LMFDB - Embedded newform 819.2.bh.a.673.64

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(589,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("819.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bh (of order $6$, degree $2$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			673.64
Character	$\chi$	$=$	819.673
Dual form			819.2.bh.a.589.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.68867i q^{2} +(1.44941 - 0.948269i) q^{3} -0.851603 q^{4} +(1.72850 - 0.997952i) q^{5} +(1.60131 + 2.44757i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.93926i q^{8} +(1.20157 - 2.74886i) q^{9} +O(q^{10})$	\(q+1.68867i q^{2} +(1.44941 - 0.948269i) q^{3} -0.851603 q^{4} +(1.72850 - 0.997952i) q^{5} +(1.60131 + 2.44757i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.93926i q^{8} +(1.20157 - 2.74886i) q^{9} +(1.68521 + 2.91887i) q^{10} +2.78788i q^{11} +(-1.23432 + 0.807548i) q^{12} +(0.954644 + 3.47687i) q^{13} +(-0.844334 - 1.46243i) q^{14} +(1.55898 - 3.08553i) q^{15} -4.97798 q^{16} +(1.71694 - 2.97383i) q^{17} +(4.64191 + 2.02906i) q^{18} +(2.55074 + 1.47267i) q^{19} +(-1.47200 + 0.849858i) q^{20} +(-0.781091 + 1.54593i) q^{21} -4.70780 q^{22} +(0.434089 - 0.751863i) q^{23} +(1.83894 + 2.81078i) q^{24} +(-0.508185 + 0.880202i) q^{25} +(-5.87129 + 1.61208i) q^{26} +(-0.865086 - 5.12363i) q^{27} +(0.737510 - 0.425801i) q^{28} -2.47019 q^{29} +(5.21043 + 2.63260i) q^{30} +(5.38232 - 3.10748i) q^{31} -4.52763i q^{32} +(2.64366 + 4.04077i) q^{33} +(5.02182 + 2.89935i) q^{34} +(-0.997952 + 1.72850i) q^{35} +(-1.02326 + 2.34094i) q^{36} +(5.93039 - 3.42391i) q^{37} +(-2.48685 + 4.30735i) q^{38} +(4.68068 + 4.13415i) q^{39} +(1.93529 + 3.35202i) q^{40} +(-1.95680 - 1.12976i) q^{41} +(-2.61056 - 1.31900i) q^{42} +(-1.31101 - 2.27074i) q^{43} -2.37416i q^{44} +(-0.666306 - 5.95052i) q^{45} +(1.26965 + 0.733032i) q^{46} +(4.45571 + 2.57250i) q^{47} +(-7.21513 + 4.72046i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-1.48637 - 0.858156i) q^{50} +(-0.331440 - 5.93843i) q^{51} +(-0.812977 - 2.96092i) q^{52} -5.32084 q^{53} +(8.65212 - 1.46084i) q^{54} +(2.78217 + 4.81885i) q^{55} +(-0.969631 - 1.67945i) q^{56} +(5.09355 - 0.284285i) q^{57} -4.17133i q^{58} -12.5330i q^{59} +(-1.32763 + 2.62764i) q^{60} +(3.33180 + 5.77085i) q^{61} +(5.24751 + 9.08896i) q^{62} +(0.333837 + 2.98137i) q^{63} -2.31029 q^{64} +(5.11986 + 5.05710i) q^{65} +(-6.82353 + 4.46426i) q^{66} +(-1.81417 - 1.04741i) q^{67} +(-1.46215 + 2.53253i) q^{68} +(-0.0837968 - 1.50139i) q^{69} +(-2.91887 - 1.68521i) q^{70} +(-8.10653 - 4.68031i) q^{71} +(5.33076 + 2.33017i) q^{72} +11.1596i q^{73} +(5.78186 + 10.0145i) q^{74} +(0.0981004 + 1.75767i) q^{75} +(-2.17222 - 1.25413i) q^{76} +(-1.39394 - 2.41437i) q^{77} +(-6.98122 + 7.90412i) q^{78} +(1.52947 - 2.64913i) q^{79} +(-8.60445 + 4.96778i) q^{80} +(-6.11245 - 6.60591i) q^{81} +(1.90778 - 3.30438i) q^{82} +(-10.1113 - 5.83777i) q^{83} +(0.665179 - 1.31652i) q^{84} -6.85371i q^{85} +(3.83453 - 2.21387i) q^{86} +(-3.58032 + 2.34240i) q^{87} -5.40643 q^{88} +(-15.1919 + 8.77105i) q^{89} +(10.0485 - 1.12517i) q^{90} +(-2.56518 - 2.53374i) q^{91} +(-0.369671 + 0.640289i) q^{92} +(4.85445 - 9.60790i) q^{93} +(-4.34411 + 7.52421i) q^{94} +5.87861 q^{95} +(-4.29341 - 6.56239i) q^{96} +(5.82839 - 3.36502i) q^{97} +(1.46243 + 0.844334i) q^{98} +(7.66348 + 3.34984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 168 q^{4} + 18 q^{6} - 2 q^{9}+O(q^{10}) $ 168 * q - 168 * q^4 + 18 * q^6 - 2 * q^9	$ 168 q - 168 q^{4} + 18 q^{6} - 2 q^{9} + 12 q^{12} + 8 q^{14} + 6 q^{15} + 168 q^{16} - 12 q^{18} + 6 q^{21} - 20 q^{23} - 36 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} - 68 q^{29} - 4 q^{30} + 16 q^{35} - 2 q^{36} - 12 q^{38} - 6 q^{39} + 24 q^{41} - 30 q^{45} + 30 q^{47} + 40 q^{48} + 84 q^{49} + 12 q^{50} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 36 q^{54} - 24 q^{56} + 54 q^{57} - 24 q^{60} + 6 q^{62} - 132 q^{64} + 74 q^{65} - 54 q^{66} + 78 q^{68} - 4 q^{69} + 24 q^{71} - 42 q^{72} + 42 q^{74} - 60 q^{75} - 16 q^{77} + 38 q^{78} - 6 q^{79} - 74 q^{81} - 6 q^{82} - 18 q^{83} - 66 q^{84} + 24 q^{86} - 38 q^{87} - 48 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 6 q^{93} - 60 q^{94} + 96 q^{95} + 24 q^{96} - 6 q^{99}+O(q^{100}) $ 168 * q - 168 * q^4 + 18 * q^6 - 2 * q^9 + 12 * q^12 + 8 * q^14 + 6 * q^15 + 168 * q^16 - 12 * q^18 + 6 * q^21 - 20 * q^23 - 36 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 - 68 * q^29 - 4 * q^30 + 16 * q^35 - 2 * q^36 - 12 * q^38 - 6 * q^39 + 24 * q^41 - 30 * q^45 + 30 * q^47 + 40 * q^48 + 84 * q^49 + 12 * q^50 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 36 * q^54 - 24 * q^56 + 54 * q^57 - 24 * q^60 + 6 * q^62 - 132 * q^64 + 74 * q^65 - 54 * q^66 + 78 * q^68 - 4 * q^69 + 24 * q^71 - 42 * q^72 + 42 * q^74 - 60 * q^75 - 16 * q^77 + 38 * q^78 - 6 * q^79 - 74 * q^81 - 6 * q^82 - 18 * q^83 - 66 * q^84 + 24 * q^86 - 38 * q^87 - 48 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 6 * q^93 - 60 * q^94 + 96 * q^95 + 24 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.68867i			1.19407i	0.802215	+	0.597035i	$0.203655\pi$
$2$			1.68867i			1.19407i	−0.802215	+	0.597035i	$0.796345\pi$
$3$	1.44941	−	0.948269i	0.836817	−	0.547483i
$3$	1.44941	−	0.948269i	0.836817	−	0.547483i
$4$	−0.851603			−0.425801
$5$	1.72850	−	0.997952i	0.773010	−	0.446298i	−0.0609373	−	0.998142i	$-0.519409\pi$
$5$	1.72850	−	0.997952i	0.773010	−	0.446298i	0.833947	+	0.551844i	$0.186076\pi$
$6$	1.60131	+	2.44757i	0.653733	+	0.999217i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$			1.93926i			0.685633i
$9$	1.20157	−	2.74886i	0.400524	−	0.916286i
$10$	1.68521	+	2.91887i	0.532910	+	0.923028i
$11$			2.78788i			0.840577i	0.907391	+	0.420288i	$0.138071\pi$
$11$			2.78788i			0.840577i	−0.907391	+	0.420288i	$0.861929\pi$
$12$	−1.23432	+	0.807548i	−0.356318	+	0.233119i
$13$	0.954644	+	3.47687i	0.264771	+	0.964311i
$13$	0.954644	+	3.47687i	0.264771	+	0.964311i
$14$	−0.844334	−	1.46243i	−0.225658	−	0.390851i
$15$	1.55898	−	3.08553i	0.402527	−	0.796679i
$16$	−4.97798			−1.24449
$17$	1.71694	−	2.97383i	0.416420	−	0.721261i	−0.579156	−	0.815216i	$-0.696618\pi$
$17$	1.71694	−	2.97383i	0.416420	−	0.721261i	0.995576	+	0.0939559i	$0.0299513\pi$
$18$	4.64191	+	2.02906i	1.09411	+	0.478254i
$19$	2.55074	+	1.47267i	0.585179	+	0.337853i	0.763189	−	0.646175i	$-0.223633\pi$
$19$	2.55074	+	1.47267i	0.585179	+	0.337853i	−0.178010	+	0.984029i	$0.556966\pi$
$20$	−1.47200	+	0.849858i	−0.329149	+	0.190034i
$21$	−0.781091	+	1.54593i	−0.170448	+	0.337349i
$22$	−4.70780			−1.00371
$23$	0.434089	−	0.751863i	0.0905137	−	0.156774i	−0.817214	−	0.576335i	$-0.804482\pi$
$23$	0.434089	−	0.751863i	0.0905137	−	0.156774i	0.907727	+	0.419560i	$0.137816\pi$
$24$	1.83894	+	2.81078i	0.375373	+	0.573749i
$25$	−0.508185	+	0.880202i	−0.101637	+	0.176040i
$26$	−5.87129	+	1.61208i	−1.15145	+	0.316154i
$27$	−0.865086	−	5.12363i	−0.166486	−	0.986044i
$28$	0.737510	−	0.425801i	0.139376	−	0.0804689i
$29$	−2.47019			−0.458703			−0.229351	−	0.973344i	$-0.573661\pi$
$29$	−2.47019			−0.458703			−0.229351	+	0.973344i	$0.573661\pi$
$30$	5.21043	+	2.63260i	0.951290	+	0.480645i
$31$	5.38232	−	3.10748i	0.966693	−	0.558121i	0.0684669	−	0.997653i	$-0.478189\pi$
$31$	5.38232	−	3.10748i	0.966693	−	0.558121i	0.898227	+	0.439533i	$0.144856\pi$
$32$		−	4.52763i		−	0.800380i
$33$	2.64366	+	4.04077i	0.460202	+	0.703409i
$34$	5.02182	+	2.89935i	0.861235	+	0.497234i
$35$	−0.997952	+	1.72850i	−0.168685	+	0.292170i
$36$	−1.02326	+	2.34094i	−0.170544	+	0.390156i
$37$	5.93039	−	3.42391i	0.974950	−	0.562888i	0.0742085	−	0.997243i	$-0.476357\pi$
$37$	5.93039	−	3.42391i	0.974950	−	0.562888i	0.900742	+	0.434355i	$0.143024\pi$
$38$	−2.48685	+	4.30735i	−0.403420	+	0.698745i
$39$	4.68068	+	4.13415i	0.749509	+	0.661994i
$40$	1.93529	+	3.35202i	0.305996	+	0.530001i
$41$	−1.95680	−	1.12976i	−0.305600	−	0.176438i	0.339356	−	0.940658i	$-0.389791\pi$
$41$	−1.95680	−	1.12976i	−0.305600	−	0.176438i	−0.644956	+	0.764220i	$0.723124\pi$
$42$	−2.61056	−	1.31900i	−0.402819	−	0.203527i
$43$	−1.31101	−	2.27074i	−0.199927	−	0.346285i	0.748577	−	0.663048i	$-0.230737\pi$
$43$	−1.31101	−	2.27074i	−0.199927	−	0.346285i	−0.948505	+	0.316763i	$0.897404\pi$
$44$		−	2.37416i		−	0.357919i
$45$	−0.666306	−	5.95052i	−0.0993270	−	0.887051i
$46$	1.26965	+	0.733032i	0.187199	+	0.108080i
$47$	4.45571	+	2.57250i	0.649932	+	0.375238i	0.788430	−	0.615125i	$-0.210894\pi$
$47$	4.45571	+	2.57250i	0.649932	+	0.375238i	−0.138498	+	0.990363i	$0.544228\pi$
$48$	−7.21513	+	4.72046i	−1.04141	+	0.681340i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−1.48637	−	0.858156i	−0.210204	−	0.121362i
$51$	−0.331440	−	5.93843i	−0.0464109	−	0.831546i
$52$	−0.812977	−	2.96092i	−0.112740	−	0.410605i
$53$	−5.32084			−0.730874			−0.365437	−	0.930836i	$-0.619080\pi$
$53$	−5.32084			−0.730874			−0.365437	+	0.930836i	$0.619080\pi$
$54$	8.65212	−	1.46084i	1.17740	−	0.198796i
$55$	2.78217	+	4.81885i	0.375147	+	0.649774i
$56$	−0.969631	−	1.67945i	−0.129572	−	0.224426i
$57$	5.09355	−	0.284285i	0.674657	−	0.0376545i
