LMFDB - Embedded newform 378.2.bf.a.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(5,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("378.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.2
Character	$\chi$	$=$	378.101
Dual form			378.2.bf.a.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642788 + 0.766044i) q^{2} +(-1.68736 + 0.390923i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-0.278956 + 0.234072i) q^{5} +(0.785149 - 1.54387i) q^{6} +(1.49966 + 2.17968i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.69436 - 1.31926i) q^{9} -0.364151i q^{10} +(2.84373 - 3.38902i) q^{11} +(0.677991 + 1.59384i) q^{12} +(-1.20667 + 3.31531i) q^{13} +(-2.63370 - 0.252266i) q^{14} +(0.379195 - 0.504014i) q^{15} +(-0.939693 + 0.342020i) q^{16} -5.47560 q^{17} +(-0.721292 + 2.91200i) q^{18} +5.51592i q^{19} +(0.278956 + 0.234072i) q^{20} +(-3.38255 - 3.09165i) q^{21} +(0.768229 + 4.35684i) q^{22} +(-1.70607 + 4.68738i) q^{23} +(-1.65676 - 0.505130i) q^{24} +(-0.845214 + 4.79345i) q^{25} +(-1.76404 - 3.05541i) q^{26} +(-4.03062 + 3.27934i) q^{27} +(1.88615 - 1.85538i) q^{28} +(-0.217053 - 0.596349i) q^{29} +(0.142355 + 0.614454i) q^{30} +(4.90787 - 0.865390i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-3.47354 + 6.83017i) q^{33} +(3.51965 - 4.19455i) q^{34} +(-0.928543 - 0.257007i) q^{35} +(-1.76708 - 2.42434i) q^{36} +(-4.30255 + 7.45224i) q^{37} +(-4.22544 - 3.54557i) q^{38} +(0.740061 - 6.06584i) q^{39} +(-0.358619 + 0.0632342i) q^{40} +(3.52911 + 1.28449i) q^{41} +(4.54261 - 0.603911i) q^{42} +(1.51425 - 8.58775i) q^{43} +(-3.83134 - 2.21203i) q^{44} +(-0.442807 + 0.998688i) q^{45} +(-2.49410 - 4.31992i) q^{46} +(-0.967922 + 5.48936i) q^{47} +(1.45189 - 0.944458i) q^{48} +(-2.50203 + 6.53757i) q^{49} +(-3.12870 - 3.72864i) q^{50} +(9.23930 - 2.14054i) q^{51} +(3.47448 + 0.612645i) q^{52} +(-7.94780 - 4.58866i) q^{53} +(0.0787098 - 5.19556i) q^{54} +1.61103i q^{55} +(0.208904 + 2.63749i) q^{56} +(-2.15630 - 9.30734i) q^{57} +(0.596349 + 0.217053i) q^{58} +(9.48190 + 3.45113i) q^{59} +(-0.562203 - 0.285913i) q^{60} +(-5.46074 - 0.962876i) q^{61} +(-2.49179 + 4.31591i) q^{62} +(6.91618 + 3.89441i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.439412 - 1.20728i) q^{65} +(-2.99947 - 7.05123i) q^{66} +(6.89583 - 5.78629i) q^{67} +(0.950828 + 5.39241i) q^{68} +(1.04634 - 8.57624i) q^{69} +(0.793735 - 0.546104i) q^{70} +(-3.24088 + 1.87112i) q^{71} +(2.99301 + 0.204670i) q^{72} +(3.79842 - 2.19302i) q^{73} +(-2.94312 - 8.08615i) q^{74} +(-0.447691 - 8.41868i) q^{75} +(5.43213 - 0.957830i) q^{76} +(11.6516 + 1.11604i) q^{77} +(4.17100 + 4.46596i) q^{78} +(12.9503 + 10.8666i) q^{79} +(0.182076 - 0.315364i) q^{80} +(5.51913 - 7.10909i) q^{81} +(-3.25244 + 1.87780i) q^{82} +(0.538728 - 0.196081i) q^{83} +(-2.45731 + 3.86803i) q^{84} +(1.52745 - 1.28169i) q^{85} +(5.60526 + 6.68009i) q^{86} +(0.599374 + 0.921404i) q^{87} +(4.15725 - 1.51312i) q^{88} -0.706622 q^{89} +(-0.480409 - 0.981154i) q^{90} +(-9.03593 + 2.34168i) q^{91} +(4.91243 + 0.866193i) q^{92} +(-7.94303 + 3.37882i) q^{93} +(-3.58293 - 4.26997i) q^{94} +(-1.29112 - 1.53870i) q^{95} +(-0.209763 + 1.71930i) q^{96} +(12.0867 + 2.13121i) q^{97} +(-3.39979 - 6.11894i) q^{98} +(3.19103 - 12.8828i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) $ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	−1.68736	+	0.390923i	−0.974197	+	0.225700i
$3$	−1.68736	+	0.390923i	−0.974197	+	0.225700i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	−0.278956	+	0.234072i	−0.124753	+	0.104680i	−0.703030	−	0.711161i	$-0.748170\pi$
$5$	−0.278956	+	0.234072i	−0.124753	+	0.104680i	0.578277	+	0.815841i	$0.303725\pi$
$6$	0.785149	−	1.54387i	0.320536	−	0.630283i
$7$	1.49966	+	2.17968i	0.566819	+	0.823843i
$7$	1.49966	+	2.17968i	0.566819	+	0.823843i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	2.69436	−	1.31926i	0.898119	−	0.439752i
$10$		−	0.364151i		−	0.115155i
$11$	2.84373	−	3.38902i	0.857416	−	1.02183i	−0.142073	−	0.989856i	$-0.545377\pi$
$11$	2.84373	−	3.38902i	0.857416	−	1.02183i	0.999489	−	0.0319720i	$-0.0101788\pi$
$12$	0.677991	+	1.59384i	0.195719	+	0.460102i
$13$	−1.20667	+	3.31531i	−0.334671	+	0.919502i	0.652208	+	0.758040i	$0.273843\pi$
$13$	−1.20667	+	3.31531i	−0.334671	+	0.919502i	−0.986879	+	0.161462i	$0.948379\pi$
$14$	−2.63370	−	0.252266i	−0.703885	−	0.0674208i
$15$	0.379195	−	0.504014i	0.0979077	−	0.130136i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−5.47560			−1.32803			−0.664014	−	0.747720i	$-0.731149\pi$
$17$	−5.47560			−1.32803			−0.664014	+	0.747720i	$0.731149\pi$
$18$	−0.721292	+	2.91200i	−0.170010	+	0.686365i
$19$			5.51592i			1.26544i	0.774381	+	0.632720i	$0.218062\pi$
$19$			5.51592i			1.26544i	−0.774381	+	0.632720i	$0.781938\pi$
$20$	0.278956	+	0.234072i	0.0623765	+	0.0523401i
$21$	−3.38255	−	3.09165i	−0.738134	−	0.674654i
$22$	0.768229	+	4.35684i	0.163787	+	0.928882i
$23$	−1.70607	+	4.68738i	−0.355740	+	0.977387i	0.624751	+	0.780824i	$0.285200\pi$
$23$	−1.70607	+	4.68738i	−0.355740	+	0.977387i	−0.980491	+	0.196563i	$0.937022\pi$
$24$	−1.65676	−	0.505130i	−0.338184	−	0.103109i
$25$	−0.845214	+	4.79345i	−0.169043	+	0.958689i
$26$	−1.76404	−	3.05541i	−0.345957	−	0.599215i
$27$	−4.03062	+	3.27934i	−0.775693	+	0.631110i
$28$	1.88615	−	1.85538i	0.356450	−	0.350633i
$29$	−0.217053	−	0.596349i	−0.0403058	−	0.110739i	0.917907	−	0.396796i	$-0.129878\pi$
$29$	−0.217053	−	0.596349i	−0.0403058	−	0.110739i	−0.958213	+	0.286056i	$0.907656\pi$
$30$	0.142355	+	0.614454i	0.0259904	+	0.112183i
$31$	4.90787	−	0.865390i	0.881479	−	0.155429i	0.285452	−	0.958393i	$-0.407856\pi$
$31$	4.90787	−	0.865390i	0.881479	−	0.155429i	0.596027	+	0.802964i	$0.296745\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	−3.47354	+	6.83017i	−0.604665	+	1.18898i
$34$	3.51965	−	4.19455i	0.603615	−	0.719360i
$35$	−0.928543	−	0.257007i	−0.156952	−	0.0434421i
$36$	−1.76708	−	2.42434i	−0.294514	−	0.404056i
$37$	−4.30255	+	7.45224i	−0.707335	+	1.22514i	0.258507	+	0.966009i	$0.416770\pi$
$37$	−4.30255	+	7.45224i	−0.707335	+	1.22514i	−0.965842	+	0.259131i	$0.916564\pi$
$38$	−4.22544	−	3.54557i	−0.685457	−	0.575167i
$39$	0.740061	−	6.06584i	0.118505	−	0.971311i
$40$	−0.358619	+	0.0632342i	−0.0567027	+	0.00999821i
$41$	3.52911	+	1.28449i	0.551154	+	0.200604i	0.602559	−	0.798074i	$-0.294148\pi$
$41$	3.52911	+	1.28449i	0.551154	+	0.200604i	−0.0514050	+	0.998678i	$0.516370\pi$
$42$	4.54261	−	0.603911i	0.700940	−	0.0931855i
$43$	1.51425	−	8.58775i	0.230921	−	1.30962i	−0.620114	−	0.784512i	$-0.712914\pi$
$43$	1.51425	−	8.58775i	0.230921	−	1.30962i	0.851035	−	0.525109i	$-0.175975\pi$
$44$	−3.83134	−	2.21203i	−0.577597	−	0.333475i
$45$	−0.442807	+	0.998688i	−0.0660098	+	0.148876i
$46$	−2.49410	−	4.31992i	−0.367736	−	0.636937i
$47$	−0.967922	+	5.48936i	−0.141186	+	0.800706i	0.829165	+	0.559004i	$0.188817\pi$
$47$	−0.967922	+	5.48936i	−0.141186	+	0.800706i	−0.970351	+	0.241701i	$0.922295\pi$
$48$	1.45189	−	0.944458i	0.209563	−	0.136321i
$49$	−2.50203	+	6.53757i	−0.357433	+	0.933939i
$50$	−3.12870	−	3.72864i	−0.442465	−	0.527309i
$51$	9.23930	−	2.14054i	1.29376	−	0.299735i
$52$	3.47448	+	0.612645i	0.481824	+	0.0849585i
$53$	−7.94780	−	4.58866i	−1.09171	−	0.630301i	−0.157681	−	0.987490i	$-0.550402\pi$
$53$	−7.94780	−	4.58866i	−1.09171	−	0.630301i	−0.934032	+	0.357189i	$0.883735\pi$
$54$	0.0787098	−	5.19556i	0.0107110	−	0.707026i
$55$			1.61103i			0.217231i
$56$	0.208904	+	2.63749i	0.0279159	+	0.352450i
$57$	−2.15630	−	9.30734i	−0.285609	−	1.23279i
$58$	0.596349	+	0.217053i	0.0783045	+	0.0285005i
$59$	9.48190	+	3.45113i	1.23444	+	0.449299i	0.875115	−	0.483915i	$-0.160786\pi$
$59$	9.48190	+	3.45113i	1.23444	+	0.449299i	0.359323	+	0.933213i	$0.383008\pi$
$60$	−0.562203	−	0.285913i	−0.0725801	−	0.0369112i
$61$	−5.46074	−	0.962876i	−0.699176	−	0.123284i	−0.187249	−	0.982312i	$-0.559957\pi$
$61$	−5.46074	−	0.962876i	−0.699176	−	0.123284i	−0.511927	+	0.859029i	$0.671068\pi$
$62$	−2.49179	+	4.31591i	−0.316458	+	0.548121i
$63$	6.91618	+	3.89441i	0.871357	+	0.490649i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.439412	−	1.20728i	−0.0545024	−	0.149744i
$66$	−2.99947	−	7.05123i	−0.369209	−	0.867947i
$67$	6.89583	−	5.78629i	0.842460	−	0.706908i	−0.115655	−	0.993289i	$-0.536897\pi$
$67$	6.89583	−	5.78629i	0.842460	−	0.706908i	0.958116	+	0.286381i	$0.0924524\pi$
$68$	0.950828	+	5.39241i	0.115305	+	0.653926i
$69$	1.04634	−	8.57624i	0.125965	−	1.03246i
$70$	0.793735	−	0.546104i	0.0948694	−	0.0652719i
$71$	−3.24088	+	1.87112i	−0.384622	+	0.222062i	−0.679827	−	0.733372i	$-0.737945\pi$
$71$	−3.24088	+	1.87112i	−0.384622	+	0.222062i	0.295205	+	0.955434i	$0.404612\pi$
$72$	2.99301	+	0.204670i	0.352730	+	0.0241206i
$73$	3.79842	−	2.19302i	0.444572	−	0.256674i	−0.260963	−	0.965349i	$-0.584040\pi$
$73$	3.79842	−	2.19302i	0.444572	−	0.256674i	0.705535	+	0.708675i	$0.250707\pi$
$74$	−2.94312	−	8.08615i	−0.342131	−	0.939996i
$75$	−0.447691	−	8.41868i	−0.0516949	−	0.972105i
$76$	5.43213	−	0.957830i	0.623108	−	0.109871i
$77$	11.6516	+	1.11604i	1.32782	+	0.127184i
$78$	4.17100	+	4.46596i	0.472273	+	0.505671i
$79$	12.9503	+	10.8666i	1.45702	+	1.22258i	0.927252	+	0.374438i	$0.122164\pi$
