27423	−	3.84151i	−0.442635	−	0.183345i	−0.592858	+	0.805307i	$0.702001\pi$
$440$	42.2828	+	7.22922i	2.01575	+	0.344640i
$441$	5.17040	−	2.14165i	0.246209	−	0.101983i
$442$	−1.81312	−	4.26815i	−0.0862414	−	0.203015i
$443$	25.2331	+	16.8602i	1.19886	+	0.801052i	0.984445	−	0.175690i	$-0.0562158\pi$
$443$	25.2331	+	16.8602i	1.19886	+	0.801052i	0.214414	+	0.976743i	$0.431216\pi$
$444$	11.8426	−	5.15712i	0.562023	−	0.244746i
$445$	−8.37013	+	42.0795i	−0.396782	+	1.99476i
$446$	−19.7684	+	13.4679i	−0.936062	+	0.637723i
$447$	19.2431			0.910168
$448$	6.33020	−	7.05402i	0.299074	−	0.333271i
$449$	−22.4612			−1.06001			−0.530004	−	0.847995i	$-0.677810\pi$
$449$	−22.4612			−1.06001			−0.530004	+	0.847995i	$0.677810\pi$
$450$	−4.02371	+	2.74128i	−0.189679	+	0.129225i
$451$	−9.42893	+	47.4024i	−0.443991	+	2.23209i
$452$	−0.141539	−	0.325023i	−0.00665744	−	0.0152878i
$453$	9.56500	+	6.39113i	0.449403	+	0.300281i
$454$	−7.66178	−	18.0361i	−0.359585	−	0.846476i
$455$	−14.2682	+	5.91008i	−0.668903	+	0.277069i
$456$	−12.1369	+	8.59273i	−0.568364	+	0.402391i
$457$	−14.0279	−	5.81056i	−0.656199	−	0.271807i	0.0296390	−	0.999561i	$-0.490564\pi$
$457$	−14.0279	−	5.81056i	−0.656199	−	0.271807i	−0.685838	+	0.727754i	$0.740564\pi$
$458$	19.2095	−	0.172979i	0.897601	−	0.00808278i
$459$	0.716860	−	0.142592i	0.0334601	−	0.00665564i
$460$	3.82694	+	17.5787i	0.178432	+	0.819611i
$461$	13.7189	−	9.16667i	0.638952	−	0.426934i	−0.193447	−	0.981111i	$-0.561967\pi$
$461$	13.7189	−	9.16667i	0.638952	−	0.426934i	0.832399	+	0.554176i	$0.186967\pi$
$462$	−4.79292	+	7.31485i	−0.222987	+	0.340317i
$463$	1.45697	−	1.45697i	0.0677111	−	0.0677111i	−0.672440	−	0.740151i	$-0.734754\pi$
$463$	1.45697	−	1.45697i	0.0677111	−	0.0677111i	0.740151	+	0.672440i	$0.234754\pi$
$464$	−1.24971	−	1.73189i	−0.0580163	−	0.0804010i
$465$	19.1860	+	19.1860i	0.889730	+	0.889730i
$466$	−24.7015	+	5.14508i	−1.14427	+	0.238341i
$467$	20.1469	+	30.1520i	0.932288	+	1.39527i	0.918525	+	0.395362i	$0.129381\pi$
$467$	20.1469	+	30.1520i	0.932288	+	1.39527i	0.0137628	+	0.999905i	$0.495619\pi$
$468$	−1.59171	+	8.83032i	−0.0735769	+	0.408182i
$469$	0.467010	+	2.34782i	0.0215645	+	0.108412i
$470$	−4.36094	+	4.44019i	−0.201155	+	0.204811i
$471$	0.675215	−	1.63011i	0.0311123	−	0.0751116i
$472$	−31.7786	−	12.1683i	−1.46273	−	0.560091i
$473$	−8.48025	−	20.4731i	−0.389922	−	0.941355i
$474$	2.86776	−	7.10365i	0.131721	−	0.326281i
$475$	10.0561	−	15.0501i	0.461408	−	0.690545i
$476$	1.20236	−	1.24646i	0.0551099	−	0.0571315i
$477$	−3.79893	−	0.755654i	−0.173941	−	0.0345990i
$478$	3.48784	−	18.3989i	0.159530	−	0.841545i
$479$		−	15.3044i		−	0.699276i	−0.936885	−	0.349638i	$-0.886305\pi$
$479$		−	15.3044i		−	0.699276i	0.936885	−	0.349638i	$-0.113695\pi$
$480$	9.73764	+	13.2418i	0.444460	+	0.604404i
$481$			28.9743i			1.32111i
$482$	−27.9341	−	5.29540i	−1.27236	−	0.241199i
$483$	−3.59722	−	0.715531i	−0.163679	−	0.0325578i
$484$	0.585046	+	32.4824i	0.0265930	+	1.47647i
$485$	6.35858	−	9.51629i	0.288728	−	0.432113i
$486$	−1.31138	−	0.529409i	−0.0594855	−	0.0240145i
$487$	6.14813	+	14.8429i	0.278599	+	0.672596i	0.999797	−	0.0201317i	$-0.00640856\pi$
$487$	6.14813	+	14.8429i	0.278599	+	0.672596i	−0.721199	+	0.692728i	$0.756409\pi$
$488$	0.965945	+	35.7486i	0.0437263	+	1.61827i
$489$	2.90817	−	7.02095i	0.131512	−	0.317499i
$490$	16.4069	+	16.1140i	0.741187	+	0.727957i
$491$	−6.85615	−	34.4682i	−0.309414	−	1.55553i	−0.752221	−	0.658911i	$-0.771017\pi$
$491$	−6.85615	−	34.4682i	−0.309414	−	1.55553i	0.442807	−	0.896617i	$-0.353983\pi$
$492$	−15.2104	+	10.5644i	−0.685738	+	0.476278i
$493$	−0.216810	−	0.324479i	−0.00976463	−	0.0146138i
$494$	−6.80206	−	32.6566i	−0.306039	−	1.46929i
$495$	−10.7241	−	10.7241i	−0.482012	−	0.482012i
$496$	25.4439	−	27.3461i	1.14246	−	1.22788i
$497$	−0.0639107	+	0.0639107i	−0.00286679	+	0.00286679i
$498$	19.0988	+	12.5141i	0.855837	+	0.560771i
$499$	25.6635	−	17.1478i	1.14885	−	0.767640i	0.172756	−	0.984965i	$-0.444733\pi$
$499$	25.6635	−	17.1478i	1.14885	−	0.767640i	0.976099	+	0.217324i	$0.0697330\pi$
$500$	7.61386	+	4.89142i	0.340502	+	0.218751i
$501$	−10.9819	+	2.18444i	−0.490636	+	0.0975935i
$502$	0.0861734	+	9.56965i	0.00384611	+	0.427114i
$503$	−14.1932	−	5.87903i	−0.632845	−	0.262133i	0.0431164	−	0.999070i	$-0.486271\pi$
$503$	−14.1932	−	5.87903i	−0.632845	−	0.262133i	−0.675961	+	0.736937i	$0.736271\pi$
$504$	−3.26770	+	0.742270i	−0.145555	+	0.0330633i
$505$	29.6576	−	12.2846i	1.31975	−	0.546657i
$506$	−21.0327	+	8.93473i	−0.935016	+	0.397197i
$507$	−5.92590	−	3.95956i	−0.263178	−	0.175850i
$508$	8.17380	−	20.7843i	0.362654	−	0.922153i
$509$	3.56893	−	17.9422i	0.158190	−	0.795275i	−0.817467	−	0.575975i	$-0.804623\pi$
$509$	3.56893	−	17.9422i	0.158190	−	0.795275i	0.975657	−	0.219300i	$-0.0703774\pi$
$510$	1.69103	+	2.48213i	0.0748802	+	0.109911i
$511$	−13.6697			−0.604713
$512$	17.7346	−	14.0529i	0.783766	−	0.621057i
$513$	5.25762			0.232129
$514$	−15.1802	−	22.2818i	−0.669571	−	0.982809i