$58$		−	4.17133i		−	0.547723i
$59$		−	12.5330i		−	1.63166i	−0.578291	−	0.815830i	$-0.696280\pi$
$59$		−	12.5330i		−	1.63166i	0.578291	−	0.815830i	$-0.303720\pi$
$60$	−1.32763	+	2.62764i	−0.171397	+	0.339227i
$61$	3.33180	+	5.77085i	0.426593	+	0.738881i	0.996568	−	0.0827812i	$-0.0263803\pi$
$61$	3.33180	+	5.77085i	0.426593	+	0.738881i	−0.569974	+	0.821662i	$0.693047\pi$
$62$	5.24751	+	9.08896i	0.666435	+	1.15430i
$63$	0.333837	+	2.98137i	0.0420595	+	0.375617i
$64$	−2.31029			−0.288786
$65$	5.11986	+	5.05710i	0.635040	+	0.627256i
$66$	−6.82353	+	4.46426i	−0.839919	+	0.549513i
$67$	−1.81417	−	1.04741i	−0.221636	−	0.127962i	0.385072	−	0.922887i	$-0.374177\pi$
$67$	−1.81417	−	1.04741i	−0.221636	−	0.127962i	−0.606708	+	0.794925i	$0.707510\pi$
$68$	−1.46215	+	2.53253i	−0.177312	+	0.307114i
$69$	−0.0837968	−	1.50139i	−0.0100879	−	0.180746i
$70$	−2.91887	−	1.68521i	−0.348872	−	0.201421i
$71$	−8.10653	−	4.68031i	−0.962068	−	0.555450i	−0.0652591	−	0.997868i	$-0.520787\pi$
$71$	−8.10653	−	4.68031i	−0.962068	−	0.555450i	−0.896809	+	0.442418i	$0.854121\pi$
$72$	5.33076	+	2.33017i	0.628236	+	0.274613i
$73$			11.1596i			1.30614i	0.757298	+	0.653069i	$0.226519\pi$
$73$			11.1596i			1.30614i	−0.757298	+	0.653069i	$0.773481\pi$
$74$	5.78186	+	10.0145i	0.672127	+	1.16416i
$75$	0.0981004	+	1.75767i	0.0113277	+	0.202958i
$76$	−2.17222	−	1.25413i	−0.249170	−	0.143858i
$77$	−1.39394	−	2.41437i	−0.158854	−	0.275143i
$78$	−6.98122	+	7.90412i	−0.790467	+	0.894965i
$79$	1.52947	−	2.64913i	0.172079	−	0.298050i	−0.767067	−	0.641567i	$-0.778285\pi$
$79$	1.52947	−	2.64913i	0.172079	−	0.298050i	0.939147	+	0.343517i	$0.111618\pi$
$80$	−8.60445	+	4.96778i	−0.962007	+	0.555415i
$81$	−6.11245	−	6.60591i	−0.679161	−	0.733990i
$82$	1.90778	−	3.30438i	0.210680	−	0.364908i
$83$	−10.1113	−	5.83777i	−1.10986	−	0.640779i	−0.171068	−	0.985259i	$-0.554722\pi$
$83$	−10.1113	−	5.83777i	−1.10986	−	0.640779i	−0.938793	+	0.344481i	$0.888055\pi$
$84$	0.665179	−	1.31652i	0.0725770	−	0.143644i
$85$		−	6.85371i		−	0.743389i
$86$	3.83453	−	2.21387i	0.413488	−	0.238727i
$87$	−3.58032	+	2.34240i	−0.383850	+	0.251132i
$88$	−5.40643			−0.576327
$89$	−15.1919	+	8.77105i	−1.61034	+	0.929729i	−0.621047	+	0.783773i	$0.713293\pi$
$89$	−15.1919	+	8.77105i	−1.61034	+	0.929729i	−0.989291	+	0.145956i	$0.953374\pi$
$90$	10.0485	−	1.12517i	1.05920	−	0.118603i
$91$	−2.56518	−	2.53374i	−0.268904	−	0.265608i
$92$	−0.369671	+	0.640289i	−0.0385409	+	0.0667547i
$93$	4.85445	−	9.60790i	0.503383	−	0.996293i
$94$	−4.34411	+	7.52421i	−0.448060	+	0.776063i
$95$	5.87861			0.603133
$96$	−4.29341	−	6.56239i	−0.438195	−	0.669771i
$97$	5.82839	−	3.36502i	0.591784	−	0.341666i	−0.174019	−	0.984742i	$-0.555675\pi$
$97$	5.82839	−	3.36502i	0.591784	−	0.341666i	0.765802	+	0.643076i	$0.222342\pi$
$98$	1.46243	+	0.844334i	0.147728	+	0.0852907i
$99$	7.66348	+	3.34984i	0.770209	+	0.336671i
$100$	0.432772	−	0.749583i	0.0432772	−	0.0749583i
$101$	−16.4124			−1.63310			−0.816549	−	0.577277i	$-0.804115\pi$
$101$	−16.4124			−1.63310			−0.816549	+	0.577277i	$0.804115\pi$
$102$	10.0280	−	0.559693i	0.992923	−	0.0554178i
$103$	−7.50261	−	12.9949i	−0.739254	−	1.28043i	−0.952831	−	0.303500i	$-0.901845\pi$
$103$	−7.50261	−	12.9949i	−0.739254	−	1.28043i	0.213577	−	0.976926i	$-0.431489\pi$
$104$	−6.74257	+	1.85130i	−0.661164	+	0.181535i
$105$	0.192645	+	3.45163i	0.0188003	+	0.336845i
$106$		−	8.98514i		−	0.872714i
$107$	0.0702618	+	0.121697i	0.00679246	+	0.0117649i	0.869402	−	0.494106i	$-0.164505\pi$
$107$	0.0702618	+	0.121697i	0.00679246	+	0.0117649i	−0.862609	+	0.505871i	$0.831171\pi$
$108$	0.736710	+	4.36330i	0.0708900	+	0.419859i
$109$			4.84617i			0.464179i	0.972694	+	0.232090i	$0.0745563\pi$
$109$			4.84617i			0.464179i	−0.972694	+	0.232090i	$0.925444\pi$
$110$	−8.13745	+	4.69816i	−0.775875	+	0.447952i
$111$	5.34877	−	10.5863i	0.507683	−	1.00480i
$112$	4.31106	−	2.48899i	0.407356	−	0.235187i
$113$	−7.35419			−0.691824			−0.345912	−	0.938267i	$-0.612430\pi$
$113$	−7.35419			−0.691824			−0.345912	+	0.938267i	$0.612430\pi$
$114$	0.480063	+	8.60132i	0.0449621	+	0.805587i
$115$		−	1.73280i		−	0.161584i
$116$	2.10362			0.195316
$117$	10.7045	+	1.55354i	0.989632	+	0.143625i
$118$	21.1641			1.94832
$119$			3.43389i			0.314784i
$120$	5.98364	+	3.02327i	0.546230	+	0.275986i
$121$	3.22774			0.293431
$122$	−9.74505	+	5.62631i	−0.882275	+	0.509382i
$123$	−3.90751	+	0.218089i	−0.352328	+	0.0196644i
$124$	−4.58360	+	2.64634i	−0.411619	+	0.237649i
$125$			12.0081i			1.07404i
$126$	−5.03454	+	0.563740i	−0.448513	+	0.0502219i
$127$	−9.45530	−	16.3771i	−0.839022	−	1.45323i	−0.890713	−	0.454566i	$-0.849794\pi$
$127$	−9.45530	−	16.3771i	−0.839022	−	1.45323i	0.0516908	−	0.998663i	$-0.483539\pi$
$128$		−	12.9566i		−	1.14521i
$129$	−4.05346	−	2.04804i	−0.356888	−	0.180320i
$130$	−8.53977	+	8.64574i	−0.748987	+	0.758282i
$131$	8.27462	+	14.3321i	0.722957	+	1.25220i	0.959809	+	0.280653i	$0.0905510\pi$
$131$	8.27462	+	14.3321i	0.722957	+	1.25220i	−0.236852	+	0.971546i	$0.576116\pi$
$132$	−2.25135	−	3.44114i	−0.195955	−	0.299512i
$133$	−2.94534			−0.255393
$134$	1.76873	−	3.06353i	0.152795	−	0.264649i
$135$	−6.60844	−	7.99290i	−0.568764	−	0.687919i
$136$	5.76705	+	3.32960i	0.494520	+	0.285511i
$137$	−11.8217	+	6.82524i	−1.00999	+	0.583119i	−0.911189	−	0.411988i	$-0.864835\pi$
$137$	−11.8217	+	6.82524i	−1.00999	+	0.583119i	−0.0988030	+	0.995107i	$0.531501\pi$
$138$	2.53535	−	0.141505i	0.215823	−	0.0120457i
$139$	−6.53972			−0.554692			−0.277346	−	0.960770i	$-0.589455\pi$
$139$	−6.53972			−0.554692			−0.277346	+	0.960770i	$0.589455\pi$
$140$	0.849858	−	1.47200i	0.0718261	−	0.124407i
$141$	8.89756	−	0.496598i	0.749310	−	0.0418211i
$142$	7.90349	−	13.6892i	0.663246	−	1.14878i
$143$	−9.69310	+	2.66143i	−0.810578	+	0.222560i
$144$	−5.98140	+	13.6838i	−0.498450	+	1.14031i
$145$	−4.26973	+	2.46513i	−0.354582	+	0.204718i
$146$	−18.8449			−1.55962
$147$	−0.0965204	−	1.72936i	−0.00796087	−	0.142635i
$148$	−5.05034	+	2.91581i	−0.415135	+	0.239678i
$149$		−	13.3440i		−	1.09318i	−0.837400	−	0.546591i	$-0.815925\pi$
$149$		−	13.3440i		−	1.09318i	0.837400	−	0.546591i	$-0.184075\pi$
$150$	−2.96812	+	0.165659i	−0.242346	+	0.0135260i
$151$	8.62281	+	4.97838i	0.701714	+	0.405135i	0.807986	−	0.589202i	$-0.200558\pi$
$151$	8.62281	+	4.97838i	0.701714	+	0.405135i	−0.106271	+	0.994337i	$0.533891\pi$
$152$	−2.85589	+	4.94655i	−0.231643	+	0.401218i
$153$	−6.11162	−	8.29291i	−0.494095	−	0.670442i
$154$	4.07708	−	2.35390i	0.328540	−	0.189683i
$155$	6.20224	−	10.7426i	0.498176	−	0.862866i
$156$	−3.98608	−	3.52066i	−0.319142	−	0.281878i
$157$	4.45576	+	7.71761i	0.355609	+	0.615932i	0.987222	−	0.159351i	$-0.0509403\pi$
$157$	4.45576	+	7.71761i	0.355609	+	0.615932i	−0.631613	+	0.775284i	$0.717607\pi$
$158$	4.47350	+	2.58277i	0.355892	+	0.205475i
$159$	−7.71208	+	5.04559i	−0.611608	+	0.400141i
$160$	−4.51836	−	7.82603i	−0.357208	−	0.618702i
$161$			0.868177i			0.0684219i
$162$	11.1552	−	10.3219i	0.876434	−	0.810965i
$163$	−3.27438	−	1.89046i	−0.256469	−	0.148072i	0.366254	−	0.930515i	$-0.380640\pi$
$163$	−3.27438	−	1.89046i	−0.256469	−	0.148072i	−0.622723	+	0.782443i	$0.713974\pi$
$164$	1.66641	+	0.962104i	0.130125	+	0.0751277i
$165$	8.60207	+	4.34625i	0.669670	+	0.338355i
$166$	9.85806	−	17.0747i	0.765134	−	1.32525i
$167$	−5.98469	−	3.45526i	−0.463109	−	0.267376i	0.250241	−	0.968183i	$-0.419490\pi$
$167$	−5.98469	−	3.45526i	−0.463109	−	0.267376i	−0.713351	+	0.700807i	$0.752823\pi$
$168$	−2.99796	−	1.51474i	−0.231298	−	0.116865i
$169$	−11.1773	+	6.63835i	−0.859793	+	0.510642i
$170$	11.5736			0.887658
$171$	7.11306	−	5.24210i	0.543949	−	0.400873i
$172$	1.11646	+	1.93377i	0.0851294	+	0.147448i
$173$	−1.25249	−	2.16938i	−0.0952253	−	0.164935i	0.814477	−	0.580195i	$-0.197024\pi$
$173$	−1.25249	−	2.16938i	−0.0952253	−	0.164935i	−0.909703	+	0.415260i	$0.863690\pi$
$174$	−3.95555	−	6.04597i	−0.299869	−	0.458344i
$175$		−	1.01637i		−	0.0768303i
$176$		−	13.8780i		−	1.04609i
$177$	−11.8847	−	18.1655i	−0.893307	−	1.36540i
$178$	−14.8114	−	25.6541i	−1.11016	−	1.92286i
$179$	3.24947	+	5.62826i	0.242877	+	0.420676i	0.961533	−	0.274691i	$-0.0885755\pi$
$179$	3.24947	+	5.62826i	0.242877	+	0.420676i	−0.718655	+	0.695366i	$0.755242\pi$
$180$	0.567428	+	5.06748i	0.0422936	+	0.377708i
$181$	3.19266			0.237308			0.118654	−	0.992936i	$-0.462142\pi$
$181$	3.19266			0.237308			0.118654	+	0.992936i	$0.462142\pi$
$182$	4.27865	−	4.33174i	0.317154	−	0.321090i
$183$	10.3015	+	5.20487i	0.761505	+	0.384755i
$184$	1.45806	+	0.841812i	0.107490	+	0.0620592i
$185$	6.83380	−	11.8365i	0.502431	−	0.870236i
$186$	16.2246	+	8.19757i	1.18964	+	0.601075i
$187$	8.29068	+	4.78663i	0.606275	+	0.350033i
$188$	−3.79449	−	2.19075i	−0.276742	−	0.159777i
$189$	3.31100	+	4.00465i	0.240840	+	0.291296i
$190$			9.92703i			0.720182i
$191$	−0.705343	−	1.22169i	−0.0510368	−	0.0883984i	0.839378	−	0.543548i	$-0.182919\pi$
$191$	−0.705343	−	1.22169i	−0.0510368	−	0.0883984i	−0.890415	+	0.455149i	$0.849586\pi$
$192$	−3.34855	+	2.19077i	−0.241661	+	0.158105i
$193$	18.0545	+	10.4238i	1.29959	+	0.750321i	0.980334	−	0.197347i	$-0.0632325\pi$