$79$	12.9503	+	10.8666i	1.45702	+	1.22258i	0.529765	+	0.848144i	$0.322280\pi$
$80$	0.182076	−	0.315364i	0.0203567	−	0.0352588i
$81$	5.51913	−	7.10909i	0.613237	−	0.789899i
$82$	−3.25244	+	1.87780i	−0.359172	+	0.207368i
$83$	0.538728	−	0.196081i	0.0591331	−	0.0215227i	−0.312284	−	0.949989i	$-0.601094\pi$
$83$	0.538728	−	0.196081i	0.0591331	−	0.0215227i	0.371417	+	0.928466i	$0.378872\pi$
$84$	−2.45731	+	3.86803i	−0.268114	+	0.422036i
$85$	1.52745	−	1.28169i	0.165676	−	0.139018i
$86$	5.60526	+	6.68009i	0.604431	+	0.720332i
$87$	0.599374	+	0.921404i	0.0642596	+	0.0987848i
$88$	4.15725	−	1.51312i	0.443164	−	0.161299i
$89$	−0.706622			−0.0749017			−0.0374509	−	0.999298i	$-0.511924\pi$
$89$	−0.706622			−0.0749017			−0.0374509	+	0.999298i	$0.511924\pi$
$90$	−0.480409	−	0.981154i	−0.0506395	−	0.103423i
$91$	−9.03593	+	2.34168i	−0.947223	+	0.245474i
$92$	4.91243	+	0.866193i	0.512156	+	0.0903069i
$93$	−7.94303	+	3.37882i	−0.823654	+	0.350368i
$94$	−3.58293	−	4.26997i	−0.369551	−	0.440413i
$95$	−1.29112	−	1.53870i	−0.132467	−	0.157867i
$96$	−0.209763	+	1.71930i	−0.0214088	+	0.175476i
$97$	12.0867	+	2.13121i	1.22722	+	0.216392i	0.749430	−	0.662083i	$-0.230327\pi$
$97$	12.0867	+	2.13121i	1.22722	+	0.216392i	0.477788	+	0.878475i	$0.341439\pi$
$98$	−3.39979	−	6.11894i	−0.343431	−	0.618106i
$99$	3.19103	−	12.8828i	0.320711	−	1.29477i
$100$	4.86739			0.486739
$101$	−13.2762	+	4.83215i	−1.32103	+	0.480817i	−0.903789	−	0.427978i	$-0.859226\pi$
$101$	−13.2762	+	4.83215i	−1.32103	+	0.480817i	−0.417244	+	0.908794i	$0.637004\pi$
$102$	−4.29916	+	8.45363i	−0.425680	+	0.837034i
$103$	−4.31372	−	5.14090i	−0.425044	−	0.506547i	0.510442	−	0.859912i	$-0.329482\pi$
$103$	−4.31372	−	5.14090i	−0.425044	−	0.506547i	−0.935486	+	0.353365i	$0.885037\pi$
$104$	−2.70267	+	2.26781i	−0.265018	+	0.222377i
$105$	1.66725	+	0.0706744i	0.162707	+	0.00689711i
$106$	8.62386	−	3.13883i	0.837624	−	0.304870i
$107$	9.16619	−	5.29210i	0.886129	−	0.511607i	0.0134544	−	0.999909i	$-0.495717\pi$
$107$	9.16619	−	5.29210i	0.886129	−	0.511607i	0.872674	+	0.488303i	$0.162384\pi$
$108$	3.92943	+	3.39993i	0.378110	+	0.327159i
$109$	−2.08606	+	3.61316i	−0.199808	+	0.346078i	−0.948466	−	0.316878i	$-0.897365\pi$
$109$	−2.08606	+	3.61316i	−0.199808	+	0.346078i	0.748658	+	0.662957i	$0.230699\pi$
$110$	−1.23412	−	1.03555i	−0.117668	−	0.0987355i
$111$	4.34669	−	14.2566i	0.412570	−	1.35317i
$112$	−2.15472	−	1.53532i	−0.203602	−	0.145074i
$113$	−9.00372	+	1.58760i	−0.846999	+	0.149349i	−0.580271	−	0.814423i	$-0.697054\pi$
$113$	−9.00372	+	1.58760i	−0.846999	+	0.149349i	−0.266728	+	0.963772i	$0.585942\pi$
$114$	8.51588	+	4.33082i	0.797586	+	0.405619i
$115$	−0.621267	−	1.70692i	−0.0579335	−	0.159171i
$116$	−0.549598	+	0.317311i	−0.0510289	+	0.0294616i
$117$	1.12253	+	10.5245i	0.103778	+	0.972995i
$118$	−8.73856	+	5.04521i	−0.804450	+	0.464449i
$119$	−8.21155	−	11.9351i	−0.752751	−	1.09409i
$120$	0.580399	−	0.246891i	0.0529830	−	0.0225380i
$121$	−1.48855	−	8.44201i	−0.135323	−	0.767455i
$122$	4.24770	−	3.56425i	0.384569	−	0.322692i
$123$	−6.45701	−	0.787786i	−0.582209	−	0.0710322i
$124$	−1.70448	−	4.68303i	−0.153067	−	0.420549i
$125$	−1.79661	−	3.11182i	−0.160694	−	0.278330i
$126$	−7.42893	+	2.79483i	−0.661821	+	0.248983i
$127$	−3.43029	+	5.94144i	−0.304389	+	0.527217i	−0.977125	−	0.212665i	$-0.931786\pi$
$127$	−3.43029	+	5.94144i	−0.304389	+	0.527217i	0.672736	+	0.739883i	$0.265119\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	0.802065	+	15.0826i	0.0706179	+	1.32795i
$130$	1.20728	+	0.439412i	0.105885	+	0.0385390i
$131$	−2.24743	−	0.817999i	−0.196359	−	0.0714689i	0.241969	−	0.970284i	$-0.422207\pi$
$131$	−2.24743	−	0.817999i	−0.196359	−	0.0714689i	−0.438328	+	0.898815i	$0.644429\pi$
$132$	7.32958	+	2.23472i	0.637958	+	0.194507i
$133$	−12.0230	+	8.27202i	−1.04252	+	0.717275i
$134$			9.00187i			0.777643i
$135$	0.356764	−	1.85825i	0.0307053	−	0.159933i
$136$	−4.74201	−	2.73780i	−0.406624	−	0.234764i
$137$	20.8605	+	3.67827i	1.78223	+	0.314256i	0.965038	−	0.262108i	$-0.0844178\pi$
$137$	20.8605	+	3.67827i	1.78223	+	0.314256i	0.817193	+	0.576364i	$0.195529\pi$
$138$	5.89720	+	6.31424i	0.502003	+	0.537504i
$139$	−13.4286	−	16.0035i	−1.13899	−	1.35740i	−0.924729	−	0.380626i	$-0.875709\pi$
$139$	−13.4286	−	16.0035i	−1.13899	−	1.35740i	−0.214266	−	0.976775i	$-0.568736\pi$
$140$	−0.0918629	+	0.959065i	−0.00776383	+	0.0810558i
$141$	−0.512686	−	9.64090i	−0.0431760	−	0.811911i
$142$	0.649835	−	3.68539i	0.0545329	−	0.309271i
$143$	7.80421	+	13.5173i	0.652620	+	1.13037i
$144$	−2.08066	+	2.16122i	−0.173388	+	0.180102i
$145$	0.200137	+	0.115549i	0.0166205	+	0.00959584i
$146$	−0.761628	+	4.31941i	−0.0630328	+	0.357477i
$147$	1.66614	−	12.0093i	0.137421	−	0.990513i
$148$	8.08615	+	2.94312i	0.664678	+	0.241923i
$149$	16.6433	−	2.93467i	1.36347	−	0.240417i	0.556423	−	0.830899i	$-0.312173\pi$
$149$	16.6433	−	2.93467i	1.36347	−	0.240417i	0.807051	+	0.590482i	$0.201062\pi$
$150$	6.73685	+	5.06847i	0.550062	+	0.413839i
$151$	0.240524	+	0.201824i	0.0195736	+	0.0164242i	0.652522	−	0.757770i	$-0.273711\pi$
$151$	0.240524	+	0.201824i	0.0195736	+	0.0164242i	−0.632948	+	0.774194i	$0.718155\pi$
$152$	−2.75796	+	4.77693i	−0.223700	+	0.387460i
$153$	−14.7532	+	7.22372i	−1.19273	+	0.584003i
$154$	−8.34445	+	8.20828i	−0.672415	+	0.661442i
$155$	−1.16652	+	1.39020i	−0.0936969	+	0.111664i
$156$	−6.10219	+	0.324504i	−0.488566	+	0.0259811i
$157$	3.31729	−	9.11418i	0.264749	−	0.727391i	−0.734083	−	0.679060i	$-0.762388\pi$
$157$	3.31729	−	9.11418i	0.264749	−	0.727391i	0.998831	−	0.0483310i	$-0.0153902\pi$
$158$	−16.6485	+	2.93558i	−1.32449	+	0.233542i
$159$	15.2046	+	4.63574i	1.20580	+	0.367638i
$160$	0.124547	+	0.342190i	0.00984632	+	0.0270525i
$161$	−12.7755	+	3.31080i	−1.00685	+	0.260928i
$162$	1.89825	+	8.79754i	0.149141	+	0.691200i
$163$	−2.36150	−	4.09023i	−0.184967	−	0.320372i	0.758599	−	0.651558i	$-0.225884\pi$
$163$	−2.36150	−	4.09023i	−0.184967	−	0.320372i	−0.943565	+	0.331187i	$0.892551\pi$
$164$	0.652153	−	3.69854i	0.0509246	−	0.288808i
$165$	−0.629787	−	2.71838i	−0.0490289	−	0.211625i
$166$	−0.196081	+	0.538728i	−0.0152188	+	0.0418134i
$167$	1.71849	+	9.74603i	0.132981	+	0.754170i	0.976245	+	0.216671i	$0.0695199\pi$
$167$	1.71849	+	9.74603i	0.132981	+	0.754170i	−0.843264	+	0.537499i	$0.819369\pi$
$168$	−1.38355	−	4.36873i	−0.106743	−	0.337055i
$169$	0.423355	+	0.355237i	0.0325657	+	0.0273259i
$170$			1.99395i			0.152929i
$171$	7.27691	+	14.8619i	0.556479	+	1.13652i
$172$	−8.72023			−0.664912
$173$	8.83584	−	3.21598i	0.671777	−	0.244507i	0.0164640	−	0.999864i	$-0.494759\pi$
$173$	8.83584	−	3.21598i	0.671777	−	0.244507i	0.655313	+	0.755358i	$0.272537\pi$
$174$	−1.09111	−	0.133120i	−0.0827165	−	0.0100918i
$175$	−11.7157	+	5.34625i	−0.885626	+	0.404138i
$176$	−1.51312	+	4.15725i	−0.114055	+	0.313364i
$177$	−17.3485	−	2.11660i	−1.30399	−	0.159093i
$178$	0.454208	−	0.541304i	0.0340443	−	0.0405724i
$179$		−	20.8101i		−	1.55542i	−0.628622	−	0.777711i	$-0.716381\pi$
$179$		−	20.8101i		−	1.55542i	0.628622	−	0.777711i	$-0.283619\pi$
$180$	1.06041	+	0.262659i	0.0790382	+	0.0195775i
$181$	−18.6917	−	10.7917i	−1.38935	−	0.802139i	−0.396105	−	0.918205i	$-0.629638\pi$
$181$	−18.6917	−	10.7917i	−1.38935	−	0.802139i	−0.993242	+	0.116066i	$0.962972\pi$
$182$	4.01435	−	8.42712i	0.297564	−	0.624660i
$183$	9.59064	−	0.510014i	0.708961	−	0.0377013i
$184$	−3.82119	+	3.20636i	−0.281702	+	0.236376i
$185$	−0.544137	−	3.08596i	−0.0400058	−	0.226884i
$186$	2.51736	−	8.25658i	0.184581	−	0.605402i
$187$	−15.5711	+	18.5569i	−1.13867	+	1.35702i
$188$	5.57404			0.406529
$189$	−13.1925	−	3.86757i	−0.959613	−	0.281324i
$190$	2.00863			0.145721
$191$	5.79562	−	6.90695i	0.419356	−	0.499769i	−0.514464	−	0.857512i	$-0.672009\pi$
$191$	5.79562	−	6.90695i	0.419356	−	0.499769i	0.933820	+	0.357743i	$0.116454\pi$
$192$	−1.18223	−	1.26583i	−0.0853200	−	0.0913537i
$193$	−0.0695836	−	0.394628i	−0.00500874	−	0.0284060i	0.982201	−	0.187833i	$-0.0601464\pi$
$193$	−0.0695836	−	0.394628i	−0.00500874	−	0.0284060i	−0.987210	+	0.159427i	$0.949035\pi$
$194$	−9.40178	+	7.88903i	−0.675009	+	0.566400i
$195$	1.21340	+	1.86533i	0.0868932	+	0.133579i
$196$	6.87272	+	1.32878i	0.490909	+	0.0949131i
$197$	−16.8084	−	9.70432i	−1.19755	−	0.691405i	−0.237540	−	0.971378i	$-0.576341\pi$
$197$	−16.8084	−	9.70432i	−1.19755	−	0.691405i	−0.960008	+	0.279973i	$0.909674\pi$
$198$	7.81767	+	10.7254i	0.555578	+	0.762221i
$199$		−	6.71542i		−	0.476044i	−0.971260	−	0.238022i	$-0.923501\pi$
$199$		−	6.71542i		−	0.476044i	0.971260	−	0.238022i	$-0.0764990\pi$
$200$	−3.12870	+	3.72864i	−0.221233	+	0.263655i
$201$	−9.37375	+	12.4593i	−0.661173	+	0.878811i
$202$	4.83215	−	13.2762i	0.339989	−	0.934112i
$203$	0.974345	−	1.36743i	0.0683856	−	0.0959747i
$204$	−3.71241	−	8.72724i	−0.259921	−	0.611029i
$205$	−1.28513	+	0.467749i	−0.0897574	+	0.0326690i
$206$	6.71096			0.467575
$207$	1.58710	+	14.8802i	0.110311	+	1.03425i
$208$		−	3.52808i		−	0.244628i
$209$	18.6936	+	15.6858i	1.29306	+	1.08501i
$210$	−1.12583	+	1.23176i	−0.0776897	+	0.0849997i
$211$	0.986224	+	5.59316i	0.0678945	+	0.385049i	0.999753	+	0.0222268i	$0.00707559\pi$