$515$	−4.19543	+	21.0919i	−0.184873	+	0.929419i
$516$	3.10761	−	7.90201i	0.136805	−	0.347867i
$517$	−6.57302	−	4.39195i	−0.289081	−	0.193158i
$518$	−9.95944	+	4.23080i	−0.437593	+	0.185891i
$519$	14.7144	−	6.09492i	0.645893	−	0.267537i
$520$	−35.9543	+	8.16716i	−1.57670	+	0.358154i
$521$	−8.89269	−	3.68347i	−0.389596	−	0.161376i	0.179282	−	0.983798i	$-0.442622\pi$
$521$	−8.89269	−	3.68347i	−0.389596	−	0.161376i	−0.568878	+	0.822422i	$0.692622\pi$
$522$	0.00679916	+	0.755053i	0.000297591	+	0.0330478i
$523$	31.2067	−	6.20740i	1.36457	−	0.271430i	0.542138	−	0.840289i	$-0.317615\pi$
$523$	31.2067	−	6.20740i	1.36457	−	0.271430i	0.822435	+	0.568859i	$0.192615\pi$
$524$	21.8457	+	14.0345i	0.954335	+	0.613099i
$525$	3.39135	−	2.26603i	0.148011	−	0.0988975i
$526$	1.94330	+	1.27331i	0.0847319	+	0.0555190i
$527$	4.82618	−	4.82618i	0.210232	−	0.210232i
$528$	−14.2219	+	15.2852i	−0.618931	+	0.665203i
$529$	9.48664	+	9.48664i	0.412463	+	0.412463i
$530$	−3.24557	−	15.5819i	−0.140978	−	0.676836i
$531$	6.68404	+	10.0034i	0.290062	+	0.434109i
$532$	10.2320	−	7.10659i	0.443612	−	0.308110i
$533$	−8.10435	−	40.7433i	−0.351038	−	1.76479i
$534$	−14.8981	−	14.6322i	−0.644703	−	0.633196i
$535$	−11.4813	+	27.7182i	−0.496378	+	1.19836i
$536$	0.154365	+	5.71288i	0.00666754	+	0.246759i
$537$	−1.90259	−	4.59326i	−0.0821028	−	0.198214i
$538$	23.6593	+	9.55131i	1.02002	+	0.411786i
$539$	−16.2286	+	24.2878i	−0.699016	+	1.04615i
$540$	−0.104651	−	5.81034i	−0.00450347	−	0.250037i
$541$	43.9467	+	8.74155i	1.88942	+	0.375829i	0.997135	−	0.0756471i	$-0.0241022\pi$
$541$	43.9467	+	8.74155i	1.88942	+	0.375829i	0.892283	+	0.451476i	$0.149102\pi$
$542$	2.11764	+	0.401436i	0.0909603	+	0.0172432i
$543$		−	21.5527i		−	0.924913i
$544$	3.33094	−	2.44947i	0.142813	−	0.105020i
$545$		−	43.7983i		−	1.87611i
$546$	1.39999	−	7.38517i	0.0599141	−	0.316056i
$547$	−4.26116	−	0.847597i	−0.182194	−	0.0362406i	0.103150	−	0.994666i	$-0.467108\pi$
$547$	−4.26116	−	0.847597i	−0.182194	−	0.0362406i	−0.285344	+	0.958425i	$0.592108\pi$
$548$	−3.36508	+	3.48852i	−0.143749	+	0.149022i
$549$	7.02445	−	10.5128i	0.299796	−	0.448677i
$550$	9.51326	−	23.5650i	0.405647	−	1.00481i
$551$	−1.07426	−	2.59349i	−0.0457650	−	0.110486i
$552$	−8.17723	−	3.13112i	−0.348046	−	0.133269i
$553$	−2.45592	+	5.92911i	−0.104436	+	0.252131i
$554$	−12.8838	+	13.1179i	−0.547380	+	0.557328i
$555$	−3.66100	−	18.4051i	−0.155401	−	0.781254i
$556$	1.06970	−	5.93435i	0.0453654	−	0.251673i
$557$	−2.86872	−	4.29334i	−0.121551	−	0.181915i	0.765704	−	0.643193i	$-0.222391\pi$
$557$	−2.86872	−	4.29334i	−0.121551	−	0.181915i	−0.887255	+	0.461279i	$0.847391\pi$
$558$	−12.9286	+	2.69290i	−0.547310	+	0.113999i
$559$	13.4682	+	13.4682i	0.569644	+	0.569644i
$560$	−8.05735	−	11.1662i	−0.340485	−	0.471856i
$561$	−2.69761	+	2.69761i	−0.113893	+	0.113893i
$562$	18.0240	−	27.5079i	0.760298	−	1.16035i
$563$	30.5462	−	20.4103i	1.28737	−	0.860193i	0.292010	−	0.956415i	$-0.405676\pi$
$563$	30.5462	−	20.4103i	1.28737	−	0.860193i	0.995360	+	0.0962225i	$0.0306760\pi$
$564$	−0.644354	−	2.95978i	−0.0271322	−	0.124629i
$565$	−0.505135	+	0.100478i	−0.0212512	+	0.00422712i
$566$	−24.0324	+	0.216409i	−1.01016	+	0.00909634i
$567$	1.09455	+	0.453379i	0.0459670	+	0.0190401i
$568$	−0.176111	+	0.124683i	−0.00738946	+	0.00523160i
$569$	−16.8518	+	6.98026i	−0.706466	+	0.292628i	−0.706841	−	0.707372i	$-0.749880\pi$
$569$	−16.8518	+	6.98026i	−0.706466	+	0.292628i	0.000375543		1.00000i	$0.499880\pi$
$570$	8.44710	+	19.8848i	0.353810	+	0.832881i
$571$	−17.3358	−	11.5834i	−0.725482	−	0.484752i	0.137171	−	0.990547i	$-0.456199\pi$
$571$	−17.3358	−	11.5834i	−0.725482	−	0.484752i	−0.862653	+	0.505796i	$0.831199\pi$
$572$	−18.6986	−	42.9385i	−0.781826	−	1.79535i
$573$	2.01771	−	10.1437i	0.0842911	−	0.423760i
$574$	12.8215	−	8.73504i	0.535158	−	0.364594i
$575$	10.6580			0.444468
$576$	−7.98833	+	0.432012i	−0.332847	+	0.0180005i
$577$	−0.646088			−0.0268970			−0.0134485	−	0.999910i	$-0.504281\pi$
$577$	−0.646088			−0.0268970			−0.0134485	+	0.999910i	$0.504281\pi$
$578$	−19.2444	+	13.1109i	−0.800463	+	0.545341i
$579$	3.42898	−	17.2386i	0.142504	−	0.716413i
$580$	−2.84475	+	1.23881i	−0.118122	+	0.0514390i
$581$	−15.9047	−	10.6272i	−0.659838	−	0.440889i
$582$	2.17800	+	5.12708i	0.0902809	+	0.212524i
$583$	18.6783	−	7.73679i	0.773575	−	0.320425i
$584$	−32.1681	−	5.49988i	−1.33113	−	0.227587i
$585$	12.0433	+	4.98851i	0.497930	+	0.206250i
$586$	−11.4941	+	0.103503i	−0.474819	+	0.00427568i
$587$	4.65120	−	0.925181i	0.191975	−	0.0381863i	−0.0981660	−	0.995170i	$-0.531298\pi$
$587$	4.65120	−	0.925181i	0.191975	−	0.0381863i	0.290142	+	0.956984i	$0.406298\pi$
$588$	−10.9366	+	2.38094i	−0.451019	+	0.0981884i
$589$	40.8219	−	27.2763i	1.68204	−	1.12390i
$590$	−27.0947	+	41.3514i	−1.11547	+	1.70241i
$591$	−4.79135	+	4.79135i	−0.197090	+	0.197090i
$592$	−25.1392	+	5.94900i	−1.03321	+	0.244502i
$593$	16.9541	+	16.9541i	0.696222	+	0.696222i	0.963594	−	0.267371i	$-0.0861550\pi$
$593$	16.9541	+	16.9541i	0.696222	+	0.696222i	−0.267371	+	0.963594i	$0.586155\pi$
