LMFDB - Embedded newform 483.2.j.a.229.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(229,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("483.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.j (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.13
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.123216 + 0.213416i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.969636 + 1.67946i) q^{4} +(-1.99266 + 3.45140i) q^{5} +0.246432i q^{6} +(-1.63265 - 2.08193i) q^{7} -0.970763 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.123216 + 0.213416i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.969636 + 1.67946i) q^{4} +(-1.99266 + 3.45140i) q^{5} +0.246432i q^{6} +(-1.63265 - 2.08193i) q^{7} -0.970763 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.491056 - 0.850535i) q^{10} +(-0.567813 + 0.327827i) q^{11} +(1.67946 + 0.969636i) q^{12} +1.72836i q^{13} +(0.645488 - 0.0919073i) q^{14} +3.98533i q^{15} +(-1.81966 + 3.15174i) q^{16} +(3.03305 + 5.25340i) q^{17} +(0.123216 + 0.213416i) q^{18} +(0.168732 - 0.292252i) q^{19} -7.72863 q^{20} +(-2.45489 - 0.986681i) q^{21} -0.161574i q^{22} +(-3.94052 + 2.73356i) q^{23} +(-0.840705 + 0.485381i) q^{24} +(-5.44142 - 9.42482i) q^{25} +(-0.368860 - 0.212961i) q^{26} -1.00000i q^{27} +(1.91344 - 4.76069i) q^{28} -4.71500 q^{29} +(-0.850535 - 0.491056i) q^{30} +(3.64518 - 2.10455i) q^{31} +(-1.41918 - 2.45810i) q^{32} +(-0.327827 + 0.567813i) q^{33} -1.49488 q^{34} +(10.4389 - 1.48634i) q^{35} +1.93927 q^{36} +(-1.40646 - 0.812022i) q^{37} +(0.0415808 + 0.0720201i) q^{38} +(0.864179 + 1.49680i) q^{39} +(1.93440 - 3.35049i) q^{40} +6.67407i q^{41} +(0.513055 - 0.402338i) q^{42} +4.20924i q^{43} +(-1.10114 - 0.635746i) q^{44} +(1.99266 + 3.45140i) q^{45} +(-0.0978515 - 1.17779i) q^{46} +(4.32275 + 2.49574i) q^{47} +3.63932i q^{48} +(-1.66889 + 6.79815i) q^{49} +2.68188 q^{50} +(5.25340 + 3.03305i) q^{51} +(-2.90271 + 1.67588i) q^{52} +(7.39119 - 4.26731i) q^{53} +(0.213416 + 0.123216i) q^{54} -2.61300i q^{55} +(1.58492 + 2.02106i) q^{56} -0.337463i q^{57} +(0.580964 - 1.00626i) q^{58} +(9.78531 - 5.64955i) q^{59} +(-6.69319 + 3.86432i) q^{60} +(2.14171 - 3.70955i) q^{61} +1.03726i q^{62} +(-2.61933 + 0.372952i) q^{63} -6.57917 q^{64} +(-5.96525 - 3.44404i) q^{65} +(-0.0807871 - 0.139927i) q^{66} +(3.69254 - 2.13189i) q^{67} +(-5.88191 + 10.1878i) q^{68} +(-2.04581 + 4.33759i) q^{69} +(-0.969032 + 2.41097i) q^{70} +2.93387 q^{71} +(-0.485381 + 0.840705i) q^{72} +(12.7226 - 7.34541i) q^{73} +(0.346598 - 0.200108i) q^{74} +(-9.42482 - 5.44142i) q^{75} +0.654432 q^{76} +(1.60956 + 0.646922i) q^{77} -0.425923 q^{78} +(9.76037 + 5.63515i) q^{79} +(-7.25194 - 12.5607i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.42436 - 0.822352i) q^{82} +12.4794 q^{83} +(-0.723255 - 5.07960i) q^{84} -24.1754 q^{85} +(-0.898321 - 0.518646i) q^{86} +(-4.08331 + 2.35750i) q^{87} +(0.551212 - 0.318242i) q^{88} +(-3.60989 + 6.25251i) q^{89} -0.982113 q^{90} +(3.59833 - 2.82181i) q^{91} +(-8.41176 - 3.96738i) q^{92} +(2.10455 - 3.64518i) q^{93} +(-1.06526 + 0.615030i) q^{94} +(0.672451 + 1.16472i) q^{95} +(-2.45810 - 1.41918i) q^{96} +14.9762 q^{97} +(-1.24520 - 1.19381i) q^{98} +0.655654i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9}+O(q^{10}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50} - 108 q^{52} - 24 q^{58} + 36 q^{59} + 168 q^{64} - 40 q^{70} - 16 q^{71} - 12 q^{72} + 48 q^{73} - 48 q^{75} - 32 q^{78} - 32 q^{81} - 24 q^{82} + 88 q^{85} + 36 q^{87} + 152 q^{92} + 24 q^{93} - 108 q^{94} - 44 q^{95} + 60 q^{96} + 112 q^{98}+O(q^{100}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.123216	+	0.213416i	−0.0871269	+	0.150908i	−0.906296	−	0.422645i	$-0.861102\pi$
$2$	−0.123216	+	0.213416i	−0.0871269	+	0.150908i	0.819169	+	0.573553i	$0.194435\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.969636	+	1.67946i	0.484818	+	0.839729i
$5$	−1.99266	+	3.45140i	−0.891147	+	1.54351i	−0.0526444	+	0.998613i	$0.516765\pi$
$5$	−1.99266	+	3.45140i	−0.891147	+	1.54351i	−0.838502	+	0.544898i	$0.816568\pi$
$6$			0.246432i			0.100605i
$7$	−1.63265	−	2.08193i	−0.617085	−	0.786897i
$7$	−1.63265	−	2.08193i	−0.617085	−	0.786897i
$8$	−0.970763			−0.343216
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.491056	−	0.850535i	−0.155286	−	0.268963i
$11$	−0.567813	+	0.327827i	−0.171202	+	0.0988436i	−0.583153	−	0.812363i	$-0.698181\pi$
$11$	−0.567813	+	0.327827i	−0.171202	+	0.0988436i	0.411950	+	0.911206i	$0.364848\pi$
$12$	1.67946	+	0.969636i	0.484818	+	0.279910i
$13$			1.72836i			0.479360i	0.970852	+	0.239680i	$0.0770426\pi$
$13$			1.72836i			0.479360i	−0.970852	+	0.239680i	$0.922957\pi$
$14$	0.645488	−	0.0919073i	0.172514	−	0.0245633i
$15$			3.98533i			1.02901i
$16$	−1.81966	+	3.15174i	−0.454914	+	0.787935i
$17$	3.03305	+	5.25340i	0.735624	+	1.27414i	0.954449	+	0.298373i	$0.0964441\pi$
$17$	3.03305	+	5.25340i	0.735624	+	1.27414i	−0.218826	+	0.975764i	$0.570223\pi$
$18$	0.123216	+	0.213416i	0.0290423	+	0.0503027i
$19$	0.168732	−	0.292252i	0.0387097	−	0.0670471i	−0.846021	−	0.533149i	$-0.821009\pi$
$19$	0.168732	−	0.292252i	0.0387097	−	0.0670471i	0.884731	+	0.466102i	$0.154342\pi$
$20$	−7.72863			−1.72818
$21$	−2.45489	−	0.986681i	−0.535700	−	0.215311i
$22$		−	0.161574i		−	0.0344477i
$23$	−3.94052	+	2.73356i	−0.821654	+	0.569986i
$23$	−3.94052	+	2.73356i	−0.821654	+	0.569986i
$24$	−0.840705	+	0.485381i	−0.171608	+	0.0990780i
$25$	−5.44142	−	9.42482i	−1.08828	−	1.88496i
$26$	−0.368860	−	0.212961i	−0.0723394	−	0.0417652i
$27$		−	1.00000i		−	0.192450i
$28$	1.91344	−	4.76069i	0.361606	−	0.899686i
$29$	−4.71500			−0.875554			−0.437777	−	0.899084i	$-0.644234\pi$
$29$	−4.71500			−0.875554			−0.437777	+	0.899084i	$0.644234\pi$
$30$	−0.850535	−	0.491056i	−0.155286	−	0.0896542i
$31$	3.64518	−	2.10455i	0.654694	−	0.377988i	−0.135558	−	0.990769i	$-0.543283\pi$
$31$	3.64518	−	2.10455i	0.654694	−	0.377988i	0.790252	+	0.612782i	$0.209950\pi$
$32$	−1.41918	−	2.45810i	−0.250879	−	0.434535i
$33$	−0.327827	+	0.567813i	−0.0570674	+	0.0988436i
$34$	−1.49488			−0.256370
$35$	10.4389	−	1.48634i	1.76450	−	0.251237i
$36$	1.93927			0.323212
$37$	−1.40646	−	0.812022i	−0.231221	−	0.133496i	0.379914	−	0.925022i	$-0.375954\pi$
$37$	−1.40646	−	0.812022i	−0.231221	−	0.133496i	−0.611135	+	0.791526i	$0.709287\pi$
$38$	0.0415808	+	0.0720201i	0.00674530	+	0.0116832i
$39$	0.864179	+	1.49680i	0.138379	+	0.239680i
$40$	1.93440	−	3.35049i	0.305856	−	0.529758i
$41$			6.67407i			1.04231i	0.853461	+	0.521157i	$0.174500\pi$
$41$			6.67407i			1.04231i	−0.853461	+	0.521157i	$0.825500\pi$
$42$	0.513055	−	0.402338i	0.0791661	−	0.0620821i
$43$			4.20924i			0.641903i	0.947096	+	0.320951i	$0.104003\pi$
$43$			4.20924i			0.641903i	−0.947096	+	0.320951i	$0.895997\pi$
$44$	−1.10114	−	0.635746i	−0.166004	−	0.0958423i
$45$	1.99266	+	3.45140i	0.297049	+	0.514504i
$46$	−0.0978515	−	1.17779i	−0.0144274	−	0.173655i
$47$	4.32275	+	2.49574i	0.630537	+	0.364041i	0.780960	−	0.624581i	$-0.214730\pi$
$47$	4.32275	+	2.49574i	0.630537	+	0.364041i	−0.150423	+	0.988622i	$0.548063\pi$
$48$			3.63932i			0.525290i
$49$	−1.66889	+	6.79815i	−0.238413	+	0.971164i
$50$	2.68188			0.379275
$51$	5.25340	+	3.03305i	0.735624	+	0.424712i
$52$	−2.90271	+	1.67588i	−0.402533	+	0.232402i
$53$	7.39119	−	4.26731i	1.01526	−	0.586160i	0.102532	−	0.994730i	$-0.467306\pi$
$53$	7.39119	−	4.26731i	1.01526	−	0.586160i	0.912727	+	0.408570i	$0.133972\pi$
$54$	0.213416	+	0.123216i	0.0290423	+	0.0167676i
$55$		−	2.61300i		−	0.352337i
$56$	1.58492	+	2.02106i	0.211794	+	0.270076i
$57$		−	0.337463i		−	0.0446981i
$58$	0.580964	−	1.00626i	0.0762843	−	0.132128i
$59$	9.78531	−	5.64955i	1.27394	−	0.735509i	0.298212	−	0.954500i	$-0.403610\pi$
$59$	9.78531	−	5.64955i	1.27394	−	0.735509i	0.975727	+	0.218991i	$0.0702764\pi$
$60$	−6.69319	+	3.86432i	−0.864088	+	0.498881i
$61$	2.14171	−	3.70955i	0.274218	−	0.474959i	−0.695720	−	0.718313i	$-0.744914\pi$
$61$	2.14171	−	3.70955i	0.274218	−	0.474959i	0.969937	+	0.243354i	$0.0782478\pi$
$62$			1.03726i			0.131732i
$63$	−2.61933	+	0.372952i	−0.330005	+	0.0469875i
$64$	−6.57917			−0.822396
$65$	−5.96525	−	3.44404i	−0.739898	−	0.427180i
$66$	−0.0807871	−	0.139927i	−0.00994421	−	0.0172239i
$67$	3.69254	−	2.13189i	0.451116	−	0.260452i	−0.257185	−	0.966362i	$-0.582795\pi$
$67$	3.69254	−	2.13189i	0.451116	−	0.260452i	0.708301	+	0.705910i	$0.249462\pi$
$68$	−5.88191	+	10.1878i	−0.713287	+	1.23545i
$69$	−2.04581	+	4.33759i	−0.246286	+	0.522184i
$70$	−0.969032	+	2.41097i	−0.115821	+	0.288166i
$71$	2.93387			0.348186			0.174093	−	0.984729i	$-0.444301\pi$
$71$	2.93387			0.348186			0.174093	+	0.984729i	$0.444301\pi$
