LMFDB - Embedded newform 504.2.bf.b.115.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(115,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 1]))

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

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

chi := DirichletCharacter("504.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bf (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.3
Character	$\chi$	$=$	504.115
Dual form			504.2.bf.b.355.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41229 - 0.0736946i) q^{2} +(-1.11864 - 1.32236i) q^{3} +(1.98914 + 0.208157i) q^{4} +(1.36131 - 2.35786i) q^{5} +(1.48240 + 1.95000i) q^{6} +(-1.25248 + 2.33051i) q^{7} +(-2.79390 - 0.440567i) q^{8} +(-0.497287 + 2.95850i) q^{9} +O(q^{10})$	\(q+(-1.41229 - 0.0736946i) q^{2} +(-1.11864 - 1.32236i) q^{3} +(1.98914 + 0.208157i) q^{4} +(1.36131 - 2.35786i) q^{5} +(1.48240 + 1.95000i) q^{6} +(-1.25248 + 2.33051i) q^{7} +(-2.79390 - 0.440567i) q^{8} +(-0.497287 + 2.95850i) q^{9} +(-2.09633 + 3.22967i) q^{10} +(-1.83065 - 3.17078i) q^{11} +(-1.94987 - 2.86322i) q^{12} +(-2.24011 - 3.87999i) q^{13} +(1.94061 - 3.19907i) q^{14} +(-4.64077 + 0.837451i) q^{15} +(3.91334 + 0.828105i) q^{16} +(1.42952 + 0.825334i) q^{17} +(0.920340 - 4.14161i) q^{18} +(-2.85950 + 1.65093i) q^{19} +(3.19864 - 4.40675i) q^{20} +(4.48286 - 0.950778i) q^{21} +(2.35174 + 4.61297i) q^{22} +(-2.28088 - 1.31686i) q^{23} +(2.54278 + 4.18739i) q^{24} +(-1.20634 - 2.08944i) q^{25} +(2.87776 + 5.64476i) q^{26} +(4.46849 - 2.65190i) q^{27} +(-2.97646 + 4.37500i) q^{28} +(-0.624720 - 0.360683i) q^{29} +(6.61583 - 0.840725i) q^{30} -2.74850 q^{31} +(-5.46575 - 1.45792i) q^{32} +(-2.14508 + 5.96774i) q^{33} +(-1.95808 - 1.27096i) q^{34} +(3.79002 + 6.12573i) q^{35} +(-1.60500 + 5.78135i) q^{36} +(-9.89755 + 5.71435i) q^{37} +(4.16011 - 2.12087i) q^{38} +(-2.62487 + 7.30256i) q^{39} +(-4.84217 + 5.98789i) q^{40} +(8.82140 - 5.09304i) q^{41} +(-6.40117 + 1.01241i) q^{42} +(-1.78801 + 3.09693i) q^{43} +(-2.98140 - 6.68818i) q^{44} +(6.29876 + 5.19997i) q^{45} +(3.12422 + 2.02789i) q^{46} -13.2778 q^{47} +(-3.28257 - 6.10121i) q^{48} +(-3.86260 - 5.83784i) q^{49} +(1.54972 + 3.03980i) q^{50} +(-0.507728 - 2.81360i) q^{51} +(-3.64825 - 8.18413i) q^{52} +(-7.03996 - 4.06452i) q^{53} +(-6.50625 + 3.41595i) q^{54} -9.96834 q^{55} +(4.52605 - 5.95943i) q^{56} +(5.38188 + 1.93450i) q^{57} +(0.855707 + 0.555428i) q^{58} +6.06180i q^{59} +(-9.40545 + 0.699798i) q^{60} +6.50731 q^{61} +(3.88169 + 0.202550i) q^{62} +(-6.27198 - 4.86439i) q^{63} +(7.61180 + 2.46180i) q^{64} -12.1980 q^{65} +(3.46927 - 8.27012i) q^{66} -3.43983 q^{67} +(2.67171 + 1.93927i) q^{68} +(0.810108 + 4.48925i) q^{69} +(-4.90118 - 8.93062i) q^{70} +4.80001i q^{71} +(2.69279 - 8.04667i) q^{72} +(5.76472 + 3.32826i) q^{73} +(14.3993 - 7.34094i) q^{74} +(-1.41354 + 3.93255i) q^{75} +(-6.03159 + 2.68871i) q^{76} +(9.68239 - 0.295027i) q^{77} +(4.24525 - 10.1199i) q^{78} +4.72138i q^{79} +(7.27983 - 8.09981i) q^{80} +(-8.50541 - 2.94245i) q^{81} +(-12.8337 + 6.54277i) q^{82} +(9.64913 + 5.57093i) q^{83} +(9.11494 - 0.958091i) q^{84} +(3.89204 - 2.24707i) q^{85} +(2.75342 - 4.24200i) q^{86} +(0.221884 + 1.22958i) q^{87} +(3.71772 + 9.66537i) q^{88} +(-7.88432 + 4.55201i) q^{89} +(-8.51248 - 7.80806i) q^{90} +(11.8481 - 0.361016i) q^{91} +(-4.26287 - 3.09421i) q^{92} +(3.07459 + 3.63452i) q^{93} +(18.7521 + 0.978502i) q^{94} +8.98973i q^{95} +(4.18632 + 8.85860i) q^{96} +(6.94214 + 4.00805i) q^{97} +(5.02490 + 8.52938i) q^{98} +(10.2911 - 3.83918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	$ 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.41229	−	0.0736946i	−0.998641	−	0.0521100i
$2$	−1.41229	−	0.0736946i	−0.998641	−	0.0521100i
$3$	−1.11864	−	1.32236i	−0.645847	−	0.763467i
$3$	−1.11864	−	1.32236i	−0.645847	−	0.763467i
$4$	1.98914	+	0.208157i	0.994569	+	0.104078i
$5$	1.36131	−	2.35786i	0.608797	−	1.05447i	−0.382642	−	0.923897i	$-0.624986\pi$
$5$	1.36131	−	2.35786i	0.608797	−	1.05447i	0.991439	−	0.130571i	$-0.0416810\pi$
$6$	1.48240	+	1.95000i	0.605186	+	0.796084i
$7$	−1.25248	+	2.33051i	−0.473392	+	0.880852i
$7$	−1.25248	+	2.33051i	−0.473392	+	0.880852i
$8$	−2.79390	−	0.440567i	−0.987794	−	0.155764i
$9$	−0.497287	+	2.95850i	−0.165762	+	0.986166i
$10$	−2.09633	+	3.22967i	−0.662918	+	1.02131i
$11$	−1.83065	−	3.17078i	−0.551962	−	0.956026i	−0.998133	−	0.0610781i	$-0.980546\pi$
$11$	−1.83065	−	3.17078i	−0.551962	−	0.956026i	0.446171	−	0.894948i	$-0.352787\pi$
$12$	−1.94987	−	2.86322i	−0.562879	−	0.826539i
$13$	−2.24011	−	3.87999i	−0.621296	−	1.07612i	−0.989245	−	0.146270i	$-0.953273\pi$
$13$	−2.24011	−	3.87999i	−0.621296	−	1.07612i	0.367949	−	0.929846i	$-0.380060\pi$
$14$	1.94061	−	3.19907i	0.518650	−	0.854987i
$15$	−4.64077	+	0.837451i	−1.19824	+	0.216229i
$16$	3.91334	+	0.828105i	0.978335	+	0.207026i
$17$	1.42952	+	0.825334i	0.346709	+	0.200173i	0.663235	−	0.748411i	$-0.269183\pi$
$17$	1.42952	+	0.825334i	0.346709	+	0.200173i	−0.316526	+	0.948584i	$0.602516\pi$
$18$	0.920340	−	4.14161i	0.216926	−	0.976188i
$19$	−2.85950	+	1.65093i	−0.656014	+	0.378750i	−0.790757	−	0.612131i	$-0.790313\pi$
$19$	−2.85950	+	1.65093i	−0.656014	+	0.378750i	0.134743	+	0.990881i	$0.456979\pi$
$20$	3.19864	−	4.40675i	0.715238	−	0.985378i
$21$	4.48286	−	0.950778i	0.978240	−	0.207477i
$22$	2.35174	+	4.61297i	0.501393	+	0.983489i
$23$	−2.28088	−	1.31686i	−0.475596	−	0.274585i	0.242984	−	0.970030i	$-0.421874\pi$
$23$	−2.28088	−	1.31686i	−0.475596	−	0.274585i	−0.718579	+	0.695445i	$0.755207\pi$
$24$	2.54278	+	4.18739i	0.519044	+	0.854748i
$25$	−1.20634	−	2.08944i	−0.241268	−	0.417888i
$26$	2.87776	+	5.64476i	0.564375	+	1.10703i
$27$	4.46849	−	2.65190i	0.859962	−	0.510358i
$28$	−2.97646	+	4.37500i	−0.562499	+	0.826798i
$29$	−0.624720	−	0.360683i	−0.116008	−	0.0669771i	0.440873	−	0.897569i	$-0.354669\pi$
$29$	−0.624720	−	0.360683i	−0.116008	−	0.0669771i	−0.556881	+	0.830592i	$0.688002\pi$
$30$	6.61583	−	0.840725i	1.20788	−	0.153495i
$31$	−2.74850			−0.493646			−0.246823	−	0.969061i	$-0.579387\pi$
$31$	−2.74850			−0.493646			−0.246823	+	0.969061i	$0.579387\pi$
$32$	−5.46575	−	1.45792i	−0.966218	−	0.257726i
$33$	−2.14508	+	5.96774i	−0.373411	+	1.03885i
$34$	−1.95808	−	1.27096i	−0.335807	−	0.217968i
$35$	3.79002	+	6.12573i	0.640630	+	1.03544i
$36$	−1.60500	+	5.78135i	−0.267501	+	0.963558i
$37$	−9.89755	+	5.71435i	−1.62715	+	0.939434i	−0.642208	+	0.766531i	$0.721981\pi$
$37$	−9.89755	+	5.71435i	−1.62715	+	0.939434i	−0.984939	+	0.172903i	$0.944685\pi$
$38$	4.16011	−	2.12087i	0.674859	−	0.344050i
$39$	−2.62487	+	7.30256i	−0.420316	+	1.16934i
$40$	−4.84217	+	5.98789i	−0.765614	+	0.946768i
$41$	8.82140	−	5.09304i	1.37767	−	0.795399i	0.385792	−	0.922586i	$-0.373928\pi$
$41$	8.82140	−	5.09304i	1.37767	−	0.795399i	0.991879	+	0.127187i	$0.0405948\pi$
$42$	−6.40117	+	1.01241i	−0.987722	+	0.156219i
$43$	−1.78801	+	3.09693i	−0.272669	+	0.472277i	−0.969544	−	0.244915i	$-0.921240\pi$
$43$	−1.78801	+	3.09693i	−0.272669	+	0.472277i	0.696875	+	0.717193i	$0.254573\pi$
$44$	−2.98140	−	6.68818i	−0.449462	−	1.00828i
$45$	6.29876	+	5.19997i	0.938964	+	0.775166i
$46$	3.12422	+	2.02789i	0.460641	+	0.298996i
$47$	−13.2778			−1.93676			−0.968382	−	0.249473i	$-0.919743\pi$
$47$	−13.2778			−1.93676			−0.968382	+	0.249473i	$0.919743\pi$
$48$	−3.28257	−	6.10121i	−0.473798	−	0.880634i
$49$	−3.86260	−	5.83784i	−0.551800	−	0.833977i
$50$	1.54972	+	3.03980i	0.219164	+	0.429893i
$51$	−0.507728	−	2.81360i	−0.0710961	−	0.393982i
$52$	−3.64825	−	8.18413i	−0.505921	−	1.13493i
$53$	−7.03996	−	4.06452i	−0.967012	−	0.558305i	−0.0686882	−	0.997638i	$-0.521881\pi$
$53$	−7.03996	−	4.06452i	−0.967012	−	0.558305i	−0.898324	+	0.439333i	$0.855215\pi$
$54$	−6.50625	+	3.41595i	−0.885388	+	0.464852i
$55$	−9.96834			−1.34413
$56$	4.52605	−	5.95943i	0.604819	−	0.796363i
$57$	5.38188	+	1.93450i	0.712848	+	0.256230i
$58$	0.855707	+	0.555428i	0.112360	+	0.0729312i
$59$			6.06180i			0.789179i	0.918857	+	0.394590i	$0.129113\pi$
$59$			6.06180i			0.789179i	−0.918857	+	0.394590i	$0.870887\pi$
$60$	−9.40545	+	0.699798i	−1.21424	+	0.0903436i
$61$	6.50731			0.833176			0.416588	−	0.909095i	$-0.363226\pi$
$61$	6.50731			0.833176			0.416588	+	0.909095i	$0.363226\pi$
$62$	3.88169	+	0.202550i	0.492975	+	0.0257239i
$63$	−6.27198	−	4.86439i	−0.790195	−	0.612855i
$64$	7.61180	+	2.46180i	0.951475	+	0.307725i
$65$	−12.1980			−1.51297
$66$	3.46927	−	8.27012i	0.427038	−	1.01798i
$67$	−3.43983			−0.420242			−0.210121	−	0.977675i	$-0.567386\pi$
$67$	−3.43983			−0.420242			−0.210121	+	0.977675i	$0.567386\pi$
$68$	2.67171	+	1.93927i	0.323993	+	0.235171i
$69$	0.810108	+	4.48925i	0.0975255	+	0.540442i
$70$	−4.90118	−	8.93062i	−0.585803	−	1.06741i
$71$			4.80001i			0.569656i	0.958579	+	0.284828i	$0.0919365\pi$
$71$			4.80001i			0.569656i	−0.958579	+	0.284828i	$0.908064\pi$
$72$	2.69279	−	8.04667i	0.317348	−	0.948309i
$73$	5.76472	+	3.32826i	0.674709	+	0.389544i	0.797859	−	0.602844i	$-0.205966\pi$
$73$	5.76472	+	3.32826i	0.674709	+	0.389544i	−0.123149	+	0.992388i	$0.539299\pi$
$74$	14.3993	−	7.34094i	1.67389	−	0.853367i
$75$	−1.41354	+	3.93255i	−0.163221	+	0.454092i
$76$	−6.03159	+	2.68871i	−0.691871	+	0.308416i
$77$	9.68239	−	0.295027i	1.10341	−	0.0336214i