$594$	7.22648	−	1.50521i	0.296506	−	0.0617593i
$595$	−1.39786	−	2.09204i	−0.0573066	−	0.0857653i
$596$	−37.8758	−	6.82732i	−1.55145	−	0.279658i
$597$	1.14122	+	5.73729i	0.0467069	+	0.234812i
$598$	13.7630	−	14.0131i	0.562812	−	0.573040i
$599$	−12.1127	+	29.2425i	−0.494910	+	1.19482i	0.457283	+	0.889321i	$0.348823\pi$
$599$	−12.1127	+	29.2425i	−0.494910	+	1.19482i	−0.952193	+	0.305497i	$0.901177\pi$
$600$	8.89237	−	3.96803i	0.363029	−	0.161994i
$601$	7.37520	+	17.8053i	0.300841	+	0.726294i	0.999937	+	0.0112656i	$0.00358604\pi$
$601$	7.37520	+	17.8053i	0.300841	+	0.726294i	−0.699096	+	0.715028i	$0.746414\pi$
$602$	−2.66286	+	6.59609i	−0.108530	+	0.268837i
$603$	1.12255	−	1.68002i	0.0457140	−	0.0684158i
$604$	−16.5591	−	15.9731i	−0.673778	−	0.649937i
$605$	46.2918	+	9.20800i	1.88203	+	0.374359i
$606$	−2.91000	+	15.3507i	−0.118211	+	0.623579i
$607$			32.3153i			1.31164i	0.754918	+	0.655819i	$0.227677\pi$
$607$			32.3153i			1.31164i	−0.754918	+	0.655819i	$0.772323\pi$
$608$	26.9375	−	12.6068i	1.09246	−	0.511273i
$609$		−	0.632561i		−	0.0256327i
$610$	51.0462	+	9.67672i	2.06680	+	0.391799i
$611$	6.66420	+	1.32559i	0.269605	+	0.0536277i
$612$	−1.46157	+	0.0263246i	−0.0590805	+	0.00106411i
$613$	6.67389	−	9.98819i	0.269556	−	0.403419i	−0.671854	−	0.740684i	$-0.734502\pi$
$613$	6.67389	−	9.98819i	0.269556	−	0.403419i	0.941410	+	0.337265i	$0.109502\pi$
$614$	34.0497	+	13.7460i	1.37414	+	0.554742i
$615$	10.2961	+	24.8571i	0.415180	+	1.00233i
$616$	12.0291	−	12.6972i	0.484664	−	0.511583i
$617$	7.44235	−	17.9674i	0.299618	−	0.723341i	−0.700337	−	0.713812i	$-0.746967\pi$
$617$	7.44235	−	17.9674i	0.299618	−	0.723341i	0.999955	−	0.00952845i	$-0.00303304\pi$
$618$	−7.46750	−	7.33421i	−0.300387	−	0.295025i
$619$	−2.22424	−	11.1820i	−0.0893998	−	0.449443i	−0.999394	−	0.0348213i	$-0.988914\pi$
$619$	−2.22424	−	11.1820i	−0.0893998	−	0.449443i	0.909994	−	0.414622i	$-0.136086\pi$
$620$	−30.9564	−	44.5705i	−1.24324	−	1.78999i
$621$	1.71992	+	2.57405i	0.0690182	+	0.103293i
$622$	1.12916	+	5.42110i	0.0452753	+	0.217366i
$623$	12.3698	+	12.3698i	0.495585	+	0.495585i
$624$	6.26587	−	16.8158i	0.250835	−	0.673171i
$625$	21.4686	−	21.4686i	0.858746	−	0.858746i
$626$	8.86206	+	5.80670i	0.354199	+	0.232082i
$627$	−22.8176	+	15.2462i	−0.911246	+	0.608875i
$628$	−1.90736	+	2.96895i	−0.0761121	+	0.118474i
$629$	−4.62974	+	0.920913i	−0.184600	+	0.0367192i
$630$	0.0438368	+	4.86812i	0.00174650	+	0.193950i
$631$	5.70909	+	2.36478i	0.227275	+	0.0941406i	0.493415	−	0.869794i	$-0.335748\pi$
$631$	5.70909	+	2.36478i	0.227275	+	0.0941406i	−0.266140	+	0.963934i	$0.585748\pi$
$632$	−8.16488	+	12.9645i	−0.324782	+	0.515700i
$633$	−17.0280	+	7.05324i	−0.676803	+	0.280341i
$634$	−31.8105	+	13.5132i	−1.26336	+	0.536677i
$635$	−26.9786	−	18.0266i	−1.07061	−	0.715362i
$636$	7.20925	+	2.83517i	0.285865	+	0.112422i
$637$	4.89817	−	24.6248i	0.194073	−	0.975669i
$638$	−2.21904	−	3.25714i	−0.0878525	−	0.128952i
$639$	0.0762898			0.00301798
$640$	−14.4683	−	29.5185i	−0.571909	−	1.16682i
$641$	−4.03696			−0.159450			−0.0797251	−	0.996817i	$-0.525404\pi$
$641$	−4.03696			−0.159450			−0.0797251	+	0.996817i	$0.525404\pi$
$642$	−8.22163	−	12.0679i	−0.324482	−	0.476281i
$643$	−9.16459	+	46.0735i	−0.361416	+	1.81696i	0.188889	+	0.981998i	$0.439511\pi$
$643$	−9.16459	+	46.0735i	−0.361416	+	1.81696i	−0.550305	+	0.834964i	$0.685489\pi$
$644$	6.82646	+	2.68463i	0.269000	+	0.105789i
$645$	−10.2571	−	6.85355i	−0.403871	−	0.269858i
$646$	5.00194	−	2.12484i	0.196799	−	0.0836007i
$647$	5.34972	−	2.21593i	0.210319	−	0.0871170i	−0.275037	−	0.961434i	$-0.588690\pi$
$647$	5.34972	−	2.21593i	0.210319	−	0.0871170i	0.485356	+	0.874317i	$0.338690\pi$
$648$	2.39334	+	1.50729i	0.0940192	+	0.0592121i
$649$	−58.0162	−	24.0311i	−2.27733	−	0.943303i
$650$	0.196684	+	21.8419i	0.00771457	+	0.856711i
$651$	10.8506	−	2.15832i	0.425269	−	0.0845913i
$652$	−8.21508	+	12.7874i	−0.321727	+	0.500793i
$653$	24.7300	−	16.5241i	0.967761	−	0.646637i	0.0320803	−	0.999485i	$-0.489787\pi$
$653$	24.7300	−	16.5241i	0.967761	−	0.646637i	0.935681	+	0.352848i	$0.114787\pi$
$654$	17.8306	+	11.6831i	0.697230	+	0.456847i
$655$	26.6742	−	26.6742i	1.04225	−	1.04225i
$656$	33.6865	−	15.3971i	1.31524	−	0.601154i
$657$	8.15873	+	8.15873i	0.318302	+	0.318302i
$658$	0.517450	+	2.48427i	0.0201723	+	0.0968470i
$659$	−14.1757	−	21.2154i	−0.552207	−	0.826435i	0.445418	−	0.895323i	$-0.353055\pi$
$659$	−14.1757	−	21.2154i	−0.552207	−	0.826435i	−0.997624	+	0.0688873i	$0.978055\pi$
$660$	17.3032	+	24.9128i	0.673525	+	0.969731i
$661$	0.276376	+	1.38944i	0.0107498	+	0.0540429i	0.985788	−	0.167995i	$-0.0537292\pi$
$661$	0.276376	+	1.38944i	0.0107498	+	0.0540429i	−0.975038	+	0.222038i	$0.928729\pi$
$662$	−9.80985	−	9.63475i	−0.381271	−	0.374465i
$663$	1.25484	−	3.02946i	0.0487341	−	0.117654i
$664$	−33.1518	−	31.4074i	−1.28654	−	1.21884i
$665$	−6.92616	−	16.7212i	−0.268585	−	0.648421i
$666$	8.46940	+	3.41912i	0.328183	+	0.132488i
$667$	0.918311	−	1.37435i	0.0355571	−	0.0532150i