$193$	18.0545	+	10.4238i	1.29959	+	0.750321i	0.319260	+	0.947667i	$0.396566\pi$
$194$	5.68241	+	9.84223i	0.407973	+	0.706631i
$195$	12.2163	+	2.47480i	0.874824	+	0.177224i
$196$	−0.425801	+	0.737510i	−0.0304144	+	0.0526793i
$197$	24.1325	−	13.9329i	1.71937	−	0.992678i	0.799290	−	0.600946i	$-0.205209\pi$
$197$	24.1325	−	13.9329i	1.71937	−	0.992678i	0.920079	−	0.391733i	$-0.128124\pi$
$198$	−5.65677	+	12.9411i	−0.402009	+	0.919683i
$199$	−7.69090	+	13.3210i	−0.545194	+	0.944303i	0.453401	+	0.891307i	$0.350211\pi$
$199$	−7.69090	+	13.3210i	−0.545194	+	0.944303i	−0.998595	+	0.0529966i	$0.983123\pi$
$200$	−1.70694	−	0.985504i	−0.120699	−	0.0696857i
$201$	−3.62270	+	0.202193i	−0.255525	+	0.0142616i
$202$		−	27.7152i		−	1.95003i
$203$	2.13925	−	1.23510i	0.150146	−	0.0866867i
$204$	0.282255	+	5.05718i	0.0197618	+	0.354073i
$205$	−4.50977			−0.314976
$206$	21.9441	−	12.6694i	1.52892	−	0.882721i
$207$	−1.54518	−	2.09667i	−0.107397	−	0.145728i
$208$	−4.75220	−	17.3078i	−0.329505	−	1.20008i
$209$	−4.10562	+	7.11114i	−0.283992	+	0.491888i
$210$	−5.82867	+	0.325314i	−0.402216	+	0.0224488i
$211$	6.34954	−	10.9977i	0.437121	−	0.757115i	−0.560345	−	0.828259i	$-0.689332\pi$
$211$	6.34954	−	10.9977i	0.437121	−	0.757115i	0.997466	+	0.0711439i	$0.0226649\pi$
$212$	4.53125			0.311207
$213$	−16.1879	+	0.903490i	−1.10917	+	0.0619061i
$214$	−0.205506	+	0.118649i	−0.0140481	+	0.00811067i
$215$	−4.53218	−	2.61665i	−0.309092	−	0.178454i
$216$	9.93607	−	1.67763i	0.676064	−	0.114148i
$217$	−3.10748	+	5.38232i	−0.210950	+	0.365376i
$218$	−8.18358			−0.554262
$219$	10.5823	+	16.1749i	0.715089	+	1.09300i
$220$	−2.36930	−	4.10375i	−0.159738	−	0.276675i
$221$	11.9787	+	3.13065i	0.805776	+	0.210590i
$222$	17.8767	+	9.03231i	1.19980	+	0.606209i
$223$		−	12.9845i		−	0.869506i	−0.900550	−	0.434753i	$-0.856836\pi$
$223$		−	12.9845i		−	0.869506i	0.900550	−	0.434753i	$-0.143164\pi$
$224$	2.26382	+	3.92104i	0.151258	+	0.261986i
$225$	1.80893	+	2.45456i	0.120595	+	0.163637i
$226$		−	12.4188i		−	0.826086i
$227$	15.0866	−	8.71026i	1.00133	−	0.578121i	0.0926914	−	0.995695i	$-0.470453\pi$
$227$	15.0866	−	8.71026i	1.00133	−	0.578121i	0.908643	+	0.417574i	$0.137120\pi$
$228$	−4.33768	+	0.242098i	−0.287270	+	0.0160333i
$229$	17.6524	−	10.1916i	1.16651	−	0.673482i	0.213651	−	0.976910i	$-0.431464\pi$
$229$	17.6524	−	10.1916i	1.16651	−	0.673482i	0.952855	+	0.303428i	$0.0981310\pi$
$230$	2.92612			0.192943
$231$	−4.30986	−	2.17758i	−0.283568	−	0.143275i
$232$		−	4.79035i		−	0.314502i
$233$	9.05169			0.592996			0.296498	−	0.955033i	$-0.404181\pi$
$233$	9.05169			0.592996			0.296498	+	0.955033i	$0.404181\pi$
$234$	−2.62341	+	18.0764i	−0.171498	+	1.18169i
$235$	10.2689			0.669871
$236$			10.6732i			0.694764i
$237$	−0.295251	−	5.29002i	−0.0191786	−	0.343624i
$238$	−5.79870			−0.375874
$239$	1.63695	−	0.945095i	0.105886	−	0.0611331i	−0.446122	−	0.894972i	$-0.647195\pi$
$239$	1.63695	−	0.945095i	0.105886	−	0.0611331i	0.552008	+	0.833839i	$0.313862\pi$
$240$	−7.76058	+	15.3597i	−0.500943	+	0.991463i
$241$	6.31844	−	3.64795i	0.407007	−	0.234985i	−0.282496	−	0.959268i	$-0.591162\pi$
$241$	6.31844	−	3.64795i	0.407007	−	0.234985i	0.689503	+	0.724283i	$0.257829\pi$
$242$			5.45058i			0.350377i
$243$	−15.1236	−	3.77842i	−0.970180	−	0.242386i
$244$	−2.83737	−	4.91447i	−0.181644	−	0.314617i
$245$		−	1.99590i		−	0.127514i
$246$	−0.368280	−	6.59849i	−0.0234807	−	0.420704i
$247$	−2.68524	+	10.2745i	−0.170858	+	0.653749i
$248$	6.02623	+	10.4377i	0.382666	+	0.662797i
$249$	−20.1912	+	1.12693i	−1.27957	+	0.0714161i
$250$	−20.2777			−1.28247
$251$	4.24362	−	7.35017i	0.267855	−	0.463938i	−0.700453	−	0.713699i	$-0.747019\pi$
$251$	4.24362	−	7.35017i	0.267855	−	0.463938i	0.968308	+	0.249760i	$0.0803519\pi$
$252$	−0.284296	−	2.53894i	−0.0179090	−	0.159938i
$253$	2.09610	+	1.21019i	0.131781	+	0.0760837i
$254$	27.6554	−	15.9669i	1.73526	−	1.00185i
$255$	−6.49916	−	9.93383i	−0.406993	−	0.622080i
$256$	17.2588			1.07867
$257$	7.40727	−	12.8298i	0.462053	−	0.800299i	−0.537010	−	0.843576i	$-0.680446\pi$
$257$	7.40727	−	12.8298i	0.462053	−	0.800299i	0.999063	+	0.0432765i	$0.0137797\pi$
$258$	3.45846	−	6.84496i	0.215314	−	0.426149i
$259$	−3.42391	+	5.93039i	−0.212752	+	0.368497i
$260$	−4.36008	−	4.30664i	−0.270401	−	0.267086i
$261$	−2.96811	+	6.79020i	−0.183722	+	0.420303i
$262$	−24.2021	+	13.9731i	−1.49521	+	0.863261i
$263$	−18.1767			−1.12082			−0.560411	−	0.828215i	$-0.689357\pi$
$263$	−18.1767			−1.12082			−0.560411	+	0.828215i	$0.689357\pi$
$264$	−7.83612	+	5.12675i	−0.482280	+	0.315529i
$265$	−9.19709	+	5.30994i	−0.564973	+	0.326187i
$266$		−	4.97370i		−	0.304957i
$267$	−13.7020	+	27.1188i	−0.838547	+	1.65965i
$268$	1.54495	+	0.891978i	0.0943729	+	0.0544862i
$269$	1.10712	−	1.91759i	0.0675022	−	0.116917i	−0.830299	−	0.557318i	$-0.811830\pi$
$269$	1.10712	−	1.91759i	0.0675022	−	0.116917i	0.897801	+	0.440401i	$0.145164\pi$
$270$	13.4974	−	11.1595i	0.821424	−	0.679144i
$271$	−27.8583	+	16.0840i	−1.69227	+	0.977032i	−0.739587	+	0.673061i	$0.764979\pi$
$271$	−27.8583	+	16.0840i	−1.69227	+	0.977032i	−0.952681	+	0.303971i	$0.901687\pi$
$272$	−8.54691	+	14.8037i	−0.518232	+	0.897605i
$273$	−6.12067	−	1.23994i	−0.370440	−	0.0750447i
$274$	−11.5256	−	19.9629i	−0.696285	−	1.20600i
$275$	−2.45390	−	1.41676i	−0.147975	−	0.0854337i
$276$	0.0713616	+	1.27859i	0.00429546	+	0.0769620i
$277$	7.28885	+	12.6247i	0.437945	+	0.758542i	0.997531	−	0.0702299i	$-0.0223733\pi$
$277$	7.28885	+	12.6247i	0.437945	+	0.758542i	−0.559586	+	0.828772i	$0.689040\pi$
$278$		−	11.0434i		−	0.662341i
$279$	−2.07479	−	18.5291i	−0.124214	−	1.10931i
$280$	−3.35202	−	1.93529i	−0.200322	−	0.115656i
$281$	10.3688	+	5.98643i	0.618551	+	0.357121i	0.776305	−	0.630358i	$-0.217092\pi$
$281$	10.3688	+	5.98643i	0.618551	+	0.357121i	−0.157754	+	0.987479i	$0.550425\pi$
$282$	0.838589	+	15.0250i	0.0499373	+	0.894728i
$283$	0.414537	−	0.718000i	0.0246417	−	0.0426807i	−0.853442	−	0.521189i	$-0.825489\pi$
$283$	0.414537	−	0.718000i	0.0246417	−	0.0426807i	0.878083	+	0.478508i	$0.158822\pi$
$284$	6.90354	+	3.98576i	0.409650	+	0.236511i
$285$	8.52051	−	5.57450i	0.504711	−	0.330205i
$286$	−4.49427	−	16.3684i	−0.265752	−	0.967886i
$287$	2.25951			0.133375
$288$	−12.4458	−	5.44028i	−0.733377	−	0.320572i
$289$	2.60421	+	4.51062i	0.153189	+	0.265331i
$290$	−4.16279	−	7.21016i	−0.244447	−	0.423395i
$291$	5.25678	−	10.4042i	0.308158	−	0.609904i
$292$		−	9.50359i		−	0.556155i
$293$		−	9.55872i		−	0.558426i	−0.960229	−	0.279213i	$-0.909926\pi$
$293$		−	9.55872i		−	0.558426i	0.960229	−	0.279213i	$-0.0900736\pi$
$294$	2.92032	−	0.162991i	0.170316	−	0.00950582i
$295$	−12.5074	−	21.6634i	−0.728206	−	1.26129i
$296$	6.63987	+	11.5006i	0.385934	+	0.668458i
$297$	14.2841	−	2.41176i	0.828845	−	0.139944i
$298$	22.5336			1.30534
$299$	3.02853	+	0.791510i	0.175145	+	0.0457742i
$300$	−0.0835426	−	1.49684i	−0.00482333	−	0.0864198i
$301$	2.27074	+	1.31101i	0.130883	+	0.0755655i
$302$	−8.40684	+	14.5611i	−0.483759	+	0.837895i
$303$	−23.7883	+	15.5634i	−1.36660	+	0.894093i
$304$	−12.6975	−	7.33091i	−0.728253	−	0.420457i
$305$	11.5181	+	6.64995i	0.659522	+	0.380775i
$306$	14.0040	−	10.3205i	0.800555	−	0.589983i
$307$			20.1396i			1.14943i	0.818354	+	0.574714i	$0.194887\pi$
$307$			20.1396i			1.14943i	−0.818354	+	0.574714i	$0.805113\pi$
$308$	1.18708	+	2.05609i	0.0676403	+	0.117156i
$309$	−23.1970	−	11.7204i	−1.31963	−	0.666753i
$310$	18.1407	+	10.4735i	1.03032	+	0.594856i
$311$	−9.02063	−	15.6242i	−0.511513	−	0.885966i	−0.999911	−	0.0133452i	$-0.995752\pi$
$311$	−9.02063	−	15.6242i	−0.511513	−	0.885966i	0.488398	−	0.872621i	$-0.337581\pi$
$312$	−8.01721	+	9.07707i	−0.453885	+	0.513888i
$313$	7.49785	−	12.9867i	0.423803	−	0.734049i	−0.572504	−	0.819902i	$-0.694028\pi$
$313$	7.49785	−	12.9867i	0.423803	−	0.734049i	0.996308	+	0.0858526i	$0.0273614\pi$
$314$	−13.0325	+	7.52431i	−0.735466	+	0.424621i
$315$	3.55230	+	4.82015i	0.200149	+	0.271585i
$316$	−1.30250	+	2.25600i	−0.0732716	+	0.126910i
$317$	14.3390	+	8.27865i	0.805361	+	0.464975i	0.845342	−	0.534225i	$-0.179396\pi$
$317$	14.3390	+	8.27865i	0.805361	+	0.464975i	−0.0399812	+	0.999200i	$0.512730\pi$
$318$	−8.52033	−	13.0231i	−0.477796	−	0.730302i
$319$		−	6.88659i		−	0.385575i
$320$	−3.99333	+	2.30555i	−0.223234	+	0.128884i
$321$	0.217240	+	0.109762i	0.0121251	+	0.00612630i
$322$	−1.46606			−0.0817005
$323$	8.75895	−	5.05698i	0.487361	−	0.281378i
$324$	5.20538	+	5.62561i	0.289188	+	0.312534i
$325$	−3.54549	−	0.926616i	−0.196668	−	0.0513994i
$326$	3.19236	−	5.52934i	0.176809	−	0.306242i
$327$	4.59548	+	7.02409i	0.254130	+	0.388433i
$328$	2.19089	−	3.79474i	0.120972	−	0.209529i
$329$	−5.14501			−0.283653
$330$	−7.33938	+	14.5260i	−0.404019	+	0.799632i
$331$	−25.5104	+	14.7284i	−1.40218	+	0.809547i	−0.994616	−	0.103631i	$-0.966954\pi$
$331$	−25.5104	+	14.7284i	−1.40218	+	0.809547i	−0.407560	+	0.913178i	$0.633620\pi$
$332$	8.61083	+	4.97146i	0.472580	+	0.272844i
$333$	−2.28606	−	20.4159i	−0.125275	−	1.11878i
$334$	5.83480	−	10.1062i	0.319266	−	0.552985i
$335$	−4.18106			−0.228436
$336$	3.88825	−	7.69560i	0.212122	−	0.419830i
$337$	4.54514	+	7.87241i	0.247590	+	0.428838i	0.962857	−	0.270014i	$-0.0870282\pi$