$78$	4.24525	−	10.1199i	0.480680	−	1.14585i
$79$			4.72138i			0.531196i	0.964084	+	0.265598i	$0.0855694\pi$
$79$			4.72138i			0.531196i	−0.964084	+	0.265598i	$0.914431\pi$
$80$	7.27983	−	8.09981i	0.813910	−	0.905586i
$81$	−8.50541	−	2.94245i	−0.945046	−	0.326938i
$82$	−12.8337	+	6.54277i	−1.41725	+	0.722528i
$83$	9.64913	+	5.57093i	1.05913	+	0.611489i	0.925191	−	0.379501i	$-0.123904\pi$
$83$	9.64913	+	5.57093i	1.05913	+	0.611489i	0.133939	+	0.990990i	$0.457238\pi$
$84$	9.11494	−	0.958091i	0.994521	−	0.104536i
$85$	3.89204	−	2.24707i	0.422151	−	0.243729i
$86$	2.75342	−	4.24200i	0.296909	−	0.457427i
$87$	0.221884	+	1.22958i	0.0237885	+	0.131825i
$88$	3.71772	+	9.66537i	0.396310	+	1.03033i
$89$	−7.88432	+	4.55201i	−0.835736	+	0.482513i	−0.855813	−	0.517286i	$-0.826942\pi$
$89$	−7.88432	+	4.55201i	−0.835736	+	0.482513i	0.0200764	+	0.999798i	$0.493609\pi$
$90$	−8.51248	−	7.80806i	−0.897295	−	0.823042i
$91$	11.8481	−	0.361016i	1.24201	−	0.0378447i
$92$	−4.26287	−	3.09421i	−0.444434	−	0.322593i
$93$	3.07459	+	3.63452i	0.318820	+	0.376882i
$94$	18.7521	+	0.978502i	1.93413	+	0.100925i
$95$			8.98973i			0.922327i
$96$	4.18632	+	8.85860i	0.427264	+	0.904127i
$97$	6.94214	+	4.00805i	0.704868	+	0.406956i	0.809158	−	0.587591i	$-0.199924\pi$
$97$	6.94214	+	4.00805i	0.704868	+	0.406956i	−0.104290	+	0.994547i	$0.533257\pi$
$98$	5.02490	+	8.52938i	0.507592	+	0.861598i
$99$	10.2911	−	3.83918i	1.03429	−	0.385853i
$100$	−1.96464	−	4.40730i	−0.196464	−	0.440730i
$101$	−7.79101	−	13.4944i	−0.775234	−	1.34274i	−0.934663	−	0.355536i	$-0.884299\pi$
$101$	−7.79101	−	13.4944i	−0.775234	−	1.34274i	0.159429	−	0.987209i	$-0.449035\pi$
$102$	0.509713	+	4.01104i	0.0504691	+	0.397152i
$103$	7.16966	−	12.4182i	0.706448	−	1.22360i	−0.259719	−	0.965684i	$-0.583630\pi$
$103$	7.16966	−	12.4182i	0.706448	−	1.22360i	0.966166	−	0.257919i	$-0.0830368\pi$
$104$	4.54927	+	11.8272i	0.446092	+	1.15976i
$105$	3.86077	−	11.8643i	0.376772	−	1.15783i
$106$	9.64294	+	6.25910i	0.936605	+	0.607937i
$107$	−6.25120	−	10.8274i	−0.604326	−	1.04672i	−0.992158	−	0.124993i	$-0.960109\pi$
$107$	−6.25120	−	10.8274i	−0.604326	−	1.04672i	0.387832	−	0.921730i	$-0.373224\pi$
$108$	9.44046	−	4.34485i	0.908409	−	0.418083i
$109$	−2.47794	−	1.43064i	−0.237344	−	0.137031i	0.376611	−	0.926371i	$-0.377089\pi$
$109$	−2.47794	−	1.43064i	−0.237344	−	0.137031i	−0.613955	+	0.789341i	$0.710423\pi$
$110$	14.0782	+	0.734613i	1.34230	+	0.0700426i
$111$	18.6282	+	6.69584i	1.76811	+	0.635541i
$112$	−6.83128	+	8.08292i	−0.645496	+	0.763764i
$113$	−8.94611	−	15.4951i	−0.841579	−	1.45766i	−0.888559	−	0.458763i	$-0.848293\pi$
$113$	−8.94611	−	15.4951i	−0.841579	−	1.45766i	0.0469795	−	0.998896i	$-0.485040\pi$
$114$	−7.45823	−	3.12869i	−0.698527	−	0.293029i
$115$	−6.20997	+	3.58533i	−0.579083	+	0.334334i
$116$	−1.16758	−	0.847487i	−0.108407	−	0.0786872i
$117$	12.5929	−	4.69790i	1.16422	−	0.434321i
$118$	0.446722	−	8.56104i	0.0411241	−	0.788107i
$119$	−3.71389	+	2.29780i	−0.340452	+	0.210639i
$120$	13.3348	−	0.295188i	1.21730	−	0.0269469i
$121$	−1.20256	+	2.08289i	−0.109323	+	0.189354i
$122$	−9.19023	−	0.479554i	−0.832044	−	0.0434168i
$123$	−16.6028	−	5.96781i	−1.49703	−	0.538100i
$124$	−5.46715	−	0.572119i	−0.490965	−	0.0513778i
$125$	7.04430			0.630061
$126$	8.49939	+	7.33215i	0.757186	+	0.653200i
$127$		−	19.8572i		−	1.76204i	−0.473077	−	0.881021i	$-0.656857\pi$
$127$		−	19.8572i		−	1.76204i	0.473077	−	0.881021i	$-0.343143\pi$
$128$	−10.5687	−	4.03774i	−0.934147	−	0.356889i
$129$	6.09541	−	1.09995i	0.536671	−	0.0968451i
$130$	17.2271	+	0.898925i	1.51092	+	0.0788410i
$131$	−5.91713	−	3.41626i	−0.516982	−	0.298480i	0.218717	−	0.975788i	$-0.429813\pi$
$131$	−5.91713	−	3.41626i	−0.516982	−	0.298480i	−0.735699	+	0.677309i	$0.763146\pi$
$132$	−5.50909	+	11.4242i	−0.479505	+	0.994345i
$133$	−0.266063	−	8.73186i	−0.0230706	−	0.757148i
$134$	4.85805	+	0.253497i	0.419671	+	0.0218988i
$135$	−0.169802	−	14.1461i	−0.0146142	−	1.21751i
$136$	−3.63033	−	2.93570i	−0.311298	−	0.251734i
$137$	−0.285962	−	0.495300i	−0.0244313	−	0.0423163i	0.853551	−	0.521009i	$-0.174444\pi$
$137$	−0.285962	−	0.495300i	−0.0244313	−	0.0423163i	−0.877983	+	0.478693i	$0.841111\pi$
$138$	−0.813276	−	6.39983i	−0.0692306	−	0.544789i
$139$	7.64742	−	4.41524i	0.648646	−	0.374496i	−0.139291	−	0.990251i	$-0.544482\pi$
$139$	7.64742	−	4.41524i	0.648646	−	0.374496i	0.787937	+	0.615755i	$0.211149\pi$
$140$	6.26376	+	12.9738i	0.529384	+	1.09649i
$141$	14.8531	+	17.5580i	1.25085	+	1.47865i
$142$	0.353735	−	6.77901i	0.0296848	−	0.568882i
$143$	−8.20173	+	14.2058i	−0.685863	+	1.18795i
$144$	−4.39600	+	11.1658i	−0.366333	+	0.930484i
$145$	−1.70088	+	0.982003i	−0.141250	+	0.0815509i
$146$	−7.89619	−	5.12531i	−0.653494	−	0.424174i
$147$	−3.39888	+	11.6382i	−0.280335	+	0.959902i
$148$	−20.8771	+	9.30639i	−1.71608	+	0.764981i
$149$	7.40150	+	4.27326i	0.606355	+	0.350079i	0.771537	−	0.636184i	$-0.219488\pi$
$149$	7.40150	+	4.27326i	0.606355	+	0.350079i	−0.165183	+	0.986263i	$0.552821\pi$
$150$	2.28614	−	5.44974i	0.186662	−	0.444970i
$151$	17.8854	−	10.3261i	1.45549	−	0.840328i	0.456707	−	0.889617i	$-0.349029\pi$
$151$	17.8854	−	10.3261i	1.45549	−	0.840328i	0.998785	+	0.0492889i	$0.0156955\pi$
$152$	8.71651	−	3.35275i	0.707002	−	0.271944i
$153$	−3.15263	+	3.81880i	−0.254875	+	0.308732i
$154$	−13.6961	−	0.296877i	−1.10366	−	0.0239230i
$155$	−3.74157	+	6.48059i	−0.300530	+	0.520533i
$156$	−6.74131	+	13.9794i	−0.539737	+	1.11925i
$157$	5.64601			0.450601			0.225300	−	0.974289i	$-0.427664\pi$
$157$	5.64601			0.450601			0.225300	+	0.974289i	$0.427664\pi$
$158$	0.347940	−	6.66796i	0.0276806	−	0.530474i
$159$	2.50041	+	13.8561i	0.198295	+	1.09886i
$160$	−10.8782	+	10.9028i	−0.859995	+	0.861943i
$161$	5.92572	−	3.66627i	0.467012	−	0.288943i
$162$	11.7953	+	4.78240i	0.926725	+	0.375741i
$163$	−5.26155	−	9.11327i	−0.412117	−	0.713807i	0.583004	−	0.812469i	$-0.301877\pi$
$163$	−5.26155	−	9.11327i	−0.412117	−	0.713807i	−0.995121	+	0.0986622i	$0.968544\pi$
$164$	18.6071	−	8.29452i	1.45297	−	0.647693i
$165$	11.1510	+	13.1818i	0.868103	+	1.02620i
$166$	−13.2168	−	8.57887i	−1.02583	−	0.665849i
$167$	−3.56890	−	6.18152i	−0.276170	−	0.478340i	0.694260	−	0.719724i	$-0.255732\pi$
$167$	−3.56890	−	6.18152i	−0.276170	−	0.478340i	−0.970430	+	0.241384i	$0.922399\pi$
$168$	−12.9436	+	0.681383i	−0.998617	+	0.0525698i
$169$	−3.53621	+	6.12490i	−0.272017	+	0.471146i
$170$	−5.66230	+	2.88670i	−0.434279	+	0.221400i
$171$	−3.46229	−	9.28081i	−0.264768	−	0.709721i
$172$	−4.20125	+	5.78803i	−0.320342	+	0.441333i
$173$	−11.5111			−0.875174			−0.437587	−	0.899176i	$-0.644167\pi$
$173$	−11.5111			−0.875174			−0.437587	+	0.899176i	$0.644167\pi$
$174$	−0.222752	−	1.75288i	−0.0168868	−	0.132885i
$175$	6.38039	−	0.194413i	0.482312	−	0.0146962i
$176$	−4.53822	−	13.9243i	−0.342081	−	1.04958i
$177$	8.01590	−	6.78098i	0.602512	−	0.509689i
$178$	11.4704	−	5.84774i	0.859745	−	0.438307i
$179$	0.873703	−	1.51330i	0.0653036	−	0.113109i	−0.831525	−	0.555487i	$-0.812532\pi$
$179$	0.873703	−	1.51330i	0.0653036	−	0.113109i	0.896829	+	0.442378i	$0.145865\pi$
$180$	11.4467	+	11.6546i	0.853187	+	0.868682i
$181$	−8.25193			−0.613361			−0.306681	−	0.951812i	$-0.599218\pi$
$181$	−8.25193			−0.613361			−0.306681	+	0.951812i	$0.599218\pi$
$182$	−16.7595	−	0.363280i	−1.24230	−	0.0269281i
$183$	−7.27935	−	8.60503i	−0.538105	−	0.636102i
$184$	5.79238	+	4.68407i	0.427020	+	0.345314i
$185$			31.1161i			2.28770i
$186$	−4.07437	−	5.35958i	−0.298747	−	0.392984i
$187$		−	6.04359i		−	0.441951i
$188$	−26.4113	−	2.76386i	−1.92625	−	0.201575i
$189$	0.583605	+	13.7353i	0.0424510	+	0.999099i
$190$	0.662495	−	12.6961i	0.0480625	−	0.921074i
$191$		−	6.49809i		−	0.470185i	−0.971973	−	0.235093i	$-0.924461\pi$
$191$		−	6.49809i		−	0.470185i	0.971973	−	0.235093i	$-0.0755394\pi$
$192$	−5.25947	−	12.8194i	−0.379570	−	0.925163i
$193$	14.6191			1.05231			0.526154	−	0.850389i	$-0.323633\pi$
$193$	14.6191			1.05231			0.526154	+	0.850389i	$0.323633\pi$
$194$	−9.50896	−	6.17213i	−0.682704	−	0.443133i
$195$	13.6451	+	16.1301i	0.977149	+	1.15510i
$196$	−6.46806	−	12.4163i	−0.462004	−	0.886878i
$197$		−	1.42349i		−	0.101419i	−0.998713	−	0.0507096i	$-0.983852\pi$
$197$		−	1.42349i		−	0.101419i	0.998713	−	0.0507096i	$-0.0161483\pi$
$198$	−14.8170	+	4.66365i	−1.05300	+	0.331431i
$199$	3.74385	−	6.48454i	0.265395	−	0.459677i	−0.702272	−	0.711908i	$-0.747831\pi$
$199$	3.74385	−	6.48454i	0.265395	−	0.459677i	0.967667	+	0.252231i	$0.0811644\pi$
$200$	2.44986	+	6.36917i	0.173231	+	0.450369i
$201$	3.84793	+	4.54870i	0.271412	+	0.320841i
$202$	10.0087	+	19.6322i	0.704210	+	1.38132i
$203$	1.62302	−	1.00417i	0.113914	−	0.0704792i
$204$	−0.424272	−	5.70232i	−0.0297050	−	0.399242i
$205$		−	27.7328i		−	1.93695i
$206$	−11.0408	+	17.0098i	−0.769250	+	1.18513i
$207$	5.03019	−	6.09311i	0.349623	−	0.423500i
$208$	−5.55329	−	17.0388i	−0.385051	−	1.18143i
$209$	10.4695	+	6.04456i	0.724189	+	0.418111i
$210$	−6.32686	+	16.4713i	−0.436595	+	1.13663i
$211$	−0.530724	−	0.919241i	−0.0365366	−	0.0632832i	0.847179	−	0.531308i	$-0.178299\pi$
$211$	−0.530724	−	0.919241i	−0.0365366	−	0.0632832i	−0.883715	+	0.468025i	$0.844966\pi$
$212$	−13.1574	−	9.55031i	−0.903653	−	0.655918i
$213$	6.34735	−	5.36948i	0.434913	−	0.367911i
$214$	8.03059	+	15.7521i	0.548960	+	1.07679i