$668$	22.3905	−	0.403280i	0.866314	−	0.0156034i
$669$	−16.5891	−	3.29978i	−0.641372	−	0.127577i
$670$	8.15753	+	1.54641i	0.315153	+	0.0597429i
$671$			65.9944i			2.54769i
$672$	6.69510	−	0.301638i	0.258269	−	0.0116359i
$673$			46.4813i			1.79172i	0.444333	+	0.895862i	$0.353441\pi$
$673$			46.4813i			1.79172i	−0.444333	+	0.895862i	$0.646559\pi$
$674$	−3.70458	+	19.5422i	−0.142695	+	0.752739i
$675$	−3.37659	−	0.671645i	−0.129965	−	0.0258516i
$676$	10.2590	+	9.89598i	0.394577	+	0.380615i
$677$	−22.5183	+	33.7010i	−0.865449	+	1.29524i	0.0887466	+	0.996054i	$0.471714\pi$
$677$	−22.5183	+	33.7010i	−0.865449	+	1.29524i	−0.954196	+	0.299182i	$0.903286\pi$
$678$	0.0938390	−	0.232446i	0.00360387	−	0.00892702i
$679$	−1.78584	−	4.31139i	−0.0685341	−	0.165456i
$680$	−2.44778	−	5.48549i	−0.0938681	−	0.210359i
$681$	5.30264	−	12.8017i	0.203198	−	0.490562i
$682$	48.2999	−	49.1776i	1.84950	−	1.88311i
$683$	−3.55473	−	17.8708i	−0.136018	−	0.683809i	−0.987270	−	0.159052i	$-0.949156\pi$
$683$	−3.55473	−	17.8708i	−0.136018	−	0.683809i	0.851252	−	0.524757i	$-0.175844\pi$
$684$	−10.3485	−	1.86536i	−0.395683	−	0.0713240i
$685$	3.91224	+	5.85507i	0.149479	+	0.223711i
$686$	20.6615	−	4.30358i	0.788859	−	0.164312i
$687$	9.60514	+	9.60514i	0.366459	+	0.366459i
$688$	−8.92022	+	14.4508i	−0.340080	+	0.550932i
$689$	−12.2875	+	12.2875i	−0.468115	+	0.468115i
$690$	−6.97197	+	10.6405i	−0.265418	+	0.405076i
$691$	−29.5073	+	19.7162i	−1.12251	+	0.750038i	−0.971157	−	0.238442i	$-0.923363\pi$
$691$	−29.5073	+	19.7162i	−1.12251	+	0.750038i	−0.151354	+	0.988480i	$0.548363\pi$
$692$	−31.1246	+	6.77593i	−1.18318	+	0.257582i
$693$	−6.06499	+	1.20640i	−0.230390	+	0.0458274i
$694$	0.611137	−	0.00550321i	0.0231985	−	0.000208899i
$695$	−8.09364	−	3.35249i	−0.307009	−	0.127167i
$696$	0.254505	−	1.48857i	0.00964698	−	0.0564240i
$697$	6.25271	−	2.58996i	0.236838	−	0.0981016i
$698$	−11.2313	−	26.4389i	−0.425112	−	1.00073i
$699$	−14.8346	−	9.91218i	−0.561097	−	0.374913i
$700$	−7.47909	+	3.25695i	−0.282683	+	0.123101i
$701$	−0.0853266	+	0.428966i	−0.00322274	+	0.0162018i	−0.982363	−	0.186983i	$-0.940129\pi$
$701$	−0.0853266	+	0.428966i	−0.00322274	+	0.0162018i	0.979140	+	0.203185i	$0.0651291\pi$
$702$	−5.24339	+	3.57223i	−0.197899	+	0.134825i
$703$	−33.9556			−1.28066
$704$	33.4158	−	25.0397i	1.25941	−	0.943719i
$705$	−4.40074			−0.165742
$706$	−10.8335	+	7.38065i	−0.407723	+	0.277774i
$707$	2.55351	−	12.8373i	0.0960345	−	0.482798i
$708$	−9.60692	−	22.0609i	−0.361050	−	0.829098i
$709$	39.9112	+	26.6678i	1.49890	+	1.00153i	0.990057	+	0.140669i	$0.0449254\pi$
$709$	39.9112	+	26.6678i	1.49890	+	1.00153i	0.508840	+	0.860861i	$0.330075\pi$
$710$	0.122570	+	0.288535i	0.00459998	+	0.0108285i
$711$	5.00458	−	2.07296i	0.187686	−	0.0777422i
$712$	24.1322	+	34.0859i	0.904392	+	1.27742i
$713$	26.7082	+	11.0629i	1.00023	+	0.414308i
$714$	1.22456	−	0.0110270i	0.0458280	−	0.000412675i
$715$	−66.7328	+	13.2740i	−2.49566	+	0.496419i
$716$	2.11517	+	9.71584i	0.0790477	+	0.363098i
$717$	11.0100	−	7.35667i	0.411178	−	0.274740i
$718$	−5.11907	+	7.81262i	−0.191042	+	0.291564i
$719$	3.35792	−	3.35792i	0.125229	−	0.125229i	−0.641714	−	0.766944i	$-0.721777\pi$
$719$	3.35792	−	3.35792i	0.125229	−	0.125229i	0.766944	+	0.641714i	$0.221777\pi$
$720$	−1.85548	+	11.4735i	−0.0691498	+	0.427592i
$721$	6.20021	+	6.20021i	0.230908	+	0.230908i
$722$	11.9656	−	2.49231i	0.445313	−	0.0927543i
$723$	−11.1693	−	16.7160i	−0.415389	−	0.621674i
$724$	−7.64673	+	42.4216i	−0.284188	+	1.57659i
$725$	0.358608	+	1.80284i	0.0133184	+	0.0669559i
$726$	−16.0969	+	16.3894i	−0.597412	+	0.608269i
$727$	2.05853	−	4.96973i	0.0763467	−	0.184317i	−0.881098	−	0.472933i	$-0.843195\pi$
$727$	2.05853	−	4.96973i	0.0763467	−	0.184317i	0.957445	+	0.288616i	$0.0931951\pi$
$728$	−5.37578	+	14.0394i	−0.199240	+	0.520333i
$729$	−0.382683	−	0.923880i	−0.0141735	−	0.0342178i
$730$	−17.7489	+	43.9652i	−0.656915	+	1.62722i
$731$	−1.72399	+	2.58013i	−0.0637640	+	0.0954295i
$732$	−17.5559	+	18.2000i	−0.648886	+	0.672690i
$733$	−11.4634	−	2.28021i	−0.423410	−	0.0842215i	−0.0212138	−	0.999775i	$-0.506753\pi$
$733$	−11.4634	−	2.28021i	−0.423410	−	0.0842215i	−0.402196	+	0.915553i	$0.631753\pi$
$734$	4.51167	−	23.7997i	0.166529	−	0.878464i
$735$			16.2611i			0.599800i
$736$	14.9842	+	9.06414i	0.552323	+	0.334109i
$737$			10.5464i			0.388480i
$738$	−12.8659	−	2.43897i	−0.473602	−	0.0897797i
$739$	31.2495	+	6.21591i	1.14953	+	0.228656i	0.732845	−	0.680395i	$-0.238192\pi$
$739$	31.2495	+	6.21591i	1.14953	+	0.228656i	0.416685	+	0.909051i	$0.363192\pi$
$740$	0.675875	+	37.5253i	0.0248457	+	1.37946i
$741$	13.1044	−	19.6121i	0.481403	−	0.720470i
$742$	−6.01782	−	2.42941i	−0.220921	−	0.0891865i
$743$	2.28742	+	5.52232i	0.0839173	+	0.202594i	0.960268	−	0.279079i	$-0.0900292\pi$
$743$	2.28742	+	5.52232i	0.0839173	+	0.202594i	−0.876351	+	0.481673i	$0.840029\pi$
$744$	26.4025	−	0.713407i	0.967962	−	0.0261548i
$745$	−21.3972	+	51.6573i	−0.783932	+	1.89258i