$337$	4.54514	+	7.87241i	0.247590	+	0.428838i	−0.715267	+	0.698851i	$0.753695\pi$
$338$	−11.2100	−	18.8748i	−0.609742	−	1.02665i
$339$	−10.6592	+	6.97375i	−0.578930	+	0.378762i
$340$			5.83664i			0.316536i
$341$	8.66329	+	15.0053i	0.469143	+	0.812580i
$342$	8.85217	+	12.0116i	0.478670	+	0.649513i
$343$			1.00000i			0.0539949i
$344$	4.40356	−	2.54240i	0.237424	−	0.137077i
$345$	−1.64316	−	2.51153i	−0.0884646	−	0.135216i
$346$	3.66337	−	2.11505i	0.196944	−	0.113706i
$347$	−19.8006			−1.06295			−0.531476	−	0.847073i	$-0.678362\pi$
$347$	−19.8006			−1.06295			−0.531476	+	0.847073i	$0.678362\pi$
$348$	3.04901	−	1.99480i	0.163444	−	0.106932i
$349$			4.94899i			0.264913i	0.991189	+	0.132457i	$0.0422865\pi$
$349$			4.94899i			0.264913i	−0.991189	+	0.132457i	$0.957713\pi$
$350$	1.71631			0.0917408
$351$	16.9884	−	7.89904i	0.906773	−	0.421620i
$352$	12.6225			0.672781
$353$			5.91312i			0.314724i	0.987541	+	0.157362i	$0.0502989\pi$
$353$			5.91312i			0.314724i	−0.987541	+	0.157362i	$0.949701\pi$
$354$	30.6755	−	20.0693i	1.63038	−	1.06667i
$355$	−18.6829			−0.991584
$356$	12.9375	−	7.46945i	0.685684	−	0.395880i
$357$	3.25625	+	4.97711i	0.172339	+	0.263416i
$358$	−9.50426	+	5.48729i	−0.502316	+	0.290012i
$359$			12.9428i			0.683097i	0.939864	+	0.341549i	$0.110951\pi$
$359$			12.9428i			0.683097i	−0.939864	+	0.341549i	$0.889049\pi$
$360$	11.5396	−	1.29214i	0.608192	−	0.0681019i
$361$	−5.16249	−	8.94170i	−0.271710	−	0.470616i
$362$			5.39134i			0.283362i
$363$	4.67831	−	3.06076i	0.245548	−	0.160648i
$364$	2.18452	+	2.15774i	0.114500	+	0.113096i
$365$	11.1368	+	19.2895i	0.582926	+	1.00966i
$366$	−8.78931	+	17.3957i	−0.459425	+	0.909290i
$367$	12.0631			0.629689			0.314844	−	0.949143i	$-0.398048\pi$
$367$	12.0631			0.629689			0.314844	+	0.949143i	$0.398048\pi$
$368$	−2.16088	+	3.74276i	−0.112644	+	0.195105i
$369$	−5.45677	+	4.02147i	−0.284068	+	0.209349i
$370$	19.9879	+	11.5400i	1.03912	+	0.599937i
$371$	4.60799	−	2.66042i	0.239235	−	0.138122i
$372$	−4.13407	+	8.18212i	−0.214341	+	0.424223i
$373$	−17.2721			−0.894314			−0.447157	−	0.894456i	$-0.647563\pi$
$373$	−17.2721			−0.894314			−0.447157	+	0.894456i	$0.647563\pi$
$374$	−8.08303	+	14.0002i	−0.417964	+	0.723934i
$375$	11.3869	+	17.4046i	0.588017	+	0.898772i
$376$	−4.98876	+	8.64078i	−0.257276	+	0.445614i
$377$	−2.35815	−	8.58854i	−0.121451	−	0.442332i
$378$	−6.76253	+	5.59119i	−0.347827	+	0.287580i
$379$	−2.37432	+	1.37082i	−0.121961	+	0.0704141i	−0.559739	−	0.828669i	$-0.689099\pi$
$379$	−2.37432	+	1.37082i	−0.121961	+	0.0704141i	0.437778	+	0.899083i	$0.355765\pi$
$380$	−5.00624			−0.256815
$381$	−29.2345	−	14.7709i	−1.49773	−	0.756736i
$382$	2.06303	−	1.19109i	0.105554	−	0.0609415i
$383$		−	17.2992i		−	0.883950i	−0.897027	−	0.441975i	$-0.854278\pi$
$383$		−	17.2992i		−	0.883950i	0.897027	−	0.441975i	$-0.145722\pi$
$384$	−12.2863	−	18.7794i	−0.626983	−	0.958331i
$385$	−4.81885	−	2.78217i	−0.245592	−	0.141792i
$386$	−17.6023	+	30.4881i	−0.895935	+	1.55180i
$387$	−7.81722	+	0.875328i	−0.397372	+	0.0444954i
$388$	−4.96348	+	2.86566i	−0.251982	+	0.145482i
$389$	15.1685	−	26.2725i	0.769071	−	1.33207i	−0.168995	−	0.985617i	$-0.554052\pi$
$389$	15.1685	−	26.2725i	0.769071	−	1.33207i	0.938067	−	0.346454i	$-0.112614\pi$
$390$	−4.17913	+	20.6292i	−0.211618	+	1.04460i
$391$	−1.49061	−	2.58181i	−0.0753834	−	0.130568i
$392$	1.67945	+	0.969631i	0.0848251	+	0.0489738i
$393$	25.5840	+	12.9265i	1.29054	+	0.652054i
$394$	23.5281	+	40.7518i	1.18533	+	2.05305i
$395$		−	6.10536i		−	0.307194i
$396$	−6.52624	−	2.85273i	−0.327956	−	0.143355i
$397$	−22.6182	−	13.0586i	−1.13518	−	0.655394i	−0.189944	−	0.981795i	$-0.560831\pi$
$397$	−22.6182	−	13.0586i	−1.13518	−	0.655394i	−0.945231	+	0.326401i	$0.894164\pi$
$398$	−22.4948	−	12.9874i	−1.12756	−	0.650999i
$399$	−4.26900	+	2.79297i	−0.213717	+	0.139823i
$400$	2.52973	−	4.38163i	0.126487	−	0.219081i
$401$	−23.2438	−	13.4198i	−1.16074	−	0.670154i	−0.209260	−	0.977860i	$-0.567105\pi$
$401$	−23.2438	−	13.4198i	−1.16074	−	0.670154i	−0.951481	+	0.307706i	$0.900439\pi$
$402$	−0.341437	−	6.11754i	−0.0170293	−	0.305115i
$403$	15.9425	+	15.7471i	0.794154	+	0.784420i
$404$	13.9769			0.695375
$405$	−17.1578	−	5.31840i	−0.852576	−	0.264274i
$406$	2.08567	+	3.61248i	0.103510	+	0.179284i
$407$	9.54545	+	16.5332i	0.473150	+	0.819520i
$408$	11.5162	−	0.642749i	0.570135	−	0.0318208i
$409$			26.0600i			1.28858i	0.764780	+	0.644292i	$0.222848\pi$
$409$			26.0600i			1.28858i	−0.764780	+	0.644292i	$0.777152\pi$
$410$		−	7.61551i		−	0.376103i
$411$	−10.6623	+	21.1027i	−0.525930	+	1.04092i
$412$	6.38925	+	11.0665i	0.314776	+	0.545207i
$413$	6.26651	+	10.8539i	0.308355	+	0.534086i
$414$	3.54058	−	2.60929i	0.174010	−	0.128240i
$415$	−23.3033			−1.14391
$416$	15.7420	−	4.32228i	0.771815	−	0.211917i
$417$	−9.47874	+	6.20142i	−0.464176	+	0.303685i
$418$	−12.0084	−	6.93303i	−0.587348	−	0.339106i
$419$	−18.4478	+	31.9525i	−0.901232	+	1.56098i	−0.0753356	+	0.997158i	$0.524003\pi$
$419$	−18.4478	+	31.9525i	−0.901232	+	1.56098i	−0.825897	+	0.563822i	$0.809331\pi$
$420$	−0.164057	−	2.93942i	−0.00800518	−	0.143429i
$421$	17.8529	+	10.3073i	0.870095	+	0.502349i	0.867380	−	0.497647i	$-0.165802\pi$
$421$	17.8529	+	10.3073i	0.870095	+	0.502349i	0.00271499	+	0.999996i	$0.499136\pi$
$422$	18.5715	+	10.7223i	0.904048	+	0.521952i
$423$	12.4253	−	9.15706i	0.604139	−	0.445231i
$424$		−	10.3185i		−	0.501111i
$425$	1.74505	+	3.02252i	0.0846474	+	0.146614i
$426$	−1.52570	−	27.3359i	−0.0739202	−	1.32443i
$427$	−5.77085	−	3.33180i	−0.279271	−	0.161237i
$428$	−0.0598351	−	0.103637i	−0.00289224	−	0.00500951i
$429$	−11.5255	+	13.0492i	−0.556457	+	0.630020i
$430$	4.41866	−	7.65335i	0.213087	−	0.369077i
$431$	20.8692	−	12.0488i	1.00523	−	0.580372i	0.0954413	−	0.995435i	$-0.469574\pi$
$431$	20.8692	−	12.0488i	1.00523	−	0.580372i	0.909793	+	0.415063i	$0.136240\pi$
$432$	4.30638	+	25.5053i	0.207191	+	1.22713i
$433$	−9.42304	+	16.3212i	−0.452842	+	0.784346i	−0.998561	−	0.0536222i	$-0.982923\pi$
$433$	−9.42304	+	16.3212i	−0.452842	+	0.784346i	0.545719	+	0.837968i	$0.316257\pi$
$434$	−9.08896	−	5.24751i	−0.436284	−	0.251889i
$435$	−3.85098	+	7.62184i	−0.184640	+	0.365439i
$436$		−	4.12702i		−	0.197648i
$437$	2.21449	−	1.27854i	0.105934	−	0.0611607i
$438$	−27.3140	+	17.8701i	−1.30512	+	0.853865i
$439$	32.9383			1.57206			0.786030	−	0.618188i	$-0.212133\pi$
$439$	32.9383			1.57206			0.786030	+	0.618188i	$0.212133\pi$
$440$	−9.34503	+	5.39535i	−0.445507	+	0.257213i
$441$	−1.77979	−	2.41502i	−0.0847521	−	0.115001i
$442$	−5.28662	+	20.2281i	−0.251459	+	0.962152i
$443$	−10.9751	+	19.0093i	−0.521440	+	0.903161i	0.478249	+	0.878225i	$0.341272\pi$
$443$	−10.9751	+	19.0093i	−0.521440	+	0.903161i	−0.999689	+	0.0249368i	$0.992062\pi$
$444$	−4.55503	+	9.01528i	−0.216172	+	0.427846i
$445$	−17.5062	+	30.3216i	−0.829872	+	1.43738i
$446$	21.9265			1.03825
$447$	−12.6537	−	19.3409i	−0.598499	−	0.914793i
$448$	2.00077	−	1.15514i	0.0945273	−	0.0545754i
$449$	−4.86626	−	2.80954i	−0.229653	−	0.132590i	0.380759	−	0.924674i	$-0.375663\pi$
$449$	−4.86626	−	2.80954i	−0.229653	−	0.132590i	−0.610412	+	0.792084i	$0.708996\pi$
$450$	−4.14493	+	3.05468i	−0.195394	+	0.143999i
$451$	3.14962	−	5.45531i	0.148310	−	0.256880i
$452$	6.26285			0.294580
$453$	17.2188	−	0.961030i	0.809011	−	0.0451531i
$454$	14.7088	+	25.4763i	0.690316	+	1.19566i
$455$	−6.96248	−	1.81965i	−0.326406	−	0.0853064i
$456$	0.551303	+	9.87773i	0.0258172	+	0.462567i
$457$			8.80377i			0.411823i	0.978571	+	0.205912i	$0.0660159\pi$
$457$			8.80377i			0.411823i	−0.978571	+	0.205912i	$0.933984\pi$
$458$	17.2103	+	29.8091i	0.804185	+	1.39289i
$459$	−16.7221	−	6.22437i	−0.780523	−	0.290529i
$460$			1.47566i			0.0688028i
$461$	−29.3357	+	16.9370i	−1.36630	+	0.788835i	−0.990454	−	0.137846i	$-0.955982\pi$
$461$	−29.3357	+	16.9370i	−1.36630	+	0.788835i	−0.375848	+	0.926681i	$0.622649\pi$
$462$	3.67722	−	7.27793i	0.171080	−	0.338600i
$463$	−7.57756	+	4.37491i	−0.352159	+	0.203319i	−0.665636	−	0.746277i	$-0.731840\pi$
$463$	−7.57756	+	4.37491i	−0.352159	+	0.203319i	0.313477	+	0.949596i	$0.398506\pi$
$464$	12.2966			0.570853
$465$	−1.19728	−	21.4518i	−0.0555227	−	0.994803i
$466$			15.2853i			0.708078i
$467$	14.8464			0.687008			0.343504	−	0.939151i	$-0.388386\pi$
$467$	14.8464			0.687008			0.343504	+	0.939151i	$0.388386\pi$
$468$	−9.11599	−	1.32300i	−0.421387	−	0.0611555i
$469$	2.09482			0.0967298
$470$			17.3408i			0.799873i
$471$	13.7766	+	6.96071i	0.634792	+	0.320733i
$472$	24.3048			1.11872
$473$	6.33054	−	3.65494i	0.291079	−	0.168054i
$474$	8.93309	−	0.498581i	0.410310	−	0.0229006i
$475$	−2.59249	+	1.49678i	−0.118952	+	0.0686768i
$476$		−	2.92431i		−	0.134035i
$477$	−6.39338	+	14.6262i	−0.292733	+	0.669690i
$478$	1.59595	+	2.76427i	0.0729972	+	0.126435i
$479$			18.8812i			0.862705i	0.902183	+	0.431353i	$0.141964\pi$
$479$			18.8812i			0.862705i	−0.902183	+	0.431353i	$0.858036\pi$
$480$	−13.9701	−	7.05849i	−0.637646	−	0.322175i
$481$	17.5659	+	17.3506i	0.800937	+	0.791120i
$482$	6.16019	+	10.6698i	0.280589	+	0.485994i
$483$	0.823265	+	1.25834i	0.0374599	+	0.0572566i
$484$	−2.74875			−0.124943