$215$	4.86809	+	8.43177i	0.332001	+	0.575042i
$216$	−13.6529	+	5.44049i	−0.928961	+	0.370178i
$217$	3.44244	−	6.40543i	0.233688	−	0.434829i
$218$	3.39415	+	2.20310i	0.229881	+	0.149212i
$219$	−2.04748	−	11.3462i	−0.138356	−	0.766704i
$220$	−19.8284	−	2.07498i	−1.33683	−	0.139895i
$221$		−	7.39536i		−	0.497466i
$222$	−25.8151	−	10.8293i	−1.73259	−	0.726814i
$223$	1.93834	−	3.35730i	0.129801	−	0.224821i	−0.793799	−	0.608181i	$-0.791900\pi$
$223$	1.93834	−	3.35730i	0.129801	−	0.224821i	0.923599	+	0.383359i	$0.125233\pi$
$224$	10.2434	−	10.9120i	0.684418	−	0.729089i
$225$	6.78150	−	2.52990i	0.452100	−	0.168660i
$226$	11.4926	+	22.5429i	0.764477	+	1.49953i
$227$	8.12512	−	4.69104i	0.539283	−	0.311355i	−0.205505	−	0.978656i	$-0.565884\pi$
$227$	8.12512	−	4.69104i	0.539283	−	0.311355i	0.744788	+	0.667301i	$0.232550\pi$
$228$	10.3026	+	4.96825i	0.682308	+	0.329031i
$229$	−14.0319	+	24.3039i	−0.927253	+	1.60605i	−0.139357	+	0.990242i	$0.544503\pi$
$229$	−14.0319	+	24.3039i	−0.927253	+	1.60605i	−0.787897	+	0.615808i	$0.788830\pi$
$230$	9.03451	−	4.60589i	0.595718	−	0.303703i
$231$	−11.2212	−	12.4736i	−0.738304	−	0.820703i
$232$	1.58650	+	1.28294i	0.104159	+	0.0842294i
$233$	12.4983	+	21.6476i	0.818789	+	1.41818i	0.906575	+	0.422045i	$0.138688\pi$
$233$	12.4983	+	21.6476i	0.818789	+	1.41818i	−0.0877855	+	0.996139i	$0.527979\pi$
$234$	−18.1311	+	5.70678i	−1.18527	+	0.373064i
$235$	−18.0752	+	31.3072i	−1.17910	+	2.04225i
$236$	−1.26180	+	12.0578i	−0.0821365	+	0.784893i
$237$	6.24337	−	5.28152i	0.405551	−	0.343072i
$238$	5.41444	−	2.97148i	0.350966	−	0.192612i
$239$	−5.98464	+	3.45523i	−0.387114	+	0.223501i	−0.680909	−	0.732368i	$-0.738415\pi$
$239$	−5.98464	+	3.45523i	−0.387114	+	0.223501i	0.293795	+	0.955869i	$0.405082\pi$
$240$	−18.8544	−	0.565812i	−1.21705	−	0.0365230i
$241$	−18.1483	+	10.4779i	−1.16903	+	0.674941i	−0.953452	−	0.301545i	$-0.902498\pi$
$241$	−18.1483	+	10.4779i	−1.16903	+	0.674941i	−0.215580	+	0.976486i	$0.569164\pi$
$242$	1.85186	−	2.85303i	0.119042	−	0.183399i
$243$	5.62352	+	14.5388i	0.360749	+	0.932663i
$244$	12.9439	+	1.35454i	0.828651	+	0.0867156i
$245$	−19.0230	+	1.16036i	−1.21534	+	0.0741324i
$246$	23.0082	+	9.65184i	1.46695	+	0.615379i
$247$	12.8112	+	7.39655i	0.815157	+	0.470631i
$248$	7.67905	+	1.21090i	0.487620	+	0.0768922i
$249$	−3.42712	−	18.9915i	−0.217185	−	1.20354i
$250$	−9.94861	−	0.519127i	−0.629205	−	0.0328325i
$251$		−	21.5246i		−	1.35862i	−0.733850	−	0.679311i	$-0.762279\pi$
$251$		−	21.5246i		−	1.35862i	0.733850	−	0.679311i	$-0.237721\pi$
$252$	−11.4633	−	10.9815i	−0.722119	−	0.691769i
$253$			9.64287i			0.606242i
$254$	−1.46337	+	28.0442i	−0.0918200	+	1.75965i
$255$	−7.32524	−	2.63303i	−0.458725	−	0.164887i
$256$	14.6285	+	6.48132i	0.914280	+	0.405082i
$257$	−5.87936	−	3.39445i	−0.366745	−	0.211740i	0.305291	−	0.952259i	$-0.401246\pi$
$257$	−5.87936	−	3.39445i	−0.366745	−	0.211740i	−0.672035	+	0.740519i	$0.734580\pi$
$258$	−8.68956	+	1.10425i	−0.540988	+	0.0687476i
$259$	−0.920922	−	30.2235i	−0.0572233	−	1.87800i
$260$	−24.2634	−	2.53909i	−1.50476	−	0.157468i
$261$	1.37774	−	1.66887i	0.0852802	−	0.103301i
$262$	8.10496	+	5.26081i	0.500726	+	0.325014i
$263$	−7.02212	+	4.05422i	−0.433003	+	0.249994i	−0.700625	−	0.713530i	$-0.747095\pi$
$263$	−7.02212	+	4.05422i	−0.433003	+	0.249994i	0.267622	+	0.963524i	$0.413762\pi$
$264$	8.62234	−	15.7283i	0.530668	−	0.968007i
$265$	−19.1672	+	11.0662i	−1.17743	+	0.679789i
$266$	−0.267732	+	12.3515i	−0.0164157	+	0.757322i
$267$	14.8391	+	5.33387i	0.908140	+	0.326427i
$268$	−6.84230	−	0.716024i	−0.417960	−	0.0437381i
$269$	9.86373	−	17.0845i	0.601402	−	1.04166i	−0.391207	−	0.920303i	$-0.627942\pi$
$269$	9.86373	−	17.0845i	0.601402	−	1.04166i	0.992609	−	0.121356i	$-0.0387243\pi$
$270$	−0.802686	+	19.9910i	−0.0488499	+	1.21661i
$271$	−2.07936	−	3.60155i	−0.126312	−	0.218779i	0.795933	−	0.605385i	$-0.206981\pi$
$271$	−2.07936	−	3.60155i	−0.126312	−	0.218779i	−0.922245	+	0.386606i	$0.873647\pi$
$272$	4.91074	+	4.41360i	0.297757	+	0.267614i
$273$	−13.7311	−	15.2636i	−0.831045	−	0.923795i
$274$	0.367360	+	0.720582i	0.0221930	+	0.0435319i
$275$	−4.41677	+	7.65007i	−0.266341	+	0.461317i
$276$	0.676950	+	9.09836i	0.0407476	+	0.547657i
$277$	−0.545452	+	0.314917i	−0.0327730	+	0.0189215i	−0.516297	−	0.856410i	$-0.672690\pi$
$277$	−0.545452	+	0.314917i	−0.0327730	+	0.0189215i	0.483524	+	0.875331i	$0.339357\pi$
$278$	−11.1258	+	5.67204i	−0.667280	+	0.340186i
$279$	1.36680	−	8.13144i	0.0818279	−	0.486816i
$280$	−7.89015	−	18.7844i	−0.471527	−	1.12259i
$281$	2.71853	−	4.70863i	0.162174	−	0.280893i	−0.773474	−	0.633828i	$-0.781483\pi$
$281$	2.71853	−	4.70863i	0.162174	−	0.280893i	0.935648	+	0.352934i	$0.114816\pi$
$282$	−19.6829	−	25.8917i	−1.17210	−	1.54183i
$283$			1.07423i			0.0638561i	0.999490	+	0.0319281i	$0.0101647\pi$
$283$			1.07423i			0.0638561i	−0.999490	+	0.0319281i	$0.989835\pi$
$284$	−0.999153	+	9.54787i	−0.0592888	+	0.566562i
$285$	11.8877	−	10.0563i	0.704166	−	0.595683i
$286$	12.6301	−	19.4583i	0.746835	−	1.15059i
$287$	0.820791	+	26.9373i	0.0484498	+	1.59006i
$288$	7.03130	−	15.4454i	0.414323	−	0.910130i
$289$	−7.13765	−	12.3628i	−0.419862	−	0.727222i
$290$	2.47451	−	1.26153i	0.145308	−	0.0740795i
$291$	−2.46567	−	13.6636i	−0.144540	−	0.800974i
$292$	10.7740	+	7.82034i	0.630502	+	0.457651i
$293$	−3.48752	−	6.04056i	−0.203743	−	0.352893i	0.745989	−	0.665959i	$-0.231977\pi$
$293$	−3.48752	−	6.04056i	−0.203743	−	0.352893i	−0.949731	+	0.313066i	$0.898644\pi$
$294$	5.65788	−	16.1861i	0.329974	−	0.943990i
$295$	14.2929	+	8.25200i	0.832164	+	0.480450i
$296$	30.1704	−	11.6048i	1.75362	−	0.674516i
$297$	−16.5888	−	9.31390i	−0.962582	−	0.540447i
$298$	−10.1382	−	6.58054i	−0.587288	−	0.381201i
$299$			11.7997i			0.682395i
$300$	−3.63031	+	7.52815i	−0.209596	+	0.434638i
$301$	−4.97799	−	8.04583i	−0.286927	−	0.463754i
$302$	−26.0204	+	13.2655i	−1.49730	+	0.763341i
$303$	−9.12918	+	25.3979i	−0.524458	+	1.45907i
$304$	−12.5573	+	4.09270i	−0.720213	+	0.234732i
$305$	8.85848	−	15.3433i	0.507235	−	0.878557i
$306$	4.73386	−	5.16093i	0.270617	−	0.295031i
$307$		−	9.84285i		−	0.561761i	−0.959743	−	0.280880i	$-0.909374\pi$
$307$		−	9.84285i		−	0.561761i	0.959743	−	0.280880i	$-0.0906264\pi$
$308$	19.3210	+	1.42861i	1.10092	+	0.0814024i
$309$	−24.4417	+	4.41063i	−1.39044	+	0.250912i
$310$	5.76177	−	8.87675i	0.327247	−	0.504165i
$311$	18.7600			1.06378			0.531890	−	0.846813i	$-0.321482\pi$
$311$	18.7600			1.06378			0.531890	+	0.846813i	$0.321482\pi$
$312$	10.5509	−	19.2462i	0.597328	−	1.08960i
$313$		−	4.60484i		−	0.260281i	−0.991496	−	0.130141i	$-0.958457\pi$
$313$		−	4.60484i		−	0.260281i	0.991496	−	0.130141i	$-0.0415429\pi$
$314$	−7.97382	−	0.416081i	−0.449988	−	0.0234808i
$315$	−20.0077	+	8.16651i	−1.12730	+	0.460131i
$316$	−0.982786	+	9.39147i	−0.0552860	+	0.528311i
$317$			25.1994i			1.41534i	0.706543	+	0.707670i	$0.250254\pi$
$317$			25.1994i			1.41534i	−0.706543	+	0.707670i	$0.749746\pi$
$318$	−2.51019	−	19.7531i	−0.140764	−	1.10770i
$319$			2.64113i			0.147875i
$320$	16.1666	−	14.5963i	0.903742	−	0.815957i
$321$	−7.32490	+	20.3783i	−0.408836	+	1.13741i
$322$	−8.63903	+	4.74116i	−0.481435	+	0.264214i
$323$	−5.45028			−0.303262
$324$	−16.3059	−	7.62339i	−0.905886	−	0.423522i
$325$	−5.40467	+	9.36117i	−0.299797	+	0.519264i
$326$	6.75925	+	13.2584i	0.374360	+	0.734312i
$327$	0.880101	+	4.87711i	0.0486697	+	0.269705i
$328$	−26.8900	+	10.3430i	−1.48475	+	0.571099i
$329$	16.6301	−	30.9441i	0.916849	−	1.70600i
$330$	−14.7770	−	19.4383i	−0.813449	−	1.07004i
$331$	23.3706			1.28456			0.642281	−	0.766469i	$-0.277988\pi$
$331$	23.3706			1.28456			0.642281	+	0.766469i	$0.277988\pi$
$332$	18.0338	+	13.0899i	0.989735	+	0.718401i
$333$	−11.9840	−	32.1235i	−0.656717	−	1.76036i
$334$	4.58478	+	8.99311i	0.250868	+	0.492081i
$335$	−4.68268	+	8.11064i	−0.255842	+	0.443132i
$336$	18.3303	−	0.00844044i	1.00000	−	0.000460464i
$337$	−10.4901	−	18.1693i	−0.571431	−	0.989747i	−0.996419	−	0.0845486i	$-0.973055\pi$
$337$	−10.4901	−	18.1693i	−0.571431	−	0.989747i	0.424988	−	0.905199i	$-0.360278\pi$
$338$	5.44554	−	8.38955i	0.296198	−	0.456332i
$339$	−10.4827	+	29.1635i	−0.569342	+	1.58394i
$340$	8.20956	−	3.65958i	0.445226	−	0.198469i
$341$	5.03155	+	8.71489i	0.272473	+	0.471938i
$342$	4.20581	+	13.3624i	0.227424	+	0.722554i
$343$	18.4430	−	1.69008i	0.995827	−	0.0912559i
$344$	6.35994	−	7.86478i	0.342905	−	0.424041i
$345$	11.6878	+	4.20114i	0.629251	+	0.226182i
$346$	16.2571	+	0.848308i	0.873985	+	0.0456053i
$347$	−11.5779			−0.621532			−0.310766	−	0.950486i	$-0.600586\pi$
$347$	−11.5779			−0.621532			−0.310766	+	0.950486i	$0.600586\pi$
$348$	0.185413	+	2.49199i	0.00993918	+	0.133585i
$349$	3.81336	−	6.60493i	0.204124	−	0.353554i	−0.745729	−	0.666249i	$-0.767899\pi$
$349$	3.81336	−	6.60493i	0.204124	−	0.353554i	0.949853	+	0.312696i	$0.101232\pi$
$350$	−9.02530	−	0.195632i	−0.482423	−	0.0104570i
$351$	−20.2993	−	11.3971i	−1.08350	−	0.608335i
$352$	5.38315	+	19.9996i	0.286923	+	1.06598i
$353$	−4.54999	+	2.62694i	−0.242172	+	0.139818i	−0.616174	−	0.787610i	$-0.711318\pi$
$353$	−4.54999	+	2.62694i	−0.242172	+	0.139818i	0.374003	+	0.927428i	$0.377985\pi$
$354$	−11.8205	+	8.98599i	−0.628253	+	0.477600i
$355$	11.3177	+	6.53430i	0.600684	+	0.346805i