$746$	27.7877	+	27.2917i	1.01738	+	0.999219i
$747$	3.14987	+	15.8355i	0.115248	+	0.579389i
$748$	6.26674	−	4.35256i	0.229135	−	0.159145i
$749$	6.79625	+	10.1713i	0.248329	+	0.371651i
$750$	1.30486	+	6.26465i	0.0476469	+	0.228753i
$751$	−18.9675	−	18.9675i	−0.692133	−	0.692133i	0.270568	−	0.962701i	$-0.412788\pi$
$751$	−18.9675	−	18.9675i	−0.692133	−	0.692133i	−0.962701	+	0.270568i	$0.912788\pi$
$752$	0.218160	+	6.05428i	0.00795549	+	0.220777i
$753$	−4.78502	+	4.78502i	−0.174376	+	0.174376i
$754$	2.83347	+	1.85658i	0.103189	+	0.0676127i
$755$	−27.7924	+	18.5703i	−1.01147	+	0.675843i
$756$	−1.99353	−	1.28072i	−0.0725041	−	0.0465792i
$757$	22.5808	−	4.49159i	0.820712	−	0.163250i	0.233162	−	0.972438i	$-0.425093\pi$
$757$	22.5808	−	4.49159i	0.820712	−	0.163250i	0.587550	+	0.809188i	$0.300093\pi$
$758$	−0.276988	−	30.7598i	−0.0100607	−	1.11725i
$759$	−14.9286	−	6.18364i	−0.541875	−	0.224452i
$760$	−9.57129	−	42.1357i	−0.347187	−	1.52842i
$761$	−2.72276	+	1.12780i	−0.0986999	+	0.0408829i	−0.431487	−	0.902119i	$-0.642011\pi$
$761$	−2.72276	+	1.12780i	−0.0986999	+	0.0408829i	0.332787	+	0.943002i	$0.392011\pi$
$762$	14.5352	−	6.17461i	0.526556	−	0.223682i
$763$	−14.8486	−	9.92149i	−0.537554	−	0.359182i
$764$	−7.57034	+	19.2498i	−0.273885	+	0.696433i
$765$	−0.414322	+	2.08294i	−0.0149798	+	0.0753087i
$766$	−2.11819	−	3.10913i	−0.0765335	−	0.112337i
$767$	53.9746			1.94891
$768$	15.8765	+	1.98388i	0.572895	+	0.0715872i
$769$	22.0370			0.794676			0.397338	−	0.917672i	$-0.369934\pi$
$769$	22.0370			0.794676			0.397338	+	0.917672i	$0.369934\pi$
$770$	−14.3070	−	21.0001i	−0.515588	−	0.756790i
$771$	3.71932	−	18.6983i	0.133948	−	0.673402i
$772$	−12.8653	+	32.7139i	−0.463034	+	1.17740i
$773$	6.95444	+	4.64681i	0.250134	+	0.167134i	0.674316	−	0.738443i	$-0.264438\pi$
$773$	6.95444	+	4.64681i	0.250134	+	0.167134i	−0.424182	+	0.905577i	$0.639438\pi$
$774$	5.52617	−	2.34754i	0.198634	−	0.0843804i
$775$	−29.7014	+	12.3027i	−1.06691	+	0.441927i
$776$	−2.46786	−	10.8643i	−0.0885908	−	0.390004i
$777$	−7.06904	−	2.92809i	−0.253600	−	0.105045i
$778$	−0.0739447	−	8.21164i	−0.00265105	−	0.294401i
$779$	47.7481	−	9.49768i	1.71075	−	0.340290i
$780$	−21.9347	−	14.0917i	−0.785390	−	0.504563i
$781$	−0.331090	+	0.221228i	−0.0118473	+	0.00791615i
$782$	2.67658	+	1.75378i	0.0957142	+	0.0627149i
$783$	−0.377542	+	0.377542i	−0.0134923	+	0.0134923i
$784$	22.3711	−	0.806121i	0.798967	−	0.0287900i
$785$	3.62517	+	3.62517i	0.129388	+	0.129388i
$786$	3.74392	+	17.9745i	0.133541	+	0.641131i
$787$	3.00589	+	4.49863i	0.107148	+	0.160359i	0.881169	−	0.472802i	$-0.156757\pi$
$787$	3.00589	+	4.49863i	0.107148	+	0.160359i	−0.774020	+	0.633161i	$0.781757\pi$
$788$	11.1306	−	7.73077i	0.396513	−	0.275397i
$789$	0.320499	+	1.61126i	0.0114101	+	0.0573623i
$790$	15.8807	+	15.5972i	0.565009	+	0.554925i
$791$	−0.0803626	+	0.194012i	−0.00285736	+	0.00689829i
$792$	−14.7578	+	0.398761i	−0.524394	+	0.0141694i
$793$	−21.7071	−	52.4057i	−0.770843	−	1.86098i
$794$	44.3960	+	17.9228i	1.57555	+	0.636056i
$795$	6.25270	−	9.35783i	0.221761	−	0.331888i
$796$	−0.210686	−	11.6975i	−0.00746755	−	0.414606i
$797$	−47.7432	−	9.49670i	−1.69115	−	0.336390i	−0.746728	−	0.665129i	$-0.768376\pi$
$797$	−47.7432	−	9.49670i	−1.69115	−	0.336390i	−0.944421	+	0.328739i	$0.893376\pi$
$798$	8.65485	+	1.64068i	0.306378	+	0.0580795i
$799$			1.10699i			0.0391626i
$800$	−18.9105	+	4.65523i	−0.668587	+	0.164587i
$801$		−	14.7657i		−	0.521721i
$802$	3.62040	−	19.0981i	0.127841	−	0.674379i
$803$	−59.0671	−	11.7492i	−2.08443	−	0.414619i
$804$	−2.80556	+	2.90848i	−0.0989445	+	0.102574i
$805$	5.92070	−	8.86095i	0.208677	−	0.312308i
$806$	−22.1789	+	54.9386i	−0.781217	+	1.93513i
$807$	6.90417	+	16.6681i	0.243038	+	0.586746i
$808$	11.1740	−	29.1820i	0.393100	−	1.02662i
$809$	3.26003	−	7.87042i	0.114617	−	0.276709i	−0.856153	−	0.516723i	$-0.827152\pi$
$809$	3.26003	−	7.87042i	0.114617	−	0.276709i	0.970770	+	0.240013i	$0.0771518\pi$
$810$	2.87936	−	2.93168i	0.101170	−	0.103009i
$811$	2.64300	+	13.2873i	0.0928084	+	0.466579i	0.999040	+	0.0437985i	$0.0139460\pi$
$811$	2.64300	+	13.2873i	0.0928084	+	0.466579i	−0.906232	+	0.422781i	$0.861054\pi$
$812$	−0.224428	+	1.24506i	−0.00787588	+	0.0436929i
$813$	0.846724	+	1.26721i	0.0296959	+	0.0444431i
$814$	−46.6713	+	9.72117i	−1.63583	+	0.340727i
$815$	15.6138	+	15.6138i	0.546926	+	0.546926i
$816$	2.88612	+	0.466741i	0.101034	+	0.0163392i
$817$	−15.7837	+	15.7837i	−0.552202	+	0.552202i
$818$	−5.01767	+	7.65786i	−0.175439	+	0.267751i
$819$	4.41935	−	2.95291i	0.154425	−	0.103183i
$820$	−11.4466	−	52.5786i	−0.399731	−	1.83613i
$821$	5.05328	−	1.00516i	0.176361	−	0.0350803i	−0.106120	−	0.994353i	$-0.533843\pi$
$821$	5.05328	−	1.00516i	0.176361	−	0.0350803i	0.282480	+	0.959273i	$0.408843\pi$
$822$	−3.42722	+	0.0308617i	−0.119538	+	0.00107642i
$823$	−44.2286	−	18.3201i	−1.54171	−	0.638598i	−0.559918	−	0.828548i	$-0.689167\pi$
$823$	−44.2286	−	18.3201i	−1.54171	−	0.638598i	−0.981794	+	0.189950i	$0.939167\pi$