$211$	0.986224	+	5.59316i	0.0678945	+	0.385049i	−0.931858	+	0.362822i	$0.881813\pi$
$212$	−3.13883	+	8.62386i	−0.215576	+	0.592289i
$213$	4.73706	−	4.42419i	0.324578	−	0.303141i
$214$	−1.83793	+	10.4234i	−0.125638	+	0.712529i
$215$	1.58774	+	2.75005i	0.108283	+	0.187552i
$216$	−5.13029	+	0.824685i	−0.349072	+	0.0561127i
$217$	9.24642	+	9.39980i	0.627688	+	0.638100i
$218$	−1.42695	−	3.92051i	−0.0966452	−	0.265531i
$219$	−5.55200	+	5.18530i	−0.375169	+	0.350390i
$220$	1.58655	−	0.279752i	0.106965	−	0.0188608i
$221$	6.60727	−	18.1533i	0.444453	−	1.22112i
$222$	8.12716	+	12.4937i	0.545459	+	0.838523i
$223$	16.3914	−	19.5345i	1.09765	−	1.30813i	0.150045	−	0.988679i	$-0.452058\pi$
$223$	16.3914	−	19.5345i	1.09765	−	1.30813i	0.947604	−	0.319447i	$-0.103497\pi$
$224$	2.56115	−	0.663725i	0.171124	−	0.0443470i
$225$	4.04647	+	14.0303i	0.269765	+	0.935354i
$226$	4.57131	−	7.91774i	0.304079	−	0.526680i
$227$	11.1725	+	9.37485i	0.741546	+	0.622231i	0.933252	−	0.359222i	$-0.116958\pi$
$227$	11.1725	+	9.37485i	0.741546	+	0.622231i	−0.191707	+	0.981452i	$0.561402\pi$
$228$	−8.79151	+	3.73975i	−0.582232	+	0.247671i
$229$	6.86286	−	1.21011i	0.453511	−	0.0799662i	0.0577730	−	0.998330i	$-0.481600\pi$
$229$	6.86286	−	1.21011i	0.453511	−	0.0799662i	0.395738	+	0.918364i	$0.370489\pi$
$230$	1.70692	+	0.621267i	0.112551	+	0.0409651i
$231$	−20.0967	+	2.67173i	−1.32227	+	0.175787i
$232$	0.110201	−	0.624980i	0.00723504	−	0.0410320i
$233$	−9.27295	−	5.35374i	−0.607491	−	0.350735i	0.164492	−	0.986378i	$-0.447402\pi$
$233$	−9.27295	−	5.35374i	−0.607491	−	0.350735i	−0.771983	+	0.635643i	$0.780735\pi$
$234$	−8.78382	−	5.90514i	−0.574216	−	0.386031i
$235$	−1.01490	−	1.75786i	−0.0662047	−	0.114670i
$236$	1.75218	−	9.93713i	0.114057	−	0.646852i
$237$	−26.0997	−	13.2732i	−1.69536	−	0.862188i
$238$	14.4211	+	1.38131i	0.934780	+	0.0895368i
$239$	13.6590	+	16.2781i	0.883526	+	1.05295i	0.998226	+	0.0595448i	$0.0189649\pi$
$239$	13.6590	+	16.2781i	0.883526	+	1.05295i	−0.114700	+	0.993400i	$0.536591\pi$
$240$	−0.183944	+	0.603311i	−0.0118735	+	0.0389435i
$241$	4.36234	+	0.769198i	0.281003	+	0.0495484i	0.312373	−	0.949959i	$-0.398876\pi$
$241$	4.36234	+	0.769198i	0.281003	+	0.0495484i	−0.0313704	+	0.999508i	$0.509987\pi$
$242$	7.42378	+	4.28612i	0.477218	+	0.275522i
$243$	−6.53364	+	14.1531i	−0.419133	+	0.907925i
$244$			5.54498i			0.354981i
$245$	−0.832305	−	2.40935i	−0.0531740	−	0.153928i
$246$	4.75397	−	4.43998i	0.303102	−	0.283083i
$247$	−18.2870	−	6.65593i	−1.16357	−	0.423506i
$248$	4.68303	+	1.70448i	0.297373	+	0.108235i
$249$	−0.832375	+	0.541460i	−0.0527496	+	0.0343137i
$250$	3.53864	+	0.623957i	0.223803	+	0.0394625i
$251$	−11.2411	+	19.4702i	−0.709533	+	1.22895i	0.255497	+	0.966810i	$0.417761\pi$
$251$	−11.2411	+	19.4702i	−0.709533	+	1.22895i	−0.965030	+	0.262138i	$0.915573\pi$
$252$	2.63426	−	7.48737i	0.165943	−	0.471660i
$253$	11.0341	+	19.1115i	0.693705	+	1.20153i
$254$	−2.34646	−	6.44684i	−0.147230	−	0.404511i
$255$	−2.07632	+	2.75978i	−0.130024	+	0.172824i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−1.16574	−	6.61124i	−0.0727169	−	0.412398i	−0.999337	−	0.0363999i	$-0.988411\pi$
$257$	−1.16574	−	6.61124i	−0.0727169	−	0.412398i	0.926620	−	0.375998i	$-0.122700\pi$
$258$	−12.0695	−	9.08048i	−0.751413	−	0.565326i
$259$	−22.6959	+	1.79764i	−1.41025	+	0.111700i
$260$	−1.11263	+	0.642378i	−0.0690024	+	0.0398386i
$261$	−1.37156	−	1.32043i	−0.0848972	−	0.0817325i
$262$	2.07125	−	1.19583i	0.127962	−	0.0738789i
$263$	3.31351	+	9.10378i	0.204320	+	0.561363i	0.998954	−	0.0457248i	$-0.0145597\pi$
$263$	3.31351	+	9.10378i	0.204320	+	0.561363i	−0.794635	+	0.607088i	$0.792338\pi$
$264$	−6.42326	+	4.17833i	−0.395324	+	0.257159i
$265$	3.29116	−	0.580321i	0.202175	−	0.0356488i
$266$	1.39148	−	14.5273i	0.0853170	−	0.890724i
$267$	1.19232	−	0.276235i	0.0729690	−	0.0169053i
$268$	−6.89583	−	5.78629i	−0.421230	−	0.353454i
$269$	2.20896	−	3.82603i	0.134683	−	0.233277i	−0.790794	−	0.612083i	$-0.790332\pi$
$269$	2.20896	−	3.82603i	0.134683	−	0.233277i	0.925476	+	0.378806i	$0.123665\pi$
$270$	1.19418	+	1.46776i	0.0726754	+	0.0893248i
$271$	2.02403	−	1.16858i	0.122951	−	0.0709859i	−0.437263	−	0.899334i	$-0.644052\pi$
$271$	2.02403	−	1.16858i	0.122951	−	0.0709859i	0.560214	+	0.828348i	$0.310719\pi$
$272$	5.14538	−	1.87277i	0.311985	−	0.113553i
$273$	14.3314	−	7.48360i	0.867378	−	0.452928i
$274$	−16.2266	+	13.6157i	−0.980283	+	0.822555i
$275$	13.8415	+	16.4957i	0.834676	+	0.994728i
$276$	−8.62764	+	0.458803i	−0.519323	+	0.0276167i
$277$	27.9213	−	10.1625i	1.67763	−	0.610608i	0.684649	−	0.728873i	$-0.259956\pi$
$277$	27.9213	−	10.1625i	1.67763	−	0.610608i	0.992982	+	0.118265i	$0.0377334\pi$
$278$	20.8911			1.25297
$279$	12.0819	−	8.80640i	0.723324	−	0.527225i
$280$	−0.675638	−	0.686846i	−0.0403771	−	0.0410469i
$281$	−19.7402	−	3.48073i	−1.17760	−	0.207643i	−0.449607	−	0.893226i	$-0.648436\pi$
$281$	−19.7402	−	3.48073i	−1.17760	−	0.207643i	−0.727994	+	0.685583i	$0.759547\pi$
$282$	7.71491	+	5.80431i	0.459416	+	0.345642i
$283$	−7.59197	−	9.04776i	−0.451296	−	0.537833i	0.491644	−	0.870796i	$-0.336396\pi$
$283$	−7.59197	−	9.04776i	−0.451296	−	0.537833i	−0.942940	+	0.332963i	$0.891952\pi$
$284$	2.40547	+	2.86673i	0.142738	+	0.170109i
$285$	2.78010	+	2.09161i	0.164679	+	0.123896i
$286$	−15.3713	−	2.71037i	−0.908923	−	0.160268i
$287$	2.49269	+	9.61864i	0.147139	+	0.567770i
$288$	−0.318170	−	2.98308i	−0.0187483	−	0.175780i
$289$	12.9822			0.763659
$290$	−0.217161	+	0.0790403i	−0.0127522	+	0.00464141i
$291$	−21.2277	+	1.12885i	−1.24439	+	0.0661746i
$292$	−2.81929	−	3.35990i	−0.164987	−	0.196623i
$293$	1.27983	−	1.07390i	0.0747683	−	0.0627380i	−0.604638	−	0.796501i	$-0.706682\pi$
$293$	1.27983	−	1.07390i	0.0747683	−	0.0627380i	0.679406	+	0.733763i	$0.262238\pi$
$294$	8.12871	+	8.99578i	0.474076	+	0.524645i
$295$	−3.45285	+	1.25673i	−0.201032	+	0.0731698i
$296$	−7.45224	+	4.30255i	−0.433153	+	0.250081i
$297$	−0.348216	+	22.9854i	−0.0202055	+	1.33375i
$298$	−8.45004	+	14.6359i	−0.489498	+	0.847835i
$299$	−13.4815	−	11.3123i	−0.779653	−	0.654207i
$300$	−8.21304	+	1.90278i	−0.474180	+	0.109857i
$301$	20.9894	−	9.57813i	1.20981	−	0.552074i
$302$	−0.309212	+	0.0545224i	−0.0177931	+	0.00313741i
$303$	20.5127	−	13.3436i	1.17843	−	0.766567i
$304$	−1.88656	−	5.18327i	−0.108201	−	0.297281i
$305$	1.74869	−	1.00961i	0.100130	−	0.0578099i
$306$	3.94951	−	15.9449i	0.225778	−	0.911512i
$307$	24.0725	−	13.8983i	1.37389	−	0.793216i	0.382475	−	0.923966i	$-0.375072\pi$
$307$	24.0725	−	13.8983i	1.37389	−	0.793216i	0.991415	+	0.130750i	$0.0417385\pi$
$308$	−0.924200	−	11.6684i	−0.0526612	−	0.664869i
$309$	9.28849	+	6.98820i	0.528404	+	0.397545i
$310$	−0.315133	−	1.78721i	−0.0178983	−	0.101507i
$311$	4.54883	−	3.81692i	0.257941	−	0.216438i	−0.504642	−	0.863329i	$-0.668376\pi$
$311$	4.54883	−	3.81692i	0.257941	−	0.216438i	0.762583	+	0.646891i	$0.223931\pi$
$312$	3.67383	−	4.88314i	0.207990	−	0.276453i
$313$	−4.49949	−	12.3623i	−0.254326	−	0.698756i	−0.999492	−	0.0318764i	$-0.989852\pi$
$313$	−4.49949	−	12.3623i	−0.254326	−	0.698756i	0.745165	−	0.666880i	$-0.232371\pi$
$314$	4.84956	+	8.39968i	0.273676	+	0.474021i
$315$	−2.84088	+	0.532515i	−0.160066	+	0.0300038i
$316$	8.45268	−	14.6405i	0.475500	−	0.823590i
$317$	20.6805	+	3.64653i	1.16153	+	0.204809i	0.721005	−	0.692930i	$-0.243680\pi$
$317$	20.6805	+	3.64653i	1.16153	+	0.204809i	0.440527	+	0.897739i	$0.354792\pi$
$318$	−13.3245	+	8.66760i	−0.747201	+	0.486055i
$319$	−2.63828	−	0.960255i	−0.147715	−	0.0537640i
$320$	−0.342190	−	0.124547i	−0.0191290	−	0.00696240i
$321$	−13.3978	+	12.5129i	−0.747794	+	0.698404i
$322$	5.67573	−	11.9148i	0.316296	−	0.663984i
$323$		−	30.2030i		−	1.68054i
$324$	−7.95948	−	4.20080i	−0.442193	−	0.233378i
$325$	−14.8719	−	8.58628i	−0.824943	−	0.476281i
$326$	4.65124	+	0.820139i	0.257608	+	0.0454233i
$327$	2.10746	−	6.91219i	0.116543	−	0.382245i
$328$	2.41405	+	2.87696i	0.133294	+	0.158853i
$329$	−13.4166	+	6.12242i	−0.739682	+	0.337540i
$330$	2.48722	+	1.26489i	0.136917	+	0.0696301i
$331$	−0.0191429	+	0.108565i	−0.00105219	+	0.00596725i	−0.985329	−	0.170664i	$-0.945409\pi$
$331$	−0.0191429	+	0.108565i	−0.00105219	+	0.00596725i	0.984277	+	0.176631i	$0.0565199\pi$
$332$	−0.286651	−	0.496495i	−0.0157320	−	0.0272487i
$333$	−1.76121	+	25.7552i	−0.0965137	+	1.41137i
$334$	−8.57051	−	4.94819i	−0.468958	−	0.270753i
$335$	−0.569227	+	3.22824i	−0.0311002	+	0.176378i
$336$	4.23597	+	1.74830i	0.231091	+	0.0953777i
$337$	−11.6718	−	4.24817i	−0.635801	−	0.231413i	0.00395335	−	0.999992i	$-0.498742\pi$
$337$	−11.6718	−	4.24817i	−0.635801	−	0.231413i	−0.639754	+	0.768580i	$0.720964\pi$
$338$	−0.544254	+	0.0959667i	−0.0296035	+	0.00521990i
$339$	14.5719	−	6.19861i	0.791436	−	0.336663i
$340$	−1.52745	−	1.28169i	−0.0828378	−	0.0695091i
$341$	11.0238	−	19.0938i	0.596973	−	1.03399i
$342$	−16.0624	−	3.97859i	−0.868553	−	0.215138i
$343$	−18.0020	+	4.35051i	−0.972018	+	0.234905i
$344$	5.60526	−	6.68009i	0.302215	−	0.360166i
$345$	1.71557	+	2.63731i	0.0923634	+	0.141988i
$346$	−3.21598	+	8.83584i	−0.172892	+	0.475018i
$347$	−5.69611	+	1.00438i	−0.305783	+	0.0539179i	−0.324434	−	0.945908i	$-0.605174\pi$
$347$	−5.69611	+	1.00438i	−0.305783	+	0.0539179i	0.0186510	+	0.999826i	$0.494063\pi$