$72$	−0.485381	+	0.840705i	−0.0572027	+	0.0990780i
$73$	12.7226	−	7.34541i	1.48907	−	0.859716i	0.489149	−	0.872200i	$-0.337307\pi$
$73$	12.7226	−	7.34541i	1.48907	−	0.859716i	0.999922	+	0.0124847i	$0.00397410\pi$
$74$	0.346598	−	0.200108i	0.0402912	−	0.0232621i
$75$	−9.42482	−	5.44142i	−1.08828	−	0.628322i
$76$	0.654432			0.0750685
$77$	1.60956	+	0.646922i	0.183426	+	0.0737235i
$78$	−0.425923			−0.0482263
$79$	9.76037	+	5.63515i	1.09813	+	0.634004i	0.935729	−	0.352721i	$-0.114743\pi$
$79$	9.76037	+	5.63515i	1.09813	+	0.634004i	0.162399	+	0.986725i	$0.448077\pi$
$80$	−7.25194	−	12.5607i	−0.810791	−	1.40433i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.42436	−	0.822352i	−0.157294	−	0.0908136i
$83$	12.4794			1.36979			0.684896	−	0.728641i	$-0.259848\pi$
$83$	12.4794			1.36979			0.684896	+	0.728641i	$0.259848\pi$
$84$	−0.723255	−	5.07960i	−0.0789136	−	0.554230i
$85$	−24.1754			−2.62219
$86$	−0.898321	−	0.518646i	−0.0968684	−	0.0559270i
$87$	−4.08331	+	2.35750i	−0.437777	+	0.252751i
$88$	0.551212	−	0.318242i	0.0587594	−	0.0339247i
$89$	−3.60989	+	6.25251i	−0.382647	+	0.662764i	−0.991440	−	0.130565i	$-0.958321\pi$
$89$	−3.60989	+	6.25251i	−0.382647	+	0.662764i	0.608793	+	0.793329i	$0.291654\pi$
$90$	−0.982113			−0.103524
$91$	3.59833	−	2.82181i	0.377207	−	0.295806i
$92$	−8.41176	−	3.96738i	−0.876987	−	0.413627i
$93$	2.10455	−	3.64518i	0.218231	−	0.377988i
$94$	−1.06526	+	0.615030i	−0.109874	+	0.0634355i
$95$	0.672451	+	1.16472i	0.0689920	+	0.119498i
$96$	−2.45810	−	1.41918i	−0.250879	−	0.144845i
$97$	14.9762			1.52060			0.760301	−	0.649571i	$-0.225052\pi$
$97$	14.9762			1.52060			0.760301	+	0.649571i	$0.225052\pi$
$98$	−1.24520	−	1.19381i	−0.125784	−	0.120593i
$99$			0.655654i			0.0658957i
$100$	10.5524	−	18.2773i	1.05524	−	1.82773i
$101$	−15.3151	+	8.84217i	−1.52391	+	0.879828i	−0.524308	+	0.851529i	$0.675676\pi$
$101$	−15.3151	+	8.84217i	−1.52391	+	0.879828i	−0.999599	+	0.0282995i	$0.990991\pi$
$102$	−1.29461	+	0.747442i	−0.128185	+	0.0740077i
$103$	5.96680	−	10.3348i	0.587927	−	1.01832i	−0.406577	−	0.913617i	$-0.633278\pi$
$103$	5.96680	−	10.3348i	0.587927	−	1.01832i	0.994504	−	0.104702i	$-0.0333890\pi$
$104$		−	1.67783i		−	0.164524i
$105$	8.29719	−	6.50666i	0.809723	−	0.634985i
$106$			2.10320i			0.204281i
$107$	−2.59532	−	1.49841i	−0.250899	−	0.144857i	0.369277	−	0.929320i	$-0.379605\pi$
$107$	−2.59532	−	1.49841i	−0.250899	−	0.144857i	−0.620176	+	0.784463i	$0.712939\pi$
$108$	1.67946	−	0.969636i	0.161606	−	0.0933032i
$109$	−11.4914	+	6.63459i	−1.10068	+	0.635478i	−0.936400	−	0.350935i	$-0.885864\pi$
$109$	−11.4914	+	6.63459i	−1.10068	+	0.635478i	−0.164281	+	0.986414i	$0.552530\pi$
$110$	0.557657	+	0.321963i	0.0531705	+	0.0306980i
$111$	−1.62404			−0.154147
$112$	9.53258	−	1.35729i	0.900744	−	0.128252i
$113$			2.69694i			0.253707i	0.991921	+	0.126854i	$0.0404878\pi$
$113$			2.69694i			0.253707i	−0.991921	+	0.126854i	$0.959512\pi$
$114$	0.0720201	+	0.0415808i	0.00674530	+	0.00389440i
$115$	−1.58247	−	19.0473i	−0.147566	−	1.77617i
$116$	−4.57184	−	7.91865i	−0.424484	−	0.735228i
$117$	1.49680	+	0.864179i	0.138379	+	0.0798934i
$118$			2.78446i			0.256330i
$119$	5.98531	−	14.8916i	0.548673	−	1.36511i
$120$		−	3.86881i		−	0.353172i
$121$	−5.28506	+	9.15399i	−0.480460	+	0.832181i
$122$	0.527785	+	0.914151i	0.0477834	+	0.0827634i
$123$	3.33703	+	5.77991i	0.300890	+	0.521157i
$124$	7.06899	+	4.08129i	0.634814	+	0.366510i
$125$	23.4451			2.09699
$126$	0.243150	−	0.604962i	0.0216615	−	0.0538943i
$127$	−3.15754			−0.280186			−0.140093	−	0.990138i	$-0.544740\pi$
$127$	−3.15754			−0.280186			−0.140093	+	0.990138i	$0.544740\pi$
$128$	3.64903	−	6.32030i	0.322532	−	0.558641i
$129$	2.10462	+	3.64531i	0.185301	+	0.320951i
$130$	1.47003	−	0.848721i	0.128930	−	0.0744378i
$131$	−16.9107	−	9.76340i	−1.47750	−	0.853032i	−0.477819	−	0.878459i	$-0.658572\pi$
$131$	−16.9107	−	9.76340i	−1.47750	−	0.853032i	−0.999677	+	0.0254262i	$0.991906\pi$
$132$	−1.27149			−0.110669
$133$	−0.883928	+	0.125858i	−0.0766463	+	0.0109132i
$134$			1.05073i			0.0907694i
$135$	3.45140	+	1.99266i	0.297049	+	0.171501i
$136$	−2.94438	−	5.09981i	−0.252478	−	0.437305i
$137$	4.17185	−	2.40862i	0.356425	−	0.205782i	−0.311086	−	0.950382i	$-0.600693\pi$
$137$	4.17185	−	2.40862i	0.356425	−	0.205782i	0.667512	+	0.744599i	$0.267359\pi$
$138$	−0.673636	−	0.971069i	−0.0573437	−	0.0826629i
$139$			14.9914i			1.27155i	0.771873	+	0.635776i	$0.219320\pi$
$139$			14.9914i			1.27155i	−0.771873	+	0.635776i	$0.780680\pi$
$140$	12.6182	+	16.0905i	1.06643	+	1.35990i
$141$	4.99148			0.420358
$142$	−0.361500	+	0.626136i	−0.0303364	+	0.0525441i
$143$	−0.566603	−	0.981385i	−0.0473817	−	0.0820675i
$144$	1.81966	+	3.15174i	0.151638	+	0.262645i
$145$	9.39542	−	16.2733i	0.780247	−	1.35143i
$146$			3.62029i			0.299617i
$147$	1.95377	+	6.72181i	0.161144	+	0.554406i
$148$		−	3.14946i		−	0.258884i
$149$	−0.619589	−	0.357720i	−0.0507587	−	0.0293056i	0.474406	−	0.880306i	$-0.342663\pi$
$149$	−0.619589	−	0.357720i	−0.0507587	−	0.0293056i	−0.525165	+	0.851001i	$0.675996\pi$
$150$	2.32258	−	1.34094i	0.189638	−	0.109487i
$151$	3.45795	+	5.98935i	0.281404	+	0.487407i	0.971731	−	0.236091i	$-0.0758665\pi$
$151$	3.45795	+	5.98935i	0.281404	+	0.487407i	−0.690327	+	0.723498i	$0.742533\pi$
$152$	−0.163798	+	0.283707i	−0.0132858	+	0.0230117i
$153$	6.06611			0.490416
$154$	−0.336387	+	0.263795i	−0.0271068	+	0.0212572i
$155$			16.7746i			1.34737i
$156$	−1.67588	+	2.90271i	−0.134178	+	0.232402i
$157$	0.122016	+	0.211339i	0.00973797	+	0.0168667i	0.870853	−	0.491543i	$-0.163567\pi$
$157$	0.122016	+	0.211339i	0.00973797	+	0.0168667i	−0.861115	+	0.508410i	$0.830234\pi$
$158$	−2.40527	+	1.38868i	−0.191353	+	0.110478i
$159$	4.26731	−	7.39119i	0.338420	−	0.586160i
$160$	11.3118			0.894279
$161$	12.1246	+	3.74094i	0.955551	+	0.294827i
$162$	0.246432			0.0193615
$163$	9.61189	−	16.6483i	0.752862	−	1.30399i	−0.193569	−	0.981087i	$-0.562006\pi$
$163$	9.61189	−	16.6483i	0.752862	−	1.30399i	0.946430	−	0.322908i	$-0.104660\pi$
$164$	−11.2088	+	6.47142i	−0.875262	+	0.505333i
$165$	−1.30650	−	2.26292i	−0.101711	−	0.176168i
$166$	−1.53766	+	2.66331i	−0.119346	+	0.206713i
$167$		−	9.42816i		−	0.729573i	−0.931091	−	0.364787i	$-0.881142\pi$
$167$		−	9.42816i		−	0.729573i	0.931091	−	0.364787i	$-0.118858\pi$
$168$	2.38311	+	0.957833i	0.183861	+	0.0738984i
$169$	10.0128			0.770214
$170$	2.97880	−	5.15943i	0.228464	−	0.395711i
$171$	−0.168732	−	0.292252i	−0.0129032	−	0.0223490i
$172$	−7.06924	+	4.08143i	−0.539025	+	0.311206i
$173$	−5.92661	−	3.42173i	−0.450592	−	0.260150i	0.257488	−	0.966281i	$-0.417105\pi$
$173$	−5.92661	−	3.42173i	−0.450592	−	0.260150i	−0.708080	+	0.706132i	$0.750439\pi$
$174$		−	1.16193i		−	0.0880855i
$175$	−10.7379	+	26.7161i	−0.811709	+	2.01955i
$176$		−	2.38613i		−	0.179862i
$177$	5.64955	−	9.78531i	0.424646	−	0.735509i
$178$	−0.889592	−	1.54082i	−0.0666777	−	0.115489i
$179$	3.44131	+	5.96052i	0.257215	+	0.445510i	0.965495	−	0.260422i	$-0.0838617\pi$
$179$	3.44131	+	5.96052i	0.257215	+	0.445510i	−0.708280	+	0.705932i	$0.750528\pi$
$180$	−3.86432	+	6.69319i	−0.288029	+	0.498881i
$181$	−19.3978			−1.44183			−0.720914	−	0.693025i	$-0.756278\pi$
$181$	−19.3978			−1.44183			−0.720914	+	0.693025i	$0.756278\pi$
$182$	0.158849	+	1.11563i	0.0117747	+	0.0826963i
$183$		−	4.28342i		−	0.316639i
$184$	3.82530	−	2.65364i	0.282005	−	0.195629i
$185$	5.60522	−	3.23618i	0.412104	−	0.237928i
$186$	0.518628	+	0.898289i	0.0380276	+	0.0658658i
$187$	−3.44442	−	1.98863i	−0.251881	−	0.145423i
$188$			9.67983i			0.705974i
$189$	−2.08193	+	1.63265i	−0.151438	+	0.118758i
$190$	−0.331427			−0.0240442
$191$	−22.6030	−	13.0499i	−1.63550	−	0.944254i	−0.982357	−	0.187017i	$-0.940118\pi$
$191$	−22.6030	−	13.0499i	−1.63550	−	0.944254i	−0.653140	−	0.757238i	$-0.726549\pi$
$192$	−5.69772	+	3.28958i	−0.411198	+	0.237405i
$193$	−5.41491	−	9.37890i	−0.389774	−	0.675108i	0.602645	−	0.798009i	$-0.294113\pi$
$193$	−5.41491	−	9.37890i	−0.389774	−	0.675108i	−0.992419	+	0.122901i	$0.960780\pi$
$194$	−1.84531	+	3.19616i	−0.132485	+	0.229471i
$195$	−6.88808			−0.493265
$196$	−13.0354	+	3.78889i	−0.931101	+	0.270635i
$197$	−9.15072			−0.651962			−0.325981	−	0.945376i	$-0.605695\pi$
$197$	−9.15072			−0.651962			−0.325981	+	0.945376i	$0.605695\pi$
$198$	−0.139927	−	0.0807871i	−0.00994421	−	0.00574129i
$199$	9.66202	+	16.7351i	0.684923	+	1.18632i	0.973461	+	0.228853i	$0.0734974\pi$
$199$	9.66202	+	16.7351i	0.684923	+	1.18632i	−0.288538	+	0.957468i	$0.593169\pi$
$200$	5.28233	+	9.14927i	0.373517	+	0.646951i
$201$	2.13189	−	3.69254i	0.150372	−	0.260452i
$202$		−	4.35799i		−	0.306627i
$203$	7.69796	+	9.81632i	0.540291	+	0.688971i
$204$			11.7638i			0.823633i