$356$	−16.6305	+	7.41341i	−0.881417	+	0.392910i
$357$	7.19304	+	2.34070i	0.380696	+	0.123883i
$358$	−1.34545	+	2.07283i	−0.0711090	+	0.109553i
$359$	−7.64157	+	4.41186i	−0.403307	+	0.232849i	−0.687910	−	0.725796i	$-0.741472\pi$
$359$	−7.64157	+	4.41186i	−0.403307	+	0.232849i	0.284603	+	0.958645i	$0.408138\pi$
$360$	−15.3072	−	17.3032i	−0.806760	−	0.911961i
$361$	−4.04884	+	7.01281i	−0.213097	+	0.369095i
$362$	11.6541	+	0.608123i	0.612528	+	0.0319623i
$363$	4.09956	−	0.739788i	0.215171	−	0.0388288i
$364$	23.6426	+	1.74815i	1.23921	+	0.0916277i
$365$	15.6952	−	9.06161i	0.821522	−	0.474306i
$366$	9.64642	+	12.6893i	0.504226	+	0.663279i
$367$	14.4287	+	24.9912i	0.753172	+	1.30453i	0.946278	+	0.323354i	$0.104810\pi$
$367$	14.4287	+	24.9912i	0.753172	+	1.30453i	−0.193106	+	0.981178i	$0.561856\pi$
$368$	−7.83535	−	7.04215i	−0.408446	−	0.367097i
$369$	10.6810	+	28.6308i	0.556029	+	1.49046i
$370$	2.29309	−	43.9450i	0.119212	−	2.28459i
$371$	18.2898	−	11.3160i	0.949560	−	0.587497i
$372$	5.35923	+	7.86955i	0.277863	+	0.408017i
$373$	−4.29000	−	2.47683i	−0.222128	−	0.128245i	0.384807	−	0.922997i	$-0.374268\pi$
$373$	−4.29000	−	2.47683i	−0.222128	−	0.128245i	−0.606935	+	0.794751i	$0.707601\pi$
$374$	−0.445380	+	8.53531i	−0.0230301	+	0.441350i
$375$	−7.88004	−	9.31512i	−0.406923	−	0.481031i
$376$	37.0969	+	5.84975i	1.91312	+	0.301678i
$377$			3.23188i			0.166450i
$378$	0.187999	−	19.4413i	0.00966964	−	0.999953i
$379$	15.6563			0.804212			0.402106	−	0.915593i	$-0.368278\pi$
$379$	15.6563			0.804212			0.402106	+	0.915593i	$0.368278\pi$
$380$	−1.87127	+	17.8818i	−0.0959943	+	0.917318i
$381$	−26.2584	+	22.2131i	−1.34526	+	1.13801i
$382$	−0.478875	+	9.17720i	−0.0245014	+	0.469547i
$383$	−3.44301	+	5.96347i	−0.175930	+	0.304719i	−0.940483	−	0.339842i	$-0.889626\pi$
$383$	−3.44301	+	5.96347i	−0.175930	+	0.304719i	0.764553	+	0.644561i	$0.222960\pi$
$384$	6.48319	+	18.4924i	0.330844	+	0.943686i
$385$	12.4851	−	23.2314i	0.636301	−	1.18398i
$386$	−20.6465	−	1.07735i	−1.05088	−	0.0548358i
$387$	−8.27310	−	6.82989i	−0.420545	−	0.347183i
$388$	12.9746	+	9.41761i	0.658684	+	0.478107i
$389$	−14.0240	+	8.09678i	−0.711047	+	0.410523i	−0.811448	−	0.584424i	$-0.801320\pi$
$389$	−14.0240	+	8.09678i	−0.711047	+	0.410523i	0.100402	+	0.994947i	$0.467987\pi$
$390$	−18.0822	−	23.7860i	−0.915629	−	1.20445i
$391$	−2.17371	−	3.76497i	−0.109929	−	0.190403i
$392$	8.21977	+	18.0121i	0.415161	+	0.909748i
$393$	2.10161	+	11.6462i	0.106012	+	0.587471i
$394$	−0.104903	+	2.01038i	−0.00528495	+	0.101281i
$395$	11.1323	+	6.42726i	0.560129	+	0.323391i
$396$	21.2696	−	5.49451i	1.06884	−	0.276109i
$397$	8.08839	+	14.0095i	0.405944	+	0.703116i	0.994431	−	0.105391i	$-0.0336093\pi$
$397$	8.08839	+	14.0095i	0.405944	+	0.703116i	−0.588486	+	0.808507i	$0.700276\pi$
$398$	−5.76529	+	8.88217i	−0.288988	+	0.445223i
$399$	−11.2491	+	10.1196i	−0.563157	+	0.506616i
$400$	−2.99054	−	9.17567i	−0.149527	−	0.458784i
$401$	−9.01122	+	15.6079i	−0.449999	+	0.779421i	−0.998385	−	0.0568040i	$-0.981909\pi$
$401$	−9.01122	+	15.6079i	−0.449999	+	0.779421i	0.548386	+	0.836225i	$0.315242\pi$
$402$	−5.09919	−	6.70767i	−0.254325	−	0.334548i
$403$	6.15696	+	10.6642i	0.306700	+	0.531220i
$404$	−12.6884	−	28.4640i	−0.631273	−	1.41614i
$405$	−18.5164	+	16.0490i	−0.920087	+	0.797481i
$406$	−2.36619	+	1.29858i	−0.117432	+	0.0644473i
$407$	36.2379	+	20.9220i	1.79625	+	1.03706i
$408$	0.178966	+	8.08460i	0.00886015	+	0.400248i
$409$			16.0408i			0.793167i	0.917999	+	0.396584i	$0.129804\pi$
$409$			16.0408i			0.793167i	−0.917999	+	0.396584i	$0.870196\pi$
$410$	−2.04376	+	39.1669i	−0.100934	+	1.93431i
$411$	−0.335078	+	0.932207i	−0.0165282	+	0.0459824i
$412$	16.8464	−	23.2091i	0.829962	−	1.14343i
$413$	−14.1271	−	7.59227i	−0.695150	−	0.373591i
$414$	−7.55313	+	8.23455i	−0.371216	+	0.404706i
$415$	26.2710	−	15.1675i	1.28959	−	0.744545i
$416$	6.58720	+	24.4730i	0.322964	+	1.19989i
$417$	−14.3933	−	5.17360i	−0.704842	−	0.253352i
$418$	−14.3405	−	9.30823i	−0.701417	−	0.455280i
$419$	17.8647	−	10.3142i	0.872748	−	0.503882i	0.00448780	−	0.999990i	$-0.498571\pi$
$419$	17.8647	−	10.3142i	0.872748	−	0.503882i	0.868261	+	0.496108i	$0.165238\pi$
$420$	10.1492	−	22.7960i	0.495231	−	1.11233i
$421$	−32.0429	−	18.5000i	−1.56168	−	0.901635i	−0.997088	−	0.0762628i	$-0.975701\pi$
$421$	−32.0429	−	18.5000i	−1.56168	−	0.901635i	−0.564589	−	0.825372i	$-0.690965\pi$
$422$	0.681794	+	1.33735i	0.0331892	+	0.0651011i
$423$	6.60287	−	39.2823i	0.321043	−	1.90997i
$424$	17.8783	+	14.4575i	0.868246	+	0.702116i
$425$		−	3.98253i		−	0.193181i
$426$	−9.36001	+	7.11551i	−0.453494	+	0.344748i
$427$	−8.15027	+	15.1654i	−0.394419	+	0.733905i
$428$	−10.1807	−	22.8384i	−0.492103	−	1.10394i
$429$	27.9600	−	5.04553i	1.34992	−	0.243601i
$430$	−6.25378	−	12.2669i	−0.301584	−	0.591561i
$431$	1.62750	+	0.939637i	0.0783938	+	0.0452607i	0.538685	−	0.842508i	$-0.318921\pi$
$431$	1.62750	+	0.939637i	0.0783938	+	0.0452607i	−0.460291	+	0.887768i	$0.652255\pi$
$432$	19.6828	−	6.67741i	0.946989	−	0.321267i
$433$			3.23860i			0.155637i	0.996968	+	0.0778186i	$0.0247955\pi$
$433$			3.23860i			0.155637i	−0.996968	+	0.0778186i	$0.975205\pi$
$434$	−5.33377	+	8.79264i	−0.256029	+	0.422060i
$435$	3.20124	+	1.15067i	0.153487	+	0.0551704i
$436$	−4.63118	−	3.36154i	−0.221793	−	0.160989i
$437$	8.69622			0.415997
$438$	2.05548	+	16.1750i	0.0982148	+	0.772872i
$439$	14.3003			0.682518			0.341259	−	0.939969i	$-0.389147\pi$
$439$	14.3003			0.682518			0.341259	+	0.939969i	$0.389147\pi$
$440$	27.8506	+	4.39172i	1.32772	+	0.209367i
$441$	19.1920	−	8.52441i	0.913907	−	0.405924i
$442$	−0.544999	+	10.4444i	−0.0259229	+	0.496790i
$443$	−29.7127			−1.41169			−0.705847	−	0.708364i	$-0.749433\pi$
$443$	−29.7127			−1.41169			−0.705847	+	0.708364i	$0.749433\pi$
$444$	35.6604	+	17.1966i	1.69237	+	0.816112i
$445$			24.7868i			1.17501i
$446$	−2.98491	+	4.59864i	−0.141340	+	0.217752i
$447$	−2.62882	−	14.5677i	−0.124339	−	0.689029i
$448$	−15.2709	+	14.6561i	−0.721481	+	0.692434i
$449$	−17.6185			−0.831467			−0.415733	−	0.909487i	$-0.636475\pi$
$449$	−17.6185			−0.831467			−0.415733	+	0.909487i	$0.636475\pi$
$450$	−9.76390	+	3.07320i	−0.460275	+	0.144872i
$451$	−32.2978	−	18.6471i	−1.52084	−	0.878059i
$452$	−14.5696	−	32.6841i	−0.685298	−	1.53733i
$453$	−33.6622	−	12.0997i	−1.58159	−	0.568495i
$454$	−11.8207	+	6.02634i	−0.554775	+	0.282830i
$455$	15.2777	−	28.4276i	0.716229	−	1.33270i
$456$	−14.1842	−	7.77587i	−0.664236	−	0.364139i
$457$	21.9674			1.02759			0.513795	−	0.857913i	$-0.328239\pi$
$457$	21.9674			1.02759			0.513795	+	0.857913i	$0.328239\pi$
$458$	21.6082	−	33.2902i	1.00968	−	1.55555i
$459$	8.57650	−	0.102947i	0.400317	−	0.00480516i
$460$	−13.0988	+	5.83906i	−0.610735	+	0.272248i
$461$	10.3351	−	17.9009i	0.481353	−	0.833727i	−0.518418	−	0.855127i	$-0.673479\pi$
$461$	10.3351	−	17.9009i	0.481353	−	0.833727i	0.999771	+	0.0214000i	$0.00681235\pi$
$462$	14.9284	+	18.4433i	0.694534	+	0.858061i
$463$	9.37939	−	5.41519i	0.435897	−	0.251665i	−0.265959	−	0.963984i	$-0.585688\pi$
$463$	9.37939	−	5.41519i	0.435897	−	0.251665i	0.701856	+	0.712319i	$0.252355\pi$
$464$	−2.14606	−	1.92881i	−0.0996284	−	0.0895427i
$465$	12.7552	−	2.30174i	0.591506	−	0.106740i
$466$	−16.0559	−	31.4939i	−0.743775	−	1.45892i
$467$	−14.4730	+	8.35599i	−0.669730	+	0.386669i	−0.795974	−	0.605330i	$-0.793041\pi$
$467$	−14.4730	+	8.35599i	−0.669730	+	0.386669i	0.126244	+	0.991999i	$0.459708\pi$
$468$	26.0270	−	6.72347i	1.20310	−	0.310793i
$469$	4.30831	−	8.01658i	0.198939	−	0.370171i
$470$	27.8346	−	42.8828i	1.28392	−	1.97804i
$471$	−6.31586	−	7.46607i	−0.291019	−	0.344019i
$472$	2.67063	−	16.9361i	0.122926	−	0.779547i
$473$	13.0929			0.602012
$474$	−9.20668	+	6.99895i	−0.422877	+	0.321472i
$475$	6.89905	+	3.98317i	0.316550	+	0.182760i
$476$	−7.86575	+	3.79758i	−0.360526	+	0.174062i
$477$	15.5258	−	18.8065i	0.710875	−	0.861088i
$478$	8.70669	−	4.43876i	0.398235	−	0.203024i
$479$	6.83657	+	11.8413i	0.312371	+	0.541042i	0.978875	−	0.204459i	$-0.0655435\pi$
$479$	6.83657	+	11.8413i	0.312371	+	0.541042i	−0.666504	+	0.745501i	$0.732210\pi$
$480$	26.5862	+	2.18856i	1.21349	+	0.0998936i
$481$	44.3433	+	25.6016i	2.02188	+	1.16733i
$482$	26.4028	−	13.4604i	1.20261	−	0.613106i
$483$	−11.4769	−	3.73471i	−0.522217	−	0.169935i
$484$	−2.82562	+	3.89283i	−0.128437	+	0.176947i
$485$	18.9008	−	10.9124i	0.858243	−	0.495507i
$486$	−6.87062	−	20.9474i	−0.311658	−	0.950194i
$487$	−26.4919	−	15.2951i	−1.20046	−	0.693088i	−0.239806	−	0.970821i	$-0.577084\pi$
$487$	−26.4919	−	15.2951i	−1.20046	−	0.693088i	−0.960658	+	0.277733i	$0.910417\pi$
$488$	−18.1808	−	2.86691i	−0.823007	−	0.129779i
$489$	−6.16527	+	17.1522i	−0.278803	+	0.775647i
$490$	26.9516	−	0.236867i	1.21755	−	0.0107006i
$491$	12.1877	+	21.1097i	0.550023	+	0.952668i	0.998272	+	0.0587592i	$0.0187144\pi$
$491$	12.1877	+	21.1097i	0.550023	+	0.952668i	−0.448249	+	0.893909i	$0.647952\pi$
$492$	−31.7831	−	15.3268i	−1.43289	−	0.690985i
$493$	−0.595367	−	1.03121i	−0.0268140	−	0.0464432i
$494$	−17.5481	−	11.3902i	−0.789525	−	0.512470i
$495$	4.95713	−	29.4913i	0.222806	−	1.32554i
$496$	−10.7558	−	2.27605i	−0.482951	−	0.102198i
$497$	−11.1865	−	6.01190i	−0.501782	−	0.269671i
$498$	3.44052	+	27.0741i	0.154173	+	1.21322i
$499$	15.1440	−	26.2302i	0.677938	−	1.17422i	−0.297663	−	0.954671i	$-0.596207\pi$