$348$	0.803325	−	0.750268i	0.0430628	−	0.0402186i
$349$	10.0647	+	27.6525i	0.538750	+	1.48020i	0.848402	+	0.529353i	$0.177565\pi$
$349$	10.0647	+	27.6525i	0.538750	+	1.48020i	−0.309652	+	0.950850i	$0.600212\pi$
$350$	3.43526	−	12.4113i	0.183622	−	0.663410i
$351$	−6.00840	−	17.3199i	−0.320705	−	0.924466i
$352$	−2.21203	−	3.83134i	−0.117901	−	0.204211i
$353$	4.21784	−	23.9206i	0.224493	−	1.27316i	−0.639159	−	0.769074i	$-0.720717\pi$
$353$	4.21784	−	23.9206i	0.224493	−	1.27316i	0.863652	−	0.504088i	$-0.168171\pi$
$354$	12.7728	−	11.9292i	0.678867	−	0.634029i
$355$	0.466086	−	1.28056i	0.0247373	−	0.0679651i
$356$	0.122704	+	0.695886i	0.00650328	+	0.0368819i
$357$	18.5215	+	16.9287i	0.980263	+	0.895960i
$358$	15.9415	+	13.3765i	0.842534	+	0.706970i
$359$			6.99542i			0.369204i	0.982813	+	0.184602i	$0.0590996\pi$
$359$			6.99542i			0.369204i	−0.982813	+	0.184602i	$0.940900\pi$
$360$	−0.882826	+	0.643486i	−0.0465290	+	0.0339147i
$361$	−11.4254			−0.601338
$362$	20.2817	−	7.38194i	1.06598	−	0.387986i
$363$	5.81190	+	13.6628i	0.305046	+	0.717110i
$364$	3.87517	+	8.49202i	0.203114	+	0.445103i
$365$	−0.546269	+	1.50086i	−0.0285930	+	0.0785587i
$366$	−5.77405	+	7.67469i	−0.301815	+	0.401162i
$367$	−11.1358	+	13.2711i	−0.581284	+	0.692747i	−0.973906	−	0.226953i	$-0.927124\pi$
$367$	−11.1358	+	13.2711i	−0.581284	+	0.692747i	0.392622	+	0.919700i	$0.371568\pi$
$368$		−	4.98821i		−	0.260028i
$369$	11.2033	−	1.19492i	0.583218	−	0.0622050i
$370$	2.71374	+	1.56678i	0.141081	+	0.0814530i
$371$	−1.91718	−	24.2051i	−0.0995348	−	1.25667i
$372$	4.70678	+	7.23563i	0.244035	+	0.375150i
$373$	2.52581	−	2.11941i	0.130781	−	0.109739i	−0.575051	−	0.818118i	$-0.695018\pi$
$373$	2.52581	−	2.11941i	0.130781	−	0.109739i	0.705832	+	0.708379i	$0.250573\pi$
$374$	−4.20651	−	23.8563i	−0.217514	−	1.23358i
$375$	4.24802	+	4.54843i	0.219367	+	0.234880i
$376$	−3.58293	+	4.26997i	−0.184775	+	0.220207i
$377$	2.23900			0.115314
$378$	11.4427	−	7.62001i	0.588549	−	0.391931i
$379$	36.0217			1.85031			0.925154	−	0.379591i	$-0.123935\pi$
$379$	36.0217			1.85031			0.925154	+	0.379591i	$0.123935\pi$
$380$	−1.29112	+	1.53870i	−0.0662333	+	0.0789337i
$381$	3.46548	−	11.3663i	0.177542	−	0.582314i
$382$	1.56568	+	8.87940i	0.0801071	+	0.454310i
$383$	9.71799	−	8.15436i	0.496566	−	0.416668i	−0.359806	−	0.933027i	$-0.617157\pi$
$383$	9.71799	−	8.15436i	0.496566	−	0.416668i	0.856372	+	0.516359i	$0.172713\pi$
$384$	1.72961	−	0.0919775i	0.0882636	−	0.00469371i
$385$	−3.51152	+	2.41599i	−0.178964	+	0.123130i
$386$	0.347030	+	0.200358i	0.0176634	+	0.0101980i
$387$	−7.24950	−	25.1362i	−0.368513	−	1.27774i
$388$		−	12.2732i		−	0.623075i
$389$	−4.90280	+	5.84293i	−0.248582	+	0.296248i	−0.875878	−	0.482532i	$-0.839717\pi$
$389$	−4.90280	+	5.84293i	−0.248582	+	0.296248i	0.627296	+	0.778781i	$0.284162\pi$
$390$	−2.20888	−	0.269494i	−0.111851	−	0.0136464i
$391$	9.34175	−	25.6662i	0.472433	−	1.29800i
$392$	−5.43561	+	4.41069i	−0.274540	+	0.222773i
$393$	4.11200	+	0.501683i	0.207423	+	0.0253066i
$394$	18.2382	−	6.63815i	0.918825	−	0.334425i
$395$	−6.15611			−0.309747
$396$	−13.2412	−	0.905473i	−0.665397	−	0.0455017i
$397$		−	2.40733i		−	0.120821i	−0.998174	−	0.0604103i	$-0.980759\pi$
$397$		−	2.40733i		−	0.120821i	0.998174	−	0.0604103i	$-0.0192409\pi$
$398$	5.14431	+	4.31659i	0.257861	+	0.216371i
$399$	17.0533	−	18.6579i	0.853734	−	0.934064i
$400$	−0.845214	−	4.79345i	−0.0422607	−	0.239672i
$401$	4.81175	−	13.2202i	0.240287	−	0.660184i	−0.759664	−	0.650316i	$-0.774637\pi$
$401$	4.81175	−	13.2202i	0.240287	−	0.660184i	0.999951	−	0.00986842i	$-0.00314127\pi$
$402$	−3.51904	−	15.1894i	−0.175514	−	0.757578i
$403$	−3.05316	+	17.3154i	−0.152089	+	0.862539i
$404$	7.06413	+	12.2354i	0.351454	+	0.608736i
$405$	0.124444	+	3.27500i	0.00618368	+	0.162736i
$406$	0.421214	+	1.62536i	0.0209045	+	0.0806652i
$407$	13.0205	+	35.7736i	0.645403	+	1.77323i
$408$	9.07174	+	2.76589i	0.449118	+	0.136932i
$409$	9.23980	−	1.62923i	0.456879	−	0.0805600i	0.0595275	−	0.998227i	$-0.481041\pi$
$409$	9.23980	−	1.62923i	0.456879	−	0.0805600i	0.397351	+	0.917667i	$0.369929\pi$
$410$	0.467749	−	1.28513i	0.0231005	−	0.0634681i
$411$	−36.6370	+	1.94829i	−1.80717	+	0.0961023i
$412$	−4.31372	+	5.14090i	−0.212522	+	0.253274i
$413$	6.69727	+	25.8430i	0.329551	+	1.27165i
$414$	−12.4191	−	8.34904i	−0.610365	−	0.410333i
$415$	−0.104384	+	0.180799i	−0.00512403	+	0.00887509i
$416$	2.70267	+	2.26781i	0.132509	+	0.111188i
$417$	28.9149	+	21.7542i	1.41597	+	1.06531i
$418$	−24.0320	+	4.23749i	−1.17544	+	0.207262i
$419$	−1.56858	−	0.570915i	−0.0766300	−	0.0278910i	0.303421	−	0.952857i	$-0.401871\pi$
$419$	−1.56858	−	0.570915i	−0.0766300	−	0.0278910i	−0.380051	+	0.924966i	$0.624093\pi$
$420$	−0.219915	−	1.65420i	−0.0107308	−	0.0807166i
$421$	1.42072	−	8.05732i	0.0692418	−	0.392690i	−0.930415	−	0.366507i	$-0.880554\pi$
$421$	1.42072	−	8.05732i	0.0692418	−	0.392690i	0.999657	−	0.0261830i	$-0.00833526\pi$
$422$	−4.91854	−	2.83972i	−0.239431	−	0.138235i
$423$	4.63394	+	16.0672i	0.225310	+	0.781216i
$424$	−4.58866	−	7.94780i	−0.222845	−	0.385979i
$425$	4.62805	−	26.2470i	0.224494	−	1.27317i
$426$	0.344203	+	6.47262i	0.0166767	+	0.313599i
$427$	−6.09050	−	13.3467i	−0.294740	−	0.645891i
$428$	−6.80339	−	8.10797i	−0.328854	−	0.391913i
$429$	−18.4527	−	19.7577i	−0.890905	−	0.953909i
$430$	−3.12724	−	0.551417i	−0.150809	−	0.0265917i
$431$	3.36070	+	1.94030i	0.161879	+	0.0934609i	0.578751	−	0.815504i	$-0.303540\pi$
$431$	3.36070	+	1.94030i	0.161879	+	0.0934609i	−0.416872	+	0.908965i	$0.636874\pi$
$432$	2.66594	−	4.46013i	0.128265	−	0.214588i
$433$			7.95078i			0.382090i	0.981581	+	0.191045i	$0.0611877\pi$
$433$			7.95078i			0.382090i	−0.981581	+	0.191045i	$0.938812\pi$
$434$	−13.1441	+	1.04109i	−0.630939	+	0.0499738i
$435$	−0.382874	−	0.116735i	−0.0183574	−	0.00559700i
$436$	3.92051	+	1.42695i	0.187759	+	0.0683385i
$437$	−25.8553	−	9.41054i	−1.23682	−	0.450167i
$438$	−0.403417	−	7.58613i	−0.0192760	−	0.362479i
$439$	−15.0276	−	2.64977i	−0.717229	−	0.126467i	−0.196889	−	0.980426i	$-0.563084\pi$
$439$	−15.0276	−	2.64977i	−0.717229	−	0.126467i	−0.520340	+	0.853959i	$0.674195\pi$
$440$	−0.805513	+	1.39519i	−0.0384013	+	0.0665130i
$441$	1.88336	+	20.9154i	0.0896836	+	0.995970i
$442$	9.65918	+	16.7302i	0.459440	+	0.795774i
$443$	6.53331	+	17.9501i	0.310407	+	0.852836i	0.992574	+	0.121640i	$0.0388153\pi$
$443$	6.53331	+	17.9501i	0.310407	+	0.852836i	−0.682167	+	0.731196i	$0.738962\pi$
$444$	−14.7948	−	1.80503i	−0.702129	−	0.0856630i
$445$	0.197116	−	0.165400i	0.00934422	−	0.00784073i
$446$	4.42811	+	25.1131i	0.209677	+	1.18914i
$447$	−26.9360	+	11.4581i	−1.27403	+	0.541949i
$448$	−1.13783	+	2.38859i	−0.0537574	+	0.112850i
$449$	−28.8723	+	16.6694i	−1.36257	+	0.786678i	−0.989965	−	0.141313i	$-0.954868\pi$
$449$	−28.8723	+	16.6694i	−1.36257	+	0.786678i	−0.372602	+	0.927991i	$0.621534\pi$
$450$	−13.3489	−	5.91874i	−0.629272	−	0.279012i
$451$	14.3890	−	8.30749i	0.677551	−	0.391184i
$452$	3.12696	+	8.59125i	0.147080	+	0.404099i
$453$	−0.484748	−	0.246522i	−0.0227754	−	0.0115826i
$454$	−14.3631	+	2.53260i	−0.674094	+	0.118861i
$455$	1.97251	−	2.76828i	0.0924726	−	0.129779i
$456$	2.78626	−	9.13855i	0.130478	−	0.427952i
$457$	7.15815	+	6.00640i	0.334844	+	0.280968i	0.794670	−	0.607041i	$-0.207644\pi$
$457$	7.15815	+	6.00640i	0.334844	+	0.280968i	−0.459826	+	0.888009i	$0.652088\pi$
$458$	−3.48437	+	6.03510i	−0.162814	+	0.282002i
$459$	22.0701	−	17.9564i	1.03014	−	0.838132i
$460$	−1.57310	+	0.908232i	−0.0733463	+	0.0423465i
$461$	−15.3507	+	5.58720i	−0.714954	+	0.260222i	−0.673782	−	0.738930i	$-0.735331\pi$
$461$	−15.3507	+	5.58720i	−0.714954	+	0.260222i	−0.0411716	+	0.999152i	$0.513109\pi$
$462$	10.8713	−	17.1124i	0.505777	−	0.796139i
$463$	−15.6985	+	13.1726i	−0.729569	+	0.612181i	−0.930014	−	0.367524i	$-0.880206\pi$
$463$	−15.6985	+	13.1726i	−0.729569	+	0.612181i	0.200445	+	0.979705i	$0.435761\pi$
$464$	0.407927	+	0.486148i	0.0189375	+	0.0225689i
$465$	1.42487	−	2.80179i	0.0660768	−	0.129930i
$466$	10.0617	−	3.66217i	0.466101	−	0.169647i
$467$	−1.85356			−0.0857724			−0.0428862	−	0.999080i	$-0.513655\pi$
$467$	−1.85356			−0.0857724			−0.0428862	+	0.999080i	$0.513655\pi$
$468$	10.1697	−	2.93304i	0.470096	−	0.135580i
$469$	22.9537	+	6.35325i	1.05990	+	0.293366i
$470$	1.99896	+	0.352470i	0.0922051	+	0.0162582i
$471$	−2.03451	+	16.6757i	−0.0937455	+	0.768376i
$472$	6.48600	+	7.72971i	0.298542	+	0.355789i
$473$	−24.7980	−	29.5531i	−1.14021	−	1.35885i
$474$	26.9444	−	11.4617i	1.23760	−	0.526452i
$475$	−26.4403	−	4.66214i	−1.21316	−	0.213914i
$476$	−10.3278	+	10.1593i	−0.473375	+	0.465651i
$477$	−27.4678	−	1.87833i	−1.25767	−	0.0860027i
$478$	−21.2496			−0.971934
$479$	−31.9967	+	11.6459i	−1.46197	+	0.532112i	−0.945906	−	0.324440i	$-0.894824\pi$
$479$	−31.9967	+	11.6459i	−1.46197	+	0.532112i	−0.516061	+	0.856552i	$0.672602\pi$
$480$	−0.343926	−	0.528710i	−0.0156980	−	0.0241322i
$481$	−19.5147	−	23.2567i	−0.889794	−	1.06042i
$482$	−3.39330	+	2.84731i	−0.154560	+	0.129692i
$483$	20.2626	−	10.5808i	0.921982	−	0.481441i
$484$	−8.05527	+	2.93188i	−0.366149	+	0.133267i
$485$	−3.87052	+	2.23464i	−0.175751	+	0.101470i