$205$	−23.0349	−	13.2992i	−1.60882	−	0.928855i
$206$	1.47041	+	2.54683i	0.102448	+	0.177446i
$207$	0.397073	+	4.77937i	0.0275985	+	0.332189i
$208$	−5.44733	−	3.14502i	−0.377705	−	0.218068i
$209$			0.221259i			0.0153048i
$210$	0.366281	+	2.57248i	0.0252758	+	0.177518i
$211$	−4.81173			−0.331253			−0.165626	−	0.986189i	$-0.552965\pi$
$211$	−4.81173			−0.331253			−0.165626	+	0.986189i	$0.552965\pi$
$212$	14.3335	+	8.27547i	0.984431	+	0.568361i
$213$	2.54081	−	1.46693i	0.174093	−	0.100513i
$214$	0.639571	−	0.369256i	0.0437201	−	0.0252418i
$215$	−14.5278	−	8.38760i	−0.990784	−	0.572030i
$216$			0.970763i			0.0660520i
$217$	−10.3328	−	4.15303i	−0.701439	−	0.281926i
$218$		−	3.26995i		−	0.221469i
$219$	7.34541	−	12.7226i	0.496357	−	0.859716i
$220$	4.38842	−	2.53366i	0.295867	−	0.170819i
$221$	−9.07976	+	5.24220i	−0.610771	+	0.352629i
$222$	0.200108	−	0.346598i	0.0134304	−	0.0232621i
$223$			22.0462i			1.47632i	0.674625	+	0.738160i	$0.264305\pi$
$223$			22.0462i			1.47632i	−0.674625	+	0.738160i	$0.735695\pi$
$224$	−2.80056	+	6.96787i	−0.187121	+	0.465560i
$225$	−10.8828			−0.725523
$226$	−0.575572	−	0.332307i	−0.0382865	−	0.0221047i
$227$	0.0667898	+	0.115683i	0.00443299	+	0.00767817i	0.868233	−	0.496156i	$-0.165256\pi$
$227$	0.0667898	+	0.115683i	0.00443299	+	0.00767817i	−0.863800	+	0.503834i	$0.831922\pi$
$228$	0.566755	−	0.327216i	0.0375343	−	0.0216704i
$229$	−13.6209	+	23.5922i	−0.900097	+	1.55901i	−0.0727313	+	0.997352i	$0.523172\pi$
$229$	−13.6209	+	23.5922i	−0.900097	+	1.55901i	−0.827366	+	0.561663i	$0.810162\pi$
$230$	4.26000	+	2.00921i	0.280896	+	0.132484i
$231$	1.71738	−	0.244528i	0.112995	−	0.0160887i
$232$	4.57715			0.300505
$233$	5.46430	−	9.46445i	0.357978	−	0.620037i	−0.629645	−	0.776883i	$-0.716799\pi$
$233$	5.46430	−	9.46445i	0.357978	−	0.620037i	0.987623	+	0.156846i	$0.0501328\pi$
$234$	−0.368860	+	0.212961i	−0.0241131	+	0.0139217i
$235$	−17.2276	+	9.94634i	−1.12380	+	0.648828i
$236$	18.9764	+	10.9560i	1.23526	+	0.713176i
$237$	11.2703			0.732085
$238$	2.44062	+	3.11225i	0.158202	+	0.201737i
$239$	−4.25183			−0.275028			−0.137514	−	0.990500i	$-0.543911\pi$
$239$	−4.25183			−0.275028			−0.137514	+	0.990500i	$0.543911\pi$
$240$	−12.5607	−	7.25194i	−0.810791	−	0.468110i
$241$	−12.0856	−	20.9328i	−0.778499	−	1.34840i	−0.932807	−	0.360377i	$-0.882648\pi$
$241$	−12.0856	−	20.9328i	−0.778499	−	1.34840i	0.154308	−	0.988023i	$-0.450685\pi$
$242$	−1.30241	−	2.25584i	−0.0837219	−	0.145011i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	8.30671			0.531782
$245$	−20.1376	−	19.3064i	−1.28654	−	1.23344i
$246$	−1.64470			−0.104863
$247$	0.505115	+	0.291628i	0.0321397	+	0.0185559i
$248$	−3.53860	+	2.04301i	−0.224702	+	0.129732i
$249$	10.8075	−	6.23970i	0.684896	−	0.395425i
$250$	−2.88881	+	5.00357i	−0.182704	+	0.316453i
$251$	−15.7258			−0.992605			−0.496303	−	0.868150i	$-0.665309\pi$
$251$	−15.7258			−0.992605			−0.496303	+	0.868150i	$0.665309\pi$
$252$	−3.16616	−	4.03743i	−0.199449	−	0.254334i
$253$	1.34134	−	2.84396i	0.0843295	−	0.178798i
$254$	0.389059	−	0.673870i	0.0244117	−	0.0422824i
$255$	−20.9365	+	12.0877i	−1.31110	+	0.756962i
$256$	−5.67993	−	9.83793i	−0.354996	−	0.614870i
$257$	16.8596	+	9.73392i	1.05168	+	0.607185i	0.923118	−	0.384517i	$-0.125632\pi$
$257$	16.8596	+	9.73392i	1.05168	+	0.607185i	0.128558	+	0.991702i	$0.458965\pi$
$258$	−1.03729			−0.0645789
$259$	0.605691	+	4.25391i	0.0376358	+	0.264325i
$260$		−	13.3578i		−	0.828419i
$261$	−2.35750	+	4.08331i	−0.145926	+	0.252751i
$262$	4.16734	−	2.40601i	0.257459	−	0.148644i
$263$	−3.70369	+	2.13833i	−0.228379	+	0.131855i	−0.609824	−	0.792537i	$-0.708760\pi$
$263$	−3.70369	+	2.13833i	−0.228379	+	0.131855i	0.381445	+	0.924392i	$0.375427\pi$
$264$	0.318242	−	0.551212i	0.0195865	−	0.0339247i
$265$			34.0133i			2.08942i
$266$	0.0820540	−	0.204152i	0.00503106	−	0.0125174i
$267$			7.21977i			0.441843i
$268$	7.16084	+	4.13431i	0.437418	+	0.252543i
$269$	16.1755	−	9.33893i	0.986238	−	0.569405i	0.0820901	−	0.996625i	$-0.473840\pi$
$269$	16.1755	−	9.33893i	0.986238	−	0.569405i	0.904148	+	0.427220i	$0.140507\pi$
$270$	−0.850535	+	0.491056i	−0.0517619	+	0.0298847i
$271$	15.9437	+	9.20509i	0.968510	+	0.559170i	0.898782	−	0.438396i	$-0.144453\pi$
$271$	15.9437	+	9.20509i	0.968510	+	0.559170i	0.0697285	+	0.997566i	$0.477787\pi$
$272$	−22.0765			−1.33858
$273$	1.70534	−	4.24292i	0.103212	−	0.256793i
$274$			1.18712i			0.0717167i
$275$	6.17943	+	3.56769i	0.372633	+	0.215140i
$276$	−9.26849	+	0.770032i	−0.557897	+	0.0463505i
$277$	−1.62257	−	2.81038i	−0.0974910	−	0.168859i	0.813154	−	0.582048i	$-0.197748\pi$
$277$	−1.62257	−	2.81038i	−0.0974910	−	0.168859i	−0.910646	+	0.413188i	$0.864415\pi$
$278$	−3.19941	−	1.84718i	−0.191888	−	0.110786i
$279$		−	4.20909i		−	0.251992i
$280$	−10.1337	+	1.44288i	−0.605604	+	0.0862286i
$281$		−	27.7593i		−	1.65598i	−0.560740	−	0.827992i	$-0.689483\pi$
$281$		−	27.7593i		−	1.65598i	0.560740	−	0.827992i	$-0.310517\pi$
$282$	−0.615030	+	1.06526i	−0.0366245	+	0.0634355i
$283$	5.75864	+	9.97426i	0.342316	+	0.592908i	0.984862	−	0.173338i	$-0.0554554\pi$
$283$	5.75864	+	9.97426i	0.342316	+	0.592908i	−0.642547	+	0.766247i	$0.722122\pi$
$284$	2.84478	+	4.92731i	0.168807	+	0.292382i
$285$	1.16472	+	0.672451i	0.0689920	+	0.0398325i
$286$	0.279258			0.0165129
$287$	13.8950	−	10.8964i	0.820194	−	0.643196i
$288$	−2.83837			−0.167252
$289$	−9.89883	+	17.1453i	−0.582284	+	1.00855i
$290$	2.31533	+	4.01027i	0.135961	+	0.235491i
$291$	12.9698	−	7.48809i	0.760301	−	0.438960i
$292$	24.6726	+	14.2447i	1.44386	+	0.833611i
$293$	1.71184			0.100007			0.0500033	−	0.998749i	$-0.484077\pi$
$293$	1.71184			0.100007			0.0500033	+	0.998749i	$0.484077\pi$
$294$	−1.67528	−	0.411268i	−0.0977044	−	0.0239857i
$295$			45.0306i			2.62179i
$296$	1.36534	+	0.788281i	0.0793589	+	0.0458179i
$297$	0.327827	+	0.567813i	0.0190225	+	0.0329479i
$298$	0.152687	−	0.0881536i	0.00884489	−	0.00510660i
$299$	−4.72457	−	6.81062i	−0.273229	−	0.393868i
$300$		−	21.1048i		−	1.21849i
$301$	8.76335	−	6.87222i	0.505111	−	0.396108i
$302$	−1.70430			−0.0980715
$303$	−8.84217	+	15.3151i	−0.507969	+	0.879828i
$304$	0.614067	+	1.06360i	0.0352192	+	0.0610014i
$305$	8.53541	+	14.7838i	0.488736	+	0.846516i
$306$	−0.747442	+	1.29461i	−0.0427284	+	0.0740077i
$307$			9.12986i			0.521069i	0.965465	+	0.260534i	$0.0838987\pi$
$307$			9.12986i			0.521069i	−0.965465	+	0.260534i	$0.916101\pi$
$308$	0.474205	+	3.33046i	0.0270204	+	0.189771i
$309$		−	11.9336i		−	0.678879i
$310$	−3.57998	−	2.06690i	−0.203329	−	0.117392i
$311$	20.3637	−	11.7570i	1.15472	−	0.666677i	0.204686	−	0.978828i	$-0.434383\pi$
$311$	20.3637	−	11.7570i	1.15472	−	0.666677i	0.950033	+	0.312150i	$0.101049\pi$
$312$	−0.838913	−	1.45304i	−0.0474941	−	0.0822622i
$313$	−11.7299	+	20.3169i	−0.663015	+	1.14838i	0.316804	+	0.948491i	$0.397390\pi$
$313$	−11.7299	+	20.3169i	−0.663015	+	1.14838i	−0.979819	+	0.199885i	$0.935943\pi$
$314$	−0.0601375			−0.00339376
$315$	3.93225	−	9.78353i	0.221557	−	0.551239i
$316$			21.8562i			1.22951i
$317$	5.50215	−	9.53000i	0.309031	−	0.535258i	−0.669119	−	0.743155i	$-0.733328\pi$
$317$	5.50215	−	9.53000i	0.309031	−	0.535258i	0.978151	+	0.207897i	$0.0666618\pi$
$318$	1.05160	+	1.82143i	0.0589709	+	0.102141i
$319$	2.67724	−	1.54571i	0.149897	−	0.0865429i
$320$	13.1101	−	22.7073i	0.732875	−	1.26938i
$321$	−2.99682			−0.167266
$322$	−2.29232	+	2.12664i	−0.127746	+	0.118513i
$323$	2.04709			0.113903
$324$	0.969636	−	1.67946i	0.0538686	−	0.0933032i
$325$	16.2895	−	9.40473i	0.903577	−	0.521681i
$326$	2.36868	+	4.10267i	0.131189	+	0.227226i
$327$	−6.63459	+	11.4914i	−0.366894	+	0.635478i
$328$		−	6.47894i		−	0.357739i
$329$	−1.86158	−	13.0743i	−0.102632	−	0.720812i
$330$	0.643926			0.0354470
$331$	3.71216	−	6.42964i	0.204039	−	0.353405i	−0.745787	−	0.666184i	$-0.767927\pi$
$331$	3.71216	−	6.42964i	0.204039	−	0.353405i	0.949826	+	0.312779i	$0.101260\pi$
$332$	12.1005	+	20.9586i	0.664099	+	1.15025i
$333$	−1.40646	+	0.812022i	−0.0770737	+	0.0444985i
$334$	2.01212	+	1.16170i	0.110099	+	0.0635654i
$335$			16.9926i			0.928403i
$336$	7.57681	−	5.94174i	0.413349	−	0.324148i
$337$		−	33.7933i		−	1.84084i	−0.390930	−	0.920420i	$-0.627847\pi$
$337$		−	33.7933i		−	1.84084i	0.390930	−	0.920420i	$-0.372153\pi$
$338$	−1.23373	+	2.13689i	−0.0671063	+	0.116232i
$339$	1.34847	+	2.33562i	0.0732389	+	0.126854i
$340$	−23.4414	−	40.6016i	−1.27129	−	2.20193i
$341$	−1.37985	+	2.38998i	−0.0747233	+	0.129425i
$342$	0.0831617			0.00449687
$343$	16.8780	−	7.62449i	0.911327	−	0.411684i
$344$		−	4.08617i		−	0.220312i
$345$	−10.8941	−	15.7043i	−0.586520	−	0.845488i
$346$	1.46051	−	0.843224i	0.0785174	−	0.0453320i
$347$	−11.0306	−	19.1055i	−0.592153	−	1.02564i	−0.993942	−	0.109907i	$-0.964945\pi$
