LMFDB - Embedded newform 483.2.j.a.229.14

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			229.14
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.14

$q$-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} +(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} +(-0.397073 + 4.77937i) 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} +(-0.971069 - 0.673636i) 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} - 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}+ \cdots + 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

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	$-0.483235\pi$
$5$	1.99266	−	3.45140i	0.891147	−	1.54351i	0.838502	−	0.544898i	$-0.183432\pi$
$6$			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	−0.411950	−	0.911206i	$-0.635152\pi$
$11$	0.567813	−	0.327827i	0.171202	−	0.0988436i	0.583153	+	0.812363i	$0.301819\pi$
$12$	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	$-0.903556\pi$
$17$	−3.03305	−	5.25340i	−0.735624	−	1.27414i	0.218826	−	0.975764i	$-0.429777\pi$
$18$	0.123216	+	0.213416i	0.0290423	+	0.0503027i
$19$	−0.168732	+	0.292252i	−0.0387097	+	0.0670471i	−0.884731	−	0.466102i	$-0.845658\pi$
$19$	−0.168732	+	0.292252i	−0.0387097	+	0.0670471i	0.846021	+	0.533149i	$0.178991\pi$
$20$	7.72863			1.72818
$21$	2.45489	+	0.986681i	0.535700	+	0.215311i
$22$			0.161574i			0.0344477i
$23$	−0.397073	+	4.77937i	−0.0827954	+	0.996567i
$23$	−0.397073	+	4.77937i	−0.0827954	+	0.996567i
$24$	−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	0.611135	−	0.791526i	$-0.290713\pi$
$37$	1.40646	+	0.812022i	0.231221	+	0.133496i	−0.379914	+	0.925022i	$0.624046\pi$
$38$	−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	$-0.895997\pi$
$43$		−	4.20924i		−	0.641903i	0.947096	−	0.320951i	$-0.104003\pi$
$44$	1.10114	+	0.635746i	0.166004	+	0.0958423i
$45$	−1.99266	−	3.45140i	−0.297049	−	0.514504i
$46$	−0.971069	−	0.673636i	−0.143176	−	0.0993222i
$47$	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	−0.912727	−	0.408570i	$-0.866028\pi$
$53$	−7.39119	+	4.26731i	−1.01526	+	0.586160i	−0.102532	+	0.994730i	$0.532694\pi$
$54$	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	−0.969937	−	0.243354i	$-0.921752\pi$
$61$	−2.14171	+	3.70955i	−0.274218	+	0.474959i	0.695720	+	0.718313i	$0.255086\pi$
$62$			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	−0.708301	−	0.705910i	$-0.750538\pi$
$67$	−3.69254	+	2.13189i	−0.451116	+	0.260452i	0.257185	+	0.966362i	$0.417205\pi$
$68$	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	−0.162399	−	0.986725i	$-0.551923\pi$
$79$	−9.76037	−	5.63515i	−1.09813	−	0.634004i	−0.935729	+	0.352721i	$0.885257\pi$
$80$	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	$-0.740152\pi$
$83$	−12.4794			−1.36979			−0.684896	+	0.728641i	$0.740152\pi$
$84$	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	−0.608793	−	0.793329i	$-0.708346\pi$
$89$	3.60989	−	6.25251i	0.382647	−	0.662764i	0.991440	+	0.130565i	$0.0416791\pi$
$90$	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	$-0.774948\pi$
$97$	−14.9762			−1.52060			−0.760301	+	0.649571i	$0.774948\pi$
$98$	−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	$0.366722\pi$
$103$	−5.96680	+	10.3348i	−0.587927	+	1.01832i	−0.994504	+	0.104702i	$0.966611\pi$
$104$		−	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	0.620176	−	0.784463i	$-0.287061\pi$
$107$	2.59532	+	1.49841i	0.250899	+	0.144857i	−0.369277	+	0.929320i	$0.620395\pi$
$108$	1.67946	−	0.969636i	0.161606	−	0.0933032i
$109$	11.4914	−	6.63459i	1.10068	−	0.635478i	0.164281	−	0.986414i	$-0.447470\pi$
$109$	11.4914	−	6.63459i	1.10068	−	0.635478i	0.936400	+	0.350935i	$0.114136\pi$
$110$	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	$-0.959512\pi$
$113$		−	2.69694i		−	0.253707i	0.991921	−	0.126854i	$-0.0404878\pi$
$114$	−0.0720201	−	0.0415808i	−0.00674530	−	0.00389440i
$115$	15.7043	+	10.8941i	1.46443	+	1.01588i