$824$	12.0960	+	17.0852i	0.421384	+	0.595191i
$825$	16.6017	−	6.87666i	0.577998	−	0.239414i
$826$	7.88133	+	18.5529i	0.274226	+	0.645538i
$827$	−23.7672	−	15.8807i	−0.826466	−	0.552227i	0.0688660	−	0.997626i	$-0.478062\pi$
$827$	−23.7672	−	15.8807i	−0.826466	−	0.552227i	−0.895332	+	0.445399i	$0.853062\pi$
$828$	−2.47204	−	5.67666i	−0.0859092	−	0.197278i
$829$	2.80642	−	14.1088i	0.0974711	−	0.490020i	−0.900954	−	0.433915i	$-0.857132\pi$
$829$	2.80642	−	14.1088i	0.0974711	−	0.490020i	0.998425	−	0.0561052i	$-0.0178682\pi$
$830$	−54.8304	+	37.3550i	−1.90319	+	1.29661i
$831$	−13.0014			−0.451013
$832$	−18.2991	+	30.8751i	−0.634407	+	1.07040i
$833$	4.09043			0.141725
$834$	3.52379	−	2.40069i	0.122019	−	0.0831293i
$835$	6.34719	−	31.9095i	0.219654	−	1.10427i
$836$	50.3206	−	21.9133i	1.74037	−	0.757887i
$837$	−7.76434	−	5.18797i	−0.268375	−	0.179322i
$838$	−8.16099	−	19.2112i	−0.281917	−	0.663641i
$839$	−47.9982	+	19.8815i	−1.65708	+	0.686386i	−0.997849	−	0.0655529i	$-0.979119\pi$
$839$	−47.9982	+	19.8815i	−1.65708	+	0.686386i	−0.659233	+	0.751939i	$0.729119\pi$
$840$	1.64089	−	9.59737i	0.0566161	−	0.331141i
$841$	−26.5291	−	10.9887i	−0.914798	−	0.378922i
$842$	29.5759	−	0.266327i	1.01925	−	0.00917825i
$843$	22.8077	−	4.53674i	0.785540	−	0.156254i
$844$	36.0184	−	7.84132i	1.23980	−	0.269909i
$845$	17.2185	−	11.5050i	0.592335	−	0.395785i
$846$	1.17389	−	1.79157i	0.0403592	−	0.0615954i
$847$	13.6080	−	13.6080i	0.467577	−	0.467577i
$848$	−13.1839	−	8.13820i	−0.452738	−	0.279467i
$849$	−12.0167	−	12.0167i	−0.412412	−	0.412412i
$850$	−3.48383	+	0.725648i	−0.119494	+	0.0248895i
$851$	−11.1079	−	16.6242i	−0.380774	−	0.569869i
$852$	−0.150160	−	0.0270671i	−0.00514438	−	0.000927303i
$853$	3.09612	+	15.5653i	0.106009	+	0.532944i	0.996897	+	0.0787203i	$0.0250834\pi$
$853$	3.09612	+	15.5653i	0.106009	+	0.532944i	−0.890888	+	0.454224i	$0.849917\pi$
$854$	14.8439	−	15.1137i	0.507949	−	0.517180i
$855$	−5.84615	+	14.1139i	−0.199934	+	0.482684i
$856$	11.9009	+	26.6699i	0.406763	+	0.911559i
$857$	−5.33851	−	12.8883i	−0.182360	−	0.440256i	0.806092	−	0.591790i	$-0.201579\pi$
$857$	−5.33851	−	12.8883i	−0.182360	−	0.440256i	−0.988452	+	0.151534i	$0.951579\pi$
$858$	12.3970	−	30.7081i	0.423225	−	1.04836i
$859$	27.4848	−	41.1339i	0.937768	−	1.40347i	0.0228908	−	0.999738i	$-0.492713\pi$
$859$	27.4848	−	41.1339i	0.937768	−	1.40347i	0.914878	−	0.403732i	$-0.132287\pi$
$860$	17.7572	+	17.1288i	0.605514	+	0.584088i
$861$	10.7594	+	2.14018i	0.366680	+	0.0729372i
$862$	−0.637695	+	3.36394i	−0.0217200	+	0.114576i
$863$			38.4116i			1.30754i	0.756691	+	0.653772i	$0.226815\pi$
$863$			38.4116i			1.30754i	−0.756691	+	0.653772i	$0.773185\pi$
$864$	−4.17598	−	3.81591i	−0.142070	−	0.129820i
$865$			46.2775i			1.57348i
$866$	27.9285	+	5.29434i	0.949048	+	0.179909i
$867$	−16.1494	−	3.21231i	−0.548462	−	0.109096i
$868$	−22.1228	+	0.398458i	−0.750896	+	0.0135245i
$869$	−15.7081	+	23.5089i	−0.532862	+	0.797485i
$870$	−2.03447	−	0.821322i	−0.0689750	−	0.0278454i
$871$	−3.46895	−	8.37479i	−0.117541	−	0.283769i
$872$	−30.9504	−	29.3218i	−1.04811	−	0.992963i
$873$	−1.50737	+	3.63911i	−0.0510167	+	0.123165i
$874$	16.4223	+	16.1292i	0.555494	+	0.545579i
$875$	−1.04583	−	5.25775i	−0.0353556	−	0.177744i
$876$	−13.1640	−	18.9533i	−0.444770	−	0.640373i
$877$	−18.3810	−	27.5091i	−0.620682	−	0.928916i	−0.999993	−	0.00364702i	$-0.998839\pi$
$877$	−18.3810	−	27.5091i	−0.620682	−	0.928916i	0.379311	−	0.925269i	$-0.376161\pi$
$878$	2.89484	+	13.8981i	0.0976960	+	0.469038i
$879$	−5.74730	−	5.74730i	−0.193852	−	0.193852i
$880$	−25.2186	−	55.1745i	−0.850118	−	1.85993i
$881$	18.4097	−	18.4097i	0.620238	−	0.620238i	−0.325354	−	0.945592i	$-0.605483\pi$
$881$	18.4097	−	18.4097i	0.620238	−	0.620238i	0.945592	+	0.325354i	$0.105483\pi$
$882$	−6.61999	−	4.33763i	−0.222907	−	0.146055i
$883$	−26.1841	+	17.4956i	−0.881164	+	0.588775i	−0.911745	−	0.410757i	$-0.865264\pi$
$883$	−26.1841	+	17.4956i	−0.881164	+	0.588775i	0.0305805	+	0.999532i	$0.490264\pi$
$884$	−3.54471	+	5.51761i	−0.119222	+	0.185577i
$885$	−34.2859	+	6.81989i	−1.15251	+	0.229248i
$886$	−0.386455	−	42.9162i	−0.0129832	−	1.44180i
$887$	13.3290	+	5.52105i	0.447544	+	0.185379i	0.595061	−	0.803681i	$-0.297128\pi$
$887$	13.3290	+	5.52105i	0.447544	+	0.185379i	−0.147517	+	0.989060i	$0.547128\pi$
$888$	−15.4571	−	9.73467i	−0.518705	−	0.326674i
$889$	−12.2228	+	5.06284i	−0.409939	+	0.169802i
$890$	55.8452	−	23.7232i	1.87194	−	0.795204i
$891$	4.33991	+	2.89983i	0.145392	+	0.0971481i
$892$	31.4813	+	12.3806i	1.05407	+	0.414533i
$893$	−1.55349	+	7.80993i	−0.0519856	+	0.261349i
$894$	−15.3223	−	22.4904i	−0.512456	−	0.752193i
$895$	14.4460			0.482876
$896$	−13.2848	−	1.78166i	−0.443815	−	0.0595212i
$897$	13.8887			0.463729
$898$	17.8847	+	26.2516i	0.596821	+	0.876026i
$899$	−0.972689	+	4.89004i	−0.0324410	+	0.163092i
$900$	6.40777	+	2.51997i	0.213592	+	0.0839991i
$901$	−2.35393	−	1.57285i	−0.0784208	−	0.0523991i
$902$	62.9096	−	26.7242i	2.09466	−	0.889817i
$903$	−4.64700	+	1.92485i	−0.154642	+	0.0640550i