$347$	−11.0306	−	19.1055i	−0.592153	−	1.02564i	0.401789	−	0.915732i	$-0.368389\pi$
$348$	−7.91865	−	4.57184i	−0.424484	−	0.245076i
$349$		−	9.37354i		−	0.501754i	−0.968019	−	0.250877i	$-0.919281\pi$
$349$		−	9.37354i		−	0.501754i	0.968019	−	0.250877i	$-0.0807190\pi$
$350$	−4.37858	−	5.58350i	−0.234045	−	0.298451i
$351$	1.72836			0.0922529
$352$	1.61166	+	0.930494i	0.0859020	+	0.0495955i
$353$	−19.5497	+	11.2870i	−1.04052	+	0.600747i	−0.919982	−	0.391962i	$-0.871797\pi$
$353$	−19.5497	+	11.2870i	−1.04052	+	0.600747i	−0.120542	+	0.992708i	$0.538463\pi$
$354$	1.39223	+	2.41141i	0.0739962	+	0.128165i
$355$	−5.84622	+	10.1259i	−0.310285	+	0.537429i
$356$	−14.0011			−0.742057
$357$	−2.26237	−	15.8892i	−0.119737	−	0.840943i
$358$	−1.69610			−0.0896415
$359$	−1.00068	−	0.577743i	−0.0528139	−	0.0304921i	0.473361	−	0.880869i	$-0.343041\pi$
$359$	−1.00068	−	0.577743i	−0.0528139	−	0.0304921i	−0.526174	+	0.850377i	$0.676374\pi$
$360$	−1.93440	−	3.35049i	−0.101952	−	0.176586i
$361$	9.44306	+	16.3559i	0.497003	+	0.860835i
$362$	2.39012	−	4.13981i	0.125622	−	0.217584i
$363$			10.5701i			0.554787i
$364$	8.22817	+	3.30711i	0.431274	+	0.173340i
$365$			58.5478i			3.06453i
$366$	0.914151	+	0.527785i	0.0477834	+	0.0275878i
$367$	0.804722	+	1.39382i	0.0420061	+	0.0727567i	0.886264	−	0.463180i	$-0.153292\pi$
$367$	0.804722	+	1.39382i	0.0420061	+	0.0727567i	−0.844258	+	0.535937i	$0.819958\pi$
$368$	−1.44507	−	17.3936i	−0.0753297	−	0.906705i
$369$	5.77991	+	3.33703i	0.300890	+	0.173719i
$370$			1.59499i			0.0829198i
$371$	−20.9515	−	8.42094i	−1.08775	−	0.437193i
$372$	8.16257			0.423210
$373$	8.02098	+	4.63092i	0.415311	+	0.239780i	0.693069	−	0.720871i	$-0.256258\pi$
$373$	8.02098	+	4.63092i	0.415311	+	0.239780i	−0.277758	+	0.960651i	$0.589591\pi$
$374$	0.848815	−	0.490063i	0.0438912	−	0.0253406i
$375$	20.3040	−	11.7225i	1.04850	−	0.605350i
$376$	−4.19636	−	2.42277i	−0.216411	−	0.124945i
$377$		−	8.14921i		−	0.419706i
$378$	−0.0919073	−	0.645488i	−0.00472720	−	0.0332003i
$379$			18.8381i			0.967650i	0.875165	+	0.483825i	$0.160753\pi$
$379$			18.8381i			0.967650i	−0.875165	+	0.483825i	$0.839247\pi$
$380$	−1.30406	+	2.25871i	−0.0668971	+	0.115869i
$381$	−2.73451	+	1.57877i	−0.140093	+	0.0808827i
$382$	5.57010	−	3.21590i	0.284991	−	0.164540i
$383$	−7.43036	+	12.8698i	−0.379674	+	0.657614i	−0.991015	−	0.133753i	$-0.957297\pi$
$383$	−7.43036	+	12.8698i	−0.379674	+	0.657614i	0.611341	+	0.791367i	$0.290630\pi$
$384$		−	7.29806i		−	0.372427i
$385$	−5.44009	+	4.26612i	−0.277253	+	0.217422i
$386$	2.66881			0.135839
$387$	3.64531	+	2.10462i	0.185301	+	0.106984i
$388$	14.5214	+	25.1519i	0.737215	+	1.27689i
$389$	19.2447	−	11.1109i	0.975744	−	0.563346i	0.0747612	−	0.997201i	$-0.476181\pi$
$389$	19.2447	−	11.1109i	0.975744	−	0.563346i	0.900982	+	0.433856i	$0.142847\pi$
$390$	0.848721	−	1.47003i	0.0429767	−	0.0744378i
$391$	−26.3123	−	12.4101i	−1.33067	−	0.627605i
$392$	1.62010	−	6.59939i	0.0818273	−	0.333319i
$393$	−19.5268			−0.984997
$394$	1.12752	−	1.95291i	0.0568034	−	0.0983864i
$395$	−38.8983	+	22.4579i	−1.95719	+	1.12998i
$396$	−1.10114	+	0.635746i	−0.0553346	+	0.0319474i
$397$	−13.9063	−	8.02882i	−0.697938	−	0.402955i	0.108641	−	0.994081i	$-0.465350\pi$
$397$	−13.9063	−	8.02882i	−0.697938	−	0.402955i	−0.806579	+	0.591126i	$0.798683\pi$
$398$	−4.76206			−0.238701
$399$	−0.702575	+	0.550960i	−0.0351728	+	0.0275825i
$400$	39.6061			1.98031
$401$	24.1971	+	13.9702i	1.20835	+	0.697640i	0.962398	−	0.271643i	$-0.0875669\pi$
$401$	24.1971	+	13.9702i	1.20835	+	0.697640i	0.245950	+	0.969283i	$0.420900\pi$
$402$	0.525366	+	0.909961i	0.0262029	+	0.0453847i
$403$	3.63741	+	6.30018i	0.181192	+	0.313834i
$404$	−29.7001	−	17.1474i	−1.47763	−	0.853113i
$405$	3.98533			0.198033
$406$	−3.04348	+	0.433343i	−0.151045	+	0.0215065i
$407$	1.06481			0.0527808
$408$	−5.09981	−	2.94438i	−0.252478	−	0.145768i
$409$	27.0614	−	15.6239i	1.33810	−	0.772551i	0.351573	−	0.936161i	$-0.385647\pi$
$409$	27.0614	−	15.6239i	1.33810	−	0.772551i	0.986525	+	0.163610i	$0.0523137\pi$
$410$	5.67653	−	3.27734i	0.280344	−	0.161856i
$411$	2.40862	−	4.17185i	0.118808	−	0.205782i
$412$	23.1425			1.14015
$413$	−27.7380	−	11.1486i	−1.36490	−	0.548587i
$414$	−1.06892	−	0.504152i	−0.0525346	−	0.0247777i
$415$	−24.8672	+	43.0713i	−1.22069	+	2.11429i
$416$	4.24848	−	2.45286i	0.208299	−	0.120261i
$417$	7.49569	+	12.9829i	0.367066	+	0.635776i
$418$	−0.0472203	−	0.0272627i	−0.00230962	−	0.00133346i
$419$	9.51570			0.464872			0.232436	−	0.972612i	$-0.425330\pi$
$419$	9.51570			0.464872			0.232436	+	0.972612i	$0.425330\pi$
$420$	18.9729	+	7.62569i	0.925783	+	0.372096i
$421$		−	24.5804i		−	1.19798i	−0.800758	−	0.598988i	$-0.795570\pi$
$421$		−	24.5804i		−	1.19798i	0.800758	−	0.598988i	$-0.204430\pi$
$422$	0.592882	−	1.02690i	0.0288610	−	0.0499888i
$423$	4.32275	−	2.49574i	0.210179	−	0.121347i
$424$	−7.17509	+	4.14254i	−0.348453	+	0.201180i
$425$	33.0083	−	57.1720i	1.60114	−	2.77325i
$426$			0.722999i			0.0350294i
$427$	−11.2197	+	1.59751i	−0.542959	+	0.0773089i
$428$		−	5.81165i		−	0.280917i
$429$	−0.981385	−	0.566603i	−0.0473817	−	0.0273558i
$430$	3.58010	−	2.06697i	0.172648	−	0.0996783i
$431$	−1.14983	+	0.663853i	−0.0553852	+	0.0319767i	−0.527437	−	0.849594i	$-0.676847\pi$
$431$	−1.14983	+	0.663853i	−0.0553852	+	0.0319767i	0.472052	+	0.881571i	$0.343514\pi$
$432$	3.15174	+	1.81966i	0.151638	+	0.0875483i
$433$	16.6799			0.801584			0.400792	−	0.916169i	$-0.368735\pi$
$433$	16.6799			0.801584			0.400792	+	0.916169i	$0.368735\pi$
$434$	2.15950	−	1.69348i	0.103659	−	0.0812895i
$435$		−	18.7908i		−	0.900952i
$436$	−22.2850	−	12.8663i	−1.06726	−	0.616183i
$437$	0.133997	+	1.61286i	0.00640997	+	0.0771535i
$438$	1.81014	+	3.13526i	0.0864921	+	0.149809i
$439$	22.9037	+	13.2235i	1.09313	+	0.631122i	0.934409	−	0.356201i	$-0.115928\pi$
$439$	22.9037	+	13.2235i	1.09313	+	0.631122i	0.158725	+	0.987323i	$0.449262\pi$
$440$			2.53660i			0.120928i
$441$	5.05292	+	4.84438i	0.240615	+	0.230685i
$442$		−	2.58369i		−	0.122894i
$443$	9.59561	−	16.6201i	0.455901	−	0.789644i	−0.542838	−	0.839837i	$-0.682650\pi$
$443$	9.59561	−	16.6201i	0.455901	−	0.789644i	0.998740	+	0.0501933i	$0.0159837\pi$
$444$	−1.57473	−	2.72751i	−0.0747334	−	0.129442i
$445$	−14.3866	−	24.9183i	−0.681990	−	1.18124i
$446$	−4.70501	−	2.71644i	−0.222789	−	0.128627i
$447$	−0.715440			−0.0338391
$448$	10.7415	+	13.6974i	0.507488	+	0.647141i
$449$	−24.2883			−1.14624			−0.573119	−	0.819472i	$-0.694267\pi$
$449$	−24.2883			−1.14624			−0.573119	+	0.819472i	$0.694267\pi$
$450$	1.34094	−	2.32258i	0.0632126	−	0.109487i
$451$	−2.18794	−	3.78963i	−0.103026	−	0.178446i
$452$	−4.52940	+	2.61505i	−0.213045	+	0.123002i
$453$	5.98935	+	3.45795i	0.281404	+	0.162469i
$454$	−0.0329183			−0.00154493
$455$	2.56892	+	18.0422i	0.120433	+	0.845830i
$456$			0.327596i			0.0153411i
$457$	11.4347	+	6.60181i	0.534892	+	0.308820i	0.743006	−	0.669285i	$-0.233399\pi$
$457$	11.4347	+	6.60181i	0.534892	+	0.308820i	−0.208114	+	0.978104i	$0.566733\pi$
$458$	−3.35664	−	5.81387i	−0.156845	−	0.271664i
$459$	5.25340	−	3.03305i	0.245208	−	0.141571i
$460$	30.4548	−	21.1267i	1.41996	−	0.985036i
$461$		−	11.2165i		−	0.522402i	−0.965284	−	0.261201i	$-0.915881\pi$
$461$		−	11.2165i		−	0.522402i	0.965284	−	0.261201i	$-0.0841186\pi$
$462$	−0.159422	+	0.396646i	−0.00741699	+	0.0184536i
$463$	7.69763			0.357739			0.178870	−	0.983873i	$-0.442756\pi$
$463$	7.69763			0.357739			0.178870	+	0.983873i	$0.442756\pi$
$464$	8.57969	−	14.8605i	0.398302	−	0.689880i
$465$	8.38731	+	14.5272i	0.388952	+	0.673685i
$466$	1.34658	+	2.33234i	0.0623791	+	0.108044i
$467$	−2.98084	+	5.16296i	−0.137937	+	0.238913i	−0.926715	−	0.375764i	$-0.877380\pi$
$467$	−2.98084	+	5.16296i	−0.137937	+	0.238913i	0.788779	+	0.614677i	$0.210714\pi$
$468$			3.35176i			0.154935i
$469$	−10.4671	−	4.20699i	−0.483325	−	0.194261i
$470$		−	4.90219i		−	0.226121i
$471$	0.211339	+	0.122016i	0.00973797	+	0.00562222i
$472$	−9.49921	+	5.48437i	−0.437237	+	0.252439i
$473$	−1.37990	−	2.39006i	−0.0634480	−	0.109895i
$474$	−1.38868	+	2.40527i	−0.0637843	+	0.110478i
$475$	−3.67256			−0.168509
$476$	30.8134	−	4.38734i	1.41233	−	0.201094i
$477$		−	8.53462i		−	0.390773i
$478$	0.523893	−	0.907409i	0.0239623	−	0.0415039i
$479$	−4.36834	−	7.56619i	−0.199595	−	0.345708i	0.748802	−	0.662793i	$-0.230629\pi$
$479$	−4.36834	−	7.56619i	−0.199595	−	0.345708i	−0.948397	+	0.317085i	$0.897296\pi$
$480$	9.79634	−	5.65592i	0.447140	−	0.258156i
$481$	1.40347	−	2.43087i	0.0639925	−	0.110838i
$482$	5.95654			0.271313
$483$	12.3707	−	2.82254i	0.562885	−	0.128430i
$484$	−20.4983			−0.931742
$485$	−29.8425	+	51.6888i	−1.35508	+	2.34707i