$499$	15.1440	−	26.2302i	0.677938	−	1.17422i	0.975601	−	0.219552i	$-0.0704596\pi$
$500$	14.0121	+	1.46632i	0.626640	+	0.0655758i
$501$	−4.18189	+	11.6343i	−0.186833	+	0.519781i
$502$	−1.58625	+	30.3991i	−0.0707978	+	1.35678i
$503$	7.30504			0.325716			0.162858	−	0.986650i	$-0.447929\pi$
$503$	7.30504			0.325716			0.162858	+	0.986650i	$0.447929\pi$
$504$	15.3802	+	16.3539i	0.685090	+	0.728459i
$505$	−42.4240			−1.88784
$506$	0.710628	−	13.6186i	0.0315913	−	0.605419i
$507$	12.0551	−	2.17541i	0.535386	−	0.0966132i
$508$	4.13341	−	39.4987i	0.183390	−	1.75247i
$509$	14.9031	−	25.8129i	0.660568	−	1.14414i	−0.319899	−	0.947452i	$-0.603649\pi$
$509$	14.9031	−	25.8129i	0.660568	−	1.14414i	0.980467	−	0.196685i	$-0.0630177\pi$
$510$	10.1513	+	4.25844i	0.449509	+	0.188567i
$511$	−14.9767	+	9.26619i	−0.662532	+	0.409912i
$512$	−20.1821	−	10.2316i	−0.891929	−	0.452175i
$513$	−8.39954	+	14.9603i	−0.370849	+	0.660513i
$514$	8.05322	+	5.22723i	0.355212	+	0.230563i
$515$	−19.5203	−	33.8101i	−0.860167	−	1.48985i
$516$	12.3536	−	0.919149i	0.543836	−	0.0404633i
$517$	24.3070	+	42.1009i	1.06902	+	1.85160i
$518$	−0.926698	+	42.7522i	−0.0407168	+	1.87843i
$519$	12.8768	+	15.2219i	0.565229	+	0.668166i
$520$	34.0800	+	5.37402i	1.49451	+	0.235666i
$521$	−24.0984	−	13.9132i	−1.05577	−	0.609549i	−0.131510	−	0.991315i	$-0.541983\pi$
$521$	−24.0984	−	13.9132i	−1.05577	−	0.609549i	−0.924259	+	0.381766i	$0.875316\pi$
$522$	−2.06876	+	2.25540i	−0.0905473	+	0.0987162i
$523$	34.4291	−	19.8777i	1.50548	−	0.869189i	0.505500	−	0.862827i	$-0.331308\pi$
$523$	34.4291	−	19.8777i	1.50548	−	0.869189i	0.999980	−	0.00636266i	$-0.00202531\pi$
$524$	−11.0589	−	8.02710i	−0.483109	−	0.350665i
$525$	−7.39444	−	8.21971i	−0.322720	−	0.358738i
$526$	10.2161	−	5.20826i	0.445441	−	0.227091i
$527$	−3.92904	−	2.26843i	−0.171152	−	0.0988144i
$528$	−13.3364	+	21.5775i	−0.580390	+	0.939039i
$529$	−8.03173	−	13.9114i	−0.349206	−	0.604842i
$530$	27.8851	−	14.2161i	1.21125	−	0.617509i
$531$	−17.9338	−	3.01446i	−0.778262	−	0.130816i
$532$	1.28836	−	17.4243i	0.0558574	−	0.755437i
$533$	−39.5219	−	22.8180i	−1.71188	−	0.988356i
$534$	−20.5641	−	8.62654i	−0.889896	−	0.373307i
$535$	−34.0393			−1.47165
$536$	9.61056	+	1.51548i	0.415113	+	0.0654586i
$537$	−2.97849	+	0.537484i	−0.128531	+	0.0231941i
$538$	−15.1895	+	23.4014i	−0.654866	+	1.00890i
$539$	−11.4394	+	22.9345i	−0.492731	+	0.987858i
$540$	2.60686	−	28.1740i	0.112181	−	1.21242i
$541$	−35.6256	+	20.5685i	−1.53167	+	0.884308i	−0.532381	+	0.846505i	$0.678703\pi$
$541$	−35.6256	+	20.5685i	−1.53167	+	0.884308i	−0.999285	+	0.0378031i	$0.987964\pi$
$542$	2.67124	+	5.23968i	0.114740	+	0.225064i
$543$	9.23095	+	10.9121i	0.396138	+	0.468281i
$544$	−6.61013	−	6.59519i	−0.283407	−	0.282767i
$545$	−6.74651	+	3.89510i	−0.288989	+	0.166848i
$546$	18.2675	+	22.5686i	0.781777	+	0.965846i
$547$	−19.2326	+	33.3119i	−0.822327	+	1.42431i	0.0816173	+	0.996664i	$0.473991\pi$
$547$	−19.2326	+	33.3119i	−0.822327	+	1.42431i	−0.903945	+	0.427649i	$0.859342\pi$
$548$	−0.465717	−	1.04474i	−0.0198944	−	0.0446293i
$549$	−3.23600	+	19.2519i	−0.138109	+	0.821650i
$550$	6.80154	−	10.4786i	0.290019	−	0.446811i
$551$	2.38185			0.101470
$552$	−0.285551	−	12.8994i	−0.0121538	−	0.549036i
$553$	−11.0032	−	5.91342i	−0.467905	−	0.251464i
$554$	0.793545	−	0.404558i	0.0337145	−	0.0171880i
$555$	41.1467	−	34.8077i	1.74658	−	1.47750i
$556$	16.1308	−	7.19067i	0.684100	−	0.304952i
$557$	27.6750	+	15.9782i	1.17263	+	0.677017i	0.954298	−	0.298858i	$-0.0966055\pi$
$557$	27.6750	+	15.9782i	1.17263	+	0.677017i	0.218331	+	0.975875i	$0.429939\pi$
$558$	−2.52956	+	11.3832i	−0.107085	+	0.481891i
$559$	16.0214			0.677633
$560$	9.75889	+	27.1106i	0.412388	+	1.14563i
$561$	−7.99181	+	6.76060i	−0.337415	+	0.285433i
$562$	−4.18636	+	6.44962i	−0.176591	+	0.272061i
$563$		−	13.5788i		−	0.572279i	−0.958188	−	0.286140i	$-0.907628\pi$
$563$		−	13.5788i		−	0.572279i	0.958188	−	0.286140i	$-0.0923721\pi$
$564$	25.8900	+	38.0171i	1.09016	+	1.60081i
$565$	−48.7138			−2.04940
$566$	0.0791647	−	1.51712i	0.00332754	−	0.0637694i
$567$	17.5103	−	16.1366i	0.735361	−	0.677675i
$568$	2.11472	−	13.4108i	0.0887318	−	0.562703i
$569$	7.32075			0.306902			0.153451	−	0.988156i	$-0.450961\pi$
$569$	7.32075			0.306902			0.153451	+	0.988156i	$0.450961\pi$
$570$	−17.5300	+	13.3263i	−0.734250	+	0.558179i
$571$	−21.8072			−0.912602			−0.456301	−	0.889826i	$-0.650826\pi$
$571$	−21.8072			−0.912602			−0.456301	+	0.889826i	$0.650826\pi$
$572$	−19.2714	+	26.5501i	−0.805778	+	1.11011i
$573$	−8.59283	+	7.26903i	−0.358971	+	0.303668i
$574$	0.825939	−	38.1039i	0.0344740	−	1.59042i
$575$			6.35435i			0.264995i
$576$	−11.0685	+	21.2953i	−0.461187	+	0.887303i
$577$	34.7896	+	20.0858i	1.44831	+	0.836183i	0.998381	−	0.0568808i	$-0.0181155\pi$
$577$	34.7896	+	20.0858i	1.44831	+	0.836183i	0.449930	+	0.893064i	$0.351449\pi$
$578$	9.16938	+	17.9859i	0.381396	+	0.748113i
$579$	−16.3536	−	19.3318i	−0.679630	−	0.803402i
$580$	−3.58769	+	1.59929i	−0.148971	+	0.0664069i
$581$	−25.0685	+	15.5100i	−1.04001	+	0.643462i
$582$	2.47531	+	19.4787i	0.102605	+	0.807418i
$583$			29.7629i			1.23265i
$584$	−14.6398	−	11.8386i	−0.605797	−	0.489884i
$585$	6.06589	−	36.0877i	0.250794	−	1.49204i
$586$	4.48024	+	8.78804i	0.185077	+	0.363031i
$587$	28.8557	+	16.6598i	1.19100	+	0.687625i	0.958534	−	0.284979i	$-0.0919868\pi$
$587$	28.8557	+	16.6598i	1.19100	+	0.687625i	0.232467	+	0.972604i	$0.425320\pi$
$588$	−9.18341	+	22.4425i	−0.378717	+	0.925512i
$589$	7.85934	−	4.53759i	0.323838	−	0.186968i
$590$	−19.5776	−	12.7075i	−0.805997	−	0.523161i
$591$	−1.88236	+	1.59237i	−0.0774301	+	0.0655013i
$592$	−43.4646	+	14.1660i	−1.78638	+	0.582219i
$593$	17.7275	−	10.2350i	0.727982	−	0.420301i	−0.0897012	−	0.995969i	$-0.528591\pi$
$593$	17.7275	−	10.2350i	0.727982	−	0.420301i	0.817684	+	0.575668i	$0.195258\pi$
$594$	22.7419	+	14.3765i	0.933111	+	0.589873i
$595$	0.362137	+	11.8849i	0.0148462	+	0.487232i
$596$	13.8331	+	10.0408i	0.566626	+	0.411286i
$597$	−12.7629	+	2.30314i	−0.522352	+	0.0942612i
$598$	0.869575	−	16.6646i	0.0355596	−	0.681467i
$599$		−	18.4021i		−	0.751890i	−0.926642	−	0.375945i	$-0.877318\pi$
$599$		−	18.4021i		−	0.751890i	0.926642	−	0.375945i	$-0.122682\pi$
$600$	5.68185	−	10.3644i	0.231960	−	0.423126i
$601$	−16.2049	−	9.35590i	−0.661011	−	0.381635i	0.131651	−	0.991296i	$-0.457972\pi$
$601$	−16.2049	−	9.35590i	−0.661011	−	0.381635i	−0.792662	+	0.609661i	$0.791306\pi$
$602$	6.43745	+	11.7299i	0.262371	+	0.478075i
$603$	1.71058	−	10.1767i	0.0696604	−	0.414428i
$604$	37.7259	−	16.8171i	1.53505	−	0.684279i
$605$	3.27411	+	5.67092i	0.133111	+	0.230556i
$606$	14.7648	−	35.1965i	0.599778	−	1.42976i
$607$	10.8864	−	18.8559i	0.441867	−	0.765336i	−0.555961	−	0.831208i	$-0.687650\pi$
$607$	10.8864	−	18.8559i	0.441867	−	0.765336i	0.997828	+	0.0658723i	$0.0209830\pi$
$608$	18.0362	−	4.85467i	0.731466	−	0.196883i
$609$	−3.14346	−	1.02292i	−0.127380	−	0.0414507i
$610$	−13.6415	+	21.0165i	−0.552328	+	0.850932i
$611$	29.7437	+	51.5177i	1.20330	+	2.08418i
$612$	−7.06592	+	6.93988i	−0.285623	+	0.280528i
$613$	7.49617	+	4.32791i	0.302767	+	0.174803i	0.643685	−	0.765290i	$-0.277405\pi$
$613$	7.49617	+	4.32791i	0.302767	+	0.174803i	−0.340918	+	0.940093i	$0.610738\pi$
$614$	−0.725365	+	13.9010i	−0.0292734	+	0.560998i
$615$	−36.6729	+	31.0231i	−1.47879	+	1.25097i
$616$	−27.1817	−	3.44147i	−1.09518	−	0.138661i
$617$	−7.40653	−	12.8285i	−0.298176	−	0.516455i	0.677543	−	0.735483i	$-0.263045\pi$
$617$	−7.40653	−	12.8285i	−0.298176	−	0.516455i	−0.975719	+	0.219028i	$0.929711\pi$
$618$	34.8438	−	4.42787i	1.40162	−	0.178115i
$619$	−16.5878	+	9.57695i	−0.666719	+	0.384930i	−0.794832	−	0.606829i	$-0.792441\pi$
$619$	−16.5878	+	9.57695i	−0.666719	+	0.384930i	0.128113	+	0.991760i	$0.459108\pi$
$620$	−8.79148	+	12.1120i	−0.353074	+	0.486428i
$621$	−13.6843	+	0.164258i	−0.549131	+	0.00659143i
$622$	−26.4946	−	1.38251i	−1.06233	−	0.0554336i
$623$	−0.733600	−	24.0758i	−0.0293911	−	0.964578i
$624$	−16.3193	+	26.4037i	−0.653295	+	1.05699i
$625$	15.6212	−	27.0567i	0.624848	−	1.08227i
$626$	−0.339352	+	6.50339i	−0.0135633	+	0.259928i
$627$	−3.71849	−	20.6061i	−0.148502	−	0.822930i
$628$	11.2307	+	1.17526i	0.448154	+	0.0468978i
$629$	−18.8650			−0.752196
$630$	28.8585	−	10.0590i	1.14975	−	0.400762i
$631$			42.6136i			1.69642i	0.529660	+	0.848210i	$0.322320\pi$
$631$			42.6136i			1.69642i	−0.529660	+	0.848210i	$0.677680\pi$
$632$	2.08008	−	13.1911i	0.0827412	−	0.524713i
$633$	−0.621881	+	1.73011i	−0.0247175	+	0.0687657i
$634$	1.85706	−	35.5889i	0.0737533	−	1.41342i
$635$	−46.8205	−	27.0318i	−1.85802	−	1.07273i
$636$	2.08941	+	28.0822i	0.0828507	+	1.11353i
$637$	−13.9981	+	28.0643i	−0.554624	+	1.11195i
$638$	0.194637	−	3.73005i	0.00770577	−	0.147674i
$639$	−14.2008	−	2.38698i	−0.561775	−	0.0944275i
$640$	−23.9077	+	19.4228i	−0.945034	+	0.767755i
$641$	15.4427	+	26.7476i	0.609951	+	1.05647i	0.991248	+	0.132013i	$0.0421442\pi$
$641$	15.4427	+	26.7476i	0.609951	+	1.05647i	−0.381297	+	0.924453i	$0.624522\pi$
$642$	11.8467	−	28.2403i	0.467551	−	1.11456i
$643$	−33.0611	+	19.0878i	−1.30380	+	0.752750i	−0.981054	−	0.193735i	$-0.937940\pi$
$643$	−33.0611	+	19.0878i	−1.30380	+	0.752750i	−0.322748	+	0.946485i	$0.604607\pi$