$486$	−6.64219	−	14.1025i	−0.301296	−	0.639704i
$487$	1.09498	−	1.89656i	0.0496182	−	0.0859412i	−0.840150	−	0.542355i	$-0.817533\pi$
$487$	1.09498	−	1.89656i	0.0496182	−	0.0859412i	0.889768	+	0.456414i	$0.150866\pi$
$488$	−4.24770	−	3.56425i	−0.192285	−	0.161346i
$489$	5.58366	+	5.97852i	0.252502	+	0.270358i
$490$	2.38067	+	0.911119i	0.107548	+	0.0411601i
$491$	−33.3404	+	5.87881i	−1.50463	+	0.265307i	−0.864372	−	0.502853i	$-0.832284\pi$
$491$	−33.3404	+	5.87881i	−1.50463	+	0.265307i	−0.640258	+	0.768160i	$0.721173\pi$
$492$	0.345431	+	6.49571i	0.0155732	+	0.292849i
$493$	1.18850	+	3.26537i	0.0535272	+	0.147065i
$494$	16.8534	−	9.73031i	0.758270	−	0.437787i
$495$	2.12535	+	4.34068i	0.0955275	+	0.195099i
$496$	−4.31591	+	2.49179i	−0.193790	+	0.111885i
$497$	−8.93868	−	4.25804i	−0.400955	−	0.190999i
$498$	0.120258	−	0.985680i	0.00538887	−	0.0441694i
$499$	1.48730	+	8.43489i	0.0665806	+	0.377598i	0.999831	+	0.0183715i	$0.00584817\pi$
$499$	1.48730	+	8.43489i	0.0665806	+	0.377598i	−0.933251	+	0.359226i	$0.883041\pi$
$500$	−2.75257	+	2.30968i	−0.123099	+	0.103292i
$501$	−6.70965	−	15.7733i	−0.299765	−	0.704697i
$502$	−7.68938	−	21.1264i	−0.343194	−	0.942917i
$503$	15.3427	+	26.5744i	0.684098	+	1.18489i	0.973719	+	0.227752i	$0.0731375\pi$
$503$	15.3427	+	26.5744i	0.684098	+	1.18489i	−0.289621	+	0.957141i	$0.593529\pi$
$504$	4.04239	+	6.83075i	0.180062	+	0.304266i
$505$	2.57241	−	4.45555i	0.114471	−	0.198269i
$506$	−21.7328	−	3.83209i	−0.966142	−	0.170357i
$507$	−0.853221	−	0.433913i	−0.0378929	−	0.0192707i
$508$	6.44684	+	2.34646i	0.286032	+	0.104107i
$509$	24.1147	+	8.77704i	1.06887	+	0.389036i	0.815753	−	0.578401i	$-0.196323\pi$
$509$	24.1147	+	8.77704i	1.06887	+	0.389036i	0.253114	+	0.967436i	$0.418545\pi$
$510$	−0.779481	−	3.36451i	−0.0345160	−	0.148983i
$511$	10.4764	+	4.99057i	0.463450	+	0.220770i
$512$			1.00000i			0.0441942i
$513$	−18.0886	−	22.2326i	−0.798632	−	0.981593i
$514$	5.81383	+	3.35662i	0.256437	+	0.148054i
$515$	2.40668	+	0.424363i	0.106051	+	0.0186996i
$516$	14.7142	−	3.40894i	0.647755	−	0.150070i
$517$	15.8511	+	18.8905i	0.697129	+	0.830805i
$518$	13.2116	−	18.5416i	0.580483	−	0.814669i
$519$	−13.6520	+	8.88065i	−0.599258	+	0.389817i
$520$	0.223095	−	1.26524i	0.00978338	−	0.0554843i
$521$	12.4012	+	21.4795i	0.543307	+	0.941036i	0.998711	+	0.0507509i	$0.0161614\pi$
$521$	12.4012	+	21.4795i	0.543307	+	0.941036i	−0.455404	+	0.890285i	$0.650505\pi$
$522$	1.89313	−	0.201917i	0.0828599	−	0.00883768i
$523$	17.6470	+	10.1885i	0.771651	+	0.445513i	0.833463	−	0.552575i	$-0.186355\pi$
$523$	17.6470	+	10.1885i	0.771651	+	0.445513i	−0.0618122	+	0.998088i	$0.519688\pi$
$524$	−0.415309	+	2.35533i	−0.0181429	+	0.102893i
$525$	17.6787	−	13.6010i	0.771560	−	0.593596i
$526$	−9.10378	−	3.31351i	−0.396944	−	0.144476i
$527$	−26.8735	+	4.73853i	−1.17063	+	0.206414i
$528$	0.928002	−	7.60628i	0.0403861	−	0.331021i
$529$	−1.44188	−	1.20988i	−0.0626902	−	0.0526033i
$530$	−1.67097	+	2.89420i	−0.0725822	+	0.125716i
$531$	30.1005	−	3.21047i	1.30625	−	0.139322i
$532$	10.2341	+	10.4039i	0.443705	+	0.451066i
$533$	−8.51697	+	10.1501i	−0.368911	+	0.439651i
$534$	−0.554803	+	1.09093i	−0.0240087	+	0.0472093i
$535$	−1.31823	+	3.62181i	−0.0569921	+	0.156585i
$536$	8.86511	−	1.56316i	0.382915	−	0.0675182i
$537$	8.13516	+	35.1142i	0.351058	+	1.51529i
$538$	1.51102	+	4.15149i	0.0651446	+	0.178983i
$539$	15.0409	+	27.0705i	0.647856	+	1.16601i
$540$	−1.89197	−	0.0286623i	−0.0814174	−	0.00123343i
$541$	−3.60386	−	6.24207i	−0.154942	−	0.268368i	0.778096	−	0.628146i	$-0.216186\pi$
$541$	−3.60386	−	6.24207i	−0.154942	−	0.268368i	−0.933038	+	0.359778i	$0.882852\pi$
$542$	−0.405842	+	2.30164i	−0.0174324	+	0.0988641i
$543$	35.7584	+	10.9024i	1.53454	+	0.467867i
$544$	−1.87277	+	5.14538i	−0.0802942	+	0.220606i
$545$	−0.263821	−	1.49620i	−0.0113009	−	0.0640903i
$546$	−3.47930	+	15.7889i	−0.148900	+	0.675702i
$547$	12.4492	+	10.4461i	0.532290	+	0.446644i	0.868891	−	0.495003i	$-0.164833\pi$
$547$	12.4492	+	10.4461i	0.532290	+	0.446644i	−0.336602	+	0.941647i	$0.609278\pi$
$548$		−	21.1823i		−	0.904863i
$549$	−15.9835	+	4.60978i	−0.682158	+	0.196741i
$550$	−21.5336			−0.918196
$551$	3.28942	−	1.19725i	0.140134	−	0.0510046i
$552$	5.19428	−	6.90407i	0.221083	−	0.293857i
$553$	−4.26464	+	44.5236i	−0.181351	+	1.89334i
$554$	−10.1625	+	27.9213i	−0.431765	+	1.18626i
$555$	2.12453	+	4.99440i	0.0901811	+	0.212000i
$556$	−13.4286	+	16.0035i	−0.569497	+	0.678701i
$557$			15.7794i			0.668594i	0.942468	+	0.334297i	$0.108499\pi$
$557$			15.7794i			0.668594i	−0.942468	+	0.334297i	$0.891501\pi$
$558$	−1.01999	+	14.9159i	−0.0431797	+	0.631441i
$559$	26.6439	+	15.3828i	1.12692	+	0.650625i
$560$	0.960446	−	0.0760725i	0.0405863	−	0.00321465i
$561$	19.0197	−	37.3993i	0.803013	−	1.57900i
$562$	15.3551	−	12.8845i	0.647718	−	0.543500i
$563$	3.00631	+	17.0496i	0.126701	+	0.718557i	0.980283	+	0.197598i	$0.0633142\pi$
$563$	3.00631	+	17.0496i	0.126701	+	0.718557i	−0.853582	+	0.520958i	$0.825575\pi$
$564$	−9.40541	+	2.17902i	−0.396039	+	0.0917534i
$565$	2.14003	−	2.55039i	0.0900318	−	0.107296i
$566$	11.8110			0.496454
$567$	23.7724	+	1.36872i	0.998347	+	0.0574809i
$568$	−3.74225			−0.157021
$569$	−16.7210	+	19.9273i	−0.700981	+	0.835397i	−0.992637	−	0.121127i	$-0.961349\pi$
$569$	−16.7210	+	19.9273i	−0.700981	+	0.835397i	0.291656	+	0.956523i	$0.405794\pi$
$570$	−3.38928	+	0.785221i	−0.141961	+	0.0328893i
$571$	−2.09906	−	11.9044i	−0.0878429	−	0.498182i	−0.996707	−	0.0810892i	$-0.974160\pi$
$571$	−2.09906	−	11.9044i	−0.0878429	−	0.498182i	0.908864	−	0.417093i	$-0.136951\pi$
$572$	11.9567	−	10.0329i	0.499936	−	0.419496i
$573$	−7.07920	+	13.9201i	−0.295738	+	0.581522i
$574$	−8.97057	−	4.27323i	−0.374424	−	0.178361i
$575$	−21.0267	−	12.1398i	−0.876875	−	0.506264i
$576$	2.48969	+	1.67375i	0.103737	+	0.0697398i
$577$		−	24.3791i		−	1.01492i	−0.861676	−	0.507458i	$-0.830585\pi$
$577$		−	24.3791i		−	1.01492i	0.861676	−	0.507458i	$-0.169415\pi$
$578$	−8.34480	+	9.94495i	−0.347098	+	0.413655i
$579$	0.271682	+	0.638678i	0.0112907	+	0.0265425i
$580$	0.0790403	−	0.217161i	0.00328197	−	0.00901714i
$581$	1.23530	+	0.880201i	0.0512491	+	0.0365169i
$582$	12.7802	−	16.9870i	0.529755	−	0.704134i
$583$	−38.1524	+	13.8863i	−1.58011	+	0.575114i
$584$	4.38604			0.181496
$585$	−2.77664	−	2.67314i	−0.114800	−	0.110521i
$586$			1.67069i			0.0690158i
$587$	−35.5459	−	29.8265i	−1.46714	−	1.23107i	−0.918746	−	0.394850i	$-0.870797\pi$
$587$	−35.5459	−	29.8265i	−1.46714	−	1.23107i	−0.548389	−	0.836223i	$-0.684759\pi$
$588$	−12.1162	+	0.444574i	−0.499664	+	0.0183339i
$589$	4.77342	+	27.0714i	0.196686	+	1.11546i
$590$	1.25673	−	3.45285i	0.0517389	−	0.142151i
$591$	32.1554	+	9.80389i	1.32270	+	0.403278i
$592$	1.49426	−	8.47437i	0.0614137	−	0.348295i
$593$	−22.2867	−	38.6017i	−0.915204	−	1.58518i	−0.806602	−	0.591095i	$-0.798696\pi$
$593$	−22.2867	−	38.6017i	−0.915204	−	1.58518i	−0.108602	−	0.994085i	$-0.534638\pi$
$594$	−17.3840	−	15.0415i	−0.713275	−	0.617160i
$595$	5.08433	+	1.40727i	0.208437	+	0.0576924i
$596$	−5.78017	−	15.8809i	−0.236765	−	0.650506i
$597$	2.62521	+	11.3313i	0.107443	+	0.463760i
$598$	17.3314	−	3.05600i	0.708735	−	0.124969i
$599$	0.724637	−	1.99092i	0.0296078	−	0.0813469i	−0.924008	−	0.382373i	$-0.875107\pi$
$599$	0.724637	−	1.99092i	0.0296078	−	0.0813469i	0.953616	+	0.301026i	$0.0973292\pi$
$600$	3.82163	−	7.51463i	0.156017	−	0.306784i
$601$	26.4199	−	31.4861i	1.07769	−	1.28434i	0.121186	−	0.992630i	$-0.461330\pi$
$601$	26.4199	−	31.4861i	1.07769	−	1.28434i	0.956506	−	0.291713i	$-0.0942252\pi$
$602$	−6.15448	+	22.2356i	−0.250838	+	0.906254i
$603$	10.9463	−	24.6877i	0.445766	−	1.00536i
$604$	0.156991	−	0.271916i	0.00638787	−	0.0110641i
$605$	2.39128	+	2.00652i	0.0972193	+	0.0815767i
$606$	−2.96359	+	24.2907i	−0.120387	+	0.986744i
$607$	33.9788	−	5.99139i	1.37916	−	0.243183i	0.565607	−	0.824675i	$-0.308642\pi$
$607$	33.9788	−	5.99139i	1.37916	−	0.243183i	0.813552	+	0.581492i	$0.197531\pi$
$608$	5.18327	+	1.88656i	0.210210	+	0.0765100i
$609$	−1.10951	+	2.68824i	−0.0449596	+	0.108933i
$610$	−0.350633	+	1.98854i	−0.0141967	+	0.0805135i
$611$	−17.0310	−	9.83284i	−0.688999	−	0.397794i
$612$	9.67584	+	13.2747i	0.391123	+	0.536598i
$613$	11.8211	+	20.4747i	0.477449	+	0.826966i	0.999666	−	0.0258467i	$-0.00822817\pi$
$613$	11.8211	+	20.4747i	0.477449	+	0.826966i	−0.522217	+	0.852813i	$0.674895\pi$
$614$	−4.82682	+	27.3742i	−0.194795	+	1.10473i
$615$	1.98562	−	1.29165i	0.0800680	−	0.0520843i
$616$	9.53258	+	6.79232i	0.384078	+	0.273671i
$617$	16.2616	+	19.3798i	0.654665	+	0.780200i	0.986610	−	0.163099i	$-0.0521491\pi$
$617$	16.2616	+	19.3798i	0.654665	+	0.780200i	−0.331944	+	0.943299i	$0.607705\pi$
$618$	−11.3238	+	2.62347i	−0.455510	+	0.105531i
$619$	−40.8702	−	7.20652i	−1.64271	−	0.289655i	−0.725551	−	0.688168i	$-0.758415\pi$
$619$	−40.8702	−	7.20652i	−1.64271	−	0.289655i	−0.917162	+	0.398514i	$0.869526\pi$
$620$	1.57164	+	0.907389i	0.0631187	+	0.0364416i
$621$	−8.49503	−	24.4878i	−0.340894	−	0.982664i
$622$			5.93808i			0.238095i
$623$	−1.05969	−	1.54021i	−0.0424557	−	0.0617072i
$624$	1.37921	+	5.95314i	0.0552125	+	0.238316i
$625$	−21.6397	−	7.87621i	−0.865588	−	0.315048i