$486$	0.213416	−	0.123216i	0.00968076	−	0.00558919i
$487$	−14.8741	−	25.7627i	−0.674010	−	1.16742i	−0.976757	−	0.214348i	$-0.931237\pi$
$487$	−14.8741	−	25.7627i	−0.674010	−	1.16742i	0.302748	−	0.953071i	$-0.402096\pi$
$488$	−2.07909	+	3.60109i	−0.0941160	+	0.163014i
$489$		−	19.2238i		−	0.869330i
$490$	6.60158	−	1.91882i	0.298229	−	0.0866836i
$491$	2.54212			0.114724			0.0573620	−	0.998353i	$-0.481731\pi$
$491$	2.54212			0.114724			0.0573620	+	0.998353i	$0.481731\pi$
$492$	−6.47142	+	11.2088i	−0.291754	+	0.505333i
$493$	−14.3009	−	24.7698i	−0.644078	−	1.11558i
$494$	−0.124477	+	0.0718666i	−0.00560047	+	0.00323343i
$495$	−2.26292	−	1.30650i	−0.101711	−	0.0587228i
$496$			15.3182i			0.687808i
$497$	−4.78999	−	6.10812i	−0.214860	−	0.273987i
$498$			3.07532i			0.137808i
$499$	10.1398	−	17.5626i	0.453918	−	0.786210i	−0.544707	−	0.838626i	$-0.683359\pi$
$499$	10.1398	−	17.5626i	0.453918	−	0.786210i	0.998625	+	0.0524168i	$0.0166924\pi$
$500$	22.7332	+	39.3750i	1.01666	+	1.76091i
$501$	−4.71408	−	8.16503i	−0.210610	−	0.364787i
$502$	1.93767	−	3.35615i	0.0864826	−	0.149792i
$503$	−16.8507			−0.751335			−0.375668	−	0.926754i	$-0.622587\pi$
$503$	−16.8507			−0.751335			−0.375668	+	0.926754i	$0.622587\pi$
$504$	2.54275	−	0.362048i	0.113263	−	0.0161269i
$505$		−	70.4779i		−	3.13622i
$506$	0.441673	+	0.636686i	0.0196347	+	0.0283041i
$507$	8.67132	−	5.00639i	0.385107	−	0.222342i
$508$	−3.06166	−	5.30295i	−0.135839	−	0.235280i
$509$	20.7071	+	11.9552i	0.917825	+	0.529906i	0.882941	−	0.469485i	$-0.155560\pi$
$509$	20.7071	+	11.9552i	0.917825	+	0.529906i	0.0348844	+	0.999391i	$0.488894\pi$
$510$		−	5.95760i		−	0.263807i
$511$	−36.0643	−	14.4952i	−1.59539	−	0.641228i
$512$	17.3955			0.768782
$513$	−0.292252	−	0.168732i	−0.0129032	−	0.00744968i
$514$	−4.15476	+	2.39875i	−0.183258	+	0.105804i
$515$	23.7797	+	41.1876i	1.04786	+	1.81494i
$516$	−4.08143	+	7.06924i	−0.179675	+	0.311206i
$517$	−3.27268			−0.143932
$518$	−0.982486	−	0.394886i	−0.0431679	−	0.0173503i
$519$	−6.84347			−0.300395
$520$	5.79084	+	3.34334i	0.253945	+	0.146615i
$521$	−8.69551	−	15.0611i	−0.380957	−	0.659837i	0.610242	−	0.792215i	$-0.291072\pi$
$521$	−8.69551	−	15.0611i	−0.380957	−	0.659837i	−0.991199	+	0.132378i	$0.957739\pi$
$522$	−0.580964	−	1.00626i	−0.0254281	−	0.0440428i
$523$	−14.4355	+	25.0030i	−0.631219	+	1.09330i	0.356084	+	0.934454i	$0.384112\pi$
$523$	−14.4355	+	25.0030i	−0.631219	+	1.09330i	−0.987303	+	0.158850i	$0.949221\pi$
$524$		−	37.8678i		−	1.65426i
$525$	4.05878	+	28.5058i	0.177140	+	1.24410i
$526$		−	1.05390i		−	0.0459524i
$527$	22.1121	+	12.7664i	0.963216	+	0.556113i
$528$	−1.19307	−	2.06645i	−0.0519216	−	0.0899308i
$529$	8.05532	−	21.5433i	0.350231	−	0.936663i
$530$	−7.25899	−	4.19098i	−0.315310	−	0.182044i
$531$		−	11.2991i		−	0.490339i
$532$	−1.06846	−	1.36248i	−0.0463236	−	0.0590712i
$533$	−11.5352			−0.499644
$534$	−1.54082	−	0.889592i	−0.0666777	−	0.0384964i
$535$	10.3432	−	5.97166i	0.447176	−	0.258177i
$536$	−3.58458	+	2.06956i	−0.154830	+	0.0893914i
$537$	5.96052	+	3.44131i	0.257215	+	0.148503i
$538$			4.60282i			0.198442i
$539$	−1.28100	−	4.40719i	−0.0551765	−	0.189831i
$540$			7.72863i			0.332587i
$541$	−17.3882	+	30.1173i	−0.747579	+	1.29484i	0.201401	+	0.979509i	$0.435451\pi$
$541$	−17.3882	+	30.1173i	−0.747579	+	1.29484i	−0.948980	+	0.315336i	$0.897883\pi$
$542$	−3.92904	+	2.26843i	−0.168767	+	0.0974374i
$543$	−16.7990	+	9.69891i	−0.720914	+	0.416220i
$544$	8.60893	−	14.9111i	0.369105	−	0.639308i
$545$		−	52.8821i		−	2.26522i
$546$	0.695384	+	0.886743i	0.0297597	+	0.0379491i
$547$	37.1612			1.58890			0.794449	−	0.607331i	$-0.207760\pi$
$547$	37.1612			1.58890			0.794449	+	0.607331i	$0.207760\pi$
$548$	8.09035	+	4.67097i	0.345603	+	0.199534i
$549$	−2.14171	−	3.70955i	−0.0914059	−	0.158320i
$550$	−1.52281	+	0.879194i	−0.0649328	+	0.0374890i
$551$	−0.795570	+	1.37797i	−0.0338924	+	0.0587034i
$552$	1.98599	−	4.21077i	0.0845295	−	0.179222i
$553$	−4.20328	−	29.5207i	−0.178742	−	1.25535i
$554$	0.799708			0.0339764
$555$	3.23618	−	5.60522i	0.137368	−	0.237928i
$556$	−25.1774	+	14.5362i	−1.06776	+	0.616471i
$557$	−12.6316	+	7.29288i	−0.535219	+	0.309009i	−0.743139	−	0.669137i	$-0.766664\pi$
$557$	−12.6316	+	7.29288i	−0.535219	+	0.309009i	0.207920	+	0.978146i	$0.433331\pi$
$558$	0.898289	+	0.518628i	0.0380276	+	0.0219553i
$559$	−7.27507			−0.307703
$560$	−14.3107	+	35.6053i	−0.604737	+	1.50460i
$561$	−3.97727			−0.167920
$562$	5.92430	+	3.42040i	0.249902	+	0.144281i
$563$	−4.97857	−	8.62314i	−0.209822	−	0.363422i	0.741837	−	0.670581i	$-0.233955\pi$
$563$	−4.97857	−	8.62314i	−0.209822	−	0.363422i	−0.951658	+	0.307159i	$0.900622\pi$
$564$	4.83991	+	8.38298i	0.203797	+	0.352987i
$565$	−9.30822	−	5.37410i	−0.391600	−	0.226090i
$566$	−2.83823			−0.119300
$567$	−0.986681	+	2.45489i	−0.0414367	+	0.103095i
$568$	−2.84809			−0.119503
$569$	40.1514	+	23.1814i	1.68323	+	0.971816i	0.959488	+	0.281749i	$0.0909146\pi$
$569$	40.1514	+	23.1814i	1.68323	+	0.971816i	0.723746	+	0.690066i	$0.242419\pi$
$570$	−0.287024	+	0.165713i	−0.0120221	+	0.00694097i
$571$	−37.5322	+	21.6692i	−1.57067	+	0.906829i	−0.574587	+	0.818443i	$0.694837\pi$
$571$	−37.5322	+	21.6692i	−1.57067	+	0.906829i	−0.996086	+	0.0883853i	$0.971829\pi$
$572$	1.09880	−	1.90317i	0.0459430	−	0.0795756i
$573$	−26.0997			−1.09033
$574$	0.613396	+	4.30803i	0.0256026	+	0.179814i
$575$	47.2053	+	22.2642i	1.96860	+	0.928482i
$576$	−3.28958	+	5.69772i	−0.137066	+	0.237405i
$577$	−5.38237	+	3.10751i	−0.224071	+	0.129367i	−0.607834	−	0.794064i	$-0.707961\pi$
$577$	−5.38237	+	3.10751i	−0.224071	+	0.129367i	0.383763	+	0.923432i	$0.374628\pi$
$578$	−2.43939	−	4.22515i	−0.101465	−	0.175743i
$579$	−9.37890	−	5.41491i	−0.389774	−	0.225036i
$580$	36.4405			1.51311
$581$	−20.3745	−	25.9813i	−0.845277	−	1.07788i
$582$			3.69061i			0.152981i
$583$	−2.79788	+	4.84607i	−0.115876	+	0.200704i
$584$	−12.3507	+	7.13065i	−0.511074	+	0.295068i
$585$	−5.96525	+	3.44404i	−0.246633	+	0.142393i
$586$	−0.210926	+	0.365334i	−0.00871326	+	0.0150918i
$587$		−	23.7269i		−	0.979315i	−0.871915	−	0.489657i	$-0.837122\pi$
$587$		−	23.7269i		−	0.979315i	0.871915	−	0.489657i	$-0.162878\pi$
$588$	−9.39456	+	9.79899i	−0.387425	+	0.404103i
$589$		−	1.42041i		−	0.0585271i
$590$	−9.61028	−	5.54850i	−0.395649	−	0.228428i
$591$	−7.92476	+	4.57536i	−0.325981	+	0.188205i
$592$	5.11857	−	2.95521i	0.210372	−	0.121458i
$593$	13.6510	+	7.88139i	0.560578	+	0.323650i	0.753378	−	0.657588i	$-0.228423\pi$
$593$	13.6510	+	7.88139i	0.560578	+	0.323650i	−0.192799	+	0.981238i	$0.561757\pi$
$594$	−0.161574			−0.00662947
$595$	39.4701	+	50.3316i	1.61812	+	2.06340i
$596$		−	1.38743i		−	0.0568314i
$597$	16.7351	+	9.66202i	0.684923	+	0.395440i
$598$	2.03564	−	0.169122i	0.0832435	−	0.00691593i
$599$	18.1368	+	31.4138i	0.741048	+	1.28353i	0.952019	+	0.306040i	$0.0990042\pi$
$599$	18.1368	+	31.4138i	0.741048	+	1.28353i	−0.210971	+	0.977492i	$0.567662\pi$
$600$	9.14927	+	5.28233i	0.373517	+	0.215650i
$601$			10.9186i			0.445381i	0.974889	+	0.222690i	$0.0714839\pi$
$601$			10.9186i			0.445381i	−0.974889	+	0.222690i	$0.928516\pi$
$602$	0.386860	+	2.71701i	0.0157672	+	0.110737i
$603$		−	4.26378i		−	0.173635i
$604$	−6.70591	+	11.6150i	−0.272860	+	0.472607i
$605$	−21.0627	−	36.4817i	−0.856320	−	1.48319i
$606$	−2.17899	−	3.77413i	−0.0885155	−	0.153313i
$607$	−34.2870	−	19.7956i	−1.39167	−	0.803479i	−0.398167	−	0.917313i	$-0.630354\pi$
$607$	−34.2870	−	19.7956i	−1.39167	−	0.803479i	−0.993500	+	0.113834i	$0.963687\pi$
$608$	−0.957845			−0.0388457
$609$	11.5748	+	4.65220i	0.469034	+	0.188517i
$610$	−4.20680			−0.170328
$611$	−4.31353	+	7.47125i	−0.174507	+	0.302255i
$612$	5.88191	+	10.1878i	0.237762	+	0.411816i
$613$	−28.0394	+	16.1885i	−1.13250	+	0.653849i	−0.944562	−	0.328332i	$-0.893513\pi$
$613$	−28.0394	+	16.1885i	−1.13250	+	0.653849i	−0.187937	+	0.982181i	$0.560180\pi$
$614$	−1.94846	−	1.12494i	−0.0786335	−	0.0453991i
$615$	−26.5984			−1.07255
$616$	−1.56250	−	0.628007i	−0.0629548	−	0.0253031i
$617$			28.7944i			1.15922i	0.814894	+	0.579610i	$0.196795\pi$
$617$			28.7944i			1.15922i	−0.814894	+	0.579610i	$0.803205\pi$
$618$	2.54683	+	1.47041i	0.102448	+	0.0591486i
$619$	−21.3808	−	37.0326i	−0.859365	−	1.48846i	−0.872535	−	0.488551i	$-0.837526\pi$
$619$	−21.3808	−	37.0326i	−0.859365	−	1.48846i	0.0131703	−	0.999913i	$-0.495808\pi$
$620$	−28.1723	+	16.2653i	−1.13143	+	0.653229i
$621$	2.73356	+	3.94052i	0.109694	+	0.158127i
$622$			5.79459i			0.232342i
$623$	18.9110	−	2.69263i	0.757653	−	0.107878i
$624$	−6.29004			−0.251803
$625$	−19.5111	+	33.7942i	−0.780443	+	1.35177i
$626$	−2.89063	−	5.00672i	−0.115533	−	0.200109i
$627$	0.110630	+	0.191616i	0.00441812	+	0.00765241i