$116$	−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	−0.667512	−	0.744599i	$-0.732641\pi$
$137$	−4.17185	+	2.40862i	−0.356425	+	0.205782i	0.311086	+	0.950382i	$0.399307\pi$
$138$	−1.17779	−	0.0978515i	−0.100260	−	0.00832967i
$139$			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	0.525165	−	0.851001i	$-0.324004\pi$
$149$	0.619589	+	0.357720i	0.0507587	+	0.0293056i	−0.474406	+	0.880306i	$0.657337\pi$
$150$	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	0.861115	−	0.508410i	$-0.169766\pi$
$157$	−0.122016	−	0.211339i	−0.00973797	−	0.0168667i	−0.870853	+	0.491543i	$0.836433\pi$
$158$	2.40527	−	1.38868i	0.191353	−	0.110478i
$159$	−4.26731	+	7.39119i	−0.338420	+	0.586160i
$160$	−11.3118			−0.894279
$161$	−10.5986	+	6.97636i	−0.835287	+	0.549814i
$162$	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	$-0.243722\pi$
$181$	19.3978			1.44183			0.720914	+	0.693025i	$0.243722\pi$
$182$	−0.158849	−	1.11563i	−0.0117747	−	0.0826963i
$183$			4.28342i			0.316639i
$184$	0.385464	−	4.63963i	0.0284168	−	0.342038i
$185$	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	$0.0598818\pi$
$191$	22.6030	+	13.0499i	1.63550	+	0.944254i	0.653140	+	0.757238i	$0.273451\pi$
$192$	−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	$-0.926503\pi$
$199$	−9.66202	−	16.7351i	−0.684923	−	1.18632i	0.288538	−	0.957468i	$-0.406831\pi$
$200$	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
$207$	3.94052	+	2.73356i	0.273885	+	0.189995i
$208$	−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	0.863800	−	0.503834i	$-0.168078\pi$
$227$	−0.0667898	−	0.115683i	−0.00443299	−	0.00767817i	−0.868233	+	0.496156i	$0.834744\pi$
$228$	−0.566755	+	0.327216i	−0.0375343	+	0.0216704i
$229$	13.6209	−	23.5922i	0.900097	−	1.55901i	0.0727313	−	0.997352i	$-0.476828\pi$
$229$	13.6209	−	23.5922i	0.900097	−	1.55901i	0.827366	−	0.561663i	$-0.189838\pi$
$230$	−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	$0.117352\pi$
$241$	12.0856	+	20.9328i	0.778499	+	1.34840i	−0.154308	+	0.988023i	$0.549315\pi$
$242$	−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	$-0.334691\pi$
$251$	15.7258			0.992605			0.496303	+	0.868150i	$0.334691\pi$
$252$	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	−0.381445	−	0.924392i	$-0.624573\pi$
$263$	3.70369	−	2.13833i	0.228379	−	0.131855i	0.609824	+	0.792537i	$0.291240\pi$
$264$	−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
$276$	−5.30111	+	7.64173i	−0.319089	+	0.459978i
$277$	−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	$0.310517\pi$
$281$			27.7593i			1.65598i	−0.560740	+	0.827992i	$0.689483\pi$
$282$	−0.615030	+	1.06526i	−0.0366245	+	0.0634355i
$283$	−5.75864	−	9.97426i	−0.342316	−	0.592908i	0.642547	−	0.766247i	$-0.277878\pi$
$283$	−5.75864	−	9.97426i	−0.342316	−	0.592908i	−0.984862	+	0.173338i	$0.944545\pi$
$284$	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	$-0.515923\pi$
$293$	−1.71184			−0.100007			−0.0500033	+	0.998749i	$0.515923\pi$
$294$	−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
$299$	−8.26045	−	0.686284i	−0.477714	−	0.0396888i
$300$		−	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	$-0.602610\pi$
$313$	11.7299	−	20.3169i	0.663015	−	1.14838i	0.979819	−	0.199885i	$-0.0640569\pi$
$314$	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
$322$	−0.182953	−	3.12151i	−0.0101956	−	0.173955i
$323$	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	$0.372153\pi$
$337$			33.7933i			1.84084i	−0.390930	+	0.920420i	$0.627847\pi$
$338$	−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
$345$	19.0473	+	1.58247i	1.02547	+	0.0851971i
$346$	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	0.526174	−	0.850377i	$-0.323626\pi$
$359$	1.00068	+	0.577743i	0.0528139	+	0.0304921i	−0.473361	+	0.880869i	$0.656959\pi$
$360$	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	0.844258	−	0.535937i	$-0.180042\pi$
$367$	−0.804722	−	1.39382i	−0.0420061	−	0.0727567i	−0.886264	+	0.463180i	$0.846708\pi$
$368$	−14.3408	−	9.94828i	−0.747565	−	0.518590i