$626$	12.3623	+	4.49949i	0.494095	+	0.179836i
$627$	−37.6747	−	19.1598i	−1.50458	−	0.765168i
$628$	−9.55176	−	1.68423i	−0.381157	−	0.0672082i
$629$	23.5591	−	40.8055i	0.939361	−	1.62702i
$630$	1.41815	−	2.51854i	0.0565006	−	0.100341i
$631$	−0.927696	−	1.60682i	−0.0369310	−	0.0639664i	0.846969	−	0.531642i	$-0.178425\pi$
$631$	−0.927696	−	1.60682i	−0.0369310	−	0.0639664i	−0.883900	+	0.467676i	$0.845092\pi$
$632$	5.78197	+	15.8858i	0.229994	+	0.631905i
$633$	−3.85061	−	9.05212i	−0.153048	−	0.359790i
$634$	−16.0866	+	13.4982i	−0.638879	+	0.536083i
$635$	−0.433824	−	2.46034i	−0.0172158	−	0.0976355i
$636$	1.92506	−	15.7786i	0.0763337	−	0.625662i
$637$	−18.6549	−	16.1837i	−0.739136	−	0.641223i
$638$	2.43145	−	1.40380i	0.0962621	−	0.0555770i
$639$	−6.26361	+	9.31703i	−0.247784	+	0.368576i
$640$	0.315364	−	0.182076i	0.0124659	−	0.00719718i
$641$	13.9697	+	38.3815i	0.551771	+	1.51598i	0.831290	+	0.555839i	$0.187603\pi$
$641$	13.9697	+	38.3815i	0.551771	+	1.51598i	−0.279518	+	0.960140i	$0.590175\pi$
$642$	−0.973508	−	18.3065i	−0.0384213	−	0.722500i
$643$	11.4195	−	2.01357i	0.450342	−	0.0794074i	0.0561227	−	0.998424i	$-0.482126\pi$
$643$	11.4195	−	2.01357i	0.450342	−	0.0794074i	0.394219	+	0.919016i	$0.371015\pi$
$644$	5.47895	+	12.0065i	0.215901	+	0.473124i
$645$	−3.75415	−	4.01964i	−0.147820	−	0.158273i
$646$	23.1368	+	19.4141i	0.910307	+	0.763838i
$647$	−5.83779	+	10.1113i	−0.229507	+	0.397518i	−0.957662	−	0.287895i	$-0.907045\pi$
$647$	−5.83779	+	10.1113i	−0.229507	+	0.397518i	0.728155	+	0.685412i	$0.240378\pi$
$648$	8.33425	−	3.39709i	0.327400	−	0.133450i
$649$	38.6599	−	22.3203i	1.51753	−	0.876148i
$650$	16.1369	−	5.87336i	0.632942	−	0.230372i
$651$	−19.2766	−	12.2462i	−0.755510	−	0.479966i
$652$	−3.61802	+	3.03588i	−0.141693	+	0.118894i
$653$	−25.9870	−	30.9701i	−1.01695	−	1.21195i	−0.977107	−	0.212747i	$-0.931759\pi$
$653$	−25.9870	−	30.9701i	−1.01695	−	1.21195i	−0.0398424	−	0.999206i	$-0.512686\pi$
$654$	3.94040	+	6.05748i	0.154082	+	0.236866i
$655$	0.818406	−	0.297875i	0.0319778	−	0.0116390i
$656$	−3.75560			−0.146632
$657$	7.34116	−	10.9199i	0.286406	−	0.426025i
$658$	3.93399	−	14.2131i	0.153363	−	0.554086i
$659$	−10.2802	−	1.81267i	−0.400459	−	0.0706117i	−0.0302084	−	0.999544i	$-0.509617\pi$
$659$	−10.2802	−	1.81267i	−0.400459	−	0.0706117i	−0.370251	+	0.928932i	$0.620728\pi$
$660$	−2.56772	+	1.09226i	−0.0999483	+	0.0425162i
$661$	25.0324	+	29.8325i	0.973648	+	1.16035i	0.987046	+	0.160439i	$0.0512909\pi$
$661$	25.0324	+	29.8325i	0.973648	+	1.16035i	−0.0133975	+	0.999910i	$0.504265\pi$
$662$	−0.0708605	−	0.0844482i	−0.00275407	−	0.00328217i
$663$	−4.05228	+	33.2141i	−0.157377	+	1.28993i
$664$	0.564593	+	0.0995530i	0.0219105	+	0.00386340i
$665$	1.41763	−	5.12177i	0.0549734	−	0.198614i
$666$	−18.5975	−	17.9043i	−0.720639	−	0.693776i
$667$	3.16563			0.122573
$668$	9.29955	−	3.38476i	0.359811	−	0.130960i
$669$	−20.0217	+	39.3695i	−0.774082	+	1.52211i
$670$	−2.10709	−	2.51113i	−0.0814039	−	0.0970134i
$671$	−18.7921	+	15.7684i	−0.725460	+	0.608733i
$672$	−4.06211	+	2.12115i	−0.156699	+	0.0818253i
$673$	20.4081	−	7.42794i	0.786675	−	0.286326i	0.0827217	−	0.996573i	$-0.473639\pi$
$673$	20.4081	−	7.42794i	0.786675	−	0.286326i	0.703953	+	0.710246i	$0.251417\pi$
$674$	10.7567	−	6.21041i	0.414334	−	0.239216i
$675$	−12.3126	−	22.0923i	−0.473913	−	0.850334i
$676$	0.276325	−	0.478609i	0.0106279	−	0.0184080i
$677$	−19.5580	−	16.4111i	−0.751674	−	0.630730i	0.184271	−	0.982876i	$-0.441008\pi$
$677$	−19.5580	−	16.4111i	−0.751674	−	0.630730i	−0.935945	+	0.352146i	$0.885452\pi$
$678$	−4.61821	+	15.1471i	−0.177361	+	0.581721i
$679$	13.4806	+	29.5413i	0.517338	+	1.13369i
$680$	1.96366	−	0.346245i	0.0753028	−	0.0132779i
$681$	−22.5169	−	11.4511i	−0.862849	−	0.438809i
$682$	7.54073	+	20.7180i	0.288749	+	0.793333i
$683$	−0.406875	+	0.234909i	−0.0155686	+	0.00898855i	−0.507764	−	0.861496i	$-0.669528\pi$
$683$	−0.406875	+	0.234909i	−0.0155686	+	0.00898855i	0.492195	+	0.870485i	$0.336195\pi$
$684$	13.3725	−	9.74710i	0.511309	−	0.372690i
$685$	−6.68014	+	3.85678i	−0.255235	+	0.147360i
$686$	8.23880	−	16.5868i	0.314559	−	0.633287i
$687$	−11.1071	+	4.72474i	−0.423760	+	0.180260i
$688$	1.51425	+	8.58775i	0.0577304	+	0.327405i
$689$	24.8032	−	20.8124i	0.944928	−	0.792889i
$690$	−3.12305	−	0.381027i	−0.118892	−	0.0145054i
$691$	−8.25105	−	22.6696i	−0.313885	−	0.862391i	−0.991863	−	0.127309i	$-0.959366\pi$
$691$	−8.25105	−	22.6696i	−0.313885	−	0.862391i	0.677978	−	0.735082i	$-0.262856\pi$
$692$	−4.70145	−	8.14316i	−0.178722	−	0.309556i
$693$	32.8660	−	12.3645i	1.24847	−	0.469687i
$694$	2.89199	−	5.00908i	0.109779	−	0.190142i
$695$	7.49196	+	1.32103i	0.284186	+	0.0501097i
$696$	0.0583709	+	1.09765i	0.00221254	+	0.0416062i
$697$	−19.3240	−	7.03336i	−0.731948	−	0.266407i
$698$	−27.6525	−	10.0647i	−1.04666	−	0.380954i
$699$	17.7397	+	5.40867i	0.670977	+	0.204575i
$700$	7.29944	+	10.6094i	0.275893	+	0.400997i
$701$			11.9842i			0.452636i	0.974053	+	0.226318i	$0.0726688\pi$
$701$			11.9842i			0.452636i	−0.974053	+	0.226318i	$0.927331\pi$
$702$	17.1299	+	6.53029i	0.646527	+	0.246470i
$703$	−41.1060	−	23.7326i	−1.55034	−	0.895090i
$704$	4.35684	+	0.768229i	0.164205	+	0.0289537i
$705$	2.39968	+	2.56938i	0.0903773	+	0.0967686i
$706$	15.6130	+	18.6069i	0.587604	+	0.700280i
$707$	−30.4424	−	21.6914i	−1.14490	−	0.815788i
$708$	0.928092	+	17.4525i	0.0348798	+	0.655904i
$709$	1.00841	−	5.71895i	0.0378715	−	0.214780i	−0.959999	−	0.280003i	$-0.909665\pi$
$709$	1.00841	−	5.71895i	0.0378715	−	0.214780i	0.997871	+	0.0652228i	$0.0207758\pi$
$710$	0.681373	+	1.18017i	0.0255715	+	0.0442911i
$711$	49.2284	+	12.1937i	1.84621	+	0.457299i
$712$	−0.611952	−	0.353311i	−0.0229339	−	0.0132409i
$713$	−4.31674	+	24.4815i	−0.161663	+	0.916839i
$714$	−24.8735	+	3.30677i	−0.930868	+	0.123753i
$715$	−5.34105	−	1.94398i	−0.199744	−	0.0727008i
$716$	−20.4940	+	3.61364i	−0.765896	+	0.135048i
$717$	−29.4111	−	22.1274i	−1.09838	−	0.826364i
$718$	−5.35880	−	4.49657i	−0.199989	−	0.167810i
$719$	12.1989	−	21.1291i	0.454943	−	0.787984i	−0.543742	−	0.839252i	$-0.682993\pi$
$719$	12.1989	−	21.1291i	0.454943	−	0.787984i	0.998685	+	0.0512684i	$0.0163264\pi$
$720$	0.0745310	−	1.08991i	0.00277761	−	0.0406185i
$721$	4.73640	−	17.1121i	0.176393	−	0.637290i
$722$	7.34412	−	8.75238i	0.273320	−	0.325730i
$723$	−7.66152	+	0.407426i	−0.284935	+	0.0151524i
$724$	−7.38194	+	20.2817i	−0.274348	+	0.753764i
$725$	3.04202	−	0.536391i	0.112978	−	0.0199211i
$726$	−14.2021	−	4.33009i	−0.527090	−	0.160705i
$727$	−9.60418	−	26.3873i	−0.356199	−	0.978650i	−0.980336	−	0.197335i	$-0.936771\pi$
$727$	−9.60418	−	26.3873i	−0.356199	−	0.978650i	0.624137	−	0.781315i	$-0.285451\pi$
$728$	−8.99618	−	2.49001i	−0.333421	−	0.0922860i
$729$	5.49181	−	26.4356i	0.203400	−	0.979096i
$730$	−0.798592	−	1.38320i	−0.0295572	−	0.0511946i
$731$	−8.29144	+	47.0231i	−0.306670	+	1.73921i
$732$	−2.16766	−	9.35638i	−0.0801191	−	0.345822i
$733$	−6.84703	+	18.8121i	−0.252901	+	0.694839i	0.746660	+	0.665206i	$0.231656\pi$
$733$	−6.84703	+	18.8121i	−0.252901	+	0.694839i	−0.999561	+	0.0296334i	$0.990566\pi$
$734$	−3.00832	−	17.0610i	−0.111039	−	0.629734i
$735$	2.34627	+	3.74007i	0.0865434	+	0.137955i
$736$	3.82119	+	3.20636i	0.140851	+	0.118188i
$737$		−	39.8248i		−	1.46696i
$738$	−6.28595	+	9.35027i	−0.231389	+	0.344188i
$739$	−42.9722			−1.58076			−0.790378	−	0.612619i	$-0.790116\pi$
$739$	−42.9722			−1.58076			−0.790378	+	0.612619i	$0.790116\pi$
$740$	−2.94458	+	1.07174i	−0.108245	+	0.0393980i
$741$	33.4587	+	4.08212i	1.22914	+	0.149960i
$742$	19.7745	+	14.0901i	0.725946	+	0.517264i
$743$	7.69035	−	21.1291i	0.282132	−	0.775150i	−0.714976	−	0.699149i	$-0.753562\pi$
$743$	7.69035	−	21.1291i	0.282132	−	0.775150i	0.997108	−	0.0760014i	$-0.0242154\pi$
$744$	−8.56828	−	1.04537i	−0.314128	−	0.0383251i
$745$	−3.95584	+	4.71438i	−0.144931	+	0.172722i
$746$			3.29721i			0.120719i
$747$	1.19285	−	1.23903i	0.0436439	−	0.0453338i
$748$	20.9789	+	12.1122i	0.767065	+	0.442865i
$749$	25.2813	+	12.0430i	0.923758	+	0.440042i
$750$	−6.21487	+	0.330496i	−0.226935	+	0.0120680i
$751$	8.36326	−	7.01761i	0.305180	−	0.256076i	−0.477317	−	0.878731i	$-0.658391\pi$
$751$	8.36326	−	7.01761i	0.305180	−	0.256076i	0.782496	+	0.622655i	$0.213946\pi$
$752$	−0.967922	−	5.48936i	−0.0352965	−	0.200176i
$753$	11.3564	−	37.2476i	0.413852	−	1.35738i
$754$	−1.43920	+	1.71517i	−0.0524125	+	0.0624628i
$755$	−0.114337			−0.00416115
$756$	−1.51796	+	13.6637i	−0.0552076	+	0.496943i
$757$	−41.5719			−1.51096			−0.755478	−	0.655174i	$-0.772595\pi$
$757$	−41.5719			−1.51096			−0.755478	+	0.655174i	$0.772595\pi$
$758$	−23.1543	+	27.5942i	−0.841001	+	1.00227i
$759$	−26.0895	−	27.9345i	−0.946990	−	1.01396i
$760$	−0.348795	−	1.97812i	−0.0126521	−	0.0717538i
$761$	−4.14738	+	3.48006i	−0.150342	+	0.126152i	−0.714856	−	0.699271i	$-0.753508\pi$
$761$	−4.14738	+	3.48006i	−0.150342	+	0.126152i	0.564514	+	0.825423i	$0.309064\pi$
$762$	6.47953	+	9.96084i	0.234729	+	0.360843i
$763$	−11.0039	+	0.871571i	−0.398369	+	0.0315530i
$764$	−7.80842	−	4.50819i	−0.282499	−	0.163101i
$765$	2.42464	−	5.46842i	0.0876629	−	0.197711i
$766$			12.6859i			0.458361i
$767$	−22.8831	+	27.2710i	−0.826262	+	0.984700i