$628$	−0.236623	+	0.409843i	−0.00944228	+	0.0163545i
$629$		−	9.85163i		−	0.392810i
$630$	1.60345	+	2.04469i	0.0638829	+	0.0814625i
$631$		−	16.7980i		−	0.668716i	−0.942446	−	0.334358i	$-0.891481\pi$
$631$		−	16.7980i		−	0.668716i	0.942446	−	0.334358i	$-0.108519\pi$
$632$	−9.47501	−	5.47040i	−0.376895	−	0.217601i
$633$	−4.16708	+	2.40586i	−0.165626	+	0.0956245i
$634$	1.35591	+	2.34850i	0.0538499	+	0.0932708i
$635$	6.29191	−	10.8979i	0.249687	−	0.432470i
$636$	16.5509			0.656287
$637$	−11.7496	−	2.88444i	−0.465537	−	0.114286i
$638$			0.761823i			0.0301609i
$639$	1.46693	−	2.54081i	0.0580310	−	0.100513i
$640$	14.5426	+	25.1885i	0.574846	+	0.995662i
$641$	−8.73067	+	5.04065i	−0.344841	+	0.199094i	−0.662411	−	0.749141i	$-0.730467\pi$
$641$	−8.73067	+	5.04065i	−0.344841	+	0.199094i	0.317570	+	0.948235i	$0.397133\pi$
$642$	0.369256	−	0.639571i	0.0145734	−	0.0252418i
$643$	32.0209			1.26278			0.631391	−	0.775464i	$-0.282484\pi$
$643$	32.0209			1.26278			0.631391	+	0.775464i	$0.282484\pi$
$644$	5.47367	+	23.9901i	0.215693	+	0.945341i
$645$	−16.7752			−0.660523
$646$	−0.252234	+	0.436882i	−0.00992401	+	0.0171889i
$647$	32.3852	−	18.6976i	1.27319	−	0.735078i	0.297605	−	0.954689i	$-0.403812\pi$
$647$	32.3852	−	18.6976i	1.27319	−	0.735078i	0.975587	+	0.219611i	$0.0704789\pi$
$648$	0.485381	+	0.840705i	0.0190676	+	0.0330260i
$649$	−3.70415	+	6.41578i	−0.145401	+	0.251841i
$650$			4.63525i			0.181810i
$651$	−11.0250	+	1.56979i	−0.432104	+	0.0615249i
$652$	37.2801			1.46000
$653$	15.1700	−	26.2752i	0.593648	−	1.02823i	−0.400088	−	0.916477i	$-0.631021\pi$
$653$	15.1700	−	26.2752i	0.593648	−	1.02823i	0.993736	−	0.111751i	$-0.0356461\pi$
$654$	−1.63498	−	2.83186i	−0.0639326	−	0.110735i
$655$	67.3947	−	38.9104i	2.63333	−	1.52035i
$656$	−21.0349	−	12.1445i	−0.821276	−	0.474164i
$657$		−	14.6908i		−	0.573144i
$658$	3.01966	+	1.21368i	0.117718	+	0.0473140i
$659$		−	8.19897i		−	0.319387i	−0.987167	−	0.159693i	$-0.948949\pi$
$659$		−	8.19897i		−	0.319387i	0.987167	−	0.159693i	$-0.0510505\pi$
$660$	2.53366	−	4.38842i	0.0986224	−	0.170819i
$661$	−13.5183	−	23.4143i	−0.525799	−	0.910711i	−0.999548	−	0.0300510i	$-0.990433\pi$
$661$	−13.5183	−	23.4143i	−0.525799	−	0.910711i	0.473749	−	0.880660i	$-0.342900\pi$
$662$	0.914794	+	1.58447i	0.0355545	+	0.0615822i
$663$	−5.24220	+	9.07976i	−0.203590	+	0.352629i
$664$	−12.1145			−0.470135
$665$	1.32699	−	3.30158i	0.0514584	−	0.128030i
$666$		−	0.400217i		−	0.0155081i
$667$	18.5795	−	12.8887i	0.719403	−	0.499054i
$668$	15.8342	−	9.14188i	0.612644	−	0.353710i
$669$	11.0231	+	19.0925i	0.426177	+	0.738160i
$670$	−3.62649	−	2.09376i	−0.140104	−	0.0808889i
$671$			2.80844i			0.108419i
$672$	1.05858	+	7.43463i	0.0408354	+	0.286797i
$673$	11.3840			0.438822			0.219411	−	0.975633i	$-0.429586\pi$
$673$	11.3840			0.438822			0.219411	+	0.975633i	$0.429586\pi$
$674$	7.21205	+	4.16388i	0.277798	+	0.160387i
$675$	−9.42482	+	5.44142i	−0.362762	+	0.209441i
$676$	9.70875	+	16.8160i	0.373413	+	0.646771i
$677$	−21.5089	+	37.2545i	−0.826654	+	1.43181i	0.0739950	+	0.997259i	$0.476425\pi$
$677$	−21.5089	+	37.2545i	−0.826654	+	1.43181i	−0.900649	+	0.434548i	$0.856908\pi$
$678$	−0.664613			−0.0255243
$679$	−24.4509	−	31.1794i	−0.938340	−	1.19656i
$680$	23.4686			0.899980
$681$	0.115683	+	0.0667898i	0.00443299	+	0.00255939i
$682$	−0.340040	−	0.588967i	−0.0130208	−	0.0225527i
$683$	10.7223	+	18.5715i	0.410276	+	0.710618i	0.994920	−	0.100672i	$-0.0320992\pi$
$683$	10.7223	+	18.5715i	0.410276	+	0.710618i	−0.584644	+	0.811290i	$0.698766\pi$
$684$	0.327216	−	0.566755i	0.0125114	−	0.0216704i
$685$			19.1983i			0.733529i
$686$	−0.452449	+	4.54150i	−0.0172746	+	0.173395i
$687$			27.2419i			1.03934i
$688$	−13.2664	−	7.65937i	−0.505778	−	0.292011i
$689$	7.37544	+	12.7746i	0.280982	+	0.486675i
$690$	4.69388	−	0.389970i	0.178693	−	0.0148459i
$691$	16.9816	+	9.80434i	0.646011	+	0.372975i	0.786926	−	0.617047i	$-0.211671\pi$
$691$	16.9816	+	9.80434i	0.646011	+	0.372975i	−0.140915	+	0.990022i	$0.545004\pi$
$692$		−	13.2713i		−	0.504500i
$693$	1.36503	−	1.07046i	0.0518531	−	0.0406633i
$694$	5.43658			0.206370
$695$	−51.7412	−	29.8728i	−1.96266	−	1.13314i
$696$	3.96393	−	2.28857i	0.150252	−	0.0867482i
$697$	−35.0616	+	20.2428i	−1.32805	+	0.766751i
$698$	2.00047	+	1.15497i	0.0757188	+	0.0437163i
$699$		−	10.9286i		−	0.413358i
$700$	−55.2805	+	7.87108i	−2.08941	+	0.297499i
$701$		−	18.8113i		−	0.710494i	−0.934773	−	0.355247i	$-0.884397\pi$
$701$		−	18.8113i		−	0.710494i	0.934773	−	0.355247i	$-0.115603\pi$
$702$	−0.212961	+	0.368860i	−0.00803771	+	0.0139217i
$703$	−0.474629	+	0.274027i	−0.0179010	+	0.0103351i
$704$	3.73574	−	2.15683i	0.140796	−	0.0812886i
$705$	−9.94634	+	17.2276i	−0.374601	+	0.648828i
$706$		−	5.56296i		−	0.209365i
$707$	43.4130	+	17.4488i	1.63271	+	0.656229i
$708$	21.9120			0.823504
$709$	23.8300	+	13.7582i	0.894954	+	0.516702i	0.875560	−	0.483110i	$-0.160493\pi$
$709$	23.8300	+	13.7582i	0.894954	+	0.516702i	0.0193940	+	0.999812i	$0.493826\pi$
$710$	−1.44070	−	2.49536i	−0.0540683	−	0.0936491i
$711$	9.76037	−	5.63515i	0.366043	−	0.211335i
$712$	3.50434	−	6.06970i	0.131331	−	0.227472i
$713$	−8.61099	+	18.2573i	−0.322484	+	0.683742i
$714$	3.66977	+	1.47497i	0.137338	+	0.0551995i
$715$	4.51620			0.168896
$716$	−6.67363	+	11.5591i	−0.249405	+	0.431982i
$717$	−3.68219	+	2.12591i	−0.137514	+	0.0793937i
$718$	0.246600	−	0.142374i	0.00920302	−	0.00531337i
$719$	8.94715	+	5.16564i	0.333672	+	0.192646i	0.657470	−	0.753480i	$-0.271626\pi$
$719$	8.94715	+	5.16564i	0.333672	+	0.192646i	−0.323798	+	0.946126i	$0.604960\pi$
$720$	−14.5039			−0.540527
$721$	−31.2581	+	4.45066i	−1.16411	+	0.165751i
$722$	−4.65414			−0.173209
$723$	−20.9328	−	12.0856i	−0.778499	−	0.449467i
$724$	−18.8088	−	32.5778i	−0.699024	−	1.21074i
$725$	25.6563	+	44.4381i	0.952852	+	1.65039i
$726$	−2.25584	−	1.30241i	−0.0837219	−	0.0483369i
$727$	−6.95672			−0.258011			−0.129005	−	0.991644i	$-0.541178\pi$
$727$	−6.95672			−0.258011			−0.129005	+	0.991644i	$0.541178\pi$
$728$	−3.49312	+	2.73931i	−0.129464	+	0.101525i
$729$	−1.00000			−0.0370370
$730$	−12.4951	−	7.21402i	−0.462463	−	0.267003i
$731$	−22.1128	+	12.7668i	−0.817873	+	0.472199i
$732$	7.19382	−	4.15335i	0.265891	−	0.153512i
$733$	24.3077	−	42.1022i	0.897826	−	1.55508i	0.0675581	−	0.997715i	$-0.478479\pi$
$733$	24.3077	−	42.1022i	0.897826	−	1.55508i	0.830268	−	0.557365i	$-0.188187\pi$
$734$	−0.396618			−0.0146394
$735$	−27.0929	−	6.65108i	−0.999335	−	0.245329i
$736$	12.3117	+	5.80676i	0.453814	+	0.214040i
$737$	−1.39778	+	2.42103i	−0.0514880	+	0.0891799i
$738$	−1.42436	+	0.822352i	−0.0524313	+	0.0302712i
$739$	11.8109	+	20.4571i	0.434471	+	0.752525i	0.997252	−	0.0740803i	$-0.0236021\pi$
$739$	11.8109	+	20.4571i	0.434471	+	0.752525i	−0.562782	+	0.826606i	$0.690269\pi$
$740$	10.8700	+	6.27582i	0.399591	+	0.230704i
$741$	0.583257			0.0214265
$742$	4.37873	−	3.43380i	0.160748	−	0.126059i
$743$		−	4.51930i		−	0.165797i	−0.996558	−	0.0828985i	$-0.973582\pi$
$743$		−	4.51930i		−	0.165797i	0.996558	−	0.0828985i	$-0.0264177\pi$
$744$	−2.04301	+	3.53860i	−0.0749005	+	0.129732i
$745$	2.46927	−	1.42563i	0.0904669	−	0.0522311i
$746$	−1.97663	+	1.14121i	−0.0723694	+	0.0417825i
$747$	6.23970	−	10.8075i	0.228299	−	0.395425i
$748$		−	7.71301i		−	0.282015i
$749$	1.11767	+	7.84967i	0.0408388	+	0.286821i
$750$			5.77762i			0.210969i
$751$	4.48893	+	2.59168i	0.163803	+	0.0945718i	0.579661	−	0.814858i	$-0.303185\pi$
$751$	4.48893	+	2.59168i	0.163803	+	0.0945718i	−0.415857	+	0.909430i	$0.636518\pi$
$752$	−15.7318	+	9.08278i	−0.573681	+	0.331215i
$753$	−13.6190	+	7.86291i	−0.496303	+	0.286540i
$754$	1.73918	+	1.00411i	0.0633371	+	0.0365677i
$755$	−27.5622			−1.00309
$756$	−4.76069	−	1.91344i	−0.173145	−	0.0695912i
$757$			4.11310i			0.149493i	0.997203	+	0.0747466i	$0.0238148\pi$
$757$			4.11310i			0.149493i	−0.997203	+	0.0747466i	$0.976185\pi$
$758$	−4.02037	−	2.32116i	−0.146026	−	0.0843083i
$759$	−0.260343	−	3.13361i	−0.00944984	−	0.113743i
$760$	−0.652790	−	1.13067i	−0.0236792	−	0.0410135i
$761$	−18.4595	−	10.6576i	−0.669155	−	0.386337i	0.126601	−	0.991954i	$-0.459593\pi$
$761$	−18.4595	−	10.6576i	−0.669155	−	0.386337i	−0.795756	+	0.605617i	$0.792926\pi$
$762$		−	0.778118i		−	0.0281882i
$763$	32.5743	+	13.0924i	1.17927	+	0.473978i
$764$		−	50.6144i		−	1.83117i
$765$	−12.0877	+	20.9365i	−0.437032	+	0.756962i
$766$	−1.83108	−	3.17152i	−0.0661595	−	0.114592i
$767$	9.76445	+	16.9125i	0.352574	+	0.610676i
$768$	−9.83793	−	5.67993i	−0.354996	−	0.204957i
$769$	19.8664			0.716399			0.358200	−	0.933645i	$-0.383391\pi$
$769$	19.8664			0.716399			0.358200	+	0.933645i	$0.383391\pi$
$770$	−0.240154	−	1.68666i	−0.00865454	−	0.0607829i
$771$	19.4678			0.701117