$644$	12.5502	−	6.05925i	0.494549	−	0.238768i
$645$	5.70423	−	15.8695i	0.224604	−	0.624861i
$646$	7.69739	+	0.401656i	0.302850	+	0.0158030i
$647$	0.556472	−	0.963838i	0.0218772	−	0.0378924i	−0.854880	−	0.518827i	$-0.826369\pi$
$647$	0.556472	−	0.963838i	0.0218772	−	0.0378924i	0.876757	+	0.480934i	$0.159702\pi$
$648$	22.4670	+	11.9681i	0.882586	+	0.470152i
$649$	19.2206	−	11.0970i	0.754476	−	0.435597i
$650$	8.32285	−	12.8224i	0.326449	−	0.502936i
$651$	−12.3211	+	2.61322i	−0.482904	+	0.102420i
$652$	−8.56896	−	19.2228i	−0.335587	−	0.752823i
$653$	−30.3822	−	17.5412i	−1.18895	−	0.686438i	−0.230879	−	0.972982i	$-0.574160\pi$
$653$	−30.3822	−	17.5412i	−1.18895	−	0.686438i	−0.958067	+	0.286544i	$0.907494\pi$
$654$	−0.883542	−	6.95277i	−0.0345492	−	0.271875i
$655$	−16.1101	+	9.30118i	−0.629474	+	0.363427i
$656$	38.7387	−	12.6257i	1.51249	−	0.492953i
$657$	−12.7134	+	15.3998i	−0.495996	+	0.600804i
$658$	−25.7670	+	42.4765i	−1.00450	+	1.65591i
$659$	−11.3498	+	19.6584i	−0.442124	+	0.765781i	−0.997847	−	0.0655866i	$-0.979108\pi$
$659$	−11.3498	+	19.6584i	−0.442124	+	0.765781i	0.555723	+	0.831367i	$0.312441\pi$
$660$	19.4370	+	28.5415i	0.756584	+	1.11098i
$661$	−13.7132			−0.533382			−0.266691	−	0.963782i	$-0.585930\pi$
$661$	−13.7132			−0.533382			−0.266691	+	0.963782i	$0.585930\pi$
$662$	−33.0061	−	1.72228i	−1.28282	−	0.0669385i
$663$	−9.77935	+	8.27275i	−0.379799	+	0.321287i
$664$	−24.5044	−	19.8157i	−0.950955	−	0.769000i
$665$	−20.9507	−	11.2594i	−0.812434	−	0.436622i
$666$	14.5575	+	46.2510i	0.564093	+	1.79219i
$667$	0.949940	+	1.64534i	0.0367818	+	0.0637080i
$668$	−5.81231	−	13.0388i	−0.224885	−	0.504486i
$669$	−6.60786	+	1.19242i	−0.255475	+	0.0461018i
$670$	7.21103	−	11.1095i	0.278586	−	0.429198i
$671$	−11.9126	−	20.6333i	−0.459881	−	0.796538i
$672$	−25.8884	−	1.33892i	−0.998665	−	0.0516501i
$673$	−19.7738	+	34.2492i	−0.762222	+	1.32021i	0.179480	+	0.983762i	$0.442558\pi$
$673$	−19.7738	+	34.2492i	−0.762222	+	1.32021i	−0.941703	+	0.336446i	$0.890775\pi$
$674$	13.4761	+	26.4335i	0.519079	+	1.01818i
$675$	−10.9315	−	6.13756i	−0.420754	−	0.236235i
$676$	−8.30896	+	11.4472i	−0.319575	+	0.440277i
$677$	21.1049			0.811129			0.405564	−	0.914066i	$-0.367075\pi$
$677$	21.1049			0.811129			0.405564	+	0.914066i	$0.367075\pi$
$678$	16.9538	−	40.4148i	0.651107	−	1.55212i
$679$	−18.0357	+	11.1588i	−0.692146	+	0.428234i
$680$	−11.8640	+	4.56340i	−0.454963	+	0.174998i
$681$	−15.2923	−	5.49677i	−0.586004	−	0.210637i
$682$	−6.46377	−	12.6788i	−0.247511	−	0.485495i
$683$	7.75822	−	13.4376i	0.296860	−	0.514177i	−0.678556	−	0.734549i	$-0.737394\pi$
$683$	7.75822	−	13.4376i	0.296860	−	0.514177i	0.975416	+	0.220372i	$0.0707271\pi$
$684$	−4.95510	−	19.1815i	−0.189463	−	0.733423i
$685$	−1.55713			−0.0594949
$686$	−26.1714	+	1.02774i	−0.999230	+	0.0392393i
$687$	47.8353	−	8.63213i	1.82503	−	0.329336i
$688$	−9.56169	+	10.6387i	−0.364536	+	0.405596i
$689$			36.4199i			1.38749i
$690$	−16.1970	−	6.79457i	−0.616610	−	0.258665i
$691$			1.04235i			0.0396529i	0.999803	+	0.0198264i	$0.00631136\pi$
$691$			1.04235i			0.0396529i	−0.999803	+	0.0198264i	$0.993689\pi$
$692$	−22.8972	−	2.39612i	−0.870421	−	0.0910867i
$693$	−3.94209	+	28.7920i	−0.149748	+	1.09372i
$694$	16.3513	+	0.853227i	0.620688	+	0.0323880i
$695$		−	24.0421i		−	0.911968i
$696$	−0.0782108	−	3.53309i	−0.00296457	−	0.133921i
$697$	16.8138			0.636869
$698$	−5.87232	+	9.04706i	−0.222271	+	0.342436i
$699$	14.6450	−	40.7432i	0.553924	−	1.54105i
$700$	12.7319	+	0.941406i	0.481222	+	0.0355818i
$701$			19.0563i			0.719746i	0.933001	+	0.359873i	$0.117180\pi$
$701$			19.0563i			0.719746i	−0.933001	+	0.359873i	$0.882820\pi$
$702$	27.8286	+	17.5921i	1.05032	+	0.663969i
$703$	18.8680	−	32.6804i	0.711621	−	1.23256i
$704$	−6.12871	−	28.6420i	−0.230984	−	1.07949i
$705$	61.6191	−	11.1195i	2.32071	−	0.418784i
$706$	6.61951	−	3.37470i	0.249129	−	0.127008i
$707$	41.2070	−	1.25559i	1.54975	−	0.0472215i
$708$	17.3562	−	11.8197i	0.652288	−	0.444213i
$709$		−	21.0390i		−	0.790136i	−0.918652	−	0.395068i	$-0.870721\pi$
$709$		−	21.0390i		−	0.790136i	0.918652	−	0.395068i	$-0.129279\pi$
$710$	−15.5024	−	10.0624i	−0.581795	−	0.377635i
$711$	−13.9682	−	2.34788i	−0.523847	−	0.0880524i
$712$	24.0335	−	9.24432i	0.900694	−	0.346446i
$713$	6.26900	+	3.61941i	0.234776	+	0.135548i
$714$	−9.98618	−	3.83584i	−0.373723	−	0.143553i
$715$	22.3302	+	38.6771i	0.835103	+	1.44644i
$716$	2.05292	−	2.82829i	0.0767212	−	0.105698i
$717$	11.2637	+	4.04870i	0.420652	+	0.151202i
$718$	11.1173	−	5.66770i	0.414893	−	0.211517i
$719$	5.64201	+	9.77225i	0.210411	+	0.364443i	0.951843	−	0.306585i	$-0.0991863\pi$
$719$	5.64201	+	9.77225i	0.210411	+	0.364443i	−0.741432	+	0.671028i	$0.765853\pi$
$720$	20.3431	+	25.5653i	0.758142	+	0.952763i
$721$	19.9610	+	32.2625i	0.743386	+	1.20152i
$722$	6.23496	−	9.60575i	0.232041	−	0.357489i
$723$	34.1570	+	12.2776i	1.27031	+	0.456608i
$724$	−16.4142	−	1.71770i	−0.610030	−	0.0638377i
$725$			1.74042i			0.0646377i
$726$	−5.84430	+	0.742681i	−0.216902	+	0.0275635i
$727$	−6.66845	+	11.5501i	−0.247319	+	0.428370i	−0.962781	−	0.270282i	$-0.912883\pi$
$727$	−6.66845	+	11.5501i	−0.247319	+	0.428370i	0.715462	+	0.698652i	$0.246216\pi$
$728$	−33.2614	−	4.21122i	−1.23275	−	0.156078i
$729$	12.9348	−	23.7000i	0.479068	−	0.877778i
$730$	−22.8339	+	11.6410i	−0.845122	+	0.430852i
$731$	−5.11200	+	2.95141i	−0.189074	+	0.109162i
$732$	−12.6884	−	18.6318i	−0.468978	−	0.688653i
$733$	16.4136	−	28.4292i	0.606250	−	1.05005i	−0.385603	−	0.922665i	$-0.626007\pi$
$733$	16.4136	−	28.4292i	0.606250	−	1.05005i	0.991853	−	0.127390i	$-0.0406601\pi$
$734$	−18.5358	−	36.3582i	−0.684169	−	1.34201i
$735$	22.8143	+	23.8573i	0.841519	+	0.879990i
$736$	10.5468	+	10.5230i	0.388761	+	0.387883i
$737$	6.29713	+	10.9069i	0.231958	+	0.401762i
$738$	−12.9747	−	41.2222i	−0.477606	−	1.51741i
$739$	−11.2535	+	19.4917i	−0.413968	+	0.717013i	−0.995319	−	0.0966393i	$-0.969191\pi$
$739$	−11.2535	+	19.4917i	−0.413968	+	0.717013i	0.581352	+	0.813652i	$0.302524\pi$
$740$	−6.47702	+	61.8941i	−0.238100	+	2.27527i
$741$	−4.55020	−	25.2151i	−0.167156	−	0.926301i
$742$	−26.6645	+	14.6336i	−0.978884	+	0.537218i
$743$	−6.99554	+	4.03887i	−0.256641	+	0.148172i	−0.622801	−	0.782380i	$-0.714006\pi$
$743$	−6.99554	+	4.03887i	−0.256641	+	0.148172i	0.366160	+	0.930552i	$0.380672\pi$
$744$	−6.98885	−	11.5091i	−0.256224	−	0.421942i
$745$	20.1515	−	11.6345i	0.738294	−	0.426254i
$746$	5.87620	+	3.81416i	0.215143	+	0.139646i
$747$	−21.2800	+	25.7766i	−0.778593	+	0.943116i
$748$	1.25801	−	12.0215i	0.0459975	−	0.439551i
$749$	33.0629	−	1.00744i	1.20809	−	0.0368110i
$750$	10.4424	+	13.7364i	0.381304	+	0.501582i
$751$	−29.1414	−	16.8248i	−1.06339	−	0.613946i	−0.137019	−	0.990568i	$-0.543752\pi$
$751$	−29.1414	−	16.8248i	−1.06339	−	0.613946i	−0.926367	+	0.376622i	$0.877085\pi$
$752$	−51.9605	−	10.9954i	−1.89480	−	0.400961i
$753$	−28.4634	+	24.0783i	−1.03726	+	0.877463i
$754$	0.238172	−	4.56436i	0.00867372	−	0.166224i
$755$		−	56.2283i		−	2.04636i
$756$	−1.69823	+	27.4430i	−0.0617641	+	0.998091i
$757$			48.5605i			1.76496i	0.470349	+	0.882480i	$0.344128\pi$
$757$			48.5605i			1.76496i	−0.470349	+	0.882480i	$0.655872\pi$
$758$	−22.1113	−	1.15379i	−0.803120	−	0.0419075i
$759$	12.7514	−	10.7869i	0.462846	−	0.391540i
$760$	3.96058	−	25.1165i	0.143665	−	0.911070i
$761$	−22.5442	−	13.0159i	−0.817228	−	0.471827i	0.0322317	−	0.999480i	$-0.489739\pi$
$761$	−22.5442	−	13.0159i	−0.817228	−	0.471827i	−0.849460	+	0.527654i	$0.823072\pi$
$762$	38.7216	−	29.4362i	1.40273	−	1.06636i
$763$	6.43770	−	3.98304i	0.233060	−	0.144196i
$764$	1.35262	−	12.9256i	0.0489361	−	0.467632i
$765$	4.71249	+	12.6320i	0.170381	+	0.456712i
$766$	5.30201	−	8.16843i	0.191570	−	0.295137i
$767$	23.5197	−	13.5791i	0.849248	−	0.490314i
$768$	−7.79336	−	26.5944i	−0.281219	−	0.959644i
$769$	−17.8317	+	10.2951i	−0.643027	+	0.371252i	−0.785779	−	0.618507i	$-0.787738\pi$
$769$	−17.8317	+	10.2951i	−0.643027	+	0.371252i	0.142753	+	0.989758i	$0.454405\pi$
$770$	−19.3447	+	31.8894i	−0.697134	+	1.14921i
$771$	2.08820	+	11.5718i	0.0752045	+	0.416749i
$772$	29.0795	+	3.04307i	1.04659	+	0.109523i
$773$	−14.3160	+	24.7960i	−0.514910	+	0.891850i	0.484941	+	0.874547i	$0.338841\pi$
$773$	−14.3160	+	24.7960i	−0.514910	+	0.891850i	−0.999850	+	0.0173026i	$0.994492\pi$
$774$	11.1807	+	10.2555i	0.401882	+	0.368626i
$775$	3.31563	+	5.74284i	0.119101	+	0.206289i
$776$	−17.6299	−	14.2566i	−0.632875	−	0.511781i
$777$	−38.9362	+	35.0270i	−1.39683	+	1.25659i
$778$	20.4027	−	10.4015i	0.731473	−	0.372913i
$779$	−16.8165	+	29.1271i	−0.602514	+	1.04359i
$780$	23.7845	+	34.9254i	0.851621	+	1.25053i
$781$	15.2198	−	8.78713i	0.544606	−	0.314428i
$782$	2.79245	+	5.47743i	0.0998578	+	0.195872i
$783$	−3.74805	+	0.0449893i	−0.133944	+	0.00160779i
$784$	−10.2813	−	26.0441i	−0.367190	−	0.930146i
$785$	7.68598	−	13.3125i	0.274324	−	0.475144i
$786$	−2.10983	−	16.6027i	−0.0752551	−	0.592197i
$787$		−	44.3647i		−	1.58143i	−0.612184	−	0.790716i	$-0.709709\pi$
$787$		−	44.3647i		−	1.58143i	0.612184	−	0.790716i	$-0.290291\pi$
$788$	0.296308	−	2.83151i	0.0105555	−	0.100868i
$789$	13.2164	+	4.75057i	0.470516	+	0.169125i
$790$	−15.2485	−	9.89757i	−0.542516	−	0.352140i
$791$	47.3164	−	1.44175i	1.68238	−	0.0512628i
$792$	−30.4438	+	6.19240i	−1.08177	+	0.220037i