$369$	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	0.277758	−	0.960651i	$-0.410409\pi$
$373$	−8.02098	−	4.63092i	−0.415311	−	0.239780i	−0.693069	+	0.720871i	$0.743742\pi$
$374$	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	$-0.839247\pi$
$379$		−	18.8381i		−	0.967650i	0.875165	−	0.483825i	$-0.160753\pi$
$380$	−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	−0.611341	−	0.791367i	$-0.709370\pi$
$383$	7.43036	−	12.8698i	0.379674	−	0.657614i	0.991015	+	0.133753i	$0.0427030\pi$
$384$		−	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	−0.900982	−	0.433856i	$-0.857153\pi$
$389$	−19.2447	+	11.1109i	−0.975744	+	0.563346i	−0.0747612	+	0.997201i	$0.523819\pi$
$390$	−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	−0.245950	−	0.969283i	$-0.579100\pi$
$401$	−24.1971	−	13.9702i	−1.20835	−	0.697640i	−0.962398	+	0.271643i	$0.912433\pi$
$402$	−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	$-0.574670\pi$
$419$	−9.51570			−0.464872			−0.232436	+	0.972612i	$0.574670\pi$
$420$	18.9729	+	7.62569i	0.925783	+	0.372096i
$421$			24.5804i			1.19798i	0.800758	+	0.598988i	$0.204430\pi$
$421$			24.5804i			1.19798i	−0.800758	+	0.598988i	$0.795570\pi$
$422$	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	−0.472052	−	0.881571i	$-0.656486\pi$
$431$	1.14983	−	0.663853i	0.0553852	−	0.0319767i	0.527437	+	0.849594i	$0.323153\pi$
$432$	3.15174	+	1.81966i	0.151638	+	0.0875483i
$433$	−16.6799			−0.801584			−0.400792	−	0.916169i	$-0.631265\pi$
$433$	−16.6799			−0.801584			−0.400792	+	0.916169i	$0.631265\pi$
$434$	−2.15950	+	1.69348i	−0.103659	+	0.0812895i
$435$			18.7908i			0.900952i
$436$	22.2850	+	12.8663i	1.06726	+	0.616183i
$437$	−1.32978	−	0.922475i	−0.0636119	−	0.0441280i
$438$	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	0.208114	−	0.978104i	$-0.433267\pi$
$457$	−11.4347	−	6.60181i	−0.534892	−	0.308820i	−0.743006	+	0.669285i	$0.766601\pi$
$458$	3.35664	+	5.81387i	0.156845	+	0.271664i
$459$	−5.25340	+	3.03305i	−0.245208	+	0.141571i
$460$	−3.06883	+	36.9380i	−0.143085	+	1.72224i
$461$		−	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	−0.788779	−	0.614677i	$-0.789286\pi$
$467$	2.98084	−	5.16296i	0.137937	−	0.238913i	0.926715	+	0.375764i	$0.122620\pi$
$468$			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	0.948397	−	0.317085i	$-0.102704\pi$
$479$	4.36834	+	7.56619i	0.199595	+	0.345708i	−0.748802	+	0.662793i	$0.769371\pi$
$480$	−9.79634	+	5.65592i	−0.447140	+	0.258156i
$481$	−1.40347	+	2.43087i	−0.0639925	+	0.110838i
$482$	−5.95654			−0.271313
$483$	−5.69048	+	11.3410i	−0.258926	+	0.516034i
$484$	−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	$-0.377413\pi$
$503$	16.8507			0.751335			0.375668	+	0.926754i	$0.377413\pi$
$504$	−2.54275	+	0.362048i	−0.113263	+	0.0161269i
$505$			70.4779i			3.13622i
$506$	−0.772222	−	0.0641568i	−0.0343295	−	0.00285212i
$507$	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	0.991199	−	0.132378i	$-0.0422612\pi$
$521$	8.69551	+	15.0611i	0.380957	+	0.659837i	−0.610242	+	0.792215i	$0.708928\pi$
$522$	−0.580964	−	1.00626i	−0.0254281	−	0.0440428i
$523$	14.4355	−	25.0030i	0.631219	−	1.09330i	−0.356084	−	0.934454i	$-0.615888\pi$
$523$	14.4355	−	25.0030i	0.631219	−	1.09330i	0.987303	−	0.158850i	$-0.0507785\pi$
$524$		−	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
$529$	−22.6847	−	3.79551i	−0.986290	−	0.165022i
$530$	−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	−0.207920	−	0.978146i	$-0.566669\pi$
$557$	12.6316	−	7.29288i	0.535219	−	0.309009i	0.743139	+	0.669137i	$0.233336\pi$
$558$	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	0.951658	−	0.307159i	$-0.0993783\pi$
$563$	4.97857	+	8.62314i	0.209822	+	0.363422i	−0.741837	+	0.670581i	$0.766045\pi$
$564$	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	$-0.909085\pi$
$569$	−40.1514	−	23.1814i	−1.68323	−	0.971816i	−0.723746	−	0.690066i	$-0.757581\pi$
$570$	−0.287024	+	0.165713i	−0.0120221	+	0.00694097i