$904$	−0.267171	+	0.424225i	−0.00888599	+	0.0141095i
$905$	57.8573	+	23.9653i	1.92324	+	0.796632i
$906$	−0.146492	−	16.2681i	−0.00486686	−	0.540470i
$907$	−23.0754	+	4.58998i	−0.766205	+	0.152408i	−0.562694	−	0.826665i	$-0.690235\pi$
$907$	−23.0754	+	4.58998i	−0.766205	+	0.152408i	−0.203511	+	0.979073i	$0.565235\pi$
$908$	−14.9790	+	23.3160i	−0.497097	+	0.773768i
$909$	−9.18598	+	6.13787i	−0.304680	+	0.203580i
$910$	18.2685	+	11.9701i	0.605594	+	0.396804i
$911$	−1.55018	+	1.55018i	−0.0513596	+	0.0513596i	−0.732320	−	0.680961i	$-0.761563\pi$
$911$	−1.55018	+	1.55018i	−0.0513596	+	0.0513596i	0.680961	+	0.732320i	$0.261563\pi$
$912$	19.7068	+	7.34312i	0.652558	+	0.243155i
$913$	−59.5903	−	59.5903i	−1.97215	−	1.97215i
$914$	4.37865	+	21.0219i	0.144833	+	0.695341i
$915$	20.4105	+	30.5465i	0.674750	+	1.00984i
$916$	−15.4978	−	22.3134i	−0.512060	−	0.737256i
$917$	−3.00070	−	15.0856i	−0.0990920	−	0.498169i
$918$	−0.737456	−	0.724293i	−0.0243397	−	0.0239052i
$919$	−4.22610	+	10.2027i	−0.139406	+	0.336556i	−0.978128	−	0.208004i	$-0.933303\pi$
$919$	−4.22610	+	10.2027i	−0.139406	+	0.336556i	0.838722	+	0.544560i	$0.183303\pi$
$920$	17.4980	−	18.4698i	0.576890	−	0.608932i
$921$	9.93628	+	23.9883i	0.327411	+	0.790441i
$922$	−21.6373	−	8.73502i	−0.712585	−	0.287673i
$923$	0.190149	−	0.284579i	0.00625884	−	0.00936702i
$924$	12.3656	−	0.222720i	0.406799	−	0.00732693i
$925$	21.8072	+	4.33773i	0.717018	+	0.142624i
$926$	−2.86295	−	0.542724i	−0.0940824	−	0.0178350i
$927$		−	7.40115i		−	0.243086i
$928$	−1.02907	+	2.83962i	−0.0337809	+	0.0932151i
$929$		−	36.3512i		−	1.19264i	−0.802745	−	0.596322i	$-0.796628\pi$
$929$		−	36.3512i		−	1.19264i	0.802745	−	0.596322i	$-0.203372\pi$
$930$	7.14683	−	37.7006i	0.234354	−	1.23625i
$931$	28.8583	+	5.74028i	0.945794	+	0.188130i
$932$	25.6819	+	24.7732i	0.841239	+	0.811472i
$933$	−2.17537	+	3.25568i	−0.0712185	+	0.106586i
$934$	19.1982	−	47.5553i	0.628185	−	1.55606i
$935$	−4.24205	−	10.2412i	−0.138730	−	0.334923i
$936$	11.5879	−	5.17083i	0.378761	−	0.169014i
$937$	6.37040	−	15.3795i	0.208112	−	0.502426i	−0.785014	−	0.619478i	$-0.787344\pi$
$937$	6.37040	−	15.3795i	0.208112	−	0.502426i	0.993126	+	0.117052i	$0.0373443\pi$
$938$	2.37216	−	2.41527i	0.0774539	−	0.0788615i
$939$	1.46158	+	7.34784i	0.0476967	+	0.239788i
$940$	8.66189	+	1.56135i	0.282520	+	0.0509257i
$941$	−6.10161	−	9.13170i	−0.198907	−	0.297685i	0.718586	−	0.695439i	$-0.244790\pi$
$941$	−6.10161	−	9.13170i	−0.198907	−	0.297685i	−0.917492	+	0.397754i	$0.869790\pi$
$942$	−2.44284	+	0.508820i	−0.0795920	+	0.0165782i
$943$	20.2697	+	20.2697i	0.660074	+	0.660074i
$944$	11.0821	+	46.8304i	0.360691	+	1.52420i
$945$	−2.43416	+	2.43416i	−0.0791832	+	0.0791832i
$946$	−17.1756	+	26.2131i	−0.558428	+	0.852260i
$947$	20.5531	−	13.7331i	0.667885	−	0.446267i	−0.174850	−	0.984595i	$-0.555944\pi$
$947$	20.5531	−	13.7331i	0.667885	−	0.446267i	0.842735	+	0.538329i	$0.180944\pi$
$948$	−10.5859	+	2.30458i	−0.343813	+	0.0748493i
$949$	50.7693	−	10.0986i	1.64804	−	0.327816i
$950$	−25.5971	+	0.230498i	−0.830478	+	0.00747835i
$951$	−22.5785	−	9.35233i	−0.732159	−	0.303270i
$952$	−2.41419	−	0.412761i	−0.0782442	−	0.0133776i
$953$	−17.9107	+	7.41886i	−0.580185	+	0.240320i	−0.653422	−	0.756994i	$-0.726667\pi$
$953$	−17.9107	+	7.41886i	−0.580185	+	0.240320i	0.0732370	+	0.997315i	$0.476667\pi$
$954$	2.14173	+	5.04170i	0.0693411	+	0.163231i
$955$	24.9868	+	16.6957i	0.808555	+	0.540259i
$956$	−24.2809	+	10.5737i	−0.785301	+	0.341978i
$957$	0.543688	−	2.73331i	0.0175749	−	0.0883552i
$958$	−17.8871	+	12.1861i	−0.577905	+	0.393717i
$959$	2.87122			0.0927166
$960$	7.72282	−	21.9247i	0.249253	−	0.707617i
$961$	−56.2000			−1.81290
$962$	33.8638	−	23.0708i	1.09181	−	0.743833i
$963$	2.01439	−	10.1270i	0.0649128	−	0.326339i
$964$	16.0535	+	36.8645i	0.517049	+	1.18733i
$965$	42.4636	+	28.3733i	1.36695	+	0.913368i
$966$	2.02801	+	4.77400i	0.0652501	+	0.153601i
$967$	35.4498	−	14.6838i	1.13999	−	0.472199i	0.268824	−	0.963189i	$-0.413365\pi$
$967$	35.4498	−	14.6838i	1.13999	−	0.472199i	0.871165	+	0.490991i	$0.163365\pi$
$968$	37.4980	−	26.5479i	1.20523	−	0.853282i
$969$	3.55029	+	1.47058i	0.114052	+	0.0472418i
$970$	−16.1852	+	0.145746i	−0.519676	+	0.00467962i
$971$	−27.8529	+	5.54028i	−0.893841	+	0.177796i	−0.620579	−	0.784144i	$-0.713103\pi$
$971$	−27.8529	+	5.54028i	−0.893841	+	0.177796i	−0.273262	+	0.961940i	$0.588103\pi$
$972$	0.425442	+	1.95423i	0.0136461	+	0.0626818i
$973$	−2.96999	+	1.98449i	−0.0952136	+	0.0636197i
$974$	12.4522	−	19.0043i	0.398995	−	0.608938i
$975$	−10.9214	+	10.9214i	−0.349765	+	0.349765i
$976$	41.0122	−	29.5939i	1.31277	−	0.947276i
$977$	21.4481	+	21.4481i	0.686186	+	0.686186i	0.961387	−	0.275201i	$-0.0887445\pi$
$977$	21.4481	+	21.4481i	0.686186	+	0.686186i	−0.275201	+	0.961387i	$0.588744\pi$
$978$	−10.5214	+	2.19151i	−0.336437	+	0.0700766i
$979$	42.8181	+	64.0818i	1.36847	+	2.04806i
$980$	5.76933	−	32.0064i	0.184294	−	1.02241i
$981$	2.94071	+	14.7839i	0.0938895	+	0.472014i