$793$	−14.5771	−	25.2483i	−0.517649	−	0.896594i
$794$	−10.3907	−	20.3816i	−0.368754	−	0.723315i
$795$	36.0746	+	12.9669i	1.27944	+	0.459888i
$796$	8.79684	−	12.1193i	0.311796	−	0.429559i
$797$	11.2656	+	19.5125i	0.399047	+	0.691169i	0.993609	−	0.112881i	$-0.0360078\pi$
$797$	11.2656	+	19.5125i	0.399047	+	0.691169i	−0.594562	+	0.804050i	$0.702674\pi$
$798$	16.6327	−	13.4629i	0.588792	−	0.476581i
$799$	−18.9809	−	10.9586i	−0.671494	−	0.387687i
$800$	3.54732	+	13.1791i	0.125417	+	0.465952i
$801$	−9.54635	−	25.5894i	−0.337304	−	0.904157i
$802$	13.8767	−	21.3788i	0.490003	−	0.754913i
$803$		−	24.3715i		−	0.860053i
$804$	6.70723	+	9.84898i	0.236546	+	0.347347i
$805$	−0.577810	−	18.9630i	−0.0203651	−	0.668357i
$806$	−7.90953	−	15.5146i	−0.278601	−	0.546480i
$807$	−33.6258	+	6.06796i	−1.18369	+	0.213602i
$808$	15.8221	+	41.1346i	0.556621	+	1.44711i
$809$	−1.50161	+	2.60086i	−0.0527937	+	0.0914414i	−0.891215	−	0.453582i	$-0.850146\pi$
$809$	−1.50161	+	2.60086i	−0.0527937	+	0.0914414i	0.838421	+	0.545023i	$0.183479\pi$
$810$	27.3333	−	21.3013i	0.960394	−	0.748452i
$811$		−	36.7840i		−	1.29166i	−0.763481	−	0.645830i	$-0.776512\pi$
$811$		−	36.7840i		−	1.29166i	0.763481	−	0.645830i	$-0.223488\pi$
$812$	3.43745	−	1.65960i	0.120631	−	0.0582404i
$813$	−2.43651	+	6.77851i	−0.0854520	+	0.237733i
$814$	−49.6366	−	32.2184i	−1.73976	−	1.12926i
$815$	−28.6504			−1.00358
$816$	0.343039	−	11.4310i	0.0120088	−	0.400165i
$817$		−	11.8076i		−	0.413094i
$818$	1.18212	−	22.6543i	0.0413319	−	0.792090i
$819$	−4.82383	+	35.2320i	−0.168558	+	1.23111i
$820$	5.77278	−	55.1645i	0.201594	−	1.92643i
$821$		−	2.61701i		−	0.0913344i	−0.998957	−	0.0456672i	$-0.985459\pi$
$821$		−	2.61701i		−	0.0913344i	0.998957	−	0.0456672i	$-0.0145414\pi$
$822$	0.541927	−	1.29186i	0.0189019	−	0.0450586i
$823$			37.6209i			1.31138i	0.755029	+	0.655691i	$0.227623\pi$
$823$			37.6209i			1.31138i	−0.755029	+	0.655691i	$0.772377\pi$
$824$	−25.5024	+	31.5366i	−0.888418	+	1.09863i
$825$	15.0569	−	2.71711i	0.524216	−	0.0945975i
$826$	19.3921	+	11.7636i	0.674738	+	0.409308i
$827$	46.6133			1.62090			0.810452	−	0.585805i	$-0.199221\pi$
$827$	46.6133			1.62090			0.810452	+	0.585805i	$0.199221\pi$
$828$	11.2741	−	11.0730i	0.391801	−	0.384812i
$829$	9.71848	−	16.8329i	0.337537	−	0.584631i	−0.646432	−	0.762972i	$-0.723740\pi$
$829$	9.71848	−	16.8329i	0.337537	−	0.584631i	0.983969	+	0.178341i	$0.0570729\pi$
$830$	−38.2200	+	19.4850i	−1.32664	+	0.676333i
$831$	1.02660	+	0.369007i	0.0356123	+	0.0128007i
$832$	−7.49952	−	35.0484i	−0.259999	−	1.21509i
$833$	−0.703498	−	11.5332i	−0.0243748	−	0.399603i
$834$	19.9462	+	8.36734i	0.690682	+	0.289737i
$835$	−19.4335			−0.672525
$836$	19.5670	+	14.2028i	0.676740	+	0.491212i
$837$	−12.2817	+	7.28876i	−0.424516	+	0.251936i
$838$	−25.9903	+	13.2501i	−0.897820	+	0.457718i
$839$	−13.6334	+	23.6138i	−0.470678	+	0.815238i	−0.999438	−	0.0335336i	$-0.989324\pi$
$839$	−13.6334	+	23.6138i	−0.470678	+	0.815238i	0.528760	+	0.848772i	$0.322657\pi$
$840$	−16.0136	+	31.4467i	−0.552522	+	1.08501i
$841$	−14.2398	−	24.6641i	−0.491028	−	0.850486i
$842$	43.8906	+	28.4888i	1.51257	+	0.981789i
$843$	−9.26757	+	1.67238i	−0.319192	+	0.0575999i
$844$	−0.864337	−	1.93897i	−0.0297517	−	0.0667421i
$845$	9.62778	+	16.6758i	0.331206	+	0.573665i
$846$	−12.2201	+	54.9915i	−0.420135	+	1.89065i
$847$	−3.34803	−	5.41135i	−0.115040	−	0.185936i
$848$	−24.1839	−	21.7357i	−0.830479	−	0.746406i
$849$	1.42052	−	1.20167i	0.0487520	−	0.0412413i
$850$	−0.293491	+	5.62450i	−0.0100667	+	0.192919i
$851$	30.1001			1.03182
$852$	13.7434	−	9.35939i	0.470843	−	0.320648i
$853$	0.850957	−	1.47390i	0.0291362	−	0.0504654i	−0.851090	−	0.525020i	$-0.824058\pi$
$853$	0.850957	−	1.47390i	0.0291362	−	0.0504654i	0.880226	+	0.474555i	$0.157391\pi$
$854$	12.6282	−	20.8173i	0.432127	−	0.712355i
$855$	−26.5961	−	4.47048i	−0.909568	−	0.152887i
$856$	12.6951	+	33.0048i	0.433908	+	1.12808i
$857$	−18.8861	+	10.9039i	−0.645137	+	0.372470i	−0.786591	−	0.617475i	$-0.788156\pi$
$857$	−18.8861	+	10.9039i	−0.645137	+	0.372470i	0.141453	+	0.989945i	$0.454822\pi$
$858$	−39.8595	+	5.06526i	−1.36078	+	0.172925i
$859$	−42.9597	−	24.8028i	−1.46577	−	0.846260i	−0.466498	−	0.884522i	$-0.654484\pi$
$859$	−42.9597	−	24.8028i	−1.46577	−	0.846260i	−0.999268	+	0.0382623i	$0.987818\pi$
$860$	7.92817	+	17.7853i	0.270348	+	0.606473i
$861$	34.7027	−	31.2186i	1.18267	−	1.06393i
$862$	−2.22926	−	1.44698i	−0.0759288	−	0.0492843i
$863$	14.8229	−	8.55802i	0.504578	−	0.291318i	−0.226024	−	0.974122i	$-0.572573\pi$
$863$	14.8229	−	8.55802i	0.504578	−	0.291318i	0.730602	+	0.682803i	$0.239239\pi$
$864$	−28.2899	+	7.97994i	−0.962443	+	0.271483i
$865$	−15.6702	+	27.1416i	−0.532804	+	0.922843i
$866$	0.238668	−	4.57385i	0.00811025	−	0.155426i
$867$	−8.36361	+	23.2681i	−0.284043	+	0.790225i
$868$	8.18082	−	12.0247i	0.277675	−	0.408145i
$869$	14.9704	−	8.64318i	0.507837	−	0.293200i
$870$	−4.43628	−	1.86100i	−0.150404	−	0.0630937i
$871$	7.70561	+	13.3465i	0.261095	+	0.452229i
$872$	6.29284	+	5.08878i	0.213103	+	0.172328i
$873$	−15.3100	+	18.5452i	−0.518166	+	0.627658i
$874$	−12.2816	−	0.640865i	−0.415431	−	0.0216776i
$875$	−8.82283	+	16.4168i	−0.298266	+	0.554991i
$876$	−1.71093	−	22.9953i	−0.0578070	−	0.776940i
$877$	36.5165	+	21.0828i	1.23308	+	0.711916i	0.967670	−	0.252221i	$-0.0811609\pi$
$877$	36.5165	+	21.0828i	1.23308	+	0.711916i	0.265405	+	0.964137i	$0.414494\pi$
$878$	−20.1962	−	1.05386i	−0.681590	−	0.0355660i
$879$	−4.08653	+	11.3690i	−0.137835	+	0.383466i
$880$	−39.0095	−	8.25483i	−1.31501	−	0.278270i
$881$		−	14.8997i		−	0.501982i	−0.967989	−	0.250991i	$-0.919243\pi$
$881$		−	14.8997i		−	0.501982i	0.967989	−	0.250991i	$-0.0807565\pi$
$882$	−27.7330	+	10.6246i	−0.933818	+	0.357749i
$883$	35.9369			1.20937			0.604686	−	0.796464i	$-0.293299\pi$
$883$	35.9369			1.20937			0.604686	+	0.796464i	$0.293299\pi$
$884$	1.53939	−	14.7104i	0.0517754	−	0.494764i
$885$	−5.07646	−	28.1314i	−0.170643	−	0.945627i
$886$	41.9630	+	2.18967i	1.40978	+	0.0735634i
$887$	9.60227	−	16.6316i	0.322413	−	0.558435i	−0.658573	−	0.752517i	$-0.728839\pi$
$887$	9.60227	−	16.6316i	0.322413	−	0.558435i	0.980985	+	0.194082i	$0.0621728\pi$
$888$	−49.0956	−	26.9145i	−1.64754	−	0.903193i
$889$	46.2775	+	24.8707i	1.55210	+	0.834137i
$890$	1.82666	−	35.0063i	0.0612297	−	1.17341i
$891$	6.24059	+	32.3554i	0.209067	+	1.08395i
$892$	4.55446	−	6.27465i	0.152495	−	0.210091i
$893$	37.9678	−	21.9207i	1.27054	−	0.733549i
$894$	2.63910	+	20.7676i	0.0882647	+	0.694572i
$895$	−2.37877	−	4.12014i	−0.0795133	−	0.137721i
$896$	22.6470	−	19.5733i	0.756584	−	0.653897i
$897$	15.6035	−	13.1996i	0.520985	−	0.440723i
$898$	24.8824	+	1.29839i	0.830337	+	0.0433277i
$899$	1.71705	+	0.991337i	0.0572667	+	0.0330629i
$900$	14.0160	−	3.62070i	0.467199	−	0.120690i
$901$	−6.70917	−	11.6206i	−0.223515	−	0.387139i
$902$	44.2397	+	28.7154i	1.47302	+	0.956117i
$903$	−5.07092	+	15.5831i	−0.168750	+	0.518573i
$904$	18.1679	+	47.2332i	0.604257	+	1.57095i
$905$	−11.2335	+	19.4569i	−0.373413	+	0.646770i
$906$	46.6492	+	19.5691i	1.54981	+	0.650139i
$907$	−4.90055	−	8.48799i	−0.162720	−	0.281839i	0.773123	−	0.634256i	$-0.218693\pi$
$907$	−4.90055	−	8.48799i	−0.162720	−	0.281839i	−0.935843	+	0.352417i	$0.885360\pi$
$908$	17.1385	−	7.63983i	0.568760	−	0.253537i
$909$	43.7976	−	16.3391i	1.45267	−	0.541933i
$910$	−23.6715	+	39.0221i	−0.784703	+	1.29357i
$911$	−51.7912	−	29.9017i	−1.71592	−	0.990687i	−0.926041	−	0.377424i	$-0.876810\pi$
$911$	−51.7912	−	29.9017i	−1.71592	−	0.990687i	−0.789879	−	0.613263i	$-0.789857\pi$
$912$	19.4592	+	12.0271i	0.644358	+	0.398257i
$913$		−	40.7937i		−	1.35007i
$914$	−31.0243	−	1.61888i	−1.02619	−	0.0535477i
$915$	−30.1989	+	5.44956i	−0.998346	+	0.180157i
$916$	−32.9704	+	45.4231i	−1.08937	+	1.50082i
$917$	15.3727	−	9.51117i	0.507652	−	0.314087i
$918$	−12.1201	−	0.486651i	−0.400023	−	0.0160619i
$919$	−6.53673	+	3.77398i	−0.215627	+	0.124492i	−0.603924	−	0.797042i	$-0.706397\pi$
$919$	−6.53673	+	3.77398i	−0.215627	+	0.124492i	0.388297	+	0.921534i	$0.373064\pi$
$920$	18.9296	−	7.28115i	0.624092	−	0.240053i
$921$	−13.0158	+	11.0106i	−0.428886	+	0.362812i
$922$	−15.9153	+	24.5196i	−0.524144	+	0.807511i
$923$	18.6240	−	10.7526i	0.613015	−	0.353925i
$924$	−19.7241	−	27.1475i	−0.648877	−	0.893088i
$925$	23.8796	+	13.7869i	0.785157	+	0.453310i
$926$	−13.6455	+	6.95662i	−0.448419	+	0.228609i
$927$	33.1739	+	27.3868i	1.08957	+	0.899502i
$928$	2.88872	+	2.88219i	0.0948270	+	0.0946126i
$929$		−	29.0322i		−	0.952516i	−0.879305	−	0.476258i	$-0.841993\pi$
$929$		−	29.0322i		−	0.952516i	0.879305	−	0.476258i	$-0.158007\pi$
$930$	−18.1836	+	2.31074i	−0.596265	+	0.0757720i
$931$	20.6830	+	10.3164i	0.677857	+	0.338106i
$932$	20.3547	+	45.6618i	0.666740	+	1.49570i
$933$	−20.9857	−	24.8075i	−0.687040	−	0.812161i
$934$	21.0559	−	10.7345i	0.688970	−	0.351244i
$935$	−14.2499	−	8.22721i	−0.466023	−	0.269058i
$936$	−37.2531	+	7.57746i	−1.21766	+	0.247677i
$937$		−	20.8956i		−	0.682628i	−0.939949	−	0.341314i	$-0.889128\pi$
$937$		−	20.8956i		−	0.682628i	0.939949	−	0.341314i	$-0.110872\pi$
$938$	−6.67537	+	11.0042i	−0.217959	+	0.359301i
$939$	−6.08928	+	5.15117i	−0.198716	+	0.168102i
$940$	−42.4709	+	58.5118i	−1.38525	+	1.90844i
$941$	0.493927			0.0161015			0.00805077	−	0.999968i	$-0.497437\pi$