$485$	6.71626	−	11.6329i	0.304970	−	0.528223i
$486$	6.38050	−	25.5388i	0.289425	−	1.15846i
$487$	19.0924	+	11.0230i	0.865161	+	0.499501i	0.865737	−	0.500499i	$-0.166850\pi$
$487$	19.0924	+	11.0230i	0.865161	+	0.499501i	−0.000576209		1.00000i	$0.500183\pi$
$488$	−11.1912	+	6.46124i	−0.506601	+	0.292486i
$489$	−6.53858	+	0.364936i	−0.295685	+	0.0165030i
$490$	3.37042			0.152260
$491$	−3.66611	+	6.34988i	−0.165449	+	0.286566i	−0.936815	−	0.349826i	$-0.886241\pi$
$491$	−3.66611	+	6.34988i	−0.165449	+	0.286566i	0.771366	+	0.636392i	$0.219574\pi$
$492$	3.32765	−	0.185725i	0.150022	−	0.00837314i
$493$	−4.24118	+	7.34594i	−0.191013	+	0.330844i
$494$	−17.3502	−	4.53448i	−0.780621	−	0.204016i
$495$	16.5893	−	1.85758i	0.745635	−	0.0834920i
$496$	−26.7931	+	15.4690i	−1.20304	+	0.694578i
$497$	9.36061			0.419881
$498$	−1.90301	−	34.0963i	−0.0852758	−	1.52789i
$499$	18.3962	−	10.6211i	0.823527	−	0.475464i	−0.0281039	−	0.999605i	$-0.508947\pi$
$499$	18.3962	−	10.6211i	0.823527	−	0.475464i	0.851631	+	0.524141i	$0.175614\pi$
$500$		−	10.2261i		−	0.457326i
$501$	−11.9508	+	0.667007i	−0.533922	+	0.0297997i
$502$	12.4120	+	7.16607i	0.553975	+	0.319837i
$503$	18.2009	−	31.5248i	0.811537	−	1.40562i	−0.100251	−	0.994962i	$-0.531965\pi$
$503$	18.2009	−	31.5248i	0.811537	−	1.40562i	0.911788	−	0.410661i	$-0.134702\pi$
$504$	−5.78166	+	0.647397i	−0.257535	+	0.0288374i
$505$	−28.3689	+	16.3788i	−1.26240	+	0.728847i
$506$	−2.04360	+	3.53962i	−0.0908492	+	0.157355i
$507$	−9.90555	+	20.2208i	−0.439921	+	0.898036i
$508$	8.05216	+	13.9468i	0.357257	+	0.618787i
$509$	27.8914	+	16.1031i	1.23627	+	0.713759i	0.968329	−	0.249677i	$-0.0803246\pi$
$509$	27.8914	+	16.1031i	1.23627	+	0.713759i	0.267937	+	0.963436i	$0.413658\pi$
$510$	16.7749	−	10.9749i	0.742807	−	0.485978i
$511$	−5.57982	−	9.66454i	−0.246837	−	0.427534i
$512$			3.23124i			0.142802i
$513$	5.33881	−	14.3430i	0.235714	−	0.633260i
$514$	21.6652	+	12.5084i	0.955613	+	0.551723i
$515$	−25.9366	−	14.9745i	−1.14290	−	0.659855i
$516$	3.45194	+	1.74412i	0.151963	+	0.0767804i
$517$	−7.17182	+	12.4220i	−0.315416	+	0.546317i
$518$	−10.0145	−	5.78186i	−0.440010	−	0.254040i
$519$	−3.87253	−	1.95662i	−0.169985	−	0.0858862i
$520$	−9.80704	+	9.92875i	−0.430067	+	0.435404i
$521$	−1.22518			−0.0536761			−0.0268381	−	0.999640i	$-0.508544\pi$
$521$	−1.22518			−0.0536761			−0.0268381	+	0.999640i	$0.508544\pi$
$522$	−11.4664	−	5.01216i	−0.501871	−	0.219376i
$523$	−8.12561	−	14.0740i	−0.355308	−	0.615412i	0.631863	−	0.775080i	$-0.282291\pi$
$523$	−8.12561	−	14.0740i	−0.355308	−	0.615412i	−0.987171	+	0.159669i	$0.948957\pi$
$524$	−7.04669	−	12.2052i	−0.307836	−	0.533188i
$525$	−0.963792	−	1.47314i	−0.0420633	−	0.0642929i
$526$		−	30.6944i		−	1.33834i
$527$		−	21.3415i		−	0.929651i
$528$	−13.1601	−	20.1149i	−0.572718	−	0.875388i
$529$	11.1231	+	19.2658i	0.483615	+	0.837645i
$530$	−8.96674	−	15.5308i	−0.389490	−	0.674617i
$531$	−34.4515	−	15.0593i	−1.49507	−	0.653520i
$532$	2.50826			0.108747
$533$	2.05998	−	7.88205i	0.0892276	−	0.341409i
$534$	−45.7947	−	23.1381i	−1.98173	−	1.00128i
$535$	0.242895	+	0.140236i	0.0105013	+	0.00606292i
$536$	2.03120	−	3.51815i	0.0877346	−	0.151961i
$537$	10.0469	+	5.07627i	0.433556	+	0.219057i
$538$	3.23817	+	1.86956i	0.139607	+	0.0806024i
$539$	2.41437	+	1.39394i	0.103994	+	0.0600412i
$540$	5.62777	+	6.80678i	0.242181	+	0.292917i
$541$		−	27.6010i		−	1.18666i	−0.804959	−	0.593331i	$-0.797813\pi$
$541$		−	27.6010i		−	1.18666i	0.804959	−	0.593331i	$-0.202187\pi$
$542$	−27.1605	−	47.0434i	−1.16664	−	2.02069i
$543$	4.62746	−	3.02750i	0.198583	−	0.129922i
$544$	−13.4644	−	7.77369i	−0.577282	−	0.333294i
$545$	4.83625	+	8.37663i	0.207162	+	0.358815i
$546$	2.09385	−	10.3358i	0.0896086	−	0.442330i
$547$	5.42150	−	9.39032i	0.231807	−	0.401501i	−0.726533	−	0.687131i	$-0.758870\pi$
$547$	5.42150	−	9.39032i	0.231807	−	0.401501i	0.958340	+	0.285630i	$0.0922030\pi$
$548$	10.0674	−	5.81239i	0.430056	−	0.248293i
$549$	19.8666	−	2.22455i	0.847888	−	0.0949417i
$550$	2.39243	−	4.14382i	0.102014	−	0.176693i
$551$	−6.30081	−	3.63777i	−0.268423	−	0.154974i
$552$	2.91159	−	0.162504i	0.123925	−	0.00691663i
$553$			3.05895i			0.130080i
$554$	−21.3189	+	12.3085i	−0.905752	+	0.522936i
$555$	−1.31920	−	23.6362i	−0.0559970	−	1.00330i
$556$	5.56925			0.236189
$557$	31.7563	−	18.3345i	1.34556	−	0.776859i	0.357942	−	0.933744i	$-0.383478\pi$
$557$	31.7563	−	18.3345i	1.34556	−	0.776859i	0.987617	+	0.156885i	$0.0501451\pi$
$558$	31.2895	−	3.50363i	1.32459	−	0.148320i
$559$	6.64353	−	6.72597i	0.280991	−	0.284478i
$560$	4.96778	−	8.60445i	0.209927	−	0.363604i
$561$	16.5556	−	0.924014i	0.698978	−	0.0390119i
$562$	−10.1091	+	17.5095i	−0.426427	+	0.738593i
$563$	7.18861			0.302964			0.151482	−	0.988460i	$-0.451595\pi$
$563$	7.18861			0.302964			0.151482	+	0.988460i	$0.451595\pi$
$564$	−7.57719	+	0.422904i	−0.319057	+	0.0178075i
$565$	−12.7117	+	7.33912i	−0.534787	+	0.308759i
$566$	1.21246	+	0.700016i	0.0509637	+	0.0294239i
$567$	8.59649	+	2.66466i	0.361019	+	0.111905i
$568$	9.07634	−	15.7207i	0.380835	−	0.659625i
$569$	9.85602			0.413186			0.206593	−	0.978427i	$-0.433762\pi$
$569$	9.85602			0.413186			0.206593	+	0.978427i	$0.433762\pi$
$570$	9.41349	+	14.3883i	0.394288	+	0.602660i
$571$	−1.02885	−	1.78201i	−0.0430558	−	0.0745749i	0.843694	−	0.536824i	$-0.180376\pi$
$571$	−1.02885	−	1.78201i	−0.0430558	−	0.0745749i	−0.886750	+	0.462249i	$0.847043\pi$
$572$	8.25467	−	2.26648i	0.345145	−	0.0947663i
$573$	−2.18082	−	1.10187i	−0.0911051	−	0.0460314i
$574$			3.81557i			0.159259i
$575$	0.441195	+	0.764171i	0.0183991	+	0.0318681i
$576$	−2.77598	+	6.35065i	−0.115666	+	0.264610i
$577$		−	23.3733i		−	0.973045i	−0.873668	−	0.486523i	$-0.838265\pi$
$577$		−	23.3733i		−	0.973045i	0.873668	−	0.486523i	$-0.161735\pi$
$578$	−7.61695	+	4.39765i	−0.316823	+	0.182918i
$579$	36.0529	−	2.01222i	1.49831	−	0.0836248i
$580$	3.63612	−	2.09931i	0.150981	−	0.0871692i
$581$	11.6755			0.484383
$582$	17.5692	+	8.87696i	0.728267	+	0.367962i
$583$		−	14.8339i		−	0.614356i
$584$	−21.6415			−0.895531
$585$	20.0531	−	7.99729i	0.829095	−	0.330647i
$586$	16.1415			0.666800
$587$			12.8526i			0.530483i	0.964182	+	0.265241i	$0.0854516\pi$
$587$			12.8526i			0.530483i	−0.964182	+	0.265241i	$0.914548\pi$
$588$	0.0821970	+	1.47273i	0.00338975	+	0.0607342i
$589$	18.3052			0.754252
$590$	36.5823	−	21.1208i	1.50607	−	0.869529i
$591$	21.7657	−	43.0786i	0.895322	−	1.77202i
$592$	−29.5214	+	17.0442i	−1.21332	+	0.700511i
$593$			25.1789i			1.03397i	0.855993	+	0.516987i	$0.172946\pi$
$593$			25.1789i			1.03397i	−0.855993	+	0.516987i	$0.827054\pi$
$594$	4.07266	+	24.1211i	0.167103	+	0.989699i
$595$	3.42685	+	5.93548i	0.140487	+	0.243331i
$596$			11.3638i			0.465479i
$597$	1.48466	+	26.6007i	0.0607630	+	1.08869i
$598$	−1.33660	+	5.11419i	−0.0546576	+	0.209135i
$599$	8.91102	+	15.4343i	0.364094	+	0.630630i	0.988630	−	0.150366i	$-0.0480453\pi$
$599$	8.91102	+	15.4343i	0.364094	+	0.630630i	−0.624536	+	0.780996i	$0.714712\pi$
$600$	−3.40858	+	0.190242i	−0.139155	+	0.00776661i
$601$	−5.18771			−0.211611			−0.105806	−	0.994387i	$-0.533742\pi$
$601$	−5.18771			−0.211611			−0.105806	+	0.994387i	$0.533742\pi$
$602$	−2.21387	+	3.83453i	−0.0902304	+	0.156284i
$603$	−5.05904	+	3.72835i	−0.206020	+	0.151830i
$604$	−7.34321	−	4.23960i	−0.298791	−	0.172507i
$605$	5.57916	−	3.22113i	0.226825	−	0.130957i
$606$	−26.2814	−	40.1706i	−1.06761	−	1.63182i
$607$	−25.1005			−1.01880			−0.509399	−	0.860530i	$-0.670132\pi$
$607$	−25.1005			−1.01880			−0.509399	+	0.860530i	$0.670132\pi$
$608$	6.66770	−	11.5488i	0.270411	−	0.468366i
$609$	1.92944	−	3.81874i	0.0781850	−	0.154743i
$610$	−11.2296	+	19.4502i	−0.454672	+	0.787515i
$611$	−4.69066	+	17.9478i	−0.189764	+	0.726088i
$612$	5.20467	+	7.06227i	0.210386	+	0.285475i
$613$	20.1389	−	11.6272i	0.813402	−	0.469618i	−0.0347336	−	0.999397i	$-0.511058\pi$
$613$	20.1389	−	11.6272i	0.813402	−	0.469618i	0.848136	+	0.529779i	$0.177725\pi$
$614$	−34.0091			−1.37250
$615$	−6.53650	+	4.27647i	−0.263577	+	0.172444i
$616$	4.68210	−	2.70321i	0.188647	−	0.108916i
$617$		−	41.4367i		−	1.66818i	−0.551631	−	0.834089i	$-0.685994\pi$
$617$		−	41.4367i		−	1.66818i	0.551631	−	0.834089i	$-0.314006\pi$
$618$	19.7919	−	39.1721i	0.796149	−	1.57573i
$619$	38.8879	+	22.4519i	1.56304	+	0.902419i	0.996947	+	0.0780753i	$0.0248774\pi$
$619$	38.8879	+	22.4519i	1.56304	+	0.902419i	0.566089	+	0.824344i	$0.308456\pi$
$620$	−5.28184	+	9.14842i	−0.212124	+	0.367409i
$621$	−4.22780	−	1.57368i	−0.169656	−	0.0631498i
$622$	26.3841	−	15.2328i	1.05790	−	0.610782i
$623$	8.77105	−	15.1919i	0.351405	−	0.608651i
$624$	−23.3003	−	20.5797i	−0.932760	−	0.823849i
$625$	9.44257	+	16.3550i	0.377703	+	0.654201i
$626$	21.9302	+	12.6614i	0.876505	+	0.506051i
$627$	0.792552	+	14.2002i	0.0316515	+	0.567101i
$628$	−3.79454	−	6.57234i	−0.151419	−	0.262265i
$629$		−	23.5147i		−	0.937591i
$630$	−8.13964	+	5.99866i	−0.324291	+	0.238992i
$631$	−21.5239	−	12.4268i	−0.856852	−	0.494704i	0.00610493	−	0.999981i	$-0.498057\pi$
$631$	−21.5239	−	12.4268i	−0.856852	−	0.494704i	−0.862957	+	0.505278i	$0.831390\pi$
$632$	5.13735	+	2.96605i	0.204353	+	0.117983i