$571$	37.5322	−	21.6692i	1.57067	−	0.906829i	0.574587	−	0.818443i	$-0.305163\pi$
$571$	37.5322	−	21.6692i	1.57067	−	0.906829i	0.996086	−	0.0883853i	$-0.0281707\pi$
$572$	−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
$598$	1.16428	−	1.67836i	0.0476111	−	0.0686330i
$599$	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	0.187937	−	0.982181i	$-0.439820\pi$
$613$	28.0394	−	16.1885i	1.13250	−	0.653849i	0.944562	+	0.328332i	$0.106487\pi$
$614$	−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	$-0.803205\pi$
$617$		−	28.7944i		−	1.15922i	0.814894	−	0.579610i	$-0.196795\pi$
$618$	−2.54683	−	1.47041i	−0.102448	−	0.0591486i
$619$	21.3808	+	37.0326i	0.859365	+	1.48846i	0.872535	+	0.488551i	$0.162474\pi$
$619$	21.3808	+	37.0326i	0.859365	+	1.48846i	−0.0131703	+	0.999913i	$0.504192\pi$
$620$	28.1723	−	16.2653i	1.13143	−	0.653229i
$621$	4.77937	+	0.397073i	0.191789	+	0.0159340i
$622$			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	$0.108519\pi$
$631$			16.7980i			0.668716i	−0.942446	+	0.334358i	$0.891481\pi$
$632$	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	−0.317570	−	0.948235i	$-0.602867\pi$
$641$	8.73067	−	5.04065i	0.344841	−	0.199094i	0.662411	+	0.749141i	$0.269533\pi$
$642$	−0.369256	+	0.639571i	−0.0145734	+	0.0252418i
$643$	−32.0209			−1.26278			−0.631391	−	0.775464i	$-0.717516\pi$
$643$	−32.0209			−1.26278			−0.631391	+	0.775464i	$0.717516\pi$
$644$	−21.9933	−	11.0354i	−0.866657	−	0.434855i
$645$	−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	$0.0510505\pi$
$659$			8.19897i			0.319387i	−0.987167	+	0.159693i	$0.948949\pi$
$660$	2.53366	−	4.38842i	0.0986224	−	0.170819i
$661$	13.5183	+	23.4143i	0.525799	+	0.910711i	0.999548	+	0.0300510i	$0.00956696\pi$
$661$	13.5183	+	23.4143i	0.525799	+	0.910711i	−0.473749	+	0.880660i	$0.657100\pi$
$662$	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
$667$	1.87220	−	22.5347i	0.0724919	−	0.872548i
$668$	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	$-0.523575\pi$
$677$	21.5089	−	37.2545i	0.826654	−	1.43181i	0.900649	−	0.434548i	$-0.143092\pi$
$678$	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
$690$	−2.68466	+	3.87003i	−0.102203	+	0.147330i
$691$	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	$0.115603\pi$
$701$			18.8113i			0.710494i	−0.934773	+	0.355247i	$0.884397\pi$
$702$	−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	−0.0193940	−	0.999812i	$-0.506174\pi$
$709$	−23.8300	−	13.7582i	−0.894954	−	0.516702i	−0.875560	+	0.483110i	$0.839507\pi$
$710$	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	$-0.458822\pi$
$727$	6.95672			0.258011			0.129005	+	0.991644i	$0.458822\pi$
$728$	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	$0.521521\pi$
$733$	−24.3077	+	42.1022i	−0.897826	+	1.55508i	−0.830268	+	0.557365i	$0.811813\pi$
$734$	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	$0.0264177\pi$
$743$			4.51930i			0.165797i	−0.996558	+	0.0828985i	$0.973582\pi$
$744$	−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	0.415857	−	0.909430i	$-0.363482\pi$
$751$	−4.48893	−	2.59168i	−0.163803	−	0.0945718i	−0.579661	+	0.814858i	$0.696815\pi$
$752$	−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	$-0.976185\pi$
$757$		−	4.11310i		−	0.149493i	0.997203	−	0.0747466i	$-0.0238148\pi$
$758$	4.02037	+	2.32116i	0.146026	+	0.0843083i
$759$	2.58362	+	1.79227i	0.0937793	+	0.0650553i
$760$	−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	$-0.616609\pi$
$769$	−19.8664			−0.716399			−0.358200	+	0.933645i	$0.616609\pi$
$770$	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	0.916878	−	0.399167i	$-0.130700\pi$
$773$	3.13480	+	5.42963i	0.112751	+	0.195290i

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} +(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} +(-0.397073 + 4.77937i) 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} +(-0.971069 - 0.673636i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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