$941$	0.493927			0.0161015			0.00805077	+	0.999968i	$0.497437\pi$
$942$	8.36962	+	11.0097i	0.272697	+	0.358716i
$943$	−26.8274			−0.873619
$944$	−5.01981	+	23.7219i	−0.163381	+	0.772082i
$945$	33.1805	+	17.3220i	1.07936	+	0.563485i
$946$	−18.4910	−	0.964877i	−0.601194	−	0.0313708i
$947$	−23.7568			−0.771991			−0.385996	−	0.922501i	$-0.626142\pi$
$947$	−23.7568			−0.771991			−0.385996	+	0.922501i	$0.626142\pi$
$948$	13.5183	−	9.20608i	0.439054	−	0.298999i
$949$		−	29.8227i		−	0.968087i
$950$	−9.44994	−	6.13382i	−0.306597	−	0.199008i
$951$	33.3228	−	28.1891i	1.08056	−	0.914094i
$952$	11.3886	−	4.78363i	0.369107	−	0.155038i
$953$	35.3699			1.14574			0.572872	−	0.819645i	$-0.305829\pi$
$953$	35.3699			1.14574			0.572872	+	0.819645i	$0.305829\pi$
$954$	−23.3128	+	25.4160i	−0.754781	+	0.822875i
$955$	−15.3216	−	8.84593i	−0.495795	−	0.286247i
$956$	−12.6235	+	5.62719i	−0.408273	+	0.181996i
$957$	3.49254	−	2.95448i	0.112898	−	0.0955047i
$958$	−8.78260	−	17.2272i	−0.283753	−	0.556585i
$959$	1.51246	−	0.0460854i	0.0488400	−	0.00148818i
$960$	−37.3862	−	5.05015i	−1.20664	−	0.162993i
$961$	−23.4457			−0.756314
$962$	−60.7389	−	39.4248i	−1.95830	−	1.27111i
$963$	35.1414	−	13.1098i	1.13242	−	0.422458i
$964$	−38.2804	+	17.0643i	−1.23293	+	0.549604i
$965$	19.9012	−	34.4699i	0.640642	−	1.10962i
$966$	15.9335	+	6.12029i	0.512652	+	0.196917i
$967$	−46.7185	+	26.9730i	−1.50237	+	0.867392i	−0.502371	+	0.864652i	$0.667539\pi$
$967$	−46.7185	+	26.9730i	−1.50237	+	0.867392i	−0.999996	+	0.00273947i	$0.999128\pi$
$968$	4.27748	−	5.28959i	0.137483	−	0.170014i
$969$	6.09690	+	7.20725i	0.195861	+	0.231530i
$970$	−27.4977	+	14.0186i	−0.882898	+	0.450110i
$971$	−35.9111	+	20.7333i	−1.15244	+	0.665363i	−0.949481	−	0.313824i	$-0.898390\pi$
$971$	−35.9111	+	20.7333i	−1.15244	+	0.665363i	−0.202961	+	0.979187i	$0.565057\pi$
$972$	8.15961	+	30.0902i	0.261719	+	0.965144i
$973$	0.711558	+	23.3524i	0.0228115	+	0.748645i
$974$	36.2872	+	23.5535i	1.16272	+	0.754703i
$975$	18.4248	−	3.32484i	0.590064	−	0.106480i
$976$	25.4653	+	5.38874i	0.815126	+	0.172489i
$977$	22.1226			0.707764			0.353882	−	0.935290i	$-0.384861\pi$
$977$	22.1226			0.707764			0.353882	+	0.935290i	$0.384861\pi$
$978$	9.97119	−	23.7695i	0.318843	−	0.760065i
$979$	28.8669	+	16.6663i	0.922589	+	0.532657i
$980$	−38.0809	−	1.65166i	−1.21645	−	0.0527604i
$981$	5.46480	−	6.61955i	0.174478	−	0.211346i
$982$	−15.6569	−	30.7112i	−0.499632	−	0.980035i
$983$	−19.8667	−	34.4102i	−0.633650	−	1.09751i	−0.986799	−	0.161947i	$-0.948223\pi$
$983$	−19.8667	−	34.4102i	−0.633650	−	1.09751i	0.353149	−	0.935567i	$-0.385111\pi$
$984$	43.7575	+	23.9882i	1.39494	+	0.764714i
$985$	−3.35638	−	1.93781i	−0.106943	−	0.0617437i
$986$	0.764837	+	1.50024i	0.0243574	+	0.0477773i
$987$	−59.5224	+	12.6242i	−1.89462	+	0.401833i
$988$	23.9436	+	17.3795i	0.761748	+	0.552916i
$989$	8.15647	−	4.70914i	0.259361	−	0.149742i
$990$	−9.17426	+	41.2850i	−0.291577	+	1.31212i
$991$	33.2384	+	19.1902i	1.05585	+	0.609596i	0.924282	−	0.381711i	$-0.124665\pi$
$991$	33.2384	+	19.1902i	1.05585	+	0.609596i	0.131570	+	0.991307i	$0.457998\pi$
$992$	15.0226	+	4.00709i	0.476969	+	0.127225i
$993$	−26.1432	−	30.9044i	−0.829631	−	0.980720i
$994$	15.3555	+	9.31494i	0.487048	+	0.295452i
$995$	−10.1931	−	17.6550i	−0.323143	−	0.559700i
$996$	−2.86380	−	38.4901i	−0.0907430	−	1.21961i
$997$	−5.30364	−	9.18617i	−0.167968	−	0.290929i	0.769737	−	0.638361i	$-0.220387\pi$
$997$	−5.30364	−	9.18617i	−0.167968	−	0.290929i	−0.937705	+	0.347432i	$0.887054\pi$
$998$	−23.3208	+	35.9286i	−0.738206	+	1.13730i
$999$	−29.0732	+	51.7818i	−0.919836	+	1.63831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bf.b.115.3	✓	180
7.5	odd	6		504.2.cz.b.187.58	yes	180
8.3	odd	2	inner	504.2.bf.b.115.4	yes	180
9.4	even	3		504.2.cz.b.283.62	yes	180
56.19	even	6		504.2.cz.b.187.62	yes	180
63.40	odd	6	inner	504.2.bf.b.355.3	yes	180
72.67	odd	6		504.2.cz.b.283.58	yes	180
504.355	even	6	inner	504.2.bf.b.355.4	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.3	✓	180	1.1	even	1	trivial
504.2.bf.b.115.4	yes	180	8.3	odd	2	inner
504.2.bf.b.355.3	yes	180	63.40	odd	6	inner
504.2.bf.b.355.4	yes	180	504.355	even	6	inner
504.2.cz.b.187.58	yes	180	7.5	odd	6
504.2.cz.b.187.62	yes	180	56.19	even	6
504.2.cz.b.283.58	yes	180	72.67	odd	6
504.2.cz.b.283.62	yes	180	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41229 - 0.0736946i) q^{2} +(-1.11864 - 1.32236i) q^{3} +(1.98914 + 0.208157i) q^{4} +(1.36131 - 2.35786i) q^{5} +(1.48240 + 1.95000i) q^{6} +(-1.25248 + 2.33051i) q^{7} +(-2.79390 - 0.440567i) q^{8} +(-0.497287 + 2.95850i) q^{9} +O(q^{10})\)	\(q+(-1.41229 - 0.0736946i) q^{2} +(-1.11864 - 1.32236i) q^{3} +(1.98914 + 0.208157i) q^{4} +(1.36131 - 2.35786i) q^{5} +(1.48240 + 1.95000i) q^{6} +(-1.25248 + 2.33051i) q^{7} +(-2.79390 - 0.440567i) q^{8} +(-0.497287 + 2.95850i) q^{9} +(-2.09633 + 3.22967i) q^{10} +(-1.83065 - 3.17078i) q^{11} +(-1.94987 - 2.86322i) q^{12} +(-2.24011 - 3.87999i) q^{13} +(1.94061 - 3.19907i) q^{14} +(-4.64077 + 0.837451i) q^{15} +(3.91334 + 0.828105i) q^{16} +(1.42952 + 0.825334i) q^{17} +(0.920340 - 4.14161i) q^{18} +(-2.85950 + 1.65093i) q^{19} +(3.19864 - 4.40675i) q^{20} +(4.48286 - 0.950778i) q^{21} +(2.35174 + 4.61297i) q^{22} +(-2.28088 - 1.31686i) q^{23} +(2.54278 + 4.18739i) q^{24} +(-1.20634 - 2.08944i) q^{25} +(2.87776 + 5.64476i) q^{26} +(4.46849 - 2.65190i) q^{27} +(-2.97646 + 4.37500i) q^{28} +(-0.624720 - 0.360683i) q^{29} +(6.61583 - 0.840725i) q^{30} -2.74850 q^{31} +(-5.46575 - 1.45792i) q^{32} +(-2.14508 + 5.96774i) q^{33} +(-1.95808 - 1.27096i) q^{34} +(3.79002 + 6.12573i) q^{35} +(-1.60500 + 5.78135i) q^{36} +(-9.89755 + 5.71435i) q^{37} +(4.16011 - 2.12087i) q^{38} +(-2.62487 + 7.30256i) q^{39} +(-4.84217 + 5.98789i) q^{40} +(8.82140 - 5.09304i) q^{41} +(-6.40117 + 1.01241i) q^{42} +(-1.78801 + 3.09693i) q^{43} +(-2.98140 - 6.68818i) q^{44} +(6.29876 + 5.19997i) q^{45} +(3.12422 + 2.02789i) q^{46} -13.2778 q^{47} +(-3.28257 - 6.10121i) q^{48} +(-3.86260 - 5.83784i) q^{49} +(1.54972 + 3.03980i) q^{50} +(-0.507728 - 2.81360i) q^{51} +(-3.64825 - 8.18413i) q^{52} +(-7.03996 - 4.06452i) q^{53} +(-6.50625 + 3.41595i) q^{54} -9.96834 q^{55} +(4.52605 - 5.95943i) q^{56} +(5.38188 + 1.93450i) q^{57} +(0.855707 + 0.555428i) q^{58} +6.06180i q^{59} +(-9.40545 + 0.699798i) q^{60} +6.50731 q^{61} +(3.88169 + 0.202550i) q^{62} +(-6.27198 - 4.86439i) q^{63} +(7.61180 + 2.46180i) q^{64} -12.1980 q^{65} +(3.46927 - 8.27012i) q^{66} -3.43983 q^{67} +(2.67171 + 1.93927i) q^{68} +(0.810108 + 4.48925i) q^{69} +(-4.90118 - 8.93062i) q^{70} +4.80001i q^{71} +(2.69279 - 8.04667i) q^{72} +(5.76472 + 3.32826i) q^{73} +(14.3993 - 7.34094i) q^{74} +(-1.41354 + 3.93255i) q^{75} +(-6.03159 + 2.68871i) q^{76} +(9.68239 - 0.295027i) q^{77} +(4.24525 - 10.1199i) q^{78} +4.72138i q^{79} +(7.27983 - 8.09981i) q^{80} +(-8.50541 - 2.94245i) q^{81} +(-12.8337 + 6.54277i) q^{82} +(9.64913 + 5.57093i) q^{83} +(9.11494 - 0.958091i) q^{84} +(3.89204 - 2.24707i) q^{85} +(2.75342 - 4.24200i) q^{86} +(0.221884 + 1.22958i) q^{87} +(3.71772 + 9.66537i) q^{88} +(-7.88432 + 4.55201i) q^{89} +(-8.51248 - 7.80806i) q^{90} +(11.8481 - 0.361016i) q^{91} +(-4.26287 - 3.09421i) q^{92} +(3.07459 + 3.63452i) q^{93} +(18.7521 + 0.978502i) q^{94} +8.98973i q^{95} +(4.18632 + 8.85860i) q^{96} +(6.94214 + 4.00805i) q^{97} +(5.02490 + 8.52938i) q^{98} +(10.2911 - 3.83918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9}+O(q^{10}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9	\( 180 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 6 q^{6} + 10 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{14} + 14 q^{16} - 18 q^{17} + 8 q^{18} - 6 q^{19} + 36 q^{20} - 16 q^{22} - 12 q^{24} - 78 q^{25} - 6 q^{26} + 16 q^{28} + q^{30} - 26 q^{32} - 36 q^{33} - 12 q^{34} - 12 q^{35} + 2 q^{36} - 27 q^{38} + 24 q^{40} - 42 q^{41} + 22 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} - 9 q^{48} + 2 q^{49} + 15 q^{50} + 9 q^{52} - 51 q^{54} + 14 q^{56} - 26 q^{57} + 19 q^{58} + 37 q^{60} - 8 q^{64} + 24 q^{65} + 6 q^{66} + 28 q^{67} + 12 q^{68} + 27 q^{70} - 28 q^{72} + 18 q^{73} + 49 q^{74} - 18 q^{75} - 12 q^{76} - 33 q^{78} - 63 q^{80} - 22 q^{81} - 54 q^{82} + 6 q^{83} + 31 q^{84} - 13 q^{86} + 29 q^{88} - 66 q^{89} - 51 q^{90} + 2 q^{91} - 60 q^{92} - 45 q^{96} - 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q - 6 * q^2 - 6 * q^3 - 2 * q^4 - 6 * q^6 + 10 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^14 + 14 * q^16 - 18 * q^17 + 8 * q^18 - 6 * q^19 + 36 * q^20 - 16 * q^22 - 12 * q^24 - 78 * q^25 - 6 * q^26 + 16 * q^28 + q^30 - 26 * q^32 - 36 * q^33 - 12 * q^34 - 12 * q^35 + 2 * q^36 - 27 * q^38 + 24 * q^40 - 42 * q^41 + 22 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 - 9 * q^48 + 2 * q^49 + 15 * q^50 + 9 * q^52 - 51 * q^54 + 14 * q^56 - 26 * q^57 + 19 * q^58 + 37 * q^60 - 8 * q^64 + 24 * q^65 + 6 * q^66 + 28 * q^67 + 12 * q^68 + 27 * q^70 - 28 * q^72 + 18 * q^73 + 49 * q^74 - 18 * q^75 - 12 * q^76 - 33 * q^78 - 63 * q^80 - 22 * q^81 - 54 * q^82 + 6 * q^83 + 31 * q^84 - 13 * q^86 + 29 * q^88 - 66 * q^89 - 51 * q^90 + 2 * q^91 - 60 * q^92 - 45 * q^96 - 6 * q^97 + 31 * q^98 + 4 * q^99

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