$633$	−1.22572	−	21.9613i	−0.0487180	−	0.872883i
$634$	−13.9799	+	24.2139i	−0.555213	+	0.961657i
$635$	−32.6870	−	18.8719i	−1.29715	−	0.748907i
$636$	6.56763	−	4.29684i	0.260423	−	0.170381i
$637$	3.48838	+	0.911692i	0.138215	+	0.0361225i
$638$	11.6292			0.460403
$639$	−22.6061	+	16.6600i	−0.894283	+	0.659058i
$640$	−12.9300	−	22.3955i	−0.511104	−	0.885259i
$641$	21.9251	+	37.9754i	0.865991	+	1.49994i	0.866060	+	0.499940i	$0.166645\pi$
$641$	21.9251	+	37.9754i	0.865991	+	1.49994i	−6.96022e−5		1.00000i	$0.500022\pi$
$642$	−0.185351	+	0.366846i	−0.00731522	+	0.0144782i
$643$		−	34.5275i		−	1.36163i	−0.732455	−	0.680816i	$-0.761625\pi$
$643$		−	34.5275i		−	1.36163i	0.732455	−	0.680816i	$-0.238375\pi$
$644$		−	0.739342i		−	0.0291342i
$645$	−9.05027	+	0.505121i	−0.356354	+	0.0198891i
$646$	8.53956	+	14.7910i	0.335985	+	0.581943i
$647$	−6.66984	−	11.5525i	−0.262218	−	0.454175i	0.704613	−	0.709592i	$-0.251121\pi$
$647$	−6.66984	−	11.5525i	−0.262218	−	0.454175i	−0.966831	+	0.255417i	$0.917787\pi$
$648$	12.8106	−	11.8536i	0.503247	−	0.465655i
$649$	34.9405			1.37154
$650$	1.56475	−	5.98716i	0.0613744	−	0.234836i
$651$	0.599871	+	10.7479i	0.0235108	+	0.421244i
$652$	2.78847	+	1.60992i	0.109205	+	0.0630494i
$653$	−5.73624	+	9.93546i	−0.224476	+	0.388805i	−0.956162	−	0.292837i	$-0.905401\pi$
$653$	−5.73624	+	9.93546i	−0.224476	+	0.388805i	0.731686	+	0.681642i	$0.238734\pi$
$654$	−11.8614	+	7.76024i	−0.463816	+	0.303449i
$655$	28.6054	+	16.5154i	1.11771	+	0.645308i
$656$	9.74088	+	5.62390i	0.380318	+	0.219576i
$657$	30.6763	+	13.4091i	1.19680	+	0.523140i
$658$		−	8.68821i		−	0.338702i
$659$	−4.88857	−	8.46725i	−0.190432	−	0.329837i	0.754962	−	0.655769i	$-0.227655\pi$
$659$	−4.88857	−	8.46725i	−0.190432	−	0.329837i	−0.945393	+	0.325932i	$0.894322\pi$
$660$	−7.32554	−	3.70128i	−0.285146	−	0.144072i
$661$	34.0855	+	19.6793i	1.32577	+	0.765435i	0.984643	−	0.174581i	$-0.0558570\pi$
$661$	34.0855	+	19.6793i	1.32577	+	0.765435i	0.341130	+	0.940016i	$0.389190\pi$
$662$	−24.8714	−	43.0786i	−0.966655	−	1.67430i
$663$	20.3308	−	6.82146i	0.789581	−	0.264923i
$664$	11.3210	−	19.6085i	0.439339	−	0.760957i
$665$	−5.09103	+	2.93931i	−0.197422	+	0.113981i
$666$	34.4757	−	3.86039i	1.33591	−	0.149587i
$667$	−1.07228	+	1.85725i	−0.0415189	+	0.0719128i
$668$	5.09658	+	2.94251i	0.197193	+	0.113849i
$669$	−12.3128	−	18.8198i	−0.476040	−	0.727617i
$670$		−	7.06043i		−	0.272768i
$671$	−16.0884	+	9.28865i	−0.621086	+	0.358584i
$672$	6.99940	+	3.53649i	0.270008	+	0.136423i
$673$	−16.6065			−0.640134			−0.320067	−	0.947395i	$-0.603705\pi$
$673$	−16.6065			−0.640134			−0.320067	+	0.947395i	$0.603705\pi$
$674$	−13.2939	+	7.67524i	−0.512062	+	0.295639i
$675$	4.94946	+	1.84230i	0.190505	+	0.0709103i
$676$	9.51863	−	5.65324i	0.366101	−	0.217432i
$677$	−11.8222	+	20.4766i	−0.454364	+	0.786981i	−0.998651	−	0.0519177i	$-0.983467\pi$
$677$	−11.8222	+	20.4766i	−0.454364	+	0.786981i	0.544288	+	0.838899i	$0.316800\pi$
$678$	−11.7764	−	17.9999i	−0.452268	−	0.691282i
$679$	−3.36502	+	5.82839i	−0.129138	+	0.223673i
$680$	13.2911			0.509692
$681$	13.6070	−	26.9309i	0.521422	−	1.03199i
$682$	−25.3389	+	14.6294i	−0.970277	+	0.560190i
$683$	−21.0903	−	12.1765i	−0.806999	−	0.465921i	0.0389139	−	0.999243i	$-0.487610\pi$
$683$	−21.0903	−	12.1765i	−0.806999	−	0.465921i	−0.845912	+	0.533322i	$0.820944\pi$
$684$	−6.05750	+	4.46419i	−0.231614	+	0.170692i
$685$	−13.6225	+	23.5949i	−0.520490	+	0.901514i
$686$	−1.68867			−0.0644737
$687$	15.9212	−	31.5111i	0.607431	−	1.20222i
$688$	6.52619	+	11.3037i	0.248809	+	0.430949i
$689$	−5.07951	−	18.4999i	−0.193514	−	0.704790i
$690$	4.24115	−	2.77475i	0.161458	−	0.105633i
$691$		−	35.0868i		−	1.33476i	−0.744716	−	0.667381i	$-0.767415\pi$
$691$		−	35.0868i		−	1.33476i	0.744716	−	0.667381i	$-0.232585\pi$
$692$	1.06663	+	1.84745i	0.0405471	+	0.0702296i
$693$	−8.31169	+	0.930696i	−0.315735	+	0.0353542i
$694$		−	33.4367i		−	1.26924i
$695$	−11.3039	+	6.52633i	−0.428783	+	0.247558i
$696$	−4.54254	−	6.94317i	−0.172184	−	0.263180i
$697$	−6.71941	+	3.87946i	−0.254516	+	0.146945i
$698$	−8.35720			−0.316325
$699$	13.1196	−	8.58344i	0.496229	−	0.324655i
$700$			0.865543i			0.0327145i
$701$	−37.8901			−1.43109			−0.715544	−	0.698567i	$-0.753821\pi$
$701$	−37.8901			−1.43109			−0.715544	+	0.698567i	$0.753821\pi$
$702$	13.3389	+	28.6878i	0.503443	+	1.08275i
$703$	20.1692			0.760694
$704$		−	6.44079i		−	0.242746i
$705$	14.8839	−	9.73771i	0.560560	−	0.366743i
$706$	−9.98530			−0.375802
$707$	14.2136	−	8.20621i	0.534557	−	0.308626i
$708$	10.1210	+	15.4698i	0.380371	+	0.581390i
$709$	−18.0974	+	10.4486i	−0.679663	+	0.392404i	−0.799728	−	0.600362i	$-0.795023\pi$
$709$	−18.0974	+	10.4486i	−0.679663	+	0.392404i	0.120065	+	0.992766i	$0.461690\pi$
$710$		−	31.5492i		−	1.18402i
$711$	−5.44430	−	7.38742i	−0.204177	−	0.277050i
$712$	−17.0094	−	29.4611i	−0.637453	−	1.10410i
$713$		−	5.39569i		−	0.202070i
$714$	−8.40469	+	5.49873i	−0.314537	+	0.205785i
$715$	−14.0986	+	14.2735i	−0.527257	+	0.533800i
$716$	−2.76726	−	4.79304i	−0.103417	−	0.179124i
$717$	1.47641	−	2.92210i	0.0551375	−	0.109128i
$718$	−21.8562			−0.815665
$719$	19.3354	−	33.4899i	0.721089	−	1.24896i	−0.239475	−	0.970903i	$-0.576975\pi$
$719$	19.3354	−	33.4899i	0.721089	−	1.24896i	0.960564	−	0.278060i	$-0.0896915\pi$
$720$	3.31686	+	29.6216i	0.123612	+	1.10393i
$721$	12.9949	+	7.50261i	0.483956	+	0.279412i
$722$	15.0996	−	8.71774i	0.561948	−	0.324441i
$723$	5.69877	−	11.2790i	0.211939	−	0.419469i
$724$	−2.71887			−0.101046
$725$	1.25531	−	2.17427i	0.0466212	−	0.0807503i
$726$	5.16862	+	7.90012i	0.191825	+	0.293201i
$727$	−25.6431	+	44.4151i	−0.951049	+	1.64726i	−0.207887	+	0.978153i	$0.566659\pi$
$727$	−25.6431	+	44.4151i	−0.951049	+	1.64726i	−0.743162	+	0.669112i	$0.766675\pi$
$728$	4.91359	−	4.97456i	0.182110	−	0.184370i
$729$	−25.5033	+	8.86477i	−0.944565	+	0.328325i
$730$	−32.5736	+	18.8063i	−1.20560	+	0.696054i
$731$	−9.00374			−0.333015
$732$	−8.77275	−	4.43249i	−0.324250	−	0.163829i
$733$	−41.6331	+	24.0369i	−1.53775	+	0.887822i	−0.538783	+	0.842444i	$0.681116\pi$
$733$	−41.6331	+	24.0369i	−1.53775	+	0.887822i	−0.998970	+	0.0453780i	$0.985551\pi$
$734$			20.3706i			0.751892i
$735$	−1.89265	−	2.89288i	−0.0698115	−	0.106705i
$736$	−3.40416	−	1.96539i	−0.125479	−	0.0724454i
$737$	2.92005	−	5.05768i	0.107561	−	0.186302i
$738$	−6.79093	−	9.21468i	−0.249978	−	0.339197i
$739$	14.7473	−	8.51437i	0.542489	−	0.313206i	−0.203598	−	0.979055i	$-0.565264\pi$
$739$	14.7473	−	8.51437i	0.542489	−	0.313206i	0.746087	+	0.665849i	$0.231930\pi$
$740$	−5.81968	+	10.0800i	−0.213936	+	0.370548i
$741$	5.85095	+	17.4382i	0.214940	+	0.640610i
$742$	4.49257	+	7.78136i	0.164927	+	0.285663i
$743$	29.3611	+	16.9517i	1.07716	+	0.621896i	0.930128	−	0.367237i	$-0.119696\pi$
$743$	29.3611	+	16.9517i	1.07716	+	0.621896i	0.147028	+	0.989132i	$0.453029\pi$
$744$	18.6322	+	9.41406i	0.683091	+	0.345136i
$745$	−13.3167	−	23.0651i	−0.487885	−	0.845041i
$746$		−	29.1668i		−	1.06787i
$747$	−28.1967	+	20.7801i	−1.03166	+	0.760303i
$748$	−7.06037	−	4.07631i	−0.258153	−	0.149045i
$749$	−0.121697	−	0.0702618i	−0.00444671	−	0.00256731i
$750$	−29.3907	+	19.2287i	−1.07320	+	0.702133i
$751$	−7.81670	+	13.5389i	−0.285235	+	0.494042i	−0.972666	−	0.232208i	$-0.925405\pi$
$751$	−7.81670	+	13.5389i	−0.285235	+	0.494042i	0.687431	+	0.726250i	$0.258738\pi$
$752$	−22.1804	−	12.8059i	−0.808836	−	0.466982i
$753$	−0.819192	−	14.6775i	−0.0298530	−	0.534877i
$754$	14.5032	−	3.98214i	0.528176	−	0.145021i
$755$	19.8727			0.723243
$756$	−2.81966	−	3.41037i	−0.102550	−	0.124034i
$757$	−22.2713	−	38.5750i	−0.809465	−	1.40203i	−0.913235	−	0.407433i	$-0.866424\pi$
$757$	−22.2713	−	38.5750i	−0.809465	−	1.40203i	0.103771	−	0.994601i	$-0.466909\pi$
$758$	−2.31486	−	4.00945i	−0.0840794	−	0.145630i
$759$	4.18569	−	0.233615i	0.151931	−	0.00847969i
$760$			11.4002i			0.413528i
$761$			52.8871i			1.91716i	0.284830	+	0.958578i	$0.408063\pi$
$761$			52.8871i			1.91716i	−0.284830	+	0.958578i	$0.591937\pi$
$762$	24.9431	−	49.3673i	0.903595	−	1.78839i
$763$	−2.42309	−	4.19691i	−0.0877216	−	0.151938i
$764$	0.600672	+	1.04039i	0.0217315	+	0.0376401i
$765$	−18.8399	−	8.23523i	−0.681157	−	0.297745i
$766$	29.2127			1.05550
$767$	43.5758	−	11.9646i	1.57343	−	0.432016i
$768$	25.0150	−	16.3660i	0.902653	−	0.590556i
$769$	26.3518	+	15.2142i	0.950271	+	0.548639i	0.893165	−	0.449729i	$-0.148479\pi$
$769$	26.3518	+	15.2142i	0.950271	+	0.548639i	0.0571059	+	0.998368i	$0.481813\pi$
$770$	4.69816	−	8.13745i	0.169310	−	0.293253i
$771$	−1.42991	−	25.6197i	−0.0514968	−	0.922670i
$772$	−15.3753	−	8.87693i	−0.553369	−	0.319488i
$773$	16.8613	+	9.73487i	0.606458	+	0.350139i	0.771578	−	0.636135i	$-0.219468\pi$
$773$	16.8613	+	9.73487i	0.606458	+	0.350139i	−0.165120	+	0.986274i	$0.552801\pi$
$774$	−1.47814	−	13.2007i	−0.0531306	−	0.474489i
$775$			6.31671i			0.226903i
$776$	6.52567	+	11.3028i	0.234258	+	0.405746i
$777$	0.660955	+	11.8424i	0.0237116	+	0.424842i
$778$	44.3656	+	25.6145i	1.59058	+	0.918325i
$779$	−3.32751	−	5.76342i	−0.119221	−	0.206496i
$780$	−10.4034	−	2.10755i	−0.372501	−	0.0754624i