$772$	10.5010	−	18.1882i	0.377939	−	0.654609i
$773$	−3.13480	−	5.42963i	−0.112751	−	0.195290i	0.804128	−	0.594457i	$-0.202633\pi$
$773$	−3.13480	−	5.42963i	−0.112751	−	0.195290i	−0.916878	+	0.399167i	$0.869300\pi$
$774$	−0.898321	+	0.518646i	−0.0322895	+	0.0186423i
$775$	−39.6700	−	22.9035i	−1.42499	−	0.822716i
$776$	−14.5383			−0.521895
$777$	2.65150	+	3.38115i	0.0951220	+	0.121298i
$778$			5.47617i			0.196330i
$779$	1.95051	+	1.12613i	0.0698842	+	0.0403476i
$780$	−6.67892	−	11.5682i	−0.239144	−	0.414209i
$781$	−1.66589	+	0.961802i	−0.0596102	+	0.0344160i
$782$	5.89061	−	4.08635i	0.210648	−	0.146128i
$783$			4.71500i			0.168500i
$784$	−18.3892	−	17.6302i	−0.656756	−	0.629650i
$785$	−0.972551			−0.0347118
$786$	2.40601	−	4.16734i	0.0858197	−	0.148644i
$787$	7.67386	+	13.2915i	0.273544	+	0.473791i	0.969767	−	0.244034i	$-0.0784709\pi$
$787$	7.67386	+	13.2915i	0.273544	+	0.473791i	−0.696223	+	0.717825i	$0.745138\pi$
$788$	−8.87286	−	15.3682i	−0.316083	−	0.547471i
$789$	−2.13833	+	3.70369i	−0.0761264	+	0.131855i
$790$		−	11.0687i		−	0.393807i
$791$	5.61486	−	4.40317i	0.199641	−	0.156559i
$792$		−	0.636485i		−	0.0226165i
$793$	6.41143	+	3.70164i	0.227676	+	0.131449i
$794$	3.42696	−	1.97856i	0.121618	−	0.0702164i
$795$	17.0066	+	29.4563i	0.603163	+	1.04471i
$796$	−18.7373	+	32.4539i	−0.664125	+	1.15030i
$797$	19.4747			0.689829			0.344914	−	0.938634i	$-0.387908\pi$
$797$	19.4747			0.689829			0.344914	+	0.938634i	$0.387908\pi$
$798$	−0.0310153	−	0.217828i	−0.00109793	−	0.00771103i
$799$			30.2788i			1.07119i
$800$	−15.4448	+	26.7511i	−0.546055	+	0.945795i
$801$	3.60989	+	6.25251i	0.127549	+	0.220921i
$802$	−5.96295	+	3.44271i	−0.210559	+	0.121566i
$803$	−4.81605	+	8.34165i	−0.169955	+	0.294370i
$804$	8.26863			0.291612
$805$	−37.0717	+	34.3923i	−1.30661	+	1.21217i
$806$	−1.79275			−0.0631469
$807$	9.33893	−	16.1755i	0.328746	−	0.569405i
$808$	14.8673	−	8.58364i	0.523030	−	0.301971i
$809$	−17.2628	−	29.9001i	−0.606928	−	1.05123i	−0.991744	−	0.128237i	$-0.959068\pi$
$809$	−17.2628	−	29.9001i	−0.606928	−	1.05123i	0.384816	−	0.922993i	$-0.374265\pi$
$810$	−0.491056	+	0.850535i	−0.0172540	+	0.0298847i
$811$		−	9.65598i		−	0.339067i	−0.985524	−	0.169534i	$-0.945774\pi$
$811$		−	9.65598i		−	0.339067i	0.985524	−	0.169534i	$-0.0542261\pi$
$812$	−9.02188	+	22.4467i	−0.316606	+	0.787723i
$813$	18.4102			0.645673
$814$	−0.131202	+	0.227248i	−0.00459862	+	0.00796505i
$815$	38.3066	+	66.3489i	1.34182	+	2.32410i
$816$	−19.1188	+	11.0382i	−0.669292	+	0.386416i
$817$	1.23016	+	0.710231i	0.0430377	+	0.0248478i
$818$			7.70045i			0.269240i
$819$	−0.644595	−	4.52715i	−0.0225240	−	0.158191i
$820$		−	51.5814i		−	1.80130i
$821$	−18.1051	+	31.3590i	−0.631872	+	1.09444i	0.355296	+	0.934754i	$0.384380\pi$
$821$	−18.1051	+	31.3590i	−0.631872	+	1.09444i	−0.987169	+	0.159681i	$0.948953\pi$
$822$	0.593561	+	1.02808i	0.0207028	+	0.0358583i
$823$	−4.35738	−	7.54721i	−0.151889	−	0.263079i	0.780033	−	0.625738i	$-0.215202\pi$
$823$	−4.35738	−	7.54721i	−0.151889	−	0.263079i	−0.931922	+	0.362659i	$0.881869\pi$
$824$	−5.79235	+	10.0326i	−0.201786	+	0.349504i
$825$	7.13539			0.248422
$826$	5.79706	−	4.54606i	0.201706	−	0.158178i
$827$		−	17.7121i		−	0.615910i	−0.951401	−	0.307955i	$-0.900355\pi$
$827$		−	17.7121i		−	0.615910i	0.951401	−	0.307955i	$-0.0996446\pi$
$828$	−7.64173	+	5.30111i	−0.265568	+	0.184226i
$829$	32.6807	−	18.8682i	1.13505	−	0.655320i	0.189848	−	0.981814i	$-0.439201\pi$
$829$	32.6807	−	18.8682i	1.13505	−	0.655320i	0.945199	+	0.326494i	$0.105867\pi$
$830$	−6.12809	−	10.6142i	−0.212709	−	0.368423i
$831$	−2.81038	−	1.62257i	−0.0974910	−	0.0562865i
$832$		−	11.3712i		−	0.394224i
$833$	−40.7752	+	11.8518i	−1.41278	+	0.410640i
$834$	−3.69436			−0.127925
$835$	32.5403	+	18.7872i	1.12610	+	0.650157i
$836$	−0.371595	+	0.214541i	−0.0128519	+	0.00742005i
$837$	−2.10455	−	3.64518i	−0.0727438	−	0.125996i
$838$	−1.17249	+	2.03081i	−0.0405029	+	0.0701530i
$839$	−38.9989			−1.34639			−0.673195	−	0.739465i	$-0.735079\pi$
$839$	−38.9989			−1.34639			−0.673195	+	0.739465i	$0.735079\pi$
$840$	−8.05460	+	6.31642i	−0.277910	+	0.217937i
$841$	−6.76874			−0.233405
$842$	5.24587	+	3.02870i	0.180785	+	0.104376i
$843$	−13.8797	−	24.0403i	−0.478041	−	0.827992i
$844$	−4.66562	−	8.08109i	−0.160597	−	0.278163i
$845$	−19.9521	+	34.5581i	−0.686373	+	1.18883i
$846$			1.23006i			0.0422903i
$847$	27.6867	−	3.94215i	0.951325	−	0.135454i
$848$			31.0602i			1.06661i
$849$	9.97426	+	5.75864i	0.342316	+	0.197636i
$850$	8.13429	+	14.0890i	0.279004	+	0.483249i
$851$	7.76190	−	0.644864i	0.266075	−	0.0221057i
$852$	4.92731	+	2.84478i	0.168807	+	0.0974607i
$853$		−	32.5570i		−	1.11473i	−0.830267	−	0.557365i	$-0.811812\pi$
$853$		−	32.5570i		−	1.11473i	0.830267	−	0.557365i	$-0.188188\pi$
$854$	1.04151	−	2.59131i	0.0356398	−	0.0886726i
$855$	1.34490			0.0459947
$856$	2.51944	+	1.45460i	0.0861127	+	0.0497172i
$857$	−28.7032	+	16.5718i	−0.980484	+	0.566083i	−0.902416	−	0.430865i	$-0.858208\pi$
$857$	−28.7032	+	16.5718i	−0.980484	+	0.566083i	−0.0780676	+	0.996948i	$0.524875\pi$
$858$	0.241845	−	0.139629i	0.00825644	−	0.00476686i
$859$	−13.8981	−	8.02407i	−0.474197	−	0.273778i	0.243798	−	0.969826i	$-0.421607\pi$
$859$	−13.8981	−	8.02407i	−0.474197	−	0.273778i	−0.717995	+	0.696048i	$0.754940\pi$
$860$		−	32.5317i		−	1.10932i
$861$	6.58518	−	16.3841i	0.224422	−	0.558368i
$862$		−	0.327189i		−	0.0111441i
$863$	−10.9828	+	19.0228i	−0.373860	+	0.647545i	−0.990156	−	0.139970i	$-0.955299\pi$
$863$	−10.9828	+	19.0228i	−0.373860	+	0.647545i	0.616296	+	0.787515i	$0.288633\pi$
$864$	−2.45810	+	1.41918i	−0.0836262	+	0.0482816i
$865$	23.6195	−	13.6367i	0.803087	−	0.463663i
$866$	−2.05523	+	3.55976i	−0.0698395	+	0.120966i
$867$			19.7977i			0.672364i
$868$	−3.04425	−	21.3805i	−0.103328	−	0.725701i
$869$	−7.38943			−0.250669
$870$	4.01027	+	2.31533i	0.135961	+	0.0784971i
$871$	3.68467	+	6.38204i	0.124850	+	0.216247i
$872$	11.1555	−	6.44061i	0.377772	−	0.218107i
$873$	7.48809	−	12.9698i	0.253434	−	0.438960i
$874$	−0.360721	−	0.170133i	−0.0122016	−	0.00575483i
$875$	−38.2777	−	48.8111i	−1.29402	−	1.65012i
$876$	28.4895			0.962571
$877$	−6.34742	+	10.9941i	−0.214337	+	0.371243i	−0.953067	−	0.302758i	$-0.902092\pi$
$877$	−6.34742	+	10.9941i	−0.214337	+	0.371243i	0.738730	+	0.674001i	$0.235426\pi$
$878$	−5.64421	+	3.25869i	−0.190483	+	0.109975i
$879$	1.48249	−	0.855918i	0.0500033	−	0.0288694i
$880$	8.23549	+	4.75476i	0.277618	+	0.160283i
$881$	7.36228			0.248041			0.124021	−	0.992280i	$-0.460421\pi$
$881$	7.36228			0.248041			0.124021	+	0.992280i	$0.460421\pi$
$882$	−1.65647	+	0.481472i	−0.0557762	+	0.0162120i
$883$	−39.1953			−1.31903			−0.659513	−	0.751693i	$-0.729237\pi$
$883$	−39.1953			−1.31903			−0.659513	+	0.751693i	$0.729237\pi$
$884$	−17.6081	−	10.1661i	−0.592225	−	0.341921i
$885$	22.5153	+	38.9977i	0.756844	+	1.31089i
$886$	2.36467	+	4.09572i	0.0794425	+	0.137598i
$887$	23.5471	+	13.5949i	0.790635	+	0.456474i	0.840186	−	0.542298i	$-0.182446\pi$
$887$	23.5471	+	13.5949i	0.790635	+	0.456474i	−0.0495508	+	0.998772i	$0.515779\pi$
$888$	1.57656			0.0529059
$889$	5.15516	+	6.57378i	0.172899	+	0.220478i
$890$	7.09063			0.237678
$891$	0.567813	+	0.327827i	0.0190225	+	0.0109826i
$892$	−37.0256	+	21.3767i	−1.23971	+	0.715746i
$893$	1.45877	−	0.842220i	0.0488158	−	0.0281838i
$894$	0.0881536	−	0.152687i	0.00294830	−	0.00510660i
$895$	−27.4295			−0.916866
$896$	−19.1160	+	2.72182i	−0.638622	+	0.0909298i
$897$	−7.49691	−	3.53589i	−0.250314	−	0.118060i
$898$	2.99271	−	5.18353i	0.0998681	−	0.172977i
$899$	−17.1870	+	9.92294i	−0.573220	+	0.330949i
$900$	−10.5524	−	18.2773i	−0.351747	−	0.609243i
$901$	44.8358	+	25.8859i	1.49370	+	0.862386i
$902$	1.07836			0.0359054
$903$	4.15318	−	10.3332i	0.138209	−	0.343867i
$904$		−	2.61809i		−	0.0870764i
$905$	38.6533	−	66.9495i	1.28488	−	2.22548i
$906$	−1.47597	+	0.852151i	−0.0490358	+	0.0283108i
$907$	26.0965	−	15.0668i	0.866521	−	0.500286i	0.000330104	−	1.00000i	$-0.499895\pi$
$907$	26.0965	−	15.0668i	0.866521	−	0.500286i	0.866190	+	0.499714i	$0.166562\pi$
$908$	−0.129523	+	0.224341i	−0.00429839	+	0.00744503i
$909$			17.6843i			0.586552i
$910$	−4.16703	−	1.67483i	−0.138136	−	0.0555202i
$911$		−	50.3390i		−	1.66780i	−0.551912	−	0.833902i	$-0.686102\pi$
$911$		−	50.3390i		−	1.66780i	0.551912	−	0.833902i	$-0.313898\pi$
$912$	1.06360	+	0.614067i	0.0352192	+	0.0203338i
$913$	−7.08597	+	4.09108i	−0.234511	+	0.135395i
$914$	−2.81787	+	1.62690i	−0.0932069	+	0.0538130i
$915$	14.7838	+	8.53541i	0.488736	+	0.282172i
$916$	−52.8294			−1.74553
$917$	7.28256	+	51.1472i	0.240491	+	1.68903i
$918$			1.49488i			0.0493385i
$919$	−16.4796	−	9.51452i	−0.543613	−	0.313855i	0.202929	−	0.979193i	$-0.434954\pi$