$768$	−1.04131	+	1.38408i	−0.0375751	+	0.0499436i
$769$	−8.02830	+	22.0576i	−0.289508	+	0.795416i	0.706628	+	0.707586i	$0.250216\pi$
$769$	−8.02830	+	22.0576i	−0.289508	+	0.795416i	−0.996135	+	0.0878306i	$0.972007\pi$
$770$	0.406406	−	4.24295i	0.0146459	−	0.152905i
$771$	4.55151	+	10.6998i	0.163919	+	0.385345i
$772$	−0.376550	+	0.137053i	−0.0135523	+	0.00493265i
$773$	51.9690			1.86920			0.934598	−	0.355706i	$-0.115759\pi$
$773$	51.9690			1.86920			0.934598	+	0.355706i	$0.115759\pi$
$774$	23.9153	+	10.6038i	0.859618	+	0.381145i
$775$			24.2570i			0.871339i
$776$	9.40178	+	7.88903i	0.337504	+	0.283200i
$777$	37.5934	−	11.9056i	1.34865	−	0.427111i
$778$	−1.32448	−	7.51153i	−0.0474851	−	0.269301i
$779$	−7.08515	+	19.4663i	−0.253852	+	0.697453i
$780$	1.62629	−	1.51888i	0.0582304	−	0.0543844i
$781$	−2.87490	+	16.3044i	−0.102872	+	0.583417i
$782$	13.6567	+	23.6541i	0.488363	+	0.845870i
$783$	2.83049	+	1.69186i	0.101154	+	0.0604623i
$784$	0.115160	−	6.99905i	0.00411285	−	0.249966i
$785$	1.20800	+	3.31894i	0.0431153	+	0.118458i
$786$	−3.02745	+	2.82750i	−0.107986	+	0.100854i
$787$	42.3137	−	7.46104i	1.50832	−	0.265957i	0.642489	−	0.766295i	$-0.277902\pi$
$787$	42.3137	−	7.46104i	1.50832	−	0.265957i	0.865830	+	0.500338i	$0.166791\pi$
$788$	−6.63815	+	18.2382i	−0.236474	+	0.649708i
$789$	−9.14995	−	14.0660i	−0.325747	−	0.500763i
$790$	3.95707	−	4.71585i	0.140786	−	0.167783i
$791$	−16.9630	−	17.2444i	−0.603135	−	0.613140i
$792$	9.20493	−	9.56135i	0.327083	−	0.339748i
$793$	9.78157	−	16.9422i	0.347354	−	0.601635i
$794$	1.84412	+	1.54740i	0.0654455	+	0.0549153i
$795$	−5.32651	+	2.26580i	−0.188912	+	0.0803597i
$796$	−6.61340	+	1.16612i	−0.234406	+	0.0413321i
$797$	−13.6311	−	4.96131i	−0.482838	−	0.175739i	0.0891211	−	0.996021i	$-0.471594\pi$
$797$	−13.6311	−	4.96131i	−0.482838	−	0.175739i	−0.571959	+	0.820282i	$0.693816\pi$
$798$	3.33113	+	25.0567i	0.117921	+	0.886997i
$799$	5.29996	−	30.0576i	0.187499	−	1.06336i
$800$	4.21529	+	2.43370i	0.149033	+	0.0860442i
$801$	−1.90389	+	0.932214i	−0.0672707	+	0.0329382i
$802$	7.03431	+	12.1838i	0.248390	+	0.430224i
$803$	3.36948	−	19.1093i	0.118906	−	0.674352i
$804$	13.8977	+	7.06781i	0.490136	+	0.249262i
$805$	2.78885	−	3.91396i	0.0982940	−	0.137949i
$806$	−11.3018	−	13.4690i	−0.398089	−	0.474424i
$807$	−2.23162	+	7.31942i	−0.0785568	+	0.257656i
$808$	−13.9136	−	2.45335i	−0.489479	−	0.0863084i
$809$	13.5722	+	7.83592i	0.477173	+	0.275496i	0.719238	−	0.694764i	$-0.244491\pi$
$809$	13.5722	+	7.83592i	0.477173	+	0.275496i	−0.242064	+	0.970260i	$0.577825\pi$
$810$	−2.58879	−	2.00980i	−0.0909607	−	0.0706172i
$811$		−	24.2880i		−	0.852865i	−0.904519	−	0.426433i	$-0.859770\pi$
$811$		−	24.2880i		−	0.852865i	0.904519	−	0.426433i	$-0.140230\pi$
$812$	−1.51585	−	0.722091i	−0.0531958	−	0.0253404i
$813$	−2.95844	+	2.76305i	−0.103757	+	0.0969043i
$814$	−35.7736	−	13.0205i	−1.25386	−	0.456369i
$815$	1.61616	+	0.588235i	0.0566117	+	0.0206050i
$816$	−7.95000	+	5.17148i	−0.278306	+	0.181038i
$817$	47.3694	+	8.35251i	1.65725	+	0.292217i
$818$	−4.69117	+	8.12534i	−0.164023	+	0.284096i
$819$	−21.2568	+	18.2300i	−0.742771	+	0.637008i
$820$	0.683804	+	1.18438i	0.0238795	+	0.0413604i
$821$	−2.27343	−	6.24620i	−0.0793433	−	0.217994i	0.893678	−	0.448709i	$-0.148116\pi$
$821$	−2.27343	−	6.24620i	−0.0793433	−	0.217994i	−0.973021	+	0.230715i	$0.925894\pi$
$822$	22.0574	−	29.3179i	0.769339	−	1.02258i
$823$	21.8046	−	18.2963i	0.760062	−	0.637768i	−0.178081	−	0.984016i	$-0.556989\pi$
$823$	21.8046	−	18.2963i	0.760062	−	0.637768i	0.938143	+	0.346248i	$0.112544\pi$
$824$	−1.16535	−	6.60901i	−0.0405968	−	0.230236i
$825$	−29.8042	−	22.4232i	−1.03765	−	0.780675i
$826$	−24.1018	−	11.4812i	−0.838610	−	0.399481i
$827$	−2.40667	+	1.38949i	−0.0836880	+	0.0483173i	−0.541260	−	0.840855i	$-0.682053\pi$
$827$	−2.40667	+	1.38949i	−0.0836880	+	0.0483173i	0.457572	+	0.889173i	$0.348719\pi$
$828$	14.3786	−	4.14691i	0.499690	−	0.144115i
$829$	9.26517	−	5.34925i	0.321793	−	0.185787i	−0.330399	−	0.943841i	$-0.607183\pi$
$829$	9.26517	−	5.34925i	0.321793	−	0.185787i	0.652191	+	0.758054i	$0.273850\pi$
$830$	−0.0714032	−	0.196179i	−0.00247844	−	0.00680946i
$831$	−43.1405	+	28.0629i	−1.49653	+	0.973493i
$832$	−3.47448	+	0.612645i	−0.120456	+	0.0212396i
$833$	13.7001	−	35.7971i	0.474681	−	1.24030i
$834$	−35.2508	+	8.16682i	−1.22064	+	0.282794i
$835$	−2.76066	−	2.31647i	−0.0955364	−	0.0801646i
$836$	12.2014	−	21.1334i	0.421993	−	0.730914i
$837$	−16.9438	+	19.5826i	−0.585665	+	0.676875i
$838$	1.44561	−	0.834622i	0.0499377	−	0.0288315i
$839$	12.9560	−	4.71560i	0.447291	−	0.162801i	−0.108547	−	0.994091i	$-0.534620\pi$
$839$	12.9560	−	4.71560i	0.447291	−	0.162801i	0.555838	+	0.831291i	$0.312398\pi$
$840$	1.40855	+	0.894833i	0.0485995	+	0.0308747i
$841$	21.9068	−	18.3820i	0.755406	−	0.633861i
$842$	5.25904	+	6.26748i	0.181239	+	0.215992i
$843$	34.6695	−	1.84366i	1.19408	−	0.0634991i
$844$	5.33693	−	1.94248i	0.183705	−	0.0668630i
$845$	−0.201248			−0.00692316
$846$	−15.2869	−	6.77802i	−0.525573	−	0.233033i
$847$	16.1686	−	15.9047i	0.555559	−	0.546493i
$848$	9.03790	+	1.59363i	0.310363	+	0.0547253i
$849$	16.3474	+	12.2989i	0.561040	+	0.422098i
$850$	17.1315	+	20.4165i	0.587606	+	0.700282i
$851$	−27.5911	−	32.8817i	−0.945809	−	1.12717i
$852$	−5.17956	−	3.89684i	−0.177449	−	0.133504i
$853$	27.4528	+	4.84068i	0.939967	+	0.165742i	0.622582	−	0.782555i	$-0.286084\pi$
$853$	27.4528	+	4.84068i	0.939967	+	0.165742i	0.317386	+	0.948297i	$0.397195\pi$
$854$	14.1390	+	3.91348i	0.483828	+	0.133917i
$855$	−5.50869	−	2.44249i	−0.188393	−	0.0835314i
$856$	10.5842			0.361760
$857$	−23.7724	+	8.65246i	−0.812051	+	0.295562i	−0.714471	−	0.699665i	$-0.753332\pi$
$857$	−23.7724	+	8.65246i	−0.812051	+	0.295562i	−0.0975801	+	0.995228i	$0.531110\pi$
$858$	26.9964	−	1.43562i	0.921642	−	0.0490113i
$859$	−19.5342	−	23.2799i	−0.666498	−	0.794301i	0.321805	−	0.946806i	$-0.395710\pi$
$859$	−19.5342	−	23.2799i	−0.666498	−	0.794301i	−0.988303	+	0.152505i	$0.951266\pi$
$860$	2.43256	−	2.04116i	0.0829497	−	0.0696031i
$861$	−7.96621	−	15.2556i	−0.271488	−	0.519911i
$862$	−3.64657	+	1.32724i	−0.124203	+	0.0452061i
$863$	35.3881	−	20.4314i	1.20463	−	0.695492i	0.243046	−	0.970015i	$-0.421853\pi$
$863$	35.3881	−	20.4314i	1.20463	−	0.695492i	0.961580	+	0.274523i	$0.0885200\pi$
$864$	1.70302	+	4.90915i	0.0579380	+	0.167013i
$865$	−1.71204	+	2.96534i	−0.0582111	+	0.100825i
$866$	−6.09065	−	5.11066i	−0.206969	−	0.173667i
$867$	−21.9056	+	5.07505i	−0.743954	+	0.172358i
$868$	7.65138	−	10.7382i	0.259705	−	0.364478i
$869$	73.6539	−	12.9872i	2.49854	−	0.440560i
$870$	0.335531	−	0.218263i	0.0113755	−	0.00739980i
$871$	10.8623	+	29.8440i	0.368056	+	1.01123i
$872$	−3.61316	+	2.08606i	−0.122357	+	0.0706430i
$873$	35.3775	−	10.2032i	1.19735	−	0.345326i
$874$	23.8283	−	13.7573i	0.806005	−	0.465347i
$875$	4.08848	−	8.58273i	0.138216	−	0.290149i
$876$	6.07062	+	4.56723i	0.205107	+	0.154313i
$877$	9.01903	+	51.1495i	0.304551	+	1.72719i	0.625611	+	0.780135i	$0.284850\pi$
$877$	9.01903	+	51.1495i	0.304551	+	1.72719i	−0.321060	+	0.947059i	$0.604039\pi$
$878$	11.6894	−	9.80858i	0.394498	−	0.331023i
$879$	−1.73971	+	2.31237i	−0.0586791	+	0.0779944i
$880$	−0.551003	−	1.51387i	−0.0185743	−	0.0510325i
$881$	5.54571	+	9.60546i	0.186840	+	0.323616i	0.944195	−	0.329387i	$-0.106842\pi$
$881$	5.54571	+	9.60546i	0.186840	+	0.323616i	−0.757355	+	0.653003i	$0.773509\pi$
$882$	−17.2327	−	12.0014i	−0.580255	−	0.404109i
$883$	−10.9736	+	19.0069i	−0.369292	+	0.639633i	−0.989455	−	0.144840i	$-0.953733\pi$
$883$	−10.9736	+	19.0069i	−0.369292	+	0.639633i	0.620163	+	0.784473i	$0.287067\pi$
$884$	−19.0249	−	3.35460i	−0.639876	−	0.112827i
$885$	5.33490	−	3.47036i	0.179331	−	0.116655i
$886$	−17.9501	−	6.53331i	−0.603046	−	0.219491i
$887$	19.5968	+	7.13264i	0.657995	+	0.239491i	0.649371	−	0.760472i	$-0.275032\pi$
$887$	19.5968	+	7.13264i	0.657995	+	0.239491i	0.00862470	+	0.999963i	$0.497255\pi$
$888$	10.8926	−	10.1732i	0.365533	−	0.341390i
$889$	−18.0947	+	1.43320i	−0.606877	+	0.0480680i
$890$			0.257317i			0.00862530i
$891$	−8.39797	−	38.9208i	−0.281342	−	1.30389i
$892$	−22.0841	−	12.7502i	−0.739429	−	0.426910i
$893$	−30.2789	−	5.33899i	−1.01324	−	0.178662i
$894$	8.53673	−	27.9993i	0.285511	−	0.936437i
$895$	4.87107	+	5.80512i	0.162822	+	0.194044i
$896$	−1.09838	−	2.40698i	−0.0366943	−	0.0804116i
$897$	27.1703	+	13.8177i	0.907190	+	0.461359i
$898$	5.78923	−	32.8323i	0.193189	−	1.09563i
$899$	−1.58134	−	2.73897i	−0.0527408	−	0.0913497i
$900$	13.1145	−	6.42134i	0.437150	−	0.214045i
$901$	43.5190	+	25.1257i	1.44983	+	0.837058i
$902$	−2.88516	+	16.3626i	−0.0960653	+	0.544813i
$903$	−31.6724	+	24.3670i	−1.05399	+	0.810883i
$904$	−8.59125	−	3.12696i	−0.285741	−	0.104001i
$905$	7.74021	−	1.36481i	0.257293	−	0.0453677i
$906$	0.500437	−	0.212877i	0.0166259	−	0.00707236i
$907$	1.18901	+	0.997699i	0.0394805	+	0.0331281i	0.662314	−	0.749226i	$-0.269574\pi$
$907$	1.18901	+	0.997699i	0.0394805	+	0.0331281i	−0.622834	+	0.782354i	$0.714019\pi$
$908$	7.29234	−	12.6307i	0.242005	−	0.419165i
$909$	−29.3961	+	30.5343i	−0.975006	+	1.01276i
$910$	0.852725	+	3.29045i	0.0282676	+	0.109077i
$911$	33.7086	−	40.1724i	1.11682	−	1.33097i	0.178995	−	0.983850i	$-0.442715\pi$