$781$	13.0481	−	22.6000i	0.466898	−	0.808692i
$782$	4.35983	−	2.51715i	0.155907	−	0.0900131i
$783$	2.13693	+	12.6564i	0.0763676	+	0.452301i
$784$	−2.48899	+	4.31106i	−0.0888925	+	0.153966i
$785$	15.4036	+	8.89327i	0.549778	+	0.317415i
$786$	−21.8285	+	43.2029i	−0.778597	+	1.54099i
$787$			34.4432i			1.22777i	0.789397	+	0.613883i	$0.210393\pi$
$787$			34.4432i			1.22777i	−0.789397	+	0.613883i	$0.789607\pi$
$788$	−20.5513	+	11.8653i	−0.732110	+	0.422684i
$789$	−26.3454	+	17.2364i	−0.937922	+	0.613631i
$790$	10.3099			0.366811
$791$	6.36891	−	3.67709i	0.226453	−	0.130742i
$792$	−6.49621	+	14.8615i	−0.230833	+	0.528080i
$793$	−16.8838	+	17.0934i	−0.599562	+	0.607003i
$794$	22.0517	−	38.1947i	0.782585	−	1.35548i
$795$	−8.29510	+	16.4176i	−0.294197	+	0.582272i
$796$	6.54960	−	11.3442i	0.232144	−	0.402086i
$797$	26.2017			0.928112			0.464056	−	0.885806i	$-0.346394\pi$
$797$	26.2017			0.928112			0.464056	+	0.885806i	$0.346394\pi$
$798$	−4.71641	−	7.20893i	−0.166959	−	0.255193i
$799$	15.3004	−	8.83369i	0.541289	−	0.312513i
$800$	3.98523	+	2.30087i	0.140899	+	0.0813482i
$801$	5.85620	+	52.2994i	0.206919	+	1.84791i
$802$	22.6616	−	39.2511i	0.800210	−	1.38601i
$803$	−31.1117			−1.09791
$804$	3.08510	−	0.172188i	0.108803	−	0.00607260i
$805$	0.866399	+	1.50065i	0.0305365	+	0.0528908i
$806$	−26.5917	+	26.9217i	−0.936651	+	0.948275i
$807$	−0.213719	−	3.82921i	−0.00752327	−	0.134795i
$808$		−	31.8280i		−	1.11971i
$809$	13.2872	+	23.0141i	0.467154	+	0.809134i	0.999296	−	0.0375210i	$-0.0119461\pi$
$809$	13.2872	+	23.0141i	0.467154	+	0.809134i	−0.532142	+	0.846655i	$0.678613\pi$
$810$	8.98102	−	28.9738i	0.315561	−	1.01803i
$811$			31.9095i			1.12050i	0.828325	+	0.560248i	$0.189294\pi$
$811$			31.9095i			1.12050i	−0.828325	+	0.560248i	$0.810706\pi$
$812$	−1.82179	+	1.05181i	−0.0639323	+	0.0369113i
$813$	−25.1261	+	49.7294i	−0.881210	+	1.74408i
$814$	−27.9191	+	16.1191i	−0.978564	+	0.564974i
$815$	−7.54636			−0.264337
$816$	1.64990	+	29.5614i	0.0577581	+	1.03485i
$817$		−	7.72275i		−	0.270185i
$818$	−44.0067			−1.53866
$819$	−10.0471	+	4.00685i	−0.351076	+	0.140011i
$820$	3.84053			0.134117
$821$		−	23.5447i		−	0.821715i	−0.911700	−	0.410858i	$-0.865229\pi$
$821$		−	23.5447i		−	0.821715i	0.911700	−	0.410858i	$-0.134771\pi$
$822$	−35.6354	−	18.0050i	−1.24293	−	0.627997i
$823$	−53.1991			−1.85440			−0.927202	−	0.374563i	$-0.877793\pi$
$823$	−53.1991			−1.85440			−0.927202	+	0.374563i	$0.877793\pi$
$824$	25.2005	−	14.5495i	0.877902	−	0.506857i
$825$	−4.90017	+	0.273492i	−0.170602	+	0.00952177i
$826$	−18.3287	+	10.5821i	−0.637736	+	0.368197i
$827$			3.18210i			0.110653i	0.998468	+	0.0553263i	$0.0176199\pi$
$827$			3.18210i			0.110653i	−0.998468	+	0.0553263i	$0.982380\pi$
$828$	1.31588	+	1.78553i	0.0457299	+	0.0620514i
$829$	11.6734	+	20.2189i	0.405433	+	0.702231i	0.994372	−	0.105947i	$-0.0337873\pi$
$829$	11.6734	+	20.2189i	0.405433	+	0.702231i	−0.588938	+	0.808178i	$0.700454\pi$
$830$		−	39.3515i		−	1.36591i
$831$	22.5361	+	11.3865i	0.781768	+	0.394993i
$832$	−2.20550	−	8.03257i	−0.0764619	−	0.278479i
$833$	−1.71694	−	2.97383i	−0.0594886	−	0.103037i
$834$	−10.4721	−	16.0064i	−0.362621	−	0.554258i
$835$	−13.7927			−0.477318
$836$	3.49636	−	6.05587i	0.120924	−	0.209447i
$837$	−20.5778	−	24.8888i	−0.711272	−	0.860283i
$838$	−53.9571	−	31.1522i	−1.86392	−	1.07613i
$839$	−32.4664	+	18.7445i	−1.12087	+	0.647132i	−0.941622	−	0.336673i	$-0.890698\pi$
$839$	−32.4664	+	18.7445i	−1.12087	+	0.647132i	−0.179244	+	0.983805i	$0.557365\pi$
$840$	−6.69363	+	0.373590i	−0.230952	+	0.0128901i
$841$	−22.8982			−0.789592
$842$	−17.4057	+	30.1476i	−0.599840	+	1.03895i
$843$	20.7054	−	1.15563i	0.713132	−	0.0398019i
$844$	−5.40729	+	9.36570i	−0.186127	+	0.322381i
$845$	−12.6953	+	22.6288i	−0.436730	+	0.778455i
$846$	15.4632	+	20.9822i	0.531637	+	0.721384i
$847$	−2.79530	+	1.61387i	−0.0960478	+	0.0554532i
$848$	26.4870			0.909569
$849$	−0.0800226	−	1.43377i	−0.00274637	−	0.0492068i
$850$	−5.10403	+	2.94681i	−0.175067	+	0.101075i
$851$		−	5.94513i		−	0.203796i
$852$	13.7856	−	0.769414i	0.472288	−	0.0263597i
$853$	25.1870	+	14.5417i	0.862385	+	0.497898i	0.864810	−	0.502099i	$-0.167439\pi$
$853$	25.1870	+	14.5417i	0.862385	+	0.497898i	−0.00242506	+	0.999997i	$0.500772\pi$
$854$	5.62631	−	9.74505i	0.192528	−	0.333469i
$855$	7.06358	−	16.1595i	0.241569	−	0.552642i
$856$	−0.236002	+	0.136256i	−0.00806640	+	0.00465714i
$857$	0.703927	−	1.21924i	0.0240457	−	0.0416484i	−0.853752	−	0.520680i	$-0.825679\pi$
$857$	0.703927	−	1.21924i	0.0240457	−	0.0416484i	0.877798	+	0.479031i	$0.159012\pi$
$858$	−22.0357	−	19.4628i	−0.752287	−	0.664448i
$859$	2.51842	+	4.36204i	0.0859275	+	0.148831i	0.905786	−	0.423735i	$-0.139281\pi$
$859$	2.51842	+	4.36204i	0.0859275	+	0.148831i	−0.819859	+	0.572566i	$0.805948\pi$
$860$	3.85961	+	2.22835i	0.131612	+	0.0759861i
$861$	3.27496	−	2.14263i	0.111610	−	0.0730205i
$862$	20.3465	+	35.2412i	0.693005	+	1.20032i
$863$		−	4.56933i		−	0.155542i	−0.996971	−	0.0777708i	$-0.975220\pi$
$863$		−	4.56933i		−	0.155542i	0.996971	−	0.0777708i	$-0.0247802\pi$
$864$	−23.1979	+	3.91679i	−0.789210	+	0.133252i
$865$	−4.32988	−	2.49986i	−0.147220	−	0.0849976i
$866$	−27.5611	−	15.9124i	−0.936564	−	0.540725i
$867$	8.05184	+	4.06825i	0.273455	+	0.138165i
$868$	2.64634	−	4.58360i	0.0898227	−	0.155578i
$869$	7.38544	+	4.26399i	0.250534	+	0.144646i
$870$	−12.8708	−	6.50303i	−0.436360	−	0.220473i
$871$	1.90983	−	7.30754i	0.0647121	−	0.247606i
$872$	−9.39800			−0.318257
$873$	−2.24674	−	20.0647i	−0.0760405	−	0.679089i
$874$	2.15903	+	3.73954i	0.0730302	+	0.126492i
$875$	−6.00405	−	10.3993i	−0.202974	−	0.351561i
$876$	−9.01195	−	13.7746i	−0.304486	−	0.465400i
$877$			18.7852i			0.634330i	0.948370	+	0.317165i	$0.102731\pi$
$877$			18.7852i			0.634330i	−0.948370	+	0.317165i	$0.897269\pi$
$878$			55.6219i			1.87715i
$879$	−9.06423	−	13.8545i	−0.305729	−	0.467300i
$880$	−13.8496	−	23.9882i	−0.466869	−	0.808640i
$881$	−0.497153	−	0.861094i	−0.0167495	−	0.0290110i	0.857529	−	0.514435i	$-0.171998\pi$
$881$	−0.497153	−	0.861094i	−0.0167495	−	0.0290110i	−0.874279	+	0.485424i	$0.838665\pi$
$882$	4.07817	−	3.00548i	0.137319	−	0.101200i
$883$	15.3052			0.515061			0.257530	−	0.966270i	$-0.417091\pi$
$883$	15.3052			0.515061			0.257530	+	0.966270i	$0.417091\pi$
$884$	−10.2011	−	2.66607i	−0.343100	−	0.0896695i
$885$	−38.6710	−	19.5388i	−1.29991	−	0.656788i
$886$	−32.1005	−	18.5332i	−1.07844	−	0.622636i
$887$	13.2557	−	22.9596i	0.445083	−	0.770906i	−0.552975	−	0.833198i	$-0.686507\pi$
$887$	13.2557	−	22.9596i	0.445083	−	0.770906i	0.998058	+	0.0622914i	$0.0198408\pi$
$888$	20.5295	+	10.3727i	0.688926	+	0.348084i
$889$	16.3771	+	9.45530i	0.549269	+	0.317121i
$890$	−51.2031	−	29.5621i	−1.71633	−	0.990924i
$891$	18.4165	−	17.0408i	0.616975	−	0.570887i
$892$			11.0576i			0.370237i
$893$	7.57689	+	13.1236i	0.253551	+	0.439163i
$894$	32.6604	−	21.3679i	1.09233	−	0.714649i
$895$	11.2335	+	6.48564i	0.375493	+	0.216791i
$896$	6.47829	+	11.2207i	0.216424	+	0.374858i
$897$	5.14015	−	1.72464i	0.171625	−	0.0575842i
$898$	4.74438	−	8.21751i	0.158322	−	0.274222i
$899$	−13.2954	+	7.67608i	−0.443425	+	0.256012i
$900$	−1.54049	−	2.09031i	−0.0513497	−	0.0696769i
$901$	−9.13559	+	15.8233i	−0.304351	+	0.527151i
$902$	9.21220	+	5.31867i	0.306733	+	0.177092i
$903$	4.53442	−	0.253079i	0.150896	−	0.00842193i
$904$		−	14.2617i		−	0.474337i
$905$	5.51851	−	3.18612i	0.183442	−	0.105910i
$906$	1.62286	+	29.0769i	0.0539160	+	0.966015i
$907$	52.6668			1.74877			0.874386	−	0.485231i	$-0.161264\pi$
$907$	52.6668			1.74877			0.874386	+	0.485231i	$0.161264\pi$
$908$	−12.8478	+	7.41769i	−0.426369	+	0.246165i
$909$	−19.7207	+	45.1154i	−0.654095	+	1.49638i
$910$	3.07278	−	11.7573i	0.101862	−	0.389751i
$911$	5.84476	−	10.1234i	0.193645	−	0.335404i	−0.752810	−	0.658238i	$-0.771302\pi$
$911$	5.84476	−	10.1234i	0.193645	−	0.335404i	0.946456	+	0.322834i	$0.104636\pi$
$912$	−25.3556	+	1.41517i	−0.839607	+	0.0468608i
$913$	16.2750	−	28.1891i	0.538624	−	0.932924i
$914$	−14.8667			−0.491745
$915$	23.0003	−	1.28371i	0.760367	−	0.0424382i
$916$	−15.0329	+	8.67923i	−0.496700	+	0.286770i
$917$	−14.3321	−	8.27462i	−0.473287	−	0.273252i
$918$	10.5109	−	28.2382i	0.346911	−	0.931998i
$919$	20.1980	−	34.9840i	0.666272	−	1.15402i	−0.312667	−	0.949863i	$-0.601222\pi$
$919$	20.1980	−	34.9840i	0.666272	−	1.15402i	0.978939	−	0.204154i	$-0.0654442\pi$
$920$	3.36035			0.110787
$921$	19.0978	+	29.1905i	0.629293	+	0.961861i
$922$	−28.6010	−	49.5384i	−0.941923	−	1.63146i
$923$	8.53399	−	32.6534i	0.280900	−	1.07480i
$924$	3.67029	+	1.85444i	0.120744	+	0.0610065i
$925$			6.95992i			0.228841i
$926$	−7.38777	−	12.7960i	−0.242777	−	0.420502i
$927$	−44.7361	+	5.00930i	−1.46933	+	0.164527i
$928$			11.1841i			0.367137i
$929$	−27.0475	+	15.6159i	−0.887398	+	0.512340i	−0.873091	−	0.487558i	$-0.837888\pi$
$929$	−27.0475	+	15.6159i	−0.887398	+	0.512340i	−0.0143078	+	0.999898i	$0.504554\pi$
$930$	36.2250	−	2.02182i	1.18786	−	0.0662980i
$931$	2.55074	−	1.47267i	0.0835970	−	0.0482648i
$932$	−7.70845			−0.252499
$933$	−27.8905	−	14.0919i	−0.913094	−	0.461347i
$934$			25.0706i			0.820335i
$935$	19.1073			0.624875