$982$	−34.8256	+	35.4585i	−1.11133	+	1.13153i
$983$	4.27208	−	10.3137i	0.136258	−	0.328957i	−0.840991	−	0.541048i	$-0.818028\pi$
$983$	4.27208	−	10.3137i	0.136258	−	0.328957i	0.977250	+	0.212092i	$0.0680276\pi$
$984$	24.4584	+	9.36531i	0.779706	+	0.298555i
$985$	−7.53449	−	18.1899i	−0.240069	−	0.579577i
$986$	−0.206601	+	0.511764i	−0.00657951	+	0.0162979i
$987$	−0.996886	+	1.49195i	−0.0317312	+	0.0474891i
$988$	−32.7514	+	33.9528i	−1.04196	+	1.08018i
$989$	−12.8908	−	2.56413i	−0.409903	−	0.0815347i
$990$	−3.99474	+	21.0729i	−0.126961	+	0.669740i
$991$			17.8630i			0.567436i	0.958908	+	0.283718i	$0.0915680\pi$
$991$			17.8630i			0.567436i	−0.958908	+	0.283718i	$0.908432\pi$
$992$	−52.2205	−	7.96323i	−1.65800	−	0.252833i
$993$		−	9.72270i		−	0.308540i
$994$	0.125585	+	0.0238069i	0.00398331	+	0.000755107i
$995$	−16.6705	−	3.31597i	−0.528490	−	0.105123i
$996$	−0.581512	−	32.2861i	−0.0184259	−	1.02303i
$997$	−9.94645	+	14.8859i	−0.315007	+	0.471442i	−0.954860	−	0.297056i	$-0.903995\pi$
$997$	−9.94645	+	14.8859i	−0.315007	+	0.471442i	0.639853	+	0.768497i	$0.278995\pi$
$998$	−40.4761	−	16.3403i	−1.28125	−	0.517244i
$999$	2.47151	+	5.96676i	0.0781952	+	0.188780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.61.4	✓	128
3.2	odd	2		576.2.bd.b.253.13		128
4.3	odd	2		768.2.r.a.337.8		128
64.21	even	16	inner	192.2.r.a.85.4	yes	128
64.43	odd	16		768.2.r.a.433.8		128
192.149	odd	16		576.2.bd.b.469.13		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.61.4	✓	128	1.1	even	1	trivial
192.2.r.a.85.4	yes	128	64.21	even	16	inner
576.2.bd.b.253.13		128	3.2	odd	2
576.2.bd.b.469.13		128	192.149	odd	16
768.2.r.a.337.8		128	4.3	odd	2
768.2.r.a.433.8		128	64.43	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.796251 - 1.16875i) q^{2} +(0.195090 - 0.980785i) q^{3} +(-0.731968 + 1.86124i) q^{4} +(2.41595 + 1.61429i) q^{5} +(-1.30164 + 0.552939i) q^{6} +(1.09455 - 0.453379i) q^{7} +(2.75816 - 0.626527i) q^{8} +(-0.923880 - 0.382683i) q^{9} +O(q^{10})\)	\(q+(-0.796251 - 1.16875i) q^{2} +(0.195090 - 0.980785i) q^{3} +(-0.731968 + 1.86124i) q^{4} +(2.41595 + 1.61429i) q^{5} +(-1.30164 + 0.552939i) q^{6} +(1.09455 - 0.453379i) q^{7} +(2.75816 - 0.626527i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(-0.0370012 - 4.10903i) q^{10} +(5.11927 - 1.01829i) q^{11} +(1.68268 + 1.08101i) q^{12} +(-3.73023 + 2.49246i) q^{13} +(-1.40143 - 0.918260i) q^{14} +(2.05460 - 2.05460i) q^{15} +(-2.92845 - 2.72474i) q^{16} +(-0.516827 - 0.516827i) q^{17} +(0.288378 + 1.38450i) q^{18} +(-2.92098 - 4.37155i) q^{19} +(-4.77298 + 3.31506i) q^{20} +(-0.231131 - 1.16197i) q^{21} +(-5.26635 - 5.17235i) q^{22} +(1.18470 - 2.86013i) q^{23} +(-0.0763975 - 2.82740i) q^{24} +(1.31748 + 3.18067i) q^{25} +(5.88328 + 2.37510i) q^{26} +(-0.555570 + 0.831470i) q^{27} +(0.0426702 + 2.36909i) q^{28} +(0.523666 + 0.104164i) q^{29} +(-4.03729 - 0.765341i) q^{30} +9.33809i q^{31} +(-0.852768 + 5.59221i) q^{32} -5.21956i q^{33} +(-0.192519 + 1.01557i) q^{34} +(3.37627 + 0.671583i) q^{35} +(1.38852 - 1.43945i) q^{36} +(3.58808 - 5.36994i) q^{37} +(-2.78343 + 6.89475i) q^{38} +(1.71684 + 4.14481i) q^{39} +(7.67498 + 2.93881i) q^{40} +(-3.54350 + 8.55477i) q^{41} +(-1.17402 + 1.19536i) q^{42} +(-0.828267 - 4.16398i) q^{43} +(-1.85186 + 10.2736i) q^{44} +(-1.61429 - 2.41595i) q^{45} +(-4.28611 + 0.892755i) q^{46} +(-1.07095 - 1.07095i) q^{47} +(-3.24370 + 2.34061i) q^{48} +(-3.95725 + 3.95725i) q^{49} +(2.66838 - 4.07242i) q^{50} +(-0.607724 + 0.406068i) q^{51} +(-1.90867 - 8.76727i) q^{52} +(3.79893 - 0.755654i) q^{53} +(1.41416 - 0.0127343i) q^{54} +(14.0117 + 5.80384i) q^{55} +(2.73491 - 1.93626i) q^{56} +(-4.85740 + 2.01200i) q^{57} +(-0.295228 - 0.694976i) q^{58} +(-10.0034 - 6.68404i) q^{59} +(2.32020 + 5.32800i) q^{60} +(-2.46666 + 12.4007i) q^{61} +(10.9139 - 7.43547i) q^{62} -1.18474 q^{63} +(7.21493 - 3.45613i) q^{64} -13.0356 q^{65} +(-6.10038 + 4.15608i) q^{66} +(-0.394189 + 1.98172i) q^{67} +(1.34024 - 0.583640i) q^{68} +(-2.57405 - 1.71992i) q^{69} +(-1.90345 - 4.48078i) q^{70} +(-0.0704826 + 0.0291948i) q^{71} +(-2.78797 - 0.476668i) q^{72} +(-10.6599 - 4.41547i) q^{73} +(-9.13314 + 0.0822428i) q^{74} +(3.37659 - 0.671645i) q^{75} +(10.2746 - 2.23681i) q^{76} +(5.14165 - 3.43554i) q^{77} +(3.47723 - 5.30687i) q^{78} +(-3.83034 + 3.83034i) q^{79} +(-2.67647 - 11.3102i) q^{80} +(0.707107 + 0.707107i) q^{81} +(12.8199 - 2.67027i) q^{82} +(-8.97007 - 13.4247i) q^{83} +(2.33189 + 0.420336i) q^{84} +(-0.414322 - 2.08294i) q^{85} +(-4.20716 + 4.28361i) q^{86} +(0.204324 - 0.493282i) q^{87} +(13.4818 - 6.01596i) q^{88} +(5.65060 + 13.6417i) q^{89} +(-1.53827 + 3.81041i) q^{90} +(-2.95291 + 4.41935i) q^{91} +(4.45623 + 4.29854i) q^{92} +(9.15866 + 1.82177i) q^{93} +(-0.398931 + 2.10442i) q^{94} -15.2767i q^{95} +(5.31839 + 1.92737i) q^{96} -3.93894i q^{97} +(7.77601 + 1.47408i) q^{98} +(-5.11927 - 1.01829i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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