$911$	33.7086	−	40.1724i	1.11682	−	1.33097i	0.937821	−	0.347120i	$-0.112840\pi$
$912$	5.20956	+	8.00854i	0.172506	+	0.265189i
$913$	0.867473	−	2.38336i	0.0287092	−	0.0788778i
$914$	−9.20234	+	1.62262i	−0.304386	+	0.0536715i
$915$	−2.55599	+	2.38717i	−0.0844984	+	0.0789175i
$916$	−2.38345	−	6.54847i	−0.0787513	−	0.216367i
$917$	−1.58741	−	6.12541i	−0.0524209	−	0.202279i
$918$	−0.430983	+	28.4488i	−0.0142246	+	0.938950i
$919$	26.4651	+	45.8389i	0.873002	+	1.51208i	0.858876	+	0.512184i	$0.171164\pi$
$919$	26.4651	+	45.8389i	0.873002	+	1.51208i	0.0141269	+	0.999900i	$0.495503\pi$
$920$	0.315426	−	1.78887i	0.0103993	−	0.0589772i
$921$	−35.1858	+	32.8619i	−1.15941	+	1.08284i
$922$	5.58720	−	15.3507i	0.184005	−	0.505548i
$923$	−2.29267	−	13.0024i	−0.0754641	−	0.427978i
$924$	6.12091	+	19.3275i	0.201363	+	0.635827i
$925$	−32.0853	−	26.9228i	−1.05496	−	0.885216i
$926$		−	20.4929i		−	0.673438i
$927$	−18.4049	−	8.16051i	−0.604495	−	0.268026i
$928$	−0.634622			−0.0208325
$929$	34.2936	−	12.4818i	1.12514	−	0.409516i	0.288611	−	0.957446i	$-0.406806\pi$
$929$	34.2936	−	12.4818i	1.12514	−	0.409516i	0.836524	+	0.547931i	$0.184584\pi$
$930$	1.23040	+	2.89247i	0.0403465	+	0.0948477i
$931$	−36.0608	−	13.8010i	−1.18184	−	0.452310i
$932$	−3.66217	+	10.0617i	−0.119959	+	0.329583i
$933$	−6.18339	+	8.21876i	−0.202435	+	0.269070i
$934$	1.19144	−	1.41991i	0.0389852	−	0.0464608i
$935$		−	8.82133i		−	0.288488i
$936$	−4.29014	+	9.67579i	−0.140227	+	0.316263i
$937$	−43.3970	−	25.0553i	−1.41772	−	0.818519i	−0.421619	−	0.906773i	$-0.638538\pi$
$937$	−43.3970	−	25.0553i	−1.41772	−	0.818519i	−0.996098	+	0.0882536i	$0.971871\pi$
$938$	−19.6212	+	13.4998i	−0.640656	+	0.440783i
$939$	12.4250	+	19.1006i	0.405473	+	0.623325i
$940$	−1.55491	+	1.30473i	−0.0507157	+	0.0425555i
$941$	−3.09167	−	17.5337i	−0.100786	−	0.571583i	−0.992820	−	0.119616i	$-0.961834\pi$
$941$	−3.09167	−	17.5337i	−0.100786	−	0.571583i	0.892035	−	0.451967i	$-0.149278\pi$
$942$	−11.4666	−	12.2775i	−0.373601	−	0.400021i
$943$	−12.0418	+	14.3509i	−0.392135	+	0.467328i
$944$	−10.0904			−0.328415
$945$	4.58542	−	2.00911i	0.149164	−	0.0653564i
$946$	38.5788			1.25430
$947$	18.8912	−	22.5136i	0.613881	−	0.731595i	−0.366124	−	0.930566i	$-0.619315\pi$
$947$	18.8912	−	22.5136i	0.613881	−	0.731595i	0.980005	+	0.198971i	$0.0637599\pi$
$948$	−8.53940	+	28.0081i	−0.277347	+	0.909660i
$949$	2.68709	+	15.2392i	0.0872265	+	0.494686i
$950$	20.5669	−	17.2577i	0.667278	−	0.559913i
$951$	−36.3209	+	1.93148i	−1.17779	+	0.0626326i
$952$	−1.14387	−	14.4418i	−0.0370731	−	0.468063i
$953$	−31.2086	−	18.0183i	−1.01095	−	0.583670i	−0.0994780	−	0.995040i	$-0.531717\pi$
$953$	−31.2086	−	18.0183i	−1.01095	−	0.583670i	−0.911469	+	0.411369i	$0.865051\pi$
$954$	19.0949	−	19.8342i	0.618219	−	0.642156i
$955$			3.28333i			0.106246i
$956$	13.6590	−	16.2781i	0.441763	−	0.526473i
$957$	4.82711	+	0.588930i	0.156038	+	0.0190374i
$958$	11.6459	−	31.9967i	0.376260	−	1.03377i
$959$	23.2662	+	50.9854i	0.751305	+	1.64640i
$960$	0.626086	+	0.0763855i	0.0202069	+	0.00246533i
$961$	−5.79220	+	2.10819i	−0.186845	+	0.0680060i
$962$	30.3595			0.978829
$963$	17.7154	−	26.3514i	0.570869	−	0.849160i
$964$		−	4.42963i		−	0.142669i
$965$	0.111782	+	0.0937965i	0.00359840	+	0.00301942i
$966$	−4.91924	+	22.3233i	−0.158274	+	0.718239i
$967$	9.90852	+	56.1940i	0.318636	+	1.80708i	0.551064	+	0.834463i	$0.314222\pi$
$967$	9.90852	+	56.1940i	0.318636	+	1.80708i	−0.232427	+	0.972614i	$0.574667\pi$
$968$	2.93188	−	8.05527i	0.0942341	−	0.258906i
$969$	11.8071	+	50.9633i	0.379297	+	1.63718i
$970$	0.776084	−	4.40139i	0.0249186	−	0.141320i
$971$	23.0207	+	39.8730i	0.738770	+	1.27959i	0.953050	+	0.302814i	$0.0979261\pi$
$971$	23.0207	+	39.8730i	0.738770	+	1.27959i	−0.214280	+	0.976772i	$0.568741\pi$
$972$	15.0727	+	3.97671i	0.483456	+	0.127553i
$973$	14.7443	−	53.2698i	0.472681	−	1.70775i
$974$	0.749008	+	2.05788i	0.0239998	+	0.0659389i
$975$	28.4508	+	8.67437i	0.911153	+	0.277802i
$976$	5.46074	−	0.962876i	0.174794	−	0.0308209i
$977$	−10.3773	+	28.5113i	−0.331998	+	0.912157i	0.655594	+	0.755114i	$0.272418\pi$
$977$	−10.3773	+	28.5113i	−0.331998	+	0.912157i	−0.987592	+	0.157043i	$0.949804\pi$
$978$	−8.16892	+	0.434409i	−0.261213	+	0.0138909i
$979$	−2.00944	+	2.39476i	−0.0642219	+	0.0765367i
$980$	−2.22822	+	1.23804i	−0.0711779	+	0.0395477i
$981$	−0.853910	+	12.4872i	−0.0272632	+	0.398686i
$982$	16.9273	−	29.3190i	0.540173	−	0.935608i
$983$	−35.7835	−	30.0259i	−1.14132	−	0.957679i	−0.141836	−	0.989890i	$-0.545301\pi$
$983$	−35.7835	−	30.0259i	−1.14132	−	0.957679i	−0.999481	+	0.0322112i	$0.989745\pi$
$984$	−5.19804	−	3.91075i	−0.165708	−	0.124670i
$985$	6.96031	−	1.22729i	0.221774	−	0.0391047i
$986$	−3.26537	−	1.18850i	−0.103991	−	0.0378495i
$987$	20.2453	−	15.5756i	0.644414	−	0.495776i
$988$	−3.37930	+	19.1650i	−0.107510	+	0.609719i
$989$	37.6707	+	21.7492i	1.19786	+	0.691584i
$990$	−4.69130	−	1.16202i	−0.149099	−	0.0369314i
$991$	−4.13692	−	7.16535i	−0.131414	−	0.227615i	0.792808	−	0.609471i	$-0.208618\pi$
$991$	−4.13692	−	7.16535i	−0.131414	−	0.227615i	−0.924222	+	0.381856i	$0.875285\pi$
$992$	0.865390	−	4.90787i	0.0274761	−	0.155825i
$993$	−0.0101395	−	0.190671i	−0.000321768	−	0.00605075i
$994$	9.00752	−	4.11041i	0.285701	−	0.130374i
$995$	1.57189	+	1.87331i	0.0498324	+	0.0593879i
$996$	0.677775	+	0.725706i	0.0214761	+	0.0229949i
$997$	4.80391	+	0.847059i	0.152141	+	0.0268266i	0.249200	−	0.968452i	$-0.419832\pi$
$997$	4.80391	+	0.847059i	0.152141	+	0.0268266i	−0.0970587	+	0.995279i	$0.530943\pi$
$998$	−7.41752	−	4.28251i	−0.234797	−	0.135560i
$999$	−7.09650	−	44.1467i	−0.224523	−	1.39674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.101.2	yes	144
7.5	odd	6		378.2.ba.a.47.18	✓	144
27.23	odd	18		378.2.ba.a.185.18	yes	144
189.131	even	18	inner	378.2.bf.a.131.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.18	✓	144	7.5	odd	6
378.2.ba.a.185.18	yes	144	27.23	odd	18
378.2.bf.a.101.2	yes	144	1.1	even	1	trivial
378.2.bf.a.131.2	yes	144	189.131	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-1.68736 + 0.390923i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-0.278956 + 0.234072i) q^{5} +(0.785149 - 1.54387i) q^{6} +(1.49966 + 2.17968i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.69436 - 1.31926i) q^{9} -0.364151i q^{10} +(2.84373 - 3.38902i) q^{11} +(0.677991 + 1.59384i) q^{12} +(-1.20667 + 3.31531i) q^{13} +(-2.63370 - 0.252266i) q^{14} +(0.379195 - 0.504014i) q^{15} +(-0.939693 + 0.342020i) q^{16} -5.47560 q^{17} +(-0.721292 + 2.91200i) q^{18} +5.51592i q^{19} +(0.278956 + 0.234072i) q^{20} +(-3.38255 - 3.09165i) q^{21} +(0.768229 + 4.35684i) q^{22} +(-1.70607 + 4.68738i) q^{23} +(-1.65676 - 0.505130i) q^{24} +(-0.845214 + 4.79345i) q^{25} +(-1.76404 - 3.05541i) q^{26} +(-4.03062 + 3.27934i) q^{27} +(1.88615 - 1.85538i) q^{28} +(-0.217053 - 0.596349i) q^{29} +(0.142355 + 0.614454i) q^{30} +(4.90787 - 0.865390i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-3.47354 + 6.83017i) q^{33} +(3.51965 - 4.19455i) q^{34} +(-0.928543 - 0.257007i) q^{35} +(-1.76708 - 2.42434i) q^{36} +(-4.30255 + 7.45224i) q^{37} +(-4.22544 - 3.54557i) q^{38} +(0.740061 - 6.06584i) q^{39} +(-0.358619 + 0.0632342i) q^{40} +(3.52911 + 1.28449i) q^{41} +(4.54261 - 0.603911i) q^{42} +(1.51425 - 8.58775i) q^{43} +(-3.83134 - 2.21203i) q^{44} +(-0.442807 + 0.998688i) q^{45} +(-2.49410 - 4.31992i) q^{46} +(-0.967922 + 5.48936i) q^{47} +(1.45189 - 0.944458i) q^{48} +(-2.50203 + 6.53757i) q^{49} +(-3.12870 - 3.72864i) q^{50} +(9.23930 - 2.14054i) q^{51} +(3.47448 + 0.612645i) q^{52} +(-7.94780 - 4.58866i) q^{53} +(0.0787098 - 5.19556i) q^{54} +1.61103i q^{55} +(0.208904 + 2.63749i) q^{56} +(-2.15630 - 9.30734i) q^{57} +(0.596349 + 0.217053i) q^{58} +(9.48190 + 3.45113i) q^{59} +(-0.562203 - 0.285913i) q^{60} +(-5.46074 - 0.962876i) q^{61} +(-2.49179 + 4.31591i) q^{62} +(6.91618 + 3.89441i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.439412 - 1.20728i) q^{65} +(-2.99947 - 7.05123i) q^{66} +(6.89583 - 5.78629i) q^{67} +(0.950828 + 5.39241i) q^{68} +(1.04634 - 8.57624i) q^{69} +(0.793735 - 0.546104i) q^{70} +(-3.24088 + 1.87112i) q^{71} +(2.99301 + 0.204670i) q^{72} +(3.79842 - 2.19302i) q^{73} +(-2.94312 - 8.08615i) q^{74} +(-0.447691 - 8.41868i) q^{75} +(5.43213 - 0.957830i) q^{76} +(11.6516 + 1.11604i) q^{77} +(4.17100 + 4.46596i) q^{78} +(12.9503 + 10.8666i) q^{79} +(0.182076 - 0.315364i) q^{80} +(5.51913 - 7.10909i) q^{81} +(-3.25244 + 1.87780i) q^{82} +(0.538728 - 0.196081i) q^{83} +(-2.45731 + 3.86803i) q^{84} +(1.52745 - 1.28169i) q^{85} +(5.60526 + 6.68009i) q^{86} +(0.599374 + 0.921404i) q^{87} +(4.15725 - 1.51312i) q^{88} -0.706622 q^{89} +(-0.480409 - 0.981154i) q^{90} +(-9.03593 + 2.34168i) q^{91} +(4.91243 + 0.866193i) q^{92} +(-7.94303 + 3.37882i) q^{93} +(-3.58293 - 4.26997i) q^{94} +(-1.29112 - 1.53870i) q^{95} +(-0.209763 + 1.71930i) q^{96} +(12.0867 + 2.13121i) q^{97} +(-3.39979 - 6.11894i) q^{98} +(3.19103 - 12.8828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) \) 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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