$936$	−3.01272	+	20.7589i	−0.0984737	+	0.678524i
$937$	18.3937			0.600895			0.300447	−	0.953798i	$-0.402864\pi$
$937$	18.3937			0.600895			0.300447	+	0.953798i	$0.402864\pi$
$938$			3.53746i			0.115502i
$939$	−1.44739	−	25.9329i	−0.0472338	−	0.846290i
$940$	−8.74505			−0.285232
$941$	−23.8224	+	13.7539i	−0.776588	+	0.448363i	−0.835220	−	0.549916i	$-0.814660\pi$
$941$	−23.8224	+	13.7539i	−0.776588	+	0.448363i	0.0586318	+	0.998280i	$0.481326\pi$
$942$	−11.7543	+	23.2641i	−0.382977	+	0.757985i
$943$	−1.69884	+	0.980828i	−0.0553220	+	0.0319402i
$944$			62.3891i			2.03059i
$945$	9.71953	+	3.61783i	0.316176	+	0.117688i
$946$	6.17199	+	10.6902i	0.200669	+	0.347568i
$947$		−	1.59842i		−	0.0519415i	−0.999663	−	0.0259708i	$-0.991732\pi$
$947$		−	1.59842i		−	0.0519415i	0.999663	−	0.0259708i	$-0.00826768\pi$
$948$	0.251436	+	4.50500i	0.00816627	+	0.146315i
$949$	−38.8007	+	10.6535i	−1.25952	+	0.345827i
$950$	−2.52756	−	4.37786i	−0.0820049	−	0.142037i
$951$	28.6335	−	1.59812i	0.928506	−	0.0518225i
$952$	−6.65921			−0.215826
$953$	5.68885	−	9.85338i	0.184280	−	0.319182i	−0.759054	−	0.651028i	$-0.774338\pi$
$953$	5.68885	−	9.85338i	0.184280	−	0.319182i	0.943334	+	0.331846i	$0.107671\pi$
$954$	−24.6989	−	10.7963i	−0.799656	−	0.349543i
$955$	−2.43837	−	1.40780i	−0.0789039	−	0.0455552i
$956$	−1.39403	+	0.804846i	−0.0450863	+	0.0260306i
$957$	−6.53034	−	9.98148i	−0.211096	−	0.322656i
$958$	−31.8841			−1.03013
$959$	6.82524	−	11.8217i	0.220398	−	0.381741i
$960$	−3.60169	+	7.12844i	−0.116244	+	0.230070i
$961$	3.81292	−	6.60418i	0.122998	−	0.213038i
$962$	−29.2994	+	29.6630i	−0.944652	+	0.956375i
$963$	0.418952	−	0.0469119i	0.0135006	−	0.00151172i
$964$	−5.38080	+	3.10661i	−0.173304	+	0.100057i
$965$	41.6097			1.33946
$966$	−2.12493	+	1.39022i	−0.0683684	+	0.0447297i
$967$	49.1602	−	28.3826i	1.58088	−	0.912724i	0.586153	−	0.810200i	$-0.300642\pi$
$967$	49.1602	−	28.3826i	1.58088	−	0.912724i	0.994731	−	0.102524i	$-0.0326917\pi$
$968$			6.25943i			0.201186i
$969$	7.89992	−	15.6355i	0.253782	−	0.502284i
$970$	19.6441	+	11.3415i	0.630735	+	0.364155i
$971$	−16.0791	+	27.8498i	−0.516002	+	0.893742i	0.483825	+	0.875164i	$0.339247\pi$
$971$	−16.0791	+	27.8498i	−0.516002	+	0.893742i	−0.999827	+	0.0185771i	$0.994086\pi$
$972$	12.8793	+	3.21771i	0.413104	+	0.103208i
$973$	5.66357	−	3.26986i	0.181566	−	0.104827i
$974$	−18.6142	+	32.2408i	−0.596439	+	1.03306i
$975$	−6.01754	+	2.01903i	−0.192716	+	0.0646607i
$976$	−16.5856	−	28.7271i	−0.530893	−	0.919534i
$977$	−6.36655	−	3.67573i	−0.203684	−	0.117597i	0.394689	−	0.918815i	$-0.370852\pi$
$977$	−6.36655	−	3.67573i	−0.203684	−	0.117597i	−0.598373	+	0.801218i	$0.704186\pi$
$978$	−0.616256	−	11.0415i	−0.0197057	−	0.353068i
$979$	−24.4526	−	42.3532i	−0.781509	−	1.35361i
$980$			1.69972i			0.0542955i
$981$	13.3214	+	5.82303i	0.425321	+	0.185915i
$982$	−10.7229	−	6.19084i	−0.342180	−	0.197558i
$983$	17.6234	+	10.1749i	0.562099	+	0.324528i	0.753988	−	0.656889i	$-0.228128\pi$
$983$	17.6234	+	10.1749i	0.562099	+	0.324528i	−0.191889	+	0.981417i	$0.561461\pi$
$984$	−0.422932	−	7.57769i	−0.0134826	−	0.241568i
$985$	27.8087	−	48.1661i	0.886060	−	1.53470i
$986$	−12.4049	−	7.16195i	−0.395051	−	0.228083i
$987$	−7.45722	+	4.87885i	−0.237366	+	0.155295i
$988$	2.28676	−	8.74977i	0.0727515	−	0.278367i
$989$	−2.27638			−0.0723847
$990$	3.13684	+	28.0139i	0.0996952	+	0.890340i
$991$	−14.3598	−	24.8719i	−0.456154	−	0.790081i	0.542600	−	0.839991i	$-0.317440\pi$
$991$	−14.3598	−	24.8719i	−0.456154	−	0.790081i	−0.998754	+	0.0499099i	$0.984107\pi$
$992$	−14.0695	−	24.3692i	−0.446709	−	0.773722i
$993$	−23.0085	+	45.5382i	−0.730151	+	1.44511i
$994$			15.8070i			0.501367i
$995$			30.7006i			0.973275i
$996$	17.1949	−	0.959695i	0.544841	−	0.0304091i
$997$	−16.8855	−	29.2465i	−0.534768	−	0.926246i	−0.999175	−	0.0406237i	$-0.987066\pi$
$997$	−16.8855	−	29.2465i	−0.534768	−	0.926246i	0.464406	−	0.885622i	$-0.346268\pi$
$998$	17.9354	+	31.0651i	0.567737	+	0.983349i
$999$	−22.6732	−	27.4232i	−0.717348	−	0.867631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bh.a.673.64	yes	168
9.4	even	3		819.2.dk.a.400.21	yes	168
13.4	even	6		819.2.dk.a.43.21	yes	168
117.4	even	6	inner	819.2.bh.a.589.21	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.bh.a.589.21	✓	168	117.4	even	6	inner
819.2.bh.a.673.64	yes	168	1.1	even	1	trivial
819.2.dk.a.43.21	yes	168	13.4	even	6
819.2.dk.a.400.21	yes	168	9.4	even	3

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.68867i q^{2} +(1.44941 - 0.948269i) q^{3} -0.851603 q^{4} +(1.72850 - 0.997952i) q^{5} +(1.60131 + 2.44757i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.93926i q^{8} +(1.20157 - 2.74886i) q^{9} +O(q^{10})\)	\(q+1.68867i q^{2} +(1.44941 - 0.948269i) q^{3} -0.851603 q^{4} +(1.72850 - 0.997952i) q^{5} +(1.60131 + 2.44757i) q^{6} +(-0.866025 + 0.500000i) q^{7} +1.93926i q^{8} +(1.20157 - 2.74886i) q^{9} +(1.68521 + 2.91887i) q^{10} +2.78788i q^{11} +(-1.23432 + 0.807548i) q^{12} +(0.954644 + 3.47687i) q^{13} +(-0.844334 - 1.46243i) q^{14} +(1.55898 - 3.08553i) q^{15} -4.97798 q^{16} +(1.71694 - 2.97383i) q^{17} +(4.64191 + 2.02906i) q^{18} +(2.55074 + 1.47267i) q^{19} +(-1.47200 + 0.849858i) q^{20} +(-0.781091 + 1.54593i) q^{21} -4.70780 q^{22} +(0.434089 - 0.751863i) q^{23} +(1.83894 + 2.81078i) q^{24} +(-0.508185 + 0.880202i) q^{25} +(-5.87129 + 1.61208i) q^{26} +(-0.865086 - 5.12363i) q^{27} +(0.737510 - 0.425801i) q^{28} -2.47019 q^{29} +(5.21043 + 2.63260i) q^{30} +(5.38232 - 3.10748i) q^{31} -4.52763i q^{32} +(2.64366 + 4.04077i) q^{33} +(5.02182 + 2.89935i) q^{34} +(-0.997952 + 1.72850i) q^{35} +(-1.02326 + 2.34094i) q^{36} +(5.93039 - 3.42391i) q^{37} +(-2.48685 + 4.30735i) q^{38} +(4.68068 + 4.13415i) q^{39} +(1.93529 + 3.35202i) q^{40} +(-1.95680 - 1.12976i) q^{41} +(-2.61056 - 1.31900i) q^{42} +(-1.31101 - 2.27074i) q^{43} -2.37416i q^{44} +(-0.666306 - 5.95052i) q^{45} +(1.26965 + 0.733032i) q^{46} +(4.45571 + 2.57250i) q^{47} +(-7.21513 + 4.72046i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-1.48637 - 0.858156i) q^{50} +(-0.331440 - 5.93843i) q^{51} +(-0.812977 - 2.96092i) q^{52} -5.32084 q^{53} +(8.65212 - 1.46084i) q^{54} +(2.78217 + 4.81885i) q^{55} +(-0.969631 - 1.67945i) q^{56} +(5.09355 - 0.284285i) q^{57} -4.17133i q^{58} -12.5330i q^{59} +(-1.32763 + 2.62764i) q^{60} +(3.33180 + 5.77085i) q^{61} +(5.24751 + 9.08896i) q^{62} +(0.333837 + 2.98137i) q^{63} -2.31029 q^{64} +(5.11986 + 5.05710i) q^{65} +(-6.82353 + 4.46426i) q^{66} +(-1.81417 - 1.04741i) q^{67} +(-1.46215 + 2.53253i) q^{68} +(-0.0837968 - 1.50139i) q^{69} +(-2.91887 - 1.68521i) q^{70} +(-8.10653 - 4.68031i) q^{71} +(5.33076 + 2.33017i) q^{72} +11.1596i q^{73} +(5.78186 + 10.0145i) q^{74} +(0.0981004 + 1.75767i) q^{75} +(-2.17222 - 1.25413i) q^{76} +(-1.39394 - 2.41437i) q^{77} +(-6.98122 + 7.90412i) q^{78} +(1.52947 - 2.64913i) q^{79} +(-8.60445 + 4.96778i) q^{80} +(-6.11245 - 6.60591i) q^{81} +(1.90778 - 3.30438i) q^{82} +(-10.1113 - 5.83777i) q^{83} +(0.665179 - 1.31652i) q^{84} -6.85371i q^{85} +(3.83453 - 2.21387i) q^{86} +(-3.58032 + 2.34240i) q^{87} -5.40643 q^{88} +(-15.1919 + 8.77105i) q^{89} +(10.0485 - 1.12517i) q^{90} +(-2.56518 - 2.53374i) q^{91} +(-0.369671 + 0.640289i) q^{92} +(4.85445 - 9.60790i) q^{93} +(-4.34411 + 7.52421i) q^{94} +5.87861 q^{95} +(-4.29341 - 6.56239i) q^{96} +(5.82839 - 3.36502i) q^{97} +(1.46243 + 0.844334i) q^{98} +(7.66348 + 3.34984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 168 q^{4} + 18 q^{6} - 2 q^{9}+O(q^{10}) \) 168 * q - 168 * q^4 + 18 * q^6 - 2 * q^9	\( 168 q - 168 q^{4} + 18 q^{6} - 2 q^{9} + 12 q^{12} + 8 q^{14} + 6 q^{15} + 168 q^{16} - 12 q^{18} + 6 q^{21} - 20 q^{23} - 36 q^{24} + 84 q^{25} + 4 q^{26} - 24 q^{27} - 68 q^{29} - 4 q^{30} + 16 q^{35} - 2 q^{36} - 12 q^{38} - 6 q^{39} + 24 q^{41} - 30 q^{45} + 30 q^{47} + 40 q^{48} + 84 q^{49} + 12 q^{50} - 38 q^{51} + 18 q^{52} - 48 q^{53} + 36 q^{54} - 24 q^{56} + 54 q^{57} - 24 q^{60} + 6 q^{62} - 132 q^{64} + 74 q^{65} - 54 q^{66} + 78 q^{68} - 4 q^{69} + 24 q^{71} - 42 q^{72} + 42 q^{74} - 60 q^{75} - 16 q^{77} + 38 q^{78} - 6 q^{79} - 74 q^{81} - 6 q^{82} - 18 q^{83} - 66 q^{84} + 24 q^{86} - 38 q^{87} - 48 q^{88} - 36 q^{89} - 44 q^{90} - 6 q^{91} + 8 q^{92} - 6 q^{93} - 60 q^{94} + 96 q^{95} + 24 q^{96} - 6 q^{99}+O(q^{100}) \) 168 * q - 168 * q^4 + 18 * q^6 - 2 * q^9 + 12 * q^12 + 8 * q^14 + 6 * q^15 + 168 * q^16 - 12 * q^18 + 6 * q^21 - 20 * q^23 - 36 * q^24 + 84 * q^25 + 4 * q^26 - 24 * q^27 - 68 * q^29 - 4 * q^30 + 16 * q^35 - 2 * q^36 - 12 * q^38 - 6 * q^39 + 24 * q^41 - 30 * q^45 + 30 * q^47 + 40 * q^48 + 84 * q^49 + 12 * q^50 - 38 * q^51 + 18 * q^52 - 48 * q^53 + 36 * q^54 - 24 * q^56 + 54 * q^57 - 24 * q^60 + 6 * q^62 - 132 * q^64 + 74 * q^65 - 54 * q^66 + 78 * q^68 - 4 * q^69 + 24 * q^71 - 42 * q^72 + 42 * q^74 - 60 * q^75 - 16 * q^77 + 38 * q^78 - 6 * q^79 - 74 * q^81 - 6 * q^82 - 18 * q^83 - 66 * q^84 + 24 * q^86 - 38 * q^87 - 48 * q^88 - 36 * q^89 - 44 * q^90 - 6 * q^91 + 8 * q^92 - 6 * q^93 - 60 * q^94 + 96 * q^95 + 24 * q^96 - 6 * q^99

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