$919$	−16.4796	−	9.51452i	−0.543613	−	0.313855i	−0.746542	+	0.665339i	$0.768287\pi$
$920$	1.53620	+	18.4904i	0.0506470	+	0.609612i
$921$	4.56493	+	7.90669i	0.150420	+	0.260534i
$922$	2.39378	+	1.38205i	0.0788348	+	0.0455153i
$923$			5.07078i			0.166907i
$924$	2.07590	+	2.64716i	0.0682922	+	0.0870852i
$925$			17.6742i			0.581125i
$926$	−0.948471	+	1.64280i	−0.0311687	+	0.0539858i
$927$	−5.96680	−	10.3348i	−0.195976	−	0.339440i
$928$	6.69146	+	11.5899i	0.219658	+	0.380459i
$929$	−14.4219	−	8.32650i	−0.473168	−	0.273184i	0.244397	−	0.969675i	$-0.421410\pi$
$929$	−14.4219	−	8.32650i	−0.473168	−	0.273184i	−0.717565	+	0.696492i	$0.754743\pi$
$930$	−4.13380			−0.135553
$931$	1.70517	+	1.63480i	0.0558848	+	0.0535783i
$932$	21.1935			0.694217
$933$	11.7570	−	20.3637i	0.384906	−	0.666677i
$934$	−0.734574	−	1.27232i	−0.0240360	−	0.0416316i
$935$	13.7271	−	7.92537i	0.448925	−	0.259187i
$936$	−1.45304	−	0.838913i	−0.0474941	−	0.0274207i
$937$	2.81729			0.0920369			0.0460185	−	0.998941i	$-0.485347\pi$
$937$	2.81729			0.0920369			0.0460185	+	0.998941i	$0.485347\pi$
$938$	2.18755	−	1.71548i	0.0714262	−	0.0560124i
$939$			23.4599i			0.765584i
$940$	−33.4089	−	19.2887i	−1.08968	−	0.629127i
$941$	13.7983	+	23.8993i	0.449810	+	0.779094i	0.998373	−	0.0570149i	$-0.0181583\pi$
$941$	13.7983	+	23.8993i	0.449810	+	0.779094i	−0.548563	+	0.836109i	$0.684825\pi$
$942$	−0.0520806	+	0.0300687i	−0.00169688	+	0.000979693i
$943$	−18.2440	−	26.2993i	−0.594105	−	0.856422i
$944$			41.1210i			1.33837i
$945$	−1.48634	−	10.4389i	−0.0483505	−	0.339578i
$946$	0.680105			0.0221121
$947$	1.79167	−	3.10326i	0.0582214	−	0.100842i	−0.835446	−	0.549573i	$-0.814790\pi$
$947$	1.79167	−	3.10326i	0.0582214	−	0.100842i	0.893667	+	0.448731i	$0.148124\pi$
$948$	10.9281	+	18.9280i	0.354928	+	0.614753i
$949$	12.6955	+	21.9893i	0.412114	+	0.713802i
$950$	0.452518	−	0.783784i	0.0146816	−	0.0254293i
$951$		−	11.0043i		−	0.356839i
$952$	−5.81032	+	14.4562i	−0.188313	+	0.468528i
$953$			15.9645i			0.517140i	0.965993	+	0.258570i	$0.0832512\pi$
$953$			15.9645i			0.517140i	−0.965993	+	0.258570i	$0.916749\pi$
$954$	1.82143	+	1.05160i	0.0589709	+	0.0340468i
$955$	90.0804	−	52.0080i	2.91493	−	1.68294i
$956$	−4.12272	−	7.14077i	−0.133338	−	0.230949i
$957$	1.54571	−	2.67724i	0.0499656	−	0.0865429i
$958$	2.15300			0.0695603
$959$	−11.8258	−	4.75308i	−0.381874	−	0.153485i
$960$		−	26.2201i		−	0.846251i
$961$	−6.64177	+	11.5039i	−0.214251	+	0.371093i
$962$	0.345859	+	0.599045i	0.0111509	+	0.0193140i
$963$	−2.59532	+	1.49841i	−0.0836331	+	0.0482856i
$964$	23.4372	−	40.5944i	0.754860	−	1.30746i
$965$	43.1604			1.38938
$966$	−0.921887	+	2.98788i	−0.0296612	+	0.0961336i
$967$	37.0897			1.19272			0.596362	−	0.802715i	$-0.296612\pi$
$967$	37.0897			1.19272			0.596362	+	0.802715i	$0.296612\pi$
$968$	5.13054	−	8.88635i	0.164902	−	0.285618i
$969$	1.77283	−	1.02354i	0.0569515	−	0.0328810i
$970$	−7.35415	−	12.7378i	−0.236128	−	0.408985i
$971$	−13.3933	+	23.1978i	−0.429810	+	0.744453i	−0.996856	−	0.0792334i	$-0.974753\pi$
$971$	−13.3933	+	23.1978i	−0.429810	+	0.744453i	0.567046	+	0.823686i	$0.308086\pi$
$972$		−	1.93927i		−	0.0622022i
$973$	31.2111	−	24.4757i	1.00058	−	0.784656i
$974$	7.33091			0.234897
$975$	9.40473	−	16.2895i	0.301192	−	0.521681i
$976$	7.79435	+	13.5002i	0.249491	+	0.432131i
$977$	52.6384	−	30.3908i	1.68405	−	0.972288i	0.725133	−	0.688609i	$-0.241778\pi$
$977$	52.6384	−	30.3908i	1.68405	−	0.972288i	0.958919	−	0.283680i	$-0.0915552\pi$
$978$	4.10267	+	2.36868i	0.131189	+	0.0757420i
$979$		−	4.73368i		−	0.151289i
$980$	12.8983	−	52.5404i	0.412020	−	1.67834i
$981$			13.2692i			0.423652i
$982$	−0.313229	+	0.542529i	−0.00999555	+	0.0173128i
$983$	−3.50649	−	6.07341i	−0.111840	−	0.193712i	0.804672	−	0.593719i	$-0.202341\pi$
$983$	−3.50649	−	6.07341i	−0.111840	−	0.193712i	−0.916512	+	0.400007i	$0.869008\pi$
$984$	−3.23947	−	5.61092i	−0.103270	−	0.178870i
$985$	18.2343	−	31.5828i	0.580994	−	1.00631i
$986$	7.04838			0.224466
$987$	−8.14935	−	10.3919i	−0.259397	−	0.330779i
$988$			1.13109i			0.0359849i
$989$	−11.5062	−	16.5866i	−0.365876	−	0.527422i
$990$	0.557657	−	0.321963i	0.0177235	−	0.0102327i
$991$	−8.39730	−	14.5445i	−0.266749	−	0.462023i	0.701271	−	0.712894i	$-0.252616\pi$
$991$	−8.39730	−	14.5445i	−0.266749	−	0.462023i	−0.968020	+	0.250872i	$0.919283\pi$
$992$	−10.3464	−	5.97348i	−0.328498	−	0.189658i
$993$		−	7.42431i		−	0.235603i
$994$	1.89378	−	0.269644i	0.0600669	−	0.00855259i
$995$	−77.0127			−2.44147
$996$	20.9586	+	12.1005i	0.664099	+	0.383418i
$997$	−22.1685	+	12.7990i	−0.702084	+	0.405348i	−0.808123	−	0.589014i	$-0.799516\pi$
$997$	−22.1685	+	12.7990i	−0.702084	+	0.405348i	0.106039	+	0.994362i	$0.466183\pi$
$998$	2.49876	+	4.32799i	0.0790970	+	0.137000i
$999$	−0.812022	+	1.40646i	−0.0256912	+	0.0444985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.j.a.229.13	✓	64
7.3	odd	6	inner	483.2.j.a.367.14	yes	64
23.22	odd	2	inner	483.2.j.a.229.14	yes	64
161.45	even	6	inner	483.2.j.a.367.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.j.a.229.13	✓	64	1.1	even	1	trivial
483.2.j.a.229.14	yes	64	23.22	odd	2	inner
483.2.j.a.367.13	yes	64	161.45	even	6	inner
483.2.j.a.367.14	yes	64	7.3	odd	6	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.123216 + 0.213416i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.969636 + 1.67946i) q^{4} +(-1.99266 + 3.45140i) q^{5} +0.246432i q^{6} +(-1.63265 - 2.08193i) q^{7} -0.970763 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.123216 + 0.213416i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.969636 + 1.67946i) q^{4} +(-1.99266 + 3.45140i) q^{5} +0.246432i q^{6} +(-1.63265 - 2.08193i) q^{7} -0.970763 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.491056 - 0.850535i) q^{10} +(-0.567813 + 0.327827i) q^{11} +(1.67946 + 0.969636i) q^{12} +1.72836i q^{13} +(0.645488 - 0.0919073i) q^{14} +3.98533i q^{15} +(-1.81966 + 3.15174i) q^{16} +(3.03305 + 5.25340i) q^{17} +(0.123216 + 0.213416i) q^{18} +(0.168732 - 0.292252i) q^{19} -7.72863 q^{20} +(-2.45489 - 0.986681i) q^{21} -0.161574i q^{22} +(-3.94052 + 2.73356i) q^{23} +(-0.840705 + 0.485381i) q^{24} +(-5.44142 - 9.42482i) q^{25} +(-0.368860 - 0.212961i) q^{26} -1.00000i q^{27} +(1.91344 - 4.76069i) q^{28} -4.71500 q^{29} +(-0.850535 - 0.491056i) q^{30} +(3.64518 - 2.10455i) q^{31} +(-1.41918 - 2.45810i) q^{32} +(-0.327827 + 0.567813i) q^{33} -1.49488 q^{34} +(10.4389 - 1.48634i) q^{35} +1.93927 q^{36} +(-1.40646 - 0.812022i) q^{37} +(0.0415808 + 0.0720201i) q^{38} +(0.864179 + 1.49680i) q^{39} +(1.93440 - 3.35049i) q^{40} +6.67407i q^{41} +(0.513055 - 0.402338i) q^{42} +4.20924i q^{43} +(-1.10114 - 0.635746i) q^{44} +(1.99266 + 3.45140i) q^{45} +(-0.0978515 - 1.17779i) q^{46} +(4.32275 + 2.49574i) q^{47} +3.63932i q^{48} +(-1.66889 + 6.79815i) q^{49} +2.68188 q^{50} +(5.25340 + 3.03305i) q^{51} +(-2.90271 + 1.67588i) q^{52} +(7.39119 - 4.26731i) q^{53} +(0.213416 + 0.123216i) q^{54} -2.61300i q^{55} +(1.58492 + 2.02106i) q^{56} -0.337463i q^{57} +(0.580964 - 1.00626i) q^{58} +(9.78531 - 5.64955i) q^{59} +(-6.69319 + 3.86432i) q^{60} +(2.14171 - 3.70955i) q^{61} +1.03726i q^{62} +(-2.61933 + 0.372952i) q^{63} -6.57917 q^{64} +(-5.96525 - 3.44404i) q^{65} +(-0.0807871 - 0.139927i) q^{66} +(3.69254 - 2.13189i) q^{67} +(-5.88191 + 10.1878i) q^{68} +(-2.04581 + 4.33759i) q^{69} +(-0.969032 + 2.41097i) q^{70} +2.93387 q^{71} +(-0.485381 + 0.840705i) q^{72} +(12.7226 - 7.34541i) q^{73} +(0.346598 - 0.200108i) q^{74} +(-9.42482 - 5.44142i) q^{75} +0.654432 q^{76} +(1.60956 + 0.646922i) q^{77} -0.425923 q^{78} +(9.76037 + 5.63515i) q^{79} +(-7.25194 - 12.5607i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.42436 - 0.822352i) q^{82} +12.4794 q^{83} +(-0.723255 - 5.07960i) q^{84} -24.1754 q^{85} +(-0.898321 - 0.518646i) q^{86} +(-4.08331 + 2.35750i) q^{87} +(0.551212 - 0.318242i) q^{88} +(-3.60989 + 6.25251i) q^{89} -0.982113 q^{90} +(3.59833 - 2.82181i) q^{91} +(-8.41176 - 3.96738i) q^{92} +(2.10455 - 3.64518i) q^{93} +(-1.06526 + 0.615030i) q^{94} +(0.672451 + 1.16472i) q^{95} +(-2.45810 - 1.41918i) q^{96} +14.9762 q^{97} +(-1.24520 - 1.19381i) q^{98} +0.655654i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9}+O(q^{10}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50} - 108 q^{52} - 24 q^{58} + 36 q^{59} + 168 q^{64} - 40 q^{70} - 16 q^{71} - 12 q^{72} + 48 q^{73} - 48 q^{75} - 32 q^{78} - 32 q^{81} - 24 q^{82} + 88 q^{85} + 36 q^{87} + 152 q^{92} + 24 q^{93} - 108 q^{94} - 44 q^{95} + 60 q^{96} + 112 q^{98}+O(q^{100}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

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